id	sid	tid	token	lemma	pos
ejpam-4242	1	1	european	european	PROPN
ejpam-4242	1	2	journal	journal	PROPN
ejpam-4242	1	3	of	of	ADP
ejpam-4242	1	4	pure	pure	ADJ
ejpam-4242	1	5	and	and	CCONJ
ejpam-4242	1	6	applied	apply	VERB
ejpam-4242	1	7	mathematics	mathematic	NOUN
ejpam-4242	1	8	vol	vol	NOUN
ejpam-4242	1	9	.	.	PROPN
ejpam-4242	2	1	15	15	NUM
ejpam-4242	2	2	,	,	PUNCT
ejpam-4242	2	3	no	no	INTJ
ejpam-4242	2	4	.	.	NOUN
ejpam-4242	2	5	1	1	NUM
ejpam-4242	2	6	,	,	PUNCT
ejpam-4242	2	7	2022	2022	NUM
ejpam-4242	2	8	,	,	PUNCT
ejpam-4242	2	9	100	100	NUM
ejpam-4242	2	10	-	-	SYM
ejpam-4242	2	11	105	105	NUM
ejpam-4242	2	12	issn	issn	PROPN
ejpam-4242	2	13	1307	1307	NUM
ejpam-4242	2	14	-	-	SYM
ejpam-4242	2	15	5543	5543	NUM
ejpam-4242	2	16	–	–	PUNCT
ejpam-4242	3	1	ejpam.com	ejpam.com	X
ejpam-4242	3	2	published	publish	VERB
ejpam-4242	3	3	by	by	ADP
ejpam-4242	3	4	new	new	PROPN
ejpam-4242	3	5	york	york	PROPN
ejpam-4242	3	6	business	business	PROPN
ejpam-4242	3	7	global	global	PROPN
ejpam-4242	3	8	a	a	DET
ejpam-4242	3	9	quadruple	quadruple	NOUN
ejpam-4242	3	10	integral	integral	ADJ
ejpam-4242	3	11	involving	involve	VERB
ejpam-4242	3	12	the	the	DET
ejpam-4242	3	13	hermite	hermite	ADJ
ejpam-4242	3	14	polynomial	polynomial	ADJ
ejpam-4242	3	15	hn(x	hn(x	NOUN
ejpam-4242	3	16	):	):	PUNCT
ejpam-4242	3	17	derivation	derivation	NOUN
ejpam-4242	3	18	and	and	CCONJ
ejpam-4242	3	19	evaluation	evaluation	NOUN
ejpam-4242	3	20	robert	robert	PROPN
ejpam-4242	3	21	reynolds1,∗	reynolds1,∗	PROPN
ejpam-4242	3	22	,	,	PUNCT
ejpam-4242	3	23	allan	allan	PROPN
ejpam-4242	3	24	stauffer1	stauffer1	PROPN
ejpam-4242	3	25	1	1	NUM
ejpam-4242	3	26	department	department	NOUN
ejpam-4242	3	27	of	of	ADP
ejpam-4242	3	28	mathematics	mathematic	NOUN
ejpam-4242	3	29	and	and	CCONJ
ejpam-4242	3	30	statistics	statistic	NOUN
ejpam-4242	3	31	,	,	PUNCT
ejpam-4242	3	32	faculty	faculty	NOUN
ejpam-4242	3	33	of	of	ADP
ejpam-4242	3	34	science	science	PROPN
ejpam-4242	3	35	,	,	PUNCT
ejpam-4242	3	36	york	york	PROPN
ejpam-4242	3	37	university	university	PROPN
ejpam-4242	3	38	,	,	PUNCT
ejpam-4242	3	39	toronto	toronto	PROPN
ejpam-4242	3	40	,	,	PUNCT
ejpam-4242	3	41	ontario	ontario	PROPN
ejpam-4242	3	42	,	,	PUNCT
ejpam-4242	3	43	canada	canada	PROPN
ejpam-4242	3	44	,	,	PUNCT
ejpam-4242	3	45	m3j1p3	m3j1p3	PROPN
ejpam-4242	3	46	abstract	abstract	NOUN
ejpam-4242	3	47	.	.	PUNCT
ejpam-4242	4	1	a	a	DET
ejpam-4242	4	2	closed	closed	ADJ
ejpam-4242	4	3	form	form	NOUN
ejpam-4242	4	4	expression	expression	NOUN
ejpam-4242	4	5	of	of	ADP
ejpam-4242	4	6	a	a	DET
ejpam-4242	4	7	quadruple	quadruple	NOUN
ejpam-4242	4	8	integral	integral	ADJ
ejpam-4242	4	9	involving	involve	VERB
ejpam-4242	4	10	the	the	DET
ejpam-4242	4	11	hermite	hermite	ADJ
ejpam-4242	4	12	polynomial	polynomial	NOUN
ejpam-4242	4	13	hn(x	hn(x	X
ejpam-4242	4	14	)	)	PUNCT
ejpam-4242	4	15	is	be	AUX
ejpam-4242	4	16	derived	derive	VERB
ejpam-4242	4	17	.	.	PUNCT
ejpam-4242	5	1	special	special	ADJ
ejpam-4242	5	2	cases	case	NOUN
ejpam-4242	5	3	are	be	AUX
ejpam-4242	5	4	expressed	express	VERB
ejpam-4242	5	5	in	in	ADP
ejpam-4242	5	6	terms	term	NOUN
ejpam-4242	5	7	of	of	ADP
ejpam-4242	5	8	special	special	ADJ
ejpam-4242	5	9	functions	function	NOUN
ejpam-4242	5	10	and	and	CCONJ
ejpam-4242	5	11	fundamental	fundamental	ADJ
ejpam-4242	5	12	constants	constant	NOUN
ejpam-4242	5	13	.	.	PUNCT
ejpam-4242	6	1	all	all	DET
ejpam-4242	6	2	the	the	DET
ejpam-4242	6	3	results	result	NOUN
ejpam-4242	6	4	in	in	ADP
ejpam-4242	6	5	this	this	DET
ejpam-4242	6	6	work	work	NOUN
ejpam-4242	6	7	are	be	AUX
ejpam-4242	6	8	new	new	ADJ
ejpam-4242	6	9	.	.	PUNCT
ejpam-4242	7	1	2020	2020	NUM
ejpam-4242	7	2	mathematics	mathematic	NOUN
ejpam-4242	7	3	subject	subject	NOUN
ejpam-4242	7	4	classifications	classification	NOUN
ejpam-4242	7	5	:	:	PUNCT
ejpam-4242	7	6	30e20	30e20	NUM
ejpam-4242	7	7	,	,	PUNCT
ejpam-4242	7	8	33	33	NUM
ejpam-4242	7	9	-	-	SYM
ejpam-4242	7	10	01	01	NUM
ejpam-4242	7	11	,	,	PUNCT
ejpam-4242	7	12	33	33	NUM
ejpam-4242	7	13	-	-	SYM
ejpam-4242	7	14	03	03	NUM
ejpam-4242	7	15	,	,	PUNCT
ejpam-4242	7	16	33	33	NUM
ejpam-4242	7	17	-	-	PUNCT
ejpam-4242	7	18	04	04	NUM
ejpam-4242	7	19	,	,	PUNCT
ejpam-4242	7	20	33	33	NUM
ejpam-4242	7	21	-	-	PUNCT
ejpam-4242	7	22	33b	33b	NUM
ejpam-4242	7	23	key	key	ADJ
ejpam-4242	7	24	words	word	NOUN
ejpam-4242	7	25	and	and	CCONJ
ejpam-4242	7	26	phrases	phrase	NOUN
ejpam-4242	7	27	:	:	PUNCT
ejpam-4242	7	28	hermite	hermite	ADJ
ejpam-4242	7	29	polynomial	polynomial	ADJ
ejpam-4242	7	30	,	,	PUNCT
ejpam-4242	7	31	quadruple	quadruple	NOUN
ejpam-4242	7	32	integral	integral	ADJ
ejpam-4242	7	33	,	,	PUNCT
ejpam-4242	7	34	hurwitz	hurwitz	PROPN
ejpam-4242	7	35	-	-	PUNCT
ejpam-4242	7	36	lerch	lerch	PROPN
ejpam-4242	7	37	zeta	zeta	PROPN
ejpam-4242	7	38	function	function	PROPN
ejpam-4242	7	39	,	,	PUNCT
ejpam-4242	7	40	cauchy	cauchy	ADJ
ejpam-4242	7	41	integral	integral	ADJ
ejpam-4242	7	42	formula	formula	NOUN
ejpam-4242	7	43	1	1	NUM
ejpam-4242	7	44	.	.	PUNCT
ejpam-4242	7	45	significance	significance	NOUN
ejpam-4242	7	46	statement	statement	NOUN
ejpam-4242	7	47	named	name	VERB
ejpam-4242	7	48	for	for	ADP
ejpam-4242	7	49	the	the	DET
ejpam-4242	7	50	frenchman	frenchman	NOUN
ejpam-4242	7	51	,	,	PUNCT
ejpam-4242	7	52	charles	charles	PROPN
ejpam-4242	7	53	hermite	hermite	ADJ
ejpam-4242	7	54	(	(	PUNCT
ejpam-4242	7	55	1822	1822	NUM
ejpam-4242	7	56	-	-	SYM
ejpam-4242	7	57	1901	1901	NUM
ejpam-4242	7	58	)	)	PUNCT
ejpam-4242	7	59	these	these	DET
ejpam-4242	7	60	polynomials	polynomial	NOUN
ejpam-4242	7	61	are	be	AUX
ejpam-4242	7	62	orthogonal	orthogonal	ADJ
ejpam-4242	7	63	on	on	ADP
ejpam-4242	7	64	the	the	DET
ejpam-4242	7	65	infinite	infinite	ADJ
ejpam-4242	7	66	interval	interval	NOUN
ejpam-4242	7	67	−∞	−∞	ADP
ejpam-4242	7	68	<	<	X
ejpam-4242	7	69	x	x	X
ejpam-4242	7	70	<	<	X
ejpam-4242	7	71	∞	∞	PROPN
ejpam-4242	7	72	with	with	ADP
ejpam-4242	7	73	a	a	DET
ejpam-4242	7	74	weight	weight	NOUN
ejpam-4242	7	75	function	function	NOUN
ejpam-4242	7	76	of	of	ADP
ejpam-4242	7	77	e−x2	e−x2	NOUN
ejpam-4242	7	78	.	.	PUNCT
ejpam-4242	8	1	they	they	PRON
ejpam-4242	8	2	arise	arise	VERB
ejpam-4242	8	3	in	in	ADP
ejpam-4242	8	4	physics	physics	NOUN
ejpam-4242	8	5	,	,	PUNCT
ejpam-4242	8	6	as	as	ADP
ejpam-4242	8	7	in	in	ADP
ejpam-4242	8	8	the	the	DET
ejpam-4242	8	9	solution	solution	NOUN
ejpam-4242	8	10	of	of	ADP
ejpam-4242	8	11	schrödinger	schrödinger	NOUN
ejpam-4242	8	12	’s	’s	PART
ejpam-4242	8	13	differential	differential	ADJ
ejpam-4242	8	14	equation	equation	NOUN
ejpam-4242	8	15	for	for	ADP
ejpam-4242	8	16	a	a	DET
ejpam-4242	8	17	simple	simple	ADJ
ejpam-4242	8	18	harmonic	harmonic	ADJ
ejpam-4242	8	19	oscillator	oscillator	NOUN
ejpam-4242	8	20	,	,	PUNCT
ejpam-4242	8	21	which	which	PRON
ejpam-4242	8	22	belongs	belong	VERB
ejpam-4242	8	23	to	to	ADP
ejpam-4242	8	24	a	a	DET
ejpam-4242	8	25	broad	broad	ADJ
ejpam-4242	8	26	class	class	NOUN
ejpam-4242	8	27	of	of	ADP
ejpam-4242	8	28	second	second	ADJ
ejpam-4242	8	29	order	order	NOUN
ejpam-4242	8	30	differential	differential	ADJ
ejpam-4242	8	31	equations	equation	NOUN
ejpam-4242	8	32	[	[	X
ejpam-4242	8	33	4	4	NUM
ejpam-4242	8	34	]	]	PUNCT
ejpam-4242	8	35	.	.	PUNCT
ejpam-4242	9	1	in	in	ADP
ejpam-4242	9	2	this	this	DET
ejpam-4242	9	3	present	present	ADJ
ejpam-4242	9	4	work	work	NOUN
ejpam-4242	9	5	we	we	PRON
ejpam-4242	9	6	investigate	investigate	VERB
ejpam-4242	9	7	the	the	DET
ejpam-4242	9	8	quadruple	quadruple	NOUN
ejpam-4242	9	9	integral	integral	ADJ
ejpam-4242	9	10	involving	involve	VERB
ejpam-4242	9	11	the	the	DET
ejpam-4242	9	12	hermite	hermite	ADJ
ejpam-4242	9	13	polynomial	polynomial	NOUN
ejpam-4242	9	14	hn(x	hn(x	ADP
ejpam-4242	9	15	)	)	PUNCT
ejpam-4242	9	16	and	and	CCONJ
ejpam-4242	9	17	the	the	DET
ejpam-4242	9	18	parameter	parameter	NOUN
ejpam-4242	9	19	n	n	PRON
ejpam-4242	9	20	dependence	dependence	NOUN
ejpam-4242	9	21	on	on	ADP
ejpam-4242	9	22	a	a	DET
ejpam-4242	9	23	constant	constant	ADJ
ejpam-4242	9	24	factor	factor	NOUN
ejpam-4242	9	25	raised	raise	VERB
ejpam-4242	9	26	to	to	ADP
ejpam-4242	9	27	a	a	DET
ejpam-4242	9	28	power	power	NOUN
ejpam-4242	9	29	and	and	CCONJ
ejpam-4242	9	30	its	its	PRON
ejpam-4242	9	31	invariance	invariance	NOUN
ejpam-4242	9	32	with	with	ADP
ejpam-4242	9	33	respect	respect	NOUN
ejpam-4242	9	34	to	to	ADP
ejpam-4242	9	35	the	the	DET
ejpam-4242	9	36	hurwitz	hurwitz	PROPN
ejpam-4242	9	37	-	-	PUNCT
ejpam-4242	9	38	lerch	lerch	PROPN
ejpam-4242	9	39	zeta	zeta	PROPN
ejpam-4242	9	40	function	function	PROPN
ejpam-4242	9	41	.	.	PUNCT
ejpam-4242	10	1	2	2	X
ejpam-4242	10	2	.	.	X
ejpam-4242	10	3	introduction	introduction	NOUN
ejpam-4242	10	4	in	in	ADP
ejpam-4242	10	5	this	this	DET
ejpam-4242	10	6	paper	paper	NOUN
ejpam-4242	10	7	we	we	PRON
ejpam-4242	10	8	derive	derive	VERB
ejpam-4242	10	9	the	the	DET
ejpam-4242	10	10	quadruple	quadruple	ADJ
ejpam-4242	10	11	definite	definite	ADJ
ejpam-4242	10	12	integral	integral	ADJ
ejpam-4242	10	13	given	give	VERB
ejpam-4242	10	14	by	by	ADP
ejpam-4242	10	15	(	(	PUNCT
ejpam-4242	10	16	1	1	NUM
ejpam-4242	10	17	)	)	PUNCT
ejpam-4242	10	18	∫	∫	PROPN
ejpam-4242	10	19	∞	∞	PROPN
ejpam-4242	10	20	0	0	NUM
ejpam-4242	11	1	∫	∫	PROPN
ejpam-4242	11	2	∞	∞	PROPN
ejpam-4242	11	3	0	0	NUM
ejpam-4242	12	1	∫	∫	PROPN
ejpam-4242	12	2	∞	∞	PROPN
ejpam-4242	12	3	0	0	NUM
ejpam-4242	13	1	∫	∫	PROPN
ejpam-4242	13	2	∞	∞	NUM
ejpam-4242	13	3	0	0	NUM
ejpam-4242	14	1	t−mxm−1z1−mym−nhn(xα)e	t−mxm−1z1−mym−nhn(xα)e	NUM
ejpam-4242	14	2	−α2x2−b	−α2x2−b	X
ejpam-4242	14	3	(	(	PUNCT
ejpam-4242	14	4	t2+y2+z2	t2+y2+z2	PROPN
ejpam-4242	14	5	)	)	PUNCT
ejpam-4242	14	6	logk	logk	NOUN
ejpam-4242	14	7	(	(	PUNCT
ejpam-4242	14	8	axy	axy	PROPN
ejpam-4242	14	9	tz	tz	PROPN
ejpam-4242	14	10	)	)	PUNCT
ejpam-4242	14	11	dxdydzdt	dxdydzdt	PROPN
ejpam-4242	14	12	∗corresponding	∗corresponde	VERB
ejpam-4242	14	13	author	author	NOUN
ejpam-4242	14	14	.	.	PUNCT
ejpam-4242	15	1	doi	doi	PROPN
ejpam-4242	15	2	:	:	PUNCT
ejpam-4242	15	3	https://doi.org/10.29020/nybg.ejpam.v15i1.4242	https://doi.org/10.29020/nybg.ejpam.v15i1.4242	PROPN
ejpam-4242	15	4	email	email	NOUN
ejpam-4242	15	5	addresses	address	NOUN
ejpam-4242	15	6	:	:	PUNCT
ejpam-4242	16	1	milver@my.yorku.ca	milver@my.yorku.ca	NOUN
ejpam-4242	16	2	(	(	PUNCT
ejpam-4242	16	3	r.	r.	PROPN
ejpam-4242	16	4	reynolds	reynolds	PROPN
ejpam-4242	16	5	)	)	PUNCT
ejpam-4242	16	6	,	,	PUNCT
ejpam-4242	16	7	stauffer@yorku.ca	stauffer@yorku.ca	NOUN
ejpam-4242	16	8	(	(	PUNCT
ejpam-4242	16	9	a.	a.	NOUN
ejpam-4242	16	10	stauffer	stauffer	PROPN
ejpam-4242	16	11	)	)	PUNCT
ejpam-4242	16	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4242	17	1	100	100	NUM
ejpam-4242	18	1	©	©	ADP
ejpam-4242	18	2	2022	2022	NUM
ejpam-4242	18	3	ejpam	ejpam	VERB
ejpam-4242	18	4	all	all	DET
ejpam-4242	18	5	rights	right	NOUN
ejpam-4242	18	6	reserved	reserve	VERB
ejpam-4242	18	7	.	.	PUNCT
ejpam-4242	19	1	r.	r.	PROPN
ejpam-4242	19	2	reynolds	reynolds	PROPN
ejpam-4242	19	3	,	,	PUNCT
ejpam-4242	19	4	a.	a.	PROPN
ejpam-4242	19	5	stauffer	stauffer	PROPN
ejpam-4242	19	6	/	/	SYM
ejpam-4242	19	7	eur	eur	PROPN
ejpam-4242	19	8	.	.	PUNCT
ejpam-4242	20	1	j.	j.	PROPN
ejpam-4242	20	2	pure	pure	PROPN
ejpam-4242	20	3	appl	appl	PROPN
ejpam-4242	20	4	.	.	PROPN
ejpam-4242	20	5	math	math	PROPN
ejpam-4242	20	6	,	,	PUNCT
ejpam-4242	20	7	15	15	NUM
ejpam-4242	20	8	(	(	PUNCT
ejpam-4242	20	9	1	1	NUM
ejpam-4242	20	10	)	)	PUNCT
ejpam-4242	20	11	(	(	PUNCT
ejpam-4242	20	12	2022	2022	NUM
ejpam-4242	20	13	)	)	PUNCT
ejpam-4242	20	14	,	,	PUNCT
ejpam-4242	20	15	100	100	NUM
ejpam-4242	20	16	-	-	SYM
ejpam-4242	20	17	105	105	NUM
ejpam-4242	20	18	101	101	NUM
ejpam-4242	20	19	where	where	SCONJ
ejpam-4242	20	20	the	the	DET
ejpam-4242	20	21	parameters	parameter	NOUN
ejpam-4242	20	22	k	k	PROPN
ejpam-4242	20	23	,	,	PUNCT
ejpam-4242	20	24	a	a	PRON
ejpam-4242	20	25	,	,	PUNCT
ejpam-4242	20	26	n	n	CCONJ
ejpam-4242	20	27	,	,	PUNCT
ejpam-4242	20	28	m	m	VERB
ejpam-4242	20	29	are	be	AUX
ejpam-4242	20	30	general	general	ADJ
ejpam-4242	20	31	complex	complex	ADJ
ejpam-4242	20	32	numbers	number	NOUN
ejpam-4242	20	33	and	and	CCONJ
ejpam-4242	20	34	re(n	re(n	NUM
ejpam-4242	20	35	)	)	PUNCT
ejpam-4242	20	36	<	<	X
ejpam-4242	20	37	re(m	re(m	NUM
ejpam-4242	20	38	)	)	PUNCT
ejpam-4242	20	39	.	.	PUNCT
ejpam-4242	21	1	this	this	DET
ejpam-4242	21	2	definite	definite	ADJ
ejpam-4242	21	3	integral	integral	ADJ
ejpam-4242	21	4	will	will	AUX
ejpam-4242	21	5	be	be	AUX
ejpam-4242	21	6	used	use	VERB
ejpam-4242	21	7	to	to	PART
ejpam-4242	21	8	derive	derive	VERB
ejpam-4242	21	9	special	special	ADJ
ejpam-4242	21	10	cases	case	NOUN
ejpam-4242	21	11	in	in	ADP
ejpam-4242	21	12	terms	term	NOUN
ejpam-4242	21	13	of	of	ADP
ejpam-4242	21	14	special	special	ADJ
ejpam-4242	21	15	functions	function	NOUN
ejpam-4242	21	16	and	and	CCONJ
ejpam-4242	21	17	fundamental	fundamental	ADJ
ejpam-4242	21	18	constants	constant	NOUN
ejpam-4242	21	19	.	.	PUNCT
ejpam-4242	22	1	the	the	DET
ejpam-4242	22	2	derivations	derivation	NOUN
ejpam-4242	22	3	follow	follow	VERB
ejpam-4242	22	4	the	the	DET
ejpam-4242	22	5	method	method	NOUN
ejpam-4242	22	6	used	use	VERB
ejpam-4242	22	7	by	by	ADP
ejpam-4242	22	8	us	we	PRON
ejpam-4242	22	9	in	in	ADP
ejpam-4242	22	10	[	[	X
ejpam-4242	22	11	5	5	NUM
ejpam-4242	22	12	]	]	PUNCT
ejpam-4242	22	13	.	.	PUNCT
ejpam-4242	23	1	this	this	DET
ejpam-4242	23	2	method	method	NOUN
ejpam-4242	23	3	involves	involve	VERB
ejpam-4242	23	4	using	use	VERB
ejpam-4242	23	5	a	a	DET
ejpam-4242	23	6	form	form	NOUN
ejpam-4242	23	7	of	of	ADP
ejpam-4242	23	8	the	the	DET
ejpam-4242	23	9	generalized	generalize	VERB
ejpam-4242	23	10	cauchy	cauchy	PROPN
ejpam-4242	23	11	’s	’s	PART
ejpam-4242	23	12	integral	integral	ADJ
ejpam-4242	23	13	formula	formula	NOUN
ejpam-4242	23	14	given	give	VERB
ejpam-4242	23	15	by	by	ADP
ejpam-4242	23	16	yk	yk	PROPN
ejpam-4242	23	17	γ(k	γ(k	PROPN
ejpam-4242	23	18	+	+	CCONJ
ejpam-4242	23	19	1	1	X
ejpam-4242	23	20	)	)	PUNCT
ejpam-4242	23	21	=	=	SYM
ejpam-4242	23	22	1	1	NUM
ejpam-4242	23	23	2πi	2πi	ADJ
ejpam-4242	23	24	∫	∫	PROPN
ejpam-4242	23	25	c	c	PROPN
ejpam-4242	23	26	ewy	ewy	PROPN
ejpam-4242	23	27	wk+1	wk+1	PROPN
ejpam-4242	23	28	dw	dw	PROPN
ejpam-4242	23	29	.	.	PUNCT
ejpam-4242	24	1	(	(	PUNCT
ejpam-4242	24	2	2	2	X
ejpam-4242	24	3	)	)	PUNCT
ejpam-4242	24	4	where	where	SCONJ
ejpam-4242	24	5	c	c	NOUN
ejpam-4242	24	6	is	be	AUX
ejpam-4242	24	7	in	in	ADP
ejpam-4242	24	8	general	general	ADJ
ejpam-4242	24	9	an	an	DET
ejpam-4242	24	10	open	open	ADJ
ejpam-4242	24	11	contour	contour	NOUN
ejpam-4242	24	12	in	in	ADP
ejpam-4242	24	13	the	the	DET
ejpam-4242	24	14	complex	complex	ADJ
ejpam-4242	24	15	plane	plane	NOUN
ejpam-4242	24	16	where	where	SCONJ
ejpam-4242	24	17	the	the	DET
ejpam-4242	24	18	bilinear	bilinear	NOUN
ejpam-4242	24	19	concomitant	concomitant	NOUN
ejpam-4242	24	20	has	have	VERB
ejpam-4242	24	21	the	the	DET
ejpam-4242	24	22	same	same	ADJ
ejpam-4242	24	23	value	value	NOUN
ejpam-4242	24	24	at	at	ADP
ejpam-4242	24	25	the	the	DET
ejpam-4242	24	26	end	end	NOUN
ejpam-4242	24	27	points	point	NOUN
ejpam-4242	24	28	of	of	ADP
ejpam-4242	24	29	the	the	DET
ejpam-4242	24	30	contour	contour	NOUN
ejpam-4242	24	31	.	.	PUNCT
ejpam-4242	25	1	we	we	PRON
ejpam-4242	25	2	then	then	ADV
ejpam-4242	25	3	multiply	multiply	VERB
ejpam-4242	25	4	both	both	DET
ejpam-4242	25	5	sides	side	NOUN
ejpam-4242	25	6	by	by	ADP
ejpam-4242	25	7	a	a	DET
ejpam-4242	25	8	function	function	NOUN
ejpam-4242	25	9	of	of	ADP
ejpam-4242	25	10	x	x	PROPN
ejpam-4242	25	11	,	,	PUNCT
ejpam-4242	25	12	y	y	PROPN
ejpam-4242	25	13	,	,	PUNCT
ejpam-4242	25	14	z	z	PROPN
ejpam-4242	25	15	and	and	CCONJ
ejpam-4242	25	16	t	t	PROPN
ejpam-4242	25	17	,	,	PUNCT
ejpam-4242	25	18	then	then	ADV
ejpam-4242	25	19	take	take	VERB
ejpam-4242	25	20	a	a	DET
ejpam-4242	25	21	definite	definite	ADJ
ejpam-4242	25	22	quadruple	quadruple	NOUN
ejpam-4242	25	23	integral	integral	ADJ
ejpam-4242	25	24	of	of	ADP
ejpam-4242	25	25	both	both	DET
ejpam-4242	25	26	sides	side	NOUN
ejpam-4242	25	27	.	.	PUNCT
ejpam-4242	26	1	this	this	PRON
ejpam-4242	26	2	yields	yield	VERB
ejpam-4242	26	3	a	a	DET
ejpam-4242	26	4	definite	definite	ADJ
ejpam-4242	26	5	integral	integral	ADJ
ejpam-4242	26	6	in	in	ADP
ejpam-4242	26	7	terms	term	NOUN
ejpam-4242	26	8	of	of	ADP
ejpam-4242	26	9	a	a	DET
ejpam-4242	26	10	contour	contour	NOUN
ejpam-4242	26	11	integral	integral	NOUN
ejpam-4242	26	12	.	.	PUNCT
ejpam-4242	27	1	then	then	ADV
ejpam-4242	27	2	we	we	PRON
ejpam-4242	27	3	multiply	multiply	VERB
ejpam-4242	27	4	both	both	DET
ejpam-4242	27	5	sides	side	NOUN
ejpam-4242	27	6	of	of	ADP
ejpam-4242	27	7	equation	equation	NOUN
ejpam-4242	27	8	(	(	PUNCT
ejpam-4242	27	9	2	2	NUM
ejpam-4242	27	10	)	)	PUNCT
ejpam-4242	27	11	by	by	ADP
ejpam-4242	27	12	another	another	DET
ejpam-4242	27	13	function	function	NOUN
ejpam-4242	27	14	of	of	ADP
ejpam-4242	27	15	x	x	PROPN
ejpam-4242	27	16	,	,	PUNCT
ejpam-4242	27	17	y	y	PROPN
ejpam-4242	27	18	,	,	PUNCT
ejpam-4242	27	19	z	z	PROPN
ejpam-4242	27	20	and	and	CCONJ
ejpam-4242	27	21	t	t	PROPN
ejpam-4242	27	22	and	and	CCONJ
ejpam-4242	27	23	take	take	VERB
ejpam-4242	27	24	the	the	DET
ejpam-4242	27	25	infinite	infinite	ADJ
ejpam-4242	27	26	sums	sum	NOUN
ejpam-4242	27	27	of	of	ADP
ejpam-4242	27	28	both	both	DET
ejpam-4242	27	29	sides	side	NOUN
ejpam-4242	27	30	such	such	ADJ
ejpam-4242	27	31	that	that	SCONJ
ejpam-4242	27	32	the	the	DET
ejpam-4242	27	33	contour	contour	NOUN
ejpam-4242	27	34	integral	integral	NOUN
ejpam-4242	27	35	of	of	ADP
ejpam-4242	27	36	both	both	DET
ejpam-4242	27	37	equations	equation	NOUN
ejpam-4242	27	38	are	be	AUX
ejpam-4242	27	39	the	the	DET
ejpam-4242	27	40	same	same	ADJ
ejpam-4242	27	41	.	.	PUNCT
ejpam-4242	28	1	3	3	X
ejpam-4242	28	2	.	.	X
ejpam-4242	28	3	definite	definite	ADJ
ejpam-4242	28	4	integral	integral	ADJ
ejpam-4242	28	5	of	of	ADP
ejpam-4242	28	6	the	the	DET
ejpam-4242	28	7	contour	contour	NOUN
ejpam-4242	28	8	integral	integral	NOUN
ejpam-4242	28	9	we	we	PRON
ejpam-4242	28	10	use	use	VERB
ejpam-4242	28	11	the	the	DET
ejpam-4242	28	12	method	method	NOUN
ejpam-4242	28	13	in	in	ADP
ejpam-4242	28	14	[	[	X
ejpam-4242	28	15	5	5	NUM
ejpam-4242	28	16	]	]	PUNCT
ejpam-4242	28	17	.	.	PUNCT
ejpam-4242	29	1	the	the	DET
ejpam-4242	29	2	variable	variable	NOUN
ejpam-4242	29	3	of	of	ADP
ejpam-4242	29	4	integration	integration	NOUN
ejpam-4242	29	5	in	in	ADP
ejpam-4242	29	6	the	the	DET
ejpam-4242	29	7	contour	contour	NOUN
ejpam-4242	29	8	integral	integral	NOUN
ejpam-4242	29	9	is	be	AUX
ejpam-4242	29	10	u	u	NOUN
ejpam-4242	29	11	=	=	PROPN
ejpam-4242	29	12	w+m	w+m	PROPN
ejpam-4242	29	13	.	.	PUNCT
ejpam-4242	30	1	the	the	DET
ejpam-4242	30	2	cut	cut	NOUN
ejpam-4242	30	3	and	and	CCONJ
ejpam-4242	30	4	contour	contour	NOUN
ejpam-4242	30	5	are	be	AUX
ejpam-4242	30	6	in	in	ADP
ejpam-4242	30	7	the	the	DET
ejpam-4242	30	8	first	first	ADJ
ejpam-4242	30	9	quadrant	quadrant	NOUN
ejpam-4242	30	10	of	of	ADP
ejpam-4242	30	11	the	the	DET
ejpam-4242	30	12	complex	complex	ADJ
ejpam-4242	30	13	u	u	NOUN
ejpam-4242	30	14	-	-	NOUN
ejpam-4242	30	15	plane	plane	NOUN
ejpam-4242	30	16	.	.	PUNCT
ejpam-4242	31	1	the	the	DET
ejpam-4242	31	2	cut	cut	NOUN
ejpam-4242	31	3	approaches	approach	VERB
ejpam-4242	31	4	the	the	DET
ejpam-4242	31	5	origin	origin	NOUN
ejpam-4242	31	6	from	from	ADP
ejpam-4242	31	7	the	the	DET
ejpam-4242	31	8	interior	interior	NOUN
ejpam-4242	31	9	of	of	ADP
ejpam-4242	31	10	the	the	DET
ejpam-4242	31	11	first	first	ADJ
ejpam-4242	31	12	quadrant	quadrant	NOUN
ejpam-4242	31	13	and	and	CCONJ
ejpam-4242	31	14	the	the	DET
ejpam-4242	31	15	contour	contour	NOUN
ejpam-4242	31	16	goes	go	VERB
ejpam-4242	31	17	round	round	ADP
ejpam-4242	31	18	the	the	DET
ejpam-4242	31	19	origin	origin	NOUN
ejpam-4242	31	20	with	with	ADP
ejpam-4242	31	21	zero	zero	NUM
ejpam-4242	31	22	radius	radius	NOUN
ejpam-4242	31	23	and	and	CCONJ
ejpam-4242	31	24	is	be	AUX
ejpam-4242	31	25	on	on	ADP
ejpam-4242	31	26	opposite	opposite	ADJ
ejpam-4242	31	27	sides	side	NOUN
ejpam-4242	31	28	of	of	ADP
ejpam-4242	31	29	the	the	DET
ejpam-4242	31	30	cut	cut	NOUN
ejpam-4242	31	31	.	.	PUNCT
ejpam-4242	32	1	using	use	VERB
ejpam-4242	32	2	a	a	DET
ejpam-4242	32	3	generalization	generalization	NOUN
ejpam-4242	32	4	of	of	ADP
ejpam-4242	32	5	cauchy	cauchy	PROPN
ejpam-4242	32	6	’s	’s	PART
ejpam-4242	32	7	integral	integral	ADJ
ejpam-4242	32	8	formula	formula	NOUN
ejpam-4242	32	9	we	we	PRON
ejpam-4242	32	10	form	form	VERB
ejpam-4242	32	11	the	the	DET
ejpam-4242	32	12	triple	triple	ADJ
ejpam-4242	32	13	integral	integral	ADJ
ejpam-4242	32	14	by	by	ADP
ejpam-4242	32	15	replacing	replace	VERB
ejpam-4242	32	16	y	y	PRON
ejpam-4242	32	17	by	by	ADP
ejpam-4242	32	18	log	log	NOUN
ejpam-4242	32	19	(	(	PUNCT
ejpam-4242	32	20	axy	axy	PROPN
ejpam-4242	32	21	tz	tz	PROPN
ejpam-4242	32	22	)	)	PUNCT
ejpam-4242	32	23	and	and	CCONJ
ejpam-4242	32	24	multiplying	multiply	VERB
ejpam-4242	32	25	by	by	ADP
ejpam-4242	32	26	t−mxm−1z1−mym−nhn(xα)e	t−mxm−1z1−mym−nhn(xα)e	NUM
ejpam-4242	32	27	α2	α2	PROPN
ejpam-4242	32	28	(	(	PUNCT
ejpam-4242	32	29	−x2	−x2	PROPN
ejpam-4242	32	30	)	)	PUNCT
ejpam-4242	32	31	−b	−b	ADV
ejpam-4242	32	32	(	(	PUNCT
ejpam-4242	32	33	t2+y2+z2	t2+y2+z2	PROPN
ejpam-4242	32	34	)	)	PUNCT
ejpam-4242	32	35	then	then	ADV
ejpam-4242	32	36	taking	take	VERB
ejpam-4242	32	37	the	the	DET
ejpam-4242	32	38	definite	definite	ADJ
ejpam-4242	32	39	integral	integral	ADJ
ejpam-4242	32	40	with	with	ADP
ejpam-4242	32	41	respect	respect	NOUN
ejpam-4242	32	42	to	to	ADP
ejpam-4242	32	43	x	x	PUNCT
ejpam-4242	32	44	∈	∈	PROPN
ejpam-4242	33	1	[	[	X
ejpam-4242	33	2	0,∞	0,∞	NOUN
ejpam-4242	33	3	)	)	PUNCT
ejpam-4242	33	4	,	,	PUNCT
ejpam-4242	33	5	y	y	PROPN
ejpam-4242	33	6	∈	∈	PROPN
ejpam-4242	34	1	[	[	X
ejpam-4242	34	2	0,∞	0,∞	NOUN
ejpam-4242	34	3	)	)	PUNCT
ejpam-4242	34	4	,	,	PUNCT
ejpam-4242	34	5	z	z	NOUN
ejpam-4242	34	6	∈	∈	PROPN
ejpam-4242	35	1	[	[	X
ejpam-4242	35	2	0,∞	0,∞	NUM
ejpam-4242	35	3	)	)	PUNCT
ejpam-4242	35	4	and	and	CCONJ
ejpam-4242	35	5	t	t	NOUN
ejpam-4242	35	6	∈	∈	PROPN
ejpam-4242	36	1	[	[	X
ejpam-4242	36	2	0,∞	0,∞	NOUN
ejpam-4242	36	3	)	)	PUNCT
ejpam-4242	36	4	to	to	PART
ejpam-4242	36	5	obtain	obtain	VERB
ejpam-4242	36	6	(	(	PUNCT
ejpam-4242	36	7	3	3	NUM
ejpam-4242	36	8	)	)	SYM
ejpam-4242	36	9	1	1	NUM
ejpam-4242	36	10	γ(k	γ(k	NOUN
ejpam-4242	36	11	+	+	CCONJ
ejpam-4242	36	12	1	1	X
ejpam-4242	36	13	)	)	PUNCT
ejpam-4242	36	14	∫	∫	PROPN
ejpam-4242	37	1	∞	∞	PROPN
ejpam-4242	37	2	0	0	NUM
ejpam-4242	38	1	∫	∫	PROPN
ejpam-4242	38	2	∞	∞	PROPN
ejpam-4242	38	3	0	0	NUM
ejpam-4242	39	1	∫	∫	PROPN
ejpam-4242	39	2	∞	∞	PROPN
ejpam-4242	39	3	0	0	NUM
ejpam-4242	39	4	∫	∫	PROPN
ejpam-4242	39	5	∞	∞	NUM
ejpam-4242	39	6	0	0	NUM
ejpam-4242	39	7	t−mxm−1z1−mym−nhn(xα)e	t−mxm−1z1−mym−nhn(xα)e	NUM
ejpam-4242	39	8	α2	α2	ADJ
ejpam-4242	39	9	(	(	PUNCT
ejpam-4242	39	10	−x2	−x2	PROPN
ejpam-4242	39	11	)	)	PUNCT
ejpam-4242	39	12	−b	−b	ADV
ejpam-4242	39	13	(	(	PUNCT
ejpam-4242	39	14	t2+y2+z2	t2+y2+z2	PROPN
ejpam-4242	39	15	)	)	PUNCT
ejpam-4242	39	16	logk	logk	NOUN
ejpam-4242	39	17	(	(	PUNCT
ejpam-4242	39	18	axy	axy	PROPN
ejpam-4242	39	19	tz	tz	PROPN
ejpam-4242	39	20	)	)	PUNCT
ejpam-4242	39	21	dxdydzdt	dxdydzdt	NOUN
ejpam-4242	39	22	=	=	SYM
ejpam-4242	39	23	1	1	NUM
ejpam-4242	39	24	2πi	2πi	NOUN
ejpam-4242	39	25	∫	∫	PROPN
ejpam-4242	40	1	∞	∞	PROPN
ejpam-4242	41	1	0	0	NUM
ejpam-4242	42	1	∫	∫	PROPN
ejpam-4242	42	2	∞	∞	PROPN
ejpam-4242	42	3	0	0	NUM
ejpam-4242	43	1	∫	∫	PROPN
ejpam-4242	43	2	∞	∞	PROPN
ejpam-4242	43	3	0	0	NUM
ejpam-4242	44	1	∫	∫	PROPN
ejpam-4242	44	2	∞	∞	PROPN
ejpam-4242	44	3	0	0	NUM
ejpam-4242	45	1	∫	∫	PROPN
ejpam-4242	45	2	c	c	PROPN
ejpam-4242	45	3	aww−k−1t−m−wxm+w−1z−m−w+1hn(xα	aww−k−1t−m−wxm+w−1z−m−w+1hn(xα	PROPN
ejpam-4242	45	4	)	)	PUNCT
ejpam-4242	45	5	ym−n+weα	ym−n+weα	PROPN
ejpam-4242	45	6	2	2	NUM
ejpam-4242	45	7	(	(	PUNCT
ejpam-4242	45	8	−x2	−x2	X
ejpam-4242	45	9	)	)	PUNCT
ejpam-4242	46	1	−b	−b	ADV
ejpam-4242	46	2	(	(	PUNCT
ejpam-4242	46	3	t2+y2+z2	t2+y2+z2	PROPN
ejpam-4242	46	4	)	)	PUNCT
ejpam-4242	46	5	dwdxdydzdt	dwdxdydzdt	NOUN
ejpam-4242	46	6	=	=	SYM
ejpam-4242	47	1	1	1	NUM
ejpam-4242	47	2	2πi	2πi	NOUN
ejpam-4242	47	3	∫	∫	PROPN
ejpam-4242	48	1	c	c	PROPN
ejpam-4242	48	2	∫	∫	PROPN
ejpam-4242	49	1	∞	∞	NUM
ejpam-4242	49	2	0	0	NUM
ejpam-4242	50	1	∫	∫	PROPN
ejpam-4242	50	2	∞	∞	PROPN
ejpam-4242	50	3	0	0	NUM
ejpam-4242	51	1	∫	∫	PROPN
ejpam-4242	51	2	∞	∞	PROPN
ejpam-4242	51	3	0	0	NUM
ejpam-4242	52	1	∫	∫	PROPN
ejpam-4242	52	2	∞	∞	PROPN
ejpam-4242	52	3	0	0	NUM
ejpam-4242	53	1	aww−k−1t−m−wxm+w−1z−m−w+1hn(xα	aww−k−1t−m−wxm+w−1z−m−w+1hn(xα	ADJ
ejpam-4242	53	2	)	)	PUNCT
ejpam-4242	53	3	ym−n+weα	ym−n+weα	PROPN
ejpam-4242	53	4	2	2	NUM
ejpam-4242	53	5	(	(	PUNCT
ejpam-4242	53	6	−x2	−x2	X
ejpam-4242	53	7	)	)	PUNCT
ejpam-4242	53	8	−b	−b	ADV
ejpam-4242	53	9	(	(	PUNCT
ejpam-4242	53	10	t2+y2+z2	t2+y2+z2	PROPN
ejpam-4242	53	11	)	)	PUNCT
ejpam-4242	53	12	dxdydzdtdw	dxdydzdtdw	NOUN
ejpam-4242	53	13	=	=	SYM
ejpam-4242	53	14	1	1	NUM
ejpam-4242	53	15	2πi	2πi	NOUN
ejpam-4242	53	16	∫	∫	PROPN
ejpam-4242	53	17	c	c	PROPN
ejpam-4242	53	18	π22n−3aww−k−1α−m−w	π22n−3aww−k−1α−m−w	ADP
ejpam-4242	53	19	csc(π(m+	csc(π(m+	PUNCT
ejpam-4242	53	20	w))b	w))b	NOUN
ejpam-4242	53	21	1	1	NUM
ejpam-4242	53	22	2	2	NUM
ejpam-4242	53	23	(	(	PUNCT
ejpam-4242	53	24	m+n+w−4)dw	m+n+w−4)dw	NOUN
ejpam-4242	53	25	from	from	ADP
ejpam-4242	53	26	equation	equation	NOUN
ejpam-4242	53	27	(	(	PUNCT
ejpam-4242	53	28	3.22.2.2	3.22.2.2	NOUN
ejpam-4242	53	29	)	)	PUNCT
ejpam-4242	53	30	in	in	ADP
ejpam-4242	53	31	[	[	X
ejpam-4242	53	32	1	1	NUM
ejpam-4242	53	33	]	]	PUNCT
ejpam-4242	53	34	and	and	CCONJ
ejpam-4242	53	35	equation	equation	NOUN
ejpam-4242	53	36	(	(	PUNCT
ejpam-4242	53	37	3.326.2	3.326.2	NOUN
ejpam-4242	53	38	)	)	PUNCT
ejpam-4242	53	39	in	in	ADP
ejpam-4242	53	40	[	[	X
ejpam-4242	53	41	3	3	X
ejpam-4242	53	42	]	]	PUNCT
ejpam-4242	53	43	where	where	SCONJ
ejpam-4242	53	44	re(π(m	re(π(m	NOUN
ejpam-4242	53	45	+	+	PROPN
ejpam-4242	53	46	w	w	NOUN
ejpam-4242	53	47	)	)	PUNCT
ejpam-4242	53	48	)	)	PUNCT
ejpam-4242	53	49	>	>	X
ejpam-4242	53	50	0	0	NUM
ejpam-4242	53	51	,	,	PUNCT
ejpam-4242	53	52	re(n	re(n	NUM
ejpam-4242	53	53	)	)	PUNCT
ejpam-4242	53	54	<	<	X
ejpam-4242	53	55	re(m	re(m	PROPN
ejpam-4242	53	56	)	)	PUNCT
ejpam-4242	53	57	,	,	PUNCT
ejpam-4242	53	58	|argα|	|argα|	NUM
ejpam-4242	53	59	<	<	X
ejpam-4242	53	60	π/4	π/4	PUNCT
ejpam-4242	53	61	and	and	CCONJ
ejpam-4242	53	62	using	use	VERB
ejpam-4242	53	63	the	the	DET
ejpam-4242	53	64	reflection	reflection	NOUN
ejpam-4242	53	65	formula	formula	NOUN
ejpam-4242	53	66	(	(	PUNCT
ejpam-4242	53	67	8.334.3	8.334.3	NUM
ejpam-4242	53	68	)	)	PUNCT
ejpam-4242	53	69	in	in	ADP
ejpam-4242	53	70	[	[	X
ejpam-4242	53	71	3	3	X
ejpam-4242	53	72	]	]	PUNCT
ejpam-4242	53	73	for	for	ADP
ejpam-4242	53	74	the	the	DET
ejpam-4242	53	75	gamma	gamma	PROPN
ejpam-4242	53	76	function	function	NOUN
ejpam-4242	53	77	.	.	PUNCT
ejpam-4242	54	1	we	we	PRON
ejpam-4242	54	2	are	be	AUX
ejpam-4242	54	3	able	able	ADJ
ejpam-4242	54	4	to	to	PART
ejpam-4242	54	5	switch	switch	VERB
ejpam-4242	54	6	the	the	DET
ejpam-4242	54	7	order	order	NOUN
ejpam-4242	54	8	of	of	ADP
ejpam-4242	54	9	integration	integration	NOUN
ejpam-4242	54	10	over	over	ADP
ejpam-4242	54	11	x	x	PROPN
ejpam-4242	54	12	,	,	PUNCT
ejpam-4242	54	13	y	y	PROPN
ejpam-4242	54	14	,	,	PUNCT
ejpam-4242	54	15	z	z	PROPN
ejpam-4242	54	16	and	and	CCONJ
ejpam-4242	54	17	t	t	PROPN
ejpam-4242	54	18	using	use	VERB
ejpam-4242	54	19	r.	r.	PROPN
ejpam-4242	54	20	reynolds	reynolds	PROPN
ejpam-4242	54	21	,	,	PUNCT
ejpam-4242	54	22	a.	a.	PROPN
ejpam-4242	54	23	stauffer	stauffer	PROPN
ejpam-4242	54	24	/	/	SYM
ejpam-4242	54	25	eur	eur	PROPN
ejpam-4242	54	26	.	.	PUNCT
ejpam-4242	55	1	j.	j.	PROPN
ejpam-4242	55	2	pure	pure	PROPN
ejpam-4242	55	3	appl	appl	PROPN
ejpam-4242	55	4	.	.	PROPN
ejpam-4242	55	5	math	math	PROPN
ejpam-4242	55	6	,	,	PUNCT
ejpam-4242	55	7	15	15	NUM
ejpam-4242	55	8	(	(	PUNCT
ejpam-4242	55	9	1	1	NUM
ejpam-4242	55	10	)	)	PUNCT
ejpam-4242	55	11	(	(	PUNCT
ejpam-4242	55	12	2022	2022	NUM
ejpam-4242	55	13	)	)	PUNCT
ejpam-4242	55	14	,	,	PUNCT
ejpam-4242	55	15	100	100	NUM
ejpam-4242	55	16	-	-	SYM
ejpam-4242	55	17	105	105	NUM
ejpam-4242	55	18	102	102	NUM
ejpam-4242	55	19	fubini	fubini	NOUN
ejpam-4242	55	20	’s	’s	PART
ejpam-4242	55	21	theorem	theorem	NOUN
ejpam-4242	55	22	since	since	SCONJ
ejpam-4242	55	23	the	the	DET
ejpam-4242	55	24	integrand	integrand	NOUN
ejpam-4242	55	25	is	be	AUX
ejpam-4242	55	26	of	of	ADP
ejpam-4242	55	27	bounded	bounded	ADJ
ejpam-4242	55	28	measure	measure	NOUN
ejpam-4242	55	29	over	over	ADP
ejpam-4242	55	30	the	the	DET
ejpam-4242	55	31	space	space	NOUN
ejpam-4242	55	32	c	c	NOUN
ejpam-4242	55	33	×	×	NOUN
ejpam-4242	56	1	[	[	X
ejpam-4242	56	2	0,∞	0,∞	NOUN
ejpam-4242	56	3	)	)	PUNCT
ejpam-4242	56	4	×	×	NOUN
ejpam-4242	57	1	[	[	X
ejpam-4242	57	2	0,∞)×	0,∞)×	NUM
ejpam-4242	57	3	[	[	X
ejpam-4242	57	4	0,∞)×	0,∞)×	NUM
ejpam-4242	57	5	[	[	X
ejpam-4242	57	6	0,∞	0,∞	NUM
ejpam-4242	57	7	)	)	PUNCT
ejpam-4242	57	8	.	.	PUNCT
ejpam-4242	58	1	4	4	X
ejpam-4242	58	2	.	.	X
ejpam-4242	58	3	the	the	DET
ejpam-4242	58	4	hurwitz	hurwitz	PROPN
ejpam-4242	58	5	-	-	PUNCT
ejpam-4242	58	6	lerch	lerch	PROPN
ejpam-4242	58	7	zeta	zeta	PROPN
ejpam-4242	58	8	function	function	PROPN
ejpam-4242	58	9	and	and	CCONJ
ejpam-4242	58	10	infinite	infinite	ADJ
ejpam-4242	58	11	sum	sum	NOUN
ejpam-4242	58	12	of	of	ADP
ejpam-4242	58	13	the	the	DET
ejpam-4242	58	14	contour	contour	NOUN
ejpam-4242	58	15	integral	integral	NOUN
ejpam-4242	58	16	in	in	ADP
ejpam-4242	58	17	this	this	DET
ejpam-4242	58	18	section	section	NOUN
ejpam-4242	58	19	we	we	PRON
ejpam-4242	58	20	use	use	VERB
ejpam-4242	58	21	equation	equation	NOUN
ejpam-4242	58	22	(	(	PUNCT
ejpam-4242	58	23	2	2	NUM
ejpam-4242	58	24	)	)	PUNCT
ejpam-4242	58	25	to	to	PART
ejpam-4242	58	26	derive	derive	VERB
ejpam-4242	58	27	the	the	DET
ejpam-4242	58	28	contour	contour	NOUN
ejpam-4242	58	29	integral	integral	ADJ
ejpam-4242	58	30	representations	representation	NOUN
ejpam-4242	58	31	for	for	ADP
ejpam-4242	58	32	the	the	DET
ejpam-4242	58	33	hurwitz	hurwitz	PROPN
ejpam-4242	58	34	-	-	PUNCT
ejpam-4242	58	35	lerch	lerch	PROPN
ejpam-4242	58	36	zeta	zeta	PROPN
ejpam-4242	58	37	function	function	PROPN
ejpam-4242	58	38	.	.	PUNCT
ejpam-4242	59	1	4.1	4.1	NUM
ejpam-4242	59	2	.	.	PUNCT
ejpam-4242	60	1	the	the	DET
ejpam-4242	60	2	hurwitz	hurwitz	PROPN
ejpam-4242	60	3	-	-	PUNCT
ejpam-4242	60	4	lerch	lerch	PROPN
ejpam-4242	60	5	zeta	zeta	PROPN
ejpam-4242	60	6	function	function	VERB
ejpam-4242	60	7	the	the	DET
ejpam-4242	60	8	hurwitz	hurwitz	PROPN
ejpam-4242	60	9	-	-	PUNCT
ejpam-4242	60	10	lerch	lerch	PROPN
ejpam-4242	60	11	zeta	zeta	PROPN
ejpam-4242	60	12	function	function	PROPN
ejpam-4242	60	13	(	(	PUNCT
ejpam-4242	60	14	25.14	25.14	NUM
ejpam-4242	60	15	)	)	PUNCT
ejpam-4242	60	16	in	in	ADP
ejpam-4242	60	17	[	[	X
ejpam-4242	60	18	2	2	X
ejpam-4242	60	19	]	]	PUNCT
ejpam-4242	60	20	has	have	VERB
ejpam-4242	60	21	a	a	DET
ejpam-4242	60	22	series	series	NOUN
ejpam-4242	60	23	representation	representation	NOUN
ejpam-4242	60	24	given	give	VERB
ejpam-4242	60	25	by	by	ADP
ejpam-4242	60	26	φ(z	φ(z	PROPN
ejpam-4242	60	27	,	,	PUNCT
ejpam-4242	60	28	s	s	NOUN
ejpam-4242	60	29	,	,	PUNCT
ejpam-4242	60	30	v	v	NOUN
ejpam-4242	60	31	)	)	PUNCT
ejpam-4242	60	32	=	=	PUNCT
ejpam-4242	61	1	∞∑	∞∑	NUM
ejpam-4242	61	2	n=0	n=0	NUM
ejpam-4242	61	3	(	(	PUNCT
ejpam-4242	61	4	v	v	NOUN
ejpam-4242	61	5	+	+	PRON
ejpam-4242	61	6	n)−szn	n)−szn	NUM
ejpam-4242	61	7	(	(	PUNCT
ejpam-4242	61	8	4	4	NUM
ejpam-4242	61	9	)	)	PUNCT
ejpam-4242	61	10	where	where	SCONJ
ejpam-4242	61	11	|z|	|z|	VERB
ejpam-4242	61	12	<	<	X
ejpam-4242	61	13	1	1	NUM
ejpam-4242	61	14	,	,	PUNCT
ejpam-4242	61	15	v	v	NOUN
ejpam-4242	61	16	6=	6=	ADP
ejpam-4242	61	17	0,−1	0,−1	PROPN
ejpam-4242	61	18	,	,	PUNCT
ejpam-4242	61	19	..	..	PUNCT
ejpam-4242	61	20	and	and	CCONJ
ejpam-4242	61	21	is	be	AUX
ejpam-4242	61	22	continued	continue	VERB
ejpam-4242	61	23	analytically	analytically	ADV
ejpam-4242	61	24	by	by	ADP
ejpam-4242	61	25	its	its	PRON
ejpam-4242	61	26	integral	integral	ADJ
ejpam-4242	61	27	representation	representation	NOUN
ejpam-4242	61	28	given	give	VERB
ejpam-4242	61	29	by	by	ADP
ejpam-4242	61	30	φ(z	φ(z	PROPN
ejpam-4242	61	31	,	,	PUNCT
ejpam-4242	61	32	s	s	NOUN
ejpam-4242	61	33	,	,	PUNCT
ejpam-4242	61	34	v	v	NOUN
ejpam-4242	61	35	)	)	PUNCT
ejpam-4242	61	36	=	=	SYM
ejpam-4242	61	37	1	1	NUM
ejpam-4242	61	38	γ(s	γ(	NOUN
ejpam-4242	61	39	)	)	PUNCT
ejpam-4242	61	40	∫	∫	PROPN
ejpam-4242	62	1	∞	∞	PROPN
ejpam-4242	62	2	0	0	NUM
ejpam-4242	63	1	ts−1e−vt	ts−1e−vt	PRON
ejpam-4242	64	1	1−	1−	NUM
ejpam-4242	64	2	ze−t	ze−t	NOUN
ejpam-4242	64	3	dt	dt	NOUN
ejpam-4242	65	1	=	=	SYM
ejpam-4242	65	2	1	1	NUM
ejpam-4242	65	3	γ(s	γ(s	PROPN
ejpam-4242	65	4	)	)	PUNCT
ejpam-4242	65	5	∫	∫	PROPN
ejpam-4242	66	1	∞	∞	NUM
ejpam-4242	66	2	0	0	NUM
ejpam-4242	67	1	ts−1e−(v−1)t	ts−1e−(v−1)t	PROPN
ejpam-4242	67	2	et	et	NOUN
ejpam-4242	67	3	−	−	NOUN
ejpam-4242	67	4	z	z	NOUN
ejpam-4242	67	5	dt	dt	X
ejpam-4242	67	6	(	(	PUNCT
ejpam-4242	67	7	5	5	NUM
ejpam-4242	67	8	)	)	PUNCT
ejpam-4242	67	9	where	where	SCONJ
ejpam-4242	67	10	re(v	re(v	NOUN
ejpam-4242	67	11	)	)	PUNCT
ejpam-4242	67	12	>	>	X
ejpam-4242	67	13	0	0	NUM
ejpam-4242	67	14	,	,	PUNCT
ejpam-4242	67	15	and	and	CCONJ
ejpam-4242	67	16	either	either	ADV
ejpam-4242	67	17	|z|≤	|z|≤	SYM
ejpam-4242	67	18	1	1	NUM
ejpam-4242	67	19	,	,	PUNCT
ejpam-4242	67	20	z	z	NOUN
ejpam-4242	67	21	6=	6=	NUM
ejpam-4242	67	22	1	1	NUM
ejpam-4242	67	23	,	,	PUNCT
ejpam-4242	67	24	re(s	re(s	ADJ
ejpam-4242	67	25	)	)	PUNCT
ejpam-4242	67	26	>	>	X
ejpam-4242	67	27	0	0	NUM
ejpam-4242	67	28	,	,	PUNCT
ejpam-4242	67	29	or	or	CCONJ
ejpam-4242	67	30	z	z	NOUN
ejpam-4242	67	31	=	=	SYM
ejpam-4242	67	32	1	1	NUM
ejpam-4242	67	33	,	,	PUNCT
ejpam-4242	67	34	re(s	re(s	ADJ
ejpam-4242	67	35	)	)	PUNCT
ejpam-4242	67	36	>	>	X
ejpam-4242	68	1	1	1	NUM
ejpam-4242	68	2	.	.	X
ejpam-4242	68	3	4.2	4.2	NUM
ejpam-4242	68	4	.	.	PUNCT
ejpam-4242	68	5	infinite	infinite	ADJ
ejpam-4242	68	6	sum	sum	NOUN
ejpam-4242	68	7	of	of	ADP
ejpam-4242	68	8	the	the	DET
ejpam-4242	68	9	contour	contour	NOUN
ejpam-4242	68	10	integral	integral	ADJ
ejpam-4242	68	11	using	use	VERB
ejpam-4242	68	12	equation	equation	NOUN
ejpam-4242	68	13	(	(	PUNCT
ejpam-4242	68	14	2	2	NUM
ejpam-4242	68	15	)	)	PUNCT
ejpam-4242	68	16	and	and	CCONJ
ejpam-4242	68	17	replacing	replace	VERB
ejpam-4242	68	18	y	y	PRON
ejpam-4242	68	19	by	by	ADP
ejpam-4242	68	20	log(a	log(a	PROPN
ejpam-4242	68	21	)	)	PUNCT
ejpam-4242	69	1	+	+	CCONJ
ejpam-4242	69	2	iπ(2y	iπ(2y	PRON
ejpam-4242	69	3	+	+	NOUN
ejpam-4242	69	4	1	1	X
ejpam-4242	69	5	)	)	PUNCT
ejpam-4242	69	6	−	−	NOUN
ejpam-4242	69	7	log(2	log(2	NOUN
ejpam-4242	69	8	)	)	PUNCT
ejpam-4242	69	9	then	then	ADV
ejpam-4242	69	10	multiplying	multiply	VERB
ejpam-4242	69	11	both	both	DET
ejpam-4242	69	12	sides	side	NOUN
ejpam-4242	69	13	by	by	ADP
ejpam-4242	69	14	−iπ221−meiπm(2y+1	−iπ221−meiπm(2y+1	NOUN
ejpam-4242	69	15	)	)	PUNCT
ejpam-4242	69	16	taking	take	VERB
ejpam-4242	69	17	the	the	DET
ejpam-4242	69	18	infinite	infinite	ADJ
ejpam-4242	69	19	sum	sum	NOUN
ejpam-4242	69	20	over	over	ADP
ejpam-4242	69	21	y	y	PROPN
ejpam-4242	69	22	∈	∈	PROPN
ejpam-4242	70	1	[	[	X
ejpam-4242	70	2	0,∞	0,∞	NOUN
ejpam-4242	70	3	)	)	PUNCT
ejpam-4242	70	4	and	and	CCONJ
ejpam-4242	70	5	simplifying	simplify	VERB
ejpam-4242	70	6	in	in	ADP
ejpam-4242	70	7	terms	term	NOUN
ejpam-4242	70	8	of	of	ADP
ejpam-4242	70	9	the	the	DET
ejpam-4242	70	10	hurwitz	hurwitz	PROPN
ejpam-4242	70	11	-	-	PUNCT
ejpam-4242	70	12	lerch	lerch	PROPN
ejpam-4242	70	13	zeta	zeta	PROPN
ejpam-4242	70	14	function	function	VERB
ejpam-4242	70	15	we	we	PRON
ejpam-4242	70	16	obtain	obtain	VERB
ejpam-4242	70	17	(	(	PUNCT
ejpam-4242	70	18	6	6	NUM
ejpam-4242	70	19	)	)	PUNCT
ejpam-4242	70	20	−	−	PROPN
ejpam-4242	70	21	1	1	NUM
ejpam-4242	71	1	γ(k	γ(k	NOUN
ejpam-4242	71	2	+	+	CCONJ
ejpam-4242	71	3	1	1	X
ejpam-4242	71	4	)	)	PUNCT
ejpam-4242	71	5	ik+1πk+2eiπm2k+n−2α−mb	ik+1πk+2eiπm2k+n−2α−mb	VERB
ejpam-4242	71	6	1	1	NUM
ejpam-4242	71	7	2	2	NUM
ejpam-4242	71	8	(	(	PUNCT
ejpam-4242	71	9	m+n−4	m+n−4	NOUN
ejpam-4242	71	10	)	)	PUNCT
ejpam-4242	71	11	φ	φ	PROPN
ejpam-4242	71	12	(	(	PUNCT
ejpam-4242	71	13	e2imπ,−k	e2imπ,−k	PROPN
ejpam-4242	71	14	,	,	PUNCT
ejpam-4242	71	15	−2i	−2i	PROPN
ejpam-4242	72	1	log(a)−	log(a)−	NOUN
ejpam-4242	72	2	i	i	PRON
ejpam-4242	72	3	log(b	log(b	PROPN
ejpam-4242	72	4	)	)	PUNCT
ejpam-4242	72	5	+	+	NUM
ejpam-4242	72	6	2i	2i	NUM
ejpam-4242	72	7	log(α	log(α	NOUN
ejpam-4242	72	8	)	)	PUNCT
ejpam-4242	73	1	+	+	NUM
ejpam-4242	73	2	2π	2π	NOUN
ejpam-4242	73	3	4π	4π	NUM
ejpam-4242	73	4	)	)	PUNCT
ejpam-4242	74	1	=	=	PUNCT
ejpam-4242	74	2	−	−	PROPN
ejpam-4242	74	3	1	1	NUM
ejpam-4242	74	4	2πi	2πi	NOUN
ejpam-4242	74	5	∞∑	∞∑	NUM
ejpam-4242	74	6	y=0	y=0	NUM
ejpam-4242	74	7	∫	∫	X
ejpam-4242	74	8	c	c	PROPN
ejpam-4242	74	9	iπ22n−2aww−k−1α−m−weiπ(2y+1)(m+w)b	iπ22n−2aww−k−1α−m−weiπ(2y+1)(m+w)b	VERB
ejpam-4242	74	10	1	1	NUM
ejpam-4242	74	11	2	2	NUM
ejpam-4242	74	12	(	(	PUNCT
ejpam-4242	74	13	m+n+w−4)dw	m+n+w−4)dw	NOUN
ejpam-4242	74	14	=	=	SYM
ejpam-4242	74	15	−	−	PROPN
ejpam-4242	74	16	1	1	NUM
ejpam-4242	74	17	2πi	2πi	NOUN
ejpam-4242	74	18	∫	∫	PROPN
ejpam-4242	75	1	c	c	NOUN
ejpam-4242	76	1	∞∑	∞∑	PRON
ejpam-4242	76	2	y=0	y=0	PRON
ejpam-4242	76	3	iπ22n−2aww−k−1α−m−weiπ(2y+1)(m+w)b	iπ22n−2aww−k−1α−m−weiπ(2y+1)(m+w)b	VERB
ejpam-4242	76	4	1	1	NUM
ejpam-4242	76	5	2	2	NUM
ejpam-4242	76	6	(	(	PUNCT
ejpam-4242	76	7	m+n+w−4)dw	m+n+w−4)dw	NOUN
ejpam-4242	76	8	=	=	SYM
ejpam-4242	76	9	1	1	NUM
ejpam-4242	76	10	2πi	2πi	NOUN
ejpam-4242	76	11	∫	∫	PROPN
ejpam-4242	76	12	c	c	PROPN
ejpam-4242	76	13	π22n−3aww−k−1α−m−w	π22n−3aww−k−1α−m−w	ADP
ejpam-4242	76	14	csc(π(m+	csc(π(m+	PUNCT
ejpam-4242	76	15	w))b	w))b	NOUN
ejpam-4242	76	16	1	1	NUM
ejpam-4242	76	17	2	2	NUM
ejpam-4242	76	18	(	(	PUNCT
ejpam-4242	76	19	m+n+w−4)dw	m+n+w−4)dw	NOUN
ejpam-4242	76	20	from	from	ADP
ejpam-4242	76	21	equation	equation	NOUN
ejpam-4242	76	22	(	(	PUNCT
ejpam-4242	76	23	1.232.3	1.232.3	NUM
ejpam-4242	76	24	)	)	PUNCT
ejpam-4242	76	25	in	in	ADP
ejpam-4242	76	26	[	[	X
ejpam-4242	76	27	3	3	X
ejpam-4242	76	28	]	]	PUNCT
ejpam-4242	76	29	where	where	SCONJ
ejpam-4242	76	30	im(π(m+	im(π(m+	NOUN
ejpam-4242	76	31	w	w	NOUN
ejpam-4242	76	32	)	)	PUNCT
ejpam-4242	76	33	)	)	PUNCT
ejpam-4242	76	34	>	>	X
ejpam-4242	76	35	0	0	PUNCT
ejpam-4242	77	1	in	in	ADP
ejpam-4242	77	2	order	order	NOUN
ejpam-4242	77	3	for	for	SCONJ
ejpam-4242	77	4	the	the	DET
ejpam-4242	77	5	sum	sum	NOUN
ejpam-4242	77	6	to	to	PART
ejpam-4242	77	7	converge	converge	VERB
ejpam-4242	77	8	.	.	PUNCT
ejpam-4242	77	9	r.	r.	PROPN
ejpam-4242	77	10	reynolds	reynolds	PROPN
ejpam-4242	77	11	,	,	PUNCT
ejpam-4242	77	12	a.	a.	PROPN
ejpam-4242	77	13	stauffer	stauffer	PROPN
ejpam-4242	77	14	/	/	SYM
ejpam-4242	77	15	eur	eur	PROPN
ejpam-4242	77	16	.	.	PUNCT
ejpam-4242	78	1	j.	j.	PROPN
ejpam-4242	78	2	pure	pure	PROPN
ejpam-4242	78	3	appl	appl	PROPN
ejpam-4242	78	4	.	.	PROPN
ejpam-4242	78	5	math	math	PROPN
ejpam-4242	78	6	,	,	PUNCT
ejpam-4242	78	7	15	15	NUM
ejpam-4242	78	8	(	(	PUNCT
ejpam-4242	78	9	1	1	NUM
ejpam-4242	78	10	)	)	PUNCT
ejpam-4242	78	11	(	(	PUNCT
ejpam-4242	78	12	2022	2022	NUM
ejpam-4242	78	13	)	)	PUNCT
ejpam-4242	78	14	,	,	PUNCT
ejpam-4242	78	15	100	100	NUM
ejpam-4242	78	16	-	-	SYM
ejpam-4242	78	17	105	105	NUM
ejpam-4242	78	18	103	103	NUM
ejpam-4242	78	19	5	5	NUM
ejpam-4242	78	20	.	.	PUNCT
ejpam-4242	79	1	definite	definite	ADJ
ejpam-4242	79	2	integral	integral	ADJ
ejpam-4242	79	3	in	in	ADP
ejpam-4242	79	4	terms	term	NOUN
ejpam-4242	79	5	of	of	ADP
ejpam-4242	79	6	the	the	DET
ejpam-4242	79	7	lerch	lerch	PROPN
ejpam-4242	79	8	function	function	PROPN
ejpam-4242	79	9	theorem	theorem	VERB
ejpam-4242	79	10	1	1	NUM
ejpam-4242	79	11	.	.	PUNCT
ejpam-4242	80	1	for	for	ADP
ejpam-4242	80	2	all	all	DET
ejpam-4242	80	3	k	k	PROPN
ejpam-4242	80	4	,	,	PUNCT
ejpam-4242	80	5	a	a	PRON
ejpam-4242	80	6	,	,	PUNCT
ejpam-4242	80	7	b	b	PROPN
ejpam-4242	80	8	,	,	PUNCT
ejpam-4242	80	9	α	α	NOUN
ejpam-4242	80	10	,	,	PUNCT
ejpam-4242	80	11	n	n	CCONJ
ejpam-4242	80	12	,	,	PUNCT
ejpam-4242	80	13	m	m	VERB
ejpam-4242	80	14	∈	∈	PROPN
ejpam-4242	80	15	c	c	NOUN
ejpam-4242	80	16	,	,	PUNCT
ejpam-4242	80	17	re(n	re(n	NUM
ejpam-4242	80	18	)	)	PUNCT
ejpam-4242	80	19	<	<	X
ejpam-4242	80	20	re(m	re(m	PROPN
ejpam-4242	80	21	)	)	PUNCT
ejpam-4242	80	22	,	,	PUNCT
ejpam-4242	80	23	|argα|	|argα|	NUM
ejpam-4242	80	24	<	<	X
ejpam-4242	80	25	π/4	π/4	NUM
ejpam-4242	80	26	,	,	PUNCT
ejpam-4242	80	27	(	(	PUNCT
ejpam-4242	80	28	7	7	X
ejpam-4242	80	29	)	)	PUNCT
ejpam-4242	80	30	∫	∫	PROPN
ejpam-4242	80	31	∞	∞	PROPN
ejpam-4242	80	32	0	0	NUM
ejpam-4242	80	33	∫	∫	PROPN
ejpam-4242	80	34	∞	∞	PROPN
ejpam-4242	80	35	0	0	NUM
ejpam-4242	80	36	∫	∫	PROPN
ejpam-4242	80	37	∞	∞	PROPN
ejpam-4242	80	38	0	0	NUM
ejpam-4242	80	39	∫	∫	PROPN
ejpam-4242	80	40	∞	∞	NUM
ejpam-4242	80	41	0	0	NUM
ejpam-4242	81	1	t−mxm−1z1−mym−nhn(xα)e	t−mxm−1z1−mym−nhn(xα)e	NUM
ejpam-4242	81	2	α2	α2	ADJ
ejpam-4242	81	3	(	(	PUNCT
ejpam-4242	81	4	−x2	−x2	PROPN
ejpam-4242	81	5	)	)	PUNCT
ejpam-4242	81	6	−b	−b	ADV
ejpam-4242	81	7	(	(	PUNCT
ejpam-4242	81	8	t2+y2+z2	t2+y2+z2	PROPN
ejpam-4242	81	9	)	)	PUNCT
ejpam-4242	81	10	logk	logk	NOUN
ejpam-4242	81	11	(	(	PUNCT
ejpam-4242	81	12	axy	axy	PROPN
ejpam-4242	81	13	tz	tz	PROPN
ejpam-4242	81	14	)	)	PUNCT
ejpam-4242	81	15	dxdydzdt	dxdydzdt	NOUN
ejpam-4242	81	16	=	=	PUNCT
ejpam-4242	81	17	−iikπk+2eiπm2k+n−2α−mb	−iikπk+2eiπm2k+n−2α−mb	PROPN
ejpam-4242	81	18	1	1	NUM
ejpam-4242	81	19	2	2	NUM
ejpam-4242	81	20	(	(	PUNCT
ejpam-4242	81	21	m+n−4	m+n−4	NOUN
ejpam-4242	81	22	)	)	PUNCT
ejpam-4242	81	23	φ	φ	PROPN
ejpam-4242	81	24	(	(	PUNCT
ejpam-4242	81	25	e2imπ,−k	e2imπ,−k	PROPN
ejpam-4242	81	26	,	,	PUNCT
ejpam-4242	81	27	−2i	−2i	PROPN
ejpam-4242	82	1	log(a)−	log(a)−	NOUN
ejpam-4242	82	2	i	i	PRON
ejpam-4242	82	3	log(b	log(b	PROPN
ejpam-4242	82	4	)	)	PUNCT
ejpam-4242	82	5	+	+	NUM
ejpam-4242	82	6	2i	2i	NUM
ejpam-4242	82	7	log(α	log(α	NOUN
ejpam-4242	82	8	)	)	PUNCT
ejpam-4242	83	1	+	+	NUM
ejpam-4242	83	2	2π	2π	NOUN
ejpam-4242	83	3	4π	4π	NUM
ejpam-4242	83	4	)	)	PUNCT
ejpam-4242	83	5	proof	proof	NOUN
ejpam-4242	83	6	.	.	PUNCT
ejpam-4242	84	1	the	the	DET
ejpam-4242	84	2	right	right	ADJ
ejpam-4242	84	3	-	-	PUNCT
ejpam-4242	84	4	hand	hand	NOUN
ejpam-4242	84	5	sides	side	NOUN
ejpam-4242	84	6	of	of	ADP
ejpam-4242	84	7	relations	relation	NOUN
ejpam-4242	84	8	(	(	PUNCT
ejpam-4242	84	9	3	3	NUM
ejpam-4242	84	10	)	)	PUNCT
ejpam-4242	84	11	and	and	CCONJ
ejpam-4242	84	12	(	(	PUNCT
ejpam-4242	84	13	6	6	NUM
ejpam-4242	84	14	)	)	PUNCT
ejpam-4242	84	15	are	be	AUX
ejpam-4242	84	16	identical	identical	ADJ
ejpam-4242	84	17	;	;	PUNCT
ejpam-4242	84	18	hence	hence	ADV
ejpam-4242	84	19	,	,	PUNCT
ejpam-4242	84	20	the	the	DET
ejpam-4242	84	21	left	leave	VERB
ejpam-4242	84	22	-	-	PUNCT
ejpam-4242	84	23	hand	hand	NOUN
ejpam-4242	84	24	sides	side	NOUN
ejpam-4242	84	25	of	of	ADP
ejpam-4242	84	26	the	the	DET
ejpam-4242	84	27	same	same	ADJ
ejpam-4242	84	28	are	be	AUX
ejpam-4242	84	29	identical	identical	ADJ
ejpam-4242	84	30	too	too	ADV
ejpam-4242	84	31	.	.	PUNCT
ejpam-4242	85	1	simplifying	simplify	VERB
ejpam-4242	85	2	with	with	ADP
ejpam-4242	85	3	the	the	DET
ejpam-4242	85	4	gamma	gamma	NOUN
ejpam-4242	85	5	function	function	NOUN
ejpam-4242	85	6	yields	yield	VERB
ejpam-4242	85	7	the	the	DET
ejpam-4242	85	8	desired	desire	VERB
ejpam-4242	85	9	conclusion	conclusion	NOUN
ejpam-4242	85	10	.	.	PUNCT
ejpam-4242	86	1	example	example	NOUN
ejpam-4242	87	1	1	1	NUM
ejpam-4242	87	2	.	.	PUNCT
ejpam-4242	88	1	the	the	DET
ejpam-4242	88	2	degenerate	degenerate	ADJ
ejpam-4242	88	3	case	case	NOUN
ejpam-4242	88	4	.	.	PUNCT
ejpam-4242	89	1	(	(	PUNCT
ejpam-4242	89	2	8)	8)	NUM
ejpam-4242	89	3	∫	∫	NOUN
ejpam-4242	89	4	∞	∞	PROPN
ejpam-4242	89	5	0	0	NUM
ejpam-4242	90	1	∫	∫	PROPN
ejpam-4242	90	2	∞	∞	PROPN
ejpam-4242	90	3	0	0	NUM
ejpam-4242	91	1	∫	∫	PROPN
ejpam-4242	91	2	∞	∞	PROPN
ejpam-4242	91	3	0	0	NUM
ejpam-4242	91	4	∫	∫	PROPN
ejpam-4242	91	5	∞	∞	NUM
ejpam-4242	91	6	0	0	NUM
ejpam-4242	91	7	t−mxm−1z1−mym−nhn(xα)e	t−mxm−1z1−mym−nhn(xα)e	NUM
ejpam-4242	91	8	α2	α2	ADJ
ejpam-4242	91	9	(	(	PUNCT
ejpam-4242	91	10	−x2	−x2	PROPN
ejpam-4242	91	11	)	)	PUNCT
ejpam-4242	92	1	−b	−b	ADV
ejpam-4242	92	2	(	(	PUNCT
ejpam-4242	92	3	t2+y2+z2	t2+y2+z2	PROPN
ejpam-4242	92	4	)	)	PUNCT
ejpam-4242	92	5	dxdydzdt	dxdydzdt	NOUN
ejpam-4242	92	6	=	=	SYM
ejpam-4242	92	7	π22n−3α−m	π22n−3α−m	NUM
ejpam-4242	92	8	csc(πm)b	csc(πm)b	NOUN
ejpam-4242	92	9	1	1	NUM
ejpam-4242	92	10	2	2	NUM
ejpam-4242	92	11	(	(	PUNCT
ejpam-4242	92	12	m+n−4	m+n−4	NOUN
ejpam-4242	92	13	)	)	PUNCT
ejpam-4242	92	14	proof	proof	NOUN
ejpam-4242	92	15	.	.	PUNCT
ejpam-4242	93	1	use	use	VERB
ejpam-4242	93	2	equation	equation	NOUN
ejpam-4242	93	3	(	(	PUNCT
ejpam-4242	93	4	7	7	NUM
ejpam-4242	93	5	)	)	PUNCT
ejpam-4242	93	6	and	and	CCONJ
ejpam-4242	93	7	set	set	VERB
ejpam-4242	93	8	k	k	PROPN
ejpam-4242	93	9	=	=	PUNCT
ejpam-4242	93	10	0	0	PUNCT
ejpam-4242	93	11	and	and	CCONJ
ejpam-4242	93	12	simplify	simplify	VERB
ejpam-4242	93	13	using	use	VERB
ejpam-4242	93	14	entry	entry	NOUN
ejpam-4242	93	15	(	(	PUNCT
ejpam-4242	93	16	2	2	NUM
ejpam-4242	93	17	)	)	PUNCT
ejpam-4242	93	18	in	in	ADP
ejpam-4242	93	19	table	table	NOUN
ejpam-4242	93	20	below	below	ADV
ejpam-4242	93	21	(	(	PUNCT
ejpam-4242	93	22	64:12:7	64:12:7	NUM
ejpam-4242	93	23	)	)	PUNCT
ejpam-4242	93	24	in	in	ADP
ejpam-4242	93	25	[	[	X
ejpam-4242	93	26	4	4	NUM
ejpam-4242	93	27	]	]	PUNCT
ejpam-4242	93	28	.	.	PUNCT
ejpam-4242	93	29	example	example	NOUN
ejpam-4242	94	1	2	2	NUM
ejpam-4242	94	2	.	.	PUNCT
ejpam-4242	94	3	(	(	PUNCT
ejpam-4242	94	4	9	9	NUM
ejpam-4242	94	5	)	)	PUNCT
ejpam-4242	94	6	∫	∫	PROPN
ejpam-4242	94	7	∞	∞	PROPN
ejpam-4242	94	8	0	0	NUM
ejpam-4242	95	1	∫	∫	PROPN
ejpam-4242	95	2	∞	∞	PROPN
ejpam-4242	95	3	0	0	NUM
ejpam-4242	96	1	∫	∫	PROPN
ejpam-4242	96	2	∞	∞	PROPN
ejpam-4242	96	3	0	0	NUM
ejpam-4242	96	4	∫	∫	PROPN
ejpam-4242	96	5	∞	∞	NUM
ejpam-4242	96	6	0	0	NUM
ejpam-4242	97	1	√	√	PROPN
ejpam-4242	97	2	zy	zy	NOUN
ejpam-4242	97	3	1	1	NUM
ejpam-4242	97	4	2	2	NUM
ejpam-4242	97	5	−nhn(xα)e	−nhn(xα)e	NOUN
ejpam-4242	97	6	α2	α2	NOUN
ejpam-4242	97	7	(	(	PUNCT
ejpam-4242	97	8	−x2	−x2	PROPN
ejpam-4242	97	9	)	)	PUNCT
ejpam-4242	98	1	−b	−b	ADV
ejpam-4242	98	2	(	(	PUNCT
ejpam-4242	98	3	t2+y2+z2	t2+y2+z2	PROPN
ejpam-4242	98	4	)	)	PUNCT
ejpam-4242	99	1	√	√	PROPN
ejpam-4242	99	2	t	t	NOUN
ejpam-4242	100	1	√	√	NOUN
ejpam-4242	101	1	x	x	SYM
ejpam-4242	102	1	log	log	NOUN
ejpam-4242	102	2	(	(	PUNCT
ejpam-4242	102	3	axy	axy	PROPN
ejpam-4242	102	4	tz	tz	PROPN
ejpam-4242	102	5	)	)	PUNCT
ejpam-4242	102	6	dxdydzdt	dxdydzdt	NOUN
ejpam-4242	103	1	=	=	SYM
ejpam-4242	103	2	1√	1√	PROPN
ejpam-4242	103	3	α	α	NOUN
ejpam-4242	103	4	iπ2n−4b	iπ2n−4b	NOUN
ejpam-4242	103	5	n	n	CCONJ
ejpam-4242	103	6	2	2	NUM
ejpam-4242	103	7	−	−	NOUN
ejpam-4242	103	8	7	7	NUM
ejpam-4242	103	9	4	4	NUM
ejpam-4242	103	10	(	(	PUNCT
ejpam-4242	103	11	ψ(0	ψ(0	NOUN
ejpam-4242	103	12	)	)	PUNCT
ejpam-4242	103	13	(	(	PUNCT
ejpam-4242	103	14	−2i	−2i	PROPN
ejpam-4242	103	15	log(a)−	log(a)−	NOUN
ejpam-4242	103	16	i	i	PRON
ejpam-4242	103	17	log(b	log(b	PROPN
ejpam-4242	103	18	)	)	PUNCT
ejpam-4242	104	1	+	+	NUM
ejpam-4242	104	2	2i	2i	NUM
ejpam-4242	104	3	log(α	log(α	NOUN
ejpam-4242	104	4	)	)	PUNCT
ejpam-4242	105	1	+	+	NUM
ejpam-4242	105	2	2π	2π	NUM
ejpam-4242	105	3	8π	8π	NUM
ejpam-4242	105	4	)	)	PUNCT
ejpam-4242	105	5	−	−	PUNCT
ejpam-4242	105	6	ψ(0	ψ(0	NOUN
ejpam-4242	105	7	)	)	PUNCT
ejpam-4242	105	8	(	(	PUNCT
ejpam-4242	105	9	−2i	−2i	PROPN
ejpam-4242	105	10	log(a)−	log(a)−	NOUN
ejpam-4242	105	11	i	i	PRON
ejpam-4242	105	12	log(b	log(b	PROPN
ejpam-4242	105	13	)	)	PUNCT
ejpam-4242	105	14	+	+	NUM
ejpam-4242	105	15	2i	2i	NUM
ejpam-4242	105	16	log(α	log(α	NOUN
ejpam-4242	105	17	)	)	PUNCT
ejpam-4242	105	18	+	+	NUM
ejpam-4242	105	19	6π	6π	NOUN
ejpam-4242	105	20	8π	8π	NUM
ejpam-4242	105	21	)	)	PUNCT
ejpam-4242	105	22	)	)	PUNCT
ejpam-4242	105	23	proof	proof	NOUN
ejpam-4242	105	24	.	.	PUNCT
ejpam-4242	106	1	use	use	VERB
ejpam-4242	106	2	equation	equation	NOUN
ejpam-4242	106	3	(	(	PUNCT
ejpam-4242	106	4	7	7	X
ejpam-4242	106	5	)	)	PUNCT
ejpam-4242	106	6	set	set	NOUN
ejpam-4242	106	7	m	m	NOUN
ejpam-4242	106	8	=	=	NOUN
ejpam-4242	106	9	1/2	1/2	NUM
ejpam-4242	106	10	and	and	CCONJ
ejpam-4242	106	11	simplify	simplify	VERB
ejpam-4242	106	12	in	in	ADP
ejpam-4242	106	13	terms	term	NOUN
ejpam-4242	106	14	of	of	ADP
ejpam-4242	106	15	the	the	DET
ejpam-4242	106	16	hurwitz	hurwitz	PROPN
ejpam-4242	106	17	zeta	zeta	PROPN
ejpam-4242	106	18	function	function	VERB
ejpam-4242	106	19	ζ(s	ζ(s	PROPN
ejpam-4242	106	20	,	,	PUNCT
ejpam-4242	106	21	v	v	NOUN
ejpam-4242	106	22	)	)	PUNCT
ejpam-4242	106	23	then	then	ADV
ejpam-4242	106	24	apply	apply	VERB
ejpam-4242	106	25	l’hopital	l’hopital	PROPN
ejpam-4242	106	26	’s	’s	PART
ejpam-4242	106	27	rule	rule	NOUN
ejpam-4242	106	28	as	as	ADP
ejpam-4242	106	29	k	k	PROPN
ejpam-4242	106	30	→	→	SYM
ejpam-4242	106	31	−1	−1	NOUN
ejpam-4242	106	32	and	and	CCONJ
ejpam-4242	106	33	simplify	simplify	VERB
ejpam-4242	106	34	in	in	ADP
ejpam-4242	106	35	terms	term	NOUN
ejpam-4242	106	36	of	of	ADP
ejpam-4242	106	37	the	the	DET
ejpam-4242	106	38	digamma	digamma	PROPN
ejpam-4242	106	39	function	function	PROPN
ejpam-4242	106	40	ψ(0)(x	ψ(0)(x	NOUN
ejpam-4242	106	41	)	)	PUNCT
ejpam-4242	106	42	using	use	VERB
ejpam-4242	106	43	equation	equation	NOUN
ejpam-4242	106	44	(	(	PUNCT
ejpam-4242	106	45	64:4:1	64:4:1	NUM
ejpam-4242	106	46	)	)	PUNCT
ejpam-4242	106	47	in	in	ADP
ejpam-4242	106	48	[	[	X
ejpam-4242	106	49	4	4	NUM
ejpam-4242	106	50	]	]	PUNCT
ejpam-4242	106	51	.	.	PUNCT
ejpam-4242	107	1	r.	r.	PROPN
ejpam-4242	107	2	reynolds	reynolds	PROPN
ejpam-4242	107	3	,	,	PUNCT
ejpam-4242	107	4	a.	a.	PROPN
ejpam-4242	107	5	stauffer	stauffer	PROPN
ejpam-4242	107	6	/	/	SYM
ejpam-4242	107	7	eur	eur	PROPN
ejpam-4242	107	8	.	.	PUNCT
ejpam-4242	108	1	j.	j.	PROPN
ejpam-4242	108	2	pure	pure	PROPN
ejpam-4242	108	3	appl	appl	PROPN
ejpam-4242	108	4	.	.	PROPN
ejpam-4242	108	5	math	math	PROPN
ejpam-4242	108	6	,	,	PUNCT
ejpam-4242	108	7	15	15	NUM
ejpam-4242	108	8	(	(	PUNCT
ejpam-4242	108	9	1	1	NUM
ejpam-4242	108	10	)	)	PUNCT
ejpam-4242	108	11	(	(	PUNCT
ejpam-4242	108	12	2022	2022	NUM
ejpam-4242	108	13	)	)	PUNCT
ejpam-4242	108	14	,	,	PUNCT
ejpam-4242	108	15	100	100	NUM
ejpam-4242	108	16	-	-	SYM
ejpam-4242	108	17	105	105	NUM
ejpam-4242	108	18	104	104	NUM
ejpam-4242	108	19	example	example	NOUN
ejpam-4242	108	20	3	3	NUM
ejpam-4242	108	21	.	.	PUNCT
ejpam-4242	109	1	(	(	PUNCT
ejpam-4242	109	2	10	10	NUM
ejpam-4242	109	3	)	)	PUNCT
ejpam-4242	109	4	∫	∫	PROPN
ejpam-4242	110	1	∞	∞	PROPN
ejpam-4242	110	2	0	0	NUM
ejpam-4242	111	1	∫	∫	PROPN
ejpam-4242	111	2	∞	∞	PROPN
ejpam-4242	111	3	0	0	NUM
ejpam-4242	112	1	∫	∫	PROPN
ejpam-4242	112	2	∞	∞	PROPN
ejpam-4242	112	3	0	0	NUM
ejpam-4242	112	4	∫	∫	PROPN
ejpam-4242	112	5	∞	∞	NUM
ejpam-4242	112	6	0	0	NUM
ejpam-4242	113	1	√	√	PROPN
ejpam-4242	113	2	zy	zy	NOUN
ejpam-4242	113	3	1	1	NUM
ejpam-4242	113	4	2	2	NUM
ejpam-4242	113	5	−nhn(xα)e	−nhn(xα)e	NOUN
ejpam-4242	113	6	−t2−α2x2−y2−z2	−t2−α2x2−y2−z2	NOUN
ejpam-4242	113	7	√	√	PROPN
ejpam-4242	113	8	t	t	NOUN
ejpam-4242	113	9	√	√	NOUN
ejpam-4242	114	1	x	x	SYM
ejpam-4242	114	2	log	log	NOUN
ejpam-4242	114	3	(	(	PUNCT
ejpam-4242	114	4	−xy	−xy	PROPN
ejpam-4242	114	5	tz	tz	PROPN
ejpam-4242	114	6	)	)	PUNCT
ejpam-4242	114	7	dxdydzdt	dxdydzdt	NOUN
ejpam-4242	114	8	=	=	SYM
ejpam-4242	114	9	−	−	NOUN
ejpam-4242	114	10	iπ2n−4	iπ2n−4	NUM
ejpam-4242	114	11	(	(	PUNCT
ejpam-4242	114	12	h	h	NOUN
ejpam-4242	114	13	i	i	NOUN
ejpam-4242	114	14	log(α	log(α	PROPN
ejpam-4242	114	15	)	)	PUNCT
ejpam-4242	114	16	4π	4π	PRON
ejpam-4242	114	17	−h	−h	VERB
ejpam-4242	114	18	i	i	PRON
ejpam-4242	114	19	log(α	log(α	PROPN
ejpam-4242	114	20	)	)	PUNCT
ejpam-4242	114	21	4π	4π	NUM
ejpam-4242	114	22	−	−	NUM
ejpam-4242	114	23	1	1	NUM
ejpam-4242	114	24	2	2	NUM
ejpam-4242	114	25	)	)	PUNCT
ejpam-4242	114	26	√	√	ADP
ejpam-4242	114	27	α	α	PRON
ejpam-4242	114	28	proof	proof	NOUN
ejpam-4242	114	29	.	.	PUNCT
ejpam-4242	115	1	use	use	VERB
ejpam-4242	115	2	equation	equation	NOUN
ejpam-4242	115	3	(	(	PUNCT
ejpam-4242	115	4	9	9	NUM
ejpam-4242	115	5	)	)	PUNCT
ejpam-4242	115	6	and	and	CCONJ
ejpam-4242	115	7	set	set	VERB
ejpam-4242	115	8	a	a	DET
ejpam-4242	115	9	=	=	SYM
ejpam-4242	115	10	−1	−1	NOUN
ejpam-4242	115	11	,	,	PUNCT
ejpam-4242	115	12	b	b	NOUN
ejpam-4242	115	13	=	=	SYM
ejpam-4242	115	14	1	1	NUM
ejpam-4242	115	15	and	and	CCONJ
ejpam-4242	115	16	simplify	simplify	VERB
ejpam-4242	115	17	in	in	ADP
ejpam-4242	115	18	terms	term	NOUN
ejpam-4242	115	19	of	of	ADP
ejpam-4242	115	20	the	the	DET
ejpam-4242	115	21	harmonic	harmonic	ADJ
ejpam-4242	115	22	number	number	NOUN
ejpam-4242	115	23	function	function	VERB
ejpam-4242	115	24	hn	hn	PROPN
ejpam-4242	115	25	.	.	PROPN
ejpam-4242	115	26	example	example	NOUN
ejpam-4242	115	27	4.∫	4.∫	NUM
ejpam-4242	115	28	∞	∞	PROPN
ejpam-4242	115	29	0	0	NUM
ejpam-4242	116	1	∫	∫	PROPN
ejpam-4242	117	1	∞	∞	PROPN
ejpam-4242	117	2	0	0	NUM
ejpam-4242	117	3	∫	∫	PROPN
ejpam-4242	117	4	∞	∞	PROPN
ejpam-4242	117	5	0	0	NUM
ejpam-4242	117	6	∫	∫	PROPN
ejpam-4242	117	7	∞	∞	PROPN
ejpam-4242	117	8	0	0	NUM
ejpam-4242	118	1	zy−nhn(x)t	zy−nhn(x)t	NOUN
ejpam-4242	118	2	−m−pe−t2−x2−y2−z2	−m−pe−t2−x2−y2−z2	NOUN
ejpam-4242	118	3	x	x	PUNCT
ejpam-4242	118	4	log	log	NOUN
ejpam-4242	118	5	(	(	PUNCT
ejpam-4242	118	6	xy	xy	PROPN
ejpam-4242	118	7	tz	tz	PROPN
ejpam-4242	118	8	)	)	PUNCT
ejpam-4242	118	9	(	(	PUNCT
ejpam-4242	118	10	tmxpypz−p	tmxpypz−p	VERB
ejpam-4242	118	11	−	−	PROPN
ejpam-4242	118	12	xmymz−mtp	xmymz−mtp	PROPN
ejpam-4242	118	13	)	)	PUNCT
ejpam-4242	118	14	dxdtdzdt	dxdtdzdt	PROPN
ejpam-4242	119	1	=	=	SYM
ejpam-4242	119	2	π2n−2	π2n−2	PROPN
ejpam-4242	119	3	(	(	PUNCT
ejpam-4242	119	4	tanh−1	tanh−1	PROPN
ejpam-4242	119	5	(	(	PUNCT
ejpam-4242	119	6	eiπm	eiπm	PROPN
ejpam-4242	119	7	)	)	PUNCT
ejpam-4242	119	8	−	−	PROPN
ejpam-4242	120	1	tanh−1	tanh−1	VERB
ejpam-4242	120	2	(	(	PUNCT
ejpam-4242	120	3	eiπp	eiπp	PROPN
ejpam-4242	120	4	)	)	PUNCT
ejpam-4242	120	5	)	)	PUNCT
ejpam-4242	121	1	(	(	PUNCT
ejpam-4242	121	2	11	11	X
ejpam-4242	121	3	)	)	PUNCT
ejpam-4242	121	4	proof	proof	NOUN
ejpam-4242	121	5	.	.	PUNCT
ejpam-4242	122	1	use	use	VERB
ejpam-4242	122	2	equation	equation	NOUN
ejpam-4242	122	3	(	(	PUNCT
ejpam-4242	122	4	7	7	NUM
ejpam-4242	122	5	)	)	PUNCT
ejpam-4242	122	6	and	and	CCONJ
ejpam-4242	122	7	form	form	VERB
ejpam-4242	122	8	a	a	DET
ejpam-4242	122	9	second	second	ADJ
ejpam-4242	122	10	equation	equation	NOUN
ejpam-4242	122	11	by	by	ADP
ejpam-4242	122	12	replacing	replace	VERB
ejpam-4242	122	13	m	m	PRON
ejpam-4242	122	14	→	→	SYM
ejpam-4242	122	15	p	p	X
ejpam-4242	122	16	and	and	CCONJ
ejpam-4242	122	17	taking	take	VERB
ejpam-4242	122	18	their	their	PRON
ejpam-4242	122	19	difference	difference	NOUN
ejpam-4242	122	20	and	and	CCONJ
ejpam-4242	122	21	setting	set	VERB
ejpam-4242	122	22	k	k	PROPN
ejpam-4242	122	23	=	=	SYM
ejpam-4242	122	24	−1	−1	NOUN
ejpam-4242	122	25	,	,	PUNCT
ejpam-4242	122	26	a	a	PRON
ejpam-4242	122	27	=	=	SYM
ejpam-4242	122	28	1	1	NUM
ejpam-4242	122	29	,	,	PUNCT
ejpam-4242	122	30	b	b	NOUN
ejpam-4242	122	31	=	=	SYM
ejpam-4242	122	32	1	1	NUM
ejpam-4242	122	33	,	,	PUNCT
ejpam-4242	122	34	α	α	NOUN
ejpam-4242	122	35	=	=	SYM
ejpam-4242	122	36	1	1	NUM
ejpam-4242	122	37	and	and	CCONJ
ejpam-4242	122	38	simplify	simplify	NOUN
ejpam-4242	122	39	.	.	PUNCT
ejpam-4242	122	40	example	example	NOUN
ejpam-4242	123	1	5	5	NUM
ejpam-4242	123	2	.	.	PUNCT
ejpam-4242	123	3	(	(	PUNCT
ejpam-4242	123	4	12	12	NUM
ejpam-4242	123	5	)	)	PUNCT
ejpam-4242	123	6	∫	∫	PROPN
ejpam-4242	123	7	∞	∞	PROPN
ejpam-4242	123	8	0	0	NUM
ejpam-4242	124	1	∫	∫	PROPN
ejpam-4242	124	2	∞	∞	PROPN
ejpam-4242	124	3	0	0	NUM
ejpam-4242	125	1	∫	∫	PROPN
ejpam-4242	125	2	∞	∞	PROPN
ejpam-4242	125	3	0	0	NUM
ejpam-4242	126	1	∫	∫	PROPN
ejpam-4242	126	2	∞	∞	NUM
ejpam-4242	126	3	0	0	NUM
ejpam-4242	126	4	3	3	NUM
ejpam-4242	127	1	√	√	NOUN
ejpam-4242	127	2	zy	zy	NOUN
ejpam-4242	127	3	1	1	NUM
ejpam-4242	127	4	2	2	NUM
ejpam-4242	127	5	−nhn(x)e	−nhn(x)e	PROPN
ejpam-4242	127	6	−t2−x2−y2−z2	−t2−x2−y2−z2	PROPN
ejpam-4242	127	7	(	(	PUNCT
ejpam-4242	127	8	6	6	NUM
ejpam-4242	127	9	√	√	NUM
ejpam-4242	127	10	x	x	SYM
ejpam-4242	127	11	6	6	NUM
ejpam-4242	127	12	√	√	NUM
ejpam-4242	127	13	y	y	NUM
ejpam-4242	127	14	−	−	PROPN
ejpam-4242	127	15	6	6	NUM
ejpam-4242	127	16	√	√	NOUN
ejpam-4242	127	17	t	t	PROPN
ejpam-4242	127	18	6	6	NUM
ejpam-4242	127	19	√	√	PROPN
ejpam-4242	127	20	z	z	NOUN
ejpam-4242	127	21	)	)	PUNCT
ejpam-4242	128	1	t2/3	t2/3	ADJ
ejpam-4242	128	2	√	√	INTJ
ejpam-4242	129	1	x	x	SYM
ejpam-4242	129	2	log	log	NOUN
ejpam-4242	129	3	(	(	PUNCT
ejpam-4242	129	4	xy	xy	PROPN
ejpam-4242	129	5	tz	tz	PROPN
ejpam-4242	129	6	)	)	PUNCT
ejpam-4242	129	7	dxdydzdt	dxdydzdt	NOUN
ejpam-4242	129	8	=	=	SYM
ejpam-4242	129	9	π2n−4	π2n−4	NOUN
ejpam-4242	129	10	log(3	log(3	ADJ
ejpam-4242	129	11	)	)	PUNCT
ejpam-4242	129	12	proof	proof	NOUN
ejpam-4242	129	13	.	.	PUNCT
ejpam-4242	130	1	use	use	VERB
ejpam-4242	130	2	equation	equation	NOUN
ejpam-4242	130	3	(	(	PUNCT
ejpam-4242	130	4	11	11	NUM
ejpam-4242	130	5	)	)	PUNCT
ejpam-4242	130	6	and	and	CCONJ
ejpam-4242	130	7	set	set	VERB
ejpam-4242	130	8	m	m	PROPN
ejpam-4242	130	9	=	=	SYM
ejpam-4242	130	10	1/2	1/2	NUM
ejpam-4242	130	11	,	,	PUNCT
ejpam-4242	130	12	p	p	X
ejpam-4242	130	13	=	=	NOUN
ejpam-4242	130	14	2/3	2/3	NUM
ejpam-4242	130	15	and	and	CCONJ
ejpam-4242	130	16	simplify	simplify	NOUN
ejpam-4242	130	17	.	.	PUNCT
ejpam-4242	131	1	6	6	X
ejpam-4242	131	2	.	.	X
ejpam-4242	131	3	discussion	discussion	NOUN
ejpam-4242	131	4	in	in	ADP
ejpam-4242	131	5	this	this	DET
ejpam-4242	131	6	paper	paper	NOUN
ejpam-4242	131	7	,	,	PUNCT
ejpam-4242	131	8	we	we	PRON
ejpam-4242	131	9	have	have	AUX
ejpam-4242	131	10	presented	present	VERB
ejpam-4242	131	11	a	a	DET
ejpam-4242	131	12	novel	novel	ADJ
ejpam-4242	131	13	method	method	NOUN
ejpam-4242	131	14	for	for	ADP
ejpam-4242	131	15	deriving	derive	VERB
ejpam-4242	131	16	a	a	DET
ejpam-4242	131	17	new	new	ADJ
ejpam-4242	131	18	integral	integral	NOUN
ejpam-4242	131	19	involving	involve	VERB
ejpam-4242	131	20	the	the	DET
ejpam-4242	131	21	hermite	hermite	ADJ
ejpam-4242	131	22	polynomial	polynomial	NOUN
ejpam-4242	131	23	hn(x	hn(x	ADP
ejpam-4242	131	24	)	)	PUNCT
ejpam-4242	131	25	along	along	ADP
ejpam-4242	131	26	with	with	ADP
ejpam-4242	131	27	some	some	DET
ejpam-4242	131	28	interesting	interesting	ADJ
ejpam-4242	131	29	definite	definite	ADJ
ejpam-4242	131	30	integrals	integral	NOUN
ejpam-4242	131	31	using	use	VERB
ejpam-4242	131	32	contour	contour	NOUN
ejpam-4242	131	33	integration	integration	NOUN
ejpam-4242	131	34	.	.	PUNCT
ejpam-4242	132	1	the	the	DET
ejpam-4242	132	2	results	result	NOUN
ejpam-4242	132	3	presented	present	VERB
ejpam-4242	132	4	were	be	AUX
ejpam-4242	132	5	numerically	numerically	ADV
ejpam-4242	132	6	verified	verify	VERB
ejpam-4242	132	7	for	for	ADP
ejpam-4242	132	8	both	both	CCONJ
ejpam-4242	132	9	real	real	ADJ
ejpam-4242	132	10	and	and	CCONJ
ejpam-4242	132	11	imaginary	imaginary	ADJ
ejpam-4242	132	12	and	and	CCONJ
ejpam-4242	132	13	complex	complex	ADJ
ejpam-4242	132	14	values	value	NOUN
ejpam-4242	132	15	of	of	ADP
ejpam-4242	132	16	the	the	DET
ejpam-4242	132	17	parameters	parameter	NOUN
ejpam-4242	132	18	in	in	ADP
ejpam-4242	132	19	the	the	DET
ejpam-4242	132	20	integrals	integral	NOUN
ejpam-4242	132	21	using	use	VERB
ejpam-4242	132	22	mathematica	mathematica	PROPN
ejpam-4242	132	23	by	by	ADP
ejpam-4242	132	24	wolfram	wolfram	PROPN
ejpam-4242	132	25	.	.	PUNCT
ejpam-4242	133	1	acknowledgements	acknowledgement	NOUN
ejpam-4242	133	2	this	this	DET
ejpam-4242	133	3	research	research	NOUN
ejpam-4242	133	4	is	be	AUX
ejpam-4242	133	5	supported	support	VERB
ejpam-4242	133	6	by	by	ADP
ejpam-4242	133	7	nserc	nserc	PROPN
ejpam-4242	133	8	canada	canada	PROPN
ejpam-4242	133	9	under	under	ADP
ejpam-4242	133	10	grant	grant	PROPN
ejpam-4242	133	11	504070	504070	NUM
ejpam-4242	133	12	.	.	PUNCT
ejpam-4242	134	1	references	reference	NOUN
ejpam-4242	134	2	105	105	NUM
ejpam-4242	134	3	references	reference	NOUN
ejpam-4242	134	4	[	[	X
ejpam-4242	134	5	1	1	NUM
ejpam-4242	134	6	]	]	PUNCT
ejpam-4242	134	7	yu	yu	PROPN
ejpam-4242	134	8	a.	a.	NOUN
ejpam-4242	134	9	brychkov	brychkov	PROPN
ejpam-4242	134	10	,	,	PUNCT
ejpam-4242	134	11	o.	o.	PROPN
ejpam-4242	134	12	i.	i.	PROPN
ejpam-4242	134	13	marichev	marichev	PROPN
ejpam-4242	134	14	,	,	PUNCT
ejpam-4242	134	15	and	and	CCONJ
ejpam-4242	134	16	n.	n.	PROPN
ejpam-4242	134	17	v.	v.	PROPN
ejpam-4242	134	18	savischenko	savischenko	PROPN
ejpam-4242	134	19	.	.	PUNCT
ejpam-4242	135	1	handbook	handbook	NOUN
ejpam-4242	135	2	of	of	ADP
ejpam-4242	135	3	mellin	mellin	PROPN
ejpam-4242	135	4	transforms	transform	VERB
ejpam-4242	135	5	.	.	PUNCT
ejpam-4242	136	1	crc	crc	PROPN
ejpam-4242	136	2	press	press	PROPN
ejpam-4242	136	3	,	,	PUNCT
ejpam-4242	136	4	10	10	NUM
ejpam-4242	136	5	2018	2018	NUM
ejpam-4242	136	6	.	.	PUNCT
ejpam-4242	137	1	[	[	X
ejpam-4242	137	2	2	2	NUM
ejpam-4242	137	3	]	]	PUNCT
ejpam-4242	137	4	nist	nist	NOUN
ejpam-4242	137	5	digital	digital	PROPN
ejpam-4242	137	6	library	library	NOUN
ejpam-4242	137	7	of	of	ADP
ejpam-4242	137	8	mathematical	mathematical	ADJ
ejpam-4242	137	9	functions	function	NOUN
ejpam-4242	137	10	.	.	PUNCT
ejpam-4242	138	1	f.	f.	PROPN
ejpam-4242	138	2	w.	w.	PROPN
ejpam-4242	138	3	j.	j.	PROPN
ejpam-4242	138	4	olver	olver	PROPN
ejpam-4242	138	5	,	,	PUNCT
ejpam-4242	138	6	a.	a.	PROPN
ejpam-4242	138	7	b.	b.	PROPN
ejpam-4242	138	8	olde	olde	PROPN
ejpam-4242	138	9	daalhuis	daalhuis	PROPN
ejpam-4242	138	10	,	,	PUNCT
ejpam-4242	138	11	d.	d.	PROPN
ejpam-4242	138	12	w.	w.	PROPN
ejpam-4242	138	13	lozier	lozier	PROPN
ejpam-4242	138	14	,	,	PUNCT
ejpam-4242	138	15	b.	b.	PROPN
ejpam-4242	138	16	i.	i.	PROPN
ejpam-4242	138	17	schneider	schneider	PROPN
ejpam-4242	138	18	,	,	PUNCT
ejpam-4242	138	19	r.	r.	PROPN
ejpam-4242	138	20	f.	f.	PROPN
ejpam-4242	138	21	boisvert	boisvert	PROPN
ejpam-4242	138	22	,	,	PUNCT
ejpam-4242	138	23	c.	c.	PROPN
ejpam-4242	138	24	w.	w.	PROPN
ejpam-4242	138	25	clark	clark	PROPN
ejpam-4242	138	26	,	,	PUNCT
ejpam-4242	138	27	b.	b.	PROPN
ejpam-4242	138	28	r.	r.	PROPN
ejpam-4242	138	29	miller	miller	PROPN
ejpam-4242	138	30	,	,	PUNCT
ejpam-4242	138	31	b.	b.	PROPN
ejpam-4242	139	1	v.	v.	PROPN
ejpam-4242	139	2	saunders	saunders	PROPN
ejpam-4242	139	3	,	,	PUNCT
ejpam-4242	139	4	h.	h.	PROPN
ejpam-4242	139	5	s.	s.	PROPN
ejpam-4242	139	6	cohl	cohl	PROPN
ejpam-4242	139	7	,	,	PUNCT
ejpam-4242	139	8	and	and	CCONJ
ejpam-4242	139	9	m.	m.	PROPN
ejpam-4242	139	10	a.	a.	PROPN
ejpam-4242	139	11	mcclain	mcclain	PROPN
ejpam-4242	139	12	,	,	PUNCT
ejpam-4242	139	13	eds	eds	PROPN
ejpam-4242	139	14	.	.	PUNCT
ejpam-4242	140	1	[	[	X
ejpam-4242	140	2	3	3	NUM
ejpam-4242	140	3	]	]	X
ejpam-4242	140	4	i.	i.	PROPN
ejpam-4242	140	5	s.	s.	PROPN
ejpam-4242	140	6	gradshteyn	gradshteyn	PROPN
ejpam-4242	140	7	and	and	CCONJ
ejpam-4242	140	8	i.	i.	PROPN
ejpam-4242	140	9	m.	m.	PROPN
ejpam-4242	140	10	ryzhik	ryzhik	PROPN
ejpam-4242	140	11	.	.	PUNCT
ejpam-4242	141	1	table	table	NOUN
ejpam-4242	141	2	of	of	ADP
ejpam-4242	141	3	integrals	integral	NOUN
ejpam-4242	141	4	,	,	PUNCT
ejpam-4242	141	5	series	series	NOUN
ejpam-4242	141	6	,	,	PUNCT
ejpam-4242	141	7	and	and	CCONJ
ejpam-4242	141	8	products	product	NOUN
ejpam-4242	141	9	.	.	PUNCT
ejpam-4242	142	1	elsevier	elsevier	NOUN
ejpam-4242	142	2	/	/	SYM
ejpam-4242	142	3	academic	academic	ADJ
ejpam-4242	142	4	press	press	NOUN
ejpam-4242	142	5	,	,	PUNCT
ejpam-4242	142	6	amsterdam	amsterdam	PROPN
ejpam-4242	142	7	,	,	PUNCT
ejpam-4242	142	8	seventh	seventh	ADJ
ejpam-4242	142	9	edition	edition	NOUN
ejpam-4242	142	10	,	,	PUNCT
ejpam-4242	142	11	2007	2007	NUM
ejpam-4242	142	12	.	.	PUNCT
ejpam-4242	143	1	[	[	X
ejpam-4242	143	2	4	4	X
ejpam-4242	143	3	]	]	PUNCT
ejpam-4242	143	4	keith	keith	PROPN
ejpam-4242	143	5	b.	b.	PROPN
ejpam-4242	143	6	oldham	oldham	PROPN
ejpam-4242	143	7	,	,	PUNCT
ejpam-4242	143	8	jan	jan	PROPN
ejpam-4242	143	9	myland	myland	PROPN
ejpam-4242	143	10	,	,	PUNCT
ejpam-4242	143	11	and	and	CCONJ
ejpam-4242	143	12	jerome	jerome	PROPN
ejpam-4242	143	13	spanier	spanier	NOUN
ejpam-4242	143	14	.	.	PUNCT
ejpam-4242	144	1	an	an	DET
ejpam-4242	144	2	atlas	atlas	PROPN
ejpam-4242	144	3	of	of	ADP
ejpam-4242	144	4	functions	function	NOUN
ejpam-4242	144	5	:	:	PUNCT
ejpam-4242	144	6	with	with	ADP
ejpam-4242	144	7	equator	equator	NOUN
ejpam-4242	144	8	,	,	PUNCT
ejpam-4242	144	9	the	the	DET
ejpam-4242	144	10	atlas	atlas	PROPN
ejpam-4242	144	11	function	function	PROPN
ejpam-4242	144	12	calculator	calculator	NOUN
ejpam-4242	144	13	.	.	PUNCT
ejpam-4242	145	1	springer	springer	NOUN
ejpam-4242	145	2	science	science	PROPN
ejpam-4242	145	3	&	&	CCONJ
ejpam-4242	145	4	business	business	NOUN
ejpam-4242	145	5	media	medium	NOUN
ejpam-4242	145	6	,	,	PUNCT
ejpam-4242	145	7	07	07	NUM
ejpam-4242	145	8	2010	2010	NUM
ejpam-4242	145	9	.	.	PUNCT
ejpam-4242	146	1	[	[	X
ejpam-4242	146	2	5	5	X
ejpam-4242	146	3	]	]	X
ejpam-4242	146	4	robert	robert	PROPN
ejpam-4242	146	5	reynolds	reynolds	PROPN
ejpam-4242	146	6	and	and	CCONJ
ejpam-4242	146	7	allan	allan	PROPN
ejpam-4242	146	8	stauffer	stauffer	PROPN
ejpam-4242	146	9	.	.	PUNCT
ejpam-4242	147	1	a	a	DET
ejpam-4242	147	2	method	method	NOUN
ejpam-4242	147	3	for	for	ADP
ejpam-4242	147	4	evaluating	evaluate	VERB
ejpam-4242	147	5	definite	definite	ADJ
ejpam-4242	147	6	integrals	integral	NOUN
ejpam-4242	147	7	in	in	ADP
ejpam-4242	147	8	terms	term	NOUN
ejpam-4242	147	9	of	of	ADP
ejpam-4242	147	10	special	special	ADJ
ejpam-4242	147	11	functions	function	NOUN
ejpam-4242	147	12	with	with	ADP
ejpam-4242	147	13	examples	example	NOUN
ejpam-4242	147	14	.	.	PUNCT
ejpam-4242	148	1	international	international	ADJ
ejpam-4242	148	2	mathematical	mathematical	PROPN
ejpam-4242	148	3	forum	forum	PROPN
ejpam-4242	148	4	,	,	PUNCT
ejpam-4242	148	5	15:235–244	15:235–244	PROPN
ejpam-4242	148	6	,	,	PUNCT
ejpam-4242	148	7	2020	2020	NUM
ejpam-4242	148	8	.	.	PUNCT