id	sid	tid	token	lemma	pos
ejpam-4085	1	1	european	european	PROPN
ejpam-4085	1	2	journal	journal	PROPN
ejpam-4085	1	3	of	of	ADP
ejpam-4085	1	4	pure	pure	ADJ
ejpam-4085	1	5	and	and	CCONJ
ejpam-4085	1	6	applied	apply	VERB
ejpam-4085	1	7	mathematics	mathematic	NOUN
ejpam-4085	1	8	vol	vol	NOUN
ejpam-4085	1	9	.	.	PUNCT
ejpam-4085	2	1	14	14	NUM
ejpam-4085	2	2	,	,	PUNCT
ejpam-4085	2	3	no	no	INTJ
ejpam-4085	2	4	.	.	NOUN
ejpam-4085	2	5	4	4	NUM
ejpam-4085	2	6	,	,	PUNCT
ejpam-4085	2	7	2021	2021	NUM
ejpam-4085	2	8	,	,	PUNCT
ejpam-4085	2	9	1337	1337	NUM
ejpam-4085	2	10	-	-	SYM
ejpam-4085	2	11	1349	1349	NUM
ejpam-4085	2	12	issn	issn	PROPN
ejpam-4085	2	13	1307	1307	NUM
ejpam-4085	2	14	-	-	SYM
ejpam-4085	2	15	5543	5543	NUM
ejpam-4085	2	16	–	–	PUNCT
ejpam-4085	2	17	ejpam.com	ejpam.com	X
ejpam-4085	2	18	published	publish	VERB
ejpam-4085	2	19	by	by	ADP
ejpam-4085	2	20	new	new	PROPN
ejpam-4085	2	21	york	york	PROPN
ejpam-4085	2	22	business	business	PROPN
ejpam-4085	2	23	global	global	ADJ
ejpam-4085	2	24	double	double	ADJ
ejpam-4085	2	25	integral	integral	ADJ
ejpam-4085	2	26	involving	involve	VERB
ejpam-4085	2	27	logarithmic	logarithmic	ADJ
ejpam-4085	2	28	and	and	CCONJ
ejpam-4085	2	29	quotient	quotient	NOUN
ejpam-4085	2	30	function	function	NOUN
ejpam-4085	2	31	with	with	ADP
ejpam-4085	2	32	powers	power	NOUN
ejpam-4085	2	33	expressed	express	VERB
ejpam-4085	2	34	in	in	ADP
ejpam-4085	2	35	terms	term	NOUN
ejpam-4085	2	36	of	of	ADP
ejpam-4085	2	37	the	the	DET
ejpam-4085	2	38	lerch	lerch	PROPN
ejpam-4085	2	39	function	function	PROPN
ejpam-4085	2	40	robert	robert	PROPN
ejpam-4085	2	41	reynolds1,∗	reynolds1,∗	PROPN
ejpam-4085	2	42	,	,	PUNCT
ejpam-4085	2	43	allan	allan	PROPN
ejpam-4085	2	44	stauffer1	stauffer1	PROPN
ejpam-4085	2	45	1	1	NUM
ejpam-4085	2	46	department	department	NOUN
ejpam-4085	2	47	of	of	ADP
ejpam-4085	2	48	mathematics	mathematic	NOUN
ejpam-4085	2	49	and	and	CCONJ
ejpam-4085	2	50	statistics	statistic	NOUN
ejpam-4085	2	51	,	,	PUNCT
ejpam-4085	2	52	faculty	faculty	NOUN
ejpam-4085	2	53	of	of	ADP
ejpam-4085	2	54	science	science	PROPN
ejpam-4085	2	55	,	,	PUNCT
ejpam-4085	2	56	york	york	PROPN
ejpam-4085	2	57	university	university	PROPN
ejpam-4085	2	58	,	,	PUNCT
ejpam-4085	2	59	toronto	toronto	PROPN
ejpam-4085	2	60	,	,	PUNCT
ejpam-4085	2	61	ontario	ontario	PROPN
ejpam-4085	2	62	,	,	PUNCT
ejpam-4085	2	63	canada	canada	PROPN
ejpam-4085	2	64	,	,	PUNCT
ejpam-4085	2	65	m3j1p3	m3j1p3	PROPN
ejpam-4085	2	66	abstract	abstract	NOUN
ejpam-4085	2	67	.	.	PUNCT
ejpam-4085	3	1	in	in	ADP
ejpam-4085	3	2	this	this	DET
ejpam-4085	3	3	work	work	NOUN
ejpam-4085	3	4	the	the	DET
ejpam-4085	3	5	authors	author	NOUN
ejpam-4085	3	6	use	use	VERB
ejpam-4085	3	7	their	their	PRON
ejpam-4085	3	8	contour	contour	NOUN
ejpam-4085	3	9	integral	integral	ADJ
ejpam-4085	3	10	method	method	NOUN
ejpam-4085	3	11	to	to	PART
ejpam-4085	3	12	derive	derive	VERB
ejpam-4085	3	13	the	the	DET
ejpam-4085	3	14	double	double	ADJ
ejpam-4085	3	15	integral	integral	NOUN
ejpam-4085	3	16	given	give	VERB
ejpam-4085	3	17	by	by	ADP
ejpam-4085	3	18	∫∞	∫∞	NOUN
ejpam-4085	3	19	0	0	NUM
ejpam-4085	3	20	∫∞	∫∞	NOUN
ejpam-4085	3	21	0	0	PUNCT
ejpam-4085	4	1	xm−1ym+	xm−1ym+	NOUN
ejpam-4085	4	2	q	q	PROPN
ejpam-4085	4	3	2	2	NUM
ejpam-4085	4	4	−1	−1	NOUN
ejpam-4085	4	5	logk(axy	logk(axy	NOUN
ejpam-4085	4	6	)	)	PUNCT
ejpam-4085	4	7	(	(	PUNCT
ejpam-4085	4	8	xq+1)2(yq+1)2	xq+1)2(yq+1)2	X
ejpam-4085	4	9	dxdy	dxdy	PROPN
ejpam-4085	4	10	in	in	ADP
ejpam-4085	4	11	terms	term	NOUN
ejpam-4085	4	12	of	of	ADP
ejpam-4085	4	13	the	the	DET
ejpam-4085	4	14	lerch	lerch	PROPN
ejpam-4085	4	15	function	function	PROPN
ejpam-4085	4	16	.	.	PUNCT
ejpam-4085	5	1	this	this	DET
ejpam-4085	5	2	integral	integral	ADJ
ejpam-4085	5	3	formula	formula	NOUN
ejpam-4085	5	4	is	be	AUX
ejpam-4085	5	5	then	then	ADV
ejpam-4085	5	6	used	use	VERB
ejpam-4085	5	7	to	to	PART
ejpam-4085	5	8	derive	derive	VERB
ejpam-4085	5	9	closed	closed	ADJ
ejpam-4085	5	10	solutions	solution	NOUN
ejpam-4085	5	11	in	in	ADP
ejpam-4085	5	12	terms	term	NOUN
ejpam-4085	5	13	of	of	ADP
ejpam-4085	5	14	fundamental	fundamental	ADJ
ejpam-4085	5	15	constants	constant	NOUN
ejpam-4085	5	16	and	and	CCONJ
ejpam-4085	5	17	special	special	ADJ
ejpam-4085	5	18	functions	function	NOUN
ejpam-4085	5	19	.	.	PUNCT
ejpam-4085	6	1	there	there	PRON
ejpam-4085	6	2	are	be	VERB
ejpam-4085	6	3	some	some	DET
ejpam-4085	6	4	useful	useful	ADJ
ejpam-4085	6	5	results	result	NOUN
ejpam-4085	6	6	relating	relate	VERB
ejpam-4085	6	7	double	double	ADJ
ejpam-4085	6	8	integrals	integral	NOUN
ejpam-4085	6	9	of	of	ADP
ejpam-4085	6	10	certain	certain	ADJ
ejpam-4085	6	11	kinds	kind	NOUN
ejpam-4085	6	12	of	of	ADP
ejpam-4085	6	13	functions	function	NOUN
ejpam-4085	6	14	to	to	ADP
ejpam-4085	6	15	ordinary	ordinary	ADJ
ejpam-4085	6	16	integrals	integral	NOUN
ejpam-4085	6	17	for	for	ADP
ejpam-4085	6	18	which	which	PRON
ejpam-4085	6	19	we	we	PRON
ejpam-4085	6	20	know	know	VERB
ejpam-4085	6	21	no	no	DET
ejpam-4085	6	22	general	general	ADJ
ejpam-4085	6	23	reference	reference	NOUN
ejpam-4085	6	24	.	.	PUNCT
ejpam-4085	7	1	thus	thus	ADV
ejpam-4085	7	2	a	a	DET
ejpam-4085	7	3	table	table	NOUN
ejpam-4085	7	4	of	of	ADP
ejpam-4085	7	5	integral	integral	ADJ
ejpam-4085	7	6	pairs	pair	NOUN
ejpam-4085	7	7	is	be	AUX
ejpam-4085	7	8	given	give	VERB
ejpam-4085	7	9	for	for	ADP
ejpam-4085	7	10	interested	interested	ADJ
ejpam-4085	7	11	readers	reader	NOUN
ejpam-4085	7	12	.	.	PUNCT
ejpam-4085	8	1	all	all	DET
ejpam-4085	8	2	the	the	DET
ejpam-4085	8	3	results	result	NOUN
ejpam-4085	8	4	in	in	ADP
ejpam-4085	8	5	this	this	DET
ejpam-4085	8	6	work	work	NOUN
ejpam-4085	8	7	are	be	AUX
ejpam-4085	8	8	new	new	ADJ
ejpam-4085	8	9	.	.	PUNCT
ejpam-4085	9	1	2020	2020	NUM
ejpam-4085	9	2	mathematics	mathematic	NOUN
ejpam-4085	9	3	subject	subject	NOUN
ejpam-4085	9	4	classifications	classification	NOUN
ejpam-4085	9	5	:	:	PUNCT
ejpam-4085	9	6	30e20	30e20	NUM
ejpam-4085	9	7	,	,	PUNCT
ejpam-4085	9	8	33	33	NUM
ejpam-4085	9	9	-	-	SYM
ejpam-4085	9	10	01	01	NUM
ejpam-4085	9	11	,	,	PUNCT
ejpam-4085	9	12	33	33	NUM
ejpam-4085	9	13	-	-	SYM
ejpam-4085	9	14	03	03	NUM
ejpam-4085	9	15	,	,	PUNCT
ejpam-4085	9	16	33	33	NUM
ejpam-4085	9	17	-	-	PUNCT
ejpam-4085	9	18	04	04	NUM
ejpam-4085	9	19	,	,	PUNCT
ejpam-4085	9	20	33	33	NUM
ejpam-4085	9	21	-	-	PUNCT
ejpam-4085	9	22	33b	33b	NUM
ejpam-4085	9	23	,	,	PUNCT
ejpam-4085	9	24	33e20	33e20	NUM
ejpam-4085	9	25	key	key	ADJ
ejpam-4085	9	26	words	word	NOUN
ejpam-4085	9	27	and	and	CCONJ
ejpam-4085	9	28	phrases	phrase	NOUN
ejpam-4085	9	29	:	:	PUNCT
ejpam-4085	9	30	catalan	catalan	NOUN
ejpam-4085	9	31	’s	’s	PART
ejpam-4085	9	32	constant	constant	ADJ
ejpam-4085	9	33	,	,	PUNCT
ejpam-4085	9	34	double	double	ADJ
ejpam-4085	9	35	integral	integral	ADJ
ejpam-4085	9	36	,	,	PUNCT
ejpam-4085	9	37	apéry	apéry	X
ejpam-4085	9	38	’s	’s	NOUN
ejpam-4085	9	39	constant	constant	ADJ
ejpam-4085	9	40	,	,	PUNCT
ejpam-4085	9	41	lerch	lerch	PROPN
ejpam-4085	9	42	function	function	PROPN
ejpam-4085	9	43	,	,	PUNCT
ejpam-4085	9	44	contour	contour	NOUN
ejpam-4085	9	45	integral	integral	ADJ
ejpam-4085	9	46	1	1	NUM
ejpam-4085	9	47	.	.	PUNCT
ejpam-4085	9	48	introduction	introduction	NOUN
ejpam-4085	9	49	the	the	DET
ejpam-4085	9	50	double	double	ADJ
ejpam-4085	9	51	integral	integral	ADJ
ejpam-4085	9	52	in	in	ADP
ejpam-4085	9	53	terms	term	NOUN
ejpam-4085	9	54	of	of	ADP
ejpam-4085	9	55	the	the	DET
ejpam-4085	9	56	lerch	lerch	PROPN
ejpam-4085	9	57	function	function	NOUN
ejpam-4085	9	58	derived	derive	VERB
ejpam-4085	9	59	in	in	ADP
ejpam-4085	9	60	this	this	DET
ejpam-4085	9	61	work	work	NOUN
ejpam-4085	9	62	is	be	AUX
ejpam-4085	9	63	used	use	VERB
ejpam-4085	9	64	to	to	PART
ejpam-4085	9	65	provide	provide	VERB
ejpam-4085	9	66	formal	formal	ADJ
ejpam-4085	9	67	derivations	derivation	NOUN
ejpam-4085	9	68	and	and	CCONJ
ejpam-4085	9	69	new	new	ADJ
ejpam-4085	9	70	formulae	formulae	NOUN
ejpam-4085	9	71	in	in	ADP
ejpam-4085	9	72	the	the	DET
ejpam-4085	9	73	form	form	NOUN
ejpam-4085	9	74	of	of	ADP
ejpam-4085	9	75	a	a	DET
ejpam-4085	9	76	summary	summary	NOUN
ejpam-4085	9	77	table	table	NOUN
ejpam-4085	9	78	of	of	ADP
ejpam-4085	9	79	integrals	integral	NOUN
ejpam-4085	9	80	.	.	PUNCT
ejpam-4085	10	1	the	the	DET
ejpam-4085	10	2	lerch	lerch	PROPN
ejpam-4085	10	3	function	function	PROPN
ejpam-4085	10	4	being	be	AUX
ejpam-4085	10	5	a	a	DET
ejpam-4085	10	6	special	special	ADJ
ejpam-4085	10	7	function	function	NOUN
ejpam-4085	10	8	has	have	VERB
ejpam-4085	10	9	the	the	DET
ejpam-4085	10	10	fundamental	fundamental	ADJ
ejpam-4085	10	11	property	property	NOUN
ejpam-4085	10	12	of	of	ADP
ejpam-4085	10	13	analytic	analytic	ADJ
ejpam-4085	10	14	continuation	continuation	NOUN
ejpam-4085	10	15	,	,	PUNCT
ejpam-4085	10	16	which	which	PRON
ejpam-4085	10	17	enables	enable	VERB
ejpam-4085	10	18	us	we	PRON
ejpam-4085	10	19	to	to	PART
ejpam-4085	10	20	widen	widen	VERB
ejpam-4085	10	21	the	the	DET
ejpam-4085	10	22	range	range	NOUN
ejpam-4085	10	23	of	of	ADP
ejpam-4085	10	24	evaluation	evaluation	NOUN
ejpam-4085	10	25	for	for	ADP
ejpam-4085	10	26	the	the	DET
ejpam-4085	10	27	parameters	parameter	NOUN
ejpam-4085	10	28	involved	involve	VERB
ejpam-4085	10	29	in	in	ADP
ejpam-4085	10	30	our	our	PRON
ejpam-4085	10	31	definite	definite	ADJ
ejpam-4085	10	32	integral	integral	NOUN
ejpam-4085	10	33	.	.	PUNCT
ejpam-4085	11	1	the	the	DET
ejpam-4085	11	2	definite	definite	ADJ
ejpam-4085	11	3	integral	integral	ADJ
ejpam-4085	11	4	derived	derived	NOUN
ejpam-4085	11	5	in	in	ADP
ejpam-4085	11	6	this	this	DET
ejpam-4085	11	7	manuscript	manuscript	NOUN
ejpam-4085	11	8	is	be	AUX
ejpam-4085	11	9	given	give	VERB
ejpam-4085	11	10	by∫	by∫	PROPN
ejpam-4085	11	11	∞	∞	PROPN
ejpam-4085	11	12	0	0	NUM
ejpam-4085	12	1	∫	∫	PROPN
ejpam-4085	12	2	∞	∞	NOUN
ejpam-4085	12	3	0	0	PUNCT
ejpam-4085	13	1	xm−1ym+	xm−1ym+	NOUN
ejpam-4085	13	2	q	q	PROPN
ejpam-4085	13	3	2	2	NUM
ejpam-4085	13	4	−1	−1	NOUN
ejpam-4085	13	5	logk(axy	logk(axy	NOUN
ejpam-4085	13	6	)	)	PUNCT
ejpam-4085	13	7	(	(	PUNCT
ejpam-4085	13	8	xq	xq	X
ejpam-4085	13	9	+	+	PROPN
ejpam-4085	13	10	1)2	1)2	NUM
ejpam-4085	13	11	(	(	PUNCT
ejpam-4085	13	12	yq	yq	PROPN
ejpam-4085	13	13	+	+	PROPN
ejpam-4085	13	14	1)2	1)2	NUM
ejpam-4085	13	15	dxdy	dxdy	NOUN
ejpam-4085	13	16	(	(	PUNCT
ejpam-4085	13	17	1	1	NUM
ejpam-4085	13	18	)	)	PUNCT
ejpam-4085	13	19	where	where	SCONJ
ejpam-4085	13	20	the	the	DET
ejpam-4085	13	21	parameters	parameter	NOUN
ejpam-4085	13	22	k	k	PROPN
ejpam-4085	13	23	,	,	PUNCT
ejpam-4085	13	24	a	a	PRON
ejpam-4085	13	25	are	be	AUX
ejpam-4085	13	26	general	general	ADJ
ejpam-4085	13	27	complex	complex	ADJ
ejpam-4085	13	28	numbers	number	NOUN
ejpam-4085	13	29	and	and	CCONJ
ejpam-4085	13	30	0	0	NUM
ejpam-4085	13	31	<	<	X
ejpam-4085	13	32	re(m	re(m	PROPN
ejpam-4085	13	33	)	)	PUNCT
ejpam-4085	13	34	<	<	X
ejpam-4085	14	1	1	1	X
ejpam-4085	14	2	.	.	PUNCT
ejpam-4085	15	1	this	this	DET
ejpam-4085	15	2	work	work	NOUN
ejpam-4085	15	3	is	be	AUX
ejpam-4085	15	4	important	important	ADJ
ejpam-4085	15	5	because	because	SCONJ
ejpam-4085	15	6	the	the	DET
ejpam-4085	15	7	authors	author	NOUN
ejpam-4085	15	8	were	be	AUX
ejpam-4085	15	9	unable	unable	ADJ
ejpam-4085	15	10	to	to	PART
ejpam-4085	15	11	find	find	VERB
ejpam-4085	15	12	similar	similar	ADJ
ejpam-4085	15	13	derivations	derivation	NOUN
ejpam-4085	15	14	in	in	ADP
ejpam-4085	15	15	current	current	ADJ
ejpam-4085	15	16	literature	literature	NOUN
ejpam-4085	15	17	.	.	PUNCT
ejpam-4085	16	1	∗corresponding	∗corresponde	VERB
ejpam-4085	16	2	author	author	NOUN
ejpam-4085	16	3	.	.	PUNCT
ejpam-4085	17	1	doi	doi	NOUN
ejpam-4085	17	2	:	:	PUNCT
ejpam-4085	17	3	https://doi.org/10.29020/nybg.ejpam.v14i4.4085	https://doi.org/10.29020/nybg.ejpam.v14i4.4085	NUM
ejpam-4085	17	4	email	email	NOUN
ejpam-4085	17	5	addresses	address	NOUN
ejpam-4085	17	6	:	:	PUNCT
ejpam-4085	18	1	milver@my.yorku.ca	milver@my.yorku.ca	NOUN
ejpam-4085	18	2	(	(	PUNCT
ejpam-4085	18	3	r.	r.	PROPN
ejpam-4085	18	4	reynolds	reynolds	PROPN
ejpam-4085	18	5	)	)	PUNCT
ejpam-4085	18	6	,	,	PUNCT
ejpam-4085	18	7	stauffer@yorku.ca	stauffer@yorku.ca	NOUN
ejpam-4085	18	8	(	(	PUNCT
ejpam-4085	18	9	a.	a.	NOUN
ejpam-4085	18	10	stauffer	stauffer	PROPN
ejpam-4085	18	11	)	)	PUNCT
ejpam-4085	18	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4085	18	13	1337	1337	NUM
ejpam-4085	19	1	©	©	PROPN
ejpam-4085	19	2	2021	2021	NUM
ejpam-4085	19	3	ejpam	ejpam	VERB
ejpam-4085	19	4	all	all	DET
ejpam-4085	19	5	rights	right	NOUN
ejpam-4085	19	6	reserved	reserve	VERB
ejpam-4085	19	7	.	.	PUNCT
ejpam-4085	20	1	r.	r.	PROPN
ejpam-4085	20	2	reynolds	reynolds	PROPN
ejpam-4085	20	3	,	,	PUNCT
ejpam-4085	20	4	a.	a.	PROPN
ejpam-4085	20	5	stauffer	stauffer	PROPN
ejpam-4085	20	6	/	/	SYM
ejpam-4085	20	7	eur	eur	PROPN
ejpam-4085	20	8	.	.	PUNCT
ejpam-4085	21	1	j.	j.	PROPN
ejpam-4085	21	2	pure	pure	PROPN
ejpam-4085	21	3	appl	appl	PROPN
ejpam-4085	21	4	.	.	PROPN
ejpam-4085	21	5	math	math	PROPN
ejpam-4085	21	6	,	,	PUNCT
ejpam-4085	21	7	14	14	NUM
ejpam-4085	21	8	(	(	PUNCT
ejpam-4085	21	9	4	4	NUM
ejpam-4085	21	10	)	)	PUNCT
ejpam-4085	21	11	(	(	PUNCT
ejpam-4085	21	12	2021	2021	NUM
ejpam-4085	21	13	)	)	PUNCT
ejpam-4085	21	14	,	,	PUNCT
ejpam-4085	21	15	1337	1337	NUM
ejpam-4085	21	16	-	-	SYM
ejpam-4085	21	17	1349	1349	NUM
ejpam-4085	21	18	1338	1338	NUM
ejpam-4085	21	19	the	the	DET
ejpam-4085	21	20	derivation	derivation	NOUN
ejpam-4085	21	21	of	of	ADP
ejpam-4085	21	22	the	the	DET
ejpam-4085	21	23	definite	definite	ADJ
ejpam-4085	21	24	integral	integral	NOUN
ejpam-4085	21	25	follows	follow	VERB
ejpam-4085	21	26	the	the	DET
ejpam-4085	21	27	method	method	NOUN
ejpam-4085	21	28	used	use	VERB
ejpam-4085	21	29	by	by	ADP
ejpam-4085	21	30	us	we	PRON
ejpam-4085	21	31	in	in	ADP
ejpam-4085	21	32	[	[	X
ejpam-4085	21	33	3	3	X
ejpam-4085	21	34	]	]	PUNCT
ejpam-4085	21	35	which	which	PRON
ejpam-4085	21	36	involves	involve	VERB
ejpam-4085	21	37	cauchy	cauchy	PROPN
ejpam-4085	21	38	’s	’s	PART
ejpam-4085	21	39	integral	integral	ADJ
ejpam-4085	21	40	formula	formula	NOUN
ejpam-4085	21	41	.	.	PUNCT
ejpam-4085	22	1	the	the	DET
ejpam-4085	22	2	generalized	generalized	ADJ
ejpam-4085	22	3	cauchy	cauchy	PROPN
ejpam-4085	22	4	’s	’s	PART
ejpam-4085	22	5	integral	integral	ADJ
ejpam-4085	22	6	formula	formula	NOUN
ejpam-4085	22	7	is	be	AUX
ejpam-4085	22	8	given	give	VERB
ejpam-4085	22	9	by	by	ADP
ejpam-4085	22	10	yk	yk	PROPN
ejpam-4085	22	11	γ(k	γ(k	PROPN
ejpam-4085	22	12	+	+	CCONJ
ejpam-4085	22	13	1	1	X
ejpam-4085	22	14	)	)	PUNCT
ejpam-4085	22	15	=	=	SYM
ejpam-4085	22	16	1	1	NUM
ejpam-4085	22	17	2πi	2πi	ADJ
ejpam-4085	22	18	∫	∫	PROPN
ejpam-4085	22	19	c	c	PROPN
ejpam-4085	22	20	ewy	ewy	PROPN
ejpam-4085	22	21	wk+1	wk+1	PROPN
ejpam-4085	22	22	dw	dw	PROPN
ejpam-4085	22	23	.	.	PUNCT
ejpam-4085	23	1	(	(	PUNCT
ejpam-4085	23	2	2	2	X
ejpam-4085	23	3	)	)	PUNCT
ejpam-4085	23	4	where	where	SCONJ
ejpam-4085	23	5	c	c	NOUN
ejpam-4085	23	6	is	be	AUX
ejpam-4085	23	7	in	in	ADP
ejpam-4085	23	8	general	general	ADJ
ejpam-4085	23	9	an	an	DET
ejpam-4085	23	10	open	open	ADJ
ejpam-4085	23	11	contour	contour	NOUN
ejpam-4085	23	12	in	in	ADP
ejpam-4085	23	13	the	the	DET
ejpam-4085	23	14	complex	complex	ADJ
ejpam-4085	23	15	plane	plane	NOUN
ejpam-4085	23	16	where	where	SCONJ
ejpam-4085	23	17	the	the	DET
ejpam-4085	23	18	bilinear	bilinear	NOUN
ejpam-4085	23	19	concomitant	concomitant	NOUN
ejpam-4085	23	20	has	have	VERB
ejpam-4085	23	21	the	the	DET
ejpam-4085	23	22	same	same	ADJ
ejpam-4085	23	23	value	value	NOUN
ejpam-4085	23	24	at	at	ADP
ejpam-4085	23	25	the	the	DET
ejpam-4085	23	26	end	end	NOUN
ejpam-4085	23	27	points	point	NOUN
ejpam-4085	23	28	of	of	ADP
ejpam-4085	23	29	the	the	DET
ejpam-4085	23	30	contour	contour	NOUN
ejpam-4085	23	31	.	.	PUNCT
ejpam-4085	24	1	this	this	DET
ejpam-4085	24	2	method	method	NOUN
ejpam-4085	24	3	involves	involve	VERB
ejpam-4085	24	4	using	use	VERB
ejpam-4085	24	5	a	a	DET
ejpam-4085	24	6	form	form	NOUN
ejpam-4085	24	7	of	of	ADP
ejpam-4085	24	8	equation	equation	NOUN
ejpam-4085	24	9	(	(	PUNCT
ejpam-4085	24	10	2	2	NUM
ejpam-4085	24	11	)	)	PUNCT
ejpam-4085	24	12	then	then	ADV
ejpam-4085	24	13	multiply	multiply	VERB
ejpam-4085	24	14	both	both	DET
ejpam-4085	24	15	sides	side	NOUN
ejpam-4085	24	16	by	by	ADP
ejpam-4085	24	17	a	a	DET
ejpam-4085	24	18	function	function	NOUN
ejpam-4085	24	19	,	,	PUNCT
ejpam-4085	24	20	then	then	ADV
ejpam-4085	24	21	take	take	VERB
ejpam-4085	24	22	a	a	DET
ejpam-4085	24	23	definite	definite	ADJ
ejpam-4085	24	24	integral	integral	NOUN
ejpam-4085	24	25	of	of	ADP
ejpam-4085	24	26	both	both	DET
ejpam-4085	24	27	sides	side	NOUN
ejpam-4085	24	28	.	.	PUNCT
ejpam-4085	25	1	this	this	PRON
ejpam-4085	25	2	yields	yield	VERB
ejpam-4085	25	3	a	a	DET
ejpam-4085	25	4	definite	definite	ADJ
ejpam-4085	25	5	integral	integral	ADJ
ejpam-4085	25	6	in	in	ADP
ejpam-4085	25	7	terms	term	NOUN
ejpam-4085	25	8	of	of	ADP
ejpam-4085	25	9	a	a	DET
ejpam-4085	25	10	contour	contour	NOUN
ejpam-4085	25	11	integral	integral	NOUN
ejpam-4085	25	12	.	.	PUNCT
ejpam-4085	26	1	a	a	DET
ejpam-4085	26	2	second	second	ADJ
ejpam-4085	26	3	contour	contour	NOUN
ejpam-4085	26	4	integral	integral	NOUN
ejpam-4085	26	5	is	be	AUX
ejpam-4085	26	6	derived	derive	VERB
ejpam-4085	26	7	by	by	ADP
ejpam-4085	26	8	multiplying	multiply	VERB
ejpam-4085	26	9	equation	equation	NOUN
ejpam-4085	26	10	(	(	PUNCT
ejpam-4085	26	11	2	2	NUM
ejpam-4085	26	12	)	)	PUNCT
ejpam-4085	26	13	by	by	ADP
ejpam-4085	26	14	a	a	DET
ejpam-4085	26	15	function	function	NOUN
ejpam-4085	26	16	and	and	CCONJ
ejpam-4085	26	17	performing	perform	VERB
ejpam-4085	26	18	some	some	DET
ejpam-4085	26	19	substitutions	substitution	NOUN
ejpam-4085	26	20	so	so	SCONJ
ejpam-4085	26	21	that	that	SCONJ
ejpam-4085	26	22	the	the	DET
ejpam-4085	26	23	contour	contour	NOUN
ejpam-4085	26	24	integrals	integral	NOUN
ejpam-4085	26	25	are	be	AUX
ejpam-4085	26	26	the	the	DET
ejpam-4085	26	27	same	same	ADJ
ejpam-4085	26	28	.	.	PUNCT
ejpam-4085	27	1	2	2	X
ejpam-4085	27	2	.	.	X
ejpam-4085	27	3	definite	definite	ADJ
ejpam-4085	27	4	integral	integral	ADJ
ejpam-4085	27	5	of	of	ADP
ejpam-4085	27	6	the	the	DET
ejpam-4085	27	7	contour	contour	NOUN
ejpam-4085	27	8	integral	integral	NOUN
ejpam-4085	27	9	we	we	PRON
ejpam-4085	27	10	use	use	VERB
ejpam-4085	27	11	the	the	DET
ejpam-4085	27	12	method	method	NOUN
ejpam-4085	27	13	in	in	ADP
ejpam-4085	27	14	[	[	X
ejpam-4085	27	15	3	3	NUM
ejpam-4085	27	16	]	]	PUNCT
ejpam-4085	27	17	.	.	PUNCT
ejpam-4085	28	1	the	the	DET
ejpam-4085	28	2	variable	variable	NOUN
ejpam-4085	28	3	of	of	ADP
ejpam-4085	28	4	integration	integration	NOUN
ejpam-4085	28	5	in	in	ADP
ejpam-4085	28	6	the	the	DET
ejpam-4085	28	7	contour	contour	NOUN
ejpam-4085	28	8	integral	integral	NOUN
ejpam-4085	28	9	is	be	AUX
ejpam-4085	28	10	t	t	X
ejpam-4085	28	11	=	=	PUNCT
ejpam-4085	28	12	m	m	VERB
ejpam-4085	28	13	+	+	X
ejpam-4085	28	14	w.	w.	NOUN
ejpam-4085	28	15	the	the	DET
ejpam-4085	28	16	cut	cut	NOUN
ejpam-4085	28	17	and	and	CCONJ
ejpam-4085	28	18	contour	contour	NOUN
ejpam-4085	28	19	are	be	AUX
ejpam-4085	28	20	in	in	ADP
ejpam-4085	28	21	the	the	DET
ejpam-4085	28	22	first	first	ADJ
ejpam-4085	28	23	quadrant	quadrant	NOUN
ejpam-4085	28	24	of	of	ADP
ejpam-4085	28	25	the	the	DET
ejpam-4085	28	26	complex	complex	ADJ
ejpam-4085	28	27	z	z	NOUN
ejpam-4085	28	28	-	-	NOUN
ejpam-4085	28	29	plane	plane	NOUN
ejpam-4085	28	30	.	.	PUNCT
ejpam-4085	29	1	the	the	DET
ejpam-4085	29	2	cut	cut	NOUN
ejpam-4085	29	3	approaches	approach	VERB
ejpam-4085	29	4	the	the	DET
ejpam-4085	29	5	origin	origin	NOUN
ejpam-4085	29	6	from	from	ADP
ejpam-4085	29	7	the	the	DET
ejpam-4085	29	8	interior	interior	NOUN
ejpam-4085	29	9	of	of	ADP
ejpam-4085	29	10	the	the	DET
ejpam-4085	29	11	first	first	ADJ
ejpam-4085	29	12	quadrant	quadrant	NOUN
ejpam-4085	29	13	and	and	CCONJ
ejpam-4085	29	14	the	the	DET
ejpam-4085	29	15	contour	contour	NOUN
ejpam-4085	29	16	goes	go	VERB
ejpam-4085	29	17	round	round	ADP
ejpam-4085	29	18	the	the	DET
ejpam-4085	29	19	origin	origin	NOUN
ejpam-4085	29	20	with	with	ADP
ejpam-4085	29	21	zero	zero	NUM
ejpam-4085	29	22	radius	radius	NOUN
ejpam-4085	29	23	and	and	CCONJ
ejpam-4085	29	24	is	be	AUX
ejpam-4085	29	25	on	on	ADP
ejpam-4085	29	26	opposite	opposite	ADJ
ejpam-4085	29	27	sides	side	NOUN
ejpam-4085	29	28	of	of	ADP
ejpam-4085	29	29	the	the	DET
ejpam-4085	29	30	cut	cut	NOUN
ejpam-4085	29	31	.	.	PUNCT
ejpam-4085	30	1	using	use	VERB
ejpam-4085	30	2	equation	equation	NOUN
ejpam-4085	30	3	(	(	PUNCT
ejpam-4085	30	4	2	2	X
ejpam-4085	30	5	)	)	PUNCT
ejpam-4085	30	6	we	we	PRON
ejpam-4085	30	7	replace	replace	VERB
ejpam-4085	30	8	y	y	PROPN
ejpam-4085	30	9	by	by	ADP
ejpam-4085	30	10	log(axy	log(axy	PROPN
ejpam-4085	30	11	)	)	PUNCT
ejpam-4085	30	12	then	then	ADV
ejpam-4085	30	13	multiply	multiply	VERB
ejpam-4085	30	14	by	by	ADP
ejpam-4085	30	15	xm−1ym+	xm−1ym+	NOUN
ejpam-4085	30	16	q	q	X
ejpam-4085	31	1	2−1	2−1	NUM
ejpam-4085	31	2	(	(	PUNCT
ejpam-4085	31	3	xq+1)2(yq+1)2	xq+1)2(yq+1)2	PROPN
ejpam-4085	31	4	.	.	PUNCT
ejpam-4085	32	1	next	next	ADV
ejpam-4085	32	2	we	we	PRON
ejpam-4085	32	3	take	take	VERB
ejpam-4085	32	4	the	the	DET
ejpam-4085	32	5	double	double	ADJ
ejpam-4085	32	6	infinite	infinite	NOUN
ejpam-4085	32	7	integral	integral	ADJ
ejpam-4085	32	8	over	over	ADP
ejpam-4085	32	9	x	x	SYM
ejpam-4085	32	10	∈	∈	PROPN
ejpam-4085	32	11	(	(	PUNCT
ejpam-4085	32	12	0,∞	0,∞	NOUN
ejpam-4085	32	13	)	)	PUNCT
ejpam-4085	32	14	and	and	CCONJ
ejpam-4085	32	15	y	y	PROPN
ejpam-4085	32	16	∈	∈	PROPN
ejpam-4085	32	17	(	(	PUNCT
ejpam-4085	32	18	0,∞	0,∞	NOUN
ejpam-4085	32	19	)	)	PUNCT
ejpam-4085	32	20	to	to	PART
ejpam-4085	32	21	get	get	VERB
ejpam-4085	32	22	(	(	PUNCT
ejpam-4085	32	23	3	3	NUM
ejpam-4085	32	24	)	)	PUNCT
ejpam-4085	32	25	1	1	NUM
ejpam-4085	32	26	γ(k	γ(k	NOUN
ejpam-4085	32	27	+	+	CCONJ
ejpam-4085	32	28	1	1	X
ejpam-4085	32	29	)	)	PUNCT
ejpam-4085	32	30	∫	∫	PROPN
ejpam-4085	33	1	∞	∞	PROPN
ejpam-4085	33	2	0	0	NUM
ejpam-4085	33	3	∫	∫	PROPN
ejpam-4085	33	4	∞	∞	NOUN
ejpam-4085	33	5	0	0	PUNCT
ejpam-4085	34	1	xm−1ym+	xm−1ym+	NOUN
ejpam-4085	34	2	q	q	PROPN
ejpam-4085	34	3	2	2	NUM
ejpam-4085	34	4	−1	−1	NOUN
ejpam-4085	34	5	logk(axy	logk(axy	NOUN
ejpam-4085	34	6	)	)	PUNCT
ejpam-4085	34	7	(	(	PUNCT
ejpam-4085	34	8	xq	xq	X
ejpam-4085	34	9	+	+	PROPN
ejpam-4085	34	10	1)2	1)2	NUM
ejpam-4085	34	11	(	(	PUNCT
ejpam-4085	34	12	yq	yq	PROPN
ejpam-4085	34	13	+	+	PROPN
ejpam-4085	34	14	1)2	1)2	NUM
ejpam-4085	34	15	dxdy	dxdy	NOUN
ejpam-4085	34	16	=	=	SYM
ejpam-4085	34	17	1	1	NUM
ejpam-4085	34	18	2πi	2πi	NOUN
ejpam-4085	34	19	∫	∫	PROPN
ejpam-4085	35	1	∞	∞	PROPN
ejpam-4085	35	2	0	0	NUM
ejpam-4085	36	1	∫	∫	PROPN
ejpam-4085	36	2	∞	∞	PROPN
ejpam-4085	36	3	0	0	NUM
ejpam-4085	37	1	∫	∫	PROPN
ejpam-4085	37	2	c	c	NOUN
ejpam-4085	37	3	aww−k−1xm+w−1ym+	aww−k−1xm+w−1ym+	NOUN
ejpam-4085	37	4	q	q	PROPN
ejpam-4085	37	5	2	2	NUM
ejpam-4085	37	6	+	+	ADJ
ejpam-4085	37	7	w−1	w−1	PROPN
ejpam-4085	37	8	(	(	PUNCT
ejpam-4085	37	9	xq	xq	PROPN
ejpam-4085	37	10	+	+	PROPN
ejpam-4085	37	11	1)2	1)2	NUM
ejpam-4085	37	12	(	(	PUNCT
ejpam-4085	37	13	yq	yq	PROPN
ejpam-4085	37	14	+	+	PROPN
ejpam-4085	38	1	1)2	1)2	NUM
ejpam-4085	38	2	dwdxdy	dwdxdy	NOUN
ejpam-4085	38	3	=	=	SYM
ejpam-4085	38	4	1	1	NUM
ejpam-4085	38	5	2πi	2πi	NOUN
ejpam-4085	38	6	∫	∫	PROPN
ejpam-4085	39	1	c	c	PROPN
ejpam-4085	39	2	∫	∫	PROPN
ejpam-4085	40	1	∞	∞	NUM
ejpam-4085	40	2	0	0	NUM
ejpam-4085	41	1	∫	∫	PROPN
ejpam-4085	41	2	∞	∞	NUM
ejpam-4085	41	3	0	0	NUM
ejpam-4085	42	1	aww−k−1xm+w−1ym+	aww−k−1xm+w−1ym+	NOUN
ejpam-4085	42	2	q	q	NOUN
ejpam-4085	43	1	2	2	NUM
ejpam-4085	43	2	+	+	ADJ
ejpam-4085	43	3	w−1	w−1	PROPN
ejpam-4085	43	4	(	(	PUNCT
ejpam-4085	43	5	xq	xq	PROPN
ejpam-4085	43	6	+	+	PROPN
ejpam-4085	43	7	1)2	1)2	NUM
ejpam-4085	43	8	(	(	PUNCT
ejpam-4085	43	9	yq	yq	PROPN
ejpam-4085	43	10	+	+	PROPN
ejpam-4085	43	11	1)2	1)2	NUM
ejpam-4085	43	12	dxdydw	dxdydw	NOUN
ejpam-4085	43	13	=	=	SYM
ejpam-4085	43	14	1	1	NUM
ejpam-4085	43	15	2πi	2πi	NOUN
ejpam-4085	43	16	∫	∫	PROPN
ejpam-4085	44	1	c	c	PROPN
ejpam-4085	44	2	π2aww−k−1(m−	π2aww−k−1(m−	PROPN
ejpam-4085	44	3	q	q	PROPN
ejpam-4085	45	1	+	+	CCONJ
ejpam-4085	46	1	w)(2m−	w)(2m−	ADV
ejpam-4085	46	2	q	q	NOUN
ejpam-4085	47	1	+	+	NUM
ejpam-4085	47	2	2w	2w	NUM
ejpam-4085	47	3	)	)	PUNCT
ejpam-4085	47	4	csc	csc	PROPN
ejpam-4085	47	5	(	(	PUNCT
ejpam-4085	47	6	2π(m+w	2π(m+w	NUM
ejpam-4085	47	7	)	)	PUNCT
ejpam-4085	47	8	q	q	NOUN
ejpam-4085	47	9	)	)	PUNCT
ejpam-4085	47	10	q4	q4	PROPN
ejpam-4085	47	11	dw	dw	PROPN
ejpam-4085	47	12	from	from	ADP
ejpam-4085	47	13	equation	equation	NOUN
ejpam-4085	47	14	(	(	PUNCT
ejpam-4085	47	15	3.241.5	3.241.5	NUM
ejpam-4085	47	16	)	)	PUNCT
ejpam-4085	47	17	in	in	ADP
ejpam-4085	47	18	[	[	X
ejpam-4085	47	19	1	1	X
ejpam-4085	47	20	]	]	PUNCT
ejpam-4085	47	21	where	where	SCONJ
ejpam-4085	47	22	re(w	re(w	ADV
ejpam-4085	47	23	+	+	NUM
ejpam-4085	47	24	m	m	NOUN
ejpam-4085	47	25	)	)	PUNCT
ejpam-4085	47	26	<	<	X
ejpam-4085	47	27	2q	2q	NUM
ejpam-4085	47	28	.	.	PUNCT
ejpam-4085	48	1	we	we	PRON
ejpam-4085	48	2	are	be	AUX
ejpam-4085	48	3	able	able	ADJ
ejpam-4085	48	4	to	to	PART
ejpam-4085	48	5	switch	switch	VERB
ejpam-4085	48	6	the	the	DET
ejpam-4085	48	7	order	order	NOUN
ejpam-4085	48	8	of	of	ADP
ejpam-4085	48	9	integration	integration	NOUN
ejpam-4085	48	10	over	over	ADP
ejpam-4085	48	11	z	z	PROPN
ejpam-4085	48	12	,	,	PUNCT
ejpam-4085	48	13	x	x	PUNCT
ejpam-4085	48	14	and	and	CCONJ
ejpam-4085	48	15	y	y	PROPN
ejpam-4085	48	16	using	use	VERB
ejpam-4085	48	17	fubini	fubini	NOUN
ejpam-4085	48	18	’s	’s	PART
ejpam-4085	48	19	theorem	theorem	NOUN
ejpam-4085	48	20	since	since	SCONJ
ejpam-4085	48	21	the	the	DET
ejpam-4085	48	22	integrand	integrand	NOUN
ejpam-4085	48	23	is	be	AUX
ejpam-4085	48	24	of	of	ADP
ejpam-4085	48	25	bounded	bounded	ADJ
ejpam-4085	48	26	measure	measure	NOUN
ejpam-4085	48	27	over	over	ADP
ejpam-4085	48	28	the	the	DET
ejpam-4085	48	29	space	space	NOUN
ejpam-4085	48	30	c	c	NOUN
ejpam-4085	48	31	×	×	PROPN
ejpam-4085	48	32	r×	r×	PROPN
ejpam-4085	48	33	r.	r.	PROPN
ejpam-4085	48	34	3	3	NUM
ejpam-4085	48	35	.	.	PUNCT
ejpam-4085	49	1	the	the	DET
ejpam-4085	49	2	lerch	lerch	PROPN
ejpam-4085	49	3	function	function	NOUN
ejpam-4085	49	4	we	we	PRON
ejpam-4085	49	5	use	use	VERB
ejpam-4085	49	6	(	(	PUNCT
ejpam-4085	49	7	9.550	9.550	NUM
ejpam-4085	49	8	)	)	PUNCT
ejpam-4085	49	9	and	and	CCONJ
ejpam-4085	49	10	(	(	PUNCT
ejpam-4085	49	11	9.556	9.556	NUM
ejpam-4085	49	12	)	)	PUNCT
ejpam-4085	49	13	in	in	ADP
ejpam-4085	49	14	[	[	X
ejpam-4085	49	15	1	1	X
ejpam-4085	49	16	]	]	PUNCT
ejpam-4085	49	17	where	where	SCONJ
ejpam-4085	49	18	φ(z	φ(z	PROPN
ejpam-4085	49	19	,	,	PUNCT
ejpam-4085	49	20	s	s	NOUN
ejpam-4085	49	21	,	,	PUNCT
ejpam-4085	49	22	v	v	NOUN
ejpam-4085	49	23	)	)	PUNCT
ejpam-4085	49	24	is	be	AUX
ejpam-4085	49	25	the	the	DET
ejpam-4085	49	26	lerch	lerch	PROPN
ejpam-4085	49	27	function	function	NOUN
ejpam-4085	49	28	which	which	PRON
ejpam-4085	49	29	is	be	AUX
ejpam-4085	49	30	a	a	DET
ejpam-4085	49	31	generalization	generalization	NOUN
ejpam-4085	49	32	of	of	ADP
ejpam-4085	49	33	the	the	DET
ejpam-4085	49	34	hurwitz	hurwitz	PROPN
ejpam-4085	49	35	zeta	zeta	PROPN
ejpam-4085	49	36	ζ(s	ζ(s	PROPN
ejpam-4085	49	37	,	,	PUNCT
ejpam-4085	49	38	v	v	NOUN
ejpam-4085	49	39	)	)	PUNCT
ejpam-4085	49	40	and	and	CCONJ
ejpam-4085	49	41	polylogarithm	polylogarithm	PROPN
ejpam-4085	49	42	functions	function	NOUN
ejpam-4085	49	43	lin(z	lin(z	PROPN
ejpam-4085	49	44	)	)	PUNCT
ejpam-4085	49	45	.	.	PUNCT
ejpam-4085	50	1	the	the	DET
ejpam-4085	50	2	lerch	lerch	PROPN
ejpam-4085	50	3	function	function	PROPN
ejpam-4085	50	4	has	have	VERB
ejpam-4085	50	5	a	a	DET
ejpam-4085	50	6	series	series	NOUN
ejpam-4085	50	7	representation	representation	NOUN
ejpam-4085	50	8	given	give	VERB
ejpam-4085	50	9	by	by	ADP
ejpam-4085	50	10	r.	r.	PROPN
ejpam-4085	50	11	reynolds	reynolds	PROPN
ejpam-4085	50	12	,	,	PUNCT
ejpam-4085	50	13	a.	a.	PROPN
ejpam-4085	50	14	stauffer	stauffer	PROPN
ejpam-4085	50	15	/	/	SYM
ejpam-4085	50	16	eur	eur	PROPN
ejpam-4085	50	17	.	.	PUNCT
ejpam-4085	51	1	j.	j.	PROPN
ejpam-4085	51	2	pure	pure	PROPN
ejpam-4085	51	3	appl	appl	PROPN
ejpam-4085	51	4	.	.	PROPN
ejpam-4085	51	5	math	math	PROPN
ejpam-4085	51	6	,	,	PUNCT
ejpam-4085	51	7	14	14	NUM
ejpam-4085	51	8	(	(	PUNCT
ejpam-4085	51	9	4	4	NUM
ejpam-4085	51	10	)	)	PUNCT
ejpam-4085	51	11	(	(	PUNCT
ejpam-4085	51	12	2021	2021	NUM
ejpam-4085	51	13	)	)	PUNCT
ejpam-4085	51	14	,	,	PUNCT
ejpam-4085	51	15	1337	1337	NUM
ejpam-4085	51	16	-	-	SYM
ejpam-4085	51	17	1349	1349	NUM
ejpam-4085	51	18	1339	1339	NUM
ejpam-4085	51	19	φ(z	φ(z	PROPN
ejpam-4085	51	20	,	,	PUNCT
ejpam-4085	51	21	s	s	NOUN
ejpam-4085	51	22	,	,	PUNCT
ejpam-4085	51	23	v	v	NOUN
ejpam-4085	51	24	)	)	PUNCT
ejpam-4085	51	25	=	=	PUNCT
ejpam-4085	52	1	∞∑	∞∑	NUM
ejpam-4085	52	2	n=0	n=0	NUM
ejpam-4085	52	3	(	(	PUNCT
ejpam-4085	52	4	v	v	NOUN
ejpam-4085	52	5	+	+	PRON
ejpam-4085	52	6	n)−szn	n)−szn	NUM
ejpam-4085	52	7	(	(	PUNCT
ejpam-4085	52	8	4	4	NUM
ejpam-4085	52	9	)	)	PUNCT
ejpam-4085	52	10	where	where	SCONJ
ejpam-4085	52	11	|z|	|z|	VERB
ejpam-4085	52	12	<	<	X
ejpam-4085	52	13	1	1	NUM
ejpam-4085	52	14	,	,	PUNCT
ejpam-4085	52	15	v	v	ADP
ejpam-4085	52	16	̸=	̸=	PROPN
ejpam-4085	52	17	0,−1	0,−1	PROPN
ejpam-4085	52	18	,	,	PUNCT
ejpam-4085	52	19	..	..	PUNCT
ejpam-4085	52	20	and	and	CCONJ
ejpam-4085	52	21	is	be	AUX
ejpam-4085	52	22	continued	continue	VERB
ejpam-4085	52	23	analytically	analytically	ADV
ejpam-4085	52	24	by	by	ADP
ejpam-4085	52	25	its	its	PRON
ejpam-4085	52	26	integral	integral	ADJ
ejpam-4085	52	27	representation	representation	NOUN
ejpam-4085	52	28	given	give	VERB
ejpam-4085	52	29	by	by	ADP
ejpam-4085	52	30	φ(z	φ(z	PROPN
ejpam-4085	52	31	,	,	PUNCT
ejpam-4085	52	32	s	s	NOUN
ejpam-4085	52	33	,	,	PUNCT
ejpam-4085	52	34	v	v	NOUN
ejpam-4085	52	35	)	)	PUNCT
ejpam-4085	52	36	=	=	SYM
ejpam-4085	52	37	1	1	NUM
ejpam-4085	52	38	γ(s	γ(	NOUN
ejpam-4085	52	39	)	)	PUNCT
ejpam-4085	52	40	∫	∫	PROPN
ejpam-4085	53	1	∞	∞	PROPN
ejpam-4085	53	2	0	0	NUM
ejpam-4085	54	1	ts−1e−vt	ts−1e−vt	PRON
ejpam-4085	55	1	1−	1−	NUM
ejpam-4085	55	2	ze−t	ze−t	NOUN
ejpam-4085	55	3	dt	dt	NOUN
ejpam-4085	56	1	=	=	SYM
ejpam-4085	56	2	1	1	NUM
ejpam-4085	56	3	γ(s	γ(s	PROPN
ejpam-4085	56	4	)	)	PUNCT
ejpam-4085	56	5	∫	∫	PROPN
ejpam-4085	57	1	∞	∞	NUM
ejpam-4085	57	2	0	0	NUM
ejpam-4085	58	1	ts−1e−(v−1)t	ts−1e−(v−1)t	PROPN
ejpam-4085	58	2	et	et	NOUN
ejpam-4085	58	3	−	−	NOUN
ejpam-4085	58	4	z	z	NOUN
ejpam-4085	58	5	dt	dt	X
ejpam-4085	58	6	(	(	PUNCT
ejpam-4085	58	7	5	5	NUM
ejpam-4085	58	8	)	)	PUNCT
ejpam-4085	58	9	where	where	SCONJ
ejpam-4085	58	10	re(v	re(v	NOUN
ejpam-4085	58	11	)	)	PUNCT
ejpam-4085	58	12	>	>	X
ejpam-4085	58	13	0	0	NUM
ejpam-4085	58	14	,	,	PUNCT
ejpam-4085	58	15	and	and	CCONJ
ejpam-4085	58	16	either	either	ADV
ejpam-4085	58	17	|z|≤	|z|≤	SYM
ejpam-4085	58	18	1	1	NUM
ejpam-4085	58	19	,	,	PUNCT
ejpam-4085	58	20	z	z	NOUN
ejpam-4085	58	21	̸=	̸=	PROPN
ejpam-4085	58	22	1	1	NUM
ejpam-4085	58	23	,	,	PUNCT
ejpam-4085	58	24	re(s	re(s	ADJ
ejpam-4085	58	25	)	)	PUNCT
ejpam-4085	58	26	>	>	X
ejpam-4085	58	27	0	0	NUM
ejpam-4085	58	28	,	,	PUNCT
ejpam-4085	58	29	or	or	CCONJ
ejpam-4085	58	30	z	z	NOUN
ejpam-4085	58	31	=	=	SYM
ejpam-4085	58	32	1	1	NUM
ejpam-4085	58	33	,	,	PUNCT
ejpam-4085	58	34	re(s	re(s	ADJ
ejpam-4085	58	35	)	)	PUNCT
ejpam-4085	58	36	>	>	X
ejpam-4085	59	1	1	1	NUM
ejpam-4085	59	2	.	.	X
ejpam-4085	59	3	4	4	NUM
ejpam-4085	59	4	.	.	X
ejpam-4085	59	5	infinite	infinite	ADJ
ejpam-4085	59	6	sum	sum	NOUN
ejpam-4085	59	7	of	of	ADP
ejpam-4085	59	8	the	the	DET
ejpam-4085	59	9	contour	contour	NOUN
ejpam-4085	59	10	integral	integral	ADJ
ejpam-4085	59	11	4.1	4.1	NUM
ejpam-4085	59	12	.	.	PUNCT
ejpam-4085	60	1	derivation	derivation	NOUN
ejpam-4085	60	2	of	of	ADP
ejpam-4085	60	3	the	the	DET
ejpam-4085	60	4	first	first	ADJ
ejpam-4085	60	5	contour	contour	NOUN
ejpam-4085	60	6	integral	integral	ADJ
ejpam-4085	60	7	in	in	ADP
ejpam-4085	60	8	this	this	DET
ejpam-4085	60	9	section	section	NOUN
ejpam-4085	60	10	we	we	PRON
ejpam-4085	60	11	will	will	AUX
ejpam-4085	60	12	again	again	ADV
ejpam-4085	60	13	use	use	VERB
ejpam-4085	60	14	cauchy	cauchy	NOUN
ejpam-4085	60	15	’s	’s	PART
ejpam-4085	60	16	integral	integral	ADJ
ejpam-4085	60	17	formula	formula	NOUN
ejpam-4085	60	18	(	(	PUNCT
ejpam-4085	60	19	2	2	NUM
ejpam-4085	60	20	)	)	PUNCT
ejpam-4085	60	21	and	and	CCONJ
ejpam-4085	60	22	taking	take	VERB
ejpam-4085	60	23	the	the	DET
ejpam-4085	60	24	infinite	infinite	ADJ
ejpam-4085	60	25	sum	sum	NOUN
ejpam-4085	60	26	to	to	PART
ejpam-4085	60	27	derive	derive	VERB
ejpam-4085	60	28	equivalent	equivalent	ADJ
ejpam-4085	60	29	sum	sum	NOUN
ejpam-4085	60	30	representations	representation	NOUN
ejpam-4085	60	31	for	for	ADP
ejpam-4085	60	32	the	the	DET
ejpam-4085	60	33	contour	contour	NOUN
ejpam-4085	60	34	integrals	integral	NOUN
ejpam-4085	60	35	.	.	PUNCT
ejpam-4085	61	1	we	we	PRON
ejpam-4085	61	2	proceed	proceed	VERB
ejpam-4085	61	3	using	use	VERB
ejpam-4085	61	4	equation	equation	NOUN
ejpam-4085	61	5	(	(	PUNCT
ejpam-4085	61	6	2	2	NUM
ejpam-4085	61	7	)	)	PUNCT
ejpam-4085	61	8	and	and	CCONJ
ejpam-4085	61	9	replace	replace	VERB
ejpam-4085	61	10	y	y	PROPN
ejpam-4085	61	11	by	by	ADP
ejpam-4085	61	12	log(a	log(a	PROPN
ejpam-4085	61	13	)	)	PUNCT
ejpam-4085	61	14	+	+	CCONJ
ejpam-4085	62	1	2iπ(2y+1	2iπ(2y+1	X
ejpam-4085	62	2	)	)	PUNCT
ejpam-4085	62	3	q	q	NOUN
ejpam-4085	62	4	and	and	CCONJ
ejpam-4085	62	5	multiply	multiply	VERB
ejpam-4085	62	6	both	both	DET
ejpam-4085	62	7	sides	side	NOUN
ejpam-4085	62	8	by	by	ADP
ejpam-4085	62	9	−4iπ2m2e	−4iπ2m2e	PROPN
ejpam-4085	62	10	2iπm(2y+1	2iπm(2y+1	NUM
ejpam-4085	62	11	)	)	PUNCT
ejpam-4085	63	1	q	q	PROPN
ejpam-4085	63	2	q4	q4	PROPN
ejpam-4085	63	3	and	and	CCONJ
ejpam-4085	63	4	take	take	VERB
ejpam-4085	63	5	the	the	DET
ejpam-4085	63	6	infinite	infinite	ADJ
ejpam-4085	63	7	sum	sum	NOUN
ejpam-4085	63	8	over	over	ADP
ejpam-4085	63	9	y	y	PROPN
ejpam-4085	63	10	∈	∈	PROPN
ejpam-4085	64	1	[	[	X
ejpam-4085	64	2	0,∞	0,∞	NOUN
ejpam-4085	64	3	)	)	PUNCT
ejpam-4085	64	4	simplifying	simplify	VERB
ejpam-4085	64	5	in	in	ADP
ejpam-4085	64	6	terms	term	NOUN
ejpam-4085	64	7	of	of	ADP
ejpam-4085	64	8	the	the	DET
ejpam-4085	64	9	lerch	lerch	PROPN
ejpam-4085	64	10	function	function	NOUN
ejpam-4085	64	11	to	to	PART
ejpam-4085	64	12	get	get	VERB
ejpam-4085	64	13	(	(	PUNCT
ejpam-4085	64	14	6	6	NUM
ejpam-4085	64	15	)	)	PUNCT
ejpam-4085	64	16	4k+1πk+2m2	4k+1πk+2m2	NUM
ejpam-4085	64	17	(	(	PUNCT
ejpam-4085	64	18	i	i	PRON
ejpam-4085	64	19	q	q	PROPN
ejpam-4085	64	20	)	)	PUNCT
ejpam-4085	65	1	k−1	k−1	PROPN
ejpam-4085	65	2	e	e	PROPN
ejpam-4085	66	1	2iπm	2iπm	NUM
ejpam-4085	66	2	q	q	X
ejpam-4085	66	3	φ	φ	X
ejpam-4085	66	4	(	(	PUNCT
ejpam-4085	66	5	e	e	PROPN
ejpam-4085	66	6	4imπ	4imπ	NUM
ejpam-4085	66	7	q	q	X
ejpam-4085	66	8	,	,	PUNCT
ejpam-4085	66	9	−k	−k	PROPN
ejpam-4085	66	10	,	,	PUNCT
ejpam-4085	66	11	12	12	NUM
ejpam-4085	66	12	−	−	NOUN
ejpam-4085	66	13	iq	iq	NOUN
ejpam-4085	66	14	log(a	log(a	PROPN
ejpam-4085	66	15	)	)	PUNCT
ejpam-4085	66	16	4π	4π	NUM
ejpam-4085	66	17	)	)	PUNCT
ejpam-4085	66	18	q5γ(k	q5γ(k	NOUN
ejpam-4085	66	19	+	+	CCONJ
ejpam-4085	66	20	1	1	X
ejpam-4085	66	21	)	)	PUNCT
ejpam-4085	66	22	=	=	SYM
ejpam-4085	66	23	−	−	PROPN
ejpam-4085	66	24	1	1	NUM
ejpam-4085	66	25	2πi	2πi	NOUN
ejpam-4085	66	26	∞∑	∞∑	NUM
ejpam-4085	66	27	y=0	y=0	NUM
ejpam-4085	66	28	∫	∫	PROPN
ejpam-4085	66	29	c	c	PROPN
ejpam-4085	66	30	4iπ2m2aww−k−1e	4iπ2m2aww−k−1e	PROPN
ejpam-4085	66	31	2iπ(2y+1)(m+w	2iπ(2y+1)(m+w	NUM
ejpam-4085	66	32	)	)	PUNCT
ejpam-4085	66	33	q	q	PROPN
ejpam-4085	66	34	q4	q4	PROPN
ejpam-4085	66	35	dw	dw	PROPN
ejpam-4085	66	36	=	=	NOUN
ejpam-4085	66	37	−	−	PROPN
ejpam-4085	66	38	1	1	NUM
ejpam-4085	66	39	2πi	2πi	NOUN
ejpam-4085	66	40	∫	∫	PROPN
ejpam-4085	66	41	c	c	NOUN
ejpam-4085	66	42	∞∑	∞∑	NUM
ejpam-4085	66	43	y=0	y=0	X
ejpam-4085	66	44	4iπ2m2aww−k−1e	4iπ2m2aww−k−1e	NOUN
ejpam-4085	66	45	2iπ(2y+1)(m+w	2iπ(2y+1)(m+w	NUM
ejpam-4085	66	46	)	)	PUNCT
ejpam-4085	66	47	q	q	PROPN
ejpam-4085	66	48	q4	q4	PROPN
ejpam-4085	66	49	dw	dw	PROPN
ejpam-4085	66	50	=	=	SYM
ejpam-4085	66	51	1	1	NUM
ejpam-4085	66	52	2πi	2πi	ADJ
ejpam-4085	66	53	∫	∫	PROPN
ejpam-4085	66	54	c	c	PROPN
ejpam-4085	66	55	2π2m2aww−k−1	2π2m2aww−k−1	NUM
ejpam-4085	66	56	csc	csc	PROPN
ejpam-4085	66	57	(	(	PUNCT
ejpam-4085	66	58	2π(m+w	2π(m+w	NUM
ejpam-4085	66	59	)	)	PUNCT
ejpam-4085	66	60	q	q	NOUN
ejpam-4085	66	61	)	)	PUNCT
ejpam-4085	66	62	q4	q4	PROPN
ejpam-4085	66	63	dw	dw	PROPN
ejpam-4085	66	64	from	from	ADP
ejpam-4085	66	65	equation	equation	NOUN
ejpam-4085	66	66	(	(	PUNCT
ejpam-4085	66	67	1.232.3	1.232.3	NUM
ejpam-4085	66	68	)	)	PUNCT
ejpam-4085	66	69	in	in	ADP
ejpam-4085	66	70	[	[	X
ejpam-4085	66	71	1	1	X
ejpam-4085	66	72	]	]	PUNCT
ejpam-4085	66	73	where	where	SCONJ
ejpam-4085	66	74	im(m+	im(m+	PROPN
ejpam-4085	66	75	w	w	NOUN
ejpam-4085	66	76	)	)	PUNCT
ejpam-4085	66	77	>	>	X
ejpam-4085	66	78	0	0	PUNCT
ejpam-4085	67	1	for	for	ADP
ejpam-4085	67	2	convergence	convergence	NOUN
ejpam-4085	67	3	of	of	ADP
ejpam-4085	67	4	the	the	DET
ejpam-4085	67	5	sum	sum	NOUN
ejpam-4085	67	6	.	.	PUNCT
ejpam-4085	68	1	4.2	4.2	NUM
ejpam-4085	68	2	.	.	PUNCT
ejpam-4085	69	1	derivation	derivation	NOUN
ejpam-4085	69	2	of	of	ADP
ejpam-4085	69	3	the	the	DET
ejpam-4085	69	4	second	second	ADJ
ejpam-4085	69	5	contour	contour	NOUN
ejpam-4085	69	6	integral	integral	ADJ
ejpam-4085	69	7	in	in	ADP
ejpam-4085	69	8	this	this	DET
ejpam-4085	69	9	section	section	NOUN
ejpam-4085	69	10	we	we	PRON
ejpam-4085	69	11	will	will	AUX
ejpam-4085	69	12	again	again	ADV
ejpam-4085	69	13	use	use	VERB
ejpam-4085	69	14	cauchy	cauchy	NOUN
ejpam-4085	69	15	’s	’s	PART
ejpam-4085	69	16	integral	integral	ADJ
ejpam-4085	69	17	formula	formula	NOUN
ejpam-4085	69	18	(	(	PUNCT
ejpam-4085	69	19	2	2	NUM
ejpam-4085	69	20	)	)	PUNCT
ejpam-4085	69	21	and	and	CCONJ
ejpam-4085	69	22	taking	take	VERB
ejpam-4085	69	23	the	the	DET
ejpam-4085	69	24	infinite	infinite	ADJ
ejpam-4085	69	25	sum	sum	NOUN
ejpam-4085	69	26	to	to	PART
ejpam-4085	69	27	derive	derive	VERB
ejpam-4085	69	28	equivalent	equivalent	ADJ
ejpam-4085	69	29	sum	sum	NOUN
ejpam-4085	69	30	representations	representation	NOUN
ejpam-4085	69	31	for	for	ADP
ejpam-4085	69	32	the	the	DET
ejpam-4085	69	33	contour	contour	NOUN
ejpam-4085	69	34	integrals	integral	NOUN
ejpam-4085	69	35	.	.	PUNCT
ejpam-4085	70	1	we	we	PRON
ejpam-4085	70	2	proceed	proceed	VERB
ejpam-4085	70	3	using	use	VERB
ejpam-4085	70	4	equation	equation	NOUN
ejpam-4085	70	5	(	(	PUNCT
ejpam-4085	70	6	2	2	NUM
ejpam-4085	70	7	)	)	PUNCT
ejpam-4085	70	8	and	and	CCONJ
ejpam-4085	70	9	replace	replace	VERB
ejpam-4085	70	10	y	y	NOUN
ejpam-4085	70	11	by	by	ADP
ejpam-4085	70	12	log(a)+	log(a)+	NOUN
ejpam-4085	70	13	2iπ(2y+1	2iπ(2y+1	NUM
ejpam-4085	70	14	)	)	PUNCT
ejpam-4085	70	15	q	q	NOUN
ejpam-4085	70	16	and	and	CCONJ
ejpam-4085	70	17	multiply	multiply	VERB
ejpam-4085	70	18	both	both	DET
ejpam-4085	70	19	sides	side	NOUN
ejpam-4085	70	20	by	by	ADP
ejpam-4085	70	21	6iπ2me	6iπ2me	PROPN
ejpam-4085	70	22	2iπm(2y+1	2iπm(2y+1	NUM
ejpam-4085	70	23	)	)	PUNCT
ejpam-4085	70	24	q	q	PROPN
ejpam-4085	70	25	q3	q3	NOUN
ejpam-4085	70	26	and	and	CCONJ
ejpam-4085	70	27	take	take	VERB
ejpam-4085	70	28	the	the	DET
ejpam-4085	70	29	infinite	infinite	ADJ
ejpam-4085	70	30	sum	sum	NOUN
ejpam-4085	70	31	over	over	ADP
ejpam-4085	70	32	y	y	PROPN
ejpam-4085	70	33	∈	∈	PROPN
ejpam-4085	71	1	[	[	X
ejpam-4085	71	2	0,∞	0,∞	NOUN
ejpam-4085	71	3	)	)	PUNCT
ejpam-4085	71	4	simplifying	simplify	VERB
ejpam-4085	71	5	in	in	ADP
ejpam-4085	71	6	terms	term	NOUN
ejpam-4085	71	7	of	of	ADP
ejpam-4085	71	8	the	the	DET
ejpam-4085	71	9	lerch	lerch	PROPN
ejpam-4085	71	10	function	function	NOUN
ejpam-4085	71	11	to	to	PART
ejpam-4085	71	12	get	get	VERB
ejpam-4085	71	13	r.	r.	PROPN
ejpam-4085	71	14	reynolds	reynolds	PROPN
ejpam-4085	71	15	,	,	PUNCT
ejpam-4085	71	16	a.	a.	PROPN
ejpam-4085	71	17	stauffer	stauffer	PROPN
ejpam-4085	71	18	/	/	SYM
ejpam-4085	71	19	eur	eur	PROPN
ejpam-4085	71	20	.	.	PUNCT
ejpam-4085	72	1	j.	j.	PROPN
ejpam-4085	72	2	pure	pure	PROPN
ejpam-4085	72	3	appl	appl	PROPN
ejpam-4085	72	4	.	.	PROPN
ejpam-4085	72	5	math	math	PROPN
ejpam-4085	72	6	,	,	PUNCT
ejpam-4085	72	7	14	14	NUM
ejpam-4085	72	8	(	(	PUNCT
ejpam-4085	72	9	4	4	NUM
ejpam-4085	72	10	)	)	PUNCT
ejpam-4085	72	11	(	(	PUNCT
ejpam-4085	72	12	2021	2021	NUM
ejpam-4085	72	13	)	)	PUNCT
ejpam-4085	72	14	,	,	PUNCT
ejpam-4085	72	15	1337	1337	NUM
ejpam-4085	72	16	-	-	SYM
ejpam-4085	72	17	1349	1349	NUM
ejpam-4085	72	18	1340	1340	NUM
ejpam-4085	72	19	(	(	PUNCT
ejpam-4085	72	20	7	7	NUM
ejpam-4085	72	21	)	)	PUNCT
ejpam-4085	72	22	3i22k+1πk+2	3i22k+1πk+2	NUM
ejpam-4085	72	23	m	m	NOUN
ejpam-4085	72	24	(	(	PUNCT
ejpam-4085	72	25	i	i	PRON
ejpam-4085	72	26	q	q	NOUN
ejpam-4085	72	27	)	)	PUNCT
ejpam-4085	73	1	k	k	X
ejpam-4085	73	2	e	e	X
ejpam-4085	73	3	2iπm	2iπm	NUM
ejpam-4085	73	4	q	q	X
ejpam-4085	73	5	φ	φ	X
ejpam-4085	73	6	(	(	PUNCT
ejpam-4085	73	7	e	e	PROPN
ejpam-4085	73	8	4imπ	4imπ	NUM
ejpam-4085	73	9	q	q	X
ejpam-4085	73	10	,	,	PUNCT
ejpam-4085	73	11	−k	−k	PROPN
ejpam-4085	73	12	,	,	PUNCT
ejpam-4085	73	13	12	12	NUM
ejpam-4085	73	14	−	−	NOUN
ejpam-4085	73	15	iq	iq	NOUN
ejpam-4085	73	16	log(a	log(a	PROPN
ejpam-4085	73	17	)	)	PUNCT
ejpam-4085	73	18	4π	4π	NUM
ejpam-4085	73	19	)	)	PUNCT
ejpam-4085	73	20	q3γ(k	q3γ(k	PROPN
ejpam-4085	73	21	+	+	CCONJ
ejpam-4085	73	22	1	1	X
ejpam-4085	73	23	)	)	PUNCT
ejpam-4085	73	24	=	=	SYM
ejpam-4085	74	1	1	1	NUM
ejpam-4085	74	2	2πi	2πi	NOUN
ejpam-4085	74	3	∞∑	∞∑	NUM
ejpam-4085	74	4	y=0	y=0	NUM
ejpam-4085	74	5	∫	∫	PROPN
ejpam-4085	74	6	c	c	PROPN
ejpam-4085	74	7	6iπ2maww−k−1e	6iπ2maww−k−1e	NOUN
ejpam-4085	74	8	2iπ(2y+1)(m+w	2iπ(2y+1)(m+w	NUM
ejpam-4085	74	9	)	)	PUNCT
ejpam-4085	74	10	q	q	PROPN
ejpam-4085	74	11	q3	q3	NOUN
ejpam-4085	74	12	dw	dw	PROPN
ejpam-4085	74	13	=	=	SYM
ejpam-4085	74	14	1	1	NUM
ejpam-4085	74	15	2πi	2πi	NOUN
ejpam-4085	74	16	∫	∫	PROPN
ejpam-4085	74	17	c	c	NOUN
ejpam-4085	74	18	∞∑	∞∑	NUM
ejpam-4085	74	19	y=0	y=0	NOUN
ejpam-4085	74	20	6iπ2maww−k−1e	6iπ2maww−k−1e	NOUN
ejpam-4085	74	21	2iπ(2y+1)(m+w	2iπ(2y+1)(m+w	NUM
ejpam-4085	74	22	)	)	PUNCT
ejpam-4085	74	23	q	q	PROPN
ejpam-4085	74	24	q3	q3	NOUN
ejpam-4085	74	25	dw	dw	PROPN
ejpam-4085	74	26	=	=	SYM
ejpam-4085	75	1	−	−	PROPN
ejpam-4085	75	2	1	1	NUM
ejpam-4085	75	3	2πi	2πi	NOUN
ejpam-4085	75	4	∫	∫	PROPN
ejpam-4085	75	5	c	c	PROPN
ejpam-4085	75	6	3π2maww−k−1	3π2maww−k−1	PROPN
ejpam-4085	75	7	csc	csc	PROPN
ejpam-4085	75	8	(	(	PUNCT
ejpam-4085	75	9	2π(m+w	2π(m+w	NUM
ejpam-4085	75	10	)	)	PUNCT
ejpam-4085	75	11	q	q	NOUN
ejpam-4085	75	12	)	)	PUNCT
ejpam-4085	75	13	q3	q3	PROPN
ejpam-4085	75	14	dw	dw	PROPN
ejpam-4085	75	15	from	from	ADP
ejpam-4085	75	16	equation	equation	NOUN
ejpam-4085	75	17	(	(	PUNCT
ejpam-4085	75	18	1.232.3	1.232.3	NUM
ejpam-4085	75	19	)	)	PUNCT
ejpam-4085	75	20	in	in	ADP
ejpam-4085	75	21	[	[	X
ejpam-4085	75	22	1	1	X
ejpam-4085	75	23	]	]	PUNCT
ejpam-4085	75	24	where	where	SCONJ
ejpam-4085	75	25	im(m+	im(m+	PROPN
ejpam-4085	75	26	w	w	NOUN
ejpam-4085	75	27	)	)	PUNCT
ejpam-4085	75	28	>	>	X
ejpam-4085	75	29	0	0	PUNCT
ejpam-4085	76	1	for	for	ADP
ejpam-4085	76	2	convergence	convergence	NOUN
ejpam-4085	76	3	of	of	ADP
ejpam-4085	76	4	the	the	DET
ejpam-4085	76	5	sum	sum	NOUN
ejpam-4085	76	6	.	.	PUNCT
ejpam-4085	77	1	4.3	4.3	NUM
ejpam-4085	77	2	.	.	PUNCT
ejpam-4085	77	3	derivation	derivation	NOUN
ejpam-4085	77	4	of	of	ADP
ejpam-4085	77	5	the	the	DET
ejpam-4085	77	6	third	third	ADJ
ejpam-4085	77	7	contour	contour	NOUN
ejpam-4085	77	8	integral	integral	ADJ
ejpam-4085	77	9	in	in	ADP
ejpam-4085	77	10	this	this	DET
ejpam-4085	77	11	section	section	NOUN
ejpam-4085	77	12	we	we	PRON
ejpam-4085	77	13	will	will	AUX
ejpam-4085	77	14	again	again	ADV
ejpam-4085	77	15	use	use	VERB
ejpam-4085	77	16	cauchy	cauchy	NOUN
ejpam-4085	77	17	’s	’s	PART
ejpam-4085	77	18	integral	integral	ADJ
ejpam-4085	77	19	formula	formula	NOUN
ejpam-4085	77	20	(	(	PUNCT
ejpam-4085	77	21	2	2	NUM
ejpam-4085	77	22	)	)	PUNCT
ejpam-4085	77	23	and	and	CCONJ
ejpam-4085	77	24	taking	take	VERB
ejpam-4085	77	25	the	the	DET
ejpam-4085	77	26	infinite	infinite	ADJ
ejpam-4085	77	27	sum	sum	NOUN
ejpam-4085	77	28	to	to	PART
ejpam-4085	77	29	derive	derive	VERB
ejpam-4085	77	30	equivalent	equivalent	ADJ
ejpam-4085	77	31	sum	sum	NOUN
ejpam-4085	77	32	representations	representation	NOUN
ejpam-4085	77	33	for	for	ADP
ejpam-4085	77	34	the	the	DET
ejpam-4085	77	35	contour	contour	NOUN
ejpam-4085	77	36	integrals	integral	NOUN
ejpam-4085	77	37	.	.	PUNCT
ejpam-4085	78	1	we	we	PRON
ejpam-4085	78	2	proceed	proceed	VERB
ejpam-4085	78	3	using	use	VERB
ejpam-4085	78	4	equation	equation	NOUN
ejpam-4085	78	5	(	(	PUNCT
ejpam-4085	78	6	2	2	NUM
ejpam-4085	78	7	)	)	PUNCT
ejpam-4085	78	8	and	and	CCONJ
ejpam-4085	78	9	replace	replace	VERB
ejpam-4085	78	10	y	y	NOUN
ejpam-4085	78	11	by	by	ADP
ejpam-4085	78	12	log(a)+	log(a)+	NOUN
ejpam-4085	78	13	2iπ(2y+1	2iπ(2y+1	NUM
ejpam-4085	78	14	)	)	PUNCT
ejpam-4085	78	15	q	q	NOUN
ejpam-4085	78	16	and	and	CCONJ
ejpam-4085	78	17	multiply	multiply	VERB
ejpam-4085	78	18	both	both	DET
ejpam-4085	78	19	sides	side	NOUN
ejpam-4085	78	20	by	by	ADP
ejpam-4085	78	21	−2iπ2e	−2iπ2e	PROPN
ejpam-4085	78	22	2iπm(2y+1	2iπm(2y+1	NUM
ejpam-4085	78	23	)	)	PUNCT
ejpam-4085	78	24	q	q	PROPN
ejpam-4085	78	25	q2	q2	NOUN
ejpam-4085	78	26	and	and	CCONJ
ejpam-4085	78	27	take	take	VERB
ejpam-4085	78	28	the	the	DET
ejpam-4085	78	29	infinite	infinite	ADJ
ejpam-4085	78	30	sum	sum	NOUN
ejpam-4085	78	31	over	over	ADP
ejpam-4085	78	32	y	y	PROPN
ejpam-4085	78	33	∈	∈	PROPN
ejpam-4085	79	1	[	[	X
ejpam-4085	79	2	0,∞	0,∞	NOUN
ejpam-4085	79	3	)	)	PUNCT
ejpam-4085	79	4	simplifying	simplify	VERB
ejpam-4085	79	5	in	in	ADP
ejpam-4085	79	6	terms	term	NOUN
ejpam-4085	79	7	of	of	ADP
ejpam-4085	79	8	the	the	DET
ejpam-4085	79	9	lerch	lerch	PROPN
ejpam-4085	79	10	function	function	NOUN
ejpam-4085	79	11	to	to	PART
ejpam-4085	79	12	get	get	VERB
ejpam-4085	79	13	(	(	PUNCT
ejpam-4085	79	14	8)	8)	NUM
ejpam-4085	79	15	22k+1πk+2	22k+1πk+2	NUM
ejpam-4085	79	16	(	(	PUNCT
ejpam-4085	79	17	i	i	PRON
ejpam-4085	79	18	q	q	NOUN
ejpam-4085	79	19	)	)	PUNCT
ejpam-4085	79	20	k−1	k−1	PROPN
ejpam-4085	79	21	e	e	PROPN
ejpam-4085	80	1	2iπm	2iπm	NUM
ejpam-4085	80	2	q	q	X
ejpam-4085	80	3	φ	φ	X
ejpam-4085	80	4	(	(	PUNCT
ejpam-4085	80	5	e	e	PROPN
ejpam-4085	80	6	4imπ	4imπ	NUM
ejpam-4085	80	7	q	q	X
ejpam-4085	80	8	,	,	PUNCT
ejpam-4085	80	9	−k	−k	PROPN
ejpam-4085	80	10	,	,	PUNCT
ejpam-4085	80	11	12	12	NUM
ejpam-4085	80	12	−	−	NOUN
ejpam-4085	80	13	iq	iq	NOUN
ejpam-4085	80	14	log(a	log(a	PROPN
ejpam-4085	80	15	)	)	PUNCT
ejpam-4085	80	16	4π	4π	NUM
ejpam-4085	80	17	)	)	PUNCT
ejpam-4085	80	18	q3γ(k	q3γ(k	PROPN
ejpam-4085	80	19	+	+	CCONJ
ejpam-4085	80	20	1	1	X
ejpam-4085	80	21	)	)	PUNCT
ejpam-4085	80	22	=	=	SYM
ejpam-4085	80	23	−	−	PROPN
ejpam-4085	80	24	1	1	NUM
ejpam-4085	80	25	2πi	2πi	NOUN
ejpam-4085	80	26	∞∑	∞∑	NUM
ejpam-4085	80	27	y=0	y=0	NUM
ejpam-4085	80	28	∫	∫	PROPN
ejpam-4085	80	29	c	c	PROPN
ejpam-4085	80	30	2iπ2aww−k−1e	2iπ2aww−k−1e	PROPN
ejpam-4085	80	31	2iπ(2y+1)(m+w	2iπ(2y+1)(m+w	NUM
ejpam-4085	80	32	)	)	PUNCT
ejpam-4085	80	33	q	q	PROPN
ejpam-4085	80	34	q2	q2	NOUN
ejpam-4085	80	35	dw	dw	NOUN
ejpam-4085	81	1	=	=	SYM
ejpam-4085	82	1	−	−	PROPN
ejpam-4085	82	2	1	1	NUM
ejpam-4085	82	3	2πi	2πi	NOUN
ejpam-4085	82	4	∫	∫	PROPN
ejpam-4085	83	1	c	c	NOUN
ejpam-4085	83	2	∞∑	∞∑	NUM
ejpam-4085	83	3	y=0	y=0	NOUN
ejpam-4085	83	4	2iπ2aww−k−1e	2iπ2aww−k−1e	PROPN
ejpam-4085	83	5	2iπ(2y+1)(m+w	2iπ(2y+1)(m+w	NUM
ejpam-4085	83	6	)	)	PUNCT
ejpam-4085	83	7	q	q	PROPN
ejpam-4085	83	8	q2	q2	NOUN
ejpam-4085	83	9	dw	dw	NOUN
ejpam-4085	83	10	=	=	SYM
ejpam-4085	83	11	1	1	NUM
ejpam-4085	83	12	2πi	2πi	NOUN
ejpam-4085	83	13	∫	∫	PROPN
ejpam-4085	83	14	c	c	X
ejpam-4085	83	15	π2aww−k−1	π2aww−k−1	PUNCT
ejpam-4085	83	16	csc	csc	PROPN
ejpam-4085	83	17	(	(	PUNCT
ejpam-4085	83	18	2π(m+w	2π(m+w	NUM
ejpam-4085	83	19	)	)	PUNCT
ejpam-4085	83	20	q	q	NOUN
ejpam-4085	83	21	)	)	PUNCT
ejpam-4085	83	22	q2	q2	PROPN
ejpam-4085	83	23	dw	dw	PROPN
ejpam-4085	83	24	from	from	ADP
ejpam-4085	83	25	equation	equation	NOUN
ejpam-4085	83	26	(	(	PUNCT
ejpam-4085	83	27	1.232.3	1.232.3	NUM
ejpam-4085	83	28	)	)	PUNCT
ejpam-4085	83	29	in	in	ADP
ejpam-4085	83	30	[	[	X
ejpam-4085	83	31	1	1	X
ejpam-4085	83	32	]	]	PUNCT
ejpam-4085	83	33	where	where	SCONJ
ejpam-4085	83	34	im(m+	im(m+	PROPN
ejpam-4085	83	35	w	w	NOUN
ejpam-4085	83	36	)	)	PUNCT
ejpam-4085	83	37	>	>	X
ejpam-4085	83	38	0	0	PUNCT
ejpam-4085	84	1	for	for	ADP
ejpam-4085	84	2	convergence	convergence	NOUN
ejpam-4085	84	3	of	of	ADP
ejpam-4085	84	4	the	the	DET
ejpam-4085	84	5	sum	sum	NOUN
ejpam-4085	84	6	.	.	PUNCT
ejpam-4085	85	1	4.4	4.4	NUM
ejpam-4085	85	2	.	.	PUNCT
ejpam-4085	86	1	derivation	derivation	NOUN
ejpam-4085	86	2	of	of	ADP
ejpam-4085	86	3	the	the	DET
ejpam-4085	86	4	fourth	fourth	ADJ
ejpam-4085	86	5	contour	contour	NOUN
ejpam-4085	86	6	integral	integral	ADJ
ejpam-4085	86	7	in	in	ADP
ejpam-4085	86	8	this	this	DET
ejpam-4085	86	9	section	section	NOUN
ejpam-4085	86	10	we	we	PRON
ejpam-4085	86	11	will	will	AUX
ejpam-4085	86	12	again	again	ADV
ejpam-4085	86	13	use	use	VERB
ejpam-4085	86	14	cauchy	cauchy	NOUN
ejpam-4085	86	15	’s	’s	PART
ejpam-4085	86	16	integral	integral	ADJ
ejpam-4085	86	17	formula	formula	NOUN
ejpam-4085	86	18	(	(	PUNCT
ejpam-4085	86	19	2	2	NUM
ejpam-4085	86	20	)	)	PUNCT
ejpam-4085	86	21	and	and	CCONJ
ejpam-4085	86	22	taking	take	VERB
ejpam-4085	86	23	the	the	DET
ejpam-4085	86	24	infinite	infinite	ADJ
ejpam-4085	86	25	sum	sum	NOUN
ejpam-4085	86	26	to	to	PART
ejpam-4085	86	27	derive	derive	VERB
ejpam-4085	86	28	equivalent	equivalent	ADJ
ejpam-4085	86	29	sum	sum	NOUN
ejpam-4085	86	30	representations	representation	NOUN
ejpam-4085	86	31	for	for	ADP
ejpam-4085	86	32	the	the	DET
ejpam-4085	86	33	contour	contour	NOUN
ejpam-4085	86	34	integrals	integral	NOUN
ejpam-4085	86	35	.	.	PUNCT
ejpam-4085	87	1	we	we	PRON
ejpam-4085	87	2	proceed	proceed	VERB
ejpam-4085	87	3	using	use	VERB
ejpam-4085	87	4	equation	equation	NOUN
ejpam-4085	87	5	(	(	PUNCT
ejpam-4085	87	6	2	2	NUM
ejpam-4085	87	7	)	)	PUNCT
ejpam-4085	87	8	and	and	CCONJ
ejpam-4085	87	9	replace	replace	VERB
ejpam-4085	87	10	y	y	NOUN
ejpam-4085	87	11	by	by	ADP
ejpam-4085	87	12	log(a)+	log(a)+	NOUN
ejpam-4085	87	13	2iπ(2y+1	2iπ(2y+1	NUM
ejpam-4085	87	14	)	)	PUNCT
ejpam-4085	87	15	q	q	NOUN
ejpam-4085	87	16	and	and	CCONJ
ejpam-4085	87	17	multiply	multiply	VERB
ejpam-4085	87	18	both	both	DET
ejpam-4085	87	19	sides	side	NOUN
ejpam-4085	87	20	by	by	ADP
ejpam-4085	87	21	−4iπ2e	−4iπ2e	PROPN
ejpam-4085	87	22	2iπm(2y+1	2iπm(2y+1	NUM
ejpam-4085	87	23	)	)	PUNCT
ejpam-4085	87	24	q	q	PROPN
ejpam-4085	87	25	q4	q4	PROPN
ejpam-4085	87	26	and	and	CCONJ
ejpam-4085	87	27	replace	replace	VERB
ejpam-4085	87	28	k	k	PROPN
ejpam-4085	87	29	→	→	PUNCT
ejpam-4085	87	30	k	k	PROPN
ejpam-4085	88	1	−	−	PROPN
ejpam-4085	88	2	2	2	NUM
ejpam-4085	89	1	and	and	CCONJ
ejpam-4085	89	2	take	take	VERB
ejpam-4085	89	3	the	the	DET
ejpam-4085	89	4	infinite	infinite	ADJ
ejpam-4085	89	5	sum	sum	NOUN
ejpam-4085	89	6	over	over	ADP
ejpam-4085	89	7	y	y	PROPN
ejpam-4085	89	8	∈	∈	PROPN
ejpam-4085	90	1	[	[	X
ejpam-4085	90	2	0,∞	0,∞	NOUN
ejpam-4085	90	3	)	)	PUNCT
ejpam-4085	90	4	simplifying	simplify	VERB
ejpam-4085	90	5	in	in	ADP
ejpam-4085	90	6	terms	term	NOUN
ejpam-4085	90	7	of	of	ADP
ejpam-4085	90	8	the	the	DET
ejpam-4085	90	9	lerch	lerch	PROPN
ejpam-4085	90	10	function	function	NOUN
ejpam-4085	90	11	to	to	PART
ejpam-4085	90	12	get	get	VERB
ejpam-4085	90	13	r.	r.	PROPN
ejpam-4085	90	14	reynolds	reynolds	PROPN
ejpam-4085	90	15	,	,	PUNCT
ejpam-4085	90	16	a.	a.	PROPN
ejpam-4085	90	17	stauffer	stauffer	PROPN
ejpam-4085	90	18	/	/	SYM
ejpam-4085	90	19	eur	eur	PROPN
ejpam-4085	90	20	.	.	PUNCT
ejpam-4085	91	1	j.	j.	PROPN
ejpam-4085	91	2	pure	pure	PROPN
ejpam-4085	91	3	appl	appl	PROPN
ejpam-4085	91	4	.	.	PROPN
ejpam-4085	91	5	math	math	PROPN
ejpam-4085	91	6	,	,	PUNCT
ejpam-4085	91	7	14	14	NUM
ejpam-4085	91	8	(	(	PUNCT
ejpam-4085	91	9	4	4	NUM
ejpam-4085	91	10	)	)	PUNCT
ejpam-4085	91	11	(	(	PUNCT
ejpam-4085	91	12	2021	2021	NUM
ejpam-4085	91	13	)	)	PUNCT
ejpam-4085	91	14	,	,	PUNCT
ejpam-4085	91	15	1337	1337	NUM
ejpam-4085	91	16	-	-	SYM
ejpam-4085	91	17	1349	1349	NUM
ejpam-4085	91	18	1341	1341	NUM
ejpam-4085	91	19	(	(	PUNCT
ejpam-4085	91	20	9	9	NUM
ejpam-4085	91	21	)	)	PUNCT
ejpam-4085	91	22	4k−1πk	4k−1πk	NOUN
ejpam-4085	91	23	(	(	PUNCT
ejpam-4085	91	24	i	i	PRON
ejpam-4085	91	25	q	q	PROPN
ejpam-4085	91	26	)	)	PUNCT
ejpam-4085	92	1	k−3	k−3	PROPN
ejpam-4085	92	2	e	e	PROPN
ejpam-4085	92	3	2iπm	2iπm	PROPN
ejpam-4085	92	4	q	q	PROPN
ejpam-4085	92	5	φ	φ	X
ejpam-4085	92	6	(	(	PUNCT
ejpam-4085	92	7	e	e	PROPN
ejpam-4085	92	8	4imπ	4imπ	NUM
ejpam-4085	92	9	q	q	PROPN
ejpam-4085	92	10	,	,	PUNCT
ejpam-4085	92	11	2−	2−	NUM
ejpam-4085	92	12	k	k	NOUN
ejpam-4085	92	13	,	,	PUNCT
ejpam-4085	92	14	12	12	NUM
ejpam-4085	92	15	−	−	NOUN
ejpam-4085	92	16	iq	iq	PROPN
ejpam-4085	92	17	log(a	log(a	PROPN
ejpam-4085	92	18	)	)	PUNCT
ejpam-4085	92	19	4π	4π	NUM
ejpam-4085	92	20	)	)	PUNCT
ejpam-4085	92	21	q5γ(k	q5γ(k	NOUN
ejpam-4085	92	22	−	−	NOUN
ejpam-4085	92	23	1	1	NUM
ejpam-4085	92	24	)	)	PUNCT
ejpam-4085	92	25	=	=	SYM
ejpam-4085	92	26	−	−	PROPN
ejpam-4085	92	27	1	1	NUM
ejpam-4085	92	28	2πi	2πi	NOUN
ejpam-4085	92	29	∞∑	∞∑	NUM
ejpam-4085	92	30	y=0	y=0	NUM
ejpam-4085	92	31	∫	∫	PROPN
ejpam-4085	92	32	c	c	PROPN
ejpam-4085	92	33	4iπ2aww1−ke	4iπ2aww1−ke	NUM
ejpam-4085	92	34	2iπ(2y+1)(m+w	2iπ(2y+1)(m+w	NUM
ejpam-4085	92	35	)	)	PUNCT
ejpam-4085	92	36	q	q	PROPN
ejpam-4085	92	37	q4	q4	PROPN
ejpam-4085	92	38	dw	dw	PROPN
ejpam-4085	92	39	=	=	NOUN
ejpam-4085	92	40	−	−	PROPN
ejpam-4085	92	41	1	1	NUM
ejpam-4085	92	42	2πi	2πi	NOUN
ejpam-4085	92	43	∫	∫	PROPN
ejpam-4085	92	44	c	c	NOUN
ejpam-4085	92	45	∞∑	∞∑	NUM
ejpam-4085	92	46	y=0	y=0	NOUN
ejpam-4085	92	47	4iπ2aww1−ke	4iπ2aww1−ke	NUM
ejpam-4085	92	48	2iπ(2y+1)(m+w	2iπ(2y+1)(m+w	NUM
ejpam-4085	92	49	)	)	PUNCT
ejpam-4085	92	50	q	q	PROPN
ejpam-4085	92	51	q4	q4	PROPN
ejpam-4085	92	52	dw	dw	PROPN
ejpam-4085	92	53	=	=	SYM
ejpam-4085	92	54	1	1	NUM
ejpam-4085	92	55	2πi	2πi	ADJ
ejpam-4085	92	56	∫	∫	PROPN
ejpam-4085	93	1	c	c	PROPN
ejpam-4085	93	2	2π2aww1−k	2π2aww1−k	NUM
ejpam-4085	93	3	csc	csc	PROPN
ejpam-4085	93	4	(	(	PUNCT
ejpam-4085	93	5	2π(m+w	2π(m+w	NUM
ejpam-4085	93	6	)	)	PUNCT
ejpam-4085	93	7	q	q	NOUN
ejpam-4085	93	8	)	)	PUNCT
ejpam-4085	93	9	q4	q4	PROPN
ejpam-4085	93	10	dw	dw	PROPN
ejpam-4085	93	11	from	from	ADP
ejpam-4085	93	12	equation	equation	NOUN
ejpam-4085	93	13	(	(	PUNCT
ejpam-4085	93	14	1.232.3	1.232.3	NUM
ejpam-4085	93	15	)	)	PUNCT
ejpam-4085	93	16	in	in	ADP
ejpam-4085	93	17	[	[	X
ejpam-4085	93	18	1	1	X
ejpam-4085	93	19	]	]	PUNCT
ejpam-4085	94	1	where	where	SCONJ
ejpam-4085	94	2	im(m+	im(m+	PROPN
ejpam-4085	94	3	w	w	NOUN
ejpam-4085	94	4	)	)	PUNCT
ejpam-4085	94	5	>	>	X
ejpam-4085	94	6	0	0	PUNCT
ejpam-4085	94	7	for	for	ADP
ejpam-4085	94	8	convergence	convergence	NOUN
ejpam-4085	94	9	of	of	ADP
ejpam-4085	94	10	the	the	DET
ejpam-4085	94	11	sum	sum	NOUN
ejpam-4085	94	12	.	.	PUNCT
ejpam-4085	95	1	4.5	4.5	NUM
ejpam-4085	95	2	.	.	PUNCT
ejpam-4085	96	1	derivation	derivation	NOUN
ejpam-4085	96	2	of	of	ADP
ejpam-4085	96	3	the	the	DET
ejpam-4085	96	4	fifth	fifth	ADJ
ejpam-4085	96	5	contour	contour	NOUN
ejpam-4085	96	6	integral	integral	ADJ
ejpam-4085	96	7	in	in	ADP
ejpam-4085	96	8	this	this	DET
ejpam-4085	96	9	section	section	NOUN
ejpam-4085	96	10	we	we	PRON
ejpam-4085	96	11	will	will	AUX
ejpam-4085	96	12	again	again	ADV
ejpam-4085	96	13	use	use	VERB
ejpam-4085	96	14	cauchy	cauchy	NOUN
ejpam-4085	96	15	’s	’s	PART
ejpam-4085	96	16	integral	integral	ADJ
ejpam-4085	96	17	formula	formula	NOUN
ejpam-4085	96	18	(	(	PUNCT
ejpam-4085	96	19	2	2	NUM
ejpam-4085	96	20	)	)	PUNCT
ejpam-4085	96	21	and	and	CCONJ
ejpam-4085	96	22	taking	take	VERB
ejpam-4085	96	23	the	the	DET
ejpam-4085	96	24	infinite	infinite	ADJ
ejpam-4085	96	25	sum	sum	NOUN
ejpam-4085	96	26	to	to	PART
ejpam-4085	96	27	derive	derive	VERB
ejpam-4085	96	28	equivalent	equivalent	ADJ
ejpam-4085	96	29	sum	sum	NOUN
ejpam-4085	96	30	representations	representation	NOUN
ejpam-4085	96	31	for	for	ADP
ejpam-4085	96	32	the	the	DET
ejpam-4085	96	33	contour	contour	NOUN
ejpam-4085	96	34	integrals	integral	NOUN
ejpam-4085	96	35	.	.	PUNCT
ejpam-4085	97	1	we	we	PRON
ejpam-4085	97	2	proceed	proceed	VERB
ejpam-4085	97	3	using	use	VERB
ejpam-4085	97	4	equation	equation	NOUN
ejpam-4085	97	5	(	(	PUNCT
ejpam-4085	97	6	2	2	NUM
ejpam-4085	97	7	)	)	PUNCT
ejpam-4085	97	8	and	and	CCONJ
ejpam-4085	97	9	replace	replace	VERB
ejpam-4085	97	10	y	y	NOUN
ejpam-4085	97	11	by	by	ADP
ejpam-4085	97	12	log(a)+	log(a)+	NOUN
ejpam-4085	97	13	2iπ(2y+1	2iπ(2y+1	NUM
ejpam-4085	97	14	)	)	PUNCT
ejpam-4085	97	15	q	q	NOUN
ejpam-4085	97	16	and	and	CCONJ
ejpam-4085	97	17	multiply	multiply	VERB
ejpam-4085	97	18	both	both	DET
ejpam-4085	97	19	sides	side	NOUN
ejpam-4085	97	20	by	by	ADP
ejpam-4085	97	21	−4iπ2e	−4iπ2e	PROPN
ejpam-4085	97	22	2iπm(2y+1	2iπm(2y+1	NUM
ejpam-4085	97	23	)	)	PUNCT
ejpam-4085	97	24	q	q	PROPN
ejpam-4085	97	25	q4	q4	PROPN
ejpam-4085	97	26	and	and	CCONJ
ejpam-4085	97	27	replace	replace	VERB
ejpam-4085	97	28	k	k	PROPN
ejpam-4085	97	29	→	→	PUNCT
ejpam-4085	97	30	k	k	PROPN
ejpam-4085	98	1	−	−	PROPN
ejpam-4085	98	2	1	1	NUM
ejpam-4085	98	3	and	and	CCONJ
ejpam-4085	98	4	take	take	VERB
ejpam-4085	98	5	the	the	DET
ejpam-4085	98	6	infinite	infinite	ADJ
ejpam-4085	98	7	sum	sum	NOUN
ejpam-4085	98	8	over	over	ADP
ejpam-4085	98	9	y	y	PROPN
ejpam-4085	98	10	∈	∈	PROPN
ejpam-4085	99	1	[	[	X
ejpam-4085	99	2	0,∞	0,∞	NOUN
ejpam-4085	99	3	)	)	PUNCT
ejpam-4085	99	4	simplifying	simplify	VERB
ejpam-4085	99	5	in	in	ADP
ejpam-4085	99	6	terms	term	NOUN
ejpam-4085	99	7	of	of	ADP
ejpam-4085	99	8	the	the	DET
ejpam-4085	99	9	lerch	lerch	PROPN
ejpam-4085	99	10	function	function	NOUN
ejpam-4085	99	11	to	to	PART
ejpam-4085	99	12	get	get	VERB
ejpam-4085	99	13	(	(	PUNCT
ejpam-4085	99	14	10	10	NUM
ejpam-4085	99	15	)	)	PUNCT
ejpam-4085	99	16	22(k−1)+3πk+1	22(k−1)+3πk+1	NUM
ejpam-4085	99	17	m	m	NOUN
ejpam-4085	99	18	(	(	PUNCT
ejpam-4085	99	19	i	i	PRON
ejpam-4085	99	20	q	q	NOUN
ejpam-4085	99	21	)	)	PUNCT
ejpam-4085	99	22	k−2	k−2	PROPN
ejpam-4085	99	23	e	e	PROPN
ejpam-4085	99	24	2iπm	2iπm	PROPN
ejpam-4085	99	25	q	q	PROPN
ejpam-4085	99	26	φ	φ	X
ejpam-4085	99	27	(	(	PUNCT
ejpam-4085	99	28	e	e	PROPN
ejpam-4085	99	29	4imπ	4imπ	NUM
ejpam-4085	99	30	q	q	PROPN
ejpam-4085	99	31	,	,	PUNCT
ejpam-4085	99	32	1−	1−	NUM
ejpam-4085	99	33	k	k	NOUN
ejpam-4085	99	34	,	,	PUNCT
ejpam-4085	99	35	12	12	NUM
ejpam-4085	99	36	−	−	NOUN
ejpam-4085	99	37	iq	iq	PROPN
ejpam-4085	99	38	log(a	log(a	PROPN
ejpam-4085	99	39	)	)	PUNCT
ejpam-4085	99	40	4π	4π	NUM
ejpam-4085	99	41	)	)	PUNCT
ejpam-4085	99	42	q5γ(k	q5γ(k	PROPN
ejpam-4085	99	43	)	)	PUNCT
ejpam-4085	100	1	=	=	PUNCT
ejpam-4085	101	1	−	−	PROPN
ejpam-4085	101	2	1	1	NUM
ejpam-4085	101	3	2πi	2πi	NOUN
ejpam-4085	101	4	∞∑	∞∑	NUM
ejpam-4085	101	5	y=0	y=0	NUM
ejpam-4085	101	6	∫	∫	PROPN
ejpam-4085	101	7	c	c	PROPN
ejpam-4085	101	8	8iπ2maww−ke	8iπ2maww−ke	PROPN
ejpam-4085	101	9	2iπ(2y+1)(m+w	2iπ(2y+1)(m+w	NUM
ejpam-4085	101	10	)	)	PUNCT
ejpam-4085	101	11	q	q	PROPN
ejpam-4085	101	12	q4	q4	PROPN
ejpam-4085	101	13	dw	dw	PROPN
ejpam-4085	101	14	=	=	NOUN
ejpam-4085	101	15	−	−	PROPN
ejpam-4085	101	16	1	1	NUM
ejpam-4085	101	17	2πi	2πi	NOUN
ejpam-4085	101	18	∫	∫	PROPN
ejpam-4085	102	1	c	c	NOUN
ejpam-4085	102	2	∞∑	∞∑	NUM
ejpam-4085	102	3	y=0	y=0	NOUN
ejpam-4085	102	4	8iπ2maww−ke	8iπ2maww−ke	PROPN
ejpam-4085	102	5	2iπ(2y+1)(m+w	2iπ(2y+1)(m+w	NUM
ejpam-4085	102	6	)	)	PUNCT
ejpam-4085	102	7	q	q	PROPN
ejpam-4085	102	8	q4	q4	PROPN
ejpam-4085	102	9	dw	dw	PROPN
ejpam-4085	102	10	=	=	SYM
ejpam-4085	102	11	1	1	NUM
ejpam-4085	102	12	2πi	2πi	NOUN
ejpam-4085	102	13	∫	∫	PROPN
ejpam-4085	103	1	c	c	PROPN
ejpam-4085	103	2	4π2maww−k	4π2maww−k	PROPN
ejpam-4085	103	3	csc	csc	PROPN
ejpam-4085	103	4	(	(	PUNCT
ejpam-4085	103	5	2π(m+w	2π(m+w	NUM
ejpam-4085	103	6	)	)	PUNCT
ejpam-4085	103	7	q	q	NOUN
ejpam-4085	103	8	)	)	PUNCT
ejpam-4085	103	9	q4	q4	PROPN
ejpam-4085	103	10	dw	dw	PROPN
ejpam-4085	103	11	from	from	ADP
ejpam-4085	103	12	equation	equation	NOUN
ejpam-4085	103	13	(	(	PUNCT
ejpam-4085	103	14	1.232.3	1.232.3	NUM
ejpam-4085	103	15	)	)	PUNCT
ejpam-4085	103	16	in	in	ADP
ejpam-4085	103	17	[	[	X
ejpam-4085	103	18	1	1	X
ejpam-4085	103	19	]	]	PUNCT
ejpam-4085	103	20	where	where	SCONJ
ejpam-4085	103	21	im(m+	im(m+	PROPN
ejpam-4085	103	22	w	w	NOUN
ejpam-4085	103	23	)	)	PUNCT
ejpam-4085	103	24	>	>	X
ejpam-4085	103	25	0	0	PUNCT
ejpam-4085	104	1	for	for	ADP
ejpam-4085	104	2	convergence	convergence	NOUN
ejpam-4085	104	3	of	of	ADP
ejpam-4085	104	4	the	the	DET
ejpam-4085	104	5	sum	sum	NOUN
ejpam-4085	104	6	.	.	PUNCT
ejpam-4085	105	1	4.6	4.6	NUM
ejpam-4085	105	2	.	.	PUNCT
ejpam-4085	105	3	derivation	derivation	NOUN
ejpam-4085	105	4	of	of	ADP
ejpam-4085	105	5	the	the	DET
ejpam-4085	105	6	sixth	sixth	ADJ
ejpam-4085	105	7	contour	contour	NOUN
ejpam-4085	105	8	integral	integral	ADJ
ejpam-4085	105	9	in	in	ADP
ejpam-4085	105	10	this	this	DET
ejpam-4085	105	11	section	section	NOUN
ejpam-4085	105	12	we	we	PRON
ejpam-4085	105	13	will	will	AUX
ejpam-4085	105	14	again	again	ADV
ejpam-4085	105	15	use	use	VERB
ejpam-4085	105	16	cauchy	cauchy	NOUN
ejpam-4085	105	17	’s	’s	PART
ejpam-4085	105	18	integral	integral	ADJ
ejpam-4085	105	19	formula	formula	NOUN
ejpam-4085	105	20	(	(	PUNCT
ejpam-4085	105	21	2	2	NUM
ejpam-4085	105	22	)	)	PUNCT
ejpam-4085	105	23	and	and	CCONJ
ejpam-4085	105	24	taking	take	VERB
ejpam-4085	105	25	the	the	DET
ejpam-4085	105	26	infinite	infinite	ADJ
ejpam-4085	105	27	sum	sum	NOUN
ejpam-4085	105	28	to	to	PART
ejpam-4085	105	29	derive	derive	VERB
ejpam-4085	105	30	equivalent	equivalent	ADJ
ejpam-4085	105	31	sum	sum	NOUN
ejpam-4085	105	32	representations	representation	NOUN
ejpam-4085	105	33	for	for	ADP
ejpam-4085	105	34	the	the	DET
ejpam-4085	105	35	contour	contour	NOUN
ejpam-4085	105	36	integrals	integral	NOUN
ejpam-4085	105	37	.	.	PUNCT
ejpam-4085	106	1	we	we	PRON
ejpam-4085	106	2	proceed	proceed	VERB
ejpam-4085	106	3	using	use	VERB
ejpam-4085	106	4	equation	equation	NOUN
ejpam-4085	106	5	(	(	PUNCT
ejpam-4085	106	6	2	2	NUM
ejpam-4085	106	7	)	)	PUNCT
ejpam-4085	106	8	and	and	CCONJ
ejpam-4085	106	9	replace	replace	VERB
ejpam-4085	106	10	y	y	PROPN
ejpam-4085	106	11	by	by	ADP
ejpam-4085	106	12	log(a	log(a	PROPN
ejpam-4085	106	13	)	)	PUNCT
ejpam-4085	106	14	+	+	CCONJ
ejpam-4085	107	1	2iπ(2y+1	2iπ(2y+1	X
ejpam-4085	107	2	)	)	PUNCT
ejpam-4085	107	3	q	q	NOUN
ejpam-4085	107	4	and	and	CCONJ
ejpam-4085	107	5	multiply	multiply	VERB
ejpam-4085	107	6	both	both	DET
ejpam-4085	107	7	sides	side	NOUN
ejpam-4085	107	8	by	by	ADP
ejpam-4085	107	9	6iπ2e	6iπ2e	PROPN
ejpam-4085	107	10	2iπm(2y+1	2iπm(2y+1	NUM
ejpam-4085	107	11	)	)	PUNCT
ejpam-4085	107	12	q	q	PROPN
ejpam-4085	107	13	q3	q3	PROPN
ejpam-4085	107	14	r.	r.	PROPN
ejpam-4085	107	15	reynolds	reynolds	PROPN
ejpam-4085	107	16	,	,	PUNCT
ejpam-4085	107	17	a.	a.	PROPN
ejpam-4085	107	18	stauffer	stauffer	PROPN
ejpam-4085	107	19	/	/	SYM
ejpam-4085	107	20	eur	eur	PROPN
ejpam-4085	107	21	.	.	PUNCT
ejpam-4085	108	1	j.	j.	PROPN
ejpam-4085	108	2	pure	pure	PROPN
ejpam-4085	108	3	appl	appl	PROPN
ejpam-4085	108	4	.	.	PROPN
ejpam-4085	108	5	math	math	PROPN
ejpam-4085	108	6	,	,	PUNCT
ejpam-4085	108	7	14	14	NUM
ejpam-4085	108	8	(	(	PUNCT
ejpam-4085	108	9	4	4	NUM
ejpam-4085	108	10	)	)	PUNCT
ejpam-4085	108	11	(	(	PUNCT
ejpam-4085	108	12	2021	2021	NUM
ejpam-4085	108	13	)	)	PUNCT
ejpam-4085	108	14	,	,	PUNCT
ejpam-4085	108	15	1337	1337	NUM
ejpam-4085	108	16	-	-	SYM
ejpam-4085	108	17	1349	1349	NUM
ejpam-4085	108	18	1342	1342	NUM
ejpam-4085	108	19	and	and	CCONJ
ejpam-4085	108	20	replace	replace	VERB
ejpam-4085	108	21	k	k	PROPN
ejpam-4085	108	22	→	→	PUNCT
ejpam-4085	108	23	k	k	PROPN
ejpam-4085	108	24	−	−	PROPN
ejpam-4085	108	25	1	1	NUM
ejpam-4085	108	26	and	and	CCONJ
ejpam-4085	108	27	take	take	VERB
ejpam-4085	108	28	the	the	DET
ejpam-4085	108	29	infinite	infinite	ADJ
ejpam-4085	108	30	sum	sum	NOUN
ejpam-4085	108	31	over	over	ADP
ejpam-4085	108	32	y	y	PROPN
ejpam-4085	108	33	∈	∈	PROPN
ejpam-4085	109	1	[	[	X
ejpam-4085	109	2	0,∞	0,∞	NOUN
ejpam-4085	109	3	)	)	PUNCT
ejpam-4085	109	4	simplifying	simplify	VERB
ejpam-4085	109	5	in	in	ADP
ejpam-4085	109	6	terms	term	NOUN
ejpam-4085	109	7	of	of	ADP
ejpam-4085	109	8	the	the	DET
ejpam-4085	109	9	lerch	lerch	PROPN
ejpam-4085	109	10	function	function	NOUN
ejpam-4085	109	11	to	to	PART
ejpam-4085	109	12	get	get	VERB
ejpam-4085	109	13	(	(	PUNCT
ejpam-4085	109	14	11	11	NUM
ejpam-4085	109	15	)	)	PUNCT
ejpam-4085	109	16	3i22(k−1)+1πk+1	3i22(k−1)+1πk+1	NUM
ejpam-4085	109	17	(	(	PUNCT
ejpam-4085	109	18	i	i	PRON
ejpam-4085	109	19	q	q	NOUN
ejpam-4085	109	20	)	)	PUNCT
ejpam-4085	110	1	k−1	k−1	PROPN
ejpam-4085	110	2	e	e	PROPN
ejpam-4085	111	1	2iπm	2iπm	NUM
ejpam-4085	111	2	q	q	X
ejpam-4085	111	3	φ	φ	X
ejpam-4085	111	4	(	(	PUNCT
ejpam-4085	111	5	e	e	PROPN
ejpam-4085	111	6	4imπ	4imπ	NUM
ejpam-4085	111	7	q	q	PROPN
ejpam-4085	111	8	,	,	PUNCT
ejpam-4085	111	9	1−	1−	NUM
ejpam-4085	111	10	k	k	NOUN
ejpam-4085	111	11	,	,	PUNCT
ejpam-4085	111	12	12	12	NUM
ejpam-4085	111	13	−	−	NOUN
ejpam-4085	111	14	iq	iq	PROPN
ejpam-4085	111	15	log(a	log(a	PROPN
ejpam-4085	111	16	)	)	PUNCT
ejpam-4085	111	17	4π	4π	NUM
ejpam-4085	111	18	)	)	PUNCT
ejpam-4085	111	19	q3γ(k	q3γ(k	PROPN
ejpam-4085	111	20	)	)	PUNCT
ejpam-4085	111	21	=	=	NOUN
ejpam-4085	112	1	1	1	NUM
ejpam-4085	112	2	2πi	2πi	NOUN
ejpam-4085	112	3	∞∑	∞∑	NUM
ejpam-4085	112	4	y=0	y=0	NUM
ejpam-4085	112	5	∫	∫	PROPN
ejpam-4085	112	6	c	c	PROPN
ejpam-4085	112	7	6iπ2aww−ke	6iπ2aww−ke	NUM
ejpam-4085	112	8	2iπ(2y+1)(m+w	2iπ(2y+1)(m+w	NUM
ejpam-4085	112	9	)	)	PUNCT
ejpam-4085	112	10	q	q	PROPN
ejpam-4085	112	11	q3	q3	NOUN
ejpam-4085	112	12	dw	dw	PROPN
ejpam-4085	112	13	=	=	SYM
ejpam-4085	112	14	1	1	NUM
ejpam-4085	112	15	2πi	2πi	NOUN
ejpam-4085	112	16	∫	∫	PROPN
ejpam-4085	112	17	c	c	NOUN
ejpam-4085	113	1	∞∑	∞∑	NUM
ejpam-4085	113	2	y=0	y=0	NOUN
ejpam-4085	113	3	6iπ2aww−ke	6iπ2aww−ke	NUM
ejpam-4085	113	4	2iπ(2y+1)(m+w	2iπ(2y+1)(m+w	NUM
ejpam-4085	113	5	)	)	PUNCT
ejpam-4085	113	6	q	q	PROPN
ejpam-4085	113	7	q3	q3	NOUN
ejpam-4085	113	8	dw	dw	PROPN
ejpam-4085	113	9	=	=	SYM
ejpam-4085	113	10	−	−	PROPN
ejpam-4085	113	11	1	1	NUM
ejpam-4085	113	12	2πi	2πi	NOUN
ejpam-4085	113	13	∫	∫	PROPN
ejpam-4085	113	14	c	c	PROPN
ejpam-4085	113	15	3π2aww−k	3π2aww−k	NUM
ejpam-4085	113	16	csc	csc	PROPN
ejpam-4085	113	17	(	(	PUNCT
ejpam-4085	113	18	2π(m+w	2π(m+w	NUM
ejpam-4085	113	19	)	)	PUNCT
ejpam-4085	113	20	q	q	NOUN
ejpam-4085	113	21	)	)	PUNCT
ejpam-4085	113	22	q3	q3	PROPN
ejpam-4085	113	23	dw	dw	PROPN
ejpam-4085	113	24	from	from	ADP
ejpam-4085	113	25	equation	equation	NOUN
ejpam-4085	113	26	(	(	PUNCT
ejpam-4085	113	27	1.232.3	1.232.3	NUM
ejpam-4085	113	28	)	)	PUNCT
ejpam-4085	113	29	in	in	ADP
ejpam-4085	113	30	[	[	X
ejpam-4085	113	31	1	1	X
ejpam-4085	113	32	]	]	PUNCT
ejpam-4085	113	33	where	where	SCONJ
ejpam-4085	113	34	im(m+	im(m+	PROPN
ejpam-4085	113	35	w	w	NOUN
ejpam-4085	113	36	)	)	PUNCT
ejpam-4085	113	37	>	>	X
ejpam-4085	113	38	0	0	PUNCT
ejpam-4085	113	39	for	for	ADP
ejpam-4085	113	40	convergence	convergence	NOUN
ejpam-4085	113	41	of	of	ADP
ejpam-4085	113	42	the	the	DET
ejpam-4085	113	43	sum	sum	NOUN
ejpam-4085	113	44	.	.	PUNCT
ejpam-4085	114	1	main	main	ADJ
ejpam-4085	114	2	results	result	NOUN
ejpam-4085	114	3	5	5	NUM
ejpam-4085	114	4	.	.	PUNCT
ejpam-4085	114	5	definite	definite	ADJ
ejpam-4085	114	6	integral	integral	ADJ
ejpam-4085	114	7	in	in	ADP
ejpam-4085	114	8	terms	term	NOUN
ejpam-4085	114	9	of	of	ADP
ejpam-4085	114	10	the	the	DET
ejpam-4085	114	11	lerch	lerch	PROPN
ejpam-4085	114	12	function	function	PROPN
ejpam-4085	114	13	theorem	theorem	VERB
ejpam-4085	114	14	1	1	NUM
ejpam-4085	114	15	.	.	X
ejpam-4085	115	1	for	for	ADP
ejpam-4085	115	2	a	a	PRON
ejpam-4085	115	3	,	,	PUNCT
ejpam-4085	115	4	k	k	PROPN
ejpam-4085	115	5	∈	∈	PROPN
ejpam-4085	115	6	c	c	PROPN
ejpam-4085	115	7	,	,	PUNCT
ejpam-4085	115	8	0	0	PUNCT
ejpam-4085	115	9	<	<	X
ejpam-4085	115	10	re(m	re(m	PROPN
ejpam-4085	115	11	)	)	PUNCT
ejpam-4085	115	12	<	<	X
ejpam-4085	115	13	1	1	NUM
ejpam-4085	115	14	,	,	PUNCT
ejpam-4085	115	15	re(q	re(q	VERB
ejpam-4085	115	16	)	)	PUNCT
ejpam-4085	115	17	>	>	X
ejpam-4085	116	1	0,∫	0,∫	X
ejpam-4085	116	2	∞	∞	NUM
ejpam-4085	116	3	0	0	NUM
ejpam-4085	117	1	∫	∫	PROPN
ejpam-4085	117	2	∞	∞	NOUN
ejpam-4085	117	3	0	0	PUNCT
ejpam-4085	118	1	xm−1ym+	xm−1ym+	NOUN
ejpam-4085	118	2	q	q	PROPN
ejpam-4085	118	3	2	2	NUM
ejpam-4085	118	4	−1	−1	NOUN
ejpam-4085	118	5	logk(axy	logk(axy	NOUN
ejpam-4085	118	6	)	)	PUNCT
ejpam-4085	118	7	(	(	PUNCT
ejpam-4085	118	8	xq	xq	X
ejpam-4085	118	9	+	+	PROPN
ejpam-4085	118	10	1)2	1)2	NUM
ejpam-4085	118	11	(	(	PUNCT
ejpam-4085	118	12	yq	yq	PROPN
ejpam-4085	118	13	+	+	PROPN
ejpam-4085	118	14	1)2	1)2	NUM
ejpam-4085	118	15	dxdy	dxdy	NOUN
ejpam-4085	118	16	=	=	SYM
ejpam-4085	118	17	4k−1πk	4k−1πk	PROPN
ejpam-4085	118	18	q4	q4	PROPN
ejpam-4085	118	19	(	(	PUNCT
ejpam-4085	118	20	i	i	PRON
ejpam-4085	118	21	q	q	NOUN
ejpam-4085	118	22	)	)	PUNCT
ejpam-4085	118	23	k	k	X
ejpam-4085	119	1	e	e	X
ejpam-4085	119	2	2iπm	2iπm	NUM
ejpam-4085	119	3	q	q	NOUN
ejpam-4085	120	1	(	(	PUNCT
ejpam-4085	120	2	i	i	PRON
ejpam-4085	120	3	(	(	PUNCT
ejpam-4085	120	4	(	(	PUNCT
ejpam-4085	120	5	k−1)kq2φ	k−1)kq2φ	X
ejpam-4085	120	6	(	(	PUNCT
ejpam-4085	120	7	e	e	X
ejpam-4085	120	8	4imπ	4imπ	NUM
ejpam-4085	120	9	q	q	PROPN
ejpam-4085	120	10	,	,	PUNCT
ejpam-4085	120	11	2−k	2−k	NUM
ejpam-4085	120	12	,	,	PUNCT
ejpam-4085	120	13	1	1	NUM
ejpam-4085	120	14	2	2	NUM
ejpam-4085	120	15	−	−	NOUN
ejpam-4085	120	16	iq	iq	NOUN
ejpam-4085	120	17	log(a	log(a	PROPN
ejpam-4085	120	18	)	)	PUNCT
ejpam-4085	120	19	4π	4π	NUM
ejpam-4085	120	20	)	)	PUNCT
ejpam-4085	121	1	−8π2(q−2m)(q−m)φ	−8π2(q−2m)(q−m)φ	PROPN
ejpam-4085	121	2	(	(	PUNCT
ejpam-4085	121	3	e	e	PROPN
ejpam-4085	121	4	4imπ	4imπ	NUM
ejpam-4085	121	5	q	q	X
ejpam-4085	121	6	,	,	PUNCT
ejpam-4085	121	7	−k	−k	PROPN
ejpam-4085	121	8	,	,	PUNCT
ejpam-4085	121	9	1	1	NUM
ejpam-4085	121	10	2	2	NUM
ejpam-4085	121	11	−	−	NOUN
ejpam-4085	121	12	iq	iq	NOUN
ejpam-4085	121	13	log(a	log(a	PROPN
ejpam-4085	121	14	)	)	PUNCT
ejpam-4085	121	15	4π	4π	NUM
ejpam-4085	121	16	)	)	PUNCT
ejpam-4085	121	17	)	)	PUNCT
ejpam-4085	122	1	+	+	CCONJ
ejpam-4085	123	1	2πkq(3q	2πkq(3q	NUM
ejpam-4085	123	2	−	−	NOUN
ejpam-4085	123	3	4m)φ	4m)φ	NUM
ejpam-4085	123	4	(	(	PUNCT
ejpam-4085	123	5	e	e	PROPN
ejpam-4085	123	6	4imπ	4imπ	NUM
ejpam-4085	123	7	q	q	PROPN
ejpam-4085	123	8	,	,	PUNCT
ejpam-4085	123	9	1−	1−	NUM
ejpam-4085	124	1	k	k	X
ejpam-4085	125	1	,	,	PUNCT
ejpam-4085	125	2	1	1	NUM
ejpam-4085	125	3	2	2	NUM
ejpam-4085	125	4	−	−	NOUN
ejpam-4085	125	5	iq	iq	NOUN
ejpam-4085	125	6	log(a	log(a	PROPN
ejpam-4085	125	7	)	)	PUNCT
ejpam-4085	125	8	4π	4π	NUM
ejpam-4085	125	9	)	)	PUNCT
ejpam-4085	125	10	)	)	PUNCT
ejpam-4085	126	1	(	(	PUNCT
ejpam-4085	126	2	12	12	X
ejpam-4085	126	3	)	)	PUNCT
ejpam-4085	126	4	proof	proof	NOUN
ejpam-4085	126	5	.	.	PUNCT
ejpam-4085	127	1	since	since	SCONJ
ejpam-4085	127	2	the	the	DET
ejpam-4085	127	3	addition	addition	NOUN
ejpam-4085	127	4	of	of	ADP
ejpam-4085	127	5	the	the	DET
ejpam-4085	127	6	right	right	ADJ
ejpam-4085	127	7	-	-	PUNCT
ejpam-4085	127	8	hand	hand	NOUN
ejpam-4085	127	9	sides	side	NOUN
ejpam-4085	127	10	of	of	ADP
ejpam-4085	127	11	equations	equation	NOUN
ejpam-4085	127	12	(	(	PUNCT
ejpam-4085	127	13	6	6	NUM
ejpam-4085	127	14	)	)	PUNCT
ejpam-4085	127	15	,	,	PUNCT
ejpam-4085	127	16	(	(	PUNCT
ejpam-4085	127	17	7	7	NUM
ejpam-4085	127	18	)	)	PUNCT
ejpam-4085	127	19	,	,	PUNCT
ejpam-4085	127	20	(	(	PUNCT
ejpam-4085	127	21	8)	8)	NUM
ejpam-4085	127	22	,	,	PUNCT
ejpam-4085	127	23	(	(	PUNCT
ejpam-4085	127	24	9	9	NUM
ejpam-4085	127	25	)	)	PUNCT
ejpam-4085	127	26	,	,	PUNCT
ejpam-4085	127	27	(	(	PUNCT
ejpam-4085	127	28	10	10	NUM
ejpam-4085	127	29	)	)	PUNCT
ejpam-4085	127	30	and	and	CCONJ
ejpam-4085	127	31	(	(	PUNCT
ejpam-4085	127	32	11	11	NUM
ejpam-4085	127	33	)	)	PUNCT
ejpam-4085	127	34	is	be	AUX
ejpam-4085	127	35	equal	equal	ADJ
ejpam-4085	127	36	to	to	ADP
ejpam-4085	127	37	the	the	DET
ejpam-4085	127	38	right	right	ADJ
ejpam-4085	127	39	-	-	PUNCT
ejpam-4085	127	40	hand	hand	NOUN
ejpam-4085	127	41	side	side	NOUN
ejpam-4085	127	42	of	of	ADP
ejpam-4085	127	43	equation	equation	NOUN
ejpam-4085	127	44	(	(	PUNCT
ejpam-4085	127	45	3	3	X
ejpam-4085	127	46	)	)	PUNCT
ejpam-4085	127	47	we	we	PRON
ejpam-4085	127	48	can	can	AUX
ejpam-4085	127	49	equate	equate	VERB
ejpam-4085	127	50	the	the	DET
ejpam-4085	127	51	left	left	ADJ
ejpam-4085	127	52	-	-	PUNCT
ejpam-4085	127	53	hand	hand	NOUN
ejpam-4085	127	54	sides	side	NOUN
ejpam-4085	127	55	and	and	CCONJ
ejpam-4085	127	56	reduce	reduce	VERB
ejpam-4085	127	57	the	the	DET
ejpam-4085	127	58	factorial	factorial	NOUN
ejpam-4085	127	59	to	to	PART
ejpam-4085	127	60	get	get	VERB
ejpam-4085	127	61	the	the	DET
ejpam-4085	127	62	stated	state	VERB
ejpam-4085	127	63	result	result	NOUN
ejpam-4085	127	64	.	.	PUNCT
ejpam-4085	128	1	r.	r.	PROPN
ejpam-4085	128	2	reynolds	reynolds	PROPN
ejpam-4085	128	3	,	,	PUNCT
ejpam-4085	128	4	a.	a.	PROPN
ejpam-4085	128	5	stauffer	stauffer	PROPN
ejpam-4085	128	6	/	/	SYM
ejpam-4085	128	7	eur	eur	PROPN
ejpam-4085	128	8	.	.	PUNCT
ejpam-4085	129	1	j.	j.	PROPN
ejpam-4085	129	2	pure	pure	PROPN
ejpam-4085	129	3	appl	appl	PROPN
ejpam-4085	129	4	.	.	PROPN
ejpam-4085	129	5	math	math	PROPN
ejpam-4085	129	6	,	,	PUNCT
ejpam-4085	129	7	14	14	NUM
ejpam-4085	129	8	(	(	PUNCT
ejpam-4085	129	9	4	4	NUM
ejpam-4085	129	10	)	)	PUNCT
ejpam-4085	129	11	(	(	PUNCT
ejpam-4085	129	12	2021	2021	NUM
ejpam-4085	129	13	)	)	PUNCT
ejpam-4085	129	14	,	,	PUNCT
ejpam-4085	129	15	1337	1337	NUM
ejpam-4085	129	16	-	-	SYM
ejpam-4085	129	17	1349	1349	NUM
ejpam-4085	129	18	1343	1343	NUM
ejpam-4085	129	19	6	6	NUM
ejpam-4085	129	20	.	.	PUNCT
ejpam-4085	129	21	integral	integral	ADJ
ejpam-4085	129	22	representation	representation	NOUN
ejpam-4085	129	23	for	for	ADP
ejpam-4085	129	24	catalan	catalan	NOUN
ejpam-4085	129	25	’s	’s	PART
ejpam-4085	129	26	constant	constant	ADJ
ejpam-4085	129	27	g	g	NOUN
ejpam-4085	129	28	,	,	PUNCT
ejpam-4085	129	29	apéry	apéry	X
ejpam-4085	129	30	’s	’s	NOUN
ejpam-4085	129	31	constant	constant	ADJ
ejpam-4085	129	32	ζ(3	ζ(3	NOUN
ejpam-4085	129	33	)	)	PUNCT
ejpam-4085	129	34	and	and	CCONJ
ejpam-4085	129	35	π	π	PROPN
ejpam-4085	129	36	proposition	proposition	NOUN
ejpam-4085	129	37	1	1	X
ejpam-4085	129	38	.	.	PUNCT
ejpam-4085	130	1	(	(	PUNCT
ejpam-4085	130	2	13	13	NUM
ejpam-4085	130	3	)	)	PUNCT
ejpam-4085	130	4	∫	∫	PROPN
ejpam-4085	131	1	∞	∞	PROPN
ejpam-4085	131	2	0	0	NUM
ejpam-4085	132	1	∫	∫	PROPN
ejpam-4085	132	2	∞	∞	PROPN
ejpam-4085	132	3	0	0	NUM
ejpam-4085	132	4	4	4	NUM
ejpam-4085	132	5	√	√	NUM
ejpam-4085	132	6	x	x	SYM
ejpam-4085	132	7	(	(	PUNCT
ejpam-4085	133	1	√	√	NUM
ejpam-4085	133	2	x	x	SYM
ejpam-4085	133	3	√	√	PROPN
ejpam-4085	133	4	y	y	NUM
ejpam-4085	133	5	−	−	NOUN
ejpam-4085	133	6	1	1	NUM
ejpam-4085	133	7	)	)	PUNCT
ejpam-4085	133	8	(	(	PUNCT
ejpam-4085	133	9	x+	x+	X
ejpam-4085	133	10	1)2	1)2	NUM
ejpam-4085	133	11	4	4	NUM
ejpam-4085	133	12	√	√	NOUN
ejpam-4085	133	13	y(y	y(y	PROPN
ejpam-4085	133	14	+	+	CCONJ
ejpam-4085	133	15	1)2	1)2	NUM
ejpam-4085	133	16	log(xy	log(xy	NOUN
ejpam-4085	133	17	)	)	PUNCT
ejpam-4085	133	18	dxdy	dxdy	NOUN
ejpam-4085	133	19	=	=	PUNCT
ejpam-4085	134	1	g	g	PROPN
ejpam-4085	134	2	proof	proof	NOUN
ejpam-4085	134	3	.	.	PUNCT
ejpam-4085	135	1	use	use	NOUN
ejpam-4085	135	2	(	(	PUNCT
ejpam-4085	135	3	12	12	NUM
ejpam-4085	135	4	)	)	PUNCT
ejpam-4085	135	5	and	and	CCONJ
ejpam-4085	135	6	form	form	VERB
ejpam-4085	135	7	a	a	DET
ejpam-4085	135	8	second	second	ADJ
ejpam-4085	135	9	equation	equation	NOUN
ejpam-4085	135	10	by	by	ADP
ejpam-4085	135	11	replacing	replace	VERB
ejpam-4085	135	12	m	m	PRON
ejpam-4085	135	13	→	→	SYM
ejpam-4085	135	14	p	p	X
ejpam-4085	135	15	and	and	CCONJ
ejpam-4085	135	16	take	take	VERB
ejpam-4085	135	17	their	their	PRON
ejpam-4085	135	18	difference	difference	NOUN
ejpam-4085	135	19	.	.	PUNCT
ejpam-4085	136	1	then	then	ADV
ejpam-4085	136	2	set	set	VERB
ejpam-4085	136	3	k	k	PROPN
ejpam-4085	136	4	=	=	PUNCT
ejpam-4085	136	5	−1	−1	NOUN
ejpam-4085	136	6	,	,	PUNCT
ejpam-4085	136	7	a	a	DET
ejpam-4085	136	8	=	=	SYM
ejpam-4085	136	9	1	1	NUM
ejpam-4085	136	10	,	,	PUNCT
ejpam-4085	136	11	q	q	NOUN
ejpam-4085	136	12	=	=	PUNCT
ejpam-4085	136	13	−1,m	−1,m	PROPN
ejpam-4085	136	14	=	=	SYM
ejpam-4085	136	15	−3/4	−3/4	NOUN
ejpam-4085	136	16	,	,	PUNCT
ejpam-4085	136	17	p	p	NOUN
ejpam-4085	136	18	=	=	X
ejpam-4085	136	19	−1/4	−1/4	NOUN
ejpam-4085	136	20	and	and	CCONJ
ejpam-4085	136	21	simplify	simplify	NOUN
ejpam-4085	136	22	using	use	VERB
ejpam-4085	136	23	entries	entry	NOUN
ejpam-4085	136	24	(	(	PUNCT
ejpam-4085	136	25	1	1	NUM
ejpam-4085	136	26	)	)	PUNCT
ejpam-4085	136	27	,	,	PUNCT
ejpam-4085	136	28	(	(	PUNCT
ejpam-4085	136	29	2	2	NUM
ejpam-4085	136	30	)	)	PUNCT
ejpam-4085	136	31	,	,	PUNCT
ejpam-4085	136	32	(	(	PUNCT
ejpam-4085	136	33	4	4	X
ejpam-4085	136	34	)	)	PUNCT
ejpam-4085	136	35	in	in	ADP
ejpam-4085	136	36	table	table	NOUN
ejpam-4085	136	37	below	below	ADV
ejpam-4085	136	38	(	(	PUNCT
ejpam-4085	136	39	64:12:7	64:12:7	NUM
ejpam-4085	136	40	)	)	PUNCT
ejpam-4085	136	41	in	in	ADP
ejpam-4085	136	42	[	[	X
ejpam-4085	136	43	2	2	NUM
ejpam-4085	136	44	]	]	PUNCT
ejpam-4085	136	45	.	.	PUNCT
ejpam-4085	137	1	proposition	proposition	NOUN
ejpam-4085	137	2	2	2	NUM
ejpam-4085	137	3	.	.	PUNCT
ejpam-4085	138	1	(	(	PUNCT
ejpam-4085	138	2	14	14	NUM
ejpam-4085	138	3	)	)	PUNCT
ejpam-4085	138	4	∫	∫	PROPN
ejpam-4085	139	1	∞	∞	PROPN
ejpam-4085	139	2	0	0	NUM
ejpam-4085	140	1	∫	∫	PROPN
ejpam-4085	140	2	∞	∞	PROPN
ejpam-4085	140	3	0	0	NUM
ejpam-4085	140	4	4	4	NUM
ejpam-4085	140	5	√	√	NUM
ejpam-4085	140	6	x	x	SYM
ejpam-4085	140	7	4	4	NUM
ejpam-4085	140	8	√	√	NUM
ejpam-4085	140	9	y	y	NUM
ejpam-4085	141	1	−	−	PROPN
ejpam-4085	141	2	1	1	NUM
ejpam-4085	141	3	x3/4(x+	x3/4(x+	X
ejpam-4085	141	4	1)2	1)2	NUM
ejpam-4085	141	5	4	4	NUM
ejpam-4085	141	6	√	√	NOUN
ejpam-4085	141	7	y(y	y(y	PROPN
ejpam-4085	141	8	+	+	CCONJ
ejpam-4085	141	9	1)2	1)2	NUM
ejpam-4085	141	10	log(xy	log(xy	NOUN
ejpam-4085	141	11	)	)	PUNCT
ejpam-4085	141	12	dxdy	dxdy	NOUN
ejpam-4085	141	13	=	=	SYM
ejpam-4085	141	14	g−	g−	PROPN
ejpam-4085	141	15	7ζ(3	7ζ(3	NUM
ejpam-4085	141	16	)	)	PUNCT
ejpam-4085	142	1	8π	8π	NUM
ejpam-4085	142	2	proof	proof	NOUN
ejpam-4085	142	3	.	.	PUNCT
ejpam-4085	143	1	use	use	NOUN
ejpam-4085	143	2	(	(	PUNCT
ejpam-4085	143	3	12	12	NUM
ejpam-4085	143	4	)	)	PUNCT
ejpam-4085	143	5	and	and	CCONJ
ejpam-4085	143	6	form	form	VERB
ejpam-4085	143	7	a	a	DET
ejpam-4085	143	8	second	second	ADJ
ejpam-4085	143	9	equation	equation	NOUN
ejpam-4085	143	10	by	by	ADP
ejpam-4085	143	11	replacing	replace	VERB
ejpam-4085	143	12	m	m	PRON
ejpam-4085	143	13	→	→	SYM
ejpam-4085	143	14	p	p	X
ejpam-4085	143	15	and	and	CCONJ
ejpam-4085	143	16	take	take	VERB
ejpam-4085	143	17	their	their	PRON
ejpam-4085	143	18	difference	difference	NOUN
ejpam-4085	143	19	.	.	PUNCT
ejpam-4085	144	1	then	then	ADV
ejpam-4085	144	2	set	set	VERB
ejpam-4085	144	3	k	k	PROPN
ejpam-4085	144	4	=	=	PUNCT
ejpam-4085	144	5	−1	−1	NOUN
ejpam-4085	144	6	,	,	PUNCT
ejpam-4085	144	7	a	a	DET
ejpam-4085	144	8	=	=	X
ejpam-4085	144	9	1,m	1,m	NOUN
ejpam-4085	144	10	=	=	SYM
ejpam-4085	144	11	1/4	1/4	NUM
ejpam-4085	144	12	,	,	PUNCT
ejpam-4085	144	13	p	p	NOUN
ejpam-4085	144	14	=	=	PROPN
ejpam-4085	144	15	1/2	1/2	NUM
ejpam-4085	144	16	.	.	PUNCT
ejpam-4085	145	1	then	then	ADV
ejpam-4085	145	2	apply	apply	VERB
ejpam-4085	145	3	l’hopital	l’hopital	PROPN
ejpam-4085	145	4	’s	’s	PART
ejpam-4085	145	5	rule	rule	NOUN
ejpam-4085	145	6	to	to	ADP
ejpam-4085	145	7	the	the	DET
ejpam-4085	145	8	right	right	ADJ
ejpam-4085	145	9	-	-	PUNCT
ejpam-4085	145	10	hand	hand	NOUN
ejpam-4085	145	11	side	side	NOUN
ejpam-4085	145	12	as	as	ADP
ejpam-4085	145	13	q	q	NOUN
ejpam-4085	145	14	→	→	SYM
ejpam-4085	145	15	1	1	NUM
ejpam-4085	145	16	and	and	CCONJ
ejpam-4085	145	17	simplify	simplify	VERB
ejpam-4085	145	18	using	use	VERB
ejpam-4085	145	19	entries	entry	NOUN
ejpam-4085	145	20	(	(	PUNCT
ejpam-4085	145	21	1	1	NUM
ejpam-4085	145	22	)	)	PUNCT
ejpam-4085	145	23	,	,	PUNCT
ejpam-4085	145	24	(	(	PUNCT
ejpam-4085	145	25	2	2	NUM
ejpam-4085	145	26	)	)	PUNCT
ejpam-4085	145	27	,	,	PUNCT
ejpam-4085	145	28	(	(	PUNCT
ejpam-4085	145	29	4	4	X
ejpam-4085	145	30	)	)	PUNCT
ejpam-4085	145	31	in	in	ADP
ejpam-4085	145	32	table	table	NOUN
ejpam-4085	145	33	below	below	ADV
ejpam-4085	145	34	(	(	PUNCT
ejpam-4085	145	35	64:12:7	64:12:7	NUM
ejpam-4085	145	36	)	)	PUNCT
ejpam-4085	145	37	,	,	PUNCT
ejpam-4085	145	38	equation	equation	NOUN
ejpam-4085	145	39	(	(	PUNCT
ejpam-4085	145	40	64:12:1	64:12:1	NUM
ejpam-4085	145	41	)	)	PUNCT
ejpam-4085	145	42	and	and	CCONJ
ejpam-4085	145	43	entry	entry	NOUN
ejpam-4085	145	44	(	(	PUNCT
ejpam-4085	145	45	2	2	NUM
ejpam-4085	145	46	)	)	PUNCT
ejpam-4085	145	47	in	in	ADP
ejpam-4085	145	48	table	table	NOUN
ejpam-4085	145	49	below	below	ADV
ejpam-4085	145	50	(	(	PUNCT
ejpam-4085	145	51	64:7	64:7	NUM
ejpam-4085	145	52	)	)	PUNCT
ejpam-4085	145	53	in	in	ADP
ejpam-4085	145	54	[	[	X
ejpam-4085	145	55	2	2	NUM
ejpam-4085	145	56	]	]	PUNCT
ejpam-4085	145	57	.	.	PUNCT
ejpam-4085	146	1	proposition	proposition	NOUN
ejpam-4085	146	2	3	3	NUM
ejpam-4085	146	3	.	.	PUNCT
ejpam-4085	147	1	(	(	PUNCT
ejpam-4085	147	2	15	15	NUM
ejpam-4085	147	3	)	)	PUNCT
ejpam-4085	147	4	∫	∫	PROPN
ejpam-4085	148	1	∞	∞	PROPN
ejpam-4085	148	2	0	0	NUM
ejpam-4085	149	1	∫	∫	PROPN
ejpam-4085	149	2	∞	∞	NOUN
ejpam-4085	149	3	0	0	PUNCT
ejpam-4085	150	1	y2	y2	INTJ
ejpam-4085	150	2	(	(	PUNCT
ejpam-4085	150	3	1−	1−	NUM
ejpam-4085	150	4	x2y2	x2y2	NUM
ejpam-4085	150	5	)	)	PUNCT
ejpam-4085	150	6	log(xy	log(xy	NOUN
ejpam-4085	150	7	)	)	PUNCT
ejpam-4085	150	8	(	(	PUNCT
ejpam-4085	150	9	x4	x4	PROPN
ejpam-4085	150	10	+	+	PROPN
ejpam-4085	150	11	1)2	1)2	NUM
ejpam-4085	150	12	(	(	PUNCT
ejpam-4085	150	13	y4	y4	PROPN
ejpam-4085	150	14	+	+	CCONJ
ejpam-4085	150	15	1)2	1)2	NUM
ejpam-4085	150	16	(	(	PUNCT
ejpam-4085	150	17	log2(xy	log2(xy	PROPN
ejpam-4085	150	18	)	)	PUNCT
ejpam-4085	150	19	+	+	CCONJ
ejpam-4085	150	20	π2	π2	ADJ
ejpam-4085	150	21	)	)	PUNCT
ejpam-4085	150	22	dxdy	dxdy	NOUN
ejpam-4085	150	23	=	=	SYM
ejpam-4085	150	24	1	1	NUM
ejpam-4085	150	25	4	4	NUM
ejpam-4085	150	26	(	(	PUNCT
ejpam-4085	150	27	g−	g−	PROPN
ejpam-4085	150	28	1	1	NUM
ejpam-4085	150	29	)	)	PUNCT
ejpam-4085	150	30	and	and	CCONJ
ejpam-4085	150	31	(	(	PUNCT
ejpam-4085	150	32	16	16	NUM
ejpam-4085	150	33	)	)	PUNCT
ejpam-4085	150	34	∫	∫	PROPN
ejpam-4085	151	1	∞	∞	PROPN
ejpam-4085	151	2	0	0	NUM
ejpam-4085	152	1	∫	∫	PROPN
ejpam-4085	152	2	∞	∞	NOUN
ejpam-4085	152	3	0	0	NUM
ejpam-4085	153	1	y2	y2	INTJ
ejpam-4085	153	2	(	(	PUNCT
ejpam-4085	153	3	x2y2	x2y2	NUM
ejpam-4085	153	4	−	−	PROPN
ejpam-4085	153	5	1	1	NUM
ejpam-4085	153	6	)	)	PUNCT
ejpam-4085	153	7	(	(	PUNCT
ejpam-4085	153	8	x4	x4	PROPN
ejpam-4085	153	9	+	+	PROPN
ejpam-4085	153	10	1)2	1)2	NUM
ejpam-4085	153	11	(	(	PUNCT
ejpam-4085	153	12	y4	y4	PROPN
ejpam-4085	153	13	+	+	CCONJ
ejpam-4085	153	14	1)2	1)2	NUM
ejpam-4085	153	15	(	(	PUNCT
ejpam-4085	153	16	log2(xy	log2(xy	PROPN
ejpam-4085	153	17	)	)	PUNCT
ejpam-4085	153	18	+	+	CCONJ
ejpam-4085	153	19	π2	π2	ADJ
ejpam-4085	153	20	)	)	PUNCT
ejpam-4085	153	21	dxdy	dxdy	NOUN
ejpam-4085	153	22	=	=	PUNCT
ejpam-4085	153	23	1	1	NUM
ejpam-4085	153	24	2π2	2π2	NUM
ejpam-4085	153	25	−	−	NUM
ejpam-4085	153	26	1	1	NUM
ejpam-4085	153	27	16	16	NUM
ejpam-4085	153	28	proof	proof	NOUN
ejpam-4085	153	29	.	.	PUNCT
ejpam-4085	154	1	use	use	NOUN
ejpam-4085	154	2	(	(	PUNCT
ejpam-4085	154	3	12	12	NUM
ejpam-4085	154	4	)	)	PUNCT
ejpam-4085	154	5	and	and	CCONJ
ejpam-4085	154	6	form	form	VERB
ejpam-4085	154	7	a	a	DET
ejpam-4085	154	8	second	second	ADJ
ejpam-4085	154	9	equation	equation	NOUN
ejpam-4085	154	10	by	by	ADP
ejpam-4085	154	11	replacing	replace	VERB
ejpam-4085	154	12	m	m	PRON
ejpam-4085	154	13	→	→	SYM
ejpam-4085	154	14	p	p	X
ejpam-4085	154	15	and	and	CCONJ
ejpam-4085	154	16	take	take	VERB
ejpam-4085	154	17	their	their	PRON
ejpam-4085	154	18	difference	difference	NOUN
ejpam-4085	154	19	.	.	PUNCT
ejpam-4085	155	1	then	then	ADV
ejpam-4085	155	2	set	set	VERB
ejpam-4085	155	3	k	k	PROPN
ejpam-4085	155	4	=	=	PUNCT
ejpam-4085	155	5	−1	−1	NOUN
ejpam-4085	155	6	,	,	PUNCT
ejpam-4085	155	7	a	a	DET
ejpam-4085	155	8	=	=	SYM
ejpam-4085	155	9	−1	−1	NOUN
ejpam-4085	155	10	,	,	PUNCT
ejpam-4085	155	11	q	q	PUNCT
ejpam-4085	156	1	=	=	SYM
ejpam-4085	156	2	4,m	4,m	NUM
ejpam-4085	156	3	=	=	SYM
ejpam-4085	156	4	3	3	NUM
ejpam-4085	156	5	,	,	PUNCT
ejpam-4085	156	6	p	p	NOUN
ejpam-4085	156	7	=	=	SYM
ejpam-4085	156	8	1	1	NUM
ejpam-4085	156	9	rationalize	rationalize	VERB
ejpam-4085	156	10	the	the	DET
ejpam-4085	156	11	denominator	denominator	NOUN
ejpam-4085	156	12	and	and	CCONJ
ejpam-4085	156	13	equate	equate	VERB
ejpam-4085	156	14	real	real	ADJ
ejpam-4085	156	15	and	and	CCONJ
ejpam-4085	156	16	imaginary	imaginary	ADJ
ejpam-4085	156	17	parts	part	NOUN
ejpam-4085	156	18	and	and	CCONJ
ejpam-4085	156	19	simplify	simplify	VERB
ejpam-4085	156	20	using	use	VERB
ejpam-4085	156	21	entries	entry	NOUN
ejpam-4085	156	22	(	(	PUNCT
ejpam-4085	156	23	1	1	NUM
ejpam-4085	156	24	)	)	PUNCT
ejpam-4085	156	25	,	,	PUNCT
ejpam-4085	156	26	(	(	PUNCT
ejpam-4085	156	27	2	2	NUM
ejpam-4085	156	28	)	)	PUNCT
ejpam-4085	156	29	,	,	PUNCT
ejpam-4085	156	30	(	(	PUNCT
ejpam-4085	156	31	4	4	X
ejpam-4085	156	32	)	)	PUNCT
ejpam-4085	156	33	in	in	ADP
ejpam-4085	156	34	table	table	NOUN
ejpam-4085	156	35	below	below	ADV
ejpam-4085	156	36	(	(	PUNCT
ejpam-4085	156	37	64:12:7	64:12:7	NUM
ejpam-4085	156	38	)	)	PUNCT
ejpam-4085	156	39	in	in	ADP
ejpam-4085	156	40	[	[	X
ejpam-4085	156	41	2	2	NUM
ejpam-4085	156	42	]	]	PUNCT
ejpam-4085	156	43	.	.	PUNCT
ejpam-4085	157	1	r.	r.	PROPN
ejpam-4085	157	2	reynolds	reynolds	PROPN
ejpam-4085	157	3	,	,	PUNCT
ejpam-4085	157	4	a.	a.	PROPN
ejpam-4085	157	5	stauffer	stauffer	PROPN
ejpam-4085	157	6	/	/	SYM
ejpam-4085	157	7	eur	eur	PROPN
ejpam-4085	157	8	.	.	PUNCT
ejpam-4085	158	1	j.	j.	PROPN
ejpam-4085	158	2	pure	pure	PROPN
ejpam-4085	158	3	appl	appl	PROPN
ejpam-4085	158	4	.	.	PROPN
ejpam-4085	158	5	math	math	PROPN
ejpam-4085	158	6	,	,	PUNCT
ejpam-4085	158	7	14	14	NUM
ejpam-4085	158	8	(	(	PUNCT
ejpam-4085	158	9	4	4	NUM
ejpam-4085	158	10	)	)	PUNCT
ejpam-4085	158	11	(	(	PUNCT
ejpam-4085	158	12	2021	2021	NUM
ejpam-4085	158	13	)	)	PUNCT
ejpam-4085	158	14	,	,	PUNCT
ejpam-4085	158	15	1337	1337	NUM
ejpam-4085	158	16	-	-	SYM
ejpam-4085	158	17	1349	1349	NUM
ejpam-4085	158	18	1344	1344	NUM
ejpam-4085	158	19	7	7	NUM
ejpam-4085	158	20	.	.	PUNCT
ejpam-4085	159	1	definite	definite	ADJ
ejpam-4085	159	2	integral	integral	ADJ
ejpam-4085	159	3	in	in	ADP
ejpam-4085	159	4	terms	term	NOUN
ejpam-4085	159	5	of	of	ADP
ejpam-4085	159	6	the	the	DET
ejpam-4085	159	7	polylogarithm	polylogarithm	PROPN
ejpam-4085	159	8	function	function	PROPN
ejpam-4085	159	9	theorem	theorem	VERB
ejpam-4085	159	10	2	2	NUM
ejpam-4085	159	11	.	.	X
ejpam-4085	159	12	for	for	ADP
ejpam-4085	159	13	k	k	PROPN
ejpam-4085	159	14	∈	∈	PROPN
ejpam-4085	159	15	c	c	PROPN
ejpam-4085	159	16	,	,	PUNCT
ejpam-4085	159	17	0	0	PUNCT
ejpam-4085	159	18	<	<	X
ejpam-4085	159	19	re(m	re(m	PROPN
ejpam-4085	159	20	)	)	PUNCT
ejpam-4085	159	21	<	<	X
ejpam-4085	159	22	1	1	NUM
ejpam-4085	159	23	,	,	PUNCT
ejpam-4085	159	24	re(q	re(q	VERB
ejpam-4085	159	25	)	)	PUNCT
ejpam-4085	159	26	>	>	X
ejpam-4085	159	27	0	0	NUM
ejpam-4085	159	28	,	,	PUNCT
ejpam-4085	159	29	(	(	PUNCT
ejpam-4085	159	30	17	17	NUM
ejpam-4085	159	31	)	)	PUNCT
ejpam-4085	159	32	∫	∫	PROPN
ejpam-4085	160	1	∞	∞	PROPN
ejpam-4085	160	2	0	0	NUM
ejpam-4085	160	3	∫	∫	PROPN
ejpam-4085	160	4	∞	∞	NOUN
ejpam-4085	160	5	0	0	PUNCT
ejpam-4085	161	1	xm−1ym+	xm−1ym+	NOUN
ejpam-4085	161	2	q	q	PROPN
ejpam-4085	161	3	2	2	NUM
ejpam-4085	161	4	−1	−1	NOUN
ejpam-4085	161	5	logk	logk	NOUN
ejpam-4085	161	6	(	(	PUNCT
ejpam-4085	161	7	e	e	NOUN
ejpam-4085	161	8	2iπ	2iπ	NOUN
ejpam-4085	161	9	q	q	X
ejpam-4085	161	10	xy	xy	PROPN
ejpam-4085	161	11	)	)	PUNCT
ejpam-4085	162	1	(	(	PUNCT
ejpam-4085	162	2	xq	xq	X
ejpam-4085	162	3	+	+	PROPN
ejpam-4085	163	1	1)2	1)2	NUM
ejpam-4085	163	2	(	(	PUNCT
ejpam-4085	163	3	yq	yq	PROPN
ejpam-4085	163	4	+	+	PROPN
ejpam-4085	163	5	1)2	1)2	NUM
ejpam-4085	163	6	dxdy	dxdy	NOUN
ejpam-4085	163	7	=	=	SYM
ejpam-4085	163	8	4k−1π	4k−1π	PROPN
ejpam-4085	163	9	q4	q4	PROPN
ejpam-4085	163	10	k	k	PROPN
ejpam-4085	163	11	(	(	PUNCT
ejpam-4085	163	12	i	i	PRON
ejpam-4085	163	13	q	q	NOUN
ejpam-4085	163	14	)	)	PUNCT
ejpam-4085	164	1	k	k	PROPN
ejpam-4085	164	2	e	e	X
ejpam-4085	164	3	−	−	PROPN
ejpam-4085	165	1	2iπm	2iπm	NUM
ejpam-4085	165	2	q	q	NOUN
ejpam-4085	166	1	(	(	PUNCT
ejpam-4085	166	2	i	i	PRON
ejpam-4085	166	3	(	(	PUNCT
ejpam-4085	166	4	(	(	PUNCT
ejpam-4085	166	5	k	k	PROPN
ejpam-4085	166	6	−	−	PROPN
ejpam-4085	166	7	1)kq2li2−k	1)kq2li2−k	NUM
ejpam-4085	166	8	(	(	PUNCT
ejpam-4085	166	9	e	e	X
ejpam-4085	166	10	4imπ	4imπ	NUM
ejpam-4085	166	11	q	q	NOUN
ejpam-4085	166	12	)	)	PUNCT
ejpam-4085	166	13	−	−	PROPN
ejpam-4085	166	14	8π2(q	8π2(q	NUM
ejpam-4085	166	15	−	−	PROPN
ejpam-4085	166	16	2m)(q	2m)(q	NUM
ejpam-4085	167	1	−m)li−k	−m)li−k	NOUN
ejpam-4085	167	2	(	(	PUNCT
ejpam-4085	167	3	e	e	X
ejpam-4085	167	4	4imπ	4imπ	NUM
ejpam-4085	167	5	q	q	NOUN
ejpam-4085	167	6	)	)	PUNCT
ejpam-4085	167	7	)	)	PUNCT
ejpam-4085	168	1	+	+	CCONJ
ejpam-4085	169	1	2πkq(3q	2πkq(3q	NUM
ejpam-4085	169	2	−	−	NOUN
ejpam-4085	169	3	4m)li1−k	4m)li1−k	NOUN
ejpam-4085	169	4	(	(	PUNCT
ejpam-4085	169	5	e	e	X
ejpam-4085	169	6	4imπ	4imπ	NUM
ejpam-4085	169	7	q	q	NOUN
ejpam-4085	169	8	)	)	PUNCT
ejpam-4085	169	9	)	)	PUNCT
ejpam-4085	169	10	proof	proof	NOUN
ejpam-4085	169	11	.	.	PUNCT
ejpam-4085	170	1	use	use	NOUN
ejpam-4085	170	2	(	(	PUNCT
ejpam-4085	170	3	12	12	NUM
ejpam-4085	170	4	)	)	PUNCT
ejpam-4085	170	5	and	and	CCONJ
ejpam-4085	170	6	replace	replace	VERB
ejpam-4085	170	7	a	a	DET
ejpam-4085	170	8	→	→	SYM
ejpam-4085	170	9	e	e	NOUN
ejpam-4085	170	10	2πi	2πi	NOUN
ejpam-4085	170	11	q	q	X
ejpam-4085	170	12	and	and	CCONJ
ejpam-4085	170	13	simplify	simplify	VERB
ejpam-4085	170	14	using	use	VERB
ejpam-4085	170	15	equation	equation	NOUN
ejpam-4085	170	16	(	(	PUNCT
ejpam-4085	170	17	64:12:2	64:12:2	NUM
ejpam-4085	170	18	)	)	PUNCT
ejpam-4085	170	19	in	in	ADP
ejpam-4085	170	20	[	[	X
ejpam-4085	170	21	2	2	NUM
ejpam-4085	170	22	]	]	PUNCT
ejpam-4085	170	23	.	.	PUNCT
ejpam-4085	170	24	8	8	X
ejpam-4085	170	25	.	.	PUNCT
ejpam-4085	170	26	definite	definite	ADJ
ejpam-4085	170	27	integral	integral	ADJ
ejpam-4085	170	28	in	in	ADP
ejpam-4085	170	29	terms	term	NOUN
ejpam-4085	170	30	of	of	ADP
ejpam-4085	170	31	the	the	DET
ejpam-4085	170	32	hurwitz	hurwitz	PROPN
ejpam-4085	170	33	zeta	zeta	PROPN
ejpam-4085	170	34	function	function	NOUN
ejpam-4085	170	35	theorem	theorem	VERB
ejpam-4085	170	36	3	3	NUM
ejpam-4085	170	37	.	.	X
ejpam-4085	170	38	for	for	ADP
ejpam-4085	170	39	k	k	PROPN
ejpam-4085	170	40	∈	∈	PROPN
ejpam-4085	170	41	c	c	PROPN
ejpam-4085	170	42	,	,	PUNCT
ejpam-4085	170	43	re(q	re(q	ADV
ejpam-4085	170	44	)	)	PUNCT
ejpam-4085	170	45	>	>	X
ejpam-4085	170	46	0	0	NUM
ejpam-4085	170	47	,	,	PUNCT
ejpam-4085	170	48	(	(	PUNCT
ejpam-4085	170	49	18	18	NUM
ejpam-4085	170	50	)	)	PUNCT
ejpam-4085	170	51	∫	∫	PROPN
ejpam-4085	171	1	∞	∞	PROPN
ejpam-4085	171	2	0	0	NUM
ejpam-4085	171	3	∫	∫	PROPN
ejpam-4085	171	4	∞	∞	NUM
ejpam-4085	171	5	0	0	NUM
ejpam-4085	172	1	x	x	SYM
ejpam-4085	172	2	q	q	PROPN
ejpam-4085	172	3	4	4	NUM
ejpam-4085	172	4	−1y	−1y	NOUN
ejpam-4085	172	5	3q	3q	NUM
ejpam-4085	172	6	4	4	NUM
ejpam-4085	172	7	−1	−1	NOUN
ejpam-4085	172	8	logk(xy	logk(xy	NOUN
ejpam-4085	172	9	)	)	PUNCT
ejpam-4085	172	10	(	(	PUNCT
ejpam-4085	172	11	xq	xq	X
ejpam-4085	172	12	+	+	PROPN
ejpam-4085	173	1	1)2	1)2	NUM
ejpam-4085	173	2	(	(	PUNCT
ejpam-4085	173	3	yq	yq	PROPN
ejpam-4085	173	4	+	+	PROPN
ejpam-4085	173	5	1)2	1)2	NUM
ejpam-4085	173	6	dxdy	dxdy	NOUN
ejpam-4085	173	7	=	=	SYM
ejpam-4085	173	8	23k−4πk	23k−4πk	NUM
ejpam-4085	173	9	q2	q2	NOUN
ejpam-4085	173	10	(	(	PUNCT
ejpam-4085	173	11	8iπkζ	8iπkζ	NUM
ejpam-4085	173	12	(	(	PUNCT
ejpam-4085	173	13	1−	1−	NUM
ejpam-4085	173	14	k	k	NOUN
ejpam-4085	173	15	,	,	PUNCT
ejpam-4085	173	16	1	1	NUM
ejpam-4085	173	17	4	4	NUM
ejpam-4085	173	18	)	)	PUNCT
ejpam-4085	173	19	−	−	PROPN
ejpam-4085	174	1	8iπkζ	8iπkζ	NUM
ejpam-4085	174	2	(	(	PUNCT
ejpam-4085	174	3	1−	1−	NUM
ejpam-4085	174	4	k	k	NOUN
ejpam-4085	174	5	,	,	PUNCT
ejpam-4085	174	6	3	3	NUM
ejpam-4085	174	7	4	4	NUM
ejpam-4085	174	8	)	)	PUNCT
ejpam-4085	174	9	−	−	PROPN
ejpam-4085	175	1	(	(	PUNCT
ejpam-4085	175	2	k	k	PROPN
ejpam-4085	175	3	−	−	PROPN
ejpam-4085	175	4	1)k	1)k	NUM
ejpam-4085	175	5	(	(	PUNCT
ejpam-4085	175	6	ζ	ζ	X
ejpam-4085	175	7	(	(	PUNCT
ejpam-4085	175	8	2−	2−	NUM
ejpam-4085	175	9	k	k	NOUN
ejpam-4085	175	10	,	,	PUNCT
ejpam-4085	175	11	1	1	NUM
ejpam-4085	175	12	4	4	NUM
ejpam-4085	175	13	)	)	PUNCT
ejpam-4085	175	14	−	−	PROPN
ejpam-4085	175	15	ζ	ζ	NOUN
ejpam-4085	175	16	(	(	PUNCT
ejpam-4085	175	17	2−	2−	NUM
ejpam-4085	175	18	k	k	NOUN
ejpam-4085	175	19	,	,	PUNCT
ejpam-4085	175	20	3	3	NUM
ejpam-4085	175	21	4	4	NUM
ejpam-4085	175	22	)	)	PUNCT
ejpam-4085	175	23	)	)	PUNCT
ejpam-4085	176	1	+	+	CCONJ
ejpam-4085	177	1	12π2	12π2	NUM
ejpam-4085	177	2	(	(	PUNCT
ejpam-4085	177	3	ζ	ζ	X
ejpam-4085	177	4	(	(	PUNCT
ejpam-4085	177	5	−k	−k	PROPN
ejpam-4085	177	6	,	,	PUNCT
ejpam-4085	177	7	1	1	NUM
ejpam-4085	177	8	4	4	NUM
ejpam-4085	177	9	)	)	PUNCT
ejpam-4085	177	10	−	−	NOUN
ejpam-4085	177	11	ζ	ζ	NOUN
ejpam-4085	177	12	(	(	PUNCT
ejpam-4085	177	13	−k	−k	PROPN
ejpam-4085	177	14	,	,	PUNCT
ejpam-4085	177	15	3	3	NUM
ejpam-4085	177	16	4	4	NUM
ejpam-4085	177	17	)	)	PUNCT
ejpam-4085	177	18	)	)	PUNCT
ejpam-4085	177	19	)	)	PUNCT
ejpam-4085	178	1	(	(	PUNCT
ejpam-4085	178	2	i	i	PRON
ejpam-4085	178	3	q	q	NOUN
ejpam-4085	178	4	)	)	PUNCT
ejpam-4085	178	5	k	k	NOUN
ejpam-4085	178	6	proof	proof	NOUN
ejpam-4085	178	7	.	.	PUNCT
ejpam-4085	179	1	use	use	NOUN
ejpam-4085	179	2	(	(	PUNCT
ejpam-4085	179	3	12	12	NUM
ejpam-4085	179	4	)	)	PUNCT
ejpam-4085	179	5	set	set	VERB
ejpam-4085	179	6	a	a	DET
ejpam-4085	179	7	=	=	SYM
ejpam-4085	179	8	1	1	NUM
ejpam-4085	179	9	and	and	CCONJ
ejpam-4085	179	10	replace	replace	VERB
ejpam-4085	179	11	m	m	PROPN
ejpam-4085	179	12	→	→	SYM
ejpam-4085	179	13	q/4	q/4	PUNCT
ejpam-4085	179	14	and	and	CCONJ
ejpam-4085	179	15	simplify	simplify	VERB
ejpam-4085	179	16	using	use	VERB
ejpam-4085	179	17	equation	equation	NOUN
ejpam-4085	179	18	(	(	PUNCT
ejpam-4085	179	19	64:12:1	64:12:1	NUM
ejpam-4085	179	20	)	)	PUNCT
ejpam-4085	179	21	and	and	CCONJ
ejpam-4085	179	22	entry	entry	NOUN
ejpam-4085	179	23	(	(	PUNCT
ejpam-4085	179	24	4	4	NUM
ejpam-4085	179	25	)	)	PUNCT
ejpam-4085	179	26	in	in	ADP
ejpam-4085	179	27	table	table	NOUN
ejpam-4085	179	28	below	below	ADV
ejpam-4085	179	29	(	(	PUNCT
ejpam-4085	179	30	64:12:7	64:12:7	NUM
ejpam-4085	179	31	)	)	PUNCT
ejpam-4085	179	32	in	in	ADP
ejpam-4085	179	33	[	[	X
ejpam-4085	179	34	2	2	NUM
ejpam-4085	179	35	]	]	PUNCT
ejpam-4085	179	36	.	.	PUNCT
ejpam-4085	180	1	r.	r.	PROPN
ejpam-4085	180	2	reynolds	reynolds	PROPN
ejpam-4085	180	3	,	,	PUNCT
ejpam-4085	180	4	a.	a.	PROPN
ejpam-4085	180	5	stauffer	stauffer	PROPN
ejpam-4085	180	6	/	/	SYM
ejpam-4085	180	7	eur	eur	PROPN
ejpam-4085	180	8	.	.	PUNCT
ejpam-4085	181	1	j.	j.	PROPN
ejpam-4085	181	2	pure	pure	PROPN
ejpam-4085	181	3	appl	appl	PROPN
ejpam-4085	181	4	.	.	PROPN
ejpam-4085	181	5	math	math	PROPN
ejpam-4085	181	6	,	,	PUNCT
ejpam-4085	181	7	14	14	NUM
ejpam-4085	181	8	(	(	PUNCT
ejpam-4085	181	9	4	4	NUM
ejpam-4085	181	10	)	)	PUNCT
ejpam-4085	181	11	(	(	PUNCT
ejpam-4085	181	12	2021	2021	NUM
ejpam-4085	181	13	)	)	PUNCT
ejpam-4085	181	14	,	,	PUNCT
ejpam-4085	181	15	1337	1337	NUM
ejpam-4085	181	16	-	-	SYM
ejpam-4085	181	17	1349	1349	NUM
ejpam-4085	181	18	1345	1345	NUM
ejpam-4085	181	19	9	9	NUM
ejpam-4085	181	20	.	.	PUNCT
ejpam-4085	182	1	derivation	derivation	NOUN
ejpam-4085	182	2	of	of	ADP
ejpam-4085	182	3	entry	entry	NOUN
ejpam-4085	182	4	3.241.5	3.241.5	NUM
ejpam-4085	182	5	in	in	ADP
ejpam-4085	182	6	[	[	PUNCT
ejpam-4085	182	7	1	1	NUM
ejpam-4085	182	8	]	]	PUNCT
ejpam-4085	182	9	proposition	proposition	NOUN
ejpam-4085	182	10	4	4	NUM
ejpam-4085	182	11	.	.	PUNCT
ejpam-4085	183	1	for	for	ADP
ejpam-4085	183	2	0	0	NUM
ejpam-4085	183	3	<	<	X
ejpam-4085	183	4	re(m	re(m	PROPN
ejpam-4085	183	5	)	)	PUNCT
ejpam-4085	183	6	<	<	X
ejpam-4085	183	7	1	1	NUM
ejpam-4085	183	8	,	,	PUNCT
ejpam-4085	183	9	0	0	NUM
ejpam-4085	183	10	<	<	X
ejpam-4085	183	11	re(p	re(p	NOUN
ejpam-4085	183	12	)	)	PUNCT
ejpam-4085	183	13	<	<	X
ejpam-4085	183	14	1	1	NUM
ejpam-4085	183	15	,	,	PUNCT
ejpam-4085	183	16	re(p	re(p	NUM
ejpam-4085	183	17	)	)	PUNCT
ejpam-4085	183	18	<	<	X
ejpam-4085	183	19	2q	2q	NUM
ejpam-4085	183	20	,	,	PUNCT
ejpam-4085	183	21	(	(	PUNCT
ejpam-4085	183	22	19	19	NUM
ejpam-4085	183	23	)	)	PUNCT
ejpam-4085	183	24	∫	∫	PROPN
ejpam-4085	183	25	∞	∞	PROPN
ejpam-4085	183	26	0	0	NUM
ejpam-4085	183	27	∫	∫	PROPN
ejpam-4085	183	28	∞	∞	PROPN
ejpam-4085	183	29	0	0	NUM
ejpam-4085	184	1	y	y	PROPN
ejpam-4085	184	2	q	q	PROPN
ejpam-4085	184	3	2	2	NUM
ejpam-4085	184	4	−1	−1	NOUN
ejpam-4085	184	5	(	(	PUNCT
ejpam-4085	184	6	xpyp	xpyp	PROPN
ejpam-4085	184	7	−	−	PROPN
ejpam-4085	184	8	xmym	xmym	PROPN
ejpam-4085	184	9	)	)	PUNCT
ejpam-4085	184	10	x	x	X
ejpam-4085	184	11	(	(	PUNCT
ejpam-4085	184	12	xq	xq	PROPN
ejpam-4085	184	13	+	+	PROPN
ejpam-4085	184	14	1)2	1)2	NUM
ejpam-4085	184	15	(	(	PUNCT
ejpam-4085	184	16	yq	yq	PROPN
ejpam-4085	184	17	+	+	PROPN
ejpam-4085	184	18	1)2	1)2	NUM
ejpam-4085	184	19	dxdy	dxdy	NOUN
ejpam-4085	184	20	=	=	SYM
ejpam-4085	184	21	π2	π2	X
ejpam-4085	184	22	(	(	PUNCT
ejpam-4085	184	23	(	(	PUNCT
ejpam-4085	184	24	2m−	2m−	PROPN
ejpam-4085	184	25	q)(q	q)(q	NOUN
ejpam-4085	184	26	−m	−m	NOUN
ejpam-4085	184	27	)	)	PUNCT
ejpam-4085	184	28	csc	csc	PROPN
ejpam-4085	184	29	(	(	PUNCT
ejpam-4085	184	30	2πm	2πm	NOUN
ejpam-4085	184	31	q	q	X
ejpam-4085	184	32	)	)	PUNCT
ejpam-4085	185	1	+	+	CCONJ
ejpam-4085	185	2	(	(	PUNCT
ejpam-4085	185	3	q	q	X
ejpam-4085	185	4	−	−	PROPN
ejpam-4085	185	5	2p)(q	2p)(q	NUM
ejpam-4085	185	6	−	−	PROPN
ejpam-4085	186	1	p	p	X
ejpam-4085	186	2	)	)	PUNCT
ejpam-4085	186	3	csc	csc	PROPN
ejpam-4085	186	4	(	(	PUNCT
ejpam-4085	186	5	2πp	2πp	PROPN
ejpam-4085	186	6	q	q	NOUN
ejpam-4085	186	7	)	)	PUNCT
ejpam-4085	186	8	)	)	PUNCT
ejpam-4085	186	9	q4	q4	PROPN
ejpam-4085	186	10	proof	proof	NOUN
ejpam-4085	186	11	.	.	PUNCT
ejpam-4085	187	1	use	use	VERB
ejpam-4085	187	2	equation	equation	NOUN
ejpam-4085	187	3	(	(	PUNCT
ejpam-4085	187	4	12	12	NUM
ejpam-4085	187	5	)	)	PUNCT
ejpam-4085	187	6	and	and	CCONJ
ejpam-4085	187	7	set	set	VERB
ejpam-4085	187	8	k	k	PROPN
ejpam-4085	187	9	=	=	PUNCT
ejpam-4085	187	10	0	0	PUNCT
ejpam-4085	187	11	and	and	CCONJ
ejpam-4085	187	12	simplify	simplify	VERB
ejpam-4085	187	13	using	use	VERB
ejpam-4085	187	14	entry	entry	NOUN
ejpam-4085	187	15	(	(	PUNCT
ejpam-4085	187	16	2	2	NUM
ejpam-4085	187	17	)	)	PUNCT
ejpam-4085	187	18	in	in	ADP
ejpam-4085	187	19	table	table	NOUN
ejpam-4085	187	20	below	below	ADV
ejpam-4085	187	21	(	(	PUNCT
ejpam-4085	187	22	64:12:7	64:12:7	NUM
ejpam-4085	187	23	)	)	PUNCT
ejpam-4085	187	24	in	in	ADP
ejpam-4085	187	25	[	[	X
ejpam-4085	187	26	2	2	NUM
ejpam-4085	187	27	]	]	PUNCT
ejpam-4085	187	28	.	.	PUNCT
ejpam-4085	188	1	proposition	proposition	NOUN
ejpam-4085	188	2	5	5	NUM
ejpam-4085	188	3	.	.	PUNCT
ejpam-4085	189	1	(	(	PUNCT
ejpam-4085	189	2	20	20	NUM
ejpam-4085	189	3	)	)	PUNCT
ejpam-4085	189	4	∫	∫	PROPN
ejpam-4085	190	1	∞	∞	PROPN
ejpam-4085	190	2	0	0	NUM
ejpam-4085	190	3	∫	∫	PROPN
ejpam-4085	190	4	∞	∞	NUM
ejpam-4085	190	5	0	0	NUM
ejpam-4085	191	1	√	√	PROPN
ejpam-4085	191	2	y	y	PROPN
ejpam-4085	191	3	log(log(xy	log(log(xy	PROPN
ejpam-4085	191	4	)	)	PUNCT
ejpam-4085	191	5	)	)	PUNCT
ejpam-4085	192	1	√	√	NUM
ejpam-4085	192	2	x	x	SYM
ejpam-4085	193	1	(	(	PUNCT
ejpam-4085	193	2	x2	x2	NOUN
ejpam-4085	193	3	+	+	CCONJ
ejpam-4085	193	4	1)2	1)2	NUM
ejpam-4085	193	5	(	(	PUNCT
ejpam-4085	193	6	y2	y2	PROPN
ejpam-4085	193	7	+	+	CCONJ
ejpam-4085	193	8	1)2	1)2	NUM
ejpam-4085	193	9	dxdy	dxdy	NOUN
ejpam-4085	193	10	=	=	SYM
ejpam-4085	193	11	1	1	NUM
ejpam-4085	193	12	64	64	NUM
ejpam-4085	193	13	(	(	PUNCT
ejpam-4085	193	14	16g+	16g+	NUM
ejpam-4085	193	15	π2	π2	NOUN
ejpam-4085	193	16	(	(	PUNCT
ejpam-4085	193	17	8i+	8i+	NUM
ejpam-4085	193	18	3iπ	3iπ	NOUN
ejpam-4085	193	19	+	+	CCONJ
ejpam-4085	193	20	2	2	NUM
ejpam-4085	193	21	log	log	NOUN
ejpam-4085	193	22	(	(	PUNCT
ejpam-4085	193	23	64π3γ	64π3γ	NUM
ejpam-4085	193	24	(	(	PUNCT
ejpam-4085	193	25	−1	−1	NOUN
ejpam-4085	193	26	4	4	NUM
ejpam-4085	193	27	)	)	SYM
ejpam-4085	193	28	6	6	NUM
ejpam-4085	193	29	729γ	729γ	NOUN
ejpam-4085	193	30	(	(	PUNCT
ejpam-4085	193	31	−3	−3	PROPN
ejpam-4085	193	32	4	4	NUM
ejpam-4085	193	33	)	)	PUNCT
ejpam-4085	193	34	6	6	NUM
ejpam-4085	193	35	)	)	PUNCT
ejpam-4085	193	36	)	)	PUNCT
ejpam-4085	193	37	)	)	PUNCT
ejpam-4085	193	38	proof	proof	NOUN
ejpam-4085	193	39	.	.	PUNCT
ejpam-4085	194	1	use	use	VERB
ejpam-4085	194	2	equation	equation	NOUN
ejpam-4085	194	3	(	(	PUNCT
ejpam-4085	194	4	18	18	NUM
ejpam-4085	194	5	)	)	PUNCT
ejpam-4085	194	6	and	and	CCONJ
ejpam-4085	194	7	take	take	VERB
ejpam-4085	194	8	the	the	DET
ejpam-4085	194	9	first	first	ADJ
ejpam-4085	194	10	partial	partial	ADJ
ejpam-4085	194	11	derivative	derivative	NOUN
ejpam-4085	194	12	with	with	ADP
ejpam-4085	194	13	respect	respect	NOUN
ejpam-4085	194	14	to	to	ADP
ejpam-4085	194	15	k	k	PROPN
ejpam-4085	194	16	and	and	CCONJ
ejpam-4085	194	17	set	set	VERB
ejpam-4085	194	18	k	k	PROPN
ejpam-4085	194	19	=	=	SYM
ejpam-4085	194	20	0	0	NUM
ejpam-4085	194	21	,	,	PUNCT
ejpam-4085	194	22	q	q	NOUN
ejpam-4085	194	23	=	=	SYM
ejpam-4085	194	24	2	2	NUM
ejpam-4085	194	25	and	and	CCONJ
ejpam-4085	194	26	simplify	simplify	VERB
ejpam-4085	194	27	using	use	VERB
ejpam-4085	194	28	equation	equation	NOUN
ejpam-4085	194	29	(	(	PUNCT
ejpam-4085	194	30	64:10:2	64:10:2	NUM
ejpam-4085	194	31	)	)	PUNCT
ejpam-4085	194	32	in	in	ADP
ejpam-4085	194	33	[	[	X
ejpam-4085	194	34	2	2	NUM
ejpam-4085	194	35	]	]	PUNCT
ejpam-4085	194	36	.	.	PUNCT
ejpam-4085	195	1	proposition	proposition	NOUN
ejpam-4085	195	2	6	6	NUM
ejpam-4085	195	3	.	.	PUNCT
ejpam-4085	196	1	(	(	PUNCT
ejpam-4085	196	2	21	21	NUM
ejpam-4085	196	3	)	)	PUNCT
ejpam-4085	196	4	∫	∫	PROPN
ejpam-4085	197	1	∞	∞	PROPN
ejpam-4085	197	2	0	0	NUM
ejpam-4085	197	3	∫	∫	PROPN
ejpam-4085	198	1	∞	∞	NUM
ejpam-4085	198	2	0	0	NUM
ejpam-4085	198	3	√	√	PROPN
ejpam-4085	198	4	y	y	PROPN
ejpam-4085	198	5	log(xy	log(xy	PROPN
ejpam-4085	198	6	)	)	PUNCT
ejpam-4085	198	7	log(log(xy	log(log(xy	NOUN
ejpam-4085	198	8	)	)	PUNCT
ejpam-4085	198	9	)	)	PUNCT
ejpam-4085	199	1	√	√	NUM
ejpam-4085	199	2	x	x	SYM
ejpam-4085	200	1	(	(	PUNCT
ejpam-4085	200	2	x2	x2	NOUN
ejpam-4085	200	3	+	+	CCONJ
ejpam-4085	200	4	1)2	1)2	NUM
ejpam-4085	200	5	(	(	PUNCT
ejpam-4085	200	6	y2	y2	PROPN
ejpam-4085	200	7	+	+	CCONJ
ejpam-4085	200	8	1)2	1)2	NUM
ejpam-4085	200	9	dxdy	dxdy	NOUN
ejpam-4085	200	10	=	=	SYM
ejpam-4085	200	11	1	1	NUM
ejpam-4085	200	12	16	16	NUM
ejpam-4085	200	13	π2	π2	NOUN
ejpam-4085	200	14	(	(	PUNCT
ejpam-4085	200	15	−6ig+	−6ig+	NOUN
ejpam-4085	200	16	(	(	PUNCT
ejpam-4085	200	17	−4−	−4−	PROPN
ejpam-4085	200	18	i)−	i)−	PROPN
ejpam-4085	200	19	2iπ	2iπ	NOUN
ejpam-4085	200	20	+	+	CCONJ
ejpam-4085	200	21	log	log	NOUN
ejpam-4085	200	22	(	(	PUNCT
ejpam-4085	200	23	6561γ	6561γ	NUM
ejpam-4085	200	24	(	(	PUNCT
ejpam-4085	200	25	−3	−3	PROPN
ejpam-4085	200	26	4	4	NUM
ejpam-4085	200	27	)	)	SYM
ejpam-4085	200	28	8	8	NUM
ejpam-4085	200	29	256π4γ	256π4γ	NUM
ejpam-4085	200	30	(	(	PUNCT
ejpam-4085	200	31	−1	−1	NOUN
ejpam-4085	200	32	4	4	NUM
ejpam-4085	200	33	)	)	PUNCT
ejpam-4085	200	34	8	8	NUM
ejpam-4085	200	35	)	)	PUNCT
ejpam-4085	200	36	)	)	PUNCT
ejpam-4085	200	37	proof	proof	NOUN
ejpam-4085	200	38	.	.	PUNCT
ejpam-4085	201	1	use	use	VERB
ejpam-4085	201	2	equation	equation	NOUN
ejpam-4085	201	3	(	(	PUNCT
ejpam-4085	201	4	18	18	NUM
ejpam-4085	201	5	)	)	PUNCT
ejpam-4085	201	6	and	and	CCONJ
ejpam-4085	201	7	apply	apply	VERB
ejpam-4085	201	8	l’hopital	l’hopital	PROPN
ejpam-4085	201	9	’s	’s	PART
ejpam-4085	201	10	rule	rule	NOUN
ejpam-4085	201	11	as	as	ADP
ejpam-4085	201	12	k	k	PROPN
ejpam-4085	201	13	→	→	SYM
ejpam-4085	201	14	1	1	NUM
ejpam-4085	201	15	and	and	CCONJ
ejpam-4085	201	16	set	set	VERB
ejpam-4085	201	17	q	q	PROPN
ejpam-4085	201	18	=	=	SYM
ejpam-4085	201	19	2	2	NUM
ejpam-4085	201	20	and	and	CCONJ
ejpam-4085	201	21	simplify	simplify	VERB
ejpam-4085	201	22	using	use	VERB
ejpam-4085	201	23	equation	equation	NOUN
ejpam-4085	201	24	(	(	PUNCT
ejpam-4085	201	25	64:10:2	64:10:2	NUM
ejpam-4085	201	26	)	)	PUNCT
ejpam-4085	201	27	in	in	ADP
ejpam-4085	201	28	[	[	X
ejpam-4085	201	29	2	2	NUM
ejpam-4085	201	30	]	]	PUNCT
ejpam-4085	201	31	.	.	PUNCT
ejpam-4085	202	1	10	10	NUM
ejpam-4085	202	2	.	.	PUNCT
ejpam-4085	203	1	definite	definite	ADJ
ejpam-4085	203	2	integral	integral	ADJ
ejpam-4085	203	3	in	in	ADP
ejpam-4085	203	4	terms	term	NOUN
ejpam-4085	203	5	of	of	ADP
ejpam-4085	203	6	the	the	DET
ejpam-4085	203	7	zeta	zeta	NOUN
ejpam-4085	203	8	function	function	NOUN
ejpam-4085	203	9	of	of	ADP
ejpam-4085	203	10	riemann	riemann	PROPN
ejpam-4085	203	11	lemma	lemma	PROPN
ejpam-4085	203	12	1	1	NUM
ejpam-4085	203	13	.	.	PUNCT
ejpam-4085	204	1	(	(	PUNCT
ejpam-4085	204	2	22	22	NUM
ejpam-4085	204	3	)	)	PUNCT
ejpam-4085	204	4	∫	∫	PROPN
ejpam-4085	205	1	∞	∞	PROPN
ejpam-4085	205	2	0	0	NUM
ejpam-4085	205	3	∫	∫	PROPN
ejpam-4085	205	4	∞	∞	NUM
ejpam-4085	205	5	0	0	NUM
ejpam-4085	206	1	√	√	PROPN
ejpam-4085	206	2	y	y	NUM
ejpam-4085	206	3	√	√	NUM
ejpam-4085	206	4	x	x	SYM
ejpam-4085	207	1	(	(	PUNCT
ejpam-4085	207	2	x2	x2	NOUN
ejpam-4085	207	3	+	+	CCONJ
ejpam-4085	207	4	1)2	1)2	NUM
ejpam-4085	207	5	(	(	PUNCT
ejpam-4085	207	6	y2	y2	PROPN
ejpam-4085	207	7	+	+	CCONJ
ejpam-4085	207	8	1)2	1)2	NUM
ejpam-4085	207	9	(	(	PUNCT
ejpam-4085	207	10	log2(xy	log2(xy	PROPN
ejpam-4085	207	11	)	)	PUNCT
ejpam-4085	207	12	+	+	CCONJ
ejpam-4085	207	13	π2	π2	ADJ
ejpam-4085	207	14	)	)	PUNCT
ejpam-4085	207	15	dxdy	dxdy	NOUN
ejpam-4085	207	16	=	=	SYM
ejpam-4085	207	17	3	3	NUM
ejpam-4085	207	18	32	32	NUM
ejpam-4085	207	19	(	(	PUNCT
ejpam-4085	207	20	2ζ	2ζ	NUM
ejpam-4085	207	21	′(−2	′(−2	PROPN
ejpam-4085	207	22	)	)	PUNCT
ejpam-4085	207	23	+	+	NUM
ejpam-4085	207	24	log(2	log(2	NOUN
ejpam-4085	207	25	)	)	PUNCT
ejpam-4085	207	26	)	)	PUNCT
ejpam-4085	208	1	r.	r.	PROPN
ejpam-4085	208	2	reynolds	reynolds	PROPN
ejpam-4085	208	3	,	,	PUNCT
ejpam-4085	208	4	a.	a.	PROPN
ejpam-4085	208	5	stauffer	stauffer	PROPN
ejpam-4085	208	6	/	/	SYM
ejpam-4085	208	7	eur	eur	PROPN
ejpam-4085	208	8	.	.	PUNCT
ejpam-4085	209	1	j.	j.	PROPN
ejpam-4085	209	2	pure	pure	PROPN
ejpam-4085	209	3	appl	appl	PROPN
ejpam-4085	209	4	.	.	PROPN
ejpam-4085	209	5	math	math	PROPN
ejpam-4085	209	6	,	,	PUNCT
ejpam-4085	209	7	14	14	NUM
ejpam-4085	209	8	(	(	PUNCT
ejpam-4085	209	9	4	4	NUM
ejpam-4085	209	10	)	)	PUNCT
ejpam-4085	209	11	(	(	PUNCT
ejpam-4085	209	12	2021	2021	NUM
ejpam-4085	209	13	)	)	PUNCT
ejpam-4085	209	14	,	,	PUNCT
ejpam-4085	209	15	1337	1337	NUM
ejpam-4085	209	16	-	-	SYM
ejpam-4085	209	17	1349	1349	NUM
ejpam-4085	209	18	1346	1346	NUM
ejpam-4085	209	19	proof	proof	NOUN
ejpam-4085	209	20	.	.	PUNCT
ejpam-4085	210	1	use	use	VERB
ejpam-4085	210	2	equation	equation	NOUN
ejpam-4085	210	3	(	(	PUNCT
ejpam-4085	210	4	12	12	NUM
ejpam-4085	210	5	)	)	PUNCT
ejpam-4085	210	6	and	and	CCONJ
ejpam-4085	210	7	set	set	VERB
ejpam-4085	210	8	m	m	PROPN
ejpam-4085	210	9	=	=	SYM
ejpam-4085	210	10	1/2	1/2	NUM
ejpam-4085	210	11	,	,	PUNCT
ejpam-4085	210	12	a	a	DET
ejpam-4085	210	13	=	=	SYM
ejpam-4085	210	14	−1	−1	NOUN
ejpam-4085	210	15	,	,	PUNCT
ejpam-4085	210	16	q	q	NOUN
ejpam-4085	210	17	=	=	SYM
ejpam-4085	210	18	2	2	NUM
ejpam-4085	210	19	and	and	CCONJ
ejpam-4085	210	20	simplify	simplify	VERB
ejpam-4085	210	21	in	in	ADP
ejpam-4085	210	22	terms	term	NOUN
ejpam-4085	210	23	of	of	ADP
ejpam-4085	210	24	the	the	DET
ejpam-4085	210	25	riemann	riemann	PROPN
ejpam-4085	210	26	zeta	zeta	PROPN
ejpam-4085	210	27	function	function	NOUN
ejpam-4085	210	28	using	use	VERB
ejpam-4085	210	29	entry	entry	NOUN
ejpam-4085	210	30	(	(	PUNCT
ejpam-4085	210	31	2	2	NUM
ejpam-4085	210	32	)	)	PUNCT
ejpam-4085	210	33	in	in	ADP
ejpam-4085	210	34	tbale	tbale	NOUN
ejpam-4085	210	35	below	below	ADV
ejpam-4085	210	36	(	(	PUNCT
ejpam-4085	210	37	64:7	64:7	NUM
ejpam-4085	210	38	)	)	PUNCT
ejpam-4085	210	39	and	and	CCONJ
ejpam-4085	210	40	entry	entry	NOUN
ejpam-4085	210	41	(	(	PUNCT
ejpam-4085	210	42	4	4	NUM
ejpam-4085	210	43	)	)	PUNCT
ejpam-4085	210	44	in	in	ADP
ejpam-4085	210	45	table	table	NOUN
ejpam-4085	210	46	below	below	ADV
ejpam-4085	210	47	(	(	PUNCT
ejpam-4085	210	48	64:12:7	64:12:7	NUM
ejpam-4085	210	49	)	)	PUNCT
ejpam-4085	210	50	in	in	ADP
ejpam-4085	210	51	[	[	X
ejpam-4085	210	52	2	2	NUM
ejpam-4085	210	53	]	]	PUNCT
ejpam-4085	210	54	to	to	PART
ejpam-4085	210	55	get	get	VERB
ejpam-4085	210	56	(	(	PUNCT
ejpam-4085	210	57	23	23	NUM
ejpam-4085	210	58	)	)	PUNCT
ejpam-4085	210	59	∫	∫	PROPN
ejpam-4085	210	60	∞	∞	PROPN
ejpam-4085	210	61	0	0	NUM
ejpam-4085	211	1	∫	∫	PROPN
ejpam-4085	212	1	∞	∞	NUM
ejpam-4085	212	2	0	0	NUM
ejpam-4085	212	3	√	√	PROPN
ejpam-4085	212	4	y	y	PROPN
ejpam-4085	212	5	logk(−xy	logk(−xy	PROPN
ejpam-4085	212	6	)	)	PUNCT
ejpam-4085	212	7	√	√	NUM
ejpam-4085	212	8	x	x	SYM
ejpam-4085	212	9	(	(	PUNCT
ejpam-4085	212	10	x2	x2	NOUN
ejpam-4085	212	11	+	+	CCONJ
ejpam-4085	212	12	1)2	1)2	NUM
ejpam-4085	212	13	(	(	PUNCT
ejpam-4085	212	14	y2	y2	PROPN
ejpam-4085	212	15	+	+	CCONJ
ejpam-4085	212	16	1)2	1)2	NUM
ejpam-4085	212	17	dxdy	dxdy	NOUN
ejpam-4085	212	18	=	=	SYM
ejpam-4085	212	19	2k−5(iπ)k	2k−5(iπ)k	PROPN
ejpam-4085	212	20	(	(	PUNCT
ejpam-4085	212	21	−8iπ	−8iπ	NOUN
ejpam-4085	212	22	(	(	PUNCT
ejpam-4085	212	23	2k	2k	NUM
ejpam-4085	212	24	−	−	NOUN
ejpam-4085	212	25	1	1	NUM
ejpam-4085	212	26	)	)	PUNCT
ejpam-4085	212	27	kζ(1−	kζ(1−	PROPN
ejpam-4085	212	28	k	k	NOUN
ejpam-4085	212	29	)	)	PUNCT
ejpam-4085	213	1	+	+	CCONJ
ejpam-4085	213	2	(	(	PUNCT
ejpam-4085	213	3	2k	2k	NUM
ejpam-4085	213	4	−	−	PROPN
ejpam-4085	213	5	2	2	NUM
ejpam-4085	213	6	)	)	PUNCT
ejpam-4085	213	7	(	(	PUNCT
ejpam-4085	213	8	k	k	X
ejpam-4085	213	9	−	−	PROPN
ejpam-4085	213	10	1)kζ(2−	1)kζ(2−	PROPN
ejpam-4085	213	11	k)−	k)−	PROPN
ejpam-4085	213	12	6π2	6π2	NUM
ejpam-4085	213	13	(	(	PUNCT
ejpam-4085	213	14	2k+1	2k+1	NOUN
ejpam-4085	213	15	−	−	NOUN
ejpam-4085	213	16	1	1	NUM
ejpam-4085	213	17	)	)	PUNCT
ejpam-4085	213	18	ζ(−k	ζ(−k	NOUN
ejpam-4085	213	19	)	)	PUNCT
ejpam-4085	213	20	)	)	PUNCT
ejpam-4085	214	1	next	next	ADV
ejpam-4085	214	2	apply	apply	VERB
ejpam-4085	214	3	l’hopital	l’hopital	PROPN
ejpam-4085	214	4	’s	’s	PART
ejpam-4085	214	5	rule	rule	NOUN
ejpam-4085	214	6	as	as	ADP
ejpam-4085	214	7	k	k	PROPN
ejpam-4085	214	8	→	→	SYM
ejpam-4085	214	9	−1	−1	NOUN
ejpam-4085	214	10	and	and	CCONJ
ejpam-4085	214	11	simplify	simplify	NOUN
ejpam-4085	214	12	.	.	PUNCT
ejpam-4085	215	1	proposition	proposition	NOUN
ejpam-4085	215	2	7	7	NUM
ejpam-4085	215	3	.	.	PUNCT
ejpam-4085	216	1	(	(	PUNCT
ejpam-4085	216	2	24	24	NUM
ejpam-4085	216	3	)	)	PUNCT
ejpam-4085	216	4	∫	∫	PROPN
ejpam-4085	217	1	∞	∞	PROPN
ejpam-4085	217	2	0	0	NUM
ejpam-4085	217	3	∫	∫	PROPN
ejpam-4085	217	4	∞	∞	NUM
ejpam-4085	217	5	0	0	NUM
ejpam-4085	218	1	√	√	PROPN
ejpam-4085	218	2	y	y	NUM
ejpam-4085	218	3	√	√	NUM
ejpam-4085	218	4	x	x	SYM
ejpam-4085	219	1	(	(	PUNCT
ejpam-4085	219	2	x2	x2	NOUN
ejpam-4085	219	3	+	+	CCONJ
ejpam-4085	219	4	1)2	1)2	NUM
ejpam-4085	219	5	(	(	PUNCT
ejpam-4085	219	6	y2	y2	PROPN
ejpam-4085	219	7	+	+	CCONJ
ejpam-4085	219	8	1)2	1)2	NUM
ejpam-4085	219	9	(	(	PUNCT
ejpam-4085	219	10	log2(xy	log2(xy	PROPN
ejpam-4085	219	11	)	)	PUNCT
ejpam-4085	219	12	+	+	CCONJ
ejpam-4085	219	13	π2	π2	ADJ
ejpam-4085	219	14	)	)	PUNCT
ejpam-4085	219	15	dxdy	dxdy	NOUN
ejpam-4085	219	16	=	=	SYM
ejpam-4085	219	17	3	3	NUM
ejpam-4085	219	18	32	32	NUM
ejpam-4085	219	19	(	(	PUNCT
ejpam-4085	219	20	2ζ	2ζ	NUM
ejpam-4085	219	21	′(−2	′(−2	PROPN
ejpam-4085	219	22	)	)	PUNCT
ejpam-4085	219	23	+	+	NUM
ejpam-4085	219	24	log(2	log(2	NOUN
ejpam-4085	219	25	)	)	PUNCT
ejpam-4085	219	26	)	)	PUNCT
ejpam-4085	220	1	and	and	CCONJ
ejpam-4085	220	2	(	(	PUNCT
ejpam-4085	220	3	25	25	NUM
ejpam-4085	220	4	)	)	PUNCT
ejpam-4085	220	5	∫	∫	PROPN
ejpam-4085	220	6	∞	∞	PROPN
ejpam-4085	220	7	0	0	NUM
ejpam-4085	221	1	∫	∫	PROPN
ejpam-4085	222	1	∞	∞	NUM
ejpam-4085	222	2	0	0	NUM
ejpam-4085	222	3	√	√	PROPN
ejpam-4085	222	4	y	y	PROPN
ejpam-4085	222	5	log(xy	log(xy	PROPN
ejpam-4085	222	6	)	)	PUNCT
ejpam-4085	222	7	√	√	DET
ejpam-4085	222	8	x	x	SYM
ejpam-4085	222	9	(	(	PUNCT
ejpam-4085	222	10	x2	x2	NOUN
ejpam-4085	222	11	+	+	CCONJ
ejpam-4085	222	12	1)2	1)2	NUM
ejpam-4085	222	13	(	(	PUNCT
ejpam-4085	222	14	y2	y2	PROPN
ejpam-4085	223	1	+	+	CCONJ
ejpam-4085	223	2	1)2	1)2	NUM
ejpam-4085	223	3	(	(	PUNCT
ejpam-4085	223	4	log2(xy	log2(xy	PROPN
ejpam-4085	223	5	)	)	PUNCT
ejpam-4085	224	1	+	+	CCONJ
ejpam-4085	224	2	π2	π2	ADJ
ejpam-4085	224	3	)	)	PUNCT
ejpam-4085	224	4	dxdy	dxdy	NOUN
ejpam-4085	224	5	=	=	SYM
ejpam-4085	224	6	−π2	−π2	PROPN
ejpam-4085	224	7	96	96	NUM
ejpam-4085	224	8	proof	proof	NOUN
ejpam-4085	224	9	.	.	PUNCT
ejpam-4085	225	1	use	use	VERB
ejpam-4085	225	2	equation	equation	NOUN
ejpam-4085	225	3	(	(	PUNCT
ejpam-4085	225	4	23	23	NUM
ejpam-4085	225	5	)	)	PUNCT
ejpam-4085	225	6	and	and	CCONJ
ejpam-4085	225	7	apply	apply	VERB
ejpam-4085	225	8	l’hopitals	l’hopital	NOUN
ejpam-4085	225	9	’	'	PUNCT
ejpam-4085	225	10	rule	rule	NOUN
ejpam-4085	225	11	as	as	SCONJ
ejpam-4085	225	12	k	k	PROPN
ejpam-4085	225	13	→	→	SYM
ejpam-4085	225	14	−1	−1	NOUN
ejpam-4085	225	15	rationalize	rationalize	VERB
ejpam-4085	225	16	the	the	DET
ejpam-4085	225	17	denominator	denominator	NOUN
ejpam-4085	225	18	and	and	CCONJ
ejpam-4085	225	19	equate	equate	VERB
ejpam-4085	225	20	real	real	ADJ
ejpam-4085	225	21	and	and	CCONJ
ejpam-4085	225	22	imaginary	imaginary	ADJ
ejpam-4085	225	23	parts	part	NOUN
ejpam-4085	225	24	to	to	PART
ejpam-4085	225	25	get	get	AUX
ejpam-4085	225	26	stated	state	VERB
ejpam-4085	225	27	result	result	NOUN
ejpam-4085	225	28	.	.	PUNCT
ejpam-4085	226	1	theorem	theorem	ADJ
ejpam-4085	226	2	4	4	NUM
ejpam-4085	226	3	.	.	X
ejpam-4085	227	1	for	for	ADP
ejpam-4085	227	2	k	k	PROPN
ejpam-4085	227	3	∈	∈	PROPN
ejpam-4085	227	4	c	c	PROPN
ejpam-4085	227	5	,	,	PUNCT
ejpam-4085	227	6	(	(	PUNCT
ejpam-4085	227	7	26	26	NUM
ejpam-4085	227	8	)	)	PUNCT
ejpam-4085	227	9	∫	∫	PROPN
ejpam-4085	228	1	∞	∞	PROPN
ejpam-4085	228	2	0	0	NUM
ejpam-4085	229	1	∫	∫	PROPN
ejpam-4085	229	2	∞	∞	NOUN
ejpam-4085	229	3	0	0	NUM
ejpam-4085	229	4	y2	y2	NOUN
ejpam-4085	229	5	logk(ixy	logk(ixy	NOUN
ejpam-4085	229	6	)	)	PUNCT
ejpam-4085	229	7	(	(	PUNCT
ejpam-4085	229	8	x4	x4	PROPN
ejpam-4085	229	9	+	+	PROPN
ejpam-4085	229	10	1)2	1)2	NUM
ejpam-4085	229	11	(	(	PUNCT
ejpam-4085	229	12	y4	y4	PROPN
ejpam-4085	229	13	+	+	PROPN
ejpam-4085	229	14	1)2	1)2	NUM
ejpam-4085	229	15	dxdy	dxdy	NOUN
ejpam-4085	229	16	=	=	SYM
ejpam-4085	229	17	1	1	NUM
ejpam-4085	229	18	128	128	NUM
ejpam-4085	229	19	(	(	PUNCT
ejpam-4085	229	20	iπ)k	iπ)k	PROPN
ejpam-4085	229	21	(	(	PUNCT
ejpam-4085	229	22	−8iπ	−8iπ	PROPN
ejpam-4085	229	23	(	(	PUNCT
ejpam-4085	229	24	2k	2k	NUM
ejpam-4085	229	25	−	−	NOUN
ejpam-4085	229	26	1	1	NUM
ejpam-4085	229	27	)	)	PUNCT
ejpam-4085	229	28	kζ(1−	kζ(1−	PROPN
ejpam-4085	229	29	k	k	NOUN
ejpam-4085	229	30	)	)	PUNCT
ejpam-4085	229	31	+	+	CCONJ
ejpam-4085	229	32	(	(	PUNCT
ejpam-4085	229	33	2k	2k	NUM
ejpam-4085	229	34	−	−	PROPN
ejpam-4085	229	35	2	2	NUM
ejpam-4085	229	36	)	)	PUNCT
ejpam-4085	229	37	(	(	PUNCT
ejpam-4085	229	38	k	k	X
ejpam-4085	229	39	−	−	PROPN
ejpam-4085	229	40	1)kζ(2−	1)kζ(2−	PROPN
ejpam-4085	229	41	k)−	k)−	PROPN
ejpam-4085	229	42	6π2	6π2	NUM
ejpam-4085	229	43	(	(	PUNCT
ejpam-4085	229	44	2k+1	2k+1	NOUN
ejpam-4085	229	45	−	−	NOUN
ejpam-4085	229	46	1	1	NUM
ejpam-4085	229	47	)	)	PUNCT
ejpam-4085	229	48	ζ(−k	ζ(−k	NOUN
ejpam-4085	229	49	)	)	PUNCT
ejpam-4085	229	50	)	)	PUNCT
ejpam-4085	229	51	proof	proof	NOUN
ejpam-4085	229	52	.	.	PUNCT
ejpam-4085	230	1	use	use	NOUN
ejpam-4085	230	2	(	(	PUNCT
ejpam-4085	230	3	12	12	NUM
ejpam-4085	230	4	)	)	PUNCT
ejpam-4085	230	5	and	and	CCONJ
ejpam-4085	230	6	set	set	VERB
ejpam-4085	230	7	m	m	PROPN
ejpam-4085	230	8	=	=	SYM
ejpam-4085	230	9	1	1	NUM
ejpam-4085	230	10	,	,	PUNCT
ejpam-4085	230	11	q	q	NOUN
ejpam-4085	230	12	=	=	NOUN
ejpam-4085	230	13	4	4	NUM
ejpam-4085	230	14	,	,	PUNCT
ejpam-4085	230	15	a	a	PRON
ejpam-4085	230	16	=	=	X
ejpam-4085	230	17	i	i	PRON
ejpam-4085	230	18	and	and	CCONJ
ejpam-4085	230	19	simplify	simplify	VERB
ejpam-4085	230	20	using	use	VERB
ejpam-4085	230	21	entry	entry	NOUN
ejpam-4085	230	22	(	(	PUNCT
ejpam-4085	230	23	4	4	NUM
ejpam-4085	230	24	)	)	PUNCT
ejpam-4085	230	25	in	in	ADP
ejpam-4085	230	26	table	table	NOUN
ejpam-4085	230	27	below	below	ADV
ejpam-4085	230	28	(	(	PUNCT
ejpam-4085	230	29	64:12:7	64:12:7	NUM
ejpam-4085	230	30	)	)	PUNCT
ejpam-4085	230	31	in	in	ADP
ejpam-4085	230	32	[	[	X
ejpam-4085	230	33	2	2	NUM
ejpam-4085	230	34	]	]	PUNCT
ejpam-4085	230	35	.	.	PUNCT
ejpam-4085	231	1	r.	r.	PROPN
ejpam-4085	231	2	reynolds	reynolds	PROPN
ejpam-4085	231	3	,	,	PUNCT
ejpam-4085	231	4	a.	a.	PROPN
ejpam-4085	231	5	stauffer	stauffer	PROPN
ejpam-4085	231	6	/	/	SYM
ejpam-4085	231	7	eur	eur	PROPN
ejpam-4085	231	8	.	.	PUNCT
ejpam-4085	232	1	j.	j.	PROPN
ejpam-4085	232	2	pure	pure	PROPN
ejpam-4085	232	3	appl	appl	PROPN
ejpam-4085	232	4	.	.	PROPN
ejpam-4085	232	5	math	math	PROPN
ejpam-4085	232	6	,	,	PUNCT
ejpam-4085	232	7	14	14	NUM
ejpam-4085	232	8	(	(	PUNCT
ejpam-4085	232	9	4	4	NUM
ejpam-4085	232	10	)	)	PUNCT
ejpam-4085	232	11	(	(	PUNCT
ejpam-4085	232	12	2021	2021	NUM
ejpam-4085	232	13	)	)	PUNCT
ejpam-4085	232	14	,	,	PUNCT
ejpam-4085	232	15	1337	1337	NUM
ejpam-4085	232	16	-	-	SYM
ejpam-4085	232	17	1349	1349	NUM
ejpam-4085	232	18	1347	1347	NUM
ejpam-4085	232	19	proposition	proposition	NOUN
ejpam-4085	232	20	8	8	NUM
ejpam-4085	232	21	.	.	PUNCT
ejpam-4085	233	1	(	(	PUNCT
ejpam-4085	233	2	27	27	NUM
ejpam-4085	233	3	)	)	PUNCT
ejpam-4085	233	4	∫	∫	PROPN
ejpam-4085	234	1	∞	∞	PROPN
ejpam-4085	234	2	0	0	NUM
ejpam-4085	235	1	∫	∫	PROPN
ejpam-4085	235	2	∞	∞	NOUN
ejpam-4085	235	3	0	0	NUM
ejpam-4085	236	1	y2	y2	INTJ
ejpam-4085	236	2	(	(	PUNCT
ejpam-4085	236	3	x4	x4	PROPN
ejpam-4085	236	4	+	+	PROPN
ejpam-4085	236	5	1)2	1)2	NUM
ejpam-4085	236	6	(	(	PUNCT
ejpam-4085	236	7	y4	y4	PROPN
ejpam-4085	236	8	+	+	CCONJ
ejpam-4085	236	9	1)2	1)2	NUM
ejpam-4085	236	10	(	(	PUNCT
ejpam-4085	236	11	4	4	NUM
ejpam-4085	236	12	log2(xy	log2(xy	ADV
ejpam-4085	236	13	)	)	PUNCT
ejpam-4085	237	1	+	+	CCONJ
ejpam-4085	237	2	π2	π2	ADJ
ejpam-4085	237	3	)	)	PUNCT
ejpam-4085	237	4	dxdy	dxdy	NOUN
ejpam-4085	237	5	=	=	SYM
ejpam-4085	237	6	3	3	NUM
ejpam-4085	237	7	128	128	NUM
ejpam-4085	237	8	(	(	PUNCT
ejpam-4085	237	9	2ζ	2ζ	NUM
ejpam-4085	237	10	′(−2	′(−2	PROPN
ejpam-4085	237	11	)	)	PUNCT
ejpam-4085	237	12	+	+	NUM
ejpam-4085	237	13	log(2	log(2	NOUN
ejpam-4085	237	14	)	)	PUNCT
ejpam-4085	237	15	)	)	PUNCT
ejpam-4085	238	1	and	and	CCONJ
ejpam-4085	238	2	(	(	PUNCT
ejpam-4085	238	3	28	28	NUM
ejpam-4085	238	4	)	)	PUNCT
ejpam-4085	238	5	∫	∫	PROPN
ejpam-4085	239	1	∞	∞	PROPN
ejpam-4085	239	2	0	0	NUM
ejpam-4085	240	1	∫	∫	PROPN
ejpam-4085	240	2	∞	∞	NOUN
ejpam-4085	240	3	0	0	NUM
ejpam-4085	240	4	y2	y2	NOUN
ejpam-4085	240	5	log(xy	log(xy	NOUN
ejpam-4085	240	6	)	)	PUNCT
ejpam-4085	240	7	(	(	PUNCT
ejpam-4085	240	8	x4	x4	PROPN
ejpam-4085	241	1	+	+	PROPN
ejpam-4085	241	2	1)2	1)2	NUM
ejpam-4085	241	3	(	(	PUNCT
ejpam-4085	241	4	y4	y4	PROPN
ejpam-4085	241	5	+	+	CCONJ
ejpam-4085	241	6	1)2	1)2	NUM
ejpam-4085	241	7	(	(	PUNCT
ejpam-4085	241	8	4	4	NUM
ejpam-4085	241	9	log2(xy	log2(xy	ADV
ejpam-4085	241	10	)	)	PUNCT
ejpam-4085	242	1	+	+	CCONJ
ejpam-4085	242	2	π2	π2	ADJ
ejpam-4085	242	3	)	)	PUNCT
ejpam-4085	242	4	dxdy	dxdy	NOUN
ejpam-4085	242	5	=	=	PUNCT
ejpam-4085	243	1	−	−	PROPN
ejpam-4085	243	2	π2	π2	ADJ
ejpam-4085	243	3	768	768	NUM
ejpam-4085	243	4	proof	proof	NOUN
ejpam-4085	243	5	.	.	PUNCT
ejpam-4085	244	1	use	use	VERB
ejpam-4085	244	2	equation	equation	NOUN
ejpam-4085	244	3	(	(	PUNCT
ejpam-4085	244	4	26	26	NUM
ejpam-4085	244	5	)	)	PUNCT
ejpam-4085	244	6	and	and	CCONJ
ejpam-4085	244	7	apply	apply	VERB
ejpam-4085	244	8	l’hopitals	l’hopital	NOUN
ejpam-4085	244	9	’	'	PUNCT
ejpam-4085	244	10	rule	rule	NOUN
ejpam-4085	244	11	as	as	SCONJ
ejpam-4085	244	12	k	k	PROPN
ejpam-4085	244	13	→	→	SYM
ejpam-4085	244	14	−1	−1	NOUN
ejpam-4085	244	15	rationalize	rationalize	VERB
ejpam-4085	244	16	the	the	DET
ejpam-4085	244	17	denominator	denominator	NOUN
ejpam-4085	244	18	and	and	CCONJ
ejpam-4085	244	19	equate	equate	VERB
ejpam-4085	244	20	real	real	ADJ
ejpam-4085	244	21	and	and	CCONJ
ejpam-4085	244	22	imaginary	imaginary	ADJ
ejpam-4085	244	23	parts	part	NOUN
ejpam-4085	244	24	to	to	PART
ejpam-4085	244	25	get	get	AUX
ejpam-4085	244	26	stated	state	VERB
ejpam-4085	244	27	result	result	NOUN
ejpam-4085	244	28	.	.	PUNCT
ejpam-4085	245	1	r.	r.	PROPN
ejpam-4085	245	2	reynolds	reynolds	PROPN
ejpam-4085	245	3	,	,	PUNCT
ejpam-4085	245	4	a.	a.	PROPN
ejpam-4085	245	5	stauffer	stauffer	PROPN
ejpam-4085	245	6	/	/	SYM
ejpam-4085	245	7	eur	eur	PROPN
ejpam-4085	245	8	.	.	PUNCT
ejpam-4085	246	1	j.	j.	PROPN
ejpam-4085	246	2	pure	pure	PROPN
ejpam-4085	246	3	appl	appl	PROPN
ejpam-4085	246	4	.	.	PROPN
ejpam-4085	246	5	math	math	PROPN
ejpam-4085	246	6	,	,	PUNCT
ejpam-4085	246	7	14	14	NUM
ejpam-4085	246	8	(	(	PUNCT
ejpam-4085	246	9	4	4	NUM
ejpam-4085	246	10	)	)	PUNCT
ejpam-4085	246	11	(	(	PUNCT
ejpam-4085	246	12	2021	2021	NUM
ejpam-4085	246	13	)	)	PUNCT
ejpam-4085	246	14	,	,	PUNCT
ejpam-4085	246	15	1337	1337	NUM
ejpam-4085	246	16	-	-	SYM
ejpam-4085	246	17	1349	1349	NUM
ejpam-4085	246	18	1348	1348	NUM
ejpam-4085	246	19	11	11	NUM
ejpam-4085	246	20	.	.	PUNCT
ejpam-4085	247	1	summary	summary	NOUN
ejpam-4085	247	2	table	table	NOUN
ejpam-4085	247	3	of	of	ADP
ejpam-4085	247	4	results	result	NOUN
ejpam-4085	247	5	f(x	f(x	PROPN
ejpam-4085	247	6	,	,	PUNCT
ejpam-4085	247	7	y	y	NOUN
ejpam-4085	247	8	)	)	PUNCT
ejpam-4085	247	9	∫∞	∫∞	NOUN
ejpam-4085	247	10	0	0	NUM
ejpam-4085	247	11	∫∞	∫∞	NOUN
ejpam-4085	247	12	0	0	NUM
ejpam-4085	248	1	f(x	f(x	PROPN
ejpam-4085	248	2	,	,	PUNCT
ejpam-4085	248	3	y)dxdy	y)dxdy	NOUN
ejpam-4085	248	4	4	4	NUM
ejpam-4085	248	5	√	√	NUM
ejpam-4085	248	6	x	x	SYM
ejpam-4085	248	7	(	(	PUNCT
ejpam-4085	248	8	√	√	NUM
ejpam-4085	248	9	x	x	SYM
ejpam-4085	248	10	√	√	NUM
ejpam-4085	248	11	y−1	y−1	PROPN
ejpam-4085	248	12	)	)	PUNCT
ejpam-4085	248	13	(	(	PUNCT
ejpam-4085	248	14	x+1)2	x+1)2	PROPN
ejpam-4085	248	15	4	4	NUM
ejpam-4085	248	16	√	√	PROPN
ejpam-4085	248	17	y(y+1)2	y(y+1)2	NUM
ejpam-4085	248	18	log(xy	log(xy	NOUN
ejpam-4085	248	19	)	)	PUNCT
ejpam-4085	248	20	g	g	ADP
ejpam-4085	248	21	4	4	NUM
ejpam-4085	248	22	√	√	NUM
ejpam-4085	248	23	x	x	SYM
ejpam-4085	248	24	4	4	X
ejpam-4085	248	25	√	√	NUM
ejpam-4085	248	26	y−1	y−1	PROPN
ejpam-4085	248	27	x3/4(x+1)2	x3/4(x+1)2	NUM
ejpam-4085	248	28	4	4	NUM
ejpam-4085	248	29	√	√	NUM
ejpam-4085	248	30	y(y+1)2	y(y+1)2	NUM
ejpam-4085	248	31	log(xy	log(xy	NOUN
ejpam-4085	248	32	)	)	PUNCT
ejpam-4085	248	33	g−	g−	PROPN
ejpam-4085	248	34	7ζ(3	7ζ(3	NUM
ejpam-4085	248	35	)	)	PUNCT
ejpam-4085	248	36	8π	8π	NOUN
ejpam-4085	248	37	y2(x2y2−1	y2(x2y2−1	NOUN
ejpam-4085	248	38	)	)	PUNCT
ejpam-4085	248	39	(	(	PUNCT
ejpam-4085	248	40	x4	x4	PROPN
ejpam-4085	248	41	+	+	NOUN
ejpam-4085	248	42	1)2(y4	1)2(y4	NUM
ejpam-4085	248	43	+	+	ADJ
ejpam-4085	248	44	1)2(log2(xy)+π2	1)2(log2(xy)+π2	NOUN
ejpam-4085	248	45	)	)	PUNCT
ejpam-4085	248	46	1	1	NUM
ejpam-4085	248	47	2π2	2π2	NUM
ejpam-4085	248	48	−	−	NUM
ejpam-4085	248	49	1	1	NUM
ejpam-4085	248	50	16	16	NUM
ejpam-4085	248	51	y2(1−x2y2	y2(1−x2y2	NOUN
ejpam-4085	248	52	)	)	PUNCT
ejpam-4085	248	53	log(xy	log(xy	NOUN
ejpam-4085	248	54	)	)	PUNCT
ejpam-4085	248	55	(	(	PUNCT
ejpam-4085	248	56	x4	x4	PROPN
ejpam-4085	248	57	+	+	NOUN
ejpam-4085	248	58	1)2(y4	1)2(y4	NUM
ejpam-4085	248	59	+	+	ADJ
ejpam-4085	248	60	1)2(log2(xy)+π2	1)2(log2(xy)+π2	NOUN
ejpam-4085	248	61	)	)	PUNCT
ejpam-4085	248	62	1	1	NUM
ejpam-4085	248	63	4(g−	4(g−	NUM
ejpam-4085	248	64	1	1	NUM
ejpam-4085	248	65	)	)	PUNCT
ejpam-4085	248	66	y	y	PROPN
ejpam-4085	248	67	q	q	PROPN
ejpam-4085	248	68	2−1(xpyp−xmym	2−1(xpyp−xmym	PROPN
ejpam-4085	248	69	)	)	PUNCT
ejpam-4085	249	1	x(xq+1)2(yq+1)2	x(xq+1)2(yq+1)2	PUNCT
ejpam-4085	249	2	π2	π2	X
ejpam-4085	249	3	(	(	PUNCT
ejpam-4085	249	4	(	(	PUNCT
ejpam-4085	249	5	2m−q)(q−m	2m−q)(q−m	NUM
ejpam-4085	249	6	)	)	PUNCT
ejpam-4085	249	7	csc	csc	PROPN
ejpam-4085	249	8	(	(	PUNCT
ejpam-4085	249	9	2πm	2πm	NOUN
ejpam-4085	249	10	q	q	X
ejpam-4085	249	11	)	)	PUNCT
ejpam-4085	250	1	+	+	ADJ
ejpam-4085	250	2	(	(	PUNCT
ejpam-4085	250	3	q−2p)(q−p	q−2p)(q−p	NOUN
ejpam-4085	250	4	)	)	PUNCT
ejpam-4085	250	5	csc	csc	PROPN
ejpam-4085	250	6	(	(	PUNCT
ejpam-4085	250	7	2πp	2πp	PROPN
ejpam-4085	250	8	q	q	NOUN
ejpam-4085	250	9	)	)	PUNCT
ejpam-4085	250	10	)	)	PUNCT
ejpam-4085	251	1	q4	q4	PROPN
ejpam-4085	251	2	√	√	PROPN
ejpam-4085	251	3	y	y	PROPN
ejpam-4085	251	4	log(log(xy	log(log(xy	PROPN
ejpam-4085	251	5	)	)	PUNCT
ejpam-4085	251	6	)	)	PUNCT
ejpam-4085	252	1	√	√	ADP
ejpam-4085	252	2	x(x2	x(x2	NOUN
ejpam-4085	253	1	+	+	NOUN
ejpam-4085	253	2	1)2(y2	1)2(y2	NUM
ejpam-4085	253	3	+	+	ADJ
ejpam-4085	253	4	1)2	1)2	NUM
ejpam-4085	253	5	1	1	NUM
ejpam-4085	253	6	64	64	NUM
ejpam-4085	253	7	(	(	PUNCT
ejpam-4085	253	8	16g+	16g+	NUM
ejpam-4085	253	9	π2	π2	NOUN
ejpam-4085	253	10	(	(	PUNCT
ejpam-4085	253	11	8i+	8i+	NUM
ejpam-4085	253	12	3iπ	3iπ	NOUN
ejpam-4085	253	13	+	+	CCONJ
ejpam-4085	253	14	2	2	NUM
ejpam-4085	253	15	log	log	NOUN
ejpam-4085	253	16	(	(	PUNCT
ejpam-4085	253	17	64π3γ(−	64π3γ(−	PROPN
ejpam-4085	253	18	1	1	NUM
ejpam-4085	253	19	4	4	NUM
ejpam-4085	253	20	)	)	PUNCT
ejpam-4085	253	21	6	6	NUM
ejpam-4085	253	22	729γ(−	729γ(−	NUM
ejpam-4085	253	23	3	3	NUM
ejpam-4085	253	24	4	4	NUM
ejpam-4085	253	25	)	)	PUNCT
ejpam-4085	253	26	6	6	NUM
ejpam-4085	253	27	)	)	PUNCT
ejpam-4085	253	28	)	)	PUNCT
ejpam-4085	253	29	)	)	PUNCT
ejpam-4085	254	1	√	√	PROPN
ejpam-4085	254	2	y	y	NUM
ejpam-4085	254	3	log(xy	log(xy	PROPN
ejpam-4085	254	4	)	)	PUNCT
ejpam-4085	254	5	log(log(xy	log(log(xy	NOUN
ejpam-4085	254	6	)	)	PUNCT
ejpam-4085	254	7	)	)	PUNCT
ejpam-4085	255	1	√	√	ADP
ejpam-4085	255	2	x(x2	x(x2	NOUN
ejpam-4085	256	1	+	+	NOUN
ejpam-4085	257	1	1)2(y2	1)2(y2	NUM
ejpam-4085	257	2	+	+	ADJ
ejpam-4085	257	3	1)2	1)2	NUM
ejpam-4085	257	4	1	1	NUM
ejpam-4085	257	5	16π	16π	SYM
ejpam-4085	257	6	2	2	NUM
ejpam-4085	257	7	(	(	PUNCT
ejpam-4085	257	8	−6ig+	−6ig+	NOUN
ejpam-4085	257	9	(	(	PUNCT
ejpam-4085	257	10	−4−	−4−	PROPN
ejpam-4085	257	11	i)−	i)−	PROPN
ejpam-4085	257	12	2iπ	2iπ	NOUN
ejpam-4085	258	1	+	+	CCONJ
ejpam-4085	258	2	log	log	NOUN
ejpam-4085	258	3	(	(	PUNCT
ejpam-4085	258	4	6561γ(−	6561γ(−	NUM
ejpam-4085	258	5	3	3	NUM
ejpam-4085	258	6	4	4	NUM
ejpam-4085	258	7	)	)	PUNCT
ejpam-4085	258	8	8	8	NUM
ejpam-4085	258	9	256π4γ(−	256π4γ(−	NUM
ejpam-4085	258	10	1	1	NUM
ejpam-4085	258	11	4	4	NUM
ejpam-4085	258	12	)	)	PUNCT
ejpam-4085	258	13	8	8	NUM
ejpam-4085	258	14	)	)	PUNCT
ejpam-4085	258	15	)	)	PUNCT
ejpam-4085	259	1	√	√	PROPN
ejpam-4085	259	2	y	y	NUM
ejpam-4085	259	3	√	√	PROPN
ejpam-4085	259	4	x(x2	x(x2	PROPN
ejpam-4085	260	1	+	+	PROPN
ejpam-4085	260	2	1)2(y2	1)2(y2	NUM
ejpam-4085	260	3	+	+	ADJ
ejpam-4085	260	4	1)2(log2(xy)+π2	1)2(log2(xy)+π2	NOUN
ejpam-4085	261	1	)	)	PUNCT
ejpam-4085	261	2	3	3	NUM
ejpam-4085	261	3	32	32	NUM
ejpam-4085	261	4	(	(	PUNCT
ejpam-4085	261	5	2ζ	2ζ	PROPN
ejpam-4085	261	6	′(−2	′(−2	PROPN
ejpam-4085	261	7	)	)	PUNCT
ejpam-4085	261	8	+	+	NUM
ejpam-4085	261	9	log(2	log(2	NOUN
ejpam-4085	261	10	)	)	PUNCT
ejpam-4085	261	11	)	)	PUNCT
ejpam-4085	262	1	√	√	PROPN
ejpam-4085	262	2	y	y	NUM
ejpam-4085	262	3	log(xy	log(xy	PROPN
ejpam-4085	262	4	)	)	PUNCT
ejpam-4085	262	5	√	√	NUM
ejpam-4085	262	6	x(x2	x(x2	PROPN
ejpam-4085	263	1	+	+	PROPN
ejpam-4085	263	2	1)2(y2	1)2(y2	NUM
ejpam-4085	263	3	+	+	ADJ
ejpam-4085	263	4	1)2(log2(xy)+π2	1)2(log2(xy)+π2	NOUN
ejpam-4085	263	5	)	)	PUNCT
ejpam-4085	263	6	−π2	−π2	NOUN
ejpam-4085	263	7	96	96	NUM
ejpam-4085	263	8	y2	y2	PROPN
ejpam-4085	263	9	(	(	PUNCT
ejpam-4085	263	10	x4	x4	PROPN
ejpam-4085	263	11	+	+	NOUN
ejpam-4085	263	12	1)2(y4	1)2(y4	NUM
ejpam-4085	263	13	+	+	ADJ
ejpam-4085	263	14	1)2(4	1)2(4	ADJ
ejpam-4085	263	15	log2(xy)+π2	log2(xy)+π2	NOUN
ejpam-4085	263	16	)	)	PUNCT
ejpam-4085	263	17	3	3	NUM
ejpam-4085	263	18	128	128	NUM
ejpam-4085	263	19	(	(	PUNCT
ejpam-4085	263	20	2ζ	2ζ	NUM
ejpam-4085	263	21	′(−2	′(−2	PROPN
ejpam-4085	263	22	)	)	PUNCT
ejpam-4085	263	23	+	+	NUM
ejpam-4085	263	24	log(2	log(2	NOUN
ejpam-4085	263	25	)	)	PUNCT
ejpam-4085	263	26	)	)	PUNCT
ejpam-4085	264	1	y2	y2	NOUN
ejpam-4085	264	2	log(xy	log(xy	NOUN
ejpam-4085	264	3	)	)	PUNCT
ejpam-4085	264	4	(	(	PUNCT
ejpam-4085	264	5	x4	x4	PROPN
ejpam-4085	264	6	+	+	NOUN
ejpam-4085	264	7	1)2(y4	1)2(y4	NUM
ejpam-4085	264	8	+	+	ADJ
ejpam-4085	264	9	1)2(4	1)2(4	ADJ
ejpam-4085	264	10	log2(xy)+π2	log2(xy)+π2	NOUN
ejpam-4085	264	11	)	)	PUNCT
ejpam-4085	264	12	−	−	PROPN
ejpam-4085	265	1	π2	π2	ADJ
ejpam-4085	265	2	768	768	NUM
ejpam-4085	265	3	12	12	NUM
ejpam-4085	265	4	.	.	PUNCT
ejpam-4085	266	1	discussion	discussion	NOUN
ejpam-4085	266	2	in	in	ADP
ejpam-4085	266	3	this	this	DET
ejpam-4085	266	4	work	work	NOUN
ejpam-4085	266	5	the	the	DET
ejpam-4085	266	6	authors	author	NOUN
ejpam-4085	266	7	derived	derive	VERB
ejpam-4085	266	8	a	a	DET
ejpam-4085	266	9	double	double	ADJ
ejpam-4085	266	10	integral	integral	ADJ
ejpam-4085	266	11	formula	formula	NOUN
ejpam-4085	266	12	in	in	ADP
ejpam-4085	266	13	terms	term	NOUN
ejpam-4085	266	14	of	of	ADP
ejpam-4085	266	15	the	the	DET
ejpam-4085	266	16	lerch	lerch	PROPN
ejpam-4085	266	17	function	function	PROPN
ejpam-4085	266	18	.	.	PUNCT
ejpam-4085	267	1	this	this	DET
ejpam-4085	267	2	integral	integral	ADJ
ejpam-4085	267	3	formula	formula	NOUN
ejpam-4085	267	4	was	be	AUX
ejpam-4085	267	5	then	then	ADV
ejpam-4085	267	6	used	use	VERB
ejpam-4085	267	7	to	to	PART
ejpam-4085	267	8	derive	derive	VERB
ejpam-4085	267	9	special	special	ADJ
ejpam-4085	267	10	cases	case	NOUN
ejpam-4085	267	11	in	in	ADP
ejpam-4085	267	12	terms	term	NOUN
ejpam-4085	267	13	of	of	ADP
ejpam-4085	267	14	fundamental	fundamental	ADJ
ejpam-4085	267	15	constants	constant	NOUN
ejpam-4085	267	16	and	and	CCONJ
ejpam-4085	267	17	special	special	ADJ
ejpam-4085	267	18	functions	function	NOUN
ejpam-4085	267	19	.	.	PUNCT
ejpam-4085	268	1	a	a	DET
ejpam-4085	268	2	table	table	NOUN
ejpam-4085	268	3	of	of	ADP
ejpam-4085	268	4	integrals	integral	NOUN
ejpam-4085	268	5	featuring	feature	VERB
ejpam-4085	268	6	some	some	PRON
ejpam-4085	268	7	of	of	ADP
ejpam-4085	268	8	the	the	DET
ejpam-4085	268	9	integral	integral	ADJ
ejpam-4085	268	10	results	result	NOUN
ejpam-4085	268	11	was	be	AUX
ejpam-4085	268	12	presented	present	VERB
ejpam-4085	268	13	for	for	ADP
ejpam-4085	268	14	the	the	DET
ejpam-4085	268	15	benefit	benefit	NOUN
ejpam-4085	268	16	of	of	ADP
ejpam-4085	268	17	interested	interested	ADJ
ejpam-4085	268	18	readers	reader	NOUN
ejpam-4085	268	19	.	.	PUNCT
ejpam-4085	269	1	we	we	PRON
ejpam-4085	269	2	used	use	VERB
ejpam-4085	269	3	wolfram	wolfram	PROPN
ejpam-4085	269	4	mathematica	mathematica	PROPN
ejpam-4085	269	5	to	to	ADP
ejpam-4085	269	6	references	reference	NOUN
ejpam-4085	269	7	1349	1349	NUM
ejpam-4085	269	8	numerically	numerically	ADV
ejpam-4085	269	9	verify	verify	VERB
ejpam-4085	269	10	the	the	DET
ejpam-4085	269	11	formulas	formula	NOUN
ejpam-4085	269	12	for	for	ADP
ejpam-4085	269	13	various	various	ADJ
ejpam-4085	269	14	ranges	range	NOUN
ejpam-4085	269	15	of	of	ADP
ejpam-4085	269	16	the	the	DET
ejpam-4085	269	17	parameters	parameter	NOUN
ejpam-4085	269	18	for	for	ADP
ejpam-4085	269	19	real	real	ADJ
ejpam-4085	269	20	and	and	CCONJ
ejpam-4085	269	21	imaginary	imaginary	ADJ
ejpam-4085	269	22	values	value	NOUN
ejpam-4085	269	23	.	.	PUNCT
ejpam-4085	270	1	we	we	PRON
ejpam-4085	270	2	will	will	AUX
ejpam-4085	270	3	use	use	VERB
ejpam-4085	270	4	our	our	PRON
ejpam-4085	270	5	contour	contour	NOUN
ejpam-4085	270	6	integral	integral	ADJ
ejpam-4085	270	7	method	method	NOUN
ejpam-4085	270	8	to	to	PART
ejpam-4085	270	9	derive	derive	VERB
ejpam-4085	270	10	other	other	ADJ
ejpam-4085	270	11	double	double	ADJ
ejpam-4085	270	12	integrals	integral	NOUN
ejpam-4085	270	13	and	and	CCONJ
ejpam-4085	270	14	produce	produce	VERB
ejpam-4085	270	15	more	more	ADJ
ejpam-4085	270	16	tables	table	NOUN
ejpam-4085	270	17	of	of	ADP
ejpam-4085	270	18	integrals	integral	NOUN
ejpam-4085	270	19	in	in	ADP
ejpam-4085	270	20	our	our	PRON
ejpam-4085	270	21	future	future	ADJ
ejpam-4085	270	22	work	work	NOUN
ejpam-4085	270	23	.	.	PUNCT
ejpam-4085	271	1	references	reference	NOUN
ejpam-4085	271	2	[	[	X
ejpam-4085	271	3	1	1	NUM
ejpam-4085	271	4	]	]	X
ejpam-4085	271	5	i.	i.	PROPN
ejpam-4085	271	6	s.	s.	PROPN
ejpam-4085	271	7	gradshteyn	gradshteyn	PROPN
ejpam-4085	271	8	and	and	CCONJ
ejpam-4085	271	9	i.	i.	PROPN
ejpam-4085	271	10	m.	m.	PROPN
ejpam-4085	271	11	ryzhik	ryzhik	PROPN
ejpam-4085	271	12	.	.	PUNCT
ejpam-4085	272	1	table	table	NOUN
ejpam-4085	272	2	of	of	ADP
ejpam-4085	272	3	integrals	integral	NOUN
ejpam-4085	272	4	,	,	PUNCT
ejpam-4085	272	5	series	series	NOUN
ejpam-4085	272	6	,	,	PUNCT
ejpam-4085	272	7	and	and	CCONJ
ejpam-4085	272	8	products	product	NOUN
ejpam-4085	272	9	.	.	PUNCT
ejpam-4085	273	1	academic	academic	ADJ
ejpam-4085	273	2	press	press	NOUN
ejpam-4085	273	3	,	,	PUNCT
ejpam-4085	273	4	05	05	NUM
ejpam-4085	273	5	2014	2014	NUM
ejpam-4085	273	6	.	.	PUNCT
ejpam-4085	274	1	[	[	X
ejpam-4085	274	2	2	2	X
ejpam-4085	274	3	]	]	PUNCT
ejpam-4085	274	4	keith	keith	PROPN
ejpam-4085	274	5	b.	b.	PROPN
ejpam-4085	274	6	oldham	oldham	PROPN
ejpam-4085	274	7	,	,	PUNCT
ejpam-4085	274	8	jan	jan	PROPN
ejpam-4085	274	9	myland	myland	PROPN
ejpam-4085	274	10	,	,	PUNCT
ejpam-4085	274	11	and	and	CCONJ
ejpam-4085	274	12	jerome	jerome	PROPN
ejpam-4085	274	13	spanier	spanier	NOUN
ejpam-4085	274	14	.	.	PUNCT
ejpam-4085	275	1	an	an	DET
ejpam-4085	275	2	atlas	atlas	PROPN
ejpam-4085	275	3	of	of	ADP
ejpam-4085	275	4	functions	function	NOUN
ejpam-4085	275	5	:	:	PUNCT
ejpam-4085	275	6	with	with	ADP
ejpam-4085	275	7	equator	equator	NOUN
ejpam-4085	275	8	,	,	PUNCT
ejpam-4085	275	9	the	the	DET
ejpam-4085	275	10	atlas	atlas	PROPN
ejpam-4085	275	11	function	function	PROPN
ejpam-4085	275	12	calculator	calculator	NOUN
ejpam-4085	275	13	.	.	PUNCT
ejpam-4085	276	1	springer	springer	NOUN
ejpam-4085	276	2	science	science	PROPN
ejpam-4085	276	3	&	&	CCONJ
ejpam-4085	276	4	business	business	NOUN
ejpam-4085	276	5	media	medium	NOUN
ejpam-4085	276	6	,	,	PUNCT
ejpam-4085	276	7	07	07	NUM
ejpam-4085	276	8	2010	2010	NUM
ejpam-4085	276	9	.	.	PUNCT
ejpam-4085	277	1	[	[	X
ejpam-4085	277	2	3	3	X
ejpam-4085	277	3	]	]	X
ejpam-4085	277	4	robert	robert	PROPN
ejpam-4085	277	5	reynolds	reynolds	PROPN
ejpam-4085	277	6	and	and	CCONJ
ejpam-4085	277	7	allan	allan	PROPN
ejpam-4085	277	8	stauffer	stauffer	PROPN
ejpam-4085	277	9	.	.	PUNCT
ejpam-4085	278	1	a	a	DET
ejpam-4085	278	2	method	method	NOUN
ejpam-4085	278	3	for	for	ADP
ejpam-4085	278	4	evaluating	evaluate	VERB
ejpam-4085	278	5	definite	definite	ADJ
ejpam-4085	278	6	integrals	integral	NOUN
ejpam-4085	278	7	in	in	ADP
ejpam-4085	278	8	terms	term	NOUN
ejpam-4085	278	9	of	of	ADP
ejpam-4085	278	10	special	special	ADJ
ejpam-4085	278	11	functions	function	NOUN
ejpam-4085	278	12	with	with	ADP
ejpam-4085	278	13	examples	example	NOUN
ejpam-4085	278	14	.	.	PUNCT
ejpam-4085	279	1	international	international	ADJ
ejpam-4085	279	2	mathematical	mathematical	PROPN
ejpam-4085	279	3	forum	forum	PROPN
ejpam-4085	279	4	,	,	PUNCT
ejpam-4085	279	5	15:235	15:235	NUM
ejpam-4085	279	6	–	–	PUNCT
ejpam-4085	279	7	244	244	NUM
ejpam-4085	279	8	,	,	PUNCT
ejpam-4085	279	9	2020	2020	NUM
ejpam-4085	279	10	.	.	PUNCT