id	sid	tid	token	lemma	pos
ejpam-4237	1	1	european	european	PROPN
ejpam-4237	1	2	journal	journal	PROPN
ejpam-4237	1	3	of	of	ADP
ejpam-4237	1	4	pure	pure	ADJ
ejpam-4237	1	5	and	and	CCONJ
ejpam-4237	1	6	applied	apply	VERB
ejpam-4237	1	7	mathematics	mathematic	NOUN
ejpam-4237	1	8	vol	vol	NOUN
ejpam-4237	1	9	.	.	PROPN
ejpam-4237	2	1	15	15	NUM
ejpam-4237	2	2	,	,	PUNCT
ejpam-4237	2	3	no	no	INTJ
ejpam-4237	2	4	.	.	NOUN
ejpam-4237	2	5	3	3	NUM
ejpam-4237	2	6	,	,	PUNCT
ejpam-4237	2	7	2022	2022	NUM
ejpam-4237	2	8	,	,	PUNCT
ejpam-4237	2	9	1113	1113	NUM
ejpam-4237	2	10	-	-	SYM
ejpam-4237	2	11	1119	1119	NUM
ejpam-4237	2	12	issn	issn	PROPN
ejpam-4237	2	13	1307	1307	NUM
ejpam-4237	2	14	-	-	SYM
ejpam-4237	2	15	5543	5543	NUM
ejpam-4237	2	16	–	–	PUNCT
ejpam-4237	3	1	ejpam.com	ejpam.com	X
ejpam-4237	3	2	published	publish	VERB
ejpam-4237	3	3	by	by	ADP
ejpam-4237	3	4	new	new	PROPN
ejpam-4237	3	5	york	york	PROPN
ejpam-4237	3	6	business	business	PROPN
ejpam-4237	3	7	global	global	PROPN
ejpam-4237	3	8	a	a	DET
ejpam-4237	3	9	quadruple	quadruple	NOUN
ejpam-4237	3	10	integral	integral	ADJ
ejpam-4237	3	11	involving	involve	VERB
ejpam-4237	3	12	the	the	DET
ejpam-4237	3	13	legendre	legendre	PROPN
ejpam-4237	3	14	function	function	NOUN
ejpam-4237	3	15	pn(x	pn(x	ADP
ejpam-4237	3	16	)	)	PUNCT
ejpam-4237	3	17	of	of	ADP
ejpam-4237	3	18	the	the	DET
ejpam-4237	3	19	first	first	ADJ
ejpam-4237	3	20	kind	kind	NOUN
ejpam-4237	3	21	:	:	PUNCT
ejpam-4237	3	22	derivation	derivation	NOUN
ejpam-4237	3	23	and	and	CCONJ
ejpam-4237	3	24	evaluation	evaluation	NOUN
ejpam-4237	3	25	robert	robert	PROPN
ejpam-4237	3	26	reynolds1,∗	reynolds1,∗	PROPN
ejpam-4237	3	27	,	,	PUNCT
ejpam-4237	3	28	allan	allan	PROPN
ejpam-4237	3	29	stauffer1	stauffer1	PROPN
ejpam-4237	3	30	1	1	NUM
ejpam-4237	3	31	department	department	NOUN
ejpam-4237	3	32	of	of	ADP
ejpam-4237	3	33	mathematics	mathematic	NOUN
ejpam-4237	3	34	and	and	CCONJ
ejpam-4237	3	35	statistics	statistic	NOUN
ejpam-4237	3	36	,	,	PUNCT
ejpam-4237	3	37	faculty	faculty	NOUN
ejpam-4237	3	38	of	of	ADP
ejpam-4237	3	39	science	science	PROPN
ejpam-4237	3	40	,	,	PUNCT
ejpam-4237	3	41	york	york	PROPN
ejpam-4237	3	42	university	university	PROPN
ejpam-4237	3	43	,	,	PUNCT
ejpam-4237	3	44	toronto	toronto	PROPN
ejpam-4237	3	45	,	,	PUNCT
ejpam-4237	3	46	ontario	ontario	PROPN
ejpam-4237	3	47	,	,	PUNCT
ejpam-4237	3	48	canada	canada	PROPN
ejpam-4237	3	49	,	,	PUNCT
ejpam-4237	3	50	m3j1p3	m3j1p3	PROPN
ejpam-4237	3	51	abstract	abstract	NOUN
ejpam-4237	3	52	.	.	PUNCT
ejpam-4237	4	1	a	a	DET
ejpam-4237	4	2	closed	closed	ADJ
ejpam-4237	4	3	form	form	NOUN
ejpam-4237	4	4	expression	expression	NOUN
ejpam-4237	4	5	of	of	ADP
ejpam-4237	4	6	a	a	DET
ejpam-4237	4	7	quadruple	quadruple	NOUN
ejpam-4237	4	8	integral	integral	ADJ
ejpam-4237	4	9	involving	involve	VERB
ejpam-4237	4	10	the	the	DET
ejpam-4237	4	11	legerndre	legerndre	NOUN
ejpam-4237	4	12	polynomial	polynomial	ADJ
ejpam-4237	4	13	pn(x	pn(x	X
ejpam-4237	4	14	)	)	PUNCT
ejpam-4237	4	15	is	be	AUX
ejpam-4237	4	16	derived	derive	VERB
ejpam-4237	4	17	.	.	PUNCT
ejpam-4237	5	1	special	special	ADJ
ejpam-4237	5	2	cases	case	NOUN
ejpam-4237	5	3	are	be	AUX
ejpam-4237	5	4	expressed	express	VERB
ejpam-4237	5	5	in	in	ADP
ejpam-4237	5	6	terms	term	NOUN
ejpam-4237	5	7	of	of	ADP
ejpam-4237	5	8	special	special	ADJ
ejpam-4237	5	9	functions	function	NOUN
ejpam-4237	5	10	and	and	CCONJ
ejpam-4237	5	11	fundamental	fundamental	ADJ
ejpam-4237	5	12	constants	constant	NOUN
ejpam-4237	5	13	.	.	PUNCT
ejpam-4237	6	1	all	all	DET
ejpam-4237	6	2	the	the	DET
ejpam-4237	6	3	results	result	NOUN
ejpam-4237	6	4	in	in	ADP
ejpam-4237	6	5	this	this	DET
ejpam-4237	6	6	work	work	NOUN
ejpam-4237	6	7	are	be	AUX
ejpam-4237	6	8	new	new	ADJ
ejpam-4237	6	9	.	.	PUNCT
ejpam-4237	7	1	2020	2020	NUM
ejpam-4237	7	2	mathematics	mathematic	NOUN
ejpam-4237	7	3	subject	subject	NOUN
ejpam-4237	7	4	classifications	classification	NOUN
ejpam-4237	7	5	:	:	PUNCT
ejpam-4237	7	6	30e20	30e20	NUM
ejpam-4237	7	7	,	,	PUNCT
ejpam-4237	7	8	33	33	NUM
ejpam-4237	7	9	-	-	SYM
ejpam-4237	7	10	01	01	NUM
ejpam-4237	7	11	,	,	PUNCT
ejpam-4237	7	12	33	33	NUM
ejpam-4237	7	13	-	-	SYM
ejpam-4237	7	14	03	03	NUM
ejpam-4237	7	15	,	,	PUNCT
ejpam-4237	7	16	33	33	NUM
ejpam-4237	7	17	-	-	PUNCT
ejpam-4237	7	18	04	04	NUM
ejpam-4237	7	19	,	,	PUNCT
ejpam-4237	7	20	33	33	NUM
ejpam-4237	7	21	-	-	PUNCT
ejpam-4237	7	22	33b	33b	NUM
ejpam-4237	7	23	key	key	ADJ
ejpam-4237	7	24	words	word	NOUN
ejpam-4237	7	25	and	and	CCONJ
ejpam-4237	7	26	phrases	phrase	NOUN
ejpam-4237	7	27	:	:	PUNCT
ejpam-4237	7	28	legendre	legendre	PROPN
ejpam-4237	7	29	polynomial	polynomial	PROPN
ejpam-4237	7	30	,	,	PUNCT
ejpam-4237	7	31	quadruple	quadruple	PROPN
ejpam-4237	7	32	integral	integral	ADJ
ejpam-4237	7	33	,	,	PUNCT
ejpam-4237	7	34	hurwitz	hurwitz	PROPN
ejpam-4237	7	35	-	-	PUNCT
ejpam-4237	7	36	lerch	lerch	PROPN
ejpam-4237	7	37	zeta	zeta	PROPN
ejpam-4237	7	38	function	function	PROPN
ejpam-4237	7	39	,	,	PUNCT
ejpam-4237	7	40	cauchy	cauchy	ADJ
ejpam-4237	7	41	integral	integral	ADJ
ejpam-4237	7	42	formula	formula	NOUN
ejpam-4237	7	43	1	1	NUM
ejpam-4237	7	44	.	.	PUNCT
ejpam-4237	7	45	significance	significance	NOUN
ejpam-4237	7	46	statement	statement	NOUN
ejpam-4237	7	47	the	the	DET
ejpam-4237	7	48	legendre	legendre	PROPN
ejpam-4237	7	49	functions	function	NOUN
ejpam-4237	7	50	are	be	AUX
ejpam-4237	7	51	the	the	DET
ejpam-4237	7	52	most	most	ADV
ejpam-4237	7	53	well	well	ADV
ejpam-4237	7	54	known	know	VERB
ejpam-4237	7	55	particular	particular	ADJ
ejpam-4237	7	56	cases	case	NOUN
ejpam-4237	7	57	of	of	ADP
ejpam-4237	7	58	the	the	DET
ejpam-4237	7	59	hypergeometric	hypergeometric	ADJ
ejpam-4237	7	60	function	function	NOUN
ejpam-4237	7	61	.	.	PUNCT
ejpam-4237	8	1	they	they	PRON
ejpam-4237	8	2	have	have	AUX
ejpam-4237	8	3	been	be	AUX
ejpam-4237	8	4	discovered	discover	VERB
ejpam-4237	8	5	by	by	ADP
ejpam-4237	8	6	laplace	laplace	NOUN
ejpam-4237	8	7	and	and	CCONJ
ejpam-4237	8	8	legendre	legendre	PROPN
ejpam-4237	8	9	as	as	ADV
ejpam-4237	8	10	early	early	ADV
ejpam-4237	8	11	as	as	ADP
ejpam-4237	8	12	in	in	ADP
ejpam-4237	8	13	the	the	DET
ejpam-4237	8	14	18th	18th	ADJ
ejpam-4237	8	15	century	century	NOUN
ejpam-4237	8	16	.	.	PUNCT
ejpam-4237	9	1	later	later	ADV
ejpam-4237	9	2	on	on	ADP
ejpam-4237	9	3	their	their	PRON
ejpam-4237	9	4	importance	importance	NOUN
ejpam-4237	9	5	has	have	AUX
ejpam-4237	9	6	grown	grow	VERB
ejpam-4237	9	7	substantially	substantially	ADV
ejpam-4237	9	8	due	due	ADJ
ejpam-4237	9	9	to	to	ADP
ejpam-4237	9	10	their	their	PRON
ejpam-4237	9	11	connections	connection	NOUN
ejpam-4237	9	12	with	with	ADP
ejpam-4237	9	13	many	many	ADJ
ejpam-4237	9	14	problems	problem	NOUN
ejpam-4237	9	15	of	of	ADP
ejpam-4237	9	16	mathematical	mathematical	ADJ
ejpam-4237	9	17	physics	physics	NOUN
ejpam-4237	9	18	[	[	X
ejpam-4237	9	19	3	3	NUM
ejpam-4237	9	20	]	]	PUNCT
ejpam-4237	9	21	.	.	PUNCT
ejpam-4237	10	1	in	in	ADP
ejpam-4237	10	2	this	this	DET
ejpam-4237	10	3	present	present	ADJ
ejpam-4237	10	4	work	work	NOUN
ejpam-4237	10	5	we	we	PRON
ejpam-4237	10	6	investigate	investigate	VERB
ejpam-4237	10	7	the	the	DET
ejpam-4237	10	8	quadruple	quadruple	NOUN
ejpam-4237	10	9	integral	integral	ADJ
ejpam-4237	10	10	involving	involve	VERB
ejpam-4237	10	11	the	the	DET
ejpam-4237	10	12	legendre	legendre	PROPN
ejpam-4237	10	13	polynomial	polynomial	ADJ
ejpam-4237	10	14	pn(x	pn(x	PUNCT
ejpam-4237	10	15	)	)	PUNCT
ejpam-4237	10	16	and	and	CCONJ
ejpam-4237	10	17	the	the	DET
ejpam-4237	10	18	invariance	invariance	NOUN
ejpam-4237	10	19	of	of	ADP
ejpam-4237	10	20	the	the	DET
ejpam-4237	10	21	parameter	parameter	NOUN
ejpam-4237	10	22	n	n	CCONJ
ejpam-4237	10	23	with	with	ADP
ejpam-4237	10	24	respect	respect	NOUN
ejpam-4237	10	25	to	to	ADP
ejpam-4237	10	26	the	the	DET
ejpam-4237	10	27	hurwitz	hurwitz	PROPN
ejpam-4237	10	28	-	-	PUNCT
ejpam-4237	10	29	lerch	lerch	PROPN
ejpam-4237	10	30	zeta	zeta	PROPN
ejpam-4237	10	31	function	function	PROPN
ejpam-4237	10	32	.	.	PUNCT
ejpam-4237	11	1	2	2	X
ejpam-4237	11	2	.	.	X
ejpam-4237	11	3	introduction	introduction	NOUN
ejpam-4237	11	4	in	in	ADP
ejpam-4237	11	5	this	this	DET
ejpam-4237	11	6	paper	paper	NOUN
ejpam-4237	11	7	we	we	PRON
ejpam-4237	11	8	derive	derive	VERB
ejpam-4237	11	9	the	the	DET
ejpam-4237	11	10	quadruple	quadruple	ADJ
ejpam-4237	11	11	definite	definite	ADJ
ejpam-4237	11	12	integral	integral	ADJ
ejpam-4237	11	13	given	give	VERB
ejpam-4237	11	14	by∫	by∫	PROPN
ejpam-4237	11	15	1	1	NUM
ejpam-4237	11	16	0	0	NUM
ejpam-4237	11	17	∫	∫	PROPN
ejpam-4237	11	18	1	1	NUM
ejpam-4237	11	19	0	0	NUM
ejpam-4237	11	20	∫	∫	PROPN
ejpam-4237	11	21	1	1	NUM
ejpam-4237	11	22	0	0	NUM
ejpam-4237	11	23	∫	∫	PROPN
ejpam-4237	11	24	1	1	NUM
ejpam-4237	11	25	0	0	NUM
ejpam-4237	11	26	xm−1pv(x	xm−1pv(x	PROPN
ejpam-4237	11	27	)	)	PUNCT
ejpam-4237	11	28	log	log	VERB
ejpam-4237	11	29	−m	−m	NOUN
ejpam-4237	11	30	(	(	PUNCT
ejpam-4237	11	31	1	1	NUM
ejpam-4237	11	32	t	t	NOUN
ejpam-4237	11	33	)	)	PUNCT
ejpam-4237	11	34	log	log	VERB
ejpam-4237	11	35	1	1	NUM
ejpam-4237	11	36	2	2	NUM
ejpam-4237	11	37	(	(	PUNCT
ejpam-4237	11	38	m−v−1	m−v−1	NOUN
ejpam-4237	11	39	)	)	PUNCT
ejpam-4237	11	40	(	(	PUNCT
ejpam-4237	11	41	1	1	NUM
ejpam-4237	11	42	y	y	NOUN
ejpam-4237	11	43	)	)	PUNCT
ejpam-4237	11	44	log	log	VERB
ejpam-4237	11	45	m+v	m+v	X
ejpam-4237	11	46	2	2	NUM
ejpam-4237	11	47	(	(	PUNCT
ejpam-4237	11	48	1	1	NUM
ejpam-4237	11	49	z	z	NOUN
ejpam-4237	11	50	)	)	PUNCT
ejpam-4237	11	51	logk	logk	ADJ
ejpam-4237	11	52	ax	ax	NOUN
ejpam-4237	11	53	√	√	NUM
ejpam-4237	12	1	log	log	NOUN
ejpam-4237	12	2	(	(	PUNCT
ejpam-4237	12	3	1	1	NUM
ejpam-4237	12	4	y	y	NOUN
ejpam-4237	12	5	)	)	PUNCT
ejpam-4237	12	6	√	√	PROPN
ejpam-4237	13	1	log	log	NOUN
ejpam-4237	13	2	(	(	PUNCT
ejpam-4237	13	3	1	1	NUM
ejpam-4237	13	4	z	z	NOUN
ejpam-4237	13	5	)	)	PUNCT
ejpam-4237	13	6	log	log	NOUN
ejpam-4237	13	7	(	(	PUNCT
ejpam-4237	13	8	1	1	NUM
ejpam-4237	13	9	t	t	NOUN
ejpam-4237	13	10	)	)	PUNCT
ejpam-4237	13	11			NOUN
ejpam-4237	13	12	dxdydzdt	dxdydzdt	NOUN
ejpam-4237	13	13	(	(	PUNCT
ejpam-4237	13	14	1	1	X
ejpam-4237	13	15	)	)	PUNCT
ejpam-4237	13	16	∗corresponding	∗corresponde	VERB
ejpam-4237	13	17	author	author	NOUN
ejpam-4237	13	18	.	.	PUNCT
ejpam-4237	14	1	doi	doi	NOUN
ejpam-4237	14	2	:	:	PUNCT
ejpam-4237	14	3	https://doi.org/10.29020/nybg.ejpam.v15i3.4237	https://doi.org/10.29020/nybg.ejpam.v15i3.4237	ADJ
ejpam-4237	14	4	email	email	NOUN
ejpam-4237	14	5	addresses	address	NOUN
ejpam-4237	14	6	:	:	PUNCT
ejpam-4237	15	1	milver@my.yorku.ca	milver@my.yorku.ca	NOUN
ejpam-4237	15	2	(	(	PUNCT
ejpam-4237	15	3	r.	r.	PROPN
ejpam-4237	15	4	reynolds	reynolds	PROPN
ejpam-4237	15	5	)	)	PUNCT
ejpam-4237	15	6	,	,	PUNCT
ejpam-4237	15	7	stauffer@yorku.ca	stauffer@yorku.ca	NOUN
ejpam-4237	15	8	(	(	PUNCT
ejpam-4237	15	9	a.	a.	NOUN
ejpam-4237	15	10	stauffer	stauffer	PROPN
ejpam-4237	15	11	)	)	PUNCT
ejpam-4237	15	12	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4237	15	13	1113	1113	NUM
ejpam-4237	16	1	©	©	ADP
ejpam-4237	16	2	2022	2022	NUM
ejpam-4237	16	3	ejpam	ejpam	VERB
ejpam-4237	16	4	all	all	DET
ejpam-4237	16	5	rights	right	NOUN
ejpam-4237	16	6	reserved	reserve	VERB
ejpam-4237	16	7	.	.	PUNCT
ejpam-4237	17	1	r.	r.	PROPN
ejpam-4237	17	2	reynolds	reynolds	PROPN
ejpam-4237	17	3	,	,	PUNCT
ejpam-4237	17	4	a.	a.	PROPN
ejpam-4237	17	5	stauffer	stauffer	PROPN
ejpam-4237	17	6	/	/	SYM
ejpam-4237	17	7	eur	eur	PROPN
ejpam-4237	17	8	.	.	PUNCT
ejpam-4237	18	1	j.	j.	PROPN
ejpam-4237	18	2	pure	pure	PROPN
ejpam-4237	18	3	appl	appl	PROPN
ejpam-4237	18	4	.	.	PROPN
ejpam-4237	18	5	math	math	PROPN
ejpam-4237	18	6	,	,	PUNCT
ejpam-4237	18	7	15	15	NUM
ejpam-4237	18	8	(	(	PUNCT
ejpam-4237	18	9	3	3	NUM
ejpam-4237	18	10	)	)	PUNCT
ejpam-4237	18	11	(	(	PUNCT
ejpam-4237	18	12	2022	2022	NUM
ejpam-4237	18	13	)	)	PUNCT
ejpam-4237	18	14	,	,	PUNCT
ejpam-4237	18	15	1113	1113	NUM
ejpam-4237	18	16	-	-	SYM
ejpam-4237	18	17	1119	1119	NUM
ejpam-4237	18	18	1114	1114	NUM
ejpam-4237	18	19	where	where	SCONJ
ejpam-4237	18	20	the	the	DET
ejpam-4237	18	21	parameters	parameter	NOUN
ejpam-4237	18	22	k	k	PROPN
ejpam-4237	18	23	,	,	PUNCT
ejpam-4237	18	24	a	a	PRON
ejpam-4237	18	25	,	,	PUNCT
ejpam-4237	18	26	v	v	NOUN
ejpam-4237	18	27	,	,	PUNCT
ejpam-4237	18	28	m	m	VERB
ejpam-4237	18	29	are	be	AUX
ejpam-4237	18	30	general	general	ADJ
ejpam-4237	18	31	complex	complex	ADJ
ejpam-4237	18	32	numbers	number	NOUN
ejpam-4237	18	33	and	and	CCONJ
ejpam-4237	18	34	re(v	re(v	NOUN
ejpam-4237	18	35	)	)	PUNCT
ejpam-4237	18	36	<	<	X
ejpam-4237	18	37	re(m	re(m	PROPN
ejpam-4237	18	38	)	)	PUNCT
ejpam-4237	18	39	<	<	X
ejpam-4237	18	40	1/2	1/2	NUM
ejpam-4237	18	41	.	.	PUNCT
ejpam-4237	19	1	this	this	DET
ejpam-4237	19	2	definite	definite	ADJ
ejpam-4237	19	3	integral	integral	ADJ
ejpam-4237	19	4	will	will	AUX
ejpam-4237	19	5	be	be	AUX
ejpam-4237	19	6	used	use	VERB
ejpam-4237	19	7	to	to	PART
ejpam-4237	19	8	derive	derive	VERB
ejpam-4237	19	9	special	special	ADJ
ejpam-4237	19	10	cases	case	NOUN
ejpam-4237	19	11	in	in	ADP
ejpam-4237	19	12	terms	term	NOUN
ejpam-4237	19	13	of	of	ADP
ejpam-4237	19	14	special	special	ADJ
ejpam-4237	19	15	functions	function	NOUN
ejpam-4237	19	16	and	and	CCONJ
ejpam-4237	19	17	fundamental	fundamental	ADJ
ejpam-4237	19	18	constants	constant	NOUN
ejpam-4237	19	19	.	.	PUNCT
ejpam-4237	20	1	the	the	DET
ejpam-4237	20	2	derivations	derivation	NOUN
ejpam-4237	20	3	follow	follow	VERB
ejpam-4237	20	4	the	the	DET
ejpam-4237	20	5	method	method	NOUN
ejpam-4237	20	6	used	use	VERB
ejpam-4237	20	7	by	by	ADP
ejpam-4237	20	8	us	we	PRON
ejpam-4237	20	9	in	in	ADP
ejpam-4237	20	10	[	[	X
ejpam-4237	20	11	6	6	NUM
ejpam-4237	20	12	]	]	PUNCT
ejpam-4237	20	13	.	.	PUNCT
ejpam-4237	21	1	this	this	DET
ejpam-4237	21	2	method	method	NOUN
ejpam-4237	21	3	involves	involve	VERB
ejpam-4237	21	4	using	use	VERB
ejpam-4237	21	5	a	a	DET
ejpam-4237	21	6	form	form	NOUN
ejpam-4237	21	7	of	of	ADP
ejpam-4237	21	8	the	the	DET
ejpam-4237	21	9	generalized	generalize	VERB
ejpam-4237	21	10	cauchy	cauchy	PROPN
ejpam-4237	21	11	’s	’s	PART
ejpam-4237	21	12	integral	integral	ADJ
ejpam-4237	21	13	formula	formula	NOUN
ejpam-4237	21	14	given	give	VERB
ejpam-4237	21	15	by	by	ADP
ejpam-4237	21	16	yk	yk	PROPN
ejpam-4237	21	17	γ(k	γ(k	PROPN
ejpam-4237	21	18	+	+	CCONJ
ejpam-4237	21	19	1	1	X
ejpam-4237	21	20	)	)	PUNCT
ejpam-4237	21	21	=	=	SYM
ejpam-4237	21	22	1	1	NUM
ejpam-4237	21	23	2πi	2πi	ADJ
ejpam-4237	21	24	∫	∫	PROPN
ejpam-4237	21	25	c	c	PROPN
ejpam-4237	21	26	ewy	ewy	PROPN
ejpam-4237	21	27	wk+1	wk+1	PROPN
ejpam-4237	21	28	dw	dw	PROPN
ejpam-4237	21	29	.	.	PUNCT
ejpam-4237	22	1	(	(	PUNCT
ejpam-4237	22	2	2	2	X
ejpam-4237	22	3	)	)	PUNCT
ejpam-4237	22	4	where	where	SCONJ
ejpam-4237	22	5	c	c	NOUN
ejpam-4237	22	6	is	be	AUX
ejpam-4237	22	7	in	in	ADP
ejpam-4237	22	8	general	general	ADJ
ejpam-4237	22	9	an	an	DET
ejpam-4237	22	10	open	open	ADJ
ejpam-4237	22	11	contour	contour	NOUN
ejpam-4237	22	12	in	in	ADP
ejpam-4237	22	13	the	the	DET
ejpam-4237	22	14	complex	complex	ADJ
ejpam-4237	22	15	plane	plane	NOUN
ejpam-4237	22	16	where	where	SCONJ
ejpam-4237	22	17	the	the	DET
ejpam-4237	22	18	bilinear	bilinear	NOUN
ejpam-4237	22	19	concomitant	concomitant	NOUN
ejpam-4237	22	20	has	have	VERB
ejpam-4237	22	21	the	the	DET
ejpam-4237	22	22	same	same	ADJ
ejpam-4237	22	23	value	value	NOUN
ejpam-4237	22	24	at	at	ADP
ejpam-4237	22	25	the	the	DET
ejpam-4237	22	26	end	end	NOUN
ejpam-4237	22	27	points	point	NOUN
ejpam-4237	22	28	of	of	ADP
ejpam-4237	22	29	the	the	DET
ejpam-4237	22	30	contour	contour	NOUN
ejpam-4237	22	31	.	.	PUNCT
ejpam-4237	23	1	we	we	PRON
ejpam-4237	23	2	then	then	ADV
ejpam-4237	23	3	multiply	multiply	VERB
ejpam-4237	23	4	both	both	DET
ejpam-4237	23	5	sides	side	NOUN
ejpam-4237	23	6	by	by	ADP
ejpam-4237	23	7	a	a	DET
ejpam-4237	23	8	function	function	NOUN
ejpam-4237	23	9	of	of	ADP
ejpam-4237	23	10	x	x	PROPN
ejpam-4237	23	11	,	,	PUNCT
ejpam-4237	23	12	y	y	PROPN
ejpam-4237	23	13	,	,	PUNCT
ejpam-4237	23	14	z	z	PROPN
ejpam-4237	23	15	and	and	CCONJ
ejpam-4237	23	16	t	t	PROPN
ejpam-4237	23	17	,	,	PUNCT
ejpam-4237	23	18	then	then	ADV
ejpam-4237	23	19	take	take	VERB
ejpam-4237	23	20	a	a	DET
ejpam-4237	23	21	definite	definite	ADJ
ejpam-4237	23	22	quadruple	quadruple	NOUN
ejpam-4237	23	23	integral	integral	ADJ
ejpam-4237	23	24	of	of	ADP
ejpam-4237	23	25	both	both	DET
ejpam-4237	23	26	sides	side	NOUN
ejpam-4237	23	27	.	.	PUNCT
ejpam-4237	24	1	this	this	PRON
ejpam-4237	24	2	yields	yield	VERB
ejpam-4237	24	3	a	a	DET
ejpam-4237	24	4	definite	definite	ADJ
ejpam-4237	24	5	integral	integral	ADJ
ejpam-4237	24	6	in	in	ADP
ejpam-4237	24	7	terms	term	NOUN
ejpam-4237	24	8	of	of	ADP
ejpam-4237	24	9	a	a	DET
ejpam-4237	24	10	contour	contour	NOUN
ejpam-4237	24	11	integral	integral	NOUN
ejpam-4237	24	12	.	.	PUNCT
ejpam-4237	25	1	then	then	ADV
ejpam-4237	25	2	we	we	PRON
ejpam-4237	25	3	multiply	multiply	VERB
ejpam-4237	25	4	both	both	DET
ejpam-4237	25	5	sides	side	NOUN
ejpam-4237	25	6	of	of	ADP
ejpam-4237	25	7	equation	equation	NOUN
ejpam-4237	25	8	(	(	PUNCT
ejpam-4237	25	9	2	2	NUM
ejpam-4237	25	10	)	)	PUNCT
ejpam-4237	25	11	by	by	ADP
ejpam-4237	25	12	another	another	DET
ejpam-4237	25	13	function	function	NOUN
ejpam-4237	25	14	of	of	ADP
ejpam-4237	25	15	x	x	PROPN
ejpam-4237	25	16	,	,	PUNCT
ejpam-4237	25	17	y	y	PROPN
ejpam-4237	25	18	,	,	PUNCT
ejpam-4237	25	19	z	z	PROPN
ejpam-4237	25	20	and	and	CCONJ
ejpam-4237	25	21	t	t	PROPN
ejpam-4237	25	22	and	and	CCONJ
ejpam-4237	25	23	take	take	VERB
ejpam-4237	25	24	the	the	DET
ejpam-4237	25	25	infinite	infinite	ADJ
ejpam-4237	25	26	sums	sum	NOUN
ejpam-4237	25	27	of	of	ADP
ejpam-4237	25	28	both	both	DET
ejpam-4237	25	29	sides	side	NOUN
ejpam-4237	25	30	such	such	ADJ
ejpam-4237	25	31	that	that	SCONJ
ejpam-4237	25	32	the	the	DET
ejpam-4237	25	33	contour	contour	NOUN
ejpam-4237	25	34	integral	integral	NOUN
ejpam-4237	25	35	of	of	ADP
ejpam-4237	25	36	both	both	DET
ejpam-4237	25	37	equations	equation	NOUN
ejpam-4237	25	38	are	be	AUX
ejpam-4237	25	39	the	the	DET
ejpam-4237	25	40	same	same	ADJ
ejpam-4237	25	41	.	.	PUNCT
ejpam-4237	26	1	3	3	X
ejpam-4237	26	2	.	.	X
ejpam-4237	26	3	definite	definite	ADJ
ejpam-4237	26	4	integral	integral	ADJ
ejpam-4237	26	5	of	of	ADP
ejpam-4237	26	6	the	the	DET
ejpam-4237	26	7	contour	contour	NOUN
ejpam-4237	26	8	integral	integral	NOUN
ejpam-4237	26	9	we	we	PRON
ejpam-4237	26	10	use	use	VERB
ejpam-4237	26	11	the	the	DET
ejpam-4237	26	12	method	method	NOUN
ejpam-4237	26	13	in	in	ADP
ejpam-4237	26	14	[	[	X
ejpam-4237	26	15	6	6	NUM
ejpam-4237	26	16	]	]	PUNCT
ejpam-4237	26	17	.	.	PUNCT
ejpam-4237	27	1	the	the	DET
ejpam-4237	27	2	variable	variable	NOUN
ejpam-4237	27	3	of	of	ADP
ejpam-4237	27	4	integration	integration	NOUN
ejpam-4237	27	5	in	in	ADP
ejpam-4237	27	6	the	the	DET
ejpam-4237	27	7	contour	contour	NOUN
ejpam-4237	27	8	integral	integral	NOUN
ejpam-4237	27	9	is	be	AUX
ejpam-4237	27	10	u	u	NOUN
ejpam-4237	27	11	=	=	PROPN
ejpam-4237	27	12	w	w	PROPN
ejpam-4237	27	13	+	+	PROPN
ejpam-4237	27	14	m.	m.	NOUN
ejpam-4237	27	15	the	the	DET
ejpam-4237	27	16	cut	cut	NOUN
ejpam-4237	27	17	and	and	CCONJ
ejpam-4237	27	18	contour	contour	NOUN
ejpam-4237	27	19	are	be	AUX
ejpam-4237	27	20	in	in	ADP
ejpam-4237	27	21	the	the	DET
ejpam-4237	27	22	first	first	ADJ
ejpam-4237	27	23	quadrant	quadrant	NOUN
ejpam-4237	27	24	of	of	ADP
ejpam-4237	27	25	the	the	DET
ejpam-4237	27	26	complex	complex	ADJ
ejpam-4237	27	27	u	u	NOUN
ejpam-4237	27	28	-	-	NOUN
ejpam-4237	27	29	plane	plane	NOUN
ejpam-4237	27	30	.	.	PUNCT
ejpam-4237	28	1	the	the	DET
ejpam-4237	28	2	cut	cut	NOUN
ejpam-4237	28	3	approaches	approach	VERB
ejpam-4237	28	4	the	the	DET
ejpam-4237	28	5	origin	origin	NOUN
ejpam-4237	28	6	from	from	ADP
ejpam-4237	28	7	the	the	DET
ejpam-4237	28	8	interior	interior	NOUN
ejpam-4237	28	9	of	of	ADP
ejpam-4237	28	10	the	the	DET
ejpam-4237	28	11	first	first	ADJ
ejpam-4237	28	12	quadrant	quadrant	NOUN
ejpam-4237	28	13	and	and	CCONJ
ejpam-4237	28	14	the	the	DET
ejpam-4237	28	15	contour	contour	NOUN
ejpam-4237	28	16	goes	go	VERB
ejpam-4237	28	17	round	round	ADP
ejpam-4237	28	18	the	the	DET
ejpam-4237	28	19	origin	origin	NOUN
ejpam-4237	28	20	with	with	ADP
ejpam-4237	28	21	zero	zero	NUM
ejpam-4237	28	22	radius	radius	NOUN
ejpam-4237	28	23	and	and	CCONJ
ejpam-4237	28	24	is	be	AUX
ejpam-4237	28	25	on	on	ADP
ejpam-4237	28	26	opposite	opposite	ADJ
ejpam-4237	28	27	sides	side	NOUN
ejpam-4237	28	28	of	of	ADP
ejpam-4237	28	29	the	the	DET
ejpam-4237	28	30	cut	cut	NOUN
ejpam-4237	28	31	.	.	PUNCT
ejpam-4237	29	1	using	use	VERB
ejpam-4237	29	2	a	a	DET
ejpam-4237	29	3	generalization	generalization	NOUN
ejpam-4237	29	4	of	of	ADP
ejpam-4237	29	5	cauchy	cauchy	PROPN
ejpam-4237	29	6	’s	’s	PART
ejpam-4237	29	7	integral	integral	ADJ
ejpam-4237	29	8	formula	formula	NOUN
ejpam-4237	29	9	we	we	PRON
ejpam-4237	29	10	form	form	VERB
ejpam-4237	29	11	the	the	DET
ejpam-4237	29	12	triple	triple	ADJ
ejpam-4237	29	13	integral	integral	ADJ
ejpam-4237	29	14	by	by	ADP
ejpam-4237	29	15	replacing	replace	VERB
ejpam-4237	29	16	y	y	PRON
ejpam-4237	29	17	by	by	ADP
ejpam-4237	29	18	log	log	PROPN
ejpam-4237	29	19	ax	ax	PROPN
ejpam-4237	29	20	√	√	PROPN
ejpam-4237	29	21	log	log	NOUN
ejpam-4237	29	22	(	(	PUNCT
ejpam-4237	29	23	1	1	NUM
ejpam-4237	29	24	y	y	NOUN
ejpam-4237	29	25	)	)	PUNCT
ejpam-4237	29	26	√	√	PROPN
ejpam-4237	30	1	log	log	NOUN
ejpam-4237	30	2	(	(	PUNCT
ejpam-4237	30	3	1	1	NUM
ejpam-4237	30	4	z	z	NOUN
ejpam-4237	30	5	)	)	PUNCT
ejpam-4237	30	6	log	log	NOUN
ejpam-4237	30	7	(	(	PUNCT
ejpam-4237	30	8	1	1	NUM
ejpam-4237	30	9	t	t	NOUN
ejpam-4237	30	10	)	)	PUNCT
ejpam-4237	30	11			PROPN
ejpam-4237	30	12	and	and	CCONJ
ejpam-4237	30	13	multiplying	multiply	VERB
ejpam-4237	30	14	by	by	ADP
ejpam-4237	30	15	xm−1pv(x	xm−1pv(x	PROPN
ejpam-4237	30	16	)	)	PUNCT
ejpam-4237	30	17	log	log	VERB
ejpam-4237	30	18	−m	−m	NOUN
ejpam-4237	30	19	(	(	PUNCT
ejpam-4237	30	20	1	1	NUM
ejpam-4237	30	21	t	t	NOUN
ejpam-4237	30	22	)	)	PUNCT
ejpam-4237	30	23	log	log	VERB
ejpam-4237	30	24	1	1	NUM
ejpam-4237	30	25	2	2	NUM
ejpam-4237	30	26	(	(	PUNCT
ejpam-4237	30	27	m−v−1	m−v−1	NOUN
ejpam-4237	30	28	)	)	PUNCT
ejpam-4237	30	29	(	(	PUNCT
ejpam-4237	30	30	1	1	NUM
ejpam-4237	30	31	y	y	NOUN
ejpam-4237	30	32	)	)	PUNCT
ejpam-4237	30	33	log	log	VERB
ejpam-4237	30	34	m+v	m+v	X
ejpam-4237	30	35	2	2	NUM
ejpam-4237	30	36	(	(	PUNCT
ejpam-4237	30	37	1	1	NUM
ejpam-4237	30	38	z	z	NOUN
ejpam-4237	30	39	)	)	PUNCT
ejpam-4237	30	40	then	then	ADV
ejpam-4237	30	41	taking	take	VERB
ejpam-4237	30	42	the	the	DET
ejpam-4237	30	43	definite	definite	ADJ
ejpam-4237	30	44	integral	integral	ADJ
ejpam-4237	30	45	with	with	ADP
ejpam-4237	30	46	respect	respect	NOUN
ejpam-4237	30	47	to	to	ADP
ejpam-4237	30	48	x	x	SYM
ejpam-4237	30	49	∈	∈	PROPN
ejpam-4237	31	1	[	[	X
ejpam-4237	31	2	0	0	NUM
ejpam-4237	31	3	,	,	PUNCT
ejpam-4237	31	4	1	1	NUM
ejpam-4237	31	5	]	]	PUNCT
ejpam-4237	31	6	,	,	PUNCT
ejpam-4237	31	7	y	y	PROPN
ejpam-4237	31	8	∈	∈	PROPN
ejpam-4237	31	9	0	0	NUM
ejpam-4237	31	10	,	,	PUNCT
ejpam-4237	31	11	1	1	NUM
ejpam-4237	31	12	]	]	PUNCT
ejpam-4237	31	13	,	,	PUNCT
ejpam-4237	31	14	z	z	PROPN
ejpam-4237	31	15	∈	∈	PROPN
ejpam-4237	31	16	0	0	NUM
ejpam-4237	31	17	,	,	PUNCT
ejpam-4237	31	18	1	1	NUM
ejpam-4237	31	19	]	]	PUNCT
ejpam-4237	31	20	and	and	CCONJ
ejpam-4237	31	21	t	t	PROPN
ejpam-4237	31	22	∈	∈	PROPN
ejpam-4237	31	23	0	0	NUM
ejpam-4237	31	24	,	,	PUNCT
ejpam-4237	31	25	1	1	NUM
ejpam-4237	31	26	]	]	PUNCT
ejpam-4237	31	27	to	to	PART
ejpam-4237	31	28	obtain	obtain	VERB
ejpam-4237	31	29	1	1	NUM
ejpam-4237	31	30	γ(k	γ(k	NOUN
ejpam-4237	31	31	+	+	CCONJ
ejpam-4237	31	32	1	1	X
ejpam-4237	31	33	)	)	PUNCT
ejpam-4237	31	34	∫	∫	NOUN
ejpam-4237	31	35	1	1	NUM
ejpam-4237	31	36	0	0	NUM
ejpam-4237	31	37	∫	∫	PROPN
ejpam-4237	31	38	1	1	NUM
ejpam-4237	31	39	0	0	NUM
ejpam-4237	31	40	∫	∫	PROPN
ejpam-4237	31	41	1	1	NUM
ejpam-4237	31	42	0	0	NUM
ejpam-4237	31	43	∫	∫	PROPN
ejpam-4237	32	1	1	1	NUM
ejpam-4237	32	2	0	0	NUM
ejpam-4237	32	3	xm−1pv(x	xm−1pv(x	PROPN
ejpam-4237	32	4	)	)	PUNCT
ejpam-4237	32	5	log	log	VERB
ejpam-4237	32	6	−m	−m	NOUN
ejpam-4237	32	7	(	(	PUNCT
ejpam-4237	32	8	1	1	NUM
ejpam-4237	32	9	t	t	NOUN
ejpam-4237	32	10	)	)	PUNCT
ejpam-4237	32	11	log	log	VERB
ejpam-4237	32	12	1	1	NUM
ejpam-4237	32	13	2	2	NUM
ejpam-4237	32	14	(	(	PUNCT
ejpam-4237	32	15	m−v−1	m−v−1	NOUN
ejpam-4237	32	16	)	)	PUNCT
ejpam-4237	32	17	(	(	PUNCT
ejpam-4237	32	18	1	1	NUM
ejpam-4237	32	19	y	y	NOUN
ejpam-4237	32	20	)	)	PUNCT
ejpam-4237	32	21	log	log	VERB
ejpam-4237	32	22	m+v	m+v	X
ejpam-4237	32	23	2	2	NUM
ejpam-4237	32	24	(	(	PUNCT
ejpam-4237	32	25	1	1	NUM
ejpam-4237	32	26	z	z	NOUN
ejpam-4237	32	27	)	)	PUNCT
ejpam-4237	32	28	logk	logk	ADJ
ejpam-4237	32	29	ax	ax	NOUN
ejpam-4237	32	30	√	√	NUM
ejpam-4237	33	1	log	log	NOUN
ejpam-4237	33	2	(	(	PUNCT
ejpam-4237	33	3	1	1	NUM
ejpam-4237	33	4	y	y	NOUN
ejpam-4237	33	5	)	)	PUNCT
ejpam-4237	33	6	√	√	PROPN
ejpam-4237	34	1	log	log	NOUN
ejpam-4237	34	2	(	(	PUNCT
ejpam-4237	34	3	1	1	NUM
ejpam-4237	34	4	z	z	NOUN
ejpam-4237	34	5	)	)	PUNCT
ejpam-4237	34	6	log	log	NOUN
ejpam-4237	34	7	(	(	PUNCT
ejpam-4237	34	8	1	1	NUM
ejpam-4237	34	9	t	t	NOUN
ejpam-4237	34	10	)	)	PUNCT
ejpam-4237	34	11			NOUN
ejpam-4237	34	12	dxdydzdt	dxdydzdt	NOUN
ejpam-4237	34	13	=	=	SYM
ejpam-4237	34	14	1	1	NUM
ejpam-4237	34	15	2πi	2πi	NOUN
ejpam-4237	34	16	∫	∫	NOUN
ejpam-4237	34	17	1	1	NUM
ejpam-4237	34	18	0	0	NUM
ejpam-4237	34	19	∫	∫	PROPN
ejpam-4237	34	20	1	1	NUM
ejpam-4237	34	21	0	0	NUM
ejpam-4237	34	22	∫	∫	PROPN
ejpam-4237	34	23	1	1	NUM
ejpam-4237	34	24	0	0	NUM
ejpam-4237	34	25	∫	∫	PROPN
ejpam-4237	34	26	1	1	NUM
ejpam-4237	34	27	0	0	NUM
ejpam-4237	34	28	∫	∫	PROPN
ejpam-4237	34	29	c	c	X
ejpam-4237	34	30	aww−k−1pv(x)x	aww−k−1pv(x)x	PROPN
ejpam-4237	34	31	m+w−1	m+w−1	PROPN
ejpam-4237	34	32	log−m−w	log−m−w	PROPN
ejpam-4237	34	33	(	(	PUNCT
ejpam-4237	34	34	1	1	NUM
ejpam-4237	34	35	t	t	NOUN
ejpam-4237	34	36	)	)	PUNCT
ejpam-4237	34	37	log	log	VERB
ejpam-4237	34	38	1	1	NUM
ejpam-4237	34	39	2	2	NUM
ejpam-4237	34	40	(	(	PUNCT
ejpam-4237	34	41	m−v+w−1	m−v+w−1	PROPN
ejpam-4237	34	42	)	)	PUNCT
ejpam-4237	34	43	(	(	PUNCT
ejpam-4237	34	44	1	1	NUM
ejpam-4237	34	45	y	y	NOUN
ejpam-4237	34	46	)	)	PUNCT
ejpam-4237	34	47	log	log	VERB
ejpam-4237	34	48	1	1	NUM
ejpam-4237	34	49	2	2	NUM
ejpam-4237	34	50	(	(	PUNCT
ejpam-4237	34	51	m+v+w	m+v+w	NOUN
ejpam-4237	34	52	)	)	PUNCT
ejpam-4237	34	53	(	(	PUNCT
ejpam-4237	34	54	1	1	NUM
ejpam-4237	34	55	z	z	NOUN
ejpam-4237	34	56	)	)	PUNCT
ejpam-4237	35	1	dwdxdydzdt	dwdxdydzdt	NOUN
ejpam-4237	35	2	=	=	SYM
ejpam-4237	36	1	1	1	NUM
ejpam-4237	36	2	2πi	2πi	NOUN
ejpam-4237	36	3	∫	∫	PROPN
ejpam-4237	36	4	c	c	NOUN
ejpam-4237	36	5	∫	∫	PROPN
ejpam-4237	36	6	1	1	NUM
ejpam-4237	36	7	0	0	NUM
ejpam-4237	36	8	∫	∫	PROPN
ejpam-4237	36	9	1	1	NUM
ejpam-4237	36	10	0	0	NUM
ejpam-4237	36	11	∫	∫	PROPN
ejpam-4237	36	12	1	1	NUM
ejpam-4237	36	13	0	0	NUM
ejpam-4237	36	14	∫	∫	PROPN
ejpam-4237	36	15	1	1	NUM
ejpam-4237	36	16	0	0	NUM
ejpam-4237	36	17	aww−k−1pv(x)x	aww−k−1pv(x)x	NOUN
ejpam-4237	36	18	m+w−1	m+w−1	X
ejpam-4237	36	19	log−m−w	log−m−w	PROPN
ejpam-4237	36	20	(	(	PUNCT
ejpam-4237	36	21	1	1	NUM
ejpam-4237	36	22	t	t	NOUN
ejpam-4237	36	23	)	)	PUNCT
ejpam-4237	36	24	r.	r.	PROPN
ejpam-4237	36	25	reynolds	reynolds	PROPN
ejpam-4237	36	26	,	,	PUNCT
ejpam-4237	36	27	a.	a.	PROPN
ejpam-4237	36	28	stauffer	stauffer	PROPN
ejpam-4237	36	29	/	/	SYM
ejpam-4237	36	30	eur	eur	PROPN
ejpam-4237	36	31	.	.	PUNCT
ejpam-4237	37	1	j.	j.	PROPN
ejpam-4237	37	2	pure	pure	PROPN
ejpam-4237	37	3	appl	appl	PROPN
ejpam-4237	37	4	.	.	PROPN
ejpam-4237	37	5	math	math	PROPN
ejpam-4237	37	6	,	,	PUNCT
ejpam-4237	37	7	15	15	NUM
ejpam-4237	37	8	(	(	PUNCT
ejpam-4237	37	9	3	3	NUM
ejpam-4237	37	10	)	)	PUNCT
ejpam-4237	37	11	(	(	PUNCT
ejpam-4237	37	12	2022	2022	NUM
ejpam-4237	37	13	)	)	PUNCT
ejpam-4237	37	14	,	,	PUNCT
ejpam-4237	37	15	1113	1113	NUM
ejpam-4237	37	16	-	-	SYM
ejpam-4237	37	17	1119	1119	NUM
ejpam-4237	37	18	1115	1115	NUM
ejpam-4237	37	19	log	log	NOUN
ejpam-4237	37	20	1	1	NUM
ejpam-4237	37	21	2	2	NUM
ejpam-4237	37	22	(	(	PUNCT
ejpam-4237	37	23	m−v+w−1	m−v+w−1	PROPN
ejpam-4237	37	24	)	)	PUNCT
ejpam-4237	37	25	(	(	PUNCT
ejpam-4237	37	26	1	1	NUM
ejpam-4237	37	27	y	y	NOUN
ejpam-4237	37	28	)	)	PUNCT
ejpam-4237	37	29	log	log	VERB
ejpam-4237	37	30	1	1	NUM
ejpam-4237	37	31	2	2	NUM
ejpam-4237	37	32	(	(	PUNCT
ejpam-4237	37	33	m+v+w	m+v+w	NOUN
ejpam-4237	37	34	)	)	PUNCT
ejpam-4237	37	35	(	(	PUNCT
ejpam-4237	37	36	1	1	NUM
ejpam-4237	37	37	z	z	NOUN
ejpam-4237	37	38	)	)	PUNCT
ejpam-4237	37	39	dxdydzdtdw	dxdydzdtdw	NOUN
ejpam-4237	37	40	=	=	NOUN
ejpam-4237	37	41	1	1	NUM
ejpam-4237	37	42	2πi	2πi	NOUN
ejpam-4237	37	43	∫	∫	PROPN
ejpam-4237	38	1	c	c	NOUN
ejpam-4237	38	2	π3/2aww−k−12−m−w	π3/2aww−k−12−m−w	PROPN
ejpam-4237	38	3	csc(π(m+	csc(π(m+	PROPN
ejpam-4237	38	4	w))dw	w))dw	NOUN
ejpam-4237	38	5	(	(	PUNCT
ejpam-4237	38	6	3	3	NUM
ejpam-4237	38	7	)	)	PUNCT
ejpam-4237	38	8	from	from	ADP
ejpam-4237	38	9	equation	equation	NOUN
ejpam-4237	38	10	(	(	PUNCT
ejpam-4237	38	11	1.8.8.1	1.8.8.1	NUM
ejpam-4237	38	12	)	)	PUNCT
ejpam-4237	38	13	in	in	ADP
ejpam-4237	38	14	[	[	X
ejpam-4237	38	15	4	4	NUM
ejpam-4237	38	16	]	]	PUNCT
ejpam-4237	38	17	and	and	CCONJ
ejpam-4237	38	18	equation	equation	NOUN
ejpam-4237	38	19	(	(	PUNCT
ejpam-4237	38	20	4.215.1	4.215.1	NUM
ejpam-4237	38	21	)	)	PUNCT
ejpam-4237	38	22	in	in	ADP
ejpam-4237	38	23	[	[	X
ejpam-4237	38	24	2	2	X
ejpam-4237	38	25	]	]	PUNCT
ejpam-4237	38	26	where	where	SCONJ
ejpam-4237	38	27	re(π(m	re(π(m	NOUN
ejpam-4237	38	28	+	+	PROPN
ejpam-4237	38	29	w	w	NOUN
ejpam-4237	38	30	)	)	PUNCT
ejpam-4237	38	31	)	)	PUNCT
ejpam-4237	38	32	>	>	X
ejpam-4237	38	33	0	0	PUNCT
ejpam-4237	38	34	and	and	CCONJ
ejpam-4237	38	35	using	use	VERB
ejpam-4237	38	36	the	the	DET
ejpam-4237	38	37	reflection	reflection	NOUN
ejpam-4237	38	38	formula	formula	NOUN
ejpam-4237	38	39	(	(	PUNCT
ejpam-4237	38	40	8.334.3	8.334.3	NUM
ejpam-4237	38	41	)	)	PUNCT
ejpam-4237	38	42	in	in	ADP
ejpam-4237	38	43	[	[	X
ejpam-4237	38	44	2	2	NUM
ejpam-4237	38	45	]	]	PUNCT
ejpam-4237	38	46	for	for	ADP
ejpam-4237	38	47	the	the	DET
ejpam-4237	38	48	gamma	gamma	PROPN
ejpam-4237	38	49	function	function	NOUN
ejpam-4237	38	50	.	.	PUNCT
ejpam-4237	39	1	we	we	PRON
ejpam-4237	39	2	are	be	AUX
ejpam-4237	39	3	able	able	ADJ
ejpam-4237	39	4	to	to	PART
ejpam-4237	39	5	switch	switch	VERB
ejpam-4237	39	6	the	the	DET
ejpam-4237	39	7	order	order	NOUN
ejpam-4237	39	8	of	of	ADP
ejpam-4237	39	9	integration	integration	NOUN
ejpam-4237	39	10	over	over	ADP
ejpam-4237	39	11	x	x	PROPN
ejpam-4237	39	12	,	,	PUNCT
ejpam-4237	39	13	y	y	PROPN
ejpam-4237	39	14	,	,	PUNCT
ejpam-4237	39	15	z	z	PROPN
ejpam-4237	39	16	and	and	CCONJ
ejpam-4237	39	17	t	t	PROPN
ejpam-4237	39	18	using	use	VERB
ejpam-4237	39	19	fubini	fubini	NOUN
ejpam-4237	39	20	’s	’s	PART
ejpam-4237	39	21	theorem	theorem	NOUN
ejpam-4237	39	22	since	since	SCONJ
ejpam-4237	39	23	the	the	DET
ejpam-4237	39	24	integrand	integrand	NOUN
ejpam-4237	39	25	is	be	AUX
ejpam-4237	39	26	of	of	ADP
ejpam-4237	39	27	bounded	bounded	ADJ
ejpam-4237	39	28	measure	measure	NOUN
ejpam-4237	39	29	over	over	ADP
ejpam-4237	39	30	the	the	DET
ejpam-4237	39	31	space	space	NOUN
ejpam-4237	39	32	c×	c×	PROPN
ejpam-4237	40	1	[	[	X
ejpam-4237	40	2	0	0	NUM
ejpam-4237	40	3	,	,	PUNCT
ejpam-4237	40	4	1]×	1]×	NUM
ejpam-4237	40	5	[	[	X
ejpam-4237	40	6	0	0	NUM
ejpam-4237	40	7	,	,	PUNCT
ejpam-4237	40	8	1]×	1]×	NUM
ejpam-4237	41	1	[	[	X
ejpam-4237	41	2	0	0	NUM
ejpam-4237	41	3	,	,	PUNCT
ejpam-4237	41	4	1]×	1]×	NUM
ejpam-4237	42	1	[	[	X
ejpam-4237	42	2	0	0	NUM
ejpam-4237	42	3	,	,	PUNCT
ejpam-4237	42	4	1	1	NUM
ejpam-4237	42	5	]	]	PUNCT
ejpam-4237	42	6	.	.	PUNCT
ejpam-4237	43	1	4	4	X
ejpam-4237	43	2	.	.	X
ejpam-4237	43	3	the	the	DET
ejpam-4237	43	4	hurwitz	hurwitz	PROPN
ejpam-4237	43	5	-	-	PUNCT
ejpam-4237	43	6	lerch	lerch	PROPN
ejpam-4237	43	7	zeta	zeta	PROPN
ejpam-4237	43	8	function	function	PROPN
ejpam-4237	43	9	and	and	CCONJ
ejpam-4237	43	10	infinite	infinite	ADJ
ejpam-4237	43	11	sum	sum	NOUN
ejpam-4237	43	12	of	of	ADP
ejpam-4237	43	13	the	the	DET
ejpam-4237	43	14	contour	contour	NOUN
ejpam-4237	43	15	integral	integral	NOUN
ejpam-4237	43	16	in	in	ADP
ejpam-4237	43	17	this	this	DET
ejpam-4237	43	18	section	section	NOUN
ejpam-4237	43	19	we	we	PRON
ejpam-4237	43	20	use	use	VERB
ejpam-4237	43	21	equation	equation	NOUN
ejpam-4237	43	22	(	(	PUNCT
ejpam-4237	43	23	2	2	NUM
ejpam-4237	43	24	)	)	PUNCT
ejpam-4237	43	25	to	to	PART
ejpam-4237	43	26	derive	derive	VERB
ejpam-4237	43	27	the	the	DET
ejpam-4237	43	28	contour	contour	NOUN
ejpam-4237	43	29	integral	integral	ADJ
ejpam-4237	43	30	representations	representation	NOUN
ejpam-4237	43	31	for	for	ADP
ejpam-4237	43	32	the	the	DET
ejpam-4237	43	33	hurwitz	hurwitz	PROPN
ejpam-4237	43	34	-	-	PUNCT
ejpam-4237	43	35	lerch	lerch	PROPN
ejpam-4237	43	36	zeta	zeta	PROPN
ejpam-4237	43	37	function	function	PROPN
ejpam-4237	43	38	.	.	PUNCT
ejpam-4237	44	1	4.1	4.1	NUM
ejpam-4237	44	2	.	.	PUNCT
ejpam-4237	45	1	the	the	DET
ejpam-4237	45	2	hurwitz	hurwitz	PROPN
ejpam-4237	45	3	-	-	PUNCT
ejpam-4237	45	4	lerch	lerch	PROPN
ejpam-4237	45	5	zeta	zeta	PROPN
ejpam-4237	45	6	function	function	VERB
ejpam-4237	45	7	the	the	DET
ejpam-4237	45	8	hurwitz	hurwitz	PROPN
ejpam-4237	45	9	-	-	PUNCT
ejpam-4237	45	10	lerch	lerch	PROPN
ejpam-4237	45	11	zeta	zeta	PROPN
ejpam-4237	45	12	function	function	PROPN
ejpam-4237	45	13	(	(	PUNCT
ejpam-4237	45	14	25.14	25.14	NUM
ejpam-4237	45	15	)	)	PUNCT
ejpam-4237	45	16	in	in	ADP
ejpam-4237	45	17	[	[	X
ejpam-4237	45	18	1	1	X
ejpam-4237	45	19	]	]	PUNCT
ejpam-4237	45	20	has	have	VERB
ejpam-4237	45	21	a	a	DET
ejpam-4237	45	22	series	series	NOUN
ejpam-4237	45	23	representation	representation	NOUN
ejpam-4237	45	24	given	give	VERB
ejpam-4237	45	25	by	by	ADP
ejpam-4237	45	26	φ(z	φ(z	PROPN
ejpam-4237	45	27	,	,	PUNCT
ejpam-4237	45	28	s	s	NOUN
ejpam-4237	45	29	,	,	PUNCT
ejpam-4237	45	30	v	v	NOUN
ejpam-4237	45	31	)	)	PUNCT
ejpam-4237	45	32	=	=	PUNCT
ejpam-4237	46	1	∞∑	∞∑	NUM
ejpam-4237	46	2	n=0	n=0	NUM
ejpam-4237	46	3	(	(	PUNCT
ejpam-4237	46	4	v	v	NOUN
ejpam-4237	46	5	+	+	PRON
ejpam-4237	46	6	n)−szn	n)−szn	NUM
ejpam-4237	46	7	(	(	PUNCT
ejpam-4237	46	8	4	4	NUM
ejpam-4237	46	9	)	)	PUNCT
ejpam-4237	46	10	where	where	SCONJ
ejpam-4237	46	11	|z|	|z|	VERB
ejpam-4237	46	12	<	<	X
ejpam-4237	46	13	1	1	NUM
ejpam-4237	46	14	,	,	PUNCT
ejpam-4237	46	15	v	v	ADP
ejpam-4237	46	16	̸=	̸=	PROPN
ejpam-4237	46	17	0,−1	0,−1	PROPN
ejpam-4237	46	18	,	,	PUNCT
ejpam-4237	46	19	..	..	PUNCT
ejpam-4237	46	20	and	and	CCONJ
ejpam-4237	46	21	is	be	AUX
ejpam-4237	46	22	continued	continue	VERB
ejpam-4237	46	23	analytically	analytically	ADV
ejpam-4237	46	24	by	by	ADP
ejpam-4237	46	25	its	its	PRON
ejpam-4237	46	26	integral	integral	ADJ
ejpam-4237	46	27	representation	representation	NOUN
ejpam-4237	46	28	given	give	VERB
ejpam-4237	46	29	by	by	ADP
ejpam-4237	46	30	φ(z	φ(z	PROPN
ejpam-4237	46	31	,	,	PUNCT
ejpam-4237	46	32	s	s	NOUN
ejpam-4237	46	33	,	,	PUNCT
ejpam-4237	46	34	v	v	NOUN
ejpam-4237	46	35	)	)	PUNCT
ejpam-4237	46	36	=	=	SYM
ejpam-4237	46	37	1	1	NUM
ejpam-4237	46	38	γ(s	γ(	NOUN
ejpam-4237	46	39	)	)	PUNCT
ejpam-4237	46	40	∫	∫	PROPN
ejpam-4237	47	1	∞	∞	PROPN
ejpam-4237	47	2	0	0	NUM
ejpam-4237	48	1	ts−1e−vt	ts−1e−vt	PRON
ejpam-4237	49	1	1−	1−	NUM
ejpam-4237	49	2	ze−t	ze−t	NOUN
ejpam-4237	49	3	dt	dt	NOUN
ejpam-4237	50	1	=	=	SYM
ejpam-4237	50	2	1	1	NUM
ejpam-4237	50	3	γ(s	γ(s	PROPN
ejpam-4237	50	4	)	)	PUNCT
ejpam-4237	50	5	∫	∫	PROPN
ejpam-4237	51	1	∞	∞	NUM
ejpam-4237	51	2	0	0	NUM
ejpam-4237	52	1	ts−1e−(v−1)t	ts−1e−(v−1)t	PROPN
ejpam-4237	52	2	et	et	NOUN
ejpam-4237	52	3	−	−	NOUN
ejpam-4237	52	4	z	z	NOUN
ejpam-4237	52	5	dt	dt	X
ejpam-4237	52	6	(	(	PUNCT
ejpam-4237	52	7	5	5	NUM
ejpam-4237	52	8	)	)	PUNCT
ejpam-4237	52	9	where	where	SCONJ
ejpam-4237	52	10	re(v	re(v	NOUN
ejpam-4237	52	11	)	)	PUNCT
ejpam-4237	52	12	>	>	X
ejpam-4237	52	13	0	0	NUM
ejpam-4237	52	14	,	,	PUNCT
ejpam-4237	52	15	and	and	CCONJ
ejpam-4237	52	16	either	either	ADV
ejpam-4237	52	17	|z|≤	|z|≤	SYM
ejpam-4237	52	18	1	1	NUM
ejpam-4237	52	19	,	,	PUNCT
ejpam-4237	52	20	z	z	NOUN
ejpam-4237	52	21	̸=	̸=	PROPN
ejpam-4237	52	22	1	1	NUM
ejpam-4237	52	23	,	,	PUNCT
ejpam-4237	52	24	re(s	re(s	ADJ
ejpam-4237	52	25	)	)	PUNCT
ejpam-4237	52	26	>	>	X
ejpam-4237	52	27	0	0	NUM
ejpam-4237	52	28	,	,	PUNCT
ejpam-4237	52	29	or	or	CCONJ
ejpam-4237	52	30	z	z	NOUN
ejpam-4237	52	31	=	=	SYM
ejpam-4237	52	32	1	1	NUM
ejpam-4237	52	33	,	,	PUNCT
ejpam-4237	52	34	re(s	re(s	ADJ
ejpam-4237	52	35	)	)	PUNCT
ejpam-4237	52	36	>	>	X
ejpam-4237	53	1	1	1	NUM
ejpam-4237	53	2	.	.	X
ejpam-4237	53	3	4.2	4.2	NUM
ejpam-4237	53	4	.	.	PUNCT
ejpam-4237	53	5	infinite	infinite	ADJ
ejpam-4237	53	6	sum	sum	NOUN
ejpam-4237	53	7	of	of	ADP
ejpam-4237	53	8	the	the	DET
ejpam-4237	53	9	contour	contour	NOUN
ejpam-4237	53	10	integral	integral	ADJ
ejpam-4237	53	11	using	use	VERB
ejpam-4237	53	12	equation	equation	NOUN
ejpam-4237	53	13	(	(	PUNCT
ejpam-4237	53	14	2	2	NUM
ejpam-4237	53	15	)	)	PUNCT
ejpam-4237	53	16	and	and	CCONJ
ejpam-4237	53	17	replacing	replace	VERB
ejpam-4237	53	18	y	y	PRON
ejpam-4237	53	19	by	by	ADP
ejpam-4237	53	20	log(a	log(a	PROPN
ejpam-4237	53	21	)	)	PUNCT
ejpam-4237	54	1	+	+	CCONJ
ejpam-4237	54	2	iπ(2y	iπ(2y	PRON
ejpam-4237	54	3	+	+	NOUN
ejpam-4237	54	4	1	1	X
ejpam-4237	54	5	)	)	PUNCT
ejpam-4237	54	6	−	−	NOUN
ejpam-4237	54	7	log(2	log(2	NOUN
ejpam-4237	54	8	)	)	PUNCT
ejpam-4237	54	9	then	then	ADV
ejpam-4237	54	10	multiplying	multiply	VERB
ejpam-4237	54	11	both	both	DET
ejpam-4237	54	12	sides	side	NOUN
ejpam-4237	54	13	by	by	ADP
ejpam-4237	54	14	−iπ3/221−meiπm(2y+1	−iπ3/221−meiπm(2y+1	NOUN
ejpam-4237	54	15	)	)	PUNCT
ejpam-4237	54	16	taking	take	VERB
ejpam-4237	54	17	the	the	DET
ejpam-4237	54	18	infinite	infinite	ADJ
ejpam-4237	54	19	sum	sum	NOUN
ejpam-4237	54	20	over	over	ADP
ejpam-4237	54	21	y	y	PROPN
ejpam-4237	54	22	∈	∈	PROPN
ejpam-4237	55	1	[	[	X
ejpam-4237	55	2	0,∞	0,∞	NOUN
ejpam-4237	55	3	)	)	PUNCT
ejpam-4237	55	4	and	and	CCONJ
ejpam-4237	55	5	simplifying	simplify	VERB
ejpam-4237	55	6	in	in	ADP
ejpam-4237	55	7	terms	term	NOUN
ejpam-4237	55	8	of	of	ADP
ejpam-4237	55	9	r.	r.	PROPN
ejpam-4237	55	10	reynolds	reynolds	PROPN
ejpam-4237	55	11	,	,	PUNCT
ejpam-4237	55	12	a.	a.	PROPN
ejpam-4237	55	13	stauffer	stauffer	PROPN
ejpam-4237	55	14	/	/	SYM
ejpam-4237	55	15	eur	eur	PROPN
ejpam-4237	55	16	.	.	PUNCT
ejpam-4237	56	1	j.	j.	PROPN
ejpam-4237	56	2	pure	pure	PROPN
ejpam-4237	56	3	appl	appl	PROPN
ejpam-4237	56	4	.	.	PROPN
ejpam-4237	56	5	math	math	PROPN
ejpam-4237	56	6	,	,	PUNCT
ejpam-4237	56	7	15	15	NUM
ejpam-4237	56	8	(	(	PUNCT
ejpam-4237	56	9	3	3	NUM
ejpam-4237	56	10	)	)	PUNCT
ejpam-4237	56	11	(	(	PUNCT
ejpam-4237	56	12	2022	2022	NUM
ejpam-4237	56	13	)	)	PUNCT
ejpam-4237	56	14	,	,	PUNCT
ejpam-4237	56	15	1113	1113	NUM
ejpam-4237	56	16	-	-	SYM
ejpam-4237	56	17	1119	1119	NUM
ejpam-4237	56	18	1116	1116	NUM
ejpam-4237	56	19	the	the	DET
ejpam-4237	56	20	hurwitz	hurwitz	PROPN
ejpam-4237	56	21	-	-	PUNCT
ejpam-4237	56	22	lerch	lerch	PROPN
ejpam-4237	56	23	zeta	zeta	PROPN
ejpam-4237	56	24	function	function	VERB
ejpam-4237	56	25	we	we	PRON
ejpam-4237	56	26	obtain	obtain	VERB
ejpam-4237	56	27	(	(	PUNCT
ejpam-4237	56	28	6	6	NUM
ejpam-4237	56	29	)	)	SYM
ejpam-4237	56	30	1	1	NUM
ejpam-4237	56	31	γ(k	γ(k	NOUN
ejpam-4237	56	32	+	+	CCONJ
ejpam-4237	56	33	1	1	X
ejpam-4237	56	34	)	)	PUNCT
ejpam-4237	56	35	ik−1πk+	ik−1πk+	NOUN
ejpam-4237	56	36	3	3	NUM
ejpam-4237	56	37	2	2	NUM
ejpam-4237	56	38	eiπm2k−m+1φ	eiπm2k−m+1φ	NOUN
ejpam-4237	56	39	(	(	PUNCT
ejpam-4237	56	40	e2imπ,−k	e2imπ,−k	NOUN
ejpam-4237	56	41	,	,	PUNCT
ejpam-4237	56	42	−i	−i	PROPN
ejpam-4237	56	43	log(a	log(a	PROPN
ejpam-4237	56	44	)	)	PUNCT
ejpam-4237	57	1	+	+	CCONJ
ejpam-4237	57	2	i	i	PRON
ejpam-4237	57	3	log(2	log(2	NOUN
ejpam-4237	57	4	)	)	PUNCT
ejpam-4237	58	1	+	+	CCONJ
ejpam-4237	58	2	π	π	PROPN
ejpam-4237	58	3	2π	2π	NOUN
ejpam-4237	58	4	)	)	PUNCT
ejpam-4237	59	1	=	=	PUNCT
ejpam-4237	59	2	−	−	PROPN
ejpam-4237	59	3	1	1	NUM
ejpam-4237	59	4	2πi	2πi	NOUN
ejpam-4237	59	5	∞∑	∞∑	NUM
ejpam-4237	59	6	y=0	y=0	NUM
ejpam-4237	59	7	∫	∫	PROPN
ejpam-4237	59	8	c	c	PROPN
ejpam-4237	60	1	iπ3/2aww−k−12−m−w+1eiπ(2y+1)(m+w)dw	iπ3/2aww−k−12−m−w+1eiπ(2y+1)(m+w)dw	PROPN
ejpam-4237	60	2	=	=	SYM
ejpam-4237	60	3	−	−	PROPN
ejpam-4237	60	4	1	1	NUM
ejpam-4237	60	5	2πi	2πi	NOUN
ejpam-4237	60	6	∫	∫	PROPN
ejpam-4237	60	7	c	c	NOUN
ejpam-4237	61	1	∞∑	∞∑	NUM
ejpam-4237	61	2	y=0	y=0	NOUN
ejpam-4237	61	3	iπ3/2aww−k−12−m−w+1eiπ(2y+1)(m+w)dw	iπ3/2aww−k−12−m−w+1eiπ(2y+1)(m+w)dw	PROPN
ejpam-4237	61	4	=	=	SYM
ejpam-4237	61	5	1	1	NUM
ejpam-4237	61	6	2πi	2πi	NOUN
ejpam-4237	61	7	∫	∫	PROPN
ejpam-4237	61	8	c	c	PROPN
ejpam-4237	61	9	π3/2aww−k−12−m−w	π3/2aww−k−12−m−w	PROPN
ejpam-4237	61	10	csc(π(m+	csc(π(m+	PROPN
ejpam-4237	61	11	w))dw	w))dw	NOUN
ejpam-4237	61	12	from	from	ADP
ejpam-4237	61	13	equation	equation	NOUN
ejpam-4237	61	14	(	(	PUNCT
ejpam-4237	61	15	1.232.3	1.232.3	NUM
ejpam-4237	61	16	)	)	PUNCT
ejpam-4237	61	17	in	in	ADP
ejpam-4237	61	18	[	[	X
ejpam-4237	61	19	2	2	X
ejpam-4237	61	20	]	]	PUNCT
ejpam-4237	61	21	where	where	SCONJ
ejpam-4237	61	22	im(π(m+	im(π(m+	NOUN
ejpam-4237	61	23	w	w	NOUN
ejpam-4237	61	24	)	)	PUNCT
ejpam-4237	61	25	)	)	PUNCT
ejpam-4237	61	26	>	>	X
ejpam-4237	61	27	0	0	PUNCT
ejpam-4237	62	1	in	in	ADP
ejpam-4237	62	2	order	order	NOUN
ejpam-4237	62	3	for	for	SCONJ
ejpam-4237	62	4	the	the	DET
ejpam-4237	62	5	sum	sum	NOUN
ejpam-4237	62	6	to	to	PART
ejpam-4237	62	7	converge	converge	VERB
ejpam-4237	62	8	.	.	PUNCT
ejpam-4237	63	1	5	5	X
ejpam-4237	63	2	.	.	X
ejpam-4237	63	3	definite	definite	ADJ
ejpam-4237	63	4	integral	integral	ADJ
ejpam-4237	63	5	in	in	ADP
ejpam-4237	63	6	terms	term	NOUN
ejpam-4237	63	7	of	of	ADP
ejpam-4237	63	8	the	the	DET
ejpam-4237	63	9	lerch	lerch	PROPN
ejpam-4237	63	10	function	function	PROPN
ejpam-4237	63	11	and	and	CCONJ
ejpam-4237	63	12	invariant	invariant	ADJ
ejpam-4237	63	13	index	index	NOUN
ejpam-4237	63	14	forms	form	NOUN
ejpam-4237	63	15	theorem	theorem	VERB
ejpam-4237	63	16	1	1	NUM
ejpam-4237	63	17	.	.	PUNCT
ejpam-4237	64	1	for	for	ADP
ejpam-4237	64	2	all	all	DET
ejpam-4237	64	3	k	k	PROPN
ejpam-4237	64	4	,	,	PUNCT
ejpam-4237	64	5	a	a	DET
ejpam-4237	64	6	,	,	PUNCT
ejpam-4237	64	7	v	v	NOUN
ejpam-4237	64	8	,	,	PUNCT
ejpam-4237	64	9	m	m	VERB
ejpam-4237	64	10	∈	∈	PROPN
ejpam-4237	64	11	c	c	NOUN
ejpam-4237	64	12	,	,	PUNCT
ejpam-4237	64	13	re(v	re(v	NOUN
ejpam-4237	64	14	)	)	PUNCT
ejpam-4237	64	15	<	<	X
ejpam-4237	64	16	re(m	re(m	X
ejpam-4237	64	17	)	)	PUNCT
ejpam-4237	64	18	≤	≤	NOUN
ejpam-4237	64	19	1/2,∫	1/2,∫	NUM
ejpam-4237	64	20	1	1	NUM
ejpam-4237	64	21	0	0	NUM
ejpam-4237	64	22	∫	∫	PROPN
ejpam-4237	64	23	1	1	NUM
ejpam-4237	64	24	0	0	NUM
ejpam-4237	64	25	∫	∫	PROPN
ejpam-4237	64	26	1	1	NUM
ejpam-4237	64	27	0	0	NUM
ejpam-4237	64	28	∫	∫	PROPN
ejpam-4237	64	29	1	1	NUM
ejpam-4237	64	30	0	0	NUM
ejpam-4237	64	31	xm−1pv(x	xm−1pv(x	PROPN
ejpam-4237	64	32	)	)	PUNCT
ejpam-4237	64	33	log	log	VERB
ejpam-4237	64	34	−m	−m	NOUN
ejpam-4237	64	35	(	(	PUNCT
ejpam-4237	64	36	1	1	NUM
ejpam-4237	64	37	t	t	NOUN
ejpam-4237	64	38	)	)	PUNCT
ejpam-4237	64	39	log	log	VERB
ejpam-4237	64	40	1	1	NUM
ejpam-4237	64	41	2	2	NUM
ejpam-4237	64	42	(	(	PUNCT
ejpam-4237	64	43	m−v−1	m−v−1	NOUN
ejpam-4237	64	44	)	)	PUNCT
ejpam-4237	64	45	(	(	PUNCT
ejpam-4237	64	46	1	1	NUM
ejpam-4237	64	47	y	y	NOUN
ejpam-4237	64	48	)	)	PUNCT
ejpam-4237	64	49	log	log	VERB
ejpam-4237	64	50	m+v	m+v	X
ejpam-4237	64	51	2	2	NUM
ejpam-4237	64	52	(	(	PUNCT
ejpam-4237	64	53	1	1	NUM
ejpam-4237	64	54	z	z	NOUN
ejpam-4237	64	55	)	)	PUNCT
ejpam-4237	64	56	logk	logk	ADJ
ejpam-4237	64	57	ax	ax	NOUN
ejpam-4237	65	1	√	√	NUM
ejpam-4237	66	1	log	log	NOUN
ejpam-4237	66	2	(	(	PUNCT
ejpam-4237	66	3	1	1	NUM
ejpam-4237	66	4	y	y	NOUN
ejpam-4237	66	5	)	)	PUNCT
ejpam-4237	66	6	√	√	PROPN
ejpam-4237	67	1	log	log	NOUN
ejpam-4237	67	2	(	(	PUNCT
ejpam-4237	67	3	1	1	NUM
ejpam-4237	67	4	z	z	NOUN
ejpam-4237	67	5	)	)	PUNCT
ejpam-4237	67	6	log	log	NOUN
ejpam-4237	67	7	(	(	PUNCT
ejpam-4237	67	8	1	1	NUM
ejpam-4237	67	9	t	t	NOUN
ejpam-4237	67	10	)	)	PUNCT
ejpam-4237	67	11			NOUN
ejpam-4237	67	12	dxdydzdt	dxdydzdt	NOUN
ejpam-4237	67	13	=	=	PUNCT
ejpam-4237	67	14	ik−1πk+	ik−1πk+	NOUN
ejpam-4237	67	15	3	3	NUM
ejpam-4237	67	16	2	2	NUM
ejpam-4237	67	17	eiπm2k−m+1φ	eiπm2k−m+1φ	NUM
ejpam-4237	67	18	(	(	PUNCT
ejpam-4237	67	19	e2imπ,−k	e2imπ,−k	NOUN
ejpam-4237	67	20	,	,	PUNCT
ejpam-4237	67	21	−i	−i	PROPN
ejpam-4237	67	22	log(a	log(a	PROPN
ejpam-4237	67	23	)	)	PUNCT
ejpam-4237	68	1	+	+	CCONJ
ejpam-4237	68	2	i	i	PRON
ejpam-4237	68	3	log(2	log(2	NOUN
ejpam-4237	68	4	)	)	PUNCT
ejpam-4237	69	1	+	+	CCONJ
ejpam-4237	69	2	π	π	PROPN
ejpam-4237	69	3	2π	2π	NOUN
ejpam-4237	69	4	)	)	PUNCT
ejpam-4237	69	5	(	(	PUNCT
ejpam-4237	69	6	7	7	X
ejpam-4237	69	7	)	)	PUNCT
ejpam-4237	69	8	proof	proof	NOUN
ejpam-4237	69	9	.	.	PUNCT
ejpam-4237	70	1	the	the	DET
ejpam-4237	70	2	right	right	ADJ
ejpam-4237	70	3	-	-	PUNCT
ejpam-4237	70	4	hand	hand	NOUN
ejpam-4237	70	5	sides	side	NOUN
ejpam-4237	70	6	of	of	ADP
ejpam-4237	70	7	relations	relation	NOUN
ejpam-4237	70	8	(	(	PUNCT
ejpam-4237	70	9	3	3	NUM
ejpam-4237	70	10	)	)	PUNCT
ejpam-4237	70	11	and	and	CCONJ
ejpam-4237	70	12	(	(	PUNCT
ejpam-4237	70	13	6	6	NUM
ejpam-4237	70	14	)	)	PUNCT
ejpam-4237	70	15	are	be	AUX
ejpam-4237	70	16	identical	identical	ADJ
ejpam-4237	70	17	;	;	PUNCT
ejpam-4237	70	18	hence	hence	ADV
ejpam-4237	70	19	,	,	PUNCT
ejpam-4237	70	20	the	the	DET
ejpam-4237	70	21	left	leave	VERB
ejpam-4237	70	22	-	-	PUNCT
ejpam-4237	70	23	hand	hand	NOUN
ejpam-4237	70	24	sides	side	NOUN
ejpam-4237	70	25	of	of	ADP
ejpam-4237	70	26	the	the	DET
ejpam-4237	70	27	same	same	ADJ
ejpam-4237	70	28	are	be	AUX
ejpam-4237	70	29	identical	identical	ADJ
ejpam-4237	70	30	too	too	ADV
ejpam-4237	70	31	.	.	PUNCT
ejpam-4237	71	1	simplifying	simplify	VERB
ejpam-4237	71	2	with	with	ADP
ejpam-4237	71	3	the	the	DET
ejpam-4237	71	4	gamma	gamma	NOUN
ejpam-4237	71	5	function	function	NOUN
ejpam-4237	71	6	yields	yield	VERB
ejpam-4237	71	7	the	the	DET
ejpam-4237	71	8	desired	desire	VERB
ejpam-4237	71	9	conclusion	conclusion	NOUN
ejpam-4237	71	10	.	.	PUNCT
ejpam-4237	72	1	example	example	NOUN
ejpam-4237	73	1	1	1	NUM
ejpam-4237	73	2	.	.	PUNCT
ejpam-4237	74	1	the	the	DET
ejpam-4237	74	2	degenerate	degenerate	ADJ
ejpam-4237	74	3	case.∫	case.∫	NOUN
ejpam-4237	74	4	1	1	NUM
ejpam-4237	74	5	0	0	NUM
ejpam-4237	74	6	∫	∫	PROPN
ejpam-4237	74	7	1	1	NUM
ejpam-4237	74	8	0	0	NUM
ejpam-4237	74	9	∫	∫	PROPN
ejpam-4237	74	10	1	1	NUM
ejpam-4237	74	11	0	0	NUM
ejpam-4237	74	12	∫	∫	PROPN
ejpam-4237	74	13	1	1	NUM
ejpam-4237	74	14	0	0	NUM
ejpam-4237	74	15	xm−1pv(x	xm−1pv(x	PROPN
ejpam-4237	74	16	)	)	PUNCT
ejpam-4237	74	17	log	log	VERB
ejpam-4237	74	18	−m	−m	NOUN
ejpam-4237	74	19	(	(	PUNCT
ejpam-4237	74	20	1	1	NUM
ejpam-4237	74	21	t	t	NOUN
ejpam-4237	74	22	)	)	PUNCT
ejpam-4237	74	23	log	log	VERB
ejpam-4237	74	24	1	1	NUM
ejpam-4237	74	25	2	2	NUM
ejpam-4237	74	26	(	(	PUNCT
ejpam-4237	74	27	m−v−1	m−v−1	NOUN
ejpam-4237	74	28	)	)	PUNCT
ejpam-4237	74	29	(	(	PUNCT
ejpam-4237	74	30	1	1	NUM
ejpam-4237	74	31	y	y	NOUN
ejpam-4237	74	32	)	)	PUNCT
ejpam-4237	74	33	log	log	VERB
ejpam-4237	74	34	m+v	m+v	X
ejpam-4237	74	35	2	2	NUM
ejpam-4237	74	36	(	(	PUNCT
ejpam-4237	74	37	1	1	NUM
ejpam-4237	74	38	z	z	NOUN
ejpam-4237	74	39	)	)	PUNCT
ejpam-4237	74	40	dxdydzdt	dxdydzdt	NOUN
ejpam-4237	74	41	=	=	SYM
ejpam-4237	75	1	π3/22−m	π3/22−m	PROPN
ejpam-4237	75	2	csc(πm	csc(πm	NOUN
ejpam-4237	75	3	)	)	PUNCT
ejpam-4237	75	4	(	(	PUNCT
ejpam-4237	75	5	8)	8)	NUM
ejpam-4237	75	6	proof	proof	NOUN
ejpam-4237	75	7	.	.	PUNCT
ejpam-4237	76	1	use	use	VERB
ejpam-4237	76	2	equation	equation	NOUN
ejpam-4237	76	3	(	(	PUNCT
ejpam-4237	76	4	7	7	NUM
ejpam-4237	76	5	)	)	PUNCT
ejpam-4237	76	6	and	and	CCONJ
ejpam-4237	76	7	set	set	VERB
ejpam-4237	76	8	k	k	PROPN
ejpam-4237	76	9	=	=	PUNCT
ejpam-4237	76	10	0	0	PUNCT
ejpam-4237	76	11	and	and	CCONJ
ejpam-4237	76	12	simplify	simplify	VERB
ejpam-4237	76	13	using	use	VERB
ejpam-4237	76	14	entry	entry	NOUN
ejpam-4237	76	15	(	(	PUNCT
ejpam-4237	76	16	2	2	NUM
ejpam-4237	76	17	)	)	PUNCT
ejpam-4237	76	18	in	in	ADP
ejpam-4237	76	19	table	table	NOUN
ejpam-4237	76	20	below	below	ADV
ejpam-4237	76	21	(	(	PUNCT
ejpam-4237	76	22	64:12:7	64:12:7	NUM
ejpam-4237	76	23	)	)	PUNCT
ejpam-4237	76	24	in	in	ADP
ejpam-4237	76	25	[	[	X
ejpam-4237	76	26	5	5	NUM
ejpam-4237	76	27	]	]	PUNCT
ejpam-4237	76	28	.	.	PUNCT
ejpam-4237	77	1	r.	r.	PROPN
ejpam-4237	77	2	reynolds	reynolds	PROPN
ejpam-4237	77	3	,	,	PUNCT
ejpam-4237	77	4	a.	a.	PROPN
ejpam-4237	77	5	stauffer	stauffer	PROPN
ejpam-4237	77	6	/	/	SYM
ejpam-4237	77	7	eur	eur	PROPN
ejpam-4237	77	8	.	.	PUNCT
ejpam-4237	78	1	j.	j.	PROPN
ejpam-4237	78	2	pure	pure	PROPN
ejpam-4237	78	3	appl	appl	PROPN
ejpam-4237	78	4	.	.	PROPN
ejpam-4237	78	5	math	math	PROPN
ejpam-4237	78	6	,	,	PUNCT
ejpam-4237	78	7	15	15	NUM
ejpam-4237	78	8	(	(	PUNCT
ejpam-4237	78	9	3	3	NUM
ejpam-4237	78	10	)	)	PUNCT
ejpam-4237	78	11	(	(	PUNCT
ejpam-4237	78	12	2022	2022	NUM
ejpam-4237	78	13	)	)	PUNCT
ejpam-4237	78	14	,	,	PUNCT
ejpam-4237	78	15	1113	1113	NUM
ejpam-4237	78	16	-	-	SYM
ejpam-4237	78	17	1119	1119	NUM
ejpam-4237	78	18	1117	1117	NUM
ejpam-4237	78	19	example	example	NOUN
ejpam-4237	78	20	2	2	NUM
ejpam-4237	78	21	.	.	PUNCT
ejpam-4237	79	1	the	the	DET
ejpam-4237	79	2	hurwitz	hurwitz	PROPN
ejpam-4237	79	3	zeta	zeta	PROPN
ejpam-4237	79	4	function	function	VERB
ejpam-4237	79	5	ζ(k	ζ(k	PROPN
ejpam-4237	79	6	,	,	PUNCT
ejpam-4237	79	7	a	a	PRON
ejpam-4237	79	8	)	)	PUNCT
ejpam-4237	79	9	,	,	PUNCT
ejpam-4237	79	10	where	where	SCONJ
ejpam-4237	79	11	the	the	DET
ejpam-4237	79	12	right	right	ADJ
ejpam-4237	79	13	-	-	PUNCT
ejpam-4237	79	14	hand	hand	NOUN
ejpam-4237	79	15	side	side	NOUN
ejpam-4237	79	16	is	be	AUX
ejpam-4237	79	17	invariant	invariant	ADJ
ejpam-4237	79	18	with	with	ADP
ejpam-4237	79	19	respect	respect	NOUN
ejpam-4237	79	20	to	to	ADP
ejpam-4237	79	21	v	v	NOUN
ejpam-4237	79	22	,	,	PUNCT
ejpam-4237	79	23	(	(	PUNCT
ejpam-4237	79	24	9	9	NUM
ejpam-4237	79	25	)	)	PUNCT
ejpam-4237	79	26	∫	∫	PROPN
ejpam-4237	79	27	1	1	NUM
ejpam-4237	79	28	0	0	NUM
ejpam-4237	79	29	∫	∫	PROPN
ejpam-4237	79	30	1	1	NUM
ejpam-4237	79	31	0	0	NUM
ejpam-4237	79	32	∫	∫	PROPN
ejpam-4237	79	33	1	1	NUM
ejpam-4237	79	34	0	0	NUM
ejpam-4237	79	35	∫	∫	PROPN
ejpam-4237	79	36	1	1	NUM
ejpam-4237	79	37	0	0	NUM
ejpam-4237	79	38	pv(x	pv(x	NUM
ejpam-4237	79	39	)	)	PUNCT
ejpam-4237	79	40	log	log	VERB
ejpam-4237	79	41	1	1	NUM
ejpam-4237	79	42	2(−v−	2(−v−	NUM
ejpam-4237	79	43	1	1	NUM
ejpam-4237	79	44	2	2	NUM
ejpam-4237	79	45	)	)	PUNCT
ejpam-4237	79	46	(	(	PUNCT
ejpam-4237	79	47	1	1	NUM
ejpam-4237	79	48	y	y	NOUN
ejpam-4237	79	49	)	)	PUNCT
ejpam-4237	79	50	log	log	VERB
ejpam-4237	79	51	1	1	NUM
ejpam-4237	79	52	2(v+	2(v+	NUM
ejpam-4237	79	53	1	1	NUM
ejpam-4237	79	54	2	2	NUM
ejpam-4237	79	55	)	)	PUNCT
ejpam-4237	79	56	(	(	PUNCT
ejpam-4237	79	57	1	1	NUM
ejpam-4237	79	58	z	z	NOUN
ejpam-4237	79	59	)	)	PUNCT
ejpam-4237	80	1	√	√	NUM
ejpam-4237	80	2	x	x	SYM
ejpam-4237	80	3	√	√	NUM
ejpam-4237	81	1	log	log	NOUN
ejpam-4237	81	2	(	(	PUNCT
ejpam-4237	81	3	1	1	NUM
ejpam-4237	81	4	t	t	NOUN
ejpam-4237	81	5	)	)	PUNCT
ejpam-4237	81	6	logk	logk	ADJ
ejpam-4237	81	7	ax	ax	NOUN
ejpam-4237	81	8	√	√	NUM
ejpam-4237	82	1	log	log	NOUN
ejpam-4237	82	2	(	(	PUNCT
ejpam-4237	82	3	1	1	NUM
ejpam-4237	82	4	y	y	NOUN
ejpam-4237	82	5	)	)	PUNCT
ejpam-4237	82	6	√	√	PROPN
ejpam-4237	83	1	log	log	NOUN
ejpam-4237	83	2	(	(	PUNCT
ejpam-4237	83	3	1	1	NUM
ejpam-4237	83	4	z	z	NOUN
ejpam-4237	83	5	)	)	PUNCT
ejpam-4237	83	6	log	log	NOUN
ejpam-4237	83	7	(	(	PUNCT
ejpam-4237	83	8	1	1	NUM
ejpam-4237	83	9	t	t	NOUN
ejpam-4237	83	10	)	)	PUNCT
ejpam-4237	83	11			NOUN
ejpam-4237	83	12	dxdydzdt	dxdydzdt	NOUN
ejpam-4237	83	13	=	=	SYM
ejpam-4237	83	14	ik2k+	ik2k+	NUM
ejpam-4237	84	1	1	1	NUM
ejpam-4237	84	2	2πk+	2πk+	NUM
ejpam-4237	84	3	3	3	NUM
ejpam-4237	84	4	2	2	NUM
ejpam-4237	84	5	(	(	PUNCT
ejpam-4237	84	6	2kζ	2kζ	ADJ
ejpam-4237	84	7	(	(	PUNCT
ejpam-4237	84	8	−k	−k	PROPN
ejpam-4237	84	9	,	,	PUNCT
ejpam-4237	84	10	−i	−i	PROPN
ejpam-4237	84	11	log(a	log(a	PROPN
ejpam-4237	84	12	)	)	PUNCT
ejpam-4237	85	1	+	+	CCONJ
ejpam-4237	85	2	i	i	PRON
ejpam-4237	85	3	log(2	log(2	NOUN
ejpam-4237	85	4	)	)	PUNCT
ejpam-4237	86	1	+	+	CCONJ
ejpam-4237	87	1	π	π	NOUN
ejpam-4237	87	2	4π	4π	NUM
ejpam-4237	87	3	)	)	PUNCT
ejpam-4237	87	4	−	−	PROPN
ejpam-4237	87	5	2kζ	2kζ	ADJ
ejpam-4237	87	6	(	(	PUNCT
ejpam-4237	87	7	−k	−k	PROPN
ejpam-4237	87	8	,	,	PUNCT
ejpam-4237	87	9	1	1	NUM
ejpam-4237	87	10	2	2	NUM
ejpam-4237	87	11	(	(	PUNCT
ejpam-4237	87	12	−i	−i	PROPN
ejpam-4237	87	13	log(a	log(a	PROPN
ejpam-4237	87	14	)	)	PUNCT
ejpam-4237	88	1	+	+	CCONJ
ejpam-4237	88	2	i	i	PRON
ejpam-4237	88	3	log(2	log(2	NOUN
ejpam-4237	88	4	)	)	PUNCT
ejpam-4237	89	1	+	+	CCONJ
ejpam-4237	89	2	π	π	NOUN
ejpam-4237	89	3	2π	2π	NOUN
ejpam-4237	89	4	+	+	CCONJ
ejpam-4237	89	5	1	1	NUM
ejpam-4237	89	6	)	)	PUNCT
ejpam-4237	89	7	)	)	PUNCT
ejpam-4237	89	8	)	)	PUNCT
ejpam-4237	90	1	proof	proof	NOUN
ejpam-4237	90	2	.	.	PUNCT
ejpam-4237	91	1	use	use	VERB
ejpam-4237	91	2	equation	equation	NOUN
ejpam-4237	91	3	(	(	PUNCT
ejpam-4237	91	4	7	7	NUM
ejpam-4237	91	5	)	)	PUNCT
ejpam-4237	91	6	and	and	CCONJ
ejpam-4237	91	7	set	set	VERB
ejpam-4237	91	8	m	m	PROPN
ejpam-4237	91	9	=	=	NOUN
ejpam-4237	91	10	1/2	1/2	NUM
ejpam-4237	91	11	and	and	CCONJ
ejpam-4237	91	12	simplify	simplify	VERB
ejpam-4237	91	13	using	use	VERB
ejpam-4237	91	14	entry	entry	NOUN
ejpam-4237	91	15	(	(	PUNCT
ejpam-4237	91	16	4	4	NUM
ejpam-4237	91	17	)	)	PUNCT
ejpam-4237	91	18	in	in	ADP
ejpam-4237	91	19	table	table	NOUN
ejpam-4237	91	20	below	below	ADV
ejpam-4237	91	21	(	(	PUNCT
ejpam-4237	91	22	64:12:7	64:12:7	NUM
ejpam-4237	91	23	)	)	PUNCT
ejpam-4237	91	24	in	in	ADP
ejpam-4237	91	25	[	[	X
ejpam-4237	91	26	5	5	NUM
ejpam-4237	91	27	]	]	PUNCT
ejpam-4237	91	28	.	.	PUNCT
ejpam-4237	91	29	example	example	NOUN
ejpam-4237	92	1	3	3	X
ejpam-4237	92	2	.	.	PUNCT
ejpam-4237	92	3	the	the	DET
ejpam-4237	92	4	zeta	zeta	PROPN
ejpam-4237	92	5	function	function	NOUN
ejpam-4237	92	6	of	of	ADP
ejpam-4237	92	7	riemann	riemann	PROPN
ejpam-4237	92	8	ζ(k	ζ(k	PROPN
ejpam-4237	92	9	)	)	PUNCT
ejpam-4237	92	10	,	,	PUNCT
ejpam-4237	92	11	∫	∫	PROPN
ejpam-4237	92	12	1	1	NUM
ejpam-4237	92	13	0	0	NUM
ejpam-4237	92	14	∫	∫	PROPN
ejpam-4237	92	15	1	1	NUM
ejpam-4237	92	16	0	0	NUM
ejpam-4237	92	17	∫	∫	PROPN
ejpam-4237	92	18	1	1	NUM
ejpam-4237	92	19	0	0	NUM
ejpam-4237	92	20	∫	∫	PROPN
ejpam-4237	92	21	1	1	NUM
ejpam-4237	92	22	0	0	NUM
ejpam-4237	92	23	pv(x	pv(x	NUM
ejpam-4237	92	24	)	)	PUNCT
ejpam-4237	92	25	log	log	NOUN
ejpam-4237	92	26	−	−	PROPN
ejpam-4237	92	27	v	v	NOUN
ejpam-4237	92	28	2	2	NUM
ejpam-4237	92	29	−	−	NOUN
ejpam-4237	92	30	1	1	NUM
ejpam-4237	92	31	4	4	NUM
ejpam-4237	92	32	(	(	PUNCT
ejpam-4237	92	33	1	1	NUM
ejpam-4237	92	34	y	y	NOUN
ejpam-4237	92	35	)	)	PUNCT
ejpam-4237	92	36	log	log	VERB
ejpam-4237	92	37	v	v	NUM
ejpam-4237	92	38	2	2	NUM
ejpam-4237	92	39	+	+	CCONJ
ejpam-4237	92	40	1	1	NUM
ejpam-4237	92	41	4	4	NUM
ejpam-4237	92	42	(	(	PUNCT
ejpam-4237	92	43	1	1	NUM
ejpam-4237	92	44	z	z	NOUN
ejpam-4237	92	45	)	)	PUNCT
ejpam-4237	93	1	√	√	NUM
ejpam-4237	93	2	x	x	SYM
ejpam-4237	93	3	√	√	NUM
ejpam-4237	93	4	log	log	NOUN
ejpam-4237	93	5	(	(	PUNCT
ejpam-4237	93	6	1	1	NUM
ejpam-4237	93	7	t	t	NOUN
ejpam-4237	93	8	)	)	PUNCT
ejpam-4237	93	9	logk	logk	NOUN
ejpam-4237	93	10	−	−	NOUN
ejpam-4237	93	11	2x	2x	NUM
ejpam-4237	93	12	√	√	INTJ
ejpam-4237	94	1	log	log	NOUN
ejpam-4237	94	2	(	(	PUNCT
ejpam-4237	94	3	1	1	NUM
ejpam-4237	94	4	y	y	NOUN
ejpam-4237	94	5	)	)	PUNCT
ejpam-4237	94	6	√	√	PROPN
ejpam-4237	95	1	log	log	NOUN
ejpam-4237	95	2	(	(	PUNCT
ejpam-4237	95	3	1	1	NUM
ejpam-4237	95	4	z	z	NOUN
ejpam-4237	95	5	)	)	PUNCT
ejpam-4237	95	6	log	log	NOUN
ejpam-4237	95	7	(	(	PUNCT
ejpam-4237	95	8	1	1	NUM
ejpam-4237	95	9	t	t	NOUN
ejpam-4237	95	10	)	)	PUNCT
ejpam-4237	95	11			NOUN
ejpam-4237	95	12	dxdydzdt	dxdydzdt	NOUN
ejpam-4237	96	1	=	=	PUNCT
ejpam-4237	96	2	−ik2k+	−ik2k+	PRON
ejpam-4237	96	3	1	1	NUM
ejpam-4237	96	4	2	2	NUM
ejpam-4237	96	5	(	(	PUNCT
ejpam-4237	96	6	2k+1	2k+1	NOUN
ejpam-4237	96	7	−	−	NOUN
ejpam-4237	96	8	1	1	NUM
ejpam-4237	96	9	)	)	PUNCT
ejpam-4237	96	10	πk+	πk+	NOUN
ejpam-4237	96	11	3	3	NUM
ejpam-4237	96	12	2	2	NUM
ejpam-4237	96	13	ζ(−k	ζ(−k	NOUN
ejpam-4237	96	14	)	)	PUNCT
ejpam-4237	96	15	(	(	PUNCT
ejpam-4237	96	16	10	10	X
ejpam-4237	96	17	)	)	PUNCT
ejpam-4237	96	18	proof	proof	NOUN
ejpam-4237	96	19	.	.	PUNCT
ejpam-4237	97	1	use	use	VERB
ejpam-4237	97	2	equation	equation	NOUN
ejpam-4237	97	3	9	9	NUM
ejpam-4237	97	4	and	and	CCONJ
ejpam-4237	97	5	set	set	VERB
ejpam-4237	97	6	a	a	DET
ejpam-4237	97	7	=	=	PUNCT
ejpam-4237	97	8	−2	−2	NOUN
ejpam-4237	97	9	and	and	CCONJ
ejpam-4237	97	10	simplify	simplify	VERB
ejpam-4237	97	11	using	use	VERB
ejpam-4237	97	12	entry	entry	NOUN
ejpam-4237	97	13	(	(	PUNCT
ejpam-4237	97	14	2	2	NUM
ejpam-4237	97	15	)	)	PUNCT
ejpam-4237	97	16	in	in	ADP
ejpam-4237	97	17	table	table	NOUN
ejpam-4237	97	18	below	below	ADV
ejpam-4237	97	19	(	(	PUNCT
ejpam-4237	97	20	64:7	64:7	NUM
ejpam-4237	97	21	)	)	PUNCT
ejpam-4237	97	22	in	in	ADP
ejpam-4237	97	23	[	[	X
ejpam-4237	97	24	5	5	NUM
ejpam-4237	97	25	]	]	PUNCT
ejpam-4237	97	26	.	.	PUNCT
ejpam-4237	97	27	example	example	NOUN
ejpam-4237	98	1	4	4	NUM
ejpam-4237	98	2	.	.	PUNCT
ejpam-4237	99	1	the	the	DET
ejpam-4237	99	2	fundamental	fundamental	ADJ
ejpam-4237	99	3	constant	constant	ADJ
ejpam-4237	99	4	log(2	log(2	NOUN
ejpam-4237	99	5	)	)	PUNCT
ejpam-4237	99	6	,	,	PUNCT
ejpam-4237	99	7	(	(	PUNCT
ejpam-4237	99	8	11	11	X
ejpam-4237	99	9	)	)	PUNCT
ejpam-4237	99	10	∫	∫	PROPN
ejpam-4237	99	11	1	1	NUM
ejpam-4237	99	12	0	0	NUM
ejpam-4237	99	13	∫	∫	PROPN
ejpam-4237	99	14	1	1	NUM
ejpam-4237	99	15	0	0	NUM
ejpam-4237	99	16	∫	∫	PROPN
ejpam-4237	99	17	1	1	NUM
ejpam-4237	99	18	0	0	NUM
ejpam-4237	99	19	∫	∫	PROPN
ejpam-4237	99	20	1	1	NUM
ejpam-4237	99	21	0	0	NUM
ejpam-4237	99	22	pv(x	pv(x	NUM
ejpam-4237	99	23	)	)	PUNCT
ejpam-4237	99	24	log	log	NOUN
ejpam-4237	99	25	−	−	PROPN
ejpam-4237	99	26	v	v	NOUN
ejpam-4237	99	27	2	2	NUM
ejpam-4237	99	28	−	−	NOUN
ejpam-4237	99	29	1	1	NUM
ejpam-4237	99	30	4	4	NUM
ejpam-4237	99	31	(	(	PUNCT
ejpam-4237	99	32	1	1	NUM
ejpam-4237	99	33	y	y	NOUN
ejpam-4237	99	34	)	)	PUNCT
ejpam-4237	99	35	log	log	VERB
ejpam-4237	99	36	v	v	NUM
ejpam-4237	99	37	2	2	NUM
ejpam-4237	99	38	+	+	CCONJ
ejpam-4237	99	39	1	1	NUM
ejpam-4237	99	40	4	4	NUM
ejpam-4237	99	41	(	(	PUNCT
ejpam-4237	99	42	1	1	NUM
ejpam-4237	99	43	z	z	NOUN
ejpam-4237	99	44	)	)	PUNCT
ejpam-4237	100	1	√	√	NUM
ejpam-4237	100	2	x	x	SYM
ejpam-4237	100	3	√	√	NUM
ejpam-4237	100	4	log	log	NOUN
ejpam-4237	100	5	(	(	PUNCT
ejpam-4237	100	6	1	1	NUM
ejpam-4237	100	7	t	t	NOUN
ejpam-4237	100	8	)	)	PUNCT
ejpam-4237	100	9	log	log	VERB
ejpam-4237	100	10	−	−	NOUN
ejpam-4237	100	11	2x	2x	NUM
ejpam-4237	100	12	√	√	ADV
ejpam-4237	101	1	log	log	NOUN
ejpam-4237	101	2	(	(	PUNCT
ejpam-4237	101	3	1	1	NUM
ejpam-4237	101	4	y	y	NOUN
ejpam-4237	101	5	)	)	PUNCT
ejpam-4237	101	6	√	√	PROPN
ejpam-4237	102	1	log	log	NOUN
ejpam-4237	102	2	(	(	PUNCT
ejpam-4237	102	3	1	1	NUM
ejpam-4237	102	4	z	z	NOUN
ejpam-4237	102	5	)	)	PUNCT
ejpam-4237	102	6	log	log	NOUN
ejpam-4237	102	7	(	(	PUNCT
ejpam-4237	102	8	1	1	NUM
ejpam-4237	102	9	t	t	NOUN
ejpam-4237	102	10	)	)	PUNCT
ejpam-4237	102	11	dxdydzdt	dxdydzdt	PUNCT
ejpam-4237	103	1	=	=	PUNCT
ejpam-4237	103	2	−i	−i	ADJ
ejpam-4237	103	3	√	√	NUM
ejpam-4237	103	4	π	π	PROPN
ejpam-4237	103	5	2	2	NUM
ejpam-4237	103	6	log(2	log(2	NOUN
ejpam-4237	103	7	)	)	PUNCT
ejpam-4237	103	8	proof	proof	NOUN
ejpam-4237	103	9	.	.	PUNCT
ejpam-4237	104	1	use	use	VERB
ejpam-4237	104	2	equation	equation	NOUN
ejpam-4237	104	3	(	(	PUNCT
ejpam-4237	104	4	10	10	NUM
ejpam-4237	104	5	)	)	PUNCT
ejpam-4237	104	6	and	and	CCONJ
ejpam-4237	104	7	apply	apply	VERB
ejpam-4237	104	8	l’hopital	l’hopital	PROPN
ejpam-4237	104	9	’s	’s	PART
ejpam-4237	104	10	rule	rule	NOUN
ejpam-4237	104	11	as	as	ADP
ejpam-4237	104	12	k	k	PROPN
ejpam-4237	104	13	→	→	SYM
ejpam-4237	104	14	−1	−1	NOUN
ejpam-4237	104	15	and	and	CCONJ
ejpam-4237	104	16	simplify	simplify	VERB
ejpam-4237	104	17	using	use	VERB
ejpam-4237	104	18	equation	equation	NOUN
ejpam-4237	104	19	(	(	PUNCT
ejpam-4237	104	20	25.6.11	25.6.11	X
ejpam-4237	104	21	)	)	PUNCT
ejpam-4237	104	22	in	in	ADP
ejpam-4237	104	23	[	[	X
ejpam-4237	104	24	1	1	NUM
ejpam-4237	104	25	]	]	PUNCT
ejpam-4237	104	26	.	.	PUNCT
ejpam-4237	105	1	r.	r.	PROPN
ejpam-4237	105	2	reynolds	reynolds	PROPN
ejpam-4237	105	3	,	,	PUNCT
ejpam-4237	105	4	a.	a.	PROPN
ejpam-4237	105	5	stauffer	stauffer	PROPN
ejpam-4237	105	6	/	/	SYM
ejpam-4237	105	7	eur	eur	PROPN
ejpam-4237	105	8	.	.	PUNCT
ejpam-4237	106	1	j.	j.	PROPN
ejpam-4237	106	2	pure	pure	PROPN
ejpam-4237	106	3	appl	appl	PROPN
ejpam-4237	106	4	.	.	PROPN
ejpam-4237	106	5	math	math	PROPN
ejpam-4237	106	6	,	,	PUNCT
ejpam-4237	106	7	15	15	NUM
ejpam-4237	106	8	(	(	PUNCT
ejpam-4237	106	9	3	3	NUM
ejpam-4237	106	10	)	)	PUNCT
ejpam-4237	106	11	(	(	PUNCT
ejpam-4237	106	12	2022	2022	NUM
ejpam-4237	106	13	)	)	PUNCT
ejpam-4237	106	14	,	,	PUNCT
ejpam-4237	106	15	1113	1113	NUM
ejpam-4237	106	16	-	-	SYM
ejpam-4237	106	17	1119	1119	NUM
ejpam-4237	106	18	1118	1118	NUM
ejpam-4237	106	19	example	example	NOUN
ejpam-4237	106	20	5	5	NUM
ejpam-4237	106	21	.	.	PUNCT
ejpam-4237	106	22	apéry	apéry	PROPN
ejpam-4237	106	23	’s	’s	NOUN
ejpam-4237	106	24	constant	constant	ADJ
ejpam-4237	106	25	ζ(3	ζ(3	NOUN
ejpam-4237	106	26	)	)	PUNCT
ejpam-4237	106	27	,	,	PUNCT
ejpam-4237	106	28	(	(	PUNCT
ejpam-4237	106	29	12	12	NUM
ejpam-4237	106	30	)	)	PUNCT
ejpam-4237	106	31	∫	∫	PROPN
ejpam-4237	107	1	1	1	NUM
ejpam-4237	107	2	0	0	NUM
ejpam-4237	107	3	∫	∫	PROPN
ejpam-4237	107	4	1	1	NUM
ejpam-4237	107	5	0	0	NUM
ejpam-4237	107	6	∫	∫	PROPN
ejpam-4237	107	7	1	1	NUM
ejpam-4237	107	8	0	0	NUM
ejpam-4237	107	9	∫	∫	PROPN
ejpam-4237	107	10	1	1	NUM
ejpam-4237	107	11	0	0	NUM
ejpam-4237	107	12	pv(x	pv(x	NUM
ejpam-4237	107	13	)	)	PUNCT
ejpam-4237	107	14	log	log	NOUN
ejpam-4237	107	15	−	−	PROPN
ejpam-4237	107	16	v	v	NOUN
ejpam-4237	107	17	2	2	NUM
ejpam-4237	107	18	−	−	NOUN
ejpam-4237	107	19	1	1	NUM
ejpam-4237	107	20	4	4	NUM
ejpam-4237	107	21	(	(	PUNCT
ejpam-4237	107	22	1	1	NUM
ejpam-4237	107	23	y	y	NOUN
ejpam-4237	107	24	)	)	PUNCT
ejpam-4237	107	25	log	log	VERB
ejpam-4237	107	26	v	v	NUM
ejpam-4237	107	27	2	2	NUM
ejpam-4237	107	28	+	+	CCONJ
ejpam-4237	107	29	1	1	NUM
ejpam-4237	107	30	4	4	NUM
ejpam-4237	107	31	(	(	PUNCT
ejpam-4237	107	32	1	1	NUM
ejpam-4237	107	33	z	z	NOUN
ejpam-4237	107	34	)	)	PUNCT
ejpam-4237	108	1	√	√	NUM
ejpam-4237	108	2	x	x	SYM
ejpam-4237	108	3	√	√	NUM
ejpam-4237	108	4	log	log	NOUN
ejpam-4237	108	5	(	(	PUNCT
ejpam-4237	108	6	1	1	NUM
ejpam-4237	108	7	t	t	NOUN
ejpam-4237	108	8	)	)	PUNCT
ejpam-4237	108	9	log3	log3	VERB
ejpam-4237	108	10	−	−	NOUN
ejpam-4237	109	1	2x	2x	NUM
ejpam-4237	109	2	√	√	ADV
ejpam-4237	109	3	log	log	NOUN
ejpam-4237	109	4	(	(	PUNCT
ejpam-4237	109	5	1	1	NUM
ejpam-4237	109	6	y	y	NOUN
ejpam-4237	109	7	)	)	PUNCT
ejpam-4237	109	8	√	√	PROPN
ejpam-4237	110	1	log	log	NOUN
ejpam-4237	110	2	(	(	PUNCT
ejpam-4237	110	3	1	1	NUM
ejpam-4237	110	4	z	z	NOUN
ejpam-4237	110	5	)	)	PUNCT
ejpam-4237	110	6	log	log	NOUN
ejpam-4237	110	7	(	(	PUNCT
ejpam-4237	110	8	1	1	NUM
ejpam-4237	110	9	t	t	NOUN
ejpam-4237	110	10	)	)	PUNCT
ejpam-4237	110	11	dxdydzdt	dxdydzdt	PUNCT
ejpam-4237	111	1	=	=	SYM
ejpam-4237	111	2	3iζ(3	3iζ(3	ADJ
ejpam-4237	111	3	)	)	PUNCT
ejpam-4237	111	4	16	16	NUM
ejpam-4237	112	1	√	√	NUM
ejpam-4237	112	2	2π3/2	2π3/2	NUM
ejpam-4237	112	3	proof	proof	NOUN
ejpam-4237	112	4	.	.	PUNCT
ejpam-4237	113	1	use	use	VERB
ejpam-4237	113	2	equation	equation	NOUN
ejpam-4237	113	3	(	(	PUNCT
ejpam-4237	113	4	10	10	NUM
ejpam-4237	113	5	)	)	PUNCT
ejpam-4237	113	6	and	and	CCONJ
ejpam-4237	113	7	set	set	VERB
ejpam-4237	113	8	k	k	PROPN
ejpam-4237	113	9	=	=	X
ejpam-4237	113	10	−3	−3	PROPN
ejpam-4237	113	11	and	and	CCONJ
ejpam-4237	113	12	simplify	simplify	VERB
ejpam-4237	113	13	.	.	PUNCT
ejpam-4237	113	14	example	example	NOUN
ejpam-4237	114	1	6	6	NUM
ejpam-4237	114	2	.	.	PUNCT
ejpam-4237	114	3	∫	∫	PROPN
ejpam-4237	114	4	1	1	NUM
ejpam-4237	114	5	0	0	NUM
ejpam-4237	114	6	∫	∫	PROPN
ejpam-4237	114	7	1	1	NUM
ejpam-4237	114	8	0	0	NUM
ejpam-4237	114	9	∫	∫	PROPN
ejpam-4237	114	10	1	1	NUM
ejpam-4237	114	11	0	0	NUM
ejpam-4237	114	12	∫	∫	PROPN
ejpam-4237	114	13	1	1	NUM
ejpam-4237	114	14	0	0	NUM
ejpam-4237	114	15	pv(x	pv(x	NUM
ejpam-4237	114	16	)	)	PUNCT
ejpam-4237	114	17	log	log	NOUN
ejpam-4237	114	18	−	−	PROPN
ejpam-4237	114	19	v	v	NOUN
ejpam-4237	114	20	2	2	NUM
ejpam-4237	114	21	−	−	NOUN
ejpam-4237	114	22	1	1	NUM
ejpam-4237	114	23	2	2	NUM
ejpam-4237	114	24	(	(	PUNCT
ejpam-4237	114	25	1	1	NUM
ejpam-4237	114	26	y	y	NOUN
ejpam-4237	114	27	)	)	PUNCT
ejpam-4237	114	28	log	log	VERB
ejpam-4237	114	29	v	v	NUM
ejpam-4237	114	30	2	2	NUM
ejpam-4237	114	31	(	(	PUNCT
ejpam-4237	114	32	1	1	NUM
ejpam-4237	114	33	z	z	NOUN
ejpam-4237	114	34	)	)	PUNCT
ejpam-4237	115	1	x	x	SYM
ejpam-4237	115	2	log	log	VERB
ejpam-4237	115	3	x	x	ADP
ejpam-4237	115	4	√	√	NOUN
ejpam-4237	115	5	log	log	NOUN
ejpam-4237	115	6	(	(	PUNCT
ejpam-4237	115	7	1	1	NUM
ejpam-4237	115	8	y	y	NOUN
ejpam-4237	115	9	)	)	PUNCT
ejpam-4237	116	1	√	√	PROPN
ejpam-4237	117	1	log	log	NOUN
ejpam-4237	117	2	(	(	PUNCT
ejpam-4237	117	3	1	1	NUM
ejpam-4237	117	4	z	z	NOUN
ejpam-4237	117	5	)	)	PUNCT
ejpam-4237	117	6	log	log	NOUN
ejpam-4237	117	7	(	(	PUNCT
ejpam-4237	117	8	1	1	NUM
ejpam-4237	117	9	t	t	NOUN
ejpam-4237	117	10	)	)	PUNCT
ejpam-4237	117	11			PROPN
ejpam-4237	118	1	(	(	PUNCT
ejpam-4237	118	2	xm	xm	PROPN
ejpam-4237	118	3	log−m	log−m	PROPN
ejpam-4237	118	4	(	(	PUNCT
ejpam-4237	118	5	1	1	NUM
ejpam-4237	118	6	t	t	NOUN
ejpam-4237	118	7	)	)	PUNCT
ejpam-4237	118	8	log	log	VERB
ejpam-4237	118	9	m	m	VERB
ejpam-4237	118	10	2	2	NUM
ejpam-4237	118	11	(	(	PUNCT
ejpam-4237	118	12	1	1	NUM
ejpam-4237	118	13	y	y	PROPN
ejpam-4237	118	14	)	)	PUNCT
ejpam-4237	118	15	log	log	VERB
ejpam-4237	118	16	m	m	VERB
ejpam-4237	118	17	2	2	NUM
ejpam-4237	118	18	(	(	PUNCT
ejpam-4237	118	19	1	1	NUM
ejpam-4237	118	20	z	z	NOUN
ejpam-4237	118	21	)	)	PUNCT
ejpam-4237	118	22	−	−	PROPN
ejpam-4237	119	1	xp	xp	INTJ
ejpam-4237	120	1	log−p	log−p	PROPN
ejpam-4237	121	1	(	(	PUNCT
ejpam-4237	121	2	1	1	NUM
ejpam-4237	121	3	t	t	NOUN
ejpam-4237	121	4	)	)	PUNCT
ejpam-4237	121	5	log	log	VERB
ejpam-4237	121	6	p	p	NOUN
ejpam-4237	121	7	2	2	NUM
ejpam-4237	121	8	(	(	PUNCT
ejpam-4237	121	9	1	1	NUM
ejpam-4237	121	10	y	y	PROPN
ejpam-4237	121	11	)	)	PUNCT
ejpam-4237	121	12	log	log	VERB
ejpam-4237	121	13	p	p	NOUN
ejpam-4237	121	14	2	2	NUM
ejpam-4237	121	15	(	(	PUNCT
ejpam-4237	121	16	1	1	NUM
ejpam-4237	121	17	z	z	NOUN
ejpam-4237	121	18	)	)	PUNCT
ejpam-4237	121	19	)	)	PUNCT
ejpam-4237	122	1	dxdydzdt	dxdydzdt	NOUN
ejpam-4237	122	2	=	=	SYM
ejpam-4237	123	1	√	√	PROPN
ejpam-4237	123	2	π	π	PROPN
ejpam-4237	123	3	(	(	PUNCT
ejpam-4237	123	4	2−peiπpφ	2−peiπpφ	X
ejpam-4237	123	5	(	(	PUNCT
ejpam-4237	123	6	e2ipπ	e2ipπ	PROPN
ejpam-4237	123	7	,	,	PUNCT
ejpam-4237	123	8	1	1	NUM
ejpam-4237	123	9	,	,	PUNCT
ejpam-4237	123	10	π	π	PROPN
ejpam-4237	123	11	+	+	CCONJ
ejpam-4237	123	12	i	i	PRON
ejpam-4237	123	13	log(2	log(2	NOUN
ejpam-4237	123	14	)	)	PUNCT
ejpam-4237	123	15	2π	2π	NOUN
ejpam-4237	123	16	)	)	PUNCT
ejpam-4237	123	17	−	−	PROPN
ejpam-4237	123	18	2−meiπmφ	2−meiπmφ	NUM
ejpam-4237	123	19	(	(	PUNCT
ejpam-4237	123	20	e2imπ	e2imπ	PROPN
ejpam-4237	123	21	,	,	PUNCT
ejpam-4237	123	22	1	1	NUM
ejpam-4237	123	23	,	,	PUNCT
ejpam-4237	123	24	π	π	PROPN
ejpam-4237	123	25	+	+	CCONJ
ejpam-4237	123	26	i	i	PRON
ejpam-4237	123	27	log(2	log(2	NOUN
ejpam-4237	123	28	)	)	PUNCT
ejpam-4237	123	29	2π	2π	NOUN
ejpam-4237	123	30	)	)	PUNCT
ejpam-4237	123	31	)	)	PUNCT
ejpam-4237	123	32	(	(	PUNCT
ejpam-4237	123	33	13	13	X
ejpam-4237	123	34	)	)	PUNCT
ejpam-4237	123	35	proof	proof	NOUN
ejpam-4237	123	36	.	.	PUNCT
ejpam-4237	124	1	use	use	VERB
ejpam-4237	124	2	equation	equation	NOUN
ejpam-4237	124	3	(	(	PUNCT
ejpam-4237	124	4	7	7	NUM
ejpam-4237	124	5	)	)	PUNCT
ejpam-4237	124	6	and	and	CCONJ
ejpam-4237	124	7	form	form	VERB
ejpam-4237	124	8	a	a	DET
ejpam-4237	124	9	second	second	ADJ
ejpam-4237	124	10	equation	equation	NOUN
ejpam-4237	124	11	by	by	ADP
ejpam-4237	124	12	replacing	replace	VERB
ejpam-4237	124	13	m	m	PRON
ejpam-4237	124	14	→	→	SYM
ejpam-4237	124	15	p	p	X
ejpam-4237	124	16	and	and	CCONJ
ejpam-4237	124	17	taking	take	VERB
ejpam-4237	124	18	their	their	PRON
ejpam-4237	124	19	difference	difference	NOUN
ejpam-4237	124	20	and	and	CCONJ
ejpam-4237	124	21	setting	set	VERB
ejpam-4237	124	22	k	k	PROPN
ejpam-4237	124	23	=	=	SYM
ejpam-4237	124	24	−1	−1	NOUN
ejpam-4237	124	25	,	,	PUNCT
ejpam-4237	124	26	a	a	DET
ejpam-4237	124	27	=	=	SYM
ejpam-4237	124	28	1	1	NUM
ejpam-4237	124	29	and	and	CCONJ
ejpam-4237	124	30	simplify	simplify	NOUN
ejpam-4237	124	31	.	.	PUNCT
ejpam-4237	124	32	example	example	NOUN
ejpam-4237	125	1	7	7	NUM
ejpam-4237	125	2	.	.	PUNCT
ejpam-4237	125	3	∫	∫	PROPN
ejpam-4237	125	4	1	1	NUM
ejpam-4237	125	5	0	0	NUM
ejpam-4237	125	6	∫	∫	PROPN
ejpam-4237	125	7	1	1	NUM
ejpam-4237	125	8	0	0	NUM
ejpam-4237	125	9	∫	∫	PROPN
ejpam-4237	125	10	1	1	NUM
ejpam-4237	125	11	0	0	NUM
ejpam-4237	125	12	∫	∫	PROPN
ejpam-4237	125	13	1	1	NUM
ejpam-4237	125	14	0	0	NUM
ejpam-4237	125	15	pv(x	pv(x	NUM
ejpam-4237	125	16	)	)	PUNCT
ejpam-4237	125	17	log	log	NOUN
ejpam-4237	125	18	−	−	PROPN
ejpam-4237	125	19	v	v	NOUN
ejpam-4237	125	20	2	2	NUM
ejpam-4237	125	21	−	−	NOUN
ejpam-4237	125	22	3	3	NUM
ejpam-4237	125	23	8	8	NUM
ejpam-4237	125	24	(	(	PUNCT
ejpam-4237	125	25	1	1	NUM
ejpam-4237	125	26	y	y	NOUN
ejpam-4237	125	27	)	)	PUNCT
ejpam-4237	125	28	log	log	VERB
ejpam-4237	125	29	v	v	NUM
ejpam-4237	125	30	2	2	NUM
ejpam-4237	125	31	+	+	CCONJ
ejpam-4237	125	32	1	1	NUM
ejpam-4237	125	33	8	8	NUM
ejpam-4237	125	34	(	(	PUNCT
ejpam-4237	125	35	1	1	NUM
ejpam-4237	125	36	z	z	NOUN
ejpam-4237	125	37	)	)	PUNCT
ejpam-4237	125	38	x3/4	x3/4	NUM
ejpam-4237	126	1	√	√	NUM
ejpam-4237	126	2	log	log	NOUN
ejpam-4237	126	3	(	(	PUNCT
ejpam-4237	126	4	1	1	NUM
ejpam-4237	126	5	t	t	NOUN
ejpam-4237	126	6	)	)	PUNCT
ejpam-4237	126	7	log	log	VERB
ejpam-4237	126	8	x	x	PRON
ejpam-4237	126	9	√	√	NOUN
ejpam-4237	126	10	log	log	NOUN
ejpam-4237	126	11	(	(	PUNCT
ejpam-4237	126	12	1	1	NUM
ejpam-4237	126	13	y	y	NOUN
ejpam-4237	126	14	)	)	PUNCT
ejpam-4237	127	1	√	√	PROPN
ejpam-4237	128	1	log	log	NOUN
ejpam-4237	128	2	(	(	PUNCT
ejpam-4237	128	3	1	1	NUM
ejpam-4237	128	4	z	z	NOUN
ejpam-4237	128	5	)	)	PUNCT
ejpam-4237	128	6	log	log	NOUN
ejpam-4237	128	7	(	(	PUNCT
ejpam-4237	128	8	1	1	NUM
ejpam-4237	128	9	t	t	NOUN
ejpam-4237	128	10	)	)	PUNCT
ejpam-4237	128	11			PROPN
ejpam-4237	128	12	(	(	PUNCT
ejpam-4237	128	13	4	4	NUM
ejpam-4237	128	14	√	√	NUM
ejpam-4237	128	15	x	x	SYM
ejpam-4237	128	16	8	8	NUM
ejpam-4237	128	17	√	√	NUM
ejpam-4237	128	18	log	log	NOUN
ejpam-4237	128	19	(	(	PUNCT
ejpam-4237	128	20	1	1	NUM
ejpam-4237	128	21	y	y	NOUN
ejpam-4237	128	22	)	)	PUNCT
ejpam-4237	128	23	8	8	NUM
ejpam-4237	128	24	√	√	NUM
ejpam-4237	128	25	log	log	NOUN
ejpam-4237	128	26	(	(	PUNCT
ejpam-4237	128	27	1	1	NUM
ejpam-4237	128	28	z	z	NOUN
ejpam-4237	128	29	)	)	PUNCT
ejpam-4237	128	30	−	−	ADP
ejpam-4237	128	31	4	4	NUM
ejpam-4237	128	32	√	√	NOUN
ejpam-4237	128	33	log	log	NOUN
ejpam-4237	128	34	(	(	PUNCT
ejpam-4237	128	35	1	1	NUM
ejpam-4237	128	36	t	t	NOUN
ejpam-4237	128	37	)	)	PUNCT
ejpam-4237	128	38	)	)	PUNCT
ejpam-4237	128	39	dxdydzdt	dxdydzdt	NOUN
ejpam-4237	128	40	=	=	PUNCT
ejpam-4237	128	41	√	√	PROPN
ejpam-4237	128	42	π	π	SYM
ejpam-4237	128	43	2	2	NUM
ejpam-4237	128	44	(	(	PUNCT
ejpam-4237	128	45	4	4	NUM
ejpam-4237	128	46	√	√	NOUN
ejpam-4237	128	47	−2φ	−2φ	PROPN
ejpam-4237	128	48	(	(	PUNCT
ejpam-4237	128	49	i	i	PROPN
ejpam-4237	128	50	,	,	PUNCT
ejpam-4237	128	51	1	1	NUM
ejpam-4237	128	52	,	,	PUNCT
ejpam-4237	128	53	π	π	PROPN
ejpam-4237	129	1	+	+	CCONJ
ejpam-4237	129	2	i	i	PRON
ejpam-4237	129	3	log(2	log(2	NOUN
ejpam-4237	129	4	)	)	PUNCT
ejpam-4237	129	5	2π	2π	NOUN
ejpam-4237	129	6	)	)	PUNCT
ejpam-4237	130	1	−	−	PROPN
ejpam-4237	130	2	iφ	iφ	NOUN
ejpam-4237	130	3	(	(	PUNCT
ejpam-4237	130	4	−1	−1	NOUN
ejpam-4237	130	5	,	,	PUNCT
ejpam-4237	130	6	1	1	NUM
ejpam-4237	130	7	,	,	PUNCT
ejpam-4237	130	8	π	π	PROPN
ejpam-4237	130	9	+	+	CCONJ
ejpam-4237	130	10	i	i	PRON
ejpam-4237	130	11	log(2	log(2	NOUN
ejpam-4237	130	12	)	)	PUNCT
ejpam-4237	130	13	2π	2π	NOUN
ejpam-4237	130	14	)	)	PUNCT
ejpam-4237	130	15	)	)	PUNCT
ejpam-4237	130	16	(	(	PUNCT
ejpam-4237	130	17	14	14	X
ejpam-4237	130	18	)	)	PUNCT
ejpam-4237	130	19	proof	proof	NOUN
ejpam-4237	130	20	.	.	PUNCT
ejpam-4237	131	1	use	use	VERB
ejpam-4237	131	2	equation	equation	NOUN
ejpam-4237	131	3	(	(	PUNCT
ejpam-4237	131	4	13	13	NUM
ejpam-4237	131	5	)	)	PUNCT
ejpam-4237	131	6	and	and	CCONJ
ejpam-4237	131	7	set	set	VERB
ejpam-4237	131	8	p	p	NOUN
ejpam-4237	131	9	=	=	SYM
ejpam-4237	131	10	1/2,m	1/2,m	NUM
ejpam-4237	131	11	=	=	SYM
ejpam-4237	131	12	1/4	1/4	NUM
ejpam-4237	131	13	and	and	CCONJ
ejpam-4237	131	14	simplify	simplify	NOUN
ejpam-4237	131	15	.	.	PUNCT
ejpam-4237	132	1	references	reference	NOUN
ejpam-4237	132	2	1119	1119	NUM
ejpam-4237	132	3	6	6	NUM
ejpam-4237	132	4	.	.	PUNCT
ejpam-4237	132	5	discussion	discussion	NOUN
ejpam-4237	132	6	in	in	ADP
ejpam-4237	132	7	this	this	DET
ejpam-4237	132	8	paper	paper	NOUN
ejpam-4237	132	9	,	,	PUNCT
ejpam-4237	132	10	we	we	PRON
ejpam-4237	132	11	have	have	AUX
ejpam-4237	132	12	presented	present	VERB
ejpam-4237	132	13	a	a	DET
ejpam-4237	132	14	novel	novel	ADJ
ejpam-4237	132	15	method	method	NOUN
ejpam-4237	132	16	for	for	ADP
ejpam-4237	132	17	deriving	derive	VERB
ejpam-4237	132	18	a	a	DET
ejpam-4237	132	19	new	new	ADJ
ejpam-4237	132	20	integral	integral	NOUN
ejpam-4237	132	21	involving	involve	VERB
ejpam-4237	132	22	the	the	DET
ejpam-4237	132	23	legendre	legendre	PROPN
ejpam-4237	132	24	polynomial	polynomial	ADJ
ejpam-4237	132	25	pn(x	pn(x	PUNCT
ejpam-4237	132	26	)	)	PUNCT
ejpam-4237	132	27	along	along	ADP
ejpam-4237	132	28	with	with	ADP
ejpam-4237	132	29	some	some	DET
ejpam-4237	132	30	interesting	interesting	ADJ
ejpam-4237	132	31	definite	definite	ADJ
ejpam-4237	132	32	integrals	integral	NOUN
ejpam-4237	132	33	using	use	VERB
ejpam-4237	132	34	contour	contour	NOUN
ejpam-4237	132	35	integration	integration	NOUN
ejpam-4237	132	36	.	.	PUNCT
ejpam-4237	133	1	the	the	DET
ejpam-4237	133	2	results	result	NOUN
ejpam-4237	133	3	presented	present	VERB
ejpam-4237	133	4	were	be	AUX
ejpam-4237	133	5	numerically	numerically	ADV
ejpam-4237	133	6	verified	verify	VERB
ejpam-4237	133	7	for	for	ADP
ejpam-4237	133	8	both	both	CCONJ
ejpam-4237	133	9	real	real	ADJ
ejpam-4237	133	10	and	and	CCONJ
ejpam-4237	133	11	imaginary	imaginary	ADJ
ejpam-4237	133	12	and	and	CCONJ
ejpam-4237	133	13	complex	complex	ADJ
ejpam-4237	133	14	values	value	NOUN
ejpam-4237	133	15	of	of	ADP
ejpam-4237	133	16	the	the	DET
ejpam-4237	133	17	parameters	parameter	NOUN
ejpam-4237	133	18	in	in	ADP
ejpam-4237	133	19	the	the	DET
ejpam-4237	133	20	integrals	integral	NOUN
ejpam-4237	133	21	using	use	VERB
ejpam-4237	133	22	mathematica	mathematica	PROPN
ejpam-4237	133	23	by	by	ADP
ejpam-4237	133	24	wolfram	wolfram	PROPN
ejpam-4237	133	25	.	.	PUNCT
ejpam-4237	134	1	references	reference	NOUN
ejpam-4237	134	2	[	[	X
ejpam-4237	134	3	1	1	NUM
ejpam-4237	134	4	]	]	PUNCT
ejpam-4237	134	5	nist	nist	NOUN
ejpam-4237	134	6	digital	digital	PROPN
ejpam-4237	134	7	library	library	NOUN
ejpam-4237	134	8	of	of	ADP
ejpam-4237	134	9	mathematical	mathematical	ADJ
ejpam-4237	134	10	functions	function	NOUN
ejpam-4237	134	11	.	.	PUNCT
ejpam-4237	135	1	f.	f.	PROPN
ejpam-4237	135	2	w.	w.	PROPN
ejpam-4237	135	3	j.	j.	PROPN
ejpam-4237	135	4	olver	olver	PROPN
ejpam-4237	135	5	,	,	PUNCT
ejpam-4237	135	6	a.	a.	PROPN
ejpam-4237	135	7	b.	b.	PROPN
ejpam-4237	135	8	olde	olde	PROPN
ejpam-4237	135	9	daalhuis	daalhuis	PROPN
ejpam-4237	135	10	,	,	PUNCT
ejpam-4237	135	11	d.	d.	PROPN
ejpam-4237	135	12	w.	w.	PROPN
ejpam-4237	135	13	lozier	lozier	PROPN
ejpam-4237	135	14	,	,	PUNCT
ejpam-4237	135	15	b.	b.	PROPN
ejpam-4237	135	16	i.	i.	PROPN
ejpam-4237	135	17	schneider	schneider	PROPN
ejpam-4237	135	18	,	,	PUNCT
ejpam-4237	135	19	r.	r.	PROPN
ejpam-4237	135	20	f.	f.	PROPN
ejpam-4237	135	21	boisvert	boisvert	PROPN
ejpam-4237	135	22	,	,	PUNCT
ejpam-4237	135	23	c.	c.	PROPN
ejpam-4237	135	24	w.	w.	PROPN
ejpam-4237	135	25	clark	clark	PROPN
ejpam-4237	135	26	,	,	PUNCT
ejpam-4237	135	27	b.	b.	PROPN
ejpam-4237	135	28	r.	r.	PROPN
ejpam-4237	135	29	miller	miller	PROPN
ejpam-4237	135	30	,	,	PUNCT
ejpam-4237	135	31	b.	b.	PROPN
ejpam-4237	136	1	v.	v.	PROPN
ejpam-4237	136	2	saunders	saunders	PROPN
ejpam-4237	136	3	,	,	PUNCT
ejpam-4237	136	4	h.	h.	PROPN
ejpam-4237	136	5	s.	s.	PROPN
ejpam-4237	136	6	cohl	cohl	PROPN
ejpam-4237	136	7	,	,	PUNCT
ejpam-4237	136	8	and	and	CCONJ
ejpam-4237	136	9	m.	m.	PROPN
ejpam-4237	136	10	a.	a.	PROPN
ejpam-4237	136	11	mcclain	mcclain	PROPN
ejpam-4237	136	12	,	,	PUNCT
ejpam-4237	136	13	eds	eds	PROPN
ejpam-4237	136	14	.	.	PUNCT
ejpam-4237	137	1	[	[	X
ejpam-4237	137	2	2	2	NUM
ejpam-4237	137	3	]	]	PUNCT
ejpam-4237	137	4	i.	i.	PROPN
ejpam-4237	137	5	s.	s.	PROPN
ejpam-4237	137	6	gradshteyn	gradshteyn	PROPN
ejpam-4237	137	7	and	and	CCONJ
ejpam-4237	137	8	i.	i.	PROPN
ejpam-4237	137	9	m.	m.	PROPN
ejpam-4237	137	10	ryzhik	ryzhik	PROPN
ejpam-4237	137	11	.	.	PUNCT
ejpam-4237	138	1	table	table	NOUN
ejpam-4237	138	2	of	of	ADP
ejpam-4237	138	3	integrals	integral	NOUN
ejpam-4237	138	4	,	,	PUNCT
ejpam-4237	138	5	series	series	NOUN
ejpam-4237	138	6	,	,	PUNCT
ejpam-4237	138	7	and	and	CCONJ
ejpam-4237	138	8	products	product	NOUN
ejpam-4237	138	9	.	.	PUNCT
ejpam-4237	139	1	elsevier	elsevier	NOUN
ejpam-4237	139	2	/	/	SYM
ejpam-4237	139	3	academic	academic	ADJ
ejpam-4237	139	4	press	press	NOUN
ejpam-4237	139	5	,	,	PUNCT
ejpam-4237	139	6	amsterdam	amsterdam	PROPN
ejpam-4237	139	7	,	,	PUNCT
ejpam-4237	139	8	seventh	seventh	ADJ
ejpam-4237	139	9	edition	edition	NOUN
ejpam-4237	139	10	,	,	PUNCT
ejpam-4237	139	11	2007	2007	NUM
ejpam-4237	139	12	.	.	PUNCT
ejpam-4237	140	1	[	[	X
ejpam-4237	140	2	3	3	NUM
ejpam-4237	140	3	]	]	X
ejpam-4237	140	4	iryna	iryna	NOUN
ejpam-4237	140	5	fedotova	fedotova	PROPN
ejpam-4237	140	6	nina	nina	PROPN
ejpam-4237	140	7	virchenko	virchenko	PROPN
ejpam-4237	140	8	.	.	PUNCT
ejpam-4237	141	1	generalized	generalize	VERB
ejpam-4237	141	2	associated	associated	PROPN
ejpam-4237	141	3	legendre	legendre	PROPN
ejpam-4237	141	4	functions	function	NOUN
ejpam-4237	141	5	and	and	CCONJ
ejpam-4237	141	6	their	their	PRON
ejpam-4237	141	7	applications	application	NOUN
ejpam-4237	141	8	.	.	PUNCT
ejpam-4237	142	1	world	world	NOUN
ejpam-4237	142	2	scientific	scientific	PROPN
ejpam-4237	142	3	,	,	PUNCT
ejpam-4237	142	4	national	national	PROPN
ejpam-4237	142	5	technical	technical	PROPN
ejpam-4237	142	6	university	university	PROPN
ejpam-4237	142	7	of	of	ADP
ejpam-4237	142	8	ukraine	ukraine	PROPN
ejpam-4237	142	9	,	,	PUNCT
ejpam-4237	142	10	singapore	singapore	PROPN
ejpam-4237	142	11	,	,	PUNCT
ejpam-4237	142	12	2001	2001	NUM
ejpam-4237	142	13	.	.	PUNCT
ejpam-4237	143	1	[	[	X
ejpam-4237	143	2	4	4	NUM
ejpam-4237	143	3	]	]	X
ejpam-4237	143	4	f.	f.	PROPN
ejpam-4237	143	5	oberhettinger	oberhettinger	PROPN
ejpam-4237	143	6	.	.	PUNCT
ejpam-4237	144	1	tables	table	NOUN
ejpam-4237	144	2	of	of	ADP
ejpam-4237	144	3	mellin	mellin	PROPN
ejpam-4237	144	4	transforms	transform	VERB
ejpam-4237	144	5	.	.	PUNCT
ejpam-4237	145	1	springer	springer	NOUN
ejpam-4237	145	2	-	-	PUNCT
ejpam-4237	145	3	verlag	verlag	PROPN
ejpam-4237	145	4	berlin	berlin	PROPN
ejpam-4237	145	5	heidelberg	heidelberg	PROPN
ejpam-4237	145	6	,	,	PUNCT
ejpam-4237	145	7	1974	1974	NUM
ejpam-4237	145	8	.	.	PUNCT
ejpam-4237	146	1	[	[	X
ejpam-4237	146	2	5	5	X
ejpam-4237	146	3	]	]	PUNCT
ejpam-4237	146	4	keith	keith	PROPN
ejpam-4237	146	5	b.	b.	PROPN
ejpam-4237	146	6	oldham	oldham	PROPN
ejpam-4237	146	7	,	,	PUNCT
ejpam-4237	146	8	jan	jan	PROPN
ejpam-4237	146	9	myland	myland	PROPN
ejpam-4237	146	10	,	,	PUNCT
ejpam-4237	146	11	and	and	CCONJ
ejpam-4237	146	12	jerome	jerome	PROPN
ejpam-4237	146	13	spanier	spanier	NOUN
ejpam-4237	146	14	.	.	PUNCT
ejpam-4237	147	1	an	an	DET
ejpam-4237	147	2	atlas	atlas	PROPN
ejpam-4237	147	3	of	of	ADP
ejpam-4237	147	4	functions	function	NOUN
ejpam-4237	147	5	:	:	PUNCT
ejpam-4237	147	6	with	with	ADP
ejpam-4237	147	7	equator	equator	NOUN
ejpam-4237	147	8	,	,	PUNCT
ejpam-4237	147	9	the	the	DET
ejpam-4237	147	10	atlas	atlas	PROPN
ejpam-4237	147	11	function	function	PROPN
ejpam-4237	147	12	calculator	calculator	NOUN
ejpam-4237	147	13	.	.	PUNCT
ejpam-4237	148	1	springer	springer	NOUN
ejpam-4237	148	2	science	science	PROPN
ejpam-4237	148	3	&	&	CCONJ
ejpam-4237	148	4	business	business	NOUN
ejpam-4237	148	5	media	medium	NOUN
ejpam-4237	148	6	,	,	PUNCT
ejpam-4237	148	7	07	07	NUM
ejpam-4237	148	8	2010	2010	NUM
ejpam-4237	148	9	.	.	PUNCT
ejpam-4237	149	1	[	[	X
ejpam-4237	149	2	6	6	NUM
ejpam-4237	149	3	]	]	X
ejpam-4237	149	4	robert	robert	PROPN
ejpam-4237	149	5	reynolds	reynolds	PROPN
ejpam-4237	149	6	and	and	CCONJ
ejpam-4237	149	7	allan	allan	PROPN
ejpam-4237	149	8	stauffer	stauffer	PROPN
ejpam-4237	149	9	.	.	PUNCT
ejpam-4237	150	1	a	a	DET
ejpam-4237	150	2	method	method	NOUN
ejpam-4237	150	3	for	for	ADP
ejpam-4237	150	4	evaluating	evaluate	VERB
ejpam-4237	150	5	definite	definite	ADJ
ejpam-4237	150	6	integrals	integral	NOUN
ejpam-4237	150	7	in	in	ADP
ejpam-4237	150	8	terms	term	NOUN
ejpam-4237	150	9	of	of	ADP
ejpam-4237	150	10	special	special	ADJ
ejpam-4237	150	11	functions	function	NOUN
ejpam-4237	150	12	with	with	ADP
ejpam-4237	150	13	examples	example	NOUN
ejpam-4237	150	14	.	.	PUNCT
ejpam-4237	151	1	international	international	ADJ
ejpam-4237	151	2	mathematical	mathematical	PROPN
ejpam-4237	151	3	forum	forum	PROPN
ejpam-4237	151	4	,	,	PUNCT
ejpam-4237	151	5	15:235	15:235	NUM
ejpam-4237	151	6	–	–	PUNCT
ejpam-4237	151	7	244	244	NUM
ejpam-4237	151	8	,	,	PUNCT
ejpam-4237	151	9	2020	2020	NUM
ejpam-4237	151	10	.	.	PUNCT