id	sid	tid	token	lemma	pos
ejpam-1372	1	1	5_xxx_kowalenko.dvi	5_xxx_kowalenko.dvi	NUM
ejpam-1372	1	2	european	european	ADJ
ejpam-1372	1	3	journal	journal	NOUN
ejpam-1372	1	4	of	of	ADP
ejpam-1372	1	5	pure	pure	ADJ
ejpam-1372	1	6	and	and	CCONJ
ejpam-1372	1	7	applied	apply	VERB
ejpam-1372	1	8	mathematics	mathematic	NOUN
ejpam-1372	1	9	vol	vol	NOUN
ejpam-1372	1	10	.	.	PROPN
ejpam-1372	1	11	4	4	NUM
ejpam-1372	1	12	,	,	PUNCT
ejpam-1372	1	13	no	no	INTJ
ejpam-1372	1	14	.	.	NOUN
ejpam-1372	1	15	4	4	NUM
ejpam-1372	1	16	,	,	PUNCT
ejpam-1372	1	17	2011	2011	NUM
ejpam-1372	1	18	,	,	PUNCT
ejpam-1372	1	19	370	370	NUM
ejpam-1372	1	20	-	-	SYM
ejpam-1372	1	21	423	423	NUM
ejpam-1372	1	22	issn	issn	PROPN
ejpam-1372	1	23	1307	1307	NUM
ejpam-1372	1	24	-	-	SYM
ejpam-1372	1	25	5543	5543	NUM
ejpam-1372	1	26	–	–	PUNCT
ejpam-1372	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-1372	1	28	euler	euler	NOUN
ejpam-1372	1	29	and	and	CCONJ
ejpam-1372	1	30	divergent	divergent	ADJ
ejpam-1372	1	31	series	series	NOUN
ejpam-1372	1	32	victor	victor	PROPN
ejpam-1372	1	33	kowalenko	kowalenko	PROPN
ejpam-1372	1	34	arc	arc	PROPN
ejpam-1372	1	35	centre	centre	NOUN
ejpam-1372	1	36	of	of	ADP
ejpam-1372	1	37	excellence	excellence	PROPN
ejpam-1372	1	38	for	for	ADP
ejpam-1372	1	39	mathematics	mathematic	NOUN
ejpam-1372	1	40	and	and	CCONJ
ejpam-1372	1	41	statistics	statistic	NOUN
ejpam-1372	1	42	of	of	ADP
ejpam-1372	1	43	complex	complex	ADJ
ejpam-1372	1	44	systems	system	NOUN
ejpam-1372	1	45	,	,	PUNCT
ejpam-1372	1	46	department	department	NOUN
ejpam-1372	1	47	of	of	ADP
ejpam-1372	1	48	mathematics	mathematics	PROPN
ejpam-1372	1	49	and	and	CCONJ
ejpam-1372	1	50	statistics	statistic	NOUN
ejpam-1372	1	51	,	,	PUNCT
ejpam-1372	1	52	the	the	DET
ejpam-1372	1	53	university	university	NOUN
ejpam-1372	1	54	of	of	ADP
ejpam-1372	1	55	melbourne	melbourne	PROPN
ejpam-1372	1	56	,	,	PUNCT
ejpam-1372	1	57	victoria	victoria	PROPN
ejpam-1372	1	58	3010	3010	NUM
ejpam-1372	1	59	,	,	PUNCT
ejpam-1372	1	60	australia	australia	PROPN
ejpam-1372	1	61	abstract	abstract	NOUN
ejpam-1372	1	62	.	.	PUNCT
ejpam-1372	2	1	euler	euler	PROPN
ejpam-1372	2	2	’s	’s	PART
ejpam-1372	2	3	reputation	reputation	NOUN
ejpam-1372	2	4	is	be	AUX
ejpam-1372	2	5	tarnished	tarnish	VERB
ejpam-1372	2	6	because	because	SCONJ
ejpam-1372	2	7	of	of	ADP
ejpam-1372	2	8	his	his	PRON
ejpam-1372	2	9	views	view	NOUN
ejpam-1372	2	10	on	on	ADP
ejpam-1372	2	11	divergent	divergent	ADJ
ejpam-1372	2	12	series	series	NOUN
ejpam-1372	2	13	.	.	PUNCT
ejpam-1372	3	1	he	he	PRON
ejpam-1372	3	2	believed	believe	VERB
ejpam-1372	3	3	that	that	SCONJ
ejpam-1372	3	4	all	all	DET
ejpam-1372	3	5	series	series	NOUN
ejpam-1372	3	6	should	should	AUX
ejpam-1372	3	7	have	have	VERB
ejpam-1372	3	8	a	a	DET
ejpam-1372	3	9	value	value	NOUN
ejpam-1372	3	10	,	,	PUNCT
ejpam-1372	3	11	not	not	PART
ejpam-1372	3	12	necessarily	necessarily	ADV
ejpam-1372	3	13	a	a	DET
ejpam-1372	3	14	limit	limit	NOUN
ejpam-1372	3	15	as	as	ADP
ejpam-1372	3	16	for	for	ADP
ejpam-1372	3	17	convergent	convergent	NOUN
ejpam-1372	3	18	series	series	NOUN
ejpam-1372	3	19	,	,	PUNCT
ejpam-1372	3	20	and	and	CCONJ
ejpam-1372	3	21	that	that	SCONJ
ejpam-1372	3	22	the	the	DET
ejpam-1372	3	23	value	value	NOUN
ejpam-1372	3	24	should	should	AUX
ejpam-1372	3	25	remain	remain	VERB
ejpam-1372	3	26	invariant	invariant	ADJ
ejpam-1372	3	27	irrespective	irrespective	ADV
ejpam-1372	3	28	of	of	ADP
ejpam-1372	3	29	the	the	DET
ejpam-1372	3	30	method	method	NOUN
ejpam-1372	3	31	of	of	ADP
ejpam-1372	3	32	evaluation	evaluation	NOUN
ejpam-1372	3	33	.	.	PUNCT
ejpam-1372	4	1	via	via	ADP
ejpam-1372	4	2	the	the	DET
ejpam-1372	4	3	key	key	ADJ
ejpam-1372	4	4	concept	concept	NOUN
ejpam-1372	4	5	of	of	ADP
ejpam-1372	4	6	regularisation	regularisation	NOUN
ejpam-1372	4	7	,	,	PUNCT
ejpam-1372	4	8	which	which	PRON
ejpam-1372	4	9	results	result	VERB
ejpam-1372	4	10	in	in	ADP
ejpam-1372	4	11	the	the	DET
ejpam-1372	4	12	removal	removal	NOUN
ejpam-1372	4	13	of	of	ADP
ejpam-1372	4	14	the	the	DET
ejpam-1372	4	15	infinity	infinity	NOUN
ejpam-1372	4	16	in	in	ADP
ejpam-1372	4	17	the	the	DET
ejpam-1372	4	18	remainder	remainder	NOUN
ejpam-1372	4	19	of	of	ADP
ejpam-1372	4	20	a	a	DET
ejpam-1372	4	21	divergent	divergent	ADJ
ejpam-1372	4	22	series	series	NOUN
ejpam-1372	4	23	,	,	PUNCT
ejpam-1372	4	24	regularised	regularise	VERB
ejpam-1372	4	25	values	value	NOUN
ejpam-1372	4	26	can	can	AUX
ejpam-1372	4	27	be	be	AUX
ejpam-1372	4	28	evaluated	evaluate	VERB
ejpam-1372	4	29	for	for	ADP
ejpam-1372	4	30	elementary	elementary	ADJ
ejpam-1372	4	31	series	series	PROPN
ejpam-1372	4	32	outside	outside	ADP
ejpam-1372	4	33	their	their	PRON
ejpam-1372	4	34	circles	circle	NOUN
ejpam-1372	4	35	of	of	ADP
ejpam-1372	4	36	absolute	absolute	ADJ
ejpam-1372	4	37	convergence	convergence	NOUN
ejpam-1372	4	38	such	such	ADJ
ejpam-1372	4	39	as	as	ADP
ejpam-1372	4	40	the	the	DET
ejpam-1372	4	41	geometric	geometric	ADJ
ejpam-1372	4	42	series	series	NOUN
ejpam-1372	4	43	and	and	CCONJ
ejpam-1372	4	44	for	for	ADP
ejpam-1372	4	45	more	more	ADV
ejpam-1372	4	46	complicated	complicated	ADJ
ejpam-1372	4	47	asymptotic	asymptotic	ADJ
ejpam-1372	4	48	series	series	NOUN
ejpam-1372	4	49	called	call	VERB
ejpam-1372	4	50	terminants	terminant	NOUN
ejpam-1372	4	51	.	.	PUNCT
ejpam-1372	5	1	two	two	NUM
ejpam-1372	5	2	different	different	ADJ
ejpam-1372	5	3	techniques	technique	NOUN
ejpam-1372	5	4	for	for	ADP
ejpam-1372	5	5	evaluating	evaluate	VERB
ejpam-1372	5	6	the	the	DET
ejpam-1372	5	7	regularised	regularise	VERB
ejpam-1372	5	8	values	value	NOUN
ejpam-1372	5	9	are	be	AUX
ejpam-1372	5	10	presented	present	VERB
ejpam-1372	5	11	:	:	PUNCT
ejpam-1372	5	12	the	the	DET
ejpam-1372	5	13	first	first	ADJ
ejpam-1372	5	14	being	be	AUX
ejpam-1372	5	15	the	the	DET
ejpam-1372	5	16	standard	standard	ADJ
ejpam-1372	5	17	technique	technique	NOUN
ejpam-1372	5	18	of	of	ADP
ejpam-1372	5	19	borel	borel	PROPN
ejpam-1372	5	20	summation	summation	NOUN
ejpam-1372	5	21	and	and	CCONJ
ejpam-1372	5	22	the	the	DET
ejpam-1372	5	23	second	second	ADJ
ejpam-1372	5	24	being	be	AUX
ejpam-1372	5	25	the	the	DET
ejpam-1372	5	26	relatively	relatively	ADV
ejpam-1372	5	27	novel	novel	NOUN
ejpam-1372	5	28	,	,	PUNCT
ejpam-1372	5	29	but	but	CCONJ
ejpam-1372	5	30	more	more	ADV
ejpam-1372	5	31	powerful	powerful	ADJ
ejpam-1372	5	32	,	,	PUNCT
ejpam-1372	5	33	mellin	mellin	PROPN
ejpam-1372	5	34	-	-	PUNCT
ejpam-1372	5	35	barnes	barnes	PROPN
ejpam-1372	5	36	regularisation	regularisation	NOUN
ejpam-1372	5	37	.	.	PUNCT
ejpam-1372	6	1	general	general	ADJ
ejpam-1372	6	2	forms	form	NOUN
ejpam-1372	6	3	for	for	ADP
ejpam-1372	6	4	the	the	DET
ejpam-1372	6	5	regularised	regularise	VERB
ejpam-1372	6	6	values	value	NOUN
ejpam-1372	6	7	of	of	ADP
ejpam-1372	6	8	the	the	DET
ejpam-1372	6	9	two	two	NUM
ejpam-1372	6	10	types	type	NOUN
ejpam-1372	6	11	of	of	ADP
ejpam-1372	6	12	terminants	terminant	NOUN
ejpam-1372	6	13	,	,	PUNCT
ejpam-1372	6	14	which	which	PRON
ejpam-1372	6	15	vary	vary	VERB
ejpam-1372	6	16	as	as	SCONJ
ejpam-1372	6	17	the	the	DET
ejpam-1372	6	18	truncation	truncation	NOUN
ejpam-1372	6	19	parameter	parameter	NOUN
ejpam-1372	6	20	is	be	AUX
ejpam-1372	6	21	altered	alter	VERB
ejpam-1372	6	22	,	,	PUNCT
ejpam-1372	6	23	are	be	AUX
ejpam-1372	6	24	presented	present	VERB
ejpam-1372	6	25	using	use	VERB
ejpam-1372	6	26	both	both	DET
ejpam-1372	6	27	techniques	technique	NOUN
ejpam-1372	6	28	over	over	ADP
ejpam-1372	6	29	the	the	DET
ejpam-1372	6	30	entire	entire	ADJ
ejpam-1372	6	31	complex	complex	ADJ
ejpam-1372	6	32	plane	plane	NOUN
ejpam-1372	6	33	.	.	PUNCT
ejpam-1372	7	1	then	then	ADV
ejpam-1372	7	2	an	an	DET
ejpam-1372	7	3	extremely	extremely	ADV
ejpam-1372	7	4	accurate	accurate	ADJ
ejpam-1372	7	5	and	and	CCONJ
ejpam-1372	7	6	extensive	extensive	ADJ
ejpam-1372	7	7	numerical	numerical	ADJ
ejpam-1372	7	8	study	study	NOUN
ejpam-1372	7	9	is	be	AUX
ejpam-1372	7	10	carried	carry	VERB
ejpam-1372	7	11	out	out	ADP
ejpam-1372	7	12	for	for	ADP
ejpam-1372	7	13	different	different	ADJ
ejpam-1372	7	14	values	value	NOUN
ejpam-1372	7	15	of	of	ADP
ejpam-1372	7	16	the	the	DET
ejpam-1372	7	17	magnitude	magnitude	NOUN
ejpam-1372	7	18	and	and	CCONJ
ejpam-1372	7	19	argument	argument	NOUN
ejpam-1372	7	20	of	of	ADP
ejpam-1372	7	21	the	the	DET
ejpam-1372	7	22	main	main	ADJ
ejpam-1372	7	23	variable	variable	NOUN
ejpam-1372	7	24	and	and	CCONJ
ejpam-1372	7	25	the	the	DET
ejpam-1372	7	26	truncation	truncation	NOUN
ejpam-1372	7	27	parameter	parameter	NOUN
ejpam-1372	7	28	.	.	PUNCT
ejpam-1372	8	1	in	in	ADP
ejpam-1372	8	2	all	all	DET
ejpam-1372	8	3	cases	case	NOUN
ejpam-1372	8	4	it	it	PRON
ejpam-1372	8	5	is	be	AUX
ejpam-1372	8	6	found	find	VERB
ejpam-1372	8	7	that	that	SCONJ
ejpam-1372	8	8	the	the	DET
ejpam-1372	8	9	mb	mb	ADJ
ejpam-1372	8	10	-	-	PUNCT
ejpam-1372	8	11	regularised	regularise	VERB
ejpam-1372	8	12	forms	form	NOUN
ejpam-1372	8	13	yield	yield	VERB
ejpam-1372	8	14	identical	identical	ADJ
ejpam-1372	8	15	values	value	NOUN
ejpam-1372	8	16	to	to	ADP
ejpam-1372	8	17	the	the	DET
ejpam-1372	8	18	borel	borel	NOUN
ejpam-1372	8	19	-	-	PUNCT
ejpam-1372	8	20	summed	sum	VERB
ejpam-1372	8	21	forms	form	NOUN
ejpam-1372	8	22	,	,	PUNCT
ejpam-1372	8	23	thereby	thereby	ADV
ejpam-1372	8	24	vindicating	vindicate	VERB
ejpam-1372	8	25	euler	euler	NOUN
ejpam-1372	8	26	’s	’s	PART
ejpam-1372	8	27	views	view	NOUN
ejpam-1372	8	28	and	and	CCONJ
ejpam-1372	8	29	restoring	restore	VERB
ejpam-1372	8	30	his	his	PRON
ejpam-1372	8	31	status	status	NOUN
ejpam-1372	8	32	as	as	ADP
ejpam-1372	8	33	perhaps	perhaps	ADV
ejpam-1372	8	34	the	the	DET
ejpam-1372	8	35	greatest	great	ADJ
ejpam-1372	8	36	of	of	ADP
ejpam-1372	8	37	all	all	DET
ejpam-1372	8	38	mathematicians	mathematician	NOUN
ejpam-1372	8	39	.	.	PUNCT
ejpam-1372	9	1	2000	2000	NUM
ejpam-1372	9	2	mathematics	mathematic	NOUN
ejpam-1372	9	3	subject	subject	NOUN
ejpam-1372	9	4	classifications	classification	NOUN
ejpam-1372	9	5	:	:	PUNCT
ejpam-1372	9	6	00a30	00a30	NUM
ejpam-1372	9	7	,	,	PUNCT
ejpam-1372	9	8	01a45	01a45	NUM
ejpam-1372	9	9	,	,	PUNCT
ejpam-1372	9	10	01a50	01a50	NUM
ejpam-1372	9	11	,	,	PUNCT
ejpam-1372	9	12	01a65	01a65	NUM
ejpam-1372	9	13	,	,	PUNCT
ejpam-1372	9	14	01a70	01a70	NUM
ejpam-1372	9	15	,	,	PUNCT
ejpam-1372	9	16	03a05	03a05	NUM
ejpam-1372	9	17	,	,	PUNCT
ejpam-1372	9	18	03b30	03b30	NOUN
ejpam-1372	9	19	,	,	PUNCT
ejpam-1372	9	20	30b10	30b10	NUM
ejpam-1372	9	21	,	,	PUNCT
ejpam-1372	9	22	30b30	30b30	NUM
ejpam-1372	9	23	,	,	PUNCT
ejpam-1372	9	24	30d20	30d20	NUM
ejpam-1372	9	25	,	,	PUNCT
ejpam-1372	9	26	30e15	30e15	NUM
ejpam-1372	9	27	,	,	PUNCT
ejpam-1372	9	28	30e20	30e20	NUM
ejpam-1372	9	29	,	,	PUNCT
ejpam-1372	9	30	34e05	34e05	NUM
ejpam-1372	9	31	,	,	PUNCT
ejpam-1372	9	32	34e10	34e10	NUM
ejpam-1372	9	33	,	,	PUNCT
ejpam-1372	9	34	40a05	40a05	NUM
ejpam-1372	9	35	,	,	PUNCT
ejpam-1372	9	36	40g10	40g10	NUM
ejpam-1372	9	37	,	,	PUNCT
ejpam-1372	9	38	40g99	40g99	NUM
ejpam-1372	9	39	key	key	ADJ
ejpam-1372	9	40	words	word	NOUN
ejpam-1372	9	41	and	and	CCONJ
ejpam-1372	9	42	phrases	phrase	NOUN
ejpam-1372	9	43	:	:	PUNCT
ejpam-1372	9	44	absolute	absolute	ADJ
ejpam-1372	9	45	convergence	convergence	NOUN
ejpam-1372	9	46	,	,	PUNCT
ejpam-1372	9	47	asymptotic	asymptotic	ADJ
ejpam-1372	9	48	form	form	NOUN
ejpam-1372	9	49	,	,	PUNCT
ejpam-1372	9	50	asymptotics	asymptotic	NOUN
ejpam-1372	9	51	,	,	PUNCT
ejpam-1372	9	52	asymptotic	asymptotic	ADJ
ejpam-1372	9	53	series	series	NOUN
ejpam-1372	9	54	,	,	PUNCT
ejpam-1372	9	55	borel	borel	PROPN
ejpam-1372	9	56	summation	summation	NOUN
ejpam-1372	9	57	,	,	PUNCT
ejpam-1372	9	58	cauchy	cauchy	PROPN
ejpam-1372	9	59	integral	integral	ADJ
ejpam-1372	9	60	,	,	PUNCT
ejpam-1372	9	61	cauchy	cauchy	ADJ
ejpam-1372	9	62	principal	principal	ADJ
ejpam-1372	9	63	value	value	NOUN
ejpam-1372	9	64	,	,	PUNCT
ejpam-1372	9	65	complete	complete	ADJ
ejpam-1372	9	66	asymptotic	asymptotic	ADJ
ejpam-1372	9	67	expansion	expansion	NOUN
ejpam-1372	9	68	,	,	PUNCT
ejpam-1372	9	69	conditional	conditional	ADJ
ejpam-1372	9	70	convergence	convergence	NOUN
ejpam-1372	9	71	,	,	PUNCT
ejpam-1372	9	72	divergent	divergent	ADJ
ejpam-1372	9	73	series	series	NOUN
ejpam-1372	9	74	,	,	PUNCT
ejpam-1372	9	75	domain	domain	NOUN
ejpam-1372	9	76	of	of	ADP
ejpam-1372	9	77	convergence	convergence	NOUN
ejpam-1372	9	78	,	,	PUNCT
ejpam-1372	9	79	dominant	dominant	ADJ
ejpam-1372	9	80	series	series	NOUN
ejpam-1372	9	81	,	,	PUNCT
ejpam-1372	9	82	equivalence	equivalence	NOUN
ejpam-1372	9	83	,	,	PUNCT
ejpam-1372	9	84	euler	euler	NOUN
ejpam-1372	9	85	’s	’s	PART
ejpam-1372	10	1	constant	constant	ADJ
ejpam-1372	10	2	,	,	PUNCT
ejpam-1372	10	3	gamma	gamma	NOUN
ejpam-1372	10	4	function	function	NOUN
ejpam-1372	10	5	,	,	PUNCT
ejpam-1372	10	6	geometric	geometric	ADJ
ejpam-1372	10	7	series	series	NOUN
ejpam-1372	10	8	,	,	PUNCT
ejpam-1372	10	9	grandi	grandi	PROPN
ejpam-1372	10	10	’s	’s	PART
ejpam-1372	10	11	series	series	NOUN
ejpam-1372	10	12	,	,	PUNCT
ejpam-1372	10	13	harmonic	harmonic	ADJ
ejpam-1372	10	14	series	series	NOUN
ejpam-1372	10	15	,	,	PUNCT
ejpam-1372	10	16	jump	jump	VERB
ejpam-1372	10	17	discontinuity	discontinuity	NOUN
ejpam-1372	10	18	,	,	PUNCT
ejpam-1372	10	19	logarithmic	logarithmic	ADJ
ejpam-1372	10	20	divergence	divergence	NOUN
ejpam-1372	10	21	,	,	PUNCT
ejpam-1372	10	22	mellin	mellin	NOUN
ejpam-1372	10	23	-	-	NOUN
ejpam-1372	10	24	barnes	barnes	PROPN
ejpam-1372	10	25	(	(	PUNCT
ejpam-1372	10	26	mb	mb	NOUN
ejpam-1372	10	27	)	)	PUNCT
ejpam-1372	10	28	regularisation	regularisation	NOUN
ejpam-1372	10	29	,	,	PUNCT
ejpam-1372	10	30	mellin	mellin	PROPN
ejpam-1372	10	31	transform	transform	NOUN
ejpam-1372	10	32	,	,	PUNCT
ejpam-1372	10	33	poincaré	poincaré	ADJ
ejpam-1372	10	34	prescription	prescription	NOUN
ejpam-1372	10	35	,	,	PUNCT
ejpam-1372	10	36	recurring	recur	VERB
ejpam-1372	10	37	series	series	NOUN
ejpam-1372	10	38	,	,	PUNCT
ejpam-1372	10	39	regularisation	regularisation	NOUN
ejpam-1372	10	40	,	,	PUNCT
ejpam-1372	10	41	regularised	regularise	VERB
ejpam-1372	10	42	value	value	NOUN
ejpam-1372	10	43	,	,	PUNCT
ejpam-1372	10	44	renormalisation	renormalisation	NOUN
ejpam-1372	10	45	,	,	PUNCT
ejpam-1372	10	46	stokes	stokes	PROPN
ejpam-1372	10	47	line	line	PROPN
ejpam-1372	10	48	,	,	PUNCT
ejpam-1372	10	49	stokes	stoke	NOUN
ejpam-1372	10	50	phenomenon	phenomenon	NOUN
ejpam-1372	10	51	,	,	PUNCT
ejpam-1372	10	52	stokes	stoke	NOUN
ejpam-1372	10	53	sector	sector	NOUN
ejpam-1372	10	54	,	,	PUNCT
ejpam-1372	10	55	subdominant	subdominant	ADJ
ejpam-1372	10	56	terms	term	NOUN
ejpam-1372	10	57	,	,	PUNCT
ejpam-1372	10	58	terminant	terminant	NOUN
ejpam-1372	10	59	,	,	PUNCT
ejpam-1372	10	60	truncation	truncation	NOUN
ejpam-1372	10	61	,	,	PUNCT
ejpam-1372	10	62	truncation	truncation	NOUN
ejpam-1372	10	63	parameter	parameter	NOUN
ejpam-1372	10	64	1	1	NUM
ejpam-1372	10	65	.	.	PUNCT
ejpam-1372	10	66	introduction	introduction	NOUN
ejpam-1372	10	67	despite	despite	SCONJ
ejpam-1372	10	68	being	be	AUX
ejpam-1372	10	69	regarded	regard	VERB
ejpam-1372	10	70	as	as	ADP
ejpam-1372	10	71	one	one	NUM
ejpam-1372	10	72	of	of	ADP
ejpam-1372	10	73	the	the	DET
ejpam-1372	10	74	four	four	NUM
ejpam-1372	10	75	greatest	great	ADJ
ejpam-1372	10	76	mathematicians	mathematician	NOUN
ejpam-1372	10	77	of	of	ADP
ejpam-1372	10	78	all	all	DET
ejpam-1372	10	79	time	time	NOUN
ejpam-1372	10	80	,	,	PUNCT
ejpam-1372	10	81	to	to	ADP
ejpam-1372	10	82	this	this	DET
ejpam-1372	10	83	day	day	NOUN
ejpam-1372	10	84	euler	euler	NOUN
ejpam-1372	10	85	’s	’s	PART
ejpam-1372	10	86	reputation	reputation	NOUN
ejpam-1372	10	87	is	be	AUX
ejpam-1372	10	88	tarnished	tarnish	VERB
ejpam-1372	10	89	because	because	SCONJ
ejpam-1372	10	90	of	of	ADP
ejpam-1372	10	91	the	the	DET
ejpam-1372	10	92	views	view	NOUN
ejpam-1372	10	93	he	he	PRON
ejpam-1372	10	94	held	hold	VERB
ejpam-1372	10	95	on	on	ADP
ejpam-1372	10	96	divergent	divergent	ADJ
ejpam-1372	10	97	series	series	NOUN
ejpam-1372	10	98	.	.	PUNCT
ejpam-1372	11	1	first	first	ADV
ejpam-1372	11	2	,	,	PUNCT
ejpam-1372	11	3	he	he	PRON
ejpam-1372	11	4	believed	believe	VERB
ejpam-1372	11	5	that	that	SCONJ
ejpam-1372	11	6	every	every	DET
ejpam-1372	11	7	series	series	NOUN
ejpam-1372	11	8	,	,	PUNCT
ejpam-1372	11	9	both	both	CCONJ
ejpam-1372	11	10	convergent	convergent	NOUN
ejpam-1372	11	11	and	and	CCONJ
ejpam-1372	11	12	divergent	divergent	ADJ
ejpam-1372	11	13	,	,	PUNCT
ejpam-1372	11	14	should	should	AUX
ejpam-1372	11	15	be	be	AUX
ejpam-1372	11	16	assigned	assign	VERB
ejpam-1372	11	17	a	a	DET
ejpam-1372	11	18	certain	certain	ADJ
ejpam-1372	11	19	value	value	NOUN
ejpam-1372	11	20	,	,	PUNCT
ejpam-1372	11	21	email	email	NOUN
ejpam-1372	11	22	addresses	address	NOUN
ejpam-1372	11	23	:	:	PUNCT
ejpam-1372	11	24	vkowa�unimelb.edu.au	vkowa�unimelb.edu.au	PROPN
ejpam-1372	11	25	,	,	PUNCT
ejpam-1372	11	26	vkowal	vkowal	PROPN
ejpam-1372	11	27	�	�	PROPN
ejpam-1372	11	28	netspa	netspa	PROPN
ejpam-1372	11	29	e.net.au	e.net.au	PROPN
ejpam-1372	11	30	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1372	12	1	370	370	NUM
ejpam-1372	12	2	c	c	X
ejpam-1372	12	3	©	©	NOUN
ejpam-1372	12	4	2011	2011	NUM
ejpam-1372	12	5	ejpam	ejpam	VERB
ejpam-1372	12	6	all	all	DET
ejpam-1372	12	7	rights	right	NOUN
ejpam-1372	12	8	reserved	reserve	VERB
ejpam-1372	12	9	.	.	PUNCT
ejpam-1372	13	1	v.	v.	ADP
ejpam-1372	13	2	kowalenko	kowalenko	PROPN
ejpam-1372	13	3	/	/	SYM
ejpam-1372	13	4	eur	eur	PROPN
ejpam-1372	13	5	.	.	PUNCT
ejpam-1372	14	1	j.	j.	PROPN
ejpam-1372	14	2	pure	pure	PROPN
ejpam-1372	14	3	appl	appl	PROPN
ejpam-1372	14	4	.	.	PROPN
ejpam-1372	14	5	math	math	PROPN
ejpam-1372	14	6	,	,	PUNCT
ejpam-1372	14	7	4	4	NUM
ejpam-1372	14	8	(	(	PUNCT
ejpam-1372	14	9	2011	2011	NUM
ejpam-1372	14	10	)	)	PUNCT
ejpam-1372	14	11	,	,	PUNCT
ejpam-1372	14	12	370	370	NUM
ejpam-1372	14	13	-	-	SYM
ejpam-1372	14	14	423	423	NUM
ejpam-1372	14	15	371	371	NUM
ejpam-1372	14	16	but	but	CCONJ
ejpam-1372	14	17	because	because	SCONJ
ejpam-1372	14	18	of	of	ADP
ejpam-1372	14	19	the	the	DET
ejpam-1372	14	20	fallacies	fallacy	NOUN
ejpam-1372	14	21	and	and	CCONJ
ejpam-1372	14	22	paradoxes	paradox	NOUN
ejpam-1372	14	23	surrounding	surround	VERB
ejpam-1372	14	24	the	the	DET
ejpam-1372	14	25	latter	latter	ADJ
ejpam-1372	14	26	type	type	NOUN
ejpam-1372	14	27	of	of	ADP
ejpam-1372	14	28	series	series	NOUN
ejpam-1372	14	29	,	,	PUNCT
ejpam-1372	14	30	he	he	PRON
ejpam-1372	14	31	felt	feel	VERB
ejpam-1372	14	32	that	that	SCONJ
ejpam-1372	14	33	such	such	DET
ejpam-1372	14	34	a	a	DET
ejpam-1372	14	35	value	value	NOUN
ejpam-1372	14	36	should	should	AUX
ejpam-1372	14	37	not	not	PART
ejpam-1372	14	38	be	be	AUX
ejpam-1372	14	39	denoted	denote	VERB
ejpam-1372	14	40	by	by	ADP
ejpam-1372	14	41	the	the	DET
ejpam-1372	14	42	name	name	NOUN
ejpam-1372	14	43	sum	sum	NOUN
ejpam-1372	15	1	[	[	X
ejpam-1372	15	2	6	6	NUM
ejpam-1372	15	3	]	]	PUNCT
ejpam-1372	15	4	.	.	PUNCT
ejpam-1372	16	1	second	second	ADJ
ejpam-1372	16	2	,	,	PUNCT
ejpam-1372	16	3	he	he	PRON
ejpam-1372	16	4	believed	believe	VERB
ejpam-1372	16	5	that	that	SCONJ
ejpam-1372	16	6	the	the	DET
ejpam-1372	16	7	value	value	NOUN
ejpam-1372	16	8	should	should	AUX
ejpam-1372	16	9	be	be	AUX
ejpam-1372	16	10	independent	independent	ADJ
ejpam-1372	16	11	of	of	ADP
ejpam-1372	16	12	the	the	DET
ejpam-1372	16	13	actual	actual	ADJ
ejpam-1372	16	14	method	method	NOUN
ejpam-1372	16	15	or	or	CCONJ
ejpam-1372	16	16	technique	technique	NOUN
ejpam-1372	16	17	used	use	VERB
ejpam-1372	16	18	to	to	PART
ejpam-1372	16	19	determine	determine	VERB
ejpam-1372	16	20	it	it	PRON
ejpam-1372	16	21	.	.	PUNCT
ejpam-1372	17	1	later	later	ADV
ejpam-1372	17	2	,	,	PUNCT
ejpam-1372	17	3	when	when	SCONJ
ejpam-1372	17	4	the	the	DET
ejpam-1372	17	5	foundations	foundation	NOUN
ejpam-1372	17	6	of	of	ADP
ejpam-1372	17	7	analysis	analysis	NOUN
ejpam-1372	17	8	were	be	AUX
ejpam-1372	17	9	laid	lay	VERB
ejpam-1372	17	10	down	down	ADP
ejpam-1372	17	11	,	,	PUNCT
ejpam-1372	17	12	initially	initially	ADV
ejpam-1372	17	13	by	by	ADP
ejpam-1372	17	14	abel	abel	PROPN
ejpam-1372	17	15	and	and	CCONJ
ejpam-1372	17	16	cauchy	cauchy	PROPN
ejpam-1372	17	17	,	,	PUNCT
ejpam-1372	17	18	and	and	CCONJ
ejpam-1372	17	19	then	then	ADV
ejpam-1372	17	20	by	by	ADP
ejpam-1372	17	21	weierstrass	weierstrass	NOUN
ejpam-1372	17	22	(	(	PUNCT
ejpam-1372	17	23	“	"	PUNCT
ejpam-1372	17	24	the	the	DET
ejpam-1372	17	25	father	father	NOUN
ejpam-1372	17	26	of	of	ADP
ejpam-1372	17	27	modern	modern	ADJ
ejpam-1372	17	28	analysis	analysis	NOUN
ejpam-1372	17	29	”	"	PUNCT
ejpam-1372	17	30	)	)	PUNCT
ejpam-1372	17	31	and	and	CCONJ
ejpam-1372	17	32	dedekind	dedekind	ADJ
ejpam-1372	17	33	,	,	PUNCT
ejpam-1372	17	34	divergent	divergent	ADJ
ejpam-1372	17	35	series	serie	NOUN
ejpam-1372	17	36	were	be	AUX
ejpam-1372	17	37	virtually	virtually	ADV
ejpam-1372	17	38	banished	banish	VERB
ejpam-1372	17	39	from	from	ADP
ejpam-1372	17	40	the	the	DET
ejpam-1372	17	41	mathematical	mathematical	ADJ
ejpam-1372	17	42	lexicon	lexicon	NOUN
ejpam-1372	17	43	.	.	PUNCT
ejpam-1372	18	1	consequently	consequently	ADV
ejpam-1372	18	2	,	,	PUNCT
ejpam-1372	18	3	euler	euler	PROPN
ejpam-1372	18	4	’s	’s	PART
ejpam-1372	18	5	reputation	reputation	NOUN
ejpam-1372	18	6	suffered	suffer	VERB
ejpam-1372	18	7	.	.	PUNCT
ejpam-1372	19	1	in	in	ADP
ejpam-1372	19	2	fact	fact	NOUN
ejpam-1372	19	3	,	,	PUNCT
ejpam-1372	19	4	the	the	DET
ejpam-1372	19	5	extremely	extremely	ADV
ejpam-1372	19	6	gifted	gifted	ADJ
ejpam-1372	19	7	abel	abel	NOUN
ejpam-1372	19	8	,	,	PUNCT
ejpam-1372	19	9	who	who	PRON
ejpam-1372	19	10	died	die	VERB
ejpam-1372	19	11	at	at	ADP
ejpam-1372	19	12	the	the	DET
ejpam-1372	19	13	tragically	tragically	ADV
ejpam-1372	19	14	young	young	ADJ
ejpam-1372	19	15	age	age	NOUN
ejpam-1372	19	16	of	of	ADP
ejpam-1372	19	17	26	26	NUM
ejpam-1372	19	18	,	,	PUNCT
ejpam-1372	19	19	described	describe	VERB
ejpam-1372	19	20	divergent	divergent	ADJ
ejpam-1372	19	21	series	series	NOUN
ejpam-1372	19	22	as	as	ADP
ejpam-1372	19	23	“	"	PUNCT
ejpam-1372	19	24	the	the	DET
ejpam-1372	19	25	invention	invention	NOUN
ejpam-1372	19	26	of	of	ADP
ejpam-1372	19	27	the	the	DET
ejpam-1372	19	28	devil	devil	NOUN
ejpam-1372	19	29	”	"	PUNCT
ejpam-1372	19	30	and	and	CCONJ
ejpam-1372	19	31	that	that	SCONJ
ejpam-1372	19	32	it	it	PRON
ejpam-1372	19	33	was	be	AUX
ejpam-1372	19	34	“	"	PUNCT
ejpam-1372	19	35	totally	totally	ADV
ejpam-1372	19	36	shameless	shameless	ADJ
ejpam-1372	19	37	to	to	PART
ejpam-1372	19	38	base	base	VERB
ejpam-1372	19	39	any	any	DET
ejpam-1372	19	40	demonstration	demonstration	NOUN
ejpam-1372	19	41	on	on	ADP
ejpam-1372	19	42	them	they	PRON
ejpam-1372	19	43	whatsoever	whatsoever	ADV
ejpam-1372	19	44	”	"	PUNCT
ejpam-1372	19	45	.	.	PUNCT
ejpam-1372	20	1	as	as	ADV
ejpam-1372	20	2	recently	recently	ADV
ejpam-1372	20	3	as	as	ADP
ejpam-1372	20	4	2007	2007	NUM
ejpam-1372	20	5	,	,	PUNCT
ejpam-1372	20	6	in	in	ADP
ejpam-1372	20	7	an	an	DET
ejpam-1372	20	8	article	article	NOUN
ejpam-1372	20	9	celebrating	celebrate	VERB
ejpam-1372	20	10	the	the	DET
ejpam-1372	20	11	tercentenary	tercentenary	PROPN
ejpam-1372	20	12	of	of	ADP
ejpam-1372	20	13	euler	euler	PROPN
ejpam-1372	20	14	’s	’s	PART
ejpam-1372	20	15	birth	birth	NOUN
ejpam-1372	20	16	varadarajan	varadarajan	NOUN
ejpam-1372	20	17	[	[	X
ejpam-1372	20	18	32	32	NUM
ejpam-1372	20	19	]	]	PUNCT
ejpam-1372	20	20	wrote	write	VERB
ejpam-1372	20	21	that	that	SCONJ
ejpam-1372	20	22	whilst	whilst	SCONJ
ejpam-1372	20	23	euler	euler	NOUN
ejpam-1372	20	24	certainly	certainly	ADV
ejpam-1372	20	25	had	have	VERB
ejpam-1372	20	26	some	some	DET
ejpam-1372	20	27	misconceptions	misconception	NOUN
ejpam-1372	20	28	regarding	regard	VERB
ejpam-1372	20	29	the	the	DET
ejpam-1372	20	30	summation	summation	NOUN
ejpam-1372	20	31	of	of	ADP
ejpam-1372	20	32	divergent	divergent	ADJ
ejpam-1372	20	33	series	series	NOUN
ejpam-1372	20	34	,	,	PUNCT
ejpam-1372	20	35	his	his	PRON
ejpam-1372	20	36	greatness	greatness	NOUN
ejpam-1372	20	37	on	on	ADP
ejpam-1372	20	38	this	this	DET
ejpam-1372	20	39	topic	topic	NOUN
ejpam-1372	20	40	was	be	AUX
ejpam-1372	20	41	not	not	PART
ejpam-1372	20	42	appreciated	appreciate	VERB
ejpam-1372	20	43	for	for	ADP
ejpam-1372	20	44	a	a	DET
ejpam-1372	20	45	century	century	NOUN
ejpam-1372	20	46	after	after	ADP
ejpam-1372	20	47	his	his	PRON
ejpam-1372	20	48	death	death	NOUN
ejpam-1372	20	49	when	when	SCONJ
ejpam-1372	20	50	mathematicians	mathematician	NOUN
ejpam-1372	20	51	began	begin	VERB
ejpam-1372	20	52	to	to	PART
ejpam-1372	20	53	consider	consider	VERB
ejpam-1372	20	54	the	the	DET
ejpam-1372	20	55	development	development	NOUN
ejpam-1372	20	56	of	of	ADP
ejpam-1372	20	57	a	a	DET
ejpam-1372	20	58	general	general	ADJ
ejpam-1372	20	59	theory	theory	NOUN
ejpam-1372	20	60	of	of	ADP
ejpam-1372	20	61	divergent	divergent	ADJ
ejpam-1372	20	62	series	series	NOUN
ejpam-1372	20	63	[	[	X
ejpam-1372	20	64	12	12	NUM
ejpam-1372	20	65	]	]	PUNCT
ejpam-1372	20	66	.	.	PUNCT
ejpam-1372	21	1	later	later	ADV
ejpam-1372	21	2	in	in	ADP
ejpam-1372	21	3	the	the	DET
ejpam-1372	21	4	same	same	ADJ
ejpam-1372	21	5	article	article	NOUN
ejpam-1372	21	6	he	he	PRON
ejpam-1372	21	7	states	state	VERB
ejpam-1372	21	8	that	that	SCONJ
ejpam-1372	21	9	although	although	SCONJ
ejpam-1372	21	10	in	in	ADP
ejpam-1372	21	11	his	his	PRON
ejpam-1372	21	12	opinion	opinion	NOUN
ejpam-1372	21	13	euler	euler	NOUN
ejpam-1372	21	14	had	have	AUX
ejpam-1372	21	15	taken	take	VERB
ejpam-1372	21	16	the	the	DET
ejpam-1372	21	17	first	first	ADJ
ejpam-1372	21	18	steps	step	NOUN
ejpam-1372	21	19	towards	towards	ADP
ejpam-1372	21	20	creating	create	VERB
ejpam-1372	21	21	a	a	DET
ejpam-1372	21	22	true	true	ADJ
ejpam-1372	21	23	theory	theory	NOUN
ejpam-1372	21	24	of	of	ADP
ejpam-1372	21	25	divergent	divergent	ADJ
ejpam-1372	21	26	series	series	NOUN
ejpam-1372	21	27	,	,	PUNCT
ejpam-1372	21	28	which	which	PRON
ejpam-1372	21	29	is	be	AUX
ejpam-1372	21	30	still	still	ADV
ejpam-1372	21	31	lacking	lack	VERB
ejpam-1372	21	32	today	today	NOUN
ejpam-1372	21	33	,	,	PUNCT
ejpam-1372	21	34	the	the	DET
ejpam-1372	21	35	situation	situation	NOUN
ejpam-1372	21	36	is	be	AUX
ejpam-1372	21	37	much	much	ADV
ejpam-1372	21	38	more	more	ADV
ejpam-1372	21	39	subtle	subtle	ADJ
ejpam-1372	21	40	than	than	ADP
ejpam-1372	21	41	euler	euler	NOUN
ejpam-1372	21	42	could	could	AUX
ejpam-1372	21	43	ever	ever	ADV
ejpam-1372	21	44	have	have	AUX
ejpam-1372	21	45	anticipated	anticipate	VERB
ejpam-1372	21	46	.	.	PUNCT
ejpam-1372	22	1	unfortunately	unfortunately	ADV
ejpam-1372	22	2	,	,	PUNCT
ejpam-1372	22	3	he	he	PRON
ejpam-1372	22	4	does	do	AUX
ejpam-1372	22	5	not	not	PART
ejpam-1372	22	6	elaborate	elaborate	VERB
ejpam-1372	22	7	on	on	ADP
ejpam-1372	22	8	exactly	exactly	ADV
ejpam-1372	22	9	what	what	PRON
ejpam-1372	22	10	he	he	PRON
ejpam-1372	22	11	means	mean	VERB
ejpam-1372	22	12	by	by	ADP
ejpam-1372	22	13	“	"	PUNCT
ejpam-1372	22	14	more	more	ADV
ejpam-1372	22	15	subtle	subtle	ADJ
ejpam-1372	22	16	”	"	PUNCT
ejpam-1372	22	17	.	.	PUNCT
ejpam-1372	23	1	over	over	ADP
ejpam-1372	23	2	the	the	DET
ejpam-1372	23	3	past	past	ADJ
ejpam-1372	23	4	few	few	ADJ
ejpam-1372	23	5	centuries	century	NOUN
ejpam-1372	23	6	mathematicians	mathematician	NOUN
ejpam-1372	23	7	have	have	AUX
ejpam-1372	23	8	,	,	PUNCT
ejpam-1372	23	9	for	for	ADP
ejpam-1372	23	10	the	the	DET
ejpam-1372	23	11	most	most	ADJ
ejpam-1372	23	12	part	part	NOUN
ejpam-1372	23	13	,	,	PUNCT
ejpam-1372	23	14	tended	tend	VERB
ejpam-1372	23	15	to	to	PART
ejpam-1372	23	16	steer	steer	VERB
ejpam-1372	23	17	clear	clear	ADJ
ejpam-1372	23	18	from	from	ADP
ejpam-1372	23	19	divergent	divergent	ADJ
ejpam-1372	23	20	series	series	NOUN
ejpam-1372	23	21	,	,	PUNCT
ejpam-1372	23	22	but	but	CCONJ
ejpam-1372	23	23	unfortunately	unfortunately	ADV
ejpam-1372	23	24	,	,	PUNCT
ejpam-1372	23	25	there	there	PRON
ejpam-1372	23	26	is	be	VERB
ejpam-1372	23	27	one	one	NUM
ejpam-1372	23	28	discipline	discipline	NOUN
ejpam-1372	23	29	or	or	CCONJ
ejpam-1372	23	30	field	field	NOUN
ejpam-1372	23	31	where	where	SCONJ
ejpam-1372	23	32	series	series	NOUN
ejpam-1372	23	33	of	of	ADP
ejpam-1372	23	34	this	this	DET
ejpam-1372	23	35	type	type	NOUN
ejpam-1372	23	36	abound	abound	NOUN
ejpam-1372	23	37	—	—	PUNCT
ejpam-1372	23	38	asymptotics	asymptotic	NOUN
ejpam-1372	23	39	.	.	PUNCT
ejpam-1372	24	1	in	in	ADP
ejpam-1372	24	2	this	this	DET
ejpam-1372	24	3	discipline	discipline	NOUN
ejpam-1372	24	4	special	special	ADJ
ejpam-1372	24	5	methods	method	NOUN
ejpam-1372	24	6	or	or	CCONJ
ejpam-1372	24	7	techniques	technique	NOUN
ejpam-1372	24	8	,	,	PUNCT
ejpam-1372	24	9	e.g.	e.g.	ADV
ejpam-1372	24	10	steepest	steepest	ADJ
ejpam-1372	24	11	descent	descent	NOUN
ejpam-1372	24	12	,	,	PUNCT
ejpam-1372	24	13	laplace	laplace	NOUN
ejpam-1372	24	14	’s	’s	PART
ejpam-1372	24	15	method	method	NOUN
ejpam-1372	24	16	and	and	CCONJ
ejpam-1372	24	17	the	the	DET
ejpam-1372	24	18	iterative	iterative	NOUN
ejpam-1372	24	19	solution	solution	NOUN
ejpam-1372	24	20	to	to	ADP
ejpam-1372	24	21	differential	differential	VERB
ejpam-1372	24	22	equations	equation	NOUN
ejpam-1372	24	23	to	to	PART
ejpam-1372	24	24	name	name	VERB
ejpam-1372	24	25	a	a	DET
ejpam-1372	24	26	few	few	ADJ
ejpam-1372	24	27	,	,	PUNCT
ejpam-1372	24	28	are	be	AUX
ejpam-1372	24	29	used	use	VERB
ejpam-1372	24	30	to	to	PART
ejpam-1372	24	31	derive	derive	VERB
ejpam-1372	24	32	solutions	solution	NOUN
ejpam-1372	24	33	in	in	ADP
ejpam-1372	24	34	form	form	NOUN
ejpam-1372	24	35	of	of	ADP
ejpam-1372	24	36	the	the	DET
ejpam-1372	24	37	power	power	NOUN
ejpam-1372	24	38	series	series	NOUN
ejpam-1372	24	39	expansions	expansion	NOUN
ejpam-1372	24	40	whose	whose	DET
ejpam-1372	24	41	coefficients	coefficient	NOUN
ejpam-1372	24	42	eventually	eventually	ADV
ejpam-1372	24	43	diverge	diverge	VERB
ejpam-1372	24	44	quite	quite	ADV
ejpam-1372	24	45	rapidly	rapidly	ADV
ejpam-1372	24	46	.	.	PUNCT
ejpam-1372	25	1	although	although	SCONJ
ejpam-1372	25	2	it	it	PRON
ejpam-1372	25	3	is	be	AUX
ejpam-1372	25	4	not	not	PART
ejpam-1372	25	5	clear	clear	ADJ
ejpam-1372	25	6	whether	whether	SCONJ
ejpam-1372	25	7	such	such	ADJ
ejpam-1372	25	8	expansions	expansion	NOUN
ejpam-1372	25	9	are	be	AUX
ejpam-1372	25	10	always	always	ADV
ejpam-1372	25	11	divergent	divergent	ADJ
ejpam-1372	25	12	,	,	PUNCT
ejpam-1372	25	13	they	they	PRON
ejpam-1372	25	14	are	be	AUX
ejpam-1372	25	15	invariably	invariably	ADV
ejpam-1372	25	16	truncated	truncate	VERB
ejpam-1372	25	17	according	accord	VERB
ejpam-1372	25	18	to	to	ADP
ejpam-1372	25	19	the	the	DET
ejpam-1372	25	20	poincaré	poincaré	PROPN
ejpam-1372	25	21	prescription	prescription	NOUN
ejpam-1372	25	22	or	or	CCONJ
ejpam-1372	25	23	definition	definition	NOUN
ejpam-1372	25	24	as	as	SCONJ
ejpam-1372	25	25	described	describe	VERB
ejpam-1372	25	26	on	on	ADP
ejpam-1372	25	27	p.	p.	PROPN
ejpam-1372	25	28	151	151	NUM
ejpam-1372	25	29	of	of	ADP
ejpam-1372	25	30	ref	ref	NOUN
ejpam-1372	25	31	.	.	PUNCT
ejpam-1372	26	1	[	[	X
ejpam-1372	26	2	33	33	NUM
ejpam-1372	26	3	]	]	PUNCT
ejpam-1372	26	4	.	.	PUNCT
ejpam-1372	27	1	generally	generally	ADV
ejpam-1372	27	2	,	,	PUNCT
ejpam-1372	27	3	this	this	PRON
ejpam-1372	27	4	involves	involve	VERB
ejpam-1372	27	5	truncating	truncate	VERB
ejpam-1372	27	6	an	an	DET
ejpam-1372	27	7	expansion	expansion	NOUN
ejpam-1372	27	8	after	after	ADP
ejpam-1372	27	9	a	a	DET
ejpam-1372	27	10	few	few	ADJ
ejpam-1372	27	11	terms	term	NOUN
ejpam-1372	27	12	.	.	PUNCT
ejpam-1372	28	1	then	then	ADV
ejpam-1372	28	2	one	one	NUM
ejpam-1372	28	3	is	be	AUX
ejpam-1372	28	4	left	leave	VERB
ejpam-1372	28	5	with	with	ADP
ejpam-1372	28	6	an	an	DET
ejpam-1372	28	7	approximation	approximation	NOUN
ejpam-1372	28	8	to	to	ADP
ejpam-1372	28	9	a	a	DET
ejpam-1372	28	10	given	give	VERB
ejpam-1372	28	11	function	function	NOUN
ejpam-1372	28	12	,	,	PUNCT
ejpam-1372	28	13	whose	whose	DET
ejpam-1372	28	14	accuracy	accuracy	NOUN
ejpam-1372	28	15	is	be	AUX
ejpam-1372	28	16	dependent	dependent	ADJ
ejpam-1372	28	17	upon	upon	SCONJ
ejpam-1372	28	18	whether	whether	SCONJ
ejpam-1372	28	19	the	the	DET
ejpam-1372	28	20	variable	variable	NOUN
ejpam-1372	28	21	in	in	ADP
ejpam-1372	28	22	the	the	DET
ejpam-1372	28	23	expansion	expansion	NOUN
ejpam-1372	28	24	tends	tend	VERB
ejpam-1372	28	25	to	to	ADP
ejpam-1372	28	26	a	a	DET
ejpam-1372	28	27	limit	limit	NOUN
ejpam-1372	28	28	point	point	NOUN
ejpam-1372	28	29	,	,	PUNCT
ejpam-1372	28	30	which	which	PRON
ejpam-1372	28	31	is	be	AUX
ejpam-1372	28	32	often	often	ADV
ejpam-1372	28	33	zero	zero	NUM
ejpam-1372	28	34	or	or	CCONJ
ejpam-1372	28	35	infinity	infinity	NOUN
ejpam-1372	28	36	.	.	PUNCT
ejpam-1372	29	1	hence	hence	ADV
ejpam-1372	29	2	,	,	PUNCT
ejpam-1372	29	3	depending	depend	VERB
ejpam-1372	29	4	upon	upon	SCONJ
ejpam-1372	29	5	whether	whether	SCONJ
ejpam-1372	29	6	the	the	DET
ejpam-1372	29	7	limit	limit	NOUN
ejpam-1372	29	8	point	point	NOUN
ejpam-1372	29	9	is	be	AUX
ejpam-1372	29	10	zero	zero	NUM
ejpam-1372	29	11	and	and	CCONJ
ejpam-1372	29	12	infinity	infinity	NOUN
ejpam-1372	29	13	,	,	PUNCT
ejpam-1372	29	14	we	we	PRON
ejpam-1372	29	15	say	say	VERB
ejpam-1372	29	16	that	that	SCONJ
ejpam-1372	29	17	a	a	DET
ejpam-1372	29	18	function	function	NOUN
ejpam-1372	29	19	“	"	PUNCT
ejpam-1372	29	20	goes	go	VERB
ejpam-1372	29	21	as	as	ADP
ejpam-1372	29	22	”	"	PUNCT
ejpam-1372	29	23	or	or	CCONJ
ejpam-1372	29	24	“	"	PUNCT
ejpam-1372	29	25	is	be	AUX
ejpam-1372	29	26	approximately	approximately	ADV
ejpam-1372	29	27	equal	equal	ADJ
ejpam-1372	29	28	to	to	ADP
ejpam-1372	29	29	”	"	PUNCT
ejpam-1372	29	30	the	the	DET
ejpam-1372	29	31	truncated	truncated	ADJ
ejpam-1372	29	32	expression	expression	NOUN
ejpam-1372	29	33	in	in	ADP
ejpam-1372	29	34	the	the	DET
ejpam-1372	29	35	limit	limit	NOUN
ejpam-1372	29	36	as	as	SCONJ
ejpam-1372	29	37	such	such	ADJ
ejpam-1372	29	38	and	and	CCONJ
ejpam-1372	29	39	such	such	ADJ
ejpam-1372	29	40	variable	variable	NOUN
ejpam-1372	29	41	goes	go	VERB
ejpam-1372	29	42	to	to	ADP
ejpam-1372	29	43	zero	zero	NUM
ejpam-1372	29	44	or	or	CCONJ
ejpam-1372	29	45	infinity	infinity	NOUN
ejpam-1372	29	46	.	.	PUNCT
ejpam-1372	30	1	in	in	ADP
ejpam-1372	30	2	other	other	ADJ
ejpam-1372	30	3	instances	instance	NOUN
ejpam-1372	30	4	the	the	DET
ejpam-1372	30	5	landau	landau	NOUN
ejpam-1372	30	6	symbols	symbol	NOUN
ejpam-1372	30	7	of	of	ADP
ejpam-1372	30	8	o	o	PROPN
ejpam-1372	30	9	(	(	PUNCT
ejpam-1372	30	10	)	)	PUNCT
ejpam-1372	30	11	and	and	CCONJ
ejpam-1372	30	12	o	o	X
ejpam-1372	30	13	(	(	PUNCT
ejpam-1372	30	14	)	)	PUNCT
ejpam-1372	30	15	,	,	PUNCT
ejpam-1372	30	16	or	or	CCONJ
ejpam-1372	30	17	even	even	ADV
ejpam-1372	30	18	+	+	PUNCT
ejpam-1372	30	19	.	.	PUNCT
ejpam-1372	30	20	.	.	PUNCT
ejpam-1372	30	21	.	.	PUNCT
ejpam-1372	31	1	,	,	PUNCT
ejpam-1372	31	2	are	be	AUX
ejpam-1372	31	3	used	use	VERB
ejpam-1372	31	4	to	to	PART
ejpam-1372	31	5	signify	signify	VERB
ejpam-1372	31	6	that	that	SCONJ
ejpam-1372	31	7	the	the	DET
ejpam-1372	31	8	remaining	remain	VERB
ejpam-1372	31	9	terms	term	NOUN
ejpam-1372	31	10	dropped	drop	VERB
ejpam-1372	31	11	from	from	ADP
ejpam-1372	31	12	the	the	DET
ejpam-1372	31	13	truncated	truncate	VERB
ejpam-1372	31	14	expression	expression	NOUN
ejpam-1372	31	15	can	can	AUX
ejpam-1372	31	16	be	be	AUX
ejpam-1372	31	17	bounded	bound	VERB
ejpam-1372	31	18	.	.	PUNCT
ejpam-1372	32	1	this	this	PRON
ejpam-1372	32	2	is	be	AUX
ejpam-1372	32	3	fiction	fiction	NOUN
ejpam-1372	32	4	of	of	ADP
ejpam-1372	32	5	course	course	NOUN
ejpam-1372	32	6	,	,	PUNCT
ejpam-1372	32	7	because	because	SCONJ
ejpam-1372	32	8	the	the	DET
ejpam-1372	32	9	remainder	remainder	NOUN
ejpam-1372	32	10	is	be	AUX
ejpam-1372	32	11	only	only	ADV
ejpam-1372	32	12	bounded	bound	VERB
ejpam-1372	32	13	as	as	ADV
ejpam-1372	32	14	long	long	ADV
ejpam-1372	32	15	as	as	SCONJ
ejpam-1372	32	16	there	there	PRON
ejpam-1372	32	17	is	be	VERB
ejpam-1372	32	18	an	an	DET
ejpam-1372	32	19	optimal	optimal	ADJ
ejpam-1372	32	20	point	point	NOUN
ejpam-1372	32	21	of	of	ADP
ejpam-1372	32	22	truncation	truncation	NOUN
ejpam-1372	32	23	[	[	X
ejpam-1372	32	24	24	24	NUM
ejpam-1372	32	25	]	]	PUNCT
ejpam-1372	32	26	.	.	PUNCT
ejpam-1372	33	1	even	even	ADV
ejpam-1372	33	2	more	more	ADV
ejpam-1372	33	3	troubling	troubling	ADJ
ejpam-1372	33	4	is	be	AUX
ejpam-1372	33	5	the	the	DET
ejpam-1372	33	6	fact	fact	NOUN
ejpam-1372	33	7	that	that	SCONJ
ejpam-1372	33	8	the	the	DET
ejpam-1372	33	9	domain	domain	NOUN
ejpam-1372	33	10	over	over	ADP
ejpam-1372	33	11	which	which	PRON
ejpam-1372	33	12	an	an	DET
ejpam-1372	33	13	optimal	optimal	ADJ
ejpam-1372	33	14	point	point	NOUN
ejpam-1372	33	15	of	of	ADP
ejpam-1372	33	16	truncation	truncation	NOUN
ejpam-1372	33	17	exists	exist	VERB
ejpam-1372	33	18	is	be	AUX
ejpam-1372	33	19	often	often	ADV
ejpam-1372	33	20	unspecified	unspecified	ADJ
ejpam-1372	33	21	or	or	CCONJ
ejpam-1372	33	22	even	even	ADV
ejpam-1372	33	23	unknown	unknown	ADJ
ejpam-1372	33	24	.	.	PUNCT
ejpam-1372	34	1	in	in	ADP
ejpam-1372	34	2	fact	fact	NOUN
ejpam-1372	34	3	,	,	PUNCT
ejpam-1372	34	4	for	for	ADP
ejpam-1372	34	5	most	most	ADJ
ejpam-1372	34	6	values	value	NOUN
ejpam-1372	34	7	of	of	ADP
ejpam-1372	34	8	the	the	DET
ejpam-1372	34	9	variable	variable	NOUN
ejpam-1372	34	10	there	there	PRON
ejpam-1372	34	11	is	be	VERB
ejpam-1372	34	12	simply	simply	ADV
ejpam-1372	34	13	no	no	DET
ejpam-1372	34	14	optimal	optimal	ADJ
ejpam-1372	34	15	point	point	NOUN
ejpam-1372	34	16	of	of	ADP
ejpam-1372	34	17	truncation	truncation	NOUN
ejpam-1372	34	18	.	.	PUNCT
ejpam-1372	35	1	so	so	ADV
ejpam-1372	35	2	,	,	PUNCT
ejpam-1372	35	3	we	we	PRON
ejpam-1372	35	4	have	have	VERB
ejpam-1372	35	5	the	the	DET
ejpam-1372	35	6	situation	situation	NOUN
ejpam-1372	35	7	today	today	NOUN
ejpam-1372	35	8	where	where	SCONJ
ejpam-1372	35	9	standard	standard	ADJ
ejpam-1372	35	10	asymptotics	asymptotic	NOUN
ejpam-1372	35	11	represents	represent	VERB
ejpam-1372	35	12	an	an	DET
ejpam-1372	35	13	inexact	inexact	ADJ
ejpam-1372	35	14	,	,	PUNCT
ejpam-1372	35	15	if	if	SCONJ
ejpam-1372	35	16	not	not	PART
ejpam-1372	35	17	crude	crude	ADJ
ejpam-1372	35	18	,	,	PUNCT
ejpam-1372	35	19	mathematical	mathematical	ADJ
ejpam-1372	35	20	discipline	discipline	NOUN
ejpam-1372	35	21	composed	compose	VERB
ejpam-1372	35	22	of	of	ADP
ejpam-1372	35	23	truncated	truncated	ADJ
ejpam-1372	35	24	asymptotic	asymptotic	ADJ
ejpam-1372	35	25	expansions	expansion	NOUN
ejpam-1372	35	26	that	that	PRON
ejpam-1372	35	27	suffer	suffer	VERB
ejpam-1372	35	28	from	from	ADP
ejpam-1372	35	29	the	the	DET
ejpam-1372	35	30	drawbacks	drawback	NOUN
ejpam-1372	35	31	of	of	ADP
ejpam-1372	35	32	vagueness	vagueness	NOUN
ejpam-1372	35	33	and	and	CCONJ
ejpam-1372	35	34	severe	severe	ADJ
ejpam-1372	35	35	limitation	limitation	NOUN
ejpam-1372	35	36	in	in	ADP
ejpam-1372	35	37	accuracy	accuracy	NOUN
ejpam-1372	35	38	and	and	CCONJ
ejpam-1372	35	39	range	range	NOUN
ejpam-1372	35	40	of	of	ADP
ejpam-1372	35	41	applicability	applicability	NOUN
ejpam-1372	35	42	as	as	ADP
ejpam-1372	35	43	a	a	DET
ejpam-1372	35	44	result	result	NOUN
ejpam-1372	35	45	of	of	ADP
ejpam-1372	35	46	an	an	DET
ejpam-1372	35	47	overly	overly	ADV
ejpam-1372	35	48	permissive	permissive	ADJ
ejpam-1372	35	49	poincaré	poincaré	ADJ
ejpam-1372	35	50	prescription	prescription	NOUN
ejpam-1372	35	51	.	.	PUNCT
ejpam-1372	36	1	it	it	PRON
ejpam-1372	36	2	is	be	AUX
ejpam-1372	36	3	no	no	DET
ejpam-1372	36	4	wonder	wonder	NOUN
ejpam-1372	36	5	that	that	SCONJ
ejpam-1372	36	6	the	the	DET
ejpam-1372	36	7	discipline	discipline	NOUN
ejpam-1372	36	8	is	be	AUX
ejpam-1372	36	9	frequently	frequently	ADV
ejpam-1372	36	10	subject	subject	ADJ
ejpam-1372	36	11	to	to	ADP
ejpam-1372	36	12	derisory	derisory	ADJ
ejpam-1372	36	13	remarks	remark	NOUN
ejpam-1372	36	14	from	from	ADP
ejpam-1372	36	15	pure	pure	ADJ
ejpam-1372	36	16	mathematicians	mathematician	NOUN
ejpam-1372	36	17	in	in	ADP
ejpam-1372	36	18	particular	particular	ADJ
ejpam-1372	36	19	,	,	PUNCT
ejpam-1372	36	20	who	who	PRON
ejpam-1372	36	21	point	point	VERB
ejpam-1372	36	22	out	out	ADP
ejpam-1372	36	23	that	that	SCONJ
ejpam-1372	36	24	mathematics	mathematic	NOUN
ejpam-1372	36	25	is	be	AUX
ejpam-1372	36	26	supposed	suppose	VERB
ejpam-1372	36	27	to	to	PART
ejpam-1372	36	28	be	be	AUX
ejpam-1372	36	29	an	an	DET
ejpam-1372	36	30	exact	exact	ADJ
ejpam-1372	36	31	science	science	NOUN
ejpam-1372	36	32	.	.	PUNCT
ejpam-1372	37	1	during	during	ADP
ejpam-1372	37	2	the	the	DET
ejpam-1372	37	3	last	last	ADJ
ejpam-1372	37	4	twenty	twenty	NUM
ejpam-1372	37	5	years	year	NOUN
ejpam-1372	37	6	or	or	CCONJ
ejpam-1372	37	7	so	so	ADV
ejpam-1372	37	8	,	,	PUNCT
ejpam-1372	37	9	outstanding	outstanding	ADJ
ejpam-1372	37	10	problems	problem	NOUN
ejpam-1372	37	11	in	in	ADP
ejpam-1372	37	12	dendritic	dendritic	ADJ
ejpam-1372	37	13	crystal	crystal	NOUN
ejpam-1372	37	14	growth	growth	NOUN
ejpam-1372	37	15	,	,	PUNCT
ejpam-1372	37	16	the	the	DET
ejpam-1372	37	17	directional	directional	ADJ
ejpam-1372	37	18	solidification	solidification	NOUN
ejpam-1372	37	19	of	of	ADP
ejpam-1372	37	20	crystals	crystal	NOUN
ejpam-1372	37	21	,	,	PUNCT
ejpam-1372	37	22	viscous	viscous	ADJ
ejpam-1372	37	23	flows	flow	NOUN
ejpam-1372	37	24	in	in	ADP
ejpam-1372	37	25	the	the	DET
ejpam-1372	37	26	presence	presence	NOUN
ejpam-1372	37	27	/	/	SYM
ejpam-1372	37	28	absence	absence	NOUN
ejpam-1372	37	29	of	of	ADP
ejpam-1372	37	30	surface	surface	NOUN
ejpam-1372	37	31	tension	tension	NOUN
ejpam-1372	37	32	,	,	PUNCT
ejpam-1372	37	33	quantum	quantum	ADJ
ejpam-1372	37	34	field	field	NOUN
ejpam-1372	37	35	theory	theory	NOUN
ejpam-1372	37	36	including	include	VERB
ejpam-1372	37	37	tunnelling	tunnel	VERB
ejpam-1372	37	38	,	,	PUNCT
ejpam-1372	37	39	ordinary	ordinary	ADJ
ejpam-1372	37	40	differential	differential	ADJ
ejpam-1372	37	41	equations	equation	NOUN
ejpam-1372	37	42	,	,	PUNCT
ejpam-1372	37	43	optics	optic	NOUN
ejpam-1372	37	44	,	,	PUNCT
ejpam-1372	37	45	number	number	NOUN
ejpam-1372	37	46	v.	v.	ADP
ejpam-1372	37	47	kowalenko	kowalenko	PROPN
ejpam-1372	37	48	/	/	SYM
ejpam-1372	37	49	eur	eur	PROPN
ejpam-1372	37	50	.	.	PUNCT
ejpam-1372	38	1	j.	j.	PROPN
ejpam-1372	38	2	pure	pure	PROPN
ejpam-1372	38	3	appl	appl	PROPN
ejpam-1372	38	4	.	.	PROPN
ejpam-1372	38	5	math	math	PROPN
ejpam-1372	38	6	,	,	PUNCT
ejpam-1372	38	7	4	4	NUM
ejpam-1372	38	8	(	(	PUNCT
ejpam-1372	38	9	2011	2011	NUM
ejpam-1372	38	10	)	)	PUNCT
ejpam-1372	38	11	,	,	PUNCT
ejpam-1372	38	12	370	370	NUM
ejpam-1372	38	13	-	-	SYM
ejpam-1372	38	14	423	423	NUM
ejpam-1372	38	15	372	372	NUM
ejpam-1372	38	16	theory	theory	NOUN
ejpam-1372	38	17	,	,	PUNCT
ejpam-1372	38	18	non	non	ADJ
ejpam-1372	38	19	-	-	ADJ
ejpam-1372	38	20	local	local	ADJ
ejpam-1372	38	21	solitary	solitary	ADJ
ejpam-1372	38	22	waves	wave	NOUN
ejpam-1372	38	23	,	,	PUNCT
ejpam-1372	38	24	fluid	fluid	ADJ
ejpam-1372	38	25	mechanics	mechanic	NOUN
ejpam-1372	38	26	and	and	CCONJ
ejpam-1372	38	27	a	a	DET
ejpam-1372	38	28	host	host	NOUN
ejpam-1372	38	29	of	of	ADP
ejpam-1372	38	30	other	other	ADJ
ejpam-1372	38	31	fields	field	NOUN
ejpam-1372	38	32	[	[	X
ejpam-1372	38	33	4	4	NUM
ejpam-1372	38	34	,	,	PUNCT
ejpam-1372	38	35	5	5	NUM
ejpam-1372	38	36	,	,	PUNCT
ejpam-1372	38	37	21	21	NUM
ejpam-1372	38	38	,	,	PUNCT
ejpam-1372	38	39	29	29	NUM
ejpam-1372	38	40	]	]	PUNCT
ejpam-1372	38	41	have	have	AUX
ejpam-1372	38	42	required	require	VERB
ejpam-1372	38	43	improved	improved	ADJ
ejpam-1372	38	44	methods	method	NOUN
ejpam-1372	38	45	aimed	aim	VERB
ejpam-1372	38	46	at	at	ADP
ejpam-1372	38	47	obtaining	obtain	VERB
ejpam-1372	38	48	meaningful	meaningful	ADJ
ejpam-1372	38	49	corrections	correction	NOUN
ejpam-1372	38	50	that	that	PRON
ejpam-1372	38	51	lie	lie	VERB
ejpam-1372	38	52	beyond	beyond	ADP
ejpam-1372	38	53	all	all	DET
ejpam-1372	38	54	orders	order	NOUN
ejpam-1372	38	55	of	of	ADP
ejpam-1372	38	56	a	a	DET
ejpam-1372	38	57	standard	standard	ADJ
ejpam-1372	38	58	asymptotic	asymptotic	ADJ
ejpam-1372	38	59	expansion	expansion	NOUN
ejpam-1372	38	60	.	.	PUNCT
ejpam-1372	39	1	in	in	ADP
ejpam-1372	39	2	addition	addition	NOUN
ejpam-1372	39	3	to	to	ADP
ejpam-1372	39	4	these	these	DET
ejpam-1372	39	5	applications	application	NOUN
ejpam-1372	39	6	,	,	PUNCT
ejpam-1372	39	7	analysts	analyst	NOUN
ejpam-1372	39	8	have	have	AUX
ejpam-1372	39	9	been	be	AUX
ejpam-1372	39	10	engaged	engage	VERB
ejpam-1372	39	11	in	in	ADP
ejpam-1372	39	12	developing	develop	VERB
ejpam-1372	39	13	exponentially	exponentially	ADV
ejpam-1372	39	14	improved	improve	VERB
ejpam-1372	39	15	asymptotics	asymptotic	NOUN
ejpam-1372	39	16	of	of	ADP
ejpam-1372	39	17	special	special	ADJ
ejpam-1372	39	18	functions	function	NOUN
ejpam-1372	39	19	such	such	ADJ
ejpam-1372	39	20	as	as	ADP
ejpam-1372	39	21	the	the	DET
ejpam-1372	39	22	confluent	confluent	ADJ
ejpam-1372	39	23	hypergeometric	hypergeometric	ADJ
ejpam-1372	39	24	and	and	CCONJ
ejpam-1372	39	25	gamma	gamma	NOUN
ejpam-1372	39	26	functions	function	NOUN
ejpam-1372	39	27	as	as	SCONJ
ejpam-1372	39	28	described	describe	VERB
ejpam-1372	39	29	in	in	ADP
ejpam-1372	39	30	ch	ch	PROPN
ejpam-1372	39	31	.	.	PROPN
ejpam-1372	39	32	6	6	NUM
ejpam-1372	39	33	of	of	ADP
ejpam-1372	39	34	ref	ref	NOUN
ejpam-1372	39	35	.	.	PUNCT
ejpam-1372	40	1	[	[	X
ejpam-1372	40	2	27	27	NUM
ejpam-1372	40	3	]	]	PUNCT
ejpam-1372	40	4	.	.	PUNCT
ejpam-1372	41	1	for	for	ADP
ejpam-1372	41	2	these	these	DET
ejpam-1372	41	3	exceptional	exceptional	ADJ
ejpam-1372	41	4	and	and	CCONJ
ejpam-1372	41	5	important	important	ADJ
ejpam-1372	41	6	problems	problem	NOUN
ejpam-1372	41	7	standard	standard	ADJ
ejpam-1372	41	8	asymptotic	asymptotic	ADJ
ejpam-1372	41	9	analysis	analysis	NOUN
ejpam-1372	41	10	is	be	AUX
ejpam-1372	41	11	simply	simply	ADV
ejpam-1372	41	12	inadequate	inadequate	ADJ
ejpam-1372	41	13	.	.	PUNCT
ejpam-1372	42	1	therefore	therefore	ADV
ejpam-1372	42	2	,	,	PUNCT
ejpam-1372	42	3	the	the	DET
ejpam-1372	42	4	sub	sub	NOUN
ejpam-1372	42	5	-	-	ADJ
ejpam-1372	42	6	discipline	discipline	ADJ
ejpam-1372	42	7	or	or	CCONJ
ejpam-1372	42	8	field	field	NOUN
ejpam-1372	42	9	known	know	VERB
ejpam-1372	42	10	as	as	ADP
ejpam-1372	42	11	exponential	exponential	ADJ
ejpam-1372	42	12	asymptotics	asymptotic	NOUN
ejpam-1372	42	13	or	or	CCONJ
ejpam-1372	42	14	asymptotics	asymptotic	NOUN
ejpam-1372	42	15	beyond	beyond	ADP
ejpam-1372	42	16	all	all	DET
ejpam-1372	42	17	orders	order	NOUN
ejpam-1372	42	18	,	,	PUNCT
ejpam-1372	42	19	also	also	ADV
ejpam-1372	42	20	occasionally	occasionally	ADV
ejpam-1372	42	21	referred	refer	VERB
ejpam-1372	42	22	to	to	ADP
ejpam-1372	42	23	as	as	ADP
ejpam-1372	42	24	hyperasymptotics	hyperasymptotic	NOUN
ejpam-1372	42	25	,	,	PUNCT
ejpam-1372	42	26	has	have	AUX
ejpam-1372	42	27	evolved	evolve	VERB
ejpam-1372	42	28	.	.	PUNCT
ejpam-1372	43	1	whilst	whilst	SCONJ
ejpam-1372	43	2	this	this	DET
ejpam-1372	43	3	field	field	NOUN
ejpam-1372	43	4	seeks	seek	VERB
ejpam-1372	43	5	to	to	PART
ejpam-1372	43	6	derive	derive	VERB
ejpam-1372	43	7	the	the	DET
ejpam-1372	43	8	terms	term	NOUN
ejpam-1372	43	9	in	in	ADP
ejpam-1372	43	10	an	an	DET
ejpam-1372	43	11	asymptotic	asymptotic	ADJ
ejpam-1372	43	12	expansion	expansion	NOUN
ejpam-1372	43	13	that	that	PRON
ejpam-1372	43	14	are	be	AUX
ejpam-1372	43	15	neglected	neglect	VERB
ejpam-1372	43	16	by	by	ADP
ejpam-1372	43	17	the	the	DET
ejpam-1372	43	18	application	application	NOUN
ejpam-1372	43	19	of	of	ADP
ejpam-1372	43	20	the	the	DET
ejpam-1372	43	21	poincaré	poincaré	ADJ
ejpam-1372	43	22	prescription	prescription	NOUN
ejpam-1372	43	23	,	,	PUNCT
ejpam-1372	43	24	as	as	SCONJ
ejpam-1372	43	25	explained	explain	VERB
ejpam-1372	43	26	at	at	ADP
ejpam-1372	43	27	the	the	DET
ejpam-1372	43	28	beginning	beginning	NOUN
ejpam-1372	43	29	to	to	ADP
ejpam-1372	43	30	sec	sec	PROPN
ejpam-1372	43	31	.	.	PROPN
ejpam-1372	43	32	3	3	NUM
ejpam-1372	43	33	here	here	ADV
ejpam-1372	43	34	,	,	PUNCT
ejpam-1372	43	35	it	it	PRON
ejpam-1372	43	36	still	still	ADV
ejpam-1372	43	37	suffers	suffer	VERB
ejpam-1372	43	38	from	from	ADP
ejpam-1372	43	39	the	the	DET
ejpam-1372	43	40	same	same	ADJ
ejpam-1372	43	41	problem	problem	NOUN
ejpam-1372	43	42	in	in	ADP
ejpam-1372	43	43	standard	standard	ADJ
ejpam-1372	43	44	asymptotics	asymptotic	NOUN
ejpam-1372	43	45	,	,	PUNCT
ejpam-1372	43	46	which	which	PRON
ejpam-1372	43	47	is	be	AUX
ejpam-1372	43	48	:	:	PUNCT
ejpam-1372	43	49	how	how	SCONJ
ejpam-1372	43	50	does	do	AUX
ejpam-1372	43	51	one	one	NUM
ejpam-1372	43	52	obtain	obtain	VERB
ejpam-1372	43	53	meaningful	meaningful	ADJ
ejpam-1372	43	54	values	value	NOUN
ejpam-1372	43	55	to	to	ADP
ejpam-1372	43	56	divergent	divergent	ADJ
ejpam-1372	43	57	series	series	NOUN
ejpam-1372	43	58	?	?	PUNCT
ejpam-1372	44	1	this	this	PRON
ejpam-1372	44	2	is	be	AUX
ejpam-1372	44	3	because	because	SCONJ
ejpam-1372	44	4	frequently	frequently	ADV
ejpam-1372	44	5	these	these	DET
ejpam-1372	44	6	subdominant	subdominant	ADJ
ejpam-1372	44	7	terms	term	NOUN
ejpam-1372	44	8	are	be	AUX
ejpam-1372	44	9	themselves	themselves	PRON
ejpam-1372	44	10	divergent	divergent	ADJ
ejpam-1372	44	11	series	series	NOUN
ejpam-1372	44	12	.	.	PUNCT
ejpam-1372	45	1	worse	bad	ADJ
ejpam-1372	45	2	still	still	ADV
ejpam-1372	45	3	,	,	PUNCT
ejpam-1372	45	4	they	they	PRON
ejpam-1372	45	5	are	be	AUX
ejpam-1372	45	6	usually	usually	ADV
ejpam-1372	45	7	masked	mask	VERB
ejpam-1372	45	8	by	by	ADP
ejpam-1372	45	9	a	a	DET
ejpam-1372	45	10	divergent	divergent	ADJ
ejpam-1372	45	11	dominant	dominant	ADJ
ejpam-1372	45	12	series	series	NOUN
ejpam-1372	45	13	.	.	PUNCT
ejpam-1372	46	1	hence	hence	ADV
ejpam-1372	46	2	,	,	PUNCT
ejpam-1372	46	3	in	in	ADP
ejpam-1372	46	4	order	order	NOUN
ejpam-1372	46	5	to	to	PART
ejpam-1372	46	6	determine	determine	VERB
ejpam-1372	46	7	both	both	DET
ejpam-1372	46	8	contributions	contribution	NOUN
ejpam-1372	46	9	to	to	ADP
ejpam-1372	46	10	the	the	DET
ejpam-1372	46	11	overall	overall	ADJ
ejpam-1372	46	12	solution	solution	NOUN
ejpam-1372	46	13	,	,	PUNCT
ejpam-1372	46	14	we	we	PRON
ejpam-1372	46	15	again	again	ADV
ejpam-1372	46	16	require	require	VERB
ejpam-1372	46	17	a	a	DET
ejpam-1372	46	18	theory	theory	NOUN
ejpam-1372	46	19	of	of	ADP
ejpam-1372	46	20	divergent	divergent	ADJ
ejpam-1372	46	21	series	series	NOUN
ejpam-1372	46	22	for	for	ADP
ejpam-1372	46	23	only	only	ADV
ejpam-1372	46	24	then	then	ADV
ejpam-1372	46	25	will	will	AUX
ejpam-1372	46	26	it	it	PRON
ejpam-1372	46	27	be	be	AUX
ejpam-1372	46	28	possible	possible	ADJ
ejpam-1372	46	29	to	to	PART
ejpam-1372	46	30	determine	determine	VERB
ejpam-1372	46	31	the	the	DET
ejpam-1372	46	32	exact	exact	ADJ
ejpam-1372	46	33	values	value	NOUN
ejpam-1372	46	34	of	of	ADP
ejpam-1372	46	35	the	the	DET
ejpam-1372	46	36	original	original	ADJ
ejpam-1372	46	37	function	function	NOUN
ejpam-1372	46	38	,	,	PUNCT
ejpam-1372	46	39	which	which	PRON
ejpam-1372	46	40	is	be	AUX
ejpam-1372	46	41	the	the	DET
ejpam-1372	46	42	ultimate	ultimate	ADJ
ejpam-1372	46	43	goal	goal	NOUN
ejpam-1372	46	44	of	of	ADP
ejpam-1372	46	45	asymptotics	asymptotic	NOUN
ejpam-1372	46	46	.	.	PUNCT
ejpam-1372	47	1	if	if	SCONJ
ejpam-1372	47	2	such	such	DET
ejpam-1372	47	3	a	a	DET
ejpam-1372	47	4	methodology	methodology	NOUN
ejpam-1372	47	5	could	could	AUX
ejpam-1372	47	6	be	be	AUX
ejpam-1372	47	7	formulated	formulate	VERB
ejpam-1372	47	8	,	,	PUNCT
ejpam-1372	47	9	then	then	ADV
ejpam-1372	47	10	asymptotics	asymptotic	NOUN
ejpam-1372	47	11	would	would	AUX
ejpam-1372	47	12	be	be	AUX
ejpam-1372	47	13	elevated	elevate	VERB
ejpam-1372	47	14	to	to	ADP
ejpam-1372	47	15	a	a	DET
ejpam-1372	47	16	true	true	ADJ
ejpam-1372	47	17	mathematical	mathematical	ADJ
ejpam-1372	47	18	discipline	discipline	NOUN
ejpam-1372	47	19	eliciting	elicit	VERB
ejpam-1372	47	20	precise	precise	ADJ
ejpam-1372	47	21	answers	answer	NOUN
ejpam-1372	47	22	.	.	PUNCT
ejpam-1372	48	1	this	this	PRON
ejpam-1372	48	2	would	would	AUX
ejpam-1372	48	3	not	not	PART
ejpam-1372	48	4	only	only	ADV
ejpam-1372	48	5	have	have	VERB
ejpam-1372	48	6	a	a	DET
ejpam-1372	48	7	profound	profound	ADJ
ejpam-1372	48	8	effect	effect	NOUN
ejpam-1372	48	9	on	on	ADP
ejpam-1372	48	10	mathematics	mathematic	NOUN
ejpam-1372	48	11	,	,	PUNCT
ejpam-1372	48	12	but	but	CCONJ
ejpam-1372	48	13	also	also	ADV
ejpam-1372	48	14	on	on	ADP
ejpam-1372	48	15	physics	physics	NOUN
ejpam-1372	48	16	and	and	CCONJ
ejpam-1372	48	17	engineering	engineering	NOUN
ejpam-1372	48	18	.	.	PUNCT
ejpam-1372	49	1	2	2	X
ejpam-1372	49	2	.	.	X
ejpam-1372	49	3	divergent	divergent	ADJ
ejpam-1372	49	4	series	series	NOUN
ejpam-1372	49	5	when	when	SCONJ
ejpam-1372	49	6	one	one	PRON
ejpam-1372	49	7	wishes	wish	VERB
ejpam-1372	49	8	to	to	PART
ejpam-1372	49	9	discuss	discuss	VERB
ejpam-1372	49	10	euler	euler	PROPN
ejpam-1372	49	11	’s	’s	PART
ejpam-1372	49	12	“	"	PUNCT
ejpam-1372	49	13	unorthodox	unorthodox	ADJ
ejpam-1372	49	14	”	"	PUNCT
ejpam-1372	49	15	views	view	NOUN
ejpam-1372	49	16	on	on	ADP
ejpam-1372	49	17	divergent	divergent	ADJ
ejpam-1372	49	18	series	series	NOUN
ejpam-1372	49	19	,	,	PUNCT
ejpam-1372	49	20	one	one	PRON
ejpam-1372	49	21	is	be	AUX
ejpam-1372	49	22	inevitably	inevitably	ADV
ejpam-1372	49	23	drawn	draw	VERB
ejpam-1372	49	24	into	into	ADP
ejpam-1372	49	25	a	a	DET
ejpam-1372	49	26	study	study	NOUN
ejpam-1372	49	27	of	of	ADP
ejpam-1372	49	28	the	the	DET
ejpam-1372	49	29	geometric	geometric	ADJ
ejpam-1372	49	30	series	series	NOUN
ejpam-1372	49	31	for	for	ADP
ejpam-1372	49	32	it	it	PRON
ejpam-1372	49	33	is	be	AUX
ejpam-1372	49	34	this	this	DET
ejpam-1372	49	35	series	series	NOUN
ejpam-1372	49	36	that	that	PRON
ejpam-1372	49	37	was	be	AUX
ejpam-1372	49	38	used	use	VERB
ejpam-1372	49	39	as	as	ADP
ejpam-1372	49	40	the	the	DET
ejpam-1372	49	41	basis	basis	NOUN
ejpam-1372	49	42	for	for	ADP
ejpam-1372	49	43	his	his	PRON
ejpam-1372	49	44	views	view	NOUN
ejpam-1372	49	45	.	.	PUNCT
ejpam-1372	50	1	we	we	PRON
ejpam-1372	50	2	shall	shall	AUX
ejpam-1372	50	3	do	do	VERB
ejpam-1372	50	4	likewise	likewise	ADV
ejpam-1372	50	5	,	,	PUNCT
ejpam-1372	50	6	although	although	SCONJ
ejpam-1372	50	7	it	it	PRON
ejpam-1372	50	8	should	should	AUX
ejpam-1372	50	9	be	be	AUX
ejpam-1372	50	10	pointed	point	VERB
ejpam-1372	50	11	out	out	ADP
ejpam-1372	50	12	that	that	SCONJ
ejpam-1372	50	13	the	the	DET
ejpam-1372	50	14	series	series	NOUN
ejpam-1372	50	15	has	have	VERB
ejpam-1372	50	16	a	a	DET
ejpam-1372	50	17	fascinating	fascinating	ADJ
ejpam-1372	50	18	history	history	NOUN
ejpam-1372	50	19	of	of	ADP
ejpam-1372	50	20	its	its	PRON
ejpam-1372	50	21	own	own	ADJ
ejpam-1372	50	22	going	go	VERB
ejpam-1372	50	23	way	way	ADV
ejpam-1372	50	24	back	back	ADV
ejpam-1372	50	25	to	to	ADP
ejpam-1372	50	26	archimedes	archimede	NOUN
ejpam-1372	50	27	,	,	PUNCT
ejpam-1372	50	28	who	who	PRON
ejpam-1372	50	29	used	use	VERB
ejpam-1372	50	30	it	it	PRON
ejpam-1372	50	31	to	to	PART
ejpam-1372	50	32	calculate	calculate	VERB
ejpam-1372	50	33	the	the	DET
ejpam-1372	50	34	area	area	NOUN
ejpam-1372	50	35	under	under	ADP
ejpam-1372	50	36	a	a	DET
ejpam-1372	50	37	parabola	parabola	NOUN
ejpam-1372	50	38	intersected	intersect	VERB
ejpam-1372	50	39	by	by	ADP
ejpam-1372	50	40	a	a	DET
ejpam-1372	50	41	line	line	NOUN
ejpam-1372	50	42	.	.	PUNCT
ejpam-1372	51	1	this	this	PRON
ejpam-1372	51	2	became	become	VERB
ejpam-1372	51	3	the	the	DET
ejpam-1372	51	4	precursor	precursor	NOUN
ejpam-1372	51	5	to	to	ADP
ejpam-1372	51	6	integral	integral	ADJ
ejpam-1372	51	7	calculus	calculus	NOUN
ejpam-1372	51	8	.	.	PUNCT
ejpam-1372	52	1	before	before	SCONJ
ejpam-1372	52	2	the	the	DET
ejpam-1372	52	3	geometric	geometric	ADJ
ejpam-1372	52	4	series	series	NOUN
ejpam-1372	52	5	can	can	AUX
ejpam-1372	52	6	be	be	AUX
ejpam-1372	52	7	introduced	introduce	VERB
ejpam-1372	52	8	,	,	PUNCT
ejpam-1372	52	9	however	however	ADV
ejpam-1372	52	10	,	,	PUNCT
ejpam-1372	52	11	we	we	PRON
ejpam-1372	52	12	first	first	ADV
ejpam-1372	52	13	need	need	VERB
ejpam-1372	52	14	to	to	PART
ejpam-1372	52	15	understand	understand	VERB
ejpam-1372	52	16	what	what	PRON
ejpam-1372	52	17	is	be	AUX
ejpam-1372	52	18	meant	mean	VERB
ejpam-1372	52	19	by	by	ADP
ejpam-1372	52	20	a	a	DET
ejpam-1372	52	21	divergent	divergent	ADJ
ejpam-1372	52	22	series	series	NOUN
ejpam-1372	52	23	.	.	PUNCT
ejpam-1372	53	1	in	in	ADP
ejpam-1372	53	2	actual	actual	ADJ
ejpam-1372	53	3	fact	fact	NOUN
ejpam-1372	53	4	,	,	PUNCT
ejpam-1372	53	5	there	there	PRON
ejpam-1372	53	6	is	be	VERB
ejpam-1372	53	7	no	no	DET
ejpam-1372	53	8	formal	formal	ADJ
ejpam-1372	53	9	or	or	CCONJ
ejpam-1372	53	10	rigorous	rigorous	ADJ
ejpam-1372	53	11	definition	definition	NOUN
ejpam-1372	53	12	of	of	ADP
ejpam-1372	53	13	a	a	DET
ejpam-1372	53	14	divergent	divergent	ADJ
ejpam-1372	53	15	series	series	NOUN
ejpam-1372	53	16	.	.	PUNCT
ejpam-1372	54	1	instead	instead	ADV
ejpam-1372	54	2	,	,	PUNCT
ejpam-1372	54	3	we	we	PRON
ejpam-1372	54	4	must	must	AUX
ejpam-1372	54	5	examine	examine	VERB
ejpam-1372	54	6	what	what	PRON
ejpam-1372	54	7	a	a	DET
ejpam-1372	54	8	convergent	convergent	NOUN
ejpam-1372	54	9	series	series	NOUN
ejpam-1372	54	10	is	be	AUX
ejpam-1372	54	11	.	.	PUNCT
ejpam-1372	55	1	then	then	ADV
ejpam-1372	55	2	by	by	ADP
ejpam-1372	55	3	a	a	DET
ejpam-1372	55	4	process	process	NOUN
ejpam-1372	55	5	of	of	ADP
ejpam-1372	55	6	elimination	elimination	NOUN
ejpam-1372	55	7	,	,	PUNCT
ejpam-1372	55	8	anything	anything	PRON
ejpam-1372	55	9	that	that	PRON
ejpam-1372	55	10	is	be	AUX
ejpam-1372	55	11	not	not	PART
ejpam-1372	55	12	a	a	DET
ejpam-1372	55	13	convergent	convergent	NOUN
ejpam-1372	55	14	series	series	NOUN
ejpam-1372	55	15	is	be	AUX
ejpam-1372	55	16	regarded	regard	VERB
ejpam-1372	55	17	as	as	ADP
ejpam-1372	55	18	being	be	AUX
ejpam-1372	55	19	divergent	divergent	ADJ
ejpam-1372	55	20	.	.	PUNCT
ejpam-1372	56	1	copson	copson	PROPN
ejpam-1372	56	2	’s	’s	PART
ejpam-1372	56	3	definition	definition	NOUN
ejpam-1372	56	4	[	[	X
ejpam-1372	56	5	7	7	X
ejpam-1372	56	6	]	]	PUNCT
ejpam-1372	56	7	begins	begin	VERB
ejpam-1372	56	8	with	with	ADP
ejpam-1372	56	9	the	the	DET
ejpam-1372	56	10	symbol	symbol	NOUN
ejpam-1372	56	11	of	of	ADP
ejpam-1372	56	12	a0+a1+a2	a0+a1+a2	PROPN
ejpam-1372	56	13	+	+	PROPN
ejpam-1372	56	14	.	.	PUNCT
ejpam-1372	56	15	.	.	PUNCT
ejpam-1372	57	1	.+ak+	.+ak+	PROPN
ejpam-1372	57	2	.	.	PUNCT
ejpam-1372	57	3	.	.	PUNCT
ejpam-1372	58	1	.	.	PUNCT
ejpam-1372	58	2	,	,	PUNCT
ejpam-1372	59	1	which	which	PRON
ejpam-1372	59	2	involves	involve	VERB
ejpam-1372	59	3	the	the	DET
ejpam-1372	59	4	sum	sum	NOUN
ejpam-1372	59	5	of	of	ADP
ejpam-1372	59	6	an	an	DET
ejpam-1372	59	7	infinite	infinite	ADJ
ejpam-1372	59	8	number	number	NOUN
ejpam-1372	59	9	of	of	ADP
ejpam-1372	59	10	complex	complex	ADJ
ejpam-1372	59	11	numbers	number	NOUN
ejpam-1372	59	12	.	.	PUNCT
ejpam-1372	60	1	to	to	PART
ejpam-1372	60	2	assign	assign	VERB
ejpam-1372	60	3	a	a	DET
ejpam-1372	60	4	meaning	meaning	NOUN
ejpam-1372	60	5	to	to	ADP
ejpam-1372	60	6	this	this	DET
ejpam-1372	60	7	symbol	symbol	NOUN
ejpam-1372	60	8	,	,	PUNCT
ejpam-1372	60	9	he	he	PRON
ejpam-1372	60	10	then	then	ADV
ejpam-1372	60	11	considers	consider	VERB
ejpam-1372	60	12	the	the	DET
ejpam-1372	60	13	partial	partial	ADJ
ejpam-1372	60	14	sums	sum	NOUN
ejpam-1372	60	15	,	,	PUNCT
ejpam-1372	60	16	s0	s0	NOUN
ejpam-1372	60	17	,	,	PUNCT
ejpam-1372	60	18	s1,s2	s1,s2	PROPN
ejpam-1372	60	19	,	,	PUNCT
ejpam-1372	60	20	.	.	PUNCT
ejpam-1372	60	21	.	.	PUNCT
ejpam-1372	61	1	.	.	PUNCT
ejpam-1372	62	1	,	,	PUNCT
ejpam-1372	62	2	where	where	SCONJ
ejpam-1372	62	3	each	each	DET
ejpam-1372	62	4	partial	partial	ADJ
ejpam-1372	62	5	sum	sum	NOUN
ejpam-1372	62	6	is	be	AUX
ejpam-1372	62	7	given	give	VERB
ejpam-1372	62	8	by	by	ADP
ejpam-1372	62	9	sk	sk	NOUN
ejpam-1372	62	10	=	=	PROPN
ejpam-1372	62	11	a0	a0	PROPN
ejpam-1372	62	12	+	+	CCONJ
ejpam-1372	62	13	a1	a1	NOUN
ejpam-1372	62	14	+	+	CCONJ
ejpam-1372	62	15	a2	a2	PROPN
ejpam-1372	62	16	+	+	X
ejpam-1372	62	17	.	.	PUNCT
ejpam-1372	62	18	.	.	PUNCT
ejpam-1372	63	1	.+	.+	NOUN
ejpam-1372	63	2	ak	ak	PROPN
ejpam-1372	63	3	.	.	PUNCT
ejpam-1372	64	1	(	(	PUNCT
ejpam-1372	64	2	1	1	X
ejpam-1372	64	3	)	)	PUNCT
ejpam-1372	64	4	if	if	SCONJ
ejpam-1372	64	5	this	this	DET
ejpam-1372	64	6	sequence	sequence	NOUN
ejpam-1372	64	7	tends	tend	VERB
ejpam-1372	64	8	to	to	ADP
ejpam-1372	64	9	a	a	DET
ejpam-1372	64	10	finite	finite	ADJ
ejpam-1372	64	11	limit	limit	NOUN
ejpam-1372	64	12	s	s	PART
ejpam-1372	64	13	,	,	PUNCT
ejpam-1372	64	14	then	then	ADV
ejpam-1372	64	15	the	the	DET
ejpam-1372	64	16	infinite	infinite	ADJ
ejpam-1372	64	17	series	series	NOUN
ejpam-1372	64	18	is	be	AUX
ejpam-1372	64	19	convergent	convergent	ADJ
ejpam-1372	64	20	with	with	ADP
ejpam-1372	64	21	the	the	DET
ejpam-1372	64	22	value	value	NOUN
ejpam-1372	64	23	of	of	ADP
ejpam-1372	64	24	the	the	DET
ejpam-1372	64	25	limit	limit	NOUN
ejpam-1372	64	26	equal	equal	ADJ
ejpam-1372	64	27	to	to	ADP
ejpam-1372	64	28	s.	s.	PROPN
ejpam-1372	64	29	that	that	PRON
ejpam-1372	64	30	is	be	AUX
ejpam-1372	64	31	,	,	PUNCT
ejpam-1372	64	32	s	s	PART
ejpam-1372	64	33	=	=	NOUN
ejpam-1372	64	34	∑∞	∑∞	NOUN
ejpam-1372	64	35	k=0	k=0	PROPN
ejpam-1372	64	36	ak	ak	PROPN
ejpam-1372	64	37	.	.	PROPN
ejpam-1372	64	38	on	on	ADP
ejpam-1372	64	39	the	the	DET
ejpam-1372	64	40	other	other	ADJ
ejpam-1372	64	41	hand	hand	NOUN
ejpam-1372	64	42	,	,	PUNCT
ejpam-1372	64	43	if	if	SCONJ
ejpam-1372	64	44	the	the	DET
ejpam-1372	64	45	sequence	sequence	NOUN
ejpam-1372	64	46	of	of	ADP
ejpam-1372	64	47	partial	partial	ADJ
ejpam-1372	64	48	sums	sum	NOUN
ejpam-1372	64	49	does	do	AUX
ejpam-1372	64	50	not	not	PART
ejpam-1372	64	51	converge	converge	VERB
ejpam-1372	64	52	,	,	PUNCT
ejpam-1372	64	53	the	the	DET
ejpam-1372	64	54	series	series	NOUN
ejpam-1372	64	55	is	be	AUX
ejpam-1372	64	56	said	say	VERB
ejpam-1372	64	57	to	to	PART
ejpam-1372	64	58	be	be	AUX
ejpam-1372	64	59	divergent	divergent	ADJ
ejpam-1372	64	60	.	.	PUNCT
ejpam-1372	65	1	this	this	PRON
ejpam-1372	65	2	is	be	AUX
ejpam-1372	65	3	certainly	certainly	ADV
ejpam-1372	65	4	a	a	DET
ejpam-1372	65	5	strange	strange	ADJ
ejpam-1372	65	6	definition	definition	NOUN
ejpam-1372	65	7	for	for	ADP
ejpam-1372	65	8	it	it	PRON
ejpam-1372	65	9	not	not	PART
ejpam-1372	65	10	only	only	ADV
ejpam-1372	65	11	includes	include	VERB
ejpam-1372	65	12	series	series	NOUN
ejpam-1372	65	13	yielding	yield	VERB
ejpam-1372	65	14	an	an	DET
ejpam-1372	65	15	obvious	obvious	ADJ
ejpam-1372	65	16	infinity	infinity	NOUN
ejpam-1372	65	17	such	such	ADJ
ejpam-1372	65	18	as	as	ADP
ejpam-1372	65	19	1	1	NUM
ejpam-1372	65	20	+	+	NUM
ejpam-1372	65	21	1	1	NUM
ejpam-1372	65	22	+	+	NUM
ejpam-1372	65	23	1	1	NUM
ejpam-1372	65	24	+	+	NUM
ejpam-1372	65	25	1	1	NUM
ejpam-1372	65	26	+	+	NUM
ejpam-1372	65	27	.	.	PUNCT
ejpam-1372	65	28	.	.	PUNCT
ejpam-1372	65	29	.	.	PUNCT
ejpam-1372	66	1	and	and	CCONJ
ejpam-1372	67	1	1	1	NUM
ejpam-1372	67	2	+	+	NUM
ejpam-1372	67	3	2	2	NUM
ejpam-1372	67	4	+	+	NUM
ejpam-1372	67	5	4	4	NUM
ejpam-1372	67	6	+	+	NUM
ejpam-1372	67	7	.	.	PUNCT
ejpam-1372	67	8	.	.	PUNCT
ejpam-1372	67	9	.	.	PUNCT
ejpam-1372	67	10	,	,	PUNCT
ejpam-1372	67	11	but	but	CCONJ
ejpam-1372	67	12	also	also	ADV
ejpam-1372	67	13	examples	example	NOUN
ejpam-1372	67	14	,	,	PUNCT
ejpam-1372	67	15	where	where	SCONJ
ejpam-1372	67	16	the	the	DET
ejpam-1372	67	17	series	series	NOUN
ejpam-1372	67	18	possess	possess	VERB
ejpam-1372	67	19	indeterminate	indeterminate	ADJ
ejpam-1372	67	20	limits	limit	NOUN
ejpam-1372	67	21	such	such	ADJ
ejpam-1372	67	22	as	as	ADP
ejpam-1372	67	23	1−	1−	NUM
ejpam-1372	67	24	1	1	NUM
ejpam-1372	67	25	+	+	SYM
ejpam-1372	67	26	1−	1−	NUM
ejpam-1372	67	27	1	1	NUM
ejpam-1372	67	28	+	+	NUM
ejpam-1372	67	29	1−	1−	NUM
ejpam-1372	67	30	1	1	NUM
ejpam-1372	67	31	+	+	NUM
ejpam-1372	67	32	.	.	PUNCT
ejpam-1372	67	33	.	.	PUNCT
ejpam-1372	68	1	..	..	PUNCT
ejpam-1372	69	1	all	all	DET
ejpam-1372	69	2	these	these	DET
ejpam-1372	69	3	examples	example	NOUN
ejpam-1372	69	4	v.	v.	ADP
ejpam-1372	69	5	kowalenko	kowalenko	PROPN
ejpam-1372	69	6	/	/	SYM
ejpam-1372	69	7	eur	eur	PROPN
ejpam-1372	69	8	.	.	PUNCT
ejpam-1372	70	1	j.	j.	PROPN
ejpam-1372	70	2	pure	pure	PROPN
ejpam-1372	70	3	appl	appl	PROPN
ejpam-1372	70	4	.	.	PROPN
ejpam-1372	70	5	math	math	PROPN
ejpam-1372	70	6	,	,	PUNCT
ejpam-1372	70	7	4	4	NUM
ejpam-1372	70	8	(	(	PUNCT
ejpam-1372	70	9	2011	2011	NUM
ejpam-1372	70	10	)	)	PUNCT
ejpam-1372	70	11	,	,	PUNCT
ejpam-1372	70	12	370	370	NUM
ejpam-1372	70	13	-	-	SYM
ejpam-1372	70	14	423	423	NUM
ejpam-1372	70	15	373	373	NUM
ejpam-1372	70	16	can	can	AUX
ejpam-1372	70	17	be	be	AUX
ejpam-1372	70	18	regarded	regard	VERB
ejpam-1372	70	19	as	as	ADP
ejpam-1372	70	20	special	special	ADJ
ejpam-1372	70	21	cases	case	NOUN
ejpam-1372	70	22	of	of	ADP
ejpam-1372	70	23	the	the	DET
ejpam-1372	70	24	geometric	geometric	ADJ
ejpam-1372	70	25	series	series	NOUN
ejpam-1372	70	26	,	,	PUNCT
ejpam-1372	70	27	although	although	SCONJ
ejpam-1372	70	28	the	the	DET
ejpam-1372	70	29	last	last	ADJ
ejpam-1372	70	30	example	example	NOUN
ejpam-1372	70	31	is	be	AUX
ejpam-1372	70	32	now	now	ADV
ejpam-1372	70	33	known	know	VERB
ejpam-1372	70	34	as	as	ADP
ejpam-1372	70	35	grandi	grandi	PROPN
ejpam-1372	70	36	’s	’s	PART
ejpam-1372	70	37	series	series	NOUN
ejpam-1372	70	38	since	since	SCONJ
ejpam-1372	70	39	he	he	PRON
ejpam-1372	70	40	was	be	AUX
ejpam-1372	70	41	the	the	DET
ejpam-1372	70	42	first	first	ADJ
ejpam-1372	70	43	to	to	PART
ejpam-1372	70	44	provide	provide	VERB
ejpam-1372	70	45	a	a	DET
ejpam-1372	70	46	simplistic	simplistic	ADJ
ejpam-1372	70	47	account	account	NOUN
ejpam-1372	70	48	of	of	ADP
ejpam-1372	70	49	it	it	PRON
ejpam-1372	70	50	in	in	ADP
ejpam-1372	70	51	1703∗.	1703∗.	NUM
ejpam-1372	70	52	in	in	ADP
ejpam-1372	70	53	particular	particular	ADJ
ejpam-1372	70	54	,	,	PUNCT
ejpam-1372	70	55	he	he	PRON
ejpam-1372	70	56	noticed	notice	VERB
ejpam-1372	70	57	that	that	SCONJ
ejpam-1372	70	58	bracketing	bracket	VERB
ejpam-1372	70	59	the	the	DET
ejpam-1372	70	60	series	series	NOUN
ejpam-1372	70	61	as	as	ADP
ejpam-1372	70	62	(	(	PUNCT
ejpam-1372	70	63	1−	1−	NUM
ejpam-1372	70	64	1	1	NUM
ejpam-1372	70	65	)	)	PUNCT
ejpam-1372	71	1	+	+	CCONJ
ejpam-1372	71	2	(	(	PUNCT
ejpam-1372	71	3	1−	1−	NUM
ejpam-1372	71	4	1	1	NUM
ejpam-1372	71	5	)	)	PUNCT
ejpam-1372	71	6	+	+	CCONJ
ejpam-1372	71	7	.	.	PUNCT
ejpam-1372	71	8	.	.	PUNCT
ejpam-1372	72	1	.	.	PUNCT
ejpam-1372	72	2	appears	appear	VERB
ejpam-1372	72	3	to	to	PART
ejpam-1372	72	4	yield	yield	VERB
ejpam-1372	72	5	a	a	DET
ejpam-1372	72	6	limit	limit	NOUN
ejpam-1372	72	7	of	of	ADP
ejpam-1372	72	8	zero	zero	NUM
ejpam-1372	72	9	,	,	PUNCT
ejpam-1372	72	10	while	while	SCONJ
ejpam-1372	72	11	bracketing	bracket	VERB
ejpam-1372	72	12	it	it	PRON
ejpam-1372	72	13	as	as	ADP
ejpam-1372	72	14	1	1	NUM
ejpam-1372	72	15	+	+	CCONJ
ejpam-1372	72	16	(	(	PUNCT
ejpam-1372	72	17	−1	−1	NOUN
ejpam-1372	72	18	+	+	NOUN
ejpam-1372	72	19	1	1	NUM
ejpam-1372	72	20	)	)	PUNCT
ejpam-1372	73	1	+	+	CCONJ
ejpam-1372	73	2	(	(	PUNCT
ejpam-1372	73	3	−1	−1	NOUN
ejpam-1372	73	4	+	+	NOUN
ejpam-1372	73	5	1	1	NUM
ejpam-1372	73	6	)	)	PUNCT
ejpam-1372	74	1	+	+	CCONJ
ejpam-1372	74	2	.	.	PUNCT
ejpam-1372	74	3	.	.	PUNCT
ejpam-1372	75	1	.	.	PUNCT
ejpam-1372	75	2	appears	appear	VERB
ejpam-1372	75	3	to	to	PART
ejpam-1372	75	4	yield	yield	VERB
ejpam-1372	75	5	a	a	DET
ejpam-1372	75	6	limit	limit	NOUN
ejpam-1372	75	7	of	of	ADP
ejpam-1372	75	8	unity	unity	NOUN
ejpam-1372	75	9	.	.	PUNCT
ejpam-1372	76	1	therefore	therefore	ADV
ejpam-1372	76	2	,	,	PUNCT
ejpam-1372	76	3	we	we	PRON
ejpam-1372	76	4	see	see	VERB
ejpam-1372	76	5	that	that	SCONJ
ejpam-1372	76	6	there	there	PRON
ejpam-1372	76	7	are	be	VERB
ejpam-1372	76	8	two	two	NUM
ejpam-1372	76	9	possible	possible	ADJ
ejpam-1372	76	10	limits	limit	NOUN
ejpam-1372	76	11	for	for	ADP
ejpam-1372	76	12	the	the	DET
ejpam-1372	76	13	series	series	NOUN
ejpam-1372	76	14	.	.	PUNCT
ejpam-1372	77	1	however	however	ADV
ejpam-1372	77	2	,	,	PUNCT
ejpam-1372	77	3	because	because	SCONJ
ejpam-1372	77	4	one	one	PRON
ejpam-1372	77	5	can	can	AUX
ejpam-1372	77	6	bound	bind	VERB
ejpam-1372	77	7	the	the	DET
ejpam-1372	77	8	series	series	NOUN
ejpam-1372	77	9	,	,	PUNCT
ejpam-1372	77	10	one	one	PRON
ejpam-1372	77	11	does	do	AUX
ejpam-1372	77	12	not	not	PART
ejpam-1372	77	13	get	get	VERB
ejpam-1372	77	14	the	the	DET
ejpam-1372	77	15	impression	impression	NOUN
ejpam-1372	77	16	that	that	SCONJ
ejpam-1372	77	17	it	it	PRON
ejpam-1372	77	18	is	be	AUX
ejpam-1372	77	19	divergent	divergent	ADJ
ejpam-1372	77	20	.	.	PUNCT
ejpam-1372	78	1	nevertheless	nevertheless	ADV
ejpam-1372	78	2	,	,	PUNCT
ejpam-1372	78	3	according	accord	VERB
ejpam-1372	78	4	to	to	ADP
ejpam-1372	78	5	copson	copson	NOUN
ejpam-1372	78	6	[	[	X
ejpam-1372	78	7	7	7	NUM
ejpam-1372	78	8	]	]	PUNCT
ejpam-1372	78	9	,	,	PUNCT
ejpam-1372	78	10	the	the	DET
ejpam-1372	78	11	series	series	NOUN
ejpam-1372	78	12	is	be	AUX
ejpam-1372	78	13	divergent	divergent	ADJ
ejpam-1372	78	14	.	.	PUNCT
ejpam-1372	79	1	in	in	ADP
ejpam-1372	79	2	fact	fact	NOUN
ejpam-1372	79	3	,	,	PUNCT
ejpam-1372	79	4	grandi	grandi	NOUN
ejpam-1372	79	5	himself	himself	PRON
ejpam-1372	79	6	did	do	AUX
ejpam-1372	79	7	not	not	PART
ejpam-1372	79	8	think	think	VERB
ejpam-1372	79	9	that	that	SCONJ
ejpam-1372	79	10	it	it	PRON
ejpam-1372	79	11	summed	sum	VERB
ejpam-1372	79	12	to	to	ADP
ejpam-1372	79	13	either	either	DET
ejpam-1372	79	14	value	value	NOUN
ejpam-1372	79	15	,	,	PUNCT
ejpam-1372	79	16	but	but	CCONJ
ejpam-1372	79	17	to	to	ADP
ejpam-1372	79	18	1/2	1/2	NUM
ejpam-1372	79	19	for	for	ADP
ejpam-1372	79	20	various	various	ADJ
ejpam-1372	79	21	reasons	reason	NOUN
ejpam-1372	79	22	,	,	PUNCT
ejpam-1372	79	23	none	none	NOUN
ejpam-1372	79	24	of	of	ADP
ejpam-1372	79	25	which	which	PRON
ejpam-1372	79	26	would	would	AUX
ejpam-1372	79	27	be	be	AUX
ejpam-1372	79	28	considered	consider	VERB
ejpam-1372	79	29	a	a	DET
ejpam-1372	79	30	mathematical	mathematical	ADJ
ejpam-1372	79	31	proof	proof	NOUN
ejpam-1372	79	32	today	today	NOUN
ejpam-1372	79	33	.	.	PUNCT
ejpam-1372	80	1	leibniz	leibniz	PROPN
ejpam-1372	80	2	went	go	VERB
ejpam-1372	80	3	further	far	ADV
ejpam-1372	80	4	by	by	ADP
ejpam-1372	80	5	introducing	introduce	VERB
ejpam-1372	80	6	a	a	DET
ejpam-1372	80	7	“	"	PUNCT
ejpam-1372	80	8	law	law	NOUN
ejpam-1372	80	9	of	of	ADP
ejpam-1372	80	10	justice	justice	NOUN
ejpam-1372	80	11	”	"	PUNCT
ejpam-1372	80	12	,	,	PUNCT
ejpam-1372	80	13	which	which	PRON
ejpam-1372	80	14	amounted	amount	VERB
ejpam-1372	80	15	to	to	ADP
ejpam-1372	80	16	averaging	average	VERB
ejpam-1372	80	17	the	the	DET
ejpam-1372	80	18	two	two	NUM
ejpam-1372	80	19	possible	possible	ADJ
ejpam-1372	80	20	limits	limit	NOUN
ejpam-1372	80	21	.	.	PUNCT
ejpam-1372	81	1	consequently	consequently	ADV
ejpam-1372	81	2	,	,	PUNCT
ejpam-1372	81	3	the	the	DET
ejpam-1372	81	4	series	series	NOUN
ejpam-1372	81	5	is	be	AUX
ejpam-1372	81	6	also	also	ADV
ejpam-1372	81	7	known	know	VERB
ejpam-1372	81	8	as	as	ADP
ejpam-1372	81	9	leibniz	leibniz	PROPN
ejpam-1372	81	10	’s	’s	PART
ejpam-1372	81	11	series	series	NOUN
ejpam-1372	81	12	.	.	PUNCT
ejpam-1372	82	1	it	it	PRON
ejpam-1372	82	2	was	be	AUX
ejpam-1372	82	3	euler	euler	NOUN
ejpam-1372	82	4	who	who	PRON
ejpam-1372	82	5	gave	give	VERB
ejpam-1372	82	6	what	what	PRON
ejpam-1372	82	7	could	could	AUX
ejpam-1372	82	8	be	be	AUX
ejpam-1372	82	9	regarded	regard	VERB
ejpam-1372	82	10	as	as	ADP
ejpam-1372	82	11	the	the	DET
ejpam-1372	82	12	first	first	ADJ
ejpam-1372	82	13	proper	proper	ADJ
ejpam-1372	82	14	mathematical	mathematical	ADJ
ejpam-1372	82	15	treatment	treatment	NOUN
ejpam-1372	82	16	of	of	ADP
ejpam-1372	82	17	grandi	grandi	PROPN
ejpam-1372	82	18	’s	’s	PART
ejpam-1372	82	19	series	series	NOUN
ejpam-1372	82	20	.	.	PUNCT
ejpam-1372	83	1	to	to	PART
ejpam-1372	83	2	do	do	VERB
ejpam-1372	83	3	so	so	ADV
ejpam-1372	83	4	,	,	PUNCT
ejpam-1372	83	5	we	we	PRON
ejpam-1372	83	6	express	express	VERB
ejpam-1372	83	7	the	the	DET
ejpam-1372	83	8	series	series	NOUN
ejpam-1372	83	9	in	in	ADP
ejpam-1372	83	10	eq	eq	PROPN
ejpam-1372	83	11	.	.	PUNCT
ejpam-1372	84	1	(	(	PUNCT
ejpam-1372	84	2	1	1	X
ejpam-1372	84	3	)	)	PUNCT
ejpam-1372	84	4	as	as	ADP
ejpam-1372	84	5	the	the	DET
ejpam-1372	84	6	geometric	geometric	ADJ
ejpam-1372	84	7	series	series	NOUN
ejpam-1372	84	8	by	by	ADP
ejpam-1372	84	9	replacing	replace	VERB
ejpam-1372	84	10	ak	ak	PROPN
ejpam-1372	84	11	by	by	ADP
ejpam-1372	84	12	x	x	PROPN
ejpam-1372	84	13	k	k	PROPN
ejpam-1372	84	14	,	,	PUNCT
ejpam-1372	84	15	where	where	SCONJ
ejpam-1372	84	16	x	x	PRON
ejpam-1372	84	17	can	can	AUX
ejpam-1372	84	18	be	be	AUX
ejpam-1372	84	19	any	any	DET
ejpam-1372	84	20	value	value	NOUN
ejpam-1372	84	21	.	.	PUNCT
ejpam-1372	85	1	when	when	SCONJ
ejpam-1372	85	2	the	the	DET
ejpam-1372	85	3	magnitude	magnitude	NOUN
ejpam-1372	85	4	of	of	ADP
ejpam-1372	85	5	x	x	SYM
ejpam-1372	85	6	is	be	AUX
ejpam-1372	85	7	less	less	ADJ
ejpam-1372	85	8	than	than	ADP
ejpam-1372	85	9	unity	unity	NOUN
ejpam-1372	85	10	,	,	PUNCT
ejpam-1372	85	11	i.e.	i.e.	X
ejpam-1372	85	12	for	for	ADP
ejpam-1372	85	13	|x	|x	PROPN
ejpam-1372	85	14	|<1	|<1	PROPN
ejpam-1372	85	15	,	,	PUNCT
ejpam-1372	85	16	the	the	DET
ejpam-1372	85	17	limit	limit	NOUN
ejpam-1372	85	18	s	s	VERB
ejpam-1372	85	19	equals	equal	VERB
ejpam-1372	85	20	1/(1−	1/(1−	NUM
ejpam-1372	85	21	x	x	NOUN
ejpam-1372	85	22	)	)	PUNCT
ejpam-1372	85	23	.	.	PUNCT
ejpam-1372	86	1	the	the	DET
ejpam-1372	86	2	series	series	NOUN
ejpam-1372	86	3	is	be	AUX
ejpam-1372	86	4	said	say	VERB
ejpam-1372	86	5	to	to	PART
ejpam-1372	86	6	be	be	AUX
ejpam-1372	86	7	absolutely	absolutely	ADV
ejpam-1372	86	8	convergent	convergent	ADJ
ejpam-1372	86	9	for	for	ADP
ejpam-1372	86	10	these	these	DET
ejpam-1372	86	11	values	value	NOUN
ejpam-1372	86	12	of	of	ADP
ejpam-1372	86	13	x	x	X
ejpam-1372	86	14	.	.	PUNCT
ejpam-1372	87	1	e.g.	e.g.	ADV
ejpam-1372	87	2	,	,	PUNCT
ejpam-1372	87	3	for	for	ADP
ejpam-1372	87	4	x=1/4	x=1/4	PROPN
ejpam-1372	87	5	,	,	PUNCT
ejpam-1372	87	6	the	the	DET
ejpam-1372	87	7	series	series	NOUN
ejpam-1372	87	8	becomes	become	VERB
ejpam-1372	87	9	1	1	NUM
ejpam-1372	87	10	+	+	NOUN
ejpam-1372	87	11	1/4	1/4	NUM
ejpam-1372	87	12	+	+	NUM
ejpam-1372	87	13	1/16	1/16	NUM
ejpam-1372	87	14	+	+	SYM
ejpam-1372	87	15	1/64	1/64	NUM
ejpam-1372	87	16	+	+	NOUN
ejpam-1372	87	17	1/256	1/256	NUM
ejpam-1372	87	18	+	+	NUM
ejpam-1372	87	19	.	.	PUNCT
ejpam-1372	87	20	.	.	PUNCT
ejpam-1372	88	1	.=	.=	VERB
ejpam-1372	89	1	1/(1−1/4	1/(1−1/4	NUM
ejpam-1372	89	2	)	)	PUNCT
ejpam-1372	89	3	=	=	SYM
ejpam-1372	89	4	4/3	4/3	NUM
ejpam-1372	89	5	.	.	PUNCT
ejpam-1372	90	1	thus	thus	ADV
ejpam-1372	90	2	,	,	PUNCT
ejpam-1372	90	3	archimedes	archimede	NOUN
ejpam-1372	90	4	was	be	AUX
ejpam-1372	90	5	able	able	ADJ
ejpam-1372	90	6	to	to	PART
ejpam-1372	90	7	show	show	VERB
ejpam-1372	90	8	that	that	SCONJ
ejpam-1372	90	9	the	the	DET
ejpam-1372	90	10	area	area	NOUN
ejpam-1372	90	11	enclosed	enclose	VERB
ejpam-1372	90	12	by	by	ADP
ejpam-1372	90	13	a	a	DET
ejpam-1372	90	14	parabola	parabola	NOUN
ejpam-1372	90	15	and	and	CCONJ
ejpam-1372	90	16	straight	straight	ADJ
ejpam-1372	90	17	line	line	NOUN
ejpam-1372	90	18	is	be	AUX
ejpam-1372	90	19	4/3	4/3	NUM
ejpam-1372	90	20	times	time	NOUN
ejpam-1372	90	21	the	the	DET
ejpam-1372	90	22	area	area	NOUN
ejpam-1372	90	23	of	of	ADP
ejpam-1372	90	24	the	the	DET
ejpam-1372	90	25	triangle	triangle	NOUN
ejpam-1372	90	26	inscribed	inscribe	VERB
ejpam-1372	90	27	within	within	ADP
ejpam-1372	90	28	this	this	DET
ejpam-1372	90	29	area	area	NOUN
ejpam-1372	90	30	.	.	PUNCT
ejpam-1372	91	1	if	if	SCONJ
ejpam-1372	91	2	we	we	PRON
ejpam-1372	91	3	replace	replace	VERB
ejpam-1372	91	4	x	x	PUNCT
ejpam-1372	91	5	by	by	ADP
ejpam-1372	91	6	the	the	DET
ejpam-1372	91	7	complex	complex	ADJ
ejpam-1372	91	8	variable	variable	ADJ
ejpam-1372	91	9	z(=	z(=	NOUN
ejpam-1372	91	10	x+	x+	PROPN
ejpam-1372	91	11	i	i	PRON
ejpam-1372	91	12	y	y	PROPN
ejpam-1372	91	13	)	)	PUNCT
ejpam-1372	91	14	,	,	PUNCT
ejpam-1372	91	15	then	then	ADV
ejpam-1372	91	16	|z|	|z|	VERB
ejpam-1372	91	17	<	<	X
ejpam-1372	91	18	1	1	NUM
ejpam-1372	91	19	represents	represent	VERB
ejpam-1372	91	20	the	the	DET
ejpam-1372	91	21	unit	unit	NOUN
ejpam-1372	91	22	disk	disk	NOUN
ejpam-1372	91	23	centred	centre	VERB
ejpam-1372	91	24	in	in	ADP
ejpam-1372	91	25	the	the	DET
ejpam-1372	91	26	complex	complex	ADJ
ejpam-1372	91	27	plane	plane	NOUN
ejpam-1372	91	28	.	.	PUNCT
ejpam-1372	92	1	furthermore	furthermore	ADV
ejpam-1372	92	2	,	,	PUNCT
ejpam-1372	92	3	if	if	SCONJ
ejpam-1372	92	4	we	we	PRON
ejpam-1372	92	5	put	put	VERB
ejpam-1372	92	6	x	x	PUNCT
ejpam-1372	92	7	equal	equal	ADJ
ejpam-1372	92	8	to	to	ADP
ejpam-1372	92	9	-1	-1	VERB
ejpam-1372	92	10	,	,	PUNCT
ejpam-1372	92	11	then	then	ADV
ejpam-1372	92	12	we	we	PRON
ejpam-1372	92	13	find	find	VERB
ejpam-1372	92	14	that	that	SCONJ
ejpam-1372	92	15	s=	s=	NOUN
ejpam-1372	92	16	1/2	1/2	NUM
ejpam-1372	92	17	,	,	PUNCT
ejpam-1372	92	18	but	but	CCONJ
ejpam-1372	92	19	the	the	DET
ejpam-1372	92	20	series	series	NOUN
ejpam-1372	92	21	is	be	AUX
ejpam-1372	92	22	no	no	ADV
ejpam-1372	92	23	longer	long	ADV
ejpam-1372	92	24	absolutely	absolutely	ADV
ejpam-1372	92	25	convergent	convergent	ADJ
ejpam-1372	92	26	,	,	PUNCT
ejpam-1372	92	27	which	which	PRON
ejpam-1372	92	28	means	mean	VERB
ejpam-1372	92	29	that	that	SCONJ
ejpam-1372	92	30	it	it	PRON
ejpam-1372	92	31	is	be	AUX
ejpam-1372	92	32	invalid	invalid	ADJ
ejpam-1372	92	33	to	to	PART
ejpam-1372	92	34	use	use	VERB
ejpam-1372	92	35	the	the	DET
ejpam-1372	92	36	limit	limit	NOUN
ejpam-1372	92	37	value	value	NOUN
ejpam-1372	92	38	of	of	ADP
ejpam-1372	92	39	1/(1	1/(1	NUM
ejpam-1372	92	40	−	−	PROPN
ejpam-1372	92	41	x	x	NOUN
ejpam-1372	92	42	)	)	PUNCT
ejpam-1372	92	43	.	.	PUNCT
ejpam-1372	93	1	instead	instead	ADV
ejpam-1372	93	2	,	,	PUNCT
ejpam-1372	93	3	euler	euler	PROPN
ejpam-1372	93	4	wrote	write	VERB
ejpam-1372	93	5	the	the	DET
ejpam-1372	93	6	series	series	NOUN
ejpam-1372	93	7	in	in	ADP
ejpam-1372	93	8	terms	term	NOUN
ejpam-1372	93	9	of	of	ADP
ejpam-1372	93	10	−x	−x	NOUN
ejpam-1372	93	11	as	as	ADP
ejpam-1372	93	12	1	1	NUM
ejpam-1372	93	13	1	1	NUM
ejpam-1372	93	14	+	+	NUM
ejpam-1372	93	15	x	x	SYM
ejpam-1372	93	16	=	=	SYM
ejpam-1372	93	17	1−	1−	NUM
ejpam-1372	93	18	x	x	PUNCT
ejpam-1372	94	1	+	+	CCONJ
ejpam-1372	94	2	x2−	x2−	PROPN
ejpam-1372	94	3	x3	x3	PROPN
ejpam-1372	94	4	+	+	NOUN
ejpam-1372	94	5	.	.	PUNCT
ejpam-1372	94	6	.	.	PUNCT
ejpam-1372	95	1	.+	.+	NOUN
ejpam-1372	95	2	(	(	PUNCT
ejpam-1372	95	3	−1)k	−1)k	PROPN
ejpam-1372	95	4	x	x	PROPN
ejpam-1372	96	1	k	k	PROPN
ejpam-1372	96	2	+	+	CCONJ
ejpam-1372	96	3	(	(	PUNCT
ejpam-1372	96	4	−x)k+1	−x)k+1	NOUN
ejpam-1372	96	5	1	1	NUM
ejpam-1372	96	6	+	+	NUM
ejpam-1372	96	7	x	x	NOUN
ejpam-1372	96	8	.	.	PUNCT
ejpam-1372	97	1	(	(	PUNCT
ejpam-1372	97	2	2	2	NUM
ejpam-1372	97	3	)	)	PUNCT
ejpam-1372	97	4	then	then	ADV
ejpam-1372	97	5	the	the	DET
ejpam-1372	97	6	main	main	ADJ
ejpam-1372	97	7	objection	objection	NOUN
ejpam-1372	97	8	to	to	ADP
ejpam-1372	97	9	the	the	DET
ejpam-1372	97	10	use	use	NOUN
ejpam-1372	97	11	of	of	ADP
ejpam-1372	97	12	1/(1	1/(1	NUM
ejpam-1372	97	13	+	+	NOUN
ejpam-1372	97	14	x	x	NOUN
ejpam-1372	97	15	)	)	PUNCT
ejpam-1372	97	16	when	when	SCONJ
ejpam-1372	97	17	x=1	x=1	PROPN
ejpam-1372	97	18	is	be	AUX
ejpam-1372	97	19	that	that	SCONJ
ejpam-1372	97	20	the	the	DET
ejpam-1372	97	21	final	final	ADJ
ejpam-1372	97	22	term	term	NOUN
ejpam-1372	97	23	or	or	CCONJ
ejpam-1372	97	24	remainder	remainder	NOUN
ejpam-1372	97	25	can	can	AUX
ejpam-1372	97	26	not	not	PART
ejpam-1372	97	27	be	be	AUX
ejpam-1372	97	28	disregarded	disregard	VERB
ejpam-1372	97	29	as	as	SCONJ
ejpam-1372	97	30	k	k	PROPN
ejpam-1372	97	31	goes	go	VERB
ejpam-1372	97	32	to	to	ADP
ejpam-1372	97	33	infinity	infinity	NOUN
ejpam-1372	97	34	.	.	PUNCT
ejpam-1372	98	1	his	his	PRON
ejpam-1372	98	2	idea	idea	NOUN
ejpam-1372	98	3	was	be	AUX
ejpam-1372	98	4	that	that	SCONJ
ejpam-1372	98	5	since	since	SCONJ
ejpam-1372	98	6	an	an	DET
ejpam-1372	98	7	infinite	infinite	ADJ
ejpam-1372	98	8	series	series	NOUN
ejpam-1372	98	9	has	have	VERB
ejpam-1372	98	10	no	no	DET
ejpam-1372	98	11	last	last	ADJ
ejpam-1372	98	12	term	term	NOUN
ejpam-1372	98	13	,	,	PUNCT
ejpam-1372	98	14	it	it	PRON
ejpam-1372	98	15	could	could	AUX
ejpam-1372	98	16	be	be	AUX
ejpam-1372	98	17	neglected	neglect	VERB
ejpam-1372	98	18	.	.	PUNCT
ejpam-1372	99	1	later	later	ADV
ejpam-1372	99	2	,	,	PUNCT
ejpam-1372	99	3	he	he	PRON
ejpam-1372	99	4	used	use	VERB
ejpam-1372	99	5	finite	finite	ADJ
ejpam-1372	99	6	differences	difference	NOUN
ejpam-1372	99	7	to	to	PART
ejpam-1372	99	8	attack	attack	VERB
ejpam-1372	99	9	the	the	DET
ejpam-1372	99	10	problem	problem	NOUN
ejpam-1372	99	11	,	,	PUNCT
ejpam-1372	99	12	but	but	CCONJ
ejpam-1372	99	13	in	in	ADP
ejpam-1372	99	14	reality	reality	NOUN
ejpam-1372	99	15	his	his	PRON
ejpam-1372	99	16	explanation	explanation	NOUN
ejpam-1372	99	17	would	would	AUX
ejpam-1372	99	18	not	not	PART
ejpam-1372	99	19	be	be	AUX
ejpam-1372	99	20	considered	consider	VERB
ejpam-1372	99	21	valid	valid	ADJ
ejpam-1372	99	22	today	today	NOUN
ejpam-1372	99	23	.	.	PUNCT
ejpam-1372	100	1	as	as	ADP
ejpam-1372	100	2	a	a	DET
ejpam-1372	100	3	consequence	consequence	NOUN
ejpam-1372	100	4	,	,	PUNCT
ejpam-1372	100	5	in	in	ADP
ejpam-1372	100	6	time	time	NOUN
ejpam-1372	100	7	his	his	PRON
ejpam-1372	100	8	belief	belief	NOUN
ejpam-1372	100	9	that	that	SCONJ
ejpam-1372	100	10	every	every	DET
ejpam-1372	100	11	series	series	NOUN
ejpam-1372	100	12	should	should	AUX
ejpam-1372	100	13	be	be	AUX
ejpam-1372	100	14	assigned	assign	VERB
ejpam-1372	100	15	a	a	DET
ejpam-1372	100	16	certain	certain	ADJ
ejpam-1372	100	17	value	value	NOUN
ejpam-1372	100	18	came	come	VERB
ejpam-1372	100	19	under	under	ADP
ejpam-1372	100	20	attack	attack	NOUN
ejpam-1372	100	21	and	and	CCONJ
ejpam-1372	100	22	his	his	PRON
ejpam-1372	100	23	reputation	reputation	NOUN
ejpam-1372	100	24	began	begin	VERB
ejpam-1372	100	25	to	to	PART
ejpam-1372	100	26	wane	wane	VERB
ejpam-1372	100	27	as	as	SCONJ
ejpam-1372	100	28	indicated	indicate	VERB
ejpam-1372	100	29	earlier	early	ADV
ejpam-1372	100	30	.	.	PUNCT
ejpam-1372	101	1	according	accord	VERB
ejpam-1372	101	2	to	to	ADP
ejpam-1372	101	3	varadarajan	varadarajan	NOUN
ejpam-1372	101	4	[	[	X
ejpam-1372	101	5	32	32	NUM
ejpam-1372	101	6	]	]	PUNCT
ejpam-1372	101	7	,	,	PUNCT
ejpam-1372	101	8	euler	euler	PROPN
ejpam-1372	101	9	had	have	VERB
ejpam-1372	101	10	several	several	ADJ
ejpam-1372	101	11	different	different	ADJ
ejpam-1372	101	12	methods	method	NOUN
ejpam-1372	101	13	for	for	ADP
ejpam-1372	101	14	summing	sum	VERB
ejpam-1372	101	15	divergent	divergent	ADJ
ejpam-1372	101	16	series	series	NOUN
ejpam-1372	101	17	,	,	PUNCT
ejpam-1372	101	18	but	but	CCONJ
ejpam-1372	101	19	most	most	ADJ
ejpam-1372	101	20	of	of	ADP
ejpam-1372	101	21	all	all	PRON
ejpam-1372	101	22	he	he	PRON
ejpam-1372	101	23	used	use	VERB
ejpam-1372	101	24	what	what	PRON
ejpam-1372	101	25	is	be	AUX
ejpam-1372	101	26	now	now	ADV
ejpam-1372	101	27	known	know	VERB
ejpam-1372	101	28	as	as	ADP
ejpam-1372	101	29	abel	abel	PROPN
ejpam-1372	101	30	summation	summation	NOUN
ejpam-1372	101	31	.	.	PUNCT
ejpam-1372	102	1	this	this	PRON
ejpam-1372	102	2	amounts	amount	VERB
ejpam-1372	102	3	to	to	ADP
ejpam-1372	102	4	extending	extend	VERB
ejpam-1372	102	5	the	the	DET
ejpam-1372	102	6	limit	limit	NOUN
ejpam-1372	102	7	inside	inside	ADP
ejpam-1372	102	8	the	the	DET
ejpam-1372	102	9	unit	unit	NOUN
ejpam-1372	102	10	disk	disk	NOUN
ejpam-1372	102	11	of	of	ADP
ejpam-1372	102	12	absolute	absolute	ADJ
ejpam-1372	102	13	convergence	convergence	NOUN
ejpam-1372	102	14	to	to	ADP
ejpam-1372	102	15	a	a	DET
ejpam-1372	102	16	domain	domain	NOUN
ejpam-1372	102	17	with	with	ADP
ejpam-1372	102	18	z	z	NOUN
ejpam-1372	102	19	=	=	SYM
ejpam-1372	102	20	1	1	X
ejpam-1372	102	21	.	.	PUNCT
ejpam-1372	103	1	unfortunately	unfortunately	ADV
ejpam-1372	103	2	,	,	PUNCT
ejpam-1372	103	3	for	for	ADP
ejpam-1372	103	4	more	more	ADV
ejpam-1372	103	5	intricate	intricate	ADJ
ejpam-1372	103	6	examples	example	NOUN
ejpam-1372	103	7	of	of	ADP
ejpam-1372	103	8	divergent	divergent	ADJ
ejpam-1372	103	9	series	series	NOUN
ejpam-1372	103	10	,	,	PUNCT
ejpam-1372	103	11	e.g.	e.g.	ADV
ejpam-1372	103	12	ak	ak	PROPN
ejpam-1372	103	13	equal	equal	ADJ
ejpam-1372	103	14	to	to	ADP
ejpam-1372	103	15	(	(	PUNCT
ejpam-1372	103	16	−1)kγ(k+1	−1)kγ(k+1	NOUN
ejpam-1372	103	17	)	)	PUNCT
ejpam-1372	103	18	,	,	PUNCT
ejpam-1372	103	19	where	where	SCONJ
ejpam-1372	103	20	γ(k+	γ(k+	ADV
ejpam-1372	103	21	1	1	X
ejpam-1372	103	22	)	)	PUNCT
ejpam-1372	103	23	=	=	SYM
ejpam-1372	103	24	k	k	X
ejpam-1372	103	25	!	!	PUNCT
ejpam-1372	104	1	=	=	PUNCT
ejpam-1372	105	1	k(k	k(k	ADJ
ejpam-1372	105	2	−	−	NOUN
ejpam-1372	105	3	1	1	NUM
ejpam-1372	105	4	)	)	PUNCT
ejpam-1372	105	5	.	.	PUNCT
ejpam-1372	105	6	.	.	PUNCT
ejpam-1372	105	7	.	.	PUNCT
ejpam-1372	106	1	2	2	NUM
ejpam-1372	106	2	·	·	SYM
ejpam-1372	106	3	1	1	NUM
ejpam-1372	106	4	,	,	PUNCT
ejpam-1372	106	5	this	this	DET
ejpam-1372	106	6	method	method	NOUN
ejpam-1372	106	7	breaks	break	VERB
ejpam-1372	106	8	down	down	ADP
ejpam-1372	106	9	completely	completely	ADV
ejpam-1372	106	10	,	,	PUNCT
ejpam-1372	106	11	which	which	PRON
ejpam-1372	106	12	is	be	AUX
ejpam-1372	106	13	why	why	SCONJ
ejpam-1372	106	14	euler	euler	PROPN
ejpam-1372	106	15	referred	refer	VERB
ejpam-1372	106	16	to	to	ADP
ejpam-1372	106	17	such	such	ADJ
ejpam-1372	106	18	series	series	NOUN
ejpam-1372	106	19	as	as	ADP
ejpam-1372	106	20	divergent	divergent	ADJ
ejpam-1372	106	21	series	series	NOUN
ejpam-1372	106	22	par	par	PROPN
ejpam-1372	106	23	excellence	excellence	PROPN
ejpam-1372	106	24	.	.	PUNCT
ejpam-1372	107	1	unlike	unlike	ADP
ejpam-1372	107	2	the	the	DET
ejpam-1372	107	3	geometric	geometric	ADJ
ejpam-1372	107	4	series	series	NOUN
ejpam-1372	107	5	,	,	PUNCT
ejpam-1372	107	6	which	which	PRON
ejpam-1372	107	7	we	we	PRON
ejpam-1372	107	8	have	have	AUX
ejpam-1372	107	9	already	already	ADV
ejpam-1372	107	10	stated	state	VERB
ejpam-1372	107	11	possesses	possesse	NOUN
ejpam-1372	107	12	a	a	DET
ejpam-1372	107	13	radius	radius	NOUN
ejpam-1372	107	14	of	of	ADP
ejpam-1372	107	15	absolute	absolute	ADJ
ejpam-1372	107	16	convergence	convergence	NOUN
ejpam-1372	107	17	equal	equal	ADJ
ejpam-1372	107	18	to	to	ADP
ejpam-1372	107	19	unity	unity	NOUN
ejpam-1372	107	20	,	,	PUNCT
ejpam-1372	107	21	the	the	DET
ejpam-1372	107	22	latter	latter	ADJ
ejpam-1372	107	23	type	type	NOUN
ejpam-1372	107	24	of	of	ADP
ejpam-1372	107	25	series	series	NOUN
ejpam-1372	107	26	possesses	possess	VERB
ejpam-1372	107	27	zero	zero	NUM
ejpam-1372	107	28	radius	radius	NOUN
ejpam-1372	107	29	of	of	ADP
ejpam-1372	107	30	absolute	absolute	ADJ
ejpam-1372	107	31	convergence	convergence	NOUN
ejpam-1372	107	32	.	.	PUNCT
ejpam-1372	108	1	we	we	PRON
ejpam-1372	108	2	shall	shall	AUX
ejpam-1372	108	3	return	return	VERB
ejpam-1372	108	4	to	to	ADP
ejpam-1372	108	5	these	these	DET
ejpam-1372	108	6	series	series	NOUN
ejpam-1372	108	7	later	later	ADV
ejpam-1372	108	8	in	in	ADP
ejpam-1372	108	9	this	this	DET
ejpam-1372	108	10	article	article	NOUN
ejpam-1372	108	11	.	.	PUNCT
ejpam-1372	109	1	despite	despite	SCONJ
ejpam-1372	109	2	the	the	DET
ejpam-1372	109	3	tone	tone	NOUN
ejpam-1372	109	4	of	of	ADP
ejpam-1372	109	5	his	his	PRON
ejpam-1372	109	6	papers	paper	NOUN
ejpam-1372	109	7	,	,	PUNCT
ejpam-1372	109	8	euler	euler	PROPN
ejpam-1372	109	9	expressed	express	VERB
ejpam-1372	109	10	doubt	doubt	NOUN
ejpam-1372	109	11	in	in	ADP
ejpam-1372	109	12	private	private	ADJ
ejpam-1372	109	13	correspondence	correspondence	NOUN
ejpam-1372	109	14	over	over	ADP
ejpam-1372	109	15	his	his	PRON
ejpam-1372	109	16	methods	method	NOUN
ejpam-1372	109	17	for	for	ADP
ejpam-1372	109	18	handling	handle	VERB
ejpam-1372	109	19	divergent	divergent	ADJ
ejpam-1372	109	20	series	series	NOUN
ejpam-1372	109	21	,	,	PUNCT
ejpam-1372	109	22	but	but	CCONJ
ejpam-1372	109	23	he	he	PRON
ejpam-1372	109	24	never	never	ADV
ejpam-1372	109	25	found	find	VERB
ejpam-1372	109	26	a	a	DET
ejpam-1372	109	27	counterexample	counterexample	NOUN
ejpam-1372	109	28	to	to	ADP
ejpam-1372	109	29	grandi	grandi	PROPN
ejpam-1372	109	30	’s	’s	PART
ejpam-1372	109	31	series	series	NOUN
ejpam-1372	109	32	∗history	∗history	NUM
ejpam-1372	109	33	of	of	ADP
ejpam-1372	109	34	grandi	grandi	PROPN
ejpam-1372	109	35	’s	’s	PART
ejpam-1372	109	36	series	series	NOUN
ejpam-1372	109	37	.	.	PUNCT
ejpam-1372	109	38	,	,	PUNCT
ejpam-1372	109	39	http://en.wikipedia.org/wiki/history_of_grandi's_series	http://en.wikipedia.org/wiki/history_of_grandi's_serie	NOUN
ejpam-1372	109	40	v.	v.	ADP
ejpam-1372	109	41	kowalenko	kowalenko	PROPN
ejpam-1372	109	42	/	/	SYM
ejpam-1372	109	43	eur	eur	PROPN
ejpam-1372	109	44	.	.	PUNCT
ejpam-1372	110	1	j.	j.	PROPN
ejpam-1372	110	2	pure	pure	PROPN
ejpam-1372	110	3	appl	appl	PROPN
ejpam-1372	110	4	.	.	PROPN
ejpam-1372	110	5	math	math	PROPN
ejpam-1372	110	6	,	,	PUNCT
ejpam-1372	110	7	4	4	NUM
ejpam-1372	110	8	(	(	PUNCT
ejpam-1372	110	9	2011	2011	NUM
ejpam-1372	110	10	)	)	PUNCT
ejpam-1372	110	11	,	,	PUNCT
ejpam-1372	110	12	370	370	NUM
ejpam-1372	110	13	-	-	SYM
ejpam-1372	110	14	423	423	NUM
ejpam-1372	110	15	374	374	NUM
ejpam-1372	110	16	equalling	equal	VERB
ejpam-1372	110	17	1/2	1/2	NUM
ejpam-1372	110	18	.	.	PUNCT
ejpam-1372	111	1	then	then	ADV
ejpam-1372	111	2	in	in	ADP
ejpam-1372	111	3	1771	1771	NUM
ejpam-1372	111	4	daniel	daniel	PROPN
ejpam-1372	111	5	bernoulli	bernoulli	PROPN
ejpam-1372	111	6	,	,	PUNCT
ejpam-1372	111	7	who	who	PRON
ejpam-1372	111	8	had	have	AUX
ejpam-1372	111	9	accepted	accept	VERB
ejpam-1372	111	10	the	the	DET
ejpam-1372	111	11	result	result	NOUN
ejpam-1372	111	12	,	,	PUNCT
ejpam-1372	111	13	noticed	notice	VERB
ejpam-1372	111	14	that	that	SCONJ
ejpam-1372	111	15	by	by	ADP
ejpam-1372	111	16	inserting	insert	VERB
ejpam-1372	111	17	zeros	zero	NOUN
ejpam-1372	111	18	into	into	ADP
ejpam-1372	111	19	the	the	DET
ejpam-1372	111	20	series	series	NOUN
ejpam-1372	111	21	,	,	PUNCT
ejpam-1372	111	22	one	one	PRON
ejpam-1372	111	23	could	could	AUX
ejpam-1372	111	24	obtain	obtain	VERB
ejpam-1372	111	25	any	any	DET
ejpam-1372	111	26	value	value	NOUN
ejpam-1372	111	27	between	between	ADP
ejpam-1372	111	28	0	0	NUM
ejpam-1372	111	29	and	and	CCONJ
ejpam-1372	111	30	1	1	NUM
ejpam-1372	111	31	.	.	X
ejpam-1372	112	1	for	for	ADP
ejpam-1372	112	2	example	example	NOUN
ejpam-1372	112	3	,	,	PUNCT
ejpam-1372	112	4	he	he	PRON
ejpam-1372	112	5	found	find	VERB
ejpam-1372	112	6	that	that	SCONJ
ejpam-1372	112	7	1	1	NUM
ejpam-1372	112	8	+	+	NOUN
ejpam-1372	112	9	0−1	0−1	ADJ
ejpam-1372	112	10	+	+	ADJ
ejpam-1372	112	11	1	1	NUM
ejpam-1372	112	12	+	+	NOUN
ejpam-1372	112	13	0−1	0−1	NOUN
ejpam-1372	112	14	+	+	NUM
ejpam-1372	112	15	.	.	PUNCT
ejpam-1372	112	16	.	.	PUNCT
ejpam-1372	113	1	.=	.=	VERB
ejpam-1372	114	1	2/3	2/3	NUM
ejpam-1372	115	1	[	[	X
ejpam-1372	115	2	12	12	NUM
ejpam-1372	115	3	]	]	PUNCT
ejpam-1372	115	4	.	.	PUNCT
ejpam-1372	116	1	this	this	PRON
ejpam-1372	116	2	is	be	AUX
ejpam-1372	116	3	really	really	ADV
ejpam-1372	116	4	counter	counter	ADJ
ejpam-1372	116	5	-	-	ADJ
ejpam-1372	116	6	intuitive	intuitive	ADJ
ejpam-1372	116	7	and	and	CCONJ
ejpam-1372	116	8	a	a	DET
ejpam-1372	116	9	theory	theory	NOUN
ejpam-1372	116	10	of	of	ADP
ejpam-1372	116	11	divergent	divergent	ADJ
ejpam-1372	116	12	series	series	NOUN
ejpam-1372	116	13	would	would	AUX
ejpam-1372	116	14	need	need	VERB
ejpam-1372	116	15	to	to	PART
ejpam-1372	116	16	account	account	VERB
ejpam-1372	116	17	for	for	ADP
ejpam-1372	116	18	how	how	SCONJ
ejpam-1372	116	19	the	the	DET
ejpam-1372	116	20	introduction	introduction	NOUN
ejpam-1372	116	21	of	of	ADP
ejpam-1372	116	22	an	an	DET
ejpam-1372	116	23	infinite	infinite	ADJ
ejpam-1372	116	24	number	number	NOUN
ejpam-1372	116	25	of	of	ADP
ejpam-1372	116	26	zeros	zero	NOUN
ejpam-1372	116	27	can	can	AUX
ejpam-1372	116	28	yield	yield	VERB
ejpam-1372	116	29	a	a	DET
ejpam-1372	116	30	different	different	ADJ
ejpam-1372	116	31	limit	limit	NOUN
ejpam-1372	116	32	.	.	PUNCT
ejpam-1372	117	1	it	it	PRON
ejpam-1372	117	2	is	be	AUX
ejpam-1372	117	3	precisely	precisely	ADV
ejpam-1372	117	4	this	this	DET
ejpam-1372	117	5	type	type	NOUN
ejpam-1372	117	6	of	of	ADP
ejpam-1372	117	7	result	result	NOUN
ejpam-1372	117	8	that	that	SCONJ
ejpam-1372	117	9	abel	abel	PROPN
ejpam-1372	117	10	was	be	AUX
ejpam-1372	117	11	referring	refer	VERB
ejpam-1372	117	12	to	to	ADP
ejpam-1372	117	13	when	when	SCONJ
ejpam-1372	117	14	criticising	criticise	VERB
ejpam-1372	117	15	divergent	divergent	ADJ
ejpam-1372	117	16	series	series	NOUN
ejpam-1372	117	17	for	for	ADP
ejpam-1372	117	18	producing	produce	VERB
ejpam-1372	117	19	fallacies	fallacy	NOUN
ejpam-1372	117	20	and	and	CCONJ
ejpam-1372	117	21	paradoxes	paradox	NOUN
ejpam-1372	117	22	.	.	PUNCT
ejpam-1372	118	1	worse	bad	ADJ
ejpam-1372	118	2	still	still	ADV
ejpam-1372	118	3	,	,	PUNCT
ejpam-1372	118	4	if	if	SCONJ
ejpam-1372	118	5	the	the	DET
ejpam-1372	118	6	zeros	zero	NOUN
ejpam-1372	118	7	and	and	CCONJ
ejpam-1372	118	8	minus	minus	NUM
ejpam-1372	118	9	ones	one	NOUN
ejpam-1372	118	10	are	be	AUX
ejpam-1372	118	11	re	re	VERB
ejpam-1372	118	12	-	-	VERB
ejpam-1372	118	13	ordered	order	VERB
ejpam-1372	118	14	so	so	SCONJ
ejpam-1372	118	15	that	that	SCONJ
ejpam-1372	118	16	the	the	DET
ejpam-1372	118	17	series	series	NOUN
ejpam-1372	118	18	becomes	become	VERB
ejpam-1372	118	19	1−	1−	NUM
ejpam-1372	118	20	1	1	NUM
ejpam-1372	118	21	+	+	NUM
ejpam-1372	118	22	0	0	NUM
ejpam-1372	118	23	+	+	SYM
ejpam-1372	118	24	1−	1−	NUM
ejpam-1372	118	25	1	1	NUM
ejpam-1372	118	26	+	+	NUM
ejpam-1372	118	27	0	0	NUM
ejpam-1372	118	28	+	+	SYM
ejpam-1372	118	29	1−	1−	NUM
ejpam-1372	118	30	1	1	NUM
ejpam-1372	118	31	+	+	NUM
ejpam-1372	118	32	.	.	PUNCT
ejpam-1372	118	33	.	.	PUNCT
ejpam-1372	119	1	.	.	PUNCT
ejpam-1372	120	1	,	,	PUNCT
ejpam-1372	120	2	then	then	ADV
ejpam-1372	120	3	we	we	PRON
ejpam-1372	120	4	would	would	AUX
ejpam-1372	120	5	obtain	obtain	VERB
ejpam-1372	120	6	a	a	DET
ejpam-1372	120	7	different	different	ADJ
ejpam-1372	120	8	limit	limit	NOUN
ejpam-1372	120	9	.	.	PUNCT
ejpam-1372	121	1	in	in	ADP
ejpam-1372	121	2	this	this	DET
ejpam-1372	121	3	case	case	NOUN
ejpam-1372	121	4	the	the	DET
ejpam-1372	121	5	limit	limit	NOUN
ejpam-1372	121	6	would	would	AUX
ejpam-1372	121	7	be	be	AUX
ejpam-1372	121	8	1/3	1/3	NUM
ejpam-1372	121	9	.	.	PUNCT
ejpam-1372	122	1	in	in	ADP
ejpam-1372	122	2	1799	1799	NUM
ejpam-1372	122	3	more	more	ADJ
ejpam-1372	122	4	than	than	ADP
ejpam-1372	122	5	a	a	PRON
ejpam-1372	122	6	decade	decade	NOUN
ejpam-1372	122	7	after	after	ADP
ejpam-1372	122	8	euler	euler	PROPN
ejpam-1372	122	9	’s	’s	PART
ejpam-1372	122	10	death	death	NOUN
ejpam-1372	122	11	,	,	PUNCT
ejpam-1372	122	12	the	the	DET
ejpam-1372	122	13	situation	situation	NOUN
ejpam-1372	122	14	became	become	VERB
ejpam-1372	122	15	even	even	ADV
ejpam-1372	122	16	worse	bad	ADJ
ejpam-1372	122	17	when	when	SCONJ
ejpam-1372	122	18	callet	callet	NOUN
ejpam-1372	122	19	pointed	point	VERB
ejpam-1372	122	20	out	out	ADP
ejpam-1372	122	21	to	to	PART
ejpam-1372	122	22	lagrange	lagrange	VERB
ejpam-1372	122	23	that	that	DET
ejpam-1372	122	24	1	1	NUM
ejpam-1372	122	25	+	+	NUM
ejpam-1372	122	26	z	z	NOUN
ejpam-1372	122	27	1	1	NUM
ejpam-1372	122	28	+	+	SYM
ejpam-1372	122	29	z	z	NOUN
ejpam-1372	122	30	+	+	NOUN
ejpam-1372	122	31	z2	z2	PROPN
ejpam-1372	122	32	=	=	SYM
ejpam-1372	122	33	1−	1−	NUM
ejpam-1372	122	34	z2	z2	PROPN
ejpam-1372	122	35	+	+	CCONJ
ejpam-1372	122	36	z3	z3	PROPN
ejpam-1372	122	37	−	−	PROPN
ejpam-1372	122	38	z5	z5	PROPN
ejpam-1372	122	39	+	+	CCONJ
ejpam-1372	122	40	z6	z6	PROPN
ejpam-1372	122	41	+	+	CCONJ
ejpam-1372	122	42	.	.	PUNCT
ejpam-1372	122	43	.	.	PUNCT
ejpam-1372	122	44	.	.	PUNCT
ejpam-1372	123	1	,	,	PUNCT
ejpam-1372	123	2	(	(	PUNCT
ejpam-1372	123	3	3	3	X
ejpam-1372	123	4	)	)	PUNCT
ejpam-1372	123	5	gives	give	VERB
ejpam-1372	123	6	grandi	grandi	PROPN
ejpam-1372	123	7	’s	’s	PART
ejpam-1372	123	8	series	series	NOUN
ejpam-1372	123	9	for	for	ADP
ejpam-1372	123	10	z	z	NOUN
ejpam-1372	123	11	=	=	SYM
ejpam-1372	123	12	1	1	NUM
ejpam-1372	123	13	,	,	PUNCT
ejpam-1372	123	14	but	but	CCONJ
ejpam-1372	123	15	now	now	ADV
ejpam-1372	123	16	the	the	DET
ejpam-1372	123	17	limit	limit	NOUN
ejpam-1372	123	18	is	be	AUX
ejpam-1372	123	19	2/3	2/3	NUM
ejpam-1372	123	20	instead	instead	ADV
ejpam-1372	123	21	of	of	ADP
ejpam-1372	123	22	1/2	1/2	NUM
ejpam-1372	123	23	.	.	PUNCT
ejpam-1372	124	1	lagrange	lagrange	PROPN
ejpam-1372	124	2	defended	defend	VERB
ejpam-1372	124	3	euler	euler	NOUN
ejpam-1372	124	4	by	by	ADP
ejpam-1372	124	5	stating	state	VERB
ejpam-1372	124	6	that	that	SCONJ
ejpam-1372	124	7	the	the	DET
ejpam-1372	124	8	rhs	rhs	PROPN
ejpam-1372	124	9	of	of	ADP
ejpam-1372	124	10	eq	eq	PROPN
ejpam-1372	124	11	.	.	PUNCT
ejpam-1372	125	1	(	(	PUNCT
ejpam-1372	125	2	3	3	X
ejpam-1372	125	3	)	)	PUNCT
ejpam-1372	125	4	is	be	AUX
ejpam-1372	125	5	not	not	PART
ejpam-1372	125	6	a	a	DET
ejpam-1372	125	7	true	true	ADJ
ejpam-1372	125	8	power	power	NOUN
ejpam-1372	125	9	series	series	NOUN
ejpam-1372	125	10	since	since	SCONJ
ejpam-1372	125	11	many	many	ADJ
ejpam-1372	125	12	powers	power	NOUN
ejpam-1372	125	13	are	be	AUX
ejpam-1372	125	14	missing	miss	VERB
ejpam-1372	125	15	.	.	PUNCT
ejpam-1372	126	1	when	when	SCONJ
ejpam-1372	126	2	these	these	PRON
ejpam-1372	126	3	are	be	AUX
ejpam-1372	126	4	included	include	VERB
ejpam-1372	126	5	by	by	ADP
ejpam-1372	126	6	writing	write	VERB
ejpam-1372	126	7	the	the	DET
ejpam-1372	126	8	series	series	NOUN
ejpam-1372	126	9	as	as	ADP
ejpam-1372	126	10	1	1	NUM
ejpam-1372	126	11	+	+	SYM
ejpam-1372	126	12	0	0	NUM
ejpam-1372	126	13	·	·	PUNCT
ejpam-1372	126	14	z	z	SYM
ejpam-1372	126	15	−	−	PROPN
ejpam-1372	126	16	z2	z2	PROPN
ejpam-1372	126	17	+	+	CCONJ
ejpam-1372	126	18	z3	z3	PROPN
ejpam-1372	126	19	+	+	CCONJ
ejpam-1372	126	20	0	0	NUM
ejpam-1372	126	21	·	·	PUNCT
ejpam-1372	126	22	z4	z4	PROPN
ejpam-1372	126	23	−	−	PROPN
ejpam-1372	126	24	z5	z5	PROPN
ejpam-1372	126	25	+	+	CCONJ
ejpam-1372	126	26	z6	z6	NOUN
ejpam-1372	126	27	+	+	CCONJ
ejpam-1372	126	28	0	0	NUM
ejpam-1372	126	29	·	·	PUNCT
ejpam-1372	126	30	z7	z7	PROPN
ejpam-1372	127	1	−	−	PROPN
ejpam-1372	127	2	z8	z8	PROPN
ejpam-1372	127	3	+	+	PUNCT
ejpam-1372	127	4	.	.	PUNCT
ejpam-1372	127	5	.	.	PUNCT
ejpam-1372	127	6	.	.	PUNCT
ejpam-1372	128	1	,	,	PUNCT
ejpam-1372	128	2	(	(	PUNCT
ejpam-1372	128	3	4	4	X
ejpam-1372	128	4	)	)	PUNCT
ejpam-1372	128	5	the	the	DET
ejpam-1372	128	6	series	series	NOUN
ejpam-1372	128	7	reduces	reduce	VERB
ejpam-1372	128	8	to	to	ADP
ejpam-1372	128	9	1	1	NUM
ejpam-1372	128	10	+	+	NOUN
ejpam-1372	128	11	0−1	0−1	ADJ
ejpam-1372	128	12	+	+	ADJ
ejpam-1372	128	13	1	1	NUM
ejpam-1372	128	14	+	+	NOUN
ejpam-1372	128	15	0−1	0−1	NOUN
ejpam-1372	128	16	+	+	NUM
ejpam-1372	128	17	.	.	PUNCT
ejpam-1372	128	18	.	.	PUNCT
ejpam-1372	128	19	.	.	PUNCT
ejpam-1372	129	1	for	for	ADP
ejpam-1372	129	2	z=1	z=1	NUM
ejpam-1372	129	3	,	,	PUNCT
ejpam-1372	129	4	which	which	PRON
ejpam-1372	129	5	as	as	SCONJ
ejpam-1372	129	6	stated	state	VERB
ejpam-1372	129	7	previously	previously	ADV
ejpam-1372	129	8	,	,	PUNCT
ejpam-1372	129	9	was	be	AUX
ejpam-1372	129	10	found	find	VERB
ejpam-1372	129	11	by	by	ADP
ejpam-1372	129	12	bernoulli	bernoulli	PROPN
ejpam-1372	129	13	to	to	PART
ejpam-1372	129	14	yield	yield	VERB
ejpam-1372	129	15	a	a	DET
ejpam-1372	129	16	limit	limit	NOUN
ejpam-1372	129	17	of	of	ADP
ejpam-1372	129	18	2/3	2/3	NUM
ejpam-1372	129	19	.	.	PUNCT
ejpam-1372	130	1	whilst	whilst	SCONJ
ejpam-1372	130	2	this	this	PRON
ejpam-1372	130	3	may	may	AUX
ejpam-1372	130	4	have	have	AUX
ejpam-1372	130	5	silenced	silence	VERB
ejpam-1372	130	6	callet	callet	ADV
ejpam-1372	130	7	,	,	PUNCT
ejpam-1372	130	8	it	it	PRON
ejpam-1372	130	9	is	be	AUX
ejpam-1372	130	10	particularly	particularly	ADV
ejpam-1372	130	11	alarming	alarming	ADJ
ejpam-1372	130	12	for	for	ADP
ejpam-1372	130	13	applied	apply	VERB
ejpam-1372	130	14	mathematicians	mathematician	NOUN
ejpam-1372	130	15	who	who	PRON
ejpam-1372	130	16	derive	derive	VERB
ejpam-1372	130	17	divergent	divergent	ADJ
ejpam-1372	130	18	series	series	NOUN
ejpam-1372	130	19	in	in	ADP
ejpam-1372	130	20	the	the	DET
ejpam-1372	130	21	form	form	NOUN
ejpam-1372	130	22	of	of	ADP
ejpam-1372	130	23	asymptotic	asymptotic	ADJ
ejpam-1372	130	24	series	series	NOUN
ejpam-1372	130	25	for	for	ADP
ejpam-1372	130	26	often	often	ADV
ejpam-1372	130	27	such	such	ADJ
ejpam-1372	130	28	series	series	NOUN
ejpam-1372	130	29	are	be	AUX
ejpam-1372	130	30	in	in	ADP
ejpam-1372	130	31	the	the	DET
ejpam-1372	130	32	form	form	NOUN
ejpam-1372	130	33	where	where	SCONJ
ejpam-1372	130	34	z	z	NOUN
ejpam-1372	130	35	is	be	AUX
ejpam-1372	130	36	a	a	DET
ejpam-1372	130	37	power	power	NOUN
ejpam-1372	130	38	of	of	ADP
ejpam-1372	130	39	another	another	DET
ejpam-1372	130	40	variable	variable	NOUN
ejpam-1372	130	41	.	.	PUNCT
ejpam-1372	131	1	for	for	ADP
ejpam-1372	131	2	example	example	NOUN
ejpam-1372	131	3	,	,	PUNCT
ejpam-1372	131	4	the	the	DET
ejpam-1372	131	5	asymptotic	asymptotic	ADJ
ejpam-1372	131	6	series	series	NOUN
ejpam-1372	131	7	for	for	ADP
ejpam-1372	131	8	the	the	DET
ejpam-1372	131	9	error	error	NOUN
ejpam-1372	131	10	function	function	NOUN
ejpam-1372	131	11	,	,	PUNCT
ejpam-1372	131	12	which	which	PRON
ejpam-1372	131	13	appears	appear	VERB
ejpam-1372	131	14	in	in	ADP
ejpam-1372	131	15	sec	sec	PROPN
ejpam-1372	131	16	.	.	PROPN
ejpam-1372	131	17	9	9	NUM
ejpam-1372	131	18	,	,	PUNCT
ejpam-1372	131	19	is	be	AUX
ejpam-1372	131	20	actually	actually	ADV
ejpam-1372	131	21	in	in	ADP
ejpam-1372	131	22	powers	power	NOUN
ejpam-1372	131	23	of	of	ADP
ejpam-1372	131	24	−1	−1	NOUN
ejpam-1372	131	25	/	/	SYM
ejpam-1372	131	26	z2	z2	PROPN
ejpam-1372	131	27	.	.	PUNCT
ejpam-1372	132	1	the	the	DET
ejpam-1372	132	2	above	above	ADJ
ejpam-1372	132	3	would	would	AUX
ejpam-1372	132	4	imply	imply	VERB
ejpam-1372	132	5	that	that	SCONJ
ejpam-1372	132	6	those	those	DET
ejpam-1372	132	7	missing	missing	ADJ
ejpam-1372	132	8	powers	power	NOUN
ejpam-1372	132	9	,	,	PUNCT
ejpam-1372	132	10	namely	namely	ADV
ejpam-1372	132	11	the	the	DET
ejpam-1372	132	12	odd	odd	ADJ
ejpam-1372	132	13	powers	power	NOUN
ejpam-1372	132	14	of	of	ADP
ejpam-1372	132	15	1	1	NUM
ejpam-1372	132	16	/	/	SYM
ejpam-1372	132	17	z	z	NOUN
ejpam-1372	132	18	,	,	PUNCT
ejpam-1372	132	19	would	would	AUX
ejpam-1372	132	20	have	have	VERB
ejpam-1372	132	21	to	to	PART
ejpam-1372	132	22	be	be	AUX
ejpam-1372	132	23	included	include	VERB
ejpam-1372	132	24	in	in	ADP
ejpam-1372	132	25	the	the	DET
ejpam-1372	132	26	analysis	analysis	NOUN
ejpam-1372	132	27	to	to	PART
ejpam-1372	132	28	obtain	obtain	VERB
ejpam-1372	132	29	the	the	DET
ejpam-1372	132	30	limit	limit	NOUN
ejpam-1372	132	31	.	.	PUNCT
ejpam-1372	133	1	since	since	SCONJ
ejpam-1372	133	2	lagrange	lagrange	NOUN
ejpam-1372	133	3	,	,	PUNCT
ejpam-1372	133	4	many	many	ADJ
ejpam-1372	133	5	mathematicians	mathematician	NOUN
ejpam-1372	133	6	have	have	AUX
ejpam-1372	133	7	introduced	introduce	VERB
ejpam-1372	133	8	various	various	ADJ
ejpam-1372	133	9	methods	method	NOUN
ejpam-1372	133	10	for	for	ADP
ejpam-1372	133	11	summing	sum	VERB
ejpam-1372	133	12	divergent	divergent	ADJ
ejpam-1372	133	13	series	series	NOUN
ejpam-1372	133	14	.	.	PUNCT
ejpam-1372	134	1	most	most	ADJ
ejpam-1372	134	2	of	of	ADP
ejpam-1372	134	3	these	these	DET
ejpam-1372	134	4	sum	sum	NOUN
ejpam-1372	134	5	grandi	grandi	PROPN
ejpam-1372	134	6	’s	’s	PART
ejpam-1372	134	7	series	series	NOUN
ejpam-1372	134	8	to	to	ADP
ejpam-1372	134	9	1/2	1/2	NUM
ejpam-1372	134	10	.	.	PUNCT
ejpam-1372	135	1	others	other	NOUN
ejpam-1372	135	2	motivated	motivate	VERB
ejpam-1372	135	3	by	by	ADP
ejpam-1372	135	4	bernoulli	bernoulli	PROPN
ejpam-1372	135	5	’s	’s	PART
ejpam-1372	135	6	treatment	treatment	NOUN
ejpam-1372	135	7	sum	sum	VERB
ejpam-1372	135	8	the	the	DET
ejpam-1372	135	9	series	series	NOUN
ejpam-1372	135	10	to	to	ADP
ejpam-1372	135	11	another	another	DET
ejpam-1372	135	12	value	value	NOUN
ejpam-1372	135	13	,	,	PUNCT
ejpam-1372	135	14	while	while	SCONJ
ejpam-1372	135	15	a	a	DET
ejpam-1372	135	16	small	small	ADJ
ejpam-1372	135	17	minority	minority	NOUN
ejpam-1372	135	18	take	take	VERB
ejpam-1372	135	19	the	the	DET
ejpam-1372	135	20	safe	safe	ADJ
ejpam-1372	135	21	option	option	NOUN
ejpam-1372	135	22	of	of	ADP
ejpam-1372	135	23	not	not	PART
ejpam-1372	135	24	bothering	bother	VERB
ejpam-1372	135	25	to	to	PART
ejpam-1372	135	26	sum	sum	VERB
ejpam-1372	135	27	it	it	PRON
ejpam-1372	135	28	at	at	ADV
ejpam-1372	135	29	all	all	ADV
ejpam-1372	135	30	.	.	PUNCT
ejpam-1372	136	1	therefore	therefore	ADV
ejpam-1372	136	2	,	,	PUNCT
ejpam-1372	136	3	the	the	DET
ejpam-1372	136	4	issue	issue	NOUN
ejpam-1372	136	5	has	have	AUX
ejpam-1372	136	6	become	become	VERB
ejpam-1372	136	7	whether	whether	SCONJ
ejpam-1372	136	8	all	all	DET
ejpam-1372	136	9	the	the	DET
ejpam-1372	136	10	inconsistencies	inconsistency	NOUN
ejpam-1372	136	11	or	or	CCONJ
ejpam-1372	136	12	apparent	apparent	ADJ
ejpam-1372	136	13	paradoxes	paradox	NOUN
ejpam-1372	136	14	that	that	PRON
ejpam-1372	136	15	have	have	AUX
ejpam-1372	136	16	been	be	AUX
ejpam-1372	136	17	raised	raise	VERB
ejpam-1372	136	18	here	here	ADV
ejpam-1372	136	19	can	can	AUX
ejpam-1372	136	20	be	be	AUX
ejpam-1372	136	21	resolved	resolve	VERB
ejpam-1372	136	22	.	.	PUNCT
ejpam-1372	137	1	3	3	X
ejpam-1372	137	2	.	.	X
ejpam-1372	137	3	regularisation	regularisation	NOUN
ejpam-1372	137	4	in	in	ADP
ejpam-1372	137	5	1993	1993	NUM
ejpam-1372	137	6	my	my	PRON
ejpam-1372	137	7	colleague	colleague	NOUN
ejpam-1372	137	8	t.	t.	PROPN
ejpam-1372	137	9	taucher	taucher	PROPN
ejpam-1372	137	10	and	and	CCONJ
ejpam-1372	137	11	i	i	PRON
ejpam-1372	137	12	carried	carry	VERB
ejpam-1372	137	13	out	out	ADP
ejpam-1372	137	14	a	a	DET
ejpam-1372	137	15	numerical	numerical	ADJ
ejpam-1372	137	16	study	study	NOUN
ejpam-1372	137	17	into	into	ADP
ejpam-1372	137	18	the	the	DET
ejpam-1372	137	19	complete	complete	ADJ
ejpam-1372	137	20	asymptotic	asymptotic	ADJ
ejpam-1372	137	21	expansion	expansion	NOUN
ejpam-1372	137	22	of	of	ADP
ejpam-1372	137	23	a	a	DET
ejpam-1372	137	24	particular	particular	ADJ
ejpam-1372	137	25	case	case	NOUN
ejpam-1372	137	26	of	of	ADP
ejpam-1372	137	27	a	a	DET
ejpam-1372	137	28	number	number	NOUN
ejpam-1372	137	29	theoretic	theoretic	ADJ
ejpam-1372	137	30	exponential	exponential	ADJ
ejpam-1372	137	31	series	series	NOUN
ejpam-1372	137	32	,	,	PUNCT
ejpam-1372	137	33	which	which	PRON
ejpam-1372	137	34	we	we	PRON
ejpam-1372	137	35	called	call	VERB
ejpam-1372	137	36	the	the	DET
ejpam-1372	137	37	generalised	generalise	VERB
ejpam-1372	137	38	euler	euler	PROPN
ejpam-1372	137	39	-	-	PUNCT
ejpam-1372	137	40	jacobi	jacobi	PROPN
ejpam-1372	137	41	series	series	NOUN
ejpam-1372	137	42	[	[	X
ejpam-1372	137	43	21	21	NUM
ejpam-1372	137	44	]	]	PUNCT
ejpam-1372	137	45	.	.	PUNCT
ejpam-1372	138	1	specifically	specifically	ADV
ejpam-1372	138	2	,	,	PUNCT
ejpam-1372	138	3	our	our	PRON
ejpam-1372	138	4	investigation	investigation	NOUN
ejpam-1372	138	5	concentrated	concentrate	VERB
ejpam-1372	138	6	on	on	ADP
ejpam-1372	138	7	the	the	DET
ejpam-1372	138	8	series	series	NOUN
ejpam-1372	138	9	,	,	PUNCT
ejpam-1372	138	10	s3(a	s3(a	PROPN
ejpam-1372	138	11	)	)	PUNCT
ejpam-1372	138	12	=	=	SYM
ejpam-1372	138	13	∑∞	∑∞	NOUN
ejpam-1372	138	14	k=0	k=0	PROPN
ejpam-1372	138	15	exp(−ak3	exp(−ak3	NUM
ejpam-1372	138	16	)	)	PUNCT
ejpam-1372	138	17	,	,	PUNCT
ejpam-1372	138	18	which	which	PRON
ejpam-1372	138	19	represented	represent	VERB
ejpam-1372	138	20	the	the	DET
ejpam-1372	138	21	p	p	PROPN
ejpam-1372	138	22	/	/	SYM
ejpam-1372	138	23	q=3	q=3	NOUN
ejpam-1372	138	24	case	case	NOUN
ejpam-1372	138	25	.	.	PUNCT
ejpam-1372	139	1	this	this	DET
ejpam-1372	139	2	series	series	NOUN
ejpam-1372	139	3	was	be	AUX
ejpam-1372	139	4	found	find	VERB
ejpam-1372	139	5	to	to	PART
ejpam-1372	139	6	possess	possess	VERB
ejpam-1372	139	7	unimportant	unimportant	ADJ
ejpam-1372	139	8	constant	constant	ADJ
ejpam-1372	139	9	terms	term	NOUN
ejpam-1372	139	10	,	,	PUNCT
ejpam-1372	139	11	which	which	PRON
ejpam-1372	139	12	were	be	AUX
ejpam-1372	139	13	removed	remove	VERB
ejpam-1372	139	14	so	so	SCONJ
ejpam-1372	139	15	that	that	SCONJ
ejpam-1372	139	16	remaining	remain	VERB
ejpam-1372	139	17	terms	term	NOUN
ejpam-1372	139	18	or	or	CCONJ
ejpam-1372	139	19	the	the	DET
ejpam-1372	139	20	tail	tail	NOUN
ejpam-1372	139	21	denoted	denote	VERB
ejpam-1372	139	22	by	by	ADP
ejpam-1372	139	23	t3(a	t3(a	PRON
ejpam-1372	139	24	)	)	PUNCT
ejpam-1372	139	25	yielded	yield	VERB
ejpam-1372	139	26	an	an	DET
ejpam-1372	139	27	asymptotic	asymptotic	ADJ
ejpam-1372	139	28	expansion	expansion	NOUN
ejpam-1372	139	29	,	,	PUNCT
ejpam-1372	139	30	which	which	PRON
ejpam-1372	139	31	was	be	AUX
ejpam-1372	139	32	composed	compose	VERB
ejpam-1372	139	33	of	of	ADP
ejpam-1372	139	34	two	two	NUM
ejpam-1372	139	35	separate	separate	ADJ
ejpam-1372	139	36	divergent	divergent	ADJ
ejpam-1372	139	37	series	series	NOUN
ejpam-1372	139	38	.	.	PUNCT
ejpam-1372	140	1	one	one	NUM
ejpam-1372	140	2	of	of	ADP
ejpam-1372	140	3	these	these	DET
ejpam-1372	140	4	series	series	NOUN
ejpam-1372	140	5	denoted	denote	VERB
ejpam-1372	140	6	by	by	ADP
ejpam-1372	140	7	t	t	PROPN
ejpam-1372	140	8	k	k	PROPN
ejpam-1372	140	9	3	3	NUM
ejpam-1372	140	10	(	(	PUNCT
ejpam-1372	140	11	a	a	NOUN
ejpam-1372	140	12	)	)	PUNCT
ejpam-1372	140	13	was	be	AUX
ejpam-1372	140	14	subdominant	subdominant	ADJ
ejpam-1372	140	15	to	to	ADP
ejpam-1372	140	16	the	the	DET
ejpam-1372	140	17	other	other	ADJ
ejpam-1372	140	18	,	,	PUNCT
ejpam-1372	140	19	which	which	PRON
ejpam-1372	140	20	was	be	AUX
ejpam-1372	140	21	denoted	denote	VERB
ejpam-1372	140	22	by	by	ADP
ejpam-1372	140	23	t	t	PROPN
ejpam-1372	140	24	l	l	NOUN
ejpam-1372	140	25	3	3	NUM
ejpam-1372	140	26	(	(	PUNCT
ejpam-1372	140	27	a	a	NOUN
ejpam-1372	140	28	)	)	PUNCT
ejpam-1372	140	29	.	.	PUNCT
ejpam-1372	141	1	specifically	specifically	ADV
ejpam-1372	141	2	,	,	PUNCT
ejpam-1372	141	3	we	we	PRON
ejpam-1372	141	4	found	find	VERB
ejpam-1372	141	5	that	that	SCONJ
ejpam-1372	141	6	t3(a	t3(a	X
ejpam-1372	141	7	)	)	PUNCT
ejpam-1372	141	8	=	=	SYM
ejpam-1372	141	9	t	t	NOUN
ejpam-1372	141	10	l	l	NOUN
ejpam-1372	141	11	3	3	X
ejpam-1372	141	12	(	(	PUNCT
ejpam-1372	141	13	a	a	NOUN
ejpam-1372	141	14	)	)	PUNCT
ejpam-1372	142	1	+	+	NUM
ejpam-1372	142	2	t	t	X
ejpam-1372	142	3	k	k	X
ejpam-1372	142	4	3	3	NUM
ejpam-1372	142	5	(	(	PUNCT
ejpam-1372	142	6	a	a	NOUN
ejpam-1372	142	7	)	)	PUNCT
ejpam-1372	142	8	,	,	PUNCT
ejpam-1372	142	9	(	(	PUNCT
ejpam-1372	142	10	5	5	X
ejpam-1372	142	11	)	)	PUNCT
ejpam-1372	142	12	v.	v.	ADP
ejpam-1372	142	13	kowalenko	kowalenko	PROPN
ejpam-1372	142	14	/	/	SYM
ejpam-1372	142	15	eur	eur	PROPN
ejpam-1372	142	16	.	.	PUNCT
ejpam-1372	143	1	j.	j.	PROPN
ejpam-1372	143	2	pure	pure	PROPN
ejpam-1372	143	3	appl	appl	PROPN
ejpam-1372	143	4	.	.	PROPN
ejpam-1372	143	5	math	math	PROPN
ejpam-1372	143	6	,	,	PUNCT
ejpam-1372	143	7	4	4	NUM
ejpam-1372	143	8	(	(	PUNCT
ejpam-1372	143	9	2011	2011	NUM
ejpam-1372	143	10	)	)	PUNCT
ejpam-1372	143	11	,	,	PUNCT
ejpam-1372	143	12	370	370	NUM
ejpam-1372	143	13	-	-	SYM
ejpam-1372	143	14	423	423	NUM
ejpam-1372	143	15	375	375	NUM
ejpam-1372	143	16	where	where	SCONJ
ejpam-1372	143	17	t	t	NOUN
ejpam-1372	143	18	l	l	NOUN
ejpam-1372	143	19	3	3	NUM
ejpam-1372	143	20	(	(	PUNCT
ejpam-1372	143	21	a	a	NOUN
ejpam-1372	143	22	)	)	PUNCT
ejpam-1372	143	23	=	=	SYM
ejpam-1372	143	24	2	2	NUM
ejpam-1372	143	25	∞	∞	NUM
ejpam-1372	143	26	∑	∑	PUNCT
ejpam-1372	143	27	k=0	k=0	PROPN
ejpam-1372	143	28	(	(	PUNCT
ejpam-1372	143	29	−1)k+1a2k+1	−1)k+1a2k+1	PUNCT
ejpam-1372	143	30	(	(	PUNCT
ejpam-1372	143	31	2π)6k+4	2π)6k+4	NUM
ejpam-1372	143	32	γ(6k+	γ(6k+	NOUN
ejpam-1372	143	33	4	4	NUM
ejpam-1372	143	34	)	)	PUNCT
ejpam-1372	143	35	γ(2k+	γ(2k+	NOUN
ejpam-1372	143	36	2	2	NUM
ejpam-1372	143	37	)	)	PUNCT
ejpam-1372	143	38	ζ(6k+	ζ(6k+	NOUN
ejpam-1372	143	39	4	4	NUM
ejpam-1372	143	40	)	)	PUNCT
ejpam-1372	143	41	,	,	PUNCT
ejpam-1372	143	42	(	(	PUNCT
ejpam-1372	143	43	6	6	NUM
ejpam-1372	143	44	)	)	PUNCT
ejpam-1372	143	45	whilst	whilst	SCONJ
ejpam-1372	143	46	the	the	DET
ejpam-1372	143	47	subdominant	subdominant	ADJ
ejpam-1372	143	48	series	series	NOUN
ejpam-1372	143	49	was	be	AUX
ejpam-1372	143	50	given	give	VERB
ejpam-1372	143	51	by	by	ADP
ejpam-1372	143	52	t	t	PROPN
ejpam-1372	143	53	k	k	PROPN
ejpam-1372	143	54	3	3	NUM
ejpam-1372	143	55	(	(	PUNCT
ejpam-1372	143	56	a	a	NOUN
ejpam-1372	143	57	)	)	PUNCT
ejpam-1372	143	58	=	=	SYM
ejpam-1372	144	1	2	2	NUM
ejpam-1372	144	2	p	p	NOUN
ejpam-1372	144	3	π	π	PROPN
ejpam-1372	144	4	γ(1	γ(1	PROPN
ejpam-1372	144	5	6	6	NUM
ejpam-1372	144	6	)	)	PUNCT
ejpam-1372	144	7	γ(5	γ(5	NOUN
ejpam-1372	144	8	6	6	NUM
ejpam-1372	144	9	)	)	PUNCT
ejpam-1372	144	10	∞	∞	PROPN
ejpam-1372	144	11	∑	∑	PUNCT
ejpam-1372	144	12	n=1	n=1	PROPN
ejpam-1372	144	13	e−	e−	PROPN
ejpam-1372	144	14	p	p	PROPN
ejpam-1372	144	15	2z	2z	PRON
ejpam-1372	144	16	(	(	PUNCT
ejpam-1372	144	17	6πna)1/4	6πna)1/4	NUM
ejpam-1372	144	18	∞	∞	NUM
ejpam-1372	144	19	∑	∑	PROPN
ejpam-1372	144	20	k=0	k=0	PUNCT
ejpam-1372	144	21	γ(k+	γ(k+	ADP
ejpam-1372	144	22	1/6	1/6	NUM
ejpam-1372	144	23	)	)	PUNCT
ejpam-1372	144	24	(	(	PUNCT
ejpam-1372	144	25	4	4	NUM
ejpam-1372	144	26	p	p	NOUN
ejpam-1372	144	27	z)k	z)k	NOUN
ejpam-1372	144	28	×	×	NOUN
ejpam-1372	144	29	γ(k+	γ(k+	SYM
ejpam-1372	144	30	5/6	5/6	NUM
ejpam-1372	144	31	)	)	PUNCT
ejpam-1372	144	32	γ(k+	γ(k+	NUM
ejpam-1372	144	33	1/2	1/2	NUM
ejpam-1372	144	34	)	)	PUNCT
ejpam-1372	144	35	cos	cos	PROPN
ejpam-1372	144	36	�	�	PROPN
ejpam-1372	144	37	p	p	NOUN
ejpam-1372	144	38	2z	2z	NUM
ejpam-1372	144	39	−	−	PROPN
ejpam-1372	144	40	π	π	NOUN
ejpam-1372	144	41	8	8	NUM
ejpam-1372	144	42	−	−	NOUN
ejpam-1372	144	43	3kπ	3kπ	ADJ
ejpam-1372	144	44	4	4	NUM
ejpam-1372	144	45	�	�	NOUN
ejpam-1372	144	46	.	.	PUNCT
ejpam-1372	145	1	(	(	PUNCT
ejpam-1372	145	2	7	7	X
ejpam-1372	145	3	)	)	PUNCT
ejpam-1372	145	4	in	in	ADP
ejpam-1372	145	5	these	these	DET
ejpam-1372	145	6	results	result	NOUN
ejpam-1372	145	7	z=(2nπ/3)3a−1	z=(2nπ/3)3a−1	NOUN
ejpam-1372	145	8	,	,	PUNCT
ejpam-1372	145	9	while	while	SCONJ
ejpam-1372	145	10	ζ(s	ζ(s	PROPN
ejpam-1372	145	11	)	)	PUNCT
ejpam-1372	145	12	represents	represent	VERB
ejpam-1372	145	13	the	the	DET
ejpam-1372	145	14	riemann	riemann	PROPN
ejpam-1372	145	15	zeta	zeta	PROPN
ejpam-1372	145	16	function	function	PROPN
ejpam-1372	145	17	.	.	PUNCT
ejpam-1372	146	1	subdominance	subdominance	NOUN
ejpam-1372	146	2	in	in	ADP
ejpam-1372	146	3	an	an	DET
ejpam-1372	146	4	asymptotic	asymptotic	ADJ
ejpam-1372	146	5	expansion	expansion	NOUN
ejpam-1372	146	6	means	mean	VERB
ejpam-1372	146	7	that	that	SCONJ
ejpam-1372	146	8	one	one	NUM
ejpam-1372	146	9	of	of	ADP
ejpam-1372	146	10	the	the	DET
ejpam-1372	146	11	component	component	NOUN
ejpam-1372	146	12	series	series	NOUN
ejpam-1372	146	13	possesses	possess	VERB
ejpam-1372	146	14	an	an	DET
ejpam-1372	146	15	exponential	exponential	ADJ
ejpam-1372	146	16	factor	factor	NOUN
ejpam-1372	146	17	that	that	PRON
ejpam-1372	146	18	causes	cause	VERB
ejpam-1372	146	19	the	the	DET
ejpam-1372	146	20	entire	entire	ADJ
ejpam-1372	146	21	series	series	NOUN
ejpam-1372	146	22	to	to	PART
ejpam-1372	146	23	vanish	vanish	VERB
ejpam-1372	146	24	as	as	SCONJ
ejpam-1372	146	25	the	the	DET
ejpam-1372	146	26	main	main	ADJ
ejpam-1372	146	27	variable	variable	NOUN
ejpam-1372	146	28	tends	tend	VERB
ejpam-1372	146	29	to	to	ADP
ejpam-1372	146	30	the	the	DET
ejpam-1372	146	31	limit	limit	NOUN
ejpam-1372	146	32	point	point	NOUN
ejpam-1372	146	33	,	,	PUNCT
ejpam-1372	146	34	which	which	PRON
ejpam-1372	146	35	in	in	ADP
ejpam-1372	146	36	the	the	DET
ejpam-1372	146	37	above	above	ADJ
ejpam-1372	146	38	example	example	NOUN
ejpam-1372	146	39	refers	refer	VERB
ejpam-1372	146	40	to	to	ADP
ejpam-1372	146	41	either	either	CCONJ
ejpam-1372	146	42	a	a	DET
ejpam-1372	146	43	→	→	SYM
ejpam-1372	146	44	0	0	NUM
ejpam-1372	146	45	or	or	CCONJ
ejpam-1372	146	46	z	z	PROPN
ejpam-1372	146	47	→	→	SYM
ejpam-1372	146	48	∞.	∞.	PROPN
ejpam-1372	146	49	that	that	PRON
ejpam-1372	146	50	is	be	AUX
ejpam-1372	146	51	,	,	PUNCT
ejpam-1372	146	52	in	in	ADP
ejpam-1372	146	53	this	this	DET
ejpam-1372	146	54	limit	limit	NOUN
ejpam-1372	146	55	the	the	DET
ejpam-1372	146	56	exponential	exponential	ADJ
ejpam-1372	146	57	factor	factor	NOUN
ejpam-1372	146	58	of	of	ADP
ejpam-1372	146	59	exp(−p2z	exp(−p2z	NOUN
ejpam-1372	146	60	)	)	PUNCT
ejpam-1372	146	61	appearing	appear	VERB
ejpam-1372	146	62	in	in	ADP
ejpam-1372	146	63	eq	eq	ADP
ejpam-1372	146	64	.	.	PUNCT
ejpam-1372	147	1	(	(	PUNCT
ejpam-1372	147	2	7	7	X
ejpam-1372	147	3	)	)	PUNCT
ejpam-1372	147	4	becomes	become	VERB
ejpam-1372	147	5	vanishingly	vanishingly	ADV
ejpam-1372	147	6	small	small	ADJ
ejpam-1372	147	7	in	in	ADP
ejpam-1372	147	8	comparison	comparison	NOUN
ejpam-1372	147	9	with	with	ADP
ejpam-1372	147	10	the	the	DET
ejpam-1372	147	11	dominant	dominant	ADJ
ejpam-1372	147	12	series	series	NOUN
ejpam-1372	147	13	given	give	VERB
ejpam-1372	147	14	in	in	ADP
ejpam-1372	147	15	eq	eq	ADP
ejpam-1372	147	16	.	.	PUNCT
ejpam-1372	148	1	(	(	PUNCT
ejpam-1372	148	2	6	6	NUM
ejpam-1372	148	3	)	)	PUNCT
ejpam-1372	148	4	.	.	PUNCT
ejpam-1372	149	1	it	it	PRON
ejpam-1372	149	2	should	should	AUX
ejpam-1372	149	3	also	also	ADV
ejpam-1372	149	4	be	be	AUX
ejpam-1372	149	5	noted	note	VERB
ejpam-1372	149	6	that	that	SCONJ
ejpam-1372	149	7	subdominant	subdominant	ADJ
ejpam-1372	149	8	terms	term	NOUN
ejpam-1372	149	9	can	can	AUX
ejpam-1372	149	10	become	become	VERB
ejpam-1372	149	11	the	the	DET
ejpam-1372	149	12	dominant	dominant	ADJ
ejpam-1372	149	13	terms	term	NOUN
ejpam-1372	149	14	and	and	CCONJ
ejpam-1372	149	15	vice	vice	NOUN
ejpam-1372	149	16	-	-	NOUN
ejpam-1372	149	17	versa	versa	NOUN
ejpam-1372	149	18	as	as	ADP
ejpam-1372	149	19	the	the	DET
ejpam-1372	149	20	main	main	ADJ
ejpam-1372	149	21	variable	variable	NOUN
ejpam-1372	149	22	or	or	CCONJ
ejpam-1372	149	23	a	a	PRON
ejpam-1372	149	24	in	in	ADP
ejpam-1372	149	25	the	the	DET
ejpam-1372	149	26	above	above	ADJ
ejpam-1372	149	27	example	example	NOUN
ejpam-1372	149	28	undergoes	undergo	VERB
ejpam-1372	149	29	changes	change	NOUN
ejpam-1372	149	30	in	in	ADP
ejpam-1372	149	31	its	its	PRON
ejpam-1372	149	32	argument	argument	NOUN
ejpam-1372	149	33	or	or	CCONJ
ejpam-1372	149	34	phase	phase	NOUN
ejpam-1372	149	35	.	.	PUNCT
ejpam-1372	150	1	however	however	ADV
ejpam-1372	150	2	,	,	PUNCT
ejpam-1372	150	3	at	at	ADP
ejpam-1372	150	4	the	the	DET
ejpam-1372	150	5	time	time	NOUN
ejpam-1372	150	6	we	we	PRON
ejpam-1372	150	7	were	be	AUX
ejpam-1372	150	8	only	only	ADV
ejpam-1372	150	9	interested	interested	ADJ
ejpam-1372	150	10	in	in	ADP
ejpam-1372	150	11	real	real	ADJ
ejpam-1372	150	12	values	value	NOUN
ejpam-1372	150	13	of	of	ADP
ejpam-1372	150	14	a.	a.	NOUN
ejpam-1372	150	15	as	as	SCONJ
ejpam-1372	150	16	described	describe	VERB
ejpam-1372	150	17	in	in	ADP
ejpam-1372	150	18	the	the	DET
ejpam-1372	150	19	introduction	introduction	NOUN
ejpam-1372	150	20	,	,	PUNCT
ejpam-1372	150	21	subdominant	subdominant	ADJ
ejpam-1372	150	22	terms	term	NOUN
ejpam-1372	150	23	such	such	ADJ
ejpam-1372	150	24	as	as	ADP
ejpam-1372	150	25	those	those	PRON
ejpam-1372	150	26	in	in	ADP
ejpam-1372	150	27	eq	eq	ADP
ejpam-1372	150	28	.	.	PUNCT
ejpam-1372	150	29	(	(	PUNCT
ejpam-1372	150	30	7	7	X
ejpam-1372	150	31	)	)	PUNCT
ejpam-1372	150	32	are	be	AUX
ejpam-1372	150	33	said	say	VERB
ejpam-1372	150	34	to	to	PART
ejpam-1372	150	35	lie	lie	VERB
ejpam-1372	150	36	beyond	beyond	ADP
ejpam-1372	150	37	all	all	DET
ejpam-1372	150	38	orders	order	NOUN
ejpam-1372	150	39	of	of	ADP
ejpam-1372	150	40	the	the	DET
ejpam-1372	150	41	dominant	dominant	ADJ
ejpam-1372	150	42	part	part	NOUN
ejpam-1372	150	43	of	of	ADP
ejpam-1372	150	44	the	the	DET
ejpam-1372	150	45	expansion	expansion	NOUN
ejpam-1372	150	46	[	[	X
ejpam-1372	150	47	4	4	NUM
ejpam-1372	150	48	,	,	PUNCT
ejpam-1372	150	49	5	5	NUM
ejpam-1372	150	50	,	,	PUNCT
ejpam-1372	150	51	29	29	NUM
ejpam-1372	150	52	]	]	PUNCT
ejpam-1372	150	53	and	and	CCONJ
ejpam-1372	150	54	are	be	AUX
ejpam-1372	150	55	generally	generally	ADV
ejpam-1372	150	56	neglected	neglect	VERB
ejpam-1372	150	57	by	by	ADP
ejpam-1372	150	58	practitioners	practitioner	NOUN
ejpam-1372	150	59	of	of	ADP
ejpam-1372	150	60	standard	standard	ADJ
ejpam-1372	150	61	asymptotics	asymptotic	NOUN
ejpam-1372	150	62	.	.	PUNCT
ejpam-1372	151	1	nevertheless	nevertheless	ADV
ejpam-1372	151	2	,	,	PUNCT
ejpam-1372	151	3	we	we	PRON
ejpam-1372	151	4	found	find	VERB
ejpam-1372	151	5	that	that	SCONJ
ejpam-1372	151	6	they	they	PRON
ejpam-1372	151	7	were	be	AUX
ejpam-1372	151	8	necessary	necessary	ADJ
ejpam-1372	151	9	for	for	ADP
ejpam-1372	151	10	obtaining	obtain	VERB
ejpam-1372	151	11	exact	exact	ADJ
ejpam-1372	151	12	values	value	NOUN
ejpam-1372	151	13	of	of	ADP
ejpam-1372	151	14	the	the	DET
ejpam-1372	151	15	series	series	NOUN
ejpam-1372	151	16	regardless	regardless	ADV
ejpam-1372	151	17	of	of	ADP
ejpam-1372	151	18	the	the	DET
ejpam-1372	151	19	size	size	NOUN
ejpam-1372	151	20	of	of	ADP
ejpam-1372	151	21	a.	a.	NOUN
ejpam-1372	151	22	for	for	ADP
ejpam-1372	151	23	example	example	NOUN
ejpam-1372	151	24	,	,	PUNCT
ejpam-1372	151	25	when	when	SCONJ
ejpam-1372	151	26	the	the	DET
ejpam-1372	151	27	first	first	ADJ
ejpam-1372	151	28	fifteen	fifteen	NUM
ejpam-1372	151	29	terms	term	NOUN
ejpam-1372	151	30	of	of	ADP
ejpam-1372	151	31	the	the	DET
ejpam-1372	151	32	dominant	dominant	ADJ
ejpam-1372	151	33	series	series	NOUN
ejpam-1372	151	34	and	and	CCONJ
ejpam-1372	151	35	the	the	DET
ejpam-1372	151	36	first	first	ADJ
ejpam-1372	151	37	twenty	twenty	NUM
ejpam-1372	151	38	-	-	PUNCT
ejpam-1372	151	39	one	one	NUM
ejpam-1372	151	40	terms	term	NOUN
ejpam-1372	151	41	of	of	ADP
ejpam-1372	151	42	the	the	DET
ejpam-1372	151	43	subdominant	subdominant	ADJ
ejpam-1372	151	44	series	series	NOUN
ejpam-1372	151	45	are	be	AUX
ejpam-1372	151	46	subtracted	subtract	VERB
ejpam-1372	151	47	from	from	ADP
ejpam-1372	151	48	t3(a	t3(a	PROPN
ejpam-1372	151	49	)	)	PUNCT
ejpam-1372	151	50	with	with	ADP
ejpam-1372	151	51	a	a	DET
ejpam-1372	151	52	equal	equal	ADJ
ejpam-1372	151	53	to	to	ADP
ejpam-1372	151	54	0.2	0.2	NUM
ejpam-1372	151	55	,	,	PUNCT
ejpam-1372	151	56	one	one	PRON
ejpam-1372	151	57	obtains	obtain	VERB
ejpam-1372	151	58	a	a	DET
ejpam-1372	151	59	value	value	NOUN
ejpam-1372	151	60	of	of	ADP
ejpam-1372	151	61	t3(0.2)−	t3(0.2)−	PROPN
ejpam-1372	151	62	t	t	PROPN
ejpam-1372	151	63	l	l	NOUN
ejpam-1372	151	64	3	3	NUM
ejpam-1372	151	65	(	(	PUNCT
ejpam-1372	151	66	0.2,15)−	0.2,15)−	NOUN
ejpam-1372	151	67	t	t	PROPN
ejpam-1372	151	68	k	k	PROPN
ejpam-1372	151	69	3	3	NUM
ejpam-1372	151	70	(	(	PUNCT
ejpam-1372	151	71	0.2,21	0.2,21	PROPN
ejpam-1372	151	72	)	)	PUNCT
ejpam-1372	151	73	=	=	PUNCT
ejpam-1372	151	74	−8.458	−8.458	NOUN
ejpam-1372	151	75	470	470	NUM
ejpam-1372	151	76	156	156	NUM
ejpam-1372	151	77	185	185	NUM
ejpam-1372	151	78	480	480	NUM
ejpam-1372	151	79	·	·	PUNCT
ejpam-1372	151	80	·	·	PUNCT
ejpam-1372	152	1	·	·	PUNCT
ejpam-1372	152	2	×	×	PROPN
ejpam-1372	152	3	10−7	10−7	NUM
ejpam-1372	152	4	.	.	PUNCT
ejpam-1372	153	1	(	(	PUNCT
ejpam-1372	153	2	8)	8)	NUM
ejpam-1372	153	3	on	on	ADP
ejpam-1372	153	4	the	the	DET
ejpam-1372	153	5	lhs	lhs	PROPN
ejpam-1372	153	6	of	of	ADP
ejpam-1372	153	7	the	the	DET
ejpam-1372	153	8	above	above	ADJ
ejpam-1372	153	9	equation	equation	NOUN
ejpam-1372	153	10	,	,	PUNCT
ejpam-1372	153	11	we	we	PRON
ejpam-1372	153	12	have	have	AUX
ejpam-1372	153	13	introduced	introduce	VERB
ejpam-1372	153	14	the	the	DET
ejpam-1372	153	15	truncation	truncation	NOUN
ejpam-1372	153	16	parameter	parameter	NOUN
ejpam-1372	153	17	n	n	CCONJ
ejpam-1372	153	18	into	into	ADP
ejpam-1372	153	19	the	the	DET
ejpam-1372	153	20	series	series	NOUN
ejpam-1372	153	21	given	give	VERB
ejpam-1372	153	22	by	by	ADP
ejpam-1372	153	23	eqs	eqs	PROPN
ejpam-1372	153	24	.	.	PUNCT
ejpam-1372	154	1	(	(	PUNCT
ejpam-1372	154	2	6	6	NUM
ejpam-1372	154	3	)	)	PUNCT
ejpam-1372	154	4	and	and	CCONJ
ejpam-1372	154	5	(	(	PUNCT
ejpam-1372	154	6	7	7	X
ejpam-1372	154	7	)	)	PUNCT
ejpam-1372	154	8	to	to	PART
ejpam-1372	154	9	indicate	indicate	VERB
ejpam-1372	154	10	that	that	SCONJ
ejpam-1372	154	11	the	the	DET
ejpam-1372	154	12	sums	sum	NOUN
ejpam-1372	154	13	over	over	ADP
ejpam-1372	154	14	k	k	PROPN
ejpam-1372	154	15	have	have	AUX
ejpam-1372	154	16	been	be	AUX
ejpam-1372	154	17	evaluated	evaluate	VERB
ejpam-1372	154	18	partially	partially	ADV
ejpam-1372	154	19	by	by	ADP
ejpam-1372	154	20	setting	set	VERB
ejpam-1372	154	21	n	n	X
ejpam-1372	154	22	=	=	SYM
ejpam-1372	154	23	15	15	NUM
ejpam-1372	154	24	in	in	ADP
ejpam-1372	154	25	the	the	DET
ejpam-1372	154	26	first	first	ADJ
ejpam-1372	154	27	series	series	NOUN
ejpam-1372	154	28	and	and	CCONJ
ejpam-1372	154	29	n	n	NOUN
ejpam-1372	154	30	=	=	NUM
ejpam-1372	154	31	21	21	NUM
ejpam-1372	154	32	in	in	ADP
ejpam-1372	154	33	the	the	DET
ejpam-1372	154	34	second	second	ADJ
ejpam-1372	154	35	series	series	NOUN
ejpam-1372	154	36	.	.	PUNCT
ejpam-1372	155	1	the	the	DET
ejpam-1372	155	2	value	value	NOUN
ejpam-1372	155	3	on	on	ADP
ejpam-1372	155	4	the	the	DET
ejpam-1372	155	5	rhs	rhs	PROPN
ejpam-1372	155	6	now	now	ADV
ejpam-1372	155	7	represents	represent	VERB
ejpam-1372	155	8	the	the	DET
ejpam-1372	155	9	combined	combined	ADJ
ejpam-1372	155	10	remainder	remainder	NOUN
ejpam-1372	155	11	of	of	ADP
ejpam-1372	155	12	two	two	NUM
ejpam-1372	155	13	divergent	divergent	ADJ
ejpam-1372	155	14	series	series	NOUN
ejpam-1372	155	15	.	.	PUNCT
ejpam-1372	156	1	by	by	ADP
ejpam-1372	156	2	using	use	VERB
ejpam-1372	156	3	our	our	PRON
ejpam-1372	156	4	newlydiscovered	newlydiscovere	VERB
ejpam-1372	156	5	mathematical	mathematical	ADJ
ejpam-1372	156	6	technique	technique	NOUN
ejpam-1372	156	7	,	,	PUNCT
ejpam-1372	156	8	we	we	PRON
ejpam-1372	156	9	were	be	AUX
ejpam-1372	156	10	able	able	ADJ
ejpam-1372	156	11	to	to	PART
ejpam-1372	156	12	evaluate	evaluate	VERB
ejpam-1372	156	13	the	the	DET
ejpam-1372	156	14	remainder	remainder	NOUN
ejpam-1372	156	15	of	of	ADP
ejpam-1372	156	16	t	t	PROPN
ejpam-1372	156	17	l	l	NOUN
ejpam-1372	156	18	3	3	NUM
ejpam-1372	156	19	(	(	PUNCT
ejpam-1372	156	20	a	a	NOUN
ejpam-1372	156	21	)	)	PUNCT
ejpam-1372	156	22	,	,	PUNCT
ejpam-1372	156	23	which	which	PRON
ejpam-1372	156	24	when	when	SCONJ
ejpam-1372	156	25	subtracted	subtract	VERB
ejpam-1372	156	26	from	from	ADP
ejpam-1372	156	27	the	the	DET
ejpam-1372	156	28	right	right	ADJ
ejpam-1372	156	29	hand	hand	NOUN
ejpam-1372	156	30	side	side	NOUN
ejpam-1372	156	31	(	(	PUNCT
ejpam-1372	156	32	rhs	rhs	PROPN
ejpam-1372	156	33	)	)	PUNCT
ejpam-1372	156	34	of	of	ADP
ejpam-1372	156	35	the	the	DET
ejpam-1372	156	36	above	above	ADJ
ejpam-1372	156	37	equation	equation	NOUN
ejpam-1372	156	38	yielded	yield	VERB
ejpam-1372	156	39	a	a	DET
ejpam-1372	156	40	value	value	NOUN
ejpam-1372	156	41	of	of	ADP
ejpam-1372	156	42	−1.588955334	−1.588955334	NOUN
ejpam-1372	156	43	·	·	PUNCT
ejpam-1372	156	44	·	·	PUNCT
ejpam-1372	156	45	·	·	PUNCT
ejpam-1372	157	1	×	×	NOUN
ejpam-1372	157	2	10−17	10−17	X
ejpam-1372	157	3	.	.	PUNCT
ejpam-1372	158	1	then	then	ADV
ejpam-1372	158	2	by	by	ADP
ejpam-1372	158	3	applying	apply	VERB
ejpam-1372	158	4	the	the	DET
ejpam-1372	158	5	same	same	ADJ
ejpam-1372	158	6	technique	technique	NOUN
ejpam-1372	158	7	to	to	ADP
ejpam-1372	158	8	the	the	DET
ejpam-1372	158	9	expression	expression	NOUN
ejpam-1372	158	10	for	for	ADP
ejpam-1372	158	11	the	the	DET
ejpam-1372	158	12	remainder	remainder	NOUN
ejpam-1372	158	13	of	of	ADP
ejpam-1372	158	14	the	the	DET
ejpam-1372	158	15	subdominant	subdominant	ADJ
ejpam-1372	158	16	series	series	NOUN
ejpam-1372	158	17	t	t	PROPN
ejpam-1372	158	18	k	k	PROPN
ejpam-1372	158	19	3	3	NUM
ejpam-1372	158	20	(	(	PUNCT
ejpam-1372	158	21	a	a	NOUN
ejpam-1372	158	22	)	)	PUNCT
ejpam-1372	158	23	,	,	PUNCT
ejpam-1372	158	24	we	we	PRON
ejpam-1372	158	25	obtained	obtain	VERB
ejpam-1372	158	26	the	the	DET
ejpam-1372	158	27	same	same	ADJ
ejpam-1372	158	28	value	value	NOUN
ejpam-1372	158	29	.	.	PUNCT
ejpam-1372	159	1	the	the	DET
ejpam-1372	159	2	analysis	analysis	NOUN
ejpam-1372	159	3	was	be	AUX
ejpam-1372	159	4	repeated	repeat	VERB
ejpam-1372	159	5	for	for	ADP
ejpam-1372	159	6	numerous	numerous	ADJ
ejpam-1372	159	7	values	value	NOUN
ejpam-1372	159	8	of	of	ADP
ejpam-1372	159	9	a	a	DET
ejpam-1372	159	10	ranging	ranging	NOUN
ejpam-1372	159	11	from	from	ADP
ejpam-1372	159	12	0.01	0.01	NUM
ejpam-1372	159	13	to	to	PART
ejpam-1372	159	14	10	10	NUM
ejpam-1372	159	15	.	.	PUNCT
ejpam-1372	160	1	on	on	ADP
ejpam-1372	160	2	each	each	DET
ejpam-1372	160	3	occasion	occasion	NOUN
ejpam-1372	160	4	we	we	PRON
ejpam-1372	160	5	obtained	obtain	VERB
ejpam-1372	160	6	the	the	DET
ejpam-1372	160	7	exact	exact	ADJ
ejpam-1372	160	8	numerical	numerical	ADJ
ejpam-1372	160	9	values	value	NOUN
ejpam-1372	160	10	of	of	ADP
ejpam-1372	160	11	the	the	DET
ejpam-1372	160	12	remainder	remainder	NOUN
ejpam-1372	160	13	for	for	ADP
ejpam-1372	160	14	the	the	DET
ejpam-1372	160	15	subdominant	subdominant	ADJ
ejpam-1372	160	16	series	series	NOUN
ejpam-1372	160	17	.	.	PUNCT
ejpam-1372	161	1	therefore	therefore	ADV
ejpam-1372	161	2	,	,	PUNCT
ejpam-1372	161	3	for	for	ADP
ejpam-1372	161	4	the	the	DET
ejpam-1372	161	5	first	first	ADJ
ejpam-1372	161	6	time	time	NOUN
ejpam-1372	161	7	in	in	ADP
ejpam-1372	161	8	the	the	DET
ejpam-1372	161	9	history	history	NOUN
ejpam-1372	161	10	of	of	ADP
ejpam-1372	161	11	mathematics	mathematic	NOUN
ejpam-1372	161	12	we	we	PRON
ejpam-1372	161	13	had	have	AUX
ejpam-1372	161	14	shown	show	VERB
ejpam-1372	161	15	that	that	SCONJ
ejpam-1372	161	16	a	a	DET
ejpam-1372	161	17	complete	complete	ADJ
ejpam-1372	161	18	asymptotic	asymptotic	ADJ
ejpam-1372	161	19	expansion	expansion	NOUN
ejpam-1372	161	20	could	could	AUX
ejpam-1372	161	21	be	be	AUX
ejpam-1372	161	22	used	use	VERB
ejpam-1372	161	23	to	to	PART
ejpam-1372	161	24	generate	generate	VERB
ejpam-1372	161	25	the	the	DET
ejpam-1372	161	26	values	value	NOUN
ejpam-1372	161	27	of	of	ADP
ejpam-1372	161	28	the	the	DET
ejpam-1372	161	29	original	original	ADJ
ejpam-1372	161	30	function	function	NOUN
ejpam-1372	161	31	it	it	PRON
ejpam-1372	161	32	represented	represent	VERB
ejpam-1372	161	33	.	.	PUNCT
ejpam-1372	162	1	all	all	DET
ejpam-1372	162	2	the	the	DET
ejpam-1372	162	3	results	result	NOUN
ejpam-1372	162	4	from	from	ADP
ejpam-1372	162	5	this	this	DET
ejpam-1372	162	6	spectacular	spectacular	ADJ
ejpam-1372	162	7	study	study	NOUN
ejpam-1372	162	8	were	be	AUX
ejpam-1372	162	9	eventually	eventually	ADV
ejpam-1372	162	10	documented	document	VERB
ejpam-1372	162	11	and	and	CCONJ
ejpam-1372	162	12	discussed	discuss	VERB
ejpam-1372	162	13	in	in	ADP
ejpam-1372	162	14	chs	ch	NOUN
ejpam-1372	162	15	.	.	PROPN
ejpam-1372	162	16	7	7	NUM
ejpam-1372	162	17	and	and	CCONJ
ejpam-1372	162	18	8	8	NUM
ejpam-1372	162	19	of	of	ADP
ejpam-1372	162	20	ref	ref	NOUN
ejpam-1372	162	21	.	.	PUNCT
ejpam-1372	163	1	[	[	X
ejpam-1372	163	2	21	21	NUM
ejpam-1372	163	3	]	]	PUNCT
ejpam-1372	163	4	.	.	PUNCT
ejpam-1372	164	1	v.	v.	ADP
ejpam-1372	164	2	kowalenko	kowalenko	PROPN
ejpam-1372	164	3	/	/	SYM
ejpam-1372	164	4	eur	eur	PROPN
ejpam-1372	164	5	.	.	PUNCT
ejpam-1372	165	1	j.	j.	PROPN
ejpam-1372	165	2	pure	pure	PROPN
ejpam-1372	165	3	appl	appl	PROPN
ejpam-1372	165	4	.	.	PROPN
ejpam-1372	165	5	math	math	PROPN
ejpam-1372	165	6	,	,	PUNCT
ejpam-1372	165	7	4	4	NUM
ejpam-1372	165	8	(	(	PUNCT
ejpam-1372	165	9	2011	2011	NUM
ejpam-1372	165	10	)	)	PUNCT
ejpam-1372	165	11	,	,	PUNCT
ejpam-1372	165	12	370	370	NUM
ejpam-1372	165	13	-	-	SYM
ejpam-1372	165	14	423	423	NUM
ejpam-1372	165	15	376	376	NUM
ejpam-1372	165	16	the	the	DET
ejpam-1372	165	17	mathematical	mathematical	ADJ
ejpam-1372	165	18	technique	technique	NOUN
ejpam-1372	165	19	mentioned	mention	VERB
ejpam-1372	165	20	in	in	ADP
ejpam-1372	165	21	the	the	DET
ejpam-1372	165	22	previous	previous	ADJ
ejpam-1372	165	23	paragraph	paragraph	NOUN
ejpam-1372	165	24	is	be	AUX
ejpam-1372	165	25	known	know	VERB
ejpam-1372	165	26	today	today	NOUN
ejpam-1372	165	27	as	as	ADP
ejpam-1372	165	28	mellin	mellin	NOUN
ejpam-1372	165	29	-	-	PUNCT
ejpam-1372	165	30	barnes	barnes	PROPN
ejpam-1372	165	31	regularisation	regularisation	NOUN
ejpam-1372	165	32	.	.	PUNCT
ejpam-1372	166	1	at	at	ADP
ejpam-1372	166	2	its	its	PRON
ejpam-1372	166	3	heart	heart	NOUN
ejpam-1372	166	4	lies	lie	VERB
ejpam-1372	166	5	the	the	DET
ejpam-1372	166	6	key	key	ADJ
ejpam-1372	166	7	concept	concept	NOUN
ejpam-1372	166	8	of	of	ADP
ejpam-1372	166	9	regularisation	regularisation	NOUN
ejpam-1372	166	10	,	,	PUNCT
ejpam-1372	166	11	which	which	PRON
ejpam-1372	166	12	is	be	AUX
ejpam-1372	166	13	defined	define	VERB
ejpam-1372	166	14	as	as	ADP
ejpam-1372	166	15	the	the	DET
ejpam-1372	166	16	removal	removal	NOUN
ejpam-1372	166	17	of	of	ADP
ejpam-1372	166	18	the	the	DET
ejpam-1372	166	19	infinity	infinity	NOUN
ejpam-1372	166	20	in	in	ADP
ejpam-1372	166	21	the	the	DET
ejpam-1372	166	22	remainder	remainder	NOUN
ejpam-1372	166	23	of	of	ADP
ejpam-1372	166	24	a	a	DET
ejpam-1372	166	25	divergent	divergent	ADJ
ejpam-1372	166	26	series	series	NOUN
ejpam-1372	166	27	so	so	SCONJ
ejpam-1372	166	28	as	as	SCONJ
ejpam-1372	166	29	to	to	PART
ejpam-1372	166	30	make	make	VERB
ejpam-1372	166	31	the	the	DET
ejpam-1372	166	32	series	series	NOUN
ejpam-1372	166	33	summable	summable	ADJ
ejpam-1372	166	34	.	.	PUNCT
ejpam-1372	167	1	it	it	PRON
ejpam-1372	167	2	is	be	AUX
ejpam-1372	167	3	the	the	DET
ejpam-1372	167	4	absence	absence	NOUN
ejpam-1372	167	5	of	of	ADP
ejpam-1372	167	6	this	this	DET
ejpam-1372	167	7	concept	concept	NOUN
ejpam-1372	167	8	that	that	PRON
ejpam-1372	167	9	has	have	AUX
ejpam-1372	167	10	resulted	result	VERB
ejpam-1372	167	11	in	in	ADP
ejpam-1372	167	12	the	the	DET
ejpam-1372	167	13	fallacies	fallacy	NOUN
ejpam-1372	167	14	and	and	CCONJ
ejpam-1372	167	15	paradoxes	paradox	NOUN
ejpam-1372	167	16	occurring	occur	VERB
ejpam-1372	167	17	in	in	ADP
ejpam-1372	167	18	divergent	divergent	ADJ
ejpam-1372	167	19	series	series	NOUN
ejpam-1372	167	20	as	as	SCONJ
ejpam-1372	167	21	described	describe	VERB
ejpam-1372	167	22	in	in	ADP
ejpam-1372	167	23	the	the	DET
ejpam-1372	167	24	previous	previous	ADJ
ejpam-1372	167	25	section	section	NOUN
ejpam-1372	167	26	.	.	PUNCT
ejpam-1372	168	1	so	so	ADV
ejpam-1372	168	2	,	,	PUNCT
ejpam-1372	168	3	let	let	VERB
ejpam-1372	168	4	us	we	PRON
ejpam-1372	168	5	examine	examine	VERB
ejpam-1372	168	6	how	how	SCONJ
ejpam-1372	168	7	regularisation	regularisation	NOUN
ejpam-1372	168	8	applies	apply	VERB
ejpam-1372	168	9	to	to	ADP
ejpam-1372	168	10	the	the	DET
ejpam-1372	168	11	geometric	geometric	ADJ
ejpam-1372	168	12	series	series	NOUN
ejpam-1372	168	13	since	since	SCONJ
ejpam-1372	168	14	it	it	PRON
ejpam-1372	168	15	represents	represent	VERB
ejpam-1372	168	16	a	a	DET
ejpam-1372	168	17	generalisation	generalisation	NOUN
ejpam-1372	168	18	of	of	ADP
ejpam-1372	168	19	grandi	grandi	PROPN
ejpam-1372	168	20	’s	’s	PART
ejpam-1372	168	21	series	series	NOUN
ejpam-1372	168	22	.	.	PUNCT
ejpam-1372	169	1	to	to	PART
ejpam-1372	169	2	do	do	VERB
ejpam-1372	169	3	so	so	ADV
ejpam-1372	169	4	,	,	PUNCT
ejpam-1372	169	5	we	we	PRON
ejpam-1372	169	6	write	write	VERB
ejpam-1372	169	7	the	the	DET
ejpam-1372	169	8	geometric	geometric	ADJ
ejpam-1372	169	9	series	series	NOUN
ejpam-1372	169	10	as	as	ADP
ejpam-1372	169	11	k	k	PROPN
ejpam-1372	169	12	∑	∑	PROPN
ejpam-1372	169	13	k=0	k=0	PROPN
ejpam-1372	169	14	zk	zk	PROPN
ejpam-1372	170	1	=	=	SYM
ejpam-1372	170	2	∞	∞	PROPN
ejpam-1372	170	3	∑	∑	PUNCT
ejpam-1372	170	4	k=0	k=0	PROPN
ejpam-1372	170	5	γ(k+	γ(k+	ADP
ejpam-1372	170	6	1	1	X
ejpam-1372	170	7	)	)	PUNCT
ejpam-1372	170	8	zk	zk	PROPN
ejpam-1372	171	1	k	k	PROPN
ejpam-1372	171	2	!	!	PUNCT
ejpam-1372	172	1	=	=	PUNCT
ejpam-1372	172	2	lim	lim	PROPN
ejpam-1372	172	3	p→∞	p→∞	ADP
ejpam-1372	172	4	∞	∞	PROPN
ejpam-1372	172	5	∑	∑	PROPN
ejpam-1372	172	6	k=0	k=0	PROPN
ejpam-1372	172	7	zk	zk	PROPN
ejpam-1372	173	1	k	k	PROPN
ejpam-1372	173	2	!	!	PUNCT
ejpam-1372	173	3	∫	∫	PROPN
ejpam-1372	174	1	p	p	NOUN
ejpam-1372	174	2	0	0	NUM
ejpam-1372	174	3	d	d	NOUN
ejpam-1372	174	4	t	t	PROPN
ejpam-1372	174	5	e−t	e−t	NOUN
ejpam-1372	174	6	tk	tk	PROPN
ejpam-1372	174	7	.	.	PUNCT
ejpam-1372	175	1	(	(	PUNCT
ejpam-1372	175	2	9	9	NUM
ejpam-1372	175	3	)	)	PUNCT
ejpam-1372	175	4	in	in	ADP
ejpam-1372	175	5	obtaining	obtain	VERB
ejpam-1372	175	6	the	the	DET
ejpam-1372	175	7	above	above	ADJ
ejpam-1372	175	8	equation	equation	NOUN
ejpam-1372	175	9	we	we	PRON
ejpam-1372	175	10	have	have	AUX
ejpam-1372	175	11	multiplied	multiply	VERB
ejpam-1372	175	12	the	the	DET
ejpam-1372	175	13	summand	summand	NOUN
ejpam-1372	175	14	zk	zk	PROPN
ejpam-1372	175	15	by	by	ADP
ejpam-1372	175	16	k!/k	k!/k	PROPN
ejpam-1372	175	17	!	!	PROPN
ejpam-1372	175	18	,	,	PUNCT
ejpam-1372	175	19	substituted	substitute	VERB
ejpam-1372	175	20	k	k	X
ejpam-1372	175	21	!	!	PUNCT
ejpam-1372	176	1	by	by	ADP
ejpam-1372	176	2	its	its	PRON
ejpam-1372	176	3	more	more	ADV
ejpam-1372	176	4	general	general	ADJ
ejpam-1372	176	5	form	form	NOUN
ejpam-1372	176	6	in	in	ADP
ejpam-1372	176	7	terms	term	NOUN
ejpam-1372	176	8	of	of	ADP
ejpam-1372	176	9	the	the	DET
ejpam-1372	176	10	gamma	gamma	NOUN
ejpam-1372	176	11	function	function	NOUN
ejpam-1372	176	12	and	and	CCONJ
ejpam-1372	176	13	then	then	ADV
ejpam-1372	176	14	introduced	introduce	VERB
ejpam-1372	176	15	the	the	DET
ejpam-1372	176	16	integral	integral	ADJ
ejpam-1372	176	17	representation	representation	NOUN
ejpam-1372	176	18	for	for	ADP
ejpam-1372	176	19	the	the	DET
ejpam-1372	176	20	latter	latter	ADJ
ejpam-1372	176	21	.	.	PUNCT
ejpam-1372	177	1	that	that	PRON
ejpam-1372	177	2	is	is	ADV
ejpam-1372	177	3	,	,	PUNCT
ejpam-1372	177	4	γ(k+1	γ(k+1	X
ejpam-1372	177	5	)	)	PUNCT
ejpam-1372	177	6	has	have	AUX
ejpam-1372	177	7	been	be	AUX
ejpam-1372	177	8	replaced	replace	VERB
ejpam-1372	177	9	by	by	ADP
ejpam-1372	177	10	its	its	PRON
ejpam-1372	177	11	integral	integral	ADJ
ejpam-1372	177	12	representation	representation	NOUN
ejpam-1372	177	13	of	of	ADP
ejpam-1372	177	14	∫∞	∫∞	NOUN
ejpam-1372	177	15	0	0	PUNCT
ejpam-1372	178	1	d	d	NOUN
ejpam-1372	178	2	t	t	PROPN
ejpam-1372	178	3	tk	tk	PROPN
ejpam-1372	178	4	exp(−t	exp(−t	PROPN
ejpam-1372	178	5	)	)	PUNCT
ejpam-1372	178	6	.	.	PUNCT
ejpam-1372	179	1	although	although	SCONJ
ejpam-1372	179	2	the	the	DET
ejpam-1372	179	3	integral	integral	NOUN
ejpam-1372	179	4	in	in	ADP
ejpam-1372	179	5	eq	eq	ADP
ejpam-1372	179	6	.	.	PUNCT
ejpam-1372	180	1	(	(	PUNCT
ejpam-1372	180	2	9	9	X
ejpam-1372	180	3	)	)	PUNCT
ejpam-1372	180	4	actually	actually	ADV
ejpam-1372	180	5	extends	extend	VERB
ejpam-1372	180	6	from	from	ADP
ejpam-1372	180	7	zero	zero	NUM
ejpam-1372	180	8	to	to	ADP
ejpam-1372	180	9	infinity	infinity	NOUN
ejpam-1372	180	10	,	,	PUNCT
ejpam-1372	180	11	the	the	DET
ejpam-1372	180	12	upper	upper	ADJ
ejpam-1372	180	13	limit	limit	NOUN
ejpam-1372	180	14	has	have	AUX
ejpam-1372	180	15	been	be	AUX
ejpam-1372	180	16	replaced	replace	VERB
ejpam-1372	180	17	by	by	ADP
ejpam-1372	180	18	the	the	DET
ejpam-1372	180	19	finite	finite	ADJ
ejpam-1372	180	20	value	value	NOUN
ejpam-1372	180	21	p	p	NOUN
ejpam-1372	180	22	,	,	PUNCT
ejpam-1372	180	23	which	which	PRON
ejpam-1372	180	24	we	we	PRON
ejpam-1372	180	25	let	let	VERB
ejpam-1372	180	26	go	go	VERB
ejpam-1372	180	27	to	to	ADP
ejpam-1372	180	28	infinity	infinity	NOUN
ejpam-1372	180	29	later	later	ADV
ejpam-1372	180	30	.	.	PUNCT
ejpam-1372	181	1	since	since	SCONJ
ejpam-1372	181	2	the	the	DET
ejpam-1372	181	3	resulting	result	VERB
ejpam-1372	181	4	integral	integral	NOUN
ejpam-1372	181	5	in	in	ADP
ejpam-1372	181	6	the	the	DET
ejpam-1372	181	7	above	above	ADJ
ejpam-1372	181	8	equation	equation	NOUN
ejpam-1372	181	9	is	be	AUX
ejpam-1372	181	10	now	now	ADV
ejpam-1372	181	11	technically	technically	ADV
ejpam-1372	181	12	finite	finite	ADJ
ejpam-1372	181	13	,	,	PUNCT
ejpam-1372	181	14	we	we	PRON
ejpam-1372	181	15	can	can	AUX
ejpam-1372	181	16	interchange	interchange	VERB
ejpam-1372	181	17	the	the	DET
ejpam-1372	181	18	order	order	NOUN
ejpam-1372	181	19	of	of	ADP
ejpam-1372	181	20	the	the	DET
ejpam-1372	181	21	summation	summation	NOUN
ejpam-1372	181	22	and	and	CCONJ
ejpam-1372	181	23	integration	integration	NOUN
ejpam-1372	181	24	.	.	PUNCT
ejpam-1372	182	1	in	in	ADP
ejpam-1372	182	2	reality	reality	NOUN
ejpam-1372	182	3	,	,	PUNCT
ejpam-1372	182	4	an	an	DET
ejpam-1372	182	5	impropriety	impropriety	NOUN
ejpam-1372	182	6	is	be	AUX
ejpam-1372	182	7	occurring	occur	VERB
ejpam-1372	182	8	here	here	ADV
ejpam-1372	182	9	,	,	PUNCT
ejpam-1372	182	10	which	which	PRON
ejpam-1372	182	11	will	will	AUX
ejpam-1372	182	12	be	be	AUX
ejpam-1372	182	13	explained	explain	VERB
ejpam-1372	182	14	shortly	shortly	ADV
ejpam-1372	182	15	.	.	PUNCT
ejpam-1372	183	1	nevertheless	nevertheless	ADV
ejpam-1372	183	2	,	,	PUNCT
ejpam-1372	183	3	if	if	SCONJ
ejpam-1372	183	4	we	we	PRON
ejpam-1372	183	5	persevere	persevere	VERB
ejpam-1372	183	6	with	with	ADP
ejpam-1372	183	7	interchanging	interchange	VERB
ejpam-1372	183	8	the	the	DET
ejpam-1372	183	9	order	order	NOUN
ejpam-1372	183	10	of	of	ADP
ejpam-1372	183	11	the	the	DET
ejpam-1372	183	12	summation	summation	NOUN
ejpam-1372	183	13	and	and	CCONJ
ejpam-1372	183	14	integration	integration	NOUN
ejpam-1372	183	15	,	,	PUNCT
ejpam-1372	183	16	then	then	ADV
ejpam-1372	183	17	we	we	PRON
ejpam-1372	183	18	find	find	VERB
ejpam-1372	183	19	that	that	SCONJ
ejpam-1372	183	20	the	the	DET
ejpam-1372	183	21	summation	summation	NOUN
ejpam-1372	183	22	is	be	AUX
ejpam-1372	183	23	not	not	PART
ejpam-1372	183	24	only	only	ADV
ejpam-1372	183	25	absolutely	absolutely	ADV
ejpam-1372	183	26	convergent	convergent	ADJ
ejpam-1372	183	27	,	,	PUNCT
ejpam-1372	183	28	but	but	CCONJ
ejpam-1372	183	29	it	it	PRON
ejpam-1372	183	30	also	also	ADV
ejpam-1372	183	31	represents	represent	VERB
ejpam-1372	183	32	the	the	DET
ejpam-1372	183	33	taylor	taylor	PROPN
ejpam-1372	183	34	series	series	PROPN
ejpam-1372	183	35	expansion	expansion	NOUN
ejpam-1372	183	36	for	for	ADP
ejpam-1372	183	37	exp(zt	exp(zt	NOUN
ejpam-1372	183	38	)	)	PUNCT
ejpam-1372	183	39	.	.	PUNCT
ejpam-1372	184	1	therefore	therefore	ADV
ejpam-1372	184	2	,	,	PUNCT
ejpam-1372	184	3	replacing	replace	VERB
ejpam-1372	184	4	the	the	DET
ejpam-1372	184	5	series	series	NOUN
ejpam-1372	184	6	by	by	ADP
ejpam-1372	184	7	this	this	DET
ejpam-1372	184	8	limit	limit	NOUN
ejpam-1372	184	9	,	,	PUNCT
ejpam-1372	184	10	we	we	PRON
ejpam-1372	184	11	find	find	VERB
ejpam-1372	184	12	that	that	SCONJ
ejpam-1372	184	13	eq	eq	ADP
ejpam-1372	184	14	.	.	PUNCT
ejpam-1372	185	1	(	(	PUNCT
ejpam-1372	185	2	9	9	X
ejpam-1372	185	3	)	)	PUNCT
ejpam-1372	185	4	becomes	become	VERB
ejpam-1372	185	5	∞	∞	PROPN
ejpam-1372	185	6	∑	∑	PROPN
ejpam-1372	185	7	k=0	k=0	PROPN
ejpam-1372	185	8	zk	zk	PROPN
ejpam-1372	186	1	=	=	PROPN
ejpam-1372	186	2	lim	lim	PROPN
ejpam-1372	186	3	p→∞	p→∞	PROPN
ejpam-1372	187	1	∫	∫	PROPN
ejpam-1372	187	2	p	p	NOUN
ejpam-1372	187	3	0	0	NUM
ejpam-1372	187	4	d	d	X
ejpam-1372	187	5	t	t	PROPN
ejpam-1372	187	6	e−t(1−z	e−t(1−z	PROPN
ejpam-1372	187	7	)	)	PUNCT
ejpam-1372	188	1	=	=	VERB
ejpam-1372	188	2	lim	lim	PROPN
ejpam-1372	188	3	p→∞	p→∞	PROPN
ejpam-1372	188	4	�	�	PROPN
ejpam-1372	188	5	−	−	PROPN
ejpam-1372	188	6	e−p(1−z	e−p(1−z	PROPN
ejpam-1372	188	7	)	)	PUNCT
ejpam-1372	188	8	1−	1−	NUM
ejpam-1372	189	1	z	z	NOUN
ejpam-1372	190	1	+	+	CCONJ
ejpam-1372	190	2	1	1	NUM
ejpam-1372	190	3	1−	1−	NUM
ejpam-1372	190	4	z	z	PROPN
ejpam-1372	190	5	�	�	PROPN
ejpam-1372	190	6	.	.	PUNCT
ejpam-1372	191	1	(	(	PUNCT
ejpam-1372	191	2	10	10	NUM
ejpam-1372	191	3	)	)	PUNCT
ejpam-1372	191	4	when	when	SCONJ
ejpam-1372	191	5	the	the	DET
ejpam-1372	191	6	real	real	ADJ
ejpam-1372	191	7	part	part	NOUN
ejpam-1372	191	8	of	of	ADP
ejpam-1372	191	9	z	z	NOUN
ejpam-1372	191	10	is	be	AUX
ejpam-1372	191	11	less	less	ADJ
ejpam-1372	191	12	than	than	ADP
ejpam-1372	191	13	unity	unity	NOUN
ejpam-1372	191	14	,	,	PUNCT
ejpam-1372	191	15	i.e.	i.e.	X
ejpam-1372	191	16	ℜ	ℜ	ADJ
ejpam-1372	191	17	z	z	NOUN
ejpam-1372	191	18	<	<	X
ejpam-1372	191	19	1	1	NUM
ejpam-1372	191	20	,	,	PUNCT
ejpam-1372	191	21	the	the	DET
ejpam-1372	191	22	first	first	ADJ
ejpam-1372	191	23	term	term	NOUN
ejpam-1372	191	24	in	in	ADP
ejpam-1372	191	25	the	the	DET
ejpam-1372	191	26	last	last	ADJ
ejpam-1372	191	27	member	member	NOUN
ejpam-1372	191	28	of	of	ADP
ejpam-1372	191	29	eq	eq	PROPN
ejpam-1372	191	30	.	.	PUNCT
ejpam-1372	192	1	(	(	PUNCT
ejpam-1372	192	2	10	10	NUM
ejpam-1372	192	3	)	)	PUNCT
ejpam-1372	192	4	vanishes	vanish	VERB
ejpam-1372	192	5	and	and	CCONJ
ejpam-1372	192	6	the	the	DET
ejpam-1372	192	7	series	series	NOUN
ejpam-1372	192	8	yields	yield	VERB
ejpam-1372	192	9	the	the	DET
ejpam-1372	192	10	finite	finite	ADJ
ejpam-1372	192	11	value	value	NOUN
ejpam-1372	192	12	of	of	ADP
ejpam-1372	192	13	1/(1−	1/(1−	NUM
ejpam-1372	192	14	z	z	NOUN
ejpam-1372	192	15	)	)	PUNCT
ejpam-1372	192	16	.	.	PUNCT
ejpam-1372	193	1	hence	hence	ADV
ejpam-1372	193	2	,	,	PUNCT
ejpam-1372	193	3	we	we	PRON
ejpam-1372	193	4	see	see	VERB
ejpam-1372	193	5	that	that	SCONJ
ejpam-1372	193	6	the	the	DET
ejpam-1372	193	7	same	same	ADJ
ejpam-1372	193	8	value	value	NOUN
ejpam-1372	193	9	is	be	AUX
ejpam-1372	193	10	obtained	obtain	VERB
ejpam-1372	193	11	for	for	ADP
ejpam-1372	193	12	the	the	DET
ejpam-1372	193	13	series	series	NOUN
ejpam-1372	193	14	when	when	SCONJ
ejpam-1372	193	15	ℜ	ℜ	PROPN
ejpam-1372	193	16	z<1	z<1	PROPN
ejpam-1372	193	17	as	as	ADP
ejpam-1372	193	18	for	for	ADP
ejpam-1372	193	19	when	when	SCONJ
ejpam-1372	193	20	lies	lie	NOUN
ejpam-1372	193	21	in	in	ADP
ejpam-1372	193	22	the	the	DET
ejpam-1372	193	23	unit	unit	NOUN
ejpam-1372	193	24	disk	disk	NOUN
ejpam-1372	193	25	of	of	ADP
ejpam-1372	193	26	absolute	absolute	ADJ
ejpam-1372	193	27	convergence	convergence	NOUN
ejpam-1372	193	28	.	.	PUNCT
ejpam-1372	194	1	according	accord	VERB
ejpam-1372	194	2	to	to	ADP
ejpam-1372	194	3	the	the	DET
ejpam-1372	194	4	definition	definition	NOUN
ejpam-1372	194	5	on	on	ADP
ejpam-1372	194	6	p.	p.	PROPN
ejpam-1372	194	7	18	18	NUM
ejpam-1372	194	8	of	of	ADP
ejpam-1372	194	9	ref	ref	NOUN
ejpam-1372	194	10	.	.	PUNCT
ejpam-1372	195	1	[	[	X
ejpam-1372	195	2	33	33	NUM
ejpam-1372	195	3	]	]	PUNCT
ejpam-1372	195	4	,	,	PUNCT
ejpam-1372	195	5	this	this	PRON
ejpam-1372	195	6	means	mean	VERB
ejpam-1372	195	7	that	that	SCONJ
ejpam-1372	195	8	the	the	DET
ejpam-1372	195	9	series	series	NOUN
ejpam-1372	195	10	is	be	AUX
ejpam-1372	195	11	conditionally	conditionally	ADV
ejpam-1372	195	12	convergent	convergent	ADJ
ejpam-1372	195	13	for	for	ADP
ejpam-1372	195	14	ℜ	ℜ	ADJ
ejpam-1372	195	15	z	z	NOUN
ejpam-1372	195	16	<	<	X
ejpam-1372	195	17	1	1	NUM
ejpam-1372	195	18	and	and	CCONJ
ejpam-1372	195	19	|z|	|z|	NOUN
ejpam-1372	195	20	>	>	X
ejpam-1372	195	21	1	1	NUM
ejpam-1372	195	22	.	.	PUNCT
ejpam-1372	196	1	that	that	PRON
ejpam-1372	196	2	is	is	ADV
ejpam-1372	196	3	,	,	PUNCT
ejpam-1372	196	4	it	it	PRON
ejpam-1372	196	5	is	be	AUX
ejpam-1372	196	6	not	not	PART
ejpam-1372	196	7	divergent	divergent	ADJ
ejpam-1372	196	8	,	,	PUNCT
ejpam-1372	196	9	but	but	CCONJ
ejpam-1372	196	10	it	it	PRON
ejpam-1372	196	11	is	be	AUX
ejpam-1372	196	12	also	also	ADV
ejpam-1372	196	13	not	not	PART
ejpam-1372	196	14	absolutely	absolutely	ADV
ejpam-1372	196	15	convergent	convergent	ADJ
ejpam-1372	196	16	either	either	ADV
ejpam-1372	196	17	.	.	PUNCT
ejpam-1372	197	1	for	for	ADP
ejpam-1372	197	2	ℜ	ℜ	PROPN
ejpam-1372	197	3	z	z	NOUN
ejpam-1372	197	4	>	>	X
ejpam-1372	197	5	1	1	NUM
ejpam-1372	197	6	,	,	PUNCT
ejpam-1372	197	7	however	however	ADV
ejpam-1372	197	8	,	,	PUNCT
ejpam-1372	197	9	the	the	DET
ejpam-1372	197	10	first	first	ADJ
ejpam-1372	197	11	term	term	NOUN
ejpam-1372	197	12	in	in	ADP
ejpam-1372	197	13	the	the	DET
ejpam-1372	197	14	last	last	ADJ
ejpam-1372	197	15	member	member	NOUN
ejpam-1372	197	16	of	of	ADP
ejpam-1372	197	17	eq	eq	PROPN
ejpam-1372	197	18	.	.	PUNCT
ejpam-1372	198	1	(	(	PUNCT
ejpam-1372	198	2	10	10	NUM
ejpam-1372	198	3	)	)	PUNCT
ejpam-1372	198	4	yields	yield	NOUN
ejpam-1372	198	5	infinity	infinity	NOUN
ejpam-1372	198	6	.	.	PUNCT
ejpam-1372	199	1	since	since	SCONJ
ejpam-1372	199	2	we	we	PRON
ejpam-1372	199	3	have	have	AUX
ejpam-1372	199	4	defined	define	VERB
ejpam-1372	199	5	regularisation	regularisation	NOUN
ejpam-1372	199	6	as	as	ADP
ejpam-1372	199	7	the	the	DET
ejpam-1372	199	8	process	process	NOUN
ejpam-1372	199	9	of	of	ADP
ejpam-1372	199	10	removing	remove	VERB
ejpam-1372	199	11	the	the	DET
ejpam-1372	199	12	infinity	infinity	NOUN
ejpam-1372	199	13	so	so	SCONJ
ejpam-1372	199	14	that	that	SCONJ
ejpam-1372	199	15	the	the	DET
ejpam-1372	199	16	series	series	NOUN
ejpam-1372	199	17	becomes	become	VERB
ejpam-1372	199	18	summable	summable	ADJ
ejpam-1372	199	19	,	,	PUNCT
ejpam-1372	199	20	we	we	PRON
ejpam-1372	199	21	remove	remove	VERB
ejpam-1372	199	22	or	or	CCONJ
ejpam-1372	199	23	neglect	neglect	VERB
ejpam-1372	199	24	the	the	DET
ejpam-1372	199	25	first	first	ADJ
ejpam-1372	199	26	term	term	NOUN
ejpam-1372	199	27	of	of	ADP
ejpam-1372	199	28	the	the	DET
ejpam-1372	199	29	last	last	ADJ
ejpam-1372	199	30	member	member	NOUN
ejpam-1372	199	31	of	of	ADP
ejpam-1372	199	32	eq	eq	PROPN
ejpam-1372	199	33	.	.	PUNCT
ejpam-1372	200	1	(	(	PUNCT
ejpam-1372	200	2	10	10	NUM
ejpam-1372	200	3	)	)	PUNCT
ejpam-1372	200	4	.	.	PUNCT
ejpam-1372	201	1	then	then	ADV
ejpam-1372	201	2	we	we	PRON
ejpam-1372	201	3	are	be	AUX
ejpam-1372	201	4	left	leave	VERB
ejpam-1372	201	5	with	with	ADP
ejpam-1372	201	6	a	a	DET
ejpam-1372	201	7	finite	finite	ADJ
ejpam-1372	201	8	result	result	NOUN
ejpam-1372	201	9	that	that	SCONJ
ejpam-1372	201	10	once	once	ADV
ejpam-1372	201	11	again	again	ADV
ejpam-1372	201	12	equals	equal	VERB
ejpam-1372	201	13	1/(1−	1/(1−	NUM
ejpam-1372	201	14	z	z	NOUN
ejpam-1372	201	15	)	)	PUNCT
ejpam-1372	201	16	.	.	PUNCT
ejpam-1372	202	1	we	we	PRON
ejpam-1372	202	2	shall	shall	AUX
ejpam-1372	202	3	call	call	VERB
ejpam-1372	202	4	this	this	DET
ejpam-1372	202	5	result	result	NOUN
ejpam-1372	202	6	the	the	DET
ejpam-1372	202	7	regularised	regularise	VERB
ejpam-1372	202	8	value	value	NOUN
ejpam-1372	202	9	of	of	ADP
ejpam-1372	202	10	the	the	DET
ejpam-1372	202	11	series	series	NOUN
ejpam-1372	202	12	when	when	SCONJ
ejpam-1372	202	13	it	it	PRON
ejpam-1372	202	14	is	be	AUX
ejpam-1372	202	15	divergent	divergent	ADJ
ejpam-1372	202	16	.	.	PUNCT
ejpam-1372	203	1	hence	hence	ADV
ejpam-1372	203	2	,	,	PUNCT
ejpam-1372	203	3	for	for	ADP
ejpam-1372	203	4	all	all	DET
ejpam-1372	203	5	complex	complex	ADJ
ejpam-1372	203	6	values	value	NOUN
ejpam-1372	203	7	of	of	ADP
ejpam-1372	203	8	z	z	NOUN
ejpam-1372	203	9	except	except	SCONJ
ejpam-1372	203	10	for	for	ADP
ejpam-1372	203	11	ℜ	ℜ	PROPN
ejpam-1372	203	12	z=1	z=1	NOUN
ejpam-1372	203	13	,	,	PUNCT
ejpam-1372	203	14	we	we	PRON
ejpam-1372	203	15	arrive	arrive	VERB
ejpam-1372	203	16	at	at	ADP
ejpam-1372	203	17	∞	∞	PROPN
ejpam-1372	203	18	∑	∑	PROPN
ejpam-1372	203	19	k=0	k=0	PROPN
ejpam-1372	203	20	zk	zk	PROPN
ejpam-1372	203	21	(	(	PUNCT
ejpam-1372	203	22	≡	≡	PROPN
ejpam-1372	203	23	1(1−	1(1−	PROPN
ejpam-1372	203	24	z	z	NOUN
ejpam-1372	203	25	)	)	PUNCT
ejpam-1372	203	26	,	,	PUNCT
ejpam-1372	203	27	ℜ	ℜ	PROPN
ejpam-1372	203	28	z	z	NOUN
ejpam-1372	203	29	>	>	X
ejpam-1372	203	30	1	1	NUM
ejpam-1372	203	31	,	,	PUNCT
ejpam-1372	203	32	=	=	SYM
ejpam-1372	203	33	1/(1−	1/(1−	NUM
ejpam-1372	203	34	z	z	NOUN
ejpam-1372	203	35	)	)	PUNCT
ejpam-1372	203	36	,	,	PUNCT
ejpam-1372	203	37	ℜ	ℜ	PROPN
ejpam-1372	203	38	z	z	NOUN
ejpam-1372	203	39	<	<	X
ejpam-1372	203	40	1	1	NUM
ejpam-1372	203	41	.	.	PUNCT
ejpam-1372	204	1	(	(	PUNCT
ejpam-1372	204	2	11	11	NUM
ejpam-1372	204	3	)	)	PUNCT
ejpam-1372	204	4	frequently	frequently	ADV
ejpam-1372	204	5	,	,	PUNCT
ejpam-1372	204	6	it	it	PRON
ejpam-1372	204	7	is	be	AUX
ejpam-1372	204	8	not	not	PART
ejpam-1372	204	9	known	know	VERB
ejpam-1372	204	10	for	for	ADP
ejpam-1372	204	11	which	which	DET
ejpam-1372	204	12	values	value	NOUN
ejpam-1372	204	13	of	of	ADP
ejpam-1372	204	14	the	the	DET
ejpam-1372	204	15	variable	variable	NOUN
ejpam-1372	204	16	,	,	PUNCT
ejpam-1372	204	17	e.g.	e.g.	ADV
ejpam-1372	204	18	z	z	NOUN
ejpam-1372	204	19	in	in	ADP
ejpam-1372	204	20	the	the	DET
ejpam-1372	204	21	above	above	ADJ
ejpam-1372	204	22	example	example	NOUN
ejpam-1372	204	23	,	,	PUNCT
ejpam-1372	204	24	an	an	DET
ejpam-1372	204	25	asymptotic	asymptotic	ADJ
ejpam-1372	204	26	series	series	NOUN
ejpam-1372	204	27	is	be	AUX
ejpam-1372	204	28	convergent	convergent	ADJ
ejpam-1372	204	29	and	and	CCONJ
ejpam-1372	204	30	for	for	ADP
ejpam-1372	204	31	which	which	PRON
ejpam-1372	204	32	it	it	PRON
ejpam-1372	204	33	is	be	AUX
ejpam-1372	204	34	divergent	divergent	ADJ
ejpam-1372	204	35	.	.	PUNCT
ejpam-1372	205	1	in	in	ADP
ejpam-1372	205	2	these	these	DET
ejpam-1372	205	3	cases	case	NOUN
ejpam-1372	205	4	we	we	PRON
ejpam-1372	205	5	replace	replace	VERB
ejpam-1372	205	6	v.	v.	ADP
ejpam-1372	205	7	kowalenko	kowalenko	PROPN
ejpam-1372	205	8	/	/	SYM
ejpam-1372	205	9	eur	eur	PROPN
ejpam-1372	205	10	.	.	PUNCT
ejpam-1372	206	1	j.	j.	PROPN
ejpam-1372	206	2	pure	pure	PROPN
ejpam-1372	206	3	appl	appl	PROPN
ejpam-1372	206	4	.	.	PROPN
ejpam-1372	206	5	math	math	PROPN
ejpam-1372	206	6	,	,	PUNCT
ejpam-1372	206	7	4	4	NUM
ejpam-1372	206	8	(	(	PUNCT
ejpam-1372	206	9	2011	2011	NUM
ejpam-1372	206	10	)	)	PUNCT
ejpam-1372	206	11	,	,	PUNCT
ejpam-1372	206	12	370	370	NUM
ejpam-1372	206	13	-	-	SYM
ejpam-1372	206	14	423	423	NUM
ejpam-1372	206	15	377	377	NUM
ejpam-1372	206	16	the	the	DET
ejpam-1372	206	17	equals	equal	VERB
ejpam-1372	206	18	sign	sign	NOUN
ejpam-1372	206	19	by	by	ADP
ejpam-1372	206	20	the	the	DET
ejpam-1372	206	21	less	less	ADV
ejpam-1372	206	22	stringent	stringent	ADJ
ejpam-1372	206	23	equivalence	equivalence	NOUN
ejpam-1372	206	24	symbol	symbol	NOUN
ejpam-1372	206	25	on	on	ADP
ejpam-1372	206	26	the	the	DET
ejpam-1372	206	27	understanding	understanding	NOUN
ejpam-1372	206	28	that	that	PRON
ejpam-1372	206	29	we	we	PRON
ejpam-1372	206	30	may	may	AUX
ejpam-1372	206	31	be	be	AUX
ejpam-1372	206	32	dealing	deal	VERB
ejpam-1372	206	33	with	with	ADP
ejpam-1372	206	34	a	a	DET
ejpam-1372	206	35	series	series	NOUN
ejpam-1372	206	36	that	that	PRON
ejpam-1372	206	37	is	be	AUX
ejpam-1372	206	38	absolutely	absolutely	ADV
ejpam-1372	206	39	convergent	convergent	ADJ
ejpam-1372	206	40	for	for	ADP
ejpam-1372	206	41	some	some	DET
ejpam-1372	206	42	values	value	NOUN
ejpam-1372	206	43	of	of	ADP
ejpam-1372	206	44	the	the	DET
ejpam-1372	206	45	variable	variable	NOUN
ejpam-1372	206	46	.	.	PUNCT
ejpam-1372	207	1	as	as	ADP
ejpam-1372	207	2	a	a	DET
ejpam-1372	207	3	result	result	NOUN
ejpam-1372	207	4	,	,	PUNCT
ejpam-1372	207	5	we	we	PRON
ejpam-1372	207	6	adopt	adopt	VERB
ejpam-1372	207	7	the	the	DET
ejpam-1372	207	8	shorthand	shorthand	NOUN
ejpam-1372	207	9	notation	notation	NOUN
ejpam-1372	207	10	of	of	ADP
ejpam-1372	207	11	∞	∞	PROPN
ejpam-1372	207	12	∑	∑	PROPN
ejpam-1372	207	13	k	k	X
ejpam-1372	207	14	=	=	PROPN
ejpam-1372	207	15	n	n	SYM
ejpam-1372	207	16	zk	zk	X
ejpam-1372	207	17	=	=	PUNCT
ejpam-1372	208	1	zn	zn	PROPN
ejpam-1372	208	2	∞	∞	NUM
ejpam-1372	208	3	∑	∑	PROPN
ejpam-1372	208	4	k=0	k=0	PROPN
ejpam-1372	208	5	zk	zk	PROPN
ejpam-1372	208	6	≡	≡	PROPN
ejpam-1372	208	7	zn	zn	PROPN
ejpam-1372	208	8	1−	1−	NUM
ejpam-1372	208	9	z	z	NOUN
ejpam-1372	208	10	.	.	PUNCT
ejpam-1372	209	1	(	(	PUNCT
ejpam-1372	209	2	12	12	NUM
ejpam-1372	209	3	)	)	PUNCT
ejpam-1372	209	4	obviously	obviously	ADV
ejpam-1372	209	5	,	,	PUNCT
ejpam-1372	209	6	such	such	ADJ
ejpam-1372	209	7	mathematical	mathematical	ADJ
ejpam-1372	209	8	statements	statement	NOUN
ejpam-1372	209	9	are	be	AUX
ejpam-1372	209	10	no	no	ADV
ejpam-1372	209	11	longer	long	ADJ
ejpam-1372	209	12	equations	equation	NOUN
ejpam-1372	209	13	for	for	ADP
ejpam-1372	209	14	it	it	PRON
ejpam-1372	209	15	is	be	AUX
ejpam-1372	209	16	simply	simply	ADV
ejpam-1372	209	17	invalid	invalid	ADJ
ejpam-1372	209	18	to	to	PART
ejpam-1372	209	19	refer	refer	VERB
ejpam-1372	209	20	to	to	ADP
ejpam-1372	209	21	the	the	DET
ejpam-1372	209	22	above	above	NOUN
ejpam-1372	209	23	as	as	ADP
ejpam-1372	209	24	an	an	DET
ejpam-1372	209	25	equation	equation	NOUN
ejpam-1372	209	26	because	because	SCONJ
ejpam-1372	209	27	the	the	DET
ejpam-1372	209	28	left	left	ADJ
ejpam-1372	209	29	hand	hand	NOUN
ejpam-1372	209	30	side	side	NOUN
ejpam-1372	209	31	(	(	PUNCT
ejpam-1372	209	32	lhs	lhs	PROPN
ejpam-1372	209	33	)	)	PUNCT
ejpam-1372	209	34	is	be	AUX
ejpam-1372	209	35	infinite	infinite	ADJ
ejpam-1372	209	36	when	when	SCONJ
ejpam-1372	209	37	ℜ	ℜ	ADJ
ejpam-1372	209	38	z	z	NOUN
ejpam-1372	209	39	>	>	X
ejpam-1372	209	40	1	1	NUM
ejpam-1372	209	41	,	,	PUNCT
ejpam-1372	209	42	while	while	SCONJ
ejpam-1372	209	43	the	the	DET
ejpam-1372	209	44	right	right	ADJ
ejpam-1372	209	45	hand	hand	NOUN
ejpam-1372	209	46	side	side	NOUN
ejpam-1372	209	47	(	(	PUNCT
ejpam-1372	209	48	rhs	rhs	PROPN
ejpam-1372	209	49	)	)	PUNCT
ejpam-1372	209	50	remains	remain	VERB
ejpam-1372	209	51	finite	finite	ADJ
ejpam-1372	209	52	for	for	ADP
ejpam-1372	209	53	these	these	DET
ejpam-1372	209	54	values	value	NOUN
ejpam-1372	209	55	of	of	ADP
ejpam-1372	209	56	z.	z.	PROPN
ejpam-1372	209	57	instead	instead	ADV
ejpam-1372	209	58	,	,	PUNCT
ejpam-1372	209	59	we	we	PRON
ejpam-1372	209	60	shall	shall	AUX
ejpam-1372	209	61	refer	refer	VERB
ejpam-1372	209	62	to	to	ADP
ejpam-1372	209	63	such	such	ADJ
ejpam-1372	209	64	results	result	NOUN
ejpam-1372	209	65	as	as	ADP
ejpam-1372	209	66	equivalence	equivalence	NOUN
ejpam-1372	209	67	statements	statement	NOUN
ejpam-1372	209	68	or	or	CCONJ
ejpam-1372	209	69	simply	simply	ADV
ejpam-1372	209	70	equivalences	equivalence	NOUN
ejpam-1372	209	71	,	,	PUNCT
ejpam-1372	209	72	for	for	ADP
ejpam-1372	209	73	short	short	ADJ
ejpam-1372	209	74	.	.	PUNCT
ejpam-1372	210	1	it	it	PRON
ejpam-1372	210	2	should	should	AUX
ejpam-1372	210	3	also	also	ADV
ejpam-1372	210	4	be	be	AUX
ejpam-1372	210	5	noted	note	VERB
ejpam-1372	210	6	that	that	SCONJ
ejpam-1372	210	7	the	the	DET
ejpam-1372	210	8	above	above	ADJ
ejpam-1372	210	9	notation	notation	NOUN
ejpam-1372	210	10	is	be	AUX
ejpam-1372	210	11	only	only	ADV
ejpam-1372	210	12	applicable	applicable	ADJ
ejpam-1372	210	13	when	when	SCONJ
ejpam-1372	210	14	the	the	DET
ejpam-1372	210	15	result	result	NOUN
ejpam-1372	210	16	for	for	ADP
ejpam-1372	210	17	the	the	DET
ejpam-1372	210	18	regularised	regularise	VERB
ejpam-1372	210	19	value	value	NOUN
ejpam-1372	210	20	of	of	ADP
ejpam-1372	210	21	a	a	DET
ejpam-1372	210	22	divergent	divergent	ADJ
ejpam-1372	210	23	series	series	NOUN
ejpam-1372	210	24	is	be	AUX
ejpam-1372	210	25	identical	identical	ADJ
ejpam-1372	210	26	to	to	ADP
ejpam-1372	210	27	the	the	DET
ejpam-1372	210	28	limiting	limit	VERB
ejpam-1372	210	29	value	value	NOUN
ejpam-1372	210	30	of	of	ADP
ejpam-1372	210	31	the	the	DET
ejpam-1372	210	32	convergent	convergent	NOUN
ejpam-1372	210	33	series	series	NOUN
ejpam-1372	210	34	.	.	PUNCT
ejpam-1372	211	1	this	this	PRON
ejpam-1372	211	2	is	be	AUX
ejpam-1372	211	3	not	not	PART
ejpam-1372	211	4	always	always	ADV
ejpam-1372	211	5	the	the	DET
ejpam-1372	211	6	case	case	NOUN
ejpam-1372	211	7	as	as	SCONJ
ejpam-1372	211	8	can	can	AUX
ejpam-1372	211	9	be	be	AUX
ejpam-1372	211	10	seen	see	VERB
ejpam-1372	211	11	from	from	ADP
ejpam-1372	211	12	the	the	DET
ejpam-1372	211	13	final	final	ADJ
ejpam-1372	211	14	example	example	NOUN
ejpam-1372	211	15	in	in	ADP
ejpam-1372	211	16	ch	ch	PROPN
ejpam-1372	211	17	.	.	PROPN
ejpam-1372	211	18	4	4	NUM
ejpam-1372	211	19	of	of	ADP
ejpam-1372	211	20	ref	ref	NOUN
ejpam-1372	211	21	.	.	PUNCT
ejpam-1372	212	1	[	[	X
ejpam-1372	212	2	17	17	NUM
ejpam-1372	212	3	]	]	PUNCT
ejpam-1372	212	4	.	.	PUNCT
ejpam-1372	213	1	an	an	DET
ejpam-1372	213	2	important	important	ADJ
ejpam-1372	213	3	property	property	NOUN
ejpam-1372	213	4	of	of	ADP
ejpam-1372	213	5	the	the	DET
ejpam-1372	213	6	above	above	ADJ
ejpam-1372	213	7	result	result	NOUN
ejpam-1372	213	8	is	be	AUX
ejpam-1372	213	9	that	that	SCONJ
ejpam-1372	213	10	it	it	PRON
ejpam-1372	213	11	is	be	AUX
ejpam-1372	213	12	one	one	NUM
ejpam-1372	213	13	-	-	PUNCT
ejpam-1372	213	14	to	to	ADP
ejpam-1372	213	15	-	-	PUNCT
ejpam-1372	213	16	one	one	NUM
ejpam-1372	213	17	or	or	CCONJ
ejpam-1372	213	18	bijective	bijective	ADJ
ejpam-1372	213	19	for	for	ADP
ejpam-1372	213	20	each	each	DET
ejpam-1372	213	21	value	value	NOUN
ejpam-1372	213	22	of	of	ADP
ejpam-1372	213	23	z	z	NOUN
ejpam-1372	213	24	in	in	ADP
ejpam-1372	213	25	the	the	DET
ejpam-1372	213	26	principal	principal	ADJ
ejpam-1372	213	27	branch	branch	NOUN
ejpam-1372	213	28	of	of	ADP
ejpam-1372	213	29	the	the	DET
ejpam-1372	213	30	complex	complex	ADJ
ejpam-1372	213	31	plane	plane	NOUN
ejpam-1372	213	32	.	.	PUNCT
ejpam-1372	214	1	this	this	PRON
ejpam-1372	214	2	is	be	AUX
ejpam-1372	214	3	critical	critical	ADJ
ejpam-1372	214	4	for	for	ADP
ejpam-1372	214	5	developing	develop	VERB
ejpam-1372	214	6	a	a	DET
ejpam-1372	214	7	theory	theory	NOUN
ejpam-1372	214	8	of	of	ADP
ejpam-1372	214	9	divergent	divergent	ADJ
ejpam-1372	214	10	series	series	NOUN
ejpam-1372	214	11	since	since	SCONJ
ejpam-1372	214	12	it	it	PRON
ejpam-1372	214	13	means	mean	VERB
ejpam-1372	214	14	that	that	SCONJ
ejpam-1372	214	15	each	each	DET
ejpam-1372	214	16	value	value	NOUN
ejpam-1372	214	17	of	of	ADP
ejpam-1372	214	18	z	z	NOUN
ejpam-1372	214	19	will	will	AUX
ejpam-1372	214	20	yield	yield	VERB
ejpam-1372	214	21	a	a	DET
ejpam-1372	214	22	unique	unique	ADJ
ejpam-1372	214	23	regularised	regularise	VERB
ejpam-1372	214	24	value	value	NOUN
ejpam-1372	214	25	,	,	PUNCT
ejpam-1372	214	26	which	which	PRON
ejpam-1372	214	27	is	be	AUX
ejpam-1372	214	28	beginning	begin	VERB
ejpam-1372	214	29	to	to	ADP
ejpam-1372	214	30	accord	accord	NOUN
ejpam-1372	214	31	with	with	ADP
ejpam-1372	214	32	euler	euler	NOUN
ejpam-1372	214	33	’s	’s	PART
ejpam-1372	214	34	belief	belief	NOUN
ejpam-1372	214	35	that	that	SCONJ
ejpam-1372	214	36	each	each	DET
ejpam-1372	214	37	series	series	NOUN
ejpam-1372	214	38	has	have	AUX
ejpam-1372	214	39	a	a	DET
ejpam-1372	214	40	specific	specific	ADJ
ejpam-1372	214	41	value	value	NOUN
ejpam-1372	214	42	.	.	PUNCT
ejpam-1372	215	1	thus	thus	ADV
ejpam-1372	215	2	,	,	PUNCT
ejpam-1372	215	3	there	there	PRON
ejpam-1372	215	4	is	be	VERB
ejpam-1372	215	5	now	now	ADV
ejpam-1372	215	6	a	a	DET
ejpam-1372	215	7	possibility	possibility	NOUN
ejpam-1372	215	8	that	that	SCONJ
ejpam-1372	215	9	the	the	DET
ejpam-1372	215	10	fallacies	fallacy	NOUN
ejpam-1372	215	11	and	and	CCONJ
ejpam-1372	215	12	paradoxes	paradox	NOUN
ejpam-1372	215	13	that	that	PRON
ejpam-1372	215	14	led	lead	VERB
ejpam-1372	215	15	to	to	ADP
ejpam-1372	215	16	the	the	DET
ejpam-1372	215	17	banishment	banishment	NOUN
ejpam-1372	215	18	of	of	ADP
ejpam-1372	215	19	divergent	divergent	ADJ
ejpam-1372	215	20	series	series	NOUN
ejpam-1372	215	21	from	from	ADP
ejpam-1372	215	22	the	the	DET
ejpam-1372	215	23	mathematical	mathematical	ADJ
ejpam-1372	215	24	lexicon	lexicon	NOUN
ejpam-1372	215	25	can	can	AUX
ejpam-1372	215	26	start	start	VERB
ejpam-1372	215	27	to	to	PART
ejpam-1372	215	28	disappear	disappear	VERB
ejpam-1372	215	29	.	.	PUNCT
ejpam-1372	216	1	at	at	ADP
ejpam-1372	216	2	the	the	DET
ejpam-1372	216	3	barrier	barrier	NOUN
ejpam-1372	216	4	of	of	ADP
ejpam-1372	216	5	ℜ	ℜ	PROPN
ejpam-1372	216	6	z=1	z=1	NOUN
ejpam-1372	216	7	,	,	PUNCT
ejpam-1372	216	8	the	the	DET
ejpam-1372	216	9	situation	situation	NOUN
ejpam-1372	216	10	appears	appear	VERB
ejpam-1372	216	11	to	to	PART
ejpam-1372	216	12	be	be	AUX
ejpam-1372	216	13	unclear	unclear	ADJ
ejpam-1372	216	14	.	.	PUNCT
ejpam-1372	217	1	for	for	ADP
ejpam-1372	217	2	z=1	z=1	PROPN
ejpam-1372	217	3	the	the	DET
ejpam-1372	217	4	last	last	ADJ
ejpam-1372	217	5	member	member	NOUN
ejpam-1372	217	6	of	of	ADP
ejpam-1372	217	7	equivalence	equivalence	NOUN
ejpam-1372	217	8	(	(	PUNCT
ejpam-1372	217	9	10	10	NUM
ejpam-1372	217	10	)	)	PUNCT
ejpam-1372	217	11	vanishes	vanish	VERB
ejpam-1372	217	12	,	,	PUNCT
ejpam-1372	217	13	which	which	PRON
ejpam-1372	217	14	is	be	AUX
ejpam-1372	217	15	consistent	consistent	ADJ
ejpam-1372	217	16	with	with	ADP
ejpam-1372	217	17	removing	remove	VERB
ejpam-1372	217	18	the	the	DET
ejpam-1372	217	19	infinity	infinity	NOUN
ejpam-1372	217	20	due	due	ADP
ejpam-1372	217	21	to	to	ADP
ejpam-1372	217	22	1/(1−z	1/(1−z	NUM
ejpam-1372	217	23	)	)	PUNCT
ejpam-1372	217	24	.	.	PUNCT
ejpam-1372	218	1	for	for	ADP
ejpam-1372	218	2	other	other	ADJ
ejpam-1372	218	3	values	value	NOUN
ejpam-1372	218	4	of	of	ADP
ejpam-1372	218	5	ℜ	ℜ	NOUN
ejpam-1372	218	6	z	z	NOUN
ejpam-1372	218	7	=	=	SYM
ejpam-1372	218	8	1	1	NUM
ejpam-1372	218	9	,	,	PUNCT
ejpam-1372	218	10	the	the	DET
ejpam-1372	218	11	last	last	ADJ
ejpam-1372	218	12	member	member	NOUN
ejpam-1372	218	13	of	of	ADP
ejpam-1372	218	14	eq	eq	PROPN
ejpam-1372	218	15	.	.	PUNCT
ejpam-1372	219	1	(	(	PUNCT
ejpam-1372	219	2	10	10	NUM
ejpam-1372	219	3	)	)	PUNCT
ejpam-1372	219	4	is	be	AUX
ejpam-1372	219	5	clearly	clearly	ADV
ejpam-1372	219	6	undefined	undefined	ADJ
ejpam-1372	219	7	,	,	PUNCT
ejpam-1372	219	8	which	which	PRON
ejpam-1372	219	9	is	be	AUX
ejpam-1372	219	10	expected	expect	VERB
ejpam-1372	219	11	because	because	SCONJ
ejpam-1372	219	12	this	this	DET
ejpam-1372	219	13	line	line	NOUN
ejpam-1372	219	14	forms	form	VERB
ejpam-1372	219	15	the	the	DET
ejpam-1372	219	16	border	border	NOUN
ejpam-1372	219	17	or	or	CCONJ
ejpam-1372	219	18	boundary	boundary	NOUN
ejpam-1372	219	19	between	between	ADP
ejpam-1372	219	20	the	the	DET
ejpam-1372	219	21	domains	domain	NOUN
ejpam-1372	219	22	of	of	ADP
ejpam-1372	219	23	convergence	convergence	NOUN
ejpam-1372	219	24	and	and	CCONJ
ejpam-1372	219	25	divergence	divergence	NOUN
ejpam-1372	219	26	for	for	ADP
ejpam-1372	219	27	the	the	DET
ejpam-1372	219	28	series	series	NOUN
ejpam-1372	219	29	.	.	PUNCT
ejpam-1372	220	1	because	because	SCONJ
ejpam-1372	220	2	the	the	DET
ejpam-1372	220	3	finite	finite	ADJ
ejpam-1372	220	4	value	value	NOUN
ejpam-1372	220	5	is	be	AUX
ejpam-1372	220	6	the	the	DET
ejpam-1372	220	7	same	same	ADJ
ejpam-1372	220	8	to	to	ADP
ejpam-1372	220	9	the	the	DET
ejpam-1372	220	10	right	right	NOUN
ejpam-1372	220	11	and	and	CCONJ
ejpam-1372	220	12	to	to	ADP
ejpam-1372	220	13	the	the	DET
ejpam-1372	220	14	left	left	NOUN
ejpam-1372	220	15	of	of	ADP
ejpam-1372	220	16	the	the	DET
ejpam-1372	220	17	barrier	barrier	NOUN
ejpam-1372	220	18	or	or	CCONJ
ejpam-1372	220	19	line	line	NOUN
ejpam-1372	220	20	at	at	ADP
ejpam-1372	220	21	ℜ	ℜ	PROPN
ejpam-1372	220	22	z=1	z=1	NOUN
ejpam-1372	220	23	and	and	CCONJ
ejpam-1372	220	24	in	in	ADP
ejpam-1372	220	25	keeping	keep	VERB
ejpam-1372	220	26	with	with	ADP
ejpam-1372	220	27	the	the	DET
ejpam-1372	220	28	fact	fact	NOUN
ejpam-1372	220	29	that	that	SCONJ
ejpam-1372	220	30	regularisation	regularisation	NOUN
ejpam-1372	220	31	is	be	AUX
ejpam-1372	220	32	effectively	effectively	ADV
ejpam-1372	220	33	the	the	DET
ejpam-1372	220	34	removal	removal	NOUN
ejpam-1372	220	35	of	of	ADP
ejpam-1372	220	36	the	the	DET
ejpam-1372	220	37	first	first	ADJ
ejpam-1372	220	38	term	term	NOUN
ejpam-1372	220	39	in	in	ADP
ejpam-1372	220	40	the	the	DET
ejpam-1372	220	41	last	last	ADJ
ejpam-1372	220	42	member	member	NOUN
ejpam-1372	220	43	or	or	CCONJ
ejpam-1372	220	44	rhs	rhs	PROPN
ejpam-1372	220	45	of	of	ADP
ejpam-1372	220	46	eq	eq	PROPN
ejpam-1372	220	47	.	.	PUNCT
ejpam-1372	221	1	(	(	PUNCT
ejpam-1372	221	2	10	10	NUM
ejpam-1372	221	3	)	)	PUNCT
ejpam-1372	221	4	,	,	PUNCT
ejpam-1372	221	5	we	we	PRON
ejpam-1372	221	6	take	take	VERB
ejpam-1372	221	7	1/(1−	1/(1−	NUM
ejpam-1372	221	8	z	z	NOUN
ejpam-1372	221	9	)	)	PUNCT
ejpam-1372	221	10	to	to	PART
ejpam-1372	221	11	be	be	AUX
ejpam-1372	221	12	the	the	DET
ejpam-1372	221	13	finite	finite	NOUN
ejpam-1372	221	14	or	or	CCONJ
ejpam-1372	221	15	regularised	regularise	VERB
ejpam-1372	221	16	value	value	NOUN
ejpam-1372	221	17	when	when	SCONJ
ejpam-1372	221	18	ℜ	ℜ	PROPN
ejpam-1372	221	19	z=1	z=1	NOUN
ejpam-1372	221	20	.	.	PUNCT
ejpam-1372	222	1	hence	hence	ADV
ejpam-1372	222	2	,	,	PUNCT
ejpam-1372	222	3	equivalence	equivalence	NOUN
ejpam-1372	222	4	(	(	PUNCT
ejpam-1372	222	5	11	11	NUM
ejpam-1372	222	6	)	)	PUNCT
ejpam-1372	222	7	becomes	become	VERB
ejpam-1372	222	8	∞	∞	PROPN
ejpam-1372	222	9	∑	∑	PROPN
ejpam-1372	222	10	k=0	k=0	PROPN
ejpam-1372	222	11	zk	zk	PROPN
ejpam-1372	222	12	(	(	PUNCT
ejpam-1372	222	13	≡	≡	PROPN
ejpam-1372	222	14	1/(1−	1/(1−	PROPN
ejpam-1372	222	15	z	z	NOUN
ejpam-1372	222	16	)	)	PUNCT
ejpam-1372	222	17	,	,	PUNCT
ejpam-1372	222	18	ℜ	ℜ	PROPN
ejpam-1372	222	19	z	z	NOUN
ejpam-1372	222	20	≥	≥	NUM
ejpam-1372	222	21	1	1	NUM
ejpam-1372	222	22	,	,	PUNCT
ejpam-1372	222	23	=	=	PUNCT
ejpam-1372	222	24	1/(1−	1/(1−	NUM
ejpam-1372	222	25	z	z	NOUN
ejpam-1372	222	26	)	)	PUNCT
ejpam-1372	222	27	,	,	PUNCT
ejpam-1372	222	28	ℜ	ℜ	PROPN
ejpam-1372	222	29	z<1	z<1	PROPN
ejpam-1372	222	30	.	.	PUNCT
ejpam-1372	223	1	(	(	PUNCT
ejpam-1372	223	2	13	13	NUM
ejpam-1372	223	3	)	)	PUNCT
ejpam-1372	223	4	since	since	SCONJ
ejpam-1372	223	5	the	the	DET
ejpam-1372	223	6	equals	equal	NOUN
ejpam-1372	223	7	sign	sign	NOUN
ejpam-1372	223	8	is	be	AUX
ejpam-1372	223	9	less	less	ADV
ejpam-1372	223	10	stringent	stringent	ADJ
ejpam-1372	223	11	than	than	ADP
ejpam-1372	223	12	the	the	DET
ejpam-1372	223	13	equivalence	equivalence	NOUN
ejpam-1372	223	14	symbol	symbol	NOUN
ejpam-1372	223	15	,	,	PUNCT
ejpam-1372	223	16	we	we	PRON
ejpam-1372	223	17	can	can	AUX
ejpam-1372	223	18	replace	replace	VERB
ejpam-1372	223	19	the	the	DET
ejpam-1372	223	20	former	former	ADJ
ejpam-1372	223	21	symbol	symbol	NOUN
ejpam-1372	223	22	by	by	ADP
ejpam-1372	223	23	the	the	DET
ejpam-1372	223	24	latter	latter	ADJ
ejpam-1372	223	25	in	in	ADP
ejpam-1372	223	26	the	the	DET
ejpam-1372	223	27	above	above	ADJ
ejpam-1372	223	28	result	result	NOUN
ejpam-1372	223	29	.	.	PUNCT
ejpam-1372	224	1	then	then	ADV
ejpam-1372	224	2	we	we	PRON
ejpam-1372	224	3	find	find	VERB
ejpam-1372	224	4	that	that	DET
ejpam-1372	224	5	equivalence	equivalence	NOUN
ejpam-1372	224	6	(	(	PUNCT
ejpam-1372	224	7	12	12	NUM
ejpam-1372	224	8	)	)	PUNCT
ejpam-1372	224	9	is	be	AUX
ejpam-1372	224	10	valid	valid	ADJ
ejpam-1372	224	11	for	for	ADP
ejpam-1372	224	12	all	all	DET
ejpam-1372	224	13	values	value	NOUN
ejpam-1372	224	14	of	of	ADP
ejpam-1372	224	15	z.	z.	PROPN
ejpam-1372	224	16	the	the	DET
ejpam-1372	224	17	standard	standard	ADJ
ejpam-1372	224	18	rules	rule	NOUN
ejpam-1372	224	19	of	of	ADP
ejpam-1372	224	20	differentiation	differentiation	NOUN
ejpam-1372	224	21	and	and	CCONJ
ejpam-1372	224	22	integration	integration	NOUN
ejpam-1372	224	23	apply	apply	VERB
ejpam-1372	224	24	to	to	ADP
ejpam-1372	224	25	an	an	DET
ejpam-1372	224	26	equivalence	equivalence	NOUN
ejpam-1372	224	27	statement	statement	NOUN
ejpam-1372	224	28	just	just	ADV
ejpam-1372	224	29	as	as	SCONJ
ejpam-1372	224	30	they	they	PRON
ejpam-1372	224	31	would	would	AUX
ejpam-1372	224	32	to	to	ADP
ejpam-1372	224	33	an	an	DET
ejpam-1372	224	34	equation	equation	NOUN
ejpam-1372	224	35	.	.	PUNCT
ejpam-1372	225	1	that	that	PRON
ejpam-1372	225	2	is	is	ADV
ejpam-1372	225	3	,	,	PUNCT
ejpam-1372	225	4	the	the	DET
ejpam-1372	225	5	regularised	regularise	VERB
ejpam-1372	225	6	value	value	NOUN
ejpam-1372	225	7	has	have	VERB
ejpam-1372	225	8	to	to	PART
ejpam-1372	225	9	be	be	AUX
ejpam-1372	225	10	either	either	CCONJ
ejpam-1372	225	11	differentiable	differentiable	ADJ
ejpam-1372	225	12	or	or	CCONJ
ejpam-1372	225	13	integrable	integrable	ADJ
ejpam-1372	225	14	in	in	ADP
ejpam-1372	225	15	order	order	NOUN
ejpam-1372	225	16	to	to	PART
ejpam-1372	225	17	operate	operate	VERB
ejpam-1372	225	18	on	on	ADP
ejpam-1372	225	19	the	the	DET
ejpam-1372	225	20	series	series	NOUN
ejpam-1372	225	21	.	.	PUNCT
ejpam-1372	226	1	for	for	ADP
ejpam-1372	226	2	example	example	NOUN
ejpam-1372	226	3	,	,	PUNCT
ejpam-1372	226	4	differentiating	differentiate	VERB
ejpam-1372	226	5	the	the	DET
ejpam-1372	226	6	preceding	precede	VERB
ejpam-1372	226	7	result	result	NOUN
ejpam-1372	226	8	j	j	PROPN
ejpam-1372	226	9	times	times	PROPN
ejpam-1372	226	10	yields	yield	VERB
ejpam-1372	226	11	∞	∞	PROPN
ejpam-1372	226	12	∑	∑	PROPN
ejpam-1372	226	13	k=	k=	PROPN
ejpam-1372	226	14	j	j	PROPN
ejpam-1372	227	1	γ(k+	γ(k+	PROPN
ejpam-1372	227	2	1	1	NUM
ejpam-1372	227	3	)	)	PUNCT
ejpam-1372	227	4	γ(k−	γ(k−	NOUN
ejpam-1372	227	5	j+	j+	NUM
ejpam-1372	227	6	1	1	NUM
ejpam-1372	227	7	)	)	PUNCT
ejpam-1372	227	8	zk−	zk−	NUM
ejpam-1372	227	9	j	j	PROPN
ejpam-1372	227	10	(	(	PUNCT
ejpam-1372	227	11	≡	≡	PROPN
ejpam-1372	227	12	(	(	PUNCT
ejpam-1372	227	13	−1	−1	NOUN
ejpam-1372	227	14	)	)	PUNCT
ejpam-1372	227	15	jγ	jγ	NOUN
ejpam-1372	227	16	(	(	PUNCT
ejpam-1372	227	17	j+	j+	NUM
ejpam-1372	227	18	1)(1−	1)(1−	PROPN
ejpam-1372	227	19	z	z	NOUN
ejpam-1372	227	20	)	)	PUNCT
ejpam-1372	228	1	j+1	j+1	NOUN
ejpam-1372	228	2	,	,	PUNCT
ejpam-1372	228	3	ℜ	ℜ	PROPN
ejpam-1372	228	4	z	z	NOUN
ejpam-1372	228	5	≥	≥	NUM
ejpam-1372	228	6	1	1	NUM
ejpam-1372	228	7	,	,	PUNCT
ejpam-1372	228	8	=	=	PRON
ejpam-1372	228	9	(	(	PUNCT
ejpam-1372	228	10	−1	−1	NOUN
ejpam-1372	228	11	)	)	PUNCT
ejpam-1372	228	12	jγ	jγ	NOUN
ejpam-1372	228	13	(	(	PUNCT
ejpam-1372	228	14	j+	j+	NUM
ejpam-1372	228	15	1)(1−	1)(1−	PROPN
ejpam-1372	228	16	z	z	NOUN
ejpam-1372	228	17	)	)	PUNCT
ejpam-1372	228	18	j+1	j+1	NOUN
ejpam-1372	228	19	,	,	PUNCT
ejpam-1372	228	20	ℜ	ℜ	NOUN
ejpam-1372	228	21	z	z	NOUN
ejpam-1372	228	22	<	<	X
ejpam-1372	228	23	1	1	NUM
ejpam-1372	228	24	,	,	PUNCT
ejpam-1372	228	25	(	(	PUNCT
ejpam-1372	228	26	14	14	NUM
ejpam-1372	228	27	)	)	PUNCT
ejpam-1372	228	28	v.	v.	ADP
ejpam-1372	228	29	kowalenko	kowalenko	PROPN
ejpam-1372	228	30	/	/	SYM
ejpam-1372	228	31	eur	eur	PROPN
ejpam-1372	228	32	.	.	PUNCT
ejpam-1372	229	1	j.	j.	PROPN
ejpam-1372	229	2	pure	pure	PROPN
ejpam-1372	229	3	appl	appl	PROPN
ejpam-1372	229	4	.	.	PROPN
ejpam-1372	229	5	math	math	PROPN
ejpam-1372	229	6	,	,	PUNCT
ejpam-1372	229	7	4	4	NUM
ejpam-1372	229	8	(	(	PUNCT
ejpam-1372	229	9	2011	2011	NUM
ejpam-1372	229	10	)	)	PUNCT
ejpam-1372	229	11	,	,	PUNCT
ejpam-1372	229	12	370	370	NUM
ejpam-1372	229	13	-	-	SYM
ejpam-1372	229	14	423	423	NUM
ejpam-1372	229	15	378	378	NUM
ejpam-1372	229	16	while	while	SCONJ
ejpam-1372	229	17	if	if	SCONJ
ejpam-1372	229	18	we	we	PRON
ejpam-1372	229	19	replace	replace	VERB
ejpam-1372	229	20	z	z	NOUN
ejpam-1372	229	21	by	by	ADP
ejpam-1372	229	22	−z	−z	NOUN
ejpam-1372	229	23	and	and	CCONJ
ejpam-1372	229	24	integrate	integrate	VERB
ejpam-1372	229	25	from	from	ADP
ejpam-1372	229	26	0	0	NUM
ejpam-1372	229	27	to	to	ADP
ejpam-1372	229	28	z	z	PROPN
ejpam-1372	229	29	,	,	PUNCT
ejpam-1372	229	30	then	then	ADV
ejpam-1372	229	31	we	we	PRON
ejpam-1372	229	32	obtain	obtain	VERB
ejpam-1372	229	33	∞	∞	PROPN
ejpam-1372	229	34	∑	∑	X
ejpam-1372	229	35	k=0	k=0	PROPN
ejpam-1372	229	36	(	(	PUNCT
ejpam-1372	229	37	−1)kzk+1	−1)kzk+1	INTJ
ejpam-1372	229	38	k+	k+	NOUN
ejpam-1372	229	39	1	1	NUM
ejpam-1372	229	40	(	(	PUNCT
ejpam-1372	229	41	≡	≡	PROPN
ejpam-1372	229	42	log(1	log(1	NOUN
ejpam-1372	229	43	+	+	PROPN
ejpam-1372	229	44	z	z	NOUN
ejpam-1372	229	45	)	)	PUNCT
ejpam-1372	229	46	,	,	PUNCT
ejpam-1372	230	1	ℜz	ℜz	VERB
ejpam-1372	230	2	≤	≤	NUM
ejpam-1372	230	3	−1	−1	NOUN
ejpam-1372	230	4	,	,	PUNCT
ejpam-1372	230	5	=	=	PUNCT
ejpam-1372	230	6	log(1	log(1	NOUN
ejpam-1372	231	1	+	+	CCONJ
ejpam-1372	231	2	z	z	NOUN
ejpam-1372	231	3	)	)	PUNCT
ejpam-1372	231	4	,	,	PUNCT
ejpam-1372	231	5	ℜz	ℜz	PROPN
ejpam-1372	231	6	>	>	X
ejpam-1372	231	7	−1	−1	NOUN
ejpam-1372	231	8	.	.	PUNCT
ejpam-1372	232	1	(	(	PUNCT
ejpam-1372	232	2	15	15	NUM
ejpam-1372	232	3	)	)	PUNCT
ejpam-1372	232	4	the	the	DET
ejpam-1372	232	5	series	series	NOUN
ejpam-1372	232	6	in	in	ADP
ejpam-1372	232	7	the	the	DET
ejpam-1372	232	8	above	above	ADJ
ejpam-1372	232	9	result	result	NOUN
ejpam-1372	232	10	is	be	AUX
ejpam-1372	232	11	often	often	ADV
ejpam-1372	232	12	used	use	VERB
ejpam-1372	232	13	as	as	ADP
ejpam-1372	232	14	a	a	DET
ejpam-1372	232	15	textbook	textbook	NOUN
ejpam-1372	232	16	example	example	NOUN
ejpam-1372	232	17	of	of	ADP
ejpam-1372	232	18	conditional	conditional	ADJ
ejpam-1372	232	19	series	series	NOUN
ejpam-1372	232	20	,	,	PUNCT
ejpam-1372	232	21	e.g.	e.g.	ADV
ejpam-1372	232	22	see	see	VERB
ejpam-1372	232	23	p.	p.	NOUN
ejpam-1372	232	24	18	18	NUM
ejpam-1372	232	25	of	of	ADP
ejpam-1372	232	26	ref	ref	NOUN
ejpam-1372	232	27	.	.	PUNCT
ejpam-1372	233	1	[	[	X
ejpam-1372	233	2	33	33	NUM
ejpam-1372	233	3	]	]	PUNCT
ejpam-1372	233	4	.	.	PUNCT
ejpam-1372	234	1	if	if	SCONJ
ejpam-1372	234	2	one	one	PRON
ejpam-1372	234	3	puts	put	VERB
ejpam-1372	234	4	z=1	z=1	PROPN
ejpam-1372	234	5	,	,	PUNCT
ejpam-1372	234	6	then	then	ADV
ejpam-1372	234	7	one	one	NUM
ejpam-1372	234	8	obtains	obtain	VERB
ejpam-1372	234	9	1−	1−	NUM
ejpam-1372	234	10	1/2	1/2	NUM
ejpam-1372	234	11	+	+	CCONJ
ejpam-1372	234	12	1/3−	1/3−	NUM
ejpam-1372	234	13	1/4	1/4	NUM
ejpam-1372	234	14	+	+	CCONJ
ejpam-1372	234	15	1/5−	1/5−	NUM
ejpam-1372	234	16	1/6	1/6	NUM
ejpam-1372	234	17	+	+	NUM
ejpam-1372	234	18	.	.	PUNCT
ejpam-1372	234	19	.	.	PUNCT
ejpam-1372	234	20	.	.	PUNCT
ejpam-1372	235	1	=	=	PRON
ejpam-1372	235	2	log	log	VERB
ejpam-1372	235	3	2	2	NUM
ejpam-1372	235	4	.	.	PUNCT
ejpam-1372	236	1	(	(	PUNCT
ejpam-1372	236	2	16	16	NUM
ejpam-1372	236	3	)	)	PUNCT
ejpam-1372	236	4	on	on	ADP
ejpam-1372	236	5	the	the	DET
ejpam-1372	236	6	other	other	ADJ
ejpam-1372	236	7	hand	hand	NOUN
ejpam-1372	236	8	,	,	PUNCT
ejpam-1372	236	9	by	by	ADP
ejpam-1372	236	10	putting	put	VERB
ejpam-1372	236	11	z	z	NOUN
ejpam-1372	236	12	=	=	NOUN
ejpam-1372	236	13	−1	−1	NOUN
ejpam-1372	236	14	in	in	ADP
ejpam-1372	236	15	equivalence	equivalence	NOUN
ejpam-1372	236	16	(	(	PUNCT
ejpam-1372	236	17	15	15	NUM
ejpam-1372	236	18	)	)	PUNCT
ejpam-1372	236	19	,	,	PUNCT
ejpam-1372	236	20	one	one	PRON
ejpam-1372	236	21	obtains	obtain	VERB
ejpam-1372	236	22	the	the	DET
ejpam-1372	236	23	logarithmically	logarithmically	ADV
ejpam-1372	236	24	divergent	divergent	ADJ
ejpam-1372	236	25	and	and	CCONJ
ejpam-1372	236	26	quite	quite	ADV
ejpam-1372	236	27	famous	famous	ADJ
ejpam-1372	236	28	harmonic	harmonic	ADJ
ejpam-1372	236	29	series	series	NOUN
ejpam-1372	236	30	of	of	ADP
ejpam-1372	236	31	1	1	NUM
ejpam-1372	236	32	+	+	NUM
ejpam-1372	236	33	1/2	1/2	NUM
ejpam-1372	236	34	+	+	NUM
ejpam-1372	236	35	1/3	1/3	NUM
ejpam-1372	236	36	+	+	NUM
ejpam-1372	236	37	1/4	1/4	NUM
ejpam-1372	236	38	+	+	NUM
ejpam-1372	236	39	.	.	PUNCT
ejpam-1372	236	40	.	.	PUNCT
ejpam-1372	237	1	..	..	PUNCT
ejpam-1372	238	1	this	this	DET
ejpam-1372	238	2	series	series	NOUN
ejpam-1372	238	3	,	,	PUNCT
ejpam-1372	238	4	which	which	PRON
ejpam-1372	238	5	,	,	PUNCT
ejpam-1372	238	6	as	as	SCONJ
ejpam-1372	238	7	described	describe	VERB
ejpam-1372	238	8	in	in	ADP
ejpam-1372	238	9	sec	sec	PROPN
ejpam-1372	238	10	.	.	PROPN
ejpam-1372	238	11	7	7	NUM
ejpam-1372	238	12	,	,	PUNCT
ejpam-1372	238	13	represents	represent	VERB
ejpam-1372	238	14	a	a	DET
ejpam-1372	238	15	very	very	ADV
ejpam-1372	238	16	different	different	ADJ
ejpam-1372	238	17	prospect	prospect	NOUN
ejpam-1372	238	18	to	to	PART
ejpam-1372	238	19	regularise	regularise	VERB
ejpam-1372	238	20	from	from	ADP
ejpam-1372	238	21	the	the	DET
ejpam-1372	238	22	geometric	geometric	ADJ
ejpam-1372	238	23	series	series	NOUN
ejpam-1372	238	24	,	,	PUNCT
ejpam-1372	238	25	was	be	AUX
ejpam-1372	238	26	studied	study	VERB
ejpam-1372	238	27	in	in	ADP
ejpam-1372	238	28	great	great	ADJ
ejpam-1372	238	29	detail	detail	NOUN
ejpam-1372	238	30	by	by	ADP
ejpam-1372	238	31	euler	euler	NOUN
ejpam-1372	239	1	[	[	X
ejpam-1372	239	2	13	13	NUM
ejpam-1372	239	3	]	]	PUNCT
ejpam-1372	239	4	.	.	PUNCT
ejpam-1372	240	1	unbeknownst	unbeknownst	ADJ
ejpam-1372	240	2	to	to	ADP
ejpam-1372	240	3	him	he	PRON
ejpam-1372	240	4	at	at	ADP
ejpam-1372	240	5	the	the	DET
ejpam-1372	240	6	time	time	NOUN
ejpam-1372	240	7	,	,	PUNCT
ejpam-1372	240	8	in	in	ADP
ejpam-1372	240	9	writing	write	VERB
ejpam-1372	240	10	down	down	ADP
ejpam-1372	240	11	the	the	DET
ejpam-1372	240	12	equation	equation	NOUN
ejpam-1372	240	13	for	for	ADP
ejpam-1372	240	14	the	the	DET
ejpam-1372	240	15	constant	constant	ADJ
ejpam-1372	240	16	that	that	SCONJ
ejpam-1372	240	17	now	now	ADV
ejpam-1372	240	18	bears	bear	VERB
ejpam-1372	240	19	his	his	PRON
ejpam-1372	240	20	name	name	NOUN
ejpam-1372	240	21	from	from	ADP
ejpam-1372	240	22	the	the	DET
ejpam-1372	240	23	harmonic	harmonic	ADJ
ejpam-1372	240	24	series	series	NOUN
ejpam-1372	240	25	,	,	PUNCT
ejpam-1372	240	26	viz	viz	PROPN
ejpam-1372	240	27	.	.	PUNCT
ejpam-1372	241	1	γ=	γ=	PROPN
ejpam-1372	241	2	lim	lim	PROPN
ejpam-1372	241	3	k→∞	k→∞	PROPN
ejpam-1372	241	4	�	�	PROPN
ejpam-1372	241	5	1	1	NUM
ejpam-1372	241	6	+	+	NUM
ejpam-1372	241	7	1	1	NUM
ejpam-1372	241	8	2	2	NUM
ejpam-1372	241	9	+	+	CCONJ
ejpam-1372	241	10	1	1	NUM
ejpam-1372	241	11	3	3	NUM
ejpam-1372	241	12	+	+	CCONJ
ejpam-1372	241	13	1	1	NUM
ejpam-1372	241	14	4	4	NUM
ejpam-1372	241	15	+	+	CCONJ
ejpam-1372	241	16	.	.	PUNCT
ejpam-1372	241	17	.	.	PUNCT
ejpam-1372	242	1	.+	.+	NOUN
ejpam-1372	242	2	1	1	NUM
ejpam-1372	243	1	k	k	NOUN
ejpam-1372	243	2	−	−	PROPN
ejpam-1372	243	3	log	log	NOUN
ejpam-1372	243	4	k	k	PROPN
ejpam-1372	243	5	�	�	PROPN
ejpam-1372	243	6	,	,	PUNCT
ejpam-1372	243	7	(	(	PUNCT
ejpam-1372	243	8	17	17	NUM
ejpam-1372	243	9	)	)	PUNCT
ejpam-1372	243	10	he	he	PRON
ejpam-1372	243	11	was	be	AUX
ejpam-1372	243	12	actually	actually	ADV
ejpam-1372	243	13	displaying	display	VERB
ejpam-1372	243	14	for	for	ADP
ejpam-1372	243	15	the	the	DET
ejpam-1372	243	16	first	first	ADJ
ejpam-1372	243	17	time	time	NOUN
ejpam-1372	243	18	ever	ever	ADV
ejpam-1372	243	19	a	a	DET
ejpam-1372	243	20	formula	formula	NOUN
ejpam-1372	243	21	for	for	ADP
ejpam-1372	243	22	regularising	regularise	VERB
ejpam-1372	243	23	a	a	DET
ejpam-1372	243	24	divergent	divergent	ADJ
ejpam-1372	243	25	series	series	NOUN
ejpam-1372	243	26	.	.	PUNCT
ejpam-1372	244	1	4	4	X
ejpam-1372	244	2	.	.	X
ejpam-1372	244	3	divergent	divergent	ADJ
ejpam-1372	244	4	integrals	integral	NOUN
ejpam-1372	244	5	as	as	SCONJ
ejpam-1372	244	6	discussed	discuss	VERB
ejpam-1372	244	7	in	in	ADP
ejpam-1372	244	8	refs	ref	NOUN
ejpam-1372	244	9	.	.	PUNCT
ejpam-1372	245	1	[	[	X
ejpam-1372	245	2	14	14	NUM
ejpam-1372	245	3	,	,	PUNCT
ejpam-1372	245	4	17	17	NUM
ejpam-1372	245	5	]	]	PUNCT
ejpam-1372	245	6	,	,	PUNCT
ejpam-1372	245	7	the	the	DET
ejpam-1372	245	8	regularised	regularise	VERB
ejpam-1372	245	9	value	value	NOUN
ejpam-1372	245	10	of	of	ADP
ejpam-1372	245	11	a	a	DET
ejpam-1372	245	12	divergent	divergent	ADJ
ejpam-1372	245	13	series	series	NOUN
ejpam-1372	245	14	is	be	AUX
ejpam-1372	245	15	analogous	analogous	ADJ
ejpam-1372	245	16	to	to	ADP
ejpam-1372	245	17	the	the	DET
ejpam-1372	245	18	hadamard	hadamard	ADJ
ejpam-1372	245	19	finite	finite	VERB
ejpam-1372	245	20	part	part	NOUN
ejpam-1372	245	21	that	that	PRON
ejpam-1372	245	22	arises	arise	VERB
ejpam-1372	245	23	in	in	ADP
ejpam-1372	245	24	the	the	DET
ejpam-1372	245	25	regularisation	regularisation	NOUN
ejpam-1372	245	26	of	of	ADP
ejpam-1372	245	27	divergent	divergent	ADJ
ejpam-1372	245	28	integrals	integral	NOUN
ejpam-1372	245	29	in	in	ADP
ejpam-1372	245	30	the	the	DET
ejpam-1372	245	31	theory	theory	NOUN
ejpam-1372	245	32	of	of	ADP
ejpam-1372	245	33	generalised	generalise	VERB
ejpam-1372	245	34	functions	function	NOUN
ejpam-1372	245	35	[	[	X
ejpam-1372	245	36	10	10	NUM
ejpam-1372	245	37	,	,	PUNCT
ejpam-1372	245	38	23	23	NUM
ejpam-1372	245	39	]	]	PUNCT
ejpam-1372	245	40	.	.	PUNCT
ejpam-1372	246	1	as	as	ADP
ejpam-1372	246	2	a	a	DET
ejpam-1372	246	3	typical	typical	ADJ
ejpam-1372	246	4	example	example	NOUN
ejpam-1372	246	5	,	,	PUNCT
ejpam-1372	246	6	let	let	VERB
ejpam-1372	246	7	us	we	PRON
ejpam-1372	246	8	consider	consider	VERB
ejpam-1372	246	9	the	the	DET
ejpam-1372	246	10	general	general	ADJ
ejpam-1372	246	11	integral	integral	ADJ
ejpam-1372	246	12	representation	representation	NOUN
ejpam-1372	246	13	of	of	ADP
ejpam-1372	246	14	the	the	DET
ejpam-1372	246	15	gamma	gamma	NOUN
ejpam-1372	246	16	function	function	NOUN
ejpam-1372	246	17	that	that	PRON
ejpam-1372	246	18	was	be	AUX
ejpam-1372	246	19	used	use	VERB
ejpam-1372	246	20	to	to	PART
ejpam-1372	246	21	derive	derive	VERB
ejpam-1372	246	22	eq	eq	ADP
ejpam-1372	246	23	.	.	PUNCT
ejpam-1372	247	1	(	(	PUNCT
ejpam-1372	247	2	9	9	NUM
ejpam-1372	247	3	)	)	PUNCT
ejpam-1372	247	4	.	.	PUNCT
ejpam-1372	248	1	this	this	PRON
ejpam-1372	248	2	is	be	AUX
ejpam-1372	248	3	γ(α	γ(α	NOUN
ejpam-1372	248	4	)	)	PUNCT
ejpam-1372	249	1	=	=	SYM
ejpam-1372	250	1	∫	∫	PROPN
ejpam-1372	251	1	∞	∞	NOUN
ejpam-1372	251	2	0	0	PUNCT
ejpam-1372	252	1	d	d	NOUN
ejpam-1372	252	2	x	x	X
ejpam-1372	252	3	xα−1e−x	xα−1e−x	PROPN
ejpam-1372	252	4	.	.	PUNCT
ejpam-1372	253	1	(	(	PUNCT
ejpam-1372	253	2	18	18	NUM
ejpam-1372	253	3	)	)	PUNCT
ejpam-1372	253	4	the	the	DET
ejpam-1372	253	5	above	above	ADJ
ejpam-1372	253	6	integral	integral	ADJ
ejpam-1372	253	7	is	be	AUX
ejpam-1372	253	8	convergent	convergent	NOUN
ejpam-1372	253	9	for	for	ADP
ejpam-1372	253	10	ℜα>0	ℜα>0	NOUN
ejpam-1372	253	11	,	,	PUNCT
ejpam-1372	253	12	but	but	CCONJ
ejpam-1372	253	13	is	be	AUX
ejpam-1372	253	14	divergent	divergent	ADJ
ejpam-1372	253	15	for	for	ADP
ejpam-1372	253	16	all	all	DET
ejpam-1372	253	17	other	other	ADJ
ejpam-1372	253	18	values	value	NOUN
ejpam-1372	253	19	of	of	ADP
ejpam-1372	253	20	α	α	NOUN
ejpam-1372	253	21	.	.	PUNCT
ejpam-1372	254	1	the	the	DET
ejpam-1372	254	2	divergence	divergence	NOUN
ejpam-1372	254	3	in	in	ADP
ejpam-1372	254	4	the	the	DET
ejpam-1372	254	5	above	above	ADJ
ejpam-1372	254	6	integral	integral	ADJ
ejpam-1372	254	7	is	be	AUX
ejpam-1372	254	8	associated	associate	VERB
ejpam-1372	254	9	with	with	ADP
ejpam-1372	254	10	the	the	DET
ejpam-1372	254	11	lower	low	ADJ
ejpam-1372	254	12	limit	limit	NOUN
ejpam-1372	254	13	.	.	PUNCT
ejpam-1372	255	1	if	if	SCONJ
ejpam-1372	255	2	the	the	DET
ejpam-1372	255	3	lower	low	ADJ
ejpam-1372	255	4	limit	limit	NOUN
ejpam-1372	255	5	is	be	AUX
ejpam-1372	255	6	replaced	replace	VERB
ejpam-1372	255	7	by	by	ADP
ejpam-1372	255	8	ε	ε	PROPN
ejpam-1372	255	9	and	and	CCONJ
ejpam-1372	255	10	the	the	DET
ejpam-1372	255	11	limit	limit	NOUN
ejpam-1372	255	12	of	of	ADP
ejpam-1372	255	13	ε→	ε→	PROPN
ejpam-1372	255	14	0	0	NUM
ejpam-1372	255	15	is	be	AUX
ejpam-1372	255	16	taken	take	VERB
ejpam-1372	255	17	,	,	PUNCT
ejpam-1372	255	18	then	then	ADV
ejpam-1372	255	19	the	the	DET
ejpam-1372	255	20	above	above	ADJ
ejpam-1372	255	21	integral	integral	NOUN
ejpam-1372	255	22	can	can	AUX
ejpam-1372	255	23	be	be	AUX
ejpam-1372	255	24	evaluated	evaluate	VERB
ejpam-1372	255	25	by	by	ADP
ejpam-1372	255	26	integrating	integrate	VERB
ejpam-1372	255	27	by	by	ADP
ejpam-1372	255	28	parts	part	NOUN
ejpam-1372	255	29	continuously	continuously	ADV
ejpam-1372	255	30	so	so	SCONJ
ejpam-1372	255	31	that	that	SCONJ
ejpam-1372	255	32	after	after	SCONJ
ejpam-1372	255	33	k	k	PROPN
ejpam-1372	255	34	integrations	integration	VERB
ejpam-1372	255	35	one	one	NUM
ejpam-1372	255	36	finds	find	VERB
ejpam-1372	255	37	that	that	SCONJ
ejpam-1372	255	38	ℜ(k+α)>0	ℜ(k+α)>0	PROPN
ejpam-1372	255	39	.	.	PUNCT
ejpam-1372	256	1	then	then	ADV
ejpam-1372	256	2	one	one	NUM
ejpam-1372	256	3	obtains	obtain	VERB
ejpam-1372	256	4	γ(k	γ(k	PROPN
ejpam-1372	256	5	+	+	CCONJ
ejpam-1372	256	6	α)/α(α+	α)/α(α+	DET
ejpam-1372	256	7	1	1	NUM
ejpam-1372	256	8	)	)	PUNCT
ejpam-1372	256	9	.	.	PUNCT
ejpam-1372	256	10	.	.	PUNCT
ejpam-1372	256	11	.	.	PUNCT
ejpam-1372	257	1	(	(	PUNCT
ejpam-1372	257	2	α+	α+	X
ejpam-1372	257	3	k	k	NOUN
ejpam-1372	257	4	−	−	NOUN
ejpam-1372	257	5	1	1	NUM
ejpam-1372	257	6	)	)	PUNCT
ejpam-1372	257	7	=	=	SYM
ejpam-1372	257	8	γ(α	γ(α	PROPN
ejpam-1372	257	9	)	)	PUNCT
ejpam-1372	257	10	plus	plus	CCONJ
ejpam-1372	257	11	a	a	DET
ejpam-1372	257	12	whole	whole	ADJ
ejpam-1372	257	13	lot	lot	NOUN
ejpam-1372	257	14	of	of	ADP
ejpam-1372	257	15	contributions	contribution	NOUN
ejpam-1372	257	16	such	such	ADJ
ejpam-1372	257	17	as	as	ADP
ejpam-1372	257	18	−εα	−εα	NOUN
ejpam-1372	257	19	exp(−ε)/α	exp(−ε)/α	NOUN
ejpam-1372	257	20	,	,	PUNCT
ejpam-1372	257	21	−εα+1	−εα+1	NOUN
ejpam-1372	257	22	exp(−ε)/α	exp(−ε)/α	NOUN
ejpam-1372	257	23	and	and	CCONJ
ejpam-1372	257	24	so	so	ADV
ejpam-1372	257	25	on	on	ADV
ejpam-1372	257	26	.	.	PUNCT
ejpam-1372	258	1	in	in	ADP
ejpam-1372	258	2	accordance	accordance	NOUN
ejpam-1372	258	3	with	with	ADP
ejpam-1372	258	4	regularisation	regularisation	NOUN
ejpam-1372	258	5	,	,	PUNCT
ejpam-1372	258	6	these	these	DET
ejpam-1372	258	7	infinities	infinity	NOUN
ejpam-1372	258	8	are	be	AUX
ejpam-1372	258	9	omitted	omit	VERB
ejpam-1372	258	10	or	or	CCONJ
ejpam-1372	258	11	removed	remove	VERB
ejpam-1372	258	12	,	,	PUNCT
ejpam-1372	258	13	leaving	leave	VERB
ejpam-1372	258	14	only	only	ADV
ejpam-1372	258	15	γ(α	γ(α	PROPN
ejpam-1372	258	16	)	)	PUNCT
ejpam-1372	258	17	,	,	PUNCT
ejpam-1372	258	18	which	which	PRON
ejpam-1372	258	19	is	be	AUX
ejpam-1372	258	20	the	the	DET
ejpam-1372	258	21	same	same	ADJ
ejpam-1372	258	22	result	result	NOUN
ejpam-1372	258	23	for	for	ADP
ejpam-1372	258	24	ℜα	ℜα	PROPN
ejpam-1372	258	25	>	>	X
ejpam-1372	258	26	0	0	NUM
ejpam-1372	258	27	.	.	PUNCT
ejpam-1372	259	1	according	accord	VERB
ejpam-1372	259	2	to	to	ADP
ejpam-1372	259	3	p.	p.	NOUN
ejpam-1372	259	4	32	32	NUM
ejpam-1372	259	5	of	of	ADP
ejpam-1372	259	6	ref	ref	NOUN
ejpam-1372	259	7	.	.	PUNCT
ejpam-1372	260	1	[	[	X
ejpam-1372	260	2	23	23	NUM
ejpam-1372	260	3	]	]	PUNCT
ejpam-1372	260	4	,	,	PUNCT
ejpam-1372	260	5	the	the	DET
ejpam-1372	260	6	remaining	remain	VERB
ejpam-1372	260	7	term	term	NOUN
ejpam-1372	260	8	was	be	AUX
ejpam-1372	260	9	called	call	VERB
ejpam-1372	260	10	the	the	DET
ejpam-1372	260	11	“	"	PUNCT
ejpam-1372	260	12	finite	finite	ADJ
ejpam-1372	260	13	part	part	NOUN
ejpam-1372	260	14	”	"	PUNCT
ejpam-1372	260	15	by	by	ADP
ejpam-1372	260	16	hadamard	hadamard	NOUN
ejpam-1372	260	17	,	,	PUNCT
ejpam-1372	260	18	who	who	PRON
ejpam-1372	260	19	showed	show	VERB
ejpam-1372	260	20	that	that	SCONJ
ejpam-1372	260	21	it	it	PRON
ejpam-1372	260	22	obeys	obey	VERB
ejpam-1372	260	23	many	many	ADJ
ejpam-1372	260	24	of	of	ADP
ejpam-1372	260	25	the	the	DET
ejpam-1372	260	26	ordinary	ordinary	ADJ
ejpam-1372	260	27	rules	rule	NOUN
ejpam-1372	260	28	of	of	ADP
ejpam-1372	260	29	integration	integration	NOUN
ejpam-1372	260	30	.	.	PUNCT
ejpam-1372	261	1	to	to	PART
ejpam-1372	261	2	demonstrate	demonstrate	VERB
ejpam-1372	261	3	the	the	DET
ejpam-1372	261	4	relationship	relationship	NOUN
ejpam-1372	261	5	between	between	ADP
ejpam-1372	261	6	the	the	DET
ejpam-1372	261	7	finite	finite	ADJ
ejpam-1372	261	8	part	part	NOUN
ejpam-1372	261	9	of	of	ADP
ejpam-1372	261	10	a	a	DET
ejpam-1372	261	11	divergent	divergent	ADJ
ejpam-1372	261	12	integral	integral	ADJ
ejpam-1372	261	13	and	and	CCONJ
ejpam-1372	261	14	the	the	DET
ejpam-1372	261	15	regularised	regularise	VERB
ejpam-1372	261	16	value	value	NOUN
ejpam-1372	261	17	of	of	ADP
ejpam-1372	261	18	a	a	DET
ejpam-1372	261	19	divergent	divergent	ADJ
ejpam-1372	261	20	series	series	NOUN
ejpam-1372	261	21	,	,	PUNCT
ejpam-1372	261	22	consider	consider	VERB
ejpam-1372	261	23	the	the	DET
ejpam-1372	261	24	following	follow	VERB
ejpam-1372	261	25	integral	integral	ADJ
ejpam-1372	261	26	:	:	PUNCT
ejpam-1372	261	27	i	i	PRON
ejpam-1372	261	28	=	=	PUNCT
ejpam-1372	262	1	∫	∫	PROPN
ejpam-1372	263	1	∞	∞	NOUN
ejpam-1372	263	2	0	0	PUNCT
ejpam-1372	264	1	d	d	NOUN
ejpam-1372	264	2	x	x	PROPN
ejpam-1372	264	3	eax	eax	NOUN
ejpam-1372	264	4	=	=	PROPN
ejpam-1372	264	5	lim	lim	PROPN
ejpam-1372	264	6	p→∞	p→∞	PROPN
ejpam-1372	265	1	∫	∫	PROPN
ejpam-1372	266	1	p	p	NOUN
ejpam-1372	266	2	0	0	NUM
ejpam-1372	266	3	d	d	NOUN
ejpam-1372	266	4	x	x	PROPN
ejpam-1372	266	5	eax	eax	NOUN
ejpam-1372	266	6	=	=	PROPN
ejpam-1372	266	7	lim	lim	PROPN
ejpam-1372	266	8	p→∞	p→∞	PROPN
ejpam-1372	266	9	�	�	PROPN
ejpam-1372	266	10	eap	eap	PROPN
ejpam-1372	266	11	−	−	PROPN
ejpam-1372	266	12	1	1	NUM
ejpam-1372	266	13	a	a	DET
ejpam-1372	266	14	�	�	PROPN
ejpam-1372	266	15	.	.	PUNCT
ejpam-1372	267	1	(	(	PUNCT
ejpam-1372	267	2	19	19	NUM
ejpam-1372	267	3	)	)	PUNCT
ejpam-1372	267	4	v.	v.	ADP
ejpam-1372	267	5	kowalenko	kowalenko	PROPN
ejpam-1372	267	6	/	/	SYM
ejpam-1372	267	7	eur	eur	PROPN
ejpam-1372	267	8	.	.	PUNCT
ejpam-1372	268	1	j.	j.	PROPN
ejpam-1372	268	2	pure	pure	PROPN
ejpam-1372	268	3	appl	appl	PROPN
ejpam-1372	268	4	.	.	PROPN
ejpam-1372	268	5	math	math	PROPN
ejpam-1372	268	6	,	,	PUNCT
ejpam-1372	268	7	4	4	NUM
ejpam-1372	268	8	(	(	PUNCT
ejpam-1372	268	9	2011	2011	NUM
ejpam-1372	268	10	)	)	PUNCT
ejpam-1372	268	11	,	,	PUNCT
ejpam-1372	268	12	370	370	NUM
ejpam-1372	268	13	-	-	SYM
ejpam-1372	268	14	423	423	NUM
ejpam-1372	268	15	379	379	NUM
ejpam-1372	268	16	for	for	ADP
ejpam-1372	268	17	ℜ	ℜ	DET
ejpam-1372	268	18	a	a	DET
ejpam-1372	268	19	<	<	X
ejpam-1372	268	20	0	0	NUM
ejpam-1372	268	21	,	,	PUNCT
ejpam-1372	268	22	the	the	DET
ejpam-1372	268	23	integral	integral	NOUN
ejpam-1372	268	24	in	in	ADP
ejpam-1372	268	25	eq	eq	PROPN
ejpam-1372	268	26	.	.	PUNCT
ejpam-1372	269	1	(	(	PUNCT
ejpam-1372	269	2	19	19	NUM
ejpam-1372	269	3	)	)	PUNCT
ejpam-1372	269	4	is	be	AUX
ejpam-1372	269	5	convergent	convergent	NOUN
ejpam-1372	269	6	,	,	PUNCT
ejpam-1372	269	7	yielding	yield	VERB
ejpam-1372	269	8	a	a	DET
ejpam-1372	269	9	value	value	NOUN
ejpam-1372	269	10	of	of	ADP
ejpam-1372	269	11	−1	−1	NOUN
ejpam-1372	269	12	/	/	SYM
ejpam-1372	269	13	a.	a.	NOUN
ejpam-1372	269	14	on	on	ADP
ejpam-1372	269	15	the	the	DET
ejpam-1372	269	16	other	other	ADJ
ejpam-1372	269	17	hand	hand	NOUN
ejpam-1372	269	18	,	,	PUNCT
ejpam-1372	269	19	for	for	ADP
ejpam-1372	269	20	ℜ	ℜ	DET
ejpam-1372	269	21	a	a	DET
ejpam-1372	269	22	>	>	X
ejpam-1372	269	23	0	0	NUM
ejpam-1372	269	24	,	,	PUNCT
ejpam-1372	269	25	it	it	PRON
ejpam-1372	269	26	is	be	AUX
ejpam-1372	269	27	divergent	divergent	ADJ
ejpam-1372	269	28	,	,	PUNCT
ejpam-1372	269	29	but	but	CCONJ
ejpam-1372	269	30	removing	remove	VERB
ejpam-1372	269	31	the	the	DET
ejpam-1372	269	32	infinity	infinity	NOUN
ejpam-1372	269	33	or	or	CCONJ
ejpam-1372	269	34	first	first	ADJ
ejpam-1372	269	35	term	term	NOUN
ejpam-1372	269	36	in	in	ADP
ejpam-1372	269	37	the	the	DET
ejpam-1372	269	38	last	last	ADJ
ejpam-1372	269	39	member	member	NOUN
ejpam-1372	269	40	yields	yield	NOUN
ejpam-1372	269	41	,	,	PUNCT
ejpam-1372	269	42	once	once	ADV
ejpam-1372	269	43	again	again	ADV
ejpam-1372	269	44	,	,	PUNCT
ejpam-1372	269	45	a	a	DET
ejpam-1372	269	46	finite	finite	ADJ
ejpam-1372	269	47	part	part	NOUN
ejpam-1372	269	48	of	of	ADP
ejpam-1372	269	49	−1	−1	NOUN
ejpam-1372	269	50	/	/	SYM
ejpam-1372	269	51	a.	a.	NOUN
ejpam-1372	269	52	now	now	ADV
ejpam-1372	269	53	to	to	PART
ejpam-1372	269	54	connect	connect	VERB
ejpam-1372	269	55	the	the	DET
ejpam-1372	269	56	above	above	ADJ
ejpam-1372	269	57	result	result	NOUN
ejpam-1372	269	58	with	with	ADP
ejpam-1372	269	59	regularisation	regularisation	NOUN
ejpam-1372	269	60	of	of	ADP
ejpam-1372	269	61	a	a	DET
ejpam-1372	269	62	divergent	divergent	ADJ
ejpam-1372	269	63	series	series	NOUN
ejpam-1372	269	64	,	,	PUNCT
ejpam-1372	269	65	we	we	PRON
ejpam-1372	269	66	write	write	VERB
ejpam-1372	269	67	the	the	DET
ejpam-1372	269	68	integral	integral	ADJ
ejpam-1372	269	69	in	in	ADP
ejpam-1372	269	70	terms	term	NOUN
ejpam-1372	269	71	of	of	ADP
ejpam-1372	269	72	an	an	DET
ejpam-1372	269	73	arbitrary	arbitrary	ADJ
ejpam-1372	269	74	positive	positive	ADJ
ejpam-1372	269	75	real	real	ADJ
ejpam-1372	269	76	parameter	parameter	NOUN
ejpam-1372	269	77	,	,	PUNCT
ejpam-1372	269	78	say	say	VERB
ejpam-1372	269	79	b	b	X
ejpam-1372	269	80	,	,	PUNCT
ejpam-1372	269	81	as	as	ADP
ejpam-1372	269	82	i	i	PRON
ejpam-1372	269	83	=	=	SYM
ejpam-1372	270	1	∫	∫	PROPN
ejpam-1372	271	1	∞	∞	NOUN
ejpam-1372	271	2	0	0	PUNCT
ejpam-1372	272	1	d	d	NOUN
ejpam-1372	272	2	x	x	PROPN
ejpam-1372	272	3	e−bx	e−bx	PROPN
ejpam-1372	272	4	e(a+b)x	e(a+b)x	PROPN
ejpam-1372	273	1	=	=	SYM
ejpam-1372	273	2	∫	∫	PROPN
ejpam-1372	274	1	∞	∞	NOUN
ejpam-1372	274	2	0	0	PUNCT
ejpam-1372	275	1	d	d	NOUN
ejpam-1372	275	2	x	x	PROPN
ejpam-1372	275	3	e−bx	e−bx	PROPN
ejpam-1372	275	4	∞	∞	NUM
ejpam-1372	275	5	∑	∑	PROPN
ejpam-1372	275	6	k=0	k=0	PROPN
ejpam-1372	275	7	(	(	PUNCT
ejpam-1372	275	8	a+	a+	X
ejpam-1372	275	9	b)k	b)k	NOUN
ejpam-1372	275	10	x	x	X
ejpam-1372	276	1	k	k	PROPN
ejpam-1372	276	2	k	k	PROPN
ejpam-1372	276	3	!	!	PUNCT
ejpam-1372	276	4	.	.	PUNCT
ejpam-1372	277	1	(	(	PUNCT
ejpam-1372	277	2	20	20	NUM
ejpam-1372	277	3	)	)	PUNCT
ejpam-1372	277	4	in	in	ADP
ejpam-1372	277	5	obtaining	obtain	VERB
ejpam-1372	277	6	this	this	DET
ejpam-1372	277	7	result	result	NOUN
ejpam-1372	277	8	we	we	PRON
ejpam-1372	277	9	have	have	AUX
ejpam-1372	277	10	employed	employ	VERB
ejpam-1372	277	11	the	the	DET
ejpam-1372	277	12	asymptotic	asymptotic	ADJ
ejpam-1372	277	13	method	method	NOUN
ejpam-1372	277	14	of	of	ADP
ejpam-1372	277	15	expanding	expand	VERB
ejpam-1372	277	16	most	most	ADJ
ejpam-1372	277	17	of	of	ADP
ejpam-1372	277	18	the	the	DET
ejpam-1372	277	19	exponential	exponential	NOUN
ejpam-1372	277	20	as	as	SCONJ
ejpam-1372	277	21	described	describe	VERB
ejpam-1372	277	22	on	on	ADP
ejpam-1372	277	23	p.	p.	PROPN
ejpam-1372	277	24	113	113	NUM
ejpam-1372	277	25	of	of	ADP
ejpam-1372	277	26	ref	ref	NOUN
ejpam-1372	277	27	.	.	PUNCT
ejpam-1372	278	1	[	[	X
ejpam-1372	278	2	8	8	NUM
ejpam-1372	278	3	]	]	PUNCT
ejpam-1372	278	4	.	.	PUNCT
ejpam-1372	279	1	next	next	ADV
ejpam-1372	279	2	we	we	PRON
ejpam-1372	279	3	interchange	interchange	VERB
ejpam-1372	279	4	the	the	DET
ejpam-1372	279	5	order	order	NOUN
ejpam-1372	279	6	of	of	ADP
ejpam-1372	279	7	the	the	DET
ejpam-1372	279	8	summation	summation	NOUN
ejpam-1372	279	9	and	and	CCONJ
ejpam-1372	279	10	integration	integration	NOUN
ejpam-1372	279	11	.	.	PUNCT
ejpam-1372	280	1	because	because	SCONJ
ejpam-1372	280	2	most	most	ADJ
ejpam-1372	280	3	of	of	ADP
ejpam-1372	280	4	the	the	DET
ejpam-1372	280	5	exponential	exponential	NOUN
ejpam-1372	280	6	has	have	AUX
ejpam-1372	280	7	been	be	AUX
ejpam-1372	280	8	expanded	expand	VERB
ejpam-1372	280	9	,	,	PUNCT
ejpam-1372	280	10	an	an	DET
ejpam-1372	280	11	impropriety	impropriety	NOUN
ejpam-1372	280	12	has	have	AUX
ejpam-1372	280	13	occurred	occur	VERB
ejpam-1372	280	14	.	.	PUNCT
ejpam-1372	281	1	evaluating	evaluate	VERB
ejpam-1372	281	2	the	the	DET
ejpam-1372	281	3	resulting	result	VERB
ejpam-1372	281	4	integral	integral	ADJ
ejpam-1372	281	5	yields	yield	NOUN
ejpam-1372	281	6	a	a	DET
ejpam-1372	281	7	divergent	divergent	ADJ
ejpam-1372	281	8	series	series	NOUN
ejpam-1372	281	9	,	,	PUNCT
ejpam-1372	281	10	depending	depend	VERB
ejpam-1372	281	11	,	,	PUNCT
ejpam-1372	281	12	of	of	ADP
ejpam-1372	281	13	course	course	NOUN
ejpam-1372	281	14	,	,	PUNCT
ejpam-1372	281	15	on	on	ADP
ejpam-1372	281	16	the	the	DET
ejpam-1372	281	17	values	value	NOUN
ejpam-1372	281	18	of	of	ADP
ejpam-1372	281	19	a	a	PRON
ejpam-1372	281	20	and	and	CCONJ
ejpam-1372	281	21	b.	b.	PROPN
ejpam-1372	281	22	as	as	ADP
ejpam-1372	281	23	a	a	DET
ejpam-1372	281	24	consequence	consequence	NOUN
ejpam-1372	281	25	,	,	PUNCT
ejpam-1372	281	26	we	we	PRON
ejpam-1372	281	27	have	have	VERB
ejpam-1372	281	28	to	to	PART
ejpam-1372	281	29	replace	replace	VERB
ejpam-1372	281	30	the	the	DET
ejpam-1372	281	31	equals	equal	NOUN
ejpam-1372	281	32	sign	sign	NOUN
ejpam-1372	281	33	by	by	ADP
ejpam-1372	281	34	an	an	DET
ejpam-1372	281	35	equivalence	equivalence	NOUN
ejpam-1372	281	36	symbol	symbol	NOUN
ejpam-1372	281	37	in	in	ADP
ejpam-1372	281	38	the	the	DET
ejpam-1372	281	39	final	final	ADJ
ejpam-1372	281	40	result	result	NOUN
ejpam-1372	281	41	.	.	PUNCT
ejpam-1372	282	1	hence	hence	ADV
ejpam-1372	282	2	,	,	PUNCT
ejpam-1372	282	3	the	the	DET
ejpam-1372	282	4	integral	integral	ADJ
ejpam-1372	282	5	i	i	PRON
ejpam-1372	282	6	becomes	become	VERB
ejpam-1372	282	7	i	i	PRON
ejpam-1372	282	8	≡	≡	PROPN
ejpam-1372	282	9	∞	∞	PROPN
ejpam-1372	282	10	∑	∑	PROPN
ejpam-1372	282	11	k=0	k=0	PROPN
ejpam-1372	282	12	(	(	PUNCT
ejpam-1372	282	13	a+	a+	X
ejpam-1372	282	14	b)k	b)k	X
ejpam-1372	282	15	k	k	X
ejpam-1372	282	16	!	!	PUNCT
ejpam-1372	282	17	∫	∫	PROPN
ejpam-1372	283	1	∞	∞	NUM
ejpam-1372	283	2	0	0	PUNCT
ejpam-1372	284	1	d	d	NOUN
ejpam-1372	284	2	x	x	X
ejpam-1372	284	3	e−bx	e−bx	NOUN
ejpam-1372	284	4	x	x	PUNCT
ejpam-1372	285	1	k	k	NOUN
ejpam-1372	285	2	=	=	SYM
ejpam-1372	285	3	1	1	NUM
ejpam-1372	285	4	a+	a+	SYM
ejpam-1372	285	5	b	b	NOUN
ejpam-1372	285	6	∞	∞	NUM
ejpam-1372	285	7	∑	∑	PUNCT
ejpam-1372	285	8	k=1	k=1	X
ejpam-1372	285	9	(	(	PUNCT
ejpam-1372	285	10	1	1	NUM
ejpam-1372	285	11	+	+	NUM
ejpam-1372	285	12	a	a	DET
ejpam-1372	285	13	/	/	SYM
ejpam-1372	285	14	b)k	b)k	NOUN
ejpam-1372	285	15	.	.	PUNCT
ejpam-1372	286	1	(	(	PUNCT
ejpam-1372	286	2	21	21	NUM
ejpam-1372	286	3	)	)	PUNCT
ejpam-1372	286	4	the	the	DET
ejpam-1372	286	5	series	series	NOUN
ejpam-1372	286	6	in	in	ADP
ejpam-1372	286	7	the	the	DET
ejpam-1372	286	8	final	final	ADJ
ejpam-1372	286	9	member	member	NOUN
ejpam-1372	286	10	of	of	ADP
ejpam-1372	286	11	the	the	DET
ejpam-1372	286	12	above	above	ADJ
ejpam-1372	286	13	result	result	NOUN
ejpam-1372	286	14	is	be	AUX
ejpam-1372	286	15	merely	merely	ADV
ejpam-1372	286	16	the	the	DET
ejpam-1372	286	17	geometric	geometric	ADJ
ejpam-1372	286	18	series	series	NOUN
ejpam-1372	286	19	with	with	ADP
ejpam-1372	286	20	the	the	DET
ejpam-1372	286	21	variable	variable	NOUN
ejpam-1372	286	22	equal	equal	ADJ
ejpam-1372	286	23	to	to	ADP
ejpam-1372	286	24	(	(	PUNCT
ejpam-1372	286	25	1	1	NUM
ejpam-1372	286	26	+	+	NUM
ejpam-1372	286	27	a	a	DET
ejpam-1372	286	28	/	/	SYM
ejpam-1372	286	29	b	b	NOUN
ejpam-1372	286	30	)	)	PUNCT
ejpam-1372	286	31	.	.	PUNCT
ejpam-1372	287	1	if	if	SCONJ
ejpam-1372	287	2	we	we	PRON
ejpam-1372	287	3	introduce	introduce	VERB
ejpam-1372	287	4	the	the	DET
ejpam-1372	287	5	regularised	regularise	VERB
ejpam-1372	287	6	value	value	NOUN
ejpam-1372	287	7	of	of	ADP
ejpam-1372	287	8	the	the	DET
ejpam-1372	287	9	series	series	NOUN
ejpam-1372	287	10	,	,	PUNCT
ejpam-1372	287	11	viz	viz	PROPN
ejpam-1372	287	12	.	.	PUNCT
ejpam-1372	288	1	−(1	−(1	ADJ
ejpam-1372	288	2	+	+	CCONJ
ejpam-1372	288	3	a	a	DET
ejpam-1372	288	4	/	/	SYM
ejpam-1372	288	5	b)/(a	b)/(a	NOUN
ejpam-1372	288	6	/	/	SYM
ejpam-1372	288	7	b	b	NOUN
ejpam-1372	288	8	)	)	PUNCT
ejpam-1372	288	9	,	,	PUNCT
ejpam-1372	288	10	into	into	ADP
ejpam-1372	288	11	the	the	DET
ejpam-1372	288	12	last	last	ADJ
ejpam-1372	288	13	member	member	NOUN
ejpam-1372	288	14	of	of	ADP
ejpam-1372	288	15	the	the	DET
ejpam-1372	288	16	above	above	ADJ
ejpam-1372	288	17	equivalence	equivalence	NOUN
ejpam-1372	288	18	,	,	PUNCT
ejpam-1372	288	19	then	then	ADV
ejpam-1372	288	20	we	we	PRON
ejpam-1372	288	21	obtain	obtain	VERB
ejpam-1372	288	22	the	the	DET
ejpam-1372	288	23	finite	finite	ADJ
ejpam-1372	288	24	value	value	NOUN
ejpam-1372	288	25	of	of	ADP
ejpam-1372	288	26	−1	−1	NOUN
ejpam-1372	288	27	/	/	SYM
ejpam-1372	288	28	a	a	NOUN
ejpam-1372	288	29	as	as	SCONJ
ejpam-1372	288	30	we	we	PRON
ejpam-1372	288	31	did	do	VERB
ejpam-1372	288	32	when	when	SCONJ
ejpam-1372	288	33	we	we	PRON
ejpam-1372	288	34	evaluated	evaluate	VERB
ejpam-1372	288	35	the	the	DET
ejpam-1372	288	36	integral	integral	NOUN
ejpam-1372	288	37	in	in	ADP
ejpam-1372	288	38	eq	eq	ADP
ejpam-1372	288	39	.	.	PUNCT
ejpam-1372	289	1	(	(	PUNCT
ejpam-1372	289	2	19	19	NUM
ejpam-1372	289	3	)	)	PUNCT
ejpam-1372	289	4	.	.	PUNCT
ejpam-1372	290	1	that	that	PRON
ejpam-1372	290	2	is	be	AUX
ejpam-1372	290	3	,	,	PUNCT
ejpam-1372	290	4	by	by	ADP
ejpam-1372	290	5	regularising	regularise	VERB
ejpam-1372	290	6	the	the	DET
ejpam-1372	290	7	series	series	NOUN
ejpam-1372	290	8	in	in	ADP
ejpam-1372	290	9	eq	eq	PROPN
ejpam-1372	290	10	.	.	PUNCT
ejpam-1372	291	1	(	(	PUNCT
ejpam-1372	291	2	21	21	NUM
ejpam-1372	291	3	)	)	PUNCT
ejpam-1372	291	4	,	,	PUNCT
ejpam-1372	291	5	we	we	PRON
ejpam-1372	291	6	have	have	AUX
ejpam-1372	291	7	found	find	VERB
ejpam-1372	291	8	that	that	SCONJ
ejpam-1372	291	9	i	i	PRON
ejpam-1372	291	10	≡	≡	PROPN
ejpam-1372	291	11	−1	−1	ADV
ejpam-1372	291	12	/	/	SYM
ejpam-1372	291	13	a	a	PRON
ejpam-1372	291	14	,	,	PUNCT
ejpam-1372	291	15	which	which	PRON
ejpam-1372	291	16	is	be	AUX
ejpam-1372	291	17	identical	identical	ADJ
ejpam-1372	291	18	to	to	ADP
ejpam-1372	291	19	the	the	DET
ejpam-1372	291	20	direct	direct	ADJ
ejpam-1372	291	21	evaluation	evaluation	NOUN
ejpam-1372	291	22	of	of	ADP
ejpam-1372	291	23	the	the	DET
ejpam-1372	291	24	divergent	divergent	ADJ
ejpam-1372	291	25	integral	integral	ADJ
ejpam-1372	291	26	and	and	CCONJ
ejpam-1372	291	27	removal	removal	NOUN
ejpam-1372	291	28	of	of	ADP
ejpam-1372	291	29	the	the	DET
ejpam-1372	291	30	infinity	infinity	NOUN
ejpam-1372	291	31	or	or	CCONJ
ejpam-1372	291	32	the	the	DET
ejpam-1372	291	33	first	first	ADJ
ejpam-1372	291	34	term	term	NOUN
ejpam-1372	291	35	in	in	ADP
ejpam-1372	291	36	the	the	DET
ejpam-1372	291	37	last	last	ADJ
ejpam-1372	291	38	member	member	NOUN
ejpam-1372	291	39	of	of	ADP
ejpam-1372	291	40	eq	eq	PROPN
ejpam-1372	291	41	.	.	PUNCT
ejpam-1372	292	1	(	(	PUNCT
ejpam-1372	292	2	19	19	NUM
ejpam-1372	292	3	)	)	PUNCT
ejpam-1372	292	4	.	.	PUNCT
ejpam-1372	293	1	hence	hence	ADV
ejpam-1372	293	2	,	,	PUNCT
ejpam-1372	293	3	regularisation	regularisation	NOUN
ejpam-1372	293	4	of	of	ADP
ejpam-1372	293	5	a	a	DET
ejpam-1372	293	6	divergent	divergent	ADJ
ejpam-1372	293	7	series	series	NOUN
ejpam-1372	293	8	is	be	AUX
ejpam-1372	293	9	equivalent	equivalent	ADJ
ejpam-1372	293	10	to	to	ADP
ejpam-1372	293	11	evaluating	evaluate	VERB
ejpam-1372	293	12	the	the	DET
ejpam-1372	293	13	finite	finite	ADJ
ejpam-1372	293	14	part	part	NOUN
ejpam-1372	293	15	of	of	ADP
ejpam-1372	293	16	a	a	DET
ejpam-1372	293	17	divergent	divergent	ADJ
ejpam-1372	293	18	integral	integral	NOUN
ejpam-1372	293	19	.	.	PUNCT
ejpam-1372	294	1	in	in	ADP
ejpam-1372	294	2	ref	ref	NOUN
ejpam-1372	294	3	.	.	PUNCT
ejpam-1372	295	1	[	[	X
ejpam-1372	295	2	9	9	NUM
ejpam-1372	295	3	]	]	PUNCT
ejpam-1372	295	4	farassat	farassat	NOUN
ejpam-1372	295	5	discusses	discuss	VERB
ejpam-1372	295	6	the	the	DET
ejpam-1372	295	7	issue	issue	NOUN
ejpam-1372	295	8	of	of	ADP
ejpam-1372	295	9	whether	whether	SCONJ
ejpam-1372	295	10	the	the	DET
ejpam-1372	295	11	appearance	appearance	NOUN
ejpam-1372	295	12	of	of	ADP
ejpam-1372	295	13	divergent	divergent	ADJ
ejpam-1372	295	14	integrals	integral	NOUN
ejpam-1372	295	15	in	in	ADP
ejpam-1372	295	16	applications	application	NOUN
ejpam-1372	295	17	constitutes	constitute	VERB
ejpam-1372	295	18	a	a	DET
ejpam-1372	295	19	breakdown	breakdown	NOUN
ejpam-1372	295	20	in	in	ADP
ejpam-1372	295	21	physics	physics	NOUN
ejpam-1372	295	22	or	or	CCONJ
ejpam-1372	295	23	mathematics	mathematic	NOUN
ejpam-1372	295	24	.	.	PUNCT
ejpam-1372	296	1	he	he	PRON
ejpam-1372	296	2	concludes	conclude	VERB
ejpam-1372	296	3	that	that	SCONJ
ejpam-1372	296	4	divergent	divergent	ADJ
ejpam-1372	296	5	integrals	integral	NOUN
ejpam-1372	296	6	arise	arise	VERB
ejpam-1372	296	7	as	as	ADP
ejpam-1372	296	8	a	a	DET
ejpam-1372	296	9	result	result	NOUN
ejpam-1372	296	10	of	of	ADP
ejpam-1372	296	11	incorrect	incorrect	ADJ
ejpam-1372	296	12	mathematics	mathematic	NOUN
ejpam-1372	296	13	because	because	SCONJ
ejpam-1372	296	14	an	an	DET
ejpam-1372	296	15	ordinary	ordinary	ADJ
ejpam-1372	296	16	derivative	derivative	NOUN
ejpam-1372	296	17	has	have	AUX
ejpam-1372	296	18	been	be	AUX
ejpam-1372	296	19	wrongly	wrongly	ADV
ejpam-1372	296	20	evaluated	evaluate	VERB
ejpam-1372	296	21	inside	inside	ADP
ejpam-1372	296	22	an	an	DET
ejpam-1372	296	23	improper	improper	ADJ
ejpam-1372	296	24	integral	integral	NOUN
ejpam-1372	296	25	.	.	PUNCT
ejpam-1372	297	1	therefore	therefore	ADV
ejpam-1372	297	2	,	,	PUNCT
ejpam-1372	297	3	he	he	PRON
ejpam-1372	297	4	finds	find	VERB
ejpam-1372	297	5	regularisation	regularisation	NOUN
ejpam-1372	297	6	of	of	ADP
ejpam-1372	297	7	a	a	DET
ejpam-1372	297	8	divergent	divergent	ADJ
ejpam-1372	297	9	integral	integral	ADJ
ejpam-1372	297	10	or	or	CCONJ
ejpam-1372	297	11	taking	take	VERB
ejpam-1372	297	12	the	the	DET
ejpam-1372	297	13	finite	finite	ADJ
ejpam-1372	297	14	part	part	NOUN
ejpam-1372	297	15	as	as	ADP
ejpam-1372	297	16	a	a	DET
ejpam-1372	297	17	necessary	necessary	ADJ
ejpam-1372	297	18	corrective	corrective	ADJ
ejpam-1372	297	19	measure	measure	NOUN
ejpam-1372	297	20	.	.	PUNCT
ejpam-1372	298	1	in	in	ADP
ejpam-1372	298	2	view	view	NOUN
ejpam-1372	298	3	of	of	ADP
ejpam-1372	298	4	the	the	DET
ejpam-1372	298	5	equivalence	equivalence	NOUN
ejpam-1372	298	6	between	between	ADP
ejpam-1372	298	7	divergent	divergent	ADJ
ejpam-1372	298	8	integrals	integral	NOUN
ejpam-1372	298	9	and	and	CCONJ
ejpam-1372	298	10	divergent	divergent	ADJ
ejpam-1372	298	11	series	series	NOUN
ejpam-1372	298	12	,	,	PUNCT
ejpam-1372	298	13	the	the	DET
ejpam-1372	298	14	same	same	ADJ
ejpam-1372	298	15	can	can	AUX
ejpam-1372	298	16	be	be	AUX
ejpam-1372	298	17	said	say	VERB
ejpam-1372	298	18	of	of	ADP
ejpam-1372	298	19	divergent	divergent	ADJ
ejpam-1372	298	20	series	series	NOUN
ejpam-1372	298	21	in	in	ADP
ejpam-1372	298	22	asymptotic	asymptotic	ADJ
ejpam-1372	298	23	expansions	expansion	NOUN
ejpam-1372	298	24	.	.	PUNCT
ejpam-1372	299	1	by	by	ADP
ejpam-1372	299	2	itself	itself	PRON
ejpam-1372	299	3	,	,	PUNCT
ejpam-1372	299	4	a	a	DET
ejpam-1372	299	5	divergent	divergent	ADJ
ejpam-1372	299	6	series	series	NOUN
ejpam-1372	299	7	yields	yield	NOUN
ejpam-1372	299	8	infinity	infinity	NOUN
ejpam-1372	299	9	,	,	PUNCT
ejpam-1372	299	10	but	but	CCONJ
ejpam-1372	299	11	when	when	SCONJ
ejpam-1372	299	12	regularised	regularise	VERB
ejpam-1372	299	13	,	,	PUNCT
ejpam-1372	299	14	one	one	PRON
ejpam-1372	299	15	obtains	obtain	VERB
ejpam-1372	299	16	a	a	DET
ejpam-1372	299	17	finite	finite	ADJ
ejpam-1372	299	18	value	value	NOUN
ejpam-1372	299	19	or	or	CCONJ
ejpam-1372	299	20	part	part	NOUN
ejpam-1372	299	21	.	.	PUNCT
ejpam-1372	300	1	yet	yet	CCONJ
ejpam-1372	300	2	the	the	DET
ejpam-1372	300	3	original	original	ADJ
ejpam-1372	300	4	function	function	NOUN
ejpam-1372	300	5	from	from	ADP
ejpam-1372	300	6	which	which	PRON
ejpam-1372	300	7	an	an	DET
ejpam-1372	300	8	asymptotic	asymptotic	ADJ
ejpam-1372	300	9	series	series	NOUN
ejpam-1372	300	10	is	be	AUX
ejpam-1372	300	11	derived	derive	VERB
ejpam-1372	300	12	is	be	AUX
ejpam-1372	300	13	finite	finite	ADJ
ejpam-1372	300	14	.	.	PUNCT
ejpam-1372	301	1	therefore	therefore	ADV
ejpam-1372	301	2	,	,	PUNCT
ejpam-1372	301	3	when	when	SCONJ
ejpam-1372	301	4	an	an	DET
ejpam-1372	301	5	asymptotic	asymptotic	ADJ
ejpam-1372	301	6	method	method	NOUN
ejpam-1372	301	7	is	be	AUX
ejpam-1372	301	8	used	use	VERB
ejpam-1372	301	9	to	to	PART
ejpam-1372	301	10	obtain	obtain	VERB
ejpam-1372	301	11	a	a	DET
ejpam-1372	301	12	power	power	NOUN
ejpam-1372	301	13	series	series	NOUN
ejpam-1372	301	14	expansion	expansion	NOUN
ejpam-1372	301	15	,	,	PUNCT
ejpam-1372	301	16	an	an	DET
ejpam-1372	301	17	impropriety	impropriety	NOUN
ejpam-1372	301	18	or	or	CCONJ
ejpam-1372	301	19	flaw	flaw	NOUN
ejpam-1372	301	20	associated	associate	VERB
ejpam-1372	301	21	with	with	ADP
ejpam-1372	301	22	the	the	DET
ejpam-1372	301	23	method	method	NOUN
ejpam-1372	301	24	has	have	AUX
ejpam-1372	301	25	been	be	AUX
ejpam-1372	301	26	invoked	invoke	VERB
ejpam-1372	301	27	.	.	PUNCT
ejpam-1372	302	1	the	the	DET
ejpam-1372	302	2	derivation	derivation	NOUN
ejpam-1372	302	3	of	of	ADP
ejpam-1372	302	4	asymptotic	asymptotic	ADJ
ejpam-1372	302	5	expansions	expansion	NOUN
ejpam-1372	302	6	from	from	ADP
ejpam-1372	302	7	integral	integral	ADJ
ejpam-1372	302	8	representations	representation	NOUN
ejpam-1372	302	9	,	,	PUNCT
ejpam-1372	302	10	e.g.	e.g.	ADV
ejpam-1372	302	11	by	by	ADP
ejpam-1372	302	12	laplace	laplace	NOUN
ejpam-1372	302	13	’s	’s	PART
ejpam-1372	302	14	method	method	NOUN
ejpam-1372	302	15	or	or	CCONJ
ejpam-1372	302	16	the	the	DET
ejpam-1372	302	17	method	method	NOUN
ejpam-1372	302	18	of	of	ADP
ejpam-1372	302	19	steepest	steep	ADJ
ejpam-1372	302	20	descent	descent	NOUN
ejpam-1372	302	21	,	,	PUNCT
ejpam-1372	302	22	invariably	invariably	ADV
ejpam-1372	302	23	involves	involve	VERB
ejpam-1372	302	24	integrating	integrate	VERB
ejpam-1372	302	25	over	over	ADP
ejpam-1372	302	26	a	a	DET
ejpam-1372	302	27	range	range	NOUN
ejpam-1372	302	28	that	that	PRON
ejpam-1372	302	29	is	be	AUX
ejpam-1372	302	30	outside	outside	ADP
ejpam-1372	302	31	the	the	DET
ejpam-1372	302	32	circle	circle	NOUN
ejpam-1372	302	33	or	or	CCONJ
ejpam-1372	302	34	disk	disk	NOUN
ejpam-1372	302	35	of	of	ADP
ejpam-1372	302	36	absolute	absolute	ADJ
ejpam-1372	302	37	convergence	convergence	NOUN
ejpam-1372	302	38	of	of	ADP
ejpam-1372	302	39	the	the	DET
ejpam-1372	302	40	expanded	expand	VERB
ejpam-1372	302	41	function	function	NOUN
ejpam-1372	302	42	.	.	PUNCT
ejpam-1372	303	1	the	the	DET
ejpam-1372	303	2	derivation	derivation	NOUN
ejpam-1372	303	3	of	of	ADP
ejpam-1372	303	4	an	an	DET
ejpam-1372	303	5	asymptotic	asymptotic	ADJ
ejpam-1372	303	6	series	series	NOUN
ejpam-1372	303	7	by	by	ADP
ejpam-1372	303	8	applying	apply	VERB
ejpam-1372	303	9	the	the	DET
ejpam-1372	303	10	iterative	iterative	NOUN
ejpam-1372	303	11	method	method	NOUN
ejpam-1372	303	12	to	to	PART
ejpam-1372	303	13	differential	differential	VERB
ejpam-1372	303	14	equations	equation	NOUN
ejpam-1372	303	15	also	also	ADV
ejpam-1372	303	16	involves	involve	VERB
ejpam-1372	303	17	introducing	introduce	VERB
ejpam-1372	303	18	an	an	DET
ejpam-1372	303	19	infinity	infinity	NOUN
ejpam-1372	303	20	as	as	SCONJ
ejpam-1372	303	21	is	be	AUX
ejpam-1372	303	22	explained	explain	VERB
ejpam-1372	303	23	in	in	ADP
ejpam-1372	303	24	ch	ch	PROPN
ejpam-1372	303	25	.	.	PROPN
ejpam-1372	303	26	2	2	NUM
ejpam-1372	303	27	of	of	ADP
ejpam-1372	303	28	ref	ref	NOUN
ejpam-1372	303	29	.	.	PUNCT
ejpam-1372	304	1	[	[	X
ejpam-1372	304	2	17	17	NUM
ejpam-1372	304	3	]	]	PUNCT
ejpam-1372	304	4	.	.	PUNCT
ejpam-1372	305	1	therefore	therefore	ADV
ejpam-1372	305	2	,	,	PUNCT
ejpam-1372	305	3	it	it	PRON
ejpam-1372	305	4	is	be	AUX
ejpam-1372	305	5	to	to	PART
ejpam-1372	305	6	be	be	AUX
ejpam-1372	305	7	expected	expect	VERB
ejpam-1372	305	8	that	that	SCONJ
ejpam-1372	305	9	series	series	NOUN
ejpam-1372	305	10	,	,	PUNCT
ejpam-1372	305	11	which	which	PRON
ejpam-1372	305	12	are	be	AUX
ejpam-1372	305	13	either	either	CCONJ
ejpam-1372	305	14	divergent	divergent	ADJ
ejpam-1372	305	15	or	or	CCONJ
ejpam-1372	305	16	conditionally	conditionally	ADV
ejpam-1372	305	17	convergent	convergent	ADJ
ejpam-1372	305	18	outside	outside	ADP
ejpam-1372	305	19	the	the	DET
ejpam-1372	305	20	radius	radius	NOUN
ejpam-1372	305	21	of	of	ADP
ejpam-1372	305	22	absolute	absolute	ADJ
ejpam-1372	305	23	v.	v.	ADP
ejpam-1372	305	24	kowalenko	kowalenko	PROPN
ejpam-1372	305	25	/	/	SYM
ejpam-1372	305	26	eur	eur	PROPN
ejpam-1372	305	27	.	.	PUNCT
ejpam-1372	306	1	j.	j.	PROPN
ejpam-1372	306	2	pure	pure	PROPN
ejpam-1372	306	3	appl	appl	PROPN
ejpam-1372	306	4	.	.	PROPN
ejpam-1372	306	5	math	math	PROPN
ejpam-1372	306	6	,	,	PUNCT
ejpam-1372	306	7	4	4	NUM
ejpam-1372	306	8	(	(	PUNCT
ejpam-1372	306	9	2011	2011	NUM
ejpam-1372	306	10	)	)	PUNCT
ejpam-1372	306	11	,	,	PUNCT
ejpam-1372	306	12	370	370	NUM
ejpam-1372	306	13	-	-	SYM
ejpam-1372	306	14	423	423	NUM
ejpam-1372	306	15	380	380	NUM
ejpam-1372	306	16	convergence	convergence	NOUN
ejpam-1372	306	17	will	will	AUX
ejpam-1372	306	18	possess	possess	VERB
ejpam-1372	306	19	vastly	vastly	ADV
ejpam-1372	306	20	different	different	ADJ
ejpam-1372	306	21	properties	property	NOUN
ejpam-1372	306	22	than	than	ADP
ejpam-1372	306	23	within	within	ADP
ejpam-1372	306	24	the	the	DET
ejpam-1372	306	25	radius	radius	NOUN
ejpam-1372	306	26	of	of	ADP
ejpam-1372	306	27	absolute	absolute	ADJ
ejpam-1372	306	28	convergence	convergence	NOUN
ejpam-1372	306	29	.	.	PUNCT
ejpam-1372	307	1	moreover	moreover	ADV
ejpam-1372	307	2	,	,	PUNCT
ejpam-1372	307	3	whilst	whilst	SCONJ
ejpam-1372	307	4	regularisation	regularisation	NOUN
ejpam-1372	307	5	has	have	AUX
ejpam-1372	307	6	been	be	AUX
ejpam-1372	307	7	presented	present	VERB
ejpam-1372	307	8	as	as	ADP
ejpam-1372	307	9	a	a	DET
ejpam-1372	307	10	mathematical	mathematical	ADJ
ejpam-1372	307	11	abstraction	abstraction	NOUN
ejpam-1372	307	12	for	for	ADP
ejpam-1372	307	13	obtaining	obtain	VERB
ejpam-1372	307	14	the	the	DET
ejpam-1372	307	15	finite	finite	ADJ
ejpam-1372	307	16	value	value	NOUN
ejpam-1372	307	17	of	of	ADP
ejpam-1372	307	18	a	a	DET
ejpam-1372	307	19	divergent	divergent	ADJ
ejpam-1372	307	20	series	series	NOUN
ejpam-1372	307	21	so	so	ADV
ejpam-1372	307	22	far	far	ADV
ejpam-1372	307	23	,	,	PUNCT
ejpam-1372	307	24	it	it	PRON
ejpam-1372	307	25	is	be	AUX
ejpam-1372	307	26	required	require	VERB
ejpam-1372	307	27	in	in	ADP
ejpam-1372	307	28	asymptotics	asymptotic	NOUN
ejpam-1372	307	29	for	for	ADP
ejpam-1372	307	30	correcting	correct	VERB
ejpam-1372	307	31	the	the	DET
ejpam-1372	307	32	impropriety	impropriety	NOUN
ejpam-1372	307	33	of	of	ADP
ejpam-1372	307	34	the	the	DET
ejpam-1372	307	35	method	method	NOUN
ejpam-1372	307	36	used	use	VERB
ejpam-1372	307	37	to	to	PART
ejpam-1372	307	38	obtain	obtain	VERB
ejpam-1372	307	39	the	the	DET
ejpam-1372	307	40	expansion	expansion	NOUN
ejpam-1372	307	41	from	from	ADP
ejpam-1372	307	42	the	the	DET
ejpam-1372	307	43	original	original	ADJ
ejpam-1372	307	44	function	function	NOUN
ejpam-1372	307	45	.	.	PUNCT
ejpam-1372	308	1	with	with	ADP
ejpam-1372	308	2	regard	regard	NOUN
ejpam-1372	308	3	to	to	ADP
ejpam-1372	308	4	the	the	DET
ejpam-1372	308	5	issue	issue	NOUN
ejpam-1372	308	6	of	of	ADP
ejpam-1372	308	7	whether	whether	SCONJ
ejpam-1372	308	8	the	the	DET
ejpam-1372	308	9	appearance	appearance	NOUN
ejpam-1372	308	10	of	of	ADP
ejpam-1372	308	11	divergent	divergent	ADJ
ejpam-1372	308	12	integrals	integral	NOUN
ejpam-1372	308	13	and	and	CCONJ
ejpam-1372	308	14	series	series	NOUN
ejpam-1372	308	15	in	in	ADP
ejpam-1372	308	16	applications	application	NOUN
ejpam-1372	308	17	constitutes	constitute	VERB
ejpam-1372	308	18	a	a	DET
ejpam-1372	308	19	breakdown	breakdown	NOUN
ejpam-1372	308	20	in	in	ADP
ejpam-1372	308	21	physics	physics	NOUN
ejpam-1372	308	22	or	or	CCONJ
ejpam-1372	308	23	mathematics	mathematic	NOUN
ejpam-1372	308	24	,	,	PUNCT
ejpam-1372	308	25	it	it	PRON
ejpam-1372	308	26	is	be	AUX
ejpam-1372	308	27	more	more	ADJ
ejpam-1372	308	28	than	than	ADP
ejpam-1372	308	29	likely	likely	ADJ
ejpam-1372	308	30	to	to	PART
ejpam-1372	308	31	be	be	AUX
ejpam-1372	308	32	a	a	DET
ejpam-1372	308	33	combination	combination	NOUN
ejpam-1372	308	34	of	of	ADP
ejpam-1372	308	35	both	both	PRON
ejpam-1372	308	36	when	when	SCONJ
ejpam-1372	308	37	dealing	deal	VERB
ejpam-1372	308	38	with	with	ADP
ejpam-1372	308	39	the	the	DET
ejpam-1372	308	40	very	very	ADV
ejpam-1372	308	41	small	small	ADJ
ejpam-1372	308	42	such	such	ADJ
ejpam-1372	308	43	as	as	ADP
ejpam-1372	308	44	the	the	DET
ejpam-1372	308	45	planck	planck	NOUN
ejpam-1372	308	46	scale	scale	NOUN
ejpam-1372	308	47	in	in	ADP
ejpam-1372	308	48	particle	particle	NOUN
ejpam-1372	308	49	physics	physics	NOUN
ejpam-1372	308	50	and	and	CCONJ
ejpam-1372	308	51	physical	physical	ADJ
ejpam-1372	308	52	cosmology	cosmology	NOUN
ejpam-1372	308	53	.	.	PUNCT
ejpam-1372	309	1	however	however	ADV
ejpam-1372	309	2	,	,	PUNCT
ejpam-1372	309	3	before	before	SCONJ
ejpam-1372	309	4	the	the	DET
ejpam-1372	309	5	physical	physical	ADJ
ejpam-1372	309	6	issues	issue	NOUN
ejpam-1372	309	7	can	can	AUX
ejpam-1372	309	8	be	be	AUX
ejpam-1372	309	9	tackled	tackle	VERB
ejpam-1372	309	10	,	,	PUNCT
ejpam-1372	309	11	the	the	DET
ejpam-1372	309	12	mathematics	mathematic	NOUN
ejpam-1372	309	13	needs	need	VERB
ejpam-1372	309	14	to	to	PART
ejpam-1372	309	15	be	be	AUX
ejpam-1372	309	16	corrected	correct	VERB
ejpam-1372	309	17	first	first	ADV
ejpam-1372	309	18	.	.	PUNCT
ejpam-1372	310	1	at	at	ADP
ejpam-1372	310	2	the	the	DET
ejpam-1372	310	3	moment	moment	NOUN
ejpam-1372	310	4	it	it	PRON
ejpam-1372	310	5	appears	appear	VERB
ejpam-1372	310	6	that	that	SCONJ
ejpam-1372	310	7	the	the	DET
ejpam-1372	310	8	wrong	wrong	ADJ
ejpam-1372	310	9	sort	sort	NOUN
ejpam-1372	310	10	of	of	ADP
ejpam-1372	310	11	mathematics	mathematic	NOUN
ejpam-1372	310	12	is	be	AUX
ejpam-1372	310	13	being	be	AUX
ejpam-1372	310	14	employed	employ	VERB
ejpam-1372	310	15	,	,	PUNCT
ejpam-1372	310	16	which	which	PRON
ejpam-1372	310	17	has	have	AUX
ejpam-1372	310	18	resulted	result	VERB
ejpam-1372	310	19	in	in	ADP
ejpam-1372	310	20	the	the	DET
ejpam-1372	310	21	rather	rather	ADV
ejpam-1372	310	22	bizarre	bizarre	ADJ
ejpam-1372	310	23	predictions	prediction	NOUN
ejpam-1372	310	24	being	be	AUX
ejpam-1372	310	25	made	make	VERB
ejpam-1372	310	26	by	by	ADP
ejpam-1372	310	27	eminent	eminent	ADJ
ejpam-1372	310	28	cosmologists	cosmologist	NOUN
ejpam-1372	310	29	and	and	CCONJ
ejpam-1372	310	30	particle	particle	NOUN
ejpam-1372	310	31	theorists	theorist	NOUN
ejpam-1372	310	32	today	today	NOUN
ejpam-1372	310	33	.	.	PUNCT
ejpam-1372	311	1	we	we	PRON
ejpam-1372	311	2	shall	shall	AUX
ejpam-1372	311	3	consider	consider	VERB
ejpam-1372	311	4	the	the	DET
ejpam-1372	311	5	physicist	physicist	NOUN
ejpam-1372	311	6	’s	’s	PART
ejpam-1372	311	7	approach	approach	NOUN
ejpam-1372	311	8	to	to	ADP
ejpam-1372	311	9	renormalisation	renormalisation	NOUN
ejpam-1372	311	10	and	and	CCONJ
ejpam-1372	311	11	compare	compare	VERB
ejpam-1372	311	12	it	it	PRON
ejpam-1372	311	13	with	with	ADP
ejpam-1372	311	14	the	the	DET
ejpam-1372	311	15	mathematical	mathematical	ADJ
ejpam-1372	311	16	concept	concept	NOUN
ejpam-1372	311	17	of	of	ADP
ejpam-1372	311	18	regularisation	regularisation	NOUN
ejpam-1372	311	19	in	in	ADP
ejpam-1372	311	20	a	a	DET
ejpam-1372	311	21	later	later	ADJ
ejpam-1372	311	22	section	section	NOUN
ejpam-1372	311	23	.	.	PUNCT
ejpam-1372	312	1	5	5	X
ejpam-1372	312	2	.	.	X
ejpam-1372	312	3	grandi	grandi	PROPN
ejpam-1372	312	4	’s	’s	PART
ejpam-1372	312	5	series	series	NOUN
ejpam-1372	312	6	revisited	revisit	VERB
ejpam-1372	312	7	let	let	VERB
ejpam-1372	312	8	us	we	PRON
ejpam-1372	312	9	now	now	ADV
ejpam-1372	312	10	return	return	VERB
ejpam-1372	312	11	to	to	ADP
ejpam-1372	312	12	grandi	grandi	PROPN
ejpam-1372	312	13	’s	’s	PART
ejpam-1372	312	14	series	series	NOUN
ejpam-1372	312	15	,	,	PUNCT
ejpam-1372	312	16	which	which	PRON
ejpam-1372	312	17	is	be	AUX
ejpam-1372	312	18	obtained	obtain	VERB
ejpam-1372	312	19	by	by	ADP
ejpam-1372	312	20	putting	put	VERB
ejpam-1372	312	21	z	z	NOUN
ejpam-1372	312	22	equal	equal	ADJ
ejpam-1372	312	23	to	to	ADP
ejpam-1372	312	24	-1	-1	VERB
ejpam-1372	312	25	in	in	ADP
ejpam-1372	312	26	the	the	DET
ejpam-1372	312	27	geometric	geometric	ADJ
ejpam-1372	312	28	series	series	NOUN
ejpam-1372	312	29	.	.	PUNCT
ejpam-1372	313	1	from	from	ADP
ejpam-1372	313	2	our	our	PRON
ejpam-1372	313	3	study	study	NOUN
ejpam-1372	313	4	of	of	ADP
ejpam-1372	313	5	the	the	DET
ejpam-1372	313	6	geometric	geometric	ADJ
ejpam-1372	313	7	series	series	NOUN
ejpam-1372	313	8	in	in	ADP
ejpam-1372	313	9	the	the	DET
ejpam-1372	313	10	previous	previous	ADJ
ejpam-1372	313	11	section	section	NOUN
ejpam-1372	313	12	we	we	PRON
ejpam-1372	313	13	know	know	VERB
ejpam-1372	313	14	that	that	SCONJ
ejpam-1372	313	15	grandi	grandi	PROPN
ejpam-1372	313	16	’s	’s	PART
ejpam-1372	313	17	series	series	NOUN
ejpam-1372	313	18	is	be	AUX
ejpam-1372	313	19	conditionally	conditionally	ADV
ejpam-1372	313	20	convergent	convergent	ADJ
ejpam-1372	313	21	,	,	PUNCT
ejpam-1372	313	22	and	and	CCONJ
ejpam-1372	313	23	not	not	PART
ejpam-1372	313	24	divergent	divergent	ADJ
ejpam-1372	313	25	according	accord	VERB
ejpam-1372	313	26	to	to	ADP
ejpam-1372	313	27	copson	copson	PROPN
ejpam-1372	313	28	’s	’s	PART
ejpam-1372	313	29	definition	definition	NOUN
ejpam-1372	313	30	.	.	PUNCT
ejpam-1372	314	1	hence	hence	ADV
ejpam-1372	314	2	,	,	PUNCT
ejpam-1372	314	3	the	the	DET
ejpam-1372	314	4	limit	limit	NOUN
ejpam-1372	314	5	of	of	ADP
ejpam-1372	314	6	the	the	DET
ejpam-1372	314	7	series	series	NOUN
ejpam-1372	314	8	is	be	AUX
ejpam-1372	314	9	simply	simply	ADV
ejpam-1372	314	10	1/(1-(-1	1/(1-(-1	NUM
ejpam-1372	314	11	)	)	PUNCT
ejpam-1372	314	12	)	)	PUNCT
ejpam-1372	314	13	or	or	CCONJ
ejpam-1372	314	14	1/2	1/2	NUM
ejpam-1372	314	15	,	,	PUNCT
ejpam-1372	314	16	a	a	DET
ejpam-1372	314	17	result	result	NOUN
ejpam-1372	314	18	which	which	PRON
ejpam-1372	314	19	is	be	AUX
ejpam-1372	314	20	entirely	entirely	ADV
ejpam-1372	314	21	consistent	consistent	ADJ
ejpam-1372	314	22	with	with	ADP
ejpam-1372	314	23	leibniz	leibniz	PROPN
ejpam-1372	314	24	’s	’s	PART
ejpam-1372	314	25	law	law	NOUN
ejpam-1372	314	26	of	of	ADP
ejpam-1372	314	27	justice	justice	NOUN
ejpam-1372	314	28	.	.	PUNCT
ejpam-1372	315	1	if	if	SCONJ
ejpam-1372	315	2	it	it	PRON
ejpam-1372	315	3	is	be	AUX
ejpam-1372	315	4	not	not	PART
ejpam-1372	315	5	divergent	divergent	ADJ
ejpam-1372	315	6	,	,	PUNCT
ejpam-1372	315	7	then	then	ADV
ejpam-1372	315	8	how	how	SCONJ
ejpam-1372	315	9	can	can	AUX
ejpam-1372	315	10	the	the	DET
ejpam-1372	315	11	introduction	introduction	NOUN
ejpam-1372	315	12	of	of	ADP
ejpam-1372	315	13	an	an	DET
ejpam-1372	315	14	infinite	infinite	ADJ
ejpam-1372	315	15	number	number	NOUN
ejpam-1372	315	16	of	of	ADP
ejpam-1372	315	17	zeros	zero	NOUN
ejpam-1372	315	18	affect	affect	VERB
ejpam-1372	315	19	the	the	DET
ejpam-1372	315	20	limit	limit	NOUN
ejpam-1372	315	21	as	as	SCONJ
ejpam-1372	315	22	bernoulli	bernoulli	PROPN
ejpam-1372	315	23	found	find	VERB
ejpam-1372	315	24	?	?	PUNCT
ejpam-1372	316	1	before	before	SCONJ
ejpam-1372	316	2	we	we	PRON
ejpam-1372	316	3	can	can	AUX
ejpam-1372	316	4	consider	consider	VERB
ejpam-1372	316	5	this	this	DET
ejpam-1372	316	6	question	question	NOUN
ejpam-1372	316	7	,	,	PUNCT
ejpam-1372	316	8	we	we	PRON
ejpam-1372	316	9	need	need	VERB
ejpam-1372	316	10	to	to	PART
ejpam-1372	316	11	examine	examine	VERB
ejpam-1372	316	12	what	what	PRON
ejpam-1372	316	13	happens	happen	VERB
ejpam-1372	316	14	when	when	SCONJ
ejpam-1372	316	15	an	an	DET
ejpam-1372	316	16	infinite	infinite	ADJ
ejpam-1372	316	17	number	number	NOUN
ejpam-1372	316	18	of	of	ADP
ejpam-1372	316	19	zeros	zero	NOUN
ejpam-1372	316	20	is	be	AUX
ejpam-1372	316	21	introduced	introduce	VERB
ejpam-1372	316	22	into	into	ADP
ejpam-1372	316	23	an	an	DET
ejpam-1372	316	24	absolutely	absolutely	ADV
ejpam-1372	316	25	convergent	convergent	ADJ
ejpam-1372	316	26	series	series	NOUN
ejpam-1372	316	27	.	.	PUNCT
ejpam-1372	317	1	therefore	therefore	ADV
ejpam-1372	317	2	,	,	PUNCT
ejpam-1372	317	3	we	we	PRON
ejpam-1372	317	4	write	write	VERB
ejpam-1372	317	5	the	the	DET
ejpam-1372	317	6	geometric	geometric	ADJ
ejpam-1372	317	7	series	series	NOUN
ejpam-1372	317	8	as	as	ADP
ejpam-1372	317	9	s(z	s(z	PROPN
ejpam-1372	317	10	)	)	PUNCT
ejpam-1372	317	11	=	=	PUNCT
ejpam-1372	318	1	1	1	NUM
ejpam-1372	318	2	+	+	NUM
ejpam-1372	318	3	0	0	NUM
ejpam-1372	318	4	+	+	NUM
ejpam-1372	318	5	z	z	NOUN
ejpam-1372	318	6	+	+	NOUN
ejpam-1372	318	7	0	0	NUM
ejpam-1372	318	8	+	+	NOUN
ejpam-1372	318	9	z2	z2	NOUN
ejpam-1372	318	10	+	+	CCONJ
ejpam-1372	318	11	0	0	NUM
ejpam-1372	318	12	+	+	NUM
ejpam-1372	318	13	z3	z3	NOUN
ejpam-1372	318	14	+	+	CCONJ
ejpam-1372	318	15	0	0	NUM
ejpam-1372	318	16	+	+	NUM
ejpam-1372	318	17	z4	z4	PROPN
ejpam-1372	318	18	+	+	CCONJ
ejpam-1372	318	19	0	0	NUM
ejpam-1372	318	20	+	+	NUM
ejpam-1372	318	21	.	.	PUNCT
ejpam-1372	318	22	.	.	PUNCT
ejpam-1372	318	23	.	.	PUNCT
ejpam-1372	318	24	.	.	PUNCT
ejpam-1372	319	1	(	(	PUNCT
ejpam-1372	319	2	22	22	NUM
ejpam-1372	319	3	)	)	PUNCT
ejpam-1372	319	4	since	since	SCONJ
ejpam-1372	319	5	every	every	DET
ejpam-1372	319	6	second	second	ADJ
ejpam-1372	319	7	element	element	NOUN
ejpam-1372	319	8	is	be	AUX
ejpam-1372	319	9	zero	zero	NUM
ejpam-1372	319	10	,	,	PUNCT
ejpam-1372	319	11	we	we	PRON
ejpam-1372	319	12	can	can	AUX
ejpam-1372	319	13	express	express	VERB
ejpam-1372	319	14	s(z	s(z	NOUN
ejpam-1372	319	15	)	)	PUNCT
ejpam-1372	319	16	alternatively	alternatively	ADV
ejpam-1372	319	17	as	as	ADP
ejpam-1372	319	18	s(z	s(z	PROPN
ejpam-1372	319	19	)	)	PUNCT
ejpam-1372	319	20	=	=	SYM
ejpam-1372	320	1	∞	∞	NUM
ejpam-1372	320	2	∑	∑	PUNCT
ejpam-1372	320	3	k=1	k=1	PROPN
ejpam-1372	320	4	�	�	PROPN
ejpam-1372	320	5	1−	1−	NUM
ejpam-1372	320	6	(	(	PUNCT
ejpam-1372	320	7	−1)k	−1)k	PROPN
ejpam-1372	320	8	2	2	NUM
ejpam-1372	320	9	�	�	PROPN
ejpam-1372	320	10	z(k−1)/2	z(k−1)/2	PROPN
ejpam-1372	320	11	+	+	CCONJ
ejpam-1372	320	12	∞	∞	PROPN
ejpam-1372	320	13	∑	∑	PROPN
ejpam-1372	320	14	k=2	k=2	PROPN
ejpam-1372	320	15	�	�	PROPN
ejpam-1372	320	16	1	1	NUM
ejpam-1372	320	17	+	+	CCONJ
ejpam-1372	320	18	(	(	PUNCT
ejpam-1372	320	19	−1)k	−1)k	NOUN
ejpam-1372	320	20	)	)	PUNCT
ejpam-1372	320	21	2	2	NUM
ejpam-1372	320	22	�	�	NOUN
ejpam-1372	320	23	0k	0k	NOUN
ejpam-1372	320	24	.	.	PUNCT
ejpam-1372	321	1	(	(	PUNCT
ejpam-1372	321	2	23	23	NUM
ejpam-1372	321	3	)	)	PUNCT
ejpam-1372	321	4	the	the	DET
ejpam-1372	321	5	above	above	ADJ
ejpam-1372	321	6	result	result	NOUN
ejpam-1372	321	7	represents	represent	VERB
ejpam-1372	321	8	the	the	DET
ejpam-1372	321	9	sum	sum	NOUN
ejpam-1372	321	10	of	of	ADP
ejpam-1372	321	11	four	four	NUM
ejpam-1372	321	12	separate	separate	ADJ
ejpam-1372	321	13	series	series	NOUN
ejpam-1372	321	14	.	.	PUNCT
ejpam-1372	322	1	hence	hence	ADV
ejpam-1372	322	2	,	,	PUNCT
ejpam-1372	322	3	separating	separate	VERB
ejpam-1372	322	4	each	each	DET
ejpam-1372	322	5	series	series	NOUN
ejpam-1372	322	6	we	we	PRON
ejpam-1372	322	7	obtain	obtain	VERB
ejpam-1372	322	8	s(z	s(z	PROPN
ejpam-1372	322	9	)	)	PUNCT
ejpam-1372	322	10	=	=	SYM
ejpam-1372	322	11	1	1	NUM
ejpam-1372	322	12	2	2	NUM
ejpam-1372	322	13	p	p	NOUN
ejpam-1372	322	14	z	z	NOUN
ejpam-1372	322	15	∞	∞	NUM
ejpam-1372	322	16	∑	∑	PUNCT
ejpam-1372	322	17	k=1	k=1	PROPN
ejpam-1372	322	18	zk/2	zk/2	VERB
ejpam-1372	322	19	−	−	PROPN
ejpam-1372	322	20	1	1	NUM
ejpam-1372	322	21	2	2	NUM
ejpam-1372	322	22	p	p	NOUN
ejpam-1372	322	23	z	z	NOUN
ejpam-1372	322	24	∞	∞	PROPN
ejpam-1372	322	25	∑	∑	PUNCT
ejpam-1372	322	26	k=1	k=1	X
ejpam-1372	322	27	(	(	PUNCT
ejpam-1372	322	28	−1)kzk/2	−1)kzk/2	X
ejpam-1372	322	29	+	+	CCONJ
ejpam-1372	322	30	1	1	NUM
ejpam-1372	322	31	2	2	NUM
ejpam-1372	322	32	∞	∞	NUM
ejpam-1372	322	33	∑	∑	PROPN
ejpam-1372	322	34	k=2	k=2	PROPN
ejpam-1372	322	35	0k	0k	NOUN
ejpam-1372	322	36	−	−	NOUN
ejpam-1372	322	37	1	1	NUM
ejpam-1372	322	38	2	2	NUM
ejpam-1372	322	39	∞	∞	NUM
ejpam-1372	322	40	∑	∑	PROPN
ejpam-1372	322	41	k=2	k=2	PROPN
ejpam-1372	322	42	(	(	PUNCT
ejpam-1372	322	43	−0)k	−0)k	X
ejpam-1372	322	44	.	.	PUNCT
ejpam-1372	323	1	(	(	PUNCT
ejpam-1372	323	2	24	24	NUM
ejpam-1372	323	3	)	)	PUNCT
ejpam-1372	323	4	the	the	DET
ejpam-1372	323	5	last	last	ADJ
ejpam-1372	323	6	two	two	NUM
ejpam-1372	323	7	terms	term	NOUN
ejpam-1372	323	8	in	in	ADP
ejpam-1372	323	9	eq	eq	ADP
ejpam-1372	323	10	.	.	PUNCT
ejpam-1372	324	1	(	(	PUNCT
ejpam-1372	324	2	24	24	NUM
ejpam-1372	324	3	)	)	PUNCT
ejpam-1372	324	4	vanish	vanish	VERB
ejpam-1372	324	5	according	accord	VERB
ejpam-1372	324	6	to	to	ADP
ejpam-1372	324	7	equivalence	equivalence	NOUN
ejpam-1372	324	8	(	(	PUNCT
ejpam-1372	324	9	13	13	NUM
ejpam-1372	324	10	)	)	PUNCT
ejpam-1372	324	11	,	,	PUNCT
ejpam-1372	324	12	which	which	PRON
ejpam-1372	324	13	now	now	ADV
ejpam-1372	324	14	becomes	become	VERB
ejpam-1372	324	15	an	an	DET
ejpam-1372	324	16	equation	equation	NOUN
ejpam-1372	324	17	since	since	SCONJ
ejpam-1372	324	18	z=	z=	PROPN
ejpam-1372	324	19	0	0	NUM
ejpam-1372	324	20	.	.	PUNCT
ejpam-1372	325	1	that	that	PRON
ejpam-1372	325	2	is	be	AUX
ejpam-1372	325	3	,	,	PUNCT
ejpam-1372	325	4	the	the	DET
ejpam-1372	325	5	equivalence	equivalence	NOUN
ejpam-1372	325	6	symbol	symbol	NOUN
ejpam-1372	325	7	can	can	AUX
ejpam-1372	325	8	be	be	AUX
ejpam-1372	325	9	replaced	replace	VERB
ejpam-1372	325	10	by	by	ADP
ejpam-1372	325	11	an	an	DET
ejpam-1372	325	12	equals	equal	NOUN
ejpam-1372	325	13	sign	sign	NOUN
ejpam-1372	325	14	.	.	PUNCT
ejpam-1372	326	1	furthermore	furthermore	ADV
ejpam-1372	326	2	,	,	PUNCT
ejpam-1372	326	3	for	for	ADP
ejpam-1372	326	4	|z|<1	|z|<1	PROPN
ejpam-1372	326	5	the	the	DET
ejpam-1372	326	6	first	first	ADJ
ejpam-1372	326	7	two	two	NUM
ejpam-1372	326	8	series	series	NOUN
ejpam-1372	326	9	can	can	AUX
ejpam-1372	326	10	be	be	AUX
ejpam-1372	326	11	evaluated	evaluate	VERB
ejpam-1372	326	12	with	with	ADP
ejpam-1372	326	13	the	the	DET
ejpam-1372	326	14	equation	equation	NOUN
ejpam-1372	326	15	form	form	NOUN
ejpam-1372	326	16	of	of	ADP
ejpam-1372	326	17	equivalence	equivalence	NOUN
ejpam-1372	326	18	(	(	PUNCT
ejpam-1372	326	19	13	13	NUM
ejpam-1372	326	20	)	)	PUNCT
ejpam-1372	326	21	.	.	PUNCT
ejpam-1372	327	1	then	then	ADV
ejpam-1372	327	2	we	we	PRON
ejpam-1372	327	3	find	find	VERB
ejpam-1372	327	4	that	that	SCONJ
ejpam-1372	327	5	s(z	s(z	NOUN
ejpam-1372	327	6	)	)	PUNCT
ejpam-1372	327	7	=	=	SYM
ejpam-1372	327	8	1	1	NUM
ejpam-1372	327	9	2	2	NUM
ejpam-1372	327	10	p	p	NOUN
ejpam-1372	327	11	z	z	NOUN
ejpam-1372	327	12	p	p	NOUN
ejpam-1372	327	13	z	z	NOUN
ejpam-1372	327	14	1−pz	1−pz	NUM
ejpam-1372	327	15	−	−	NUM
ejpam-1372	327	16	1	1	NUM
ejpam-1372	327	17	2	2	NUM
ejpam-1372	327	18	p	p	PROPN
ejpam-1372	327	19	z	z	PROPN
ejpam-1372	327	20	�	�	PROPN
ejpam-1372	327	21	−pz	−pz	PROPN
ejpam-1372	327	22	�	�	PROPN
ejpam-1372	327	23	1	1	NUM
ejpam-1372	327	24	+	+	PROPN
ejpam-1372	327	25	p	p	NOUN
ejpam-1372	327	26	z	z	NOUN
ejpam-1372	327	27	=	=	SYM
ejpam-1372	327	28	1	1	NUM
ejpam-1372	327	29	1−	1−	NUM
ejpam-1372	327	30	z	z	NOUN
ejpam-1372	327	31	.	.	PUNCT
ejpam-1372	328	1	(	(	PUNCT
ejpam-1372	328	2	25	25	NUM
ejpam-1372	328	3	)	)	PUNCT
ejpam-1372	328	4	v.	v.	ADP
ejpam-1372	328	5	kowalenko	kowalenko	PROPN
ejpam-1372	328	6	/	/	SYM
ejpam-1372	328	7	eur	eur	PROPN
ejpam-1372	328	8	.	.	PUNCT
ejpam-1372	329	1	j.	j.	PROPN
ejpam-1372	329	2	pure	pure	PROPN
ejpam-1372	329	3	appl	appl	PROPN
ejpam-1372	329	4	.	.	PROPN
ejpam-1372	329	5	math	math	PROPN
ejpam-1372	329	6	,	,	PUNCT
ejpam-1372	329	7	4	4	NUM
ejpam-1372	329	8	(	(	PUNCT
ejpam-1372	329	9	2011	2011	NUM
ejpam-1372	329	10	)	)	PUNCT
ejpam-1372	329	11	,	,	PUNCT
ejpam-1372	329	12	370	370	NUM
ejpam-1372	329	13	-	-	SYM
ejpam-1372	329	14	423	423	NUM
ejpam-1372	329	15	381	381	NUM
ejpam-1372	329	16	hence	hence	ADV
ejpam-1372	329	17	,	,	PUNCT
ejpam-1372	329	18	we	we	PRON
ejpam-1372	329	19	see	see	VERB
ejpam-1372	329	20	that	that	SCONJ
ejpam-1372	329	21	the	the	DET
ejpam-1372	329	22	introduction	introduction	NOUN
ejpam-1372	329	23	of	of	ADP
ejpam-1372	329	24	an	an	DET
ejpam-1372	329	25	infinite	infinite	ADJ
ejpam-1372	329	26	number	number	NOUN
ejpam-1372	329	27	of	of	ADP
ejpam-1372	329	28	zeros	zero	NOUN
ejpam-1372	329	29	into	into	ADP
ejpam-1372	329	30	the	the	DET
ejpam-1372	329	31	geometric	geometric	ADJ
ejpam-1372	329	32	series	series	NOUN
ejpam-1372	329	33	has	have	VERB
ejpam-1372	329	34	no	no	DET
ejpam-1372	329	35	effect	effect	NOUN
ejpam-1372	329	36	on	on	ADP
ejpam-1372	329	37	its	its	PRON
ejpam-1372	329	38	limit	limit	NOUN
ejpam-1372	329	39	when	when	SCONJ
ejpam-1372	329	40	|z|<1	|z|<1	PROPN
ejpam-1372	329	41	.	.	PUNCT
ejpam-1372	330	1	let	let	VERB
ejpam-1372	330	2	us	we	PRON
ejpam-1372	330	3	now	now	ADV
ejpam-1372	330	4	consider	consider	VERB
ejpam-1372	330	5	the	the	DET
ejpam-1372	330	6	introduction	introduction	NOUN
ejpam-1372	330	7	of	of	ADP
ejpam-1372	330	8	an	an	DET
ejpam-1372	330	9	infinite	infinite	ADJ
ejpam-1372	330	10	number	number	NOUN
ejpam-1372	330	11	of	of	ADP
ejpam-1372	330	12	zeros	zero	NOUN
ejpam-1372	330	13	into	into	ADP
ejpam-1372	330	14	grandi	grandi	PROPN
ejpam-1372	330	15	’s	’s	PART
ejpam-1372	330	16	series	series	NOUN
ejpam-1372	330	17	as	as	SCONJ
ejpam-1372	330	18	bernoulli	bernoulli	PROPN
ejpam-1372	330	19	did	do	VERB
ejpam-1372	330	20	.	.	PUNCT
ejpam-1372	331	1	then	then	ADV
ejpam-1372	331	2	we	we	PRON
ejpam-1372	331	3	can	can	AUX
ejpam-1372	331	4	write	write	VERB
ejpam-1372	331	5	the	the	DET
ejpam-1372	331	6	modified	modify	VERB
ejpam-1372	331	7	version	version	NOUN
ejpam-1372	331	8	of	of	ADP
ejpam-1372	331	9	grandi	grandi	PROPN
ejpam-1372	331	10	’s	’s	PART
ejpam-1372	331	11	series	series	NOUN
ejpam-1372	331	12	as	as	ADP
ejpam-1372	331	13	s3(1,0,−1	s3(1,0,−1	PROPN
ejpam-1372	331	14	)	)	PUNCT
ejpam-1372	331	15	=	=	PUNCT
ejpam-1372	332	1	1	1	NUM
ejpam-1372	332	2	+	+	NUM
ejpam-1372	332	3	0−	0−	NUM
ejpam-1372	332	4	1	1	NUM
ejpam-1372	332	5	+	+	NUM
ejpam-1372	332	6	1	1	NUM
ejpam-1372	332	7	+	+	NUM
ejpam-1372	332	8	0−	0−	NUM
ejpam-1372	332	9	1	1	NUM
ejpam-1372	332	10	+	+	NUM
ejpam-1372	332	11	.	.	PUNCT
ejpam-1372	332	12	.	.	PUNCT
ejpam-1372	332	13	.	.	PUNCT
ejpam-1372	333	1	=	=	PUNCT
ejpam-1372	334	1	1	1	NUM
ejpam-1372	334	2	+	+	NUM
ejpam-1372	334	3	0	0	NUM
ejpam-1372	334	4	+	+	NUM
ejpam-1372	334	5	0	0	NUM
ejpam-1372	334	6	+	+	NUM
ejpam-1372	334	7	1	1	NUM
ejpam-1372	334	8	+	+	NUM
ejpam-1372	334	9	0	0	NUM
ejpam-1372	334	10	+	+	NUM
ejpam-1372	334	11	0	0	NUM
ejpam-1372	334	12	+	+	NUM
ejpam-1372	334	13	1	1	NUM
ejpam-1372	334	14	+	+	NUM
ejpam-1372	334	15	.	.	PUNCT
ejpam-1372	334	16	.	.	PUNCT
ejpam-1372	334	17	.	.	PUNCT
ejpam-1372	335	1	+	+	CCONJ
ejpam-1372	335	2	0	0	NUM
ejpam-1372	335	3	+	+	NUM
ejpam-1372	335	4	0−	0−	NUM
ejpam-1372	335	5	1	1	NUM
ejpam-1372	335	6	+	+	NUM
ejpam-1372	335	7	0	0	NUM
ejpam-1372	335	8	+	+	NUM
ejpam-1372	335	9	0−	0−	NUM
ejpam-1372	335	10	1	1	NUM
ejpam-1372	335	11	+	+	NUM
ejpam-1372	335	12	0	0	NUM
ejpam-1372	335	13	+	+	NUM
ejpam-1372	335	14	.	.	PUNCT
ejpam-1372	335	15	.	.	PUNCT
ejpam-1372	335	16	.	.	PUNCT
ejpam-1372	336	1	.	.	PUNCT
ejpam-1372	337	1	(	(	PUNCT
ejpam-1372	337	2	26	26	NUM
ejpam-1372	337	3	)	)	PUNCT
ejpam-1372	337	4	that	that	PRON
ejpam-1372	337	5	is	be	AUX
ejpam-1372	337	6	,	,	PUNCT
ejpam-1372	337	7	grandi	grandi	PROPN
ejpam-1372	337	8	’s	’s	PART
ejpam-1372	337	9	series	series	NOUN
ejpam-1372	337	10	represents	represent	VERB
ejpam-1372	337	11	the	the	DET
ejpam-1372	337	12	sum	sum	NOUN
ejpam-1372	337	13	of	of	ADP
ejpam-1372	337	14	two	two	NUM
ejpam-1372	337	15	separate	separate	ADJ
ejpam-1372	337	16	series	series	NOUN
ejpam-1372	337	17	,	,	PUNCT
ejpam-1372	337	18	s3(1,0,0	s3(1,0,0	NOUN
ejpam-1372	337	19	)	)	PUNCT
ejpam-1372	337	20	and	and	CCONJ
ejpam-1372	337	21	s3(0,0,−1	s3(0,0,−1	PROPN
ejpam-1372	337	22	)	)	PUNCT
ejpam-1372	337	23	.	.	PUNCT
ejpam-1372	338	1	the	the	DET
ejpam-1372	338	2	first	first	ADJ
ejpam-1372	338	3	series	series	NOUN
ejpam-1372	338	4	in	in	ADP
ejpam-1372	338	5	eq	eq	PROPN
ejpam-1372	338	6	.	.	PUNCT
ejpam-1372	339	1	(	(	PUNCT
ejpam-1372	339	2	26	26	NUM
ejpam-1372	339	3	)	)	PUNCT
ejpam-1372	339	4	can	can	AUX
ejpam-1372	339	5	be	be	AUX
ejpam-1372	339	6	written	write	VERB
ejpam-1372	339	7	alternatively	alternatively	ADV
ejpam-1372	339	8	as	as	ADP
ejpam-1372	339	9	s3(1,0,0	s3(1,0,0	NOUN
ejpam-1372	339	10	)	)	PUNCT
ejpam-1372	339	11	=	=	SYM
ejpam-1372	340	1	1	1	NUM
ejpam-1372	340	2	3	3	NUM
ejpam-1372	340	3	∞	∞	NUM
ejpam-1372	340	4	∑	∑	PUNCT
ejpam-1372	340	5	k=0	k=0	PUNCT
ejpam-1372	340	6	�	�	PROPN
ejpam-1372	340	7	1k	1k	X
ejpam-1372	340	8	+	+	CCONJ
ejpam-1372	340	9	e2πik/3	e2πik/3	PROPN
ejpam-1372	340	10	+	+	CCONJ
ejpam-1372	340	11	e4πik/3	e4πik/3	PROPN
ejpam-1372	340	12	�	�	PROPN
ejpam-1372	340	13	,	,	PUNCT
ejpam-1372	340	14	(	(	PUNCT
ejpam-1372	340	15	27	27	NUM
ejpam-1372	340	16	)	)	PUNCT
ejpam-1372	340	17	while	while	SCONJ
ejpam-1372	340	18	the	the	DET
ejpam-1372	340	19	other	other	ADJ
ejpam-1372	340	20	series	series	NOUN
ejpam-1372	340	21	can	can	AUX
ejpam-1372	340	22	be	be	AUX
ejpam-1372	340	23	expressed	express	VERB
ejpam-1372	340	24	as	as	ADP
ejpam-1372	340	25	s3(0,0,−1	s3(0,0,−1	PROPN
ejpam-1372	340	26	)	)	PUNCT
ejpam-1372	340	27	=	=	SYM
ejpam-1372	340	28	−1	−1	NOUN
ejpam-1372	340	29	3	3	NUM
ejpam-1372	340	30	∞	∞	NUM
ejpam-1372	340	31	∑	∑	PUNCT
ejpam-1372	340	32	k=0	k=0	PUNCT
ejpam-1372	340	33	�	�	PROPN
ejpam-1372	340	34	1k	1k	X
ejpam-1372	340	35	+	+	CCONJ
ejpam-1372	340	36	e2πi(k−2)/3	e2πi(k−2)/3	ADJ
ejpam-1372	340	37	+	+	CCONJ
ejpam-1372	340	38	e4πi(k−2)/3	e4πi(k−2)/3	ADJ
ejpam-1372	340	39	�	�	PROPN
ejpam-1372	340	40	.	.	PUNCT
ejpam-1372	341	1	(	(	PUNCT
ejpam-1372	341	2	28	28	NUM
ejpam-1372	341	3	)	)	PUNCT
ejpam-1372	341	4	therefore	therefore	ADV
ejpam-1372	341	5	,	,	PUNCT
ejpam-1372	341	6	we	we	PRON
ejpam-1372	341	7	see	see	VERB
ejpam-1372	341	8	that	that	SCONJ
ejpam-1372	341	9	both	both	DET
ejpam-1372	341	10	s3(1,0,0	s3(1,0,0	NOUN
ejpam-1372	341	11	)	)	PUNCT
ejpam-1372	341	12	and	and	CCONJ
ejpam-1372	341	13	s3(0,0,−1	s3(0,0,−1	PROPN
ejpam-1372	341	14	)	)	PUNCT
ejpam-1372	341	15	are	be	AUX
ejpam-1372	341	16	themselves	themselves	PRON
ejpam-1372	341	17	the	the	DET
ejpam-1372	341	18	sums	sum	NOUN
ejpam-1372	341	19	of	of	ADP
ejpam-1372	341	20	three	three	NUM
ejpam-1372	341	21	specific	specific	ADJ
ejpam-1372	341	22	geometric	geometric	ADJ
ejpam-1372	341	23	series	series	NOUN
ejpam-1372	341	24	.	.	PUNCT
ejpam-1372	342	1	in	in	ADP
ejpam-1372	342	2	each	each	DET
ejpam-1372	342	3	case	case	NOUN
ejpam-1372	342	4	the	the	DET
ejpam-1372	342	5	first	first	ADJ
ejpam-1372	342	6	series	series	NOUN
ejpam-1372	342	7	yields	yield	VERB
ejpam-1372	342	8	a	a	DET
ejpam-1372	342	9	regularised	regularise	VERB
ejpam-1372	342	10	value	value	NOUN
ejpam-1372	342	11	of	of	ADP
ejpam-1372	342	12	infinity	infinity	NOUN
ejpam-1372	342	13	,	,	PUNCT
ejpam-1372	342	14	but	but	CCONJ
ejpam-1372	342	15	as	as	SCONJ
ejpam-1372	342	16	we	we	PRON
ejpam-1372	342	17	are	be	AUX
ejpam-1372	342	18	interested	interested	ADJ
ejpam-1372	342	19	in	in	ADP
ejpam-1372	342	20	the	the	DET
ejpam-1372	342	21	sum	sum	NOUN
ejpam-1372	342	22	of	of	ADP
ejpam-1372	342	23	s3(1,0,0	s3(1,0,0	NOUN
ejpam-1372	342	24	)	)	PUNCT
ejpam-1372	342	25	and	and	CCONJ
ejpam-1372	342	26	s3(0,0,−1	s3(0,0,−1	PROPN
ejpam-1372	342	27	)	)	PUNCT
ejpam-1372	342	28	,	,	PUNCT
ejpam-1372	342	29	these	these	DET
ejpam-1372	342	30	infinities	infinity	NOUN
ejpam-1372	342	31	cancel	cancel	VERB
ejpam-1372	342	32	.	.	PUNCT
ejpam-1372	343	1	in	in	ADP
ejpam-1372	343	2	order	order	NOUN
ejpam-1372	343	3	to	to	PART
ejpam-1372	343	4	evaluate	evaluate	VERB
ejpam-1372	343	5	the	the	DET
ejpam-1372	343	6	other	other	ADJ
ejpam-1372	343	7	series	series	NOUN
ejpam-1372	343	8	in	in	ADP
ejpam-1372	343	9	eqs	eqs	PROPN
ejpam-1372	343	10	.	.	PUNCT
ejpam-1372	344	1	(	(	PUNCT
ejpam-1372	344	2	27	27	NUM
ejpam-1372	344	3	)	)	PUNCT
ejpam-1372	344	4	and	and	CCONJ
ejpam-1372	344	5	(	(	PUNCT
ejpam-1372	344	6	28	28	NUM
ejpam-1372	344	7	)	)	PUNCT
ejpam-1372	344	8	,	,	PUNCT
ejpam-1372	344	9	we	we	PRON
ejpam-1372	344	10	introduce	introduce	VERB
ejpam-1372	344	11	the	the	DET
ejpam-1372	344	12	rhs	rh	NOUN
ejpam-1372	344	13	of	of	ADP
ejpam-1372	344	14	equivalence	equivalence	NOUN
ejpam-1372	344	15	(	(	PUNCT
ejpam-1372	344	16	13	13	NUM
ejpam-1372	344	17	)	)	PUNCT
ejpam-1372	344	18	.	.	PUNCT
ejpam-1372	345	1	as	as	SCONJ
ejpam-1372	345	2	z	z	NOUN
ejpam-1372	345	3	is	be	AUX
ejpam-1372	345	4	equal	equal	ADJ
ejpam-1372	345	5	to	to	ADP
ejpam-1372	345	6	either	either	CCONJ
ejpam-1372	345	7	exp(2πi/3	exp(2πi/3	PROPN
ejpam-1372	345	8	)	)	PUNCT
ejpam-1372	345	9	or	or	CCONJ
ejpam-1372	345	10	exp(4πi/3	exp(4πi/3	NOUN
ejpam-1372	345	11	)	)	PUNCT
ejpam-1372	345	12	in	in	ADP
ejpam-1372	345	13	these	these	DET
ejpam-1372	345	14	series	series	NOUN
ejpam-1372	345	15	,	,	PUNCT
ejpam-1372	345	16	we	we	PRON
ejpam-1372	345	17	have	have	VERB
ejpam-1372	345	18	ℜ	ℜ	ADJ
ejpam-1372	345	19	z<1	z<1	NOUN
ejpam-1372	345	20	.	.	PUNCT
ejpam-1372	346	1	hence	hence	ADV
ejpam-1372	346	2	,	,	PUNCT
ejpam-1372	346	3	the	the	DET
ejpam-1372	346	4	equivalence	equivalence	NOUN
ejpam-1372	346	5	symbol	symbol	NOUN
ejpam-1372	346	6	can	can	AUX
ejpam-1372	346	7	be	be	AUX
ejpam-1372	346	8	replaced	replace	VERB
ejpam-1372	346	9	by	by	ADP
ejpam-1372	346	10	an	an	DET
ejpam-1372	346	11	equals	equal	NOUN
ejpam-1372	346	12	sign	sign	NOUN
ejpam-1372	346	13	,	,	PUNCT
ejpam-1372	346	14	resulting	result	VERB
ejpam-1372	346	15	in	in	ADP
ejpam-1372	346	16	an	an	DET
ejpam-1372	346	17	equation	equation	NOUN
ejpam-1372	346	18	.	.	PUNCT
ejpam-1372	347	1	combining	combine	VERB
ejpam-1372	347	2	the	the	DET
ejpam-1372	347	3	regularised	regularise	VERB
ejpam-1372	347	4	values	value	NOUN
ejpam-1372	347	5	of	of	ADP
ejpam-1372	347	6	all	all	DET
ejpam-1372	347	7	the	the	DET
ejpam-1372	347	8	series	series	NOUN
ejpam-1372	347	9	gives	give	VERB
ejpam-1372	347	10	s3(1,0,−1	s3(1,0,−1	PROPN
ejpam-1372	347	11	)	)	PUNCT
ejpam-1372	347	12	=	=	SYM
ejpam-1372	347	13	1	1	NUM
ejpam-1372	347	14	3	3	NUM
ejpam-1372	347	15	�	�	PROPN
ejpam-1372	347	16	1−	1−	NUM
ejpam-1372	347	17	e−4πi/3	e−4πi/3	NOUN
ejpam-1372	347	18	1−	1−	NUM
ejpam-1372	347	19	e2πi/3	e2πi/3	NOUN
ejpam-1372	348	1	+	+	CCONJ
ejpam-1372	348	2	1−	1−	NUM
ejpam-1372	348	3	e−2πi/3	e−2πi/3	NOUN
ejpam-1372	348	4	1−	1−	NUM
ejpam-1372	348	5	e4πi/3	e4πi/3	PROPN
ejpam-1372	348	6	�	�	PROPN
ejpam-1372	348	7	=	=	NOUN
ejpam-1372	348	8	2	2	NUM
ejpam-1372	348	9	3	3	NUM
ejpam-1372	348	10	,	,	PUNCT
ejpam-1372	348	11	(	(	PUNCT
ejpam-1372	348	12	29	29	NUM
ejpam-1372	348	13	)	)	PUNCT
ejpam-1372	348	14	which	which	PRON
ejpam-1372	348	15	is	be	AUX
ejpam-1372	348	16	the	the	DET
ejpam-1372	348	17	identical	identical	ADJ
ejpam-1372	348	18	result	result	NOUN
ejpam-1372	348	19	obtained	obtain	VERB
ejpam-1372	348	20	by	by	ADP
ejpam-1372	348	21	bernoulli	bernoulli	PROPN
ejpam-1372	348	22	.	.	PUNCT
ejpam-1372	349	1	in	in	ADP
ejpam-1372	349	2	addition	addition	NOUN
ejpam-1372	349	3	,	,	PUNCT
ejpam-1372	349	4	if	if	SCONJ
ejpam-1372	349	5	the	the	DET
ejpam-1372	349	6	series	series	NOUN
ejpam-1372	349	7	had	have	AUX
ejpam-1372	349	8	been	be	AUX
ejpam-1372	349	9	given	give	VERB
ejpam-1372	349	10	by	by	ADP
ejpam-1372	349	11	1−	1−	NUM
ejpam-1372	349	12	1	1	NUM
ejpam-1372	349	13	+	+	NUM
ejpam-1372	349	14	0	0	NUM
ejpam-1372	349	15	+	+	SYM
ejpam-1372	349	16	1−	1−	NUM
ejpam-1372	349	17	1	1	NUM
ejpam-1372	349	18	+	+	NUM
ejpam-1372	349	19	0	0	NUM
ejpam-1372	349	20	+	+	NUM
ejpam-1372	349	21	.	.	PUNCT
ejpam-1372	349	22	.	.	PUNCT
ejpam-1372	350	1	.	.	PUNCT
ejpam-1372	351	1	,	,	PUNCT
ejpam-1372	351	2	then	then	ADV
ejpam-1372	351	3	the	the	DET
ejpam-1372	351	4	series	series	NOUN
ejpam-1372	351	5	would	would	AUX
ejpam-1372	351	6	have	have	AUX
ejpam-1372	351	7	become	become	VERB
ejpam-1372	351	8	s3(1,−1,0	s3(1,−1,0	NOUN
ejpam-1372	351	9	)	)	PUNCT
ejpam-1372	351	10	,	,	PUNCT
ejpam-1372	351	11	which	which	PRON
ejpam-1372	351	12	is	be	AUX
ejpam-1372	351	13	the	the	DET
ejpam-1372	351	14	sum	sum	NOUN
ejpam-1372	351	15	of	of	ADP
ejpam-1372	351	16	s3(1,0,0	s3(1,0,0	NOUN
ejpam-1372	351	17	)	)	PUNCT
ejpam-1372	351	18	and	and	CCONJ
ejpam-1372	351	19	s3(0,−1,0	s3(0,−1,0	PROPN
ejpam-1372	351	20	)	)	PUNCT
ejpam-1372	351	21	.	.	PUNCT
ejpam-1372	352	1	the	the	DET
ejpam-1372	352	2	limit	limit	NOUN
ejpam-1372	352	3	of	of	ADP
ejpam-1372	352	4	the	the	DET
ejpam-1372	352	5	latter	latter	ADJ
ejpam-1372	352	6	series	series	NOUN
ejpam-1372	352	7	is	be	AUX
ejpam-1372	352	8	given	give	VERB
ejpam-1372	352	9	by	by	ADP
ejpam-1372	352	10	s3(0,−1,0	s3(0,−1,0	PROPN
ejpam-1372	352	11	)	)	PUNCT
ejpam-1372	352	12	=	=	SYM
ejpam-1372	352	13	−1	−1	NOUN
ejpam-1372	352	14	3	3	NUM
ejpam-1372	352	15	∞	∞	NUM
ejpam-1372	352	16	∑	∑	PUNCT
ejpam-1372	352	17	k=0	k=0	PUNCT
ejpam-1372	352	18	�	�	PROPN
ejpam-1372	352	19	1k	1k	X
ejpam-1372	352	20	+	+	CCONJ
ejpam-1372	352	21	e2πi(k−1)/3	e2πi(k−1)/3	ADJ
ejpam-1372	352	22	+	+	CCONJ
ejpam-1372	352	23	e4πi(k−1)/3	e4πi(k−1)/3	NOUN
ejpam-1372	352	24	�	�	PROPN
ejpam-1372	352	25	.	.	PUNCT
ejpam-1372	353	1	(	(	PUNCT
ejpam-1372	353	2	30	30	NUM
ejpam-1372	353	3	)	)	PUNCT
ejpam-1372	353	4	by	by	ADP
ejpam-1372	353	5	combining	combine	VERB
ejpam-1372	353	6	this	this	DET
ejpam-1372	353	7	result	result	NOUN
ejpam-1372	353	8	with	with	ADP
ejpam-1372	353	9	the	the	DET
ejpam-1372	353	10	limit	limit	NOUN
ejpam-1372	353	11	for	for	ADP
ejpam-1372	353	12	s3(1,0,0	s3(1,0,0	NOUN
ejpam-1372	353	13	)	)	PUNCT
ejpam-1372	353	14	,	,	PUNCT
ejpam-1372	353	15	we	we	PRON
ejpam-1372	353	16	arrive	arrive	VERB
ejpam-1372	353	17	at	at	ADP
ejpam-1372	353	18	s3(1,−1,0	s3(1,−1,0	PROPN
ejpam-1372	353	19	)	)	PUNCT
ejpam-1372	353	20	=	=	SYM
ejpam-1372	354	1	1	1	NUM
ejpam-1372	354	2	3	3	NUM
ejpam-1372	354	3	�	�	PROPN
ejpam-1372	354	4	1−	1−	NUM
ejpam-1372	354	5	e−2πi/3	e−2πi/3	NOUN
ejpam-1372	354	6	1−	1−	NUM
ejpam-1372	354	7	e2πi/3	e2πi/3	NOUN
ejpam-1372	355	1	+	+	CCONJ
ejpam-1372	355	2	1−	1−	NUM
ejpam-1372	355	3	e−4πi/3	e−4πi/3	NUM
ejpam-1372	355	4	1−	1−	NUM
ejpam-1372	355	5	e4πi/3	e4πi/3	PROPN
ejpam-1372	355	6	�	�	PROPN
ejpam-1372	355	7	.	.	PUNCT
ejpam-1372	356	1	(	(	PUNCT
ejpam-1372	356	2	31	31	NUM
ejpam-1372	356	3	)	)	PUNCT
ejpam-1372	356	4	after	after	ADP
ejpam-1372	356	5	a	a	DET
ejpam-1372	356	6	little	little	ADJ
ejpam-1372	356	7	algebra	algebra	NOUN
ejpam-1372	356	8	we	we	PRON
ejpam-1372	356	9	find	find	VERB
ejpam-1372	356	10	that	that	SCONJ
ejpam-1372	356	11	s3(1,−1,0	s3(1,−1,0	PUNCT
ejpam-1372	356	12	)	)	PUNCT
ejpam-1372	356	13	equals	equal	VERB
ejpam-1372	356	14	1/3	1/3	NUM
ejpam-1372	356	15	,	,	PUNCT
ejpam-1372	356	16	once	once	ADV
ejpam-1372	356	17	again	again	ADV
ejpam-1372	356	18	demonstrating	demonstrate	VERB
ejpam-1372	356	19	that	that	SCONJ
ejpam-1372	356	20	the	the	DET
ejpam-1372	356	21	position	position	NOUN
ejpam-1372	356	22	of	of	ADP
ejpam-1372	356	23	the	the	DET
ejpam-1372	356	24	infinite	infinite	ADJ
ejpam-1372	356	25	number	number	NOUN
ejpam-1372	356	26	of	of	ADP
ejpam-1372	356	27	zeros	zero	NOUN
ejpam-1372	356	28	in	in	ADP
ejpam-1372	356	29	a	a	DET
ejpam-1372	356	30	conditionally	conditionally	ADV
ejpam-1372	356	31	convergent	convergent	ADJ
ejpam-1372	356	32	series	series	NOUN
ejpam-1372	356	33	affects	affect	VERB
ejpam-1372	356	34	the	the	DET
ejpam-1372	356	35	limit	limit	NOUN
ejpam-1372	356	36	value	value	NOUN
ejpam-1372	356	37	.	.	PUNCT
ejpam-1372	357	1	v.	v.	ADP
ejpam-1372	357	2	kowalenko	kowalenko	PROPN
ejpam-1372	357	3	/	/	SYM
ejpam-1372	357	4	eur	eur	PROPN
ejpam-1372	357	5	.	.	PUNCT
ejpam-1372	358	1	j.	j.	PROPN
ejpam-1372	358	2	pure	pure	PROPN
ejpam-1372	358	3	appl	appl	PROPN
ejpam-1372	358	4	.	.	PROPN
ejpam-1372	358	5	math	math	PROPN
ejpam-1372	358	6	,	,	PUNCT
ejpam-1372	358	7	4	4	NUM
ejpam-1372	358	8	(	(	PUNCT
ejpam-1372	358	9	2011	2011	NUM
ejpam-1372	358	10	)	)	PUNCT
ejpam-1372	358	11	,	,	PUNCT
ejpam-1372	358	12	370	370	NUM
ejpam-1372	358	13	-	-	SYM
ejpam-1372	358	14	423	423	NUM
ejpam-1372	358	15	382	382	NUM
ejpam-1372	358	16	6	6	NUM
ejpam-1372	358	17	.	.	PUNCT
ejpam-1372	358	18	recurring	recur	VERB
ejpam-1372	358	19	series	series	NOUN
ejpam-1372	358	20	as	as	ADP
ejpam-1372	358	21	a	a	DET
ejpam-1372	358	22	result	result	NOUN
ejpam-1372	358	23	of	of	ADP
ejpam-1372	358	24	the	the	DET
ejpam-1372	358	25	foregoing	forego	VERB
ejpam-1372	358	26	analysis	analysis	NOUN
ejpam-1372	358	27	,	,	PUNCT
ejpam-1372	358	28	we	we	PRON
ejpam-1372	358	29	can	can	AUX
ejpam-1372	358	30	consider	consider	VERB
ejpam-1372	358	31	any	any	DET
ejpam-1372	358	32	periodically	periodically	ADV
ejpam-1372	358	33	recurring	recur	VERB
ejpam-1372	358	34	series	series	NOUN
ejpam-1372	358	35	of	of	ADP
ejpam-1372	358	36	the	the	DET
ejpam-1372	358	37	form	form	NOUN
ejpam-1372	358	38	where	where	SCONJ
ejpam-1372	358	39	sk(a1	sk(a1	NOUN
ejpam-1372	358	40	,	,	PUNCT
ejpam-1372	358	41	a2	a2	PROPN
ejpam-1372	358	42	,	,	PUNCT
ejpam-1372	358	43	a3	a3	NOUN
ejpam-1372	358	44	,	,	PUNCT
ejpam-1372	358	45	.	.	PUNCT
ejpam-1372	358	46	.	.	PUNCT
ejpam-1372	359	1	.	.	PUNCT
ejpam-1372	360	1	,	,	PUNCT
ejpam-1372	360	2	ak	ak	PROPN
ejpam-1372	360	3	)	)	PUNCT
ejpam-1372	360	4	=	=	SYM
ejpam-1372	360	5	a1	a1	NOUN
ejpam-1372	360	6	+	+	NUM
ejpam-1372	360	7	a2	a2	PROPN
ejpam-1372	360	8	+	+	X
ejpam-1372	360	9	.	.	PUNCT
ejpam-1372	360	10	.	.	PUNCT
ejpam-1372	361	1	.+	.+	PROPN
ejpam-1372	361	2	ak	ak	PROPN
ejpam-1372	361	3	+	+	CCONJ
ejpam-1372	361	4	a1	a1	NOUN
ejpam-1372	361	5	+	+	CCONJ
ejpam-1372	361	6	a2	a2	PROPN
ejpam-1372	361	7	+	+	X
ejpam-1372	361	8	.	.	PUNCT
ejpam-1372	361	9	.	.	PUNCT
ejpam-1372	362	1	.+	.+	PROPN
ejpam-1372	362	2	ak	ak	PROPN
ejpam-1372	363	1	+	+	PROPN
ejpam-1372	363	2	.	.	PUNCT
ejpam-1372	363	3	.	.	PUNCT
ejpam-1372	363	4	.	.	PUNCT
ejpam-1372	364	1	.	.	PUNCT
ejpam-1372	365	1	(	(	PUNCT
ejpam-1372	365	2	32	32	NUM
ejpam-1372	365	3	)	)	PUNCT
ejpam-1372	365	4	from	from	ADP
ejpam-1372	365	5	the	the	DET
ejpam-1372	365	6	previous	previous	ADJ
ejpam-1372	365	7	section	section	NOUN
ejpam-1372	365	8	we	we	PRON
ejpam-1372	365	9	know	know	VERB
ejpam-1372	365	10	that	that	DET
ejpam-1372	365	11	sk(a1	sk(a1	NOUN
ejpam-1372	365	12	,	,	PUNCT
ejpam-1372	365	13	a2	a2	PROPN
ejpam-1372	365	14	,	,	PUNCT
ejpam-1372	365	15	a3	a3	NOUN
ejpam-1372	365	16	,	,	PUNCT
ejpam-1372	365	17	.	.	PUNCT
ejpam-1372	365	18	.	.	PUNCT
ejpam-1372	366	1	.	.	PUNCT
ejpam-1372	367	1	,	,	PUNCT
ejpam-1372	367	2	ak	ak	PROPN
ejpam-1372	367	3	)	)	PUNCT
ejpam-1372	367	4	can	can	AUX
ejpam-1372	367	5	be	be	AUX
ejpam-1372	367	6	expressed	express	VERB
ejpam-1372	367	7	as	as	ADP
ejpam-1372	367	8	a	a	DET
ejpam-1372	367	9	finite	finite	ADJ
ejpam-1372	367	10	sum	sum	NOUN
ejpam-1372	367	11	of	of	ADP
ejpam-1372	367	12	series	series	NOUN
ejpam-1372	367	13	involving	involve	VERB
ejpam-1372	367	14	zeros	zero	NOUN
ejpam-1372	367	15	and	and	CCONJ
ejpam-1372	367	16	one	one	NUM
ejpam-1372	367	17	.	.	PUNCT
ejpam-1372	368	1	that	that	PRON
ejpam-1372	368	2	is	is	ADV
ejpam-1372	368	3	,	,	PUNCT
ejpam-1372	368	4	the	the	DET
ejpam-1372	368	5	above	above	ADJ
ejpam-1372	368	6	can	can	AUX
ejpam-1372	368	7	be	be	AUX
ejpam-1372	368	8	written	write	VERB
ejpam-1372	368	9	as	as	ADP
ejpam-1372	368	10	sk(a1	sk(a1	NOUN
ejpam-1372	368	11	,	,	PUNCT
ejpam-1372	368	12	a2	a2	PROPN
ejpam-1372	368	13	,	,	PUNCT
ejpam-1372	368	14	a3	a3	NOUN
ejpam-1372	368	15	,	,	PUNCT
ejpam-1372	368	16	.	.	PUNCT
ejpam-1372	368	17	.	.	PUNCT
ejpam-1372	368	18	.	.	PUNCT
ejpam-1372	369	1	,	,	PUNCT
ejpam-1372	369	2	ak	ak	PROPN
ejpam-1372	369	3	)	)	PUNCT
ejpam-1372	369	4	=	=	SYM
ejpam-1372	369	5	a1sk(1,0,0	a1sk(1,0,0	NOUN
ejpam-1372	369	6	,	,	PUNCT
ejpam-1372	369	7	.	.	PUNCT
ejpam-1372	369	8	.	.	PUNCT
ejpam-1372	370	1	.	.	PUNCT
ejpam-1372	371	1	,	,	PUNCT
ejpam-1372	371	2	0	0	NUM
ejpam-1372	371	3	)	)	PUNCT
ejpam-1372	371	4	+	+	NUM
ejpam-1372	371	5	a2sk(0,1,0	a2sk(0,1,0	NOUN
ejpam-1372	371	6	,	,	PUNCT
ejpam-1372	371	7	.	.	PUNCT
ejpam-1372	371	8	.	.	PUNCT
ejpam-1372	372	1	.	.	PUNCT
ejpam-1372	373	1	,	,	PUNCT
ejpam-1372	373	2	0	0	X
ejpam-1372	373	3	)	)	PUNCT
ejpam-1372	373	4	+	+	CCONJ
ejpam-1372	373	5	.	.	PUNCT
ejpam-1372	373	6	.	.	PUNCT
ejpam-1372	373	7	.	.	PUNCT
ejpam-1372	374	1	+	+	PUNCT
ejpam-1372	374	2	aksk(0,0,0	aksk(0,0,0	NOUN
ejpam-1372	374	3	,	,	PUNCT
ejpam-1372	374	4	.	.	PUNCT
ejpam-1372	374	5	.	.	PUNCT
ejpam-1372	375	1	.	.	PUNCT
ejpam-1372	376	1	,	,	PUNCT
ejpam-1372	376	2	1	1	X
ejpam-1372	376	3	)	)	PUNCT
ejpam-1372	376	4	.	.	PUNCT
ejpam-1372	377	1	(	(	PUNCT
ejpam-1372	377	2	33	33	NUM
ejpam-1372	377	3	)	)	PUNCT
ejpam-1372	377	4	each	each	DET
ejpam-1372	377	5	series	series	NOUN
ejpam-1372	377	6	on	on	ADP
ejpam-1372	377	7	the	the	DET
ejpam-1372	377	8	rhs	rhs	PROPN
ejpam-1372	377	9	of	of	ADP
ejpam-1372	377	10	eq	eq	PROPN
ejpam-1372	377	11	.	.	PUNCT
ejpam-1372	378	1	(	(	PUNCT
ejpam-1372	378	2	33	33	NUM
ejpam-1372	378	3	)	)	PUNCT
ejpam-1372	378	4	possesses	possess	VERB
ejpam-1372	378	5	an	an	DET
ejpam-1372	378	6	infinite	infinite	ADJ
ejpam-1372	378	7	sum	sum	NOUN
ejpam-1372	378	8	over	over	ADP
ejpam-1372	378	9	unity	unity	NOUN
ejpam-1372	378	10	,	,	PUNCT
ejpam-1372	378	11	just	just	ADV
ejpam-1372	378	12	as	as	ADP
ejpam-1372	378	13	in	in	ADP
ejpam-1372	378	14	eqs	eqs	PROPN
ejpam-1372	378	15	.	.	PUNCT
ejpam-1372	379	1	(	(	PUNCT
ejpam-1372	379	2	27	27	NUM
ejpam-1372	379	3	)	)	PUNCT
ejpam-1372	379	4	and	and	CCONJ
ejpam-1372	379	5	(	(	PUNCT
ejpam-1372	379	6	28	28	NUM
ejpam-1372	379	7	)	)	PUNCT
ejpam-1372	379	8	.	.	PUNCT
ejpam-1372	380	1	in	in	ADP
ejpam-1372	380	2	the	the	DET
ejpam-1372	380	3	preceding	precede	VERB
ejpam-1372	380	4	cases	case	NOUN
ejpam-1372	380	5	we	we	PRON
ejpam-1372	380	6	found	find	VERB
ejpam-1372	380	7	that	that	SCONJ
ejpam-1372	380	8	they	they	PRON
ejpam-1372	380	9	eventually	eventually	ADV
ejpam-1372	380	10	cancelled	cancel	VERB
ejpam-1372	380	11	each	each	DET
ejpam-1372	380	12	other	other	ADJ
ejpam-1372	380	13	when	when	SCONJ
ejpam-1372	380	14	evaluating	evaluate	VERB
ejpam-1372	380	15	the	the	DET
ejpam-1372	380	16	limits	limit	NOUN
ejpam-1372	380	17	for	for	ADP
ejpam-1372	380	18	s3(1,0,−1	s3(1,0,−1	NOUN
ejpam-1372	380	19	)	)	PUNCT
ejpam-1372	380	20	and	and	CCONJ
ejpam-1372	380	21	s3(1,−1,0	s3(1,−1,0	PROPN
ejpam-1372	380	22	)	)	PUNCT
ejpam-1372	380	23	.	.	PUNCT
ejpam-1372	381	1	in	in	ADP
ejpam-1372	381	2	the	the	DET
ejpam-1372	381	3	above	above	ADJ
ejpam-1372	381	4	result	result	VERB
ejpam-1372	381	5	the	the	DET
ejpam-1372	381	6	sums	sum	NOUN
ejpam-1372	381	7	over	over	ADP
ejpam-1372	381	8	unity	unity	NOUN
ejpam-1372	381	9	will	will	AUX
ejpam-1372	381	10	cancel	cancel	VERB
ejpam-1372	381	11	each	each	DET
ejpam-1372	381	12	other	other	ADJ
ejpam-1372	381	13	if	if	SCONJ
ejpam-1372	382	1	and	and	CCONJ
ejpam-1372	382	2	only	only	ADV
ejpam-1372	382	3	if	if	SCONJ
ejpam-1372	382	4	∑k	∑k	PROPN
ejpam-1372	382	5	j=1	j=1	PROPN
ejpam-1372	382	6	a	a	DET
ejpam-1372	382	7	j=0	j=0	PROPN
ejpam-1372	382	8	.	.	PUNCT
ejpam-1372	383	1	otherwise	otherwise	ADV
ejpam-1372	383	2	,	,	PUNCT
ejpam-1372	383	3	one	one	NOUN
ejpam-1372	383	4	obtains	obtain	VERB
ejpam-1372	383	5	infinity	infinity	NOUN
ejpam-1372	383	6	.	.	PUNCT
ejpam-1372	384	1	hence	hence	ADV
ejpam-1372	384	2	,	,	PUNCT
ejpam-1372	384	3	we	we	PRON
ejpam-1372	384	4	need	need	VERB
ejpam-1372	384	5	to	to	PART
ejpam-1372	384	6	make	make	VERB
ejpam-1372	384	7	this	this	DET
ejpam-1372	384	8	assumption	assumption	NOUN
ejpam-1372	384	9	or	or	CCONJ
ejpam-1372	384	10	condition	condition	NOUN
ejpam-1372	384	11	to	to	PART
ejpam-1372	384	12	obtain	obtain	VERB
ejpam-1372	384	13	a	a	DET
ejpam-1372	384	14	finite	finite	ADJ
ejpam-1372	384	15	limit	limit	NOUN
ejpam-1372	384	16	for	for	ADP
ejpam-1372	384	17	sk(a1	sk(a1	NOUN
ejpam-1372	384	18	,	,	PUNCT
ejpam-1372	384	19	a2	a2	PROPN
ejpam-1372	384	20	,	,	PUNCT
ejpam-1372	384	21	a3	a3	NOUN
ejpam-1372	384	22	,	,	PUNCT
ejpam-1372	384	23	.	.	PUNCT
ejpam-1372	384	24	.	.	PUNCT
ejpam-1372	384	25	.	.	PUNCT
ejpam-1372	385	1	,	,	PUNCT
ejpam-1372	385	2	ak	ak	PROPN
ejpam-1372	385	3	)	)	PUNCT
ejpam-1372	385	4	.	.	PUNCT
ejpam-1372	386	1	in	in	ADP
ejpam-1372	386	2	addition	addition	NOUN
ejpam-1372	386	3	,	,	PUNCT
ejpam-1372	386	4	if	if	SCONJ
ejpam-1372	386	5	we	we	PRON
ejpam-1372	386	6	denote	denote	VERB
ejpam-1372	386	7	sk(0	sk(0	NOUN
ejpam-1372	386	8	,	,	PUNCT
ejpam-1372	386	9	.	.	PUNCT
ejpam-1372	386	10	.	.	PUNCT
ejpam-1372	387	1	.	.	PUNCT
ejpam-1372	388	1	,	,	PUNCT
ejpam-1372	388	2	i	i	PRON
ejpam-1372	388	3	j	j	PROPN
ejpam-1372	388	4	,	,	PUNCT
ejpam-1372	388	5	.	.	PUNCT
ejpam-1372	388	6	.	.	PUNCT
ejpam-1372	388	7	.	.	PUNCT
ejpam-1372	389	1	,	,	PUNCT
ejpam-1372	389	2	0	0	X
ejpam-1372	389	3	)	)	PUNCT
ejpam-1372	389	4	as	as	SCONJ
ejpam-1372	389	5	the	the	DET
ejpam-1372	389	6	series	series	NOUN
ejpam-1372	389	7	composed	compose	VERB
ejpam-1372	389	8	of	of	ADP
ejpam-1372	389	9	zeros	zero	NOUN
ejpam-1372	389	10	and	and	CCONJ
ejpam-1372	389	11	ones	one	NOUN
ejpam-1372	389	12	,	,	PUNCT
ejpam-1372	389	13	where	where	SCONJ
ejpam-1372	389	14	the	the	DET
ejpam-1372	389	15	ones	one	NOUN
ejpam-1372	389	16	only	only	ADV
ejpam-1372	389	17	appear	appear	VERB
ejpam-1372	389	18	at	at	ADP
ejpam-1372	389	19	the	the	DET
ejpam-1372	389	20	j	j	PROPN
ejpam-1372	389	21	-	-	PUNCT
ejpam-1372	389	22	th	th	VERB
ejpam-1372	389	23	position	position	NOUN
ejpam-1372	389	24	of	of	ADP
ejpam-1372	389	25	each	each	DET
ejpam-1372	389	26	cycle	cycle	NOUN
ejpam-1372	389	27	of	of	ADP
ejpam-1372	389	28	k	k	PROPN
ejpam-1372	389	29	terms	term	NOUN
ejpam-1372	389	30	,	,	PUNCT
ejpam-1372	389	31	e.g.	e.g.	ADV
ejpam-1372	389	32	s3(0,12	s3(0,12	PROPN
ejpam-1372	389	33	,	,	PUNCT
ejpam-1372	389	34	0	0	NUM
ejpam-1372	389	35	)	)	PUNCT
ejpam-1372	389	36	has	have	AUX
ejpam-1372	389	37	unity	unity	NOUN
ejpam-1372	389	38	appearing	appear	VERB
ejpam-1372	389	39	at	at	ADP
ejpam-1372	389	40	the	the	DET
ejpam-1372	389	41	second	second	ADJ
ejpam-1372	389	42	position	position	NOUN
ejpam-1372	389	43	of	of	ADP
ejpam-1372	389	44	every	every	DET
ejpam-1372	389	45	triple	triple	ADJ
ejpam-1372	389	46	(	(	PUNCT
ejpam-1372	389	47	0,1,0	0,1,0	NUM
ejpam-1372	389	48	)	)	PUNCT
ejpam-1372	389	49	,	,	PUNCT
ejpam-1372	389	50	then	then	ADV
ejpam-1372	389	51	the	the	DET
ejpam-1372	389	52	above	above	ADJ
ejpam-1372	389	53	equation	equation	NOUN
ejpam-1372	389	54	can	can	AUX
ejpam-1372	389	55	be	be	AUX
ejpam-1372	389	56	represented	represent	VERB
ejpam-1372	389	57	as	as	ADP
ejpam-1372	389	58	sk(a1	sk(a1	NOUN
ejpam-1372	389	59	,	,	PUNCT
ejpam-1372	389	60	a2	a2	PROPN
ejpam-1372	389	61	,	,	PUNCT
ejpam-1372	389	62	a3	a3	NOUN
ejpam-1372	389	63	,	,	PUNCT
ejpam-1372	389	64	.	.	PUNCT
ejpam-1372	389	65	.	.	PUNCT
ejpam-1372	390	1	.	.	PUNCT
ejpam-1372	391	1	,	,	PUNCT
ejpam-1372	391	2	ak	ak	PROPN
ejpam-1372	391	3	)	)	PUNCT
ejpam-1372	391	4	=	=	SYM
ejpam-1372	392	1	k	k	PROPN
ejpam-1372	392	2	∑	∑	PUNCT
ejpam-1372	392	3	j=1	j=1	PROPN
ejpam-1372	392	4	a	a	DET
ejpam-1372	392	5	jsk(0,0	jsk(0,0	NOUN
ejpam-1372	392	6	,	,	PUNCT
ejpam-1372	392	7	.	.	PUNCT
ejpam-1372	392	8	.	.	PUNCT
ejpam-1372	393	1	.	.	PUNCT
ejpam-1372	394	1	,	,	PUNCT
ejpam-1372	394	2	1	1	NUM
ejpam-1372	394	3	j	j	NOUN
ejpam-1372	394	4	,	,	PUNCT
ejpam-1372	394	5	.	.	PUNCT
ejpam-1372	394	6	.	.	PUNCT
ejpam-1372	395	1	.	.	PUNCT
ejpam-1372	396	1	,	,	PUNCT
ejpam-1372	396	2	0	0	X
ejpam-1372	396	3	)	)	PUNCT
ejpam-1372	396	4	=	=	SYM
ejpam-1372	397	1	1	1	NUM
ejpam-1372	397	2	k	k	X
ejpam-1372	397	3	k	k	X
ejpam-1372	397	4	∑	∑	PUNCT
ejpam-1372	397	5	j=1	j=1	PROPN
ejpam-1372	397	6	a	a	DET
ejpam-1372	397	7	j	j	PROPN
ejpam-1372	397	8	k−1	k−1	PROPN
ejpam-1372	397	9	∑	∑	PUNCT
ejpam-1372	397	10	l=1	l=1	PROPN
ejpam-1372	397	11	∞	∞	NUM
ejpam-1372	397	12	∑	∑	PROPN
ejpam-1372	397	13	n=0	n=0	X
ejpam-1372	397	14	e2(n−	e2(n−	X
ejpam-1372	397	15	j+1)lπi	j+1)lπi	AUX
ejpam-1372	397	16	/	/	SYM
ejpam-1372	397	17	k	k	X
ejpam-1372	397	18	.	.	PUNCT
ejpam-1372	398	1	(	(	PUNCT
ejpam-1372	398	2	34	34	NUM
ejpam-1372	398	3	)	)	PUNCT
ejpam-1372	398	4	the	the	DET
ejpam-1372	398	5	infinite	infinite	ADJ
ejpam-1372	398	6	sum	sum	NOUN
ejpam-1372	398	7	over	over	ADP
ejpam-1372	398	8	n	n	NOUN
ejpam-1372	398	9	can	can	AUX
ejpam-1372	398	10	be	be	AUX
ejpam-1372	398	11	removed	remove	VERB
ejpam-1372	398	12	by	by	ADP
ejpam-1372	398	13	introducing	introduce	VERB
ejpam-1372	398	14	the	the	DET
ejpam-1372	398	15	rhs	rh	NOUN
ejpam-1372	398	16	of	of	ADP
ejpam-1372	398	17	equivalence	equivalence	NOUN
ejpam-1372	398	18	(	(	PUNCT
ejpam-1372	398	19	13	13	NUM
ejpam-1372	398	20	)	)	PUNCT
ejpam-1372	398	21	except	except	SCONJ
ejpam-1372	398	22	that	that	SCONJ
ejpam-1372	398	23	because	because	SCONJ
ejpam-1372	398	24	ℜ	ℜ	ADJ
ejpam-1372	398	25	exp(2lπi	exp(2lπi	NOUN
ejpam-1372	398	26	/	/	SYM
ejpam-1372	398	27	k)<1	k)<1	PROPN
ejpam-1372	398	28	for	for	ADP
ejpam-1372	398	29	all	all	DET
ejpam-1372	398	30	values	value	NOUN
ejpam-1372	398	31	of	of	ADP
ejpam-1372	398	32	l	l	NOUN
ejpam-1372	398	33	in	in	ADP
ejpam-1372	398	34	the	the	DET
ejpam-1372	398	35	above	above	ADJ
ejpam-1372	398	36	result	result	NOUN
ejpam-1372	398	37	,	,	PUNCT
ejpam-1372	398	38	the	the	DET
ejpam-1372	398	39	equivalence	equivalence	NOUN
ejpam-1372	398	40	symbol	symbol	NOUN
ejpam-1372	398	41	can	can	AUX
ejpam-1372	398	42	be	be	AUX
ejpam-1372	398	43	replaced	replace	VERB
ejpam-1372	398	44	by	by	ADP
ejpam-1372	398	45	an	an	DET
ejpam-1372	398	46	equals	equal	NOUN
ejpam-1372	398	47	sign	sign	NOUN
ejpam-1372	398	48	.	.	PUNCT
ejpam-1372	399	1	then	then	ADV
ejpam-1372	399	2	eq	eq	X
ejpam-1372	399	3	.	.	PUNCT
ejpam-1372	400	1	(	(	PUNCT
ejpam-1372	400	2	34	34	NUM
ejpam-1372	400	3	)	)	PUNCT
ejpam-1372	400	4	reduces	reduce	VERB
ejpam-1372	400	5	to	to	PART
ejpam-1372	400	6	sk(a1	sk(a1	VERB
ejpam-1372	400	7	,	,	PUNCT
ejpam-1372	400	8	a2	a2	PROPN
ejpam-1372	400	9	,	,	PUNCT
ejpam-1372	400	10	a3	a3	NOUN
ejpam-1372	400	11	,	,	PUNCT
ejpam-1372	400	12	.	.	PUNCT
ejpam-1372	400	13	.	.	PUNCT
ejpam-1372	401	1	.	.	PUNCT
ejpam-1372	402	1	,	,	PUNCT
ejpam-1372	402	2	ak	ak	PROPN
ejpam-1372	402	3	)	)	PUNCT
ejpam-1372	402	4	=	=	PUNCT
ejpam-1372	403	1	i	i	PRON
ejpam-1372	403	2	2k	2k	NOUN
ejpam-1372	403	3	k−1	k−1	PROPN
ejpam-1372	403	4	∑	∑	PUNCT
ejpam-1372	403	5	l=1	l=1	PROPN
ejpam-1372	403	6	1	1	NUM
ejpam-1372	403	7	sin(lπ	sin(lπ	NOUN
ejpam-1372	403	8	/	/	SYM
ejpam-1372	403	9	k	k	NOUN
ejpam-1372	403	10	)	)	PUNCT
ejpam-1372	404	1	k	k	NOUN
ejpam-1372	405	1	∑	∑	PUNCT
ejpam-1372	405	2	j=1	j=1	PROPN
ejpam-1372	405	3	a	a	DET
ejpam-1372	405	4	j	j	PROPN
ejpam-1372	405	5	e−(2	e−(2	PROPN
ejpam-1372	405	6	j−1)lπi	j−1)lπi	PROPN
ejpam-1372	405	7	/	/	SYM
ejpam-1372	405	8	k	k	PROPN
ejpam-1372	405	9	.	.	PUNCT
ejpam-1372	406	1	(	(	PUNCT
ejpam-1372	406	2	35	35	NUM
ejpam-1372	406	3	)	)	PUNCT
ejpam-1372	406	4	therefore	therefore	ADV
ejpam-1372	406	5	,	,	PUNCT
ejpam-1372	406	6	we	we	PRON
ejpam-1372	406	7	arrive	arrive	VERB
ejpam-1372	406	8	at	at	ADP
ejpam-1372	406	9	a	a	DET
ejpam-1372	406	10	finite	finite	ADJ
ejpam-1372	406	11	double	double	ADJ
ejpam-1372	406	12	sum	sum	NOUN
ejpam-1372	406	13	that	that	PRON
ejpam-1372	406	14	is	be	AUX
ejpam-1372	406	15	very	very	ADV
ejpam-1372	406	16	much	much	ADV
ejpam-1372	406	17	dependent	dependent	ADJ
ejpam-1372	406	18	upon	upon	SCONJ
ejpam-1372	406	19	the	the	DET
ejpam-1372	406	20	values	value	NOUN
ejpam-1372	406	21	of	of	ADP
ejpam-1372	406	22	the	the	DET
ejpam-1372	406	23	a	a	DET
ejpam-1372	406	24	j.	j.	PROPN
ejpam-1372	406	25	it	it	PRON
ejpam-1372	406	26	should	should	AUX
ejpam-1372	406	27	be	be	AUX
ejpam-1372	406	28	noted	note	VERB
ejpam-1372	406	29	that	that	SCONJ
ejpam-1372	406	30	in	in	ADP
ejpam-1372	406	31	eq	eq	ADP
ejpam-1372	406	32	.	.	PUNCT
ejpam-1372	406	33	(	(	PUNCT
ejpam-1372	406	34	35	35	NUM
ejpam-1372	406	35	)	)	PUNCT
ejpam-1372	406	36	the	the	DET
ejpam-1372	406	37	a	a	DET
ejpam-1372	406	38	j	j	NOUN
ejpam-1372	406	39	need	need	AUX
ejpam-1372	406	40	not	not	PART
ejpam-1372	406	41	necessarily	necessarily	ADV
ejpam-1372	406	42	be	be	AUX
ejpam-1372	406	43	real	real	ADJ
ejpam-1372	406	44	.	.	PUNCT
ejpam-1372	407	1	that	that	PRON
ejpam-1372	407	2	is	is	ADV
ejpam-1372	407	3	,	,	PUNCT
ejpam-1372	407	4	they	they	PRON
ejpam-1372	407	5	can	can	AUX
ejpam-1372	407	6	be	be	AUX
ejpam-1372	407	7	complex	complex	ADJ
ejpam-1372	407	8	provided	provide	VERB
ejpam-1372	407	9	that	that	SCONJ
ejpam-1372	407	10	∑k	∑k	PROPN
ejpam-1372	407	11	j=1	j=1	PROPN
ejpam-1372	407	12	a	a	DET
ejpam-1372	407	13	j=0	j=0	PROPN
ejpam-1372	407	14	.	.	PUNCT
ejpam-1372	408	1	on	on	ADP
ejpam-1372	408	2	the	the	DET
ejpam-1372	408	3	other	other	ADJ
ejpam-1372	408	4	hand	hand	NOUN
ejpam-1372	408	5	,	,	PUNCT
ejpam-1372	408	6	if	if	SCONJ
ejpam-1372	408	7	they	they	PRON
ejpam-1372	408	8	are	be	AUX
ejpam-1372	408	9	purely	purely	ADV
ejpam-1372	408	10	real	real	ADJ
ejpam-1372	408	11	,	,	PUNCT
ejpam-1372	408	12	then	then	ADV
ejpam-1372	408	13	eq	eq	ADP
ejpam-1372	408	14	.	.	PUNCT
ejpam-1372	409	1	(	(	PUNCT
ejpam-1372	409	2	32	32	NUM
ejpam-1372	409	3	)	)	PUNCT
ejpam-1372	409	4	can	can	AUX
ejpam-1372	409	5	be	be	AUX
ejpam-1372	409	6	simplified	simplify	VERB
ejpam-1372	409	7	even	even	ADV
ejpam-1372	409	8	further	far	ADV
ejpam-1372	409	9	because	because	SCONJ
ejpam-1372	409	10	the	the	DET
ejpam-1372	409	11	real	real	ADJ
ejpam-1372	409	12	part	part	NOUN
ejpam-1372	409	13	of	of	ADP
ejpam-1372	409	14	the	the	DET
ejpam-1372	409	15	final	final	ADJ
ejpam-1372	409	16	sum	sum	NOUN
ejpam-1372	409	17	,	,	PUNCT
ejpam-1372	409	18	viz	viz	PROPN
ejpam-1372	409	19	.	.	PUNCT
ejpam-1372	410	1	the	the	DET
ejpam-1372	410	2	sum	sum	NOUN
ejpam-1372	410	3	over	over	ADP
ejpam-1372	410	4	j	j	PROPN
ejpam-1372	410	5	,	,	PUNCT
ejpam-1372	410	6	must	must	AUX
ejpam-1372	410	7	vanish	vanish	VERB
ejpam-1372	410	8	.	.	PUNCT
ejpam-1372	411	1	therefore	therefore	ADV
ejpam-1372	411	2	,	,	PUNCT
ejpam-1372	411	3	in	in	ADP
ejpam-1372	411	4	this	this	DET
ejpam-1372	411	5	case	case	NOUN
ejpam-1372	411	6	eq	eq	ADP
ejpam-1372	411	7	.	.	PUNCT
ejpam-1372	412	1	(	(	PUNCT
ejpam-1372	412	2	35	35	NUM
ejpam-1372	412	3	)	)	PUNCT
ejpam-1372	412	4	yields	yield	NOUN
ejpam-1372	412	5	sk(a1	sk(a1	NOUN
ejpam-1372	412	6	,	,	PUNCT
ejpam-1372	412	7	a2	a2	PROPN
ejpam-1372	412	8	,	,	PUNCT
ejpam-1372	412	9	a3	a3	NOUN
ejpam-1372	412	10	,	,	PUNCT
ejpam-1372	412	11	.	.	PUNCT
ejpam-1372	412	12	.	.	PUNCT
ejpam-1372	413	1	.	.	PUNCT
ejpam-1372	414	1	,	,	PUNCT
ejpam-1372	414	2	ak	ak	PROPN
ejpam-1372	414	3	)	)	PUNCT
ejpam-1372	414	4	=	=	SYM
ejpam-1372	414	5	a1	a1	NOUN
ejpam-1372	414	6	2	2	NUM
ejpam-1372	414	7	�	�	NOUN
ejpam-1372	414	8	1−	1−	NUM
ejpam-1372	414	9	1	1	NUM
ejpam-1372	414	10	k	k	X
ejpam-1372	414	11	�	�	PROPN
ejpam-1372	415	1	+	+	CCONJ
ejpam-1372	416	1	i	i	PROPN
ejpam-1372	416	2	2k	2k	NOUN
ejpam-1372	416	3	k−1	k−1	PROPN
ejpam-1372	416	4	∑	∑	PUNCT
ejpam-1372	416	5	l=1	l=1	PROPN
ejpam-1372	416	6	1	1	NUM
ejpam-1372	416	7	sin(lπ	sin(lπ	NOUN
ejpam-1372	416	8	/	/	SYM
ejpam-1372	416	9	k	k	NOUN
ejpam-1372	416	10	)	)	PUNCT
ejpam-1372	417	1	v.	v.	ADP
ejpam-1372	417	2	kowalenko	kowalenko	PROPN
ejpam-1372	417	3	/	/	SYM
ejpam-1372	417	4	eur	eur	PROPN
ejpam-1372	417	5	.	.	PUNCT
ejpam-1372	418	1	j.	j.	PROPN
ejpam-1372	418	2	pure	pure	PROPN
ejpam-1372	418	3	appl	appl	PROPN
ejpam-1372	418	4	.	.	PROPN
ejpam-1372	418	5	math	math	PROPN
ejpam-1372	418	6	,	,	PUNCT
ejpam-1372	418	7	4	4	NUM
ejpam-1372	418	8	(	(	PUNCT
ejpam-1372	418	9	2011	2011	NUM
ejpam-1372	418	10	)	)	PUNCT
ejpam-1372	418	11	,	,	PUNCT
ejpam-1372	418	12	370	370	NUM
ejpam-1372	418	13	-	-	SYM
ejpam-1372	418	14	423	423	NUM
ejpam-1372	418	15	383	383	NUM
ejpam-1372	418	16	×	×	NOUN
ejpam-1372	418	17	k	k	PROPN
ejpam-1372	418	18	∑	∑	PUNCT
ejpam-1372	418	19	j=2	j=2	PROPN
ejpam-1372	418	20	a	a	DET
ejpam-1372	418	21	j	j	PROPN
ejpam-1372	418	22	�	�	PROPN
ejpam-1372	418	23	sin((2	sin((2	NOUN
ejpam-1372	418	24	j−	j−	PROPN
ejpam-1372	418	25	1)lπ	1)lπ	PROPN
ejpam-1372	418	26	/	/	SYM
ejpam-1372	418	27	k	k	NOUN
ejpam-1372	418	28	)	)	PUNCT
ejpam-1372	418	29	sin(lπ	sin(lπ	NOUN
ejpam-1372	418	30	/	/	SYM
ejpam-1372	418	31	k	k	NOUN
ejpam-1372	418	32	)	)	PUNCT
ejpam-1372	418	33	�	�	PROPN
ejpam-1372	418	34	.	.	PUNCT
ejpam-1372	419	1	(	(	PUNCT
ejpam-1372	419	2	36	36	NUM
ejpam-1372	419	3	)	)	PUNCT
ejpam-1372	419	4	if	if	SCONJ
ejpam-1372	419	5	we	we	PRON
ejpam-1372	419	6	let	let	VERB
ejpam-1372	419	7	a1=1	a1=1	PROPN
ejpam-1372	419	8	,	,	PUNCT
ejpam-1372	419	9	a2=0	a2=0	PROPN
ejpam-1372	419	10	,	,	PUNCT
ejpam-1372	419	11	a3=−1	a3=−1	NOUN
ejpam-1372	419	12	,	,	PUNCT
ejpam-1372	419	13	and	and	CCONJ
ejpam-1372	419	14	k=3	k=3	X
ejpam-1372	419	15	in	in	ADP
ejpam-1372	419	16	the	the	DET
ejpam-1372	419	17	above	above	ADJ
ejpam-1372	419	18	equation	equation	NOUN
ejpam-1372	419	19	,	,	PUNCT
ejpam-1372	419	20	then	then	ADV
ejpam-1372	419	21	,	,	PUNCT
ejpam-1372	419	22	as	as	SCONJ
ejpam-1372	419	23	expected	expect	VERB
ejpam-1372	419	24	,	,	PUNCT
ejpam-1372	419	25	we	we	PRON
ejpam-1372	419	26	find	find	VERB
ejpam-1372	419	27	that	that	SCONJ
ejpam-1372	419	28	s3(1,0,−1)=2/3	s3(1,0,−1)=2/3	ADP
ejpam-1372	419	29	,	,	PUNCT
ejpam-1372	419	30	while	while	SCONJ
ejpam-1372	419	31	for	for	ADP
ejpam-1372	419	32	a1=1	a1=1	NOUN
ejpam-1372	419	33	,	,	PUNCT
ejpam-1372	419	34	a2=−1	a2=−1	NOUN
ejpam-1372	419	35	,	,	PUNCT
ejpam-1372	419	36	a3=0	a3=0	NOUN
ejpam-1372	419	37	,	,	PUNCT
ejpam-1372	419	38	and	and	CCONJ
ejpam-1372	419	39	k=3	k=3	X
ejpam-1372	419	40	,	,	PUNCT
ejpam-1372	419	41	we	we	PRON
ejpam-1372	419	42	find	find	VERB
ejpam-1372	419	43	that	that	SCONJ
ejpam-1372	419	44	s3(1,−1,0)=1/3	s3(1,−1,0)=1/3	ADJ
ejpam-1372	419	45	.	.	PUNCT
ejpam-1372	420	1	for	for	ADP
ejpam-1372	420	2	a	a	DET
ejpam-1372	420	3	more	more	ADV
ejpam-1372	420	4	complicated	complicated	ADJ
ejpam-1372	420	5	series	series	NOUN
ejpam-1372	420	6	such	such	ADJ
ejpam-1372	420	7	as	as	ADP
ejpam-1372	420	8	s4(3,2,−4,−1	s4(3,2,−4,−1	PROPN
ejpam-1372	420	9	)	)	PUNCT
ejpam-1372	420	10	,	,	PUNCT
ejpam-1372	420	11	we	we	PRON
ejpam-1372	420	12	obtain	obtain	VERB
ejpam-1372	420	13	a	a	DET
ejpam-1372	420	14	limit	limit	NOUN
ejpam-1372	420	15	value	value	NOUN
ejpam-1372	420	16	of	of	ADP
ejpam-1372	420	17	9/4	9/4	NUM
ejpam-1372	420	18	.	.	PUNCT
ejpam-1372	421	1	since	since	SCONJ
ejpam-1372	421	2	we	we	PRON
ejpam-1372	421	3	have	have	AUX
ejpam-1372	421	4	seen	see	VERB
ejpam-1372	421	5	that	that	SCONJ
ejpam-1372	421	6	grandi	grandi	PROPN
ejpam-1372	421	7	’s	’s	PART
ejpam-1372	421	8	series	series	NOUN
ejpam-1372	421	9	is	be	AUX
ejpam-1372	421	10	conditionally	conditionally	ADV
ejpam-1372	421	11	convergent	convergent	ADJ
ejpam-1372	421	12	rather	rather	ADV
ejpam-1372	421	13	than	than	ADP
ejpam-1372	421	14	divergent	divergent	ADJ
ejpam-1372	421	15	,	,	PUNCT
ejpam-1372	421	16	we	we	PRON
ejpam-1372	421	17	now	now	ADV
ejpam-1372	421	18	turn	turn	VERB
ejpam-1372	421	19	to	to	ADP
ejpam-1372	421	20	the	the	DET
ejpam-1372	421	21	question	question	NOUN
ejpam-1372	421	22	of	of	ADP
ejpam-1372	421	23	who	who	PRON
ejpam-1372	421	24	is	be	AUX
ejpam-1372	421	25	correct	correct	ADJ
ejpam-1372	421	26	:	:	PUNCT
ejpam-1372	421	27	callet	callet	NOUN
ejpam-1372	421	28	or	or	CCONJ
ejpam-1372	421	29	lagrange	lagrange	VERB
ejpam-1372	421	30	?	?	PUNCT
ejpam-1372	422	1	in	in	ADP
ejpam-1372	422	2	actual	actual	ADJ
ejpam-1372	422	3	fact	fact	NOUN
ejpam-1372	422	4	,	,	PUNCT
ejpam-1372	422	5	both	both	PRON
ejpam-1372	422	6	are	be	AUX
ejpam-1372	422	7	correct	correct	ADJ
ejpam-1372	422	8	,	,	PUNCT
ejpam-1372	422	9	but	but	CCONJ
ejpam-1372	422	10	for	for	ADP
ejpam-1372	422	11	different	different	ADJ
ejpam-1372	422	12	reasons	reason	NOUN
ejpam-1372	422	13	.	.	PUNCT
ejpam-1372	423	1	first	first	ADV
ejpam-1372	423	2	,	,	PUNCT
ejpam-1372	423	3	we	we	PRON
ejpam-1372	423	4	note	note	VERB
ejpam-1372	423	5	that	that	SCONJ
ejpam-1372	423	6	grandi	grandi	PROPN
ejpam-1372	423	7	’s	’s	PART
ejpam-1372	423	8	series	series	PROPN
ejpam-1372	423	9	admits	admit	VERB
ejpam-1372	423	10	an	an	DET
ejpam-1372	423	11	infinite	infinite	ADJ
ejpam-1372	423	12	number	number	NOUN
ejpam-1372	423	13	of	of	ADP
ejpam-1372	423	14	encodings	encoding	NOUN
ejpam-1372	423	15	.	.	PUNCT
ejpam-1372	424	1	to	to	PART
ejpam-1372	424	2	see	see	VERB
ejpam-1372	424	3	this	this	PRON
ejpam-1372	424	4	more	more	ADV
ejpam-1372	424	5	clearly	clearly	ADV
ejpam-1372	424	6	,	,	PUNCT
ejpam-1372	424	7	consider	consider	VERB
ejpam-1372	424	8	the	the	DET
ejpam-1372	424	9	following	follow	VERB
ejpam-1372	424	10	series	series	NOUN
ejpam-1372	424	11	:	:	PUNCT
ejpam-1372	424	12	lim	lim	PROPN
ejpam-1372	424	13	z→1	z→1	PROPN
ejpam-1372	424	14	s(z	s(z	PROPN
ejpam-1372	424	15	)	)	PUNCT
ejpam-1372	425	1	=	=	SYM
ejpam-1372	425	2	lim	lim	PROPN
ejpam-1372	425	3	z→1	z→1	PROPN
ejpam-1372	425	4	(	(	PUNCT
ejpam-1372	425	5	1−	1−	NUM
ejpam-1372	425	6	zp	zp	NOUN
ejpam-1372	425	7	)	)	PUNCT
ejpam-1372	425	8	�	�	PROPN
ejpam-1372	425	9	1	1	NUM
ejpam-1372	425	10	+	+	NUM
ejpam-1372	425	11	zq	zq	PROPN
ejpam-1372	425	12	+	+	CCONJ
ejpam-1372	425	13	z2q	z2q	PROPN
ejpam-1372	426	1	+	+	CCONJ
ejpam-1372	426	2	z3q	z3q	PROPN
ejpam-1372	426	3	+	+	PUNCT
ejpam-1372	426	4	.	.	PUNCT
ejpam-1372	426	5	.	.	PUNCT
ejpam-1372	426	6	.	.	PUNCT
ejpam-1372	427	1	�	�	PROPN
ejpam-1372	427	2	=	=	SYM
ejpam-1372	427	3	lim	lim	PROPN
ejpam-1372	427	4	z→1	z→1	PROPN
ejpam-1372	427	5	(	(	PUNCT
ejpam-1372	427	6	1−	1−	NUM
ejpam-1372	427	7	zp	zp	X
ejpam-1372	427	8	)	)	PUNCT
ejpam-1372	427	9	∞	∞	PROPN
ejpam-1372	427	10	∑	∑	PROPN
ejpam-1372	427	11	k=0	k=0	PROPN
ejpam-1372	427	12	zqk	zqk	PROPN
ejpam-1372	427	13	,	,	PUNCT
ejpam-1372	427	14	(	(	PUNCT
ejpam-1372	427	15	37	37	NUM
ejpam-1372	427	16	)	)	PUNCT
ejpam-1372	427	17	where	where	SCONJ
ejpam-1372	427	18	both	both	DET
ejpam-1372	427	19	ℜ	ℜ	ADJ
ejpam-1372	427	20	p	p	NOUN
ejpam-1372	427	21	and	and	CCONJ
ejpam-1372	427	22	ℜq	ℜq	PROPN
ejpam-1372	427	23	are	be	AUX
ejpam-1372	427	24	greater	great	ADJ
ejpam-1372	427	25	than	than	ADP
ejpam-1372	427	26	zero	zero	NUM
ejpam-1372	427	27	.	.	PUNCT
ejpam-1372	428	1	it	it	PRON
ejpam-1372	428	2	is	be	AUX
ejpam-1372	428	3	obvious	obvious	ADJ
ejpam-1372	428	4	that	that	SCONJ
ejpam-1372	428	5	if	if	SCONJ
ejpam-1372	428	6	we	we	PRON
ejpam-1372	428	7	put	put	VERB
ejpam-1372	428	8	z=1	z=1	PROPN
ejpam-1372	428	9	in	in	ADP
ejpam-1372	428	10	the	the	DET
ejpam-1372	428	11	above	above	ADJ
ejpam-1372	428	12	result	result	NOUN
ejpam-1372	428	13	,	,	PUNCT
ejpam-1372	428	14	then	then	ADV
ejpam-1372	428	15	we	we	PRON
ejpam-1372	428	16	will	will	AUX
ejpam-1372	428	17	obtain	obtain	VERB
ejpam-1372	428	18	grandi	grandi	PROPN
ejpam-1372	428	19	’s	’s	PART
ejpam-1372	428	20	series	series	NOUN
ejpam-1372	428	21	.	.	PUNCT
ejpam-1372	429	1	introducing	introduce	VERB
ejpam-1372	429	2	the	the	DET
ejpam-1372	429	3	regularised	regularise	VERB
ejpam-1372	429	4	value	value	NOUN
ejpam-1372	429	5	of	of	ADP
ejpam-1372	429	6	the	the	DET
ejpam-1372	429	7	geometric	geometric	ADJ
ejpam-1372	429	8	series	series	NOUN
ejpam-1372	429	9	,	,	PUNCT
ejpam-1372	429	10	viz	viz	PROPN
ejpam-1372	429	11	.	.	PUNCT
ejpam-1372	430	1	equivalence	equivalence	NOUN
ejpam-1372	430	2	(	(	PUNCT
ejpam-1372	430	3	13	13	NUM
ejpam-1372	430	4	)	)	PUNCT
ejpam-1372	430	5	,	,	PUNCT
ejpam-1372	430	6	into	into	ADP
ejpam-1372	430	7	the	the	DET
ejpam-1372	430	8	above	above	ADJ
ejpam-1372	430	9	result	result	NOUN
ejpam-1372	430	10	,	,	PUNCT
ejpam-1372	430	11	we	we	PRON
ejpam-1372	430	12	arrive	arrive	VERB
ejpam-1372	430	13	at	at	ADP
ejpam-1372	430	14	lim	lim	PROPN
ejpam-1372	430	15	z→1	z→1	PROPN
ejpam-1372	430	16	s(z	s(z	PROPN
ejpam-1372	430	17	)	)	PUNCT
ejpam-1372	431	1	=	=	SYM
ejpam-1372	431	2	lim	lim	PROPN
ejpam-1372	431	3	z→1	z→1	PROPN
ejpam-1372	431	4	�	�	PROPN
ejpam-1372	431	5	1−	1−	NUM
ejpam-1372	431	6	zp	zp	PROPN
ejpam-1372	431	7	1−	1−	NUM
ejpam-1372	431	8	zq	zq	PROPN
ejpam-1372	431	9	�	�	PROPN
ejpam-1372	431	10	=	=	PUNCT
ejpam-1372	432	1	p	p	X
ejpam-1372	432	2	q	q	X
ejpam-1372	432	3	.	.	PUNCT
ejpam-1372	433	1	(	(	PUNCT
ejpam-1372	433	2	38	38	NUM
ejpam-1372	433	3	)	)	PUNCT
ejpam-1372	433	4	eq	eq	NOUN
ejpam-1372	433	5	.	.	PUNCT
ejpam-1372	434	1	(	(	PUNCT
ejpam-1372	434	2	38	38	NUM
ejpam-1372	434	3	)	)	PUNCT
ejpam-1372	434	4	has	have	AUX
ejpam-1372	434	5	been	be	AUX
ejpam-1372	434	6	obtained	obtain	VERB
ejpam-1372	434	7	by	by	ADP
ejpam-1372	434	8	applying	apply	VERB
ejpam-1372	434	9	l’hospital	l’hospital	PROPN
ejpam-1372	434	10	’s	’s	PART
ejpam-1372	434	11	rule	rule	NOUN
ejpam-1372	434	12	[	[	X
ejpam-1372	434	13	30	30	NUM
ejpam-1372	434	14	]	]	PUNCT
ejpam-1372	434	15	.	.	PUNCT
ejpam-1372	435	1	note	note	VERB
ejpam-1372	435	2	that	that	SCONJ
ejpam-1372	435	3	there	there	PRON
ejpam-1372	435	4	is	be	VERB
ejpam-1372	435	5	no	no	DET
ejpam-1372	435	6	equivalence	equivalence	NOUN
ejpam-1372	435	7	symbol	symbol	NOUN
ejpam-1372	435	8	in	in	ADP
ejpam-1372	435	9	eq	eq	ADP
ejpam-1372	435	10	.	.	PUNCT
ejpam-1372	436	1	(	(	PUNCT
ejpam-1372	436	2	38	38	NUM
ejpam-1372	436	3	)	)	PUNCT
ejpam-1372	436	4	because	because	SCONJ
ejpam-1372	436	5	the	the	DET
ejpam-1372	436	6	infinity	infinity	NOUN
ejpam-1372	436	7	in	in	ADP
ejpam-1372	436	8	the	the	DET
ejpam-1372	436	9	series	series	NOUN
ejpam-1372	436	10	is	be	AUX
ejpam-1372	436	11	cancelled	cancel	VERB
ejpam-1372	436	12	by	by	ADP
ejpam-1372	436	13	the	the	DET
ejpam-1372	436	14	factor	factor	NOUN
ejpam-1372	436	15	of	of	ADP
ejpam-1372	436	16	(	(	PUNCT
ejpam-1372	436	17	1−	1−	NUM
ejpam-1372	436	18	zp	zp	NOUN
ejpam-1372	436	19	)	)	PUNCT
ejpam-1372	436	20	preceding	precede	VERB
ejpam-1372	436	21	it	it	PRON
ejpam-1372	436	22	.	.	PUNCT
ejpam-1372	437	1	for	for	ADP
ejpam-1372	437	2	p=1	p=1	PROPN
ejpam-1372	437	3	and	and	CCONJ
ejpam-1372	437	4	q=2	q=2	PROPN
ejpam-1372	437	5	,	,	PUNCT
ejpam-1372	437	6	we	we	PRON
ejpam-1372	437	7	find	find	VERB
ejpam-1372	437	8	that	that	SCONJ
ejpam-1372	437	9	s(z	s(z	NOUN
ejpam-1372	437	10	)	)	PUNCT
ejpam-1372	437	11	=	=	SYM
ejpam-1372	438	1	1−	1−	NUM
ejpam-1372	438	2	z	z	NOUN
ejpam-1372	438	3	+	+	NOUN
ejpam-1372	438	4	z2	z2	PROPN
ejpam-1372	438	5	−	−	PROPN
ejpam-1372	438	6	z3	z3	PROPN
ejpam-1372	438	7	+	+	CCONJ
ejpam-1372	438	8	z4	z4	PROPN
ejpam-1372	438	9	−	−	PROPN
ejpam-1372	438	10	z5	z5	PROPN
ejpam-1372	438	11	+	+	CCONJ
ejpam-1372	438	12	z6	z6	PROPN
ejpam-1372	438	13	+	+	CCONJ
ejpam-1372	438	14	.	.	PUNCT
ejpam-1372	438	15	.	.	PUNCT
ejpam-1372	438	16	.	.	PUNCT
ejpam-1372	439	1	,	,	PUNCT
ejpam-1372	439	2	(	(	PUNCT
ejpam-1372	439	3	39	39	NUM
ejpam-1372	439	4	)	)	PUNCT
ejpam-1372	439	5	while	while	SCONJ
ejpam-1372	439	6	if	if	SCONJ
ejpam-1372	439	7	p=2	p=2	PROPN
ejpam-1372	439	8	and	and	CCONJ
ejpam-1372	439	9	q=3	q=3	PROPN
ejpam-1372	439	10	,	,	PUNCT
ejpam-1372	439	11	then	then	ADV
ejpam-1372	439	12	s(z	s(z	PROPN
ejpam-1372	439	13	)	)	PUNCT
ejpam-1372	439	14	becomes	become	VERB
ejpam-1372	439	15	s(z	s(z	PROPN
ejpam-1372	439	16	)	)	PUNCT
ejpam-1372	439	17	=	=	SYM
ejpam-1372	440	1	1−	1−	NUM
ejpam-1372	440	2	0	0	NUM
ejpam-1372	440	3	·	·	PUNCT
ejpam-1372	440	4	z	z	X
ejpam-1372	441	1	−	−	PROPN
ejpam-1372	441	2	z2	z2	PROPN
ejpam-1372	441	3	+	+	CCONJ
ejpam-1372	441	4	z3	z3	PROPN
ejpam-1372	441	5	+	+	CCONJ
ejpam-1372	441	6	0	0	NUM
ejpam-1372	441	7	·	·	PUNCT
ejpam-1372	441	8	z4	z4	PROPN
ejpam-1372	441	9	−	−	PROPN
ejpam-1372	441	10	z5	z5	PROPN
ejpam-1372	441	11	+	+	CCONJ
ejpam-1372	441	12	z6	z6	PROPN
ejpam-1372	441	13	+	+	CCONJ
ejpam-1372	441	14	.	.	PUNCT
ejpam-1372	441	15	.	.	PUNCT
ejpam-1372	441	16	.	.	PUNCT
ejpam-1372	441	17	.	.	PUNCT
ejpam-1372	442	1	(	(	PUNCT
ejpam-1372	442	2	40	40	NUM
ejpam-1372	442	3	)	)	PUNCT
ejpam-1372	442	4	therefore	therefore	ADV
ejpam-1372	442	5	,	,	PUNCT
ejpam-1372	442	6	in	in	ADP
ejpam-1372	442	7	the	the	DET
ejpam-1372	442	8	first	first	ADJ
ejpam-1372	442	9	instance	instance	NOUN
ejpam-1372	442	10	we	we	PRON
ejpam-1372	442	11	recover	recover	VERB
ejpam-1372	442	12	the	the	DET
ejpam-1372	442	13	geometric	geometric	ADJ
ejpam-1372	442	14	series	series	NOUN
ejpam-1372	442	15	with	with	ADP
ejpam-1372	442	16	z	z	PROPN
ejpam-1372	442	17	replaced	replace	VERB
ejpam-1372	442	18	by	by	ADP
ejpam-1372	442	19	−z	−z	NOUN
ejpam-1372	442	20	,	,	PUNCT
ejpam-1372	442	21	while	while	SCONJ
ejpam-1372	442	22	in	in	ADP
ejpam-1372	442	23	the	the	DET
ejpam-1372	442	24	second	second	ADJ
ejpam-1372	442	25	case	case	NOUN
ejpam-1372	442	26	we	we	PRON
ejpam-1372	442	27	recover	recover	VERB
ejpam-1372	442	28	the	the	DET
ejpam-1372	442	29	callet	callet	NOUN
ejpam-1372	442	30	/	/	SYM
ejpam-1372	442	31	lagrange	lagrange	PROPN
ejpam-1372	442	32	example	example	NOUN
ejpam-1372	442	33	.	.	PUNCT
ejpam-1372	443	1	for	for	ADP
ejpam-1372	443	2	p=4	p=4	ADP
ejpam-1372	443	3	and	and	CCONJ
ejpam-1372	443	4	q=5	q=5	PROPN
ejpam-1372	443	5	,	,	PUNCT
ejpam-1372	443	6	however	however	ADV
ejpam-1372	443	7	,	,	PUNCT
ejpam-1372	443	8	we	we	PRON
ejpam-1372	443	9	find	find	VERB
ejpam-1372	443	10	that	that	SCONJ
ejpam-1372	443	11	s(z	s(z	NOUN
ejpam-1372	443	12	)	)	PUNCT
ejpam-1372	443	13	=	=	SYM
ejpam-1372	443	14	1−	1−	NUM
ejpam-1372	443	15	z4	z4	X
ejpam-1372	443	16	+	+	CCONJ
ejpam-1372	443	17	z5	z5	PROPN
ejpam-1372	443	18	−	−	PROPN
ejpam-1372	443	19	z9	z9	PROPN
ejpam-1372	443	20	+	+	CCONJ
ejpam-1372	443	21	z10	z10	PROPN
ejpam-1372	443	22	−	−	PROPN
ejpam-1372	443	23	z14	z14	PROPN
ejpam-1372	444	1	+	+	X
ejpam-1372	444	2	.	.	PUNCT
ejpam-1372	444	3	.	.	PUNCT
ejpam-1372	445	1	.	.	PUNCT
ejpam-1372	446	1	.	.	PUNCT
ejpam-1372	447	1	(	(	PUNCT
ejpam-1372	447	2	41	41	NUM
ejpam-1372	447	3	)	)	PUNCT
ejpam-1372	447	4	in	in	ADP
ejpam-1372	447	5	the	the	DET
ejpam-1372	447	6	three	three	NUM
ejpam-1372	447	7	preceding	precede	VERB
ejpam-1372	447	8	examples	example	NOUN
ejpam-1372	447	9	putting	put	VERB
ejpam-1372	447	10	z	z	NOUN
ejpam-1372	447	11	=	=	SYM
ejpam-1372	447	12	1	1	NUM
ejpam-1372	447	13	always	always	ADV
ejpam-1372	447	14	yields	yield	VERB
ejpam-1372	447	15	grandi	grandi	PROPN
ejpam-1372	447	16	’s	’s	PART
ejpam-1372	447	17	series	series	NOUN
ejpam-1372	447	18	.	.	PUNCT
ejpam-1372	448	1	in	in	ADP
ejpam-1372	448	2	fact	fact	NOUN
ejpam-1372	448	3	,	,	PUNCT
ejpam-1372	448	4	eq	eq	NOUN
ejpam-1372	448	5	.	.	PUNCT
ejpam-1372	449	1	(	(	PUNCT
ejpam-1372	449	2	38	38	NUM
ejpam-1372	449	3	)	)	PUNCT
ejpam-1372	449	4	admits	admit	VERB
ejpam-1372	449	5	an	an	DET
ejpam-1372	449	6	infinite	infinite	ADJ
ejpam-1372	449	7	number	number	NOUN
ejpam-1372	449	8	of	of	ADP
ejpam-1372	449	9	representations	representation	NOUN
ejpam-1372	449	10	for	for	ADP
ejpam-1372	449	11	grandi	grandi	PROPN
ejpam-1372	449	12	’s	’s	PART
ejpam-1372	449	13	series	series	NOUN
ejpam-1372	449	14	.	.	PUNCT
ejpam-1372	450	1	therefore	therefore	ADV
ejpam-1372	450	2	,	,	PUNCT
ejpam-1372	450	3	the	the	DET
ejpam-1372	450	4	problem	problem	NOUN
ejpam-1372	450	5	is	be	AUX
ejpam-1372	450	6	that	that	SCONJ
ejpam-1372	450	7	grandi	grandi	PROPN
ejpam-1372	450	8	’s	’s	PART
ejpam-1372	450	9	series	series	NOUN
ejpam-1372	450	10	does	do	AUX
ejpam-1372	450	11	not	not	PART
ejpam-1372	450	12	possess	possess	VERB
ejpam-1372	450	13	a	a	DET
ejpam-1372	450	14	unique	unique	ADJ
ejpam-1372	450	15	representation	representation	NOUN
ejpam-1372	450	16	.	.	PUNCT
ejpam-1372	451	1	to	to	PART
ejpam-1372	451	2	obtain	obtain	VERB
ejpam-1372	451	3	a	a	DET
ejpam-1372	451	4	specific	specific	ADJ
ejpam-1372	451	5	representation	representation	NOUN
ejpam-1372	451	6	,	,	PUNCT
ejpam-1372	451	7	we	we	PRON
ejpam-1372	451	8	need	need	VERB
ejpam-1372	451	9	to	to	PART
ejpam-1372	451	10	impose	impose	VERB
ejpam-1372	451	11	conditions	condition	NOUN
ejpam-1372	451	12	so	so	SCONJ
ejpam-1372	451	13	that	that	SCONJ
ejpam-1372	451	14	one	one	NUM
ejpam-1372	451	15	specific	specific	ADJ
ejpam-1372	451	16	representation	representation	NOUN
ejpam-1372	451	17	can	can	AUX
ejpam-1372	451	18	be	be	AUX
ejpam-1372	451	19	isolated	isolate	VERB
ejpam-1372	451	20	for	for	ADP
ejpam-1372	451	21	s(z	s(z	PROPN
ejpam-1372	451	22	)	)	PUNCT
ejpam-1372	451	23	.	.	PUNCT
ejpam-1372	452	1	this	this	PRON
ejpam-1372	452	2	is	be	AUX
ejpam-1372	452	3	essentially	essentially	ADV
ejpam-1372	452	4	what	what	PRON
ejpam-1372	452	5	lagrange	lagrange	NOUN
ejpam-1372	452	6	did	do	VERB
ejpam-1372	452	7	by	by	ADP
ejpam-1372	452	8	stipulating	stipulate	VERB
ejpam-1372	452	9	that	that	SCONJ
ejpam-1372	452	10	s(z	s(z	PROPN
ejpam-1372	452	11	)	)	PUNCT
ejpam-1372	452	12	had	have	VERB
ejpam-1372	452	13	to	to	PART
ejpam-1372	452	14	be	be	AUX
ejpam-1372	452	15	a	a	DET
ejpam-1372	452	16	“	"	PUNCT
ejpam-1372	452	17	true	true	ADJ
ejpam-1372	452	18	”	"	PUNCT
ejpam-1372	452	19	power	power	NOUN
ejpam-1372	452	20	series	series	NOUN
ejpam-1372	452	21	.	.	PUNCT
ejpam-1372	453	1	consequently	consequently	ADV
ejpam-1372	453	2	,	,	PUNCT
ejpam-1372	453	3	the	the	DET
ejpam-1372	453	4	powers	power	NOUN
ejpam-1372	453	5	of	of	ADP
ejpam-1372	453	6	z	z	PROPN
ejpam-1372	453	7	in	in	ADP
ejpam-1372	453	8	s(z	s(z	PROPN
ejpam-1372	453	9	)	)	PUNCT
ejpam-1372	453	10	had	have	VERB
ejpam-1372	453	11	to	to	PART
ejpam-1372	453	12	be	be	AUX
ejpam-1372	453	13	positive	positive	ADJ
ejpam-1372	453	14	integers	integer	NOUN
ejpam-1372	453	15	,	,	PUNCT
ejpam-1372	453	16	which	which	PRON
ejpam-1372	453	17	automatically	automatically	ADV
ejpam-1372	453	18	excludes	exclude	VERB
ejpam-1372	453	19	p	p	NOUN
ejpam-1372	453	20	and	and	CCONJ
ejpam-1372	453	21	q	q	NOUN
ejpam-1372	453	22	from	from	ADP
ejpam-1372	453	23	being	be	AUX
ejpam-1372	453	24	anything	anything	PRON
ejpam-1372	453	25	other	other	ADJ
ejpam-1372	453	26	than	than	ADP
ejpam-1372	453	27	positive	positive	ADJ
ejpam-1372	453	28	integers	integer	NOUN
ejpam-1372	453	29	.	.	PUNCT
ejpam-1372	454	1	it	it	PRON
ejpam-1372	454	2	also	also	ADV
ejpam-1372	454	3	implies	imply	VERB
ejpam-1372	454	4	that	that	SCONJ
ejpam-1372	454	5	all	all	DET
ejpam-1372	454	6	coefficients	coefficient	NOUN
ejpam-1372	454	7	of	of	ADP
ejpam-1372	454	8	s(z	s(z	PROPN
ejpam-1372	454	9	)	)	PUNCT
ejpam-1372	454	10	have	have	VERB
ejpam-1372	454	11	to	to	PART
ejpam-1372	454	12	be	be	AUX
ejpam-1372	454	13	non	non	ADJ
ejpam-1372	454	14	-	-	ADJ
ejpam-1372	454	15	zero	zero	NUM
ejpam-1372	454	16	.	.	PUNCT
ejpam-1372	455	1	then	then	ADV
ejpam-1372	455	2	one	one	NUM
ejpam-1372	455	3	finds	find	VERB
ejpam-1372	455	4	that	that	SCONJ
ejpam-1372	455	5	p=	p=	NOUN
ejpam-1372	455	6	1	1	NUM
ejpam-1372	455	7	and	and	CCONJ
ejpam-1372	455	8	q=	q=	ADV
ejpam-1372	455	9	2	2	NUM
ejpam-1372	455	10	,	,	PUNCT
ejpam-1372	455	11	which	which	PRON
ejpam-1372	455	12	yields	yield	VERB
ejpam-1372	455	13	v.	v.	ADP
ejpam-1372	455	14	kowalenko	kowalenko	PROPN
ejpam-1372	455	15	/	/	SYM
ejpam-1372	455	16	eur	eur	PROPN
ejpam-1372	455	17	.	.	PUNCT
ejpam-1372	456	1	j.	j.	PROPN
ejpam-1372	456	2	pure	pure	PROPN
ejpam-1372	456	3	appl	appl	PROPN
ejpam-1372	456	4	.	.	PROPN
ejpam-1372	456	5	math	math	PROPN
ejpam-1372	456	6	,	,	PUNCT
ejpam-1372	456	7	4	4	NUM
ejpam-1372	456	8	(	(	PUNCT
ejpam-1372	456	9	2011	2011	NUM
ejpam-1372	456	10	)	)	PUNCT
ejpam-1372	456	11	,	,	PUNCT
ejpam-1372	456	12	370	370	NUM
ejpam-1372	456	13	-	-	SYM
ejpam-1372	456	14	423	423	NUM
ejpam-1372	456	15	384	384	NUM
ejpam-1372	456	16	the	the	DET
ejpam-1372	456	17	value	value	NOUN
ejpam-1372	456	18	for	for	ADP
ejpam-1372	456	19	the	the	DET
ejpam-1372	456	20	limit	limit	NOUN
ejpam-1372	456	21	of	of	ADP
ejpam-1372	456	22	the	the	DET
ejpam-1372	456	23	series	series	NOUN
ejpam-1372	456	24	obtained	obtain	VERB
ejpam-1372	456	25	by	by	ADP
ejpam-1372	456	26	grandi	grandi	PROPN
ejpam-1372	456	27	,	,	PUNCT
ejpam-1372	456	28	euler	euler	NOUN
ejpam-1372	456	29	and	and	CCONJ
ejpam-1372	456	30	leibniz	leibniz	PROPN
ejpam-1372	456	31	,	,	PUNCT
ejpam-1372	456	32	not	not	PART
ejpam-1372	456	33	to	to	PART
ejpam-1372	456	34	mention	mention	VERB
ejpam-1372	456	35	lagrange	lagrange	NOUN
ejpam-1372	456	36	,	,	PUNCT
ejpam-1372	456	37	of	of	ADP
ejpam-1372	456	38	course	course	NOUN
ejpam-1372	456	39	.	.	PUNCT
ejpam-1372	457	1	the	the	DET
ejpam-1372	457	2	problem	problem	NOUN
ejpam-1372	457	3	concerning	concern	VERB
ejpam-1372	457	4	uniqueness	uniqueness	NOUN
ejpam-1372	457	5	does	do	AUX
ejpam-1372	457	6	not	not	PART
ejpam-1372	457	7	arise	arise	VERB
ejpam-1372	457	8	in	in	ADP
ejpam-1372	457	9	asymptotics	asymptotic	NOUN
ejpam-1372	457	10	because	because	SCONJ
ejpam-1372	457	11	an	an	DET
ejpam-1372	457	12	asymptotic	asymptotic	ADJ
ejpam-1372	457	13	expansion	expansion	NOUN
ejpam-1372	457	14	is	be	AUX
ejpam-1372	457	15	generally	generally	ADV
ejpam-1372	457	16	determined	determine	VERB
ejpam-1372	457	17	over	over	ADP
ejpam-1372	457	18	a	a	DET
ejpam-1372	457	19	range	range	NOUN
ejpam-1372	457	20	of	of	ADP
ejpam-1372	457	21	values	value	NOUN
ejpam-1372	457	22	for	for	ADP
ejpam-1372	457	23	the	the	DET
ejpam-1372	457	24	variable	variable	NOUN
ejpam-1372	457	25	.	.	PUNCT
ejpam-1372	458	1	hence	hence	ADV
ejpam-1372	458	2	,	,	PUNCT
ejpam-1372	458	3	the	the	DET
ejpam-1372	458	4	asymptotic	asymptotic	ADJ
ejpam-1372	458	5	expansion	expansion	NOUN
ejpam-1372	458	6	is	be	AUX
ejpam-1372	458	7	valid	valid	ADJ
ejpam-1372	458	8	for	for	ADP
ejpam-1372	458	9	an	an	DET
ejpam-1372	458	10	infinite	infinite	ADJ
ejpam-1372	458	11	number	number	NOUN
ejpam-1372	458	12	of	of	ADP
ejpam-1372	458	13	values	value	NOUN
ejpam-1372	458	14	of	of	ADP
ejpam-1372	458	15	the	the	DET
ejpam-1372	458	16	variable	variable	NOUN
ejpam-1372	458	17	,	,	PUNCT
ejpam-1372	458	18	which	which	PRON
ejpam-1372	458	19	guarantees	guarantee	VERB
ejpam-1372	458	20	its	its	PRON
ejpam-1372	458	21	uniqueness	uniqueness	NOUN
ejpam-1372	458	22	.	.	PUNCT
ejpam-1372	459	1	however	however	ADV
ejpam-1372	459	2	,	,	PUNCT
ejpam-1372	459	3	grandi	grandi	PROPN
ejpam-1372	459	4	’s	’s	PART
ejpam-1372	459	5	series	series	NOUN
ejpam-1372	459	6	represents	represent	VERB
ejpam-1372	459	7	an	an	DET
ejpam-1372	459	8	infinite	infinite	ADJ
ejpam-1372	459	9	series	series	NOUN
ejpam-1372	459	10	for	for	ADP
ejpam-1372	459	11	one	one	NUM
ejpam-1372	459	12	value	value	NOUN
ejpam-1372	459	13	of	of	ADP
ejpam-1372	459	14	the	the	DET
ejpam-1372	459	15	variable	variable	NOUN
ejpam-1372	459	16	,	,	PUNCT
ejpam-1372	459	17	viz	viz	PROPN
ejpam-1372	459	18	.	.	PUNCT
ejpam-1372	459	19	z=	z=	PROPN
ejpam-1372	460	1	1	1	X
ejpam-1372	460	2	.	.	PUNCT
ejpam-1372	460	3	consequently	consequently	ADV
ejpam-1372	460	4	,	,	PUNCT
ejpam-1372	460	5	a	a	DET
ejpam-1372	460	6	multitude	multitude	NOUN
ejpam-1372	460	7	of	of	ADP
ejpam-1372	460	8	valid	valid	ADJ
ejpam-1372	460	9	representations	representation	NOUN
ejpam-1372	460	10	exist	exist	VERB
ejpam-1372	460	11	for	for	ADP
ejpam-1372	460	12	such	such	DET
ejpam-1372	460	13	a	a	DET
ejpam-1372	460	14	series	series	NOUN
ejpam-1372	460	15	as	as	SCONJ
ejpam-1372	460	16	we	we	PRON
ejpam-1372	460	17	have	have	AUX
ejpam-1372	460	18	witnessed	witness	VERB
ejpam-1372	460	19	above	above	ADV
ejpam-1372	460	20	.	.	PUNCT
ejpam-1372	461	1	this	this	DET
ejpam-1372	461	2	situation	situation	NOUN
ejpam-1372	461	3	resembles	resemble	VERB
ejpam-1372	461	4	the	the	DET
ejpam-1372	461	5	application	application	NOUN
ejpam-1372	461	6	of	of	ADP
ejpam-1372	461	7	boundary	boundary	ADJ
ejpam-1372	461	8	conditions	condition	NOUN
ejpam-1372	461	9	in	in	ADP
ejpam-1372	461	10	order	order	NOUN
ejpam-1372	461	11	to	to	PART
ejpam-1372	461	12	derive	derive	VERB
ejpam-1372	461	13	a	a	DET
ejpam-1372	461	14	specific	specific	ADJ
ejpam-1372	461	15	solution	solution	NOUN
ejpam-1372	461	16	from	from	ADP
ejpam-1372	461	17	the	the	DET
ejpam-1372	461	18	general	general	ADJ
ejpam-1372	461	19	solution	solution	NOUN
ejpam-1372	461	20	to	to	ADP
ejpam-1372	461	21	a	a	DET
ejpam-1372	461	22	differential	differential	ADJ
ejpam-1372	461	23	equation	equation	NOUN
ejpam-1372	461	24	.	.	PUNCT
ejpam-1372	462	1	7	7	X
ejpam-1372	462	2	.	.	X
ejpam-1372	462	3	logarithmic	logarithmic	ADJ
ejpam-1372	462	4	divergence	divergence	NOUN
ejpam-1372	462	5	it	it	PRON
ejpam-1372	462	6	should	should	AUX
ejpam-1372	462	7	be	be	AUX
ejpam-1372	462	8	emphasised	emphasise	VERB
ejpam-1372	462	9	again	again	ADV
ejpam-1372	462	10	that	that	SCONJ
ejpam-1372	462	11	the	the	DET
ejpam-1372	462	12	regularisation	regularisation	NOUN
ejpam-1372	462	13	of	of	ADP
ejpam-1372	462	14	series	series	NOUN
ejpam-1372	462	15	which	which	PRON
ejpam-1372	462	16	diverge	diverge	VERB
ejpam-1372	462	17	logarithmically	logarithmically	ADV
ejpam-1372	462	18	such	such	ADJ
ejpam-1372	462	19	as	as	ADP
ejpam-1372	462	20	the	the	DET
ejpam-1372	462	21	harmonic	harmonic	ADJ
ejpam-1372	462	22	series	series	NOUN
ejpam-1372	462	23	presented	present	VERB
ejpam-1372	462	24	earlier	early	ADV
ejpam-1372	462	25	is	be	AUX
ejpam-1372	462	26	a	a	DET
ejpam-1372	462	27	much	much	ADV
ejpam-1372	462	28	different	different	ADJ
ejpam-1372	462	29	proposition	proposition	NOUN
ejpam-1372	462	30	from	from	ADP
ejpam-1372	462	31	that	that	PRON
ejpam-1372	462	32	for	for	ADP
ejpam-1372	462	33	the	the	DET
ejpam-1372	462	34	geometric	geometric	ADJ
ejpam-1372	462	35	series	series	NOUN
ejpam-1372	462	36	.	.	PUNCT
ejpam-1372	463	1	to	to	PART
ejpam-1372	463	2	see	see	VERB
ejpam-1372	463	3	this	this	PRON
ejpam-1372	463	4	more	more	ADV
ejpam-1372	463	5	clearly	clearly	ADV
ejpam-1372	463	6	,	,	PUNCT
ejpam-1372	463	7	if	if	SCONJ
ejpam-1372	463	8	we	we	PRON
ejpam-1372	463	9	put	put	VERB
ejpam-1372	463	10	z=−1	z=−1	NUM
ejpam-1372	463	11	in	in	ADP
ejpam-1372	463	12	equivalence	equivalence	NOUN
ejpam-1372	463	13	(	(	PUNCT
ejpam-1372	463	14	15	15	NUM
ejpam-1372	463	15	)	)	PUNCT
ejpam-1372	463	16	,	,	PUNCT
ejpam-1372	463	17	then	then	ADV
ejpam-1372	463	18	we	we	PRON
ejpam-1372	463	19	obtain	obtain	VERB
ejpam-1372	463	20	∞	∞	NUM
ejpam-1372	463	21	∑	∑	PROPN
ejpam-1372	463	22	k=0	k=0	PROPN
ejpam-1372	463	23	1	1	NUM
ejpam-1372	463	24	k+	k+	NOUN
ejpam-1372	463	25	1	1	NUM
ejpam-1372	463	26	−	−	NOUN
ejpam-1372	463	27	log(∞)≡	log(∞)≡	NOUN
ejpam-1372	463	28	0	0	PUNCT
ejpam-1372	463	29	.	.	PUNCT
ejpam-1372	464	1	(	(	PUNCT
ejpam-1372	464	2	42	42	NUM
ejpam-1372	464	3	)	)	PUNCT
ejpam-1372	464	4	where	where	SCONJ
ejpam-1372	464	5	−	−	PROPN
ejpam-1372	464	6	log(0	log(0	NOUN
ejpam-1372	464	7	)	)	PUNCT
ejpam-1372	464	8	has	have	AUX
ejpam-1372	464	9	been	be	AUX
ejpam-1372	464	10	replaced	replace	VERB
ejpam-1372	464	11	by	by	ADP
ejpam-1372	464	12	log(∞	log(∞	PROPN
ejpam-1372	464	13	)	)	PUNCT
ejpam-1372	464	14	.	.	PUNCT
ejpam-1372	465	1	the	the	DET
ejpam-1372	465	2	problem	problem	NOUN
ejpam-1372	465	3	with	with	ADP
ejpam-1372	465	4	this	this	DET
ejpam-1372	465	5	result	result	NOUN
ejpam-1372	465	6	is	be	AUX
ejpam-1372	465	7	that	that	SCONJ
ejpam-1372	465	8	it	it	PRON
ejpam-1372	465	9	has	have	AUX
ejpam-1372	465	10	been	be	AUX
ejpam-1372	465	11	obtained	obtain	VERB
ejpam-1372	465	12	by	by	ADP
ejpam-1372	465	13	integrating	integrate	VERB
ejpam-1372	465	14	the	the	DET
ejpam-1372	465	15	singularity	singularity	NOUN
ejpam-1372	465	16	in	in	ADP
ejpam-1372	465	17	the	the	DET
ejpam-1372	465	18	geometric	geometric	ADJ
ejpam-1372	465	19	series	series	NOUN
ejpam-1372	465	20	,	,	PUNCT
ejpam-1372	465	21	bearing	bear	VERB
ejpam-1372	465	22	in	in	ADP
ejpam-1372	465	23	mind	mind	NOUN
ejpam-1372	465	24	that	that	SCONJ
ejpam-1372	465	25	the	the	DET
ejpam-1372	465	26	singularity	singularity	NOUN
ejpam-1372	465	27	is	be	AUX
ejpam-1372	465	28	now	now	ADV
ejpam-1372	465	29	situated	situate	VERB
ejpam-1372	465	30	at	at	ADP
ejpam-1372	465	31	z=−1	z=−1	NUM
ejpam-1372	465	32	rather	rather	ADV
ejpam-1372	465	33	than	than	ADP
ejpam-1372	465	34	at	at	ADP
ejpam-1372	465	35	z=1	z=1	NUM
ejpam-1372	465	36	due	due	ADP
ejpam-1372	465	37	to	to	ADP
ejpam-1372	465	38	fact	fact	NOUN
ejpam-1372	465	39	that	that	SCONJ
ejpam-1372	465	40	z	z	NOUN
ejpam-1372	465	41	has	have	AUX
ejpam-1372	465	42	been	be	AUX
ejpam-1372	465	43	replaced	replace	VERB
ejpam-1372	465	44	by	by	ADP
ejpam-1372	465	45	−z	−z	NOUN
ejpam-1372	465	46	in	in	ADP
ejpam-1372	465	47	the	the	DET
ejpam-1372	465	48	derivation	derivation	NOUN
ejpam-1372	465	49	of	of	ADP
ejpam-1372	465	50	equivalence	equivalence	NOUN
ejpam-1372	465	51	(	(	PUNCT
ejpam-1372	465	52	15	15	NUM
ejpam-1372	465	53	)	)	PUNCT
ejpam-1372	465	54	.	.	PUNCT
ejpam-1372	466	1	as	as	ADV
ejpam-1372	466	2	yet	yet	ADV
ejpam-1372	466	3	,	,	PUNCT
ejpam-1372	466	4	a	a	DET
ejpam-1372	466	5	theory	theory	NOUN
ejpam-1372	466	6	of	of	ADP
ejpam-1372	466	7	integrating	integrating	NOUN
ejpam-1372	466	8	singularities	singularity	NOUN
ejpam-1372	466	9	does	do	AUX
ejpam-1372	466	10	not	not	PART
ejpam-1372	466	11	exist	exist	VERB
ejpam-1372	466	12	and	and	CCONJ
ejpam-1372	466	13	it	it	PRON
ejpam-1372	466	14	could	could	AUX
ejpam-1372	466	15	well	well	ADV
ejpam-1372	466	16	be	be	AUX
ejpam-1372	466	17	that	that	SCONJ
ejpam-1372	466	18	there	there	PRON
ejpam-1372	466	19	may	may	AUX
ejpam-1372	466	20	be	be	AUX
ejpam-1372	466	21	a	a	DET
ejpam-1372	466	22	missing	missing	ADJ
ejpam-1372	466	23	term	term	NOUN
ejpam-1372	466	24	like	like	ADP
ejpam-1372	466	25	a	a	DET
ejpam-1372	466	26	constant	constant	NOUN
ejpam-1372	466	27	of	of	ADP
ejpam-1372	466	28	integration	integration	NOUN
ejpam-1372	466	29	.	.	PUNCT
ejpam-1372	467	1	this	this	PRON
ejpam-1372	467	2	means	mean	VERB
ejpam-1372	467	3	that	that	SCONJ
ejpam-1372	467	4	more	more	ADJ
ejpam-1372	467	5	rigorous	rigorous	ADJ
ejpam-1372	467	6	mathematics	mathematic	NOUN
ejpam-1372	467	7	is	be	AUX
ejpam-1372	467	8	required	require	VERB
ejpam-1372	467	9	to	to	PART
ejpam-1372	467	10	establish	establish	VERB
ejpam-1372	467	11	whether	whether	SCONJ
ejpam-1372	467	12	the	the	DET
ejpam-1372	467	13	above	above	ADJ
ejpam-1372	467	14	equivalence	equivalence	NOUN
ejpam-1372	467	15	is	be	AUX
ejpam-1372	467	16	correct	correct	ADJ
ejpam-1372	467	17	.	.	PUNCT
ejpam-1372	468	1	as	as	SCONJ
ejpam-1372	468	2	indicated	indicate	VERB
ejpam-1372	468	3	earlier	early	ADV
ejpam-1372	468	4	,	,	PUNCT
ejpam-1372	468	5	the	the	DET
ejpam-1372	468	6	quantity	quantity	NOUN
ejpam-1372	468	7	on	on	ADP
ejpam-1372	468	8	the	the	DET
ejpam-1372	468	9	left	left	ADJ
ejpam-1372	468	10	hand	hand	NOUN
ejpam-1372	468	11	side	side	NOUN
ejpam-1372	468	12	of	of	ADP
ejpam-1372	468	13	the	the	DET
ejpam-1372	468	14	above	above	ADJ
ejpam-1372	468	15	result	result	NOUN
ejpam-1372	468	16	was	be	AUX
ejpam-1372	468	17	made	make	VERB
ejpam-1372	468	18	famous	famous	ADJ
ejpam-1372	468	19	,	,	PUNCT
ejpam-1372	468	20	again	again	ADV
ejpam-1372	468	21	by	by	ADP
ejpam-1372	468	22	euler	euler	PROPN
ejpam-1372	468	23	,	,	PUNCT
ejpam-1372	468	24	who	who	PRON
ejpam-1372	468	25	found	find	VERB
ejpam-1372	468	26	that	that	SCONJ
ejpam-1372	468	27	it	it	PRON
ejpam-1372	468	28	yielded	yield	VERB
ejpam-1372	468	29	a	a	DET
ejpam-1372	468	30	constant	constant	ADJ
ejpam-1372	468	31	.	.	PUNCT
ejpam-1372	469	1	in	in	ADP
ejpam-1372	469	2	fact	fact	NOUN
ejpam-1372	469	3	,	,	PUNCT
ejpam-1372	469	4	he	he	PRON
ejpam-1372	469	5	was	be	AUX
ejpam-1372	469	6	effectively	effectively	ADV
ejpam-1372	469	7	regularising	regularise	VERB
ejpam-1372	469	8	the	the	DET
ejpam-1372	469	9	series	series	NOUN
ejpam-1372	469	10	.	.	PUNCT
ejpam-1372	470	1	today	today	NOUN
ejpam-1372	470	2	,	,	PUNCT
ejpam-1372	470	3	the	the	DET
ejpam-1372	470	4	constant	constant	ADJ
ejpam-1372	470	5	that	that	PRON
ejpam-1372	470	6	remains	remain	VERB
ejpam-1372	470	7	in	in	ADP
ejpam-1372	470	8	this	this	DET
ejpam-1372	470	9	regularisation	regularisation	NOUN
ejpam-1372	470	10	process	process	NOUN
ejpam-1372	470	11	is	be	AUX
ejpam-1372	470	12	known	know	VERB
ejpam-1372	470	13	as	as	ADP
ejpam-1372	470	14	euler	euler	NOUN
ejpam-1372	470	15	’s	’s	PART
ejpam-1372	470	16	constant	constant	ADJ
ejpam-1372	470	17	[	[	X
ejpam-1372	470	18	13	13	NUM
ejpam-1372	470	19	]	]	PUNCT
ejpam-1372	470	20	.	.	PUNCT
ejpam-1372	471	1	sometimes	sometimes	ADV
ejpam-1372	471	2	it	it	PRON
ejpam-1372	471	3	is	be	AUX
ejpam-1372	471	4	called	call	VERB
ejpam-1372	471	5	the	the	DET
ejpam-1372	471	6	euler	euler	NOUN
ejpam-1372	471	7	-	-	PUNCT
ejpam-1372	471	8	mascheroni	mascheroni	NOUN
ejpam-1372	471	9	constant	constant	ADJ
ejpam-1372	471	10	because	because	SCONJ
ejpam-1372	471	11	the	the	DET
ejpam-1372	471	12	latter	latter	NOUN
ejpam-1372	471	13	calculated	calculate	VERB
ejpam-1372	471	14	it	it	PRON
ejpam-1372	471	15	to	to	ADP
ejpam-1372	471	16	32	32	NUM
ejpam-1372	471	17	decimal	decimal	ADJ
ejpam-1372	471	18	places	place	NOUN
ejpam-1372	471	19	.	.	PUNCT
ejpam-1372	472	1	not	not	PART
ejpam-1372	472	2	long	long	ADV
ejpam-1372	472	3	afterwards	afterwards	ADV
ejpam-1372	472	4	,	,	PUNCT
ejpam-1372	472	5	a	a	DET
ejpam-1372	472	6	controversy	controversy	NOUN
ejpam-1372	472	7	arose	arise	VERB
ejpam-1372	472	8	,	,	PUNCT
ejpam-1372	472	9	where	where	SCONJ
ejpam-1372	472	10	it	it	PRON
ejpam-1372	472	11	was	be	AUX
ejpam-1372	472	12	found	find	VERB
ejpam-1372	472	13	that	that	SCONJ
ejpam-1372	472	14	the	the	DET
ejpam-1372	472	15	last	last	ADJ
ejpam-1372	472	16	12	12	NUM
ejpam-1372	472	17	decimal	decimal	ADJ
ejpam-1372	472	18	places	place	NOUN
ejpam-1372	472	19	mascheroni	mascheroni	PROPN
ejpam-1372	472	20	had	have	AUX
ejpam-1372	472	21	calculated	calculate	VERB
ejpam-1372	472	22	were	be	AUX
ejpam-1372	472	23	incorrect	incorrect	ADJ
ejpam-1372	472	24	.	.	PUNCT
ejpam-1372	473	1	specifically	specifically	ADV
ejpam-1372	473	2	,	,	PUNCT
ejpam-1372	473	3	euler	euler	PROPN
ejpam-1372	473	4	found	find	VERB
ejpam-1372	473	5	that	that	SCONJ
ejpam-1372	473	6	∞	∞	PROPN
ejpam-1372	473	7	∑	∑	SYM
ejpam-1372	473	8	k=0	k=0	PROPN
ejpam-1372	473	9	1	1	NUM
ejpam-1372	473	10	k+	k+	NOUN
ejpam-1372	473	11	1	1	NUM
ejpam-1372	473	12	−	−	NOUN
ejpam-1372	473	13	log(∞	log(∞	PROPN
ejpam-1372	473	14	)	)	PUNCT
ejpam-1372	473	15	=	=	PUNCT
ejpam-1372	473	16	γ=	γ=	PROPN
ejpam-1372	473	17	0.577	0.577	NUM
ejpam-1372	473	18	215	215	NUM
ejpam-1372	473	19	664	664	NUM
ejpam-1372	473	20	901	901	NUM
ejpam-1372	473	21	.	.	PUNCT
ejpam-1372	473	22	.	.	PUNCT
ejpam-1372	473	23	.	.	PUNCT
ejpam-1372	473	24	.	.	PUNCT
ejpam-1372	474	1	(	(	PUNCT
ejpam-1372	474	2	43	43	NUM
ejpam-1372	474	3	)	)	PUNCT
ejpam-1372	474	4	because	because	SCONJ
ejpam-1372	474	5	of	of	ADP
ejpam-1372	474	6	this	this	DET
ejpam-1372	474	7	result	result	NOUN
ejpam-1372	474	8	,	,	PUNCT
ejpam-1372	474	9	one	one	PRON
ejpam-1372	474	10	can	can	AUX
ejpam-1372	474	11	not	not	PART
ejpam-1372	474	12	simply	simply	ADV
ejpam-1372	474	13	subtract	subtract	VERB
ejpam-1372	474	14	a	a	DET
ejpam-1372	474	15	logarithmic	logarithmic	ADJ
ejpam-1372	474	16	infinity	infinity	NOUN
ejpam-1372	474	17	from	from	ADP
ejpam-1372	474	18	an	an	DET
ejpam-1372	474	19	integrated	integrate	VERB
ejpam-1372	474	20	divergent	divergent	ADJ
ejpam-1372	474	21	series	series	NOUN
ejpam-1372	474	22	at	at	ADP
ejpam-1372	474	23	its	its	PRON
ejpam-1372	474	24	most	most	ADV
ejpam-1372	474	25	singular	singular	ADJ
ejpam-1372	474	26	point	point	NOUN
ejpam-1372	474	27	as	as	ADP
ejpam-1372	474	28	in	in	ADP
ejpam-1372	474	29	equivalence	equivalence	NOUN
ejpam-1372	474	30	(	(	PUNCT
ejpam-1372	474	31	42	42	NUM
ejpam-1372	474	32	)	)	PUNCT
ejpam-1372	474	33	.	.	PUNCT
ejpam-1372	475	1	previously	previously	ADV
ejpam-1372	475	2	,	,	PUNCT
ejpam-1372	475	3	we	we	PRON
ejpam-1372	475	4	were	be	AUX
ejpam-1372	475	5	successful	successful	ADJ
ejpam-1372	475	6	in	in	ADP
ejpam-1372	475	7	regularising	regularise	VERB
ejpam-1372	475	8	the	the	DET
ejpam-1372	475	9	geometric	geometric	ADJ
ejpam-1372	475	10	series	series	NOUN
ejpam-1372	475	11	by	by	ADP
ejpam-1372	475	12	introducing	introduce	VERB
ejpam-1372	475	13	the	the	DET
ejpam-1372	475	14	gamma	gamma	NOUN
ejpam-1372	475	15	function	function	NOUN
ejpam-1372	475	16	into	into	ADP
ejpam-1372	475	17	the	the	DET
ejpam-1372	475	18	analysis	analysis	NOUN
ejpam-1372	475	19	.	.	PUNCT
ejpam-1372	476	1	let	let	VERB
ejpam-1372	476	2	us	we	PRON
ejpam-1372	476	3	do	do	VERB
ejpam-1372	476	4	the	the	DET
ejpam-1372	476	5	same	same	ADJ
ejpam-1372	476	6	here	here	ADV
ejpam-1372	476	7	by	by	ADP
ejpam-1372	476	8	multiplying	multiply	VERB
ejpam-1372	476	9	the	the	DET
ejpam-1372	476	10	summand	summand	NOUN
ejpam-1372	476	11	of	of	ADP
ejpam-1372	476	12	1/(k+1	1/(k+1	NUM
ejpam-1372	476	13	)	)	PUNCT
ejpam-1372	476	14	by	by	ADP
ejpam-1372	476	15	k!/k	k!/k	PROPN
ejpam-1372	476	16	!	!	PUNCT
ejpam-1372	477	1	and	and	CCONJ
ejpam-1372	477	2	introducing	introduce	VERB
ejpam-1372	477	3	the	the	DET
ejpam-1372	477	4	integral	integral	ADJ
ejpam-1372	477	5	representation	representation	NOUN
ejpam-1372	477	6	for	for	ADP
ejpam-1372	477	7	the	the	DET
ejpam-1372	477	8	gamma	gamma	NOUN
ejpam-1372	477	9	function	function	NOUN
ejpam-1372	477	10	in	in	ADP
ejpam-1372	477	11	the	the	DET
ejpam-1372	477	12	numerator	numerator	NOUN
ejpam-1372	477	13	.	.	PUNCT
ejpam-1372	478	1	then	then	ADV
ejpam-1372	478	2	the	the	DET
ejpam-1372	478	3	harmonic	harmonic	ADJ
ejpam-1372	478	4	series	series	NOUN
ejpam-1372	478	5	v.	v.	ADP
ejpam-1372	478	6	kowalenko	kowalenko	PROPN
ejpam-1372	478	7	/	/	SYM
ejpam-1372	478	8	eur	eur	PROPN
ejpam-1372	478	9	.	.	PUNCT
ejpam-1372	479	1	j.	j.	PROPN
ejpam-1372	479	2	pure	pure	PROPN
ejpam-1372	479	3	appl	appl	PROPN
ejpam-1372	479	4	.	.	PROPN
ejpam-1372	479	5	math	math	PROPN
ejpam-1372	479	6	,	,	PUNCT
ejpam-1372	479	7	4	4	NUM
ejpam-1372	479	8	(	(	PUNCT
ejpam-1372	479	9	2011	2011	NUM
ejpam-1372	479	10	)	)	PUNCT
ejpam-1372	479	11	,	,	PUNCT
ejpam-1372	479	12	370	370	NUM
ejpam-1372	479	13	-	-	SYM
ejpam-1372	479	14	423	423	NUM
ejpam-1372	479	15	385	385	NUM
ejpam-1372	479	16	can	can	AUX
ejpam-1372	479	17	be	be	AUX
ejpam-1372	479	18	written	write	VERB
ejpam-1372	479	19	as	as	ADP
ejpam-1372	479	20	∞	∞	PROPN
ejpam-1372	479	21	∑	∑	PROPN
ejpam-1372	479	22	k=1	k=1	PROPN
ejpam-1372	479	23	1	1	NUM
ejpam-1372	479	24	k	k	X
ejpam-1372	479	25	=	=	SYM
ejpam-1372	479	26	∫	∫	PROPN
ejpam-1372	480	1	∞	∞	NUM
ejpam-1372	480	2	0	0	PUNCT
ejpam-1372	481	1	d	d	NOUN
ejpam-1372	481	2	t	t	PROPN
ejpam-1372	481	3	e−t	e−t	NOUN
ejpam-1372	481	4	∞	∞	PROPN
ejpam-1372	481	5	∑	∑	PUNCT
ejpam-1372	481	6	k=1	k=1	PROPN
ejpam-1372	481	7	tk−1	tk−1	PROPN
ejpam-1372	481	8	k	k	PROPN
ejpam-1372	481	9	!	!	PUNCT
ejpam-1372	482	1	=	=	PUNCT
ejpam-1372	483	1	∫	∫	PROPN
ejpam-1372	484	1	∞	∞	NOUN
ejpam-1372	484	2	0	0	PUNCT
ejpam-1372	485	1	d	d	PRON
ejpam-1372	485	2	t	t	PROPN
ejpam-1372	485	3	�	�	PROPN
ejpam-1372	485	4	1−	1−	NUM
ejpam-1372	485	5	e−t	e−t	NOUN
ejpam-1372	485	6	�	�	PROPN
ejpam-1372	485	7	/t	/t	PUNCT
ejpam-1372	485	8	.	.	PUNCT
ejpam-1372	486	1	(	(	PUNCT
ejpam-1372	486	2	44	44	NUM
ejpam-1372	486	3	)	)	PUNCT
ejpam-1372	486	4	the	the	DET
ejpam-1372	486	5	integral	integral	ADJ
ejpam-1372	486	6	in	in	ADP
ejpam-1372	486	7	the	the	DET
ejpam-1372	486	8	above	above	ADJ
ejpam-1372	486	9	result	result	NOUN
ejpam-1372	486	10	is	be	AUX
ejpam-1372	486	11	not	not	PART
ejpam-1372	486	12	singular	singular	ADJ
ejpam-1372	486	13	at	at	ADP
ejpam-1372	486	14	the	the	DET
ejpam-1372	486	15	lower	low	ADJ
ejpam-1372	486	16	limit	limit	NOUN
ejpam-1372	486	17	,	,	PUNCT
ejpam-1372	486	18	but	but	CCONJ
ejpam-1372	486	19	is	be	AUX
ejpam-1372	486	20	logarithmically	logarithmically	ADV
ejpam-1372	486	21	divergent	divergent	ADJ
ejpam-1372	486	22	at	at	ADP
ejpam-1372	486	23	the	the	DET
ejpam-1372	486	24	upper	upper	ADJ
ejpam-1372	486	25	limit	limit	NOUN
ejpam-1372	486	26	.	.	PUNCT
ejpam-1372	487	1	since	since	SCONJ
ejpam-1372	487	2	log	log	PROPN
ejpam-1372	487	3	t	t	PROPN
ejpam-1372	487	4	is	be	AUX
ejpam-1372	487	5	obtained	obtain	VERB
ejpam-1372	487	6	by	by	ADP
ejpam-1372	487	7	integrating	integrate	VERB
ejpam-1372	487	8	1	1	NUM
ejpam-1372	487	9	/	/	SYM
ejpam-1372	487	10	t	t	NOUN
ejpam-1372	487	11	between	between	ADP
ejpam-1372	487	12	0	0	NUM
ejpam-1372	487	13	and	and	CCONJ
ejpam-1372	487	14	t	t	PROPN
ejpam-1372	487	15	,	,	PUNCT
ejpam-1372	487	16	we	we	PRON
ejpam-1372	487	17	subtract	subtract	VERB
ejpam-1372	487	18	the	the	DET
ejpam-1372	487	19	integral	integral	ADJ
ejpam-1372	487	20	∫	∫	PROPN
ejpam-1372	487	21	1	1	NUM
ejpam-1372	487	22	0	0	NUM
ejpam-1372	487	23	d	d	NOUN
ejpam-1372	487	24	t	t	X
ejpam-1372	487	25	t−1	t−1	PROPN
ejpam-1372	487	26	from	from	ADP
ejpam-1372	487	27	the	the	DET
ejpam-1372	487	28	rhs	rhs	PROPN
ejpam-1372	487	29	of	of	ADP
ejpam-1372	487	30	the	the	DET
ejpam-1372	487	31	above	above	ADJ
ejpam-1372	487	32	result	result	NOUN
ejpam-1372	487	33	in	in	ADP
ejpam-1372	487	34	order	order	NOUN
ejpam-1372	487	35	to	to	PART
ejpam-1372	487	36	regularise	regularise	VERB
ejpam-1372	487	37	it	it	PRON
ejpam-1372	487	38	.	.	PUNCT
ejpam-1372	488	1	thus	thus	ADV
ejpam-1372	488	2	,	,	PUNCT
ejpam-1372	488	3	the	the	DET
ejpam-1372	488	4	rhs	rhs	PROPN
ejpam-1372	488	5	becomes	become	VERB
ejpam-1372	488	6	i	i	PRON
ejpam-1372	488	7	=	=	PUNCT
ejpam-1372	488	8	∫	∫	PROPN
ejpam-1372	489	1	1	1	NUM
ejpam-1372	489	2	0	0	NUM
ejpam-1372	490	1	d	d	NOUN
ejpam-1372	490	2	t	t	PROPN
ejpam-1372	490	3	�	�	PROPN
ejpam-1372	490	4	1	1	NUM
ejpam-1372	490	5	log	log	NOUN
ejpam-1372	490	6	t	t	NOUN
ejpam-1372	490	7	+	+	CCONJ
ejpam-1372	490	8	1	1	NUM
ejpam-1372	490	9	1−	1−	NUM
ejpam-1372	490	10	t	t	PROPN
ejpam-1372	490	11	�	�	PROPN
ejpam-1372	490	12	,	,	PUNCT
ejpam-1372	490	13	(	(	PUNCT
ejpam-1372	490	14	45	45	NUM
ejpam-1372	490	15	)	)	PUNCT
ejpam-1372	491	1	which	which	PRON
ejpam-1372	491	2	,	,	PUNCT
ejpam-1372	491	3	according	accord	VERB
ejpam-1372	491	4	to	to	ADP
ejpam-1372	491	5	no	no	PROPN
ejpam-1372	491	6	.	.	PUNCT
ejpam-1372	491	7	8.367(6	8.367(6	NUM
ejpam-1372	491	8	)	)	PUNCT
ejpam-1372	491	9	of	of	ADP
ejpam-1372	491	10	ref	ref	NOUN
ejpam-1372	491	11	.	.	PUNCT
ejpam-1372	492	1	[	[	X
ejpam-1372	492	2	11	11	NUM
ejpam-1372	492	3	]	]	PUNCT
ejpam-1372	492	4	,	,	PUNCT
ejpam-1372	492	5	is	be	AUX
ejpam-1372	492	6	the	the	DET
ejpam-1372	492	7	integral	integral	ADJ
ejpam-1372	492	8	representation	representation	NOUN
ejpam-1372	492	9	for	for	ADP
ejpam-1372	492	10	euler	euler	PROPN
ejpam-1372	492	11	’s	’s	PART
ejpam-1372	492	12	constant	constant	ADJ
ejpam-1372	492	13	.	.	PUNCT
ejpam-1372	493	1	that	that	PRON
ejpam-1372	493	2	is	is	ADV
ejpam-1372	493	3	,	,	PUNCT
ejpam-1372	493	4	the	the	DET
ejpam-1372	493	5	above	above	ADJ
ejpam-1372	493	6	result	result	NOUN
ejpam-1372	493	7	is	be	AUX
ejpam-1372	493	8	finite	finite	ADJ
ejpam-1372	493	9	,	,	PUNCT
ejpam-1372	493	10	not	not	PART
ejpam-1372	493	11	equal	equal	ADJ
ejpam-1372	493	12	to	to	ADP
ejpam-1372	493	13	zero	zero	NUM
ejpam-1372	493	14	as	as	SCONJ
ejpam-1372	493	15	implied	imply	VERB
ejpam-1372	493	16	by	by	ADP
ejpam-1372	493	17	equivalence	equivalence	NOUN
ejpam-1372	493	18	(	(	PUNCT
ejpam-1372	493	19	42	42	NUM
ejpam-1372	493	20	)	)	PUNCT
ejpam-1372	493	21	.	.	PUNCT
ejpam-1372	494	1	euler	euler	PROPN
ejpam-1372	494	2	’s	’s	PART
ejpam-1372	494	3	regularisation	regularisation	NOUN
ejpam-1372	494	4	formula	formula	NOUN
ejpam-1372	494	5	provides	provide	VERB
ejpam-1372	494	6	us	we	PRON
ejpam-1372	494	7	with	with	ADP
ejpam-1372	494	8	a	a	DET
ejpam-1372	494	9	method	method	NOUN
ejpam-1372	494	10	or	or	CCONJ
ejpam-1372	494	11	scheme	scheme	NOUN
ejpam-1372	494	12	for	for	ADP
ejpam-1372	494	13	regularising	regularise	VERB
ejpam-1372	494	14	logarithmically	logarithmically	ADV
ejpam-1372	494	15	divergent	divergent	ADJ
ejpam-1372	494	16	series	series	NOUN
ejpam-1372	494	17	with	with	ADP
ejpam-1372	494	18	far	far	ADV
ejpam-1372	494	19	more	more	ADV
ejpam-1372	494	20	complicated	complicated	ADJ
ejpam-1372	494	21	summands	summand	NOUN
ejpam-1372	494	22	than	than	ADP
ejpam-1372	494	23	that	that	PRON
ejpam-1372	494	24	in	in	ADP
ejpam-1372	494	25	the	the	DET
ejpam-1372	494	26	harmonic	harmonic	ADJ
ejpam-1372	494	27	series	series	NOUN
ejpam-1372	494	28	.	.	PUNCT
ejpam-1372	495	1	in	in	ADP
ejpam-1372	495	2	such	such	ADJ
ejpam-1372	495	3	cases	case	NOUN
ejpam-1372	495	4	,	,	PUNCT
ejpam-1372	495	5	all	all	PRON
ejpam-1372	495	6	we	we	PRON
ejpam-1372	495	7	need	need	VERB
ejpam-1372	495	8	to	to	PART
ejpam-1372	495	9	do	do	VERB
ejpam-1372	495	10	is	be	AUX
ejpam-1372	495	11	subtract	subtract	VERB
ejpam-1372	495	12	the	the	DET
ejpam-1372	495	13	entire	entire	ADJ
ejpam-1372	495	14	harmonic	harmonic	ADJ
ejpam-1372	495	15	series	series	NOUN
ejpam-1372	495	16	and	and	CCONJ
ejpam-1372	495	17	add	add	VERB
ejpam-1372	495	18	euler	euler	PROPN
ejpam-1372	495	19	’s	’s	PART
ejpam-1372	495	20	constant	constant	ADJ
ejpam-1372	495	21	.	.	PUNCT
ejpam-1372	496	1	e.g.	e.g.	ADV
ejpam-1372	496	2	,	,	PUNCT
ejpam-1372	496	3	consider	consider	VERB
ejpam-1372	496	4	the	the	DET
ejpam-1372	496	5	following	follow	VERB
ejpam-1372	496	6	series	series	NOUN
ejpam-1372	496	7	s(z	s(z	PROPN
ejpam-1372	496	8	)	)	PUNCT
ejpam-1372	496	9	=	=	SYM
ejpam-1372	497	1	∞	∞	NUM
ejpam-1372	497	2	∑	∑	SYM
ejpam-1372	497	3	k=0	k=0	PROPN
ejpam-1372	497	4	1	1	NUM
ejpam-1372	497	5	k+	k+	NOUN
ejpam-1372	497	6	z	z	NOUN
ejpam-1372	497	7	.	.	PUNCT
ejpam-1372	498	1	(	(	PUNCT
ejpam-1372	498	2	46	46	NUM
ejpam-1372	498	3	)	)	PUNCT
ejpam-1372	498	4	by	by	ADP
ejpam-1372	498	5	introducing	introduce	VERB
ejpam-1372	498	6	euler	euler	NOUN
ejpam-1372	498	7	’s	’s	PART
ejpam-1372	498	8	regularisation	regularisation	NOUN
ejpam-1372	498	9	formula	formula	NOUN
ejpam-1372	498	10	into	into	ADP
ejpam-1372	498	11	the	the	DET
ejpam-1372	498	12	above	above	ADJ
ejpam-1372	498	13	result	result	NOUN
ejpam-1372	498	14	,	,	PUNCT
ejpam-1372	498	15	we	we	PRON
ejpam-1372	498	16	find	find	VERB
ejpam-1372	498	17	that	that	SCONJ
ejpam-1372	498	18	s(z	s(z	PROPN
ejpam-1372	498	19	)	)	PUNCT
ejpam-1372	498	20	−∑∞k=0	−∑∞k=0	NOUN
ejpam-1372	498	21	1/(k	1/(k	NUM
ejpam-1372	498	22	+	+	CCONJ
ejpam-1372	498	23	1	1	NUM
ejpam-1372	498	24	)	)	PUNCT
ejpam-1372	498	25	+	+	CCONJ
ejpam-1372	498	26	γ	γ	X
ejpam-1372	498	27	is	be	AUX
ejpam-1372	498	28	now	now	ADV
ejpam-1372	498	29	finite	finite	ADJ
ejpam-1372	498	30	.	.	PUNCT
ejpam-1372	499	1	in	in	ADP
ejpam-1372	499	2	fact	fact	NOUN
ejpam-1372	499	3	,	,	PUNCT
ejpam-1372	499	4	multiplying	multiply	VERB
ejpam-1372	499	5	this	this	DET
ejpam-1372	499	6	result	result	NOUN
ejpam-1372	499	7	by	by	ADP
ejpam-1372	499	8	-1	-1	PUNCT
ejpam-1372	499	9	,	,	PUNCT
ejpam-1372	499	10	we	we	PRON
ejpam-1372	499	11	see	see	VERB
ejpam-1372	499	12	that	that	SCONJ
ejpam-1372	499	13	according	accord	VERB
ejpam-1372	499	14	to	to	ADP
ejpam-1372	499	15	no	no	PROPN
ejpam-1372	499	16	.	.	PUNCT
ejpam-1372	499	17	8.362(1	8.362(1	NUM
ejpam-1372	499	18	)	)	PUNCT
ejpam-1372	499	19	of	of	ADP
ejpam-1372	499	20	ref	ref	NOUN
ejpam-1372	499	21	.	.	PUNCT
ejpam-1372	500	1	[	[	X
ejpam-1372	500	2	11	11	NUM
ejpam-1372	500	3	]	]	PUNCT
ejpam-1372	500	4	,	,	PUNCT
ejpam-1372	500	5	it	it	PRON
ejpam-1372	500	6	is	be	AUX
ejpam-1372	500	7	the	the	DET
ejpam-1372	500	8	representation	representation	NOUN
ejpam-1372	500	9	for	for	ADP
ejpam-1372	500	10	the	the	DET
ejpam-1372	500	11	digamma	digamma	PROPN
ejpam-1372	500	12	function	function	NOUN
ejpam-1372	500	13	,	,	PUNCT
ejpam-1372	500	14	which	which	PRON
ejpam-1372	500	15	is	be	AUX
ejpam-1372	500	16	defined	define	VERB
ejpam-1372	500	17	as	as	ADP
ejpam-1372	500	18	ψ(z	ψ(z	NOUN
ejpam-1372	500	19	)	)	PUNCT
ejpam-1372	500	20	=	=	PUNCT
ejpam-1372	501	1	d	d	PROPN
ejpam-1372	501	2	logγ(z)/dz	logγ(z)/dz	PROPN
ejpam-1372	501	3	.	.	PUNCT
ejpam-1372	502	1	the	the	DET
ejpam-1372	502	2	reason	reason	NOUN
ejpam-1372	502	3	why	why	SCONJ
ejpam-1372	502	4	regularisation	regularisation	NOUN
ejpam-1372	502	5	of	of	ADP
ejpam-1372	502	6	a	a	DET
ejpam-1372	502	7	logarithmically	logarithmically	ADV
ejpam-1372	502	8	divergent	divergent	ADJ
ejpam-1372	502	9	series	series	NOUN
ejpam-1372	502	10	is	be	AUX
ejpam-1372	502	11	a	a	DET
ejpam-1372	502	12	much	much	ADV
ejpam-1372	502	13	different	different	ADJ
ejpam-1372	502	14	proposition	proposition	NOUN
ejpam-1372	502	15	than	than	ADP
ejpam-1372	502	16	regularisation	regularisation	NOUN
ejpam-1372	502	17	of	of	ADP
ejpam-1372	502	18	a	a	DET
ejpam-1372	502	19	divergent	divergent	ADJ
ejpam-1372	502	20	series	series	NOUN
ejpam-1372	502	21	with	with	ADP
ejpam-1372	502	22	an	an	DET
ejpam-1372	502	23	algebraic	algebraic	ADJ
ejpam-1372	502	24	infinity	infinity	NOUN
ejpam-1372	502	25	such	such	ADJ
ejpam-1372	502	26	as	as	ADP
ejpam-1372	502	27	the	the	DET
ejpam-1372	502	28	geometric	geometric	ADJ
ejpam-1372	502	29	series	series	NOUN
ejpam-1372	502	30	is	be	AUX
ejpam-1372	502	31	because	because	SCONJ
ejpam-1372	502	32	we	we	PRON
ejpam-1372	502	33	can	can	AUX
ejpam-1372	502	34	truncate	truncate	VERB
ejpam-1372	502	35	the	the	DET
ejpam-1372	502	36	series	series	NOUN
ejpam-1372	502	37	at	at	ADP
ejpam-1372	502	38	n	n	PROPN
ejpam-1372	502	39	in	in	ADP
ejpam-1372	502	40	the	the	DET
ejpam-1372	502	41	sum	sum	NOUN
ejpam-1372	502	42	,	,	PUNCT
ejpam-1372	502	43	replace	replace	VERB
ejpam-1372	502	44	the	the	DET
ejpam-1372	502	45	logarithmic	logarithmic	ADJ
ejpam-1372	502	46	infinity	infinity	NOUN
ejpam-1372	502	47	by	by	ADP
ejpam-1372	502	48	log	log	NOUN
ejpam-1372	502	49	n	n	NOUN
ejpam-1372	502	50	and	and	CCONJ
ejpam-1372	502	51	still	still	ADV
ejpam-1372	502	52	come	come	VERB
ejpam-1372	502	53	up	up	ADP
ejpam-1372	502	54	with	with	ADP
ejpam-1372	502	55	an	an	DET
ejpam-1372	502	56	accurate	accurate	ADJ
ejpam-1372	502	57	approximation	approximation	NOUN
ejpam-1372	502	58	to	to	ADP
ejpam-1372	502	59	γ	γ	PROPN
ejpam-1372	502	60	.	.	PROPN
ejpam-1372	503	1	that	that	PRON
ejpam-1372	503	2	is	is	ADV
ejpam-1372	503	3	,	,	PUNCT
ejpam-1372	503	4	eq	eq	ADJ
ejpam-1372	503	5	.	.	PUNCT
ejpam-1372	504	1	(	(	PUNCT
ejpam-1372	504	2	43	43	NUM
ejpam-1372	504	3	)	)	PUNCT
ejpam-1372	504	4	can	can	AUX
ejpam-1372	504	5	be	be	AUX
ejpam-1372	504	6	written	write	VERB
ejpam-1372	504	7	as	as	ADP
ejpam-1372	504	8	an	an	DET
ejpam-1372	504	9	approximation	approximation	NOUN
ejpam-1372	504	10	given	give	VERB
ejpam-1372	504	11	by	by	ADP
ejpam-1372	504	12	n	n	CCONJ
ejpam-1372	504	13	∑	∑	ADV
ejpam-1372	504	14	k=0	k=0	PROPN
ejpam-1372	504	15	1	1	NUM
ejpam-1372	504	16	k+	k+	NOUN
ejpam-1372	504	17	1	1	NUM
ejpam-1372	504	18	−	−	NOUN
ejpam-1372	504	19	log	log	NOUN
ejpam-1372	504	20	n	n	PROPN
ejpam-1372	504	21	≈	≈	PROPN
ejpam-1372	504	22	γ	γ	X
ejpam-1372	504	23	.	.	PUNCT
ejpam-1372	505	1	(	(	PUNCT
ejpam-1372	505	2	47	47	NUM
ejpam-1372	505	3	)	)	PUNCT
ejpam-1372	505	4	as	as	ADP
ejpam-1372	505	5	n	n	PRON
ejpam-1372	505	6	increases	increase	NOUN
ejpam-1372	505	7	,	,	PUNCT
ejpam-1372	505	8	the	the	DET
ejpam-1372	505	9	lhs	lhs	PROPN
ejpam-1372	505	10	becomes	become	VERB
ejpam-1372	505	11	more	more	ADV
ejpam-1372	505	12	and	and	CCONJ
ejpam-1372	505	13	more	more	ADV
ejpam-1372	505	14	accurate	accurate	ADJ
ejpam-1372	505	15	as	as	ADP
ejpam-1372	505	16	an	an	DET
ejpam-1372	505	17	approximation	approximation	NOUN
ejpam-1372	505	18	to	to	PART
ejpam-1372	505	19	euler	euler	VERB
ejpam-1372	505	20	’s	’s	PART
ejpam-1372	505	21	constant	constant	ADJ
ejpam-1372	505	22	.	.	PUNCT
ejpam-1372	506	1	in	in	ADP
ejpam-1372	506	2	fact	fact	NOUN
ejpam-1372	506	3	,	,	PUNCT
ejpam-1372	506	4	this	this	PRON
ejpam-1372	506	5	is	be	AUX
ejpam-1372	506	6	the	the	DET
ejpam-1372	506	7	standard	standard	ADJ
ejpam-1372	506	8	approach	approach	NOUN
ejpam-1372	506	9	for	for	ADP
ejpam-1372	506	10	determining	determine	VERB
ejpam-1372	506	11	numerical	numerical	ADJ
ejpam-1372	506	12	values	value	NOUN
ejpam-1372	506	13	of	of	ADP
ejpam-1372	506	14	γ	γ	PROPN
ejpam-1372	506	15	.	.	PROPN
ejpam-1372	506	16	in	in	ADP
ejpam-1372	506	17	our	our	PRON
ejpam-1372	506	18	study	study	NOUN
ejpam-1372	506	19	of	of	ADP
ejpam-1372	506	20	the	the	DET
ejpam-1372	506	21	geometric	geometric	ADJ
ejpam-1372	506	22	series	series	NOUN
ejpam-1372	506	23	we	we	PRON
ejpam-1372	506	24	could	could	AUX
ejpam-1372	506	25	not	not	PART
ejpam-1372	506	26	expect	expect	VERB
ejpam-1372	506	27	to	to	PART
ejpam-1372	506	28	obtain	obtain	VERB
ejpam-1372	506	29	an	an	DET
ejpam-1372	506	30	accurate	accurate	ADJ
ejpam-1372	506	31	approximation	approximation	NOUN
ejpam-1372	506	32	to	to	ADP
ejpam-1372	506	33	the	the	DET
ejpam-1372	506	34	limit	limit	NOUN
ejpam-1372	506	35	of	of	ADP
ejpam-1372	506	36	1/(1−	1/(1−	NUM
ejpam-1372	506	37	z	z	NOUN
ejpam-1372	506	38	)	)	PUNCT
ejpam-1372	506	39	for	for	ADP
ejpam-1372	506	40	z	z	PROPN
ejpam-1372	506	41	outside	outside	ADP
ejpam-1372	506	42	the	the	DET
ejpam-1372	506	43	disk	disk	NOUN
ejpam-1372	506	44	of	of	ADP
ejpam-1372	506	45	absolute	absolute	ADJ
ejpam-1372	506	46	convergence	convergence	NOUN
ejpam-1372	506	47	by	by	ADP
ejpam-1372	506	48	truncating	truncate	VERB
ejpam-1372	506	49	the	the	DET
ejpam-1372	506	50	series	series	NOUN
ejpam-1372	506	51	at	at	ADP
ejpam-1372	506	52	ever	ever	ADV
ejpam-1372	506	53	increasing	increase	VERB
ejpam-1372	506	54	values	value	NOUN
ejpam-1372	506	55	of	of	ADP
ejpam-1372	506	56	n	n	PRON
ejpam-1372	506	57	and	and	CCONJ
ejpam-1372	506	58	then	then	ADV
ejpam-1372	506	59	subtracting	subtract	VERB
ejpam-1372	506	60	values	value	NOUN
ejpam-1372	506	61	of	of	ADP
ejpam-1372	506	62	n	n	PRON
ejpam-1372	506	63	instead	instead	ADV
ejpam-1372	506	64	of	of	ADP
ejpam-1372	506	65	infinity	infinity	NOUN
ejpam-1372	506	66	.	.	PUNCT
ejpam-1372	507	1	euler	euler	PROPN
ejpam-1372	507	2	’s	’s	PART
ejpam-1372	507	3	formula	formula	NOUN
ejpam-1372	507	4	for	for	ADP
ejpam-1372	507	5	γ	γ	X
ejpam-1372	507	6	is	be	AUX
ejpam-1372	507	7	a	a	DET
ejpam-1372	507	8	unique	unique	ADJ
ejpam-1372	507	9	example	example	NOUN
ejpam-1372	507	10	of	of	ADP
ejpam-1372	507	11	a	a	DET
ejpam-1372	507	12	mathematical	mathematical	ADJ
ejpam-1372	507	13	quantity	quantity	NOUN
ejpam-1372	507	14	that	that	PRON
ejpam-1372	507	15	has	have	AUX
ejpam-1372	507	16	been	be	AUX
ejpam-1372	507	17	first	first	ADV
ejpam-1372	507	18	evaluated	evaluate	VERB
ejpam-1372	507	19	by	by	ADP
ejpam-1372	507	20	employing	employ	VERB
ejpam-1372	507	21	the	the	DET
ejpam-1372	507	22	concept	concept	NOUN
ejpam-1372	507	23	of	of	ADP
ejpam-1372	507	24	regularisation	regularisation	NOUN
ejpam-1372	507	25	,	,	PUNCT
ejpam-1372	507	26	albeit	albeit	SCONJ
ejpam-1372	507	27	of	of	ADP
ejpam-1372	507	28	a	a	DET
ejpam-1372	507	29	logarithmically	logarithmically	ADV
ejpam-1372	507	30	diverging	diverging	ADJ
ejpam-1372	507	31	series	series	NOUN
ejpam-1372	507	32	.	.	PUNCT
ejpam-1372	508	1	only	only	ADV
ejpam-1372	508	2	recently	recently	ADV
ejpam-1372	508	3	has	have	VERB
ejpam-1372	508	4	a	a	DET
ejpam-1372	508	5	rapidly	rapidly	ADV
ejpam-1372	508	6	converging	converge	VERB
ejpam-1372	508	7	formula	formula	NOUN
ejpam-1372	508	8	for	for	SCONJ
ejpam-1372	508	9	γ	γ	NOUN
ejpam-1372	508	10	been	be	AUX
ejpam-1372	508	11	discovered	discover	VERB
ejpam-1372	508	12	in	in	ADP
ejpam-1372	508	13	terms	term	NOUN
ejpam-1372	508	14	of	of	ADP
ejpam-1372	508	15	v.	v.	ADP
ejpam-1372	508	16	kowalenko	kowalenko	PROPN
ejpam-1372	508	17	/	/	SYM
ejpam-1372	508	18	eur	eur	PROPN
ejpam-1372	508	19	.	.	PUNCT
ejpam-1372	509	1	j.	j.	PROPN
ejpam-1372	509	2	pure	pure	PROPN
ejpam-1372	509	3	appl	appl	PROPN
ejpam-1372	509	4	.	.	PROPN
ejpam-1372	509	5	math	math	PROPN
ejpam-1372	509	6	,	,	PUNCT
ejpam-1372	509	7	4	4	NUM
ejpam-1372	509	8	(	(	PUNCT
ejpam-1372	509	9	2011	2011	NUM
ejpam-1372	509	10	)	)	PUNCT
ejpam-1372	509	11	,	,	PUNCT
ejpam-1372	509	12	370	370	NUM
ejpam-1372	509	13	-	-	SYM
ejpam-1372	509	14	423	423	NUM
ejpam-1372	509	15	386	386	NUM
ejpam-1372	509	16	an	an	DET
ejpam-1372	509	17	infinite	infinite	ADJ
ejpam-1372	509	18	set	set	NOUN
ejpam-1372	509	19	of	of	ADP
ejpam-1372	509	20	relatively	relatively	ADV
ejpam-1372	509	21	novel	novel	ADJ
ejpam-1372	509	22	numbers	number	NOUN
ejpam-1372	509	23	known	know	VERB
ejpam-1372	509	24	as	as	ADP
ejpam-1372	509	25	the	the	DET
ejpam-1372	509	26	reciprocal	reciprocal	ADJ
ejpam-1372	509	27	logarithm	logarithm	NOUN
ejpam-1372	509	28	numbers	number	NOUN
ejpam-1372	509	29	or	or	CCONJ
ejpam-1372	509	30	ak	ak	PROPN
ejpam-1372	509	31	given	give	VERB
ejpam-1372	509	32	in	in	ADP
ejpam-1372	509	33	ref	ref	NOUN
ejpam-1372	509	34	.	.	PUNCT
ejpam-1372	510	1	[	[	X
ejpam-1372	510	2	18	18	NUM
ejpam-1372	510	3	]	]	PUNCT
ejpam-1372	510	4	.	.	PUNCT
ejpam-1372	511	1	according	accord	VERB
ejpam-1372	511	2	to	to	ADP
ejpam-1372	511	3	p.	p.	NOUN
ejpam-1372	511	4	137	137	NUM
ejpam-1372	511	5	of	of	ADP
ejpam-1372	511	6	ref	ref	NOUN
ejpam-1372	511	7	.	.	PUNCT
ejpam-1372	512	1	[	[	X
ejpam-1372	512	2	2	2	NUM
ejpam-1372	512	3	]	]	PUNCT
ejpam-1372	512	4	,	,	PUNCT
ejpam-1372	512	5	the	the	DET
ejpam-1372	512	6	magnitudes	magnitude	NOUN
ejpam-1372	512	7	of	of	ADP
ejpam-1372	512	8	these	these	DET
ejpam-1372	512	9	numbers	number	NOUN
ejpam-1372	512	10	have	have	AUX
ejpam-1372	512	11	been	be	AUX
ejpam-1372	512	12	referred	refer	VERB
ejpam-1372	512	13	to	to	ADP
ejpam-1372	512	14	in	in	ADP
ejpam-1372	512	15	the	the	DET
ejpam-1372	512	16	past	past	NOUN
ejpam-1372	512	17	as	as	SCONJ
ejpam-1372	512	18	either	either	CCONJ
ejpam-1372	512	19	the	the	DET
ejpam-1372	512	20	gregory	gregory	NOUN
ejpam-1372	512	21	or	or	CCONJ
ejpam-1372	512	22	the	the	DET
ejpam-1372	512	23	cauchy	cauchy	ADJ
ejpam-1372	512	24	numbers	number	NOUN
ejpam-1372	512	25	,	,	PUNCT
ejpam-1372	512	26	but	but	CCONJ
ejpam-1372	512	27	important	important	ADJ
ejpam-1372	512	28	properties	property	NOUN
ejpam-1372	512	29	for	for	ADP
ejpam-1372	512	30	them	they	PRON
ejpam-1372	512	31	have	have	AUX
ejpam-1372	512	32	only	only	ADV
ejpam-1372	512	33	appeared	appear	VERB
ejpam-1372	512	34	for	for	ADP
ejpam-1372	512	35	the	the	DET
ejpam-1372	512	36	first	first	ADJ
ejpam-1372	512	37	time	time	NOUN
ejpam-1372	512	38	in	in	ADP
ejpam-1372	512	39	ref	ref	NOUN
ejpam-1372	512	40	.	.	PUNCT
ejpam-1372	513	1	[	[	X
ejpam-1372	513	2	18	18	NUM
ejpam-1372	513	3	]	]	PUNCT
ejpam-1372	513	4	.	.	PUNCT
ejpam-1372	514	1	there	there	ADV
ejpam-1372	514	2	,	,	PUNCT
ejpam-1372	514	3	the	the	DET
ejpam-1372	514	4	new	new	ADJ
ejpam-1372	514	5	result	result	NOUN
ejpam-1372	514	6	for	for	ADP
ejpam-1372	514	7	γ	γ	PROPN
ejpam-1372	514	8	,	,	PUNCT
ejpam-1372	514	9	which	which	PRON
ejpam-1372	514	10	is	be	AUX
ejpam-1372	514	11	known	know	VERB
ejpam-1372	514	12	as	as	ADP
ejpam-1372	514	13	hurst	hurst	PROPN
ejpam-1372	514	14	’s	’s	PART
ejpam-1372	514	15	formula	formula	NOUN
ejpam-1372	514	16	,	,	PUNCT
ejpam-1372	514	17	is	be	AUX
ejpam-1372	514	18	given	give	VERB
ejpam-1372	514	19	as	as	ADP
ejpam-1372	514	20	γ=	γ=	PROPN
ejpam-1372	514	21	∞	∞	PROPN
ejpam-1372	514	22	∑	∑	PROPN
ejpam-1372	514	23	k=1	k=1	X
ejpam-1372	514	24	(	(	PUNCT
ejpam-1372	514	25	−1)k+1	−1)k+1	VERB
ejpam-1372	514	26	k	k	PROPN
ejpam-1372	514	27	ak	ak	PROPN
ejpam-1372	514	28	,	,	PUNCT
ejpam-1372	514	29	(	(	PUNCT
ejpam-1372	514	30	48	48	NUM
ejpam-1372	514	31	)	)	PUNCT
ejpam-1372	515	1	where	where	SCONJ
ejpam-1372	515	2	a0=1	a0=1	PROPN
ejpam-1372	515	3	,	,	PUNCT
ejpam-1372	515	4	a1=1/2	a1=1/2	PROPN
ejpam-1372	515	5	,	,	PUNCT
ejpam-1372	515	6	a2=−1/12	a2=−1/12	PROPN
ejpam-1372	515	7	,	,	PUNCT
ejpam-1372	515	8	and	and	CCONJ
ejpam-1372	515	9	ak	ak	PROPN
ejpam-1372	515	10	=	=	SYM
ejpam-1372	515	11	(	(	PUNCT
ejpam-1372	515	12	−1)k	−1)k	PROPN
ejpam-1372	515	13	k	k	X
ejpam-1372	515	14	!	!	PUNCT
ejpam-1372	515	15	∫	∫	PROPN
ejpam-1372	516	1	1	1	NUM
ejpam-1372	516	2	0	0	NUM
ejpam-1372	516	3	d	d	NOUN
ejpam-1372	516	4	t	t	NOUN
ejpam-1372	516	5	γ(k+	γ(k+	PROPN
ejpam-1372	516	6	t	t	PROPN
ejpam-1372	516	7	−	−	NOUN
ejpam-1372	516	8	1	1	NUM
ejpam-1372	516	9	)	)	PUNCT
ejpam-1372	516	10	γ(t	γ(t	NOUN
ejpam-1372	516	11	−	−	PROPN
ejpam-1372	516	12	1	1	NUM
ejpam-1372	516	13	)	)	PUNCT
ejpam-1372	516	14	.	.	PUNCT
ejpam-1372	517	1	(	(	PUNCT
ejpam-1372	517	2	49	49	NUM
ejpam-1372	517	3	)	)	PUNCT
ejpam-1372	517	4	furthermore	furthermore	ADV
ejpam-1372	517	5	,	,	PUNCT
ejpam-1372	517	6	by	by	ADP
ejpam-1372	517	7	using	use	VERB
ejpam-1372	517	8	the	the	DET
ejpam-1372	517	9	properties	property	NOUN
ejpam-1372	517	10	of	of	ADP
ejpam-1372	517	11	volterra	volterra	NOUN
ejpam-1372	517	12	functions	function	NOUN
ejpam-1372	517	13	and	and	CCONJ
ejpam-1372	517	14	the	the	DET
ejpam-1372	517	15	orthogonality	orthogonality	NOUN
ejpam-1372	517	16	of	of	ADP
ejpam-1372	517	17	laguerre	laguerre	NOUN
ejpam-1372	517	18	polynomials	polynomial	NOUN
ejpam-1372	517	19	,	,	PUNCT
ejpam-1372	517	20	apelblat	apelblat	NOUN
ejpam-1372	517	21	obtains	obtain	VERB
ejpam-1372	517	22	on	on	ADP
ejpam-1372	517	23	p.	p.	PROPN
ejpam-1372	517	24	156	156	NUM
ejpam-1372	517	25	of	of	ADP
ejpam-1372	517	26	ref	ref	NOUN
ejpam-1372	517	27	.	.	PUNCT
ejpam-1372	518	1	[	[	X
ejpam-1372	518	2	2	2	X
ejpam-1372	518	3	]	]	PUNCT
ejpam-1372	518	4	an	an	DET
ejpam-1372	518	5	alternative	alternative	ADJ
ejpam-1372	518	6	result	result	NOUN
ejpam-1372	518	7	for	for	ADP
ejpam-1372	518	8	the	the	DET
ejpam-1372	518	9	ak	ak	PROPN
ejpam-1372	518	10	,	,	PUNCT
ejpam-1372	518	11	which	which	PRON
ejpam-1372	518	12	for	for	ADP
ejpam-1372	518	13	k	k	PROPN
ejpam-1372	518	14	≥	≥	NUM
ejpam-1372	518	15	1	1	NUM
ejpam-1372	518	16	is	be	AUX
ejpam-1372	518	17	given	give	VERB
ejpam-1372	518	18	by	by	ADP
ejpam-1372	518	19	ak	ak	PROPN
ejpam-1372	518	20	=	=	PROPN
ejpam-1372	518	21	(	(	PUNCT
ejpam-1372	518	22	−1)k	−1)k	PROPN
ejpam-1372	518	23	∫	∫	PROPN
ejpam-1372	518	24	∞	∞	PROPN
ejpam-1372	518	25	0	0	PUNCT
ejpam-1372	519	1	d	d	PRON
ejpam-1372	519	2	t	t	PROPN
ejpam-1372	519	3	1	1	NUM
ejpam-1372	519	4	(	(	PUNCT
ejpam-1372	519	5	t	t	PROPN
ejpam-1372	519	6	+	+	X
ejpam-1372	519	7	1)k	1)k	NUM
ejpam-1372	519	8	(	(	PUNCT
ejpam-1372	519	9	π2	π2	X
ejpam-1372	519	10	+	+	CCONJ
ejpam-1372	519	11	log2	log2	PROPN
ejpam-1372	519	12	t	t	PROPN
ejpam-1372	519	13	)	)	PUNCT
ejpam-1372	519	14	.	.	PUNCT
ejpam-1372	520	1	(	(	PUNCT
ejpam-1372	520	2	50	50	NUM
ejpam-1372	520	3	)	)	PUNCT
ejpam-1372	520	4	if	if	SCONJ
ejpam-1372	520	5	this	this	DET
ejpam-1372	520	6	result	result	NOUN
ejpam-1372	520	7	is	be	AUX
ejpam-1372	520	8	introduced	introduce	VERB
ejpam-1372	520	9	into	into	ADP
ejpam-1372	520	10	hurst	hurst	PROPN
ejpam-1372	520	11	’s	’s	PART
ejpam-1372	520	12	formula	formula	NOUN
ejpam-1372	520	13	and	and	CCONJ
ejpam-1372	520	14	the	the	DET
ejpam-1372	520	15	order	order	NOUN
ejpam-1372	520	16	of	of	ADP
ejpam-1372	520	17	the	the	DET
ejpam-1372	520	18	integration	integration	NOUN
ejpam-1372	520	19	and	and	CCONJ
ejpam-1372	520	20	summation	summation	NOUN
ejpam-1372	520	21	are	be	AUX
ejpam-1372	520	22	interchanged	interchange	VERB
ejpam-1372	520	23	,	,	PUNCT
ejpam-1372	520	24	then	then	ADV
ejpam-1372	520	25	with	with	ADP
ejpam-1372	520	26	the	the	DET
ejpam-1372	520	27	aid	aid	NOUN
ejpam-1372	520	28	of	of	ADP
ejpam-1372	520	29	the	the	DET
ejpam-1372	520	30	lower	low	ADJ
ejpam-1372	520	31	result	result	NOUN
ejpam-1372	520	32	in	in	ADP
ejpam-1372	520	33	equivalence	equivalence	NOUN
ejpam-1372	520	34	(	(	PUNCT
ejpam-1372	520	35	15	15	NUM
ejpam-1372	520	36	)	)	PUNCT
ejpam-1372	520	37	,	,	PUNCT
ejpam-1372	520	38	i.e.	i.e.	X
ejpam-1372	520	39	the	the	DET
ejpam-1372	520	40	equation	equation	NOUN
ejpam-1372	520	41	form	form	NOUN
ejpam-1372	520	42	,	,	PUNCT
ejpam-1372	520	43	we	we	PRON
ejpam-1372	520	44	arrive	arrive	VERB
ejpam-1372	520	45	at	at	ADP
ejpam-1372	520	46	a	a	DET
ejpam-1372	520	47	new	new	ADJ
ejpam-1372	520	48	integral	integral	ADJ
ejpam-1372	520	49	representation	representation	NOUN
ejpam-1372	520	50	for	for	ADP
ejpam-1372	520	51	euler	euler	PROPN
ejpam-1372	520	52	’s	’s	PART
ejpam-1372	520	53	constant	constant	ADJ
ejpam-1372	520	54	,	,	PUNCT
ejpam-1372	520	55	which	which	PRON
ejpam-1372	520	56	is	be	AUX
ejpam-1372	520	57	γ=	γ=	PROPN
ejpam-1372	520	58	−	−	PROPN
ejpam-1372	520	59	∫	∫	PROPN
ejpam-1372	520	60	∞	∞	PROPN
ejpam-1372	520	61	0	0	PUNCT
ejpam-1372	521	1	d	d	PRON
ejpam-1372	521	2	t	t	PROPN
ejpam-1372	521	3	π2	π2	X
ejpam-1372	521	4	+	+	CCONJ
ejpam-1372	521	5	log2	log2	PROPN
ejpam-1372	521	6	t	t	PROPN
ejpam-1372	521	7	log	log	PROPN
ejpam-1372	521	8	�	�	PROPN
ejpam-1372	521	9	t	t	PROPN
ejpam-1372	521	10	t	t	PROPN
ejpam-1372	521	11	+	+	CCONJ
ejpam-1372	521	12	1	1	NUM
ejpam-1372	521	13	�	�	PROPN
ejpam-1372	521	14	.	.	PUNCT
ejpam-1372	522	1	(	(	PUNCT
ejpam-1372	522	2	51	51	NUM
ejpam-1372	522	3	)	)	PUNCT
ejpam-1372	522	4	8	8	NUM
ejpam-1372	522	5	.	.	PUNCT
ejpam-1372	523	1	regularisation	regularisation	NOUN
ejpam-1372	523	2	versus	versus	ADP
ejpam-1372	523	3	renormalisation	renormalisation	NOUN
ejpam-1372	523	4	the	the	DET
ejpam-1372	523	5	regularisation	regularisation	NOUN
ejpam-1372	523	6	formula	formula	NOUN
ejpam-1372	523	7	discovered	discover	VERB
ejpam-1372	523	8	by	by	ADP
ejpam-1372	523	9	euler	euler	NOUN
ejpam-1372	523	10	can	can	AUX
ejpam-1372	523	11	also	also	ADV
ejpam-1372	523	12	be	be	AUX
ejpam-1372	523	13	used	use	VERB
ejpam-1372	523	14	to	to	PART
ejpam-1372	523	15	see	see	VERB
ejpam-1372	523	16	whether	whether	SCONJ
ejpam-1372	523	17	it	it	PRON
ejpam-1372	523	18	is	be	AUX
ejpam-1372	523	19	consistent	consistent	ADJ
ejpam-1372	523	20	with	with	ADP
ejpam-1372	523	21	the	the	DET
ejpam-1372	523	22	physicist	physicist	NOUN
ejpam-1372	523	23	’s	’s	PART
ejpam-1372	523	24	concept	concept	NOUN
ejpam-1372	523	25	of	of	ADP
ejpam-1372	523	26	renormalisation	renormalisation	NOUN
ejpam-1372	523	27	.	.	PUNCT
ejpam-1372	524	1	the	the	DET
ejpam-1372	524	2	longitudinal	longitudinal	ADJ
ejpam-1372	524	3	dielectric	dielectric	ADJ
ejpam-1372	524	4	response	response	NOUN
ejpam-1372	524	5	function	function	NOUN
ejpam-1372	524	6	of	of	ADP
ejpam-1372	524	7	an	an	DET
ejpam-1372	524	8	electron	electron	NOUN
ejpam-1372	524	9	-	-	PUNCT
ejpam-1372	524	10	positron	positron	NOUN
ejpam-1372	524	11	plasma	plasma	NOUN
ejpam-1372	524	12	in	in	ADP
ejpam-1372	524	13	an	an	DET
ejpam-1372	524	14	external	external	ADJ
ejpam-1372	524	15	magnetic	magnetic	ADJ
ejpam-1372	524	16	field	field	NOUN
ejpam-1372	524	17	denoted	denote	VERB
ejpam-1372	524	18	by	by	ADP
ejpam-1372	524	19	ε(q	ε(q	PROPN
ejpam-1372	524	20	,	,	PUNCT
ejpam-1372	524	21	ω	ω	PROPN
ejpam-1372	524	22	,	,	PUNCT
ejpam-1372	524	23	b	b	NOUN
ejpam-1372	524	24	)	)	PUNCT
ejpam-1372	524	25	arises	arise	VERB
ejpam-1372	524	26	in	in	ADP
ejpam-1372	524	27	the	the	DET
ejpam-1372	524	28	response	response	NOUN
ejpam-1372	524	29	theory	theory	NOUN
ejpam-1372	524	30	of	of	ADP
ejpam-1372	524	31	particle	particle	NOUN
ejpam-1372	524	32	-	-	PUNCT
ejpam-1372	524	33	anti	anti	ADJ
ejpam-1372	524	34	-	-	ADJ
ejpam-1372	524	35	particle	particle	ADJ
ejpam-1372	524	36	plasmas	plasma	NOUN
ejpam-1372	524	37	[	[	X
ejpam-1372	524	38	22	22	NUM
ejpam-1372	524	39	]	]	PUNCT
ejpam-1372	524	40	.	.	PUNCT
ejpam-1372	525	1	this	this	DET
ejpam-1372	525	2	quantity	quantity	NOUN
ejpam-1372	525	3	can	can	AUX
ejpam-1372	525	4	be	be	AUX
ejpam-1372	525	5	separated	separate	VERB
ejpam-1372	525	6	into	into	ADP
ejpam-1372	525	7	particle	particle	NOUN
ejpam-1372	525	8	and	and	CCONJ
ejpam-1372	525	9	vacuum	vacuum	NOUN
ejpam-1372	525	10	parts	part	NOUN
ejpam-1372	525	11	denoted	denote	VERB
ejpam-1372	525	12	by	by	ADP
ejpam-1372	525	13	the	the	DET
ejpam-1372	525	14	subscripts	subscript	NOUN
ejpam-1372	525	15	p	p	NOUN
ejpam-1372	525	16	and	and	CCONJ
ejpam-1372	525	17	v	v	ADP
ejpam-1372	525	18	respectively	respectively	ADV
ejpam-1372	525	19	.	.	PUNCT
ejpam-1372	526	1	because	because	SCONJ
ejpam-1372	526	2	it	it	PRON
ejpam-1372	526	3	is	be	AUX
ejpam-1372	526	4	derived	derive	VERB
ejpam-1372	526	5	via	via	ADP
ejpam-1372	526	6	quantum	quantum	ADJ
ejpam-1372	526	7	mechanics	mechanic	NOUN
ejpam-1372	526	8	,	,	PUNCT
ejpam-1372	526	9	it	it	PRON
ejpam-1372	526	10	needs	need	VERB
ejpam-1372	526	11	to	to	PART
ejpam-1372	526	12	be	be	AUX
ejpam-1372	526	13	renormalised	renormalise	VERB
ejpam-1372	526	14	in	in	ADP
ejpam-1372	526	15	accordance	accordance	NOUN
ejpam-1372	526	16	with	with	ADP
ejpam-1372	526	17	standard	standard	ADJ
ejpam-1372	526	18	quantum	quantum	ADJ
ejpam-1372	526	19	electrodynamic	electrodynamic	ADJ
ejpam-1372	526	20	theory	theory	NOUN
ejpam-1372	526	21	(	(	PUNCT
ejpam-1372	526	22	qed	qed	PROPN
ejpam-1372	526	23	)	)	PUNCT
ejpam-1372	526	24	.	.	PUNCT
ejpam-1372	527	1	hence	hence	ADV
ejpam-1372	527	2	,	,	PUNCT
ejpam-1372	527	3	the	the	DET
ejpam-1372	527	4	divergent	divergent	ADJ
ejpam-1372	527	5	vacuum	vacuum	NOUN
ejpam-1372	527	6	polarisation	polarisation	NOUN
ejpam-1372	527	7	term	term	NOUN
ejpam-1372	527	8	must	must	AUX
ejpam-1372	527	9	be	be	AUX
ejpam-1372	527	10	removed	remove	VERB
ejpam-1372	527	11	,	,	PUNCT
ejpam-1372	527	12	which	which	PRON
ejpam-1372	527	13	means	mean	VERB
ejpam-1372	527	14	evaluating	evaluate	VERB
ejpam-1372	527	15	ℜ	ℜ	PROPN
ejpam-1372	527	16	ε̄(q	ε̄(q	PROPN
ejpam-1372	527	17	,	,	PUNCT
ejpam-1372	527	18	ω	ω	PROPN
ejpam-1372	527	19	,	,	PUNCT
ejpam-1372	527	20	b	b	NOUN
ejpam-1372	527	21	)	)	PUNCT
ejpam-1372	527	22	=	=	SYM
ejpam-1372	527	23	ℜεp(q	ℜεp(q	X
ejpam-1372	527	24	,	,	PUNCT
ejpam-1372	527	25	ω	ω	PROPN
ejpam-1372	527	26	,	,	PUNCT
ejpam-1372	527	27	b	b	NOUN
ejpam-1372	527	28	)	)	PUNCT
ejpam-1372	528	1	+	+	ADJ
ejpam-1372	528	2	ℜεv	ℜεv	PROPN
ejpam-1372	528	3	(	(	PUNCT
ejpam-1372	528	4	q	q	PROPN
ejpam-1372	528	5	,	,	PUNCT
ejpam-1372	528	6	ω	ω	PROPN
ejpam-1372	528	7	,	,	PUNCT
ejpam-1372	528	8	b)−ℜεv	b)−ℜεv	ADV
ejpam-1372	528	9	(	(	PUNCT
ejpam-1372	528	10	0,0,0	0,0,0	NOUN
ejpam-1372	528	11	)	)	PUNCT
ejpam-1372	528	12	.	.	PUNCT
ejpam-1372	529	1	(	(	PUNCT
ejpam-1372	529	2	52	52	NUM
ejpam-1372	529	3	)	)	PUNCT
ejpam-1372	529	4	in	in	ADP
ejpam-1372	529	5	this	this	DET
ejpam-1372	529	6	equation	equation	NOUN
ejpam-1372	529	7	the	the	DET
ejpam-1372	529	8	field	field	NOUN
ejpam-1372	529	9	-	-	PUNCT
ejpam-1372	529	10	free	free	ADJ
ejpam-1372	529	11	vacuum	vacuum	NOUN
ejpam-1372	529	12	term	term	NOUN
ejpam-1372	529	13	is	be	AUX
ejpam-1372	529	14	given	give	VERB
ejpam-1372	529	15	by	by	ADP
ejpam-1372	529	16	the	the	DET
ejpam-1372	529	17	following	follow	VERB
ejpam-1372	529	18	divergent	divergent	ADJ
ejpam-1372	529	19	integral	integral	ADJ
ejpam-1372	529	20	:	:	PUNCT
ejpam-1372	529	21	ℜεv	ℜεv	PROPN
ejpam-1372	529	22	(	(	PUNCT
ejpam-1372	529	23	0,0,0	0,0,0	NUM
ejpam-1372	529	24	)	)	PUNCT
ejpam-1372	529	25	=	=	SYM
ejpam-1372	529	26	e2	e2	PROPN
ejpam-1372	529	27	4π2	4π2	NUM
ejpam-1372	529	28	∫	∫	PROPN
ejpam-1372	529	29	d3p	d3p	PROPN
ejpam-1372	529	30	�	�	PROPN
ejpam-1372	529	31	m2	m2	PROPN
ejpam-1372	529	32	+	+	PROPN
ejpam-1372	529	33	2p2/3	2p2/3	NUM
ejpam-1372	529	34	(	(	PUNCT
ejpam-1372	529	35	p2	p2	PROPN
ejpam-1372	529	36	+	+	PROPN
ejpam-1372	529	37	m2)5/2	m2)5/2	ADJ
ejpam-1372	529	38	�	�	PROPN
ejpam-1372	529	39	.	.	PUNCT
ejpam-1372	530	1	(	(	PUNCT
ejpam-1372	530	2	53	53	NUM
ejpam-1372	530	3	)	)	PUNCT
ejpam-1372	530	4	v.	v.	ADP
ejpam-1372	530	5	kowalenko	kowalenko	PROPN
ejpam-1372	530	6	/	/	SYM
ejpam-1372	530	7	eur	eur	PROPN
ejpam-1372	530	8	.	.	PUNCT
ejpam-1372	531	1	j.	j.	PROPN
ejpam-1372	531	2	pure	pure	PROPN
ejpam-1372	531	3	appl	appl	PROPN
ejpam-1372	531	4	.	.	PROPN
ejpam-1372	531	5	math	math	PROPN
ejpam-1372	531	6	,	,	PUNCT
ejpam-1372	531	7	4	4	NUM
ejpam-1372	531	8	(	(	PUNCT
ejpam-1372	531	9	2011	2011	NUM
ejpam-1372	531	10	)	)	PUNCT
ejpam-1372	531	11	,	,	PUNCT
ejpam-1372	531	12	370	370	NUM
ejpam-1372	531	13	-	-	SYM
ejpam-1372	531	14	423	423	NUM
ejpam-1372	531	15	387	387	NUM
ejpam-1372	531	16	because	because	SCONJ
ejpam-1372	531	17	the	the	DET
ejpam-1372	531	18	last	last	ADJ
ejpam-1372	531	19	two	two	NUM
ejpam-1372	531	20	terms	term	NOUN
ejpam-1372	531	21	of	of	ADP
ejpam-1372	531	22	eq	eq	NOUN
ejpam-1372	531	23	.	.	PUNCT
ejpam-1372	532	1	(	(	PUNCT
ejpam-1372	532	2	52	52	NUM
ejpam-1372	532	3	)	)	PUNCT
ejpam-1372	532	4	diverge	diverge	NOUN
ejpam-1372	532	5	,	,	PUNCT
ejpam-1372	532	6	they	they	PRON
ejpam-1372	532	7	are	be	AUX
ejpam-1372	532	8	both	both	PRON
ejpam-1372	532	9	renormalised	renormalise	VERB
ejpam-1372	532	10	by	by	ADP
ejpam-1372	532	11	introducing	introduce	VERB
ejpam-1372	532	12	−ℜεv	−ℜεv	PROPN
ejpam-1372	532	13	(	(	PUNCT
ejpam-1372	532	14	0,0	0,0	NOUN
ejpam-1372	532	15	,	,	PUNCT
ejpam-1372	532	16	b	b	NOUN
ejpam-1372	532	17	)	)	PUNCT
ejpam-1372	532	18	after	after	ADP
ejpam-1372	532	19	the	the	DET
ejpam-1372	532	20	second	second	ADJ
ejpam-1372	532	21	term	term	NOUN
ejpam-1372	532	22	on	on	ADP
ejpam-1372	532	23	the	the	DET
ejpam-1372	532	24	rhs	rhs	PROPN
ejpam-1372	532	25	and	and	CCONJ
ejpam-1372	532	26	+	+	ADJ
ejpam-1372	532	27	ℜεv	ℜεv	PROPN
ejpam-1372	532	28	(	(	PUNCT
ejpam-1372	532	29	0,0	0,0	NOUN
ejpam-1372	532	30	,	,	PUNCT
ejpam-1372	532	31	b	b	NOUN
ejpam-1372	532	32	)	)	PUNCT
ejpam-1372	532	33	before	before	ADP
ejpam-1372	532	34	the	the	DET
ejpam-1372	532	35	final	final	ADJ
ejpam-1372	532	36	term	term	NOUN
ejpam-1372	532	37	.	.	PUNCT
ejpam-1372	533	1	this	this	DET
ejpam-1372	533	2	results	result	VERB
ejpam-1372	533	3	in	in	ADP
ejpam-1372	533	4	the	the	DET
ejpam-1372	533	5	emergence	emergence	NOUN
ejpam-1372	533	6	of	of	ADP
ejpam-1372	533	7	a	a	DET
ejpam-1372	533	8	quantity	quantity	NOUN
ejpam-1372	533	9	known	know	VERB
ejpam-1372	533	10	as	as	ADP
ejpam-1372	533	11	the	the	DET
ejpam-1372	533	12	longitudinal	longitudinal	ADJ
ejpam-1372	533	13	static	static	ADJ
ejpam-1372	533	14	uniform	uniform	ADJ
ejpam-1372	533	15	polarisability	polarisability	NOUN
ejpam-1372	533	16	,	,	PUNCT
ejpam-1372	533	17	which	which	PRON
ejpam-1372	533	18	is	be	AUX
ejpam-1372	533	19	defined	define	VERB
ejpam-1372	533	20	as	as	ADP
ejpam-1372	533	21	α‖(b	α‖(b	NOUN
ejpam-1372	533	22	)	)	PUNCT
ejpam-1372	533	23	=	=	VERB
ejpam-1372	533	24	ℜεv	ℜεv	PROPN
ejpam-1372	533	25	(	(	PUNCT
ejpam-1372	533	26	0,0	0,0	NOUN
ejpam-1372	533	27	,	,	PUNCT
ejpam-1372	533	28	b)−ℜεv	b)−ℜεv	X
ejpam-1372	533	29	(	(	PUNCT
ejpam-1372	533	30	0,0,0	0,0,0	NOUN
ejpam-1372	533	31	)	)	PUNCT
ejpam-1372	533	32	=	=	SYM
ejpam-1372	533	33	e3b	e3b	PROPN
ejpam-1372	533	34	4π	4π	NUM
ejpam-1372	533	35	∞	∞	PROPN
ejpam-1372	533	36	∑	∑	PROPN
ejpam-1372	533	37	n=0	n=0	X
ejpam-1372	533	38	an	an	DET
ejpam-1372	533	39	×	×	NOUN
ejpam-1372	533	40	∫	∫	NOUN
ejpam-1372	533	41	∞	∞	PROPN
ejpam-1372	533	42	−∞	−∞	ADP
ejpam-1372	533	43	dpz	dpz	PROPN
ejpam-1372	533	44	�	�	PROPN
ejpam-1372	533	45	m2	m2	PROPN
ejpam-1372	533	46	+	+	CCONJ
ejpam-1372	533	47	2neb	2neb	PROPN
ejpam-1372	533	48	(	(	PUNCT
ejpam-1372	533	49	p2	p2	PROPN
ejpam-1372	533	50	z	z	PROPN
ejpam-1372	533	51	+	+	PROPN
ejpam-1372	533	52	m2	m2	PROPN
ejpam-1372	533	53	+	+	PROPN
ejpam-1372	533	54	2neb)5/2	2neb)5/2	NUM
ejpam-1372	533	55	�	�	PROPN
ejpam-1372	533	56	−	−	PROPN
ejpam-1372	533	57	e2	e2	PROPN
ejpam-1372	533	58	4π2	4π2	NUM
ejpam-1372	533	59	∫	∫	PROPN
ejpam-1372	533	60	d3p	d3p	PROPN
ejpam-1372	533	61	�	�	PROPN
ejpam-1372	533	62	m2	m2	PROPN
ejpam-1372	533	63	+	+	PROPN
ejpam-1372	533	64	2p2/3	2p2/3	NUM
ejpam-1372	533	65	(	(	PUNCT
ejpam-1372	533	66	p2	p2	PROPN
ejpam-1372	533	67	+	+	PROPN
ejpam-1372	533	68	m2)5/2	m2)5/2	ADJ
ejpam-1372	533	69	�	�	PROPN
ejpam-1372	533	70	.	.	PUNCT
ejpam-1372	534	1	(	(	PUNCT
ejpam-1372	534	2	54	54	NUM
ejpam-1372	534	3	)	)	PUNCT
ejpam-1372	534	4	in	in	ADP
ejpam-1372	534	5	eq	eq	ADP
ejpam-1372	534	6	.	.	PUNCT
ejpam-1372	535	1	(	(	PUNCT
ejpam-1372	535	2	54	54	NUM
ejpam-1372	535	3	)	)	PUNCT
ejpam-1372	535	4	,	,	PUNCT
ejpam-1372	535	5	an=2	an=2	PROPN
ejpam-1372	535	6	for	for	ADP
ejpam-1372	535	7	n>0	n>0	NUM
ejpam-1372	535	8	,	,	PUNCT
ejpam-1372	535	9	while	while	SCONJ
ejpam-1372	535	10	for	for	ADP
ejpam-1372	535	11	n=0	n=0	NUM
ejpam-1372	535	12	,	,	PUNCT
ejpam-1372	535	13	an=1	an=1	PROPN
ejpam-1372	535	14	.	.	PUNCT
ejpam-1372	536	1	for	for	ADP
ejpam-1372	536	2	those	those	PRON
ejpam-1372	536	3	with	with	ADP
ejpam-1372	536	4	a	a	DET
ejpam-1372	536	5	physical	physical	ADJ
ejpam-1372	536	6	bent	bent	NOUN
ejpam-1372	536	7	,	,	PUNCT
ejpam-1372	536	8	e	e	NOUN
ejpam-1372	536	9	and	and	CCONJ
ejpam-1372	536	10	m	m	AUX
ejpam-1372	536	11	represent	represent	VERB
ejpam-1372	536	12	the	the	DET
ejpam-1372	536	13	charge	charge	NOUN
ejpam-1372	536	14	and	and	CCONJ
ejpam-1372	536	15	mass	mass	NOUN
ejpam-1372	536	16	of	of	ADP
ejpam-1372	536	17	an	an	DET
ejpam-1372	536	18	electron	electron	NOUN
ejpam-1372	536	19	,	,	PUNCT
ejpam-1372	536	20	while	while	SCONJ
ejpam-1372	536	21	the	the	DET
ejpam-1372	536	22	momentum	momentum	NOUN
ejpam-1372	536	23	p	p	NOUN
ejpam-1372	536	24	is	be	AUX
ejpam-1372	536	25	expressed	express	VERB
ejpam-1372	536	26	in	in	ADP
ejpam-1372	536	27	components	component	NOUN
ejpam-1372	536	28	px	px	PROPN
ejpam-1372	536	29	,	,	PUNCT
ejpam-1372	536	30	py	py	PROPN
ejpam-1372	536	31	and	and	CCONJ
ejpam-1372	536	32	pz	pz	PROPN
ejpam-1372	536	33	.	.	PROPN
ejpam-1372	536	34	hence	hence	ADV
ejpam-1372	536	35	,	,	PUNCT
ejpam-1372	536	36	in	in	ADP
ejpam-1372	536	37	the	the	DET
ejpam-1372	536	38	vacuum	vacuum	NOUN
ejpam-1372	536	39	term	term	NOUN
ejpam-1372	536	40	d3p	d3p	PROPN
ejpam-1372	536	41	=	=	SYM
ejpam-1372	536	42	dpx	dpx	PROPN
ejpam-1372	536	43	dpy	dpy	PROPN
ejpam-1372	536	44	dpz	dpz	PROPN
ejpam-1372	536	45	,	,	PUNCT
ejpam-1372	536	46	where	where	SCONJ
ejpam-1372	536	47	each	each	DET
ejpam-1372	536	48	component	component	NOUN
ejpam-1372	536	49	of	of	ADP
ejpam-1372	536	50	the	the	DET
ejpam-1372	536	51	momentum	momentum	NOUN
ejpam-1372	536	52	ranges	range	VERB
ejpam-1372	536	53	from	from	ADP
ejpam-1372	536	54	−∞	−∞	X
ejpam-1372	536	55	to	to	ADP
ejpam-1372	536	56	∞.	∞.	PROPN
ejpam-1372	536	57	the	the	DET
ejpam-1372	536	58	summation	summation	NOUN
ejpam-1372	536	59	over	over	ADP
ejpam-1372	536	60	n	n	PROPN
ejpam-1372	536	61	arises	arise	VERB
ejpam-1372	536	62	from	from	ADP
ejpam-1372	536	63	summing	sum	VERB
ejpam-1372	536	64	over	over	ADP
ejpam-1372	536	65	the	the	DET
ejpam-1372	536	66	landau	landau	NOUN
ejpam-1372	536	67	levels	level	NOUN
ejpam-1372	536	68	that	that	PRON
ejpam-1372	536	69	result	result	VERB
ejpam-1372	536	70	from	from	ADP
ejpam-1372	536	71	the	the	DET
ejpam-1372	536	72	solutions	solution	NOUN
ejpam-1372	536	73	for	for	ADP
ejpam-1372	536	74	the	the	DET
ejpam-1372	536	75	dirac	dirac	NOUN
ejpam-1372	536	76	equation	equation	NOUN
ejpam-1372	536	77	.	.	PUNCT
ejpam-1372	537	1	the	the	DET
ejpam-1372	537	2	introduction	introduction	NOUN
ejpam-1372	537	3	of	of	ADP
ejpam-1372	537	4	a	a	DET
ejpam-1372	537	5	magnetic	magnetic	ADJ
ejpam-1372	537	6	field	field	NOUN
ejpam-1372	537	7	into	into	ADP
ejpam-1372	537	8	response	response	NOUN
ejpam-1372	537	9	theory	theory	NOUN
ejpam-1372	537	10	has	have	VERB
ejpam-1372	537	11	the	the	DET
ejpam-1372	537	12	effect	effect	NOUN
ejpam-1372	537	13	of	of	ADP
ejpam-1372	537	14	suppressing	suppress	VERB
ejpam-1372	537	15	the	the	DET
ejpam-1372	537	16	x	x	NOUN
ejpam-1372	537	17	and	and	CCONJ
ejpam-1372	537	18	y	y	PROPN
ejpam-1372	537	19	components	component	NOUN
ejpam-1372	537	20	of	of	ADP
ejpam-1372	537	21	the	the	DET
ejpam-1372	537	22	momentum	momentum	NOUN
ejpam-1372	537	23	.	.	PUNCT
ejpam-1372	538	1	that	that	PRON
ejpam-1372	538	2	is	is	ADV
ejpam-1372	538	3	,	,	PUNCT
ejpam-1372	538	4	2neb	2neb	PROPN
ejpam-1372	538	5	takes	take	VERB
ejpam-1372	538	6	on	on	ADP
ejpam-1372	538	7	the	the	DET
ejpam-1372	538	8	role	role	NOUN
ejpam-1372	538	9	of	of	ADP
ejpam-1372	538	10	p2	p2	PROPN
ejpam-1372	538	11	x	x	PUNCT
ejpam-1372	539	1	+	+	CCONJ
ejpam-1372	539	2	p2	p2	PROPN
ejpam-1372	539	3	y	y	NOUN
ejpam-1372	539	4	=	=	NOUN
ejpam-1372	539	5	p2	p2	PROPN
ejpam-1372	539	6	⊥	⊥	NOUN
ejpam-1372	539	7	.	.	PUNCT
ejpam-1372	540	1	the	the	DET
ejpam-1372	540	2	first	first	ADJ
ejpam-1372	540	3	term	term	NOUN
ejpam-1372	540	4	on	on	ADP
ejpam-1372	540	5	the	the	DET
ejpam-1372	540	6	rhs	rhs	PROPN
ejpam-1372	540	7	of	of	ADP
ejpam-1372	540	8	eq	eq	PROPN
ejpam-1372	540	9	.	.	PUNCT
ejpam-1372	540	10	(	(	PUNCT
ejpam-1372	540	11	54	54	NUM
ejpam-1372	540	12	)	)	PUNCT
ejpam-1372	540	13	is	be	AUX
ejpam-1372	540	14	logarithmically	logarithmically	ADV
ejpam-1372	540	15	divergent	divergent	ADJ
ejpam-1372	540	16	,	,	PUNCT
ejpam-1372	540	17	which	which	PRON
ejpam-1372	540	18	can	can	AUX
ejpam-1372	540	19	be	be	AUX
ejpam-1372	540	20	observed	observe	VERB
ejpam-1372	540	21	by	by	ADP
ejpam-1372	540	22	evaluating	evaluate	VERB
ejpam-1372	540	23	the	the	DET
ejpam-1372	540	24	integral	integral	ADJ
ejpam-1372	540	25	over	over	ADP
ejpam-1372	540	26	pz	pz	PROPN
ejpam-1372	540	27	.	.	PUNCT
ejpam-1372	541	1	with	with	ADP
ejpam-1372	541	2	the	the	DET
ejpam-1372	541	3	aid	aid	NOUN
ejpam-1372	541	4	of	of	ADP
ejpam-1372	541	5	no	no	NOUN
ejpam-1372	541	6	.	.	NOUN
ejpam-1372	541	7	2.271(6	2.271(6	NUM
ejpam-1372	541	8	)	)	PUNCT
ejpam-1372	541	9	in	in	ADP
ejpam-1372	541	10	ref	ref	NOUN
ejpam-1372	541	11	.	.	PUNCT
ejpam-1372	542	1	[	[	X
ejpam-1372	542	2	11	11	NUM
ejpam-1372	542	3	]	]	PUNCT
ejpam-1372	542	4	,	,	PUNCT
ejpam-1372	542	5	we	we	PRON
ejpam-1372	542	6	find	find	VERB
ejpam-1372	542	7	that	that	SCONJ
ejpam-1372	542	8	e3b	e3b	PROPN
ejpam-1372	542	9	4π	4π	NUM
ejpam-1372	542	10	∞	∞	PROPN
ejpam-1372	542	11	∑	∑	PROPN
ejpam-1372	542	12	n=0	n=0	X
ejpam-1372	542	13	an	an	DET
ejpam-1372	542	14	∫	∫	PROPN
ejpam-1372	542	15	∞	∞	PROPN
ejpam-1372	542	16	−∞	−∞	ADP
ejpam-1372	542	17	dpz	dpz	PROPN
ejpam-1372	542	18	�	�	PROPN
ejpam-1372	542	19	m2	m2	PROPN
ejpam-1372	542	20	+	+	CCONJ
ejpam-1372	542	21	2neb	2neb	PROPN
ejpam-1372	542	22	(	(	PUNCT
ejpam-1372	542	23	p2	p2	PROPN
ejpam-1372	542	24	z	z	PROPN
ejpam-1372	542	25	+	+	PROPN
ejpam-1372	542	26	m2	m2	PROPN
ejpam-1372	542	27	+	+	PROPN
ejpam-1372	542	28	2neb)5/2	2neb)5/2	NUM
ejpam-1372	542	29	�	�	PROPN
ejpam-1372	542	30	=	=	SYM
ejpam-1372	542	31	e3b	e3b	PROPN
ejpam-1372	542	32	3π	3π	NUM
ejpam-1372	542	33	�	�	NOUN
ejpam-1372	542	34	1	1	NUM
ejpam-1372	542	35	m2	m2	PROPN
ejpam-1372	542	36	+	+	CCONJ
ejpam-1372	542	37	1	1	NUM
ejpam-1372	542	38	eb	eb	PROPN
ejpam-1372	542	39	∞	∞	NUM
ejpam-1372	542	40	∑	∑	PUNCT
ejpam-1372	542	41	n=1	n=1	PROPN
ejpam-1372	542	42	1	1	NUM
ejpam-1372	542	43	n+m2/2eb	n+m2/2eb	PROPN
ejpam-1372	542	44	!	!	PUNCT
ejpam-1372	542	45	.	.	PUNCT
ejpam-1372	543	1	(	(	PUNCT
ejpam-1372	543	2	55	55	NUM
ejpam-1372	543	3	)	)	PUNCT
ejpam-1372	543	4	the	the	DET
ejpam-1372	543	5	series	series	NOUN
ejpam-1372	543	6	in	in	ADP
ejpam-1372	543	7	eq	eq	PROPN
ejpam-1372	543	8	.	.	PUNCT
ejpam-1372	544	1	(	(	PUNCT
ejpam-1372	544	2	55	55	NUM
ejpam-1372	544	3	)	)	PUNCT
ejpam-1372	544	4	can	can	AUX
ejpam-1372	544	5	be	be	AUX
ejpam-1372	544	6	regularised	regularise	VERB
ejpam-1372	544	7	by	by	ADP
ejpam-1372	544	8	introducing	introduce	VERB
ejpam-1372	544	9	euler	euler	NOUN
ejpam-1372	544	10	’s	’s	PART
ejpam-1372	544	11	regularisation	regularisation	NOUN
ejpam-1372	544	12	formula	formula	NOUN
ejpam-1372	544	13	.	.	PUNCT
ejpam-1372	545	1	denoting	denote	VERB
ejpam-1372	545	2	the	the	DET
ejpam-1372	545	3	finite	finite	ADJ
ejpam-1372	545	4	part	part	NOUN
ejpam-1372	545	5	by	by	ADP
ejpam-1372	545	6	p(b	p(b	PROPN
ejpam-1372	545	7	)	)	PUNCT
ejpam-1372	545	8	,	,	PUNCT
ejpam-1372	545	9	where	where	SCONJ
ejpam-1372	545	10	b=2eb	b=2eb	X
ejpam-1372	545	11	/	/	SYM
ejpam-1372	545	12	m2	m2	PROPN
ejpam-1372	545	13	,	,	PUNCT
ejpam-1372	545	14	we	we	PRON
ejpam-1372	545	15	obtain	obtain	VERB
ejpam-1372	545	16	p(b	p(b	NOUN
ejpam-1372	545	17	)	)	PUNCT
ejpam-1372	545	18	=	=	SYM
ejpam-1372	546	1	∞	∞	NUM
ejpam-1372	546	2	∑	∑	PUNCT
ejpam-1372	546	3	n=1	n=1	PROPN
ejpam-1372	546	4	1	1	NUM
ejpam-1372	546	5	n+	n+	SYM
ejpam-1372	546	6	1	1	NUM
ejpam-1372	546	7	/	/	SYM
ejpam-1372	546	8	b	b	NOUN
ejpam-1372	546	9	−	−	NOUN
ejpam-1372	546	10	∞	∞	NUM
ejpam-1372	546	11	∑	∑	PROPN
ejpam-1372	546	12	n=0	n=0	PROPN
ejpam-1372	546	13	1	1	NUM
ejpam-1372	546	14	n+	n+	SYM
ejpam-1372	546	15	1	1	NUM
ejpam-1372	546	16	+	+	CCONJ
ejpam-1372	546	17	γ	γ	X
ejpam-1372	546	18	.	.	PUNCT
ejpam-1372	547	1	(	(	PUNCT
ejpam-1372	547	2	56	56	NUM
ejpam-1372	547	3	)	)	PUNCT
ejpam-1372	547	4	from	from	ADP
ejpam-1372	547	5	no	no	PROPN
ejpam-1372	547	6	.	.	PUNCT
ejpam-1372	547	7	8.362(1	8.362(1	NUM
ejpam-1372	547	8	)	)	PUNCT
ejpam-1372	547	9	of	of	ADP
ejpam-1372	547	10	ref	ref	NOUN
ejpam-1372	547	11	.	.	PUNCT
ejpam-1372	548	1	[	[	X
ejpam-1372	548	2	11	11	NUM
ejpam-1372	548	3	]	]	PUNCT
ejpam-1372	548	4	,	,	PUNCT
ejpam-1372	548	5	which	which	PRON
ejpam-1372	548	6	states	state	VERB
ejpam-1372	548	7	that	that	SCONJ
ejpam-1372	548	8	the	the	DET
ejpam-1372	548	9	digamma	digamma	PROPN
ejpam-1372	548	10	function	function	NOUN
ejpam-1372	548	11	is	be	AUX
ejpam-1372	548	12	given	give	VERB
ejpam-1372	548	13	by	by	ADP
ejpam-1372	548	14	ψ(x	ψ(x	NOUN
ejpam-1372	548	15	)	)	PUNCT
ejpam-1372	548	16	=	=	SYM
ejpam-1372	548	17	−γ−	−γ−	NOUN
ejpam-1372	548	18	∞	∞	PROPN
ejpam-1372	548	19	∑	∑	PROPN
ejpam-1372	548	20	n=0	n=0	PROPN
ejpam-1372	548	21	�	�	PROPN
ejpam-1372	548	22	1	1	NUM
ejpam-1372	548	23	n+	n+	NOUN
ejpam-1372	548	24	x	x	PUNCT
ejpam-1372	548	25	−	−	PROPN
ejpam-1372	548	26	1	1	NUM
ejpam-1372	548	27	n+	n+	SYM
ejpam-1372	548	28	1	1	NUM
ejpam-1372	548	29	�	�	PROPN
ejpam-1372	548	30	.	.	PUNCT
ejpam-1372	549	1	(	(	PUNCT
ejpam-1372	549	2	57	57	NUM
ejpam-1372	549	3	)	)	PUNCT
ejpam-1372	549	4	we	we	PRON
ejpam-1372	549	5	arrive	arrive	VERB
ejpam-1372	549	6	at	at	ADP
ejpam-1372	549	7	p(b	p(b	NOUN
ejpam-1372	549	8	)	)	PUNCT
ejpam-1372	549	9	=	=	SYM
ejpam-1372	550	1	−ψ(1	−ψ(1	PROPN
ejpam-1372	550	2	/	/	SYM
ejpam-1372	550	3	b)−	b)−	PROPN
ejpam-1372	550	4	b	b	PROPN
ejpam-1372	550	5	.	.	PUNCT
ejpam-1372	551	1	(	(	PUNCT
ejpam-1372	551	2	58	58	NUM
ejpam-1372	551	3	)	)	PUNCT
ejpam-1372	551	4	then	then	ADV
ejpam-1372	551	5	by	by	ADP
ejpam-1372	551	6	introducing	introduce	VERB
ejpam-1372	551	7	this	this	DET
ejpam-1372	551	8	result	result	NOUN
ejpam-1372	551	9	into	into	ADP
ejpam-1372	551	10	eq	eq	NOUN
ejpam-1372	551	11	.	.	PUNCT
ejpam-1372	552	1	(	(	PUNCT
ejpam-1372	552	2	53	53	NUM
ejpam-1372	552	3	)	)	PUNCT
ejpam-1372	552	4	we	we	PRON
ejpam-1372	552	5	obtain	obtain	VERB
ejpam-1372	552	6	e3b	e3b	PROPN
ejpam-1372	552	7	4π	4π	NUM
ejpam-1372	552	8	∞	∞	PROPN
ejpam-1372	552	9	∑	∑	PROPN
ejpam-1372	552	10	n=0	n=0	X
ejpam-1372	552	11	an	an	DET
ejpam-1372	552	12	∫	∫	PROPN
ejpam-1372	552	13	∞	∞	PROPN
ejpam-1372	552	14	−∞	−∞	ADP
ejpam-1372	552	15	dpz	dpz	PROPN
ejpam-1372	552	16	�	�	PROPN
ejpam-1372	552	17	m2	m2	PROPN
ejpam-1372	552	18	+	+	CCONJ
ejpam-1372	552	19	2neb	2neb	PROPN
ejpam-1372	552	20	(	(	PUNCT
ejpam-1372	552	21	p2	p2	PROPN
ejpam-1372	552	22	z	z	PROPN
ejpam-1372	552	23	+	+	PROPN
ejpam-1372	552	24	m2	m2	PROPN
ejpam-1372	552	25	+	+	CCONJ
ejpam-1372	553	1	2neb)5/2	2neb)5/2	NUM
ejpam-1372	553	2	�	�	PROPN
ejpam-1372	553	3	≡	≡	PROPN
ejpam-1372	553	4	−	−	PROPN
ejpam-1372	553	5	e2	e2	PROPN
ejpam-1372	553	6	3π	3π	NUM
ejpam-1372	553	7	h	h	NOUN
ejpam-1372	553	8	b/2+ψ(1	b/2+ψ(1	NOUN
ejpam-1372	553	9	/	/	SYM
ejpam-1372	553	10	b	b	NOUN
ejpam-1372	553	11	)	)	PUNCT
ejpam-1372	553	12	i	i	PRON
ejpam-1372	553	13	.	.	PUNCT
ejpam-1372	554	1	(	(	PUNCT
ejpam-1372	554	2	59	59	NUM
ejpam-1372	554	3	)	)	PUNCT
ejpam-1372	554	4	v.	v.	ADP
ejpam-1372	554	5	kowalenko	kowalenko	PROPN
ejpam-1372	554	6	/	/	SYM
ejpam-1372	554	7	eur	eur	PROPN
ejpam-1372	554	8	.	.	PUNCT
ejpam-1372	555	1	j.	j.	PROPN
ejpam-1372	555	2	pure	pure	PROPN
ejpam-1372	555	3	appl	appl	PROPN
ejpam-1372	555	4	.	.	PROPN
ejpam-1372	555	5	math	math	PROPN
ejpam-1372	555	6	,	,	PUNCT
ejpam-1372	555	7	4	4	NUM
ejpam-1372	555	8	(	(	PUNCT
ejpam-1372	555	9	2011	2011	NUM
ejpam-1372	555	10	)	)	PUNCT
ejpam-1372	555	11	,	,	PUNCT
ejpam-1372	555	12	370	370	NUM
ejpam-1372	555	13	-	-	SYM
ejpam-1372	555	14	423	423	NUM
ejpam-1372	555	15	388	388	NUM
ejpam-1372	555	16	now	now	ADV
ejpam-1372	555	17	let	let	VERB
ejpam-1372	555	18	us	we	PRON
ejpam-1372	555	19	examine	examine	VERB
ejpam-1372	555	20	when	when	SCONJ
ejpam-1372	555	21	the	the	DET
ejpam-1372	555	22	static	static	ADJ
ejpam-1372	555	23	uniform	uniform	ADJ
ejpam-1372	555	24	polarisability	polarisability	NOUN
ejpam-1372	555	25	is	be	AUX
ejpam-1372	555	26	renormalised	renormalise	VERB
ejpam-1372	555	27	according	accord	VERB
ejpam-1372	555	28	to	to	ADP
ejpam-1372	555	29	the	the	DET
ejpam-1372	555	30	physicist	physicist	NOUN
ejpam-1372	555	31	’s	’s	PART
ejpam-1372	555	32	approach	approach	NOUN
ejpam-1372	555	33	.	.	PUNCT
ejpam-1372	556	1	first	first	ADV
ejpam-1372	556	2	,	,	PUNCT
ejpam-1372	556	3	it	it	PRON
ejpam-1372	556	4	is	be	AUX
ejpam-1372	556	5	found	find	VERB
ejpam-1372	556	6	that	that	SCONJ
ejpam-1372	556	7	the	the	DET
ejpam-1372	556	8	free	free	ADJ
ejpam-1372	556	9	-	-	PUNCT
ejpam-1372	556	10	field	field	NOUN
ejpam-1372	556	11	vacuum	vacuum	NOUN
ejpam-1372	556	12	term	term	NOUN
ejpam-1372	556	13	or	or	CCONJ
ejpam-1372	556	14	the	the	DET
ejpam-1372	556	15	second	second	ADJ
ejpam-1372	556	16	term	term	NOUN
ejpam-1372	556	17	on	on	ADP
ejpam-1372	556	18	the	the	DET
ejpam-1372	556	19	rhs	rhs	PROPN
ejpam-1372	556	20	of	of	ADP
ejpam-1372	556	21	eq	eq	PROPN
ejpam-1372	556	22	.	.	PUNCT
ejpam-1372	557	1	(	(	PUNCT
ejpam-1372	557	2	54	54	NUM
ejpam-1372	557	3	)	)	PUNCT
ejpam-1372	557	4	is	be	AUX
ejpam-1372	557	5	logarithmically	logarithmically	ADV
ejpam-1372	557	6	divergent	divergent	ADJ
ejpam-1372	557	7	,	,	PUNCT
ejpam-1372	557	8	but	but	CCONJ
ejpam-1372	557	9	does	do	AUX
ejpam-1372	557	10	not	not	PART
ejpam-1372	557	11	match	match	VERB
ejpam-1372	557	12	the	the	DET
ejpam-1372	557	13	b	b	PROPN
ejpam-1372	557	14	→	→	SYM
ejpam-1372	557	15	0	0	NUM
ejpam-1372	557	16	limit	limit	NOUN
ejpam-1372	557	17	of	of	ADP
ejpam-1372	557	18	the	the	DET
ejpam-1372	557	19	preceding	precede	VERB
ejpam-1372	557	20	term	term	NOUN
ejpam-1372	557	21	,	,	PUNCT
ejpam-1372	557	22	which	which	PRON
ejpam-1372	557	23	is	be	AUX
ejpam-1372	557	24	also	also	ADV
ejpam-1372	557	25	logarithmically	logarithmically	ADV
ejpam-1372	557	26	divergent	divergent	ADJ
ejpam-1372	557	27	.	.	PUNCT
ejpam-1372	558	1	consequently	consequently	ADV
ejpam-1372	558	2	,	,	PUNCT
ejpam-1372	558	3	the	the	DET
ejpam-1372	558	4	second	second	ADJ
ejpam-1372	558	5	term	term	NOUN
ejpam-1372	558	6	on	on	ADP
ejpam-1372	558	7	the	the	DET
ejpam-1372	558	8	rhs	rhs	PROPN
ejpam-1372	558	9	is	be	AUX
ejpam-1372	558	10	replaced	replace	VERB
ejpam-1372	558	11	by	by	ADP
ejpam-1372	558	12	the	the	DET
ejpam-1372	558	13	b	b	PROPN
ejpam-1372	558	14	→	→	SYM
ejpam-1372	558	15	0	0	NUM
ejpam-1372	558	16	limit	limit	NOUN
ejpam-1372	558	17	of	of	ADP
ejpam-1372	558	18	the	the	DET
ejpam-1372	558	19	first	first	ADJ
ejpam-1372	558	20	term	term	NOUN
ejpam-1372	558	21	.	.	PUNCT
ejpam-1372	559	1	then	then	ADV
ejpam-1372	559	2	with	with	ADP
ejpam-1372	559	3	the	the	DET
ejpam-1372	559	4	aid	aid	NOUN
ejpam-1372	559	5	of	of	ADP
ejpam-1372	559	6	eq	eq	PROPN
ejpam-1372	559	7	.	.	PUNCT
ejpam-1372	560	1	(	(	PUNCT
ejpam-1372	560	2	55	55	NUM
ejpam-1372	560	3	)	)	PUNCT
ejpam-1372	560	4	the	the	DET
ejpam-1372	560	5	longitudinal	longitudinal	ADJ
ejpam-1372	560	6	static	static	ADJ
ejpam-1372	560	7	uniform	uniform	ADJ
ejpam-1372	560	8	polarisability	polarisability	NOUN
ejpam-1372	560	9	becomes	become	VERB
ejpam-1372	560	10	α‖(b	α‖(b	ADV
ejpam-1372	560	11	)	)	PUNCT
ejpam-1372	560	12	=	=	SYM
ejpam-1372	560	13	e2	e2	PROPN
ejpam-1372	560	14	b	b	NUM
ejpam-1372	560	15	3π	3π	NUM
ejpam-1372	560	16	∞	∞	NUM
ejpam-1372	560	17	∑	∑	PROPN
ejpam-1372	560	18	n=0	n=0	PROPN
ejpam-1372	560	19	�	�	PROPN
ejpam-1372	560	20	1	1	NUM
ejpam-1372	560	21	1	1	NUM
ejpam-1372	560	22	+	+	NUM
ejpam-1372	560	23	nb	nb	PROPN
ejpam-1372	560	24	�	�	PROPN
ejpam-1372	560	25	−	−	PROPN
ejpam-1372	560	26	e2	e2	PROPN
ejpam-1372	560	27	b	b	PROPN
ejpam-1372	560	28	6π	6π	NOUN
ejpam-1372	560	29	−	−	PROPN
ejpam-1372	560	30	lim	lim	PROPN
ejpam-1372	560	31	b→0	b→0	PROPN
ejpam-1372	560	32	e2	e2	PROPN
ejpam-1372	560	33	b	b	PROPN
ejpam-1372	560	34	3π	3π	NUM
ejpam-1372	560	35	∞	∞	NUM
ejpam-1372	560	36	∑	∑	PROPN
ejpam-1372	560	37	n=0	n=0	PROPN
ejpam-1372	560	38	�	�	PROPN
ejpam-1372	560	39	1	1	NUM
ejpam-1372	560	40	1	1	NUM
ejpam-1372	560	41	+	+	NUM
ejpam-1372	560	42	nb	nb	PROPN
ejpam-1372	560	43	�	�	PROPN
ejpam-1372	560	44	.	.	PUNCT
ejpam-1372	561	1	(	(	PUNCT
ejpam-1372	561	2	60	60	X
ejpam-1372	561	3	)	)	PUNCT
ejpam-1372	561	4	converting	convert	VERB
ejpam-1372	561	5	the	the	DET
ejpam-1372	561	6	last	last	ADJ
ejpam-1372	561	7	term	term	NOUN
ejpam-1372	561	8	to	to	ADP
ejpam-1372	561	9	an	an	DET
ejpam-1372	561	10	integral	integral	ADJ
ejpam-1372	561	11	yields	yield	NOUN
ejpam-1372	561	12	a	a	DET
ejpam-1372	561	13	logarithmically	logarithmically	ADV
ejpam-1372	561	14	divergent	divergent	ADJ
ejpam-1372	561	15	integral	integral	ADJ
ejpam-1372	561	16	,	,	PUNCT
ejpam-1372	561	17	but	but	CCONJ
ejpam-1372	561	18	the	the	DET
ejpam-1372	561	19	resulting	result	VERB
ejpam-1372	561	20	integral	integral	ADJ
ejpam-1372	561	21	is	be	AUX
ejpam-1372	561	22	difficult	difficult	ADJ
ejpam-1372	561	23	to	to	PART
ejpam-1372	561	24	match	match	VERB
ejpam-1372	561	25	with	with	ADP
ejpam-1372	561	26	the	the	DET
ejpam-1372	561	27	first	first	ADJ
ejpam-1372	561	28	term	term	NOUN
ejpam-1372	561	29	when	when	SCONJ
ejpam-1372	561	30	the	the	DET
ejpam-1372	561	31	latter	latter	NOUN
ejpam-1372	561	32	is	be	AUX
ejpam-1372	561	33	also	also	ADV
ejpam-1372	561	34	converted	convert	VERB
ejpam-1372	561	35	into	into	ADP
ejpam-1372	561	36	an	an	DET
ejpam-1372	561	37	integral	integral	ADJ
ejpam-1372	561	38	.	.	PUNCT
ejpam-1372	562	1	instead	instead	ADV
ejpam-1372	562	2	,	,	PUNCT
ejpam-1372	562	3	the	the	DET
ejpam-1372	562	4	process	process	NOUN
ejpam-1372	562	5	of	of	ADP
ejpam-1372	562	6	renormalisation	renormalisation	NOUN
ejpam-1372	562	7	involves	involve	VERB
ejpam-1372	562	8	:	:	PUNCT
ejpam-1372	562	9	1	1	X
ejpam-1372	562	10	.	.	X
ejpam-1372	562	11	converting	convert	VERB
ejpam-1372	562	12	the	the	DET
ejpam-1372	562	13	first	first	ADJ
ejpam-1372	562	14	term	term	NOUN
ejpam-1372	562	15	into	into	ADP
ejpam-1372	562	16	an	an	DET
ejpam-1372	562	17	integral	integral	ADJ
ejpam-1372	562	18	by	by	ADP
ejpam-1372	562	19	replacing	replace	VERB
ejpam-1372	562	20	1/(1	1/(1	NUM
ejpam-1372	562	21	+	+	PROPN
ejpam-1372	562	22	nb	nb	NOUN
ejpam-1372	562	23	)	)	PUNCT
ejpam-1372	562	24	with	with	ADP
ejpam-1372	562	25	∫∞	∫∞	NOUN
ejpam-1372	562	26	0	0	PUNCT
ejpam-1372	563	1	d	d	NOUN
ejpam-1372	563	2	t	t	PROPN
ejpam-1372	563	3	exp(−(1	exp(−(1	NOUN
ejpam-1372	564	1	+	+	CCONJ
ejpam-1372	564	2	nb)t	nb)t	PROPN
ejpam-1372	564	3	)	)	PUNCT
ejpam-1372	565	1	,	,	PUNCT
ejpam-1372	565	2	2	2	X
ejpam-1372	565	3	.	.	X
ejpam-1372	565	4	interchanging	interchange	VERB
ejpam-1372	565	5	the	the	DET
ejpam-1372	565	6	order	order	NOUN
ejpam-1372	565	7	of	of	ADP
ejpam-1372	565	8	the	the	DET
ejpam-1372	565	9	summation	summation	NOUN
ejpam-1372	565	10	and	and	CCONJ
ejpam-1372	565	11	integration	integration	NOUN
ejpam-1372	565	12	,	,	PUNCT
ejpam-1372	565	13	3	3	X
ejpam-1372	565	14	.	.	X
ejpam-1372	565	15	subtracting	subtract	VERB
ejpam-1372	565	16	the	the	DET
ejpam-1372	565	17	b→	b→	PROPN
ejpam-1372	565	18	0	0	NUM
ejpam-1372	565	19	limit	limit	NOUN
ejpam-1372	565	20	of	of	ADP
ejpam-1372	565	21	the	the	DET
ejpam-1372	565	22	resulting	result	VERB
ejpam-1372	565	23	integral	integral	ADJ
ejpam-1372	565	24	.	.	PUNCT
ejpam-1372	566	1	carrying	carry	VERB
ejpam-1372	566	2	out	out	ADP
ejpam-1372	566	3	these	these	DET
ejpam-1372	566	4	steps	step	NOUN
ejpam-1372	566	5	yields	yield	NOUN
ejpam-1372	566	6	α‖(b	α‖(b	ADV
ejpam-1372	566	7	)	)	PUNCT
ejpam-1372	566	8	=	=	SYM
ejpam-1372	566	9	e2	e2	PROPN
ejpam-1372	566	10	3π	3π	NUM
ejpam-1372	566	11	�	�	PROPN
ejpam-1372	566	12	∫	∫	PROPN
ejpam-1372	566	13	∞	∞	PROPN
ejpam-1372	566	14	0	0	PUNCT
ejpam-1372	567	1	d	d	PRON
ejpam-1372	567	2	t	t	PROPN
ejpam-1372	567	3	�	�	PROPN
ejpam-1372	567	4	be−t	be−t	NOUN
ejpam-1372	567	5	1−	1−	NUM
ejpam-1372	567	6	e−bt	e−bt	NOUN
ejpam-1372	567	7	−	−	ADP
ejpam-1372	567	8	e−t	e−t	NOUN
ejpam-1372	567	9	t	t	PROPN
ejpam-1372	567	10	�	�	PROPN
ejpam-1372	568	1	−	−	ADP
ejpam-1372	568	2	b	b	SYM
ejpam-1372	568	3	2	2	NUM
ejpam-1372	568	4	�	�	PROPN
ejpam-1372	568	5	.	.	PUNCT
ejpam-1372	569	1	(	(	PUNCT
ejpam-1372	569	2	61	61	NUM
ejpam-1372	569	3	)	)	PUNCT
ejpam-1372	569	4	by	by	ADP
ejpam-1372	569	5	introducing	introduce	VERB
ejpam-1372	569	6	some	some	PRON
ejpam-1372	569	7	of	of	ADP
ejpam-1372	569	8	the	the	DET
ejpam-1372	569	9	integral	integral	ADJ
ejpam-1372	569	10	identities	identity	NOUN
ejpam-1372	569	11	that	that	PRON
ejpam-1372	569	12	appear	appear	VERB
ejpam-1372	569	13	in	in	ADP
ejpam-1372	569	14	secs	sec	NOUN
ejpam-1372	569	15	.	.	PUNCT
ejpam-1372	570	1	8.361	8.361	NUM
ejpam-1372	570	2	and	and	CCONJ
ejpam-1372	570	3	8.367	8.367	NUM
ejpam-1372	570	4	of	of	ADP
ejpam-1372	570	5	ref	ref	NOUN
ejpam-1372	570	6	.	.	PUNCT
ejpam-1372	571	1	[	[	X
ejpam-1372	571	2	11	11	NUM
ejpam-1372	571	3	]	]	PUNCT
ejpam-1372	571	4	,	,	PUNCT
ejpam-1372	571	5	one	one	PRON
ejpam-1372	571	6	eventually	eventually	ADV
ejpam-1372	571	7	arrives	arrive	VERB
ejpam-1372	571	8	at	at	ADP
ejpam-1372	571	9	α‖(b	α‖(b	NOUN
ejpam-1372	571	10	)	)	PUNCT
ejpam-1372	571	11	=	=	SYM
ejpam-1372	571	12	−(e2/3π	−(e2/3π	PROPN
ejpam-1372	571	13	)	)	PUNCT
ejpam-1372	571	14	�	�	PROPN
ejpam-1372	571	15	b/2	b/2	PROPN
ejpam-1372	571	16	+	+	SYM
ejpam-1372	571	17	log(b	log(b	PROPN
ejpam-1372	571	18	)	)	PUNCT
ejpam-1372	571	19	+	+	NOUN
ejpam-1372	571	20	ψ(1	ψ(1	PROPN
ejpam-1372	571	21	/	/	SYM
ejpam-1372	571	22	b	b	NOUN
ejpam-1372	571	23	)	)	PUNCT
ejpam-1372	571	24	�	�	PROPN
ejpam-1372	571	25	.	.	PUNCT
ejpam-1372	572	1	(	(	PUNCT
ejpam-1372	572	2	62	62	NUM
ejpam-1372	572	3	)	)	PUNCT
ejpam-1372	572	4	this	this	DET
ejpam-1372	572	5	result	result	NOUN
ejpam-1372	572	6	was	be	AUX
ejpam-1372	572	7	first	first	ADV
ejpam-1372	572	8	obtained	obtain	VERB
ejpam-1372	572	9	by	by	ADP
ejpam-1372	572	10	bakshi	bakshi	PROPN
ejpam-1372	572	11	,	,	PUNCT
ejpam-1372	572	12	cover	cover	VERB
ejpam-1372	572	13	and	and	CCONJ
ejpam-1372	572	14	kalman	kalman	NOUN
ejpam-1372	572	15	in	in	ADP
ejpam-1372	572	16	ref	ref	NOUN
ejpam-1372	572	17	.	.	PUNCT
ejpam-1372	573	1	[	[	X
ejpam-1372	573	2	3	3	NUM
ejpam-1372	573	3	]	]	PUNCT
ejpam-1372	573	4	.	.	PUNCT
ejpam-1372	574	1	by	by	ADP
ejpam-1372	574	2	comparing	compare	VERB
ejpam-1372	574	3	the	the	DET
ejpam-1372	574	4	rhs	rhs	PROPN
ejpam-1372	574	5	of	of	ADP
ejpam-1372	574	6	equivalence	equivalence	NOUN
ejpam-1372	574	7	(	(	PUNCT
ejpam-1372	574	8	62	62	NUM
ejpam-1372	574	9	)	)	PUNCT
ejpam-1372	574	10	with	with	ADP
ejpam-1372	574	11	the	the	DET
ejpam-1372	574	12	rhs	rhs	PROPN
ejpam-1372	574	13	of	of	ADP
ejpam-1372	574	14	eq	eq	PROPN
ejpam-1372	574	15	.	.	PUNCT
ejpam-1372	575	1	(	(	PUNCT
ejpam-1372	575	2	59	59	NUM
ejpam-1372	575	3	)	)	PUNCT
ejpam-1372	575	4	,	,	PUNCT
ejpam-1372	575	5	we	we	PRON
ejpam-1372	575	6	see	see	VERB
ejpam-1372	575	7	that	that	SCONJ
ejpam-1372	575	8	there	there	PRON
ejpam-1372	575	9	is	be	VERB
ejpam-1372	575	10	a	a	DET
ejpam-1372	575	11	discrepancy	discrepancy	NOUN
ejpam-1372	575	12	of	of	ADP
ejpam-1372	575	13	log(b	log(b	PROPN
ejpam-1372	575	14	)	)	PUNCT
ejpam-1372	575	15	in	in	ADP
ejpam-1372	575	16	the	the	DET
ejpam-1372	575	17	bracketed	bracketed	ADJ
ejpam-1372	575	18	terms	term	NOUN
ejpam-1372	575	19	.	.	PUNCT
ejpam-1372	576	1	hence	hence	ADV
ejpam-1372	576	2	,	,	PUNCT
ejpam-1372	576	3	we	we	PRON
ejpam-1372	576	4	have	have	AUX
ejpam-1372	576	5	seen	see	VERB
ejpam-1372	576	6	that	that	SCONJ
ejpam-1372	576	7	the	the	DET
ejpam-1372	576	8	mathematical	mathematical	ADJ
ejpam-1372	576	9	approach	approach	NOUN
ejpam-1372	576	10	to	to	ADP
ejpam-1372	576	11	regularising	regularise	VERB
ejpam-1372	576	12	a	a	DET
ejpam-1372	576	13	divergent	divergent	ADJ
ejpam-1372	576	14	series	series	NOUN
ejpam-1372	576	15	can	can	AUX
ejpam-1372	576	16	yield	yield	VERB
ejpam-1372	576	17	a	a	DET
ejpam-1372	576	18	different	different	ADJ
ejpam-1372	576	19	result	result	NOUN
ejpam-1372	576	20	from	from	ADP
ejpam-1372	576	21	the	the	DET
ejpam-1372	576	22	physicist	physicist	NOUN
ejpam-1372	576	23	’s	’s	PART
ejpam-1372	576	24	approach	approach	NOUN
ejpam-1372	576	25	of	of	ADP
ejpam-1372	576	26	renormalisation	renormalisation	NOUN
ejpam-1372	576	27	.	.	PUNCT
ejpam-1372	577	1	that	that	PRON
ejpam-1372	577	2	is	is	ADV
ejpam-1372	577	3	,	,	PUNCT
ejpam-1372	577	4	regularising	regularise	VERB
ejpam-1372	577	5	a	a	DET
ejpam-1372	577	6	divergent	divergent	ADJ
ejpam-1372	577	7	mathematical	mathematical	ADJ
ejpam-1372	577	8	quantity	quantity	NOUN
ejpam-1372	577	9	arising	arise	VERB
ejpam-1372	577	10	out	out	ADP
ejpam-1372	577	11	of	of	ADP
ejpam-1372	577	12	a	a	DET
ejpam-1372	577	13	physical	physical	ADJ
ejpam-1372	577	14	theory	theory	NOUN
ejpam-1372	577	15	may	may	AUX
ejpam-1372	577	16	not	not	PART
ejpam-1372	577	17	necessarily	necessarily	ADV
ejpam-1372	577	18	yield	yield	VERB
ejpam-1372	577	19	the	the	DET
ejpam-1372	577	20	correct	correct	ADJ
ejpam-1372	577	21	physical	physical	ADJ
ejpam-1372	577	22	result	result	NOUN
ejpam-1372	577	23	.	.	PUNCT
ejpam-1372	578	1	this	this	PRON
ejpam-1372	578	2	vindicates	vindicate	VERB
ejpam-1372	578	3	the	the	DET
ejpam-1372	578	4	statements	statement	NOUN
ejpam-1372	578	5	made	make	VERB
ejpam-1372	578	6	earlier	early	ADV
ejpam-1372	578	7	concerning	concern	VERB
ejpam-1372	578	8	whether	whether	SCONJ
ejpam-1372	578	9	the	the	DET
ejpam-1372	578	10	appearance	appearance	NOUN
ejpam-1372	578	11	of	of	ADP
ejpam-1372	578	12	divergent	divergent	ADJ
ejpam-1372	578	13	series	series	NOUN
ejpam-1372	578	14	and	and	CCONJ
ejpam-1372	578	15	integrals	integral	NOUN
ejpam-1372	578	16	in	in	ADP
ejpam-1372	578	17	theoretical	theoretical	ADJ
ejpam-1372	578	18	physics	physics	NOUN
ejpam-1372	578	19	constitutes	constitute	VERB
ejpam-1372	578	20	a	a	DET
ejpam-1372	578	21	breakdown	breakdown	NOUN
ejpam-1372	578	22	in	in	ADP
ejpam-1372	578	23	the	the	DET
ejpam-1372	578	24	mathematics	mathematic	NOUN
ejpam-1372	578	25	or	or	CCONJ
ejpam-1372	578	26	the	the	DET
ejpam-1372	578	27	physical	physical	ADJ
ejpam-1372	578	28	theory	theory	NOUN
ejpam-1372	578	29	.	.	PUNCT
ejpam-1372	579	1	it	it	PRON
ejpam-1372	579	2	is	be	AUX
ejpam-1372	579	3	likely	likely	ADJ
ejpam-1372	579	4	to	to	PART
ejpam-1372	579	5	be	be	AUX
ejpam-1372	579	6	a	a	DET
ejpam-1372	579	7	combination	combination	NOUN
ejpam-1372	579	8	of	of	ADP
ejpam-1372	579	9	both	both	PRON
ejpam-1372	579	10	with	with	ADP
ejpam-1372	579	11	the	the	DET
ejpam-1372	579	12	creation	creation	NOUN
ejpam-1372	579	13	of	of	ADP
ejpam-1372	579	14	a	a	DET
ejpam-1372	579	15	physical	physical	ADJ
ejpam-1372	579	16	theory	theory	NOUN
ejpam-1372	579	17	out	out	ADP
ejpam-1372	579	18	of	of	ADP
ejpam-1372	579	19	new	new	ADJ
ejpam-1372	579	20	mathematics	mathematic	NOUN
ejpam-1372	579	21	.	.	PUNCT
ejpam-1372	580	1	9	9	X
ejpam-1372	580	2	.	.	X
ejpam-1372	580	3	terminants	terminant	NOUN
ejpam-1372	580	4	all	all	DET
ejpam-1372	580	5	the	the	DET
ejpam-1372	580	6	divergent	divergent	ADJ
ejpam-1372	580	7	series	series	NOUN
ejpam-1372	580	8	that	that	PRON
ejpam-1372	580	9	have	have	AUX
ejpam-1372	580	10	been	be	AUX
ejpam-1372	580	11	considered	consider	VERB
ejpam-1372	580	12	so	so	ADV
ejpam-1372	580	13	far	far	ADV
ejpam-1372	580	14	have	have	AUX
ejpam-1372	580	15	been	be	AUX
ejpam-1372	580	16	relatively	relatively	ADV
ejpam-1372	580	17	elementary	elementary	ADJ
ejpam-1372	580	18	,	,	PUNCT
ejpam-1372	580	19	but	but	CCONJ
ejpam-1372	580	20	in	in	ADP
ejpam-1372	580	21	order	order	NOUN
ejpam-1372	580	22	to	to	PART
ejpam-1372	580	23	develop	develop	VERB
ejpam-1372	580	24	a	a	DET
ejpam-1372	580	25	theory	theory	NOUN
ejpam-1372	580	26	of	of	ADP
ejpam-1372	580	27	divergent	divergent	ADJ
ejpam-1372	580	28	series	series	NOUN
ejpam-1372	580	29	,	,	PUNCT
ejpam-1372	580	30	more	more	ADV
ejpam-1372	580	31	complicated	complicated	ADJ
ejpam-1372	580	32	examples	example	NOUN
ejpam-1372	580	33	will	will	AUX
ejpam-1372	580	34	need	need	VERB
ejpam-1372	580	35	to	to	PART
ejpam-1372	580	36	v.	v.	ADP
ejpam-1372	580	37	kowalenko	kowalenko	PROPN
ejpam-1372	580	38	/	/	SYM
ejpam-1372	580	39	eur	eur	PROPN
ejpam-1372	580	40	.	.	PUNCT
ejpam-1372	581	1	j.	j.	PROPN
ejpam-1372	581	2	pure	pure	PROPN
ejpam-1372	581	3	appl	appl	PROPN
ejpam-1372	581	4	.	.	PROPN
ejpam-1372	581	5	math	math	PROPN
ejpam-1372	581	6	,	,	PUNCT
ejpam-1372	581	7	4	4	NUM
ejpam-1372	581	8	(	(	PUNCT
ejpam-1372	581	9	2011	2011	NUM
ejpam-1372	581	10	)	)	PUNCT
ejpam-1372	581	11	,	,	PUNCT
ejpam-1372	581	12	370	370	NUM
ejpam-1372	581	13	-	-	SYM
ejpam-1372	581	14	423	423	NUM
ejpam-1372	581	15	389	389	NUM
ejpam-1372	581	16	be	be	AUX
ejpam-1372	581	17	analysed	analyse	VERB
ejpam-1372	581	18	.	.	PUNCT
ejpam-1372	582	1	although	although	SCONJ
ejpam-1372	582	2	this	this	PRON
ejpam-1372	582	3	is	be	AUX
ejpam-1372	582	4	well	well	ADJ
ejpam-1372	582	5	and	and	CCONJ
ejpam-1372	582	6	truly	truly	ADV
ejpam-1372	582	7	beyond	beyond	ADP
ejpam-1372	582	8	the	the	DET
ejpam-1372	582	9	scope	scope	NOUN
ejpam-1372	582	10	of	of	ADP
ejpam-1372	582	11	the	the	DET
ejpam-1372	582	12	present	present	ADJ
ejpam-1372	582	13	work	work	NOUN
ejpam-1372	582	14	,	,	PUNCT
ejpam-1372	582	15	we	we	PRON
ejpam-1372	582	16	can	can	AUX
ejpam-1372	582	17	at	at	ADP
ejpam-1372	582	18	least	least	ADJ
ejpam-1372	582	19	discuss	discuss	VERB
ejpam-1372	582	20	the	the	DET
ejpam-1372	582	21	issue	issue	NOUN
ejpam-1372	582	22	of	of	ADP
ejpam-1372	582	23	regularising	regularise	VERB
ejpam-1372	582	24	those	those	DET
ejpam-1372	582	25	series	series	NOUN
ejpam-1372	582	26	,	,	PUNCT
ejpam-1372	582	27	which	which	PRON
ejpam-1372	582	28	euler	euler	NOUN
ejpam-1372	582	29	referred	refer	VERB
ejpam-1372	582	30	to	to	ADP
ejpam-1372	582	31	as	as	ADP
ejpam-1372	582	32	divergent	divergent	ADJ
ejpam-1372	582	33	par	par	NOUN
ejpam-1372	582	34	excellence	excellence	NOUN
ejpam-1372	582	35	.	.	PUNCT
ejpam-1372	583	1	previously	previously	ADV
ejpam-1372	583	2	,	,	PUNCT
ejpam-1372	583	3	it	it	PRON
ejpam-1372	583	4	was	be	AUX
ejpam-1372	583	5	remarked	remark	VERB
ejpam-1372	583	6	that	that	SCONJ
ejpam-1372	583	7	such	such	ADJ
ejpam-1372	583	8	series	series	NOUN
ejpam-1372	583	9	had	have	AUX
ejpam-1372	583	10	rapidly	rapidly	ADV
ejpam-1372	583	11	diverging	diverge	VERB
ejpam-1372	583	12	coefficients	coefficient	NOUN
ejpam-1372	583	13	ak	ak	PROPN
ejpam-1372	583	14	,	,	PUNCT
ejpam-1372	583	15	which	which	PRON
ejpam-1372	583	16	were	be	AUX
ejpam-1372	583	17	equal	equal	ADJ
ejpam-1372	583	18	to	to	ADP
ejpam-1372	583	19	(	(	PUNCT
ejpam-1372	583	20	−1)kk	−1)kk	PROPN
ejpam-1372	583	21	!	!	PUNCT
ejpam-1372	583	22	.	.	PUNCT
ejpam-1372	584	1	in	in	ADP
ejpam-1372	584	2	fact	fact	NOUN
ejpam-1372	584	3	,	,	PUNCT
ejpam-1372	584	4	these	these	DET
ejpam-1372	584	5	series	series	NOUN
ejpam-1372	584	6	can	can	AUX
ejpam-1372	584	7	be	be	AUX
ejpam-1372	584	8	generalised	generalise	VERB
ejpam-1372	584	9	by	by	ADP
ejpam-1372	584	10	replacing	replace	VERB
ejpam-1372	584	11	the	the	DET
ejpam-1372	584	12	k	k	PROPN
ejpam-1372	584	13	!	!	PUNCT
ejpam-1372	584	14	factor	factor	NOUN
ejpam-1372	584	15	in	in	ADP
ejpam-1372	584	16	the	the	DET
ejpam-1372	584	17	coefficients	coefficient	NOUN
ejpam-1372	584	18	by	by	ADP
ejpam-1372	584	19	the	the	DET
ejpam-1372	584	20	gamma	gamma	NOUN
ejpam-1372	584	21	function	function	PROPN
ejpam-1372	584	22	γ(k+α	γ(k+α	PROPN
ejpam-1372	584	23	)	)	PUNCT
ejpam-1372	584	24	.	.	PUNCT
ejpam-1372	585	1	then	then	ADV
ejpam-1372	585	2	they	they	PRON
ejpam-1372	585	3	become	become	VERB
ejpam-1372	585	4	what	what	PRON
ejpam-1372	585	5	are	be	AUX
ejpam-1372	585	6	known	know	VERB
ejpam-1372	585	7	today	today	NOUN
ejpam-1372	585	8	as	as	ADP
ejpam-1372	585	9	terminants	terminant	NOUN
ejpam-1372	585	10	.	.	PUNCT
ejpam-1372	586	1	this	this	DET
ejpam-1372	586	2	terminology	terminology	NOUN
ejpam-1372	586	3	was	be	AUX
ejpam-1372	586	4	introduced	introduce	VERB
ejpam-1372	586	5	by	by	ADP
ejpam-1372	586	6	dingle	dingle	NOUN
ejpam-1372	586	7	[	[	X
ejpam-1372	586	8	8	8	NUM
ejpam-1372	586	9	]	]	PUNCT
ejpam-1372	586	10	after	after	SCONJ
ejpam-1372	586	11	he	he	PRON
ejpam-1372	586	12	noticed	notice	VERB
ejpam-1372	586	13	that	that	SCONJ
ejpam-1372	586	14	the	the	DET
ejpam-1372	586	15	late	late	ADJ
ejpam-1372	586	16	terms	term	NOUN
ejpam-1372	586	17	in	in	ADP
ejpam-1372	586	18	many	many	ADJ
ejpam-1372	586	19	asymptotic	asymptotic	ADJ
ejpam-1372	586	20	expansions	expansion	NOUN
ejpam-1372	586	21	for	for	ADP
ejpam-1372	586	22	the	the	DET
ejpam-1372	586	23	special	special	ADJ
ejpam-1372	586	24	functions	function	NOUN
ejpam-1372	586	25	of	of	ADP
ejpam-1372	586	26	mathematical	mathematical	ADJ
ejpam-1372	586	27	physics	physics	NOUN
ejpam-1372	586	28	could	could	AUX
ejpam-1372	586	29	be	be	AUX
ejpam-1372	586	30	approximated	approximate	VERB
ejpam-1372	586	31	by	by	ADP
ejpam-1372	586	32	them	they	PRON
ejpam-1372	586	33	.	.	PUNCT
ejpam-1372	587	1	specifically	specifically	ADV
ejpam-1372	587	2	,	,	PUNCT
ejpam-1372	587	3	there	there	PRON
ejpam-1372	587	4	are	be	VERB
ejpam-1372	587	5	two	two	NUM
ejpam-1372	587	6	types	type	NOUN
ejpam-1372	587	7	of	of	ADP
ejpam-1372	587	8	such	such	ADJ
ejpam-1372	587	9	series	series	NOUN
ejpam-1372	587	10	:	:	PUNCT
ejpam-1372	587	11	the	the	DET
ejpam-1372	587	12	first	first	ADJ
ejpam-1372	587	13	type	type	NOUN
ejpam-1372	587	14	is	be	AUX
ejpam-1372	587	15	defined	define	VERB
ejpam-1372	587	16	as	as	ADP
ejpam-1372	587	17	ti	ti	PROPN
ejpam-1372	587	18	(	(	PUNCT
ejpam-1372	587	19	n	n	X
ejpam-1372	587	20	,	,	PUNCT
ejpam-1372	587	21	α	α	NOUN
ejpam-1372	587	22	,	,	PUNCT
ejpam-1372	587	23	z	z	NOUN
ejpam-1372	587	24	)	)	PUNCT
ejpam-1372	587	25	=	=	SYM
ejpam-1372	588	1	∞	∞	NUM
ejpam-1372	588	2	∑	∑	PUNCT
ejpam-1372	588	3	k	k	X
ejpam-1372	588	4	=	=	NOUN
ejpam-1372	588	5	n	n	PRON
ejpam-1372	588	6	γ(k+α)(−z)k	γ(k+α)(−z)k	NOUN
ejpam-1372	588	7	,	,	PUNCT
ejpam-1372	588	8	(	(	PUNCT
ejpam-1372	588	9	63	63	NUM
ejpam-1372	588	10	)	)	PUNCT
ejpam-1372	588	11	while	while	SCONJ
ejpam-1372	588	12	the	the	DET
ejpam-1372	588	13	second	second	ADJ
ejpam-1372	588	14	type	type	NOUN
ejpam-1372	588	15	is	be	AUX
ejpam-1372	588	16	defined	define	VERB
ejpam-1372	588	17	as	as	ADP
ejpam-1372	588	18	ti	ti	PROPN
ejpam-1372	588	19	i(n	i(n	PROPN
ejpam-1372	588	20	,	,	PUNCT
ejpam-1372	588	21	α	α	NOUN
ejpam-1372	588	22	,	,	PUNCT
ejpam-1372	588	23	z	z	NOUN
ejpam-1372	588	24	)	)	PUNCT
ejpam-1372	589	1	=	=	SYM
ejpam-1372	589	2	∞	∞	NUM
ejpam-1372	589	3	∑	∑	PUNCT
ejpam-1372	589	4	k	k	X
ejpam-1372	589	5	=	=	NOUN
ejpam-1372	589	6	n	n	NOUN
ejpam-1372	589	7	γ(k+α)zk	γ(k+α)zk	NOUN
ejpam-1372	589	8	.	.	PUNCT
ejpam-1372	590	1	(	(	PUNCT
ejpam-1372	590	2	64	64	NUM
ejpam-1372	590	3	)	)	PUNCT
ejpam-1372	590	4	in	in	ADP
ejpam-1372	590	5	these	these	DET
ejpam-1372	590	6	results	result	NOUN
ejpam-1372	590	7	n	n	VERB
ejpam-1372	590	8	is	be	AUX
ejpam-1372	590	9	referred	refer	VERB
ejpam-1372	590	10	to	to	ADP
ejpam-1372	590	11	as	as	ADP
ejpam-1372	590	12	the	the	DET
ejpam-1372	590	13	truncation	truncation	NOUN
ejpam-1372	590	14	parameter	parameter	NOUN
ejpam-1372	590	15	.	.	PUNCT
ejpam-1372	591	1	since	since	SCONJ
ejpam-1372	591	2	the	the	DET
ejpam-1372	591	3	limit	limit	NOUN
ejpam-1372	591	4	point	point	NOUN
ejpam-1372	591	5	is	be	AUX
ejpam-1372	591	6	zero	zero	NUM
ejpam-1372	591	7	in	in	ADP
ejpam-1372	591	8	the	the	DET
ejpam-1372	591	9	above	above	ADJ
ejpam-1372	591	10	series	series	NOUN
ejpam-1372	591	11	,	,	PUNCT
ejpam-1372	591	12	both	both	DET
ejpam-1372	591	13	types	type	NOUN
ejpam-1372	591	14	of	of	ADP
ejpam-1372	591	15	terminants	terminant	NOUN
ejpam-1372	591	16	represent	represent	VERB
ejpam-1372	591	17	small	small	ADJ
ejpam-1372	591	18	z	z	NOUN
ejpam-1372	591	19	asymptotic	asymptotic	ADJ
ejpam-1372	591	20	series	series	NOUN
ejpam-1372	591	21	.	.	PUNCT
ejpam-1372	592	1	had	have	AUX
ejpam-1372	592	2	they	they	PRON
ejpam-1372	592	3	been	be	AUX
ejpam-1372	592	4	expressed	express	VERB
ejpam-1372	592	5	in	in	ADP
ejpam-1372	592	6	terms	term	NOUN
ejpam-1372	592	7	of	of	ADP
ejpam-1372	592	8	powers	power	NOUN
ejpam-1372	592	9	of	of	ADP
ejpam-1372	592	10	1	1	NUM
ejpam-1372	592	11	/	/	SYM
ejpam-1372	592	12	z	z	NOUN
ejpam-1372	592	13	,	,	PUNCT
ejpam-1372	592	14	which	which	PRON
ejpam-1372	592	15	is	be	AUX
ejpam-1372	592	16	how	how	SCONJ
ejpam-1372	592	17	dingle	dingle	ADJ
ejpam-1372	592	18	defined	define	VERB
ejpam-1372	592	19	them	they	PRON
ejpam-1372	592	20	originally	originally	ADV
ejpam-1372	592	21	in	in	ADP
ejpam-1372	592	22	ref	ref	NOUN
ejpam-1372	592	23	.	.	PUNCT
ejpam-1372	593	1	[	[	X
ejpam-1372	593	2	8	8	NUM
ejpam-1372	593	3	]	]	PUNCT
ejpam-1372	593	4	,	,	PUNCT
ejpam-1372	593	5	then	then	ADV
ejpam-1372	593	6	they	they	PRON
ejpam-1372	593	7	would	would	AUX
ejpam-1372	593	8	have	have	AUX
ejpam-1372	593	9	represented	represent	VERB
ejpam-1372	593	10	large	large	ADJ
ejpam-1372	593	11	z	z	NOUN
ejpam-1372	593	12	asymptotic	asymptotic	ADJ
ejpam-1372	593	13	series	series	NOUN
ejpam-1372	593	14	.	.	PUNCT
ejpam-1372	594	1	by	by	ADP
ejpam-1372	594	2	asymptotic	asymptotic	ADJ
ejpam-1372	594	3	,	,	PUNCT
ejpam-1372	594	4	we	we	PRON
ejpam-1372	594	5	mean	mean	VERB
ejpam-1372	594	6	here	here	ADV
ejpam-1372	594	7	according	accord	VERB
ejpam-1372	594	8	to	to	ADP
ejpam-1372	594	9	the	the	DET
ejpam-1372	594	10	standard	standard	ADJ
ejpam-1372	594	11	poincaré	poincaré	ADJ
ejpam-1372	594	12	prescription	prescription	NOUN
ejpam-1372	594	13	discussed	discuss	VERB
ejpam-1372	594	14	on	on	ADP
ejpam-1372	594	15	p.	p.	PROPN
ejpam-1372	594	16	151	151	NUM
ejpam-1372	594	17	of	of	ADP
ejpam-1372	594	18	ref	ref	NOUN
ejpam-1372	594	19	.	.	PUNCT
ejpam-1372	595	1	[	[	X
ejpam-1372	595	2	33	33	NUM
ejpam-1372	595	3	]	]	PUNCT
ejpam-1372	595	4	.	.	PUNCT
ejpam-1372	596	1	as	as	SCONJ
ejpam-1372	596	2	mentioned	mention	VERB
ejpam-1372	596	3	in	in	ADP
ejpam-1372	596	4	the	the	DET
ejpam-1372	596	5	introduction	introduction	NOUN
ejpam-1372	596	6	,	,	PUNCT
ejpam-1372	596	7	by	by	ADP
ejpam-1372	596	8	adopting	adopt	VERB
ejpam-1372	596	9	this	this	DET
ejpam-1372	596	10	prescription	prescription	NOUN
ejpam-1372	596	11	for	for	ADP
ejpam-1372	596	12	sufficiently	sufficiently	ADV
ejpam-1372	596	13	small	small	ADJ
ejpam-1372	596	14	values	value	NOUN
ejpam-1372	596	15	of	of	ADP
ejpam-1372	596	16	z	z	NOUN
ejpam-1372	596	17	,	,	PUNCT
ejpam-1372	596	18	namely	namely	ADV
ejpam-1372	596	19	|z|	|z|	NOUN
ejpam-1372	596	20	≪	≪	ADJ
ejpam-1372	596	21	1	1	NUM
ejpam-1372	596	22	,	,	PUNCT
ejpam-1372	596	23	one	one	PRON
ejpam-1372	596	24	can	can	AUX
ejpam-1372	596	25	truncate	truncate	VERB
ejpam-1372	596	26	the	the	DET
ejpam-1372	596	27	series	series	NOUN
ejpam-1372	596	28	after	after	ADP
ejpam-1372	596	29	only	only	ADV
ejpam-1372	596	30	a	a	DET
ejpam-1372	596	31	few	few	ADJ
ejpam-1372	596	32	terms	term	NOUN
ejpam-1372	596	33	and	and	CCONJ
ejpam-1372	596	34	still	still	ADV
ejpam-1372	596	35	produce	produce	VERB
ejpam-1372	596	36	an	an	DET
ejpam-1372	596	37	accurate	accurate	ADJ
ejpam-1372	596	38	approximation	approximation	NOUN
ejpam-1372	596	39	to	to	ADP
ejpam-1372	596	40	the	the	DET
ejpam-1372	596	41	actual	actual	ADJ
ejpam-1372	596	42	value	value	NOUN
ejpam-1372	596	43	of	of	ADP
ejpam-1372	596	44	the	the	DET
ejpam-1372	596	45	original	original	ADJ
ejpam-1372	596	46	function	function	NOUN
ejpam-1372	596	47	from	from	ADP
ejpam-1372	596	48	which	which	PRON
ejpam-1372	596	49	the	the	DET
ejpam-1372	596	50	series	series	NOUN
ejpam-1372	596	51	has	have	AUX
ejpam-1372	596	52	been	be	AUX
ejpam-1372	596	53	derived	derive	VERB
ejpam-1372	596	54	.	.	PUNCT
ejpam-1372	597	1	furthermore	furthermore	ADV
ejpam-1372	597	2	,	,	PUNCT
ejpam-1372	597	3	the	the	DET
ejpam-1372	597	4	point	point	NOUN
ejpam-1372	597	5	at	at	ADP
ejpam-1372	597	6	which	which	PRON
ejpam-1372	597	7	the	the	DET
ejpam-1372	597	8	approximation	approximation	NOUN
ejpam-1372	597	9	begins	begin	VERB
ejpam-1372	597	10	to	to	PART
ejpam-1372	597	11	break	break	VERB
ejpam-1372	597	12	down	down	ADP
ejpam-1372	597	13	,	,	PUNCT
ejpam-1372	597	14	known	know	VERB
ejpam-1372	597	15	as	as	ADP
ejpam-1372	597	16	the	the	DET
ejpam-1372	597	17	optimal	optimal	ADJ
ejpam-1372	597	18	point	point	NOUN
ejpam-1372	597	19	of	of	ADP
ejpam-1372	597	20	truncation	truncation	NOUN
ejpam-1372	597	21	and	and	CCONJ
ejpam-1372	597	22	denoted	denote	VERB
ejpam-1372	597	23	by	by	ADP
ejpam-1372	597	24	nt	not	PART
ejpam-1372	597	25	in	in	ADP
ejpam-1372	597	26	this	this	DET
ejpam-1372	597	27	work	work	NOUN
ejpam-1372	597	28	,	,	PUNCT
ejpam-1372	597	29	increases	increase	VERB
ejpam-1372	597	30	or	or	CCONJ
ejpam-1372	597	31	diverges	diverge	NOUN
ejpam-1372	597	32	to	to	ADP
ejpam-1372	597	33	infinity	infinity	NOUN
ejpam-1372	597	34	as	as	ADP
ejpam-1372	597	35	z	z	NOUN
ejpam-1372	597	36	→	→	SYM
ejpam-1372	597	37	0	0	NUM
ejpam-1372	597	38	.	.	PUNCT
ejpam-1372	598	1	for	for	ADP
ejpam-1372	598	2	those	those	PRON
ejpam-1372	598	3	seeking	seek	VERB
ejpam-1372	598	4	an	an	DET
ejpam-1372	598	5	understanding	understanding	NOUN
ejpam-1372	598	6	of	of	ADP
ejpam-1372	598	7	the	the	DET
ejpam-1372	598	8	important	important	ADJ
ejpam-1372	598	9	concept	concept	NOUN
ejpam-1372	598	10	of	of	ADP
ejpam-1372	598	11	optimal	optimal	ADJ
ejpam-1372	598	12	truncation	truncation	NOUN
ejpam-1372	598	13	,	,	PUNCT
ejpam-1372	598	14	they	they	PRON
ejpam-1372	598	15	should	should	AUX
ejpam-1372	598	16	consult	consult	VERB
ejpam-1372	598	17	sec	sec	PROPN
ejpam-1372	598	18	.	.	PROPN
ejpam-1372	598	19	4.6	4.6	NUM
ejpam-1372	598	20	of	of	ADP
ejpam-1372	598	21	ref	ref	NOUN
ejpam-1372	598	22	.	.	PUNCT
ejpam-1372	599	1	[	[	X
ejpam-1372	599	2	24	24	NUM
ejpam-1372	599	3	]	]	PUNCT
ejpam-1372	599	4	.	.	PUNCT
ejpam-1372	600	1	as	as	ADV
ejpam-1372	600	2	long	long	ADV
ejpam-1372	600	3	as	as	ADP
ejpam-1372	600	4	n	n	CCONJ
ejpam-1372	600	5	<	<	X
ejpam-1372	600	6	nt	not	PART
ejpam-1372	600	7	or	or	CCONJ
ejpam-1372	600	8	even	even	ADV
ejpam-1372	600	9	for	for	ADP
ejpam-1372	600	10	n	n	PROPN
ejpam-1372	600	11	≈	≈	PROPN
ejpam-1372	601	1	nt	not	PART
ejpam-1372	601	2	,	,	PUNCT
ejpam-1372	601	3	one	one	PRON
ejpam-1372	601	4	can	can	AUX
ejpam-1372	601	5	still	still	ADV
ejpam-1372	601	6	obtain	obtain	VERB
ejpam-1372	601	7	an	an	DET
ejpam-1372	601	8	accurate	accurate	ADJ
ejpam-1372	601	9	approximation	approximation	NOUN
ejpam-1372	601	10	to	to	ADP
ejpam-1372	601	11	the	the	DET
ejpam-1372	601	12	original	original	ADJ
ejpam-1372	601	13	function	function	NOUN
ejpam-1372	601	14	.	.	PUNCT
ejpam-1372	602	1	however	however	ADV
ejpam-1372	602	2	,	,	PUNCT
ejpam-1372	602	3	the	the	DET
ejpam-1372	602	4	accuracy	accuracy	NOUN
ejpam-1372	602	5	of	of	ADP
ejpam-1372	602	6	the	the	DET
ejpam-1372	602	7	approximation	approximation	NOUN
ejpam-1372	602	8	wanes	wane	VERB
ejpam-1372	602	9	dramatically	dramatically	ADV
ejpam-1372	602	10	as	as	ADP
ejpam-1372	602	11	nt	not	PART
ejpam-1372	602	12	→	→	SYM
ejpam-1372	602	13	0	0	NUM
ejpam-1372	602	14	,	,	PUNCT
ejpam-1372	602	15	so	so	SCONJ
ejpam-1372	602	16	that	that	SCONJ
ejpam-1372	602	17	truncation	truncation	NOUN
ejpam-1372	602	18	of	of	ADP
ejpam-1372	602	19	the	the	DET
ejpam-1372	602	20	series	series	NOUN
ejpam-1372	602	21	is	be	AUX
ejpam-1372	602	22	no	no	ADV
ejpam-1372	602	23	longer	long	ADV
ejpam-1372	602	24	a	a	DET
ejpam-1372	602	25	valid	valid	ADJ
ejpam-1372	602	26	option	option	NOUN
ejpam-1372	602	27	for	for	ADP
ejpam-1372	602	28	those	those	DET
ejpam-1372	602	29	values	value	NOUN
ejpam-1372	602	30	of	of	ADP
ejpam-1372	602	31	z	z	NOUN
ejpam-1372	602	32	in	in	ADP
ejpam-1372	602	33	either	either	CCONJ
ejpam-1372	602	34	the	the	DET
ejpam-1372	602	35	intermediate	intermediate	ADJ
ejpam-1372	602	36	region	region	NOUN
ejpam-1372	602	37	,	,	PUNCT
ejpam-1372	602	38	typically	typically	ADV
ejpam-1372	602	39	given	give	VERB
ejpam-1372	602	40	by	by	ADP
ejpam-1372	602	41	0.1	0.1	NUM
ejpam-1372	602	42	<	<	X
ejpam-1372	602	43	|z|	|z|	NOUN
ejpam-1372	602	44	<	<	X
ejpam-1372	602	45	2	2	NUM
ejpam-1372	602	46	,	,	PUNCT
ejpam-1372	602	47	or	or	CCONJ
ejpam-1372	602	48	for	for	ADP
ejpam-1372	602	49	“	"	PUNCT
ejpam-1372	602	50	large	large	ADJ
ejpam-1372	602	51	values	value	NOUN
ejpam-1372	602	52	”	"	PUNCT
ejpam-1372	602	53	of	of	ADP
ejpam-1372	602	54	|z|	|z|	NOUN
ejpam-1372	602	55	greater	great	ADJ
ejpam-1372	602	56	than	than	ADP
ejpam-1372	602	57	2	2	NUM
ejpam-1372	602	58	.	.	PUNCT
ejpam-1372	602	59	as	as	SCONJ
ejpam-1372	602	60	was	be	AUX
ejpam-1372	602	61	also	also	ADV
ejpam-1372	602	62	discussed	discuss	VERB
ejpam-1372	602	63	in	in	ADP
ejpam-1372	602	64	the	the	DET
ejpam-1372	602	65	introduction	introduction	NOUN
ejpam-1372	602	66	,	,	PUNCT
ejpam-1372	602	67	since	since	SCONJ
ejpam-1372	602	68	asymptotic	asymptotic	ADJ
ejpam-1372	602	69	series	series	NOUN
ejpam-1372	602	70	possess	possess	VERB
ejpam-1372	602	71	limited	limited	ADJ
ejpam-1372	602	72	ranges	range	NOUN
ejpam-1372	602	73	of	of	ADP
ejpam-1372	602	74	applicability	applicability	NOUN
ejpam-1372	602	75	and	and	CCONJ
ejpam-1372	602	76	suffer	suffer	VERB
ejpam-1372	602	77	from	from	ADP
ejpam-1372	602	78	deficiencies	deficiency	NOUN
ejpam-1372	602	79	in	in	ADP
ejpam-1372	602	80	accuracy	accuracy	NOUN
ejpam-1372	602	81	,	,	PUNCT
ejpam-1372	602	82	asymptotics	asymptotic	NOUN
ejpam-1372	602	83	as	as	ADP
ejpam-1372	602	84	a	a	DET
ejpam-1372	602	85	mathematical	mathematical	ADJ
ejpam-1372	602	86	discipline	discipline	NOUN
ejpam-1372	602	87	has	have	AUX
ejpam-1372	602	88	often	often	ADV
ejpam-1372	602	89	been	be	AUX
ejpam-1372	602	90	ridiculed	ridicule	VERB
ejpam-1372	602	91	by	by	ADP
ejpam-1372	602	92	pure	pure	ADJ
ejpam-1372	602	93	mathematicians	mathematician	NOUN
ejpam-1372	602	94	,	,	PUNCT
ejpam-1372	602	95	who	who	PRON
ejpam-1372	602	96	point	point	VERB
ejpam-1372	602	97	out	out	ADP
ejpam-1372	602	98	that	that	SCONJ
ejpam-1372	602	99	mathematics	mathematic	NOUN
ejpam-1372	602	100	is	be	AUX
ejpam-1372	602	101	supposed	suppose	VERB
ejpam-1372	602	102	to	to	PART
ejpam-1372	602	103	be	be	AUX
ejpam-1372	602	104	an	an	DET
ejpam-1372	602	105	exact	exact	ADJ
ejpam-1372	602	106	science	science	NOUN
ejpam-1372	602	107	,	,	PUNCT
ejpam-1372	602	108	not	not	PART
ejpam-1372	602	109	composed	compose	VERB
ejpam-1372	602	110	of	of	ADP
ejpam-1372	602	111	vague	vague	ADJ
ejpam-1372	602	112	concepts	concept	NOUN
ejpam-1372	602	113	and	and	CCONJ
ejpam-1372	602	114	quantities	quantity	NOUN
ejpam-1372	602	115	.	.	PUNCT
ejpam-1372	603	1	in	in	ADP
ejpam-1372	603	2	reality	reality	NOUN
ejpam-1372	603	3	,	,	PUNCT
ejpam-1372	603	4	the	the	DET
ejpam-1372	603	5	cause	cause	NOUN
ejpam-1372	603	6	for	for	ADP
ejpam-1372	603	7	this	this	DET
ejpam-1372	603	8	state	state	NOUN
ejpam-1372	603	9	of	of	ADP
ejpam-1372	603	10	affairs	affair	NOUN
ejpam-1372	603	11	is	be	AUX
ejpam-1372	603	12	the	the	DET
ejpam-1372	603	13	adoption	adoption	NOUN
ejpam-1372	603	14	of	of	ADP
ejpam-1372	603	15	the	the	DET
ejpam-1372	603	16	poincaré	poincaré	ADJ
ejpam-1372	603	17	prescription	prescription	NOUN
ejpam-1372	603	18	,	,	PUNCT
ejpam-1372	603	19	particularly	particularly	ADV
ejpam-1372	603	20	truncating	truncate	VERB
ejpam-1372	603	21	asymptotic	asymptotic	ADJ
ejpam-1372	603	22	series	series	NOUN
ejpam-1372	603	23	.	.	PUNCT
ejpam-1372	604	1	because	because	SCONJ
ejpam-1372	604	2	of	of	ADP
ejpam-1372	604	3	the	the	DET
ejpam-1372	604	4	rapid	rapid	ADJ
ejpam-1372	604	5	divergence	divergence	NOUN
ejpam-1372	604	6	in	in	ADP
ejpam-1372	604	7	the	the	DET
ejpam-1372	604	8	coefficients	coefficient	NOUN
ejpam-1372	604	9	of	of	ADP
ejpam-1372	604	10	both	both	DET
ejpam-1372	604	11	types	type	NOUN
ejpam-1372	604	12	of	of	ADP
ejpam-1372	604	13	terminants	terminant	NOUN
ejpam-1372	604	14	,	,	PUNCT
ejpam-1372	604	15	which	which	PRON
ejpam-1372	604	16	results	result	VERB
ejpam-1372	604	17	in	in	ADP
ejpam-1372	604	18	a	a	DET
ejpam-1372	604	19	zero	zero	NUM
ejpam-1372	604	20	radius	radius	NOUN
ejpam-1372	604	21	of	of	ADP
ejpam-1372	604	22	absolute	absolute	ADJ
ejpam-1372	604	23	convergence	convergence	NOUN
ejpam-1372	604	24	,	,	PUNCT
ejpam-1372	604	25	they	they	PRON
ejpam-1372	604	26	too	too	ADV
ejpam-1372	604	27	represent	represent	VERB
ejpam-1372	604	28	a	a	DET
ejpam-1372	604	29	different	different	ADJ
ejpam-1372	604	30	proposition	proposition	NOUN
ejpam-1372	604	31	to	to	PART
ejpam-1372	604	32	regularise	regularise	VERB
ejpam-1372	604	33	compared	compare	VERB
ejpam-1372	604	34	with	with	ADP
ejpam-1372	604	35	the	the	DET
ejpam-1372	604	36	geometric	geometric	ADJ
ejpam-1372	604	37	series	series	NOUN
ejpam-1372	604	38	studied	study	VERB
ejpam-1372	604	39	earlier	early	ADV
ejpam-1372	604	40	.	.	PUNCT
ejpam-1372	605	1	thus	thus	ADV
ejpam-1372	605	2	,	,	PUNCT
ejpam-1372	605	3	the	the	DET
ejpam-1372	605	4	question	question	NOUN
ejpam-1372	605	5	becomes	become	VERB
ejpam-1372	605	6	:	:	PUNCT
ejpam-1372	605	7	how	how	SCONJ
ejpam-1372	605	8	do	do	AUX
ejpam-1372	605	9	we	we	PRON
ejpam-1372	605	10	regularise	regularise	VERB
ejpam-1372	605	11	them	they	PRON
ejpam-1372	605	12	?	?	PUNCT
ejpam-1372	606	1	when	when	SCONJ
ejpam-1372	606	2	discussing	discuss	VERB
ejpam-1372	606	3	regularisation	regularisation	NOUN
ejpam-1372	606	4	of	of	ADP
ejpam-1372	606	5	the	the	DET
ejpam-1372	606	6	geometric	geometric	ADJ
ejpam-1372	606	7	series	series	NOUN
ejpam-1372	606	8	above	above	ADV
ejpam-1372	606	9	,	,	PUNCT
ejpam-1372	606	10	we	we	PRON
ejpam-1372	606	11	v.	v.	VERB
ejpam-1372	606	12	kowalenko	kowalenko	PROPN
ejpam-1372	606	13	/	/	SYM
ejpam-1372	606	14	eur	eur	PROPN
ejpam-1372	606	15	.	.	PUNCT
ejpam-1372	607	1	j.	j.	PROPN
ejpam-1372	607	2	pure	pure	PROPN
ejpam-1372	607	3	appl	appl	PROPN
ejpam-1372	607	4	.	.	PROPN
ejpam-1372	607	5	math	math	PROPN
ejpam-1372	607	6	,	,	PUNCT
ejpam-1372	607	7	4	4	NUM
ejpam-1372	607	8	(	(	PUNCT
ejpam-1372	607	9	2011	2011	NUM
ejpam-1372	607	10	)	)	PUNCT
ejpam-1372	607	11	,	,	PUNCT
ejpam-1372	607	12	370	370	NUM
ejpam-1372	607	13	-	-	SYM
ejpam-1372	607	14	423	423	NUM
ejpam-1372	607	15	390	390	NUM
ejpam-1372	607	16	introduced	introduce	VERB
ejpam-1372	607	17	the	the	DET
ejpam-1372	607	18	integral	integral	ADJ
ejpam-1372	607	19	representation	representation	NOUN
ejpam-1372	607	20	for	for	ADP
ejpam-1372	607	21	the	the	DET
ejpam-1372	607	22	gamma	gamma	NOUN
ejpam-1372	607	23	function	function	NOUN
ejpam-1372	607	24	in	in	ADP
ejpam-1372	607	25	the	the	DET
ejpam-1372	607	26	numerator	numerator	NOUN
ejpam-1372	607	27	,	,	PUNCT
ejpam-1372	607	28	interchanged	interchange	VERB
ejpam-1372	607	29	the	the	DET
ejpam-1372	607	30	order	order	NOUN
ejpam-1372	607	31	of	of	ADP
ejpam-1372	607	32	the	the	DET
ejpam-1372	607	33	summation	summation	NOUN
ejpam-1372	607	34	and	and	CCONJ
ejpam-1372	607	35	integration	integration	NOUN
ejpam-1372	607	36	and	and	CCONJ
ejpam-1372	607	37	finally	finally	ADV
ejpam-1372	607	38	evaluated	evaluate	VERB
ejpam-1372	607	39	the	the	DET
ejpam-1372	607	40	sum	sum	NOUN
ejpam-1372	607	41	.	.	PUNCT
ejpam-1372	608	1	this	this	DET
ejpam-1372	608	2	approach	approach	NOUN
ejpam-1372	608	3	to	to	ADP
ejpam-1372	608	4	obtaining	obtain	VERB
ejpam-1372	608	5	limits	limit	NOUN
ejpam-1372	608	6	to	to	ADP
ejpam-1372	608	7	divergent	divergent	ADJ
ejpam-1372	608	8	series	series	NOUN
ejpam-1372	608	9	is	be	AUX
ejpam-1372	608	10	known	know	VERB
ejpam-1372	608	11	more	more	ADV
ejpam-1372	608	12	commonly	commonly	ADV
ejpam-1372	608	13	as	as	ADP
ejpam-1372	608	14	borel	borel	NOUN
ejpam-1372	608	15	summation	summation	NOUN
ejpam-1372	608	16	.	.	PUNCT
ejpam-1372	609	1	so	so	ADV
ejpam-1372	609	2	let	let	VERB
ejpam-1372	609	3	us	we	PRON
ejpam-1372	609	4	do	do	VERB
ejpam-1372	609	5	the	the	DET
ejpam-1372	609	6	same	same	ADJ
ejpam-1372	609	7	to	to	ADP
ejpam-1372	609	8	the	the	DET
ejpam-1372	609	9	first	first	ADJ
ejpam-1372	609	10	type	type	NOUN
ejpam-1372	609	11	of	of	ADP
ejpam-1372	609	12	terminant	terminant	NOUN
ejpam-1372	609	13	.	.	PUNCT
ejpam-1372	610	1	then	then	ADV
ejpam-1372	610	2	we	we	PRON
ejpam-1372	610	3	find	find	VERB
ejpam-1372	610	4	that	that	SCONJ
ejpam-1372	610	5	ti(n	ti(n	NUM
ejpam-1372	610	6	,	,	PUNCT
ejpam-1372	610	7	α	α	NOUN
ejpam-1372	610	8	,	,	PUNCT
ejpam-1372	610	9	z	z	NOUN
ejpam-1372	610	10	)	)	PUNCT
ejpam-1372	610	11	=	=	SYM
ejpam-1372	611	1	∫	∫	PROPN
ejpam-1372	612	1	∞	∞	NUM
ejpam-1372	612	2	0	0	PUNCT
ejpam-1372	613	1	d	d	PRON
ejpam-1372	613	2	t	t	NOUN
ejpam-1372	613	3	tα−1	tα−1	NOUN
ejpam-1372	613	4	e−t	e−t	NOUN
ejpam-1372	613	5	∞	∞	PROPN
ejpam-1372	613	6	∑	∑	PROPN
ejpam-1372	613	7	k	k	X
ejpam-1372	613	8	=	=	PROPN
ejpam-1372	613	9	n	n	X
ejpam-1372	613	10	(	(	PUNCT
ejpam-1372	613	11	−zt)k	−zt)k	PROPN
ejpam-1372	613	12	.	.	PUNCT
ejpam-1372	614	1	(	(	PUNCT
ejpam-1372	614	2	65	65	NUM
ejpam-1372	614	3	)	)	PUNCT
ejpam-1372	614	4	now	now	ADV
ejpam-1372	614	5	we	we	PRON
ejpam-1372	614	6	see	see	VERB
ejpam-1372	614	7	that	that	SCONJ
ejpam-1372	614	8	the	the	DET
ejpam-1372	614	9	first	first	ADJ
ejpam-1372	614	10	type	type	NOUN
ejpam-1372	614	11	of	of	ADP
ejpam-1372	614	12	terminant	terminant	NOUN
ejpam-1372	614	13	has	have	AUX
ejpam-1372	614	14	been	be	AUX
ejpam-1372	614	15	expressed	express	VERB
ejpam-1372	614	16	in	in	ADP
ejpam-1372	614	17	terms	term	NOUN
ejpam-1372	614	18	of	of	ADP
ejpam-1372	614	19	the	the	DET
ejpam-1372	614	20	geometric	geometric	ADJ
ejpam-1372	614	21	series	series	NOUN
ejpam-1372	614	22	.	.	PUNCT
ejpam-1372	615	1	therefore	therefore	ADV
ejpam-1372	615	2	,	,	PUNCT
ejpam-1372	615	3	if	if	SCONJ
ejpam-1372	615	4	we	we	PRON
ejpam-1372	615	5	introduce	introduce	VERB
ejpam-1372	615	6	the	the	DET
ejpam-1372	615	7	regularised	regularise	VERB
ejpam-1372	615	8	value	value	NOUN
ejpam-1372	615	9	of	of	ADP
ejpam-1372	615	10	the	the	DET
ejpam-1372	615	11	latter	latter	ADJ
ejpam-1372	615	12	series	series	NOUN
ejpam-1372	615	13	into	into	ADP
ejpam-1372	615	14	the	the	DET
ejpam-1372	615	15	above	above	ADJ
ejpam-1372	615	16	result	result	NOUN
ejpam-1372	615	17	,	,	PUNCT
ejpam-1372	615	18	then	then	ADV
ejpam-1372	615	19	we	we	PRON
ejpam-1372	615	20	obtain	obtain	VERB
ejpam-1372	615	21	the	the	DET
ejpam-1372	615	22	regularised	regularise	VERB
ejpam-1372	615	23	value	value	NOUN
ejpam-1372	615	24	of	of	ADP
ejpam-1372	615	25	the	the	DET
ejpam-1372	615	26	first	first	ADJ
ejpam-1372	615	27	type	type	NOUN
ejpam-1372	615	28	of	of	ADP
ejpam-1372	615	29	terminant	terminant	NOUN
ejpam-1372	615	30	.	.	PUNCT
ejpam-1372	616	1	in	in	ADP
ejpam-1372	616	2	addition	addition	NOUN
ejpam-1372	616	3	,	,	PUNCT
ejpam-1372	616	4	according	accord	VERB
ejpam-1372	616	5	to	to	ADP
ejpam-1372	616	6	our	our	PRON
ejpam-1372	616	7	analysis	analysis	NOUN
ejpam-1372	616	8	of	of	ADP
ejpam-1372	616	9	the	the	DET
ejpam-1372	616	10	geometric	geometric	ADJ
ejpam-1372	616	11	series	series	NOUN
ejpam-1372	616	12	,	,	PUNCT
ejpam-1372	616	13	it	it	PRON
ejpam-1372	616	14	is	be	AUX
ejpam-1372	616	15	conditionally	conditionally	ADV
ejpam-1372	616	16	convergent	convergent	ADJ
ejpam-1372	616	17	for	for	ADP
ejpam-1372	616	18	ℜ(−zt	ℜ(−zt	PROPN
ejpam-1372	616	19	)	)	PUNCT
ejpam-1372	616	20	<	<	X
ejpam-1372	617	1	1	1	X
ejpam-1372	617	2	.	.	PUNCT
ejpam-1372	617	3	as	as	SCONJ
ejpam-1372	617	4	t	t	PROPN
ejpam-1372	617	5	ranges	range	VERB
ejpam-1372	617	6	from	from	ADP
ejpam-1372	617	7	0	0	NUM
ejpam-1372	617	8	to	to	ADP
ejpam-1372	617	9	infinity	infinity	NOUN
ejpam-1372	617	10	,	,	PUNCT
ejpam-1372	617	11	this	this	PRON
ejpam-1372	617	12	means	mean	VERB
ejpam-1372	617	13	that	that	SCONJ
ejpam-1372	617	14	the	the	DET
ejpam-1372	617	15	terminant	terminant	NOUN
ejpam-1372	617	16	is	be	AUX
ejpam-1372	617	17	conditionally	conditionally	ADV
ejpam-1372	617	18	convergent	convergent	ADJ
ejpam-1372	617	19	for	for	ADP
ejpam-1372	617	20	ℜ	ℜ	ADJ
ejpam-1372	617	21	z	z	NOUN
ejpam-1372	617	22	>	>	X
ejpam-1372	617	23	0	0	PUNCT
ejpam-1372	617	24	and	and	CCONJ
ejpam-1372	617	25	divergent	divergent	ADJ
ejpam-1372	617	26	for	for	ADP
ejpam-1372	617	27	all	all	DET
ejpam-1372	617	28	other	other	ADJ
ejpam-1372	617	29	values	value	NOUN
ejpam-1372	617	30	of	of	ADP
ejpam-1372	617	31	z.	z.	PROPN
ejpam-1372	617	32	as	as	ADP
ejpam-1372	617	33	a	a	DET
ejpam-1372	617	34	consequence	consequence	NOUN
ejpam-1372	617	35	,	,	PUNCT
ejpam-1372	617	36	we	we	PRON
ejpam-1372	617	37	observe	observe	VERB
ejpam-1372	617	38	that	that	SCONJ
ejpam-1372	617	39	an	an	DET
ejpam-1372	617	40	asymptotic	asymptotic	ADJ
ejpam-1372	617	41	series	series	NOUN
ejpam-1372	617	42	need	need	AUX
ejpam-1372	617	43	not	not	PART
ejpam-1372	617	44	necessarily	necessarily	ADV
ejpam-1372	617	45	be	be	AUX
ejpam-1372	617	46	divergent	divergent	ADJ
ejpam-1372	617	47	.	.	PUNCT
ejpam-1372	618	1	that	that	PRON
ejpam-1372	618	2	is	is	ADV
ejpam-1372	618	3	,	,	PUNCT
ejpam-1372	618	4	an	an	DET
ejpam-1372	618	5	asymptotic	asymptotic	ADJ
ejpam-1372	618	6	expansion	expansion	NOUN
ejpam-1372	618	7	is	be	AUX
ejpam-1372	618	8	not	not	PART
ejpam-1372	618	9	always	always	ADV
ejpam-1372	618	10	divergent	divergent	ADJ
ejpam-1372	618	11	;	;	PUNCT
ejpam-1372	618	12	it	it	PRON
ejpam-1372	618	13	can	can	AUX
ejpam-1372	618	14	also	also	ADV
ejpam-1372	618	15	be	be	AUX
ejpam-1372	618	16	conditionally	conditionally	ADV
ejpam-1372	618	17	convergent	convergent	ADJ
ejpam-1372	618	18	.	.	PUNCT
ejpam-1372	619	1	the	the	DET
ejpam-1372	619	2	introduction	introduction	NOUN
ejpam-1372	619	3	of	of	ADP
ejpam-1372	619	4	the	the	DET
ejpam-1372	619	5	regularised	regularise	VERB
ejpam-1372	619	6	value	value	NOUN
ejpam-1372	619	7	of	of	ADP
ejpam-1372	619	8	the	the	DET
ejpam-1372	619	9	geometric	geometric	ADJ
ejpam-1372	619	10	series	series	NOUN
ejpam-1372	619	11	into	into	ADP
ejpam-1372	619	12	eq	eq	PROPN
ejpam-1372	619	13	.	.	PUNCT
ejpam-1372	620	1	(	(	PUNCT
ejpam-1372	620	2	65	65	NUM
ejpam-1372	620	3	)	)	PUNCT
ejpam-1372	620	4	yields	yield	VERB
ejpam-1372	620	5	ti	ti	NOUN
ejpam-1372	620	6	(	(	PUNCT
ejpam-1372	620	7	n	n	PROPN
ejpam-1372	620	8	,	,	PUNCT
ejpam-1372	620	9	α	α	PROPN
ejpam-1372	620	10	,	,	PUNCT
ejpam-1372	620	11	z	z	NOUN
ejpam-1372	620	12	)	)	PUNCT
ejpam-1372	620	13	≡	≡	PROPN
ejpam-1372	620	14	(	(	PUNCT
ejpam-1372	620	15	−z)n	−z)n	X
ejpam-1372	620	16	∫	∫	PROPN
ejpam-1372	620	17	∞	∞	PROPN
ejpam-1372	620	18	0	0	PUNCT
ejpam-1372	621	1	d	d	PRON
ejpam-1372	621	2	t	t	NOUN
ejpam-1372	621	3	tn+α−1	tn+α−1	NOUN
ejpam-1372	621	4	e−t	e−t	NOUN
ejpam-1372	621	5	1	1	NUM
ejpam-1372	621	6	+	+	NUM
ejpam-1372	621	7	zt	zt	PROPN
ejpam-1372	621	8	.	.	PUNCT
ejpam-1372	622	1	(	(	PUNCT
ejpam-1372	622	2	66	66	NUM
ejpam-1372	622	3	)	)	PUNCT
ejpam-1372	622	4	since	since	SCONJ
ejpam-1372	622	5	we	we	PRON
ejpam-1372	622	6	have	have	AUX
ejpam-1372	622	7	already	already	ADV
ejpam-1372	622	8	stated	state	VERB
ejpam-1372	622	9	that	that	SCONJ
ejpam-1372	622	10	the	the	DET
ejpam-1372	622	11	geometric	geometric	ADJ
ejpam-1372	622	12	series	series	NOUN
ejpam-1372	622	13	is	be	AUX
ejpam-1372	622	14	bijective	bijective	ADJ
ejpam-1372	622	15	within	within	ADP
ejpam-1372	622	16	the	the	DET
ejpam-1372	622	17	principal	principal	ADJ
ejpam-1372	622	18	branch	branch	NOUN
ejpam-1372	622	19	of	of	ADP
ejpam-1372	622	20	the	the	DET
ejpam-1372	622	21	complex	complex	ADJ
ejpam-1372	622	22	plane	plane	NOUN
ejpam-1372	622	23	,	,	PUNCT
ejpam-1372	622	24	i.e.	i.e.	X
ejpam-1372	622	25	for	for	ADP
ejpam-1372	622	26	|arg	|arg	NOUN
ejpam-1372	622	27	z|<π	z|<π	PROPN
ejpam-1372	622	28	,	,	PUNCT
ejpam-1372	622	29	the	the	DET
ejpam-1372	622	30	regularised	regularise	VERB
ejpam-1372	622	31	value	value	NOUN
ejpam-1372	622	32	of	of	ADP
ejpam-1372	622	33	the	the	DET
ejpam-1372	622	34	first	first	ADJ
ejpam-1372	622	35	type	type	NOUN
ejpam-1372	622	36	of	of	ADP
ejpam-1372	622	37	terminant	terminant	NOUN
ejpam-1372	622	38	given	give	VERB
ejpam-1372	622	39	by	by	ADP
ejpam-1372	622	40	the	the	DET
ejpam-1372	622	41	above	above	ADJ
ejpam-1372	622	42	cauchy	cauchy	PROPN
ejpam-1372	622	43	integral	integral	NOUN
ejpam-1372	622	44	is	be	AUX
ejpam-1372	622	45	also	also	ADV
ejpam-1372	622	46	bijective	bijective	ADJ
ejpam-1372	622	47	.	.	PUNCT
ejpam-1372	623	1	that	that	PRON
ejpam-1372	623	2	is	be	AUX
ejpam-1372	623	3	,	,	PUNCT
ejpam-1372	623	4	there	there	PRON
ejpam-1372	623	5	is	be	VERB
ejpam-1372	623	6	a	a	DET
ejpam-1372	623	7	definite	definite	ADJ
ejpam-1372	623	8	value	value	NOUN
ejpam-1372	623	9	for	for	ADP
ejpam-1372	623	10	each	each	DET
ejpam-1372	623	11	value	value	NOUN
ejpam-1372	623	12	of	of	ADP
ejpam-1372	623	13	z	z	NOUN
ejpam-1372	623	14	within	within	ADP
ejpam-1372	623	15	the	the	DET
ejpam-1372	623	16	principal	principal	ADJ
ejpam-1372	623	17	branch	branch	NOUN
ejpam-1372	623	18	of	of	ADP
ejpam-1372	623	19	the	the	DET
ejpam-1372	623	20	complex	complex	ADJ
ejpam-1372	623	21	plane	plane	NOUN
ejpam-1372	623	22	,	,	PUNCT
ejpam-1372	623	23	which	which	PRON
ejpam-1372	623	24	means	mean	VERB
ejpam-1372	623	25	,	,	PUNCT
ejpam-1372	623	26	in	in	ADP
ejpam-1372	623	27	turn	turn	NOUN
ejpam-1372	623	28	,	,	PUNCT
ejpam-1372	623	29	that	that	SCONJ
ejpam-1372	623	30	we	we	PRON
ejpam-1372	623	31	are	be	AUX
ejpam-1372	623	32	moving	move	VERB
ejpam-1372	623	33	closer	close	ADV
ejpam-1372	623	34	to	to	PART
ejpam-1372	623	35	euler	euler	VERB
ejpam-1372	623	36	’s	’s	PART
ejpam-1372	623	37	unorthodox	unorthodox	ADJ
ejpam-1372	623	38	view	view	NOUN
ejpam-1372	623	39	of	of	ADP
ejpam-1372	623	40	there	there	PRON
ejpam-1372	623	41	being	be	AUX
ejpam-1372	623	42	a	a	DET
ejpam-1372	623	43	definite	definite	ADJ
ejpam-1372	623	44	value	value	NOUN
ejpam-1372	623	45	connected	connect	VERB
ejpam-1372	623	46	with	with	ADP
ejpam-1372	623	47	each	each	DET
ejpam-1372	623	48	divergent	divergent	ADJ
ejpam-1372	623	49	series	series	NOUN
ejpam-1372	623	50	.	.	PUNCT
ejpam-1372	624	1	on	on	ADP
ejpam-1372	624	2	the	the	DET
ejpam-1372	624	3	other	other	ADJ
ejpam-1372	624	4	hand	hand	NOUN
ejpam-1372	624	5	,	,	PUNCT
ejpam-1372	624	6	if	if	SCONJ
ejpam-1372	624	7	in	in	ADP
ejpam-1372	624	8	equivalence	equivalence	NOUN
ejpam-1372	624	9	(	(	PUNCT
ejpam-1372	624	10	66	66	NUM
ejpam-1372	624	11	)	)	PUNCT
ejpam-1372	624	12	we	we	PRON
ejpam-1372	624	13	replace	replace	VERB
ejpam-1372	624	14	z	z	NOUN
ejpam-1372	624	15	with	with	ADP
ejpam-1372	624	16	z	z	PROPN
ejpam-1372	624	17	exp(−2ilπ	exp(−2ilπ	PROPN
ejpam-1372	624	18	)	)	PUNCT
ejpam-1372	624	19	,	,	PUNCT
ejpam-1372	624	20	where	where	SCONJ
ejpam-1372	624	21	l	l	NOUN
ejpam-1372	624	22	is	be	AUX
ejpam-1372	624	23	an	an	DET
ejpam-1372	624	24	arbitrary	arbitrary	ADJ
ejpam-1372	624	25	integer	integer	NOUN
ejpam-1372	624	26	,	,	PUNCT
ejpam-1372	624	27	then	then	ADV
ejpam-1372	624	28	we	we	PRON
ejpam-1372	624	29	find	find	VERB
ejpam-1372	624	30	that	that	SCONJ
ejpam-1372	624	31	ti	ti	NOUN
ejpam-1372	624	32	(	(	PUNCT
ejpam-1372	624	33	n	n	X
ejpam-1372	624	34	,	,	PUNCT
ejpam-1372	624	35	α	α	PROPN
ejpam-1372	624	36	,	,	PUNCT
ejpam-1372	624	37	z	z	NOUN
ejpam-1372	624	38	exp(−2ilπ))≡	exp(−2ilπ))≡	NUM
ejpam-1372	624	39	(	(	PUNCT
ejpam-1372	624	40	−z)n	−z)n	X
ejpam-1372	624	41	∫	∫	PROPN
ejpam-1372	624	42	∞	∞	PROPN
ejpam-1372	624	43	0	0	PUNCT
ejpam-1372	624	44	d	d	PRON
ejpam-1372	624	45	t	t	NOUN
ejpam-1372	624	46	tn+α−1	tn+α−1	NOUN
ejpam-1372	624	47	e−t	e−t	NOUN
ejpam-1372	624	48	1	1	NUM
ejpam-1372	624	49	+	+	SYM
ejpam-1372	624	50	z	z	NOUN
ejpam-1372	624	51	exp(−2ilπ)t	exp(−2ilπ)t	NOUN
ejpam-1372	624	52	.	.	PUNCT
ejpam-1372	625	1	(	(	PUNCT
ejpam-1372	625	2	67	67	NUM
ejpam-1372	625	3	)	)	PUNCT
ejpam-1372	625	4	we	we	PRON
ejpam-1372	625	5	can	can	AUX
ejpam-1372	625	6	express	express	VERB
ejpam-1372	625	7	the	the	DET
ejpam-1372	625	8	above	above	ADJ
ejpam-1372	625	9	result	result	NOUN
ejpam-1372	625	10	as	as	ADP
ejpam-1372	625	11	a	a	DET
ejpam-1372	625	12	contour	contour	NOUN
ejpam-1372	625	13	integral	integral	ADJ
ejpam-1372	625	14	in	in	ADP
ejpam-1372	625	15	terms	term	NOUN
ejpam-1372	625	16	of	of	ADP
ejpam-1372	625	17	the	the	DET
ejpam-1372	625	18	complex	complex	ADJ
ejpam-1372	625	19	variable	variable	NOUN
ejpam-1372	625	20	s	s	NOUN
ejpam-1372	625	21	and	and	CCONJ
ejpam-1372	625	22	c	c	PROPN
ejpam-1372	625	23	,	,	PUNCT
ejpam-1372	625	24	the	the	DET
ejpam-1372	625	25	line	line	NOUN
ejpam-1372	625	26	contour	contour	NOUN
ejpam-1372	625	27	along	along	ADP
ejpam-1372	625	28	the	the	DET
ejpam-1372	625	29	positive	positive	ADJ
ejpam-1372	625	30	real	real	ADJ
ejpam-1372	625	31	axis	axis	NOUN
ejpam-1372	625	32	.	.	PUNCT
ejpam-1372	626	1	then	then	ADV
ejpam-1372	626	2	equivalence	equivalence	NOUN
ejpam-1372	626	3	(	(	PUNCT
ejpam-1372	626	4	67	67	NUM
ejpam-1372	626	5	)	)	PUNCT
ejpam-1372	626	6	becomes	become	VERB
ejpam-1372	626	7	ti	ti	NOUN
ejpam-1372	626	8	(	(	PUNCT
ejpam-1372	626	9	n	n	X
ejpam-1372	626	10	,	,	PUNCT
ejpam-1372	626	11	α	α	PROPN
ejpam-1372	626	12	,	,	PUNCT
ejpam-1372	626	13	z	z	NOUN
ejpam-1372	626	14	exp(−2ilπ))≡	exp(−2ilπ))≡	NOUN
ejpam-1372	626	15	(	(	PUNCT
ejpam-1372	626	16	−1)nzn−1	−1)nzn−1	NOUN
ejpam-1372	626	17	∫	∫	X
ejpam-1372	626	18	c	c	PROPN
ejpam-1372	626	19	ds	ds	PROPN
ejpam-1372	626	20	sn+α−1	sn+α−1	PROPN
ejpam-1372	626	21	e−s	e−s	ADV
ejpam-1372	626	22	s−	s−	PROPN
ejpam-1372	626	23	(	(	PUNCT
ejpam-1372	626	24	z−1	z−1	PROPN
ejpam-1372	626	25	exp((2l	exp((2l	PROPN
ejpam-1372	626	26	−	−	NOUN
ejpam-1372	626	27	1)iπ	1)iπ	NUM
ejpam-1372	626	28	)	)	PUNCT
ejpam-1372	626	29	)	)	PUNCT
ejpam-1372	626	30	,	,	PUNCT
ejpam-1372	626	31	(	(	PUNCT
ejpam-1372	626	32	68	68	NUM
ejpam-1372	626	33	)	)	PUNCT
ejpam-1372	626	34	where	where	SCONJ
ejpam-1372	626	35	−π	−π	PROPN
ejpam-1372	626	36	<	<	X
ejpam-1372	626	37	arg(z	arg(z	PROPN
ejpam-1372	626	38	exp(−2ilπ))<π	exp(−2ilπ))<π	PROPN
ejpam-1372	626	39	or(2l	or(2l	NOUN
ejpam-1372	626	40	−	−	PROPN
ejpam-1372	626	41	1)π	1)π	NUM
ejpam-1372	626	42	<	<	X
ejpam-1372	626	43	arg	arg	NOUN
ejpam-1372	626	44	z	z	X
ejpam-1372	626	45	<	<	X
ejpam-1372	626	46	(	(	PUNCT
ejpam-1372	626	47	2l	2l	X
ejpam-1372	626	48	+	+	SYM
ejpam-1372	626	49	1)π	1)π	NUM
ejpam-1372	626	50	.	.	PUNCT
ejpam-1372	627	1	the	the	DET
ejpam-1372	627	2	problem	problem	NOUN
ejpam-1372	627	3	with	with	ADP
ejpam-1372	627	4	equivalence	equivalence	NOUN
ejpam-1372	627	5	(	(	PUNCT
ejpam-1372	627	6	68	68	NUM
ejpam-1372	627	7	)	)	PUNCT
ejpam-1372	627	8	is	be	AUX
ejpam-1372	627	9	that	that	SCONJ
ejpam-1372	627	10	it	it	PRON
ejpam-1372	627	11	appears	appear	VERB
ejpam-1372	627	12	to	to	PART
ejpam-1372	627	13	yield	yield	VERB
ejpam-1372	627	14	the	the	DET
ejpam-1372	627	15	same	same	ADJ
ejpam-1372	627	16	regularised	regularise	VERB
ejpam-1372	627	17	value	value	NOUN
ejpam-1372	627	18	for	for	ADP
ejpam-1372	627	19	any	any	DET
ejpam-1372	627	20	value	value	NOUN
ejpam-1372	627	21	of	of	ADP
ejpam-1372	627	22	l.	l.	NOUN
ejpam-1372	627	23	that	that	PRON
ejpam-1372	627	24	is	be	AUX
ejpam-1372	627	25	,	,	PUNCT
ejpam-1372	627	26	the	the	DET
ejpam-1372	627	27	regularised	regularise	VERB
ejpam-1372	627	28	value	value	NOUN
ejpam-1372	627	29	appears	appear	VERB
ejpam-1372	627	30	to	to	PART
ejpam-1372	627	31	be	be	AUX
ejpam-1372	627	32	the	the	DET
ejpam-1372	627	33	same	same	ADJ
ejpam-1372	627	34	for	for	ADP
ejpam-1372	627	35	all	all	DET
ejpam-1372	627	36	branches	branch	NOUN
ejpam-1372	627	37	of	of	ADP
ejpam-1372	627	38	the	the	DET
ejpam-1372	627	39	complex	complex	ADJ
ejpam-1372	627	40	plane	plane	NOUN
ejpam-1372	627	41	when	when	SCONJ
ejpam-1372	627	42	we	we	PRON
ejpam-1372	627	43	might	might	AUX
ejpam-1372	627	44	expect	expect	VERB
ejpam-1372	627	45	it	it	PRON
ejpam-1372	627	46	to	to	PART
ejpam-1372	627	47	be	be	AUX
ejpam-1372	627	48	different	different	ADJ
ejpam-1372	627	49	.	.	PUNCT
ejpam-1372	628	1	this	this	PRON
ejpam-1372	628	2	is	be	AUX
ejpam-1372	628	3	because	because	SCONJ
ejpam-1372	628	4	when	when	SCONJ
ejpam-1372	628	5	asymptotic	asymptotic	ADJ
ejpam-1372	628	6	series	series	NOUN
ejpam-1372	628	7	including	include	VERB
ejpam-1372	628	8	terminants	terminant	NOUN
ejpam-1372	628	9	are	be	AUX
ejpam-1372	628	10	derived	derive	VERB
ejpam-1372	628	11	,	,	PUNCT
ejpam-1372	628	12	they	they	PRON
ejpam-1372	628	13	are	be	AUX
ejpam-1372	628	14	usually	usually	ADV
ejpam-1372	628	15	expressed	express	VERB
ejpam-1372	628	16	in	in	ADP
ejpam-1372	628	17	powers	power	NOUN
ejpam-1372	628	18	of	of	ADP
ejpam-1372	628	19	z	z	NOUN
ejpam-1372	628	20	such	such	ADJ
ejpam-1372	628	21	as	as	ADP
ejpam-1372	628	22	zβ	zβ	PROPN
ejpam-1372	628	23	,	,	PUNCT
ejpam-1372	628	24	where	where	SCONJ
ejpam-1372	628	25	β	β	X
ejpam-1372	628	26	>	>	X
ejpam-1372	628	27	1	1	NUM
ejpam-1372	628	28	.	.	PUNCT
ejpam-1372	629	1	for	for	ADP
ejpam-1372	629	2	example	example	NOUN
ejpam-1372	629	3	,	,	PUNCT
ejpam-1372	629	4	v.	v.	ADP
ejpam-1372	629	5	kowalenko	kowalenko	PROPN
ejpam-1372	629	6	/	/	SYM
ejpam-1372	629	7	eur	eur	PROPN
ejpam-1372	629	8	.	.	PUNCT
ejpam-1372	630	1	j.	j.	PROPN
ejpam-1372	630	2	pure	pure	PROPN
ejpam-1372	630	3	appl	appl	PROPN
ejpam-1372	630	4	.	.	PROPN
ejpam-1372	630	5	math	math	PROPN
ejpam-1372	630	6	,	,	PUNCT
ejpam-1372	630	7	4	4	NUM
ejpam-1372	630	8	(	(	PUNCT
ejpam-1372	630	9	2011	2011	NUM
ejpam-1372	630	10	)	)	PUNCT
ejpam-1372	630	11	,	,	PUNCT
ejpam-1372	630	12	370	370	NUM
ejpam-1372	630	13	-	-	SYM
ejpam-1372	630	14	423	423	NUM
ejpam-1372	630	15	391	391	NUM
ejpam-1372	630	16	the	the	DET
ejpam-1372	630	17	asymptotic	asymptotic	ADJ
ejpam-1372	630	18	expansion	expansion	NOUN
ejpam-1372	630	19	for	for	ADP
ejpam-1372	630	20	the	the	DET
ejpam-1372	630	21	complementary	complementary	ADJ
ejpam-1372	630	22	error	error	NOUN
ejpam-1372	630	23	function	function	NOUN
ejpam-1372	630	24	,	,	PUNCT
ejpam-1372	630	25	which	which	PRON
ejpam-1372	630	26	is	be	AUX
ejpam-1372	630	27	given	give	VERB
ejpam-1372	630	28	as	as	ADP
ejpam-1372	630	29	no	no	NOUN
ejpam-1372	630	30	.	.	PUNCT
ejpam-1372	631	1	7.1.23	7.1.23	NUM
ejpam-1372	631	2	in	in	ADP
ejpam-1372	631	3	ref	ref	NOUN
ejpam-1372	631	4	.	.	PUNCT
ejpam-1372	632	1	[	[	X
ejpam-1372	632	2	1	1	NUM
ejpam-1372	632	3	]	]	PUNCT
ejpam-1372	632	4	,	,	PUNCT
ejpam-1372	632	5	is	be	AUX
ejpam-1372	632	6	erfc(z	erfc(z	NOUN
ejpam-1372	632	7	)	)	PUNCT
ejpam-1372	632	8	≡	≡	PROPN
ejpam-1372	632	9	e−z2	e−z2	ADV
ejpam-1372	632	10	πz	πz	VERB
ejpam-1372	632	11	∞	∞	PROPN
ejpam-1372	632	12	∑	∑	ADP
ejpam-1372	632	13	k=0	k=0	PUNCT
ejpam-1372	632	14	γ(k+	γ(k+	ADP
ejpam-1372	632	15	1/2	1/2	NUM
ejpam-1372	632	16	)	)	PUNCT
ejpam-1372	632	17	(	(	PUNCT
ejpam-1372	632	18	−z2)k	−z2)k	NOUN
ejpam-1372	632	19	,	,	PUNCT
ejpam-1372	632	20	|arg	|arg	VERB
ejpam-1372	632	21	z|	z|	PROPN
ejpam-1372	632	22	<	<	X
ejpam-1372	632	23	3π/4	3π/4	NUM
ejpam-1372	632	24	.	.	PUNCT
ejpam-1372	633	1	(	(	PUNCT
ejpam-1372	633	2	69	69	NUM
ejpam-1372	633	3	)	)	PUNCT
ejpam-1372	633	4	note	note	NOUN
ejpam-1372	633	5	that	that	SCONJ
ejpam-1372	633	6	it	it	PRON
ejpam-1372	633	7	has	have	AUX
ejpam-1372	633	8	been	be	AUX
ejpam-1372	633	9	necessary	necessary	ADJ
ejpam-1372	633	10	to	to	PART
ejpam-1372	633	11	introduce	introduce	VERB
ejpam-1372	633	12	the	the	DET
ejpam-1372	633	13	equivalence	equivalence	NOUN
ejpam-1372	633	14	symbol	symbol	NOUN
ejpam-1372	633	15	into	into	ADP
ejpam-1372	633	16	this	this	DET
ejpam-1372	633	17	result	result	NOUN
ejpam-1372	633	18	as	as	ADP
ejpam-1372	633	19	a	a	DET
ejpam-1372	633	20	consequence	consequence	NOUN
ejpam-1372	633	21	of	of	ADP
ejpam-1372	633	22	our	our	PRON
ejpam-1372	633	23	previous	previous	ADJ
ejpam-1372	633	24	discussion	discussion	NOUN
ejpam-1372	633	25	on	on	ADP
ejpam-1372	633	26	the	the	DET
ejpam-1372	633	27	properties	property	NOUN
ejpam-1372	633	28	of	of	ADP
ejpam-1372	633	29	an	an	DET
ejpam-1372	633	30	asymptotic	asymptotic	ADJ
ejpam-1372	633	31	series	series	NOUN
ejpam-1372	633	32	.	.	PUNCT
ejpam-1372	634	1	according	accord	VERB
ejpam-1372	634	2	to	to	ADP
ejpam-1372	634	3	equivalence	equivalence	NOUN
ejpam-1372	634	4	(	(	PUNCT
ejpam-1372	634	5	68	68	NUM
ejpam-1372	634	6	)	)	PUNCT
ejpam-1372	634	7	the	the	DET
ejpam-1372	634	8	value	value	NOUN
ejpam-1372	634	9	of	of	ADP
ejpam-1372	634	10	erfc(exp(−3πi/8	erfc(exp(−3πi/8	PROPN
ejpam-1372	634	11	)	)	PUNCT
ejpam-1372	634	12	)	)	PUNCT
ejpam-1372	634	13	is	be	AUX
ejpam-1372	634	14	expected	expect	VERB
ejpam-1372	634	15	to	to	PART
ejpam-1372	634	16	be	be	AUX
ejpam-1372	634	17	equal	equal	ADJ
ejpam-1372	634	18	to	to	ADP
ejpam-1372	634	19	erfc(exp(5πi/8	erfc(exp(5πi/8	NUM
ejpam-1372	634	20	)	)	PUNCT
ejpam-1372	634	21	)	)	PUNCT
ejpam-1372	634	22	.	.	PUNCT
ejpam-1372	635	1	yet	yet	ADV
ejpam-1372	635	2	,	,	PUNCT
ejpam-1372	635	3	the	the	DET
ejpam-1372	635	4	former	former	ADJ
ejpam-1372	635	5	yields	yield	VERB
ejpam-1372	635	6	a	a	DET
ejpam-1372	635	7	value	value	NOUN
ejpam-1372	635	8	of	of	ADP
ejpam-1372	635	9	0.663	0.663	NUM
ejpam-1372	635	10	282	282	NUM
ejpam-1372	635	11	.	.	PUNCT
ejpam-1372	635	12	.	.	PUNCT
ejpam-1372	636	1	.	.	PUNCT
ejpam-1372	637	1	,	,	PUNCT
ejpam-1372	637	2	while	while	SCONJ
ejpam-1372	637	3	the	the	DET
ejpam-1372	637	4	latter	latter	NOUN
ejpam-1372	637	5	equals	equal	VERB
ejpam-1372	637	6	7.117	7.117	NUM
ejpam-1372	637	7	400	400	NUM
ejpam-1372	637	8	.	.	PUNCT
ejpam-1372	637	9	.	.	PUNCT
ejpam-1372	638	1	.×	.×	PROPN
ejpam-1372	638	2	10−24	10−24	PROPN
ejpam-1372	638	3	.	.	PUNCT
ejpam-1372	639	1	therefore	therefore	ADV
ejpam-1372	639	2	,	,	PUNCT
ejpam-1372	639	3	equivalence	equivalence	NOUN
ejpam-1372	639	4	(	(	PUNCT
ejpam-1372	639	5	68	68	NUM
ejpam-1372	639	6	)	)	PUNCT
ejpam-1372	639	7	must	must	AUX
ejpam-1372	639	8	be	be	AUX
ejpam-1372	639	9	restricted	restrict	VERB
ejpam-1372	639	10	to	to	ADP
ejpam-1372	639	11	one	one	NUM
ejpam-1372	639	12	branch	branch	NOUN
ejpam-1372	639	13	given	give	VERB
ejpam-1372	639	14	by	by	ADP
ejpam-1372	639	15	either	either	DET
ejpam-1372	639	16	2lπ	2lπ	NOUN
ejpam-1372	639	17	<	<	X
ejpam-1372	639	18	arg(−z2	arg(−z2	NOUN
ejpam-1372	639	19	)	)	PUNCT
ejpam-1372	639	20	<	<	X
ejpam-1372	639	21	(	(	PUNCT
ejpam-1372	639	22	2l	2l	X
ejpam-1372	639	23	+	+	X
ejpam-1372	639	24	2)π	2)π	NUM
ejpam-1372	639	25	or	or	CCONJ
ejpam-1372	639	26	(	(	PUNCT
ejpam-1372	639	27	l	l	NOUN
ejpam-1372	640	1	−	−	PROPN
ejpam-1372	640	2	1/2)π	1/2)π	NUM
ejpam-1372	640	3	<	<	X
ejpam-1372	640	4	arg	arg	NOUN
ejpam-1372	640	5	z	z	X
ejpam-1372	640	6	<	<	X
ejpam-1372	640	7	(	(	PUNCT
ejpam-1372	640	8	l	l	NOUN
ejpam-1372	640	9	+	+	NOUN
ejpam-1372	640	10	1/2)π	1/2)π	X
ejpam-1372	640	11	.	.	PUNCT
ejpam-1372	640	12	then	then	ADV
ejpam-1372	640	13	we	we	PRON
ejpam-1372	640	14	are	be	AUX
ejpam-1372	640	15	left	leave	VERB
ejpam-1372	640	16	with	with	ADP
ejpam-1372	640	17	the	the	DET
ejpam-1372	640	18	problem	problem	NOUN
ejpam-1372	640	19	of	of	ADP
ejpam-1372	640	20	deciding	decide	VERB
ejpam-1372	640	21	whether	whether	SCONJ
ejpam-1372	640	22	the	the	DET
ejpam-1372	640	23	equivalence	equivalence	NOUN
ejpam-1372	640	24	is	be	AUX
ejpam-1372	640	25	valid	valid	ADJ
ejpam-1372	640	26	for	for	ADP
ejpam-1372	640	27	either	either	DET
ejpam-1372	640	28	−3π/2	−3π/2	PROPN
ejpam-1372	640	29	<	<	X
ejpam-1372	640	30	arg	arg	NOUN
ejpam-1372	640	31	z	z	X
ejpam-1372	640	32	<	<	X
ejpam-1372	640	33	−π/2	−π/2	PROPN
ejpam-1372	640	34	,	,	PUNCT
ejpam-1372	640	35	|arg	|arg	NOUN
ejpam-1372	640	36	z|<π/2	z|<π/2	PROPN
ejpam-1372	640	37	,	,	PUNCT
ejpam-1372	640	38	or	or	CCONJ
ejpam-1372	640	39	for	for	ADP
ejpam-1372	640	40	π/2	π/2	NUM
ejpam-1372	640	41	<	<	X
ejpam-1372	640	42	arg	arg	NOUN
ejpam-1372	640	43	z<3π/2	z<3π/2	PROPN
ejpam-1372	640	44	within	within	ADP
ejpam-1372	640	45	the	the	DET
ejpam-1372	640	46	principal	principal	ADJ
ejpam-1372	640	47	branch	branch	NOUN
ejpam-1372	640	48	of	of	ADP
ejpam-1372	640	49	the	the	DET
ejpam-1372	640	50	complex	complex	ADJ
ejpam-1372	640	51	plane	plane	NOUN
ejpam-1372	640	52	.	.	PUNCT
ejpam-1372	641	1	another	another	DET
ejpam-1372	641	2	problem	problem	NOUN
ejpam-1372	641	3	with	with	ADP
ejpam-1372	641	4	equivalences	equivalence	NOUN
ejpam-1372	641	5	(	(	PUNCT
ejpam-1372	641	6	66	66	NUM
ejpam-1372	641	7	)	)	PUNCT
ejpam-1372	641	8	and	and	CCONJ
ejpam-1372	641	9	(	(	PUNCT
ejpam-1372	641	10	67	67	NUM
ejpam-1372	641	11	)	)	PUNCT
ejpam-1372	641	12	is	be	AUX
ejpam-1372	641	13	:	:	PUNCT
ejpam-1372	641	14	what	what	PRON
ejpam-1372	641	15	do	do	AUX
ejpam-1372	641	16	we	we	PRON
ejpam-1372	641	17	do	do	VERB
ejpam-1372	641	18	when	when	SCONJ
ejpam-1372	641	19	arg	arg	VERB
ejpam-1372	641	20	z	z	NOUN
ejpam-1372	641	21	=	=	PUNCT
ejpam-1372	641	22	±π	±π	PROPN
ejpam-1372	641	23	?	?	PROPN
ejpam-1372	641	24	for	for	ADP
ejpam-1372	641	25	these	these	DET
ejpam-1372	641	26	values	value	NOUN
ejpam-1372	641	27	of	of	ADP
ejpam-1372	641	28	z	z	NOUN
ejpam-1372	641	29	the	the	DET
ejpam-1372	641	30	cauchy	cauchy	ADJ
ejpam-1372	641	31	integral	integral	NOUN
ejpam-1372	641	32	is	be	AUX
ejpam-1372	641	33	singular	singular	ADJ
ejpam-1372	641	34	.	.	PUNCT
ejpam-1372	642	1	whilst	whilst	SCONJ
ejpam-1372	642	2	this	this	PRON
ejpam-1372	642	3	might	might	AUX
ejpam-1372	642	4	not	not	PART
ejpam-1372	642	5	be	be	AUX
ejpam-1372	642	6	a	a	DET
ejpam-1372	642	7	serious	serious	ADJ
ejpam-1372	642	8	problem	problem	NOUN
ejpam-1372	642	9	with	with	ADP
ejpam-1372	642	10	equivalence	equivalence	NOUN
ejpam-1372	642	11	(	(	PUNCT
ejpam-1372	642	12	66	66	NUM
ejpam-1372	642	13	)	)	PUNCT
ejpam-1372	642	14	where	where	SCONJ
ejpam-1372	642	15	nearly	nearly	ADV
ejpam-1372	642	16	all	all	DET
ejpam-1372	642	17	the	the	DET
ejpam-1372	642	18	principal	principal	ADJ
ejpam-1372	642	19	branch	branch	NOUN
ejpam-1372	642	20	of	of	ADP
ejpam-1372	642	21	the	the	DET
ejpam-1372	642	22	complex	complex	ADJ
ejpam-1372	642	23	plane	plane	NOUN
ejpam-1372	642	24	has	have	AUX
ejpam-1372	642	25	been	be	AUX
ejpam-1372	642	26	covered	cover	VERB
ejpam-1372	642	27	anyway	anyway	ADV
ejpam-1372	642	28	,	,	PUNCT
ejpam-1372	642	29	for	for	ADP
ejpam-1372	642	30	asymptotic	asymptotic	ADJ
ejpam-1372	642	31	expansions	expansion	NOUN
ejpam-1372	642	32	written	write	VERB
ejpam-1372	642	33	in	in	ADP
ejpam-1372	642	34	terms	term	NOUN
ejpam-1372	642	35	of	of	ADP
ejpam-1372	642	36	zβ	zβ	PROPN
ejpam-1372	642	37	,	,	PUNCT
ejpam-1372	642	38	where	where	SCONJ
ejpam-1372	642	39	β	β	X
ejpam-1372	642	40	>	>	X
ejpam-1372	642	41	1	1	NUM
ejpam-1372	642	42	,	,	PUNCT
ejpam-1372	642	43	it	it	PRON
ejpam-1372	642	44	will	will	AUX
ejpam-1372	642	45	mean	mean	VERB
ejpam-1372	642	46	that	that	SCONJ
ejpam-1372	642	47	the	the	DET
ejpam-1372	642	48	regularised	regularise	VERB
ejpam-1372	642	49	value	value	NOUN
ejpam-1372	642	50	will	will	AUX
ejpam-1372	642	51	be	be	AUX
ejpam-1372	642	52	singular	singular	ADJ
ejpam-1372	642	53	well	well	ADV
ejpam-1372	642	54	within	within	ADP
ejpam-1372	642	55	inside	inside	ADP
ejpam-1372	642	56	the	the	DET
ejpam-1372	642	57	principal	principal	ADJ
ejpam-1372	642	58	branch	branch	NOUN
ejpam-1372	642	59	.	.	PUNCT
ejpam-1372	643	1	for	for	ADP
ejpam-1372	643	2	example	example	NOUN
ejpam-1372	643	3	,	,	PUNCT
ejpam-1372	643	4	in	in	ADP
ejpam-1372	643	5	the	the	DET
ejpam-1372	643	6	case	case	NOUN
ejpam-1372	643	7	of	of	ADP
ejpam-1372	643	8	the	the	DET
ejpam-1372	643	9	complementary	complementary	ADJ
ejpam-1372	643	10	error	error	NOUN
ejpam-1372	643	11	function	function	NOUN
ejpam-1372	643	12	mentioned	mention	VERB
ejpam-1372	643	13	above	above	ADV
ejpam-1372	643	14	,	,	PUNCT
ejpam-1372	643	15	the	the	DET
ejpam-1372	643	16	cauchy	cauchy	ADJ
ejpam-1372	643	17	integral	integral	NOUN
ejpam-1372	643	18	is	be	AUX
ejpam-1372	643	19	singular	singular	ADJ
ejpam-1372	643	20	along	along	ADP
ejpam-1372	643	21	the	the	DET
ejpam-1372	643	22	positive	positive	ADJ
ejpam-1372	643	23	and	and	CCONJ
ejpam-1372	643	24	negative	negative	ADJ
ejpam-1372	643	25	imaginary	imaginary	ADJ
ejpam-1372	643	26	axes	axis	NOUN
ejpam-1372	643	27	.	.	PUNCT
ejpam-1372	644	1	these	these	DET
ejpam-1372	644	2	issues	issue	NOUN
ejpam-1372	644	3	can	can	AUX
ejpam-1372	644	4	be	be	AUX
ejpam-1372	644	5	resolved	resolve	VERB
ejpam-1372	644	6	as	as	ADP
ejpam-1372	644	7	a	a	DET
ejpam-1372	644	8	result	result	NOUN
ejpam-1372	644	9	of	of	ADP
ejpam-1372	644	10	a	a	DET
ejpam-1372	644	11	remarkable	remarkable	ADJ
ejpam-1372	644	12	discovery	discovery	NOUN
ejpam-1372	644	13	made	make	VERB
ejpam-1372	644	14	in	in	ADP
ejpam-1372	644	15	1857	1857	NUM
ejpam-1372	644	16	by	by	ADP
ejpam-1372	644	17	stokes	stoke	NOUN
ejpam-1372	644	18	[	[	X
ejpam-1372	644	19	31	31	NUM
ejpam-1372	644	20	]	]	PUNCT
ejpam-1372	644	21	of	of	ADP
ejpam-1372	644	22	what	what	PRON
ejpam-1372	644	23	is	be	AUX
ejpam-1372	644	24	known	know	VERB
ejpam-1372	644	25	today	today	NOUN
ejpam-1372	644	26	as	as	ADP
ejpam-1372	644	27	the	the	DET
ejpam-1372	644	28	stokes	stoke	NOUN
ejpam-1372	644	29	phenomenon	phenomenon	NOUN
ejpam-1372	644	30	.	.	PUNCT
ejpam-1372	645	1	stokes	stoke	NOUN
ejpam-1372	645	2	found	find	VERB
ejpam-1372	645	3	that	that	SCONJ
ejpam-1372	645	4	as	as	SCONJ
ejpam-1372	645	5	one	one	NUM
ejpam-1372	645	6	moved	move	VERB
ejpam-1372	645	7	across	across	ADP
ejpam-1372	645	8	specific	specific	ADJ
ejpam-1372	645	9	sectors	sector	NOUN
ejpam-1372	645	10	of	of	ADP
ejpam-1372	645	11	the	the	DET
ejpam-1372	645	12	complex	complex	ADJ
ejpam-1372	645	13	plane	plane	NOUN
ejpam-1372	645	14	,	,	PUNCT
ejpam-1372	645	15	called	call	VERB
ejpam-1372	645	16	stokes	stoke	NOUN
ejpam-1372	645	17	sectors	sector	NOUN
ejpam-1372	645	18	,	,	PUNCT
ejpam-1372	645	19	asymptotic	asymptotic	ADJ
ejpam-1372	645	20	expansions	expansion	NOUN
ejpam-1372	645	21	suddenly	suddenly	ADV
ejpam-1372	645	22	acquired	acquire	VERB
ejpam-1372	645	23	extra	extra	ADJ
ejpam-1372	645	24	or	or	CCONJ
ejpam-1372	645	25	jump	jump	VERB
ejpam-1372	645	26	discontinuous	discontinuous	ADJ
ejpam-1372	645	27	terms	term	NOUN
ejpam-1372	645	28	.	.	PUNCT
ejpam-1372	646	1	these	these	DET
ejpam-1372	646	2	terms	term	NOUN
ejpam-1372	646	3	appear	appear	VERB
ejpam-1372	646	4	at	at	ADP
ejpam-1372	646	5	specific	specific	ADJ
ejpam-1372	646	6	rays	ray	NOUN
ejpam-1372	646	7	in	in	ADP
ejpam-1372	646	8	the	the	DET
ejpam-1372	646	9	complex	complex	ADJ
ejpam-1372	646	10	plane	plane	NOUN
ejpam-1372	646	11	known	know	VERB
ejpam-1372	646	12	as	as	ADP
ejpam-1372	646	13	stokes	stoke	NOUN
ejpam-1372	646	14	lines	line	NOUN
ejpam-1372	646	15	.	.	PUNCT
ejpam-1372	647	1	along	along	ADP
ejpam-1372	647	2	these	these	DET
ejpam-1372	647	3	lines	line	NOUN
ejpam-1372	647	4	the	the	DET
ejpam-1372	647	5	regularised	regularise	VERB
ejpam-1372	647	6	value	value	NOUN
ejpam-1372	647	7	as	as	SCONJ
ejpam-1372	647	8	indicated	indicate	VERB
ejpam-1372	647	9	by	by	ADP
ejpam-1372	647	10	the	the	DET
ejpam-1372	647	11	cauchy	cauchy	PROPN
ejpam-1372	647	12	integral	integral	ADJ
ejpam-1372	647	13	in	in	ADP
ejpam-1372	647	14	equivalence	equivalence	NOUN
ejpam-1372	647	15	(	(	PUNCT
ejpam-1372	647	16	65	65	NUM
ejpam-1372	647	17	)	)	PUNCT
ejpam-1372	647	18	is	be	AUX
ejpam-1372	647	19	singular	singular	ADJ
ejpam-1372	647	20	.	.	PUNCT
ejpam-1372	648	1	moreover	moreover	ADV
ejpam-1372	648	2	,	,	PUNCT
ejpam-1372	648	3	ch	ch	PROPN
ejpam-1372	648	4	.	.	PROPN
ejpam-1372	648	5	1	1	NUM
ejpam-1372	648	6	of	of	ADP
ejpam-1372	648	7	ref	ref	NOUN
ejpam-1372	648	8	.	.	PUNCT
ejpam-1372	649	1	[	[	X
ejpam-1372	649	2	8	8	NUM
ejpam-1372	649	3	]	]	PUNCT
ejpam-1372	649	4	states	state	VERB
ejpam-1372	649	5	that	that	SCONJ
ejpam-1372	649	6	the	the	DET
ejpam-1372	649	7	stokes	stokes	PROPN
ejpam-1372	649	8	lines	line	NOUN
ejpam-1372	649	9	occur	occur	VERB
ejpam-1372	649	10	at	at	ADP
ejpam-1372	649	11	those	those	DET
ejpam-1372	649	12	values	value	NOUN
ejpam-1372	649	13	of	of	ADP
ejpam-1372	649	14	arg	arg	NOUN
ejpam-1372	649	15	z	z	PROPN
ejpam-1372	649	16	,	,	PUNCT
ejpam-1372	649	17	where	where	SCONJ
ejpam-1372	649	18	all	all	DET
ejpam-1372	649	19	the	the	DET
ejpam-1372	649	20	terms	term	NOUN
ejpam-1372	649	21	in	in	ADP
ejpam-1372	649	22	the	the	DET
ejpam-1372	649	23	terminants	terminant	NOUN
ejpam-1372	649	24	are	be	AUX
ejpam-1372	649	25	of	of	ADP
ejpam-1372	649	26	the	the	DET
ejpam-1372	649	27	same	same	ADJ
ejpam-1372	649	28	sign	sign	NOUN
ejpam-1372	649	29	and	and	CCONJ
ejpam-1372	649	30	homogeneous	homogeneous	ADJ
ejpam-1372	649	31	in	in	ADP
ejpam-1372	649	32	phase	phase	NOUN
ejpam-1372	649	33	.	.	PUNCT
ejpam-1372	650	1	for	for	ADP
ejpam-1372	650	2	the	the	DET
ejpam-1372	650	3	first	first	ADJ
ejpam-1372	650	4	type	type	NOUN
ejpam-1372	650	5	of	of	ADP
ejpam-1372	650	6	terminant	terminant	NOUN
ejpam-1372	650	7	this	this	PRON
ejpam-1372	650	8	means	mean	VERB
ejpam-1372	650	9	they	they	PRON
ejpam-1372	650	10	occur	occur	VERB
ejpam-1372	650	11	whenever	whenever	SCONJ
ejpam-1372	650	12	arg	arg	NOUN
ejpam-1372	650	13	z	z	NOUN
ejpam-1372	650	14	=	=	SYM
ejpam-1372	650	15	(	(	PUNCT
ejpam-1372	650	16	2k	2k	NUM
ejpam-1372	650	17	+	+	CCONJ
ejpam-1372	650	18	1)π	1)π	NUM
ejpam-1372	650	19	,	,	PUNCT
ejpam-1372	650	20	where	where	SCONJ
ejpam-1372	650	21	k	k	PROPN
ejpam-1372	650	22	is	be	AUX
ejpam-1372	650	23	an	an	DET
ejpam-1372	650	24	arbitrary	arbitrary	ADJ
ejpam-1372	650	25	integer	integer	NOUN
ejpam-1372	650	26	.	.	PUNCT
ejpam-1372	651	1	hence	hence	ADV
ejpam-1372	651	2	,	,	PUNCT
ejpam-1372	651	3	the	the	DET
ejpam-1372	651	4	regularised	regularise	VERB
ejpam-1372	651	5	value	value	NOUN
ejpam-1372	651	6	given	give	VERB
ejpam-1372	651	7	by	by	ADP
ejpam-1372	651	8	equivalence	equivalence	NOUN
ejpam-1372	651	9	(	(	PUNCT
ejpam-1372	651	10	67	67	NUM
ejpam-1372	651	11	)	)	PUNCT
ejpam-1372	651	12	develops	develop	VERB
ejpam-1372	651	13	extra	extra	ADJ
ejpam-1372	651	14	terms	term	NOUN
ejpam-1372	651	15	as	as	ADP
ejpam-1372	651	16	arg	arg	NOUN
ejpam-1372	651	17	z	z	NOUN
ejpam-1372	651	18	moves	move	VERB
ejpam-1372	651	19	across	across	ADP
ejpam-1372	651	20	these	these	DET
ejpam-1372	651	21	lines	line	NOUN
ejpam-1372	651	22	.	.	PUNCT
ejpam-1372	652	1	in	in	ADP
ejpam-1372	652	2	addition	addition	NOUN
ejpam-1372	652	3	,	,	PUNCT
ejpam-1372	652	4	on	on	ADP
ejpam-1372	652	5	the	the	DET
ejpam-1372	652	6	lines	line	NOUN
ejpam-1372	652	7	the	the	DET
ejpam-1372	652	8	cauchy	cauchy	ADJ
ejpam-1372	652	9	integral	integral	NOUN
ejpam-1372	652	10	will	will	AUX
ejpam-1372	652	11	need	need	VERB
ejpam-1372	652	12	to	to	PART
ejpam-1372	652	13	be	be	AUX
ejpam-1372	652	14	modified	modify	VERB
ejpam-1372	652	15	.	.	PUNCT
ejpam-1372	653	1	it	it	PRON
ejpam-1372	653	2	should	should	AUX
ejpam-1372	653	3	be	be	AUX
ejpam-1372	653	4	emphasised	emphasise	VERB
ejpam-1372	653	5	that	that	SCONJ
ejpam-1372	653	6	stokes	stoke	VERB
ejpam-1372	653	7	sectors	sector	NOUN
ejpam-1372	653	8	and	and	CCONJ
ejpam-1372	653	9	lines	line	NOUN
ejpam-1372	653	10	are	be	AUX
ejpam-1372	653	11	fictitious	fictitious	ADJ
ejpam-1372	653	12	with	with	ADP
ejpam-1372	653	13	regard	regard	NOUN
ejpam-1372	653	14	to	to	ADP
ejpam-1372	653	15	the	the	DET
ejpam-1372	653	16	original	original	ADJ
ejpam-1372	653	17	function	function	NOUN
ejpam-1372	653	18	from	from	ADP
ejpam-1372	653	19	which	which	PRON
ejpam-1372	653	20	an	an	DET
ejpam-1372	653	21	asymptotic	asymptotic	ADJ
ejpam-1372	653	22	expansion	expansion	NOUN
ejpam-1372	653	23	is	be	AUX
ejpam-1372	653	24	derived	derive	VERB
ejpam-1372	653	25	.	.	PUNCT
ejpam-1372	654	1	that	that	PRON
ejpam-1372	654	2	is	be	AUX
ejpam-1372	654	3	,	,	PUNCT
ejpam-1372	654	4	although	although	SCONJ
ejpam-1372	654	5	the	the	DET
ejpam-1372	654	6	asymptotic	asymptotic	ADJ
ejpam-1372	654	7	expansion	expansion	NOUN
ejpam-1372	654	8	develops	develop	VERB
ejpam-1372	654	9	jump	jump	VERB
ejpam-1372	654	10	discontinuities	discontinuity	NOUN
ejpam-1372	654	11	as	as	ADP
ejpam-1372	654	12	the	the	DET
ejpam-1372	654	13	argument	argument	NOUN
ejpam-1372	654	14	of	of	ADP
ejpam-1372	654	15	variable	variable	NOUN
ejpam-1372	654	16	in	in	ADP
ejpam-1372	654	17	the	the	DET
ejpam-1372	654	18	expansion	expansion	NOUN
ejpam-1372	654	19	changes	change	NOUN
ejpam-1372	654	20	in	in	ADP
ejpam-1372	654	21	the	the	DET
ejpam-1372	654	22	complex	complex	ADJ
ejpam-1372	654	23	plane	plane	NOUN
ejpam-1372	654	24	,	,	PUNCT
ejpam-1372	654	25	it	it	PRON
ejpam-1372	654	26	does	do	AUX
ejpam-1372	654	27	not	not	PART
ejpam-1372	654	28	necessarily	necessarily	ADV
ejpam-1372	654	29	mean	mean	VERB
ejpam-1372	654	30	that	that	SCONJ
ejpam-1372	654	31	the	the	DET
ejpam-1372	654	32	original	original	ADJ
ejpam-1372	654	33	function	function	NOUN
ejpam-1372	654	34	is	be	AUX
ejpam-1372	654	35	discontinuous	discontinuous	ADJ
ejpam-1372	654	36	.	.	PUNCT
ejpam-1372	655	1	in	in	ADP
ejpam-1372	655	2	fact	fact	NOUN
ejpam-1372	655	3	,	,	PUNCT
ejpam-1372	655	4	it	it	PRON
ejpam-1372	655	5	is	be	AUX
ejpam-1372	655	6	more	more	ADV
ejpam-1372	655	7	often	often	ADV
ejpam-1372	655	8	than	than	ADP
ejpam-1372	655	9	not	not	PART
ejpam-1372	655	10	continuous	continuous	ADJ
ejpam-1372	655	11	across	across	ADP
ejpam-1372	655	12	the	the	DET
ejpam-1372	655	13	stokes	stokes	PROPN
ejpam-1372	655	14	lines	line	NOUN
ejpam-1372	655	15	of	of	ADP
ejpam-1372	655	16	discontinuity	discontinuity	NOUN
ejpam-1372	655	17	.	.	PUNCT
ejpam-1372	656	1	now	now	ADV
ejpam-1372	656	2	the	the	DET
ejpam-1372	656	3	only	only	ADJ
ejpam-1372	656	4	problem	problem	NOUN
ejpam-1372	656	5	that	that	PRON
ejpam-1372	656	6	remains	remain	VERB
ejpam-1372	656	7	is	be	AUX
ejpam-1372	656	8	determining	determine	VERB
ejpam-1372	656	9	the	the	DET
ejpam-1372	656	10	value	value	NOUN
ejpam-1372	656	11	of	of	ADP
ejpam-1372	656	12	l	l	NOUN
ejpam-1372	656	13	for	for	ADP
ejpam-1372	656	14	which	which	DET
ejpam-1372	656	15	equivalence	equivalence	NOUN
ejpam-1372	656	16	(	(	PUNCT
ejpam-1372	656	17	67	67	NUM
ejpam-1372	656	18	)	)	PUNCT
ejpam-1372	656	19	is	be	AUX
ejpam-1372	656	20	valid	valid	ADJ
ejpam-1372	656	21	.	.	PUNCT
ejpam-1372	657	1	in	in	ADP
ejpam-1372	657	2	actual	actual	ADJ
ejpam-1372	657	3	fact	fact	NOUN
ejpam-1372	657	4	,	,	PUNCT
ejpam-1372	657	5	this	this	DET
ejpam-1372	657	6	value	value	NOUN
ejpam-1372	657	7	is	be	AUX
ejpam-1372	657	8	arbitrary	arbitrary	ADJ
ejpam-1372	657	9	,	,	PUNCT
ejpam-1372	657	10	but	but	CCONJ
ejpam-1372	657	11	once	once	SCONJ
ejpam-1372	657	12	it	it	PRON
ejpam-1372	657	13	is	be	AUX
ejpam-1372	657	14	fixed	fix	VERB
ejpam-1372	657	15	,	,	PUNCT
ejpam-1372	657	16	the	the	DET
ejpam-1372	657	17	regularised	regularise	VERB
ejpam-1372	657	18	value	value	NOUN
ejpam-1372	657	19	will	will	AUX
ejpam-1372	657	20	change	change	VERB
ejpam-1372	657	21	on	on	ADP
ejpam-1372	657	22	reaching	reach	VERB
ejpam-1372	657	23	the	the	DET
ejpam-1372	657	24	stokes	stoke	NOUN
ejpam-1372	657	25	lines	line	NOUN
ejpam-1372	657	26	at	at	ADP
ejpam-1372	657	27	its	its	PRON
ejpam-1372	657	28	boundaries	boundary	NOUN
ejpam-1372	657	29	and	and	CCONJ
ejpam-1372	657	30	then	then	ADV
ejpam-1372	657	31	from	from	ADP
ejpam-1372	657	32	each	each	DET
ejpam-1372	657	33	stokes	stoke	NOUN
ejpam-1372	657	34	line	line	NOUN
ejpam-1372	657	35	to	to	ADP
ejpam-1372	657	36	the	the	DET
ejpam-1372	657	37	adjacent	adjacent	ADJ
ejpam-1372	657	38	stokes	stoke	NOUN
ejpam-1372	657	39	sectors	sector	NOUN
ejpam-1372	657	40	.	.	PUNCT
ejpam-1372	658	1	because	because	SCONJ
ejpam-1372	658	2	of	of	ADP
ejpam-1372	658	3	the	the	DET
ejpam-1372	658	4	arbitrariness	arbitrariness	NOUN
ejpam-1372	658	5	in	in	ADP
ejpam-1372	658	6	the	the	DET
ejpam-1372	658	7	choice	choice	NOUN
ejpam-1372	658	8	of	of	ADP
ejpam-1372	658	9	a	a	DET
ejpam-1372	658	10	primary	primary	ADJ
ejpam-1372	658	11	stokes	stoke	NOUN
ejpam-1372	658	12	sector	sector	NOUN
ejpam-1372	658	13	,	,	PUNCT
ejpam-1372	658	14	one	one	PRON
ejpam-1372	658	15	can	can	AUX
ejpam-1372	658	16	no	no	ADV
ejpam-1372	658	17	longer	long	ADV
ejpam-1372	658	18	only	only	ADV
ejpam-1372	658	19	provide	provide	VERB
ejpam-1372	658	20	a	a	DET
ejpam-1372	658	21	regularised	regularise	VERB
ejpam-1372	658	22	value	value	NOUN
ejpam-1372	658	23	to	to	ADP
ejpam-1372	658	24	a	a	DET
ejpam-1372	658	25	series	series	NOUN
ejpam-1372	658	26	expansion	expansion	NOUN
ejpam-1372	658	27	to	to	PART
ejpam-1372	658	28	represent	represent	VERB
ejpam-1372	658	29	a	a	DET
ejpam-1372	658	30	function	function	NOUN
ejpam-1372	658	31	.	.	PUNCT
ejpam-1372	659	1	accompanying	accompany	VERB
ejpam-1372	659	2	the	the	DET
ejpam-1372	659	3	regularised	regularise	VERB
ejpam-1372	659	4	value	value	NOUN
ejpam-1372	659	5	must	must	AUX
ejpam-1372	659	6	also	also	ADV
ejpam-1372	659	7	be	be	AUX
ejpam-1372	659	8	the	the	DET
ejpam-1372	659	9	values	value	NOUN
ejpam-1372	659	10	of	of	ADP
ejpam-1372	659	11	arg	arg	NOUN
ejpam-1372	659	12	z	z	NOUN
ejpam-1372	659	13	for	for	ADP
ejpam-1372	659	14	which	which	PRON
ejpam-1372	659	15	it	it	PRON
ejpam-1372	659	16	is	be	AUX
ejpam-1372	659	17	v.	v.	ADP
ejpam-1372	659	18	kowalenko	kowalenko	PROPN
ejpam-1372	659	19	/	/	SYM
ejpam-1372	659	20	eur	eur	PROPN
ejpam-1372	659	21	.	.	PUNCT
ejpam-1372	660	1	j.	j.	PROPN
ejpam-1372	660	2	pure	pure	PROPN
ejpam-1372	660	3	appl	appl	PROPN
ejpam-1372	660	4	.	.	PROPN
ejpam-1372	660	5	math	math	PROPN
ejpam-1372	660	6	,	,	PUNCT
ejpam-1372	660	7	4	4	NUM
ejpam-1372	660	8	(	(	PUNCT
ejpam-1372	660	9	2011	2011	NUM
ejpam-1372	660	10	)	)	PUNCT
ejpam-1372	660	11	,	,	PUNCT
ejpam-1372	660	12	370	370	NUM
ejpam-1372	660	13	-	-	SYM
ejpam-1372	660	14	423	423	NUM
ejpam-1372	660	15	392	392	NUM
ejpam-1372	660	16	valid	valid	NOUN
ejpam-1372	660	17	.	.	PUNCT
ejpam-1372	661	1	this	this	PRON
ejpam-1372	661	2	applies	apply	VERB
ejpam-1372	661	3	to	to	ADP
ejpam-1372	661	4	both	both	DET
ejpam-1372	661	5	stokes	stoke	NOUN
ejpam-1372	661	6	sectors	sector	NOUN
ejpam-1372	661	7	and	and	CCONJ
ejpam-1372	661	8	lines	line	NOUN
ejpam-1372	661	9	.	.	PUNCT
ejpam-1372	662	1	we	we	PRON
ejpam-1372	662	2	shall	shall	AUX
ejpam-1372	662	3	refer	refer	VERB
ejpam-1372	662	4	to	to	ADP
ejpam-1372	662	5	the	the	DET
ejpam-1372	662	6	combination	combination	NOUN
ejpam-1372	662	7	of	of	ADP
ejpam-1372	662	8	the	the	DET
ejpam-1372	662	9	series	series	NOUN
ejpam-1372	662	10	expansion	expansion	NOUN
ejpam-1372	662	11	,	,	PUNCT
ejpam-1372	662	12	regularised	regularise	VERB
ejpam-1372	662	13	value	value	NOUN
ejpam-1372	662	14	and	and	CCONJ
ejpam-1372	662	15	the	the	DET
ejpam-1372	662	16	stokes	stoke	NOUN
ejpam-1372	662	17	sector	sector	NOUN
ejpam-1372	662	18	over	over	ADP
ejpam-1372	662	19	which	which	PRON
ejpam-1372	662	20	the	the	DET
ejpam-1372	662	21	latter	latter	ADJ
ejpam-1372	662	22	is	be	AUX
ejpam-1372	662	23	valid	valid	ADJ
ejpam-1372	662	24	as	as	ADP
ejpam-1372	662	25	an	an	DET
ejpam-1372	662	26	asymptotic	asymptotic	ADJ
ejpam-1372	662	27	form	form	NOUN
ejpam-1372	662	28	.	.	PUNCT
ejpam-1372	663	1	frequently	frequently	ADV
ejpam-1372	663	2	,	,	PUNCT
ejpam-1372	663	3	asymptotic	asymptotic	ADJ
ejpam-1372	663	4	expansions	expansion	NOUN
ejpam-1372	663	5	are	be	AUX
ejpam-1372	663	6	derived	derive	VERB
ejpam-1372	663	7	when	when	SCONJ
ejpam-1372	663	8	the	the	DET
ejpam-1372	663	9	argument	argument	NOUN
ejpam-1372	663	10	of	of	ADP
ejpam-1372	663	11	the	the	DET
ejpam-1372	663	12	variable	variable	NOUN
ejpam-1372	663	13	is	be	AUX
ejpam-1372	663	14	real	real	ADJ
ejpam-1372	663	15	,	,	PUNCT
ejpam-1372	663	16	positive	positive	ADJ
ejpam-1372	663	17	and	and	CCONJ
ejpam-1372	663	18	situated	situate	VERB
ejpam-1372	663	19	in	in	ADP
ejpam-1372	663	20	the	the	DET
ejpam-1372	663	21	principal	principal	ADJ
ejpam-1372	663	22	branch	branch	NOUN
ejpam-1372	663	23	of	of	ADP
ejpam-1372	663	24	the	the	DET
ejpam-1372	663	25	complex	complex	ADJ
ejpam-1372	663	26	plane	plane	NOUN
ejpam-1372	663	27	.	.	PUNCT
ejpam-1372	664	1	if	if	SCONJ
ejpam-1372	664	2	this	this	PRON
ejpam-1372	664	3	is	be	AUX
ejpam-1372	664	4	the	the	DET
ejpam-1372	664	5	case	case	NOUN
ejpam-1372	664	6	,	,	PUNCT
ejpam-1372	664	7	then	then	ADV
ejpam-1372	664	8	we	we	PRON
ejpam-1372	664	9	let	let	VERB
ejpam-1372	664	10	the	the	DET
ejpam-1372	664	11	primary	primary	ADJ
ejpam-1372	664	12	stokes	stoke	NOUN
ejpam-1372	664	13	sector	sector	NOUN
ejpam-1372	664	14	for	for	ADP
ejpam-1372	664	15	equivalence	equivalence	NOUN
ejpam-1372	664	16	(	(	PUNCT
ejpam-1372	664	17	67	67	NUM
ejpam-1372	664	18	)	)	PUNCT
ejpam-1372	664	19	be	be	AUX
ejpam-1372	664	20	given	give	VERB
ejpam-1372	664	21	by	by	ADP
ejpam-1372	664	22	the	the	DET
ejpam-1372	664	23	l=0	l=0	PROPN
ejpam-1372	664	24	value	value	NOUN
ejpam-1372	664	25	or	or	CCONJ
ejpam-1372	664	26	in	in	ADP
ejpam-1372	664	27	other	other	ADJ
ejpam-1372	664	28	words	word	NOUN
ejpam-1372	664	29	,	,	PUNCT
ejpam-1372	664	30	by	by	ADP
ejpam-1372	664	31	|arg	|arg	NOUN
ejpam-1372	664	32	z|<π	z|<π	PROPN
ejpam-1372	664	33	.	.	PUNCT
ejpam-1372	665	1	hence	hence	ADV
ejpam-1372	665	2	,	,	PUNCT
ejpam-1372	665	3	equivalence	equivalence	NOUN
ejpam-1372	665	4	(	(	PUNCT
ejpam-1372	665	5	66	66	NUM
ejpam-1372	665	6	)	)	PUNCT
ejpam-1372	665	7	as	as	ADP
ejpam-1372	665	8	an	an	DET
ejpam-1372	665	9	asymptotic	asymptotic	ADJ
ejpam-1372	665	10	form	form	NOUN
ejpam-1372	665	11	becomes	become	VERB
ejpam-1372	665	12	ti	ti	NOUN
ejpam-1372	665	13	(	(	PUNCT
ejpam-1372	665	14	n	n	X
ejpam-1372	665	15	,	,	PUNCT
ejpam-1372	665	16	α	α	PROPN
ejpam-1372	665	17	,	,	PUNCT
ejpam-1372	665	18	z	z	NOUN
ejpam-1372	665	19	)	)	PUNCT
ejpam-1372	665	20	≡	≡	PROPN
ejpam-1372	665	21	(	(	PUNCT
ejpam-1372	665	22	−z)n	−z)n	X
ejpam-1372	665	23	∫	∫	PROPN
ejpam-1372	665	24	∞	∞	PROPN
ejpam-1372	665	25	0	0	PUNCT
ejpam-1372	666	1	d	d	PRON
ejpam-1372	666	2	t	t	NOUN
ejpam-1372	666	3	tn+α−1	tn+α−1	NOUN
ejpam-1372	666	4	e−t	e−t	NOUN
ejpam-1372	666	5	1	1	NUM
ejpam-1372	666	6	+	+	NUM
ejpam-1372	666	7	zt	zt	PROPN
ejpam-1372	666	8	,	,	PUNCT
ejpam-1372	666	9	|arg	|arg	VERB
ejpam-1372	666	10	z|	z|	PROPN
ejpam-1372	666	11	<	<	X
ejpam-1372	666	12	π	π	X
ejpam-1372	666	13	.	.	PUNCT
ejpam-1372	667	1	(	(	PUNCT
ejpam-1372	667	2	70	70	X
ejpam-1372	667	3	)	)	PUNCT
ejpam-1372	667	4	let	let	VERB
ejpam-1372	667	5	us	we	PRON
ejpam-1372	667	6	now	now	ADV
ejpam-1372	667	7	turn	turn	VERB
ejpam-1372	667	8	our	our	PRON
ejpam-1372	667	9	attention	attention	NOUN
ejpam-1372	667	10	to	to	ADP
ejpam-1372	667	11	the	the	DET
ejpam-1372	667	12	second	second	ADJ
ejpam-1372	667	13	type	type	NOUN
ejpam-1372	667	14	of	of	ADP
ejpam-1372	667	15	terminant	terminant	NOUN
ejpam-1372	667	16	given	give	VERB
ejpam-1372	667	17	by	by	ADP
ejpam-1372	667	18	eq	eq	PROPN
ejpam-1372	667	19	.	.	PUNCT
ejpam-1372	668	1	(	(	PUNCT
ejpam-1372	668	2	64	64	NUM
ejpam-1372	668	3	)	)	PUNCT
ejpam-1372	668	4	.	.	PUNCT
ejpam-1372	669	1	borel	borel	PROPN
ejpam-1372	669	2	summation	summation	NOUN
ejpam-1372	669	3	of	of	ADP
ejpam-1372	669	4	this	this	DET
ejpam-1372	669	5	result	result	NOUN
ejpam-1372	669	6	yields	yield	VERB
ejpam-1372	669	7	ti	ti	NOUN
ejpam-1372	669	8	i(n	i(n	PROPN
ejpam-1372	669	9	,	,	PUNCT
ejpam-1372	670	1	α	α	NOUN
ejpam-1372	670	2	,	,	PUNCT
ejpam-1372	670	3	z	z	NOUN
ejpam-1372	670	4	)	)	PUNCT
ejpam-1372	670	5	≡	≡	PROPN
ejpam-1372	671	1	zn	zn	PROPN
ejpam-1372	671	2	∫	∫	PROPN
ejpam-1372	672	1	∞	∞	PROPN
ejpam-1372	672	2	0	0	PUNCT
ejpam-1372	673	1	d	d	PRON
ejpam-1372	673	2	t	t	NOUN
ejpam-1372	673	3	tn+α−1	tn+α−1	PROPN
ejpam-1372	673	4	e−t	e−t	NOUN
ejpam-1372	673	5	1−	1−	NUM
ejpam-1372	673	6	zt	zt	INTJ
ejpam-1372	673	7	.	.	PUNCT
ejpam-1372	674	1	(	(	PUNCT
ejpam-1372	674	2	71	71	NUM
ejpam-1372	674	3	)	)	PUNCT
ejpam-1372	674	4	if	if	SCONJ
ejpam-1372	674	5	z	z	NOUN
ejpam-1372	674	6	is	be	AUX
ejpam-1372	674	7	replaced	replace	VERB
ejpam-1372	674	8	by	by	ADP
ejpam-1372	674	9	z	z	PROPN
ejpam-1372	674	10	exp(−2l	exp(−2l	NOUN
ejpam-1372	674	11	iπ	iπ	NOUN
ejpam-1372	674	12	)	)	PUNCT
ejpam-1372	674	13	,	,	PUNCT
ejpam-1372	674	14	where	where	SCONJ
ejpam-1372	674	15	l	l	NOUN
ejpam-1372	674	16	is	be	AUX
ejpam-1372	674	17	an	an	DET
ejpam-1372	674	18	arbitrary	arbitrary	ADJ
ejpam-1372	674	19	integer	integer	NOUN
ejpam-1372	674	20	integer	integer	NOUN
ejpam-1372	674	21	,	,	PUNCT
ejpam-1372	674	22	then	then	ADV
ejpam-1372	674	23	equivalence	equivalence	NOUN
ejpam-1372	674	24	(	(	PUNCT
ejpam-1372	674	25	71	71	NUM
ejpam-1372	674	26	)	)	PUNCT
ejpam-1372	674	27	becomes	become	VERB
ejpam-1372	674	28	ti	ti	PROPN
ejpam-1372	674	29	i(n	i(n	PROPN
ejpam-1372	674	30	,	,	PUNCT
ejpam-1372	674	31	α	α	X
ejpam-1372	674	32	,	,	PUNCT
ejpam-1372	674	33	z	z	NOUN
ejpam-1372	674	34	exp(−2ilπ))≡	exp(−2ilπ))≡	X
ejpam-1372	675	1	zn	zn	X
ejpam-1372	675	2	∫	∫	PROPN
ejpam-1372	675	3	∞	∞	PROPN
ejpam-1372	675	4	0	0	PUNCT
ejpam-1372	676	1	d	d	PRON
ejpam-1372	676	2	t	t	NOUN
ejpam-1372	676	3	tn+α−1	tn+α−1	NOUN
ejpam-1372	676	4	e−t	e−t	NOUN
ejpam-1372	676	5	1−	1−	NUM
ejpam-1372	676	6	z	z	NOUN
ejpam-1372	676	7	exp(−2ilπ)t	exp(−2ilπ)t	NOUN
ejpam-1372	676	8	.	.	PUNCT
ejpam-1372	677	1	(	(	PUNCT
ejpam-1372	677	2	72	72	NUM
ejpam-1372	677	3	)	)	PUNCT
ejpam-1372	677	4	whilst	whilst	SCONJ
ejpam-1372	677	5	the	the	DET
ejpam-1372	677	6	integral	integral	ADJ
ejpam-1372	677	7	in	in	ADP
ejpam-1372	677	8	the	the	DET
ejpam-1372	677	9	above	above	ADJ
ejpam-1372	677	10	equivalence	equivalence	NOUN
ejpam-1372	677	11	is	be	AUX
ejpam-1372	677	12	defined	define	VERB
ejpam-1372	677	13	for	for	ADP
ejpam-1372	677	14	complex	complex	ADJ
ejpam-1372	677	15	values	value	NOUN
ejpam-1372	677	16	of	of	ADP
ejpam-1372	677	17	z	z	NOUN
ejpam-1372	677	18	,	,	PUNCT
ejpam-1372	677	19	it	it	PRON
ejpam-1372	677	20	is	be	AUX
ejpam-1372	677	21	singular	singular	ADJ
ejpam-1372	677	22	for	for	ADP
ejpam-1372	677	23	positive	positive	ADJ
ejpam-1372	677	24	real	real	ADJ
ejpam-1372	677	25	values	value	NOUN
ejpam-1372	677	26	of	of	ADP
ejpam-1372	677	27	z.	z.	PROPN
ejpam-1372	677	28	this	this	PRON
ejpam-1372	677	29	is	be	AUX
ejpam-1372	677	30	a	a	DET
ejpam-1372	677	31	problem	problem	NOUN
ejpam-1372	677	32	since	since	SCONJ
ejpam-1372	677	33	it	it	PRON
ejpam-1372	677	34	has	have	AUX
ejpam-1372	677	35	already	already	ADV
ejpam-1372	677	36	been	be	AUX
ejpam-1372	677	37	stated	state	VERB
ejpam-1372	677	38	that	that	SCONJ
ejpam-1372	677	39	whenever	whenever	SCONJ
ejpam-1372	677	40	a	a	DET
ejpam-1372	677	41	type	type	NOUN
ejpam-1372	677	42	ii	ii	NOUN
ejpam-1372	677	43	asymptotic	asymptotic	ADJ
ejpam-1372	677	44	expansion	expansion	NOUN
ejpam-1372	677	45	is	be	AUX
ejpam-1372	677	46	derived	derive	VERB
ejpam-1372	677	47	,	,	PUNCT
ejpam-1372	677	48	it	it	PRON
ejpam-1372	677	49	is	be	AUX
ejpam-1372	677	50	usually	usually	ADV
ejpam-1372	677	51	for	for	ADP
ejpam-1372	677	52	these	these	DET
ejpam-1372	677	53	values	value	NOUN
ejpam-1372	677	54	of	of	ADP
ejpam-1372	677	55	z.	z.	PROPN
ejpam-1372	677	56	the	the	DET
ejpam-1372	677	57	situation	situation	NOUN
ejpam-1372	677	58	can	can	AUX
ejpam-1372	677	59	be	be	AUX
ejpam-1372	677	60	resolved	resolve	VERB
ejpam-1372	677	61	by	by	ADP
ejpam-1372	677	62	noting	note	VERB
ejpam-1372	677	63	that	that	SCONJ
ejpam-1372	677	64	the	the	DET
ejpam-1372	677	65	stokes	stokes	PROPN
ejpam-1372	677	66	lines	line	NOUN
ejpam-1372	677	67	for	for	ADP
ejpam-1372	677	68	this	this	DET
ejpam-1372	677	69	type	type	NOUN
ejpam-1372	677	70	of	of	ADP
ejpam-1372	677	71	terminant	terminant	NOUN
ejpam-1372	677	72	occur	occur	VERB
ejpam-1372	677	73	at	at	ADP
ejpam-1372	677	74	arg	arg	NOUN
ejpam-1372	677	75	z=	z=	NOUN
ejpam-1372	677	76	2kπ	2kπ	NOUN
ejpam-1372	677	77	,	,	PUNCT
ejpam-1372	677	78	where	where	SCONJ
ejpam-1372	677	79	k	k	PROPN
ejpam-1372	677	80	is	be	AUX
ejpam-1372	677	81	an	an	DET
ejpam-1372	677	82	arbitrary	arbitrary	ADJ
ejpam-1372	677	83	integer	integer	NOUN
ejpam-1372	677	84	.	.	PUNCT
ejpam-1372	678	1	consequently	consequently	ADV
ejpam-1372	678	2	,	,	PUNCT
ejpam-1372	678	3	instead	instead	ADV
ejpam-1372	678	4	of	of	ADP
ejpam-1372	678	5	nominating	nominate	VERB
ejpam-1372	678	6	a	a	DET
ejpam-1372	678	7	primary	primary	ADJ
ejpam-1372	678	8	stokes	stoke	NOUN
ejpam-1372	678	9	sector	sector	NOUN
ejpam-1372	678	10	,	,	PUNCT
ejpam-1372	678	11	we	we	PRON
ejpam-1372	678	12	must	must	AUX
ejpam-1372	678	13	now	now	ADV
ejpam-1372	678	14	nominate	nominate	VERB
ejpam-1372	678	15	a	a	DET
ejpam-1372	678	16	primary	primary	ADJ
ejpam-1372	678	17	stokes	stoke	NOUN
ejpam-1372	678	18	line	line	NOUN
ejpam-1372	678	19	.	.	PUNCT
ejpam-1372	679	1	again	again	ADV
ejpam-1372	679	2	,	,	PUNCT
ejpam-1372	679	3	this	this	PRON
ejpam-1372	679	4	is	be	AUX
ejpam-1372	679	5	arbitrary	arbitrary	ADJ
ejpam-1372	679	6	,	,	PUNCT
ejpam-1372	679	7	but	but	CCONJ
ejpam-1372	679	8	we	we	PRON
ejpam-1372	679	9	shall	shall	AUX
ejpam-1372	679	10	take	take	VERB
ejpam-1372	679	11	it	it	PRON
ejpam-1372	679	12	to	to	PART
ejpam-1372	679	13	be	be	AUX
ejpam-1372	679	14	the	the	DET
ejpam-1372	679	15	k=	k=	ADJ
ejpam-1372	679	16	0	0	NUM
ejpam-1372	679	17	line	line	NOUN
ejpam-1372	679	18	.	.	PUNCT
ejpam-1372	680	1	furthermore	furthermore	ADV
ejpam-1372	680	2	,	,	PUNCT
ejpam-1372	680	3	in	in	ADP
ejpam-1372	680	4	accordance	accordance	NOUN
ejpam-1372	680	5	with	with	ADP
ejpam-1372	680	6	the	the	DET
ejpam-1372	680	7	rules	rule	NOUN
ejpam-1372	680	8	for	for	ADP
ejpam-1372	680	9	the	the	DET
ejpam-1372	680	10	stokes	stoke	NOUN
ejpam-1372	680	11	phenomenon	phenomenon	NOUN
ejpam-1372	680	12	given	give	VERB
ejpam-1372	680	13	in	in	ADP
ejpam-1372	680	14	ch	ch	PROPN
ejpam-1372	680	15	.	.	PROPN
ejpam-1372	680	16	1	1	NUM
ejpam-1372	680	17	of	of	ADP
ejpam-1372	680	18	ref	ref	NOUN
ejpam-1372	680	19	.	.	PUNCT
ejpam-1372	681	1	[	[	X
ejpam-1372	681	2	8	8	NUM
ejpam-1372	681	3	]	]	PUNCT
ejpam-1372	681	4	,	,	PUNCT
ejpam-1372	681	5	as	as	ADV
ejpam-1372	681	6	soon	soon	ADV
ejpam-1372	681	7	as	as	SCONJ
ejpam-1372	681	8	arg	arg	NOUN
ejpam-1372	681	9	z	z	NOUN
ejpam-1372	681	10	moves	move	VERB
ejpam-1372	681	11	off	off	ADP
ejpam-1372	681	12	this	this	DET
ejpam-1372	681	13	line	line	NOUN
ejpam-1372	681	14	in	in	ADP
ejpam-1372	681	15	either	either	DET
ejpam-1372	681	16	direction	direction	NOUN
ejpam-1372	681	17	,	,	PUNCT
ejpam-1372	681	18	the	the	DET
ejpam-1372	681	19	regularised	regularise	VERB
ejpam-1372	681	20	value	value	NOUN
ejpam-1372	681	21	must	must	AUX
ejpam-1372	681	22	acquire	acquire	VERB
ejpam-1372	681	23	jump	jump	NOUN
ejpam-1372	681	24	discontinuous	discontinuous	ADJ
ejpam-1372	681	25	terms	term	NOUN
ejpam-1372	681	26	.	.	PUNCT
ejpam-1372	682	1	this	this	PRON
ejpam-1372	682	2	produces	produce	VERB
ejpam-1372	682	3	two	two	NUM
ejpam-1372	682	4	more	more	ADJ
ejpam-1372	682	5	problems	problem	NOUN
ejpam-1372	682	6	:	:	PUNCT
ejpam-1372	682	7	1	1	X
ejpam-1372	682	8	.	.	PUNCT
ejpam-1372	682	9	because	because	SCONJ
ejpam-1372	682	10	of	of	ADP
ejpam-1372	682	11	the	the	DET
ejpam-1372	682	12	singularity	singularity	NOUN
ejpam-1372	682	13	occurring	occur	VERB
ejpam-1372	682	14	at	at	ADP
ejpam-1372	682	15	t=1	t=1	PROPN
ejpam-1372	682	16	/	/	SYM
ejpam-1372	682	17	z	z	NOUN
ejpam-1372	682	18	,	,	PUNCT
ejpam-1372	682	19	how	how	SCONJ
ejpam-1372	682	20	do	do	AUX
ejpam-1372	682	21	we	we	PRON
ejpam-1372	682	22	interpret	interpret	VERB
ejpam-1372	682	23	equivalence	equivalence	NOUN
ejpam-1372	682	24	(	(	PUNCT
ejpam-1372	682	25	72	72	NUM
ejpam-1372	682	26	)	)	PUNCT
ejpam-1372	682	27	along	along	ADP
ejpam-1372	682	28	the	the	DET
ejpam-1372	682	29	primary	primary	ADJ
ejpam-1372	682	30	stokes	stoke	NOUN
ejpam-1372	682	31	line	line	NOUN
ejpam-1372	682	32	?	?	PUNCT
ejpam-1372	683	1	2	2	X
ejpam-1372	683	2	.	.	X
ejpam-1372	683	3	what	what	PRON
ejpam-1372	683	4	are	be	AUX
ejpam-1372	683	5	the	the	DET
ejpam-1372	683	6	jump	jump	NOUN
ejpam-1372	683	7	discontinuous	discontinuous	ADJ
ejpam-1372	683	8	terms	term	NOUN
ejpam-1372	683	9	when	when	SCONJ
ejpam-1372	683	10	arg	arg	VERB
ejpam-1372	683	11	z	z	PROPN
ejpam-1372	683	12	6=	6=	PROPN
ejpam-1372	683	13	0	0	X
ejpam-1372	683	14	?	?	PUNCT
ejpam-1372	684	1	note	note	VERB
ejpam-1372	684	2	that	that	SCONJ
ejpam-1372	684	3	these	these	DET
ejpam-1372	684	4	problems	problem	NOUN
ejpam-1372	684	5	apply	apply	VERB
ejpam-1372	684	6	to	to	ADP
ejpam-1372	684	7	the	the	DET
ejpam-1372	684	8	first	first	ADJ
ejpam-1372	684	9	type	type	NOUN
ejpam-1372	684	10	of	of	ADP
ejpam-1372	684	11	terminant	terminant	NOUN
ejpam-1372	684	12	when	when	SCONJ
ejpam-1372	684	13	arg	arg	NOUN
ejpam-1372	684	14	z	z	PROPN
ejpam-1372	684	15	reaches	reach	VERB
ejpam-1372	684	16	the	the	DET
ejpam-1372	684	17	boundary	boundary	NOUN
ejpam-1372	684	18	of	of	ADP
ejpam-1372	684	19	the	the	DET
ejpam-1372	684	20	principal	principal	ADJ
ejpam-1372	684	21	branch	branch	NOUN
ejpam-1372	684	22	of	of	ADP
ejpam-1372	684	23	the	the	DET
ejpam-1372	684	24	complex	complex	ADJ
ejpam-1372	684	25	plane	plane	NOUN
ejpam-1372	684	26	,	,	PUNCT
ejpam-1372	684	27	i.e.	i.e.	X
ejpam-1372	684	28	when	when	SCONJ
ejpam-1372	684	29	arg	arg	NOUN
ejpam-1372	684	30	z=±π	z=±π	PROPN
ejpam-1372	684	31	.	.	PUNCT
ejpam-1372	685	1	we	we	PRON
ejpam-1372	685	2	shall	shall	AUX
ejpam-1372	685	3	be	be	AUX
ejpam-1372	685	4	able	able	ADJ
ejpam-1372	685	5	to	to	PART
ejpam-1372	685	6	consider	consider	VERB
ejpam-1372	685	7	this	this	DET
ejpam-1372	685	8	situation	situation	NOUN
ejpam-1372	685	9	when	when	SCONJ
ejpam-1372	685	10	the	the	DET
ejpam-1372	685	11	type	type	NOUN
ejpam-1372	685	12	ii	ii	NOUN
ejpam-1372	685	13	situation	situation	NOUN
ejpam-1372	685	14	has	have	AUX
ejpam-1372	685	15	been	be	AUX
ejpam-1372	685	16	resolved	resolve	VERB
ejpam-1372	685	17	.	.	PUNCT
ejpam-1372	686	1	both	both	CCONJ
ejpam-1372	686	2	the	the	DET
ejpam-1372	686	3	problems	problem	NOUN
ejpam-1372	686	4	mentioned	mention	VERB
ejpam-1372	686	5	in	in	ADP
ejpam-1372	686	6	the	the	DET
ejpam-1372	686	7	previous	previous	ADJ
ejpam-1372	686	8	paragraph	paragraph	NOUN
ejpam-1372	686	9	are	be	AUX
ejpam-1372	686	10	addressed	address	VERB
ejpam-1372	686	11	and	and	CCONJ
ejpam-1372	686	12	actually	actually	ADV
ejpam-1372	686	13	resolved	resolve	VERB
ejpam-1372	686	14	by	by	ADP
ejpam-1372	686	15	dingle	dingle	NOUN
ejpam-1372	686	16	in	in	ADP
ejpam-1372	686	17	ref	ref	NOUN
ejpam-1372	686	18	.	.	PUNCT
ejpam-1372	687	1	[	[	X
ejpam-1372	687	2	8	8	NUM
ejpam-1372	687	3	]	]	PUNCT
ejpam-1372	687	4	.	.	PUNCT
ejpam-1372	688	1	for	for	ADP
ejpam-1372	688	2	the	the	DET
ejpam-1372	688	3	first	first	ADJ
ejpam-1372	688	4	problem	problem	NOUN
ejpam-1372	688	5	he	he	PRON
ejpam-1372	688	6	points	point	VERB
ejpam-1372	688	7	out	out	ADP
ejpam-1372	688	8	that	that	SCONJ
ejpam-1372	688	9	since	since	SCONJ
ejpam-1372	688	10	the	the	DET
ejpam-1372	688	11	variable	variable	NOUN
ejpam-1372	688	12	and	and	CCONJ
ejpam-1372	688	13	terms	term	NOUN
ejpam-1372	688	14	in	in	ADP
ejpam-1372	688	15	the	the	DET
ejpam-1372	688	16	series	series	NOUN
ejpam-1372	688	17	are	be	AUX
ejpam-1372	688	18	all	all	ADV
ejpam-1372	688	19	positive	positive	ADJ
ejpam-1372	688	20	and	and	CCONJ
ejpam-1372	688	21	real	real	ADJ
ejpam-1372	688	22	along	along	ADP
ejpam-1372	688	23	the	the	DET
ejpam-1372	688	24	primary	primary	ADJ
ejpam-1372	688	25	stokes	stokes	PROPN
ejpam-1372	688	26	line	line	NOUN
ejpam-1372	688	27	,	,	PUNCT
ejpam-1372	688	28	which	which	PRON
ejpam-1372	688	29	we	we	PRON
ejpam-1372	688	30	have	have	VERB
ejpam-1372	688	31	v.	v.	ADP
ejpam-1372	688	32	kowalenko	kowalenko	PROPN
ejpam-1372	688	33	/	/	SYM
ejpam-1372	688	34	eur	eur	PROPN
ejpam-1372	688	35	.	.	PUNCT
ejpam-1372	689	1	j.	j.	PROPN
ejpam-1372	689	2	pure	pure	PROPN
ejpam-1372	689	3	appl	appl	PROPN
ejpam-1372	689	4	.	.	PROPN
ejpam-1372	689	5	math	math	PROPN
ejpam-1372	689	6	,	,	PUNCT
ejpam-1372	689	7	4	4	NUM
ejpam-1372	689	8	(	(	PUNCT
ejpam-1372	689	9	2011	2011	NUM
ejpam-1372	689	10	)	)	PUNCT
ejpam-1372	689	11	,	,	PUNCT
ejpam-1372	689	12	370	370	NUM
ejpam-1372	689	13	-	-	SYM
ejpam-1372	689	14	423	423	NUM
ejpam-1372	689	15	393	393	NUM
ejpam-1372	689	16	taken	take	VERB
ejpam-1372	689	17	to	to	PART
ejpam-1372	689	18	be	be	AUX
ejpam-1372	689	19	arg	arg	NOUN
ejpam-1372	689	20	z	z	NOUN
ejpam-1372	689	21	=	=	SYM
ejpam-1372	689	22	0	0	NUM
ejpam-1372	689	23	,	,	PUNCT
ejpam-1372	689	24	an	an	DET
ejpam-1372	689	25	initially	initially	ADV
ejpam-1372	689	26	real	real	ADJ
ejpam-1372	689	27	function	function	NOUN
ejpam-1372	689	28	can	can	AUX
ejpam-1372	689	29	not	not	PART
ejpam-1372	689	30	acquire	acquire	VERB
ejpam-1372	689	31	an	an	DET
ejpam-1372	689	32	imaginary	imaginary	ADJ
ejpam-1372	689	33	part	part	NOUN
ejpam-1372	689	34	.	.	PUNCT
ejpam-1372	690	1	this	this	DET
ejpam-1372	690	2	concept	concept	NOUN
ejpam-1372	690	3	is	be	AUX
ejpam-1372	690	4	based	base	VERB
ejpam-1372	690	5	on	on	ADP
ejpam-1372	690	6	the	the	DET
ejpam-1372	690	7	pioneering	pioneering	ADJ
ejpam-1372	690	8	work	work	NOUN
ejpam-1372	690	9	of	of	ADP
ejpam-1372	690	10	zwaan	zwaan	PROPN
ejpam-1372	690	11	[	[	X
ejpam-1372	690	12	35	35	NUM
ejpam-1372	690	13	]	]	PUNCT
ejpam-1372	690	14	and	and	CCONJ
ejpam-1372	690	15	is	be	AUX
ejpam-1372	690	16	referred	refer	VERB
ejpam-1372	690	17	to	to	ADP
ejpam-1372	690	18	as	as	ADP
ejpam-1372	690	19	the	the	DET
ejpam-1372	690	20	zwaan	zwaan	NOUN
ejpam-1372	690	21	-	-	PUNCT
ejpam-1372	690	22	dingle	dingle	NOUN
ejpam-1372	690	23	principle	principle	NOUN
ejpam-1372	690	24	in	in	ADP
ejpam-1372	690	25	ref	ref	NOUN
ejpam-1372	690	26	.	.	PUNCT
ejpam-1372	691	1	[	[	X
ejpam-1372	691	2	17	17	NUM
ejpam-1372	691	3	]	]	PUNCT
ejpam-1372	691	4	.	.	PUNCT
ejpam-1372	692	1	basically	basically	ADV
ejpam-1372	692	2	,	,	PUNCT
ejpam-1372	692	3	it	it	PRON
ejpam-1372	692	4	means	mean	VERB
ejpam-1372	692	5	that	that	SCONJ
ejpam-1372	692	6	the	the	DET
ejpam-1372	692	7	regularised	regularise	VERB
ejpam-1372	692	8	value	value	NOUN
ejpam-1372	692	9	must	must	AUX
ejpam-1372	692	10	be	be	AUX
ejpam-1372	692	11	real	real	ADJ
ejpam-1372	692	12	when	when	SCONJ
ejpam-1372	692	13	arg	arg	NOUN
ejpam-1372	692	14	z	z	PROPN
ejpam-1372	692	15	is	be	AUX
ejpam-1372	692	16	situated	situate	VERB
ejpam-1372	692	17	on	on	ADP
ejpam-1372	692	18	a	a	DET
ejpam-1372	692	19	stokes	stoke	NOUN
ejpam-1372	692	20	line	line	NOUN
ejpam-1372	692	21	initially	initially	ADV
ejpam-1372	692	22	.	.	PUNCT
ejpam-1372	693	1	furthermore	furthermore	ADV
ejpam-1372	693	2	,	,	PUNCT
ejpam-1372	693	3	the	the	DET
ejpam-1372	693	4	singularity	singularity	NOUN
ejpam-1372	693	5	at	at	ADP
ejpam-1372	693	6	t=1	t=1	PROPN
ejpam-1372	693	7	/	/	SYM
ejpam-1372	693	8	z	z	NOUN
ejpam-1372	693	9	results	result	NOUN
ejpam-1372	693	10	in	in	ADP
ejpam-1372	693	11	a	a	DET
ejpam-1372	693	12	complex	complex	ADJ
ejpam-1372	693	13	term	term	NOUN
ejpam-1372	693	14	according	accord	VERB
ejpam-1372	693	15	to	to	ADP
ejpam-1372	693	16	cauchy	cauchy	PROPN
ejpam-1372	693	17	’s	’s	PART
ejpam-1372	693	18	residue	residue	NOUN
ejpam-1372	693	19	theorem	theorem	NOUN
ejpam-1372	693	20	.	.	PUNCT
ejpam-1372	694	1	so	so	ADV
ejpam-1372	694	2	,	,	PUNCT
ejpam-1372	694	3	in	in	ADP
ejpam-1372	694	4	order	order	NOUN
ejpam-1372	694	5	to	to	PART
ejpam-1372	694	6	guarantee	guarantee	VERB
ejpam-1372	694	7	that	that	SCONJ
ejpam-1372	694	8	the	the	DET
ejpam-1372	694	9	regularised	regularise	VERB
ejpam-1372	694	10	value	value	NOUN
ejpam-1372	694	11	is	be	AUX
ejpam-1372	694	12	real	real	ADJ
ejpam-1372	694	13	along	along	ADP
ejpam-1372	694	14	the	the	DET
ejpam-1372	694	15	primary	primary	ADJ
ejpam-1372	694	16	stokes	stoke	NOUN
ejpam-1372	694	17	line	line	NOUN
ejpam-1372	694	18	,	,	PUNCT
ejpam-1372	694	19	we	we	PRON
ejpam-1372	694	20	need	need	VERB
ejpam-1372	694	21	to	to	PART
ejpam-1372	694	22	evaluate	evaluate	VERB
ejpam-1372	694	23	the	the	DET
ejpam-1372	694	24	cauchy	cauchy	ADJ
ejpam-1372	694	25	principal	principal	ADJ
ejpam-1372	694	26	value	value	NOUN
ejpam-1372	694	27	of	of	ADP
ejpam-1372	694	28	the	the	DET
ejpam-1372	694	29	integral	integral	ADJ
ejpam-1372	694	30	in	in	ADP
ejpam-1372	694	31	equivalence	equivalence	NOUN
ejpam-1372	694	32	(	(	PUNCT
ejpam-1372	694	33	66	66	NUM
ejpam-1372	694	34	)	)	PUNCT
ejpam-1372	694	35	.	.	PUNCT
ejpam-1372	695	1	hence	hence	ADV
ejpam-1372	695	2	,	,	PUNCT
ejpam-1372	695	3	the	the	DET
ejpam-1372	695	4	asymptotic	asymptotic	ADJ
ejpam-1372	695	5	form	form	NOUN
ejpam-1372	695	6	for	for	ADP
ejpam-1372	695	7	the	the	DET
ejpam-1372	695	8	second	second	ADJ
ejpam-1372	695	9	type	type	NOUN
ejpam-1372	695	10	of	of	ADP
ejpam-1372	695	11	terminant	terminant	NOUN
ejpam-1372	695	12	becomes	become	VERB
ejpam-1372	695	13	ti	ti	PROPN
ejpam-1372	695	14	i(n	i(n	PROPN
ejpam-1372	695	15	,	,	PUNCT
ejpam-1372	695	16	α	α	NOUN
ejpam-1372	695	17	,	,	PUNCT
ejpam-1372	695	18	z	z	NOUN
ejpam-1372	695	19	)	)	PUNCT
ejpam-1372	695	20	≡	≡	PROPN
ejpam-1372	695	21	zn	zn	PROPN
ejpam-1372	695	22	∫	∫	PROPN
ejpam-1372	696	1	∞	∞	PROPN
ejpam-1372	696	2	0	0	PUNCT
ejpam-1372	697	1	d	d	PRON
ejpam-1372	697	2	t	t	NOUN
ejpam-1372	697	3	tn+α−1	tn+α−1	PROPN
ejpam-1372	697	4	e−t	e−t	NOUN
ejpam-1372	697	5	1−	1−	NUM
ejpam-1372	697	6	zt	zt	PROPN
ejpam-1372	697	7	,	,	PUNCT
ejpam-1372	697	8	arg	arg	NOUN
ejpam-1372	697	9	z	z	NOUN
ejpam-1372	697	10	=	=	SYM
ejpam-1372	697	11	0	0	PROPN
ejpam-1372	697	12	.	.	PUNCT
ejpam-1372	698	1	(	(	PUNCT
ejpam-1372	698	2	73	73	NUM
ejpam-1372	698	3	)	)	PUNCT
ejpam-1372	698	4	in	in	ADP
ejpam-1372	698	5	regard	regard	NOUN
ejpam-1372	698	6	to	to	ADP
ejpam-1372	698	7	the	the	DET
ejpam-1372	698	8	second	second	ADJ
ejpam-1372	698	9	question	question	NOUN
ejpam-1372	698	10	,	,	PUNCT
ejpam-1372	698	11	by	by	ADP
ejpam-1372	698	12	using	use	VERB
ejpam-1372	698	13	remarkable	remarkable	ADJ
ejpam-1372	698	14	insight	insight	NOUN
ejpam-1372	698	15	,	,	PUNCT
ejpam-1372	698	16	dingle	dingle	NOUN
ejpam-1372	698	17	points	point	VERB
ejpam-1372	698	18	out	out	ADP
ejpam-1372	698	19	on	on	ADP
ejpam-1372	698	20	p.	p.	PROPN
ejpam-1372	698	21	411	411	NUM
ejpam-1372	698	22	of	of	ADP
ejpam-1372	698	23	ref	ref	NOUN
ejpam-1372	698	24	.	.	PUNCT
ejpam-1372	699	1	[	[	X
ejpam-1372	699	2	8	8	X
ejpam-1372	699	3	]	]	PUNCT
ejpam-1372	699	4	that	that	SCONJ
ejpam-1372	699	5	the	the	DET
ejpam-1372	699	6	discontinuous	discontinuous	ADJ
ejpam-1372	699	7	terms	term	NOUN
ejpam-1372	699	8	in	in	ADP
ejpam-1372	699	9	the	the	DET
ejpam-1372	699	10	stokes	stoke	NOUN
ejpam-1372	699	11	phenomenon	phenomenon	NOUN
ejpam-1372	699	12	arise	arise	VERB
ejpam-1372	699	13	from	from	ADP
ejpam-1372	699	14	the	the	DET
ejpam-1372	699	15	pole	pole	NOUN
ejpam-1372	699	16	in	in	ADP
ejpam-1372	699	17	the	the	DET
ejpam-1372	699	18	singular	singular	ADJ
ejpam-1372	699	19	integral	integral	NOUN
ejpam-1372	699	20	of	of	ADP
ejpam-1372	699	21	equivalence	equivalence	NOUN
ejpam-1372	699	22	(	(	PUNCT
ejpam-1372	699	23	72	72	NUM
ejpam-1372	699	24	)	)	PUNCT
ejpam-1372	699	25	.	.	PUNCT
ejpam-1372	700	1	in	in	ADP
ejpam-1372	700	2	fact	fact	NOUN
ejpam-1372	700	3	,	,	PUNCT
ejpam-1372	700	4	the	the	DET
ejpam-1372	700	5	jump	jump	NOUN
ejpam-1372	700	6	discontinuous	discontinuous	ADJ
ejpam-1372	700	7	terms	term	NOUN
ejpam-1372	700	8	in	in	ADP
ejpam-1372	700	9	the	the	DET
ejpam-1372	700	10	regularised	regularise	VERB
ejpam-1372	700	11	value	value	NOUN
ejpam-1372	700	12	when	when	SCONJ
ejpam-1372	700	13	arg	arg	NOUN
ejpam-1372	700	14	z	z	PROPN
ejpam-1372	700	15	moves	move	VERB
ejpam-1372	700	16	off	off	ADP
ejpam-1372	700	17	the	the	DET
ejpam-1372	700	18	primary	primary	ADJ
ejpam-1372	700	19	stokes	stoke	NOUN
ejpam-1372	700	20	line	line	NOUN
ejpam-1372	700	21	in	in	ADP
ejpam-1372	700	22	either	either	DET
ejpam-1372	700	23	direction	direction	NOUN
ejpam-1372	700	24	are	be	AUX
ejpam-1372	700	25	related	relate	VERB
ejpam-1372	700	26	to	to	ADP
ejpam-1372	700	27	the	the	DET
ejpam-1372	700	28	residue	residue	NOUN
ejpam-1372	700	29	at	at	ADP
ejpam-1372	700	30	t=1	t=1	PROPN
ejpam-1372	700	31	/	/	SYM
ejpam-1372	700	32	z	z	NOUN
ejpam-1372	700	33	.	.	PUNCT
ejpam-1372	701	1	this	this	PRON
ejpam-1372	701	2	is	be	AUX
ejpam-1372	701	3	found	find	VERB
ejpam-1372	701	4	to	to	PART
ejpam-1372	701	5	be	be	AUX
ejpam-1372	701	6	iγres	iγre	NOUN
ejpam-1372	701	7	ii	ii	PROPN
ejpam-1372	701	8	i(z	i(z	NOUN
ejpam-1372	701	9	,	,	PUNCT
ejpam-1372	701	10	α	α	X
ejpam-1372	701	11	)	)	PUNCT
ejpam-1372	701	12	=	=	PUNCT
ejpam-1372	701	13	−izn−1	−izn−1	ADJ
ejpam-1372	701	14	∫	∫	PROPN
ejpam-1372	701	15	γ	γ	PROPN
ejpam-1372	701	16	0	0	PROPN
ejpam-1372	701	17	dθ	dθ	PROPN
ejpam-1372	701	18	(	(	PUNCT
ejpam-1372	701	19	1	1	NUM
ejpam-1372	701	20	/	/	SYM
ejpam-1372	701	21	z)n+α−1e−1	z)n+α−1e−1	PROPN
ejpam-1372	701	22	/	/	SYM
ejpam-1372	701	23	z	z	NOUN
ejpam-1372	701	24	.	.	PUNCT
ejpam-1372	702	1	(	(	PUNCT
ejpam-1372	702	2	74	74	X
ejpam-1372	702	3	)	)	PUNCT
ejpam-1372	702	4	the	the	DET
ejpam-1372	702	5	above	above	ADJ
ejpam-1372	702	6	result	result	NOUN
ejpam-1372	702	7	has	have	AUX
ejpam-1372	702	8	been	be	AUX
ejpam-1372	702	9	derived	derive	VERB
ejpam-1372	702	10	by	by	ADP
ejpam-1372	702	11	converting	convert	VERB
ejpam-1372	702	12	the	the	DET
ejpam-1372	702	13	integral	integral	ADJ
ejpam-1372	702	14	in	in	ADP
ejpam-1372	702	15	equivalence	equivalence	NOUN
ejpam-1372	702	16	(	(	PUNCT
ejpam-1372	702	17	72	72	NUM
ejpam-1372	702	18	)	)	PUNCT
ejpam-1372	702	19	to	to	ADP
ejpam-1372	702	20	a	a	DET
ejpam-1372	702	21	complex	complex	ADJ
ejpam-1372	702	22	integral	integral	ADJ
ejpam-1372	702	23	along	along	ADP
ejpam-1372	702	24	the	the	DET
ejpam-1372	702	25	positive	positive	ADJ
ejpam-1372	702	26	real	real	ADJ
ejpam-1372	702	27	axis	axis	NOUN
ejpam-1372	702	28	where	where	SCONJ
ejpam-1372	702	29	the	the	DET
ejpam-1372	702	30	variable	variable	ADJ
ejpam-1372	702	31	t	t	PROPN
ejpam-1372	702	32	has	have	AUX
ejpam-1372	702	33	been	be	AUX
ejpam-1372	702	34	replaced	replace	VERB
ejpam-1372	702	35	by	by	ADP
ejpam-1372	702	36	the	the	DET
ejpam-1372	702	37	complex	complex	ADJ
ejpam-1372	702	38	variable	variable	NOUN
ejpam-1372	702	39	s.	s.	PROPN
ejpam-1372	702	40	eq	eq	PROPN
ejpam-1372	702	41	.	.	PUNCT
ejpam-1372	703	1	(	(	PUNCT
ejpam-1372	703	2	74	74	NUM
ejpam-1372	703	3	)	)	PUNCT
ejpam-1372	703	4	follows	follow	VERB
ejpam-1372	703	5	once	once	ADV
ejpam-1372	703	6	s	s	NOUN
ejpam-1372	703	7	is	be	AUX
ejpam-1372	703	8	set	set	VERB
ejpam-1372	703	9	equal	equal	ADJ
ejpam-1372	703	10	to	to	ADP
ejpam-1372	703	11	1	1	NUM
ejpam-1372	703	12	/	/	SYM
ejpam-1372	703	13	z+εexp(iθ	z+εexp(iθ	NUM
ejpam-1372	703	14	)	)	PUNCT
ejpam-1372	703	15	in	in	ADP
ejpam-1372	703	16	the	the	DET
ejpam-1372	703	17	vicinity	vicinity	NOUN
ejpam-1372	703	18	of	of	ADP
ejpam-1372	703	19	the	the	DET
ejpam-1372	703	20	singularity	singularity	NOUN
ejpam-1372	703	21	and	and	CCONJ
ejpam-1372	703	22	the	the	DET
ejpam-1372	703	23	limit	limit	NOUN
ejpam-1372	703	24	ε→	ε→	X
ejpam-1372	703	25	0	0	NUM
ejpam-1372	703	26	is	be	AUX
ejpam-1372	703	27	taken	take	VERB
ejpam-1372	703	28	.	.	PUNCT
ejpam-1372	704	1	moreover	moreover	ADV
ejpam-1372	704	2	,	,	PUNCT
ejpam-1372	704	3	the	the	DET
ejpam-1372	704	4	question	question	NOUN
ejpam-1372	704	5	of	of	ADP
ejpam-1372	704	6	whether	whether	SCONJ
ejpam-1372	704	7	an	an	DET
ejpam-1372	704	8	anti	anti	ADJ
ejpam-1372	704	9	-	-	ADJ
ejpam-1372	704	10	clockwise	clockwise	ADJ
ejpam-1372	704	11	rotation	rotation	NOUN
ejpam-1372	704	12	or	or	CCONJ
ejpam-1372	704	13	clockwise	clockwise	NOUN
ejpam-1372	704	14	rotation	rotation	NOUN
ejpam-1372	704	15	around	around	ADP
ejpam-1372	704	16	the	the	DET
ejpam-1372	704	17	residue	residue	NOUN
ejpam-1372	704	18	should	should	AUX
ejpam-1372	704	19	be	be	AUX
ejpam-1372	704	20	taken	take	VERB
ejpam-1372	704	21	has	have	AUX
ejpam-1372	704	22	been	be	AUX
ejpam-1372	704	23	left	leave	VERB
ejpam-1372	704	24	open	open	ADJ
ejpam-1372	704	25	for	for	ADP
ejpam-1372	704	26	the	the	DET
ejpam-1372	704	27	time	time	NOUN
ejpam-1372	704	28	being	be	AUX
ejpam-1372	704	29	with	with	ADP
ejpam-1372	704	30	the	the	DET
ejpam-1372	704	31	introduction	introduction	NOUN
ejpam-1372	704	32	of	of	ADP
ejpam-1372	704	33	γ	γ	NOUN
ejpam-1372	704	34	in	in	ADP
ejpam-1372	704	35	the	the	DET
ejpam-1372	704	36	upper	upper	ADJ
ejpam-1372	704	37	limit	limit	NOUN
ejpam-1372	704	38	of	of	ADP
ejpam-1372	704	39	the	the	DET
ejpam-1372	704	40	integral	integral	ADJ
ejpam-1372	704	41	.	.	PUNCT
ejpam-1372	705	1	if	if	SCONJ
ejpam-1372	705	2	arg	arg	NOUN
ejpam-1372	705	3	z	z	NOUN
ejpam-1372	705	4	is	be	AUX
ejpam-1372	705	5	situated	situate	VERB
ejpam-1372	705	6	just	just	ADV
ejpam-1372	705	7	above	above	ADP
ejpam-1372	705	8	the	the	DET
ejpam-1372	705	9	positive	positive	ADJ
ejpam-1372	705	10	real	real	ADJ
ejpam-1372	705	11	axis	axis	NOUN
ejpam-1372	705	12	,	,	PUNCT
ejpam-1372	705	13	then	then	ADV
ejpam-1372	705	14	the	the	DET
ejpam-1372	705	15	semi	semi	ADJ
ejpam-1372	705	16	-	-	ADJ
ejpam-1372	705	17	circular	circular	ADJ
ejpam-1372	705	18	contour	contour	NOUN
ejpam-1372	705	19	around	around	ADP
ejpam-1372	705	20	t	t	NOUN
ejpam-1372	705	21	=	=	SYM
ejpam-1372	705	22	1	1	NUM
ejpam-1372	705	23	/	/	SYM
ejpam-1372	705	24	z	z	NOUN
ejpam-1372	705	25	is	be	AUX
ejpam-1372	705	26	taken	take	VERB
ejpam-1372	705	27	in	in	ADP
ejpam-1372	705	28	a	a	DET
ejpam-1372	705	29	clockwise	clockwise	NOUN
ejpam-1372	705	30	direction	direction	NOUN
ejpam-1372	705	31	in	in	ADP
ejpam-1372	705	32	order	order	NOUN
ejpam-1372	705	33	to	to	PART
ejpam-1372	705	34	be	be	AUX
ejpam-1372	705	35	consistent	consistent	ADJ
ejpam-1372	705	36	with	with	ADP
ejpam-1372	705	37	attempting	attempt	VERB
ejpam-1372	705	38	to	to	PART
ejpam-1372	705	39	avoid	avoid	VERB
ejpam-1372	705	40	its	its	PRON
ejpam-1372	705	41	contribution	contribution	NOUN
ejpam-1372	705	42	as	as	SCONJ
ejpam-1372	705	43	we	we	PRON
ejpam-1372	705	44	did	do	VERB
ejpam-1372	705	45	when	when	SCONJ
ejpam-1372	705	46	evaluating	evaluate	VERB
ejpam-1372	705	47	the	the	DET
ejpam-1372	705	48	cauchy	cauchy	ADJ
ejpam-1372	705	49	principal	principal	ADJ
ejpam-1372	705	50	value	value	NOUN
ejpam-1372	705	51	.	.	PUNCT
ejpam-1372	706	1	hence	hence	ADV
ejpam-1372	706	2	,	,	PUNCT
ejpam-1372	706	3	in	in	ADP
ejpam-1372	706	4	this	this	DET
ejpam-1372	706	5	case	case	NOUN
ejpam-1372	706	6	γ=−π	γ=−π	NOUN
ejpam-1372	706	7	.	.	PUNCT
ejpam-1372	707	1	conversely	conversely	ADV
ejpam-1372	707	2	,	,	PUNCT
ejpam-1372	707	3	if	if	SCONJ
ejpam-1372	707	4	arg	arg	NOUN
ejpam-1372	707	5	z	z	NOUN
ejpam-1372	707	6	is	be	AUX
ejpam-1372	707	7	situated	situate	VERB
ejpam-1372	707	8	just	just	ADV
ejpam-1372	707	9	below	below	ADP
ejpam-1372	707	10	the	the	DET
ejpam-1372	707	11	positive	positive	ADJ
ejpam-1372	707	12	real	real	ADJ
ejpam-1372	707	13	axis	axis	NOUN
ejpam-1372	707	14	,	,	PUNCT
ejpam-1372	707	15	then	then	ADV
ejpam-1372	707	16	the	the	DET
ejpam-1372	707	17	semi	semi	ADJ
ejpam-1372	707	18	-	-	ADJ
ejpam-1372	707	19	circular	circular	ADJ
ejpam-1372	707	20	contour	contour	NOUN
ejpam-1372	707	21	is	be	AUX
ejpam-1372	707	22	taken	take	VERB
ejpam-1372	707	23	in	in	ADP
ejpam-1372	707	24	an	an	DET
ejpam-1372	707	25	anti	anti	ADJ
ejpam-1372	707	26	-	-	ADJ
ejpam-1372	707	27	clockwise	clockwise	ADJ
ejpam-1372	707	28	direction	direction	NOUN
ejpam-1372	707	29	,	,	PUNCT
ejpam-1372	707	30	i.e.	i.e.	X
ejpam-1372	707	31	γ	γ	X
ejpam-1372	707	32	=	=	SYM
ejpam-1372	707	33	π	π	PROPN
ejpam-1372	707	34	.	.	PUNCT
ejpam-1372	708	1	in	in	ADP
ejpam-1372	708	2	both	both	DET
ejpam-1372	708	3	cases	case	NOUN
ejpam-1372	708	4	because	because	SCONJ
ejpam-1372	708	5	the	the	DET
ejpam-1372	708	6	semi	semi	ADJ
ejpam-1372	708	7	-	-	ADJ
ejpam-1372	708	8	residue	residue	ADJ
ejpam-1372	708	9	contribution	contribution	NOUN
ejpam-1372	708	10	is	be	AUX
ejpam-1372	708	11	removed	remove	VERB
ejpam-1372	708	12	completely	completely	ADV
ejpam-1372	708	13	in	in	ADP
ejpam-1372	708	14	the	the	DET
ejpam-1372	708	15	process	process	NOUN
ejpam-1372	708	16	of	of	ADP
ejpam-1372	708	17	evaluating	evaluate	VERB
ejpam-1372	708	18	the	the	DET
ejpam-1372	708	19	cauchy	cauchy	ADJ
ejpam-1372	708	20	principal	principal	ADJ
ejpam-1372	708	21	value	value	NOUN
ejpam-1372	708	22	in	in	ADP
ejpam-1372	708	23	equivalence	equivalence	NOUN
ejpam-1372	708	24	(	(	PUNCT
ejpam-1372	708	25	73	73	NUM
ejpam-1372	708	26	)	)	PUNCT
ejpam-1372	708	27	,	,	PUNCT
ejpam-1372	708	28	we	we	PRON
ejpam-1372	708	29	must	must	AUX
ejpam-1372	708	30	remove	remove	VERB
ejpam-1372	708	31	the	the	DET
ejpam-1372	708	32	semi	semi	ADJ
ejpam-1372	708	33	-	-	ADJ
ejpam-1372	708	34	residue	residue	ADJ
ejpam-1372	708	35	contributions	contribution	NOUN
ejpam-1372	708	36	from	from	ADP
ejpam-1372	708	37	the	the	DET
ejpam-1372	708	38	integral	integral	ADJ
ejpam-1372	708	39	in	in	ADP
ejpam-1372	708	40	equivalence	equivalence	NOUN
ejpam-1372	708	41	(	(	PUNCT
ejpam-1372	708	42	72	72	NUM
ejpam-1372	708	43	)	)	PUNCT
ejpam-1372	708	44	.	.	PUNCT
ejpam-1372	709	1	therefore	therefore	ADV
ejpam-1372	709	2	,	,	PUNCT
ejpam-1372	709	3	the	the	DET
ejpam-1372	709	4	regularised	regularise	VERB
ejpam-1372	709	5	value	value	NOUN
ejpam-1372	709	6	of	of	ADP
ejpam-1372	709	7	the	the	DET
ejpam-1372	709	8	second	second	ADJ
ejpam-1372	709	9	type	type	NOUN
ejpam-1372	709	10	of	of	ADP
ejpam-1372	709	11	terminant	terminant	NOUN
ejpam-1372	709	12	becomes	become	VERB
ejpam-1372	709	13	ti	ti	NOUN
ejpam-1372	709	14	i	i	PRON
ejpam-1372	709	15	(	(	PUNCT
ejpam-1372	709	16	n	n	X
ejpam-1372	709	17	,	,	PUNCT
ejpam-1372	709	18	α	α	NOUN
ejpam-1372	709	19	,	,	PUNCT
ejpam-1372	709	20	z	z	NOUN
ejpam-1372	709	21	)	)	PUNCT
ejpam-1372	709	22	≡	≡	PROPN
ejpam-1372	709	23			VERB
ejpam-1372	709	24			ADP
ejpam-1372	709	25			PROPN
ejpam-1372	709	26	zn	zn	PROPN
ejpam-1372	709	27	∫∞	∫∞	NOUN
ejpam-1372	709	28	0	0	PROPN
ejpam-1372	710	1	d	d	NOUN
ejpam-1372	710	2	t	t	PROPN
ejpam-1372	710	3	tn+α−1	tn+α−1	NOUN
ejpam-1372	710	4	e−t	e−t	NOUN
ejpam-1372	710	5	1−zt	1−zt	NUM
ejpam-1372	710	6	−	−	NUM
ejpam-1372	710	7	iπz−αe−1	iπz−αe−1	PROPN
ejpam-1372	710	8	/	/	SYM
ejpam-1372	710	9	z	z	NOUN
ejpam-1372	710	10	,	,	PUNCT
ejpam-1372	710	11	arg	arg	NOUN
ejpam-1372	710	12	z	z	NOUN
ejpam-1372	710	13	=	=	SYM
ejpam-1372	710	14	0	0	PUNCT
ejpam-1372	710	15	zn	zn	PROPN
ejpam-1372	710	16	p	p	NOUN
ejpam-1372	710	17	∫∞	∫∞	NOUN
ejpam-1372	710	18	0	0	PUNCT
ejpam-1372	711	1	d	d	NOUN
ejpam-1372	711	2	t	t	PROPN
ejpam-1372	711	3	tn+α−1	tn+α−1	NOUN
ejpam-1372	711	4	e−t	e−t	PROPN
ejpam-1372	711	5	1−zt	1−zt	NUM
ejpam-1372	711	6	,	,	PUNCT
ejpam-1372	711	7	arg	arg	NOUN
ejpam-1372	711	8	z	z	NOUN
ejpam-1372	711	9	=	=	SYM
ejpam-1372	711	10	0	0	NUM
ejpam-1372	711	11	,	,	PUNCT
ejpam-1372	711	12	zn	zn	PROPN
ejpam-1372	711	13	∫∞	∫∞	NOUN
ejpam-1372	711	14	0	0	NUM
ejpam-1372	712	1	d	d	NOUN
ejpam-1372	712	2	t	t	NOUN
ejpam-1372	712	3	tn+α−1	tn+α−1	NOUN
ejpam-1372	712	4	e−t	e−t	NOUN
ejpam-1372	712	5	1−zt	1−zt	NUM
ejpam-1372	713	1	+	+	CCONJ
ejpam-1372	713	2	iπz−αe−1	iπz−αe−1	ADJ
ejpam-1372	713	3	/	/	SYM
ejpam-1372	713	4	z	z	NOUN
ejpam-1372	713	5	,	,	PUNCT
ejpam-1372	713	6	−2π	−2π	PROPN
ejpam-1372	713	7	<	<	X
ejpam-1372	713	8	arg	arg	X
ejpam-1372	713	9	z	z	X
ejpam-1372	713	10	<	<	X
ejpam-1372	713	11	0	0	NUM
ejpam-1372	713	12	.	.	PUNCT
ejpam-1372	713	13	(	(	PUNCT
ejpam-1372	713	14	75	75	NUM
ejpam-1372	713	15	)	)	PUNCT
ejpam-1372	713	16	since	since	SCONJ
ejpam-1372	713	17	we	we	PRON
ejpam-1372	713	18	have	have	AUX
ejpam-1372	713	19	seen	see	VERB
ejpam-1372	713	20	that	that	SCONJ
ejpam-1372	713	21	it	it	PRON
ejpam-1372	713	22	is	be	AUX
ejpam-1372	713	23	the	the	DET
ejpam-1372	713	24	residues	residue	NOUN
ejpam-1372	713	25	of	of	ADP
ejpam-1372	713	26	the	the	DET
ejpam-1372	713	27	cauchy	cauchy	NOUN
ejpam-1372	713	28	integrals	integral	NOUN
ejpam-1372	713	29	which	which	PRON
ejpam-1372	713	30	are	be	AUX
ejpam-1372	713	31	responsible	responsible	ADJ
ejpam-1372	713	32	for	for	ADP
ejpam-1372	713	33	the	the	DET
ejpam-1372	713	34	jump	jump	NOUN
ejpam-1372	713	35	discontinuities	discontinuity	NOUN
ejpam-1372	713	36	in	in	ADP
ejpam-1372	713	37	the	the	DET
ejpam-1372	713	38	stokes	stoke	NOUN
ejpam-1372	713	39	phenomenon	phenomenon	NOUN
ejpam-1372	713	40	,	,	PUNCT
ejpam-1372	713	41	we	we	PRON
ejpam-1372	713	42	can	can	AUX
ejpam-1372	713	43	now	now	ADV
ejpam-1372	713	44	examine	examine	VERB
ejpam-1372	713	45	the	the	DET
ejpam-1372	713	46	change	change	NOUN
ejpam-1372	713	47	in	in	ADP
ejpam-1372	713	48	the	the	DET
ejpam-1372	713	49	regularised	regularise	VERB
ejpam-1372	713	50	value	value	NOUN
ejpam-1372	713	51	when	when	SCONJ
ejpam-1372	713	52	z	z	PROPN
ejpam-1372	713	53	encounters	encounter	VERB
ejpam-1372	713	54	a	a	DET
ejpam-1372	713	55	stokes	stoke	NOUN
ejpam-1372	713	56	line	line	NOUN
ejpam-1372	713	57	,	,	PUNCT
ejpam-1372	713	58	viz	viz	PROPN
ejpam-1372	713	59	.	.	PUNCT
ejpam-1372	714	1	when	when	SCONJ
ejpam-1372	714	2	arg	arg	NOUN
ejpam-1372	714	3	z	z	NOUN
ejpam-1372	714	4	=	=	SYM
ejpam-1372	714	5	±π	±π	PROPN
ejpam-1372	714	6	,	,	PUNCT
ejpam-1372	714	7	for	for	ADP
ejpam-1372	714	8	the	the	DET
ejpam-1372	714	9	first	first	ADJ
ejpam-1372	714	10	type	type	NOUN
ejpam-1372	714	11	of	of	ADP
ejpam-1372	714	12	terminant	terminant	NOUN
ejpam-1372	714	13	or	or	CCONJ
ejpam-1372	714	14	ti	ti	NOUN
ejpam-1372	714	15	(	(	PUNCT
ejpam-1372	714	16	n	n	X
ejpam-1372	714	17	,	,	PUNCT
ejpam-1372	714	18	α	α	NOUN
ejpam-1372	714	19	,	,	PUNCT
ejpam-1372	714	20	z	z	NOUN
ejpam-1372	714	21	)	)	PUNCT
ejpam-1372	714	22	.	.	PUNCT
ejpam-1372	715	1	in	in	ADP
ejpam-1372	715	2	both	both	DET
ejpam-1372	715	3	cases	case	NOUN
ejpam-1372	715	4	we	we	PRON
ejpam-1372	715	5	expect	expect	VERB
ejpam-1372	715	6	that	that	SCONJ
ejpam-1372	715	7	the	the	DET
ejpam-1372	715	8	cauchy	cauchy	ADJ
ejpam-1372	715	9	integral	integral	NOUN
ejpam-1372	715	10	given	give	VERB
ejpam-1372	715	11	v.	v.	ADP
ejpam-1372	715	12	kowalenko	kowalenko	PROPN
ejpam-1372	715	13	/	/	SYM
ejpam-1372	715	14	eur	eur	PROPN
ejpam-1372	715	15	.	.	PUNCT
ejpam-1372	716	1	j.	j.	PROPN
ejpam-1372	716	2	pure	pure	PROPN
ejpam-1372	716	3	appl	appl	PROPN
ejpam-1372	716	4	.	.	PROPN
ejpam-1372	716	5	math	math	PROPN
ejpam-1372	716	6	,	,	PUNCT
ejpam-1372	716	7	4	4	NUM
ejpam-1372	716	8	(	(	PUNCT
ejpam-1372	716	9	2011	2011	NUM
ejpam-1372	716	10	)	)	PUNCT
ejpam-1372	716	11	,	,	PUNCT
ejpam-1372	716	12	370	370	NUM
ejpam-1372	716	13	-	-	SYM
ejpam-1372	716	14	423	423	NUM
ejpam-1372	716	15	394	394	NUM
ejpam-1372	716	16	in	in	ADP
ejpam-1372	716	17	equivalence	equivalence	NOUN
ejpam-1372	716	18	(	(	PUNCT
ejpam-1372	716	19	68	68	NUM
ejpam-1372	716	20	)	)	PUNCT
ejpam-1372	716	21	will	will	AUX
ejpam-1372	716	22	form	form	VERB
ejpam-1372	716	23	part	part	NOUN
ejpam-1372	716	24	of	of	ADP
ejpam-1372	716	25	the	the	DET
ejpam-1372	716	26	regularised	regularise	VERB
ejpam-1372	716	27	value	value	NOUN
ejpam-1372	716	28	except	except	SCONJ
ejpam-1372	716	29	that	that	SCONJ
ejpam-1372	716	30	it	it	PRON
ejpam-1372	716	31	will	will	AUX
ejpam-1372	716	32	have	have	AUX
ejpam-1372	716	33	to	to	PART
ejpam-1372	716	34	be	be	AUX
ejpam-1372	716	35	modified	modify	VERB
ejpam-1372	716	36	so	so	SCONJ
ejpam-1372	716	37	that	that	SCONJ
ejpam-1372	716	38	only	only	ADV
ejpam-1372	716	39	the	the	DET
ejpam-1372	716	40	principal	principal	ADJ
ejpam-1372	716	41	value	value	NOUN
ejpam-1372	716	42	is	be	AUX
ejpam-1372	716	43	evaluated	evaluate	VERB
ejpam-1372	716	44	.	.	PUNCT
ejpam-1372	717	1	furthermore	furthermore	ADV
ejpam-1372	717	2	,	,	PUNCT
ejpam-1372	717	3	the	the	DET
ejpam-1372	717	4	extra	extra	ADJ
ejpam-1372	717	5	terms	term	NOUN
ejpam-1372	717	6	or	or	CCONJ
ejpam-1372	717	7	jump	jump	VERB
ejpam-1372	717	8	discontinuous	discontinuous	ADJ
ejpam-1372	717	9	terms	term	NOUN
ejpam-1372	717	10	to	to	ADP
ejpam-1372	717	11	the	the	DET
ejpam-1372	717	12	regularised	regularise	VERB
ejpam-1372	717	13	value	value	NOUN
ejpam-1372	717	14	along	along	ADP
ejpam-1372	717	15	the	the	DET
ejpam-1372	717	16	stokes	stoke	NOUN
ejpam-1372	717	17	lines	line	NOUN
ejpam-1372	717	18	will	will	AUX
ejpam-1372	717	19	be	be	AUX
ejpam-1372	717	20	dependent	dependent	ADJ
ejpam-1372	717	21	upon	upon	SCONJ
ejpam-1372	717	22	the	the	DET
ejpam-1372	717	23	semi	semi	ADJ
ejpam-1372	717	24	-	-	ADJ
ejpam-1372	717	25	residue	residue	ADJ
ejpam-1372	717	26	contributions	contribution	NOUN
ejpam-1372	717	27	,	,	PUNCT
ejpam-1372	717	28	while	while	SCONJ
ejpam-1372	717	29	as	as	SCONJ
ejpam-1372	717	30	arg	arg	NOUN
ejpam-1372	717	31	z	z	NOUN
ejpam-1372	717	32	moves	move	VERB
ejpam-1372	717	33	off	off	ADP
ejpam-1372	717	34	the	the	DET
ejpam-1372	717	35	stokes	stoke	NOUN
ejpam-1372	717	36	lines	line	NOUN
ejpam-1372	717	37	,	,	PUNCT
ejpam-1372	717	38	the	the	DET
ejpam-1372	717	39	extra	extra	ADJ
ejpam-1372	717	40	contributions	contribution	NOUN
ejpam-1372	717	41	to	to	ADP
ejpam-1372	717	42	the	the	DET
ejpam-1372	717	43	regularised	regularise	VERB
ejpam-1372	717	44	value	value	NOUN
ejpam-1372	717	45	will	will	AUX
ejpam-1372	717	46	become	become	VERB
ejpam-1372	717	47	full	full	ADJ
ejpam-1372	717	48	-	-	PUNCT
ejpam-1372	717	49	residue	residue	NOUN
ejpam-1372	717	50	contributions	contribution	NOUN
ejpam-1372	717	51	.	.	PUNCT
ejpam-1372	718	1	as	as	SCONJ
ejpam-1372	718	2	discussed	discuss	VERB
ejpam-1372	718	3	in	in	ADP
ejpam-1372	718	4	ref	ref	NOUN
ejpam-1372	718	5	.	.	PUNCT
ejpam-1372	719	1	[	[	X
ejpam-1372	719	2	17	17	NUM
ejpam-1372	719	3	]	]	PUNCT
ejpam-1372	719	4	,	,	PUNCT
ejpam-1372	719	5	where	where	SCONJ
ejpam-1372	719	6	both	both	DET
ejpam-1372	719	7	types	type	NOUN
ejpam-1372	719	8	of	of	ADP
ejpam-1372	719	9	terminants	terminant	NOUN
ejpam-1372	719	10	are	be	AUX
ejpam-1372	719	11	generalised	generalise	VERB
ejpam-1372	719	12	by	by	ADP
ejpam-1372	719	13	replacing	replace	VERB
ejpam-1372	719	14	γ(k	γ(k	PROPN
ejpam-1372	719	15	+	+	CCONJ
ejpam-1372	719	16	α	α	X
ejpam-1372	719	17	)	)	PUNCT
ejpam-1372	719	18	and	and	CCONJ
ejpam-1372	719	19	z	z	NOUN
ejpam-1372	719	20	with	with	ADP
ejpam-1372	719	21	γ(pk	γ(pk	PRON
ejpam-1372	719	22	+	+	CCONJ
ejpam-1372	719	23	q	q	X
ejpam-1372	719	24	)	)	PUNCT
ejpam-1372	719	25	and	and	CCONJ
ejpam-1372	719	26	zβ	zβ	PROPN
ejpam-1372	719	27	respectively	respectively	ADV
ejpam-1372	719	28	,	,	PUNCT
ejpam-1372	719	29	moving	move	VERB
ejpam-1372	719	30	to	to	ADP
ejpam-1372	719	31	a	a	DET
ejpam-1372	719	32	higher	high	ADJ
ejpam-1372	719	33	stokes	stoke	NOUN
ejpam-1372	719	34	sector	sector	NOUN
ejpam-1372	719	35	means	mean	VERB
ejpam-1372	719	36	that	that	SCONJ
ejpam-1372	719	37	either	either	CCONJ
ejpam-1372	719	38	z	z	NOUN
ejpam-1372	719	39	or	or	CCONJ
ejpam-1372	719	40	zβ	zβ	PROPN
ejpam-1372	719	41	undergoes	undergo	VERB
ejpam-1372	719	42	an	an	DET
ejpam-1372	719	43	anti	anti	ADJ
ejpam-1372	719	44	-	-	ADJ
ejpam-1372	719	45	clockwise	clockwise	ADJ
ejpam-1372	719	46	rotation	rotation	NOUN
ejpam-1372	719	47	of	of	ADP
ejpam-1372	719	48	2π	2π	NOUN
ejpam-1372	719	49	.	.	PUNCT
ejpam-1372	720	1	this	this	PRON
ejpam-1372	720	2	means	mean	VERB
ejpam-1372	720	3	that	that	SCONJ
ejpam-1372	720	4	we	we	PRON
ejpam-1372	720	5	need	need	VERB
ejpam-1372	720	6	to	to	PART
ejpam-1372	720	7	consider	consider	VERB
ejpam-1372	720	8	terminants	terminant	NOUN
ejpam-1372	720	9	with	with	ADP
ejpam-1372	720	10	z	z	PROPN
ejpam-1372	720	11	exp(2iπ	exp(2iπ	NOUN
ejpam-1372	720	12	)	)	PUNCT
ejpam-1372	720	13	or	or	CCONJ
ejpam-1372	720	14	l=−1	l=−1	ADV
ejpam-1372	720	15	in	in	ADP
ejpam-1372	720	16	equivalence	equivalence	NOUN
ejpam-1372	720	17	(	(	PUNCT
ejpam-1372	720	18	68	68	NUM
ejpam-1372	720	19	)	)	PUNCT
ejpam-1372	720	20	.	.	PUNCT
ejpam-1372	721	1	according	accord	VERB
ejpam-1372	721	2	to	to	ADP
ejpam-1372	721	3	sec	sec	PROPN
ejpam-1372	721	4	.	.	PROPN
ejpam-1372	721	5	10.1	10.1	NUM
ejpam-1372	721	6	of	of	ADP
ejpam-1372	721	7	ref	ref	NOUN
ejpam-1372	721	8	.	.	PUNCT
ejpam-1372	722	1	[	[	X
ejpam-1372	722	2	17	17	NUM
ejpam-1372	722	3	]	]	PUNCT
ejpam-1372	722	4	,	,	PUNCT
ejpam-1372	722	5	the	the	DET
ejpam-1372	722	6	difference	difference	NOUN
ejpam-1372	722	7	between	between	ADP
ejpam-1372	722	8	the	the	DET
ejpam-1372	722	9	regularised	regularise	VERB
ejpam-1372	722	10	value	value	NOUN
ejpam-1372	722	11	of	of	ADP
ejpam-1372	722	12	the	the	DET
ejpam-1372	722	13	first	first	ADJ
ejpam-1372	722	14	terminant	terminant	NOUN
ejpam-1372	722	15	for	for	ADP
ejpam-1372	722	16	z	z	PROPN
ejpam-1372	722	17	exp(2iπ	exp(2iπ	NOUN
ejpam-1372	722	18	)	)	PUNCT
ejpam-1372	722	19	and	and	CCONJ
ejpam-1372	722	20	that	that	SCONJ
ejpam-1372	722	21	for	for	ADP
ejpam-1372	722	22	z	z	NOUN
ejpam-1372	722	23	can	can	AUX
ejpam-1372	722	24	be	be	AUX
ejpam-1372	722	25	derived	derive	VERB
ejpam-1372	722	26	via	via	ADP
ejpam-1372	722	27	the	the	DET
ejpam-1372	722	28	theory	theory	NOUN
ejpam-1372	722	29	of	of	ADP
ejpam-1372	722	30	mellin	mellin	PROPN
ejpam-1372	722	31	transforms	transform	VERB
ejpam-1372	722	32	[	[	X
ejpam-1372	722	33	25	25	NUM
ejpam-1372	722	34	]	]	PUNCT
ejpam-1372	722	35	and	and	CCONJ
ejpam-1372	722	36	is	be	AUX
ejpam-1372	722	37	given	give	VERB
ejpam-1372	722	38	by	by	ADP
ejpam-1372	722	39	ti	ti	PROPN
ejpam-1372	722	40	(	(	PUNCT
ejpam-1372	722	41	n	n	X
ejpam-1372	722	42	,	,	PUNCT
ejpam-1372	722	43	α	α	PROPN
ejpam-1372	722	44	,	,	PUNCT
ejpam-1372	722	45	z	z	NOUN
ejpam-1372	722	46	exp(2iπ))−	exp(2iπ))−	PROPN
ejpam-1372	722	47	ti	ti	NOUN
ejpam-1372	722	48	(	(	PUNCT
ejpam-1372	722	49	n	n	X
ejpam-1372	722	50	,	,	PUNCT
ejpam-1372	722	51	α	α	PROPN
ejpam-1372	722	52	,	,	PUNCT
ejpam-1372	722	53	z	z	NOUN
ejpam-1372	722	54	)	)	PUNCT
ejpam-1372	722	55	≡	≡	PROPN
ejpam-1372	722	56	2πi	2πi	PROPN
ejpam-1372	722	57	res	res	PROPN
ejpam-1372	722	58	�	�	PROPN
ejpam-1372	722	59	ii	ii	PROPN
ejpam-1372	722	60	(	(	PUNCT
ejpam-1372	722	61	z	z	NOUN
ejpam-1372	722	62	,	,	PUNCT
ejpam-1372	722	63	exp(−iπ),α	exp(−iπ),α	NOUN
ejpam-1372	722	64	)	)	PUNCT
ejpam-1372	722	65	,	,	PUNCT
ejpam-1372	722	66	(	(	PUNCT
ejpam-1372	722	67	76	76	NUM
ejpam-1372	722	68	)	)	PUNCT
ejpam-1372	722	69	where	where	SCONJ
ejpam-1372	722	70	ii	ii	X
ejpam-1372	722	71	(	(	PUNCT
ejpam-1372	722	72	z	z	PROPN
ejpam-1372	722	73	,	,	PUNCT
ejpam-1372	722	74	α	α	NOUN
ejpam-1372	722	75	)	)	PUNCT
ejpam-1372	722	76	represents	represent	VERB
ejpam-1372	722	77	the	the	DET
ejpam-1372	722	78	integral	integral	ADJ
ejpam-1372	722	79	on	on	ADP
ejpam-1372	722	80	the	the	DET
ejpam-1372	722	81	rhs	rhs	PROPN
ejpam-1372	722	82	of	of	ADP
ejpam-1372	722	83	equivalence	equivalence	NOUN
ejpam-1372	722	84	(	(	PUNCT
ejpam-1372	722	85	68	68	NUM
ejpam-1372	722	86	)	)	PUNCT
ejpam-1372	722	87	.	.	PUNCT
ejpam-1372	723	1	the	the	DET
ejpam-1372	723	2	residue	residue	NOUN
ejpam-1372	723	3	for	for	ADP
ejpam-1372	723	4	this	this	DET
ejpam-1372	723	5	integral	integral	ADJ
ejpam-1372	723	6	is	be	AUX
ejpam-1372	723	7	found	find	VERB
ejpam-1372	723	8	to	to	PART
ejpam-1372	723	9	be	be	AUX
ejpam-1372	723	10	iγres	iγre	NOUN
ejpam-1372	723	11	�	�	PROPN
ejpam-1372	723	12	ii	ii	PROPN
ejpam-1372	723	13	(	(	PUNCT
ejpam-1372	723	14	z	z	NOUN
ejpam-1372	723	15	exp(−iπ),α	exp(−iπ),α	NOUN
ejpam-1372	723	16	)	)	PUNCT
ejpam-1372	724	1	=	=	SYM
ejpam-1372	724	2	−i	−i	ADJ
ejpam-1372	724	3	∫	∫	PROPN
ejpam-1372	724	4	γ	γ	X
ejpam-1372	724	5	0	0	PROPN
ejpam-1372	724	6	dθ	dθ	PROPN
ejpam-1372	724	7	(	(	PUNCT
ejpam-1372	724	8	1	1	NUM
ejpam-1372	724	9	/	/	SYM
ejpam-1372	724	10	z)αe−iπα	z)αe−iπα	NOUN
ejpam-1372	724	11	e1	e1	NOUN
ejpam-1372	724	12	/	/	SYM
ejpam-1372	724	13	z	z	NOUN
ejpam-1372	724	14	.	.	PUNCT
ejpam-1372	725	1	(	(	PUNCT
ejpam-1372	725	2	77	77	NUM
ejpam-1372	725	3	)	)	PUNCT
ejpam-1372	725	4	by	by	ADP
ejpam-1372	725	5	introducing	introduce	VERB
ejpam-1372	725	6	the	the	DET
ejpam-1372	725	7	regularised	regularise	VERB
ejpam-1372	725	8	value	value	NOUN
ejpam-1372	725	9	given	give	VERB
ejpam-1372	725	10	by	by	ADP
ejpam-1372	725	11	equivalence	equivalence	NOUN
ejpam-1372	725	12	(	(	PUNCT
ejpam-1372	725	13	70	70	NUM
ejpam-1372	725	14	)	)	PUNCT
ejpam-1372	725	15	for	for	ADP
ejpam-1372	725	16	the	the	DET
ejpam-1372	725	17	second	second	ADJ
ejpam-1372	725	18	term	term	NOUN
ejpam-1372	725	19	on	on	ADP
ejpam-1372	725	20	the	the	DET
ejpam-1372	725	21	lhs	lhs	NOUN
ejpam-1372	725	22	of	of	ADP
ejpam-1372	725	23	equivalence	equivalence	NOUN
ejpam-1372	725	24	(	(	PUNCT
ejpam-1372	725	25	76	76	NUM
ejpam-1372	725	26	)	)	PUNCT
ejpam-1372	725	27	and	and	CCONJ
ejpam-1372	725	28	eq	eq	NOUN
ejpam-1372	725	29	.	.	PUNCT
ejpam-1372	726	1	(	(	PUNCT
ejpam-1372	726	2	77	77	NUM
ejpam-1372	726	3	)	)	PUNCT
ejpam-1372	726	4	into	into	ADP
ejpam-1372	726	5	its	its	PRON
ejpam-1372	726	6	rhs	rhs	PROPN
ejpam-1372	726	7	,	,	PUNCT
ejpam-1372	726	8	one	one	NOUN
ejpam-1372	726	9	obtains	obtain	VERB
ejpam-1372	726	10	the	the	DET
ejpam-1372	726	11	regularised	regularise	VERB
ejpam-1372	726	12	value	value	NOUN
ejpam-1372	726	13	of	of	ADP
ejpam-1372	726	14	the	the	DET
ejpam-1372	726	15	first	first	ADJ
ejpam-1372	726	16	series	series	NOUN
ejpam-1372	726	17	on	on	ADP
ejpam-1372	726	18	the	the	DET
ejpam-1372	726	19	lhs	lhs	PROPN
ejpam-1372	726	20	.	.	PUNCT
ejpam-1372	727	1	this	this	DET
ejpam-1372	727	2	yields	yield	NOUN
ejpam-1372	727	3	ti(n	ti(n	X
ejpam-1372	727	4	,	,	PUNCT
ejpam-1372	727	5	α	α	NOUN
ejpam-1372	727	6	,	,	PUNCT
ejpam-1372	727	7	z	z	NOUN
ejpam-1372	727	8	)	)	PUNCT
ejpam-1372	727	9	≡	≡	PROPN
ejpam-1372	727	10	(	(	PUNCT
ejpam-1372	727	11	−1)nzn−1	−1)nzn−1	NUM
ejpam-1372	727	12	−1	−1	NOUN
ejpam-1372	727	13	∫	∫	X
ejpam-1372	727	14	c	c	PROPN
ejpam-1372	727	15	ds	ds	PROPN
ejpam-1372	727	16	sn+α−1	sn+α−1	PROPN
ejpam-1372	727	17	e−s	e−s	ADV
ejpam-1372	727	18	s−	s−	PROPN
ejpam-1372	727	19	(	(	PUNCT
ejpam-1372	727	20	z−1	z−1	PROPN
ejpam-1372	727	21	−1	−1	NOUN
ejpam-1372	727	22	)	)	PUNCT
ejpam-1372	727	23	−	−	PROPN
ejpam-1372	727	24	2πi	2πi	ADJ
ejpam-1372	727	25	z−α−1	z−α−1	ADJ
ejpam-1372	727	26	e−iπαe1	e−iπαe1	X
ejpam-1372	727	27	/	/	SYM
ejpam-1372	727	28	z−1	z−1	PROPN
ejpam-1372	727	29	.	.	PUNCT
ejpam-1372	728	1	(	(	PUNCT
ejpam-1372	728	2	78	78	NUM
ejpam-1372	728	3	)	)	PUNCT
ejpam-1372	728	4	in	in	ADP
ejpam-1372	728	5	the	the	DET
ejpam-1372	728	6	above	above	ADJ
ejpam-1372	728	7	result	result	NOUN
ejpam-1372	728	8	c	c	PROPN
ejpam-1372	728	9	is	be	AUX
ejpam-1372	728	10	,	,	PUNCT
ejpam-1372	728	11	again	again	ADV
ejpam-1372	728	12	,	,	PUNCT
ejpam-1372	728	13	the	the	DET
ejpam-1372	728	14	line	line	NOUN
ejpam-1372	728	15	contour	contour	NOUN
ejpam-1372	728	16	along	along	ADP
ejpam-1372	728	17	the	the	DET
ejpam-1372	728	18	positive	positive	ADJ
ejpam-1372	728	19	real	real	ADJ
ejpam-1372	728	20	axis	axis	NOUN
ejpam-1372	728	21	and	and	CCONJ
ejpam-1372	728	22	π	π	NOUN
ejpam-1372	728	23	<	<	X
ejpam-1372	728	24	arg	arg	NOUN
ejpam-1372	728	25	z<3π	z<3π	NOUN
ejpam-1372	728	26	,	,	PUNCT
ejpam-1372	728	27	while	while	SCONJ
ejpam-1372	728	28	z−1	z−1	PROPN
ejpam-1372	728	29	=	=	SYM
ejpam-1372	728	30	z	z	PROPN
ejpam-1372	728	31	exp(−2iπ	exp(−2iπ	NOUN
ejpam-1372	728	32	)	)	PUNCT
ejpam-1372	728	33	.	.	PUNCT
ejpam-1372	729	1	to	to	PART
ejpam-1372	729	2	obtain	obtain	VERB
ejpam-1372	729	3	the	the	DET
ejpam-1372	729	4	regularised	regularise	VERB
ejpam-1372	729	5	value	value	NOUN
ejpam-1372	729	6	when	when	SCONJ
ejpam-1372	729	7	arg	arg	NOUN
ejpam-1372	729	8	z	z	PROPN
ejpam-1372	729	9	=	=	SYM
ejpam-1372	729	10	π	π	PROPN
ejpam-1372	729	11	,	,	PUNCT
ejpam-1372	729	12	all	all	PRON
ejpam-1372	729	13	we	we	PRON
ejpam-1372	729	14	need	need	VERB
ejpam-1372	729	15	to	to	PART
ejpam-1372	729	16	do	do	VERB
ejpam-1372	729	17	is	be	AUX
ejpam-1372	729	18	average	average	ADJ
ejpam-1372	729	19	the	the	DET
ejpam-1372	729	20	results	result	NOUN
ejpam-1372	729	21	for	for	ADP
ejpam-1372	729	22	the	the	DET
ejpam-1372	729	23	adjacent	adjacent	ADJ
ejpam-1372	729	24	stokes	stoke	NOUN
ejpam-1372	729	25	sectors	sector	NOUN
ejpam-1372	729	26	,	,	PUNCT
ejpam-1372	729	27	viz	viz	PROPN
ejpam-1372	729	28	.	.	PUNCT
ejpam-1372	730	1	equivalences	equivalences	PROPN
ejpam-1372	730	2	(	(	PUNCT
ejpam-1372	730	3	67	67	NUM
ejpam-1372	730	4	)	)	PUNCT
ejpam-1372	730	5	and	and	CCONJ
ejpam-1372	730	6	(	(	PUNCT
ejpam-1372	730	7	75	75	NUM
ejpam-1372	730	8	)	)	PUNCT
ejpam-1372	730	9	,	,	PUNCT
ejpam-1372	730	10	while	while	SCONJ
ejpam-1372	730	11	ensuring	ensure	VERB
ejpam-1372	730	12	that	that	SCONJ
ejpam-1372	730	13	only	only	ADV
ejpam-1372	730	14	the	the	DET
ejpam-1372	730	15	cauchy	cauchy	ADJ
ejpam-1372	730	16	principal	principal	ADJ
ejpam-1372	730	17	value	value	NOUN
ejpam-1372	730	18	is	be	AUX
ejpam-1372	730	19	evaluated	evaluate	VERB
ejpam-1372	730	20	in	in	ADP
ejpam-1372	730	21	the	the	DET
ejpam-1372	730	22	resulting	result	VERB
ejpam-1372	730	23	integral	integral	ADJ
ejpam-1372	730	24	.	.	PUNCT
ejpam-1372	731	1	then	then	ADV
ejpam-1372	731	2	for	for	ADP
ejpam-1372	731	3	arg	arg	NOUN
ejpam-1372	731	4	z	z	PROPN
ejpam-1372	731	5	=	=	SYM
ejpam-1372	731	6	π	π	PROPN
ejpam-1372	731	7	,	,	PUNCT
ejpam-1372	731	8	we	we	PRON
ejpam-1372	731	9	find	find	VERB
ejpam-1372	731	10	that	that	SCONJ
ejpam-1372	731	11	the	the	DET
ejpam-1372	731	12	regularised	regularise	VERB
ejpam-1372	731	13	value	value	NOUN
ejpam-1372	731	14	of	of	ADP
ejpam-1372	731	15	the	the	DET
ejpam-1372	731	16	first	first	ADJ
ejpam-1372	731	17	type	type	NOUN
ejpam-1372	731	18	of	of	ADP
ejpam-1372	731	19	terminant	terminant	NOUN
ejpam-1372	731	20	is	be	AUX
ejpam-1372	731	21	given	give	VERB
ejpam-1372	731	22	by	by	ADP
ejpam-1372	731	23	ti	ti	PROPN
ejpam-1372	731	24	(	(	PUNCT
ejpam-1372	731	25	n	n	X
ejpam-1372	731	26	,	,	PUNCT
ejpam-1372	731	27	α	α	PROPN
ejpam-1372	731	28	,	,	PUNCT
ejpam-1372	731	29	z	z	NOUN
ejpam-1372	731	30	)	)	PUNCT
ejpam-1372	731	31	≡	≡	PROPN
ejpam-1372	732	1	|z|n	|z|n	ADP
ejpam-1372	732	2	p	p	X
ejpam-1372	732	3	∫	∫	PROPN
ejpam-1372	732	4	∞	∞	NOUN
ejpam-1372	732	5	0	0	PUNCT
ejpam-1372	733	1	d	d	PRON
ejpam-1372	733	2	t	t	NOUN
ejpam-1372	733	3	tn+α−1	tn+α−1	PROPN
ejpam-1372	733	4	e−t	e−t	NOUN
ejpam-1372	733	5	1−	1−	NUM
ejpam-1372	733	6	|z|t	|z|t	X
ejpam-1372	733	7	−πi	−πi	NOUN
ejpam-1372	733	8	|z|−α	|z|−α	PROPN
ejpam-1372	733	9	e−1/|z|	e−1/|z|	NOUN
ejpam-1372	733	10	.	.	PUNCT
ejpam-1372	734	1	(	(	PUNCT
ejpam-1372	734	2	79	79	NUM
ejpam-1372	734	3	)	)	PUNCT
ejpam-1372	734	4	to	to	PART
ejpam-1372	734	5	determine	determine	VERB
ejpam-1372	734	6	the	the	DET
ejpam-1372	734	7	asymptotic	asymptotic	ADJ
ejpam-1372	734	8	forms	form	NOUN
ejpam-1372	734	9	for	for	ADP
ejpam-1372	734	10	the	the	DET
ejpam-1372	734	11	other	other	ADJ
ejpam-1372	734	12	or	or	CCONJ
ejpam-1372	734	13	higher	high	ADJ
ejpam-1372	734	14	stokes	stoke	NOUN
ejpam-1372	734	15	sectors	sector	NOUN
ejpam-1372	734	16	and	and	CCONJ
ejpam-1372	734	17	lines	line	NOUN
ejpam-1372	734	18	,	,	PUNCT
ejpam-1372	734	19	we	we	PRON
ejpam-1372	734	20	continue	continue	VERB
ejpam-1372	734	21	with	with	ADP
ejpam-1372	734	22	more	more	ADJ
ejpam-1372	734	23	anti	anti	ADJ
ejpam-1372	734	24	-	-	ADJ
ejpam-1372	734	25	clockwise	clockwise	ADJ
ejpam-1372	734	26	rotations	rotation	NOUN
ejpam-1372	734	27	of	of	ADP
ejpam-1372	734	28	2π	2π	NOUN
ejpam-1372	734	29	.	.	PUNCT
ejpam-1372	735	1	in	in	ADP
ejpam-1372	735	2	fact	fact	NOUN
ejpam-1372	735	3	,	,	PUNCT
ejpam-1372	735	4	the	the	DET
ejpam-1372	735	5	generalisation	generalisation	NOUN
ejpam-1372	735	6	of	of	ADP
ejpam-1372	735	7	equivalence	equivalence	NOUN
ejpam-1372	735	8	(	(	PUNCT
ejpam-1372	735	9	76	76	NUM
ejpam-1372	735	10	)	)	PUNCT
ejpam-1372	735	11	to	to	ADP
ejpam-1372	735	12	l	l	NOUN
ejpam-1372	735	13	rotations	rotation	NOUN
ejpam-1372	735	14	yields	yield	NOUN
ejpam-1372	735	15	ti	ti	X
ejpam-1372	735	16	(	(	PUNCT
ejpam-1372	735	17	n	n	PROPN
ejpam-1372	735	18	,	,	PUNCT
ejpam-1372	735	19	α	α	NOUN
ejpam-1372	735	20	,	,	PUNCT
ejpam-1372	735	21	z	z	PROPN
ejpam-1372	735	22	exp(2l	exp(2l	VERB
ejpam-1372	735	23	iπ))−	iπ))−	ADV
ejpam-1372	735	24	ti	ti	NOUN
ejpam-1372	735	25	(	(	PUNCT
ejpam-1372	735	26	n	n	X
ejpam-1372	735	27	,	,	PUNCT
ejpam-1372	735	28	α	α	PROPN
ejpam-1372	735	29	,	,	PUNCT
ejpam-1372	735	30	z	z	NOUN
ejpam-1372	735	31	exp(2(l	exp(2(l	NOUN
ejpam-1372	735	32	−	−	PROPN
ejpam-1372	735	33	1)iπ	1)iπ	NUM
ejpam-1372	735	34	)	)	PUNCT
ejpam-1372	735	35	)	)	PUNCT
ejpam-1372	736	1	≡	≡	PROPN
ejpam-1372	736	2	2πi	2πi	PROPN
ejpam-1372	736	3	res	res	PROPN
ejpam-1372	736	4	�	�	PROPN
ejpam-1372	736	5	ii	ii	PROPN
ejpam-1372	736	6	(	(	PUNCT
ejpam-1372	736	7	z	z	PROPN
ejpam-1372	736	8	exp(−(2l	exp(−(2l	PROPN
ejpam-1372	736	9	−	−	NOUN
ejpam-1372	736	10	1)iπ),α	1)iπ),α	NUM
ejpam-1372	736	11	)	)	PUNCT
ejpam-1372	736	12	.	.	PUNCT
ejpam-1372	737	1	(	(	PUNCT
ejpam-1372	737	2	80	80	NUM
ejpam-1372	737	3	)	)	PUNCT
ejpam-1372	737	4	for	for	ADP
ejpam-1372	737	5	l	l	PROPN
ejpam-1372	737	6	>	>	X
ejpam-1372	737	7	1	1	NUM
ejpam-1372	737	8	,	,	PUNCT
ejpam-1372	737	9	we	we	PRON
ejpam-1372	737	10	replace	replace	VERB
ejpam-1372	737	11	the	the	DET
ejpam-1372	737	12	second	second	ADJ
ejpam-1372	737	13	term	term	NOUN
ejpam-1372	737	14	on	on	ADP
ejpam-1372	737	15	the	the	DET
ejpam-1372	737	16	lhs	lhs	NOUN
ejpam-1372	737	17	by	by	ADP
ejpam-1372	737	18	introducing	introduce	VERB
ejpam-1372	737	19	the	the	DET
ejpam-1372	737	20	l	l	NOUN
ejpam-1372	737	21	=	=	PUNCT
ejpam-1372	737	22	l−1	l−1	PROPN
ejpam-1372	737	23	version	version	NOUN
ejpam-1372	737	24	of	of	ADP
ejpam-1372	737	25	equivalence	equivalence	NOUN
ejpam-1372	737	26	(	(	PUNCT
ejpam-1372	737	27	80	80	NUM
ejpam-1372	737	28	)	)	PUNCT
ejpam-1372	737	29	.	.	PUNCT
ejpam-1372	738	1	we	we	PRON
ejpam-1372	738	2	continue	continue	VERB
ejpam-1372	738	3	this	this	DET
ejpam-1372	738	4	process	process	NOUN
ejpam-1372	738	5	recursively	recursively	ADV
ejpam-1372	738	6	stopping	stop	VERB
ejpam-1372	738	7	only	only	ADV
ejpam-1372	738	8	when	when	SCONJ
ejpam-1372	738	9	we	we	PRON
ejpam-1372	738	10	reach	reach	VERB
ejpam-1372	738	11	the	the	DET
ejpam-1372	738	12	rhs	rhs	PROPN
ejpam-1372	738	13	v.	v.	ADP
ejpam-1372	738	14	kowalenko	kowalenko	PROPN
ejpam-1372	738	15	/	/	SYM
ejpam-1372	738	16	eur	eur	PROPN
ejpam-1372	738	17	.	.	PUNCT
ejpam-1372	739	1	j.	j.	PROPN
ejpam-1372	739	2	pure	pure	PROPN
ejpam-1372	739	3	appl	appl	PROPN
ejpam-1372	739	4	.	.	PROPN
ejpam-1372	739	5	math	math	PROPN
ejpam-1372	739	6	,	,	PUNCT
ejpam-1372	739	7	4	4	NUM
ejpam-1372	739	8	(	(	PUNCT
ejpam-1372	739	9	2011	2011	NUM
ejpam-1372	739	10	)	)	PUNCT
ejpam-1372	739	11	,	,	PUNCT
ejpam-1372	739	12	370	370	NUM
ejpam-1372	739	13	-	-	SYM
ejpam-1372	739	14	423	423	NUM
ejpam-1372	739	15	395	395	NUM
ejpam-1372	739	16	of	of	ADP
ejpam-1372	739	17	equivalence	equivalence	NOUN
ejpam-1372	739	18	(	(	PUNCT
ejpam-1372	739	19	73	73	NUM
ejpam-1372	739	20	)	)	PUNCT
ejpam-1372	739	21	.	.	PUNCT
ejpam-1372	740	1	hence	hence	ADV
ejpam-1372	740	2	,	,	PUNCT
ejpam-1372	740	3	we	we	PRON
ejpam-1372	740	4	see	see	VERB
ejpam-1372	740	5	that	that	PRON
ejpam-1372	740	6	for	for	ADP
ejpam-1372	740	7	the	the	DET
ejpam-1372	740	8	higher	high	ADJ
ejpam-1372	740	9	stokes	stoke	NOUN
ejpam-1372	740	10	sectors	sector	NOUN
ejpam-1372	740	11	the	the	DET
ejpam-1372	740	12	regularised	regularise	VERB
ejpam-1372	740	13	value	value	NOUN
ejpam-1372	740	14	is	be	AUX
ejpam-1372	740	15	given	give	VERB
ejpam-1372	740	16	by	by	ADP
ejpam-1372	740	17	the	the	DET
ejpam-1372	740	18	rhs	rhs	PROPN
ejpam-1372	740	19	of	of	ADP
ejpam-1372	740	20	equivalence	equivalence	NOUN
ejpam-1372	740	21	(	(	PUNCT
ejpam-1372	740	22	76	76	NUM
ejpam-1372	740	23	)	)	PUNCT
ejpam-1372	740	24	except	except	SCONJ
ejpam-1372	740	25	the	the	DET
ejpam-1372	740	26	second	second	ADJ
ejpam-1372	740	27	term	term	NOUN
ejpam-1372	740	28	becomes	become	VERB
ejpam-1372	740	29	a	a	DET
ejpam-1372	740	30	sum	sum	NOUN
ejpam-1372	740	31	over	over	ADP
ejpam-1372	740	32	all	all	DET
ejpam-1372	740	33	the	the	DET
ejpam-1372	740	34	residues	residue	NOUN
ejpam-1372	740	35	from	from	ADP
ejpam-1372	740	36	k=1	k=1	PRON
ejpam-1372	740	37	to	to	AUX
ejpam-1372	740	38	l.	l.	PROPN
ejpam-1372	740	39	this	this	PRON
ejpam-1372	740	40	means	mean	VERB
ejpam-1372	740	41	that	that	SCONJ
ejpam-1372	740	42	ti	ti	PROPN
ejpam-1372	740	43	(	(	PUNCT
ejpam-1372	740	44	n	n	X
ejpam-1372	740	45	,	,	PUNCT
ejpam-1372	740	46	α	α	NOUN
ejpam-1372	740	47	,	,	PUNCT
ejpam-1372	740	48	z	z	PROPN
ejpam-1372	740	49	exp(2l	exp(2l	VERB
ejpam-1372	740	50	iπ))−	iπ))−	ADV
ejpam-1372	740	51	ti	ti	NOUN
ejpam-1372	740	52	(	(	PUNCT
ejpam-1372	740	53	n	n	PROPN
ejpam-1372	740	54	,	,	PUNCT
ejpam-1372	740	55	α	α	PROPN
ejpam-1372	740	56	,	,	PUNCT
ejpam-1372	740	57	z	z	NOUN
ejpam-1372	740	58	)	)	PUNCT
ejpam-1372	740	59	≡	≡	PROPN
ejpam-1372	740	60	2πi	2πi	PROPN
ejpam-1372	741	1	l	l	NOUN
ejpam-1372	741	2	∑	∑	PUNCT
ejpam-1372	741	3	k=1	k=1	PROPN
ejpam-1372	741	4	res	res	PROPN
ejpam-1372	741	5	�	�	PROPN
ejpam-1372	741	6	ii	ii	PROPN
ejpam-1372	741	7	(	(	PUNCT
ejpam-1372	741	8	z	z	NOUN
ejpam-1372	741	9	exp(−(2k−	exp(−(2k−	NOUN
ejpam-1372	741	10	1)iπ),α	1)iπ),α	NUM
ejpam-1372	741	11	)	)	PUNCT
ejpam-1372	741	12	.	.	PUNCT
ejpam-1372	742	1	(	(	PUNCT
ejpam-1372	742	2	81	81	NUM
ejpam-1372	742	3	)	)	PUNCT
ejpam-1372	742	4	replacing	replace	VERB
ejpam-1372	742	5	z	z	NOUN
ejpam-1372	742	6	exp(2l	exp(2l	VERB
ejpam-1372	742	7	iπ	iπ	NOUN
ejpam-1372	742	8	)	)	PUNCT
ejpam-1372	742	9	by	by	ADP
ejpam-1372	742	10	z	z	PROPN
ejpam-1372	742	11	,	,	PUNCT
ejpam-1372	742	12	where(2l	where(2l	VERB
ejpam-1372	742	13	−	−	PROPN
ejpam-1372	742	14	1)π	1)π	NOUN
ejpam-1372	742	15	<	<	X
ejpam-1372	742	16	arg	arg	NOUN
ejpam-1372	742	17	z	z	X
ejpam-1372	742	18	<	<	X
ejpam-1372	742	19	(	(	PUNCT
ejpam-1372	742	20	2l	2l	X
ejpam-1372	742	21	+	+	CCONJ
ejpam-1372	742	22	1)π	1)π	NUM
ejpam-1372	742	23	,	,	PUNCT
ejpam-1372	742	24	and	and	CCONJ
ejpam-1372	742	25	carrying	carry	VERB
ejpam-1372	742	26	out	out	ADP
ejpam-1372	742	27	the	the	DET
ejpam-1372	742	28	finite	finite	ADJ
ejpam-1372	742	29	sum	sum	NOUN
ejpam-1372	742	30	,	,	PUNCT
ejpam-1372	742	31	we	we	PRON
ejpam-1372	742	32	find	find	VERB
ejpam-1372	742	33	that	that	SCONJ
ejpam-1372	742	34	the	the	DET
ejpam-1372	742	35	regularised	regularise	VERB
ejpam-1372	742	36	value	value	NOUN
ejpam-1372	742	37	of	of	ADP
ejpam-1372	742	38	the	the	DET
ejpam-1372	742	39	first	first	ADJ
ejpam-1372	742	40	type	type	NOUN
ejpam-1372	742	41	of	of	ADP
ejpam-1372	742	42	terminant	terminant	NOUN
ejpam-1372	742	43	reduces	reduce	VERB
ejpam-1372	742	44	to	to	ADP
ejpam-1372	742	45	ti	ti	PROPN
ejpam-1372	742	46	(	(	PUNCT
ejpam-1372	742	47	n	n	X
ejpam-1372	742	48	,	,	PUNCT
ejpam-1372	742	49	α	α	PROPN
ejpam-1372	742	50	,	,	PUNCT
ejpam-1372	742	51	z	z	NOUN
ejpam-1372	742	52	)	)	PUNCT
ejpam-1372	742	53	≡	≡	PROPN
ejpam-1372	742	54	(	(	PUNCT
ejpam-1372	742	55	−z−l	−z−l	PROPN
ejpam-1372	742	56	)	)	PUNCT
ejpam-1372	742	57	n	n	CCONJ
ejpam-1372	743	1	∫	∫	NOUN
ejpam-1372	743	2	∞	∞	NUM
ejpam-1372	743	3	0	0	NUM
ejpam-1372	744	1	d	d	PRON
ejpam-1372	744	2	t	t	NOUN
ejpam-1372	744	3	tn+α−1	tn+α−1	NOUN
ejpam-1372	744	4	e−t	e−t	NOUN
ejpam-1372	744	5	1	1	NUM
ejpam-1372	744	6	+	+	NUM
ejpam-1372	744	7	z−l	z−l	PROPN
ejpam-1372	744	8	t	t	NOUN
ejpam-1372	744	9	−	−	PROPN
ejpam-1372	744	10	2πi	2πi	NOUN
ejpam-1372	744	11	z−α−l	z−α−l	NOUN
ejpam-1372	744	12	e−l	e−l	PROPN
ejpam-1372	744	13	iπαe1	iπαe1	PROPN
ejpam-1372	744	14	/	/	SYM
ejpam-1372	744	15	z−l	z−l	PROPN
ejpam-1372	744	16	sin(lπα	sin(lπα	NOUN
ejpam-1372	744	17	)	)	PUNCT
ejpam-1372	744	18	sin(πα	sin(πα	VERB
ejpam-1372	744	19	)	)	PUNCT
ejpam-1372	744	20	,	,	PUNCT
ejpam-1372	744	21	(	(	PUNCT
ejpam-1372	744	22	82	82	NUM
ejpam-1372	744	23	)	)	PUNCT
ejpam-1372	744	24	where	where	SCONJ
ejpam-1372	744	25	z−l	z−l	PROPN
ejpam-1372	744	26	=	=	PROPN
ejpam-1372	744	27	z	z	PROPN
ejpam-1372	744	28	exp(−2l	exp(−2l	NOUN
ejpam-1372	744	29	iπ	iπ	NOUN
ejpam-1372	744	30	)	)	PUNCT
ejpam-1372	744	31	.	.	PUNCT
ejpam-1372	745	1	for	for	ADP
ejpam-1372	745	2	the	the	DET
ejpam-1372	745	3	stokes	stoke	NOUN
ejpam-1372	745	4	line	line	NOUN
ejpam-1372	745	5	of	of	ADP
ejpam-1372	745	6	arg	arg	NOUN
ejpam-1372	745	7	z=(2l+1)π	z=(2l+1)π	PROPN
ejpam-1372	745	8	,	,	PUNCT
ejpam-1372	745	9	the	the	DET
ejpam-1372	745	10	regularised	regularise	VERB
ejpam-1372	745	11	value	value	NOUN
ejpam-1372	745	12	of	of	ADP
ejpam-1372	745	13	the	the	DET
ejpam-1372	745	14	first	first	ADJ
ejpam-1372	745	15	type	type	NOUN
ejpam-1372	745	16	of	of	ADP
ejpam-1372	745	17	terminant	terminant	NOUN
ejpam-1372	745	18	is	be	AUX
ejpam-1372	745	19	obtained	obtain	VERB
ejpam-1372	745	20	by	by	ADP
ejpam-1372	745	21	averaging	average	VERB
ejpam-1372	745	22	the	the	DET
ejpam-1372	745	23	regularised	regularise	VERB
ejpam-1372	745	24	values	value	NOUN
ejpam-1372	745	25	of	of	ADP
ejpam-1372	745	26	the	the	DET
ejpam-1372	745	27	abutting	abutting	NOUN
ejpam-1372	745	28	stokes	stoke	VERB
ejpam-1372	745	29	sectors	sector	NOUN
ejpam-1372	745	30	,	,	PUNCT
ejpam-1372	745	31	whilst	whilst	SCONJ
ejpam-1372	745	32	ensuring	ensure	VERB
ejpam-1372	745	33	that	that	SCONJ
ejpam-1372	745	34	the	the	DET
ejpam-1372	745	35	principal	principal	ADJ
ejpam-1372	745	36	value	value	NOUN
ejpam-1372	745	37	is	be	AUX
ejpam-1372	745	38	evaluated	evaluate	VERB
ejpam-1372	745	39	in	in	ADP
ejpam-1372	745	40	the	the	DET
ejpam-1372	745	41	resulting	result	VERB
ejpam-1372	745	42	contour	contour	NOUN
ejpam-1372	745	43	integral	integral	ADJ
ejpam-1372	745	44	.	.	PUNCT
ejpam-1372	746	1	thus	thus	ADV
ejpam-1372	746	2	,	,	PUNCT
ejpam-1372	746	3	we	we	PRON
ejpam-1372	746	4	find	find	VERB
ejpam-1372	746	5	that	that	SCONJ
ejpam-1372	746	6	ti	ti	NOUN
ejpam-1372	746	7	(	(	PUNCT
ejpam-1372	746	8	n	n	X
ejpam-1372	746	9	,	,	PUNCT
ejpam-1372	746	10	α	α	PROPN
ejpam-1372	746	11	,	,	PUNCT
ejpam-1372	746	12	z	z	NOUN
ejpam-1372	746	13	)	)	PUNCT
ejpam-1372	746	14	≡	≡	PROPN
ejpam-1372	747	1	|z|n−1p	|z|n−1p	PROPN
ejpam-1372	747	2	∫	∫	PROPN
ejpam-1372	747	3	∞	∞	NOUN
ejpam-1372	747	4	0	0	PUNCT
ejpam-1372	748	1	d	d	PRON
ejpam-1372	748	2	t	t	PROPN
ejpam-1372	748	3	tn+α−1	tn+α−1	PROPN
ejpam-1372	748	4	e−t	e−t	NOUN
ejpam-1372	748	5	t	t	NOUN
ejpam-1372	748	6	−	−	NOUN
ejpam-1372	748	7	|z|	|z|	VERB
ejpam-1372	748	8	−πi	−πi	NOUN
ejpam-1372	748	9	|z|−αe−1/|z|	|z|−αe−1/|z|	NOUN
ejpam-1372	748	10	×	×	PROPN
ejpam-1372	748	11	�	�	PROPN
ejpam-1372	748	12	2e−(l+1)iπα	2e−(l+1)iπα	NUM
ejpam-1372	748	13	sin(lπα	sin(lπα	NOUN
ejpam-1372	748	14	)	)	PUNCT
ejpam-1372	748	15	sin(πα	sin(πα	VERB
ejpam-1372	748	16	)	)	PUNCT
ejpam-1372	749	1	+	+	CCONJ
ejpam-1372	749	2	1	1	NUM
ejpam-1372	749	3	�	�	NOUN
ejpam-1372	749	4	.	.	PUNCT
ejpam-1372	750	1	(	(	PUNCT
ejpam-1372	750	2	83	83	NUM
ejpam-1372	750	3	)	)	PUNCT
ejpam-1372	750	4	to	to	PART
ejpam-1372	750	5	determine	determine	VERB
ejpam-1372	750	6	the	the	DET
ejpam-1372	750	7	regularised	regularise	VERB
ejpam-1372	750	8	value	value	NOUN
ejpam-1372	750	9	for	for	ADP
ejpam-1372	750	10	arg	arg	NOUN
ejpam-1372	750	11	z	z	NOUN
ejpam-1372	750	12	less	less	ADJ
ejpam-1372	750	13	than	than	ADP
ejpam-1372	750	14	zero	zero	NUM
ejpam-1372	750	15	,	,	PUNCT
ejpam-1372	750	16	we	we	PRON
ejpam-1372	750	17	need	need	VERB
ejpam-1372	750	18	to	to	PART
ejpam-1372	750	19	consider	consider	VERB
ejpam-1372	750	20	clockwise	clockwise	NOUN
ejpam-1372	750	21	rotations	rotation	NOUN
ejpam-1372	750	22	of	of	ADP
ejpam-1372	750	23	2π	2π	NOUN
ejpam-1372	750	24	.	.	PUNCT
ejpam-1372	751	1	for	for	ADP
ejpam-1372	751	2	example	example	NOUN
ejpam-1372	751	3	,	,	PUNCT
ejpam-1372	751	4	equivalence	equivalence	NOUN
ejpam-1372	751	5	(	(	PUNCT
ejpam-1372	751	6	76	76	NUM
ejpam-1372	751	7	)	)	PUNCT
ejpam-1372	751	8	becomes	become	VERB
ejpam-1372	751	9	ti	ti	NOUN
ejpam-1372	751	10	(	(	PUNCT
ejpam-1372	751	11	n	n	X
ejpam-1372	751	12	,	,	PUNCT
ejpam-1372	751	13	α	α	NOUN
ejpam-1372	751	14	,	,	PUNCT
ejpam-1372	751	15	z	z	NOUN
ejpam-1372	751	16	exp(−2iπ))−	exp(−2iπ))−	ADJ
ejpam-1372	751	17	ti	ti	X
ejpam-1372	751	18	(	(	PUNCT
ejpam-1372	751	19	n	n	PROPN
ejpam-1372	751	20	,	,	PUNCT
ejpam-1372	751	21	α	α	PROPN
ejpam-1372	751	22	,	,	PUNCT
ejpam-1372	751	23	z	z	NOUN
ejpam-1372	751	24	)	)	PUNCT
ejpam-1372	751	25	≡	≡	PROPN
ejpam-1372	751	26	−2πi	−2πi	PROPN
ejpam-1372	751	27	res	res	PROPN
ejpam-1372	751	28	�	�	PROPN
ejpam-1372	751	29	ii	ii	PROPN
ejpam-1372	751	30	(	(	PUNCT
ejpam-1372	751	31	z	z	NOUN
ejpam-1372	751	32	,	,	PUNCT
ejpam-1372	751	33	exp(iπ),α	exp(iπ),α	PROPN
ejpam-1372	751	34	)	)	PUNCT
ejpam-1372	751	35	,	,	PUNCT
ejpam-1372	751	36	(	(	PUNCT
ejpam-1372	751	37	84	84	NUM
ejpam-1372	751	38	)	)	PUNCT
ejpam-1372	751	39	which	which	PRON
ejpam-1372	751	40	is	be	AUX
ejpam-1372	751	41	merely	merely	ADV
ejpam-1372	751	42	the	the	DET
ejpam-1372	751	43	complex	complex	ADJ
ejpam-1372	751	44	conjugate	conjugate	NOUN
ejpam-1372	751	45	of	of	ADP
ejpam-1372	751	46	equivalence	equivalence	NOUN
ejpam-1372	751	47	(	(	PUNCT
ejpam-1372	751	48	76	76	NUM
ejpam-1372	751	49	)	)	PUNCT
ejpam-1372	751	50	.	.	PUNCT
ejpam-1372	752	1	consequently	consequently	ADV
ejpam-1372	752	2	,	,	PUNCT
ejpam-1372	752	3	the	the	DET
ejpam-1372	752	4	regularised	regularise	VERB
ejpam-1372	752	5	value	value	NOUN
ejpam-1372	752	6	of	of	ADP
ejpam-1372	752	7	the	the	DET
ejpam-1372	752	8	first	first	ADJ
ejpam-1372	752	9	type	type	NOUN
ejpam-1372	752	10	of	of	ADP
ejpam-1372	752	11	terminant	terminant	NOUN
ejpam-1372	752	12	for	for	ADP
ejpam-1372	752	13	negative	negative	ADJ
ejpam-1372	752	14	values	value	NOUN
ejpam-1372	752	15	of	of	ADP
ejpam-1372	752	16	arg	arg	NOUN
ejpam-1372	752	17	z	z	NOUN
ejpam-1372	752	18	will	will	AUX
ejpam-1372	752	19	be	be	AUX
ejpam-1372	752	20	the	the	DET
ejpam-1372	752	21	complex	complex	ADJ
ejpam-1372	752	22	conjugate	conjugate	NOUN
ejpam-1372	752	23	of	of	ADP
ejpam-1372	752	24	the	the	DET
ejpam-1372	752	25	corresponding	corresponding	ADJ
ejpam-1372	752	26	regularised	regularise	VERB
ejpam-1372	752	27	value	value	NOUN
ejpam-1372	752	28	for	for	ADP
ejpam-1372	752	29	the	the	DET
ejpam-1372	752	30	complex	complex	ADJ
ejpam-1372	752	31	conjugate	conjugate	NOUN
ejpam-1372	752	32	of	of	ADP
ejpam-1372	752	33	z.	z.	PROPN
ejpam-1372	752	34	hence	hence	PROPN
ejpam-1372	752	35	,	,	PUNCT
ejpam-1372	752	36	the	the	DET
ejpam-1372	752	37	regularised	regularise	VERB
ejpam-1372	752	38	value	value	NOUN
ejpam-1372	752	39	of	of	ADP
ejpam-1372	752	40	the	the	DET
ejpam-1372	752	41	first	first	ADJ
ejpam-1372	752	42	type	type	NOUN
ejpam-1372	752	43	terminant	terminant	NOUN
ejpam-1372	752	44	for	for	ADP
ejpam-1372	752	45	−(2l	−(2l	NOUN
ejpam-1372	752	46	+	+	NOUN
ejpam-1372	752	47	1)π	1)π	NUM
ejpam-1372	752	48	<	<	X
ejpam-1372	752	49	arg	arg	NOUN
ejpam-1372	752	50	z<−(2l	z<−(2l	NUM
ejpam-1372	752	51	−	−	NOUN
ejpam-1372	752	52	1)π	1)π	NUM
ejpam-1372	752	53	is	be	AUX
ejpam-1372	752	54	given	give	VERB
ejpam-1372	752	55	by	by	ADP
ejpam-1372	752	56	ti	ti	PROPN
ejpam-1372	752	57	(	(	PUNCT
ejpam-1372	752	58	n	n	X
ejpam-1372	752	59	,	,	PUNCT
ejpam-1372	752	60	α	α	PROPN
ejpam-1372	752	61	,	,	PUNCT
ejpam-1372	752	62	z	z	NOUN
ejpam-1372	752	63	)	)	PUNCT
ejpam-1372	752	64	≡	≡	PROPN
ejpam-1372	752	65	(	(	PUNCT
ejpam-1372	752	66	−zl	−zl	PROPN
ejpam-1372	752	67	)	)	PUNCT
ejpam-1372	752	68	n	n	CCONJ
ejpam-1372	752	69	∫	∫	NOUN
ejpam-1372	753	1	∞	∞	NUM
ejpam-1372	753	2	0	0	NUM
ejpam-1372	754	1	d	d	PRON
ejpam-1372	754	2	t	t	NOUN
ejpam-1372	754	3	tn+α−1	tn+α−1	NOUN
ejpam-1372	754	4	e−t	e−t	NOUN
ejpam-1372	754	5	1	1	NUM
ejpam-1372	754	6	+	+	SYM
ejpam-1372	754	7	zl	zl	NUM
ejpam-1372	754	8	t	t	NOUN
ejpam-1372	754	9	+	+	CCONJ
ejpam-1372	754	10	2πi	2πi	ADJ
ejpam-1372	754	11	z−α	z−α	PROPN
ejpam-1372	754	12	l	l	X
ejpam-1372	754	13	eiπαe1	eiπαe1	PROPN
ejpam-1372	754	14	/	/	SYM
ejpam-1372	754	15	zl	zl	PROPN
ejpam-1372	754	16	sin(lπα	sin(lπα	NOUN
ejpam-1372	754	17	)	)	PUNCT
ejpam-1372	754	18	sin(πα	sin(πα	VERB
ejpam-1372	754	19	)	)	PUNCT
ejpam-1372	754	20	,	,	PUNCT
ejpam-1372	754	21	(	(	PUNCT
ejpam-1372	754	22	85	85	NUM
ejpam-1372	754	23	)	)	PUNCT
ejpam-1372	754	24	where	where	SCONJ
ejpam-1372	754	25	zl	zl	NOUN
ejpam-1372	754	26	=	=	SYM
ejpam-1372	754	27	z	z	PROPN
ejpam-1372	754	28	exp(2l	exp(2l	VERB
ejpam-1372	754	29	iπ	iπ	NOUN
ejpam-1372	754	30	)	)	PUNCT
ejpam-1372	754	31	.	.	PUNCT
ejpam-1372	755	1	similarly	similarly	ADV
ejpam-1372	755	2	,	,	PUNCT
ejpam-1372	755	3	for	for	ADP
ejpam-1372	755	4	the	the	DET
ejpam-1372	755	5	stokes	stokes	PROPN
ejpam-1372	755	6	lines	line	NOUN
ejpam-1372	755	7	,	,	PUNCT
ejpam-1372	755	8	where	where	SCONJ
ejpam-1372	755	9	arg	arg	VERB
ejpam-1372	755	10	z=−(2l	z=−(2l	PROPN
ejpam-1372	755	11	+	+	CCONJ
ejpam-1372	755	12	1)π	1)π	NUM
ejpam-1372	755	13	,	,	PUNCT
ejpam-1372	755	14	we	we	PRON
ejpam-1372	755	15	find	find	VERB
ejpam-1372	755	16	that	that	SCONJ
ejpam-1372	756	1	ti	ti	NOUN
ejpam-1372	756	2	(	(	PUNCT
ejpam-1372	756	3	n	n	X
ejpam-1372	756	4	,	,	PUNCT
ejpam-1372	756	5	α	α	PROPN
ejpam-1372	756	6	,	,	PUNCT
ejpam-1372	756	7	z	z	NOUN
ejpam-1372	756	8	)	)	PUNCT
ejpam-1372	756	9	≡	≡	PROPN
ejpam-1372	757	1	|z|n−1p	|z|n−1p	PROPN
ejpam-1372	757	2	∫	∫	PROPN
ejpam-1372	757	3	∞	∞	NOUN
ejpam-1372	757	4	0	0	PUNCT
ejpam-1372	758	1	d	d	PRON
ejpam-1372	758	2	t	t	PROPN
ejpam-1372	758	3	tn+α−1	tn+α−1	PROPN
ejpam-1372	758	4	e−t	e−t	NOUN
ejpam-1372	758	5	t	t	NOUN
ejpam-1372	758	6	−	−	NOUN
ejpam-1372	758	7	|z|	|z|	NOUN
ejpam-1372	758	8	+	+	NOUN
ejpam-1372	758	9	πi	πi	ADP
ejpam-1372	758	10	|z|−αe−1/|z|	|z|−αe−1/|z|	NOUN
ejpam-1372	758	11	×	×	PROPN
ejpam-1372	758	12	�	�	PROPN
ejpam-1372	758	13	2e(l+1)iπα	2e(l+1)iπα	PROPN
ejpam-1372	758	14	sin(lπα	sin(lπα	NOUN
ejpam-1372	758	15	)	)	PUNCT
ejpam-1372	758	16	sin(πα	sin(πα	VERB
ejpam-1372	758	17	)	)	PUNCT
ejpam-1372	759	1	+	+	CCONJ
ejpam-1372	759	2	1	1	NUM
ejpam-1372	759	3	�	�	NOUN
ejpam-1372	759	4	.	.	PUNCT
ejpam-1372	760	1	(	(	PUNCT
ejpam-1372	760	2	86	86	NUM
ejpam-1372	760	3	)	)	PUNCT
ejpam-1372	760	4	v.	v.	ADP
ejpam-1372	760	5	kowalenko	kowalenko	PROPN
ejpam-1372	760	6	/	/	SYM
ejpam-1372	760	7	eur	eur	PROPN
ejpam-1372	760	8	.	.	PUNCT
ejpam-1372	761	1	j.	j.	PROPN
ejpam-1372	761	2	pure	pure	PROPN
ejpam-1372	761	3	appl	appl	PROPN
ejpam-1372	761	4	.	.	PROPN
ejpam-1372	761	5	math	math	PROPN
ejpam-1372	761	6	,	,	PUNCT
ejpam-1372	761	7	4	4	NUM
ejpam-1372	761	8	(	(	PUNCT
ejpam-1372	761	9	2011	2011	NUM
ejpam-1372	761	10	)	)	PUNCT
ejpam-1372	761	11	,	,	PUNCT
ejpam-1372	761	12	370	370	NUM
ejpam-1372	761	13	-	-	SYM
ejpam-1372	761	14	423	423	NUM
ejpam-1372	761	15	396	396	NUM
ejpam-1372	761	16	naturally	naturally	ADV
ejpam-1372	761	17	,	,	PUNCT
ejpam-1372	761	18	higher	high	ADJ
ejpam-1372	761	19	stokes	stoke	NOUN
ejpam-1372	761	20	sectors	sector	NOUN
ejpam-1372	761	21	or	or	CCONJ
ejpam-1372	761	22	branches	branch	NOUN
ejpam-1372	761	23	of	of	ADP
ejpam-1372	761	24	the	the	DET
ejpam-1372	761	25	complex	complex	ADJ
ejpam-1372	761	26	plane	plane	NOUN
ejpam-1372	761	27	will	will	AUX
ejpam-1372	761	28	also	also	ADV
ejpam-1372	761	29	affect	affect	VERB
ejpam-1372	761	30	the	the	DET
ejpam-1372	761	31	regularised	regularise	VERB
ejpam-1372	761	32	value	value	NOUN
ejpam-1372	761	33	of	of	ADP
ejpam-1372	761	34	the	the	DET
ejpam-1372	761	35	second	second	ADJ
ejpam-1372	761	36	type	type	NOUN
ejpam-1372	761	37	of	of	ADP
ejpam-1372	761	38	terminant	terminant	NOUN
ejpam-1372	761	39	.	.	PUNCT
ejpam-1372	762	1	for	for	ADP
ejpam-1372	762	2	this	this	DET
ejpam-1372	762	3	type	type	NOUN
ejpam-1372	762	4	of	of	ADP
ejpam-1372	762	5	terminant	terminant	NOUN
ejpam-1372	762	6	the	the	DET
ejpam-1372	762	7	theory	theory	NOUN
ejpam-1372	762	8	of	of	ADP
ejpam-1372	762	9	mellin	mellin	PROPN
ejpam-1372	762	10	transforms	transform	VERB
ejpam-1372	762	11	[	[	X
ejpam-1372	762	12	25	25	NUM
ejpam-1372	762	13	]	]	PUNCT
ejpam-1372	762	14	yields	yield	NOUN
ejpam-1372	762	15	ti	ti	PROPN
ejpam-1372	762	16	i(n	i(n	PROPN
ejpam-1372	762	17	,	,	PUNCT
ejpam-1372	762	18	α	α	X
ejpam-1372	762	19	,	,	PUNCT
ejpam-1372	762	20	z	z	NOUN
ejpam-1372	762	21	exp(−2l	exp(−2l	NOUN
ejpam-1372	763	1	iπ))−	iπ))−	PROPN
ejpam-1372	763	2	ti	ti	PROPN
ejpam-1372	763	3	i(n	i(n	PROPN
ejpam-1372	763	4	,	,	PUNCT
ejpam-1372	763	5	α	α	X
ejpam-1372	763	6	,	,	PUNCT
ejpam-1372	763	7	z	z	PROPN
ejpam-1372	763	8	exp(−2(l	exp(−2(l	PROPN
ejpam-1372	763	9	−	−	PROPN
ejpam-1372	763	10	1)iπ	1)iπ	NUM
ejpam-1372	763	11	)	)	PUNCT
ejpam-1372	763	12	)	)	PUNCT
ejpam-1372	764	1	≡	≡	PROPN
ejpam-1372	764	2	2πi	2πi	PROPN
ejpam-1372	764	3	z−α	z−α	PROPN
ejpam-1372	764	4	e2l	e2l	PROPN
ejpam-1372	764	5	iπα	iπα	PROPN
ejpam-1372	764	6	e−z−α	e−z−α	NOUN
ejpam-1372	764	7	.	.	PUNCT
ejpam-1372	765	1	(	(	PUNCT
ejpam-1372	765	2	87	87	NUM
ejpam-1372	765	3	)	)	PUNCT
ejpam-1372	765	4	the	the	DET
ejpam-1372	765	5	second	second	ADJ
ejpam-1372	765	6	series	series	NOUN
ejpam-1372	765	7	on	on	ADP
ejpam-1372	765	8	the	the	DET
ejpam-1372	765	9	lhs	lhs	PROPN
ejpam-1372	765	10	can	can	AUX
ejpam-1372	765	11	be	be	AUX
ejpam-1372	765	12	expressed	express	VERB
ejpam-1372	765	13	in	in	ADP
ejpam-1372	765	14	terms	term	NOUN
ejpam-1372	765	15	of	of	ADP
ejpam-1372	765	16	ti	ti	NOUN
ejpam-1372	765	17	i(n	i(n	PROPN
ejpam-1372	765	18	,	,	PUNCT
ejpam-1372	765	19	α	α	X
ejpam-1372	765	20	,	,	PUNCT
ejpam-1372	765	21	z	z	PROPN
ejpam-1372	765	22	exp(−2(l	exp(−2(l	PROPN
ejpam-1372	765	23	−	−	PROPN
ejpam-1372	765	24	2)iπ	2)iπ	NOUN
ejpam-1372	765	25	)	)	PUNCT
ejpam-1372	765	26	by	by	ADP
ejpam-1372	765	27	replacing	replace	VERB
ejpam-1372	765	28	l	l	NOUN
ejpam-1372	765	29	with	with	ADP
ejpam-1372	765	30	l	l	NOUN
ejpam-1372	765	31	−	−	PROPN
ejpam-1372	765	32	1	1	NUM
ejpam-1372	765	33	in	in	ADP
ejpam-1372	765	34	the	the	DET
ejpam-1372	765	35	above	above	ADJ
ejpam-1372	765	36	result	result	NOUN
ejpam-1372	765	37	.	.	PUNCT
ejpam-1372	766	1	we	we	PRON
ejpam-1372	766	2	continue	continue	VERB
ejpam-1372	766	3	this	this	DET
ejpam-1372	766	4	process	process	NOUN
ejpam-1372	766	5	stopping	stop	VERB
ejpam-1372	766	6	at	at	ADP
ejpam-1372	766	7	l	l	NOUN
ejpam-1372	766	8	=	=	NOUN
ejpam-1372	767	1	1	1	X
ejpam-1372	767	2	.	.	PUNCT
ejpam-1372	767	3	then	then	ADV
ejpam-1372	767	4	with	with	ADP
ejpam-1372	767	5	the	the	DET
ejpam-1372	767	6	introduction	introduction	NOUN
ejpam-1372	767	7	of	of	ADP
ejpam-1372	767	8	the	the	DET
ejpam-1372	767	9	lower	low	ADJ
ejpam-1372	767	10	form	form	NOUN
ejpam-1372	767	11	of	of	ADP
ejpam-1372	767	12	equivalence	equivalence	NOUN
ejpam-1372	767	13	(	(	PUNCT
ejpam-1372	767	14	72	72	NUM
ejpam-1372	767	15	)	)	PUNCT
ejpam-1372	767	16	we	we	PRON
ejpam-1372	767	17	obtain	obtain	VERB
ejpam-1372	767	18	the	the	DET
ejpam-1372	767	19	regularised	regularise	VERB
ejpam-1372	767	20	value	value	NOUN
ejpam-1372	767	21	of	of	ADP
ejpam-1372	767	22	the	the	DET
ejpam-1372	767	23	second	second	ADJ
ejpam-1372	767	24	type	type	NOUN
ejpam-1372	767	25	of	of	ADP
ejpam-1372	767	26	terminant	terminant	NOUN
ejpam-1372	767	27	for	for	ADP
ejpam-1372	767	28	−2(l	−2(l	NOUN
ejpam-1372	767	29	+	+	CCONJ
ejpam-1372	767	30	1)π	1)π	NUM
ejpam-1372	767	31	<	<	X
ejpam-1372	767	32	argz<−2lπ	argz<−2lπ	PROPN
ejpam-1372	767	33	.	.	PUNCT
ejpam-1372	768	1	this	this	PRON
ejpam-1372	768	2	is	be	AUX
ejpam-1372	768	3	given	give	VERB
ejpam-1372	768	4	by	by	ADP
ejpam-1372	768	5	ti	ti	PROPN
ejpam-1372	768	6	i(n	i(n	PROPN
ejpam-1372	768	7	,	,	PUNCT
ejpam-1372	768	8	α	α	NOUN
ejpam-1372	768	9	,	,	PUNCT
ejpam-1372	768	10	z	z	NOUN
ejpam-1372	768	11	)	)	PUNCT
ejpam-1372	768	12	≡	≡	PROPN
ejpam-1372	768	13	−zn	−zn	PROPN
ejpam-1372	768	14	∫	∫	PROPN
ejpam-1372	768	15	c	c	PROPN
ejpam-1372	768	16	ds	ds	PROPN
ejpam-1372	768	17	sn+α−1	sn+α−1	PROPN
ejpam-1372	768	18	e−s	e−s	PROPN
ejpam-1372	768	19	1−	1−	NUM
ejpam-1372	768	20	zs	zs	PUNCT
ejpam-1372	769	1	+	+	NOUN
ejpam-1372	769	2	πi	πi	ADP
ejpam-1372	769	3	|z|−αe−1/|z|	|z|−αe−1/|z|	NOUN
ejpam-1372	769	4	×	×	PROPN
ejpam-1372	769	5	�	�	PROPN
ejpam-1372	769	6	2e−(l+1)iπα	2e−(l+1)iπα	NUM
ejpam-1372	769	7	sin(lπα	sin(lπα	NOUN
ejpam-1372	769	8	)	)	PUNCT
ejpam-1372	769	9	sin(πα	sin(πα	VERB
ejpam-1372	769	10	)	)	PUNCT
ejpam-1372	770	1	+	+	CCONJ
ejpam-1372	770	2	1	1	NUM
ejpam-1372	770	3	�	�	NOUN
ejpam-1372	770	4	.	.	PUNCT
ejpam-1372	771	1	(	(	PUNCT
ejpam-1372	771	2	88	88	NUM
ejpam-1372	771	3	)	)	PUNCT
ejpam-1372	771	4	in	in	ADP
ejpam-1372	771	5	equivalence	equivalence	NOUN
ejpam-1372	771	6	(	(	PUNCT
ejpam-1372	771	7	88	88	NUM
ejpam-1372	771	8	)	)	PUNCT
ejpam-1372	771	9	c	c	NOUN
ejpam-1372	771	10	represents	represent	VERB
ejpam-1372	771	11	the	the	DET
ejpam-1372	771	12	line	line	NOUN
ejpam-1372	771	13	contour	contour	NOUN
ejpam-1372	771	14	along	along	ADP
ejpam-1372	771	15	the	the	DET
ejpam-1372	771	16	positive	positive	ADJ
ejpam-1372	771	17	real	real	ADJ
ejpam-1372	771	18	axis	axis	NOUN
ejpam-1372	771	19	as	as	ADP
ejpam-1372	771	20	before	before	ADV
ejpam-1372	771	21	.	.	PUNCT
ejpam-1372	772	1	for	for	ADP
ejpam-1372	772	2	2lπ	2lπ	NOUN
ejpam-1372	772	3	<	<	X
ejpam-1372	772	4	arg	arg	X
ejpam-1372	772	5	z	z	NOUN
ejpam-1372	772	6	<	<	X
ejpam-1372	772	7	2(l	2(l	NUM
ejpam-1372	772	8	+	+	CCONJ
ejpam-1372	772	9	1)π	1)π	NUM
ejpam-1372	772	10	,	,	PUNCT
ejpam-1372	772	11	the	the	DET
ejpam-1372	772	12	regularised	regularise	VERB
ejpam-1372	772	13	value	value	NOUN
ejpam-1372	772	14	is	be	AUX
ejpam-1372	772	15	simply	simply	ADV
ejpam-1372	772	16	the	the	DET
ejpam-1372	772	17	complex	complex	ADJ
ejpam-1372	772	18	conjugate	conjugate	NOUN
ejpam-1372	772	19	of	of	ADP
ejpam-1372	772	20	the	the	DET
ejpam-1372	772	21	above	above	ADJ
ejpam-1372	772	22	result	result	NOUN
ejpam-1372	772	23	.	.	PUNCT
ejpam-1372	773	1	for	for	ADP
ejpam-1372	773	2	the	the	DET
ejpam-1372	773	3	stokes	stoke	NOUN
ejpam-1372	773	4	line	line	NOUN
ejpam-1372	773	5	of	of	ADP
ejpam-1372	773	6	arg	arg	NOUN
ejpam-1372	773	7	z=−2lπ	z=−2lπ	PROPN
ejpam-1372	773	8	,	,	PUNCT
ejpam-1372	773	9	we	we	PRON
ejpam-1372	773	10	can	can	AUX
ejpam-1372	773	11	again	again	ADV
ejpam-1372	773	12	average	average	VERB
ejpam-1372	773	13	the	the	DET
ejpam-1372	773	14	regularised	regularise	VERB
ejpam-1372	773	15	value	value	NOUN
ejpam-1372	773	16	for	for	ADP
ejpam-1372	773	17	each	each	PRON
ejpam-1372	773	18	of	of	ADP
ejpam-1372	773	19	the	the	DET
ejpam-1372	773	20	abutting	abutting	NOUN
ejpam-1372	773	21	stokes	stoke	VERB
ejpam-1372	773	22	sectors	sector	NOUN
ejpam-1372	773	23	,	,	PUNCT
ejpam-1372	773	24	whilst	whilst	SCONJ
ejpam-1372	773	25	at	at	ADP
ejpam-1372	773	26	the	the	DET
ejpam-1372	773	27	same	same	ADJ
ejpam-1372	773	28	time	time	NOUN
ejpam-1372	773	29	ensuring	ensure	VERB
ejpam-1372	773	30	that	that	SCONJ
ejpam-1372	773	31	only	only	ADV
ejpam-1372	773	32	the	the	DET
ejpam-1372	773	33	principal	principal	ADJ
ejpam-1372	773	34	value	value	NOUN
ejpam-1372	773	35	of	of	ADP
ejpam-1372	773	36	the	the	DET
ejpam-1372	773	37	resulting	result	VERB
ejpam-1372	773	38	integral	integral	ADJ
ejpam-1372	773	39	is	be	AUX
ejpam-1372	773	40	evaluated	evaluate	VERB
ejpam-1372	773	41	.	.	PUNCT
ejpam-1372	774	1	then	then	ADV
ejpam-1372	774	2	the	the	DET
ejpam-1372	774	3	regularised	regularise	VERB
ejpam-1372	774	4	value	value	NOUN
ejpam-1372	774	5	of	of	ADP
ejpam-1372	774	6	this	this	DET
ejpam-1372	774	7	terminant	terminant	NOUN
ejpam-1372	774	8	can	can	AUX
ejpam-1372	774	9	be	be	AUX
ejpam-1372	774	10	expressed	express	VERB
ejpam-1372	774	11	as	as	ADP
ejpam-1372	774	12	ti	ti	PROPN
ejpam-1372	774	13	i(n	i(n	PROPN
ejpam-1372	774	14	,	,	PUNCT
ejpam-1372	774	15	α	α	NOUN
ejpam-1372	774	16	,	,	PUNCT
ejpam-1372	774	17	z	z	NOUN
ejpam-1372	774	18	)	)	PUNCT
ejpam-1372	774	19	≡	≡	PROPN
ejpam-1372	774	20	|z|n−1	|z|n−1	PROPN
ejpam-1372	775	1	p	p	X
ejpam-1372	775	2	∫	∫	PROPN
ejpam-1372	775	3	∞	∞	PROPN
ejpam-1372	775	4	0	0	PUNCT
ejpam-1372	776	1	d	d	PRON
ejpam-1372	776	2	t	t	PROPN
ejpam-1372	776	3	tn+α−1	tn+α−1	PROPN
ejpam-1372	776	4	e−t	e−t	NOUN
ejpam-1372	776	5	t	t	NOUN
ejpam-1372	776	6	−	−	NOUN
ejpam-1372	776	7	1/|z|	1/|z|	NOUN
ejpam-1372	776	8	−	−	NOUN
ejpam-1372	776	9	2πi	2πi	NOUN
ejpam-1372	776	10	|z|−α	|z|−α	PROPN
ejpam-1372	777	1	e−1/|z|	e−1/|z|	NOUN
ejpam-1372	777	2	×	×	PROPN
ejpam-1372	777	3	el	el	PROPN
ejpam-1372	777	4	iπα	iπα	PROPN
ejpam-1372	777	5	sin(lπα	sin(lπα	PROPN
ejpam-1372	777	6	)	)	PUNCT
ejpam-1372	777	7	sin(πα	sin(πα	VERB
ejpam-1372	777	8	)	)	PUNCT
ejpam-1372	777	9	cos(πα	cos(πα	NUM
ejpam-1372	777	10	)	)	PUNCT
ejpam-1372	777	11	.	.	PUNCT
ejpam-1372	778	1	(	(	PUNCT
ejpam-1372	778	2	89	89	NUM
ejpam-1372	778	3	)	)	PUNCT
ejpam-1372	778	4	for	for	ADP
ejpam-1372	778	5	arg	arg	NOUN
ejpam-1372	778	6	z=2lπ	z=2lπ	NUM
ejpam-1372	778	7	,	,	PUNCT
ejpam-1372	778	8	the	the	DET
ejpam-1372	778	9	regularised	regularise	VERB
ejpam-1372	778	10	value	value	NOUN
ejpam-1372	778	11	of	of	ADP
ejpam-1372	778	12	ti	ti	PROPN
ejpam-1372	778	13	i(n	i(n	PROPN
ejpam-1372	778	14	,	,	PUNCT
ejpam-1372	778	15	α	α	X
ejpam-1372	778	16	,	,	PUNCT
ejpam-1372	778	17	z	z	NOUN
ejpam-1372	778	18	)	)	PUNCT
ejpam-1372	778	19	is	be	AUX
ejpam-1372	778	20	given	give	VERB
ejpam-1372	778	21	by	by	ADP
ejpam-1372	778	22	the	the	DET
ejpam-1372	778	23	complex	complex	ADJ
ejpam-1372	778	24	conjugate	conjugate	NOUN
ejpam-1372	778	25	of	of	ADP
ejpam-1372	778	26	the	the	DET
ejpam-1372	778	27	above	above	ADJ
ejpam-1372	778	28	result	result	NOUN
ejpam-1372	778	29	.	.	PUNCT
ejpam-1372	779	1	as	as	SCONJ
ejpam-1372	779	2	mentioned	mention	VERB
ejpam-1372	779	3	previously	previously	ADV
ejpam-1372	779	4	,	,	PUNCT
ejpam-1372	779	5	the	the	DET
ejpam-1372	779	6	preceding	precede	VERB
ejpam-1372	779	7	analysis	analysis	NOUN
ejpam-1372	779	8	is	be	AUX
ejpam-1372	779	9	applied	apply	VERB
ejpam-1372	779	10	in	in	ADP
ejpam-1372	779	11	ref	ref	NOUN
ejpam-1372	779	12	.	.	PUNCT
ejpam-1372	780	1	[	[	X
ejpam-1372	780	2	17	17	NUM
ejpam-1372	780	3	]	]	PUNCT
ejpam-1372	780	4	to	to	ADP
ejpam-1372	780	5	generalised	generalise	VERB
ejpam-1372	780	6	versions	version	NOUN
ejpam-1372	780	7	of	of	ADP
ejpam-1372	780	8	both	both	DET
ejpam-1372	780	9	types	type	NOUN
ejpam-1372	780	10	of	of	ADP
ejpam-1372	780	11	terminants	terminant	NOUN
ejpam-1372	780	12	.	.	PUNCT
ejpam-1372	781	1	there	there	ADV
ejpam-1372	781	2	,	,	PUNCT
ejpam-1372	781	3	expressions	expression	NOUN
ejpam-1372	781	4	for	for	ADP
ejpam-1372	781	5	the	the	DET
ejpam-1372	781	6	regularised	regularise	VERB
ejpam-1372	781	7	values	value	NOUN
ejpam-1372	781	8	of	of	ADP
ejpam-1372	781	9	both	both	DET
ejpam-1372	781	10	types	type	NOUN
ejpam-1372	781	11	of	of	ADP
ejpam-1372	781	12	terminant	terminant	NOUN
ejpam-1372	781	13	are	be	AUX
ejpam-1372	781	14	derived	derive	VERB
ejpam-1372	781	15	for	for	ADP
ejpam-1372	781	16	all	all	DET
ejpam-1372	781	17	values	value	NOUN
ejpam-1372	781	18	of	of	ADP
ejpam-1372	781	19	arg	arg	NOUN
ejpam-1372	781	20	z.	z.	PROPN
ejpam-1372	781	21	these	these	DET
ejpam-1372	781	22	expressions	expression	NOUN
ejpam-1372	781	23	simplify	simplify	VERB
ejpam-1372	781	24	drastically	drastically	ADV
ejpam-1372	781	25	for	for	ADP
ejpam-1372	781	26	the	the	DET
ejpam-1372	781	27	cases	case	NOUN
ejpam-1372	781	28	of	of	ADP
ejpam-1372	781	29	p	p	NOUN
ejpam-1372	781	30	equal	equal	ADJ
ejpam-1372	781	31	to	to	ADP
ejpam-1372	781	32	the	the	DET
ejpam-1372	781	33	reciprocal	reciprocal	NOUN
ejpam-1372	781	34	of	of	ADP
ejpam-1372	781	35	an	an	DET
ejpam-1372	781	36	integer	integer	NOUN
ejpam-1372	781	37	including	include	VERB
ejpam-1372	781	38	unity	unity	NOUN
ejpam-1372	781	39	and	and	CCONJ
ejpam-1372	781	40	p=2	p=2	PROPN
ejpam-1372	781	41	.	.	PUNCT
ejpam-1372	782	1	in	in	ADP
ejpam-1372	782	2	addition	addition	NOUN
ejpam-1372	782	3	,	,	PUNCT
ejpam-1372	782	4	borel	borel	PROPN
ejpam-1372	782	5	summation	summation	NOUN
ejpam-1372	782	6	is	be	AUX
ejpam-1372	782	7	extended	extend	VERB
ejpam-1372	782	8	in	in	ADP
ejpam-1372	782	9	the	the	DET
ejpam-1372	782	10	following	follow	VERB
ejpam-1372	782	11	chapter	chapter	NOUN
ejpam-1372	782	12	by	by	ADP
ejpam-1372	782	13	eliminating	eliminate	VERB
ejpam-1372	782	14	the	the	DET
ejpam-1372	782	15	need	need	NOUN
ejpam-1372	782	16	for	for	SCONJ
ejpam-1372	782	17	the	the	DET
ejpam-1372	782	18	gamma	gamma	NOUN
ejpam-1372	782	19	function	function	NOUN
ejpam-1372	782	20	to	to	PART
ejpam-1372	782	21	appear	appear	VERB
ejpam-1372	782	22	in	in	ADP
ejpam-1372	782	23	the	the	DET
ejpam-1372	782	24	coefficients	coefficient	NOUN
ejpam-1372	782	25	of	of	ADP
ejpam-1372	782	26	the	the	DET
ejpam-1372	782	27	asymptotic	asymptotic	ADJ
ejpam-1372	782	28	series	series	NOUN
ejpam-1372	782	29	.	.	PUNCT
ejpam-1372	783	1	instead	instead	ADV
ejpam-1372	783	2	,	,	PUNCT
ejpam-1372	783	3	since	since	SCONJ
ejpam-1372	783	4	it	it	PRON
ejpam-1372	783	5	is	be	AUX
ejpam-1372	783	6	regularisation	regularisation	NOUN
ejpam-1372	783	7	of	of	ADP
ejpam-1372	783	8	the	the	DET
ejpam-1372	783	9	geometric	geometric	ADJ
ejpam-1372	783	10	series	series	NOUN
ejpam-1372	783	11	,	,	PUNCT
ejpam-1372	783	12	which	which	PRON
ejpam-1372	783	13	lies	lie	VERB
ejpam-1372	783	14	at	at	ADP
ejpam-1372	783	15	the	the	DET
ejpam-1372	783	16	heart	heart	NOUN
ejpam-1372	783	17	of	of	ADP
ejpam-1372	783	18	borel	borel	PROPN
ejpam-1372	783	19	summation	summation	NOUN
ejpam-1372	783	20	,	,	PUNCT
ejpam-1372	783	21	all	all	PRON
ejpam-1372	783	22	we	we	PRON
ejpam-1372	783	23	need	need	VERB
ejpam-1372	783	24	to	to	PART
ejpam-1372	783	25	do	do	VERB
ejpam-1372	783	26	in	in	ADP
ejpam-1372	783	27	order	order	NOUN
ejpam-1372	783	28	to	to	PART
ejpam-1372	783	29	derive	derive	VERB
ejpam-1372	783	30	the	the	DET
ejpam-1372	783	31	regularised	regularise	VERB
ejpam-1372	783	32	value	value	NOUN
ejpam-1372	783	33	is	be	AUX
ejpam-1372	783	34	to	to	PART
ejpam-1372	783	35	replace	replace	VERB
ejpam-1372	783	36	ak	ak	PROPN
ejpam-1372	783	37	in	in	ADP
ejpam-1372	783	38	eq	eq	ADP
ejpam-1372	783	39	.	.	PUNCT
ejpam-1372	784	1	(	(	PUNCT
ejpam-1372	784	2	1	1	NUM
ejpam-1372	784	3	)	)	PUNCT
ejpam-1372	784	4	by	by	ADP
ejpam-1372	784	5	f	f	PROPN
ejpam-1372	784	6	(	(	PUNCT
ejpam-1372	784	7	k)zk	k)zk	PROPN
ejpam-1372	784	8	where	where	SCONJ
ejpam-1372	784	9	f	f	PROPN
ejpam-1372	784	10	(	(	PUNCT
ejpam-1372	784	11	k	k	NOUN
ejpam-1372	784	12	)	)	PUNCT
ejpam-1372	784	13	can	can	AUX
ejpam-1372	784	14	be	be	AUX
ejpam-1372	784	15	expressed	express	VERB
ejpam-1372	784	16	as	as	ADP
ejpam-1372	784	17	a	a	DET
ejpam-1372	784	18	mellin	mellin	PROPN
ejpam-1372	784	19	transform	transform	NOUN
ejpam-1372	784	20	,	,	PUNCT
ejpam-1372	784	21	viz	viz	PROPN
ejpam-1372	784	22	.	.	PUNCT
ejpam-1372	785	1	f	f	PROPN
ejpam-1372	785	2	(	(	PUNCT
ejpam-1372	785	3	k)=	k)=	VERB
ejpam-1372	785	4	∫∞	∫∞	NOUN
ejpam-1372	785	5	0	0	PUNCT
ejpam-1372	786	1	d	d	NOUN
ejpam-1372	786	2	x	x	X
ejpam-1372	786	3	x	x	SYM
ejpam-1372	786	4	k−1f(x	k−1f(x	PROPN
ejpam-1372	786	5	)	)	PUNCT
ejpam-1372	786	6	.	.	PUNCT
ejpam-1372	787	1	we	we	PRON
ejpam-1372	787	2	shall	shall	AUX
ejpam-1372	787	3	return	return	VERB
ejpam-1372	787	4	to	to	ADP
ejpam-1372	787	5	this	this	DET
ejpam-1372	787	6	issue	issue	NOUN
ejpam-1372	787	7	at	at	ADP
ejpam-1372	787	8	the	the	DET
ejpam-1372	787	9	end	end	NOUN
ejpam-1372	787	10	of	of	ADP
ejpam-1372	787	11	sec	sec	PROPN
ejpam-1372	787	12	.	.	PROPN
ejpam-1372	787	13	11	11	NUM
ejpam-1372	787	14	.	.	PUNCT
ejpam-1372	788	1	v.	v.	ADP
ejpam-1372	788	2	kowalenko	kowalenko	PROPN
ejpam-1372	788	3	/	/	SYM
ejpam-1372	788	4	eur	eur	PROPN
ejpam-1372	788	5	.	.	PUNCT
ejpam-1372	789	1	j.	j.	PROPN
ejpam-1372	789	2	pure	pure	PROPN
ejpam-1372	789	3	appl	appl	PROPN
ejpam-1372	789	4	.	.	PROPN
ejpam-1372	789	5	math	math	PROPN
ejpam-1372	789	6	,	,	PUNCT
ejpam-1372	789	7	4	4	NUM
ejpam-1372	789	8	(	(	PUNCT
ejpam-1372	789	9	2011	2011	NUM
ejpam-1372	789	10	)	)	PUNCT
ejpam-1372	789	11	,	,	PUNCT
ejpam-1372	789	12	370	370	NUM
ejpam-1372	789	13	-	-	SYM
ejpam-1372	789	14	423	423	NUM
ejpam-1372	789	15	397	397	NUM
ejpam-1372	789	16	10	10	NUM
ejpam-1372	789	17	.	.	PUNCT
ejpam-1372	790	1	mellin	mellin	NOUN
ejpam-1372	790	2	-	-	PUNCT
ejpam-1372	790	3	barnes	barnes	PROPN
ejpam-1372	790	4	regularisation	regularisation	NOUN
ejpam-1372	790	5	as	as	SCONJ
ejpam-1372	790	6	stated	state	VERB
ejpam-1372	790	7	in	in	ADP
ejpam-1372	790	8	sec	sec	PROPN
ejpam-1372	790	9	.	.	PROPN
ejpam-1372	790	10	3	3	NUM
ejpam-1372	790	11	,	,	PUNCT
ejpam-1372	790	12	mellin	mellin	NOUN
ejpam-1372	790	13	-	-	PUNCT
ejpam-1372	790	14	barnes	barnes	PROPN
ejpam-1372	790	15	(	(	PUNCT
ejpam-1372	790	16	mb	mb	NOUN
ejpam-1372	790	17	)	)	PUNCT
ejpam-1372	790	18	regularisation	regularisation	NOUN
ejpam-1372	790	19	was	be	AUX
ejpam-1372	790	20	first	first	ADV
ejpam-1372	790	21	introduced	introduce	VERB
ejpam-1372	790	22	in	in	ADP
ejpam-1372	790	23	ref	ref	NOUN
ejpam-1372	790	24	.	.	PUNCT
ejpam-1372	791	1	[	[	X
ejpam-1372	791	2	21	21	NUM
ejpam-1372	791	3	]	]	PUNCT
ejpam-1372	791	4	to	to	PART
ejpam-1372	791	5	determine	determine	VERB
ejpam-1372	791	6	the	the	DET
ejpam-1372	791	7	regularised	regularise	VERB
ejpam-1372	791	8	value	value	NOUN
ejpam-1372	791	9	of	of	ADP
ejpam-1372	791	10	the	the	DET
ejpam-1372	791	11	complete	complete	ADJ
ejpam-1372	791	12	asymptotic	asymptotic	ADJ
ejpam-1372	791	13	expansion	expansion	NOUN
ejpam-1372	791	14	for	for	ADP
ejpam-1372	791	15	a	a	DET
ejpam-1372	791	16	particular	particular	ADJ
ejpam-1372	791	17	case	case	NOUN
ejpam-1372	791	18	of	of	ADP
ejpam-1372	791	19	the	the	DET
ejpam-1372	791	20	generalised	generalise	VERB
ejpam-1372	791	21	euler	euler	PROPN
ejpam-1372	791	22	-	-	PUNCT
ejpam-1372	791	23	jacobi	jacobi	PROPN
ejpam-1372	791	24	series	series	PROPN
ejpam-1372	791	25	,	,	PUNCT
ejpam-1372	791	26	viz	viz	PROPN
ejpam-1372	791	27	.	.	PUNCT
ejpam-1372	792	1	s3(a)=	s3(a)=	PROPN
ejpam-1372	792	2	∑∞	∑∞	NOUN
ejpam-1372	792	3	k=0	k=0	PROPN
ejpam-1372	792	4	exp(−ak3	exp(−ak3	NUM
ejpam-1372	792	5	)	)	PUNCT
ejpam-1372	792	6	.	.	PUNCT
ejpam-1372	793	1	this	this	DET
ejpam-1372	793	2	fascinating	fascinating	ADJ
ejpam-1372	793	3	technique	technique	NOUN
ejpam-1372	793	4	for	for	ADP
ejpam-1372	793	5	obtaining	obtain	VERB
ejpam-1372	793	6	the	the	DET
ejpam-1372	793	7	regularised	regularise	VERB
ejpam-1372	793	8	value	value	NOUN
ejpam-1372	793	9	of	of	ADP
ejpam-1372	793	10	a	a	DET
ejpam-1372	793	11	divergent	divergent	ADJ
ejpam-1372	793	12	series	series	NOUN
ejpam-1372	793	13	has	have	VERB
ejpam-1372	793	14	several	several	ADJ
ejpam-1372	793	15	advantages	advantage	NOUN
ejpam-1372	793	16	over	over	ADP
ejpam-1372	793	17	borel	borel	NOUN
ejpam-1372	793	18	summation	summation	NOUN
ejpam-1372	793	19	.	.	PUNCT
ejpam-1372	794	1	first	first	ADV
ejpam-1372	794	2	and	and	CCONJ
ejpam-1372	794	3	foremost	foremost	ADV
ejpam-1372	794	4	,	,	PUNCT
ejpam-1372	794	5	the	the	DET
ejpam-1372	794	6	regularised	regularise	VERB
ejpam-1372	794	7	values	value	NOUN
ejpam-1372	794	8	,	,	PUNCT
ejpam-1372	794	9	which	which	PRON
ejpam-1372	794	10	are	be	AUX
ejpam-1372	794	11	expressed	express	VERB
ejpam-1372	794	12	in	in	ADP
ejpam-1372	794	13	terms	term	NOUN
ejpam-1372	794	14	of	of	ADP
ejpam-1372	794	15	mb	mb	ADP
ejpam-1372	794	16	integrals	integral	NOUN
ejpam-1372	794	17	,	,	PUNCT
ejpam-1372	794	18	are	be	AUX
ejpam-1372	794	19	often	often	ADV
ejpam-1372	794	20	more	more	ADV
ejpam-1372	794	21	amenable	amenable	ADJ
ejpam-1372	794	22	,	,	PUNCT
ejpam-1372	794	23	but	but	CCONJ
ejpam-1372	794	24	not	not	PART
ejpam-1372	794	25	always	always	ADV
ejpam-1372	794	26	as	as	SCONJ
ejpam-1372	794	27	we	we	PRON
ejpam-1372	794	28	shall	shall	AUX
ejpam-1372	794	29	see	see	VERB
ejpam-1372	794	30	later	later	ADV
ejpam-1372	794	31	in	in	ADP
ejpam-1372	794	32	this	this	DET
ejpam-1372	794	33	article	article	NOUN
ejpam-1372	794	34	,	,	PUNCT
ejpam-1372	794	35	to	to	ADP
ejpam-1372	794	36	numerical	numerical	ADJ
ejpam-1372	794	37	computation	computation	NOUN
ejpam-1372	794	38	than	than	ADP
ejpam-1372	794	39	the	the	DET
ejpam-1372	794	40	cauchy	cauchy	NOUN
ejpam-1372	794	41	integrals	integral	NOUN
ejpam-1372	794	42	obtained	obtain	VERB
ejpam-1372	794	43	via	via	ADP
ejpam-1372	794	44	borel	borel	PROPN
ejpam-1372	794	45	summation	summation	NOUN
ejpam-1372	794	46	.	.	PUNCT
ejpam-1372	795	1	second	second	ADJ
ejpam-1372	795	2	,	,	PUNCT
ejpam-1372	795	3	the	the	DET
ejpam-1372	795	4	technique	technique	NOUN
ejpam-1372	795	5	is	be	AUX
ejpam-1372	795	6	not	not	PART
ejpam-1372	795	7	limited	limit	VERB
ejpam-1372	795	8	to	to	ADP
ejpam-1372	795	9	series	series	NOUN
ejpam-1372	795	10	where	where	SCONJ
ejpam-1372	795	11	the	the	DET
ejpam-1372	795	12	coefficients	coefficient	NOUN
ejpam-1372	795	13	are	be	AUX
ejpam-1372	795	14	expressed	express	VERB
ejpam-1372	795	15	in	in	ADP
ejpam-1372	795	16	terms	term	NOUN
ejpam-1372	795	17	of	of	ADP
ejpam-1372	795	18	the	the	DET
ejpam-1372	795	19	gamma	gamma	NOUN
ejpam-1372	795	20	function	function	NOUN
ejpam-1372	795	21	.	.	PUNCT
ejpam-1372	796	1	although	although	SCONJ
ejpam-1372	796	2	it	it	PRON
ejpam-1372	796	3	was	be	AUX
ejpam-1372	796	4	mentioned	mention	VERB
ejpam-1372	796	5	at	at	ADP
ejpam-1372	796	6	the	the	DET
ejpam-1372	796	7	end	end	NOUN
ejpam-1372	796	8	of	of	ADP
ejpam-1372	796	9	the	the	DET
ejpam-1372	796	10	previous	previous	ADJ
ejpam-1372	796	11	section	section	NOUN
ejpam-1372	796	12	that	that	PRON
ejpam-1372	796	13	borel	borel	PROPN
ejpam-1372	796	14	summation	summation	NOUN
ejpam-1372	796	15	can	can	AUX
ejpam-1372	796	16	be	be	AUX
ejpam-1372	796	17	extended	extend	VERB
ejpam-1372	796	18	to	to	ADP
ejpam-1372	796	19	coefficients	coefficient	NOUN
ejpam-1372	796	20	that	that	PRON
ejpam-1372	796	21	can	can	AUX
ejpam-1372	796	22	be	be	AUX
ejpam-1372	796	23	expressed	express	VERB
ejpam-1372	796	24	in	in	ADP
ejpam-1372	796	25	terms	term	NOUN
ejpam-1372	796	26	of	of	ADP
ejpam-1372	796	27	mellin	mellin	PROPN
ejpam-1372	796	28	transforms	transform	VERB
ejpam-1372	796	29	,	,	PUNCT
ejpam-1372	796	30	this	this	PRON
ejpam-1372	796	31	is	be	AUX
ejpam-1372	796	32	also	also	ADV
ejpam-1372	796	33	not	not	PART
ejpam-1372	796	34	necessary	necessary	ADJ
ejpam-1372	796	35	for	for	ADP
ejpam-1372	796	36	carrying	carry	VERB
ejpam-1372	796	37	out	out	ADP
ejpam-1372	796	38	the	the	DET
ejpam-1372	796	39	mb	mb	ADJ
ejpam-1372	796	40	regularisation	regularisation	NOUN
ejpam-1372	796	41	of	of	ADP
ejpam-1372	796	42	a	a	DET
ejpam-1372	796	43	series	series	NOUN
ejpam-1372	796	44	.	.	PUNCT
ejpam-1372	797	1	in	in	ADP
ejpam-1372	797	2	fact	fact	NOUN
ejpam-1372	797	3	,	,	PUNCT
ejpam-1372	797	4	mb	mb	ADP
ejpam-1372	797	5	regularisation	regularisation	NOUN
ejpam-1372	797	6	can	can	AUX
ejpam-1372	797	7	be	be	AUX
ejpam-1372	797	8	applied	apply	VERB
ejpam-1372	797	9	to	to	ADP
ejpam-1372	797	10	a	a	DET
ejpam-1372	797	11	series	series	NOUN
ejpam-1372	797	12	with	with	ADP
ejpam-1372	797	13	a	a	DET
ejpam-1372	797	14	finite	finite	ADJ
ejpam-1372	797	15	radius	radius	NOUN
ejpam-1372	797	16	of	of	ADP
ejpam-1372	797	17	absolute	absolute	ADJ
ejpam-1372	797	18	convergence	convergence	NOUN
ejpam-1372	797	19	such	such	ADJ
ejpam-1372	797	20	as	as	ADP
ejpam-1372	797	21	the	the	DET
ejpam-1372	797	22	geometric	geometric	ADJ
ejpam-1372	797	23	series	series	NOUN
ejpam-1372	797	24	as	as	SCONJ
ejpam-1372	797	25	is	be	AUX
ejpam-1372	797	26	done	do	VERB
ejpam-1372	797	27	in	in	ADP
ejpam-1372	797	28	ref	ref	NOUN
ejpam-1372	797	29	.	.	PUNCT
ejpam-1372	798	1	[	[	X
ejpam-1372	798	2	15	15	NUM
ejpam-1372	798	3	]	]	PUNCT
ejpam-1372	798	4	and	and	CCONJ
ejpam-1372	798	5	even	even	ADV
ejpam-1372	798	6	to	to	ADP
ejpam-1372	798	7	convergent	convergent	NOUN
ejpam-1372	798	8	series	series	NOUN
ejpam-1372	798	9	.	.	PUNCT
ejpam-1372	799	1	another	another	DET
ejpam-1372	799	2	feature	feature	NOUN
ejpam-1372	799	3	of	of	ADP
ejpam-1372	799	4	mb	mb	ADP
ejpam-1372	799	5	regularisation	regularisation	NOUN
ejpam-1372	799	6	,	,	PUNCT
ejpam-1372	799	7	which	which	PRON
ejpam-1372	799	8	will	will	AUX
ejpam-1372	799	9	be	be	AUX
ejpam-1372	799	10	seen	see	VERB
ejpam-1372	799	11	shortly	shortly	ADV
ejpam-1372	799	12	,	,	PUNCT
ejpam-1372	799	13	is	be	AUX
ejpam-1372	799	14	that	that	SCONJ
ejpam-1372	799	15	the	the	DET
ejpam-1372	799	16	mb	mb	PROPN
ejpam-1372	799	17	integrals	integral	NOUN
ejpam-1372	799	18	resulting	result	VERB
ejpam-1372	799	19	from	from	ADP
ejpam-1372	799	20	this	this	DET
ejpam-1372	799	21	technique	technique	NOUN
ejpam-1372	799	22	are	be	AUX
ejpam-1372	799	23	valid	valid	ADJ
ejpam-1372	799	24	over	over	ADP
ejpam-1372	799	25	domains	domain	NOUN
ejpam-1372	799	26	of	of	ADP
ejpam-1372	799	27	convergence	convergence	NOUN
ejpam-1372	799	28	,	,	PUNCT
ejpam-1372	799	29	whose	whose	DET
ejpam-1372	799	30	ranges	range	NOUN
ejpam-1372	799	31	are	be	AUX
ejpam-1372	799	32	generally	generally	ADV
ejpam-1372	799	33	greater	great	ADJ
ejpam-1372	799	34	than	than	ADP
ejpam-1372	799	35	stokes	stoke	NOUN
ejpam-1372	799	36	sectors	sector	NOUN
ejpam-1372	799	37	.	.	PUNCT
ejpam-1372	800	1	this	this	PRON
ejpam-1372	800	2	means	mean	VERB
ejpam-1372	800	3	that	that	SCONJ
ejpam-1372	800	4	not	not	PART
ejpam-1372	800	5	only	only	ADV
ejpam-1372	800	6	are	be	AUX
ejpam-1372	800	7	stokes	stokes	PROPN
ejpam-1372	800	8	lines	line	NOUN
ejpam-1372	800	9	non	non	ADJ
ejpam-1372	800	10	-	-	ADJ
ejpam-1372	800	11	existent	existent	ADJ
ejpam-1372	800	12	and	and	CCONJ
ejpam-1372	800	13	the	the	DET
ejpam-1372	800	14	resulting	result	VERB
ejpam-1372	800	15	mb	mb	ADV
ejpam-1372	800	16	-	-	PUNCT
ejpam-1372	800	17	regularised	regularise	VERB
ejpam-1372	800	18	values	value	NOUN
ejpam-1372	800	19	more	more	ADV
ejpam-1372	800	20	compact	compact	ADJ
ejpam-1372	800	21	,	,	PUNCT
ejpam-1372	800	22	but	but	CCONJ
ejpam-1372	800	23	that	that	SCONJ
ejpam-1372	800	24	the	the	DET
ejpam-1372	800	25	mb	mb	ADJ
ejpam-1372	800	26	-	-	PUNCT
ejpam-1372	800	27	regularised	regularise	VERB
ejpam-1372	800	28	forms	form	NOUN
ejpam-1372	800	29	for	for	ADP
ejpam-1372	800	30	the	the	DET
ejpam-1372	800	31	regularised	regularise	VERB
ejpam-1372	800	32	value	value	NOUN
ejpam-1372	800	33	overlap	overlap	NOUN
ejpam-1372	800	34	.	.	PUNCT
ejpam-1372	801	1	hence	hence	ADV
ejpam-1372	801	2	,	,	PUNCT
ejpam-1372	801	3	in	in	ADP
ejpam-1372	801	4	these	these	DET
ejpam-1372	801	5	overlapping	overlap	VERB
ejpam-1372	801	6	sectors	sector	NOUN
ejpam-1372	801	7	or	or	CCONJ
ejpam-1372	801	8	common	common	ADJ
ejpam-1372	801	9	regions	region	NOUN
ejpam-1372	801	10	we	we	PRON
ejpam-1372	801	11	have	have	VERB
ejpam-1372	801	12	two	two	NUM
ejpam-1372	801	13	representations	representation	NOUN
ejpam-1372	801	14	for	for	ADP
ejpam-1372	801	15	the	the	DET
ejpam-1372	801	16	same	same	ADJ
ejpam-1372	801	17	regularised	regularise	VERB
ejpam-1372	801	18	value	value	NOUN
ejpam-1372	801	19	of	of	ADP
ejpam-1372	801	20	a	a	DET
ejpam-1372	801	21	series	series	NOUN
ejpam-1372	801	22	.	.	PUNCT
ejpam-1372	802	1	consequently	consequently	ADV
ejpam-1372	802	2	,	,	PUNCT
ejpam-1372	802	3	the	the	DET
ejpam-1372	802	4	values	value	NOUN
ejpam-1372	802	5	obtained	obtain	VERB
ejpam-1372	802	6	from	from	ADP
ejpam-1372	802	7	mb	mb	NOUN
ejpam-1372	802	8	-	-	NOUN
ejpam-1372	802	9	regularisation	regularisation	NOUN
ejpam-1372	802	10	can	can	AUX
ejpam-1372	802	11	be	be	AUX
ejpam-1372	802	12	checked	check	VERB
ejpam-1372	802	13	against	against	ADP
ejpam-1372	802	14	each	each	DET
ejpam-1372	802	15	other	other	ADJ
ejpam-1372	802	16	in	in	ADP
ejpam-1372	802	17	these	these	DET
ejpam-1372	802	18	common	common	ADJ
ejpam-1372	802	19	regions	region	NOUN
ejpam-1372	802	20	of	of	ADP
ejpam-1372	802	21	the	the	DET
ejpam-1372	802	22	domains	domain	NOUN
ejpam-1372	802	23	of	of	ADP
ejpam-1372	802	24	convergence	convergence	NOUN
ejpam-1372	802	25	.	.	PUNCT
ejpam-1372	803	1	such	such	ADJ
ejpam-1372	803	2	checks	check	NOUN
ejpam-1372	803	3	can	can	AUX
ejpam-1372	803	4	not	not	PART
ejpam-1372	803	5	be	be	AUX
ejpam-1372	803	6	accomplished	accomplish	VERB
ejpam-1372	803	7	with	with	ADP
ejpam-1372	803	8	borel	borel	NOUN
ejpam-1372	803	9	-	-	PUNCT
ejpam-1372	803	10	summed	sum	VERB
ejpam-1372	803	11	forms	form	NOUN
ejpam-1372	803	12	since	since	SCONJ
ejpam-1372	803	13	we	we	PRON
ejpam-1372	803	14	have	have	AUX
ejpam-1372	803	15	already	already	ADV
ejpam-1372	803	16	seen	see	VERB
ejpam-1372	803	17	that	that	SCONJ
ejpam-1372	803	18	the	the	DET
ejpam-1372	803	19	latter	latter	ADJ
ejpam-1372	803	20	forms	form	NOUN
ejpam-1372	803	21	only	only	ADV
ejpam-1372	803	22	apply	apply	VERB
ejpam-1372	803	23	over	over	ADP
ejpam-1372	803	24	specific	specific	ADJ
ejpam-1372	803	25	non	non	ADJ
ejpam-1372	803	26	-	-	ADJ
ejpam-1372	803	27	overlapping	overlapping	ADJ
ejpam-1372	803	28	sectors	sector	NOUN
ejpam-1372	803	29	and	and	CCONJ
ejpam-1372	803	30	lines	line	NOUN
ejpam-1372	803	31	in	in	ADP
ejpam-1372	803	32	the	the	DET
ejpam-1372	803	33	complex	complex	ADJ
ejpam-1372	803	34	plane	plane	NOUN
ejpam-1372	803	35	.	.	PUNCT
ejpam-1372	804	1	as	as	SCONJ
ejpam-1372	804	2	discussed	discuss	VERB
ejpam-1372	804	3	in	in	ADP
ejpam-1372	804	4	ch	ch	NOUN
ejpam-1372	804	5	.	.	PROPN
ejpam-1372	804	6	7	7	NUM
ejpam-1372	804	7	of	of	ADP
ejpam-1372	804	8	ref	ref	NOUN
ejpam-1372	804	9	.	.	PUNCT
ejpam-1372	805	1	[	[	X
ejpam-1372	805	2	17	17	NUM
ejpam-1372	805	3	]	]	PUNCT
ejpam-1372	805	4	,	,	PUNCT
ejpam-1372	805	5	we	we	PRON
ejpam-1372	805	6	still	still	ADV
ejpam-1372	805	7	need	need	VERB
ejpam-1372	805	8	to	to	PART
ejpam-1372	805	9	consider	consider	VERB
ejpam-1372	805	10	both	both	DET
ejpam-1372	805	11	types	type	NOUN
ejpam-1372	805	12	of	of	ADP
ejpam-1372	805	13	asymptotic	asymptotic	ADJ
ejpam-1372	805	14	series	series	NOUN
ejpam-1372	805	15	studied	study	VERB
ejpam-1372	805	16	in	in	ADP
ejpam-1372	805	17	the	the	DET
ejpam-1372	805	18	previous	previous	ADJ
ejpam-1372	805	19	section	section	NOUN
ejpam-1372	805	20	separately	separately	ADV
ejpam-1372	805	21	when	when	SCONJ
ejpam-1372	805	22	carrying	carry	VERB
ejpam-1372	805	23	out	out	ADP
ejpam-1372	805	24	mb	mb	ADP
ejpam-1372	805	25	regularisation	regularisation	NOUN
ejpam-1372	805	26	,	,	PUNCT
ejpam-1372	805	27	but	but	CCONJ
ejpam-1372	805	28	now	now	ADV
ejpam-1372	805	29	we	we	PRON
ejpam-1372	805	30	can	can	AUX
ejpam-1372	805	31	make	make	VERB
ejpam-1372	805	32	them	they	PRON
ejpam-1372	805	33	more	more	ADV
ejpam-1372	805	34	general	general	ADJ
ejpam-1372	805	35	.	.	PUNCT
ejpam-1372	806	1	specifically	specifically	ADV
ejpam-1372	806	2	,	,	PUNCT
ejpam-1372	806	3	the	the	DET
ejpam-1372	806	4	first	first	ADJ
ejpam-1372	806	5	type	type	NOUN
ejpam-1372	806	6	of	of	ADP
ejpam-1372	806	7	general	general	ADJ
ejpam-1372	806	8	series	series	NOUN
ejpam-1372	806	9	is	be	AUX
ejpam-1372	806	10	represented	represent	VERB
ejpam-1372	806	11	in	in	ADP
ejpam-1372	806	12	terms	term	NOUN
ejpam-1372	806	13	of	of	ADP
ejpam-1372	806	14	the	the	DET
ejpam-1372	806	15	general	general	ADJ
ejpam-1372	806	16	form	form	NOUN
ejpam-1372	806	17	below	below	ADP
ejpam-1372	806	18	eq	eq	PROPN
ejpam-1372	806	19	.	.	PUNCT
ejpam-1372	807	1	(	(	PUNCT
ejpam-1372	807	2	1	1	NUM
ejpam-1372	807	3	)	)	PUNCT
ejpam-1372	807	4	with	with	ADP
ejpam-1372	807	5	ak=(−1)k	ak=(−1)k	PROPN
ejpam-1372	807	6	f	f	PROPN
ejpam-1372	807	7	(	(	PUNCT
ejpam-1372	807	8	k	k	PROPN
ejpam-1372	807	9	)	)	PUNCT
ejpam-1372	807	10	zk	zk	PROPN
ejpam-1372	807	11	,	,	PUNCT
ejpam-1372	807	12	while	while	SCONJ
ejpam-1372	807	13	in	in	ADP
ejpam-1372	807	14	the	the	DET
ejpam-1372	807	15	second	second	ADJ
ejpam-1372	807	16	type	type	NOUN
ejpam-1372	807	17	of	of	ADP
ejpam-1372	807	18	general	general	ADJ
ejpam-1372	807	19	series	series	NOUN
ejpam-1372	807	20	the	the	DET
ejpam-1372	807	21	terms	term	NOUN
ejpam-1372	807	22	are	be	AUX
ejpam-1372	807	23	given	give	VERB
ejpam-1372	807	24	by	by	ADP
ejpam-1372	807	25	ak=	ak=	PROPN
ejpam-1372	807	26	f	f	PROPN
ejpam-1372	807	27	(	(	PUNCT
ejpam-1372	807	28	k	k	NOUN
ejpam-1372	807	29	)	)	PUNCT
ejpam-1372	807	30	zk	zk	PROPN
ejpam-1372	807	31	.	.	PUNCT
ejpam-1372	808	1	hence	hence	ADV
ejpam-1372	808	2	,	,	PUNCT
ejpam-1372	808	3	terminants	terminant	NOUN
ejpam-1372	808	4	form	form	NOUN
ejpam-1372	808	5	classes	class	NOUN
ejpam-1372	808	6	within	within	ADP
ejpam-1372	808	7	these	these	DET
ejpam-1372	808	8	general	general	ADJ
ejpam-1372	808	9	types	type	NOUN
ejpam-1372	808	10	of	of	ADP
ejpam-1372	808	11	series	series	NOUN
ejpam-1372	808	12	.	.	PUNCT
ejpam-1372	809	1	according	accord	VERB
ejpam-1372	809	2	to	to	ADP
ejpam-1372	809	3	proposition	proposition	NOUN
ejpam-1372	809	4	3	3	NUM
ejpam-1372	809	5	of	of	ADP
ejpam-1372	809	6	the	the	DET
ejpam-1372	809	7	same	same	ADJ
ejpam-1372	809	8	reference	reference	NOUN
ejpam-1372	809	9	,	,	PUNCT
ejpam-1372	809	10	if	if	SCONJ
ejpam-1372	809	11	there	there	PRON
ejpam-1372	809	12	exists	exist	VERB
ejpam-1372	809	13	a	a	DET
ejpam-1372	809	14	real	real	ADJ
ejpam-1372	809	15	number	number	NOUN
ejpam-1372	809	16	c	c	NOUN
ejpam-1372	809	17	such	such	ADJ
ejpam-1372	809	18	that	that	SCONJ
ejpam-1372	809	19	the	the	DET
ejpam-1372	809	20	poles	pole	NOUN
ejpam-1372	809	21	of	of	ADP
ejpam-1372	809	22	γ(n−s	γ(n−s	NOUN
ejpam-1372	809	23	)	)	PUNCT
ejpam-1372	809	24	lie	lie	NOUN
ejpam-1372	809	25	to	to	ADP
ejpam-1372	809	26	the	the	DET
ejpam-1372	809	27	right	right	NOUN
ejpam-1372	809	28	of	of	ADP
ejpam-1372	809	29	the	the	DET
ejpam-1372	809	30	line	line	NOUN
ejpam-1372	809	31	given	give	VERB
ejpam-1372	809	32	by	by	ADP
ejpam-1372	809	33	n−1	n−1	PROPN
ejpam-1372	809	34	<	<	X
ejpam-1372	809	35	c	c	NOUN
ejpam-1372	809	36	=	=	SYM
ejpam-1372	809	37	ℜ	ℜ	PROPN
ejpam-1372	809	38	s	s	PART
ejpam-1372	809	39	<	<	X
ejpam-1372	809	40	n	n	NOUN
ejpam-1372	809	41	and	and	CCONJ
ejpam-1372	809	42	the	the	DET
ejpam-1372	809	43	poles	pole	NOUN
ejpam-1372	809	44	of	of	ADP
ejpam-1372	809	45	f	f	PROPN
ejpam-1372	809	46	(	(	PUNCT
ejpam-1372	809	47	s)γ(s	s)γ(s	PROPN
ejpam-1372	809	48	+	+	SYM
ejpam-1372	809	49	1−	1−	NUM
ejpam-1372	809	50	n	n	CCONJ
ejpam-1372	809	51	)	)	PUNCT
ejpam-1372	809	52	to	to	ADP
ejpam-1372	809	53	the	the	DET
ejpam-1372	809	54	left	left	NOUN
ejpam-1372	809	55	of	of	ADP
ejpam-1372	809	56	it	it	PRON
ejpam-1372	809	57	,	,	PUNCT
ejpam-1372	809	58	then	then	ADV
ejpam-1372	809	59	the	the	DET
ejpam-1372	809	60	mb	mb	ADJ
ejpam-1372	809	61	-	-	PUNCT
ejpam-1372	809	62	regularised	regularise	VERB
ejpam-1372	809	63	value	value	NOUN
ejpam-1372	809	64	of	of	ADP
ejpam-1372	809	65	the	the	DET
ejpam-1372	809	66	first	first	ADJ
ejpam-1372	809	67	type	type	NOUN
ejpam-1372	809	68	of	of	ADP
ejpam-1372	809	69	series	series	NOUN
ejpam-1372	809	70	is	be	AUX
ejpam-1372	809	71	found	find	VERB
ejpam-1372	809	72	to	to	PART
ejpam-1372	809	73	be	be	AUX
ejpam-1372	809	74	si(n	si(n	NOUN
ejpam-1372	809	75	,	,	PUNCT
ejpam-1372	809	76	z	z	X
ejpam-1372	809	77	)	)	PUNCT
ejpam-1372	809	78	=	=	SYM
ejpam-1372	810	1	∞	∞	NUM
ejpam-1372	810	2	∑	∑	PUNCT
ejpam-1372	810	3	k	k	X
ejpam-1372	810	4	=	=	PROPN
ejpam-1372	810	5	n	n	PROPN
ejpam-1372	810	6	f	f	X
ejpam-1372	810	7	(	(	PUNCT
ejpam-1372	810	8	k)(−z)k	k)(−z)k	NOUN
ejpam-1372	810	9	≡	≡	PROPN
ejpam-1372	810	10	∫	∫	PROPN
ejpam-1372	810	11	c+i∞	c+i∞	PROPN
ejpam-1372	811	1	c−i∞	c−i∞	PROPN
ejpam-1372	811	2	ds	ds	PROPN
ejpam-1372	811	3	zs	zs	PROPN
ejpam-1372	811	4	f	f	PROPN
ejpam-1372	811	5	(	(	PUNCT
ejpam-1372	811	6	s	s	NOUN
ejpam-1372	811	7	)	)	PUNCT
ejpam-1372	811	8	e−iπs	e−iπs	NOUN
ejpam-1372	811	9	−	−	PROPN
ejpam-1372	811	10	eiπs	eiπs	PROPN
ejpam-1372	811	11	.	.	PUNCT
ejpam-1372	812	1	(	(	PUNCT
ejpam-1372	812	2	90	90	NUM
ejpam-1372	812	3	)	)	PUNCT
ejpam-1372	812	4	this	this	DET
ejpam-1372	812	5	result	result	NOUN
ejpam-1372	812	6	is	be	AUX
ejpam-1372	812	7	subject	subject	ADJ
ejpam-1372	812	8	to	to	ADP
ejpam-1372	812	9	the	the	DET
ejpam-1372	812	10	following	following	ADJ
ejpam-1372	812	11	conditions	condition	NOUN
ejpam-1372	812	12	:	:	PUNCT
ejpam-1372	812	13	1	1	X
ejpam-1372	812	14	.	.	X
ejpam-1372	812	15	as	as	ADP
ejpam-1372	812	16	l→∞	l→∞	NUM
ejpam-1372	812	17	,	,	PUNCT
ejpam-1372	813	1	|	|	ADV
ejpam-1372	813	2	f	f	X
ejpam-1372	813	3	(	(	PUNCT
ejpam-1372	813	4	s)|	s)|	NOUN
ejpam-1372	813	5	=	=	PUNCT
ejpam-1372	813	6	o(exp(−ε1	o(exp(−ε1	PROPN
ejpam-1372	813	7	l	l	NOUN
ejpam-1372	813	8	)	)	PUNCT
ejpam-1372	813	9	)	)	PUNCT
ejpam-1372	813	10	for	for	ADP
ejpam-1372	813	11	s=	s=	NOUN
ejpam-1372	813	12	c+	c+	VERB
ejpam-1372	813	13	i	i	NOUN
ejpam-1372	813	14	l	l	NOUN
ejpam-1372	814	1	and	and	CCONJ
ejpam-1372	814	2	|	|	ADV
ejpam-1372	814	3	f	f	PROPN
ejpam-1372	814	4	(	(	PUNCT
ejpam-1372	814	5	s)|	s)|	NOUN
ejpam-1372	814	6	=	=	PUNCT
ejpam-1372	814	7	o(exp(−ε2	o(exp(−ε2	PROPN
ejpam-1372	814	8	l	l	NOUN
ejpam-1372	814	9	)	)	PUNCT
ejpam-1372	814	10	)	)	PUNCT
ejpam-1372	814	11	for	for	ADP
ejpam-1372	814	12	s=	s=	NOUN
ejpam-1372	814	13	c−	c−	PROPN
ejpam-1372	814	14	i	i	PRON
ejpam-1372	814	15	l	l	NOUN
ejpam-1372	814	16	,	,	PUNCT
ejpam-1372	815	1	where	where	SCONJ
ejpam-1372	815	2	ε1	ε1	PROPN
ejpam-1372	815	3	,	,	PUNCT
ejpam-1372	815	4	ε2>0	ε2>0	NOUN
ejpam-1372	815	5	,	,	PUNCT
ejpam-1372	815	6	2	2	NUM
ejpam-1372	815	7	.	.	PUNCT
ejpam-1372	816	1	−π	−π	PROPN
ejpam-1372	816	2	<	<	X
ejpam-1372	816	3	θ	θ	X
ejpam-1372	816	4	=	=	PUNCT
ejpam-1372	816	5	arg	arg	VERB
ejpam-1372	816	6	z	z	X
ejpam-1372	816	7	<	<	X
ejpam-1372	816	8	π	π	PROPN
ejpam-1372	816	9	,	,	PUNCT
ejpam-1372	816	10	3	3	NUM
ejpam-1372	816	11	.	.	PUNCT
ejpam-1372	817	1	zs	zs	PROPN
ejpam-1372	817	2	f	f	PROPN
ejpam-1372	817	3	(	(	PUNCT
ejpam-1372	817	4	s)γ(1	s)γ(1	PROPN
ejpam-1372	817	5	+	+	CCONJ
ejpam-1372	817	6	s−n)γ(n	s−n)γ(n	PROPN
ejpam-1372	817	7	−	−	NUM
ejpam-1372	817	8	s	s	NOUN
ejpam-1372	817	9	)	)	PUNCT
ejpam-1372	817	10	is	be	AUX
ejpam-1372	817	11	single	single	ADV
ejpam-1372	817	12	-	-	PUNCT
ejpam-1372	817	13	valued	value	VERB
ejpam-1372	817	14	to	to	ADP
ejpam-1372	817	15	the	the	DET
ejpam-1372	817	16	right	right	NOUN
ejpam-1372	817	17	of	of	ADP
ejpam-1372	817	18	the	the	DET
ejpam-1372	817	19	line	line	NOUN
ejpam-1372	817	20	.	.	PUNCT
ejpam-1372	818	1	v.	v.	ADP
ejpam-1372	818	2	kowalenko	kowalenko	PROPN
ejpam-1372	818	3	/	/	SYM
ejpam-1372	818	4	eur	eur	PROPN
ejpam-1372	818	5	.	.	PUNCT
ejpam-1372	819	1	j.	j.	PROPN
ejpam-1372	819	2	pure	pure	PROPN
ejpam-1372	819	3	appl	appl	PROPN
ejpam-1372	819	4	.	.	PROPN
ejpam-1372	819	5	math	math	PROPN
ejpam-1372	819	6	,	,	PUNCT
ejpam-1372	819	7	4	4	NUM
ejpam-1372	819	8	(	(	PUNCT
ejpam-1372	819	9	2011	2011	NUM
ejpam-1372	819	10	)	)	PUNCT
ejpam-1372	819	11	,	,	PUNCT
ejpam-1372	819	12	370	370	NUM
ejpam-1372	819	13	-	-	SYM
ejpam-1372	819	14	423	423	NUM
ejpam-1372	819	15	398	398	NUM
ejpam-1372	819	16	in	in	ADP
ejpam-1372	819	17	addition	addition	NOUN
ejpam-1372	819	18	,	,	PUNCT
ejpam-1372	819	19	as	as	SCONJ
ejpam-1372	819	20	the	the	DET
ejpam-1372	819	21	offset	offset	NOUN
ejpam-1372	819	22	c	c	NOUN
ejpam-1372	819	23	continues	continue	VERB
ejpam-1372	819	24	to	to	PART
ejpam-1372	819	25	increase	increase	VERB
ejpam-1372	819	26	,	,	PUNCT
ejpam-1372	819	27	the	the	DET
ejpam-1372	819	28	mb	mb	NOUN
ejpam-1372	819	29	integral	integral	ADJ
ejpam-1372	819	30	in	in	ADP
ejpam-1372	819	31	the	the	DET
ejpam-1372	819	32	above	above	ADJ
ejpam-1372	819	33	result	result	NOUN
ejpam-1372	819	34	will	will	AUX
ejpam-1372	819	35	eventually	eventually	ADV
ejpam-1372	819	36	increase	increase	VERB
ejpam-1372	819	37	exponentially	exponentially	ADV
ejpam-1372	819	38	regardless	regardless	ADV
ejpam-1372	819	39	of	of	ADP
ejpam-1372	819	40	the	the	DET
ejpam-1372	819	41	magnitude	magnitude	NOUN
ejpam-1372	819	42	of	of	ADP
ejpam-1372	819	43	z.	z.	PROPN
ejpam-1372	819	44	it	it	PRON
ejpam-1372	819	45	should	should	AUX
ejpam-1372	819	46	also	also	ADV
ejpam-1372	819	47	be	be	AUX
ejpam-1372	819	48	noted	note	VERB
ejpam-1372	819	49	that	that	SCONJ
ejpam-1372	819	50	the	the	DET
ejpam-1372	819	51	situation	situation	NOUN
ejpam-1372	819	52	can	can	AUX
ejpam-1372	819	53	be	be	AUX
ejpam-1372	819	54	adjusted	adjust	VERB
ejpam-1372	819	55	when	when	SCONJ
ejpam-1372	819	56	the	the	DET
ejpam-1372	819	57	poles	pole	NOUN
ejpam-1372	819	58	of	of	ADP
ejpam-1372	819	59	f	f	PROPN
ejpam-1372	819	60	(	(	PUNCT
ejpam-1372	819	61	s)γ(s+	s)γ(s+	NOUN
ejpam-1372	819	62	1−	1−	NUM
ejpam-1372	819	63	n	n	CCONJ
ejpam-1372	819	64	)	)	PUNCT
ejpam-1372	819	65	do	do	AUX
ejpam-1372	819	66	not	not	PART
ejpam-1372	819	67	lie	lie	VERB
ejpam-1372	819	68	to	to	ADP
ejpam-1372	819	69	the	the	DET
ejpam-1372	819	70	left	left	NOUN
ejpam-1372	819	71	of	of	ADP
ejpam-1372	819	72	the	the	DET
ejpam-1372	819	73	line	line	NOUN
ejpam-1372	819	74	c=ℜ	c=ℜ	ADV
ejpam-1372	819	75	s	s	PART
ejpam-1372	819	76	,	,	PUNCT
ejpam-1372	819	77	but	but	CCONJ
ejpam-1372	819	78	then	then	ADV
ejpam-1372	819	79	we	we	PRON
ejpam-1372	819	80	must	must	AUX
ejpam-1372	819	81	consider	consider	VERB
ejpam-1372	819	82	the	the	DET
ejpam-1372	819	83	specific	specific	ADJ
ejpam-1372	819	84	form	form	NOUN
ejpam-1372	819	85	of	of	ADP
ejpam-1372	819	86	f	f	PROPN
ejpam-1372	819	87	(	(	PUNCT
ejpam-1372	819	88	s	s	NOUN
ejpam-1372	819	89	)	)	PUNCT
ejpam-1372	819	90	.	.	PUNCT
ejpam-1372	820	1	in	in	ADP
ejpam-1372	820	2	order	order	NOUN
ejpam-1372	820	3	to	to	PART
ejpam-1372	820	4	derive	derive	VERB
ejpam-1372	820	5	equivalence	equivalence	NOUN
ejpam-1372	820	6	(	(	PUNCT
ejpam-1372	820	7	90	90	NUM
ejpam-1372	820	8	)	)	PUNCT
ejpam-1372	820	9	we	we	PRON
ejpam-1372	820	10	need	need	VERB
ejpam-1372	820	11	to	to	PART
ejpam-1372	820	12	study	study	VERB
ejpam-1372	820	13	the	the	DET
ejpam-1372	820	14	following	follow	VERB
ejpam-1372	820	15	contour	contour	NOUN
ejpam-1372	820	16	integral	integral	ADJ
ejpam-1372	820	17	:	:	PUNCT
ejpam-1372	821	1	i	i	PRON
ejpam-1372	821	2	=	=	SYM
ejpam-1372	821	3	(	(	PUNCT
ejpam-1372	821	4	−1)n	−1)n	PROPN
ejpam-1372	821	5	∫	∫	PROPN
ejpam-1372	821	6	c+i∞	c+i∞	PROPN
ejpam-1372	821	7	c−i∞	c−i∞	PROPN
ejpam-1372	821	8	ds	ds	PROPN
ejpam-1372	821	9	zs	zs	PROPN
ejpam-1372	821	10	f	f	PROPN
ejpam-1372	821	11	(	(	PUNCT
ejpam-1372	821	12	s)γ(1	s)γ(1	PROPN
ejpam-1372	821	13	+	+	X
ejpam-1372	821	14	s−	s−	PROPN
ejpam-1372	821	15	n)γ(n	n)γ(n	PUNCT
ejpam-1372	821	16	−	−	PROPN
ejpam-1372	821	17	s	s	PART
ejpam-1372	821	18	)	)	PUNCT
ejpam-1372	821	19	,	,	PUNCT
ejpam-1372	821	20	(	(	PUNCT
ejpam-1372	821	21	91	91	NUM
ejpam-1372	821	22	)	)	PUNCT
ejpam-1372	821	23	where	where	SCONJ
ejpam-1372	821	24	n	n	ADV
ejpam-1372	821	25	−	−	PROPN
ejpam-1372	821	26	1	1	NUM
ejpam-1372	821	27	<	<	X
ejpam-1372	821	28	c	c	NOUN
ejpam-1372	821	29	=	=	SYM
ejpam-1372	821	30	ℜ	ℜ	PROPN
ejpam-1372	821	31	s	s	PART
ejpam-1372	821	32	<	<	X
ejpam-1372	821	33	n	n	NOUN
ejpam-1372	821	34	.	.	PUNCT
ejpam-1372	822	1	the	the	DET
ejpam-1372	822	2	first	first	ADJ
ejpam-1372	822	3	two	two	NUM
ejpam-1372	822	4	conditions	condition	NOUN
ejpam-1372	822	5	given	give	VERB
ejpam-1372	822	6	above	above	ADV
ejpam-1372	822	7	ensure	ensure	VERB
ejpam-1372	822	8	that	that	SCONJ
ejpam-1372	822	9	the	the	DET
ejpam-1372	822	10	contour	contour	NOUN
ejpam-1372	822	11	integral	integral	NOUN
ejpam-1372	822	12	in	in	ADP
ejpam-1372	822	13	eq	eq	ADP
ejpam-1372	822	14	.	.	PUNCT
ejpam-1372	823	1	(	(	PUNCT
ejpam-1372	823	2	91	91	NUM
ejpam-1372	823	3	)	)	PUNCT
ejpam-1372	823	4	decays	decay	VERB
ejpam-1372	823	5	exponentially	exponentially	ADV
ejpam-1372	823	6	at	at	ADP
ejpam-1372	823	7	the	the	DET
ejpam-1372	823	8	endpoints	endpoint	NOUN
ejpam-1372	823	9	.	.	PUNCT
ejpam-1372	824	1	since	since	SCONJ
ejpam-1372	824	2	i	i	PRON
ejpam-1372	824	3	is	be	AUX
ejpam-1372	824	4	defined	define	VERB
ejpam-1372	824	5	,	,	PUNCT
ejpam-1372	824	6	it	it	PRON
ejpam-1372	824	7	can	can	AUX
ejpam-1372	824	8	be	be	AUX
ejpam-1372	824	9	closed	close	VERB
ejpam-1372	824	10	to	to	ADP
ejpam-1372	824	11	the	the	DET
ejpam-1372	824	12	right	right	NOUN
ejpam-1372	824	13	by	by	ADP
ejpam-1372	824	14	introducing	introduce	VERB
ejpam-1372	824	15	a	a	DET
ejpam-1372	824	16	contour	contour	NOUN
ejpam-1372	824	17	integral	integral	ADJ
ejpam-1372	824	18	along	along	ADP
ejpam-1372	824	19	the	the	DET
ejpam-1372	824	20	great	great	ADJ
ejpam-1372	824	21	arc	arc	NOUN
ejpam-1372	824	22	from	from	ADP
ejpam-1372	824	23	c−	c−	NOUN
ejpam-1372	824	24	i∞	i∞	NOUN
ejpam-1372	824	25	to	to	PART
ejpam-1372	824	26	c+	c+	VERB
ejpam-1372	824	27	i∞.	i∞.	ADP
ejpam-1372	824	28	the	the	DET
ejpam-1372	824	29	condition	condition	NOUN
ejpam-1372	824	30	on	on	ADP
ejpam-1372	824	31	arg	arg	NOUN
ejpam-1372	824	32	z	z	NOUN
ejpam-1372	824	33	ensures	ensure	VERB
ejpam-1372	824	34	that	that	SCONJ
ejpam-1372	824	35	the	the	DET
ejpam-1372	824	36	contour	contour	NOUN
ejpam-1372	824	37	integral	integral	ADJ
ejpam-1372	824	38	remains	remain	VERB
ejpam-1372	824	39	single	single	ADV
ejpam-1372	824	40	-	-	PUNCT
ejpam-1372	824	41	valued	value	VERB
ejpam-1372	824	42	.	.	PUNCT
ejpam-1372	825	1	consequently	consequently	ADV
ejpam-1372	825	2	,	,	PUNCT
ejpam-1372	825	3	we	we	PRON
ejpam-1372	825	4	can	can	AUX
ejpam-1372	825	5	apply	apply	VERB
ejpam-1372	825	6	the	the	DET
ejpam-1372	825	7	cauchy	cauchy	ADJ
ejpam-1372	825	8	residue	residue	NOUN
ejpam-1372	825	9	theorem	theorem	NOUN
ejpam-1372	825	10	[	[	X
ejpam-1372	825	11	7	7	NUM
ejpam-1372	825	12	,	,	PUNCT
ejpam-1372	825	13	30	30	NUM
ejpam-1372	825	14	,	,	PUNCT
ejpam-1372	825	15	33	33	NUM
ejpam-1372	825	16	]	]	PUNCT
ejpam-1372	825	17	.	.	PUNCT
ejpam-1372	826	1	the	the	DET
ejpam-1372	826	2	third	third	ADJ
ejpam-1372	826	3	condition	condition	NOUN
ejpam-1372	826	4	means	mean	VERB
ejpam-1372	826	5	that	that	SCONJ
ejpam-1372	826	6	when	when	SCONJ
ejpam-1372	826	7	the	the	DET
ejpam-1372	826	8	residues	residue	NOUN
ejpam-1372	826	9	of	of	ADP
ejpam-1372	826	10	the	the	DET
ejpam-1372	826	11	contour	contour	NOUN
ejpam-1372	826	12	integral	integral	NOUN
ejpam-1372	826	13	are	be	AUX
ejpam-1372	826	14	evaluated	evaluate	VERB
ejpam-1372	826	15	,	,	PUNCT
ejpam-1372	826	16	one	one	PRON
ejpam-1372	826	17	obtains	obtain	VERB
ejpam-1372	826	18	the	the	DET
ejpam-1372	826	19	series	series	NOUN
ejpam-1372	826	20	on	on	ADP
ejpam-1372	826	21	the	the	DET
ejpam-1372	826	22	lhs	lhs	PROPN
ejpam-1372	826	23	of	of	ADP
ejpam-1372	826	24	equivalence	equivalence	NOUN
ejpam-1372	826	25	(	(	PUNCT
ejpam-1372	826	26	87	87	NUM
ejpam-1372	826	27	)	)	PUNCT
ejpam-1372	826	28	.	.	PUNCT
ejpam-1372	827	1	where	where	SCONJ
ejpam-1372	827	2	regularisation	regularisation	NOUN
ejpam-1372	827	3	becomes	become	VERB
ejpam-1372	827	4	an	an	DET
ejpam-1372	827	5	issue	issue	NOUN
ejpam-1372	827	6	is	be	AUX
ejpam-1372	827	7	when	when	SCONJ
ejpam-1372	827	8	we	we	PRON
ejpam-1372	827	9	wish	wish	VERB
ejpam-1372	827	10	to	to	PART
ejpam-1372	827	11	evaluate	evaluate	VERB
ejpam-1372	827	12	the	the	DET
ejpam-1372	827	13	contour	contour	NOUN
ejpam-1372	827	14	integral	integral	ADJ
ejpam-1372	827	15	along	along	ADP
ejpam-1372	827	16	the	the	DET
ejpam-1372	827	17	great	great	ADJ
ejpam-1372	827	18	arc	arc	NOUN
ejpam-1372	827	19	.	.	PUNCT
ejpam-1372	828	1	in	in	ADP
ejpam-1372	828	2	the	the	DET
ejpam-1372	828	3	case	case	NOUN
ejpam-1372	828	4	of	of	ADP
ejpam-1372	828	5	a	a	DET
ejpam-1372	828	6	convergent	convergent	NOUN
ejpam-1372	828	7	series	series	NOUN
ejpam-1372	828	8	the	the	DET
ejpam-1372	828	9	integral	integral	ADJ
ejpam-1372	828	10	along	along	ADP
ejpam-1372	828	11	the	the	DET
ejpam-1372	828	12	great	great	ADJ
ejpam-1372	828	13	arc	arc	NOUN
ejpam-1372	828	14	vanishes	vanish	VERB
ejpam-1372	828	15	and	and	CCONJ
ejpam-1372	828	16	equivalence	equivalence	NOUN
ejpam-1372	828	17	(	(	PUNCT
ejpam-1372	828	18	90	90	NUM
ejpam-1372	828	19	)	)	PUNCT
ejpam-1372	828	20	becomes	become	VERB
ejpam-1372	828	21	an	an	DET
ejpam-1372	828	22	equation	equation	NOUN
ejpam-1372	828	23	.	.	PUNCT
ejpam-1372	829	1	for	for	ADP
ejpam-1372	829	2	ε1=	ε1=	PROPN
ejpam-1372	829	3	ln	ln	ADJ
ejpam-1372	829	4	|z|	|z|	NOUN
ejpam-1372	829	5	and	and	CCONJ
ejpam-1372	829	6	ε2=	ε2=	PRON
ejpam-1372	829	7	ln	ln	ADJ
ejpam-1372	829	8	|z|	|z|	NOUN
ejpam-1372	829	9	,	,	PUNCT
ejpam-1372	829	10	the	the	DET
ejpam-1372	829	11	integral	integral	ADJ
ejpam-1372	829	12	along	along	ADP
ejpam-1372	829	13	the	the	DET
ejpam-1372	829	14	great	great	ADJ
ejpam-1372	829	15	arc	arc	NOUN
ejpam-1372	829	16	can	can	AUX
ejpam-1372	829	17	vanish	vanish	VERB
ejpam-1372	829	18	,	,	PUNCT
ejpam-1372	829	19	but	but	CCONJ
ejpam-1372	829	20	it	it	PRON
ejpam-1372	829	21	will	will	AUX
ejpam-1372	829	22	depend	depend	VERB
ejpam-1372	829	23	upon	upon	SCONJ
ejpam-1372	829	24	the	the	DET
ejpam-1372	829	25	algebraic	algebraic	ADJ
ejpam-1372	829	26	part	part	NOUN
ejpam-1372	829	27	of	of	ADP
ejpam-1372	829	28	f	f	PROPN
ejpam-1372	829	29	(	(	PUNCT
ejpam-1372	829	30	s	s	NOUN
ejpam-1372	829	31	)	)	PUNCT
ejpam-1372	829	32	.	.	PUNCT
ejpam-1372	830	1	however	however	ADV
ejpam-1372	830	2	,	,	PUNCT
ejpam-1372	830	3	if	if	SCONJ
ejpam-1372	830	4	ε1	ε1	VERB
ejpam-1372	830	5	<	<	X
ejpam-1372	830	6	ln	ln	ADJ
ejpam-1372	830	7	|z|	|z|	NOUN
ejpam-1372	830	8	or	or	CCONJ
ejpam-1372	830	9	ε2	ε2	NOUN
ejpam-1372	830	10	<	<	X
ejpam-1372	830	11	ln	ln	ADJ
ejpam-1372	830	12	|z|	|z|	NOUN
ejpam-1372	830	13	,	,	PUNCT
ejpam-1372	830	14	then	then	ADV
ejpam-1372	830	15	the	the	DET
ejpam-1372	830	16	integral	integral	ADJ
ejpam-1372	830	17	along	along	ADP
ejpam-1372	830	18	the	the	DET
ejpam-1372	830	19	great	great	ADJ
ejpam-1372	830	20	arc	arc	NOUN
ejpam-1372	830	21	is	be	AUX
ejpam-1372	830	22	infinity	infinity	NOUN
ejpam-1372	830	23	.	.	PUNCT
ejpam-1372	831	1	in	in	ADP
ejpam-1372	831	2	this	this	DET
ejpam-1372	831	3	situation	situation	NOUN
ejpam-1372	831	4	we	we	PRON
ejpam-1372	831	5	neglect	neglect	VERB
ejpam-1372	831	6	the	the	DET
ejpam-1372	831	7	integral	integral	ADJ
ejpam-1372	831	8	,	,	PUNCT
ejpam-1372	831	9	which	which	PRON
ejpam-1372	831	10	is	be	AUX
ejpam-1372	831	11	equivalent	equivalent	ADJ
ejpam-1372	831	12	to	to	ADP
ejpam-1372	831	13	removing	remove	VERB
ejpam-1372	831	14	the	the	DET
ejpam-1372	831	15	infinity	infinity	NOUN
ejpam-1372	831	16	in	in	ADP
ejpam-1372	831	17	accordance	accordance	NOUN
ejpam-1372	831	18	with	with	ADP
ejpam-1372	831	19	the	the	DET
ejpam-1372	831	20	process	process	NOUN
ejpam-1372	831	21	of	of	ADP
ejpam-1372	831	22	regularisation	regularisation	NOUN
ejpam-1372	831	23	.	.	PUNCT
ejpam-1372	832	1	for	for	ADP
ejpam-1372	832	2	more	more	ADJ
ejpam-1372	832	3	details	detail	NOUN
ejpam-1372	832	4	on	on	ADP
ejpam-1372	832	5	this	this	DET
ejpam-1372	832	6	issue	issue	NOUN
ejpam-1372	832	7	the	the	DET
ejpam-1372	832	8	reader	reader	NOUN
ejpam-1372	832	9	is	be	AUX
ejpam-1372	832	10	referred	refer	VERB
ejpam-1372	832	11	to	to	ADP
ejpam-1372	832	12	either	either	PRON
ejpam-1372	832	13	p.	p.	NOUN
ejpam-1372	832	14	85	85	NUM
ejpam-1372	832	15	of	of	ADP
ejpam-1372	832	16	ref	ref	NOUN
ejpam-1372	832	17	.	.	PUNCT
ejpam-1372	833	1	[	[	X
ejpam-1372	833	2	17	17	NUM
ejpam-1372	833	3	]	]	PUNCT
ejpam-1372	833	4	or	or	CCONJ
ejpam-1372	833	5	ref	ref	NOUN
ejpam-1372	833	6	.	.	PUNCT
ejpam-1372	834	1	[	[	X
ejpam-1372	834	2	15	15	NUM
ejpam-1372	834	3	]	]	PUNCT
ejpam-1372	834	4	.	.	PUNCT
ejpam-1372	835	1	if	if	SCONJ
ejpam-1372	835	2	we	we	PRON
ejpam-1372	835	3	introduce	introduce	VERB
ejpam-1372	835	4	the	the	DET
ejpam-1372	835	5	seemingly	seemingly	ADV
ejpam-1372	835	6	innocuous	innocuous	ADJ
ejpam-1372	835	7	factor	factor	NOUN
ejpam-1372	835	8	of	of	ADP
ejpam-1372	835	9	1k	1k	NUM
ejpam-1372	835	10	in	in	ADP
ejpam-1372	835	11	the	the	DET
ejpam-1372	835	12	form	form	NOUN
ejpam-1372	835	13	of	of	ADP
ejpam-1372	835	14	exp(−2πilk	exp(−2πilk	NOUN
ejpam-1372	835	15	)	)	PUNCT
ejpam-1372	835	16	,	,	PUNCT
ejpam-1372	835	17	where	where	SCONJ
ejpam-1372	835	18	l	l	NOUN
ejpam-1372	835	19	is	be	AUX
ejpam-1372	835	20	an	an	DET
ejpam-1372	835	21	arbitrary	arbitrary	ADJ
ejpam-1372	835	22	integer	integer	NOUN
ejpam-1372	835	23	,	,	PUNCT
ejpam-1372	835	24	into	into	ADP
ejpam-1372	835	25	si(n	si(n	X
ejpam-1372	835	26	,	,	PUNCT
ejpam-1372	835	27	z	z	NOUN
ejpam-1372	835	28	)	)	PUNCT
ejpam-1372	835	29	,	,	PUNCT
ejpam-1372	835	30	then	then	ADV
ejpam-1372	835	31	the	the	DET
ejpam-1372	835	32	mb	mb	ADJ
ejpam-1372	835	33	-	-	PUNCT
ejpam-1372	835	34	regularised	regularise	VERB
ejpam-1372	835	35	value	value	NOUN
ejpam-1372	835	36	of	of	ADP
ejpam-1372	835	37	the	the	DET
ejpam-1372	835	38	modified	modify	VERB
ejpam-1372	835	39	series	series	NOUN
ejpam-1372	835	40	becomes	become	VERB
ejpam-1372	835	41	si	si	PROPN
ejpam-1372	835	42	�	�	PROPN
ejpam-1372	835	43	n	n	PROPN
ejpam-1372	835	44	,	,	PUNCT
ejpam-1372	835	45	z	z	PROPN
ejpam-1372	835	46	exp(−2l	exp(−2l	NOUN
ejpam-1372	835	47	iπ	iπ	NOUN
ejpam-1372	835	48	)	)	PUNCT
ejpam-1372	835	49	�	�	PROPN
ejpam-1372	835	50	=	=	SYM
ejpam-1372	835	51	∞	∞	PROPN
ejpam-1372	835	52	∑	∑	PUNCT
ejpam-1372	835	53	k	k	X
ejpam-1372	835	54	=	=	PROPN
ejpam-1372	835	55	n	n	PROPN
ejpam-1372	835	56	f	f	X
ejpam-1372	835	57	(	(	PUNCT
ejpam-1372	835	58	k	k	NOUN
ejpam-1372	835	59	)	)	PUNCT
ejpam-1372	835	60	�	�	PROPN
ejpam-1372	835	61	−z	−z	PROPN
ejpam-1372	835	62	exp(−2l	exp(−2l	X
ejpam-1372	835	63	iπ	iπ	NOUN
ejpam-1372	835	64	)	)	PUNCT
ejpam-1372	835	65	�	�	PROPN
ejpam-1372	835	66	k	k	PROPN
ejpam-1372	835	67	≡	≡	PROPN
ejpam-1372	835	68	il(z	il(z	PROPN
ejpam-1372	835	69	)	)	PUNCT
ejpam-1372	835	70	=	=	SYM
ejpam-1372	836	1	∫	∫	PROPN
ejpam-1372	836	2	c+i∞	c+i∞	NOUN
ejpam-1372	836	3	c−i∞	c−i∞	PROPN
ejpam-1372	836	4	ds	ds	VERB
ejpam-1372	836	5	zs	zs	PROPN
ejpam-1372	836	6	e−2l	e−2l	PROPN
ejpam-1372	836	7	iπs	iπs	PROPN
ejpam-1372	836	8	f	f	PROPN
ejpam-1372	836	9	(	(	PUNCT
ejpam-1372	836	10	s	s	NOUN
ejpam-1372	836	11	)	)	PUNCT
ejpam-1372	836	12	e−iπs	e−iπs	NOUN
ejpam-1372	836	13	−	−	PROPN
ejpam-1372	836	14	eiπs	eiπs	PROPN
ejpam-1372	836	15	,	,	PUNCT
ejpam-1372	836	16	(	(	PUNCT
ejpam-1372	836	17	92	92	NUM
ejpam-1372	836	18	)	)	PUNCT
ejpam-1372	836	19	where	where	SCONJ
ejpam-1372	836	20	,	,	PUNCT
ejpam-1372	836	21	again	again	ADV
ejpam-1372	836	22	,	,	PUNCT
ejpam-1372	836	23	n−1	n−1	PROPN
ejpam-1372	836	24	<	<	X
ejpam-1372	836	25	c	c	X
ejpam-1372	836	26	=	=	SYM
ejpam-1372	836	27	ℜ	ℜ	PROPN
ejpam-1372	836	28	s	s	PART
ejpam-1372	836	29	<	<	X
ejpam-1372	836	30	n	n	X
ejpam-1372	836	31	.	.	PUNCT
ejpam-1372	837	1	using	use	VERB
ejpam-1372	837	2	the	the	DET
ejpam-1372	837	3	conditions	condition	NOUN
ejpam-1372	837	4	on	on	ADP
ejpam-1372	837	5	f	f	PROPN
ejpam-1372	837	6	(	(	PUNCT
ejpam-1372	837	7	s	s	NOUN
ejpam-1372	837	8	)	)	PUNCT
ejpam-1372	837	9	below	below	ADP
ejpam-1372	837	10	equivalence	equivalence	NOUN
ejpam-1372	837	11	(	(	PUNCT
ejpam-1372	837	12	90	90	NUM
ejpam-1372	837	13	)	)	PUNCT
ejpam-1372	837	14	,	,	PUNCT
ejpam-1372	837	15	one	one	PRON
ejpam-1372	837	16	finds	find	VERB
ejpam-1372	837	17	that	that	SCONJ
ejpam-1372	837	18	the	the	DET
ejpam-1372	837	19	above	above	ADJ
ejpam-1372	837	20	integral	integral	ADJ
ejpam-1372	837	21	is	be	AUX
ejpam-1372	837	22	convergent	convergent	ADJ
ejpam-1372	837	23	when	when	SCONJ
ejpam-1372	837	24	(	(	PUNCT
ejpam-1372	837	25	2l	2l	NUM
ejpam-1372	837	26	−	−	PROPN
ejpam-1372	837	27	1)π−	1)π−	NUM
ejpam-1372	837	28	ε1	ε1	VERB
ejpam-1372	837	29	<	<	X
ejpam-1372	837	30	arg	arg	NOUN
ejpam-1372	837	31	z	z	X
ejpam-1372	837	32	<	<	X
ejpam-1372	837	33	(	(	PUNCT
ejpam-1372	837	34	2l	2l	NOUN
ejpam-1372	837	35	+	+	CCONJ
ejpam-1372	837	36	1)π+	1)π+	NUM
ejpam-1372	837	37	ε2	ε2	ADJ
ejpam-1372	837	38	.	.	PUNCT
ejpam-1372	838	1	(	(	PUNCT
ejpam-1372	838	2	93	93	NUM
ejpam-1372	838	3	)	)	PUNCT
ejpam-1372	838	4	if	if	SCONJ
ejpam-1372	838	5	we	we	PRON
ejpam-1372	838	6	put	put	VERB
ejpam-1372	838	7	l=	l=	ADJ
ejpam-1372	838	8	l	l	PROPN
ejpam-1372	839	1	+	+	CCONJ
ejpam-1372	839	2	1	1	NUM
ejpam-1372	839	3	in	in	ADP
ejpam-1372	839	4	equivalence	equivalence	NOUN
ejpam-1372	839	5	(	(	PUNCT
ejpam-1372	839	6	90	90	NUM
ejpam-1372	839	7	)	)	PUNCT
ejpam-1372	839	8	,	,	PUNCT
ejpam-1372	839	9	then	then	ADV
ejpam-1372	839	10	the	the	DET
ejpam-1372	839	11	domain	domain	NOUN
ejpam-1372	839	12	of	of	ADP
ejpam-1372	839	13	convergence	convergence	NOUN
ejpam-1372	839	14	for	for	ADP
ejpam-1372	839	15	il+1(z	il+1(z	PROPN
ejpam-1372	839	16	)	)	PUNCT
ejpam-1372	839	17	becomes	become	VERB
ejpam-1372	839	18	(	(	PUNCT
ejpam-1372	839	19	2l	2l	X
ejpam-1372	839	20	+	+	CCONJ
ejpam-1372	839	21	1)π−	1)π−	NUM
ejpam-1372	839	22	ε1	ε1	VERB
ejpam-1372	839	23	<	<	X
ejpam-1372	839	24	arg	arg	NOUN
ejpam-1372	839	25	z<(2l	z<(2l	PROPN
ejpam-1372	839	26	+	+	CCONJ
ejpam-1372	839	27	3)π+	3)π+	NUM
ejpam-1372	839	28	ε2	ε2	ADJ
ejpam-1372	839	29	.	.	PUNCT
ejpam-1372	840	1	therefore	therefore	ADV
ejpam-1372	840	2	,	,	PUNCT
ejpam-1372	840	3	there	there	PRON
ejpam-1372	840	4	is	be	VERB
ejpam-1372	840	5	a	a	DET
ejpam-1372	840	6	common	common	ADJ
ejpam-1372	840	7	sector	sector	NOUN
ejpam-1372	840	8	which	which	PRON
ejpam-1372	840	9	is	be	AUX
ejpam-1372	840	10	given	give	VERB
ejpam-1372	840	11	by	by	ADP
ejpam-1372	840	12	(	(	PUNCT
ejpam-1372	840	13	2l+1)π−ε1	2l+1)π−ε1	PROPN
ejpam-1372	840	14	<	<	X
ejpam-1372	840	15	arg	arg	NOUN
ejpam-1372	840	16	z<(2l+1)π+ε2	z<(2l+1)π+ε2	PROPN
ejpam-1372	840	17	,	,	PUNCT
ejpam-1372	840	18	where	where	SCONJ
ejpam-1372	840	19	the	the	DET
ejpam-1372	840	20	regularised	regularise	VERB
ejpam-1372	840	21	value	value	NOUN
ejpam-1372	840	22	can	can	AUX
ejpam-1372	840	23	be	be	AUX
ejpam-1372	840	24	evaluated	evaluate	VERB
ejpam-1372	840	25	by	by	ADP
ejpam-1372	840	26	either	either	PRON
ejpam-1372	840	27	il(z	il(z	NOUN
ejpam-1372	840	28	)	)	PUNCT
ejpam-1372	840	29	or	or	CCONJ
ejpam-1372	840	30	il+1(z	il+1(z	PROPN
ejpam-1372	840	31	)	)	PUNCT
ejpam-1372	840	32	.	.	PUNCT
ejpam-1372	841	1	without	without	ADP
ejpam-1372	841	2	loss	loss	NOUN
ejpam-1372	841	3	of	of	ADP
ejpam-1372	841	4	generality	generality	NOUN
ejpam-1372	841	5	α	α	NOUN
ejpam-1372	841	6	is	be	AUX
ejpam-1372	841	7	assumed	assume	VERB
ejpam-1372	841	8	to	to	PART
ejpam-1372	841	9	be	be	AUX
ejpam-1372	841	10	positive	positive	ADJ
ejpam-1372	841	11	and	and	CCONJ
ejpam-1372	841	12	real	real	ADJ
ejpam-1372	841	13	since	since	SCONJ
ejpam-1372	841	14	if	if	SCONJ
ejpam-1372	841	15	it	it	PRON
ejpam-1372	841	16	is	be	AUX
ejpam-1372	841	17	negative	negative	ADJ
ejpam-1372	841	18	,	,	PUNCT
ejpam-1372	841	19	we	we	PRON
ejpam-1372	841	20	can	can	AUX
ejpam-1372	841	21	separate	separate	VERB
ejpam-1372	841	22	the	the	DET
ejpam-1372	841	23	finite	finite	ADJ
ejpam-1372	841	24	number	number	NOUN
ejpam-1372	841	25	of	of	ADP
ejpam-1372	841	26	terms	term	NOUN
ejpam-1372	841	27	up	up	ADP
ejpam-1372	841	28	to	to	ADP
ejpam-1372	841	29	the	the	DET
ejpam-1372	841	30	first	first	ADJ
ejpam-1372	841	31	value	value	NOUN
ejpam-1372	841	32	where	where	SCONJ
ejpam-1372	841	33	k+α	k+α	PROPN
ejpam-1372	841	34	becomes	become	VERB
ejpam-1372	841	35	v.	v.	ADP
ejpam-1372	841	36	kowalenko	kowalenko	PROPN
ejpam-1372	841	37	/	/	SYM
ejpam-1372	841	38	eur	eur	PROPN
ejpam-1372	841	39	.	.	PUNCT
ejpam-1372	842	1	j.	j.	PROPN
ejpam-1372	842	2	pure	pure	PROPN
ejpam-1372	842	3	appl	appl	PROPN
ejpam-1372	842	4	.	.	PROPN
ejpam-1372	842	5	math	math	PROPN
ejpam-1372	842	6	,	,	PUNCT
ejpam-1372	842	7	4	4	NUM
ejpam-1372	842	8	(	(	PUNCT
ejpam-1372	842	9	2011	2011	NUM
ejpam-1372	842	10	)	)	PUNCT
ejpam-1372	842	11	,	,	PUNCT
ejpam-1372	842	12	370	370	NUM
ejpam-1372	842	13	-	-	SYM
ejpam-1372	842	14	423	423	NUM
ejpam-1372	842	15	399	399	NUM
ejpam-1372	842	16	positive	positive	ADJ
ejpam-1372	842	17	and	and	CCONJ
ejpam-1372	842	18	re	re	VERB
ejpam-1372	842	19	-	-	VERB
ejpam-1372	842	20	define	define	VERB
ejpam-1372	842	21	α	α	NOUN
ejpam-1372	842	22	in	in	ADP
ejpam-1372	842	23	the	the	DET
ejpam-1372	842	24	remaining	remain	VERB
ejpam-1372	842	25	infinite	infinite	ADJ
ejpam-1372	842	26	series	series	NOUN
ejpam-1372	842	27	.	.	PUNCT
ejpam-1372	843	1	furthermore	furthermore	ADV
ejpam-1372	843	2	,	,	PUNCT
ejpam-1372	843	3	we	we	PRON
ejpam-1372	843	4	can	can	AUX
ejpam-1372	843	5	evaluate	evaluate	VERB
ejpam-1372	843	6	the	the	DET
ejpam-1372	843	7	difference	difference	NOUN
ejpam-1372	843	8	of	of	ADP
ejpam-1372	843	9	the	the	DET
ejpam-1372	843	10	integrals	integral	NOUN
ejpam-1372	843	11	over	over	ADP
ejpam-1372	843	12	the	the	DET
ejpam-1372	843	13	common	common	ADJ
ejpam-1372	843	14	sector	sector	NOUN
ejpam-1372	843	15	.	.	PUNCT
ejpam-1372	844	1	as	as	ADP
ejpam-1372	844	2	a	a	DET
ejpam-1372	844	3	result	result	NOUN
ejpam-1372	844	4	,	,	PUNCT
ejpam-1372	844	5	we	we	PRON
ejpam-1372	844	6	find	find	VERB
ejpam-1372	844	7	that	that	SCONJ
ejpam-1372	844	8	∆il+1,l(z	∆il+1,l(z	NOUN
ejpam-1372	844	9	)	)	PUNCT
ejpam-1372	844	10	=	=	SYM
ejpam-1372	844	11	il+1(z)−	il+1(z)−	NOUN
ejpam-1372	844	12	il(z	il(z	NOUN
ejpam-1372	844	13	)	)	PUNCT
ejpam-1372	845	1	=	=	SYM
ejpam-1372	845	2	∫	∫	PROPN
ejpam-1372	845	3	c+i∞	c+i∞	PROPN
ejpam-1372	845	4	c−i∞	c−i∞	PROPN
ejpam-1372	845	5	ds	ds	PROPN
ejpam-1372	845	6	zse−(2l+1)iπs	zse−(2l+1)iπs	PROPN
ejpam-1372	845	7	f	f	PROPN
ejpam-1372	845	8	(	(	PUNCT
ejpam-1372	845	9	s	s	PROPN
ejpam-1372	845	10	)	)	PUNCT
ejpam-1372	845	11	.	.	PUNCT
ejpam-1372	846	1	(	(	PUNCT
ejpam-1372	846	2	94	94	NUM
ejpam-1372	846	3	)	)	PUNCT
ejpam-1372	846	4	hence	hence	ADV
ejpam-1372	846	5	,	,	PUNCT
ejpam-1372	846	6	the	the	DET
ejpam-1372	846	7	difference	difference	NOUN
ejpam-1372	846	8	between	between	ADP
ejpam-1372	846	9	consecutive	consecutive	ADJ
ejpam-1372	846	10	values	value	NOUN
ejpam-1372	846	11	of	of	ADP
ejpam-1372	846	12	l	l	NOUN
ejpam-1372	846	13	for	for	ADP
ejpam-1372	846	14	il(z	il(z	NOUN
ejpam-1372	846	15	)	)	PUNCT
ejpam-1372	846	16	yields	yield	VERB
ejpam-1372	846	17	a	a	DET
ejpam-1372	846	18	standard	standard	ADJ
ejpam-1372	846	19	inverse	inverse	NOUN
ejpam-1372	846	20	mellin	mellin	NOUN
ejpam-1372	846	21	transform	transform	NOUN
ejpam-1372	846	22	[	[	X
ejpam-1372	846	23	25	25	NUM
ejpam-1372	846	24	]	]	PUNCT
ejpam-1372	846	25	.	.	PUNCT
ejpam-1372	847	1	in	in	ADP
ejpam-1372	847	2	particular	particular	ADJ
ejpam-1372	847	3	,	,	PUNCT
ejpam-1372	847	4	for	for	ADP
ejpam-1372	847	5	those	those	DET
ejpam-1372	847	6	series	series	NOUN
ejpam-1372	847	7	which	which	DET
ejpam-1372	847	8	euler	euler	PROPN
ejpam-1372	847	9	referred	refer	VERB
ejpam-1372	847	10	to	to	ADP
ejpam-1372	847	11	as	as	ADP
ejpam-1372	847	12	divergent	divergent	ADJ
ejpam-1372	847	13	par	par	NOUN
ejpam-1372	847	14	excellence	excellence	NOUN
ejpam-1372	847	15	,	,	PUNCT
ejpam-1372	847	16	or	or	CCONJ
ejpam-1372	847	17	more	more	ADJ
ejpam-1372	847	18	generally	generally	ADV
ejpam-1372	847	19	standard	standard	ADJ
ejpam-1372	847	20	terminants	terminant	NOUN
ejpam-1372	847	21	,	,	PUNCT
ejpam-1372	847	22	f	f	PROPN
ejpam-1372	847	23	(	(	PUNCT
ejpam-1372	847	24	s)=γ(s+α	s)=γ(s+α	NOUN
ejpam-1372	847	25	)	)	PUNCT
ejpam-1372	847	26	.	.	PUNCT
ejpam-1372	848	1	then	then	ADV
ejpam-1372	848	2	we	we	PRON
ejpam-1372	848	3	obtain	obtain	VERB
ejpam-1372	848	4	∆il+1,l(z	∆il+1,l(z	NOUN
ejpam-1372	848	5	)	)	PUNCT
ejpam-1372	848	6	=	=	SYM
ejpam-1372	848	7	2πi	2πi	NOUN
ejpam-1372	848	8	z−α	z−α	PROPN
ejpam-1372	848	9	e(2l+1)iπα	e(2l+1)iπα	PROPN
ejpam-1372	848	10	e1	e1	PROPN
ejpam-1372	848	11	/	/	SYM
ejpam-1372	848	12	z	z	NOUN
ejpam-1372	848	13	.	.	PUNCT
ejpam-1372	849	1	(	(	PUNCT
ejpam-1372	849	2	95	95	NUM
ejpam-1372	849	3	)	)	PUNCT
ejpam-1372	849	4	since	since	SCONJ
ejpam-1372	849	5	i0(a	i0(a	PROPN
ejpam-1372	849	6	)	)	PUNCT
ejpam-1372	849	7	represents	represent	VERB
ejpam-1372	849	8	the	the	DET
ejpam-1372	849	9	regularised	regularise	VERB
ejpam-1372	849	10	value	value	NOUN
ejpam-1372	849	11	of	of	ADP
ejpam-1372	849	12	s1(n	s1(n	PRON
ejpam-1372	849	13	,	,	PUNCT
ejpam-1372	849	14	z	z	NOUN
ejpam-1372	849	15	)	)	PUNCT
ejpam-1372	849	16	for	for	ADP
ejpam-1372	849	17	−π	−π	PROPN
ejpam-1372	849	18	<	<	X
ejpam-1372	849	19	arg	arg	NOUN
ejpam-1372	849	20	z	z	X
ejpam-1372	849	21	<	<	X
ejpam-1372	849	22	π	π	PROPN
ejpam-1372	849	23	,	,	PUNCT
ejpam-1372	849	24	we	we	PRON
ejpam-1372	849	25	see	see	VERB
ejpam-1372	849	26	from	from	ADP
ejpam-1372	849	27	eq	eq	PROPN
ejpam-1372	849	28	.	.	PUNCT
ejpam-1372	850	1	(	(	PUNCT
ejpam-1372	850	2	94	94	NUM
ejpam-1372	850	3	)	)	PUNCT
ejpam-1372	850	4	that	that	PRON
ejpam-1372	850	5	i1(z)−∆i1,0(z	i1(z)−∆i1,0(z	PROPN
ejpam-1372	850	6	)	)	PUNCT
ejpam-1372	850	7	is	be	AUX
ejpam-1372	850	8	also	also	ADV
ejpam-1372	850	9	the	the	DET
ejpam-1372	850	10	regularised	regularise	VERB
ejpam-1372	850	11	value	value	NOUN
ejpam-1372	850	12	of	of	ADP
ejpam-1372	850	13	the	the	DET
ejpam-1372	850	14	series	series	NOUN
ejpam-1372	850	15	,	,	PUNCT
ejpam-1372	850	16	but	but	CCONJ
ejpam-1372	850	17	only	only	ADV
ejpam-1372	850	18	over	over	ADP
ejpam-1372	850	19	the	the	DET
ejpam-1372	850	20	sector	sector	NOUN
ejpam-1372	850	21	of	of	ADP
ejpam-1372	850	22	π−	π−	PROPN
ejpam-1372	850	23	ε1	ε1	PROPN
ejpam-1372	850	24	<	<	X
ejpam-1372	850	25	arg	arg	NOUN
ejpam-1372	850	26	z	z	X
ejpam-1372	850	27	<	<	X
ejpam-1372	850	28	π	π	X
ejpam-1372	850	29	.	.	PUNCT
ejpam-1372	851	1	however	however	ADV
ejpam-1372	851	2	,	,	PUNCT
ejpam-1372	851	3	we	we	PRON
ejpam-1372	851	4	know	know	VERB
ejpam-1372	851	5	that	that	PRON
ejpam-1372	851	6	i1(z	i1(z	PROPN
ejpam-1372	851	7	)	)	PUNCT
ejpam-1372	851	8	is	be	AUX
ejpam-1372	851	9	defined	define	VERB
ejpam-1372	851	10	over	over	ADP
ejpam-1372	851	11	π−	π−	PROPN
ejpam-1372	851	12	ε1	ε1	PROPN
ejpam-1372	851	13	<	<	X
ejpam-1372	851	14	arg	arg	NOUN
ejpam-1372	851	15	z<3π+	z<3π+	X
ejpam-1372	851	16	ε2	ε2	ADJ
ejpam-1372	851	17	.	.	PUNCT
ejpam-1372	852	1	so	so	ADV
ejpam-1372	852	2	,	,	PUNCT
ejpam-1372	852	3	if	if	SCONJ
ejpam-1372	852	4	∆i1,0(z	∆i1,0(z	PROPN
ejpam-1372	852	5	)	)	PUNCT
ejpam-1372	852	6	is	be	AUX
ejpam-1372	852	7	defined	define	VERB
ejpam-1372	852	8	over	over	ADP
ejpam-1372	852	9	the	the	DET
ejpam-1372	852	10	same	same	ADJ
ejpam-1372	852	11	region	region	NOUN
ejpam-1372	852	12	,	,	PUNCT
ejpam-1372	852	13	which	which	PRON
ejpam-1372	852	14	is	be	AUX
ejpam-1372	852	15	the	the	DET
ejpam-1372	852	16	case	case	NOUN
ejpam-1372	852	17	with	with	ADP
ejpam-1372	852	18	standard	standard	ADJ
ejpam-1372	852	19	terminants	terminant	NOUN
ejpam-1372	852	20	according	accord	VERB
ejpam-1372	852	21	to	to	ADP
ejpam-1372	852	22	eq	eq	PROPN
ejpam-1372	852	23	.	.	PUNCT
ejpam-1372	853	1	(	(	PUNCT
ejpam-1372	853	2	95	95	NUM
ejpam-1372	853	3	)	)	PUNCT
ejpam-1372	853	4	,	,	PUNCT
ejpam-1372	853	5	then	then	ADV
ejpam-1372	853	6	by	by	ADP
ejpam-1372	853	7	analytic	analytic	ADJ
ejpam-1372	853	8	continuation	continuation	NOUN
ejpam-1372	853	9	i1(z)−∆i1,0(z	i1(z)−∆i1,0(z	PROPN
ejpam-1372	853	10	)	)	PUNCT
ejpam-1372	853	11	becomes	become	VERB
ejpam-1372	853	12	the	the	DET
ejpam-1372	853	13	regularised	regularise	VERB
ejpam-1372	853	14	value	value	NOUN
ejpam-1372	853	15	of	of	ADP
ejpam-1372	853	16	over	over	ADP
ejpam-1372	853	17	the	the	DET
ejpam-1372	853	18	entire	entire	ADJ
ejpam-1372	853	19	branch	branch	NOUN
ejpam-1372	853	20	given	give	VERB
ejpam-1372	853	21	by	by	ADP
ejpam-1372	853	22	π−	π−	PROPN
ejpam-1372	853	23	ε1	ε1	PROPN
ejpam-1372	853	24	<	<	X
ejpam-1372	853	25	arg	arg	NOUN
ejpam-1372	853	26	z<3π+	z<3π+	X
ejpam-1372	853	27	ε2	ε2	ADJ
ejpam-1372	853	28	.	.	PUNCT
ejpam-1372	854	1	because	because	SCONJ
ejpam-1372	854	2	of	of	ADP
ejpam-1372	854	3	eq	eq	ADP
ejpam-1372	854	4	.	.	PUNCT
ejpam-1372	854	5	(	(	PUNCT
ejpam-1372	854	6	94	94	NUM
ejpam-1372	854	7	)	)	PUNCT
ejpam-1372	854	8	we	we	PRON
ejpam-1372	854	9	can	can	AUX
ejpam-1372	854	10	replace	replace	VERB
ejpam-1372	854	11	i1(z	i1(z	PROPN
ejpam-1372	854	12	)	)	PUNCT
ejpam-1372	854	13	by	by	ADP
ejpam-1372	854	14	i2(z)−∆i2,1(z	i2(z)−∆i2,1(z	PROPN
ejpam-1372	854	15	)	)	PUNCT
ejpam-1372	854	16	for	for	ADP
ejpam-1372	854	17	3π−	3π−	PROPN
ejpam-1372	854	18	ε1	ε1	PROPN
ejpam-1372	854	19	<	<	X
ejpam-1372	854	20	arg	arg	NOUN
ejpam-1372	854	21	z<3π+	z<3π+	X
ejpam-1372	854	22	ε2	ε2	ADJ
ejpam-1372	854	23	.	.	PUNCT
ejpam-1372	855	1	however	however	ADV
ejpam-1372	855	2	,	,	PUNCT
ejpam-1372	855	3	the	the	DET
ejpam-1372	855	4	domain	domain	NOUN
ejpam-1372	855	5	of	of	ADP
ejpam-1372	855	6	convergence	convergence	NOUN
ejpam-1372	855	7	for	for	ADP
ejpam-1372	855	8	i2(z	i2(z	PRON
ejpam-1372	855	9	)	)	PUNCT
ejpam-1372	855	10	is	be	AUX
ejpam-1372	855	11	3π	3π	NUM
ejpam-1372	855	12	−	−	NOUN
ejpam-1372	855	13	ε1	ε1	VERB
ejpam-1372	855	14	<	<	X
ejpam-1372	855	15	arg	arg	NOUN
ejpam-1372	855	16	z	z	X
ejpam-1372	855	17	<	<	X
ejpam-1372	855	18	5π	5π	PROPN
ejpam-1372	855	19	+	+	CCONJ
ejpam-1372	855	20	ε2	ε2	ADJ
ejpam-1372	855	21	.	.	PUNCT
ejpam-1372	856	1	if	if	SCONJ
ejpam-1372	856	2	∆i2,1(z	∆i2,1(z	NOUN
ejpam-1372	856	3	)	)	PUNCT
ejpam-1372	856	4	is	be	AUX
ejpam-1372	856	5	defined	define	VERB
ejpam-1372	856	6	over	over	ADP
ejpam-1372	856	7	the	the	DET
ejpam-1372	856	8	same	same	ADJ
ejpam-1372	856	9	sector	sector	NOUN
ejpam-1372	856	10	,	,	PUNCT
ejpam-1372	856	11	which	which	PRON
ejpam-1372	856	12	is	be	AUX
ejpam-1372	856	13	valid	valid	ADJ
ejpam-1372	856	14	for	for	ADP
ejpam-1372	856	15	standard	standard	ADJ
ejpam-1372	856	16	terminants	terminant	NOUN
ejpam-1372	856	17	,	,	PUNCT
ejpam-1372	856	18	then	then	ADV
ejpam-1372	856	19	i2(z)−∆i2,1(z	i2(z)−∆i2,1(z	VERB
ejpam-1372	856	20	)	)	PUNCT
ejpam-1372	856	21	is	be	AUX
ejpam-1372	856	22	the	the	DET
ejpam-1372	856	23	regularised	regularise	VERB
ejpam-1372	856	24	value	value	NOUN
ejpam-1372	856	25	of	of	ADP
ejpam-1372	856	26	si(n	si(n	NOUN
ejpam-1372	856	27	,	,	PUNCT
ejpam-1372	856	28	z	z	NOUN
ejpam-1372	856	29	)	)	PUNCT
ejpam-1372	856	30	over	over	ADP
ejpam-1372	856	31	3π−	3π−	PROPN
ejpam-1372	856	32	ε1	ε1	VERB
ejpam-1372	856	33	<	<	X
ejpam-1372	856	34	arg	arg	X
ejpam-1372	856	35	z	z	X
ejpam-1372	856	36	<	<	X
ejpam-1372	856	37	5π+	5π+	NUM
ejpam-1372	856	38	ε2	ε2	ADJ
ejpam-1372	856	39	.	.	PUNCT
ejpam-1372	857	1	by	by	ADP
ejpam-1372	857	2	continuing	continue	VERB
ejpam-1372	857	3	this	this	DET
ejpam-1372	857	4	process	process	NOUN
ejpam-1372	857	5	further	far	ADV
ejpam-1372	857	6	,	,	PUNCT
ejpam-1372	857	7	one	one	PRON
ejpam-1372	857	8	can	can	AUX
ejpam-1372	857	9	obtain	obtain	VERB
ejpam-1372	857	10	the	the	DET
ejpam-1372	857	11	regularised	regularise	VERB
ejpam-1372	857	12	value	value	NOUN
ejpam-1372	857	13	of	of	ADP
ejpam-1372	857	14	si(n	si(n	NOUN
ejpam-1372	857	15	,	,	PUNCT
ejpam-1372	857	16	z	z	NOUN
ejpam-1372	857	17	)	)	PUNCT
ejpam-1372	857	18	for	for	ADP
ejpam-1372	857	19	all	all	DET
ejpam-1372	857	20	branches	branch	NOUN
ejpam-1372	857	21	of	of	ADP
ejpam-1372	857	22	the	the	DET
ejpam-1372	857	23	complex	complex	ADJ
ejpam-1372	857	24	plane	plane	NOUN
ejpam-1372	857	25	.	.	PUNCT
ejpam-1372	858	1	consequently	consequently	ADV
ejpam-1372	858	2	,	,	PUNCT
ejpam-1372	858	3	we	we	PRON
ejpam-1372	858	4	arrive	arrive	VERB
ejpam-1372	858	5	at	at	ADP
ejpam-1372	858	6	the	the	DET
ejpam-1372	858	7	result	result	NOUN
ejpam-1372	858	8	given	give	VERB
ejpam-1372	858	9	in	in	ADP
ejpam-1372	858	10	proposition	proposition	NOUN
ejpam-1372	858	11	4	4	NUM
ejpam-1372	858	12	of	of	ADP
ejpam-1372	858	13	ref	ref	NOUN
ejpam-1372	858	14	.	.	PUNCT
ejpam-1372	859	1	[	[	X
ejpam-1372	859	2	17	17	NUM
ejpam-1372	859	3	]	]	PUNCT
ejpam-1372	859	4	for	for	ADP
ejpam-1372	859	5	the	the	DET
ejpam-1372	859	6	regularised	regularise	VERB
ejpam-1372	859	7	value	value	NOUN
ejpam-1372	859	8	of	of	ADP
ejpam-1372	859	9	a	a	DET
ejpam-1372	859	10	generalised	generalised	ADJ
ejpam-1372	859	11	terminant	terminant	NOUN
ejpam-1372	859	12	.	.	PUNCT
ejpam-1372	860	1	for	for	ADP
ejpam-1372	860	2	a	a	DET
ejpam-1372	860	3	standard	standard	ADJ
ejpam-1372	860	4	type	type	NOUN
ejpam-1372	860	5	i	i	PRON
ejpam-1372	860	6	terminant	terminant	VERB
ejpam-1372	860	7	the	the	DET
ejpam-1372	860	8	mb	mb	ADJ
ejpam-1372	860	9	-	-	PUNCT
ejpam-1372	860	10	regularised	regularise	VERB
ejpam-1372	860	11	value	value	NOUN
ejpam-1372	860	12	simplifies	simplifie	NOUN
ejpam-1372	860	13	to	to	ADP
ejpam-1372	860	14	ti(n	ti(n	X
ejpam-1372	860	15	,	,	PUNCT
ejpam-1372	860	16	α	α	NOUN
ejpam-1372	860	17	,	,	PUNCT
ejpam-1372	860	18	z	z	NOUN
ejpam-1372	860	19	)	)	PUNCT
ejpam-1372	860	20	≡	≡	PROPN
ejpam-1372	860	21	∫	∫	PROPN
ejpam-1372	860	22	c+i∞	c+i∞	PROPN
ejpam-1372	860	23	c−i∞	c−i∞	PROPN
ejpam-1372	860	24	ds	ds	PROPN
ejpam-1372	860	25	zs	zs	PROPN
ejpam-1372	860	26	e∓2miπsγ(s+α	e∓2miπsγ(s+α	NOUN
ejpam-1372	860	27	)	)	PUNCT
ejpam-1372	860	28	e−iπs	e−iπs	NOUN
ejpam-1372	860	29	−	−	PROPN
ejpam-1372	861	1	eiπs	eiπs	PROPN
ejpam-1372	861	2	∓	∓	PROPN
ejpam-1372	861	3	2πiz−α	2πiz−α	NUM
ejpam-1372	861	4	×	×	NOUN
ejpam-1372	861	5	e1	e1	NOUN
ejpam-1372	861	6	/	/	SYM
ejpam-1372	861	7	z	z	PROPN
ejpam-1372	861	8	e±miπα	e±miπα	X
ejpam-1372	861	9	sin(mπα	sin(mπα	PROPN
ejpam-1372	861	10	)	)	PUNCT
ejpam-1372	861	11	sin(πα	sin(πα	NOUN
ejpam-1372	861	12	)	)	PUNCT
ejpam-1372	861	13	,	,	PUNCT
ejpam-1372	861	14	(	(	PUNCT
ejpam-1372	861	15	96	96	NUM
ejpam-1372	861	16	)	)	PUNCT
ejpam-1372	861	17	where	where	SCONJ
ejpam-1372	861	18	(	(	PUNCT
ejpam-1372	861	19	±2	±2	NOUN
ejpam-1372	861	20	m	m	NOUN
ejpam-1372	861	21	−	−	NOUN
ejpam-1372	861	22	3/2)π	3/2)π	NUM
ejpam-1372	861	23	<	<	X
ejpam-1372	861	24	arg	arg	NOUN
ejpam-1372	862	1	z	z	X
ejpam-1372	862	2	<	<	X
ejpam-1372	862	3	(	(	PUNCT
ejpam-1372	862	4	±2	±2	NOUN
ejpam-1372	862	5	m	m	NOUN
ejpam-1372	862	6	+	+	NOUN
ejpam-1372	862	7	3/2)π	3/2)π	NUM
ejpam-1372	862	8	since	since	SCONJ
ejpam-1372	862	9	ε1=	ε1=	PROPN
ejpam-1372	862	10	ε2	ε2	PROPN
ejpam-1372	862	11	=	=	NOUN
ejpam-1372	862	12	π/2	π/2	NUM
ejpam-1372	862	13	.	.	PUNCT
ejpam-1372	863	1	in	in	ADP
ejpam-1372	863	2	the	the	DET
ejpam-1372	863	3	event	event	NOUN
ejpam-1372	863	4	that	that	SCONJ
ejpam-1372	863	5	−α	−α	NOUN
ejpam-1372	863	6	is	be	AUX
ejpam-1372	863	7	greater	great	ADJ
ejpam-1372	863	8	than	than	ADP
ejpam-1372	863	9	-1	-1	ADV
ejpam-1372	863	10	,	,	PUNCT
ejpam-1372	863	11	we	we	PRON
ejpam-1372	863	12	alter	alter	VERB
ejpam-1372	863	13	the	the	DET
ejpam-1372	863	14	lower	lower	ADV
ejpam-1372	863	15	bound	bind	VERB
ejpam-1372	863	16	on	on	ADP
ejpam-1372	863	17	the	the	DET
ejpam-1372	863	18	offset	offset	NOUN
ejpam-1372	863	19	c	c	NOUN
ejpam-1372	863	20	to	to	AUX
ejpam-1372	863	21	max{n	max{n	VERB
ejpam-1372	863	22	−	−	PROPN
ejpam-1372	863	23	1,−α	1,−α	NOUN
ejpam-1372	863	24	}	}	PUNCT
ejpam-1372	863	25	<	<	X
ejpam-1372	863	26	c	c	NOUN
ejpam-1372	863	27	=	=	SYM
ejpam-1372	863	28	ℜ	ℜ	PROPN
ejpam-1372	863	29	s	s	PART
ejpam-1372	863	30	<	<	X
ejpam-1372	863	31	n	n	NUM
ejpam-1372	863	32	.	.	PUNCT
ejpam-1372	864	1	this	this	PRON
ejpam-1372	864	2	ensures	ensure	VERB
ejpam-1372	864	3	that	that	SCONJ
ejpam-1372	864	4	the	the	DET
ejpam-1372	864	5	singularity	singularity	NOUN
ejpam-1372	864	6	at	at	ADP
ejpam-1372	864	7	s=−α	s=−α	ADV
ejpam-1372	864	8	remains	remain	VERB
ejpam-1372	864	9	to	to	ADP
ejpam-1372	864	10	the	the	DET
ejpam-1372	864	11	left	left	NOUN
ejpam-1372	864	12	of	of	ADP
ejpam-1372	864	13	the	the	DET
ejpam-1372	864	14	line	line	NOUN
ejpam-1372	864	15	contour	contour	NOUN
ejpam-1372	864	16	when	when	SCONJ
ejpam-1372	864	17	the	the	DET
ejpam-1372	864	18	truncation	truncation	NOUN
ejpam-1372	864	19	parameter	parameter	NOUN
ejpam-1372	864	20	equals	equal	VERB
ejpam-1372	864	21	zero	zero	NUM
ejpam-1372	864	22	,	,	PUNCT
ejpam-1372	864	23	i.e.	i.e.	X
ejpam-1372	864	24	for	for	ADP
ejpam-1372	864	25	n=0	n=0	NUM
ejpam-1372	864	26	.	.	PUNCT
ejpam-1372	865	1	next	next	ADV
ejpam-1372	865	2	we	we	PRON
ejpam-1372	865	3	turn	turn	VERB
ejpam-1372	865	4	our	our	PRON
ejpam-1372	865	5	attention	attention	NOUN
ejpam-1372	865	6	to	to	ADP
ejpam-1372	865	7	the	the	DET
ejpam-1372	865	8	issue	issue	NOUN
ejpam-1372	865	9	of	of	ADP
ejpam-1372	865	10	the	the	DET
ejpam-1372	865	11	mb	mb	ADJ
ejpam-1372	865	12	regularisation	regularisation	NOUN
ejpam-1372	865	13	of	of	ADP
ejpam-1372	865	14	the	the	DET
ejpam-1372	865	15	second	second	ADJ
ejpam-1372	865	16	type	type	NOUN
ejpam-1372	865	17	of	of	ADP
ejpam-1372	865	18	general	general	ADJ
ejpam-1372	865	19	series	series	NOUN
ejpam-1372	865	20	,	,	PUNCT
ejpam-1372	865	21	where	where	SCONJ
ejpam-1372	865	22	the	the	DET
ejpam-1372	865	23	terms	term	NOUN
ejpam-1372	865	24	in	in	ADP
ejpam-1372	865	25	eq	eq	ADP
ejpam-1372	865	26	.	.	PUNCT
ejpam-1372	866	1	(	(	PUNCT
ejpam-1372	866	2	1	1	X
ejpam-1372	866	3	)	)	PUNCT
ejpam-1372	866	4	are	be	AUX
ejpam-1372	866	5	given	give	VERB
ejpam-1372	866	6	by	by	ADP
ejpam-1372	866	7	ak	ak	PROPN
ejpam-1372	866	8	=	=	PROPN
ejpam-1372	866	9	f	f	PROPN
ejpam-1372	866	10	(	(	PUNCT
ejpam-1372	866	11	k	k	NOUN
ejpam-1372	866	12	)	)	PUNCT
ejpam-1372	866	13	zk	zk	PROPN
ejpam-1372	866	14	.	.	PUNCT
ejpam-1372	867	1	as	as	SCONJ
ejpam-1372	867	2	discussed	discuss	VERB
ejpam-1372	867	3	in	in	ADP
ejpam-1372	867	4	the	the	DET
ejpam-1372	867	5	previous	previous	ADJ
ejpam-1372	867	6	section	section	NOUN
ejpam-1372	867	7	,	,	PUNCT
ejpam-1372	867	8	this	this	DET
ejpam-1372	867	9	type	type	NOUN
ejpam-1372	867	10	of	of	ADP
ejpam-1372	867	11	series	series	NOUN
ejpam-1372	867	12	is	be	AUX
ejpam-1372	867	13	often	often	ADV
ejpam-1372	867	14	derived	derive	VERB
ejpam-1372	867	15	where	where	SCONJ
ejpam-1372	867	16	the	the	DET
ejpam-1372	867	17	values	value	NOUN
ejpam-1372	867	18	of	of	ADP
ejpam-1372	867	19	z	z	NOUN
ejpam-1372	867	20	are	be	AUX
ejpam-1372	867	21	situated	situate	VERB
ejpam-1372	867	22	initially	initially	ADV
ejpam-1372	867	23	on	on	ADP
ejpam-1372	867	24	a	a	DET
ejpam-1372	867	25	stokes	stoke	NOUN
ejpam-1372	867	26	line	line	NOUN
ejpam-1372	867	27	,	,	PUNCT
ejpam-1372	867	28	e.g.	e.g.	ADV
ejpam-1372	867	29	for	for	ADP
ejpam-1372	867	30	arg	arg	NOUN
ejpam-1372	867	31	z	z	NOUN
ejpam-1372	867	32	=	=	SYM
ejpam-1372	868	1	0	0	X
ejpam-1372	868	2	.	.	PUNCT
ejpam-1372	869	1	as	as	ADV
ejpam-1372	869	2	soon	soon	ADV
ejpam-1372	869	3	as	as	SCONJ
ejpam-1372	869	4	arg	arg	NOUN
ejpam-1372	869	5	z	z	PROPN
ejpam-1372	869	6	moves	move	VERB
ejpam-1372	869	7	off	off	ADP
ejpam-1372	869	8	the	the	DET
ejpam-1372	869	9	initial	initial	ADJ
ejpam-1372	869	10	stokes	stoke	NOUN
ejpam-1372	869	11	line	line	NOUN
ejpam-1372	869	12	,	,	PUNCT
ejpam-1372	869	13	the	the	DET
ejpam-1372	869	14	regularised	regularise	VERB
ejpam-1372	869	15	value	value	NOUN
ejpam-1372	869	16	will	will	AUX
ejpam-1372	869	17	acquire	acquire	VERB
ejpam-1372	869	18	jump	jump	VERB
ejpam-1372	869	19	discontinuous	discontinuous	ADJ
ejpam-1372	869	20	terms	term	NOUN
ejpam-1372	869	21	in	in	ADP
ejpam-1372	869	22	either	either	DET
ejpam-1372	869	23	direction	direction	NOUN
ejpam-1372	869	24	.	.	PUNCT
ejpam-1372	870	1	therefore	therefore	ADV
ejpam-1372	870	2	,	,	PUNCT
ejpam-1372	870	3	if	if	SCONJ
ejpam-1372	870	4	we	we	PRON
ejpam-1372	870	5	carry	carry	VERB
ejpam-1372	870	6	out	out	ADP
ejpam-1372	870	7	the	the	DET
ejpam-1372	870	8	mb	mb	ADJ
ejpam-1372	870	9	regularisation	regularisation	NOUN
ejpam-1372	870	10	of	of	ADP
ejpam-1372	870	11	the	the	DET
ejpam-1372	870	12	second	second	ADJ
ejpam-1372	870	13	type	type	NOUN
ejpam-1372	870	14	of	of	ADP
ejpam-1372	870	15	series	series	NOUN
ejpam-1372	870	16	,	,	PUNCT
ejpam-1372	870	17	then	then	ADV
ejpam-1372	870	18	whilst	whilst	SCONJ
ejpam-1372	870	19	the	the	DET
ejpam-1372	870	20	resulting	result	VERB
ejpam-1372	870	21	regularised	regularise	VERB
ejpam-1372	870	22	value	value	NOUN
ejpam-1372	870	23	will	will	AUX
ejpam-1372	870	24	be	be	AUX
ejpam-1372	870	25	valid	valid	ADJ
ejpam-1372	870	26	for	for	ADP
ejpam-1372	870	27	the	the	DET
ejpam-1372	870	28	initial	initial	ADJ
ejpam-1372	870	29	stokes	stoke	NOUN
ejpam-1372	870	30	line	line	NOUN
ejpam-1372	870	31	,	,	PUNCT
ejpam-1372	870	32	it	it	PRON
ejpam-1372	870	33	will	will	AUX
ejpam-1372	870	34	not	not	PART
ejpam-1372	870	35	be	be	AUX
ejpam-1372	870	36	valid	valid	ADJ
ejpam-1372	870	37	for	for	ADP
ejpam-1372	870	38	the	the	DET
ejpam-1372	870	39	abutting	abutting	NOUN
ejpam-1372	870	40	stokes	stoke	VERB
ejpam-1372	870	41	sectors	sector	NOUN
ejpam-1372	870	42	despite	despite	SCONJ
ejpam-1372	870	43	the	the	DET
ejpam-1372	870	44	fact	fact	NOUN
ejpam-1372	870	45	that	that	SCONJ
ejpam-1372	870	46	we	we	PRON
ejpam-1372	870	47	have	have	AUX
ejpam-1372	870	48	seen	see	VERB
ejpam-1372	870	49	mb	mb	ADP
ejpam-1372	870	50	regularisation	regularisation	NOUN
ejpam-1372	870	51	is	be	AUX
ejpam-1372	870	52	unaffected	unaffected	ADJ
ejpam-1372	870	53	by	by	ADP
ejpam-1372	870	54	stokes	stoke	NOUN
ejpam-1372	870	55	v.	v.	ADP
ejpam-1372	870	56	kowalenko	kowalenko	PROPN
ejpam-1372	870	57	/	/	SYM
ejpam-1372	870	58	eur	eur	PROPN
ejpam-1372	870	59	.	.	PUNCT
ejpam-1372	871	1	j.	j.	PROPN
ejpam-1372	871	2	pure	pure	PROPN
ejpam-1372	871	3	appl	appl	PROPN
ejpam-1372	871	4	.	.	PROPN
ejpam-1372	871	5	math	math	PROPN
ejpam-1372	871	6	,	,	PUNCT
ejpam-1372	871	7	4	4	NUM
ejpam-1372	871	8	(	(	PUNCT
ejpam-1372	871	9	2011	2011	NUM
ejpam-1372	871	10	)	)	PUNCT
ejpam-1372	871	11	,	,	PUNCT
ejpam-1372	871	12	370	370	NUM
ejpam-1372	871	13	-	-	SYM
ejpam-1372	871	14	423	423	NUM
ejpam-1372	871	15	400	400	NUM
ejpam-1372	871	16	lines	line	NOUN
ejpam-1372	871	17	and	and	CCONJ
ejpam-1372	871	18	sectors	sector	NOUN
ejpam-1372	871	19	.	.	PUNCT
ejpam-1372	872	1	therefore	therefore	ADV
ejpam-1372	872	2	,	,	PUNCT
ejpam-1372	872	3	we	we	PRON
ejpam-1372	872	4	have	have	VERB
ejpam-1372	872	5	a	a	DET
ejpam-1372	872	6	situation	situation	NOUN
ejpam-1372	872	7	where	where	SCONJ
ejpam-1372	872	8	a	a	DET
ejpam-1372	872	9	stokes	stoke	NOUN
ejpam-1372	872	10	line	line	NOUN
ejpam-1372	872	11	is	be	AUX
ejpam-1372	872	12	critically	critically	ADV
ejpam-1372	872	13	important	important	ADJ
ejpam-1372	872	14	initially	initially	ADV
ejpam-1372	872	15	,	,	PUNCT
ejpam-1372	872	16	but	but	CCONJ
ejpam-1372	872	17	that	that	SCONJ
ejpam-1372	872	18	the	the	DET
ejpam-1372	872	19	other	other	ADJ
ejpam-1372	872	20	stokes	stoke	NOUN
ejpam-1372	872	21	lines	line	NOUN
ejpam-1372	872	22	do	do	AUX
ejpam-1372	872	23	not	not	PART
ejpam-1372	872	24	affect	affect	VERB
ejpam-1372	872	25	the	the	DET
ejpam-1372	872	26	regularised	regularise	VERB
ejpam-1372	872	27	value	value	NOUN
ejpam-1372	872	28	.	.	PUNCT
ejpam-1372	873	1	we	we	PRON
ejpam-1372	873	2	refer	refer	VERB
ejpam-1372	873	3	to	to	ADP
ejpam-1372	873	4	this	this	DET
ejpam-1372	873	5	line	line	NOUN
ejpam-1372	873	6	as	as	ADP
ejpam-1372	873	7	the	the	DET
ejpam-1372	873	8	primary	primary	ADJ
ejpam-1372	873	9	stokes	stokes	PROPN
ejpam-1372	873	10	line	line	NOUN
ejpam-1372	873	11	.	.	PUNCT
ejpam-1372	874	1	a	a	DET
ejpam-1372	874	2	property	property	NOUN
ejpam-1372	874	3	of	of	ADP
ejpam-1372	874	4	the	the	DET
ejpam-1372	874	5	primary	primary	ADJ
ejpam-1372	874	6	stokes	stoke	NOUN
ejpam-1372	874	7	line	line	NOUN
ejpam-1372	874	8	is	be	AUX
ejpam-1372	874	9	that	that	SCONJ
ejpam-1372	874	10	it	it	PRON
ejpam-1372	874	11	is	be	AUX
ejpam-1372	874	12	completely	completely	ADV
ejpam-1372	874	13	arbitrary	arbitrary	ADJ
ejpam-1372	874	14	since	since	SCONJ
ejpam-1372	874	15	it	it	PRON
ejpam-1372	874	16	can	can	AUX
ejpam-1372	874	17	be	be	AUX
ejpam-1372	874	18	set	set	VERB
ejpam-1372	874	19	by	by	ADP
ejpam-1372	874	20	letting	let	VERB
ejpam-1372	874	21	arg	arg	NOUN
ejpam-1372	874	22	z=2kπ	z=2kπ	NUM
ejpam-1372	874	23	,	,	PUNCT
ejpam-1372	874	24	where	where	SCONJ
ejpam-1372	874	25	k	k	PROPN
ejpam-1372	874	26	is	be	AUX
ejpam-1372	874	27	an	an	DET
ejpam-1372	874	28	arbitrary	arbitrary	ADJ
ejpam-1372	874	29	integer	integer	NOUN
ejpam-1372	874	30	.	.	PUNCT
ejpam-1372	875	1	without	without	ADP
ejpam-1372	875	2	loss	loss	NOUN
ejpam-1372	875	3	of	of	ADP
ejpam-1372	875	4	generality	generality	NOUN
ejpam-1372	875	5	we	we	PRON
ejpam-1372	875	6	shall	shall	AUX
ejpam-1372	875	7	choose	choose	VERB
ejpam-1372	875	8	the	the	DET
ejpam-1372	875	9	primary	primary	ADJ
ejpam-1372	875	10	stokes	stoke	NOUN
ejpam-1372	875	11	line	line	NOUN
ejpam-1372	875	12	to	to	PART
ejpam-1372	875	13	be	be	AUX
ejpam-1372	875	14	the	the	DET
ejpam-1372	875	15	k=0	k=0	PROPN
ejpam-1372	875	16	line	line	NOUN
ejpam-1372	875	17	or	or	CCONJ
ejpam-1372	875	18	arg	arg	VERB
ejpam-1372	875	19	z=0	z=0	PROPN
ejpam-1372	875	20	.	.	PUNCT
ejpam-1372	876	1	choosing	choose	VERB
ejpam-1372	876	2	another	another	DET
ejpam-1372	876	3	primary	primary	ADJ
ejpam-1372	876	4	stokes	stoke	NOUN
ejpam-1372	876	5	line	line	NOUN
ejpam-1372	876	6	will	will	AUX
ejpam-1372	876	7	only	only	ADV
ejpam-1372	876	8	result	result	VERB
ejpam-1372	876	9	in	in	ADP
ejpam-1372	876	10	a	a	DET
ejpam-1372	876	11	shift	shift	NOUN
ejpam-1372	876	12	in	in	ADP
ejpam-1372	876	13	the	the	DET
ejpam-1372	876	14	domains	domain	NOUN
ejpam-1372	876	15	of	of	ADP
ejpam-1372	876	16	convergence	convergence	NOUN
ejpam-1372	876	17	,	,	PUNCT
ejpam-1372	876	18	as	as	SCONJ
ejpam-1372	876	19	is	be	AUX
ejpam-1372	876	20	explained	explain	VERB
ejpam-1372	876	21	later	later	ADV
ejpam-1372	876	22	.	.	PUNCT
ejpam-1372	877	1	we	we	PRON
ejpam-1372	877	2	are	be	AUX
ejpam-1372	877	3	now	now	ADV
ejpam-1372	877	4	in	in	ADP
ejpam-1372	877	5	a	a	DET
ejpam-1372	877	6	position	position	NOUN
ejpam-1372	877	7	to	to	PART
ejpam-1372	877	8	consider	consider	VERB
ejpam-1372	877	9	mb	mb	ADP
ejpam-1372	877	10	regularisation	regularisation	NOUN
ejpam-1372	877	11	of	of	ADP
ejpam-1372	877	12	the	the	DET
ejpam-1372	877	13	second	second	ADJ
ejpam-1372	877	14	type	type	NOUN
ejpam-1372	877	15	of	of	ADP
ejpam-1372	877	16	general	general	ADJ
ejpam-1372	877	17	series	series	NOUN
ejpam-1372	877	18	with	with	ADP
ejpam-1372	877	19	the	the	DET
ejpam-1372	877	20	same	same	ADJ
ejpam-1372	877	21	conditions	condition	NOUN
ejpam-1372	877	22	applying	apply	VERB
ejpam-1372	877	23	to	to	ADP
ejpam-1372	877	24	f	f	PROPN
ejpam-1372	877	25	(	(	PUNCT
ejpam-1372	877	26	s	s	NOUN
ejpam-1372	877	27	)	)	PUNCT
ejpam-1372	877	28	as	as	ADP
ejpam-1372	877	29	in	in	ADP
ejpam-1372	877	30	the	the	DET
ejpam-1372	877	31	derivation	derivation	NOUN
ejpam-1372	877	32	of	of	ADP
ejpam-1372	877	33	equivalence	equivalence	NOUN
ejpam-1372	877	34	(	(	PUNCT
ejpam-1372	877	35	90	90	NUM
ejpam-1372	877	36	)	)	PUNCT
ejpam-1372	877	37	.	.	PUNCT
ejpam-1372	878	1	then	then	ADV
ejpam-1372	878	2	we	we	PRON
ejpam-1372	878	3	arrive	arrive	VERB
ejpam-1372	878	4	at	at	ADP
ejpam-1372	878	5	si	si	PROPN
ejpam-1372	878	6	i(n	i(n	PROPN
ejpam-1372	878	7	,	,	PUNCT
ejpam-1372	878	8	z	z	NOUN
ejpam-1372	878	9	)	)	PUNCT
ejpam-1372	878	10	=	=	SYM
ejpam-1372	879	1	∞	∞	NUM
ejpam-1372	879	2	∑	∑	PUNCT
ejpam-1372	879	3	k	k	X
ejpam-1372	879	4	=	=	PROPN
ejpam-1372	879	5	n	n	PROPN
ejpam-1372	879	6	f	f	NOUN
ejpam-1372	879	7	(	(	PUNCT
ejpam-1372	879	8	k)zk	k)zk	PROPN
ejpam-1372	879	9	≡	≡	PROPN
ejpam-1372	879	10	∫	∫	PROPN
ejpam-1372	879	11	c+i∞	c+i∞	PROPN
ejpam-1372	879	12	c−i∞	c−i∞	PROPN
ejpam-1372	879	13	ds	ds	X
ejpam-1372	879	14	(	(	PUNCT
ejpam-1372	879	15	−z)s	−z)s	NOUN
ejpam-1372	879	16	f	f	X
ejpam-1372	879	17	(	(	PUNCT
ejpam-1372	879	18	s	s	NOUN
ejpam-1372	879	19	)	)	PUNCT
ejpam-1372	879	20	e−iπs	e−iπs	NOUN
ejpam-1372	879	21	−	−	PROPN
ejpam-1372	879	22	eiπs	eiπs	PROPN
ejpam-1372	879	23	,	,	PUNCT
ejpam-1372	879	24	(	(	PUNCT
ejpam-1372	879	25	97	97	NUM
ejpam-1372	879	26	)	)	PUNCT
ejpam-1372	879	27	where	where	SCONJ
ejpam-1372	879	28	,	,	PUNCT
ejpam-1372	879	29	again	again	ADV
ejpam-1372	879	30	,	,	PUNCT
ejpam-1372	879	31	the	the	DET
ejpam-1372	879	32	offset	offset	NOUN
ejpam-1372	879	33	is	be	AUX
ejpam-1372	879	34	defined	define	VERB
ejpam-1372	879	35	by	by	ADP
ejpam-1372	879	36	n−1	n−1	PROPN
ejpam-1372	879	37	<	<	X
ejpam-1372	879	38	c	c	NOUN
ejpam-1372	879	39	=	=	SYM
ejpam-1372	879	40	ℜ	ℜ	PROPN
ejpam-1372	879	41	s	s	PART
ejpam-1372	879	42	<	<	X
ejpam-1372	879	43	n	n	NUM
ejpam-1372	879	44	.	.	PUNCT
ejpam-1372	880	1	the	the	DET
ejpam-1372	880	2	principal	principal	ADJ
ejpam-1372	880	3	difference	difference	NOUN
ejpam-1372	880	4	between	between	ADP
ejpam-1372	880	5	this	this	DET
ejpam-1372	880	6	result	result	NOUN
ejpam-1372	880	7	and	and	CCONJ
ejpam-1372	880	8	equivalence	equivalence	NOUN
ejpam-1372	880	9	(	(	PUNCT
ejpam-1372	880	10	90	90	NUM
ejpam-1372	880	11	)	)	PUNCT
ejpam-1372	880	12	is	be	AUX
ejpam-1372	880	13	the	the	DET
ejpam-1372	880	14	appearance	appearance	NOUN
ejpam-1372	880	15	of	of	ADP
ejpam-1372	880	16	the	the	DET
ejpam-1372	880	17	multi	multi	ADJ
ejpam-1372	880	18	-	-	ADJ
ejpam-1372	880	19	valued	value	VERB
ejpam-1372	880	20	factor	factor	NOUN
ejpam-1372	880	21	of	of	ADP
ejpam-1372	880	22	(	(	PUNCT
ejpam-1372	880	23	−1)s	−1)s	NUM
ejpam-1372	880	24	in	in	ADP
ejpam-1372	880	25	the	the	DET
ejpam-1372	880	26	integrand	integrand	NOUN
ejpam-1372	880	27	of	of	ADP
ejpam-1372	880	28	the	the	DET
ejpam-1372	880	29	above	above	NOUN
ejpam-1372	880	30	mb	mb	ADP
ejpam-1372	880	31	integral	integral	ADJ
ejpam-1372	880	32	.	.	PUNCT
ejpam-1372	881	1	because	because	SCONJ
ejpam-1372	881	2	of	of	ADP
ejpam-1372	881	3	this	this	DET
ejpam-1372	881	4	factor	factor	NOUN
ejpam-1372	881	5	the	the	DET
ejpam-1372	881	6	regularised	regularise	VERB
ejpam-1372	881	7	value	value	NOUN
ejpam-1372	881	8	of	of	ADP
ejpam-1372	881	9	the	the	DET
ejpam-1372	881	10	series	series	NOUN
ejpam-1372	881	11	has	have	AUX
ejpam-1372	881	12	become	become	VERB
ejpam-1372	881	13	ambiguous	ambiguous	ADJ
ejpam-1372	881	14	since	since	SCONJ
ejpam-1372	881	15	it	it	PRON
ejpam-1372	881	16	can	can	AUX
ejpam-1372	881	17	be	be	AUX
ejpam-1372	881	18	interpreted	interpret	VERB
ejpam-1372	881	19	as	as	ADP
ejpam-1372	881	20	being	be	AUX
ejpam-1372	881	21	either	either	CCONJ
ejpam-1372	881	22	exp(iπs	exp(iπs	PROPN
ejpam-1372	881	23	)	)	PUNCT
ejpam-1372	881	24	,	,	PUNCT
ejpam-1372	881	25	exp(−iπs	exp(−iπs	PROPN
ejpam-1372	881	26	)	)	PUNCT
ejpam-1372	881	27	or	or	CCONJ
ejpam-1372	881	28	even	even	ADV
ejpam-1372	881	29	exp((2l	exp((2l	PROPN
ejpam-1372	881	30	+	+	CCONJ
ejpam-1372	881	31	1)iπs	1)iπs	NUM
ejpam-1372	881	32	)	)	PUNCT
ejpam-1372	881	33	,	,	PUNCT
ejpam-1372	881	34	where	where	SCONJ
ejpam-1372	881	35	l	l	NOUN
ejpam-1372	881	36	is	be	AUX
ejpam-1372	881	37	an	an	DET
ejpam-1372	881	38	arbitrary	arbitrary	ADJ
ejpam-1372	881	39	integer	integer	NOUN
ejpam-1372	881	40	.	.	PUNCT
ejpam-1372	882	1	we	we	PRON
ejpam-1372	882	2	can	can	AUX
ejpam-1372	882	3	drop	drop	VERB
ejpam-1372	882	4	the	the	DET
ejpam-1372	882	5	last	last	ADJ
ejpam-1372	882	6	possibility	possibility	NOUN
ejpam-1372	882	7	because	because	SCONJ
ejpam-1372	882	8	the	the	DET
ejpam-1372	882	9	primary	primary	ADJ
ejpam-1372	882	10	stokes	stoke	NOUN
ejpam-1372	882	11	line	line	NOUN
ejpam-1372	882	12	can	can	AUX
ejpam-1372	882	13	be	be	AUX
ejpam-1372	882	14	shifted	shift	VERB
ejpam-1372	882	15	to	to	PART
ejpam-1372	882	16	compensate	compensate	VERB
ejpam-1372	882	17	.	.	PUNCT
ejpam-1372	883	1	nevertheless	nevertheless	ADV
ejpam-1372	883	2	,	,	PUNCT
ejpam-1372	883	3	the	the	DET
ejpam-1372	883	4	mb	mb	NOUN
ejpam-1372	883	5	integral	integral	ADJ
ejpam-1372	883	6	in	in	ADP
ejpam-1372	883	7	equivalence	equivalence	NOUN
ejpam-1372	883	8	(	(	PUNCT
ejpam-1372	883	9	94	94	NUM
ejpam-1372	883	10	)	)	PUNCT
ejpam-1372	883	11	can	can	AUX
ejpam-1372	883	12	be	be	AUX
ejpam-1372	883	13	expressed	express	VERB
ejpam-1372	883	14	more	more	ADV
ejpam-1372	883	15	generally	generally	ADV
ejpam-1372	883	16	as	as	ADP
ejpam-1372	883	17	i∗l	i∗l	NUM
ejpam-1372	883	18	(	(	PUNCT
ejpam-1372	883	19	z	z	NOUN
ejpam-1372	883	20	)	)	PUNCT
ejpam-1372	883	21	=	=	SYM
ejpam-1372	884	1	∫	∫	PROPN
ejpam-1372	884	2	c+i∞	c+i∞	NOUN
ejpam-1372	884	3	c−i∞	c−i∞	PROPN
ejpam-1372	884	4	ds	ds	PROPN
ejpam-1372	884	5	zs	zs	X
ejpam-1372	884	6	e−(2l	e−(2l	VERB
ejpam-1372	884	7	i+1)πs	i+1)πs	PROPN
ejpam-1372	884	8	f	f	PROPN
ejpam-1372	884	9	(	(	PUNCT
ejpam-1372	884	10	s	s	NOUN
ejpam-1372	884	11	)	)	PUNCT
ejpam-1372	884	12	e−iπs	e−iπs	NOUN
ejpam-1372	884	13	−	−	PROPN
ejpam-1372	884	14	eiπs	eiπs	PROPN
ejpam-1372	884	15	.	.	PUNCT
ejpam-1372	885	1	(	(	PUNCT
ejpam-1372	885	2	98	98	NUM
ejpam-1372	885	3	)	)	PUNCT
ejpam-1372	885	4	in	in	ADP
ejpam-1372	885	5	addition	addition	NOUN
ejpam-1372	885	6	to	to	ADP
ejpam-1372	885	7	introducing	introduce	VERB
ejpam-1372	885	8	ambiguity	ambiguity	NOUN
ejpam-1372	885	9	when	when	SCONJ
ejpam-1372	885	10	the	the	DET
ejpam-1372	885	11	second	second	ADJ
ejpam-1372	885	12	type	type	NOUN
ejpam-1372	885	13	of	of	ADP
ejpam-1372	885	14	general	general	ADJ
ejpam-1372	885	15	series	series	NOUN
ejpam-1372	885	16	is	be	AUX
ejpam-1372	885	17	mb	mb	ADV
ejpam-1372	885	18	-	-	ADJ
ejpam-1372	885	19	regularised	regularise	VERB
ejpam-1372	885	20	,	,	PUNCT
ejpam-1372	885	21	the	the	DET
ejpam-1372	885	22	multi	multi	ADJ
ejpam-1372	885	23	-	-	ADJ
ejpam-1372	885	24	valued	value	VERB
ejpam-1372	885	25	factor	factor	NOUN
ejpam-1372	885	26	of	of	ADP
ejpam-1372	885	27	(	(	PUNCT
ejpam-1372	885	28	−1)s	−1)s	PRON
ejpam-1372	885	29	affects	affect	VERB
ejpam-1372	885	30	the	the	DET
ejpam-1372	885	31	domain	domain	NOUN
ejpam-1372	885	32	of	of	ADP
ejpam-1372	885	33	convergence	convergence	NOUN
ejpam-1372	885	34	of	of	ADP
ejpam-1372	885	35	the	the	DET
ejpam-1372	885	36	mb	mb	NOUN
ejpam-1372	885	37	integral	integral	ADJ
ejpam-1372	885	38	.	.	PUNCT
ejpam-1372	886	1	if	if	SCONJ
ejpam-1372	886	2	we	we	PRON
ejpam-1372	886	3	consider	consider	VERB
ejpam-1372	886	4	the	the	DET
ejpam-1372	886	5	first	first	ADJ
ejpam-1372	886	6	interpretation	interpretation	NOUN
ejpam-1372	886	7	,	,	PUNCT
ejpam-1372	886	8	where	where	SCONJ
ejpam-1372	886	9	(	(	PUNCT
ejpam-1372	886	10	−1)s	−1)s	X
ejpam-1372	886	11	=	=	SYM
ejpam-1372	886	12	exp(iπs	exp(iπs	NOUN
ejpam-1372	886	13	)	)	PUNCT
ejpam-1372	886	14	or	or	CCONJ
ejpam-1372	886	15	l=−1	l=−1	ADJ
ejpam-1372	886	16	in	in	ADP
ejpam-1372	886	17	the	the	DET
ejpam-1372	886	18	above	above	ADJ
ejpam-1372	886	19	equation	equation	NOUN
ejpam-1372	886	20	,	,	PUNCT
ejpam-1372	886	21	then	then	ADV
ejpam-1372	886	22	the	the	DET
ejpam-1372	886	23	domain	domain	NOUN
ejpam-1372	886	24	of	of	ADP
ejpam-1372	886	25	convergence	convergence	NOUN
ejpam-1372	886	26	for	for	ADP
ejpam-1372	886	27	the	the	DET
ejpam-1372	886	28	mb	mb	NOUN
ejpam-1372	886	29	integral	integral	ADJ
ejpam-1372	886	30	in	in	ADP
ejpam-1372	886	31	equivalence	equivalence	NOUN
ejpam-1372	886	32	(	(	PUNCT
ejpam-1372	886	33	97	97	NUM
ejpam-1372	886	34	)	)	PUNCT
ejpam-1372	886	35	is	be	AUX
ejpam-1372	886	36	found	find	VERB
ejpam-1372	886	37	to	to	PART
ejpam-1372	886	38	be	be	AUX
ejpam-1372	886	39	−ε1	−ε1	PROPN
ejpam-1372	886	40	<	<	X
ejpam-1372	886	41	arg	arg	NOUN
ejpam-1372	886	42	z<2π+ε2	z<2π+ε2	NOUN
ejpam-1372	886	43	.	.	PUNCT
ejpam-1372	887	1	on	on	ADP
ejpam-1372	887	2	the	the	DET
ejpam-1372	887	3	other	other	ADJ
ejpam-1372	887	4	hand	hand	NOUN
ejpam-1372	887	5	,	,	PUNCT
ejpam-1372	887	6	for	for	ADP
ejpam-1372	887	7	(	(	PUNCT
ejpam-1372	887	8	−1)s	−1)s	X
ejpam-1372	887	9	=	=	NOUN
ejpam-1372	887	10	exp(−iπs	exp(−iπs	NUM
ejpam-1372	887	11	)	)	PUNCT
ejpam-1372	887	12	or	or	CCONJ
ejpam-1372	887	13	l=0	l=0	PROPN
ejpam-1372	887	14	in	in	ADP
ejpam-1372	887	15	the	the	DET
ejpam-1372	887	16	above	above	ADJ
ejpam-1372	887	17	equation	equation	NOUN
ejpam-1372	887	18	the	the	DET
ejpam-1372	887	19	domain	domain	NOUN
ejpam-1372	887	20	of	of	ADP
ejpam-1372	887	21	convergence	convergence	NOUN
ejpam-1372	887	22	is	be	AUX
ejpam-1372	887	23	given	give	VERB
ejpam-1372	887	24	by	by	ADP
ejpam-1372	887	25	−2π	−2π	PROPN
ejpam-1372	887	26	−	−	PROPN
ejpam-1372	887	27	ε1	ε1	VERB
ejpam-1372	887	28	<	<	X
ejpam-1372	887	29	arg	arg	NOUN
ejpam-1372	887	30	z	z	X
ejpam-1372	887	31	<	<	X
ejpam-1372	887	32	ε2	ε2	PROPN
ejpam-1372	887	33	.	.	PUNCT
ejpam-1372	888	1	therefore	therefore	ADV
ejpam-1372	888	2	,	,	PUNCT
ejpam-1372	888	3	the	the	DET
ejpam-1372	888	4	domains	domain	NOUN
ejpam-1372	888	5	of	of	ADP
ejpam-1372	888	6	convergence	convergence	NOUN
ejpam-1372	888	7	overlap	overlap	NOUN
ejpam-1372	888	8	over	over	ADP
ejpam-1372	888	9	the	the	DET
ejpam-1372	888	10	primary	primary	ADJ
ejpam-1372	888	11	stokes	stokes	PROPN
ejpam-1372	888	12	line	line	NOUN
ejpam-1372	888	13	,	,	PUNCT
ejpam-1372	888	14	which	which	PRON
ejpam-1372	888	15	means	mean	VERB
ejpam-1372	888	16	that	that	SCONJ
ejpam-1372	888	17	either	either	CCONJ
ejpam-1372	888	18	i∗0(z	i∗0(z	PROPN
ejpam-1372	888	19	)	)	PUNCT
ejpam-1372	888	20	or	or	CCONJ
ejpam-1372	888	21	i∗−1(z	i∗−1(z	NOUN
ejpam-1372	888	22	)	)	PUNCT
ejpam-1372	888	23	is	be	AUX
ejpam-1372	888	24	valid	valid	ADJ
ejpam-1372	888	25	in	in	ADP
ejpam-1372	888	26	the	the	DET
ejpam-1372	888	27	vicinity	vicinity	NOUN
ejpam-1372	888	28	of	of	ADP
ejpam-1372	888	29	the	the	DET
ejpam-1372	888	30	primary	primary	ADJ
ejpam-1372	888	31	stokes	stokes	PROPN
ejpam-1372	888	32	line	line	NOUN
ejpam-1372	888	33	.	.	PUNCT
ejpam-1372	889	1	unfortunately	unfortunately	ADV
ejpam-1372	889	2	,	,	PUNCT
ejpam-1372	889	3	neither	neither	DET
ejpam-1372	889	4	form	form	NOUN
ejpam-1372	889	5	possesses	possess	VERB
ejpam-1372	889	6	extra	extra	ADJ
ejpam-1372	889	7	terms	term	NOUN
ejpam-1372	889	8	to	to	PART
ejpam-1372	889	9	reflect	reflect	VERB
ejpam-1372	889	10	the	the	DET
ejpam-1372	889	11	discontinuity	discontinuity	NOUN
ejpam-1372	889	12	occurring	occur	VERB
ejpam-1372	889	13	at	at	ADP
ejpam-1372	889	14	the	the	DET
ejpam-1372	889	15	primary	primary	ADJ
ejpam-1372	889	16	stokes	stoke	NOUN
ejpam-1372	889	17	line	line	NOUN
ejpam-1372	889	18	as	as	SCONJ
ejpam-1372	889	19	indicated	indicate	VERB
ejpam-1372	889	20	by	by	ADP
ejpam-1372	889	21	the	the	DET
ejpam-1372	889	22	borelsummed	borelsumme	VERB
ejpam-1372	889	23	regularised	regularise	VERB
ejpam-1372	889	24	value	value	NOUN
ejpam-1372	889	25	of	of	ADP
ejpam-1372	889	26	the	the	DET
ejpam-1372	889	27	second	second	ADJ
ejpam-1372	889	28	type	type	NOUN
ejpam-1372	889	29	of	of	ADP
ejpam-1372	889	30	terminant	terminant	NOUN
ejpam-1372	889	31	,	,	PUNCT
ejpam-1372	889	32	viz	viz	PROPN
ejpam-1372	889	33	.	.	PUNCT
ejpam-1372	889	34	equivalence	equivalence	NOUN
ejpam-1372	889	35	(	(	PUNCT
ejpam-1372	889	36	75	75	NUM
ejpam-1372	889	37	)	)	PUNCT
ejpam-1372	889	38	.	.	PUNCT
ejpam-1372	890	1	moreover	moreover	ADV
ejpam-1372	890	2	,	,	PUNCT
ejpam-1372	890	3	both	both	DET
ejpam-1372	890	4	results	result	VERB
ejpam-1372	890	5	yield	yield	VERB
ejpam-1372	890	6	complex	complex	ADJ
ejpam-1372	890	7	values	value	NOUN
ejpam-1372	890	8	along	along	ADP
ejpam-1372	890	9	the	the	DET
ejpam-1372	890	10	primary	primary	ADJ
ejpam-1372	890	11	stokes	stoke	NOUN
ejpam-1372	890	12	line	line	NOUN
ejpam-1372	890	13	,	,	PUNCT
ejpam-1372	890	14	whereas	whereas	SCONJ
ejpam-1372	890	15	from	from	ADP
ejpam-1372	890	16	the	the	DET
ejpam-1372	890	17	zwaandingle	zwaandingle	ADJ
ejpam-1372	890	18	principle	principle	NOUN
ejpam-1372	890	19	we	we	PRON
ejpam-1372	890	20	expect	expect	VERB
ejpam-1372	890	21	the	the	DET
ejpam-1372	890	22	regularised	regularise	VERB
ejpam-1372	890	23	value	value	NOUN
ejpam-1372	890	24	to	to	PART
ejpam-1372	890	25	be	be	AUX
ejpam-1372	890	26	real	real	ADJ
ejpam-1372	890	27	.	.	PUNCT
ejpam-1372	891	1	as	as	SCONJ
ejpam-1372	891	2	stated	state	VERB
ejpam-1372	891	3	on	on	ADP
ejpam-1372	891	4	p.	p.	PROPN
ejpam-1372	891	5	103	103	NUM
ejpam-1372	891	6	of	of	ADP
ejpam-1372	891	7	ref	ref	NOUN
ejpam-1372	891	8	.	.	PUNCT
ejpam-1372	892	1	[	[	X
ejpam-1372	892	2	17	17	NUM
ejpam-1372	892	3	]	]	PUNCT
ejpam-1372	892	4	the	the	DET
ejpam-1372	892	5	problem	problem	NOUN
ejpam-1372	892	6	can	can	AUX
ejpam-1372	892	7	be	be	AUX
ejpam-1372	892	8	resolved	resolve	VERB
ejpam-1372	892	9	by	by	ADP
ejpam-1372	892	10	introducing	introduce	VERB
ejpam-1372	892	11	extra	extra	ADJ
ejpam-1372	892	12	terms	term	NOUN
ejpam-1372	892	13	into	into	ADP
ejpam-1372	892	14	the	the	DET
ejpam-1372	892	15	regularised	regularise	VERB
ejpam-1372	892	16	value	value	NOUN
ejpam-1372	892	17	of	of	ADP
ejpam-1372	892	18	the	the	DET
ejpam-1372	892	19	series	series	NOUN
ejpam-1372	892	20	such	such	ADJ
ejpam-1372	892	21	that	that	SCONJ
ejpam-1372	892	22	si	si	PROPN
ejpam-1372	892	23	i(n	i(n	PROPN
ejpam-1372	892	24	,	,	PUNCT
ejpam-1372	892	25	z	z	NOUN
ejpam-1372	892	26	)	)	PUNCT
ejpam-1372	892	27	≡	≡	PROPN
ejpam-1372	892	28	(	(	PUNCT
ejpam-1372	892	29	i∗0(z	i∗0(z	ADV
ejpam-1372	892	30	)	)	PUNCT
ejpam-1372	892	31	+	+	NUM
ejpam-1372	892	32	ic(z	ic(z	NOUN
ejpam-1372	892	33	)	)	PUNCT
ejpam-1372	892	34	,	,	PUNCT
ejpam-1372	893	1	0	0	NUM
ejpam-1372	893	2	<	<	X
ejpam-1372	893	3	arg	arg	NOUN
ejpam-1372	893	4	z	z	X
ejpam-1372	893	5	<	<	X
ejpam-1372	893	6	2π+	2π+	NUM
ejpam-1372	893	7	ε1	ε1	PROPN
ejpam-1372	893	8	,	,	PUNCT
ejpam-1372	893	9	i∗−1(z	i∗−1(z	NOUN
ejpam-1372	893	10	)	)	PUNCT
ejpam-1372	893	11	+	+	NUM
ejpam-1372	893	12	id(z	id(z	NOUN
ejpam-1372	893	13	)	)	PUNCT
ejpam-1372	893	14	,	,	PUNCT
ejpam-1372	893	15	−2π−	−2π−	NOUN
ejpam-1372	893	16	ε1	ε1	VERB
ejpam-1372	893	17	<	<	X
ejpam-1372	893	18	arg	arg	NOUN
ejpam-1372	893	19	z	z	NOUN
ejpam-1372	893	20	<	<	X
ejpam-1372	893	21	0	0	PUNCT
ejpam-1372	893	22	.	.	PUNCT
ejpam-1372	894	1	(	(	PUNCT
ejpam-1372	894	2	99	99	NUM
ejpam-1372	894	3	)	)	PUNCT
ejpam-1372	894	4	for	for	ADP
ejpam-1372	894	5	z	z	NOUN
ejpam-1372	894	6	lying	lie	VERB
ejpam-1372	894	7	on	on	ADP
ejpam-1372	894	8	the	the	DET
ejpam-1372	894	9	primary	primary	ADJ
ejpam-1372	894	10	stokes	stoke	NOUN
ejpam-1372	894	11	line	line	NOUN
ejpam-1372	894	12	we	we	PRON
ejpam-1372	894	13	simply	simply	ADV
ejpam-1372	894	14	average	average	VERB
ejpam-1372	894	15	the	the	DET
ejpam-1372	894	16	two	two	NUM
ejpam-1372	894	17	regularised	regularise	VERB
ejpam-1372	894	18	values	value	NOUN
ejpam-1372	894	19	as	as	SCONJ
ejpam-1372	894	20	we	we	PRON
ejpam-1372	894	21	did	do	VERB
ejpam-1372	894	22	when	when	SCONJ
ejpam-1372	894	23	analysing	analyse	VERB
ejpam-1372	894	24	the	the	DET
ejpam-1372	894	25	first	first	ADJ
ejpam-1372	894	26	type	type	NOUN
ejpam-1372	894	27	of	of	ADP
ejpam-1372	894	28	series	series	NOUN
ejpam-1372	894	29	.	.	PUNCT
ejpam-1372	895	1	then	then	ADV
ejpam-1372	895	2	we	we	PRON
ejpam-1372	895	3	find	find	VERB
ejpam-1372	895	4	that	that	SCONJ
ejpam-1372	895	5	the	the	DET
ejpam-1372	895	6	average	average	NOUN
ejpam-1372	895	7	of	of	ADP
ejpam-1372	895	8	both	both	PRON
ejpam-1372	895	9	mb	mb	ADP
ejpam-1372	895	10	integrals	integral	NOUN
ejpam-1372	895	11	v.	v.	ADP
ejpam-1372	895	12	kowalenko	kowalenko	PROPN
ejpam-1372	895	13	/	/	SYM
ejpam-1372	895	14	eur	eur	PROPN
ejpam-1372	895	15	.	.	PUNCT
ejpam-1372	896	1	j.	j.	PROPN
ejpam-1372	896	2	pure	pure	PROPN
ejpam-1372	896	3	appl	appl	PROPN
ejpam-1372	896	4	.	.	PROPN
ejpam-1372	896	5	math	math	PROPN
ejpam-1372	896	6	,	,	PUNCT
ejpam-1372	896	7	4	4	NUM
ejpam-1372	896	8	(	(	PUNCT
ejpam-1372	896	9	2011	2011	NUM
ejpam-1372	896	10	)	)	PUNCT
ejpam-1372	896	11	,	,	PUNCT
ejpam-1372	896	12	370	370	NUM
ejpam-1372	896	13	-	-	SYM
ejpam-1372	896	14	423	423	NUM
ejpam-1372	896	15	401	401	NUM
ejpam-1372	896	16	yields	yield	NOUN
ejpam-1372	896	17	a	a	DET
ejpam-1372	896	18	real	real	ADV
ejpam-1372	896	19	valued	value	VERB
ejpam-1372	896	20	quantity	quantity	NOUN
ejpam-1372	896	21	.	.	PUNCT
ejpam-1372	897	1	this	this	PRON
ejpam-1372	897	2	means	mean	VERB
ejpam-1372	897	3	that	that	SCONJ
ejpam-1372	897	4	we	we	PRON
ejpam-1372	897	5	are	be	AUX
ejpam-1372	897	6	essentially	essentially	ADV
ejpam-1372	897	7	treating	treat	VERB
ejpam-1372	897	8	(	(	PUNCT
ejpam-1372	897	9	−z)s	−z)s	ADV
ejpam-1372	897	10	in	in	ADP
ejpam-1372	897	11	the	the	DET
ejpam-1372	897	12	mb	mb	PROPN
ejpam-1372	897	13	integrals	integral	NOUN
ejpam-1372	897	14	as	as	ADP
ejpam-1372	897	15	(	(	PUNCT
ejpam-1372	897	16	−z)s	−z)s	ADV
ejpam-1372	897	17	≡	≡	PROPN
ejpam-1372	897	18			VERB
ejpam-1372	897	19			ADP
ejpam-1372	897	20			NOUN
ejpam-1372	897	21	zs	zs	PROPN
ejpam-1372	897	22	exp(iπs	exp(iπs	PROPN
ejpam-1372	897	23	)	)	PUNCT
ejpam-1372	897	24	,	,	PUNCT
ejpam-1372	897	25	arg	arg	NOUN
ejpam-1372	897	26	z	z	NOUN
ejpam-1372	897	27	>	>	X
ejpam-1372	897	28	0	0	NUM
ejpam-1372	897	29	,	,	PUNCT
ejpam-1372	897	30	zs	zs	PROPN
ejpam-1372	897	31	cos(πs	cos(π	NOUN
ejpam-1372	897	32	)	)	PUNCT
ejpam-1372	897	33	,	,	PUNCT
ejpam-1372	897	34	arg	arg	NOUN
ejpam-1372	897	35	z	z	NOUN
ejpam-1372	897	36	=	=	SYM
ejpam-1372	897	37	0	0	PROPN
ejpam-1372	897	38	,	,	PUNCT
ejpam-1372	897	39	zs	zs	PROPN
ejpam-1372	897	40	exp(−iπs	exp(−iπs	NUM
ejpam-1372	897	41	)	)	PUNCT
ejpam-1372	897	42	,	,	PUNCT
ejpam-1372	897	43	arg	arg	NOUN
ejpam-1372	897	44	z	z	NOUN
ejpam-1372	897	45	<	<	X
ejpam-1372	897	46	0	0	PUNCT
ejpam-1372	897	47	.	.	PUNCT
ejpam-1372	898	1	(	(	PUNCT
ejpam-1372	898	2	100	100	NUM
ejpam-1372	898	3	)	)	PUNCT
ejpam-1372	898	4	according	accord	VERB
ejpam-1372	898	5	to	to	ADP
ejpam-1372	898	6	p.	p.	NOUN
ejpam-1372	898	7	12	12	NUM
ejpam-1372	898	8	of	of	ADP
ejpam-1372	898	9	ref	ref	NOUN
ejpam-1372	898	10	.	.	PUNCT
ejpam-1372	899	1	[	[	X
ejpam-1372	899	2	8	8	NUM
ejpam-1372	899	3	]	]	PUNCT
ejpam-1372	899	4	,	,	PUNCT
ejpam-1372	899	5	this	this	DET
ejpam-1372	899	6	customary	customary	ADJ
ejpam-1372	899	7	convention	convention	NOUN
ejpam-1372	899	8	for	for	ADP
ejpam-1372	899	9	dealing	deal	VERB
ejpam-1372	899	10	with	with	ADP
ejpam-1372	899	11	the	the	DET
ejpam-1372	899	12	multi	multi	ADJ
ejpam-1372	899	13	-	-	ADJ
ejpam-1372	899	14	valued	value	VERB
ejpam-1372	899	15	factor	factor	NOUN
ejpam-1372	899	16	of	of	ADP
ejpam-1372	899	17	(	(	PUNCT
ejpam-1372	899	18	−z)s	−z)s	ADV
ejpam-1372	899	19	in	in	ADP
ejpam-1372	899	20	asymptotic	asymptotic	ADJ
ejpam-1372	899	21	expansions	expansion	NOUN
ejpam-1372	899	22	is	be	AUX
ejpam-1372	899	23	an	an	DET
ejpam-1372	899	24	indication	indication	NOUN
ejpam-1372	899	25	that	that	SCONJ
ejpam-1372	899	26	the	the	DET
ejpam-1372	899	27	stokes	stoke	NOUN
ejpam-1372	899	28	phenomenon	phenomenon	NOUN
ejpam-1372	899	29	has	have	AUX
ejpam-1372	899	30	occurred	occur	VERB
ejpam-1372	899	31	.	.	PUNCT
ejpam-1372	900	1	moreover	moreover	ADV
ejpam-1372	900	2	,	,	PUNCT
ejpam-1372	900	3	because	because	SCONJ
ejpam-1372	900	4	the	the	DET
ejpam-1372	900	5	regularised	regularise	VERB
ejpam-1372	900	6	value	value	NOUN
ejpam-1372	900	7	is	be	AUX
ejpam-1372	900	8	real	real	ADJ
ejpam-1372	900	9	along	along	ADP
ejpam-1372	900	10	the	the	DET
ejpam-1372	900	11	primary	primary	ADJ
ejpam-1372	900	12	stokes	stokes	PROPN
ejpam-1372	900	13	line	line	NOUN
ejpam-1372	900	14	,	,	PUNCT
ejpam-1372	900	15	c(z	c(z	NUM
ejpam-1372	900	16	)	)	PUNCT
ejpam-1372	900	17	must	must	AUX
ejpam-1372	900	18	equal	equal	VERB
ejpam-1372	900	19	−d(z	−d(z	NOUN
ejpam-1372	900	20	)	)	PUNCT
ejpam-1372	900	21	.	.	PUNCT
ejpam-1372	901	1	we	we	PRON
ejpam-1372	901	2	have	have	AUX
ejpam-1372	901	3	already	already	ADV
ejpam-1372	901	4	seen	see	VERB
ejpam-1372	901	5	that	that	SCONJ
ejpam-1372	901	6	mb	mb	ADP
ejpam-1372	901	7	regularisation	regularisation	NOUN
ejpam-1372	901	8	is	be	AUX
ejpam-1372	901	9	different	different	ADJ
ejpam-1372	901	10	from	from	ADP
ejpam-1372	901	11	borel	borel	PROPN
ejpam-1372	901	12	summation	summation	NOUN
ejpam-1372	901	13	in	in	ADP
ejpam-1372	901	14	that	that	SCONJ
ejpam-1372	901	15	the	the	DET
ejpam-1372	901	16	mb	mb	ADJ
ejpam-1372	901	17	-	-	PUNCT
ejpam-1372	901	18	regularised	regularise	VERB
ejpam-1372	901	19	forms	form	NOUN
ejpam-1372	901	20	for	for	ADP
ejpam-1372	901	21	the	the	DET
ejpam-1372	901	22	regularised	regularise	VERB
ejpam-1372	901	23	value	value	NOUN
ejpam-1372	901	24	share	share	VERB
ejpam-1372	901	25	common	common	ADJ
ejpam-1372	901	26	regions	region	NOUN
ejpam-1372	901	27	and	and	CCONJ
ejpam-1372	901	28	that	that	SCONJ
ejpam-1372	901	29	there	there	PRON
ejpam-1372	901	30	are	be	VERB
ejpam-1372	901	31	no	no	DET
ejpam-1372	901	32	lines	line	NOUN
ejpam-1372	901	33	of	of	ADP
ejpam-1372	901	34	discontinuity	discontinuity	NOUN
ejpam-1372	901	35	,	,	PUNCT
ejpam-1372	901	36	which	which	PRON
ejpam-1372	901	37	are	be	AUX
ejpam-1372	901	38	fictitious	fictitious	ADJ
ejpam-1372	901	39	if	if	SCONJ
ejpam-1372	901	40	the	the	DET
ejpam-1372	901	41	original	original	ADJ
ejpam-1372	901	42	function	function	NOUN
ejpam-1372	901	43	is	be	AUX
ejpam-1372	901	44	continuous	continuous	ADJ
ejpam-1372	901	45	.	.	PUNCT
ejpam-1372	902	1	hence	hence	ADV
ejpam-1372	902	2	,	,	PUNCT
ejpam-1372	902	3	the	the	DET
ejpam-1372	902	4	results	result	NOUN
ejpam-1372	902	5	in	in	ADP
ejpam-1372	902	6	equivalence	equivalence	NOUN
ejpam-1372	902	7	(	(	PUNCT
ejpam-1372	902	8	99	99	NUM
ejpam-1372	902	9	)	)	PUNCT
ejpam-1372	902	10	will	will	AUX
ejpam-1372	902	11	be	be	AUX
ejpam-1372	902	12	equal	equal	ADJ
ejpam-1372	902	13	to	to	ADP
ejpam-1372	902	14	another	another	PRON
ejpam-1372	902	15	in	in	ADP
ejpam-1372	902	16	the	the	DET
ejpam-1372	902	17	common	common	ADJ
ejpam-1372	902	18	region	region	NOUN
ejpam-1372	902	19	,	,	PUNCT
ejpam-1372	902	20	which	which	PRON
ejpam-1372	902	21	includes	include	VERB
ejpam-1372	902	22	the	the	DET
ejpam-1372	902	23	stokes	stoke	NOUN
ejpam-1372	902	24	line	line	NOUN
ejpam-1372	902	25	of	of	ADP
ejpam-1372	902	26	discontinuity	discontinuity	NOUN
ejpam-1372	902	27	.	.	PUNCT
ejpam-1372	903	1	subtracting	subtract	VERB
ejpam-1372	903	2	both	both	DET
ejpam-1372	903	3	results	result	NOUN
ejpam-1372	903	4	in	in	ADP
ejpam-1372	903	5	equivalence	equivalence	NOUN
ejpam-1372	903	6	(	(	PUNCT
ejpam-1372	903	7	99	99	NUM
ejpam-1372	903	8	)	)	PUNCT
ejpam-1372	903	9	from	from	ADP
ejpam-1372	903	10	each	each	DET
ejpam-1372	903	11	other	other	ADJ
ejpam-1372	903	12	yields	yield	NOUN
ejpam-1372	903	13	c(z	c(z	NOUN
ejpam-1372	903	14	)	)	PUNCT
ejpam-1372	904	1	=	=	SYM
ejpam-1372	904	2	i	i	PRON
ejpam-1372	904	3	2	2	NUM
ejpam-1372	904	4	∆i∗0,−1(z	∆i∗0,−1(z	PROPN
ejpam-1372	904	5	)	)	PUNCT
ejpam-1372	904	6	=	=	SYM
ejpam-1372	904	7	1	1	NUM
ejpam-1372	904	8	2	2	NUM
ejpam-1372	904	9	�	�	PROPN
ejpam-1372	904	10	i∗0(z)−	i∗0(z)−	PROPN
ejpam-1372	904	11	i∗−1(z	i∗−1(z	PROPN
ejpam-1372	904	12	)	)	PUNCT
ejpam-1372	904	13	�	�	PROPN
ejpam-1372	904	14	.	.	PUNCT
ejpam-1372	905	1	(	(	PUNCT
ejpam-1372	905	2	101	101	NUM
ejpam-1372	905	3	)	)	PUNCT
ejpam-1372	905	4	as	as	ADP
ejpam-1372	905	5	a	a	DET
ejpam-1372	905	6	consequence	consequence	NOUN
ejpam-1372	905	7	,	,	PUNCT
ejpam-1372	905	8	equivalence	equivalence	NOUN
ejpam-1372	905	9	(	(	PUNCT
ejpam-1372	905	10	99	99	NUM
ejpam-1372	905	11	)	)	PUNCT
ejpam-1372	905	12	can	can	AUX
ejpam-1372	905	13	be	be	AUX
ejpam-1372	905	14	expressed	express	VERB
ejpam-1372	905	15	more	more	ADV
ejpam-1372	905	16	precisely	precisely	ADV
ejpam-1372	905	17	as	as	ADP
ejpam-1372	905	18	si	si	PROPN
ejpam-1372	905	19	i(n	i(n	PROPN
ejpam-1372	905	20	,	,	PUNCT
ejpam-1372	905	21	z)≡	z)≡	PROPN
ejpam-1372	905	22			PROPN
ejpam-1372	905	23			NOUN
ejpam-1372	905	24			NOUN
ejpam-1372	905	25	i∗0(z)−	i∗0(z)−	NUM
ejpam-1372	905	26	1	1	NUM
ejpam-1372	905	27	2	2	NUM
ejpam-1372	905	28	∆i∗0,−1(z	∆i∗0,−1(z	PROPN
ejpam-1372	905	29	)	)	PUNCT
ejpam-1372	905	30	,	,	PUNCT
ejpam-1372	906	1	0	0	NUM
ejpam-1372	906	2	<	<	X
ejpam-1372	906	3	arg	arg	NOUN
ejpam-1372	906	4	z	z	X
ejpam-1372	906	5	<	<	X
ejpam-1372	906	6	2π+	2π+	NUM
ejpam-1372	906	7	ε1	ε1	PROPN
ejpam-1372	906	8	,	,	PUNCT
ejpam-1372	906	9	1	1	NUM
ejpam-1372	906	10	2	2	NUM
ejpam-1372	906	11	�	�	PROPN
ejpam-1372	906	12	i∗0(z	i∗0(z	ADV
ejpam-1372	906	13	)	)	PUNCT
ejpam-1372	906	14	+	+	NUM
ejpam-1372	906	15	i∗−1(z	i∗−1(z	NOUN
ejpam-1372	906	16	)	)	PUNCT
ejpam-1372	906	17	�	�	PROPN
ejpam-1372	906	18	,	,	PUNCT
ejpam-1372	906	19	arg	arg	NOUN
ejpam-1372	906	20	z	z	NOUN
ejpam-1372	906	21	=	=	SYM
ejpam-1372	906	22	0	0	NUM
ejpam-1372	906	23	,	,	PUNCT
ejpam-1372	906	24	i∗−1(z	i∗−1(z	NOUN
ejpam-1372	906	25	)	)	PUNCT
ejpam-1372	906	26	+	+	CCONJ
ejpam-1372	906	27	1	1	NUM
ejpam-1372	906	28	2	2	NUM
ejpam-1372	906	29	∆i∗0,−1(z	∆i∗0,−1(z	PROPN
ejpam-1372	906	30	)	)	PUNCT
ejpam-1372	906	31	,	,	PUNCT
ejpam-1372	906	32	−2π−	−2π−	NOUN
ejpam-1372	906	33	ε1	ε1	VERB
ejpam-1372	906	34	<	<	X
ejpam-1372	906	35	arg	arg	NOUN
ejpam-1372	906	36	z	z	NOUN
ejpam-1372	906	37	<	<	X
ejpam-1372	906	38	0	0	PUNCT
ejpam-1372	906	39	.	.	PUNCT
ejpam-1372	907	1	(	(	PUNCT
ejpam-1372	907	2	102	102	NUM
ejpam-1372	907	3	)	)	PUNCT
ejpam-1372	907	4	all	all	DET
ejpam-1372	907	5	these	these	DET
ejpam-1372	907	6	results	result	NOUN
ejpam-1372	907	7	are	be	AUX
ejpam-1372	907	8	identical	identical	ADJ
ejpam-1372	907	9	to	to	ADP
ejpam-1372	907	10	each	each	DET
ejpam-1372	907	11	other	other	ADJ
ejpam-1372	907	12	in	in	ADP
ejpam-1372	907	13	common	common	ADJ
ejpam-1372	907	14	region	region	NOUN
ejpam-1372	907	15	of	of	ADP
ejpam-1372	907	16	−ε1	−ε1	PROPN
ejpam-1372	907	17	<	<	X
ejpam-1372	907	18	argz	argz	NOUN
ejpam-1372	907	19	<	<	X
ejpam-1372	907	20	ε2	ε2	NOUN
ejpam-1372	907	21	.	.	PUNCT
ejpam-1372	908	1	so	so	ADV
ejpam-1372	908	2	,	,	PUNCT
ejpam-1372	908	3	whilst	whilst	SCONJ
ejpam-1372	908	4	we	we	PRON
ejpam-1372	908	5	have	have	AUX
ejpam-1372	908	6	allowed	allow	VERB
ejpam-1372	908	7	for	for	ADP
ejpam-1372	908	8	the	the	DET
ejpam-1372	908	9	jump	jump	NOUN
ejpam-1372	908	10	discontinuity	discontinuity	NOUN
ejpam-1372	908	11	occurring	occur	VERB
ejpam-1372	908	12	in	in	ADP
ejpam-1372	908	13	the	the	DET
ejpam-1372	908	14	borel	borel	NOUN
ejpam-1372	908	15	-	-	PUNCT
ejpam-1372	908	16	summed	sum	VERB
ejpam-1372	908	17	forms	form	NOUN
ejpam-1372	908	18	,	,	PUNCT
ejpam-1372	908	19	there	there	PRON
ejpam-1372	908	20	is	be	VERB
ejpam-1372	908	21	no	no	DET
ejpam-1372	908	22	jump	jump	NOUN
ejpam-1372	908	23	discontinuity	discontinuity	NOUN
ejpam-1372	908	24	in	in	ADP
ejpam-1372	908	25	the	the	DET
ejpam-1372	908	26	final	final	ADJ
ejpam-1372	908	27	mb	mb	ADJ
ejpam-1372	908	28	-	-	PUNCT
ejpam-1372	908	29	regularised	regularise	VERB
ejpam-1372	908	30	forms	form	NOUN
ejpam-1372	908	31	for	for	ADP
ejpam-1372	908	32	the	the	DET
ejpam-1372	908	33	regularised	regularise	VERB
ejpam-1372	908	34	value	value	NOUN
ejpam-1372	908	35	of	of	ADP
ejpam-1372	908	36	a	a	DET
ejpam-1372	908	37	type	type	NOUN
ejpam-1372	908	38	ii	ii	NOUN
ejpam-1372	908	39	terminant	terminant	NOUN
ejpam-1372	908	40	at	at	ADP
ejpam-1372	908	41	the	the	DET
ejpam-1372	908	42	primary	primary	ADJ
ejpam-1372	908	43	stokes	stokes	PROPN
ejpam-1372	908	44	line	line	NOUN
ejpam-1372	908	45	.	.	PUNCT
ejpam-1372	909	1	compared	compare	VERB
ejpam-1372	909	2	with	with	ADP
ejpam-1372	909	3	the	the	DET
ejpam-1372	909	4	first	first	ADJ
ejpam-1372	909	5	type	type	NOUN
ejpam-1372	909	6	of	of	ADP
ejpam-1372	909	7	series	series	NOUN
ejpam-1372	909	8	or	or	CCONJ
ejpam-1372	909	9	si	si	PROPN
ejpam-1372	909	10	(	(	PUNCT
ejpam-1372	909	11	n	n	X
ejpam-1372	909	12	,	,	PUNCT
ejpam-1372	909	13	z	z	X
ejpam-1372	909	14	)	)	PUNCT
ejpam-1372	909	15	we	we	PRON
ejpam-1372	909	16	see	see	VERB
ejpam-1372	909	17	that	that	SCONJ
ejpam-1372	909	18	the	the	DET
ejpam-1372	909	19	regularised	regularise	VERB
ejpam-1372	909	20	value	value	NOUN
ejpam-1372	909	21	of	of	ADP
ejpam-1372	909	22	the	the	DET
ejpam-1372	909	23	second	second	ADJ
ejpam-1372	909	24	type	type	NOUN
ejpam-1372	909	25	of	of	ADP
ejpam-1372	909	26	general	general	ADJ
ejpam-1372	909	27	series	series	NOUN
ejpam-1372	909	28	has	have	AUX
ejpam-1372	909	29	acquired	acquire	VERB
ejpam-1372	909	30	half	half	DET
ejpam-1372	909	31	the	the	DET
ejpam-1372	909	32	difference	difference	NOUN
ejpam-1372	909	33	between	between	ADP
ejpam-1372	909	34	the	the	DET
ejpam-1372	909	35	l	l	NOUN
ejpam-1372	909	36	=	=	SYM
ejpam-1372	909	37	0	0	NUM
ejpam-1372	909	38	and	and	CCONJ
ejpam-1372	909	39	l	l	NOUN
ejpam-1372	909	40	=	=	NOUN
ejpam-1372	909	41	−1	−1	NOUN
ejpam-1372	909	42	versions	version	NOUN
ejpam-1372	909	43	of	of	ADP
ejpam-1372	909	44	the	the	DET
ejpam-1372	909	45	resulting	result	VERB
ejpam-1372	909	46	mb	mb	ADP
ejpam-1372	909	47	integral	integral	ADJ
ejpam-1372	909	48	derived	derive	VERB
ejpam-1372	909	49	via	via	ADP
ejpam-1372	909	50	mb	mb	ADP
ejpam-1372	909	51	regularisation	regularisation	NOUN
ejpam-1372	909	52	.	.	PUNCT
ejpam-1372	910	1	this	this	PRON
ejpam-1372	910	2	simply	simply	ADV
ejpam-1372	910	3	did	do	AUX
ejpam-1372	910	4	not	not	PART
ejpam-1372	910	5	occur	occur	VERB
ejpam-1372	910	6	in	in	ADP
ejpam-1372	910	7	the	the	DET
ejpam-1372	910	8	first	first	ADJ
ejpam-1372	910	9	type	type	NOUN
ejpam-1372	910	10	of	of	ADP
ejpam-1372	910	11	series	series	NOUN
ejpam-1372	910	12	because	because	SCONJ
ejpam-1372	910	13	its	its	PRON
ejpam-1372	910	14	mb	mb	ADJ
ejpam-1372	910	15	-	-	PUNCT
ejpam-1372	910	16	regularised	regularise	VERB
ejpam-1372	910	17	value	value	NOUN
ejpam-1372	910	18	was	be	AUX
ejpam-1372	910	19	derived	derive	VERB
ejpam-1372	910	20	within	within	ADP
ejpam-1372	910	21	a	a	DET
ejpam-1372	910	22	stokes	stoke	NOUN
ejpam-1372	910	23	sector	sector	NOUN
ejpam-1372	910	24	rather	rather	ADV
ejpam-1372	910	25	than	than	ADP
ejpam-1372	910	26	on	on	ADP
ejpam-1372	910	27	a	a	DET
ejpam-1372	910	28	singular	singular	ADJ
ejpam-1372	910	29	stokes	stoke	NOUN
ejpam-1372	910	30	line	line	NOUN
ejpam-1372	910	31	initially	initially	ADV
ejpam-1372	910	32	.	.	PUNCT
ejpam-1372	911	1	had	have	AUX
ejpam-1372	911	2	we	we	PRON
ejpam-1372	911	3	been	be	AUX
ejpam-1372	911	4	considering	consider	VERB
ejpam-1372	911	5	a	a	DET
ejpam-1372	911	6	primary	primary	ADJ
ejpam-1372	911	7	stokes	stoke	NOUN
ejpam-1372	911	8	sector	sector	NOUN
ejpam-1372	911	9	rather	rather	ADV
ejpam-1372	911	10	than	than	ADP
ejpam-1372	911	11	a	a	DET
ejpam-1372	911	12	primary	primary	ADJ
ejpam-1372	911	13	stokes	stoke	NOUN
ejpam-1372	911	14	line	line	NOUN
ejpam-1372	911	15	,	,	PUNCT
ejpam-1372	911	16	then	then	ADV
ejpam-1372	911	17	c(z	c(z	NUM
ejpam-1372	911	18	)	)	PUNCT
ejpam-1372	911	19	would	would	AUX
ejpam-1372	911	20	be	be	AUX
ejpam-1372	911	21	zero	zero	NUM
ejpam-1372	911	22	,	,	PUNCT
ejpam-1372	911	23	but	but	CCONJ
ejpam-1372	911	24	the	the	DET
ejpam-1372	911	25	ensuing	ensue	VERB
ejpam-1372	911	26	expressions	expression	NOUN
ejpam-1372	911	27	for	for	ADP
ejpam-1372	911	28	the	the	DET
ejpam-1372	911	29	regularised	regularise	VERB
ejpam-1372	911	30	value	value	NOUN
ejpam-1372	911	31	would	would	AUX
ejpam-1372	911	32	still	still	ADV
ejpam-1372	911	33	be	be	AUX
ejpam-1372	911	34	equal	equal	ADJ
ejpam-1372	911	35	to	to	ADP
ejpam-1372	911	36	each	each	DET
ejpam-1372	911	37	other	other	ADJ
ejpam-1372	911	38	in	in	ADP
ejpam-1372	911	39	the	the	DET
ejpam-1372	911	40	common	common	ADJ
ejpam-1372	911	41	region	region	NOUN
ejpam-1372	911	42	.	.	PUNCT
ejpam-1372	912	1	to	to	PART
ejpam-1372	912	2	derive	derive	VERB
ejpam-1372	912	3	the	the	DET
ejpam-1372	912	4	regularised	regularise	VERB
ejpam-1372	912	5	value	value	NOUN
ejpam-1372	912	6	for	for	ADP
ejpam-1372	912	7	other	other	ADJ
ejpam-1372	912	8	riemann	riemann	PROPN
ejpam-1372	912	9	sheets	sheet	NOUN
ejpam-1372	912	10	in	in	ADP
ejpam-1372	912	11	the	the	DET
ejpam-1372	912	12	complex	complex	ADJ
ejpam-1372	912	13	plane	plane	NOUN
ejpam-1372	912	14	,	,	PUNCT
ejpam-1372	912	15	we	we	PRON
ejpam-1372	912	16	adopt	adopt	VERB
ejpam-1372	912	17	a	a	DET
ejpam-1372	912	18	similar	similar	ADJ
ejpam-1372	912	19	approach	approach	NOUN
ejpam-1372	912	20	to	to	ADP
ejpam-1372	912	21	the	the	DET
ejpam-1372	912	22	analysis	analysis	NOUN
ejpam-1372	912	23	of	of	ADP
ejpam-1372	912	24	the	the	DET
ejpam-1372	912	25	first	first	ADJ
ejpam-1372	912	26	type	type	NOUN
ejpam-1372	912	27	of	of	ADP
ejpam-1372	912	28	series	series	NOUN
ejpam-1372	912	29	.	.	PUNCT
ejpam-1372	913	1	that	that	PRON
ejpam-1372	913	2	is	is	ADV
ejpam-1372	913	3	,	,	PUNCT
ejpam-1372	913	4	we	we	PRON
ejpam-1372	913	5	replace	replace	VERB
ejpam-1372	913	6	the	the	DET
ejpam-1372	913	7	mb	mb	PROPN
ejpam-1372	913	8	integrals	integral	NOUN
ejpam-1372	913	9	in	in	ADP
ejpam-1372	913	10	the	the	DET
ejpam-1372	913	11	first	first	ADJ
ejpam-1372	913	12	and	and	CCONJ
ejpam-1372	913	13	third	third	ADJ
ejpam-1372	913	14	results	result	NOUN
ejpam-1372	913	15	of	of	ADP
ejpam-1372	913	16	equivalence	equivalence	NOUN
ejpam-1372	913	17	(	(	PUNCT
ejpam-1372	913	18	102	102	NUM
ejpam-1372	913	19	)	)	PUNCT
ejpam-1372	913	20	by	by	ADP
ejpam-1372	913	21	the	the	DET
ejpam-1372	913	22	mb	mb	PROPN
ejpam-1372	913	23	integrals	integral	NOUN
ejpam-1372	913	24	that	that	PRON
ejpam-1372	913	25	overlap	overlap	VERB
ejpam-1372	913	26	with	with	ADP
ejpam-1372	913	27	them	they	PRON
ejpam-1372	913	28	.	.	PUNCT
ejpam-1372	914	1	in	in	ADP
ejpam-1372	914	2	the	the	DET
ejpam-1372	914	3	case	case	NOUN
ejpam-1372	914	4	of	of	ADP
ejpam-1372	914	5	i∗0(z	i∗0(z	PROPN
ejpam-1372	914	6	)	)	PUNCT
ejpam-1372	914	7	it	it	PRON
ejpam-1372	914	8	can	can	AUX
ejpam-1372	914	9	be	be	AUX
ejpam-1372	914	10	replaced	replace	VERB
ejpam-1372	914	11	by	by	ADP
ejpam-1372	914	12	i∗1(z	i∗1(z	PROPN
ejpam-1372	914	13	)	)	PUNCT
ejpam-1372	914	14	−∆i∗1,0(z	−∆i∗1,0(z	NUM
ejpam-1372	914	15	)	)	PUNCT
ejpam-1372	914	16	,	,	PUNCT
ejpam-1372	914	17	while	while	SCONJ
ejpam-1372	914	18	i∗−1(z	i∗−1(z	NOUN
ejpam-1372	914	19	)	)	PUNCT
ejpam-1372	914	20	can	can	AUX
ejpam-1372	914	21	be	be	AUX
ejpam-1372	914	22	replaced	replace	VERB
ejpam-1372	914	23	by	by	ADP
ejpam-1372	914	24	i∗−2(z	i∗−2(z	NOUN
ejpam-1372	914	25	)	)	PUNCT
ejpam-1372	914	26	+	+	CCONJ
ejpam-1372	914	27	∆i∗−1,−2(z	∆i∗−1,−2(z	NOUN
ejpam-1372	914	28	)	)	PUNCT
ejpam-1372	914	29	.	.	PUNCT
ejpam-1372	915	1	of	of	ADP
ejpam-1372	915	2	course	course	NOUN
ejpam-1372	915	3	,	,	PUNCT
ejpam-1372	915	4	the	the	DET
ejpam-1372	915	5	reason	reason	NOUN
ejpam-1372	915	6	we	we	PRON
ejpam-1372	915	7	can	can	AUX
ejpam-1372	915	8	do	do	VERB
ejpam-1372	915	9	these	these	DET
ejpam-1372	915	10	replacements	replacement	NOUN
ejpam-1372	915	11	is	be	AUX
ejpam-1372	915	12	because	because	SCONJ
ejpam-1372	915	13	of	of	ADP
ejpam-1372	915	14	the	the	DET
ejpam-1372	915	15	existence	existence	NOUN
ejpam-1372	915	16	of	of	ADP
ejpam-1372	915	17	a	a	DET
ejpam-1372	915	18	common	common	ADJ
ejpam-1372	915	19	region	region	NOUN
ejpam-1372	915	20	between	between	ADP
ejpam-1372	915	21	the	the	DET
ejpam-1372	915	22	domains	domain	NOUN
ejpam-1372	915	23	of	of	ADP
ejpam-1372	915	24	convergence	convergence	NOUN
ejpam-1372	915	25	for	for	ADP
ejpam-1372	915	26	the	the	DET
ejpam-1372	915	27	mb	mb	PROPN
ejpam-1372	915	28	integrals	integral	NOUN
ejpam-1372	915	29	.	.	PUNCT
ejpam-1372	916	1	once	once	ADV
ejpam-1372	916	2	each	each	DET
ejpam-1372	916	3	replacement	replacement	NOUN
ejpam-1372	916	4	has	have	AUX
ejpam-1372	916	5	taken	take	VERB
ejpam-1372	916	6	place	place	NOUN
ejpam-1372	916	7	,	,	PUNCT
ejpam-1372	916	8	we	we	PRON
ejpam-1372	916	9	can	can	AUX
ejpam-1372	916	10	analytically	analytically	ADV
ejpam-1372	916	11	continue	continue	VERB
ejpam-1372	916	12	the	the	DET
ejpam-1372	916	13	results	result	NOUN
ejpam-1372	916	14	to	to	ADP
ejpam-1372	916	15	the	the	DET
ejpam-1372	916	16	next	next	NOUN
ejpam-1372	916	17	mb	mb	ADP
ejpam-1372	916	18	v.	v.	CCONJ
ejpam-1372	916	19	kowalenko	kowalenko	PROPN
ejpam-1372	916	20	/	/	SYM
ejpam-1372	916	21	eur	eur	PROPN
ejpam-1372	916	22	.	.	PUNCT
ejpam-1372	917	1	j.	j.	PROPN
ejpam-1372	917	2	pure	pure	PROPN
ejpam-1372	917	3	appl	appl	PROPN
ejpam-1372	917	4	.	.	PROPN
ejpam-1372	917	5	math	math	PROPN
ejpam-1372	917	6	,	,	PUNCT
ejpam-1372	917	7	4	4	NUM
ejpam-1372	917	8	(	(	PUNCT
ejpam-1372	917	9	2011	2011	NUM
ejpam-1372	917	10	)	)	PUNCT
ejpam-1372	917	11	,	,	PUNCT
ejpam-1372	917	12	370	370	NUM
ejpam-1372	917	13	-	-	SYM
ejpam-1372	917	14	423	423	NUM
ejpam-1372	917	15	402	402	NUM
ejpam-1372	917	16	integral	integral	ADJ
ejpam-1372	917	17	provided	provide	VERB
ejpam-1372	917	18	both	both	PRON
ejpam-1372	917	19	∆i∗1,0(z	∆i∗1,0(z	NUM
ejpam-1372	917	20	)	)	PUNCT
ejpam-1372	917	21	and	and	CCONJ
ejpam-1372	917	22	∆i∗−1,−2(z	∆i∗−1,−2(z	NOUN
ejpam-1372	917	23	)	)	PUNCT
ejpam-1372	917	24	can	can	AUX
ejpam-1372	917	25	be	be	AUX
ejpam-1372	917	26	analytically	analytically	ADV
ejpam-1372	917	27	continued	continue	VERB
ejpam-1372	917	28	.	.	PUNCT
ejpam-1372	918	1	for	for	ADP
ejpam-1372	918	2	a	a	DET
ejpam-1372	918	3	standard	standard	ADJ
ejpam-1372	918	4	type	type	NOUN
ejpam-1372	918	5	ii	ii	NOUN
ejpam-1372	918	6	terminant	terminant	NOUN
ejpam-1372	918	7	,	,	PUNCT
ejpam-1372	918	8	where	where	SCONJ
ejpam-1372	918	9	f	f	PROPN
ejpam-1372	918	10	(	(	PUNCT
ejpam-1372	918	11	s	s	NOUN
ejpam-1372	918	12	)	)	PUNCT
ejpam-1372	918	13	=	=	PUNCT
ejpam-1372	918	14	γ(s+α	γ(s+α	PROPN
ejpam-1372	918	15	)	)	PUNCT
ejpam-1372	918	16	,	,	PUNCT
ejpam-1372	918	17	we	we	PRON
ejpam-1372	918	18	find	find	VERB
ejpam-1372	918	19	for	for	ADP
ejpam-1372	918	20	any	any	DET
ejpam-1372	918	21	value	value	NOUN
ejpam-1372	918	22	of	of	ADP
ejpam-1372	918	23	l	l	NOUN
ejpam-1372	918	24	that	that	PRON
ejpam-1372	918	25	∆i∗l+1,l(z	∆i∗l+1,l(z	VERB
ejpam-1372	918	26	)	)	PUNCT
ejpam-1372	918	27	=	=	SYM
ejpam-1372	918	28	i∗l+1(z)−	i∗l+1(z)−	PROPN
ejpam-1372	918	29	i∗l	i∗l	NUM
ejpam-1372	918	30	(	(	PUNCT
ejpam-1372	918	31	z	z	NOUN
ejpam-1372	918	32	)	)	PUNCT
ejpam-1372	918	33	=	=	SYM
ejpam-1372	918	34	∫	∫	PROPN
ejpam-1372	918	35	c+i∞	c+i∞	PROPN
ejpam-1372	918	36	c−i∞	c−i∞	PROPN
ejpam-1372	918	37	ds	ds	PROPN
ejpam-1372	918	38	zs	zs	PROPN
ejpam-1372	918	39	e−(2l+2)iπs	e−(2l+2)iπs	PROPN
ejpam-1372	918	40	γ(s+α	γ(s+α	PROPN
ejpam-1372	918	41	)	)	PUNCT
ejpam-1372	918	42	.	.	PUNCT
ejpam-1372	919	1	(	(	PUNCT
ejpam-1372	919	2	103	103	NUM
ejpam-1372	919	3	)	)	PUNCT
ejpam-1372	919	4	from	from	ADP
ejpam-1372	919	5	ref	ref	NOUN
ejpam-1372	919	6	.	.	PUNCT
ejpam-1372	920	1	[	[	X
ejpam-1372	920	2	25	25	NUM
ejpam-1372	920	3	]	]	X
ejpam-1372	920	4	we	we	PRON
ejpam-1372	920	5	eventually	eventually	ADV
ejpam-1372	920	6	arrive	arrive	VERB
ejpam-1372	920	7	at	at	ADP
ejpam-1372	920	8	∆i∗	∆i∗	PROPN
ejpam-1372	920	9	l+1,l	l+1,l	PROPN
ejpam-1372	920	10	(	(	PUNCT
ejpam-1372	920	11	z	z	NOUN
ejpam-1372	920	12	)	)	PUNCT
ejpam-1372	920	13	=	=	SYM
ejpam-1372	920	14	2πi	2πi	PROPN
ejpam-1372	920	15	z−α	z−α	PROPN
ejpam-1372	920	16	e2(l+1)iπα	e2(l+1)iπα	PROPN
ejpam-1372	920	17	e−1	e−1	PROPN
ejpam-1372	920	18	/	/	SYM
ejpam-1372	920	19	z	z	NOUN
ejpam-1372	920	20	,	,	PUNCT
ejpam-1372	920	21	(	(	PUNCT
ejpam-1372	920	22	104	104	NUM
ejpam-1372	920	23	)	)	PUNCT
ejpam-1372	920	24	which	which	PRON
ejpam-1372	920	25	can	can	AUX
ejpam-1372	920	26	be	be	AUX
ejpam-1372	920	27	analytically	analytically	ADV
ejpam-1372	920	28	continued	continue	VERB
ejpam-1372	920	29	through	through	ADP
ejpam-1372	920	30	to	to	ADP
ejpam-1372	920	31	all	all	DET
ejpam-1372	920	32	riemann	riemann	PROPN
ejpam-1372	920	33	sheets	sheet	NOUN
ejpam-1372	920	34	.	.	PUNCT
ejpam-1372	921	1	consequently	consequently	ADV
ejpam-1372	921	2	,	,	PUNCT
ejpam-1372	921	3	we	we	PRON
ejpam-1372	921	4	can	can	AUX
ejpam-1372	921	5	keep	keep	VERB
ejpam-1372	921	6	replacing	replace	VERB
ejpam-1372	921	7	mb	mb	ADP
ejpam-1372	921	8	integrals	integral	NOUN
ejpam-1372	921	9	and	and	CCONJ
ejpam-1372	921	10	analytically	analytically	ADV
ejpam-1372	921	11	continuing	continue	VERB
ejpam-1372	921	12	the	the	DET
ejpam-1372	921	13	results	result	NOUN
ejpam-1372	921	14	to	to	ADP
ejpam-1372	921	15	the	the	DET
ejpam-1372	921	16	next	next	ADJ
ejpam-1372	921	17	riemann	riemann	PROPN
ejpam-1372	921	18	sheet	sheet	NOUN
ejpam-1372	921	19	over	over	ADP
ejpam-1372	921	20	the	the	DET
ejpam-1372	921	21	entire	entire	ADJ
ejpam-1372	921	22	complex	complex	ADJ
ejpam-1372	921	23	plane	plane	NOUN
ejpam-1372	921	24	.	.	PUNCT
ejpam-1372	922	1	the	the	DET
ejpam-1372	922	2	procedure	procedure	NOUN
ejpam-1372	922	3	outlined	outline	VERB
ejpam-1372	922	4	in	in	ADP
ejpam-1372	922	5	the	the	DET
ejpam-1372	922	6	preceding	precede	VERB
ejpam-1372	922	7	paragraph	paragraph	NOUN
ejpam-1372	922	8	is	be	AUX
ejpam-1372	922	9	the	the	DET
ejpam-1372	922	10	method	method	NOUN
ejpam-1372	922	11	used	use	VERB
ejpam-1372	922	12	in	in	ADP
ejpam-1372	922	13	ref	ref	NOUN
ejpam-1372	922	14	.	.	PUNCT
ejpam-1372	923	1	[	[	X
ejpam-1372	923	2	17	17	NUM
ejpam-1372	923	3	]	]	PUNCT
ejpam-1372	923	4	to	to	PART
ejpam-1372	923	5	derive	derive	VERB
ejpam-1372	923	6	the	the	DET
ejpam-1372	923	7	regularised	regularise	VERB
ejpam-1372	923	8	value	value	NOUN
ejpam-1372	923	9	of	of	ADP
ejpam-1372	923	10	the	the	DET
ejpam-1372	923	11	generalised	generalise	VERB
ejpam-1372	923	12	type	type	NOUN
ejpam-1372	923	13	ii	ii	NOUN
ejpam-1372	923	14	terminant	terminant	NOUN
ejpam-1372	923	15	given	give	VERB
ejpam-1372	923	16	in	in	ADP
ejpam-1372	923	17	proposition	proposition	NOUN
ejpam-1372	923	18	5	5	NUM
ejpam-1372	923	19	.	.	PUNCT
ejpam-1372	924	1	for	for	ADP
ejpam-1372	924	2	a	a	DET
ejpam-1372	924	3	standard	standard	ADJ
ejpam-1372	924	4	terminant	terminant	NOUN
ejpam-1372	924	5	this	this	DET
ejpam-1372	924	6	result	result	NOUN
ejpam-1372	924	7	reduces	reduce	VERB
ejpam-1372	924	8	to	to	ADP
ejpam-1372	924	9	ti	ti	PROPN
ejpam-1372	924	10	i(n	i(n	PROPN
ejpam-1372	924	11	,	,	PUNCT
ejpam-1372	924	12	α	α	NOUN
ejpam-1372	924	13	,	,	PUNCT
ejpam-1372	924	14	z	z	NOUN
ejpam-1372	924	15	)	)	PUNCT
ejpam-1372	924	16	≡	≡	PROPN
ejpam-1372	924	17	∫	∫	PROPN
ejpam-1372	924	18	c+i∞	c+i∞	PROPN
ejpam-1372	924	19	c−i∞	c−i∞	PROPN
ejpam-1372	924	20	ds	ds	PROPN
ejpam-1372	924	21	zs	zs	PROPN
ejpam-1372	924	22	e∓(2m+1)iπsγ(s+α	e∓(2m+1)iπsγ(s+α	PROPN
ejpam-1372	924	23	)	)	PUNCT
ejpam-1372	924	24	e−iπs	e−iπs	NOUN
ejpam-1372	924	25	−	−	PROPN
ejpam-1372	924	26	eiπs	eiπs	PROPN
ejpam-1372	924	27	∓	∓	PROPN
ejpam-1372	924	28	2πiz−αe−1	2πiz−αe−1	NUM
ejpam-1372	924	29	/	/	SYM
ejpam-1372	924	30	z	z	PROPN
ejpam-1372	924	31	×	×	PROPN
ejpam-1372	924	32	e±(m+1)iπα	e±(m+1)iπα	PROPN
ejpam-1372	924	33	sin(mπα	sin(mπα	PROPN
ejpam-1372	924	34	)	)	PUNCT
ejpam-1372	924	35	sin(πα	sin(πα	PROPN
ejpam-1372	924	36	)	)	PUNCT
ejpam-1372	925	1	∓π	∓π	PROPN
ejpam-1372	926	1	i	i	PRON
ejpam-1372	926	2	z−α	z−α	NUM
ejpam-1372	926	3	e−1	e−1	PROPN
ejpam-1372	926	4	/	/	SYM
ejpam-1372	926	5	z	z	PROPN
ejpam-1372	926	6	,	,	PUNCT
ejpam-1372	926	7	(	(	PUNCT
ejpam-1372	926	8	105	105	NUM
ejpam-1372	926	9	)	)	PUNCT
ejpam-1372	926	10	where	where	SCONJ
ejpam-1372	926	11	for	for	ADP
ejpam-1372	926	12	the	the	DET
ejpam-1372	926	13	upper	upper	ADV
ejpam-1372	926	14	-	-	PUNCT
ejpam-1372	926	15	signed	sign	VERB
ejpam-1372	926	16	result	result	NOUN
ejpam-1372	926	17	,	,	PUNCT
ejpam-1372	926	18	(	(	PUNCT
ejpam-1372	926	19	2	2	NUM
ejpam-1372	926	20	m	m	NOUN
ejpam-1372	926	21	−	−	NOUN
ejpam-1372	926	22	1/2)π	1/2)π	NUM
ejpam-1372	926	23	<	<	X
ejpam-1372	926	24	arg	arg	NOUN
ejpam-1372	926	25	z	z	NOUN
ejpam-1372	926	26	<	<	X
ejpam-1372	926	27	(	(	PUNCT
ejpam-1372	926	28	2	2	NUM
ejpam-1372	926	29	m	m	NOUN
ejpam-1372	926	30	+	+	NOUN
ejpam-1372	926	31	5/2)π	5/2)π	NUM
ejpam-1372	926	32	,	,	PUNCT
ejpam-1372	926	33	and	and	CCONJ
ejpam-1372	926	34	for	for	ADP
ejpam-1372	926	35	the	the	DET
ejpam-1372	926	36	lowersigned	lowersigned	ADJ
ejpam-1372	926	37	result	result	NOUN
ejpam-1372	926	38	,	,	PUNCT
ejpam-1372	926	39	−(2	−(2	PROPN
ejpam-1372	926	40	m	m	VERB
ejpam-1372	926	41	+	+	NOUN
ejpam-1372	926	42	5/2)π	5/2)π	NUM
ejpam-1372	926	43	<	<	X
ejpam-1372	926	44	argz	argz	NOUN
ejpam-1372	926	45	<	<	X
ejpam-1372	926	46	(	(	PUNCT
ejpam-1372	926	47	−2	−2	NOUN
ejpam-1372	926	48	m	m	VERB
ejpam-1372	926	49	+	+	NOUN
ejpam-1372	926	50	1/2)π	1/2)π	X
ejpam-1372	926	51	.	.	PUNCT
ejpam-1372	926	52	once	once	ADV
ejpam-1372	926	53	again	again	ADV
ejpam-1372	926	54	,	,	PUNCT
ejpam-1372	926	55	the	the	DET
ejpam-1372	926	56	offset	offset	NOUN
ejpam-1372	926	57	is	be	AUX
ejpam-1372	926	58	the	the	DET
ejpam-1372	926	59	same	same	ADJ
ejpam-1372	926	60	as	as	ADP
ejpam-1372	926	61	that	that	PRON
ejpam-1372	926	62	given	give	VERB
ejpam-1372	926	63	below	below	ADP
ejpam-1372	926	64	equivalence	equivalence	NOUN
ejpam-1372	926	65	(	(	PUNCT
ejpam-1372	926	66	96	96	NUM
ejpam-1372	926	67	)	)	PUNCT
ejpam-1372	926	68	,	,	PUNCT
ejpam-1372	926	69	viz	viz	PROPN
ejpam-1372	926	70	.	.	PUNCT
ejpam-1372	927	1	max[n	max[n	NOUN
ejpam-1372	928	1	−	−	PROPN
ejpam-1372	928	2	1,−α	1,−α	PROPN
ejpam-1372	928	3	]	]	X
ejpam-1372	928	4	<	<	X
ejpam-1372	928	5	c	c	X
ejpam-1372	928	6	=	=	SYM
ejpam-1372	928	7	ℜ	ℜ	PROPN
ejpam-1372	928	8	s	s	PART
ejpam-1372	928	9	<	<	X
ejpam-1372	928	10	n	n	NUM
ejpam-1372	928	11	.	.	PUNCT
ejpam-1372	929	1	to	to	PART
ejpam-1372	929	2	complete	complete	VERB
ejpam-1372	929	3	this	this	DET
ejpam-1372	929	4	section	section	NOUN
ejpam-1372	929	5	,	,	PUNCT
ejpam-1372	929	6	we	we	PRON
ejpam-1372	929	7	now	now	ADV
ejpam-1372	929	8	turn	turn	VERB
ejpam-1372	929	9	to	to	ADP
ejpam-1372	929	10	an	an	DET
ejpam-1372	929	11	example	example	NOUN
ejpam-1372	929	12	where	where	SCONJ
ejpam-1372	929	13	the	the	DET
ejpam-1372	929	14	second	second	ADJ
ejpam-1372	929	15	type	type	NOUN
ejpam-1372	929	16	of	of	ADP
ejpam-1372	929	17	terminant	terminant	NOUN
ejpam-1372	929	18	series	series	NOUN
ejpam-1372	929	19	is	be	AUX
ejpam-1372	929	20	only	only	ADV
ejpam-1372	929	21	valid	valid	ADJ
ejpam-1372	929	22	initially	initially	ADV
ejpam-1372	929	23	over	over	ADP
ejpam-1372	929	24	a	a	DET
ejpam-1372	929	25	sector	sector	NOUN
ejpam-1372	929	26	of	of	ADP
ejpam-1372	929	27	complex	complex	ADJ
ejpam-1372	929	28	plane	plane	NOUN
ejpam-1372	929	29	rather	rather	ADV
ejpam-1372	929	30	than	than	ADP
ejpam-1372	929	31	on	on	ADP
ejpam-1372	929	32	a	a	DET
ejpam-1372	929	33	line	line	NOUN
ejpam-1372	929	34	of	of	ADP
ejpam-1372	929	35	discontinuity	discontinuity	NOUN
ejpam-1372	929	36	as	as	SCONJ
ejpam-1372	929	37	is	be	AUX
ejpam-1372	929	38	the	the	DET
ejpam-1372	929	39	usual	usual	ADJ
ejpam-1372	929	40	case	case	NOUN
ejpam-1372	929	41	discussed	discuss	VERB
ejpam-1372	929	42	above	above	ADV
ejpam-1372	929	43	.	.	PUNCT
ejpam-1372	930	1	in	in	ADP
ejpam-1372	930	2	a	a	DET
ejpam-1372	930	3	recent	recent	ADJ
ejpam-1372	930	4	work	work	NOUN
ejpam-1372	930	5	[	[	X
ejpam-1372	930	6	31	31	NUM
ejpam-1372	930	7	]	]	PUNCT
ejpam-1372	930	8	a	a	DET
ejpam-1372	930	9	series	series	NOUN
ejpam-1372	930	10	expansion	expansion	NOUN
ejpam-1372	930	11	for	for	ADP
ejpam-1372	930	12	the	the	DET
ejpam-1372	930	13	trigonometric	trigonometric	ADJ
ejpam-1372	930	14	cosecant	cosecant	ADJ
ejpam-1372	930	15	function	function	NOUN
ejpam-1372	930	16	was	be	AUX
ejpam-1372	930	17	derived	derive	VERB
ejpam-1372	930	18	by	by	ADP
ejpam-1372	930	19	using	use	VERB
ejpam-1372	930	20	the	the	DET
ejpam-1372	930	21	partition	partition	NOUN
ejpam-1372	930	22	method	method	NOUN
ejpam-1372	930	23	for	for	ADP
ejpam-1372	930	24	a	a	DET
ejpam-1372	930	25	power	power	NOUN
ejpam-1372	930	26	series	series	NOUN
ejpam-1372	930	27	expansion	expansion	NOUN
ejpam-1372	931	1	[	[	X
ejpam-1372	931	2	16	16	NUM
ejpam-1372	931	3	,	,	PUNCT
ejpam-1372	931	4	18	18	NUM
ejpam-1372	931	5	]	]	PUNCT
ejpam-1372	931	6	,	,	PUNCT
ejpam-1372	931	7	in	in	ADP
ejpam-1372	931	8	which	which	PRON
ejpam-1372	931	9	the	the	DET
ejpam-1372	931	10	ak	ak	PROPN
ejpam-1372	931	11	in	in	ADP
ejpam-1372	931	12	eq	eq	PROPN
ejpam-1372	931	13	.	.	PUNCT
ejpam-1372	932	1	(	(	PUNCT
ejpam-1372	932	2	1	1	X
ejpam-1372	932	3	)	)	PUNCT
ejpam-1372	932	4	were	be	AUX
ejpam-1372	932	5	expressed	express	VERB
ejpam-1372	932	6	in	in	ADP
ejpam-1372	932	7	terms	term	NOUN
ejpam-1372	932	8	of	of	ADP
ejpam-1372	932	9	special	special	ADJ
ejpam-1372	932	10	numbers	number	NOUN
ejpam-1372	932	11	known	know	VERB
ejpam-1372	932	12	as	as	ADP
ejpam-1372	932	13	the	the	DET
ejpam-1372	932	14	cosecant	cosecant	ADJ
ejpam-1372	932	15	numbers	number	NOUN
ejpam-1372	932	16	.	.	PUNCT
ejpam-1372	933	1	specifically	specifically	ADV
ejpam-1372	933	2	,	,	PUNCT
ejpam-1372	933	3	the	the	DET
ejpam-1372	933	4	following	following	ADJ
ejpam-1372	933	5	result	result	NOUN
ejpam-1372	933	6	was	be	AUX
ejpam-1372	933	7	derived	derive	VERB
ejpam-1372	933	8	z	z	PROPN
ejpam-1372	933	9	csc(z	csc(z	PROPN
ejpam-1372	933	10	)	)	PUNCT
ejpam-1372	933	11	≡	≡	PROPN
ejpam-1372	933	12	∞	∞	PROPN
ejpam-1372	933	13	∑	∑	PROPN
ejpam-1372	933	14	k=0	k=0	PROPN
ejpam-1372	933	15	ckz2k	ckz2k	PROPN
ejpam-1372	933	16	,	,	PUNCT
ejpam-1372	933	17	(	(	PUNCT
ejpam-1372	933	18	106	106	NUM
ejpam-1372	933	19	)	)	PUNCT
ejpam-1372	934	1	where	where	SCONJ
ejpam-1372	934	2	c0=1	c0=1	PROPN
ejpam-1372	934	3	,	,	PUNCT
ejpam-1372	934	4	c1=1/6	c1=1/6	PROPN
ejpam-1372	934	5	,	,	PUNCT
ejpam-1372	934	6	c2=7/360	c2=7/360	NOUN
ejpam-1372	934	7	,	,	PUNCT
ejpam-1372	934	8	etc	etc	X
ejpam-1372	934	9	.	.	X
ejpam-1372	935	1	a	a	DET
ejpam-1372	935	2	more	more	ADV
ejpam-1372	935	3	general	general	ADJ
ejpam-1372	935	4	formulation	formulation	NOUN
ejpam-1372	935	5	for	for	ADP
ejpam-1372	935	6	the	the	DET
ejpam-1372	935	7	cosecant	cosecant	ADJ
ejpam-1372	935	8	numbers	number	NOUN
ejpam-1372	935	9	in	in	ADP
ejpam-1372	935	10	terms	term	NOUN
ejpam-1372	935	11	of	of	ADP
ejpam-1372	935	12	the	the	DET
ejpam-1372	935	13	riemann	riemann	PROPN
ejpam-1372	935	14	zeta	zeta	PROPN
ejpam-1372	935	15	function	function	PROPN
ejpam-1372	935	16	is	be	AUX
ejpam-1372	935	17	ck	ck	PROPN
ejpam-1372	935	18	=	=	SYM
ejpam-1372	935	19	2	2	NUM
ejpam-1372	935	20	�	�	PROPN
ejpam-1372	935	21	1−	1−	NUM
ejpam-1372	935	22	21−2k	21−2k	NUM
ejpam-1372	935	23	�	�	NOUN
ejpam-1372	935	24	ζ(2k	ζ(2k	NUM
ejpam-1372	935	25	)	)	PUNCT
ejpam-1372	935	26	π2k	π2k	NOUN
ejpam-1372	935	27	.	.	PUNCT
ejpam-1372	936	1	(	(	PUNCT
ejpam-1372	936	2	107	107	NUM
ejpam-1372	936	3	)	)	PUNCT
ejpam-1372	936	4	the	the	DET
ejpam-1372	936	5	power	power	NOUN
ejpam-1372	936	6	series	series	PROPN
ejpam-1372	936	7	expansion	expansion	NOUN
ejpam-1372	936	8	given	give	VERB
ejpam-1372	936	9	by	by	ADP
ejpam-1372	936	10	equivalence	equivalence	NOUN
ejpam-1372	936	11	(	(	PUNCT
ejpam-1372	936	12	106	106	NUM
ejpam-1372	936	13	)	)	PUNCT
ejpam-1372	936	14	was	be	AUX
ejpam-1372	936	15	also	also	ADV
ejpam-1372	936	16	found	find	VERB
ejpam-1372	936	17	to	to	PART
ejpam-1372	936	18	possess	possess	VERB
ejpam-1372	936	19	a	a	DET
ejpam-1372	936	20	finite	finite	ADJ
ejpam-1372	936	21	radius	radius	NOUN
ejpam-1372	936	22	of	of	ADP
ejpam-1372	936	23	absolute	absolute	ADJ
ejpam-1372	936	24	convergence	convergence	NOUN
ejpam-1372	936	25	given	give	VERB
ejpam-1372	936	26	by	by	ADP
ejpam-1372	936	27	|z|<π	|z|<π	PROPN
ejpam-1372	936	28	.	.	PUNCT
ejpam-1372	937	1	the	the	DET
ejpam-1372	937	2	simplest	simple	ADJ
ejpam-1372	937	3	method	method	NOUN
ejpam-1372	937	4	of	of	ADP
ejpam-1372	937	5	deriving	derive	VERB
ejpam-1372	937	6	an	an	DET
ejpam-1372	937	7	asymptotic	asymptotic	ADJ
ejpam-1372	937	8	series	series	NOUN
ejpam-1372	937	9	with	with	ADP
ejpam-1372	937	10	the	the	DET
ejpam-1372	937	11	cosecant	cosecant	ADJ
ejpam-1372	937	12	numbers	number	NOUN
ejpam-1372	937	13	in	in	ADP
ejpam-1372	937	14	it	it	PRON
ejpam-1372	937	15	is	be	AUX
ejpam-1372	937	16	to	to	PART
ejpam-1372	937	17	evaluate	evaluate	VERB
ejpam-1372	937	18	the	the	DET
ejpam-1372	937	19	laplace	laplace	NOUN
ejpam-1372	937	20	transform	transform	NOUN
ejpam-1372	937	21	of	of	ADP
ejpam-1372	937	22	z	z	NOUN
ejpam-1372	937	23	csc(az	csc(az	NOUN
ejpam-1372	937	24	)	)	PUNCT
ejpam-1372	937	25	.	.	PUNCT
ejpam-1372	938	1	this	this	DET
ejpam-1372	938	2	yields	yield	VERB
ejpam-1372	938	3	icsc(p	icsc(p	PROPN
ejpam-1372	938	4	,	,	PUNCT
ejpam-1372	938	5	a	a	PRON
ejpam-1372	938	6	)	)	PUNCT
ejpam-1372	938	7	=	=	PUNCT
ejpam-1372	939	1	z	z	NOUN
ejpam-1372	939	2	∫	∫	PROPN
ejpam-1372	940	1	∞	∞	NOUN
ejpam-1372	940	2	0	0	NUM
ejpam-1372	941	1	dz	dz	PROPN
ejpam-1372	941	2	z	z	PROPN
ejpam-1372	941	3	e−pz	e−pz	PROPN
ejpam-1372	941	4	csc(z)≡	csc(z)≡	PROPN
ejpam-1372	941	5	1	1	NUM
ejpam-1372	941	6	ap	ap	NOUN
ejpam-1372	942	1	+	+	NOUN
ejpam-1372	942	2	1	1	NUM
ejpam-1372	942	3	ap	ap	NUM
ejpam-1372	942	4	∞	∞	PROPN
ejpam-1372	942	5	∑	∑	PUNCT
ejpam-1372	943	1	k=1	k=1	PROPN
ejpam-1372	943	2	γ(2k+	γ(2k+	PROPN
ejpam-1372	943	3	1)ck	1)ck	PROPN
ejpam-1372	943	4	�	�	PROPN
ejpam-1372	943	5	a	a	DET
ejpam-1372	943	6	p	p	X
ejpam-1372	943	7	�	�	PROPN
ejpam-1372	943	8	2k	2k	NUM
ejpam-1372	943	9	.	.	PUNCT
ejpam-1372	944	1	(	(	PUNCT
ejpam-1372	944	2	108	108	NUM
ejpam-1372	944	3	)	)	PUNCT
ejpam-1372	944	4	v.	v.	ADP
ejpam-1372	944	5	kowalenko	kowalenko	PROPN
ejpam-1372	944	6	/	/	SYM
ejpam-1372	944	7	eur	eur	PROPN
ejpam-1372	944	8	.	.	PUNCT
ejpam-1372	945	1	j.	j.	PROPN
ejpam-1372	945	2	pure	pure	PROPN
ejpam-1372	945	3	appl	appl	PROPN
ejpam-1372	945	4	.	.	PROPN
ejpam-1372	945	5	math	math	PROPN
ejpam-1372	945	6	,	,	PUNCT
ejpam-1372	945	7	4	4	NUM
ejpam-1372	945	8	(	(	PUNCT
ejpam-1372	945	9	2011	2011	NUM
ejpam-1372	945	10	)	)	PUNCT
ejpam-1372	945	11	,	,	PUNCT
ejpam-1372	945	12	370	370	NUM
ejpam-1372	945	13	-	-	SYM
ejpam-1372	945	14	423	423	NUM
ejpam-1372	945	15	403	403	NUM
ejpam-1372	945	16	if	if	SCONJ
ejpam-1372	945	17	we	we	PRON
ejpam-1372	945	18	introduce	introduce	VERB
ejpam-1372	945	19	eq	eq	NOUN
ejpam-1372	945	20	.	.	PUNCT
ejpam-1372	946	1	(	(	PUNCT
ejpam-1372	946	2	107	107	NUM
ejpam-1372	946	3	)	)	PUNCT
ejpam-1372	946	4	into	into	ADP
ejpam-1372	946	5	the	the	DET
ejpam-1372	946	6	above	above	ADJ
ejpam-1372	946	7	result	result	NOUN
ejpam-1372	946	8	and	and	CCONJ
ejpam-1372	946	9	replace	replace	VERB
ejpam-1372	946	10	the	the	DET
ejpam-1372	946	11	zeta	zeta	NOUN
ejpam-1372	946	12	function	function	NOUN
ejpam-1372	946	13	by	by	ADP
ejpam-1372	946	14	its	its	PRON
ejpam-1372	946	15	dirichlet	dirichlet	PROPN
ejpam-1372	946	16	series	series	NOUN
ejpam-1372	946	17	form	form	NOUN
ejpam-1372	946	18	,	,	PUNCT
ejpam-1372	946	19	i.e.	i.e.	X
ejpam-1372	946	20	by	by	ADP
ejpam-1372	946	21	ζ(2k)=	ζ(2k)=	NOUN
ejpam-1372	946	22	∑∞	∑∞	NOUN
ejpam-1372	946	23	j=1	j=1	PROPN
ejpam-1372	946	24	1/	1/	PROPN
ejpam-1372	946	25	j2k	j2k	PROPN
ejpam-1372	946	26	,	,	PUNCT
ejpam-1372	946	27	then	then	ADV
ejpam-1372	946	28	we	we	PRON
ejpam-1372	946	29	obtain	obtain	VERB
ejpam-1372	946	30	icsc(p	icsc(p	NOUN
ejpam-1372	946	31	,	,	PUNCT
ejpam-1372	946	32	a	a	PRON
ejpam-1372	946	33	)	)	PUNCT
ejpam-1372	946	34	≡	≡	PROPN
ejpam-1372	946	35	1	1	NUM
ejpam-1372	946	36	ap	ap	NOUN
ejpam-1372	947	1	+	+	PROPN
ejpam-1372	947	2	2	2	NUM
ejpam-1372	947	3	ap	ap	NUM
ejpam-1372	947	4	∞	∞	PROPN
ejpam-1372	947	5	∑	∑	PROPN
ejpam-1372	947	6	j=1	j=1	NOUN
ejpam-1372	947	7	∞	∞	PROPN
ejpam-1372	947	8	∑	∑	PUNCT
ejpam-1372	947	9	k=1	k=1	PROPN
ejpam-1372	947	10	γ(2k+	γ(2k+	PROPN
ejpam-1372	947	11	1	1	NUM
ejpam-1372	947	12	)	)	PUNCT
ejpam-1372	947	13	�	�	PROPN
ejpam-1372	947	14	a	a	DET
ejpam-1372	947	15	jpπ	jpπ	NOUN
ejpam-1372	947	16	�	�	PROPN
ejpam-1372	947	17	2k	2k	NOUN
ejpam-1372	947	18	−	−	ADP
ejpam-1372	947	19	2	2	NUM
ejpam-1372	947	20	∞	∞	NUM
ejpam-1372	947	21	∑	∑	PUNCT
ejpam-1372	947	22	k=1	k=1	PROPN
ejpam-1372	947	23	γ(2k+	γ(2k+	PROPN
ejpam-1372	947	24	1	1	NUM
ejpam-1372	947	25	)	)	PUNCT
ejpam-1372	947	26	�	�	PROPN
ejpam-1372	947	27	a	a	DET
ejpam-1372	947	28	2	2	NUM
ejpam-1372	947	29	jpπ	jpπ	NOUN
ejpam-1372	947	30	�	�	NOUN
ejpam-1372	947	31	2k	2k	PROPN
ejpam-1372	947	32	!	!	PUNCT
ejpam-1372	947	33	.	.	PUNCT
ejpam-1372	948	1	(	(	PUNCT
ejpam-1372	948	2	109	109	NUM
ejpam-1372	948	3	)	)	PUNCT
ejpam-1372	948	4	therefore	therefore	ADV
ejpam-1372	948	5	,	,	PUNCT
ejpam-1372	948	6	we	we	PRON
ejpam-1372	948	7	see	see	VERB
ejpam-1372	948	8	that	that	SCONJ
ejpam-1372	948	9	the	the	DET
ejpam-1372	948	10	asymptotic	asymptotic	ADJ
ejpam-1372	948	11	expansion	expansion	NOUN
ejpam-1372	948	12	for	for	ADP
ejpam-1372	948	13	icsc(p	icsc(p	PROPN
ejpam-1372	948	14	,	,	PUNCT
ejpam-1372	948	15	a	a	PRON
ejpam-1372	948	16	)	)	PUNCT
ejpam-1372	948	17	is	be	AUX
ejpam-1372	948	18	composed	compose	VERB
ejpam-1372	948	19	of	of	ADP
ejpam-1372	948	20	an	an	DET
ejpam-1372	948	21	infinite	infinite	ADJ
ejpam-1372	948	22	series	series	NOUN
ejpam-1372	948	23	of	of	ADP
ejpam-1372	948	24	generalised	generalise	VERB
ejpam-1372	948	25	terminants	terminant	NOUN
ejpam-1372	948	26	,	,	PUNCT
ejpam-1372	948	27	which	which	PRON
ejpam-1372	948	28	is	be	AUX
ejpam-1372	948	29	not	not	PART
ejpam-1372	948	30	so	so	ADV
ejpam-1372	948	31	surprising	surprising	ADJ
ejpam-1372	948	32	as	as	SCONJ
ejpam-1372	948	33	each	each	DET
ejpam-1372	948	34	terminant	terminant	NOUN
ejpam-1372	948	35	corresponds	correspond	VERB
ejpam-1372	948	36	to	to	ADP
ejpam-1372	948	37	each	each	DET
ejpam-1372	948	38	singularity	singularity	NOUN
ejpam-1372	948	39	lying	lie	VERB
ejpam-1372	948	40	on	on	ADP
ejpam-1372	948	41	the	the	DET
ejpam-1372	948	42	real	real	ADJ
ejpam-1372	948	43	axis	axis	NOUN
ejpam-1372	948	44	.	.	PUNCT
ejpam-1372	949	1	there	there	PRON
ejpam-1372	949	2	is	be	VERB
ejpam-1372	949	3	an	an	DET
ejpam-1372	949	4	interesting	interesting	ADJ
ejpam-1372	949	5	anomaly	anomaly	NOUN
ejpam-1372	949	6	arising	arise	VERB
ejpam-1372	949	7	out	out	ADP
ejpam-1372	949	8	of	of	ADP
ejpam-1372	949	9	equivalences	equivalence	NOUN
ejpam-1372	949	10	(	(	PUNCT
ejpam-1372	949	11	108	108	NUM
ejpam-1372	949	12	)	)	PUNCT
ejpam-1372	949	13	and	and	CCONJ
ejpam-1372	949	14	(	(	PUNCT
ejpam-1372	949	15	109	109	NUM
ejpam-1372	949	16	)	)	PUNCT
ejpam-1372	949	17	.	.	PUNCT
ejpam-1372	950	1	that	that	PRON
ejpam-1372	950	2	is	be	AUX
ejpam-1372	950	3	,	,	PUNCT
ejpam-1372	950	4	for	for	ADP
ejpam-1372	950	5	either	either	CCONJ
ejpam-1372	950	6	large	large	ADJ
ejpam-1372	950	7	values	value	NOUN
ejpam-1372	950	8	of	of	ADP
ejpam-1372	950	9	p	p	NOUN
ejpam-1372	950	10	or	or	CCONJ
ejpam-1372	950	11	small	small	ADJ
ejpam-1372	950	12	values	value	NOUN
ejpam-1372	950	13	of	of	ADP
ejpam-1372	950	14	a	a	PRON
ejpam-1372	950	15	,	,	PUNCT
ejpam-1372	950	16	we	we	PRON
ejpam-1372	950	17	can	can	AUX
ejpam-1372	950	18	truncate	truncate	VERB
ejpam-1372	950	19	the	the	DET
ejpam-1372	950	20	expansion	expansion	NOUN
ejpam-1372	950	21	on	on	ADP
ejpam-1372	950	22	the	the	DET
ejpam-1372	950	23	rhs	rhs	PROPN
ejpam-1372	950	24	of	of	ADP
ejpam-1372	950	25	equivalence	equivalence	NOUN
ejpam-1372	950	26	(	(	PUNCT
ejpam-1372	950	27	106	106	NUM
ejpam-1372	950	28	)	)	PUNCT
ejpam-1372	950	29	,	,	PUNCT
ejpam-1372	950	30	thereby	thereby	ADV
ejpam-1372	950	31	yielding	yield	VERB
ejpam-1372	950	32	a	a	DET
ejpam-1372	950	33	finite	finite	ADJ
ejpam-1372	950	34	value	value	NOUN
ejpam-1372	950	35	when	when	SCONJ
ejpam-1372	950	36	both	both	DET
ejpam-1372	950	37	a	a	PRON
ejpam-1372	950	38	and	and	CCONJ
ejpam-1372	950	39	p	p	NOUN
ejpam-1372	950	40	are	be	AUX
ejpam-1372	950	41	real	real	ADJ
ejpam-1372	950	42	.	.	PUNCT
ejpam-1372	951	1	yet	yet	CCONJ
ejpam-1372	951	2	for	for	ADP
ejpam-1372	951	3	these	these	DET
ejpam-1372	951	4	values	value	NOUN
ejpam-1372	951	5	of	of	ADP
ejpam-1372	951	6	a	a	PRON
ejpam-1372	951	7	and	and	CCONJ
ejpam-1372	951	8	p	p	X
ejpam-1372	951	9	the	the	DET
ejpam-1372	951	10	original	original	ADJ
ejpam-1372	951	11	integral	integral	NOUN
ejpam-1372	951	12	on	on	ADP
ejpam-1372	951	13	the	the	DET
ejpam-1372	951	14	lhs	lhs	PROPN
ejpam-1372	951	15	of	of	ADP
ejpam-1372	951	16	equivalence	equivalence	NOUN
ejpam-1372	951	17	(	(	PUNCT
ejpam-1372	951	18	108	108	NUM
ejpam-1372	951	19	)	)	PUNCT
ejpam-1372	951	20	is	be	AUX
ejpam-1372	951	21	singular	singular	ADJ
ejpam-1372	951	22	or	or	CCONJ
ejpam-1372	951	23	undefined	undefined	ADJ
ejpam-1372	951	24	.	.	PUNCT
ejpam-1372	952	1	this	this	PRON
ejpam-1372	952	2	is	be	AUX
ejpam-1372	952	3	a	a	DET
ejpam-1372	952	4	situation	situation	NOUN
ejpam-1372	952	5	where	where	SCONJ
ejpam-1372	952	6	a	a	DET
ejpam-1372	952	7	regularised	regularise	VERB
ejpam-1372	952	8	value	value	NOUN
ejpam-1372	952	9	can	can	AUX
ejpam-1372	952	10	be	be	AUX
ejpam-1372	952	11	obtained	obtain	VERB
ejpam-1372	952	12	,	,	PUNCT
ejpam-1372	952	13	but	but	CCONJ
ejpam-1372	952	14	it	it	PRON
ejpam-1372	952	15	does	do	AUX
ejpam-1372	952	16	not	not	PART
ejpam-1372	952	17	represent	represent	VERB
ejpam-1372	952	18	the	the	DET
ejpam-1372	952	19	actual	actual	ADJ
ejpam-1372	952	20	function	function	NOUN
ejpam-1372	952	21	.	.	PUNCT
ejpam-1372	953	1	since	since	SCONJ
ejpam-1372	953	2	a2	a2	PROPN
ejpam-1372	953	3	/	/	SYM
ejpam-1372	953	4	p2	p2	NOUN
ejpam-1372	953	5	,	,	PUNCT
ejpam-1372	953	6	not	not	PART
ejpam-1372	953	7	z	z	NOUN
ejpam-1372	953	8	,	,	PUNCT
ejpam-1372	953	9	represents	represent	VERB
ejpam-1372	953	10	the	the	DET
ejpam-1372	953	11	variable	variable	NOUN
ejpam-1372	953	12	in	in	ADP
ejpam-1372	953	13	the	the	DET
ejpam-1372	953	14	above	above	ADJ
ejpam-1372	953	15	asymptotic	asymptotic	ADJ
ejpam-1372	953	16	series	series	NOUN
ejpam-1372	953	17	,	,	PUNCT
ejpam-1372	953	18	the	the	DET
ejpam-1372	953	19	rhs	rhs	PROPN
ejpam-1372	953	20	of	of	ADP
ejpam-1372	953	21	equivalence	equivalence	NOUN
ejpam-1372	953	22	(	(	PUNCT
ejpam-1372	953	23	108	108	NUM
ejpam-1372	953	24	)	)	PUNCT
ejpam-1372	953	25	can	can	AUX
ejpam-1372	953	26	only	only	ADV
ejpam-1372	953	27	apply	apply	VERB
ejpam-1372	953	28	to	to	ADP
ejpam-1372	953	29	the	the	DET
ejpam-1372	953	30	stokes	stoke	NOUN
ejpam-1372	953	31	sectors	sector	NOUN
ejpam-1372	953	32	given	give	VERB
ejpam-1372	953	33	by	by	ADP
ejpam-1372	953	34	(	(	PUNCT
ejpam-1372	953	35	j−	j−	PROPN
ejpam-1372	953	36	1)π	1)π	PROPN
ejpam-1372	953	37	<	<	X
ejpam-1372	953	38	(	(	PUNCT
ejpam-1372	953	39	a	a	NOUN
ejpam-1372	953	40	/	/	SYM
ejpam-1372	953	41	p	p	NOUN
ejpam-1372	953	42	)	)	PUNCT
ejpam-1372	953	43	<	<	X
ejpam-1372	953	44	jπ	jπ	PROPN
ejpam-1372	953	45	,	,	PUNCT
ejpam-1372	953	46	where	where	SCONJ
ejpam-1372	953	47	j	j	PROPN
ejpam-1372	953	48	is	be	AUX
ejpam-1372	953	49	an	an	DET
ejpam-1372	953	50	arbitrary	arbitrary	ADJ
ejpam-1372	953	51	integer	integer	NOUN
ejpam-1372	953	52	.	.	PUNCT
ejpam-1372	954	1	that	that	PRON
ejpam-1372	954	2	is	is	ADV
ejpam-1372	954	3	,	,	PUNCT
ejpam-1372	954	4	the	the	DET
ejpam-1372	954	5	real	real	ADJ
ejpam-1372	954	6	axis	axis	NOUN
ejpam-1372	954	7	represents	represent	VERB
ejpam-1372	954	8	a	a	DET
ejpam-1372	954	9	line	line	NOUN
ejpam-1372	954	10	of	of	ADP
ejpam-1372	954	11	discontinuity	discontinuity	NOUN
ejpam-1372	954	12	for	for	ADP
ejpam-1372	954	13	icsc(p	icsc(p	PROPN
ejpam-1372	954	14	,	,	PUNCT
ejpam-1372	954	15	a	a	NOUN
ejpam-1372	954	16	)	)	PUNCT
ejpam-1372	954	17	with	with	ADP
ejpam-1372	954	18	the	the	DET
ejpam-1372	954	19	expansion	expansion	NOUN
ejpam-1372	954	20	on	on	ADP
ejpam-1372	954	21	the	the	DET
ejpam-1372	954	22	rhs	rhs	PROPN
ejpam-1372	954	23	of	of	ADP
ejpam-1372	954	24	equivalence	equivalence	NOUN
ejpam-1372	954	25	(	(	PUNCT
ejpam-1372	954	26	108	108	NUM
ejpam-1372	954	27	)	)	PUNCT
ejpam-1372	954	28	being	be	AUX
ejpam-1372	954	29	applicable	applicable	ADJ
ejpam-1372	954	30	to	to	ADP
ejpam-1372	954	31	each	each	DET
ejpam-1372	954	32	sector	sector	NOUN
ejpam-1372	954	33	.	.	PUNCT
ejpam-1372	955	1	because	because	SCONJ
ejpam-1372	955	2	the	the	DET
ejpam-1372	955	3	riemann	riemann	PROPN
ejpam-1372	955	4	zeta	zeta	PROPN
ejpam-1372	955	5	function	function	PROPN
ejpam-1372	955	6	can	can	AUX
ejpam-1372	955	7	be	be	AUX
ejpam-1372	955	8	analytically	analytically	ADV
ejpam-1372	955	9	continued	continue	VERB
ejpam-1372	955	10	into	into	ADP
ejpam-1372	955	11	the	the	DET
ejpam-1372	955	12	complex	complex	ADJ
ejpam-1372	955	13	plane	plane	NOUN
ejpam-1372	955	14	,	,	PUNCT
ejpam-1372	955	15	the	the	DET
ejpam-1372	955	16	cosecant	cosecant	ADJ
ejpam-1372	955	17	numbers	number	NOUN
ejpam-1372	955	18	can	can	AUX
ejpam-1372	955	19	also	also	ADV
ejpam-1372	955	20	be	be	AUX
ejpam-1372	955	21	continued	continue	VERB
ejpam-1372	955	22	in	in	ADP
ejpam-1372	955	23	the	the	DET
ejpam-1372	955	24	complex	complex	ADJ
ejpam-1372	955	25	plane	plane	NOUN
ejpam-1372	955	26	.	.	PUNCT
ejpam-1372	956	1	that	that	PRON
ejpam-1372	956	2	is	be	AUX
ejpam-1372	956	3	,	,	PUNCT
ejpam-1372	956	4	ck	ck	ADJ
ejpam-1372	956	5	=	=	SYM
ejpam-1372	956	6	c(k	c(k	NOUN
ejpam-1372	956	7	)	)	PUNCT
ejpam-1372	956	8	.	.	PUNCT
ejpam-1372	957	1	as	as	ADP
ejpam-1372	957	2	a	a	DET
ejpam-1372	957	3	consequence	consequence	NOUN
ejpam-1372	957	4	,	,	PUNCT
ejpam-1372	957	5	equivalence	equivalence	NOUN
ejpam-1372	957	6	(	(	PUNCT
ejpam-1372	957	7	108	108	NUM
ejpam-1372	957	8	)	)	PUNCT
ejpam-1372	957	9	can	can	AUX
ejpam-1372	957	10	undergo	undergo	VERB
ejpam-1372	957	11	mb	mb	ADP
ejpam-1372	957	12	regularisation	regularisation	NOUN
ejpam-1372	957	13	directly	directly	ADV
ejpam-1372	957	14	without	without	ADP
ejpam-1372	957	15	the	the	DET
ejpam-1372	957	16	need	need	NOUN
ejpam-1372	957	17	to	to	PART
ejpam-1372	957	18	consider	consider	VERB
ejpam-1372	957	19	the	the	DET
ejpam-1372	957	20	infinite	infinite	ADJ
ejpam-1372	957	21	sum	sum	NOUN
ejpam-1372	957	22	of	of	ADP
ejpam-1372	957	23	generalised	generalise	VERB
ejpam-1372	957	24	terminants	terminant	NOUN
ejpam-1372	957	25	in	in	ADP
ejpam-1372	957	26	equivalence	equivalence	NOUN
ejpam-1372	957	27	(	(	PUNCT
ejpam-1372	957	28	109	109	NUM
ejpam-1372	957	29	)	)	PUNCT
ejpam-1372	957	30	arising	arise	VERB
ejpam-1372	957	31	from	from	ADP
ejpam-1372	957	32	borel	borel	PROPN
ejpam-1372	957	33	summation	summation	NOUN
ejpam-1372	958	1	[	[	X
ejpam-1372	958	2	19	19	NUM
ejpam-1372	958	3	]	]	PUNCT
ejpam-1372	958	4	.	.	PUNCT
ejpam-1372	959	1	therefore	therefore	ADV
ejpam-1372	959	2	,	,	PUNCT
ejpam-1372	959	3	for	for	ADP
ejpam-1372	959	4	n	n	NOUN
ejpam-1372	959	5	=	=	SYM
ejpam-1372	959	6	1	1	NUM
ejpam-1372	959	7	and	and	CCONJ
ejpam-1372	959	8	−π	−π	PRON
ejpam-1372	959	9	<	<	X
ejpam-1372	959	10	arg	arg	X
ejpam-1372	959	11	(	(	PUNCT
ejpam-1372	959	12	a	a	NOUN
ejpam-1372	959	13	/	/	SYM
ejpam-1372	959	14	p	p	NOUN
ejpam-1372	959	15	)	)	PUNCT
ejpam-1372	959	16	<	<	X
ejpam-1372	959	17	0	0	PROPN
ejpam-1372	959	18	,	,	PUNCT
ejpam-1372	959	19	the	the	DET
ejpam-1372	959	20	mb	mb	ADJ
ejpam-1372	959	21	-	-	PUNCT
ejpam-1372	959	22	regularised	regularise	VERB
ejpam-1372	959	23	value	value	NOUN
ejpam-1372	959	24	of	of	ADP
ejpam-1372	959	25	icsc(p	icsc(p	PROPN
ejpam-1372	959	26	,	,	PUNCT
ejpam-1372	959	27	a	a	PRON
ejpam-1372	959	28	)	)	PUNCT
ejpam-1372	959	29	is	be	AUX
ejpam-1372	959	30	given	give	VERB
ejpam-1372	959	31	by	by	ADP
ejpam-1372	959	32	icsc(p	icsc(p	PROPN
ejpam-1372	959	33	,	,	PUNCT
ejpam-1372	959	34	a	a	PRON
ejpam-1372	959	35	)	)	PUNCT
ejpam-1372	959	36	≡	≡	PROPN
ejpam-1372	959	37	1	1	NUM
ejpam-1372	959	38	ap	ap	PROPN
ejpam-1372	959	39	1	1	NUM
ejpam-1372	959	40	+	+	NUM
ejpam-1372	959	41	∫	∫	PROPN
ejpam-1372	959	42	c+i∞	c+i∞	ADJ
ejpam-1372	959	43	c−i∞	c−i∞	PROPN
ejpam-1372	959	44	ds	ds	ADJ
ejpam-1372	959	45	γ(s+	γ(s+	NOUN
ejpam-1372	959	46	1	1	NUM
ejpam-1372	959	47	)	)	PUNCT
ejpam-1372	959	48	eiπs/2	eiπs/2	PROPN
ejpam-1372	959	49	e−iπs/2	e−iπs/2	ADJ
ejpam-1372	959	50	−	−	PROPN
ejpam-1372	959	51	eiπs/2	eiπs/2	PROPN
ejpam-1372	959	52	�	�	PROPN
ejpam-1372	959	53	a	a	DET
ejpam-1372	959	54	pπ	pπ	PROPN
ejpam-1372	959	55	�	�	PROPN
ejpam-1372	959	56	s	s	PART
ejpam-1372	959	57	�	�	PROPN
ejpam-1372	959	58	1−	1−	NUM
ejpam-1372	959	59	21−s	21−s	NUM
ejpam-1372	959	60	�	�	PROPN
ejpam-1372	959	61	ζ(s	ζ(s	PROPN
ejpam-1372	959	62	)	)	PUNCT
ejpam-1372	959	63	!	!	PUNCT
ejpam-1372	960	1	,	,	PUNCT
ejpam-1372	960	2	(	(	PUNCT
ejpam-1372	960	3	110	110	NUM
ejpam-1372	960	4	)	)	PUNCT
ejpam-1372	960	5	while	while	SCONJ
ejpam-1372	960	6	for	for	ADP
ejpam-1372	960	7	0	0	NUM
ejpam-1372	960	8	<	<	X
ejpam-1372	960	9	arg	arg	X
ejpam-1372	960	10	(	(	PUNCT
ejpam-1372	960	11	a	a	DET
ejpam-1372	960	12	/	/	SYM
ejpam-1372	960	13	p)<π	p)<π	NOUN
ejpam-1372	960	14	,	,	PUNCT
ejpam-1372	960	15	mb	mb	ADP
ejpam-1372	960	16	regularisation	regularisation	NOUN
ejpam-1372	960	17	yields	yield	NOUN
ejpam-1372	960	18	icsc(p	icsc(p	PROPN
ejpam-1372	960	19	,	,	PUNCT
ejpam-1372	960	20	a	a	PRON
ejpam-1372	960	21	)	)	PUNCT
ejpam-1372	960	22	≡	≡	PROPN
ejpam-1372	960	23	1	1	NUM
ejpam-1372	960	24	ap	ap	PROPN
ejpam-1372	960	25	1	1	NUM
ejpam-1372	960	26	+	+	NUM
ejpam-1372	960	27	∫	∫	PROPN
ejpam-1372	960	28	c+i∞	c+i∞	ADJ
ejpam-1372	960	29	c−i∞	c−i∞	PROPN
ejpam-1372	960	30	ds	ds	ADJ
ejpam-1372	960	31	γ(s+	γ(s+	NOUN
ejpam-1372	960	32	1	1	NUM
ejpam-1372	960	33	)	)	PUNCT
ejpam-1372	960	34	e−iπs/2	e−iπs/2	X
ejpam-1372	960	35	e−iπs/2	e−iπs/2	PUNCT
ejpam-1372	960	36	−	−	PROPN
ejpam-1372	960	37	eiπs/2	eiπs/2	PROPN
ejpam-1372	960	38	�	�	PROPN
ejpam-1372	960	39	a	a	DET
ejpam-1372	960	40	pπ	pπ	PROPN
ejpam-1372	960	41	�	�	PROPN
ejpam-1372	960	42	s	s	PART
ejpam-1372	960	43	�	�	PROPN
ejpam-1372	960	44	1−	1−	NUM
ejpam-1372	960	45	21−s	21−s	NUM
ejpam-1372	960	46	�	�	PROPN
ejpam-1372	960	47	ζ(s	ζ(s	PROPN
ejpam-1372	960	48	)	)	PUNCT
ejpam-1372	960	49	!	!	PUNCT
ejpam-1372	960	50	.	.	PUNCT
ejpam-1372	961	1	(	(	PUNCT
ejpam-1372	961	2	111	111	NUM
ejpam-1372	961	3	)	)	PUNCT
ejpam-1372	961	4	in	in	ADP
ejpam-1372	961	5	both	both	PRON
ejpam-1372	961	6	of	of	ADP
ejpam-1372	961	7	these	these	DET
ejpam-1372	961	8	results	result	VERB
ejpam-1372	961	9	the	the	DET
ejpam-1372	961	10	offset	offset	NOUN
ejpam-1372	961	11	c	c	NOUN
ejpam-1372	961	12	is	be	AUX
ejpam-1372	961	13	given	give	VERB
ejpam-1372	961	14	by	by	ADP
ejpam-1372	961	15	0	0	NUM
ejpam-1372	961	16	<	<	X
ejpam-1372	961	17	c	c	NOUN
ejpam-1372	961	18	=	=	SYM
ejpam-1372	961	19	ℜ(s/2)<1	ℜ(s/2)<1	PROPN
ejpam-1372	961	20	.	.	PUNCT
ejpam-1372	962	1	the	the	DET
ejpam-1372	962	2	mb	mb	PROPN
ejpam-1372	962	3	integrals	integral	NOUN
ejpam-1372	962	4	in	in	ADP
ejpam-1372	962	5	the	the	DET
ejpam-1372	962	6	above	above	ADJ
ejpam-1372	962	7	results	result	NOUN
ejpam-1372	962	8	can	can	AUX
ejpam-1372	962	9	be	be	AUX
ejpam-1372	962	10	expressed	express	VERB
ejpam-1372	962	11	more	more	ADV
ejpam-1372	962	12	generally	generally	ADV
ejpam-1372	962	13	as	as	SCONJ
ejpam-1372	962	14	imb	imb	PROPN
ejpam-1372	962	15	(	(	PUNCT
ejpam-1372	962	16	j)≡	j)≡	PROPN
ejpam-1372	962	17	∫	∫	PROPN
ejpam-1372	962	18	c+i∞	c+i∞	PROPN
ejpam-1372	962	19	c−i∞	c−i∞	PROPN
ejpam-1372	962	20	ds	ds	PROPN
ejpam-1372	962	21	γ(s+	γ(s+	ADJ
ejpam-1372	962	22	1)e	1)e	NUM
ejpam-1372	962	23	(	(	PUNCT
ejpam-1372	962	24	j+1/2)iπs	j+1/2)iπs	PROPN
ejpam-1372	962	25	e−iπs/2	e−iπs/2	PART
ejpam-1372	962	26	−	−	PROPN
ejpam-1372	962	27	eiπs/2	eiπs/2	PROPN
ejpam-1372	962	28	�	�	PROPN
ejpam-1372	962	29	a	a	DET
ejpam-1372	962	30	pπ	pπ	PROPN
ejpam-1372	962	31	�	�	PROPN
ejpam-1372	962	32	s	s	PART
ejpam-1372	962	33	�	�	PROPN
ejpam-1372	962	34	1−	1−	NUM
ejpam-1372	962	35	21−s	21−s	NUM
ejpam-1372	962	36	�	�	PROPN
ejpam-1372	962	37	ζ(s	ζ(s	PROPN
ejpam-1372	962	38	)	)	PUNCT
ejpam-1372	962	39	.	.	PUNCT
ejpam-1372	963	1	(	(	PUNCT
ejpam-1372	963	2	112	112	NUM
ejpam-1372	963	3	)	)	PUNCT
ejpam-1372	963	4	hence	hence	ADV
ejpam-1372	963	5	,	,	PUNCT
ejpam-1372	963	6	the	the	DET
ejpam-1372	963	7	mb	mb	NOUN
ejpam-1372	963	8	integral	integral	ADJ
ejpam-1372	963	9	in	in	ADP
ejpam-1372	963	10	equivalence	equivalence	NOUN
ejpam-1372	963	11	(	(	PUNCT
ejpam-1372	963	12	110	110	NUM
ejpam-1372	963	13	)	)	PUNCT
ejpam-1372	963	14	is	be	AUX
ejpam-1372	963	15	basically	basically	ADV
ejpam-1372	963	16	imb(0	imb(0	ADJ
ejpam-1372	963	17	)	)	PUNCT
ejpam-1372	963	18	,	,	PUNCT
ejpam-1372	963	19	while	while	SCONJ
ejpam-1372	963	20	that	that	SCONJ
ejpam-1372	963	21	in	in	ADP
ejpam-1372	963	22	equivalence	equivalence	NOUN
ejpam-1372	963	23	(	(	PUNCT
ejpam-1372	963	24	111	111	NUM
ejpam-1372	963	25	)	)	PUNCT
ejpam-1372	963	26	is	be	AUX
ejpam-1372	963	27	imb(−1	imb(−1	NOUN
ejpam-1372	963	28	)	)	PUNCT
ejpam-1372	963	29	.	.	PUNCT
ejpam-1372	964	1	in	in	ADP
ejpam-1372	964	2	addition	addition	NOUN
ejpam-1372	964	3	,	,	PUNCT
ejpam-1372	964	4	the	the	DET
ejpam-1372	964	5	domain	domain	NOUN
ejpam-1372	964	6	of	of	ADP
ejpam-1372	964	7	convergence	convergence	NOUN
ejpam-1372	964	8	for	for	ADP
ejpam-1372	964	9	the	the	DET
ejpam-1372	964	10	integral	integral	NOUN
ejpam-1372	964	11	in	in	ADP
ejpam-1372	964	12	eq	eq	ADP
ejpam-1372	964	13	.	.	PUNCT
ejpam-1372	965	1	(	(	PUNCT
ejpam-1372	965	2	112	112	NUM
ejpam-1372	965	3	)	)	PUNCT
ejpam-1372	965	4	is	be	AUX
ejpam-1372	965	5	v.	v.	ADP
ejpam-1372	965	6	kowalenko	kowalenko	PROPN
ejpam-1372	965	7	/	/	SYM
ejpam-1372	965	8	eur	eur	PROPN
ejpam-1372	965	9	.	.	PUNCT
ejpam-1372	966	1	j.	j.	PROPN
ejpam-1372	966	2	pure	pure	PROPN
ejpam-1372	966	3	appl	appl	PROPN
ejpam-1372	966	4	.	.	PROPN
ejpam-1372	966	5	math	math	PROPN
ejpam-1372	966	6	,	,	PUNCT
ejpam-1372	966	7	4	4	NUM
ejpam-1372	966	8	(	(	PUNCT
ejpam-1372	966	9	2011	2011	NUM
ejpam-1372	966	10	)	)	PUNCT
ejpam-1372	966	11	,	,	PUNCT
ejpam-1372	966	12	370	370	NUM
ejpam-1372	966	13	-	-	SYM
ejpam-1372	966	14	423	423	NUM
ejpam-1372	966	15	404	404	NUM
ejpam-1372	966	16	−	−	NOUN
ejpam-1372	966	17	(	(	PUNCT
ejpam-1372	966	18	j+	j+	NUM
ejpam-1372	966	19	3/2)π	3/2)π	NUM
ejpam-1372	966	20	<	<	X
ejpam-1372	966	21	arg(a	arg(a	PROPN
ejpam-1372	966	22	/	/	SYM
ejpam-1372	966	23	p)<−	p)<−	PROPN
ejpam-1372	966	24	(	(	PUNCT
ejpam-1372	966	25	j−	j−	PROPN
ejpam-1372	966	26	1/2)π	1/2)π	NUM
ejpam-1372	966	27	,	,	PUNCT
ejpam-1372	966	28	which	which	PRON
ejpam-1372	966	29	means	mean	VERB
ejpam-1372	966	30	that	that	SCONJ
ejpam-1372	966	31	both	both	DET
ejpam-1372	966	32	imb(0	imb(0	NOUN
ejpam-1372	966	33	)	)	PUNCT
ejpam-1372	966	34	and	and	CCONJ
ejpam-1372	966	35	imb(−1	imb(−1	NOUN
ejpam-1372	966	36	)	)	PUNCT
ejpam-1372	966	37	are	be	AUX
ejpam-1372	966	38	valid	valid	ADJ
ejpam-1372	966	39	over	over	ADP
ejpam-1372	966	40	the	the	DET
ejpam-1372	966	41	common	common	ADJ
ejpam-1372	966	42	region	region	NOUN
ejpam-1372	966	43	or	or	CCONJ
ejpam-1372	966	44	sector	sector	NOUN
ejpam-1372	966	45	given	give	VERB
ejpam-1372	966	46	by	by	ADP
ejpam-1372	966	47	−π/2	−π/2	PROPN
ejpam-1372	966	48	<	<	X
ejpam-1372	966	49	arg(a	arg(a	PROPN
ejpam-1372	966	50	/	/	SYM
ejpam-1372	966	51	p)<π/2	p)<π/2	ADJ
ejpam-1372	966	52	.	.	PUNCT
ejpam-1372	967	1	on	on	ADP
ejpam-1372	967	2	the	the	DET
ejpam-1372	967	3	other	other	ADJ
ejpam-1372	967	4	hand	hand	NOUN
ejpam-1372	967	5	,	,	PUNCT
ejpam-1372	967	6	the	the	DET
ejpam-1372	967	7	difference	difference	NOUN
ejpam-1372	967	8	between	between	ADP
ejpam-1372	967	9	the	the	DET
ejpam-1372	967	10	mb	mb	PROPN
ejpam-1372	967	11	integrals	integral	NOUN
ejpam-1372	967	12	is	be	AUX
ejpam-1372	967	13	found	find	VERB
ejpam-1372	967	14	from	from	ADP
ejpam-1372	967	15	the	the	DET
ejpam-1372	967	16	theory	theory	NOUN
ejpam-1372	967	17	of	of	ADP
ejpam-1372	967	18	mellin	mellin	PROPN
ejpam-1372	967	19	transforms	transform	VERB
ejpam-1372	967	20	[	[	X
ejpam-1372	967	21	25	25	NUM
ejpam-1372	967	22	]	]	PUNCT
ejpam-1372	967	23	to	to	PART
ejpam-1372	967	24	be	be	AUX
ejpam-1372	967	25	∆i	∆i	PROPN
ejpam-1372	967	26	(	(	PUNCT
ejpam-1372	967	27	−1.0	−1.0	PROPN
ejpam-1372	967	28	)	)	PUNCT
ejpam-1372	968	1	mb	mb	PROPN
ejpam-1372	968	2	=	=	SYM
ejpam-1372	968	3	imb(−1)−	imb(−1)−	PROPN
ejpam-1372	968	4	imb(0	imb(0	NOUN
ejpam-1372	968	5	)	)	PUNCT
ejpam-1372	969	1	=	=	SYM
ejpam-1372	969	2	2πi	2πi	PROPN
ejpam-1372	969	3	�	�	PROPN
ejpam-1372	969	4	pπ	pπ	VERB
ejpam-1372	969	5	a	a	DET
ejpam-1372	969	6	�	�	PROPN
ejpam-1372	969	7	e−pπ	e−pπ	PROPN
ejpam-1372	969	8	/	/	SYM
ejpam-1372	969	9	a	a	PRON
ejpam-1372	969	10	(	(	PUNCT
ejpam-1372	969	11	e−pπ	e−pπ	NOUN
ejpam-1372	969	12	/	/	SYM
ejpam-1372	969	13	a	a	DET
ejpam-1372	969	14	+	+	X
ejpam-1372	969	15	1)2	1)2	NUM
ejpam-1372	969	16	.	.	PUNCT
ejpam-1372	970	1	(	(	PUNCT
ejpam-1372	970	2	113	113	NUM
ejpam-1372	970	3	)	)	PUNCT
ejpam-1372	970	4	therefore	therefore	ADV
ejpam-1372	970	5	,	,	PUNCT
ejpam-1372	970	6	for	for	ADP
ejpam-1372	970	7	n	n	PRON
ejpam-1372	970	8	=	=	SYM
ejpam-1372	970	9	1	1	NUM
ejpam-1372	970	10	and	and	CCONJ
ejpam-1372	970	11	−π/2	−π/2	PROPN
ejpam-1372	970	12	<	<	X
ejpam-1372	970	13	arg(a	arg(a	PROPN
ejpam-1372	970	14	/	/	SYM
ejpam-1372	970	15	p)<0	p)<0	PROPN
ejpam-1372	970	16	,	,	PUNCT
ejpam-1372	970	17	the	the	DET
ejpam-1372	970	18	regularised	regularise	VERB
ejpam-1372	970	19	value	value	NOUN
ejpam-1372	970	20	of	of	ADP
ejpam-1372	970	21	icsc(p	icsc(p	PROPN
ejpam-1372	970	22	,	,	PUNCT
ejpam-1372	970	23	a	a	PRON
ejpam-1372	970	24	)	)	PUNCT
ejpam-1372	970	25	can	can	AUX
ejpam-1372	970	26	also	also	ADV
ejpam-1372	970	27	be	be	AUX
ejpam-1372	970	28	written	write	VERB
ejpam-1372	970	29	as	as	ADP
ejpam-1372	970	30	icsc(p	icsc(p	PROPN
ejpam-1372	970	31	,	,	PUNCT
ejpam-1372	970	32	a	a	PRON
ejpam-1372	970	33	)	)	PUNCT
ejpam-1372	970	34	≡	≡	PROPN
ejpam-1372	970	35	1	1	NUM
ejpam-1372	970	36	ap	ap	PROPN
ejpam-1372	970	37	1	1	NUM
ejpam-1372	970	38	+	+	NUM
ejpam-1372	970	39	∫	∫	PROPN
ejpam-1372	970	40	c+i∞	c+i∞	ADJ
ejpam-1372	970	41	c−i∞	c−i∞	PROPN
ejpam-1372	970	42	ds	ds	PROPN
ejpam-1372	970	43	γ(s+	γ(s+	VERB
ejpam-1372	970	44	1)e−iπs/2	1)e−iπs/2	NUM
ejpam-1372	970	45	e−i	e−i	NOUN
ejpam-1372	970	46	pis/2−	pis/2−	NUM
ejpam-1372	970	47	eiπs/2	eiπs/2	PROPN
ejpam-1372	970	48	�	�	PROPN
ejpam-1372	970	49	a	a	DET
ejpam-1372	970	50	pπ	pπ	PROPN
ejpam-1372	970	51	�	�	PROPN
ejpam-1372	970	52	s	s	PART
ejpam-1372	970	53	�	�	PROPN
ejpam-1372	970	54	1−	1−	NUM
ejpam-1372	970	55	21−s	21−s	NUM
ejpam-1372	970	56	�	�	PROPN
ejpam-1372	970	57	ζ(s	ζ(s	PROPN
ejpam-1372	970	58	)	)	PUNCT
ejpam-1372	970	59	!	!	PUNCT
ejpam-1372	971	1	−	−	PROPN
ejpam-1372	971	2	2πi	2πi	PROPN
ejpam-1372	971	3	�	�	PROPN
ejpam-1372	971	4	pπ	pπ	VERB
ejpam-1372	971	5	a	a	DET
ejpam-1372	971	6	�	�	PROPN
ejpam-1372	971	7	e−pπ	e−pπ	PROPN
ejpam-1372	971	8	/	/	SYM
ejpam-1372	971	9	a	a	PRON
ejpam-1372	971	10	(	(	PUNCT
ejpam-1372	971	11	e−pπ	e−pπ	NOUN
ejpam-1372	971	12	/	/	SYM
ejpam-1372	971	13	a	a	DET
ejpam-1372	971	14	+	+	X
ejpam-1372	971	15	1)2	1)2	NUM
ejpam-1372	971	16	,	,	PUNCT
ejpam-1372	971	17	(	(	PUNCT
ejpam-1372	971	18	114	114	NUM
ejpam-1372	971	19	)	)	PUNCT
ejpam-1372	971	20	while	while	SCONJ
ejpam-1372	971	21	for	for	ADP
ejpam-1372	971	22	n=1	n=1	PUNCT
ejpam-1372	971	23	and	and	CCONJ
ejpam-1372	971	24	0	0	NUM
ejpam-1372	971	25	<	<	X
ejpam-1372	971	26	arg(a	arg(a	X
ejpam-1372	971	27	/	/	SYM
ejpam-1372	971	28	p)<π/2	p)<π/2	ADJ
ejpam-1372	971	29	,	,	PUNCT
ejpam-1372	971	30	we	we	PRON
ejpam-1372	971	31	find	find	VERB
ejpam-1372	971	32	that	that	SCONJ
ejpam-1372	971	33	icsc(p	icsc(p	NOUN
ejpam-1372	971	34	,	,	PUNCT
ejpam-1372	971	35	a	a	PRON
ejpam-1372	971	36	)	)	PUNCT
ejpam-1372	971	37	≡	≡	PROPN
ejpam-1372	971	38	1	1	NUM
ejpam-1372	971	39	ap	ap	PROPN
ejpam-1372	971	40	1	1	NUM
ejpam-1372	971	41	+	+	NUM
ejpam-1372	971	42	∫	∫	PROPN
ejpam-1372	971	43	c+i∞	c+i∞	ADJ
ejpam-1372	971	44	c−i∞	c−i∞	PROPN
ejpam-1372	971	45	ds	ds	PROPN
ejpam-1372	971	46	γ(s+	γ(s+	VERB
ejpam-1372	971	47	1)eiπs/2	1)eiπs/2	NUM
ejpam-1372	971	48	e−iπs/2	e−iπs/2	PUNCT
ejpam-1372	971	49	−	−	PROPN
ejpam-1372	971	50	eiπs/2	eiπs/2	PROPN
ejpam-1372	971	51	�	�	PROPN
ejpam-1372	971	52	a	a	DET
ejpam-1372	971	53	pπ	pπ	PROPN
ejpam-1372	971	54	�	�	PROPN
ejpam-1372	971	55	s	s	PART
ejpam-1372	971	56	�	�	PROPN
ejpam-1372	971	57	1−	1−	NUM
ejpam-1372	971	58	21−s	21−s	NUM
ejpam-1372	971	59	�	�	PROPN
ejpam-1372	971	60	ζ(s	ζ(s	PROPN
ejpam-1372	971	61	)	)	PUNCT
ejpam-1372	971	62	!	!	PUNCT
ejpam-1372	972	1	+	+	CCONJ
ejpam-1372	972	2	2πi	2πi	ADJ
ejpam-1372	972	3	�	�	PROPN
ejpam-1372	972	4	pπ	pπ	VERB
ejpam-1372	972	5	a	a	DET
ejpam-1372	972	6	�	�	PROPN
ejpam-1372	972	7	e−pπ	e−pπ	PROPN
ejpam-1372	972	8	/	/	SYM
ejpam-1372	972	9	a	a	PRON
ejpam-1372	972	10	(	(	PUNCT
ejpam-1372	972	11	e−pπ	e−pπ	NOUN
ejpam-1372	972	12	/	/	SYM
ejpam-1372	972	13	a	a	DET
ejpam-1372	972	14	+	+	X
ejpam-1372	972	15	1)2	1)2	NUM
ejpam-1372	972	16	.	.	PUNCT
ejpam-1372	973	1	(	(	PUNCT
ejpam-1372	973	2	115	115	NUM
ejpam-1372	973	3	)	)	PUNCT
ejpam-1372	973	4	by	by	ADP
ejpam-1372	973	5	combining	combine	VERB
ejpam-1372	973	6	equivalence	equivalence	NOUN
ejpam-1372	973	7	(	(	PUNCT
ejpam-1372	973	8	115	115	NUM
ejpam-1372	973	9	)	)	PUNCT
ejpam-1372	973	10	with	with	ADP
ejpam-1372	973	11	equivalence	equivalence	NOUN
ejpam-1372	973	12	(	(	PUNCT
ejpam-1372	973	13	110	110	NUM
ejpam-1372	973	14	)	)	PUNCT
ejpam-1372	973	15	or	or	CCONJ
ejpam-1372	973	16	equivalence	equivalence	NOUN
ejpam-1372	973	17	(	(	PUNCT
ejpam-1372	973	18	114	114	NUM
ejpam-1372	973	19	)	)	PUNCT
ejpam-1372	973	20	with	with	ADP
ejpam-1372	973	21	equivalence	equivalence	NOUN
ejpam-1372	973	22	(	(	PUNCT
ejpam-1372	973	23	111	111	NUM
ejpam-1372	973	24	)	)	PUNCT
ejpam-1372	973	25	,	,	PUNCT
ejpam-1372	973	26	and	and	CCONJ
ejpam-1372	973	27	then	then	ADV
ejpam-1372	973	28	comparing	compare	VERB
ejpam-1372	973	29	either	either	CCONJ
ejpam-1372	973	30	result	result	NOUN
ejpam-1372	973	31	with	with	ADP
ejpam-1372	973	32	the	the	DET
ejpam-1372	973	33	regularised	regularise	VERB
ejpam-1372	973	34	value	value	NOUN
ejpam-1372	973	35	of	of	ADP
ejpam-1372	973	36	a	a	DET
ejpam-1372	973	37	general	general	ADJ
ejpam-1372	973	38	type	type	NOUN
ejpam-1372	973	39	ii	ii	PROPN
ejpam-1372	973	40	terminant	terminant	NOUN
ejpam-1372	973	41	,	,	PUNCT
ejpam-1372	973	42	viz	viz	PROPN
ejpam-1372	973	43	.	.	PUNCT
ejpam-1372	973	44	equivalence	equivalence	NOUN
ejpam-1372	973	45	(	(	PUNCT
ejpam-1372	973	46	102	102	NUM
ejpam-1372	973	47	)	)	PUNCT
ejpam-1372	973	48	,	,	PUNCT
ejpam-1372	973	49	we	we	PRON
ejpam-1372	973	50	see	see	VERB
ejpam-1372	973	51	that	that	SCONJ
ejpam-1372	973	52	in	in	ADP
ejpam-1372	973	53	this	this	DET
ejpam-1372	973	54	anomalous	anomalous	ADJ
ejpam-1372	973	55	case	case	NOUN
ejpam-1372	973	56	where	where	SCONJ
ejpam-1372	973	57	the	the	DET
ejpam-1372	973	58	asymptotic	asymptotic	ADJ
ejpam-1372	973	59	expansion	expansion	NOUN
ejpam-1372	973	60	has	have	AUX
ejpam-1372	973	61	been	be	AUX
ejpam-1372	973	62	derived	derive	VERB
ejpam-1372	973	63	initially	initially	ADV
ejpam-1372	973	64	in	in	ADP
ejpam-1372	973	65	a	a	DET
ejpam-1372	973	66	stokes	stoke	NOUN
ejpam-1372	973	67	sector	sector	NOUN
ejpam-1372	973	68	rather	rather	ADV
ejpam-1372	973	69	than	than	ADP
ejpam-1372	973	70	on	on	ADP
ejpam-1372	973	71	a	a	DET
ejpam-1372	973	72	primary	primary	ADJ
ejpam-1372	973	73	stokes	stoke	NOUN
ejpam-1372	973	74	line	line	NOUN
ejpam-1372	973	75	,	,	PUNCT
ejpam-1372	973	76	there	there	PRON
ejpam-1372	973	77	is	be	VERB
ejpam-1372	973	78	a	a	DET
ejpam-1372	973	79	discontinuity	discontinuity	NOUN
ejpam-1372	973	80	on	on	ADP
ejpam-1372	973	81	reaching	reach	VERB
ejpam-1372	973	82	the	the	DET
ejpam-1372	973	83	line	line	NOUN
ejpam-1372	973	84	at	at	ADP
ejpam-1372	973	85	arg(a	arg(a	PROPN
ejpam-1372	973	86	/	/	SYM
ejpam-1372	973	87	p)=0	p)=0	ADJ
ejpam-1372	973	88	,	,	PUNCT
ejpam-1372	973	89	while	while	SCONJ
ejpam-1372	973	90	on	on	ADP
ejpam-1372	973	91	moving	move	VERB
ejpam-1372	973	92	to	to	ADP
ejpam-1372	973	93	the	the	DET
ejpam-1372	973	94	adjacent	adjacent	ADJ
ejpam-1372	973	95	stokes	stoke	NOUN
ejpam-1372	973	96	sector	sector	NOUN
ejpam-1372	973	97	twice	twice	DET
ejpam-1372	973	98	the	the	DET
ejpam-1372	973	99	discontinuity	discontinuity	NOUN
ejpam-1372	973	100	applies	apply	VERB
ejpam-1372	973	101	.	.	PUNCT
ejpam-1372	974	1	previously	previously	ADV
ejpam-1372	974	2	,	,	PUNCT
ejpam-1372	974	3	we	we	PRON
ejpam-1372	974	4	found	find	VERB
ejpam-1372	974	5	that	that	SCONJ
ejpam-1372	974	6	half	half	DET
ejpam-1372	974	7	the	the	DET
ejpam-1372	974	8	difference	difference	NOUN
ejpam-1372	974	9	between	between	ADP
ejpam-1372	974	10	the	the	DET
ejpam-1372	974	11	mb	mb	PROPN
ejpam-1372	974	12	integrals	integral	NOUN
ejpam-1372	974	13	was	be	AUX
ejpam-1372	974	14	involved	involve	VERB
ejpam-1372	974	15	when	when	SCONJ
ejpam-1372	974	16	moving	move	VERB
ejpam-1372	974	17	in	in	ADV
ejpam-1372	974	18	either	either	DET
ejpam-1372	974	19	direction	direction	NOUN
ejpam-1372	974	20	off	off	ADP
ejpam-1372	974	21	the	the	DET
ejpam-1372	974	22	primary	primary	ADJ
ejpam-1372	974	23	stokes	stokes	PROPN
ejpam-1372	974	24	line	line	NOUN
ejpam-1372	974	25	.	.	PUNCT
ejpam-1372	975	1	now	now	ADV
ejpam-1372	975	2	half	half	DET
ejpam-1372	975	3	the	the	DET
ejpam-1372	975	4	discontinuity	discontinuity	NOUN
ejpam-1372	975	5	occurs	occur	VERB
ejpam-1372	975	6	on	on	ADP
ejpam-1372	975	7	reaching	reach	VERB
ejpam-1372	975	8	the	the	DET
ejpam-1372	975	9	line	line	NOUN
ejpam-1372	975	10	and	and	CCONJ
ejpam-1372	975	11	the	the	DET
ejpam-1372	975	12	entire	entire	ADJ
ejpam-1372	975	13	discontinuity	discontinuity	NOUN
ejpam-1372	975	14	occurs	occur	VERB
ejpam-1372	975	15	when	when	SCONJ
ejpam-1372	975	16	moving	move	VERB
ejpam-1372	975	17	off	off	ADP
ejpam-1372	975	18	the	the	DET
ejpam-1372	975	19	line	line	NOUN
ejpam-1372	975	20	into	into	ADP
ejpam-1372	975	21	the	the	DET
ejpam-1372	975	22	adjacent	adjacent	ADJ
ejpam-1372	975	23	stokes	stoke	NOUN
ejpam-1372	975	24	sector	sector	NOUN
ejpam-1372	975	25	.	.	PUNCT
ejpam-1372	976	1	whether	whether	SCONJ
ejpam-1372	976	2	half	half	NOUN
ejpam-1372	976	3	or	or	CCONJ
ejpam-1372	976	4	the	the	DET
ejpam-1372	976	5	entire	entire	ADJ
ejpam-1372	976	6	discontinuity	discontinuity	NOUN
ejpam-1372	976	7	is	be	AUX
ejpam-1372	976	8	involved	involve	VERB
ejpam-1372	976	9	is	be	AUX
ejpam-1372	976	10	connected	connect	VERB
ejpam-1372	976	11	to	to	ADP
ejpam-1372	976	12	whether	whether	SCONJ
ejpam-1372	976	13	there	there	PRON
ejpam-1372	976	14	is	be	VERB
ejpam-1372	976	15	a	a	DET
ejpam-1372	976	16	semi	semi	ADJ
ejpam-1372	976	17	-	-	ADJ
ejpam-1372	976	18	residue	residue	ADJ
ejpam-1372	976	19	or	or	CCONJ
ejpam-1372	976	20	full	full	ADJ
ejpam-1372	976	21	residue	residue	NOUN
ejpam-1372	976	22	around	around	ADP
ejpam-1372	976	23	the	the	DET
ejpam-1372	976	24	singularity	singularity	NOUN
ejpam-1372	976	25	.	.	PUNCT
ejpam-1372	977	1	although	although	SCONJ
ejpam-1372	977	2	icsc(p	icsc(p	PROPN
ejpam-1372	977	3	,	,	PUNCT
ejpam-1372	977	4	a	a	PRON
ejpam-1372	977	5	)	)	PUNCT
ejpam-1372	977	6	is	be	AUX
ejpam-1372	977	7	undefined	undefined	ADJ
ejpam-1372	977	8	along	along	ADP
ejpam-1372	977	9	the	the	DET
ejpam-1372	977	10	real	real	ADJ
ejpam-1372	977	11	axis	axis	NOUN
ejpam-1372	977	12	,	,	PUNCT
ejpam-1372	977	13	its	its	PRON
ejpam-1372	977	14	cauchy	cauchy	ADJ
ejpam-1372	977	15	principal	principal	ADJ
ejpam-1372	977	16	value	value	NOUN
ejpam-1372	977	17	,	,	PUNCT
ejpam-1372	977	18	however	however	ADV
ejpam-1372	977	19	,	,	PUNCT
ejpam-1372	977	20	exists	exist	VERB
ejpam-1372	977	21	.	.	PUNCT
ejpam-1372	978	1	we	we	PRON
ejpam-1372	978	2	can	can	AUX
ejpam-1372	978	3	obtain	obtain	VERB
ejpam-1372	978	4	this	this	DET
ejpam-1372	978	5	value	value	NOUN
ejpam-1372	978	6	simply	simply	ADV
ejpam-1372	978	7	by	by	ADP
ejpam-1372	978	8	averaging	average	VERB
ejpam-1372	978	9	equivalences	equivalence	NOUN
ejpam-1372	978	10	(	(	PUNCT
ejpam-1372	978	11	110	110	NUM
ejpam-1372	978	12	)	)	PUNCT
ejpam-1372	978	13	and	and	CCONJ
ejpam-1372	978	14	(	(	PUNCT
ejpam-1372	978	15	111	111	NUM
ejpam-1372	978	16	)	)	PUNCT
ejpam-1372	978	17	or	or	CCONJ
ejpam-1372	978	18	by	by	ADP
ejpam-1372	978	19	evaluating	evaluate	VERB
ejpam-1372	978	20	either	either	DET
ejpam-1372	978	21	equivalence	equivalence	NOUN
ejpam-1372	978	22	(	(	PUNCT
ejpam-1372	978	23	114	114	NUM
ejpam-1372	978	24	)	)	PUNCT
ejpam-1372	978	25	or	or	CCONJ
ejpam-1372	978	26	(	(	PUNCT
ejpam-1372	978	27	115	115	NUM
ejpam-1372	978	28	)	)	PUNCT
ejpam-1372	978	29	with	with	ADP
ejpam-1372	978	30	only	only	ADV
ejpam-1372	978	31	half	half	NOUN
ejpam-1372	978	32	of	of	ADP
ejpam-1372	978	33	their	their	PRON
ejpam-1372	978	34	second	second	ADJ
ejpam-1372	978	35	terms	term	NOUN
ejpam-1372	978	36	on	on	ADP
ejpam-1372	978	37	the	the	DET
ejpam-1372	978	38	rhs	rhs	PROPN
ejpam-1372	978	39	.	.	PUNCT
ejpam-1372	979	1	for	for	ADP
ejpam-1372	979	2	more	more	ADJ
ejpam-1372	979	3	details	detail	NOUN
ejpam-1372	979	4	the	the	DET
ejpam-1372	979	5	reader	reader	NOUN
ejpam-1372	979	6	is	be	AUX
ejpam-1372	979	7	referred	refer	VERB
ejpam-1372	979	8	to	to	AUX
ejpam-1372	979	9	ref	ref	VERB
ejpam-1372	979	10	.	.	PUNCT
ejpam-1372	980	1	[	[	X
ejpam-1372	980	2	19	19	NUM
ejpam-1372	980	3	]	]	X
ejpam-1372	980	4	,	,	PUNCT
ejpam-1372	980	5	where	where	SCONJ
ejpam-1372	980	6	a	a	DET
ejpam-1372	980	7	spectacular	spectacular	ADJ
ejpam-1372	980	8	numerical	numerical	ADJ
ejpam-1372	980	9	study	study	NOUN
ejpam-1372	980	10	involving	involve	VERB
ejpam-1372	980	11	these	these	DET
ejpam-1372	980	12	forms	form	NOUN
ejpam-1372	980	13	for	for	ADP
ejpam-1372	980	14	the	the	DET
ejpam-1372	980	15	regularised	regularise	VERB
ejpam-1372	980	16	value	value	NOUN
ejpam-1372	980	17	of	of	ADP
ejpam-1372	980	18	icsc(p	icsc(p	PROPN
ejpam-1372	980	19	,	,	PUNCT
ejpam-1372	980	20	a	a	PRON
ejpam-1372	980	21	)	)	PUNCT
ejpam-1372	980	22	is	be	AUX
ejpam-1372	980	23	presented	present	VERB
ejpam-1372	980	24	.	.	PUNCT
ejpam-1372	981	1	11	11	NUM
ejpam-1372	981	2	.	.	PUNCT
ejpam-1372	981	3	examples	example	NOUN
ejpam-1372	981	4	by	by	ADP
ejpam-1372	981	5	presenting	present	VERB
ejpam-1372	981	6	numerical	numerical	ADJ
ejpam-1372	981	7	examples	example	NOUN
ejpam-1372	981	8	to	to	ADP
ejpam-1372	981	9	extremely	extremely	ADV
ejpam-1372	981	10	high	high	ADJ
ejpam-1372	981	11	precision	precision	NOUN
ejpam-1372	981	12	,	,	PUNCT
ejpam-1372	981	13	we	we	PRON
ejpam-1372	981	14	shall	shall	AUX
ejpam-1372	981	15	not	not	PART
ejpam-1372	981	16	only	only	ADV
ejpam-1372	981	17	be	be	AUX
ejpam-1372	981	18	able	able	ADJ
ejpam-1372	981	19	to	to	PART
ejpam-1372	981	20	verify	verify	VERB
ejpam-1372	981	21	the	the	DET
ejpam-1372	981	22	various	various	ADJ
ejpam-1372	981	23	expressions	expression	NOUN
ejpam-1372	981	24	for	for	ADP
ejpam-1372	981	25	the	the	DET
ejpam-1372	981	26	regularised	regularise	VERB
ejpam-1372	981	27	value	value	NOUN
ejpam-1372	981	28	of	of	ADP
ejpam-1372	981	29	both	both	DET
ejpam-1372	981	30	type	type	NOUN
ejpam-1372	981	31	i	i	PRON
ejpam-1372	981	32	and	and	CCONJ
ejpam-1372	981	33	ii	ii	PROPN
ejpam-1372	981	34	series	series	NOUN
ejpam-1372	981	35	,	,	PUNCT
ejpam-1372	981	36	but	but	CCONJ
ejpam-1372	982	1	v.	v.	ADP
ejpam-1372	982	2	kowalenko	kowalenko	PROPN
ejpam-1372	982	3	/	/	SYM
ejpam-1372	982	4	eur	eur	PROPN
ejpam-1372	982	5	.	.	PUNCT
ejpam-1372	983	1	j.	j.	PROPN
ejpam-1372	983	2	pure	pure	PROPN
ejpam-1372	983	3	appl	appl	PROPN
ejpam-1372	983	4	.	.	PROPN
ejpam-1372	983	5	math	math	PROPN
ejpam-1372	983	6	,	,	PUNCT
ejpam-1372	983	7	4	4	NUM
ejpam-1372	983	8	(	(	PUNCT
ejpam-1372	983	9	2011	2011	NUM
ejpam-1372	983	10	)	)	PUNCT
ejpam-1372	983	11	,	,	PUNCT
ejpam-1372	983	12	370	370	NUM
ejpam-1372	983	13	-	-	SYM
ejpam-1372	983	14	423	423	NUM
ejpam-1372	983	15	405	405	NUM
ejpam-1372	983	16	we	we	PRON
ejpam-1372	983	17	shall	shall	AUX
ejpam-1372	983	18	also	also	ADV
ejpam-1372	983	19	be	be	AUX
ejpam-1372	983	20	in	in	ADP
ejpam-1372	983	21	a	a	DET
ejpam-1372	983	22	position	position	NOUN
ejpam-1372	983	23	to	to	PART
ejpam-1372	983	24	see	see	VERB
ejpam-1372	983	25	for	for	ADP
ejpam-1372	983	26	ourselves	ourselves	PRON
ejpam-1372	983	27	whether	whether	SCONJ
ejpam-1372	983	28	euler	euler	VERB
ejpam-1372	983	29	’s	’s	PART
ejpam-1372	983	30	“	"	PUNCT
ejpam-1372	983	31	unorthodox	unorthodox	ADJ
ejpam-1372	983	32	”	"	PUNCT
ejpam-1372	983	33	views	view	NOUN
ejpam-1372	983	34	are	be	AUX
ejpam-1372	983	35	indeed	indeed	ADV
ejpam-1372	983	36	valid	valid	ADJ
ejpam-1372	983	37	or	or	CCONJ
ejpam-1372	983	38	not	not	PART
ejpam-1372	983	39	.	.	PUNCT
ejpam-1372	984	1	underlying	underlie	VERB
ejpam-1372	984	2	numerical	numerical	ADJ
ejpam-1372	984	3	demonstrations	demonstration	NOUN
ejpam-1372	984	4	is	be	AUX
ejpam-1372	984	5	the	the	DET
ejpam-1372	984	6	fact	fact	NOUN
ejpam-1372	984	7	that	that	SCONJ
ejpam-1372	984	8	numbers	number	NOUN
ejpam-1372	984	9	do	do	AUX
ejpam-1372	984	10	not	not	PART
ejpam-1372	984	11	lie	lie	VERB
ejpam-1372	984	12	.	.	PUNCT
ejpam-1372	985	1	this	this	PRON
ejpam-1372	985	2	is	be	AUX
ejpam-1372	985	3	generally	generally	ADV
ejpam-1372	985	4	ignored	ignore	VERB
ejpam-1372	985	5	by	by	ADP
ejpam-1372	985	6	practitioners	practitioner	NOUN
ejpam-1372	985	7	in	in	ADP
ejpam-1372	985	8	standard	standard	ADJ
ejpam-1372	985	9	asymptotics	asymptotic	NOUN
ejpam-1372	985	10	,	,	PUNCT
ejpam-1372	985	11	who	who	PRON
ejpam-1372	985	12	instead	instead	ADV
ejpam-1372	985	13	rely	rely	VERB
ejpam-1372	985	14	on	on	ADP
ejpam-1372	985	15	“	"	PUNCT
ejpam-1372	985	16	proving	prove	VERB
ejpam-1372	985	17	theorems	theorem	NOUN
ejpam-1372	985	18	”	"	PUNCT
ejpam-1372	985	19	by	by	ADP
ejpam-1372	985	20	invoking	invoke	VERB
ejpam-1372	985	21	such	such	ADJ
ejpam-1372	985	22	vague	vague	ADJ
ejpam-1372	985	23	symbols	symbol	NOUN
ejpam-1372	985	24	as	as	ADP
ejpam-1372	985	25	∼	∼	NOUN
ejpam-1372	985	26	,	,	PUNCT
ejpam-1372	985	27	≈	≈	PROPN
ejpam-1372	985	28	,	,	PUNCT
ejpam-1372	985	29	o	o	NOUN
ejpam-1372	985	30	(	(	PUNCT
ejpam-1372	985	31	)	)	PUNCT
ejpam-1372	985	32	,	,	PUNCT
ejpam-1372	985	33	o	o	NOUN
ejpam-1372	985	34	(	(	PUNCT
ejpam-1372	985	35	)	)	PUNCT
ejpam-1372	985	36	,	,	PUNCT
ejpam-1372	985	37	+	+	CCONJ
ejpam-1372	985	38	.	.	PUNCT
ejpam-1372	985	39	.	.	PUNCT
ejpam-1372	986	1	.	.	PUNCT
ejpam-1372	986	2	,	,	PUNCT
ejpam-1372	986	3	≥	≥	NUM
ejpam-1372	986	4	,	,	PUNCT
ejpam-1372	986	5	and	and	CCONJ
ejpam-1372	986	6	≤.	≤.	NOUN
ejpam-1372	986	7	as	as	ADP
ejpam-1372	986	8	a	a	DET
ejpam-1372	986	9	consequence	consequence	NOUN
ejpam-1372	987	1	,	,	PUNCT
ejpam-1372	987	2	no	no	DET
ejpam-1372	987	3	one	one	NOUN
ejpam-1372	987	4	knows	know	VERB
ejpam-1372	987	5	exactly	exactly	ADV
ejpam-1372	987	6	just	just	ADV
ejpam-1372	987	7	how	how	SCONJ
ejpam-1372	987	8	accurate	accurate	ADJ
ejpam-1372	987	9	the	the	DET
ejpam-1372	987	10	resulting	result	VERB
ejpam-1372	987	11	expansions	expansion	NOUN
ejpam-1372	987	12	are	be	AUX
ejpam-1372	987	13	or	or	CCONJ
ejpam-1372	987	14	even	even	ADV
ejpam-1372	987	15	the	the	DET
ejpam-1372	987	16	specific	specific	ADJ
ejpam-1372	987	17	ranges	range	NOUN
ejpam-1372	987	18	over	over	ADP
ejpam-1372	987	19	which	which	PRON
ejpam-1372	987	20	they	they	PRON
ejpam-1372	987	21	are	be	AUX
ejpam-1372	987	22	valid	valid	ADJ
ejpam-1372	987	23	.	.	PUNCT
ejpam-1372	988	1	as	as	SCONJ
ejpam-1372	988	2	indicated	indicate	VERB
ejpam-1372	988	3	earlier	early	ADV
ejpam-1372	988	4	,	,	PUNCT
ejpam-1372	988	5	it	it	PRON
ejpam-1372	988	6	is	be	AUX
ejpam-1372	988	7	these	these	DET
ejpam-1372	988	8	deficiencies	deficiency	NOUN
ejpam-1372	988	9	arising	arise	VERB
ejpam-1372	988	10	from	from	ADP
ejpam-1372	988	11	the	the	DET
ejpam-1372	988	12	overly	overly	ADV
ejpam-1372	988	13	-	-	PUNCT
ejpam-1372	988	14	permissive	permissive	ADJ
ejpam-1372	988	15	poincaré	poincaré	NOUN
ejpam-1372	988	16	prescription	prescription	NOUN
ejpam-1372	988	17	that	that	PRON
ejpam-1372	988	18	are	be	AUX
ejpam-1372	988	19	responsible	responsible	ADJ
ejpam-1372	988	20	for	for	ADP
ejpam-1372	988	21	giving	give	VERB
ejpam-1372	988	22	asymptotics	asymptotic	NOUN
ejpam-1372	988	23	a	a	DET
ejpam-1372	988	24	bad	bad	ADJ
ejpam-1372	988	25	name	name	NOUN
ejpam-1372	988	26	.	.	PUNCT
ejpam-1372	989	1	on	on	ADP
ejpam-1372	989	2	the	the	DET
ejpam-1372	989	3	other	other	ADJ
ejpam-1372	989	4	hand	hand	NOUN
ejpam-1372	989	5	,	,	PUNCT
ejpam-1372	989	6	an	an	DET
ejpam-1372	989	7	effective	effective	ADJ
ejpam-1372	989	8	numerical	numerical	ADJ
ejpam-1372	989	9	study	study	NOUN
ejpam-1372	989	10	such	such	ADJ
ejpam-1372	989	11	as	as	ADP
ejpam-1372	989	12	that	that	PRON
ejpam-1372	989	13	presented	present	VERB
ejpam-1372	989	14	in	in	ADP
ejpam-1372	989	15	this	this	DET
ejpam-1372	989	16	section	section	NOUN
ejpam-1372	989	17	is	be	AUX
ejpam-1372	989	18	able	able	ADJ
ejpam-1372	989	19	to	to	PART
ejpam-1372	989	20	expose	expose	VERB
ejpam-1372	989	21	the	the	DET
ejpam-1372	989	22	deficiencies	deficiency	NOUN
ejpam-1372	989	23	in	in	ADP
ejpam-1372	989	24	standard	standard	ADJ
ejpam-1372	989	25	asymptotics	asymptotic	NOUN
ejpam-1372	989	26	,	,	PUNCT
ejpam-1372	989	27	where	where	SCONJ
ejpam-1372	989	28	a	a	DET
ejpam-1372	989	29	so	so	ADV
ejpam-1372	989	30	-	-	PUNCT
ejpam-1372	989	31	called	call	VERB
ejpam-1372	989	32	mathematical	mathematical	ADJ
ejpam-1372	989	33	proof	proof	NOUN
ejpam-1372	989	34	can	can	AUX
ejpam-1372	989	35	not	not	PART
ejpam-1372	989	36	.	.	PUNCT
ejpam-1372	990	1	in	in	ADP
ejpam-1372	990	2	fact	fact	NOUN
ejpam-1372	990	3	,	,	PUNCT
ejpam-1372	990	4	in	in	ADP
ejpam-1372	990	5	these	these	DET
ejpam-1372	990	6	times	time	NOUN
ejpam-1372	990	7	where	where	SCONJ
ejpam-1372	990	8	computing	computing	NOUN
ejpam-1372	990	9	is	be	AUX
ejpam-1372	990	10	continually	continually	ADV
ejpam-1372	990	11	being	be	AUX
ejpam-1372	990	12	taken	take	VERB
ejpam-1372	990	13	to	to	ADP
ejpam-1372	990	14	new	new	ADJ
ejpam-1372	990	15	levels	level	NOUN
ejpam-1372	990	16	of	of	ADP
ejpam-1372	990	17	accuracy	accuracy	NOUN
ejpam-1372	990	18	,	,	PUNCT
ejpam-1372	990	19	the	the	DET
ejpam-1372	990	20	reader	reader	NOUN
ejpam-1372	990	21	will	will	AUX
ejpam-1372	990	22	be	be	AUX
ejpam-1372	990	23	surprised	surprise	VERB
ejpam-1372	990	24	,	,	PUNCT
ejpam-1372	990	25	or	or	CCONJ
ejpam-1372	990	26	even	even	ADV
ejpam-1372	990	27	alarmed	alarmed	ADJ
ejpam-1372	990	28	,	,	PUNCT
ejpam-1372	990	29	to	to	PART
ejpam-1372	990	30	see	see	VERB
ejpam-1372	990	31	just	just	ADV
ejpam-1372	990	32	how	how	SCONJ
ejpam-1372	990	33	bad	bad	ADJ
ejpam-1372	990	34	standard	standard	ADJ
ejpam-1372	990	35	asymptotics	asymptotic	NOUN
ejpam-1372	990	36	is	be	AUX
ejpam-1372	990	37	when	when	SCONJ
ejpam-1372	990	38	compared	compare	VERB
ejpam-1372	990	39	with	with	ADP
ejpam-1372	990	40	the	the	DET
ejpam-1372	990	41	results	result	NOUN
ejpam-1372	990	42	obtained	obtain	VERB
ejpam-1372	990	43	from	from	ADP
ejpam-1372	990	44	an	an	DET
ejpam-1372	990	45	accurate	accurate	ADJ
ejpam-1372	990	46	numerical	numerical	ADJ
ejpam-1372	990	47	investigation	investigation	NOUN
ejpam-1372	990	48	.	.	PUNCT
ejpam-1372	991	1	frequently	frequently	ADV
ejpam-1372	991	2	,	,	PUNCT
ejpam-1372	991	3	the	the	DET
ejpam-1372	991	4	situation	situation	NOUN
ejpam-1372	991	5	is	be	AUX
ejpam-1372	991	6	covered	cover	VERB
ejpam-1372	991	7	up	up	ADP
ejpam-1372	991	8	by	by	ADP
ejpam-1372	991	9	practitioners	practitioner	NOUN
ejpam-1372	991	10	in	in	ADP
ejpam-1372	991	11	asymptotics	asymptotic	NOUN
ejpam-1372	991	12	by	by	ADP
ejpam-1372	991	13	using	use	VERB
ejpam-1372	991	14	either	either	CCONJ
ejpam-1372	991	15	considerably	considerably	ADV
ejpam-1372	991	16	small	small	ADJ
ejpam-1372	991	17	values	value	NOUN
ejpam-1372	991	18	in	in	ADP
ejpam-1372	991	19	their	their	PRON
ejpam-1372	991	20	studies	study	NOUN
ejpam-1372	991	21	of	of	ADP
ejpam-1372	991	22	small	small	ADJ
ejpam-1372	991	23	variable	variable	ADJ
ejpam-1372	991	24	expansions	expansion	NOUN
ejpam-1372	991	25	or	or	CCONJ
ejpam-1372	991	26	large	large	ADJ
ejpam-1372	991	27	values	value	NOUN
ejpam-1372	991	28	when	when	SCONJ
ejpam-1372	991	29	dealing	deal	VERB
ejpam-1372	991	30	with	with	ADP
ejpam-1372	991	31	large	large	ADJ
ejpam-1372	991	32	variable	variable	ADJ
ejpam-1372	991	33	expansions	expansion	NOUN
ejpam-1372	991	34	.	.	PUNCT
ejpam-1372	992	1	a	a	DET
ejpam-1372	992	2	typical	typical	ADJ
ejpam-1372	992	3	example	example	NOUN
ejpam-1372	992	4	is	be	AUX
ejpam-1372	992	5	the	the	DET
ejpam-1372	992	6	recent	recent	ADJ
ejpam-1372	992	7	study	study	NOUN
ejpam-1372	992	8	by	by	ADP
ejpam-1372	992	9	paris	paris	PROPN
ejpam-1372	992	10	into	into	ADP
ejpam-1372	992	11	the	the	DET
ejpam-1372	992	12	asymptotics	asymptotic	NOUN
ejpam-1372	992	13	of	of	ADP
ejpam-1372	992	14	n	n	CCONJ
ejpam-1372	992	15	-	-	PUNCT
ejpam-1372	992	16	dimensional	dimensional	ADJ
ejpam-1372	992	17	faxén	faxén	NOUN
ejpam-1372	992	18	-	-	PUNCT
ejpam-1372	992	19	type	type	NOUN
ejpam-1372	992	20	integrals	integral	NOUN
ejpam-1372	992	21	[	[	X
ejpam-1372	992	22	26	26	NUM
ejpam-1372	992	23	]	]	PUNCT
ejpam-1372	992	24	.	.	PUNCT
ejpam-1372	993	1	although	although	SCONJ
ejpam-1372	993	2	this	this	DET
ejpam-1372	993	3	reference	reference	NOUN
ejpam-1372	993	4	considers	consider	VERB
ejpam-1372	993	5	values	value	NOUN
ejpam-1372	993	6	of	of	ADP
ejpam-1372	993	7	|z|	|z|	NOUN
ejpam-1372	993	8	that	that	PRON
ejpam-1372	993	9	are	be	AUX
ejpam-1372	993	10	not	not	PART
ejpam-1372	993	11	very	very	ADV
ejpam-1372	993	12	large	large	ADJ
ejpam-1372	993	13	such	such	ADJ
ejpam-1372	993	14	as	as	ADP
ejpam-1372	993	15	|z|=	|z|=	NOUN
ejpam-1372	993	16	15	15	NUM
ejpam-1372	993	17	,	,	PUNCT
ejpam-1372	993	18	the	the	DET
ejpam-1372	993	19	main	main	ADJ
ejpam-1372	993	20	asymptotic	asymptotic	ADJ
ejpam-1372	993	21	expansion	expansion	NOUN
ejpam-1372	993	22	is	be	AUX
ejpam-1372	993	23	in	in	ADP
ejpam-1372	993	24	powers	power	NOUN
ejpam-1372	993	25	of	of	ADP
ejpam-1372	993	26	(	(	PUNCT
ejpam-1372	993	27	5/48)(z3/3)4/5	5/48)(z3/3)4/5	NOUN
ejpam-1372	993	28	.	.	PUNCT
ejpam-1372	994	1	when	when	SCONJ
ejpam-1372	994	2	z	z	NOUN
ejpam-1372	994	3	=	=	SYM
ejpam-1372	994	4	15	15	NUM
ejpam-1372	994	5	is	be	AUX
ejpam-1372	994	6	introduced	introduce	VERB
ejpam-1372	994	7	into	into	ADP
ejpam-1372	994	8	the	the	DET
ejpam-1372	994	9	“	"	PUNCT
ejpam-1372	994	10	actual	actual	ADJ
ejpam-1372	994	11	variable	variable	NOUN
ejpam-1372	994	12	”	"	PUNCT
ejpam-1372	994	13	,	,	PUNCT
ejpam-1372	994	14	it	it	PRON
ejpam-1372	994	15	becomes	become	VERB
ejpam-1372	994	16	quite	quite	ADV
ejpam-1372	994	17	large	large	ADJ
ejpam-1372	994	18	resulting	result	VERB
ejpam-1372	994	19	in	in	ADP
ejpam-1372	994	20	a	a	DET
ejpam-1372	994	21	large	large	ADJ
ejpam-1372	994	22	optimal	optimal	ADJ
ejpam-1372	994	23	point	point	NOUN
ejpam-1372	994	24	of	of	ADP
ejpam-1372	994	25	truncation	truncation	NOUN
ejpam-1372	994	26	.	.	PUNCT
ejpam-1372	995	1	because	because	SCONJ
ejpam-1372	995	2	small	small	ADJ
ejpam-1372	995	3	values	value	NOUN
ejpam-1372	995	4	of	of	ADP
ejpam-1372	995	5	|z|	|z|	NOUN
ejpam-1372	995	6	,	,	PUNCT
ejpam-1372	995	7	say	say	VERB
ejpam-1372	995	8	less	less	ADJ
ejpam-1372	995	9	than	than	ADP
ejpam-1372	995	10	unity	unity	NOUN
ejpam-1372	995	11	,	,	PUNCT
ejpam-1372	995	12	have	have	AUX
ejpam-1372	995	13	not	not	PART
ejpam-1372	995	14	been	be	AUX
ejpam-1372	995	15	considered	consider	VERB
ejpam-1372	995	16	,	,	PUNCT
ejpam-1372	995	17	where	where	SCONJ
ejpam-1372	995	18	the	the	DET
ejpam-1372	995	19	optimal	optimal	ADJ
ejpam-1372	995	20	point	point	NOUN
ejpam-1372	995	21	of	of	ADP
ejpam-1372	995	22	truncation	truncation	NOUN
ejpam-1372	995	23	is	be	AUX
ejpam-1372	995	24	non	non	ADJ
ejpam-1372	995	25	-	-	ADJ
ejpam-1372	995	26	existent	existent	ADJ
ejpam-1372	995	27	,	,	PUNCT
ejpam-1372	995	28	the	the	DET
ejpam-1372	995	29	reader	reader	NOUN
ejpam-1372	995	30	is	be	AUX
ejpam-1372	995	31	misled	mislead	VERB
ejpam-1372	995	32	as	as	ADP
ejpam-1372	995	33	to	to	ADP
ejpam-1372	995	34	the	the	DET
ejpam-1372	995	35	accuracy	accuracy	NOUN
ejpam-1372	995	36	of	of	ADP
ejpam-1372	995	37	the	the	DET
ejpam-1372	995	38	asymptotic	asymptotic	ADJ
ejpam-1372	995	39	expansion	expansion	NOUN
ejpam-1372	995	40	.	.	PUNCT
ejpam-1372	996	1	finally	finally	ADV
ejpam-1372	996	2	,	,	PUNCT
ejpam-1372	996	3	we	we	PRON
ejpam-1372	996	4	have	have	AUX
ejpam-1372	996	5	seen	see	VERB
ejpam-1372	996	6	throughout	throughout	ADP
ejpam-1372	996	7	this	this	DET
ejpam-1372	996	8	work	work	NOUN
ejpam-1372	996	9	that	that	PRON
ejpam-1372	996	10	the	the	DET
ejpam-1372	996	11	most	most	ADV
ejpam-1372	996	12	important	important	ADJ
ejpam-1372	996	13	problem	problem	NOUN
ejpam-1372	996	14	in	in	ADP
ejpam-1372	996	15	asymptotics	asymptotic	NOUN
ejpam-1372	996	16	is	be	AUX
ejpam-1372	996	17	regularising	regularise	VERB
ejpam-1372	996	18	the	the	DET
ejpam-1372	996	19	remainder	remainder	NOUN
ejpam-1372	996	20	when	when	SCONJ
ejpam-1372	996	21	it	it	PRON
ejpam-1372	996	22	becomes	become	VERB
ejpam-1372	996	23	divergent	divergent	ADJ
ejpam-1372	996	24	.	.	PUNCT
ejpam-1372	997	1	this	this	PRON
ejpam-1372	997	2	,	,	PUNCT
ejpam-1372	997	3	too	too	ADV
ejpam-1372	997	4	,	,	PUNCT
ejpam-1372	997	5	is	be	AUX
ejpam-1372	997	6	completely	completely	ADV
ejpam-1372	997	7	disregarded	disregarded	ADJ
ejpam-1372	997	8	in	in	ADP
ejpam-1372	997	9	ref	ref	NOUN
ejpam-1372	997	10	.	.	PUNCT
ejpam-1372	998	1	[	[	X
ejpam-1372	998	2	26	26	NUM
ejpam-1372	998	3	]	]	PUNCT
ejpam-1372	998	4	.	.	PUNCT
ejpam-1372	999	1	instead	instead	ADV
ejpam-1372	999	2	,	,	PUNCT
ejpam-1372	999	3	the	the	DET
ejpam-1372	999	4	author	author	NOUN
ejpam-1372	999	5	is	be	AUX
ejpam-1372	999	6	content	content	ADJ
ejpam-1372	999	7	to	to	PART
ejpam-1372	999	8	truncate	truncate	VERB
ejpam-1372	999	9	the	the	DET
ejpam-1372	999	10	main	main	ADJ
ejpam-1372	999	11	expansion	expansion	NOUN
ejpam-1372	999	12	,	,	PUNCT
ejpam-1372	999	13	albeit	albeit	SCONJ
ejpam-1372	999	14	to	to	ADP
ejpam-1372	999	15	the	the	DET
ejpam-1372	999	16	optimal	optimal	ADJ
ejpam-1372	999	17	point	point	NOUN
ejpam-1372	999	18	of	of	ADP
ejpam-1372	999	19	truncation	truncation	NOUN
ejpam-1372	999	20	and	and	CCONJ
ejpam-1372	999	21	then	then	ADV
ejpam-1372	999	22	introduce	introduce	VERB
ejpam-1372	999	23	the	the	DET
ejpam-1372	999	24	ubiquitous	ubiquitous	ADJ
ejpam-1372	999	25	tilde	tilde	NOUN
ejpam-1372	999	26	or	or	CCONJ
ejpam-1372	999	27	∼	∼	NOUN
ejpam-1372	999	28	into	into	ADP
ejpam-1372	999	29	the	the	DET
ejpam-1372	999	30	main	main	ADJ
ejpam-1372	999	31	results	result	NOUN
ejpam-1372	999	32	.	.	PUNCT
ejpam-1372	1000	1	here	here	ADV
ejpam-1372	1000	2	we	we	PRON
ejpam-1372	1000	3	shall	shall	AUX
ejpam-1372	1000	4	present	present	VERB
ejpam-1372	1000	5	a	a	DET
ejpam-1372	1000	6	numerical	numerical	ADJ
ejpam-1372	1000	7	demonstration	demonstration	NOUN
ejpam-1372	1000	8	involving	involve	VERB
ejpam-1372	1000	9	a	a	DET
ejpam-1372	1000	10	particular	particular	ADJ
ejpam-1372	1000	11	type	type	NOUN
ejpam-1372	1000	12	i	i	PRON
ejpam-1372	1000	13	terminant	terminant	VERB
ejpam-1372	1000	14	since	since	SCONJ
ejpam-1372	1000	15	spectacular	spectacular	ADJ
ejpam-1372	1000	16	demonstrations	demonstration	NOUN
ejpam-1372	1000	17	involving	involve	VERB
ejpam-1372	1000	18	type	type	NOUN
ejpam-1372	1000	19	ii	ii	PROPN
ejpam-1372	1000	20	generalised	generalise	VERB
ejpam-1372	1000	21	terminants	terminant	NOUN
ejpam-1372	1000	22	have	have	AUX
ejpam-1372	1000	23	already	already	ADV
ejpam-1372	1000	24	been	be	AUX
ejpam-1372	1000	25	presented	present	VERB
ejpam-1372	1000	26	in	in	ADP
ejpam-1372	1000	27	chs	ch	NOUN
ejpam-1372	1000	28	.	.	PROPN
ejpam-1372	1000	29	9	9	NUM
ejpam-1372	1000	30	and	and	CCONJ
ejpam-1372	1000	31	10	10	NUM
ejpam-1372	1000	32	of	of	ADP
ejpam-1372	1000	33	ref	ref	NOUN
ejpam-1372	1000	34	.	.	PUNCT
ejpam-1372	1001	1	[	[	X
ejpam-1372	1001	2	17	17	NUM
ejpam-1372	1001	3	]	]	PUNCT
ejpam-1372	1001	4	.	.	PUNCT
ejpam-1372	1002	1	specifically	specifically	ADV
ejpam-1372	1002	2	,	,	PUNCT
ejpam-1372	1002	3	it	it	PRON
ejpam-1372	1002	4	was	be	AUX
ejpam-1372	1002	5	found	find	VERB
ejpam-1372	1002	6	to	to	ADP
ejpam-1372	1002	7	astonishing	astonishing	ADJ
ejpam-1372	1002	8	accuracy	accuracy	NOUN
ejpam-1372	1002	9	that	that	SCONJ
ejpam-1372	1002	10	the	the	DET
ejpam-1372	1002	11	borel	borel	NOUN
ejpam-1372	1002	12	-	-	PUNCT
ejpam-1372	1002	13	summed	sum	VERB
ejpam-1372	1002	14	and	and	CCONJ
ejpam-1372	1002	15	mb	mb	ADJ
ejpam-1372	1002	16	-	-	PUNCT
ejpam-1372	1002	17	regularised	regularise	VERB
ejpam-1372	1002	18	forms	form	NOUN
ejpam-1372	1002	19	for	for	ADP
ejpam-1372	1002	20	the	the	DET
ejpam-1372	1002	21	regularised	regularise	VERB
ejpam-1372	1002	22	value	value	NOUN
ejpam-1372	1002	23	of	of	ADP
ejpam-1372	1002	24	a	a	DET
ejpam-1372	1002	25	type	type	NOUN
ejpam-1372	1002	26	ii	ii	PROPN
ejpam-1372	1002	27	series	series	NOUN
ejpam-1372	1002	28	agreed	agree	VERB
ejpam-1372	1002	29	with	with	ADP
ejpam-1372	1002	30	each	each	DET
ejpam-1372	1002	31	other	other	ADJ
ejpam-1372	1002	32	,	,	PUNCT
ejpam-1372	1002	33	but	but	CCONJ
ejpam-1372	1002	34	no	no	DET
ejpam-1372	1002	35	such	such	ADJ
ejpam-1372	1002	36	analysis	analysis	NOUN
ejpam-1372	1002	37	was	be	AUX
ejpam-1372	1002	38	ever	ever	ADV
ejpam-1372	1002	39	applied	apply	VERB
ejpam-1372	1002	40	to	to	AUX
ejpam-1372	1002	41	type	type	NOUN
ejpam-1372	1002	42	i	i	PRON
ejpam-1372	1002	43	series	series	NOUN
ejpam-1372	1002	44	.	.	PUNCT
ejpam-1372	1003	1	we	we	PRON
ejpam-1372	1003	2	shall	shall	AUX
ejpam-1372	1003	3	rectify	rectify	VERB
ejpam-1372	1003	4	the	the	DET
ejpam-1372	1003	5	situation	situation	NOUN
ejpam-1372	1003	6	here	here	ADV
ejpam-1372	1003	7	,	,	PUNCT
ejpam-1372	1003	8	whilst	whilst	SCONJ
ejpam-1372	1003	9	at	at	ADP
ejpam-1372	1003	10	the	the	DET
ejpam-1372	1003	11	same	same	ADJ
ejpam-1372	1003	12	time	time	NOUN
ejpam-1372	1003	13	providing	provide	VERB
ejpam-1372	1003	14	the	the	DET
ejpam-1372	1003	15	reader	reader	NOUN
ejpam-1372	1003	16	with	with	ADP
ejpam-1372	1003	17	a	a	DET
ejpam-1372	1003	18	clearer	clear	ADJ
ejpam-1372	1003	19	idea	idea	NOUN
ejpam-1372	1003	20	of	of	ADP
ejpam-1372	1003	21	exactly	exactly	ADV
ejpam-1372	1003	22	the	the	DET
ejpam-1372	1003	23	type	type	NOUN
ejpam-1372	1003	24	of	of	ADP
ejpam-1372	1003	25	numerics	numeric	NOUN
ejpam-1372	1003	26	we	we	PRON
ejpam-1372	1003	27	have	have	VERB
ejpam-1372	1003	28	in	in	ADP
ejpam-1372	1003	29	mind	mind	NOUN
ejpam-1372	1003	30	in	in	ADP
ejpam-1372	1003	31	carrying	carry	VERB
ejpam-1372	1003	32	out	out	ADP
ejpam-1372	1003	33	such	such	DET
ejpam-1372	1003	34	an	an	DET
ejpam-1372	1003	35	investigation	investigation	NOUN
ejpam-1372	1003	36	.	.	PUNCT
ejpam-1372	1004	1	at	at	ADP
ejpam-1372	1004	2	the	the	DET
ejpam-1372	1004	3	end	end	NOUN
ejpam-1372	1004	4	of	of	ADP
ejpam-1372	1004	5	this	this	DET
ejpam-1372	1004	6	section	section	NOUN
ejpam-1372	1004	7	,	,	PUNCT
ejpam-1372	1004	8	however	however	ADV
ejpam-1372	1004	9	,	,	PUNCT
ejpam-1372	1004	10	we	we	PRON
ejpam-1372	1004	11	shall	shall	AUX
ejpam-1372	1004	12	explain	explain	VERB
ejpam-1372	1004	13	how	how	SCONJ
ejpam-1372	1004	14	borel	borel	PROPN
ejpam-1372	1004	15	summation	summation	NOUN
ejpam-1372	1004	16	can	can	AUX
ejpam-1372	1004	17	be	be	AUX
ejpam-1372	1004	18	extended	extend	VERB
ejpam-1372	1004	19	to	to	ADP
ejpam-1372	1004	20	general	general	ADJ
ejpam-1372	1004	21	type	type	NOUN
ejpam-1372	1004	22	ii	ii	PROPN
ejpam-1372	1004	23	series	series	NOUN
ejpam-1372	1004	24	by	by	ADP
ejpam-1372	1004	25	discussing	discuss	VERB
ejpam-1372	1004	26	the	the	DET
ejpam-1372	1004	27	final	final	ADJ
ejpam-1372	1004	28	example	example	NOUN
ejpam-1372	1004	29	in	in	ADP
ejpam-1372	1004	30	ref	ref	NOUN
ejpam-1372	1004	31	.	.	PUNCT
ejpam-1372	1005	1	[	[	X
ejpam-1372	1005	2	17	17	NUM
ejpam-1372	1005	3	]	]	PUNCT
ejpam-1372	1005	4	.	.	PUNCT
ejpam-1372	1006	1	the	the	DET
ejpam-1372	1006	2	first	first	ADJ
ejpam-1372	1006	3	point	point	NOUN
ejpam-1372	1006	4	to	to	PART
ejpam-1372	1006	5	be	be	AUX
ejpam-1372	1006	6	made	make	VERB
ejpam-1372	1006	7	here	here	ADV
ejpam-1372	1006	8	is	be	AUX
ejpam-1372	1006	9	that	that	SCONJ
ejpam-1372	1006	10	z	z	NOUN
ejpam-1372	1006	11	will	will	AUX
ejpam-1372	1006	12	be	be	AUX
ejpam-1372	1006	13	replaced	replace	VERB
ejpam-1372	1006	14	by	by	ADP
ejpam-1372	1006	15	z3	z3	PROPN
ejpam-1372	1006	16	in	in	ADP
ejpam-1372	1006	17	the	the	DET
ejpam-1372	1006	18	general	general	ADJ
ejpam-1372	1006	19	forms	form	NOUN
ejpam-1372	1006	20	for	for	ADP
ejpam-1372	1006	21	the	the	DET
ejpam-1372	1006	22	regularised	regularise	VERB
ejpam-1372	1006	23	value	value	NOUN
ejpam-1372	1006	24	presented	present	VERB
ejpam-1372	1006	25	in	in	ADP
ejpam-1372	1006	26	the	the	DET
ejpam-1372	1006	27	previous	previous	ADJ
ejpam-1372	1006	28	sections	section	NOUN
ejpam-1372	1006	29	.	.	PUNCT
ejpam-1372	1007	1	this	this	PRON
ejpam-1372	1007	2	is	be	AUX
ejpam-1372	1007	3	necessary	necessary	ADJ
ejpam-1372	1007	4	so	so	SCONJ
ejpam-1372	1007	5	that	that	SCONJ
ejpam-1372	1007	6	we	we	PRON
ejpam-1372	1007	7	can	can	AUX
ejpam-1372	1007	8	observe	observe	VERB
ejpam-1372	1007	9	the	the	DET
ejpam-1372	1007	10	effect	effect	NOUN
ejpam-1372	1007	11	of	of	ADP
ejpam-1372	1007	12	other	other	ADJ
ejpam-1372	1007	13	stokes	stoke	NOUN
ejpam-1372	1007	14	sectors	sector	NOUN
ejpam-1372	1007	15	and	and	CCONJ
ejpam-1372	1007	16	domains	domain	NOUN
ejpam-1372	1007	17	of	of	ADP
ejpam-1372	1007	18	convergence	convergence	NOUN
ejpam-1372	1007	19	within	within	ADP
ejpam-1372	1007	20	the	the	DET
ejpam-1372	1007	21	principal	principal	ADJ
ejpam-1372	1007	22	branch	branch	NOUN
ejpam-1372	1007	23	of	of	ADP
ejpam-1372	1007	24	the	the	DET
ejpam-1372	1007	25	complex	complex	ADJ
ejpam-1372	1007	26	plane	plane	NOUN
ejpam-1372	1007	27	for	for	ADP
ejpam-1372	1007	28	z.	z.	PROPN
ejpam-1372	1007	29	next	next	ADV
ejpam-1372	1007	30	,	,	PUNCT
ejpam-1372	1007	31	we	we	PRON
ejpam-1372	1007	32	shall	shall	AUX
ejpam-1372	1007	33	let	let	VERB
ejpam-1372	1007	34	α=	α=	NOUN
ejpam-1372	1007	35	3/7	3/7	NUM
ejpam-1372	1007	36	rather	rather	ADV
ejpam-1372	1007	37	than	than	ADP
ejpam-1372	1007	38	a	a	DET
ejpam-1372	1007	39	simple	simple	ADJ
ejpam-1372	1007	40	value	value	NOUN
ejpam-1372	1007	41	like	like	ADP
ejpam-1372	1007	42	unity	unity	NOUN
ejpam-1372	1007	43	or	or	CCONJ
ejpam-1372	1007	44	a	a	DET
ejpam-1372	1007	45	half	half	NOUN
ejpam-1372	1007	46	,	,	PUNCT
ejpam-1372	1007	47	so	so	SCONJ
ejpam-1372	1007	48	that	that	SCONJ
ejpam-1372	1007	49	the	the	DET
ejpam-1372	1007	50	terminant	terminant	NOUN
ejpam-1372	1007	51	can	can	AUX
ejpam-1372	1007	52	no	no	ADV
ejpam-1372	1007	53	longer	long	ADV
ejpam-1372	1007	54	be	be	AUX
ejpam-1372	1007	55	identified	identify	VERB
ejpam-1372	1007	56	with	with	ADP
ejpam-1372	1007	57	a	a	DET
ejpam-1372	1007	58	known	know	VERB
ejpam-1372	1007	59	special	special	ADJ
ejpam-1372	1007	60	function	function	NOUN
ejpam-1372	1007	61	.	.	PUNCT
ejpam-1372	1008	1	that	that	PRON
ejpam-1372	1008	2	is	is	ADV
ejpam-1372	1008	3	,	,	PUNCT
ejpam-1372	1008	4	this	this	PRON
ejpam-1372	1008	5	is	be	AUX
ejpam-1372	1008	6	a	a	DET
ejpam-1372	1008	7	situation	situation	NOUN
ejpam-1372	1008	8	where	where	SCONJ
ejpam-1372	1008	9	only	only	ADV
ejpam-1372	1008	10	an	an	DET
ejpam-1372	1008	11	asymptotic	asymptotic	ADJ
ejpam-1372	1008	12	solution	solution	NOUN
ejpam-1372	1008	13	exists	exist	VERB
ejpam-1372	1008	14	.	.	PUNCT
ejpam-1372	1009	1	after	after	ADV
ejpam-1372	1009	2	all	all	ADV
ejpam-1372	1009	3	,	,	PUNCT
ejpam-1372	1009	4	there	there	PRON
ejpam-1372	1009	5	is	be	VERB
ejpam-1372	1009	6	little	little	ADJ
ejpam-1372	1009	7	point	point	NOUN
ejpam-1372	1009	8	in	in	ADP
ejpam-1372	1009	9	developing	develop	VERB
ejpam-1372	1009	10	a	a	DET
ejpam-1372	1009	11	new	new	ADJ
ejpam-1372	1009	12	approach	approach	NOUN
ejpam-1372	1009	13	to	to	ADP
ejpam-1372	1009	14	handling	handle	VERB
ejpam-1372	1009	15	divergent	divergent	ADJ
ejpam-1372	1009	16	series	series	NOUN
ejpam-1372	1009	17	if	if	SCONJ
ejpam-1372	1009	18	all	all	PRON
ejpam-1372	1009	19	it	it	PRON
ejpam-1372	1009	20	does	do	VERB
ejpam-1372	1009	21	is	be	AUX
ejpam-1372	1009	22	provide	provide	VERB
ejpam-1372	1009	23	another	another	DET
ejpam-1372	1009	24	explanation	explanation	NOUN
ejpam-1372	1009	25	of	of	ADP
ejpam-1372	1009	26	existing	exist	VERB
ejpam-1372	1009	27	problems	problem	NOUN
ejpam-1372	1009	28	without	without	ADP
ejpam-1372	1009	29	possessing	possess	VERB
ejpam-1372	1009	30	the	the	DET
ejpam-1372	1009	31	capacity	capacity	NOUN
ejpam-1372	1009	32	to	to	PART
ejpam-1372	1009	33	explore	explore	VERB
ejpam-1372	1009	34	the	the	DET
ejpam-1372	1009	35	unknown	unknown	NOUN
ejpam-1372	1009	36	.	.	PUNCT
ejpam-1372	1010	1	since	since	SCONJ
ejpam-1372	1010	2	the	the	DET
ejpam-1372	1010	3	forms	form	NOUN
ejpam-1372	1010	4	for	for	ADP
ejpam-1372	1010	5	both	both	DET
ejpam-1372	1010	6	types	type	NOUN
ejpam-1372	1010	7	of	of	ADP
ejpam-1372	1010	8	terminant	terminant	NOUN
ejpam-1372	1010	9	as	as	SCONJ
ejpam-1372	1010	10	given	give	VERB
ejpam-1372	1010	11	by	by	ADP
ejpam-1372	1010	12	eqs	eqs	PROPN
ejpam-1372	1010	13	.	.	PUNCT
ejpam-1372	1010	14	(	(	PUNCT
ejpam-1372	1010	15	63	63	NUM
ejpam-1372	1010	16	)	)	PUNCT
ejpam-1372	1010	17	and	and	CCONJ
ejpam-1372	1010	18	(	(	PUNCT
ejpam-1372	1010	19	64	64	NUM
ejpam-1372	1010	20	)	)	PUNCT
ejpam-1372	1010	21	represent	represent	VERB
ejpam-1372	1010	22	small	small	ADJ
ejpam-1372	1010	23	z	z	NOUN
ejpam-1372	1010	24	v.	v.	ADP
ejpam-1372	1010	25	kowalenko	kowalenko	PROPN
ejpam-1372	1010	26	/	/	SYM
ejpam-1372	1010	27	eur	eur	PROPN
ejpam-1372	1010	28	.	.	PUNCT
ejpam-1372	1011	1	j.	j.	PROPN
ejpam-1372	1011	2	pure	pure	PROPN
ejpam-1372	1011	3	appl	appl	PROPN
ejpam-1372	1011	4	.	.	PROPN
ejpam-1372	1011	5	math	math	PROPN
ejpam-1372	1011	6	,	,	PUNCT
ejpam-1372	1011	7	4	4	NUM
ejpam-1372	1011	8	(	(	PUNCT
ejpam-1372	1011	9	2011	2011	NUM
ejpam-1372	1011	10	)	)	PUNCT
ejpam-1372	1011	11	,	,	PUNCT
ejpam-1372	1011	12	370	370	NUM
ejpam-1372	1011	13	-	-	SYM
ejpam-1372	1011	14	423	423	NUM
ejpam-1372	1011	15	406	406	NUM
ejpam-1372	1011	16	asymptotic	asymptotic	ADJ
ejpam-1372	1011	17	series	series	NOUN
ejpam-1372	1011	18	,	,	PUNCT
ejpam-1372	1011	19	we	we	PRON
ejpam-1372	1011	20	shall	shall	AUX
ejpam-1372	1011	21	consider	consider	VERB
ejpam-1372	1011	22	values	value	NOUN
ejpam-1372	1011	23	of	of	ADP
ejpam-1372	1011	24	|z|	|z|	NOUN
ejpam-1372	1011	25	or	or	CCONJ
ejpam-1372	1011	26	rather	rather	ADV
ejpam-1372	1011	27	|z3|	|z3|	PROPN
ejpam-1372	1011	28	,	,	PUNCT
ejpam-1372	1011	29	where	where	SCONJ
ejpam-1372	1011	30	truncation	truncation	NOUN
ejpam-1372	1011	31	is	be	AUX
ejpam-1372	1011	32	unable	unable	ADJ
ejpam-1372	1011	33	to	to	PART
ejpam-1372	1011	34	provide	provide	VERB
ejpam-1372	1011	35	an	an	DET
ejpam-1372	1011	36	accurate	accurate	ADJ
ejpam-1372	1011	37	estimate	estimate	NOUN
ejpam-1372	1011	38	.	.	PUNCT
ejpam-1372	1012	1	therefore	therefore	ADV
ejpam-1372	1012	2	,	,	PUNCT
ejpam-1372	1012	3	in	in	ADP
ejpam-1372	1012	4	the	the	DET
ejpam-1372	1012	5	first	first	ADJ
ejpam-1372	1012	6	instance	instance	NOUN
ejpam-1372	1012	7	,	,	PUNCT
ejpam-1372	1012	8	|z3|	|z3|	PROPN
ejpam-1372	1012	9	will	will	AUX
ejpam-1372	1012	10	be	be	AUX
ejpam-1372	1012	11	set	set	VERB
ejpam-1372	1012	12	equal	equal	ADJ
ejpam-1372	1012	13	to	to	ADP
ejpam-1372	1012	14	a	a	DET
ejpam-1372	1012	15	value	value	NOUN
ejpam-1372	1012	16	lying	lie	VERB
ejpam-1372	1012	17	in	in	ADP
ejpam-1372	1012	18	the	the	DET
ejpam-1372	1012	19	intermediate	intermediate	ADJ
ejpam-1372	1012	20	region	region	NOUN
ejpam-1372	1012	21	of	of	ADP
ejpam-1372	1012	22	0.1	0.1	NUM
ejpam-1372	1012	23	<	<	NOUN
ejpam-1372	1012	24	|z3|<2	|z3|<2	NOUN
ejpam-1372	1012	25	and	and	CCONJ
ejpam-1372	1012	26	in	in	ADP
ejpam-1372	1012	27	the	the	DET
ejpam-1372	1012	28	second	second	ADJ
ejpam-1372	1012	29	instance	instance	NOUN
ejpam-1372	1012	30	to	to	ADP
ejpam-1372	1012	31	a	a	DET
ejpam-1372	1012	32	“	"	PUNCT
ejpam-1372	1012	33	large	large	ADJ
ejpam-1372	1012	34	”	"	PUNCT
ejpam-1372	1012	35	value	value	NOUN
ejpam-1372	1012	36	,	,	PUNCT
ejpam-1372	1012	37	where	where	SCONJ
ejpam-1372	1012	38	|z3|	|z3|	NOUN
ejpam-1372	1012	39	>	>	X
ejpam-1372	1012	40	2	2	NUM
ejpam-1372	1012	41	.	.	PUNCT
ejpam-1372	1012	42	both	both	PRON
ejpam-1372	1012	43	of	of	ADP
ejpam-1372	1012	44	these	these	DET
ejpam-1372	1012	45	situations	situation	NOUN
ejpam-1372	1012	46	would	would	AUX
ejpam-1372	1012	47	never	never	ADV
ejpam-1372	1012	48	be	be	AUX
ejpam-1372	1012	49	considered	consider	VERB
ejpam-1372	1012	50	in	in	ADP
ejpam-1372	1012	51	standard	standard	ADJ
ejpam-1372	1012	52	asymptotics	asymptotic	NOUN
ejpam-1372	1012	53	.	.	PUNCT
ejpam-1372	1013	1	the	the	DET
ejpam-1372	1013	2	numerical	numerical	ADJ
ejpam-1372	1013	3	study	study	NOUN
ejpam-1372	1013	4	will	will	AUX
ejpam-1372	1013	5	also	also	ADV
ejpam-1372	1013	6	consider	consider	VERB
ejpam-1372	1013	7	a	a	DET
ejpam-1372	1013	8	wide	wide	ADJ
ejpam-1372	1013	9	range	range	NOUN
ejpam-1372	1013	10	of	of	ADP
ejpam-1372	1013	11	values	value	NOUN
ejpam-1372	1013	12	for	for	ADP
ejpam-1372	1013	13	the	the	DET
ejpam-1372	1013	14	truncation	truncation	NOUN
ejpam-1372	1013	15	parameter	parameter	NOUN
ejpam-1372	1013	16	.	.	PUNCT
ejpam-1372	1014	1	as	as	SCONJ
ejpam-1372	1014	2	we	we	PRON
ejpam-1372	1014	3	shall	shall	AUX
ejpam-1372	1014	4	see	see	VERB
ejpam-1372	1014	5	,	,	PUNCT
ejpam-1372	1014	6	altering	alter	VERB
ejpam-1372	1014	7	the	the	DET
ejpam-1372	1014	8	truncation	truncation	NOUN
ejpam-1372	1014	9	parameter	parameter	NOUN
ejpam-1372	1014	10	is	be	AUX
ejpam-1372	1014	11	effectively	effectively	ADV
ejpam-1372	1014	12	employing	employ	VERB
ejpam-1372	1014	13	a	a	DET
ejpam-1372	1014	14	different	different	ADJ
ejpam-1372	1014	15	method	method	NOUN
ejpam-1372	1014	16	for	for	ADP
ejpam-1372	1014	17	evaluating	evaluate	VERB
ejpam-1372	1014	18	the	the	DET
ejpam-1372	1014	19	regularised	regularise	VERB
ejpam-1372	1014	20	value	value	NOUN
ejpam-1372	1014	21	.	.	PUNCT
ejpam-1372	1015	1	the	the	DET
ejpam-1372	1015	2	regularised	regularise	VERB
ejpam-1372	1015	3	value	value	NOUN
ejpam-1372	1015	4	of	of	ADP
ejpam-1372	1015	5	the	the	DET
ejpam-1372	1015	6	particular	particular	ADJ
ejpam-1372	1015	7	terminant	terminant	NOUN
ejpam-1372	1015	8	mentioned	mention	VERB
ejpam-1372	1015	9	in	in	ADP
ejpam-1372	1015	10	the	the	DET
ejpam-1372	1015	11	preceding	precede	VERB
ejpam-1372	1015	12	paragraph	paragraph	NOUN
ejpam-1372	1015	13	can	can	AUX
ejpam-1372	1015	14	be	be	AUX
ejpam-1372	1015	15	obtained	obtain	VERB
ejpam-1372	1015	16	by	by	ADP
ejpam-1372	1015	17	substituting	substitute	VERB
ejpam-1372	1015	18	the	the	DET
ejpam-1372	1015	19	appropriate	appropriate	ADJ
ejpam-1372	1015	20	values	value	NOUN
ejpam-1372	1015	21	into	into	ADP
ejpam-1372	1015	22	the	the	DET
ejpam-1372	1015	23	borel	borel	NOUN
ejpam-1372	1015	24	-	-	PUNCT
ejpam-1372	1015	25	summed	sum	VERB
ejpam-1372	1015	26	forms	form	NOUN
ejpam-1372	1015	27	given	give	VERB
ejpam-1372	1015	28	by	by	ADP
ejpam-1372	1015	29	equivalences	equivalence	NOUN
ejpam-1372	1015	30	(	(	PUNCT
ejpam-1372	1015	31	82	82	NUM
ejpam-1372	1015	32	)	)	PUNCT
ejpam-1372	1015	33	and	and	CCONJ
ejpam-1372	1015	34	(	(	PUNCT
ejpam-1372	1015	35	85	85	NUM
ejpam-1372	1015	36	)	)	PUNCT
ejpam-1372	1015	37	.	.	PUNCT
ejpam-1372	1016	1	then	then	ADV
ejpam-1372	1016	2	we	we	PRON
ejpam-1372	1016	3	find	find	VERB
ejpam-1372	1016	4	that	that	SCONJ
ejpam-1372	1016	5	ti(n	ti(n	NUM
ejpam-1372	1016	6	,	,	PUNCT
ejpam-1372	1016	7	3/7	3/7	NUM
ejpam-1372	1016	8	,	,	PUNCT
ejpam-1372	1016	9	z3)≡	z3)≡	NOUN
ejpam-1372	1016	10	(	(	PUNCT
ejpam-1372	1016	11	−z3)n	−z3)n	NOUN
ejpam-1372	1016	12	∫	∫	PROPN
ejpam-1372	1016	13	∞	∞	NOUN
ejpam-1372	1016	14	0	0	PUNCT
ejpam-1372	1017	1	d	d	NOUN
ejpam-1372	1017	2	t	t	NOUN
ejpam-1372	1017	3	tn−4/7	tn−4/7	NUM
ejpam-1372	1017	4	e−t	e−t	NOUN
ejpam-1372	1017	5	1	1	NUM
ejpam-1372	1017	6	+	+	NUM
ejpam-1372	1017	7	z3	z3	PROPN
ejpam-1372	1017	8	t	t	PROPN
ejpam-1372	1017	9	∓	∓	PROPN
ejpam-1372	1017	10	2πi	2πi	NOUN
ejpam-1372	1018	1	z−9/7e1	z−9/7e1	X
ejpam-1372	1018	2	/	/	SYM
ejpam-1372	1018	3	z3	z3	PROPN
ejpam-1372	1018	4	e3iπ/7	e3iπ/7	PROPN
ejpam-1372	1018	5	sin(3lπ/7	sin(3lπ/7	ADJ
ejpam-1372	1018	6	)	)	PUNCT
ejpam-1372	1018	7	sin(3π/7	sin(3π/7	NOUN
ejpam-1372	1018	8	)	)	PUNCT
ejpam-1372	1018	9	,	,	PUNCT
ejpam-1372	1018	10	(	(	PUNCT
ejpam-1372	1018	11	116	116	NUM
ejpam-1372	1018	12	)	)	PUNCT
ejpam-1372	1018	13	where	where	SCONJ
ejpam-1372	1018	14	the	the	DET
ejpam-1372	1018	15	upper	upper	ADJ
ejpam-1372	1018	16	sign	sign	NOUN
ejpam-1372	1018	17	is	be	AUX
ejpam-1372	1018	18	valid	valid	ADJ
ejpam-1372	1018	19	for	for	ADP
ejpam-1372	1018	20	(	(	PUNCT
ejpam-1372	1018	21	2l	2l	NUM
ejpam-1372	1018	22	−	−	PROPN
ejpam-1372	1018	23	1)π/3	1)π/3	NUM
ejpam-1372	1018	24	<	<	X
ejpam-1372	1018	25	arg	arg	X
ejpam-1372	1018	26	z	z	X
ejpam-1372	1018	27	<	<	X
ejpam-1372	1018	28	(	(	PUNCT
ejpam-1372	1018	29	2l	2l	PROPN
ejpam-1372	1018	30	+	+	X
ejpam-1372	1018	31	1)π/3	1)π/3	NUM
ejpam-1372	1018	32	and	and	CCONJ
ejpam-1372	1018	33	the	the	DET
ejpam-1372	1018	34	lower	low	ADJ
ejpam-1372	1018	35	sign	sign	NOUN
ejpam-1372	1018	36	is	be	AUX
ejpam-1372	1018	37	valid	valid	ADJ
ejpam-1372	1018	38	for	for	ADP
ejpam-1372	1018	39	−(2l	−(2l	PROPN
ejpam-1372	1018	40	+	+	NOUN
ejpam-1372	1018	41	1)π/3	1)π/3	NUM
ejpam-1372	1018	42	<	<	X
ejpam-1372	1018	43	arg	arg	X
ejpam-1372	1018	44	z	z	NOUN
ejpam-1372	1018	45	<	<	X
ejpam-1372	1018	46	−(2l	−(2l	PROPN
ejpam-1372	1018	47	−	−	PROPN
ejpam-1372	1018	48	1)π/3	1)π/3	NUM
ejpam-1372	1018	49	.	.	PUNCT
ejpam-1372	1019	1	in	in	ADP
ejpam-1372	1019	2	both	both	DET
ejpam-1372	1019	3	cases	case	NOUN
ejpam-1372	1019	4	l	l	NOUN
ejpam-1372	1019	5	is	be	AUX
ejpam-1372	1019	6	a	a	DET
ejpam-1372	1019	7	non	non	ADJ
ejpam-1372	1019	8	-	-	ADJ
ejpam-1372	1019	9	negative	negative	ADJ
ejpam-1372	1019	10	integer	integer	NOUN
ejpam-1372	1019	11	,	,	PUNCT
ejpam-1372	1019	12	while	while	SCONJ
ejpam-1372	1019	13	the	the	DET
ejpam-1372	1019	14	offset	offset	NOUN
ejpam-1372	1019	15	c	c	NOUN
ejpam-1372	1019	16	is	be	AUX
ejpam-1372	1019	17	given	give	VERB
ejpam-1372	1019	18	by	by	ADP
ejpam-1372	1019	19	max[n	max[n	PROPN
ejpam-1372	1019	20	−	−	PROPN
ejpam-1372	1019	21	1,−3/7	1,−3/7	NOUN
ejpam-1372	1019	22	]	]	X
ejpam-1372	1019	23	<	<	X
ejpam-1372	1019	24	c	c	X
ejpam-1372	1019	25	=	=	SYM
ejpam-1372	1019	26	ℜ	ℜ	PROPN
ejpam-1372	1019	27	s	s	PART
ejpam-1372	1019	28	<	<	X
ejpam-1372	1019	29	n	n	NOUN
ejpam-1372	1019	30	.	.	PUNCT
ejpam-1372	1020	1	for	for	ADP
ejpam-1372	1020	2	the	the	DET
ejpam-1372	1020	3	stokes	stokes	PROPN
ejpam-1372	1020	4	lines	line	NOUN
ejpam-1372	1020	5	,	,	PUNCT
ejpam-1372	1020	6	where	where	SCONJ
ejpam-1372	1020	7	arg	arg	VERB
ejpam-1372	1020	8	z=±(2l	z=±(2l	PROPN
ejpam-1372	1020	9	+	+	CCONJ
ejpam-1372	1020	10	1)π/3	1)π/3	PROPN
ejpam-1372	1020	11	,	,	PUNCT
ejpam-1372	1020	12	the	the	DET
ejpam-1372	1020	13	regularised	regularise	VERB
ejpam-1372	1020	14	value	value	NOUN
ejpam-1372	1020	15	derived	derive	VERB
ejpam-1372	1020	16	from	from	ADP
ejpam-1372	1020	17	equivalences	equivalence	NOUN
ejpam-1372	1020	18	(	(	PUNCT
ejpam-1372	1020	19	83	83	NUM
ejpam-1372	1020	20	)	)	PUNCT
ejpam-1372	1020	21	and	and	CCONJ
ejpam-1372	1020	22	(	(	PUNCT
ejpam-1372	1020	23	86	86	NUM
ejpam-1372	1020	24	)	)	PUNCT
ejpam-1372	1020	25	is	be	AUX
ejpam-1372	1020	26	given	give	VERB
ejpam-1372	1020	27	by	by	ADP
ejpam-1372	1020	28	ti	ti	PROPN
ejpam-1372	1020	29	(	(	PUNCT
ejpam-1372	1020	30	n	n	X
ejpam-1372	1020	31	,	,	PUNCT
ejpam-1372	1020	32	3/7	3/7	NUM
ejpam-1372	1020	33	,	,	PUNCT
ejpam-1372	1021	1	z3	z3	PROPN
ejpam-1372	1021	2	)	)	PUNCT
ejpam-1372	1021	3	≡	≡	PROPN
ejpam-1372	1021	4	|z|3n−3p	|z|3n−3p	PROPN
ejpam-1372	1022	1	∫	∫	PROPN
ejpam-1372	1022	2	∞	∞	PROPN
ejpam-1372	1022	3	0	0	PUNCT
ejpam-1372	1023	1	d	d	NOUN
ejpam-1372	1023	2	t	t	NUM
ejpam-1372	1023	3	tn−4/7	tn−4/7	NUM
ejpam-1372	1023	4	e−t	e−t	NOUN
ejpam-1372	1023	5	t	t	NOUN
ejpam-1372	1023	6	−	−	PROPN
ejpam-1372	1023	7	|z|3	|z|3	PROPN
ejpam-1372	1023	8	−πi	−πi	NOUN
ejpam-1372	1023	9	|z|−9/7e−1/|z|3	|z|−9/7e−1/|z|3	ADJ
ejpam-1372	1023	10	×	×	PROPN
ejpam-1372	1023	11	�	�	PROPN
ejpam-1372	1023	12	2e∓3(l+1)iπ/7	2e∓3(l+1)iπ/7	NUM
ejpam-1372	1023	13	sin(3lπ/7	sin(3lπ/7	ADJ
ejpam-1372	1023	14	)	)	PUNCT
ejpam-1372	1023	15	sin(3π/7	sin(3π/7	NOUN
ejpam-1372	1023	16	)	)	PUNCT
ejpam-1372	1024	1	+	+	CCONJ
ejpam-1372	1024	2	1	1	NUM
ejpam-1372	1024	3	�	�	NOUN
ejpam-1372	1024	4	.	.	PUNCT
ejpam-1372	1025	1	(	(	PUNCT
ejpam-1372	1025	2	117	117	NUM
ejpam-1372	1025	3	)	)	PUNCT
ejpam-1372	1025	4	the	the	DET
ejpam-1372	1025	5	mb	mb	ADJ
ejpam-1372	1025	6	-	-	PUNCT
ejpam-1372	1025	7	regularised	regularise	VERB
ejpam-1372	1025	8	value	value	NOUN
ejpam-1372	1025	9	of	of	ADP
ejpam-1372	1025	10	the	the	DET
ejpam-1372	1025	11	series	series	NOUN
ejpam-1372	1025	12	can	can	AUX
ejpam-1372	1025	13	be	be	AUX
ejpam-1372	1025	14	obtained	obtain	VERB
ejpam-1372	1025	15	by	by	ADP
ejpam-1372	1025	16	introducing	introduce	VERB
ejpam-1372	1025	17	the	the	DET
ejpam-1372	1025	18	appropriate	appropriate	ADJ
ejpam-1372	1025	19	values	value	NOUN
ejpam-1372	1025	20	into	into	ADP
ejpam-1372	1025	21	equivalence	equivalence	NOUN
ejpam-1372	1025	22	(	(	PUNCT
ejpam-1372	1025	23	96	96	NUM
ejpam-1372	1025	24	)	)	PUNCT
ejpam-1372	1025	25	.	.	PUNCT
ejpam-1372	1026	1	this	this	DET
ejpam-1372	1026	2	yields	yield	NOUN
ejpam-1372	1026	3	ti	ti	X
ejpam-1372	1026	4	(	(	PUNCT
ejpam-1372	1026	5	n	n	X
ejpam-1372	1026	6	,	,	PUNCT
ejpam-1372	1026	7	3/7	3/7	NUM
ejpam-1372	1026	8	,	,	PUNCT
ejpam-1372	1026	9	z3)≡	z3)≡	PROPN
ejpam-1372	1026	10	∫	∫	PROPN
ejpam-1372	1026	11	c+i∞	c+i∞	PROPN
ejpam-1372	1026	12	c−i∞	c−i∞	PROPN
ejpam-1372	1026	13	ds	ds	PROPN
ejpam-1372	1026	14	z3s	z3	NOUN
ejpam-1372	1026	15	e∓2l	e∓2l	X
ejpam-1372	1026	16	iπsγ(s+	iπsγ(s+	NOUN
ejpam-1372	1026	17	3/7	3/7	NUM
ejpam-1372	1026	18	)	)	PUNCT
ejpam-1372	1026	19	e−iπs	e−iπs	NOUN
ejpam-1372	1026	20	−	−	PROPN
ejpam-1372	1026	21	eiπs	eiπs	PROPN
ejpam-1372	1026	22	∓	∓	PROPN
ejpam-1372	1026	23	2πiz−9/7e1	2πiz−9/7e1	X
ejpam-1372	1026	24	/	/	SYM
ejpam-1372	1026	25	z3	z3	PROPN
ejpam-1372	1026	26	×	×	PROPN
ejpam-1372	1026	27	e±3l	e±3l	ADJ
ejpam-1372	1026	28	iπ/7	iπ/7	PROPN
ejpam-1372	1026	29	sin(3lπ/7	sin(3lπ/7	NOUN
ejpam-1372	1026	30	)	)	PUNCT
ejpam-1372	1026	31	sin(3π/7	sin(3π/7	NOUN
ejpam-1372	1026	32	)	)	PUNCT
ejpam-1372	1026	33	,	,	PUNCT
ejpam-1372	1026	34	(	(	PUNCT
ejpam-1372	1026	35	118	118	NUM
ejpam-1372	1026	36	)	)	PUNCT
ejpam-1372	1026	37	where	where	SCONJ
ejpam-1372	1026	38	(	(	PUNCT
ejpam-1372	1026	39	±2l	±2l	PROPN
ejpam-1372	1026	40	−	−	PROPN
ejpam-1372	1026	41	3/2)π/3	3/2)π/3	NUM
ejpam-1372	1026	42	<	<	X
ejpam-1372	1026	43	arg	arg	NOUN
ejpam-1372	1026	44	z	z	X
ejpam-1372	1026	45	<	<	X
ejpam-1372	1026	46	(	(	PUNCT
ejpam-1372	1026	47	±2l	±2l	PROPN
ejpam-1372	1026	48	+	+	CCONJ
ejpam-1372	1026	49	3/2)π/3	3/2)π/3	NUM
ejpam-1372	1026	50	.	.	PUNCT
ejpam-1372	1027	1	therefore	therefore	ADV
ejpam-1372	1027	2	,	,	PUNCT
ejpam-1372	1027	3	we	we	PRON
ejpam-1372	1027	4	find	find	VERB
ejpam-1372	1027	5	that	that	SCONJ
ejpam-1372	1027	6	there	there	PRON
ejpam-1372	1027	7	are	be	VERB
ejpam-1372	1027	8	three	three	NUM
ejpam-1372	1027	9	different	different	ADJ
ejpam-1372	1027	10	forms	form	NOUN
ejpam-1372	1027	11	covering	cover	VERB
ejpam-1372	1027	12	the	the	DET
ejpam-1372	1027	13	principal	principal	ADJ
ejpam-1372	1027	14	branch	branch	NOUN
ejpam-1372	1027	15	of	of	ADP
ejpam-1372	1027	16	the	the	DET
ejpam-1372	1027	17	complex	complex	ADJ
ejpam-1372	1027	18	plane	plane	NOUN
ejpam-1372	1027	19	for	for	ADP
ejpam-1372	1027	20	z.	z.	PROPN
ejpam-1372	1028	1	the	the	DET
ejpam-1372	1028	2	l=0	l=0	PROPN
ejpam-1372	1028	3	form	form	NOUN
ejpam-1372	1028	4	is	be	AUX
ejpam-1372	1028	5	valid	valid	ADJ
ejpam-1372	1028	6	over	over	ADP
ejpam-1372	1028	7	−π/2	−π/2	PROPN
ejpam-1372	1028	8	<	<	X
ejpam-1372	1028	9	argz	argz	NOUN
ejpam-1372	1028	10	<	<	NOUN
ejpam-1372	1028	11	π/2	π/2	NUM
ejpam-1372	1028	12	,	,	PUNCT
ejpam-1372	1028	13	while	while	SCONJ
ejpam-1372	1028	14	the	the	DET
ejpam-1372	1028	15	l=1	l=1	NOUN
ejpam-1372	1028	16	and	and	CCONJ
ejpam-1372	1028	17	l=−1	l=−1	ADJ
ejpam-1372	1028	18	forms	form	NOUN
ejpam-1372	1028	19	are	be	AUX
ejpam-1372	1028	20	valid	valid	ADJ
ejpam-1372	1028	21	over	over	ADP
ejpam-1372	1028	22	π/6	π/6	NOUN
ejpam-1372	1028	23	<	<	X
ejpam-1372	1028	24	argz<7π/6	argz<7π/6	PROPN
ejpam-1372	1028	25	and	and	CCONJ
ejpam-1372	1028	26	−7π/6	−7π/6	NOUN
ejpam-1372	1028	27	<	<	X
ejpam-1372	1028	28	arg	arg	NOUN
ejpam-1372	1028	29	z	z	X
ejpam-1372	1028	30	<	<	X
ejpam-1372	1028	31	−π/6	−π/6	PROPN
ejpam-1372	1028	32	,	,	PUNCT
ejpam-1372	1028	33	respectively	respectively	ADV
ejpam-1372	1028	34	.	.	PUNCT
ejpam-1372	1029	1	hence	hence	ADV
ejpam-1372	1029	2	,	,	PUNCT
ejpam-1372	1029	3	the	the	DET
ejpam-1372	1029	4	l	l	NOUN
ejpam-1372	1029	5	=	=	SYM
ejpam-1372	1029	6	0	0	NUM
ejpam-1372	1029	7	and	and	CCONJ
ejpam-1372	1029	8	l	l	NOUN
ejpam-1372	1029	9	=	=	SYM
ejpam-1372	1029	10	1	1	NUM
ejpam-1372	1029	11	forms	form	NOUN
ejpam-1372	1029	12	share	share	VERB
ejpam-1372	1029	13	a	a	DET
ejpam-1372	1029	14	common	common	ADJ
ejpam-1372	1029	15	region	region	NOUN
ejpam-1372	1029	16	of	of	ADP
ejpam-1372	1029	17	π/6	π/6	PROPN
ejpam-1372	1029	18	<	<	X
ejpam-1372	1029	19	arg	arg	NOUN
ejpam-1372	1029	20	z	z	PROPN
ejpam-1372	1029	21	<	<	X
ejpam-1372	1029	22	π/2	π/2	NUM
ejpam-1372	1029	23	,	,	PUNCT
ejpam-1372	1029	24	which	which	PRON
ejpam-1372	1029	25	is	be	AUX
ejpam-1372	1029	26	where	where	SCONJ
ejpam-1372	1029	27	we	we	PRON
ejpam-1372	1029	28	expect	expect	VERB
ejpam-1372	1029	29	both	both	DET
ejpam-1372	1029	30	forms	form	NOUN
ejpam-1372	1029	31	to	to	PART
ejpam-1372	1029	32	yield	yield	VERB
ejpam-1372	1029	33	identical	identical	ADJ
ejpam-1372	1029	34	results	result	NOUN
ejpam-1372	1029	35	for	for	ADP
ejpam-1372	1029	36	the	the	DET
ejpam-1372	1029	37	regularised	regularise	VERB
ejpam-1372	1029	38	value	value	NOUN
ejpam-1372	1029	39	.	.	PUNCT
ejpam-1372	1030	1	if	if	SCONJ
ejpam-1372	1030	2	this	this	PRON
ejpam-1372	1030	3	does	do	AUX
ejpam-1372	1030	4	not	not	PART
ejpam-1372	1030	5	occur	occur	VERB
ejpam-1372	1030	6	,	,	PUNCT
ejpam-1372	1030	7	then	then	ADV
ejpam-1372	1030	8	we	we	PRON
ejpam-1372	1030	9	know	know	VERB
ejpam-1372	1030	10	that	that	SCONJ
ejpam-1372	1030	11	the	the	DET
ejpam-1372	1030	12	results	result	NOUN
ejpam-1372	1030	13	of	of	ADP
ejpam-1372	1030	14	the	the	DET
ejpam-1372	1030	15	previous	previous	ADJ
ejpam-1372	1030	16	section	section	NOUN
ejpam-1372	1030	17	are	be	AUX
ejpam-1372	1030	18	invalid	invalid	ADJ
ejpam-1372	1030	19	.	.	PUNCT
ejpam-1372	1031	1	on	on	ADP
ejpam-1372	1031	2	the	the	DET
ejpam-1372	1031	3	other	other	ADJ
ejpam-1372	1031	4	hand	hand	NOUN
ejpam-1372	1031	5	,	,	PUNCT
ejpam-1372	1031	6	the	the	DET
ejpam-1372	1031	7	common	common	ADJ
ejpam-1372	1031	8	region	region	NOUN
ejpam-1372	1031	9	for	for	ADP
ejpam-1372	1031	10	the	the	DET
ejpam-1372	1031	11	l	l	NOUN
ejpam-1372	1031	12	=	=	SYM
ejpam-1372	1031	13	0	0	NUM
ejpam-1372	1031	14	and	and	CCONJ
ejpam-1372	1031	15	l	l	NOUN
ejpam-1372	1031	16	=	=	NOUN
ejpam-1372	1031	17	−1	−1	NOUN
ejpam-1372	1031	18	forms	form	NOUN
ejpam-1372	1031	19	is	be	AUX
ejpam-1372	1031	20	−π/2	−π/2	PROPN
ejpam-1372	1031	21	<	<	X
ejpam-1372	1031	22	arg	arg	NOUN
ejpam-1372	1031	23	z	z	X
ejpam-1372	1031	24	<	<	X
ejpam-1372	1031	25	−π/6	−π/6	PROPN
ejpam-1372	1031	26	.	.	PUNCT
ejpam-1372	1031	27	hence	hence	ADV
ejpam-1372	1031	28	,	,	PUNCT
ejpam-1372	1031	29	these	these	DET
ejpam-1372	1031	30	forms	form	NOUN
ejpam-1372	1031	31	are	be	AUX
ejpam-1372	1031	32	expected	expect	VERB
ejpam-1372	1031	33	to	to	PART
ejpam-1372	1031	34	yield	yield	VERB
ejpam-1372	1031	35	identical	identical	ADJ
ejpam-1372	1031	36	values	value	NOUN
ejpam-1372	1031	37	for	for	ADP
ejpam-1372	1031	38	the	the	DET
ejpam-1372	1031	39	regularised	regularise	VERB
ejpam-1372	1031	40	value	value	NOUN
ejpam-1372	1031	41	when	when	SCONJ
ejpam-1372	1031	42	z	z	NOUN
ejpam-1372	1031	43	is	be	AUX
ejpam-1372	1031	44	situated	situate	VERB
ejpam-1372	1031	45	within	within	ADP
ejpam-1372	1031	46	this	this	DET
ejpam-1372	1031	47	sector	sector	NOUN
ejpam-1372	1031	48	of	of	ADP
ejpam-1372	1031	49	the	the	DET
ejpam-1372	1031	50	complex	complex	ADJ
ejpam-1372	1031	51	plane	plane	NOUN
ejpam-1372	1031	52	.	.	PUNCT
ejpam-1372	1032	1	v.	v.	ADP
ejpam-1372	1032	2	kowalenko	kowalenko	PROPN
ejpam-1372	1032	3	/	/	SYM
ejpam-1372	1032	4	eur	eur	PROPN
ejpam-1372	1032	5	.	.	PUNCT
ejpam-1372	1033	1	j.	j.	PROPN
ejpam-1372	1033	2	pure	pure	PROPN
ejpam-1372	1033	3	appl	appl	PROPN
ejpam-1372	1033	4	.	.	PROPN
ejpam-1372	1033	5	math	math	PROPN
ejpam-1372	1033	6	,	,	PUNCT
ejpam-1372	1033	7	4	4	NUM
ejpam-1372	1033	8	(	(	PUNCT
ejpam-1372	1033	9	2011	2011	NUM
ejpam-1372	1033	10	)	)	PUNCT
ejpam-1372	1033	11	,	,	PUNCT
ejpam-1372	1033	12	370	370	NUM
ejpam-1372	1033	13	-	-	SYM
ejpam-1372	1033	14	423	423	NUM
ejpam-1372	1033	15	407	407	NUM
ejpam-1372	1033	16	table	table	NOUN
ejpam-1372	1033	17	1	1	NUM
ejpam-1372	1033	18	in	in	ADP
ejpam-1372	1033	19	the	the	DET
ejpam-1372	1033	20	appendix	appendix	NOUN
ejpam-1372	1033	21	presents	present	VERB
ejpam-1372	1033	22	a	a	DET
ejpam-1372	1033	23	small	small	ADJ
ejpam-1372	1033	24	sample	sample	NOUN
ejpam-1372	1033	25	of	of	ADP
ejpam-1372	1033	26	the	the	DET
ejpam-1372	1033	27	results	result	NOUN
ejpam-1372	1033	28	obtained	obtain	VERB
ejpam-1372	1033	29	by	by	ADP
ejpam-1372	1033	30	programming	programming	NOUN
ejpam-1372	1033	31	equivalence	equivalence	NOUN
ejpam-1372	1033	32	(	(	PUNCT
ejpam-1372	1033	33	118	118	NUM
ejpam-1372	1033	34	)	)	PUNCT
ejpam-1372	1033	35	as	as	ADP
ejpam-1372	1033	36	a	a	DET
ejpam-1372	1033	37	module	module	NOUN
ejpam-1372	1033	38	in	in	ADP
ejpam-1372	1033	39	mathematica	mathematica	PROPN
ejpam-1372	1033	40	[	[	X
ejpam-1372	1033	41	34	34	NUM
ejpam-1372	1033	42	]	]	PUNCT
ejpam-1372	1033	43	.	.	PUNCT
ejpam-1372	1034	1	only	only	ADV
ejpam-1372	1034	2	a	a	DET
ejpam-1372	1034	3	summary	summary	NOUN
ejpam-1372	1034	4	of	of	ADP
ejpam-1372	1034	5	the	the	DET
ejpam-1372	1034	6	various	various	ADJ
ejpam-1372	1034	7	modules	module	NOUN
ejpam-1372	1034	8	used	use	VERB
ejpam-1372	1034	9	to	to	PART
ejpam-1372	1034	10	produce	produce	VERB
ejpam-1372	1034	11	the	the	DET
ejpam-1372	1034	12	numerical	numerical	ADJ
ejpam-1372	1034	13	results	result	NOUN
ejpam-1372	1034	14	in	in	ADP
ejpam-1372	1034	15	this	this	DET
ejpam-1372	1034	16	work	work	NOUN
ejpam-1372	1034	17	is	be	AUX
ejpam-1372	1034	18	presented	present	VERB
ejpam-1372	1034	19	.	.	PUNCT
ejpam-1372	1035	1	the	the	DET
ejpam-1372	1035	2	actual	actual	ADJ
ejpam-1372	1035	3	modules	module	NOUN
ejpam-1372	1035	4	will	will	AUX
ejpam-1372	1035	5	appear	appear	VERB
ejpam-1372	1035	6	elsewhere	elsewhere	ADV
ejpam-1372	1035	7	[	[	X
ejpam-1372	1035	8	20	20	NUM
ejpam-1372	1035	9	]	]	PUNCT
ejpam-1372	1035	10	.	.	PUNCT
ejpam-1372	1036	1	specifically	specifically	ADV
ejpam-1372	1036	2	,	,	PUNCT
ejpam-1372	1036	3	the	the	DET
ejpam-1372	1036	4	table	table	NOUN
ejpam-1372	1036	5	is	be	AUX
ejpam-1372	1036	6	composed	compose	VERB
ejpam-1372	1036	7	of	of	ADP
ejpam-1372	1036	8	the	the	DET
ejpam-1372	1036	9	various	various	ADJ
ejpam-1372	1036	10	terms	term	NOUN
ejpam-1372	1036	11	on	on	ADP
ejpam-1372	1036	12	the	the	DET
ejpam-1372	1036	13	rhs	rhs	PROPN
ejpam-1372	1036	14	of	of	ADP
ejpam-1372	1036	15	equivalence	equivalence	NOUN
ejpam-1372	1036	16	(	(	PUNCT
ejpam-1372	1036	17	118	118	NUM
ejpam-1372	1036	18	)	)	PUNCT
ejpam-1372	1036	19	plus	plus	CCONJ
ejpam-1372	1036	20	the	the	DET
ejpam-1372	1036	21	truncated	truncated	ADJ
ejpam-1372	1036	22	series	series	NOUN
ejpam-1372	1036	23	up	up	ADP
ejpam-1372	1036	24	to	to	ADP
ejpam-1372	1036	25	n−1	n−1	PROPN
ejpam-1372	1036	26	since	since	SCONJ
ejpam-1372	1036	27	ti	ti	PROPN
ejpam-1372	1036	28	(	(	PUNCT
ejpam-1372	1036	29	0,α	0,α	PROPN
ejpam-1372	1036	30	,	,	PUNCT
ejpam-1372	1036	31	z	z	NOUN
ejpam-1372	1036	32	)	)	PUNCT
ejpam-1372	1036	33	=	=	SYM
ejpam-1372	1036	34	ti	ti	X
ejpam-1372	1036	35	(	(	PUNCT
ejpam-1372	1036	36	n	n	PROPN
ejpam-1372	1036	37	,	,	PUNCT
ejpam-1372	1036	38	α	α	NOUN
ejpam-1372	1036	39	,	,	PUNCT
ejpam-1372	1036	40	z	z	NOUN
ejpam-1372	1036	41	)	)	PUNCT
ejpam-1372	1036	42	+	+	CCONJ
ejpam-1372	1036	43	n1	n1	ADJ
ejpam-1372	1036	44	∑	∑	ADP
ejpam-1372	1036	45	k=0	k=0	NOUN
ejpam-1372	1036	46	γ(k+α)(−z)k	γ(k+α)(−z)k	NOUN
ejpam-1372	1036	47	.	.	PUNCT
ejpam-1372	1037	1	(	(	PUNCT
ejpam-1372	1037	2	119	119	NUM
ejpam-1372	1037	3	)	)	PUNCT
ejpam-1372	1037	4	that	that	PRON
ejpam-1372	1037	5	is	be	AUX
ejpam-1372	1037	6	,	,	PUNCT
ejpam-1372	1037	7	the	the	DET
ejpam-1372	1037	8	regularised	regularise	VERB
ejpam-1372	1037	9	value	value	NOUN
ejpam-1372	1037	10	of	of	ADP
ejpam-1372	1037	11	the	the	DET
ejpam-1372	1037	12	entire	entire	ADJ
ejpam-1372	1037	13	series	series	NOUN
ejpam-1372	1037	14	on	on	ADP
ejpam-1372	1037	15	the	the	DET
ejpam-1372	1037	16	lhs	lhs	PROPN
ejpam-1372	1037	17	of	of	ADP
ejpam-1372	1037	18	the	the	DET
ejpam-1372	1037	19	above	above	ADJ
ejpam-1372	1037	20	equation	equation	NOUN
ejpam-1372	1037	21	or	or	CCONJ
ejpam-1372	1037	22	ti	ti	NOUN
ejpam-1372	1037	23	(	(	PUNCT
ejpam-1372	1037	24	0,α	0,α	PROPN
ejpam-1372	1037	25	,	,	PUNCT
ejpam-1372	1037	26	z	z	NOUN
ejpam-1372	1037	27	)	)	PUNCT
ejpam-1372	1037	28	is	be	AUX
ejpam-1372	1037	29	equivalent	equivalent	ADJ
ejpam-1372	1037	30	to	to	ADP
ejpam-1372	1037	31	the	the	DET
ejpam-1372	1037	32	truncated	truncated	ADJ
ejpam-1372	1037	33	series	series	NOUN
ejpam-1372	1037	34	plus	plus	CCONJ
ejpam-1372	1037	35	the	the	DET
ejpam-1372	1037	36	regularised	regularise	VERB
ejpam-1372	1037	37	value	value	NOUN
ejpam-1372	1037	38	on	on	ADP
ejpam-1372	1037	39	the	the	DET
ejpam-1372	1037	40	rhs	rhs	PROPN
ejpam-1372	1037	41	of	of	ADP
ejpam-1372	1037	42	equivalence	equivalence	NOUN
ejpam-1372	1037	43	(	(	PUNCT
ejpam-1372	1037	44	118	118	NUM
ejpam-1372	1037	45	)	)	PUNCT
ejpam-1372	1037	46	.	.	PUNCT
ejpam-1372	1038	1	hence	hence	ADV
ejpam-1372	1038	2	,	,	PUNCT
ejpam-1372	1038	3	eq	eq	ADJ
ejpam-1372	1038	4	.	.	PUNCT
ejpam-1372	1039	1	(	(	PUNCT
ejpam-1372	1039	2	119	119	NUM
ejpam-1372	1039	3	)	)	PUNCT
ejpam-1372	1039	4	represents	represent	VERB
ejpam-1372	1039	5	a	a	DET
ejpam-1372	1039	6	method	method	NOUN
ejpam-1372	1039	7	for	for	ADP
ejpam-1372	1039	8	checking	check	VERB
ejpam-1372	1039	9	the	the	DET
ejpam-1372	1039	10	concept	concept	NOUN
ejpam-1372	1039	11	of	of	ADP
ejpam-1372	1039	12	regularisation	regularisation	NOUN
ejpam-1372	1039	13	since	since	SCONJ
ejpam-1372	1039	14	by	by	ADP
ejpam-1372	1039	15	varying	vary	VERB
ejpam-1372	1039	16	the	the	DET
ejpam-1372	1039	17	value	value	NOUN
ejpam-1372	1039	18	of	of	ADP
ejpam-1372	1039	19	the	the	DET
ejpam-1372	1039	20	truncation	truncation	NOUN
ejpam-1372	1039	21	parameter	parameter	NOUN
ejpam-1372	1039	22	n	n	PROPN
ejpam-1372	1039	23	,	,	PUNCT
ejpam-1372	1039	24	we	we	PRON
ejpam-1372	1039	25	are	be	AUX
ejpam-1372	1039	26	calculating	calculate	VERB
ejpam-1372	1039	27	completely	completely	ADV
ejpam-1372	1039	28	different	different	ADJ
ejpam-1372	1039	29	values	value	NOUN
ejpam-1372	1039	30	for	for	ADP
ejpam-1372	1039	31	both	both	CCONJ
ejpam-1372	1039	32	the	the	DET
ejpam-1372	1039	33	truncated	truncated	ADJ
ejpam-1372	1039	34	series	series	NOUN
ejpam-1372	1039	35	and	and	CCONJ
ejpam-1372	1039	36	the	the	DET
ejpam-1372	1039	37	mb	mb	NOUN
ejpam-1372	1039	38	integral	integral	ADJ
ejpam-1372	1039	39	in	in	ADP
ejpam-1372	1039	40	the	the	DET
ejpam-1372	1039	41	regularised	regularise	VERB
ejpam-1372	1039	42	value	value	NOUN
ejpam-1372	1039	43	of	of	ADP
ejpam-1372	1039	44	ti	ti	PROPN
ejpam-1372	1039	45	(	(	PUNCT
ejpam-1372	1039	46	0,α	0,α	PROPN
ejpam-1372	1039	47	,	,	PUNCT
ejpam-1372	1039	48	z	z	NOUN
ejpam-1372	1039	49	)	)	PUNCT
ejpam-1372	1039	50	.	.	PUNCT
ejpam-1372	1040	1	the	the	DET
ejpam-1372	1040	2	first	first	ADJ
ejpam-1372	1040	3	column	column	NOUN
ejpam-1372	1040	4	of	of	ADP
ejpam-1372	1040	5	table	table	NOUN
ejpam-1372	1040	6	1	1	NUM
ejpam-1372	1040	7	displays	display	VERB
ejpam-1372	1040	8	the	the	DET
ejpam-1372	1040	9	value	value	NOUN
ejpam-1372	1040	10	of	of	ADP
ejpam-1372	1040	11	the	the	DET
ejpam-1372	1040	12	truncation	truncation	NOUN
ejpam-1372	1040	13	parameter	parameter	NOUN
ejpam-1372	1040	14	.	.	PUNCT
ejpam-1372	1041	1	because	because	SCONJ
ejpam-1372	1041	2	arg	arg	NOUN
ejpam-1372	1041	3	z	z	PROPN
ejpam-1372	1041	4	has	have	AUX
ejpam-1372	1041	5	been	be	AUX
ejpam-1372	1041	6	set	set	VERB
ejpam-1372	1041	7	equal	equal	ADJ
ejpam-1372	1041	8	to	to	ADP
ejpam-1372	1041	9	π/4	π/4	NUM
ejpam-1372	1041	10	,	,	PUNCT
ejpam-1372	1041	11	the	the	DET
ejpam-1372	1041	12	regularised	regularise	VERB
ejpam-1372	1041	13	value	value	NOUN
ejpam-1372	1041	14	of	of	ADP
ejpam-1372	1041	15	this	this	DET
ejpam-1372	1041	16	particular	particular	ADJ
ejpam-1372	1041	17	terminant	terminant	NOUN
ejpam-1372	1041	18	can	can	AUX
ejpam-1372	1041	19	be	be	AUX
ejpam-1372	1041	20	determined	determine	VERB
ejpam-1372	1041	21	by	by	ADP
ejpam-1372	1041	22	setting	set	VERB
ejpam-1372	1041	23	l	l	NOUN
ejpam-1372	1041	24	=	=	SYM
ejpam-1372	1041	25	0	0	NUM
ejpam-1372	1041	26	and	and	CCONJ
ejpam-1372	1041	27	l	l	NOUN
ejpam-1372	1041	28	=	=	SYM
ejpam-1372	1041	29	1	1	NUM
ejpam-1372	1041	30	in	in	ADP
ejpam-1372	1041	31	the	the	DET
ejpam-1372	1041	32	rhs	rhs	PROPN
ejpam-1372	1041	33	of	of	ADP
ejpam-1372	1041	34	equivalence	equivalence	NOUN
ejpam-1372	1041	35	(	(	PUNCT
ejpam-1372	1041	36	118	118	NUM
ejpam-1372	1041	37	)	)	PUNCT
ejpam-1372	1041	38	.	.	PUNCT
ejpam-1372	1042	1	therefore	therefore	ADV
ejpam-1372	1042	2	,	,	PUNCT
ejpam-1372	1042	3	the	the	DET
ejpam-1372	1042	4	second	second	ADJ
ejpam-1372	1042	5	column	column	NOUN
ejpam-1372	1042	6	displays	display	VERB
ejpam-1372	1042	7	the	the	DET
ejpam-1372	1042	8	value	value	NOUN
ejpam-1372	1042	9	of	of	ADP
ejpam-1372	1042	10	l	l	NOUN
ejpam-1372	1042	11	used	use	VERB
ejpam-1372	1042	12	to	to	PART
ejpam-1372	1042	13	obtain	obtain	VERB
ejpam-1372	1042	14	the	the	DET
ejpam-1372	1042	15	regularised	regularise	VERB
ejpam-1372	1042	16	value	value	NOUN
ejpam-1372	1042	17	for	for	ADP
ejpam-1372	1042	18	the	the	DET
ejpam-1372	1042	19	entire	entire	ADJ
ejpam-1372	1042	20	series	series	NOUN
ejpam-1372	1042	21	via	via	ADP
ejpam-1372	1042	22	eq	eq	PROPN
ejpam-1372	1042	23	.	.	PUNCT
ejpam-1372	1043	1	(	(	PUNCT
ejpam-1372	1043	2	119	119	NUM
ejpam-1372	1043	3	)	)	PUNCT
ejpam-1372	1043	4	.	.	PUNCT
ejpam-1372	1044	1	the	the	DET
ejpam-1372	1044	2	next	next	ADJ
ejpam-1372	1044	3	column	column	NOUN
ejpam-1372	1044	4	presents	present	VERB
ejpam-1372	1044	5	the	the	DET
ejpam-1372	1044	6	value	value	NOUN
ejpam-1372	1044	7	of	of	ADP
ejpam-1372	1044	8	the	the	DET
ejpam-1372	1044	9	truncated	truncated	ADJ
ejpam-1372	1044	10	series	series	NOUN
ejpam-1372	1044	11	or	or	CCONJ
ejpam-1372	1044	12	the	the	DET
ejpam-1372	1044	13	first	first	ADJ
ejpam-1372	1044	14	term	term	NOUN
ejpam-1372	1044	15	on	on	ADP
ejpam-1372	1044	16	the	the	DET
ejpam-1372	1044	17	rhs	rhs	PROPN
ejpam-1372	1044	18	of	of	ADP
ejpam-1372	1044	19	eq	eq	PROPN
ejpam-1372	1044	20	.	.	PUNCT
ejpam-1372	1045	1	(	(	PUNCT
ejpam-1372	1045	2	119	119	NUM
ejpam-1372	1045	3	)	)	PUNCT
ejpam-1372	1045	4	with	with	ADP
ejpam-1372	1045	5	z	z	NOUN
ejpam-1372	1045	6	equal	equal	ADJ
ejpam-1372	1045	7	to	to	ADP
ejpam-1372	1045	8	(	(	PUNCT
ejpam-1372	1045	9	4/5)exp(iπ/4	4/5)exp(iπ/4	NOUN
ejpam-1372	1045	10	)	)	PUNCT
ejpam-1372	1045	11	.	.	PUNCT
ejpam-1372	1046	1	the	the	DET
ejpam-1372	1046	2	fourth	fourth	ADJ
ejpam-1372	1046	3	column	column	NOUN
ejpam-1372	1046	4	lists	list	VERB
ejpam-1372	1046	5	the	the	DET
ejpam-1372	1046	6	value	value	NOUN
ejpam-1372	1046	7	of	of	ADP
ejpam-1372	1046	8	the	the	DET
ejpam-1372	1046	9	mb	mb	NOUN
ejpam-1372	1046	10	integral	integral	ADJ
ejpam-1372	1046	11	on	on	ADP
ejpam-1372	1046	12	the	the	DET
ejpam-1372	1046	13	rhs	rhs	PROPN
ejpam-1372	1046	14	of	of	ADP
ejpam-1372	1046	15	equivalence	equivalence	NOUN
ejpam-1372	1046	16	(	(	PUNCT
ejpam-1372	1046	17	118	118	NUM
ejpam-1372	1046	18	)	)	PUNCT
ejpam-1372	1046	19	,	,	PUNCT
ejpam-1372	1046	20	while	while	SCONJ
ejpam-1372	1046	21	the	the	DET
ejpam-1372	1046	22	fifth	fifth	ADJ
ejpam-1372	1046	23	column	column	NOUN
ejpam-1372	1046	24	labelled	label	VERB
ejpam-1372	1046	25	discontinuity	discontinuity	NOUN
ejpam-1372	1046	26	displays	display	VERB
ejpam-1372	1046	27	the	the	DET
ejpam-1372	1046	28	values	value	NOUN
ejpam-1372	1046	29	for	for	ADP
ejpam-1372	1046	30	the	the	DET
ejpam-1372	1046	31	second	second	ADJ
ejpam-1372	1046	32	term	term	NOUN
ejpam-1372	1046	33	on	on	ADP
ejpam-1372	1046	34	the	the	DET
ejpam-1372	1046	35	rhs	rhs	PROPN
ejpam-1372	1046	36	of	of	ADP
ejpam-1372	1046	37	the	the	DET
ejpam-1372	1046	38	equivalence	equivalence	NOUN
ejpam-1372	1046	39	statement	statement	NOUN
ejpam-1372	1046	40	.	.	PUNCT
ejpam-1372	1047	1	this	this	DET
ejpam-1372	1047	2	term	term	NOUN
ejpam-1372	1047	3	vanishes	vanish	VERB
ejpam-1372	1047	4	for	for	ADP
ejpam-1372	1047	5	l=0	l=0	PROPN
ejpam-1372	1047	6	,	,	PUNCT
ejpam-1372	1047	7	but	but	CCONJ
ejpam-1372	1047	8	remains	remain	VERB
ejpam-1372	1047	9	fixed	fix	VERB
ejpam-1372	1047	10	for	for	ADP
ejpam-1372	1047	11	l=1	l=1	PROPN
ejpam-1372	1047	12	.	.	PUNCT
ejpam-1372	1048	1	the	the	DET
ejpam-1372	1048	2	final	final	ADJ
ejpam-1372	1048	3	column	column	NOUN
ejpam-1372	1048	4	displays	display	VERB
ejpam-1372	1048	5	the	the	DET
ejpam-1372	1048	6	regularised	regularise	VERB
ejpam-1372	1048	7	value	value	NOUN
ejpam-1372	1048	8	of	of	ADP
ejpam-1372	1048	9	the	the	DET
ejpam-1372	1048	10	entire	entire	ADJ
ejpam-1372	1048	11	series	series	NOUN
ejpam-1372	1048	12	,	,	PUNCT
ejpam-1372	1048	13	which	which	PRON
ejpam-1372	1048	14	is	be	AUX
ejpam-1372	1048	15	determined	determine	VERB
ejpam-1372	1048	16	by	by	ADP
ejpam-1372	1048	17	summing	sum	VERB
ejpam-1372	1048	18	the	the	DET
ejpam-1372	1048	19	quantities	quantity	NOUN
ejpam-1372	1048	20	in	in	ADP
ejpam-1372	1048	21	the	the	DET
ejpam-1372	1048	22	third	third	ADJ
ejpam-1372	1048	23	,	,	PUNCT
ejpam-1372	1048	24	fourth	fourth	ADJ
ejpam-1372	1048	25	and	and	CCONJ
ejpam-1372	1048	26	fifth	fifth	ADJ
ejpam-1372	1048	27	columns	column	NOUN
ejpam-1372	1048	28	of	of	ADP
ejpam-1372	1048	29	the	the	DET
ejpam-1372	1048	30	table	table	NOUN
ejpam-1372	1048	31	.	.	PUNCT
ejpam-1372	1049	1	the	the	DET
ejpam-1372	1049	2	results	result	NOUN
ejpam-1372	1049	3	in	in	ADP
ejpam-1372	1049	4	table	table	NOUN
ejpam-1372	1049	5	1	1	NUM
ejpam-1372	1049	6	have	have	AUX
ejpam-1372	1049	7	been	be	AUX
ejpam-1372	1049	8	obtained	obtain	VERB
ejpam-1372	1049	9	by	by	ADP
ejpam-1372	1049	10	running	run	VERB
ejpam-1372	1049	11	mathematica	mathematica	PROPN
ejpam-1372	1049	12	4.1	4.1	NUM
ejpam-1372	1049	13	on	on	ADP
ejpam-1372	1049	14	a	a	DET
ejpam-1372	1049	15	pentium	pentium	NOUN
ejpam-1372	1049	16	computer	computer	NOUN
ejpam-1372	1049	17	.	.	PUNCT
ejpam-1372	1050	1	the	the	DET
ejpam-1372	1050	2	numerical	numerical	ADJ
ejpam-1372	1050	3	integration	integration	NOUN
ejpam-1372	1050	4	routine	routine	ADJ
ejpam-1372	1050	5	in	in	ADP
ejpam-1372	1050	6	this	this	DET
ejpam-1372	1050	7	software	software	NOUN
ejpam-1372	1050	8	package	package	NOUN
ejpam-1372	1050	9	known	know	VERB
ejpam-1372	1050	10	as	as	ADP
ejpam-1372	1050	11	nintegrate	nintegrate	NOUN
ejpam-1372	1050	12	was	be	AUX
ejpam-1372	1050	13	used	use	VERB
ejpam-1372	1050	14	to	to	PART
ejpam-1372	1050	15	evaluate	evaluate	VERB
ejpam-1372	1050	16	the	the	DET
ejpam-1372	1050	17	mb	mb	NOUN
ejpam-1372	1050	18	integral	integral	ADJ
ejpam-1372	1050	19	in	in	ADP
ejpam-1372	1050	20	equivalence	equivalence	NOUN
ejpam-1372	1050	21	(	(	PUNCT
ejpam-1372	1050	22	118	118	NUM
ejpam-1372	1050	23	)	)	PUNCT
ejpam-1372	1050	24	.	.	PUNCT
ejpam-1372	1051	1	this	this	PRON
ejpam-1372	1051	2	was	be	AUX
ejpam-1372	1051	3	achieved	achieve	VERB
ejpam-1372	1051	4	by	by	ADP
ejpam-1372	1051	5	expressing	express	VERB
ejpam-1372	1051	6	each	each	DET
ejpam-1372	1051	7	mb	mb	NOUN
ejpam-1372	1051	8	integral	integral	ADJ
ejpam-1372	1051	9	as	as	ADP
ejpam-1372	1051	10	the	the	DET
ejpam-1372	1051	11	sum	sum	NOUN
ejpam-1372	1051	12	of	of	ADP
ejpam-1372	1051	13	two	two	NUM
ejpam-1372	1051	14	separate	separate	ADJ
ejpam-1372	1051	15	integrals	integral	NOUN
ejpam-1372	1051	16	ranging	range	VERB
ejpam-1372	1051	17	from	from	ADP
ejpam-1372	1051	18	zero	zero	NUM
ejpam-1372	1051	19	to	to	ADP
ejpam-1372	1051	20	infinity	infinity	NOUN
ejpam-1372	1051	21	.	.	PUNCT
ejpam-1372	1052	1	because	because	SCONJ
ejpam-1372	1052	2	the	the	DET
ejpam-1372	1052	3	nintegrate	nintegrate	ADJ
ejpam-1372	1052	4	routine	routine	NOUN
ejpam-1372	1052	5	can	can	AUX
ejpam-1372	1052	6	miss	miss	VERB
ejpam-1372	1052	7	sudden	sudden	ADJ
ejpam-1372	1052	8	peaks	peak	NOUN
ejpam-1372	1052	9	occurring	occur	VERB
ejpam-1372	1052	10	in	in	ADP
ejpam-1372	1052	11	the	the	DET
ejpam-1372	1052	12	integrand	integrand	NOUN
ejpam-1372	1052	13	,	,	PUNCT
ejpam-1372	1052	14	it	it	PRON
ejpam-1372	1052	15	is	be	AUX
ejpam-1372	1052	16	advisable	advisable	ADJ
ejpam-1372	1052	17	to	to	PART
ejpam-1372	1052	18	divide	divide	VERB
ejpam-1372	1052	19	the	the	DET
ejpam-1372	1052	20	range	range	NOUN
ejpam-1372	1052	21	of	of	ADP
ejpam-1372	1052	22	integration	integration	NOUN
ejpam-1372	1052	23	into	into	ADP
ejpam-1372	1052	24	several	several	ADJ
ejpam-1372	1052	25	smaller	small	ADJ
ejpam-1372	1052	26	intervals	interval	NOUN
ejpam-1372	1052	27	.	.	PUNCT
ejpam-1372	1053	1	in	in	ADP
ejpam-1372	1053	2	addition	addition	NOUN
ejpam-1372	1053	3	,	,	PUNCT
ejpam-1372	1053	4	the	the	DET
ejpam-1372	1053	5	routine	routine	NOUN
ejpam-1372	1053	6	can	can	AUX
ejpam-1372	1053	7	be	be	AUX
ejpam-1372	1053	8	fine	fine	ADV
ejpam-1372	1053	9	-	-	PUNCT
ejpam-1372	1053	10	tuned	tune	VERB
ejpam-1372	1053	11	by	by	ADP
ejpam-1372	1053	12	setting	set	VERB
ejpam-1372	1053	13	the	the	DET
ejpam-1372	1053	14	options	option	NOUN
ejpam-1372	1053	15	of	of	ADP
ejpam-1372	1053	16	accuracygoal	accuracygoal	NOUN
ejpam-1372	1053	17	,	,	PUNCT
ejpam-1372	1053	18	precisiongoal	precisiongoal	NOUN
ejpam-1372	1053	19	and	and	CCONJ
ejpam-1372	1053	20	workingprecision	workingprecision	NOUN
ejpam-1372	1053	21	to	to	ADP
ejpam-1372	1053	22	high	high	ADJ
ejpam-1372	1053	23	values	value	NOUN
ejpam-1372	1053	24	.	.	PUNCT
ejpam-1372	1054	1	because	because	SCONJ
ejpam-1372	1054	2	mathematica	mathematica	PROPN
ejpam-1372	1054	3	4.1	4.1	NUM
ejpam-1372	1054	4	is	be	AUX
ejpam-1372	1054	5	limited	limit	VERB
ejpam-1372	1054	6	by	by	ADP
ejpam-1372	1054	7	the	the	DET
ejpam-1372	1054	8	machine	machine	NOUN
ejpam-1372	1054	9	precision	precision	NOUN
ejpam-1372	1054	10	of	of	ADP
ejpam-1372	1054	11	the	the	DET
ejpam-1372	1054	12	computer	computer	NOUN
ejpam-1372	1054	13	,	,	PUNCT
ejpam-1372	1054	14	which	which	PRON
ejpam-1372	1054	15	in	in	ADP
ejpam-1372	1054	16	this	this	DET
ejpam-1372	1054	17	case	case	NOUN
ejpam-1372	1054	18	was	be	AUX
ejpam-1372	1054	19	16	16	NUM
ejpam-1372	1054	20	decimal	decimal	ADJ
ejpam-1372	1054	21	places	place	NOUN
ejpam-1372	1054	22	,	,	PUNCT
ejpam-1372	1054	23	working	working	NOUN
ejpam-1372	1054	24	precision	precision	NOUN
ejpam-1372	1054	25	was	be	AUX
ejpam-1372	1054	26	set	set	VERB
ejpam-1372	1054	27	equal	equal	ADJ
ejpam-1372	1054	28	to	to	ADP
ejpam-1372	1054	29	16	16	NUM
ejpam-1372	1054	30	,	,	PUNCT
ejpam-1372	1054	31	while	while	SCONJ
ejpam-1372	1054	32	the	the	DET
ejpam-1372	1054	33	other	other	ADJ
ejpam-1372	1054	34	options	option	NOUN
ejpam-1372	1054	35	were	be	AUX
ejpam-1372	1054	36	set	set	VERB
ejpam-1372	1054	37	equal	equal	ADJ
ejpam-1372	1054	38	to	to	ADP
ejpam-1372	1054	39	14	14	NUM
ejpam-1372	1054	40	.	.	PUNCT
ejpam-1372	1055	1	this	this	DET
ejpam-1372	1055	2	limitation	limitation	NOUN
ejpam-1372	1055	3	in	in	ADP
ejpam-1372	1055	4	the	the	DET
ejpam-1372	1055	5	precision	precision	NOUN
ejpam-1372	1055	6	of	of	ADP
ejpam-1372	1055	7	the	the	DET
ejpam-1372	1055	8	results	result	NOUN
ejpam-1372	1055	9	due	due	ADP
ejpam-1372	1055	10	to	to	ADP
ejpam-1372	1055	11	machine	machine	NOUN
ejpam-1372	1055	12	precision	precision	NOUN
ejpam-1372	1055	13	does	do	AUX
ejpam-1372	1055	14	not	not	PART
ejpam-1372	1055	15	apply	apply	VERB
ejpam-1372	1055	16	to	to	ADP
ejpam-1372	1055	17	more	more	ADV
ejpam-1372	1055	18	recent	recent	ADJ
ejpam-1372	1055	19	versions	version	NOUN
ejpam-1372	1055	20	of	of	ADP
ejpam-1372	1055	21	the	the	DET
ejpam-1372	1055	22	software	software	NOUN
ejpam-1372	1055	23	package	package	NOUN
ejpam-1372	1055	24	such	such	ADJ
ejpam-1372	1055	25	as	as	ADP
ejpam-1372	1055	26	versions	version	NOUN
ejpam-1372	1055	27	6.0	6.0	NUM
ejpam-1372	1055	28	to	to	PART
ejpam-1372	1055	29	8.0	8.0	NUM
ejpam-1372	1055	30	.	.	PUNCT
ejpam-1372	1056	1	provided	provide	VERB
ejpam-1372	1056	2	the	the	DET
ejpam-1372	1056	3	input	input	NOUN
ejpam-1372	1056	4	variables	variable	NOUN
ejpam-1372	1056	5	are	be	AUX
ejpam-1372	1056	6	not	not	PART
ejpam-1372	1056	7	expressed	express	VERB
ejpam-1372	1056	8	as	as	ADP
ejpam-1372	1056	9	decimal	decimal	ADJ
ejpam-1372	1056	10	numbers	number	NOUN
ejpam-1372	1056	11	in	in	ADP
ejpam-1372	1056	12	these	these	DET
ejpam-1372	1056	13	versions	version	NOUN
ejpam-1372	1056	14	,	,	PUNCT
ejpam-1372	1056	15	the	the	DET
ejpam-1372	1056	16	results	result	NOUN
ejpam-1372	1056	17	can	can	AUX
ejpam-1372	1056	18	be	be	AUX
ejpam-1372	1056	19	obtained	obtain	VERB
ejpam-1372	1056	20	to	to	ADP
ejpam-1372	1056	21	unlimited	unlimited	ADJ
ejpam-1372	1056	22	precision	precision	NOUN
ejpam-1372	1056	23	,	,	PUNCT
ejpam-1372	1056	24	but	but	CCONJ
ejpam-1372	1056	25	it	it	PRON
ejpam-1372	1056	26	will	will	AUX
ejpam-1372	1056	27	come	come	VERB
ejpam-1372	1056	28	at	at	ADP
ejpam-1372	1056	29	a	a	DET
ejpam-1372	1056	30	cost	cost	NOUN
ejpam-1372	1056	31	in	in	ADP
ejpam-1372	1056	32	the	the	DET
ejpam-1372	1056	33	time	time	NOUN
ejpam-1372	1056	34	taken	take	VERB
ejpam-1372	1056	35	to	to	PART
ejpam-1372	1056	36	carry	carry	VERB
ejpam-1372	1056	37	out	out	ADP
ejpam-1372	1056	38	the	the	DET
ejpam-1372	1056	39	computation	computation	NOUN
ejpam-1372	1056	40	of	of	ADP
ejpam-1372	1056	41	the	the	DET
ejpam-1372	1056	42	integrals	integral	NOUN
ejpam-1372	1056	43	.	.	PUNCT
ejpam-1372	1057	1	finally	finally	ADV
ejpam-1372	1057	2	,	,	PUNCT
ejpam-1372	1057	3	in	in	ADP
ejpam-1372	1057	4	obtaining	obtain	VERB
ejpam-1372	1057	5	the	the	DET
ejpam-1372	1057	6	results	result	NOUN
ejpam-1372	1057	7	for	for	ADP
ejpam-1372	1057	8	the	the	DET
ejpam-1372	1057	9	mb	mb	PROPN
ejpam-1372	1057	10	integrals	integral	NOUN
ejpam-1372	1057	11	,	,	PUNCT
ejpam-1372	1057	12	the	the	DET
ejpam-1372	1057	13	options	option	NOUN
ejpam-1372	1057	14	of	of	ADP
ejpam-1372	1057	15	minrecursion	minrecursion	NOUN
ejpam-1372	1057	16	and	and	CCONJ
ejpam-1372	1057	17	maxrecursion	maxrecursion	NOUN
ejpam-1372	1057	18	,	,	PUNCT
ejpam-1372	1057	19	which	which	PRON
ejpam-1372	1057	20	determine	determine	VERB
ejpam-1372	1057	21	the	the	DET
ejpam-1372	1057	22	minimum	minimum	ADJ
ejpam-1372	1057	23	and	and	CCONJ
ejpam-1372	1057	24	maximum	maximum	ADJ
ejpam-1372	1057	25	number	number	NOUN
ejpam-1372	1057	26	of	of	ADP
ejpam-1372	1057	27	sample	sample	NOUN
ejpam-1372	1057	28	points	point	NOUN
ejpam-1372	1057	29	used	use	VERB
ejpam-1372	1057	30	in	in	ADP
ejpam-1372	1057	31	the	the	DET
ejpam-1372	1057	32	nintegrate	nintegrate	ADJ
ejpam-1372	1057	33	routine	routine	NOUN
ejpam-1372	1057	34	,	,	PUNCT
ejpam-1372	1057	35	were	be	AUX
ejpam-1372	1057	36	set	set	VERB
ejpam-1372	1057	37	equal	equal	ADJ
ejpam-1372	1057	38	to	to	ADP
ejpam-1372	1057	39	3	3	NUM
ejpam-1372	1057	40	and	and	CCONJ
ejpam-1372	1057	41	10	10	NUM
ejpam-1372	1057	42	respectively	respectively	ADV
ejpam-1372	1057	43	.	.	PUNCT
ejpam-1372	1058	1	again	again	ADV
ejpam-1372	1058	2	,	,	PUNCT
ejpam-1372	1058	3	these	these	PRON
ejpam-1372	1058	4	can	can	AUX
ejpam-1372	1058	5	be	be	AUX
ejpam-1372	1058	6	adjusted	adjust	VERB
ejpam-1372	1058	7	,	,	PUNCT
ejpam-1372	1058	8	but	but	CCONJ
ejpam-1372	1058	9	at	at	ADP
ejpam-1372	1058	10	the	the	DET
ejpam-1372	1058	11	expense	expense	NOUN
ejpam-1372	1058	12	of	of	ADP
ejpam-1372	1058	13	the	the	DET
ejpam-1372	1058	14	cpu	cpu	NOUN
ejpam-1372	1058	15	time	time	NOUN
ejpam-1372	1058	16	.	.	PUNCT
ejpam-1372	1059	1	v.	v.	ADP
ejpam-1372	1059	2	kowalenko	kowalenko	PROPN
ejpam-1372	1059	3	/	/	SYM
ejpam-1372	1059	4	eur	eur	PROPN
ejpam-1372	1059	5	.	.	PUNCT
ejpam-1372	1060	1	j.	j.	PROPN
ejpam-1372	1060	2	pure	pure	PROPN
ejpam-1372	1060	3	appl	appl	PROPN
ejpam-1372	1060	4	.	.	PROPN
ejpam-1372	1060	5	math	math	PROPN
ejpam-1372	1060	6	,	,	PUNCT
ejpam-1372	1060	7	4	4	NUM
ejpam-1372	1060	8	(	(	PUNCT
ejpam-1372	1060	9	2011	2011	NUM
ejpam-1372	1060	10	)	)	PUNCT
ejpam-1372	1060	11	,	,	PUNCT
ejpam-1372	1060	12	370	370	NUM
ejpam-1372	1060	13	-	-	SYM
ejpam-1372	1060	14	423	423	NUM
ejpam-1372	1060	15	408	408	NUM
ejpam-1372	1060	16	because	because	SCONJ
ejpam-1372	1060	17	of	of	ADP
ejpam-1372	1060	18	the	the	DET
ejpam-1372	1060	19	limitation	limitation	NOUN
ejpam-1372	1060	20	on	on	ADP
ejpam-1372	1060	21	the	the	DET
ejpam-1372	1060	22	working	work	VERB
ejpam-1372	1060	23	precision	precision	NOUN
ejpam-1372	1060	24	in	in	ADP
ejpam-1372	1060	25	the	the	DET
ejpam-1372	1060	26	evaluation	evaluation	NOUN
ejpam-1372	1060	27	of	of	ADP
ejpam-1372	1060	28	the	the	DET
ejpam-1372	1060	29	mb	mb	NOUN
ejpam-1372	1060	30	integral	integral	ADJ
ejpam-1372	1060	31	in	in	ADP
ejpam-1372	1060	32	equivalence	equivalence	NOUN
ejpam-1372	1060	33	(	(	PUNCT
ejpam-1372	1060	34	118	118	NUM
ejpam-1372	1060	35	)	)	PUNCT
ejpam-1372	1060	36	and	and	CCONJ
ejpam-1372	1060	37	the	the	DET
ejpam-1372	1060	38	fact	fact	NOUN
ejpam-1372	1060	39	that	that	SCONJ
ejpam-1372	1060	40	the	the	DET
ejpam-1372	1060	41	accuracy	accuracy	NOUN
ejpam-1372	1060	42	and	and	CCONJ
ejpam-1372	1060	43	precision	precision	NOUN
ejpam-1372	1060	44	goals	goal	NOUN
ejpam-1372	1060	45	were	be	AUX
ejpam-1372	1060	46	set	set	VERB
ejpam-1372	1060	47	to	to	ADP
ejpam-1372	1060	48	14	14	NUM
ejpam-1372	1060	49	,	,	PUNCT
ejpam-1372	1060	50	we	we	PRON
ejpam-1372	1060	51	can	can	AUX
ejpam-1372	1060	52	at	at	ADP
ejpam-1372	1060	53	best	good	ADJ
ejpam-1372	1060	54	expect	expect	VERB
ejpam-1372	1060	55	that	that	SCONJ
ejpam-1372	1060	56	the	the	DET
ejpam-1372	1060	57	above	above	ADJ
ejpam-1372	1060	58	results	result	NOUN
ejpam-1372	1060	59	will	will	AUX
ejpam-1372	1060	60	only	only	ADV
ejpam-1372	1060	61	be	be	AUX
ejpam-1372	1060	62	accurate	accurate	ADJ
ejpam-1372	1060	63	to	to	ADP
ejpam-1372	1060	64	about	about	ADV
ejpam-1372	1060	65	14	14	NUM
ejpam-1372	1060	66	significant	significant	ADJ
ejpam-1372	1060	67	figures	figure	NOUN
ejpam-1372	1060	68	.	.	PUNCT
ejpam-1372	1061	1	this	this	DET
ejpam-1372	1061	2	situation	situation	NOUN
ejpam-1372	1061	3	applies	apply	VERB
ejpam-1372	1061	4	to	to	ADP
ejpam-1372	1061	5	all	all	DET
ejpam-1372	1061	6	the	the	DET
ejpam-1372	1061	7	values	value	NOUN
ejpam-1372	1061	8	in	in	ADP
ejpam-1372	1061	9	the	the	DET
ejpam-1372	1061	10	table	table	NOUN
ejpam-1372	1061	11	for	for	ADP
ejpam-1372	1061	12	n	n	PRON
ejpam-1372	1061	13	≤5	≤5	VERB
ejpam-1372	1061	14	.	.	PUNCT
ejpam-1372	1062	1	the	the	DET
ejpam-1372	1062	2	n	n	PROPN
ejpam-1372	1062	3	=	=	NOUN
ejpam-1372	1062	4	1	1	NUM
ejpam-1372	1062	5	and	and	CCONJ
ejpam-1372	1062	6	n	n	CCONJ
ejpam-1372	1062	7	=	=	SYM
ejpam-1372	1062	8	2	2	NUM
ejpam-1372	1062	9	values	value	NOUN
ejpam-1372	1062	10	in	in	ADP
ejpam-1372	1062	11	the	the	DET
ejpam-1372	1062	12	third	third	ADJ
ejpam-1372	1062	13	column	column	NOUN
ejpam-1372	1062	14	represent	represent	VERB
ejpam-1372	1062	15	the	the	DET
ejpam-1372	1062	16	values	value	NOUN
ejpam-1372	1062	17	one	one	PRON
ejpam-1372	1062	18	would	would	AUX
ejpam-1372	1062	19	obtain	obtain	VERB
ejpam-1372	1062	20	by	by	ADP
ejpam-1372	1062	21	adopting	adopt	VERB
ejpam-1372	1062	22	“	"	PUNCT
ejpam-1372	1062	23	standard	standard	ADJ
ejpam-1372	1062	24	asymptotics	asymptotic	NOUN
ejpam-1372	1062	25	”	"	PUNCT
ejpam-1372	1062	26	.	.	PUNCT
ejpam-1372	1063	1	here	here	ADV
ejpam-1372	1063	2	,	,	PUNCT
ejpam-1372	1063	3	we	we	PRON
ejpam-1372	1063	4	see	see	VERB
ejpam-1372	1063	5	that	that	SCONJ
ejpam-1372	1063	6	the	the	DET
ejpam-1372	1063	7	truncated	truncated	ADJ
ejpam-1372	1063	8	values	value	NOUN
ejpam-1372	1063	9	are	be	AUX
ejpam-1372	1063	10	quite	quite	ADV
ejpam-1372	1063	11	inaccurate	inaccurate	ADJ
ejpam-1372	1063	12	and	and	CCONJ
ejpam-1372	1063	13	can	can	AUX
ejpam-1372	1063	14	only	only	ADV
ejpam-1372	1063	15	be	be	AUX
ejpam-1372	1063	16	regarded	regard	VERB
ejpam-1372	1063	17	as	as	ADP
ejpam-1372	1063	18	estimates	estimate	NOUN
ejpam-1372	1063	19	despite	despite	SCONJ
ejpam-1372	1063	20	the	the	DET
ejpam-1372	1063	21	fact	fact	NOUN
ejpam-1372	1063	22	that	that	SCONJ
ejpam-1372	1063	23	we	we	PRON
ejpam-1372	1063	24	are	be	AUX
ejpam-1372	1063	25	effectively	effectively	ADV
ejpam-1372	1063	26	carrying	carry	VERB
ejpam-1372	1063	27	out	out	ADP
ejpam-1372	1063	28	our	our	PRON
ejpam-1372	1063	29	investigation	investigation	NOUN
ejpam-1372	1063	30	for	for	ADP
ejpam-1372	1063	31	|z3|	|z3|	NOUN
ejpam-1372	1063	32	,	,	PUNCT
ejpam-1372	1063	33	which	which	PRON
ejpam-1372	1063	34	is	be	AUX
ejpam-1372	1063	35	much	much	ADV
ejpam-1372	1063	36	smaller	small	ADJ
ejpam-1372	1063	37	than	than	ADP
ejpam-1372	1063	38	|z|	|z|	NOUN
ejpam-1372	1063	39	or	or	CCONJ
ejpam-1372	1063	40	4/5	4/5	NOUN
ejpam-1372	1063	41	.	.	PUNCT
ejpam-1372	1064	1	the	the	DET
ejpam-1372	1064	2	inaccuarcy	inaccuarcy	NOUN
ejpam-1372	1064	3	is	be	AUX
ejpam-1372	1064	4	expected	expect	VERB
ejpam-1372	1064	5	because	because	SCONJ
ejpam-1372	1064	6	for	for	ADP
ejpam-1372	1064	7	this	this	DET
ejpam-1372	1064	8	value	value	NOUN
ejpam-1372	1064	9	of	of	ADP
ejpam-1372	1064	10	z	z	PROPN
ejpam-1372	1064	11	,	,	PUNCT
ejpam-1372	1064	12	the	the	DET
ejpam-1372	1064	13	optimal	optimal	ADJ
ejpam-1372	1064	14	point	point	NOUN
ejpam-1372	1064	15	of	of	ADP
ejpam-1372	1064	16	truncation	truncation	NOUN
ejpam-1372	1064	17	nt	not	PART
ejpam-1372	1064	18	is	be	AUX
ejpam-1372	1064	19	equal	equal	ADJ
ejpam-1372	1064	20	to	to	ADP
ejpam-1372	1064	21	unity	unity	NOUN
ejpam-1372	1064	22	.	.	PUNCT
ejpam-1372	1065	1	for	for	ADP
ejpam-1372	1065	2	values	value	NOUN
ejpam-1372	1065	3	of	of	ADP
ejpam-1372	1065	4	n	n	X
ejpam-1372	1065	5	greater	great	ADJ
ejpam-1372	1065	6	than	than	ADP
ejpam-1372	1065	7	5	5	NUM
ejpam-1372	1065	8	,	,	PUNCT
ejpam-1372	1065	9	we	we	PRON
ejpam-1372	1065	10	find	find	VERB
ejpam-1372	1065	11	that	that	SCONJ
ejpam-1372	1065	12	the	the	DET
ejpam-1372	1065	13	regularised	regularise	VERB
ejpam-1372	1065	14	value	value	NOUN
ejpam-1372	1065	15	in	in	ADP
ejpam-1372	1065	16	the	the	DET
ejpam-1372	1065	17	final	final	ADJ
ejpam-1372	1065	18	column	column	NOUN
ejpam-1372	1065	19	is	be	AUX
ejpam-1372	1065	20	not	not	PART
ejpam-1372	1065	21	as	as	ADV
ejpam-1372	1065	22	accurate	accurate	ADJ
ejpam-1372	1065	23	as	as	ADP
ejpam-1372	1065	24	the	the	DET
ejpam-1372	1065	25	n≤5	n≤5	PROPN
ejpam-1372	1065	26	results	result	NOUN
ejpam-1372	1065	27	.	.	PUNCT
ejpam-1372	1066	1	this	this	PRON
ejpam-1372	1066	2	is	be	AUX
ejpam-1372	1066	3	because	because	SCONJ
ejpam-1372	1066	4	the	the	DET
ejpam-1372	1066	5	truncated	truncated	ADJ
ejpam-1372	1066	6	series	series	NOUN
ejpam-1372	1066	7	begins	begin	VERB
ejpam-1372	1066	8	to	to	PART
ejpam-1372	1066	9	grow	grow	VERB
ejpam-1372	1066	10	dramatically	dramatically	ADV
ejpam-1372	1066	11	or	or	CCONJ
ejpam-1372	1066	12	rather	rather	ADV
ejpam-1372	1066	13	,	,	PUNCT
ejpam-1372	1066	14	diverges	diverge	VERB
ejpam-1372	1066	15	.	.	PUNCT
ejpam-1372	1067	1	to	to	PART
ejpam-1372	1067	2	compensate	compensate	VERB
ejpam-1372	1067	3	for	for	ADP
ejpam-1372	1067	4	the	the	DET
ejpam-1372	1067	5	divergence	divergence	NOUN
ejpam-1372	1067	6	of	of	ADP
ejpam-1372	1067	7	the	the	DET
ejpam-1372	1067	8	truncated	truncated	ADJ
ejpam-1372	1067	9	series	series	NOUN
ejpam-1372	1067	10	,	,	PUNCT
ejpam-1372	1067	11	the	the	DET
ejpam-1372	1067	12	value	value	NOUN
ejpam-1372	1067	13	of	of	ADP
ejpam-1372	1067	14	the	the	DET
ejpam-1372	1067	15	mb	mb	NOUN
ejpam-1372	1067	16	integral	integral	ADJ
ejpam-1372	1067	17	diverges	diverge	NOUN
ejpam-1372	1067	18	in	in	ADP
ejpam-1372	1067	19	the	the	DET
ejpam-1372	1067	20	opposite	opposite	ADJ
ejpam-1372	1067	21	sense	sense	NOUN
ejpam-1372	1067	22	such	such	ADJ
ejpam-1372	1067	23	that	that	SCONJ
ejpam-1372	1067	24	when	when	SCONJ
ejpam-1372	1067	25	the	the	DET
ejpam-1372	1067	26	latter	latter	ADJ
ejpam-1372	1067	27	is	be	AUX
ejpam-1372	1067	28	combined	combine	VERB
ejpam-1372	1067	29	with	with	ADP
ejpam-1372	1067	30	the	the	DET
ejpam-1372	1067	31	value	value	NOUN
ejpam-1372	1067	32	for	for	ADP
ejpam-1372	1067	33	the	the	DET
ejpam-1372	1067	34	truncated	truncated	ADJ
ejpam-1372	1067	35	series	series	NOUN
ejpam-1372	1067	36	,	,	PUNCT
ejpam-1372	1067	37	it	it	PRON
ejpam-1372	1067	38	yields	yield	VERB
ejpam-1372	1067	39	a	a	DET
ejpam-1372	1067	40	less	less	ADV
ejpam-1372	1067	41	accurate	accurate	ADJ
ejpam-1372	1067	42	regularised	regularise	VERB
ejpam-1372	1067	43	value	value	NOUN
ejpam-1372	1067	44	due	due	ADP
ejpam-1372	1067	45	to	to	ADP
ejpam-1372	1067	46	the	the	DET
ejpam-1372	1067	47	cancellation	cancellation	NOUN
ejpam-1372	1067	48	of	of	ADP
ejpam-1372	1067	49	redundant	redundant	ADJ
ejpam-1372	1067	50	decimal	decimal	ADJ
ejpam-1372	1067	51	places	place	NOUN
ejpam-1372	1067	52	.	.	PUNCT
ejpam-1372	1068	1	hence	hence	ADV
ejpam-1372	1068	2	,	,	PUNCT
ejpam-1372	1068	3	by	by	ADP
ejpam-1372	1068	4	the	the	DET
ejpam-1372	1068	5	time	time	NOUN
ejpam-1372	1068	6	the	the	DET
ejpam-1372	1068	7	truncation	truncation	NOUN
ejpam-1372	1068	8	parameter	parameter	NOUN
ejpam-1372	1068	9	reaches	reach	VERB
ejpam-1372	1068	10	a	a	DET
ejpam-1372	1068	11	value	value	NOUN
ejpam-1372	1068	12	of	of	ADP
ejpam-1372	1068	13	20	20	NUM
ejpam-1372	1068	14	,	,	PUNCT
ejpam-1372	1068	15	we	we	PRON
ejpam-1372	1068	16	find	find	VERB
ejpam-1372	1068	17	that	that	SCONJ
ejpam-1372	1068	18	the	the	DET
ejpam-1372	1068	19	truncated	truncated	ADJ
ejpam-1372	1068	20	series	series	NOUN
ejpam-1372	1068	21	is	be	AUX
ejpam-1372	1068	22	of	of	ADP
ejpam-1372	1068	23	the	the	DET
ejpam-1372	1068	24	order	order	NOUN
ejpam-1372	1068	25	of	of	ADP
ejpam-1372	1068	26	1010	1010	NUM
ejpam-1372	1068	27	,	,	PUNCT
ejpam-1372	1068	28	which	which	PRON
ejpam-1372	1068	29	means	mean	VERB
ejpam-1372	1068	30	that	that	SCONJ
ejpam-1372	1068	31	the	the	DET
ejpam-1372	1068	32	first	first	ADJ
ejpam-1372	1068	33	10	10	NUM
ejpam-1372	1068	34	significant	significant	ADJ
ejpam-1372	1068	35	figures	figure	NOUN
ejpam-1372	1068	36	will	will	AUX
ejpam-1372	1068	37	be	be	AUX
ejpam-1372	1068	38	cancelled	cancel	VERB
ejpam-1372	1068	39	before	before	ADP
ejpam-1372	1068	40	the	the	DET
ejpam-1372	1068	41	regularised	regularise	VERB
ejpam-1372	1068	42	value	value	NOUN
ejpam-1372	1068	43	for	for	ADP
ejpam-1372	1068	44	the	the	DET
ejpam-1372	1068	45	series	series	NOUN
ejpam-1372	1068	46	on	on	ADP
ejpam-1372	1068	47	the	the	DET
ejpam-1372	1068	48	lhs	lhs	PROPN
ejpam-1372	1068	49	of	of	ADP
ejpam-1372	1068	50	eq	eq	PROPN
ejpam-1372	1068	51	.	.	PUNCT
ejpam-1372	1069	1	(	(	PUNCT
ejpam-1372	1069	2	119	119	NUM
ejpam-1372	1069	3	)	)	PUNCT
ejpam-1372	1069	4	can	can	AUX
ejpam-1372	1069	5	be	be	AUX
ejpam-1372	1069	6	obtained	obtain	VERB
ejpam-1372	1069	7	.	.	PUNCT
ejpam-1372	1070	1	consequently	consequently	ADV
ejpam-1372	1070	2	,	,	PUNCT
ejpam-1372	1070	3	the	the	DET
ejpam-1372	1070	4	regularised	regularise	VERB
ejpam-1372	1070	5	value	value	NOUN
ejpam-1372	1070	6	in	in	ADP
ejpam-1372	1070	7	the	the	DET
ejpam-1372	1070	8	final	final	ADJ
ejpam-1372	1070	9	column	column	NOUN
ejpam-1372	1070	10	for	for	ADP
ejpam-1372	1070	11	the	the	DET
ejpam-1372	1070	12	l	l	NOUN
ejpam-1372	1070	13	=	=	SYM
ejpam-1372	1070	14	0	0	NUM
ejpam-1372	1070	15	form	form	NOUN
ejpam-1372	1070	16	will	will	AUX
ejpam-1372	1070	17	only	only	ADV
ejpam-1372	1070	18	be	be	AUX
ejpam-1372	1070	19	accurate	accurate	ADJ
ejpam-1372	1070	20	to	to	ADP
ejpam-1372	1070	21	5	5	NUM
ejpam-1372	1070	22	decimal	decimal	ADJ
ejpam-1372	1070	23	places	place	NOUN
ejpam-1372	1070	24	,	,	PUNCT
ejpam-1372	1070	25	courtesy	courtesy	NOUN
ejpam-1372	1070	26	of	of	ADP
ejpam-1372	1070	27	the	the	DET
ejpam-1372	1070	28	machine	machine	NOUN
ejpam-1372	1070	29	precision	precision	NOUN
ejpam-1372	1070	30	of	of	ADP
ejpam-1372	1070	31	the	the	DET
ejpam-1372	1070	32	computing	computing	NOUN
ejpam-1372	1070	33	system	system	NOUN
ejpam-1372	1070	34	.	.	PUNCT
ejpam-1372	1071	1	it	it	PRON
ejpam-1372	1071	2	should	should	AUX
ejpam-1372	1071	3	also	also	ADV
ejpam-1372	1071	4	be	be	AUX
ejpam-1372	1071	5	noted	note	VERB
ejpam-1372	1071	6	that	that	SCONJ
ejpam-1372	1071	7	all	all	DET
ejpam-1372	1071	8	the	the	DET
ejpam-1372	1071	9	values	value	NOUN
ejpam-1372	1071	10	displayed	display	VERB
ejpam-1372	1071	11	in	in	ADP
ejpam-1372	1071	12	this	this	PRON
ejpam-1372	1071	13	and	and	CCONJ
ejpam-1372	1071	14	subsequent	subsequent	ADJ
ejpam-1372	1071	15	tables	table	NOUN
ejpam-1372	1071	16	are	be	AUX
ejpam-1372	1071	17	not	not	PART
ejpam-1372	1071	18	rounded	round	VERB
ejpam-1372	1071	19	off	off	ADP
ejpam-1372	1071	20	at	at	ADP
ejpam-1372	1071	21	any	any	DET
ejpam-1372	1071	22	stage	stage	NOUN
ejpam-1372	1071	23	.	.	PUNCT
ejpam-1372	1072	1	that	that	PRON
ejpam-1372	1072	2	is	is	ADV
ejpam-1372	1072	3	,	,	PUNCT
ejpam-1372	1072	4	the	the	DET
ejpam-1372	1072	5	final	final	ADJ
ejpam-1372	1072	6	digit	digit	NOUN
ejpam-1372	1072	7	presented	present	VERB
ejpam-1372	1072	8	in	in	ADP
ejpam-1372	1072	9	the	the	DET
ejpam-1372	1072	10	tables	table	NOUN
ejpam-1372	1072	11	represents	represent	VERB
ejpam-1372	1072	12	in	in	ADP
ejpam-1372	1072	13	all	all	DET
ejpam-1372	1072	14	cases	case	NOUN
ejpam-1372	1072	15	the	the	DET
ejpam-1372	1072	16	output	output	NOUN
ejpam-1372	1072	17	as	as	SCONJ
ejpam-1372	1072	18	derived	derive	VERB
ejpam-1372	1072	19	from	from	ADP
ejpam-1372	1072	20	running	run	VERB
ejpam-1372	1072	21	the	the	DET
ejpam-1372	1072	22	computer	computer	NOUN
ejpam-1372	1072	23	programs	program	NOUN
ejpam-1372	1072	24	.	.	PUNCT
ejpam-1372	1073	1	another	another	DET
ejpam-1372	1073	2	point	point	NOUN
ejpam-1372	1073	3	requiring	require	VERB
ejpam-1372	1073	4	mention	mention	NOUN
ejpam-1372	1073	5	is	be	AUX
ejpam-1372	1073	6	that	that	SCONJ
ejpam-1372	1073	7	the	the	DET
ejpam-1372	1073	8	values	value	NOUN
ejpam-1372	1073	9	of	of	ADP
ejpam-1372	1073	10	the	the	DET
ejpam-1372	1073	11	l	l	NOUN
ejpam-1372	1073	12	=	=	SYM
ejpam-1372	1073	13	1	1	NUM
ejpam-1372	1073	14	mb	mb	NOUN
ejpam-1372	1073	15	integrals	integral	NOUN
ejpam-1372	1073	16	for	for	ADP
ejpam-1372	1073	17	n	n	X
ejpam-1372	1073	18	≥	≥	NOUN
ejpam-1372	1073	19	5	5	NUM
ejpam-1372	1073	20	in	in	ADP
ejpam-1372	1073	21	the	the	DET
ejpam-1372	1073	22	table	table	NOUN
ejpam-1372	1073	23	have	have	AUX
ejpam-1372	1073	24	been	be	AUX
ejpam-1372	1073	25	asterisked	asterisk	VERB
ejpam-1372	1073	26	because	because	SCONJ
ejpam-1372	1073	27	problems	problem	NOUN
ejpam-1372	1073	28	occurred	occur	VERB
ejpam-1372	1073	29	during	during	ADP
ejpam-1372	1073	30	their	their	PRON
ejpam-1372	1073	31	computation	computation	NOUN
ejpam-1372	1073	32	.	.	PUNCT
ejpam-1372	1074	1	in	in	ADP
ejpam-1372	1074	2	fact	fact	NOUN
ejpam-1372	1074	3	,	,	PUNCT
ejpam-1372	1074	4	for	for	ADP
ejpam-1372	1074	5	n=20	n=20	NOUN
ejpam-1372	1074	6	the	the	DET
ejpam-1372	1074	7	regularised	regularise	VERB
ejpam-1372	1074	8	value	value	NOUN
ejpam-1372	1074	9	in	in	ADP
ejpam-1372	1074	10	the	the	DET
ejpam-1372	1074	11	final	final	ADJ
ejpam-1372	1074	12	column	column	NOUN
ejpam-1372	1074	13	is	be	AUX
ejpam-1372	1074	14	not	not	PART
ejpam-1372	1074	15	even	even	ADV
ejpam-1372	1074	16	correct	correct	ADJ
ejpam-1372	1074	17	.	.	PUNCT
ejpam-1372	1075	1	this	this	PRON
ejpam-1372	1075	2	is	be	AUX
ejpam-1372	1075	3	an	an	DET
ejpam-1372	1075	4	indication	indication	NOUN
ejpam-1372	1075	5	that	that	SCONJ
ejpam-1372	1075	6	numerical	numerical	ADJ
ejpam-1372	1075	7	integration	integration	NOUN
ejpam-1372	1075	8	is	be	AUX
ejpam-1372	1075	9	largely	largely	ADV
ejpam-1372	1075	10	a	a	DET
ejpam-1372	1075	11	“	"	PUNCT
ejpam-1372	1075	12	black	black	ADJ
ejpam-1372	1075	13	art	art	NOUN
ejpam-1372	1075	14	”	"	PUNCT
ejpam-1372	1075	15	relying	rely	VERB
ejpam-1372	1075	16	on	on	ADP
ejpam-1372	1075	17	the	the	DET
ejpam-1372	1075	18	intuition	intuition	NOUN
ejpam-1372	1075	19	of	of	ADP
ejpam-1372	1075	20	the	the	DET
ejpam-1372	1075	21	programmer	programmer	NOUN
ejpam-1372	1075	22	to	to	PART
ejpam-1372	1075	23	gauge	gauge	VERB
ejpam-1372	1075	24	the	the	DET
ejpam-1372	1075	25	limitations	limitation	NOUN
ejpam-1372	1075	26	of	of	ADP
ejpam-1372	1075	27	the	the	DET
ejpam-1372	1075	28	software	software	NOUN
ejpam-1372	1075	29	being	be	AUX
ejpam-1372	1075	30	used	use	VERB
ejpam-1372	1075	31	.	.	PUNCT
ejpam-1372	1076	1	in	in	ADP
ejpam-1372	1076	2	this	this	DET
ejpam-1372	1076	3	instance	instance	NOUN
ejpam-1372	1076	4	,	,	PUNCT
ejpam-1372	1076	5	the	the	DET
ejpam-1372	1076	6	integrand	integrand	NOUN
ejpam-1372	1076	7	outside	outside	ADP
ejpam-1372	1076	8	the	the	DET
ejpam-1372	1076	9	mathematica	mathematica	PROPN
ejpam-1372	1076	10	module	module	NOUN
ejpam-1372	1076	11	has	have	AUX
ejpam-1372	1076	12	been	be	AUX
ejpam-1372	1076	13	set	set	VERB
ejpam-1372	1076	14	equal	equal	ADJ
ejpam-1372	1076	15	to	to	ADP
ejpam-1372	1076	16	intgrd[z−	intgrd[z−	NOUN
ejpam-1372	1076	17	,	,	PUNCT
ejpam-1372	1076	18	s−	s−	PROPN
ejpam-1372	1076	19	,	,	PUNCT
ejpam-1372	1076	20	l−	l−	PROPN
ejpam-1372	1076	21	]	]	PUNCT
ejpam-1372	1076	22	:	:	PUNCT
ejpam-1372	1077	1	=	=	SYM
ejpam-1372	1077	2	(	(	PUNCT
ejpam-1372	1077	3	z	z	NOUN
ejpam-1372	1077	4	∧	∧	PROPN
ejpam-1372	1078	1	3)∧	3)∧	PROPN
ejpam-1372	1078	2	s	s	PART
ejpam-1372	1078	3	exp[−2	exp[−2	NOUN
ejpam-1372	1079	1	i	i	NOUN
ejpam-1372	1079	2	l	l	NOUN
ejpam-1372	1079	3	pi	pi	NOUN
ejpam-1372	1079	4	s	s	X
ejpam-1372	1079	5	]	]	X
ejpam-1372	1079	6	gamma[s+	gamma[s+	PROPN
ejpam-1372	1079	7	3/7]/	3/7]/	NUM
ejpam-1372	1079	8	(	(	PUNCT
ejpam-1372	1079	9	exp[−i	exp[−i	NOUN
ejpam-1372	1079	10	pi	pi	NOUN
ejpam-1372	1079	11	s]−	s]−	PROPN
ejpam-1372	1079	12	exp[i	exp[i	NOUN
ejpam-1372	1079	13	pi	pi	NOUN
ejpam-1372	1079	14	s	s	X
ejpam-1372	1079	15	]	]	X
ejpam-1372	1079	16	)	)	PUNCT
ejpam-1372	1079	17	.	.	PUNCT
ejpam-1372	1080	1	the	the	DET
ejpam-1372	1080	2	main	main	ADJ
ejpam-1372	1080	3	module	module	NOUN
ejpam-1372	1080	4	requires	require	VERB
ejpam-1372	1080	5	the	the	DET
ejpam-1372	1080	6	value	value	NOUN
ejpam-1372	1080	7	of	of	ADP
ejpam-1372	1080	8	|z|	|z|	NOUN
ejpam-1372	1080	9	and	and	CCONJ
ejpam-1372	1080	10	arg	arg	NOUN
ejpam-1372	1080	11	z	z	PROPN
ejpam-1372	1080	12	as	as	ADP
ejpam-1372	1080	13	input	input	NOUN
ejpam-1372	1080	14	before	before	ADP
ejpam-1372	1080	15	calculating	calculate	VERB
ejpam-1372	1080	16	the	the	DET
ejpam-1372	1080	17	value	value	NOUN
ejpam-1372	1080	18	of	of	ADP
ejpam-1372	1080	19	z(=	z(=	PROPN
ejpam-1372	1080	20	|z|exp(iarg	|z|exp(iarg	PROPN
ejpam-1372	1080	21	z	z	NOUN
ejpam-1372	1080	22	)	)	PUNCT
ejpam-1372	1080	23	)	)	PUNCT
ejpam-1372	1080	24	.	.	PUNCT
ejpam-1372	1081	1	the	the	DET
ejpam-1372	1081	2	problem	problem	NOUN
ejpam-1372	1081	3	with	with	ADP
ejpam-1372	1081	4	the	the	DET
ejpam-1372	1081	5	above	above	ADJ
ejpam-1372	1081	6	form	form	NOUN
ejpam-1372	1081	7	for	for	ADP
ejpam-1372	1081	8	the	the	DET
ejpam-1372	1081	9	integrand	integrand	NOUN
ejpam-1372	1081	10	is	be	AUX
ejpam-1372	1081	11	that	that	SCONJ
ejpam-1372	1081	12	z3s	z3	NOUN
ejpam-1372	1081	13	may	may	AUX
ejpam-1372	1081	14	become	become	VERB
ejpam-1372	1081	15	very	very	ADV
ejpam-1372	1081	16	large	large	ADJ
ejpam-1372	1081	17	or	or	CCONJ
ejpam-1372	1081	18	very	very	ADV
ejpam-1372	1081	19	small	small	ADJ
ejpam-1372	1081	20	before	before	SCONJ
ejpam-1372	1081	21	it	it	PRON
ejpam-1372	1081	22	can	can	AUX
ejpam-1372	1081	23	be	be	AUX
ejpam-1372	1081	24	countered	counter	VERB
ejpam-1372	1081	25	by	by	ADP
ejpam-1372	1081	26	the	the	DET
ejpam-1372	1081	27	factor	factor	NOUN
ejpam-1372	1081	28	of	of	ADP
ejpam-1372	1081	29	exp(2iπs	exp(2iπs	PROPN
ejpam-1372	1081	30	)	)	PUNCT
ejpam-1372	1081	31	and/or	and/or	CCONJ
ejpam-1372	1081	32	the	the	DET
ejpam-1372	1081	33	other	other	ADJ
ejpam-1372	1081	34	factors	factor	NOUN
ejpam-1372	1081	35	in	in	ADP
ejpam-1372	1081	36	the	the	DET
ejpam-1372	1081	37	integrand	integrand	NOUN
ejpam-1372	1081	38	.	.	PUNCT
ejpam-1372	1082	1	when	when	SCONJ
ejpam-1372	1082	2	this	this	PRON
ejpam-1372	1082	3	occurs	occur	VERB
ejpam-1372	1082	4	,	,	PUNCT
ejpam-1372	1082	5	mathematica	mathematica	PROPN
ejpam-1372	1082	6	alerts	alert	VERB
ejpam-1372	1082	7	the	the	DET
ejpam-1372	1082	8	user	user	NOUN
ejpam-1372	1082	9	that	that	PRON
ejpam-1372	1082	10	it	it	PRON
ejpam-1372	1082	11	is	be	AUX
ejpam-1372	1082	12	experiencing	experience	VERB
ejpam-1372	1082	13	convergence	convergence	NOUN
ejpam-1372	1082	14	problems	problem	NOUN
ejpam-1372	1082	15	in	in	ADP
ejpam-1372	1082	16	the	the	DET
ejpam-1372	1082	17	numerical	numerical	ADJ
ejpam-1372	1082	18	integration	integration	NOUN
ejpam-1372	1082	19	.	.	PUNCT
ejpam-1372	1083	1	the	the	DET
ejpam-1372	1083	2	asterisked	asterisked	ADJ
ejpam-1372	1083	3	results	result	NOUN
ejpam-1372	1083	4	in	in	ADP
ejpam-1372	1083	5	table	table	NOUN
ejpam-1372	1083	6	1	1	NUM
ejpam-1372	1083	7	are	be	AUX
ejpam-1372	1083	8	examples	example	NOUN
ejpam-1372	1083	9	of	of	ADP
ejpam-1372	1083	10	this	this	DET
ejpam-1372	1083	11	type	type	NOUN
ejpam-1372	1083	12	of	of	ADP
ejpam-1372	1083	13	occurrence	occurrence	NOUN
ejpam-1372	1083	14	.	.	PUNCT
ejpam-1372	1084	1	in	in	ADP
ejpam-1372	1084	2	fact	fact	NOUN
ejpam-1372	1084	3	,	,	PUNCT
ejpam-1372	1084	4	what	what	PRON
ejpam-1372	1084	5	is	be	AUX
ejpam-1372	1084	6	surprising	surprising	ADJ
ejpam-1372	1084	7	about	about	ADP
ejpam-1372	1084	8	these	these	DET
ejpam-1372	1084	9	results	result	NOUN
ejpam-1372	1084	10	is	be	AUX
ejpam-1372	1084	11	that	that	SCONJ
ejpam-1372	1084	12	although	although	SCONJ
ejpam-1372	1084	13	convergence	convergence	NOUN
ejpam-1372	1084	14	problems	problem	NOUN
ejpam-1372	1084	15	did	do	AUX
ejpam-1372	1084	16	arise	arise	VERB
ejpam-1372	1084	17	in	in	ADP
ejpam-1372	1084	18	the	the	DET
ejpam-1372	1084	19	evaluation	evaluation	NOUN
ejpam-1372	1084	20	of	of	ADP
ejpam-1372	1084	21	the	the	DET
ejpam-1372	1084	22	mb	mb	NOUN
ejpam-1372	1084	23	integral	integral	ADJ
ejpam-1372	1084	24	,	,	PUNCT
ejpam-1372	1084	25	the	the	DET
ejpam-1372	1084	26	software	software	NOUN
ejpam-1372	1084	27	package	package	NOUN
ejpam-1372	1084	28	was	be	AUX
ejpam-1372	1084	29	still	still	ADV
ejpam-1372	1084	30	able	able	ADJ
ejpam-1372	1084	31	to	to	PART
ejpam-1372	1084	32	give	give	VERB
ejpam-1372	1084	33	accurate	accurate	ADJ
ejpam-1372	1084	34	values	value	NOUN
ejpam-1372	1084	35	for	for	ADP
ejpam-1372	1084	36	the	the	DET
ejpam-1372	1084	37	regularised	regularise	VERB
ejpam-1372	1084	38	value	value	NOUN
ejpam-1372	1084	39	in	in	ADV
ejpam-1372	1084	40	all	all	ADV
ejpam-1372	1084	41	,	,	PUNCT
ejpam-1372	1084	42	but	but	CCONJ
ejpam-1372	1084	43	the	the	DET
ejpam-1372	1084	44	last	last	ADJ
ejpam-1372	1084	45	calculation	calculation	NOUN
ejpam-1372	1084	46	,	,	PUNCT
ejpam-1372	1084	47	i.e.	i.e.	X
ejpam-1372	1084	48	for	for	ADP
ejpam-1372	1084	49	n=20	n=20	NOUN
ejpam-1372	1084	50	and	and	CCONJ
ejpam-1372	1084	51	l=1	l=1	PROPN
ejpam-1372	1084	52	.	.	PUNCT
ejpam-1372	1085	1	let	let	VERB
ejpam-1372	1085	2	us	we	PRON
ejpam-1372	1085	3	raise	raise	VERB
ejpam-1372	1085	4	the	the	DET
ejpam-1372	1085	5	ante	ante	NOUN
ejpam-1372	1085	6	by	by	ADP
ejpam-1372	1085	7	carrying	carry	VERB
ejpam-1372	1085	8	out	out	ADP
ejpam-1372	1085	9	calculations	calculation	NOUN
ejpam-1372	1085	10	using	use	VERB
ejpam-1372	1085	11	a	a	DET
ejpam-1372	1085	12	later	later	ADJ
ejpam-1372	1085	13	version	version	NOUN
ejpam-1372	1085	14	of	of	ADP
ejpam-1372	1085	15	the	the	DET
ejpam-1372	1085	16	software	software	NOUN
ejpam-1372	1085	17	,	,	PUNCT
ejpam-1372	1085	18	namely	namely	ADV
ejpam-1372	1085	19	version	version	NOUN
ejpam-1372	1085	20	7.0	7.0	NUM
ejpam-1372	1085	21	,	,	PUNCT
ejpam-1372	1085	22	on	on	ADP
ejpam-1372	1085	23	a	a	DET
ejpam-1372	1085	24	powermac	powermac	ADJ
ejpam-1372	1085	25	g5	g5	NOUN
ejpam-1372	1085	26	with	with	ADP
ejpam-1372	1085	27	1.25	1.25	NUM
ejpam-1372	1085	28	gb	gb	NOUN
ejpam-1372	1085	29	of	of	ADP
ejpam-1372	1085	30	ram	ram	NOUN
ejpam-1372	1085	31	.	.	PUNCT
ejpam-1372	1086	1	we	we	PRON
ejpam-1372	1086	2	shall	shall	AUX
ejpam-1372	1086	3	also	also	ADV
ejpam-1372	1086	4	carry	carry	VERB
ejpam-1372	1086	5	out	out	ADP
ejpam-1372	1086	6	calculations	calculation	NOUN
ejpam-1372	1086	7	for	for	ADP
ejpam-1372	1086	8	both	both	DET
ejpam-1372	1086	9	|z|=	|z|=	NOUN
ejpam-1372	1086	10	4/5	4/5	NUM
ejpam-1372	1086	11	and	and	CCONJ
ejpam-1372	1086	12	|z|=	|z|=	NOUN
ejpam-1372	1086	13	2	2	NUM
ejpam-1372	1086	14	.	.	PUNCT
ejpam-1372	1086	15	two	two	NUM
ejpam-1372	1086	16	separate	separate	ADJ
ejpam-1372	1086	17	tables	table	NOUN
ejpam-1372	1086	18	of	of	ADP
ejpam-1372	1086	19	results	result	NOUN
ejpam-1372	1086	20	will	will	AUX
ejpam-1372	1086	21	be	be	AUX
ejpam-1372	1086	22	presented	present	VERB
ejpam-1372	1086	23	in	in	ADP
ejpam-1372	1086	24	the	the	DET
ejpam-1372	1086	25	v.	v.	ADP
ejpam-1372	1086	26	kowalenko	kowalenko	PROPN
ejpam-1372	1086	27	/	/	SYM
ejpam-1372	1086	28	eur	eur	PROPN
ejpam-1372	1086	29	.	.	PUNCT
ejpam-1372	1087	1	j.	j.	PROPN
ejpam-1372	1087	2	pure	pure	PROPN
ejpam-1372	1087	3	appl	appl	PROPN
ejpam-1372	1087	4	.	.	PROPN
ejpam-1372	1087	5	math	math	PROPN
ejpam-1372	1087	6	,	,	PUNCT
ejpam-1372	1087	7	4	4	NUM
ejpam-1372	1087	8	(	(	PUNCT
ejpam-1372	1087	9	2011	2011	NUM
ejpam-1372	1087	10	)	)	PUNCT
ejpam-1372	1087	11	,	,	PUNCT
ejpam-1372	1087	12	370	370	NUM
ejpam-1372	1087	13	-	-	SYM
ejpam-1372	1087	14	423	423	NUM
ejpam-1372	1087	15	409	409	NUM
ejpam-1372	1087	16	appendix	appendix	NOUN
ejpam-1372	1087	17	:	:	PUNCT
ejpam-1372	1087	18	the	the	DET
ejpam-1372	1087	19	first	first	ADV
ejpam-1372	1087	20	displaying	display	VERB
ejpam-1372	1087	21	the	the	DET
ejpam-1372	1087	22	results	result	NOUN
ejpam-1372	1087	23	obtained	obtain	VERB
ejpam-1372	1087	24	for	for	ADP
ejpam-1372	1087	25	|z|=4/5	|z|=4/5	ADV
ejpam-1372	1087	26	and	and	CCONJ
ejpam-1372	1087	27	arg	arg	NOUN
ejpam-1372	1087	28	z	z	NOUN
ejpam-1372	1087	29	situated	situate	VERB
ejpam-1372	1087	30	in	in	ADP
ejpam-1372	1087	31	the	the	DET
ejpam-1372	1087	32	upper	upper	ADJ
ejpam-1372	1087	33	half	half	NOUN
ejpam-1372	1087	34	of	of	ADP
ejpam-1372	1087	35	the	the	DET
ejpam-1372	1087	36	principal	principal	ADJ
ejpam-1372	1087	37	branch	branch	NOUN
ejpam-1372	1087	38	,	,	PUNCT
ejpam-1372	1087	39	viz	viz	PROPN
ejpam-1372	1087	40	.	.	NOUN
ejpam-1372	1087	41	0	0	PUNCT
ejpam-1372	1087	42	<	<	X
ejpam-1372	1087	43	argz	argz	X
ejpam-1372	1087	44	<	<	X
ejpam-1372	1087	45	π	π	X
ejpam-1372	1087	46	,	,	PUNCT
ejpam-1372	1087	47	and	and	CCONJ
ejpam-1372	1087	48	the	the	DET
ejpam-1372	1087	49	second	second	ADJ
ejpam-1372	1087	50	table	table	NOUN
ejpam-1372	1087	51	displaying	display	VERB
ejpam-1372	1087	52	the	the	DET
ejpam-1372	1087	53	results	result	NOUN
ejpam-1372	1087	54	for	for	ADP
ejpam-1372	1087	55	|z|=2	|z|=2	ADJ
ejpam-1372	1087	56	and	and	CCONJ
ejpam-1372	1087	57	−π	−π	NOUN
ejpam-1372	1087	58	<	<	X
ejpam-1372	1087	59	argz<0	argz<0	PROPN
ejpam-1372	1087	60	.	.	PUNCT
ejpam-1372	1088	1	it	it	PRON
ejpam-1372	1088	2	would	would	AUX
ejpam-1372	1088	3	simply	simply	ADV
ejpam-1372	1088	4	be	be	AUX
ejpam-1372	1088	5	inconceivable	inconceivable	ADJ
ejpam-1372	1088	6	to	to	PART
ejpam-1372	1088	7	consider	consider	VERB
ejpam-1372	1088	8	the	the	DET
ejpam-1372	1088	9	second	second	ADJ
ejpam-1372	1088	10	lot	lot	NOUN
ejpam-1372	1088	11	of	of	ADP
ejpam-1372	1088	12	values	value	NOUN
ejpam-1372	1088	13	for	for	ADP
ejpam-1372	1088	14	|z|	|z|	NOUN
ejpam-1372	1088	15	in	in	ADP
ejpam-1372	1088	16	standard	standard	ADJ
ejpam-1372	1088	17	asymptotics	asymptotic	NOUN
ejpam-1372	1088	18	as	as	SCONJ
ejpam-1372	1088	19	truncation	truncation	NOUN
ejpam-1372	1088	20	would	would	AUX
ejpam-1372	1088	21	result	result	VERB
ejpam-1372	1088	22	in	in	ADP
ejpam-1372	1088	23	extremely	extremely	ADV
ejpam-1372	1088	24	inaccurate	inaccurate	ADJ
ejpam-1372	1088	25	results	result	NOUN
ejpam-1372	1088	26	.	.	PUNCT
ejpam-1372	1089	1	furthermore	furthermore	ADV
ejpam-1372	1089	2	,	,	PUNCT
ejpam-1372	1089	3	as	as	ADP
ejpam-1372	1089	4	a	a	DET
ejpam-1372	1089	5	result	result	NOUN
ejpam-1372	1089	6	of	of	ADP
ejpam-1372	1089	7	the	the	DET
ejpam-1372	1089	8	discussion	discussion	NOUN
ejpam-1372	1089	9	in	in	ADP
ejpam-1372	1089	10	the	the	DET
ejpam-1372	1089	11	preceding	precede	VERB
ejpam-1372	1089	12	paragraph	paragraph	NOUN
ejpam-1372	1089	13	,	,	PUNCT
ejpam-1372	1089	14	we	we	PRON
ejpam-1372	1089	15	shall	shall	AUX
ejpam-1372	1089	16	re	re	VERB
ejpam-1372	1089	17	-	-	VERB
ejpam-1372	1089	18	write	write	VERB
ejpam-1372	1089	19	the	the	DET
ejpam-1372	1089	20	integrand	integrand	NOUN
ejpam-1372	1089	21	for	for	ADP
ejpam-1372	1089	22	the	the	DET
ejpam-1372	1089	23	nintegrate	nintegrate	ADJ
ejpam-1372	1089	24	routine	routine	NOUN
ejpam-1372	1089	25	in	in	ADP
ejpam-1372	1089	26	the	the	DET
ejpam-1372	1089	27	mathematica	mathematica	PROPN
ejpam-1372	1089	28	7.0	7.0	NUM
ejpam-1372	1089	29	module	module	NOUN
ejpam-1372	1089	30	as	as	ADP
ejpam-1372	1089	31	intgrd[modz−	intgrd[modz−	SYM
ejpam-1372	1089	32	,	,	PUNCT
ejpam-1372	1089	33	argz−	argz−	NOUN
ejpam-1372	1089	34	,	,	PUNCT
ejpam-1372	1089	35	s−	s−	PROPN
ejpam-1372	1089	36	,	,	PUNCT
ejpam-1372	1089	37	l−	l−	PROPN
ejpam-1372	1089	38	]	]	PUNCT
ejpam-1372	1089	39	:	:	PUNCT
ejpam-1372	1089	40	=	=	SYM
ejpam-1372	1089	41	modz∧	modz∧	ADJ
ejpam-1372	1089	42	(	(	PUNCT
ejpam-1372	1089	43	3s)exp[(3	3s)exp[(3	NUM
ejpam-1372	1089	44	argz−	argz−	ADJ
ejpam-1372	1089	45	2	2	NUM
ejpam-1372	1089	46	l	l	NOUN
ejpam-1372	1089	47	pi	pi	NOUN
ejpam-1372	1089	48	)	)	PUNCT
ejpam-1372	1089	49	i	i	PRON
ejpam-1372	1089	50	s	s	VERB
ejpam-1372	1089	51	]	]	X
ejpam-1372	1089	52	gamma[s+	gamma[s+	PROPN
ejpam-1372	1089	53	3/7]/(exp[−i	3/7]/(exp[−i	NUM
ejpam-1372	1089	54	pi	pi	NOUN
ejpam-1372	1089	55	s]−	s]−	PROPN
ejpam-1372	1089	56	exp[i	exp[i	NOUN
ejpam-1372	1089	57	pi	pi	NOUN
ejpam-1372	1089	58	s	s	X
ejpam-1372	1089	59	]	]	X
ejpam-1372	1089	60	)	)	PUNCT
ejpam-1372	1089	61	.	.	PUNCT
ejpam-1372	1090	1	this	this	PRON
ejpam-1372	1090	2	provides	provide	VERB
ejpam-1372	1090	3	us	we	PRON
ejpam-1372	1090	4	with	with	ADP
ejpam-1372	1090	5	the	the	DET
ejpam-1372	1090	6	best	good	ADJ
ejpam-1372	1090	7	opportunity	opportunity	NOUN
ejpam-1372	1090	8	to	to	PART
ejpam-1372	1090	9	avoid	avoid	VERB
ejpam-1372	1090	10	convergence	convergence	NOUN
ejpam-1372	1090	11	problems	problem	NOUN
ejpam-1372	1090	12	that	that	PRON
ejpam-1372	1090	13	arose	arise	VERB
ejpam-1372	1090	14	in	in	ADP
ejpam-1372	1090	15	presenting	present	VERB
ejpam-1372	1090	16	the	the	DET
ejpam-1372	1090	17	results	result	NOUN
ejpam-1372	1090	18	in	in	ADP
ejpam-1372	1090	19	table	table	NOUN
ejpam-1372	1090	20	1	1	NUM
ejpam-1372	1090	21	.	.	PUNCT
ejpam-1372	1090	22	before	before	SCONJ
ejpam-1372	1090	23	the	the	DET
ejpam-1372	1090	24	code	code	NOUN
ejpam-1372	1090	25	was	be	AUX
ejpam-1372	1090	26	used	use	VERB
ejpam-1372	1090	27	to	to	PART
ejpam-1372	1090	28	generate	generate	VERB
ejpam-1372	1090	29	the	the	DET
ejpam-1372	1090	30	results	result	NOUN
ejpam-1372	1090	31	for	for	ADP
ejpam-1372	1090	32	various	various	ADJ
ejpam-1372	1090	33	values	value	NOUN
ejpam-1372	1090	34	of	of	ADP
ejpam-1372	1090	35	arg	arg	NOUN
ejpam-1372	1090	36	z	z	PROPN
ejpam-1372	1090	37	,	,	PUNCT
ejpam-1372	1090	38	it	it	PRON
ejpam-1372	1090	39	was	be	AUX
ejpam-1372	1090	40	rerun	rerun	VERB
ejpam-1372	1090	41	for	for	ADP
ejpam-1372	1090	42	the	the	DET
ejpam-1372	1090	43	same	same	ADJ
ejpam-1372	1090	44	set	set	NOUN
ejpam-1372	1090	45	of	of	ADP
ejpam-1372	1090	46	values	value	NOUN
ejpam-1372	1090	47	in	in	ADP
ejpam-1372	1090	48	table	table	NOUN
ejpam-1372	1090	49	1	1	NUM
ejpam-1372	1090	50	in	in	ADP
ejpam-1372	1090	51	order	order	NOUN
ejpam-1372	1090	52	to	to	PART
ejpam-1372	1090	53	enable	enable	VERB
ejpam-1372	1090	54	a	a	DET
ejpam-1372	1090	55	comparison	comparison	NOUN
ejpam-1372	1090	56	between	between	ADP
ejpam-1372	1090	57	the	the	DET
ejpam-1372	1090	58	two	two	NUM
ejpam-1372	1090	59	computing	computing	NOUN
ejpam-1372	1090	60	systems	system	NOUN
ejpam-1372	1090	61	.	.	PUNCT
ejpam-1372	1091	1	not	not	PART
ejpam-1372	1091	2	only	only	ADV
ejpam-1372	1091	3	was	be	AUX
ejpam-1372	1091	4	the	the	DET
ejpam-1372	1091	5	second	second	ADJ
ejpam-1372	1091	6	computing	computing	NOUN
ejpam-1372	1091	7	system	system	NOUN
ejpam-1372	1091	8	much	much	ADV
ejpam-1372	1091	9	quicker	quick	ADV
ejpam-1372	1091	10	,	,	PUNCT
ejpam-1372	1091	11	it	it	PRON
ejpam-1372	1091	12	was	be	AUX
ejpam-1372	1091	13	also	also	ADV
ejpam-1372	1091	14	able	able	ADJ
ejpam-1372	1091	15	to	to	PART
ejpam-1372	1091	16	generate	generate	VERB
ejpam-1372	1091	17	values	value	NOUN
ejpam-1372	1091	18	for	for	ADP
ejpam-1372	1091	19	much	much	ADV
ejpam-1372	1091	20	larger	large	ADJ
ejpam-1372	1091	21	values	value	NOUN
ejpam-1372	1091	22	of	of	ADP
ejpam-1372	1091	23	the	the	DET
ejpam-1372	1091	24	truncation	truncation	NOUN
ejpam-1372	1091	25	parameter	parameter	NOUN
ejpam-1372	1091	26	,	,	PUNCT
ejpam-1372	1091	27	i.e.	i.e.	X
ejpam-1372	1091	28	for	for	ADP
ejpam-1372	1091	29	values	value	NOUN
ejpam-1372	1091	30	of	of	ADP
ejpam-1372	1091	31	n	n	PRON
ejpam-1372	1091	32	where	where	SCONJ
ejpam-1372	1091	33	the	the	DET
ejpam-1372	1091	34	pentium	pentium	NOUN
ejpam-1372	1091	35	plus	plus	CCONJ
ejpam-1372	1091	36	mathematica	mathematica	PROPN
ejpam-1372	1091	37	4.1	4.1	NUM
ejpam-1372	1091	38	system	system	NOUN
ejpam-1372	1091	39	experienced	experience	VERB
ejpam-1372	1091	40	convergence	convergence	NOUN
ejpam-1372	1091	41	problems	problem	NOUN
ejpam-1372	1091	42	.	.	PUNCT
ejpam-1372	1092	1	in	in	ADP
ejpam-1372	1092	2	addition	addition	NOUN
ejpam-1372	1092	3	,	,	PUNCT
ejpam-1372	1092	4	for	for	ADP
ejpam-1372	1092	5	n	n	X
ejpam-1372	1092	6	<	<	X
ejpam-1372	1092	7	10	10	NUM
ejpam-1372	1092	8	,	,	PUNCT
ejpam-1372	1092	9	many	many	ADJ
ejpam-1372	1092	10	of	of	ADP
ejpam-1372	1092	11	the	the	DET
ejpam-1372	1092	12	results	result	NOUN
ejpam-1372	1092	13	took	take	VERB
ejpam-1372	1092	14	less	less	ADJ
ejpam-1372	1092	15	than	than	ADP
ejpam-1372	1092	16	30	30	NUM
ejpam-1372	1092	17	seconds	second	NOUN
ejpam-1372	1092	18	of	of	ADP
ejpam-1372	1092	19	cpu	cpu	ADJ
ejpam-1372	1092	20	time	time	NOUN
ejpam-1372	1092	21	with	with	ADP
ejpam-1372	1092	22	the	the	DET
ejpam-1372	1092	23	more	more	ADV
ejpam-1372	1092	24	powerful	powerful	ADJ
ejpam-1372	1092	25	computing	computing	NOUN
ejpam-1372	1092	26	system	system	NOUN
ejpam-1372	1092	27	,	,	PUNCT
ejpam-1372	1092	28	whereas	whereas	SCONJ
ejpam-1372	1092	29	they	they	PRON
ejpam-1372	1092	30	took	take	VERB
ejpam-1372	1092	31	several	several	ADJ
ejpam-1372	1092	32	minutes	minute	NOUN
ejpam-1372	1092	33	to	to	PART
ejpam-1372	1092	34	compute	compute	VERB
ejpam-1372	1092	35	using	use	VERB
ejpam-1372	1092	36	the	the	DET
ejpam-1372	1092	37	first	first	ADJ
ejpam-1372	1092	38	system	system	NOUN
ejpam-1372	1092	39	despite	despite	SCONJ
ejpam-1372	1092	40	the	the	DET
ejpam-1372	1092	41	fact	fact	NOUN
ejpam-1372	1092	42	that	that	SCONJ
ejpam-1372	1092	43	the	the	DET
ejpam-1372	1092	44	precision	precision	NOUN
ejpam-1372	1092	45	and	and	CCONJ
ejpam-1372	1092	46	accuracy	accuracy	NOUN
ejpam-1372	1092	47	goals	goal	NOUN
ejpam-1372	1092	48	were	be	AUX
ejpam-1372	1092	49	much	much	ADV
ejpam-1372	1092	50	lower	low	ADJ
ejpam-1372	1092	51	in	in	ADP
ejpam-1372	1092	52	the	the	DET
ejpam-1372	1092	53	former	former	ADJ
ejpam-1372	1092	54	system	system	NOUN
ejpam-1372	1092	55	.	.	PUNCT
ejpam-1372	1093	1	nevertheless	nevertheless	ADV
ejpam-1372	1093	2	,	,	PUNCT
ejpam-1372	1093	3	irrespective	irrespective	ADV
ejpam-1372	1093	4	of	of	ADP
ejpam-1372	1093	5	the	the	DET
ejpam-1372	1093	6	value	value	NOUN
ejpam-1372	1093	7	of	of	ADP
ejpam-1372	1093	8	z	z	PROPN
ejpam-1372	1093	9	,	,	PUNCT
ejpam-1372	1093	10	it	it	PRON
ejpam-1372	1093	11	must	must	AUX
ejpam-1372	1093	12	be	be	AUX
ejpam-1372	1093	13	emphasised	emphasise	VERB
ejpam-1372	1093	14	that	that	SCONJ
ejpam-1372	1093	15	problems	problem	NOUN
ejpam-1372	1093	16	with	with	ADP
ejpam-1372	1093	17	convergence	convergence	NOUN
ejpam-1372	1093	18	as	as	ADV
ejpam-1372	1093	19	well	well	ADV
ejpam-1372	1093	20	as	as	ADP
ejpam-1372	1093	21	with	with	ADP
ejpam-1372	1093	22	precision	precision	NOUN
ejpam-1372	1093	23	and	and	CCONJ
ejpam-1372	1093	24	accuracy	accuracy	NOUN
ejpam-1372	1093	25	goals	goal	NOUN
ejpam-1372	1093	26	will	will	AUX
ejpam-1372	1093	27	also	also	ADV
ejpam-1372	1093	28	arise	arise	VERB
ejpam-1372	1093	29	in	in	ADP
ejpam-1372	1093	30	the	the	DET
ejpam-1372	1093	31	more	more	ADV
ejpam-1372	1093	32	powerful	powerful	ADJ
ejpam-1372	1093	33	system	system	NOUN
ejpam-1372	1093	34	,	,	PUNCT
ejpam-1372	1093	35	once	once	SCONJ
ejpam-1372	1093	36	the	the	DET
ejpam-1372	1093	37	truncation	truncation	NOUN
ejpam-1372	1093	38	parameter	parameter	NOUN
ejpam-1372	1093	39	becomes	become	VERB
ejpam-1372	1093	40	sufficiently	sufficiently	ADV
ejpam-1372	1093	41	large	large	ADJ
ejpam-1372	1093	42	.	.	PUNCT
ejpam-1372	1094	1	this	this	PRON
ejpam-1372	1094	2	will	will	AUX
ejpam-1372	1094	3	be	be	AUX
ejpam-1372	1094	4	discussed	discuss	VERB
ejpam-1372	1094	5	shortly	shortly	ADV
ejpam-1372	1094	6	when	when	SCONJ
ejpam-1372	1094	7	we	we	PRON
ejpam-1372	1094	8	consider	consider	VERB
ejpam-1372	1094	9	the	the	DET
ejpam-1372	1094	10	case	case	NOUN
ejpam-1372	1094	11	of	of	ADP
ejpam-1372	1094	12	|z|=2	|z|=2	NOUN
ejpam-1372	1094	13	and	and	CCONJ
ejpam-1372	1094	14	arg	arg	VERB
ejpam-1372	1094	15	z=−π/4	z=−π/4	NOUN
ejpam-1372	1094	16	.	.	PUNCT
ejpam-1372	1095	1	table	table	NOUN
ejpam-1372	1095	2	2	2	NUM
ejpam-1372	1095	3	presents	present	VERB
ejpam-1372	1095	4	a	a	DET
ejpam-1372	1095	5	sample	sample	NOUN
ejpam-1372	1095	6	of	of	ADP
ejpam-1372	1095	7	the	the	DET
ejpam-1372	1095	8	results	result	NOUN
ejpam-1372	1095	9	obtained	obtain	VERB
ejpam-1372	1095	10	by	by	ADP
ejpam-1372	1095	11	running	run	VERB
ejpam-1372	1095	12	the	the	DET
ejpam-1372	1095	13	modified	modify	VERB
ejpam-1372	1095	14	mathematica	mathematica	PROPN
ejpam-1372	1095	15	module	module	NOUN
ejpam-1372	1095	16	on	on	ADP
ejpam-1372	1095	17	the	the	DET
ejpam-1372	1095	18	power	power	NOUN
ejpam-1372	1095	19	mac	mac	PROPN
ejpam-1372	1095	20	g5	g5	PROPN
ejpam-1372	1095	21	plus	plus	CCONJ
ejpam-1372	1095	22	mathematica	mathematica	PROPN
ejpam-1372	1095	23	7.0	7.0	NUM
ejpam-1372	1095	24	system	system	NOUN
ejpam-1372	1095	25	.	.	PUNCT
ejpam-1372	1096	1	not	not	PART
ejpam-1372	1096	2	all	all	DET
ejpam-1372	1096	3	the	the	DET
ejpam-1372	1096	4	decimal	decimal	ADJ
ejpam-1372	1096	5	places	place	NOUN
ejpam-1372	1096	6	for	for	ADP
ejpam-1372	1096	7	the	the	DET
ejpam-1372	1096	8	various	various	ADJ
ejpam-1372	1096	9	results	result	NOUN
ejpam-1372	1096	10	are	be	AUX
ejpam-1372	1096	11	displayed	display	VERB
ejpam-1372	1096	12	in	in	ADP
ejpam-1372	1096	13	the	the	DET
ejpam-1372	1096	14	table	table	NOUN
ejpam-1372	1096	15	due	due	ADP
ejpam-1372	1096	16	to	to	ADP
ejpam-1372	1096	17	limited	limited	ADJ
ejpam-1372	1096	18	space	space	NOUN
ejpam-1372	1096	19	.	.	PUNCT
ejpam-1372	1097	1	because	because	SCONJ
ejpam-1372	1097	2	the	the	DET
ejpam-1372	1097	3	truncation	truncation	NOUN
ejpam-1372	1097	4	parameter	parameter	NOUN
ejpam-1372	1097	5	was	be	AUX
ejpam-1372	1097	6	not	not	PART
ejpam-1372	1097	7	very	very	ADV
ejpam-1372	1097	8	large	large	ADJ
ejpam-1372	1097	9	,	,	PUNCT
ejpam-1372	1097	10	i.e.	i.e.	X
ejpam-1372	1097	11	n	n	PRON
ejpam-1372	1097	12	was	be	AUX
ejpam-1372	1097	13	generally	generally	ADV
ejpam-1372	1097	14	taken	take	VERB
ejpam-1372	1097	15	to	to	PART
ejpam-1372	1097	16	be	be	AUX
ejpam-1372	1097	17	less	less	ADJ
ejpam-1372	1097	18	than	than	ADP
ejpam-1372	1097	19	25	25	NUM
ejpam-1372	1097	20	,	,	PUNCT
ejpam-1372	1097	21	the	the	DET
ejpam-1372	1097	22	regularised	regularise	VERB
ejpam-1372	1097	23	values	value	NOUN
ejpam-1372	1097	24	in	in	ADP
ejpam-1372	1097	25	the	the	DET
ejpam-1372	1097	26	final	final	ADJ
ejpam-1372	1097	27	column	column	NOUN
ejpam-1372	1097	28	are	be	AUX
ejpam-1372	1097	29	accurate	accurate	ADJ
ejpam-1372	1097	30	to	to	ADP
ejpam-1372	1097	31	at	at	ADV
ejpam-1372	1097	32	least	least	ADV
ejpam-1372	1097	33	30	30	NUM
ejpam-1372	1097	34	decimal	decimal	ADJ
ejpam-1372	1097	35	places	place	NOUN
ejpam-1372	1097	36	.	.	PUNCT
ejpam-1372	1098	1	as	as	ADP
ejpam-1372	1098	2	a	a	DET
ejpam-1372	1098	3	consequence	consequence	NOUN
ejpam-1372	1098	4	,	,	PUNCT
ejpam-1372	1098	5	one	one	NUM
ejpam-1372	1098	6	is	be	AUX
ejpam-1372	1098	7	not	not	PART
ejpam-1372	1098	8	able	able	ADJ
ejpam-1372	1098	9	to	to	PART
ejpam-1372	1098	10	observe	observe	VERB
ejpam-1372	1098	11	any	any	DET
ejpam-1372	1098	12	variation	variation	NOUN
ejpam-1372	1098	13	in	in	ADP
ejpam-1372	1098	14	any	any	PRON
ejpam-1372	1098	15	of	of	ADP
ejpam-1372	1098	16	the	the	DET
ejpam-1372	1098	17	regularised	regularise	VERB
ejpam-1372	1098	18	values	value	NOUN
ejpam-1372	1098	19	appearing	appear	VERB
ejpam-1372	1098	20	in	in	ADP
ejpam-1372	1098	21	the	the	DET
ejpam-1372	1098	22	final	final	ADJ
ejpam-1372	1098	23	column	column	NOUN
ejpam-1372	1098	24	.	.	PUNCT
ejpam-1372	1099	1	from	from	ADP
ejpam-1372	1099	2	the	the	DET
ejpam-1372	1099	3	table	table	NOUN
ejpam-1372	1099	4	we	we	PRON
ejpam-1372	1099	5	see	see	VERB
ejpam-1372	1099	6	that	that	SCONJ
ejpam-1372	1099	7	for	for	ADP
ejpam-1372	1099	8	those	those	DET
ejpam-1372	1099	9	values	value	NOUN
ejpam-1372	1099	10	of	of	ADP
ejpam-1372	1099	11	arg	arg	NOUN
ejpam-1372	1099	12	z	z	PROPN
ejpam-1372	1099	13	,	,	PUNCT
ejpam-1372	1099	14	where	where	SCONJ
ejpam-1372	1099	15	both	both	CCONJ
ejpam-1372	1099	16	the	the	DET
ejpam-1372	1099	17	l=0	l=0	PROPN
ejpam-1372	1099	18	and	and	CCONJ
ejpam-1372	1099	19	l=1	l=1	PROPN
ejpam-1372	1099	20	forms	form	NOUN
ejpam-1372	1099	21	of	of	ADP
ejpam-1372	1099	22	equivalence	equivalence	NOUN
ejpam-1372	1099	23	(	(	PUNCT
ejpam-1372	1099	24	118	118	NUM
ejpam-1372	1099	25	)	)	PUNCT
ejpam-1372	1099	26	are	be	AUX
ejpam-1372	1099	27	valid	valid	ADJ
ejpam-1372	1099	28	,	,	PUNCT
ejpam-1372	1099	29	we	we	PRON
ejpam-1372	1099	30	ultimately	ultimately	ADV
ejpam-1372	1099	31	obtain	obtain	VERB
ejpam-1372	1099	32	the	the	DET
ejpam-1372	1099	33	same	same	ADJ
ejpam-1372	1099	34	regularised	regularise	VERB
ejpam-1372	1099	35	value	value	NOUN
ejpam-1372	1099	36	.	.	PUNCT
ejpam-1372	1100	1	therefore	therefore	ADV
ejpam-1372	1100	2	,	,	PUNCT
ejpam-1372	1100	3	we	we	PRON
ejpam-1372	1100	4	have	have	VERB
ejpam-1372	1100	5	two	two	NUM
ejpam-1372	1100	6	completely	completely	ADV
ejpam-1372	1100	7	different	different	ADJ
ejpam-1372	1100	8	forms	form	NOUN
ejpam-1372	1100	9	for	for	ADP
ejpam-1372	1100	10	the	the	DET
ejpam-1372	1100	11	regularised	regularise	VERB
ejpam-1372	1100	12	value	value	NOUN
ejpam-1372	1100	13	yielding	yield	VERB
ejpam-1372	1100	14	identical	identical	ADJ
ejpam-1372	1100	15	results	result	NOUN
ejpam-1372	1100	16	,	,	PUNCT
ejpam-1372	1100	17	which	which	PRON
ejpam-1372	1100	18	is	be	AUX
ejpam-1372	1100	19	in	in	ADP
ejpam-1372	1100	20	accordance	accordance	NOUN
ejpam-1372	1100	21	with	with	ADP
ejpam-1372	1100	22	euler	euler	NOUN
ejpam-1372	1100	23	’s	’s	PART
ejpam-1372	1100	24	so	so	ADV
ejpam-1372	1100	25	-	-	PUNCT
ejpam-1372	1100	26	called	call	VERB
ejpam-1372	1100	27	“	"	PUNCT
ejpam-1372	1100	28	unorthodox	unorthodox	ADJ
ejpam-1372	1100	29	”	"	PUNCT
ejpam-1372	1100	30	views	view	NOUN
ejpam-1372	1100	31	about	about	ADP
ejpam-1372	1100	32	divergent	divergent	ADJ
ejpam-1372	1100	33	series	series	NOUN
ejpam-1372	1100	34	.	.	PUNCT
ejpam-1372	1101	1	moreover	moreover	ADV
ejpam-1372	1101	2	,	,	PUNCT
ejpam-1372	1101	3	we	we	PRON
ejpam-1372	1101	4	see	see	VERB
ejpam-1372	1101	5	that	that	SCONJ
ejpam-1372	1101	6	altering	alter	VERB
ejpam-1372	1101	7	the	the	DET
ejpam-1372	1101	8	truncation	truncation	NOUN
ejpam-1372	1101	9	parameter	parameter	NOUN
ejpam-1372	1101	10	for	for	ADP
ejpam-1372	1101	11	the	the	DET
ejpam-1372	1101	12	same	same	ADJ
ejpam-1372	1101	13	value	value	NOUN
ejpam-1372	1101	14	of	of	ADP
ejpam-1372	1101	15	z	z	NOUN
ejpam-1372	1101	16	yields	yield	NOUN
ejpam-1372	1101	17	the	the	DET
ejpam-1372	1101	18	same	same	ADJ
ejpam-1372	1101	19	regularised	regularise	VERB
ejpam-1372	1101	20	value	value	NOUN
ejpam-1372	1101	21	even	even	ADV
ejpam-1372	1101	22	though	though	SCONJ
ejpam-1372	1101	23	the	the	DET
ejpam-1372	1101	24	truncated	truncated	ADJ
ejpam-1372	1101	25	series	series	NOUN
ejpam-1372	1101	26	and	and	CCONJ
ejpam-1372	1101	27	mb	mb	NOUN
ejpam-1372	1101	28	integrals	integral	NOUN
ejpam-1372	1101	29	are	be	AUX
ejpam-1372	1101	30	different	different	ADJ
ejpam-1372	1101	31	for	for	ADP
ejpam-1372	1101	32	each	each	DET
ejpam-1372	1101	33	value	value	NOUN
ejpam-1372	1101	34	of	of	ADP
ejpam-1372	1101	35	n	n	PROPN
ejpam-1372	1101	36	.	.	PUNCT
ejpam-1372	1102	1	this	this	PRON
ejpam-1372	1102	2	also	also	ADV
ejpam-1372	1102	3	vindicates	vindicate	VERB
ejpam-1372	1102	4	euler	euler	PROPN
ejpam-1372	1102	5	’s	’s	PART
ejpam-1372	1102	6	second	second	ADJ
ejpam-1372	1102	7	view	view	NOUN
ejpam-1372	1102	8	that	that	SCONJ
ejpam-1372	1102	9	one	one	PRON
ejpam-1372	1102	10	should	should	AUX
ejpam-1372	1102	11	obtain	obtain	VERB
ejpam-1372	1102	12	the	the	DET
ejpam-1372	1102	13	same	same	ADJ
ejpam-1372	1102	14	value	value	NOUN
ejpam-1372	1102	15	irrespective	irrespective	ADV
ejpam-1372	1102	16	of	of	ADP
ejpam-1372	1102	17	what	what	PRON
ejpam-1372	1102	18	method	method	NOUN
ejpam-1372	1102	19	or	or	CCONJ
ejpam-1372	1102	20	approach	approach	NOUN
ejpam-1372	1102	21	is	be	AUX
ejpam-1372	1102	22	used	use	VERB
ejpam-1372	1102	23	.	.	PUNCT
ejpam-1372	1103	1	table	table	NOUN
ejpam-1372	1103	2	3	3	NUM
ejpam-1372	1103	3	presents	present	VERB
ejpam-1372	1103	4	a	a	DET
ejpam-1372	1103	5	sample	sample	NOUN
ejpam-1372	1103	6	of	of	ADP
ejpam-1372	1103	7	the	the	DET
ejpam-1372	1103	8	results	result	NOUN
ejpam-1372	1103	9	obtained	obtain	VERB
ejpam-1372	1103	10	by	by	ADP
ejpam-1372	1103	11	running	run	VERB
ejpam-1372	1103	12	the	the	DET
ejpam-1372	1103	13	mathematica	mathematica	PROPN
ejpam-1372	1103	14	module	module	NOUN
ejpam-1372	1103	15	used	use	VERB
ejpam-1372	1103	16	to	to	PART
ejpam-1372	1103	17	obtain	obtain	VERB
ejpam-1372	1103	18	table	table	NOUN
ejpam-1372	1103	19	2	2	NUM
ejpam-1372	1103	20	again	again	ADV
ejpam-1372	1103	21	on	on	ADP
ejpam-1372	1103	22	the	the	DET
ejpam-1372	1103	23	same	same	ADJ
ejpam-1372	1103	24	power	power	NOUN
ejpam-1372	1103	25	mac	mac	PROPN
ejpam-1372	1103	26	g5	g5	PROPN
ejpam-1372	1103	27	plus	plus	CCONJ
ejpam-1372	1103	28	mathematica	mathematica	PROPN
ejpam-1372	1103	29	7.0	7.0	NUM
ejpam-1372	1103	30	system	system	NOUN
ejpam-1372	1103	31	,	,	PUNCT
ejpam-1372	1103	32	but	but	CCONJ
ejpam-1372	1103	33	on	on	ADP
ejpam-1372	1103	34	this	this	DET
ejpam-1372	1103	35	occasion	occasion	NOUN
ejpam-1372	1103	36	,	,	PUNCT
ejpam-1372	1103	37	|z|	|z|	NOUN
ejpam-1372	1103	38	has	have	AUX
ejpam-1372	1103	39	been	be	AUX
ejpam-1372	1103	40	set	set	VERB
ejpam-1372	1103	41	equal	equal	ADJ
ejpam-1372	1103	42	to	to	ADP
ejpam-1372	1103	43	2	2	NUM
ejpam-1372	1103	44	and	and	CCONJ
ejpam-1372	1103	45	arg	arg	NOUN
ejpam-1372	1103	46	z	z	NOUN
ejpam-1372	1103	47	is	be	AUX
ejpam-1372	1103	48	less	less	ADJ
ejpam-1372	1103	49	than	than	ADP
ejpam-1372	1103	50	zero	zero	NUM
ejpam-1372	1103	51	.	.	PUNCT
ejpam-1372	1104	1	this	this	PRON
ejpam-1372	1104	2	means	mean	VERB
ejpam-1372	1104	3	that	that	SCONJ
ejpam-1372	1104	4	the	the	DET
ejpam-1372	1104	5	mb	mb	ADJ
ejpam-1372	1104	6	-	-	PUNCT
ejpam-1372	1104	7	regularised	regularise	VERB
ejpam-1372	1104	8	values	value	NOUN
ejpam-1372	1104	9	can	can	AUX
ejpam-1372	1104	10	only	only	ADV
ejpam-1372	1104	11	be	be	AUX
ejpam-1372	1104	12	evaluated	evaluate	VERB
ejpam-1372	1104	13	by	by	ADP
ejpam-1372	1104	14	using	use	VERB
ejpam-1372	1104	15	the	the	DET
ejpam-1372	1104	16	l	l	NOUN
ejpam-1372	1104	17	=	=	SYM
ejpam-1372	1104	18	0	0	NUM
ejpam-1372	1104	19	and	and	CCONJ
ejpam-1372	1104	20	l	l	NOUN
ejpam-1372	1104	21	=	=	NOUN
ejpam-1372	1104	22	−1	−1	NOUN
ejpam-1372	1104	23	forms	form	NOUN
ejpam-1372	1104	24	of	of	ADP
ejpam-1372	1104	25	equivalence	equivalence	NOUN
ejpam-1372	1104	26	(	(	PUNCT
ejpam-1372	1104	27	118	118	NUM
ejpam-1372	1104	28	)	)	PUNCT
ejpam-1372	1104	29	.	.	PUNCT
ejpam-1372	1105	1	as	as	ADP
ejpam-1372	1105	2	in	in	ADP
ejpam-1372	1105	3	the	the	DET
ejpam-1372	1105	4	case	case	NOUN
ejpam-1372	1105	5	of	of	ADP
ejpam-1372	1105	6	the	the	DET
ejpam-1372	1105	7	previous	previous	ADJ
ejpam-1372	1105	8	table	table	NOUN
ejpam-1372	1105	9	not	not	PART
ejpam-1372	1105	10	all	all	DET
ejpam-1372	1105	11	the	the	DET
ejpam-1372	1105	12	decimal	decimal	ADJ
ejpam-1372	1105	13	places	place	NOUN
ejpam-1372	1105	14	of	of	ADP
ejpam-1372	1105	15	the	the	DET
ejpam-1372	1105	16	values	value	NOUN
ejpam-1372	1105	17	v.	v.	ADP
ejpam-1372	1105	18	kowalenko	kowalenko	PROPN
ejpam-1372	1105	19	/	/	SYM
ejpam-1372	1105	20	eur	eur	PROPN
ejpam-1372	1105	21	.	.	PUNCT
ejpam-1372	1106	1	j.	j.	PROPN
ejpam-1372	1106	2	pure	pure	PROPN
ejpam-1372	1106	3	appl	appl	PROPN
ejpam-1372	1106	4	.	.	PROPN
ejpam-1372	1106	5	math	math	PROPN
ejpam-1372	1106	6	,	,	PUNCT
ejpam-1372	1106	7	4	4	NUM
ejpam-1372	1106	8	(	(	PUNCT
ejpam-1372	1106	9	2011	2011	NUM
ejpam-1372	1106	10	)	)	PUNCT
ejpam-1372	1106	11	,	,	PUNCT
ejpam-1372	1106	12	370	370	NUM
ejpam-1372	1106	13	-	-	SYM
ejpam-1372	1106	14	423	423	NUM
ejpam-1372	1106	15	410	410	NUM
ejpam-1372	1106	16	in	in	ADP
ejpam-1372	1106	17	the	the	DET
ejpam-1372	1106	18	various	various	ADJ
ejpam-1372	1106	19	columns	column	NOUN
ejpam-1372	1106	20	were	be	AUX
ejpam-1372	1106	21	able	able	ADJ
ejpam-1372	1106	22	to	to	PART
ejpam-1372	1106	23	be	be	AUX
ejpam-1372	1106	24	displayed	display	VERB
ejpam-1372	1106	25	here	here	ADV
ejpam-1372	1106	26	.	.	PUNCT
ejpam-1372	1107	1	the	the	DET
ejpam-1372	1107	2	major	major	ADJ
ejpam-1372	1107	3	difference	difference	NOUN
ejpam-1372	1107	4	between	between	ADP
ejpam-1372	1107	5	this	this	PRON
ejpam-1372	1107	6	and	and	CCONJ
ejpam-1372	1107	7	the	the	DET
ejpam-1372	1107	8	previous	previous	ADJ
ejpam-1372	1107	9	table	table	NOUN
ejpam-1372	1107	10	is	be	AUX
ejpam-1372	1107	11	that	that	SCONJ
ejpam-1372	1107	12	the	the	DET
ejpam-1372	1107	13	truncation	truncation	NOUN
ejpam-1372	1107	14	parameter	parameter	NOUN
ejpam-1372	1107	15	need	need	AUX
ejpam-1372	1107	16	not	not	PART
ejpam-1372	1107	17	be	be	AUX
ejpam-1372	1107	18	reasonably	reasonably	ADV
ejpam-1372	1107	19	large	large	ADJ
ejpam-1372	1107	20	before	before	ADP
ejpam-1372	1107	21	the	the	DET
ejpam-1372	1107	22	truncated	truncated	ADJ
ejpam-1372	1107	23	series	series	NOUN
ejpam-1372	1107	24	and	and	CCONJ
ejpam-1372	1107	25	the	the	DET
ejpam-1372	1107	26	mb	mb	ADJ
ejpam-1372	1107	27	integral	integral	ADJ
ejpam-1372	1107	28	begin	begin	NOUN
ejpam-1372	1107	29	to	to	PART
ejpam-1372	1107	30	diverge	diverge	VERB
ejpam-1372	1107	31	rapidly	rapidly	ADV
ejpam-1372	1107	32	.	.	PUNCT
ejpam-1372	1108	1	e.g.	e.g.	ADV
ejpam-1372	1108	2	,	,	PUNCT
ejpam-1372	1108	3	for	for	ADP
ejpam-1372	1108	4	n=6	n=6	NOUN
ejpam-1372	1108	5	,	,	PUNCT
ejpam-1372	1108	6	the	the	DET
ejpam-1372	1108	7	magnitude	magnitude	NOUN
ejpam-1372	1108	8	of	of	ADP
ejpam-1372	1108	9	both	both	CCONJ
ejpam-1372	1108	10	the	the	DET
ejpam-1372	1108	11	truncated	truncated	ADJ
ejpam-1372	1108	12	series	series	NOUN
ejpam-1372	1108	13	and	and	CCONJ
ejpam-1372	1108	14	mb	mb	ADP
ejpam-1372	1108	15	integral	integral	ADJ
ejpam-1372	1108	16	is	be	AUX
ejpam-1372	1108	17	of	of	ADP
ejpam-1372	1108	18	the	the	DET
ejpam-1372	1108	19	order	order	NOUN
ejpam-1372	1108	20	of	of	ADP
ejpam-1372	1108	21	105	105	NUM
ejpam-1372	1108	22	.	.	PUNCT
ejpam-1372	1109	1	nevertheless	nevertheless	ADV
ejpam-1372	1109	2	,	,	PUNCT
ejpam-1372	1109	3	as	as	SCONJ
ejpam-1372	1109	4	they	they	PRON
ejpam-1372	1109	5	diverge	diverge	VERB
ejpam-1372	1109	6	in	in	ADP
ejpam-1372	1109	7	opposite	opposite	ADJ
ejpam-1372	1109	8	directions	direction	NOUN
ejpam-1372	1109	9	,	,	PUNCT
ejpam-1372	1109	10	there	there	PRON
ejpam-1372	1109	11	is	be	VERB
ejpam-1372	1109	12	a	a	DET
ejpam-1372	1109	13	great	great	ADJ
ejpam-1372	1109	14	cancellation	cancellation	NOUN
ejpam-1372	1109	15	of	of	ADP
ejpam-1372	1109	16	decimal	decimal	ADJ
ejpam-1372	1109	17	places	place	NOUN
ejpam-1372	1109	18	in	in	ADP
ejpam-1372	1109	19	the	the	DET
ejpam-1372	1109	20	process	process	NOUN
ejpam-1372	1109	21	of	of	ADP
ejpam-1372	1109	22	arriving	arrive	VERB
ejpam-1372	1109	23	at	at	ADP
ejpam-1372	1109	24	the	the	DET
ejpam-1372	1109	25	regularised	regularise	VERB
ejpam-1372	1109	26	value	value	NOUN
ejpam-1372	1109	27	of	of	ADP
ejpam-1372	1109	28	the	the	DET
ejpam-1372	1109	29	series	series	NOUN
ejpam-1372	1109	30	.	.	PUNCT
ejpam-1372	1110	1	the	the	DET
ejpam-1372	1110	2	main	main	ADJ
ejpam-1372	1110	3	characteristics	characteristic	NOUN
ejpam-1372	1110	4	or	or	CCONJ
ejpam-1372	1110	5	features	feature	NOUN
ejpam-1372	1110	6	of	of	ADP
ejpam-1372	1110	7	table	table	NOUN
ejpam-1372	1110	8	2	2	NUM
ejpam-1372	1110	9	are	be	AUX
ejpam-1372	1110	10	also	also	ADV
ejpam-1372	1110	11	evident	evident	ADJ
ejpam-1372	1110	12	in	in	ADP
ejpam-1372	1110	13	table	table	NOUN
ejpam-1372	1110	14	3	3	NUM
ejpam-1372	1110	15	.	.	PUNCT
ejpam-1372	1111	1	although	although	SCONJ
ejpam-1372	1111	2	the	the	DET
ejpam-1372	1111	3	common	common	ADJ
ejpam-1372	1111	4	region	region	NOUN
ejpam-1372	1111	5	is	be	AUX
ejpam-1372	1111	6	different	different	ADJ
ejpam-1372	1111	7	,	,	PUNCT
ejpam-1372	1111	8	viz	viz	NOUN
ejpam-1372	1111	9	.	.	PUNCT
ejpam-1372	1112	1	−π/2	−π/2	PRON
ejpam-1372	1112	2	<	<	X
ejpam-1372	1112	3	arg	arg	NOUN
ejpam-1372	1112	4	z	z	X
ejpam-1372	1112	5	<	<	X
ejpam-1372	1112	6	−π/6	−π/6	PROPN
ejpam-1372	1112	7	,	,	PUNCT
ejpam-1372	1112	8	both	both	PRON
ejpam-1372	1112	9	the	the	DET
ejpam-1372	1112	10	l	l	NOUN
ejpam-1372	1112	11	=	=	SYM
ejpam-1372	1112	12	0	0	NUM
ejpam-1372	1112	13	and	and	CCONJ
ejpam-1372	1112	14	l	l	NOUN
ejpam-1372	1112	15	=	=	NOUN
ejpam-1372	1112	16	−1	−1	NOUN
ejpam-1372	1112	17	forms	form	NOUN
ejpam-1372	1112	18	of	of	ADP
ejpam-1372	1112	19	equivalence	equivalence	NOUN
ejpam-1372	1112	20	(	(	PUNCT
ejpam-1372	1112	21	118	118	NUM
ejpam-1372	1112	22	)	)	PUNCT
ejpam-1372	1112	23	yield	yield	NOUN
ejpam-1372	1112	24	identical	identical	ADJ
ejpam-1372	1112	25	results	result	NOUN
ejpam-1372	1112	26	for	for	ADP
ejpam-1372	1112	27	the	the	DET
ejpam-1372	1112	28	regularised	regularise	VERB
ejpam-1372	1112	29	value	value	NOUN
ejpam-1372	1112	30	of	of	ADP
ejpam-1372	1112	31	ti	ti	PROPN
ejpam-1372	1112	32	(	(	PUNCT
ejpam-1372	1112	33	0,3/7	0,3/7	PROPN
ejpam-1372	1112	34	,	,	PUNCT
ejpam-1372	1112	35	z3	z3	PROPN
ejpam-1372	1112	36	)	)	PUNCT
ejpam-1372	1112	37	.	.	PUNCT
ejpam-1372	1113	1	this	this	PRON
ejpam-1372	1113	2	is	be	AUX
ejpam-1372	1113	3	despite	despite	SCONJ
ejpam-1372	1113	4	the	the	DET
ejpam-1372	1113	5	fact	fact	NOUN
ejpam-1372	1113	6	that	that	SCONJ
ejpam-1372	1113	7	the	the	DET
ejpam-1372	1113	8	jump	jump	NOUN
ejpam-1372	1113	9	discontinuity	discontinuity	NOUN
ejpam-1372	1113	10	is	be	AUX
ejpam-1372	1113	11	different	different	ADJ
ejpam-1372	1113	12	for	for	ADP
ejpam-1372	1113	13	both	both	DET
ejpam-1372	1113	14	forms	form	NOUN
ejpam-1372	1113	15	.	.	PUNCT
ejpam-1372	1114	1	in	in	ADP
ejpam-1372	1114	2	addition	addition	NOUN
ejpam-1372	1114	3	,	,	PUNCT
ejpam-1372	1114	4	altering	alter	VERB
ejpam-1372	1114	5	the	the	DET
ejpam-1372	1114	6	truncation	truncation	NOUN
ejpam-1372	1114	7	parameter	parameter	NOUN
ejpam-1372	1114	8	for	for	ADP
ejpam-1372	1114	9	a	a	DET
ejpam-1372	1114	10	fixed	fix	VERB
ejpam-1372	1114	11	value	value	NOUN
ejpam-1372	1114	12	of	of	ADP
ejpam-1372	1114	13	arg	arg	NOUN
ejpam-1372	1114	14	z	z	VERB
ejpam-1372	1114	15	always	always	ADV
ejpam-1372	1114	16	yields	yield	VERB
ejpam-1372	1114	17	the	the	DET
ejpam-1372	1114	18	same	same	ADJ
ejpam-1372	1114	19	value	value	NOUN
ejpam-1372	1114	20	for	for	ADP
ejpam-1372	1114	21	the	the	DET
ejpam-1372	1114	22	regularised	regularise	VERB
ejpam-1372	1114	23	value	value	NOUN
ejpam-1372	1114	24	of	of	ADP
ejpam-1372	1114	25	ti	ti	PROPN
ejpam-1372	1114	26	(	(	PUNCT
ejpam-1372	1114	27	0,3/7	0,3/7	PROPN
ejpam-1372	1114	28	,	,	PUNCT
ejpam-1372	1114	29	z3	z3	PROPN
ejpam-1372	1114	30	)	)	PUNCT
ejpam-1372	1114	31	even	even	ADV
ejpam-1372	1114	32	though	though	SCONJ
ejpam-1372	1114	33	the	the	DET
ejpam-1372	1114	34	truncated	truncated	ADJ
ejpam-1372	1114	35	series	series	NOUN
ejpam-1372	1114	36	and	and	CCONJ
ejpam-1372	1114	37	mb	mb	NOUN
ejpam-1372	1114	38	integrals	integral	NOUN
ejpam-1372	1114	39	vary	vary	VERB
ejpam-1372	1114	40	for	for	ADP
ejpam-1372	1114	41	each	each	DET
ejpam-1372	1114	42	value	value	NOUN
ejpam-1372	1114	43	of	of	ADP
ejpam-1372	1114	44	n	n	PROPN
ejpam-1372	1114	45	.	.	PUNCT
ejpam-1372	1115	1	in	in	ADP
ejpam-1372	1115	2	fact	fact	NOUN
ejpam-1372	1115	3	,	,	PUNCT
ejpam-1372	1115	4	the	the	DET
ejpam-1372	1115	5	only	only	ADJ
ejpam-1372	1115	6	difference	difference	NOUN
ejpam-1372	1115	7	between	between	ADP
ejpam-1372	1115	8	choosing	choose	VERB
ejpam-1372	1115	9	a	a	DET
ejpam-1372	1115	10	value	value	NOUN
ejpam-1372	1115	11	of	of	ADP
ejpam-1372	1115	12	|z|	|z|	NOUN
ejpam-1372	1115	13	in	in	ADP
ejpam-1372	1115	14	the	the	DET
ejpam-1372	1115	15	intermediate	intermediate	ADJ
ejpam-1372	1115	16	region	region	NOUN
ejpam-1372	1115	17	and	and	CCONJ
ejpam-1372	1115	18	one	one	NUM
ejpam-1372	1115	19	in	in	ADP
ejpam-1372	1115	20	the	the	DET
ejpam-1372	1115	21	large	large	ADJ
ejpam-1372	1115	22	region	region	NOUN
ejpam-1372	1115	23	is	be	AUX
ejpam-1372	1115	24	that	that	SCONJ
ejpam-1372	1115	25	the	the	DET
ejpam-1372	1115	26	truncated	truncated	ADJ
ejpam-1372	1115	27	series	series	NOUN
ejpam-1372	1115	28	and	and	CCONJ
ejpam-1372	1115	29	mb	mb	NOUN
ejpam-1372	1115	30	integrals	integral	NOUN
ejpam-1372	1115	31	do	do	AUX
ejpam-1372	1115	32	not	not	PART
ejpam-1372	1115	33	diverge	diverge	VERB
ejpam-1372	1115	34	as	as	ADV
ejpam-1372	1115	35	rapidly	rapidly	ADV
ejpam-1372	1115	36	in	in	ADP
ejpam-1372	1115	37	the	the	DET
ejpam-1372	1115	38	former	former	ADJ
ejpam-1372	1115	39	case	case	NOUN
ejpam-1372	1115	40	as	as	SCONJ
ejpam-1372	1115	41	they	they	PRON
ejpam-1372	1115	42	do	do	VERB
ejpam-1372	1115	43	in	in	ADP
ejpam-1372	1115	44	the	the	DET
ejpam-1372	1115	45	latter	latter	ADJ
ejpam-1372	1115	46	case	case	NOUN
ejpam-1372	1115	47	.	.	PUNCT
ejpam-1372	1116	1	table	table	NOUN
ejpam-1372	1116	2	4	4	NUM
ejpam-1372	1116	3	,	,	PUNCT
ejpam-1372	1116	4	which	which	PRON
ejpam-1372	1116	5	also	also	ADV
ejpam-1372	1116	6	appears	appear	VERB
ejpam-1372	1116	7	in	in	ADP
ejpam-1372	1116	8	the	the	DET
ejpam-1372	1116	9	appendix	appendix	NOUN
ejpam-1372	1116	10	,	,	PUNCT
ejpam-1372	1116	11	presents	present	VERB
ejpam-1372	1116	12	a	a	DET
ejpam-1372	1116	13	small	small	ADJ
ejpam-1372	1116	14	sample	sample	NOUN
ejpam-1372	1116	15	of	of	ADP
ejpam-1372	1116	16	the	the	DET
ejpam-1372	1116	17	results	result	NOUN
ejpam-1372	1116	18	for	for	ADP
ejpam-1372	1116	19	the	the	DET
ejpam-1372	1116	20	regularised	regularise	VERB
ejpam-1372	1116	21	value	value	NOUN
ejpam-1372	1116	22	of	of	ADP
ejpam-1372	1116	23	ti(0,3/7	ti(0,3/7	ADJ
ejpam-1372	1116	24	,	,	PUNCT
ejpam-1372	1116	25	z3	z3	PROPN
ejpam-1372	1116	26	)	)	PUNCT
ejpam-1372	1116	27	obtained	obtain	VERB
ejpam-1372	1116	28	from	from	ADP
ejpam-1372	1116	29	the	the	DET
ejpam-1372	1116	30	borel	borel	NOUN
ejpam-1372	1116	31	-	-	PUNCT
ejpam-1372	1116	32	summed	sum	VERB
ejpam-1372	1116	33	forms	form	NOUN
ejpam-1372	1116	34	given	give	VERB
ejpam-1372	1116	35	by	by	ADP
ejpam-1372	1116	36	equivalence	equivalence	NOUN
ejpam-1372	1116	37	(	(	PUNCT
ejpam-1372	1116	38	116	116	NUM
ejpam-1372	1116	39	)	)	PUNCT
ejpam-1372	1116	40	.	.	PUNCT
ejpam-1372	1117	1	this	this	PRON
ejpam-1372	1117	2	means	mean	VERB
ejpam-1372	1117	3	that	that	SCONJ
ejpam-1372	1117	4	another	another	DET
ejpam-1372	1117	5	mathematica	mathematica	PROPN
ejpam-1372	1117	6	module	module	NOUN
ejpam-1372	1117	7	was	be	AUX
ejpam-1372	1117	8	created	create	VERB
ejpam-1372	1117	9	,	,	PUNCT
ejpam-1372	1117	10	which	which	PRON
ejpam-1372	1117	11	evaluates	evaluate	VERB
ejpam-1372	1117	12	all	all	DET
ejpam-1372	1117	13	the	the	DET
ejpam-1372	1117	14	quantities	quantity	NOUN
ejpam-1372	1117	15	on	on	ADP
ejpam-1372	1117	16	the	the	DET
ejpam-1372	1117	17	rhs	rhs	PROPN
ejpam-1372	1117	18	of	of	ADP
ejpam-1372	1117	19	this	this	DET
ejpam-1372	1117	20	equivalence	equivalence	NOUN
ejpam-1372	1117	21	.	.	PUNCT
ejpam-1372	1118	1	the	the	DET
ejpam-1372	1118	2	values	value	NOUN
ejpam-1372	1118	3	in	in	ADP
ejpam-1372	1118	4	the	the	DET
ejpam-1372	1118	5	table	table	NOUN
ejpam-1372	1118	6	have	have	AUX
ejpam-1372	1118	7	been	be	AUX
ejpam-1372	1118	8	obtained	obtain	VERB
ejpam-1372	1118	9	by	by	ADP
ejpam-1372	1118	10	running	run	VERB
ejpam-1372	1118	11	the	the	DET
ejpam-1372	1118	12	new	new	PROPN
ejpam-1372	1118	13	mathematica	mathematica	PROPN
ejpam-1372	1118	14	module	module	NOUN
ejpam-1372	1118	15	with	with	ADP
ejpam-1372	1118	16	|z|=4/5	|z|=4/5	ADV
ejpam-1372	1118	17	and	and	CCONJ
ejpam-1372	1118	18	arg	arg	VERB
ejpam-1372	1118	19	z>0	z>0	NOUN
ejpam-1372	1118	20	on	on	ADP
ejpam-1372	1118	21	the	the	DET
ejpam-1372	1118	22	same	same	ADJ
ejpam-1372	1118	23	power	power	NOUN
ejpam-1372	1118	24	mac	mac	PROPN
ejpam-1372	1118	25	g5	g5	PROPN
ejpam-1372	1118	26	computer	computer	NOUN
ejpam-1372	1118	27	plus	plus	CCONJ
ejpam-1372	1118	28	mathematica	mathematica	PROPN
ejpam-1372	1118	29	7.0	7.0	NUM
ejpam-1372	1118	30	system	system	NOUN
ejpam-1372	1118	31	.	.	PUNCT
ejpam-1372	1119	1	in	in	ADP
ejpam-1372	1119	2	this	this	DET
ejpam-1372	1119	3	code	code	NOUN
ejpam-1372	1119	4	the	the	DET
ejpam-1372	1119	5	options	option	NOUN
ejpam-1372	1119	6	in	in	ADP
ejpam-1372	1119	7	the	the	DET
ejpam-1372	1119	8	call	call	NOUN
ejpam-1372	1119	9	to	to	ADP
ejpam-1372	1119	10	the	the	DET
ejpam-1372	1119	11	nintegrate	nintegrate	ADJ
ejpam-1372	1119	12	routine	routine	NOUN
ejpam-1372	1119	13	were	be	AUX
ejpam-1372	1119	14	set	set	VERB
ejpam-1372	1119	15	to	to	ADP
ejpam-1372	1119	16	the	the	DET
ejpam-1372	1119	17	same	same	ADJ
ejpam-1372	1119	18	values	value	NOUN
ejpam-1372	1119	19	as	as	ADP
ejpam-1372	1119	20	in	in	ADP
ejpam-1372	1119	21	the	the	DET
ejpam-1372	1119	22	module	module	NOUN
ejpam-1372	1119	23	that	that	PRON
ejpam-1372	1119	24	was	be	AUX
ejpam-1372	1119	25	used	use	VERB
ejpam-1372	1119	26	to	to	PART
ejpam-1372	1119	27	obtain	obtain	VERB
ejpam-1372	1119	28	the	the	DET
ejpam-1372	1119	29	results	result	NOUN
ejpam-1372	1119	30	in	in	ADP
ejpam-1372	1119	31	tables	table	NOUN
ejpam-1372	1119	32	2	2	NUM
ejpam-1372	1119	33	and	and	CCONJ
ejpam-1372	1119	34	3	3	NUM
ejpam-1372	1119	35	.	.	PUNCT
ejpam-1372	1120	1	hence	hence	ADV
ejpam-1372	1120	2	,	,	PUNCT
ejpam-1372	1120	3	where	where	SCONJ
ejpam-1372	1120	4	the	the	DET
ejpam-1372	1120	5	same	same	ADJ
ejpam-1372	1120	6	value	value	NOUN
ejpam-1372	1120	7	of	of	ADP
ejpam-1372	1120	8	z	z	NOUN
ejpam-1372	1120	9	is	be	AUX
ejpam-1372	1120	10	involved	involve	VERB
ejpam-1372	1120	11	,	,	PUNCT
ejpam-1372	1120	12	the	the	DET
ejpam-1372	1120	13	results	result	NOUN
ejpam-1372	1120	14	in	in	ADP
ejpam-1372	1120	15	table	table	NOUN
ejpam-1372	1120	16	4	4	NUM
ejpam-1372	1120	17	can	can	AUX
ejpam-1372	1120	18	be	be	AUX
ejpam-1372	1120	19	compared	compare	VERB
ejpam-1372	1120	20	directly	directly	ADV
ejpam-1372	1120	21	with	with	ADP
ejpam-1372	1120	22	those	those	PRON
ejpam-1372	1120	23	in	in	ADP
ejpam-1372	1120	24	table	table	NOUN
ejpam-1372	1120	25	2	2	NUM
ejpam-1372	1120	26	.	.	PUNCT
ejpam-1372	1120	27	as	as	SCONJ
ejpam-1372	1120	28	was	be	AUX
ejpam-1372	1120	29	the	the	DET
ejpam-1372	1120	30	case	case	NOUN
ejpam-1372	1120	31	in	in	ADP
ejpam-1372	1120	32	the	the	DET
ejpam-1372	1120	33	two	two	NUM
ejpam-1372	1120	34	preceding	precede	VERB
ejpam-1372	1120	35	tables	table	NOUN
ejpam-1372	1120	36	,	,	PUNCT
ejpam-1372	1120	37	not	not	PART
ejpam-1372	1120	38	all	all	DET
ejpam-1372	1120	39	the	the	DET
ejpam-1372	1120	40	decimal	decimal	ADJ
ejpam-1372	1120	41	places	place	NOUN
ejpam-1372	1120	42	for	for	ADP
ejpam-1372	1120	43	the	the	DET
ejpam-1372	1120	44	results	result	NOUN
ejpam-1372	1120	45	were	be	AUX
ejpam-1372	1120	46	able	able	ADJ
ejpam-1372	1120	47	to	to	PART
ejpam-1372	1120	48	be	be	AUX
ejpam-1372	1120	49	displayed	display	VERB
ejpam-1372	1120	50	due	due	ADP
ejpam-1372	1120	51	to	to	ADP
ejpam-1372	1120	52	limited	limited	ADJ
ejpam-1372	1120	53	space	space	NOUN
ejpam-1372	1120	54	.	.	PUNCT
ejpam-1372	1121	1	one	one	NUM
ejpam-1372	1121	2	interesting	interesting	ADJ
ejpam-1372	1121	3	feature	feature	NOUN
ejpam-1372	1121	4	about	about	ADP
ejpam-1372	1121	5	these	these	DET
ejpam-1372	1121	6	results	result	NOUN
ejpam-1372	1121	7	is	be	AUX
ejpam-1372	1121	8	that	that	SCONJ
ejpam-1372	1121	9	they	they	PRON
ejpam-1372	1121	10	took	take	VERB
ejpam-1372	1121	11	considerably	considerably	ADV
ejpam-1372	1121	12	less	less	ADJ
ejpam-1372	1121	13	time	time	NOUN
ejpam-1372	1121	14	to	to	PART
ejpam-1372	1121	15	compute	compute	VERB
ejpam-1372	1121	16	than	than	ADP
ejpam-1372	1121	17	their	their	PRON
ejpam-1372	1121	18	mb	mb	ADJ
ejpam-1372	1121	19	-	-	PUNCT
ejpam-1372	1121	20	regularised	regularise	VERB
ejpam-1372	1121	21	counterparts	counterpart	NOUN
ejpam-1372	1121	22	.	.	PUNCT
ejpam-1372	1122	1	in	in	ADP
ejpam-1372	1122	2	fact	fact	NOUN
ejpam-1372	1122	3	,	,	PUNCT
ejpam-1372	1122	4	they	they	PRON
ejpam-1372	1122	5	generally	generally	ADV
ejpam-1372	1122	6	took	take	VERB
ejpam-1372	1122	7	only	only	ADV
ejpam-1372	1122	8	a	a	DET
ejpam-1372	1122	9	few	few	ADJ
ejpam-1372	1122	10	cpu	cpu	NOUN
ejpam-1372	1122	11	seconds	second	NOUN
ejpam-1372	1122	12	to	to	PART
ejpam-1372	1122	13	compute	compute	VERB
ejpam-1372	1122	14	compared	compare	VERB
ejpam-1372	1122	15	with	with	ADP
ejpam-1372	1122	16	the	the	DET
ejpam-1372	1122	17	mb	mb	ADV
ejpam-1372	1122	18	-	-	PUNCT
ejpam-1372	1122	19	regularised	regularise	VERB
ejpam-1372	1122	20	values	value	NOUN
ejpam-1372	1122	21	,	,	PUNCT
ejpam-1372	1122	22	which	which	PRON
ejpam-1372	1122	23	took	take	VERB
ejpam-1372	1122	24	between	between	ADP
ejpam-1372	1122	25	20	20	NUM
ejpam-1372	1122	26	and	and	CCONJ
ejpam-1372	1122	27	90	90	NUM
ejpam-1372	1122	28	seconds	second	NOUN
ejpam-1372	1122	29	and	and	CCONJ
ejpam-1372	1122	30	even	even	ADV
ejpam-1372	1122	31	longer	long	ADV
ejpam-1372	1122	32	on	on	ADP
ejpam-1372	1122	33	the	the	DET
ejpam-1372	1122	34	pentium	pentium	NOUN
ejpam-1372	1122	35	computer	computer	NOUN
ejpam-1372	1122	36	plus	plus	CCONJ
ejpam-1372	1122	37	mathematica	mathematica	PROPN
ejpam-1372	1122	38	4.1	4.1	NUM
ejpam-1372	1122	39	system	system	NOUN
ejpam-1372	1122	40	.	.	PUNCT
ejpam-1372	1123	1	this	this	PRON
ejpam-1372	1123	2	is	be	AUX
ejpam-1372	1123	3	quite	quite	ADV
ejpam-1372	1123	4	surprising	surprising	ADJ
ejpam-1372	1123	5	because	because	SCONJ
ejpam-1372	1123	6	the	the	DET
ejpam-1372	1123	7	opposite	opposite	NOUN
ejpam-1372	1123	8	was	be	AUX
ejpam-1372	1123	9	found	find	VERB
ejpam-1372	1123	10	to	to	PART
ejpam-1372	1123	11	apply	apply	VERB
ejpam-1372	1123	12	when	when	SCONJ
ejpam-1372	1123	13	determining	determine	VERB
ejpam-1372	1123	14	the	the	DET
ejpam-1372	1123	15	regularised	regularise	VERB
ejpam-1372	1123	16	values	value	NOUN
ejpam-1372	1123	17	from	from	ADP
ejpam-1372	1123	18	the	the	DET
ejpam-1372	1123	19	mb	mb	NOUN
ejpam-1372	1123	20	-	-	PUNCT
ejpam-1372	1123	21	regularised	regularise	VERB
ejpam-1372	1123	22	and	and	CCONJ
ejpam-1372	1123	23	borel	borel	NOUN
ejpam-1372	1123	24	-	-	PUNCT
ejpam-1372	1123	25	summed	sum	VERB
ejpam-1372	1123	26	forms	form	NOUN
ejpam-1372	1123	27	for	for	ADP
ejpam-1372	1123	28	the	the	DET
ejpam-1372	1123	29	complete	complete	ADJ
ejpam-1372	1123	30	asymptotic	asymptotic	ADJ
ejpam-1372	1123	31	expansion	expansion	NOUN
ejpam-1372	1123	32	of	of	ADP
ejpam-1372	1123	33	the	the	DET
ejpam-1372	1123	34	generalised	generalise	VERB
ejpam-1372	1123	35	euler	euler	PROPN
ejpam-1372	1123	36	-	-	PUNCT
ejpam-1372	1123	37	jacobi	jacobi	PROPN
ejpam-1372	1123	38	series	series	NOUN
ejpam-1372	1123	39	for	for	ADP
ejpam-1372	1123	40	p	p	PROPN
ejpam-1372	1123	41	/	/	SYM
ejpam-1372	1123	42	q=3	q=3	PROPN
ejpam-1372	1123	43	in	in	ADP
ejpam-1372	1123	44	ref	ref	NOUN
ejpam-1372	1123	45	.	.	PUNCT
ejpam-1372	1124	1	[	[	X
ejpam-1372	1124	2	21	21	NUM
ejpam-1372	1124	3	]	]	PUNCT
ejpam-1372	1124	4	.	.	PUNCT
ejpam-1372	1125	1	the	the	DET
ejpam-1372	1125	2	first	first	ADJ
ejpam-1372	1125	3	column	column	NOUN
ejpam-1372	1125	4	in	in	ADP
ejpam-1372	1125	5	table	table	NOUN
ejpam-1372	1125	6	4	4	NUM
ejpam-1372	1125	7	presents	present	VERB
ejpam-1372	1125	8	the	the	DET
ejpam-1372	1125	9	value	value	NOUN
ejpam-1372	1125	10	of	of	ADP
ejpam-1372	1125	11	the	the	DET
ejpam-1372	1125	12	truncation	truncation	NOUN
ejpam-1372	1125	13	parameter	parameter	NOUN
ejpam-1372	1125	14	or	or	CCONJ
ejpam-1372	1125	15	n	n	PROPN
ejpam-1372	1125	16	that	that	PRON
ejpam-1372	1125	17	was	be	AUX
ejpam-1372	1125	18	used	use	VERB
ejpam-1372	1125	19	to	to	PART
ejpam-1372	1125	20	evaluate	evaluate	VERB
ejpam-1372	1125	21	the	the	DET
ejpam-1372	1125	22	various	various	ADJ
ejpam-1372	1125	23	quantities	quantity	NOUN
ejpam-1372	1125	24	on	on	ADP
ejpam-1372	1125	25	the	the	DET
ejpam-1372	1125	26	rhs	rhs	PROPN
ejpam-1372	1125	27	of	of	ADP
ejpam-1372	1125	28	equivalence	equivalence	NOUN
ejpam-1372	1125	29	(	(	PUNCT
ejpam-1372	1125	30	116	116	NUM
ejpam-1372	1125	31	)	)	PUNCT
ejpam-1372	1125	32	.	.	PUNCT
ejpam-1372	1126	1	the	the	DET
ejpam-1372	1126	2	next	next	ADJ
ejpam-1372	1126	3	column	column	NOUN
ejpam-1372	1126	4	displays	display	VERB
ejpam-1372	1126	5	the	the	DET
ejpam-1372	1126	6	values	value	NOUN
ejpam-1372	1126	7	of	of	ADP
ejpam-1372	1126	8	l	l	NOUN
ejpam-1372	1126	9	used	use	VERB
ejpam-1372	1126	10	in	in	ADP
ejpam-1372	1126	11	evaluating	evaluate	VERB
ejpam-1372	1126	12	the	the	DET
ejpam-1372	1126	13	stokes	stokes	PROPN
ejpam-1372	1126	14	discontinuity	discontinuity	NOUN
ejpam-1372	1126	15	term	term	NOUN
ejpam-1372	1126	16	appearing	appear	VERB
ejpam-1372	1126	17	in	in	ADP
ejpam-1372	1126	18	the	the	DET
ejpam-1372	1126	19	equivalence	equivalence	NOUN
ejpam-1372	1126	20	statement	statement	NOUN
ejpam-1372	1126	21	.	.	PUNCT
ejpam-1372	1127	1	as	as	SCONJ
ejpam-1372	1127	2	indicated	indicate	VERB
ejpam-1372	1127	3	previously	previously	ADV
ejpam-1372	1127	4	,	,	PUNCT
ejpam-1372	1127	5	these	these	DET
ejpam-1372	1127	6	integers	integer	NOUN
ejpam-1372	1127	7	are	be	AUX
ejpam-1372	1127	8	dependent	dependent	ADJ
ejpam-1372	1127	9	on	on	ADP
ejpam-1372	1127	10	the	the	DET
ejpam-1372	1127	11	value	value	NOUN
ejpam-1372	1127	12	of	of	ADP
ejpam-1372	1127	13	arg	arg	NOUN
ejpam-1372	1127	14	z	z	PROPN
ejpam-1372	1127	15	,	,	PUNCT
ejpam-1372	1127	16	which	which	PRON
ejpam-1372	1127	17	appear	appear	VERB
ejpam-1372	1127	18	in	in	ADP
ejpam-1372	1127	19	the	the	DET
ejpam-1372	1127	20	third	third	ADJ
ejpam-1372	1127	21	column	column	NOUN
ejpam-1372	1127	22	of	of	ADP
ejpam-1372	1127	23	the	the	DET
ejpam-1372	1127	24	table	table	NOUN
ejpam-1372	1127	25	.	.	PUNCT
ejpam-1372	1128	1	the	the	DET
ejpam-1372	1128	2	next	next	ADJ
ejpam-1372	1128	3	column	column	NOUN
ejpam-1372	1128	4	displays	display	VERB
ejpam-1372	1128	5	the	the	DET
ejpam-1372	1128	6	values	value	NOUN
ejpam-1372	1128	7	of	of	ADP
ejpam-1372	1128	8	the	the	DET
ejpam-1372	1128	9	truncated	truncated	ADJ
ejpam-1372	1128	10	series	series	NOUN
ejpam-1372	1128	11	,	,	PUNCT
ejpam-1372	1128	12	viz	viz	PROPN
ejpam-1372	1128	13	.	.	PUNCT
ejpam-1372	1129	1	the	the	DET
ejpam-1372	1129	2	second	second	ADJ
ejpam-1372	1129	3	term	term	NOUN
ejpam-1372	1129	4	on	on	ADP
ejpam-1372	1129	5	the	the	DET
ejpam-1372	1129	6	rhs	rhs	PROPN
ejpam-1372	1129	7	of	of	ADP
ejpam-1372	1129	8	eq	eq	PROPN
ejpam-1372	1129	9	.	.	PUNCT
ejpam-1372	1130	1	(	(	PUNCT
ejpam-1372	1130	2	119	119	NUM
ejpam-1372	1130	3	)	)	PUNCT
ejpam-1372	1130	4	,	,	PUNCT
ejpam-1372	1130	5	while	while	SCONJ
ejpam-1372	1130	6	the	the	DET
ejpam-1372	1130	7	fifth	fifth	ADJ
ejpam-1372	1130	8	and	and	CCONJ
ejpam-1372	1130	9	sixth	sixth	ADJ
ejpam-1372	1130	10	columns	column	NOUN
ejpam-1372	1130	11	display	display	VERB
ejpam-1372	1130	12	the	the	DET
ejpam-1372	1130	13	values	value	NOUN
ejpam-1372	1130	14	corresponding	correspond	VERB
ejpam-1372	1130	15	to	to	ADP
ejpam-1372	1130	16	the	the	DET
ejpam-1372	1130	17	other	other	ADJ
ejpam-1372	1130	18	terms	term	NOUN
ejpam-1372	1130	19	on	on	ADP
ejpam-1372	1130	20	the	the	DET
ejpam-1372	1130	21	rhs	rhs	PROPN
ejpam-1372	1130	22	of	of	ADP
ejpam-1372	1130	23	equivalence	equivalence	NOUN
ejpam-1372	1130	24	(	(	PUNCT
ejpam-1372	1130	25	116	116	NUM
ejpam-1372	1130	26	)	)	PUNCT
ejpam-1372	1130	27	.	.	PUNCT
ejpam-1372	1131	1	the	the	DET
ejpam-1372	1131	2	integral	integral	ADJ
ejpam-1372	1131	3	on	on	ADP
ejpam-1372	1131	4	the	the	DET
ejpam-1372	1131	5	rhs	rhs	PROPN
ejpam-1372	1131	6	of	of	ADP
ejpam-1372	1131	7	equivalence	equivalence	NOUN
ejpam-1372	1131	8	(	(	PUNCT
ejpam-1372	1131	9	116	116	NUM
ejpam-1372	1131	10	)	)	PUNCT
ejpam-1372	1131	11	is	be	AUX
ejpam-1372	1131	12	referred	refer	VERB
ejpam-1372	1131	13	to	to	ADP
ejpam-1372	1131	14	here	here	ADV
ejpam-1372	1131	15	as	as	ADP
ejpam-1372	1131	16	the	the	DET
ejpam-1372	1131	17	borel	borel	NOUN
ejpam-1372	1131	18	integral	integral	ADJ
ejpam-1372	1131	19	.	.	PUNCT
ejpam-1372	1132	1	the	the	DET
ejpam-1372	1132	2	final	final	ADJ
ejpam-1372	1132	3	column	column	NOUN
ejpam-1372	1132	4	presents	present	VERB
ejpam-1372	1132	5	the	the	DET
ejpam-1372	1132	6	borel	borel	NOUN
ejpam-1372	1132	7	-	-	PUNCT
ejpam-1372	1132	8	summed	sum	VERB
ejpam-1372	1132	9	regularised	regularise	VERB
ejpam-1372	1132	10	values	value	NOUN
ejpam-1372	1132	11	of	of	ADP
ejpam-1372	1132	12	ti	ti	PROPN
ejpam-1372	1132	13	(	(	PUNCT
ejpam-1372	1132	14	0,3/7	0,3/7	PROPN
ejpam-1372	1132	15	,	,	PUNCT
ejpam-1372	1132	16	z3	z3	PROPN
ejpam-1372	1132	17	)	)	PUNCT
ejpam-1372	1132	18	,	,	PUNCT
ejpam-1372	1132	19	which	which	PRON
ejpam-1372	1132	20	have	have	AUX
ejpam-1372	1132	21	been	be	AUX
ejpam-1372	1132	22	calculated	calculate	VERB
ejpam-1372	1132	23	by	by	ADP
ejpam-1372	1132	24	summing	sum	VERB
ejpam-1372	1132	25	the	the	DET
ejpam-1372	1132	26	respective	respective	ADJ
ejpam-1372	1132	27	quantities	quantity	NOUN
ejpam-1372	1132	28	in	in	ADP
ejpam-1372	1132	29	the	the	DET
ejpam-1372	1132	30	three	three	NUM
ejpam-1372	1132	31	preceding	precede	VERB
ejpam-1372	1132	32	columns	column	NOUN
ejpam-1372	1132	33	.	.	PUNCT
ejpam-1372	1133	1	from	from	ADP
ejpam-1372	1133	2	table	table	NOUN
ejpam-1372	1133	3	4	4	NUM
ejpam-1372	1133	4	it	it	PRON
ejpam-1372	1133	5	can	can	AUX
ejpam-1372	1133	6	be	be	AUX
ejpam-1372	1133	7	seen	see	VERB
ejpam-1372	1133	8	that	that	SCONJ
ejpam-1372	1133	9	the	the	DET
ejpam-1372	1133	10	regularised	regularise	VERB
ejpam-1372	1133	11	value	value	NOUN
ejpam-1372	1133	12	of	of	ADP
ejpam-1372	1133	13	ti	ti	PROPN
ejpam-1372	1133	14	(	(	PUNCT
ejpam-1372	1133	15	0,3/7	0,3/7	PROPN
ejpam-1372	1133	16	,	,	PUNCT
ejpam-1372	1133	17	z3	z3	PROPN
ejpam-1372	1133	18	)	)	PUNCT
ejpam-1372	1133	19	remains	remain	VERB
ejpam-1372	1133	20	invariant	invariant	ADJ
ejpam-1372	1133	21	v.	v.	ADP
ejpam-1372	1133	22	kowalenko	kowalenko	PROPN
ejpam-1372	1133	23	/	/	SYM
ejpam-1372	1133	24	eur	eur	PROPN
ejpam-1372	1133	25	.	.	PUNCT
ejpam-1372	1134	1	j.	j.	PROPN
ejpam-1372	1134	2	pure	pure	PROPN
ejpam-1372	1134	3	appl	appl	PROPN
ejpam-1372	1134	4	.	.	PROPN
ejpam-1372	1134	5	math	math	PROPN
ejpam-1372	1134	6	,	,	PUNCT
ejpam-1372	1134	7	4	4	NUM
ejpam-1372	1134	8	(	(	PUNCT
ejpam-1372	1134	9	2011	2011	NUM
ejpam-1372	1134	10	)	)	PUNCT
ejpam-1372	1134	11	,	,	PUNCT
ejpam-1372	1134	12	370	370	NUM
ejpam-1372	1134	13	-	-	SYM
ejpam-1372	1134	14	423	423	NUM
ejpam-1372	1134	15	411	411	NUM
ejpam-1372	1134	16	for	for	ADP
ejpam-1372	1134	17	each	each	DET
ejpam-1372	1134	18	value	value	NOUN
ejpam-1372	1134	19	of	of	ADP
ejpam-1372	1134	20	arg	arg	NOUN
ejpam-1372	1134	21	z.	z.	PROPN
ejpam-1372	1134	22	that	that	ADV
ejpam-1372	1134	23	is	be	AUX
ejpam-1372	1134	24	,	,	PUNCT
ejpam-1372	1134	25	irrespective	irrespective	ADV
ejpam-1372	1134	26	of	of	ADP
ejpam-1372	1134	27	the	the	DET
ejpam-1372	1134	28	value	value	NOUN
ejpam-1372	1134	29	selected	select	VERB
ejpam-1372	1134	30	for	for	ADP
ejpam-1372	1134	31	the	the	DET
ejpam-1372	1134	32	truncation	truncation	NOUN
ejpam-1372	1134	33	parameter	parameter	NOUN
ejpam-1372	1135	1	,	,	PUNCT
ejpam-1372	1135	2	we	we	PRON
ejpam-1372	1135	3	end	end	VERB
ejpam-1372	1135	4	up	up	ADP
ejpam-1372	1135	5	with	with	ADP
ejpam-1372	1135	6	the	the	DET
ejpam-1372	1135	7	same	same	ADJ
ejpam-1372	1135	8	regularised	regularise	VERB
ejpam-1372	1135	9	value	value	NOUN
ejpam-1372	1135	10	for	for	ADP
ejpam-1372	1135	11	the	the	DET
ejpam-1372	1135	12	entire	entire	ADJ
ejpam-1372	1135	13	series	series	NOUN
ejpam-1372	1135	14	.	.	PUNCT
ejpam-1372	1136	1	each	each	DET
ejpam-1372	1136	2	value	value	NOUN
ejpam-1372	1136	3	of	of	ADP
ejpam-1372	1136	4	n	n	NOUN
ejpam-1372	1136	5	results	result	NOUN
ejpam-1372	1136	6	in	in	ADP
ejpam-1372	1136	7	a	a	DET
ejpam-1372	1136	8	completely	completely	ADV
ejpam-1372	1136	9	different	different	ADJ
ejpam-1372	1136	10	integrand	integrand	NOUN
ejpam-1372	1136	11	being	be	AUX
ejpam-1372	1136	12	computed	compute	VERB
ejpam-1372	1136	13	by	by	ADP
ejpam-1372	1136	14	the	the	DET
ejpam-1372	1136	15	nintegrate	nintegrate	ADJ
ejpam-1372	1136	16	routine	routine	NOUN
ejpam-1372	1136	17	,	,	PUNCT
ejpam-1372	1136	18	which	which	PRON
ejpam-1372	1136	19	means	mean	VERB
ejpam-1372	1136	20	effectively	effectively	ADV
ejpam-1372	1136	21	that	that	SCONJ
ejpam-1372	1136	22	different	different	ADJ
ejpam-1372	1136	23	methods	method	NOUN
ejpam-1372	1136	24	are	be	AUX
ejpam-1372	1136	25	being	be	AUX
ejpam-1372	1136	26	employed	employ	VERB
ejpam-1372	1136	27	to	to	PART
ejpam-1372	1136	28	evaluate	evaluate	VERB
ejpam-1372	1136	29	the	the	DET
ejpam-1372	1136	30	regularised	regularise	VERB
ejpam-1372	1136	31	value	value	NOUN
ejpam-1372	1136	32	.	.	PUNCT
ejpam-1372	1137	1	nevertheless	nevertheless	ADV
ejpam-1372	1137	2	,	,	PUNCT
ejpam-1372	1137	3	the	the	DET
ejpam-1372	1137	4	regularised	regularise	VERB
ejpam-1372	1137	5	value	value	NOUN
ejpam-1372	1137	6	remains	remain	VERB
ejpam-1372	1137	7	invariant	invariant	ADJ
ejpam-1372	1137	8	as	as	SCONJ
ejpam-1372	1137	9	it	it	PRON
ejpam-1372	1137	10	did	do	VERB
ejpam-1372	1137	11	when	when	SCONJ
ejpam-1372	1137	12	the	the	DET
ejpam-1372	1137	13	truncation	truncation	NOUN
ejpam-1372	1137	14	parameter	parameter	NOUN
ejpam-1372	1137	15	was	be	AUX
ejpam-1372	1137	16	altered	alter	VERB
ejpam-1372	1137	17	in	in	ADP
ejpam-1372	1137	18	the	the	DET
ejpam-1372	1137	19	mb	mb	ADJ
ejpam-1372	1137	20	-	-	PUNCT
ejpam-1372	1137	21	regularised	regularise	VERB
ejpam-1372	1137	22	forms	form	NOUN
ejpam-1372	1137	23	of	of	ADP
ejpam-1372	1137	24	the	the	DET
ejpam-1372	1137	25	regularised	regularise	VERB
ejpam-1372	1137	26	value	value	NOUN
ejpam-1372	1137	27	.	.	PUNCT
ejpam-1372	1138	1	from	from	ADP
ejpam-1372	1138	2	the	the	DET
ejpam-1372	1138	3	table	table	NOUN
ejpam-1372	1138	4	it	it	PRON
ejpam-1372	1138	5	can	can	AUX
ejpam-1372	1138	6	be	be	AUX
ejpam-1372	1138	7	seen	see	VERB
ejpam-1372	1138	8	that	that	SCONJ
ejpam-1372	1138	9	for	for	ADP
ejpam-1372	1138	10	n	n	PROPN
ejpam-1372	1138	11	>	>	X
ejpam-1372	1138	12	10	10	NUM
ejpam-1372	1138	13	,	,	PUNCT
ejpam-1372	1138	14	the	the	DET
ejpam-1372	1138	15	truncated	truncated	ADJ
ejpam-1372	1138	16	series	series	NOUN
ejpam-1372	1138	17	diverges	diverge	VERB
ejpam-1372	1138	18	rapidly	rapidly	ADV
ejpam-1372	1138	19	,	,	PUNCT
ejpam-1372	1138	20	while	while	SCONJ
ejpam-1372	1138	21	the	the	DET
ejpam-1372	1138	22	borel	borel	NOUN
ejpam-1372	1138	23	integral	integral	ADJ
ejpam-1372	1138	24	obliges	oblige	NOUN
ejpam-1372	1138	25	by	by	ADP
ejpam-1372	1138	26	diverging	diverge	VERB
ejpam-1372	1138	27	in	in	ADP
ejpam-1372	1138	28	the	the	DET
ejpam-1372	1138	29	opposite	opposite	ADJ
ejpam-1372	1138	30	direction	direction	NOUN
ejpam-1372	1138	31	.	.	PUNCT
ejpam-1372	1139	1	even	even	ADV
ejpam-1372	1139	2	for	for	ADP
ejpam-1372	1139	3	the	the	DET
ejpam-1372	1139	4	smaller	small	ADJ
ejpam-1372	1139	5	values	value	NOUN
ejpam-1372	1139	6	of	of	ADP
ejpam-1372	1139	7	the	the	DET
ejpam-1372	1139	8	truncation	truncation	NOUN
ejpam-1372	1139	9	parameter	parameter	NOUN
ejpam-1372	1139	10	the	the	DET
ejpam-1372	1139	11	truncated	truncated	ADJ
ejpam-1372	1139	12	series	series	NOUN
ejpam-1372	1139	13	represents	represent	VERB
ejpam-1372	1139	14	a	a	DET
ejpam-1372	1139	15	poor	poor	ADJ
ejpam-1372	1139	16	approximation	approximation	NOUN
ejpam-1372	1139	17	to	to	ADP
ejpam-1372	1139	18	the	the	DET
ejpam-1372	1139	19	regularised	regularise	VERB
ejpam-1372	1139	20	value	value	NOUN
ejpam-1372	1139	21	,	,	PUNCT
ejpam-1372	1139	22	which	which	PRON
ejpam-1372	1139	23	emphasises	emphasise	VERB
ejpam-1372	1139	24	the	the	DET
ejpam-1372	1139	25	fact	fact	NOUN
ejpam-1372	1139	26	that	that	SCONJ
ejpam-1372	1139	27	the	the	DET
ejpam-1372	1139	28	truncated	truncated	ADJ
ejpam-1372	1139	29	series	series	NOUN
ejpam-1372	1139	30	is	be	AUX
ejpam-1372	1139	31	only	only	ADV
ejpam-1372	1139	32	a	a	DET
ejpam-1372	1139	33	good	good	ADJ
ejpam-1372	1139	34	approximation	approximation	NOUN
ejpam-1372	1139	35	when	when	SCONJ
ejpam-1372	1139	36	|z|	|z|	NOUN
ejpam-1372	1139	37	is	be	AUX
ejpam-1372	1139	38	very	very	ADV
ejpam-1372	1139	39	small	small	ADJ
ejpam-1372	1139	40	,	,	PUNCT
ejpam-1372	1139	41	namely	namely	ADV
ejpam-1372	1139	42	less	less	ADJ
ejpam-1372	1139	43	than	than	ADP
ejpam-1372	1139	44	0.01	0.01	NUM
ejpam-1372	1139	45	.	.	PUNCT
ejpam-1372	1140	1	as	as	SCONJ
ejpam-1372	1140	2	mentioned	mention	VERB
ejpam-1372	1140	3	previously	previously	ADV
ejpam-1372	1140	4	,	,	PUNCT
ejpam-1372	1140	5	because	because	SCONJ
ejpam-1372	1140	6	the	the	DET
ejpam-1372	1140	7	regularised	regularise	VERB
ejpam-1372	1140	8	values	value	NOUN
ejpam-1372	1140	9	in	in	ADP
ejpam-1372	1140	10	table	table	NOUN
ejpam-1372	1140	11	4	4	NUM
ejpam-1372	1140	12	have	have	AUX
ejpam-1372	1140	13	been	be	AUX
ejpam-1372	1140	14	evaluated	evaluate	VERB
ejpam-1372	1140	15	by	by	ADP
ejpam-1372	1140	16	using	use	VERB
ejpam-1372	1140	17	the	the	DET
ejpam-1372	1140	18	same	same	ADJ
ejpam-1372	1140	19	options	option	NOUN
ejpam-1372	1140	20	in	in	ADP
ejpam-1372	1140	21	the	the	DET
ejpam-1372	1140	22	nintegrate	nintegrate	ADJ
ejpam-1372	1140	23	routine	routine	NOUN
ejpam-1372	1140	24	as	as	ADP
ejpam-1372	1140	25	those	those	PRON
ejpam-1372	1140	26	in	in	ADP
ejpam-1372	1140	27	table	table	NOUN
ejpam-1372	1140	28	2	2	NUM
ejpam-1372	1140	29	,	,	PUNCT
ejpam-1372	1140	30	we	we	PRON
ejpam-1372	1140	31	can	can	AUX
ejpam-1372	1140	32	compare	compare	VERB
ejpam-1372	1140	33	corresponding	corresponding	ADJ
ejpam-1372	1140	34	results	result	NOUN
ejpam-1372	1140	35	.	.	PUNCT
ejpam-1372	1141	1	as	as	ADP
ejpam-1372	1141	2	a	a	DET
ejpam-1372	1141	3	result	result	NOUN
ejpam-1372	1141	4	,	,	PUNCT
ejpam-1372	1141	5	we	we	PRON
ejpam-1372	1141	6	find	find	VERB
ejpam-1372	1141	7	that	that	SCONJ
ejpam-1372	1141	8	for	for	ADP
ejpam-1372	1141	9	the	the	DET
ejpam-1372	1141	10	same	same	ADJ
ejpam-1372	1141	11	value	value	NOUN
ejpam-1372	1141	12	of	of	ADP
ejpam-1372	1141	13	arg	arg	NOUN
ejpam-1372	1141	14	z	z	PROPN
ejpam-1372	1141	15	that	that	SCONJ
ejpam-1372	1141	16	the	the	DET
ejpam-1372	1141	17	regularised	regularise	VERB
ejpam-1372	1141	18	values	value	NOUN
ejpam-1372	1141	19	are	be	AUX
ejpam-1372	1141	20	identical	identical	ADJ
ejpam-1372	1141	21	to	to	ADP
ejpam-1372	1141	22	one	one	NUM
ejpam-1372	1141	23	another	another	DET
ejpam-1372	1141	24	within	within	ADP
ejpam-1372	1141	25	the	the	DET
ejpam-1372	1141	26	precision	precision	NOUN
ejpam-1372	1141	27	and	and	CCONJ
ejpam-1372	1141	28	accuracy	accuracy	NOUN
ejpam-1372	1141	29	goals	goal	NOUN
ejpam-1372	1141	30	set	set	VERB
ejpam-1372	1141	31	in	in	ADP
ejpam-1372	1141	32	both	both	DET
ejpam-1372	1141	33	programs	program	NOUN
ejpam-1372	1141	34	.	.	PUNCT
ejpam-1372	1142	1	this	this	PRON
ejpam-1372	1142	2	means	mean	VERB
ejpam-1372	1142	3	that	that	SCONJ
ejpam-1372	1142	4	the	the	DET
ejpam-1372	1142	5	regularised	regularise	VERB
ejpam-1372	1142	6	value	value	NOUN
ejpam-1372	1142	7	of	of	ADP
ejpam-1372	1142	8	ti(0,3/7	ti(0,3/7	ADJ
ejpam-1372	1142	9	,	,	PUNCT
ejpam-1372	1142	10	z3	z3	PROPN
ejpam-1372	1142	11	)	)	PUNCT
ejpam-1372	1142	12	can	can	AUX
ejpam-1372	1142	13	be	be	AUX
ejpam-1372	1142	14	evaluated	evaluate	VERB
ejpam-1372	1142	15	by	by	ADP
ejpam-1372	1142	16	combining	combine	VERB
ejpam-1372	1142	17	eq	eq	ADP
ejpam-1372	1142	18	.	.	PUNCT
ejpam-1372	1143	1	(	(	PUNCT
ejpam-1372	1143	2	119	119	NUM
ejpam-1372	1143	3	)	)	PUNCT
ejpam-1372	1143	4	with	with	ADP
ejpam-1372	1143	5	either	either	CCONJ
ejpam-1372	1143	6	the	the	DET
ejpam-1372	1143	7	borel	borel	NOUN
ejpam-1372	1143	8	-	-	PUNCT
ejpam-1372	1143	9	summed	sum	VERB
ejpam-1372	1143	10	form	form	NOUN
ejpam-1372	1143	11	given	give	VERB
ejpam-1372	1143	12	by	by	ADP
ejpam-1372	1143	13	equivalence	equivalence	NOUN
ejpam-1372	1143	14	(	(	PUNCT
ejpam-1372	1143	15	116	116	NUM
ejpam-1372	1143	16	)	)	PUNCT
ejpam-1372	1143	17	or	or	CCONJ
ejpam-1372	1143	18	the	the	DET
ejpam-1372	1143	19	mb	mb	ADJ
ejpam-1372	1143	20	-	-	PUNCT
ejpam-1372	1143	21	regularised	regularise	VERB
ejpam-1372	1143	22	form	form	NOUN
ejpam-1372	1143	23	given	give	VERB
ejpam-1372	1143	24	by	by	ADP
ejpam-1372	1143	25	equivalence	equivalence	NOUN
ejpam-1372	1143	26	(	(	PUNCT
ejpam-1372	1143	27	118	118	NUM
ejpam-1372	1143	28	)	)	PUNCT
ejpam-1372	1143	29	.	.	PUNCT
ejpam-1372	1144	1	in	in	ADP
ejpam-1372	1144	2	other	other	ADJ
ejpam-1372	1144	3	words	word	NOUN
ejpam-1372	1144	4	,	,	PUNCT
ejpam-1372	1144	5	we	we	PRON
ejpam-1372	1144	6	have	have	VERB
ejpam-1372	1144	7	two	two	NUM
ejpam-1372	1144	8	totally	totally	ADV
ejpam-1372	1144	9	different	different	ADJ
ejpam-1372	1144	10	methods	method	NOUN
ejpam-1372	1144	11	yielding	yield	VERB
ejpam-1372	1144	12	the	the	DET
ejpam-1372	1144	13	same	same	ADJ
ejpam-1372	1144	14	regularised	regularise	VERB
ejpam-1372	1144	15	value	value	NOUN
ejpam-1372	1144	16	,	,	PUNCT
ejpam-1372	1144	17	which	which	PRON
ejpam-1372	1144	18	is	be	AUX
ejpam-1372	1144	19	,	,	PUNCT
ejpam-1372	1144	20	again	again	ADV
ejpam-1372	1144	21	,	,	PUNCT
ejpam-1372	1144	22	in	in	ADP
ejpam-1372	1144	23	accordance	accordance	NOUN
ejpam-1372	1144	24	with	with	ADP
ejpam-1372	1144	25	euler	euler	PROPN
ejpam-1372	1144	26	’s	’s	PART
ejpam-1372	1144	27	second	second	ADJ
ejpam-1372	1144	28	view	view	NOUN
ejpam-1372	1144	29	on	on	ADP
ejpam-1372	1144	30	divergent	divergent	ADJ
ejpam-1372	1144	31	series	series	NOUN
ejpam-1372	1144	32	.	.	PUNCT
ejpam-1372	1145	1	table	table	NOUN
ejpam-1372	1145	2	5	5	NUM
ejpam-1372	1145	3	in	in	ADP
ejpam-1372	1145	4	the	the	DET
ejpam-1372	1145	5	appendix	appendix	NOUN
ejpam-1372	1145	6	presents	present	VERB
ejpam-1372	1145	7	another	another	DET
ejpam-1372	1145	8	small	small	ADJ
ejpam-1372	1145	9	sample	sample	NOUN
ejpam-1372	1145	10	of	of	ADP
ejpam-1372	1145	11	the	the	DET
ejpam-1372	1145	12	results	result	NOUN
ejpam-1372	1145	13	obtained	obtain	VERB
ejpam-1372	1145	14	by	by	ADP
ejpam-1372	1145	15	running	run	VERB
ejpam-1372	1145	16	the	the	DET
ejpam-1372	1145	17	second	second	ADJ
ejpam-1372	1145	18	module	module	NOUN
ejpam-1372	1145	19	on	on	ADP
ejpam-1372	1145	20	the	the	DET
ejpam-1372	1145	21	same	same	ADJ
ejpam-1372	1145	22	power	power	NOUN
ejpam-1372	1145	23	mac	mac	PROPN
ejpam-1372	1145	24	g5	g5	PROPN
ejpam-1372	1145	25	with	with	ADP
ejpam-1372	1145	26	mathematica	mathematica	PROPN
ejpam-1372	1145	27	7.0	7.0	NUM
ejpam-1372	1145	28	,	,	PUNCT
ejpam-1372	1145	29	but	but	CCONJ
ejpam-1372	1145	30	now	now	ADV
ejpam-1372	1145	31	we	we	PRON
ejpam-1372	1145	32	set	set	VERB
ejpam-1372	1145	33	|z|=2	|z|=2	NOUN
ejpam-1372	1145	34	and	and	CCONJ
ejpam-1372	1145	35	consider	consider	VERB
ejpam-1372	1145	36	the	the	DET
ejpam-1372	1145	37	lower	low	ADJ
ejpam-1372	1145	38	half	half	NOUN
ejpam-1372	1145	39	of	of	ADP
ejpam-1372	1145	40	the	the	DET
ejpam-1372	1145	41	principal	principal	ADJ
ejpam-1372	1145	42	branch	branch	NOUN
ejpam-1372	1145	43	of	of	ADP
ejpam-1372	1145	44	the	the	DET
ejpam-1372	1145	45	complex	complex	ADJ
ejpam-1372	1145	46	plane	plane	NOUN
ejpam-1372	1145	47	,	,	PUNCT
ejpam-1372	1145	48	viz	viz	PROPN
ejpam-1372	1145	49	.	.	PUNCT
ejpam-1372	1146	1	arg	arg	PROPN
ejpam-1372	1146	2	z<0	z<0	PROPN
ejpam-1372	1146	3	.	.	PUNCT
ejpam-1372	1147	1	the	the	DET
ejpam-1372	1147	2	new	new	ADJ
ejpam-1372	1147	3	table	table	NOUN
ejpam-1372	1147	4	is	be	AUX
ejpam-1372	1147	5	composed	compose	VERB
ejpam-1372	1147	6	of	of	ADP
ejpam-1372	1147	7	the	the	DET
ejpam-1372	1147	8	same	same	ADJ
ejpam-1372	1147	9	quantities	quantity	NOUN
ejpam-1372	1147	10	appearing	appear	VERB
ejpam-1372	1147	11	in	in	ADP
ejpam-1372	1147	12	table	table	NOUN
ejpam-1372	1147	13	4	4	NUM
ejpam-1372	1147	14	.	.	PUNCT
ejpam-1372	1148	1	as	as	SCONJ
ejpam-1372	1148	2	was	be	AUX
ejpam-1372	1148	3	found	find	VERB
ejpam-1372	1148	4	to	to	PART
ejpam-1372	1148	5	be	be	AUX
ejpam-1372	1148	6	the	the	DET
ejpam-1372	1148	7	case	case	NOUN
ejpam-1372	1148	8	for	for	ADP
ejpam-1372	1148	9	the	the	DET
ejpam-1372	1148	10	results	result	NOUN
ejpam-1372	1148	11	in	in	ADP
ejpam-1372	1148	12	the	the	DET
ejpam-1372	1148	13	previous	previous	ADJ
ejpam-1372	1148	14	table	table	NOUN
ejpam-1372	1148	15	,	,	PUNCT
ejpam-1372	1148	16	they	they	PRON
ejpam-1372	1148	17	were	be	AUX
ejpam-1372	1148	18	computed	compute	VERB
ejpam-1372	1148	19	far	far	ADV
ejpam-1372	1148	20	more	more	ADV
ejpam-1372	1148	21	quickly	quickly	ADV
ejpam-1372	1148	22	than	than	ADP
ejpam-1372	1148	23	their	their	PRON
ejpam-1372	1148	24	mb	mb	ADJ
ejpam-1372	1148	25	-	-	PUNCT
ejpam-1372	1148	26	regularised	regularise	VERB
ejpam-1372	1148	27	counterparts	counterpart	NOUN
ejpam-1372	1148	28	displayed	display	VERB
ejpam-1372	1148	29	in	in	ADP
ejpam-1372	1148	30	table	table	NOUN
ejpam-1372	1148	31	3	3	NUM
ejpam-1372	1148	32	.	.	PUNCT
ejpam-1372	1149	1	once	once	ADV
ejpam-1372	1149	2	again	again	ADV
ejpam-1372	1149	3	,	,	PUNCT
ejpam-1372	1149	4	we	we	PRON
ejpam-1372	1149	5	see	see	VERB
ejpam-1372	1149	6	that	that	PRON
ejpam-1372	1149	7	for	for	ADP
ejpam-1372	1149	8	fixed	fix	VERB
ejpam-1372	1149	9	values	value	NOUN
ejpam-1372	1149	10	of	of	ADP
ejpam-1372	1149	11	arg	arg	NOUN
ejpam-1372	1149	12	z	z	PROPN
ejpam-1372	1149	13	,	,	PUNCT
ejpam-1372	1149	14	the	the	DET
ejpam-1372	1149	15	regularised	regularise	VERB
ejpam-1372	1149	16	value	value	NOUN
ejpam-1372	1149	17	of	of	ADP
ejpam-1372	1149	18	ti	ti	PROPN
ejpam-1372	1149	19	(	(	PUNCT
ejpam-1372	1149	20	0,3/7	0,3/7	PROPN
ejpam-1372	1149	21	,	,	PUNCT
ejpam-1372	1149	22	z3	z3	PROPN
ejpam-1372	1149	23	)	)	PUNCT
ejpam-1372	1149	24	remains	remain	VERB
ejpam-1372	1149	25	invariant	invariant	ADJ
ejpam-1372	1149	26	despite	despite	SCONJ
ejpam-1372	1149	27	the	the	DET
ejpam-1372	1149	28	variation	variation	NOUN
ejpam-1372	1149	29	in	in	ADP
ejpam-1372	1149	30	the	the	DET
ejpam-1372	1149	31	truncation	truncation	NOUN
ejpam-1372	1149	32	parameter	parameter	NOUN
ejpam-1372	1149	33	.	.	PUNCT
ejpam-1372	1150	1	of	of	ADP
ejpam-1372	1150	2	course	course	NOUN
ejpam-1372	1150	3	,	,	PUNCT
ejpam-1372	1150	4	this	this	PRON
ejpam-1372	1150	5	is	be	AUX
ejpam-1372	1150	6	provided	provide	VERB
ejpam-1372	1150	7	that	that	SCONJ
ejpam-1372	1150	8	n	n	PRON
ejpam-1372	1150	9	is	be	AUX
ejpam-1372	1150	10	not	not	PART
ejpam-1372	1150	11	sufficiently	sufficiently	ADV
ejpam-1372	1150	12	large	large	ADJ
ejpam-1372	1150	13	to	to	PART
ejpam-1372	1150	14	cause	cause	VERB
ejpam-1372	1150	15	convergence	convergence	NOUN
ejpam-1372	1150	16	problems	problem	NOUN
ejpam-1372	1150	17	when	when	SCONJ
ejpam-1372	1150	18	the	the	DET
ejpam-1372	1150	19	nintegrate	nintegrate	ADJ
ejpam-1372	1150	20	routine	routine	NOUN
ejpam-1372	1150	21	is	be	AUX
ejpam-1372	1150	22	called	call	VERB
ejpam-1372	1150	23	.	.	PUNCT
ejpam-1372	1151	1	as	as	SCONJ
ejpam-1372	1151	2	can	can	AUX
ejpam-1372	1151	3	be	be	AUX
ejpam-1372	1151	4	seen	see	VERB
ejpam-1372	1151	5	from	from	ADP
ejpam-1372	1151	6	the	the	DET
ejpam-1372	1151	7	table	table	NOUN
ejpam-1372	1151	8	,	,	PUNCT
ejpam-1372	1151	9	the	the	DET
ejpam-1372	1151	10	truncated	truncated	ADJ
ejpam-1372	1151	11	series	series	NOUN
ejpam-1372	1151	12	diverges	diverge	VERB
ejpam-1372	1151	13	rapidly	rapidly	ADV
ejpam-1372	1151	14	as	as	ADV
ejpam-1372	1151	15	soon	soon	ADV
ejpam-1372	1151	16	as	as	SCONJ
ejpam-1372	1151	17	n	n	PRON
ejpam-1372	1151	18	becomes	become	VERB
ejpam-1372	1151	19	greater	great	ADJ
ejpam-1372	1151	20	than	than	ADP
ejpam-1372	1151	21	3	3	NUM
ejpam-1372	1151	22	.	.	PUNCT
ejpam-1372	1152	1	as	as	SCONJ
ejpam-1372	1152	2	expected	expect	VERB
ejpam-1372	1152	3	,	,	PUNCT
ejpam-1372	1152	4	the	the	DET
ejpam-1372	1152	5	divergence	divergence	NOUN
ejpam-1372	1152	6	is	be	AUX
ejpam-1372	1152	7	much	much	ADV
ejpam-1372	1152	8	greater	great	ADJ
ejpam-1372	1152	9	and	and	CCONJ
ejpam-1372	1152	10	more	more	ADV
ejpam-1372	1152	11	rapid	rapid	ADJ
ejpam-1372	1152	12	than	than	ADP
ejpam-1372	1152	13	the	the	DET
ejpam-1372	1152	14	truncated	truncated	ADJ
ejpam-1372	1152	15	series	series	NOUN
ejpam-1372	1152	16	for	for	ADP
ejpam-1372	1152	17	|z|=	|z|=	NOUN
ejpam-1372	1152	18	4/5	4/5	ADV
ejpam-1372	1152	19	again	again	ADV
ejpam-1372	1152	20	confirming	confirm	VERB
ejpam-1372	1152	21	that	that	SCONJ
ejpam-1372	1152	22	the	the	DET
ejpam-1372	1152	23	truncated	truncated	ADJ
ejpam-1372	1152	24	series	series	NOUN
ejpam-1372	1152	25	will	will	AUX
ejpam-1372	1152	26	only	only	ADV
ejpam-1372	1152	27	be	be	AUX
ejpam-1372	1152	28	accurate	accurate	ADJ
ejpam-1372	1152	29	for	for	ADP
ejpam-1372	1152	30	very	very	ADV
ejpam-1372	1152	31	small	small	ADJ
ejpam-1372	1152	32	values	value	NOUN
ejpam-1372	1152	33	of	of	ADP
ejpam-1372	1152	34	|z|	|z|	NOUN
ejpam-1372	1152	35	,	,	PUNCT
ejpam-1372	1152	36	where	where	SCONJ
ejpam-1372	1152	37	an	an	DET
ejpam-1372	1152	38	optimal	optimal	ADJ
ejpam-1372	1152	39	point	point	NOUN
ejpam-1372	1152	40	of	of	ADP
ejpam-1372	1152	41	truncation	truncation	NOUN
ejpam-1372	1152	42	exists	exist	VERB
ejpam-1372	1152	43	.	.	PUNCT
ejpam-1372	1153	1	furthermore	furthermore	ADV
ejpam-1372	1153	2	,	,	PUNCT
ejpam-1372	1153	3	we	we	PRON
ejpam-1372	1153	4	find	find	VERB
ejpam-1372	1153	5	that	that	SCONJ
ejpam-1372	1153	6	for	for	ADP
ejpam-1372	1153	7	the	the	DET
ejpam-1372	1153	8	same	same	ADJ
ejpam-1372	1153	9	value	value	NOUN
ejpam-1372	1153	10	of	of	ADP
ejpam-1372	1153	11	arg	arg	NOUN
ejpam-1372	1153	12	z	z	PROPN
ejpam-1372	1153	13	that	that	SCONJ
ejpam-1372	1153	14	the	the	DET
ejpam-1372	1153	15	regularised	regularise	VERB
ejpam-1372	1153	16	value	value	NOUN
ejpam-1372	1153	17	given	give	VERB
ejpam-1372	1153	18	in	in	ADP
ejpam-1372	1153	19	the	the	DET
ejpam-1372	1153	20	final	final	ADJ
ejpam-1372	1153	21	column	column	NOUN
ejpam-1372	1153	22	of	of	ADP
ejpam-1372	1153	23	table	table	NOUN
ejpam-1372	1153	24	5	5	NUM
ejpam-1372	1153	25	is	be	AUX
ejpam-1372	1153	26	identical	identical	ADJ
ejpam-1372	1153	27	to	to	ADP
ejpam-1372	1153	28	the	the	DET
ejpam-1372	1153	29	corresponding	corresponding	ADJ
ejpam-1372	1153	30	value	value	NOUN
ejpam-1372	1153	31	in	in	ADP
ejpam-1372	1153	32	table	table	NOUN
ejpam-1372	1153	33	3	3	NUM
ejpam-1372	1153	34	.	.	PUNCT
ejpam-1372	1154	1	hence	hence	ADV
ejpam-1372	1154	2	,	,	PUNCT
ejpam-1372	1154	3	both	both	DET
ejpam-1372	1154	4	mb	mb	ADV
ejpam-1372	1154	5	-	-	ADJ
ejpam-1372	1154	6	regularised	regularise	VERB
ejpam-1372	1154	7	and	and	CCONJ
ejpam-1372	1154	8	borelsummed	borelsumme	VERB
ejpam-1372	1154	9	forms	form	NOUN
ejpam-1372	1154	10	again	again	ADV
ejpam-1372	1154	11	yield	yield	VERB
ejpam-1372	1154	12	identical	identical	ADJ
ejpam-1372	1154	13	values	value	NOUN
ejpam-1372	1154	14	for	for	ADP
ejpam-1372	1154	15	the	the	DET
ejpam-1372	1154	16	regularised	regularise	VERB
ejpam-1372	1154	17	value	value	NOUN
ejpam-1372	1154	18	of	of	ADP
ejpam-1372	1154	19	ti	ti	PROPN
ejpam-1372	1154	20	(	(	PUNCT
ejpam-1372	1154	21	0,3/7	0,3/7	PROPN
ejpam-1372	1154	22	,	,	PUNCT
ejpam-1372	1154	23	z3	z3	PROPN
ejpam-1372	1154	24	)	)	PUNCT
ejpam-1372	1154	25	.	.	PUNCT
ejpam-1372	1155	1	now	now	ADV
ejpam-1372	1155	2	let	let	VERB
ejpam-1372	1155	3	us	we	PRON
ejpam-1372	1155	4	examine	examine	VERB
ejpam-1372	1155	5	the	the	DET
ejpam-1372	1155	6	evaluation	evaluation	NOUN
ejpam-1372	1155	7	of	of	ADP
ejpam-1372	1155	8	the	the	DET
ejpam-1372	1155	9	regularised	regularise	VERB
ejpam-1372	1155	10	values	value	NOUN
ejpam-1372	1155	11	of	of	ADP
ejpam-1372	1155	12	ti	ti	PROPN
ejpam-1372	1155	13	(	(	PUNCT
ejpam-1372	1155	14	0,3/7	0,3/7	PROPN
ejpam-1372	1155	15	,	,	PUNCT
ejpam-1372	1155	16	z3	z3	PROPN
ejpam-1372	1155	17	)	)	PUNCT
ejpam-1372	1155	18	via	via	ADP
ejpam-1372	1155	19	the	the	DET
ejpam-1372	1155	20	borelsummed	borelsumme	VERB
ejpam-1372	1155	21	forms	form	NOUN
ejpam-1372	1155	22	given	give	VERB
ejpam-1372	1155	23	in	in	ADP
ejpam-1372	1155	24	equivalence	equivalence	NOUN
ejpam-1372	1155	25	(	(	PUNCT
ejpam-1372	1155	26	116	116	NUM
ejpam-1372	1155	27	)	)	PUNCT
ejpam-1372	1155	28	.	.	PUNCT
ejpam-1372	1156	1	although	although	SCONJ
ejpam-1372	1156	2	the	the	DET
ejpam-1372	1156	3	stokes	stokes	PROPN
ejpam-1372	1156	4	discontinuity	discontinuity	NOUN
ejpam-1372	1156	5	term	term	NOUN
ejpam-1372	1156	6	or	or	CCONJ
ejpam-1372	1156	7	the	the	DET
ejpam-1372	1156	8	second	second	ADJ
ejpam-1372	1156	9	term	term	NOUN
ejpam-1372	1156	10	on	on	ADP
ejpam-1372	1156	11	the	the	DET
ejpam-1372	1156	12	rhs	rhs	PROPN
ejpam-1372	1156	13	of	of	ADP
ejpam-1372	1156	14	equivalence	equivalence	NOUN
ejpam-1372	1156	15	(	(	PUNCT
ejpam-1372	1156	16	116	116	NUM
ejpam-1372	1156	17	)	)	PUNCT
ejpam-1372	1156	18	is	be	AUX
ejpam-1372	1156	19	identical	identical	ADJ
ejpam-1372	1156	20	to	to	ADP
ejpam-1372	1156	21	the	the	DET
ejpam-1372	1156	22	extra	extra	ADJ
ejpam-1372	1156	23	term	term	NOUN
ejpam-1372	1156	24	on	on	ADP
ejpam-1372	1156	25	the	the	DET
ejpam-1372	1156	26	rhs	rhs	PROPN
ejpam-1372	1156	27	of	of	ADP
ejpam-1372	1156	28	the	the	DET
ejpam-1372	1156	29	mb	mb	ADJ
ejpam-1372	1156	30	-	-	ADJ
ejpam-1372	1156	31	regularised	regularise	VERB
ejpam-1372	1156	32	value	value	NOUN
ejpam-1372	1156	33	given	give	VERB
ejpam-1372	1156	34	by	by	ADP
ejpam-1372	1156	35	equivalence	equivalence	NOUN
ejpam-1372	1156	36	(	(	PUNCT
ejpam-1372	1156	37	118	118	NUM
ejpam-1372	1156	38	)	)	PUNCT
ejpam-1372	1156	39	,	,	PUNCT
ejpam-1372	1156	40	it	it	PRON
ejpam-1372	1156	41	appears	appear	VERB
ejpam-1372	1156	42	for	for	ADP
ejpam-1372	1156	43	different	different	ADJ
ejpam-1372	1156	44	values	value	NOUN
ejpam-1372	1156	45	of	of	ADP
ejpam-1372	1156	46	arg	arg	NOUN
ejpam-1372	1156	47	z	z	NOUN
ejpam-1372	1156	48	in	in	ADP
ejpam-1372	1156	49	the	the	DET
ejpam-1372	1156	50	principal	principal	ADJ
ejpam-1372	1156	51	branch	branch	NOUN
ejpam-1372	1156	52	of	of	ADP
ejpam-1372	1156	53	the	the	DET
ejpam-1372	1156	54	complex	complex	ADJ
ejpam-1372	1156	55	plane	plane	NOUN
ejpam-1372	1156	56	for	for	ADP
ejpam-1372	1156	57	z.	z.	PROPN
ejpam-1372	1156	58	we	we	PRON
ejpam-1372	1156	59	have	have	AUX
ejpam-1372	1156	60	already	already	ADV
ejpam-1372	1156	61	noticed	notice	VERB
ejpam-1372	1156	62	that	that	SCONJ
ejpam-1372	1156	63	the	the	DET
ejpam-1372	1156	64	mb	mb	ADJ
ejpam-1372	1156	65	-	-	PUNCT
ejpam-1372	1156	66	regularised	regularise	VERB
ejpam-1372	1156	67	value	value	NOUN
ejpam-1372	1156	68	for	for	ADP
ejpam-1372	1156	69	π/6	π/6	NOUN
ejpam-1372	1156	70	<	<	X
ejpam-1372	1156	71	|arg	|arg	NOUN
ejpam-1372	1156	72	z|<π/2	z|<π/2	PROPN
ejpam-1372	1156	73	can	can	AUX
ejpam-1372	1156	74	be	be	AUX
ejpam-1372	1156	75	written	write	VERB
ejpam-1372	1156	76	in	in	ADP
ejpam-1372	1156	77	terms	term	NOUN
ejpam-1372	1156	78	of	of	ADP
ejpam-1372	1156	79	an	an	DET
ejpam-1372	1156	80	mb	mb	NOUN
ejpam-1372	1156	81	integral	integral	ADJ
ejpam-1372	1156	82	without	without	ADP
ejpam-1372	1156	83	the	the	DET
ejpam-1372	1156	84	extra	extra	ADJ
ejpam-1372	1156	85	term	term	NOUN
ejpam-1372	1156	86	,	,	PUNCT
ejpam-1372	1156	87	i.e.	i.e.	X
ejpam-1372	1156	88	l	l	X
ejpam-1372	1156	89	=	=	SYM
ejpam-1372	1156	90	0	0	NUM
ejpam-1372	1157	1	in	in	ADP
ejpam-1372	1157	2	equivalence	equivalence	NOUN
ejpam-1372	1157	3	(	(	PUNCT
ejpam-1372	1157	4	118	118	NUM
ejpam-1372	1157	5	)	)	PUNCT
ejpam-1372	1157	6	,	,	PUNCT
ejpam-1372	1157	7	or	or	CCONJ
ejpam-1372	1157	8	it	it	PRON
ejpam-1372	1157	9	can	can	AUX
ejpam-1372	1157	10	be	be	AUX
ejpam-1372	1157	11	expressed	express	VERB
ejpam-1372	1157	12	in	in	ADP
ejpam-1372	1157	13	terms	term	NOUN
ejpam-1372	1157	14	of	of	ADP
ejpam-1372	1157	15	another	another	PRON
ejpam-1372	1157	16	mb	mb	ADP
ejpam-1372	1157	17	integral	integral	ADJ
ejpam-1372	1157	18	with	with	ADP
ejpam-1372	1157	19	v.	v.	ADP
ejpam-1372	1157	20	kowalenko	kowalenko	PROPN
ejpam-1372	1157	21	/	/	SYM
ejpam-1372	1157	22	eur	eur	PROPN
ejpam-1372	1157	23	.	.	PUNCT
ejpam-1372	1158	1	j.	j.	PROPN
ejpam-1372	1158	2	pure	pure	PROPN
ejpam-1372	1158	3	appl	appl	PROPN
ejpam-1372	1158	4	.	.	PROPN
ejpam-1372	1158	5	math	math	PROPN
ejpam-1372	1158	6	,	,	PUNCT
ejpam-1372	1158	7	4	4	NUM
ejpam-1372	1158	8	(	(	PUNCT
ejpam-1372	1158	9	2011	2011	NUM
ejpam-1372	1158	10	)	)	PUNCT
ejpam-1372	1158	11	,	,	PUNCT
ejpam-1372	1158	12	370	370	NUM
ejpam-1372	1158	13	-	-	SYM
ejpam-1372	1158	14	423	423	NUM
ejpam-1372	1158	15	412	412	NUM
ejpam-1372	1158	16	the	the	DET
ejpam-1372	1158	17	l	l	NOUN
ejpam-1372	1158	18	=	=	SYM
ejpam-1372	1158	19	1	1	NUM
ejpam-1372	1158	20	value	value	NOUN
ejpam-1372	1158	21	of	of	ADP
ejpam-1372	1158	22	the	the	DET
ejpam-1372	1158	23	extra	extra	ADJ
ejpam-1372	1158	24	term	term	NOUN
ejpam-1372	1158	25	on	on	ADP
ejpam-1372	1158	26	the	the	DET
ejpam-1372	1158	27	rhs	rhs	PROPN
ejpam-1372	1158	28	of	of	ADP
ejpam-1372	1158	29	equivalence	equivalence	NOUN
ejpam-1372	1158	30	(	(	PUNCT
ejpam-1372	1158	31	118	118	NUM
ejpam-1372	1158	32	)	)	PUNCT
ejpam-1372	1158	33	.	.	PUNCT
ejpam-1372	1159	1	however	however	ADV
ejpam-1372	1159	2	,	,	PUNCT
ejpam-1372	1159	3	the	the	DET
ejpam-1372	1159	4	extra	extra	ADJ
ejpam-1372	1159	5	term	term	NOUN
ejpam-1372	1159	6	or	or	CCONJ
ejpam-1372	1159	7	stokes	stoke	VERB
ejpam-1372	1159	8	discontinuity	discontinuity	NOUN
ejpam-1372	1159	9	term	term	NOUN
ejpam-1372	1159	10	is	be	AUX
ejpam-1372	1159	11	zero	zero	NUM
ejpam-1372	1159	12	for	for	ADP
ejpam-1372	1159	13	borel	borel	NOUN
ejpam-1372	1159	14	-	-	PUNCT
ejpam-1372	1159	15	summed	sum	VERB
ejpam-1372	1159	16	regularised	regularise	VERB
ejpam-1372	1159	17	values	value	NOUN
ejpam-1372	1159	18	when	when	SCONJ
ejpam-1372	1159	19	|arg	|arg	NOUN
ejpam-1372	1159	20	z|<π/3	z|<π/3	PROPN
ejpam-1372	1159	21	,	,	PUNCT
ejpam-1372	1159	22	but	but	CCONJ
ejpam-1372	1159	23	yields	yield	VERB
ejpam-1372	1159	24	a	a	DET
ejpam-1372	1159	25	contribution	contribution	NOUN
ejpam-1372	1159	26	when	when	SCONJ
ejpam-1372	1159	27	π/3	π/3	X
ejpam-1372	1159	28	<	<	X
ejpam-1372	1159	29	|arg	|arg	NOUN
ejpam-1372	1159	30	z|	z|	PROPN
ejpam-1372	1159	31	<	<	X
ejpam-1372	1159	32	π	π	X
ejpam-1372	1159	33	.	.	PUNCT
ejpam-1372	1160	1	that	that	PRON
ejpam-1372	1160	2	is	be	AUX
ejpam-1372	1160	3	,	,	PUNCT
ejpam-1372	1160	4	l	l	NOUN
ejpam-1372	1160	5	=	=	SYM
ejpam-1372	1160	6	0	0	NUM
ejpam-1372	1160	7	in	in	ADP
ejpam-1372	1160	8	equivalence	equivalence	NOUN
ejpam-1372	1160	9	(	(	PUNCT
ejpam-1372	1160	10	116	116	NUM
ejpam-1372	1160	11	)	)	PUNCT
ejpam-1372	1160	12	for	for	ADP
ejpam-1372	1160	13	|arg	|arg	VERB
ejpam-1372	1160	14	z|	z|	PRON
ejpam-1372	1160	15	<	<	X
ejpam-1372	1160	16	π/3	π/3	PROPN
ejpam-1372	1160	17	,	,	PUNCT
ejpam-1372	1160	18	while	while	SCONJ
ejpam-1372	1160	19	for	for	ADP
ejpam-1372	1160	20	π/3	π/3	X
ejpam-1372	1160	21	<	<	X
ejpam-1372	1160	22	arg	arg	X
ejpam-1372	1160	23	z	z	X
ejpam-1372	1160	24	<	<	X
ejpam-1372	1160	25	π	π	X
ejpam-1372	1160	26	,	,	PUNCT
ejpam-1372	1160	27	we	we	PRON
ejpam-1372	1160	28	put	put	VERB
ejpam-1372	1160	29	l	l	NOUN
ejpam-1372	1160	30	=	=	NOUN
ejpam-1372	1160	31	1	1	NUM
ejpam-1372	1160	32	in	in	ADP
ejpam-1372	1160	33	the	the	DET
ejpam-1372	1160	34	upper	upper	ADV
ejpam-1372	1160	35	-	-	PUNCT
ejpam-1372	1160	36	signed	sign	VERB
ejpam-1372	1160	37	version	version	NOUN
ejpam-1372	1160	38	and	and	CCONJ
ejpam-1372	1160	39	for	for	ADP
ejpam-1372	1160	40	−π/	−π/	X
ejpam-1372	1160	41	<	<	X
ejpam-1372	1160	42	arg	arg	NOUN
ejpam-1372	1160	43	z	z	X
ejpam-1372	1160	44	<	<	X
ejpam-1372	1160	45	−π/3	−π/3	PROPN
ejpam-1372	1160	46	,	,	PUNCT
ejpam-1372	1160	47	we	we	PRON
ejpam-1372	1160	48	put	put	VERB
ejpam-1372	1160	49	l	l	NOUN
ejpam-1372	1160	50	=	=	NOUN
ejpam-1372	1160	51	1	1	NUM
ejpam-1372	1160	52	in	in	ADP
ejpam-1372	1160	53	the	the	DET
ejpam-1372	1160	54	lower	lower	ADV
ejpam-1372	1160	55	-	-	PUNCT
ejpam-1372	1160	56	signed	sign	VERB
ejpam-1372	1160	57	version	version	NOUN
ejpam-1372	1160	58	.	.	PUNCT
ejpam-1372	1161	1	notwithstanding	notwithstanding	ADV
ejpam-1372	1161	2	,	,	PUNCT
ejpam-1372	1161	3	we	we	PRON
ejpam-1372	1161	4	find	find	VERB
ejpam-1372	1161	5	that	that	SCONJ
ejpam-1372	1161	6	whichever	whichever	DET
ejpam-1372	1161	7	form	form	NOUN
ejpam-1372	1161	8	is	be	AUX
ejpam-1372	1161	9	used	use	VERB
ejpam-1372	1161	10	to	to	PART
ejpam-1372	1161	11	evaluate	evaluate	VERB
ejpam-1372	1161	12	the	the	DET
ejpam-1372	1161	13	regularised	regularise	VERB
ejpam-1372	1161	14	value	value	NOUN
ejpam-1372	1161	15	,	,	PUNCT
ejpam-1372	1161	16	we	we	PRON
ejpam-1372	1161	17	get	get	VERB
ejpam-1372	1161	18	the	the	DET
ejpam-1372	1161	19	same	same	ADJ
ejpam-1372	1161	20	result	result	NOUN
ejpam-1372	1161	21	despite	despite	SCONJ
ejpam-1372	1161	22	varying	vary	VERB
ejpam-1372	1161	23	the	the	DET
ejpam-1372	1161	24	truncation	truncation	NOUN
ejpam-1372	1161	25	parameter	parameter	NOUN
ejpam-1372	1161	26	.	.	PUNCT
ejpam-1372	1162	1	all	all	PRON
ejpam-1372	1162	2	that	that	PRON
ejpam-1372	1162	3	remains	remain	VERB
ejpam-1372	1162	4	is	be	AUX
ejpam-1372	1162	5	to	to	PART
ejpam-1372	1162	6	describe	describe	VERB
ejpam-1372	1162	7	the	the	DET
ejpam-1372	1162	8	evaluation	evaluation	NOUN
ejpam-1372	1162	9	of	of	ADP
ejpam-1372	1162	10	the	the	DET
ejpam-1372	1162	11	borel	borel	NOUN
ejpam-1372	1162	12	-	-	PUNCT
ejpam-1372	1162	13	summed	sum	VERB
ejpam-1372	1162	14	forms	form	NOUN
ejpam-1372	1162	15	for	for	ADP
ejpam-1372	1162	16	the	the	DET
ejpam-1372	1162	17	regularised	regularise	VERB
ejpam-1372	1162	18	value	value	NOUN
ejpam-1372	1162	19	of	of	ADP
ejpam-1372	1162	20	ti	ti	PROPN
ejpam-1372	1162	21	(	(	PUNCT
ejpam-1372	1162	22	0,3/7	0,3/7	PROPN
ejpam-1372	1162	23	,	,	PUNCT
ejpam-1372	1162	24	z3	z3	PROPN
ejpam-1372	1162	25	)	)	PUNCT
ejpam-1372	1162	26	along	along	ADP
ejpam-1372	1162	27	the	the	DET
ejpam-1372	1162	28	stokes	stoke	NOUN
ejpam-1372	1162	29	lines	line	NOUN
ejpam-1372	1162	30	of	of	ADP
ejpam-1372	1162	31	arg	arg	NOUN
ejpam-1372	1162	32	z	z	NOUN
ejpam-1372	1162	33	=	=	SYM
ejpam-1372	1162	34	±π/3	±π/3	PROPN
ejpam-1372	1162	35	.	.	PUNCT
ejpam-1372	1162	36	to	to	PART
ejpam-1372	1162	37	accomplish	accomplish	VERB
ejpam-1372	1162	38	this	this	PRON
ejpam-1372	1162	39	,	,	PUNCT
ejpam-1372	1162	40	another	another	DET
ejpam-1372	1162	41	mathematica	mathematica	PROPN
ejpam-1372	1162	42	module	module	NOUN
ejpam-1372	1162	43	is	be	AUX
ejpam-1372	1162	44	required	require	VERB
ejpam-1372	1162	45	in	in	ADP
ejpam-1372	1162	46	order	order	NOUN
ejpam-1372	1162	47	to	to	PART
ejpam-1372	1162	48	evaluate	evaluate	VERB
ejpam-1372	1162	49	all	all	DET
ejpam-1372	1162	50	the	the	DET
ejpam-1372	1162	51	terms	term	NOUN
ejpam-1372	1162	52	on	on	ADP
ejpam-1372	1162	53	the	the	DET
ejpam-1372	1162	54	rhs	rhs	PROPN
ejpam-1372	1162	55	of	of	ADP
ejpam-1372	1162	56	equivalence	equivalence	NOUN
ejpam-1372	1162	57	(	(	PUNCT
ejpam-1372	1162	58	117	117	NUM
ejpam-1372	1162	59	)	)	PUNCT
ejpam-1372	1162	60	,	,	PUNCT
ejpam-1372	1162	61	particularly	particularly	ADV
ejpam-1372	1162	62	the	the	DET
ejpam-1372	1162	63	cauchy	cauchy	ADJ
ejpam-1372	1162	64	principal	principal	ADJ
ejpam-1372	1162	65	value	value	NOUN
ejpam-1372	1162	66	.	.	PUNCT
ejpam-1372	1163	1	in	in	ADP
ejpam-1372	1163	2	mathematica	mathematica	PROPN
ejpam-1372	1163	3	7.0	7.0	NUM
ejpam-1372	1163	4	this	this	PRON
ejpam-1372	1163	5	is	be	AUX
ejpam-1372	1163	6	achieved	achieve	VERB
ejpam-1372	1163	7	by	by	ADP
ejpam-1372	1163	8	specifying	specify	VERB
ejpam-1372	1163	9	method→‘principalvalue	method→‘principalvalue	NOUN
ejpam-1372	1163	10	’	'	PUNCT
ejpam-1372	1163	11	in	in	ADP
ejpam-1372	1163	12	the	the	DET
ejpam-1372	1163	13	call	call	NOUN
ejpam-1372	1163	14	to	to	ADP
ejpam-1372	1163	15	the	the	DET
ejpam-1372	1163	16	nintegrate	nintegrate	ADJ
ejpam-1372	1163	17	routine	routine	NOUN
ejpam-1372	1163	18	.	.	PUNCT
ejpam-1372	1164	1	unfortunately	unfortunately	ADV
ejpam-1372	1164	2	,	,	PUNCT
ejpam-1372	1164	3	this	this	PRON
ejpam-1372	1164	4	can	can	AUX
ejpam-1372	1164	5	fail	fail	VERB
ejpam-1372	1164	6	,	,	PUNCT
ejpam-1372	1164	7	as	as	SCONJ
ejpam-1372	1164	8	described	describe	VERB
ejpam-1372	1164	9	in	in	ADP
ejpam-1372	1164	10	sec	sec	PROPN
ejpam-1372	1164	11	.	.	PROPN
ejpam-1372	1165	1	11.3	11.3	NUM
ejpam-1372	1165	2	of	of	ADP
ejpam-1372	1165	3	ref	ref	NOUN
ejpam-1372	1165	4	.	.	PUNCT
ejpam-1372	1166	1	[	[	X
ejpam-1372	1166	2	17	17	NUM
ejpam-1372	1166	3	]	]	PUNCT
ejpam-1372	1166	4	.	.	PUNCT
ejpam-1372	1167	1	a	a	DET
ejpam-1372	1167	2	better	well	ADJ
ejpam-1372	1167	3	approach	approach	NOUN
ejpam-1372	1167	4	is	be	AUX
ejpam-1372	1167	5	either	either	CCONJ
ejpam-1372	1167	6	to	to	PART
ejpam-1372	1167	7	evaluate	evaluate	VERB
ejpam-1372	1167	8	the	the	DET
ejpam-1372	1167	9	cauchy	cauchy	ADJ
ejpam-1372	1167	10	principal	principal	NOUN
ejpam-1372	1167	11	value	value	NOUN
ejpam-1372	1167	12	by	by	ADP
ejpam-1372	1167	13	using	use	VERB
ejpam-1372	1167	14	the	the	DET
ejpam-1372	1167	15	special	special	ADJ
ejpam-1372	1167	16	add	add	VERB
ejpam-1372	1167	17	-	-	PUNCT
ejpam-1372	1167	18	on	on	ADP
ejpam-1372	1167	19	package	package	NOUN
ejpam-1372	1167	20	in	in	ADP
ejpam-1372	1167	21	mathematica	mathematica	PROPN
ejpam-1372	1167	22	4.1	4.1	NUM
ejpam-1372	1167	23	or	or	CCONJ
ejpam-1372	1167	24	to	to	PART
ejpam-1372	1167	25	specify	specify	VERB
ejpam-1372	1167	26	the	the	DET
ejpam-1372	1167	27	singularity	singularity	NOUN
ejpam-1372	1167	28	in	in	ADP
ejpam-1372	1167	29	the	the	DET
ejpam-1372	1167	30	range	range	NOUN
ejpam-1372	1167	31	of	of	ADP
ejpam-1372	1167	32	integration	integration	NOUN
ejpam-1372	1167	33	.	.	PUNCT
ejpam-1372	1168	1	the	the	DET
ejpam-1372	1168	2	second	second	ADJ
ejpam-1372	1168	3	option	option	NOUN
ejpam-1372	1168	4	has	have	AUX
ejpam-1372	1168	5	been	be	AUX
ejpam-1372	1168	6	adopted	adopt	VERB
ejpam-1372	1168	7	here	here	ADV
ejpam-1372	1168	8	,	,	PUNCT
ejpam-1372	1168	9	which	which	PRON
ejpam-1372	1168	10	means	mean	VERB
ejpam-1372	1168	11	that	that	SCONJ
ejpam-1372	1168	12	separate	separate	ADJ
ejpam-1372	1168	13	modules	module	NOUN
ejpam-1372	1168	14	are	be	AUX
ejpam-1372	1168	15	required	require	VERB
ejpam-1372	1168	16	for	for	ADP
ejpam-1372	1168	17	|z|=4/5	|z|=4/5	ADV
ejpam-1372	1168	18	and	and	CCONJ
ejpam-1372	1168	19	|z|=2	|z|=2	ADJ
ejpam-1372	1168	20	.	.	PUNCT
ejpam-1372	1169	1	for	for	ADP
ejpam-1372	1169	2	the	the	DET
ejpam-1372	1169	3	sake	sake	NOUN
ejpam-1372	1169	4	of	of	ADP
ejpam-1372	1169	5	brevity	brevity	NOUN
ejpam-1372	1169	6	we	we	PRON
ejpam-1372	1169	7	shall	shall	AUX
ejpam-1372	1169	8	only	only	ADV
ejpam-1372	1169	9	consider	consider	VERB
ejpam-1372	1169	10	the	the	DET
ejpam-1372	1169	11	latter	latter	ADJ
ejpam-1372	1169	12	case	case	NOUN
ejpam-1372	1169	13	.	.	PUNCT
ejpam-1372	1170	1	because	because	SCONJ
ejpam-1372	1170	2	the	the	DET
ejpam-1372	1170	3	singularity	singularity	NOUN
ejpam-1372	1170	4	in	in	ADP
ejpam-1372	1170	5	the	the	DET
ejpam-1372	1170	6	cauchy	cauchy	ADJ
ejpam-1372	1170	7	integral	integral	PROPN
ejpam-1372	1170	8	occurs	occur	VERB
ejpam-1372	1170	9	at	at	ADP
ejpam-1372	1170	10	t=1/8	t=1/8	NOUN
ejpam-1372	1170	11	in	in	ADP
ejpam-1372	1170	12	this	this	DET
ejpam-1372	1170	13	case	case	NOUN
ejpam-1372	1170	14	,	,	PUNCT
ejpam-1372	1170	15	1/8	1/8	NUM
ejpam-1372	1170	16	has	have	VERB
ejpam-1372	1170	17	to	to	PART
ejpam-1372	1170	18	be	be	AUX
ejpam-1372	1170	19	introduced	introduce	VERB
ejpam-1372	1170	20	into	into	ADP
ejpam-1372	1170	21	the	the	DET
ejpam-1372	1170	22	subdivision	subdivision	NOUN
ejpam-1372	1170	23	of	of	ADP
ejpam-1372	1170	24	the	the	DET
ejpam-1372	1170	25	range	range	NOUN
ejpam-1372	1170	26	of	of	ADP
ejpam-1372	1170	27	integration	integration	NOUN
ejpam-1372	1170	28	in	in	ADP
ejpam-1372	1170	29	the	the	DET
ejpam-1372	1170	30	nintegrate	nintegrate	ADJ
ejpam-1372	1170	31	routine	routine	NOUN
ejpam-1372	1170	32	.	.	PUNCT
ejpam-1372	1171	1	the	the	DET
ejpam-1372	1171	2	other	other	ADJ
ejpam-1372	1171	3	options	option	NOUN
ejpam-1372	1171	4	of	of	ADP
ejpam-1372	1171	5	workingprecision	workingprecision	NOUN
ejpam-1372	1171	6	,	,	PUNCT
ejpam-1372	1171	7	accuracygoal	accuracygoal	NOUN
ejpam-1372	1171	8	,	,	PUNCT
ejpam-1372	1171	9	precisiongoal	precisiongoal	NOUN
ejpam-1372	1171	10	,	,	PUNCT
ejpam-1372	1171	11	minrecursion	minrecursion	NOUN
ejpam-1372	1171	12	and	and	CCONJ
ejpam-1372	1171	13	maxrecursion	maxrecursion	NOUN
ejpam-1372	1171	14	in	in	ADP
ejpam-1372	1171	15	the	the	DET
ejpam-1372	1171	16	nintegrate	nintegrate	ADJ
ejpam-1372	1171	17	routine	routine	NOUN
ejpam-1372	1171	18	were	be	AUX
ejpam-1372	1171	19	set	set	VERB
ejpam-1372	1171	20	to	to	ADP
ejpam-1372	1171	21	the	the	DET
ejpam-1372	1171	22	same	same	ADJ
ejpam-1372	1171	23	values	value	NOUN
ejpam-1372	1171	24	used	use	VERB
ejpam-1372	1171	25	to	to	PART
ejpam-1372	1171	26	obtain	obtain	VERB
ejpam-1372	1171	27	the	the	DET
ejpam-1372	1171	28	results	result	NOUN
ejpam-1372	1171	29	displayed	display	VERB
ejpam-1372	1171	30	in	in	ADP
ejpam-1372	1171	31	tables	table	NOUN
ejpam-1372	1171	32	2	2	NUM
ejpam-1372	1171	33	to	to	PART
ejpam-1372	1171	34	5	5	NUM
ejpam-1372	1171	35	.	.	PUNCT
ejpam-1372	1171	36	table	table	NOUN
ejpam-1372	1171	37	6	6	NUM
ejpam-1372	1171	38	,	,	PUNCT
ejpam-1372	1171	39	also	also	ADV
ejpam-1372	1171	40	in	in	ADP
ejpam-1372	1171	41	the	the	DET
ejpam-1372	1171	42	appendix	appendix	NOUN
ejpam-1372	1171	43	,	,	PUNCT
ejpam-1372	1171	44	presents	present	VERB
ejpam-1372	1171	45	a	a	DET
ejpam-1372	1171	46	sample	sample	NOUN
ejpam-1372	1171	47	of	of	ADP
ejpam-1372	1171	48	the	the	DET
ejpam-1372	1171	49	results	result	NOUN
ejpam-1372	1171	50	obtained	obtain	VERB
ejpam-1372	1171	51	by	by	ADP
ejpam-1372	1171	52	setting	set	VERB
ejpam-1372	1171	53	arg	arg	NOUN
ejpam-1372	1171	54	z=−π/3	z=−π/3	PROPN
ejpam-1372	1171	55	and	and	CCONJ
ejpam-1372	1171	56	then	then	ADV
ejpam-1372	1171	57	varying	vary	VERB
ejpam-1372	1171	58	the	the	DET
ejpam-1372	1171	59	truncation	truncation	NOUN
ejpam-1372	1171	60	parameter	parameter	NOUN
ejpam-1372	1171	61	n	n	PROPN
ejpam-1372	1171	62	.	.	PUNCT
ejpam-1372	1172	1	again	again	ADV
ejpam-1372	1172	2	,	,	PUNCT
ejpam-1372	1172	3	all	all	DET
ejpam-1372	1172	4	the	the	DET
ejpam-1372	1172	5	values	value	NOUN
ejpam-1372	1172	6	appearing	appear	VERB
ejpam-1372	1172	7	in	in	ADP
ejpam-1372	1172	8	the	the	DET
ejpam-1372	1172	9	table	table	NOUN
ejpam-1372	1172	10	were	be	AUX
ejpam-1372	1172	11	computed	compute	VERB
ejpam-1372	1172	12	in	in	ADP
ejpam-1372	1172	13	only	only	ADV
ejpam-1372	1172	14	a	a	DET
ejpam-1372	1172	15	few	few	ADJ
ejpam-1372	1172	16	cpu	cpu	NOUN
ejpam-1372	1172	17	seconds	second	NOUN
ejpam-1372	1172	18	.	.	PUNCT
ejpam-1372	1173	1	as	as	SCONJ
ejpam-1372	1173	2	we	we	PRON
ejpam-1372	1173	3	have	have	AUX
ejpam-1372	1173	4	seen	see	VERB
ejpam-1372	1173	5	in	in	ADP
ejpam-1372	1173	6	the	the	DET
ejpam-1372	1173	7	other	other	ADJ
ejpam-1372	1173	8	tables	table	NOUN
ejpam-1372	1173	9	with	with	ADP
ejpam-1372	1173	10	|z|=2	|z|=2	ADJ
ejpam-1372	1173	11	,	,	PUNCT
ejpam-1372	1173	12	the	the	DET
ejpam-1372	1173	13	truncated	truncated	ADJ
ejpam-1372	1173	14	series	series	NOUN
ejpam-1372	1173	15	begins	begin	VERB
ejpam-1372	1173	16	to	to	PART
ejpam-1372	1173	17	diverge	diverge	VERB
ejpam-1372	1173	18	rapidly	rapidly	ADV
ejpam-1372	1173	19	for	for	ADP
ejpam-1372	1173	20	fairly	fairly	ADV
ejpam-1372	1173	21	small	small	ADJ
ejpam-1372	1173	22	values	value	NOUN
ejpam-1372	1173	23	of	of	ADP
ejpam-1372	1173	24	the	the	DET
ejpam-1372	1173	25	truncation	truncation	NOUN
ejpam-1372	1173	26	parameter	parameter	NOUN
ejpam-1372	1173	27	,	,	PUNCT
ejpam-1372	1173	28	but	but	CCONJ
ejpam-1372	1173	29	is	be	AUX
ejpam-1372	1173	30	countered	counter	VERB
ejpam-1372	1173	31	by	by	ADP
ejpam-1372	1173	32	the	the	DET
ejpam-1372	1173	33	divergence	divergence	NOUN
ejpam-1372	1173	34	in	in	ADP
ejpam-1372	1173	35	the	the	DET
ejpam-1372	1173	36	value	value	NOUN
ejpam-1372	1173	37	of	of	ADP
ejpam-1372	1173	38	the	the	DET
ejpam-1372	1173	39	cauchy	cauchy	ADJ
ejpam-1372	1173	40	principal	principal	ADJ
ejpam-1372	1173	41	value	value	NOUN
ejpam-1372	1173	42	integral	integral	ADJ
ejpam-1372	1173	43	,	,	PUNCT
ejpam-1372	1173	44	whose	whose	DET
ejpam-1372	1173	45	values	value	NOUN
ejpam-1372	1173	46	appear	appear	VERB
ejpam-1372	1173	47	in	in	ADP
ejpam-1372	1173	48	the	the	DET
ejpam-1372	1173	49	column	column	NOUN
ejpam-1372	1173	50	denoted	denote	VERB
ejpam-1372	1173	51	by	by	ADP
ejpam-1372	1173	52	pv	pv	PROPN
ejpam-1372	1173	53	integral	integral	PROPN
ejpam-1372	1173	54	.	.	PUNCT
ejpam-1372	1174	1	as	as	SCONJ
ejpam-1372	1174	2	is	be	AUX
ejpam-1372	1174	3	typical	typical	ADJ
ejpam-1372	1174	4	for	for	ADP
ejpam-1372	1174	5	this	this	DET
ejpam-1372	1174	6	stokes	stoke	NOUN
ejpam-1372	1174	7	line	line	NOUN
ejpam-1372	1174	8	,	,	PUNCT
ejpam-1372	1174	9	the	the	DET
ejpam-1372	1174	10	stokes	stokes	PROPN
ejpam-1372	1174	11	discontinuity	discontinuity	NOUN
ejpam-1372	1174	12	term	term	NOUN
ejpam-1372	1174	13	is	be	AUX
ejpam-1372	1174	14	purely	purely	ADV
ejpam-1372	1174	15	imaginary	imaginary	ADJ
ejpam-1372	1174	16	.	.	PUNCT
ejpam-1372	1175	1	in	in	ADP
ejpam-1372	1175	2	ch	ch	PROPN
ejpam-1372	1175	3	.	.	PROPN
ejpam-1372	1175	4	1	1	NUM
ejpam-1372	1175	5	of	of	ADP
ejpam-1372	1175	6	ref	ref	NOUN
ejpam-1372	1175	7	.	.	PUNCT
ejpam-1372	1176	1	[	[	X
ejpam-1372	1176	2	8	8	NUM
ejpam-1372	1176	3	]	]	PUNCT
ejpam-1372	1176	4	,	,	PUNCT
ejpam-1372	1176	5	dingle	dingle	PROPN
ejpam-1372	1176	6	gives	give	VERB
ejpam-1372	1176	7	a	a	DET
ejpam-1372	1176	8	rule	rule	NOUN
ejpam-1372	1176	9	based	base	VERB
ejpam-1372	1176	10	on	on	ADP
ejpam-1372	1176	11	this	this	DET
ejpam-1372	1176	12	behaviour	behaviour	NOUN
ejpam-1372	1176	13	for	for	ADP
ejpam-1372	1176	14	continuing	continue	VERB
ejpam-1372	1176	15	asymptotic	asymptotic	ADJ
ejpam-1372	1176	16	expansions	expansion	NOUN
ejpam-1372	1176	17	across	across	ADP
ejpam-1372	1176	18	a	a	DET
ejpam-1372	1176	19	stokes	stoke	NOUN
ejpam-1372	1176	20	line	line	NOUN
ejpam-1372	1176	21	.	.	PUNCT
ejpam-1372	1177	1	in	in	ADP
ejpam-1372	1177	2	particular	particular	ADJ
ejpam-1372	1177	3	,	,	PUNCT
ejpam-1372	1177	4	he	he	PRON
ejpam-1372	1177	5	states	state	VERB
ejpam-1372	1177	6	that	that	SCONJ
ejpam-1372	1177	7	an	an	DET
ejpam-1372	1177	8	asymptotic	asymptotic	ADJ
ejpam-1372	1177	9	series	series	NOUN
ejpam-1372	1177	10	generates	generate	VERB
ejpam-1372	1177	11	a	a	DET
ejpam-1372	1177	12	discontinuity	discontinuity	NOUN
ejpam-1372	1177	13	that	that	PRON
ejpam-1372	1177	14	is	be	AUX
ejpam-1372	1177	15	π/2	π/2	NUM
ejpam-1372	1177	16	out	out	ADP
ejpam-1372	1177	17	of	of	ADP
ejpam-1372	1177	18	phase	phase	NOUN
ejpam-1372	1177	19	or	or	CCONJ
ejpam-1372	1177	20	imaginary	imaginary	ADJ
ejpam-1372	1177	21	with	with	ADP
ejpam-1372	1177	22	the	the	DET
ejpam-1372	1177	23	series	series	NOUN
ejpam-1372	1177	24	.	.	PUNCT
ejpam-1372	1178	1	although	although	SCONJ
ejpam-1372	1178	2	this	this	PRON
ejpam-1372	1178	3	occurs	occur	VERB
ejpam-1372	1178	4	in	in	ADP
ejpam-1372	1178	5	the	the	DET
ejpam-1372	1178	6	fourth	fourth	ADJ
ejpam-1372	1178	7	column	column	NOUN
ejpam-1372	1178	8	of	of	ADP
ejpam-1372	1178	9	table	table	NOUN
ejpam-1372	1178	10	6	6	NUM
ejpam-1372	1178	11	,	,	PUNCT
ejpam-1372	1178	12	it	it	PRON
ejpam-1372	1178	13	only	only	ADV
ejpam-1372	1178	14	occurs	occur	VERB
ejpam-1372	1178	15	because	because	SCONJ
ejpam-1372	1178	16	l	l	NOUN
ejpam-1372	1178	17	=	=	SYM
ejpam-1372	1178	18	0	0	NUM
ejpam-1372	1178	19	for	for	ADP
ejpam-1372	1178	20	the	the	DET
ejpam-1372	1178	21	stokes	stokes	PROPN
ejpam-1372	1178	22	discontinuity	discontinuity	NOUN
ejpam-1372	1178	23	.	.	PUNCT
ejpam-1372	1179	1	for	for	ADP
ejpam-1372	1179	2	other	other	ADJ
ejpam-1372	1179	3	values	value	NOUN
ejpam-1372	1179	4	of	of	ADP
ejpam-1372	1179	5	l	l	NOUN
ejpam-1372	1179	6	,	,	PUNCT
ejpam-1372	1179	7	this	this	PRON
ejpam-1372	1179	8	need	need	AUX
ejpam-1372	1179	9	not	not	PART
ejpam-1372	1179	10	necessarily	necessarily	ADV
ejpam-1372	1179	11	be	be	AUX
ejpam-1372	1179	12	the	the	DET
ejpam-1372	1179	13	case	case	NOUN
ejpam-1372	1179	14	.	.	PUNCT
ejpam-1372	1180	1	for	for	ADP
ejpam-1372	1180	2	all	all	DET
ejpam-1372	1180	3	values	value	NOUN
ejpam-1372	1180	4	of	of	ADP
ejpam-1372	1180	5	the	the	DET
ejpam-1372	1180	6	truncation	truncation	NOUN
ejpam-1372	1180	7	parameter	parameter	NOUN
ejpam-1372	1180	8	we	we	PRON
ejpam-1372	1180	9	obtain	obtain	VERB
ejpam-1372	1180	10	the	the	DET
ejpam-1372	1180	11	same	same	ADJ
ejpam-1372	1180	12	regularised	regularise	VERB
ejpam-1372	1180	13	value	value	NOUN
ejpam-1372	1180	14	,	,	PUNCT
ejpam-1372	1180	15	which	which	PRON
ejpam-1372	1180	16	can	can	AUX
ejpam-1372	1180	17	be	be	AUX
ejpam-1372	1180	18	checked	check	VERB
ejpam-1372	1180	19	with	with	ADP
ejpam-1372	1180	20	the	the	DET
ejpam-1372	1180	21	value	value	NOUN
ejpam-1372	1180	22	obtained	obtain	VERB
ejpam-1372	1180	23	from	from	ADP
ejpam-1372	1180	24	the	the	DET
ejpam-1372	1180	25	mb	mb	ADJ
ejpam-1372	1180	26	-	-	PUNCT
ejpam-1372	1180	27	regularised	regularise	VERB
ejpam-1372	1180	28	form	form	NOUN
ejpam-1372	1180	29	displayed	display	VERB
ejpam-1372	1180	30	in	in	ADP
ejpam-1372	1180	31	table	table	NOUN
ejpam-1372	1180	32	3	3	NUM
ejpam-1372	1180	33	.	.	PUNCT
ejpam-1372	1181	1	although	although	SCONJ
ejpam-1372	1181	2	the	the	DET
ejpam-1372	1181	3	correct	correct	ADJ
ejpam-1372	1181	4	value	value	NOUN
ejpam-1372	1181	5	was	be	AUX
ejpam-1372	1181	6	obtained	obtain	VERB
ejpam-1372	1181	7	for	for	ADP
ejpam-1372	1181	8	n	n	NOUN
ejpam-1372	1181	9	=	=	SYM
ejpam-1372	1181	10	30	30	NUM
ejpam-1372	1181	11	,	,	PUNCT
ejpam-1372	1181	12	mathematica	mathematica	PROPN
ejpam-1372	1181	13	did	do	AUX
ejpam-1372	1181	14	indicate	indicate	VERB
ejpam-1372	1181	15	problems	problem	NOUN
ejpam-1372	1181	16	with	with	ADP
ejpam-1372	1181	17	internal	internal	ADJ
ejpam-1372	1181	18	precision	precision	NOUN
ejpam-1372	1181	19	when	when	SCONJ
ejpam-1372	1181	20	calculating	calculate	VERB
ejpam-1372	1181	21	the	the	DET
ejpam-1372	1181	22	cauchy	cauchy	ADJ
ejpam-1372	1181	23	principal	principal	ADJ
ejpam-1372	1181	24	value	value	NOUN
ejpam-1372	1181	25	.	.	PUNCT
ejpam-1372	1182	1	this	this	PRON
ejpam-1372	1182	2	is	be	AUX
ejpam-1372	1182	3	presumably	presumably	ADV
ejpam-1372	1182	4	due	due	ADJ
ejpam-1372	1182	5	to	to	ADP
ejpam-1372	1182	6	the	the	DET
ejpam-1372	1182	7	fact	fact	NOUN
ejpam-1372	1182	8	that	that	SCONJ
ejpam-1372	1182	9	56	56	NUM
ejpam-1372	1182	10	decimal	decimal	ADJ
ejpam-1372	1182	11	places	place	NOUN
ejpam-1372	1182	12	had	have	AUX
ejpam-1372	1182	13	to	to	PART
ejpam-1372	1182	14	be	be	AUX
ejpam-1372	1182	15	cancelled	cancel	VERB
ejpam-1372	1182	16	before	before	ADP
ejpam-1372	1182	17	yielding	yield	VERB
ejpam-1372	1182	18	the	the	DET
ejpam-1372	1182	19	regularised	regularise	VERB
ejpam-1372	1182	20	value	value	NOUN
ejpam-1372	1182	21	.	.	PUNCT
ejpam-1372	1183	1	consequently	consequently	ADV
ejpam-1372	1183	2	,	,	PUNCT
ejpam-1372	1183	3	this	this	DET
ejpam-1372	1183	4	value	value	NOUN
ejpam-1372	1183	5	is	be	AUX
ejpam-1372	1183	6	asterisked	asterisk	VERB
ejpam-1372	1183	7	in	in	ADP
ejpam-1372	1183	8	the	the	DET
ejpam-1372	1183	9	table	table	NOUN
ejpam-1372	1183	10	.	.	PUNCT
ejpam-1372	1184	1	again	again	ADV
ejpam-1372	1184	2	,	,	PUNCT
ejpam-1372	1184	3	the	the	DET
ejpam-1372	1184	4	results	result	NOUN
ejpam-1372	1184	5	in	in	ADP
ejpam-1372	1184	6	this	this	DET
ejpam-1372	1184	7	table	table	NOUN
ejpam-1372	1184	8	vindicate	vindicate	NOUN
ejpam-1372	1184	9	euler	euler	PROPN
ejpam-1372	1184	10	’s	’s	PART
ejpam-1372	1184	11	view	view	NOUN
ejpam-1372	1184	12	that	that	SCONJ
ejpam-1372	1184	13	the	the	DET
ejpam-1372	1184	14	value	value	NOUN
ejpam-1372	1184	15	assigned	assign	VERB
ejpam-1372	1184	16	to	to	ADP
ejpam-1372	1184	17	an	an	DET
ejpam-1372	1184	18	infinite	infinite	ADJ
ejpam-1372	1184	19	series	series	NOUN
ejpam-1372	1184	20	should	should	AUX
ejpam-1372	1184	21	be	be	AUX
ejpam-1372	1184	22	independent	independent	ADJ
ejpam-1372	1184	23	of	of	ADP
ejpam-1372	1184	24	the	the	DET
ejpam-1372	1184	25	method	method	NOUN
ejpam-1372	1184	26	used	use	VERB
ejpam-1372	1184	27	to	to	PART
ejpam-1372	1184	28	determine	determine	VERB
ejpam-1372	1184	29	it	it	PRON
ejpam-1372	1184	30	.	.	PUNCT
ejpam-1372	1185	1	at	at	ADP
ejpam-1372	1185	2	the	the	DET
ejpam-1372	1185	3	beginning	beginning	NOUN
ejpam-1372	1185	4	of	of	ADP
ejpam-1372	1185	5	this	this	DET
ejpam-1372	1185	6	section	section	NOUN
ejpam-1372	1185	7	it	it	PRON
ejpam-1372	1185	8	was	be	AUX
ejpam-1372	1185	9	mentioned	mention	VERB
ejpam-1372	1185	10	that	that	SCONJ
ejpam-1372	1185	11	a	a	DET
ejpam-1372	1185	12	numerical	numerical	ADJ
ejpam-1372	1185	13	study	study	NOUN
ejpam-1372	1185	14	of	of	ADP
ejpam-1372	1185	15	generalised	generalised	ADJ
ejpam-1372	1185	16	type	type	NOUN
ejpam-1372	1185	17	ii	ii	NOUN
ejpam-1372	1185	18	terminants	terminant	NOUN
ejpam-1372	1185	19	had	have	AUX
ejpam-1372	1185	20	already	already	ADV
ejpam-1372	1185	21	been	be	AUX
ejpam-1372	1185	22	carried	carry	VERB
ejpam-1372	1185	23	out	out	ADP
ejpam-1372	1185	24	in	in	ADP
ejpam-1372	1185	25	ref	ref	NOUN
ejpam-1372	1185	26	.	.	PUNCT
ejpam-1372	1186	1	[	[	X
ejpam-1372	1186	2	17	17	NUM
ejpam-1372	1186	3	]	]	PUNCT
ejpam-1372	1186	4	.	.	PUNCT
ejpam-1372	1187	1	so	so	ADV
ejpam-1372	1187	2	,	,	PUNCT
ejpam-1372	1187	3	there	there	PRON
ejpam-1372	1187	4	is	be	VERB
ejpam-1372	1187	5	no	no	DET
ejpam-1372	1187	6	need	need	NOUN
ejpam-1372	1187	7	to	to	PART
ejpam-1372	1187	8	present	present	VERB
ejpam-1372	1187	9	v.	v.	ADP
ejpam-1372	1187	10	kowalenko	kowalenko	PROPN
ejpam-1372	1187	11	/	/	SYM
ejpam-1372	1187	12	eur	eur	PROPN
ejpam-1372	1187	13	.	.	PUNCT
ejpam-1372	1188	1	j.	j.	PROPN
ejpam-1372	1188	2	pure	pure	PROPN
ejpam-1372	1188	3	appl	appl	PROPN
ejpam-1372	1188	4	.	.	PROPN
ejpam-1372	1188	5	math	math	PROPN
ejpam-1372	1188	6	,	,	PUNCT
ejpam-1372	1188	7	4	4	NUM
ejpam-1372	1188	8	(	(	PUNCT
ejpam-1372	1188	9	2011	2011	NUM
ejpam-1372	1188	10	)	)	PUNCT
ejpam-1372	1188	11	,	,	PUNCT
ejpam-1372	1188	12	370	370	NUM
ejpam-1372	1188	13	-	-	SYM
ejpam-1372	1188	14	423	423	NUM
ejpam-1372	1188	15	413	413	NUM
ejpam-1372	1188	16	a	a	DET
ejpam-1372	1188	17	numerical	numerical	ADJ
ejpam-1372	1188	18	study	study	NOUN
ejpam-1372	1188	19	of	of	ADP
ejpam-1372	1188	20	this	this	DET
ejpam-1372	1188	21	type	type	NOUN
ejpam-1372	1188	22	of	of	ADP
ejpam-1372	1188	23	terminant	terminant	NOUN
ejpam-1372	1188	24	here	here	ADV
ejpam-1372	1188	25	.	.	PUNCT
ejpam-1372	1189	1	nevertheless	nevertheless	ADV
ejpam-1372	1189	2	,	,	PUNCT
ejpam-1372	1189	3	it	it	PRON
ejpam-1372	1189	4	was	be	AUX
ejpam-1372	1189	5	found	find	VERB
ejpam-1372	1189	6	that	that	SCONJ
ejpam-1372	1189	7	both	both	CCONJ
ejpam-1372	1189	8	the	the	DET
ejpam-1372	1189	9	mb	mb	ADV
ejpam-1372	1189	10	-	-	PUNCT
ejpam-1372	1189	11	regularised	regularise	VERB
ejpam-1372	1189	12	and	and	CCONJ
ejpam-1372	1189	13	borel	borel	NOUN
ejpam-1372	1189	14	-	-	PUNCT
ejpam-1372	1189	15	summed	sum	VERB
ejpam-1372	1189	16	forms	form	NOUN
ejpam-1372	1189	17	for	for	ADP
ejpam-1372	1189	18	the	the	DET
ejpam-1372	1189	19	regularised	regularise	VERB
ejpam-1372	1189	20	value	value	NOUN
ejpam-1372	1189	21	of	of	ADP
ejpam-1372	1189	22	a	a	DET
ejpam-1372	1189	23	generalised	generalise	VERB
ejpam-1372	1189	24	type	type	NOUN
ejpam-1372	1189	25	ii	ii	NOUN
ejpam-1372	1189	26	terminant	terminant	NOUN
ejpam-1372	1189	27	yielded	yield	VERB
ejpam-1372	1189	28	identical	identical	ADJ
ejpam-1372	1189	29	results	result	NOUN
ejpam-1372	1189	30	for	for	ADP
ejpam-1372	1189	31	all	all	DET
ejpam-1372	1189	32	values	value	NOUN
ejpam-1372	1189	33	of	of	ADP
ejpam-1372	1189	34	variable	variable	NOUN
ejpam-1372	1189	35	over	over	ADP
ejpam-1372	1189	36	the	the	DET
ejpam-1372	1189	37	principal	principal	ADJ
ejpam-1372	1189	38	branch	branch	NOUN
ejpam-1372	1189	39	of	of	ADP
ejpam-1372	1189	40	the	the	DET
ejpam-1372	1189	41	complex	complex	ADJ
ejpam-1372	1189	42	plane	plane	NOUN
ejpam-1372	1189	43	as	as	SCONJ
ejpam-1372	1189	44	we	we	PRON
ejpam-1372	1189	45	have	have	AUX
ejpam-1372	1189	46	observed	observe	VERB
ejpam-1372	1189	47	here	here	ADV
ejpam-1372	1189	48	with	with	ADP
ejpam-1372	1189	49	type	type	NOUN
ejpam-1372	1189	50	i	i	PROPN
ejpam-1372	1189	51	terminants	terminant	NOUN
ejpam-1372	1189	52	.	.	PUNCT
ejpam-1372	1190	1	since	since	SCONJ
ejpam-1372	1190	2	the	the	DET
ejpam-1372	1190	3	regularised	regularise	VERB
ejpam-1372	1190	4	value	value	NOUN
ejpam-1372	1190	5	remains	remain	VERB
ejpam-1372	1190	6	invariant	invariant	ADJ
ejpam-1372	1190	7	when	when	SCONJ
ejpam-1372	1190	8	both	both	DET
ejpam-1372	1190	9	regularisation	regularisation	NOUN
ejpam-1372	1190	10	techniques	technique	NOUN
ejpam-1372	1190	11	are	be	AUX
ejpam-1372	1190	12	applied	apply	VERB
ejpam-1372	1190	13	to	to	ADP
ejpam-1372	1190	14	type	type	NOUN
ejpam-1372	1190	15	ii	ii	NOUN
ejpam-1372	1190	16	terminants	terminant	NOUN
ejpam-1372	1190	17	,	,	PUNCT
ejpam-1372	1190	18	this	this	PRON
ejpam-1372	1190	19	means	mean	VERB
ejpam-1372	1190	20	that	that	SCONJ
ejpam-1372	1190	21	euler	euler	NOUN
ejpam-1372	1190	22	’s	’s	PART
ejpam-1372	1190	23	views	view	NOUN
ejpam-1372	1190	24	hold	hold	VERB
ejpam-1372	1190	25	regardless	regardless	ADV
ejpam-1372	1190	26	of	of	ADP
ejpam-1372	1190	27	the	the	DET
ejpam-1372	1190	28	type	type	NOUN
ejpam-1372	1190	29	of	of	ADP
ejpam-1372	1190	30	terminant	terminant	NOUN
ejpam-1372	1190	31	.	.	PUNCT
ejpam-1372	1191	1	ref	ref	NOUN
ejpam-1372	1191	2	.	.	PUNCT
ejpam-1372	1192	1	[	[	X
ejpam-1372	1192	2	17	17	NUM
ejpam-1372	1192	3	]	]	PUNCT
ejpam-1372	1192	4	also	also	ADV
ejpam-1372	1192	5	concludes	conclude	VERB
ejpam-1372	1192	6	with	with	ADP
ejpam-1372	1192	7	a	a	DET
ejpam-1372	1192	8	numerical	numerical	ADJ
ejpam-1372	1192	9	study	study	NOUN
ejpam-1372	1192	10	of	of	ADP
ejpam-1372	1192	11	the	the	DET
ejpam-1372	1192	12	following	follow	VERB
ejpam-1372	1192	13	series	series	NOUN
ejpam-1372	1192	14	:	:	PUNCT
ejpam-1372	1192	15	p(z	p(z	NOUN
ejpam-1372	1192	16	)	)	PUNCT
ejpam-1372	1192	17	=	=	SYM
ejpam-1372	1193	1	∞	∞	NUM
ejpam-1372	1193	2	∑	∑	PUNCT
ejpam-1372	1193	3	k=1	k=1	PROPN
ejpam-1372	1193	4	γ(2k)γ(k+	γ(2k)γ(k+	PUNCT
ejpam-1372	1193	5	ν/2	ν/2	NUM
ejpam-1372	1193	6	)	)	PUNCT
ejpam-1372	1194	1	γ(ν/2−	γ(ν/2−	NUM
ejpam-1372	1194	2	k+	k+	NOUN
ejpam-1372	1194	3	1	1	X
ejpam-1372	1194	4	)	)	PUNCT
ejpam-1372	1194	5	z7k/3	z7k/3	NOUN
ejpam-1372	1194	6	.	.	PUNCT
ejpam-1372	1195	1	(	(	PUNCT
ejpam-1372	1195	2	120	120	NUM
ejpam-1372	1195	3	)	)	PUNCT
ejpam-1372	1195	4	this	this	DET
ejpam-1372	1195	5	example	example	NOUN
ejpam-1372	1195	6	of	of	ADP
ejpam-1372	1195	7	a	a	DET
ejpam-1372	1195	8	general	general	ADJ
ejpam-1372	1195	9	type	type	NOUN
ejpam-1372	1195	10	ii	ii	PROPN
ejpam-1372	1195	11	series	series	NOUN
ejpam-1372	1195	12	can	can	AUX
ejpam-1372	1195	13	be	be	AUX
ejpam-1372	1195	14	mb	mb	VERB
ejpam-1372	1195	15	-	-	ADJ
ejpam-1372	1195	16	regularised	regularise	VERB
ejpam-1372	1195	17	by	by	ADP
ejpam-1372	1195	18	following	follow	VERB
ejpam-1372	1195	19	the	the	DET
ejpam-1372	1195	20	approach	approach	NOUN
ejpam-1372	1195	21	presented	present	VERB
ejpam-1372	1195	22	in	in	ADP
ejpam-1372	1195	23	the	the	DET
ejpam-1372	1195	24	previous	previous	ADJ
ejpam-1372	1195	25	section	section	NOUN
ejpam-1372	1195	26	,	,	PUNCT
ejpam-1372	1195	27	but	but	CCONJ
ejpam-1372	1195	28	it	it	PRON
ejpam-1372	1195	29	is	be	AUX
ejpam-1372	1195	30	not	not	PART
ejpam-1372	1195	31	borel	borel	NOUN
ejpam-1372	1195	32	-	-	PUNCT
ejpam-1372	1195	33	summable	summable	ADJ
ejpam-1372	1195	34	.	.	PUNCT
ejpam-1372	1196	1	however	however	ADV
ejpam-1372	1196	2	,	,	PUNCT
ejpam-1372	1196	3	at	at	ADP
ejpam-1372	1196	4	the	the	DET
ejpam-1372	1196	5	end	end	NOUN
ejpam-1372	1196	6	of	of	ADP
ejpam-1372	1196	7	sec	sec	PROPN
ejpam-1372	1196	8	.	.	PROPN
ejpam-1372	1196	9	9	9	NUM
ejpam-1372	1196	10	it	it	PRON
ejpam-1372	1196	11	was	be	AUX
ejpam-1372	1196	12	mentioned	mention	VERB
ejpam-1372	1196	13	that	that	SCONJ
ejpam-1372	1196	14	borel	borel	PROPN
ejpam-1372	1196	15	summation	summation	NOUN
ejpam-1372	1196	16	can	can	AUX
ejpam-1372	1196	17	be	be	AUX
ejpam-1372	1196	18	extended	extend	VERB
ejpam-1372	1196	19	to	to	ADP
ejpam-1372	1196	20	general	general	ADJ
ejpam-1372	1196	21	type	type	NOUN
ejpam-1372	1196	22	i	i	PRON
ejpam-1372	1196	23	and	and	CCONJ
ejpam-1372	1196	24	type	type	PROPN
ejpam-1372	1196	25	ii	ii	PROPN
ejpam-1372	1196	26	series	series	NOUN
ejpam-1372	1196	27	provided	provide	VERB
ejpam-1372	1196	28	f	f	PROPN
ejpam-1372	1196	29	(	(	PUNCT
ejpam-1372	1196	30	k	k	NOUN
ejpam-1372	1196	31	)	)	PUNCT
ejpam-1372	1196	32	can	can	AUX
ejpam-1372	1196	33	be	be	AUX
ejpam-1372	1196	34	expressed	express	VERB
ejpam-1372	1196	35	as	as	ADP
ejpam-1372	1196	36	a	a	DET
ejpam-1372	1196	37	mellin	mellin	NOUN
ejpam-1372	1196	38	transform	transform	NOUN
ejpam-1372	1196	39	.	.	PUNCT
ejpam-1372	1197	1	to	to	PART
ejpam-1372	1197	2	see	see	VERB
ejpam-1372	1197	3	how	how	SCONJ
ejpam-1372	1197	4	this	this	PRON
ejpam-1372	1197	5	applies	apply	VERB
ejpam-1372	1197	6	to	to	ADP
ejpam-1372	1197	7	eq	eq	PROPN
ejpam-1372	1197	8	.	.	PUNCT
ejpam-1372	1198	1	(	(	PUNCT
ejpam-1372	1198	2	120	120	NUM
ejpam-1372	1198	3	)	)	PUNCT
ejpam-1372	1198	4	,	,	PUNCT
ejpam-1372	1198	5	we	we	PRON
ejpam-1372	1198	6	note	note	VERB
ejpam-1372	1198	7	that	that	SCONJ
ejpam-1372	1198	8	the	the	DET
ejpam-1372	1198	9	quotient	quotient	NOUN
ejpam-1372	1198	10	of	of	ADP
ejpam-1372	1198	11	the	the	DET
ejpam-1372	1198	12	gamma	gamma	NOUN
ejpam-1372	1198	13	functions	function	NOUN
ejpam-1372	1198	14	in	in	ADP
ejpam-1372	1198	15	the	the	DET
ejpam-1372	1198	16	coefficients	coefficient	NOUN
ejpam-1372	1198	17	of	of	ADP
ejpam-1372	1198	18	p(z	p(z	NOUN
ejpam-1372	1198	19	)	)	PUNCT
ejpam-1372	1198	20	appears	appear	VERB
ejpam-1372	1198	21	in	in	ADP
ejpam-1372	1198	22	a	a	DET
ejpam-1372	1198	23	more	more	ADV
ejpam-1372	1198	24	general	general	ADJ
ejpam-1372	1198	25	form	form	NOUN
ejpam-1372	1198	26	in	in	ADP
ejpam-1372	1198	27	the	the	DET
ejpam-1372	1198	28	integral	integral	ADJ
ejpam-1372	1198	29	given	give	VERB
ejpam-1372	1198	30	by	by	ADP
ejpam-1372	1198	31	no	no	PRON
ejpam-1372	1198	32	.	.	PROPN
ejpam-1372	1198	33	1.16.21(1	1.16.21(1	NUM
ejpam-1372	1198	34	)	)	PUNCT
ejpam-1372	1198	35	in	in	ADP
ejpam-1372	1198	36	ref	ref	NOUN
ejpam-1372	1198	37	.	.	PUNCT
ejpam-1372	1199	1	[	[	X
ejpam-1372	1199	2	28	28	NUM
ejpam-1372	1199	3	]	]	PUNCT
ejpam-1372	1199	4	.	.	PUNCT
ejpam-1372	1200	1	this	this	PRON
ejpam-1372	1200	2	is	be	AUX
ejpam-1372	1200	3	∫	∫	PROPN
ejpam-1372	1200	4	∞	∞	PROPN
ejpam-1372	1200	5	0	0	PUNCT
ejpam-1372	1201	1	d	d	NOUN
ejpam-1372	1201	2	x	x	PUNCT
ejpam-1372	1201	3	x	x	X
ejpam-1372	1201	4	pk+q−1	pk+q−1	NOUN
ejpam-1372	1201	5	jν(ax)kν(ax	jν(ax)kν(ax	NOUN
ejpam-1372	1201	6	)	)	PUNCT
ejpam-1372	1201	7	=	=	SYM
ejpam-1372	1202	1	2pk+q−3	2pk+q−3	NUM
ejpam-1372	1202	2	apk+	apk+	NOUN
ejpam-1372	1202	3	q	q	ADJ
ejpam-1372	1202	4	γ((pk+	γ((pk+	PROPN
ejpam-1372	1202	5	q)/4	q)/4	PROPN
ejpam-1372	1202	6	+	+	ADJ
ejpam-1372	1202	7	ν/2	ν/2	NUM
ejpam-1372	1202	8	)	)	PUNCT
ejpam-1372	1202	9	γ(1−	γ(1−	NOUN
ejpam-1372	1202	10	(	(	PUNCT
ejpam-1372	1202	11	pk+	pk+	NOUN
ejpam-1372	1202	12	q)/4	q)/4	PROPN
ejpam-1372	1202	13	+	+	SYM
ejpam-1372	1202	14	ν/2	ν/2	NUM
ejpam-1372	1202	15	)	)	PUNCT
ejpam-1372	1202	16	×	×	PROPN
ejpam-1372	1202	17	γ((pk+	γ((pk+	PROPN
ejpam-1372	1202	18	q)/2	q)/2	PROPN
ejpam-1372	1202	19	)	)	PUNCT
ejpam-1372	1202	20	.	.	PUNCT
ejpam-1372	1203	1	(	(	PUNCT
ejpam-1372	1203	2	121	121	NUM
ejpam-1372	1203	3	)	)	PUNCT
ejpam-1372	1203	4	hence	hence	ADV
ejpam-1372	1203	5	,	,	PUNCT
ejpam-1372	1203	6	putting	put	VERB
ejpam-1372	1203	7	k=2k	k=2k	NOUN
ejpam-1372	1203	8	,	,	PUNCT
ejpam-1372	1203	9	p=2	p=2	PROPN
ejpam-1372	1203	10	,	,	PUNCT
ejpam-1372	1203	11	q=2	q=2	NOUN
ejpam-1372	1203	12	and	and	CCONJ
ejpam-1372	1203	13	a=2	a=2	PROPN
ejpam-1372	1203	14	in	in	ADP
ejpam-1372	1203	15	the	the	DET
ejpam-1372	1203	16	above	above	ADJ
ejpam-1372	1203	17	result	result	NOUN
ejpam-1372	1203	18	produces	produce	VERB
ejpam-1372	1203	19	the	the	DET
ejpam-1372	1203	20	precise	precise	ADJ
ejpam-1372	1203	21	form	form	NOUN
ejpam-1372	1203	22	for	for	ADP
ejpam-1372	1203	23	the	the	DET
ejpam-1372	1203	24	quotient	quotient	NOUN
ejpam-1372	1203	25	of	of	ADP
ejpam-1372	1203	26	gamma	gamma	NOUN
ejpam-1372	1203	27	functions	function	NOUN
ejpam-1372	1203	28	appearing	appear	VERB
ejpam-1372	1203	29	in	in	ADP
ejpam-1372	1203	30	eq	eq	ADP
ejpam-1372	1203	31	.	.	PUNCT
ejpam-1372	1204	1	(	(	PUNCT
ejpam-1372	1204	2	120	120	NUM
ejpam-1372	1204	3	)	)	PUNCT
ejpam-1372	1204	4	.	.	PUNCT
ejpam-1372	1205	1	by	by	ADP
ejpam-1372	1205	2	introducing	introduce	VERB
ejpam-1372	1205	3	the	the	DET
ejpam-1372	1205	4	resulting	result	VERB
ejpam-1372	1205	5	integral	integral	ADJ
ejpam-1372	1205	6	into	into	ADP
ejpam-1372	1205	7	eq	eq	PROPN
ejpam-1372	1205	8	.	.	PUNCT
ejpam-1372	1206	1	(	(	PUNCT
ejpam-1372	1206	2	120	120	NUM
ejpam-1372	1206	3	)	)	PUNCT
ejpam-1372	1206	4	and	and	CCONJ
ejpam-1372	1206	5	interchanging	interchange	VERB
ejpam-1372	1206	6	the	the	DET
ejpam-1372	1206	7	order	order	NOUN
ejpam-1372	1206	8	of	of	ADP
ejpam-1372	1206	9	the	the	DET
ejpam-1372	1206	10	summation	summation	NOUN
ejpam-1372	1206	11	and	and	CCONJ
ejpam-1372	1206	12	integration	integration	NOUN
ejpam-1372	1206	13	,	,	PUNCT
ejpam-1372	1206	14	we	we	PRON
ejpam-1372	1206	15	arrive	arrive	VERB
ejpam-1372	1206	16	at	at	ADP
ejpam-1372	1206	17	a	a	DET
ejpam-1372	1206	18	series	series	NOUN
ejpam-1372	1206	19	where	where	SCONJ
ejpam-1372	1206	20	the	the	DET
ejpam-1372	1206	21	summation	summation	NOUN
ejpam-1372	1206	22	over	over	ADP
ejpam-1372	1206	23	k	k	PROPN
ejpam-1372	1206	24	is	be	AUX
ejpam-1372	1206	25	only	only	ADV
ejpam-1372	1206	26	in	in	ADP
ejpam-1372	1206	27	powers	power	NOUN
ejpam-1372	1206	28	of	of	ADP
ejpam-1372	1206	29	k.	k.	PROPN
ejpam-1372	1206	30	since	since	SCONJ
ejpam-1372	1206	31	the	the	DET
ejpam-1372	1206	32	resulting	result	VERB
ejpam-1372	1206	33	series	series	NOUN
ejpam-1372	1206	34	is	be	AUX
ejpam-1372	1206	35	a	a	DET
ejpam-1372	1206	36	variant	variant	NOUN
ejpam-1372	1206	37	of	of	ADP
ejpam-1372	1206	38	the	the	DET
ejpam-1372	1206	39	geometric	geometric	ADJ
ejpam-1372	1206	40	series	series	NOUN
ejpam-1372	1206	41	,	,	PUNCT
ejpam-1372	1206	42	it	it	PRON
ejpam-1372	1206	43	can	can	AUX
ejpam-1372	1206	44	be	be	AUX
ejpam-1372	1206	45	regularised	regularise	VERB
ejpam-1372	1206	46	.	.	PUNCT
ejpam-1372	1207	1	e.g.	e.g.	ADV
ejpam-1372	1207	2	,	,	PUNCT
ejpam-1372	1207	3	for	for	ADP
ejpam-1372	1207	4	the	the	DET
ejpam-1372	1207	5	stokes	stoke	NOUN
ejpam-1372	1207	6	sector	sector	NOUN
ejpam-1372	1207	7	of	of	ADP
ejpam-1372	1207	8	0	0	NUM
ejpam-1372	1207	9	<	<	X
ejpam-1372	1207	10	argz	argz	NOUN
ejpam-1372	1207	11	<	<	X
ejpam-1372	1207	12	6π/7	6π/7	NUM
ejpam-1372	1207	13	,	,	PUNCT
ejpam-1372	1207	14	the	the	DET
ejpam-1372	1207	15	extended	extend	VERB
ejpam-1372	1207	16	borel	borel	NOUN
ejpam-1372	1207	17	-	-	PUNCT
ejpam-1372	1207	18	summed	sum	VERB
ejpam-1372	1207	19	form	form	NOUN
ejpam-1372	1207	20	of	of	ADP
ejpam-1372	1207	21	the	the	DET
ejpam-1372	1207	22	regularised	regularise	VERB
ejpam-1372	1207	23	value	value	NOUN
ejpam-1372	1207	24	of	of	ADP
ejpam-1372	1207	25	p(z	p(z	NOUN
ejpam-1372	1207	26	)	)	PUNCT
ejpam-1372	1207	27	is	be	AUX
ejpam-1372	1207	28	found	find	VERB
ejpam-1372	1207	29	to	to	PART
ejpam-1372	1207	30	be	be	AUX
ejpam-1372	1207	31	p(z	p(z	VERB
ejpam-1372	1207	32	)	)	PUNCT
ejpam-1372	1208	1	≡	≡	PROPN
ejpam-1372	1208	2	−2	−2	PROPN
ejpam-1372	1208	3	∫	∫	PROPN
ejpam-1372	1209	1	∞	∞	NOUN
ejpam-1372	1209	2	0	0	PUNCT
ejpam-1372	1210	1	d	d	PRON
ejpam-1372	1210	2	t	t	PROPN
ejpam-1372	1210	3	jν	jν	PROPN
ejpam-1372	1210	4	�	�	PROPN
ejpam-1372	1210	5	2t1/4	2t1/4	NUM
ejpam-1372	1210	6	�	�	PROPN
ejpam-1372	1210	7	kν	kν	PROPN
ejpam-1372	1210	8	�	�	PROPN
ejpam-1372	1210	9	t1/4	t1/4	PROPN
ejpam-1372	1210	10	�	�	PROPN
ejpam-1372	1210	11	t	t	PROPN
ejpam-1372	1210	12	−	−	PROPN
ejpam-1372	1210	13	z−7/3	z−7/3	PROPN
ejpam-1372	1211	1	−	−	PROPN
ejpam-1372	1211	2	2πi	2πi	PROPN
ejpam-1372	1211	3	jν	jν	PROPN
ejpam-1372	1211	4	�	�	PROPN
ejpam-1372	1211	5	2z−7/12	2z−7/12	PROPN
ejpam-1372	1211	6	�	�	PROPN
ejpam-1372	1211	7	kν	kν	PROPN
ejpam-1372	1211	8	�	�	PROPN
ejpam-1372	1211	9	2z−7/12	2z−7/12	PROPN
ejpam-1372	1211	10	�	�	PROPN
ejpam-1372	1211	11	.	.	PUNCT
ejpam-1372	1212	1	(	(	PUNCT
ejpam-1372	1212	2	122	122	NUM
ejpam-1372	1212	3	)	)	PUNCT
ejpam-1372	1212	4	the	the	DET
ejpam-1372	1212	5	above	above	ADJ
ejpam-1372	1212	6	result	result	NOUN
ejpam-1372	1212	7	,	,	PUNCT
ejpam-1372	1212	8	which	which	PRON
ejpam-1372	1212	9	is	be	AUX
ejpam-1372	1212	10	composed	compose	VERB
ejpam-1372	1212	11	of	of	ADP
ejpam-1372	1212	12	a	a	DET
ejpam-1372	1212	13	cauchy	cauchy	ADJ
ejpam-1372	1212	14	integral	integral	ADJ
ejpam-1372	1212	15	and	and	CCONJ
ejpam-1372	1212	16	a	a	DET
ejpam-1372	1212	17	jump	jump	NOUN
ejpam-1372	1212	18	discontinuity	discontinuity	NOUN
ejpam-1372	1212	19	term	term	NOUN
ejpam-1372	1212	20	,	,	PUNCT
ejpam-1372	1212	21	is	be	AUX
ejpam-1372	1212	22	typical	typical	ADJ
ejpam-1372	1212	23	of	of	ADP
ejpam-1372	1212	24	the	the	DET
ejpam-1372	1212	25	extended	extend	VERB
ejpam-1372	1212	26	borel	borel	NOUN
ejpam-1372	1212	27	-	-	PUNCT
ejpam-1372	1212	28	summed	sum	VERB
ejpam-1372	1212	29	forms	form	NOUN
ejpam-1372	1212	30	presented	present	VERB
ejpam-1372	1212	31	in	in	ADP
ejpam-1372	1212	32	sec	sec	PROPN
ejpam-1372	1212	33	.	.	PROPN
ejpam-1372	1212	34	9	9	NUM
ejpam-1372	1212	35	.	.	X
ejpam-1372	1213	1	therefore	therefore	ADV
ejpam-1372	1213	2	,	,	PUNCT
ejpam-1372	1213	3	we	we	PRON
ejpam-1372	1213	4	see	see	VERB
ejpam-1372	1213	5	that	that	DET
ejpam-1372	1213	6	borel	borel	PROPN
ejpam-1372	1213	7	summation	summation	NOUN
ejpam-1372	1213	8	can	can	AUX
ejpam-1372	1213	9	be	be	AUX
ejpam-1372	1213	10	extended	extend	VERB
ejpam-1372	1213	11	to	to	ADP
ejpam-1372	1213	12	more	more	ADV
ejpam-1372	1213	13	complicated	complicated	ADJ
ejpam-1372	1213	14	series	series	NOUN
ejpam-1372	1213	15	other	other	ADJ
ejpam-1372	1213	16	than	than	ADP
ejpam-1372	1213	17	those	those	PRON
ejpam-1372	1213	18	with	with	ADP
ejpam-1372	1213	19	gamma	gamma	NOUN
ejpam-1372	1213	20	function	function	NOUN
ejpam-1372	1213	21	growth	growth	NOUN
ejpam-1372	1213	22	in	in	ADP
ejpam-1372	1213	23	their	their	PRON
ejpam-1372	1213	24	coefficients	coefficient	NOUN
ejpam-1372	1213	25	as	as	ADP
ejpam-1372	1213	26	in	in	ADP
ejpam-1372	1213	27	generalised	generalised	ADJ
ejpam-1372	1213	28	terminants	terminant	NOUN
ejpam-1372	1213	29	,	,	PUNCT
ejpam-1372	1213	30	but	but	CCONJ
ejpam-1372	1213	31	only	only	ADV
ejpam-1372	1213	32	on	on	ADP
ejpam-1372	1213	33	the	the	DET
ejpam-1372	1213	34	condition	condition	NOUN
ejpam-1372	1213	35	that	that	SCONJ
ejpam-1372	1213	36	the	the	DET
ejpam-1372	1213	37	coefficients	coefficient	NOUN
ejpam-1372	1213	38	must	must	AUX
ejpam-1372	1213	39	be	be	AUX
ejpam-1372	1213	40	expressible	expressible	ADJ
ejpam-1372	1213	41	in	in	ADP
ejpam-1372	1213	42	terms	term	NOUN
ejpam-1372	1213	43	of	of	ADP
ejpam-1372	1213	44	a	a	DET
ejpam-1372	1213	45	mellin	mellin	PROPN
ejpam-1372	1213	46	transform	transform	NOUN
ejpam-1372	1213	47	.	.	PUNCT
ejpam-1372	1214	1	by	by	ADP
ejpam-1372	1214	2	using	use	VERB
ejpam-1372	1214	3	the	the	DET
ejpam-1372	1214	4	borel	borel	NOUN
ejpam-1372	1214	5	-	-	PUNCT
ejpam-1372	1214	6	summed	sum	VERB
ejpam-1372	1214	7	forms	form	NOUN
ejpam-1372	1214	8	such	such	ADJ
ejpam-1372	1214	9	as	as	ADP
ejpam-1372	1214	10	equivalence	equivalence	NOUN
ejpam-1372	1214	11	(	(	PUNCT
ejpam-1372	1214	12	122	122	NUM
ejpam-1372	1214	13	)	)	PUNCT
ejpam-1372	1214	14	,	,	PUNCT
ejpam-1372	1214	15	an	an	DET
ejpam-1372	1214	16	extensive	extensive	ADJ
ejpam-1372	1214	17	numerical	numerical	ADJ
ejpam-1372	1214	18	study	study	NOUN
ejpam-1372	1214	19	is	be	AUX
ejpam-1372	1214	20	undertaken	undertake	VERB
ejpam-1372	1214	21	in	in	ADP
ejpam-1372	1214	22	conjunction	conjunction	NOUN
ejpam-1372	1214	23	with	with	ADP
ejpam-1372	1214	24	the	the	DET
ejpam-1372	1214	25	mb	mb	ADV
ejpam-1372	1214	26	-	-	PUNCT
ejpam-1372	1214	27	regularised	regularise	VERB
ejpam-1372	1214	28	forms	form	NOUN
ejpam-1372	1214	29	for	for	ADP
ejpam-1372	1214	30	the	the	DET
ejpam-1372	1214	31	regularised	regularise	VERB
ejpam-1372	1214	32	value	value	NOUN
ejpam-1372	1214	33	of	of	ADP
ejpam-1372	1214	34	p(z	p(z	NOUN
ejpam-1372	1214	35	)	)	PUNCT
ejpam-1372	1214	36	in	in	ADP
ejpam-1372	1214	37	ch	ch	PROPN
ejpam-1372	1214	38	.	.	PROPN
ejpam-1372	1214	39	11	11	NUM
ejpam-1372	1214	40	of	of	ADP
ejpam-1372	1214	41	ref	ref	NOUN
ejpam-1372	1214	42	.	.	PUNCT
ejpam-1372	1215	1	[	[	X
ejpam-1372	1215	2	17	17	NUM
ejpam-1372	1215	3	]	]	PUNCT
ejpam-1372	1215	4	.	.	PUNCT
ejpam-1372	1216	1	again	again	ADV
ejpam-1372	1216	2	,	,	PUNCT
ejpam-1372	1216	3	it	it	PRON
ejpam-1372	1216	4	is	be	AUX
ejpam-1372	1216	5	found	find	VERB
ejpam-1372	1216	6	that	that	SCONJ
ejpam-1372	1216	7	the	the	DET
ejpam-1372	1216	8	regularised	regularise	VERB
ejpam-1372	1216	9	values	value	NOUN
ejpam-1372	1216	10	evaluated	evaluate	VERB
ejpam-1372	1216	11	by	by	ADP
ejpam-1372	1216	12	the	the	DET
ejpam-1372	1216	13	different	different	ADJ
ejpam-1372	1216	14	forms	form	NOUN
ejpam-1372	1216	15	agree	agree	VERB
ejpam-1372	1216	16	with	with	ADP
ejpam-1372	1216	17	each	each	DET
ejpam-1372	1216	18	other	other	ADJ
ejpam-1372	1216	19	for	for	ADP
ejpam-1372	1216	20	a	a	DET
ejpam-1372	1216	21	great	great	ADJ
ejpam-1372	1216	22	number	number	NOUN
ejpam-1372	1216	23	of	of	ADP
ejpam-1372	1216	24	values	value	NOUN
ejpam-1372	1216	25	of	of	ADP
ejpam-1372	1216	26	z	z	NOUN
ejpam-1372	1216	27	situated	situate	VERB
ejpam-1372	1216	28	in	in	ADP
ejpam-1372	1216	29	the	the	DET
ejpam-1372	1216	30	principal	principal	ADJ
ejpam-1372	1216	31	branch	branch	NOUN
ejpam-1372	1216	32	of	of	ADP
ejpam-1372	1216	33	the	the	DET
ejpam-1372	1216	34	complex	complex	ADJ
ejpam-1372	1216	35	plane	plane	NOUN
ejpam-1372	1216	36	.	.	PUNCT
ejpam-1372	1217	1	hence	hence	ADV
ejpam-1372	1217	2	,	,	PUNCT
ejpam-1372	1217	3	the	the	DET
ejpam-1372	1217	4	two	two	NUM
ejpam-1372	1217	5	entirely	entirely	ADV
ejpam-1372	1217	6	different	different	ADJ
ejpam-1372	1217	7	methods	method	NOUN
ejpam-1372	1217	8	for	for	ADP
ejpam-1372	1217	9	regularising	regularise	VERB
ejpam-1372	1217	10	asymptotic	asymptotic	ADJ
ejpam-1372	1217	11	series	series	NOUN
ejpam-1372	1217	12	yield	yield	VERB
ejpam-1372	1217	13	the	the	DET
ejpam-1372	1217	14	same	same	ADJ
ejpam-1372	1217	15	v.	v.	ADP
ejpam-1372	1217	16	kowalenko	kowalenko	PROPN
ejpam-1372	1217	17	/	/	SYM
ejpam-1372	1217	18	eur	eur	PROPN
ejpam-1372	1217	19	.	.	PUNCT
ejpam-1372	1218	1	j.	j.	PROPN
ejpam-1372	1218	2	pure	pure	PROPN
ejpam-1372	1218	3	appl	appl	PROPN
ejpam-1372	1218	4	.	.	PROPN
ejpam-1372	1218	5	math	math	PROPN
ejpam-1372	1218	6	,	,	PUNCT
ejpam-1372	1218	7	4	4	NUM
ejpam-1372	1218	8	(	(	PUNCT
ejpam-1372	1218	9	2011	2011	NUM
ejpam-1372	1218	10	)	)	PUNCT
ejpam-1372	1218	11	,	,	PUNCT
ejpam-1372	1218	12	370	370	NUM
ejpam-1372	1218	13	-	-	SYM
ejpam-1372	1218	14	423	423	NUM
ejpam-1372	1218	15	414	414	NUM
ejpam-1372	1218	16	regularised	regularise	VERB
ejpam-1372	1218	17	values	value	NOUN
ejpam-1372	1218	18	of	of	ADP
ejpam-1372	1218	19	this	this	DET
ejpam-1372	1218	20	general	general	ADJ
ejpam-1372	1218	21	type	type	NOUN
ejpam-1372	1218	22	ii	ii	PROPN
ejpam-1372	1218	23	series	series	NOUN
ejpam-1372	1218	24	.	.	PUNCT
ejpam-1372	1219	1	as	as	ADP
ejpam-1372	1219	2	a	a	DET
ejpam-1372	1219	3	consequence	consequence	NOUN
ejpam-1372	1219	4	,	,	PUNCT
ejpam-1372	1219	5	we	we	PRON
ejpam-1372	1219	6	can	can	AUX
ejpam-1372	1219	7	be	be	AUX
ejpam-1372	1219	8	confident	confident	ADJ
ejpam-1372	1219	9	that	that	SCONJ
ejpam-1372	1219	10	the	the	DET
ejpam-1372	1219	11	mb	mb	ADJ
ejpam-1372	1219	12	-	-	PUNCT
ejpam-1372	1219	13	regularised	regularise	VERB
ejpam-1372	1219	14	forms	form	NOUN
ejpam-1372	1219	15	will	will	AUX
ejpam-1372	1219	16	yield	yield	VERB
ejpam-1372	1219	17	the	the	DET
ejpam-1372	1219	18	correct	correct	ADJ
ejpam-1372	1219	19	regularised	regularise	VERB
ejpam-1372	1219	20	value	value	NOUN
ejpam-1372	1219	21	of	of	ADP
ejpam-1372	1219	22	the	the	DET
ejpam-1372	1219	23	asymptotic	asymptotic	ADJ
ejpam-1372	1219	24	expansion	expansion	NOUN
ejpam-1372	1219	25	for	for	ADP
ejpam-1372	1219	26	the	the	DET
ejpam-1372	1219	27	original	original	ADJ
ejpam-1372	1219	28	function	function	NOUN
ejpam-1372	1219	29	even	even	ADV
ejpam-1372	1219	30	when	when	SCONJ
ejpam-1372	1219	31	extended	extended	ADJ
ejpam-1372	1219	32	borel	borel	NOUN
ejpam-1372	1219	33	-	-	PUNCT
ejpam-1372	1219	34	summed	sum	VERB
ejpam-1372	1219	35	forms	form	NOUN
ejpam-1372	1219	36	can	can	AUX
ejpam-1372	1219	37	not	not	PART
ejpam-1372	1219	38	be	be	AUX
ejpam-1372	1219	39	determined	determine	VERB
ejpam-1372	1219	40	.	.	PUNCT
ejpam-1372	1220	1	more	more	ADV
ejpam-1372	1220	2	importantly	importantly	ADV
ejpam-1372	1220	3	,	,	PUNCT
ejpam-1372	1220	4	we	we	PRON
ejpam-1372	1220	5	find	find	VERB
ejpam-1372	1220	6	that	that	PRON
ejpam-1372	1220	7	euler	euler	NOUN
ejpam-1372	1220	8	’s	’s	PART
ejpam-1372	1220	9	views	view	NOUN
ejpam-1372	1220	10	hold	hold	VERB
ejpam-1372	1220	11	yet	yet	ADV
ejpam-1372	1220	12	again	again	ADV
ejpam-1372	1220	13	.	.	PUNCT
ejpam-1372	1221	1	because	because	SCONJ
ejpam-1372	1221	2	on	on	ADP
ejpam-1372	1221	3	this	this	DET
ejpam-1372	1221	4	occasion	occasion	NOUN
ejpam-1372	1221	5	a	a	DET
ejpam-1372	1221	6	far	far	ADV
ejpam-1372	1221	7	more	more	ADV
ejpam-1372	1221	8	complicated	complicated	ADJ
ejpam-1372	1221	9	series	series	NOUN
ejpam-1372	1221	10	than	than	SCONJ
ejpam-1372	1221	11	a	a	DET
ejpam-1372	1221	12	terminant	terminant	NOUN
ejpam-1372	1221	13	is	be	AUX
ejpam-1372	1221	14	being	be	AUX
ejpam-1372	1221	15	considered	consider	VERB
ejpam-1372	1221	16	,	,	PUNCT
ejpam-1372	1221	17	we	we	PRON
ejpam-1372	1221	18	can	can	AUX
ejpam-1372	1221	19	see	see	VERB
ejpam-1372	1221	20	that	that	SCONJ
ejpam-1372	1221	21	his	his	PRON
ejpam-1372	1221	22	views	view	NOUN
ejpam-1372	1221	23	are	be	AUX
ejpam-1372	1221	24	going	go	VERB
ejpam-1372	1221	25	to	to	PART
ejpam-1372	1221	26	hold	hold	VERB
ejpam-1372	1221	27	for	for	ADP
ejpam-1372	1221	28	all	all	DET
ejpam-1372	1221	29	divergent	divergent	ADJ
ejpam-1372	1221	30	series	series	NOUN
ejpam-1372	1221	31	when	when	SCONJ
ejpam-1372	1221	32	a	a	DET
ejpam-1372	1221	33	theory	theory	NOUN
ejpam-1372	1221	34	of	of	ADP
ejpam-1372	1221	35	divergent	divergent	ADJ
ejpam-1372	1221	36	series	series	NOUN
ejpam-1372	1221	37	is	be	AUX
ejpam-1372	1221	38	finally	finally	ADV
ejpam-1372	1221	39	realised	realise	VERB
ejpam-1372	1221	40	.	.	PUNCT
ejpam-1372	1222	1	12	12	NUM
ejpam-1372	1222	2	.	.	PUNCT
ejpam-1372	1223	1	conclusion	conclusion	NOUN
ejpam-1372	1223	2	this	this	DET
ejpam-1372	1223	3	article	article	NOUN
ejpam-1372	1223	4	has	have	AUX
ejpam-1372	1223	5	been	be	AUX
ejpam-1372	1223	6	concerned	concern	VERB
ejpam-1372	1223	7	with	with	ADP
ejpam-1372	1223	8	re	re	ADJ
ejpam-1372	1223	9	-	-	ADJ
ejpam-1372	1223	10	evaluating	evaluate	VERB
ejpam-1372	1223	11	euler	euler	NOUN
ejpam-1372	1223	12	’s	’s	PART
ejpam-1372	1223	13	views	view	NOUN
ejpam-1372	1223	14	on	on	ADP
ejpam-1372	1223	15	infinite	infinite	ADJ
ejpam-1372	1223	16	series	series	NOUN
ejpam-1372	1223	17	as	as	ADP
ejpam-1372	1223	18	a	a	DET
ejpam-1372	1223	19	result	result	NOUN
ejpam-1372	1223	20	of	of	ADP
ejpam-1372	1223	21	recent	recent	ADJ
ejpam-1372	1223	22	developments	development	NOUN
ejpam-1372	1223	23	aimed	aim	VERB
ejpam-1372	1223	24	at	at	ADP
ejpam-1372	1223	25	obtaining	obtain	VERB
ejpam-1372	1223	26	meaningful	meaningful	ADJ
ejpam-1372	1223	27	results	result	NOUN
ejpam-1372	1223	28	for	for	ADP
ejpam-1372	1223	29	divergent	divergent	ADJ
ejpam-1372	1223	30	series	series	NOUN
ejpam-1372	1223	31	.	.	PUNCT
ejpam-1372	1224	1	basically	basically	ADV
ejpam-1372	1224	2	,	,	PUNCT
ejpam-1372	1224	3	euler	euler	PROPN
ejpam-1372	1224	4	believed	believe	VERB
ejpam-1372	1224	5	that	that	SCONJ
ejpam-1372	1224	6	all	all	DET
ejpam-1372	1224	7	series	series	NOUN
ejpam-1372	1224	8	,	,	PUNCT
ejpam-1372	1224	9	whether	whether	SCONJ
ejpam-1372	1224	10	they	they	PRON
ejpam-1372	1224	11	are	be	AUX
ejpam-1372	1224	12	convergent	convergent	ADJ
ejpam-1372	1224	13	or	or	CCONJ
ejpam-1372	1224	14	divergent	divergent	ADJ
ejpam-1372	1224	15	,	,	PUNCT
ejpam-1372	1224	16	could	could	AUX
ejpam-1372	1224	17	be	be	AUX
ejpam-1372	1224	18	summed	sum	VERB
ejpam-1372	1224	19	to	to	ADP
ejpam-1372	1224	20	a	a	DET
ejpam-1372	1224	21	particular	particular	ADJ
ejpam-1372	1224	22	value	value	NOUN
ejpam-1372	1224	23	and	and	CCONJ
ejpam-1372	1224	24	that	that	SCONJ
ejpam-1372	1224	25	this	this	DET
ejpam-1372	1224	26	value	value	NOUN
ejpam-1372	1224	27	should	should	AUX
ejpam-1372	1224	28	remain	remain	VERB
ejpam-1372	1224	29	invariant	invariant	ADJ
ejpam-1372	1224	30	whatever	whatever	DET
ejpam-1372	1224	31	method	method	NOUN
ejpam-1372	1224	32	was	be	AUX
ejpam-1372	1224	33	employed	employ	VERB
ejpam-1372	1224	34	.	.	PUNCT
ejpam-1372	1225	1	in	in	ADP
ejpam-1372	1225	2	relation	relation	NOUN
ejpam-1372	1225	3	to	to	ADP
ejpam-1372	1225	4	divergent	divergent	ADJ
ejpam-1372	1225	5	series	series	NOUN
ejpam-1372	1225	6	these	these	DET
ejpam-1372	1225	7	views	view	NOUN
ejpam-1372	1225	8	are	be	AUX
ejpam-1372	1225	9	not	not	PART
ejpam-1372	1225	10	only	only	ADV
ejpam-1372	1225	11	regarded	regard	VERB
ejpam-1372	1225	12	as	as	ADP
ejpam-1372	1225	13	unorthodox	unorthodox	ADJ
ejpam-1372	1225	14	,	,	PUNCT
ejpam-1372	1225	15	but	but	CCONJ
ejpam-1372	1225	16	also	also	ADV
ejpam-1372	1225	17	totally	totally	ADV
ejpam-1372	1225	18	unfounded	unfounded	ADJ
ejpam-1372	1225	19	by	by	ADP
ejpam-1372	1225	20	the	the	DET
ejpam-1372	1225	21	mathematical	mathematical	ADJ
ejpam-1372	1225	22	community	community	NOUN
ejpam-1372	1225	23	today	today	NOUN
ejpam-1372	1225	24	.	.	PUNCT
ejpam-1372	1226	1	to	to	PART
ejpam-1372	1226	2	emphasise	emphasise	VERB
ejpam-1372	1226	3	this	this	DET
ejpam-1372	1226	4	point	point	NOUN
ejpam-1372	1226	5	,	,	PUNCT
ejpam-1372	1226	6	varadarajan	varadarajan	ADJ
ejpam-1372	1226	7	[	[	X
ejpam-1372	1226	8	32	32	NUM
ejpam-1372	1226	9	]	]	PUNCT
ejpam-1372	1226	10	wrote	write	VERB
ejpam-1372	1226	11	on	on	ADP
ejpam-1372	1226	12	the	the	DET
ejpam-1372	1226	13	occasion	occasion	NOUN
ejpam-1372	1226	14	of	of	ADP
ejpam-1372	1226	15	the	the	DET
ejpam-1372	1226	16	tercentenary	tercentenary	PROPN
ejpam-1372	1226	17	of	of	ADP
ejpam-1372	1226	18	euler	euler	PROPN
ejpam-1372	1226	19	’s	’s	PART
ejpam-1372	1226	20	birth	birth	NOUN
ejpam-1372	1226	21	in	in	ADP
ejpam-1372	1226	22	2007	2007	NUM
ejpam-1372	1226	23	that	that	SCONJ
ejpam-1372	1226	24	although	although	SCONJ
ejpam-1372	1226	25	euler	euler	NOUN
ejpam-1372	1226	26	was	be	AUX
ejpam-1372	1226	27	unsure	unsure	ADJ
ejpam-1372	1226	28	about	about	ADP
ejpam-1372	1226	29	calling	call	VERB
ejpam-1372	1226	30	the	the	DET
ejpam-1372	1226	31	limit	limit	NOUN
ejpam-1372	1226	32	value	value	NOUN
ejpam-1372	1226	33	a	a	DET
ejpam-1372	1226	34	sum	sum	NOUN
ejpam-1372	1226	35	,	,	PUNCT
ejpam-1372	1226	36	he	he	PRON
ejpam-1372	1226	37	was	be	AUX
ejpam-1372	1226	38	unable	unable	ADJ
ejpam-1372	1226	39	to	to	PART
ejpam-1372	1226	40	appreciate	appreciate	VERB
ejpam-1372	1226	41	just	just	ADV
ejpam-1372	1226	42	how	how	SCONJ
ejpam-1372	1226	43	subtle	subtle	ADJ
ejpam-1372	1226	44	divergent	divergent	ADJ
ejpam-1372	1226	45	series	series	NOUN
ejpam-1372	1226	46	are	be	AUX
ejpam-1372	1226	47	.	.	PUNCT
ejpam-1372	1227	1	yet	yet	ADV
ejpam-1372	1227	2	in	in	ADP
ejpam-1372	1227	3	this	this	DET
ejpam-1372	1227	4	article	article	NOUN
ejpam-1372	1227	5	we	we	PRON
ejpam-1372	1227	6	have	have	AUX
ejpam-1372	1227	7	seen	see	VERB
ejpam-1372	1227	8	the	the	DET
ejpam-1372	1227	9	opposite	opposite	ADJ
ejpam-1372	1227	10	,	,	PUNCT
ejpam-1372	1227	11	namely	namely	ADV
ejpam-1372	1227	12	that	that	DET
ejpam-1372	1227	13	euler	euler	NOUN
ejpam-1372	1227	14	’s	’s	PART
ejpam-1372	1227	15	views	view	NOUN
ejpam-1372	1227	16	are	be	AUX
ejpam-1372	1227	17	indeed	indeed	ADV
ejpam-1372	1227	18	valid	valid	ADJ
ejpam-1372	1227	19	and	and	CCONJ
ejpam-1372	1227	20	that	that	SCONJ
ejpam-1372	1227	21	the	the	DET
ejpam-1372	1227	22	current	current	ADJ
ejpam-1372	1227	23	dogma	dogma	NOUN
ejpam-1372	1227	24	is	be	AUX
ejpam-1372	1227	25	,	,	PUNCT
ejpam-1372	1227	26	therefore	therefore	ADV
ejpam-1372	1227	27	,	,	PUNCT
ejpam-1372	1227	28	misguided	misguided	ADJ
ejpam-1372	1227	29	.	.	PUNCT
ejpam-1372	1228	1	the	the	DET
ejpam-1372	1228	2	concept	concept	NOUN
ejpam-1372	1228	3	that	that	PRON
ejpam-1372	1228	4	euler	euler	NOUN
ejpam-1372	1228	5	seems	seem	VERB
ejpam-1372	1228	6	to	to	PART
ejpam-1372	1228	7	have	have	AUX
ejpam-1372	1228	8	missed	miss	VERB
ejpam-1372	1228	9	or	or	CCONJ
ejpam-1372	1228	10	not	not	PART
ejpam-1372	1228	11	been	be	AUX
ejpam-1372	1228	12	aware	aware	ADJ
ejpam-1372	1228	13	of	of	ADP
ejpam-1372	1228	14	is	be	AUX
ejpam-1372	1228	15	regularisation	regularisation	NOUN
ejpam-1372	1228	16	.	.	PUNCT
ejpam-1372	1229	1	even	even	ADV
ejpam-1372	1229	2	here	here	ADV
ejpam-1372	1229	3	the	the	DET
ejpam-1372	1229	4	situation	situation	NOUN
ejpam-1372	1229	5	is	be	AUX
ejpam-1372	1229	6	uncanny	uncanny	ADJ
ejpam-1372	1229	7	because	because	SCONJ
ejpam-1372	1229	8	he	he	PRON
ejpam-1372	1229	9	was	be	AUX
ejpam-1372	1229	10	the	the	DET
ejpam-1372	1229	11	first	first	ADJ
ejpam-1372	1229	12	mathematician	mathematician	NOUN
ejpam-1372	1229	13	to	to	PART
ejpam-1372	1229	14	uncover	uncover	VERB
ejpam-1372	1229	15	the	the	DET
ejpam-1372	1229	16	concept	concept	NOUN
ejpam-1372	1229	17	in	in	ADP
ejpam-1372	1229	18	the	the	DET
ejpam-1372	1229	19	course	course	NOUN
ejpam-1372	1229	20	of	of	ADP
ejpam-1372	1229	21	calculating	calculate	VERB
ejpam-1372	1229	22	the	the	DET
ejpam-1372	1229	23	constant	constant	ADJ
ejpam-1372	1229	24	that	that	SCONJ
ejpam-1372	1229	25	now	now	ADV
ejpam-1372	1229	26	bears	bear	VERB
ejpam-1372	1229	27	his	his	PRON
ejpam-1372	1229	28	name	name	NOUN
ejpam-1372	1229	29	from	from	ADP
ejpam-1372	1229	30	the	the	DET
ejpam-1372	1229	31	logarithmically	logarithmically	ADV
ejpam-1372	1229	32	divergent	divergent	ADJ
ejpam-1372	1229	33	harmonic	harmonic	ADJ
ejpam-1372	1229	34	series	series	NOUN
ejpam-1372	1229	35	[	[	X
ejpam-1372	1229	36	13	13	NUM
ejpam-1372	1229	37	]	]	PUNCT
ejpam-1372	1229	38	.	.	PUNCT
ejpam-1372	1230	1	nevertheless	nevertheless	ADV
ejpam-1372	1230	2	,	,	PUNCT
ejpam-1372	1230	3	it	it	PRON
ejpam-1372	1230	4	is	be	AUX
ejpam-1372	1230	5	true	true	ADJ
ejpam-1372	1230	6	that	that	SCONJ
ejpam-1372	1230	7	like	like	INTJ
ejpam-1372	1230	8	so	so	ADV
ejpam-1372	1230	9	many	many	ADJ
ejpam-1372	1230	10	others	other	NOUN
ejpam-1372	1230	11	after	after	ADP
ejpam-1372	1230	12	him	he	PRON
ejpam-1372	1230	13	he	he	PRON
ejpam-1372	1230	14	did	do	AUX
ejpam-1372	1230	15	not	not	PART
ejpam-1372	1230	16	apply	apply	VERB
ejpam-1372	1230	17	the	the	DET
ejpam-1372	1230	18	concept	concept	NOUN
ejpam-1372	1230	19	to	to	ADP
ejpam-1372	1230	20	more	more	ADV
ejpam-1372	1230	21	complicated	complicated	ADJ
ejpam-1372	1230	22	divergent	divergent	ADJ
ejpam-1372	1230	23	series	series	NOUN
ejpam-1372	1230	24	,	,	PUNCT
ejpam-1372	1230	25	particularly	particularly	ADV
ejpam-1372	1230	26	those	those	PRON
ejpam-1372	1230	27	appearing	appear	VERB
ejpam-1372	1230	28	in	in	ADP
ejpam-1372	1230	29	asymptotic	asymptotic	ADJ
ejpam-1372	1230	30	expansions	expansion	NOUN
ejpam-1372	1230	31	.	.	PUNCT
ejpam-1372	1231	1	in	in	ADP
ejpam-1372	1231	2	short	short	ADJ
ejpam-1372	1231	3	,	,	PUNCT
ejpam-1372	1231	4	the	the	DET
ejpam-1372	1231	5	concept	concept	NOUN
ejpam-1372	1231	6	was	be	AUX
ejpam-1372	1231	7	left	leave	VERB
ejpam-1372	1231	8	for	for	SCONJ
ejpam-1372	1231	9	others	other	NOUN
ejpam-1372	1231	10	to	to	PART
ejpam-1372	1231	11	enunciate	enunciate	VERB
ejpam-1372	1231	12	.	.	PUNCT
ejpam-1372	1232	1	instead	instead	ADV
ejpam-1372	1232	2	of	of	ADP
ejpam-1372	1232	3	referring	refer	VERB
ejpam-1372	1232	4	to	to	ADP
ejpam-1372	1232	5	a	a	DET
ejpam-1372	1232	6	limit	limit	NOUN
ejpam-1372	1232	7	sum	sum	NOUN
ejpam-1372	1232	8	for	for	ADP
ejpam-1372	1232	9	a	a	DET
ejpam-1372	1232	10	divergent	divergent	ADJ
ejpam-1372	1232	11	series	series	NOUN
ejpam-1372	1232	12	,	,	PUNCT
ejpam-1372	1232	13	we	we	PRON
ejpam-1372	1232	14	now	now	ADV
ejpam-1372	1232	15	refer	refer	VERB
ejpam-1372	1232	16	to	to	ADP
ejpam-1372	1232	17	a	a	DET
ejpam-1372	1232	18	regularised	regularise	VERB
ejpam-1372	1232	19	value	value	NOUN
ejpam-1372	1232	20	,	,	PUNCT
ejpam-1372	1232	21	which	which	PRON
ejpam-1372	1232	22	is	be	AUX
ejpam-1372	1232	23	defined	define	VERB
ejpam-1372	1232	24	as	as	ADP
ejpam-1372	1232	25	the	the	DET
ejpam-1372	1232	26	removal	removal	NOUN
ejpam-1372	1232	27	of	of	ADP
ejpam-1372	1232	28	the	the	DET
ejpam-1372	1232	29	infinity	infinity	NOUN
ejpam-1372	1232	30	in	in	ADP
ejpam-1372	1232	31	the	the	DET
ejpam-1372	1232	32	remainder	remainder	NOUN
ejpam-1372	1232	33	so	so	SCONJ
ejpam-1372	1232	34	as	as	SCONJ
ejpam-1372	1232	35	to	to	PART
ejpam-1372	1232	36	make	make	VERB
ejpam-1372	1232	37	the	the	DET
ejpam-1372	1232	38	entire	entire	ADJ
ejpam-1372	1232	39	series	series	NOUN
ejpam-1372	1232	40	summable	summable	ADJ
ejpam-1372	1232	41	.	.	PUNCT
ejpam-1372	1233	1	on	on	ADP
ejpam-1372	1233	2	its	its	PRON
ejpam-1372	1233	3	own	own	ADJ
ejpam-1372	1233	4	,	,	PUNCT
ejpam-1372	1233	5	regularisation	regularisation	NOUN
ejpam-1372	1233	6	represents	represent	VERB
ejpam-1372	1233	7	a	a	DET
ejpam-1372	1233	8	mathematical	mathematical	ADJ
ejpam-1372	1233	9	abstraction	abstraction	NOUN
ejpam-1372	1233	10	,	,	PUNCT
ejpam-1372	1233	11	but	but	CCONJ
ejpam-1372	1233	12	it	it	PRON
ejpam-1372	1233	13	is	be	AUX
ejpam-1372	1233	14	necessary	necessary	ADJ
ejpam-1372	1233	15	in	in	ADP
ejpam-1372	1233	16	asymptotics	asymptotic	NOUN
ejpam-1372	1233	17	for	for	ADP
ejpam-1372	1233	18	correcting	correct	VERB
ejpam-1372	1233	19	the	the	DET
ejpam-1372	1233	20	improprieties	impropriety	NOUN
ejpam-1372	1233	21	due	due	ADP
ejpam-1372	1233	22	to	to	ADP
ejpam-1372	1233	23	the	the	DET
ejpam-1372	1233	24	various	various	ADJ
ejpam-1372	1233	25	asymptotic	asymptotic	ADJ
ejpam-1372	1233	26	methods	method	NOUN
ejpam-1372	1233	27	that	that	PRON
ejpam-1372	1233	28	are	be	AUX
ejpam-1372	1233	29	used	use	VERB
ejpam-1372	1233	30	to	to	PART
ejpam-1372	1233	31	derive	derive	VERB
ejpam-1372	1233	32	asymptotic	asymptotic	ADJ
ejpam-1372	1233	33	power	power	NOUN
ejpam-1372	1233	34	series	series	NOUN
ejpam-1372	1233	35	expansions	expansion	NOUN
ejpam-1372	1233	36	from	from	ADP
ejpam-1372	1233	37	their	their	PRON
ejpam-1372	1233	38	original	original	ADJ
ejpam-1372	1233	39	functions	function	NOUN
ejpam-1372	1233	40	or	or	CCONJ
ejpam-1372	1233	41	integrals	integral	NOUN
ejpam-1372	1233	42	.	.	PUNCT
ejpam-1372	1234	1	from	from	ADP
ejpam-1372	1234	2	the	the	DET
ejpam-1372	1234	3	material	material	NOUN
ejpam-1372	1234	4	presented	present	VERB
ejpam-1372	1234	5	in	in	ADP
ejpam-1372	1234	6	this	this	DET
ejpam-1372	1234	7	article	article	NOUN
ejpam-1372	1234	8	,	,	PUNCT
ejpam-1372	1234	9	it	it	PRON
ejpam-1372	1234	10	is	be	AUX
ejpam-1372	1234	11	obvious	obvious	ADJ
ejpam-1372	1234	12	that	that	SCONJ
ejpam-1372	1234	13	euler	euler	NOUN
ejpam-1372	1234	14	was	be	AUX
ejpam-1372	1234	15	clearly	clearly	ADV
ejpam-1372	1234	16	well	well	ADV
ejpam-1372	1234	17	ahead	ahead	ADV
ejpam-1372	1234	18	of	of	ADP
ejpam-1372	1234	19	his	his	PRON
ejpam-1372	1234	20	time	time	NOUN
ejpam-1372	1234	21	,	,	PUNCT
ejpam-1372	1234	22	whilst	whilst	SCONJ
ejpam-1372	1234	23	those	those	PRON
ejpam-1372	1234	24	following	follow	VERB
ejpam-1372	1234	25	him	he	PRON
ejpam-1372	1234	26	such	such	ADJ
ejpam-1372	1234	27	as	as	ADP
ejpam-1372	1234	28	abel	abel	PROPN
ejpam-1372	1234	29	and	and	CCONJ
ejpam-1372	1234	30	cauchy	cauchy	PROPN
ejpam-1372	1234	31	were	be	AUX
ejpam-1372	1234	32	simply	simply	ADV
ejpam-1372	1234	33	wrong	wrong	ADJ
ejpam-1372	1234	34	to	to	PART
ejpam-1372	1234	35	ridicule	ridicule	VERB
ejpam-1372	1234	36	his	his	PRON
ejpam-1372	1234	37	views	view	NOUN
ejpam-1372	1234	38	on	on	ADP
ejpam-1372	1234	39	divergent	divergent	ADJ
ejpam-1372	1234	40	series	series	NOUN
ejpam-1372	1234	41	.	.	PUNCT
ejpam-1372	1235	1	unfortunately	unfortunately	ADV
ejpam-1372	1235	2	,	,	PUNCT
ejpam-1372	1235	3	because	because	SCONJ
ejpam-1372	1235	4	their	their	PRON
ejpam-1372	1235	5	attitudes	attitude	NOUN
ejpam-1372	1235	6	prevailed	prevail	VERB
ejpam-1372	1235	7	,	,	PUNCT
ejpam-1372	1235	8	weierstrass	weierstrass	VERB
ejpam-1372	1235	9	only	only	ADV
ejpam-1372	1235	10	concentrated	concentrate	VERB
ejpam-1372	1235	11	upon	upon	SCONJ
ejpam-1372	1235	12	convergence	convergence	NOUN
ejpam-1372	1235	13	when	when	SCONJ
ejpam-1372	1235	14	laying	lay	VERB
ejpam-1372	1235	15	down	down	ADP
ejpam-1372	1235	16	the	the	DET
ejpam-1372	1235	17	foundations	foundation	NOUN
ejpam-1372	1235	18	of	of	ADP
ejpam-1372	1235	19	classical	classical	ADJ
ejpam-1372	1235	20	analysis	analysis	NOUN
ejpam-1372	1235	21	.	.	PUNCT
ejpam-1372	1236	1	consequently	consequently	ADV
ejpam-1372	1236	2	,	,	PUNCT
ejpam-1372	1236	3	a	a	DET
ejpam-1372	1236	4	vast	vast	ADJ
ejpam-1372	1236	5	and	and	CCONJ
ejpam-1372	1236	6	important	important	ADJ
ejpam-1372	1236	7	frontier	frontier	NOUN
ejpam-1372	1236	8	in	in	ADP
ejpam-1372	1236	9	mathematics	mathematic	NOUN
ejpam-1372	1236	10	was	be	AUX
ejpam-1372	1236	11	largely	largely	ADV
ejpam-1372	1236	12	ignored	ignore	VERB
ejpam-1372	1236	13	for	for	ADP
ejpam-1372	1236	14	about	about	ADV
ejpam-1372	1236	15	a	a	PRON
ejpam-1372	1236	16	century	century	NOUN
ejpam-1372	1236	17	.	.	PUNCT
ejpam-1372	1237	1	today	today	NOUN
ejpam-1372	1237	2	,	,	PUNCT
ejpam-1372	1237	3	understanding	understand	VERB
ejpam-1372	1237	4	divergent	divergent	ADJ
ejpam-1372	1237	5	series	series	NOUN
ejpam-1372	1237	6	and	and	CCONJ
ejpam-1372	1237	7	developing	develop	VERB
ejpam-1372	1237	8	techniques	technique	NOUN
ejpam-1372	1237	9	for	for	ADP
ejpam-1372	1237	10	obtaining	obtain	VERB
ejpam-1372	1237	11	meaningful	meaningful	ADJ
ejpam-1372	1237	12	values	value	NOUN
ejpam-1372	1237	13	from	from	ADP
ejpam-1372	1237	14	them	they	PRON
ejpam-1372	1237	15	have	have	AUX
ejpam-1372	1237	16	become	become	VERB
ejpam-1372	1237	17	a	a	DET
ejpam-1372	1237	18	top	top	ADJ
ejpam-1372	1237	19	priority	priority	NOUN
ejpam-1372	1237	20	in	in	ADP
ejpam-1372	1237	21	mathematics	mathematic	NOUN
ejpam-1372	1237	22	because	because	SCONJ
ejpam-1372	1237	23	in	in	ADP
ejpam-1372	1237	24	general	general	ADJ
ejpam-1372	1237	25	,	,	PUNCT
ejpam-1372	1237	26	the	the	DET
ejpam-1372	1237	27	most	most	ADV
ejpam-1372	1237	28	important	important	ADJ
ejpam-1372	1237	29	and	and	CCONJ
ejpam-1372	1237	30	difficult	difficult	ADJ
ejpam-1372	1237	31	problems	problem	NOUN
ejpam-1372	1237	32	in	in	ADP
ejpam-1372	1237	33	applied	applied	ADJ
ejpam-1372	1237	34	mathematics	mathematic	NOUN
ejpam-1372	1237	35	and	and	CCONJ
ejpam-1372	1237	36	modern	modern	ADJ
ejpam-1372	1237	37	theoretical	theoretical	ADJ
ejpam-1372	1237	38	physics	physics	NOUN
ejpam-1372	1237	39	are	be	AUX
ejpam-1372	1237	40	either	either	CCONJ
ejpam-1372	1237	41	asymptotic	asymptotic	ADJ
ejpam-1372	1237	42	or	or	CCONJ
ejpam-1372	1237	43	divergent	divergent	ADJ
ejpam-1372	1237	44	in	in	ADP
ejpam-1372	1237	45	nature	nature	NOUN
ejpam-1372	1237	46	.	.	PUNCT
ejpam-1372	1238	1	the	the	DET
ejpam-1372	1238	2	indifference	indifference	NOUN
ejpam-1372	1238	3	towards	towards	ADP
ejpam-1372	1238	4	divergent	divergent	ADJ
ejpam-1372	1238	5	series	series	NOUN
ejpam-1372	1238	6	in	in	ADP
ejpam-1372	1238	7	the	the	DET
ejpam-1372	1238	8	nineteenth	nineteenth	ADJ
ejpam-1372	1238	9	century	century	NOUN
ejpam-1372	1238	10	was	be	AUX
ejpam-1372	1238	11	also	also	ADV
ejpam-1372	1238	12	responsible	responsible	ADJ
ejpam-1372	1238	13	for	for	ADP
ejpam-1372	1238	14	the	the	DET
ejpam-1372	1238	15	limited	limited	ADJ
ejpam-1372	1238	16	and	and	CCONJ
ejpam-1372	1238	17	inadequate	inadequate	ADJ
ejpam-1372	1238	18	poincaré	poincaré	ADJ
ejpam-1372	1238	19	prescription	prescription	NOUN
ejpam-1372	1238	20	or	or	CCONJ
ejpam-1372	1238	21	definition	definition	NOUN
ejpam-1372	1238	22	being	be	AUX
ejpam-1372	1238	23	applied	apply	VERB
ejpam-1372	1238	24	universally	universally	ADV
ejpam-1372	1238	25	in	in	ADP
ejpam-1372	1238	26	asymptotics	asymptotic	NOUN
ejpam-1372	1238	27	.	.	PUNCT
ejpam-1372	1239	1	over	over	ADP
ejpam-1372	1239	2	the	the	DET
ejpam-1372	1239	3	past	past	ADJ
ejpam-1372	1239	4	two	two	NUM
ejpam-1372	1239	5	decades	decade	NOUN
ejpam-1372	1239	6	the	the	DET
ejpam-1372	1239	7	subject	subject	NOUN
ejpam-1372	1239	8	of	of	ADP
ejpam-1372	1239	9	asymptotics	asymptotic	NOUN
ejpam-1372	1239	10	beyond	beyond	ADP
ejpam-1372	1239	11	all	all	DET
ejpam-1372	1239	12	orders	order	NOUN
ejpam-1372	1239	13	or	or	CCONJ
ejpam-1372	1239	14	exponential	exponential	ADJ
ejpam-1372	1239	15	asymptotics	asymptotic	NOUN
ejpam-1372	1239	16	[	[	X
ejpam-1372	1239	17	4	4	NUM
ejpam-1372	1239	18	,	,	PUNCT
ejpam-1372	1239	19	5	5	NUM
ejpam-1372	1239	20	,	,	PUNCT
ejpam-1372	1239	21	21	21	NUM
ejpam-1372	1239	22	,	,	PUNCT
ejpam-1372	1239	23	27	27	NUM
ejpam-1372	1239	24	,	,	PUNCT
ejpam-1372	1239	25	29	29	NUM
ejpam-1372	1239	26	]	]	PUNCT
ejpam-1372	1239	27	has	have	AUX
ejpam-1372	1239	28	evolved	evolve	VERB
ejpam-1372	1239	29	with	with	ADP
ejpam-1372	1239	30	researchers	researcher	NOUN
ejpam-1372	1239	31	actively	actively	ADV
ejpam-1372	1239	32	engaged	engage	VERB
ejpam-1372	1239	33	in	in	ADP
ejpam-1372	1239	34	references	reference	NOUN
ejpam-1372	1239	35	415	415	NUM
ejpam-1372	1239	36	the	the	DET
ejpam-1372	1239	37	derivation	derivation	NOUN
ejpam-1372	1239	38	and	and	CCONJ
ejpam-1372	1239	39	formulation	formulation	NOUN
ejpam-1372	1239	40	of	of	ADP
ejpam-1372	1239	41	methods	method	NOUN
ejpam-1372	1239	42	aimed	aim	VERB
ejpam-1372	1239	43	at	at	ADP
ejpam-1372	1239	44	isolating	isolate	VERB
ejpam-1372	1239	45	subdominant	subdominant	ADJ
ejpam-1372	1239	46	exponential	exponential	ADJ
ejpam-1372	1239	47	terms	term	NOUN
ejpam-1372	1239	48	in	in	ADP
ejpam-1372	1239	49	asymptotic	asymptotic	ADJ
ejpam-1372	1239	50	expansions	expansion	NOUN
ejpam-1372	1239	51	.	.	PUNCT
ejpam-1372	1240	1	for	for	ADP
ejpam-1372	1240	2	these	these	DET
ejpam-1372	1240	3	problems	problem	NOUN
ejpam-1372	1240	4	the	the	DET
ejpam-1372	1240	5	poincaré	poincaré	ADJ
ejpam-1372	1240	6	prescription	prescription	NOUN
ejpam-1372	1240	7	is	be	AUX
ejpam-1372	1240	8	basically	basically	ADV
ejpam-1372	1240	9	useless	useless	ADJ
ejpam-1372	1240	10	,	,	PUNCT
ejpam-1372	1240	11	but	but	CCONJ
ejpam-1372	1240	12	in	in	ADP
ejpam-1372	1240	13	order	order	NOUN
ejpam-1372	1240	14	to	to	PART
ejpam-1372	1240	15	obtain	obtain	VERB
ejpam-1372	1240	16	meaningful	meaningful	ADJ
ejpam-1372	1240	17	numerical	numerical	ADJ
ejpam-1372	1240	18	values	value	NOUN
ejpam-1372	1240	19	for	for	ADP
ejpam-1372	1240	20	these	these	DET
ejpam-1372	1240	21	terms	term	NOUN
ejpam-1372	1240	22	,	,	PUNCT
ejpam-1372	1240	23	which	which	PRON
ejpam-1372	1240	24	become	become	VERB
ejpam-1372	1240	25	dominant	dominant	ADJ
ejpam-1372	1240	26	with	with	ADP
ejpam-1372	1240	27	further	further	ADJ
ejpam-1372	1240	28	movement	movement	NOUN
ejpam-1372	1240	29	in	in	ADP
ejpam-1372	1240	30	the	the	DET
ejpam-1372	1240	31	complex	complex	ADJ
ejpam-1372	1240	32	plane	plane	NOUN
ejpam-1372	1240	33	,	,	PUNCT
ejpam-1372	1240	34	again	again	ADV
ejpam-1372	1240	35	a	a	DET
ejpam-1372	1240	36	theory	theory	NOUN
ejpam-1372	1240	37	of	of	ADP
ejpam-1372	1240	38	divergent	divergent	ADJ
ejpam-1372	1240	39	series	series	NOUN
ejpam-1372	1240	40	is	be	AUX
ejpam-1372	1240	41	required	require	VERB
ejpam-1372	1240	42	as	as	SCONJ
ejpam-1372	1240	43	can	can	AUX
ejpam-1372	1240	44	be	be	AUX
ejpam-1372	1240	45	seen	see	VERB
ejpam-1372	1240	46	by	by	ADP
ejpam-1372	1240	47	the	the	DET
ejpam-1372	1240	48	subdominant	subdominant	ADJ
ejpam-1372	1240	49	series	series	NOUN
ejpam-1372	1240	50	appearing	appear	VERB
ejpam-1372	1240	51	in	in	ADP
ejpam-1372	1240	52	eq	eq	ADP
ejpam-1372	1240	53	.	.	PUNCT
ejpam-1372	1241	1	(	(	PUNCT
ejpam-1372	1241	2	7	7	NUM
ejpam-1372	1241	3	)	)	PUNCT
ejpam-1372	1241	4	.	.	PUNCT
ejpam-1372	1242	1	although	although	SCONJ
ejpam-1372	1242	2	this	this	DET
ejpam-1372	1242	3	article	article	NOUN
ejpam-1372	1242	4	has	have	AUX
ejpam-1372	1242	5	described	describe	VERB
ejpam-1372	1242	6	the	the	DET
ejpam-1372	1242	7	initial	initial	ADJ
ejpam-1372	1242	8	steps	step	NOUN
ejpam-1372	1242	9	and	and	CCONJ
ejpam-1372	1242	10	presented	present	VERB
ejpam-1372	1242	11	many	many	ADJ
ejpam-1372	1242	12	examples	example	NOUN
ejpam-1372	1242	13	for	for	ADP
ejpam-1372	1242	14	developing	develop	VERB
ejpam-1372	1242	15	a	a	DET
ejpam-1372	1242	16	fully	fully	ADV
ejpam-1372	1242	17	-	-	PUNCT
ejpam-1372	1242	18	fledged	fledge	VERB
ejpam-1372	1242	19	theory	theory	NOUN
ejpam-1372	1242	20	of	of	ADP
ejpam-1372	1242	21	divergent	divergent	ADJ
ejpam-1372	1242	22	series	series	NOUN
ejpam-1372	1242	23	,	,	PUNCT
ejpam-1372	1242	24	more	more	ADV
ejpam-1372	1242	25	complicated	complicated	ADJ
ejpam-1372	1242	26	examples	example	NOUN
ejpam-1372	1242	27	will	will	AUX
ejpam-1372	1242	28	need	need	VERB
ejpam-1372	1242	29	to	to	PART
ejpam-1372	1242	30	be	be	AUX
ejpam-1372	1242	31	studied	study	VERB
ejpam-1372	1242	32	in	in	ADP
ejpam-1372	1242	33	the	the	DET
ejpam-1372	1242	34	future	future	NOUN
ejpam-1372	1242	35	before	before	SCONJ
ejpam-1372	1242	36	such	such	DET
ejpam-1372	1242	37	a	a	DET
ejpam-1372	1242	38	theory	theory	NOUN
ejpam-1372	1242	39	can	can	AUX
ejpam-1372	1242	40	be	be	AUX
ejpam-1372	1242	41	realised	realise	VERB
ejpam-1372	1242	42	.	.	PUNCT
ejpam-1372	1243	1	for	for	ADP
ejpam-1372	1243	2	example	example	NOUN
ejpam-1372	1243	3	,	,	PUNCT
ejpam-1372	1243	4	extending	extend	VERB
ejpam-1372	1243	5	the	the	DET
ejpam-1372	1243	6	asymptotics	asymptotic	NOUN
ejpam-1372	1243	7	of	of	ADP
ejpam-1372	1243	8	the	the	DET
ejpam-1372	1243	9	gamma	gamma	NOUN
ejpam-1372	1243	10	function	function	NOUN
ejpam-1372	1243	11	to	to	ADP
ejpam-1372	1243	12	the	the	DET
ejpam-1372	1243	13	entire	entire	ADJ
ejpam-1372	1243	14	complex	complex	ADJ
ejpam-1372	1243	15	plane	plane	NOUN
ejpam-1372	1243	16	involves	involve	VERB
ejpam-1372	1243	17	further	further	ADJ
ejpam-1372	1243	18	development	development	NOUN
ejpam-1372	1243	19	of	of	ADP
ejpam-1372	1243	20	the	the	DET
ejpam-1372	1243	21	material	material	NOUN
ejpam-1372	1243	22	presented	present	VERB
ejpam-1372	1243	23	here	here	ADV
ejpam-1372	1243	24	so	so	SCONJ
ejpam-1372	1243	25	that	that	SCONJ
ejpam-1372	1243	26	an	an	DET
ejpam-1372	1243	27	infinite	infinite	ADJ
ejpam-1372	1243	28	number	number	NOUN
ejpam-1372	1243	29	of	of	ADP
ejpam-1372	1243	30	singularities	singularity	NOUN
ejpam-1372	1243	31	situated	situate	VERB
ejpam-1372	1243	32	on	on	ADP
ejpam-1372	1243	33	stokes	stoke	NOUN
ejpam-1372	1243	34	lines	line	NOUN
ejpam-1372	1243	35	can	can	AUX
ejpam-1372	1243	36	be	be	AUX
ejpam-1372	1243	37	handled	handle	VERB
ejpam-1372	1243	38	rather	rather	ADV
ejpam-1372	1243	39	than	than	ADP
ejpam-1372	1243	40	a	a	DET
ejpam-1372	1243	41	single	single	ADJ
ejpam-1372	1243	42	singularity	singularity	NOUN
ejpam-1372	1243	43	.	.	PUNCT
ejpam-1372	1244	1	another	another	DET
ejpam-1372	1244	2	problem	problem	NOUN
ejpam-1372	1244	3	is	be	AUX
ejpam-1372	1244	4	whether	whether	SCONJ
ejpam-1372	1244	5	the	the	DET
ejpam-1372	1244	6	techniques	technique	NOUN
ejpam-1372	1244	7	of	of	ADP
ejpam-1372	1244	8	borel	borel	PROPN
ejpam-1372	1244	9	summation	summation	NOUN
ejpam-1372	1244	10	and	and	CCONJ
ejpam-1372	1244	11	mb	mb	ADP
ejpam-1372	1244	12	regularisation	regularisation	NOUN
ejpam-1372	1244	13	can	can	AUX
ejpam-1372	1244	14	be	be	AUX
ejpam-1372	1244	15	used	use	VERB
ejpam-1372	1244	16	to	to	PART
ejpam-1372	1244	17	develop	develop	VERB
ejpam-1372	1244	18	the	the	DET
ejpam-1372	1244	19	complete	complete	ADJ
ejpam-1372	1244	20	asymptotic	asymptotic	ADJ
ejpam-1372	1244	21	forms	form	NOUN
ejpam-1372	1244	22	for	for	ADP
ejpam-1372	1244	23	the	the	DET
ejpam-1372	1244	24	confluent	confluent	ADJ
ejpam-1372	1244	25	hypergeometric	hypergeometric	ADJ
ejpam-1372	1244	26	functions	function	NOUN
ejpam-1372	1244	27	throughout	throughout	ADP
ejpam-1372	1244	28	the	the	DET
ejpam-1372	1244	29	entire	entire	ADJ
ejpam-1372	1244	30	complex	complex	ADJ
ejpam-1372	1244	31	plane	plane	NOUN
ejpam-1372	1244	32	.	.	PUNCT
ejpam-1372	1245	1	the	the	DET
ejpam-1372	1245	2	subdominant	subdominant	ADJ
ejpam-1372	1245	3	terms	term	NOUN
ejpam-1372	1245	4	in	in	ADP
ejpam-1372	1245	5	these	these	DET
ejpam-1372	1245	6	expansions	expansion	NOUN
ejpam-1372	1245	7	are	be	AUX
ejpam-1372	1245	8	expected	expect	VERB
ejpam-1372	1245	9	to	to	PART
ejpam-1372	1245	10	become	become	VERB
ejpam-1372	1245	11	divergent	divergent	ADJ
ejpam-1372	1245	12	series	series	NOUN
ejpam-1372	1245	13	similar	similar	ADJ
ejpam-1372	1245	14	in	in	ADP
ejpam-1372	1245	15	form	form	NOUN
ejpam-1372	1245	16	to	to	ADP
ejpam-1372	1245	17	t	t	PROPN
ejpam-1372	1245	18	k	k	PROPN
ejpam-1372	1245	19	3	3	NUM
ejpam-1372	1245	20	(	(	PUNCT
ejpam-1372	1245	21	a	a	NOUN
ejpam-1372	1245	22	)	)	PUNCT
ejpam-1372	1245	23	in	in	ADP
ejpam-1372	1245	24	eq	eq	ADP
ejpam-1372	1245	25	.	.	PUNCT
ejpam-1372	1246	1	(	(	PUNCT
ejpam-1372	1246	2	7	7	NUM
ejpam-1372	1246	3	)	)	PUNCT
ejpam-1372	1246	4	.	.	PUNCT
ejpam-1372	1247	1	whilst	whilst	SCONJ
ejpam-1372	1247	2	such	such	ADJ
ejpam-1372	1247	3	series	series	NOUN
ejpam-1372	1247	4	are	be	AUX
ejpam-1372	1247	5	not	not	PART
ejpam-1372	1247	6	expected	expect	VERB
ejpam-1372	1247	7	to	to	PART
ejpam-1372	1247	8	pose	pose	VERB
ejpam-1372	1247	9	a	a	DET
ejpam-1372	1247	10	problem	problem	NOUN
ejpam-1372	1247	11	for	for	ADP
ejpam-1372	1247	12	mb	mb	ADP
ejpam-1372	1247	13	regularisation	regularisation	NOUN
ejpam-1372	1247	14	as	as	ADP
ejpam-1372	1247	15	a	a	DET
ejpam-1372	1247	16	result	result	NOUN
ejpam-1372	1247	17	of	of	ADP
ejpam-1372	1247	18	the	the	DET
ejpam-1372	1247	19	numerical	numerical	ADJ
ejpam-1372	1247	20	study	study	NOUN
ejpam-1372	1247	21	in	in	ADP
ejpam-1372	1247	22	ref	ref	NOUN
ejpam-1372	1247	23	.	.	PUNCT
ejpam-1372	1248	1	[	[	X
ejpam-1372	1248	2	21	21	NUM
ejpam-1372	1248	3	]	]	PUNCT
ejpam-1372	1248	4	,	,	PUNCT
ejpam-1372	1248	5	the	the	DET
ejpam-1372	1248	6	question	question	NOUN
ejpam-1372	1248	7	is	be	AUX
ejpam-1372	1248	8	whether	whether	SCONJ
ejpam-1372	1248	9	borel	borel	PROPN
ejpam-1372	1248	10	summation	summation	NOUN
ejpam-1372	1248	11	can	can	AUX
ejpam-1372	1248	12	be	be	AUX
ejpam-1372	1248	13	extended	extend	VERB
ejpam-1372	1248	14	even	even	ADV
ejpam-1372	1248	15	further	far	ADV
ejpam-1372	1248	16	not	not	PART
ejpam-1372	1248	17	only	only	ADV
ejpam-1372	1248	18	to	to	PART
ejpam-1372	1248	19	produce	produce	VERB
ejpam-1372	1248	20	such	such	ADJ
ejpam-1372	1248	21	series	series	NOUN
ejpam-1372	1248	22	,	,	PUNCT
ejpam-1372	1248	23	but	but	CCONJ
ejpam-1372	1248	24	also	also	ADV
ejpam-1372	1248	25	to	to	PART
ejpam-1372	1248	26	handle	handle	VERB
ejpam-1372	1248	27	them	they	PRON
ejpam-1372	1248	28	.	.	PUNCT
ejpam-1372	1249	1	furthermore	furthermore	ADV
ejpam-1372	1249	2	,	,	PUNCT
ejpam-1372	1249	3	this	this	DET
ejpam-1372	1249	4	problem	problem	NOUN
ejpam-1372	1249	5	has	have	VERB
ejpam-1372	1249	6	the	the	DET
ejpam-1372	1249	7	advantage	advantage	NOUN
ejpam-1372	1249	8	that	that	PRON
ejpam-1372	1249	9	for	for	ADP
ejpam-1372	1249	10	particular	particular	ADJ
ejpam-1372	1249	11	values	value	NOUN
ejpam-1372	1249	12	of	of	ADP
ejpam-1372	1249	13	their	their	PRON
ejpam-1372	1249	14	parameters	parameter	NOUN
ejpam-1372	1249	15	the	the	DET
ejpam-1372	1249	16	confluent	confluent	ADJ
ejpam-1372	1249	17	hypergeometric	hypergeometric	ADJ
ejpam-1372	1249	18	functions	function	NOUN
ejpam-1372	1249	19	reduce	reduce	VERB
ejpam-1372	1249	20	to	to	ADP
ejpam-1372	1249	21	the	the	DET
ejpam-1372	1249	22	family	family	NOUN
ejpam-1372	1249	23	of	of	ADP
ejpam-1372	1249	24	bessel	bessel	NOUN
ejpam-1372	1249	25	and	and	CCONJ
ejpam-1372	1249	26	hankel	hankel	NOUN
ejpam-1372	1249	27	functions	function	NOUN
ejpam-1372	1249	28	.	.	PUNCT
ejpam-1372	1250	1	so	so	ADV
ejpam-1372	1250	2	far	far	ADV
ejpam-1372	1250	3	,	,	PUNCT
ejpam-1372	1250	4	mb	mb	ADP
ejpam-1372	1250	5	regularisation	regularisation	NOUN
ejpam-1372	1250	6	has	have	AUX
ejpam-1372	1250	7	only	only	ADV
ejpam-1372	1250	8	been	be	AUX
ejpam-1372	1250	9	applied	apply	VERB
ejpam-1372	1250	10	to	to	ADP
ejpam-1372	1250	11	positive	positive	ADJ
ejpam-1372	1250	12	real	real	ADJ
ejpam-1372	1250	13	values	value	NOUN
ejpam-1372	1250	14	of	of	ADP
ejpam-1372	1250	15	the	the	DET
ejpam-1372	1250	16	variable	variable	NOUN
ejpam-1372	1250	17	in	in	ADP
ejpam-1372	1250	18	the	the	DET
ejpam-1372	1250	19	asymptotic	asymptotic	ADJ
ejpam-1372	1250	20	expansions	expansion	NOUN
ejpam-1372	1250	21	of	of	ADP
ejpam-1372	1250	22	these	these	DET
ejpam-1372	1250	23	special	special	ADJ
ejpam-1372	1250	24	functions	function	NOUN
ejpam-1372	1250	25	[	[	X
ejpam-1372	1250	26	15	15	NUM
ejpam-1372	1250	27	]	]	PUNCT
ejpam-1372	1250	28	.	.	PUNCT
ejpam-1372	1251	1	nevertheless	nevertheless	ADV
ejpam-1372	1251	2	from	from	ADP
ejpam-1372	1251	3	the	the	DET
ejpam-1372	1251	4	material	material	NOUN
ejpam-1372	1251	5	presented	present	VERB
ejpam-1372	1251	6	in	in	ADP
ejpam-1372	1251	7	this	this	DET
ejpam-1372	1251	8	work	work	NOUN
ejpam-1372	1251	9	,	,	PUNCT
ejpam-1372	1251	10	we	we	PRON
ejpam-1372	1251	11	have	have	AUX
ejpam-1372	1251	12	seen	see	VERB
ejpam-1372	1251	13	that	that	DET
ejpam-1372	1251	14	euler	euler	VERB
ejpam-1372	1251	15	’s	’s	PART
ejpam-1372	1251	16	so	so	ADV
ejpam-1372	1251	17	-	-	PUNCT
ejpam-1372	1251	18	called	call	VERB
ejpam-1372	1251	19	unorthodox	unorthodox	ADJ
ejpam-1372	1251	20	views	view	NOUN
ejpam-1372	1251	21	on	on	ADP
ejpam-1372	1251	22	divergent	divergent	ADJ
ejpam-1372	1251	23	series	serie	NOUN
ejpam-1372	1251	24	hold	hold	VERB
ejpam-1372	1251	25	true	true	ADJ
ejpam-1372	1251	26	.	.	PUNCT
ejpam-1372	1252	1	with	with	SCONJ
ejpam-1372	1252	2	his	his	PRON
ejpam-1372	1252	3	reputation	reputation	NOUN
ejpam-1372	1252	4	restored	restore	VERB
ejpam-1372	1252	5	,	,	PUNCT
ejpam-1372	1252	6	perhaps	perhaps	ADV
ejpam-1372	1252	7	he	he	PRON
ejpam-1372	1252	8	can	can	AUX
ejpam-1372	1252	9	now	now	ADV
ejpam-1372	1252	10	be	be	AUX
ejpam-1372	1252	11	regarded	regard	VERB
ejpam-1372	1252	12	as	as	ADP
ejpam-1372	1252	13	the	the	DET
ejpam-1372	1252	14	greatest	great	ADJ
ejpam-1372	1252	15	of	of	ADP
ejpam-1372	1252	16	all	all	DET
ejpam-1372	1252	17	mathematicians	mathematician	NOUN
ejpam-1372	1252	18	.	.	PUNCT
ejpam-1372	1253	1	references	reference	NOUN
ejpam-1372	1253	2	[	[	X
ejpam-1372	1253	3	1	1	NUM
ejpam-1372	1253	4	]	]	PUNCT
ejpam-1372	1253	5	m	m	NOUN
ejpam-1372	1253	6	abramowitz	abramowitz	NOUN
ejpam-1372	1253	7	and	and	CCONJ
ejpam-1372	1253	8	i	i	PRON
ejpam-1372	1253	9	stegun	stegun	VERB
ejpam-1372	1253	10	,	,	PUNCT
ejpam-1372	1253	11	editors	editor	NOUN
ejpam-1372	1253	12	.	.	PUNCT
ejpam-1372	1254	1	handbook	handbook	NOUN
ejpam-1372	1254	2	of	of	ADP
ejpam-1372	1254	3	mathematical	mathematical	ADJ
ejpam-1372	1254	4	functions	function	NOUN
ejpam-1372	1254	5	.	.	PUNCT
ejpam-1372	1255	1	dover	dover	PROPN
ejpam-1372	1255	2	,	,	PUNCT
ejpam-1372	1255	3	new	new	PROPN
ejpam-1372	1255	4	york	york	PROPN
ejpam-1372	1255	5	,	,	PUNCT
ejpam-1372	1255	6	1970	1970	NUM
ejpam-1372	1255	7	.	.	PUNCT
ejpam-1372	1256	1	[	[	X
ejpam-1372	1256	2	2	2	X
ejpam-1372	1256	3	]	]	PUNCT
ejpam-1372	1256	4	a	a	DET
ejpam-1372	1256	5	apelblat	apelblat	NOUN
ejpam-1372	1256	6	.	.	PUNCT
ejpam-1372	1257	1	volterra	volterra	NOUN
ejpam-1372	1257	2	functions	function	NOUN
ejpam-1372	1257	3	.	.	PUNCT
ejpam-1372	1258	1	nova	nova	PROPN
ejpam-1372	1258	2	science	science	NOUN
ejpam-1372	1258	3	publishers	publisher	NOUN
ejpam-1372	1258	4	,	,	PUNCT
ejpam-1372	1258	5	new	new	PROPN
ejpam-1372	1258	6	york	york	PROPN
ejpam-1372	1258	7	,	,	PUNCT
ejpam-1372	1258	8	2008	2008	NUM
ejpam-1372	1258	9	.	.	PUNCT
ejpam-1372	1259	1	[	[	X
ejpam-1372	1259	2	3	3	X
ejpam-1372	1259	3	]	]	X
ejpam-1372	1259	4	p	p	X
ejpam-1372	1259	5	bakshi	bakshi	PROPN
ejpam-1372	1259	6	,	,	PUNCT
ejpam-1372	1259	7	r	r	NOUN
ejpam-1372	1259	8	cover	cover	NOUN
ejpam-1372	1259	9	,	,	PUNCT
ejpam-1372	1259	10	and	and	CCONJ
ejpam-1372	1259	11	g	g	PROPN
ejpam-1372	1259	12	kalman	kalman	PROPN
ejpam-1372	1259	13	.	.	PUNCT
ejpam-1372	1260	1	polarization	polarization	NOUN
ejpam-1372	1260	2	and	and	CCONJ
ejpam-1372	1260	3	electromagnetic	electromagnetic	ADJ
ejpam-1372	1260	4	properties	property	NOUN
ejpam-1372	1260	5	of	of	ADP
ejpam-1372	1260	6	the	the	DET
ejpam-1372	1260	7	vacuum	vacuum	NOUN
ejpam-1372	1260	8	in	in	ADP
ejpam-1372	1260	9	the	the	DET
ejpam-1372	1260	10	static	static	ADJ
ejpam-1372	1260	11	limit	limit	NOUN
ejpam-1372	1260	12	for	for	ADP
ejpam-1372	1260	13	strong	strong	ADJ
ejpam-1372	1260	14	magnetic	magnetic	ADJ
ejpam-1372	1260	15	fields	field	NOUN
ejpam-1372	1260	16	.	.	PUNCT
ejpam-1372	1261	1	ann	ann	PROPN
ejpam-1372	1261	2	.	.	PUNCT
ejpam-1372	1261	3	n.	n.	PROPN
ejpam-1372	1261	4	y.	y.	PROPN
ejpam-1372	1261	5	acad	acad	PROPN
ejpam-1372	1261	6	.	.	PUNCT
ejpam-1372	1262	1	sci	sci	PROPN
ejpam-1372	1262	2	.	.	PROPN
ejpam-1372	1262	3	,	,	PUNCT
ejpam-1372	1262	4	257:95–107	257:95–107	NUM
ejpam-1372	1262	5	,	,	PUNCT
ejpam-1372	1262	6	1975	1975	NUM
ejpam-1372	1262	7	.	.	PUNCT
ejpam-1372	1263	1	[	[	X
ejpam-1372	1263	2	4	4	NUM
ejpam-1372	1263	3	]	]	X
ejpam-1372	1263	4	j	j	PROPN
ejpam-1372	1263	5	boyd	boyd	PROPN
ejpam-1372	1263	6	.	.	PUNCT
ejpam-1372	1264	1	weakly	weakly	ADJ
ejpam-1372	1264	2	nonlocal	nonlocal	ADJ
ejpam-1372	1264	3	solitary	solitary	ADJ
ejpam-1372	1264	4	waves	wave	NOUN
ejpam-1372	1264	5	and	and	CCONJ
ejpam-1372	1264	6	beyond	beyond	ADP
ejpam-1372	1264	7	-	-	PUNCT
ejpam-1372	1264	8	all	all	DET
ejpam-1372	1264	9	-	-	PUNCT
ejpam-1372	1264	10	orders	order	NOUN
ejpam-1372	1264	11	asymptotics	asymptotic	NOUN
ejpam-1372	1264	12	beyond	beyond	ADP
ejpam-1372	1264	13	all	all	DET
ejpam-1372	1264	14	orders	order	NOUN
ejpam-1372	1264	15	:	:	PUNCT
ejpam-1372	1264	16	generalized	generalized	ADJ
ejpam-1372	1264	17	solutions	solution	NOUN
ejpam-1372	1264	18	and	and	CCONJ
ejpam-1372	1264	19	hyperasymptotic	hyperasymptotic	ADJ
ejpam-1372	1264	20	perturbation	perturbation	NOUN
ejpam-1372	1264	21	theory	theory	NOUN
ejpam-1372	1264	22	.	.	PUNCT
ejpam-1372	1265	1	kluwer	kluwer	NOUN
ejpam-1372	1265	2	,	,	PUNCT
ejpam-1372	1265	3	amsterdam	amsterdam	PROPN
ejpam-1372	1265	4	,	,	PUNCT
ejpam-1372	1265	5	1998	1998	NUM
ejpam-1372	1265	6	.	.	PUNCT
ejpam-1372	1266	1	[	[	X
ejpam-1372	1266	2	5	5	NUM
ejpam-1372	1266	3	]	]	X
ejpam-1372	1266	4	j	j	PROPN
ejpam-1372	1266	5	boyd	boyd	PROPN
ejpam-1372	1266	6	.	.	PUNCT
ejpam-1372	1267	1	the	the	DET
ejpam-1372	1267	2	devil	devil	NOUN
ejpam-1372	1267	3	’s	’s	PART
ejpam-1372	1267	4	invention	invention	NOUN
ejpam-1372	1267	5	.	.	PUNCT
ejpam-1372	1268	1	asymptotic	asymptotic	ADJ
ejpam-1372	1268	2	,	,	PUNCT
ejpam-1372	1268	3	superasymptotic	superasymptotic	ADJ
ejpam-1372	1268	4	and	and	CCONJ
ejpam-1372	1268	5	hyperasymptotic	hyperasymptotic	ADJ
ejpam-1372	1268	6	series	series	NOUN
ejpam-1372	1268	7	.	.	PUNCT
ejpam-1372	1269	1	acta	acta	PROPN
ejpam-1372	1269	2	.	.	PUNCT
ejpam-1372	1270	1	appl	appl	PROPN
ejpam-1372	1270	2	.	.	PROPN
ejpam-1372	1270	3	math	math	PROPN
ejpam-1372	1270	4	.	.	PUNCT
ejpam-1372	1270	5	,	,	PUNCT
ejpam-1372	1270	6	56:1–98	56:1–98	NUM
ejpam-1372	1270	7	,	,	PUNCT
ejpam-1372	1270	8	1999	1999	NUM
ejpam-1372	1270	9	.	.	PUNCT
ejpam-1372	1271	1	[	[	X
ejpam-1372	1271	2	6	6	NUM
ejpam-1372	1271	3	]	]	PUNCT
ejpam-1372	1271	4	t	t	PROPN
ejpam-1372	1271	5	bromwich	bromwich	PROPN
ejpam-1372	1271	6	.	.	PUNCT
ejpam-1372	1272	1	an	an	DET
ejpam-1372	1272	2	introduction	introduction	NOUN
ejpam-1372	1272	3	to	to	ADP
ejpam-1372	1272	4	the	the	DET
ejpam-1372	1272	5	theory	theory	NOUN
ejpam-1372	1272	6	of	of	ADP
ejpam-1372	1272	7	infinite	infinite	ADJ
ejpam-1372	1272	8	series	series	NOUN
ejpam-1372	1272	9	,	,	PUNCT
ejpam-1372	1272	10	second	second	ADJ
ejpam-1372	1272	11	edition	edition	NOUN
ejpam-1372	1272	12	revised	revise	VERB
ejpam-1372	1272	13	.	.	PUNCT
ejpam-1372	1273	1	macmillan	macmillan	PROPN
ejpam-1372	1273	2	,	,	PUNCT
ejpam-1372	1273	3	london	london	PROPN
ejpam-1372	1273	4	,	,	PUNCT
ejpam-1372	1273	5	1965	1965	NUM
ejpam-1372	1273	6	.	.	PUNCT
ejpam-1372	1274	1	references	reference	NOUN
ejpam-1372	1274	2	416	416	NUM
ejpam-1372	1275	1	[	[	X
ejpam-1372	1275	2	7	7	NUM
ejpam-1372	1275	3	]	]	X
ejpam-1372	1275	4	e	e	PROPN
ejpam-1372	1275	5	copson	copson	PROPN
ejpam-1372	1275	6	.	.	PUNCT
ejpam-1372	1276	1	introduction	introduction	NOUN
ejpam-1372	1276	2	to	to	ADP
ejpam-1372	1276	3	the	the	DET
ejpam-1372	1276	4	theory	theory	NOUN
ejpam-1372	1276	5	of	of	ADP
ejpam-1372	1276	6	functions	function	NOUN
ejpam-1372	1276	7	of	of	ADP
ejpam-1372	1276	8	a	a	DET
ejpam-1372	1276	9	complex	complex	ADJ
ejpam-1372	1276	10	variable	variable	NOUN
ejpam-1372	1276	11	.	.	PUNCT
ejpam-1372	1277	1	clarendon	clarendon	PROPN
ejpam-1372	1277	2	,	,	PUNCT
ejpam-1372	1277	3	oxford	oxford	NOUN
ejpam-1372	1277	4	,	,	PUNCT
ejpam-1372	1277	5	1976	1976	NUM
ejpam-1372	1277	6	.	.	PUNCT
ejpam-1372	1278	1	[	[	X
ejpam-1372	1278	2	8	8	NUM
ejpam-1372	1278	3	]	]	X
ejpam-1372	1278	4	r	r	NOUN
ejpam-1372	1278	5	dingle	dingle	NOUN
ejpam-1372	1278	6	.	.	PUNCT
ejpam-1372	1279	1	asymptotic	asymptotic	ADJ
ejpam-1372	1279	2	expansions	expansion	NOUN
ejpam-1372	1279	3	:	:	PUNCT
ejpam-1372	1279	4	their	their	PRON
ejpam-1372	1279	5	derivation	derivation	NOUN
ejpam-1372	1279	6	and	and	CCONJ
ejpam-1372	1279	7	interpretation	interpretation	NOUN
ejpam-1372	1279	8	.	.	PUNCT
ejpam-1372	1280	1	academic	academic	ADJ
ejpam-1372	1280	2	press	press	PROPN
ejpam-1372	1280	3	,	,	PUNCT
ejpam-1372	1280	4	london	london	PROPN
ejpam-1372	1280	5	,	,	PUNCT
ejpam-1372	1280	6	1973	1973	NUM
ejpam-1372	1280	7	.	.	PUNCT
ejpam-1372	1281	1	[	[	X
ejpam-1372	1281	2	9	9	NUM
ejpam-1372	1281	3	]	]	X
ejpam-1372	1281	4	f	f	PROPN
ejpam-1372	1281	5	farassat	farassat	NOUN
ejpam-1372	1281	6	.	.	PUNCT
ejpam-1372	1282	1	introduction	introduction	NOUN
ejpam-1372	1282	2	to	to	ADP
ejpam-1372	1282	3	generalized	generalized	ADJ
ejpam-1372	1282	4	functions	function	NOUN
ejpam-1372	1282	5	with	with	ADP
ejpam-1372	1282	6	applications	application	NOUN
ejpam-1372	1282	7	in	in	ADP
ejpam-1372	1282	8	aerodynamics	aerodynamic	NOUN
ejpam-1372	1282	9	and	and	CCONJ
ejpam-1372	1282	10	aeronautics	aeronautic	NOUN
ejpam-1372	1282	11	.	.	PUNCT
ejpam-1372	1283	1	nasa	nasa	PROPN
ejpam-1372	1283	2	technical	technical	PROPN
ejpam-1372	1283	3	paper	paper	PROPN
ejpam-1372	1283	4	3428	3428	NUM
ejpam-1372	1283	5	,	,	PUNCT
ejpam-1372	1283	6	langley	langley	PROPN
ejpam-1372	1283	7	research	research	NOUN
ejpam-1372	1283	8	center	center	PROPN
ejpam-1372	1283	9	,	,	PUNCT
ejpam-1372	1283	10	virginia	virginia	PROPN
ejpam-1372	1283	11	,	,	PUNCT
ejpam-1372	1283	12	usa	usa	PROPN
ejpam-1372	1283	13	,	,	PUNCT
ejpam-1372	1283	14	1994	1994	NUM
ejpam-1372	1283	15	.	.	PUNCT
ejpam-1372	1284	1	[	[	X
ejpam-1372	1284	2	10	10	NUM
ejpam-1372	1284	3	]	]	X
ejpam-1372	1284	4	i	i	PRON
ejpam-1372	1284	5	gel’fand	gel’fand	VERB
ejpam-1372	1284	6	and	and	CCONJ
ejpam-1372	1284	7	g	g	PROPN
ejpam-1372	1284	8	shilov	shilov	NOUN
ejpam-1372	1284	9	.	.	PUNCT
ejpam-1372	1285	1	generalized	generalized	ADJ
ejpam-1372	1285	2	functions	function	NOUN
ejpam-1372	1285	3	:	:	PUNCT
ejpam-1372	1285	4	vol	vol	NOUN
ejpam-1372	1285	5	.	.	PUNCT
ejpam-1372	1285	6	iproperties	ipropertie	NOUN
ejpam-1372	1285	7	and	and	CCONJ
ejpam-1372	1285	8	applications	application	NOUN
ejpam-1372	1285	9	.	.	PUNCT
ejpam-1372	1286	1	academic	academic	ADJ
ejpam-1372	1286	2	press	press	NOUN
ejpam-1372	1286	3	,	,	PUNCT
ejpam-1372	1286	4	new	new	PROPN
ejpam-1372	1286	5	york	york	PROPN
ejpam-1372	1286	6	,	,	PUNCT
ejpam-1372	1286	7	1964	1964	NUM
ejpam-1372	1286	8	.	.	PUNCT
ejpam-1372	1287	1	[	[	X
ejpam-1372	1287	2	11	11	NUM
ejpam-1372	1287	3	]	]	X
ejpam-1372	1287	4	i	i	PRON
ejpam-1372	1287	5	gradshteyn	gradshteyn	VERB
ejpam-1372	1287	6	and	and	CCONJ
ejpam-1372	1287	7	i	i	PRON
ejpam-1372	1287	8	ryzhik	ryzhik	ADJ
ejpam-1372	1287	9	.	.	PUNCT
ejpam-1372	1288	1	table	table	NOUN
ejpam-1372	1288	2	of	of	ADP
ejpam-1372	1288	3	integrals	integral	NOUN
ejpam-1372	1288	4	,	,	PUNCT
ejpam-1372	1288	5	series	series	NOUN
ejpam-1372	1288	6	and	and	CCONJ
ejpam-1372	1288	7	products	product	NOUN
ejpam-1372	1288	8	5	5	NUM
ejpam-1372	1288	9	-	-	PUNCT
ejpam-1372	1288	10	th	th	X
ejpam-1372	1288	11	edition	edition	NOUN
ejpam-1372	1288	12	.	.	PUNCT
ejpam-1372	1289	1	academic	academic	ADJ
ejpam-1372	1289	2	press	press	PROPN
ejpam-1372	1289	3	,	,	PUNCT
ejpam-1372	1289	4	london	london	PROPN
ejpam-1372	1289	5	,	,	PUNCT
ejpam-1372	1289	6	1994	1994	NUM
ejpam-1372	1289	7	.	.	PUNCT
ejpam-1372	1290	1	[	[	X
ejpam-1372	1290	2	12	12	NUM
ejpam-1372	1290	3	]	]	X
ejpam-1372	1290	4	g	g	NOUN
ejpam-1372	1290	5	hardy	hardy	ADJ
ejpam-1372	1290	6	.	.	PUNCT
ejpam-1372	1291	1	divergent	divergent	ADJ
ejpam-1372	1291	2	series	series	NOUN
ejpam-1372	1291	3	.	.	PUNCT
ejpam-1372	1292	1	clarendon	clarendon	PROPN
ejpam-1372	1292	2	press	press	PROPN
ejpam-1372	1292	3	,	,	PUNCT
ejpam-1372	1292	4	oxford	oxford	PROPN
ejpam-1372	1292	5	,	,	PUNCT
ejpam-1372	1292	6	1963	1963	NUM
ejpam-1372	1292	7	.	.	PUNCT
ejpam-1372	1293	1	[	[	X
ejpam-1372	1293	2	13	13	NUM
ejpam-1372	1293	3	]	]	X
ejpam-1372	1293	4	j	j	PROPN
ejpam-1372	1293	5	havil	havil	NOUN
ejpam-1372	1293	6	.	.	PUNCT
ejpam-1372	1294	1	gammaexploring	gammaexploring	PROPN
ejpam-1372	1294	2	euler	euler	PROPN
ejpam-1372	1294	3	’s	’s	PART
ejpam-1372	1294	4	constant	constant	ADJ
ejpam-1372	1294	5	.	.	PUNCT
ejpam-1372	1295	1	princeton	princeton	PROPN
ejpam-1372	1295	2	university	university	PROPN
ejpam-1372	1295	3	press	press	PROPN
ejpam-1372	1295	4	,	,	PUNCT
ejpam-1372	1295	5	princeton	princeton	PROPN
ejpam-1372	1295	6	,	,	PUNCT
ejpam-1372	1295	7	1976	1976	NUM
ejpam-1372	1295	8	.	.	PUNCT
ejpam-1372	1296	1	[	[	X
ejpam-1372	1296	2	14	14	NUM
ejpam-1372	1296	3	]	]	SYM
ejpam-1372	1296	4	v	v	X
ejpam-1372	1296	5	kowalenko	kowalenko	PROPN
ejpam-1372	1296	6	.	.	PUNCT
ejpam-1372	1297	1	towards	towards	ADP
ejpam-1372	1297	2	a	a	DET
ejpam-1372	1297	3	theory	theory	NOUN
ejpam-1372	1297	4	of	of	ADP
ejpam-1372	1297	5	divergent	divergent	ADJ
ejpam-1372	1297	6	series	series	NOUN
ejpam-1372	1297	7	and	and	CCONJ
ejpam-1372	1297	8	its	its	PRON
ejpam-1372	1297	9	importance	importance	NOUN
ejpam-1372	1297	10	to	to	ADP
ejpam-1372	1297	11	asymptotics	asymptotic	NOUN
ejpam-1372	1297	12	.	.	PUNCT
ejpam-1372	1298	1	in	in	ADP
ejpam-1372	1298	2	s	s	PROPN
ejpam-1372	1298	3	pandalai	pandalai	PROPN
ejpam-1372	1298	4	,	,	PUNCT
ejpam-1372	1298	5	editor	editor	NOUN
ejpam-1372	1298	6	,	,	PUNCT
ejpam-1372	1298	7	recent	recent	ADJ
ejpam-1372	1298	8	research	research	NOUN
ejpam-1372	1298	9	developments	development	NOUN
ejpam-1372	1298	10	in	in	ADP
ejpam-1372	1298	11	physics	physics	NOUN
ejpam-1372	1298	12	,	,	PUNCT
ejpam-1372	1298	13	volume	volume	NOUN
ejpam-1372	1298	14	2	2	NUM
ejpam-1372	1298	15	,	,	PUNCT
ejpam-1372	1298	16	pages	page	NOUN
ejpam-1372	1298	17	17–68	17–68	NUM
ejpam-1372	1298	18	.	.	PUNCT
ejpam-1372	1299	1	transworld	transworld	PROPN
ejpam-1372	1299	2	research	research	NOUN
ejpam-1372	1299	3	network	network	PROPN
ejpam-1372	1299	4	,	,	PUNCT
ejpam-1372	1299	5	trivandrum	trivandrum	PROPN
ejpam-1372	1299	6	,	,	PUNCT
ejpam-1372	1299	7	india	india	PROPN
ejpam-1372	1299	8	,	,	PUNCT
ejpam-1372	1299	9	2001	2001	NUM
ejpam-1372	1299	10	.	.	PUNCT
ejpam-1372	1300	1	[	[	X
ejpam-1372	1300	2	15	15	NUM
ejpam-1372	1300	3	]	]	SYM
ejpam-1372	1300	4	v	v	ADP
ejpam-1372	1300	5	kowalenko	kowalenko	PROPN
ejpam-1372	1300	6	.	.	PUNCT
ejpam-1372	1301	1	exactification	exactification	NOUN
ejpam-1372	1301	2	of	of	ADP
ejpam-1372	1301	3	the	the	DET
ejpam-1372	1301	4	asymptotics	asymptotic	NOUN
ejpam-1372	1301	5	for	for	ADP
ejpam-1372	1301	6	bessel	bessel	NOUN
ejpam-1372	1301	7	and	and	CCONJ
ejpam-1372	1301	8	hankel	hankel	NOUN
ejpam-1372	1301	9	functions	function	NOUN
ejpam-1372	1301	10	.	.	PUNCT
ejpam-1372	1302	1	appl	appl	PROPN
ejpam-1372	1302	2	.	.	PROPN
ejpam-1372	1302	3	math	math	PROPN
ejpam-1372	1302	4	.	.	PUNCT
ejpam-1372	1303	1	comput	comput	NOUN
ejpam-1372	1303	2	.	.	PUNCT
ejpam-1372	1303	3	,	,	PUNCT
ejpam-1372	1303	4	133:487–518	133:487–518	NUM
ejpam-1372	1303	5	,	,	PUNCT
ejpam-1372	1303	6	2002	2002	NUM
ejpam-1372	1303	7	.	.	PUNCT
ejpam-1372	1304	1	[	[	X
ejpam-1372	1304	2	16	16	NUM
ejpam-1372	1304	3	]	]	PUNCT
ejpam-1372	1304	4	v	v	X
ejpam-1372	1304	5	kowalenko	kowalenko	NOUN
ejpam-1372	1304	6	.	.	PUNCT
ejpam-1372	1305	1	generalizing	generalize	VERB
ejpam-1372	1305	2	the	the	DET
ejpam-1372	1305	3	reciprocal	reciprocal	ADJ
ejpam-1372	1305	4	logarithm	logarithm	NOUN
ejpam-1372	1305	5	numbers	number	NOUN
ejpam-1372	1305	6	by	by	ADP
ejpam-1372	1305	7	adapting	adapt	VERB
ejpam-1372	1305	8	the	the	DET
ejpam-1372	1305	9	partition	partition	NOUN
ejpam-1372	1305	10	method	method	NOUN
ejpam-1372	1305	11	for	for	ADP
ejpam-1372	1305	12	a	a	DET
ejpam-1372	1305	13	power	power	NOUN
ejpam-1372	1305	14	series	series	NOUN
ejpam-1372	1305	15	exapnsion	exapnsion	NOUN
ejpam-1372	1305	16	.	.	PUNCT
ejpam-1372	1306	1	acta	acta	PROPN
ejpam-1372	1306	2	.	.	PUNCT
ejpam-1372	1307	1	appl	appl	PROPN
ejpam-1372	1307	2	.	.	PROPN
ejpam-1372	1307	3	math	math	PROPN
ejpam-1372	1307	4	.	.	PUNCT
ejpam-1372	1307	5	,	,	PUNCT
ejpam-1372	1307	6	106:369–420	106:369–420	NUM
ejpam-1372	1307	7	,	,	PUNCT
ejpam-1372	1307	8	2009	2009	NUM
ejpam-1372	1307	9	.	.	PUNCT
ejpam-1372	1308	1	[	[	X
ejpam-1372	1308	2	17	17	NUM
ejpam-1372	1308	3	]	]	SYM
ejpam-1372	1308	4	v	v	ADP
ejpam-1372	1308	5	kowalenko	kowalenko	PROPN
ejpam-1372	1308	6	.	.	PUNCT
ejpam-1372	1309	1	the	the	DET
ejpam-1372	1309	2	stokes	stoke	NOUN
ejpam-1372	1309	3	phenomenon	phenomenon	NOUN
ejpam-1372	1309	4	,	,	PUNCT
ejpam-1372	1309	5	borel	borel	PROPN
ejpam-1372	1309	6	summation	summation	NOUN
ejpam-1372	1309	7	and	and	CCONJ
ejpam-1372	1309	8	mellin	mellin	PROPN
ejpam-1372	1309	9	-	-	PUNCT
ejpam-1372	1309	10	barnes	barnes	PROPN
ejpam-1372	1309	11	regularisation	regularisation	NOUN
ejpam-1372	1309	12	.	.	PUNCT
ejpam-1372	1310	1	bentham	bentham	PROPN
ejpam-1372	1310	2	science	science	NOUN
ejpam-1372	1310	3	publishers	publisher	NOUN
ejpam-1372	1310	4	,	,	PUNCT
ejpam-1372	1310	5	http://www.bentham.org./ebooks	http://www.bentham.org./ebook	NOUN
ejpam-1372	1310	6	,	,	PUNCT
ejpam-1372	1310	7	2009	2009	NUM
ejpam-1372	1310	8	.	.	PUNCT
ejpam-1372	1311	1	[	[	X
ejpam-1372	1311	2	18	18	NUM
ejpam-1372	1311	3	]	]	SYM
ejpam-1372	1311	4	v	v	ADP
ejpam-1372	1311	5	kowalenko	kowalenko	NOUN
ejpam-1372	1311	6	.	.	PUNCT
ejpam-1372	1312	1	properties	property	NOUN
ejpam-1372	1312	2	and	and	CCONJ
ejpam-1372	1312	3	applications	application	NOUN
ejpam-1372	1312	4	of	of	ADP
ejpam-1372	1312	5	the	the	DET
ejpam-1372	1312	6	reciprocal	reciprocal	ADJ
ejpam-1372	1312	7	logarithm	logarithm	NOUN
ejpam-1372	1312	8	numbers	number	NOUN
ejpam-1372	1312	9	.	.	PUNCT
ejpam-1372	1313	1	acta	acta	PROPN
ejpam-1372	1313	2	.	.	PUNCT
ejpam-1372	1314	1	appl	appl	PROPN
ejpam-1372	1314	2	.	.	PROPN
ejpam-1372	1314	3	math	math	PROPN
ejpam-1372	1314	4	.	.	PUNCT
ejpam-1372	1314	5	,	,	PUNCT
ejpam-1372	1314	6	109:413–437	109:413–437	NUM
ejpam-1372	1314	7	,	,	PUNCT
ejpam-1372	1314	8	2010	2010	NUM
ejpam-1372	1314	9	.	.	PUNCT
ejpam-1372	1315	1	[	[	X
ejpam-1372	1315	2	19	19	NUM
ejpam-1372	1315	3	]	]	SYM
ejpam-1372	1315	4	v	v	ADP
ejpam-1372	1315	5	kowalenko	kowalenko	NOUN
ejpam-1372	1315	6	.	.	PUNCT
ejpam-1372	1316	1	applications	application	NOUN
ejpam-1372	1316	2	of	of	ADP
ejpam-1372	1316	3	the	the	DET
ejpam-1372	1316	4	cosecant	cosecant	ADJ
ejpam-1372	1316	5	and	and	CCONJ
ejpam-1372	1316	6	related	related	ADJ
ejpam-1372	1316	7	numbers	number	NOUN
ejpam-1372	1316	8	.	.	PUNCT
ejpam-1372	1317	1	acta	acta	PROPN
ejpam-1372	1317	2	appl	appl	PROPN
ejpam-1372	1317	3	.	.	PROPN
ejpam-1372	1317	4	math	math	PROPN
ejpam-1372	1317	5	.	.	PUNCT
ejpam-1372	1317	6	,	,	PUNCT
ejpam-1372	1317	7	114:15–134	114:15–134	NUM
ejpam-1372	1317	8	,	,	PUNCT
ejpam-1372	1317	9	2011	2011	NUM
ejpam-1372	1317	10	.	.	PUNCT
ejpam-1372	1318	1	[	[	X
ejpam-1372	1318	2	20	20	NUM
ejpam-1372	1318	3	]	]	SYM
ejpam-1372	1318	4	v	v	X
ejpam-1372	1318	5	kowalenko	kowalenko	PROPN
ejpam-1372	1318	6	.	.	PUNCT
ejpam-1372	1319	1	euler	euler	NOUN
ejpam-1372	1319	2	and	and	CCONJ
ejpam-1372	1319	3	divergent	divergent	ADJ
ejpam-1372	1319	4	mathematics	mathematic	NOUN
ejpam-1372	1319	5	.	.	PUNCT
ejpam-1372	1320	1	bestthinking	bestthinking	ADJ
ejpam-1372	1320	2	science	science	NOUN
ejpam-1372	1320	3	,	,	PUNCT
ejpam-1372	1320	4	http://www.bestthinking	http://www.bestthinke	VERB
ejpam-1372	1320	5	.	.	PUNCT
ejpam-1372	1321	1	om	om	PROPN
ejpam-1372	1321	2	/	/	SYM
ejpam-1372	1321	3	arti	arti	NOUN
ejpam-1372	1321	4	le	le	X
ejpam-1372	1321	5	/	/	SYM
ejpam-1372	1321	6	permalink/1255?tab	permalink/1255?tab	NOUN
ejpam-1372	1321	7	=	=	NOUN
ejpam-1372	1321	8	arti	arti	NOUN
ejpam-1372	1321	9	le&title	le&title	NOUN
ejpam-1372	1321	10	=	=	SYM
ejpam-1372	1321	11	euler	euler	VERB
ejpam-1372	1321	12	-	-	PUNCT
ejpam-1372	1321	13	and	and	CCONJ
ejpam-1372	1321	14	-	-	PUNCT
ejpam-1372	1321	15	divergent	divergent	ADJ
ejpam-1372	1321	16	-	-	PUNCT
ejpam-1372	1321	17	mathemati	mathemati	NOUN
ejpam-1372	1321	18	s	s	NOUN
ejpam-1372	1321	19	,	,	PUNCT
ejpam-1372	1321	20	2011	2011	NUM
ejpam-1372	1321	21	.	.	PUNCT
ejpam-1372	1322	1	[	[	X
ejpam-1372	1322	2	21	21	NUM
ejpam-1372	1322	3	]	]	SYM
ejpam-1372	1322	4	v	v	ADP
ejpam-1372	1322	5	kowalenko	kowalenko	PROPN
ejpam-1372	1322	6	,	,	PUNCT
ejpam-1372	1322	7	n	n	PRON
ejpam-1372	1322	8	frankel	frankel	NOUN
ejpam-1372	1322	9	,	,	PUNCT
ejpam-1372	1322	10	m	m	PROPN
ejpam-1372	1322	11	glasser	glasser	NOUN
ejpam-1372	1322	12	,	,	PUNCT
ejpam-1372	1322	13	and	and	CCONJ
ejpam-1372	1322	14	t	t	PROPN
ejpam-1372	1322	15	taucher	taucher	NOUN
ejpam-1372	1322	16	.	.	PUNCT
ejpam-1372	1323	1	generalised	generalise	VERB
ejpam-1372	1323	2	euler	euler	PROPN
ejpam-1372	1323	3	-	-	PUNCT
ejpam-1372	1323	4	jacobi	jacobi	PROPN
ejpam-1372	1323	5	inversion	inversion	NOUN
ejpam-1372	1323	6	formula	formula	NOUN
ejpam-1372	1323	7	and	and	CCONJ
ejpam-1372	1323	8	asymptotics	asymptotic	NOUN
ejpam-1372	1323	9	beyond	beyond	ADP
ejpam-1372	1323	10	all	all	DET
ejpam-1372	1323	11	orders	order	NOUN
ejpam-1372	1323	12	.	.	PUNCT
ejpam-1372	1324	1	in	in	ADP
ejpam-1372	1324	2	london	london	PROPN
ejpam-1372	1324	3	mathematical	mathematical	ADJ
ejpam-1372	1324	4	society	society	NOUN
ejpam-1372	1324	5	lecture	lecture	NOUN
ejpam-1372	1324	6	note	note	NOUN
ejpam-1372	1324	7	,	,	PUNCT
ejpam-1372	1324	8	number	number	NOUN
ejpam-1372	1324	9	214	214	NUM
ejpam-1372	1324	10	.	.	PUNCT
ejpam-1372	1325	1	cambridge	cambridge	PROPN
ejpam-1372	1325	2	university	university	PROPN
ejpam-1372	1325	3	press	press	PROPN
ejpam-1372	1325	4	,	,	PUNCT
ejpam-1372	1325	5	cambridge	cambridge	PROPN
ejpam-1372	1325	6	,	,	PUNCT
ejpam-1372	1325	7	1995	1995	NUM
ejpam-1372	1325	8	.	.	PUNCT
ejpam-1372	1326	1	[	[	X
ejpam-1372	1326	2	22	22	NUM
ejpam-1372	1326	3	]	]	SYM
ejpam-1372	1326	4	v	v	X
ejpam-1372	1326	5	kowalenko	kowalenko	PROPN
ejpam-1372	1326	6	,	,	PUNCT
ejpam-1372	1326	7	n	n	PRON
ejpam-1372	1326	8	frankel	frankel	NOUN
ejpam-1372	1326	9	,	,	PUNCT
ejpam-1372	1326	10	and	and	CCONJ
ejpam-1372	1326	11	k	k	PROPN
ejpam-1372	1326	12	hines	hine	NOUN
ejpam-1372	1326	13	.	.	PUNCT
ejpam-1372	1327	1	the	the	DET
ejpam-1372	1327	2	response	response	NOUN
ejpam-1372	1327	3	theory	theory	NOUN
ejpam-1372	1327	4	of	of	ADP
ejpam-1372	1327	5	particle	particle	NOUN
ejpam-1372	1327	6	-	-	PUNCT
ejpam-1372	1327	7	anti	anti	ADJ
ejpam-1372	1327	8	-	-	ADJ
ejpam-1372	1327	9	particle	particle	ADJ
ejpam-1372	1327	10	plasmas	plasma	NOUN
ejpam-1372	1327	11	.	.	PUNCT
ejpam-1372	1328	1	physics	physics	NOUN
ejpam-1372	1328	2	reports	report	NOUN
ejpam-1372	1328	3	,	,	PUNCT
ejpam-1372	1328	4	126(3):109–187	126(3):109–187	NUM
ejpam-1372	1328	5	,	,	PUNCT
ejpam-1372	1328	6	1985	1985	NUM
ejpam-1372	1328	7	.	.	PUNCT
ejpam-1372	1329	1	references	reference	NOUN
ejpam-1372	1329	2	417	417	NUM
ejpam-1372	1330	1	[	[	X
ejpam-1372	1330	2	23	23	NUM
ejpam-1372	1330	3	]	]	X
ejpam-1372	1330	4	m	m	VERB
ejpam-1372	1330	5	lighthill	lighthill	ADJ
ejpam-1372	1330	6	.	.	PUNCT
ejpam-1372	1331	1	fourier	fourier	ADJ
ejpam-1372	1331	2	analysis	analysis	NOUN
ejpam-1372	1331	3	and	and	CCONJ
ejpam-1372	1331	4	generalised	generalised	ADJ
ejpam-1372	1331	5	functions	function	NOUN
ejpam-1372	1331	6	.	.	PUNCT
ejpam-1372	1332	1	students	student	NOUN
ejpam-1372	1332	2	edition	edition	PROPN
ejpam-1372	1332	3	.	.	PUNCT
ejpam-1372	1333	1	cambridge	cambridge	PROPN
ejpam-1372	1333	2	university	university	PROPN
ejpam-1372	1333	3	press	press	PROPN
ejpam-1372	1333	4	,	,	PUNCT
ejpam-1372	1333	5	cambridge	cambridge	PROPN
ejpam-1372	1333	6	,	,	PUNCT
ejpam-1372	1333	7	1975	1975	NUM
ejpam-1372	1333	8	.	.	PUNCT
ejpam-1372	1334	1	[	[	X
ejpam-1372	1334	2	24	24	NUM
ejpam-1372	1334	3	]	]	X
ejpam-1372	1334	4	p	p	NOUN
ejpam-1372	1334	5	morse	morse	NOUN
ejpam-1372	1334	6	and	and	CCONJ
ejpam-1372	1334	7	feshbach	feshbach	NOUN
ejpam-1372	1334	8	.	.	PUNCT
ejpam-1372	1335	1	methods	method	NOUN
ejpam-1372	1335	2	of	of	ADP
ejpam-1372	1335	3	theoretical	theoretical	ADJ
ejpam-1372	1335	4	physics	physics	NOUN
ejpam-1372	1335	5	,	,	PUNCT
ejpam-1372	1335	6	part	part	PROPN
ejpam-1372	1335	7	i.	i.	PROPN
ejpam-1372	1335	8	mcgraw	mcgraw	PROPN
ejpam-1372	1335	9	-	-	PUNCT
ejpam-1372	1335	10	hill	hill	PROPN
ejpam-1372	1335	11	,	,	PUNCT
ejpam-1372	1335	12	new	new	PROPN
ejpam-1372	1335	13	york	york	PROPN
ejpam-1372	1335	14	,	,	PUNCT
ejpam-1372	1335	15	1953	1953	NUM
ejpam-1372	1335	16	.	.	PUNCT
ejpam-1372	1336	1	[	[	X
ejpam-1372	1336	2	25	25	NUM
ejpam-1372	1336	3	]	]	X
ejpam-1372	1336	4	f	f	PROPN
ejpam-1372	1336	5	oberhettinger	oberhettinger	PROPN
ejpam-1372	1336	6	.	.	PUNCT
ejpam-1372	1337	1	tables	table	NOUN
ejpam-1372	1337	2	of	of	ADP
ejpam-1372	1337	3	mellin	mellin	PROPN
ejpam-1372	1337	4	transforms	transform	VERB
ejpam-1372	1337	5	.	.	PUNCT
ejpam-1372	1338	1	springer	springer	NOUN
ejpam-1372	1338	2	-	-	PUNCT
ejpam-1372	1338	3	verlag	verlag	PROPN
ejpam-1372	1338	4	,	,	PUNCT
ejpam-1372	1338	5	berlin	berlin	PROPN
ejpam-1372	1338	6	,	,	PUNCT
ejpam-1372	1338	7	1974	1974	NUM
ejpam-1372	1338	8	.	.	PUNCT
ejpam-1372	1339	1	[	[	X
ejpam-1372	1339	2	26	26	NUM
ejpam-1372	1339	3	]	]	X
ejpam-1372	1339	4	r	r	NOUN
ejpam-1372	1339	5	paris	paris	PROPN
ejpam-1372	1339	6	.	.	PUNCT
ejpam-1372	1340	1	asymptotic	asymptotic	ADJ
ejpam-1372	1340	2	expansion	expansion	NOUN
ejpam-1372	1340	3	of	of	ADP
ejpam-1372	1340	4	n	n	CCONJ
ejpam-1372	1340	5	-	-	PUNCT
ejpam-1372	1340	6	dimensional	dimensional	ADJ
ejpam-1372	1340	7	faxén	faxén	ADJ
ejpam-1372	1340	8	-	-	PUNCT
ejpam-1372	1340	9	type	type	NOUN
ejpam-1372	1340	10	integrals	integral	NOUN
ejpam-1372	1340	11	.	.	PUNCT
ejpam-1372	1341	1	eur	eur	PROPN
ejpam-1372	1341	2	.	.	PUNCT
ejpam-1372	1342	1	j.	j.	PROPN
ejpam-1372	1342	2	pure	pure	PROPN
ejpam-1372	1342	3	apppl	apppl	PROPN
ejpam-1372	1342	4	.	.	PUNCT
ejpam-1372	1343	1	math	math	PROPN
ejpam-1372	1343	2	.	.	PUNCT
ejpam-1372	1343	3	,	,	PUNCT
ejpam-1372	1344	1	3(6):1006–1031	3(6):1006–1031	PROPN
ejpam-1372	1344	2	,	,	PUNCT
ejpam-1372	1344	3	2010	2010	NUM
ejpam-1372	1344	4	.	.	PUNCT
ejpam-1372	1345	1	[	[	X
ejpam-1372	1345	2	27	27	NUM
ejpam-1372	1345	3	]	]	X
ejpam-1372	1345	4	r	r	NOUN
ejpam-1372	1345	5	paris	paris	PROPN
ejpam-1372	1345	6	and	and	CCONJ
ejpam-1372	1345	7	d	d	PROPN
ejpam-1372	1345	8	kaminski	kaminski	PROPN
ejpam-1372	1345	9	.	.	PUNCT
ejpam-1372	1346	1	asymptotics	asymptotic	NOUN
ejpam-1372	1346	2	and	and	CCONJ
ejpam-1372	1346	3	mellin	mellin	PROPN
ejpam-1372	1346	4	-	-	PUNCT
ejpam-1372	1346	5	barnes	barnes	PROPN
ejpam-1372	1346	6	integrals	integral	NOUN
ejpam-1372	1346	7	.	.	PUNCT
ejpam-1372	1347	1	cambridge	cambridge	PROPN
ejpam-1372	1347	2	university	university	PROPN
ejpam-1372	1347	3	press	press	PROPN
ejpam-1372	1347	4	,	,	PUNCT
ejpam-1372	1347	5	cambridge	cambridge	PROPN
ejpam-1372	1347	6	,	,	PUNCT
ejpam-1372	1347	7	2001	2001	NUM
ejpam-1372	1347	8	.	.	PUNCT
ejpam-1372	1348	1	[	[	X
ejpam-1372	1348	2	28	28	NUM
ejpam-1372	1348	3	]	]	X
ejpam-1372	1348	4	a	a	DET
ejpam-1372	1348	5	prudnikov	prudnikov	NOUN
ejpam-1372	1348	6	,	,	PUNCT
ejpam-1372	1348	7	yu	yu	PROPN
ejpam-1372	1348	8	brychkov	brychkov	PROPN
ejpam-1372	1348	9	,	,	PUNCT
ejpam-1372	1348	10	and	and	CCONJ
ejpam-1372	1348	11	o	o	X
ejpam-1372	1348	12	marichev	marichev	PROPN
ejpam-1372	1348	13	.	.	PUNCT
ejpam-1372	1349	1	integrals	integral	NOUN
ejpam-1372	1349	2	and	and	CCONJ
ejpam-1372	1349	3	series	series	NOUN
ejpam-1372	1349	4	,	,	PUNCT
ejpam-1372	1349	5	volume	volume	NOUN
ejpam-1372	1349	6	2	2	NUM
ejpam-1372	1349	7	:	:	PUNCT
ejpam-1372	1349	8	special	special	ADJ
ejpam-1372	1349	9	functions	function	NOUN
ejpam-1372	1349	10	.	.	PUNCT
ejpam-1372	1350	1	gordon	gordon	PROPN
ejpam-1372	1350	2	and	and	CCONJ
ejpam-1372	1350	3	breach	breach	PROPN
ejpam-1372	1350	4	,	,	PUNCT
ejpam-1372	1350	5	new	new	PROPN
ejpam-1372	1350	6	york	york	PROPN
ejpam-1372	1350	7	,	,	PUNCT
ejpam-1372	1350	8	1986	1986	NUM
ejpam-1372	1350	9	.	.	PUNCT
ejpam-1372	1351	1	[	[	X
ejpam-1372	1351	2	29	29	NUM
ejpam-1372	1351	3	]	]	X
ejpam-1372	1351	4	h	h	NOUN
ejpam-1372	1351	5	segur	segur	NOUN
ejpam-1372	1351	6	,	,	PUNCT
ejpam-1372	1351	7	s	s	VERB
ejpam-1372	1351	8	tanveer	tanveer	NOUN
ejpam-1372	1351	9	,	,	PUNCT
ejpam-1372	1351	10	and	and	CCONJ
ejpam-1372	1351	11	h	h	PROPN
ejpam-1372	1351	12	levine	levine	PROPN
ejpam-1372	1351	13	,	,	PUNCT
ejpam-1372	1351	14	editors	editor	NOUN
ejpam-1372	1351	15	.	.	PUNCT
ejpam-1372	1352	1	asymptotics	asymptotic	NOUN
ejpam-1372	1352	2	beyond	beyond	ADP
ejpam-1372	1352	3	all	all	DET
ejpam-1372	1352	4	orders	order	NOUN
ejpam-1372	1352	5	.	.	PUNCT
ejpam-1372	1353	1	plenum	plenum	PROPN
ejpam-1372	1353	2	press	press	PROPN
ejpam-1372	1353	3	,	,	PUNCT
ejpam-1372	1353	4	new	new	PROPN
ejpam-1372	1353	5	york	york	PROPN
ejpam-1372	1353	6	,	,	PUNCT
ejpam-1372	1353	7	1991	1991	NUM
ejpam-1372	1353	8	.	.	PUNCT
ejpam-1372	1354	1	[	[	X
ejpam-1372	1354	2	30	30	NUM
ejpam-1372	1354	3	]	]	X
ejpam-1372	1354	4	m	m	PROPN
ejpam-1372	1354	5	spiegel	spiegel	PROPN
ejpam-1372	1354	6	.	.	PUNCT
ejpam-1372	1355	1	schaum	schaum	PROPN
ejpam-1372	1355	2	’s	’s	PART
ejpam-1372	1355	3	outline	outline	NOUN
ejpam-1372	1355	4	of	of	ADP
ejpam-1372	1355	5	theory	theory	NOUN
ejpam-1372	1355	6	and	and	CCONJ
ejpam-1372	1355	7	problems	problem	NOUN
ejpam-1372	1355	8	of	of	ADP
ejpam-1372	1355	9	complex	complex	ADJ
ejpam-1372	1355	10	variables	variable	NOUN
ejpam-1372	1355	11	,	,	PUNCT
ejpam-1372	1355	12	si(metric	si(metric	NOUN
ejpam-1372	1355	13	)	)	PUNCT
ejpam-1372	1355	14	edition	edition	NOUN
ejpam-1372	1355	15	.	.	PUNCT
ejpam-1372	1356	1	mcgraw	mcgraw	PROPN
ejpam-1372	1356	2	-	-	PUNCT
ejpam-1372	1356	3	hill	hill	PROPN
ejpam-1372	1356	4	,	,	PUNCT
ejpam-1372	1356	5	new	new	PROPN
ejpam-1372	1356	6	york	york	PROPN
ejpam-1372	1356	7	,	,	PUNCT
ejpam-1372	1356	8	1974	1974	NUM
ejpam-1372	1356	9	.	.	PUNCT
ejpam-1372	1357	1	[	[	X
ejpam-1372	1357	2	31	31	NUM
ejpam-1372	1357	3	]	]	X
ejpam-1372	1357	4	g	g	PROPN
ejpam-1372	1357	5	stokes	stokes	PROPN
ejpam-1372	1357	6	.	.	PUNCT
ejpam-1372	1358	1	on	on	ADP
ejpam-1372	1358	2	the	the	DET
ejpam-1372	1358	3	discontinuity	discontinuity	NOUN
ejpam-1372	1358	4	of	of	ADP
ejpam-1372	1358	5	arbitrary	arbitrary	ADJ
ejpam-1372	1358	6	constants	constant	NOUN
ejpam-1372	1358	7	which	which	PRON
ejpam-1372	1358	8	appear	appear	VERB
ejpam-1372	1358	9	in	in	ADP
ejpam-1372	1358	10	deivergent	deivergent	NOUN
ejpam-1372	1358	11	developments	development	NOUN
ejpam-1372	1358	12	.	.	PUNCT
ejpam-1372	1359	1	in	in	ADP
ejpam-1372	1359	2	collected	collect	VERB
ejpam-1372	1359	3	mathematical	mathematical	ADJ
ejpam-1372	1359	4	and	and	CCONJ
ejpam-1372	1359	5	physical	physical	ADJ
ejpam-1372	1359	6	papers	paper	NOUN
ejpam-1372	1359	7	,	,	PUNCT
ejpam-1372	1359	8	volume	volume	NOUN
ejpam-1372	1359	9	4	4	NUM
ejpam-1372	1359	10	,	,	PUNCT
ejpam-1372	1359	11	pages	page	NOUN
ejpam-1372	1359	12	77–109	77–109	NUM
ejpam-1372	1359	13	.	.	PUNCT
ejpam-1372	1360	1	cambridge	cambridge	PROPN
ejpam-1372	1360	2	university	university	PROPN
ejpam-1372	1360	3	press	press	PROPN
ejpam-1372	1360	4	,	,	PUNCT
ejpam-1372	1360	5	cambridge	cambridge	PROPN
ejpam-1372	1360	6	,	,	PUNCT
ejpam-1372	1360	7	1904	1904	NUM
ejpam-1372	1360	8	.	.	PUNCT
ejpam-1372	1361	1	[	[	X
ejpam-1372	1361	2	32	32	NUM
ejpam-1372	1361	3	]	]	SYM
ejpam-1372	1361	4	v	v	ADP
ejpam-1372	1361	5	varadarajan	varadarajan	NOUN
ejpam-1372	1361	6	.	.	PUNCT
ejpam-1372	1361	7	euler	euler	PROPN
ejpam-1372	1361	8	and	and	CCONJ
ejpam-1372	1361	9	his	his	PRON
ejpam-1372	1361	10	work	work	NOUN
ejpam-1372	1361	11	on	on	ADP
ejpam-1372	1361	12	infinite	infinite	ADJ
ejpam-1372	1361	13	series	series	NOUN
ejpam-1372	1361	14	.	.	PUNCT
ejpam-1372	1362	1	bulletin	bulletin	NOUN
ejpam-1372	1362	2	(	(	PUNCT
ejpam-1372	1362	3	new	new	ADJ
ejpam-1372	1362	4	series	series	NOUN
ejpam-1372	1362	5	)	)	PUNCT
ejpam-1372	1362	6	of	of	ADP
ejpam-1372	1362	7	the	the	DET
ejpam-1372	1362	8	american	american	PROPN
ejpam-1372	1362	9	mathematical	mathematical	PROPN
ejpam-1372	1362	10	society	society	NOUN
ejpam-1372	1362	11	,	,	PUNCT
ejpam-1372	1362	12	44(4):515–539	44(4):515–539	PROPN
ejpam-1372	1362	13	,	,	PUNCT
ejpam-1372	1362	14	2007	2007	NUM
ejpam-1372	1362	15	.	.	PUNCT
ejpam-1372	1363	1	[	[	X
ejpam-1372	1363	2	33	33	NUM
ejpam-1372	1363	3	]	]	PUNCT
ejpam-1372	1363	4	e	e	X
ejpam-1372	1363	5	whittaker	whittaker	PROPN
ejpam-1372	1363	6	and	and	CCONJ
ejpam-1372	1363	7	g	g	PROPN
ejpam-1372	1363	8	watson	watson	PROPN
ejpam-1372	1363	9	.	.	PUNCT
ejpam-1372	1364	1	a	a	DET
ejpam-1372	1364	2	course	course	NOUN
ejpam-1372	1364	3	in	in	ADP
ejpam-1372	1364	4	modern	modern	ADJ
ejpam-1372	1364	5	analysis	analysis	NOUN
ejpam-1372	1364	6	.	.	PUNCT
ejpam-1372	1365	1	cambridge	cambridge	PROPN
ejpam-1372	1365	2	university	university	PROPN
ejpam-1372	1365	3	press	press	PROPN
ejpam-1372	1365	4	,	,	PUNCT
ejpam-1372	1365	5	cambridge	cambridge	PROPN
ejpam-1372	1365	6	,	,	PUNCT
ejpam-1372	1365	7	1973	1973	NUM
ejpam-1372	1365	8	.	.	PUNCT
ejpam-1372	1366	1	[	[	X
ejpam-1372	1366	2	34	34	NUM
ejpam-1372	1366	3	]	]	SYM
ejpam-1372	1366	4	s	s	PART
ejpam-1372	1366	5	wolfram	wolfram	PROPN
ejpam-1372	1366	6	.	.	PUNCT
ejpam-1372	1367	1	mathematicaa	mathematicaa	NOUN
ejpam-1372	1367	2	system	system	NOUN
ejpam-1372	1367	3	for	for	ADP
ejpam-1372	1367	4	doing	do	VERB
ejpam-1372	1367	5	mathematics	mathematic	NOUN
ejpam-1372	1367	6	by	by	ADP
ejpam-1372	1367	7	computer	computer	NOUN
ejpam-1372	1367	8	.	.	PUNCT
ejpam-1372	1368	1	addison	addison	PROPN
ejpam-1372	1368	2	-	-	PUNCT
ejpam-1372	1368	3	wesley	wesley	PROPN
ejpam-1372	1368	4	,	,	PUNCT
ejpam-1372	1368	5	reading	reading	NOUN
ejpam-1372	1368	6	,	,	PUNCT
ejpam-1372	1368	7	massachusetts	massachusetts	PROPN
ejpam-1372	1368	8	,	,	PUNCT
ejpam-1372	1368	9	1992	1992	NUM
ejpam-1372	1368	10	.	.	PUNCT
ejpam-1372	1369	1	[	[	X
ejpam-1372	1369	2	35	35	NUM
ejpam-1372	1369	3	]	]	PUNCT
ejpam-1372	1369	4	a	a	DET
ejpam-1372	1369	5	zwaan	zwaan	X
ejpam-1372	1369	6	.	.	PUNCT
ejpam-1372	1369	7	intensitäten	intensitäten	VERB
ejpam-1372	1369	8	in	in	ADP
ejpam-1372	1369	9	ca	ca	NOUN
ejpam-1372	1369	10	-	-	PUNCT
ejpam-1372	1369	11	funkenspektrum	funkenspektrum	NOUN
ejpam-1372	1369	12	.	.	PUNCT
ejpam-1372	1370	1	arch	arch	PROPN
ejpam-1372	1370	2	,	,	PUNCT
ejpam-1372	1370	3	nederlandaises	nederlandaises	PROPN
ejpam-1372	1370	4	des	des	PROPN
ejpam-1372	1370	5	sciences	sciences	PROPN
ejpam-1372	1370	6	exactes	exacte	NOUN
ejpam-1372	1370	7	,	,	PUNCT
ejpam-1372	1370	8	12:1–76	12:1–76	NUM
ejpam-1372	1370	9	,	,	PUNCT
ejpam-1372	1370	10	1929	1929	NUM
ejpam-1372	1370	11	.	.	PUNCT
ejpam-1372	1371	1	references	reference	NOUN
ejpam-1372	1371	2	418	418	NUM
ejpam-1372	1371	3	appendix	appendix	NOUN
ejpam-1372	1371	4	:	:	PUNCT
ejpam-1372	1371	5	tablestable	tablestable	ADJ
ejpam-1372	1371	6	1	1	NUM
ejpam-1372	1371	7	:	:	PUNCT
ejpam-1372	1371	8	mb	mb	ADJ
ejpam-1372	1371	9	-	-	PUNCT
ejpam-1372	1371	10	regularised	regularise	VERB
ejpam-1372	1371	11	values	value	NOUN
ejpam-1372	1371	12	of	of	ADP
ejpam-1372	1371	13	ti	ti	PROPN
ejpam-1372	1371	14	(	(	PUNCT
ejpam-1372	1371	15	0	0	NUM
ejpam-1372	1371	16	,	,	PUNCT
ejpam-1372	1371	17	3/7	3/7	NUM
ejpam-1372	1371	18	,	,	PUNCT
ejpam-1372	1371	19	z3	z3	PROPN
ejpam-1372	1371	20	)	)	PUNCT
ejpam-1372	1371	21	for	for	ADP
ejpam-1372	1371	22	various	various	ADJ
ejpam-1372	1371	23	values	value	NOUN
ejpam-1372	1371	24	of	of	ADP
ejpam-1372	1371	25	n	n	PRON
ejpam-1372	1371	26	with	with	ADP
ejpam-1372	1371	27	z	z	NOUN
ejpam-1372	1371	28	=	=	SYM
ejpam-1372	1371	29	(	(	PUNCT
ejpam-1372	1371	30	4/5)exp(iπ/4	4/5)exp(iπ/4	NOUN
ejpam-1372	1371	31	)	)	PUNCT
ejpam-1372	1371	32	.	.	PUNCT
ejpam-1372	1372	1	n	n	CCONJ
ejpam-1372	1372	2	l	l	NOUN
ejpam-1372	1372	3	truncated	truncate	VERB
ejpam-1372	1372	4	series	series	NOUN
ejpam-1372	1372	5	mb	mb	ADP
ejpam-1372	1372	6	integral	integral	ADJ
ejpam-1372	1372	7	discontinuity	discontinuity	NOUN
ejpam-1372	1372	8	regularised	regularise	VERB
ejpam-1372	1372	9	value	value	NOUN
ejpam-1372	1372	10	0	0	NUM
ejpam-1372	1372	11	0	0	NUM
ejpam-1372	1372	12	0	0	NUM
ejpam-1372	1372	13	2.11636689711647	2.11636689711647	NUM
ejpam-1372	1372	14	0	0	NUM
ejpam-1372	1372	15	2.11636689711647	2.11636689711647	NUM
ejpam-1372	1372	16	−0.47053628409637	−0.47053628409637	VERB
ejpam-1372	1373	1	i	i	PRON
ejpam-1372	1373	2	0	0	PUNCT
ejpam-1372	1374	1	−0.47053628409637	−0.47053628409637	ADJ
ejpam-1372	1375	1	i	i	PRON
ejpam-1372	1375	2	0	0	NUM
ejpam-1372	1375	3	1	1	NUM
ejpam-1372	1375	4	0	0	NUM
ejpam-1372	1375	5	3.93536614918420	3.93536614918420	NUM
ejpam-1372	1375	6	−1.81899925206772	−1.81899925206772	NOUN
ejpam-1372	1375	7	2.116366897116477	2.116366897116477	NUM
ejpam-1372	1375	8	+0.58629220846559	+0.58629220846559	NOUN
ejpam-1372	1376	1	i	i	PRON
ejpam-1372	1376	2	−1.05682849256197	−1.05682849256197	VERB
ejpam-1372	1377	1	i	i	PRON
ejpam-1372	1377	2	−0.47053628409637	−0.47053628409637	VERB
ejpam-1372	1377	3	i	i	PRON
ejpam-1372	1378	1	1	1	NUM
ejpam-1372	1378	2	0	0	NUM
ejpam-1372	1378	3	2.06751172656022	2.06751172656022	NUM
ejpam-1372	1378	4	0.04885517055624	0.04885517055624	NUM
ejpam-1372	1378	5	0	0	NUM
ejpam-1372	1379	1	2.11636689711647	2.11636689711647	NUM
ejpam-1372	1380	1	−0.47053628409637	−0.47053628409637	VERB
ejpam-1372	1381	1	i	i	PRON
ejpam-1372	1381	2	−0.47053628409637	−0.47053628409637	VERB
ejpam-1372	1382	1	i	i	PRON
ejpam-1372	1382	2	1	1	NUM
ejpam-1372	1382	3	1	1	NUM
ejpam-1372	1382	4	2.06751172656022	2.06751172656022	NUM
ejpam-1372	1382	5	1.867854422623970	1.867854422623970	NUM
ejpam-1372	1382	6	−1.81899925206772	−1.81899925206772	NOUN
ejpam-1372	1382	7	2.11636689711647	2.11636689711647	NUM
ejpam-1372	1382	8	+0.58629222084655	+0.58629222084655	NOUN
ejpam-1372	1383	1	i	i	PRON
ejpam-1372	1383	2	−1.05682849256197	−1.05682849256197	VERB
ejpam-1372	1384	1	i	i	PRON
ejpam-1372	1384	2	−0.47053628409637	−0.47053628409637	VERB
ejpam-1372	1384	3	i	i	PRON
ejpam-1372	1384	4	2	2	NUM
ejpam-1372	1384	5	0	0	NUM
ejpam-1372	1384	6	2.38830566931499	2.38830566931499	NUM
ejpam-1372	1384	7	−0.27193877219851	−0.27193877219851	NOUN
ejpam-1372	1384	8	0	0	NUM
ejpam-1372	1384	9	2.11636689711647	2.11636689711647	NUM
ejpam-1372	1384	10	−0.32079394275467	−0.32079394275467	NOUN
ejpam-1372	1384	11	i	i	PRON
ejpam-1372	1384	12	−0.14974234134161	−0.14974234134161	VERB
ejpam-1372	1384	13	i	i	PRON
ejpam-1372	1384	14	−0.47053628409637	−0.47053628409637	VERB
ejpam-1372	1385	1	i	i	PRON
ejpam-1372	1385	2	2	2	NUM
ejpam-1372	1385	3	1	1	NUM
ejpam-1372	1385	4	2.38830566931499	2.38830566931499	NUM
ejpam-1372	1385	5	1.54706047986920	1.54706047986920	NUM
ejpam-1372	1385	6	−1.81899925206772	−1.81899925206772	NOUN
ejpam-1372	1385	7	2.11636689711647	2.11636689711647	NUM
ejpam-1372	1385	8	−0.32079394275467	−0.32079394275467	NOUN
ejpam-1372	1385	9	i	i	PRON
ejpam-1372	1385	10	+0.90708615122036	+0.90708615122036	NOUN
ejpam-1372	1386	1	i	i	PRON
ejpam-1372	1386	2	−1.05682849256197	−1.05682849256197	VERB
ejpam-1372	1387	1	i	i	PRON
ejpam-1372	1387	2	−0.47053628409637	−0.47053628409637	VERB
ejpam-1372	1387	3	i	i	PRON
ejpam-1372	1388	1	5	5	NUM
ejpam-1372	1388	2	0	0	NUM
ejpam-1372	1388	3	1.37225259445007	1.37225259445007	NUM
ejpam-1372	1388	4	0.74411430266640	0.74411430266640	NUM
ejpam-1372	1388	5	0	0	NUM
ejpam-1372	1388	6	2.11636689711647	2.11636689711647	NUM
ejpam-1372	1388	7	−0.94437739311064	−0.94437739311064	NUM
ejpam-1372	1388	8	i	i	PRON
ejpam-1372	1388	9	+0.47384110901427	+0.47384110901427	VERB
ejpam-1372	1388	10	i	i	PRON
ejpam-1372	1388	11	−0.47053628409637	−0.47053628409637	VERB
ejpam-1372	1388	12	i	i	PRON
ejpam-1372	1388	13	5	5	NUM
ejpam-1372	1388	14	1	1	NUM
ejpam-1372	1388	15	1.37225259445007	1.37225259445007	NUM
ejpam-1372	1388	16	2.56311355473412	2.56311355473412	NUM
ejpam-1372	1388	17	*	*	PUNCT
ejpam-1372	1388	18	−1.81899925206772	−1.81899925206772	X
ejpam-1372	1388	19	2.11636689711647	2.11636689711647	NUM
ejpam-1372	1388	20	−0.94437739311064	−0.94437739311064	NUM
ejpam-1372	1388	21	i	i	PRON
ejpam-1372	1388	22	+1.53066960157624	+1.53066960157624	VERB
ejpam-1372	1388	23	i	i	PRON
ejpam-1372	1388	24	*	*	PUNCT
ejpam-1372	1388	25	−1.05682849256197	−1.05682849256197	PUNCT
ejpam-1372	1389	1	i	i	PRON
ejpam-1372	1389	2	−0.47053628409637	−0.47053628409637	VERB
ejpam-1372	1390	1	i	i	PRON
ejpam-1372	1391	1	10	10	NUM
ejpam-1372	1391	2	0	0	NUM
ejpam-1372	1391	3	242.349288466045	242.349288466045	NUM
ejpam-1372	1391	4	−240.232921568929	−240.232921568929	NOUN
ejpam-1372	1391	5	0	0	NUM
ejpam-1372	1391	6	2.11636689711576	2.11636689711576	NUM
ejpam-1372	1391	7	−158.966005072758	−158.966005072758	NOUN
ejpam-1372	1391	8	i	i	PRON
ejpam-1372	1391	9	+158.495468788662	+158.495468788662	PROPN
ejpam-1372	1391	10	i	i	PROPN
ejpam-1372	1391	11	−0.47053628409614	−0.47053628409614	NOUN
ejpam-1372	1391	12	i	i	PRON
ejpam-1372	1391	13	10	10	NUM
ejpam-1372	1391	14	1	1	NUM
ejpam-1372	1391	15	242.349288466045	242.349288466045	NUM
ejpam-1372	1391	16	−238.413922316848	−238.413922316848	NOUN
ejpam-1372	1391	17	*	*	PUNCT
ejpam-1372	1391	18	−1.81899925206772	−1.81899925206772	X
ejpam-1372	1391	19	2.11636689712853	2.11636689712853	NUM
ejpam-1372	1391	20	−158.966005072758	−158.966005072758	NOUN
ejpam-1372	1391	21	i	i	PRON
ejpam-1372	1391	22	+159.552297281241	+159.552297281241	PROPN
ejpam-1372	1391	23	i	i	PRON
ejpam-1372	1391	24	*	*	PUNCT
ejpam-1372	1391	25	−1.05682849256197	−1.05682849256197	PUNCT
ejpam-1372	1392	1	i	i	PRON
ejpam-1372	1392	2	−0.47053628407897	−0.47053628407897	PROPN
ejpam-1372	1393	1	i	i	PRON
ejpam-1372	1393	2	15	15	NUM
ejpam-1372	1393	3	0	0	NUM
ejpam-1372	1393	4	−208800.24691375	−208800.24691375	NOUN
ejpam-1372	1394	1	208802.36328065	208802.36328065	NUM
ejpam-1372	1394	2	0	0	SYM
ejpam-1372	1394	3	2.11636690574232	2.11636690574232	NUM
ejpam-1372	1394	4	+1.788757490	+1.788757490	NUM
ejpam-1372	1394	5	×	×	NOUN
ejpam-1372	1394	6	106	106	NUM
ejpam-1372	1395	1	i	i	PRON
ejpam-1372	1395	2	−1.788757960	−1.788757960	PROPN
ejpam-1372	1395	3	×	×	NOUN
ejpam-1372	1395	4	106	106	NUM
ejpam-1372	1396	1	i	i	PRON
ejpam-1372	1396	2	−0.47053628531284	−0.47053628531284	VERB
ejpam-1372	1396	3	i	i	PRON
ejpam-1372	1396	4	15	15	NUM
ejpam-1372	1396	5	1	1	NUM
ejpam-1372	1396	6	−208800.24691375	−208800.24691375	NUM
ejpam-1372	1396	7	208804.182279090	208804.182279090	NOUN
ejpam-1372	1396	8	*	*	PUNCT
ejpam-1372	1396	9	−1.81899925206772	−1.81899925206772	X
ejpam-1372	1396	10	2.11636608755697	2.11636608755697	NUM
ejpam-1372	1396	11	+1.788757490	+1.788757490	NUM
ejpam-1372	1396	12	×	×	NOUN
ejpam-1372	1396	13	106	106	NUM
ejpam-1372	1396	14	i	i	NOUN
ejpam-1372	1397	1	−1.788756903	−1.788756903	ADJ
ejpam-1372	1397	2	×	×	NOUN
ejpam-1372	1397	3	106	106	NUM
ejpam-1372	1398	1	i	i	PRON
ejpam-1372	1398	2	*	*	PROPN
ejpam-1372	1398	3	−1.05682849256197	−1.05682849256197	PUNCT
ejpam-1372	1399	1	i	i	PRON
ejpam-1372	1399	2	−0.47053533281075	−0.47053533281075	VERB
ejpam-1372	1399	3	i	i	PRON
ejpam-1372	1400	1	20	20	NUM
ejpam-1372	1400	2	0	0	NUM
ejpam-1372	1400	3	−4.688631796	−4.688631796	AUX
ejpam-1372	1400	4	×	×	VERB
ejpam-1372	1400	5	1010	1010	NUM
ejpam-1372	1400	6	4.688631796	4.688631796	NUM
ejpam-1372	1400	7	×	×	NOUN
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ejpam-1372	1400	9	0	0	NUM
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ejpam-1372	1400	11	−5.523649527	−5.523649527	ADJ
ejpam-1372	1400	12	×	×	NOUN
ejpam-1372	1400	13	1010	1010	NUM
ejpam-1372	1401	1	i	i	PRON
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ejpam-1372	1401	3	×	×	NOUN
ejpam-1372	1401	4	1010	1010	NUM
ejpam-1372	1401	5	i	i	PRON
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ejpam-1372	1401	7	i	i	ADV
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ejpam-1372	1401	9	1	1	NUM
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ejpam-1372	1401	11	×	×	NOUN
ejpam-1372	1401	12	1010	1010	NUM
ejpam-1372	1401	13	4.6886317966	4.6886317966	NUM
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ejpam-1372	1401	16	*	*	PUNCT
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ejpam-1372	1401	20	×	×	NOUN
ejpam-1372	1401	21	1010	1010	NUM
ejpam-1372	1402	1	i	i	PRON
ejpam-1372	1402	2	+5.5236495272	+5.5236495272	X
ejpam-1372	1403	1	×	×	VERB
ejpam-1372	1403	2	1010	1010	NUM
ejpam-1372	1403	3	i	i	PRON
ejpam-1372	1403	4	*	*	PUNCT
ejpam-1372	1403	5	+0.20513439806302	+0.20513439806302	PROPN
ejpam-1372	1404	1	i	i	PRON
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ejpam-1372	1405	2	references	reference	VERB
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ejpam-1372	1405	5	2	2	NUM
ejpam-1372	1405	6	:	:	PUNCT
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ejpam-1372	1405	8	-	-	PUNCT
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ejpam-1372	1405	20	=	=	SYM
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ejpam-1372	1405	24	z	z	PROPN
ejpam-1372	1405	25	>	>	X
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ejpam-1372	1410	3	1	1	NUM
ejpam-1372	1410	4	π/5	π/5	NUM
ejpam-1372	1410	5	0	0	NUM
ejpam-1372	1411	1	6.405352445877721	6.405352445877721	NUM
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ejpam-1372	1411	3	1.971898996789572	1.971898996789572	NUM
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ejpam-1372	1412	1	i	i	PRON
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ejpam-1372	1413	3	i	i	PRON
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ejpam-1372	1420	1	i	i	PRON
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ejpam-1372	1420	3	i	i	PRON
ejpam-1372	1420	4	1	1	NUM
ejpam-1372	1420	5	0	0	NUM
ejpam-1372	1420	6	3π/7	3π/7	NUM
ejpam-1372	1420	7	2.0675117265602293	2.0675117265602293	NUM
ejpam-1372	1420	8	2.2614145153684305	2.2614145153684305	NUM
ejpam-1372	1420	9	0	0	NUM
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ejpam-1372	1422	2	−0.5800987411949	−0.5800987411949	VERB
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ejpam-1372	1423	5	i	i	ADV
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ejpam-1372	1426	4	2π/3	2π/3	NUM
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ejpam-1372	1428	7	1	1	NUM
ejpam-1372	1428	8	8π/9	8π/9	NUM
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ejpam-1372	1432	4	8π/9	8π/9	NUM
ejpam-1372	1432	5	2.17482659335582993	2.17482659335582993	NUM
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ejpam-1372	1432	8	4.276241548706656	4.276241548706656	NUM
ejpam-1372	1432	9	+1.36926557120305	+1.36926557120305	NOUN
ejpam-1372	1432	10	i	i	PRON
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ejpam-1372	1434	5	:	:	PUNCT
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ejpam-1372	1434	7	-	-	PUNCT
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ejpam-1372	1434	16	)	)	PUNCT
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ejpam-1372	1434	18	|z|=	|z|=	NOUN
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