id	sid	tid	token	lemma	pos
ejpam-4022	1	1	european	european	PROPN
ejpam-4022	1	2	journal	journal	PROPN
ejpam-4022	1	3	of	of	ADP
ejpam-4022	1	4	pure	pure	ADJ
ejpam-4022	1	5	and	and	CCONJ
ejpam-4022	1	6	applied	apply	VERB
ejpam-4022	1	7	mathematics	mathematic	NOUN
ejpam-4022	1	8	vol	vol	NOUN
ejpam-4022	1	9	.	.	PUNCT
ejpam-4022	2	1	14	14	NUM
ejpam-4022	2	2	,	,	PUNCT
ejpam-4022	2	3	no	no	INTJ
ejpam-4022	2	4	.	.	NOUN
ejpam-4022	2	5	4	4	NUM
ejpam-4022	2	6	,	,	PUNCT
ejpam-4022	2	7	2021	2021	NUM
ejpam-4022	2	8	,	,	PUNCT
ejpam-4022	2	9	1200	1200	NUM
ejpam-4022	2	10	-	-	SYM
ejpam-4022	2	11	1211	1211	NUM
ejpam-4022	2	12	issn	issn	PROPN
ejpam-4022	2	13	1307	1307	NUM
ejpam-4022	2	14	-	-	SYM
ejpam-4022	2	15	5543	5543	NUM
ejpam-4022	2	16	–	–	PUNCT
ejpam-4022	2	17	ejpam.com	ejpam.com	X
ejpam-4022	2	18	published	publish	VERB
ejpam-4022	2	19	by	by	ADP
ejpam-4022	2	20	new	new	PROPN
ejpam-4022	2	21	york	york	PROPN
ejpam-4022	2	22	business	business	PROPN
ejpam-4022	2	23	global	global	ADJ
ejpam-4022	2	24	double	double	ADJ
ejpam-4022	2	25	integrals	integral	NOUN
ejpam-4022	2	26	of	of	ADP
ejpam-4022	2	27	logarithm	logarithm	NOUN
ejpam-4022	2	28	and	and	CCONJ
ejpam-4022	2	29	exponential	exponential	ADJ
ejpam-4022	2	30	function	function	NOUN
ejpam-4022	2	31	expressed	express	VERB
ejpam-4022	2	32	in	in	ADP
ejpam-4022	2	33	terms	term	NOUN
ejpam-4022	2	34	of	of	ADP
ejpam-4022	2	35	the	the	DET
ejpam-4022	2	36	lerch	lerch	PROPN
ejpam-4022	2	37	function	function	PROPN
ejpam-4022	2	38	robert	robert	PROPN
ejpam-4022	2	39	reynolds1,∗	reynolds1,∗	PROPN
ejpam-4022	2	40	,	,	PUNCT
ejpam-4022	2	41	allan	allan	PROPN
ejpam-4022	2	42	stauffer1	stauffer1	PROPN
ejpam-4022	2	43	1	1	NUM
ejpam-4022	2	44	department	department	NOUN
ejpam-4022	2	45	of	of	ADP
ejpam-4022	2	46	mathematics	mathematic	NOUN
ejpam-4022	2	47	and	and	CCONJ
ejpam-4022	2	48	statistics	statistic	NOUN
ejpam-4022	2	49	,	,	PUNCT
ejpam-4022	2	50	faculty	faculty	NOUN
ejpam-4022	2	51	of	of	ADP
ejpam-4022	2	52	science	science	PROPN
ejpam-4022	2	53	,	,	PUNCT
ejpam-4022	2	54	york	york	PROPN
ejpam-4022	2	55	university	university	PROPN
ejpam-4022	2	56	,	,	PUNCT
ejpam-4022	2	57	toronto	toronto	PROPN
ejpam-4022	2	58	,	,	PUNCT
ejpam-4022	2	59	ontario	ontario	PROPN
ejpam-4022	2	60	,	,	PUNCT
ejpam-4022	2	61	canada	canada	PROPN
ejpam-4022	2	62	,	,	PUNCT
ejpam-4022	2	63	m3j1p3	m3j1p3	PROPN
ejpam-4022	2	64	abstract	abstract	NOUN
ejpam-4022	2	65	.	.	PUNCT
ejpam-4022	3	1	this	this	DET
ejpam-4022	3	2	paper	paper	NOUN
ejpam-4022	3	3	contains	contain	VERB
ejpam-4022	3	4	new	new	ADJ
ejpam-4022	3	5	explicit	explicit	ADJ
ejpam-4022	3	6	computations	computation	NOUN
ejpam-4022	3	7	of	of	ADP
ejpam-4022	3	8	some	some	DET
ejpam-4022	3	9	integrals	integral	NOUN
ejpam-4022	3	10	containing	contain	VERB
ejpam-4022	3	11	elementary	elementary	ADJ
ejpam-4022	3	12	functions	function	NOUN
ejpam-4022	3	13	,	,	PUNCT
ejpam-4022	3	14	such	such	ADJ
ejpam-4022	3	15	as	as	ADP
ejpam-4022	3	16	powers	power	NOUN
ejpam-4022	3	17	,	,	PUNCT
ejpam-4022	3	18	logarithms	logarithm	NOUN
ejpam-4022	3	19	and	and	CCONJ
ejpam-4022	3	20	exponentials	exponential	NOUN
ejpam-4022	3	21	.	.	PUNCT
ejpam-4022	4	1	in	in	ADP
ejpam-4022	4	2	this	this	DET
ejpam-4022	4	3	work	work	NOUN
ejpam-4022	4	4	the	the	DET
ejpam-4022	4	5	authors	author	NOUN
ejpam-4022	4	6	use	use	VERB
ejpam-4022	4	7	their	their	PRON
ejpam-4022	4	8	contour	contour	NOUN
ejpam-4022	4	9	integral	integral	ADJ
ejpam-4022	4	10	method	method	NOUN
ejpam-4022	4	11	to	to	PART
ejpam-4022	4	12	derive	derive	VERB
ejpam-4022	4	13	a	a	DET
ejpam-4022	4	14	double	double	ADJ
ejpam-4022	4	15	integral	integral	ADJ
ejpam-4022	4	16	connected	connect	VERB
ejpam-4022	4	17	to	to	ADP
ejpam-4022	4	18	the	the	DET
ejpam-4022	4	19	modified	modify	VERB
ejpam-4022	4	20	bessel	bessel	NOUN
ejpam-4022	4	21	function	function	NOUN
ejpam-4022	4	22	of	of	ADP
ejpam-4022	4	23	the	the	DET
ejpam-4022	4	24	second	second	ADJ
ejpam-4022	4	25	kind	kind	NOUN
ejpam-4022	4	26	kν(z	kν(z	NOUN
ejpam-4022	4	27	)	)	PUNCT
ejpam-4022	4	28	and	and	CCONJ
ejpam-4022	4	29	express	express	VERB
ejpam-4022	4	30	it	it	PRON
ejpam-4022	4	31	in	in	ADP
ejpam-4022	4	32	terms	term	NOUN
ejpam-4022	4	33	of	of	ADP
ejpam-4022	4	34	the	the	DET
ejpam-4022	4	35	lerch	lerch	PROPN
ejpam-4022	4	36	function	function	PROPN
ejpam-4022	4	37	.	.	PUNCT
ejpam-4022	5	1	a	a	DET
ejpam-4022	5	2	table	table	NOUN
ejpam-4022	5	3	of	of	ADP
ejpam-4022	5	4	integral	integral	ADJ
ejpam-4022	5	5	pairs	pair	NOUN
ejpam-4022	5	6	is	be	AUX
ejpam-4022	5	7	given	give	VERB
ejpam-4022	5	8	for	for	ADP
ejpam-4022	5	9	interested	interested	ADJ
ejpam-4022	5	10	readers	reader	NOUN
ejpam-4022	5	11	.	.	PUNCT
ejpam-4022	6	1	the	the	DET
ejpam-4022	6	2	majority	majority	NOUN
ejpam-4022	6	3	of	of	ADP
ejpam-4022	6	4	the	the	DET
ejpam-4022	6	5	results	result	NOUN
ejpam-4022	6	6	in	in	ADP
ejpam-4022	6	7	this	this	DET
ejpam-4022	6	8	work	work	NOUN
ejpam-4022	6	9	are	be	AUX
ejpam-4022	6	10	new	new	ADJ
ejpam-4022	6	11	.	.	PUNCT
ejpam-4022	7	1	2020	2020	NUM
ejpam-4022	7	2	mathematics	mathematic	NOUN
ejpam-4022	7	3	subject	subject	NOUN
ejpam-4022	7	4	classifications	classification	NOUN
ejpam-4022	7	5	:	:	PUNCT
ejpam-4022	7	6	30e20,33	30e20,33	NUM
ejpam-4022	7	7	-	-	SYM
ejpam-4022	7	8	01	01	NUM
ejpam-4022	7	9	,	,	PUNCT
ejpam-4022	7	10	33	33	NUM
ejpam-4022	7	11	-	-	SYM
ejpam-4022	7	12	03	03	NUM
ejpam-4022	7	13	,	,	PUNCT
ejpam-4022	7	14	33	33	NUM
ejpam-4022	7	15	-	-	PUNCT
ejpam-4022	7	16	04	04	NUM
ejpam-4022	7	17	,	,	PUNCT
ejpam-4022	7	18	33	33	NUM
ejpam-4022	7	19	-	-	PUNCT
ejpam-4022	7	20	33b	33b	NUM
ejpam-4022	7	21	,	,	PUNCT
ejpam-4022	7	22	33e20	33e20	NUM
ejpam-4022	7	23	,	,	PUNCT
ejpam-4022	7	24	33e33c	33e33c	NUM
ejpam-4022	7	25	key	key	ADJ
ejpam-4022	7	26	words	word	NOUN
ejpam-4022	7	27	and	and	CCONJ
ejpam-4022	7	28	phrases	phrase	NOUN
ejpam-4022	7	29	:	:	PUNCT
ejpam-4022	7	30	double	double	ADJ
ejpam-4022	7	31	integral	integral	ADJ
ejpam-4022	7	32	,	,	PUNCT
ejpam-4022	7	33	lerch	lerch	PROPN
ejpam-4022	7	34	function	function	PROPN
ejpam-4022	7	35	,	,	PUNCT
ejpam-4022	7	36	contour	contour	NOUN
ejpam-4022	7	37	integral	integral	ADJ
ejpam-4022	7	38	,	,	PUNCT
ejpam-4022	7	39	glaisher	glaisher	PROPN
ejpam-4022	7	40	’s	’s	PART
ejpam-4022	7	41	constant	constant	ADJ
ejpam-4022	7	42	,	,	PUNCT
ejpam-4022	7	43	modified	modified	ADJ
ejpam-4022	7	44	bessel	bessel	NOUN
ejpam-4022	7	45	function	function	NOUN
ejpam-4022	7	46	of	of	ADP
ejpam-4022	7	47	the	the	DET
ejpam-4022	7	48	second	second	ADJ
ejpam-4022	7	49	kind	kind	NOUN
ejpam-4022	7	50	1	1	NUM
ejpam-4022	7	51	.	.	NOUN
ejpam-4022	7	52	significance	significance	NOUN
ejpam-4022	7	53	statement	statement	NOUN
ejpam-4022	7	54	double	double	ADJ
ejpam-4022	7	55	integrals	integral	NOUN
ejpam-4022	7	56	play	play	VERB
ejpam-4022	7	57	a	a	DET
ejpam-4022	7	58	significant	significant	ADJ
ejpam-4022	7	59	role	role	NOUN
ejpam-4022	7	60	in	in	ADP
ejpam-4022	7	61	the	the	DET
ejpam-4022	7	62	area	area	NOUN
ejpam-4022	7	63	of	of	ADP
ejpam-4022	7	64	mathematics	mathematic	NOUN
ejpam-4022	7	65	,	,	PUNCT
ejpam-4022	7	66	namely	namely	ADV
ejpam-4022	7	67	in	in	ADP
ejpam-4022	7	68	the	the	DET
ejpam-4022	7	69	evaluation	evaluation	NOUN
ejpam-4022	7	70	of	of	ADP
ejpam-4022	7	71	moment	moment	NOUN
ejpam-4022	7	72	of	of	ADP
ejpam-4022	7	73	inertia	inertia	NOUN
ejpam-4022	7	74	,	,	PUNCT
ejpam-4022	7	75	centre	centre	NOUN
ejpam-4022	7	76	of	of	ADP
ejpam-4022	7	77	mass	mass	NOUN
ejpam-4022	7	78	,	,	PUNCT
ejpam-4022	7	79	volumes	volume	NOUN
ejpam-4022	7	80	of	of	ADP
ejpam-4022	7	81	solids	solid	NOUN
ejpam-4022	7	82	of	of	ADP
ejpam-4022	7	83	revolution	revolution	NOUN
ejpam-4022	7	84	,	,	PUNCT
ejpam-4022	7	85	averages	average	NOUN
ejpam-4022	7	86	and	and	CCONJ
ejpam-4022	7	87	in	in	ADP
ejpam-4022	7	88	error	error	NOUN
ejpam-4022	7	89	analysis	analysis	NOUN
ejpam-4022	7	90	of	of	ADP
ejpam-4022	7	91	integrals	integral	NOUN
ejpam-4022	7	92	,	,	PUNCT
ejpam-4022	7	93	discrete	discrete	ADJ
ejpam-4022	7	94	transforms	transform	VERB
ejpam-4022	7	95	[	[	X
ejpam-4022	7	96	3	3	NUM
ejpam-4022	7	97	]	]	PUNCT
ejpam-4022	7	98	and	and	CCONJ
ejpam-4022	7	99	the	the	DET
ejpam-4022	7	100	evaluation	evaluation	NOUN
ejpam-4022	7	101	of	of	ADP
ejpam-4022	7	102	special	special	ADJ
ejpam-4022	7	103	functions	function	NOUN
ejpam-4022	7	104	.	.	PUNCT
ejpam-4022	8	1	regarding	regard	VERB
ejpam-4022	8	2	the	the	DET
ejpam-4022	8	3	evaluation	evaluation	NOUN
ejpam-4022	8	4	of	of	ADP
ejpam-4022	8	5	the	the	DET
ejpam-4022	8	6	double	double	ADJ
ejpam-4022	8	7	integral	integral	NOUN
ejpam-4022	8	8	of	of	ADP
ejpam-4022	8	9	special	special	ADJ
ejpam-4022	8	10	functions	function	NOUN
ejpam-4022	8	11	,	,	PUNCT
ejpam-4022	8	12	research	research	NOUN
ejpam-4022	8	13	has	have	AUX
ejpam-4022	8	14	been	be	AUX
ejpam-4022	8	15	done	do	VERB
ejpam-4022	8	16	in	in	ADP
ejpam-4022	8	17	the	the	DET
ejpam-4022	8	18	evaluation	evaluation	NOUN
ejpam-4022	8	19	of	of	ADP
ejpam-4022	8	20	double	double	ADJ
ejpam-4022	8	21	integrals	integral	NOUN
ejpam-4022	8	22	involving	involve	VERB
ejpam-4022	8	23	the	the	DET
ejpam-4022	8	24	bessel	bessel	ADJ
ejpam-4022	8	25	function	function	NOUN
ejpam-4022	8	26	[	[	X
ejpam-4022	8	27	9	9	NUM
ejpam-4022	8	28	]	]	PUNCT
ejpam-4022	8	29	and	and	CCONJ
ejpam-4022	8	30	the	the	DET
ejpam-4022	8	31	bessel	bessel	ADJ
ejpam-4022	8	32	function	function	NOUN
ejpam-4022	8	33	of	of	ADP
ejpam-4022	8	34	the	the	DET
ejpam-4022	8	35	second	second	ADJ
ejpam-4022	8	36	kind	kind	NOUN
ejpam-4022	8	37	[	[	X
ejpam-4022	8	38	4	4	NUM
ejpam-4022	8	39	,	,	PUNCT
ejpam-4022	8	40	7	7	NUM
ejpam-4022	8	41	]	]	PUNCT
ejpam-4022	8	42	.	.	PUNCT
ejpam-4022	9	1	one	one	NUM
ejpam-4022	9	2	of	of	ADP
ejpam-4022	9	3	the	the	DET
ejpam-4022	9	4	aims	aim	NOUN
ejpam-4022	9	5	of	of	ADP
ejpam-4022	9	6	this	this	DET
ejpam-4022	9	7	present	present	ADJ
ejpam-4022	9	8	work	work	NOUN
ejpam-4022	9	9	is	be	AUX
ejpam-4022	9	10	to	to	PART
ejpam-4022	9	11	expand	expand	VERB
ejpam-4022	9	12	on	on	ADP
ejpam-4022	9	13	the	the	DET
ejpam-4022	9	14	research	research	NOUN
ejpam-4022	9	15	in	in	ADP
ejpam-4022	9	16	the	the	DET
ejpam-4022	9	17	area	area	NOUN
ejpam-4022	9	18	of	of	ADP
ejpam-4022	9	19	the	the	DET
ejpam-4022	9	20	double	double	ADJ
ejpam-4022	9	21	integral	integral	NOUN
ejpam-4022	9	22	of	of	ADP
ejpam-4022	9	23	special	special	ADJ
ejpam-4022	9	24	functions	function	NOUN
ejpam-4022	9	25	by	by	ADP
ejpam-4022	9	26	deriving	derive	VERB
ejpam-4022	9	27	and	and	CCONJ
ejpam-4022	9	28	evaluating	evaluate	VERB
ejpam-4022	9	29	the	the	DET
ejpam-4022	9	30	laplace	laplace	NOUN
ejpam-4022	9	31	transform	transform	NOUN
ejpam-4022	9	32	of	of	ADP
ejpam-4022	9	33	kernels	kernel	NOUN
ejpam-4022	9	34	involving	involve	VERB
ejpam-4022	9	35	the	the	DET
ejpam-4022	9	36	modified	modify	VERB
ejpam-4022	9	37	bessel	bessel	NOUN
ejpam-4022	9	38	function	function	NOUN
ejpam-4022	9	39	.	.	PUNCT
ejpam-4022	10	1	for	for	ADP
ejpam-4022	10	2	certain	certain	ADJ
ejpam-4022	10	3	values	value	NOUN
ejpam-4022	10	4	of	of	ADP
ejpam-4022	10	5	the	the	DET
ejpam-4022	10	6	parameters	parameter	NOUN
ejpam-4022	10	7	the	the	DET
ejpam-4022	10	8	integrand	integrand	NOUN
ejpam-4022	10	9	of	of	ADP
ejpam-4022	10	10	this	this	DET
ejpam-4022	10	11	derived	derive	VERB
ejpam-4022	10	12	integral	integral	ADJ
ejpam-4022	10	13	formula	formula	NOUN
ejpam-4022	10	14	involved	involve	VERB
ejpam-4022	10	15	the	the	DET
ejpam-4022	10	16	modified	modify	VERB
ejpam-4022	10	17	bessel	bessel	NOUN
ejpam-4022	10	18	function	function	NOUN
ejpam-4022	10	19	of	of	ADP
ejpam-4022	10	20	the	the	DET
ejpam-4022	10	21	second	second	ADJ
ejpam-4022	10	22	kind	kind	NOUN
ejpam-4022	10	23	kn(z	kn(z	NOUN
ejpam-4022	10	24	)	)	PUNCT
ejpam-4022	10	25	.	.	PUNCT
ejpam-4022	11	1	∗corresponding	∗corresponde	VERB
ejpam-4022	11	2	author	author	NOUN
ejpam-4022	11	3	.	.	PUNCT
ejpam-4022	12	1	doi	doi	NOUN
ejpam-4022	12	2	:	:	PUNCT
ejpam-4022	12	3	https://doi.org/10.29020/nybg.ejpam.v14i4.4022	https://doi.org/10.29020/nybg.ejpam.v14i4.4022	PROPN
ejpam-4022	12	4	email	email	NOUN
ejpam-4022	12	5	addresses	address	NOUN
ejpam-4022	12	6	:	:	PUNCT
ejpam-4022	13	1	milver@my.yorku.ca	milver@my.yorku.ca	NOUN
ejpam-4022	13	2	(	(	PUNCT
ejpam-4022	13	3	r.	r.	PROPN
ejpam-4022	13	4	reynolds	reynolds	PROPN
ejpam-4022	13	5	)	)	PUNCT
ejpam-4022	13	6	,	,	PUNCT
ejpam-4022	13	7	stauffer@yorku.ca	stauffer@yorku.ca	NOUN
ejpam-4022	13	8	(	(	PUNCT
ejpam-4022	13	9	a.	a.	NOUN
ejpam-4022	13	10	stauffer	stauffer	PROPN
ejpam-4022	13	11	)	)	PUNCT
ejpam-4022	13	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4022	13	13	1200	1200	NUM
ejpam-4022	14	1	©	©	PROPN
ejpam-4022	14	2	2021	2021	NUM
ejpam-4022	14	3	ejpam	ejpam	VERB
ejpam-4022	14	4	all	all	DET
ejpam-4022	14	5	rights	right	NOUN
ejpam-4022	14	6	reserved	reserve	VERB
ejpam-4022	14	7	.	.	PUNCT
ejpam-4022	15	1	r.	r.	PROPN
ejpam-4022	15	2	reynolds	reynolds	PROPN
ejpam-4022	15	3	,	,	PUNCT
ejpam-4022	15	4	a.	a.	PROPN
ejpam-4022	15	5	stauffer	stauffer	PROPN
ejpam-4022	15	6	/	/	SYM
ejpam-4022	15	7	eur	eur	PROPN
ejpam-4022	15	8	.	.	PUNCT
ejpam-4022	16	1	j.	j.	PROPN
ejpam-4022	16	2	pure	pure	PROPN
ejpam-4022	16	3	appl	appl	PROPN
ejpam-4022	16	4	.	.	PROPN
ejpam-4022	16	5	math	math	PROPN
ejpam-4022	16	6	,	,	PUNCT
ejpam-4022	16	7	14	14	NUM
ejpam-4022	16	8	(	(	PUNCT
ejpam-4022	16	9	4	4	NUM
ejpam-4022	16	10	)	)	PUNCT
ejpam-4022	16	11	(	(	PUNCT
ejpam-4022	16	12	2021	2021	NUM
ejpam-4022	16	13	)	)	PUNCT
ejpam-4022	16	14	,	,	PUNCT
ejpam-4022	16	15	1200	1200	NUM
ejpam-4022	16	16	-	-	SYM
ejpam-4022	16	17	1211	1211	NUM
ejpam-4022	16	18	1201	1201	NUM
ejpam-4022	16	19	2	2	NUM
ejpam-4022	16	20	.	.	PUNCT
ejpam-4022	16	21	introduction	introduction	NOUN
ejpam-4022	16	22	in	in	ADP
ejpam-4022	16	23	1986	1986	NUM
ejpam-4022	16	24	a.p	a.p	PROPN
ejpam-4022	16	25	.	.	PROPN
ejpam-4022	16	26	prudnikov	prudnikov	PROPN
ejpam-4022	16	27	et	et	PROPN
ejpam-4022	16	28	al	al	PROPN
ejpam-4022	16	29	.	.	PUNCT
ejpam-4022	17	1	[	[	X
ejpam-4022	17	2	6	6	NUM
ejpam-4022	17	3	]	]	PUNCT
ejpam-4022	17	4	produced	produce	VERB
ejpam-4022	17	5	volume	volume	NOUN
ejpam-4022	17	6	1	1	NUM
ejpam-4022	17	7	of	of	ADP
ejpam-4022	17	8	their	their	PRON
ejpam-4022	17	9	five	five	NUM
ejpam-4022	17	10	volume	volume	NOUN
ejpam-4022	17	11	collection	collection	NOUN
ejpam-4022	17	12	on	on	ADP
ejpam-4022	17	13	integrals	integral	NOUN
ejpam-4022	17	14	and	and	CCONJ
ejpam-4022	17	15	series	series	NOUN
ejpam-4022	17	16	.	.	PUNCT
ejpam-4022	18	1	in	in	ADP
ejpam-4022	18	2	this	this	DET
ejpam-4022	18	3	work	work	NOUN
ejpam-4022	18	4	,	,	PUNCT
ejpam-4022	18	5	the	the	DET
ejpam-4022	18	6	authors	author	NOUN
ejpam-4022	18	7	used	use	VERB
ejpam-4022	18	8	their	their	PRON
ejpam-4022	18	9	contour	contour	NOUN
ejpam-4022	18	10	integral	integral	ADJ
ejpam-4022	18	11	method	method	NOUN
ejpam-4022	18	12	and	and	CCONJ
ejpam-4022	18	13	applied	apply	VERB
ejpam-4022	18	14	it	it	PRON
ejpam-4022	18	15	to	to	ADP
ejpam-4022	18	16	an	an	DET
ejpam-4022	18	17	interesting	interesting	ADJ
ejpam-4022	18	18	integral	integral	NOUN
ejpam-4022	18	19	in	in	ADP
ejpam-4022	18	20	the	the	DET
ejpam-4022	18	21	book	book	NOUN
ejpam-4022	18	22	of	of	ADP
ejpam-4022	18	23	prudnikov	prudnikov	PROPN
ejpam-4022	18	24	et	et	PROPN
ejpam-4022	18	25	al	al	PROPN
ejpam-4022	18	26	.	.	PUNCT
ejpam-4022	19	1	[	[	X
ejpam-4022	19	2	6	6	NUM
ejpam-4022	19	3	]	]	PUNCT
ejpam-4022	19	4	and	and	CCONJ
ejpam-4022	19	5	expressed	express	VERB
ejpam-4022	19	6	its	its	PRON
ejpam-4022	19	7	closed	closed	ADJ
ejpam-4022	19	8	form	form	NOUN
ejpam-4022	19	9	in	in	ADP
ejpam-4022	19	10	terms	term	NOUN
ejpam-4022	19	11	of	of	ADP
ejpam-4022	19	12	the	the	DET
ejpam-4022	19	13	lerch	lerch	PROPN
ejpam-4022	19	14	function	function	PROPN
ejpam-4022	19	15	.	.	PUNCT
ejpam-4022	20	1	this	this	DET
ejpam-4022	20	2	integral	integral	ADJ
ejpam-4022	20	3	formula	formula	NOUN
ejpam-4022	20	4	was	be	AUX
ejpam-4022	20	5	then	then	ADV
ejpam-4022	20	6	used	use	VERB
ejpam-4022	20	7	to	to	PART
ejpam-4022	20	8	provide	provide	VERB
ejpam-4022	20	9	formal	formal	ADJ
ejpam-4022	20	10	derivations	derivation	NOUN
ejpam-4022	20	11	in	in	ADP
ejpam-4022	20	12	terms	term	NOUN
ejpam-4022	20	13	of	of	ADP
ejpam-4022	20	14	new	new	ADJ
ejpam-4022	20	15	formulae	formulae	NOUN
ejpam-4022	20	16	in	in	ADP
ejpam-4022	20	17	the	the	DET
ejpam-4022	20	18	form	form	NOUN
ejpam-4022	20	19	of	of	ADP
ejpam-4022	20	20	a	a	DET
ejpam-4022	20	21	summary	summary	NOUN
ejpam-4022	20	22	table	table	NOUN
ejpam-4022	20	23	(	(	PUNCT
ejpam-4022	20	24	1	1	NUM
ejpam-4022	20	25	)	)	PUNCT
ejpam-4022	20	26	of	of	ADP
ejpam-4022	20	27	integrals	integral	NOUN
ejpam-4022	20	28	.	.	PUNCT
ejpam-4022	21	1	the	the	DET
ejpam-4022	21	2	lerch	lerch	PROPN
ejpam-4022	21	3	function	function	PROPN
ejpam-4022	21	4	being	be	AUX
ejpam-4022	21	5	a	a	DET
ejpam-4022	21	6	special	special	ADJ
ejpam-4022	21	7	function	function	NOUN
ejpam-4022	21	8	has	have	VERB
ejpam-4022	21	9	the	the	DET
ejpam-4022	21	10	fundamental	fundamental	ADJ
ejpam-4022	21	11	property	property	NOUN
ejpam-4022	21	12	of	of	ADP
ejpam-4022	21	13	analytic	analytic	ADJ
ejpam-4022	21	14	continuation	continuation	NOUN
ejpam-4022	21	15	,	,	PUNCT
ejpam-4022	21	16	which	which	PRON
ejpam-4022	21	17	enables	enable	VERB
ejpam-4022	21	18	us	we	PRON
ejpam-4022	21	19	to	to	PART
ejpam-4022	21	20	widen	widen	VERB
ejpam-4022	21	21	the	the	DET
ejpam-4022	21	22	range	range	NOUN
ejpam-4022	21	23	of	of	ADP
ejpam-4022	21	24	evaluation	evaluation	NOUN
ejpam-4022	21	25	for	for	ADP
ejpam-4022	21	26	the	the	DET
ejpam-4022	21	27	parameters	parameter	NOUN
ejpam-4022	21	28	involved	involve	VERB
ejpam-4022	21	29	in	in	ADP
ejpam-4022	21	30	our	our	PRON
ejpam-4022	21	31	definite	definite	ADJ
ejpam-4022	21	32	integral	integral	NOUN
ejpam-4022	21	33	.	.	PUNCT
ejpam-4022	22	1	the	the	DET
ejpam-4022	22	2	definite	definite	ADJ
ejpam-4022	22	3	integral	integral	ADJ
ejpam-4022	22	4	derived	derived	NOUN
ejpam-4022	22	5	in	in	ADP
ejpam-4022	22	6	this	this	DET
ejpam-4022	22	7	manuscript	manuscript	NOUN
ejpam-4022	22	8	is	be	AUX
ejpam-4022	22	9	given	give	VERB
ejpam-4022	22	10	by∫	by∫	PROPN
ejpam-4022	22	11	∞	∞	PROPN
ejpam-4022	22	12	0	0	NUM
ejpam-4022	23	1	∫	∫	PROPN
ejpam-4022	23	2	∞	∞	NOUN
ejpam-4022	23	3	0	0	NUM
ejpam-4022	24	1	xmy−m−1e	xmy−m−1e	PROPN
ejpam-4022	24	2	−px−qy−x2	−px−qy−x2	VERB
ejpam-4022	24	3	4y	4y	NUM
ejpam-4022	24	4	logk	logk	NOUN
ejpam-4022	24	5	(	(	PUNCT
ejpam-4022	24	6	ax	ax	NOUN
ejpam-4022	24	7	y	y	PROPN
ejpam-4022	24	8	)	)	PUNCT
ejpam-4022	24	9	dxdy	dxdy	PROPN
ejpam-4022	24	10	(	(	PUNCT
ejpam-4022	24	11	1	1	NUM
ejpam-4022	24	12	)	)	PUNCT
ejpam-4022	24	13	where	where	SCONJ
ejpam-4022	24	14	the	the	DET
ejpam-4022	24	15	parameters	parameter	NOUN
ejpam-4022	24	16	k	k	PROPN
ejpam-4022	24	17	,	,	PUNCT
ejpam-4022	24	18	a	a	PRON
ejpam-4022	24	19	,	,	PUNCT
ejpam-4022	24	20	p	p	NOUN
ejpam-4022	24	21	and	and	CCONJ
ejpam-4022	24	22	q	q	NOUN
ejpam-4022	24	23	are	be	AUX
ejpam-4022	24	24	general	general	ADJ
ejpam-4022	24	25	complex	complex	ADJ
ejpam-4022	24	26	numbers	number	NOUN
ejpam-4022	24	27	and	and	CCONJ
ejpam-4022	24	28	−1	−1	NOUN
ejpam-4022	24	29	<	<	X
ejpam-4022	24	30	re(m	re(m	NOUN
ejpam-4022	24	31	)	)	PUNCT
ejpam-4022	24	32	≤	≤	NOUN
ejpam-4022	24	33	−1/2,−1	−1/2,−1	ADV
ejpam-4022	24	34	<	<	X
ejpam-4022	24	35	im(m	im(m	NOUN
ejpam-4022	24	36	)	)	PUNCT
ejpam-4022	24	37	<	<	X
ejpam-4022	25	1	−1/2	−1/2	ADJ
ejpam-4022	25	2	.	.	PUNCT
ejpam-4022	26	1	this	this	DET
ejpam-4022	26	2	work	work	NOUN
ejpam-4022	26	3	is	be	AUX
ejpam-4022	26	4	important	important	ADJ
ejpam-4022	26	5	because	because	SCONJ
ejpam-4022	26	6	the	the	DET
ejpam-4022	26	7	authors	author	NOUN
ejpam-4022	26	8	were	be	AUX
ejpam-4022	26	9	unable	unable	ADJ
ejpam-4022	26	10	to	to	PART
ejpam-4022	26	11	find	find	VERB
ejpam-4022	26	12	similar	similar	ADJ
ejpam-4022	26	13	derivations	derivation	NOUN
ejpam-4022	26	14	in	in	ADP
ejpam-4022	26	15	current	current	ADJ
ejpam-4022	26	16	literature	literature	NOUN
ejpam-4022	26	17	.	.	PUNCT
ejpam-4022	27	1	the	the	DET
ejpam-4022	27	2	derivation	derivation	NOUN
ejpam-4022	27	3	of	of	ADP
ejpam-4022	27	4	the	the	DET
ejpam-4022	27	5	definite	definite	ADJ
ejpam-4022	27	6	integral	integral	NOUN
ejpam-4022	27	7	follows	follow	VERB
ejpam-4022	27	8	the	the	DET
ejpam-4022	27	9	method	method	NOUN
ejpam-4022	27	10	used	use	VERB
ejpam-4022	27	11	by	by	ADP
ejpam-4022	27	12	us	we	PRON
ejpam-4022	27	13	in	in	ADP
ejpam-4022	27	14	[	[	X
ejpam-4022	27	15	8	8	NUM
ejpam-4022	27	16	]	]	PUNCT
ejpam-4022	27	17	which	which	PRON
ejpam-4022	27	18	involves	involve	VERB
ejpam-4022	27	19	cauchy	cauchy	PROPN
ejpam-4022	27	20	’s	’s	PART
ejpam-4022	27	21	integral	integral	ADJ
ejpam-4022	27	22	formula	formula	NOUN
ejpam-4022	27	23	.	.	PUNCT
ejpam-4022	28	1	the	the	DET
ejpam-4022	28	2	generalized	generalized	ADJ
ejpam-4022	28	3	cauchy	cauchy	PROPN
ejpam-4022	28	4	’s	’s	PART
ejpam-4022	28	5	integral	integral	ADJ
ejpam-4022	28	6	formula	formula	NOUN
ejpam-4022	28	7	is	be	AUX
ejpam-4022	28	8	given	give	VERB
ejpam-4022	28	9	by	by	ADP
ejpam-4022	28	10	yk	yk	PROPN
ejpam-4022	28	11	γ(k	γ(k	PROPN
ejpam-4022	28	12	+	+	CCONJ
ejpam-4022	28	13	1	1	X
ejpam-4022	28	14	)	)	PUNCT
ejpam-4022	28	15	=	=	SYM
ejpam-4022	28	16	1	1	NUM
ejpam-4022	28	17	2πi	2πi	ADJ
ejpam-4022	28	18	∫	∫	PROPN
ejpam-4022	28	19	c	c	PROPN
ejpam-4022	28	20	ewy	ewy	PROPN
ejpam-4022	28	21	wk+1	wk+1	PROPN
ejpam-4022	28	22	dw	dw	PROPN
ejpam-4022	28	23	(	(	PUNCT
ejpam-4022	28	24	2	2	NUM
ejpam-4022	28	25	)	)	PUNCT
ejpam-4022	28	26	where	where	SCONJ
ejpam-4022	28	27	c	c	NOUN
ejpam-4022	28	28	is	be	AUX
ejpam-4022	28	29	in	in	ADP
ejpam-4022	28	30	general	general	ADJ
ejpam-4022	28	31	an	an	DET
ejpam-4022	28	32	open	open	ADJ
ejpam-4022	28	33	contour	contour	NOUN
ejpam-4022	28	34	in	in	ADP
ejpam-4022	28	35	the	the	DET
ejpam-4022	28	36	complex	complex	ADJ
ejpam-4022	28	37	plane	plane	NOUN
ejpam-4022	28	38	where	where	SCONJ
ejpam-4022	28	39	the	the	DET
ejpam-4022	28	40	bilinear	bilinear	NOUN
ejpam-4022	28	41	concomitant	concomitant	NOUN
ejpam-4022	28	42	has	have	VERB
ejpam-4022	28	43	the	the	DET
ejpam-4022	28	44	same	same	ADJ
ejpam-4022	28	45	value	value	NOUN
ejpam-4022	28	46	at	at	ADP
ejpam-4022	28	47	the	the	DET
ejpam-4022	28	48	end	end	NOUN
ejpam-4022	28	49	points	point	NOUN
ejpam-4022	28	50	of	of	ADP
ejpam-4022	28	51	the	the	DET
ejpam-4022	28	52	contour	contour	NOUN
ejpam-4022	28	53	.	.	PUNCT
ejpam-4022	29	1	this	this	DET
ejpam-4022	29	2	method	method	NOUN
ejpam-4022	29	3	involves	involve	VERB
ejpam-4022	29	4	using	use	VERB
ejpam-4022	29	5	a	a	DET
ejpam-4022	29	6	form	form	NOUN
ejpam-4022	29	7	of	of	ADP
ejpam-4022	29	8	equation	equation	NOUN
ejpam-4022	29	9	(	(	PUNCT
ejpam-4022	29	10	2	2	NUM
ejpam-4022	29	11	)	)	PUNCT
ejpam-4022	29	12	then	then	ADV
ejpam-4022	29	13	multiply	multiply	VERB
ejpam-4022	29	14	both	both	DET
ejpam-4022	29	15	sides	side	NOUN
ejpam-4022	29	16	by	by	ADP
ejpam-4022	29	17	a	a	DET
ejpam-4022	29	18	function	function	NOUN
ejpam-4022	29	19	,	,	PUNCT
ejpam-4022	29	20	then	then	ADV
ejpam-4022	29	21	take	take	VERB
ejpam-4022	29	22	a	a	DET
ejpam-4022	29	23	definite	definite	ADJ
ejpam-4022	29	24	integral	integral	NOUN
ejpam-4022	29	25	of	of	ADP
ejpam-4022	29	26	both	both	DET
ejpam-4022	29	27	sides	side	NOUN
ejpam-4022	29	28	.	.	PUNCT
ejpam-4022	30	1	this	this	PRON
ejpam-4022	30	2	yields	yield	VERB
ejpam-4022	30	3	a	a	DET
ejpam-4022	30	4	definite	definite	ADJ
ejpam-4022	30	5	integral	integral	ADJ
ejpam-4022	30	6	in	in	ADP
ejpam-4022	30	7	terms	term	NOUN
ejpam-4022	30	8	of	of	ADP
ejpam-4022	30	9	a	a	DET
ejpam-4022	30	10	contour	contour	NOUN
ejpam-4022	30	11	integral	integral	NOUN
ejpam-4022	30	12	.	.	PUNCT
ejpam-4022	31	1	a	a	DET
ejpam-4022	31	2	second	second	ADJ
ejpam-4022	31	3	contour	contour	NOUN
ejpam-4022	31	4	integral	integral	NOUN
ejpam-4022	31	5	is	be	AUX
ejpam-4022	31	6	derived	derive	VERB
ejpam-4022	31	7	by	by	ADP
ejpam-4022	31	8	multiplying	multiply	VERB
ejpam-4022	31	9	equation	equation	NOUN
ejpam-4022	31	10	(	(	PUNCT
ejpam-4022	31	11	2	2	NUM
ejpam-4022	31	12	)	)	PUNCT
ejpam-4022	31	13	by	by	ADP
ejpam-4022	31	14	a	a	DET
ejpam-4022	31	15	function	function	NOUN
ejpam-4022	31	16	and	and	CCONJ
ejpam-4022	31	17	performing	perform	VERB
ejpam-4022	31	18	some	some	DET
ejpam-4022	31	19	substitutions	substitution	NOUN
ejpam-4022	31	20	so	so	SCONJ
ejpam-4022	31	21	that	that	SCONJ
ejpam-4022	31	22	the	the	DET
ejpam-4022	31	23	contour	contour	NOUN
ejpam-4022	31	24	integrals	integral	NOUN
ejpam-4022	31	25	are	be	AUX
ejpam-4022	31	26	the	the	DET
ejpam-4022	31	27	same	same	ADJ
ejpam-4022	31	28	.	.	PUNCT
ejpam-4022	32	1	3	3	X
ejpam-4022	32	2	.	.	X
ejpam-4022	32	3	definite	definite	ADJ
ejpam-4022	32	4	integral	integral	ADJ
ejpam-4022	32	5	of	of	ADP
ejpam-4022	32	6	the	the	DET
ejpam-4022	32	7	contour	contour	NOUN
ejpam-4022	32	8	integral	integral	NOUN
ejpam-4022	32	9	we	we	PRON
ejpam-4022	32	10	use	use	VERB
ejpam-4022	32	11	the	the	DET
ejpam-4022	32	12	method	method	NOUN
ejpam-4022	32	13	in	in	ADP
ejpam-4022	32	14	[	[	X
ejpam-4022	32	15	8	8	NUM
ejpam-4022	32	16	]	]	PUNCT
ejpam-4022	32	17	.	.	PUNCT
ejpam-4022	33	1	the	the	DET
ejpam-4022	33	2	cut	cut	NOUN
ejpam-4022	33	3	and	and	CCONJ
ejpam-4022	33	4	contour	contour	NOUN
ejpam-4022	33	5	are	be	AUX
ejpam-4022	33	6	in	in	ADP
ejpam-4022	33	7	the	the	DET
ejpam-4022	33	8	second	second	ADJ
ejpam-4022	33	9	quadrant	quadrant	NOUN
ejpam-4022	33	10	of	of	ADP
ejpam-4022	33	11	the	the	DET
ejpam-4022	33	12	complex	complex	ADJ
ejpam-4022	33	13	z	z	NOUN
ejpam-4022	33	14	-	-	PUNCT
ejpam-4022	33	15	plane	plane	NOUN
ejpam-4022	33	16	where	where	SCONJ
ejpam-4022	33	17	z	z	NOUN
ejpam-4022	33	18	=	=	SYM
ejpam-4022	33	19	w	w	PROPN
ejpam-4022	33	20	+	+	NUM
ejpam-4022	33	21	m.	m.	NOUN
ejpam-4022	33	22	the	the	DET
ejpam-4022	33	23	cut	cut	NOUN
ejpam-4022	33	24	approaches	approach	VERB
ejpam-4022	33	25	the	the	DET
ejpam-4022	33	26	origin	origin	NOUN
ejpam-4022	33	27	from	from	ADP
ejpam-4022	33	28	the	the	DET
ejpam-4022	33	29	interior	interior	NOUN
ejpam-4022	33	30	of	of	ADP
ejpam-4022	33	31	the	the	DET
ejpam-4022	33	32	second	second	ADJ
ejpam-4022	33	33	quadrant	quadrant	NOUN
ejpam-4022	33	34	and	and	CCONJ
ejpam-4022	33	35	the	the	DET
ejpam-4022	33	36	contour	contour	NOUN
ejpam-4022	33	37	goes	go	VERB
ejpam-4022	33	38	round	round	ADP
ejpam-4022	33	39	the	the	DET
ejpam-4022	33	40	origin	origin	NOUN
ejpam-4022	33	41	with	with	ADP
ejpam-4022	33	42	zero	zero	NUM
ejpam-4022	33	43	radius	radius	NOUN
ejpam-4022	33	44	and	and	CCONJ
ejpam-4022	33	45	is	be	AUX
ejpam-4022	33	46	on	on	ADP
ejpam-4022	33	47	opposite	opposite	ADJ
ejpam-4022	33	48	sides	side	NOUN
ejpam-4022	33	49	of	of	ADP
ejpam-4022	33	50	the	the	DET
ejpam-4022	33	51	cut	cut	NOUN
ejpam-4022	33	52	.	.	PUNCT
ejpam-4022	34	1	using	use	VERB
ejpam-4022	34	2	equation	equation	NOUN
ejpam-4022	34	3	(	(	PUNCT
ejpam-4022	34	4	2	2	X
ejpam-4022	34	5	)	)	PUNCT
ejpam-4022	34	6	we	we	PRON
ejpam-4022	34	7	replace	replace	VERB
ejpam-4022	34	8	y	y	PROPN
ejpam-4022	34	9	by	by	ADP
ejpam-4022	34	10	log(axy	log(axy	PROPN
ejpam-4022	34	11	)	)	PUNCT
ejpam-4022	34	12	then	then	ADV
ejpam-4022	34	13	multiply	multiply	VERB
ejpam-4022	34	14	by	by	ADP
ejpam-4022	34	15	xmy−m−1e	xmy−m−1e	PROPN
ejpam-4022	34	16	−px−qy−x2	−px−qy−x2	PROPN
ejpam-4022	34	17	4y	4y	PROPN
ejpam-4022	34	18	.	.	PUNCT
ejpam-4022	35	1	next	next	ADV
ejpam-4022	35	2	we	we	PRON
ejpam-4022	35	3	take	take	VERB
ejpam-4022	35	4	the	the	DET
ejpam-4022	35	5	double	double	ADJ
ejpam-4022	35	6	infinite	infinite	NOUN
ejpam-4022	35	7	integral	integral	ADJ
ejpam-4022	35	8	over	over	ADP
ejpam-4022	35	9	x	x	PUNCT
ejpam-4022	35	10	∈	∈	PROPN
ejpam-4022	35	11	[	[	X
ejpam-4022	35	12	0,∞	0,∞	NOUN
ejpam-4022	35	13	)	)	PUNCT
ejpam-4022	35	14	and	and	CCONJ
ejpam-4022	35	15	y	y	PROPN
ejpam-4022	35	16	∈	∈	PROPN
ejpam-4022	36	1	[	[	X
ejpam-4022	36	2	0,∞	0,∞	NOUN
ejpam-4022	36	3	)	)	PUNCT
ejpam-4022	36	4	to	to	PART
ejpam-4022	36	5	get	get	VERB
ejpam-4022	36	6	r.	r.	PROPN
ejpam-4022	36	7	reynolds	reynolds	PROPN
ejpam-4022	36	8	,	,	PUNCT
ejpam-4022	36	9	a.	a.	PROPN
ejpam-4022	36	10	stauffer	stauffer	PROPN
ejpam-4022	36	11	/	/	SYM
ejpam-4022	36	12	eur	eur	PROPN
ejpam-4022	36	13	.	.	PUNCT
ejpam-4022	37	1	j.	j.	PROPN
ejpam-4022	37	2	pure	pure	PROPN
ejpam-4022	37	3	appl	appl	PROPN
ejpam-4022	37	4	.	.	PROPN
ejpam-4022	37	5	math	math	PROPN
ejpam-4022	37	6	,	,	PUNCT
ejpam-4022	37	7	14	14	NUM
ejpam-4022	37	8	(	(	PUNCT
ejpam-4022	37	9	4	4	NUM
ejpam-4022	37	10	)	)	PUNCT
ejpam-4022	37	11	(	(	PUNCT
ejpam-4022	37	12	2021	2021	NUM
ejpam-4022	37	13	)	)	PUNCT
ejpam-4022	37	14	,	,	PUNCT
ejpam-4022	37	15	1200	1200	NUM
ejpam-4022	37	16	-	-	SYM
ejpam-4022	37	17	1211	1211	NUM
ejpam-4022	37	18	1202	1202	NUM
ejpam-4022	37	19	(	(	PUNCT
ejpam-4022	37	20	3	3	NUM
ejpam-4022	37	21	)	)	SYM
ejpam-4022	37	22	1	1	NUM
ejpam-4022	37	23	γ(k	γ(k	NOUN
ejpam-4022	37	24	+	+	CCONJ
ejpam-4022	37	25	1	1	X
ejpam-4022	37	26	)	)	PUNCT
ejpam-4022	37	27	∫	∫	PROPN
ejpam-4022	38	1	∞	∞	PROPN
ejpam-4022	38	2	0	0	NUM
ejpam-4022	39	1	∫	∫	PROPN
ejpam-4022	39	2	∞	∞	NOUN
ejpam-4022	39	3	0	0	NUM
ejpam-4022	40	1	xmy−m−1e	xmy−m−1e	PROPN
ejpam-4022	40	2	−px−qy−x2	−px−qy−x2	VERB
ejpam-4022	40	3	4y	4y	NUM
ejpam-4022	40	4	logk	logk	NOUN
ejpam-4022	40	5	(	(	PUNCT
ejpam-4022	40	6	ax	ax	NOUN
ejpam-4022	40	7	y	y	PROPN
ejpam-4022	40	8	)	)	PUNCT
ejpam-4022	40	9	dxdy	dxdy	PROPN
ejpam-4022	40	10	=	=	SYM
ejpam-4022	41	1	1	1	NUM
ejpam-4022	41	2	2πi	2πi	NOUN
ejpam-4022	41	3	∫	∫	PROPN
ejpam-4022	41	4	∞	∞	PROPN
ejpam-4022	41	5	0	0	NUM
ejpam-4022	41	6	∫	∫	PROPN
ejpam-4022	41	7	∞	∞	PROPN
ejpam-4022	41	8	0	0	NUM
ejpam-4022	41	9	∫	∫	PROPN
ejpam-4022	41	10	c	c	PROPN
ejpam-4022	41	11	aww−k−1xm+wy−m−w−1e	aww−k−1xm+wy−m−w−1e	PRON
ejpam-4022	41	12	−px−qy−x2	−px−qy−x2	VERB
ejpam-4022	41	13	4y	4y	PROPN
ejpam-4022	41	14	dwdxdy	dwdxdy	X
ejpam-4022	41	15	=	=	SYM
ejpam-4022	41	16	1	1	NUM
ejpam-4022	41	17	2πi	2πi	NOUN
ejpam-4022	41	18	∫	∫	PROPN
ejpam-4022	41	19	c	c	PROPN
ejpam-4022	41	20	∫	∫	PROPN
ejpam-4022	42	1	∞	∞	NUM
ejpam-4022	42	2	0	0	NUM
ejpam-4022	42	3	∫	∫	PROPN
ejpam-4022	42	4	∞	∞	PROPN
ejpam-4022	42	5	0	0	NUM
ejpam-4022	43	1	aww−k−1xm+wy−m−w−1e	aww−k−1xm+wy−m−w−1e	X
ejpam-4022	43	2	−px−qy−x2	−px−qy−x2	PROPN
ejpam-4022	43	3	4y	4y	NUM
ejpam-4022	43	4	dxdydw	dxdydw	NOUN
ejpam-4022	43	5	=	=	SYM
ejpam-4022	43	6	1	1	NUM
ejpam-4022	43	7	2πi	2πi	NOUN
ejpam-4022	43	8	∫	∫	PROPN
ejpam-4022	43	9	c	c	PROPN
ejpam-4022	43	10	πaww−k−12m+w+1q	πaww−k−12m+w+1q	X
ejpam-4022	43	11	m+w	m+w	X
ejpam-4022	43	12	2	2	NUM
ejpam-4022	43	13	csc(π(m+	csc(π(m+	NOUN
ejpam-4022	43	14	w	w	NOUN
ejpam-4022	43	15	)	)	PUNCT
ejpam-4022	43	16	)	)	PUNCT
ejpam-4022	43	17	sinh	sinh	NOUN
ejpam-4022	43	18	(	(	PUNCT
ejpam-4022	43	19	(	(	PUNCT
ejpam-4022	43	20	m+	m+	NUM
ejpam-4022	43	21	w	w	NOUN
ejpam-4022	43	22	)	)	PUNCT
ejpam-4022	43	23	cosh−1	cosh−1	NOUN
ejpam-4022	43	24	(	(	PUNCT
ejpam-4022	43	25	p√	p√	X
ejpam-4022	43	26	q	q	PROPN
ejpam-4022	43	27	)	)	PUNCT
ejpam-4022	43	28	)	)	PUNCT
ejpam-4022	44	1	√	√	PROPN
ejpam-4022	44	2	p2	p2	NOUN
ejpam-4022	45	1	−	−	PROPN
ejpam-4022	45	2	q	q	PROPN
ejpam-4022	45	3	dw	dw	PROPN
ejpam-4022	45	4	from	from	ADP
ejpam-4022	45	5	equation	equation	NOUN
ejpam-4022	45	6	(	(	PUNCT
ejpam-4022	45	7	3.1.3.48	3.1.3.48	NUM
ejpam-4022	45	8	)	)	PUNCT
ejpam-4022	45	9	in	in	ADP
ejpam-4022	45	10	[	[	X
ejpam-4022	45	11	6	6	NUM
ejpam-4022	45	12	]	]	PUNCT
ejpam-4022	45	13	where	where	SCONJ
ejpam-4022	45	14	|re(m+w)|	|re(m+w)|	X
ejpam-4022	45	15	<	<	X
ejpam-4022	45	16	1	1	NUM
ejpam-4022	45	17	.	.	PUNCT
ejpam-4022	46	1	we	we	PRON
ejpam-4022	46	2	are	be	AUX
ejpam-4022	46	3	able	able	ADJ
ejpam-4022	46	4	to	to	PART
ejpam-4022	46	5	switch	switch	VERB
ejpam-4022	46	6	the	the	DET
ejpam-4022	46	7	order	order	NOUN
ejpam-4022	46	8	of	of	ADP
ejpam-4022	46	9	integration	integration	NOUN
ejpam-4022	46	10	over	over	ADP
ejpam-4022	46	11	z	z	PROPN
ejpam-4022	46	12	,	,	PUNCT
ejpam-4022	46	13	x	x	PUNCT
ejpam-4022	46	14	and	and	CCONJ
ejpam-4022	46	15	y	y	PROPN
ejpam-4022	46	16	using	use	VERB
ejpam-4022	46	17	fubini	fubini	NOUN
ejpam-4022	46	18	’s	’s	PART
ejpam-4022	46	19	theorem	theorem	NOUN
ejpam-4022	46	20	since	since	SCONJ
ejpam-4022	46	21	the	the	DET
ejpam-4022	46	22	integrand	integrand	NOUN
ejpam-4022	46	23	is	be	AUX
ejpam-4022	46	24	of	of	ADP
ejpam-4022	46	25	bounded	bounded	ADJ
ejpam-4022	46	26	measure	measure	NOUN
ejpam-4022	46	27	over	over	ADP
ejpam-4022	46	28	the	the	DET
ejpam-4022	46	29	space	space	NOUN
ejpam-4022	46	30	c	c	NOUN
ejpam-4022	46	31	×	×	NOUN
ejpam-4022	47	1	[	[	X
ejpam-4022	47	2	0,∞)×	0,∞)×	NUM
ejpam-4022	47	3	[	[	X
ejpam-4022	47	4	0,∞	0,∞	NUM
ejpam-4022	47	5	)	)	PUNCT
ejpam-4022	47	6	.	.	PUNCT
ejpam-4022	48	1	4	4	X
ejpam-4022	48	2	.	.	X
ejpam-4022	48	3	the	the	DET
ejpam-4022	48	4	lerch	lerch	PROPN
ejpam-4022	48	5	function	function	NOUN
ejpam-4022	48	6	we	we	PRON
ejpam-4022	48	7	use	use	VERB
ejpam-4022	48	8	(	(	PUNCT
ejpam-4022	48	9	9.550	9.550	NUM
ejpam-4022	48	10	)	)	PUNCT
ejpam-4022	48	11	and	and	CCONJ
ejpam-4022	48	12	(	(	PUNCT
ejpam-4022	48	13	9.556	9.556	NUM
ejpam-4022	48	14	)	)	PUNCT
ejpam-4022	48	15	in	in	ADP
ejpam-4022	48	16	[	[	X
ejpam-4022	48	17	2	2	NUM
ejpam-4022	48	18	]	]	PUNCT
ejpam-4022	48	19	where	where	SCONJ
ejpam-4022	48	20	φ(z	φ(z	PROPN
ejpam-4022	48	21	,	,	PUNCT
ejpam-4022	48	22	s	s	NOUN
ejpam-4022	48	23	,	,	PUNCT
ejpam-4022	48	24	v	v	NOUN
ejpam-4022	48	25	)	)	PUNCT
ejpam-4022	48	26	is	be	AUX
ejpam-4022	48	27	the	the	DET
ejpam-4022	48	28	lerch	lerch	PROPN
ejpam-4022	48	29	function	function	NOUN
ejpam-4022	48	30	which	which	PRON
ejpam-4022	48	31	is	be	AUX
ejpam-4022	48	32	a	a	DET
ejpam-4022	48	33	generalization	generalization	NOUN
ejpam-4022	48	34	of	of	ADP
ejpam-4022	48	35	the	the	DET
ejpam-4022	48	36	hurwitz	hurwitz	PROPN
ejpam-4022	48	37	zeta	zeta	PROPN
ejpam-4022	48	38	ζ(s	ζ(s	PROPN
ejpam-4022	48	39	,	,	PUNCT
ejpam-4022	48	40	v	v	NOUN
ejpam-4022	48	41	)	)	PUNCT
ejpam-4022	48	42	and	and	CCONJ
ejpam-4022	48	43	polylogarithm	polylogarithm	PROPN
ejpam-4022	48	44	functions	function	NOUN
ejpam-4022	48	45	lin(z	lin(z	PROPN
ejpam-4022	48	46	)	)	PUNCT
ejpam-4022	48	47	.	.	PUNCT
ejpam-4022	49	1	the	the	DET
ejpam-4022	49	2	lerch	lerch	PROPN
ejpam-4022	49	3	function	function	PROPN
ejpam-4022	49	4	has	have	VERB
ejpam-4022	49	5	a	a	DET
ejpam-4022	49	6	series	series	NOUN
ejpam-4022	49	7	representation	representation	NOUN
ejpam-4022	49	8	given	give	VERB
ejpam-4022	49	9	by	by	ADP
ejpam-4022	49	10	φ(z	φ(z	PROPN
ejpam-4022	49	11	,	,	PUNCT
ejpam-4022	49	12	s	s	NOUN
ejpam-4022	49	13	,	,	PUNCT
ejpam-4022	49	14	v	v	NOUN
ejpam-4022	49	15	)	)	PUNCT
ejpam-4022	49	16	=	=	PUNCT
ejpam-4022	50	1	∞∑	∞∑	NUM
ejpam-4022	50	2	n=0	n=0	NUM
ejpam-4022	50	3	(	(	PUNCT
ejpam-4022	50	4	v	v	NOUN
ejpam-4022	50	5	+	+	PRON
ejpam-4022	50	6	n)−szn	n)−szn	NUM
ejpam-4022	50	7	(	(	PUNCT
ejpam-4022	50	8	4	4	NUM
ejpam-4022	50	9	)	)	PUNCT
ejpam-4022	50	10	where	where	SCONJ
ejpam-4022	50	11	|z|	|z|	VERB
ejpam-4022	50	12	<	<	X
ejpam-4022	50	13	1	1	NUM
ejpam-4022	50	14	,	,	PUNCT
ejpam-4022	50	15	v	v	ADP
ejpam-4022	50	16	̸=	̸=	PROPN
ejpam-4022	50	17	0,−1	0,−1	PROPN
ejpam-4022	50	18	,	,	PUNCT
ejpam-4022	50	19	..	..	PUNCT
ejpam-4022	50	20	and	and	CCONJ
ejpam-4022	50	21	is	be	AUX
ejpam-4022	50	22	continued	continue	VERB
ejpam-4022	50	23	analytically	analytically	ADV
ejpam-4022	50	24	by	by	ADP
ejpam-4022	50	25	its	its	PRON
ejpam-4022	50	26	integral	integral	ADJ
ejpam-4022	50	27	representation	representation	NOUN
ejpam-4022	50	28	given	give	VERB
ejpam-4022	50	29	by	by	ADP
ejpam-4022	50	30	φ(z	φ(z	PROPN
ejpam-4022	50	31	,	,	PUNCT
ejpam-4022	50	32	s	s	NOUN
ejpam-4022	50	33	,	,	PUNCT
ejpam-4022	50	34	v	v	NOUN
ejpam-4022	50	35	)	)	PUNCT
ejpam-4022	50	36	=	=	SYM
ejpam-4022	50	37	1	1	NUM
ejpam-4022	50	38	γ(s	γ(	NOUN
ejpam-4022	50	39	)	)	PUNCT
ejpam-4022	50	40	∫	∫	PROPN
ejpam-4022	51	1	∞	∞	PROPN
ejpam-4022	51	2	0	0	NUM
ejpam-4022	52	1	ts−1e−vt	ts−1e−vt	PRON
ejpam-4022	53	1	1−	1−	NUM
ejpam-4022	53	2	ze−t	ze−t	NOUN
ejpam-4022	53	3	dt	dt	NOUN
ejpam-4022	54	1	=	=	SYM
ejpam-4022	54	2	1	1	NUM
ejpam-4022	54	3	γ(s	γ(s	PROPN
ejpam-4022	54	4	)	)	PUNCT
ejpam-4022	54	5	∫	∫	PROPN
ejpam-4022	55	1	∞	∞	NUM
ejpam-4022	55	2	0	0	NUM
ejpam-4022	56	1	ts−1e−(v−1)t	ts−1e−(v−1)t	PROPN
ejpam-4022	56	2	et	et	NOUN
ejpam-4022	56	3	−	−	NOUN
ejpam-4022	56	4	z	z	NOUN
ejpam-4022	56	5	dt	dt	X
ejpam-4022	56	6	(	(	PUNCT
ejpam-4022	56	7	5	5	NUM
ejpam-4022	56	8	)	)	PUNCT
ejpam-4022	56	9	where	where	SCONJ
ejpam-4022	56	10	re(v	re(v	NOUN
ejpam-4022	56	11	)	)	PUNCT
ejpam-4022	56	12	>	>	X
ejpam-4022	56	13	0	0	NUM
ejpam-4022	56	14	,	,	PUNCT
ejpam-4022	56	15	and	and	CCONJ
ejpam-4022	56	16	either	either	ADV
ejpam-4022	56	17	|z|≤	|z|≤	SYM
ejpam-4022	56	18	1	1	NUM
ejpam-4022	56	19	,	,	PUNCT
ejpam-4022	56	20	z	z	NOUN
ejpam-4022	56	21	̸=	̸=	PROPN
ejpam-4022	56	22	1,re(s	1,re(s	NUM
ejpam-4022	56	23	)	)	PUNCT
ejpam-4022	56	24	>	>	X
ejpam-4022	56	25	0	0	NUM
ejpam-4022	56	26	,	,	PUNCT
ejpam-4022	56	27	or	or	CCONJ
ejpam-4022	56	28	z	z	NOUN
ejpam-4022	56	29	=	=	SYM
ejpam-4022	56	30	1,re(s	1,re(s	NOUN
ejpam-4022	56	31	)	)	PUNCT
ejpam-4022	56	32	>	>	X
ejpam-4022	57	1	1	1	NUM
ejpam-4022	57	2	.	.	X
ejpam-4022	57	3	5	5	NUM
ejpam-4022	57	4	.	.	X
ejpam-4022	57	5	infinite	infinite	ADJ
ejpam-4022	57	6	sum	sum	NOUN
ejpam-4022	57	7	of	of	ADP
ejpam-4022	57	8	the	the	DET
ejpam-4022	57	9	contour	contour	NOUN
ejpam-4022	57	10	integral	integral	NOUN
ejpam-4022	57	11	in	in	ADP
ejpam-4022	57	12	this	this	DET
ejpam-4022	57	13	section	section	NOUN
ejpam-4022	57	14	we	we	PRON
ejpam-4022	57	15	will	will	AUX
ejpam-4022	57	16	again	again	ADV
ejpam-4022	57	17	use	use	VERB
ejpam-4022	57	18	cauchy	cauchy	NOUN
ejpam-4022	57	19	’s	’s	PART
ejpam-4022	57	20	integral	integral	ADJ
ejpam-4022	57	21	formula	formula	NOUN
ejpam-4022	57	22	(	(	PUNCT
ejpam-4022	57	23	2	2	NUM
ejpam-4022	57	24	)	)	PUNCT
ejpam-4022	57	25	and	and	CCONJ
ejpam-4022	57	26	taking	take	VERB
ejpam-4022	57	27	the	the	DET
ejpam-4022	57	28	infinite	infinite	ADJ
ejpam-4022	57	29	sum	sum	NOUN
ejpam-4022	57	30	to	to	PART
ejpam-4022	57	31	derive	derive	VERB
ejpam-4022	57	32	equivalent	equivalent	ADJ
ejpam-4022	57	33	sum	sum	NOUN
ejpam-4022	57	34	representations	representation	NOUN
ejpam-4022	57	35	for	for	ADP
ejpam-4022	57	36	the	the	DET
ejpam-4022	57	37	contour	contour	NOUN
ejpam-4022	57	38	integrals	integral	NOUN
ejpam-4022	57	39	.	.	PUNCT
ejpam-4022	58	1	we	we	PRON
ejpam-4022	58	2	proceed	proceed	VERB
ejpam-4022	58	3	using	use	VERB
ejpam-4022	58	4	equation	equation	NOUN
ejpam-4022	58	5	(	(	PUNCT
ejpam-4022	58	6	2	2	NUM
ejpam-4022	58	7	)	)	PUNCT
ejpam-4022	58	8	to	to	PART
ejpam-4022	58	9	form	form	VERB
ejpam-4022	58	10	two	two	NUM
ejpam-4022	58	11	equations	equation	NOUN
ejpam-4022	58	12	and	and	CCONJ
ejpam-4022	58	13	take	take	VERB
ejpam-4022	58	14	their	their	PRON
ejpam-4022	58	15	difference	difference	NOUN
ejpam-4022	58	16	.	.	PUNCT
ejpam-4022	59	1	firstly	firstly	ADV
ejpam-4022	59	2	,	,	PUNCT
ejpam-4022	59	3	replace	replace	VERB
ejpam-4022	59	4	y	y	PROPN
ejpam-4022	59	5	→	→	SYM
ejpam-4022	59	6	y	y	PROPN
ejpam-4022	60	1	+	+	CCONJ
ejpam-4022	60	2	x	x	PUNCT
ejpam-4022	60	3	and	and	CCONJ
ejpam-4022	60	4	multiply	multiply	VERB
ejpam-4022	60	5	both	both	DET
ejpam-4022	60	6	sides	side	NOUN
ejpam-4022	60	7	by	by	ADP
ejpam-4022	60	8	emx	emx	NOUN
ejpam-4022	60	9	and	and	CCONJ
ejpam-4022	60	10	secondly	secondly	ADV
ejpam-4022	60	11	,	,	PUNCT
ejpam-4022	60	12	replace	replace	VERB
ejpam-4022	60	13	x	x	INTJ
ejpam-4022	60	14	→	→	SYM
ejpam-4022	60	15	−x	−x	NOUN
ejpam-4022	60	16	in	in	ADP
ejpam-4022	60	17	the	the	DET
ejpam-4022	60	18	first	first	ADJ
ejpam-4022	60	19	equation	equation	NOUN
ejpam-4022	60	20	to	to	PART
ejpam-4022	60	21	get	get	VERB
ejpam-4022	60	22	the	the	DET
ejpam-4022	60	23	second	second	ADJ
ejpam-4022	60	24	equation	equation	NOUN
ejpam-4022	60	25	and	and	CCONJ
ejpam-4022	60	26	subtract	subtract	VERB
ejpam-4022	60	27	to	to	PART
ejpam-4022	60	28	get	get	VERB
ejpam-4022	60	29	(	(	PUNCT
ejpam-4022	60	30	6	6	NUM
ejpam-4022	60	31	)	)	PUNCT
ejpam-4022	60	32	emx(x+	emx(x+	VERB
ejpam-4022	60	33	y)k	y)k	ADJ
ejpam-4022	60	34	−	−	ADP
ejpam-4022	60	35	e−mx(y	e−mx(y	NOUN
ejpam-4022	60	36	−	−	NOUN
ejpam-4022	60	37	x)k	x)k	NOUN
ejpam-4022	60	38	2γ(k	2γ(k	NUM
ejpam-4022	61	1	+	+	CCONJ
ejpam-4022	61	2	1	1	X
ejpam-4022	61	3	)	)	PUNCT
ejpam-4022	61	4	=	=	SYM
ejpam-4022	61	5	1	1	NUM
ejpam-4022	61	6	2πi	2πi	ADJ
ejpam-4022	61	7	∫	∫	PROPN
ejpam-4022	61	8	c	c	PROPN
ejpam-4022	61	9	w−k−1ewy	w−k−1ewy	PROPN
ejpam-4022	61	10	sinh(x(m+	sinh(x(m+	AUX
ejpam-4022	61	11	w))dw	w))dw	NOUN
ejpam-4022	62	1	next	next	ADV
ejpam-4022	62	2	we	we	PRON
ejpam-4022	62	3	replace	replace	VERB
ejpam-4022	62	4	y	y	PROPN
ejpam-4022	62	5	→	→	SYM
ejpam-4022	62	6	log(a	log(a	PROPN
ejpam-4022	62	7	)	)	PUNCT
ejpam-4022	62	8	+	+	CCONJ
ejpam-4022	62	9	log(q	log(q	PROPN
ejpam-4022	62	10	)	)	PUNCT
ejpam-4022	62	11	2	2	NUM
ejpam-4022	63	1	+	+	CCONJ
ejpam-4022	63	2	iπ(2y	iπ(2y	PRON
ejpam-4022	63	3	+	+	NOUN
ejpam-4022	63	4	1	1	X
ejpam-4022	63	5	)	)	PUNCT
ejpam-4022	63	6	+	+	NUM
ejpam-4022	63	7	log(2	log(2	NOUN
ejpam-4022	63	8	)	)	PUNCT
ejpam-4022	63	9	and	and	CCONJ
ejpam-4022	63	10	multiply	multiply	VERB
ejpam-4022	63	11	both	both	DET
ejpam-4022	63	12	sides	side	NOUN
ejpam-4022	63	13	by	by	ADP
ejpam-4022	63	14	eiπm(2y+1	eiπm(2y+1	ADJ
ejpam-4022	63	15	)	)	PUNCT
ejpam-4022	63	16	and	and	CCONJ
ejpam-4022	63	17	take	take	VERB
ejpam-4022	63	18	the	the	DET
ejpam-4022	63	19	infinite	infinite	ADJ
ejpam-4022	63	20	sum	sum	NOUN
ejpam-4022	63	21	over	over	ADP
ejpam-4022	63	22	y	y	PROPN
ejpam-4022	63	23	∈	∈	PROPN
ejpam-4022	64	1	[	[	X
ejpam-4022	64	2	0,∞	0,∞	NOUN
ejpam-4022	64	3	)	)	PUNCT
ejpam-4022	64	4	to	to	PART
ejpam-4022	64	5	get	get	VERB
ejpam-4022	64	6	r.	r.	PROPN
ejpam-4022	64	7	reynolds	reynolds	PROPN
ejpam-4022	64	8	,	,	PUNCT
ejpam-4022	64	9	a.	a.	PROPN
ejpam-4022	64	10	stauffer	stauffer	PROPN
ejpam-4022	64	11	/	/	SYM
ejpam-4022	64	12	eur	eur	PROPN
ejpam-4022	64	13	.	.	PUNCT
ejpam-4022	65	1	j.	j.	PROPN
ejpam-4022	65	2	pure	pure	PROPN
ejpam-4022	65	3	appl	appl	PROPN
ejpam-4022	65	4	.	.	PROPN
ejpam-4022	65	5	math	math	PROPN
ejpam-4022	65	6	,	,	PUNCT
ejpam-4022	65	7	14	14	NUM
ejpam-4022	65	8	(	(	PUNCT
ejpam-4022	65	9	4	4	NUM
ejpam-4022	65	10	)	)	PUNCT
ejpam-4022	65	11	(	(	PUNCT
ejpam-4022	65	12	2021	2021	NUM
ejpam-4022	65	13	)	)	PUNCT
ejpam-4022	65	14	,	,	PUNCT
ejpam-4022	65	15	1200	1200	NUM
ejpam-4022	65	16	-	-	SYM
ejpam-4022	65	17	1211	1211	NUM
ejpam-4022	65	18	1203	1203	NUM
ejpam-4022	65	19	(	(	PUNCT
ejpam-4022	65	20	7	7	NUM
ejpam-4022	65	21	)	)	PUNCT
ejpam-4022	65	22	2k−1πke−mx+	2k−1πke−mx+	NUM
ejpam-4022	65	23	1	1	NUM
ejpam-4022	65	24	2	2	NUM
ejpam-4022	65	25	iπ(k+2	iπ(k+2	NOUN
ejpam-4022	65	26	m	m	NOUN
ejpam-4022	65	27	)	)	PUNCT
ejpam-4022	65	28	γ(k	γ(k	NOUN
ejpam-4022	65	29	+	+	CCONJ
ejpam-4022	65	30	1	1	X
ejpam-4022	65	31	)	)	PUNCT
ejpam-4022	65	32	(	(	PUNCT
ejpam-4022	65	33	e2mxφ	e2mxφ	X
ejpam-4022	65	34	(	(	PUNCT
ejpam-4022	65	35	e2imπ,−k,−2ix+	e2imπ,−k,−2ix+	PROPN
ejpam-4022	65	36	2i	2i	PROPN
ejpam-4022	65	37	log(2a	log(2a	ADJ
ejpam-4022	65	38	)	)	PUNCT
ejpam-4022	66	1	+	+	CCONJ
ejpam-4022	66	2	i	i	PRON
ejpam-4022	66	3	log(q)−	log(q)−	VERB
ejpam-4022	66	4	2π	2π	NOUN
ejpam-4022	66	5	4π	4π	NUM
ejpam-4022	66	6	)	)	PUNCT
ejpam-4022	66	7	−	−	PROPN
ejpam-4022	67	1	φ	φ	PROPN
ejpam-4022	67	2	(	(	PUNCT
ejpam-4022	67	3	e2imπ,−k	e2imπ,−k	NOUN
ejpam-4022	67	4	,	,	PUNCT
ejpam-4022	67	5	2ix−	2ix−	NUM
ejpam-4022	67	6	2i	2i	NUM
ejpam-4022	67	7	log(2a)−	log(2a)−	NOUN
ejpam-4022	67	8	i	i	PRON
ejpam-4022	67	9	log(q	log(q	PROPN
ejpam-4022	67	10	)	)	PUNCT
ejpam-4022	67	11	+	+	NUM
ejpam-4022	67	12	2π	2π	NOUN
ejpam-4022	67	13	4π	4π	NUM
ejpam-4022	67	14	)	)	PUNCT
ejpam-4022	67	15	)	)	PUNCT
ejpam-4022	68	1	=	=	SYM
ejpam-4022	69	1	1	1	NUM
ejpam-4022	69	2	2πi	2πi	NOUN
ejpam-4022	69	3	∞∑	∞∑	NUM
ejpam-4022	69	4	y=0	y=0	NUM
ejpam-4022	69	5	∫	∫	PROPN
ejpam-4022	69	6	c	c	PROPN
ejpam-4022	69	7	2waww−k−1qw/2eiπ(2y+1)(m+w	2waww−k−1qw/2eiπ(2y+1)(m+w	NUM
ejpam-4022	69	8	)	)	PUNCT
ejpam-4022	69	9	sinh(x(m+	sinh(x(m+	NOUN
ejpam-4022	69	10	w))dw	w))dw	NOUN
ejpam-4022	69	11	=	=	SYM
ejpam-4022	69	12	1	1	NUM
ejpam-4022	69	13	2πi	2πi	NOUN
ejpam-4022	69	14	∫	∫	PROPN
ejpam-4022	70	1	c	c	NOUN
ejpam-4022	70	2	∞∑	∞∑	NUM
ejpam-4022	70	3	y=0	y=0	NOUN
ejpam-4022	70	4	2waww−k−1qw/2eiπ(2y+1)(m+w	2waww−k−1qw/2eiπ(2y+1)(m+w	NUM
ejpam-4022	70	5	)	)	PUNCT
ejpam-4022	70	6	sinh(x(m+	sinh(x(m+	NOUN
ejpam-4022	70	7	w))dw	w))dw	NOUN
ejpam-4022	70	8	=	=	SYM
ejpam-4022	70	9	1	1	NUM
ejpam-4022	70	10	2πi	2πi	ADJ
ejpam-4022	70	11	∫	∫	PROPN
ejpam-4022	71	1	c	c	PROPN
ejpam-4022	71	2	i2w−1aww−k−1qw/2	i2w−1aww−k−1qw/2	PROPN
ejpam-4022	71	3	csc(π(m+	csc(π(m+	PROPN
ejpam-4022	71	4	w	w	NOUN
ejpam-4022	71	5	)	)	PUNCT
ejpam-4022	71	6	)	)	PUNCT
ejpam-4022	72	1	sinh(x(m+	sinh(x(m+	NOUN
ejpam-4022	72	2	w))dw	w))dw	NOUN
ejpam-4022	72	3	from	from	ADP
ejpam-4022	72	4	equation	equation	NOUN
ejpam-4022	72	5	(	(	PUNCT
ejpam-4022	72	6	1.232.3	1.232.3	NUM
ejpam-4022	72	7	)	)	PUNCT
ejpam-4022	72	8	in	in	ADP
ejpam-4022	72	9	[	[	X
ejpam-4022	72	10	2	2	NUM
ejpam-4022	72	11	]	]	PUNCT
ejpam-4022	72	12	where	where	SCONJ
ejpam-4022	72	13	im(m	im(m	PUNCT
ejpam-4022	72	14	+	+	CCONJ
ejpam-4022	72	15	w	w	X
ejpam-4022	72	16	)	)	PUNCT
ejpam-4022	72	17	>	>	X
ejpam-4022	73	1	0	0	X
ejpam-4022	73	2	.	.	PUNCT
ejpam-4022	74	1	next	next	ADV
ejpam-4022	74	2	we	we	PRON
ejpam-4022	74	3	multiply	multiply	VERB
ejpam-4022	74	4	by	by	ADP
ejpam-4022	74	5	−	−	PROPN
ejpam-4022	74	6	iπ2m+2qm/2√	iπ2m+2qm/2√	NOUN
ejpam-4022	74	7	p2−q	p2−q	VERB
ejpam-4022	74	8	and	and	CCONJ
ejpam-4022	74	9	replace	replace	VERB
ejpam-4022	74	10	x	x	X
ejpam-4022	74	11	→	→	SYM
ejpam-4022	74	12	cosh−1	cosh−1	NOUN
ejpam-4022	74	13	(	(	PUNCT
ejpam-4022	74	14	p√	p√	X
ejpam-4022	74	15	q	q	X
ejpam-4022	74	16	)	)	PUNCT
ejpam-4022	74	17	simplifying	simplify	VERB
ejpam-4022	74	18	to	to	PART
ejpam-4022	74	19	get	get	VERB
ejpam-4022	74	20	s̄	s̄	NOUN
ejpam-4022	74	21	e	e	ADJ
ejpam-4022	74	22	2	2	NUM
ejpam-4022	74	23	m	m	NOUN
ejpam-4022	74	24	cosh−1	cosh−1	NOUN
ejpam-4022	74	25	(	(	PUNCT
ejpam-4022	74	26	p√	p√	PROPN
ejpam-4022	74	27	q	q	X
ejpam-4022	74	28	)	)	PUNCT
ejpam-4022	74	29	φ	φ	PROPN
ejpam-4022	74	30	e2imπ,−k,−	e2imπ,−k,−	ADP
ejpam-4022	74	31	2i	2i	PROPN
ejpam-4022	74	32	cosh−1	cosh−1	NOUN
ejpam-4022	74	33	(	(	PUNCT
ejpam-4022	74	34	p√	p√	X
ejpam-4022	74	35	q	q	X
ejpam-4022	74	36	)	)	PUNCT
ejpam-4022	75	1	+	+	CCONJ
ejpam-4022	75	2	2i	2i	NUM
ejpam-4022	75	3	log(2a	log(2a	ADJ
ejpam-4022	75	4	)	)	PUNCT
ejpam-4022	76	1	+	+	CCONJ
ejpam-4022	76	2	i	i	PRON
ejpam-4022	76	3	log(q)−	log(q)−	VERB
ejpam-4022	76	4	2π	2π	NOUN
ejpam-4022	76	5	4π	4π	NUM
ejpam-4022	76	6			PROPN
ejpam-4022	76	7	−	−	PROPN
ejpam-4022	76	8	φ	φ	NOUN
ejpam-4022	76	9	e2imπ,−k	e2imπ,−k	PROPN
ejpam-4022	76	10	,	,	PUNCT
ejpam-4022	76	11	2i	2i	NOUN
ejpam-4022	76	12	cosh−1	cosh−1	NOUN
ejpam-4022	76	13	(	(	PUNCT
ejpam-4022	76	14	p√	p√	X
ejpam-4022	76	15	q	q	PROPN
ejpam-4022	76	16	)	)	PUNCT
ejpam-4022	76	17	−	−	PROPN
ejpam-4022	76	18	2i	2i	NOUN
ejpam-4022	76	19	log(2a)−	log(2a)−	VERB
ejpam-4022	76	20	i	i	PRON
ejpam-4022	76	21	log(q	log(q	PROPN
ejpam-4022	76	22	)	)	PUNCT
ejpam-4022	76	23	+	+	NUM
ejpam-4022	76	24	2π	2π	NOUN
ejpam-4022	76	25	4π	4π	NUM
ejpam-4022	77	1			NOUN
ejpam-4022	77	2	=	=	SYM
ejpam-4022	77	3	1	1	NUM
ejpam-4022	77	4	2πi	2πi	NOUN
ejpam-4022	77	5	∫	∫	PROPN
ejpam-4022	78	1	c	c	PROPN
ejpam-4022	78	2	πaww−k−12m+w+1q	πaww−k−12m+w+1q	PROPN
ejpam-4022	78	3	m	m	VERB
ejpam-4022	78	4	2	2	NUM
ejpam-4022	78	5	+	+	NOUN
ejpam-4022	78	6	w	w	PROPN
ejpam-4022	78	7	2	2	NUM
ejpam-4022	78	8	csc(π(m+	csc(π(m+	NOUN
ejpam-4022	78	9	w	w	NOUN
ejpam-4022	78	10	)	)	PUNCT
ejpam-4022	78	11	)	)	PUNCT
ejpam-4022	78	12	sinh	sinh	NOUN
ejpam-4022	78	13	(	(	PUNCT
ejpam-4022	78	14	(	(	PUNCT
ejpam-4022	78	15	m+	m+	NUM
ejpam-4022	78	16	w	w	NOUN
ejpam-4022	78	17	)	)	PUNCT
ejpam-4022	78	18	cosh−1	cosh−1	NOUN
ejpam-4022	78	19	(	(	PUNCT
ejpam-4022	78	20	p√	p√	X
ejpam-4022	78	21	q	q	PROPN
ejpam-4022	78	22	)	)	PUNCT
ejpam-4022	78	23	)	)	PUNCT
ejpam-4022	79	1	√	√	PROPN
ejpam-4022	79	2	p2	p2	NOUN
ejpam-4022	80	1	−	−	PROPN
ejpam-4022	80	2	q	q	PROPN
ejpam-4022	80	3	dw	dw	PROPN
ejpam-4022	80	4	(	(	PUNCT
ejpam-4022	80	5	8)	8)	NUM
ejpam-4022	80	6	where	where	SCONJ
ejpam-4022	80	7	s̄	s̄	NOUN
ejpam-4022	80	8	=	=	PUNCT
ejpam-4022	80	9	−	−	PROPN
ejpam-4022	80	10	iπk+12k+m+1qm/2e	iπk+12k+m+1qm/2e	ADJ
ejpam-4022	80	11	−m	−m	NOUN
ejpam-4022	80	12	cosh−1	cosh−1	PROPN
ejpam-4022	80	13	(	(	PUNCT
ejpam-4022	80	14	p√	p√	PROPN
ejpam-4022	80	15	q	q	PROPN
ejpam-4022	80	16	)	)	PUNCT
ejpam-4022	80	17	+1	+1	PROPN
ejpam-4022	80	18	2	2	NUM
ejpam-4022	80	19	iπ(k+2	iπ(k+2	NOUN
ejpam-4022	80	20	m	m	NOUN
ejpam-4022	80	21	)	)	PUNCT
ejpam-4022	80	22	γ(k+1	γ(k+1	VERB
ejpam-4022	80	23	)	)	PUNCT
ejpam-4022	80	24	√	√	ADP
ejpam-4022	80	25	p2−q	p2−q	PROPN
ejpam-4022	80	26	.	.	PUNCT
ejpam-4022	81	1	r.	r.	PROPN
ejpam-4022	81	2	reynolds	reynolds	PROPN
ejpam-4022	81	3	,	,	PUNCT
ejpam-4022	81	4	a.	a.	PROPN
ejpam-4022	81	5	stauffer	stauffer	PROPN
ejpam-4022	81	6	/	/	SYM
ejpam-4022	81	7	eur	eur	PROPN
ejpam-4022	81	8	.	.	PUNCT
ejpam-4022	82	1	j.	j.	PROPN
ejpam-4022	82	2	pure	pure	PROPN
ejpam-4022	82	3	appl	appl	PROPN
ejpam-4022	82	4	.	.	PROPN
ejpam-4022	82	5	math	math	PROPN
ejpam-4022	82	6	,	,	PUNCT
ejpam-4022	82	7	14	14	NUM
ejpam-4022	82	8	(	(	PUNCT
ejpam-4022	82	9	4	4	NUM
ejpam-4022	82	10	)	)	PUNCT
ejpam-4022	82	11	(	(	PUNCT
ejpam-4022	82	12	2021	2021	NUM
ejpam-4022	82	13	)	)	PUNCT
ejpam-4022	82	14	,	,	PUNCT
ejpam-4022	82	15	1200	1200	NUM
ejpam-4022	82	16	-	-	SYM
ejpam-4022	82	17	1211	1211	NUM
ejpam-4022	82	18	1204	1204	NUM
ejpam-4022	82	19	6	6	NUM
ejpam-4022	82	20	.	.	PUNCT
ejpam-4022	82	21	double	double	ADJ
ejpam-4022	82	22	integral	integral	ADJ
ejpam-4022	82	23	in	in	ADP
ejpam-4022	82	24	terms	term	NOUN
ejpam-4022	82	25	of	of	ADP
ejpam-4022	82	26	the	the	DET
ejpam-4022	82	27	lerch	lerch	PROPN
ejpam-4022	82	28	function	function	PROPN
ejpam-4022	82	29	theorem	theorem	VERB
ejpam-4022	82	30	1	1	NUM
ejpam-4022	82	31	.	.	X
ejpam-4022	82	32	for	for	ADP
ejpam-4022	82	33	a	a	DET
ejpam-4022	82	34	,	,	PUNCT
ejpam-4022	82	35	p	p	X
ejpam-4022	82	36	,	,	PUNCT
ejpam-4022	82	37	q	q	PUNCT
ejpam-4022	82	38	∈	∈	PROPN
ejpam-4022	82	39	c	c	NOUN
ejpam-4022	82	40	,	,	PUNCT
ejpam-4022	82	41	im(k	im(k	NUM
ejpam-4022	82	42	)	)	PUNCT
ejpam-4022	82	43	≤	≤	PUNCT
ejpam-4022	83	1	0,−1	0,−1	PROPN
ejpam-4022	83	2	<	<	X
ejpam-4022	83	3	re(m	re(m	X
ejpam-4022	83	4	)	)	PUNCT
ejpam-4022	83	5	≤	≤	NOUN
ejpam-4022	83	6	−1/2,−1	−1/2,−1	ADV
ejpam-4022	83	7	<	<	X
ejpam-4022	83	8	im(m	im(m	NOUN
ejpam-4022	83	9	)	)	PUNCT
ejpam-4022	84	1	<	<	X
ejpam-4022	85	1	−1/2	−1/2	ADJ
ejpam-4022	85	2	,	,	PUNCT
ejpam-4022	85	3	(	(	PUNCT
ejpam-4022	85	4	9	9	NUM
ejpam-4022	85	5	)	)	PUNCT
ejpam-4022	85	6	∫	∫	PROPN
ejpam-4022	86	1	∞	∞	PROPN
ejpam-4022	86	2	0	0	NUM
ejpam-4022	86	3	∫	∫	PROPN
ejpam-4022	86	4	∞	∞	NOUN
ejpam-4022	86	5	0	0	NUM
ejpam-4022	87	1	xmy−m−1e	xmy−m−1e	PROPN
ejpam-4022	87	2	−px−qy−x2	−px−qy−x2	VERB
ejpam-4022	87	3	4y	4y	NUM
ejpam-4022	87	4	logk	logk	NOUN
ejpam-4022	87	5	(	(	PUNCT
ejpam-4022	87	6	ax	ax	NOUN
ejpam-4022	87	7	y	y	PROPN
ejpam-4022	87	8	)	)	PUNCT
ejpam-4022	87	9	dxdy	dxdy	PROPN
ejpam-4022	87	10	=	=	SYM
ejpam-4022	87	11	r̄	r̄	NOUN
ejpam-4022	87	12	e	e	ADJ
ejpam-4022	87	13	2	2	NUM
ejpam-4022	87	14	m	m	NOUN
ejpam-4022	87	15	cosh−1	cosh−1	NOUN
ejpam-4022	87	16	(	(	PUNCT
ejpam-4022	87	17	p√	p√	PROPN
ejpam-4022	87	18	q	q	X
ejpam-4022	87	19	)	)	PUNCT
ejpam-4022	87	20	φ	φ	PROPN
ejpam-4022	87	21	e2imπ,−k,−	e2imπ,−k,−	ADP
ejpam-4022	87	22	2i	2i	PROPN
ejpam-4022	87	23	cosh−1	cosh−1	NOUN
ejpam-4022	87	24	(	(	PUNCT
ejpam-4022	87	25	p√	p√	X
ejpam-4022	87	26	q	q	X
ejpam-4022	87	27	)	)	PUNCT
ejpam-4022	88	1	+	+	CCONJ
ejpam-4022	88	2	2i	2i	NUM
ejpam-4022	88	3	log(2a	log(2a	ADJ
ejpam-4022	88	4	)	)	PUNCT
ejpam-4022	89	1	+	+	CCONJ
ejpam-4022	89	2	i	i	PRON
ejpam-4022	89	3	log(q)−	log(q)−	VERB
ejpam-4022	89	4	2π	2π	NOUN
ejpam-4022	89	5	4π	4π	NUM
ejpam-4022	89	6			PROPN
ejpam-4022	89	7	−	−	PROPN
ejpam-4022	89	8	φ	φ	NOUN
ejpam-4022	89	9	e2imπ,−k	e2imπ,−k	PROPN
ejpam-4022	89	10	,	,	PUNCT
ejpam-4022	89	11	2i	2i	NOUN
ejpam-4022	89	12	cosh−1	cosh−1	NOUN
ejpam-4022	89	13	(	(	PUNCT
ejpam-4022	89	14	p√	p√	X
ejpam-4022	89	15	q	q	PROPN
ejpam-4022	89	16	)	)	PUNCT
ejpam-4022	89	17	−	−	PROPN
ejpam-4022	89	18	2i	2i	NOUN
ejpam-4022	89	19	log(2a)−	log(2a)−	VERB
ejpam-4022	89	20	i	i	PRON
ejpam-4022	89	21	log(q	log(q	PROPN
ejpam-4022	89	22	)	)	PUNCT
ejpam-4022	89	23	+	+	NUM
ejpam-4022	89	24	2π	2π	NOUN
ejpam-4022	89	25	4π	4π	NUM
ejpam-4022	90	1			PROPN
ejpam-4022	90	2	where	where	SCONJ
ejpam-4022	90	3	r̄	r̄	NOUN
ejpam-4022	90	4	=	=	PUNCT
ejpam-4022	90	5	γ(k	γ(k	PROPN
ejpam-4022	90	6	+	+	CCONJ
ejpam-4022	90	7	1)s̄	1)s̄	NUM
ejpam-4022	90	8	=	=	SYM
ejpam-4022	90	9	−	−	PROPN
ejpam-4022	90	10	iπk+12k+m+1qm/2e	iπk+12k+m+1qm/2e	PROPN
ejpam-4022	90	11	−m	−m	NOUN
ejpam-4022	90	12	cosh−1	cosh−1	PROPN
ejpam-4022	90	13	(	(	PUNCT
ejpam-4022	90	14	p√	p√	PROPN
ejpam-4022	90	15	q	q	PROPN
ejpam-4022	90	16	)	)	PUNCT
ejpam-4022	90	17	+1	+1	PROPN
ejpam-4022	90	18	2	2	NUM
ejpam-4022	90	19	iπ(k+2	iπ(k+2	NOUN
ejpam-4022	90	20	m	m	NOUN
ejpam-4022	90	21	)	)	PUNCT
ejpam-4022	90	22	√	√	ADP
ejpam-4022	90	23	p2−q	p2−q	PROPN
ejpam-4022	90	24	proof	proof	NOUN
ejpam-4022	90	25	.	.	PUNCT
ejpam-4022	91	1	since	since	SCONJ
ejpam-4022	91	2	the	the	DET
ejpam-4022	91	3	right	right	ADJ
ejpam-4022	91	4	-	-	PUNCT
ejpam-4022	91	5	hand	hand	NOUN
ejpam-4022	91	6	sides	side	NOUN
ejpam-4022	91	7	of	of	ADP
ejpam-4022	91	8	equations	equation	NOUN
ejpam-4022	91	9	(	(	PUNCT
ejpam-4022	91	10	3	3	NUM
ejpam-4022	91	11	)	)	PUNCT
ejpam-4022	91	12	and	and	CCONJ
ejpam-4022	91	13	(	(	PUNCT
ejpam-4022	91	14	8)	8)	NUM
ejpam-4022	91	15	are	be	AUX
ejpam-4022	91	16	equal	equal	ADJ
ejpam-4022	91	17	we	we	PRON
ejpam-4022	91	18	can	can	AUX
ejpam-4022	91	19	equate	equate	VERB
ejpam-4022	91	20	the	the	DET
ejpam-4022	91	21	left	left	ADJ
ejpam-4022	91	22	-	-	PUNCT
ejpam-4022	91	23	hand	hand	NOUN
ejpam-4022	91	24	sides	side	NOUN
ejpam-4022	91	25	and	and	CCONJ
ejpam-4022	91	26	simplify	simplify	VERB
ejpam-4022	91	27	the	the	DET
ejpam-4022	91	28	gamma	gamma	NOUN
ejpam-4022	91	29	function	function	NOUN
ejpam-4022	91	30	to	to	PART
ejpam-4022	91	31	get	get	VERB
ejpam-4022	91	32	the	the	DET
ejpam-4022	91	33	stated	state	VERB
ejpam-4022	91	34	result	result	NOUN
ejpam-4022	91	35	.	.	PUNCT
ejpam-4022	92	1	main	main	ADJ
ejpam-4022	92	2	results	result	NOUN
ejpam-4022	92	3	in	in	ADP
ejpam-4022	92	4	this	this	DET
ejpam-4022	92	5	section	section	NOUN
ejpam-4022	92	6	we	we	PRON
ejpam-4022	92	7	will	will	AUX
ejpam-4022	92	8	present	present	VERB
ejpam-4022	92	9	evaluations	evaluation	NOUN
ejpam-4022	92	10	of	of	ADP
ejpam-4022	92	11	equation	equation	NOUN
ejpam-4022	92	12	(	(	PUNCT
ejpam-4022	92	13	9	9	NUM
ejpam-4022	92	14	)	)	PUNCT
ejpam-4022	92	15	when	when	SCONJ
ejpam-4022	92	16	k	k	PROPN
ejpam-4022	92	17	is	be	AUX
ejpam-4022	92	18	a	a	DET
ejpam-4022	92	19	positive	positive	ADJ
ejpam-4022	92	20	integer	integer	NOUN
ejpam-4022	92	21	and	and	CCONJ
ejpam-4022	92	22	when	when	SCONJ
ejpam-4022	92	23	k	k	PROPN
ejpam-4022	92	24	is	be	AUX
ejpam-4022	92	25	otherwise	otherwise	ADV
ejpam-4022	92	26	.	.	PUNCT
ejpam-4022	93	1	when	when	SCONJ
ejpam-4022	93	2	k	k	PROPN
ejpam-4022	93	3	is	be	AUX
ejpam-4022	93	4	a	a	DET
ejpam-4022	93	5	positive	positive	ADJ
ejpam-4022	93	6	integer	integer	NOUN
ejpam-4022	93	7	the	the	DET
ejpam-4022	93	8	kernel	kernel	NOUN
ejpam-4022	93	9	reduces	reduce	VERB
ejpam-4022	93	10	to	to	ADP
ejpam-4022	93	11	the	the	DET
ejpam-4022	93	12	laplace	laplace	NOUN
ejpam-4022	93	13	transform	transform	NOUN
ejpam-4022	93	14	of	of	ADP
ejpam-4022	93	15	the	the	DET
ejpam-4022	93	16	modified	modify	VERB
ejpam-4022	93	17	bessel	bessel	NOUN
ejpam-4022	93	18	function	function	NOUN
ejpam-4022	93	19	of	of	ADP
ejpam-4022	93	20	the	the	DET
ejpam-4022	93	21	second	second	ADJ
ejpam-4022	93	22	kind	kind	NOUN
ejpam-4022	93	23	kν(z	kν(z	NOUN
ejpam-4022	93	24	)	)	PUNCT
ejpam-4022	93	25	.	.	PUNCT
ejpam-4022	94	1	examples	example	NOUN
ejpam-4022	94	2	of	of	ADP
ejpam-4022	94	3	these	these	DET
ejpam-4022	94	4	evaluations	evaluation	NOUN
ejpam-4022	94	5	are	be	AUX
ejpam-4022	94	6	7	7	NUM
ejpam-4022	94	7	.	.	PUNCT
ejpam-4022	95	1	derivation	derivation	NOUN
ejpam-4022	95	2	of	of	ADP
ejpam-4022	95	3	entry	entry	NOUN
ejpam-4022	95	4	3.1.3.48	3.1.3.48	NUM
ejpam-4022	95	5	in	in	ADP
ejpam-4022	95	6	[	[	X
ejpam-4022	95	7	6	6	NUM
ejpam-4022	95	8	]	]	PUNCT
ejpam-4022	95	9	theorem	theorem	NOUN
ejpam-4022	95	10	2	2	NUM
ejpam-4022	95	11	.	.	PUNCT
ejpam-4022	95	12	for	for	ADP
ejpam-4022	95	13	p	p	NOUN
ejpam-4022	95	14	,	,	PUNCT
ejpam-4022	95	15	q	q	NOUN
ejpam-4022	95	16	∈	∈	PROPN
ejpam-4022	95	17	c,−1	c,−1	NOUN
ejpam-4022	95	18	<	<	X
ejpam-4022	95	19	re(m	re(m	NOUN
ejpam-4022	95	20	)	)	PUNCT
ejpam-4022	95	21	≤	≤	NOUN
ejpam-4022	95	22	−1/2,−1	−1/2,−1	ADV
ejpam-4022	95	23	<	<	X
ejpam-4022	95	24	im(m	im(m	NOUN
ejpam-4022	95	25	)	)	PUNCT
ejpam-4022	95	26	<	<	X
ejpam-4022	96	1	−1/2	−1/2	ADJ
ejpam-4022	96	2	,	,	PUNCT
ejpam-4022	96	3	(	(	PUNCT
ejpam-4022	96	4	10	10	NUM
ejpam-4022	96	5	)	)	PUNCT
ejpam-4022	96	6	∫	∫	PROPN
ejpam-4022	97	1	∞	∞	PROPN
ejpam-4022	97	2	0	0	NUM
ejpam-4022	97	3	∫	∫	PROPN
ejpam-4022	97	4	∞	∞	NOUN
ejpam-4022	97	5	0	0	NUM
ejpam-4022	98	1	xmy−m−1e	xmy−m−1e	PROPN
ejpam-4022	98	2	−px−qy−x2	−px−qy−x2	VERB
ejpam-4022	98	3	4y	4y	PROPN
ejpam-4022	98	4	dxdy	dxdy	NOUN
ejpam-4022	98	5	=	=	SYM
ejpam-4022	98	6	π2m+1qm/2	π2m+1qm/2	PROPN
ejpam-4022	98	7	csc(πm	csc(πm	NOUN
ejpam-4022	98	8	)	)	PUNCT
ejpam-4022	98	9	sinh	sinh	NOUN
ejpam-4022	98	10	(	(	PUNCT
ejpam-4022	98	11	m	m	NOUN
ejpam-4022	98	12	cosh−1	cosh−1	NOUN
ejpam-4022	98	13	(	(	PUNCT
ejpam-4022	98	14	p√	p√	PROPN
ejpam-4022	98	15	q	q	PROPN
ejpam-4022	98	16	)	)	PUNCT
ejpam-4022	98	17	)	)	PUNCT
ejpam-4022	99	1	√	√	PROPN
ejpam-4022	100	1	p2	p2	NOUN
ejpam-4022	101	1	−	−	NOUN
ejpam-4022	101	2	q	q	NOUN
ejpam-4022	101	3	proof	proof	NOUN
ejpam-4022	101	4	.	.	PUNCT
ejpam-4022	102	1	use	use	VERB
ejpam-4022	102	2	equation	equation	NOUN
ejpam-4022	102	3	(	(	PUNCT
ejpam-4022	102	4	9	9	NUM
ejpam-4022	102	5	)	)	PUNCT
ejpam-4022	102	6	and	and	CCONJ
ejpam-4022	102	7	set	set	VERB
ejpam-4022	102	8	k	k	PROPN
ejpam-4022	102	9	=	=	PUNCT
ejpam-4022	102	10	0	0	PUNCT
ejpam-4022	102	11	and	and	CCONJ
ejpam-4022	102	12	simplify	simplify	VERB
ejpam-4022	102	13	using	use	VERB
ejpam-4022	102	14	entry	entry	NOUN
ejpam-4022	102	15	(	(	PUNCT
ejpam-4022	102	16	2	2	NUM
ejpam-4022	102	17	)	)	PUNCT
ejpam-4022	102	18	in	in	ADP
ejpam-4022	102	19	table	table	NOUN
ejpam-4022	102	20	below	below	ADV
ejpam-4022	102	21	(	(	PUNCT
ejpam-4022	102	22	64:12:7	64:12:7	NUM
ejpam-4022	102	23	)	)	PUNCT
ejpam-4022	102	24	in	in	ADP
ejpam-4022	102	25	[	[	X
ejpam-4022	102	26	5	5	NUM
ejpam-4022	102	27	]	]	PUNCT
ejpam-4022	102	28	.	.	PUNCT
ejpam-4022	103	1	8	8	X
ejpam-4022	103	2	.	.	X
ejpam-4022	103	3	derivation	derivation	NOUN
ejpam-4022	103	4	of	of	ADP
ejpam-4022	103	5	new	new	ADJ
ejpam-4022	103	6	entry	entry	NOUN
ejpam-4022	103	7	3.1.3.59	3.1.3.59	NUM
ejpam-4022	103	8	in	in	ADP
ejpam-4022	103	9	[	[	X
ejpam-4022	103	10	6	6	NUM
ejpam-4022	103	11	]	]	PUNCT
ejpam-4022	103	12	in	in	ADP
ejpam-4022	103	13	this	this	DET
ejpam-4022	103	14	example	example	NOUN
ejpam-4022	103	15	we	we	PRON
ejpam-4022	103	16	look	look	VERB
ejpam-4022	103	17	at	at	ADP
ejpam-4022	103	18	a	a	DET
ejpam-4022	103	19	double	double	ADJ
ejpam-4022	103	20	integral	integral	NOUN
ejpam-4022	103	21	where	where	SCONJ
ejpam-4022	103	22	the	the	DET
ejpam-4022	103	23	kernel	kernel	NOUN
ejpam-4022	103	24	involves	involve	VERB
ejpam-4022	103	25	the	the	DET
ejpam-4022	103	26	modified	modify	VERB
ejpam-4022	103	27	bessel	bessel	NOUN
ejpam-4022	103	28	function	function	NOUN
ejpam-4022	103	29	of	of	ADP
ejpam-4022	103	30	the	the	DET
ejpam-4022	103	31	second	second	ADJ
ejpam-4022	103	32	kind	kind	NOUN
ejpam-4022	103	33	kν(z	kν(z	NOUN
ejpam-4022	103	34	)	)	PUNCT
ejpam-4022	103	35	and	and	CCONJ
ejpam-4022	103	36	its	its	PRON
ejpam-4022	103	37	first	first	ADJ
ejpam-4022	103	38	partial	partial	ADJ
ejpam-4022	103	39	derivative	derivative	ADJ
ejpam-4022	103	40	∂	∂	NUM
ejpam-4022	103	41	∂νkν(z	∂νkν(z	NOUN
ejpam-4022	103	42	)	)	PUNCT
ejpam-4022	103	43	and	and	CCONJ
ejpam-4022	103	44	express	express	VERB
ejpam-4022	103	45	it	it	PRON
ejpam-4022	103	46	in	in	ADP
ejpam-4022	103	47	terms	term	NOUN
ejpam-4022	103	48	of	of	ADP
ejpam-4022	103	49	elementary	elementary	ADJ
ejpam-4022	103	50	functions	function	NOUN
ejpam-4022	103	51	.	.	PUNCT
ejpam-4022	104	1	r.	r.	PROPN
ejpam-4022	104	2	reynolds	reynolds	PROPN
ejpam-4022	104	3	,	,	PUNCT
ejpam-4022	104	4	a.	a.	PROPN
ejpam-4022	104	5	stauffer	stauffer	PROPN
ejpam-4022	104	6	/	/	SYM
ejpam-4022	104	7	eur	eur	PROPN
ejpam-4022	104	8	.	.	PUNCT
ejpam-4022	105	1	j.	j.	PROPN
ejpam-4022	105	2	pure	pure	PROPN
ejpam-4022	105	3	appl	appl	PROPN
ejpam-4022	105	4	.	.	PROPN
ejpam-4022	105	5	math	math	PROPN
ejpam-4022	105	6	,	,	PUNCT
ejpam-4022	105	7	14	14	NUM
ejpam-4022	105	8	(	(	PUNCT
ejpam-4022	105	9	4	4	NUM
ejpam-4022	105	10	)	)	PUNCT
ejpam-4022	105	11	(	(	PUNCT
ejpam-4022	105	12	2021	2021	NUM
ejpam-4022	105	13	)	)	PUNCT
ejpam-4022	105	14	,	,	PUNCT
ejpam-4022	105	15	1200	1200	NUM
ejpam-4022	105	16	-	-	SYM
ejpam-4022	105	17	1211	1211	NUM
ejpam-4022	105	18	1205	1205	NUM
ejpam-4022	105	19	theorem	theorem	NOUN
ejpam-4022	105	20	3	3	NUM
ejpam-4022	105	21	.	.	X
ejpam-4022	106	1	for	for	ADP
ejpam-4022	106	2	p	p	NOUN
ejpam-4022	106	3	,	,	PUNCT
ejpam-4022	106	4	q	q	NOUN
ejpam-4022	106	5	∈	∈	PROPN
ejpam-4022	106	6	c,−1	c,−1	NOUN
ejpam-4022	106	7	<	<	X
ejpam-4022	106	8	re(m	re(m	NOUN
ejpam-4022	106	9	)	)	PUNCT
ejpam-4022	106	10	≤	≤	NOUN
ejpam-4022	106	11	−1/2,−1	−1/2,−1	ADV
ejpam-4022	106	12	<	<	X
ejpam-4022	106	13	im(m	im(m	NOUN
ejpam-4022	106	14	)	)	PUNCT
ejpam-4022	106	15	<	<	X
ejpam-4022	107	1	−1/2,∫	−1/2,∫	X
ejpam-4022	107	2	∞	∞	PROPN
ejpam-4022	107	3	0	0	NUM
ejpam-4022	107	4	∫	∫	PROPN
ejpam-4022	107	5	∞	∞	PROPN
ejpam-4022	107	6	0	0	PROPN
ejpam-4022	107	7	xmy−m−1	xmy−m−1	PROPN
ejpam-4022	107	8	log	log	NOUN
ejpam-4022	107	9	(	(	PUNCT
ejpam-4022	107	10	ax	ax	NOUN
ejpam-4022	107	11	y	y	PROPN
ejpam-4022	107	12	)	)	PUNCT
ejpam-4022	107	13	e	e	PROPN
ejpam-4022	107	14	−px−qy−x2	−px−qy−x2	PROPN
ejpam-4022	107	15	4y	4y	PROPN
ejpam-4022	107	16	dxdy	dxdy	NOUN
ejpam-4022	107	17	=	=	PUNCT
ejpam-4022	107	18	−π2mqm/2	−π2mqm/2	X
ejpam-4022	107	19	csc(πm)√	csc(πm)√	ADJ
ejpam-4022	107	20	p2	p2	NOUN
ejpam-4022	108	1	−	−	PROPN
ejpam-4022	108	2	q	q	NOUN
ejpam-4022	109	1	(	(	PUNCT
ejpam-4022	109	2	(	(	PUNCT
ejpam-4022	109	3	−2	−2	PROPN
ejpam-4022	109	4	log(a	log(a	PROPN
ejpam-4022	109	5	)	)	PUNCT
ejpam-4022	110	1	+	+	NUM
ejpam-4022	110	2	2π	2π	PROPN
ejpam-4022	110	3	cot(πm)−	cot(πm)−	NOUN
ejpam-4022	110	4	log(4q	log(4q	ADJ
ejpam-4022	110	5	)	)	PUNCT
ejpam-4022	110	6	)	)	PUNCT
ejpam-4022	111	1	sinh	sinh	NOUN
ejpam-4022	111	2	(	(	PUNCT
ejpam-4022	111	3	m	m	NOUN
ejpam-4022	111	4	cosh−1	cosh−1	NOUN
ejpam-4022	111	5	(	(	PUNCT
ejpam-4022	111	6	p	p	NOUN
ejpam-4022	111	7	√	√	PROPN
ejpam-4022	111	8	q	q	NOUN
ejpam-4022	111	9	)	)	PUNCT
ejpam-4022	111	10	)	)	PUNCT
ejpam-4022	112	1	−	−	ADP
ejpam-4022	112	2	2	2	NUM
ejpam-4022	112	3	cosh−1	cosh−1	PROPN
ejpam-4022	112	4	(	(	PUNCT
ejpam-4022	112	5	p	p	NOUN
ejpam-4022	112	6	√	√	PROPN
ejpam-4022	112	7	q	q	NOUN
ejpam-4022	112	8	)	)	PUNCT
ejpam-4022	112	9	cosh	cosh	NOUN
ejpam-4022	112	10	(	(	PUNCT
ejpam-4022	112	11	m	m	NOUN
ejpam-4022	112	12	cosh−1	cosh−1	NOUN
ejpam-4022	112	13	(	(	PUNCT
ejpam-4022	112	14	p	p	NOUN
ejpam-4022	112	15	√	√	PROPN
ejpam-4022	112	16	q	q	NOUN
ejpam-4022	112	17	)	)	PUNCT
ejpam-4022	112	18	)	)	PUNCT
ejpam-4022	112	19	)	)	PUNCT
ejpam-4022	112	20	(	(	PUNCT
ejpam-4022	112	21	11	11	X
ejpam-4022	112	22	)	)	PUNCT
ejpam-4022	112	23	proof	proof	NOUN
ejpam-4022	112	24	.	.	PUNCT
ejpam-4022	113	1	use	use	VERB
ejpam-4022	113	2	equation	equation	NOUN
ejpam-4022	113	3	(	(	PUNCT
ejpam-4022	113	4	9	9	NUM
ejpam-4022	113	5	)	)	PUNCT
ejpam-4022	113	6	and	and	CCONJ
ejpam-4022	113	7	set	set	VERB
ejpam-4022	113	8	k	k	PROPN
ejpam-4022	113	9	=	=	SYM
ejpam-4022	113	10	1	1	NUM
ejpam-4022	113	11	and	and	CCONJ
ejpam-4022	113	12	simplify	simplify	VERB
ejpam-4022	113	13	using	use	VERB
ejpam-4022	113	14	entry	entry	NOUN
ejpam-4022	113	15	(	(	PUNCT
ejpam-4022	113	16	1	1	NUM
ejpam-4022	113	17	)	)	PUNCT
ejpam-4022	113	18	in	in	ADP
ejpam-4022	113	19	table	table	NOUN
ejpam-4022	113	20	below	below	ADV
ejpam-4022	113	21	(	(	PUNCT
ejpam-4022	113	22	64:12:7	64:12:7	NUM
ejpam-4022	113	23	)	)	PUNCT
ejpam-4022	113	24	in	in	ADP
ejpam-4022	113	25	[	[	X
ejpam-4022	113	26	5	5	NUM
ejpam-4022	113	27	]	]	PUNCT
ejpam-4022	113	28	and	and	CCONJ
ejpam-4022	113	29	equation	equation	NOUN
ejpam-4022	113	30	(	(	PUNCT
ejpam-4022	113	31	11.125	11.125	NUM
ejpam-4022	113	32	)	)	PUNCT
ejpam-4022	113	33	in	in	ADP
ejpam-4022	113	34	[	[	X
ejpam-4022	113	35	1	1	NUM
ejpam-4022	113	36	]	]	PUNCT
ejpam-4022	113	37	.	.	PUNCT
ejpam-4022	114	1	9	9	X
ejpam-4022	114	2	.	.	X
ejpam-4022	114	3	derivation	derivation	NOUN
ejpam-4022	114	4	of	of	ADP
ejpam-4022	114	5	new	new	ADJ
ejpam-4022	114	6	entry	entry	NOUN
ejpam-4022	114	7	3.1.3.60	3.1.3.60	NUM
ejpam-4022	114	8	in	in	ADP
ejpam-4022	114	9	[	[	X
ejpam-4022	114	10	6	6	NUM
ejpam-4022	114	11	]	]	PUNCT
ejpam-4022	114	12	in	in	ADP
ejpam-4022	114	13	this	this	DET
ejpam-4022	114	14	example	example	NOUN
ejpam-4022	114	15	we	we	PRON
ejpam-4022	114	16	look	look	VERB
ejpam-4022	114	17	at	at	ADP
ejpam-4022	114	18	the	the	DET
ejpam-4022	114	19	laplace	laplace	NOUN
ejpam-4022	114	20	transform	transform	NOUN
ejpam-4022	114	21	of	of	ADP
ejpam-4022	114	22	the	the	DET
ejpam-4022	114	23	first	first	ADJ
ejpam-4022	114	24	partial	partial	ADJ
ejpam-4022	114	25	derivative	derivative	NOUN
ejpam-4022	114	26	with	with	ADP
ejpam-4022	114	27	respect	respect	NOUN
ejpam-4022	114	28	to	to	ADP
ejpam-4022	114	29	ν	ν	NOUN
ejpam-4022	114	30	of	of	ADP
ejpam-4022	114	31	the	the	DET
ejpam-4022	114	32	modified	modify	VERB
ejpam-4022	114	33	bessel	bessel	NOUN
ejpam-4022	114	34	function	function	NOUN
ejpam-4022	114	35	of	of	ADP
ejpam-4022	114	36	the	the	DET
ejpam-4022	114	37	second	second	ADJ
ejpam-4022	114	38	kind	kind	NOUN
ejpam-4022	114	39	kν(x	kν(x	PROPN
ejpam-4022	114	40	)	)	PUNCT
ejpam-4022	114	41	where	where	SCONJ
ejpam-4022	114	42	ν	ν	X
ejpam-4022	114	43	=	=	SYM
ejpam-4022	114	44	−1/2	−1/2	ADJ
ejpam-4022	114	45	,	,	PUNCT
ejpam-4022	114	46	x	x	X
ejpam-4022	114	47	=	=	PUNCT
ejpam-4022	114	48	x/2	x/2	NUM
ejpam-4022	114	49	.	.	PUNCT
ejpam-4022	115	1	details	detail	NOUN
ejpam-4022	115	2	about	about	ADP
ejpam-4022	115	3	this	this	DET
ejpam-4022	115	4	function	function	NOUN
ejpam-4022	115	5	are	be	AUX
ejpam-4022	115	6	listed	list	VERB
ejpam-4022	115	7	in	in	ADP
ejpam-4022	115	8	equation	equation	NOUN
ejpam-4022	115	9	(	(	PUNCT
ejpam-4022	115	10	51:4:1	51:4:1	NUM
ejpam-4022	115	11	)	)	PUNCT
ejpam-4022	115	12	in	in	ADP
ejpam-4022	115	13	[	[	X
ejpam-4022	115	14	5	5	NUM
ejpam-4022	115	15	]	]	PUNCT
ejpam-4022	115	16	and	and	CCONJ
ejpam-4022	115	17	equation	equation	NOUN
ejpam-4022	115	18	(	(	PUNCT
ejpam-4022	115	19	11.123a	11.123a	NOUN
ejpam-4022	115	20	)	)	PUNCT
ejpam-4022	115	21	in	in	ADP
ejpam-4022	115	22	[	[	X
ejpam-4022	115	23	1	1	NUM
ejpam-4022	115	24	]	]	PUNCT
ejpam-4022	115	25	.	.	PUNCT
ejpam-4022	116	1	proposition	proposition	NOUN
ejpam-4022	116	2	1	1	NUM
ejpam-4022	116	3	.	.	PUNCT
ejpam-4022	117	1	(	(	PUNCT
ejpam-4022	117	2	12	12	NUM
ejpam-4022	117	3	)	)	PUNCT
ejpam-4022	117	4	∫	∫	PROPN
ejpam-4022	118	1	∞	∞	PROPN
ejpam-4022	118	2	0	0	NUM
ejpam-4022	118	3	∫	∫	PROPN
ejpam-4022	118	4	∞	∞	NOUN
ejpam-4022	118	5	0	0	PUNCT
ejpam-4022	119	1	e	e	X
ejpam-4022	119	2	−x2	−x2	PROPN
ejpam-4022	119	3	+	+	NOUN
ejpam-4022	119	4	4xy+y2	4xy+y2	NOUN
ejpam-4022	119	5	4y	4y	NUM
ejpam-4022	119	6	log	log	NOUN
ejpam-4022	119	7	(	(	PUNCT
ejpam-4022	119	8	x	x	NOUN
ejpam-4022	119	9	y	y	PROPN
ejpam-4022	119	10	)	)	PUNCT
ejpam-4022	119	11	√	√	PROPN
ejpam-4022	120	1	x	x	SYM
ejpam-4022	120	2	√	√	NUM
ejpam-4022	120	3	y	y	PROPN
ejpam-4022	120	4	dxdy	dxdy	PROPN
ejpam-4022	120	5	=	=	PUNCT
ejpam-4022	120	6	−2	−2	PROPN
ejpam-4022	120	7	√	√	PROPN
ejpam-4022	120	8	2π	2π	NUM
ejpam-4022	120	9	cosh−1(2	cosh−1(2	PROPN
ejpam-4022	120	10	)	)	PUNCT
ejpam-4022	120	11	proof	proof	NOUN
ejpam-4022	120	12	.	.	PUNCT
ejpam-4022	121	1	use	use	VERB
ejpam-4022	121	2	equation	equation	NOUN
ejpam-4022	121	3	(	(	PUNCT
ejpam-4022	121	4	9	9	NUM
ejpam-4022	121	5	)	)	PUNCT
ejpam-4022	121	6	and	and	CCONJ
ejpam-4022	121	7	set	set	VERB
ejpam-4022	121	8	m	m	PROPN
ejpam-4022	121	9	=	=	SYM
ejpam-4022	121	10	−1/2	−1/2	ADJ
ejpam-4022	121	11	,	,	PUNCT
ejpam-4022	121	12	a	a	DET
ejpam-4022	121	13	=	=	SYM
ejpam-4022	121	14	1	1	NUM
ejpam-4022	121	15	and	and	CCONJ
ejpam-4022	121	16	simplify	simplify	VERB
ejpam-4022	121	17	in	in	ADP
ejpam-4022	121	18	terms	term	NOUN
ejpam-4022	121	19	of	of	ADP
ejpam-4022	121	20	the	the	DET
ejpam-4022	121	21	hurwitz	hurwitz	PROPN
ejpam-4022	121	22	zeta	zeta	PROPN
ejpam-4022	121	23	function	function	NOUN
ejpam-4022	121	24	using	use	VERB
ejpam-4022	121	25	entry	entry	NOUN
ejpam-4022	121	26	(	(	PUNCT
ejpam-4022	121	27	4	4	NUM
ejpam-4022	121	28	)	)	PUNCT
ejpam-4022	121	29	in	in	ADP
ejpam-4022	121	30	table	table	NOUN
ejpam-4022	121	31	below	below	ADV
ejpam-4022	121	32	(	(	PUNCT
ejpam-4022	121	33	64:12:7	64:12:7	NUM
ejpam-4022	121	34	)	)	PUNCT
ejpam-4022	121	35	in	in	ADP
ejpam-4022	121	36	[	[	X
ejpam-4022	121	37	5	5	NUM
ejpam-4022	121	38	]	]	PUNCT
ejpam-4022	121	39	.	.	PUNCT
ejpam-4022	122	1	next	next	ADJ
ejpam-4022	122	2	set	set	VERB
ejpam-4022	122	3	k	k	PROPN
ejpam-4022	123	1	=	=	PUNCT
ejpam-4022	123	2	p	p	NOUN
ejpam-4022	123	3	=	=	SYM
ejpam-4022	123	4	1	1	NUM
ejpam-4022	123	5	,	,	PUNCT
ejpam-4022	123	6	q	q	NOUN
ejpam-4022	123	7	=	=	SYM
ejpam-4022	123	8	1/4	1/4	NUM
ejpam-4022	123	9	and	and	CCONJ
ejpam-4022	123	10	simplify	simplify	VERB
ejpam-4022	123	11	using	use	VERB
ejpam-4022	123	12	entry	entry	NOUN
ejpam-4022	123	13	(	(	PUNCT
ejpam-4022	123	14	2	2	NUM
ejpam-4022	123	15	)	)	PUNCT
ejpam-4022	123	16	in	in	ADP
ejpam-4022	123	17	table	table	NOUN
ejpam-4022	123	18	below	below	ADV
ejpam-4022	123	19	(	(	PUNCT
ejpam-4022	123	20	64:4:1	64:4:1	NUM
ejpam-4022	123	21	)	)	PUNCT
ejpam-4022	123	22	in	in	ADP
ejpam-4022	123	23	[	[	X
ejpam-4022	123	24	5	5	NUM
ejpam-4022	123	25	]	]	PUNCT
ejpam-4022	123	26	.	.	PUNCT
ejpam-4022	124	1	10	10	NUM
ejpam-4022	124	2	.	.	PUNCT
ejpam-4022	125	1	derivation	derivation	NOUN
ejpam-4022	125	2	of	of	ADP
ejpam-4022	125	3	new	new	ADJ
ejpam-4022	125	4	entry	entry	NOUN
ejpam-4022	125	5	3.1.3.61	3.1.3.61	NOUN
ejpam-4022	125	6	in	in	ADP
ejpam-4022	125	7	[	[	X
ejpam-4022	125	8	6	6	NUM
ejpam-4022	125	9	]	]	PUNCT
ejpam-4022	125	10	proposition	proposition	NOUN
ejpam-4022	125	11	2	2	NUM
ejpam-4022	125	12	.	.	PUNCT
ejpam-4022	126	1	(	(	PUNCT
ejpam-4022	126	2	13	13	NUM
ejpam-4022	126	3	)	)	PUNCT
ejpam-4022	126	4	∫	∫	PROPN
ejpam-4022	127	1	∞	∞	PROPN
ejpam-4022	127	2	0	0	NUM
ejpam-4022	128	1	∫	∫	PROPN
ejpam-4022	128	2	∞	∞	NOUN
ejpam-4022	128	3	0	0	PUNCT
ejpam-4022	129	1	e	e	X
ejpam-4022	129	2	−x2	−x2	PROPN
ejpam-4022	129	3	+	+	NOUN
ejpam-4022	129	4	4xy+y2	4xy+y2	NOUN
ejpam-4022	129	5	4y	4y	PROPN
ejpam-4022	129	6	log2	log2	PROPN
ejpam-4022	129	7	(	(	PUNCT
ejpam-4022	129	8	x	x	NOUN
ejpam-4022	129	9	y	y	PROPN
ejpam-4022	129	10	)	)	PUNCT
ejpam-4022	129	11	√	√	PROPN
ejpam-4022	129	12	x	x	SYM
ejpam-4022	129	13	√	√	NUM
ejpam-4022	129	14	y	y	PROPN
ejpam-4022	129	15	dxdy	dxdy	PROPN
ejpam-4022	129	16	=	=	PROPN
ejpam-4022	129	17	2	2	NUM
ejpam-4022	129	18	√	√	NUM
ejpam-4022	129	19	2	2	NUM
ejpam-4022	129	20	3	3	NUM
ejpam-4022	129	21	π	π	NOUN
ejpam-4022	129	22	(	(	PUNCT
ejpam-4022	129	23	π2	π2	X
ejpam-4022	129	24	+	+	CCONJ
ejpam-4022	129	25	(	(	PUNCT
ejpam-4022	129	26	cosh−1(2))2	cosh−1(2))2	NOUN
ejpam-4022	129	27	)	)	PUNCT
ejpam-4022	129	28	r.	r.	PROPN
ejpam-4022	129	29	reynolds	reynolds	PROPN
ejpam-4022	129	30	,	,	PUNCT
ejpam-4022	129	31	a.	a.	PROPN
ejpam-4022	129	32	stauffer	stauffer	PROPN
ejpam-4022	129	33	/	/	SYM
ejpam-4022	129	34	eur	eur	PROPN
ejpam-4022	129	35	.	.	PUNCT
ejpam-4022	130	1	j.	j.	PROPN
ejpam-4022	130	2	pure	pure	PROPN
ejpam-4022	130	3	appl	appl	PROPN
ejpam-4022	130	4	.	.	PROPN
ejpam-4022	130	5	math	math	PROPN
ejpam-4022	130	6	,	,	PUNCT
ejpam-4022	130	7	14	14	NUM
ejpam-4022	130	8	(	(	PUNCT
ejpam-4022	130	9	4	4	NUM
ejpam-4022	130	10	)	)	PUNCT
ejpam-4022	130	11	(	(	PUNCT
ejpam-4022	130	12	2021	2021	NUM
ejpam-4022	130	13	)	)	PUNCT
ejpam-4022	130	14	,	,	PUNCT
ejpam-4022	130	15	1200	1200	NUM
ejpam-4022	130	16	-	-	SYM
ejpam-4022	130	17	1211	1211	NUM
ejpam-4022	130	18	1206	1206	NUM
ejpam-4022	130	19	proof	proof	NOUN
ejpam-4022	130	20	.	.	PUNCT
ejpam-4022	131	1	use	use	VERB
ejpam-4022	131	2	equation	equation	NOUN
ejpam-4022	131	3	(	(	PUNCT
ejpam-4022	131	4	9	9	NUM
ejpam-4022	131	5	)	)	PUNCT
ejpam-4022	131	6	and	and	CCONJ
ejpam-4022	131	7	set	set	VERB
ejpam-4022	131	8	m	m	PROPN
ejpam-4022	131	9	=	=	SYM
ejpam-4022	131	10	−1/2	−1/2	ADJ
ejpam-4022	131	11	,	,	PUNCT
ejpam-4022	131	12	a	a	DET
ejpam-4022	131	13	=	=	SYM
ejpam-4022	131	14	1	1	NUM
ejpam-4022	131	15	and	and	CCONJ
ejpam-4022	131	16	simplify	simplify	VERB
ejpam-4022	131	17	in	in	ADP
ejpam-4022	131	18	terms	term	NOUN
ejpam-4022	131	19	of	of	ADP
ejpam-4022	131	20	the	the	DET
ejpam-4022	131	21	hurwitz	hurwitz	PROPN
ejpam-4022	131	22	zeta	zeta	PROPN
ejpam-4022	131	23	function	function	NOUN
ejpam-4022	131	24	using	use	VERB
ejpam-4022	131	25	entry	entry	NOUN
ejpam-4022	131	26	(	(	PUNCT
ejpam-4022	131	27	4	4	NUM
ejpam-4022	131	28	)	)	PUNCT
ejpam-4022	131	29	in	in	ADP
ejpam-4022	131	30	table	table	NOUN
ejpam-4022	131	31	below	below	ADV
ejpam-4022	131	32	(	(	PUNCT
ejpam-4022	131	33	64:12:7	64:12:7	NUM
ejpam-4022	131	34	)	)	PUNCT
ejpam-4022	131	35	in	in	ADP
ejpam-4022	131	36	[	[	X
ejpam-4022	131	37	5	5	NUM
ejpam-4022	131	38	]	]	PUNCT
ejpam-4022	131	39	.	.	PUNCT
ejpam-4022	132	1	next	next	ADJ
ejpam-4022	132	2	set	set	VERB
ejpam-4022	132	3	k	k	PROPN
ejpam-4022	132	4	=	=	SYM
ejpam-4022	132	5	2	2	NUM
ejpam-4022	132	6	,	,	PUNCT
ejpam-4022	132	7	p	p	NOUN
ejpam-4022	132	8	=	=	NOUN
ejpam-4022	132	9	1	1	NUM
ejpam-4022	132	10	,	,	PUNCT
ejpam-4022	132	11	q	q	NOUN
ejpam-4022	132	12	=	=	SYM
ejpam-4022	132	13	1/4	1/4	NUM
ejpam-4022	132	14	and	and	CCONJ
ejpam-4022	132	15	simplify	simplify	VERB
ejpam-4022	132	16	using	use	VERB
ejpam-4022	132	17	entry	entry	NOUN
ejpam-4022	132	18	(	(	PUNCT
ejpam-4022	132	19	3	3	NUM
ejpam-4022	132	20	)	)	PUNCT
ejpam-4022	132	21	in	in	ADP
ejpam-4022	132	22	table	table	NOUN
ejpam-4022	132	23	below	below	ADV
ejpam-4022	132	24	(	(	PUNCT
ejpam-4022	132	25	64:4:1	64:4:1	NUM
ejpam-4022	132	26	)	)	PUNCT
ejpam-4022	132	27	in	in	ADP
ejpam-4022	132	28	[	[	X
ejpam-4022	132	29	5	5	NUM
ejpam-4022	132	30	]	]	PUNCT
ejpam-4022	132	31	.	.	PUNCT
ejpam-4022	133	1	11	11	NUM
ejpam-4022	133	2	.	.	PUNCT
ejpam-4022	134	1	derivation	derivation	NOUN
ejpam-4022	134	2	of	of	ADP
ejpam-4022	134	3	new	new	ADJ
ejpam-4022	134	4	entry	entry	NOUN
ejpam-4022	134	5	3.1.3.62	3.1.3.62	NUM
ejpam-4022	134	6	in	in	ADP
ejpam-4022	134	7	[	[	X
ejpam-4022	134	8	6	6	NUM
ejpam-4022	134	9	]	]	PUNCT
ejpam-4022	134	10	proposition	proposition	NOUN
ejpam-4022	134	11	3	3	NUM
ejpam-4022	134	12	.	.	PUNCT
ejpam-4022	134	13	for	for	ADP
ejpam-4022	134	14	re(k	re(k	NOUN
ejpam-4022	134	15	)	)	PUNCT
ejpam-4022	134	16	>	>	X
ejpam-4022	134	17	0	0	NUM
ejpam-4022	134	18	,	,	PUNCT
ejpam-4022	134	19	im(k	im(k	NUM
ejpam-4022	134	20	)	)	PUNCT
ejpam-4022	134	21	<	<	X
ejpam-4022	134	22	0	0	NUM
ejpam-4022	134	23	,	,	PUNCT
ejpam-4022	134	24	(	(	PUNCT
ejpam-4022	134	25	14	14	NUM
ejpam-4022	134	26	)	)	PUNCT
ejpam-4022	134	27	∫	∫	PROPN
ejpam-4022	135	1	∞	∞	PROPN
ejpam-4022	135	2	0	0	NUM
ejpam-4022	136	1	∫	∫	PROPN
ejpam-4022	136	2	∞	∞	NOUN
ejpam-4022	136	3	0	0	PUNCT
ejpam-4022	137	1	e	e	PROPN
ejpam-4022	137	2	−x2+xy+y2	−x2+xy+y2	PROPN
ejpam-4022	137	3	4y	4y	PROPN
ejpam-4022	137	4	(	(	PUNCT
ejpam-4022	137	5	x−	x−	PROPN
ejpam-4022	137	6	y	y	PROPN
ejpam-4022	137	7	)	)	PUNCT
ejpam-4022	137	8	logk	logk	NOUN
ejpam-4022	137	9	(	(	PUNCT
ejpam-4022	137	10	x	x	NOUN
ejpam-4022	137	11	y	y	PROPN
ejpam-4022	137	12	)	)	PUNCT
ejpam-4022	137	13	√	√	PROPN
ejpam-4022	137	14	xy3/2	xy3/2	PROPN
ejpam-4022	137	15	dxdy	dxdy	PROPN
ejpam-4022	137	16	=	=	SYM
ejpam-4022	137	17	i22k+3e	i22k+3e	PROPN
ejpam-4022	137	18	iπk	iπk	NOUN
ejpam-4022	137	19	2	2	NUM
ejpam-4022	137	20	πk+1	πk+1	NOUN
ejpam-4022	137	21	(	(	PUNCT
ejpam-4022	137	22	ζ	ζ	NOUN
ejpam-4022	137	23	(	(	PUNCT
ejpam-4022	137	24	−k	−k	PROPN
ejpam-4022	137	25	,	,	PUNCT
ejpam-4022	137	26	1	1	NUM
ejpam-4022	137	27	6	6	NUM
ejpam-4022	137	28	)	)	PUNCT
ejpam-4022	138	1	+	+	CCONJ
ejpam-4022	138	2	ζ	ζ	X
ejpam-4022	138	3	(	(	PUNCT
ejpam-4022	138	4	−k	−k	PROPN
ejpam-4022	138	5	,	,	PUNCT
ejpam-4022	138	6	5	5	NUM
ejpam-4022	138	7	6	6	NUM
ejpam-4022	138	8	)	)	PUNCT
ejpam-4022	138	9	+	+	CCONJ
ejpam-4022	138	10	(	(	PUNCT
ejpam-4022	138	11	1−	1−	NUM
ejpam-4022	138	12	3−k	3−k	NUM
ejpam-4022	138	13	)	)	PUNCT
ejpam-4022	138	14	ζ(−k	ζ(−k	NOUN
ejpam-4022	138	15	)	)	PUNCT
ejpam-4022	138	16	)	)	PUNCT
ejpam-4022	138	17	proof	proof	NOUN
ejpam-4022	138	18	.	.	PUNCT
ejpam-4022	139	1	use	use	VERB
ejpam-4022	139	2	equation	equation	NOUN
ejpam-4022	139	3	(	(	PUNCT
ejpam-4022	139	4	9	9	NUM
ejpam-4022	139	5	)	)	PUNCT
ejpam-4022	139	6	and	and	CCONJ
ejpam-4022	139	7	set	set	VERB
ejpam-4022	139	8	a	a	DET
ejpam-4022	139	9	=	=	X
ejpam-4022	139	10	1,m	1,m	NOUN
ejpam-4022	139	11	=	=	SYM
ejpam-4022	139	12	−1/2	−1/2	PROPN
ejpam-4022	139	13	,	,	PUNCT
ejpam-4022	139	14	q	q	NOUN
ejpam-4022	140	1	=	=	PUNCT
ejpam-4022	140	2	p	p	NOUN
ejpam-4022	140	3	and	and	CCONJ
ejpam-4022	140	4	simplify	simplify	VERB
ejpam-4022	140	5	in	in	ADP
ejpam-4022	140	6	terms	term	NOUN
ejpam-4022	140	7	of	of	ADP
ejpam-4022	140	8	the	the	DET
ejpam-4022	140	9	hurwitz	hurwitz	PROPN
ejpam-4022	140	10	zeta	zeta	PROPN
ejpam-4022	140	11	functions	function	NOUN
ejpam-4022	140	12	using	use	VERB
ejpam-4022	140	13	entry	entry	NOUN
ejpam-4022	140	14	(	(	PUNCT
ejpam-4022	140	15	4	4	NUM
ejpam-4022	140	16	)	)	PUNCT
ejpam-4022	140	17	in	in	ADP
ejpam-4022	140	18	table	table	NOUN
ejpam-4022	140	19	below	below	ADV
ejpam-4022	140	20	(	(	PUNCT
ejpam-4022	140	21	64:12:7	64:12:7	NUM
ejpam-4022	140	22	)	)	PUNCT
ejpam-4022	140	23	in	in	ADP
ejpam-4022	140	24	[	[	X
ejpam-4022	140	25	5	5	NUM
ejpam-4022	140	26	]	]	PUNCT
ejpam-4022	140	27	.	.	PUNCT
ejpam-4022	141	1	next	next	ADJ
ejpam-4022	141	2	set	set	VERB
ejpam-4022	141	3	p	p	PROPN
ejpam-4022	141	4	=	=	NOUN
ejpam-4022	141	5	1/4	1/4	NUM
ejpam-4022	141	6	and	and	CCONJ
ejpam-4022	141	7	simplify	simplify	VERB
ejpam-4022	141	8	using	use	VERB
ejpam-4022	141	9	entry	entry	NOUN
ejpam-4022	141	10	(	(	PUNCT
ejpam-4022	141	11	2	2	NUM
ejpam-4022	141	12	)	)	PUNCT
ejpam-4022	141	13	in	in	ADP
ejpam-4022	141	14	table	table	NOUN
ejpam-4022	141	15	below	below	ADV
ejpam-4022	141	16	(	(	PUNCT
ejpam-4022	141	17	64:7	64:7	NUM
ejpam-4022	141	18	)	)	PUNCT
ejpam-4022	141	19	in	in	ADP
ejpam-4022	141	20	[	[	X
ejpam-4022	141	21	5	5	NUM
ejpam-4022	141	22	]	]	PUNCT
ejpam-4022	141	23	.	.	PUNCT
ejpam-4022	142	1	12	12	NUM
ejpam-4022	142	2	.	.	PUNCT
ejpam-4022	143	1	derivation	derivation	NOUN
ejpam-4022	143	2	of	of	ADP
ejpam-4022	143	3	new	new	ADJ
ejpam-4022	143	4	entry	entry	NOUN
ejpam-4022	143	5	3.1.3.63	3.1.3.63	NUM
ejpam-4022	143	6	in	in	ADP
ejpam-4022	143	7	[	[	X
ejpam-4022	143	8	6	6	NUM
ejpam-4022	143	9	]	]	PUNCT
ejpam-4022	143	10	proposition	proposition	NOUN
ejpam-4022	143	11	4	4	NUM
ejpam-4022	143	12	.	.	PUNCT
ejpam-4022	144	1	(	(	PUNCT
ejpam-4022	144	2	15	15	NUM
ejpam-4022	144	3	)	)	PUNCT
ejpam-4022	144	4	∫	∫	PROPN
ejpam-4022	145	1	∞	∞	PROPN
ejpam-4022	145	2	0	0	NUM
ejpam-4022	146	1	∫	∫	PROPN
ejpam-4022	146	2	∞	∞	NOUN
ejpam-4022	146	3	0	0	PUNCT
ejpam-4022	147	1	e	e	PROPN
ejpam-4022	147	2	−x2+xy+y2	−x2+xy+y2	PROPN
ejpam-4022	147	3	4y	4y	PROPN
ejpam-4022	147	4	(	(	PUNCT
ejpam-4022	147	5	x−	x−	PROPN
ejpam-4022	147	6	y	y	PROPN
ejpam-4022	147	7	)	)	PUNCT
ejpam-4022	147	8	log	log	NOUN
ejpam-4022	147	9	(	(	PUNCT
ejpam-4022	147	10	x	x	NOUN
ejpam-4022	147	11	y	y	PROPN
ejpam-4022	147	12	)	)	PUNCT
ejpam-4022	147	13	log	log	NOUN
ejpam-4022	147	14	(	(	PUNCT
ejpam-4022	147	15	log	log	NOUN
ejpam-4022	147	16	(	(	PUNCT
ejpam-4022	147	17	x	x	NOUN
ejpam-4022	147	18	y	y	PROPN
ejpam-4022	147	19	)	)	PUNCT
ejpam-4022	147	20	)	)	PUNCT
ejpam-4022	148	1	√	√	PROPN
ejpam-4022	148	2	xy3/2	xy3/2	PROPN
ejpam-4022	148	3	dxdy	dxdy	PROPN
ejpam-4022	148	4	=	=	NOUN
ejpam-4022	148	5	4	4	NUM
ejpam-4022	148	6	9	9	NUM
ejpam-4022	148	7	π2	π2	NOUN
ejpam-4022	148	8	(	(	PUNCT
ejpam-4022	148	9	6	6	NUM
ejpam-4022	148	10	+	+	SYM
ejpam-4022	148	11	3πi+	3πi+	NUM
ejpam-4022	148	12	log	log	NOUN
ejpam-4022	148	13	(	(	PUNCT
ejpam-4022	148	14	21433π6	21433π6	NOUN
ejpam-4022	148	15	a72	a72	NOUN
ejpam-4022	148	16	)	)	PUNCT
ejpam-4022	148	17	)	)	PUNCT
ejpam-4022	148	18	proof	proof	NOUN
ejpam-4022	148	19	.	.	PUNCT
ejpam-4022	149	1	use	use	VERB
ejpam-4022	149	2	equation	equation	NOUN
ejpam-4022	149	3	(	(	PUNCT
ejpam-4022	149	4	14	14	NUM
ejpam-4022	149	5	)	)	PUNCT
ejpam-4022	149	6	and	and	CCONJ
ejpam-4022	149	7	take	take	VERB
ejpam-4022	149	8	the	the	DET
ejpam-4022	149	9	first	first	ADJ
ejpam-4022	149	10	partial	partial	ADJ
ejpam-4022	149	11	derivative	derivative	NOUN
ejpam-4022	149	12	with	with	ADP
ejpam-4022	149	13	respect	respect	NOUN
ejpam-4022	149	14	to	to	ADP
ejpam-4022	149	15	k	k	PROPN
ejpam-4022	149	16	then	then	ADV
ejpam-4022	149	17	set	set	VERB
ejpam-4022	149	18	k	k	PROPN
ejpam-4022	149	19	=	=	SYM
ejpam-4022	149	20	1	1	NUM
ejpam-4022	149	21	and	and	CCONJ
ejpam-4022	149	22	simplify	simplify	VERB
ejpam-4022	149	23	in	in	ADP
ejpam-4022	149	24	terms	term	NOUN
ejpam-4022	149	25	of	of	ADP
ejpam-4022	149	26	glaisher	glaisher	PROPN
ejpam-4022	149	27	’s	’s	PART
ejpam-4022	149	28	constant	constant	ADJ
ejpam-4022	149	29	a	a	PRON
ejpam-4022	149	30	,	,	PUNCT
ejpam-4022	149	31	using	use	VERB
ejpam-4022	149	32	equations	equation	NOUN
ejpam-4022	149	33	(	(	PUNCT
ejpam-4022	149	34	a11	a11	PROPN
ejpam-4022	149	35	)	)	PUNCT
ejpam-4022	149	36	and	and	CCONJ
ejpam-4022	149	37	(	(	PUNCT
ejpam-4022	149	38	a12	a12	NOUN
ejpam-4022	149	39	)	)	PUNCT
ejpam-4022	149	40	in	in	ADP
ejpam-4022	149	41	[	[	X
ejpam-4022	149	42	10	10	NUM
ejpam-4022	149	43	]	]	PUNCT
ejpam-4022	149	44	.	.	PUNCT
ejpam-4022	150	1	r.	r.	PROPN
ejpam-4022	150	2	reynolds	reynolds	PROPN
ejpam-4022	150	3	,	,	PUNCT
ejpam-4022	150	4	a.	a.	PROPN
ejpam-4022	150	5	stauffer	stauffer	PROPN
ejpam-4022	150	6	/	/	SYM
ejpam-4022	150	7	eur	eur	PROPN
ejpam-4022	150	8	.	.	PUNCT
ejpam-4022	151	1	j.	j.	PROPN
ejpam-4022	151	2	pure	pure	PROPN
ejpam-4022	151	3	appl	appl	PROPN
ejpam-4022	151	4	.	.	PROPN
ejpam-4022	151	5	math	math	PROPN
ejpam-4022	151	6	,	,	PUNCT
ejpam-4022	151	7	14	14	NUM
ejpam-4022	151	8	(	(	PUNCT
ejpam-4022	151	9	4	4	NUM
ejpam-4022	151	10	)	)	PUNCT
ejpam-4022	151	11	(	(	PUNCT
ejpam-4022	151	12	2021	2021	NUM
ejpam-4022	151	13	)	)	PUNCT
ejpam-4022	151	14	,	,	PUNCT
ejpam-4022	151	15	1200	1200	NUM
ejpam-4022	151	16	-	-	SYM
ejpam-4022	151	17	1211	1211	NUM
ejpam-4022	151	18	1207	1207	NUM
ejpam-4022	151	19	13	13	NUM
ejpam-4022	151	20	.	.	PUNCT
ejpam-4022	152	1	derivation	derivation	NOUN
ejpam-4022	152	2	of	of	ADP
ejpam-4022	152	3	new	new	ADJ
ejpam-4022	152	4	entry	entry	NOUN
ejpam-4022	152	5	3.1.3.64	3.1.3.64	NUM
ejpam-4022	152	6	in	in	ADP
ejpam-4022	152	7	[	[	X
ejpam-4022	152	8	6	6	NUM
ejpam-4022	152	9	]	]	PUNCT
ejpam-4022	152	10	proposition	proposition	NOUN
ejpam-4022	152	11	5	5	NUM
ejpam-4022	152	12	.	.	PUNCT
ejpam-4022	153	1	(	(	PUNCT
ejpam-4022	153	2	16	16	NUM
ejpam-4022	153	3	)	)	PUNCT
ejpam-4022	153	4	∫	∫	PROPN
ejpam-4022	154	1	∞	∞	PROPN
ejpam-4022	154	2	0	0	NUM
ejpam-4022	155	1	∫	∫	PROPN
ejpam-4022	155	2	∞	∞	NOUN
ejpam-4022	155	3	0	0	PUNCT
ejpam-4022	156	1	e	e	PROPN
ejpam-4022	156	2	−x2+xy+y2	−x2+xy+y2	NOUN
ejpam-4022	156	3	4y	4y	PROPN
ejpam-4022	156	4	(	(	PUNCT
ejpam-4022	156	5	4	4	NUM
ejpam-4022	156	6	√	√	NOUN
ejpam-4022	156	7	y	y	NUM
ejpam-4022	156	8	−	−	PROPN
ejpam-4022	156	9	4	4	NUM
ejpam-4022	156	10	√	√	PROPN
ejpam-4022	156	11	x	x	SYM
ejpam-4022	156	12	)	)	PUNCT
ejpam-4022	156	13	x3/4	x3/4	NUM
ejpam-4022	156	14	√	√	NUM
ejpam-4022	157	1	y	y	PROPN
ejpam-4022	157	2	log	log	NOUN
ejpam-4022	157	3	(	(	PUNCT
ejpam-4022	157	4	x	x	NOUN
ejpam-4022	157	5	y	y	PROPN
ejpam-4022	157	6	)	)	PUNCT
ejpam-4022	157	7	dxdy	dxdy	NOUN
ejpam-4022	157	8	=	=	NOUN
ejpam-4022	157	9	4	4	NUM
ejpam-4022	157	10	log	log	NOUN
ejpam-4022	157	11	(	(	PUNCT
ejpam-4022	157	12	4−	4−	NOUN
ejpam-4022	157	13	2	2	NUM
ejpam-4022	157	14	√	√	NUM
ejpam-4022	157	15	3	3	NUM
ejpam-4022	157	16	)	)	PUNCT
ejpam-4022	157	17	proof	proof	NOUN
ejpam-4022	157	18	.	.	PUNCT
ejpam-4022	158	1	use	use	VERB
ejpam-4022	158	2	equation	equation	NOUN
ejpam-4022	158	3	(	(	PUNCT
ejpam-4022	158	4	9	9	NUM
ejpam-4022	158	5	)	)	PUNCT
ejpam-4022	158	6	and	and	CCONJ
ejpam-4022	158	7	replace	replace	VERB
ejpam-4022	158	8	m	m	PROPN
ejpam-4022	158	9	→	→	SYM
ejpam-4022	158	10	t	t	NOUN
ejpam-4022	158	11	to	to	PART
ejpam-4022	158	12	form	form	VERB
ejpam-4022	158	13	a	a	DET
ejpam-4022	158	14	second	second	ADJ
ejpam-4022	158	15	equation	equation	NOUN
ejpam-4022	158	16	and	and	CCONJ
ejpam-4022	158	17	take	take	VERB
ejpam-4022	158	18	their	their	PRON
ejpam-4022	158	19	difference	difference	NOUN
ejpam-4022	158	20	.	.	PUNCT
ejpam-4022	159	1	next	next	ADJ
ejpam-4022	159	2	set	set	VERB
ejpam-4022	159	3	m	m	PROPN
ejpam-4022	159	4	=	=	SYM
ejpam-4022	159	5	−1/2	−1/2	ADJ
ejpam-4022	159	6	,	,	PUNCT
ejpam-4022	159	7	t	t	NOUN
ejpam-4022	159	8	=	=	SYM
ejpam-4022	159	9	−3/4	−3/4	PROPN
ejpam-4022	159	10	,	,	PUNCT
ejpam-4022	159	11	a	a	DET
ejpam-4022	159	12	=	=	SYM
ejpam-4022	159	13	1	1	NUM
ejpam-4022	159	14	,	,	PUNCT
ejpam-4022	159	15	q	q	NOUN
ejpam-4022	159	16	=	=	PUNCT
ejpam-4022	159	17	p	p	NOUN
ejpam-4022	159	18	and	and	CCONJ
ejpam-4022	159	19	simplify	simplify	VERB
ejpam-4022	159	20	the	the	DET
ejpam-4022	159	21	right	right	ADJ
ejpam-4022	159	22	-	-	PUNCT
ejpam-4022	159	23	hand	hand	NOUN
ejpam-4022	159	24	side	side	NOUN
ejpam-4022	159	25	in	in	ADP
ejpam-4022	159	26	terms	term	NOUN
ejpam-4022	159	27	of	of	ADP
ejpam-4022	159	28	the	the	DET
ejpam-4022	159	29	hurwitz	hurwitz	PROPN
ejpam-4022	159	30	zeta	zeta	PROPN
ejpam-4022	159	31	function	function	NOUN
ejpam-4022	159	32	using	use	VERB
ejpam-4022	159	33	entry	entry	NOUN
ejpam-4022	159	34	(	(	PUNCT
ejpam-4022	159	35	4	4	NUM
ejpam-4022	159	36	)	)	PUNCT
ejpam-4022	159	37	in	in	ADP
ejpam-4022	159	38	table	table	NOUN
ejpam-4022	159	39	below	below	ADV
ejpam-4022	159	40	(	(	PUNCT
ejpam-4022	159	41	64:12:7	64:12:7	NUM
ejpam-4022	159	42	)	)	PUNCT
ejpam-4022	159	43	in	in	ADP
ejpam-4022	159	44	[	[	X
ejpam-4022	159	45	5	5	NUM
ejpam-4022	159	46	]	]	PUNCT
ejpam-4022	159	47	.	.	PUNCT
ejpam-4022	160	1	next	next	ADJ
ejpam-4022	160	2	apply	apply	VERB
ejpam-4022	160	3	l’hopital	l’hopital	PROPN
ejpam-4022	160	4	’s	’s	PART
ejpam-4022	160	5	rule	rule	NOUN
ejpam-4022	160	6	to	to	ADP
ejpam-4022	160	7	the	the	DET
ejpam-4022	160	8	right	right	ADJ
ejpam-4022	160	9	-	-	PUNCT
ejpam-4022	160	10	hand	hand	NOUN
ejpam-4022	160	11	side	side	NOUN
ejpam-4022	160	12	as	as	ADP
ejpam-4022	160	13	k	k	PROPN
ejpam-4022	160	14	→	→	SYM
ejpam-4022	160	15	−1	−1	NOUN
ejpam-4022	160	16	and	and	CCONJ
ejpam-4022	160	17	simplify	simplify	VERB
ejpam-4022	160	18	using	use	VERB
ejpam-4022	160	19	entry	entry	NOUN
ejpam-4022	160	20	(	(	PUNCT
ejpam-4022	160	21	1	1	NUM
ejpam-4022	160	22	)	)	PUNCT
ejpam-4022	160	23	in	in	ADP
ejpam-4022	160	24	table	table	NOUN
ejpam-4022	160	25	below	below	ADV
ejpam-4022	160	26	(	(	PUNCT
ejpam-4022	160	27	64:12:7	64:12:7	NUM
ejpam-4022	160	28	)	)	PUNCT
ejpam-4022	160	29	and	and	CCONJ
ejpam-4022	160	30	equation	equation	NOUN
ejpam-4022	160	31	(	(	PUNCT
ejpam-4022	160	32	64:4:1	64:4:1	NUM
ejpam-4022	160	33	)	)	PUNCT
ejpam-4022	160	34	in	in	ADP
ejpam-4022	160	35	[	[	X
ejpam-4022	160	36	5	5	NUM
ejpam-4022	160	37	]	]	PUNCT
ejpam-4022	160	38	.	.	PUNCT
ejpam-4022	161	1	14	14	NUM
ejpam-4022	161	2	.	.	PUNCT
ejpam-4022	162	1	derivation	derivation	NOUN
ejpam-4022	162	2	of	of	ADP
ejpam-4022	162	3	new	new	ADJ
ejpam-4022	162	4	entry	entry	NOUN
ejpam-4022	162	5	3.1.3.65	3.1.3.65	NUM
ejpam-4022	162	6	in	in	ADP
ejpam-4022	162	7	[	[	X
ejpam-4022	162	8	6	6	NUM
ejpam-4022	162	9	]	]	PUNCT
ejpam-4022	162	10	proposition	proposition	NOUN
ejpam-4022	162	11	6	6	NUM
ejpam-4022	162	12	.	.	PUNCT
ejpam-4022	163	1	for	for	ADP
ejpam-4022	163	2	−1	−1	NOUN
ejpam-4022	163	3	<	<	X
ejpam-4022	163	4	re(m	re(m	NOUN
ejpam-4022	163	5	)	)	PUNCT
ejpam-4022	163	6	≤	≤	NOUN
ejpam-4022	163	7	−1/2,−1	−1/2,−1	ADV
ejpam-4022	163	8	<	<	X
ejpam-4022	163	9	im(m	im(m	NOUN
ejpam-4022	163	10	)	)	PUNCT
ejpam-4022	163	11	<	<	X
ejpam-4022	163	12	−1/2,−1	−1/2,−1	ADV
ejpam-4022	163	13	<	<	X
ejpam-4022	163	14	re(t	re(t	PRON
ejpam-4022	163	15	)	)	PUNCT
ejpam-4022	163	16	≤	≤	NOUN
ejpam-4022	163	17	−1/2,−1	−1/2,−1	ADV
ejpam-4022	163	18	<	<	X
ejpam-4022	163	19	im(t	im(t	NUM
ejpam-4022	163	20	)	)	PUNCT
ejpam-4022	163	21	<	<	X
ejpam-4022	164	1	−1/2	−1/2	ADJ
ejpam-4022	164	2	,	,	PUNCT
ejpam-4022	164	3	(	(	PUNCT
ejpam-4022	164	4	17	17	NUM
ejpam-4022	164	5	)	)	PUNCT
ejpam-4022	164	6	∫	∫	PROPN
ejpam-4022	165	1	∞	∞	PROPN
ejpam-4022	165	2	0	0	NUM
ejpam-4022	166	1	∫	∫	PROPN
ejpam-4022	166	2	∞	∞	NOUN
ejpam-4022	166	3	0	0	PUNCT
ejpam-4022	167	1	e	e	PROPN
ejpam-4022	167	2	−x2+xy+y2	−x2+xy+y2	NOUN
ejpam-4022	167	3	4y	4y	NUM
ejpam-4022	167	4	y−m−t−1	y−m−t−1	PROPN
ejpam-4022	167	5	(	(	PUNCT
ejpam-4022	167	6	ymxt	ymxt	ADV
ejpam-4022	167	7	−	−	NOUN
ejpam-4022	167	8	xmyt	xmyt	PROPN
ejpam-4022	167	9	)	)	PUNCT
ejpam-4022	167	10	log	log	NOUN
ejpam-4022	167	11	(	(	PUNCT
ejpam-4022	167	12	x	x	SYM
ejpam-4022	167	13	y	y	PROPN
ejpam-4022	167	14	)	)	PUNCT
ejpam-4022	167	15	dxdy	dxdy	PROPN
ejpam-4022	167	16	=	=	SYM
ejpam-4022	167	17	2i	2i	NUM
ejpam-4022	167	18	√	√	NUM
ejpam-4022	167	19	3	3	NUM
ejpam-4022	167	20	(	(	PUNCT
ejpam-4022	167	21	2e	2e	NOUN
ejpam-4022	167	22	2iπm	2iπm	NUM
ejpam-4022	167	23	3	3	NUM
ejpam-4022	167	24	2f1	2f1	NUM
ejpam-4022	167	25	(	(	PUNCT
ejpam-4022	167	26	1	1	NUM
ejpam-4022	167	27	3	3	NUM
ejpam-4022	167	28	,	,	PUNCT
ejpam-4022	167	29	1	1	NUM
ejpam-4022	167	30	;	;	PUNCT
ejpam-4022	167	31	4	4	NUM
ejpam-4022	167	32	3	3	NUM
ejpam-4022	167	33	;	;	PUNCT
ejpam-4022	167	34	e2imπ	e2imπ	PROPN
ejpam-4022	167	35	)	)	PUNCT
ejpam-4022	167	36	−	−	PUNCT
ejpam-4022	168	1	e	e	X
ejpam-4022	168	2	4iπm	4iπm	PROPN
ejpam-4022	168	3	3	3	NUM
ejpam-4022	168	4	2f1	2f1	NUM
ejpam-4022	168	5	(	(	PUNCT
ejpam-4022	168	6	2	2	NUM
ejpam-4022	168	7	3	3	NUM
ejpam-4022	168	8	,	,	PUNCT
ejpam-4022	168	9	1	1	NUM
ejpam-4022	168	10	;	;	PUNCT
ejpam-4022	168	11	5	5	NUM
ejpam-4022	168	12	3	3	NUM
ejpam-4022	168	13	;	;	PUNCT
ejpam-4022	168	14	e2imπ	e2imπ	PROPN
ejpam-4022	168	15	)	)	PUNCT
ejpam-4022	169	1	−	−	PROPN
ejpam-4022	169	2	2e	2e	NOUN
ejpam-4022	169	3	2iπt	2iπt	NUM
ejpam-4022	169	4	3	3	NUM
ejpam-4022	169	5	2f1	2f1	NUM
ejpam-4022	169	6	(	(	PUNCT
ejpam-4022	169	7	1	1	NUM
ejpam-4022	169	8	3	3	NUM
ejpam-4022	169	9	,	,	PUNCT
ejpam-4022	169	10	1	1	NUM
ejpam-4022	169	11	;	;	PUNCT
ejpam-4022	169	12	4	4	NUM
ejpam-4022	169	13	3	3	NUM
ejpam-4022	169	14	;	;	PUNCT
ejpam-4022	169	15	e2iπt	e2iπt	X
ejpam-4022	169	16	)	)	PUNCT
ejpam-4022	170	1	+	+	CCONJ
ejpam-4022	170	2	e	e	X
ejpam-4022	170	3	4iπt	4iπt	NUM
ejpam-4022	170	4	3	3	NUM
ejpam-4022	170	5	2f1	2f1	NUM
ejpam-4022	170	6	(	(	PUNCT
ejpam-4022	170	7	2	2	NUM
ejpam-4022	170	8	3	3	NUM
ejpam-4022	170	9	,	,	PUNCT
ejpam-4022	170	10	1	1	NUM
ejpam-4022	170	11	;	;	PUNCT
ejpam-4022	170	12	5	5	NUM
ejpam-4022	170	13	3	3	NUM
ejpam-4022	170	14	;	;	PUNCT
ejpam-4022	170	15	e2iπt	e2iπt	X
ejpam-4022	170	16	)	)	PUNCT
ejpam-4022	170	17	)	)	PUNCT
ejpam-4022	170	18	proof	proof	NOUN
ejpam-4022	170	19	.	.	PUNCT
ejpam-4022	171	1	use	use	VERB
ejpam-4022	171	2	equation	equation	NOUN
ejpam-4022	171	3	(	(	PUNCT
ejpam-4022	171	4	9	9	NUM
ejpam-4022	171	5	)	)	PUNCT
ejpam-4022	171	6	and	and	CCONJ
ejpam-4022	171	7	set	set	VERB
ejpam-4022	171	8	k	k	PROPN
ejpam-4022	171	9	=	=	PUNCT
ejpam-4022	171	10	−1	−1	NOUN
ejpam-4022	171	11	,	,	PUNCT
ejpam-4022	171	12	a	a	DET
ejpam-4022	171	13	=	=	NOUN
ejpam-4022	171	14	1	1	NUM
ejpam-4022	171	15	,	,	PUNCT
ejpam-4022	171	16	p	p	NOUN
ejpam-4022	171	17	=	=	X
ejpam-4022	171	18	q	q	NOUN
ejpam-4022	171	19	=	=	SYM
ejpam-4022	171	20	1/4	1/4	NUM
ejpam-4022	171	21	and	and	CCONJ
ejpam-4022	171	22	simplify	simplify	VERB
ejpam-4022	171	23	using	use	VERB
ejpam-4022	171	24	(	(	PUNCT
ejpam-4022	171	25	9.559	9.559	NUM
ejpam-4022	171	26	)	)	PUNCT
ejpam-4022	171	27	in	in	ADP
ejpam-4022	171	28	[	[	X
ejpam-4022	171	29	2	2	NUM
ejpam-4022	171	30	]	]	PUNCT
ejpam-4022	171	31	.	.	PUNCT
ejpam-4022	172	1	15	15	NUM
ejpam-4022	172	2	.	.	PUNCT
ejpam-4022	173	1	derivation	derivation	NOUN
ejpam-4022	173	2	of	of	ADP
ejpam-4022	173	3	new	new	ADJ
ejpam-4022	173	4	entry	entry	NOUN
ejpam-4022	173	5	3.1.3.66	3.1.3.66	NUM
ejpam-4022	173	6	in	in	ADP
ejpam-4022	173	7	[	[	X
ejpam-4022	173	8	6	6	NUM
ejpam-4022	173	9	]	]	PUNCT
ejpam-4022	173	10	proposition	proposition	NOUN
ejpam-4022	173	11	7	7	NUM
ejpam-4022	173	12	.	.	PUNCT
ejpam-4022	174	1	(	(	PUNCT
ejpam-4022	174	2	18	18	NUM
ejpam-4022	174	3	)	)	PUNCT
ejpam-4022	174	4	∫	∫	PROPN
ejpam-4022	175	1	∞	∞	PROPN
ejpam-4022	175	2	0	0	NUM
ejpam-4022	176	1	∫	∫	PROPN
ejpam-4022	176	2	∞	∞	NOUN
ejpam-4022	176	3	0	0	PUNCT
ejpam-4022	177	1	e	e	PROPN
ejpam-4022	177	2	−x2+xy+y2	−x2+xy+y2	PROPN
ejpam-4022	177	3	4y	4y	PROPN
ejpam-4022	177	4	(	(	PUNCT
ejpam-4022	177	5	6	6	NUM
ejpam-4022	177	6	√	√	NUM
ejpam-4022	177	7	y	y	NUM
ejpam-4022	177	8	−	−	PROPN
ejpam-4022	177	9	6	6	NUM
ejpam-4022	177	10	√	√	PROPN
ejpam-4022	177	11	x	x	SYM
ejpam-4022	177	12	)	)	PUNCT
ejpam-4022	177	13	x2/3	x2/3	NUM
ejpam-4022	177	14	√	√	NUM
ejpam-4022	178	1	y	y	PROPN
ejpam-4022	178	2	log	log	NOUN
ejpam-4022	178	3	(	(	PUNCT
ejpam-4022	178	4	x	x	NOUN
ejpam-4022	178	5	y	y	PROPN
ejpam-4022	178	6	)	)	PUNCT
ejpam-4022	178	7	dxdy	dxdy	PROPN
ejpam-4022	178	8	=	=	SYM
ejpam-4022	178	9	log	log	PROPN
ejpam-4022	178	10	(	(	PUNCT
ejpam-4022	178	11	sec4	sec4	NOUN
ejpam-4022	178	12	(	(	PUNCT
ejpam-4022	178	13	π	π	PROPN
ejpam-4022	178	14	9	9	NUM
ejpam-4022	178	15	)	)	PUNCT
ejpam-4022	178	16	4	4	NUM
ejpam-4022	178	17	(	(	PUNCT
ejpam-4022	178	18	sin	sin	NOUN
ejpam-4022	178	19	(	(	PUNCT
ejpam-4022	178	20	π	π	NOUN
ejpam-4022	178	21	36	36	NUM
ejpam-4022	178	22	)	)	PUNCT
ejpam-4022	179	1	+	+	CCONJ
ejpam-4022	179	2	cos	cos	X
ejpam-4022	179	3	(	(	PUNCT
ejpam-4022	179	4	π	π	PROPN
ejpam-4022	179	5	36	36	NUM
ejpam-4022	179	6	)	)	PUNCT
ejpam-4022	179	7	)	)	PUNCT
ejpam-4022	179	8	4	4	X
ejpam-4022	179	9	)	)	PUNCT
ejpam-4022	179	10	r.	r.	PROPN
ejpam-4022	179	11	reynolds	reynolds	PROPN
ejpam-4022	179	12	,	,	PUNCT
ejpam-4022	179	13	a.	a.	PROPN
ejpam-4022	179	14	stauffer	stauffer	PROPN
ejpam-4022	179	15	/	/	SYM
ejpam-4022	179	16	eur	eur	PROPN
ejpam-4022	179	17	.	.	PUNCT
ejpam-4022	180	1	j.	j.	PROPN
ejpam-4022	180	2	pure	pure	PROPN
ejpam-4022	180	3	appl	appl	PROPN
ejpam-4022	180	4	.	.	PROPN
ejpam-4022	180	5	math	math	PROPN
ejpam-4022	180	6	,	,	PUNCT
ejpam-4022	180	7	14	14	NUM
ejpam-4022	180	8	(	(	PUNCT
ejpam-4022	180	9	4	4	NUM
ejpam-4022	180	10	)	)	PUNCT
ejpam-4022	180	11	(	(	PUNCT
ejpam-4022	180	12	2021	2021	NUM
ejpam-4022	180	13	)	)	PUNCT
ejpam-4022	180	14	,	,	PUNCT
ejpam-4022	180	15	1200	1200	NUM
ejpam-4022	180	16	-	-	SYM
ejpam-4022	180	17	1211	1211	NUM
ejpam-4022	180	18	1208	1208	NUM
ejpam-4022	180	19	proof	proof	NOUN
ejpam-4022	180	20	.	.	PUNCT
ejpam-4022	181	1	use	use	VERB
ejpam-4022	181	2	equation	equation	NOUN
ejpam-4022	181	3	(	(	PUNCT
ejpam-4022	181	4	17	17	NUM
ejpam-4022	181	5	)	)	PUNCT
ejpam-4022	181	6	and	and	CCONJ
ejpam-4022	181	7	set	set	VERB
ejpam-4022	181	8	m	m	PROPN
ejpam-4022	181	9	=	=	SYM
ejpam-4022	181	10	−1/2	−1/2	ADJ
ejpam-4022	181	11	,	,	PUNCT
ejpam-4022	181	12	t	t	PROPN
ejpam-4022	181	13	=	=	SYM
ejpam-4022	181	14	−2/3	−2/3	PROPN
ejpam-4022	181	15	and	and	CCONJ
ejpam-4022	181	16	simplify	simplify	VERB
ejpam-4022	181	17	using	use	VERB
ejpam-4022	181	18	(	(	PUNCT
ejpam-4022	181	19	9.559	9.559	NUM
ejpam-4022	181	20	)	)	PUNCT
ejpam-4022	181	21	in	in	ADP
ejpam-4022	181	22	[	[	X
ejpam-4022	181	23	2	2	NUM
ejpam-4022	181	24	]	]	PUNCT
ejpam-4022	181	25	.	.	PUNCT
ejpam-4022	182	1	16	16	NUM
ejpam-4022	182	2	.	.	PUNCT
ejpam-4022	183	1	derivation	derivation	NOUN
ejpam-4022	183	2	of	of	ADP
ejpam-4022	183	3	new	new	ADJ
ejpam-4022	183	4	entry	entry	NOUN
ejpam-4022	183	5	3.1.3.67	3.1.3.67	NUM
ejpam-4022	183	6	in	in	ADP
ejpam-4022	183	7	[	[	X
ejpam-4022	183	8	6	6	NUM
ejpam-4022	183	9	]	]	PUNCT
ejpam-4022	183	10	proposition	proposition	NOUN
ejpam-4022	183	11	8	8	NUM
ejpam-4022	183	12	.	.	PUNCT
ejpam-4022	184	1	(	(	PUNCT
ejpam-4022	184	2	19	19	NUM
ejpam-4022	184	3	)	)	PUNCT
ejpam-4022	184	4	∫	∫	PROPN
ejpam-4022	185	1	∞	∞	PROPN
ejpam-4022	185	2	0	0	NUM
ejpam-4022	186	1	∫	∫	PROPN
ejpam-4022	186	2	∞	∞	NOUN
ejpam-4022	186	3	0	0	PUNCT
ejpam-4022	187	1	e	e	PROPN
ejpam-4022	187	2	−x2+xy+y2	−x2+xy+y2	PROPN
ejpam-4022	187	3	4y	4y	PROPN
ejpam-4022	187	4	(	(	PUNCT
ejpam-4022	187	5	12	12	NUM
ejpam-4022	187	6	√	√	NUM
ejpam-4022	187	7	y	y	NUM
ejpam-4022	187	8	−	−	PROPN
ejpam-4022	187	9	12	12	NUM
ejpam-4022	187	10	√	√	NUM
ejpam-4022	187	11	x	x	SYM
ejpam-4022	187	12	)	)	PUNCT
ejpam-4022	187	13	x3/4	x3/4	NOUN
ejpam-4022	187	14	3	3	NUM
ejpam-4022	187	15	√	√	PROPN
ejpam-4022	187	16	y	y	PROPN
ejpam-4022	187	17	log	log	NOUN
ejpam-4022	187	18	(	(	PUNCT
ejpam-4022	187	19	x	x	NOUN
ejpam-4022	187	20	y	y	PROPN
ejpam-4022	187	21	)	)	PUNCT
ejpam-4022	187	22	dxdy	dxdy	PROPN
ejpam-4022	187	23	=	=	SYM
ejpam-4022	187	24	2	2	NUM
ejpam-4022	187	25	(	(	PUNCT
ejpam-4022	187	26	log	log	NOUN
ejpam-4022	187	27	(	(	PUNCT
ejpam-4022	187	28	7	7	NUM
ejpam-4022	187	29	4	4	NUM
ejpam-4022	187	30	−	−	NOUN
ejpam-4022	187	31	√	√	NUM
ejpam-4022	187	32	3	3	NUM
ejpam-4022	187	33	)	)	PUNCT
ejpam-4022	188	1	+	+	CCONJ
ejpam-4022	188	2	2	2	NUM
ejpam-4022	188	3	log	log	NOUN
ejpam-4022	188	4	(	(	PUNCT
ejpam-4022	188	5	csc	csc	PROPN
ejpam-4022	188	6	(	(	PUNCT
ejpam-4022	188	7	π	π	PROPN
ejpam-4022	188	8	18	18	NUM
ejpam-4022	188	9	)	)	PUNCT
ejpam-4022	188	10	)	)	PUNCT
ejpam-4022	188	11	)	)	PUNCT
ejpam-4022	188	12	proof	proof	NOUN
ejpam-4022	188	13	.	.	PUNCT
ejpam-4022	189	1	use	use	VERB
ejpam-4022	189	2	equation	equation	NOUN
ejpam-4022	189	3	(	(	PUNCT
ejpam-4022	189	4	17	17	NUM
ejpam-4022	189	5	)	)	PUNCT
ejpam-4022	189	6	and	and	CCONJ
ejpam-4022	189	7	set	set	VERB
ejpam-4022	189	8	m	m	PROPN
ejpam-4022	189	9	=	=	SYM
ejpam-4022	189	10	−2/3	−2/3	PROPN
ejpam-4022	189	11	,	,	PUNCT
ejpam-4022	189	12	t	t	NOUN
ejpam-4022	189	13	=	=	SYM
ejpam-4022	189	14	−3/4	−3/4	NOUN
ejpam-4022	189	15	and	and	CCONJ
ejpam-4022	189	16	simplify	simplify	VERB
ejpam-4022	189	17	using	use	VERB
ejpam-4022	189	18	(	(	PUNCT
ejpam-4022	189	19	9.559	9.559	NUM
ejpam-4022	189	20	)	)	PUNCT
ejpam-4022	189	21	in	in	ADP
ejpam-4022	189	22	[	[	X
ejpam-4022	189	23	2	2	NUM
ejpam-4022	189	24	]	]	PUNCT
ejpam-4022	189	25	.	.	PUNCT
ejpam-4022	190	1	17	17	NUM
ejpam-4022	190	2	.	.	PUNCT
ejpam-4022	191	1	derivation	derivation	NOUN
ejpam-4022	191	2	of	of	ADP
ejpam-4022	191	3	new	new	ADJ
ejpam-4022	191	4	entry	entry	NOUN
ejpam-4022	191	5	3.1.3.68	3.1.3.68	NUM
ejpam-4022	191	6	in	in	ADP
ejpam-4022	191	7	[	[	PUNCT
ejpam-4022	191	8	6	6	NUM
ejpam-4022	191	9	]	]	PUNCT
ejpam-4022	191	10	proposition	proposition	NOUN
ejpam-4022	191	11	9	9	NUM
ejpam-4022	191	12	.	.	PUNCT
ejpam-4022	192	1	(	(	PUNCT
ejpam-4022	192	2	20	20	NUM
ejpam-4022	192	3	)	)	PUNCT
ejpam-4022	192	4	∫	∫	PROPN
ejpam-4022	193	1	∞	∞	PROPN
ejpam-4022	193	2	0	0	NUM
ejpam-4022	194	1	∫	∫	PROPN
ejpam-4022	194	2	∞	∞	NOUN
ejpam-4022	194	3	0	0	PUNCT
ejpam-4022	195	1	e	e	PROPN
ejpam-4022	195	2	−x2+xy+y2	−x2+xy+y2	PROPN
ejpam-4022	195	3	4y	4y	PROPN
ejpam-4022	195	4	(	(	PUNCT
ejpam-4022	195	5	6	6	NUM
ejpam-4022	195	6	√	√	NUM
ejpam-4022	195	7	y	y	NUM
ejpam-4022	195	8	−	−	PROPN
ejpam-4022	195	9	6	6	NUM
ejpam-4022	195	10	√	√	PROPN
ejpam-4022	195	11	x	x	SYM
ejpam-4022	195	12	)	)	PUNCT
ejpam-4022	195	13	√	√	PROPN
ejpam-4022	196	1	xy2/3	xy2/3	PROPN
ejpam-4022	196	2	log	log	NOUN
ejpam-4022	196	3	(	(	PUNCT
ejpam-4022	196	4	x	x	SYM
ejpam-4022	196	5	y	y	PROPN
ejpam-4022	196	6	)	)	PUNCT
ejpam-4022	196	7	dxdy	dxdy	NOUN
ejpam-4022	196	8	=	=	SYM
ejpam-4022	196	9	2	2	NUM
ejpam-4022	196	10	log	log	NOUN
ejpam-4022	196	11	(	(	PUNCT
ejpam-4022	196	12	1	1	NUM
ejpam-4022	196	13	+	+	CCONJ
ejpam-4022	196	14	cos	cos	X
ejpam-4022	196	15	(	(	PUNCT
ejpam-4022	196	16	π	π	PROPN
ejpam-4022	196	17	9	9	NUM
ejpam-4022	196	18	)	)	PUNCT
ejpam-4022	196	19	4−	4−	NOUN
ejpam-4022	196	20	4	4	NUM
ejpam-4022	196	21	sin	sin	NOUN
ejpam-4022	196	22	(	(	PUNCT
ejpam-4022	196	23	π	π	PROPN
ejpam-4022	196	24	18	18	NUM
ejpam-4022	196	25	)	)	PUNCT
ejpam-4022	196	26	)	)	PUNCT
ejpam-4022	196	27	proof	proof	NOUN
ejpam-4022	196	28	.	.	PUNCT
ejpam-4022	197	1	use	use	VERB
ejpam-4022	197	2	equation	equation	NOUN
ejpam-4022	197	3	(	(	PUNCT
ejpam-4022	197	4	17	17	NUM
ejpam-4022	197	5	)	)	PUNCT
ejpam-4022	197	6	and	and	CCONJ
ejpam-4022	197	7	set	set	VERB
ejpam-4022	197	8	m	m	PROPN
ejpam-4022	197	9	=	=	NOUN
ejpam-4022	197	10	−1/3	−1/3	ADJ
ejpam-4022	197	11	,	,	PUNCT
ejpam-4022	197	12	t	t	NOUN
ejpam-4022	197	13	=	=	SYM
ejpam-4022	197	14	−1/2	−1/2	VERB
ejpam-4022	197	15	and	and	CCONJ
ejpam-4022	197	16	simplify	simplify	VERB
ejpam-4022	197	17	using	use	VERB
ejpam-4022	197	18	(	(	PUNCT
ejpam-4022	197	19	9.559	9.559	NUM
ejpam-4022	197	20	)	)	PUNCT
ejpam-4022	197	21	in	in	ADP
ejpam-4022	197	22	[	[	X
ejpam-4022	197	23	2	2	NUM
ejpam-4022	197	24	]	]	PUNCT
ejpam-4022	197	25	.	.	PUNCT
ejpam-4022	198	1	18	18	NUM
ejpam-4022	198	2	.	.	PUNCT
ejpam-4022	198	3	derivation	derivation	NOUN
ejpam-4022	198	4	of	of	ADP
ejpam-4022	198	5	new	new	ADJ
ejpam-4022	198	6	entry	entry	NOUN
ejpam-4022	198	7	3.1.3.69	3.1.3.69	NUM
ejpam-4022	198	8	in	in	ADP
ejpam-4022	198	9	[	[	X
ejpam-4022	198	10	6	6	NUM
ejpam-4022	198	11	]	]	PUNCT
ejpam-4022	198	12	proposition	proposition	NOUN
ejpam-4022	198	13	10	10	NUM
ejpam-4022	198	14	.	.	PUNCT
ejpam-4022	199	1	(	(	PUNCT
ejpam-4022	199	2	21	21	NUM
ejpam-4022	199	3	)	)	PUNCT
ejpam-4022	199	4	∫	∫	PROPN
ejpam-4022	200	1	∞	∞	PROPN
ejpam-4022	200	2	0	0	NUM
ejpam-4022	201	1	∫	∫	PROPN
ejpam-4022	201	2	∞	∞	NOUN
ejpam-4022	201	3	0	0	PUNCT
ejpam-4022	202	1	e	e	PROPN
ejpam-4022	202	2	−x2+xy+y2	−x2+xy+y2	NOUN
ejpam-4022	202	3	4y	4y	PROPN
ejpam-4022	202	4	(	(	PUNCT
ejpam-4022	202	5	4	4	NUM
ejpam-4022	202	6	√	√	NOUN
ejpam-4022	202	7	y	y	NUM
ejpam-4022	202	8	−	−	PROPN
ejpam-4022	202	9	4	4	NUM
ejpam-4022	202	10	√	√	PROPN
ejpam-4022	202	11	x	x	SYM
ejpam-4022	202	12	)	)	PUNCT
ejpam-4022	202	13	x3/4	x3/4	NUM
ejpam-4022	202	14	√	√	NUM
ejpam-4022	203	1	y	y	PROPN
ejpam-4022	203	2	log	log	NOUN
ejpam-4022	203	3	(	(	PUNCT
ejpam-4022	203	4	x	x	NOUN
ejpam-4022	203	5	y	y	PROPN
ejpam-4022	203	6	)	)	PUNCT
ejpam-4022	203	7	dxdy	dxdy	NOUN
ejpam-4022	203	8	=	=	NOUN
ejpam-4022	203	9	4	4	NUM
ejpam-4022	203	10	log	log	NOUN
ejpam-4022	203	11	(	(	PUNCT
ejpam-4022	203	12	4−	4−	NOUN
ejpam-4022	203	13	2	2	NUM
ejpam-4022	203	14	√	√	NUM
ejpam-4022	203	15	3	3	NUM
ejpam-4022	203	16	)	)	PUNCT
ejpam-4022	203	17	proof	proof	NOUN
ejpam-4022	203	18	.	.	PUNCT
ejpam-4022	204	1	use	use	VERB
ejpam-4022	204	2	equation	equation	NOUN
ejpam-4022	204	3	(	(	PUNCT
ejpam-4022	204	4	17	17	NUM
ejpam-4022	204	5	)	)	PUNCT
ejpam-4022	204	6	and	and	CCONJ
ejpam-4022	204	7	set	set	VERB
ejpam-4022	204	8	m	m	PROPN
ejpam-4022	204	9	=	=	SYM
ejpam-4022	204	10	−1/2	−1/2	ADJ
ejpam-4022	204	11	,	,	PUNCT
ejpam-4022	204	12	t	t	NOUN
ejpam-4022	204	13	=	=	SYM
ejpam-4022	204	14	−3/4	−3/4	NOUN
ejpam-4022	204	15	and	and	CCONJ
ejpam-4022	204	16	simplify	simplify	VERB
ejpam-4022	204	17	using	use	VERB
ejpam-4022	204	18	(	(	PUNCT
ejpam-4022	204	19	9.559	9.559	NUM
ejpam-4022	204	20	)	)	PUNCT
ejpam-4022	204	21	in	in	ADP
ejpam-4022	204	22	[	[	X
ejpam-4022	204	23	2	2	NUM
ejpam-4022	204	24	]	]	PUNCT
ejpam-4022	204	25	.	.	PUNCT
ejpam-4022	205	1	r.	r.	PROPN
ejpam-4022	205	2	reynolds	reynolds	PROPN
ejpam-4022	205	3	,	,	PUNCT
ejpam-4022	205	4	a.	a.	PROPN
ejpam-4022	205	5	stauffer	stauffer	PROPN
ejpam-4022	205	6	/	/	SYM
ejpam-4022	205	7	eur	eur	PROPN
ejpam-4022	205	8	.	.	PUNCT
ejpam-4022	206	1	j.	j.	PROPN
ejpam-4022	206	2	pure	pure	PROPN
ejpam-4022	206	3	appl	appl	PROPN
ejpam-4022	206	4	.	.	PROPN
ejpam-4022	206	5	math	math	PROPN
ejpam-4022	206	6	,	,	PUNCT
ejpam-4022	206	7	14	14	NUM
ejpam-4022	206	8	(	(	PUNCT
ejpam-4022	206	9	4	4	NUM
ejpam-4022	206	10	)	)	PUNCT
ejpam-4022	206	11	(	(	PUNCT
ejpam-4022	206	12	2021	2021	NUM
ejpam-4022	206	13	)	)	PUNCT
ejpam-4022	206	14	,	,	PUNCT
ejpam-4022	206	15	1200	1200	NUM
ejpam-4022	206	16	-	-	SYM
ejpam-4022	206	17	1211	1211	NUM
ejpam-4022	206	18	1209	1209	NUM
ejpam-4022	206	19	19	19	NUM
ejpam-4022	206	20	.	.	PUNCT
ejpam-4022	207	1	derivation	derivation	NOUN
ejpam-4022	207	2	of	of	ADP
ejpam-4022	207	3	new	new	ADJ
ejpam-4022	207	4	entry	entry	NOUN
ejpam-4022	207	5	3.1.3.70	3.1.3.70	NUM
ejpam-4022	207	6	in	in	ADP
ejpam-4022	207	7	[	[	X
ejpam-4022	207	8	6	6	NUM
ejpam-4022	207	9	]	]	PUNCT
ejpam-4022	207	10	in	in	ADP
ejpam-4022	207	11	this	this	DET
ejpam-4022	207	12	section	section	NOUN
ejpam-4022	207	13	we	we	PRON
ejpam-4022	207	14	will	will	AUX
ejpam-4022	207	15	look	look	VERB
ejpam-4022	207	16	at	at	ADP
ejpam-4022	207	17	the	the	DET
ejpam-4022	207	18	limiting	limit	VERB
ejpam-4022	207	19	case	case	NOUN
ejpam-4022	207	20	of	of	ADP
ejpam-4022	207	21	equation	equation	NOUN
ejpam-4022	207	22	(	(	PUNCT
ejpam-4022	207	23	9	9	NUM
ejpam-4022	207	24	)	)	PUNCT
ejpam-4022	207	25	when	when	SCONJ
ejpam-4022	207	26	p	p	NOUN
ejpam-4022	207	27	=	=	X
ejpam-4022	207	28	q	q	X
ejpam-4022	207	29	and	and	CCONJ
ejpam-4022	207	30	apply	apply	VERB
ejpam-4022	207	31	l’hopitals	l’hopital	NOUN
ejpam-4022	207	32	’	'	PUNCT
ejpam-4022	207	33	rule	rule	NOUN
ejpam-4022	207	34	as	as	ADP
ejpam-4022	207	35	q	q	NOUN
ejpam-4022	207	36	→	→	SYM
ejpam-4022	207	37	1	1	NUM
ejpam-4022	207	38	and	and	CCONJ
ejpam-4022	207	39	express	express	VERB
ejpam-4022	207	40	the	the	DET
ejpam-4022	207	41	integral	integral	ADJ
ejpam-4022	207	42	in	in	ADP
ejpam-4022	207	43	terms	term	NOUN
ejpam-4022	207	44	of	of	ADP
ejpam-4022	207	45	the	the	DET
ejpam-4022	207	46	hypergeometric	hypergeometric	ADJ
ejpam-4022	207	47	function	function	NOUN
ejpam-4022	207	48	section	section	NOUN
ejpam-4022	207	49	(	(	PUNCT
ejpam-4022	207	50	9.1	9.1	NUM
ejpam-4022	207	51	)	)	PUNCT
ejpam-4022	207	52	and	and	CCONJ
ejpam-4022	207	53	equation	equation	NOUN
ejpam-4022	207	54	(	(	PUNCT
ejpam-4022	207	55	9.559	9.559	NUM
ejpam-4022	207	56	)	)	PUNCT
ejpam-4022	207	57	in	in	ADP
ejpam-4022	207	58	[	[	X
ejpam-4022	207	59	2	2	NUM
ejpam-4022	207	60	]	]	PUNCT
ejpam-4022	207	61	.	.	PUNCT
ejpam-4022	208	1	proposition	proposition	NOUN
ejpam-4022	208	2	11	11	NUM
ejpam-4022	208	3	.	.	PUNCT
ejpam-4022	209	1	for	for	ADP
ejpam-4022	209	2	−1	−1	NOUN
ejpam-4022	209	3	<	<	X
ejpam-4022	209	4	re(m	re(m	NOUN
ejpam-4022	209	5	)	)	PUNCT
ejpam-4022	209	6	≤	≤	NOUN
ejpam-4022	209	7	−1/2,−1	−1/2,−1	ADV
ejpam-4022	209	8	<	<	X
ejpam-4022	209	9	im(m	im(m	NOUN
ejpam-4022	209	10	)	)	PUNCT
ejpam-4022	209	11	<	<	X
ejpam-4022	209	12	−1/2,−1	−1/2,−1	ADV
ejpam-4022	209	13	<	<	X
ejpam-4022	209	14	re(t	re(t	PRON
ejpam-4022	209	15	)	)	PUNCT
ejpam-4022	209	16	≤	≤	NOUN
ejpam-4022	209	17	−1/2,−1	−1/2,−1	ADV
ejpam-4022	209	18	<	<	X
ejpam-4022	209	19	im(t	im(t	NUM
ejpam-4022	209	20	)	)	PUNCT
ejpam-4022	209	21	<	<	X
ejpam-4022	210	1	−1/2	−1/2	ADJ
ejpam-4022	210	2	,	,	PUNCT
ejpam-4022	210	3	(	(	PUNCT
ejpam-4022	210	4	22	22	NUM
ejpam-4022	210	5	)	)	PUNCT
ejpam-4022	210	6	∫	∫	PROPN
ejpam-4022	211	1	∞	∞	PROPN
ejpam-4022	211	2	0	0	NUM
ejpam-4022	211	3	∫	∫	PROPN
ejpam-4022	211	4	∞	∞	NUM
ejpam-4022	211	5	0	0	PUNCT
ejpam-4022	212	1	e	e	X
ejpam-4022	212	2	−	−	PROPN
ejpam-4022	212	3	(	(	PUNCT
ejpam-4022	212	4	x+2y)2	x+2y)2	PRON
ejpam-4022	212	5	4y	4y	PROPN
ejpam-4022	212	6	y−m−t−1	y−m−t−1	PROPN
ejpam-4022	212	7	(	(	PUNCT
ejpam-4022	212	8	ymxt	ymxt	ADV
ejpam-4022	212	9	−	−	NOUN
ejpam-4022	212	10	xmyt	xmyt	PROPN
ejpam-4022	212	11	)	)	PUNCT
ejpam-4022	212	12	log	log	NOUN
ejpam-4022	212	13	(	(	PUNCT
ejpam-4022	212	14	x	x	SYM
ejpam-4022	212	15	y	y	PROPN
ejpam-4022	212	16	)	)	PUNCT
ejpam-4022	212	17	dxdy	dxdy	PROPN
ejpam-4022	212	18	=	=	PUNCT
ejpam-4022	213	1	2meiπm	2meiπm	NUM
ejpam-4022	213	2	π	π	NOUN
ejpam-4022	213	3	(	(	PUNCT
ejpam-4022	213	4	2πmφ	2πmφ	NUM
ejpam-4022	213	5	(	(	PUNCT
ejpam-4022	213	6	e2imπ	e2imπ	PROPN
ejpam-4022	213	7	,	,	PUNCT
ejpam-4022	213	8	1	1	NUM
ejpam-4022	213	9	,	,	PUNCT
ejpam-4022	213	10	π	π	PROPN
ejpam-4022	213	11	−	−	PROPN
ejpam-4022	213	12	i	i	PRON
ejpam-4022	213	13	log(2	log(2	VERB
ejpam-4022	213	14	)	)	PUNCT
ejpam-4022	213	15	2π	2π	NOUN
ejpam-4022	213	16	)	)	PUNCT
ejpam-4022	214	1	+	+	CCONJ
ejpam-4022	214	2	iφ	iφ	NOUN
ejpam-4022	214	3	(	(	PUNCT
ejpam-4022	214	4	e2imπ	e2imπ	PROPN
ejpam-4022	214	5	,	,	PUNCT
ejpam-4022	214	6	2	2	NUM
ejpam-4022	214	7	,	,	PUNCT
ejpam-4022	214	8	π	π	PROPN
ejpam-4022	214	9	−	−	PROPN
ejpam-4022	214	10	i	i	PRON
ejpam-4022	214	11	log(2	log(2	VERB
ejpam-4022	214	12	)	)	PUNCT
ejpam-4022	214	13	2π	2π	NOUN
ejpam-4022	214	14	)	)	PUNCT
ejpam-4022	214	15	)	)	PUNCT
ejpam-4022	215	1	−	−	PROPN
ejpam-4022	216	1	2teiπt	2teiπt	NUM
ejpam-4022	216	2	(	(	PUNCT
ejpam-4022	216	3	2πtφ	2πtφ	PROPN
ejpam-4022	216	4	(	(	PUNCT
ejpam-4022	216	5	e2iπt	e2iπt	PROPN
ejpam-4022	216	6	,	,	PUNCT
ejpam-4022	216	7	1	1	NUM
ejpam-4022	216	8	,	,	PUNCT
ejpam-4022	216	9	π	π	PROPN
ejpam-4022	216	10	−	−	PROPN
ejpam-4022	216	11	i	i	PRON
ejpam-4022	216	12	log(2	log(2	VERB
ejpam-4022	216	13	)	)	PUNCT
ejpam-4022	216	14	2π	2π	NOUN
ejpam-4022	216	15	)	)	PUNCT
ejpam-4022	217	1	+	+	CCONJ
ejpam-4022	217	2	iφ	iφ	NOUN
ejpam-4022	217	3	(	(	PUNCT
ejpam-4022	217	4	e2iπt	e2iπt	PROPN
ejpam-4022	217	5	,	,	PUNCT
ejpam-4022	217	6	2	2	NUM
ejpam-4022	217	7	,	,	PUNCT
ejpam-4022	217	8	π	π	PROPN
ejpam-4022	217	9	−	−	PROPN
ejpam-4022	217	10	i	i	PRON
ejpam-4022	217	11	log(2	log(2	VERB
ejpam-4022	217	12	)	)	PUNCT
ejpam-4022	217	13	2π	2π	NOUN
ejpam-4022	217	14	)	)	PUNCT
ejpam-4022	217	15	)	)	PUNCT
ejpam-4022	217	16	proof	proof	NOUN
ejpam-4022	217	17	.	.	PUNCT
ejpam-4022	218	1	use	use	VERB
ejpam-4022	218	2	equation	equation	NOUN
ejpam-4022	218	3	(	(	PUNCT
ejpam-4022	218	4	9	9	NUM
ejpam-4022	218	5	)	)	PUNCT
ejpam-4022	218	6	and	and	CCONJ
ejpam-4022	218	7	set	set	VERB
ejpam-4022	218	8	p	p	NOUN
ejpam-4022	218	9	=	=	NOUN
ejpam-4022	218	10	q	q	X
ejpam-4022	218	11	and	and	CCONJ
ejpam-4022	218	12	apply	apply	VERB
ejpam-4022	218	13	l’hopital	l’hopital	PROPN
ejpam-4022	218	14	’s	’s	PART
ejpam-4022	218	15	’	'	PUNCT
ejpam-4022	218	16	rule	rule	NOUN
ejpam-4022	218	17	as	as	ADP
ejpam-4022	218	18	q	q	NOUN
ejpam-4022	218	19	→	→	SYM
ejpam-4022	218	20	1	1	NUM
ejpam-4022	218	21	to	to	ADP
ejpam-4022	218	22	the	the	DET
ejpam-4022	218	23	right	right	ADJ
ejpam-4022	218	24	-	-	PUNCT
ejpam-4022	218	25	hand	hand	NOUN
ejpam-4022	218	26	side	side	NOUN
ejpam-4022	218	27	and	and	CCONJ
ejpam-4022	218	28	simplify	simplify	VERB
ejpam-4022	218	29	.	.	PUNCT
ejpam-4022	219	1	next	next	ADJ
ejpam-4022	219	2	form	form	NOUN
ejpam-4022	219	3	a	a	DET
ejpam-4022	219	4	second	second	ADJ
ejpam-4022	219	5	integral	integral	ADJ
ejpam-4022	219	6	by	by	ADP
ejpam-4022	219	7	replacing	replace	VERB
ejpam-4022	219	8	m	m	PRON
ejpam-4022	219	9	→	→	SYM
ejpam-4022	219	10	t	t	NOUN
ejpam-4022	219	11	and	and	CCONJ
ejpam-4022	219	12	take	take	VERB
ejpam-4022	219	13	their	their	PRON
ejpam-4022	219	14	difference	difference	NOUN
ejpam-4022	219	15	.	.	PUNCT
ejpam-4022	220	1	r.	r.	PROPN
ejpam-4022	220	2	reynolds	reynolds	PROPN
ejpam-4022	220	3	,	,	PUNCT
ejpam-4022	220	4	a.	a.	PROPN
ejpam-4022	220	5	stauffer	stauffer	PROPN
ejpam-4022	220	6	/	/	SYM
ejpam-4022	220	7	eur	eur	PROPN
ejpam-4022	220	8	.	.	PUNCT
ejpam-4022	221	1	j.	j.	PROPN
ejpam-4022	221	2	pure	pure	PROPN
ejpam-4022	221	3	appl	appl	PROPN
ejpam-4022	221	4	.	.	PROPN
ejpam-4022	221	5	math	math	PROPN
ejpam-4022	221	6	,	,	PUNCT
ejpam-4022	221	7	14	14	NUM
ejpam-4022	221	8	(	(	PUNCT
ejpam-4022	221	9	4	4	NUM
ejpam-4022	221	10	)	)	PUNCT
ejpam-4022	221	11	(	(	PUNCT
ejpam-4022	221	12	2021	2021	NUM
ejpam-4022	221	13	)	)	PUNCT
ejpam-4022	221	14	,	,	PUNCT
ejpam-4022	221	15	1200	1200	NUM
ejpam-4022	221	16	-	-	SYM
ejpam-4022	221	17	1211	1211	NUM
ejpam-4022	221	18	1210	1210	NUM
ejpam-4022	221	19	20	20	NUM
ejpam-4022	221	20	.	.	PUNCT
ejpam-4022	222	1	summary	summary	NOUN
ejpam-4022	222	2	table	table	NOUN
ejpam-4022	222	3	of	of	ADP
ejpam-4022	222	4	results	result	NOUN
ejpam-4022	222	5	f(x	f(x	PROPN
ejpam-4022	222	6	,	,	PUNCT
ejpam-4022	222	7	y	y	NOUN
ejpam-4022	222	8	)	)	PUNCT
ejpam-4022	222	9	∫∞	∫∞	NOUN
ejpam-4022	222	10	0	0	NUM
ejpam-4022	222	11	∫∞	∫∞	NOUN
ejpam-4022	222	12	0	0	PUNCT
ejpam-4022	223	1	f(x	f(x	PROPN
ejpam-4022	223	2	,	,	PUNCT
ejpam-4022	223	3	y)dxdy	y)dxdy	X
ejpam-4022	223	4	xmy−m−1e	xmy−m−1e	PROPN
ejpam-4022	223	5	−px−qy−x2	−px−qy−x2	VERB
ejpam-4022	223	6	4y	4y	NUM
ejpam-4022	223	7	π2m+1qm/2	π2m+1qm/2	PROPN
ejpam-4022	223	8	csc(πm	csc(πm	NOUN
ejpam-4022	223	9	)	)	PUNCT
ejpam-4022	223	10	sinh	sinh	NOUN
ejpam-4022	223	11	(	(	PUNCT
ejpam-4022	223	12	m	m	NOUN
ejpam-4022	223	13	cosh−1	cosh−1	NOUN
ejpam-4022	223	14	(	(	PUNCT
ejpam-4022	223	15	p√	p√	PROPN
ejpam-4022	223	16	q	q	PROPN
ejpam-4022	223	17	)	)	PUNCT
ejpam-4022	223	18	)	)	PUNCT
ejpam-4022	223	19	√	√	ADP
ejpam-4022	224	1	p2−q	p2−q	PROPN
ejpam-4022	224	2	e	e	X
ejpam-4022	224	3	−x2	−x2	PROPN
ejpam-4022	224	4	+	+	NOUN
ejpam-4022	224	5	4xy+y2	4xy+y2	NOUN
ejpam-4022	224	6	4y	4y	PROPN
ejpam-4022	224	7	log2	log2	PROPN
ejpam-4022	224	8	(	(	PUNCT
ejpam-4022	224	9	x	x	NOUN
ejpam-4022	224	10	y	y	PROPN
ejpam-4022	224	11	)	)	PUNCT
ejpam-4022	224	12	√	√	PROPN
ejpam-4022	224	13	x	x	SYM
ejpam-4022	224	14	√	√	NUM
ejpam-4022	224	15	y	y	NUM
ejpam-4022	224	16	2	2	NUM
ejpam-4022	224	17	√	√	ADP
ejpam-4022	224	18	2	2	NUM
ejpam-4022	224	19	3π	3π	NOUN
ejpam-4022	224	20	(	(	PUNCT
ejpam-4022	224	21	π2	π2	X
ejpam-4022	224	22	+	+	CCONJ
ejpam-4022	224	23	cosh−1(2)2	cosh−1(2)2	NOUN
ejpam-4022	224	24	)	)	PUNCT
ejpam-4022	224	25	e	e	PROPN
ejpam-4022	224	26	−x2+xy+y2	−x2+xy+y2	PROPN
ejpam-4022	224	27	4y	4y	PROPN
ejpam-4022	224	28	(	(	PUNCT
ejpam-4022	224	29	x−y	x−y	PROPN
ejpam-4022	224	30	)	)	PUNCT
ejpam-4022	224	31	logk	logk	NOUN
ejpam-4022	224	32	(	(	PUNCT
ejpam-4022	224	33	x	x	NOUN
ejpam-4022	224	34	y	y	PROPN
ejpam-4022	224	35	)	)	PUNCT
ejpam-4022	224	36	√	√	PROPN
ejpam-4022	224	37	xy3/2	xy3/2	PUNCT
ejpam-4022	225	1	i22k+3e	i22k+3e	PRON
ejpam-4022	225	2	iπk	iπk	NOUN
ejpam-4022	225	3	2	2	NUM
ejpam-4022	225	4	πk+1	πk+1	NOUN
ejpam-4022	225	5	(	(	PUNCT
ejpam-4022	225	6	ζ	ζ	NOUN
ejpam-4022	225	7	(	(	PUNCT
ejpam-4022	225	8	−k	−k	PROPN
ejpam-4022	225	9	,	,	PUNCT
ejpam-4022	225	10	16	16	NUM
ejpam-4022	225	11	)	)	PUNCT
ejpam-4022	226	1	+	+	CCONJ
ejpam-4022	226	2	ζ	ζ	X
ejpam-4022	226	3	(	(	PUNCT
ejpam-4022	226	4	−k	−k	PROPN
ejpam-4022	226	5	,	,	PUNCT
ejpam-4022	226	6	56	56	NUM
ejpam-4022	226	7	)	)	PUNCT
ejpam-4022	226	8	+	+	CCONJ
ejpam-4022	226	9	(	(	PUNCT
ejpam-4022	226	10	1−	1−	NUM
ejpam-4022	226	11	3−k	3−k	NUM
ejpam-4022	226	12	)	)	PUNCT
ejpam-4022	226	13	ζ(−k	ζ(−k	NOUN
ejpam-4022	226	14	)	)	PUNCT
ejpam-4022	226	15	)	)	PUNCT
ejpam-4022	227	1	e	e	X
ejpam-4022	227	2	−x2+xy+y2	−x2+xy+y2	NOUN
ejpam-4022	227	3	4y	4y	PROPN
ejpam-4022	227	4	(	(	PUNCT
ejpam-4022	227	5	x−y	x−y	PROPN
ejpam-4022	227	6	)	)	PUNCT
ejpam-4022	227	7	log	log	NOUN
ejpam-4022	227	8	(	(	PUNCT
ejpam-4022	227	9	x	x	NOUN
ejpam-4022	227	10	y	y	PROPN
ejpam-4022	227	11	)	)	PUNCT
ejpam-4022	227	12	log	log	NOUN
ejpam-4022	227	13	(	(	PUNCT
ejpam-4022	227	14	log	log	NOUN
ejpam-4022	227	15	(	(	PUNCT
ejpam-4022	227	16	x	x	NOUN
ejpam-4022	227	17	y	y	PROPN
ejpam-4022	227	18	)	)	PUNCT
ejpam-4022	227	19	)	)	PUNCT
ejpam-4022	228	1	√	√	PROPN
ejpam-4022	228	2	xy3/2	xy3/2	PROPN
ejpam-4022	228	3	4	4	NUM
ejpam-4022	228	4	9π	9π	NUM
ejpam-4022	228	5	2	2	NUM
ejpam-4022	228	6	(	(	PUNCT
ejpam-4022	228	7	6	6	NUM
ejpam-4022	228	8	+	+	SYM
ejpam-4022	228	9	3πi+	3πi+	NUM
ejpam-4022	228	10	log	log	NOUN
ejpam-4022	228	11	(	(	PUNCT
ejpam-4022	228	12	21433π6	21433π6	NOUN
ejpam-4022	228	13	a72	a72	NOUN
ejpam-4022	228	14	)	)	PUNCT
ejpam-4022	228	15	)	)	PUNCT
ejpam-4022	229	1	e	e	X
ejpam-4022	229	2	−x2+xy+y2	−x2+xy+y2	NOUN
ejpam-4022	229	3	4y	4y	PROPN
ejpam-4022	229	4	(	(	PUNCT
ejpam-4022	229	5	4	4	NUM
ejpam-4022	229	6	√	√	NUM
ejpam-4022	229	7	y−	y−	NOUN
ejpam-4022	229	8	4	4	NUM
ejpam-4022	229	9	√	√	NOUN
ejpam-4022	229	10	x	x	SYM
ejpam-4022	229	11	)	)	PUNCT
ejpam-4022	229	12	x3/4√y	x3/4√y	PUNCT
ejpam-4022	230	1	log	log	NOUN
ejpam-4022	230	2	(	(	PUNCT
ejpam-4022	230	3	x	x	SYM
ejpam-4022	230	4	y	y	PROPN
ejpam-4022	230	5	)	)	PUNCT
ejpam-4022	230	6	4	4	NUM
ejpam-4022	230	7	log	log	NOUN
ejpam-4022	230	8	(	(	PUNCT
ejpam-4022	230	9	4−	4−	NOUN
ejpam-4022	230	10	2	2	NUM
ejpam-4022	230	11	√	√	NUM
ejpam-4022	230	12	3	3	NUM
ejpam-4022	230	13	)	)	PUNCT
ejpam-4022	231	1	e	e	NOUN
ejpam-4022	231	2	−x2+xy+y2	−x2+xy+y2	PROPN
ejpam-4022	231	3	4y	4y	PROPN
ejpam-4022	231	4	(	(	PUNCT
ejpam-4022	231	5	6	6	NUM
ejpam-4022	231	6	√	√	NUM
ejpam-4022	231	7	y−	y−	NOUN
ejpam-4022	231	8	6	6	NUM
ejpam-4022	231	9	√	√	NUM
ejpam-4022	231	10	x	x	SYM
ejpam-4022	231	11	)	)	PUNCT
ejpam-4022	231	12	x2/3√y	x2/3√y	X
ejpam-4022	232	1	log	log	NOUN
ejpam-4022	232	2	(	(	PUNCT
ejpam-4022	232	3	x	x	NOUN
ejpam-4022	232	4	y	y	PROPN
ejpam-4022	232	5	)	)	PUNCT
ejpam-4022	232	6	log	log	PROPN
ejpam-4022	232	7	(	(	PUNCT
ejpam-4022	232	8	sec4(π	sec4(π	NOUN
ejpam-4022	232	9	9	9	NUM
ejpam-4022	232	10	)	)	PUNCT
ejpam-4022	232	11	4(sin	4(sin	NOUN
ejpam-4022	232	12	(	(	PUNCT
ejpam-4022	232	13	π	π	PROPN
ejpam-4022	232	14	36)+cos	36)+cos	PROPN
ejpam-4022	232	15	(	(	PUNCT
ejpam-4022	232	16	π	π	PROPN
ejpam-4022	232	17	36	36	NUM
ejpam-4022	232	18	)	)	PUNCT
ejpam-4022	232	19	)	)	PUNCT
ejpam-4022	232	20	4	4	NUM
ejpam-4022	232	21	)	)	PUNCT
ejpam-4022	232	22	e	e	X
ejpam-4022	232	23	−x2+xy+y2	−x2+xy+y2	PROPN
ejpam-4022	232	24	4y	4y	PROPN
ejpam-4022	232	25	(	(	PUNCT
ejpam-4022	232	26	12	12	NUM
ejpam-4022	232	27	√	√	NUM
ejpam-4022	232	28	y−	y−	NOUN
ejpam-4022	232	29	12	12	NUM
ejpam-4022	232	30	√	√	NUM
ejpam-4022	232	31	x	x	SYM
ejpam-4022	232	32	)	)	PUNCT
ejpam-4022	232	33	x3/4	x3/4	NOUN
ejpam-4022	232	34	3	3	NUM
ejpam-4022	232	35	√	√	PROPN
ejpam-4022	232	36	y	y	PROPN
ejpam-4022	232	37	log	log	NOUN
ejpam-4022	232	38	(	(	PUNCT
ejpam-4022	232	39	x	x	NOUN
ejpam-4022	232	40	y	y	PROPN
ejpam-4022	232	41	)	)	PUNCT
ejpam-4022	232	42	2	2	NUM
ejpam-4022	232	43	(	(	PUNCT
ejpam-4022	232	44	log	log	NOUN
ejpam-4022	232	45	(	(	PUNCT
ejpam-4022	232	46	7	7	NUM
ejpam-4022	232	47	4	4	NUM
ejpam-4022	232	48	−	−	NOUN
ejpam-4022	232	49	√	√	NUM
ejpam-4022	232	50	3	3	NUM
ejpam-4022	232	51	)	)	PUNCT
ejpam-4022	233	1	+	+	CCONJ
ejpam-4022	233	2	2	2	NUM
ejpam-4022	233	3	log	log	NOUN
ejpam-4022	233	4	(	(	PUNCT
ejpam-4022	233	5	csc	csc	PROPN
ejpam-4022	233	6	(	(	PUNCT
ejpam-4022	233	7	π	π	PROPN
ejpam-4022	233	8	18	18	NUM
ejpam-4022	233	9	)	)	PUNCT
ejpam-4022	233	10	)	)	PUNCT
ejpam-4022	233	11	)	)	PUNCT
ejpam-4022	234	1	e	e	X
ejpam-4022	234	2	−x2+xy+y2	−x2+xy+y2	NOUN
ejpam-4022	234	3	4y	4y	PROPN
ejpam-4022	234	4	(	(	PUNCT
ejpam-4022	234	5	6	6	NUM
ejpam-4022	234	6	√	√	NUM
ejpam-4022	234	7	y−	y−	NOUN
ejpam-4022	234	8	6	6	NUM
ejpam-4022	234	9	√	√	NUM
ejpam-4022	234	10	x	x	SYM
ejpam-4022	234	11	)	)	PUNCT
ejpam-4022	234	12	√	√	PROPN
ejpam-4022	235	1	xy2/3	xy2/3	PROPN
ejpam-4022	235	2	log	log	NOUN
ejpam-4022	235	3	(	(	PUNCT
ejpam-4022	235	4	x	x	SYM
ejpam-4022	235	5	y	y	PROPN
ejpam-4022	235	6	)	)	PUNCT
ejpam-4022	235	7	2	2	NUM
ejpam-4022	235	8	log	log	NOUN
ejpam-4022	235	9	(	(	PUNCT
ejpam-4022	235	10	1+cos(π	1+cos(π	NUM
ejpam-4022	235	11	9	9	NUM
ejpam-4022	235	12	)	)	PUNCT
ejpam-4022	235	13	4−4	4−4	NUM
ejpam-4022	235	14	sin	sin	NOUN
ejpam-4022	235	15	(	(	PUNCT
ejpam-4022	235	16	π	π	PROPN
ejpam-4022	235	17	18	18	NUM
ejpam-4022	235	18	)	)	PUNCT
ejpam-4022	235	19	)	)	PUNCT
ejpam-4022	236	1	e	e	X
ejpam-4022	236	2	−x2+xy+y2	−x2+xy+y2	NOUN
ejpam-4022	236	3	4y	4y	PROPN
ejpam-4022	236	4	(	(	PUNCT
ejpam-4022	236	5	4	4	NUM
ejpam-4022	236	6	√	√	NUM
ejpam-4022	236	7	y−	y−	NOUN
ejpam-4022	236	8	4	4	NUM
ejpam-4022	236	9	√	√	NOUN
ejpam-4022	236	10	x	x	SYM
ejpam-4022	236	11	)	)	PUNCT
ejpam-4022	236	12	x3/4√y	x3/4√y	PUNCT
ejpam-4022	237	1	log	log	NOUN
ejpam-4022	237	2	(	(	PUNCT
ejpam-4022	237	3	x	x	SYM
ejpam-4022	237	4	y	y	PROPN
ejpam-4022	237	5	)	)	PUNCT
ejpam-4022	237	6	4	4	NUM
ejpam-4022	237	7	log	log	NOUN
ejpam-4022	237	8	(	(	PUNCT
ejpam-4022	237	9	4−	4−	NOUN
ejpam-4022	237	10	2	2	NUM
ejpam-4022	237	11	√	√	NUM
ejpam-4022	237	12	3	3	NUM
ejpam-4022	237	13	)	)	PUNCT
ejpam-4022	237	14	table	table	NOUN
ejpam-4022	237	15	1	1	NUM
ejpam-4022	237	16	:	:	PUNCT
ejpam-4022	237	17	table	table	NOUN
ejpam-4022	237	18	of	of	ADP
ejpam-4022	237	19	definite	definite	ADJ
ejpam-4022	237	20	integrals	integral	NOUN
ejpam-4022	237	21	21	21	NUM
ejpam-4022	237	22	.	.	PUNCT
ejpam-4022	238	1	discussion	discussion	NOUN
ejpam-4022	238	2	in	in	ADP
ejpam-4022	238	3	this	this	DET
ejpam-4022	238	4	work	work	NOUN
ejpam-4022	238	5	the	the	DET
ejpam-4022	238	6	authors	author	NOUN
ejpam-4022	238	7	derived	derive	VERB
ejpam-4022	238	8	a	a	DET
ejpam-4022	238	9	double	double	ADJ
ejpam-4022	238	10	integral	integral	ADJ
ejpam-4022	238	11	formula	formula	NOUN
ejpam-4022	238	12	in	in	ADP
ejpam-4022	238	13	terms	term	NOUN
ejpam-4022	238	14	of	of	ADP
ejpam-4022	238	15	the	the	DET
ejpam-4022	238	16	lerch	lerch	PROPN
ejpam-4022	238	17	function	function	PROPN
ejpam-4022	238	18	.	.	PUNCT
ejpam-4022	239	1	this	this	DET
ejpam-4022	239	2	integral	integral	ADJ
ejpam-4022	239	3	formula	formula	NOUN
ejpam-4022	239	4	was	be	AUX
ejpam-4022	239	5	then	then	ADV
ejpam-4022	239	6	used	use	VERB
ejpam-4022	239	7	to	to	PART
ejpam-4022	239	8	derive	derive	VERB
ejpam-4022	239	9	special	special	ADJ
ejpam-4022	239	10	cases	case	NOUN
ejpam-4022	239	11	in	in	ADP
ejpam-4022	239	12	terms	term	NOUN
ejpam-4022	239	13	of	of	ADP
ejpam-4022	239	14	fundamental	fundamental	ADJ
ejpam-4022	239	15	constants	constant	NOUN
ejpam-4022	239	16	and	and	CCONJ
ejpam-4022	239	17	special	special	ADJ
ejpam-4022	239	18	functions	function	NOUN
ejpam-4022	239	19	.	.	PUNCT
ejpam-4022	240	1	a	a	DET
ejpam-4022	240	2	table	table	NOUN
ejpam-4022	240	3	(	(	PUNCT
ejpam-4022	240	4	1	1	NUM
ejpam-4022	240	5	)	)	PUNCT
ejpam-4022	240	6	of	of	ADP
ejpam-4022	240	7	integrals	integral	NOUN
ejpam-4022	240	8	featuring	feature	VERB
ejpam-4022	240	9	some	some	PRON
ejpam-4022	240	10	of	of	ADP
ejpam-4022	240	11	the	the	DET
ejpam-4022	240	12	integral	integral	ADJ
ejpam-4022	240	13	results	result	NOUN
ejpam-4022	240	14	was	be	AUX
ejpam-4022	240	15	presented	present	VERB
ejpam-4022	240	16	for	for	ADP
ejpam-4022	240	17	the	the	DET
ejpam-4022	240	18	benefit	benefit	NOUN
ejpam-4022	240	19	of	of	ADP
ejpam-4022	240	20	interested	interested	ADJ
ejpam-4022	240	21	readers	reader	NOUN
ejpam-4022	240	22	.	.	PUNCT
ejpam-4022	241	1	we	we	PRON
ejpam-4022	241	2	used	use	VERB
ejpam-4022	241	3	wolfram	wolfram	PROPN
ejpam-4022	241	4	mathematica	mathematica	PROPN
ejpam-4022	241	5	to	to	PART
ejpam-4022	241	6	numerically	numerically	ADV
ejpam-4022	241	7	verify	verify	VERB
ejpam-4022	241	8	the	the	DET
ejpam-4022	241	9	formulas	formula	NOUN
ejpam-4022	241	10	for	for	ADP
ejpam-4022	241	11	various	various	ADJ
ejpam-4022	241	12	ranges	range	NOUN
ejpam-4022	241	13	of	of	ADP
ejpam-4022	241	14	the	the	DET
ejpam-4022	241	15	parameters	parameter	NOUN
ejpam-4022	241	16	for	for	ADP
ejpam-4022	241	17	real	real	ADJ
ejpam-4022	241	18	and	and	CCONJ
ejpam-4022	241	19	imaginary	imaginary	ADJ
ejpam-4022	241	20	values	value	NOUN
ejpam-4022	241	21	.	.	PUNCT
ejpam-4022	242	1	we	we	PRON
ejpam-4022	242	2	will	will	AUX
ejpam-4022	242	3	use	use	VERB
ejpam-4022	242	4	our	our	PRON
ejpam-4022	242	5	contour	contour	NOUN
ejpam-4022	242	6	integral	integral	ADJ
ejpam-4022	242	7	method	method	NOUN
ejpam-4022	242	8	to	to	PART
ejpam-4022	242	9	derive	derive	VERB
ejpam-4022	242	10	other	other	ADJ
ejpam-4022	242	11	double	double	ADJ
ejpam-4022	242	12	integrals	integral	NOUN
ejpam-4022	242	13	and	and	CCONJ
ejpam-4022	242	14	produce	produce	VERB
ejpam-4022	242	15	more	more	ADJ
ejpam-4022	242	16	tables	table	NOUN
ejpam-4022	242	17	of	of	ADP
ejpam-4022	242	18	integrals	integral	NOUN
ejpam-4022	242	19	in	in	ADP
ejpam-4022	242	20	our	our	PRON
ejpam-4022	242	21	future	future	ADJ
ejpam-4022	242	22	work	work	NOUN
ejpam-4022	242	23	.	.	PUNCT
ejpam-4022	243	1	references	reference	NOUN
ejpam-4022	243	2	1211	1211	NUM
ejpam-4022	243	3	references	reference	NOUN
ejpam-4022	243	4	[	[	X
ejpam-4022	243	5	1	1	NUM
ejpam-4022	243	6	]	]	X
ejpam-4022	243	7	george	george	PROPN
ejpam-4022	243	8	b.	b.	PROPN
ejpam-4022	243	9	arfken	arfken	PROPN
ejpam-4022	243	10	and	and	CCONJ
ejpam-4022	243	11	hans	hans	PROPN
ejpam-4022	243	12	j.	j.	PROPN
ejpam-4022	243	13	weber	weber	PROPN
ejpam-4022	243	14	.	.	PUNCT
ejpam-4022	244	1	mathematical	mathematical	ADJ
ejpam-4022	244	2	methods	method	NOUN
ejpam-4022	244	3	for	for	ADP
ejpam-4022	244	4	physicists	physicist	NOUN
ejpam-4022	244	5	international	international	PROPN
ejpam-4022	244	6	student	student	NOUN
ejpam-4022	244	7	edition	edition	NOUN
ejpam-4022	244	8	.	.	PUNCT
ejpam-4022	245	1	elsevier	elsevier	PROPN
ejpam-4022	245	2	,	,	PUNCT
ejpam-4022	245	3	07	07	NUM
ejpam-4022	245	4	2005	2005	NUM
ejpam-4022	245	5	.	.	PUNCT
ejpam-4022	246	1	[	[	X
ejpam-4022	246	2	2	2	NUM
ejpam-4022	246	3	]	]	PUNCT
ejpam-4022	246	4	i.	i.	PROPN
ejpam-4022	246	5	s.	s.	PROPN
ejpam-4022	246	6	gradshteyn	gradshteyn	PROPN
ejpam-4022	246	7	,	,	PUNCT
ejpam-4022	246	8	i.	i.	PROPN
ejpam-4022	246	9	m.	m.	PROPN
ejpam-4022	246	10	ryzhik	ryzhik	PROPN
ejpam-4022	246	11	,	,	PUNCT
ejpam-4022	246	12	alan	alan	PROPN
ejpam-4022	246	13	jeffrey	jeffrey	PROPN
ejpam-4022	246	14	,	,	PUNCT
ejpam-4022	246	15	and	and	CCONJ
ejpam-4022	246	16	daniel	daniel	PROPN
ejpam-4022	246	17	zwillinger	zwillinger	PROPN
ejpam-4022	246	18	.	.	PUNCT
ejpam-4022	246	19	table	table	NOUN
ejpam-4022	246	20	of	of	ADP
ejpam-4022	246	21	integrals	integral	NOUN
ejpam-4022	246	22	,	,	PUNCT
ejpam-4022	246	23	series	series	NOUN
ejpam-4022	246	24	,	,	PUNCT
ejpam-4022	246	25	and	and	CCONJ
ejpam-4022	246	26	products	product	NOUN
ejpam-4022	246	27	.	.	PUNCT
ejpam-4022	247	1	academic	academic	ADJ
ejpam-4022	247	2	press	press	NOUN
ejpam-4022	247	3	;	;	PUNCT
ejpam-4022	247	4	6th	6th	ADJ
ejpam-4022	247	5	edition	edition	NOUN
ejpam-4022	247	6	(	(	PUNCT
ejpam-4022	247	7	aug	aug	PROPN
ejpam-4022	247	8	.	.	PROPN
ejpam-4022	247	9	24	24	NUM
ejpam-4022	247	10	2000	2000	NUM
ejpam-4022	247	11	)	)	PUNCT
ejpam-4022	247	12	,	,	PUNCT
ejpam-4022	247	13	08	08	NUM
ejpam-4022	247	14	2000	2000	NUM
ejpam-4022	247	15	.	.	PUNCT
ejpam-4022	248	1	[	[	X
ejpam-4022	248	2	3	3	X
ejpam-4022	248	3	]	]	X
ejpam-4022	248	4	abdul	abdul	PROPN
ejpam-4022	248	5	jerri	jerri	PROPN
ejpam-4022	248	6	.	.	PUNCT
ejpam-4022	248	7	integral	integral	ADJ
ejpam-4022	248	8	and	and	CCONJ
ejpam-4022	248	9	discrete	discrete	ADJ
ejpam-4022	248	10	transforms	transform	VERB
ejpam-4022	248	11	with	with	ADP
ejpam-4022	248	12	applications	application	NOUN
ejpam-4022	248	13	and	and	CCONJ
ejpam-4022	248	14	error	error	NOUN
ejpam-4022	248	15	analysis	analysis	NOUN
ejpam-4022	248	16	.	.	PUNCT
ejpam-4022	249	1	chapman	chapman	PROPN
ejpam-4022	249	2	&	&	CCONJ
ejpam-4022	249	3	hall	hall	PROPN
ejpam-4022	249	4	/	/	SYM
ejpam-4022	249	5	crc	crc	NOUN
ejpam-4022	249	6	pure	pure	ADJ
ejpam-4022	249	7	and	and	CCONJ
ejpam-4022	249	8	applied	applied	ADJ
ejpam-4022	249	9	mathematics	mathematic	NOUN
ejpam-4022	249	10	,	,	PUNCT
ejpam-4022	249	11	06	06	NUM
ejpam-4022	249	12	1992	1992	NUM
ejpam-4022	249	13	.	.	PUNCT
ejpam-4022	250	1	[	[	X
ejpam-4022	250	2	4	4	X
ejpam-4022	250	3	]	]	PUNCT
ejpam-4022	250	4	t.	t.	PROPN
ejpam-4022	250	5	m.	m.	PROPN
ejpam-4022	250	6	macrobert	macrobert	PROPN
ejpam-4022	250	7	.	.	PUNCT
ejpam-4022	251	1	integrals	integral	NOUN
ejpam-4022	251	2	involving	involve	VERB
ejpam-4022	251	3	a	a	DET
ejpam-4022	251	4	modified	modify	VERB
ejpam-4022	251	5	bessel	bessel	NOUN
ejpam-4022	251	6	function	function	NOUN
ejpam-4022	251	7	of	of	ADP
ejpam-4022	251	8	the	the	DET
ejpam-4022	251	9	second	second	ADJ
ejpam-4022	251	10	kind	kind	NOUN
ejpam-4022	251	11	and	and	CCONJ
ejpam-4022	251	12	an	an	DET
ejpam-4022	251	13	e	e	NOUN
ejpam-4022	251	14	-	-	NOUN
ejpam-4022	251	15	function	function	NOUN
ejpam-4022	251	16	.	.	PUNCT
ejpam-4022	252	1	proceedings	proceeding	NOUN
ejpam-4022	252	2	of	of	ADP
ejpam-4022	252	3	the	the	DET
ejpam-4022	252	4	glasgow	glasgow	PROPN
ejpam-4022	252	5	mathematical	mathematical	PROPN
ejpam-4022	252	6	association	association	PROPN
ejpam-4022	252	7	,	,	PUNCT
ejpam-4022	252	8	2:93–96	2:93–96	PROPN
ejpam-4022	252	9	,	,	PUNCT
ejpam-4022	252	10	10	10	NUM
ejpam-4022	252	11	1954	1954	NUM
ejpam-4022	252	12	.	.	PUNCT
ejpam-4022	253	1	[	[	X
ejpam-4022	253	2	5	5	X
ejpam-4022	253	3	]	]	PUNCT
ejpam-4022	253	4	keith	keith	PROPN
ejpam-4022	253	5	b.	b.	PROPN
ejpam-4022	253	6	oldham	oldham	PROPN
ejpam-4022	253	7	,	,	PUNCT
ejpam-4022	253	8	jan	jan	PROPN
ejpam-4022	253	9	myland	myland	PROPN
ejpam-4022	253	10	,	,	PUNCT
ejpam-4022	253	11	and	and	CCONJ
ejpam-4022	253	12	jerome	jerome	PROPN
ejpam-4022	253	13	spanier	spanier	NOUN
ejpam-4022	253	14	.	.	PUNCT
ejpam-4022	254	1	an	an	DET
ejpam-4022	254	2	atlas	atlas	PROPN
ejpam-4022	254	3	of	of	ADP
ejpam-4022	254	4	functions	function	NOUN
ejpam-4022	254	5	:	:	PUNCT
ejpam-4022	254	6	with	with	ADP
ejpam-4022	254	7	equator	equator	NOUN
ejpam-4022	254	8	,	,	PUNCT
ejpam-4022	254	9	the	the	DET
ejpam-4022	254	10	atlas	atlas	PROPN
ejpam-4022	254	11	function	function	PROPN
ejpam-4022	254	12	calculator	calculator	NOUN
ejpam-4022	254	13	.	.	PUNCT
ejpam-4022	255	1	springer	springer	NOUN
ejpam-4022	255	2	science	science	PROPN
ejpam-4022	255	3	&	&	CCONJ
ejpam-4022	255	4	business	business	NOUN
ejpam-4022	255	5	media	medium	NOUN
ejpam-4022	255	6	,	,	PUNCT
ejpam-4022	255	7	07	07	NUM
ejpam-4022	255	8	2010	2010	NUM
ejpam-4022	255	9	.	.	PUNCT
ejpam-4022	256	1	[	[	X
ejpam-4022	256	2	6	6	X
ejpam-4022	256	3	]	]	PUNCT
ejpam-4022	256	4	anatolĭı	anatolĭı	PROPN
ejpam-4022	256	5	platonovich	platonovich	PROPN
ejpam-4022	256	6	prudnikov	prudnikov	PROPN
ejpam-4022	256	7	,	,	PUNCT
ejpam-4022	256	8	yu	yu	PROPN
ejpam-4022	256	9	a.	a.	NOUN
ejpam-4022	256	10	brychkov	brychkov	PROPN
ejpam-4022	256	11	,	,	PUNCT
ejpam-4022	256	12	and	and	CCONJ
ejpam-4022	256	13	oleg	oleg	PROPN
ejpam-4022	256	14	igorevich	igorevich	PROPN
ejpam-4022	256	15	marichev	marichev	PROPN
ejpam-4022	256	16	.	.	PUNCT
ejpam-4022	256	17	integrals	integral	NOUN
ejpam-4022	256	18	and	and	CCONJ
ejpam-4022	256	19	series	series	NOUN
ejpam-4022	256	20	:	:	PUNCT
ejpam-4022	256	21	more	more	ADJ
ejpam-4022	256	22	special	special	ADJ
ejpam-4022	256	23	functions	function	NOUN
ejpam-4022	256	24	.	.	PUNCT
ejpam-4022	257	1	gordon	gordon	PROPN
ejpam-4022	257	2	and	and	CCONJ
ejpam-4022	257	3	breach	breach	VERB
ejpam-4022	257	4	science	science	NOUN
ejpam-4022	257	5	publishers	publisher	NOUN
ejpam-4022	257	6	,	,	PUNCT
ejpam-4022	257	7	1986	1986	NUM
ejpam-4022	257	8	.	.	PUNCT
ejpam-4022	258	1	[	[	X
ejpam-4022	258	2	7	7	X
ejpam-4022	258	3	]	]	X
ejpam-4022	258	4	fouad	fouad	PROPN
ejpam-4022	258	5	m.	m.	PROPN
ejpam-4022	258	6	ragab	ragab	PROPN
ejpam-4022	258	7	.	.	PUNCT
ejpam-4022	259	1	an	an	DET
ejpam-4022	259	2	integral	integral	ADJ
ejpam-4022	259	3	involving	involve	VERB
ejpam-4022	259	4	a	a	DET
ejpam-4022	259	5	modified	modify	VERB
ejpam-4022	259	6	bessel	bessel	NOUN
ejpam-4022	259	7	function	function	NOUN
ejpam-4022	259	8	of	of	ADP
ejpam-4022	259	9	the	the	DET
ejpam-4022	259	10	second	second	ADJ
ejpam-4022	259	11	kind	kind	NOUN
ejpam-4022	259	12	and	and	CCONJ
ejpam-4022	259	13	an	an	DET
ejpam-4022	259	14	e	e	NOUN
ejpam-4022	259	15	-	-	NOUN
ejpam-4022	259	16	function	function	NOUN
ejpam-4022	259	17	.	.	PUNCT
ejpam-4022	260	1	proceedings	proceeding	NOUN
ejpam-4022	260	2	of	of	ADP
ejpam-4022	260	3	the	the	DET
ejpam-4022	260	4	glasgow	glasgow	PROPN
ejpam-4022	260	5	mathematical	mathematical	PROPN
ejpam-4022	260	6	association	association	PROPN
ejpam-4022	260	7	,	,	PUNCT
ejpam-4022	260	8	1:119–120	1:119–120	NUM
ejpam-4022	260	9	,	,	PUNCT
ejpam-4022	260	10	09	09	NUM
ejpam-4022	260	11	1953	1953	NUM
ejpam-4022	260	12	.	.	PUNCT
ejpam-4022	261	1	[	[	X
ejpam-4022	261	2	8	8	NUM
ejpam-4022	261	3	]	]	X
ejpam-4022	261	4	robert	robert	PROPN
ejpam-4022	261	5	reynolds	reynolds	PROPN
ejpam-4022	261	6	and	and	CCONJ
ejpam-4022	261	7	allan	allan	PROPN
ejpam-4022	261	8	stauffer	stauffer	PROPN
ejpam-4022	261	9	.	.	PUNCT
ejpam-4022	262	1	a	a	DET
ejpam-4022	262	2	method	method	NOUN
ejpam-4022	262	3	for	for	ADP
ejpam-4022	262	4	evaluating	evaluate	VERB
ejpam-4022	262	5	definite	definite	ADJ
ejpam-4022	262	6	integrals	integral	NOUN
ejpam-4022	262	7	in	in	ADP
ejpam-4022	262	8	terms	term	NOUN
ejpam-4022	262	9	of	of	ADP
ejpam-4022	262	10	special	special	ADJ
ejpam-4022	262	11	functions	function	NOUN
ejpam-4022	262	12	with	with	ADP
ejpam-4022	262	13	examples	example	NOUN
ejpam-4022	262	14	.	.	PUNCT
ejpam-4022	263	1	international	international	ADJ
ejpam-4022	263	2	mathematical	mathematical	PROPN
ejpam-4022	263	3	forum	forum	PROPN
ejpam-4022	263	4	,	,	PUNCT
ejpam-4022	263	5	15:235	15:235	NUM
ejpam-4022	263	6	–	–	PUNCT
ejpam-4022	263	7	244	244	NUM
ejpam-4022	263	8	,	,	PUNCT
ejpam-4022	263	9	2020	2020	NUM
ejpam-4022	263	10	.	.	PUNCT
ejpam-4022	264	1	[	[	X
ejpam-4022	264	2	9	9	NUM
ejpam-4022	264	3	]	]	X
ejpam-4022	264	4	n.	n.	NOUN
ejpam-4022	264	5	m.	m.	NOUN
ejpam-4022	264	6	temme	temme	PROPN
ejpam-4022	264	7	.	.	PUNCT
ejpam-4022	265	1	a	a	DET
ejpam-4022	265	2	double	double	ADJ
ejpam-4022	265	3	integral	integral	ADJ
ejpam-4022	265	4	containing	contain	VERB
ejpam-4022	265	5	the	the	DET
ejpam-4022	265	6	modified	modify	VERB
ejpam-4022	265	7	bessel	bessel	NOUN
ejpam-4022	265	8	function	function	NOUN
ejpam-4022	265	9	:	:	PUNCT
ejpam-4022	265	10	asymptotics	asymptotic	NOUN
ejpam-4022	265	11	and	and	CCONJ
ejpam-4022	265	12	computation	computation	NOUN
ejpam-4022	265	13	.	.	PUNCT
ejpam-4022	266	1	mathematics	mathematic	NOUN
ejpam-4022	266	2	of	of	ADP
ejpam-4022	266	3	computation	computation	NOUN
ejpam-4022	266	4	,	,	PUNCT
ejpam-4022	266	5	47:683–683	47:683–683	PROPN
ejpam-4022	266	6	,	,	PUNCT
ejpam-4022	266	7	1986	1986	NUM
ejpam-4022	266	8	.	.	PUNCT
ejpam-4022	267	1	[	[	X
ejpam-4022	267	2	10	10	NUM
ejpam-4022	267	3	]	]	PUNCT
ejpam-4022	267	4	a.	a.	NOUN
ejpam-4022	267	5	voros	voros	PROPN
ejpam-4022	267	6	.	.	PUNCT
ejpam-4022	268	1	spectral	spectral	ADJ
ejpam-4022	268	2	functions	function	NOUN
ejpam-4022	268	3	,	,	PUNCT
ejpam-4022	268	4	special	special	ADJ
ejpam-4022	268	5	functions	function	NOUN
ejpam-4022	268	6	and	and	CCONJ
ejpam-4022	268	7	the	the	DET
ejpam-4022	268	8	selberg	selberg	NOUN
ejpam-4022	268	9	zeta	zeta	PROPN
ejpam-4022	268	10	function	function	PROPN
ejpam-4022	268	11	.	.	PUNCT
ejpam-4022	269	1	communications	communication	NOUN
ejpam-4022	269	2	in	in	ADP
ejpam-4022	269	3	mathematical	mathematical	ADJ
ejpam-4022	269	4	physics	physics	NOUN
ejpam-4022	269	5	,	,	PUNCT
ejpam-4022	269	6	110:439–465	110:439–465	NUM
ejpam-4022	269	7	,	,	PUNCT
ejpam-4022	269	8	01	01	NUM
ejpam-4022	269	9	1987	1987	NUM
ejpam-4022	269	10	.	.	PUNCT