id	sid	tid	token	lemma	pos
ejpam-2461	1	1	compile	compile	NOUN
ejpam-2461	1	2	/	/	SYM
ejpam-2461	1	3	output.dvi	output.dvi	NOUN
ejpam-2461	1	4	european	european	ADJ
ejpam-2461	1	5	journal	journal	NOUN
ejpam-2461	1	6	of	of	ADP
ejpam-2461	1	7	pure	pure	ADJ
ejpam-2461	1	8	and	and	CCONJ
ejpam-2461	1	9	applied	apply	VERB
ejpam-2461	1	10	mathematics	mathematic	NOUN
ejpam-2461	1	11	vol	vol	NOUN
ejpam-2461	1	12	.	.	PROPN
ejpam-2461	2	1	9	9	NUM
ejpam-2461	2	2	,	,	PUNCT
ejpam-2461	2	3	no	no	INTJ
ejpam-2461	2	4	.	.	NOUN
ejpam-2461	2	5	1	1	NUM
ejpam-2461	2	6	,	,	PUNCT
ejpam-2461	2	7	2016	2016	NUM
ejpam-2461	2	8	,	,	PUNCT
ejpam-2461	2	9	3	3	NUM
ejpam-2461	2	10	-	-	SYM
ejpam-2461	2	11	18	18	NUM
ejpam-2461	2	12	issn	issn	PROPN
ejpam-2461	2	13	1307	1307	NUM
ejpam-2461	2	14	-	-	SYM
ejpam-2461	2	15	5543	5543	NUM
ejpam-2461	2	16	–	–	PUNCT
ejpam-2461	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2461	2	18	the	the	DET
ejpam-2461	2	19	asymptotic	asymptotic	ADJ
ejpam-2461	2	20	expansion	expansion	NOUN
ejpam-2461	2	21	of	of	ADP
ejpam-2461	2	22	a	a	DET
ejpam-2461	2	23	generalisation	generalisation	NOUN
ejpam-2461	2	24	of	of	ADP
ejpam-2461	2	25	the	the	DET
ejpam-2461	2	26	euler	euler	PROPN
ejpam-2461	2	27	-	-	PUNCT
ejpam-2461	2	28	jacobi	jacobi	PROPN
ejpam-2461	2	29	series	series	PROPN
ejpam-2461	2	30	richard	richard	PROPN
ejpam-2461	2	31	b.	b.	PROPN
ejpam-2461	2	32	paris	paris	PROPN
ejpam-2461	2	33	division	division	NOUN
ejpam-2461	2	34	of	of	ADP
ejpam-2461	2	35	computing	computing	NOUN
ejpam-2461	2	36	and	and	CCONJ
ejpam-2461	2	37	mathematics	mathematic	NOUN
ejpam-2461	2	38	,	,	PUNCT
ejpam-2461	2	39	university	university	NOUN
ejpam-2461	2	40	of	of	ADP
ejpam-2461	2	41	abertay	abertay	PROPN
ejpam-2461	2	42	dundee	dundee	PROPN
ejpam-2461	2	43	,	,	PUNCT
ejpam-2461	2	44	dundee	dundee	PROPN
ejpam-2461	2	45	dd1	dd1	PROPN
ejpam-2461	2	46	1hg	1hg	PROPN
ejpam-2461	2	47	,	,	PUNCT
ejpam-2461	2	48	uk	uk	PROPN
ejpam-2461	2	49	abstract	abstract	NOUN
ejpam-2461	2	50	.	.	PUNCT
ejpam-2461	3	1	we	we	PRON
ejpam-2461	3	2	consider	consider	VERB
ejpam-2461	3	3	the	the	DET
ejpam-2461	3	4	asymptotic	asymptotic	ADJ
ejpam-2461	3	5	expansion	expansion	NOUN
ejpam-2461	3	6	of	of	ADP
ejpam-2461	3	7	the	the	DET
ejpam-2461	3	8	sum	sum	NOUN
ejpam-2461	3	9	sp(a	sp(a	NOUN
ejpam-2461	3	10	;	;	PUNCT
ejpam-2461	3	11	w	w	X
ejpam-2461	3	12	)	)	PUNCT
ejpam-2461	3	13	=	=	SYM
ejpam-2461	4	1	∞	∞	NUM
ejpam-2461	4	2	∑	∑	PUNCT
ejpam-2461	4	3	n=1	n=1	PROPN
ejpam-2461	4	4	e−anp	e−anp	VERB
ejpam-2461	4	5	nw	nw	PROPN
ejpam-2461	4	6	as	as	ADP
ejpam-2461	4	7	a→	a→	X
ejpam-2461	4	8	0	0	NUM
ejpam-2461	4	9	in	in	ADP
ejpam-2461	4	10	|arg	|arg	NOUN
ejpam-2461	4	11	a|	a|	PROPN
ejpam-2461	4	12	<	<	X
ejpam-2461	4	13	1	1	NUM
ejpam-2461	4	14	2π	2π	NOUN
ejpam-2461	4	15	for	for	ADP
ejpam-2461	4	16	arbitrary	arbitrary	ADJ
ejpam-2461	4	17	finite	finite	NOUN
ejpam-2461	4	18	p	p	PROPN
ejpam-2461	4	19	>	>	X
ejpam-2461	4	20	0	0	PUNCT
ejpam-2461	4	21	and	and	CCONJ
ejpam-2461	4	22	w	w	ADP
ejpam-2461	4	23	>	>	X
ejpam-2461	4	24	0	0	X
ejpam-2461	4	25	.	.	PUNCT
ejpam-2461	5	1	our	our	PRON
ejpam-2461	5	2	attention	attention	NOUN
ejpam-2461	5	3	is	be	AUX
ejpam-2461	5	4	concentrated	concentrate	VERB
ejpam-2461	5	5	mainly	mainly	ADV
ejpam-2461	5	6	on	on	ADP
ejpam-2461	5	7	the	the	DET
ejpam-2461	5	8	case	case	NOUN
ejpam-2461	5	9	when	when	SCONJ
ejpam-2461	5	10	p	p	PROPN
ejpam-2461	5	11	and	and	CCONJ
ejpam-2461	5	12	w	w	PROPN
ejpam-2461	5	13	are	be	AUX
ejpam-2461	5	14	both	both	PRON
ejpam-2461	5	15	even	even	ADV
ejpam-2461	5	16	integers	integer	NOUN
ejpam-2461	5	17	,	,	PUNCT
ejpam-2461	5	18	where	where	SCONJ
ejpam-2461	5	19	the	the	DET
ejpam-2461	5	20	expansion	expansion	NOUN
ejpam-2461	5	21	consists	consist	VERB
ejpam-2461	5	22	of	of	ADP
ejpam-2461	5	23	a	a	DET
ejpam-2461	5	24	finite	finite	ADJ
ejpam-2461	5	25	algebraic	algebraic	ADJ
ejpam-2461	5	26	expansion	expansion	NOUN
ejpam-2461	5	27	together	together	ADV
ejpam-2461	5	28	with	with	ADP
ejpam-2461	5	29	a	a	DET
ejpam-2461	5	30	sequence	sequence	NOUN
ejpam-2461	5	31	of	of	ADP
ejpam-2461	5	32	increasingly	increasingly	ADV
ejpam-2461	5	33	subdominant	subdominant	ADJ
ejpam-2461	5	34	exponential	exponential	ADJ
ejpam-2461	5	35	expansions	expansion	NOUN
ejpam-2461	5	36	.	.	PUNCT
ejpam-2461	6	1	this	this	DET
ejpam-2461	6	2	exponentially	exponentially	ADV
ejpam-2461	6	3	small	small	ADJ
ejpam-2461	6	4	component	component	NOUN
ejpam-2461	6	5	produces	produce	VERB
ejpam-2461	6	6	a	a	DET
ejpam-2461	6	7	transformation	transformation	NOUN
ejpam-2461	6	8	for	for	ADP
ejpam-2461	6	9	sp(a	sp(a	PROPN
ejpam-2461	6	10	;	;	PUNCT
ejpam-2461	6	11	w	w	X
ejpam-2461	6	12	)	)	PUNCT
ejpam-2461	6	13	analogous	analogous	ADJ
ejpam-2461	6	14	to	to	ADP
ejpam-2461	6	15	the	the	DET
ejpam-2461	6	16	well	well	ADV
ejpam-2461	6	17	-	-	PUNCT
ejpam-2461	6	18	known	know	VERB
ejpam-2461	6	19	poisson	poisson	NOUN
ejpam-2461	6	20	-	-	PROPN
ejpam-2461	6	21	jacobi	jacobi	PROPN
ejpam-2461	6	22	transformation	transformation	NOUN
ejpam-2461	6	23	for	for	ADP
ejpam-2461	6	24	the	the	DET
ejpam-2461	6	25	sum	sum	NOUN
ejpam-2461	6	26	with	with	ADP
ejpam-2461	6	27	p	p	NOUN
ejpam-2461	6	28	=	=	SYM
ejpam-2461	6	29	2	2	NUM
ejpam-2461	6	30	and	and	CCONJ
ejpam-2461	6	31	w=	w=	NOUN
ejpam-2461	6	32	0	0	NUM
ejpam-2461	6	33	.	.	PUNCT
ejpam-2461	7	1	numerical	numerical	ADJ
ejpam-2461	7	2	results	result	NOUN
ejpam-2461	7	3	are	be	AUX
ejpam-2461	7	4	given	give	VERB
ejpam-2461	7	5	to	to	PART
ejpam-2461	7	6	illustrate	illustrate	VERB
ejpam-2461	7	7	the	the	DET
ejpam-2461	7	8	accuracy	accuracy	NOUN
ejpam-2461	7	9	of	of	ADP
ejpam-2461	7	10	the	the	DET
ejpam-2461	7	11	expansion	expansion	NOUN
ejpam-2461	7	12	obtained	obtain	VERB
ejpam-2461	7	13	.	.	PUNCT
ejpam-2461	8	1	2010	2010	NUM
ejpam-2461	8	2	mathematics	mathematic	NOUN
ejpam-2461	8	3	subject	subject	NOUN
ejpam-2461	8	4	classifications	classification	NOUN
ejpam-2461	8	5	:	:	PUNCT
ejpam-2461	8	6	30e15	30e15	NUM
ejpam-2461	8	7	,	,	PUNCT
ejpam-2461	8	8	33b10	33b10	NUM
ejpam-2461	8	9	,	,	PUNCT
ejpam-2461	8	10	34e05	34e05	NUM
ejpam-2461	8	11	,	,	PUNCT
ejpam-2461	8	12	41a30	41a30	DET
ejpam-2461	8	13	key	key	ADJ
ejpam-2461	8	14	words	word	NOUN
ejpam-2461	8	15	and	and	CCONJ
ejpam-2461	8	16	phrases	phrase	NOUN
ejpam-2461	8	17	:	:	PUNCT
ejpam-2461	8	18	euler	euler	NOUN
ejpam-2461	8	19	-	-	PUNCT
ejpam-2461	8	20	jacobi	jacobi	PROPN
ejpam-2461	8	21	series	series	PROPN
ejpam-2461	8	22	,	,	PUNCT
ejpam-2461	8	23	poisson	poisson	PROPN
ejpam-2461	8	24	-	-	PROPN
ejpam-2461	8	25	jacobi	jacobi	PROPN
ejpam-2461	8	26	transformation	transformation	NOUN
ejpam-2461	8	27	,	,	PUNCT
ejpam-2461	8	28	asymptotic	asymptotic	ADJ
ejpam-2461	8	29	expansion	expansion	NOUN
ejpam-2461	8	30	,	,	PUNCT
ejpam-2461	8	31	inverse	inverse	NOUN
ejpam-2461	8	32	factorial	factorial	NOUN
ejpam-2461	8	33	expansion	expansion	NOUN
ejpam-2461	8	34	1	1	NUM
ejpam-2461	8	35	.	.	PUNCT
ejpam-2461	9	1	introduction	introduction	NOUN
ejpam-2461	9	2	we	we	PRON
ejpam-2461	9	3	consider	consider	VERB
ejpam-2461	9	4	the	the	DET
ejpam-2461	9	5	asymptotic	asymptotic	ADJ
ejpam-2461	9	6	expansion	expansion	NOUN
ejpam-2461	9	7	of	of	ADP
ejpam-2461	9	8	the	the	DET
ejpam-2461	9	9	sum	sum	NOUN
ejpam-2461	9	10	sp(a	sp(a	NOUN
ejpam-2461	9	11	;	;	PUNCT
ejpam-2461	9	12	w	w	X
ejpam-2461	9	13	)	)	PUNCT
ejpam-2461	9	14	=	=	SYM
ejpam-2461	10	1	∞	∞	NUM
ejpam-2461	10	2	∑	∑	PUNCT
ejpam-2461	10	3	n=1	n=1	PROPN
ejpam-2461	10	4	e−anp	e−anp	VERB
ejpam-2461	10	5	nw	nw	PROPN
ejpam-2461	11	1	(	(	PUNCT
ejpam-2461	11	2	1	1	NUM
ejpam-2461	11	3	)	)	PUNCT
ejpam-2461	11	4	as	as	ADP
ejpam-2461	11	5	the	the	DET
ejpam-2461	11	6	parameter	parameter	NOUN
ejpam-2461	11	7	a→	a→	PUNCT
ejpam-2461	11	8	0	0	NUM
ejpam-2461	11	9	in	in	ADP
ejpam-2461	11	10	|arg	|arg	NOUN
ejpam-2461	11	11	a|	a|	PROPN
ejpam-2461	11	12	<	<	X
ejpam-2461	11	13	1	1	NUM
ejpam-2461	11	14	2π	2π	NOUN
ejpam-2461	11	15	,	,	PUNCT
ejpam-2461	11	16	where	where	SCONJ
ejpam-2461	11	17	p	p	NOUN
ejpam-2461	11	18	>	>	X
ejpam-2461	11	19	0	0	PUNCT
ejpam-2461	12	1	and	and	CCONJ
ejpam-2461	12	2	,	,	PUNCT
ejpam-2461	12	3	for	for	ADP
ejpam-2461	12	4	convenience	convenience	NOUN
ejpam-2461	12	5	,	,	PUNCT
ejpam-2461	12	6	w	w	PROPN
ejpam-2461	12	7	will	will	AUX
ejpam-2461	12	8	be	be	AUX
ejpam-2461	12	9	supposed	suppose	VERB
ejpam-2461	12	10	throughout	throughout	ADP
ejpam-2461	12	11	to	to	PART
ejpam-2461	12	12	be	be	AUX
ejpam-2461	12	13	real	real	ADJ
ejpam-2461	12	14	and	and	CCONJ
ejpam-2461	12	15	positive	positive	ADJ
ejpam-2461	12	16	.	.	PUNCT
ejpam-2461	13	1	when	when	SCONJ
ejpam-2461	13	2	w=	w=	PROPN
ejpam-2461	13	3	0	0	NUM
ejpam-2461	13	4	,	,	PUNCT
ejpam-2461	13	5	this	this	DET
ejpam-2461	13	6	sum	sum	NOUN
ejpam-2461	13	7	is	be	AUX
ejpam-2461	13	8	known	know	VERB
ejpam-2461	13	9	as	as	ADP
ejpam-2461	13	10	the	the	DET
ejpam-2461	13	11	euler	euler	PROPN
ejpam-2461	13	12	-	-	PUNCT
ejpam-2461	13	13	jacobi	jacobi	PROPN
ejpam-2461	13	14	series	series	NOUN
ejpam-2461	13	15	and	and	CCONJ
ejpam-2461	13	16	when	when	SCONJ
ejpam-2461	13	17	a	a	DET
ejpam-2461	13	18	=	=	SYM
ejpam-2461	13	19	0	0	X
ejpam-2461	13	20	then	then	ADV
ejpam-2461	13	21	sp(0	sp(0	NOUN
ejpam-2461	13	22	;	;	PUNCT
ejpam-2461	13	23	w	w	X
ejpam-2461	13	24	)	)	PUNCT
ejpam-2461	13	25	reduces	reduce	VERB
ejpam-2461	13	26	to	to	ADP
ejpam-2461	13	27	the	the	DET
ejpam-2461	13	28	riemann	riemann	PROPN
ejpam-2461	13	29	zeta	zeta	PROPN
ejpam-2461	13	30	function	function	PROPN
ejpam-2461	13	31	ζ(w	ζ(w	PROPN
ejpam-2461	13	32	)	)	PUNCT
ejpam-2461	13	33	(	(	PUNCT
ejpam-2461	13	34	providedℜ(w	providedℜ(w	NOUN
ejpam-2461	13	35	)	)	PUNCT
ejpam-2461	13	36	>	>	X
ejpam-2461	13	37	1	1	NUM
ejpam-2461	13	38	)	)	PUNCT
ejpam-2461	13	39	.	.	PUNCT
ejpam-2461	14	1	consequently	consequently	ADV
ejpam-2461	14	2	,	,	PUNCT
ejpam-2461	14	3	the	the	DET
ejpam-2461	14	4	series	series	NOUN
ejpam-2461	14	5	in	in	ADP
ejpam-2461	14	6	(	(	PUNCT
ejpam-2461	14	7	1	1	X
ejpam-2461	14	8	)	)	PUNCT
ejpam-2461	14	9	can	can	AUX
ejpam-2461	14	10	also	also	ADV
ejpam-2461	14	11	be	be	AUX
ejpam-2461	14	12	viewed	view	VERB
ejpam-2461	14	13	as	as	ADP
ejpam-2461	14	14	a	a	DET
ejpam-2461	14	15	smoothed	smoothed	ADJ
ejpam-2461	14	16	dirichlet	dirichlet	PROPN
ejpam-2461	14	17	series	series	NOUN
ejpam-2461	14	18	for	for	ADP
ejpam-2461	14	19	ζ(w	ζ(w	PROPN
ejpam-2461	14	20	)	)	PUNCT
ejpam-2461	14	21	.	.	PUNCT
ejpam-2461	15	1	the	the	DET
ejpam-2461	15	2	asymptotics	asymptotic	NOUN
ejpam-2461	15	3	of	of	ADP
ejpam-2461	15	4	sp(a	sp(a	PROPN
ejpam-2461	15	5	;	;	PUNCT
ejpam-2461	15	6	w	w	X
ejpam-2461	15	7	)	)	PUNCT
ejpam-2461	15	8	as	as	ADP
ejpam-2461	15	9	a→	a→	X
ejpam-2461	15	10	0	0	NUM
ejpam-2461	15	11	+	+	X
ejpam-2461	15	12	for	for	ADP
ejpam-2461	15	13	p	p	DET
ejpam-2461	15	14	a	a	DET
ejpam-2461	15	15	rational	rational	ADJ
ejpam-2461	15	16	fraction	fraction	NOUN
ejpam-2461	15	17	and	and	CCONJ
ejpam-2461	15	18	w	w	NOUN
ejpam-2461	15	19	<	<	X
ejpam-2461	15	20	0	0	NUM
ejpam-2461	15	21	was	be	AUX
ejpam-2461	15	22	considered	consider	VERB
ejpam-2461	15	23	by	by	ADP
ejpam-2461	15	24	ramanujan	ramanujan	NOUN
ejpam-2461	15	25	and	and	CCONJ
ejpam-2461	15	26	is	be	AUX
ejpam-2461	15	27	discussed	discuss	VERB
ejpam-2461	15	28	in	in	ADP
ejpam-2461	15	29	[	[	X
ejpam-2461	15	30	1	1	NUM
ejpam-2461	15	31	,	,	PUNCT
ejpam-2461	15	32	chapter	chapter	NOUN
ejpam-2461	15	33	15	15	NUM
ejpam-2461	15	34	]	]	PUNCT
ejpam-2461	15	35	.	.	PUNCT
ejpam-2461	16	1	it	it	PRON
ejpam-2461	16	2	was	be	AUX
ejpam-2461	16	3	shown	show	VERB
ejpam-2461	16	4	that	that	SCONJ
ejpam-2461	16	5	the	the	DET
ejpam-2461	16	6	expansion	expansion	NOUN
ejpam-2461	16	7	in	in	ADP
ejpam-2461	16	8	this	this	DET
ejpam-2461	16	9	email	email	NOUN
ejpam-2461	16	10	address	address	NOUN
ejpam-2461	16	11	:	:	PUNCT
ejpam-2461	16	12	r.paris@abertay.ac.uk	r.paris@abertay.ac.uk	PROPN
ejpam-2461	16	13	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2461	17	1	3	3	NUM
ejpam-2461	17	2	c	c	X
ejpam-2461	17	3	©	©	PROPN
ejpam-2461	17	4	2016	2016	NUM
ejpam-2461	17	5	ejpam	ejpam	VERB
ejpam-2461	17	6	all	all	DET
ejpam-2461	17	7	rights	right	NOUN
ejpam-2461	17	8	reserved	reserve	VERB
ejpam-2461	17	9	.	.	PUNCT
ejpam-2461	18	1	r.	r.	PROPN
ejpam-2461	18	2	paris	paris	PROPN
ejpam-2461	18	3	/	/	SYM
ejpam-2461	18	4	eur	eur	PROPN
ejpam-2461	18	5	.	.	PUNCT
ejpam-2461	19	1	j.	j.	PROPN
ejpam-2461	19	2	pure	pure	PROPN
ejpam-2461	19	3	appl	appl	PROPN
ejpam-2461	19	4	.	.	PROPN
ejpam-2461	19	5	math	math	PROPN
ejpam-2461	19	6	,	,	PUNCT
ejpam-2461	19	7	9	9	NUM
ejpam-2461	19	8	(	(	PUNCT
ejpam-2461	19	9	2016	2016	NUM
ejpam-2461	19	10	)	)	PUNCT
ejpam-2461	19	11	,	,	PUNCT
ejpam-2461	19	12	3	3	NUM
ejpam-2461	19	13	-	-	SYM
ejpam-2461	19	14	18	18	NUM
ejpam-2461	19	15	4	4	NUM
ejpam-2461	19	16	case	case	NOUN
ejpam-2461	19	17	consisted	consist	VERB
ejpam-2461	19	18	of	of	ADP
ejpam-2461	19	19	an	an	DET
ejpam-2461	19	20	asymptotic	asymptotic	ADJ
ejpam-2461	19	21	sum	sum	NOUN
ejpam-2461	19	22	involving	involve	VERB
ejpam-2461	19	23	the	the	DET
ejpam-2461	19	24	riemann	riemann	PROPN
ejpam-2461	19	25	zeta	zeta	PROPN
ejpam-2461	19	26	function	function	PROPN
ejpam-2461	19	27	.	.	PUNCT
ejpam-2461	20	1	a	a	DET
ejpam-2461	20	2	hypergeometric	hypergeometric	ADJ
ejpam-2461	20	3	function	function	NOUN
ejpam-2461	20	4	approach	approach	NOUN
ejpam-2461	20	5	for	for	ADP
ejpam-2461	20	6	the	the	DET
ejpam-2461	20	7	euler	euler	PROPN
ejpam-2461	20	8	-	-	PUNCT
ejpam-2461	20	9	jacobi	jacobi	PROPN
ejpam-2461	20	10	series	series	PROPN
ejpam-2461	20	11	when	when	SCONJ
ejpam-2461	20	12	p	p	NOUN
ejpam-2461	20	13	is	be	AUX
ejpam-2461	20	14	a	a	DET
ejpam-2461	20	15	rational	rational	ADJ
ejpam-2461	20	16	fraction	fraction	NOUN
ejpam-2461	20	17	and	and	CCONJ
ejpam-2461	20	18	w=	w=	NOUN
ejpam-2461	20	19	0	0	NUM
ejpam-2461	20	20	has	have	AUX
ejpam-2461	20	21	been	be	AUX
ejpam-2461	20	22	discussed	discuss	VERB
ejpam-2461	20	23	at	at	ADP
ejpam-2461	20	24	length	length	NOUN
ejpam-2461	20	25	in	in	ADP
ejpam-2461	20	26	the	the	DET
ejpam-2461	20	27	monograph	monograph	NOUN
ejpam-2461	21	1	[	[	X
ejpam-2461	21	2	3	3	NUM
ejpam-2461	21	3	]	]	PUNCT
ejpam-2461	21	4	,	,	PUNCT
ejpam-2461	21	5	where	where	SCONJ
ejpam-2461	21	6	great	great	ADJ
ejpam-2461	21	7	emphasis	emphasis	NOUN
ejpam-2461	21	8	was	be	AUX
ejpam-2461	21	9	placed	place	VERB
ejpam-2461	21	10	on	on	ADP
ejpam-2461	21	11	obtaining	obtain	VERB
ejpam-2461	21	12	exponentially	exponentially	ADV
ejpam-2461	21	13	small	small	ADJ
ejpam-2461	21	14	expansions	expansion	NOUN
ejpam-2461	21	15	.	.	PUNCT
ejpam-2461	22	1	the	the	DET
ejpam-2461	22	2	case	case	NOUN
ejpam-2461	22	3	w=	w=	NOUN
ejpam-2461	22	4	0	0	NUM
ejpam-2461	22	5	and	and	CCONJ
ejpam-2461	22	6	arbitrary	arbitrary	ADJ
ejpam-2461	22	7	p	p	X
ejpam-2461	22	8	>	>	X
ejpam-2461	22	9	0	0	NUM
ejpam-2461	22	10	,	,	PUNCT
ejpam-2461	22	11	thus	thus	ADV
ejpam-2461	22	12	generalising	generalise	VERB
ejpam-2461	22	13	the	the	DET
ejpam-2461	22	14	work	work	NOUN
ejpam-2461	22	15	in	in	ADP
ejpam-2461	22	16	[	[	X
ejpam-2461	22	17	3	3	NUM
ejpam-2461	22	18	]	]	PUNCT
ejpam-2461	22	19	,	,	PUNCT
ejpam-2461	22	20	has	have	AUX
ejpam-2461	22	21	been	be	AUX
ejpam-2461	22	22	investigated	investigate	VERB
ejpam-2461	22	23	in	in	ADP
ejpam-2461	22	24	[	[	X
ejpam-2461	22	25	5	5	NUM
ejpam-2461	22	26	,	,	PUNCT
ejpam-2461	22	27	§	§	NOUN
ejpam-2461	22	28	8.1	8.1	NUM
ejpam-2461	22	29	]	]	PUNCT
ejpam-2461	22	30	also	also	ADV
ejpam-2461	22	31	for	for	ADP
ejpam-2461	22	32	a→	a→	X
ejpam-2461	22	33	0	0	NUM
ejpam-2461	22	34	+	+	CCONJ
ejpam-2461	22	35	using	use	VERB
ejpam-2461	22	36	both	both	CCONJ
ejpam-2461	22	37	a	a	DET
ejpam-2461	22	38	mellin	mellin	NOUN
ejpam-2461	22	39	-	-	PUNCT
ejpam-2461	22	40	barnes	barnes	NOUN
ejpam-2461	22	41	integral	integral	ADJ
ejpam-2461	22	42	approach	approach	NOUN
ejpam-2461	22	43	and	and	CCONJ
ejpam-2461	22	44	also	also	ADV
ejpam-2461	22	45	a	a	DET
ejpam-2461	22	46	saddle	saddle	NOUN
ejpam-2461	22	47	point	point	NOUN
ejpam-2461	22	48	analysis	analysis	NOUN
ejpam-2461	22	49	of	of	ADP
ejpam-2461	22	50	a	a	DET
ejpam-2461	22	51	laplace	laplace	NOUN
ejpam-2461	22	52	-	-	PUNCT
ejpam-2461	22	53	type	type	NOUN
ejpam-2461	22	54	integral	integral	ADJ
ejpam-2461	22	55	representation	representation	NOUN
ejpam-2461	22	56	.	.	PUNCT
ejpam-2461	23	1	a	a	DET
ejpam-2461	23	2	similar	similar	ADJ
ejpam-2461	23	3	mellin	mellin	PROPN
ejpam-2461	23	4	-	-	PUNCT
ejpam-2461	23	5	barnes	barnes	NOUN
ejpam-2461	23	6	integral	integral	ADJ
ejpam-2461	23	7	approach	approach	NOUN
ejpam-2461	23	8	for	for	ADP
ejpam-2461	23	9	this	this	DET
ejpam-2461	23	10	latter	latter	ADJ
ejpam-2461	23	11	case	case	NOUN
ejpam-2461	23	12	has	have	AUX
ejpam-2461	23	13	also	also	ADV
ejpam-2461	23	14	been	be	AUX
ejpam-2461	23	15	independently	independently	ADV
ejpam-2461	23	16	considered	consider	VERB
ejpam-2461	23	17	.	.	PUNCT
ejpam-2461	24	1	the	the	DET
ejpam-2461	24	2	saddle	saddle	NOUN
ejpam-2461	24	3	point	point	NOUN
ejpam-2461	24	4	approach	approach	NOUN
ejpam-2461	24	5	is	be	AUX
ejpam-2461	24	6	instructive	instructive	ADJ
ejpam-2461	24	7	for	for	ADP
ejpam-2461	24	8	understanding	understand	VERB
ejpam-2461	24	9	the	the	DET
ejpam-2461	24	10	appearance	appearance	NOUN
ejpam-2461	24	11	of	of	ADP
ejpam-2461	24	12	exponentially	exponentially	ADV
ejpam-2461	24	13	small	small	ADJ
ejpam-2461	24	14	terms	term	NOUN
ejpam-2461	24	15	in	in	ADP
ejpam-2461	24	16	the	the	DET
ejpam-2461	24	17	expansion	expansion	NOUN
ejpam-2461	24	18	as	as	ADP
ejpam-2461	24	19	the	the	DET
ejpam-2461	24	20	parameter	parameter	NOUN
ejpam-2461	24	21	p	p	NOUN
ejpam-2461	24	22	increases	increase	NOUN
ejpam-2461	24	23	.	.	PUNCT
ejpam-2461	25	1	it	it	PRON
ejpam-2461	25	2	was	be	AUX
ejpam-2461	25	3	established	establish	VERB
ejpam-2461	25	4	in	in	ADP
ejpam-2461	25	5	[	[	X
ejpam-2461	25	6	5	5	NUM
ejpam-2461	25	7	,	,	PUNCT
ejpam-2461	25	8	§	§	NOUN
ejpam-2461	25	9	8.1	8.1	NUM
ejpam-2461	25	10	]	]	PUNCT
ejpam-2461	25	11	that	that	SCONJ
ejpam-2461	25	12	an	an	DET
ejpam-2461	25	13	additional	additional	ADJ
ejpam-2461	25	14	exponentially	exponentially	ADV
ejpam-2461	25	15	small	small	ADJ
ejpam-2461	25	16	contribution	contribution	NOUN
ejpam-2461	25	17	appears	appear	VERB
ejpam-2461	25	18	when	when	SCONJ
ejpam-2461	25	19	p	p	PROPN
ejpam-2461	25	20	=	=	NOUN
ejpam-2461	25	21	2	2	NUM
ejpam-2461	25	22	+	+	NUM
ejpam-2461	25	23	4k	4k	NOUN
ejpam-2461	25	24	,	,	PUNCT
ejpam-2461	25	25	k	k	PROPN
ejpam-2461	26	1	=	=	PUNCT
ejpam-2461	26	2	0,1,2	0,1,2	NUM
ejpam-2461	26	3	,	,	PUNCT
ejpam-2461	26	4	.	.	PUNCT
ejpam-2461	26	5	.	.	PUNCT
ejpam-2461	26	6	.	.	PUNCT
ejpam-2461	26	7	.	.	PUNCT
ejpam-2461	27	1	indeed	indeed	ADV
ejpam-2461	27	2	,	,	PUNCT
ejpam-2461	27	3	the	the	DET
ejpam-2461	27	4	appearance	appearance	NOUN
ejpam-2461	27	5	of	of	ADP
ejpam-2461	27	6	the	the	DET
ejpam-2461	27	7	first	first	ADJ
ejpam-2461	27	8	exponentially	exponentially	ADV
ejpam-2461	27	9	small	small	ADJ
ejpam-2461	27	10	expansion	expansion	NOUN
ejpam-2461	27	11	as	as	SCONJ
ejpam-2461	27	12	p	p	NOUN
ejpam-2461	27	13	passes	pass	VERB
ejpam-2461	27	14	through	through	ADP
ejpam-2461	27	15	the	the	DET
ejpam-2461	27	16	‘	'	PUNCT
ejpam-2461	27	17	classical	classical	ADJ
ejpam-2461	27	18	’	'	PUNCT
ejpam-2461	27	19	value	value	NOUN
ejpam-2461	27	20	p	p	NOUN
ejpam-2461	27	21	=	=	SYM
ejpam-2461	27	22	2	2	NUM
ejpam-2461	27	23	was	be	AUX
ejpam-2461	27	24	demonstrated	demonstrate	VERB
ejpam-2461	27	25	to	to	PART
ejpam-2461	27	26	be	be	AUX
ejpam-2461	27	27	associated	associate	VERB
ejpam-2461	27	28	with	with	ADP
ejpam-2461	27	29	a	a	DET
ejpam-2461	27	30	stokes	stoke	NOUN
ejpam-2461	27	31	phenomenon	phenomenon	NOUN
ejpam-2461	28	1	[	[	X
ejpam-2461	28	2	5	5	NUM
ejpam-2461	28	3	,	,	PUNCT
ejpam-2461	28	4	§	§	NOUN
ejpam-2461	28	5	8.1.7	8.1.7	NUM
ejpam-2461	28	6	]	]	PUNCT
ejpam-2461	28	7	.	.	PUNCT
ejpam-2461	29	1	in	in	ADP
ejpam-2461	29	2	the	the	DET
ejpam-2461	29	3	case	case	NOUN
ejpam-2461	29	4	p	p	X
ejpam-2461	29	5	=	=	SYM
ejpam-2461	29	6	2	2	NUM
ejpam-2461	29	7	,	,	PUNCT
ejpam-2461	29	8	w=	w=	NOUN
ejpam-2461	29	9	0	0	NUM
ejpam-2461	30	1	the	the	DET
ejpam-2461	30	2	behaviour	behaviour	NOUN
ejpam-2461	30	3	of	of	ADP
ejpam-2461	30	4	the	the	DET
ejpam-2461	30	5	sum	sum	NOUN
ejpam-2461	30	6	s2(a	s2(a	PROPN
ejpam-2461	30	7	;	;	PUNCT
ejpam-2461	30	8	0	0	NUM
ejpam-2461	30	9	)	)	PUNCT
ejpam-2461	30	10	as	as	ADP
ejpam-2461	30	11	a→	a→	X
ejpam-2461	30	12	0	0	NUM
ejpam-2461	30	13	can	can	AUX
ejpam-2461	30	14	be	be	AUX
ejpam-2461	30	15	obtained	obtain	VERB
ejpam-2461	30	16	from	from	ADP
ejpam-2461	30	17	the	the	DET
ejpam-2461	30	18	classical	classical	ADJ
ejpam-2461	30	19	poisson	poisson	NOUN
ejpam-2461	30	20	-	-	PUNCT
ejpam-2461	30	21	jacobi	jacobi	PROPN
ejpam-2461	30	22	transformation	transformation	NOUN
ejpam-2461	30	23	given	give	VERB
ejpam-2461	30	24	by	by	ADP
ejpam-2461	30	25	s2(a	s2(a	PROPN
ejpam-2461	30	26	;	;	PUNCT
ejpam-2461	30	27	0	0	X
ejpam-2461	30	28	)	)	PUNCT
ejpam-2461	30	29	=	=	SYM
ejpam-2461	31	1	∞	∞	NUM
ejpam-2461	31	2	∑	∑	PUNCT
ejpam-2461	31	3	n=1	n=1	PROPN
ejpam-2461	31	4	e−an2	e−an2	PROPN
ejpam-2461	31	5	=	=	SYM
ejpam-2461	31	6	1	1	NUM
ejpam-2461	31	7	2	2	NUM
ejpam-2461	31	8	s	s	NOUN
ejpam-2461	31	9	π	π	NOUN
ejpam-2461	31	10	a	a	DET
ejpam-2461	31	11	−	−	NUM
ejpam-2461	31	12	1	1	NUM
ejpam-2461	31	13	2	2	NUM
ejpam-2461	31	14	+	+	SYM
ejpam-2461	31	15	s	s	NOUN
ejpam-2461	31	16	π	π	NOUN
ejpam-2461	31	17	a	a	DET
ejpam-2461	31	18	∞	∞	PROPN
ejpam-2461	31	19	∑	∑	PROPN
ejpam-2461	31	20	n=1	n=1	PROPN
ejpam-2461	31	21	e−π	e−π	VERB
ejpam-2461	31	22	2n2	2n2	NUM
ejpam-2461	31	23	/	/	SYM
ejpam-2461	31	24	a	a	DET
ejpam-2461	31	25	(	(	PUNCT
ejpam-2461	31	26	2	2	NUM
ejpam-2461	31	27	)	)	PUNCT
ejpam-2461	31	28	valid	valid	NOUN
ejpam-2461	31	29	for	for	ADP
ejpam-2461	31	30	all	all	DET
ejpam-2461	31	31	values	value	NOUN
ejpam-2461	31	32	of	of	ADP
ejpam-2461	31	33	a	a	PRON
ejpam-2461	31	34	in	in	ADP
ejpam-2461	31	35	|arg	|arg	NOUN
ejpam-2461	31	36	a|	a|	PROPN
ejpam-2461	31	37	<	<	X
ejpam-2461	31	38	1	1	NUM
ejpam-2461	31	39	2π	2π	NOUN
ejpam-2461	31	40	.	.	PUNCT
ejpam-2461	32	1	this	this	DET
ejpam-2461	32	2	well	well	ADV
ejpam-2461	32	3	-	-	PUNCT
ejpam-2461	32	4	known	know	VERB
ejpam-2461	32	5	transformation	transformation	NOUN
ejpam-2461	32	6	relates	relate	VERB
ejpam-2461	32	7	a	a	DET
ejpam-2461	32	8	sum	sum	NOUN
ejpam-2461	32	9	of	of	ADP
ejpam-2461	32	10	gaussian	gaussian	ADJ
ejpam-2461	32	11	exponentials	exponential	NOUN
ejpam-2461	32	12	involving	involve	VERB
ejpam-2461	32	13	the	the	DET
ejpam-2461	32	14	parameter	parameter	NOUN
ejpam-2461	32	15	a	a	PRON
ejpam-2461	32	16	to	to	ADP
ejpam-2461	32	17	a	a	DET
ejpam-2461	32	18	similar	similar	ADJ
ejpam-2461	32	19	sum	sum	NOUN
ejpam-2461	32	20	with	with	ADP
ejpam-2461	32	21	parameter	parameter	NOUN
ejpam-2461	32	22	π2	π2	PROPN
ejpam-2461	32	23	/	/	SYM
ejpam-2461	32	24	a.	a.	NOUN
ejpam-2461	32	25	in	in	ADP
ejpam-2461	32	26	the	the	DET
ejpam-2461	32	27	small	small	ADJ
ejpam-2461	32	28	-	-	PUNCT
ejpam-2461	32	29	a	a	DET
ejpam-2461	32	30	limit	limit	NOUN
ejpam-2461	32	31	,	,	PUNCT
ejpam-2461	32	32	the	the	DET
ejpam-2461	32	33	convergence	convergence	NOUN
ejpam-2461	32	34	of	of	ADP
ejpam-2461	32	35	the	the	DET
ejpam-2461	32	36	sum	sum	NOUN
ejpam-2461	32	37	on	on	ADP
ejpam-2461	32	38	the	the	DET
ejpam-2461	32	39	left	left	ADJ
ejpam-2461	32	40	-	-	PUNCT
ejpam-2461	32	41	hand	hand	NOUN
ejpam-2461	32	42	side	side	NOUN
ejpam-2461	32	43	becomes	become	VERB
ejpam-2461	32	44	slow	slow	ADJ
ejpam-2461	32	45	,	,	PUNCT
ejpam-2461	32	46	whereas	whereas	SCONJ
ejpam-2461	32	47	the	the	DET
ejpam-2461	32	48	sum	sum	NOUN
ejpam-2461	32	49	on	on	ADP
ejpam-2461	32	50	the	the	DET
ejpam-2461	32	51	right	right	ADJ
ejpam-2461	32	52	-	-	PUNCT
ejpam-2461	32	53	hand	hand	NOUN
ejpam-2461	32	54	side	side	NOUN
ejpam-2461	32	55	converges	converge	VERB
ejpam-2461	32	56	rapidly	rapidly	ADV
ejpam-2461	32	57	.	.	PUNCT
ejpam-2461	33	1	various	various	ADJ
ejpam-2461	33	2	proofs	proof	NOUN
ejpam-2461	33	3	of	of	ADP
ejpam-2461	33	4	(	(	PUNCT
ejpam-2461	33	5	2	2	X
ejpam-2461	33	6	)	)	PUNCT
ejpam-2461	33	7	exist	exist	VERB
ejpam-2461	33	8	in	in	ADP
ejpam-2461	33	9	the	the	DET
ejpam-2461	33	10	literature	literature	NOUN
ejpam-2461	33	11	;	;	PUNCT
ejpam-2461	33	12	see	see	VERB
ejpam-2461	33	13	,	,	PUNCT
ejpam-2461	33	14	for	for	ADP
ejpam-2461	33	15	example	example	NOUN
ejpam-2461	33	16	,	,	PUNCT
ejpam-2461	33	17	[	[	X
ejpam-2461	33	18	5	5	NUM
ejpam-2461	33	19	,	,	PUNCT
ejpam-2461	33	20	p.	p.	NOUN
ejpam-2461	33	21	120	120	NUM
ejpam-2461	33	22	]	]	PUNCT
ejpam-2461	33	23	,	,	PUNCT
ejpam-2461	33	24	[	[	X
ejpam-2461	33	25	7	7	NUM
ejpam-2461	33	26	,	,	PUNCT
ejpam-2461	33	27	p.	p.	NOUN
ejpam-2461	33	28	60	60	NUM
ejpam-2461	33	29	]	]	PUNCT
ejpam-2461	33	30	and	and	CCONJ
ejpam-2461	33	31	[	[	X
ejpam-2461	33	32	8	8	NUM
ejpam-2461	33	33	,	,	PUNCT
ejpam-2461	33	34	p.	p.	NOUN
ejpam-2461	33	35	124	124	NUM
ejpam-2461	33	36	]	]	PUNCT
ejpam-2461	33	37	.	.	PUNCT
ejpam-2461	34	1	the	the	DET
ejpam-2461	34	2	dominant	dominant	ADJ
ejpam-2461	34	3	asymptotic	asymptotic	ADJ
ejpam-2461	34	4	expansion	expansion	NOUN
ejpam-2461	34	5	of	of	ADP
ejpam-2461	34	6	sp(a	sp(a	PROPN
ejpam-2461	34	7	;	;	PUNCT
ejpam-2461	34	8	w	w	X
ejpam-2461	34	9	)	)	PUNCT
ejpam-2461	34	10	as	as	ADP
ejpam-2461	34	11	a	a	DET
ejpam-2461	34	12	→	→	SYM
ejpam-2461	34	13	0	0	NUM
ejpam-2461	34	14	in	in	ADP
ejpam-2461	34	15	|arg	|arg	NOUN
ejpam-2461	34	16	a|	a|	PROPN
ejpam-2461	34	17	<	<	X
ejpam-2461	34	18	1	1	NUM
ejpam-2461	34	19	2π	2π	NOUN
ejpam-2461	34	20	for	for	ADP
ejpam-2461	34	21	general	general	ADJ
ejpam-2461	34	22	p	p	X
ejpam-2461	34	23	>	>	X
ejpam-2461	34	24	0	0	PUNCT
ejpam-2461	35	1	and	and	CCONJ
ejpam-2461	35	2	w	w	PROPN
ejpam-2461	35	3	>	>	X
ejpam-2461	35	4	0	0	PUNCT
ejpam-2461	35	5	is	be	AUX
ejpam-2461	35	6	relatively	relatively	ADV
ejpam-2461	35	7	straightforward	straightforward	ADJ
ejpam-2461	35	8	and	and	CCONJ
ejpam-2461	35	9	is	be	AUX
ejpam-2461	35	10	found	find	VERB
ejpam-2461	35	11	to	to	PART
ejpam-2461	35	12	consist	consist	VERB
ejpam-2461	35	13	,	,	PUNCT
ejpam-2461	35	14	in	in	ADP
ejpam-2461	35	15	general	general	ADJ
ejpam-2461	35	16	,	,	PUNCT
ejpam-2461	35	17	of	of	ADP
ejpam-2461	35	18	a	a	DET
ejpam-2461	35	19	single	single	ADJ
ejpam-2461	35	20	term	term	NOUN
ejpam-2461	35	21	proportional	proportional	ADJ
ejpam-2461	35	22	to	to	ADP
ejpam-2461	35	23	a(w−1)/p	a(w−1)/p	NOUN
ejpam-2461	35	24	,	,	PUNCT
ejpam-2461	35	25	together	together	ADV
ejpam-2461	35	26	with	with	ADP
ejpam-2461	35	27	a	a	DET
ejpam-2461	35	28	series	series	NOUN
ejpam-2461	35	29	in	in	ADP
ejpam-2461	35	30	ascending	ascend	VERB
ejpam-2461	35	31	powers	power	NOUN
ejpam-2461	35	32	of	of	ADP
ejpam-2461	35	33	a	a	PRON
ejpam-2461	35	34	with	with	ADP
ejpam-2461	35	35	coefficients	coefficient	NOUN
ejpam-2461	35	36	involving	involve	VERB
ejpam-2461	35	37	the	the	DET
ejpam-2461	35	38	riemann	riemann	PROPN
ejpam-2461	35	39	zeta	zeta	PROPN
ejpam-2461	35	40	function	function	PROPN
ejpam-2461	35	41	(	(	PUNCT
ejpam-2461	35	42	the	the	DET
ejpam-2461	35	43	algebraic	algebraic	ADJ
ejpam-2461	35	44	expansion	expansion	NOUN
ejpam-2461	35	45	)	)	PUNCT
ejpam-2461	35	46	.	.	PUNCT
ejpam-2461	36	1	when	when	SCONJ
ejpam-2461	36	2	0	0	PUNCT
ejpam-2461	36	3	<	<	X
ejpam-2461	36	4	p	p	X
ejpam-2461	36	5	≤	≤	NUM
ejpam-2461	36	6	1	1	NUM
ejpam-2461	36	7	,	,	PUNCT
ejpam-2461	36	8	the	the	DET
ejpam-2461	36	9	expansion	expansion	NOUN
ejpam-2461	36	10	is	be	AUX
ejpam-2461	36	11	convergent	convergent	ADJ
ejpam-2461	36	12	and	and	CCONJ
ejpam-2461	36	13	the	the	DET
ejpam-2461	36	14	result	result	NOUN
ejpam-2461	36	15	is	be	AUX
ejpam-2461	36	16	exact	exact	ADJ
ejpam-2461	36	17	;	;	PUNCT
ejpam-2461	36	18	when	when	SCONJ
ejpam-2461	36	19	p	p	NOUN
ejpam-2461	36	20	>	>	X
ejpam-2461	36	21	1	1	NUM
ejpam-2461	36	22	the	the	DET
ejpam-2461	36	23	expansion	expansion	NOUN
ejpam-2461	36	24	is	be	AUX
ejpam-2461	36	25	asymptotic	asymptotic	ADJ
ejpam-2461	36	26	as	as	ADP
ejpam-2461	36	27	a→	a→	X
ejpam-2461	36	28	0	0	NUM
ejpam-2461	36	29	.	.	PUNCT
ejpam-2461	37	1	the	the	DET
ejpam-2461	37	2	most	most	ADV
ejpam-2461	37	3	interesting	interesting	ADJ
ejpam-2461	37	4	case	case	NOUN
ejpam-2461	37	5	arises	arise	VERB
ejpam-2461	37	6	when	when	SCONJ
ejpam-2461	37	7	p	p	NOUN
ejpam-2461	37	8	and	and	CCONJ
ejpam-2461	37	9	w	w	PROPN
ejpam-2461	37	10	are	be	AUX
ejpam-2461	37	11	both	both	PRON
ejpam-2461	37	12	even	even	ADV
ejpam-2461	37	13	integers	integer	NOUN
ejpam-2461	37	14	.	.	PUNCT
ejpam-2461	38	1	the	the	DET
ejpam-2461	38	2	above	above	ADV
ejpam-2461	38	3	-	-	PUNCT
ejpam-2461	38	4	mentioned	mention	VERB
ejpam-2461	38	5	algebraic	algebraic	ADJ
ejpam-2461	38	6	expansion	expansion	NOUN
ejpam-2461	38	7	then	then	ADV
ejpam-2461	38	8	terminates	terminate	VERB
ejpam-2461	38	9	after	after	ADP
ejpam-2461	38	10	a	a	DET
ejpam-2461	38	11	finite	finite	ADJ
ejpam-2461	38	12	number	number	NOUN
ejpam-2461	38	13	of	of	ADP
ejpam-2461	38	14	terms	term	NOUN
ejpam-2461	38	15	,	,	PUNCT
ejpam-2461	38	16	and	and	CCONJ
ejpam-2461	38	17	it	it	PRON
ejpam-2461	38	18	becomes	become	VERB
ejpam-2461	38	19	essential	essential	ADJ
ejpam-2461	38	20	for	for	ADP
ejpam-2461	38	21	accurate	accurate	ADJ
ejpam-2461	38	22	estimation	estimation	NOUN
ejpam-2461	38	23	to	to	PART
ejpam-2461	38	24	also	also	ADV
ejpam-2461	38	25	include	include	VERB
ejpam-2461	38	26	a	a	DET
ejpam-2461	38	27	subdominant	subdominant	ADJ
ejpam-2461	38	28	sequence	sequence	NOUN
ejpam-2461	38	29	of	of	ADP
ejpam-2461	38	30	exponentially	exponentially	ADV
ejpam-2461	38	31	small	small	ADJ
ejpam-2461	38	32	expansions	expansion	NOUN
ejpam-2461	38	33	.	.	PUNCT
ejpam-2461	39	1	this	this	DET
ejpam-2461	39	2	exponentially	exponentially	ADV
ejpam-2461	39	3	small	small	ADJ
ejpam-2461	39	4	component	component	NOUN
ejpam-2461	39	5	produces	produce	VERB
ejpam-2461	39	6	a	a	DET
ejpam-2461	39	7	transformation	transformation	NOUN
ejpam-2461	39	8	for	for	ADP
ejpam-2461	39	9	sp(a	sp(a	PROPN
ejpam-2461	39	10	;	;	PUNCT
ejpam-2461	39	11	w	w	X
ejpam-2461	39	12	)	)	PUNCT
ejpam-2461	39	13	analogous	analogous	ADJ
ejpam-2461	39	14	to	to	ADP
ejpam-2461	39	15	the	the	DET
ejpam-2461	39	16	poisson	poisson	PROPN
ejpam-2461	39	17	-	-	PROPN
ejpam-2461	39	18	jacobi	jacobi	PROPN
ejpam-2461	39	19	transformation	transformation	NOUN
ejpam-2461	39	20	in	in	ADP
ejpam-2461	39	21	(	(	PUNCT
ejpam-2461	39	22	2	2	NUM
ejpam-2461	39	23	)	)	PUNCT
ejpam-2461	39	24	,	,	PUNCT
ejpam-2461	39	25	but	but	CCONJ
ejpam-2461	39	26	valid	valid	ADJ
ejpam-2461	39	27	as	as	ADP
ejpam-2461	39	28	a→	a→	X
ejpam-2461	39	29	0	0	NUM
ejpam-2461	39	30	in	in	ADP
ejpam-2461	39	31	|arg	|arg	NOUN
ejpam-2461	39	32	a|	a|	PROPN
ejpam-2461	39	33	<	<	X
ejpam-2461	39	34	1	1	NUM
ejpam-2461	39	35	2π	2π	NOUN
ejpam-2461	39	36	.	.	PUNCT
ejpam-2461	40	1	this	this	PRON
ejpam-2461	40	2	similarly	similarly	ADV
ejpam-2461	40	3	involves	involve	VERB
ejpam-2461	40	4	a	a	DET
ejpam-2461	40	5	finite	finite	ADJ
ejpam-2461	40	6	sequence	sequence	NOUN
ejpam-2461	40	7	of	of	ADP
ejpam-2461	40	8	series	series	NOUN
ejpam-2461	40	9	similar	similar	ADJ
ejpam-2461	40	10	to	to	ADP
ejpam-2461	40	11	(	(	PUNCT
ejpam-2461	40	12	2	2	NUM
ejpam-2461	40	13	)	)	PUNCT
ejpam-2461	40	14	with	with	ADP
ejpam-2461	40	15	a	a	PRON
ejpam-2461	40	16	in	in	ADP
ejpam-2461	40	17	the	the	DET
ejpam-2461	40	18	exponential	exponential	NOUN
ejpam-2461	40	19	replaced	replace	VERB
ejpam-2461	40	20	by	by	ADP
ejpam-2461	40	21	an	an	DET
ejpam-2461	40	22	inverse	inverse	NOUN
ejpam-2461	40	23	power	power	NOUN
ejpam-2461	40	24	of	of	ADP
ejpam-2461	40	25	a	a	PRON
ejpam-2461	40	26	,	,	PUNCT
ejpam-2461	40	27	but	but	CCONJ
ejpam-2461	40	28	with	with	ADP
ejpam-2461	40	29	each	each	DET
ejpam-2461	40	30	term	term	NOUN
ejpam-2461	40	31	decorated	decorate	VERB
ejpam-2461	40	32	by	by	ADP
ejpam-2461	40	33	an	an	DET
ejpam-2461	40	34	asymptotic	asymptotic	ADJ
ejpam-2461	40	35	series	series	NOUN
ejpam-2461	40	36	in	in	ADP
ejpam-2461	40	37	ascending	ascend	VERB
ejpam-2461	40	38	powers	power	NOUN
ejpam-2461	40	39	of	of	ADP
ejpam-2461	40	40	a1/(p−1	a1/(p−1	NOUN
ejpam-2461	40	41	)	)	PUNCT
ejpam-2461	40	42	.	.	PUNCT
ejpam-2461	41	1	the	the	DET
ejpam-2461	41	2	approach	approach	NOUN
ejpam-2461	41	3	we	we	PRON
ejpam-2461	41	4	employ	employ	VERB
ejpam-2461	41	5	in	in	ADP
ejpam-2461	41	6	this	this	DET
ejpam-2461	41	7	paper	paper	NOUN
ejpam-2461	41	8	is	be	AUX
ejpam-2461	41	9	based	base	VERB
ejpam-2461	41	10	on	on	ADP
ejpam-2461	41	11	a	a	DET
ejpam-2461	41	12	mellin	mellin	NOUN
ejpam-2461	41	13	-	-	PUNCT
ejpam-2461	41	14	barnes	barnes	NOUN
ejpam-2461	41	15	integral	integral	ADJ
ejpam-2461	41	16	representation	representation	NOUN
ejpam-2461	41	17	for	for	ADP
ejpam-2461	41	18	sp(a	sp(a	PROPN
ejpam-2461	41	19	;	;	PUNCT
ejpam-2461	41	20	w	w	X
ejpam-2461	41	21	)	)	PUNCT
ejpam-2461	41	22	and	and	CCONJ
ejpam-2461	41	23	is	be	AUX
ejpam-2461	41	24	similar	similar	ADJ
ejpam-2461	41	25	to	to	ADP
ejpam-2461	41	26	that	that	PRON
ejpam-2461	41	27	described	describe	VERB
ejpam-2461	41	28	in	in	ADP
ejpam-2461	41	29	[	[	X
ejpam-2461	41	30	5	5	NUM
ejpam-2461	41	31	,	,	PUNCT
ejpam-2461	41	32	§	§	NOUN
ejpam-2461	41	33	8.1.4	8.1.4	NOUN
ejpam-2461	41	34	]	]	X
ejpam-2461	41	35	.	.	PUNCT
ejpam-2461	42	1	an	an	DET
ejpam-2461	42	2	algorithm	algorithm	NOUN
ejpam-2461	42	3	for	for	ADP
ejpam-2461	42	4	the	the	DET
ejpam-2461	42	5	determination	determination	NOUN
ejpam-2461	42	6	of	of	ADP
ejpam-2461	42	7	the	the	DET
ejpam-2461	42	8	coefficients	coefficient	NOUN
ejpam-2461	42	9	in	in	ADP
ejpam-2461	42	10	the	the	DET
ejpam-2461	42	11	exponentially	exponentially	ADV
ejpam-2461	42	12	small	small	ADJ
ejpam-2461	42	13	asymptotic	asymptotic	ADJ
ejpam-2461	42	14	series	series	NOUN
ejpam-2461	42	15	is	be	AUX
ejpam-2461	42	16	described	describe	VERB
ejpam-2461	42	17	.	.	PUNCT
ejpam-2461	43	1	the	the	DET
ejpam-2461	43	2	case	case	NOUN
ejpam-2461	43	3	p	p	X
ejpam-2461	43	4	=	=	NOUN
ejpam-2461	43	5	2	2	NUM
ejpam-2461	43	6	when	when	SCONJ
ejpam-2461	43	7	w	w	NOUN
ejpam-2461	43	8	is	be	AUX
ejpam-2461	43	9	an	an	DET
ejpam-2461	43	10	even	even	ADJ
ejpam-2461	43	11	integer	integer	NOUN
ejpam-2461	43	12	has	have	AUX
ejpam-2461	43	13	been	be	AUX
ejpam-2461	43	14	recently	recently	ADV
ejpam-2461	43	15	discussed	discuss	VERB
ejpam-2461	43	16	in	in	ADP
ejpam-2461	43	17	[	[	X
ejpam-2461	43	18	6	6	NUM
ejpam-2461	43	19	]	]	PUNCT
ejpam-2461	43	20	,	,	PUNCT
ejpam-2461	43	21	where	where	SCONJ
ejpam-2461	43	22	the	the	DET
ejpam-2461	43	23	coefficients	coefficient	NOUN
ejpam-2461	43	24	in	in	ADP
ejpam-2461	43	25	the	the	DET
ejpam-2461	43	26	decorating	decorate	VERB
ejpam-2461	43	27	asymptotic	asymptotic	ADJ
ejpam-2461	43	28	series	series	NOUN
ejpam-2461	43	29	can	can	AUX
ejpam-2461	43	30	be	be	AUX
ejpam-2461	43	31	given	give	VERB
ejpam-2461	43	32	in	in	ADP
ejpam-2461	43	33	closed	closed	ADJ
ejpam-2461	43	34	form	form	NOUN
ejpam-2461	43	35	.	.	PUNCT
ejpam-2461	44	1	an	an	DET
ejpam-2461	44	2	application	application	NOUN
ejpam-2461	44	3	of	of	ADP
ejpam-2461	44	4	the	the	DET
ejpam-2461	44	5	series	series	NOUN
ejpam-2461	44	6	when	when	SCONJ
ejpam-2461	44	7	p	p	PROPN
ejpam-2461	44	8	=	=	NOUN
ejpam-2461	44	9	2	2	NUM
ejpam-2461	44	10	,	,	PUNCT
ejpam-2461	44	11	with	with	ADP
ejpam-2461	44	12	w	w	NOUN
ejpam-2461	44	13	=	=	SYM
ejpam-2461	44	14	2	2	NUM
ejpam-2461	44	15	and	and	CCONJ
ejpam-2461	44	16	w	w	NOUN
ejpam-2461	44	17	=	=	NOUN
ejpam-2461	44	18	4	4	NUM
ejpam-2461	44	19	,	,	PUNCT
ejpam-2461	44	20	has	have	AUX
ejpam-2461	44	21	arisen	arise	VERB
ejpam-2461	44	22	in	in	ADP
ejpam-2461	44	23	the	the	DET
ejpam-2461	44	24	geological	geological	ADJ
ejpam-2461	44	25	problem	problem	NOUN
ejpam-2461	44	26	of	of	ADP
ejpam-2461	44	27	thermochronometry	thermochronometry	NOUN
ejpam-2461	44	28	in	in	ADP
ejpam-2461	44	29	spherical	spherical	ADJ
ejpam-2461	44	30	geometry	geometry	NOUN
ejpam-2461	44	31	[	[	X
ejpam-2461	44	32	9	9	NUM
ejpam-2461	44	33	]	]	PUNCT
ejpam-2461	44	34	.	.	PUNCT
ejpam-2461	45	1	r.	r.	PROPN
ejpam-2461	45	2	paris	paris	PROPN
ejpam-2461	45	3	/	/	SYM
ejpam-2461	45	4	eur	eur	PROPN
ejpam-2461	45	5	.	.	PUNCT
ejpam-2461	46	1	j.	j.	PROPN
ejpam-2461	46	2	pure	pure	PROPN
ejpam-2461	46	3	appl	appl	PROPN
ejpam-2461	46	4	.	.	PROPN
ejpam-2461	46	5	math	math	PROPN
ejpam-2461	46	6	,	,	PUNCT
ejpam-2461	46	7	9	9	NUM
ejpam-2461	46	8	(	(	PUNCT
ejpam-2461	46	9	2016	2016	NUM
ejpam-2461	46	10	)	)	PUNCT
ejpam-2461	46	11	,	,	PUNCT
ejpam-2461	46	12	3	3	NUM
ejpam-2461	46	13	-	-	SYM
ejpam-2461	46	14	18	18	NUM
ejpam-2461	46	15	5	5	NUM
ejpam-2461	46	16	2	2	NUM
ejpam-2461	46	17	.	.	PUNCT
ejpam-2461	47	1	an	an	DET
ejpam-2461	47	2	expansion	expansion	NOUN
ejpam-2461	47	3	for	for	ADP
ejpam-2461	47	4	sp(a	sp(a	ADJ
ejpam-2461	47	5	;	;	PUNCT
ejpam-2461	47	6	w	w	X
ejpam-2461	47	7	)	)	PUNCT
ejpam-2461	47	8	as	as	ADP
ejpam-2461	47	9	a→	a→	X
ejpam-2461	47	10	0	0	NUM
ejpam-2461	47	11	when	when	SCONJ
ejpam-2461	47	12	w	w	ADP
ejpam-2461	47	13	,	,	PUNCT
ejpam-2461	47	14	p	p	NOUN
ejpam-2461	47	15	6=	6=	PROPN
ejpam-2461	47	16	2	2	NUM
ejpam-2461	47	17	,	,	PUNCT
ejpam-2461	47	18	4	4	NUM
ejpam-2461	47	19	,	,	PUNCT
ejpam-2461	47	20	.	.	PUNCT
ejpam-2461	47	21	.	.	PUNCT
ejpam-2461	47	22	.	.	PUNCT
ejpam-2461	48	1	we	we	PRON
ejpam-2461	48	2	examine	examine	VERB
ejpam-2461	48	3	the	the	DET
ejpam-2461	48	4	expansion	expansion	NOUN
ejpam-2461	48	5	of	of	ADP
ejpam-2461	48	6	the	the	DET
ejpam-2461	48	7	series	series	NOUN
ejpam-2461	48	8	sp(a	sp(a	PROPN
ejpam-2461	48	9	;	;	PUNCT
ejpam-2461	48	10	w	w	X
ejpam-2461	48	11	)	)	PUNCT
ejpam-2461	48	12	defined	define	VERB
ejpam-2461	48	13	in	in	ADP
ejpam-2461	48	14	(	(	PUNCT
ejpam-2461	48	15	1	1	NUM
ejpam-2461	48	16	)	)	PUNCT
ejpam-2461	48	17	as	as	ADP
ejpam-2461	48	18	a	a	DET
ejpam-2461	48	19	→	→	SYM
ejpam-2461	48	20	0	0	NUM
ejpam-2461	48	21	in	in	ADP
ejpam-2461	48	22	the	the	DET
ejpam-2461	48	23	sector	sector	NOUN
ejpam-2461	48	24	|arg	|arg	PROPN
ejpam-2461	48	25	a|	a|	PROPN
ejpam-2461	48	26	<	<	X
ejpam-2461	48	27	1	1	NUM
ejpam-2461	48	28	2π	2π	NOUN
ejpam-2461	48	29	,	,	PUNCT
ejpam-2461	48	30	where	where	SCONJ
ejpam-2461	48	31	p	p	NOUN
ejpam-2461	48	32	>	>	X
ejpam-2461	48	33	0	0	PUNCT
ejpam-2461	48	34	and	and	CCONJ
ejpam-2461	48	35	for	for	ADP
ejpam-2461	48	36	simplicity	simplicity	NOUN
ejpam-2461	48	37	in	in	ADP
ejpam-2461	48	38	presentation	presentation	NOUN
ejpam-2461	48	39	we	we	PRON
ejpam-2461	48	40	shall	shall	AUX
ejpam-2461	48	41	assume	assume	VERB
ejpam-2461	48	42	throughout	throughout	ADP
ejpam-2461	48	43	real	real	ADJ
ejpam-2461	48	44	values	value	NOUN
ejpam-2461	48	45	of	of	ADP
ejpam-2461	48	46	w	w	PROPN
ejpam-2461	48	47	>	>	X
ejpam-2461	48	48	0	0	NUM
ejpam-2461	48	49	.	.	PUNCT
ejpam-2461	49	1	the	the	DET
ejpam-2461	49	2	case	case	NOUN
ejpam-2461	49	3	p	p	X
ejpam-2461	49	4	=	=	NOUN
ejpam-2461	49	5	1	1	NUM
ejpam-2461	49	6	,	,	PUNCT
ejpam-2461	49	7	w	w	NOUN
ejpam-2461	49	8	=	=	SYM
ejpam-2461	49	9	0	0	NUM
ejpam-2461	49	10	may	may	AUX
ejpam-2461	49	11	be	be	AUX
ejpam-2461	49	12	excluded	exclude	VERB
ejpam-2461	49	13	from	from	ADP
ejpam-2461	49	14	our	our	PRON
ejpam-2461	49	15	consideration	consideration	NOUN
ejpam-2461	49	16	since	since	SCONJ
ejpam-2461	49	17	the	the	DET
ejpam-2461	49	18	series	series	NOUN
ejpam-2461	49	19	in	in	ADP
ejpam-2461	49	20	this	this	DET
ejpam-2461	49	21	case	case	NOUN
ejpam-2461	49	22	is	be	AUX
ejpam-2461	49	23	summable	summable	ADJ
ejpam-2461	49	24	as	as	ADP
ejpam-2461	49	25	a	a	DET
ejpam-2461	49	26	geometric	geometric	ADJ
ejpam-2461	49	27	progression	progression	NOUN
ejpam-2461	49	28	.	.	PUNCT
ejpam-2461	50	1	our	our	PRON
ejpam-2461	50	2	starting	starting	NOUN
ejpam-2461	50	3	point	point	NOUN
ejpam-2461	50	4	is	be	AUX
ejpam-2461	50	5	the	the	DET
ejpam-2461	50	6	well	well	ADV
ejpam-2461	50	7	-	-	PUNCT
ejpam-2461	50	8	known	know	VERB
ejpam-2461	50	9	cahen	cahen	NOUN
ejpam-2461	50	10	-	-	PUNCT
ejpam-2461	50	11	mellin	mellin	ADV
ejpam-2461	50	12	integral	integral	ADJ
ejpam-2461	50	13	(	(	PUNCT
ejpam-2461	50	14	see	see	VERB
ejpam-2461	50	15	,	,	PUNCT
ejpam-2461	50	16	for	for	ADP
ejpam-2461	50	17	example	example	NOUN
ejpam-2461	50	18	,	,	PUNCT
ejpam-2461	50	19	[	[	X
ejpam-2461	50	20	5	5	NUM
ejpam-2461	50	21	,	,	PUNCT
ejpam-2461	50	22	§	§	NOUN
ejpam-2461	50	23	3.3.1	3.3.1	NUM
ejpam-2461	50	24	]	]	X
ejpam-2461	50	25	)	)	PUNCT
ejpam-2461	50	26	zαe−z	zαe−z	NOUN
ejpam-2461	50	27	=	=	SYM
ejpam-2461	50	28	1	1	NUM
ejpam-2461	50	29	2πi	2πi	NOUN
ejpam-2461	50	30	∫	∫	PROPN
ejpam-2461	50	31	c+∞i	c+∞i	ADJ
ejpam-2461	50	32	c−∞i	c−∞i	PROPN
ejpam-2461	50	33	γ(α−	γ(α−	NOUN
ejpam-2461	50	34	s)zsds	s)zsds	NOUN
ejpam-2461	50	35	(	(	PUNCT
ejpam-2461	50	36	z	z	NOUN
ejpam-2461	50	37	6=	6=	NUM
ejpam-2461	50	38	0	0	NUM
ejpam-2461	50	39	,	,	PUNCT
ejpam-2461	50	40	|arg	|arg	VERB
ejpam-2461	50	41	z|	z|	PROPN
ejpam-2461	50	42	<	<	X
ejpam-2461	50	43	1	1	NUM
ejpam-2461	50	44	2	2	NUM
ejpam-2461	50	45	π	π	NOUN
ejpam-2461	50	46	)	)	PUNCT
ejpam-2461	50	47	,	,	PUNCT
ejpam-2461	50	48	(	(	PUNCT
ejpam-2461	50	49	3	3	X
ejpam-2461	50	50	)	)	PUNCT
ejpam-2461	50	51	where	where	SCONJ
ejpam-2461	50	52	c	c	X
ejpam-2461	50	53	<	<	X
ejpam-2461	50	54	ℜ(α	ℜ(α	PROPN
ejpam-2461	50	55	)	)	PUNCT
ejpam-2461	50	56	so	so	SCONJ
ejpam-2461	50	57	that	that	SCONJ
ejpam-2461	50	58	the	the	DET
ejpam-2461	50	59	integration	integration	NOUN
ejpam-2461	50	60	path	path	NOUN
ejpam-2461	50	61	passes	pass	VERB
ejpam-2461	50	62	to	to	ADP
ejpam-2461	50	63	the	the	DET
ejpam-2461	50	64	left	left	NOUN
ejpam-2461	50	65	of	of	ADP
ejpam-2461	50	66	all	all	DET
ejpam-2461	50	67	the	the	DET
ejpam-2461	50	68	poles	pole	NOUN
ejpam-2461	50	69	of	of	ADP
ejpam-2461	50	70	γ(α	γ(α	PROPN
ejpam-2461	50	71	−	−	PROPN
ejpam-2461	50	72	s	s	PART
ejpam-2461	50	73	)	)	PUNCT
ejpam-2461	50	74	situated	situate	VERB
ejpam-2461	50	75	at	at	ADP
ejpam-2461	50	76	s	s	PROPN
ejpam-2461	50	77	=	=	X
ejpam-2461	50	78	k+α	k+α	PROPN
ejpam-2461	50	79	(	(	PUNCT
ejpam-2461	50	80	k	k	NOUN
ejpam-2461	50	81	=	=	SYM
ejpam-2461	50	82	0,1,2	0,1,2	NUM
ejpam-2461	50	83	,	,	PUNCT
ejpam-2461	50	84	.	.	PUNCT
ejpam-2461	50	85	.	.	PUNCT
ejpam-2461	50	86	.	.	PUNCT
ejpam-2461	50	87	)	)	PUNCT
ejpam-2461	50	88	.	.	PUNCT
ejpam-2461	51	1	then	then	ADV
ejpam-2461	51	2	,	,	PUNCT
ejpam-2461	51	3	it	it	PRON
ejpam-2461	51	4	follows	follow	VERB
ejpam-2461	51	5	that	that	PRON
ejpam-2461	51	6	sp(a	sp(a	ADP
ejpam-2461	51	7	;	;	PUNCT
ejpam-2461	51	8	w	w	X
ejpam-2461	51	9	)	)	PUNCT
ejpam-2461	51	10	=	=	SYM
ejpam-2461	52	1	∞	∞	NUM
ejpam-2461	52	2	∑	∑	PUNCT
ejpam-2461	52	3	n=1	n=1	PROPN
ejpam-2461	52	4	e−anp	e−anp	VERB
ejpam-2461	52	5	nw	nw	PUNCT
ejpam-2461	52	6	=	=	PUNCT
ejpam-2461	53	1	∞	∞	NUM
ejpam-2461	53	2	∑	∑	PUNCT
ejpam-2461	53	3	n=1	n=1	PROPN
ejpam-2461	53	4	n−w	n−w	NUM
ejpam-2461	53	5	2πi	2πi	NOUN
ejpam-2461	53	6	∫	∫	PROPN
ejpam-2461	54	1	−c+∞i	−c+∞i	PRON
ejpam-2461	54	2	−c−∞i	−c−∞i	ADJ
ejpam-2461	54	3	γ(−s)(anp)sds	γ(−s)(anp)sds	NOUN
ejpam-2461	54	4	=	=	SYM
ejpam-2461	54	5	1	1	NUM
ejpam-2461	54	6	2πi	2πi	ADJ
ejpam-2461	54	7	∫	∫	PROPN
ejpam-2461	55	1	−c+∞i	−c+∞i	PRON
ejpam-2461	55	2	−c−∞i	−c−∞i	ADJ
ejpam-2461	55	3	γ(−s)ζ(w−	γ(−s)ζ(w−	ADJ
ejpam-2461	55	4	ps)asds	ps)asds	NOUN
ejpam-2461	55	5	(	(	PUNCT
ejpam-2461	55	6	|arg	|arg	NOUN
ejpam-2461	55	7	a|	a|	PROPN
ejpam-2461	55	8	<	<	X
ejpam-2461	55	9	1	1	NUM
ejpam-2461	55	10	2	2	NUM
ejpam-2461	55	11	π	π	NOUN
ejpam-2461	55	12	)	)	PUNCT
ejpam-2461	55	13	,	,	PUNCT
ejpam-2461	55	14	(	(	PUNCT
ejpam-2461	55	15	4	4	X
ejpam-2461	55	16	)	)	PUNCT
ejpam-2461	55	17	upon	upon	SCONJ
ejpam-2461	55	18	reversal	reversal	NOUN
ejpam-2461	55	19	of	of	ADP
ejpam-2461	55	20	the	the	DET
ejpam-2461	55	21	order	order	NOUN
ejpam-2461	55	22	of	of	ADP
ejpam-2461	55	23	summation	summation	NOUN
ejpam-2461	55	24	and	and	CCONJ
ejpam-2461	55	25	integration	integration	NOUN
ejpam-2461	55	26	,	,	PUNCT
ejpam-2461	55	27	which	which	PRON
ejpam-2461	55	28	is	be	AUX
ejpam-2461	55	29	justified	justify	VERB
ejpam-2461	55	30	when	when	SCONJ
ejpam-2461	55	31	c	c	PROPN
ejpam-2461	55	32	>	>	X
ejpam-2461	55	33	max{0	max{0	PROPN
ejpam-2461	55	34	,	,	PUNCT
ejpam-2461	55	35	(	(	PUNCT
ejpam-2461	55	36	w−1)/p	w−1)/p	NOUN
ejpam-2461	55	37	}	}	PUNCT
ejpam-2461	55	38	,	,	PUNCT
ejpam-2461	55	39	and	and	CCONJ
ejpam-2461	55	40	evaluation	evaluation	NOUN
ejpam-2461	55	41	of	of	ADP
ejpam-2461	55	42	the	the	DET
ejpam-2461	55	43	inner	inner	ADJ
ejpam-2461	55	44	sum	sum	NOUN
ejpam-2461	55	45	in	in	ADP
ejpam-2461	55	46	terms	term	NOUN
ejpam-2461	55	47	of	of	ADP
ejpam-2461	55	48	the	the	DET
ejpam-2461	55	49	riemann	riemann	PROPN
ejpam-2461	55	50	zeta	zeta	PROPN
ejpam-2461	55	51	function	function	PROPN
ejpam-2461	55	52	.	.	PUNCT
ejpam-2461	56	1	the	the	DET
ejpam-2461	56	2	integrand	integrand	NOUN
ejpam-2461	56	3	in	in	ADP
ejpam-2461	56	4	(	(	PUNCT
ejpam-2461	56	5	4	4	X
ejpam-2461	56	6	)	)	PUNCT
ejpam-2461	56	7	possesses	possess	VERB
ejpam-2461	56	8	simple	simple	ADJ
ejpam-2461	56	9	poles	pole	NOUN
ejpam-2461	56	10	at	at	ADP
ejpam-2461	56	11	s	s	PROPN
ejpam-2461	56	12	=	=	X
ejpam-2461	56	13	k	k	X
ejpam-2461	56	14	(	(	PUNCT
ejpam-2461	56	15	k	k	NOUN
ejpam-2461	56	16	=	=	SYM
ejpam-2461	56	17	0,1,2	0,1,2	NUM
ejpam-2461	56	18	,	,	PUNCT
ejpam-2461	56	19	.	.	PUNCT
ejpam-2461	56	20	.	.	PUNCT
ejpam-2461	57	1	.	.	PUNCT
ejpam-2461	57	2	)	)	PUNCT
ejpam-2461	58	1	and	and	CCONJ
ejpam-2461	58	2	s	s	NOUN
ejpam-2461	58	3	=	=	PUNCT
ejpam-2461	58	4	s0	s0	PROPN
ejpam-2461	58	5	≡	≡	PROPN
ejpam-2461	58	6	(	(	PUNCT
ejpam-2461	58	7	w−1)/p	w−1)/p	NOUN
ejpam-2461	58	8	,	,	PUNCT
ejpam-2461	58	9	except	except	SCONJ
ejpam-2461	58	10	if	if	SCONJ
ejpam-2461	58	11	s0	s0	PROPN
ejpam-2461	58	12	=	=	VERB
ejpam-2461	58	13	m	m	PROPN
ejpam-2461	58	14	(	(	PUNCT
ejpam-2461	58	15	that	that	ADV
ejpam-2461	58	16	is	be	AUX
ejpam-2461	58	17	,	,	PUNCT
ejpam-2461	58	18	w	w	PROPN
ejpam-2461	58	19	=	=	PUNCT
ejpam-2461	58	20	pm	pm	NOUN
ejpam-2461	58	21	+	+	NOUN
ejpam-2461	58	22	1	1	NUM
ejpam-2461	58	23	)	)	PUNCT
ejpam-2461	58	24	,	,	PUNCT
ejpam-2461	58	25	where	where	SCONJ
ejpam-2461	58	26	m	m	NOUN
ejpam-2461	58	27	is	be	AUX
ejpam-2461	58	28	a	a	DET
ejpam-2461	58	29	non	non	ADJ
ejpam-2461	58	30	-	-	ADJ
ejpam-2461	58	31	negative	negative	ADJ
ejpam-2461	58	32	integer	integer	NOUN
ejpam-2461	58	33	,	,	PUNCT
ejpam-2461	58	34	when	when	SCONJ
ejpam-2461	58	35	the	the	DET
ejpam-2461	58	36	pole	pole	NOUN
ejpam-2461	58	37	at	at	ADP
ejpam-2461	58	38	s	s	NOUN
ejpam-2461	58	39	=	=	SYM
ejpam-2461	58	40	s0	s0	PROPN
ejpam-2461	58	41	is	be	AUX
ejpam-2461	58	42	double	double	ADJ
ejpam-2461	58	43	.	.	PUNCT
ejpam-2461	59	1	the	the	DET
ejpam-2461	59	2	residue	residue	NOUN
ejpam-2461	59	3	at	at	ADP
ejpam-2461	59	4	the	the	DET
ejpam-2461	59	5	double	double	ADJ
ejpam-2461	59	6	pole	pole	NOUN
ejpam-2461	59	7	is	be	AUX
ejpam-2461	59	8	obtained	obtain	VERB
ejpam-2461	59	9	by	by	ADP
ejpam-2461	59	10	making	make	VERB
ejpam-2461	59	11	use	use	NOUN
ejpam-2461	59	12	of	of	ADP
ejpam-2461	59	13	the	the	DET
ejpam-2461	59	14	fact	fact	NOUN
ejpam-2461	59	15	that	that	SCONJ
ejpam-2461	59	16	ζ(s)≃	ζ(s)≃	NOUN
ejpam-2461	59	17	1/(s−	1/(s−	NUM
ejpam-2461	59	18	1	1	NUM
ejpam-2461	59	19	)	)	PUNCT
ejpam-2461	60	1	+	+	CCONJ
ejpam-2461	60	2	γ	γ	NOUN
ejpam-2461	60	3	in	in	ADP
ejpam-2461	60	4	the	the	DET
ejpam-2461	60	5	neighbourhood	neighbourhood	NOUN
ejpam-2461	60	6	of	of	ADP
ejpam-2461	60	7	s	s	NOUN
ejpam-2461	60	8	=	=	SYM
ejpam-2461	60	9	1	1	NUM
ejpam-2461	60	10	,	,	PUNCT
ejpam-2461	60	11	where	where	SCONJ
ejpam-2461	60	12	γ	γ	PROPN
ejpam-2461	60	13	is	be	AUX
ejpam-2461	60	14	euler	euler	NOUN
ejpam-2461	60	15	’s	’s	NOUN
ejpam-2461	60	16	constant	constant	ADJ
ejpam-2461	60	17	,	,	PUNCT
ejpam-2461	60	18	to	to	PART
ejpam-2461	60	19	find	find	VERB
ejpam-2461	60	20	(	(	PUNCT
ejpam-2461	60	21	−a)m	−a)m	NOUN
ejpam-2461	60	22	m	m	PROPN
ejpam-2461	60	23	!	!	PUNCT
ejpam-2461	61	1	§	§	PROPN
ejpam-2461	61	2	γ−	γ−	NUM
ejpam-2461	61	3	1	1	NUM
ejpam-2461	61	4	p	p	NOUN
ejpam-2461	61	5	log	log	NOUN
ejpam-2461	61	6	a+	a+	PUNCT
ejpam-2461	61	7	1	1	NUM
ejpam-2461	61	8	p	p	NOUN
ejpam-2461	61	9	ψ(m	ψ(m	PROPN
ejpam-2461	61	10	+	+	CCONJ
ejpam-2461	61	11	1	1	X
ejpam-2461	61	12	)	)	PUNCT
ejpam-2461	61	13	ª	ª	PROPN
ejpam-2461	61	14	(	(	PUNCT
ejpam-2461	61	15	m	m	VERB
ejpam-2461	61	16	=	=	NOUN
ejpam-2461	61	17	0,1,2	0,1,2	NUM
ejpam-2461	61	18	,	,	PUNCT
ejpam-2461	61	19	.	.	PUNCT
ejpam-2461	61	20	.	.	PUNCT
ejpam-2461	61	21	.	.	PUNCT
ejpam-2461	61	22	)	)	PUNCT
ejpam-2461	61	23	,	,	PUNCT
ejpam-2461	61	24	where	where	SCONJ
ejpam-2461	61	25	ψ(x	ψ(x	NOUN
ejpam-2461	61	26	)	)	PUNCT
ejpam-2461	61	27	is	be	AUX
ejpam-2461	61	28	the	the	DET
ejpam-2461	61	29	logarithmic	logarithmic	ADJ
ejpam-2461	61	30	derivative	derivative	NOUN
ejpam-2461	61	31	of	of	ADP
ejpam-2461	61	32	the	the	DET
ejpam-2461	61	33	gamma	gamma	NOUN
ejpam-2461	61	34	function	function	NOUN
ejpam-2461	61	35	.	.	PUNCT
ejpam-2461	62	1	the	the	DET
ejpam-2461	62	2	case	case	NOUN
ejpam-2461	62	3	when	when	SCONJ
ejpam-2461	62	4	w	w	NOUN
ejpam-2461	62	5	and	and	CCONJ
ejpam-2461	62	6	p	p	NOUN
ejpam-2461	62	7	are	be	AUX
ejpam-2461	62	8	even	even	ADV
ejpam-2461	62	9	positive	positive	ADJ
ejpam-2461	62	10	integers	integer	NOUN
ejpam-2461	62	11	requires	require	VERB
ejpam-2461	62	12	a	a	DET
ejpam-2461	62	13	separate	separate	ADJ
ejpam-2461	62	14	treatment	treatment	NOUN
ejpam-2461	62	15	which	which	PRON
ejpam-2461	62	16	is	be	AUX
ejpam-2461	62	17	discussed	discuss	VERB
ejpam-2461	62	18	in	in	ADP
ejpam-2461	62	19	section	section	NOUN
ejpam-2461	62	20	3	3	NUM
ejpam-2461	62	21	.	.	NOUN
ejpam-2461	62	22	2.1	2.1	NUM
ejpam-2461	62	23	.	.	PUNCT
ejpam-2461	63	1	the	the	DET
ejpam-2461	63	2	case	case	NOUN
ejpam-2461	63	3	0	0	PUNCT
ejpam-2461	63	4	<	<	X
ejpam-2461	63	5	p	p	X
ejpam-2461	63	6	<	<	X
ejpam-2461	63	7	1	1	NUM
ejpam-2461	63	8	we	we	PRON
ejpam-2461	63	9	first	first	ADV
ejpam-2461	63	10	consider	consider	VERB
ejpam-2461	63	11	the	the	DET
ejpam-2461	63	12	case	case	NOUN
ejpam-2461	63	13	0	0	PUNCT
ejpam-2461	63	14	<	<	X
ejpam-2461	63	15	p	p	X
ejpam-2461	63	16	<	<	X
ejpam-2461	63	17	1	1	NUM
ejpam-2461	63	18	.	.	PUNCT
ejpam-2461	64	1	the	the	DET
ejpam-2461	64	2	integration	integration	NOUN
ejpam-2461	64	3	path	path	NOUN
ejpam-2461	64	4	in	in	ADP
ejpam-2461	64	5	(	(	PUNCT
ejpam-2461	64	6	4	4	X
ejpam-2461	64	7	)	)	PUNCT
ejpam-2461	64	8	can	can	AUX
ejpam-2461	64	9	be	be	AUX
ejpam-2461	64	10	made	make	VERB
ejpam-2461	64	11	to	to	PART
ejpam-2461	64	12	coincide	coincide	VERB
ejpam-2461	64	13	with	with	ADP
ejpam-2461	64	14	the	the	DET
ejpam-2461	64	15	imaginary	imaginary	ADJ
ejpam-2461	64	16	s	s	NOUN
ejpam-2461	64	17	-	-	NOUN
ejpam-2461	64	18	axis	axis	NOUN
ejpam-2461	64	19	together	together	ADV
ejpam-2461	64	20	with	with	ADP
ejpam-2461	64	21	a	a	DET
ejpam-2461	64	22	suitable	suitable	ADJ
ejpam-2461	64	23	indentation	indentation	NOUN
ejpam-2461	64	24	to	to	PART
ejpam-2461	64	25	lie	lie	VERB
ejpam-2461	64	26	to	to	ADP
ejpam-2461	64	27	the	the	DET
ejpam-2461	64	28	left	left	NOUN
ejpam-2461	64	29	of	of	ADP
ejpam-2461	64	30	the	the	DET
ejpam-2461	64	31	poles	pole	NOUN
ejpam-2461	64	32	at	at	ADP
ejpam-2461	64	33	s	s	NOUN
ejpam-2461	64	34	=	=	SYM
ejpam-2461	64	35	0	0	NUM
ejpam-2461	64	36	and	and	CCONJ
ejpam-2461	64	37	s	s	NOUN
ejpam-2461	64	38	=	=	SYM
ejpam-2461	64	39	s0	s0	PROPN
ejpam-2461	64	40	(	(	PUNCT
ejpam-2461	64	41	when	when	SCONJ
ejpam-2461	64	42	0	0	PUNCT
ejpam-2461	64	43	<	<	X
ejpam-2461	64	44	w	w	X
ejpam-2461	64	45	<	<	X
ejpam-2461	64	46	1	1	NUM
ejpam-2461	64	47	)	)	PUNCT
ejpam-2461	64	48	.	.	PUNCT
ejpam-2461	65	1	then	then	ADV
ejpam-2461	65	2	use	use	NOUN
ejpam-2461	65	3	of	of	ADP
ejpam-2461	65	4	the	the	DET
ejpam-2461	65	5	functional	functional	ADJ
ejpam-2461	65	6	relation	relation	NOUN
ejpam-2461	65	7	for	for	ADP
ejpam-2461	65	8	ζ(s	ζ(s	NOUN
ejpam-2461	65	9	)	)	PUNCT
ejpam-2461	65	10	given	give	VERB
ejpam-2461	65	11	by	by	ADP
ejpam-2461	65	12	[	[	X
ejpam-2461	65	13	8	8	NUM
ejpam-2461	65	14	,	,	PUNCT
ejpam-2461	65	15	p.	p.	NOUN
ejpam-2461	65	16	269	269	NUM
ejpam-2461	65	17	]	]	PUNCT
ejpam-2461	65	18	ζ(s	ζ(s	PROPN
ejpam-2461	65	19	)	)	PUNCT
ejpam-2461	65	20	=	=	PUNCT
ejpam-2461	66	1	2sπs−1ζ(1−	2sπs−1ζ(1−	NUM
ejpam-2461	66	2	s)γ(1−	s)γ(1−	PROPN
ejpam-2461	66	3	s	s	PART
ejpam-2461	66	4	)	)	PUNCT
ejpam-2461	66	5	sin	sin	NOUN
ejpam-2461	66	6	1	1	NUM
ejpam-2461	66	7	2	2	NUM
ejpam-2461	66	8	πs	πs	ADP
ejpam-2461	66	9	(	(	PUNCT
ejpam-2461	66	10	5	5	NUM
ejpam-2461	66	11	)	)	PUNCT
ejpam-2461	66	12	shows	show	VERB
ejpam-2461	66	13	that	that	SCONJ
ejpam-2461	66	14	the	the	DET
ejpam-2461	66	15	integrand	integrand	NOUN
ejpam-2461	66	16	can	can	AUX
ejpam-2461	66	17	be	be	AUX
ejpam-2461	66	18	written	write	VERB
ejpam-2461	66	19	as	as	ADP
ejpam-2461	66	20	(	(	PUNCT
ejpam-2461	66	21	2π)wζ(1−w+	2π)wζ(1−w+	NUM
ejpam-2461	66	22	ps	ps	NOUN
ejpam-2461	66	23	)	)	PUNCT
ejpam-2461	66	24	γ(1−w+	γ(1−w+	PROPN
ejpam-2461	66	25	ps	ps	NOUN
ejpam-2461	66	26	)	)	PUNCT
ejpam-2461	66	27	γ(1	γ(1	PROPN
ejpam-2461	66	28	+	+	SYM
ejpam-2461	66	29	s	s	NOUN
ejpam-2461	66	30	)	)	PUNCT
ejpam-2461	66	31	sin	sin	NOUN
ejpam-2461	66	32	1	1	NUM
ejpam-2461	66	33	2π(ps−w	2π(ps−w	NUM
ejpam-2461	66	34	)	)	PUNCT
ejpam-2461	66	35	sinπs	sinπs	PROPN
ejpam-2461	66	36	as	as	ADP
ejpam-2461	66	37	(	(	PUNCT
ejpam-2461	66	38	2π)ps	2π)ps	NUM
ejpam-2461	66	39	.	.	PUNCT
ejpam-2461	67	1	r.	r.	PROPN
ejpam-2461	67	2	paris	paris	PROPN
ejpam-2461	67	3	/	/	SYM
ejpam-2461	67	4	eur	eur	PROPN
ejpam-2461	67	5	.	.	PUNCT
ejpam-2461	68	1	j.	j.	PROPN
ejpam-2461	68	2	pure	pure	PROPN
ejpam-2461	68	3	appl	appl	PROPN
ejpam-2461	68	4	.	.	PROPN
ejpam-2461	68	5	math	math	PROPN
ejpam-2461	68	6	,	,	PUNCT
ejpam-2461	68	7	9	9	NUM
ejpam-2461	68	8	(	(	PUNCT
ejpam-2461	68	9	2016	2016	NUM
ejpam-2461	68	10	)	)	PUNCT
ejpam-2461	68	11	,	,	PUNCT
ejpam-2461	68	12	3	3	NUM
ejpam-2461	68	13	-	-	SYM
ejpam-2461	68	14	18	18	NUM
ejpam-2461	68	15	6	6	NUM
ejpam-2461	68	16	with	with	ADP
ejpam-2461	68	17	s	s	NOUN
ejpam-2461	68	18	=	=	VERB
ejpam-2461	68	19	reiθ	reiθ	PROPN
ejpam-2461	68	20	,	,	PUNCT
ejpam-2461	68	21	where	where	SCONJ
ejpam-2461	68	22	r→∞	r→∞	NUM
ejpam-2461	68	23	and	and	CCONJ
ejpam-2461	68	24	is	be	AUX
ejpam-2461	68	25	chosen	choose	VERB
ejpam-2461	68	26	so	so	SCONJ
ejpam-2461	68	27	that	that	SCONJ
ejpam-2461	68	28	the	the	DET
ejpam-2461	68	29	arc	arc	NOUN
ejpam-2461	68	30	passes	pass	VERB
ejpam-2461	68	31	between	between	ADP
ejpam-2461	68	32	the	the	DET
ejpam-2461	68	33	poles	pole	NOUN
ejpam-2461	68	34	on	on	ADP
ejpam-2461	68	35	the	the	DET
ejpam-2461	68	36	positive	positive	ADJ
ejpam-2461	68	37	real	real	ADJ
ejpam-2461	68	38	axis	axis	NOUN
ejpam-2461	68	39	,	,	PUNCT
ejpam-2461	68	40	the	the	DET
ejpam-2461	68	41	logarithm	logarithm	NOUN
ejpam-2461	68	42	of	of	ADP
ejpam-2461	68	43	the	the	DET
ejpam-2461	68	44	dominant	dominant	ADJ
ejpam-2461	68	45	real	real	ADJ
ejpam-2461	68	46	part	part	NOUN
ejpam-2461	68	47	of	of	ADP
ejpam-2461	68	48	the	the	DET
ejpam-2461	68	49	integrand	integrand	NOUN
ejpam-2461	68	50	is	be	AUX
ejpam-2461	68	51	controlled	control	VERB
ejpam-2461	68	52	by	by	ADP
ejpam-2461	68	53	(	(	PUNCT
ejpam-2461	68	54	p−	p−	PROPN
ejpam-2461	68	55	1)r	1)r	PROPN
ejpam-2461	68	56	cosθ	cosθ	PROPN
ejpam-2461	68	57	log	log	NOUN
ejpam-2461	68	58	r+o(r	r+o(r	NOUN
ejpam-2461	68	59	)	)	PUNCT
ejpam-2461	68	60	.	.	PUNCT
ejpam-2461	69	1	when	when	SCONJ
ejpam-2461	69	2	|θ	|θ	PRON
ejpam-2461	69	3	|	|	ADV
ejpam-2461	69	4	<	<	X
ejpam-2461	69	5	1	1	NUM
ejpam-2461	69	6	2π	2π	NOUN
ejpam-2461	69	7	,	,	PUNCT
ejpam-2461	69	8	this	this	DET
ejpam-2461	69	9	last	last	ADJ
ejpam-2461	69	10	expression	expression	NOUN
ejpam-2461	69	11	tends	tend	VERB
ejpam-2461	69	12	to	to	ADP
ejpam-2461	69	13	−∞	−∞	PUNCT
ejpam-2461	69	14	when	when	SCONJ
ejpam-2461	69	15	0	0	PUNCT
ejpam-2461	69	16	<	<	X
ejpam-2461	69	17	p	p	X
ejpam-2461	69	18	<	<	X
ejpam-2461	69	19	1	1	NUM
ejpam-2461	69	20	.	.	PUNCT
ejpam-2461	69	21	consequently	consequently	ADV
ejpam-2461	69	22	,	,	PUNCT
ejpam-2461	69	23	the	the	DET
ejpam-2461	69	24	integration	integration	NOUN
ejpam-2461	69	25	path	path	NOUN
ejpam-2461	69	26	can	can	AUX
ejpam-2461	69	27	be	be	AUX
ejpam-2461	69	28	bent	bent	ADJ
ejpam-2461	69	29	back	back	ADV
ejpam-2461	69	30	to	to	PART
ejpam-2461	69	31	enclose	enclose	VERB
ejpam-2461	69	32	the	the	DET
ejpam-2461	69	33	poles	pole	NOUN
ejpam-2461	69	34	of	of	ADP
ejpam-2461	69	35	the	the	DET
ejpam-2461	69	36	integrand	integrand	NOUN
ejpam-2461	69	37	to	to	PART
ejpam-2461	69	38	yield	yield	VERB
ejpam-2461	69	39	the	the	DET
ejpam-2461	69	40	convergent	convergent	NOUN
ejpam-2461	69	41	result	result	NOUN
ejpam-2461	69	42	sp(a	sp(a	ADP
ejpam-2461	69	43	;	;	PUNCT
ejpam-2461	69	44	w	w	X
ejpam-2461	69	45	)	)	PUNCT
ejpam-2461	69	46	=	=	PUNCT
ejpam-2461	69	47	jp(a	jp(a	NOUN
ejpam-2461	69	48	;	;	PUNCT
ejpam-2461	69	49	w	w	X
ejpam-2461	69	50	)	)	PUNCT
ejpam-2461	70	1	+	+	CCONJ
ejpam-2461	70	2	∞	∞	NUM
ejpam-2461	70	3	∑	∑	PUNCT
ejpam-2461	70	4	k=0	k=0	PROPN
ejpam-2461	70	5	′	′	NUM
ejpam-2461	70	6	(	(	PUNCT
ejpam-2461	70	7	−)k	−)k	PROPN
ejpam-2461	70	8	k	k	X
ejpam-2461	70	9	!	!	PROPN
ejpam-2461	70	10	ζ(w−	ζ(w−	ADJ
ejpam-2461	70	11	kp)ak	kp)ak	X
ejpam-2461	70	12	(	(	PUNCT
ejpam-2461	70	13	0	0	PUNCT
ejpam-2461	70	14	<	<	X
ejpam-2461	70	15	p	p	X
ejpam-2461	70	16	<	<	X
ejpam-2461	70	17	1	1	NUM
ejpam-2461	70	18	)	)	PUNCT
ejpam-2461	70	19	,	,	PUNCT
ejpam-2461	70	20	(	(	PUNCT
ejpam-2461	70	21	6	6	NUM
ejpam-2461	70	22	)	)	PUNCT
ejpam-2461	70	23	where	where	SCONJ
ejpam-2461	70	24	jp(a	jp(a	NOUN
ejpam-2461	70	25	;	;	PUNCT
ejpam-2461	70	26	w	w	X
ejpam-2461	70	27	)	)	PUNCT
ejpam-2461	70	28	=	=	SYM
ejpam-2461	71	1			PROPN
ejpam-2461	71	2			ADV
ejpam-2461	71	3			PRON
ejpam-2461	71	4			ADJ
ejpam-2461	71	5			NOUN
ejpam-2461	71	6	1	1	NUM
ejpam-2461	71	7	p	p	PROPN
ejpam-2461	71	8	γ	γ	X
ejpam-2461	71	9	�	�	PROPN
ejpam-2461	71	10	1−w	1−w	PROPN
ejpam-2461	71	11	p	p	PROPN
ejpam-2461	71	12	�	�	PROPN
ejpam-2461	71	13	a(w−1)/p	a(w−1)/p	PROPN
ejpam-2461	71	14	(	(	PUNCT
ejpam-2461	71	15	w	w	PROPN
ejpam-2461	71	16	6=	6=	PROPN
ejpam-2461	71	17	pm	pm	NOUN
ejpam-2461	71	18	+	+	NOUN
ejpam-2461	71	19	1	1	NUM
ejpam-2461	71	20	)	)	PUNCT
ejpam-2461	71	21	(	(	PUNCT
ejpam-2461	71	22	−a)m	−a)m	NOUN
ejpam-2461	71	23	m	m	PROPN
ejpam-2461	71	24	!	!	PUNCT
ejpam-2461	72	1	{	{	PUNCT
ejpam-2461	72	2	γ−	γ−	NUM
ejpam-2461	72	3	1	1	NUM
ejpam-2461	72	4	p	p	NOUN
ejpam-2461	72	5	log	log	NOUN
ejpam-2461	72	6	a+	a+	PUNCT
ejpam-2461	72	7	1	1	NUM
ejpam-2461	72	8	p	p	NOUN
ejpam-2461	72	9	ψ(m	ψ(m	PROPN
ejpam-2461	72	10	+	+	CCONJ
ejpam-2461	72	11	1	1	NUM
ejpam-2461	72	12	)	)	PUNCT
ejpam-2461	72	13	}	}	PUNCT
ejpam-2461	72	14	(	(	PUNCT
ejpam-2461	72	15	w=	w=	NOUN
ejpam-2461	72	16	pm	pm	NOUN
ejpam-2461	72	17	+	+	CCONJ
ejpam-2461	72	18	1	1	NUM
ejpam-2461	72	19	)	)	PUNCT
ejpam-2461	72	20	and	and	CCONJ
ejpam-2461	72	21	the	the	DET
ejpam-2461	72	22	prime	prime	NOUN
ejpam-2461	72	23	on	on	ADP
ejpam-2461	72	24	the	the	DET
ejpam-2461	72	25	sum	sum	NOUN
ejpam-2461	72	26	over	over	ADP
ejpam-2461	72	27	k	k	PROPN
ejpam-2461	72	28	denotes	denote	VERB
ejpam-2461	72	29	the	the	DET
ejpam-2461	72	30	omission	omission	NOUN
ejpam-2461	72	31	of	of	ADP
ejpam-2461	72	32	the	the	DET
ejpam-2461	72	33	term	term	NOUN
ejpam-2461	72	34	corresponding	correspond	VERB
ejpam-2461	72	35	to	to	ADP
ejpam-2461	72	36	k	k	PROPN
ejpam-2461	73	1	=	=	PUNCT
ejpam-2461	73	2	m	m	VERB
ejpam-2461	73	3	when	when	SCONJ
ejpam-2461	73	4	w=	w=	PRON
ejpam-2461	73	5	pm	pm	VERB
ejpam-2461	73	6	+	+	NOUN
ejpam-2461	73	7	1	1	X
ejpam-2461	73	8	.	.	PUNCT
ejpam-2461	73	9	when	when	SCONJ
ejpam-2461	73	10	p	p	NOUN
ejpam-2461	73	11	=	=	NOUN
ejpam-2461	73	12	1	1	NUM
ejpam-2461	73	13	,	,	PUNCT
ejpam-2461	73	14	the	the	DET
ejpam-2461	73	15	sum	sum	NOUN
ejpam-2461	73	16	s1(a	s1(a	ADP
ejpam-2461	73	17	;	;	PUNCT
ejpam-2461	73	18	w	w	X
ejpam-2461	73	19	)	)	PUNCT
ejpam-2461	73	20	is	be	AUX
ejpam-2461	73	21	given	give	VERB
ejpam-2461	73	22	by	by	ADP
ejpam-2461	73	23	(	(	PUNCT
ejpam-2461	73	24	6	6	NUM
ejpam-2461	73	25	)	)	PUNCT
ejpam-2461	73	26	but	but	CCONJ
ejpam-2461	73	27	now	now	ADV
ejpam-2461	73	28	the	the	DET
ejpam-2461	73	29	sum	sum	NOUN
ejpam-2461	73	30	over	over	ADP
ejpam-2461	73	31	k	k	PROPN
ejpam-2461	73	32	on	on	ADP
ejpam-2461	73	33	the	the	DET
ejpam-2461	73	34	right	right	ADJ
ejpam-2461	73	35	-	-	PUNCT
ejpam-2461	73	36	hand	hand	NOUN
ejpam-2461	73	37	side	side	NOUN
ejpam-2461	73	38	converges	converge	NOUN
ejpam-2461	73	39	when	when	SCONJ
ejpam-2461	73	40	|a|	|a|	PROPN
ejpam-2461	73	41	<	<	X
ejpam-2461	73	42	2π	2π	NOUN
ejpam-2461	73	43	;	;	PUNCT
ejpam-2461	73	44	see	see	VERB
ejpam-2461	73	45	[	[	X
ejpam-2461	73	46	5	5	NUM
ejpam-2461	73	47	,	,	PUNCT
ejpam-2461	73	48	§	§	NOUN
ejpam-2461	73	49	4.2.2	4.2.2	NUM
ejpam-2461	73	50	]	]	PUNCT
ejpam-2461	73	51	for	for	ADP
ejpam-2461	73	52	details	detail	NOUN
ejpam-2461	73	53	.	.	PUNCT
ejpam-2461	74	1	if	if	SCONJ
ejpam-2461	74	2	we	we	PRON
ejpam-2461	74	3	let	let	VERB
ejpam-2461	74	4	p	p	NOUN
ejpam-2461	74	5	=	=	NOUN
ejpam-2461	74	6	1	1	NUM
ejpam-2461	74	7	,	,	PUNCT
ejpam-2461	74	8	w	w	NOUN
ejpam-2461	74	9	=	=	NOUN
ejpam-2461	74	10	0	0	NUM
ejpam-2461	74	11	then	then	ADV
ejpam-2461	74	12	use	use	NOUN
ejpam-2461	74	13	of	of	ADP
ejpam-2461	74	14	the	the	DET
ejpam-2461	74	15	facts	fact	NOUN
ejpam-2461	74	16	that	that	PRON
ejpam-2461	74	17	ζ(1−	ζ(1−	PROPN
ejpam-2461	74	18	2k	2k	NUM
ejpam-2461	74	19	)	)	PUNCT
ejpam-2461	74	20	=	=	SYM
ejpam-2461	74	21	−b2k/(2k	−b2k/(2k	NOUN
ejpam-2461	74	22	)	)	PUNCT
ejpam-2461	74	23	and	and	CCONJ
ejpam-2461	74	24	ζ(−2k	ζ(−2k	NUM
ejpam-2461	74	25	)	)	PUNCT
ejpam-2461	74	26	=	=	SYM
ejpam-2461	74	27	0	0	NUM
ejpam-2461	74	28	,	,	PUNCT
ejpam-2461	74	29	where	where	SCONJ
ejpam-2461	74	30	b2k	b2k	PROPN
ejpam-2461	74	31	are	be	AUX
ejpam-2461	74	32	even	even	ADV
ejpam-2461	74	33	-	-	PUNCT
ejpam-2461	74	34	order	order	NOUN
ejpam-2461	74	35	bernoulli	bernoulli	NOUN
ejpam-2461	74	36	numbers	number	NOUN
ejpam-2461	74	37	,	,	PUNCT
ejpam-2461	74	38	shows	show	VERB
ejpam-2461	74	39	that	that	SCONJ
ejpam-2461	74	40	s1(a	s1(a	ADP
ejpam-2461	74	41	;	;	PUNCT
ejpam-2461	74	42	0	0	NUM
ejpam-2461	74	43	)	)	PUNCT
ejpam-2461	74	44	=	=	SYM
ejpam-2461	74	45	1	1	NUM
ejpam-2461	74	46	a	a	DET
ejpam-2461	74	47	−	−	NUM
ejpam-2461	74	48	1	1	NUM
ejpam-2461	74	49	2	2	NUM
ejpam-2461	74	50	+	+	CCONJ
ejpam-2461	74	51	1	1	NUM
ejpam-2461	74	52	a	a	DET
ejpam-2461	74	53	∞	∞	NUM
ejpam-2461	74	54	∑	∑	PUNCT
ejpam-2461	74	55	k=1	k=1	PROPN
ejpam-2461	74	56	b2k	b2k	PROPN
ejpam-2461	74	57	(	(	PUNCT
ejpam-2461	74	58	2k	2k	NUM
ejpam-2461	74	59	)	)	PUNCT
ejpam-2461	74	60	!	!	PUNCT
ejpam-2461	75	1	a2k	a2k	PROPN
ejpam-2461	75	2	(	(	PUNCT
ejpam-2461	75	3	|a|	|a|	ADP
ejpam-2461	75	4	<	<	X
ejpam-2461	75	5	2π	2π	NOUN
ejpam-2461	75	6	)	)	PUNCT
ejpam-2461	75	7	,	,	PUNCT
ejpam-2461	75	8	which	which	PRON
ejpam-2461	75	9	correctly	correctly	ADV
ejpam-2461	75	10	reduces	reduce	VERB
ejpam-2461	75	11	to	to	ADP
ejpam-2461	75	12	the	the	DET
ejpam-2461	75	13	trivial	trivial	ADJ
ejpam-2461	75	14	summation	summation	NOUN
ejpam-2461	75	15	1/(ea−1	1/(ea−1	NUM
ejpam-2461	75	16	)	)	PUNCT
ejpam-2461	75	17	by	by	ADP
ejpam-2461	75	18	application	application	NOUN
ejpam-2461	75	19	of	of	ADP
ejpam-2461	75	20	[	[	X
ejpam-2461	75	21	4	4	NUM
ejpam-2461	75	22	,	,	PUNCT
ejpam-2461	75	23	eq	eq	NOUN
ejpam-2461	75	24	.	.	PUNCT
ejpam-2461	75	25	(	(	PUNCT
ejpam-2461	75	26	24.2.1	24.2.1	NUM
ejpam-2461	75	27	)	)	PUNCT
ejpam-2461	75	28	]	]	PUNCT
ejpam-2461	75	29	.	.	PUNCT
ejpam-2461	76	1	2.2	2.2	NUM
ejpam-2461	76	2	.	.	PUNCT
ejpam-2461	77	1	the	the	DET
ejpam-2461	77	2	case	case	NOUN
ejpam-2461	77	3	p	p	X
ejpam-2461	77	4	>	>	X
ejpam-2461	77	5	1	1	NUM
ejpam-2461	77	6	when	when	SCONJ
ejpam-2461	77	7	p	p	NOUN
ejpam-2461	77	8	>	>	X
ejpam-2461	77	9	1	1	NUM
ejpam-2461	77	10	,	,	PUNCT
ejpam-2461	77	11	the	the	DET
ejpam-2461	77	12	integration	integration	NOUN
ejpam-2461	77	13	path	path	NOUN
ejpam-2461	77	14	in	in	ADP
ejpam-2461	77	15	(	(	PUNCT
ejpam-2461	77	16	4	4	X
ejpam-2461	77	17	)	)	PUNCT
ejpam-2461	77	18	can	can	AUX
ejpam-2461	77	19	not	not	PART
ejpam-2461	77	20	be	be	AUX
ejpam-2461	77	21	bent	bent	ADJ
ejpam-2461	77	22	back	back	ADV
ejpam-2461	77	23	over	over	ADP
ejpam-2461	77	24	the	the	DET
ejpam-2461	77	25	poles	pole	NOUN
ejpam-2461	77	26	and	and	CCONJ
ejpam-2461	77	27	we	we	PRON
ejpam-2461	77	28	proceed	proceed	VERB
ejpam-2461	77	29	in	in	ADP
ejpam-2461	77	30	a	a	DET
ejpam-2461	77	31	similar	similar	ADJ
ejpam-2461	77	32	manner	manner	NOUN
ejpam-2461	77	33	to	to	ADP
ejpam-2461	77	34	that	that	PRON
ejpam-2461	77	35	described	describe	VERB
ejpam-2461	77	36	for	for	ADP
ejpam-2461	77	37	the	the	DET
ejpam-2461	77	38	case	case	NOUN
ejpam-2461	77	39	w	w	NOUN
ejpam-2461	77	40	=	=	NOUN
ejpam-2461	77	41	0	0	NUM
ejpam-2461	77	42	in	in	ADP
ejpam-2461	77	43	[	[	X
ejpam-2461	77	44	5	5	NUM
ejpam-2461	77	45	,	,	PUNCT
ejpam-2461	77	46	§	§	NOUN
ejpam-2461	77	47	8.1.4	8.1.4	NOUN
ejpam-2461	77	48	]	]	PUNCT
ejpam-2461	77	49	.	.	PUNCT
ejpam-2461	78	1	consider	consider	VERB
ejpam-2461	78	2	the	the	DET
ejpam-2461	78	3	integral	integral	ADJ
ejpam-2461	78	4	taken	take	VERB
ejpam-2461	78	5	round	round	ADP
ejpam-2461	78	6	the	the	DET
ejpam-2461	78	7	rectangular	rectangular	ADJ
ejpam-2461	78	8	contour	contour	NOUN
ejpam-2461	78	9	with	with	ADP
ejpam-2461	78	10	vertices	vertex	NOUN
ejpam-2461	78	11	at	at	ADP
ejpam-2461	78	12	−c	−c	ADJ
ejpam-2461	78	13	±	±	NUM
ejpam-2461	78	14	it	it	PRON
ejpam-2461	78	15	,	,	PUNCT
ejpam-2461	78	16	c′	c′	NOUN
ejpam-2461	78	17	±	±	NUM
ejpam-2461	79	1	it	it	PRON
ejpam-2461	79	2	,	,	PUNCT
ejpam-2461	79	3	where	where	SCONJ
ejpam-2461	79	4	c′	c′	ADV
ejpam-2461	79	5	>	>	X
ejpam-2461	79	6	0	0	X
ejpam-2461	79	7	.	.	PUNCT
ejpam-2461	80	1	the	the	DET
ejpam-2461	80	2	contribution	contribution	NOUN
ejpam-2461	80	3	from	from	ADP
ejpam-2461	80	4	the	the	DET
ejpam-2461	80	5	upper	upper	ADJ
ejpam-2461	80	6	and	and	CCONJ
ejpam-2461	80	7	lower	low	ADJ
ejpam-2461	80	8	sides	side	NOUN
ejpam-2461	80	9	s	s	PART
ejpam-2461	80	10	=	=	SYM
ejpam-2461	80	11	σ	σ	X
ejpam-2461	80	12	±	±	NUM
ejpam-2461	80	13	it	it	PRON
ejpam-2461	80	14	,	,	PUNCT
ejpam-2461	80	15	−c	−c	ADJ
ejpam-2461	80	16	≤	≤	NUM
ejpam-2461	80	17	σ	σ	NOUN
ejpam-2461	80	18	≤	≤	PROPN
ejpam-2461	80	19	c′	c′	NOUN
ejpam-2461	80	20	,	,	PUNCT
ejpam-2461	80	21	vanishes	vanish	VERB
ejpam-2461	80	22	as	as	ADP
ejpam-2461	80	23	t	t	PROPN
ejpam-2461	80	24	→∞	→∞	PROPN
ejpam-2461	80	25	provided	provide	VERB
ejpam-2461	80	26	|arg	|arg	PROPN
ejpam-2461	80	27	a|	a|	PROPN
ejpam-2461	80	28	<	<	X
ejpam-2461	80	29	1	1	NUM
ejpam-2461	80	30	2π	2π	NOUN
ejpam-2461	80	31	,	,	PUNCT
ejpam-2461	80	32	since	since	SCONJ
ejpam-2461	80	33	from	from	ADP
ejpam-2461	80	34	the	the	DET
ejpam-2461	80	35	behaviour	behaviour	NOUN
ejpam-2461	80	36	γ(σ±	γ(σ±	NOUN
ejpam-2461	80	37	i	i	PROPN
ejpam-2461	80	38	t	t	PROPN
ejpam-2461	80	39	)	)	PUNCT
ejpam-2461	81	1	=	=	VERB
ejpam-2461	81	2	o(tσ−	o(tσ−	VERB
ejpam-2461	81	3	1	1	NUM
ejpam-2461	81	4	2	2	NUM
ejpam-2461	81	5	e−	e−	PROPN
ejpam-2461	81	6	1	1	NUM
ejpam-2461	81	7	2πt	2πt	NOUN
ejpam-2461	81	8	)	)	PUNCT
ejpam-2461	81	9	,	,	PUNCT
ejpam-2461	81	10	ζ(σ±	ζ(σ±	NOUN
ejpam-2461	82	1	i	i	PROPN
ejpam-2461	82	2	t	t	PROPN
ejpam-2461	82	3	)	)	PUNCT
ejpam-2461	82	4	=	=	SYM
ejpam-2461	82	5	o(tµ(σ	o(tµ(σ	PROPN
ejpam-2461	82	6	)	)	PUNCT
ejpam-2461	82	7	loga	loga	PROPN
ejpam-2461	82	8	t	t	PROPN
ejpam-2461	82	9	)	)	PUNCT
ejpam-2461	82	10	(	(	PUNCT
ejpam-2461	82	11	t	t	PROPN
ejpam-2461	82	12	→∞	→∞	NUM
ejpam-2461	82	13	)	)	PUNCT
ejpam-2461	82	14	,	,	PUNCT
ejpam-2461	82	15	where	where	SCONJ
ejpam-2461	82	16	for	for	ADP
ejpam-2461	82	17	σ	σ	PROPN
ejpam-2461	82	18	and	and	CCONJ
ejpam-2461	82	19	t	t	PROPN
ejpam-2461	82	20	real	real	ADJ
ejpam-2461	82	21	µ(σ	µ(σ	PROPN
ejpam-2461	82	22	)	)	PUNCT
ejpam-2461	82	23	=	=	SYM
ejpam-2461	82	24	0	0	PUNCT
ejpam-2461	82	25	(	(	PUNCT
ejpam-2461	82	26	σ	σ	X
ejpam-2461	82	27	>	>	X
ejpam-2461	82	28	1	1	NUM
ejpam-2461	82	29	)	)	PUNCT
ejpam-2461	82	30	,	,	PUNCT
ejpam-2461	82	31	1	1	NUM
ejpam-2461	82	32	2	2	NUM
ejpam-2461	82	33	−	−	NOUN
ejpam-2461	82	34	1	1	NUM
ejpam-2461	82	35	2	2	NUM
ejpam-2461	82	36	σ	σ	NOUN
ejpam-2461	82	37	(	(	PUNCT
ejpam-2461	82	38	0≤	0≤	PROPN
ejpam-2461	82	39	σ	σ	NUM
ejpam-2461	82	40	≤	≤	NUM
ejpam-2461	82	41	1	1	NUM
ejpam-2461	82	42	)	)	PUNCT
ejpam-2461	82	43	,	,	PUNCT
ejpam-2461	82	44	1	1	NUM
ejpam-2461	82	45	2	2	NUM
ejpam-2461	82	46	−σ	−σ	NOUN
ejpam-2461	82	47	(	(	PUNCT
ejpam-2461	82	48	σ	σ	X
ejpam-2461	82	49	<	<	X
ejpam-2461	82	50	0	0	NUM
ejpam-2461	82	51	)	)	PUNCT
ejpam-2461	82	52	,	,	PUNCT
ejpam-2461	82	53	a=	a=	PROPN
ejpam-2461	82	54	1	1	NUM
ejpam-2461	82	55	(	(	PUNCT
ejpam-2461	82	56	0≤	0≤	PROPN
ejpam-2461	82	57	σ	σ	NUM
ejpam-2461	82	58	≤	≤	NUM
ejpam-2461	82	59	1	1	NUM
ejpam-2461	82	60	)	)	PUNCT
ejpam-2461	82	61	,	,	PUNCT
ejpam-2461	82	62	a=	a=	PROPN
ejpam-2461	82	63	0	0	PUNCT
ejpam-2461	83	1	otherwise	otherwise	ADV
ejpam-2461	83	2	,	,	PUNCT
ejpam-2461	83	3	r.	r.	PROPN
ejpam-2461	83	4	paris	paris	PROPN
ejpam-2461	83	5	/	/	SYM
ejpam-2461	83	6	eur	eur	PROPN
ejpam-2461	83	7	.	.	PUNCT
ejpam-2461	84	1	j.	j.	PROPN
ejpam-2461	84	2	pure	pure	PROPN
ejpam-2461	84	3	appl	appl	PROPN
ejpam-2461	84	4	.	.	PROPN
ejpam-2461	84	5	math	math	PROPN
ejpam-2461	84	6	,	,	PUNCT
ejpam-2461	84	7	9	9	NUM
ejpam-2461	84	8	(	(	PUNCT
ejpam-2461	84	9	2016	2016	NUM
ejpam-2461	84	10	)	)	PUNCT
ejpam-2461	84	11	,	,	PUNCT
ejpam-2461	84	12	3	3	NUM
ejpam-2461	84	13	-	-	SYM
ejpam-2461	84	14	18	18	NUM
ejpam-2461	84	15	7	7	NUM
ejpam-2461	84	16	the	the	DET
ejpam-2461	84	17	modulus	modulus	NOUN
ejpam-2461	84	18	of	of	ADP
ejpam-2461	84	19	the	the	DET
ejpam-2461	84	20	integrand	integrand	NOUN
ejpam-2461	84	21	is	be	AUX
ejpam-2461	84	22	controlled	control	VERB
ejpam-2461	84	23	by	by	ADP
ejpam-2461	84	24	o(tσ+µ(σ)−	o(tσ+µ(σ)−	PROPN
ejpam-2461	84	25	1	1	NUM
ejpam-2461	84	26	2	2	NUM
ejpam-2461	84	27	log	log	NOUN
ejpam-2461	84	28	te−∆t	te−∆t	PROPN
ejpam-2461	84	29	)	)	PUNCT
ejpam-2461	84	30	,	,	PUNCT
ejpam-2461	84	31	with∆=	with∆=	ADV
ejpam-2461	84	32	1	1	NUM
ejpam-2461	84	33	2π−|arg	2π−|arg	PROPN
ejpam-2461	84	34	a|	a|	PROPN
ejpam-2461	84	35	.	.	PUNCT
ejpam-2461	85	1	displacement	displacement	NOUN
ejpam-2461	85	2	of	of	ADP
ejpam-2461	85	3	the	the	DET
ejpam-2461	85	4	integration	integration	NOUN
ejpam-2461	85	5	path	path	NOUN
ejpam-2461	85	6	to	to	ADP
ejpam-2461	85	7	the	the	DET
ejpam-2461	85	8	right	right	NOUN
ejpam-2461	85	9	over	over	ADP
ejpam-2461	85	10	a	a	DET
ejpam-2461	85	11	finite	finite	ADJ
ejpam-2461	85	12	set	set	NOUN
ejpam-2461	85	13	of	of	ADP
ejpam-2461	85	14	poles	pole	NOUN
ejpam-2461	85	15	then	then	ADV
ejpam-2461	85	16	yields	yield	VERB
ejpam-2461	85	17	(	(	PUNCT
ejpam-2461	85	18	provided	provide	VERB
ejpam-2461	85	19	w	w	PROPN
ejpam-2461	85	20	and	and	CCONJ
ejpam-2461	85	21	p	p	NOUN
ejpam-2461	85	22	are	be	AUX
ejpam-2461	85	23	not	not	PART
ejpam-2461	85	24	even	even	ADV
ejpam-2461	85	25	integers	integer	NOUN
ejpam-2461	85	26	)	)	PUNCT
ejpam-2461	85	27	sp(a	sp(a	PUNCT
ejpam-2461	85	28	;	;	PUNCT
ejpam-2461	85	29	w	w	X
ejpam-2461	85	30	)	)	PUNCT
ejpam-2461	85	31	=	=	PUNCT
ejpam-2461	85	32	jp(a	jp(a	NOUN
ejpam-2461	85	33	;	;	PUNCT
ejpam-2461	85	34	w	w	X
ejpam-2461	85	35	)	)	PUNCT
ejpam-2461	85	36	+	+	CCONJ
ejpam-2461	85	37	n−1	n−1	PROPN
ejpam-2461	85	38	∑	∑	PUNCT
ejpam-2461	85	39	k=0	k=0	PROPN
ejpam-2461	85	40	′	′	NUM
ejpam-2461	85	41	(	(	PUNCT
ejpam-2461	85	42	−)k	−)k	PROPN
ejpam-2461	85	43	k	k	X
ejpam-2461	85	44	!	!	PUNCT
ejpam-2461	85	45	ζ(w−	ζ(w−	NUM
ejpam-2461	86	1	kp)ak	kp)ak	X
ejpam-2461	87	1	+	+	CCONJ
ejpam-2461	87	2	rn	rn	PROPN
ejpam-2461	87	3	,	,	PUNCT
ejpam-2461	87	4	(	(	PUNCT
ejpam-2461	87	5	7	7	X
ejpam-2461	87	6	)	)	PUNCT
ejpam-2461	87	7	where	where	SCONJ
ejpam-2461	87	8	n	n	PRON
ejpam-2461	87	9	is	be	AUX
ejpam-2461	87	10	a	a	DET
ejpam-2461	87	11	positive	positive	ADJ
ejpam-2461	87	12	integer	integer	NOUN
ejpam-2461	87	13	such	such	ADJ
ejpam-2461	87	14	that	that	SCONJ
ejpam-2461	87	15	n	n	NOUN
ejpam-2461	87	16	>	>	X
ejpam-2461	87	17	s0	s0	X
ejpam-2461	87	18	+	+	CCONJ
ejpam-2461	87	19	3	3	NUM
ejpam-2461	87	20	2	2	NUM
ejpam-2461	87	21	and	and	CCONJ
ejpam-2461	87	22	the	the	DET
ejpam-2461	87	23	prime	prime	NOUN
ejpam-2461	87	24	on	on	ADP
ejpam-2461	87	25	the	the	DET
ejpam-2461	87	26	sum	sum	NOUN
ejpam-2461	87	27	over	over	ADP
ejpam-2461	87	28	k	k	PROPN
ejpam-2461	87	29	again	again	ADV
ejpam-2461	87	30	denotes	denote	VERB
ejpam-2461	87	31	the	the	DET
ejpam-2461	87	32	omission	omission	NOUN
ejpam-2461	87	33	of	of	ADP
ejpam-2461	87	34	the	the	DET
ejpam-2461	87	35	term	term	NOUN
ejpam-2461	87	36	corresponding	correspond	VERB
ejpam-2461	87	37	to	to	ADP
ejpam-2461	87	38	k	k	PROPN
ejpam-2461	87	39	=	=	PUNCT
ejpam-2461	87	40	m	m	VERB
ejpam-2461	87	41	when	when	SCONJ
ejpam-2461	87	42	w=	w=	PRON
ejpam-2461	87	43	pm	pm	VERB
ejpam-2461	87	44	+	+	NOUN
ejpam-2461	87	45	1	1	X
ejpam-2461	87	46	.	.	PUNCT
ejpam-2461	88	1	the	the	DET
ejpam-2461	88	2	remainder	remainder	NOUN
ejpam-2461	88	3	rn	rn	PROPN
ejpam-2461	88	4	is	be	AUX
ejpam-2461	88	5	given	give	VERB
ejpam-2461	88	6	by	by	ADP
ejpam-2461	88	7	rn	rn	PROPN
ejpam-2461	88	8	=	=	SYM
ejpam-2461	88	9	1	1	NUM
ejpam-2461	88	10	2πi	2πi	NOUN
ejpam-2461	88	11	∫	∫	PROPN
ejpam-2461	88	12	c+∞i	c+∞i	ADJ
ejpam-2461	88	13	c−∞i	c−∞i	ADJ
ejpam-2461	88	14	γ(−s)ζ(w−	γ(−s)ζ(w−	NOUN
ejpam-2461	88	15	ps)asds	ps)asds	NOUN
ejpam-2461	88	16	=	=	PUNCT
ejpam-2461	88	17	(	(	PUNCT
ejpam-2461	88	18	2π)w	2π)w	NUM
ejpam-2461	88	19	2πi	2πi	NOUN
ejpam-2461	88	20	∫	∫	PROPN
ejpam-2461	88	21	c+∞i	c+∞i	ADJ
ejpam-2461	88	22	c−∞i	c−∞i	PROPN
ejpam-2461	88	23	ζ(1−w+	ζ(1−w+	PROPN
ejpam-2461	88	24	ps	ps	NOUN
ejpam-2461	88	25	)	)	PUNCT
ejpam-2461	88	26	γ(1−w+	γ(1−w+	PROPN
ejpam-2461	88	27	ps	ps	NOUN
ejpam-2461	88	28	)	)	PUNCT
ejpam-2461	88	29	γ(1	γ(1	PROPN
ejpam-2461	88	30	+	+	SYM
ejpam-2461	88	31	s	s	NOUN
ejpam-2461	88	32	)	)	PUNCT
ejpam-2461	88	33	sin	sin	NOUN
ejpam-2461	88	34	1	1	NUM
ejpam-2461	88	35	2π(ps−w	2π(ps−w	NUM
ejpam-2461	88	36	)	)	PUNCT
ejpam-2461	88	37	sinπs	sinπs	PROPN
ejpam-2461	88	38	as	as	ADP
ejpam-2461	88	39	(	(	PUNCT
ejpam-2461	88	40	2π)ps	2π)ps	NUM
ejpam-2461	88	41	ds	ds	VERB
ejpam-2461	88	42	where	where	SCONJ
ejpam-2461	88	43	c	c	NOUN
ejpam-2461	88	44	=	=	SYM
ejpam-2461	88	45	n	n	CCONJ
ejpam-2461	88	46	−	−	NUM
ejpam-2461	88	47	1	1	NUM
ejpam-2461	88	48	2	2	NUM
ejpam-2461	88	49	and	and	CCONJ
ejpam-2461	88	50	the	the	DET
ejpam-2461	88	51	second	second	ADJ
ejpam-2461	88	52	expression	expression	NOUN
ejpam-2461	88	53	follows	follow	VERB
ejpam-2461	88	54	from	from	ADP
ejpam-2461	88	55	(	(	PUNCT
ejpam-2461	88	56	5	5	NUM
ejpam-2461	88	57	)	)	PUNCT
ejpam-2461	88	58	.	.	PUNCT
ejpam-2461	89	1	upon	upon	SCONJ
ejpam-2461	89	2	use	use	NOUN
ejpam-2461	89	3	of	of	ADP
ejpam-2461	89	4	the	the	DET
ejpam-2461	89	5	result	result	NOUN
ejpam-2461	89	6	|ζ(x	|ζ(x	PROPN
ejpam-2461	90	1	+	+	PROPN
ejpam-2461	90	2	i	i	PRON
ejpam-2461	90	3	y)|	y)|	VERB
ejpam-2461	90	4	<	<	X
ejpam-2461	90	5	ζ(x	ζ(x	NOUN
ejpam-2461	90	6	)	)	PUNCT
ejpam-2461	90	7	when	when	SCONJ
ejpam-2461	90	8	x	x	X
ejpam-2461	90	9	>	>	X
ejpam-2461	90	10	1	1	NUM
ejpam-2461	90	11	,	,	PUNCT
ejpam-2461	90	12	we	we	PRON
ejpam-2461	90	13	obtain	obtain	VERB
ejpam-2461	90	14	the	the	DET
ejpam-2461	90	15	bound	bound	ADJ
ejpam-2461	90	16	|rn	|rn	NUM
ejpam-2461	90	17	|	|	ADV
ejpam-2461	90	18	<	<	X
ejpam-2461	90	19	(	(	PUNCT
ejpam-2461	90	20	2π)w−1ζ(pn−p(s0−	2π)w−1ζ(pn−p(s0−	NUM
ejpam-2461	90	21	1	1	NUM
ejpam-2461	90	22	2	2	NUM
ejpam-2461	90	23	)	)	PUNCT
ejpam-2461	90	24	)	)	PUNCT
ejpam-2461	91	1	�	�	PROPN
ejpam-2461	91	2	a	a	DET
ejpam-2461	91	3	(	(	PUNCT
ejpam-2461	91	4	2π)p	2π)p	NUM
ejpam-2461	91	5	�	�	PROPN
ejpam-2461	91	6	n−	n−	NOUN
ejpam-2461	91	7	1	1	NUM
ejpam-2461	91	8	2	2	NUM
ejpam-2461	91	9	∫	∫	NOUN
ejpam-2461	91	10	∞	∞	PROPN
ejpam-2461	91	11	−∞	−∞	ADP
ejpam-2461	91	12	e−φ	e−φ	PROPN
ejpam-2461	91	13	t	t	PROPN
ejpam-2461	91	14	f(t	f(t	PROPN
ejpam-2461	91	15	)	)	PUNCT
ejpam-2461	91	16	d	d	PROPN
ejpam-2461	91	17	t	t	PROPN
ejpam-2461	91	18	,	,	PUNCT
ejpam-2461	91	19	(	(	PUNCT
ejpam-2461	91	20	8)	8)	NUM
ejpam-2461	91	21	where	where	SCONJ
ejpam-2461	91	22	φ	φ	PROPN
ejpam-2461	91	23	=	=	SYM
ejpam-2461	91	24	arg	arg	VERB
ejpam-2461	91	25	a	a	PRON
ejpam-2461	91	26	and	and	CCONJ
ejpam-2461	91	27	f(t	f(t	NOUN
ejpam-2461	91	28	)	)	PUNCT
ejpam-2461	91	29	=	=	SYM
ejpam-2461	91	30	�	�	PROPN
ejpam-2461	91	31	�	�	PROPN
ejpam-2461	91	32	�	�	PROPN
ejpam-2461	91	33	�	�	PROPN
ejpam-2461	91	34	γ(1−w+	γ(1−w+	PROPN
ejpam-2461	91	35	ps	ps	NOUN
ejpam-2461	91	36	)	)	PUNCT
ejpam-2461	91	37	γ(1	γ(1	PROPN
ejpam-2461	91	38	+	+	CCONJ
ejpam-2461	91	39	s	s	X
ejpam-2461	91	40	)	)	PUNCT
ejpam-2461	91	41	�	�	PROPN
ejpam-2461	91	42	�	�	PROPN
ejpam-2461	91	43	�	�	PROPN
ejpam-2461	91	44	�	�	PROPN
ejpam-2461	91	45	cosh	cosh	PROPN
ejpam-2461	91	46	1	1	NUM
ejpam-2461	91	47	2πpt	2πpt	PROPN
ejpam-2461	91	48	coshπt	coshπt	NOUN
ejpam-2461	91	49	(	(	PUNCT
ejpam-2461	91	50	s	s	NOUN
ejpam-2461	91	51	=	=	PUNCT
ejpam-2461	91	52	n	n	CCONJ
ejpam-2461	91	53	−	−	NUM
ejpam-2461	91	54	1	1	NUM
ejpam-2461	91	55	2	2	NUM
ejpam-2461	91	56	+	+	NUM
ejpam-2461	91	57	i	i	PROPN
ejpam-2461	91	58	t	t	PROPN
ejpam-2461	91	59	)	)	PUNCT
ejpam-2461	91	60	.	.	PUNCT
ejpam-2461	92	1	on	on	ADP
ejpam-2461	92	2	the	the	DET
ejpam-2461	92	3	integration	integration	NOUN
ejpam-2461	92	4	path	path	NOUN
ejpam-2461	92	5	,	,	PUNCT
ejpam-2461	92	6	f(t	f(t	PROPN
ejpam-2461	92	7	)	)	PUNCT
ejpam-2461	92	8	is	be	AUX
ejpam-2461	92	9	regular	regular	ADJ
ejpam-2461	92	10	and	and	CCONJ
ejpam-2461	92	11	satisfies	satisfy	VERB
ejpam-2461	92	12	f(t	f(t	NOUN
ejpam-2461	92	13	)	)	PUNCT
ejpam-2461	93	1	=	=	SYM
ejpam-2461	93	2	o(e−	o(e−	PROPN
ejpam-2461	93	3	1	1	NUM
ejpam-2461	93	4	2π|t|	2π|t|	NUM
ejpam-2461	93	5	)	)	PUNCT
ejpam-2461	93	6	as	as	ADP
ejpam-2461	93	7	t	t	PROPN
ejpam-2461	93	8	→±∞.	→±∞.	NOUN
ejpam-2461	93	9	hence	hence	ADV
ejpam-2461	93	10	the	the	DET
ejpam-2461	93	11	integral	integral	ADJ
ejpam-2461	93	12	in	in	ADP
ejpam-2461	93	13	(	(	PUNCT
ejpam-2461	93	14	8)	8)	NUM
ejpam-2461	93	15	is	be	AUX
ejpam-2461	93	16	convergent	convergent	NOUN
ejpam-2461	93	17	and	and	CCONJ
ejpam-2461	93	18	independent	independent	ADJ
ejpam-2461	93	19	of	of	ADP
ejpam-2461	93	20	|a|	|a|	PROPN
ejpam-2461	93	21	provided	provide	VERB
ejpam-2461	93	22	|φ|	|φ|	PROPN
ejpam-2461	93	23	<	<	X
ejpam-2461	93	24	1	1	NUM
ejpam-2461	93	25	2π	2π	NOUN
ejpam-2461	93	26	.	.	PUNCT
ejpam-2461	94	1	it	it	PRON
ejpam-2461	94	2	then	then	ADV
ejpam-2461	94	3	follows	follow	VERB
ejpam-2461	94	4	that	that	PRON
ejpam-2461	94	5	rn	rn	PROPN
ejpam-2461	95	1	=	=	NOUN
ejpam-2461	96	1	o(an−	o(an−	NUM
ejpam-2461	97	1	1	1	NUM
ejpam-2461	97	2	2	2	NUM
ejpam-2461	97	3	)	)	PUNCT
ejpam-2461	97	4	(	(	PUNCT
ejpam-2461	97	5	a→	a→	X
ejpam-2461	97	6	0	0	NUM
ejpam-2461	97	7	in	in	ADP
ejpam-2461	97	8	|arg	|arg	NOUN
ejpam-2461	97	9	a|	a|	PROPN
ejpam-2461	97	10	<	<	X
ejpam-2461	97	11	1	1	NUM
ejpam-2461	97	12	2	2	NUM
ejpam-2461	97	13	π	π	NOUN
ejpam-2461	97	14	)	)	PUNCT
ejpam-2461	97	15	.	.	PUNCT
ejpam-2461	98	1	the	the	DET
ejpam-2461	98	2	expansion	expansion	NOUN
ejpam-2461	98	3	(	(	PUNCT
ejpam-2461	98	4	7	7	X
ejpam-2461	98	5	)	)	PUNCT
ejpam-2461	98	6	is	be	AUX
ejpam-2461	98	7	the	the	DET
ejpam-2461	98	8	dominant	dominant	ADJ
ejpam-2461	98	9	algebraic	algebraic	ADJ
ejpam-2461	98	10	expansion	expansion	NOUN
ejpam-2461	98	11	associated	associate	VERB
ejpam-2461	98	12	with	with	ADP
ejpam-2461	98	13	sp(a	sp(a	PROPN
ejpam-2461	98	14	;	;	PUNCT
ejpam-2461	98	15	w	w	X
ejpam-2461	98	16	)	)	PUNCT
ejpam-2461	98	17	valid	valid	ADJ
ejpam-2461	98	18	as	as	ADP
ejpam-2461	98	19	a→	a→	X
ejpam-2461	98	20	0	0	NUM
ejpam-2461	98	21	in	in	ADP
ejpam-2461	98	22	|arg	|arg	NOUN
ejpam-2461	98	23	a|	a|	PROPN
ejpam-2461	98	24	<	<	X
ejpam-2461	98	25	1	1	NUM
ejpam-2461	98	26	2π	2π	NOUN
ejpam-2461	98	27	,	,	PUNCT
ejpam-2461	98	28	provided	provide	VERB
ejpam-2461	98	29	w	w	PROPN
ejpam-2461	98	30	(	(	PUNCT
ejpam-2461	98	31	>	>	X
ejpam-2461	98	32	0	0	NUM
ejpam-2461	98	33	)	)	PUNCT
ejpam-2461	98	34	and	and	CCONJ
ejpam-2461	98	35	p	p	NOUN
ejpam-2461	98	36	are	be	AUX
ejpam-2461	98	37	not	not	PART
ejpam-2461	98	38	even	even	ADV
ejpam-2461	98	39	integers	integer	NOUN
ejpam-2461	98	40	when	when	SCONJ
ejpam-2461	98	41	the	the	DET
ejpam-2461	98	42	sum	sum	NOUN
ejpam-2461	98	43	in	in	ADP
ejpam-2461	98	44	(	(	PUNCT
ejpam-2461	98	45	7	7	X
ejpam-2461	98	46	)	)	PUNCT
ejpam-2461	98	47	is	be	AUX
ejpam-2461	98	48	finite	finite	ADJ
ejpam-2461	98	49	.	.	PUNCT
ejpam-2461	99	1	the	the	DET
ejpam-2461	99	2	same	same	ADJ
ejpam-2461	99	3	analysis	analysis	NOUN
ejpam-2461	99	4	can	can	AUX
ejpam-2461	99	5	be	be	AUX
ejpam-2461	99	6	applied	apply	VERB
ejpam-2461	99	7	to	to	ADP
ejpam-2461	99	8	the	the	DET
ejpam-2461	99	9	case	case	NOUN
ejpam-2461	99	10	with	with	ADP
ejpam-2461	99	11	non	non	ADJ
ejpam-2461	99	12	-	-	ADJ
ejpam-2461	99	13	positive	positive	ADJ
ejpam-2461	99	14	w	w	NOUN
ejpam-2461	99	15	to	to	PART
ejpam-2461	99	16	yield	yield	VERB
ejpam-2461	99	17	the	the	DET
ejpam-2461	99	18	berndtramanujan	berndtramanujan	NOUN
ejpam-2461	99	19	result	result	NOUN
ejpam-2461	100	1	[	[	X
ejpam-2461	100	2	1	1	NUM
ejpam-2461	100	3	,	,	PUNCT
ejpam-2461	100	4	theorem	theorem	VERB
ejpam-2461	100	5	3.1	3.1	NUM
ejpam-2461	100	6	,	,	PUNCT
ejpam-2461	100	7	p.	p.	NOUN
ejpam-2461	100	8	306	306	NUM
ejpam-2461	100	9	]	]	PUNCT
ejpam-2461	100	10	sp(a;−w	sp(a;−w	X
ejpam-2461	100	11	)	)	PUNCT
ejpam-2461	100	12	=	=	NOUN
ejpam-2461	101	1	1	1	NUM
ejpam-2461	101	2	p	p	NOUN
ejpam-2461	101	3	γ	γ	X
ejpam-2461	101	4	�	�	PROPN
ejpam-2461	101	5	1+w	1+w	NUM
ejpam-2461	101	6	p	p	PROPN
ejpam-2461	101	7	�	�	PROPN
ejpam-2461	101	8	a−(1+w)/p	a−(1+w)/p	PROPN
ejpam-2461	101	9	+	+	CCONJ
ejpam-2461	101	10	n−1	n−1	PROPN
ejpam-2461	101	11	∑	∑	ADP
ejpam-2461	101	12	k=0	k=0	PROPN
ejpam-2461	101	13	(	(	PUNCT
ejpam-2461	101	14	−)k	−)k	PROPN
ejpam-2461	101	15	k	k	PROPN
ejpam-2461	101	16	!	!	PUNCT
ejpam-2461	101	17	ζ(−w−	ζ(−w−	PUNCT
ejpam-2461	101	18	kp	kp	PROPN
ejpam-2461	101	19	)	)	PUNCT
ejpam-2461	101	20	ak	ak	PROPN
ejpam-2461	102	1	+	+	PROPN
ejpam-2461	102	2	o(an−	o(an−	NUM
ejpam-2461	102	3	1	1	NUM
ejpam-2461	102	4	2	2	NUM
ejpam-2461	102	5	)	)	PUNCT
ejpam-2461	102	6	(	(	PUNCT
ejpam-2461	102	7	w≥	w≥	PROPN
ejpam-2461	102	8	0	0	NUM
ejpam-2461	102	9	)	)	PUNCT
ejpam-2461	102	10	as	as	ADP
ejpam-2461	102	11	a→	a→	X
ejpam-2461	102	12	0	0	NUM
ejpam-2461	102	13	in	in	ADP
ejpam-2461	102	14	|arg	|arg	NOUN
ejpam-2461	102	15	a|	a|	PROPN
ejpam-2461	102	16	<	<	X
ejpam-2461	102	17	1	1	NUM
ejpam-2461	102	18	2π	2π	NOUN
ejpam-2461	102	19	.	.	PUNCT
ejpam-2461	103	1	the	the	DET
ejpam-2461	103	2	reflection	reflection	NOUN
ejpam-2461	103	3	formula	formula	NOUN
ejpam-2461	103	4	(	(	PUNCT
ejpam-2461	103	5	5	5	X
ejpam-2461	103	6	)	)	PUNCT
ejpam-2461	103	7	can	can	AUX
ejpam-2461	103	8	be	be	AUX
ejpam-2461	103	9	employed	employ	VERB
ejpam-2461	103	10	to	to	PART
ejpam-2461	103	11	convert	convert	VERB
ejpam-2461	103	12	the	the	DET
ejpam-2461	103	13	argument	argument	NOUN
ejpam-2461	103	14	of	of	ADP
ejpam-2461	103	15	the	the	DET
ejpam-2461	103	16	zeta	zeta	PROPN
ejpam-2461	103	17	function	function	NOUN
ejpam-2461	103	18	to	to	ADP
ejpam-2461	103	19	a	a	DET
ejpam-2461	103	20	positive	positive	ADJ
ejpam-2461	103	21	form	form	NOUN
ejpam-2461	103	22	.	.	PUNCT
ejpam-2461	104	1	r.	r.	PROPN
ejpam-2461	104	2	paris	paris	PROPN
ejpam-2461	104	3	/	/	SYM
ejpam-2461	104	4	eur	eur	PROPN
ejpam-2461	104	5	.	.	PUNCT
ejpam-2461	105	1	j.	j.	PROPN
ejpam-2461	105	2	pure	pure	PROPN
ejpam-2461	105	3	appl	appl	PROPN
ejpam-2461	105	4	.	.	PROPN
ejpam-2461	105	5	math	math	PROPN
ejpam-2461	105	6	,	,	PUNCT
ejpam-2461	105	7	9	9	NUM
ejpam-2461	105	8	(	(	PUNCT
ejpam-2461	105	9	2016	2016	NUM
ejpam-2461	105	10	)	)	PUNCT
ejpam-2461	105	11	,	,	PUNCT
ejpam-2461	105	12	3	3	NUM
ejpam-2461	105	13	-	-	SYM
ejpam-2461	105	14	18	18	NUM
ejpam-2461	105	15	8	8	NUM
ejpam-2461	105	16	3	3	NUM
ejpam-2461	105	17	.	.	PUNCT
ejpam-2461	106	1	the	the	DET
ejpam-2461	106	2	expansion	expansion	NOUN
ejpam-2461	106	3	of	of	ADP
ejpam-2461	106	4	sp(a	sp(a	PROPN
ejpam-2461	106	5	;	;	PUNCT
ejpam-2461	106	6	w	w	X
ejpam-2461	106	7	)	)	PUNCT
ejpam-2461	106	8	when	when	SCONJ
ejpam-2461	106	9	w	w	NOUN
ejpam-2461	106	10	and	and	CCONJ
ejpam-2461	106	11	p	p	NOUN
ejpam-2461	106	12	are	be	AUX
ejpam-2461	106	13	even	even	ADV
ejpam-2461	106	14	integers	integer	NOUN
ejpam-2461	106	15	throughout	throughout	ADP
ejpam-2461	106	16	this	this	DET
ejpam-2461	106	17	section	section	NOUN
ejpam-2461	106	18	we	we	PRON
ejpam-2461	106	19	let	let	VERB
ejpam-2461	106	20	w	w	NOUN
ejpam-2461	106	21	and	and	CCONJ
ejpam-2461	106	22	p	p	NOUN
ejpam-2461	106	23	be	be	AUX
ejpam-2461	106	24	even	even	ADV
ejpam-2461	106	25	positive	positive	ADJ
ejpam-2461	106	26	integers	integer	NOUN
ejpam-2461	106	27	,	,	PUNCT
ejpam-2461	106	28	with	with	ADP
ejpam-2461	106	29	w	w	PROPN
ejpam-2461	106	30	=	=	SYM
ejpam-2461	106	31	2	2	NUM
ejpam-2461	106	32	m	m	NOUN
ejpam-2461	106	33	where	where	SCONJ
ejpam-2461	106	34	m	m	VERB
ejpam-2461	106	35	=	=	SYM
ejpam-2461	106	36	1,2	1,2	NUM
ejpam-2461	106	37	,	,	PUNCT
ejpam-2461	106	38	.	.	PUNCT
ejpam-2461	106	39	.	.	PUNCT
ejpam-2461	106	40	.	.	PUNCT
ejpam-2461	107	1	.	.	PUNCT
ejpam-2461	108	1	in	in	ADP
ejpam-2461	108	2	this	this	DET
ejpam-2461	108	3	case	case	NOUN
ejpam-2461	108	4	s0	s0	NOUN
ejpam-2461	108	5	=	=	SYM
ejpam-2461	108	6	(	(	PUNCT
ejpam-2461	108	7	2m−	2m−	PROPN
ejpam-2461	108	8	1)/p	1)/p	NUM
ejpam-2461	108	9	,	,	PUNCT
ejpam-2461	108	10	which	which	PRON
ejpam-2461	108	11	can	can	AUX
ejpam-2461	108	12	not	not	PART
ejpam-2461	108	13	equal	equal	VERB
ejpam-2461	108	14	an	an	DET
ejpam-2461	108	15	integer	integer	NOUN
ejpam-2461	108	16	and	and	CCONJ
ejpam-2461	108	17	so	so	ADV
ejpam-2461	108	18	no	no	DET
ejpam-2461	108	19	double	double	ADJ
ejpam-2461	108	20	pole	pole	NOUN
ejpam-2461	108	21	can	can	AUX
ejpam-2461	108	22	arise	arise	VERB
ejpam-2461	108	23	.	.	PUNCT
ejpam-2461	109	1	more	more	ADV
ejpam-2461	109	2	importantly	importantly	ADV
ejpam-2461	109	3	,	,	PUNCT
ejpam-2461	109	4	there	there	PRON
ejpam-2461	109	5	is	be	VERB
ejpam-2461	109	6	now	now	ADV
ejpam-2461	109	7	only	only	ADV
ejpam-2461	109	8	a	a	DET
ejpam-2461	109	9	finite	finite	ADJ
ejpam-2461	109	10	set	set	NOUN
ejpam-2461	109	11	of	of	ADP
ejpam-2461	109	12	poles	pole	NOUN
ejpam-2461	109	13	of	of	ADP
ejpam-2461	109	14	the	the	DET
ejpam-2461	109	15	integrand	integrand	NOUN
ejpam-2461	109	16	in	in	ADP
ejpam-2461	109	17	(	(	PUNCT
ejpam-2461	109	18	4	4	NUM
ejpam-2461	109	19	)	)	PUNCT
ejpam-2461	109	20	at	at	ADP
ejpam-2461	109	21	s	s	NOUN
ejpam-2461	109	22	=	=	VERB
ejpam-2461	109	23	s0	s0	PROPN
ejpam-2461	109	24	and	and	CCONJ
ejpam-2461	109	25	s	s	NOUN
ejpam-2461	109	26	=	=	NOUN
ejpam-2461	109	27	0,1,2	0,1,2	NUM
ejpam-2461	109	28	,	,	PUNCT
ejpam-2461	109	29	.	.	PUNCT
ejpam-2461	109	30	.	.	PUNCT
ejpam-2461	109	31	.	.	PUNCT
ejpam-2461	110	1	,	,	PUNCT
ejpam-2461	111	1	k	k	X
ejpam-2461	111	2	,	,	PUNCT
ejpam-2461	111	3	where	where	SCONJ
ejpam-2461	111	4	k	k	PROPN
ejpam-2461	111	5	=	=	SYM
ejpam-2461	111	6	⌊w	⌊w	PROPN
ejpam-2461	111	7	/	/	SYM
ejpam-2461	111	8	p⌋	p⌋	PROPN
ejpam-2461	111	9	,	,	PUNCT
ejpam-2461	111	10	since	since	SCONJ
ejpam-2461	111	11	the	the	DET
ejpam-2461	111	12	poles	pole	NOUN
ejpam-2461	111	13	of	of	ADP
ejpam-2461	111	14	γ(−s	γ(−	NOUN
ejpam-2461	111	15	)	)	PUNCT
ejpam-2461	111	16	at	at	ADP
ejpam-2461	111	17	s	s	NOUN
ejpam-2461	111	18	=	=	PUNCT
ejpam-2461	111	19	k	k	PROPN
ejpam-2461	112	1	+	+	CCONJ
ejpam-2461	112	2	k	k	X
ejpam-2461	112	3	(	(	PUNCT
ejpam-2461	112	4	k	k	NOUN
ejpam-2461	112	5	=	=	SYM
ejpam-2461	112	6	1,2	1,2	NUM
ejpam-2461	112	7	,	,	PUNCT
ejpam-2461	112	8	.	.	PUNCT
ejpam-2461	112	9	.	.	PUNCT
ejpam-2461	112	10	.	.	PUNCT
ejpam-2461	112	11	)	)	PUNCT
ejpam-2461	113	1	are	be	AUX
ejpam-2461	113	2	cancelled	cancel	VERB
ejpam-2461	113	3	by	by	ADP
ejpam-2461	113	4	the	the	DET
ejpam-2461	113	5	trivial	trivial	ADJ
ejpam-2461	113	6	zeros	zero	NOUN
ejpam-2461	113	7	of	of	ADP
ejpam-2461	113	8	the	the	DET
ejpam-2461	113	9	zeta	zeta	PROPN
ejpam-2461	113	10	function	function	NOUN
ejpam-2461	113	11	ζ(s	ζ(s	PROPN
ejpam-2461	113	12	)	)	PUNCT
ejpam-2461	113	13	at	at	ADP
ejpam-2461	113	14	s	s	NOUN
ejpam-2461	113	15	=	=	NOUN
ejpam-2461	113	16	−2,−4	−2,−4	PROPN
ejpam-2461	113	17	,	,	PUNCT
ejpam-2461	113	18	.	.	PUNCT
ejpam-2461	113	19	.	.	PUNCT
ejpam-2461	114	1	..	..	PUNCT
ejpam-2461	115	1	this	this	PRON
ejpam-2461	115	2	has	have	VERB
ejpam-2461	115	3	the	the	DET
ejpam-2461	115	4	consequence	consequence	NOUN
ejpam-2461	115	5	that	that	SCONJ
ejpam-2461	115	6	the	the	DET
ejpam-2461	115	7	integrand	integrand	NOUN
ejpam-2461	115	8	is	be	AUX
ejpam-2461	115	9	holomorphic	holomorphic	ADJ
ejpam-2461	115	10	in	in	ADP
ejpam-2461	115	11	ℜ(s	ℜ(s	PROPN
ejpam-2461	115	12	)	)	PUNCT
ejpam-2461	115	13	>	>	X
ejpam-2461	116	1	max{s0	max{s0	NOUN
ejpam-2461	116	2	,	,	PUNCT
ejpam-2461	116	3	k	k	NOUN
ejpam-2461	116	4	}	}	PUNCT
ejpam-2461	116	5	,	,	PUNCT
ejpam-2461	116	6	so	so	SCONJ
ejpam-2461	116	7	that	that	SCONJ
ejpam-2461	116	8	further	further	ADJ
ejpam-2461	116	9	displacement	displacement	NOUN
ejpam-2461	116	10	of	of	ADP
ejpam-2461	116	11	the	the	DET
ejpam-2461	116	12	contour	contour	NOUN
ejpam-2461	116	13	can	can	AUX
ejpam-2461	116	14	produce	produce	VERB
ejpam-2461	116	15	no	no	DET
ejpam-2461	116	16	additional	additional	ADJ
ejpam-2461	116	17	algebraic	algebraic	ADJ
ejpam-2461	116	18	terms	term	NOUN
ejpam-2461	116	19	in	in	ADP
ejpam-2461	116	20	the	the	DET
ejpam-2461	116	21	expansion	expansion	NOUN
ejpam-2461	116	22	of	of	ADP
ejpam-2461	116	23	sp(a	sp(a	PROPN
ejpam-2461	116	24	;	;	PUNCT
ejpam-2461	116	25	w	w	X
ejpam-2461	116	26	)	)	PUNCT
ejpam-2461	116	27	.	.	PUNCT
ejpam-2461	117	1	thus	thus	ADV
ejpam-2461	117	2	,	,	PUNCT
ejpam-2461	117	3	we	we	PRON
ejpam-2461	117	4	find	find	VERB
ejpam-2461	117	5	from	from	ADP
ejpam-2461	117	6	(	(	PUNCT
ejpam-2461	117	7	6	6	NUM
ejpam-2461	117	8	)	)	PUNCT
ejpam-2461	117	9	upon	upon	SCONJ
ejpam-2461	117	10	displacement	displacement	NOUN
ejpam-2461	117	11	of	of	ADP
ejpam-2461	117	12	the	the	DET
ejpam-2461	117	13	integration	integration	NOUN
ejpam-2461	117	14	path	path	NOUN
ejpam-2461	117	15	to	to	ADP
ejpam-2461	117	16	the	the	DET
ejpam-2461	117	17	right	right	NOUN
ejpam-2461	117	18	over	over	ADP
ejpam-2461	117	19	the	the	DET
ejpam-2461	117	20	poles	pole	NOUN
ejpam-2461	117	21	of	of	ADP
ejpam-2461	117	22	the	the	DET
ejpam-2461	117	23	integrand	integrand	NOUN
ejpam-2461	117	24	sp(a	sp(a	NOUN
ejpam-2461	117	25	;	;	PUNCT
ejpam-2461	117	26	w	w	X
ejpam-2461	117	27	)	)	PUNCT
ejpam-2461	117	28	=	=	SYM
ejpam-2461	118	1	1	1	NUM
ejpam-2461	118	2	p	p	NOUN
ejpam-2461	118	3	γ	γ	X
ejpam-2461	118	4	�	�	PROPN
ejpam-2461	118	5	1−w	1−w	NUM
ejpam-2461	118	6	p	p	X
ejpam-2461	118	7	�	�	PROPN
ejpam-2461	118	8	a(w−1)/p	a(w−1)/p	PROPN
ejpam-2461	119	1	+	+	CCONJ
ejpam-2461	119	2	k	k	PROPN
ejpam-2461	119	3	∑	∑	PUNCT
ejpam-2461	119	4	k=0	k=0	PROPN
ejpam-2461	119	5	(	(	PUNCT
ejpam-2461	119	6	−)k	−)k	PROPN
ejpam-2461	119	7	k	k	PROPN
ejpam-2461	119	8	!	!	PROPN
ejpam-2461	119	9	ζ(w−	ζ(w−	PROPN
ejpam-2461	119	10	pk	pk	PROPN
ejpam-2461	119	11	)	)	PUNCT
ejpam-2461	119	12	ak	ak	PROPN
ejpam-2461	119	13	+	+	CCONJ
ejpam-2461	119	14	(	(	PUNCT
ejpam-2461	119	15	−)m(2π)w	−)m(2π)w	NUM
ejpam-2461	119	16	il	il	PROPN
ejpam-2461	119	17	,	,	PUNCT
ejpam-2461	119	18	(	(	PUNCT
ejpam-2461	119	19	9	9	X
ejpam-2461	119	20	)	)	PUNCT
ejpam-2461	119	21	where	where	SCONJ
ejpam-2461	119	22	il	il	PROPN
ejpam-2461	119	23	=	=	SYM
ejpam-2461	119	24	(	(	PUNCT
ejpam-2461	119	25	−)m(2π)−w	−)m(2π)−w	PROPN
ejpam-2461	119	26	2πi	2πi	PROPN
ejpam-2461	119	27	∫	∫	PROPN
ejpam-2461	120	1	l	l	NOUN
ejpam-2461	120	2	γ(−s)ζ(w−	γ(−s)ζ(w−	ADJ
ejpam-2461	120	3	ps)asds	ps)asds	NOUN
ejpam-2461	120	4	(	(	PUNCT
ejpam-2461	120	5	10	10	NUM
ejpam-2461	120	6	)	)	PUNCT
ejpam-2461	120	7	and	and	CCONJ
ejpam-2461	120	8	l	l	NOUN
ejpam-2461	120	9	denotes	denote	VERB
ejpam-2461	120	10	a	a	DET
ejpam-2461	120	11	path	path	NOUN
ejpam-2461	120	12	parallel	parallel	NOUN
ejpam-2461	120	13	to	to	ADP
ejpam-2461	120	14	the	the	DET
ejpam-2461	120	15	imaginary	imaginary	ADJ
ejpam-2461	120	16	axis	axis	NOUN
ejpam-2461	120	17	withℜ(s	withℜ(s	PROPN
ejpam-2461	120	18	)	)	PUNCT
ejpam-2461	120	19	>	>	X
ejpam-2461	121	1	(	(	PUNCT
ejpam-2461	121	2	w	w	NOUN
ejpam-2461	121	3	/	/	SYM
ejpam-2461	121	4	p)+δ	p)+δ	NOUN
ejpam-2461	121	5	,	,	PUNCT
ejpam-2461	121	6	with	with	ADP
ejpam-2461	121	7	δ	δ	PROPN
ejpam-2461	121	8	denoting	denote	VERB
ejpam-2461	121	9	an	an	DET
ejpam-2461	121	10	arbitrary	arbitrary	ADJ
ejpam-2461	121	11	positive	positive	ADJ
ejpam-2461	121	12	quantity	quantity	NOUN
ejpam-2461	121	13	.	.	PUNCT
ejpam-2461	122	1	this	this	PRON
ejpam-2461	122	2	is	be	AUX
ejpam-2461	122	3	easily	easily	ADV
ejpam-2461	122	4	seen	see	VERB
ejpam-2461	122	5	to	to	PART
ejpam-2461	122	6	satisfy	satisfy	VERB
ejpam-2461	122	7	the	the	DET
ejpam-2461	122	8	requirement	requirement	NOUN
ejpam-2461	122	9	ℜ(s	ℜ(s	NOUN
ejpam-2461	122	10	)	)	PUNCT
ejpam-2461	122	11	>	>	X
ejpam-2461	123	1	max{s0	max{s0	PROPN
ejpam-2461	123	2	,	,	PUNCT
ejpam-2461	123	3	k0	k0	PROPN
ejpam-2461	123	4	}	}	PUNCT
ejpam-2461	123	5	necessary	necessary	ADJ
ejpam-2461	123	6	for	for	ADP
ejpam-2461	123	7	the	the	DET
ejpam-2461	123	8	validity	validity	NOUN
ejpam-2461	123	9	of	of	ADP
ejpam-2461	123	10	(	(	PUNCT
ejpam-2461	123	11	9	9	NUM
ejpam-2461	123	12	)	)	PUNCT
ejpam-2461	123	13	.	.	PUNCT
ejpam-2461	124	1	we	we	PRON
ejpam-2461	124	2	now	now	ADV
ejpam-2461	124	3	employ	employ	VERB
ejpam-2461	124	4	the	the	DET
ejpam-2461	124	5	functional	functional	ADJ
ejpam-2461	124	6	relation	relation	NOUN
ejpam-2461	124	7	for	for	ADP
ejpam-2461	124	8	ζ(s	ζ(s	PROPN
ejpam-2461	124	9	)	)	PUNCT
ejpam-2461	124	10	in	in	ADP
ejpam-2461	124	11	(	(	PUNCT
ejpam-2461	124	12	5	5	NUM
ejpam-2461	124	13	)	)	PUNCT
ejpam-2461	124	14	to	to	PART
ejpam-2461	124	15	convert	convert	VERB
ejpam-2461	124	16	the	the	DET
ejpam-2461	124	17	argument	argument	NOUN
ejpam-2461	124	18	of	of	ADP
ejpam-2461	124	19	the	the	DET
ejpam-2461	124	20	zeta	zeta	NOUN
ejpam-2461	124	21	function	function	NOUN
ejpam-2461	124	22	in	in	ADP
ejpam-2461	124	23	(	(	PUNCT
ejpam-2461	124	24	10	10	NUM
ejpam-2461	124	25	)	)	PUNCT
ejpam-2461	124	26	into	into	ADP
ejpam-2461	124	27	one	one	NUM
ejpam-2461	124	28	with	with	ADP
ejpam-2461	124	29	real	real	ADJ
ejpam-2461	124	30	part	part	NOUN
ejpam-2461	124	31	greater	great	ADJ
ejpam-2461	124	32	than	than	ADP
ejpam-2461	124	33	unity	unity	NOUN
ejpam-2461	124	34	.	.	PUNCT
ejpam-2461	125	1	the	the	DET
ejpam-2461	125	2	integral	integral	ADJ
ejpam-2461	125	3	in	in	ADP
ejpam-2461	125	4	(	(	PUNCT
ejpam-2461	125	5	10	10	NUM
ejpam-2461	125	6	)	)	PUNCT
ejpam-2461	125	7	can	can	AUX
ejpam-2461	125	8	then	then	ADV
ejpam-2461	125	9	be	be	AUX
ejpam-2461	125	10	written	write	VERB
ejpam-2461	125	11	in	in	ADP
ejpam-2461	125	12	the	the	DET
ejpam-2461	125	13	form	form	NOUN
ejpam-2461	125	14	il	il	PROPN
ejpam-2461	125	15	=	=	SYM
ejpam-2461	125	16	1	1	NUM
ejpam-2461	125	17	2πi	2πi	ADJ
ejpam-2461	125	18	∫	∫	PROPN
ejpam-2461	125	19	l	l	PROPN
ejpam-2461	125	20	ζ(1−w+	ζ(1−w+	PROPN
ejpam-2461	125	21	ps	ps	NOUN
ejpam-2461	125	22	)	)	PUNCT
ejpam-2461	125	23	γ(1−w+	γ(1−w+	PROPN
ejpam-2461	125	24	ps	ps	NOUN
ejpam-2461	125	25	)	)	PUNCT
ejpam-2461	125	26	γ(1	γ(1	PROPN
ejpam-2461	125	27	+	+	SYM
ejpam-2461	125	28	s	s	NOUN
ejpam-2461	125	29	)	)	PUNCT
ejpam-2461	125	30	sin	sin	NOUN
ejpam-2461	125	31	1	1	NUM
ejpam-2461	125	32	2πps	2πps	NUM
ejpam-2461	125	33	sinπs	sinπs	PROPN
ejpam-2461	125	34	χ−sds	χ−sds	NOUN
ejpam-2461	125	35	,	,	PUNCT
ejpam-2461	125	36	where	where	SCONJ
ejpam-2461	125	37	χ	χ	X
ejpam-2461	125	38	=	=	X
ejpam-2461	125	39	(	(	PUNCT
ejpam-2461	125	40	2π)pa−1	2π)pa−1	NOUN
ejpam-2461	125	41	.	.	PUNCT
ejpam-2461	126	1	in	in	ADP
ejpam-2461	126	2	[	[	X
ejpam-2461	126	3	5	5	NUM
ejpam-2461	126	4	,	,	PUNCT
ejpam-2461	126	5	§	§	NOUN
ejpam-2461	126	6	8.1.4	8.1.4	NOUN
ejpam-2461	126	7	]	]	X
ejpam-2461	126	8	,	,	PUNCT
ejpam-2461	126	9	the	the	DET
ejpam-2461	126	10	zeta	zeta	NOUN
ejpam-2461	126	11	function	function	NOUN
ejpam-2461	126	12	appearing	appear	VERB
ejpam-2461	126	13	in	in	ADP
ejpam-2461	126	14	the	the	DET
ejpam-2461	126	15	above	above	ADJ
ejpam-2461	126	16	integrand	integrand	NOUN
ejpam-2461	126	17	was	be	AUX
ejpam-2461	126	18	written	write	VERB
ejpam-2461	126	19	as	as	ADP
ejpam-2461	126	20	an	an	DET
ejpam-2461	126	21	infinite	infinite	ADJ
ejpam-2461	126	22	series	series	NOUN
ejpam-2461	126	23	.	.	PUNCT
ejpam-2461	127	1	here	here	ADV
ejpam-2461	127	2	we	we	PRON
ejpam-2461	127	3	follow	follow	VERB
ejpam-2461	127	4	a	a	DET
ejpam-2461	127	5	suggestion	suggestion	NOUN
ejpam-2461	127	6	made	make	VERB
ejpam-2461	127	7	by	by	ADP
ejpam-2461	127	8	j.	j.	PROPN
ejpam-2461	127	9	boersma	boersma	PROPN
ejpam-2461	127	10	and	and	CCONJ
ejpam-2461	127	11	retain	retain	VERB
ejpam-2461	127	12	this	this	DET
ejpam-2461	127	13	function	function	NOUN
ejpam-2461	127	14	in	in	ADP
ejpam-2461	127	15	the	the	DET
ejpam-2461	127	16	integrand	integrand	NOUN
ejpam-2461	127	17	;	;	PUNCT
ejpam-2461	127	18	see	see	VERB
ejpam-2461	127	19	also	also	ADV
ejpam-2461	127	20	[	[	X
ejpam-2461	127	21	3	3	NUM
ejpam-2461	127	22	,	,	PUNCT
ejpam-2461	127	23	§	§	NOUN
ejpam-2461	127	24	8	8	NUM
ejpam-2461	127	25	]	]	PUNCT
ejpam-2461	127	26	.	.	PUNCT
ejpam-2461	128	1	making	make	VERB
ejpam-2461	128	2	use	use	NOUN
ejpam-2461	128	3	of	of	ADP
ejpam-2461	128	4	the	the	DET
ejpam-2461	128	5	expansion	expansion	NOUN
ejpam-2461	128	6	(	(	PUNCT
ejpam-2461	128	7	see	see	VERB
ejpam-2461	128	8	,	,	PUNCT
ejpam-2461	128	9	for	for	ADP
ejpam-2461	128	10	example	example	NOUN
ejpam-2461	128	11	,	,	PUNCT
ejpam-2461	128	12	[	[	X
ejpam-2461	128	13	5	5	NUM
ejpam-2461	128	14	,	,	PUNCT
ejpam-2461	128	15	p.	p.	NOUN
ejpam-2461	128	16	368	368	NUM
ejpam-2461	128	17	]	]	PUNCT
ejpam-2461	128	18	)	)	PUNCT
ejpam-2461	128	19	sin	sin	NOUN
ejpam-2461	128	20	1	1	NUM
ejpam-2461	128	21	2πps	2πps	NUM
ejpam-2461	128	22	sinπs	sinπs	NOUN
ejpam-2461	128	23	=	=	SYM
ejpam-2461	128	24	2	2	NUM
ejpam-2461	128	25	n−1	n−1	PROPN
ejpam-2461	128	26	∑	∑	PUNCT
ejpam-2461	128	27	r=0	r=0	PROPN
ejpam-2461	128	28	cosπ	cosπ	NOUN
ejpam-2461	128	29	(	(	PUNCT
ejpam-2461	128	30	1	1	NUM
ejpam-2461	128	31	2	2	NUM
ejpam-2461	128	32	p−2r−1)s+	p−2r−1)s+	NOUN
ejpam-2461	128	33	¨	¨	NOUN
ejpam-2461	128	34	0	0	NUM
ejpam-2461	128	35	(	(	PUNCT
ejpam-2461	128	36	p/2	p/2	NOUN
ejpam-2461	128	37	even	even	ADV
ejpam-2461	128	38	)	)	PUNCT
ejpam-2461	128	39	1	1	NUM
ejpam-2461	128	40	(	(	PUNCT
ejpam-2461	128	41	p/2	p/2	NOUN
ejpam-2461	128	42	odd	odd	ADJ
ejpam-2461	128	43	)	)	PUNCT
ejpam-2461	128	44	,	,	PUNCT
ejpam-2461	128	45	n	n	NOUN
ejpam-2461	128	46	=	=	PUNCT
ejpam-2461	129	1	[	[	PUNCT
ejpam-2461	129	2	1	1	NUM
ejpam-2461	129	3	4	4	NUM
ejpam-2461	129	4	p	p	NOUN
ejpam-2461	129	5	]	]	X
ejpam-2461	129	6	,	,	PUNCT
ejpam-2461	129	7	where	where	SCONJ
ejpam-2461	129	8	square	square	ADJ
ejpam-2461	129	9	brackets	bracket	NOUN
ejpam-2461	129	10	denote	denote	VERB
ejpam-2461	129	11	the	the	DET
ejpam-2461	129	12	nearest	near	ADJ
ejpam-2461	129	13	integer	integer	ADJ
ejpam-2461	129	14	part∗	part∗	NOUN
ejpam-2461	129	15	,	,	PUNCT
ejpam-2461	129	16	we	we	PRON
ejpam-2461	129	17	obtain	obtain	VERB
ejpam-2461	129	18	il	il	PROPN
ejpam-2461	129	19	=	=	SYM
ejpam-2461	129	20	n−1	n−1	PROPN
ejpam-2461	129	21	∑	∑	PUNCT
ejpam-2461	129	22	r=0	r=0	PROPN
ejpam-2461	129	23	{	{	PUNCT
ejpam-2461	129	24	j+r	j+r	X
ejpam-2461	129	25	+	+	NUM
ejpam-2461	129	26	j−r	j−r	NOUN
ejpam-2461	129	27	}	}	PUNCT
ejpam-2461	129	28	+	+	PUNCT
ejpam-2461	129	29	¨	¨	NOUN
ejpam-2461	129	30	0	0	NUM
ejpam-2461	129	31	(	(	PUNCT
ejpam-2461	129	32	p/2	p/2	NOUN
ejpam-2461	129	33	even	even	ADV
ejpam-2461	129	34	)	)	PUNCT
ejpam-2461	129	35	j	j	PROPN
ejpam-2461	129	36	(	(	PUNCT
ejpam-2461	129	37	p/2	p/2	NOUN
ejpam-2461	129	38	odd	odd	ADJ
ejpam-2461	129	39	)	)	PUNCT
ejpam-2461	129	40	.	.	PUNCT
ejpam-2461	130	1	(	(	PUNCT
ejpam-2461	130	2	11	11	NUM
ejpam-2461	130	3	)	)	PUNCT
ejpam-2461	130	4	∗the	∗the	DET
ejpam-2461	130	5	nearest	near	ADJ
ejpam-2461	130	6	integer	integer	NOUN
ejpam-2461	130	7	part	part	NOUN
ejpam-2461	130	8	corresponds	correspond	VERB
ejpam-2461	130	9	to	to	ADP
ejpam-2461	130	10	[	[	X
ejpam-2461	130	11	x	x	X
ejpam-2461	130	12	]	]	X
ejpam-2461	130	13	=	=	SYM
ejpam-2461	130	14	n	n	NOUN
ejpam-2461	130	15	when	when	SCONJ
ejpam-2461	130	16	x	x	PRON
ejpam-2461	130	17	is	be	AUX
ejpam-2461	130	18	in	in	ADP
ejpam-2461	130	19	the	the	DET
ejpam-2461	130	20	interval	interval	NOUN
ejpam-2461	130	21	(	(	PUNCT
ejpam-2461	130	22	n	n	CCONJ
ejpam-2461	130	23	−	−	PROPN
ejpam-2461	130	24	1	1	NUM
ejpam-2461	130	25	2	2	NUM
ejpam-2461	130	26	,	,	PUNCT
ejpam-2461	130	27	n	n	PROPN
ejpam-2461	130	28	+	+	CCONJ
ejpam-2461	130	29	1	1	NUM
ejpam-2461	130	30	2	2	NUM
ejpam-2461	130	31	]	]	PUNCT
ejpam-2461	130	32	.	.	PUNCT
ejpam-2461	131	1	note	note	VERB
ejpam-2461	131	2	that	that	SCONJ
ejpam-2461	131	3	when	when	SCONJ
ejpam-2461	131	4	p	p	PROPN
ejpam-2461	131	5	=	=	NOUN
ejpam-2461	131	6	2	2	NUM
ejpam-2461	131	7	,	,	PUNCT
ejpam-2461	131	8	we	we	PRON
ejpam-2461	131	9	have	have	VERB
ejpam-2461	131	10	n	n	NOUN
ejpam-2461	131	11	=	=	SYM
ejpam-2461	131	12	0	0	NUM
ejpam-2461	131	13	and	and	CCONJ
ejpam-2461	131	14	the	the	DET
ejpam-2461	131	15	above	above	ADJ
ejpam-2461	131	16	expansion	expansion	NOUN
ejpam-2461	131	17	contains	contain	VERB
ejpam-2461	131	18	no	no	DET
ejpam-2461	131	19	information	information	NOUN
ejpam-2461	131	20	.	.	PUNCT
ejpam-2461	132	1	r.	r.	PROPN
ejpam-2461	132	2	paris	paris	PROPN
ejpam-2461	132	3	/	/	SYM
ejpam-2461	132	4	eur	eur	PROPN
ejpam-2461	132	5	.	.	PUNCT
ejpam-2461	133	1	j.	j.	PROPN
ejpam-2461	133	2	pure	pure	PROPN
ejpam-2461	133	3	appl	appl	PROPN
ejpam-2461	133	4	.	.	PROPN
ejpam-2461	133	5	math	math	PROPN
ejpam-2461	133	6	,	,	PUNCT
ejpam-2461	133	7	9	9	NUM
ejpam-2461	133	8	(	(	PUNCT
ejpam-2461	133	9	2016	2016	NUM
ejpam-2461	133	10	)	)	PUNCT
ejpam-2461	133	11	,	,	PUNCT
ejpam-2461	133	12	3	3	NUM
ejpam-2461	133	13	-	-	SYM
ejpam-2461	133	14	18	18	NUM
ejpam-2461	133	15	9	9	NUM
ejpam-2461	133	16	here	here	ADV
ejpam-2461	133	17	we	we	PRON
ejpam-2461	133	18	have	have	AUX
ejpam-2461	133	19	defined	define	VERB
ejpam-2461	133	20	the	the	DET
ejpam-2461	133	21	integrals	integral	NOUN
ejpam-2461	133	22	j±r	j±r	PROPN
ejpam-2461	133	23	and	and	CCONJ
ejpam-2461	133	24	j	j	PROPN
ejpam-2461	133	25	by	by	ADP
ejpam-2461	133	26	j±r	j±r	PROPN
ejpam-2461	133	27	=	=	SYM
ejpam-2461	133	28	1	1	NUM
ejpam-2461	133	29	2πi	2πi	ADJ
ejpam-2461	133	30	∫	∫	PROPN
ejpam-2461	133	31	l	l	PROPN
ejpam-2461	133	32	ζ(1−w+	ζ(1−w+	PROPN
ejpam-2461	133	33	ps	ps	NOUN
ejpam-2461	133	34	)	)	PUNCT
ejpam-2461	133	35	γ(1−w+	γ(1−w+	PROPN
ejpam-2461	133	36	ps	ps	NOUN
ejpam-2461	133	37	)	)	PUNCT
ejpam-2461	134	1	γ(1	γ(1	PROPN
ejpam-2461	134	2	+	+	SYM
ejpam-2461	134	3	s	s	NOUN
ejpam-2461	134	4	)	)	PUNCT
ejpam-2461	134	5	(	(	PUNCT
ejpam-2461	134	6	χe∓πi(p/2−2r−1))−sds	χe∓πi(p/2−2r−1))−sds	X
ejpam-2461	134	7	(	(	PUNCT
ejpam-2461	134	8	12	12	NUM
ejpam-2461	134	9	)	)	PUNCT
ejpam-2461	134	10	and	and	CCONJ
ejpam-2461	134	11	j	j	X
ejpam-2461	134	12	=	=	SYM
ejpam-2461	134	13	1	1	NUM
ejpam-2461	134	14	2πi	2πi	ADJ
ejpam-2461	134	15	∫	∫	PROPN
ejpam-2461	134	16	l	l	PROPN
ejpam-2461	134	17	ζ(1−w+	ζ(1−w+	PROPN
ejpam-2461	134	18	ps	ps	NOUN
ejpam-2461	134	19	)	)	PUNCT
ejpam-2461	134	20	γ(1−w+	γ(1−w+	PROPN
ejpam-2461	134	21	ps	ps	NOUN
ejpam-2461	134	22	)	)	PUNCT
ejpam-2461	134	23	γ(1	γ(1	PROPN
ejpam-2461	134	24	+	+	CCONJ
ejpam-2461	134	25	s	s	NOUN
ejpam-2461	134	26	)	)	PUNCT
ejpam-2461	134	27	χ−sds	χ−sds	NOUN
ejpam-2461	134	28	.	.	PUNCT
ejpam-2461	135	1	(	(	PUNCT
ejpam-2461	135	2	13	13	NUM
ejpam-2461	135	3	)	)	PUNCT
ejpam-2461	135	4	3.1	3.1	NUM
ejpam-2461	135	5	.	.	PUNCT
ejpam-2461	136	1	asymptotic	asymptotic	ADJ
ejpam-2461	136	2	evaluation	evaluation	NOUN
ejpam-2461	136	3	of	of	ADP
ejpam-2461	136	4	j±	j±	PROPN
ejpam-2461	136	5	r	r	PROPN
ejpam-2461	136	6	and	and	CCONJ
ejpam-2461	136	7	j	j	NOUN
ejpam-2461	136	8	the	the	DET
ejpam-2461	136	9	integrals	integral	NOUN
ejpam-2461	136	10	j±r	j±r	PROPN
ejpam-2461	136	11	and	and	CCONJ
ejpam-2461	136	12	j	j	PROPN
ejpam-2461	136	13	have	have	VERB
ejpam-2461	136	14	no	no	DET
ejpam-2461	136	15	poles	pole	NOUN
ejpam-2461	136	16	in	in	ADP
ejpam-2461	136	17	the	the	DET
ejpam-2461	136	18	half	half	ADJ
ejpam-2461	136	19	-	-	PUNCT
ejpam-2461	136	20	plane	plane	NOUN
ejpam-2461	136	21	ℜ(s	ℜ(s	NOUN
ejpam-2461	136	22	)	)	PUNCT
ejpam-2461	136	23	>	>	X
ejpam-2461	137	1	(	(	PUNCT
ejpam-2461	137	2	w	w	NOUN
ejpam-2461	137	3	/	/	SYM
ejpam-2461	137	4	p	p	NOUN
ejpam-2461	137	5	)	)	PUNCT
ejpam-2461	137	6	+	+	CCONJ
ejpam-2461	137	7	δ	δ	PROPN
ejpam-2461	137	8	,	,	PUNCT
ejpam-2461	137	9	so	so	SCONJ
ejpam-2461	137	10	that	that	SCONJ
ejpam-2461	137	11	we	we	PRON
ejpam-2461	137	12	can	can	AUX
ejpam-2461	137	13	displace	displace	VERB
ejpam-2461	137	14	the	the	DET
ejpam-2461	137	15	path	path	NOUN
ejpam-2461	137	16	l	l	NOUN
ejpam-2461	137	17	as	as	ADV
ejpam-2461	137	18	far	far	ADV
ejpam-2461	137	19	to	to	ADP
ejpam-2461	137	20	the	the	DET
ejpam-2461	137	21	right	right	NOUN
ejpam-2461	137	22	as	as	SCONJ
ejpam-2461	137	23	we	we	PRON
ejpam-2461	137	24	please	please	VERB
ejpam-2461	137	25	.	.	PUNCT
ejpam-2461	138	1	on	on	ADP
ejpam-2461	138	2	such	such	DET
ejpam-2461	138	3	a	a	DET
ejpam-2461	138	4	displaced	displace	VERB
ejpam-2461	138	5	path	path	NOUN
ejpam-2461	138	6	|s|	|s|	PROPN
ejpam-2461	138	7	is	be	AUX
ejpam-2461	138	8	everywhere	everywhere	ADV
ejpam-2461	138	9	large	large	ADJ
ejpam-2461	138	10	.	.	PUNCT
ejpam-2461	139	1	let	let	VERB
ejpam-2461	139	2	m	m	PRON
ejpam-2461	139	3	denote	denote	VERB
ejpam-2461	139	4	an	an	DET
ejpam-2461	139	5	arbitrary	arbitrary	ADJ
ejpam-2461	139	6	positive	positive	ADJ
ejpam-2461	139	7	integer	integer	NOUN
ejpam-2461	139	8	.	.	PUNCT
ejpam-2461	140	1	the	the	DET
ejpam-2461	140	2	ratio	ratio	NOUN
ejpam-2461	140	3	of	of	ADP
ejpam-2461	140	4	gamma	gamma	NOUN
ejpam-2461	140	5	functions	function	NOUN
ejpam-2461	140	6	appearing	appear	VERB
ejpam-2461	140	7	in	in	ADP
ejpam-2461	140	8	(	(	PUNCT
ejpam-2461	140	9	12	12	NUM
ejpam-2461	140	10	)	)	PUNCT
ejpam-2461	140	11	and	and	CCONJ
ejpam-2461	140	12	(	(	PUNCT
ejpam-2461	140	13	13	13	NUM
ejpam-2461	140	14	)	)	PUNCT
ejpam-2461	140	15	may	may	AUX
ejpam-2461	140	16	then	then	ADV
ejpam-2461	140	17	be	be	AUX
ejpam-2461	140	18	expanded	expand	VERB
ejpam-2461	140	19	by	by	ADP
ejpam-2461	140	20	making	make	VERB
ejpam-2461	140	21	use	use	NOUN
ejpam-2461	140	22	of	of	ADP
ejpam-2461	140	23	the	the	DET
ejpam-2461	140	24	result	result	NOUN
ejpam-2461	140	25	(	(	PUNCT
ejpam-2461	140	26	for	for	ADP
ejpam-2461	140	27	p	p	ADJ
ejpam-2461	140	28	>	>	X
ejpam-2461	140	29	1	1	NUM
ejpam-2461	140	30	)	)	PUNCT
ejpam-2461	140	31	given	give	VERB
ejpam-2461	140	32	in	in	ADP
ejpam-2461	140	33	[	[	NOUN
ejpam-2461	140	34	5	5	NUM
ejpam-2461	140	35	,	,	PUNCT
ejpam-2461	140	36	p.	p.	NOUN
ejpam-2461	140	37	53	53	NUM
ejpam-2461	140	38	]	]	PUNCT
ejpam-2461	140	39	γ(1−w+	γ(1−w+	PROPN
ejpam-2461	140	40	ps	ps	NOUN
ejpam-2461	140	41	)	)	PUNCT
ejpam-2461	141	1	γ(1	γ(1	PROPN
ejpam-2461	141	2	+	+	SYM
ejpam-2461	141	3	s	s	NOUN
ejpam-2461	141	4	)	)	PUNCT
ejpam-2461	141	5	=	=	PUNCT
ejpam-2461	141	6	a	a	DET
ejpam-2461	141	7	2π	2π	NOUN
ejpam-2461	141	8	(	(	PUNCT
ejpam-2461	141	9	hκκ)−s	hκκ)−s	PROPN
ejpam-2461	141	10	§	§	PROPN
ejpam-2461	141	11	m−1	m−1	PROPN
ejpam-2461	141	12	∑	∑	PUNCT
ejpam-2461	141	13	j=0	j=0	PROPN
ejpam-2461	141	14	(	(	PUNCT
ejpam-2461	141	15	−	−	PROPN
ejpam-2461	141	16	)	)	PUNCT
ejpam-2461	141	17	jc	jc	PROPN
ejpam-2461	141	18	jγ(κs+	jγ(κs+	PROPN
ejpam-2461	141	19	ϑ−	ϑ−	PROPN
ejpam-2461	141	20	j	j	PROPN
ejpam-2461	141	21	)	)	PUNCT
ejpam-2461	142	1	+	+	NOUN
ejpam-2461	142	2	ρm	ρm	INTJ
ejpam-2461	142	3	(	(	PUNCT
ejpam-2461	142	4	s)γ(κs+	s)γ(κs+	NOUN
ejpam-2461	142	5	ϑ−m	ϑ−m	PROPN
ejpam-2461	142	6	)	)	PUNCT
ejpam-2461	142	7	ª	ª	PRON
ejpam-2461	142	8	,	,	PUNCT
ejpam-2461	142	9	(	(	PUNCT
ejpam-2461	142	10	14	14	NUM
ejpam-2461	142	11	)	)	PUNCT
ejpam-2461	142	12	where	where	SCONJ
ejpam-2461	142	13	c0	c0	NOUN
ejpam-2461	142	14	=	=	PROPN
ejpam-2461	142	15	1	1	NUM
ejpam-2461	142	16	,	,	PUNCT
ejpam-2461	142	17	ρm	ρm	PROPN
ejpam-2461	142	18	(	(	PUNCT
ejpam-2461	142	19	s	s	NOUN
ejpam-2461	142	20	)	)	PUNCT
ejpam-2461	142	21	=	=	SYM
ejpam-2461	142	22	o(1	o(1	NOUN
ejpam-2461	142	23	)	)	PUNCT
ejpam-2461	142	24	as	as	ADP
ejpam-2461	142	25	|s|	|s|	NOUN
ejpam-2461	142	26	→∞	→∞	PROPN
ejpam-2461	142	27	in	in	ADP
ejpam-2461	142	28	|arg	|arg	NOUN
ejpam-2461	142	29	s|	s|	VERB
ejpam-2461	142	30	<	<	X
ejpam-2461	142	31	π	π	X
ejpam-2461	142	32	and	and	CCONJ
ejpam-2461	142	33	κ=	κ=	VERB
ejpam-2461	142	34	p−	p−	NOUN
ejpam-2461	142	35	1	1	NUM
ejpam-2461	142	36	,	,	PUNCT
ejpam-2461	142	37	h=	h=	PRON
ejpam-2461	142	38	p−p	p−p	PROPN
ejpam-2461	142	39	,	,	PUNCT
ejpam-2461	142	40	ϑ	ϑ	X
ejpam-2461	142	41	=	=	SYM
ejpam-2461	142	42	1	1	NUM
ejpam-2461	142	43	2	2	NUM
ejpam-2461	142	44	−	−	NOUN
ejpam-2461	142	45	w	w	NOUN
ejpam-2461	142	46	,	,	PUNCT
ejpam-2461	142	47	a=	a=	X
ejpam-2461	142	48	(	(	PUNCT
ejpam-2461	142	49	2π	2π	NOUN
ejpam-2461	142	50	)	)	PUNCT
ejpam-2461	142	51	1	1	NUM
ejpam-2461	142	52	2	2	NUM
ejpam-2461	142	53	κ	κ	NOUN
ejpam-2461	142	54	1	1	NUM
ejpam-2461	142	55	2−ϑpϑ.	2−ϑpϑ.	NUM
ejpam-2461	142	56	(	(	PUNCT
ejpam-2461	142	57	15	15	NUM
ejpam-2461	142	58	)	)	PUNCT
ejpam-2461	142	59	the	the	DET
ejpam-2461	142	60	coefficients	coefficient	NOUN
ejpam-2461	142	61	c	c	PROPN
ejpam-2461	142	62	j	j	PROPN
ejpam-2461	142	63	≡	≡	PROPN
ejpam-2461	142	64	c	c	PROPN
ejpam-2461	142	65	j(w	j(w	PROPN
ejpam-2461	142	66	,	,	PUNCT
ejpam-2461	142	67	p	p	NOUN
ejpam-2461	142	68	)	)	PUNCT
ejpam-2461	142	69	(	(	PUNCT
ejpam-2461	142	70	0	0	NUM
ejpam-2461	142	71	≤	≤	NUM
ejpam-2461	142	72	j	j	PROPN
ejpam-2461	142	73	≤	≤	ADV
ejpam-2461	142	74	4	4	NUM
ejpam-2461	142	75	)	)	PUNCT
ejpam-2461	142	76	are	be	AUX
ejpam-2461	142	77	listed	list	VERB
ejpam-2461	142	78	in	in	ADP
ejpam-2461	142	79	[	[	X
ejpam-2461	142	80	5	5	NUM
ejpam-2461	142	81	,	,	PUNCT
ejpam-2461	142	82	pp	pp	ADJ
ejpam-2461	142	83	.	.	PUNCT
ejpam-2461	143	1	46–48	46–48	NUM
ejpam-2461	143	2	]	]	PUNCT
ejpam-2461	143	3	where	where	SCONJ
ejpam-2461	143	4	an	an	DET
ejpam-2461	143	5	algorithm	algorithm	NOUN
ejpam-2461	143	6	for	for	ADP
ejpam-2461	143	7	their	their	PRON
ejpam-2461	143	8	determination	determination	NOUN
ejpam-2461	143	9	is	be	AUX
ejpam-2461	143	10	described	describe	VERB
ejpam-2461	143	11	;	;	PUNCT
ejpam-2461	143	12	see	see	VERB
ejpam-2461	143	13	section	section	NOUN
ejpam-2461	143	14	4	4	NUM
ejpam-2461	143	15	for	for	ADP
ejpam-2461	143	16	details	detail	NOUN
ejpam-2461	143	17	.	.	PUNCT
ejpam-2461	144	1	substitution	substitution	NOUN
ejpam-2461	144	2	of	of	ADP
ejpam-2461	144	3	the	the	DET
ejpam-2461	144	4	expansion	expansion	NOUN
ejpam-2461	144	5	(	(	PUNCT
ejpam-2461	144	6	14	14	NUM
ejpam-2461	144	7	)	)	PUNCT
ejpam-2461	144	8	into	into	ADP
ejpam-2461	144	9	the	the	DET
ejpam-2461	144	10	integrals	integral	NOUN
ejpam-2461	144	11	j±r	j±r	PROPN
ejpam-2461	145	1	in	in	ADP
ejpam-2461	145	2	(	(	PUNCT
ejpam-2461	145	3	12	12	NUM
ejpam-2461	145	4	)	)	PUNCT
ejpam-2461	145	5	then	then	ADV
ejpam-2461	145	6	produces	produce	VERB
ejpam-2461	145	7	j±r	j±r	PROPN
ejpam-2461	145	8	=	=	PUNCT
ejpam-2461	145	9	a	a	DET
ejpam-2461	145	10	2π	2π	NUM
ejpam-2461	145	11	m−1	m−1	PROPN
ejpam-2461	145	12	∑	∑	PUNCT
ejpam-2461	145	13	j=0	j=0	PROPN
ejpam-2461	145	14	(	(	PUNCT
ejpam-2461	145	15	−	−	PROPN
ejpam-2461	145	16	)	)	PUNCT
ejpam-2461	145	17	jc	jc	PROPN
ejpam-2461	145	18	j	j	PROPN
ejpam-2461	145	19	2πi	2πi	PROPN
ejpam-2461	145	20	∫	∫	PROPN
ejpam-2461	146	1	l	l	PROPN
ejpam-2461	146	2	ζ(1−w+	ζ(1−w+	PROPN
ejpam-2461	146	3	ps)γ(κs+	ps)γ(κs+	PROPN
ejpam-2461	146	4	ϑ−	ϑ−	PROPN
ejpam-2461	146	5	j	j	PROPN
ejpam-2461	146	6	)	)	PUNCT
ejpam-2461	146	7	(	(	PUNCT
ejpam-2461	146	8	x	x	PROPN
ejpam-2461	146	9	e∓πiψr	e∓πiψr	PROPN
ejpam-2461	146	10	)	)	PUNCT
ejpam-2461	146	11	−κsds+r±m	−κsds+r±m	PROPN
ejpam-2461	146	12	,	,	PUNCT
ejpam-2461	146	13	r	r	NOUN
ejpam-2461	146	14	=	=	PUNCT
ejpam-2461	146	15	a	a	DET
ejpam-2461	146	16	2πκ	2πκ	ADJ
ejpam-2461	146	17	m−1	m−1	PROPN
ejpam-2461	146	18	∑	∑	PUNCT
ejpam-2461	146	19	j=0	j=0	PROPN
ejpam-2461	146	20	(	(	PUNCT
ejpam-2461	146	21	x	x	NOUN
ejpam-2461	146	22	e∓πiψr	e∓πiψr	PROPN
ejpam-2461	146	23	)	)	PUNCT
ejpam-2461	146	24	ϑ−	ϑ−	PROPN
ejpam-2461	146	25	j	j	NOUN
ejpam-2461	146	26	(	(	PUNCT
ejpam-2461	146	27	−	−	PROPN
ejpam-2461	146	28	)	)	PUNCT
ejpam-2461	146	29	jc	jc	PROPN
ejpam-2461	146	30	j	j	PROPN
ejpam-2461	146	31	2πi	2πi	PROPN
ejpam-2461	146	32	∫	∫	PROPN
ejpam-2461	146	33	l′	l′	VERB
ejpam-2461	146	34	γ(u)ζ(qu+λ	γ(u)ζ(qu+λ	NOUN
ejpam-2461	146	35	j)(x	j)(x	PROPN
ejpam-2461	146	36	e∓πiψr	e∓πiψr	PROPN
ejpam-2461	146	37	)	)	PUNCT
ejpam-2461	147	1	−udu+r±m	−udu+r±m	NOUN
ejpam-2461	147	2	,	,	PUNCT
ejpam-2461	147	3	r	r	NOUN
ejpam-2461	147	4	.	.	PUNCT
ejpam-2461	148	1	here	here	ADV
ejpam-2461	148	2	we	we	PRON
ejpam-2461	148	3	have	have	AUX
ejpam-2461	148	4	made	make	VERB
ejpam-2461	148	5	the	the	DET
ejpam-2461	148	6	change	change	NOUN
ejpam-2461	148	7	of	of	ADP
ejpam-2461	148	8	variable	variable	ADJ
ejpam-2461	148	9	u	u	NOUN
ejpam-2461	148	10	→	→	X
ejpam-2461	148	11	κs	κs	NOUN
ejpam-2461	148	12	+	+	CCONJ
ejpam-2461	148	13	ϑ	ϑ	X
ejpam-2461	148	14	−	−	PROPN
ejpam-2461	148	15	j	j	PROPN
ejpam-2461	148	16	,	,	PUNCT
ejpam-2461	148	17	with	with	ADP
ejpam-2461	148	18	l′	l′	NUM
ejpam-2461	148	19	denoting	denote	VERB
ejpam-2461	148	20	the	the	DET
ejpam-2461	148	21	modified	modify	VERB
ejpam-2461	148	22	integration	integration	NOUN
ejpam-2461	148	23	path	path	NOUN
ejpam-2461	148	24	,	,	PUNCT
ejpam-2461	148	25	and	and	CCONJ
ejpam-2461	148	26	have	have	AUX
ejpam-2461	148	27	defined	define	VERB
ejpam-2461	148	28	x	x	X
ejpam-2461	148	29	:	:	PUNCT
ejpam-2461	148	30	=	=	SYM
ejpam-2461	148	31	κ(hχ)1	κ(hχ)1	X
ejpam-2461	148	32	/	/	SYM
ejpam-2461	148	33	κ	κ	NOUN
ejpam-2461	148	34	,	,	PUNCT
ejpam-2461	148	35	ψr	ψr	ADP
ejpam-2461	148	36	:	:	PUNCT
ejpam-2461	148	37	=	=	SYM
ejpam-2461	148	38	1	1	NUM
ejpam-2461	148	39	2	2	NUM
ejpam-2461	148	40	p−2r−1	p−2r−1	PROPN
ejpam-2461	148	41	κ	κ	NOUN
ejpam-2461	148	42	,	,	PUNCT
ejpam-2461	148	43	q	q	X
ejpam-2461	148	44	:	:	PUNCT
ejpam-2461	148	45	=	=	SYM
ejpam-2461	148	46	p	p	X
ejpam-2461	148	47	κ	κ	NOUN
ejpam-2461	148	48	,	,	PUNCT
ejpam-2461	148	49	λ	λ	X
ejpam-2461	148	50	j	j	NOUN
ejpam-2461	148	51	:	:	PUNCT
ejpam-2461	148	52	=	=	SYM
ejpam-2461	149	1	1	1	NUM
ejpam-2461	149	2	+	+	SYM
ejpam-2461	149	3	1	1	NUM
ejpam-2461	149	4	κ	κ	NOUN
ejpam-2461	149	5	(	(	PUNCT
ejpam-2461	149	6	w+	w+	NOUN
ejpam-2461	149	7	p	p	X
ejpam-2461	149	8	(	(	PUNCT
ejpam-2461	149	9	j	j	PROPN
ejpam-2461	149	10	−	−	PROPN
ejpam-2461	149	11	1	1	NUM
ejpam-2461	149	12	2	2	NUM
ejpam-2461	149	13	)	)	PUNCT
ejpam-2461	149	14	)	)	PUNCT
ejpam-2461	149	15	(	(	PUNCT
ejpam-2461	149	16	16	16	NUM
ejpam-2461	149	17	)	)	PUNCT
ejpam-2461	149	18	together	together	ADV
ejpam-2461	149	19	with	with	ADP
ejpam-2461	149	20	the	the	DET
ejpam-2461	149	21	remainders	remainder	NOUN
ejpam-2461	149	22	r±m	r±m	PROPN
ejpam-2461	149	23	,	,	PUNCT
ejpam-2461	149	24	r	r	NOUN
ejpam-2461	149	25	=	=	PUNCT
ejpam-2461	149	26	a	a	DET
ejpam-2461	149	27	4πi	4πi	ADJ
ejpam-2461	149	28	∫	∫	PROPN
ejpam-2461	149	29	l	l	NOUN
ejpam-2461	149	30	ρm	ρm	PROPN
ejpam-2461	150	1	(	(	PUNCT
ejpam-2461	150	2	s)ζ(1−w+	s)ζ(1−w+	X
ejpam-2461	150	3	ps)γ(κs+	ps)γ(κs+	NOUN
ejpam-2461	150	4	ϑ−m	ϑ−m	PROPN
ejpam-2461	150	5	)	)	PUNCT
ejpam-2461	150	6	(	(	PUNCT
ejpam-2461	150	7	x	x	X
ejpam-2461	150	8	e∓πiψr	e∓πiψr	PROPN
ejpam-2461	150	9	)	)	PUNCT
ejpam-2461	150	10	−κsds	−κsds	PROPN
ejpam-2461	150	11	.	.	PUNCT
ejpam-2461	151	1	(	(	PUNCT
ejpam-2461	151	2	17	17	NUM
ejpam-2461	151	3	)	)	PUNCT
ejpam-2461	151	4	we	we	PRON
ejpam-2461	151	5	note	note	VERB
ejpam-2461	151	6	that	that	SCONJ
ejpam-2461	151	7	λ	λ	PROPN
ejpam-2461	151	8	j	j	X
ejpam-2461	151	9	>	>	X
ejpam-2461	151	10	0	0	PUNCT
ejpam-2461	152	1	for	for	ADP
ejpam-2461	152	2	j	j	PROPN
ejpam-2461	152	3	≥	≥	X
ejpam-2461	152	4	0	0	PUNCT
ejpam-2461	152	5	when	when	SCONJ
ejpam-2461	152	6	w	w	ADP
ejpam-2461	152	7	>	>	X
ejpam-2461	152	8	0	0	PUNCT
ejpam-2461	153	1	and	and	CCONJ
ejpam-2461	153	2	p	p	X
ejpam-2461	153	3	≥	≥	NUM
ejpam-2461	153	4	2	2	NUM
ejpam-2461	153	5	.	.	PUNCT
ejpam-2461	154	1	the	the	DET
ejpam-2461	154	2	above	above	ADJ
ejpam-2461	154	3	integrals	integral	NOUN
ejpam-2461	154	4	appearing	appear	VERB
ejpam-2461	154	5	in	in	ADP
ejpam-2461	154	6	j±r	j±r	PROPN
ejpam-2461	154	7	may	may	AUX
ejpam-2461	154	8	now	now	ADV
ejpam-2461	154	9	be	be	AUX
ejpam-2461	154	10	evaluated	evaluate	VERB
ejpam-2461	154	11	by	by	ADP
ejpam-2461	154	12	means	mean	NOUN
ejpam-2461	154	13	of	of	ADP
ejpam-2461	154	14	(	(	PUNCT
ejpam-2461	154	15	4	4	NUM
ejpam-2461	154	16	)	)	PUNCT
ejpam-2461	154	17	,	,	PUNCT
ejpam-2461	154	18	when	when	SCONJ
ejpam-2461	154	19	we	we	PRON
ejpam-2461	154	20	replace	replace	VERB
ejpam-2461	154	21	s	s	PRON
ejpam-2461	154	22	by	by	ADP
ejpam-2461	154	23	−s	−s	NOUN
ejpam-2461	154	24	and	and	CCONJ
ejpam-2461	154	25	allow	allow	VERB
ejpam-2461	154	26	the	the	DET
ejpam-2461	154	27	integration	integration	NOUN
ejpam-2461	154	28	r.	r.	PROPN
ejpam-2461	154	29	paris	paris	PROPN
ejpam-2461	154	30	/	/	SYM
ejpam-2461	154	31	eur	eur	PROPN
ejpam-2461	154	32	.	.	PUNCT
ejpam-2461	155	1	j.	j.	PROPN
ejpam-2461	155	2	pure	pure	PROPN
ejpam-2461	155	3	appl	appl	PROPN
ejpam-2461	155	4	.	.	PROPN
ejpam-2461	155	5	math	math	PROPN
ejpam-2461	155	6	,	,	PUNCT
ejpam-2461	155	7	9	9	NUM
ejpam-2461	155	8	(	(	PUNCT
ejpam-2461	155	9	2016	2016	NUM
ejpam-2461	155	10	)	)	PUNCT
ejpam-2461	155	11	,	,	PUNCT
ejpam-2461	155	12	3	3	NUM
ejpam-2461	155	13	-	-	SYM
ejpam-2461	155	14	18	18	NUM
ejpam-2461	155	15	10	10	NUM
ejpam-2461	155	16	path	path	NOUN
ejpam-2461	155	17	(	(	PUNCT
ejpam-2461	155	18	c−∞i	c−∞i	NOUN
ejpam-2461	155	19	,	,	PUNCT
ejpam-2461	155	20	c+∞i	c+∞i	ADJ
ejpam-2461	155	21	)	)	PUNCT
ejpam-2461	155	22	to	to	PART
ejpam-2461	155	23	coincide	coincide	VERB
ejpam-2461	155	24	with	with	ADP
ejpam-2461	155	25	the	the	DET
ejpam-2461	155	26	path	path	NOUN
ejpam-2461	155	27	l′	l′	NOUN
ejpam-2461	155	28	,	,	PUNCT
ejpam-2461	155	29	to	to	PART
ejpam-2461	155	30	yield	yield	VERB
ejpam-2461	155	31	the	the	DET
ejpam-2461	155	32	sum	sum	NOUN
ejpam-2461	155	33	sq(x	sq(x	NUM
ejpam-2461	155	34	e∓πiψr	e∓πiψr	PROPN
ejpam-2461	155	35	;	;	PUNCT
ejpam-2461	155	36	λ	λ	PROPN
ejpam-2461	155	37	j	j	PROPN
ejpam-2461	155	38	)	)	PUNCT
ejpam-2461	155	39	as	as	SCONJ
ejpam-2461	155	40	defined	define	VERB
ejpam-2461	155	41	in	in	ADP
ejpam-2461	155	42	(	(	PUNCT
ejpam-2461	155	43	1	1	NUM
ejpam-2461	155	44	)	)	PUNCT
ejpam-2461	155	45	.	.	PUNCT
ejpam-2461	156	1	this	this	DET
ejpam-2461	156	2	evaluation	evaluation	NOUN
ejpam-2461	156	3	is	be	AUX
ejpam-2461	156	4	valid	valid	ADJ
ejpam-2461	156	5	provided	provide	VERB
ejpam-2461	156	6	that	that	SCONJ
ejpam-2461	156	7	the	the	DET
ejpam-2461	156	8	variable	variable	NOUN
ejpam-2461	156	9	x	x	SYM
ejpam-2461	156	10	e∓πiψr	e∓πiψr	PROPN
ejpam-2461	156	11	satisfies	satisfy	VERB
ejpam-2461	156	12	the	the	DET
ejpam-2461	156	13	convergence	convergence	NOUN
ejpam-2461	156	14	condition	condition	NOUN
ejpam-2461	156	15	|arg(x	|arg(x	VERB
ejpam-2461	156	16	e∓πiψr	e∓πiψr	PROPN
ejpam-2461	156	17	)	)	PUNCT
ejpam-2461	156	18	|	|	CCONJ
ejpam-2461	156	19	<	<	X
ejpam-2461	156	20	1	1	NUM
ejpam-2461	156	21	2π	2π	NOUN
ejpam-2461	156	22	;	;	PUNCT
ejpam-2461	156	23	that	that	PRON
ejpam-2461	156	24	is	be	AUX
ejpam-2461	156	25	�	�	PROPN
ejpam-2461	156	26	�	�	PROPN
ejpam-2461	156	27	�	�	PROPN
ejpam-2461	156	28	arg	arg	VERB
ejpam-2461	156	29	a	a	DET
ejpam-2461	156	30	κ	κ	PROPN
ejpam-2461	156	31	∓πψr	∓πψr	PROPN
ejpam-2461	156	32	�	�	PROPN
ejpam-2461	156	33	�	�	PROPN
ejpam-2461	156	34	�	�	PROPN
ejpam-2461	156	35	<	<	X
ejpam-2461	156	36	1	1	NUM
ejpam-2461	156	37	2	2	NUM
ejpam-2461	156	38	π	π	NOUN
ejpam-2461	156	39	(	(	PUNCT
ejpam-2461	156	40	0≤	0≤	NUM
ejpam-2461	156	41	r	r	NOUN
ejpam-2461	156	42	≤	≤	NOUN
ejpam-2461	156	43	n	n	CCONJ
ejpam-2461	156	44	−	−	PROPN
ejpam-2461	156	45	1	1	NUM
ejpam-2461	156	46	)	)	PUNCT
ejpam-2461	156	47	.	.	PUNCT
ejpam-2461	157	1	it	it	PRON
ejpam-2461	157	2	is	be	AUX
ejpam-2461	157	3	routine	routine	ADJ
ejpam-2461	157	4	to	to	PART
ejpam-2461	157	5	verify	verify	VERB
ejpam-2461	157	6	that	that	SCONJ
ejpam-2461	157	7	these	these	DET
ejpam-2461	157	8	conditions	condition	NOUN
ejpam-2461	157	9	are	be	AUX
ejpam-2461	157	10	met	meet	VERB
ejpam-2461	157	11	when	when	SCONJ
ejpam-2461	157	12	|arg	|arg	NOUN
ejpam-2461	157	13	a|	a|	PROPN
ejpam-2461	157	14	<	<	X
ejpam-2461	157	15	1	1	NUM
ejpam-2461	157	16	2π	2π	NOUN
ejpam-2461	157	17	.	.	PUNCT
ejpam-2461	158	1	thus	thus	ADV
ejpam-2461	158	2	we	we	PRON
ejpam-2461	158	3	find	find	VERB
ejpam-2461	158	4	j±r	j±r	NOUN
ejpam-2461	158	5	=	=	PUNCT
ejpam-2461	158	6	a	a	DET
ejpam-2461	158	7	2πκ	2πκ	ADJ
ejpam-2461	158	8	m−1	m−1	PROPN
ejpam-2461	158	9	∑	∑	PUNCT
ejpam-2461	158	10	j=0	j=0	PROPN
ejpam-2461	158	11	(	(	PUNCT
ejpam-2461	158	12	−	−	PROPN
ejpam-2461	158	13	)	)	PUNCT
ejpam-2461	158	14	jc	jc	PROPN
ejpam-2461	158	15	j(x	j(x	PROPN
ejpam-2461	158	16	e∓πiψr	e∓πiψr	PROPN
ejpam-2461	158	17	)	)	PUNCT
ejpam-2461	158	18	ϑ−	ϑ−	PROPN
ejpam-2461	158	19	j	j	PROPN
ejpam-2461	158	20	sq(x	sq(x	X
ejpam-2461	158	21	e∓πiψr	e∓πiψr	PROPN
ejpam-2461	158	22	;	;	PUNCT
ejpam-2461	158	23	λ	λ	PROPN
ejpam-2461	158	24	j	j	PROPN
ejpam-2461	158	25	)	)	PUNCT
ejpam-2461	159	1	+	+	PROPN
ejpam-2461	159	2	r±m	r±m	PROPN
ejpam-2461	159	3	,	,	PUNCT
ejpam-2461	159	4	r	r	NOUN
ejpam-2461	159	5	.	.	PUNCT
ejpam-2461	160	1	(	(	PUNCT
ejpam-2461	160	2	18	18	NUM
ejpam-2461	160	3	)	)	PUNCT
ejpam-2461	160	4	bounds	bound	NOUN
ejpam-2461	160	5	for	for	ADP
ejpam-2461	160	6	the	the	DET
ejpam-2461	160	7	remainders	remainder	NOUN
ejpam-2461	160	8	of	of	ADP
ejpam-2461	160	9	the	the	DET
ejpam-2461	160	10	type	type	NOUN
ejpam-2461	160	11	r±m	r±m	PROPN
ejpam-2461	160	12	,	,	PUNCT
ejpam-2461	160	13	r	r	NOUN
ejpam-2461	160	14	have	have	AUX
ejpam-2461	160	15	been	be	AUX
ejpam-2461	160	16	considered	consider	VERB
ejpam-2461	160	17	in	in	ADP
ejpam-2461	160	18	[	[	X
ejpam-2461	160	19	5	5	NUM
ejpam-2461	160	20	,	,	PUNCT
ejpam-2461	160	21	p.	p.	NOUN
ejpam-2461	160	22	71	71	NUM
ejpam-2461	160	23	,	,	PUNCT
ejpam-2461	160	24	lemma	lemma	PROPN
ejpam-2461	160	25	2.7	2.7	NUM
ejpam-2461	160	26	]	]	PUNCT
ejpam-2461	160	27	;	;	PUNCT
ejpam-2461	160	28	see	see	VERB
ejpam-2461	160	29	also	also	ADV
ejpam-2461	160	30	[	[	X
ejpam-2461	160	31	2	2	NUM
ejpam-2461	160	32	,	,	PUNCT
ejpam-2461	160	33	§	§	NOUN
ejpam-2461	160	34	10.1	10.1	NUM
ejpam-2461	160	35	]	]	PUNCT
ejpam-2461	160	36	.	.	PUNCT
ejpam-2461	161	1	the	the	DET
ejpam-2461	161	2	integration	integration	NOUN
ejpam-2461	161	3	path	path	NOUN
ejpam-2461	161	4	in	in	ADP
ejpam-2461	161	5	(	(	PUNCT
ejpam-2461	161	6	17	17	NUM
ejpam-2461	161	7	)	)	PUNCT
ejpam-2461	161	8	is	be	AUX
ejpam-2461	161	9	such	such	ADJ
ejpam-2461	161	10	that	that	SCONJ
ejpam-2461	161	11	ℜ(1−	ℜ(1−	ADJ
ejpam-2461	161	12	w+	w+	VERB
ejpam-2461	161	13	ps	ps	NOUN
ejpam-2461	161	14	)	)	PUNCT
ejpam-2461	161	15	>	>	X
ejpam-2461	161	16	1	1	NUM
ejpam-2461	161	17	,	,	PUNCT
ejpam-2461	161	18	so	so	SCONJ
ejpam-2461	161	19	that	that	SCONJ
ejpam-2461	161	20	we	we	PRON
ejpam-2461	161	21	may	may	AUX
ejpam-2461	161	22	employ	employ	VERB
ejpam-2461	161	23	the	the	DET
ejpam-2461	161	24	bound	bound	ADJ
ejpam-2461	161	25	|ζ(x	|ζ(x	PROPN
ejpam-2461	162	1	+	+	CCONJ
ejpam-2461	162	2	i	i	PRON
ejpam-2461	162	3	y)|	y)|	VERB
ejpam-2461	162	4	≤	≤	X
ejpam-2461	162	5	ζ(x	ζ(x	NOUN
ejpam-2461	162	6	)	)	PUNCT
ejpam-2461	162	7	for	for	ADP
ejpam-2461	162	8	x	x	SYM
ejpam-2461	162	9	>	>	X
ejpam-2461	162	10	1	1	NUM
ejpam-2461	162	11	.	.	PUNCT
ejpam-2461	162	12	a	a	DET
ejpam-2461	162	13	slight	slight	ADJ
ejpam-2461	162	14	modification	modification	NOUN
ejpam-2461	162	15	of	of	ADP
ejpam-2461	162	16	lemma	lemma	PROPN
ejpam-2461	162	17	2.7	2.7	NUM
ejpam-2461	162	18	in	in	ADP
ejpam-2461	162	19	[	[	X
ejpam-2461	162	20	5	5	NUM
ejpam-2461	162	21	,	,	PUNCT
ejpam-2461	162	22	p.	p.	NOUN
ejpam-2461	162	23	71	71	NUM
ejpam-2461	162	24	]	]	PUNCT
ejpam-2461	162	25	then	then	ADV
ejpam-2461	162	26	shows	show	VERB
ejpam-2461	162	27	that	that	SCONJ
ejpam-2461	162	28	r±m	r±m	PROPN
ejpam-2461	162	29	,	,	PUNCT
ejpam-2461	162	30	r	r	NOUN
ejpam-2461	162	31	=	=	SYM
ejpam-2461	162	32	o	o	X
ejpam-2461	162	33	�	�	PROPN
ejpam-2461	162	34	x	x	PUNCT
ejpam-2461	162	35	ϑ−m	ϑ−m	VERB
ejpam-2461	162	36	e−x	e−x	PROPN
ejpam-2461	162	37	e∓πiψr	e∓πiψr	PROPN
ejpam-2461	162	38	�	�	PROPN
ejpam-2461	162	39	(	(	PUNCT
ejpam-2461	162	40	19	19	NUM
ejpam-2461	162	41	)	)	PUNCT
ejpam-2461	162	42	as	as	ADP
ejpam-2461	162	43	a→	a→	X
ejpam-2461	162	44	0	0	NUM
ejpam-2461	162	45	in	in	ADP
ejpam-2461	162	46	the	the	DET
ejpam-2461	162	47	sector	sector	NOUN
ejpam-2461	162	48	|arg	|arg	PROPN
ejpam-2461	162	49	a|	a|	PROPN
ejpam-2461	162	50	<	<	X
ejpam-2461	162	51	1	1	NUM
ejpam-2461	162	52	2π	2π	NOUN
ejpam-2461	162	53	.	.	PUNCT
ejpam-2461	163	1	an	an	DET
ejpam-2461	163	2	analogous	analogous	ADJ
ejpam-2461	163	3	procedure	procedure	NOUN
ejpam-2461	163	4	applied	apply	VERB
ejpam-2461	163	5	to	to	ADP
ejpam-2461	163	6	j	j	PROPN
ejpam-2461	163	7	in	in	ADP
ejpam-2461	163	8	(	(	PUNCT
ejpam-2461	163	9	13	13	NUM
ejpam-2461	163	10	)	)	PUNCT
ejpam-2461	163	11	shows	show	VERB
ejpam-2461	163	12	that	that	SCONJ
ejpam-2461	163	13	j	j	PROPN
ejpam-2461	163	14	=	=	PUNCT
ejpam-2461	163	15	a	a	DET
ejpam-2461	163	16	2πκ	2πκ	ADJ
ejpam-2461	163	17	m−1	m−1	PROPN
ejpam-2461	163	18	∑	∑	PUNCT
ejpam-2461	163	19	j=0	j=0	PROPN
ejpam-2461	163	20	(	(	PUNCT
ejpam-2461	163	21	−	−	PROPN
ejpam-2461	163	22	)	)	PUNCT
ejpam-2461	163	23	jc	jc	PROPN
ejpam-2461	163	24	jx	jx	PROPN
ejpam-2461	163	25	ϑ−	ϑ−	PROPN
ejpam-2461	163	26	jsq(x	jsq(x	PROPN
ejpam-2461	163	27	;	;	PUNCT
ejpam-2461	163	28	λ	λ	PROPN
ejpam-2461	163	29	j	j	PROPN
ejpam-2461	163	30	)	)	PUNCT
ejpam-2461	164	1	+	+	ADJ
ejpam-2461	164	2	o(x	o(x	ADJ
ejpam-2461	164	3	ϑ−m	ϑ−m	VERB
ejpam-2461	164	4	e−x	e−x	NOUN
ejpam-2461	164	5	)	)	PUNCT
ejpam-2461	164	6	(	(	PUNCT
ejpam-2461	164	7	20	20	NUM
ejpam-2461	164	8	)	)	PUNCT
ejpam-2461	164	9	as	as	ADP
ejpam-2461	164	10	a→	a→	X
ejpam-2461	164	11	0	0	NUM
ejpam-2461	164	12	in	in	ADP
ejpam-2461	164	13	|arg	|arg	NOUN
ejpam-2461	164	14	a|	a|	PROPN
ejpam-2461	164	15	<	<	X
ejpam-2461	164	16	1	1	NUM
ejpam-2461	164	17	2π	2π	NOUN
ejpam-2461	164	18	.	.	PUNCT
ejpam-2461	165	1	3.2	3.2	NUM
ejpam-2461	165	2	.	.	PUNCT
ejpam-2461	166	1	the	the	DET
ejpam-2461	166	2	expansion	expansion	NOUN
ejpam-2461	166	3	of	of	ADP
ejpam-2461	166	4	sp(a	sp(a	PROPN
ejpam-2461	166	5	;	;	PUNCT
ejpam-2461	166	6	w	w	X
ejpam-2461	166	7	)	)	PUNCT
ejpam-2461	166	8	the	the	DET
ejpam-2461	166	9	expansion	expansion	NOUN
ejpam-2461	166	10	of	of	ADP
ejpam-2461	166	11	il	il	PROPN
ejpam-2461	166	12	as	as	ADP
ejpam-2461	166	13	a→	a→	X
ejpam-2461	166	14	0	0	NUM
ejpam-2461	166	15	in	in	ADP
ejpam-2461	166	16	|arg	|arg	NOUN
ejpam-2461	166	17	a|	a|	PROPN
ejpam-2461	166	18	<	<	X
ejpam-2461	166	19	1	1	NUM
ejpam-2461	166	20	2π	2π	NOUN
ejpam-2461	166	21	then	then	ADV
ejpam-2461	166	22	follows	follow	VERB
ejpam-2461	166	23	from	from	ADP
ejpam-2461	166	24	(	(	PUNCT
ejpam-2461	166	25	9	9	NUM
ejpam-2461	166	26	)	)	PUNCT
ejpam-2461	166	27	,	,	PUNCT
ejpam-2461	166	28	(	(	PUNCT
ejpam-2461	166	29	11	11	NUM
ejpam-2461	166	30	)	)	PUNCT
ejpam-2461	166	31	,	,	PUNCT
ejpam-2461	166	32	(	(	PUNCT
ejpam-2461	166	33	18	18	NUM
ejpam-2461	166	34	)	)	PUNCT
ejpam-2461	166	35	and	and	CCONJ
ejpam-2461	166	36	(	(	PUNCT
ejpam-2461	166	37	20	20	NUM
ejpam-2461	166	38	)	)	PUNCT
ejpam-2461	166	39	.	.	PUNCT
ejpam-2461	167	1	we	we	PRON
ejpam-2461	167	2	obtain	obtain	VERB
ejpam-2461	167	3	the	the	DET
ejpam-2461	167	4	following	follow	VERB
ejpam-2461	167	5	theorem	theorem	VERB
ejpam-2461	167	6	.	.	PUNCT
ejpam-2461	167	7	theorem	theorem	NOUN
ejpam-2461	167	8	1	1	NUM
ejpam-2461	167	9	.	.	PUNCT
ejpam-2461	168	1	let	let	VERB
ejpam-2461	168	2	m	m	PRON
ejpam-2461	168	3	and	and	CCONJ
ejpam-2461	168	4	m	m	AUX
ejpam-2461	168	5	be	be	AUX
ejpam-2461	168	6	positive	positive	ADJ
ejpam-2461	168	7	integers	integer	NOUN
ejpam-2461	168	8	.	.	PUNCT
ejpam-2461	169	1	then	then	ADV
ejpam-2461	169	2	,	,	PUNCT
ejpam-2461	169	3	when	when	SCONJ
ejpam-2461	169	4	w=	w=	PRON
ejpam-2461	169	5	2	2	NUM
ejpam-2461	169	6	m	m	VERB
ejpam-2461	169	7	and	and	CCONJ
ejpam-2461	169	8	p	p	NOUN
ejpam-2461	169	9	is	be	AUX
ejpam-2461	169	10	also	also	ADV
ejpam-2461	169	11	an	an	DET
ejpam-2461	169	12	even	even	ADV
ejpam-2461	169	13	positive	positive	ADJ
ejpam-2461	169	14	integer	integer	NOUN
ejpam-2461	169	15	,	,	PUNCT
ejpam-2461	169	16	with	with	ADP
ejpam-2461	169	17	k	k	PROPN
ejpam-2461	169	18	=	=	PUNCT
ejpam-2461	169	19	⌊w	⌊w	PROPN
ejpam-2461	169	20	/	/	SYM
ejpam-2461	169	21	p⌋	p⌋	PROPN
ejpam-2461	169	22	and	and	CCONJ
ejpam-2461	169	23	n	n	NOUN
ejpam-2461	169	24	=	=	PUNCT
ejpam-2461	170	1	[	[	X
ejpam-2461	170	2	1	1	NUM
ejpam-2461	170	3	4	4	NUM
ejpam-2461	170	4	p	p	NOUN
ejpam-2461	170	5	]	]	PUNCT
ejpam-2461	170	6	(	(	PUNCT
ejpam-2461	170	7	with	with	ADP
ejpam-2461	170	8	square	square	ADJ
ejpam-2461	170	9	brackets	bracket	NOUN
ejpam-2461	170	10	denoting	denote	VERB
ejpam-2461	170	11	the	the	DET
ejpam-2461	170	12	nearest	near	ADJ
ejpam-2461	170	13	integer	integer	ADJ
ejpam-2461	170	14	part	part	NOUN
ejpam-2461	170	15	)	)	PUNCT
ejpam-2461	170	16	,	,	PUNCT
ejpam-2461	170	17	we	we	PRON
ejpam-2461	170	18	have	have	VERB
ejpam-2461	170	19	the	the	DET
ejpam-2461	170	20	expansion	expansion	NOUN
ejpam-2461	170	21	valid	valid	ADJ
ejpam-2461	170	22	as	as	ADP
ejpam-2461	170	23	a→	a→	X
ejpam-2461	170	24	0	0	NUM
ejpam-2461	170	25	in	in	ADP
ejpam-2461	170	26	|arg	|arg	NOUN
ejpam-2461	170	27	a|	a|	PROPN
ejpam-2461	170	28	<	<	X
ejpam-2461	170	29	1	1	NUM
ejpam-2461	170	30	2π	2π	NOUN
ejpam-2461	170	31	sp(a	sp(a	NOUN
ejpam-2461	170	32	;	;	PUNCT
ejpam-2461	170	33	w	w	X
ejpam-2461	170	34	)	)	PUNCT
ejpam-2461	170	35	=	=	SYM
ejpam-2461	170	36	1	1	NUM
ejpam-2461	170	37	p	p	NOUN
ejpam-2461	170	38	γ	γ	X
ejpam-2461	170	39	�	�	PROPN
ejpam-2461	170	40	1−w	1−w	NUM
ejpam-2461	170	41	p	p	X
ejpam-2461	170	42	�	�	PROPN
ejpam-2461	170	43	a(w−1)/p	a(w−1)/p	PROPN
ejpam-2461	171	1	+	+	CCONJ
ejpam-2461	171	2	k	k	PROPN
ejpam-2461	171	3	∑	∑	PUNCT
ejpam-2461	171	4	k=0	k=0	PROPN
ejpam-2461	171	5	(	(	PUNCT
ejpam-2461	171	6	−)k	−)k	PROPN
ejpam-2461	171	7	k	k	PROPN
ejpam-2461	171	8	!	!	PROPN
ejpam-2461	171	9	ζ(w−	ζ(w−	PROPN
ejpam-2461	171	10	pk	pk	PROPN
ejpam-2461	171	11	)	)	PUNCT
ejpam-2461	171	12	ak	ak	PROPN
ejpam-2461	171	13	+	+	CCONJ
ejpam-2461	171	14	(	(	PUNCT
ejpam-2461	171	15	−)m(2π)w	−)m(2π)w	NUM
ejpam-2461	171	16	il	il	PROPN
ejpam-2461	171	17	,	,	PUNCT
ejpam-2461	171	18	(	(	PUNCT
ejpam-2461	171	19	21	21	NUM
ejpam-2461	171	20	)	)	PUNCT
ejpam-2461	171	21	with	with	ADP
ejpam-2461	171	22	il	il	PROPN
ejpam-2461	171	23	=	=	SYM
ejpam-2461	171	24	n−1	n−1	PROPN
ejpam-2461	171	25	∑	∑	PUNCT
ejpam-2461	171	26	r=0	r=0	PROPN
ejpam-2461	171	27	er(a	er(a	PROPN
ejpam-2461	171	28	;	;	PUNCT
ejpam-2461	171	29	w	w	X
ejpam-2461	171	30	,	,	PUNCT
ejpam-2461	171	31	p	p	NOUN
ejpam-2461	171	32	)	)	PUNCT
ejpam-2461	172	1	+	+	ADP
ejpam-2461	172	2	δpp∗	δpp∗	NOUN
ejpam-2461	172	3	ên	ên	PROPN
ejpam-2461	172	4	(	(	PUNCT
ejpam-2461	172	5	a	a	PRON
ejpam-2461	172	6	;	;	PUNCT
ejpam-2461	172	7	w	w	PROPN
ejpam-2461	172	8	,	,	PUNCT
ejpam-2461	172	9	p	p	NOUN
ejpam-2461	172	10	)	)	PUNCT
ejpam-2461	172	11	,	,	PUNCT
ejpam-2461	172	12	(	(	PUNCT
ejpam-2461	172	13	22	22	X
ejpam-2461	172	14	)	)	PUNCT
ejpam-2461	172	15	r.	r.	PROPN
ejpam-2461	172	16	paris	paris	PROPN
ejpam-2461	172	17	/	/	SYM
ejpam-2461	172	18	eur	eur	PROPN
ejpam-2461	172	19	.	.	PUNCT
ejpam-2461	173	1	j.	j.	PROPN
ejpam-2461	173	2	pure	pure	PROPN
ejpam-2461	173	3	appl	appl	PROPN
ejpam-2461	173	4	.	.	PROPN
ejpam-2461	173	5	math	math	PROPN
ejpam-2461	173	6	,	,	PUNCT
ejpam-2461	173	7	9	9	NUM
ejpam-2461	173	8	(	(	PUNCT
ejpam-2461	173	9	2016	2016	NUM
ejpam-2461	173	10	)	)	PUNCT
ejpam-2461	173	11	,	,	PUNCT
ejpam-2461	173	12	3	3	NUM
ejpam-2461	173	13	-	-	SYM
ejpam-2461	173	14	18	18	NUM
ejpam-2461	173	15	11	11	NUM
ejpam-2461	173	16	where	where	SCONJ
ejpam-2461	173	17	δpp∗	δpp∗	NOUN
ejpam-2461	173	18	is	be	AUX
ejpam-2461	173	19	the	the	DET
ejpam-2461	173	20	kronecker	kronecker	NOUN
ejpam-2461	173	21	symbol	symbol	NOUN
ejpam-2461	173	22	with	with	ADP
ejpam-2461	173	23	p∗	p∗	NOUN
ejpam-2461	173	24	=	=	PUNCT
ejpam-2461	173	25	4n	4n	NOUN
ejpam-2461	173	26	+	+	NOUN
ejpam-2461	173	27	2	2	X
ejpam-2461	173	28	.	.	X
ejpam-2461	174	1	the	the	DET
ejpam-2461	174	2	sums	sum	NOUN
ejpam-2461	174	3	er(a	er(a	NUM
ejpam-2461	174	4	;	;	PUNCT
ejpam-2461	174	5	w	w	X
ejpam-2461	174	6	,	,	PUNCT
ejpam-2461	174	7	p	p	NOUN
ejpam-2461	174	8	)	)	PUNCT
ejpam-2461	174	9	are	be	AUX
ejpam-2461	174	10	given	give	VERB
ejpam-2461	174	11	by†	by†	PROPN
ejpam-2461	174	12	er(a	er(a	NUM
ejpam-2461	174	13	;	;	PUNCT
ejpam-2461	174	14	w	w	X
ejpam-2461	174	15	,	,	PUNCT
ejpam-2461	174	16	p	p	NOUN
ejpam-2461	174	17	)	)	PUNCT
ejpam-2461	174	18	=	=	PUNCT
ejpam-2461	174	19	a	a	DET
ejpam-2461	174	20	2πκ	2πκ	NOUN
ejpam-2461	174	21	∑	∑	ADP
ejpam-2461	174	22	±	±	NOUN
ejpam-2461	174	23	m−1	m−1	PROPN
ejpam-2461	174	24	∑	∑	PUNCT
ejpam-2461	174	25	j=0	j=0	PROPN
ejpam-2461	174	26	(	(	PUNCT
ejpam-2461	174	27	−	−	PROPN
ejpam-2461	174	28	)	)	PUNCT
ejpam-2461	174	29	jc	jc	PROPN
ejpam-2461	174	30	j(x	j(x	PROPN
ejpam-2461	174	31	e∓πiψr	e∓πiψr	PROPN
ejpam-2461	174	32	)	)	PUNCT
ejpam-2461	174	33	ϑ−	ϑ−	PROPN
ejpam-2461	174	34	j	j	PROPN
ejpam-2461	174	35	sq(x	sq(x	X
ejpam-2461	174	36	e∓πiψr	e∓πiψr	PROPN
ejpam-2461	174	37	;	;	PUNCT
ejpam-2461	174	38	λ	λ	PROPN
ejpam-2461	174	39	j	j	PROPN
ejpam-2461	174	40	)	)	PUNCT
ejpam-2461	175	1	+	+	CCONJ
ejpam-2461	175	2	rm	rm	NOUN
ejpam-2461	175	3	,	,	PUNCT
ejpam-2461	175	4	r	r	NOUN
ejpam-2461	175	5	(	(	PUNCT
ejpam-2461	175	6	23	23	NUM
ejpam-2461	175	7	)	)	PUNCT
ejpam-2461	175	8	for	for	ADP
ejpam-2461	175	9	0	0	NUM
ejpam-2461	175	10	≤	≤	NUM
ejpam-2461	175	11	r	r	NOUN
ejpam-2461	175	12	≤	≤	NOUN
ejpam-2461	175	13	n	n	CCONJ
ejpam-2461	175	14	−	−	PROPN
ejpam-2461	175	15	1	1	NUM
ejpam-2461	175	16	,	,	PUNCT
ejpam-2461	175	17	where	where	SCONJ
ejpam-2461	175	18	x	x	ADP
ejpam-2461	175	19	=	=	SYM
ejpam-2461	175	20	κ(h(2π)p	κ(h(2π)p	PROPN
ejpam-2461	175	21	/	/	SYM
ejpam-2461	175	22	a)1	a)1	PROPN
ejpam-2461	175	23	/	/	SYM
ejpam-2461	175	24	κ	κ	PROPN
ejpam-2461	175	25	,	,	PUNCT
ejpam-2461	175	26	ψr	ψr	ADP
ejpam-2461	175	27	=	=	SYM
ejpam-2461	175	28	(	(	PUNCT
ejpam-2461	175	29	1	1	NUM
ejpam-2461	175	30	2	2	NUM
ejpam-2461	175	31	p−2r−1)/κ	p−2r−1)/κ	NOUN
ejpam-2461	175	32	(	(	PUNCT
ejpam-2461	175	33	0	0	NUM
ejpam-2461	175	34	≤	≤	NUM
ejpam-2461	175	35	r	r	NOUN
ejpam-2461	175	36	≤	≤	NOUN
ejpam-2461	175	37	n	n	CCONJ
ejpam-2461	175	38	−	−	PROPN
ejpam-2461	175	39	1	1	NUM
ejpam-2461	175	40	)	)	PUNCT
ejpam-2461	175	41	,	,	PUNCT
ejpam-2461	175	42	λ	λ	X
ejpam-2461	175	43	j	j	NOUN
ejpam-2461	175	44	=	=	SYM
ejpam-2461	175	45	1	1	NUM
ejpam-2461	175	46	+	+	CCONJ
ejpam-2461	175	47	(	(	PUNCT
ejpam-2461	175	48	w+	w+	X
ejpam-2461	175	49	p	p	X
ejpam-2461	175	50	(	(	PUNCT
ejpam-2461	175	51	j	j	PROPN
ejpam-2461	175	52	−	−	PROPN
ejpam-2461	175	53	1	1	NUM
ejpam-2461	175	54	2))/κ	2))/κ	NUM
ejpam-2461	175	55	,	,	PUNCT
ejpam-2461	175	56	q	q	NOUN
ejpam-2461	176	1	=	=	SYM
ejpam-2461	176	2	p	p	NOUN
ejpam-2461	176	3	/	/	SYM
ejpam-2461	176	4	κ	κ	NOUN
ejpam-2461	176	5	and	and	CCONJ
ejpam-2461	176	6	the	the	DET
ejpam-2461	176	7	parameters	parameter	NOUN
ejpam-2461	176	8	κ	κ	VERB
ejpam-2461	176	9	,	,	PUNCT
ejpam-2461	176	10	h	h	NOUN
ejpam-2461	176	11	,	,	PUNCT
ejpam-2461	176	12	ϑ	ϑ	X
ejpam-2461	176	13	and	and	CCONJ
ejpam-2461	176	14	a	a	PRON
ejpam-2461	176	15	are	be	AUX
ejpam-2461	176	16	defined	define	VERB
ejpam-2461	176	17	in	in	ADP
ejpam-2461	176	18	(	(	PUNCT
ejpam-2461	176	19	15	15	NUM
ejpam-2461	176	20	)	)	PUNCT
ejpam-2461	176	21	.	.	PUNCT
ejpam-2461	177	1	the	the	DET
ejpam-2461	177	2	leading	lead	VERB
ejpam-2461	177	3	coefficient	coefficient	NOUN
ejpam-2461	177	4	c0	c0	NOUN
ejpam-2461	177	5	=	=	PROPN
ejpam-2461	177	6	1	1	NUM
ejpam-2461	177	7	and	and	CCONJ
ejpam-2461	177	8	c	c	PROPN
ejpam-2461	177	9	j	j	PROPN
ejpam-2461	177	10	≡	≡	PROPN
ejpam-2461	177	11	c	c	PROPN
ejpam-2461	177	12	j(w	j(w	PROPN
ejpam-2461	177	13	,	,	PUNCT
ejpam-2461	177	14	p	p	NOUN
ejpam-2461	177	15	)	)	PUNCT
ejpam-2461	177	16	(	(	PUNCT
ejpam-2461	177	17	j	j	PROPN
ejpam-2461	177	18	≥	≥	NUM
ejpam-2461	177	19	1	1	NUM
ejpam-2461	177	20	)	)	PUNCT
ejpam-2461	177	21	are	be	AUX
ejpam-2461	177	22	discussed	discuss	VERB
ejpam-2461	177	23	in	in	ADP
ejpam-2461	177	24	section	section	NOUN
ejpam-2461	177	25	4	4	NUM
ejpam-2461	177	26	.	.	PUNCT
ejpam-2461	178	1	the	the	DET
ejpam-2461	178	2	sum	sum	NOUN
ejpam-2461	178	3	ên	ên	PROPN
ejpam-2461	178	4	(	(	PUNCT
ejpam-2461	178	5	a	a	PROPN
ejpam-2461	178	6	;	;	PUNCT
ejpam-2461	178	7	w	w	PROPN
ejpam-2461	178	8	,	,	PUNCT
ejpam-2461	178	9	p	p	NOUN
ejpam-2461	178	10	)	)	PUNCT
ejpam-2461	178	11	is	be	AUX
ejpam-2461	178	12	also	also	ADV
ejpam-2461	178	13	given	give	VERB
ejpam-2461	178	14	by	by	ADP
ejpam-2461	178	15	(	(	PUNCT
ejpam-2461	178	16	21	21	NUM
ejpam-2461	178	17	)	)	PUNCT
ejpam-2461	178	18	when	when	SCONJ
ejpam-2461	178	19	we	we	PRON
ejpam-2461	178	20	put	put	VERB
ejpam-2461	178	21	ψn	ψn	VERB
ejpam-2461	178	22	≡	≡	PROPN
ejpam-2461	178	23	0	0	PUNCT
ejpam-2461	178	24	and	and	CCONJ
ejpam-2461	178	25	omit	omit	VERB
ejpam-2461	178	26	the	the	DET
ejpam-2461	178	27	summation	summation	NOUN
ejpam-2461	178	28	∑	∑	PUNCT
ejpam-2461	178	29	±.	±.	VERB
ejpam-2461	178	30	the	the	DET
ejpam-2461	178	31	remainders	remainder	NOUN
ejpam-2461	178	32	rm	rm	PROPN
ejpam-2461	178	33	,	,	PUNCT
ejpam-2461	178	34	r	r	NOUN
ejpam-2461	178	35	satisfy	satisfy	NOUN
ejpam-2461	178	36	the	the	DET
ejpam-2461	178	37	bound	bound	ADJ
ejpam-2461	178	38	rm	rm	NOUN
ejpam-2461	178	39	,	,	PUNCT
ejpam-2461	178	40	r	r	NOUN
ejpam-2461	178	41	=	=	NOUN
ejpam-2461	178	42	o(max{x	o(max{x	ADV
ejpam-2461	178	43	ϑ−m	ϑ−m	VERB
ejpam-2461	178	44	e−x	e−x	ADJ
ejpam-2461	178	45	e±πiψr	e±πiψr	PROPN
ejpam-2461	178	46	}	}	PUNCT
ejpam-2461	178	47	)	)	PUNCT
ejpam-2461	179	1	(	(	PUNCT
ejpam-2461	179	2	0≤	0≤	NUM
ejpam-2461	179	3	r	r	NOUN
ejpam-2461	179	4	≤	≤	NUM
ejpam-2461	179	5	n	n	CCONJ
ejpam-2461	179	6	)	)	PUNCT
ejpam-2461	179	7	.	.	PUNCT
ejpam-2461	180	1	it	it	PRON
ejpam-2461	180	2	is	be	AUX
ejpam-2461	180	3	seen	see	VERB
ejpam-2461	180	4	from	from	ADP
ejpam-2461	180	5	(	(	PUNCT
ejpam-2461	180	6	21	21	NUM
ejpam-2461	180	7	)	)	PUNCT
ejpam-2461	180	8	,	,	PUNCT
ejpam-2461	180	9	(	(	PUNCT
ejpam-2461	180	10	22	22	NUM
ejpam-2461	180	11	)	)	PUNCT
ejpam-2461	180	12	and	and	CCONJ
ejpam-2461	180	13	(	(	PUNCT
ejpam-2461	180	14	23	23	NUM
ejpam-2461	180	15	)	)	PUNCT
ejpam-2461	180	16	that	that	SCONJ
ejpam-2461	180	17	the	the	DET
ejpam-2461	180	18	sum	sum	NOUN
ejpam-2461	180	19	sp(a	sp(a	ADP
ejpam-2461	180	20	;	;	PUNCT
ejpam-2461	180	21	w	w	X
ejpam-2461	180	22	)	)	PUNCT
ejpam-2461	180	23	has	have	AUX
ejpam-2461	180	24	been	be	AUX
ejpam-2461	180	25	expressed	express	VERB
ejpam-2461	180	26	in	in	ADP
ejpam-2461	180	27	terms	term	NOUN
ejpam-2461	180	28	of	of	ADP
ejpam-2461	180	29	the	the	DET
ejpam-2461	180	30	sums	sum	NOUN
ejpam-2461	180	31	sq(x	sq(x	NUM
ejpam-2461	180	32	e∓πiψr	e∓πiψr	PROPN
ejpam-2461	180	33	;	;	PUNCT
ejpam-2461	180	34	λ	λ	PROPN
ejpam-2461	180	35	j	j	PROPN
ejpam-2461	180	36	)	)	PUNCT
ejpam-2461	180	37	,	,	PUNCT
ejpam-2461	180	38	which	which	PRON
ejpam-2461	180	39	involve	involve	VERB
ejpam-2461	180	40	the	the	DET
ejpam-2461	180	41	reciprocal	reciprocal	ADJ
ejpam-2461	180	42	power	power	NOUN
ejpam-2461	180	43	of	of	ADP
ejpam-2461	180	44	the	the	DET
ejpam-2461	180	45	asymptotic	asymptotic	ADJ
ejpam-2461	180	46	variable	variable	NOUN
ejpam-2461	180	47	a	a	DET
ejpam-2461	180	48	scaling	scaling	NOUN
ejpam-2461	180	49	like	like	ADP
ejpam-2461	180	50	a−1	a−1	PROPN
ejpam-2461	180	51	/	/	SYM
ejpam-2461	180	52	κ	κ	NOUN
ejpam-2461	180	53	.	.	PUNCT
ejpam-2461	181	1	thus	thus	ADV
ejpam-2461	181	2	,	,	PUNCT
ejpam-2461	181	3	as	as	ADP
ejpam-2461	181	4	a	a	DET
ejpam-2461	181	5	→	→	SYM
ejpam-2461	181	6	0	0	NUM
ejpam-2461	181	7	the	the	DET
ejpam-2461	181	8	argument	argument	NOUN
ejpam-2461	181	9	x	x	INTJ
ejpam-2461	181	10	→	→	SYM
ejpam-2461	181	11	∞.	∞.	PROPN
ejpam-2461	181	12	it	it	PRON
ejpam-2461	181	13	is	be	AUX
ejpam-2461	181	14	obvious	obvious	ADJ
ejpam-2461	181	15	from	from	ADP
ejpam-2461	181	16	the	the	DET
ejpam-2461	181	17	definition	definition	NOUN
ejpam-2461	181	18	in	in	ADP
ejpam-2461	181	19	(	(	PUNCT
ejpam-2461	181	20	1	1	NUM
ejpam-2461	181	21	)	)	PUNCT
ejpam-2461	181	22	(	(	PUNCT
ejpam-2461	181	23	when	when	SCONJ
ejpam-2461	181	24	q	q	X
ejpam-2461	181	25	>	>	X
ejpam-2461	181	26	0	0	NUM
ejpam-2461	181	27	)	)	PUNCT
ejpam-2461	181	28	that	that	PRON
ejpam-2461	181	29	sq(z;λ	sq(z;λ	PROPN
ejpam-2461	181	30	j)∼	j)∼	VERB
ejpam-2461	181	31	e−z	e−z	PROPN
ejpam-2461	181	32	(	(	PUNCT
ejpam-2461	181	33	z→∞	z→∞	NUM
ejpam-2461	181	34	in	in	ADP
ejpam-2461	181	35	|arg	|arg	VERB
ejpam-2461	181	36	z|	z|	PROPN
ejpam-2461	181	37	<	<	X
ejpam-2461	181	38	1	1	NUM
ejpam-2461	181	39	2	2	NUM
ejpam-2461	181	40	π	π	NOUN
ejpam-2461	181	41	)	)	PUNCT
ejpam-2461	181	42	,	,	PUNCT
ejpam-2461	181	43	so	so	SCONJ
ejpam-2461	181	44	that	that	SCONJ
ejpam-2461	181	45	the	the	DET
ejpam-2461	181	46	er(a	er(a	NUM
ejpam-2461	181	47	;	;	PUNCT
ejpam-2461	181	48	w	w	X
ejpam-2461	181	49	,	,	PUNCT
ejpam-2461	181	50	p	p	NOUN
ejpam-2461	181	51	)	)	PUNCT
ejpam-2461	181	52	represent	represent	VERB
ejpam-2461	181	53	a	a	DET
ejpam-2461	181	54	series	series	NOUN
ejpam-2461	181	55	of	of	ADP
ejpam-2461	181	56	exponentially	exponentially	ADV
ejpam-2461	181	57	small	small	ADJ
ejpam-2461	181	58	expansions	expansion	NOUN
ejpam-2461	181	59	of	of	ADP
ejpam-2461	181	60	increasing	increase	VERB
ejpam-2461	181	61	subdominance	subdominance	NOUN
ejpam-2461	181	62	in	in	ADP
ejpam-2461	181	63	the	the	DET
ejpam-2461	181	64	small	small	ADJ
ejpam-2461	181	65	-	-	PUNCT
ejpam-2461	181	66	a	a	DET
ejpam-2461	181	67	limit	limit	NOUN
ejpam-2461	181	68	.	.	PUNCT
ejpam-2461	182	1	in	in	ADP
ejpam-2461	182	2	addition	addition	NOUN
ejpam-2461	182	3	,	,	PUNCT
ejpam-2461	182	4	the	the	DET
ejpam-2461	182	5	number	number	NOUN
ejpam-2461	182	6	of	of	ADP
ejpam-2461	182	7	exponentially	exponentially	ADV
ejpam-2461	182	8	small	small	ADJ
ejpam-2461	182	9	expansions	expansion	NOUN
ejpam-2461	182	10	increases	increase	NOUN
ejpam-2461	182	11	by	by	ADP
ejpam-2461	182	12	one	one	NUM
ejpam-2461	182	13	each	each	DET
ejpam-2461	182	14	time	time	NOUN
ejpam-2461	182	15	p	p	NOUN
ejpam-2461	182	16	increases	increase	NOUN
ejpam-2461	182	17	by	by	ADP
ejpam-2461	182	18	4	4	NUM
ejpam-2461	182	19	.	.	PUNCT
ejpam-2461	182	20	by	by	ADP
ejpam-2461	182	21	means	mean	NOUN
ejpam-2461	182	22	of	of	ADP
ejpam-2461	182	23	a	a	DET
ejpam-2461	182	24	saddle	saddle	NOUN
ejpam-2461	182	25	-	-	PUNCT
ejpam-2461	182	26	point	point	NOUN
ejpam-2461	182	27	analysis	analysis	NOUN
ejpam-2461	182	28	in	in	ADP
ejpam-2461	182	29	the	the	DET
ejpam-2461	182	30	case	case	NOUN
ejpam-2461	182	31	w	w	NOUN
ejpam-2461	182	32	=	=	SYM
ejpam-2461	182	33	0	0	PROPN
ejpam-2461	182	34	,	,	PUNCT
ejpam-2461	182	35	this	this	PRON
ejpam-2461	182	36	was	be	AUX
ejpam-2461	182	37	demonstrated	demonstrate	VERB
ejpam-2461	182	38	to	to	PART
ejpam-2461	182	39	correspond	correspond	VERB
ejpam-2461	182	40	to	to	ADP
ejpam-2461	182	41	a	a	DET
ejpam-2461	182	42	stokes	stoke	NOUN
ejpam-2461	182	43	phenomenon	phenomenon	NOUN
ejpam-2461	182	44	when	when	SCONJ
ejpam-2461	182	45	p	p	NOUN
ejpam-2461	182	46	was	be	AUX
ejpam-2461	182	47	allowed	allow	VERB
ejpam-2461	182	48	to	to	PART
ejpam-2461	182	49	vary	vary	VERB
ejpam-2461	182	50	continuously	continuously	ADV
ejpam-2461	182	51	through	through	ADP
ejpam-2461	182	52	the	the	DET
ejpam-2461	182	53	values	value	NOUN
ejpam-2461	182	54	p	p	X
ejpam-2461	182	55	=	=	SYM
ejpam-2461	182	56	2,6,10	2,6,10	NUM
ejpam-2461	182	57	,	,	PUNCT
ejpam-2461	182	58	.	.	PUNCT
ejpam-2461	182	59	.	.	PUNCT
ejpam-2461	183	1	.	.	PUNCT
ejpam-2461	183	2	;	;	PUNCT
ejpam-2461	183	3	see	see	VERB
ejpam-2461	183	4	[	[	X
ejpam-2461	183	5	5	5	NUM
ejpam-2461	183	6	,	,	PUNCT
ejpam-2461	183	7	§	§	NOUN
ejpam-2461	183	8	§	§	NOUN
ejpam-2461	183	9	8.1.2	8.1.2	NUM
ejpam-2461	183	10	,	,	PUNCT
ejpam-2461	183	11	8.1.7	8.1.7	NUM
ejpam-2461	183	12	]	]	PUNCT
ejpam-2461	183	13	.	.	PUNCT
ejpam-2461	184	1	finally	finally	ADV
ejpam-2461	184	2	,	,	PUNCT
ejpam-2461	184	3	we	we	PRON
ejpam-2461	184	4	remark	remark	VERB
ejpam-2461	184	5	that	that	SCONJ
ejpam-2461	184	6	the	the	DET
ejpam-2461	184	7	exponents	exponent	NOUN
ejpam-2461	184	8	p	p	NOUN
ejpam-2461	184	9	and	and	CCONJ
ejpam-2461	184	10	q	q	NOUN
ejpam-2461	184	11	are	be	AUX
ejpam-2461	184	12	conjugate	conjugate	ADJ
ejpam-2461	184	13	exponents	exponent	NOUN
ejpam-2461	184	14	,	,	PUNCT
ejpam-2461	184	15	since	since	SCONJ
ejpam-2461	184	16	1	1	NUM
ejpam-2461	184	17	p	p	NOUN
ejpam-2461	185	1	+	+	NOUN
ejpam-2461	185	2	1	1	NUM
ejpam-2461	185	3	q	q	NOUN
ejpam-2461	185	4	=	=	ADJ
ejpam-2461	185	5	1	1	X
ejpam-2461	185	6	.	.	PUNCT
ejpam-2461	185	7	when	when	SCONJ
ejpam-2461	185	8	a	a	PRON
ejpam-2461	185	9	is	be	AUX
ejpam-2461	185	10	a	a	DET
ejpam-2461	185	11	real	real	ADJ
ejpam-2461	185	12	parameter	parameter	NOUN
ejpam-2461	185	13	,	,	PUNCT
ejpam-2461	185	14	the	the	DET
ejpam-2461	185	15	expansion	expansion	NOUN
ejpam-2461	185	16	in	in	ADP
ejpam-2461	185	17	theorem	theorem	NOUN
ejpam-2461	185	18	1	1	NUM
ejpam-2461	185	19	can	can	AUX
ejpam-2461	185	20	be	be	AUX
ejpam-2461	185	21	expressed	express	VERB
ejpam-2461	185	22	in	in	ADP
ejpam-2461	185	23	a	a	DET
ejpam-2461	185	24	different	different	ADJ
ejpam-2461	185	25	form	form	NOUN
ejpam-2461	185	26	by	by	ADP
ejpam-2461	185	27	using	use	VERB
ejpam-2461	185	28	(	(	PUNCT
ejpam-2461	185	29	1	1	NUM
ejpam-2461	185	30	)	)	PUNCT
ejpam-2461	185	31	to	to	PART
ejpam-2461	185	32	represent	represent	VERB
ejpam-2461	185	33	the	the	DET
ejpam-2461	185	34	sq(x	sq(x	NUM
ejpam-2461	185	35	e∓πiψr	e∓πiψr	PROPN
ejpam-2461	185	36	;	;	PUNCT
ejpam-2461	185	37	λ	λ	PROPN
ejpam-2461	185	38	j	j	PROPN
ejpam-2461	185	39	)	)	PUNCT
ejpam-2461	185	40	as	as	ADP
ejpam-2461	185	41	infinite	infinite	ADJ
ejpam-2461	185	42	sums	sum	NOUN
ejpam-2461	185	43	.	.	PUNCT
ejpam-2461	186	1	then	then	ADV
ejpam-2461	186	2	from	from	ADP
ejpam-2461	186	3	(	(	PUNCT
ejpam-2461	186	4	23	23	NUM
ejpam-2461	186	5	)	)	PUNCT
ejpam-2461	186	6	we	we	PRON
ejpam-2461	186	7	obtain	obtain	VERB
ejpam-2461	186	8	the	the	DET
ejpam-2461	186	9	following	follow	VERB
ejpam-2461	186	10	theorem	theorem	NOUN
ejpam-2461	186	11	:	:	PUNCT
ejpam-2461	186	12	theorem	theorem	NOUN
ejpam-2461	186	13	2	2	NUM
ejpam-2461	186	14	.	.	PUNCT
ejpam-2461	187	1	let	let	VERB
ejpam-2461	187	2	w	w	NOUN
ejpam-2461	188	1	and	and	CCONJ
ejpam-2461	188	2	p	p	NOUN
ejpam-2461	188	3	be	be	AUX
ejpam-2461	188	4	even	even	ADV
ejpam-2461	188	5	positive	positive	ADJ
ejpam-2461	188	6	integers	integer	NOUN
ejpam-2461	188	7	,	,	PUNCT
ejpam-2461	188	8	n	n	NOUN
ejpam-2461	188	9	=	=	PUNCT
ejpam-2461	189	1	[	[	X
ejpam-2461	189	2	1	1	NUM
ejpam-2461	189	3	4	4	NUM
ejpam-2461	189	4	p	p	NOUN
ejpam-2461	189	5	]	]	PUNCT
ejpam-2461	189	6	and	and	CCONJ
ejpam-2461	189	7	m	m	AUX
ejpam-2461	189	8	be	be	AUX
ejpam-2461	189	9	a	a	DET
ejpam-2461	189	10	positive	positive	ADJ
ejpam-2461	189	11	integer	integer	NOUN
ejpam-2461	189	12	.	.	PUNCT
ejpam-2461	190	1	then	then	ADV
ejpam-2461	190	2	,	,	PUNCT
ejpam-2461	190	3	the	the	DET
ejpam-2461	190	4	exponentially	exponentially	ADV
ejpam-2461	190	5	small	small	ADJ
ejpam-2461	190	6	expansions	expansion	NOUN
ejpam-2461	190	7	in	in	ADP
ejpam-2461	190	8	(	(	PUNCT
ejpam-2461	190	9	23	23	NUM
ejpam-2461	190	10	)	)	PUNCT
ejpam-2461	190	11	valid	valid	ADJ
ejpam-2461	190	12	as	as	ADP
ejpam-2461	190	13	a→	a→	X
ejpam-2461	190	14	0	0	NUM
ejpam-2461	190	15	+	+	CCONJ
ejpam-2461	190	16	can	can	AUX
ejpam-2461	190	17	be	be	AUX
ejpam-2461	190	18	written	write	VERB
ejpam-2461	190	19	in	in	ADP
ejpam-2461	190	20	the	the	DET
ejpam-2461	190	21	form	form	NOUN
ejpam-2461	190	22	er(a	er(a	NUM
ejpam-2461	190	23	;	;	PUNCT
ejpam-2461	190	24	w	w	X
ejpam-2461	190	25	,	,	PUNCT
ejpam-2461	190	26	p	p	NOUN
ejpam-2461	190	27	)	)	PUNCT
ejpam-2461	190	28	=	=	PUNCT
ejpam-2461	190	29	a	a	PRON
ejpam-2461	190	30	πκ	πκ	NOUN
ejpam-2461	190	31	∞	∞	PROPN
ejpam-2461	190	32	∑	∑	PROPN
ejpam-2461	190	33	n=1	n=1	PROPN
ejpam-2461	190	34	nw−1x	nw−1x	NUM
ejpam-2461	190	35	ϑn	ϑn	PROPN
ejpam-2461	190	36	e−xn	e−xn	PROPN
ejpam-2461	190	37	cosπψr	cosπψr	PROPN
ejpam-2461	190	38	υn	υn	NOUN
ejpam-2461	190	39	,	,	PUNCT
ejpam-2461	190	40	r	r	NOUN
ejpam-2461	190	41	(	(	PUNCT
ejpam-2461	190	42	0≤	0≤	NUM
ejpam-2461	190	43	r	r	NOUN
ejpam-2461	190	44	≤	≤	NOUN
ejpam-2461	190	45	n	n	CCONJ
ejpam-2461	190	46	−	−	PROPN
ejpam-2461	190	47	1	1	NUM
ejpam-2461	190	48	)	)	PUNCT
ejpam-2461	190	49	,	,	PUNCT
ejpam-2461	190	50	(	(	PUNCT
ejpam-2461	190	51	24	24	NUM
ejpam-2461	190	52	)	)	PUNCT
ejpam-2461	190	53	ên	ên	PROPN
ejpam-2461	190	54	(	(	PUNCT
ejpam-2461	190	55	a	a	X
ejpam-2461	190	56	;	;	PUNCT
ejpam-2461	190	57	w	w	PROPN
ejpam-2461	190	58	,	,	PUNCT
ejpam-2461	190	59	p	p	NOUN
ejpam-2461	190	60	)	)	PUNCT
ejpam-2461	190	61	=	=	PUNCT
ejpam-2461	190	62	a	a	DET
ejpam-2461	190	63	2πκ	2πκ	ADJ
ejpam-2461	190	64	∞	∞	PROPN
ejpam-2461	190	65	∑	∑	PROPN
ejpam-2461	190	66	n=1	n=1	PROPN
ejpam-2461	190	67	nw−1x	nw−1x	NUM
ejpam-2461	190	68	ϑn	ϑn	NOUN
ejpam-2461	190	69	e−xnυn	e−xnυn	NUM
ejpam-2461	190	70	,	,	PUNCT
ejpam-2461	190	71	n	n	X
ejpam-2461	190	72	.	.	PUNCT
ejpam-2461	191	1	(	(	PUNCT
ejpam-2461	191	2	25	25	NUM
ejpam-2461	191	3	)	)	PUNCT
ejpam-2461	191	4	the	the	DET
ejpam-2461	191	5	υn	υn	NOUN
ejpam-2461	191	6	,	,	PUNCT
ejpam-2461	191	7	r	r	NOUN
ejpam-2461	191	8	(	(	PUNCT
ejpam-2461	191	9	0≤	0≤	NUM
ejpam-2461	191	10	r	r	NOUN
ejpam-2461	191	11	≤	≤	NUM
ejpam-2461	191	12	n	n	CCONJ
ejpam-2461	191	13	)	)	PUNCT
ejpam-2461	191	14	have	have	VERB
ejpam-2461	191	15	the	the	DET
ejpam-2461	191	16	asymptotic	asymptotic	ADJ
ejpam-2461	191	17	expansions	expansion	NOUN
ejpam-2461	191	18	υn	υn	VERB
ejpam-2461	191	19	,	,	PUNCT
ejpam-2461	191	20	r	r	NOUN
ejpam-2461	191	21	=	=	SYM
ejpam-2461	191	22	m−1	m−1	PROPN
ejpam-2461	191	23	∑	∑	PUNCT
ejpam-2461	191	24	j=0	j=0	PROPN
ejpam-2461	191	25	(	(	PUNCT
ejpam-2461	191	26	−	−	PROPN
ejpam-2461	191	27	)	)	PUNCT
ejpam-2461	191	28	jc	jc	PROPN
ejpam-2461	191	29	jx	jx	PROPN
ejpam-2461	192	1	−	−	PROPN
ejpam-2461	192	2	j	j	PROPN
ejpam-2461	192	3	n	n	PRON
ejpam-2461	192	4	cos[xn	cos[xn	NOUN
ejpam-2461	192	5	sinπψr	sinπψr	NOUN
ejpam-2461	193	1	+	+	PROPN
ejpam-2461	193	2	π	π	PROPN
ejpam-2461	193	3	(	(	PUNCT
ejpam-2461	193	4	j	j	PROPN
ejpam-2461	193	5	−	−	PROPN
ejpam-2461	193	6	ϑ)ψr	ϑ)ψr	PROPN
ejpam-2461	193	7	]	]	X
ejpam-2461	193	8	+	+	NOUN
ejpam-2461	193	9	o(x−m	o(x−m	NOUN
ejpam-2461	193	10	n	n	PRON
ejpam-2461	193	11	)	)	PUNCT
ejpam-2461	193	12	,	,	PUNCT
ejpam-2461	193	13	(	(	PUNCT
ejpam-2461	193	14	26	26	NUM
ejpam-2461	193	15	)	)	PUNCT
ejpam-2461	193	16	†the	†the	DET
ejpam-2461	193	17	symbol	symbol	NOUN
ejpam-2461	193	18	∑	∑	PUNCT
ejpam-2461	193	19	±	±	NOUN
ejpam-2461	193	20	signifies	signifie	NOUN
ejpam-2461	193	21	that	that	SCONJ
ejpam-2461	193	22	the	the	DET
ejpam-2461	193	23	series	series	NOUN
ejpam-2461	193	24	with	with	ADP
ejpam-2461	193	25	±	±	NOUN
ejpam-2461	193	26	signs	sign	NOUN
ejpam-2461	193	27	are	be	AUX
ejpam-2461	193	28	to	to	PART
ejpam-2461	193	29	be	be	AUX
ejpam-2461	193	30	added	add	VERB
ejpam-2461	193	31	.	.	PUNCT
ejpam-2461	194	1	r.	r.	PROPN
ejpam-2461	194	2	paris	paris	PROPN
ejpam-2461	194	3	/	/	SYM
ejpam-2461	194	4	eur	eur	PROPN
ejpam-2461	194	5	.	.	PUNCT
ejpam-2461	195	1	j.	j.	PROPN
ejpam-2461	195	2	pure	pure	PROPN
ejpam-2461	195	3	appl	appl	PROPN
ejpam-2461	195	4	.	.	PROPN
ejpam-2461	195	5	math	math	PROPN
ejpam-2461	195	6	,	,	PUNCT
ejpam-2461	195	7	9	9	NUM
ejpam-2461	195	8	(	(	PUNCT
ejpam-2461	195	9	2016	2016	NUM
ejpam-2461	195	10	)	)	PUNCT
ejpam-2461	195	11	,	,	PUNCT
ejpam-2461	195	12	3	3	NUM
ejpam-2461	195	13	-	-	SYM
ejpam-2461	195	14	18	18	NUM
ejpam-2461	195	15	12	12	NUM
ejpam-2461	195	16	where	where	SCONJ
ejpam-2461	195	17	xn	xn	PUNCT
ejpam-2461	196	1	=	=	SYM
ejpam-2461	196	2	x	x	SYM
ejpam-2461	196	3	np	np	PROPN
ejpam-2461	196	4	/	/	SYM
ejpam-2461	196	5	κ	κ	NOUN
ejpam-2461	196	6	=	=	PUNCT
ejpam-2461	196	7	κ(h(2πn)p	κ(h(2πn)p	NOUN
ejpam-2461	196	8	/	/	SYM
ejpam-2461	196	9	a)1	a)1	PROPN
ejpam-2461	196	10	/	/	SYM
ejpam-2461	196	11	κ	κ	PROPN
ejpam-2461	196	12	,	,	PUNCT
ejpam-2461	196	13	ψr	ψr	ADP
ejpam-2461	196	14	=	=	SYM
ejpam-2461	196	15	(	(	PUNCT
ejpam-2461	196	16	1	1	NUM
ejpam-2461	196	17	2	2	NUM
ejpam-2461	196	18	p−2r	p−2r	NOUN
ejpam-2461	196	19	−1)/κ	−1)/κ	PROPN
ejpam-2461	196	20	,	,	PUNCT
ejpam-2461	196	21	ψn	ψn	VERB
ejpam-2461	196	22	≡	≡	PROPN
ejpam-2461	196	23	0	0	PUNCT
ejpam-2461	196	24	and	and	CCONJ
ejpam-2461	196	25	the	the	DET
ejpam-2461	196	26	other	other	ADJ
ejpam-2461	196	27	quantities	quantity	NOUN
ejpam-2461	196	28	are	be	AUX
ejpam-2461	196	29	as	as	ADV
ejpam-2461	196	30	defined	define	VERB
ejpam-2461	196	31	in	in	ADP
ejpam-2461	196	32	theorem	theorem	NOUN
ejpam-2461	196	33	1	1	NUM
ejpam-2461	196	34	.	.	PUNCT
ejpam-2461	197	1	the	the	DET
ejpam-2461	197	2	result	result	NOUN
ejpam-2461	197	3	in	in	ADP
ejpam-2461	197	4	(	(	PUNCT
ejpam-2461	197	5	21	21	NUM
ejpam-2461	197	6	)	)	PUNCT
ejpam-2461	197	7	and	and	CCONJ
ejpam-2461	197	8	(	(	PUNCT
ejpam-2461	197	9	22	22	NUM
ejpam-2461	197	10	)	)	PUNCT
ejpam-2461	197	11	is	be	AUX
ejpam-2461	197	12	the	the	DET
ejpam-2461	197	13	analogue	analogue	NOUN
ejpam-2461	197	14	of	of	ADP
ejpam-2461	197	15	the	the	DET
ejpam-2461	197	16	poisson	poisson	PROPN
ejpam-2461	197	17	-	-	PROPN
ejpam-2461	197	18	jacobi	jacobi	PROPN
ejpam-2461	197	19	transformation	transformation	NOUN
ejpam-2461	197	20	in	in	ADP
ejpam-2461	197	21	(	(	PUNCT
ejpam-2461	197	22	2	2	X
ejpam-2461	197	23	)	)	PUNCT
ejpam-2461	197	24	corresponding	correspond	VERB
ejpam-2461	197	25	to	to	ADP
ejpam-2461	197	26	w	w	PROPN
ejpam-2461	197	27	=	=	NOUN
ejpam-2461	197	28	0	0	NUM
ejpam-2461	197	29	,	,	PUNCT
ejpam-2461	197	30	p	p	NOUN
ejpam-2461	197	31	=	=	NOUN
ejpam-2461	197	32	2	2	X
ejpam-2461	197	33	.	.	PUNCT
ejpam-2461	198	1	in	in	ADP
ejpam-2461	198	2	this	this	DET
ejpam-2461	198	3	latter	latter	ADJ
ejpam-2461	198	4	case	case	NOUN
ejpam-2461	198	5	,	,	PUNCT
ejpam-2461	198	6	n	n	NOUN
ejpam-2461	198	7	=	=	SYM
ejpam-2461	198	8	0	0	NUM
ejpam-2461	199	1	and	and	CCONJ
ejpam-2461	199	2	,	,	PUNCT
ejpam-2461	199	3	from	from	ADP
ejpam-2461	199	4	(	(	PUNCT
ejpam-2461	199	5	22	22	NUM
ejpam-2461	199	6	)	)	PUNCT
ejpam-2461	199	7	,	,	PUNCT
ejpam-2461	199	8	il	il	PROPN
ejpam-2461	199	9	=	=	SYM
ejpam-2461	199	10	e0(a	e0(a	PROPN
ejpam-2461	199	11	;	;	PUNCT
ejpam-2461	199	12	0	0	NUM
ejpam-2461	199	13	,	,	PUNCT
ejpam-2461	199	14	2	2	NUM
ejpam-2461	199	15	)	)	PUNCT
ejpam-2461	199	16	.	.	PUNCT
ejpam-2461	200	1	the	the	DET
ejpam-2461	200	2	ratio	ratio	NOUN
ejpam-2461	200	3	of	of	ADP
ejpam-2461	200	4	gamma	gamma	NOUN
ejpam-2461	200	5	functions	function	NOUN
ejpam-2461	200	6	in	in	ADP
ejpam-2461	200	7	(	(	PUNCT
ejpam-2461	200	8	14	14	NUM
ejpam-2461	200	9	)	)	PUNCT
ejpam-2461	200	10	is	be	AUX
ejpam-2461	200	11	replaced	replace	VERB
ejpam-2461	200	12	by	by	ADP
ejpam-2461	200	13	the	the	DET
ejpam-2461	200	14	single	single	ADJ
ejpam-2461	200	15	gamma	gamma	NOUN
ejpam-2461	200	16	function	function	NOUN
ejpam-2461	200	17	γ(s	γ(s	PROPN
ejpam-2461	200	18	+	+	CCONJ
ejpam-2461	200	19	1	1	NUM
ejpam-2461	200	20	2	2	NUM
ejpam-2461	200	21	)	)	PUNCT
ejpam-2461	200	22	by	by	ADP
ejpam-2461	200	23	the	the	DET
ejpam-2461	200	24	duplication	duplication	NOUN
ejpam-2461	200	25	formula	formula	NOUN
ejpam-2461	200	26	for	for	ADP
ejpam-2461	200	27	the	the	DET
ejpam-2461	200	28	gamma	gamma	PROPN
ejpam-2461	200	29	function	function	NOUN
ejpam-2461	200	30	,	,	PUNCT
ejpam-2461	200	31	with	with	ADP
ejpam-2461	200	32	the	the	DET
ejpam-2461	200	33	result	result	NOUN
ejpam-2461	200	34	that	that	SCONJ
ejpam-2461	200	35	c0	c0	NOUN
ejpam-2461	200	36	=	=	PROPN
ejpam-2461	200	37	1	1	NUM
ejpam-2461	200	38	,	,	PUNCT
ejpam-2461	200	39	c	c	PROPN
ejpam-2461	200	40	j	j	PROPN
ejpam-2461	200	41	=	=	SYM
ejpam-2461	200	42	0	0	PROPN
ejpam-2461	201	1	(	(	PUNCT
ejpam-2461	201	2	j	j	PROPN
ejpam-2461	201	3	≥	≥	NUM
ejpam-2461	201	4	1	1	NUM
ejpam-2461	201	5	)	)	PUNCT
ejpam-2461	201	6	and	and	CCONJ
ejpam-2461	201	7	consequently	consequently	ADV
ejpam-2461	201	8	υn	υn	NOUN
ejpam-2461	201	9	,	,	PUNCT
ejpam-2461	201	10	n	n	NOUN
ejpam-2461	201	11	=	=	SYM
ejpam-2461	201	12	1	1	NUM
ejpam-2461	201	13	for	for	ADP
ejpam-2461	201	14	all	all	DET
ejpam-2461	201	15	n	n	PRON
ejpam-2461	201	16	≥	≥	NOUN
ejpam-2461	201	17	1	1	NUM
ejpam-2461	201	18	.	.	PUNCT
ejpam-2461	202	1	then	then	ADV
ejpam-2461	202	2	,	,	PUNCT
ejpam-2461	202	3	since	since	SCONJ
ejpam-2461	202	4	k	k	PROPN
ejpam-2461	202	5	=	=	SYM
ejpam-2461	202	6	0	0	PROPN
ejpam-2461	202	7	and	and	CCONJ
ejpam-2461	202	8	ζ(0	ζ(0	NOUN
ejpam-2461	202	9	)	)	PUNCT
ejpam-2461	202	10	=	=	SYM
ejpam-2461	202	11	−1	−1	NOUN
ejpam-2461	202	12	2	2	NUM
ejpam-2461	202	13	,	,	PUNCT
ejpam-2461	202	14	(	(	PUNCT
ejpam-2461	202	15	21	21	NUM
ejpam-2461	202	16	)	)	PUNCT
ejpam-2461	202	17	,	,	PUNCT
ejpam-2461	202	18	(	(	PUNCT
ejpam-2461	202	19	22	22	NUM
ejpam-2461	202	20	)	)	PUNCT
ejpam-2461	202	21	and	and	CCONJ
ejpam-2461	202	22	(	(	PUNCT
ejpam-2461	202	23	25	25	NUM
ejpam-2461	202	24	)	)	PUNCT
ejpam-2461	202	25	reduce	reduce	VERB
ejpam-2461	202	26	to	to	ADP
ejpam-2461	202	27	(	(	PUNCT
ejpam-2461	202	28	2	2	NUM
ejpam-2461	202	29	)	)	PUNCT
ejpam-2461	202	30	.	.	PUNCT
ejpam-2461	203	1	the	the	DET
ejpam-2461	203	2	resulting	result	VERB
ejpam-2461	203	3	expansion	expansion	NOUN
ejpam-2461	203	4	is	be	AUX
ejpam-2461	203	5	valid	valid	ADJ
ejpam-2461	203	6	for	for	ADP
ejpam-2461	203	7	all	all	DET
ejpam-2461	203	8	values	value	NOUN
ejpam-2461	203	9	of	of	ADP
ejpam-2461	203	10	the	the	DET
ejpam-2461	203	11	parameter	parameter	NOUN
ejpam-2461	203	12	a	a	DET
ejpam-2461	203	13	(	(	PUNCT
ejpam-2461	203	14	not	not	PART
ejpam-2461	203	15	just	just	ADV
ejpam-2461	203	16	a	a	DET
ejpam-2461	203	17	→	→	SYM
ejpam-2461	203	18	0	0	NUM
ejpam-2461	203	19	)	)	PUNCT
ejpam-2461	203	20	satisfying	satisfy	VERB
ejpam-2461	203	21	|arg	|arg	NOUN
ejpam-2461	203	22	a|	a|	PROPN
ejpam-2461	203	23	<	<	X
ejpam-2461	203	24	1	1	NUM
ejpam-2461	203	25	2π	2π	NOUN
ejpam-2461	203	26	.	.	PUNCT
ejpam-2461	204	1	when	when	SCONJ
ejpam-2461	204	2	w	w	PROPN
ejpam-2461	204	3	=	=	NOUN
ejpam-2461	204	4	0	0	NUM
ejpam-2461	204	5	,	,	PUNCT
ejpam-2461	204	6	p	p	NOUN
ejpam-2461	204	7	=	=	PROPN
ejpam-2461	204	8	2	2	NUM
ejpam-2461	204	9	m	m	NOUN
ejpam-2461	204	10	,	,	PUNCT
ejpam-2461	204	11	the	the	DET
ejpam-2461	204	12	expansions	expansion	NOUN
ejpam-2461	204	13	(	(	PUNCT
ejpam-2461	204	14	24	24	NUM
ejpam-2461	204	15	)	)	PUNCT
ejpam-2461	204	16	and	and	CCONJ
ejpam-2461	204	17	(	(	PUNCT
ejpam-2461	204	18	25	25	NUM
ejpam-2461	204	19	)	)	PUNCT
ejpam-2461	204	20	reduce	reduce	VERB
ejpam-2461	204	21	to	to	ADP
ejpam-2461	204	22	those	those	PRON
ejpam-2461	204	23	given	give	VERB
ejpam-2461	204	24	in	in	ADP
ejpam-2461	204	25	[	[	X
ejpam-2461	204	26	6	6	NUM
ejpam-2461	204	27	]	]	PUNCT
ejpam-2461	204	28	;	;	PUNCT
ejpam-2461	204	29	see	see	VERB
ejpam-2461	204	30	section	section	NOUN
ejpam-2461	204	31	5	5	NUM
ejpam-2461	204	32	.	.	PUNCT
ejpam-2461	205	1	we	we	PRON
ejpam-2461	205	2	observe	observe	VERB
ejpam-2461	205	3	that	that	SCONJ
ejpam-2461	205	4	the	the	DET
ejpam-2461	205	5	n	n	NOUN
ejpam-2461	205	6	-	-	PUNCT
ejpam-2461	205	7	dependence	dependence	NOUN
ejpam-2461	205	8	in	in	ADP
ejpam-2461	205	9	the	the	DET
ejpam-2461	205	10	sums	sum	NOUN
ejpam-2461	205	11	er(a	er(a	NUM
ejpam-2461	205	12	;	;	PUNCT
ejpam-2461	205	13	w	w	X
ejpam-2461	205	14	,	,	PUNCT
ejpam-2461	205	15	p	p	NOUN
ejpam-2461	205	16	)	)	PUNCT
ejpam-2461	205	17	from	from	ADP
ejpam-2461	205	18	the	the	DET
ejpam-2461	205	19	factor	factor	NOUN
ejpam-2461	205	20	nw−1x	nw−1x	PROPN
ejpam-2461	205	21	ϑn	ϑn	NOUN
ejpam-2461	205	22	is	be	AUX
ejpam-2461	205	23	given	give	VERB
ejpam-2461	205	24	by	by	ADP
ejpam-2461	205	25	nw−1	nw−1	NOUN
ejpam-2461	205	26	npϑ/κ	npϑ/κ	NOUN
ejpam-2461	205	27	=	=	SYM
ejpam-2461	205	28	n−(2w+p−2)/(2κ	n−(2w+p−2)/(2κ	NOUN
ejpam-2461	205	29	)	)	PUNCT
ejpam-2461	205	30	.	.	PUNCT
ejpam-2461	206	1	since	since	SCONJ
ejpam-2461	206	2	p	p	PROPN
ejpam-2461	206	3	≥	≥	NUM
ejpam-2461	206	4	2	2	NUM
ejpam-2461	206	5	and	and	CCONJ
ejpam-2461	206	6	w	w	NOUN
ejpam-2461	206	7	>	>	X
ejpam-2461	206	8	0	0	NUM
ejpam-2461	206	9	,	,	PUNCT
ejpam-2461	206	10	this	this	PRON
ejpam-2461	206	11	is	be	AUX
ejpam-2461	206	12	seen	see	VERB
ejpam-2461	206	13	to	to	PART
ejpam-2461	206	14	correspond	correspond	VERB
ejpam-2461	206	15	to	to	ADP
ejpam-2461	206	16	a	a	DET
ejpam-2461	206	17	negative	negative	ADJ
ejpam-2461	206	18	power	power	NOUN
ejpam-2461	206	19	of	of	ADP
ejpam-2461	206	20	n.	n.	PROPN
ejpam-2461	206	21	4	4	NUM
ejpam-2461	206	22	.	.	PUNCT
ejpam-2461	207	1	the	the	DET
ejpam-2461	207	2	coefficients	coefficient	NOUN
ejpam-2461	207	3	c	c	VERB
ejpam-2461	207	4	j	j	NOUN
ejpam-2461	207	5	we	we	PRON
ejpam-2461	207	6	describe	describe	VERB
ejpam-2461	207	7	an	an	DET
ejpam-2461	207	8	algorithm	algorithm	NOUN
ejpam-2461	207	9	for	for	ADP
ejpam-2461	207	10	the	the	DET
ejpam-2461	207	11	computation	computation	NOUN
ejpam-2461	207	12	of	of	ADP
ejpam-2461	207	13	the	the	DET
ejpam-2461	207	14	coefficients	coefficient	NOUN
ejpam-2461	207	15	c	c	PROPN
ejpam-2461	207	16	j	j	PROPN
ejpam-2461	207	17	≡	≡	PROPN
ejpam-2461	207	18	c	c	PROPN
ejpam-2461	207	19	j(w	j(w	PROPN
ejpam-2461	207	20	,	,	PUNCT
ejpam-2461	207	21	p	p	NOUN
ejpam-2461	207	22	)	)	PUNCT
ejpam-2461	207	23	that	that	PRON
ejpam-2461	207	24	appear	appear	VERB
ejpam-2461	207	25	in	in	ADP
ejpam-2461	207	26	the	the	DET
ejpam-2461	207	27	exponentially	exponentially	ADV
ejpam-2461	207	28	small	small	ADJ
ejpam-2461	207	29	expansions	expansion	NOUN
ejpam-2461	207	30	er(a	er(a	NUM
ejpam-2461	207	31	;	;	PUNCT
ejpam-2461	207	32	w	w	X
ejpam-2461	207	33	,	,	PUNCT
ejpam-2461	207	34	p	p	NOUN
ejpam-2461	207	35	)	)	PUNCT
ejpam-2461	207	36	in	in	ADP
ejpam-2461	207	37	(	(	PUNCT
ejpam-2461	207	38	23	23	NUM
ejpam-2461	207	39	)	)	PUNCT
ejpam-2461	207	40	and	and	CCONJ
ejpam-2461	207	41	(	(	PUNCT
ejpam-2461	207	42	26	26	NUM
ejpam-2461	207	43	)	)	PUNCT
ejpam-2461	207	44	.	.	PUNCT
ejpam-2461	208	1	the	the	DET
ejpam-2461	208	2	expression	expression	NOUN
ejpam-2461	208	3	for	for	ADP
ejpam-2461	208	4	the	the	DET
ejpam-2461	208	5	ratio	ratio	NOUN
ejpam-2461	208	6	of	of	ADP
ejpam-2461	208	7	two	two	NUM
ejpam-2461	208	8	gamma	gamma	NOUN
ejpam-2461	208	9	functions	function	NOUN
ejpam-2461	208	10	in	in	ADP
ejpam-2461	208	11	(	(	PUNCT
ejpam-2461	208	12	14	14	NUM
ejpam-2461	208	13	)	)	PUNCT
ejpam-2461	208	14	,	,	PUNCT
ejpam-2461	208	15	with	with	ADP
ejpam-2461	208	16	α≡	α≡	NUM
ejpam-2461	208	17	1−w	1−w	NUM
ejpam-2461	208	18	for	for	ADP
ejpam-2461	208	19	convenience	convenience	NOUN
ejpam-2461	208	20	,	,	PUNCT
ejpam-2461	208	21	takes	take	VERB
ejpam-2461	208	22	the	the	DET
ejpam-2461	208	23	form	form	NOUN
ejpam-2461	208	24	γ(α+	γ(α+	DET
ejpam-2461	208	25	ps	ps	NOUN
ejpam-2461	208	26	)	)	PUNCT
ejpam-2461	208	27	γ(1	γ(1	PROPN
ejpam-2461	209	1	+	+	CCONJ
ejpam-2461	209	2	s)γ(κs+	s)γ(κs+	NOUN
ejpam-2461	209	3	ϑ	ϑ	NOUN
ejpam-2461	209	4	)	)	PUNCT
ejpam-2461	209	5	=	=	PUNCT
ejpam-2461	209	6	a	a	DET
ejpam-2461	209	7	2π	2π	NOUN
ejpam-2461	209	8	(	(	PUNCT
ejpam-2461	209	9	hκκ)−s	hκκ)−s	PROPN
ejpam-2461	209	10	§	§	PROPN
ejpam-2461	209	11	m−1	m−1	PROPN
ejpam-2461	209	12	∑	∑	PUNCT
ejpam-2461	209	13	j=0	j=0	PROPN
ejpam-2461	209	14	c	c	PROPN
ejpam-2461	209	15	j	j	PROPN
ejpam-2461	209	16	(	(	PUNCT
ejpam-2461	209	17	1−	1−	NUM
ejpam-2461	209	18	κs−	κs−	SYM
ejpam-2461	209	19	ϑ	ϑ	X
ejpam-2461	209	20	)	)	PUNCT
ejpam-2461	209	21	j	j	PROPN
ejpam-2461	210	1	+	+	CCONJ
ejpam-2461	210	2	ρm	ρm	PROPN
ejpam-2461	210	3	(	(	PUNCT
ejpam-2461	210	4	s	s	NOUN
ejpam-2461	210	5	)	)	PUNCT
ejpam-2461	210	6	(	(	PUNCT
ejpam-2461	210	7	1−	1−	NUM
ejpam-2461	210	8	κs−	κs−	NOUN
ejpam-2461	210	9	ϑ)m	ϑ)m	X
ejpam-2461	210	10	ª	ª	VERB
ejpam-2461	210	11	,	,	PUNCT
ejpam-2461	210	12	where	where	SCONJ
ejpam-2461	210	13	the	the	DET
ejpam-2461	210	14	parameters	parameter	NOUN
ejpam-2461	210	15	κ	κ	VERB
ejpam-2461	210	16	,	,	PUNCT
ejpam-2461	210	17	h	h	NOUN
ejpam-2461	210	18	,	,	PUNCT
ejpam-2461	210	19	ϑ	ϑ	X
ejpam-2461	210	20	and	and	CCONJ
ejpam-2461	210	21	a	a	PRON
ejpam-2461	210	22	are	be	AUX
ejpam-2461	210	23	defined	define	VERB
ejpam-2461	210	24	in	in	ADP
ejpam-2461	210	25	(	(	PUNCT
ejpam-2461	210	26	15	15	NUM
ejpam-2461	210	27	)	)	PUNCT
ejpam-2461	210	28	and	and	CCONJ
ejpam-2461	210	29	(	(	PUNCT
ejpam-2461	210	30	α	α	NOUN
ejpam-2461	210	31	)	)	PUNCT
ejpam-2461	210	32	j	j	PROPN
ejpam-2461	210	33	=	=	PUNCT
ejpam-2461	210	34	γ(α	γ(α	PROPN
ejpam-2461	210	35	+	+	CCONJ
ejpam-2461	210	36	j)/γ(α	j)/γ(α	PROPN
ejpam-2461	210	37	)	)	PUNCT
ejpam-2461	210	38	is	be	AUX
ejpam-2461	210	39	the	the	DET
ejpam-2461	210	40	pochhammer	pochhammer	NOUN
ejpam-2461	210	41	symbol	symbol	NOUN
ejpam-2461	210	42	.	.	PUNCT
ejpam-2461	211	1	if	if	SCONJ
ejpam-2461	211	2	we	we	PRON
ejpam-2461	211	3	introduce	introduce	VERB
ejpam-2461	211	4	the	the	DET
ejpam-2461	211	5	scaled	scale	VERB
ejpam-2461	211	6	gamma	gamma	NOUN
ejpam-2461	211	7	function	function	PROPN
ejpam-2461	211	8	γ∗(z	γ∗(z	NOUN
ejpam-2461	211	9	)	)	PUNCT
ejpam-2461	211	10	=	=	SYM
ejpam-2461	212	1	γ(z)/	γ(z)/	ADJ
ejpam-2461	212	2	(	(	PUNCT
ejpam-2461	212	3	p	p	X
ejpam-2461	212	4	2π	2π	PROPN
ejpam-2461	212	5	zz−	zz−	NUM
ejpam-2461	212	6	1	1	NUM
ejpam-2461	212	7	2	2	NUM
ejpam-2461	212	8	e−z	e−z	NOUN
ejpam-2461	212	9	)	)	PUNCT
ejpam-2461	212	10	,	,	PUNCT
ejpam-2461	212	11	then	then	ADV
ejpam-2461	212	12	we	we	PRON
ejpam-2461	212	13	have	have	AUX
ejpam-2461	212	14	γ(βs+	γ(βs+	NOUN
ejpam-2461	212	15	γ	γ	NOUN
ejpam-2461	212	16	)	)	PUNCT
ejpam-2461	212	17	=	=	SYM
ejpam-2461	213	1	γ∗(βs+	γ∗(βs+	ADJ
ejpam-2461	213	2	γ)(2π	γ)(2π	PROPN
ejpam-2461	213	3	)	)	PUNCT
ejpam-2461	213	4	1	1	NUM
ejpam-2461	213	5	2	2	NUM
ejpam-2461	213	6	e−βs(βs)βs+γ−	e−βs(βs)βs+γ−	NOUN
ejpam-2461	213	7	1	1	NUM
ejpam-2461	213	8	2	2	NUM
ejpam-2461	213	9	e(βs;γ	e(βs;γ	PROPN
ejpam-2461	213	10	)	)	PUNCT
ejpam-2461	213	11	,	,	PUNCT
ejpam-2461	213	12	where	where	SCONJ
ejpam-2461	213	13	e(βs;γ	e(βs;γ	PROPN
ejpam-2461	213	14	)	)	PUNCT
ejpam-2461	213	15	:	:	PUNCT
ejpam-2461	213	16	=	=	NUM
ejpam-2461	213	17	exp	exp	PRON
ejpam-2461	213	18	�	�	PROPN
ejpam-2461	213	19	(	(	PUNCT
ejpam-2461	213	20	βs+	βs+	NOUN
ejpam-2461	213	21	γ−	γ−	NUM
ejpam-2461	213	22	1	1	NUM
ejpam-2461	213	23	2	2	NUM
ejpam-2461	213	24	)	)	PUNCT
ejpam-2461	213	25	log(1	log(1	NOUN
ejpam-2461	213	26	+	+	CCONJ
ejpam-2461	213	27	γ	γ	X
ejpam-2461	213	28	βs	βs	PRON
ejpam-2461	213	29	)	)	PUNCT
ejpam-2461	213	30	−	−	PROPN
ejpam-2461	213	31	γ	γ	PROPN
ejpam-2461	213	32	�	�	PROPN
ejpam-2461	213	33	.	.	PUNCT
ejpam-2461	214	1	the	the	DET
ejpam-2461	214	2	above	above	ADJ
ejpam-2461	214	3	ratio	ratio	NOUN
ejpam-2461	214	4	of	of	ADP
ejpam-2461	214	5	gamma	gamma	NOUN
ejpam-2461	214	6	functions	function	NOUN
ejpam-2461	214	7	may	may	AUX
ejpam-2461	214	8	therefore	therefore	ADV
ejpam-2461	214	9	be	be	AUX
ejpam-2461	214	10	rewritten	rewrite	VERB
ejpam-2461	214	11	as	as	ADP
ejpam-2461	214	12	r(s)g(s	r(s)g(s	NOUN
ejpam-2461	214	13	)	)	PUNCT
ejpam-2461	215	1	=	=	SYM
ejpam-2461	215	2	m−1	m−1	PROPN
ejpam-2461	215	3	∑	∑	PUNCT
ejpam-2461	215	4	j=0	j=0	PROPN
ejpam-2461	215	5	c	c	PROPN
ejpam-2461	215	6	j	j	PROPN
ejpam-2461	215	7	(	(	PUNCT
ejpam-2461	215	8	1−	1−	NUM
ejpam-2461	215	9	κs−	κs−	SYM
ejpam-2461	215	10	ϑ	ϑ	X
ejpam-2461	215	11	)	)	PUNCT
ejpam-2461	215	12	j	j	PROPN
ejpam-2461	216	1	+	+	CCONJ
ejpam-2461	216	2	ρm	ρm	PROPN
ejpam-2461	216	3	(	(	PUNCT
ejpam-2461	216	4	s	s	NOUN
ejpam-2461	216	5	)	)	PUNCT
ejpam-2461	216	6	(	(	PUNCT
ejpam-2461	216	7	1−	1−	NUM
ejpam-2461	216	8	κs−	κs−	NOUN
ejpam-2461	216	9	ϑ)m	ϑ)m	X
ejpam-2461	216	10	(	(	PUNCT
ejpam-2461	216	11	27	27	NUM
ejpam-2461	216	12	)	)	PUNCT
ejpam-2461	216	13	as	as	ADP
ejpam-2461	216	14	|s|	|s|	NOUN
ejpam-2461	216	15	→∞	→∞	PROPN
ejpam-2461	216	16	in	in	ADP
ejpam-2461	216	17	|arg	|arg	NOUN
ejpam-2461	216	18	s|	s|	VERB
ejpam-2461	216	19	<	<	X
ejpam-2461	216	20	π	π	PROPN
ejpam-2461	216	21	,	,	PUNCT
ejpam-2461	216	22	where	where	SCONJ
ejpam-2461	216	23	r(s	r(s	NOUN
ejpam-2461	216	24	)	)	PUNCT
ejpam-2461	216	25	=	=	SYM
ejpam-2461	216	26	e(ps;α	e(ps;α	NOUN
ejpam-2461	216	27	)	)	PUNCT
ejpam-2461	216	28	e(s	e(s	PROPN
ejpam-2461	216	29	;	;	PUNCT
ejpam-2461	216	30	1)e(κs;ϑ	1)e(κs;ϑ	NUM
ejpam-2461	216	31	)	)	PUNCT
ejpam-2461	216	32	,	,	PUNCT
ejpam-2461	216	33	g(s	g(s	NOUN
ejpam-2461	216	34	)	)	PUNCT
ejpam-2461	216	35	=	=	SYM
ejpam-2461	216	36	γ∗(α+	γ∗(α+	PRON
ejpam-2461	216	37	ps	ps	NOUN
ejpam-2461	216	38	)	)	PUNCT
ejpam-2461	216	39	γ∗(1	γ∗(1	PROPN
ejpam-2461	216	40	+	+	CCONJ
ejpam-2461	216	41	s)γ∗(κs+	s)γ∗(κs+	PROPN
ejpam-2461	216	42	ϑ	ϑ	NOUN
ejpam-2461	216	43	)	)	PUNCT
ejpam-2461	216	44	.	.	PUNCT
ejpam-2461	217	1	we	we	PRON
ejpam-2461	217	2	now	now	ADV
ejpam-2461	217	3	let	let	VERB
ejpam-2461	217	4	ξ	ξ	X
ejpam-2461	217	5	:	:	PUNCT
ejpam-2461	217	6	=	=	SYM
ejpam-2461	217	7	(	(	PUNCT
ejpam-2461	217	8	κs)−1	κs)−1	PRON
ejpam-2461	217	9	and	and	CCONJ
ejpam-2461	217	10	expand	expand	VERB
ejpam-2461	217	11	r(s	r(s	NUM
ejpam-2461	217	12	)	)	PUNCT
ejpam-2461	217	13	and	and	CCONJ
ejpam-2461	217	14	g(s	g(	NOUN
ejpam-2461	217	15	)	)	PUNCT
ejpam-2461	217	16	for	for	ADP
ejpam-2461	217	17	ξ→	ξ→	PROPN
ejpam-2461	217	18	0	0	NUM
ejpam-2461	217	19	making	make	VERB
ejpam-2461	217	20	use	use	NOUN
ejpam-2461	217	21	of	of	ADP
ejpam-2461	217	22	the	the	DET
ejpam-2461	217	23	well	well	ADV
ejpam-2461	217	24	-	-	PUNCT
ejpam-2461	217	25	known	know	VERB
ejpam-2461	217	26	expansion	expansion	NOUN
ejpam-2461	217	27	[	[	X
ejpam-2461	217	28	5	5	NUM
ejpam-2461	217	29	,	,	PUNCT
ejpam-2461	217	30	p.	p.	NOUN
ejpam-2461	217	31	71	71	NUM
ejpam-2461	217	32	]	]	SYM
ejpam-2461	217	33	γ∗(z)∼	γ∗(z)∼	X
ejpam-2461	217	34	∞	∞	PROPN
ejpam-2461	217	35	∑	∑	PROPN
ejpam-2461	217	36	k=0	k=0	X
ejpam-2461	217	37	(	(	PUNCT
ejpam-2461	217	38	−)kγkz−k	−)kγkz−k	NOUN
ejpam-2461	217	39	(	(	PUNCT
ejpam-2461	217	40	|z|	|z|	NOUN
ejpam-2461	217	41	→∞	→∞	NOUN
ejpam-2461	217	42	;	;	PUNCT
ejpam-2461	217	43	|arg	|arg	VERB
ejpam-2461	217	44	z|	z|	PROPN
ejpam-2461	217	45	<	<	X
ejpam-2461	217	46	π	π	PROPN
ejpam-2461	217	47	)	)	PUNCT
ejpam-2461	217	48	,	,	PUNCT
ejpam-2461	217	49	r.	r.	PROPN
ejpam-2461	217	50	paris	paris	PROPN
ejpam-2461	217	51	/	/	SYM
ejpam-2461	217	52	eur	eur	PROPN
ejpam-2461	217	53	.	.	PUNCT
ejpam-2461	218	1	j.	j.	PROPN
ejpam-2461	218	2	pure	pure	PROPN
ejpam-2461	218	3	appl	appl	PROPN
ejpam-2461	218	4	.	.	PROPN
ejpam-2461	218	5	math	math	PROPN
ejpam-2461	218	6	,	,	PUNCT
ejpam-2461	218	7	9	9	NUM
ejpam-2461	218	8	(	(	PUNCT
ejpam-2461	218	9	2016	2016	NUM
ejpam-2461	218	10	)	)	PUNCT
ejpam-2461	218	11	,	,	PUNCT
ejpam-2461	218	12	3	3	NUM
ejpam-2461	218	13	-	-	SYM
ejpam-2461	218	14	18	18	NUM
ejpam-2461	218	15	13	13	NUM
ejpam-2461	218	16	where	where	SCONJ
ejpam-2461	218	17	γk	γk	PROPN
ejpam-2461	218	18	are	be	AUX
ejpam-2461	218	19	the	the	DET
ejpam-2461	218	20	stirling	stirling	NOUN
ejpam-2461	218	21	coefficients	coefficient	NOUN
ejpam-2461	218	22	,	,	PUNCT
ejpam-2461	218	23	with	with	ADP
ejpam-2461	218	24	γ0	γ0	NOUN
ejpam-2461	218	25	=	=	SYM
ejpam-2461	218	26	1	1	NUM
ejpam-2461	218	27	,	,	PUNCT
ejpam-2461	218	28	γ1	γ1	NOUN
ejpam-2461	218	29	=	=	SYM
ejpam-2461	218	30	−	−	PROPN
ejpam-2461	218	31	1	1	NUM
ejpam-2461	218	32	12	12	NUM
ejpam-2461	218	33	,	,	PUNCT
ejpam-2461	218	34	γ2	γ2	NOUN
ejpam-2461	218	35	=	=	SYM
ejpam-2461	218	36	1	1	NUM
ejpam-2461	218	37	288	288	NUM
ejpam-2461	218	38	,	,	PUNCT
ejpam-2461	218	39	γ3	γ3	NOUN
ejpam-2461	218	40	=	=	SYM
ejpam-2461	218	41	139	139	NUM
ejpam-2461	218	42	51840	51840	NUM
ejpam-2461	218	43	,	,	PUNCT
ejpam-2461	218	44	γ4	γ4	NOUN
ejpam-2461	218	45	=	=	SYM
ejpam-2461	218	46	−	−	PROPN
ejpam-2461	218	47	571	571	NUM
ejpam-2461	218	48	2488320	2488320	NUM
ejpam-2461	218	49	,	,	PUNCT
ejpam-2461	218	50	.	.	PUNCT
ejpam-2461	218	51	.	.	PUNCT
ejpam-2461	218	52	.	.	PUNCT
ejpam-2461	219	1	.	.	PUNCT
ejpam-2461	220	1	after	after	ADP
ejpam-2461	220	2	some	some	DET
ejpam-2461	220	3	straightforward	straightforward	ADJ
ejpam-2461	220	4	algebra	algebra	NOUN
ejpam-2461	220	5	we	we	PRON
ejpam-2461	220	6	find	find	VERB
ejpam-2461	220	7	that	that	SCONJ
ejpam-2461	220	8	r(s	r(s	NOUN
ejpam-2461	220	9	)	)	PUNCT
ejpam-2461	220	10	=	=	PUNCT
ejpam-2461	220	11	1	1	NUM
ejpam-2461	220	12	+	+	SYM
ejpam-2461	220	13	ξ	ξ	SYM
ejpam-2461	220	14	2	2	NUM
ejpam-2461	220	15	§	§	PROPN
ejpam-2461	220	16	α(α−	α(α−	PROPN
ejpam-2461	220	17	1)κ	1)κ	NUM
ejpam-2461	220	18	p	p	NOUN
ejpam-2461	220	19	−	−	NOUN
ejpam-2461	220	20	ϑ(ϑ−	ϑ(ϑ−	NOUN
ejpam-2461	220	21	1	1	NUM
ejpam-2461	220	22	)	)	PUNCT
ejpam-2461	220	23	ª	ª	VERB
ejpam-2461	220	24	+	+	NOUN
ejpam-2461	220	25	o(ξ2	o(ξ2	NOUN
ejpam-2461	220	26	)	)	PUNCT
ejpam-2461	220	27	,	,	PUNCT
ejpam-2461	220	28	g(s	g(s	NOUN
ejpam-2461	220	29	)	)	PUNCT
ejpam-2461	220	30	=	=	PUNCT
ejpam-2461	220	31	1	1	NUM
ejpam-2461	220	32	+	+	SYM
ejpam-2461	220	33	ξ	ξ	SYM
ejpam-2461	220	34	12	12	NUM
ejpam-2461	220	35	�	�	NOUN
ejpam-2461	220	36	1−	1−	NUM
ejpam-2461	220	37	p−	p−	NOUN
ejpam-2461	220	38	1	1	NUM
ejpam-2461	220	39	p	p	X
ejpam-2461	220	40	�	�	PROPN
ejpam-2461	220	41	+	+	PROPN
ejpam-2461	220	42	o(ξ2	o(ξ2	NOUN
ejpam-2461	220	43	)	)	PUNCT
ejpam-2461	220	44	,	,	PUNCT
ejpam-2461	220	45	so	so	SCONJ
ejpam-2461	220	46	that	that	SCONJ
ejpam-2461	220	47	upon	upon	SCONJ
ejpam-2461	220	48	equating	equate	VERB
ejpam-2461	220	49	coefficients	coefficient	NOUN
ejpam-2461	220	50	of	of	ADP
ejpam-2461	220	51	ξ	ξ	PROPN
ejpam-2461	220	52	in	in	ADP
ejpam-2461	220	53	(	(	PUNCT
ejpam-2461	220	54	27	27	NUM
ejpam-2461	220	55	)	)	PUNCT
ejpam-2461	220	56	)	)	PUNCT
ejpam-2461	220	57	we	we	PRON
ejpam-2461	220	58	can	can	AUX
ejpam-2461	220	59	obtain	obtain	VERB
ejpam-2461	220	60	c1	c1	PROPN
ejpam-2461	220	61	.	.	PUNCT
ejpam-2461	221	1	the	the	DET
ejpam-2461	221	2	higher	high	ADJ
ejpam-2461	221	3	coefficients	coefficient	NOUN
ejpam-2461	221	4	can	can	AUX
ejpam-2461	221	5	be	be	AUX
ejpam-2461	221	6	obtained	obtain	VERB
ejpam-2461	221	7	by	by	ADP
ejpam-2461	221	8	matching	match	VERB
ejpam-2461	221	9	coefficients	coefficient	NOUN
ejpam-2461	221	10	recursively	recursively	ADV
ejpam-2461	221	11	with	with	ADP
ejpam-2461	221	12	the	the	DET
ejpam-2461	221	13	aid	aid	NOUN
ejpam-2461	221	14	of	of	ADP
ejpam-2461	221	15	mathematica	mathematica	PROPN
ejpam-2461	221	16	to	to	PART
ejpam-2461	221	17	find	find	VERB
ejpam-2461	221	18	[	[	X
ejpam-2461	221	19	5	5	NUM
ejpam-2461	221	20	,	,	PUNCT
ejpam-2461	221	21	p.	p.	NOUN
ejpam-2461	221	22	47	47	NUM
ejpam-2461	221	23	]	]	X
ejpam-2461	222	1	c0	c0	PROPN
ejpam-2461	222	2	=	=	PROPN
ejpam-2461	222	3	1	1	NUM
ejpam-2461	222	4	,	,	PUNCT
ejpam-2461	222	5	c1	c1	NOUN
ejpam-2461	222	6	=	=	NOUN
ejpam-2461	222	7	1	1	NUM
ejpam-2461	222	8	24p	24p	NOUN
ejpam-2461	222	9	(	(	PUNCT
ejpam-2461	222	10	2−	2−	NUM
ejpam-2461	222	11	5p+	5p+	NUM
ejpam-2461	222	12	2p2	2p2	NUM
ejpam-2461	222	13	−	−	NOUN
ejpam-2461	222	14	12w+	12w+	NUM
ejpam-2461	222	15	12pw+	12pw+	NUM
ejpam-2461	222	16	12w2	12w2	NUM
ejpam-2461	222	17	)	)	PUNCT
ejpam-2461	222	18	,	,	PUNCT
ejpam-2461	222	19	c2	c2	PROPN
ejpam-2461	222	20	=	=	SYM
ejpam-2461	222	21	1	1	NUM
ejpam-2461	222	22	1152p2	1152p2	NUM
ejpam-2461	222	23	(	(	PUNCT
ejpam-2461	222	24	4	4	NUM
ejpam-2461	222	25	+	+	NUM
ejpam-2461	222	26	28p−	28p−	NUM
ejpam-2461	222	27	87p2	87p2	NUM
ejpam-2461	222	28	+	+	NUM
ejpam-2461	222	29	28p3	28p3	NUM
ejpam-2461	222	30	+	+	NUM
ejpam-2461	222	31	4p4	4p4	NUM
ejpam-2461	222	32	+	+	SYM
ejpam-2461	222	33	48w−	48w−	NUM
ejpam-2461	222	34	216pw+	216pw+	NUM
ejpam-2461	222	35	24p2w+	24p2w+	NOUN
ejpam-2461	223	1	144p3w	144p3w	NUM
ejpam-2461	223	2	−96w2	−96w2	PUNCT
ejpam-2461	224	1	−	−	PROPN
ejpam-2461	224	2	120pw2	120pw2	NUM
ejpam-2461	225	1	+	+	NUM
ejpam-2461	225	2	480p2w2	480p2w2	NUM
ejpam-2461	225	3	−	−	NOUN
ejpam-2461	225	4	96w3	96w3	NUM
ejpam-2461	225	5	+	+	CCONJ
ejpam-2461	225	6	480pw3	480pw3	NUM
ejpam-2461	225	7	+	+	NUM
ejpam-2461	225	8	144w4	144w4	NUM
ejpam-2461	225	9	)	)	PUNCT
ejpam-2461	225	10	,	,	PUNCT
ejpam-2461	225	11	.	.	PUNCT
ejpam-2461	225	12	.	.	PUNCT
ejpam-2461	225	13	.	.	PUNCT
ejpam-2461	225	14	.	.	PUNCT
ejpam-2461	226	1	(	(	PUNCT
ejpam-2461	226	2	28	28	NUM
ejpam-2461	226	3	)	)	PUNCT
ejpam-2461	226	4	the	the	DET
ejpam-2461	226	5	rapidly	rapidly	ADV
ejpam-2461	226	6	increasing	increase	VERB
ejpam-2461	226	7	complexity	complexity	NOUN
ejpam-2461	226	8	of	of	ADP
ejpam-2461	226	9	the	the	DET
ejpam-2461	226	10	coefficients	coefficient	NOUN
ejpam-2461	226	11	with	with	ADP
ejpam-2461	226	12	j	j	PROPN
ejpam-2461	226	13	≥	≥	NUM
ejpam-2461	226	14	3	3	NUM
ejpam-2461	226	15	prevents	prevent	VERB
ejpam-2461	226	16	their	their	PRON
ejpam-2461	226	17	presentation	presentation	NOUN
ejpam-2461	226	18	.	.	PUNCT
ejpam-2461	227	1	however	however	ADV
ejpam-2461	227	2	,	,	PUNCT
ejpam-2461	227	3	this	this	DET
ejpam-2461	227	4	procedure	procedure	NOUN
ejpam-2461	227	5	is	be	AUX
ejpam-2461	227	6	found	find	VERB
ejpam-2461	227	7	to	to	PART
ejpam-2461	227	8	work	work	VERB
ejpam-2461	227	9	well	well	ADV
ejpam-2461	227	10	in	in	ADP
ejpam-2461	227	11	specific	specific	ADJ
ejpam-2461	227	12	cases	case	NOUN
ejpam-2461	227	13	when	when	SCONJ
ejpam-2461	227	14	the	the	DET
ejpam-2461	227	15	various	various	ADJ
ejpam-2461	227	16	parameters	parameter	NOUN
ejpam-2461	227	17	have	have	VERB
ejpam-2461	227	18	numerical	numerical	ADJ
ejpam-2461	227	19	values	value	NOUN
ejpam-2461	227	20	,	,	PUNCT
ejpam-2461	227	21	where	where	SCONJ
ejpam-2461	227	22	up	up	ADP
ejpam-2461	227	23	to	to	ADP
ejpam-2461	227	24	a	a	DET
ejpam-2461	227	25	maximum	maximum	NOUN
ejpam-2461	227	26	of	of	ADP
ejpam-2461	227	27	100	100	NUM
ejpam-2461	227	28	coefficients	coefficient	NOUN
ejpam-2461	227	29	have	have	AUX
ejpam-2461	227	30	been	be	AUX
ejpam-2461	227	31	so	so	ADV
ejpam-2461	227	32	calculated	calculate	VERB
ejpam-2461	227	33	.	.	PUNCT
ejpam-2461	228	1	in	in	ADP
ejpam-2461	228	2	table	table	NOUN
ejpam-2461	228	3	1	1	NUM
ejpam-2461	228	4	we	we	PRON
ejpam-2461	228	5	present	present	VERB
ejpam-2461	228	6	the	the	DET
ejpam-2461	228	7	values‡	values‡	NOUN
ejpam-2461	228	8	of	of	ADP
ejpam-2461	228	9	the	the	DET
ejpam-2461	228	10	coefficients	coefficient	NOUN
ejpam-2461	228	11	c	c	PROPN
ejpam-2461	228	12	j	j	PROPN
ejpam-2461	228	13	for	for	ADP
ejpam-2461	228	14	1	1	NUM
ejpam-2461	228	15	≤	≤	NUM
ejpam-2461	229	1	j	j	PROPN
ejpam-2461	229	2	≤	≤	ADV
ejpam-2461	229	3	8	8	NUM
ejpam-2461	229	4	in	in	ADP
ejpam-2461	229	5	the	the	DET
ejpam-2461	229	6	specific	specific	ADJ
ejpam-2461	229	7	examples	example	NOUN
ejpam-2461	229	8	considered	consider	VERB
ejpam-2461	229	9	in	in	ADP
ejpam-2461	229	10	section	section	NOUN
ejpam-2461	229	11	5	5	NUM
ejpam-2461	229	12	.	.	PUNCT
ejpam-2461	229	13	table	table	NOUN
ejpam-2461	229	14	1	1	NUM
ejpam-2461	229	15	:	:	PUNCT
ejpam-2461	229	16	the	the	DET
ejpam-2461	229	17	coefficients	coefficient	NOUN
ejpam-2461	229	18	c	c	PROPN
ejpam-2461	229	19	j	j	PROPN
ejpam-2461	229	20	(	(	PUNCT
ejpam-2461	229	21	1≤	1≤	NUM
ejpam-2461	229	22	j	j	PROPN
ejpam-2461	229	23	≤	≤	PROPN
ejpam-2461	229	24	8)	8)	NUM
ejpam-2461	229	25	for	for	ADP
ejpam-2461	229	26	different	different	ADJ
ejpam-2461	229	27	p	p	NOUN
ejpam-2461	229	28	and	and	CCONJ
ejpam-2461	229	29	w.	w.	PROPN
ejpam-2461	229	30	j	j	PROPN
ejpam-2461	230	1	p	p	X
ejpam-2461	230	2	=	=	PROPN
ejpam-2461	230	3	4	4	NUM
ejpam-2461	230	4	,	,	PUNCT
ejpam-2461	230	5	w=	w=	NOUN
ejpam-2461	230	6	2	2	NUM
ejpam-2461	230	7	p	p	NOUN
ejpam-2461	230	8	=	=	NOUN
ejpam-2461	230	9	4	4	NUM
ejpam-2461	230	10	,	,	PUNCT
ejpam-2461	230	11	w=	w=	AUX
ejpam-2461	230	12	4	4	NUM
ejpam-2461	230	13	p	p	NOUN
ejpam-2461	230	14	=	=	NOUN
ejpam-2461	230	15	6	6	NUM
ejpam-2461	230	16	,	,	PUNCT
ejpam-2461	230	17	w=	w=	NOUN
ejpam-2461	230	18	2	2	NUM
ejpam-2461	230	19	p	p	NOUN
ejpam-2461	230	20	=	=	SYM
ejpam-2461	230	21	6	6	NUM
ejpam-2461	230	22	,	,	PUNCT
ejpam-2461	230	23	w=	w=	NOUN
ejpam-2461	230	24	4	4	NUM
ejpam-2461	230	25	1	1	NUM
ejpam-2461	230	26	1.395833	1.395833	NUM
ejpam-2461	230	27	(	(	PUNCT
ejpam-2461	230	28	0	0	NUM
ejpam-2461	230	29	)	)	PUNCT
ejpam-2461	230	30	3.645833	3.645833	NUM
ejpam-2461	230	31	(	(	PUNCT
ejpam-2461	230	32	0	0	NUM
ejpam-2461	230	33	)	)	PUNCT
ejpam-2461	230	34	1.472222	1.472222	NUM
ejpam-2461	230	35	(	(	PUNCT
ejpam-2461	230	36	0	0	NUM
ejpam-2461	230	37	)	)	PUNCT
ejpam-2461	230	38	3.305556	3.305556	NUM
ejpam-2461	230	39	(	(	PUNCT
ejpam-2461	230	40	0	0	NUM
ejpam-2461	230	41	)	)	PUNCT
ejpam-2461	230	42	2	2	NUM
ejpam-2461	230	43	3.495009	3.495009	NUM
ejpam-2461	230	44	(	(	PUNCT
ejpam-2461	230	45	0	0	NUM
ejpam-2461	230	46	)	)	PUNCT
ejpam-2461	230	47	1.648980	1.648980	NUM
ejpam-2461	230	48	(	(	PUNCT
ejpam-2461	230	49	1	1	NUM
ejpam-2461	230	50	)	)	PUNCT
ejpam-2461	230	51	3.861497	3.861497	NUM
ejpam-2461	230	52	(	(	PUNCT
ejpam-2461	230	53	0	0	NUM
ejpam-2461	230	54	)	)	PUNCT
ejpam-2461	230	55	1.469946	1.469946	NUM
ejpam-2461	230	56	(	(	PUNCT
ejpam-2461	230	57	1	1	NUM
ejpam-2461	230	58	)	)	PUNCT
ejpam-2461	230	59	3	3	NUM
ejpam-2461	230	60	1.230179	1.230179	NUM
ejpam-2461	230	61	(	(	PUNCT
ejpam-2461	230	62	1	1	NUM
ejpam-2461	230	63	)	)	PUNCT
ejpam-2461	230	64	9.075366	9.075366	NUM
ejpam-2461	230	65	(	(	PUNCT
ejpam-2461	230	66	1	1	NUM
ejpam-2461	230	67	)	)	PUNCT
ejpam-2461	230	68	1.380091	1.380091	NUM
ejpam-2461	230	69	(	(	PUNCT
ejpam-2461	230	70	1	1	NUM
ejpam-2461	230	71	)	)	PUNCT
ejpam-2461	230	72	8.081628	8.081628	NUM
ejpam-2461	230	73	(	(	PUNCT
ejpam-2461	230	74	1	1	NUM
ejpam-2461	230	75	)	)	PUNCT
ejpam-2461	230	76	4	4	NUM
ejpam-2461	230	77	5.555372	5.555372	NUM
ejpam-2461	230	78	(	(	PUNCT
ejpam-2461	230	79	1	1	NUM
ejpam-2461	230	80	)	)	PUNCT
ejpam-2461	230	81	5.899040	5.899040	NUM
ejpam-2461	230	82	(	(	PUNCT
ejpam-2461	230	83	2	2	NUM
ejpam-2461	230	84	)	)	PUNCT
ejpam-2461	230	85	6.207979	6.207979	NUM
ejpam-2461	230	86	(	(	PUNCT
ejpam-2461	230	87	1	1	NUM
ejpam-2461	230	88	)	)	PUNCT
ejpam-2461	230	89	5.260968	5.260968	NUM
ejpam-2461	230	90	(	(	PUNCT
ejpam-2461	230	91	2	2	NUM
ejpam-2461	230	92	)	)	PUNCT
ejpam-2461	230	93	5	5	NUM
ejpam-2461	230	94	3.060544	3.060544	NUM
ejpam-2461	230	95	(	(	PUNCT
ejpam-2461	230	96	2	2	NUM
ejpam-2461	230	97	)	)	PUNCT
ejpam-2461	230	98	4.424055	4.424055	NUM
ejpam-2461	230	99	(	(	PUNCT
ejpam-2461	230	100	3	3	NUM
ejpam-2461	230	101	)	)	PUNCT
ejpam-2461	230	102	3.387328	3.387328	NUM
ejpam-2461	230	103	(	(	PUNCT
ejpam-2461	230	104	2	2	NUM
ejpam-2461	230	105	)	)	PUNCT
ejpam-2461	230	106	3.949570	3.949570	NUM
ejpam-2461	230	107	(	(	PUNCT
ejpam-2461	230	108	3	3	NUM
ejpam-2461	230	109	)	)	PUNCT
ejpam-2461	230	110	6	6	NUM
ejpam-2461	230	111	1.990604	1.990604	NUM
ejpam-2461	230	112	(	(	PUNCT
ejpam-2461	230	113	3	3	NUM
ejpam-2461	230	114	)	)	PUNCT
ejpam-2461	230	115	3.760330	3.760330	NUM
ejpam-2461	230	116	(	(	PUNCT
ejpam-2461	230	117	4	4	NUM
ejpam-2461	230	118	)	)	PUNCT
ejpam-2461	230	119	2.188492	2.188492	NUM
ejpam-2461	230	120	(	(	PUNCT
ejpam-2461	230	121	3	3	NUM
ejpam-2461	230	122	)	)	PUNCT
ejpam-2461	230	123	3.358058	3.358058	NUM
ejpam-2461	230	124	(	(	PUNCT
ejpam-2461	230	125	4	4	NUM
ejpam-2461	230	126	)	)	PUNCT
ejpam-2461	230	127	7	7	NUM
ejpam-2461	230	128	1.493190	1.493190	NUM
ejpam-2461	230	129	(	(	PUNCT
ejpam-2461	230	130	4	4	NUM
ejpam-2461	230	131	)	)	PUNCT
ejpam-2461	230	132	3.572267	3.572267	NUM
ejpam-2461	230	133	(	(	PUNCT
ejpam-2461	230	134	5	5	NUM
ejpam-2461	230	135	)	)	PUNCT
ejpam-2461	230	136	1.639364	1.639364	NUM
ejpam-2461	230	137	(	(	PUNCT
ejpam-2461	230	138	4	4	NUM
ejpam-2461	230	139	)	)	PUNCT
ejpam-2461	230	140	3.189927	3.189927	NUM
ejpam-2461	230	141	(	(	PUNCT
ejpam-2461	230	142	5	5	NUM
ejpam-2461	230	143	)	)	PUNCT
ejpam-2461	230	144	8	8	NUM
ejpam-2461	230	145	1.269216	1.269216	NUM
ejpam-2461	230	146	(	(	PUNCT
ejpam-2461	230	147	5	5	NUM
ejpam-2461	230	148	)	)	PUNCT
ejpam-2461	230	149	3.750863	3.750863	NUM
ejpam-2461	230	150	(	(	PUNCT
ejpam-2461	230	151	6	6	NUM
ejpam-2461	230	152	)	)	PUNCT
ejpam-2461	230	153	1.396172	1.396172	NUM
ejpam-2461	230	154	(	(	PUNCT
ejpam-2461	230	155	5	5	NUM
ejpam-2461	230	156	)	)	PUNCT
ejpam-2461	230	157	3.348999	3.348999	NUM
ejpam-2461	230	158	(	(	PUNCT
ejpam-2461	230	159	6	6	NUM
ejpam-2461	230	160	)	)	PUNCT
ejpam-2461	230	161	when	when	SCONJ
ejpam-2461	230	162	p	p	NOUN
ejpam-2461	230	163	=	=	NOUN
ejpam-2461	230	164	2	2	NUM
ejpam-2461	230	165	,	,	PUNCT
ejpam-2461	230	166	use	use	NOUN
ejpam-2461	230	167	of	of	ADP
ejpam-2461	230	168	the	the	DET
ejpam-2461	230	169	duplication	duplication	NOUN
ejpam-2461	230	170	formula	formula	NOUN
ejpam-2461	230	171	shows	show	VERB
ejpam-2461	230	172	that	that	SCONJ
ejpam-2461	230	173	the	the	DET
ejpam-2461	230	174	ratio	ratio	NOUN
ejpam-2461	230	175	of	of	ADP
ejpam-2461	230	176	gamma	gamma	NOUN
ejpam-2461	230	177	functions	function	NOUN
ejpam-2461	230	178	in	in	ADP
ejpam-2461	230	179	(	(	PUNCT
ejpam-2461	230	180	14	14	NUM
ejpam-2461	230	181	)	)	PUNCT
ejpam-2461	230	182	becomes	become	VERB
ejpam-2461	230	183	γ(1	γ(1	PROPN
ejpam-2461	230	184	2−	2−	NUM
ejpam-2461	230	185	1	1	NUM
ejpam-2461	230	186	2	2	NUM
ejpam-2461	230	187	w+s)γ(1−	w+s)γ(1−	NOUN
ejpam-2461	230	188	1	1	NUM
ejpam-2461	230	189	2	2	NUM
ejpam-2461	230	190	w+s	w+s	NUM
ejpam-2461	230	191	)	)	PUNCT
ejpam-2461	231	1	γ(1	γ(1	PROPN
ejpam-2461	231	2	+	+	NUM
ejpam-2461	231	3	s	s	PART
ejpam-2461	231	4	)	)	PUNCT
ejpam-2461	231	5	=	=	SYM
ejpam-2461	231	6	m−1	m−1	PROPN
ejpam-2461	231	7	∑	∑	PUNCT
ejpam-2461	231	8	j=0	j=0	PROPN
ejpam-2461	231	9	(	(	PUNCT
ejpam-2461	231	10	−	−	NOUN
ejpam-2461	231	11	)	)	PUNCT
ejpam-2461	231	12	jc	jc	PROPN
ejpam-2461	231	13	jγ(s+	jγ(s+	PROPN
ejpam-2461	231	14	1	1	NUM
ejpam-2461	231	15	2	2	NUM
ejpam-2461	231	16	−w−	−w−	NOUN
ejpam-2461	231	17	j	j	NOUN
ejpam-2461	231	18	)	)	PUNCT
ejpam-2461	232	1	+	+	NOUN
ejpam-2461	232	2	ρm	ρm	INTJ
ejpam-2461	232	3	(	(	PUNCT
ejpam-2461	232	4	s)γ(s+	s)γ(s+	NOUN
ejpam-2461	232	5	1	1	NUM
ejpam-2461	232	6	2	2	NUM
ejpam-2461	232	7	−w−m	−w−m	PROPN
ejpam-2461	232	8	)	)	PUNCT
ejpam-2461	232	9	.	.	PUNCT
ejpam-2461	233	1	‡in	‡in	PROPN
ejpam-2461	234	1	the	the	DET
ejpam-2461	234	2	tables	table	NOUN
ejpam-2461	234	3	we	we	PRON
ejpam-2461	234	4	write	write	VERB
ejpam-2461	234	5	the	the	DET
ejpam-2461	234	6	values	value	NOUN
ejpam-2461	234	7	as	as	ADP
ejpam-2461	234	8	x(y	x(y	PROPN
ejpam-2461	234	9	)	)	PUNCT
ejpam-2461	234	10	instead	instead	ADV
ejpam-2461	234	11	of	of	ADP
ejpam-2461	234	12	x	x	SYM
ejpam-2461	234	13	×	×	PROPN
ejpam-2461	234	14	10y	10y	PROPN
ejpam-2461	234	15	.	.	PUNCT
ejpam-2461	235	1	r.	r.	PROPN
ejpam-2461	235	2	paris	paris	PROPN
ejpam-2461	235	3	/	/	SYM
ejpam-2461	235	4	eur	eur	PROPN
ejpam-2461	235	5	.	.	PUNCT
ejpam-2461	236	1	j.	j.	PROPN
ejpam-2461	236	2	pure	pure	PROPN
ejpam-2461	236	3	appl	appl	PROPN
ejpam-2461	236	4	.	.	PROPN
ejpam-2461	236	5	math	math	PROPN
ejpam-2461	236	6	,	,	PUNCT
ejpam-2461	236	7	9	9	NUM
ejpam-2461	236	8	(	(	PUNCT
ejpam-2461	236	9	2016	2016	NUM
ejpam-2461	236	10	)	)	PUNCT
ejpam-2461	236	11	,	,	PUNCT
ejpam-2461	236	12	3	3	NUM
ejpam-2461	236	13	-	-	SYM
ejpam-2461	236	14	18	18	NUM
ejpam-2461	236	15	14	14	NUM
ejpam-2461	236	16	the	the	DET
ejpam-2461	236	17	coefficients	coefficient	NOUN
ejpam-2461	237	1	c	c	PROPN
ejpam-2461	237	2	j	j	PROPN
ejpam-2461	237	3	in	in	ADP
ejpam-2461	237	4	this	this	DET
ejpam-2461	237	5	case	case	NOUN
ejpam-2461	237	6	can	can	AUX
ejpam-2461	237	7	be	be	AUX
ejpam-2461	237	8	expressed	express	VERB
ejpam-2461	237	9	in	in	ADP
ejpam-2461	237	10	closed	closed	ADJ
ejpam-2461	237	11	form	form	NOUN
ejpam-2461	237	12	as	as	ADP
ejpam-2461	237	13	[	[	X
ejpam-2461	237	14	5	5	NUM
ejpam-2461	237	15	,	,	PUNCT
ejpam-2461	237	16	p.	p.	NOUN
ejpam-2461	237	17	53	53	NUM
ejpam-2461	237	18	]	]	X
ejpam-2461	238	1	c	c	PROPN
ejpam-2461	238	2	j	j	PROPN
ejpam-2461	238	3	=	=	PUNCT
ejpam-2461	238	4	(	(	PUNCT
ejpam-2461	238	5	1	1	NUM
ejpam-2461	238	6	2	2	NUM
ejpam-2461	238	7	w	w	PROPN
ejpam-2461	238	8	)	)	PUNCT
ejpam-2461	238	9	j	j	NOUN
ejpam-2461	238	10	(	(	PUNCT
ejpam-2461	238	11	1	1	NUM
ejpam-2461	238	12	2	2	NUM
ejpam-2461	238	13	+	+	CCONJ
ejpam-2461	238	14	1	1	NUM
ejpam-2461	238	15	2	2	NUM
ejpam-2461	238	16	w	w	NOUN
ejpam-2461	238	17	)	)	PUNCT
ejpam-2461	238	18	j	j	PROPN
ejpam-2461	238	19	j	j	PROPN
ejpam-2461	238	20	!	!	PUNCT
ejpam-2461	238	21	=	=	PUNCT
ejpam-2461	239	1	2−2	2−2	NUM
ejpam-2461	239	2	j(w)2	j(w)2	PROPN
ejpam-2461	239	3	j	j	PROPN
ejpam-2461	239	4	j	j	PROPN
ejpam-2461	239	5	!	!	PUNCT
ejpam-2461	240	1	(	(	PUNCT
ejpam-2461	240	2	p	p	NOUN
ejpam-2461	240	3	=	=	NOUN
ejpam-2461	240	4	2	2	NUM
ejpam-2461	240	5	)	)	PUNCT
ejpam-2461	240	6	.	.	PUNCT
ejpam-2461	241	1	(	(	PUNCT
ejpam-2461	241	2	29	29	NUM
ejpam-2461	241	3	)	)	PUNCT
ejpam-2461	241	4	finally	finally	ADV
ejpam-2461	241	5	,	,	PUNCT
ejpam-2461	241	6	we	we	PRON
ejpam-2461	241	7	mention	mention	VERB
ejpam-2461	241	8	that	that	SCONJ
ejpam-2461	241	9	when	when	SCONJ
ejpam-2461	241	10	w=	w=	PRON
ejpam-2461	241	11	0	0	PUNCT
ejpam-2461	242	1	(	(	PUNCT
ejpam-2461	242	2	corresponding	correspond	VERB
ejpam-2461	242	3	to	to	ADP
ejpam-2461	242	4	the	the	DET
ejpam-2461	242	5	euler	euler	PROPN
ejpam-2461	242	6	-	-	PUNCT
ejpam-2461	242	7	jacobi	jacobi	PROPN
ejpam-2461	242	8	series	series	PROPN
ejpam-2461	242	9	)	)	PUNCT
ejpam-2461	242	10	the	the	DET
ejpam-2461	242	11	coefficients	coefficient	NOUN
ejpam-2461	242	12	c	c	PROPN
ejpam-2461	242	13	j	j	PROPN
ejpam-2461	242	14	are	be	AUX
ejpam-2461	242	15	listed	list	VERB
ejpam-2461	242	16	for	for	ADP
ejpam-2461	242	17	p	p	PROPN
ejpam-2461	242	18	≥	≥	NUM
ejpam-2461	242	19	2	2	NUM
ejpam-2461	242	20	and	and	CCONJ
ejpam-2461	242	21	j	j	PROPN
ejpam-2461	242	22	≤	≤	ADV
ejpam-2461	242	23	8	8	NUM
ejpam-2461	242	24	in	in	ADP
ejpam-2461	242	25	[	[	X
ejpam-2461	242	26	5	5	NUM
ejpam-2461	242	27	,	,	PUNCT
ejpam-2461	242	28	p.	p.	NOUN
ejpam-2461	242	29	374	374	NUM
ejpam-2461	242	30	]	]	PUNCT
ejpam-2461	242	31	.	.	PUNCT
ejpam-2461	243	1	5	5	X
ejpam-2461	243	2	.	.	X
ejpam-2461	243	3	numerical	numerical	ADJ
ejpam-2461	243	4	results	result	NOUN
ejpam-2461	243	5	and	and	CCONJ
ejpam-2461	243	6	concluding	conclude	VERB
ejpam-2461	243	7	remarks	remark	NOUN
ejpam-2461	243	8	we	we	PRON
ejpam-2461	243	9	present	present	VERB
ejpam-2461	243	10	some	some	DET
ejpam-2461	243	11	examples	example	NOUN
ejpam-2461	243	12	of	of	ADP
ejpam-2461	243	13	the	the	DET
ejpam-2461	243	14	expansion	expansion	NOUN
ejpam-2461	243	15	of	of	ADP
ejpam-2461	243	16	sp(a	sp(a	PROPN
ejpam-2461	243	17	;	;	PUNCT
ejpam-2461	243	18	w	w	X
ejpam-2461	243	19	)	)	PUNCT
ejpam-2461	243	20	given	give	VERB
ejpam-2461	243	21	in	in	ADP
ejpam-2461	243	22	theorem	theorem	NOUN
ejpam-2461	243	23	1	1	NUM
ejpam-2461	243	24	when	when	SCONJ
ejpam-2461	243	25	p	p	PRON
ejpam-2461	243	26	and	and	CCONJ
ejpam-2461	243	27	w=	w=	NUM
ejpam-2461	243	28	2	2	NUM
ejpam-2461	243	29	m	m	NOUN
ejpam-2461	243	30	are	be	AUX
ejpam-2461	243	31	even	even	ADV
ejpam-2461	243	32	integers	integer	NOUN
ejpam-2461	243	33	.	.	PUNCT
ejpam-2461	244	1	for	for	ADP
ejpam-2461	244	2	convenience	convenience	NOUN
ejpam-2461	244	3	in	in	ADP
ejpam-2461	244	4	presentation	presentation	NOUN
ejpam-2461	244	5	,	,	PUNCT
ejpam-2461	244	6	we	we	PRON
ejpam-2461	244	7	extract	extract	VERB
ejpam-2461	244	8	the	the	DET
ejpam-2461	244	9	factor	factor	NOUN
ejpam-2461	244	10	e−z	e−z	NOUN
ejpam-2461	244	11	from	from	ADP
ejpam-2461	244	12	the	the	DET
ejpam-2461	244	13	sum	sum	NOUN
ejpam-2461	244	14	sq(z;λ	sq(z;λ	PROPN
ejpam-2461	244	15	j	j	PROPN
ejpam-2461	244	16	)	)	PUNCT
ejpam-2461	244	17	by	by	ADP
ejpam-2461	244	18	writing	write	VERB
ejpam-2461	244	19	sq(z;λ	sq(z;λ	PROPN
ejpam-2461	244	20	j	j	PROPN
ejpam-2461	244	21	)	)	PUNCT
ejpam-2461	245	1	=	=	SYM
ejpam-2461	245	2	e−z	e−z	PROPN
ejpam-2461	245	3	ŝ2(z;λ	ŝ2(z;λ	PROPN
ejpam-2461	245	4	j	j	PROPN
ejpam-2461	245	5	)	)	PUNCT
ejpam-2461	245	6	,	,	PUNCT
ejpam-2461	245	7	ŝq(z;λ	ŝq(z;λ	PROPN
ejpam-2461	245	8	j	j	PROPN
ejpam-2461	245	9	)	)	PUNCT
ejpam-2461	245	10	:	:	PUNCT
ejpam-2461	246	1	=	=	SYM
ejpam-2461	246	2	∞	∞	NUM
ejpam-2461	246	3	∑	∑	PUNCT
ejpam-2461	246	4	n=1	n=1	PROPN
ejpam-2461	246	5	e−z(nq−1	e−z(nq−1	NOUN
ejpam-2461	246	6	)	)	PUNCT
ejpam-2461	246	7	nλ	nλ	NUM
ejpam-2461	246	8	j	j	PROPN
ejpam-2461	246	9	.	.	PUNCT
ejpam-2461	247	1	it	it	PRON
ejpam-2461	247	2	follows	follow	VERB
ejpam-2461	247	3	that	that	SCONJ
ejpam-2461	247	4	,	,	PUNCT
ejpam-2461	247	5	when	when	SCONJ
ejpam-2461	247	6	q	q	X
ejpam-2461	247	7	>	>	X
ejpam-2461	247	8	0	0	PROPN
ejpam-2461	247	9	,	,	PUNCT
ejpam-2461	247	10	ŝq(z;λ	ŝq(z;λ	PROPN
ejpam-2461	247	11	j	j	PROPN
ejpam-2461	247	12	)	)	PUNCT
ejpam-2461	247	13	=	=	SYM
ejpam-2461	247	14	o(1	o(1	PROPN
ejpam-2461	247	15	)	)	PUNCT
ejpam-2461	247	16	as	as	ADP
ejpam-2461	247	17	z→∞	z→∞	NUM
ejpam-2461	247	18	in	in	ADP
ejpam-2461	247	19	|arg	|arg	VERB
ejpam-2461	247	20	z|	z|	PROPN
ejpam-2461	247	21	<	<	X
ejpam-2461	247	22	1	1	NUM
ejpam-2461	247	23	2π	2π	NOUN
ejpam-2461	247	24	.	.	PUNCT
ejpam-2461	248	1	example	example	NOUN
ejpam-2461	249	1	1	1	NUM
ejpam-2461	249	2	.	.	PUNCT
ejpam-2461	250	1	in	in	ADP
ejpam-2461	250	2	the	the	DET
ejpam-2461	250	3	case	case	NOUN
ejpam-2461	250	4	p	p	X
ejpam-2461	250	5	=	=	NOUN
ejpam-2461	250	6	2	2	NUM
ejpam-2461	250	7	,	,	PUNCT
ejpam-2461	250	8	we	we	PRON
ejpam-2461	250	9	have	have	VERB
ejpam-2461	250	10	κ	κ	NOUN
ejpam-2461	250	11	=	=	SYM
ejpam-2461	250	12	1	1	NUM
ejpam-2461	250	13	,	,	PUNCT
ejpam-2461	250	14	q	q	NOUN
ejpam-2461	250	15	=	=	SYM
ejpam-2461	250	16	2	2	NUM
ejpam-2461	250	17	,	,	PUNCT
ejpam-2461	250	18	n	n	NOUN
ejpam-2461	250	19	=	=	SYM
ejpam-2461	250	20	0	0	NUM
ejpam-2461	250	21	,	,	PUNCT
ejpam-2461	250	22	k	k	NOUN
ejpam-2461	250	23	=	=	PUNCT
ejpam-2461	250	24	m	m	PROPN
ejpam-2461	250	25	,	,	PUNCT
ejpam-2461	250	26	p∗	p∗	ADJ
ejpam-2461	250	27	=	=	SYM
ejpam-2461	250	28	2	2	NUM
ejpam-2461	250	29	,	,	PUNCT
ejpam-2461	250	30	ψ0	ψ0	ADJ
ejpam-2461	250	31	≡	≡	PROPN
ejpam-2461	250	32	0	0	PUNCT
ejpam-2461	251	1	and	and	CCONJ
ejpam-2461	251	2	x	x	X
ejpam-2461	251	3	=	=	SYM
ejpam-2461	251	4	π2	π2	PROPN
ejpam-2461	251	5	/	/	SYM
ejpam-2461	251	6	a.	a.	NOUN
ejpam-2461	251	7	the	the	DET
ejpam-2461	251	8	quantity	quantity	NOUN
ejpam-2461	251	9	δpp∗	δpp∗	NOUN
ejpam-2461	251	10	=	=	SYM
ejpam-2461	251	11	1	1	NUM
ejpam-2461	251	12	so	so	SCONJ
ejpam-2461	251	13	that	that	SCONJ
ejpam-2461	251	14	the	the	DET
ejpam-2461	251	15	exponentially	exponentially	ADV
ejpam-2461	251	16	small	small	ADJ
ejpam-2461	251	17	component	component	NOUN
ejpam-2461	251	18	of	of	ADP
ejpam-2461	251	19	s2(a	s2(a	PROPN
ejpam-2461	251	20	;	;	PUNCT
ejpam-2461	251	21	2	2	NUM
ejpam-2461	251	22	m	m	NOUN
ejpam-2461	251	23	)	)	PUNCT
ejpam-2461	251	24	consists	consist	VERB
ejpam-2461	251	25	of	of	ADP
ejpam-2461	251	26	the	the	DET
ejpam-2461	251	27	single	single	ADJ
ejpam-2461	251	28	term	term	NOUN
ejpam-2461	251	29	ê0(a	ê0(a	PROPN
ejpam-2461	251	30	;	;	PUNCT
ejpam-2461	251	31	2	2	NUM
ejpam-2461	251	32	m	m	NOUN
ejpam-2461	251	33	,	,	PUNCT
ejpam-2461	251	34	2	2	NUM
ejpam-2461	251	35	)	)	PUNCT
ejpam-2461	251	36	.	.	PUNCT
ejpam-2461	252	1	from	from	ADP
ejpam-2461	252	2	(	(	PUNCT
ejpam-2461	252	3	21	21	NUM
ejpam-2461	252	4	)	)	PUNCT
ejpam-2461	252	5	,	,	PUNCT
ejpam-2461	252	6	(	(	PUNCT
ejpam-2461	252	7	22	22	NUM
ejpam-2461	252	8	)	)	PUNCT
ejpam-2461	252	9	,	,	PUNCT
ejpam-2461	252	10	(	(	PUNCT
ejpam-2461	252	11	23	23	NUM
ejpam-2461	252	12	)	)	PUNCT
ejpam-2461	252	13	and	and	CCONJ
ejpam-2461	252	14	(	(	PUNCT
ejpam-2461	252	15	29	29	NUM
ejpam-2461	252	16	)	)	PUNCT
ejpam-2461	252	17	we	we	PRON
ejpam-2461	252	18	therefore	therefore	ADV
ejpam-2461	252	19	find	find	VERB
ejpam-2461	252	20	s2(a	s2(a	NOUN
ejpam-2461	252	21	;	;	PUNCT
ejpam-2461	252	22	2m)−1	2m)−1	NUM
ejpam-2461	252	23	2	2	NUM
ejpam-2461	252	24	γ	γ	X
ejpam-2461	252	25	�	�	PROPN
ejpam-2461	252	26	1−	1−	NUM
ejpam-2461	252	27	2	2	NUM
ejpam-2461	252	28	m	m	NUM
ejpam-2461	252	29	2	2	NUM
ejpam-2461	252	30	�	�	PROPN
ejpam-2461	252	31	am−	am−	NUM
ejpam-2461	252	32	1	1	NUM
ejpam-2461	252	33	2	2	NUM
ejpam-2461	252	34	−	−	NOUN
ejpam-2461	252	35	m	m	PROPN
ejpam-2461	252	36	∑	∑	PUNCT
ejpam-2461	252	37	k=0	k=0	PROPN
ejpam-2461	252	38	(	(	PUNCT
ejpam-2461	252	39	−)k	−)k	PROPN
ejpam-2461	252	40	k	k	PROPN
ejpam-2461	252	41	!	!	PUNCT
ejpam-2461	253	1	ζ(2m−	ζ(2m−	PROPN
ejpam-2461	253	2	2k)ak	2k)ak	NUM
ejpam-2461	253	3	=(	=(	PROPN
ejpam-2461	253	4	−)m	−)m	PROPN
ejpam-2461	253	5	�	�	PROPN
ejpam-2461	254	1	a	a	DET
ejpam-2461	254	2	π	π	PROPN
ejpam-2461	254	3	�	�	PROPN
ejpam-2461	254	4	2m−	2m−	PROPN
ejpam-2461	254	5	1	1	NUM
ejpam-2461	254	6	2	2	NUM
ejpam-2461	254	7	e−π	e−π	NUM
ejpam-2461	254	8	2	2	NUM
ejpam-2461	254	9	/	/	SYM
ejpam-2461	254	10	a	a	DET
ejpam-2461	254	11	§	§	ADJ
ejpam-2461	254	12	m−1	m−1	PROPN
ejpam-2461	254	13	∑	∑	PUNCT
ejpam-2461	254	14	j=0	j=0	PROPN
ejpam-2461	254	15	(	(	PUNCT
ejpam-2461	254	16	−	−	PROPN
ejpam-2461	254	17	)	)	PUNCT
ejpam-2461	254	18	j(2m)2	j(2m)2	PROPN
ejpam-2461	254	19	j	j	PROPN
ejpam-2461	254	20	j	j	PROPN
ejpam-2461	254	21	!	!	PROPN
ejpam-2461	254	22	�	�	PROPN
ejpam-2461	255	1	a	a	DET
ejpam-2461	255	2	4π2	4π2	NUM
ejpam-2461	255	3	�	�	PROPN
ejpam-2461	255	4	j	j	PROPN
ejpam-2461	255	5	ŝ2(π	ŝ2(π	VERB
ejpam-2461	255	6	2	2	NUM
ejpam-2461	255	7	/	/	SYM
ejpam-2461	255	8	a	a	NOUN
ejpam-2461	255	9	;	;	PUNCT
ejpam-2461	255	10	2m+	2m+	NUM
ejpam-2461	255	11	2	2	NUM
ejpam-2461	255	12	j	j	NOUN
ejpam-2461	255	13	)	)	PUNCT
ejpam-2461	256	1	+	+	ADP
ejpam-2461	256	2	o(am	o(am	X
ejpam-2461	256	3	)	)	PUNCT
ejpam-2461	257	1	ª	ª	X
ejpam-2461	257	2	(	(	PUNCT
ejpam-2461	257	3	30	30	NUM
ejpam-2461	257	4	)	)	PUNCT
ejpam-2461	257	5	as	as	ADP
ejpam-2461	257	6	a→	a→	X
ejpam-2461	257	7	0	0	NUM
ejpam-2461	257	8	in	in	ADP
ejpam-2461	257	9	the	the	DET
ejpam-2461	257	10	sector	sector	NOUN
ejpam-2461	257	11	|arg	|arg	NOUN
ejpam-2461	257	12	a|	a|	PROPN
ejpam-2461	257	13	<	<	X
ejpam-2461	257	14	1	1	NUM
ejpam-2461	257	15	2π	2π	NOUN
ejpam-2461	257	16	.	.	PUNCT
ejpam-2461	258	1	the	the	DET
ejpam-2461	258	2	expansion	expansion	NOUN
ejpam-2461	258	3	in	in	ADP
ejpam-2461	258	4	this	this	DET
ejpam-2461	258	5	case	case	NOUN
ejpam-2461	258	6	has	have	AUX
ejpam-2461	258	7	been	be	AUX
ejpam-2461	258	8	given	give	VERB
ejpam-2461	258	9	in	in	ADP
ejpam-2461	258	10	an	an	DET
ejpam-2461	258	11	equivalent	equivalent	ADJ
ejpam-2461	258	12	form	form	NOUN
ejpam-2461	258	13	in	in	ADP
ejpam-2461	258	14	[	[	X
ejpam-2461	258	15	6	6	NUM
ejpam-2461	258	16	]	]	PUNCT
ejpam-2461	258	17	.	.	PUNCT
ejpam-2461	259	1	example	example	NOUN
ejpam-2461	260	1	2	2	NUM
ejpam-2461	260	2	.	.	PUNCT
ejpam-2461	260	3	when	when	SCONJ
ejpam-2461	260	4	p	p	NOUN
ejpam-2461	260	5	=	=	NOUN
ejpam-2461	260	6	4	4	NUM
ejpam-2461	260	7	,	,	PUNCT
ejpam-2461	260	8	we	we	PRON
ejpam-2461	260	9	have	have	AUX
ejpam-2461	260	10	κ=	κ=	VERB
ejpam-2461	260	11	3	3	NUM
ejpam-2461	260	12	,	,	PUNCT
ejpam-2461	260	13	q	q	NOUN
ejpam-2461	261	1	=	=	NOUN
ejpam-2461	261	2	4	4	NUM
ejpam-2461	261	3	3	3	NUM
ejpam-2461	261	4	,	,	PUNCT
ejpam-2461	261	5	n	n	NOUN
ejpam-2461	261	6	=	=	SYM
ejpam-2461	261	7	1	1	NUM
ejpam-2461	261	8	,	,	PUNCT
ejpam-2461	261	9	k	k	X
ejpam-2461	261	10	=	=	X
ejpam-2461	261	11	⌊12	⌊12	PROPN
ejpam-2461	261	12	m⌋	m⌋	PROPN
ejpam-2461	261	13	,	,	PUNCT
ejpam-2461	261	14	p∗	p∗	NOUN
ejpam-2461	261	15	=	=	SYM
ejpam-2461	261	16	6	6	NUM
ejpam-2461	261	17	and	and	CCONJ
ejpam-2461	261	18	x	x	X
ejpam-2461	261	19	=	=	SYM
ejpam-2461	261	20	3	3	NUM
ejpam-2461	261	21	(	(	PUNCT
ejpam-2461	261	22	1	1	NUM
ejpam-2461	261	23	2	2	NUM
ejpam-2461	261	24	π)4/3	π)4/3	ADP
ejpam-2461	261	25	a−1/3	a−1/3	PROPN
ejpam-2461	261	26	,	,	PUNCT
ejpam-2461	261	27	λ	λ	X
ejpam-2461	261	28	j	j	NOUN
ejpam-2461	261	29	=	=	SYM
ejpam-2461	261	30	1	1	NUM
ejpam-2461	261	31	3	3	NUM
ejpam-2461	261	32	(	(	PUNCT
ejpam-2461	261	33	2m+	2m+	NUM
ejpam-2461	261	34	4	4	NUM
ejpam-2461	261	35	j	j	NOUN
ejpam-2461	261	36	+	+	NOUN
ejpam-2461	261	37	1	1	NUM
ejpam-2461	261	38	)	)	PUNCT
ejpam-2461	261	39	.	.	PUNCT
ejpam-2461	262	1	the	the	DET
ejpam-2461	262	2	quantity	quantity	NOUN
ejpam-2461	262	3	δpp∗	δpp∗	NOUN
ejpam-2461	262	4	=	=	SYM
ejpam-2461	262	5	0	0	PUNCT
ejpam-2461	262	6	so	so	SCONJ
ejpam-2461	262	7	that	that	SCONJ
ejpam-2461	262	8	there	there	PRON
ejpam-2461	262	9	is	be	VERB
ejpam-2461	262	10	the	the	DET
ejpam-2461	262	11	single	single	ADJ
ejpam-2461	262	12	exponentially	exponentially	ADV
ejpam-2461	262	13	small	small	ADJ
ejpam-2461	262	14	term	term	NOUN
ejpam-2461	262	15	e0(a	e0(a	NOUN
ejpam-2461	262	16	;	;	PUNCT
ejpam-2461	262	17	2	2	NUM
ejpam-2461	262	18	m	m	NOUN
ejpam-2461	262	19	,	,	PUNCT
ejpam-2461	262	20	4	4	NUM
ejpam-2461	262	21	)	)	PUNCT
ejpam-2461	262	22	with	with	ADP
ejpam-2461	262	23	ψ0	ψ0	PROPN
ejpam-2461	262	24	=	=	SYM
ejpam-2461	262	25	1	1	NUM
ejpam-2461	262	26	3	3	NUM
ejpam-2461	262	27	.	.	PUNCT
ejpam-2461	263	1	then	then	ADV
ejpam-2461	263	2	we	we	PRON
ejpam-2461	263	3	find	find	VERB
ejpam-2461	263	4	the	the	DET
ejpam-2461	263	5	expansion	expansion	NOUN
ejpam-2461	263	6	as	as	ADP
ejpam-2461	263	7	a→	a→	X
ejpam-2461	263	8	0	0	NUM
ejpam-2461	263	9	in	in	ADP
ejpam-2461	263	10	|arg	|arg	NOUN
ejpam-2461	263	11	a|	a|	PROPN
ejpam-2461	263	12	<	<	X
ejpam-2461	263	13	1	1	NUM
ejpam-2461	263	14	2π	2π	NOUN
ejpam-2461	263	15	given	give	VERB
ejpam-2461	263	16	by	by	ADP
ejpam-2461	263	17	s4(a	s4(a	PROPN
ejpam-2461	263	18	;	;	PUNCT
ejpam-2461	263	19	2m)−1	2m)−1	NUM
ejpam-2461	263	20	4	4	NUM
ejpam-2461	263	21	γ	γ	X
ejpam-2461	263	22	�	�	PROPN
ejpam-2461	263	23	1−	1−	NUM
ejpam-2461	263	24	2	2	NUM
ejpam-2461	263	25	m	m	NOUN
ejpam-2461	263	26	4	4	NUM
ejpam-2461	263	27	�	�	NOUN
ejpam-2461	263	28	a(2m−1)/4	a(2m−1)/4	NOUN
ejpam-2461	263	29	−	−	PROPN
ejpam-2461	263	30	k	k	INTJ
ejpam-2461	263	31	∑	∑	PUNCT
ejpam-2461	263	32	k=0	k=0	PROPN
ejpam-2461	263	33	(	(	PUNCT
ejpam-2461	264	1	−)k	−)k	PROPN
ejpam-2461	264	2	k	k	PROPN
ejpam-2461	264	3	!	!	PUNCT
ejpam-2461	264	4	ζ(2m−	ζ(2m−	PROPN
ejpam-2461	264	5	4k)ak	4k)ak	NUM
ejpam-2461	264	6	r.	r.	PROPN
ejpam-2461	264	7	paris	paris	PROPN
ejpam-2461	264	8	/	/	SYM
ejpam-2461	264	9	eur	eur	PROPN
ejpam-2461	264	10	.	.	PUNCT
ejpam-2461	265	1	j.	j.	PROPN
ejpam-2461	265	2	pure	pure	PROPN
ejpam-2461	265	3	appl	appl	PROPN
ejpam-2461	265	4	.	.	PROPN
ejpam-2461	265	5	math	math	PROPN
ejpam-2461	265	6	,	,	PUNCT
ejpam-2461	265	7	9	9	NUM
ejpam-2461	265	8	(	(	PUNCT
ejpam-2461	265	9	2016	2016	NUM
ejpam-2461	265	10	)	)	PUNCT
ejpam-2461	265	11	,	,	PUNCT
ejpam-2461	265	12	3	3	NUM
ejpam-2461	265	13	-	-	SYM
ejpam-2461	265	14	18	18	NUM
ejpam-2461	265	15	15	15	NUM
ejpam-2461	265	16	=(	=(	NOUN
ejpam-2461	265	17	−)m	−)m	PROPN
ejpam-2461	265	18	�	�	PROPN
ejpam-2461	265	19	2a	2a	NUM
ejpam-2461	265	20	π	π	PROPN
ejpam-2461	265	21	�	�	PROPN
ejpam-2461	265	22	(	(	PUNCT
ejpam-2461	265	23	4m−1)/6∑	4m−1)/6∑	PROPN
ejpam-2461	265	24	±	±	NUM
ejpam-2461	265	25	e−x	e−x	PROPN
ejpam-2461	265	26	e	e	PROPN
ejpam-2461	265	27	∓	∓	PROPN
ejpam-2461	265	28	1	1	NUM
ejpam-2461	265	29	3	3	NUM
ejpam-2461	265	30	πi∓	πi∓	NOUN
ejpam-2461	265	31	1	1	NUM
ejpam-2461	265	32	3πiϑ	3πiϑ	NUM
ejpam-2461	265	33	§	§	PROPN
ejpam-2461	265	34	m−1	m−1	PROPN
ejpam-2461	265	35	∑	∑	PUNCT
ejpam-2461	265	36	j=0	j=0	PROPN
ejpam-2461	265	37	(	(	PUNCT
ejpam-2461	265	38	−	−	PROPN
ejpam-2461	265	39	)	)	PUNCT
ejpam-2461	265	40	jc	jc	PROPN
ejpam-2461	265	41	j	j	PROPN
ejpam-2461	265	42	(	(	PUNCT
ejpam-2461	265	43	x	x	PROPN
ejpam-2461	265	44	e∓	e∓	PROPN
ejpam-2461	265	45	1	1	NUM
ejpam-2461	265	46	3πi	3πi	NOUN
ejpam-2461	265	47	)	)	PUNCT
ejpam-2461	265	48	j	j	NOUN
ejpam-2461	265	49	ŝ	ŝ	VERB
ejpam-2461	265	50	4	4	NUM
ejpam-2461	265	51	3	3	NUM
ejpam-2461	265	52	(	(	PUNCT
ejpam-2461	265	53	x	x	SYM
ejpam-2461	265	54	e∓	e∓	PROPN
ejpam-2461	265	55	1	1	NUM
ejpam-2461	265	56	3πi;λ	3πi;λ	NUM
ejpam-2461	265	57	j	j	NOUN
ejpam-2461	265	58	)	)	PUNCT
ejpam-2461	266	1	+	+	NOUN
ejpam-2461	266	2	o(am/3	o(am/3	ADJ
ejpam-2461	266	3	)	)	PUNCT
ejpam-2461	266	4	ª	ª	PROPN
ejpam-2461	266	5	(	(	PUNCT
ejpam-2461	266	6	31	31	NUM
ejpam-2461	266	7	)	)	PUNCT
ejpam-2461	266	8	where	where	SCONJ
ejpam-2461	266	9	the	the	DET
ejpam-2461	266	10	coefficients	coefficient	NOUN
ejpam-2461	267	1	c	c	PROPN
ejpam-2461	267	2	j	j	PROPN
ejpam-2461	267	3	≡	≡	PROPN
ejpam-2461	267	4	c	c	PROPN
ejpam-2461	267	5	j(2	j(2	PROPN
ejpam-2461	267	6	m	m	PROPN
ejpam-2461	267	7	,	,	PUNCT
ejpam-2461	267	8	4	4	NUM
ejpam-2461	267	9	)	)	PUNCT
ejpam-2461	267	10	can	can	AUX
ejpam-2461	267	11	be	be	AUX
ejpam-2461	267	12	obtained	obtain	VERB
ejpam-2461	267	13	from	from	ADP
ejpam-2461	267	14	(	(	PUNCT
ejpam-2461	267	15	28	28	NUM
ejpam-2461	267	16	)	)	PUNCT
ejpam-2461	267	17	and	and	CCONJ
ejpam-2461	267	18	[	[	X
ejpam-2461	267	19	5	5	NUM
ejpam-2461	267	20	,	,	PUNCT
ejpam-2461	267	21	p.	p.	NOUN
ejpam-2461	267	22	47	47	NUM
ejpam-2461	267	23	]	]	PUNCT
ejpam-2461	267	24	as	as	ADP
ejpam-2461	267	25	c0	c0	PROPN
ejpam-2461	267	26	=	=	PROPN
ejpam-2461	267	27	1	1	NUM
ejpam-2461	267	28	,	,	PUNCT
ejpam-2461	267	29	c1	c1	NOUN
ejpam-2461	267	30	=	=	NOUN
ejpam-2461	267	31	1	1	NUM
ejpam-2461	267	32	48	48	NUM
ejpam-2461	267	33	(	(	PUNCT
ejpam-2461	267	34	7	7	NUM
ejpam-2461	267	35	+	+	NUM
ejpam-2461	267	36	36m+	36m+	NUM
ejpam-2461	267	37	24m2	24m2	NUM
ejpam-2461	267	38	)	)	PUNCT
ejpam-2461	267	39	,	,	PUNCT
ejpam-2461	267	40	c2	c2	PROPN
ejpam-2461	267	41	=	=	PUNCT
ejpam-2461	267	42	1	1	NUM
ejpam-2461	267	43	4608	4608	NUM
ejpam-2461	267	44	(	(	PUNCT
ejpam-2461	267	45	385	385	NUM
ejpam-2461	267	46	+	+	NUM
ejpam-2461	267	47	4392m+	4392m+	NUM
ejpam-2461	267	48	7104m2	7104m2	NUM
ejpam-2461	267	49	+	+	CCONJ
ejpam-2461	267	50	3648m3	3648m3	NUM
ejpam-2461	267	51	+	+	NUM
ejpam-2461	267	52	576m4	576m4	NUM
ejpam-2461	267	53	)	)	PUNCT
ejpam-2461	267	54	,	,	PUNCT
ejpam-2461	267	55	c3	c3	NOUN
ejpam-2461	267	56	=	=	PUNCT
ejpam-2461	267	57	1	1	NUM
ejpam-2461	267	58	663552	663552	NUM
ejpam-2461	267	59	(	(	PUNCT
ejpam-2461	267	60	39655	39655	NUM
ejpam-2461	267	61	+	+	SYM
ejpam-2461	267	62	1191132m+	1191132m+	NUM
ejpam-2461	267	63	2970936m2	2970936m2	NUM
ejpam-2461	268	1	+	+	CCONJ
ejpam-2461	268	2	2666880m3	2666880m3	NUM
ejpam-2461	268	3	+	+	CCONJ
ejpam-2461	268	4	1080000m4	1080000m4	NUM
ejpam-2461	268	5	+	+	CCONJ
ejpam-2461	268	6	200448m5	200448m5	NUM
ejpam-2461	268	7	+	+	CCONJ
ejpam-2461	268	8	13824m6	13824m6	NUM
ejpam-2461	268	9	)	)	PUNCT
ejpam-2461	268	10	,	,	PUNCT
ejpam-2461	268	11	.	.	PUNCT
ejpam-2461	268	12	.	.	PUNCT
ejpam-2461	268	13	.	.	PUNCT
ejpam-2461	269	1	.	.	PUNCT
ejpam-2461	270	1	these	these	DET
ejpam-2461	270	2	coefficients	coefficient	NOUN
ejpam-2461	270	3	are	be	AUX
ejpam-2461	270	4	listed	list	VERB
ejpam-2461	270	5	in	in	ADP
ejpam-2461	270	6	table	table	NOUN
ejpam-2461	270	7	1	1	NUM
ejpam-2461	270	8	for	for	ADP
ejpam-2461	270	9	1≤	1≤	NUM
ejpam-2461	270	10	j	j	PROPN
ejpam-2461	270	11	≤	≤	ADV
ejpam-2461	270	12	8	8	NUM
ejpam-2461	270	13	when	when	SCONJ
ejpam-2461	270	14	m=	m=	AUX
ejpam-2461	270	15	1	1	NUM
ejpam-2461	270	16	and	and	CCONJ
ejpam-2461	270	17	m=	m=	ADJ
ejpam-2461	270	18	2	2	NUM
ejpam-2461	270	19	.	.	PUNCT
ejpam-2461	270	20	example	example	NOUN
ejpam-2461	271	1	3	3	NUM
ejpam-2461	271	2	.	.	PUNCT
ejpam-2461	271	3	when	when	SCONJ
ejpam-2461	271	4	p	p	NOUN
ejpam-2461	271	5	=	=	NOUN
ejpam-2461	271	6	6	6	NUM
ejpam-2461	271	7	,	,	PUNCT
ejpam-2461	271	8	we	we	PRON
ejpam-2461	271	9	have	have	AUX
ejpam-2461	271	10	κ=	κ=	VERB
ejpam-2461	271	11	5	5	NUM
ejpam-2461	271	12	,	,	PUNCT
ejpam-2461	271	13	q	q	NOUN
ejpam-2461	272	1	=	=	NOUN
ejpam-2461	272	2	6	6	NUM
ejpam-2461	272	3	5	5	NUM
ejpam-2461	272	4	,	,	PUNCT
ejpam-2461	272	5	n	n	NOUN
ejpam-2461	272	6	=	=	SYM
ejpam-2461	272	7	1	1	NUM
ejpam-2461	272	8	,	,	PUNCT
ejpam-2461	272	9	k	k	X
ejpam-2461	272	10	=	=	PUNCT
ejpam-2461	272	11	⌊13	⌊13	PROPN
ejpam-2461	272	12	m⌋	m⌋	PROPN
ejpam-2461	272	13	and	and	CCONJ
ejpam-2461	272	14	x	x	SYM
ejpam-2461	272	15	=	=	SYM
ejpam-2461	272	16	5	5	NUM
ejpam-2461	272	17	(	(	PUNCT
ejpam-2461	272	18	1	1	NUM
ejpam-2461	272	19	3	3	NUM
ejpam-2461	272	20	π)6/5	π)6/5	SYM
ejpam-2461	272	21	a−1/5	a−1/5	PROPN
ejpam-2461	272	22	,	,	PUNCT
ejpam-2461	272	23	λ	λ	PROPN
ejpam-2461	272	24	j	j	NOUN
ejpam-2461	272	25	=	=	SYM
ejpam-2461	272	26	1	1	NUM
ejpam-2461	272	27	5	5	NUM
ejpam-2461	272	28	(	(	PUNCT
ejpam-2461	272	29	2m+	2m+	NUM
ejpam-2461	272	30	6	6	NUM
ejpam-2461	272	31	j	j	NOUN
ejpam-2461	272	32	+	+	PROPN
ejpam-2461	272	33	2	2	NUM
ejpam-2461	272	34	)	)	PUNCT
ejpam-2461	272	35	.	.	PUNCT
ejpam-2461	273	1	in	in	ADP
ejpam-2461	273	2	this	this	DET
ejpam-2461	273	3	case	case	NOUN
ejpam-2461	273	4	p∗	p∗	ADJ
ejpam-2461	273	5	=	=	SYM
ejpam-2461	273	6	6	6	NUM
ejpam-2461	273	7	,	,	PUNCT
ejpam-2461	273	8	so	so	SCONJ
ejpam-2461	273	9	that	that	SCONJ
ejpam-2461	273	10	δpp∗	δpp∗	NOUN
ejpam-2461	273	11	=	=	SYM
ejpam-2461	273	12	1	1	NUM
ejpam-2461	273	13	and	and	CCONJ
ejpam-2461	273	14	there	there	PRON
ejpam-2461	273	15	are	be	VERB
ejpam-2461	273	16	now	now	ADV
ejpam-2461	273	17	two	two	NUM
ejpam-2461	273	18	exponentially	exponentially	ADV
ejpam-2461	273	19	small	small	ADJ
ejpam-2461	273	20	expansions	expansion	NOUN
ejpam-2461	273	21	e0(a	e0(a	NOUN
ejpam-2461	273	22	;	;	PUNCT
ejpam-2461	273	23	2	2	NUM
ejpam-2461	273	24	m	m	NOUN
ejpam-2461	273	25	,	,	PUNCT
ejpam-2461	273	26	6	6	NUM
ejpam-2461	273	27	)	)	PUNCT
ejpam-2461	273	28	,	,	PUNCT
ejpam-2461	273	29	with	with	ADP
ejpam-2461	273	30	ψ0	ψ0	ADJ
ejpam-2461	273	31	=	=	SYM
ejpam-2461	273	32	2	2	NUM
ejpam-2461	273	33	5	5	NUM
ejpam-2461	273	34	,	,	PUNCT
ejpam-2461	273	35	and	and	CCONJ
ejpam-2461	273	36	ê1(a	ê1(a	NOUN
ejpam-2461	273	37	;	;	PUNCT
ejpam-2461	273	38	2	2	NUM
ejpam-2461	273	39	m	m	NOUN
ejpam-2461	273	40	,	,	PUNCT
ejpam-2461	273	41	6	6	NUM
ejpam-2461	273	42	)	)	PUNCT
ejpam-2461	273	43	.	.	PUNCT
ejpam-2461	274	1	then	then	ADV
ejpam-2461	274	2	,	,	PUNCT
ejpam-2461	274	3	as	as	ADP
ejpam-2461	274	4	a	a	DET
ejpam-2461	274	5	→	→	SYM
ejpam-2461	274	6	0	0	NUM
ejpam-2461	274	7	in	in	ADP
ejpam-2461	274	8	|arg	|arg	NOUN
ejpam-2461	274	9	a|	a|	PROPN
ejpam-2461	274	10	<	<	X
ejpam-2461	274	11	1	1	NUM
ejpam-2461	274	12	2π	2π	NOUN
ejpam-2461	274	13	,	,	PUNCT
ejpam-2461	274	14	we	we	PRON
ejpam-2461	274	15	have	have	VERB
ejpam-2461	274	16	the	the	DET
ejpam-2461	274	17	expansion	expansion	NOUN
ejpam-2461	274	18	s6(a	s6(a	NOUN
ejpam-2461	274	19	;	;	PUNCT
ejpam-2461	274	20	2m)−1	2m)−1	NUM
ejpam-2461	274	21	6	6	NUM
ejpam-2461	274	22	γ	γ	X
ejpam-2461	274	23	�	�	PROPN
ejpam-2461	274	24	1−	1−	NUM
ejpam-2461	274	25	2	2	NUM
ejpam-2461	274	26	m	m	NOUN
ejpam-2461	274	27	6	6	NUM
ejpam-2461	274	28	�	�	PROPN
ejpam-2461	274	29	a(2m−1)/6	a(2m−1)/6	NOUN
ejpam-2461	274	30	−	−	PROPN
ejpam-2461	274	31	k	k	PROPN
ejpam-2461	274	32	∑	∑	PUNCT
ejpam-2461	274	33	k=0	k=0	PROPN
ejpam-2461	274	34	(	(	PUNCT
ejpam-2461	274	35	−)k	−)k	PROPN
ejpam-2461	274	36	k	k	PROPN
ejpam-2461	274	37	!	!	PUNCT
ejpam-2461	274	38	ζ(2m−	ζ(2m−	PROPN
ejpam-2461	275	1	6k)ak	6k)ak	NUM
ejpam-2461	275	2	=(	=(	PROPN
ejpam-2461	275	3	−)m	−)m	PROPN
ejpam-2461	275	4	�	�	PROPN
ejpam-2461	275	5	3a	3a	PROPN
ejpam-2461	275	6	π	π	PROPN
ejpam-2461	275	7	�	�	PROPN
ejpam-2461	275	8	(	(	PUNCT
ejpam-2461	275	9	4m−1)/10∑	4m−1)/10∑	NUM
ejpam-2461	275	10	±	±	NUM
ejpam-2461	275	11	e−x	e−x	PROPN
ejpam-2461	275	12	e	e	PROPN
ejpam-2461	275	13	∓	∓	PROPN
ejpam-2461	275	14	2	2	NUM
ejpam-2461	275	15	5πi∓	5πi∓	NUM
ejpam-2461	275	16	2	2	NUM
ejpam-2461	275	17	5πiϑ	5πiϑ	PROPN
ejpam-2461	275	18	§	§	PROPN
ejpam-2461	275	19	m−1	m−1	PROPN
ejpam-2461	275	20	∑	∑	PUNCT
ejpam-2461	275	21	j=0	j=0	PROPN
ejpam-2461	275	22	(	(	PUNCT
ejpam-2461	275	23	−	−	PROPN
ejpam-2461	275	24	)	)	PUNCT
ejpam-2461	275	25	jc	jc	PROPN
ejpam-2461	275	26	j	j	PROPN
ejpam-2461	275	27	(	(	PUNCT
ejpam-2461	275	28	x	x	PROPN
ejpam-2461	275	29	e∓	e∓	PROPN
ejpam-2461	275	30	2	2	NUM
ejpam-2461	275	31	5πi	5πi	NOUN
ejpam-2461	275	32	)	)	PUNCT
ejpam-2461	275	33	j	j	NOUN
ejpam-2461	275	34	ŝ	ŝ	VERB
ejpam-2461	275	35	6	6	NUM
ejpam-2461	275	36	5	5	NUM
ejpam-2461	275	37	(	(	PUNCT
ejpam-2461	275	38	x	x	SYM
ejpam-2461	275	39	e∓	e∓	PROPN
ejpam-2461	275	40	2	2	NUM
ejpam-2461	275	41	5πi;λ	5πi;λ	NUM
ejpam-2461	275	42	j	j	NOUN
ejpam-2461	275	43	)	)	PUNCT
ejpam-2461	276	1	+	+	NOUN
ejpam-2461	276	2	o(am/5	o(am/5	NOUN
ejpam-2461	276	3	)	)	PUNCT
ejpam-2461	277	1	ª	ª	PRON
ejpam-2461	277	2	+	+	CCONJ
ejpam-2461	277	3	(	(	PUNCT
ejpam-2461	277	4	−)m	−)m	PROPN
ejpam-2461	277	5	�	�	PROPN
ejpam-2461	277	6	3a	3a	PROPN
ejpam-2461	277	7	π	π	PROPN
ejpam-2461	277	8	�	�	PROPN
ejpam-2461	277	9	(	(	PUNCT
ejpam-2461	277	10	4m−1)/10	4m−1)/10	NUM
ejpam-2461	277	11	e−x	e−x	PROPN
ejpam-2461	277	12	§	§	PROPN
ejpam-2461	277	13	m−1	m−1	PROPN
ejpam-2461	277	14	∑	∑	PUNCT
ejpam-2461	277	15	j=0	j=0	PROPN
ejpam-2461	277	16	(	(	PUNCT
ejpam-2461	277	17	−	−	PROPN
ejpam-2461	277	18	)	)	PUNCT
ejpam-2461	278	1	jc	jc	PROPN
ejpam-2461	278	2	j	j	PROPN
ejpam-2461	278	3	x	x	X
ejpam-2461	278	4	j	j	PROPN
ejpam-2461	278	5	ŝ	ŝ	NUM
ejpam-2461	278	6	6	6	NUM
ejpam-2461	278	7	5	5	NUM
ejpam-2461	278	8	(	(	PUNCT
ejpam-2461	278	9	x	x	PROPN
ejpam-2461	278	10	;	;	PUNCT
ejpam-2461	278	11	λ	λ	PROPN
ejpam-2461	278	12	j	j	PROPN
ejpam-2461	278	13	)	)	PUNCT
ejpam-2461	278	14	+	+	NOUN
ejpam-2461	278	15	o(am/5	o(am/5	NOUN
ejpam-2461	278	16	)	)	PUNCT
ejpam-2461	278	17	ª	ª	X
ejpam-2461	278	18	.	.	PUNCT
ejpam-2461	279	1	(	(	PUNCT
ejpam-2461	279	2	32	32	NUM
ejpam-2461	279	3	)	)	PUNCT
ejpam-2461	279	4	the	the	DET
ejpam-2461	279	5	first	first	ADJ
ejpam-2461	279	6	few	few	ADJ
ejpam-2461	279	7	coefficients	coefficient	NOUN
ejpam-2461	279	8	c	c	PROPN
ejpam-2461	279	9	j	j	PROPN
ejpam-2461	279	10	≡	≡	PROPN
ejpam-2461	279	11	c	c	PROPN
ejpam-2461	279	12	j(2	j(2	PROPN
ejpam-2461	279	13	m	m	PROPN
ejpam-2461	279	14	,	,	PUNCT
ejpam-2461	279	15	6	6	NUM
ejpam-2461	279	16	)	)	PUNCT
ejpam-2461	279	17	are	be	AUX
ejpam-2461	279	18	c0	c0	NOUN
ejpam-2461	279	19	=	=	NOUN
ejpam-2461	279	20	1	1	NUM
ejpam-2461	279	21	,	,	PUNCT
ejpam-2461	279	22	c1	c1	NOUN
ejpam-2461	279	23	=	=	NOUN
ejpam-2461	279	24	1	1	NUM
ejpam-2461	279	25	36	36	NUM
ejpam-2461	279	26	(	(	PUNCT
ejpam-2461	279	27	11	11	NUM
ejpam-2461	279	28	+	+	NUM
ejpam-2461	279	29	30m+	30m+	NUM
ejpam-2461	279	30	12m2	12m2	NUM
ejpam-2461	279	31	)	)	PUNCT
ejpam-2461	279	32	,	,	PUNCT
ejpam-2461	279	33	c2	c2	PROPN
ejpam-2461	279	34	=	=	SYM
ejpam-2461	279	35	1	1	NUM
ejpam-2461	279	36	2592	2592	NUM
ejpam-2461	279	37	(	(	PUNCT
ejpam-2461	279	38	517	517	NUM
ejpam-2461	279	39	+	+	NUM
ejpam-2461	279	40	3840m+	3840m+	NUM
ejpam-2461	279	41	4116m2	4116m2	NUM
ejpam-2461	280	1	+	+	CCONJ
ejpam-2461	280	2	1392m3	1392m3	NUM
ejpam-2461	281	1	+	+	CCONJ
ejpam-2461	281	2	144m4	144m4	NUM
ejpam-2461	281	3	)	)	PUNCT
ejpam-2461	281	4	,	,	PUNCT
ejpam-2461	281	5	c3	c3	NOUN
ejpam-2461	281	6	=	=	PUNCT
ejpam-2461	281	7	1	1	NUM
ejpam-2461	281	8	1399680	1399680	NUM
ejpam-2461	281	9	(	(	PUNCT
ejpam-2461	281	10	−22253	−22253	ADJ
ejpam-2461	281	11	+	+	SYM
ejpam-2461	281	12	426550m+	426550m+	NUM
ejpam-2461	282	1	8181720m2	8181720m2	NOUN
ejpam-2461	283	1	+	+	CCONJ
ejpam-2461	283	2	5237640m3	5237640m3	NUM
ejpam-2461	283	3	+	+	CCONJ
ejpam-2461	283	4	1468800m4	1468800m4	NUM
ejpam-2461	283	5	+	+	CCONJ
ejpam-2461	283	6	185760m5	185760m5	NUM
ejpam-2461	283	7	+	+	NUM
ejpam-2461	283	8	8640m6	8640m6	NUM
ejpam-2461	283	9	)	)	PUNCT
ejpam-2461	283	10	.	.	PUNCT
ejpam-2461	284	1	these	these	DET
ejpam-2461	284	2	coefficients	coefficient	NOUN
ejpam-2461	284	3	are	be	AUX
ejpam-2461	284	4	listed	list	VERB
ejpam-2461	284	5	in	in	ADP
ejpam-2461	284	6	table	table	NOUN
ejpam-2461	284	7	1	1	NUM
ejpam-2461	284	8	for	for	ADP
ejpam-2461	284	9	1≤	1≤	NUM
ejpam-2461	284	10	j	j	PROPN
ejpam-2461	284	11	≤	≤	ADV
ejpam-2461	284	12	8	8	NUM
ejpam-2461	284	13	when	when	SCONJ
ejpam-2461	284	14	m=	m=	AUX
ejpam-2461	284	15	1	1	NUM
ejpam-2461	284	16	and	and	CCONJ
ejpam-2461	284	17	m=	m=	X
ejpam-2461	284	18	2	2	NUM
ejpam-2461	284	19	.	.	X
ejpam-2461	284	20	r.	r.	PROPN
ejpam-2461	284	21	paris	paris	PROPN
ejpam-2461	284	22	/	/	SYM
ejpam-2461	284	23	eur	eur	PROPN
ejpam-2461	284	24	.	.	PUNCT
ejpam-2461	285	1	j.	j.	PROPN
ejpam-2461	285	2	pure	pure	PROPN
ejpam-2461	285	3	appl	appl	PROPN
ejpam-2461	285	4	.	.	PROPN
ejpam-2461	285	5	math	math	PROPN
ejpam-2461	285	6	,	,	PUNCT
ejpam-2461	285	7	9	9	NUM
ejpam-2461	285	8	(	(	PUNCT
ejpam-2461	285	9	2016	2016	NUM
ejpam-2461	285	10	)	)	PUNCT
ejpam-2461	285	11	,	,	PUNCT
ejpam-2461	285	12	3	3	NUM
ejpam-2461	285	13	-	-	SYM
ejpam-2461	285	14	18	18	NUM
ejpam-2461	285	15	16	16	NUM
ejpam-2461	285	16	table	table	NOUN
ejpam-2461	285	17	2	2	NUM
ejpam-2461	285	18	:	:	PUNCT
ejpam-2461	285	19	values	value	NOUN
ejpam-2461	285	20	of	of	ADP
ejpam-2461	285	21	the	the	DET
ejpam-2461	285	22	absolute	absolute	ADJ
ejpam-2461	285	23	error	error	NOUN
ejpam-2461	285	24	in	in	ADP
ejpam-2461	285	25	the	the	DET
ejpam-2461	285	26	computation	computation	NOUN
ejpam-2461	285	27	of	of	ADP
ejpam-2461	285	28	sp(a	sp(a	PROPN
ejpam-2461	285	29	;	;	PUNCT
ejpam-2461	285	30	w	w	X
ejpam-2461	285	31	)	)	PUNCT
ejpam-2461	285	32	defined	define	VERB
ejpam-2461	285	33	in	in	ADP
ejpam-2461	285	34	(	(	PUNCT
ejpam-2461	285	35	33	33	NUM
ejpam-2461	285	36	)	)	PUNCT
ejpam-2461	285	37	using	use	VERB
ejpam-2461	285	38	the	the	DET
ejpam-2461	285	39	expansions	expansion	NOUN
ejpam-2461	285	40	(	(	PUNCT
ejpam-2461	285	41	30	30	NUM
ejpam-2461	285	42	)	)	PUNCT
ejpam-2461	285	43	and	and	CCONJ
ejpam-2461	285	44	(	(	PUNCT
ejpam-2461	285	45	31	31	NUM
ejpam-2461	285	46	)	)	PUNCT
ejpam-2461	285	47	.	.	PUNCT
ejpam-2461	286	1	the	the	DET
ejpam-2461	286	2	value	value	NOUN
ejpam-2461	286	3	of	of	ADP
ejpam-2461	286	4	the	the	DET
ejpam-2461	286	5	index	index	NOUN
ejpam-2461	286	6	j0	j0	PROPN
ejpam-2461	286	7	corresponds	correspond	VERB
ejpam-2461	286	8	to	to	ADP
ejpam-2461	286	9	optimal	optimal	ADJ
ejpam-2461	286	10	truncation	truncation	NOUN
ejpam-2461	286	11	of	of	ADP
ejpam-2461	286	12	the	the	DET
ejpam-2461	286	13	subdominant	subdominant	ADJ
ejpam-2461	286	14	expansion	expansion	NOUN
ejpam-2461	286	15	e0(a	e0(a	NOUN
ejpam-2461	286	16	;	;	PUNCT
ejpam-2461	286	17	w	w	PROPN
ejpam-2461	286	18	,	,	PUNCT
ejpam-2461	286	19	p	p	NOUN
ejpam-2461	286	20	)	)	PUNCT
ejpam-2461	286	21	.	.	PUNCT
ejpam-2461	287	1	p	p	X
ejpam-2461	287	2	=	=	NOUN
ejpam-2461	287	3	2	2	NUM
ejpam-2461	287	4	,	,	PUNCT
ejpam-2461	287	5	w=	w=	NOUN
ejpam-2461	287	6	2	2	NUM
ejpam-2461	287	7	p	p	NOUN
ejpam-2461	287	8	=	=	NOUN
ejpam-2461	287	9	2	2	NUM
ejpam-2461	287	10	,	,	PUNCT
ejpam-2461	287	11	w=	w=	NOUN
ejpam-2461	287	12	4	4	NUM
ejpam-2461	287	13	a	a	DET
ejpam-2461	287	14	|sp	|sp	NOUN
ejpam-2461	287	15	,	,	PUNCT
ejpam-2461	287	16	w|	w|	NOUN
ejpam-2461	287	17	|sp	|sp	NUM
ejpam-2461	287	18	,	,	PUNCT
ejpam-2461	287	19	w	w	ADP
ejpam-2461	287	20	−	−	PROPN
ejpam-2461	287	21	e0|	e0|	PROPN
ejpam-2461	287	22	j0	j0	PROPN
ejpam-2461	287	23	|sp	|sp	NUM
ejpam-2461	287	24	,	,	PUNCT
ejpam-2461	287	25	w|	w|	NOUN
ejpam-2461	287	26	|sp	|sp	NUM
ejpam-2461	287	27	,	,	PUNCT
ejpam-2461	287	28	w	w	ADP
ejpam-2461	287	29	−	−	PROPN
ejpam-2461	287	30	e0|	e0|	VERB
ejpam-2461	287	31	j0	j0	PROPN
ejpam-2461	287	32	1.00	1.00	NUM
ejpam-2461	287	33	8.146(−06	8.146(−06	NUM
ejpam-2461	287	34	)	)	PUNCT
ejpam-2461	287	35	6.637(−09	6.637(−09	NUM
ejpam-2461	287	36	)	)	PUNCT
ejpam-2461	287	37	8	8	NUM
ejpam-2461	287	38	6.252(−07	6.252(−07	NUM
ejpam-2461	287	39	)	)	PUNCT
ejpam-2461	288	1	3.642(−08	3.642(−08	NUM
ejpam-2461	288	2	)	)	PUNCT
ejpam-2461	288	3	6	6	NUM
ejpam-2461	288	4	0.75	0.75	NUM
ejpam-2461	288	5	2.031(−07	2.031(−07	NUM
ejpam-2461	288	6	)	)	PUNCT
ejpam-2461	288	7	8.089(−12	8.089(−12	NOUN
ejpam-2461	288	8	)	)	PUNCT
ejpam-2461	288	9	11	11	NUM
ejpam-2461	288	10	9.296(−09	9.296(−09	NUM
ejpam-2461	288	11	)	)	PUNCT
ejpam-2461	288	12	4.659(−11	4.659(−11	NUM
ejpam-2461	288	13	)	)	PUNCT
ejpam-2461	288	14	9	9	NUM
ejpam-2461	288	15	0.50	0.50	NUM
ejpam-2461	288	16	1.584(−10	1.584(−10	NUM
ejpam-2461	288	17	)	)	PUNCT
ejpam-2461	288	18	1.260(−17	1.260(−17	NUM
ejpam-2461	288	19	)	)	PUNCT
ejpam-2461	288	20	18	18	NUM
ejpam-2461	288	21	3.437(−12	3.437(−12	NUM
ejpam-2461	288	22	)	)	PUNCT
ejpam-2461	288	23	7.635(−17	7.635(−17	NOUN
ejpam-2461	288	24	)	)	PUNCT
ejpam-2461	288	25	16	16	NUM
ejpam-2461	288	26	0.20	0.20	NUM
ejpam-2461	288	27	5.774(−24	5.774(−24	NUM
ejpam-2461	288	28	)	)	PUNCT
ejpam-2461	288	29	1.542(−43	1.542(−43	NUM
ejpam-2461	288	30	)	)	PUNCT
ejpam-2461	288	31	47	47	NUM
ejpam-2461	288	32	2.189(−26	2.189(−26	NUM
ejpam-2461	288	33	)	)	PUNCT
ejpam-2461	288	34	9.830(−43	9.830(−43	NUM
ejpam-2461	288	35	)	)	PUNCT
ejpam-2461	288	36	45	45	NUM
ejpam-2461	288	37	0.10	0.10	NUM
ejpam-2461	288	38	7.667(−46	7.667(−46	NUM
ejpam-2461	288	39	)	)	PUNCT
ejpam-2461	288	40	1.486(−86	1.486(−86	NUM
ejpam-2461	288	41	)	)	PUNCT
ejpam-2461	288	42	97	97	NUM
ejpam-2461	288	43	7.506(−49	7.506(−49	NUM
ejpam-2461	288	44	)	)	PUNCT
ejpam-2461	288	45	9.631(−86	9.631(−86	PROPN
ejpam-2461	288	46	)	)	PUNCT
ejpam-2461	288	47	95	95	NUM
ejpam-2461	288	48	p	p	NOUN
ejpam-2461	288	49	=	=	NOUN
ejpam-2461	288	50	4	4	NUM
ejpam-2461	288	51	,	,	PUNCT
ejpam-2461	288	52	w=	w=	NOUN
ejpam-2461	288	53	2	2	NUM
ejpam-2461	288	54	p	p	NOUN
ejpam-2461	288	55	=	=	NOUN
ejpam-2461	288	56	4	4	NUM
ejpam-2461	288	57	,	,	PUNCT
ejpam-2461	288	58	w=	w=	AUX
ejpam-2461	288	59	4	4	NUM
ejpam-2461	288	60	a	a	DET
ejpam-2461	288	61	|sp	|sp	NOUN
ejpam-2461	288	62	,	,	PUNCT
ejpam-2461	288	63	w|	w|	NOUN
ejpam-2461	288	64	|sp	|sp	NUM
ejpam-2461	288	65	,	,	PUNCT
ejpam-2461	288	66	w	w	ADP
ejpam-2461	288	67	−	−	PROPN
ejpam-2461	288	68	e0|	e0|	PROPN
ejpam-2461	288	69	j0	j0	PROPN
ejpam-2461	288	70	|sp	|sp	NUM
ejpam-2461	288	71	,	,	PUNCT
ejpam-2461	288	72	w|	w|	NOUN
ejpam-2461	288	73	|sp	|sp	NUM
ejpam-2461	288	74	,	,	PUNCT
ejpam-2461	288	75	w	w	ADP
ejpam-2461	288	76	−	−	PROPN
ejpam-2461	288	77	e0|	e0|	PROPN
ejpam-2461	288	78	j0	j0	PROPN
ejpam-2461	288	79	0.200	0.200	NUM
ejpam-2461	288	80	3.473(−03	3.473(−03	NUM
ejpam-2461	288	81	)	)	PUNCT
ejpam-2461	288	82	1.329(−06	1.329(−06	NUM
ejpam-2461	288	83	)	)	PUNCT
ejpam-2461	288	84	7	7	NUM
ejpam-2461	288	85	3.919(−04	3.919(−04	NUM
ejpam-2461	288	86	)	)	PUNCT
ejpam-2461	288	87	8.742(−06	8.742(−06	NUM
ejpam-2461	288	88	)	)	PUNCT
ejpam-2461	288	89	6	6	NUM
ejpam-2461	288	90	0.100	0.100	NUM
ejpam-2461	288	91	4.863(−04	4.863(−04	NUM
ejpam-2461	288	92	)	)	PUNCT
ejpam-2461	288	93	2.749(−08	2.749(−08	NUM
ejpam-2461	288	94	)	)	PUNCT
ejpam-2461	288	95	11	11	NUM
ejpam-2461	288	96	4.805(−05	4.805(−05	NUM
ejpam-2461	288	97	)	)	PUNCT
ejpam-2461	288	98	4.879(−07	4.879(−07	NUM
ejpam-2461	288	99	)	)	PUNCT
ejpam-2461	289	1	8	8	NUM
ejpam-2461	289	2	0.050	0.050	NUM
ejpam-2461	289	3	2.737(−05	2.737(−05	NUM
ejpam-2461	289	4	)	)	PUNCT
ejpam-2461	289	5	2.156(−10	2.156(−10	NUM
ejpam-2461	289	6	)	)	PUNCT
ejpam-2461	289	7	14	14	NUM
ejpam-2461	289	8	8.456(−06	8.456(−06	NUM
ejpam-2461	289	9	)	)	PUNCT
ejpam-2461	289	10	1.420(−09	1.420(−09	NUM
ejpam-2461	289	11	)	)	PUNCT
ejpam-2461	289	12	11	11	NUM
ejpam-2461	289	13	0.010	0.010	NUM
ejpam-2461	289	14	4.221(−09	4.221(−09	NUM
ejpam-2461	289	15	)	)	PUNCT
ejpam-2461	289	16	4.621(−17	4.621(−17	NUM
ejpam-2461	289	17	)	)	PUNCT
ejpam-2461	289	18	23	23	NUM
ejpam-2461	289	19	7.982(−09	7.982(−09	NUM
ejpam-2461	289	20	)	)	PUNCT
ejpam-2461	289	21	3.041(−16	3.041(−16	NUM
ejpam-2461	289	22	)	)	PUNCT
ejpam-2461	289	23	21	21	NUM
ejpam-2461	289	24	0.001	0.001	NUM
ejpam-2461	289	25	1.064(−14	1.064(−14	NUM
ejpam-2461	289	26	)	)	PUNCT
ejpam-2461	289	27	1.033(−36	1.033(−36	NUM
ejpam-2461	289	28	)	)	PUNCT
ejpam-2461	289	29	53	53	NUM
ejpam-2461	289	30	1.876(−16	1.876(−16	NUM
ejpam-2461	289	31	)	)	PUNCT
ejpam-2461	289	32	6.799(−36	6.799(−36	NUM
ejpam-2461	289	33	)	)	PUNCT
ejpam-2461	289	34	51	51	NUM
ejpam-2461	289	35	we	we	PRON
ejpam-2461	289	36	show	show	VERB
ejpam-2461	289	37	the	the	DET
ejpam-2461	289	38	results	result	NOUN
ejpam-2461	289	39	of	of	ADP
ejpam-2461	289	40	numerical	numerical	ADJ
ejpam-2461	289	41	calculations	calculation	NOUN
ejpam-2461	289	42	to	to	PART
ejpam-2461	289	43	demonstrate	demonstrate	VERB
ejpam-2461	289	44	the	the	DET
ejpam-2461	289	45	achievable	achievable	ADJ
ejpam-2461	289	46	accuracy	accuracy	NOUN
ejpam-2461	289	47	of	of	ADP
ejpam-2461	289	48	the	the	DET
ejpam-2461	289	49	expansion	expansion	NOUN
ejpam-2461	289	50	in	in	ADP
ejpam-2461	289	51	theorem	theorem	NOUN
ejpam-2461	289	52	1	1	X
ejpam-2461	289	53	.	.	PUNCT
ejpam-2461	290	1	we	we	PRON
ejpam-2461	290	2	define	define	VERB
ejpam-2461	290	3	the	the	DET
ejpam-2461	290	4	difference	difference	NOUN
ejpam-2461	290	5	between	between	ADP
ejpam-2461	290	6	sp(a	sp(a	NOUN
ejpam-2461	290	7	;	;	PUNCT
ejpam-2461	290	8	w	w	X
ejpam-2461	290	9	)	)	PUNCT
ejpam-2461	290	10	and	and	CCONJ
ejpam-2461	290	11	the	the	DET
ejpam-2461	290	12	finite	finite	ADJ
ejpam-2461	290	13	algebraic	algebraic	ADJ
ejpam-2461	290	14	expansion	expansion	NOUN
ejpam-2461	290	15	by	by	ADP
ejpam-2461	290	16	sp	sp	PROPN
ejpam-2461	290	17	,	,	PUNCT
ejpam-2461	290	18	w	w	PROPN
ejpam-2461	290	19	≡	≡	PROPN
ejpam-2461	290	20	sp	sp	PROPN
ejpam-2461	290	21	,	,	PUNCT
ejpam-2461	290	22	w(a	w(a	NOUN
ejpam-2461	290	23	)	)	PUNCT
ejpam-2461	290	24	:	:	PUNCT
ejpam-2461	290	25	=	=	NOUN
ejpam-2461	290	26	sp(a	sp(a	ADJ
ejpam-2461	290	27	;	;	PUNCT
ejpam-2461	290	28	w)−	w)−	PROPN
ejpam-2461	290	29	1	1	NUM
ejpam-2461	290	30	p	p	PROPN
ejpam-2461	290	31	γ	γ	X
ejpam-2461	290	32	�	�	PROPN
ejpam-2461	290	33	1−	1−	NUM
ejpam-2461	290	34	w	w	PROPN
ejpam-2461	290	35	p	p	X
ejpam-2461	290	36	�	�	PROPN
ejpam-2461	290	37	a(w−1)/p	a(w−1)/p	ADP
ejpam-2461	290	38	−	−	PROPN
ejpam-2461	291	1	k	k	PROPN
ejpam-2461	291	2	∑	∑	PUNCT
ejpam-2461	291	3	k=0	k=0	PROPN
ejpam-2461	291	4	(	(	PUNCT
ejpam-2461	291	5	−)k	−)k	PROPN
ejpam-2461	291	6	k	k	PROPN
ejpam-2461	291	7	!	!	PROPN
ejpam-2461	291	8	ζ(w−	ζ(w−	PROPN
ejpam-2461	291	9	pk	pk	PROPN
ejpam-2461	291	10	)	)	PUNCT
ejpam-2461	291	11	ak	ak	PROPN
ejpam-2461	291	12	.	.	PROPN
ejpam-2461	292	1	(	(	PUNCT
ejpam-2461	292	2	33	33	NUM
ejpam-2461	292	3	)	)	PUNCT
ejpam-2461	292	4	in	in	ADP
ejpam-2461	292	5	table	table	NOUN
ejpam-2461	292	6	2	2	NUM
ejpam-2461	292	7	we	we	PRON
ejpam-2461	292	8	present	present	VERB
ejpam-2461	292	9	the	the	DET
ejpam-2461	292	10	absolute	absolute	ADJ
ejpam-2461	292	11	error	error	NOUN
ejpam-2461	292	12	in	in	ADP
ejpam-2461	292	13	the	the	DET
ejpam-2461	292	14	computation	computation	NOUN
ejpam-2461	292	15	of	of	ADP
ejpam-2461	292	16	sp(a	sp(a	PROPN
ejpam-2461	292	17	;	;	PUNCT
ejpam-2461	292	18	w	w	X
ejpam-2461	292	19	)	)	PUNCT
ejpam-2461	292	20	for	for	ADP
ejpam-2461	292	21	different	different	ADJ
ejpam-2461	292	22	values	value	NOUN
ejpam-2461	292	23	of	of	ADP
ejpam-2461	292	24	the	the	DET
ejpam-2461	292	25	parameter	parameter	NOUN
ejpam-2461	292	26	a	a	PRON
ejpam-2461	292	27	in	in	ADP
ejpam-2461	292	28	the	the	DET
ejpam-2461	292	29	two	two	NUM
ejpam-2461	292	30	cases	case	NOUN
ejpam-2461	292	31	p	p	X
ejpam-2461	292	32	=	=	SYM
ejpam-2461	292	33	2	2	NUM
ejpam-2461	292	34	and	and	CCONJ
ejpam-2461	292	35	p	p	NOUN
ejpam-2461	292	36	=	=	NOUN
ejpam-2461	292	37	4	4	NUM
ejpam-2461	292	38	,	,	PUNCT
ejpam-2461	292	39	with	with	ADP
ejpam-2461	292	40	w=	w=	PROPN
ejpam-2461	292	41	2	2	NUM
ejpam-2461	292	42	and	and	CCONJ
ejpam-2461	292	43	w=	w=	NOUN
ejpam-2461	292	44	4	4	NUM
ejpam-2461	292	45	using	use	VERB
ejpam-2461	292	46	the	the	DET
ejpam-2461	292	47	expansions	expansion	NOUN
ejpam-2461	292	48	given	give	VERB
ejpam-2461	292	49	in	in	ADP
ejpam-2461	292	50	(	(	PUNCT
ejpam-2461	292	51	30	30	NUM
ejpam-2461	292	52	)	)	PUNCT
ejpam-2461	292	53	and	and	CCONJ
ejpam-2461	292	54	(	(	PUNCT
ejpam-2461	292	55	31	31	NUM
ejpam-2461	292	56	)	)	PUNCT
ejpam-2461	292	57	.	.	PUNCT
ejpam-2461	293	1	the	the	DET
ejpam-2461	293	2	first	first	ADJ
ejpam-2461	293	3	column	column	NOUN
ejpam-2461	293	4	in	in	ADP
ejpam-2461	293	5	each	each	DET
ejpam-2461	293	6	entry	entry	NOUN
ejpam-2461	293	7	displays	display	VERB
ejpam-2461	293	8	the	the	DET
ejpam-2461	293	9	absolute	absolute	ADJ
ejpam-2461	293	10	value	value	NOUN
ejpam-2461	293	11	of	of	ADP
ejpam-2461	293	12	sp	sp	NOUN
ejpam-2461	293	13	,	,	PUNCT
ejpam-2461	293	14	w	w	PROPN
ejpam-2461	293	15	;	;	PUNCT
ejpam-2461	293	16	that	that	PRON
ejpam-2461	293	17	is	is	ADV
ejpam-2461	293	18	,	,	PUNCT
ejpam-2461	293	19	the	the	DET
ejpam-2461	293	20	accuracy	accuracy	NOUN
ejpam-2461	293	21	achievable	achievable	ADJ
ejpam-2461	293	22	with	with	ADP
ejpam-2461	293	23	just	just	ADV
ejpam-2461	293	24	the	the	DET
ejpam-2461	293	25	algebraic	algebraic	ADJ
ejpam-2461	293	26	expansion	expansion	NOUN
ejpam-2461	293	27	and	and	CCONJ
ejpam-2461	293	28	no	no	DET
ejpam-2461	293	29	subdominant	subdominant	ADJ
ejpam-2461	293	30	exponential	exponential	ADJ
ejpam-2461	293	31	terms	term	NOUN
ejpam-2461	293	32	.	.	PUNCT
ejpam-2461	294	1	the	the	DET
ejpam-2461	294	2	second	second	ADJ
ejpam-2461	294	3	column	column	NOUN
ejpam-2461	294	4	shows	show	VERB
ejpam-2461	294	5	the	the	DET
ejpam-2461	294	6	absolute	absolute	ADJ
ejpam-2461	294	7	error	error	NOUN
ejpam-2461	294	8	when	when	SCONJ
ejpam-2461	294	9	the	the	DET
ejpam-2461	294	10	single	single	ADJ
ejpam-2461	294	11	optimally	optimally	ADV
ejpam-2461	294	12	truncated	truncate	VERB
ejpam-2461	294	13	exponential	exponential	ADJ
ejpam-2461	294	14	expansion	expansion	NOUN
ejpam-2461	294	15	e0(a	e0(a	NOUN
ejpam-2461	294	16	;	;	PUNCT
ejpam-2461	294	17	w	w	PROPN
ejpam-2461	294	18	,	,	PUNCT
ejpam-2461	294	19	p	p	NOUN
ejpam-2461	294	20	)	)	PUNCT
ejpam-2461	294	21	(	(	PUNCT
ejpam-2461	294	22	denoted	denote	VERB
ejpam-2461	294	23	by	by	ADP
ejpam-2461	294	24	e0	e0	PROPN
ejpam-2461	294	25	in	in	ADP
ejpam-2461	294	26	the	the	DET
ejpam-2461	294	27	table	table	NOUN
ejpam-2461	294	28	)	)	PUNCT
ejpam-2461	294	29	is	be	AUX
ejpam-2461	294	30	included	include	VERB
ejpam-2461	294	31	.	.	PUNCT
ejpam-2461	295	1	the	the	DET
ejpam-2461	295	2	optimal	optimal	ADJ
ejpam-2461	295	3	truncation	truncation	NOUN
ejpam-2461	295	4	index	index	NOUN
ejpam-2461	295	5	j0	j0	PROPN
ejpam-2461	295	6	,	,	PUNCT
ejpam-2461	295	7	corresponding	correspond	VERB
ejpam-2461	295	8	to	to	ADP
ejpam-2461	295	9	truncation	truncation	NOUN
ejpam-2461	295	10	of	of	ADP
ejpam-2461	295	11	the	the	DET
ejpam-2461	295	12	exponential	exponential	ADJ
ejpam-2461	295	13	expansion	expansion	NOUN
ejpam-2461	295	14	e0(a	e0(a	NOUN
ejpam-2461	295	15	;	;	PUNCT
ejpam-2461	295	16	w	w	PROPN
ejpam-2461	295	17	,	,	PUNCT
ejpam-2461	295	18	p	p	NOUN
ejpam-2461	295	19	)	)	PUNCT
ejpam-2461	295	20	at	at	ADP
ejpam-2461	295	21	,	,	PUNCT
ejpam-2461	295	22	or	or	CCONJ
ejpam-2461	295	23	near	near	ADV
ejpam-2461	295	24	,	,	PUNCT
ejpam-2461	295	25	the	the	DET
ejpam-2461	295	26	least	least	ADJ
ejpam-2461	295	27	term	term	NOUN
ejpam-2461	295	28	in	in	ADP
ejpam-2461	295	29	magnitude	magnitude	NOUN
ejpam-2461	295	30	,	,	PUNCT
ejpam-2461	295	31	is	be	AUX
ejpam-2461	295	32	indicated	indicate	VERB
ejpam-2461	295	33	in	in	ADP
ejpam-2461	295	34	the	the	DET
ejpam-2461	295	35	final	final	ADJ
ejpam-2461	295	36	column	column	NOUN
ejpam-2461	295	37	.	.	PUNCT
ejpam-2461	296	1	the	the	DET
ejpam-2461	296	2	situation	situation	NOUN
ejpam-2461	296	3	when	when	SCONJ
ejpam-2461	296	4	there	there	PRON
ejpam-2461	296	5	is	be	VERB
ejpam-2461	296	6	only	only	ADV
ejpam-2461	296	7	a	a	DET
ejpam-2461	296	8	single	single	ADJ
ejpam-2461	296	9	subdominant	subdominant	ADJ
ejpam-2461	296	10	exponentially	exponentially	ADV
ejpam-2461	296	11	small	small	ADJ
ejpam-2461	296	12	expansion	expansion	NOUN
ejpam-2461	296	13	present	present	ADJ
ejpam-2461	296	14	is	be	AUX
ejpam-2461	296	15	straightforward	straightforward	ADJ
ejpam-2461	296	16	:	:	PUNCT
ejpam-2461	296	17	this	this	DET
ejpam-2461	296	18	sum	sum	NOUN
ejpam-2461	296	19	is	be	AUX
ejpam-2461	296	20	truncated	truncate	VERB
ejpam-2461	296	21	at	at	ADP
ejpam-2461	296	22	some	some	DET
ejpam-2461	296	23	suitable	suitable	ADJ
ejpam-2461	296	24	point	point	NOUN
ejpam-2461	296	25	thereby	thereby	ADV
ejpam-2461	296	26	introducing	introduce	VERB
ejpam-2461	296	27	a	a	DET
ejpam-2461	296	28	truncation	truncation	NOUN
ejpam-2461	296	29	error	error	NOUN
ejpam-2461	296	30	.	.	PUNCT
ejpam-2461	297	1	if	if	SCONJ
ejpam-2461	297	2	truncation	truncation	NOUN
ejpam-2461	297	3	is	be	AUX
ejpam-2461	297	4	optimal	optimal	ADJ
ejpam-2461	297	5	,	,	PUNCT
ejpam-2461	297	6	then	then	ADV
ejpam-2461	297	7	the	the	DET
ejpam-2461	297	8	resulting	result	VERB
ejpam-2461	297	9	error	error	NOUN
ejpam-2461	297	10	is	be	AUX
ejpam-2461	297	11	exponentially	exponentially	ADV
ejpam-2461	297	12	more	more	ADV
ejpam-2461	297	13	recessive	recessive	ADJ
ejpam-2461	297	14	than	than	ADP
ejpam-2461	297	15	the	the	DET
ejpam-2461	297	16	parent	parent	NOUN
ejpam-2461	297	17	exponential	exponential	ADJ
ejpam-2461	297	18	expansion	expansion	NOUN
ejpam-2461	297	19	.	.	PUNCT
ejpam-2461	298	1	however	however	ADV
ejpam-2461	298	2	,	,	PUNCT
ejpam-2461	298	3	in	in	ADP
ejpam-2461	298	4	the	the	DET
ejpam-2461	298	5	case	case	NOUN
ejpam-2461	298	6	of	of	ADP
ejpam-2461	298	7	two	two	NUM
ejpam-2461	298	8	,	,	PUNCT
ejpam-2461	298	9	or	or	CCONJ
ejpam-2461	298	10	more	more	ADJ
ejpam-2461	298	11	,	,	PUNCT
ejpam-2461	298	12	exponential	exponential	ADJ
ejpam-2461	298	13	expansions	expansion	NOUN
ejpam-2461	298	14	of	of	ADP
ejpam-2461	298	15	different	different	ADJ
ejpam-2461	298	16	degrees	degree	NOUN
ejpam-2461	298	17	of	of	ADP
ejpam-2461	298	18	subdominance	subdominance	NOUN
ejpam-2461	298	19	(	(	PUNCT
ejpam-2461	298	20	corresponding	correspond	VERB
ejpam-2461	298	21	to	to	ADP
ejpam-2461	298	22	p	p	PROPN
ejpam-2461	298	23	≥	≥	NUM
ejpam-2461	298	24	6	6	NUM
ejpam-2461	298	25	)	)	PUNCT
ejpam-2461	298	26	the	the	DET
ejpam-2461	298	27	situation	situation	NOUN
ejpam-2461	298	28	is	be	AUX
ejpam-2461	298	29	not	not	PART
ejpam-2461	298	30	so	so	ADV
ejpam-2461	298	31	obvious	obvious	ADJ
ejpam-2461	298	32	.	.	PUNCT
ejpam-2461	299	1	it	it	PRON
ejpam-2461	299	2	is	be	AUX
ejpam-2461	299	3	not	not	PART
ejpam-2461	299	4	clear	clear	ADJ
ejpam-2461	299	5	,	,	PUNCT
ejpam-2461	299	6	without	without	ADP
ejpam-2461	299	7	further	further	ADJ
ejpam-2461	299	8	investigation	investigation	NOUN
ejpam-2461	299	9	,	,	PUNCT
ejpam-2461	299	10	how	how	SCONJ
ejpam-2461	299	11	the	the	DET
ejpam-2461	299	12	error	error	NOUN
ejpam-2461	299	13	from	from	ADP
ejpam-2461	299	14	the	the	DET
ejpam-2461	299	15	truncated	truncated	ADJ
ejpam-2461	299	16	leading	lead	VERB
ejpam-2461	299	17	exponential	exponential	ADJ
ejpam-2461	299	18	series	series	NOUN
ejpam-2461	299	19	compares	compare	VERB
ejpam-2461	299	20	with	with	ADP
ejpam-2461	299	21	the	the	DET
ejpam-2461	299	22	contribution	contribution	NOUN
ejpam-2461	299	23	from	from	ADP
ejpam-2461	299	24	the	the	DET
ejpam-2461	299	25	next	next	ADJ
ejpam-2461	299	26	series	series	NOUN
ejpam-2461	299	27	.	.	PUNCT
ejpam-2461	300	1	we	we	PRON
ejpam-2461	300	2	illustrate	illustrate	VERB
ejpam-2461	300	3	this	this	PRON
ejpam-2461	300	4	by	by	ADP
ejpam-2461	300	5	considering	consider	VERB
ejpam-2461	300	6	the	the	DET
ejpam-2461	300	7	case	case	NOUN
ejpam-2461	300	8	p	p	X
ejpam-2461	300	9	=	=	SYM
ejpam-2461	300	10	6	6	NUM
ejpam-2461	300	11	and	and	CCONJ
ejpam-2461	300	12	w	w	NOUN
ejpam-2461	300	13	=	=	NOUN
ejpam-2461	300	14	2	2	NUM
ejpam-2461	300	15	given	give	VERB
ejpam-2461	300	16	in	in	ADP
ejpam-2461	300	17	(	(	PUNCT
ejpam-2461	300	18	32	32	NUM
ejpam-2461	300	19	)	)	PUNCT
ejpam-2461	300	20	.	.	PUNCT
ejpam-2461	301	1	in	in	ADP
ejpam-2461	301	2	table	table	NOUN
ejpam-2461	301	3	3	3	NUM
ejpam-2461	301	4	we	we	PRON
ejpam-2461	301	5	present	present	VERB
ejpam-2461	301	6	the	the	DET
ejpam-2461	301	7	absolute	absolute	ADJ
ejpam-2461	301	8	error	error	NOUN
ejpam-2461	301	9	in	in	ADP
ejpam-2461	301	10	the	the	DET
ejpam-2461	301	11	computation	computation	NOUN
ejpam-2461	301	12	of	of	ADP
ejpam-2461	301	13	s6(a	s6(a	PROPN
ejpam-2461	301	14	;	;	PUNCT
ejpam-2461	301	15	2	2	NUM
ejpam-2461	301	16	)	)	PUNCT
ejpam-2461	301	17	as	as	ADP
ejpam-2461	301	18	a	a	DET
ejpam-2461	301	19	function	function	NOUN
ejpam-2461	301	20	of	of	ADP
ejpam-2461	301	21	the	the	DET
ejpam-2461	301	22	parameter	parameter	NOUN
ejpam-2461	301	23	a.	a.	NOUN
ejpam-2461	301	24	we	we	PRON
ejpam-2461	301	25	show	show	VERB
ejpam-2461	301	26	,	,	PUNCT
ejpam-2461	301	27	in	in	ADP
ejpam-2461	301	28	order	order	NOUN
ejpam-2461	301	29	,	,	PUNCT
ejpam-2461	301	30	the	the	DET
ejpam-2461	301	31	value	value	NOUN
ejpam-2461	301	32	of	of	ADP
ejpam-2461	301	33	|s6,2|	|s6,2|	NOUN
ejpam-2461	301	34	and	and	CCONJ
ejpam-2461	301	35	the	the	DET
ejpam-2461	301	36	absolute	absolute	ADJ
ejpam-2461	301	37	error	error	NOUN
ejpam-2461	301	38	in	in	ADP
ejpam-2461	301	39	s6,2−	s6,2−	PROPN
ejpam-2461	301	40	e0(a	e0(a	PROPN
ejpam-2461	301	41	;	;	PUNCT
ejpam-2461	301	42	2	2	NUM
ejpam-2461	301	43	,	,	PUNCT
ejpam-2461	301	44	6	6	NUM
ejpam-2461	301	45	)	)	PUNCT
ejpam-2461	301	46	when	when	SCONJ
ejpam-2461	301	47	the	the	DET
ejpam-2461	301	48	leading	lead	VERB
ejpam-2461	301	49	references	reference	NOUN
ejpam-2461	301	50	17	17	NUM
ejpam-2461	301	51	subdominant	subdominant	ADJ
ejpam-2461	301	52	exponential	exponential	ADJ
ejpam-2461	301	53	expansion	expansion	NOUN
ejpam-2461	301	54	e0(a	e0(a	NOUN
ejpam-2461	301	55	;	;	PUNCT
ejpam-2461	301	56	2	2	NUM
ejpam-2461	301	57	,	,	PUNCT
ejpam-2461	301	58	6	6	NUM
ejpam-2461	301	59	)	)	PUNCT
ejpam-2461	301	60	is	be	AUX
ejpam-2461	301	61	optimally	optimally	ADV
ejpam-2461	301	62	truncated	truncate	VERB
ejpam-2461	301	63	at	at	ADP
ejpam-2461	301	64	index	index	NOUN
ejpam-2461	301	65	j0	j0	PROPN
ejpam-2461	301	66	.	.	PUNCT
ejpam-2461	302	1	the	the	DET
ejpam-2461	302	2	fourth	fourth	ADJ
ejpam-2461	302	3	column	column	NOUN
ejpam-2461	302	4	gives	give	VERB
ejpam-2461	302	5	the	the	DET
ejpam-2461	302	6	absolute	absolute	ADJ
ejpam-2461	302	7	error	error	NOUN
ejpam-2461	302	8	when	when	SCONJ
ejpam-2461	302	9	the	the	DET
ejpam-2461	302	10	first	first	ADJ
ejpam-2461	302	11	few	few	ADJ
ejpam-2461	302	12	terms	term	NOUN
ejpam-2461	302	13	of	of	ADP
ejpam-2461	302	14	the	the	DET
ejpam-2461	302	15	second	second	ADJ
ejpam-2461	302	16	exponential	exponential	ADJ
ejpam-2461	302	17	expansion	expansion	NOUN
ejpam-2461	302	18	ê1(a	ê1(a	NOUN
ejpam-2461	302	19	;	;	PUNCT
ejpam-2461	302	20	2	2	NUM
ejpam-2461	302	21	,	,	PUNCT
ejpam-2461	302	22	6	6	NUM
ejpam-2461	302	23	)	)	PUNCT
ejpam-2461	302	24	are	be	AUX
ejpam-2461	302	25	included	include	VERB
ejpam-2461	302	26	(	(	PUNCT
ejpam-2461	302	27	for	for	ADP
ejpam-2461	302	28	brevity	brevity	NOUN
ejpam-2461	302	29	in	in	ADP
ejpam-2461	302	30	the	the	DET
ejpam-2461	302	31	table	table	NOUN
ejpam-2461	302	32	these	these	DET
ejpam-2461	302	33	exponential	exponential	ADJ
ejpam-2461	302	34	expansions	expansion	NOUN
ejpam-2461	302	35	are	be	AUX
ejpam-2461	302	36	labelled	label	VERB
ejpam-2461	302	37	e0	e0	PROPN
ejpam-2461	302	38	and	and	CCONJ
ejpam-2461	302	39	e1	e1	NOUN
ejpam-2461	302	40	,	,	PUNCT
ejpam-2461	302	41	and	and	CCONJ
ejpam-2461	302	42	their	their	PRON
ejpam-2461	302	43	sum	sum	NOUN
ejpam-2461	302	44	is	be	AUX
ejpam-2461	302	45	denoted	denote	VERB
ejpam-2461	302	46	by	by	ADP
ejpam-2461	302	47	e0,1	e0,1	NOUN
ejpam-2461	302	48	)	)	PUNCT
ejpam-2461	302	49	.	.	PUNCT
ejpam-2461	303	1	the	the	DET
ejpam-2461	303	2	final	final	ADJ
ejpam-2461	303	3	two	two	NUM
ejpam-2461	303	4	columns	column	NOUN
ejpam-2461	303	5	show	show	VERB
ejpam-2461	303	6	the	the	DET
ejpam-2461	303	7	values	value	NOUN
ejpam-2461	303	8	of	of	ADP
ejpam-2461	303	9	the	the	DET
ejpam-2461	303	10	least	least	ADJ
ejpam-2461	303	11	term	term	NOUN
ejpam-2461	303	12	(	(	PUNCT
ejpam-2461	303	13	including	include	VERB
ejpam-2461	303	14	prefactors	prefactor	NOUN
ejpam-2461	303	15	)	)	PUNCT
ejpam-2461	303	16	in	in	ADP
ejpam-2461	303	17	e0(a	e0(a	PROPN
ejpam-2461	303	18	;	;	PUNCT
ejpam-2461	303	19	2	2	NUM
ejpam-2461	303	20	,	,	PUNCT
ejpam-2461	303	21	6	6	NUM
ejpam-2461	303	22	)	)	PUNCT
ejpam-2461	303	23	at	at	ADP
ejpam-2461	303	24	optimal	optimal	ADJ
ejpam-2461	303	25	truncation	truncation	NOUN
ejpam-2461	303	26	and	and	CCONJ
ejpam-2461	303	27	the	the	DET
ejpam-2461	303	28	values	value	NOUN
ejpam-2461	303	29	of	of	ADP
ejpam-2461	303	30	the	the	DET
ejpam-2461	303	31	leading	lead	VERB
ejpam-2461	303	32	term	term	NOUN
ejpam-2461	303	33	(	(	PUNCT
ejpam-2461	303	34	j	j	NOUN
ejpam-2461	303	35	=	=	SYM
ejpam-2461	303	36	0	0	NUM
ejpam-2461	303	37	)	)	PUNCT
ejpam-2461	303	38	of	of	ADP
ejpam-2461	303	39	the	the	DET
ejpam-2461	303	40	sub	sub	ADJ
ejpam-2461	303	41	-	-	ADJ
ejpam-2461	303	42	subdominant	subdominant	ADJ
ejpam-2461	303	43	expansion	expansion	NOUN
ejpam-2461	303	44	ê1(a	ê1(a	NOUN
ejpam-2461	303	45	;	;	PUNCT
ejpam-2461	303	46	2	2	NUM
ejpam-2461	303	47	,	,	PUNCT
ejpam-2461	303	48	6	6	NUM
ejpam-2461	303	49	)	)	PUNCT
ejpam-2461	303	50	.	.	PUNCT
ejpam-2461	304	1	a	a	DET
ejpam-2461	304	2	cursory	cursory	NOUN
ejpam-2461	304	3	inspection	inspection	NOUN
ejpam-2461	304	4	of	of	ADP
ejpam-2461	304	5	table	table	NOUN
ejpam-2461	304	6	3	3	NUM
ejpam-2461	304	7	shows	show	VERB
ejpam-2461	304	8	that	that	SCONJ
ejpam-2461	304	9	for	for	ADP
ejpam-2461	304	10	a	a	DET
ejpam-2461	304	11	≃	≃	NOUN
ejpam-2461	304	12	0.1	0.1	NUM
ejpam-2461	304	13	the	the	DET
ejpam-2461	304	14	leading	leading	ADJ
ejpam-2461	304	15	term	term	NOUN
ejpam-2461	304	16	of	of	ADP
ejpam-2461	304	17	ê1(a	ê1(a	NOUN
ejpam-2461	304	18	;	;	PUNCT
ejpam-2461	304	19	2	2	NUM
ejpam-2461	304	20	,	,	PUNCT
ejpam-2461	304	21	6	6	NUM
ejpam-2461	304	22	)	)	PUNCT
ejpam-2461	304	23	is	be	AUX
ejpam-2461	304	24	less	less	ADJ
ejpam-2461	304	25	than	than	ADP
ejpam-2461	304	26	the	the	DET
ejpam-2461	304	27	minimum	minimum	ADJ
ejpam-2461	304	28	term	term	NOUN
ejpam-2461	304	29	of	of	ADP
ejpam-2461	304	30	e0(a	e0(a	NOUN
ejpam-2461	304	31	;	;	PUNCT
ejpam-2461	304	32	2	2	NUM
ejpam-2461	304	33	,	,	PUNCT
ejpam-2461	304	34	6	6	NUM
ejpam-2461	304	35	)	)	PUNCT
ejpam-2461	304	36	and	and	CCONJ
ejpam-2461	304	37	consequently	consequently	ADV
ejpam-2461	304	38	that	that	SCONJ
ejpam-2461	304	39	inclusion	inclusion	NOUN
ejpam-2461	304	40	of	of	ADP
ejpam-2461	304	41	ê1(a	ê1(a	NOUN
ejpam-2461	304	42	;	;	PUNCT
ejpam-2461	304	43	2	2	NUM
ejpam-2461	304	44	,	,	PUNCT
ejpam-2461	304	45	6	6	NUM
ejpam-2461	304	46	)	)	PUNCT
ejpam-2461	304	47	can	can	AUX
ejpam-2461	304	48	not	not	PART
ejpam-2461	304	49	improve	improve	VERB
ejpam-2461	304	50	the	the	DET
ejpam-2461	304	51	accuracy	accuracy	NOUN
ejpam-2461	304	52	.	.	PUNCT
ejpam-2461	305	1	for	for	ADP
ejpam-2461	305	2	a<∼0.01	a<∼0.01	PROPN
ejpam-2461	305	3	,	,	PUNCT
ejpam-2461	305	4	the	the	DET
ejpam-2461	305	5	reverse	reverse	NOUN
ejpam-2461	305	6	is	be	AUX
ejpam-2461	305	7	true	true	ADJ
ejpam-2461	305	8	:	:	PUNCT
ejpam-2461	305	9	the	the	DET
ejpam-2461	305	10	leading	lead	VERB
ejpam-2461	305	11	terms	term	NOUN
ejpam-2461	305	12	of	of	ADP
ejpam-2461	305	13	ê1(a	ê1(a	NOUN
ejpam-2461	305	14	;	;	PUNCT
ejpam-2461	305	15	2	2	NUM
ejpam-2461	305	16	,	,	PUNCT
ejpam-2461	305	17	6	6	NUM
ejpam-2461	305	18	)	)	PUNCT
ejpam-2461	305	19	are	be	AUX
ejpam-2461	305	20	greater	great	ADJ
ejpam-2461	305	21	than	than	ADP
ejpam-2461	305	22	the	the	DET
ejpam-2461	305	23	minimum	minimum	ADJ
ejpam-2461	305	24	term	term	NOUN
ejpam-2461	305	25	of	of	ADP
ejpam-2461	305	26	e0(a	e0(a	NOUN
ejpam-2461	305	27	;	;	PUNCT
ejpam-2461	305	28	2	2	NUM
ejpam-2461	305	29	,	,	PUNCT
ejpam-2461	305	30	6	6	NUM
ejpam-2461	305	31	)	)	PUNCT
ejpam-2461	305	32	and	and	CCONJ
ejpam-2461	305	33	their	their	PRON
ejpam-2461	305	34	inclusion	inclusion	NOUN
ejpam-2461	305	35	therefore	therefore	ADV
ejpam-2461	305	36	increases	increase	VERB
ejpam-2461	305	37	the	the	DET
ejpam-2461	305	38	overall	overall	ADJ
ejpam-2461	305	39	accuracy	accuracy	NOUN
ejpam-2461	305	40	.	.	PUNCT
ejpam-2461	306	1	however	however	ADV
ejpam-2461	306	2	,	,	PUNCT
ejpam-2461	306	3	it	it	PRON
ejpam-2461	306	4	is	be	AUX
ejpam-2461	306	5	clear	clear	ADJ
ejpam-2461	306	6	that	that	SCONJ
ejpam-2461	306	7	in	in	ADP
ejpam-2461	306	8	both	both	DET
ejpam-2461	306	9	cases	case	NOUN
ejpam-2461	306	10	the	the	DET
ejpam-2461	306	11	final	final	ADJ
ejpam-2461	306	12	accuracy	accuracy	NOUN
ejpam-2461	306	13	achievable	achievable	ADJ
ejpam-2461	306	14	is	be	AUX
ejpam-2461	306	15	limited	limit	VERB
ejpam-2461	306	16	by	by	ADP
ejpam-2461	306	17	the	the	DET
ejpam-2461	306	18	optimal	optimal	ADJ
ejpam-2461	306	19	truncation	truncation	NOUN
ejpam-2461	306	20	of	of	ADP
ejpam-2461	306	21	the	the	DET
ejpam-2461	306	22	leading	lead	VERB
ejpam-2461	306	23	subdominant	subdominant	ADJ
ejpam-2461	306	24	expansion	expansion	NOUN
ejpam-2461	306	25	e0(a	e0(a	NOUN
ejpam-2461	306	26	;	;	PUNCT
ejpam-2461	306	27	2	2	NUM
ejpam-2461	306	28	,	,	PUNCT
ejpam-2461	306	29	6	6	NUM
ejpam-2461	306	30	)	)	PUNCT
ejpam-2461	306	31	.	.	PUNCT
ejpam-2461	307	1	further	further	ADJ
ejpam-2461	307	2	improvement	improvement	NOUN
ejpam-2461	307	3	in	in	ADP
ejpam-2461	307	4	the	the	DET
ejpam-2461	307	5	accuracy	accuracy	NOUN
ejpam-2461	307	6	would	would	AUX
ejpam-2461	307	7	require	require	VERB
ejpam-2461	307	8	a	a	DET
ejpam-2461	307	9	hyperasymptotic	hyperasymptotic	ADJ
ejpam-2461	307	10	treatment	treatment	NOUN
ejpam-2461	307	11	in	in	ADP
ejpam-2461	307	12	order	order	NOUN
ejpam-2461	307	13	to	to	PART
ejpam-2461	307	14	deal	deal	VERB
ejpam-2461	307	15	with	with	ADP
ejpam-2461	307	16	the	the	DET
ejpam-2461	307	17	divergent	divergent	ADJ
ejpam-2461	307	18	tails	tail	NOUN
ejpam-2461	307	19	of	of	ADP
ejpam-2461	307	20	e0(a	e0(a	NOUN
ejpam-2461	307	21	;	;	PUNCT
ejpam-2461	307	22	2	2	NUM
ejpam-2461	307	23	,	,	PUNCT
ejpam-2461	307	24	6	6	NUM
ejpam-2461	307	25	)	)	PUNCT
ejpam-2461	307	26	and	and	CCONJ
ejpam-2461	307	27	ê1(a	ê1(a	PROPN
ejpam-2461	307	28	;	;	PUNCT
ejpam-2461	307	29	2	2	NUM
ejpam-2461	307	30	,	,	PUNCT
ejpam-2461	307	31	6	6	NUM
ejpam-2461	307	32	)	)	PUNCT
ejpam-2461	307	33	.	.	PUNCT
ejpam-2461	308	1	a	a	DET
ejpam-2461	308	2	possible	possible	ADJ
ejpam-2461	308	3	hyperasymptotic	hyperasymptotic	ADJ
ejpam-2461	308	4	scheme	scheme	NOUN
ejpam-2461	308	5	for	for	ADP
ejpam-2461	308	6	the	the	DET
ejpam-2461	308	7	euler	euler	PROPN
ejpam-2461	308	8	-	-	PUNCT
ejpam-2461	308	9	jacobi	jacobi	PROPN
ejpam-2461	308	10	series	series	PROPN
ejpam-2461	308	11	with	with	ADP
ejpam-2461	308	12	p	p	NOUN
ejpam-2461	308	13	=	=	PROPN
ejpam-2461	308	14	3	3	NUM
ejpam-2461	308	15	and	and	CCONJ
ejpam-2461	308	16	w=	w=	NOUN
ejpam-2461	308	17	0	0	NUM
ejpam-2461	308	18	has	have	AUX
ejpam-2461	308	19	been	be	AUX
ejpam-2461	308	20	discussed	discuss	VERB
ejpam-2461	308	21	in	in	ADP
ejpam-2461	308	22	[	[	X
ejpam-2461	308	23	3	3	NUM
ejpam-2461	308	24	,	,	PUNCT
ejpam-2461	308	25	§	§	NOUN
ejpam-2461	308	26	8	8	NUM
ejpam-2461	308	27	]	]	X
ejpam-2461	308	28	.	.	PUNCT
ejpam-2461	309	1	table	table	NOUN
ejpam-2461	309	2	3	3	NUM
ejpam-2461	309	3	:	:	PUNCT
ejpam-2461	309	4	values	value	NOUN
ejpam-2461	309	5	of	of	ADP
ejpam-2461	309	6	the	the	DET
ejpam-2461	309	7	absolute	absolute	ADJ
ejpam-2461	309	8	error	error	NOUN
ejpam-2461	309	9	in	in	ADP
ejpam-2461	309	10	the	the	DET
ejpam-2461	309	11	computation	computation	NOUN
ejpam-2461	309	12	of	of	ADP
ejpam-2461	309	13	s6(a	s6(a	PROPN
ejpam-2461	309	14	;	;	PUNCT
ejpam-2461	309	15	2	2	NUM
ejpam-2461	309	16	)	)	PUNCT
ejpam-2461	309	17	defined	define	VERB
ejpam-2461	309	18	by	by	ADP
ejpam-2461	309	19	(	(	PUNCT
ejpam-2461	309	20	33	33	NUM
ejpam-2461	309	21	)	)	PUNCT
ejpam-2461	309	22	using	use	VERB
ejpam-2461	309	23	the	the	DET
ejpam-2461	309	24	expansion	expansion	NOUN
ejpam-2461	309	25	(	(	PUNCT
ejpam-2461	309	26	32	32	NUM
ejpam-2461	309	27	)	)	PUNCT
ejpam-2461	309	28	.	.	PUNCT
ejpam-2461	310	1	the	the	DET
ejpam-2461	310	2	value	value	NOUN
ejpam-2461	310	3	of	of	ADP
ejpam-2461	310	4	the	the	DET
ejpam-2461	310	5	index	index	NOUN
ejpam-2461	310	6	j0	j0	PROPN
ejpam-2461	310	7	corresponds	correspond	VERB
ejpam-2461	310	8	to	to	ADP
ejpam-2461	310	9	optimal	optimal	ADJ
ejpam-2461	310	10	truncation	truncation	NOUN
ejpam-2461	310	11	of	of	ADP
ejpam-2461	310	12	the	the	DET
ejpam-2461	310	13	expansion	expansion	NOUN
ejpam-2461	310	14	e0(a	e0(a	NOUN
ejpam-2461	310	15	;	;	PUNCT
ejpam-2461	310	16	2	2	NUM
ejpam-2461	310	17	,	,	PUNCT
ejpam-2461	310	18	6	6	NUM
ejpam-2461	310	19	)	)	PUNCT
ejpam-2461	310	20	.	.	PUNCT
ejpam-2461	311	1	a	a	DET
ejpam-2461	311	2	|s6,2|	|s6,2|	NOUN
ejpam-2461	311	3	|s6,2	|s6,2	NOUN
ejpam-2461	311	4	−	−	NOUN
ejpam-2461	311	5	e0|	e0|	PROPN
ejpam-2461	311	6	j0	j0	PROPN
ejpam-2461	311	7	|s6,2	|s6,2	NOUN
ejpam-2461	311	8	−	−	PROPN
ejpam-2461	311	9	e0,1|	e0,1|	PROPN
ejpam-2461	311	10	min	min	PROPN
ejpam-2461	311	11	|e0|	|e0|	NUM
ejpam-2461	311	12	e1	e1	PROPN
ejpam-2461	311	13	(	(	PUNCT
ejpam-2461	311	14	j	j	NOUN
ejpam-2461	311	15	=	=	SYM
ejpam-2461	311	16	0	0	NUM
ejpam-2461	311	17	)	)	PUNCT
ejpam-2461	311	18	1×10−1	1×10−1	NOUN
ejpam-2461	311	19	2.935(−02	2.935(−02	NUM
ejpam-2461	311	20	)	)	PUNCT
ejpam-2461	311	21	3.780(−05	3.780(−05	NUM
ejpam-2461	311	22	)	)	PUNCT
ejpam-2461	311	23	6	6	NUM
ejpam-2461	311	24	−−	−−	NOUN
ejpam-2461	311	25	9.422(−05	9.422(−05	NUM
ejpam-2461	311	26	)	)	PUNCT
ejpam-2461	311	27	5.095(−05	5.095(−05	NUM
ejpam-2461	311	28	)	)	PUNCT
ejpam-2461	312	1	5×10−2	5×10−2	NUM
ejpam-2461	312	2	1.617(−03	1.617(−03	NUM
ejpam-2461	312	3	)	)	PUNCT
ejpam-2461	312	4	3.037(−05	3.037(−05	NUM
ejpam-2461	312	5	)	)	PUNCT
ejpam-2461	312	6	8	8	NUM
ejpam-2461	312	7	1.200(−05	1.200(−05	NUM
ejpam-2461	312	8	)	)	PUNCT
ejpam-2461	312	9	1.729(−05	1.729(−05	NUM
ejpam-2461	312	10	)	)	PUNCT
ejpam-2461	312	11	1.191(−05	1.191(−05	NUM
ejpam-2461	312	12	)	)	PUNCT
ejpam-2461	313	1	1×10−2	1×10−2	NUM
ejpam-2461	313	2	9.512(−04	9.512(−04	NUM
ejpam-2461	313	3	)	)	PUNCT
ejpam-2461	313	4	1.193(−07	1.193(−07	NUM
ejpam-2461	313	5	)	)	PUNCT
ejpam-2461	313	6	12	12	NUM
ejpam-2461	313	7	5.339(−08	5.339(−08	NUM
ejpam-2461	313	8	)	)	PUNCT
ejpam-2461	313	9	1.228(−07	1.228(−07	NUM
ejpam-2461	313	10	)	)	PUNCT
ejpam-2461	313	11	1.904(−07	1.904(−07	NUM
ejpam-2461	313	12	)	)	PUNCT
ejpam-2461	313	13	5×10−3	5×10−3	NUM
ejpam-2461	313	14	1.292(−03	1.292(−03	NUM
ejpam-2461	313	15	)	)	PUNCT
ejpam-2461	313	16	1.099(−08	1.099(−08	NUM
ejpam-2461	313	17	)	)	PUNCT
ejpam-2461	313	18	13	13	NUM
ejpam-2461	313	19	8.713(−09	8.713(−09	NUM
ejpam-2461	313	20	)	)	PUNCT
ejpam-2461	313	21	9.090(−09	9.090(−09	NUM
ejpam-2461	313	22	)	)	PUNCT
ejpam-2461	313	23	2.148(−08	2.148(−08	NUM
ejpam-2461	313	24	)	)	PUNCT
ejpam-2461	313	25	1×10−3	1×10−3	NUM
ejpam-2461	313	26	1.604(−04	1.604(−04	NUM
ejpam-2461	313	27	)	)	PUNCT
ejpam-2461	313	28	3.452(−11	3.452(−11	NUM
ejpam-2461	313	29	)	)	PUNCT
ejpam-2461	313	30	19	19	NUM
ejpam-2461	313	31	3.483(−12	3.483(−12	NUM
ejpam-2461	313	32	)	)	PUNCT
ejpam-2461	313	33	3.757(−12	3.757(−12	NUM
ejpam-2461	313	34	)	)	PUNCT
ejpam-2461	313	35	4.053(−11	4.053(−11	NUM
ejpam-2461	313	36	)	)	PUNCT
ejpam-2461	314	1	1×10−4	1×10−4	PROPN
ejpam-2461	314	2	9.894(−07	9.894(−07	NUM
ejpam-2461	314	3	)	)	PUNCT
ejpam-2461	314	4	8.801(−17	8.801(−17	NUM
ejpam-2461	314	5	)	)	PUNCT
ejpam-2461	314	6	31	31	NUM
ejpam-2461	314	7	2.230(−19	2.230(−19	NUM
ejpam-2461	314	8	)	)	PUNCT
ejpam-2461	314	9	3.024(−19	3.024(−19	NUM
ejpam-2461	314	10	)	)	PUNCT
ejpam-2461	314	11	9.201(−17	9.201(−17	NUM
ejpam-2461	314	12	)	)	PUNCT
ejpam-2461	314	13	1×10−5	1×10−5	PROPN
ejpam-2461	314	14	6.209(−10	6.209(−10	NUM
ejpam-2461	314	15	)	)	PUNCT
ejpam-2461	314	16	1.522(−25	1.522(−25	NUM
ejpam-2461	314	17	)	)	PUNCT
ejpam-2461	314	18	51	51	NUM
ejpam-2461	314	19	1.963(−30	1.963(−30	NUM
ejpam-2461	314	20	)	)	PUNCT
ejpam-2461	314	21	1.964(−30	1.964(−30	NUM
ejpam-2461	314	22	)	)	PUNCT
ejpam-2461	314	23	1.564(−25	1.564(−25	NUM
ejpam-2461	314	24	)	)	PUNCT
ejpam-2461	315	1	finally	finally	ADV
ejpam-2461	315	2	we	we	PRON
ejpam-2461	315	3	remark	remark	VERB
ejpam-2461	315	4	that	that	SCONJ
ejpam-2461	315	5	the	the	DET
ejpam-2461	315	6	asymptotics	asymptotic	NOUN
ejpam-2461	315	7	of	of	ADP
ejpam-2461	315	8	the	the	DET
ejpam-2461	315	9	alternating	alternate	VERB
ejpam-2461	315	10	version	version	NOUN
ejpam-2461	315	11	of	of	ADP
ejpam-2461	315	12	(	(	PUNCT
ejpam-2461	315	13	1	1	X
ejpam-2461	315	14	)	)	PUNCT
ejpam-2461	315	15	can	can	AUX
ejpam-2461	315	16	be	be	AUX
ejpam-2461	315	17	deduced	deduce	VERB
ejpam-2461	315	18	from	from	ADP
ejpam-2461	315	19	the	the	DET
ejpam-2461	315	20	result	result	NOUN
ejpam-2461	315	21	in	in	ADP
ejpam-2461	315	22	theorem	theorem	NOUN
ejpam-2461	315	23	1	1	NUM
ejpam-2461	315	24	by	by	ADP
ejpam-2461	315	25	making	make	VERB
ejpam-2461	315	26	use	use	NOUN
ejpam-2461	315	27	of	of	ADP
ejpam-2461	315	28	the	the	DET
ejpam-2461	315	29	identity	identity	NOUN
ejpam-2461	315	30	∞	∞	PROPN
ejpam-2461	315	31	∑	∑	PROPN
ejpam-2461	315	32	n=1	n=1	PROPN
ejpam-2461	315	33	(	(	PUNCT
ejpam-2461	315	34	−)n	−)n	PROPN
ejpam-2461	315	35	e−anp	e−anp	VERB
ejpam-2461	315	36	nw	nw	PROPN
ejpam-2461	316	1	=	=	PROPN
ejpam-2461	316	2	21−wsp(2	21−wsp(2	NUM
ejpam-2461	316	3	pa	pa	NOUN
ejpam-2461	316	4	;	;	PUNCT
ejpam-2461	316	5	w)−	w)−	PROPN
ejpam-2461	316	6	sp(a	sp(a	NOUN
ejpam-2461	316	7	;	;	PUNCT
ejpam-2461	316	8	w	w	X
ejpam-2461	316	9	)	)	PUNCT
ejpam-2461	316	10	.	.	PUNCT
ejpam-2461	317	1	acknowledgements	acknowledgement	VERB
ejpam-2461	317	2	the	the	DET
ejpam-2461	317	3	author	author	NOUN
ejpam-2461	317	4	wishes	wish	VERB
ejpam-2461	317	5	to	to	PART
ejpam-2461	317	6	acknowledge	acknowledge	VERB
ejpam-2461	317	7	helpful	helpful	ADJ
ejpam-2461	317	8	correspondence	correspondence	NOUN
ejpam-2461	317	9	with	with	ADP
ejpam-2461	317	10	j.	j.	PROPN
ejpam-2461	317	11	boersma	boersma	PROPN
ejpam-2461	317	12	who	who	PRON
ejpam-2461	317	13	pointed	point	VERB
ejpam-2461	317	14	out	out	ADP
ejpam-2461	317	15	the	the	DET
ejpam-2461	317	16	conjugate	conjugate	ADJ
ejpam-2461	317	17	nature	nature	NOUN
ejpam-2461	317	18	of	of	ADP
ejpam-2461	317	19	the	the	DET
ejpam-2461	317	20	exponents	exponent	NOUN
ejpam-2461	317	21	in	in	ADP
ejpam-2461	317	22	section	section	NOUN
ejpam-2461	317	23	3.2	3.2	NUM
ejpam-2461	317	24	.	.	PUNCT
ejpam-2461	318	1	references	reference	NOUN
ejpam-2461	318	2	[	[	X
ejpam-2461	318	3	1	1	NUM
ejpam-2461	318	4	]	]	X
ejpam-2461	318	5	b.c	b.c	PROPN
ejpam-2461	318	6	.	.	PROPN
ejpam-2461	318	7	berndt	berndt	PROPN
ejpam-2461	318	8	.	.	PUNCT
ejpam-2461	319	1	ramanujan	ramanujan	PROPN
ejpam-2461	319	2	’s	’s	PART
ejpam-2461	319	3	notebooks	notebook	NOUN
ejpam-2461	319	4	,	,	PUNCT
ejpam-2461	319	5	part	part	PROPN
ejpam-2461	319	6	ii	ii	PROPN
ejpam-2461	319	7	.	.	PUNCT
ejpam-2461	319	8	springer	springer	NOUN
ejpam-2461	319	9	-	-	PUNCT
ejpam-2461	319	10	verlag	verlag	PROPN
ejpam-2461	319	11	,	,	PUNCT
ejpam-2461	319	12	new	new	PROPN
ejpam-2461	319	13	york	york	PROPN
ejpam-2461	319	14	,	,	PUNCT
ejpam-2461	319	15	1985	1985	NUM
ejpam-2461	319	16	.	.	PUNCT
ejpam-2461	320	1	[	[	X
ejpam-2461	320	2	2	2	NUM
ejpam-2461	320	3	]	]	X
ejpam-2461	320	4	b.l.j	b.l.j	NOUN
ejpam-2461	320	5	.	.	PUNCT
ejpam-2461	320	6	braaksma	braaksma	PROPN
ejpam-2461	320	7	.	.	PUNCT
ejpam-2461	321	1	asymptotic	asymptotic	ADJ
ejpam-2461	321	2	expansions	expansion	NOUN
ejpam-2461	321	3	and	and	CCONJ
ejpam-2461	321	4	analytic	analytic	ADJ
ejpam-2461	321	5	continuations	continuation	NOUN
ejpam-2461	321	6	for	for	ADP
ejpam-2461	321	7	a	a	DET
ejpam-2461	321	8	class	class	NOUN
ejpam-2461	321	9	of	of	ADP
ejpam-2461	321	10	barnes	barnes	PROPN
ejpam-2461	321	11	integrals	integrals	PROPN
ejpam-2461	321	12	,	,	PUNCT
ejpam-2461	321	13	compositio	compositio	PROPN
ejpam-2461	321	14	mathematica	mathematica	PROPN
ejpam-2461	321	15	15	15	NUM
ejpam-2461	321	16	,	,	PUNCT
ejpam-2461	321	17	239–341	239–341	NUM
ejpam-2461	321	18	,	,	PUNCT
ejpam-2461	321	19	1963	1963	NUM
ejpam-2461	321	20	.	.	PUNCT
ejpam-2461	322	1	references	reference	NOUN
ejpam-2461	322	2	18	18	NUM
ejpam-2461	322	3	[	[	X
ejpam-2461	322	4	3	3	NUM
ejpam-2461	322	5	]	]	PUNCT
ejpam-2461	322	6	v.	v.	CCONJ
ejpam-2461	322	7	kowalenko	kowalenko	PROPN
ejpam-2461	322	8	,	,	PUNCT
ejpam-2461	322	9	n.e	n.e	PROPN
ejpam-2461	322	10	.	.	PROPN
ejpam-2461	322	11	frankel	frankel	PROPN
ejpam-2461	322	12	,	,	PUNCT
ejpam-2461	322	13	m.l	m.l	PROPN
ejpam-2461	322	14	.	.	PROPN
ejpam-2461	322	15	glasser	glasser	PROPN
ejpam-2461	322	16	,	,	PUNCT
ejpam-2461	322	17	and	and	CCONJ
ejpam-2461	322	18	t.	t.	PROPN
ejpam-2461	322	19	taucher	taucher	PROPN
ejpam-2461	322	20	.	.	PUNCT
ejpam-2461	323	1	generalised	generalise	VERB
ejpam-2461	323	2	euler	euler	PROPN
ejpam-2461	323	3	-	-	PUNCT
ejpam-2461	323	4	jacobi	jacobi	PROPN
ejpam-2461	323	5	inversion	inversion	NOUN
ejpam-2461	323	6	formula	formula	NOUN
ejpam-2461	323	7	and	and	CCONJ
ejpam-2461	323	8	asymptotics	asymptotic	NOUN
ejpam-2461	323	9	beyond	beyond	ADP
ejpam-2461	323	10	all	all	DET
ejpam-2461	323	11	orders	order	NOUN
ejpam-2461	323	12	,	,	PUNCT
ejpam-2461	323	13	london	london	PROPN
ejpam-2461	323	14	math	math	PROPN
ejpam-2461	323	15	.	.	PUNCT
ejpam-2461	324	1	soc	soc	PROPN
ejpam-2461	324	2	.	.	PUNCT
ejpam-2461	325	1	lecture	lecture	NOUN
ejpam-2461	325	2	notes	note	VERB
ejpam-2461	325	3	series	series	PROPN
ejpam-2461	325	4	214	214	NUM
ejpam-2461	325	5	,	,	PUNCT
ejpam-2461	325	6	cambridge	cambridge	PROPN
ejpam-2461	325	7	university	university	PROPN
ejpam-2461	325	8	press	press	PROPN
ejpam-2461	325	9	,	,	PUNCT
ejpam-2461	325	10	cambridge	cambridge	PROPN
ejpam-2461	325	11	,	,	PUNCT
ejpam-2461	325	12	1995	1995	NUM
ejpam-2461	325	13	.	.	PUNCT
ejpam-2461	326	1	[	[	X
ejpam-2461	326	2	4	4	NUM
ejpam-2461	326	3	]	]	X
ejpam-2461	326	4	f.w.j	f.w.j	NOUN
ejpam-2461	326	5	.	.	PUNCT
ejpam-2461	326	6	olver	olver	PROPN
ejpam-2461	326	7	,	,	PUNCT
ejpam-2461	326	8	d.w	d.w	PROPN
ejpam-2461	326	9	.	.	PROPN
ejpam-2461	326	10	lozier	lozier	PROPN
ejpam-2461	326	11	,	,	PUNCT
ejpam-2461	326	12	r.f	r.f	PROPN
ejpam-2461	326	13	.	.	PROPN
ejpam-2461	326	14	boisvert	boisvert	PROPN
ejpam-2461	326	15	,	,	PUNCT
ejpam-2461	326	16	and	and	CCONJ
ejpam-2461	326	17	c.w	c.w	PROPN
ejpam-2461	326	18	.	.	PROPN
ejpam-2461	326	19	clark	clark	PROPN
ejpam-2461	326	20	(	(	PUNCT
ejpam-2461	326	21	eds	eds	PROPN
ejpam-2461	326	22	.	.	PUNCT
ejpam-2461	326	23	)	)	PUNCT
ejpam-2461	326	24	.	.	PUNCT
ejpam-2461	327	1	nist	nist	PROPN
ejpam-2461	327	2	handbook	handbook	NOUN
ejpam-2461	327	3	of	of	ADP
ejpam-2461	327	4	mathematical	mathematical	ADJ
ejpam-2461	327	5	functions	function	NOUN
ejpam-2461	327	6	,	,	PUNCT
ejpam-2461	327	7	cambridge	cambridge	PROPN
ejpam-2461	327	8	university	university	PROPN
ejpam-2461	327	9	press	press	PROPN
ejpam-2461	327	10	,	,	PUNCT
ejpam-2461	327	11	cambridge	cambridge	PROPN
ejpam-2461	327	12	,	,	PUNCT
ejpam-2461	327	13	2010	2010	NUM
ejpam-2461	327	14	.	.	PUNCT
ejpam-2461	328	1	[	[	X
ejpam-2461	328	2	5	5	X
ejpam-2461	328	3	]	]	X
ejpam-2461	328	4	r.b	r.b	PROPN
ejpam-2461	328	5	.	.	PROPN
ejpam-2461	328	6	paris	paris	PROPN
ejpam-2461	328	7	and	and	CCONJ
ejpam-2461	328	8	d.	d.	PROPN
ejpam-2461	328	9	kaminski	kaminski	PROPN
ejpam-2461	328	10	.	.	PUNCT
ejpam-2461	329	1	asymptotics	asymptotic	NOUN
ejpam-2461	329	2	and	and	CCONJ
ejpam-2461	329	3	mellin	mellin	PROPN
ejpam-2461	329	4	-	-	PUNCT
ejpam-2461	329	5	barnes	barnes	PROPN
ejpam-2461	329	6	integrals	integral	NOUN
ejpam-2461	329	7	,	,	PUNCT
ejpam-2461	329	8	cambridge	cambridge	PROPN
ejpam-2461	329	9	university	university	PROPN
ejpam-2461	329	10	press	press	PROPN
ejpam-2461	329	11	,	,	PUNCT
ejpam-2461	329	12	cambridge	cambridge	PROPN
ejpam-2461	329	13	,	,	PUNCT
ejpam-2461	329	14	2001	2001	NUM
ejpam-2461	329	15	.	.	PUNCT
ejpam-2461	330	1	[	[	X
ejpam-2461	330	2	6	6	NUM
ejpam-2461	330	3	]	]	X
ejpam-2461	330	4	r.b	r.b	PROPN
ejpam-2461	330	5	.	.	PROPN
ejpam-2461	330	6	paris	paris	PROPN
ejpam-2461	330	7	.	.	PUNCT
ejpam-2461	331	1	a	a	DET
ejpam-2461	331	2	poisson	poisson	PROPN
ejpam-2461	331	3	-	-	PUNCT
ejpam-2461	331	4	jacobi	jacobi	NOUN
ejpam-2461	331	5	-	-	PUNCT
ejpam-2461	331	6	type	type	NOUN
ejpam-2461	331	7	transformation	transformation	NOUN
ejpam-2461	331	8	for	for	ADP
ejpam-2461	331	9	the	the	DET
ejpam-2461	331	10	sum	sum	NOUN
ejpam-2461	331	11	∑∞	∑∞	NOUN
ejpam-2461	331	12	n=1	n=1	PROPN
ejpam-2461	331	13	n−2	n−2	PROPN
ejpam-2461	331	14	m	m	NOUN
ejpam-2461	331	15	exp(−an2	exp(−an2	NUM
ejpam-2461	331	16	)	)	PUNCT
ejpam-2461	331	17	for	for	ADP
ejpam-2461	331	18	positive	positive	ADJ
ejpam-2461	331	19	integer	integer	NOUN
ejpam-2461	331	20	m	m	NOUN
ejpam-2461	331	21	,	,	PUNCT
ejpam-2461	331	22	arxiv:1501.00685	arxiv:1501.00685	X
ejpam-2461	331	23	.	.	PUNCT
ejpam-2461	332	1	http://arxiv.org/abs/1501.00685	http://arxiv.org/abs/1501.00685	PROPN
ejpam-2461	332	2	2015	2015	NUM
ejpam-2461	332	3	.	.	PUNCT
ejpam-2461	333	1	[	[	X
ejpam-2461	333	2	7	7	X
ejpam-2461	333	3	]	]	X
ejpam-2461	333	4	e.c	e.c	PROPN
ejpam-2461	333	5	.	.	PROPN
ejpam-2461	333	6	titchmarsh	titchmarsh	NOUN
ejpam-2461	333	7	.	.	PUNCT
ejpam-2461	334	1	introduction	introduction	NOUN
ejpam-2461	334	2	to	to	ADP
ejpam-2461	334	3	the	the	DET
ejpam-2461	334	4	theory	theory	NOUN
ejpam-2461	334	5	of	of	ADP
ejpam-2461	334	6	fourier	fourier	NOUN
ejpam-2461	334	7	integrals	integral	NOUN
ejpam-2461	334	8	,	,	PUNCT
ejpam-2461	334	9	oxford	oxford	PROPN
ejpam-2461	334	10	university	university	PROPN
ejpam-2461	334	11	press	press	NOUN
ejpam-2461	334	12	,	,	PUNCT
ejpam-2461	334	13	oxford	oxford	PROPN
ejpam-2461	334	14	,	,	PUNCT
ejpam-2461	334	15	1975	1975	NUM
ejpam-2461	334	16	.	.	PUNCT
ejpam-2461	335	1	[	[	X
ejpam-2461	335	2	8	8	NUM
ejpam-2461	335	3	]	]	X
ejpam-2461	335	4	e.t	e.t	PROPN
ejpam-2461	335	5	.	.	PROPN
ejpam-2461	335	6	whittaker	whittaker	PROPN
ejpam-2461	335	7	and	and	CCONJ
ejpam-2461	335	8	g.n	g.n	PROPN
ejpam-2461	335	9	.	.	PROPN
ejpam-2461	335	10	watson	watson	PROPN
ejpam-2461	335	11	.	.	PUNCT
ejpam-2461	336	1	modern	modern	ADJ
ejpam-2461	336	2	analysis	analysis	NOUN
ejpam-2461	336	3	,	,	PUNCT
ejpam-2461	336	4	cambridge	cambridge	PROPN
ejpam-2461	336	5	university	university	PROPN
ejpam-2461	336	6	press	press	PROPN
ejpam-2461	336	7	,	,	PUNCT
ejpam-2461	336	8	cambridge	cambridge	PROPN
ejpam-2461	336	9	,	,	PUNCT
ejpam-2461	336	10	1952	1952	NUM
ejpam-2461	336	11	.	.	PUNCT
ejpam-2461	337	1	[	[	X
ejpam-2461	337	2	9	9	NUM
ejpam-2461	337	3	]	]	X
ejpam-2461	337	4	r.a	r.a	PROPN
ejpam-2461	337	5	.	.	PROPN
ejpam-2461	337	6	wolf	wolf	PROPN
ejpam-2461	337	7	,	,	PUNCT
ejpam-2461	337	8	k.a	k.a	PROPN
ejpam-2461	337	9	.	.	PROPN
ejpam-2461	337	10	farley	farley	PROPN
ejpam-2461	337	11	,	,	PUNCT
ejpam-2461	337	12	and	and	CCONJ
ejpam-2461	337	13	d.m	d.m	PROPN
ejpam-2461	337	14	.	.	PUNCT
ejpam-2461	337	15	kass	kass	PROPN
ejpam-2461	337	16	.	.	PUNCT
ejpam-2461	338	1	modeling	modeling	NOUN
ejpam-2461	338	2	of	of	ADP
ejpam-2461	338	3	the	the	DET
ejpam-2461	338	4	temperature	temperature	NOUN
ejpam-2461	338	5	sensitivity	sensitivity	NOUN
ejpam-2461	338	6	of	of	ADP
ejpam-2461	338	7	the	the	DET
ejpam-2461	338	8	apatite	apatite	NOUN
ejpam-2461	338	9	(	(	PUNCT
ejpam-2461	338	10	u	u	NOUN
ejpam-2461	338	11	-	-	ADJ
ejpam-2461	338	12	th)/he	th)/he	ADJ
ejpam-2461	338	13	thermochronometer	thermochronometer	NOUN
ejpam-2461	338	14	,	,	PUNCT
ejpam-2461	338	15	chemical	chemical	NOUN
ejpam-2461	338	16	geology	geology	NOUN
ejpam-2461	338	17	,	,	PUNCT
ejpam-2461	338	18	148	148	NUM
ejpam-2461	338	19	,	,	PUNCT
ejpam-2461	338	20	105–114	105–114	NUM
ejpam-2461	338	21	,	,	PUNCT
ejpam-2461	338	22	1998	1998	NUM
ejpam-2461	338	23	.	.	PUNCT