id	sid	tid	token	lemma	pos
ejpam-4064	1	1	european	european	PROPN
ejpam-4064	1	2	journal	journal	PROPN
ejpam-4064	1	3	of	of	ADP
ejpam-4064	1	4	pure	pure	ADJ
ejpam-4064	1	5	and	and	CCONJ
ejpam-4064	1	6	applied	apply	VERB
ejpam-4064	1	7	mathematics	mathematic	NOUN
ejpam-4064	1	8	vol	vol	NOUN
ejpam-4064	1	9	.	.	PUNCT
ejpam-4064	2	1	14	14	NUM
ejpam-4064	2	2	,	,	PUNCT
ejpam-4064	2	3	no	no	INTJ
ejpam-4064	2	4	.	.	NOUN
ejpam-4064	2	5	4	4	NUM
ejpam-4064	2	6	,	,	PUNCT
ejpam-4064	2	7	2021	2021	NUM
ejpam-4064	2	8	,	,	PUNCT
ejpam-4064	2	9	1295	1295	NUM
ejpam-4064	2	10	-	-	SYM
ejpam-4064	2	11	1305	1305	NUM
ejpam-4064	2	12	issn	issn	VERB
ejpam-4064	2	13	1307	1307	NUM
ejpam-4064	2	14	-	-	SYM
ejpam-4064	2	15	5543	5543	NUM
ejpam-4064	2	16	–	–	PUNCT
ejpam-4064	2	17	ejpam.com	ejpam.com	X
ejpam-4064	2	18	published	publish	VERB
ejpam-4064	2	19	by	by	ADP
ejpam-4064	2	20	new	new	PROPN
ejpam-4064	2	21	york	york	PROPN
ejpam-4064	2	22	business	business	PROPN
ejpam-4064	2	23	global	global	ADJ
ejpam-4064	2	24	definite	definite	ADJ
ejpam-4064	2	25	integral	integral	ADJ
ejpam-4064	2	26	of	of	ADP
ejpam-4064	2	27	exponential	exponential	ADJ
ejpam-4064	2	28	polynomial	polynomial	ADJ
ejpam-4064	2	29	and	and	CCONJ
ejpam-4064	2	30	hyperbolic	hyperbolic	ADJ
ejpam-4064	2	31	function	function	NOUN
ejpam-4064	2	32	in	in	ADP
ejpam-4064	2	33	terms	term	NOUN
ejpam-4064	2	34	of	of	ADP
ejpam-4064	2	35	the	the	DET
ejpam-4064	2	36	incomplete	incomplete	ADJ
ejpam-4064	2	37	gamma	gamma	PROPN
ejpam-4064	2	38	function	function	PROPN
ejpam-4064	2	39	robert	robert	PROPN
ejpam-4064	2	40	reynolds1,∗	reynolds1,∗	PROPN
ejpam-4064	2	41	,	,	PUNCT
ejpam-4064	2	42	allan	allan	PROPN
ejpam-4064	2	43	stauffer1	stauffer1	PROPN
ejpam-4064	2	44	1	1	NUM
ejpam-4064	2	45	department	department	NOUN
ejpam-4064	2	46	of	of	ADP
ejpam-4064	2	47	mathematics	mathematic	NOUN
ejpam-4064	2	48	and	and	CCONJ
ejpam-4064	2	49	statistics	statistic	NOUN
ejpam-4064	2	50	,	,	PUNCT
ejpam-4064	2	51	faculty	faculty	NOUN
ejpam-4064	2	52	of	of	ADP
ejpam-4064	2	53	science	science	PROPN
ejpam-4064	2	54	,	,	PUNCT
ejpam-4064	2	55	york	york	PROPN
ejpam-4064	2	56	university	university	PROPN
ejpam-4064	2	57	,	,	PUNCT
ejpam-4064	2	58	toronto	toronto	PROPN
ejpam-4064	2	59	,	,	PUNCT
ejpam-4064	2	60	ontario	ontario	PROPN
ejpam-4064	2	61	,	,	PUNCT
ejpam-4064	2	62	canada	canada	PROPN
ejpam-4064	2	63	,	,	PUNCT
ejpam-4064	2	64	m3j1p3	m3j1p3	PROPN
ejpam-4064	2	65	abstract	abstract	NOUN
ejpam-4064	2	66	.	.	PUNCT
ejpam-4064	3	1	this	this	DET
ejpam-4064	3	2	current	current	ADJ
ejpam-4064	3	3	paper	paper	NOUN
ejpam-4064	3	4	is	be	AUX
ejpam-4064	3	5	a	a	DET
ejpam-4064	3	6	table	table	NOUN
ejpam-4064	3	7	of	of	ADP
ejpam-4064	3	8	definite	definite	ADJ
ejpam-4064	3	9	integrals	integral	NOUN
ejpam-4064	3	10	involving	involve	VERB
ejpam-4064	3	11	hyperbolic	hyperbolic	ADJ
ejpam-4064	3	12	and	and	CCONJ
ejpam-4064	3	13	logarithmic	logarithmic	ADJ
ejpam-4064	3	14	functions	function	NOUN
ejpam-4064	3	15	expressed	express	VERB
ejpam-4064	3	16	in	in	ADP
ejpam-4064	3	17	terms	term	NOUN
ejpam-4064	3	18	of	of	ADP
ejpam-4064	3	19	the	the	DET
ejpam-4064	3	20	incomplete	incomplete	ADJ
ejpam-4064	3	21	gamma	gamma	NOUN
ejpam-4064	3	22	function	function	NOUN
ejpam-4064	3	23	and	and	CCONJ
ejpam-4064	3	24	fundamental	fundamental	ADJ
ejpam-4064	3	25	constants	constant	NOUN
ejpam-4064	3	26	.	.	PUNCT
ejpam-4064	4	1	all	all	DET
ejpam-4064	4	2	the	the	DET
ejpam-4064	4	3	results	result	NOUN
ejpam-4064	4	4	in	in	ADP
ejpam-4064	4	5	this	this	DET
ejpam-4064	4	6	work	work	NOUN
ejpam-4064	4	7	are	be	AUX
ejpam-4064	4	8	new	new	ADJ
ejpam-4064	4	9	.	.	PUNCT
ejpam-4064	5	1	2020	2020	NUM
ejpam-4064	5	2	mathematics	mathematic	NOUN
ejpam-4064	5	3	subject	subject	NOUN
ejpam-4064	5	4	classifications	classification	NOUN
ejpam-4064	5	5	:	:	PUNCT
ejpam-4064	5	6	30e20,33	30e20,33	NUM
ejpam-4064	5	7	-	-	SYM
ejpam-4064	5	8	01	01	NUM
ejpam-4064	5	9	,	,	PUNCT
ejpam-4064	5	10	33	33	NUM
ejpam-4064	5	11	-	-	SYM
ejpam-4064	5	12	03	03	NUM
ejpam-4064	5	13	,	,	PUNCT
ejpam-4064	5	14	33	33	NUM
ejpam-4064	5	15	-	-	PUNCT
ejpam-4064	5	16	04	04	NUM
ejpam-4064	5	17	,	,	PUNCT
ejpam-4064	5	18	33	33	NUM
ejpam-4064	5	19	-	-	PUNCT
ejpam-4064	5	20	33b	33b	NUM
ejpam-4064	5	21	,	,	PUNCT
ejpam-4064	5	22	33e20	33e20	NUM
ejpam-4064	5	23	key	key	ADJ
ejpam-4064	5	24	words	word	NOUN
ejpam-4064	5	25	and	and	CCONJ
ejpam-4064	5	26	phrases	phrase	NOUN
ejpam-4064	5	27	:	:	PUNCT
ejpam-4064	5	28	entry	entry	NOUN
ejpam-4064	5	29	in	in	ADP
ejpam-4064	5	30	oberhettinger	oberhettinger	NOUN
ejpam-4064	5	31	,	,	PUNCT
ejpam-4064	5	32	incomplete	incomplete	ADJ
ejpam-4064	5	33	gamma	gamma	NOUN
ejpam-4064	5	34	function	function	PROPN
ejpam-4064	5	35	,	,	PUNCT
ejpam-4064	5	36	definite	definite	ADJ
ejpam-4064	5	37	integral	integral	ADJ
ejpam-4064	5	38	,	,	PUNCT
ejpam-4064	5	39	euler	euler	NOUN
ejpam-4064	5	40	’s	’s	NOUN
ejpam-4064	5	41	constant	constant	ADJ
ejpam-4064	5	42	,	,	PUNCT
ejpam-4064	5	43	contour	contour	ADJ
ejpam-4064	5	44	integral	integral	ADJ
ejpam-4064	5	45	1	1	NUM
ejpam-4064	5	46	.	.	NOUN
ejpam-4064	5	47	significance	significance	NOUN
ejpam-4064	5	48	statement	statement	NOUN
ejpam-4064	5	49	in	in	ADP
ejpam-4064	5	50	1990	1990	NUM
ejpam-4064	5	51	,	,	PUNCT
ejpam-4064	5	52	fritz	fritz	PROPN
ejpam-4064	5	53	oberhettinger	oberhettinger	NOUN
ejpam-4064	6	1	[	[	X
ejpam-4064	6	2	5	5	NUM
ejpam-4064	6	3	]	]	PUNCT
ejpam-4064	6	4	published	publish	VERB
ejpam-4064	6	5	his	his	PRON
ejpam-4064	6	6	book	book	NOUN
ejpam-4064	6	7	on	on	ADP
ejpam-4064	6	8	fourier	fourier	NOUN
ejpam-4064	6	9	transforms	transform	VERB
ejpam-4064	6	10	inter	inter	ADJ
ejpam-4064	6	11	alia	alia	NOUN
ejpam-4064	6	12	.	.	PUNCT
ejpam-4064	7	1	in	in	ADP
ejpam-4064	7	2	his	his	PRON
ejpam-4064	7	3	book	book	NOUN
ejpam-4064	7	4	a	a	DET
ejpam-4064	7	5	vast	vast	ADJ
ejpam-4064	7	6	number	number	NOUN
ejpam-4064	7	7	of	of	ADP
ejpam-4064	7	8	definite	definite	ADJ
ejpam-4064	7	9	integrals	integral	NOUN
ejpam-4064	7	10	and	and	CCONJ
ejpam-4064	7	11	transforms	transform	NOUN
ejpam-4064	7	12	are	be	AUX
ejpam-4064	7	13	summarized	summarize	VERB
ejpam-4064	7	14	and	and	CCONJ
ejpam-4064	7	15	tables	table	NOUN
ejpam-4064	7	16	produced	produce	VERB
ejpam-4064	7	17	.	.	PUNCT
ejpam-4064	8	1	these	these	DET
ejpam-4064	8	2	tables	table	NOUN
ejpam-4064	8	3	are	be	AUX
ejpam-4064	8	4	used	use	VERB
ejpam-4064	8	5	in	in	ADP
ejpam-4064	8	6	a	a	DET
ejpam-4064	8	7	wide	wide	ADJ
ejpam-4064	8	8	area	area	NOUN
ejpam-4064	8	9	of	of	ADP
ejpam-4064	8	10	mathematics	mathematic	NOUN
ejpam-4064	8	11	namely	namely	ADV
ejpam-4064	8	12	probability	probability	NOUN
ejpam-4064	8	13	and	and	CCONJ
ejpam-4064	8	14	mathematical	mathematical	ADJ
ejpam-4064	8	15	statistics	statistic	NOUN
ejpam-4064	9	1	[	[	X
ejpam-4064	9	2	3	3	NUM
ejpam-4064	9	3	]	]	PUNCT
ejpam-4064	9	4	,	,	PUNCT
ejpam-4064	9	5	fourier	fourier	ADJ
ejpam-4064	9	6	series	series	NOUN
ejpam-4064	9	7	for	for	ADP
ejpam-4064	9	8	a	a	DET
ejpam-4064	9	9	combination	combination	NOUN
ejpam-4064	9	10	of	of	ADP
ejpam-4064	9	11	jacobian	jacobian	ADJ
ejpam-4064	9	12	elliptic	elliptic	ADJ
ejpam-4064	9	13	functions	function	NOUN
ejpam-4064	9	14	[	[	X
ejpam-4064	9	15	8	8	NUM
ejpam-4064	9	16	]	]	PUNCT
ejpam-4064	9	17	,	,	PUNCT
ejpam-4064	9	18	traveling	travel	VERB
ejpam-4064	9	19	wave	wave	NOUN
ejpam-4064	9	20	solutions	solution	NOUN
ejpam-4064	9	21	to	to	ADP
ejpam-4064	9	22	the	the	DET
ejpam-4064	9	23	two	two	NUM
ejpam-4064	9	24	-	-	PUNCT
ejpam-4064	9	25	dimensional	dimensional	ADJ
ejpam-4064	9	26	korteweg	korteweg	NOUN
ejpam-4064	9	27	-	-	PUNCT
ejpam-4064	9	28	devries	devries	PROPN
ejpam-4064	9	29	equation	equation	NOUN
ejpam-4064	9	30	[	[	X
ejpam-4064	9	31	2	2	NUM
ejpam-4064	9	32	]	]	PUNCT
ejpam-4064	9	33	,	,	PUNCT
ejpam-4064	9	34	and	and	CCONJ
ejpam-4064	9	35	fundamental	fundamental	ADJ
ejpam-4064	9	36	solution	solution	NOUN
ejpam-4064	9	37	of	of	ADP
ejpam-4064	9	38	hyperbolic	hyperbolic	ADJ
ejpam-4064	9	39	differential	differential	NOUN
ejpam-4064	9	40	operators	operator	NOUN
ejpam-4064	9	41	and	and	CCONJ
ejpam-4064	9	42	the	the	DET
ejpam-4064	9	43	poisson	poisson	NOUN
ejpam-4064	9	44	summation	summation	NOUN
ejpam-4064	9	45	formula	formula	NOUN
ejpam-4064	10	1	[	[	X
ejpam-4064	10	2	7	7	X
ejpam-4064	10	3	]	]	PUNCT
ejpam-4064	10	4	to	to	PART
ejpam-4064	10	5	name	name	VERB
ejpam-4064	10	6	a	a	DET
ejpam-4064	10	7	few	few	ADJ
ejpam-4064	10	8	.	.	PUNCT
ejpam-4064	11	1	since	since	SCONJ
ejpam-4064	11	2	there	there	PRON
ejpam-4064	11	3	is	be	VERB
ejpam-4064	11	4	vast	vast	ADJ
ejpam-4064	11	5	usage	usage	NOUN
ejpam-4064	11	6	of	of	ADP
ejpam-4064	11	7	integrals	integral	NOUN
ejpam-4064	11	8	in	in	ADP
ejpam-4064	11	9	the	the	DET
ejpam-4064	11	10	book	book	NOUN
ejpam-4064	11	11	of	of	ADP
ejpam-4064	11	12	oberhettinger	oberhettinger	NOUN
ejpam-4064	11	13	[	[	X
ejpam-4064	11	14	5	5	NUM
ejpam-4064	11	15	]	]	PUNCT
ejpam-4064	11	16	,	,	PUNCT
ejpam-4064	11	17	in	in	ADP
ejpam-4064	11	18	this	this	DET
ejpam-4064	11	19	paper	paper	NOUN
ejpam-4064	11	20	the	the	DET
ejpam-4064	11	21	authors	author	NOUN
ejpam-4064	11	22	aim	aim	VERB
ejpam-4064	11	23	to	to	PART
ejpam-4064	11	24	expand	expand	VERB
ejpam-4064	11	25	on	on	ADP
ejpam-4064	11	26	these	these	DET
ejpam-4064	11	27	tables	table	NOUN
ejpam-4064	11	28	of	of	ADP
ejpam-4064	11	29	integral	integral	ADJ
ejpam-4064	11	30	formula	formula	NOUN
ejpam-4064	11	31	involving	involve	VERB
ejpam-4064	11	32	exponential	exponential	ADJ
ejpam-4064	11	33	and	and	CCONJ
ejpam-4064	11	34	hyperbolic	hyperbolic	ADJ
ejpam-4064	11	35	functions	function	NOUN
ejpam-4064	11	36	by	by	ADP
ejpam-4064	11	37	providing	provide	VERB
ejpam-4064	11	38	new	new	ADJ
ejpam-4064	11	39	formulae	formulae	NOUN
ejpam-4064	11	40	derived	derive	VERB
ejpam-4064	11	41	in	in	ADP
ejpam-4064	11	42	this	this	DET
ejpam-4064	11	43	work	work	NOUN
ejpam-4064	11	44	.	.	PUNCT
ejpam-4064	12	1	another	another	DET
ejpam-4064	12	2	aim	aim	NOUN
ejpam-4064	12	3	in	in	ADP
ejpam-4064	12	4	this	this	DET
ejpam-4064	12	5	work	work	NOUN
ejpam-4064	12	6	is	be	AUX
ejpam-4064	12	7	to	to	PART
ejpam-4064	12	8	provide	provide	VERB
ejpam-4064	12	9	the	the	DET
ejpam-4064	12	10	correct	correct	ADJ
ejpam-4064	12	11	derivation	derivation	NOUN
ejpam-4064	12	12	of	of	ADP
ejpam-4064	12	13	one	one	NUM
ejpam-4064	12	14	of	of	ADP
ejpam-4064	12	15	the	the	DET
ejpam-4064	12	16	integrals	integral	NOUN
ejpam-4064	12	17	tables	table	VERB
ejpam-4064	12	18	in	in	ADP
ejpam-4064	12	19	[	[	X
ejpam-4064	12	20	5	5	NUM
ejpam-4064	12	21	]	]	PUNCT
ejpam-4064	12	22	,	,	PUNCT
ejpam-4064	12	23	which	which	PRON
ejpam-4064	12	24	is	be	AUX
ejpam-4064	12	25	of	of	ADP
ejpam-4064	12	26	importance	importance	NOUN
ejpam-4064	12	27	since	since	SCONJ
ejpam-4064	12	28	the	the	DET
ejpam-4064	12	29	book	book	NOUN
ejpam-4064	12	30	of	of	ADP
ejpam-4064	12	31	oberhettinger	oberhettinger	NOUN
ejpam-4064	12	32	is	be	AUX
ejpam-4064	12	33	so	so	ADV
ejpam-4064	12	34	widely	widely	ADV
ejpam-4064	12	35	used	use	VERB
ejpam-4064	12	36	.	.	PUNCT
ejpam-4064	13	1	providing	provide	VERB
ejpam-4064	13	2	an	an	DET
ejpam-4064	13	3	updated	update	VERB
ejpam-4064	13	4	version	version	NOUN
ejpam-4064	13	5	of	of	ADP
ejpam-4064	13	6	these	these	DET
ejpam-4064	13	7	tables	table	NOUN
ejpam-4064	13	8	will	will	AUX
ejpam-4064	13	9	also	also	ADV
ejpam-4064	13	10	assist	assist	VERB
ejpam-4064	13	11	in	in	ADP
ejpam-4064	13	12	expanding	expand	VERB
ejpam-4064	13	13	current	current	ADJ
ejpam-4064	13	14	and	and	CCONJ
ejpam-4064	13	15	future	future	ADJ
ejpam-4064	13	16	research	research	NOUN
ejpam-4064	13	17	where	where	SCONJ
ejpam-4064	13	18	these	these	DET
ejpam-4064	13	19	types	type	NOUN
ejpam-4064	13	20	of	of	ADP
ejpam-4064	13	21	integrals	integral	NOUN
ejpam-4064	13	22	are	be	AUX
ejpam-4064	13	23	used	use	VERB
ejpam-4064	13	24	.	.	PUNCT
ejpam-4064	14	1	∗corresponding	∗corresponde	VERB
ejpam-4064	14	2	author	author	NOUN
ejpam-4064	14	3	.	.	PUNCT
ejpam-4064	15	1	doi	doi	NOUN
ejpam-4064	15	2	:	:	PUNCT
ejpam-4064	15	3	https://doi.org/10.29020/nybg.ejpam.v14i4.4064	https://doi.org/10.29020/nybg.ejpam.v14i4.4064	PRON
ejpam-4064	15	4	email	email	NOUN
ejpam-4064	15	5	addresses	address	NOUN
ejpam-4064	15	6	:	:	PUNCT
ejpam-4064	16	1	milver@my.yorku.ca	milver@my.yorku.ca	NOUN
ejpam-4064	16	2	(	(	PUNCT
ejpam-4064	16	3	r.	r.	PROPN
ejpam-4064	16	4	reynolds	reynolds	PROPN
ejpam-4064	16	5	)	)	PUNCT
ejpam-4064	16	6	,	,	PUNCT
ejpam-4064	16	7	stauffer@yorku.ca	stauffer@yorku.ca	NOUN
ejpam-4064	16	8	(	(	PUNCT
ejpam-4064	16	9	a.	a.	NOUN
ejpam-4064	16	10	stauffer	stauffer	PROPN
ejpam-4064	16	11	)	)	PUNCT
ejpam-4064	16	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4064	17	1	1295	1295	NUM
ejpam-4064	17	2	©	©	PROPN
ejpam-4064	17	3	2021	2021	NUM
ejpam-4064	17	4	ejpam	ejpam	VERB
ejpam-4064	17	5	all	all	DET
ejpam-4064	17	6	rights	right	NOUN
ejpam-4064	17	7	reserved	reserve	VERB
ejpam-4064	17	8	.	.	PUNCT
ejpam-4064	18	1	r.	r.	PROPN
ejpam-4064	18	2	reynolds	reynolds	PROPN
ejpam-4064	18	3	,	,	PUNCT
ejpam-4064	18	4	a.	a.	PROPN
ejpam-4064	18	5	stauffer	stauffer	PROPN
ejpam-4064	18	6	/	/	SYM
ejpam-4064	18	7	eur	eur	PROPN
ejpam-4064	18	8	.	.	PUNCT
ejpam-4064	19	1	j.	j.	PROPN
ejpam-4064	19	2	pure	pure	PROPN
ejpam-4064	19	3	appl	appl	PROPN
ejpam-4064	19	4	.	.	PROPN
ejpam-4064	19	5	math	math	PROPN
ejpam-4064	19	6	,	,	PUNCT
ejpam-4064	19	7	14	14	NUM
ejpam-4064	19	8	(	(	PUNCT
ejpam-4064	19	9	4	4	NUM
ejpam-4064	19	10	)	)	PUNCT
ejpam-4064	19	11	(	(	PUNCT
ejpam-4064	19	12	2021	2021	NUM
ejpam-4064	19	13	)	)	PUNCT
ejpam-4064	19	14	,	,	PUNCT
ejpam-4064	19	15	1295	1295	NUM
ejpam-4064	19	16	-	-	SYM
ejpam-4064	19	17	1305	1305	NUM
ejpam-4064	19	18	1296	1296	NUM
ejpam-4064	19	19	2	2	NUM
ejpam-4064	19	20	.	.	PUNCT
ejpam-4064	19	21	introduction	introduction	NOUN
ejpam-4064	19	22	in	in	ADP
ejpam-4064	19	23	this	this	DET
ejpam-4064	19	24	paper	paper	NOUN
ejpam-4064	19	25	we	we	PRON
ejpam-4064	19	26	derive	derive	VERB
ejpam-4064	19	27	the	the	DET
ejpam-4064	19	28	definite	definite	ADJ
ejpam-4064	19	29	integral	integral	NOUN
ejpam-4064	19	30	given	give	VERB
ejpam-4064	19	31	by	by	ADP
ejpam-4064	19	32	(	(	PUNCT
ejpam-4064	19	33	1	1	NUM
ejpam-4064	19	34	)	)	PUNCT
ejpam-4064	19	35	∫	∫	PROPN
ejpam-4064	19	36	∞	∞	PROPN
ejpam-4064	19	37	0	0	NUM
ejpam-4064	19	38	log(tanh(αx	log(tanh(αx	NOUN
ejpam-4064	19	39	)	)	PUNCT
ejpam-4064	19	40	)	)	PUNCT
ejpam-4064	20	1	(	(	PUNCT
ejpam-4064	20	2	eimx(log(a	eimx(log(a	NOUN
ejpam-4064	20	3	)	)	PUNCT
ejpam-4064	20	4	+	+	CCONJ
ejpam-4064	20	5	ix)k	ix)k	PROPN
ejpam-4064	20	6	+	+	CCONJ
ejpam-4064	20	7	e−imx(log(a)−	e−imx(log(a)−	NOUN
ejpam-4064	20	8	ix)k	ix)k	NOUN
ejpam-4064	20	9	)	)	PUNCT
ejpam-4064	20	10	dx	dx	PROPN
ejpam-4064	20	11	where	where	SCONJ
ejpam-4064	20	12	the	the	DET
ejpam-4064	20	13	parameters	parameter	NOUN
ejpam-4064	20	14	k	k	PROPN
ejpam-4064	20	15	,	,	PUNCT
ejpam-4064	20	16	a	a	PRON
ejpam-4064	20	17	are	be	AUX
ejpam-4064	20	18	general	general	ADJ
ejpam-4064	20	19	complex	complex	ADJ
ejpam-4064	20	20	numbers	number	NOUN
ejpam-4064	20	21	,	,	PUNCT
ejpam-4064	20	22	re(α	re(α	NOUN
ejpam-4064	20	23	)	)	PUNCT
ejpam-4064	20	24	>	>	X
ejpam-4064	20	25	0	0	PUNCT
ejpam-4064	20	26	and	and	CCONJ
ejpam-4064	20	27	−1	−1	NOUN
ejpam-4064	20	28	<	<	X
ejpam-4064	20	29	re(m	re(m	PROPN
ejpam-4064	20	30	)	)	PUNCT
ejpam-4064	20	31	<	<	X
ejpam-4064	20	32	0	0	X
ejpam-4064	20	33	.	.	PUNCT
ejpam-4064	21	1	the	the	DET
ejpam-4064	21	2	integral	integral	ADJ
ejpam-4064	21	3	will	will	AUX
ejpam-4064	21	4	be	be	AUX
ejpam-4064	21	5	used	use	VERB
ejpam-4064	21	6	to	to	PART
ejpam-4064	21	7	derive	derive	VERB
ejpam-4064	21	8	special	special	ADJ
ejpam-4064	21	9	cases	case	NOUN
ejpam-4064	21	10	in	in	ADP
ejpam-4064	21	11	terms	term	NOUN
ejpam-4064	21	12	of	of	ADP
ejpam-4064	21	13	special	special	ADJ
ejpam-4064	21	14	functions	function	NOUN
ejpam-4064	21	15	and	and	CCONJ
ejpam-4064	21	16	fundamental	fundamental	ADJ
ejpam-4064	21	17	constants	constant	NOUN
ejpam-4064	21	18	.	.	PUNCT
ejpam-4064	22	1	the	the	DET
ejpam-4064	22	2	derivations	derivation	NOUN
ejpam-4064	22	3	follow	follow	VERB
ejpam-4064	22	4	the	the	DET
ejpam-4064	22	5	method	method	NOUN
ejpam-4064	22	6	used	use	VERB
ejpam-4064	22	7	by	by	ADP
ejpam-4064	22	8	us	we	PRON
ejpam-4064	22	9	in	in	ADP
ejpam-4064	22	10	[	[	X
ejpam-4064	22	11	9	9	NUM
ejpam-4064	22	12	]	]	PUNCT
ejpam-4064	22	13	.	.	PUNCT
ejpam-4064	23	1	this	this	DET
ejpam-4064	23	2	method	method	NOUN
ejpam-4064	23	3	involves	involve	VERB
ejpam-4064	23	4	using	use	VERB
ejpam-4064	23	5	a	a	DET
ejpam-4064	23	6	form	form	NOUN
ejpam-4064	23	7	of	of	ADP
ejpam-4064	23	8	the	the	DET
ejpam-4064	23	9	generalized	generalize	VERB
ejpam-4064	23	10	cauchy	cauchy	PROPN
ejpam-4064	23	11	’s	’s	PART
ejpam-4064	23	12	integral	integral	ADJ
ejpam-4064	23	13	formula	formula	NOUN
ejpam-4064	23	14	given	give	VERB
ejpam-4064	23	15	by	by	ADP
ejpam-4064	23	16	yk	yk	PROPN
ejpam-4064	23	17	γ(k	γ(k	PROPN
ejpam-4064	23	18	+	+	CCONJ
ejpam-4064	23	19	1	1	X
ejpam-4064	23	20	)	)	PUNCT
ejpam-4064	23	21	=	=	SYM
ejpam-4064	23	22	1	1	NUM
ejpam-4064	23	23	2πi	2πi	ADJ
ejpam-4064	23	24	∫	∫	PROPN
ejpam-4064	23	25	c	c	PROPN
ejpam-4064	23	26	ewy	ewy	PROPN
ejpam-4064	23	27	wk+1	wk+1	PROPN
ejpam-4064	23	28	dw	dw	PROPN
ejpam-4064	23	29	.	.	PUNCT
ejpam-4064	24	1	(	(	PUNCT
ejpam-4064	24	2	2	2	X
ejpam-4064	24	3	)	)	PUNCT
ejpam-4064	24	4	where	where	SCONJ
ejpam-4064	24	5	c	c	NOUN
ejpam-4064	24	6	is	be	AUX
ejpam-4064	24	7	in	in	ADP
ejpam-4064	24	8	general	general	ADJ
ejpam-4064	24	9	an	an	DET
ejpam-4064	24	10	open	open	ADJ
ejpam-4064	24	11	contour	contour	NOUN
ejpam-4064	24	12	in	in	ADP
ejpam-4064	24	13	the	the	DET
ejpam-4064	24	14	complex	complex	ADJ
ejpam-4064	24	15	plane	plane	NOUN
ejpam-4064	24	16	where	where	SCONJ
ejpam-4064	24	17	the	the	DET
ejpam-4064	24	18	bilinear	bilinear	NOUN
ejpam-4064	24	19	concomitant	concomitant	NOUN
ejpam-4064	25	1	[	[	X
ejpam-4064	25	2	9	9	NUM
ejpam-4064	25	3	]	]	PUNCT
ejpam-4064	25	4	has	have	VERB
ejpam-4064	25	5	the	the	DET
ejpam-4064	25	6	same	same	ADJ
ejpam-4064	25	7	value	value	NOUN
ejpam-4064	25	8	at	at	ADP
ejpam-4064	25	9	the	the	DET
ejpam-4064	25	10	end	end	NOUN
ejpam-4064	25	11	points	point	NOUN
ejpam-4064	25	12	of	of	ADP
ejpam-4064	25	13	the	the	DET
ejpam-4064	25	14	contour	contour	NOUN
ejpam-4064	25	15	.	.	PUNCT
ejpam-4064	26	1	we	we	PRON
ejpam-4064	26	2	then	then	ADV
ejpam-4064	26	3	multiply	multiply	VERB
ejpam-4064	26	4	both	both	DET
ejpam-4064	26	5	sides	side	NOUN
ejpam-4064	26	6	by	by	ADP
ejpam-4064	26	7	a	a	DET
ejpam-4064	26	8	function	function	NOUN
ejpam-4064	26	9	of	of	ADP
ejpam-4064	26	10	x	x	PUNCT
ejpam-4064	26	11	and	and	CCONJ
ejpam-4064	26	12	then	then	ADV
ejpam-4064	26	13	take	take	VERB
ejpam-4064	26	14	a	a	DET
ejpam-4064	26	15	definite	definite	ADJ
ejpam-4064	26	16	integral	integral	NOUN
ejpam-4064	26	17	of	of	ADP
ejpam-4064	26	18	both	both	DET
ejpam-4064	26	19	sides	side	NOUN
ejpam-4064	26	20	.	.	PUNCT
ejpam-4064	27	1	this	this	PRON
ejpam-4064	27	2	yields	yield	VERB
ejpam-4064	27	3	a	a	DET
ejpam-4064	27	4	definite	definite	ADJ
ejpam-4064	27	5	integral	integral	ADJ
ejpam-4064	27	6	in	in	ADP
ejpam-4064	27	7	terms	term	NOUN
ejpam-4064	27	8	of	of	ADP
ejpam-4064	27	9	a	a	DET
ejpam-4064	27	10	contour	contour	NOUN
ejpam-4064	27	11	integral	integral	NOUN
ejpam-4064	27	12	.	.	PUNCT
ejpam-4064	28	1	then	then	ADV
ejpam-4064	28	2	we	we	PRON
ejpam-4064	28	3	multiply	multiply	VERB
ejpam-4064	28	4	both	both	DET
ejpam-4064	28	5	sides	side	NOUN
ejpam-4064	28	6	of	of	ADP
ejpam-4064	28	7	equation	equation	NOUN
ejpam-4064	28	8	(	(	PUNCT
ejpam-4064	28	9	2	2	NUM
ejpam-4064	28	10	)	)	PUNCT
ejpam-4064	28	11	by	by	ADP
ejpam-4064	28	12	another	another	DET
ejpam-4064	28	13	function	function	NOUN
ejpam-4064	28	14	of	of	ADP
ejpam-4064	28	15	x	x	PUNCT
ejpam-4064	28	16	and	and	CCONJ
ejpam-4064	28	17	take	take	VERB
ejpam-4064	28	18	the	the	DET
ejpam-4064	28	19	infinite	infinite	ADJ
ejpam-4064	28	20	sums	sum	NOUN
ejpam-4064	28	21	of	of	ADP
ejpam-4064	28	22	both	both	DET
ejpam-4064	28	23	sides	side	NOUN
ejpam-4064	28	24	such	such	ADJ
ejpam-4064	28	25	that	that	SCONJ
ejpam-4064	28	26	the	the	DET
ejpam-4064	28	27	contour	contour	NOUN
ejpam-4064	28	28	integral	integral	NOUN
ejpam-4064	28	29	of	of	ADP
ejpam-4064	28	30	both	both	DET
ejpam-4064	28	31	equations	equation	NOUN
ejpam-4064	28	32	are	be	AUX
ejpam-4064	28	33	the	the	DET
ejpam-4064	28	34	same	same	ADJ
ejpam-4064	28	35	.	.	PUNCT
ejpam-4064	29	1	3	3	X
ejpam-4064	29	2	.	.	X
ejpam-4064	29	3	definite	definite	ADJ
ejpam-4064	29	4	integral	integral	ADJ
ejpam-4064	29	5	of	of	ADP
ejpam-4064	29	6	the	the	DET
ejpam-4064	29	7	contour	contour	NOUN
ejpam-4064	29	8	integral	integral	NOUN
ejpam-4064	29	9	we	we	PRON
ejpam-4064	29	10	use	use	VERB
ejpam-4064	29	11	the	the	DET
ejpam-4064	29	12	method	method	NOUN
ejpam-4064	29	13	in	in	ADP
ejpam-4064	29	14	[	[	X
ejpam-4064	29	15	9	9	NUM
ejpam-4064	29	16	]	]	PUNCT
ejpam-4064	29	17	.	.	PUNCT
ejpam-4064	30	1	the	the	DET
ejpam-4064	30	2	variable	variable	NOUN
ejpam-4064	30	3	of	of	ADP
ejpam-4064	30	4	integration	integration	NOUN
ejpam-4064	30	5	in	in	ADP
ejpam-4064	30	6	the	the	DET
ejpam-4064	30	7	contour	contour	NOUN
ejpam-4064	30	8	integral	integral	NOUN
ejpam-4064	30	9	is	be	AUX
ejpam-4064	30	10	t	t	NOUN
ejpam-4064	30	11	=	=	PUNCT
ejpam-4064	30	12	m+w	m+w	NOUN
ejpam-4064	30	13	.	.	PUNCT
ejpam-4064	31	1	the	the	DET
ejpam-4064	31	2	cut	cut	NOUN
ejpam-4064	31	3	and	and	CCONJ
ejpam-4064	31	4	contour	contour	NOUN
ejpam-4064	31	5	are	be	AUX
ejpam-4064	31	6	in	in	ADP
ejpam-4064	31	7	the	the	DET
ejpam-4064	31	8	second	second	ADJ
ejpam-4064	31	9	quadrant	quadrant	NOUN
ejpam-4064	31	10	of	of	ADP
ejpam-4064	31	11	the	the	DET
ejpam-4064	31	12	complex	complex	ADJ
ejpam-4064	31	13	z	z	NOUN
ejpam-4064	31	14	-	-	NOUN
ejpam-4064	31	15	plane	plane	NOUN
ejpam-4064	31	16	.	.	PUNCT
ejpam-4064	32	1	the	the	DET
ejpam-4064	32	2	cut	cut	NOUN
ejpam-4064	32	3	approaches	approach	VERB
ejpam-4064	32	4	the	the	DET
ejpam-4064	32	5	origin	origin	NOUN
ejpam-4064	32	6	from	from	ADP
ejpam-4064	32	7	the	the	DET
ejpam-4064	32	8	interior	interior	NOUN
ejpam-4064	32	9	of	of	ADP
ejpam-4064	32	10	the	the	DET
ejpam-4064	32	11	first	first	ADJ
ejpam-4064	32	12	quadrant	quadrant	NOUN
ejpam-4064	32	13	and	and	CCONJ
ejpam-4064	32	14	the	the	DET
ejpam-4064	32	15	contour	contour	NOUN
ejpam-4064	32	16	goes	go	VERB
ejpam-4064	32	17	round	round	ADP
ejpam-4064	32	18	the	the	DET
ejpam-4064	32	19	origin	origin	NOUN
ejpam-4064	32	20	with	with	ADP
ejpam-4064	32	21	zero	zero	NUM
ejpam-4064	32	22	radius	radius	NOUN
ejpam-4064	32	23	and	and	CCONJ
ejpam-4064	32	24	is	be	AUX
ejpam-4064	32	25	on	on	ADP
ejpam-4064	32	26	opposite	opposite	ADJ
ejpam-4064	32	27	sides	side	NOUN
ejpam-4064	32	28	of	of	ADP
ejpam-4064	32	29	the	the	DET
ejpam-4064	32	30	cut	cut	NOUN
ejpam-4064	32	31	.	.	PUNCT
ejpam-4064	33	1	using	use	VERB
ejpam-4064	33	2	equation	equation	NOUN
ejpam-4064	33	3	(	(	PUNCT
ejpam-4064	33	4	2	2	X
ejpam-4064	33	5	)	)	PUNCT
ejpam-4064	33	6	we	we	PRON
ejpam-4064	33	7	replace	replace	VERB
ejpam-4064	33	8	y	y	PROPN
ejpam-4064	33	9	→	→	SYM
ejpam-4064	33	10	iy	iy	PROPN
ejpam-4064	33	11	+	+	CCONJ
ejpam-4064	33	12	log(a	log(a	PROPN
ejpam-4064	33	13	)	)	PUNCT
ejpam-4064	33	14	and	and	CCONJ
ejpam-4064	33	15	multiply	multiply	ADV
ejpam-4064	33	16	by	by	ADP
ejpam-4064	33	17	eimy	eimy	NOUN
ejpam-4064	33	18	.	.	PUNCT
ejpam-4064	34	1	next	next	ADV
ejpam-4064	34	2	we	we	PRON
ejpam-4064	34	3	replace	replace	VERB
ejpam-4064	34	4	y	y	PROPN
ejpam-4064	34	5	→	→	SYM
ejpam-4064	34	6	−y	−y	VERB
ejpam-4064	34	7	to	to	PART
ejpam-4064	34	8	form	form	VERB
ejpam-4064	34	9	a	a	DET
ejpam-4064	34	10	second	second	ADJ
ejpam-4064	34	11	equation	equation	NOUN
ejpam-4064	34	12	and	and	CCONJ
ejpam-4064	34	13	add	add	VERB
ejpam-4064	34	14	both	both	PRON
ejpam-4064	34	15	to	to	PART
ejpam-4064	34	16	get	get	VERB
ejpam-4064	34	17	(	(	PUNCT
ejpam-4064	34	18	3	3	NUM
ejpam-4064	34	19	)	)	PUNCT
ejpam-4064	34	20	(	(	PUNCT
ejpam-4064	34	21	eimy(log(a	eimy(log(a	PROPN
ejpam-4064	34	22	)	)	PUNCT
ejpam-4064	35	1	+	+	PROPN
ejpam-4064	36	1	iy)k	iy)k	PROPN
ejpam-4064	36	2	+	+	NUM
ejpam-4064	36	3	e−imy(log(a)−	e−imy(log(a)−	PROPN
ejpam-4064	36	4	iy)k	iy)k	PROPN
ejpam-4064	36	5	)	)	PUNCT
ejpam-4064	36	6	γ(k	γ(k	PROPN
ejpam-4064	36	7	+	+	CCONJ
ejpam-4064	36	8	1	1	X
ejpam-4064	36	9	)	)	PUNCT
ejpam-4064	36	10	=	=	SYM
ejpam-4064	36	11	1	1	NUM
ejpam-4064	36	12	2πi	2πi	ADJ
ejpam-4064	36	13	∫	∫	PROPN
ejpam-4064	37	1	c	c	NOUN
ejpam-4064	37	2	2aww−k−1	2aww−k−1	NUM
ejpam-4064	37	3	cos(y(m+	cos(y(m+	NOUN
ejpam-4064	37	4	w))dw	w))dw	NOUN
ejpam-4064	37	5	next	next	ADV
ejpam-4064	37	6	we	we	PRON
ejpam-4064	37	7	replace	replace	VERB
ejpam-4064	37	8	y	y	PROPN
ejpam-4064	37	9	→	→	SYM
ejpam-4064	37	10	x	x	X
ejpam-4064	37	11	,	,	PUNCT
ejpam-4064	37	12	multiply	multiply	VERB
ejpam-4064	37	13	both	both	DET
ejpam-4064	37	14	sides	side	NOUN
ejpam-4064	37	15	by	by	ADP
ejpam-4064	37	16	1	1	NUM
ejpam-4064	37	17	2	2	NUM
ejpam-4064	37	18	log(tanh(αx	log(tanh(αx	NOUN
ejpam-4064	37	19	)	)	PUNCT
ejpam-4064	37	20	)	)	PUNCT
ejpam-4064	37	21	and	and	CCONJ
ejpam-4064	37	22	take	take	VERB
ejpam-4064	37	23	the	the	DET
ejpam-4064	37	24	definite	definite	ADJ
ejpam-4064	37	25	integral	integral	ADJ
ejpam-4064	37	26	over	over	ADP
ejpam-4064	37	27	x	x	PUNCT
ejpam-4064	37	28	∈	∈	PROPN
ejpam-4064	38	1	[	[	X
ejpam-4064	38	2	0,∞	0,∞	NOUN
ejpam-4064	38	3	)	)	PUNCT
ejpam-4064	38	4	to	to	PART
ejpam-4064	38	5	get	get	VERB
ejpam-4064	38	6	(	(	PUNCT
ejpam-4064	38	7	4	4	NUM
ejpam-4064	38	8	)	)	PUNCT
ejpam-4064	38	9	∫	∫	PROPN
ejpam-4064	39	1	∞	∞	PROPN
ejpam-4064	39	2	0	0	NUM
ejpam-4064	39	3	log(tanh(αx	log(tanh(αx	NOUN
ejpam-4064	39	4	)	)	PUNCT
ejpam-4064	39	5	)	)	PUNCT
ejpam-4064	40	1	(	(	PUNCT
ejpam-4064	40	2	eimx(log(a	eimx(log(a	NOUN
ejpam-4064	40	3	)	)	PUNCT
ejpam-4064	40	4	+	+	CCONJ
ejpam-4064	40	5	ix)k	ix)k	PROPN
ejpam-4064	40	6	+	+	CCONJ
ejpam-4064	40	7	e−imx(log(a)−	e−imx(log(a)−	NOUN
ejpam-4064	40	8	ix)k	ix)k	NOUN
ejpam-4064	40	9	)	)	PUNCT
ejpam-4064	40	10	2γ(k	2γ(k	NUM
ejpam-4064	41	1	+	+	CCONJ
ejpam-4064	41	2	1	1	X
ejpam-4064	41	3	)	)	PUNCT
ejpam-4064	41	4	dx	dx	PROPN
ejpam-4064	41	5	=	=	SYM
ejpam-4064	41	6	1	1	NUM
ejpam-4064	41	7	2πi	2πi	NOUN
ejpam-4064	41	8	∫	∫	PROPN
ejpam-4064	42	1	∞	∞	NUM
ejpam-4064	42	2	0	0	NUM
ejpam-4064	43	1	∫	∫	PROPN
ejpam-4064	43	2	c	c	NOUN
ejpam-4064	43	3	aww−k−1	aww−k−1	NOUN
ejpam-4064	43	4	cos(x(m+	cos(x(m+	NOUN
ejpam-4064	43	5	w	w	NOUN
ejpam-4064	43	6	)	)	PUNCT
ejpam-4064	43	7	)	)	PUNCT
ejpam-4064	43	8	log(tanh(αx))dwdx	log(tanh(αx))dwdx	PROPN
ejpam-4064	43	9	=	=	SYM
ejpam-4064	43	10	1	1	NUM
ejpam-4064	43	11	2πi	2πi	NOUN
ejpam-4064	43	12	∫	∫	PROPN
ejpam-4064	44	1	c	c	PROPN
ejpam-4064	44	2	∫	∫	PROPN
ejpam-4064	44	3	∞	∞	NUM
ejpam-4064	44	4	0	0	NUM
ejpam-4064	44	5	aww−k−1	aww−k−1	NOUN
ejpam-4064	44	6	cos(x(m+	cos(x(m+	NOUN
ejpam-4064	44	7	w	w	NOUN
ejpam-4064	44	8	)	)	PUNCT
ejpam-4064	44	9	)	)	PUNCT
ejpam-4064	45	1	log(tanh(αx))dxdw	log(tanh(αx))dxdw	ADJ
ejpam-4064	45	2	−	−	NOUN
ejpam-4064	45	3	1	1	NUM
ejpam-4064	45	4	2πi	2πi	NOUN
ejpam-4064	45	5	∫	∫	PROPN
ejpam-4064	45	6	c	c	PROPN
ejpam-4064	46	1	πaww−k−1	πaww−k−1	PROPN
ejpam-4064	46	2	tanh	tanh	PROPN
ejpam-4064	46	3	(	(	PUNCT
ejpam-4064	46	4	π(m+w	π(m+w	NOUN
ejpam-4064	46	5	)	)	PUNCT
ejpam-4064	46	6	4α	4α	NOUN
ejpam-4064	46	7	)	)	PUNCT
ejpam-4064	46	8	2(m+	2(m+	X
ejpam-4064	46	9	w	w	X
ejpam-4064	46	10	)	)	PUNCT
ejpam-4064	46	11	dw	dw	PROPN
ejpam-4064	46	12	r.	r.	PROPN
ejpam-4064	46	13	reynolds	reynolds	PROPN
ejpam-4064	46	14	,	,	PUNCT
ejpam-4064	46	15	a.	a.	PROPN
ejpam-4064	46	16	stauffer	stauffer	PROPN
ejpam-4064	46	17	/	/	SYM
ejpam-4064	46	18	eur	eur	PROPN
ejpam-4064	46	19	.	.	PUNCT
ejpam-4064	47	1	j.	j.	PROPN
ejpam-4064	47	2	pure	pure	PROPN
ejpam-4064	47	3	appl	appl	PROPN
ejpam-4064	47	4	.	.	PROPN
ejpam-4064	47	5	math	math	PROPN
ejpam-4064	47	6	,	,	PUNCT
ejpam-4064	47	7	14	14	NUM
ejpam-4064	47	8	(	(	PUNCT
ejpam-4064	47	9	4	4	NUM
ejpam-4064	47	10	)	)	PUNCT
ejpam-4064	47	11	(	(	PUNCT
ejpam-4064	47	12	2021	2021	NUM
ejpam-4064	47	13	)	)	PUNCT
ejpam-4064	47	14	,	,	PUNCT
ejpam-4064	47	15	1295	1295	NUM
ejpam-4064	47	16	-	-	SYM
ejpam-4064	47	17	1305	1305	NUM
ejpam-4064	47	18	1297	1297	NUM
ejpam-4064	47	19	from	from	ADP
ejpam-4064	47	20	equation	equation	NOUN
ejpam-4064	47	21	(	(	PUNCT
ejpam-4064	47	22	1.7.7.112	1.7.7.112	NUM
ejpam-4064	47	23	)	)	PUNCT
ejpam-4064	47	24	in	in	ADP
ejpam-4064	47	25	[	[	X
ejpam-4064	47	26	5	5	NUM
ejpam-4064	47	27	]	]	PUNCT
ejpam-4064	47	28	where	where	SCONJ
ejpam-4064	47	29	0	0	X
ejpam-4064	47	30	<	<	X
ejpam-4064	47	31	re(w+m	re(w+m	PROPN
ejpam-4064	47	32	)	)	PUNCT
ejpam-4064	47	33	<	<	X
ejpam-4064	48	1	1	1	X
ejpam-4064	48	2	.	.	PUNCT
ejpam-4064	48	3	we	we	PRON
ejpam-4064	48	4	are	be	AUX
ejpam-4064	48	5	able	able	ADJ
ejpam-4064	48	6	to	to	PART
ejpam-4064	48	7	switch	switch	VERB
ejpam-4064	48	8	the	the	DET
ejpam-4064	48	9	order	order	NOUN
ejpam-4064	48	10	of	of	ADP
ejpam-4064	48	11	integration	integration	NOUN
ejpam-4064	48	12	over	over	ADP
ejpam-4064	48	13	w+m	w+m	PROPN
ejpam-4064	48	14	and	and	CCONJ
ejpam-4064	48	15	x	x	SYM
ejpam-4064	48	16	using	use	VERB
ejpam-4064	48	17	fubini	fubini	NOUN
ejpam-4064	48	18	’s	’s	PART
ejpam-4064	48	19	theorem	theorem	NOUN
ejpam-4064	48	20	since	since	SCONJ
ejpam-4064	48	21	the	the	DET
ejpam-4064	48	22	integrand	integrand	NOUN
ejpam-4064	48	23	is	be	AUX
ejpam-4064	48	24	of	of	ADP
ejpam-4064	48	25	bounded	bounded	ADJ
ejpam-4064	48	26	measure	measure	NOUN
ejpam-4064	48	27	over	over	ADP
ejpam-4064	48	28	the	the	DET
ejpam-4064	48	29	space	space	NOUN
ejpam-4064	48	30	c×	c×	PROPN
ejpam-4064	49	1	[	[	X
ejpam-4064	49	2	0,∞	0,∞	NOUN
ejpam-4064	49	3	)	)	PUNCT
ejpam-4064	49	4	.	.	PUNCT
ejpam-4064	50	1	note	note	VERB
ejpam-4064	50	2	the	the	DET
ejpam-4064	50	3	equation	equation	NOUN
ejpam-4064	50	4	quoted	quote	VERB
ejpam-4064	50	5	in	in	ADP
ejpam-4064	50	6	[	[	X
ejpam-4064	50	7	5	5	NUM
ejpam-4064	50	8	]	]	PUNCT
ejpam-4064	50	9	is	be	AUX
ejpam-4064	50	10	in	in	ADP
ejpam-4064	50	11	error	error	NOUN
ejpam-4064	50	12	.	.	PUNCT
ejpam-4064	51	1	4	4	X
ejpam-4064	51	2	.	.	X
ejpam-4064	51	3	the	the	DET
ejpam-4064	51	4	incomplete	incomplete	ADJ
ejpam-4064	51	5	gamma	gamma	NOUN
ejpam-4064	51	6	function	function	NOUN
ejpam-4064	51	7	and	and	CCONJ
ejpam-4064	51	8	its	its	PRON
ejpam-4064	51	9	contour	contour	ADJ
ejpam-4064	51	10	integral	integral	ADJ
ejpam-4064	51	11	representation	representation	NOUN
ejpam-4064	51	12	the	the	DET
ejpam-4064	51	13	incomplete	incomplete	ADJ
ejpam-4064	51	14	gamma	gamma	NOUN
ejpam-4064	51	15	functions	function	NOUN
ejpam-4064	52	1	[	[	X
ejpam-4064	52	2	1	1	NUM
ejpam-4064	52	3	]	]	PUNCT
ejpam-4064	52	4	,	,	PUNCT
ejpam-4064	52	5	γ(a	γ(a	PROPN
ejpam-4064	52	6	,	,	PUNCT
ejpam-4064	52	7	z	z	NOUN
ejpam-4064	52	8	)	)	PUNCT
ejpam-4064	52	9	and	and	CCONJ
ejpam-4064	52	10	γ(a	γ(a	PROPN
ejpam-4064	52	11	,	,	PUNCT
ejpam-4064	52	12	z	z	NOUN
ejpam-4064	52	13	)	)	PUNCT
ejpam-4064	52	14	,	,	PUNCT
ejpam-4064	52	15	are	be	AUX
ejpam-4064	52	16	defined	define	VERB
ejpam-4064	52	17	by	by	ADP
ejpam-4064	52	18	γ(a	γ(a	NOUN
ejpam-4064	52	19	,	,	PUNCT
ejpam-4064	52	20	z	z	NOUN
ejpam-4064	52	21	)	)	PUNCT
ejpam-4064	53	1	=	=	SYM
ejpam-4064	53	2	∫	∫	PROPN
ejpam-4064	53	3	z	z	PROPN
ejpam-4064	53	4	0	0	NUM
ejpam-4064	53	5	ta−1e−tdt	ta−1e−tdt	PROPN
ejpam-4064	53	6	(	(	PUNCT
ejpam-4064	53	7	5	5	NUM
ejpam-4064	53	8	)	)	PUNCT
ejpam-4064	53	9	and	and	CCONJ
ejpam-4064	53	10	γ(a	γ(a	PROPN
ejpam-4064	53	11	,	,	PUNCT
ejpam-4064	53	12	z	z	NOUN
ejpam-4064	53	13	)	)	PUNCT
ejpam-4064	53	14	=	=	SYM
ejpam-4064	54	1	∫	∫	PROPN
ejpam-4064	54	2	∞	∞	PROPN
ejpam-4064	54	3	z	z	PROPN
ejpam-4064	54	4	ta−1e−tdt	ta−1e−tdt	PROPN
ejpam-4064	54	5	(	(	PUNCT
ejpam-4064	54	6	6	6	NUM
ejpam-4064	54	7	)	)	PUNCT
ejpam-4064	54	8	where	where	SCONJ
ejpam-4064	54	9	re(a	re(a	NOUN
ejpam-4064	54	10	)	)	PUNCT
ejpam-4064	54	11	>	>	X
ejpam-4064	55	1	0	0	X
ejpam-4064	55	2	.	.	PUNCT
ejpam-4064	56	1	the	the	DET
ejpam-4064	56	2	incomplete	incomplete	ADJ
ejpam-4064	56	3	gamma	gamma	NOUN
ejpam-4064	56	4	function	function	NOUN
ejpam-4064	56	5	has	have	VERB
ejpam-4064	56	6	a	a	DET
ejpam-4064	56	7	recurrence	recurrence	NOUN
ejpam-4064	56	8	relation	relation	NOUN
ejpam-4064	56	9	given	give	VERB
ejpam-4064	56	10	by	by	ADP
ejpam-4064	56	11	γ(a	γ(a	NOUN
ejpam-4064	56	12	,	,	PUNCT
ejpam-4064	56	13	z	z	NOUN
ejpam-4064	56	14	)	)	PUNCT
ejpam-4064	57	1	+	+	PUNCT
ejpam-4064	57	2	γ(a	γ(a	PROPN
ejpam-4064	57	3	,	,	PUNCT
ejpam-4064	57	4	z	z	NOUN
ejpam-4064	57	5	)	)	PUNCT
ejpam-4064	57	6	=	=	SYM
ejpam-4064	57	7	γ(a	γ(a	PROPN
ejpam-4064	57	8	)	)	PUNCT
ejpam-4064	57	9	(	(	PUNCT
ejpam-4064	57	10	7	7	X
ejpam-4064	57	11	)	)	PUNCT
ejpam-4064	57	12	where	where	SCONJ
ejpam-4064	57	13	a	a	DET
ejpam-4064	57	14	̸=	̸=	PROPN
ejpam-4064	57	15	0,−1,−2	0,−1,−2	NUM
ejpam-4064	57	16	,	,	PUNCT
ejpam-4064	57	17	...	...	PUNCT
ejpam-4064	58	1	the	the	DET
ejpam-4064	58	2	incomplete	incomplete	ADJ
ejpam-4064	58	3	gamma	gamma	NOUN
ejpam-4064	58	4	function	function	NOUN
ejpam-4064	58	5	is	be	AUX
ejpam-4064	58	6	continued	continue	VERB
ejpam-4064	58	7	analytically	analytically	ADV
ejpam-4064	58	8	by	by	ADP
ejpam-4064	58	9	γ(a	γ(a	PROPN
ejpam-4064	58	10	,	,	PUNCT
ejpam-4064	58	11	ze2mπi	ze2mπi	PROPN
ejpam-4064	58	12	)	)	PUNCT
ejpam-4064	58	13	=	=	PUNCT
ejpam-4064	59	1	e2πmiaγ(a	e2πmiaγ(a	PROPN
ejpam-4064	59	2	,	,	PUNCT
ejpam-4064	59	3	z	z	NOUN
ejpam-4064	59	4	)	)	PUNCT
ejpam-4064	59	5	(	(	PUNCT
ejpam-4064	59	6	8)	8)	NUM
ejpam-4064	59	7	and	and	CCONJ
ejpam-4064	59	8	γ(a	γ(a	PROPN
ejpam-4064	59	9	,	,	PUNCT
ejpam-4064	59	10	ze2mπi	ze2mπi	PROPN
ejpam-4064	59	11	)	)	PUNCT
ejpam-4064	59	12	=	=	PUNCT
ejpam-4064	60	1	e2πmiaγ(a	e2πmiaγ(a	PROPN
ejpam-4064	60	2	,	,	PUNCT
ejpam-4064	60	3	z	z	NOUN
ejpam-4064	60	4	)	)	PUNCT
ejpam-4064	60	5	+	+	CCONJ
ejpam-4064	60	6	(	(	PUNCT
ejpam-4064	60	7	1−	1−	NUM
ejpam-4064	60	8	e2πmia)γ(a	e2πmia)γ(a	NOUN
ejpam-4064	60	9	)	)	PUNCT
ejpam-4064	60	10	(	(	PUNCT
ejpam-4064	60	11	9	9	X
ejpam-4064	60	12	)	)	PUNCT
ejpam-4064	60	13	where	where	SCONJ
ejpam-4064	60	14	m	m	VERB
ejpam-4064	60	15	∈	∈	PROPN
ejpam-4064	60	16	z	z	PROPN
ejpam-4064	60	17	,	,	PUNCT
ejpam-4064	60	18	γ∗(a	γ∗(a	PROPN
ejpam-4064	60	19	,	,	PUNCT
ejpam-4064	60	20	z	z	NOUN
ejpam-4064	60	21	)	)	PUNCT
ejpam-4064	60	22	=	=	SYM
ejpam-4064	60	23	z−a	z−a	NOUN
ejpam-4064	60	24	γ(a)γ(a	γ(a)γ(a	NOUN
ejpam-4064	60	25	,	,	PUNCT
ejpam-4064	60	26	z	z	NOUN
ejpam-4064	60	27	)	)	PUNCT
ejpam-4064	60	28	is	be	AUX
ejpam-4064	60	29	entire	entire	ADJ
ejpam-4064	60	30	in	in	ADP
ejpam-4064	60	31	z	z	NOUN
ejpam-4064	60	32	and	and	CCONJ
ejpam-4064	60	33	a.	a.	NOUN
ejpam-4064	60	34	when	when	SCONJ
ejpam-4064	60	35	z	z	PROPN
ejpam-4064	60	36	̸=	̸=	PROPN
ejpam-4064	60	37	0	0	NUM
ejpam-4064	60	38	,	,	PUNCT
ejpam-4064	60	39	γ(a	γ(a	PROPN
ejpam-4064	60	40	,	,	PUNCT
ejpam-4064	60	41	z	z	NOUN
ejpam-4064	60	42	)	)	PUNCT
ejpam-4064	60	43	is	be	AUX
ejpam-4064	60	44	an	an	DET
ejpam-4064	60	45	entire	entire	ADJ
ejpam-4064	60	46	function	function	NOUN
ejpam-4064	60	47	of	of	ADP
ejpam-4064	60	48	a	a	DET
ejpam-4064	60	49	and	and	CCONJ
ejpam-4064	60	50	γ(a	γ(a	PROPN
ejpam-4064	60	51	,	,	PUNCT
ejpam-4064	60	52	z	z	NOUN
ejpam-4064	60	53	)	)	PUNCT
ejpam-4064	60	54	is	be	AUX
ejpam-4064	60	55	meromorphic	meromorphic	ADJ
ejpam-4064	60	56	with	with	ADP
ejpam-4064	60	57	simple	simple	ADJ
ejpam-4064	60	58	poles	pole	NOUN
ejpam-4064	60	59	at	at	ADP
ejpam-4064	60	60	a	a	DET
ejpam-4064	60	61	=	=	NOUN
ejpam-4064	60	62	−n	−n	NOUN
ejpam-4064	60	63	for	for	ADP
ejpam-4064	60	64	n	n	NOUN
ejpam-4064	60	65	=	=	SYM
ejpam-4064	60	66	0	0	NUM
ejpam-4064	60	67	,	,	PUNCT
ejpam-4064	60	68	1	1	NUM
ejpam-4064	60	69	,	,	PUNCT
ejpam-4064	60	70	2	2	NUM
ejpam-4064	60	71	,	,	PUNCT
ejpam-4064	60	72	...	...	PUNCT
ejpam-4064	60	73	with	with	ADP
ejpam-4064	60	74	residue	residue	NOUN
ejpam-4064	60	75	(	(	PUNCT
ejpam-4064	60	76	−1)n	−1)n	NOUN
ejpam-4064	60	77	n	n	CCONJ
ejpam-4064	60	78	!	!	PUNCT
ejpam-4064	60	79	.	.	PUNCT
ejpam-4064	61	1	these	these	DET
ejpam-4064	61	2	definitions	definition	NOUN
ejpam-4064	61	3	are	be	AUX
ejpam-4064	61	4	listed	list	VERB
ejpam-4064	61	5	in	in	ADP
ejpam-4064	61	6	section	section	NOUN
ejpam-4064	61	7	8.2(i	8.2(i	NUM
ejpam-4064	61	8	)	)	PUNCT
ejpam-4064	61	9	and	and	CCONJ
ejpam-4064	61	10	(	(	PUNCT
ejpam-4064	61	11	ii	ii	NOUN
ejpam-4064	61	12	)	)	PUNCT
ejpam-4064	61	13	in	in	ADP
ejpam-4064	61	14	[	[	X
ejpam-4064	61	15	1	1	NUM
ejpam-4064	61	16	]	]	PUNCT
ejpam-4064	61	17	.	.	PUNCT
ejpam-4064	62	1	4.1	4.1	NUM
ejpam-4064	62	2	.	.	PUNCT
ejpam-4064	62	3	infinite	infinite	ADJ
ejpam-4064	62	4	sum	sum	NOUN
ejpam-4064	62	5	of	of	ADP
ejpam-4064	62	6	the	the	DET
ejpam-4064	62	7	contour	contour	ADJ
ejpam-4064	62	8	integral	integral	ADJ
ejpam-4064	62	9	use	use	NOUN
ejpam-4064	62	10	equation	equation	NOUN
ejpam-4064	62	11	(	(	PUNCT
ejpam-4064	62	12	2	2	NUM
ejpam-4064	62	13	)	)	PUNCT
ejpam-4064	62	14	and	and	CCONJ
ejpam-4064	62	15	multiply	multiply	VERB
ejpam-4064	62	16	both	both	DET
ejpam-4064	62	17	sides	side	NOUN
ejpam-4064	62	18	by	by	ADP
ejpam-4064	62	19	emy	emy	PROPN
ejpam-4064	62	20	and	and	CCONJ
ejpam-4064	62	21	integrate	integrate	VERB
ejpam-4064	62	22	over	over	ADP
ejpam-4064	62	23	y	y	PROPN
ejpam-4064	62	24	∈	∈	PROPN
ejpam-4064	63	1	[	[	X
ejpam-4064	63	2	−∞	−∞	NOUN
ejpam-4064	63	3	,	,	PUNCT
ejpam-4064	63	4	y	y	NOUN
ejpam-4064	63	5	)	)	PUNCT
ejpam-4064	63	6	to	to	PART
ejpam-4064	63	7	get	get	VERB
ejpam-4064	63	8	(	(	PUNCT
ejpam-4064	63	9	−1)km−kγ(k	−1)km−kγ(k	PROPN
ejpam-4064	63	10	+	+	CCONJ
ejpam-4064	63	11	1	1	NUM
ejpam-4064	63	12	)	)	PUNCT
ejpam-4064	64	1	+	+	NUM
ejpam-4064	64	2	yk(−my)−k(γ(k	yk(−my)−k(γ(k	NOUN
ejpam-4064	64	3	+	+	NOUN
ejpam-4064	64	4	1,−my)−	1,−my)−	NUM
ejpam-4064	64	5	kγ(k	kγ(k	NOUN
ejpam-4064	64	6	)	)	PUNCT
ejpam-4064	64	7	)	)	PUNCT
ejpam-4064	64	8	mγ(k	mγ(k	PUNCT
ejpam-4064	65	1	+	+	CCONJ
ejpam-4064	65	2	1	1	X
ejpam-4064	65	3	)	)	PUNCT
ejpam-4064	65	4	=	=	SYM
ejpam-4064	65	5	1	1	NUM
ejpam-4064	65	6	2πi	2πi	ADJ
ejpam-4064	65	7	∫	∫	PROPN
ejpam-4064	65	8	c	c	NOUN
ejpam-4064	65	9	w−k−1ey(m+w	w−k−1ey(m+w	NOUN
ejpam-4064	65	10	)	)	PUNCT
ejpam-4064	66	1	m+	m+	NOUN
ejpam-4064	66	2	w	w	PROPN
ejpam-4064	66	3	dw	dw	PROPN
ejpam-4064	66	4	(	(	PUNCT
ejpam-4064	66	5	10	10	NUM
ejpam-4064	66	6	)	)	PUNCT
ejpam-4064	66	7	where	where	SCONJ
ejpam-4064	66	8	im(w	im(w	PUNCT
ejpam-4064	66	9	+	+	NOUN
ejpam-4064	66	10	m	m	NOUN
ejpam-4064	66	11	)	)	PUNCT
ejpam-4064	66	12	>	>	X
ejpam-4064	66	13	0	0	X
ejpam-4064	66	14	.	.	PUNCT
ejpam-4064	67	1	next	next	ADV
ejpam-4064	67	2	we	we	PRON
ejpam-4064	67	3	multiply	multiply	VERB
ejpam-4064	67	4	both	both	DET
ejpam-4064	67	5	sides	side	NOUN
ejpam-4064	67	6	by	by	ADP
ejpam-4064	67	7	e−my	e−my	NOUN
ejpam-4064	67	8	and	and	CCONJ
ejpam-4064	67	9	replace	replace	VERB
ejpam-4064	67	10	y	y	PROPN
ejpam-4064	67	11	→	→	SYM
ejpam-4064	67	12	log(a	log(a	PROPN
ejpam-4064	67	13	)	)	PUNCT
ejpam-4064	67	14	+	+	NUM
ejpam-4064	67	15	2π(y+1	2π(y+1	NUM
ejpam-4064	67	16	)	)	PUNCT
ejpam-4064	67	17	b	b	NOUN
ejpam-4064	67	18	to	to	PART
ejpam-4064	67	19	get	get	VERB
ejpam-4064	67	20	r.	r.	PROPN
ejpam-4064	67	21	reynolds	reynolds	PROPN
ejpam-4064	67	22	,	,	PUNCT
ejpam-4064	67	23	a.	a.	PROPN
ejpam-4064	67	24	stauffer	stauffer	PROPN
ejpam-4064	67	25	/	/	SYM
ejpam-4064	67	26	eur	eur	PROPN
ejpam-4064	67	27	.	.	PUNCT
ejpam-4064	68	1	j.	j.	PROPN
ejpam-4064	68	2	pure	pure	PROPN
ejpam-4064	68	3	appl	appl	PROPN
ejpam-4064	68	4	.	.	PROPN
ejpam-4064	68	5	math	math	PROPN
ejpam-4064	68	6	,	,	PUNCT
ejpam-4064	68	7	14	14	NUM
ejpam-4064	68	8	(	(	PUNCT
ejpam-4064	68	9	4	4	NUM
ejpam-4064	68	10	)	)	PUNCT
ejpam-4064	68	11	(	(	PUNCT
ejpam-4064	68	12	2021	2021	NUM
ejpam-4064	68	13	)	)	PUNCT
ejpam-4064	68	14	,	,	PUNCT
ejpam-4064	68	15	1295	1295	NUM
ejpam-4064	68	16	-	-	SYM
ejpam-4064	68	17	1305	1305	NUM
ejpam-4064	68	18	1298	1298	NUM
ejpam-4064	68	19	(	(	PUNCT
ejpam-4064	68	20	11	11	NUM
ejpam-4064	68	21	)	)	PUNCT
ejpam-4064	68	22	1	1	NUM
ejpam-4064	68	23	mγ(k	mγ(k	NOUN
ejpam-4064	68	24	+	+	NOUN
ejpam-4064	68	25	1	1	X
ejpam-4064	68	26	)	)	PUNCT
ejpam-4064	68	27	e	e	X
ejpam-4064	68	28	−m	−m	NOUN
ejpam-4064	68	29	(	(	PUNCT
ejpam-4064	68	30	log(a)+	log(a)+	NOUN
ejpam-4064	68	31	2π(y+1	2π(y+1	NOUN
ejpam-4064	68	32	)	)	PUNCT
ejpam-4064	68	33	b	b	NOUN
ejpam-4064	68	34	)	)	PUNCT
ejpam-4064	68	35	(	(	PUNCT
ejpam-4064	68	36	(	(	PUNCT
ejpam-4064	68	37	log(a	log(a	PROPN
ejpam-4064	68	38	)	)	PUNCT
ejpam-4064	69	1	+	+	NUM
ejpam-4064	69	2	2π(y	2π(y	NUM
ejpam-4064	70	1	+	+	CCONJ
ejpam-4064	70	2	1	1	X
ejpam-4064	70	3	)	)	PUNCT
ejpam-4064	70	4	b	b	NOUN
ejpam-4064	70	5	)	)	PUNCT
ejpam-4064	71	1	k	k	NOUN
ejpam-4064	71	2	(	(	PUNCT
ejpam-4064	71	3	−m	−m	INTJ
ejpam-4064	71	4	(	(	PUNCT
ejpam-4064	71	5	log(a	log(a	PROPN
ejpam-4064	71	6	)	)	PUNCT
ejpam-4064	72	1	+	+	NUM
ejpam-4064	72	2	2π(y	2π(y	NUM
ejpam-4064	73	1	+	+	CCONJ
ejpam-4064	73	2	1	1	X
ejpam-4064	73	3	)	)	PUNCT
ejpam-4064	73	4	b	b	NOUN
ejpam-4064	73	5	)	)	PUNCT
ejpam-4064	73	6	)	)	PUNCT
ejpam-4064	74	1	−k	−k	PROPN
ejpam-4064	74	2	(	(	PUNCT
ejpam-4064	74	3	γ	γ	X
ejpam-4064	74	4	(	(	PUNCT
ejpam-4064	74	5	k	k	PROPN
ejpam-4064	74	6	+	+	NUM
ejpam-4064	74	7	1,−m	1,−m	NUM
ejpam-4064	74	8	(	(	PUNCT
ejpam-4064	74	9	2π(y	2π(y	NUM
ejpam-4064	74	10	+	+	CCONJ
ejpam-4064	74	11	1	1	X
ejpam-4064	74	12	)	)	PUNCT
ejpam-4064	74	13	b	b	NOUN
ejpam-4064	74	14	+	+	CCONJ
ejpam-4064	74	15	log(a	log(a	PROPN
ejpam-4064	74	16	)	)	PUNCT
ejpam-4064	74	17	)	)	PUNCT
ejpam-4064	74	18	)	)	PUNCT
ejpam-4064	75	1	−	−	PROPN
ejpam-4064	75	2	kγ(k	kγ(k	NOUN
ejpam-4064	75	3	)	)	PUNCT
ejpam-4064	75	4	)	)	PUNCT
ejpam-4064	76	1	+	+	CCONJ
ejpam-4064	76	2	(	(	PUNCT
ejpam-4064	76	3	−1)km−kγ(k	−1)km−kγ(k	PROPN
ejpam-4064	76	4	+	+	CCONJ
ejpam-4064	76	5	1	1	NUM
ejpam-4064	76	6	)	)	PUNCT
ejpam-4064	76	7	)	)	PUNCT
ejpam-4064	77	1	=	=	SYM
ejpam-4064	77	2	1	1	NUM
ejpam-4064	77	3	2πi	2πi	ADJ
ejpam-4064	77	4	∫	∫	PROPN
ejpam-4064	78	1	c	c	PROPN
ejpam-4064	78	2	w−k−1e	w−k−1e	ADJ
ejpam-4064	78	3	w	w	NOUN
ejpam-4064	78	4	(	(	PUNCT
ejpam-4064	78	5	log(a)+	log(a)+	NOUN
ejpam-4064	78	6	2π(y+1	2π(y+1	NOUN
ejpam-4064	78	7	)	)	PUNCT
ejpam-4064	78	8	b	b	PROPN
ejpam-4064	78	9	)	)	PUNCT
ejpam-4064	79	1	m+	m+	PROPN
ejpam-4064	80	1	w	w	PROPN
ejpam-4064	80	2	dw	dw	PROPN
ejpam-4064	80	3	next	next	ADV
ejpam-4064	80	4	we	we	PRON
ejpam-4064	80	5	multiply	multiply	VERB
ejpam-4064	80	6	both	both	DET
ejpam-4064	80	7	sides	side	NOUN
ejpam-4064	80	8	by	by	ADP
ejpam-4064	80	9	(	(	PUNCT
ejpam-4064	80	10	−1)ye	−1)ye	PROPN
ejpam-4064	80	11	2πm(y+1	2πm(y+1	NUM
ejpam-4064	80	12	)	)	PUNCT
ejpam-4064	80	13	b	b	NOUN
ejpam-4064	80	14	and	and	CCONJ
ejpam-4064	80	15	take	take	VERB
ejpam-4064	80	16	the	the	DET
ejpam-4064	80	17	infinite	infinite	ADJ
ejpam-4064	80	18	sum	sum	NOUN
ejpam-4064	80	19	over	over	ADP
ejpam-4064	80	20	y	y	PROPN
ejpam-4064	80	21	∈	∈	PROPN
ejpam-4064	81	1	[	[	X
ejpam-4064	81	2	0,∞	0,∞	NOUN
ejpam-4064	81	3	)	)	PUNCT
ejpam-4064	81	4	and	and	CCONJ
ejpam-4064	81	5	simplify	simplify	VERB
ejpam-4064	81	6	in	in	ADP
ejpam-4064	81	7	terms	term	NOUN
ejpam-4064	81	8	of	of	ADP
ejpam-4064	81	9	the	the	DET
ejpam-4064	81	10	incomplete	incomplete	ADJ
ejpam-4064	81	11	gamma	gamma	NOUN
ejpam-4064	81	12	function	function	NOUN
ejpam-4064	81	13	to	to	PART
ejpam-4064	81	14	get	get	VERB
ejpam-4064	81	15	(	(	PUNCT
ejpam-4064	81	16	12	12	NUM
ejpam-4064	81	17	)	)	PUNCT
ejpam-4064	81	18	∞∑	∞∑	NUM
ejpam-4064	81	19	y	y	NOUN
ejpam-4064	81	20	=	=	SYM
ejpam-4064	81	21	0	0	NUM
ejpam-4064	81	22	π(−1)ya−m	π(−1)ya−m	PROPN
ejpam-4064	81	23	mγ(k	mγ(k	PUNCT
ejpam-4064	81	24	+	+	CCONJ
ejpam-4064	81	25	1	1	X
ejpam-4064	81	26	)	)	PUNCT
ejpam-4064	81	27	(	(	PUNCT
ejpam-4064	81	28	(	(	PUNCT
ejpam-4064	81	29	2	2	NUM
ejpam-4064	81	30	log(a	log(a	PROPN
ejpam-4064	81	31	)	)	PUNCT
ejpam-4064	82	1	+	+	CCONJ
ejpam-4064	83	1	π(y	π(y	PROPN
ejpam-4064	83	2	+	+	CCONJ
ejpam-4064	83	3	1	1	X
ejpam-4064	83	4	)	)	PUNCT
ejpam-4064	83	5	α	α	NOUN
ejpam-4064	83	6	)	)	PUNCT
ejpam-4064	83	7	k	k	NOUN
ejpam-4064	83	8	(	(	PUNCT
ejpam-4064	83	9	−m(2α	−m(2α	NUM
ejpam-4064	83	10	log(a	log(a	PROPN
ejpam-4064	83	11	)	)	PUNCT
ejpam-4064	84	1	+	+	NUM
ejpam-4064	84	2	πy	πy	X
ejpam-4064	84	3	+	+	NUM
ejpam-4064	84	4	π	π	X
ejpam-4064	84	5	)	)	PUNCT
ejpam-4064	84	6	α	α	NOUN
ejpam-4064	84	7	)	)	PUNCT
ejpam-4064	84	8	−k	−k	PROPN
ejpam-4064	84	9	(	(	PUNCT
ejpam-4064	84	10	γ(k	γ(k	PROPN
ejpam-4064	84	11	+	+	PROPN
ejpam-4064	84	12	1)−	1)−	PROPN
ejpam-4064	84	13	γ	γ	X
ejpam-4064	84	14	(	(	PUNCT
ejpam-4064	84	15	k	k	PROPN
ejpam-4064	84	16	+	+	PROPN
ejpam-4064	84	17	1,−m	1,−m	NUM
ejpam-4064	84	18	(	(	PUNCT
ejpam-4064	84	19	π(y	π(y	PROPN
ejpam-4064	84	20	+	+	NOUN
ejpam-4064	84	21	1	1	X
ejpam-4064	84	22	)	)	PUNCT
ejpam-4064	84	23	2α	2α	NOUN
ejpam-4064	84	24	+	+	X
ejpam-4064	84	25	log(a	log(a	PROPN
ejpam-4064	84	26	)	)	PUNCT
ejpam-4064	84	27	)	)	PUNCT
ejpam-4064	84	28	)	)	PUNCT
ejpam-4064	84	29	)	)	PUNCT
ejpam-4064	85	1	+	+	CCONJ
ejpam-4064	85	2	(	(	PUNCT
ejpam-4064	85	3	−1)k+1m−kγ(k	−1)k+1m−kγ(k	X
ejpam-4064	85	4	+	+	NOUN
ejpam-4064	85	5	1	1	NUM
ejpam-4064	85	6	)	)	PUNCT
ejpam-4064	85	7	)	)	PUNCT
ejpam-4064	86	1	=	=	SYM
ejpam-4064	86	2	1	1	NUM
ejpam-4064	86	3	2πi	2πi	NOUN
ejpam-4064	86	4	∞∑	∞∑	NUM
ejpam-4064	86	5	y=0	y=0	NUM
ejpam-4064	86	6	∫	∫	X
ejpam-4064	86	7	c	c	PROPN
ejpam-4064	86	8	(	(	PUNCT
ejpam-4064	86	9	−1)yaww−k−1e	−1)yaww−k−1e	NOUN
ejpam-4064	86	10	2π(y+1)(m+w	2π(y+1)(m+w	NUM
ejpam-4064	86	11	)	)	PUNCT
ejpam-4064	86	12	b	b	NOUN
ejpam-4064	86	13	m+	m+	NUM
ejpam-4064	86	14	w	w	PROPN
ejpam-4064	86	15	dw	dw	NOUN
ejpam-4064	86	16	=	=	SYM
ejpam-4064	86	17	1	1	NUM
ejpam-4064	86	18	2πi	2πi	NOUN
ejpam-4064	86	19	∫	∫	PROPN
ejpam-4064	86	20	c	c	NOUN
ejpam-4064	86	21	∞∑	∞∑	NUM
ejpam-4064	86	22	y=0	y=0	NOUN
ejpam-4064	86	23	(	(	PUNCT
ejpam-4064	86	24	−1)yaww−k−1e	−1)yaww−k−1e	NOUN
ejpam-4064	86	25	2π(y+1)(m+w	2π(y+1)(m+w	NUM
ejpam-4064	86	26	)	)	PUNCT
ejpam-4064	86	27	b	b	NOUN
ejpam-4064	86	28	m+	m+	NUM
ejpam-4064	86	29	w	w	PROPN
ejpam-4064	86	30	dw	dw	PROPN
ejpam-4064	86	31	=	=	SYM
ejpam-4064	86	32	−	−	PROPN
ejpam-4064	86	33	1	1	NUM
ejpam-4064	86	34	2πi	2πi	NOUN
ejpam-4064	86	35	∫	∫	PROPN
ejpam-4064	86	36	c	c	PROPN
ejpam-4064	87	1	πaww−k−1	πaww−k−1	PROPN
ejpam-4064	87	2	(	(	PUNCT
ejpam-4064	87	3	tanh	tanh	PROPN
ejpam-4064	87	4	(	(	PUNCT
ejpam-4064	87	5	π(m+w	π(m+w	NOUN
ejpam-4064	87	6	)	)	PUNCT
ejpam-4064	87	7	4α	4α	NOUN
ejpam-4064	87	8	)	)	PUNCT
ejpam-4064	88	1	+	+	CCONJ
ejpam-4064	88	2	1	1	NUM
ejpam-4064	88	3	)	)	PUNCT
ejpam-4064	88	4	2(m+	2(m+	NUM
ejpam-4064	88	5	w	w	X
ejpam-4064	88	6	)	)	PUNCT
ejpam-4064	88	7	dw	dw	NOUN
ejpam-4064	88	8	from	from	ADP
ejpam-4064	88	9	equation	equation	NOUN
ejpam-4064	88	10	(	(	PUNCT
ejpam-4064	88	11	1.232.1	1.232.1	NUM
ejpam-4064	88	12	)	)	PUNCT
ejpam-4064	88	13	in	in	ADP
ejpam-4064	88	14	[	[	X
ejpam-4064	88	15	4	4	X
ejpam-4064	88	16	]	]	PUNCT
ejpam-4064	88	17	where	where	SCONJ
ejpam-4064	88	18	im(w	im(w	PUNCT
ejpam-4064	88	19	+	+	NOUN
ejpam-4064	88	20	m	m	VERB
ejpam-4064	88	21	)	)	PUNCT
ejpam-4064	88	22	>	>	X
ejpam-4064	88	23	0	0	PUNCT
ejpam-4064	89	1	in	in	ADP
ejpam-4064	89	2	order	order	NOUN
ejpam-4064	89	3	for	for	SCONJ
ejpam-4064	89	4	the	the	DET
ejpam-4064	89	5	sum	sum	NOUN
ejpam-4064	89	6	to	to	PART
ejpam-4064	89	7	converge	converge	VERB
ejpam-4064	89	8	.	.	PUNCT
ejpam-4064	89	9	r.	r.	PROPN
ejpam-4064	89	10	reynolds	reynolds	PROPN
ejpam-4064	89	11	,	,	PUNCT
ejpam-4064	89	12	a.	a.	PROPN
ejpam-4064	89	13	stauffer	stauffer	PROPN
ejpam-4064	89	14	/	/	SYM
ejpam-4064	89	15	eur	eur	PROPN
ejpam-4064	89	16	.	.	PUNCT
ejpam-4064	90	1	j.	j.	PROPN
ejpam-4064	90	2	pure	pure	PROPN
ejpam-4064	90	3	appl	appl	PROPN
ejpam-4064	90	4	.	.	PROPN
ejpam-4064	90	5	math	math	PROPN
ejpam-4064	90	6	,	,	PUNCT
ejpam-4064	90	7	14	14	NUM
ejpam-4064	90	8	(	(	PUNCT
ejpam-4064	90	9	4	4	NUM
ejpam-4064	90	10	)	)	PUNCT
ejpam-4064	90	11	(	(	PUNCT
ejpam-4064	90	12	2021	2021	NUM
ejpam-4064	90	13	)	)	PUNCT
ejpam-4064	90	14	,	,	PUNCT
ejpam-4064	90	15	1295	1295	NUM
ejpam-4064	90	16	-	-	SYM
ejpam-4064	90	17	1305	1305	NUM
ejpam-4064	90	18	1299	1299	NUM
ejpam-4064	90	19	4.1.1	4.1.1	NUM
ejpam-4064	90	20	.	.	PUNCT
ejpam-4064	91	1	derivation	derivation	NOUN
ejpam-4064	91	2	of	of	ADP
ejpam-4064	91	3	the	the	DET
ejpam-4064	91	4	additional	additional	ADJ
ejpam-4064	91	5	contour	contour	NOUN
ejpam-4064	91	6	use	use	NOUN
ejpam-4064	91	7	equation	equation	NOUN
ejpam-4064	91	8	(	(	PUNCT
ejpam-4064	91	9	2	2	NUM
ejpam-4064	91	10	)	)	PUNCT
ejpam-4064	91	11	and	and	CCONJ
ejpam-4064	91	12	replace	replace	VERB
ejpam-4064	91	13	y	y	PROPN
ejpam-4064	91	14	→	→	SYM
ejpam-4064	91	15	log(a	log(a	PROPN
ejpam-4064	91	16	)	)	PUNCT
ejpam-4064	92	1	+	+	CCONJ
ejpam-4064	92	2	y	y	PROPN
ejpam-4064	92	3	and	and	CCONJ
ejpam-4064	92	4	multiply	multiply	VERB
ejpam-4064	92	5	both	both	DET
ejpam-4064	92	6	sides	side	NOUN
ejpam-4064	92	7	by	by	ADP
ejpam-4064	92	8	emy	emy	PROPN
ejpam-4064	92	9	and	and	CCONJ
ejpam-4064	92	10	take	take	VERB
ejpam-4064	92	11	the	the	DET
ejpam-4064	92	12	definite	definite	ADJ
ejpam-4064	92	13	integral	integral	ADJ
ejpam-4064	92	14	over	over	ADP
ejpam-4064	92	15	y	y	PROPN
ejpam-4064	92	16	∈	∈	PROPN
ejpam-4064	93	1	[	[	X
ejpam-4064	93	2	0,∞	0,∞	NOUN
ejpam-4064	93	3	)	)	PUNCT
ejpam-4064	93	4	to	to	PART
ejpam-4064	93	5	get	get	VERB
ejpam-4064	93	6	(	(	PUNCT
ejpam-4064	93	7	13	13	NUM
ejpam-4064	93	8	)	)	PUNCT
ejpam-4064	93	9	πa−m(−m)−k−1γ(k	πa−m(−m)−k−1γ(k	X
ejpam-4064	93	10	+	+	X
ejpam-4064	93	11	1,−m	1,−m	NUM
ejpam-4064	93	12	log(a	log(a	PROPN
ejpam-4064	93	13	)	)	PUNCT
ejpam-4064	93	14	)	)	PUNCT
ejpam-4064	93	15	2γ(k	2γ(k	NUM
ejpam-4064	94	1	+	+	CCONJ
ejpam-4064	94	2	1	1	X
ejpam-4064	94	3	)	)	PUNCT
ejpam-4064	94	4	=	=	SYM
ejpam-4064	95	1	−	−	PROPN
ejpam-4064	95	2	1	1	NUM
ejpam-4064	95	3	2πi	2πi	NOUN
ejpam-4064	95	4	∫	∫	PROPN
ejpam-4064	95	5	c	c	PROPN
ejpam-4064	95	6	πaww−k−1	πaww−k−1	PROPN
ejpam-4064	95	7	2(m+	2(m+	NUM
ejpam-4064	95	8	w	w	NOUN
ejpam-4064	95	9	)	)	PUNCT
ejpam-4064	95	10	dw	dw	NOUN
ejpam-4064	95	11	where	where	SCONJ
ejpam-4064	95	12	−1	−1	NOUN
ejpam-4064	95	13	<	<	X
ejpam-4064	95	14	re(m	re(m	PROPN
ejpam-4064	95	15	)	)	PUNCT
ejpam-4064	95	16	<	<	X
ejpam-4064	95	17	0	0	NUM
ejpam-4064	95	18	.	.	NOUN
ejpam-4064	95	19	5	5	NUM
ejpam-4064	95	20	.	.	X
ejpam-4064	95	21	definite	definite	ADJ
ejpam-4064	95	22	integral	integral	ADJ
ejpam-4064	95	23	in	in	ADP
ejpam-4064	95	24	terms	term	NOUN
ejpam-4064	95	25	of	of	ADP
ejpam-4064	95	26	the	the	DET
ejpam-4064	95	27	incomplete	incomplete	ADJ
ejpam-4064	95	28	gamma	gamma	NOUN
ejpam-4064	95	29	function	function	NOUN
ejpam-4064	95	30	theorem	theorem	VERB
ejpam-4064	95	31	1	1	NUM
ejpam-4064	95	32	.	.	X
ejpam-4064	95	33	for	for	ADP
ejpam-4064	95	34	−1	−1	NOUN
ejpam-4064	95	35	<	<	X
ejpam-4064	95	36	re(m	re(m	PROPN
ejpam-4064	95	37	)	)	PUNCT
ejpam-4064	95	38	<	<	X
ejpam-4064	95	39	0	0	NUM
ejpam-4064	95	40	,	,	PUNCT
ejpam-4064	95	41	k	k	NOUN
ejpam-4064	95	42	,	,	PUNCT
ejpam-4064	95	43	a	a	DET
ejpam-4064	95	44	∈	∈	PROPN
ejpam-4064	95	45	c	c	NOUN
ejpam-4064	95	46	,	,	PUNCT
ejpam-4064	95	47	re(α	re(α	PROPN
ejpam-4064	95	48	)	)	PUNCT
ejpam-4064	95	49	>	>	X
ejpam-4064	95	50	0	0	PUNCT
ejpam-4064	96	1	(	(	PUNCT
ejpam-4064	96	2	14	14	NUM
ejpam-4064	96	3	)	)	PUNCT
ejpam-4064	96	4	∫	∫	PROPN
ejpam-4064	97	1	∞	∞	PROPN
ejpam-4064	97	2	0	0	NUM
ejpam-4064	97	3	log(tanh(αx	log(tanh(αx	NOUN
ejpam-4064	97	4	)	)	PUNCT
ejpam-4064	97	5	)	)	PUNCT
ejpam-4064	98	1	(	(	PUNCT
ejpam-4064	98	2	eimx(log(a	eimx(log(a	NOUN
ejpam-4064	98	3	)	)	PUNCT
ejpam-4064	98	4	+	+	CCONJ
ejpam-4064	98	5	ix)k	ix)k	PROPN
ejpam-4064	98	6	+	+	CCONJ
ejpam-4064	98	7	e−imx(log(a)−	e−imx(log(a)−	NOUN
ejpam-4064	98	8	ix)k	ix)k	NOUN
ejpam-4064	98	9	)	)	PUNCT
ejpam-4064	98	10	dx	dx	PROPN
ejpam-4064	99	1	=	=	NOUN
ejpam-4064	100	1	∞∑	∞∑	NUM
ejpam-4064	100	2	y=0	y=0	NOUN
ejpam-4064	100	3	2π(−1)ya−m	2π(−1)ya−m	NUM
ejpam-4064	100	4	m	m	VERB
ejpam-4064	100	5	(	(	PUNCT
ejpam-4064	100	6	(	(	PUNCT
ejpam-4064	100	7	2	2	NUM
ejpam-4064	100	8	log(a	log(a	PROPN
ejpam-4064	100	9	)	)	PUNCT
ejpam-4064	100	10	+	+	CCONJ
ejpam-4064	100	11	π(y	π(y	PROPN
ejpam-4064	100	12	+	+	CCONJ
ejpam-4064	100	13	1	1	X
ejpam-4064	100	14	)	)	PUNCT
ejpam-4064	100	15	α	α	NOUN
ejpam-4064	100	16	)	)	PUNCT
ejpam-4064	100	17	k	k	NOUN
ejpam-4064	100	18	(	(	PUNCT
ejpam-4064	100	19	−m(2α	−m(2α	NUM
ejpam-4064	100	20	log(a	log(a	PROPN
ejpam-4064	100	21	)	)	PUNCT
ejpam-4064	100	22	+	+	NUM
ejpam-4064	100	23	πy	πy	X
ejpam-4064	100	24	+	+	NUM
ejpam-4064	100	25	π	π	X
ejpam-4064	100	26	)	)	PUNCT
ejpam-4064	100	27	α	α	NOUN
ejpam-4064	100	28	)	)	PUNCT
ejpam-4064	100	29	−k	−k	PROPN
ejpam-4064	100	30	(	(	PUNCT
ejpam-4064	100	31	γ(k	γ(k	PROPN
ejpam-4064	100	32	+	+	PROPN
ejpam-4064	100	33	1)−	1)−	PROPN
ejpam-4064	100	34	γ	γ	X
ejpam-4064	100	35	(	(	PUNCT
ejpam-4064	100	36	k	k	PROPN
ejpam-4064	100	37	+	+	PROPN
ejpam-4064	100	38	1,−m	1,−m	NUM
ejpam-4064	100	39	(	(	PUNCT
ejpam-4064	100	40	π(y	π(y	PROPN
ejpam-4064	100	41	+	+	NOUN
ejpam-4064	100	42	1	1	X
ejpam-4064	100	43	)	)	PUNCT
ejpam-4064	100	44	2α	2α	NOUN
ejpam-4064	100	45	+	+	X
ejpam-4064	100	46	log(a	log(a	PROPN
ejpam-4064	100	47	)	)	PUNCT
ejpam-4064	100	48	)	)	PUNCT
ejpam-4064	100	49	)	)	PUNCT
ejpam-4064	100	50	)	)	PUNCT
ejpam-4064	101	1	+	+	CCONJ
ejpam-4064	101	2	(	(	PUNCT
ejpam-4064	101	3	−1)k+1m−kγ(k	−1)k+1m−kγ(k	X
ejpam-4064	101	4	+	+	NOUN
ejpam-4064	101	5	1	1	NUM
ejpam-4064	101	6	)	)	PUNCT
ejpam-4064	101	7	)	)	PUNCT
ejpam-4064	102	1	+	+	CCONJ
ejpam-4064	102	2	π	π	X
ejpam-4064	102	3	(	(	PUNCT
ejpam-4064	102	4	−a−m	−a−m	PROPN
ejpam-4064	102	5	)	)	PUNCT
ejpam-4064	102	6	(	(	PUNCT
ejpam-4064	102	7	−m)−k−1γ(k	−m)−k−1γ(k	NOUN
ejpam-4064	102	8	+	+	CCONJ
ejpam-4064	102	9	1,−m	1,−m	NUM
ejpam-4064	102	10	log(a	log(a	PROPN
ejpam-4064	102	11	)	)	PUNCT
ejpam-4064	102	12	)	)	PUNCT
ejpam-4064	102	13	proof	proof	NOUN
ejpam-4064	102	14	.	.	PUNCT
ejpam-4064	103	1	since	since	SCONJ
ejpam-4064	103	2	the	the	DET
ejpam-4064	103	3	right	right	ADJ
ejpam-4064	103	4	-	-	PUNCT
ejpam-4064	103	5	hand	hand	NOUN
ejpam-4064	103	6	side	side	NOUN
ejpam-4064	103	7	of	of	ADP
ejpam-4064	103	8	equation	equation	NOUN
ejpam-4064	103	9	(	(	PUNCT
ejpam-4064	103	10	4	4	X
ejpam-4064	103	11	)	)	PUNCT
ejpam-4064	103	12	is	be	AUX
ejpam-4064	103	13	equal	equal	ADJ
ejpam-4064	103	14	to	to	ADP
ejpam-4064	103	15	the	the	DET
ejpam-4064	103	16	sum	sum	NOUN
ejpam-4064	103	17	of	of	ADP
ejpam-4064	103	18	the	the	DET
ejpam-4064	103	19	right	right	ADJ
ejpam-4064	103	20	-	-	PUNCT
ejpam-4064	103	21	hand	hand	NOUN
ejpam-4064	103	22	sides	side	NOUN
ejpam-4064	103	23	of	of	ADP
ejpam-4064	103	24	equations	equation	NOUN
ejpam-4064	103	25	(	(	PUNCT
ejpam-4064	103	26	12	12	NUM
ejpam-4064	103	27	)	)	PUNCT
ejpam-4064	103	28	and	and	CCONJ
ejpam-4064	103	29	(	(	PUNCT
ejpam-4064	103	30	13	13	X
ejpam-4064	103	31	)	)	PUNCT
ejpam-4064	103	32	we	we	PRON
ejpam-4064	103	33	can	can	AUX
ejpam-4064	103	34	equate	equate	VERB
ejpam-4064	103	35	the	the	DET
ejpam-4064	103	36	left	left	ADJ
ejpam-4064	103	37	-	-	PUNCT
ejpam-4064	103	38	hand	hand	NOUN
ejpam-4064	103	39	sides	side	NOUN
ejpam-4064	103	40	to	to	PART
ejpam-4064	103	41	get	get	VERB
ejpam-4064	103	42	the	the	DET
ejpam-4064	103	43	stated	state	VERB
ejpam-4064	103	44	result	result	NOUN
ejpam-4064	103	45	.	.	PUNCT
ejpam-4064	104	1	6	6	X
ejpam-4064	104	2	.	.	X
ejpam-4064	104	3	table	table	NOUN
ejpam-4064	104	4	of	of	ADP
ejpam-4064	104	5	definite	definite	ADJ
ejpam-4064	104	6	integrals	integral	NOUN
ejpam-4064	104	7	in	in	ADP
ejpam-4064	104	8	this	this	DET
ejpam-4064	104	9	section	section	NOUN
ejpam-4064	104	10	we	we	PRON
ejpam-4064	104	11	will	will	AUX
ejpam-4064	104	12	evaluate	evaluate	VERB
ejpam-4064	104	13	equation	equation	NOUN
ejpam-4064	104	14	(	(	PUNCT
ejpam-4064	104	15	14	14	NUM
ejpam-4064	104	16	)	)	PUNCT
ejpam-4064	104	17	for	for	ADP
ejpam-4064	104	18	various	various	ADJ
ejpam-4064	104	19	values	value	NOUN
ejpam-4064	104	20	of	of	ADP
ejpam-4064	104	21	the	the	DET
ejpam-4064	104	22	parameters	parameter	NOUN
ejpam-4064	104	23	and	and	CCONJ
ejpam-4064	104	24	express	express	VERB
ejpam-4064	104	25	these	these	DET
ejpam-4064	104	26	integrals	integral	NOUN
ejpam-4064	104	27	in	in	ADP
ejpam-4064	104	28	terms	term	NOUN
ejpam-4064	104	29	of	of	ADP
ejpam-4064	104	30	fundamental	fundamental	ADJ
ejpam-4064	104	31	constants	constant	NOUN
ejpam-4064	104	32	where	where	SCONJ
ejpam-4064	104	33	possible	possible	ADJ
ejpam-4064	104	34	.	.	PUNCT
ejpam-4064	105	1	some	some	DET
ejpam-4064	105	2	special	special	ADJ
ejpam-4064	105	3	functions	function	NOUN
ejpam-4064	105	4	and	and	CCONJ
ejpam-4064	105	5	fundamental	fundamental	ADJ
ejpam-4064	105	6	constants	constant	NOUN
ejpam-4064	105	7	which	which	PRON
ejpam-4064	105	8	occur	occur	VERB
ejpam-4064	105	9	in	in	ADP
ejpam-4064	105	10	this	this	DET
ejpam-4064	105	11	section	section	NOUN
ejpam-4064	105	12	are	be	AUX
ejpam-4064	105	13	euler	euler	NOUN
ejpam-4064	105	14	’s	’s	PART
ejpam-4064	105	15	constant	constant	ADJ
ejpam-4064	105	16	γ	γ	PROPN
ejpam-4064	105	17	section	section	NOUN
ejpam-4064	105	18	(	(	PUNCT
ejpam-4064	105	19	8.367	8.367	NUM
ejpam-4064	105	20	)	)	PUNCT
ejpam-4064	105	21	in	in	ADP
ejpam-4064	105	22	[	[	X
ejpam-4064	105	23	4	4	NUM
ejpam-4064	105	24	]	]	PUNCT
ejpam-4064	105	25	,	,	PUNCT
ejpam-4064	105	26	exponential	exponential	ADJ
ejpam-4064	105	27	integral	integral	ADJ
ejpam-4064	105	28	function	function	NOUN
ejpam-4064	105	29	ei(x	ei(x	NOUN
ejpam-4064	105	30	)	)	PUNCT
ejpam-4064	105	31	equation	equation	NOUN
ejpam-4064	105	32	(	(	PUNCT
ejpam-4064	105	33	5.231.1	5.231.1	NOUN
ejpam-4064	105	34	)	)	PUNCT
ejpam-4064	105	35	in	in	ADP
ejpam-4064	105	36	[	[	X
ejpam-4064	105	37	4	4	NUM
ejpam-4064	105	38	]	]	PUNCT
ejpam-4064	105	39	,	,	PUNCT
ejpam-4064	105	40	the	the	DET
ejpam-4064	105	41	imaginary	imaginary	ADJ
ejpam-4064	105	42	error	error	NOUN
ejpam-4064	105	43	function	function	NOUN
ejpam-4064	105	44	erfi(iz)/i	erfi(iz)/i	PROPN
ejpam-4064	105	45	see	see	VERB
ejpam-4064	105	46	equation	equation	NOUN
ejpam-4064	105	47	(	(	PUNCT
ejpam-4064	105	48	8.253.1	8.253.1	NUM
ejpam-4064	105	49	)	)	PUNCT
ejpam-4064	105	50	in	in	ADP
ejpam-4064	105	51	[	[	X
ejpam-4064	105	52	4	4	NUM
ejpam-4064	105	53	]	]	PUNCT
ejpam-4064	105	54	and	and	CCONJ
ejpam-4064	105	55	equation	equation	NOUN
ejpam-4064	105	56	(	(	PUNCT
ejpam-4064	105	57	40:12:2	40:12:2	NOUN
ejpam-4064	105	58	)	)	PUNCT
ejpam-4064	105	59	in	in	ADP
ejpam-4064	105	60	[	[	X
ejpam-4064	105	61	6	6	NUM
ejpam-4064	105	62	]	]	PUNCT
ejpam-4064	105	63	.	.	PUNCT
ejpam-4064	106	1	r.	r.	PROPN
ejpam-4064	106	2	reynolds	reynolds	PROPN
ejpam-4064	106	3	,	,	PUNCT
ejpam-4064	106	4	a.	a.	PROPN
ejpam-4064	106	5	stauffer	stauffer	PROPN
ejpam-4064	106	6	/	/	SYM
ejpam-4064	106	7	eur	eur	PROPN
ejpam-4064	106	8	.	.	PUNCT
ejpam-4064	107	1	j.	j.	PROPN
ejpam-4064	107	2	pure	pure	PROPN
ejpam-4064	107	3	appl	appl	PROPN
ejpam-4064	107	4	.	.	PROPN
ejpam-4064	107	5	math	math	PROPN
ejpam-4064	107	6	,	,	PUNCT
ejpam-4064	107	7	14	14	NUM
ejpam-4064	107	8	(	(	PUNCT
ejpam-4064	107	9	4	4	NUM
ejpam-4064	107	10	)	)	PUNCT
ejpam-4064	107	11	(	(	PUNCT
ejpam-4064	107	12	2021	2021	NUM
ejpam-4064	107	13	)	)	PUNCT
ejpam-4064	107	14	,	,	PUNCT
ejpam-4064	107	15	1295	1295	NUM
ejpam-4064	107	16	-	-	SYM
ejpam-4064	107	17	1305	1305	NUM
ejpam-4064	107	18	1300	1300	NUM
ejpam-4064	107	19	6.1	6.1	NUM
ejpam-4064	107	20	.	.	PUNCT
ejpam-4064	108	1	derivation	derivation	NOUN
ejpam-4064	108	2	of	of	ADP
ejpam-4064	108	3	entry	entry	NOUN
ejpam-4064	108	4	1.7.7.112	1.7.7.112	NUM
ejpam-4064	108	5	in	in	ADP
ejpam-4064	108	6	[	[	PUNCT
ejpam-4064	108	7	5	5	NUM
ejpam-4064	108	8	]	]	X
ejpam-4064	108	9	lemma	lemma	PROPN
ejpam-4064	108	10	1	1	NUM
ejpam-4064	108	11	.	.	PUNCT
ejpam-4064	109	1	(	(	PUNCT
ejpam-4064	109	2	15	15	NUM
ejpam-4064	109	3	)	)	PUNCT
ejpam-4064	109	4	∫	∫	PROPN
ejpam-4064	109	5	∞	∞	PROPN
ejpam-4064	109	6	0	0	NUM
ejpam-4064	109	7	cos(mx	cos(mx	NOUN
ejpam-4064	109	8	)	)	PUNCT
ejpam-4064	109	9	log(tanh(αx))dx	log(tanh(αx))dx	NOUN
ejpam-4064	109	10	=	=	SYM
ejpam-4064	109	11	−	−	PROPN
ejpam-4064	109	12	π	π	X
ejpam-4064	109	13	tanh	tanh	PROPN
ejpam-4064	109	14	(	(	PUNCT
ejpam-4064	109	15	πm	πm	ADP
ejpam-4064	109	16	4α	4α	NOUN
ejpam-4064	109	17	)	)	PUNCT
ejpam-4064	110	1	2	2	NUM
ejpam-4064	110	2	m	m	NOUN
ejpam-4064	110	3	proof	proof	NOUN
ejpam-4064	110	4	.	.	PUNCT
ejpam-4064	111	1	use	use	VERB
ejpam-4064	111	2	equation	equation	NOUN
ejpam-4064	111	3	(	(	PUNCT
ejpam-4064	111	4	14	14	NUM
ejpam-4064	111	5	)	)	PUNCT
ejpam-4064	111	6	and	and	CCONJ
ejpam-4064	111	7	set	set	VERB
ejpam-4064	111	8	k	k	PROPN
ejpam-4064	111	9	=	=	PUNCT
ejpam-4064	111	10	0	0	NUM
ejpam-4064	111	11	and	and	CCONJ
ejpam-4064	111	12	simplify	simplify	NOUN
ejpam-4064	111	13	.	.	PUNCT
ejpam-4064	112	1	note	note	VERB
ejpam-4064	112	2	the	the	DET
ejpam-4064	112	3	equation	equation	NOUN
ejpam-4064	112	4	quoted	quote	VERB
ejpam-4064	112	5	in	in	ADP
ejpam-4064	112	6	[	[	X
ejpam-4064	112	7	5	5	NUM
ejpam-4064	112	8	]	]	PUNCT
ejpam-4064	112	9	is	be	AUX
ejpam-4064	112	10	in	in	ADP
ejpam-4064	112	11	error	error	NOUN
ejpam-4064	112	12	.	.	PUNCT
ejpam-4064	113	1	proposition	proposition	NOUN
ejpam-4064	113	2	1	1	NUM
ejpam-4064	113	3	.	.	PUNCT
ejpam-4064	114	1	(	(	PUNCT
ejpam-4064	114	2	16	16	NUM
ejpam-4064	114	3	)	)	PUNCT
ejpam-4064	114	4	∫	∫	PROPN
ejpam-4064	115	1	∞	∞	PROPN
ejpam-4064	115	2	0	0	NUM
ejpam-4064	116	1	xk	xk	PROPN
ejpam-4064	116	2	(	(	PUNCT
ejpam-4064	116	3	(	(	PUNCT
ejpam-4064	116	4	−1)−ke−imx	−1)−ke−imx	X
ejpam-4064	116	5	+	+	CCONJ
ejpam-4064	116	6	eimx	eimx	ADJ
ejpam-4064	116	7	)	)	PUNCT
ejpam-4064	116	8	log(tanh(αx))dx	log(tanh(αx))dx	NOUN
ejpam-4064	116	9	=	=	NOUN
ejpam-4064	117	1	∞∑	∞∑	NUM
ejpam-4064	117	2	y=0	y=0	NOUN
ejpam-4064	117	3	2πi−k(−1)y	2πi−k(−1)y	NUM
ejpam-4064	117	4	m	m	NOUN
ejpam-4064	117	5	(	(	PUNCT
ejpam-4064	117	6	(	(	PUNCT
ejpam-4064	117	7	−1)k+1m−kγ(k	−1)k+1m−kγ(k	X
ejpam-4064	117	8	+	+	CCONJ
ejpam-4064	117	9	1	1	X
ejpam-4064	117	10	)	)	PUNCT
ejpam-4064	117	11	+	+	CCONJ
ejpam-4064	117	12	(	(	PUNCT
ejpam-4064	117	13	−m)−k	−m)−k	INTJ
ejpam-4064	117	14	(	(	PUNCT
ejpam-4064	117	15	γ(k	γ(k	PROPN
ejpam-4064	117	16	+	+	PROPN
ejpam-4064	117	17	1)−	1)−	PROPN
ejpam-4064	117	18	γ	γ	X
ejpam-4064	117	19	(	(	PUNCT
ejpam-4064	117	20	k	k	PROPN
ejpam-4064	117	21	+	+	CCONJ
ejpam-4064	117	22	1,−mπ(y	1,−mπ(y	NUM
ejpam-4064	117	23	+	+	CCONJ
ejpam-4064	117	24	1	1	X
ejpam-4064	117	25	)	)	PUNCT
ejpam-4064	117	26	2α	2α	NOUN
ejpam-4064	117	27	)	)	PUNCT
ejpam-4064	117	28	)	)	PUNCT
ejpam-4064	117	29	)	)	PUNCT
ejpam-4064	118	1	+	+	CCONJ
ejpam-4064	118	2	π	π	X
ejpam-4064	118	3	(	(	PUNCT
ejpam-4064	118	4	−i−k	−i−k	PROPN
ejpam-4064	118	5	)	)	PUNCT
ejpam-4064	118	6	(	(	PUNCT
ejpam-4064	118	7	−m)−k−1γ(k	−m)−k−1γ(k	NOUN
ejpam-4064	118	8	+	+	CCONJ
ejpam-4064	118	9	1	1	X
ejpam-4064	118	10	)	)	PUNCT
ejpam-4064	118	11	proof	proof	NOUN
ejpam-4064	118	12	.	.	PUNCT
ejpam-4064	119	1	use	use	VERB
ejpam-4064	119	2	equation	equation	NOUN
ejpam-4064	119	3	(	(	PUNCT
ejpam-4064	119	4	14	14	NUM
ejpam-4064	119	5	)	)	PUNCT
ejpam-4064	119	6	and	and	CCONJ
ejpam-4064	119	7	set	set	VERB
ejpam-4064	119	8	a	a	DET
ejpam-4064	119	9	=	=	SYM
ejpam-4064	119	10	1	1	NUM
ejpam-4064	119	11	and	and	CCONJ
ejpam-4064	119	12	simplify	simplify	NOUN
ejpam-4064	119	13	.	.	PUNCT
ejpam-4064	120	1	proposition	proposition	NOUN
ejpam-4064	120	2	2	2	NUM
ejpam-4064	120	3	.	.	PUNCT
ejpam-4064	121	1	(	(	PUNCT
ejpam-4064	121	2	17	17	NUM
ejpam-4064	121	3	)	)	PUNCT
ejpam-4064	121	4	∫	∫	PROPN
ejpam-4064	122	1	∞	∞	PROPN
ejpam-4064	122	2	0	0	NUM
ejpam-4064	122	3	log(tanh(αx))(log(a	log(tanh(αx))(log(a	PROPN
ejpam-4064	122	4	)	)	PUNCT
ejpam-4064	122	5	cos(mx	cos(mx	PROPN
ejpam-4064	122	6	)	)	PUNCT
ejpam-4064	123	1	+	+	CCONJ
ejpam-4064	123	2	x	x	SYM
ejpam-4064	123	3	sin(mx	sin(mx	NOUN
ejpam-4064	123	4	)	)	PUNCT
ejpam-4064	123	5	)	)	PUNCT
ejpam-4064	123	6	log2(a	log2(a	NUM
ejpam-4064	123	7	)	)	PUNCT
ejpam-4064	124	1	+	+	CCONJ
ejpam-4064	125	1	x2	x2	PROPN
ejpam-4064	125	2	dx	dx	PROPN
ejpam-4064	125	3	=	=	PROPN
ejpam-4064	126	1	π	π	PROPN
ejpam-4064	126	2	∞∑	∞∑	NUM
ejpam-4064	126	3	y=0	y=0	NOUN
ejpam-4064	126	4	(	(	PUNCT
ejpam-4064	126	5	−1)ya−m	−1)ya−m	NOUN
ejpam-4064	126	6	(	(	PUNCT
ejpam-4064	126	7	log	log	NOUN
ejpam-4064	126	8	(	(	PUNCT
ejpam-4064	126	9	−m(2α	−m(2α	NUM
ejpam-4064	126	10	log(a	log(a	PROPN
ejpam-4064	126	11	)	)	PUNCT
ejpam-4064	127	1	+	+	NUM
ejpam-4064	127	2	πy	πy	X
ejpam-4064	127	3	+	+	NUM
ejpam-4064	127	4	π	π	X
ejpam-4064	127	5	)	)	PUNCT
ejpam-4064	127	6	α	α	NOUN
ejpam-4064	127	7	)	)	PUNCT
ejpam-4064	128	1	+	+	CCONJ
ejpam-4064	128	2	γ	γ	X
ejpam-4064	128	3	(	(	PUNCT
ejpam-4064	128	4	0,−m(πy	0,−m(πy	NUM
ejpam-4064	128	5	+	+	CCONJ
ejpam-4064	128	6	2α	2α	PROPN
ejpam-4064	128	7	log(a	log(a	PROPN
ejpam-4064	128	8	)	)	PUNCT
ejpam-4064	128	9	+	+	NUM
ejpam-4064	128	10	π	π	X
ejpam-4064	128	11	)	)	PUNCT
ejpam-4064	128	12	2α	2α	NOUN
ejpam-4064	128	13	)	)	PUNCT
ejpam-4064	129	1	−	−	PROPN
ejpam-4064	129	2	log	log	NOUN
ejpam-4064	129	3	(	(	PUNCT
ejpam-4064	129	4	2	2	NUM
ejpam-4064	129	5	log(a	log(a	PROPN
ejpam-4064	129	6	)	)	PUNCT
ejpam-4064	129	7	+	+	CCONJ
ejpam-4064	129	8	π(y	π(y	PROPN
ejpam-4064	129	9	+	+	CCONJ
ejpam-4064	129	10	1	1	X
ejpam-4064	129	11	)	)	PUNCT
ejpam-4064	129	12	α	α	NOUN
ejpam-4064	129	13	)	)	PUNCT
ejpam-4064	129	14	−	−	ADP
ejpam-4064	130	1	log(m	log(m	PROPN
ejpam-4064	130	2	)	)	PUNCT
ejpam-4064	131	1	+	+	CCONJ
ejpam-4064	131	2	iπ	iπ	NOUN
ejpam-4064	131	3	)	)	PUNCT
ejpam-4064	132	1	−	−	NOUN
ejpam-4064	132	2	1	1	NUM
ejpam-4064	132	3	2	2	NUM
ejpam-4064	132	4	πa−mγ(0,−m	πa−mγ(0,−m	X
ejpam-4064	132	5	log(a	log(a	PROPN
ejpam-4064	132	6	)	)	PUNCT
ejpam-4064	132	7	)	)	PUNCT
ejpam-4064	132	8	proof	proof	NOUN
ejpam-4064	132	9	.	.	PUNCT
ejpam-4064	133	1	use	use	VERB
ejpam-4064	133	2	equation	equation	NOUN
ejpam-4064	133	3	(	(	PUNCT
ejpam-4064	133	4	14	14	NUM
ejpam-4064	133	5	)	)	PUNCT
ejpam-4064	133	6	and	and	CCONJ
ejpam-4064	133	7	apply	apply	VERB
ejpam-4064	133	8	l’hopital	l’hopital	PROPN
ejpam-4064	133	9	’s	’s	PART
ejpam-4064	133	10	rule	rule	NOUN
ejpam-4064	133	11	as	as	ADP
ejpam-4064	133	12	k	k	PROPN
ejpam-4064	133	13	→	→	SYM
ejpam-4064	133	14	−1	−1	NOUN
ejpam-4064	133	15	and	and	CCONJ
ejpam-4064	133	16	simplify	simplify	NOUN
ejpam-4064	133	17	.	.	PUNCT
ejpam-4064	134	1	lemma	lemma	PROPN
ejpam-4064	134	2	2	2	NUM
ejpam-4064	134	3	.	.	PUNCT
ejpam-4064	135	1	(	(	PUNCT
ejpam-4064	135	2	18	18	NUM
ejpam-4064	135	3	)	)	PUNCT
ejpam-4064	135	4	∫	∫	PROPN
ejpam-4064	135	5	∞	∞	PROPN
ejpam-4064	135	6	0	0	NUM
ejpam-4064	136	1	log(tanh(3x	log(tanh(3x	PROPN
ejpam-4064	136	2	)	)	PUNCT
ejpam-4064	136	3	)	)	PUNCT
ejpam-4064	136	4	(	(	PUNCT
ejpam-4064	136	5	log(2	log(2	NOUN
ejpam-4064	136	6	)	)	PUNCT
ejpam-4064	137	1	cos	cos	ADP
ejpam-4064	137	2	(	(	PUNCT
ejpam-4064	137	3	3x	3x	NUM
ejpam-4064	137	4	4	4	NUM
ejpam-4064	137	5	)	)	PUNCT
ejpam-4064	137	6	−	−	NOUN
ejpam-4064	137	7	x	x	SYM
ejpam-4064	137	8	sin	sin	NOUN
ejpam-4064	137	9	(	(	PUNCT
ejpam-4064	137	10	3x	3x	NUM
ejpam-4064	137	11	4	4	NUM
ejpam-4064	137	12	)	)	PUNCT
ejpam-4064	137	13	)	)	PUNCT
ejpam-4064	138	1	x2	x2	PROPN
ejpam-4064	139	1	+	+	PUNCT
ejpam-4064	139	2	log2(2	log2(2	ADJ
ejpam-4064	139	3	)	)	PUNCT
ejpam-4064	139	4	dx	dx	PROPN
ejpam-4064	140	1	=	=	SYM
ejpam-4064	140	2	23/4π	23/4π	NUM
ejpam-4064	140	3	∞∑	∞∑	NUM
ejpam-4064	140	4	y=0	y=0	NOUN
ejpam-4064	140	5	(	(	PUNCT
ejpam-4064	140	6	−1)yγ	−1)yγ	PROPN
ejpam-4064	140	7	(	(	PUNCT
ejpam-4064	140	8	0	0	NUM
ejpam-4064	140	9	,	,	PUNCT
ejpam-4064	140	10	1	1	NUM
ejpam-4064	140	11	8	8	NUM
ejpam-4064	140	12	(	(	PUNCT
ejpam-4064	140	13	πy	πy	NOUN
ejpam-4064	140	14	+	+	NUM
ejpam-4064	140	15	log(64	log(64	NOUN
ejpam-4064	140	16	)	)	PUNCT
ejpam-4064	141	1	+	+	NUM
ejpam-4064	141	2	π	π	X
ejpam-4064	141	3	)	)	PUNCT
ejpam-4064	141	4	)	)	PUNCT
ejpam-4064	142	1	+	+	CCONJ
ejpam-4064	142	2	πei	πei	NOUN
ejpam-4064	142	3	(	(	PUNCT
ejpam-4064	142	4	−3	−3	PROPN
ejpam-4064	142	5	log(2	log(2	NOUN
ejpam-4064	142	6	)	)	PUNCT
ejpam-4064	142	7	4	4	NUM
ejpam-4064	142	8	)	)	PUNCT
ejpam-4064	142	9	4	4	NUM
ejpam-4064	142	10	√	√	NUM
ejpam-4064	142	11	2	2	NUM
ejpam-4064	142	12	r.	r.	PROPN
ejpam-4064	142	13	reynolds	reynolds	PROPN
ejpam-4064	142	14	,	,	PUNCT
ejpam-4064	142	15	a.	a.	PROPN
ejpam-4064	142	16	stauffer	stauffer	PROPN
ejpam-4064	142	17	/	/	SYM
ejpam-4064	142	18	eur	eur	PROPN
ejpam-4064	142	19	.	.	PUNCT
ejpam-4064	143	1	j.	j.	PROPN
ejpam-4064	143	2	pure	pure	PROPN
ejpam-4064	143	3	appl	appl	PROPN
ejpam-4064	143	4	.	.	PROPN
ejpam-4064	143	5	math	math	PROPN
ejpam-4064	143	6	,	,	PUNCT
ejpam-4064	143	7	14	14	NUM
ejpam-4064	143	8	(	(	PUNCT
ejpam-4064	143	9	4	4	NUM
ejpam-4064	143	10	)	)	PUNCT
ejpam-4064	143	11	(	(	PUNCT
ejpam-4064	143	12	2021	2021	NUM
ejpam-4064	143	13	)	)	PUNCT
ejpam-4064	143	14	,	,	PUNCT
ejpam-4064	143	15	1295	1295	NUM
ejpam-4064	143	16	-	-	SYM
ejpam-4064	143	17	1305	1305	NUM
ejpam-4064	143	18	1301	1301	NUM
ejpam-4064	143	19	proof	proof	NOUN
ejpam-4064	143	20	.	.	PUNCT
ejpam-4064	144	1	use	use	VERB
ejpam-4064	144	2	equation	equation	NOUN
ejpam-4064	144	3	(	(	PUNCT
ejpam-4064	144	4	17	17	NUM
ejpam-4064	144	5	)	)	PUNCT
ejpam-4064	144	6	and	and	CCONJ
ejpam-4064	144	7	set	set	VERB
ejpam-4064	144	8	a	a	DET
ejpam-4064	144	9	=	=	SYM
ejpam-4064	144	10	2	2	NUM
ejpam-4064	144	11	,	,	PUNCT
ejpam-4064	144	12	α	α	NOUN
ejpam-4064	144	13	=	=	SYM
ejpam-4064	145	1	3,m	3,m	NUM
ejpam-4064	145	2	=	=	NOUN
ejpam-4064	145	3	−3/4	−3/4	NOUN
ejpam-4064	145	4	and	and	CCONJ
ejpam-4064	145	5	simplify	simplify	NOUN
ejpam-4064	145	6	.	.	PUNCT
ejpam-4064	146	1	lemma	lemma	PROPN
ejpam-4064	146	2	3	3	NUM
ejpam-4064	146	3	.	.	PUNCT
ejpam-4064	147	1	(	(	PUNCT
ejpam-4064	147	2	19	19	NUM
ejpam-4064	147	3	)	)	PUNCT
ejpam-4064	147	4	∫	∫	PROPN
ejpam-4064	148	1	∞	∞	PROPN
ejpam-4064	148	2	0	0	NUM
ejpam-4064	148	3	log(tanh(3x	log(tanh(3x	PROPN
ejpam-4064	148	4	)	)	PUNCT
ejpam-4064	148	5	)	)	PUNCT
ejpam-4064	149	1	(	(	PUNCT
ejpam-4064	149	2	x	x	X
ejpam-4064	149	3	sin	sin	NOUN
ejpam-4064	149	4	(	(	PUNCT
ejpam-4064	149	5	3x	3x	NUM
ejpam-4064	149	6	4	4	NUM
ejpam-4064	149	7	)	)	PUNCT
ejpam-4064	149	8	−	−	ADP
ejpam-4064	149	9	iπ	iπ	INTJ
ejpam-4064	149	10	cos	cos	PROPN
ejpam-4064	149	11	(	(	PUNCT
ejpam-4064	149	12	3x	3x	NUM
ejpam-4064	149	13	4	4	NUM
ejpam-4064	149	14	)	)	PUNCT
ejpam-4064	149	15	)	)	PUNCT
ejpam-4064	150	1	π2	π2	ADV
ejpam-4064	150	2	−	−	PROPN
ejpam-4064	150	3	x2	x2	NOUN
ejpam-4064	150	4	dx	dx	PROPN
ejpam-4064	150	5	=	=	PROPN
ejpam-4064	151	1	π	π	PROPN
ejpam-4064	151	2	∞∑	∞∑	NUM
ejpam-4064	151	3	y=0	y=0	NOUN
ejpam-4064	151	4	(	(	PUNCT
ejpam-4064	151	5	−1)y+	−1)y+	NOUN
ejpam-4064	151	6	3	3	NUM
ejpam-4064	151	7	4γ	4γ	NOUN
ejpam-4064	151	8	(	(	PUNCT
ejpam-4064	151	9	0	0	NUM
ejpam-4064	151	10	,	,	PUNCT
ejpam-4064	151	11	1	1	NUM
ejpam-4064	151	12	8	8	NUM
ejpam-4064	151	13	π(y	π(y	NOUN
ejpam-4064	151	14	+	+	CCONJ
ejpam-4064	151	15	(	(	PUNCT
ejpam-4064	151	16	1	1	NUM
ejpam-4064	151	17	+	+	NUM
ejpam-4064	151	18	6i	6i	NUM
ejpam-4064	151	19	)	)	PUNCT
ejpam-4064	151	20	)	)	PUNCT
ejpam-4064	151	21	)	)	PUNCT
ejpam-4064	152	1	−	−	NOUN
ejpam-4064	152	2	1	1	NUM
ejpam-4064	152	3	2	2	NUM
ejpam-4064	152	4	(	(	PUNCT
ejpam-4064	152	5	−1)3/4πγ	−1)3/4πγ	PROPN
ejpam-4064	152	6	(	(	PUNCT
ejpam-4064	152	7	0	0	NUM
ejpam-4064	152	8	,	,	PUNCT
ejpam-4064	152	9	3iπ	3iπ	ADJ
ejpam-4064	152	10	4	4	NUM
ejpam-4064	152	11	)	)	PUNCT
ejpam-4064	152	12	proof	proof	NOUN
ejpam-4064	152	13	.	.	PUNCT
ejpam-4064	153	1	use	use	VERB
ejpam-4064	153	2	equation	equation	NOUN
ejpam-4064	153	3	(	(	PUNCT
ejpam-4064	153	4	17	17	NUM
ejpam-4064	153	5	)	)	PUNCT
ejpam-4064	153	6	and	and	CCONJ
ejpam-4064	153	7	set	set	VERB
ejpam-4064	153	8	a	a	DET
ejpam-4064	153	9	=	=	SYM
ejpam-4064	153	10	−1	−1	NOUN
ejpam-4064	153	11	,	,	PUNCT
ejpam-4064	153	12	α	α	X
ejpam-4064	153	13	=	=	SYM
ejpam-4064	154	1	3,m	3,m	NUM
ejpam-4064	154	2	=	=	NOUN
ejpam-4064	154	3	−3/4	−3/4	NOUN
ejpam-4064	154	4	and	and	CCONJ
ejpam-4064	154	5	simplify	simplify	NOUN
ejpam-4064	154	6	.	.	PUNCT
ejpam-4064	155	1	lemma	lemma	PROPN
ejpam-4064	155	2	4	4	NUM
ejpam-4064	155	3	.	.	PUNCT
ejpam-4064	156	1	(	(	PUNCT
ejpam-4064	156	2	20	20	NUM
ejpam-4064	156	3	)	)	PUNCT
ejpam-4064	156	4	∫	∫	PROPN
ejpam-4064	157	1	∞	∞	PROPN
ejpam-4064	157	2	0	0	NUM
ejpam-4064	157	3	log(tanh(x	log(tanh(x	NOUN
ejpam-4064	157	4	)	)	PUNCT
ejpam-4064	157	5	)	)	PUNCT
ejpam-4064	158	1	(	(	PUNCT
ejpam-4064	158	2	cos	cos	X
ejpam-4064	158	3	(	(	PUNCT
ejpam-4064	158	4	2x	2x	NUM
ejpam-4064	158	5	3	3	NUM
ejpam-4064	158	6	)	)	PUNCT
ejpam-4064	158	7	−	−	NOUN
ejpam-4064	158	8	x	x	SYM
ejpam-4064	158	9	sin	sin	NOUN
ejpam-4064	158	10	(	(	PUNCT
ejpam-4064	158	11	2x	2x	NUM
ejpam-4064	158	12	3	3	NUM
ejpam-4064	158	13	)	)	PUNCT
ejpam-4064	158	14	)	)	PUNCT
ejpam-4064	159	1	x2	x2	PROPN
ejpam-4064	160	1	+	+	CCONJ
ejpam-4064	160	2	1	1	NUM
ejpam-4064	160	3	dx	dx	NOUN
ejpam-4064	160	4	=	=	VERB
ejpam-4064	160	5	e2/3π	e2/3π	ADJ
ejpam-4064	160	6	∞∑	∞∑	NUM
ejpam-4064	160	7	y=0	y=0	NOUN
ejpam-4064	160	8	(	(	PUNCT
ejpam-4064	160	9	−1)yγ	−1)yγ	PROPN
ejpam-4064	160	10	(	(	PUNCT
ejpam-4064	160	11	0	0	NUM
ejpam-4064	160	12	,	,	PUNCT
ejpam-4064	160	13	1	1	NUM
ejpam-4064	160	14	3	3	NUM
ejpam-4064	160	15	(	(	PUNCT
ejpam-4064	160	16	πy	πy	NOUN
ejpam-4064	161	1	+	+	X
ejpam-4064	161	2	π	π	X
ejpam-4064	161	3	+	+	CCONJ
ejpam-4064	161	4	2	2	NUM
ejpam-4064	161	5	)	)	PUNCT
ejpam-4064	161	6	)	)	PUNCT
ejpam-4064	162	1	+	+	CCONJ
ejpam-4064	162	2	1	1	NUM
ejpam-4064	162	3	2	2	NUM
ejpam-4064	162	4	e2/3πei	e2/3πei	NOUN
ejpam-4064	162	5	(	(	PUNCT
ejpam-4064	162	6	−2	−2	NOUN
ejpam-4064	162	7	3	3	NUM
ejpam-4064	162	8	)	)	PUNCT
ejpam-4064	162	9	proof	proof	NOUN
ejpam-4064	162	10	.	.	PUNCT
ejpam-4064	163	1	use	use	VERB
ejpam-4064	163	2	equation	equation	NOUN
ejpam-4064	163	3	(	(	PUNCT
ejpam-4064	163	4	17	17	NUM
ejpam-4064	163	5	)	)	PUNCT
ejpam-4064	163	6	and	and	CCONJ
ejpam-4064	163	7	set	set	VERB
ejpam-4064	163	8	a	a	DET
ejpam-4064	163	9	=	=	SYM
ejpam-4064	163	10	e	e	NOUN
ejpam-4064	163	11	,	,	PUNCT
ejpam-4064	163	12	α	α	NOUN
ejpam-4064	163	13	=	=	SYM
ejpam-4064	163	14	1,m	1,m	PROPN
ejpam-4064	163	15	=	=	SYM
ejpam-4064	163	16	−2/3	−2/3	PROPN
ejpam-4064	163	17	and	and	CCONJ
ejpam-4064	163	18	simplify	simplify	NOUN
ejpam-4064	163	19	.	.	PUNCT
ejpam-4064	164	1	proposition	proposition	NOUN
ejpam-4064	164	2	3	3	NUM
ejpam-4064	164	3	.	.	PUNCT
ejpam-4064	165	1	(	(	PUNCT
ejpam-4064	165	2	21	21	NUM
ejpam-4064	165	3	)	)	PUNCT
ejpam-4064	165	4	∫	∫	PROPN
ejpam-4064	165	5	∞	∞	PROPN
ejpam-4064	165	6	0	0	PUNCT
ejpam-4064	166	1	(	(	PUNCT
ejpam-4064	166	2	x	x	X
ejpam-4064	166	3	sin(mx)−	sin(mx)−	VERB
ejpam-4064	166	4	iπ	iπ	PRON
ejpam-4064	166	5	cos(mx	cos(mx	NOUN
ejpam-4064	166	6	)	)	PUNCT
ejpam-4064	166	7	)	)	PUNCT
ejpam-4064	166	8	log(tanh(αx))dx	log(tanh(αx))dx	NOUN
ejpam-4064	166	9	=	=	PUNCT
ejpam-4064	166	10	∞∑	∞∑	NUM
ejpam-4064	166	11	y=0	y=0	NOUN
ejpam-4064	166	12	π(−1)−m+y+1γ	π(−1)−m+y+1γ	NUM
ejpam-4064	166	13	(	(	PUNCT
ejpam-4064	166	14	2,−mπ(y+2iα+1	2,−mπ(y+2iα+1	NUM
ejpam-4064	166	15	)	)	PUNCT
ejpam-4064	166	16	2α	2α	NOUN
ejpam-4064	166	17	)	)	PUNCT
ejpam-4064	167	1	m2	m2	PROPN
ejpam-4064	167	2	+	+	CCONJ
ejpam-4064	167	3	π(1−	π(1−	PROPN
ejpam-4064	167	4	iπm	iπm	PROPN
ejpam-4064	167	5	)	)	PUNCT
ejpam-4064	167	6	2m2	2m2	NUM
ejpam-4064	167	7	proof	proof	NOUN
ejpam-4064	167	8	.	.	PUNCT
ejpam-4064	168	1	use	use	VERB
ejpam-4064	168	2	equation	equation	NOUN
ejpam-4064	168	3	(	(	PUNCT
ejpam-4064	168	4	14	14	NUM
ejpam-4064	168	5	)	)	PUNCT
ejpam-4064	168	6	and	and	CCONJ
ejpam-4064	168	7	set	set	VERB
ejpam-4064	168	8	k	k	PROPN
ejpam-4064	168	9	=	=	SYM
ejpam-4064	168	10	1	1	NUM
ejpam-4064	168	11	,	,	PUNCT
ejpam-4064	168	12	a	a	DET
ejpam-4064	168	13	=	=	X
ejpam-4064	168	14	−1	−1	NOUN
ejpam-4064	168	15	and	and	CCONJ
ejpam-4064	168	16	simplify	simplify	NOUN
ejpam-4064	168	17	.	.	PUNCT
ejpam-4064	169	1	proposition	proposition	NOUN
ejpam-4064	169	2	4	4	NUM
ejpam-4064	169	3	.	.	PUNCT
ejpam-4064	170	1	(	(	PUNCT
ejpam-4064	170	2	22	22	NUM
ejpam-4064	170	3	)	)	PUNCT
ejpam-4064	170	4	∫	∫	PROPN
ejpam-4064	171	1	∞	∞	NOUN
ejpam-4064	171	2	0	0	NUM
ejpam-4064	172	1	e−	e−	ADJ
ejpam-4064	172	2	2ix	2ix	NOUN
ejpam-4064	172	3	3	3	NUM
ejpam-4064	172	4	(	(	PUNCT
ejpam-4064	172	5	e	e	NOUN
ejpam-4064	172	6	4ix	4ix	NOUN
ejpam-4064	172	7	3	3	NUM
ejpam-4064	172	8	log(i(π	log(i(π	VERB
ejpam-4064	172	9	−	−	NOUN
ejpam-4064	172	10	x	x	NOUN
ejpam-4064	172	11	)	)	PUNCT
ejpam-4064	172	12	)	)	PUNCT
ejpam-4064	173	1	+	+	CCONJ
ejpam-4064	173	2	log(i(x+	log(i(x+	ADP
ejpam-4064	173	3	π	π	NOUN
ejpam-4064	173	4	)	)	PUNCT
ejpam-4064	173	5	)	)	PUNCT
ejpam-4064	173	6	)	)	PUNCT
ejpam-4064	174	1	log(tanh(αx))dx	log(tanh(αx))dx	NOUN
ejpam-4064	174	2	=	=	SYM
ejpam-4064	174	3	3	3	NUM
ejpam-4064	174	4	2	2	NUM
ejpam-4064	174	5	π	π	NOUN
ejpam-4064	174	6	∞∑	∞∑	NUM
ejpam-4064	174	7	y=0	y=0	NOUN
ejpam-4064	174	8	(	(	PUNCT
ejpam-4064	174	9	−1)y	−1)y	X
ejpam-4064	174	10	(	(	PUNCT
ejpam-4064	174	11	i	i	PRON
ejpam-4064	174	12	(	(	PUNCT
ejpam-4064	174	13	√	√	PROPN
ejpam-4064	174	14	3	3	NUM
ejpam-4064	174	15	+	+	CCONJ
ejpam-4064	174	16	i	i	NOUN
ejpam-4064	174	17	)	)	PUNCT
ejpam-4064	174	18	e1	e1	PROPN
ejpam-4064	174	19	(	(	PUNCT
ejpam-4064	174	20	π(y	π(y	PROPN
ejpam-4064	174	21	+	+	CCONJ
ejpam-4064	174	22	2iα+	2iα+	NUM
ejpam-4064	174	23	1	1	NUM
ejpam-4064	174	24	)	)	PUNCT
ejpam-4064	174	25	3α	3α	NOUN
ejpam-4064	174	26	)	)	PUNCT
ejpam-4064	175	1	+	+	CCONJ
ejpam-4064	175	2	2e−	2e−	PROPN
ejpam-4064	175	3	π(y+1	π(y+1	NUM
ejpam-4064	175	4	)	)	PUNCT
ejpam-4064	175	5	3α	3α	NUM
ejpam-4064	175	6	log	log	NOUN
ejpam-4064	175	7	(	(	PUNCT
ejpam-4064	175	8	π(2iα+	π(2iα+	NOUN
ejpam-4064	175	9	y	y	PROPN
ejpam-4064	175	10	+	+	CCONJ
ejpam-4064	175	11	1	1	X
ejpam-4064	175	12	)	)	PUNCT
ejpam-4064	175	13	2α	2α	NOUN
ejpam-4064	175	14	)	)	PUNCT
ejpam-4064	175	15	)	)	PUNCT
ejpam-4064	176	1	−	−	NOUN
ejpam-4064	176	2	3	3	NUM
ejpam-4064	176	3	2	2	NUM
ejpam-4064	176	4	π	π	NOUN
ejpam-4064	176	5	(	(	PUNCT
ejpam-4064	176	6	log(iπ	log(iπ	X
ejpam-4064	176	7	)	)	PUNCT
ejpam-4064	177	1	+	+	CCONJ
ejpam-4064	177	2	(	(	PUNCT
ejpam-4064	177	3	−1)2/3γ	−1)2/3γ	PRON
ejpam-4064	177	4	(	(	PUNCT
ejpam-4064	177	5	0	0	NUM
ejpam-4064	177	6	,	,	PUNCT
ejpam-4064	177	7	2iπ	2iπ	NOUN
ejpam-4064	177	8	3	3	NUM
ejpam-4064	177	9	)	)	PUNCT
ejpam-4064	177	10	)	)	PUNCT
ejpam-4064	177	11	r.	r.	PROPN
ejpam-4064	177	12	reynolds	reynolds	PROPN
ejpam-4064	177	13	,	,	PUNCT
ejpam-4064	177	14	a.	a.	PROPN
ejpam-4064	177	15	stauffer	stauffer	PROPN
ejpam-4064	177	16	/	/	SYM
ejpam-4064	177	17	eur	eur	PROPN
ejpam-4064	177	18	.	.	PUNCT
ejpam-4064	178	1	j.	j.	PROPN
ejpam-4064	178	2	pure	pure	PROPN
ejpam-4064	178	3	appl	appl	PROPN
ejpam-4064	178	4	.	.	PROPN
ejpam-4064	178	5	math	math	PROPN
ejpam-4064	178	6	,	,	PUNCT
ejpam-4064	178	7	14	14	NUM
ejpam-4064	178	8	(	(	PUNCT
ejpam-4064	178	9	4	4	NUM
ejpam-4064	178	10	)	)	PUNCT
ejpam-4064	178	11	(	(	PUNCT
ejpam-4064	178	12	2021	2021	NUM
ejpam-4064	178	13	)	)	PUNCT
ejpam-4064	178	14	,	,	PUNCT
ejpam-4064	178	15	1295	1295	NUM
ejpam-4064	178	16	-	-	SYM
ejpam-4064	178	17	1305	1305	NUM
ejpam-4064	178	18	1302	1302	NUM
ejpam-4064	178	19	proof	proof	NOUN
ejpam-4064	178	20	.	.	PUNCT
ejpam-4064	179	1	use	use	VERB
ejpam-4064	179	2	equation	equation	NOUN
ejpam-4064	179	3	(	(	PUNCT
ejpam-4064	179	4	14	14	NUM
ejpam-4064	179	5	)	)	PUNCT
ejpam-4064	179	6	take	take	VERB
ejpam-4064	179	7	the	the	DET
ejpam-4064	179	8	first	first	ADJ
ejpam-4064	179	9	partial	partial	ADJ
ejpam-4064	179	10	derivative	derivative	NOUN
ejpam-4064	179	11	with	with	ADP
ejpam-4064	179	12	respect	respect	NOUN
ejpam-4064	179	13	to	to	ADP
ejpam-4064	179	14	k	k	PROPN
ejpam-4064	179	15	then	then	ADV
ejpam-4064	179	16	set	set	VERB
ejpam-4064	179	17	k	k	PROPN
ejpam-4064	180	1	=	=	PUNCT
ejpam-4064	181	1	0,m	0,m	PUNCT
ejpam-4064	182	1	=	=	SYM
ejpam-4064	182	2	−2/3	−2/3	PROPN
ejpam-4064	182	3	,	,	PUNCT
ejpam-4064	182	4	a	a	DET
ejpam-4064	182	5	=	=	X
ejpam-4064	182	6	−1	−1	NOUN
ejpam-4064	182	7	and	and	CCONJ
ejpam-4064	182	8	simplify	simplify	NOUN
ejpam-4064	182	9	.	.	PUNCT
ejpam-4064	183	1	lemma	lemma	PROPN
ejpam-4064	183	2	5.∫	5.∫	PROPN
ejpam-4064	183	3	∞	∞	PROPN
ejpam-4064	183	4	0	0	NUM
ejpam-4064	183	5	log(tanh(3x	log(tanh(3x	PROPN
ejpam-4064	183	6	)	)	PUNCT
ejpam-4064	183	7	)	)	PUNCT
ejpam-4064	184	1	(	(	PUNCT
ejpam-4064	184	2	cos	cos	X
ejpam-4064	184	3	(	(	PUNCT
ejpam-4064	184	4	2x	2x	NUM
ejpam-4064	184	5	3	3	NUM
ejpam-4064	184	6	)	)	PUNCT
ejpam-4064	184	7	−	−	NOUN
ejpam-4064	184	8	sin	sin	NOUN
ejpam-4064	184	9	(	(	PUNCT
ejpam-4064	184	10	2x	2x	NUM
ejpam-4064	184	11	3	3	NUM
ejpam-4064	184	12	)	)	PUNCT
ejpam-4064	184	13	)	)	PUNCT
ejpam-4064	185	1	√	√	NUM
ejpam-4064	186	1	x	x	X
ejpam-4064	186	2	dx	dx	PROPN
ejpam-4064	186	3	=	=	SYM
ejpam-4064	186	4	√	√	NUM
ejpam-4064	186	5	3π	3π	NOUN
ejpam-4064	186	6	∞∑	∞∑	NUM
ejpam-4064	186	7	y=0	y=0	NOUN
ejpam-4064	186	8	(	(	PUNCT
ejpam-4064	186	9	−1)yγ	−1)yγ	PROPN
ejpam-4064	186	10	(	(	PUNCT
ejpam-4064	186	11	1	1	NUM
ejpam-4064	186	12	2	2	NUM
ejpam-4064	186	13	,	,	PUNCT
ejpam-4064	186	14	1	1	NUM
ejpam-4064	186	15	9	9	NUM
ejpam-4064	186	16	π(y	π(y	NOUN
ejpam-4064	186	17	+	+	CCONJ
ejpam-4064	186	18	1	1	NUM
ejpam-4064	186	19	)	)	PUNCT
ejpam-4064	186	20	)	)	PUNCT
ejpam-4064	187	1	−	−	NOUN
ejpam-4064	188	1	1	1	NUM
ejpam-4064	188	2	2	2	NUM
ejpam-4064	188	3	√	√	NUM
ejpam-4064	188	4	3π3/2	3π3/2	NUM
ejpam-4064	188	5	(	(	PUNCT
ejpam-4064	188	6	23	23	NUM
ejpam-4064	188	7	)	)	PUNCT
ejpam-4064	188	8	proof	proof	NOUN
ejpam-4064	188	9	.	.	PUNCT
ejpam-4064	189	1	use	use	VERB
ejpam-4064	189	2	equation	equation	NOUN
ejpam-4064	189	3	(	(	PUNCT
ejpam-4064	189	4	14	14	NUM
ejpam-4064	189	5	)	)	PUNCT
ejpam-4064	189	6	and	and	CCONJ
ejpam-4064	189	7	set	set	VERB
ejpam-4064	189	8	k	k	X
ejpam-4064	189	9	=	=	PUNCT
ejpam-4064	189	10	−1/2	−1/2	ADJ
ejpam-4064	189	11	,	,	PUNCT
ejpam-4064	190	1	a	a	DET
ejpam-4064	190	2	=	=	X
ejpam-4064	190	3	1,m	1,m	PROPN
ejpam-4064	190	4	=	=	SYM
ejpam-4064	190	5	−2/3	−2/3	PROPN
ejpam-4064	190	6	,	,	PUNCT
ejpam-4064	190	7	α	α	X
ejpam-4064	190	8	=	=	SYM
ejpam-4064	190	9	3	3	NUM
ejpam-4064	190	10	and	and	CCONJ
ejpam-4064	190	11	simplify	simplify	NOUN
ejpam-4064	190	12	.	.	PUNCT
ejpam-4064	191	1	lemma	lemma	PROPN
ejpam-4064	191	2	6	6	NUM
ejpam-4064	191	3	.	.	PUNCT
ejpam-4064	192	1	(	(	PUNCT
ejpam-4064	192	2	24	24	NUM
ejpam-4064	192	3	)	)	PUNCT
ejpam-4064	192	4	∫	∫	PROPN
ejpam-4064	193	1	∞	∞	PROPN
ejpam-4064	193	2	0	0	NUM
ejpam-4064	193	3	(	(	PUNCT
ejpam-4064	193	4	sin(mx	sin(mx	X
ejpam-4064	193	5	)	)	PUNCT
ejpam-4064	193	6	+	+	SYM
ejpam-4064	193	7	cos(mx	cos(mx	NOUN
ejpam-4064	193	8	)	)	PUNCT
ejpam-4064	193	9	)	)	PUNCT
ejpam-4064	193	10	log(tanh(αx))√	log(tanh(αx))√	NOUN
ejpam-4064	194	1	x	x	X
ejpam-4064	194	2	dx	dx	PROPN
ejpam-4064	194	3	=	=	PUNCT
ejpam-4064	195	1	∞∑	∞∑	NUM
ejpam-4064	195	2	y=0	y=0	NOUN
ejpam-4064	195	3	√	√	NUM
ejpam-4064	195	4	2π3/2(−1)y+1	2π3/2(−1)y+1	NUM
ejpam-4064	195	5	(	(	PUNCT
ejpam-4064	195	6	erfi	erfi	NOUN
ejpam-4064	195	7	(	(	PUNCT
ejpam-4064	195	8	√	√	PROPN
ejpam-4064	195	9	π	π	PROPN
ejpam-4064	195	10	2	2	NUM
ejpam-4064	195	11	√	√	NUM
ejpam-4064	195	12	m	m	VERB
ejpam-4064	195	13	√	√	VERB
ejpam-4064	195	14	y+1	y+1	PRON
ejpam-4064	195	15	α	α	PROPN
ejpam-4064	195	16	)	)	PUNCT
ejpam-4064	196	1	−	−	PROPN
ejpam-4064	196	2	i	i	INTJ
ejpam-4064	196	3	)	)	PUNCT
ejpam-4064	197	1	√	√	PROPN
ejpam-4064	197	2	m	m	VERB
ejpam-4064	197	3	+	+	NUM
ejpam-4064	197	4	π3/2m√	π3/2m√	NOUN
ejpam-4064	197	5	2(−m)3/2	2(−m)3/2	ADJ
ejpam-4064	197	6	proof	proof	NOUN
ejpam-4064	197	7	.	.	PUNCT
ejpam-4064	198	1	use	use	VERB
ejpam-4064	198	2	equation	equation	NOUN
ejpam-4064	198	3	(	(	PUNCT
ejpam-4064	198	4	14	14	NUM
ejpam-4064	198	5	)	)	PUNCT
ejpam-4064	198	6	and	and	CCONJ
ejpam-4064	198	7	set	set	VERB
ejpam-4064	198	8	k	k	X
ejpam-4064	198	9	=	=	PUNCT
ejpam-4064	198	10	−1/2	−1/2	ADJ
ejpam-4064	198	11	,	,	PUNCT
ejpam-4064	198	12	a	a	DET
ejpam-4064	198	13	=	=	SYM
ejpam-4064	198	14	1	1	NUM
ejpam-4064	198	15	and	and	CCONJ
ejpam-4064	198	16	simplify	simplify	NOUN
ejpam-4064	198	17	.	.	PUNCT
ejpam-4064	199	1	lemma	lemma	PROPN
ejpam-4064	199	2	7	7	NUM
ejpam-4064	199	3	.	.	PUNCT
ejpam-4064	200	1	(	(	PUNCT
ejpam-4064	200	2	25	25	NUM
ejpam-4064	200	3	)	)	PUNCT
ejpam-4064	200	4	∫	∫	PROPN
ejpam-4064	200	5	∞	∞	PROPN
ejpam-4064	200	6	0	0	NUM
ejpam-4064	200	7	log(tanh(x	log(tanh(x	NOUN
ejpam-4064	200	8	)	)	PUNCT
ejpam-4064	200	9	)	)	PUNCT
ejpam-4064	201	1	(	(	PUNCT
ejpam-4064	201	2	cos	cos	X
ejpam-4064	201	3	(	(	PUNCT
ejpam-4064	201	4	x	x	SYM
ejpam-4064	201	5	2	2	X
ejpam-4064	201	6	)	)	PUNCT
ejpam-4064	201	7	−	−	NOUN
ejpam-4064	201	8	sin	sin	NOUN
ejpam-4064	201	9	(	(	PUNCT
ejpam-4064	201	10	x	x	NOUN
ejpam-4064	201	11	2	2	NUM
ejpam-4064	201	12	)	)	PUNCT
ejpam-4064	201	13	)	)	PUNCT
ejpam-4064	202	1	√	√	NUM
ejpam-4064	203	1	x	x	X
ejpam-4064	203	2	dx	dx	PROPN
ejpam-4064	203	3	=	=	PUNCT
ejpam-4064	203	4	2π	2π	PROPN
ejpam-4064	203	5	∞∑	∞∑	NUM
ejpam-4064	203	6	y=0	y=0	NOUN
ejpam-4064	203	7	(	(	PUNCT
ejpam-4064	203	8	−1)yγ	−1)yγ	PROPN
ejpam-4064	203	9	(	(	PUNCT
ejpam-4064	203	10	1	1	NUM
ejpam-4064	203	11	2	2	NUM
ejpam-4064	203	12	,	,	PUNCT
ejpam-4064	203	13	1	1	NUM
ejpam-4064	203	14	4	4	NUM
ejpam-4064	203	15	π(y	π(y	NOUN
ejpam-4064	203	16	+	+	CCONJ
ejpam-4064	203	17	1	1	NUM
ejpam-4064	203	18	)	)	PUNCT
ejpam-4064	203	19	)	)	PUNCT
ejpam-4064	204	1	−	−	PROPN
ejpam-4064	204	2	π3/2	π3/2	NOUN
ejpam-4064	204	3	proof	proof	NOUN
ejpam-4064	204	4	.	.	PUNCT
ejpam-4064	205	1	use	use	VERB
ejpam-4064	205	2	equation	equation	NOUN
ejpam-4064	205	3	(	(	PUNCT
ejpam-4064	205	4	14	14	NUM
ejpam-4064	205	5	)	)	PUNCT
ejpam-4064	205	6	and	and	CCONJ
ejpam-4064	205	7	set	set	VERB
ejpam-4064	205	8	k	k	X
ejpam-4064	205	9	=	=	PUNCT
ejpam-4064	205	10	−1/2	−1/2	ADJ
ejpam-4064	205	11	,	,	PUNCT
ejpam-4064	205	12	a	a	PRON
ejpam-4064	205	13	=	=	X
ejpam-4064	205	14	1,m	1,m	NOUN
ejpam-4064	205	15	=	=	SYM
ejpam-4064	205	16	−1/2	−1/2	PROPN
ejpam-4064	205	17	,	,	PUNCT
ejpam-4064	205	18	α	α	NOUN
ejpam-4064	205	19	=	=	SYM
ejpam-4064	205	20	1	1	NUM
ejpam-4064	205	21	and	and	CCONJ
ejpam-4064	205	22	simplify	simplify	NOUN
ejpam-4064	205	23	.	.	PUNCT
ejpam-4064	206	1	lemma	lemma	PROPN
ejpam-4064	206	2	8	8	NUM
ejpam-4064	206	3	.	.	PUNCT
ejpam-4064	207	1	(	(	PUNCT
ejpam-4064	207	2	26	26	NUM
ejpam-4064	207	3	)	)	PUNCT
ejpam-4064	207	4	∫	∫	PROPN
ejpam-4064	208	1	∞	∞	NUM
ejpam-4064	208	2	0	0	NUM
ejpam-4064	209	1	√	√	NUM
ejpam-4064	209	2	x	x	SYM
ejpam-4064	209	3	log(tanh(x	log(tanh(x	NOUN
ejpam-4064	209	4	)	)	PUNCT
ejpam-4064	209	5	)	)	PUNCT
ejpam-4064	210	1	(	(	PUNCT
ejpam-4064	210	2	sin	sin	NOUN
ejpam-4064	210	3	(	(	PUNCT
ejpam-4064	210	4	x	x	NOUN
ejpam-4064	210	5	2	2	X
ejpam-4064	210	6	)	)	PUNCT
ejpam-4064	210	7	+	+	CCONJ
ejpam-4064	210	8	cos	cos	X
ejpam-4064	210	9	(	(	PUNCT
ejpam-4064	210	10	x	x	PROPN
ejpam-4064	210	11	2	2	NUM
ejpam-4064	210	12	)	)	PUNCT
ejpam-4064	210	13	)	)	PUNCT
ejpam-4064	210	14	dx	dx	PROPN
ejpam-4064	211	1	=	=	SYM
ejpam-4064	211	2	4π	4π	PRON
ejpam-4064	211	3	∞∑	∞∑	NUM
ejpam-4064	211	4	y=0	y=0	NOUN
ejpam-4064	211	5	(	(	PUNCT
ejpam-4064	211	6	−1)yγ	−1)yγ	PROPN
ejpam-4064	211	7	(	(	PUNCT
ejpam-4064	211	8	3	3	NUM
ejpam-4064	211	9	2	2	NUM
ejpam-4064	211	10	,	,	PUNCT
ejpam-4064	211	11	1	1	NUM
ejpam-4064	211	12	4	4	NUM
ejpam-4064	211	13	π(y	π(y	NOUN
ejpam-4064	211	14	+	+	CCONJ
ejpam-4064	211	15	1	1	NUM
ejpam-4064	211	16	)	)	PUNCT
ejpam-4064	211	17	)	)	PUNCT
ejpam-4064	212	1	−	−	PROPN
ejpam-4064	212	2	π3/2	π3/2	NOUN
ejpam-4064	212	3	proof	proof	NOUN
ejpam-4064	212	4	.	.	PUNCT
ejpam-4064	213	1	use	use	VERB
ejpam-4064	213	2	equation	equation	NOUN
ejpam-4064	213	3	(	(	PUNCT
ejpam-4064	213	4	14	14	NUM
ejpam-4064	213	5	)	)	PUNCT
ejpam-4064	213	6	and	and	CCONJ
ejpam-4064	213	7	set	set	VERB
ejpam-4064	213	8	k	k	PROPN
ejpam-4064	213	9	=	=	SYM
ejpam-4064	213	10	1/2	1/2	NUM
ejpam-4064	213	11	,	,	PUNCT
ejpam-4064	213	12	a	a	DET
ejpam-4064	213	13	=	=	X
ejpam-4064	213	14	1,m	1,m	NOUN
ejpam-4064	213	15	=	=	SYM
ejpam-4064	213	16	−1/2	−1/2	PROPN
ejpam-4064	213	17	,	,	PUNCT
ejpam-4064	213	18	α	α	NOUN
ejpam-4064	213	19	=	=	SYM
ejpam-4064	213	20	1	1	NUM
ejpam-4064	213	21	and	and	CCONJ
ejpam-4064	213	22	simplify	simplify	NOUN
ejpam-4064	213	23	.	.	PUNCT
ejpam-4064	214	1	r.	r.	PROPN
ejpam-4064	214	2	reynolds	reynolds	PROPN
ejpam-4064	214	3	,	,	PUNCT
ejpam-4064	214	4	a.	a.	PROPN
ejpam-4064	214	5	stauffer	stauffer	PROPN
ejpam-4064	214	6	/	/	SYM
ejpam-4064	214	7	eur	eur	PROPN
ejpam-4064	214	8	.	.	PUNCT
ejpam-4064	215	1	j.	j.	PROPN
ejpam-4064	215	2	pure	pure	PROPN
ejpam-4064	215	3	appl	appl	PROPN
ejpam-4064	215	4	.	.	PROPN
ejpam-4064	215	5	math	math	PROPN
ejpam-4064	215	6	,	,	PUNCT
ejpam-4064	215	7	14	14	NUM
ejpam-4064	215	8	(	(	PUNCT
ejpam-4064	215	9	4	4	NUM
ejpam-4064	215	10	)	)	PUNCT
ejpam-4064	215	11	(	(	PUNCT
ejpam-4064	215	12	2021	2021	NUM
ejpam-4064	215	13	)	)	PUNCT
ejpam-4064	215	14	,	,	PUNCT
ejpam-4064	215	15	1295	1295	NUM
ejpam-4064	215	16	-	-	SYM
ejpam-4064	215	17	1305	1305	NUM
ejpam-4064	215	18	1303	1303	NUM
ejpam-4064	215	19	lemma	lemma	PROPN
ejpam-4064	215	20	9	9	NUM
ejpam-4064	215	21	.	.	PUNCT
ejpam-4064	216	1	(	(	PUNCT
ejpam-4064	216	2	27	27	NUM
ejpam-4064	216	3	)	)	PUNCT
ejpam-4064	216	4	∫	∫	PROPN
ejpam-4064	217	1	∞	∞	NOUN
ejpam-4064	217	2	0	0	NUM
ejpam-4064	218	1	e−	e−	PROPN
ejpam-4064	218	2	ix	ix	ADP
ejpam-4064	218	3	2	2	NUM
ejpam-4064	218	4	(	(	PUNCT
ejpam-4064	218	5	√	√	PROPN
ejpam-4064	218	6	π	π	PROPN
ejpam-4064	218	7	−	−	PROPN
ejpam-4064	218	8	x+	x+	PUNCT
ejpam-4064	218	9	eix	eix	PROPN
ejpam-4064	218	10	√	√	ADP
ejpam-4064	218	11	x+	x+	PROPN
ejpam-4064	218	12	π	π	PROPN
ejpam-4064	218	13	)	)	PUNCT
ejpam-4064	218	14	log(tanh(πx	log(tanh(πx	NOUN
ejpam-4064	218	15	)	)	PUNCT
ejpam-4064	218	16	)	)	PUNCT
ejpam-4064	219	1	√	√	PROPN
ejpam-4064	219	2	π2	π2	ADV
ejpam-4064	219	3	−	−	PROPN
ejpam-4064	220	1	x2	x2	PROPN
ejpam-4064	220	2	dx	dx	PROPN
ejpam-4064	220	3	=	=	SYM
ejpam-4064	220	4	2i	2i	NUM
ejpam-4064	220	5	√	√	PROPN
ejpam-4064	220	6	2π	2π	NOUN
ejpam-4064	221	1	∞∑	∞∑	NUM
ejpam-4064	221	2	y=0	y=0	NOUN
ejpam-4064	221	3	(	(	PUNCT
ejpam-4064	221	4	−1)y+	−1)y+	NOUN
ejpam-4064	221	5	1	1	NUM
ejpam-4064	221	6	4γ	4γ	NOUN
ejpam-4064	221	7	(	(	PUNCT
ejpam-4064	221	8	1	1	NUM
ejpam-4064	221	9	2	2	NUM
ejpam-4064	221	10	,	,	PUNCT
ejpam-4064	221	11	1	1	NUM
ejpam-4064	221	12	4	4	NUM
ejpam-4064	221	13	(	(	PUNCT
ejpam-4064	221	14	y	y	PROPN
ejpam-4064	221	15	+	+	CCONJ
ejpam-4064	221	16	2iπ	2iπ	ADJ
ejpam-4064	221	17	+	+	NOUN
ejpam-4064	221	18	1	1	NUM
ejpam-4064	221	19	)	)	PUNCT
ejpam-4064	221	20	)	)	PUNCT
ejpam-4064	222	1	+	+	CCONJ
ejpam-4064	222	2	(	(	PUNCT
ejpam-4064	222	3	1−	1−	NUM
ejpam-4064	222	4	i)πγ	i)πγ	PROPN
ejpam-4064	222	5	(	(	PUNCT
ejpam-4064	222	6	1	1	NUM
ejpam-4064	222	7	2	2	NUM
ejpam-4064	222	8	,	,	PUNCT
ejpam-4064	222	9	iπ	iπ	ADV
ejpam-4064	222	10	2	2	X
ejpam-4064	222	11	)	)	PUNCT
ejpam-4064	222	12	proof	proof	NOUN
ejpam-4064	222	13	.	.	PUNCT
ejpam-4064	223	1	use	use	VERB
ejpam-4064	223	2	equation	equation	NOUN
ejpam-4064	223	3	(	(	PUNCT
ejpam-4064	223	4	14	14	NUM
ejpam-4064	223	5	)	)	PUNCT
ejpam-4064	223	6	and	and	CCONJ
ejpam-4064	223	7	set	set	VERB
ejpam-4064	223	8	k	k	X
ejpam-4064	223	9	=	=	PUNCT
ejpam-4064	223	10	−1/2	−1/2	ADJ
ejpam-4064	223	11	,	,	PUNCT
ejpam-4064	223	12	a	a	DET
ejpam-4064	223	13	=	=	X
ejpam-4064	223	14	−1,m	−1,m	PROPN
ejpam-4064	223	15	=	=	SYM
ejpam-4064	224	1	−1/2	−1/2	ADJ
ejpam-4064	224	2	,	,	PUNCT
ejpam-4064	224	3	α	α	X
ejpam-4064	224	4	=	=	SYM
ejpam-4064	224	5	π	π	PROPN
ejpam-4064	224	6	and	and	CCONJ
ejpam-4064	224	7	simplify	simplify	NOUN
ejpam-4064	224	8	.	.	PUNCT
ejpam-4064	225	1	lemma	lemma	PROPN
ejpam-4064	225	2	10	10	NUM
ejpam-4064	225	3	.	.	PUNCT
ejpam-4064	226	1	(	(	PUNCT
ejpam-4064	226	2	28	28	NUM
ejpam-4064	226	3	)	)	PUNCT
ejpam-4064	226	4	∫	∫	PROPN
ejpam-4064	227	1	∞	∞	NOUN
ejpam-4064	227	2	0	0	NUM
ejpam-4064	228	1	e−	e−	PROPN
ejpam-4064	228	2	ix	ix	ADP
ejpam-4064	228	3	2	2	NUM
ejpam-4064	228	4	(	(	PUNCT
ejpam-4064	228	5	eix	eix	PROPN
ejpam-4064	228	6	log(−ix	log(−ix	PROPN
ejpam-4064	228	7	)	)	PUNCT
ejpam-4064	228	8	+	+	CCONJ
ejpam-4064	228	9	log(ix	log(ix	X
ejpam-4064	228	10	)	)	PUNCT
ejpam-4064	228	11	)	)	PUNCT
ejpam-4064	228	12	log(tanh(πx))dx	log(tanh(πx))dx	NOUN
ejpam-4064	228	13	=	=	SYM
ejpam-4064	228	14	4π	4π	PRON
ejpam-4064	229	1	∞∑	∞∑	NUM
ejpam-4064	229	2	y=0	y=0	NOUN
ejpam-4064	229	3	(	(	PUNCT
ejpam-4064	229	4	−1)y	−1)y	X
ejpam-4064	229	5	(	(	PUNCT
ejpam-4064	229	6	e−	e−	X
ejpam-4064	229	7	y	y	PROPN
ejpam-4064	229	8	4	4	NUM
ejpam-4064	229	9	−	−	NOUN
ejpam-4064	229	10	1	1	NUM
ejpam-4064	229	11	4	4	NUM
ejpam-4064	229	12	log	log	NOUN
ejpam-4064	229	13	(	(	PUNCT
ejpam-4064	229	14	y	y	NOUN
ejpam-4064	229	15	+	+	NOUN
ejpam-4064	229	16	1	1	NUM
ejpam-4064	229	17	2	2	NUM
ejpam-4064	229	18	)	)	PUNCT
ejpam-4064	229	19	+	+	CCONJ
ejpam-4064	229	20	γ	γ	X
ejpam-4064	229	21	(	(	PUNCT
ejpam-4064	229	22	0	0	NUM
ejpam-4064	229	23	,	,	PUNCT
ejpam-4064	229	24	y	y	PROPN
ejpam-4064	229	25	+	+	NOUN
ejpam-4064	229	26	1	1	NUM
ejpam-4064	229	27	4	4	NUM
ejpam-4064	229	28	)	)	PUNCT
ejpam-4064	229	29	)	)	PUNCT
ejpam-4064	230	1	+	+	CCONJ
ejpam-4064	230	2	2π(γ	2π(γ	ADJ
ejpam-4064	230	3	−	−	NOUN
ejpam-4064	230	4	log(2	log(2	NOUN
ejpam-4064	230	5	)	)	PUNCT
ejpam-4064	230	6	)	)	PUNCT
ejpam-4064	230	7	proof	proof	NOUN
ejpam-4064	230	8	.	.	PUNCT
ejpam-4064	231	1	use	use	VERB
ejpam-4064	231	2	equation	equation	NOUN
ejpam-4064	231	3	(	(	PUNCT
ejpam-4064	231	4	14	14	NUM
ejpam-4064	231	5	)	)	PUNCT
ejpam-4064	231	6	and	and	CCONJ
ejpam-4064	231	7	set	set	VERB
ejpam-4064	231	8	a	a	DET
ejpam-4064	231	9	=	=	X
ejpam-4064	231	10	1,m	1,m	NOUN
ejpam-4064	231	11	=	=	SYM
ejpam-4064	231	12	−1/2	−1/2	PROPN
ejpam-4064	231	13	,	,	PUNCT
ejpam-4064	231	14	α	α	X
ejpam-4064	231	15	=	=	NOUN
ejpam-4064	231	16	π	π	NOUN
ejpam-4064	231	17	then	then	ADV
ejpam-4064	231	18	take	take	VERB
ejpam-4064	231	19	the	the	DET
ejpam-4064	231	20	first	first	ADJ
ejpam-4064	231	21	partial	partial	ADJ
ejpam-4064	231	22	derivative	derivative	NOUN
ejpam-4064	231	23	with	with	ADP
ejpam-4064	231	24	respect	respect	NOUN
ejpam-4064	231	25	to	to	ADP
ejpam-4064	231	26	k	k	PROPN
ejpam-4064	231	27	and	and	CCONJ
ejpam-4064	231	28	set	set	VERB
ejpam-4064	231	29	k	k	PROPN
ejpam-4064	231	30	=	=	PUNCT
ejpam-4064	231	31	0	0	PUNCT
ejpam-4064	231	32	and	and	CCONJ
ejpam-4064	231	33	simplify	simplify	VERB
ejpam-4064	231	34	.	.	PUNCT
ejpam-4064	232	1	lemma	lemma	PROPN
ejpam-4064	232	2	11	11	NUM
ejpam-4064	232	3	.	.	PUNCT
ejpam-4064	233	1	(	(	PUNCT
ejpam-4064	233	2	29	29	NUM
ejpam-4064	233	3	)	)	PUNCT
ejpam-4064	233	4	∫	∫	PROPN
ejpam-4064	234	1	∞	∞	NOUN
ejpam-4064	234	2	0	0	PUNCT
ejpam-4064	235	1	e	e	NOUN
ejpam-4064	235	2	ix	ix	ADP
ejpam-4064	235	3	2	2	NUM
ejpam-4064	235	4	(	(	PUNCT
ejpam-4064	235	5	e−ix	e−ix	NOUN
ejpam-4064	235	6	3	3	NUM
ejpam-4064	235	7	√	√	PROPN
ejpam-4064	235	8	i(x+	i(x+	PROPN
ejpam-4064	235	9	π	π	PROPN
ejpam-4064	235	10	)	)	PUNCT
ejpam-4064	235	11	+	+	CCONJ
ejpam-4064	235	12	1	1	NUM
ejpam-4064	235	13	3	3	NUM
ejpam-4064	235	14	√	√	ADP
ejpam-4064	235	15	i(π	i(π	NUM
ejpam-4064	235	16	−	−	PROPN
ejpam-4064	235	17	x	x	SYM
ejpam-4064	235	18	)	)	PUNCT
ejpam-4064	235	19	)	)	PUNCT
ejpam-4064	236	1	log(tanh(2πx))dx	log(tanh(2πx))dx	NOUN
ejpam-4064	236	2	=	=	PUNCT
ejpam-4064	237	1	2i22/3π	2i22/3π	PROPN
ejpam-4064	237	2	∞∑	∞∑	NUM
ejpam-4064	237	3	y=0	y=0	NOUN
ejpam-4064	237	4	(	(	PUNCT
ejpam-4064	237	5	−1)yγ	−1)yγ	PROPN
ejpam-4064	237	6	(	(	PUNCT
ejpam-4064	237	7	2	2	NUM
ejpam-4064	237	8	3	3	NUM
ejpam-4064	237	9	,	,	PUNCT
ejpam-4064	237	10	1	1	NUM
ejpam-4064	237	11	8	8	NUM
ejpam-4064	237	12	(	(	PUNCT
ejpam-4064	237	13	y	y	NOUN
ejpam-4064	237	14	+	+	CCONJ
ejpam-4064	237	15	4iπ	4iπ	ADJ
ejpam-4064	237	16	+	+	NOUN
ejpam-4064	237	17	1	1	NUM
ejpam-4064	237	18	)	)	PUNCT
ejpam-4064	237	19	)	)	PUNCT
ejpam-4064	238	1	−	−	ADP
ejpam-4064	238	2	i22/3πγ	i22/3πγ	NOUN
ejpam-4064	238	3	(	(	PUNCT
ejpam-4064	238	4	2	2	NUM
ejpam-4064	238	5	3	3	NUM
ejpam-4064	238	6	,	,	PUNCT
ejpam-4064	238	7	iπ	iπ	ADV
ejpam-4064	238	8	2	2	X
ejpam-4064	238	9	)	)	PUNCT
ejpam-4064	238	10	proof	proof	NOUN
ejpam-4064	238	11	.	.	PUNCT
ejpam-4064	239	1	use	use	VERB
ejpam-4064	239	2	equation	equation	NOUN
ejpam-4064	239	3	(	(	PUNCT
ejpam-4064	239	4	14	14	NUM
ejpam-4064	239	5	)	)	PUNCT
ejpam-4064	239	6	and	and	CCONJ
ejpam-4064	239	7	set	set	VERB
ejpam-4064	239	8	k	k	NOUN
ejpam-4064	239	9	=	=	NOUN
ejpam-4064	239	10	−1/3	−1/3	ADJ
ejpam-4064	239	11	,	,	PUNCT
ejpam-4064	239	12	a	a	DET
ejpam-4064	239	13	=	=	NOUN
ejpam-4064	239	14	−1	−1	NOUN
ejpam-4064	239	15	,	,	PUNCT
ejpam-4064	239	16	α	α	X
ejpam-4064	239	17	=	=	PUNCT
ejpam-4064	239	18	2π	2π	NOUN
ejpam-4064	239	19	,	,	PUNCT
ejpam-4064	239	20	m	m	VERB
ejpam-4064	239	21	=	=	X
ejpam-4064	239	22	−1/2	−1/2	ADJ
ejpam-4064	239	23	and	and	CCONJ
ejpam-4064	239	24	simplify	simplify	NOUN
ejpam-4064	239	25	.	.	PUNCT
ejpam-4064	240	1	lemma	lemma	PROPN
ejpam-4064	240	2	12	12	NUM
ejpam-4064	240	3	.	.	PUNCT
ejpam-4064	241	1	(	(	PUNCT
ejpam-4064	241	2	30	30	NUM
ejpam-4064	241	3	)	)	PUNCT
ejpam-4064	241	4	∫	∫	PROPN
ejpam-4064	242	1	∞	∞	NOUN
ejpam-4064	242	2	0	0	NUM
ejpam-4064	243	1	e−	e−	PROPN
ejpam-4064	243	2	ix	ix	ADP
ejpam-4064	243	3	2	2	NUM
ejpam-4064	243	4	(	(	PUNCT
ejpam-4064	243	5	−	−	PROPN
ejpam-4064	243	6	1	1	NUM
ejpam-4064	243	7	(	(	PUNCT
ejpam-4064	243	8	x+	x+	X
ejpam-4064	243	9	π)2	π)2	PROPN
ejpam-4064	243	10	−	−	PROPN
ejpam-4064	243	11	eix	eix	PROPN
ejpam-4064	243	12	(	(	PUNCT
ejpam-4064	243	13	π	π	PROPN
ejpam-4064	243	14	−	−	PROPN
ejpam-4064	243	15	x)2	x)2	PROPN
ejpam-4064	243	16	)	)	PUNCT
ejpam-4064	244	1	log(tanh(2πx))dx	log(tanh(2πx))dx	NOUN
ejpam-4064	244	2	=	=	PUNCT
ejpam-4064	245	1	iπ	iπ	PRON
ejpam-4064	245	2	∞∑	∞∑	NUM
ejpam-4064	245	3	y=0	y=0	NOUN
ejpam-4064	245	4	(	(	PUNCT
ejpam-4064	245	5	−1)yγ	−1)yγ	PROPN
ejpam-4064	245	6	(	(	PUNCT
ejpam-4064	245	7	−1	−1	NOUN
ejpam-4064	245	8	,	,	PUNCT
ejpam-4064	245	9	1	1	NUM
ejpam-4064	245	10	8	8	NUM
ejpam-4064	245	11	(	(	PUNCT
ejpam-4064	245	12	y	y	NOUN
ejpam-4064	245	13	+	+	CCONJ
ejpam-4064	245	14	4iπ	4iπ	ADJ
ejpam-4064	245	15	+	+	NOUN
ejpam-4064	245	16	1	1	NUM
ejpam-4064	245	17	)	)	PUNCT
ejpam-4064	245	18	)	)	PUNCT
ejpam-4064	246	1	−	−	PROPN
ejpam-4064	246	2	e2	e2	PROPN
ejpam-4064	246	3	(	(	PUNCT
ejpam-4064	246	4	iπ	iπ	ADV
ejpam-4064	246	5	2	2	X
ejpam-4064	246	6	)	)	PUNCT
ejpam-4064	246	7	references	reference	NOUN
ejpam-4064	246	8	1304	1304	NUM
ejpam-4064	246	9	proof	proof	NOUN
ejpam-4064	246	10	.	.	PUNCT
ejpam-4064	247	1	use	use	VERB
ejpam-4064	247	2	equation	equation	NOUN
ejpam-4064	247	3	(	(	PUNCT
ejpam-4064	247	4	14	14	NUM
ejpam-4064	247	5	)	)	PUNCT
ejpam-4064	247	6	set	set	VERB
ejpam-4064	247	7	a	a	DET
ejpam-4064	247	8	=	=	SYM
ejpam-4064	247	9	−1	−1	NOUN
ejpam-4064	247	10	,	,	PUNCT
ejpam-4064	247	11	α	α	X
ejpam-4064	247	12	=	=	PUNCT
ejpam-4064	247	13	2π	2π	NOUN
ejpam-4064	247	14	,	,	PUNCT
ejpam-4064	247	15	m	m	VERB
ejpam-4064	247	16	=	=	X
ejpam-4064	247	17	−1/2	−1/2	ADJ
ejpam-4064	247	18	and	and	CCONJ
ejpam-4064	247	19	apply	apply	VERB
ejpam-4064	247	20	l’hopital	l’hopital	PROPN
ejpam-4064	247	21	’s	’s	PART
ejpam-4064	247	22	rule	rule	NOUN
ejpam-4064	247	23	as	as	ADP
ejpam-4064	247	24	k	k	PROPN
ejpam-4064	247	25	→	→	SYM
ejpam-4064	247	26	−2	−2	NOUN
ejpam-4064	247	27	and	and	CCONJ
ejpam-4064	247	28	simplify	simplify	NOUN
ejpam-4064	247	29	.	.	PUNCT
ejpam-4064	248	1	lemma	lemma	PROPN
ejpam-4064	248	2	13	13	NUM
ejpam-4064	248	3	.	.	PUNCT
ejpam-4064	249	1	(	(	PUNCT
ejpam-4064	249	2	31	31	NUM
ejpam-4064	249	3	)	)	PUNCT
ejpam-4064	249	4	∫	∫	PROPN
ejpam-4064	250	1	∞	∞	NUM
ejpam-4064	250	2	0	0	PUNCT
ejpam-4064	251	1	ie−	ie−	PUNCT
ejpam-4064	251	2	ix	ix	ADP
ejpam-4064	251	3	2	2	NUM
ejpam-4064	251	4	(	(	PUNCT
ejpam-4064	251	5	1	1	NUM
ejpam-4064	251	6	(	(	PUNCT
ejpam-4064	251	7	x+	x+	X
ejpam-4064	251	8	π)3	π)3	PROPN
ejpam-4064	251	9	+	+	CCONJ
ejpam-4064	251	10	eix	eix	PROPN
ejpam-4064	251	11	(	(	PUNCT
ejpam-4064	251	12	π	π	PROPN
ejpam-4064	251	13	−	−	PROPN
ejpam-4064	251	14	x)3	x)3	PROPN
ejpam-4064	251	15	)	)	PUNCT
ejpam-4064	252	1	log(tanh(3πx))dx	log(tanh(3πx))dx	ADJ
ejpam-4064	252	2	=	=	NOUN
ejpam-4064	252	3	1	1	NUM
ejpam-4064	252	4	2	2	NUM
ejpam-4064	252	5	iπ	iπ	NOUN
ejpam-4064	252	6	∞∑	∞∑	NUM
ejpam-4064	252	7	y=0	y=0	NOUN
ejpam-4064	252	8	(	(	PUNCT
ejpam-4064	252	9	−1)yγ	−1)yγ	PROPN
ejpam-4064	252	10	(	(	PUNCT
ejpam-4064	252	11	−2	−2	PROPN
ejpam-4064	252	12	,	,	PUNCT
ejpam-4064	252	13	1	1	NUM
ejpam-4064	252	14	12	12	NUM
ejpam-4064	252	15	(	(	PUNCT
ejpam-4064	252	16	y	y	PROPN
ejpam-4064	252	17	+	+	CCONJ
ejpam-4064	252	18	6iπ	6iπ	ADJ
ejpam-4064	252	19	+	+	CCONJ
ejpam-4064	252	20	1	1	NUM
ejpam-4064	252	21	)	)	PUNCT
ejpam-4064	252	22	)	)	PUNCT
ejpam-4064	253	1	+	+	CCONJ
ejpam-4064	253	2	ie3	ie3	NOUN
ejpam-4064	253	3	(	(	PUNCT
ejpam-4064	253	4	iπ	iπ	NOUN
ejpam-4064	253	5	2	2	X
ejpam-4064	253	6	)	)	PUNCT
ejpam-4064	253	7	π	π	NOUN
ejpam-4064	253	8	proof	proof	NOUN
ejpam-4064	253	9	.	.	PUNCT
ejpam-4064	254	1	use	use	VERB
ejpam-4064	254	2	equation	equation	NOUN
ejpam-4064	254	3	(	(	PUNCT
ejpam-4064	254	4	14	14	NUM
ejpam-4064	254	5	)	)	PUNCT
ejpam-4064	254	6	set	set	VERB
ejpam-4064	254	7	a	a	DET
ejpam-4064	254	8	=	=	SYM
ejpam-4064	254	9	−1	−1	NOUN
ejpam-4064	254	10	,	,	PUNCT
ejpam-4064	254	11	α	α	X
ejpam-4064	254	12	=	=	PUNCT
ejpam-4064	254	13	2π	2π	NOUN
ejpam-4064	254	14	,	,	PUNCT
ejpam-4064	254	15	m	m	VERB
ejpam-4064	254	16	=	=	X
ejpam-4064	254	17	−1/2	−1/2	ADJ
ejpam-4064	254	18	and	and	CCONJ
ejpam-4064	254	19	apply	apply	VERB
ejpam-4064	254	20	l’hopital	l’hopital	PROPN
ejpam-4064	254	21	’s	’s	PART
ejpam-4064	254	22	rule	rule	NOUN
ejpam-4064	254	23	as	as	ADP
ejpam-4064	254	24	k	k	PROPN
ejpam-4064	254	25	→	→	X
ejpam-4064	254	26	−3	−3	PROPN
ejpam-4064	254	27	and	and	CCONJ
ejpam-4064	254	28	simplify	simplify	VERB
ejpam-4064	254	29	.	.	PUNCT
ejpam-4064	255	1	7	7	X
ejpam-4064	255	2	.	.	X
ejpam-4064	255	3	discussion	discussion	NOUN
ejpam-4064	255	4	in	in	ADP
ejpam-4064	255	5	this	this	DET
ejpam-4064	255	6	work	work	NOUN
ejpam-4064	255	7	the	the	DET
ejpam-4064	255	8	authors	author	NOUN
ejpam-4064	255	9	derived	derive	VERB
ejpam-4064	255	10	new	new	ADJ
ejpam-4064	255	11	definite	definite	ADJ
ejpam-4064	255	12	integral	integral	ADJ
ejpam-4064	255	13	formulae	formulae	NOUN
ejpam-4064	255	14	involving	involve	VERB
ejpam-4064	255	15	exponential	exponential	ADJ
ejpam-4064	255	16	and	and	CCONJ
ejpam-4064	255	17	hyperbolic	hyperbolic	ADJ
ejpam-4064	255	18	functions	function	NOUN
ejpam-4064	255	19	and	and	CCONJ
ejpam-4064	255	20	expressed	express	VERB
ejpam-4064	255	21	this	this	DET
ejpam-4064	255	22	integral	integral	ADJ
ejpam-4064	255	23	in	in	ADP
ejpam-4064	255	24	terms	term	NOUN
ejpam-4064	255	25	of	of	ADP
ejpam-4064	255	26	the	the	DET
ejpam-4064	255	27	incomplete	incomplete	ADJ
ejpam-4064	255	28	gamma	gamma	NOUN
ejpam-4064	255	29	function	function	NOUN
ejpam-4064	255	30	.	.	PUNCT
ejpam-4064	256	1	the	the	DET
ejpam-4064	256	2	authors	author	NOUN
ejpam-4064	256	3	also	also	ADV
ejpam-4064	256	4	derived	derive	VERB
ejpam-4064	256	5	the	the	DET
ejpam-4064	256	6	correct	correct	ADJ
ejpam-4064	256	7	version	version	NOUN
ejpam-4064	256	8	for	for	ADP
ejpam-4064	256	9	an	an	DET
ejpam-4064	256	10	integral	integral	ADJ
ejpam-4064	256	11	in	in	ADP
ejpam-4064	256	12	the	the	DET
ejpam-4064	256	13	[	[	X
ejpam-4064	256	14	5	5	NUM
ejpam-4064	256	15	]	]	PUNCT
ejpam-4064	256	16	.	.	PUNCT
ejpam-4064	257	1	using	use	VERB
ejpam-4064	257	2	this	this	DET
ejpam-4064	257	3	derived	derive	VERB
ejpam-4064	257	4	integral	integral	ADJ
ejpam-4064	257	5	formula	formula	NOUN
ejpam-4064	257	6	we	we	PRON
ejpam-4064	257	7	derived	derive	VERB
ejpam-4064	257	8	special	special	ADJ
ejpam-4064	257	9	cases	case	NOUN
ejpam-4064	257	10	in	in	ADP
ejpam-4064	257	11	terms	term	NOUN
ejpam-4064	257	12	of	of	ADP
ejpam-4064	257	13	fundamental	fundamental	ADJ
ejpam-4064	257	14	constants	constant	NOUN
ejpam-4064	257	15	and	and	CCONJ
ejpam-4064	257	16	special	special	ADJ
ejpam-4064	257	17	functions	function	NOUN
ejpam-4064	257	18	.	.	PUNCT
ejpam-4064	258	1	the	the	DET
ejpam-4064	258	2	authors	author	NOUN
ejpam-4064	258	3	used	use	VERB
ejpam-4064	258	4	their	their	PRON
ejpam-4064	258	5	contour	contour	NOUN
ejpam-4064	258	6	integral	integral	ADJ
ejpam-4064	258	7	method	method	NOUN
ejpam-4064	258	8	to	to	PART
ejpam-4064	258	9	derive	derive	VERB
ejpam-4064	258	10	the	the	DET
ejpam-4064	258	11	integral	integral	ADJ
ejpam-4064	258	12	formula	formula	NOUN
ejpam-4064	258	13	expressed	express	VERB
ejpam-4064	258	14	in	in	ADP
ejpam-4064	258	15	terms	term	NOUN
ejpam-4064	258	16	of	of	ADP
ejpam-4064	258	17	the	the	DET
ejpam-4064	258	18	incomplete	incomplete	ADJ
ejpam-4064	258	19	gamma	gamma	NOUN
ejpam-4064	258	20	function	function	NOUN
ejpam-4064	258	21	.	.	PUNCT
ejpam-4064	259	1	the	the	DET
ejpam-4064	259	2	results	result	NOUN
ejpam-4064	259	3	presented	present	VERB
ejpam-4064	259	4	were	be	AUX
ejpam-4064	259	5	numerically	numerically	ADV
ejpam-4064	259	6	verified	verify	VERB
ejpam-4064	259	7	for	for	ADP
ejpam-4064	259	8	both	both	CCONJ
ejpam-4064	259	9	real	real	ADJ
ejpam-4064	259	10	and	and	CCONJ
ejpam-4064	259	11	imaginary	imaginary	ADJ
ejpam-4064	259	12	and	and	CCONJ
ejpam-4064	259	13	complex	complex	ADJ
ejpam-4064	259	14	values	value	NOUN
ejpam-4064	259	15	of	of	ADP
ejpam-4064	259	16	the	the	DET
ejpam-4064	259	17	parameters	parameter	NOUN
ejpam-4064	259	18	in	in	ADP
ejpam-4064	259	19	the	the	DET
ejpam-4064	259	20	integrals	integral	NOUN
ejpam-4064	259	21	using	use	VERB
ejpam-4064	259	22	mathematica	mathematica	PROPN
ejpam-4064	259	23	by	by	ADP
ejpam-4064	259	24	wolfram	wolfram	PROPN
ejpam-4064	259	25	.	.	PUNCT
ejpam-4064	260	1	references	reference	NOUN
ejpam-4064	260	2	[	[	X
ejpam-4064	260	3	1	1	NUM
ejpam-4064	260	4	]	]	PUNCT
ejpam-4064	260	5	nist	nist	NOUN
ejpam-4064	260	6	digital	digital	PROPN
ejpam-4064	260	7	library	library	NOUN
ejpam-4064	260	8	of	of	ADP
ejpam-4064	260	9	mathematical	mathematical	ADJ
ejpam-4064	260	10	functions	function	NOUN
ejpam-4064	260	11	.	.	PUNCT
ejpam-4064	260	12	”	"	PUNCT
ejpam-4064	261	1	f.	f.	PROPN
ejpam-4064	261	2	w.	w.	PROPN
ejpam-4064	261	3	j.	j.	PROPN
ejpam-4064	261	4	olver	olver	PROPN
ejpam-4064	261	5	,	,	PUNCT
ejpam-4064	261	6	a.	a.	PROPN
ejpam-4064	261	7	b.	b.	PROPN
ejpam-4064	261	8	olde	olde	PROPN
ejpam-4064	261	9	daalhuis	daalhuis	PROPN
ejpam-4064	261	10	,	,	PUNCT
ejpam-4064	261	11	d.	d.	PROPN
ejpam-4064	261	12	w.	w.	PROPN
ejpam-4064	261	13	lozier	lozier	PROPN
ejpam-4064	261	14	,	,	PUNCT
ejpam-4064	261	15	b.	b.	PROPN
ejpam-4064	261	16	i.	i.	PROPN
ejpam-4064	261	17	schneider	schneider	PROPN
ejpam-4064	261	18	,	,	PUNCT
ejpam-4064	261	19	r.	r.	PROPN
ejpam-4064	261	20	f.	f.	PROPN
ejpam-4064	261	21	boisvert	boisvert	PROPN
ejpam-4064	261	22	,	,	PUNCT
ejpam-4064	261	23	c.	c.	PROPN
ejpam-4064	261	24	w.	w.	PROPN
ejpam-4064	261	25	clark	clark	PROPN
ejpam-4064	261	26	,	,	PUNCT
ejpam-4064	261	27	b.	b.	PROPN
ejpam-4064	261	28	r.	r.	PROPN
ejpam-4064	261	29	miller	miller	PROPN
ejpam-4064	261	30	,	,	PUNCT
ejpam-4064	261	31	b.	b.	PROPN
ejpam-4064	262	1	v.	v.	PROPN
ejpam-4064	262	2	saunders	saunders	PROPN
ejpam-4064	262	3	,	,	PUNCT
ejpam-4064	262	4	h.	h.	PROPN
ejpam-4064	262	5	s.	s.	PROPN
ejpam-4064	262	6	cohl	cohl	PROPN
ejpam-4064	262	7	,	,	PUNCT
ejpam-4064	262	8	and	and	CCONJ
ejpam-4064	262	9	m.	m.	PROPN
ejpam-4064	262	10	a.	a.	PROPN
ejpam-4064	262	11	mcclain	mcclain	PROPN
ejpam-4064	262	12	,	,	PUNCT
ejpam-4064	262	13	eds	ed	NOUN
ejpam-4064	262	14	”	"	PUNCT
ejpam-4064	262	15	.	.	PUNCT
ejpam-4064	263	1	[	[	X
ejpam-4064	263	2	2	2	X
ejpam-4064	263	3	]	]	PUNCT
ejpam-4064	263	4	yunkai	yunkai	PROPN
ejpam-4064	263	5	chen	chen	PROPN
ejpam-4064	263	6	and	and	CCONJ
ejpam-4064	263	7	shih	shih	PROPN
ejpam-4064	263	8	-	-	PUNCT
ejpam-4064	263	9	liang	liang	PROPN
ejpam-4064	263	10	wen	wen	PROPN
ejpam-4064	263	11	.	.	PUNCT
ejpam-4064	264	1	traveling	travel	VERB
ejpam-4064	264	2	wave	wave	NOUN
ejpam-4064	264	3	solutions	solution	NOUN
ejpam-4064	264	4	to	to	ADP
ejpam-4064	264	5	the	the	DET
ejpam-4064	264	6	two	two	NUM
ejpam-4064	264	7	-	-	PUNCT
ejpam-4064	264	8	dimensional	dimensional	ADJ
ejpam-4064	264	9	korteweg	korteweg	NOUN
ejpam-4064	264	10	-	-	PUNCT
ejpam-4064	264	11	devries	devries	PROPN
ejpam-4064	264	12	equation	equation	NOUN
ejpam-4064	264	13	.	.	PUNCT
ejpam-4064	265	1	journal	journal	PROPN
ejpam-4064	265	2	of	of	ADP
ejpam-4064	265	3	mathematical	mathematical	ADJ
ejpam-4064	265	4	analysis	analysis	NOUN
ejpam-4064	265	5	and	and	CCONJ
ejpam-4064	265	6	applications	application	NOUN
ejpam-4064	265	7	,	,	PUNCT
ejpam-4064	265	8	127:226–236	127:226–236	NUM
ejpam-4064	265	9	,	,	PUNCT
ejpam-4064	265	10	10	10	NUM
ejpam-4064	265	11	1987	1987	NUM
ejpam-4064	265	12	.	.	PUNCT
ejpam-4064	266	1	[	[	X
ejpam-4064	266	2	3	3	NUM
ejpam-4064	266	3	]	]	SYM
ejpam-4064	266	4	narayan	narayan	PROPN
ejpam-4064	266	5	c.	c.	PROPN
ejpam-4064	266	6	giri	giri	PROPN
ejpam-4064	266	7	.	.	PUNCT
ejpam-4064	267	1	multivariate	multivariate	VERB
ejpam-4064	267	2	statistical	statistical	ADJ
ejpam-4064	267	3	inference	inference	NOUN
ejpam-4064	267	4	.	.	PUNCT
ejpam-4064	268	1	academic	academic	ADJ
ejpam-4064	268	2	press	press	NOUN
ejpam-4064	268	3	,	,	PUNCT
ejpam-4064	268	4	1977	1977	NUM
ejpam-4064	268	5	.	.	PUNCT
ejpam-4064	269	1	[	[	X
ejpam-4064	269	2	4	4	X
ejpam-4064	269	3	]	]	X
ejpam-4064	269	4	i.	i.	PROPN
ejpam-4064	269	5	s.	s.	PROPN
ejpam-4064	269	6	gradshteyn	gradshteyn	PROPN
ejpam-4064	269	7	and	and	CCONJ
ejpam-4064	269	8	i.	i.	PROPN
ejpam-4064	269	9	m.	m.	PROPN
ejpam-4064	269	10	ryzhik	ryzhik	PROPN
ejpam-4064	269	11	.	.	PUNCT
ejpam-4064	270	1	table	table	NOUN
ejpam-4064	270	2	of	of	ADP
ejpam-4064	270	3	integrals	integral	NOUN
ejpam-4064	270	4	,	,	PUNCT
ejpam-4064	270	5	series	series	NOUN
ejpam-4064	270	6	,	,	PUNCT
ejpam-4064	270	7	and	and	CCONJ
ejpam-4064	270	8	products	product	NOUN
ejpam-4064	270	9	.	.	PUNCT
ejpam-4064	271	1	academic	academic	ADJ
ejpam-4064	271	2	press	press	NOUN
ejpam-4064	271	3	,	,	PUNCT
ejpam-4064	271	4	05	05	NUM
ejpam-4064	271	5	2014	2014	NUM
ejpam-4064	271	6	.	.	PUNCT
ejpam-4064	272	1	[	[	X
ejpam-4064	272	2	5	5	NUM
ejpam-4064	272	3	]	]	X
ejpam-4064	272	4	fritz	fritz	PROPN
ejpam-4064	272	5	oberhettinger	oberhettinger	PROPN
ejpam-4064	272	6	.	.	PUNCT
ejpam-4064	273	1	tables	table	NOUN
ejpam-4064	273	2	of	of	ADP
ejpam-4064	273	3	fourier	fourier	NOUN
ejpam-4064	273	4	transforms	transform	VERB
ejpam-4064	273	5	and	and	CCONJ
ejpam-4064	273	6	fourier	fourier	NOUN
ejpam-4064	273	7	transforms	transform	NOUN
ejpam-4064	273	8	of	of	ADP
ejpam-4064	273	9	distributions	distribution	NOUN
ejpam-4064	273	10	.	.	PUNCT
ejpam-4064	274	1	springer	springer	PROPN
ejpam-4064	274	2	berlin	berlin	PROPN
ejpam-4064	274	3	heidelberg	heidelberg	PROPN
ejpam-4064	274	4	,	,	PUNCT
ejpam-4064	274	5	04	04	NUM
ejpam-4064	274	6	1990	1990	NUM
ejpam-4064	274	7	.	.	PUNCT
ejpam-4064	275	1	[	[	X
ejpam-4064	275	2	6	6	NUM
ejpam-4064	275	3	]	]	PUNCT
ejpam-4064	275	4	keith	keith	PROPN
ejpam-4064	275	5	b.	b.	PROPN
ejpam-4064	275	6	oldham	oldham	PROPN
ejpam-4064	275	7	,	,	PUNCT
ejpam-4064	275	8	jan	jan	PROPN
ejpam-4064	275	9	myland	myland	PROPN
ejpam-4064	275	10	,	,	PUNCT
ejpam-4064	275	11	and	and	CCONJ
ejpam-4064	275	12	jerome	jerome	PROPN
ejpam-4064	275	13	spanier	spanier	NOUN
ejpam-4064	275	14	.	.	PUNCT
ejpam-4064	276	1	an	an	DET
ejpam-4064	276	2	atlas	atlas	PROPN
ejpam-4064	276	3	of	of	ADP
ejpam-4064	276	4	functions	function	NOUN
ejpam-4064	276	5	:	:	PUNCT
ejpam-4064	276	6	with	with	ADP
ejpam-4064	276	7	equator	equator	NOUN
ejpam-4064	276	8	,	,	PUNCT
ejpam-4064	276	9	the	the	DET
ejpam-4064	276	10	atlas	atlas	PROPN
ejpam-4064	276	11	function	function	PROPN
ejpam-4064	276	12	calculator	calculator	NOUN
ejpam-4064	276	13	.	.	PUNCT
ejpam-4064	277	1	springer	springer	NOUN
ejpam-4064	277	2	science	science	PROPN
ejpam-4064	277	3	&	&	CCONJ
ejpam-4064	277	4	business	business	NOUN
ejpam-4064	277	5	media	medium	NOUN
ejpam-4064	277	6	,	,	PUNCT
ejpam-4064	277	7	07	07	NUM
ejpam-4064	277	8	2010	2010	NUM
ejpam-4064	277	9	.	.	PUNCT
ejpam-4064	278	1	references	reference	NOUN
ejpam-4064	278	2	1305	1305	NUM
ejpam-4064	279	1	[	[	X
ejpam-4064	279	2	7	7	X
ejpam-4064	279	3	]	]	X
ejpam-4064	279	4	norbert	norbert	PROPN
ejpam-4064	279	5	ortner	ortner	PROPN
ejpam-4064	279	6	and	and	CCONJ
ejpam-4064	279	7	peter	peter	PROPN
ejpam-4064	279	8	wagner	wagner	PROPN
ejpam-4064	279	9	.	.	PUNCT
ejpam-4064	280	1	fundamental	fundamental	ADJ
ejpam-4064	280	2	solution	solution	NOUN
ejpam-4064	280	3	of	of	ADP
ejpam-4064	280	4	hyperbolic	hyperbolic	ADJ
ejpam-4064	280	5	differential	differential	NOUN
ejpam-4064	280	6	operators	operator	NOUN
ejpam-4064	280	7	and	and	CCONJ
ejpam-4064	280	8	the	the	DET
ejpam-4064	280	9	poisson	poisson	NOUN
ejpam-4064	280	10	summation	summation	NOUN
ejpam-4064	280	11	formula	formula	NOUN
ejpam-4064	280	12	.	.	PUNCT
ejpam-4064	281	1	integral	integral	ADJ
ejpam-4064	281	2	transforms	transform	NOUN
ejpam-4064	281	3	and	and	CCONJ
ejpam-4064	281	4	special	special	ADJ
ejpam-4064	281	5	functions	function	NOUN
ejpam-4064	281	6	,	,	PUNCT
ejpam-4064	281	7	1:183–196	1:183–196	NUM
ejpam-4064	281	8	,	,	PUNCT
ejpam-4064	281	9	12	12	NUM
ejpam-4064	281	10	1993	1993	NUM
ejpam-4064	281	11	.	.	PUNCT
ejpam-4064	282	1	[	[	X
ejpam-4064	282	2	8	8	NUM
ejpam-4064	282	3	]	]	X
ejpam-4064	282	4	n.	n.	PROPN
ejpam-4064	282	5	r.	r.	PROPN
ejpam-4064	282	6	pereira	pereira	PROPN
ejpam-4064	282	7	.	.	PUNCT
ejpam-4064	283	1	fourier	fourier	PROPN
ejpam-4064	283	2	series	series	PROPN
ejpam-4064	283	3	for	for	ADP
ejpam-4064	283	4	a	a	DET
ejpam-4064	283	5	combination	combination	NOUN
ejpam-4064	283	6	of	of	ADP
ejpam-4064	283	7	jacobian	jacobian	ADJ
ejpam-4064	283	8	elliptic	elliptic	ADJ
ejpam-4064	283	9	functions	function	NOUN
ejpam-4064	283	10	:	:	PUNCT
ejpam-4064	283	11	problem	problem	NOUN
ejpam-4064	283	12	79	79	NUM
ejpam-4064	283	13	-	-	SYM
ejpam-4064	283	14	9	9	NUM
ejpam-4064	283	15	.	.	PUNCT
ejpam-4064	284	1	siam	siam	PROPN
ejpam-4064	284	2	review	review	PROPN
ejpam-4064	284	3	,	,	PUNCT
ejpam-4064	284	4	22:232–234	22:232–234	NUM
ejpam-4064	284	5	,	,	PUNCT
ejpam-4064	284	6	1980	1980	NUM
ejpam-4064	284	7	.	.	PUNCT
ejpam-4064	285	1	[	[	X
ejpam-4064	285	2	9	9	NUM
ejpam-4064	285	3	]	]	X
ejpam-4064	285	4	robert	robert	PROPN
ejpam-4064	285	5	reynolds	reynolds	PROPN
ejpam-4064	285	6	and	and	CCONJ
ejpam-4064	285	7	allan	allan	PROPN
ejpam-4064	285	8	stauffer	stauffer	PROPN
ejpam-4064	285	9	.	.	PUNCT
ejpam-4064	286	1	a	a	DET
ejpam-4064	286	2	method	method	NOUN
ejpam-4064	286	3	for	for	ADP
ejpam-4064	286	4	evaluating	evaluate	VERB
ejpam-4064	286	5	definite	definite	ADJ
ejpam-4064	286	6	integrals	integral	NOUN
ejpam-4064	286	7	in	in	ADP
ejpam-4064	286	8	terms	term	NOUN
ejpam-4064	286	9	of	of	ADP
ejpam-4064	286	10	special	special	ADJ
ejpam-4064	286	11	functions	function	NOUN
ejpam-4064	286	12	with	with	ADP
ejpam-4064	286	13	examples	example	NOUN
ejpam-4064	286	14	.	.	PUNCT
ejpam-4064	287	1	international	international	ADJ
ejpam-4064	287	2	mathematical	mathematical	PROPN
ejpam-4064	287	3	forum	forum	PROPN
ejpam-4064	287	4	,	,	PUNCT
ejpam-4064	287	5	15:235	15:235	NUM
ejpam-4064	287	6	–	–	PUNCT
ejpam-4064	287	7	244	244	NUM
ejpam-4064	287	8	,	,	PUNCT
ejpam-4064	287	9	2020	2020	NUM
ejpam-4064	287	10	.	.	PUNCT