id	sid	tid	token	lemma	pos
ejpam-4181	1	1	european	european	PROPN
ejpam-4181	1	2	journal	journal	PROPN
ejpam-4181	1	3	of	of	ADP
ejpam-4181	1	4	pure	pure	ADJ
ejpam-4181	1	5	and	and	CCONJ
ejpam-4181	1	6	applied	apply	VERB
ejpam-4181	1	7	mathematics	mathematic	NOUN
ejpam-4181	1	8	vol	vol	NOUN
ejpam-4181	1	9	.	.	PROPN
ejpam-4181	2	1	15	15	NUM
ejpam-4181	2	2	,	,	PUNCT
ejpam-4181	2	3	no	no	INTJ
ejpam-4181	2	4	.	.	NOUN
ejpam-4181	2	5	1	1	NUM
ejpam-4181	2	6	,	,	PUNCT
ejpam-4181	2	7	2022	2022	NUM
ejpam-4181	2	8	,	,	PUNCT
ejpam-4181	2	9	30	30	NUM
ejpam-4181	2	10	-	-	SYM
ejpam-4181	2	11	35	35	NUM
ejpam-4181	2	12	issn	issn	PROPN
ejpam-4181	2	13	1307	1307	NUM
ejpam-4181	2	14	-	-	SYM
ejpam-4181	2	15	5543	5543	NUM
ejpam-4181	2	16	–	–	PUNCT
ejpam-4181	2	17	ejpam.com	ejpam.com	X
ejpam-4181	2	18	published	publish	VERB
ejpam-4181	2	19	by	by	ADP
ejpam-4181	2	20	new	new	PROPN
ejpam-4181	2	21	york	york	PROPN
ejpam-4181	2	22	business	business	PROPN
ejpam-4181	2	23	global	global	PROPN
ejpam-4181	2	24	extended	extend	VERB
ejpam-4181	2	25	apelblat	apelblat	NOUN
ejpam-4181	2	26	integrals	integral	NOUN
ejpam-4181	2	27	for	for	ADP
ejpam-4181	2	28	fractional	fractional	ADJ
ejpam-4181	2	29	calculus	calculus	PROPN
ejpam-4181	2	30	robert	robert	PROPN
ejpam-4181	2	31	reynolds1,∗	reynolds1,∗	PROPN
ejpam-4181	2	32	,	,	PUNCT
ejpam-4181	2	33	allan	allan	PROPN
ejpam-4181	2	34	stauffer1	stauffer1	PROPN
ejpam-4181	2	35	1	1	NUM
ejpam-4181	2	36	department	department	NOUN
ejpam-4181	2	37	of	of	ADP
ejpam-4181	2	38	mathematics	mathematic	NOUN
ejpam-4181	2	39	and	and	CCONJ
ejpam-4181	2	40	statistics	statistic	NOUN
ejpam-4181	2	41	,	,	PUNCT
ejpam-4181	2	42	faculty	faculty	NOUN
ejpam-4181	2	43	of	of	ADP
ejpam-4181	2	44	science	science	PROPN
ejpam-4181	2	45	,	,	PUNCT
ejpam-4181	2	46	york	york	PROPN
ejpam-4181	2	47	university	university	PROPN
ejpam-4181	2	48	,	,	PUNCT
ejpam-4181	2	49	toronto	toronto	PROPN
ejpam-4181	2	50	,	,	PUNCT
ejpam-4181	2	51	ontario	ontario	PROPN
ejpam-4181	2	52	,	,	PUNCT
ejpam-4181	2	53	canada	canada	PROPN
ejpam-4181	2	54	,	,	PUNCT
ejpam-4181	2	55	m3j1p3	m3j1p3	PROPN
ejpam-4181	2	56	abstract	abstract	NOUN
ejpam-4181	2	57	.	.	PUNCT
ejpam-4181	3	1	a	a	DET
ejpam-4181	3	2	quadruple	quadruple	NOUN
ejpam-4181	3	3	integral	integral	ADJ
ejpam-4181	3	4	involving	involve	VERB
ejpam-4181	3	5	the	the	DET
ejpam-4181	3	6	logarithmic	logarithmic	ADJ
ejpam-4181	3	7	,	,	PUNCT
ejpam-4181	3	8	exponential	exponential	ADJ
ejpam-4181	3	9	,	,	PUNCT
ejpam-4181	3	10	polynomial	polynomial	ADJ
ejpam-4181	3	11	and	and	CCONJ
ejpam-4181	3	12	gamma	gamma	NOUN
ejpam-4181	3	13	functions	function	NOUN
ejpam-4181	3	14	is	be	AUX
ejpam-4181	3	15	derived	derive	VERB
ejpam-4181	3	16	in	in	ADP
ejpam-4181	3	17	terms	term	NOUN
ejpam-4181	3	18	of	of	ADP
ejpam-4181	3	19	the	the	DET
ejpam-4181	3	20	hurwitz	hurwitz	PROPN
ejpam-4181	3	21	-	-	PUNCT
ejpam-4181	3	22	lerch	lerch	PROPN
ejpam-4181	3	23	zeta	zeta	PROPN
ejpam-4181	3	24	function	function	PROPN
ejpam-4181	3	25	.	.	PUNCT
ejpam-4181	4	1	special	special	ADJ
ejpam-4181	4	2	cases	case	NOUN
ejpam-4181	4	3	of	of	ADP
ejpam-4181	4	4	this	this	DET
ejpam-4181	4	5	integral	integral	ADJ
ejpam-4181	4	6	are	be	AUX
ejpam-4181	4	7	evaluated	evaluate	VERB
ejpam-4181	4	8	in	in	ADP
ejpam-4181	4	9	terms	term	NOUN
ejpam-4181	4	10	of	of	ADP
ejpam-4181	4	11	special	special	ADJ
ejpam-4181	4	12	functions	function	NOUN
ejpam-4181	4	13	and	and	CCONJ
ejpam-4181	4	14	fundamental	fundamental	ADJ
ejpam-4181	4	15	constants	constant	NOUN
ejpam-4181	4	16	.	.	PUNCT
ejpam-4181	5	1	almost	almost	ADV
ejpam-4181	5	2	all	all	DET
ejpam-4181	5	3	hurwitz	hurwitz	PROPN
ejpam-4181	5	4	-	-	PUNCT
ejpam-4181	5	5	lerch	lerch	PROPN
ejpam-4181	5	6	zeta	zeta	PROPN
ejpam-4181	5	7	functions	function	NOUN
ejpam-4181	5	8	have	have	VERB
ejpam-4181	5	9	an	an	DET
ejpam-4181	5	10	asymmetrical	asymmetrical	ADJ
ejpam-4181	5	11	zero	zero	NUM
ejpam-4181	5	12	-	-	PUNCT
ejpam-4181	5	13	distribution	distribution	NOUN
ejpam-4181	5	14	.	.	PUNCT
ejpam-4181	6	1	the	the	DET
ejpam-4181	6	2	majority	majority	NOUN
ejpam-4181	6	3	of	of	ADP
ejpam-4181	6	4	the	the	DET
ejpam-4181	6	5	results	result	NOUN
ejpam-4181	6	6	in	in	ADP
ejpam-4181	6	7	this	this	DET
ejpam-4181	6	8	work	work	NOUN
ejpam-4181	6	9	are	be	AUX
ejpam-4181	6	10	new	new	ADJ
ejpam-4181	6	11	.	.	PUNCT
ejpam-4181	7	1	2020	2020	NUM
ejpam-4181	7	2	mathematics	mathematic	NOUN
ejpam-4181	7	3	subject	subject	NOUN
ejpam-4181	7	4	classifications	classification	NOUN
ejpam-4181	7	5	:	:	PUNCT
ejpam-4181	7	6	30e20	30e20	NUM
ejpam-4181	7	7	,	,	PUNCT
ejpam-4181	7	8	33	33	NUM
ejpam-4181	7	9	-	-	SYM
ejpam-4181	7	10	01	01	NUM
ejpam-4181	7	11	,	,	PUNCT
ejpam-4181	7	12	33	33	NUM
ejpam-4181	7	13	-	-	SYM
ejpam-4181	7	14	03	03	NUM
ejpam-4181	7	15	,	,	PUNCT
ejpam-4181	7	16	33	33	NUM
ejpam-4181	7	17	-	-	PUNCT
ejpam-4181	7	18	04	04	NUM
ejpam-4181	7	19	,	,	PUNCT
ejpam-4181	7	20	33	33	NUM
ejpam-4181	7	21	-	-	PUNCT
ejpam-4181	7	22	33b	33b	NUM
ejpam-4181	7	23	key	key	ADJ
ejpam-4181	7	24	words	word	NOUN
ejpam-4181	7	25	and	and	CCONJ
ejpam-4181	7	26	phrases	phrase	NOUN
ejpam-4181	7	27	:	:	PUNCT
ejpam-4181	7	28	volterra	volterra	NOUN
ejpam-4181	7	29	function	function	PROPN
ejpam-4181	7	30	,	,	PUNCT
ejpam-4181	7	31	hurwitz	hurwitz	PROPN
ejpam-4181	7	32	-	-	PUNCT
ejpam-4181	7	33	lerch	lerch	PROPN
ejpam-4181	7	34	zeta	zeta	PROPN
ejpam-4181	7	35	function	function	PROPN
ejpam-4181	7	36	,	,	PUNCT
ejpam-4181	7	37	gamma	gamma	NOUN
ejpam-4181	7	38	function	function	PROPN
ejpam-4181	7	39	,	,	PUNCT
ejpam-4181	7	40	quadruple	quadruple	NOUN
ejpam-4181	7	41	integral	integral	ADJ
ejpam-4181	7	42	,	,	PUNCT
ejpam-4181	7	43	contour	contour	NOUN
ejpam-4181	7	44	integral	integral	ADJ
ejpam-4181	7	45	,	,	PUNCT
ejpam-4181	7	46	logarithmic	logarithmic	ADJ
ejpam-4181	7	47	function	function	NOUN
ejpam-4181	7	48	1	1	NUM
ejpam-4181	7	49	.	.	NOUN
ejpam-4181	7	50	significance	significance	NOUN
ejpam-4181	7	51	statement	statement	NOUN
ejpam-4181	8	1	apelblat	apelblat	NOUN
ejpam-4181	8	2	[	[	X
ejpam-4181	8	3	1	1	X
ejpam-4181	8	4	]	]	PUNCT
ejpam-4181	8	5	evaluated	evaluate	VERB
ejpam-4181	8	6	a	a	DET
ejpam-4181	8	7	triple	triple	ADJ
ejpam-4181	8	8	integral	integral	ADJ
ejpam-4181	8	9	involving	involve	VERB
ejpam-4181	8	10	the	the	DET
ejpam-4181	8	11	volterra	volterra	NOUN
ejpam-4181	8	12	function	function	NOUN
ejpam-4181	8	13	in	in	ADP
ejpam-4181	8	14	terms	term	NOUN
ejpam-4181	8	15	of	of	ADP
ejpam-4181	8	16	the	the	DET
ejpam-4181	8	17	gamma	gamma	NOUN
ejpam-4181	8	18	function	function	NOUN
ejpam-4181	8	19	which	which	PRON
ejpam-4181	8	20	is	be	AUX
ejpam-4181	8	21	used	use	VERB
ejpam-4181	8	22	in	in	ADP
ejpam-4181	8	23	fractional	fractional	ADJ
ejpam-4181	8	24	calculus	calculus	NOUN
ejpam-4181	8	25	.	.	PUNCT
ejpam-4181	9	1	in	in	ADP
ejpam-4181	9	2	this	this	DET
ejpam-4181	9	3	work	work	NOUN
ejpam-4181	9	4	the	the	DET
ejpam-4181	9	5	authors	author	NOUN
ejpam-4181	9	6	expand	expand	VERB
ejpam-4181	9	7	on	on	ADP
ejpam-4181	9	8	apelblat	apelblat	NOUN
ejpam-4181	9	9	’s	’s	PART
ejpam-4181	9	10	work	work	NOUN
ejpam-4181	9	11	by	by	ADP
ejpam-4181	9	12	deriving	derive	VERB
ejpam-4181	9	13	a	a	DET
ejpam-4181	9	14	quadruple	quadruple	NOUN
ejpam-4181	9	15	integral	integral	ADJ
ejpam-4181	9	16	involving	involve	VERB
ejpam-4181	9	17	the	the	DET
ejpam-4181	9	18	volterra	volterra	NOUN
ejpam-4181	9	19	function	function	NOUN
ejpam-4181	9	20	and	and	CCONJ
ejpam-4181	9	21	express	express	VERB
ejpam-4181	9	22	it	it	PRON
ejpam-4181	9	23	in	in	ADP
ejpam-4181	9	24	terms	term	NOUN
ejpam-4181	9	25	of	of	ADP
ejpam-4181	9	26	the	the	DET
ejpam-4181	9	27	hurwitz	hurwitz	PROPN
ejpam-4181	9	28	-	-	PUNCT
ejpam-4181	9	29	lerch	lerch	PROPN
ejpam-4181	9	30	zeta	zeta	PROPN
ejpam-4181	9	31	function	function	PROPN
ejpam-4181	9	32	.	.	PUNCT
ejpam-4181	10	1	our	our	PRON
ejpam-4181	10	2	hope	hope	NOUN
ejpam-4181	10	3	is	be	AUX
ejpam-4181	10	4	researchers	researcher	NOUN
ejpam-4181	10	5	will	will	AUX
ejpam-4181	10	6	find	find	VERB
ejpam-4181	10	7	the	the	DET
ejpam-4181	10	8	results	result	NOUN
ejpam-4181	10	9	in	in	ADP
ejpam-4181	10	10	this	this	DET
ejpam-4181	10	11	work	work	NOUN
ejpam-4181	10	12	useful	useful	ADJ
ejpam-4181	10	13	where	where	SCONJ
ejpam-4181	10	14	applicable	applicable	ADJ
ejpam-4181	10	15	.	.	PUNCT
ejpam-4181	11	1	2	2	X
ejpam-4181	11	2	.	.	X
ejpam-4181	11	3	introduction	introduction	NOUN
ejpam-4181	11	4	in	in	ADP
ejpam-4181	11	5	this	this	DET
ejpam-4181	11	6	paper	paper	NOUN
ejpam-4181	11	7	we	we	PRON
ejpam-4181	11	8	derive	derive	VERB
ejpam-4181	11	9	the	the	DET
ejpam-4181	11	10	quadruple	quadruple	ADJ
ejpam-4181	11	11	definite	definite	ADJ
ejpam-4181	11	12	integral	integral	ADJ
ejpam-4181	11	13	given	give	VERB
ejpam-4181	11	14	by∫	by∫	PROPN
ejpam-4181	11	15	∞	∞	PROPN
ejpam-4181	11	16	0	0	NUM
ejpam-4181	12	1	∫	∫	PROPN
ejpam-4181	12	2	∞	∞	PROPN
ejpam-4181	12	3	0	0	NUM
ejpam-4181	13	1	∫	∫	PROPN
ejpam-4181	13	2	∞	∞	PROPN
ejpam-4181	13	3	0	0	NUM
ejpam-4181	14	1	∫	∫	PROPN
ejpam-4181	15	1	∞	∞	PROPN
ejpam-4181	15	2	0	0	NUM
ejpam-4181	15	3	ym−1z−me−bz−pxxα+u+y	ym−1z−me−bz−pxxα+u+y	PROPN
ejpam-4181	15	4	logk	logk	NOUN
ejpam-4181	15	5	(	(	PUNCT
ejpam-4181	15	6	ay	ay	NOUN
ejpam-4181	15	7	z	z	NOUN
ejpam-4181	15	8	)	)	PUNCT
ejpam-4181	15	9	γ(u+	γ(u+	PROPN
ejpam-4181	16	1	y	y	PROPN
ejpam-4181	16	2	+	+	CCONJ
ejpam-4181	16	3	α+	α+	PUNCT
ejpam-4181	16	4	1	1	X
ejpam-4181	16	5	)	)	PUNCT
ejpam-4181	16	6	dxdydudz	dxdydudz	NOUN
ejpam-4181	16	7	(	(	PUNCT
ejpam-4181	16	8	1	1	NUM
ejpam-4181	16	9	)	)	PUNCT
ejpam-4181	16	10	where	where	SCONJ
ejpam-4181	16	11	the	the	DET
ejpam-4181	16	12	parameters	parameter	NOUN
ejpam-4181	16	13	k	k	PROPN
ejpam-4181	16	14	,	,	PUNCT
ejpam-4181	16	15	a	a	PRON
ejpam-4181	16	16	,	,	PUNCT
ejpam-4181	16	17	p	p	X
ejpam-4181	16	18	,	,	PUNCT
ejpam-4181	16	19	b	b	PROPN
ejpam-4181	16	20	,	,	PUNCT
ejpam-4181	16	21	α	α	PROPN
ejpam-4181	16	22	and	and	CCONJ
ejpam-4181	16	23	m	m	PROPN
ejpam-4181	16	24	are	be	AUX
ejpam-4181	16	25	general	general	ADJ
ejpam-4181	16	26	complex	complex	ADJ
ejpam-4181	16	27	numbers	number	NOUN
ejpam-4181	16	28	and	and	CCONJ
ejpam-4181	16	29	the	the	DET
ejpam-4181	16	30	volterra	volterra	NOUN
ejpam-4181	16	31	function	function	NOUN
ejpam-4181	16	32	is	be	AUX
ejpam-4181	16	33	given	give	VERB
ejpam-4181	16	34	in	in	ADP
ejpam-4181	16	35	equation	equation	NOUN
ejpam-4181	16	36	(	(	PUNCT
ejpam-4181	16	37	1.2.1	1.2.1	NUM
ejpam-4181	16	38	)	)	PUNCT
ejpam-4181	16	39	in	in	ADP
ejpam-4181	16	40	[	[	X
ejpam-4181	16	41	1	1	NUM
ejpam-4181	16	42	]	]	PUNCT
ejpam-4181	16	43	.	.	PUNCT
ejpam-4181	17	1	this	this	DET
ejpam-4181	17	2	definite	definite	ADJ
ejpam-4181	17	3	integral	integral	ADJ
ejpam-4181	17	4	will	will	AUX
ejpam-4181	17	5	be	be	AUX
ejpam-4181	17	6	used	use	VERB
ejpam-4181	17	7	to	to	PART
ejpam-4181	17	8	derive	derive	VERB
ejpam-4181	17	9	special	special	ADJ
ejpam-4181	17	10	cases	case	NOUN
ejpam-4181	17	11	in	in	ADP
ejpam-4181	17	12	terms	term	NOUN
ejpam-4181	17	13	of	of	ADP
ejpam-4181	17	14	special	special	ADJ
ejpam-4181	17	15	functions	function	NOUN
ejpam-4181	17	16	and	and	CCONJ
ejpam-4181	17	17	fundamental	fundamental	ADJ
ejpam-4181	17	18	constants	constant	NOUN
ejpam-4181	17	19	.	.	PUNCT
ejpam-4181	18	1	the	the	DET
ejpam-4181	18	2	derivations	derivation	NOUN
ejpam-4181	18	3	∗corresponding	∗corresponde	VERB
ejpam-4181	18	4	author	author	NOUN
ejpam-4181	18	5	.	.	PUNCT
ejpam-4181	19	1	doi	doi	NOUN
ejpam-4181	19	2	:	:	PUNCT
ejpam-4181	19	3	https://doi.org/10.29020/nybg.ejpam.v15i1.4181	https://doi.org/10.29020/nybg.ejpam.v15i1.4181	NUM
ejpam-4181	19	4	email	email	NOUN
ejpam-4181	19	5	addresses	address	NOUN
ejpam-4181	19	6	:	:	PUNCT
ejpam-4181	20	1	milver@my.yorku.ca	milver@my.yorku.ca	NOUN
ejpam-4181	20	2	(	(	PUNCT
ejpam-4181	20	3	r.	r.	PROPN
ejpam-4181	20	4	reynolds	reynolds	PROPN
ejpam-4181	20	5	)	)	PUNCT
ejpam-4181	20	6	,	,	PUNCT
ejpam-4181	20	7	stauffer@yorku.ca	stauffer@yorku.ca	NOUN
ejpam-4181	20	8	(	(	PUNCT
ejpam-4181	20	9	a.	a.	NOUN
ejpam-4181	20	10	stauffer	stauffer	PROPN
ejpam-4181	20	11	)	)	PUNCT
ejpam-4181	20	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4181	21	1	30	30	NUM
ejpam-4181	21	2	©	©	PROPN
ejpam-4181	21	3	2022	2022	NUM
ejpam-4181	21	4	ejpam	ejpam	VERB
ejpam-4181	21	5	all	all	DET
ejpam-4181	21	6	rights	right	NOUN
ejpam-4181	21	7	reserved	reserve	VERB
ejpam-4181	21	8	.	.	PUNCT
ejpam-4181	22	1	r.	r.	PROPN
ejpam-4181	22	2	reynolds	reynolds	PROPN
ejpam-4181	22	3	,	,	PUNCT
ejpam-4181	22	4	a.	a.	PROPN
ejpam-4181	22	5	stauffer	stauffer	PROPN
ejpam-4181	22	6	/	/	SYM
ejpam-4181	22	7	eur	eur	PROPN
ejpam-4181	22	8	.	.	PUNCT
ejpam-4181	23	1	j.	j.	PROPN
ejpam-4181	23	2	pure	pure	PROPN
ejpam-4181	23	3	appl	appl	PROPN
ejpam-4181	23	4	.	.	PROPN
ejpam-4181	23	5	math	math	PROPN
ejpam-4181	23	6	,	,	PUNCT
ejpam-4181	23	7	15	15	NUM
ejpam-4181	23	8	(	(	PUNCT
ejpam-4181	23	9	1	1	NUM
ejpam-4181	23	10	)	)	PUNCT
ejpam-4181	23	11	(	(	PUNCT
ejpam-4181	23	12	2022	2022	NUM
ejpam-4181	23	13	)	)	PUNCT
ejpam-4181	23	14	,	,	PUNCT
ejpam-4181	23	15	30	30	NUM
ejpam-4181	23	16	-	-	SYM
ejpam-4181	23	17	35	35	NUM
ejpam-4181	23	18	31	31	NUM
ejpam-4181	23	19	follow	follow	VERB
ejpam-4181	23	20	the	the	DET
ejpam-4181	23	21	method	method	NOUN
ejpam-4181	23	22	used	use	VERB
ejpam-4181	23	23	by	by	ADP
ejpam-4181	23	24	us	we	PRON
ejpam-4181	23	25	in	in	ADP
ejpam-4181	23	26	[	[	X
ejpam-4181	23	27	5	5	NUM
ejpam-4181	23	28	]	]	PUNCT
ejpam-4181	23	29	.	.	PUNCT
ejpam-4181	24	1	this	this	DET
ejpam-4181	24	2	method	method	NOUN
ejpam-4181	24	3	involves	involve	VERB
ejpam-4181	24	4	using	use	VERB
ejpam-4181	24	5	a	a	DET
ejpam-4181	24	6	form	form	NOUN
ejpam-4181	24	7	of	of	ADP
ejpam-4181	24	8	the	the	DET
ejpam-4181	24	9	generalized	generalize	VERB
ejpam-4181	24	10	cauchy	cauchy	PROPN
ejpam-4181	24	11	’s	’s	PART
ejpam-4181	24	12	integral	integral	ADJ
ejpam-4181	24	13	formula	formula	NOUN
ejpam-4181	24	14	given	give	VERB
ejpam-4181	24	15	by	by	ADP
ejpam-4181	24	16	yk	yk	PROPN
ejpam-4181	24	17	γ(k	γ(k	PROPN
ejpam-4181	24	18	+	+	CCONJ
ejpam-4181	24	19	1	1	X
ejpam-4181	24	20	)	)	PUNCT
ejpam-4181	24	21	=	=	SYM
ejpam-4181	24	22	1	1	NUM
ejpam-4181	24	23	2πi	2πi	ADJ
ejpam-4181	24	24	∫	∫	PROPN
ejpam-4181	24	25	c	c	PROPN
ejpam-4181	24	26	ewy	ewy	PROPN
ejpam-4181	24	27	wk+1	wk+1	PROPN
ejpam-4181	24	28	dw	dw	PROPN
ejpam-4181	24	29	.	.	PUNCT
ejpam-4181	25	1	(	(	PUNCT
ejpam-4181	25	2	2	2	X
ejpam-4181	25	3	)	)	PUNCT
ejpam-4181	25	4	where	where	SCONJ
ejpam-4181	25	5	c	c	NOUN
ejpam-4181	25	6	is	be	AUX
ejpam-4181	25	7	in	in	ADP
ejpam-4181	25	8	general	general	ADJ
ejpam-4181	25	9	an	an	DET
ejpam-4181	25	10	open	open	ADJ
ejpam-4181	25	11	contour	contour	NOUN
ejpam-4181	25	12	in	in	ADP
ejpam-4181	25	13	the	the	DET
ejpam-4181	25	14	complex	complex	ADJ
ejpam-4181	25	15	plane	plane	NOUN
ejpam-4181	25	16	where	where	SCONJ
ejpam-4181	25	17	the	the	DET
ejpam-4181	25	18	bilinear	bilinear	NOUN
ejpam-4181	25	19	concomitant	concomitant	NOUN
ejpam-4181	25	20	has	have	VERB
ejpam-4181	25	21	the	the	DET
ejpam-4181	25	22	same	same	ADJ
ejpam-4181	25	23	value	value	NOUN
ejpam-4181	25	24	at	at	ADP
ejpam-4181	25	25	the	the	DET
ejpam-4181	25	26	end	end	NOUN
ejpam-4181	25	27	points	point	NOUN
ejpam-4181	25	28	of	of	ADP
ejpam-4181	25	29	the	the	DET
ejpam-4181	25	30	contour	contour	NOUN
ejpam-4181	25	31	.	.	PUNCT
ejpam-4181	26	1	we	we	PRON
ejpam-4181	26	2	then	then	ADV
ejpam-4181	26	3	multiply	multiply	VERB
ejpam-4181	26	4	both	both	DET
ejpam-4181	26	5	sides	side	NOUN
ejpam-4181	26	6	by	by	ADP
ejpam-4181	26	7	a	a	DET
ejpam-4181	26	8	function	function	NOUN
ejpam-4181	26	9	of	of	ADP
ejpam-4181	26	10	x	x	PROPN
ejpam-4181	26	11	,	,	PUNCT
ejpam-4181	26	12	y	y	PROPN
ejpam-4181	26	13	,	,	PUNCT
ejpam-4181	26	14	u	u	NOUN
ejpam-4181	26	15	and	and	CCONJ
ejpam-4181	26	16	z	z	PROPN
ejpam-4181	26	17	,	,	PUNCT
ejpam-4181	26	18	then	then	ADV
ejpam-4181	26	19	take	take	VERB
ejpam-4181	26	20	a	a	DET
ejpam-4181	26	21	definite	definite	ADJ
ejpam-4181	26	22	quadruple	quadruple	NOUN
ejpam-4181	26	23	integral	integral	ADJ
ejpam-4181	26	24	of	of	ADP
ejpam-4181	26	25	both	both	DET
ejpam-4181	26	26	sides	side	NOUN
ejpam-4181	26	27	.	.	PUNCT
ejpam-4181	27	1	this	this	PRON
ejpam-4181	27	2	yields	yield	VERB
ejpam-4181	27	3	a	a	DET
ejpam-4181	27	4	definite	definite	ADJ
ejpam-4181	27	5	integral	integral	ADJ
ejpam-4181	27	6	in	in	ADP
ejpam-4181	27	7	terms	term	NOUN
ejpam-4181	27	8	of	of	ADP
ejpam-4181	27	9	a	a	DET
ejpam-4181	27	10	contour	contour	NOUN
ejpam-4181	27	11	integral	integral	NOUN
ejpam-4181	27	12	.	.	PUNCT
ejpam-4181	28	1	then	then	ADV
ejpam-4181	28	2	we	we	PRON
ejpam-4181	28	3	multiply	multiply	VERB
ejpam-4181	28	4	both	both	DET
ejpam-4181	28	5	sides	side	NOUN
ejpam-4181	28	6	of	of	ADP
ejpam-4181	28	7	equation	equation	NOUN
ejpam-4181	28	8	(	(	PUNCT
ejpam-4181	28	9	2	2	NUM
ejpam-4181	28	10	)	)	PUNCT
ejpam-4181	28	11	by	by	ADP
ejpam-4181	28	12	another	another	DET
ejpam-4181	28	13	function	function	NOUN
ejpam-4181	28	14	of	of	ADP
ejpam-4181	28	15	x	x	PROPN
ejpam-4181	28	16	,	,	PUNCT
ejpam-4181	28	17	y	y	PROPN
ejpam-4181	28	18	,	,	PUNCT
ejpam-4181	28	19	u	u	NOUN
ejpam-4181	28	20	and	and	CCONJ
ejpam-4181	28	21	z	z	PROPN
ejpam-4181	28	22	and	and	CCONJ
ejpam-4181	28	23	take	take	VERB
ejpam-4181	28	24	the	the	DET
ejpam-4181	28	25	infinite	infinite	ADJ
ejpam-4181	28	26	sums	sum	NOUN
ejpam-4181	28	27	of	of	ADP
ejpam-4181	28	28	both	both	DET
ejpam-4181	28	29	sides	side	NOUN
ejpam-4181	28	30	such	such	ADJ
ejpam-4181	28	31	that	that	SCONJ
ejpam-4181	28	32	the	the	DET
ejpam-4181	28	33	contour	contour	NOUN
ejpam-4181	28	34	integral	integral	NOUN
ejpam-4181	28	35	of	of	ADP
ejpam-4181	28	36	both	both	DET
ejpam-4181	28	37	equations	equation	NOUN
ejpam-4181	28	38	are	be	AUX
ejpam-4181	28	39	the	the	DET
ejpam-4181	28	40	same	same	ADJ
ejpam-4181	28	41	.	.	PUNCT
ejpam-4181	29	1	3	3	X
ejpam-4181	29	2	.	.	X
ejpam-4181	29	3	definite	definite	ADJ
ejpam-4181	29	4	integral	integral	ADJ
ejpam-4181	29	5	of	of	ADP
ejpam-4181	29	6	the	the	DET
ejpam-4181	29	7	contour	contour	NOUN
ejpam-4181	29	8	integral	integral	NOUN
ejpam-4181	29	9	we	we	PRON
ejpam-4181	29	10	use	use	VERB
ejpam-4181	29	11	the	the	DET
ejpam-4181	29	12	method	method	NOUN
ejpam-4181	29	13	in	in	ADP
ejpam-4181	29	14	[	[	X
ejpam-4181	29	15	5	5	NUM
ejpam-4181	29	16	]	]	PUNCT
ejpam-4181	29	17	.	.	PUNCT
ejpam-4181	30	1	the	the	DET
ejpam-4181	30	2	variable	variable	NOUN
ejpam-4181	30	3	of	of	ADP
ejpam-4181	30	4	integration	integration	NOUN
ejpam-4181	30	5	in	in	ADP
ejpam-4181	30	6	the	the	DET
ejpam-4181	30	7	contour	contour	NOUN
ejpam-4181	30	8	integral	integral	NOUN
ejpam-4181	30	9	is	be	AUX
ejpam-4181	30	10	t	t	X
ejpam-4181	30	11	=	=	SYM
ejpam-4181	30	12	w	w	PROPN
ejpam-4181	30	13	+	+	NUM
ejpam-4181	30	14	m.	m.	NOUN
ejpam-4181	30	15	the	the	DET
ejpam-4181	30	16	cut	cut	NOUN
ejpam-4181	30	17	and	and	CCONJ
ejpam-4181	30	18	contour	contour	NOUN
ejpam-4181	30	19	are	be	AUX
ejpam-4181	30	20	in	in	ADP
ejpam-4181	30	21	the	the	DET
ejpam-4181	30	22	first	first	ADJ
ejpam-4181	30	23	quadrant	quadrant	NOUN
ejpam-4181	30	24	of	of	ADP
ejpam-4181	30	25	the	the	DET
ejpam-4181	30	26	complex	complex	ADJ
ejpam-4181	30	27	t	t	NOUN
ejpam-4181	30	28	-	-	PUNCT
ejpam-4181	30	29	plane	plane	NOUN
ejpam-4181	30	30	.	.	PUNCT
ejpam-4181	31	1	the	the	DET
ejpam-4181	31	2	cut	cut	NOUN
ejpam-4181	31	3	approaches	approach	VERB
ejpam-4181	31	4	the	the	DET
ejpam-4181	31	5	origin	origin	NOUN
ejpam-4181	31	6	from	from	ADP
ejpam-4181	31	7	the	the	DET
ejpam-4181	31	8	interior	interior	NOUN
ejpam-4181	31	9	of	of	ADP
ejpam-4181	31	10	the	the	DET
ejpam-4181	31	11	first	first	ADJ
ejpam-4181	31	12	quadrant	quadrant	NOUN
ejpam-4181	31	13	and	and	CCONJ
ejpam-4181	31	14	the	the	DET
ejpam-4181	31	15	contour	contour	NOUN
ejpam-4181	31	16	goes	go	VERB
ejpam-4181	31	17	round	round	ADP
ejpam-4181	31	18	the	the	DET
ejpam-4181	31	19	origin	origin	NOUN
ejpam-4181	31	20	with	with	ADP
ejpam-4181	31	21	zero	zero	NUM
ejpam-4181	31	22	radius	radius	NOUN
ejpam-4181	31	23	and	and	CCONJ
ejpam-4181	31	24	is	be	AUX
ejpam-4181	31	25	on	on	ADP
ejpam-4181	31	26	opposite	opposite	ADJ
ejpam-4181	31	27	sides	side	NOUN
ejpam-4181	31	28	of	of	ADP
ejpam-4181	31	29	the	the	DET
ejpam-4181	31	30	cut	cut	NOUN
ejpam-4181	31	31	.	.	PUNCT
ejpam-4181	32	1	using	use	VERB
ejpam-4181	32	2	a	a	DET
ejpam-4181	32	3	generalization	generalization	NOUN
ejpam-4181	32	4	of	of	ADP
ejpam-4181	32	5	cauchy	cauchy	PROPN
ejpam-4181	32	6	’s	’s	PART
ejpam-4181	32	7	integral	integral	ADJ
ejpam-4181	32	8	formula	formula	NOUN
ejpam-4181	32	9	we	we	PRON
ejpam-4181	32	10	form	form	VERB
ejpam-4181	32	11	the	the	DET
ejpam-4181	32	12	quadruple	quadruple	NOUN
ejpam-4181	32	13	integral	integral	ADJ
ejpam-4181	32	14	by	by	ADP
ejpam-4181	32	15	replacing	replace	VERB
ejpam-4181	32	16	y	y	PRON
ejpam-4181	32	17	by	by	ADP
ejpam-4181	32	18	log	log	NOUN
ejpam-4181	32	19	(	(	PUNCT
ejpam-4181	32	20	ay	ay	NOUN
ejpam-4181	32	21	z	z	NOUN
ejpam-4181	32	22	)	)	PUNCT
ejpam-4181	32	23	and	and	CCONJ
ejpam-4181	32	24	multiplying	multiply	VERB
ejpam-4181	32	25	by	by	ADP
ejpam-4181	32	26	ym−1z−me−bz−pxxα+u+y	ym−1z−me−bz−pxxα+u+y	PROPN
ejpam-4181	32	27	γ(u+y+α+1	γ(u+y+α+1	NOUN
ejpam-4181	32	28	)	)	PUNCT
ejpam-4181	32	29	then	then	ADV
ejpam-4181	32	30	taking	take	VERB
ejpam-4181	32	31	the	the	DET
ejpam-4181	32	32	definite	definite	ADJ
ejpam-4181	32	33	integral	integral	ADJ
ejpam-4181	32	34	with	with	ADP
ejpam-4181	32	35	respect	respect	NOUN
ejpam-4181	32	36	to	to	ADP
ejpam-4181	32	37	x	x	PUNCT
ejpam-4181	32	38	∈	∈	PROPN
ejpam-4181	33	1	[	[	X
ejpam-4181	33	2	0,∞	0,∞	NOUN
ejpam-4181	33	3	)	)	PUNCT
ejpam-4181	33	4	,	,	PUNCT
ejpam-4181	33	5	y	y	PROPN
ejpam-4181	33	6	∈	∈	PROPN
ejpam-4181	34	1	[	[	X
ejpam-4181	34	2	0,∞	0,∞	NOUN
ejpam-4181	34	3	)	)	PUNCT
ejpam-4181	34	4	,	,	PUNCT
ejpam-4181	34	5	u	u	PROPN
ejpam-4181	34	6	∈	∈	PROPN
ejpam-4181	35	1	[	[	X
ejpam-4181	35	2	0,∞	0,∞	NUM
ejpam-4181	35	3	)	)	PUNCT
ejpam-4181	35	4	and	and	CCONJ
ejpam-4181	35	5	z	z	NOUN
ejpam-4181	35	6	∈	∈	PROPN
ejpam-4181	36	1	[	[	X
ejpam-4181	36	2	0,∞	0,∞	NOUN
ejpam-4181	36	3	)	)	PUNCT
ejpam-4181	36	4	to	to	PART
ejpam-4181	36	5	obtain	obtain	VERB
ejpam-4181	36	6	(	(	PUNCT
ejpam-4181	36	7	3	3	NUM
ejpam-4181	36	8	)	)	PUNCT
ejpam-4181	36	9	∫	∫	PROPN
ejpam-4181	37	1	∞	∞	PROPN
ejpam-4181	37	2	0	0	NUM
ejpam-4181	38	1	∫	∫	PROPN
ejpam-4181	38	2	∞	∞	PROPN
ejpam-4181	38	3	0	0	NUM
ejpam-4181	39	1	∫	∫	PROPN
ejpam-4181	39	2	∞	∞	PROPN
ejpam-4181	39	3	0	0	NUM
ejpam-4181	40	1	∫	∫	PROPN
ejpam-4181	41	1	∞	∞	PROPN
ejpam-4181	41	2	0	0	NUM
ejpam-4181	41	3	ym−1z−me−bz−pxxα+u+y	ym−1z−me−bz−pxxα+u+y	PROPN
ejpam-4181	41	4	logk	logk	NOUN
ejpam-4181	41	5	(	(	PUNCT
ejpam-4181	41	6	ay	ay	NOUN
ejpam-4181	41	7	z	z	NOUN
ejpam-4181	41	8	)	)	PUNCT
ejpam-4181	42	1	γ(k	γ(k	PROPN
ejpam-4181	42	2	+	+	CCONJ
ejpam-4181	42	3	1)γ(u+	1)γ(u+	PROPN
ejpam-4181	42	4	y	y	NOUN
ejpam-4181	42	5	+	+	CCONJ
ejpam-4181	42	6	α+	α+	PUNCT
ejpam-4181	42	7	1	1	X
ejpam-4181	42	8	)	)	PUNCT
ejpam-4181	42	9	dxdydudz	dxdydudz	NOUN
ejpam-4181	42	10	=	=	SYM
ejpam-4181	42	11	1	1	NUM
ejpam-4181	42	12	2πi	2πi	NOUN
ejpam-4181	42	13	∫	∫	PROPN
ejpam-4181	43	1	∞	∞	PROPN
ejpam-4181	43	2	0	0	NUM
ejpam-4181	44	1	∫	∫	PROPN
ejpam-4181	44	2	∞	∞	PROPN
ejpam-4181	44	3	0	0	NUM
ejpam-4181	45	1	∫	∫	PROPN
ejpam-4181	45	2	∞	∞	PROPN
ejpam-4181	45	3	0	0	NUM
ejpam-4181	46	1	∫	∫	PROPN
ejpam-4181	46	2	∞	∞	PROPN
ejpam-4181	46	3	0	0	NUM
ejpam-4181	47	1	∫	∫	PROPN
ejpam-4181	48	1	c	c	PROPN
ejpam-4181	48	2	aww−k−1ym+w−1z−m−we−bz−pxxα+u+y	aww−k−1ym+w−1z−m−we−bz−pxxα+u+y	PROPN
ejpam-4181	48	3	γ(u+	γ(u+	PROPN
ejpam-4181	49	1	y	y	NOUN
ejpam-4181	49	2	+	+	CCONJ
ejpam-4181	49	3	α+	α+	PUNCT
ejpam-4181	49	4	1	1	NUM
ejpam-4181	49	5	)	)	PUNCT
ejpam-4181	49	6	dwdxdydudz	dwdxdydudz	NOUN
ejpam-4181	49	7	=	=	SYM
ejpam-4181	49	8	1	1	NUM
ejpam-4181	49	9	2πi	2πi	NOUN
ejpam-4181	49	10	∫	∫	PROPN
ejpam-4181	50	1	c	c	PROPN
ejpam-4181	50	2	∫	∫	PROPN
ejpam-4181	51	1	∞	∞	NUM
ejpam-4181	51	2	0	0	NUM
ejpam-4181	52	1	∫	∫	PROPN
ejpam-4181	52	2	∞	∞	PROPN
ejpam-4181	52	3	0	0	NUM
ejpam-4181	53	1	∫	∫	PROPN
ejpam-4181	53	2	∞	∞	PROPN
ejpam-4181	53	3	0	0	NUM
ejpam-4181	54	1	∫	∫	PROPN
ejpam-4181	54	2	∞	∞	NOUN
ejpam-4181	54	3	0	0	NUM
ejpam-4181	55	1	aww−k−1ym+w−1z−m−we−bz−pxxα+u+y	aww−k−1ym+w−1z−m−we−bz−pxxα+u+y	PROPN
ejpam-4181	55	2	γ(u+	γ(u+	PROPN
ejpam-4181	56	1	y	y	NOUN
ejpam-4181	56	2	+	+	CCONJ
ejpam-4181	56	3	α+	α+	PUNCT
ejpam-4181	56	4	1	1	NUM
ejpam-4181	56	5	)	)	PUNCT
ejpam-4181	56	6	dxdydudzdw	dxdydudzdw	NOUN
ejpam-4181	56	7	=	=	SYM
ejpam-4181	57	1	1	1	NUM
ejpam-4181	57	2	2πi	2πi	ADJ
ejpam-4181	57	3	∫	∫	PROPN
ejpam-4181	57	4	c	c	PROPN
ejpam-4181	57	5	πaww−k−1p−α−1bm+w−1	πaww−k−1p−α−1bm+w−1	X
ejpam-4181	57	6	csc(π(m+	csc(π(m+	PROPN
ejpam-4181	57	7	w	w	NOUN
ejpam-4181	57	8	)	)	PUNCT
ejpam-4181	57	9	)	)	PUNCT
ejpam-4181	57	10	log−m−w−1(p)dw	log−m−w−1(p)dw	PROPN
ejpam-4181	57	11	from	from	ADP
ejpam-4181	57	12	equation	equation	NOUN
ejpam-4181	57	13	(	(	PUNCT
ejpam-4181	57	14	9.67.9	9.67.9	NUM
ejpam-4181	57	15	)	)	PUNCT
ejpam-4181	57	16	in	in	ADP
ejpam-4181	57	17	[	[	X
ejpam-4181	57	18	1	1	NUM
ejpam-4181	57	19	]	]	PUNCT
ejpam-4181	57	20	and	and	CCONJ
ejpam-4181	57	21	equation	equation	NOUN
ejpam-4181	57	22	(	(	PUNCT
ejpam-4181	57	23	3.326.2	3.326.2	NOUN
ejpam-4181	57	24	)	)	PUNCT
ejpam-4181	57	25	in	in	ADP
ejpam-4181	57	26	[	[	X
ejpam-4181	57	27	3	3	X
ejpam-4181	57	28	]	]	PUNCT
ejpam-4181	57	29	where	where	SCONJ
ejpam-4181	57	30	re(α	re(α	NOUN
ejpam-4181	57	31	)	)	PUNCT
ejpam-4181	57	32	>	>	X
ejpam-4181	57	33	−1	−1	NOUN
ejpam-4181	57	34	,	,	PUNCT
ejpam-4181	57	35	re(p	re(p	PROPN
ejpam-4181	57	36	)	)	PUNCT
ejpam-4181	57	37	>	>	X
ejpam-4181	57	38	1	1	NUM
ejpam-4181	57	39	,	,	PUNCT
ejpam-4181	57	40	re(w+m	re(w+m	PROPN
ejpam-4181	57	41	)	)	PUNCT
ejpam-4181	57	42	>	>	X
ejpam-4181	57	43	0	0	PUNCT
ejpam-4181	57	44	and	and	CCONJ
ejpam-4181	57	45	using	use	VERB
ejpam-4181	57	46	the	the	DET
ejpam-4181	57	47	reflection	reflection	NOUN
ejpam-4181	57	48	formula	formula	NOUN
ejpam-4181	57	49	(	(	PUNCT
ejpam-4181	57	50	8.334.3	8.334.3	NUM
ejpam-4181	57	51	)	)	PUNCT
ejpam-4181	57	52	in	in	ADP
ejpam-4181	57	53	[	[	X
ejpam-4181	57	54	3	3	X
ejpam-4181	57	55	]	]	PUNCT
ejpam-4181	57	56	for	for	ADP
ejpam-4181	57	57	the	the	DET
ejpam-4181	57	58	gamma	gamma	PROPN
ejpam-4181	57	59	function	function	NOUN
ejpam-4181	57	60	.	.	PUNCT
ejpam-4181	58	1	we	we	PRON
ejpam-4181	58	2	are	be	AUX
ejpam-4181	58	3	able	able	ADJ
ejpam-4181	58	4	to	to	PART
ejpam-4181	58	5	switch	switch	VERB
ejpam-4181	58	6	the	the	DET
ejpam-4181	58	7	order	order	NOUN
ejpam-4181	58	8	of	of	ADP
ejpam-4181	58	9	integration	integration	NOUN
ejpam-4181	58	10	over	over	ADP
ejpam-4181	58	11	t	t	PROPN
ejpam-4181	58	12	,	,	PUNCT
ejpam-4181	58	13	x	x	X
ejpam-4181	58	14	,	,	PUNCT
ejpam-4181	58	15	y	y	PROPN
ejpam-4181	58	16	,	,	PUNCT
ejpam-4181	58	17	u	u	NOUN
ejpam-4181	58	18	and	and	CCONJ
ejpam-4181	58	19	z	z	NOUN
ejpam-4181	58	20	using	use	VERB
ejpam-4181	58	21	fubini	fubini	NOUN
ejpam-4181	58	22	’s	’s	PART
ejpam-4181	58	23	theorem	theorem	NOUN
ejpam-4181	58	24	since	since	SCONJ
ejpam-4181	58	25	the	the	DET
ejpam-4181	58	26	integrand	integrand	NOUN
ejpam-4181	58	27	is	be	AUX
ejpam-4181	58	28	of	of	ADP
ejpam-4181	58	29	bounded	bounded	ADJ
ejpam-4181	58	30	measure	measure	NOUN
ejpam-4181	58	31	over	over	ADP
ejpam-4181	58	32	the	the	DET
ejpam-4181	58	33	space	space	NOUN
ejpam-4181	58	34	c×[0,∞)×[0,∞)×[0,∞)×[0,∞	c×[0,∞)×[0,∞)×[0,∞)×[0,∞	PROPN
ejpam-4181	58	35	)	)	PUNCT
ejpam-4181	58	36	.	.	PUNCT
ejpam-4181	59	1	4	4	X
ejpam-4181	59	2	.	.	X
ejpam-4181	59	3	the	the	DET
ejpam-4181	59	4	hurwitz	hurwitz	PROPN
ejpam-4181	59	5	-	-	PUNCT
ejpam-4181	59	6	lerch	lerch	PROPN
ejpam-4181	59	7	zeta	zeta	PROPN
ejpam-4181	59	8	function	function	PROPN
ejpam-4181	59	9	and	and	CCONJ
ejpam-4181	59	10	infinite	infinite	ADJ
ejpam-4181	59	11	sum	sum	NOUN
ejpam-4181	59	12	of	of	ADP
ejpam-4181	59	13	the	the	DET
ejpam-4181	59	14	contour	contour	NOUN
ejpam-4181	59	15	integral	integral	NOUN
ejpam-4181	59	16	in	in	ADP
ejpam-4181	59	17	this	this	DET
ejpam-4181	59	18	section	section	NOUN
ejpam-4181	59	19	we	we	PRON
ejpam-4181	59	20	use	use	VERB
ejpam-4181	59	21	equation	equation	NOUN
ejpam-4181	59	22	(	(	PUNCT
ejpam-4181	59	23	2	2	NUM
ejpam-4181	59	24	)	)	PUNCT
ejpam-4181	59	25	to	to	PART
ejpam-4181	59	26	derive	derive	VERB
ejpam-4181	59	27	the	the	DET
ejpam-4181	59	28	contour	contour	NOUN
ejpam-4181	59	29	integral	integral	ADJ
ejpam-4181	59	30	representations	representation	NOUN
ejpam-4181	59	31	for	for	ADP
ejpam-4181	59	32	the	the	DET
ejpam-4181	59	33	hurwitz	hurwitz	PROPN
ejpam-4181	59	34	-	-	PUNCT
ejpam-4181	59	35	lerch	lerch	PROPN
ejpam-4181	59	36	zeta	zeta	PROPN
ejpam-4181	59	37	function	function	PROPN
ejpam-4181	59	38	.	.	PUNCT
ejpam-4181	60	1	r.	r.	PROPN
ejpam-4181	60	2	reynolds	reynolds	PROPN
ejpam-4181	60	3	,	,	PUNCT
ejpam-4181	60	4	a.	a.	PROPN
ejpam-4181	60	5	stauffer	stauffer	PROPN
ejpam-4181	60	6	/	/	SYM
ejpam-4181	60	7	eur	eur	PROPN
ejpam-4181	60	8	.	.	PUNCT
ejpam-4181	61	1	j.	j.	PROPN
ejpam-4181	61	2	pure	pure	PROPN
ejpam-4181	61	3	appl	appl	PROPN
ejpam-4181	61	4	.	.	PROPN
ejpam-4181	61	5	math	math	PROPN
ejpam-4181	61	6	,	,	PUNCT
ejpam-4181	61	7	15	15	NUM
ejpam-4181	61	8	(	(	PUNCT
ejpam-4181	61	9	1	1	NUM
ejpam-4181	61	10	)	)	PUNCT
ejpam-4181	61	11	(	(	PUNCT
ejpam-4181	61	12	2022	2022	NUM
ejpam-4181	61	13	)	)	PUNCT
ejpam-4181	61	14	,	,	PUNCT
ejpam-4181	61	15	30	30	NUM
ejpam-4181	61	16	-	-	SYM
ejpam-4181	61	17	35	35	NUM
ejpam-4181	61	18	32	32	NUM
ejpam-4181	61	19	4.1	4.1	NUM
ejpam-4181	61	20	.	.	PUNCT
ejpam-4181	62	1	the	the	DET
ejpam-4181	62	2	hurwitz	hurwitz	PROPN
ejpam-4181	62	3	-	-	PUNCT
ejpam-4181	62	4	lerch	lerch	PROPN
ejpam-4181	62	5	zeta	zeta	PROPN
ejpam-4181	62	6	function	function	VERB
ejpam-4181	62	7	the	the	DET
ejpam-4181	62	8	hurwitz	hurwitz	PROPN
ejpam-4181	62	9	-	-	PUNCT
ejpam-4181	62	10	lerch	lerch	PROPN
ejpam-4181	62	11	zeta	zeta	PROPN
ejpam-4181	62	12	function	function	PROPN
ejpam-4181	62	13	(	(	PUNCT
ejpam-4181	62	14	25.14	25.14	NUM
ejpam-4181	62	15	)	)	PUNCT
ejpam-4181	62	16	in	in	ADP
ejpam-4181	62	17	[	[	X
ejpam-4181	62	18	2	2	X
ejpam-4181	62	19	]	]	PUNCT
ejpam-4181	62	20	has	have	VERB
ejpam-4181	62	21	a	a	DET
ejpam-4181	62	22	series	series	NOUN
ejpam-4181	62	23	representation	representation	NOUN
ejpam-4181	62	24	given	give	VERB
ejpam-4181	62	25	by	by	ADP
ejpam-4181	62	26	φ(z	φ(z	PROPN
ejpam-4181	62	27	,	,	PUNCT
ejpam-4181	62	28	s	s	NOUN
ejpam-4181	62	29	,	,	PUNCT
ejpam-4181	62	30	v	v	NOUN
ejpam-4181	62	31	)	)	PUNCT
ejpam-4181	62	32	=	=	PUNCT
ejpam-4181	63	1	∞∑	∞∑	NUM
ejpam-4181	63	2	n=0	n=0	NUM
ejpam-4181	63	3	(	(	PUNCT
ejpam-4181	63	4	v	v	NOUN
ejpam-4181	63	5	+	+	PRON
ejpam-4181	63	6	n)−szn	n)−szn	NUM
ejpam-4181	63	7	(	(	PUNCT
ejpam-4181	63	8	4	4	NUM
ejpam-4181	63	9	)	)	PUNCT
ejpam-4181	63	10	where	where	SCONJ
ejpam-4181	63	11	|z|	|z|	VERB
ejpam-4181	63	12	<	<	X
ejpam-4181	63	13	1	1	NUM
ejpam-4181	63	14	,	,	PUNCT
ejpam-4181	63	15	v	v	ADP
ejpam-4181	63	16	̸=	̸=	PROPN
ejpam-4181	63	17	0,−1	0,−1	PROPN
ejpam-4181	63	18	,	,	PUNCT
ejpam-4181	63	19	..	..	PUNCT
ejpam-4181	63	20	and	and	CCONJ
ejpam-4181	63	21	is	be	AUX
ejpam-4181	63	22	continued	continue	VERB
ejpam-4181	63	23	analytically	analytically	ADV
ejpam-4181	63	24	by	by	ADP
ejpam-4181	63	25	its	its	PRON
ejpam-4181	63	26	integral	integral	ADJ
ejpam-4181	63	27	representation	representation	NOUN
ejpam-4181	63	28	given	give	VERB
ejpam-4181	63	29	by	by	ADP
ejpam-4181	63	30	φ(z	φ(z	PROPN
ejpam-4181	63	31	,	,	PUNCT
ejpam-4181	63	32	s	s	NOUN
ejpam-4181	63	33	,	,	PUNCT
ejpam-4181	63	34	v	v	NOUN
ejpam-4181	63	35	)	)	PUNCT
ejpam-4181	63	36	=	=	SYM
ejpam-4181	63	37	1	1	NUM
ejpam-4181	63	38	γ(s	γ(	NOUN
ejpam-4181	63	39	)	)	PUNCT
ejpam-4181	63	40	∫	∫	PROPN
ejpam-4181	64	1	∞	∞	PROPN
ejpam-4181	64	2	0	0	NUM
ejpam-4181	65	1	ts−1e−vt	ts−1e−vt	PRON
ejpam-4181	66	1	1−	1−	NUM
ejpam-4181	66	2	ze−t	ze−t	NOUN
ejpam-4181	66	3	dt	dt	NOUN
ejpam-4181	67	1	=	=	SYM
ejpam-4181	67	2	1	1	NUM
ejpam-4181	67	3	γ(s	γ(s	PROPN
ejpam-4181	67	4	)	)	PUNCT
ejpam-4181	67	5	∫	∫	PROPN
ejpam-4181	68	1	∞	∞	NUM
ejpam-4181	68	2	0	0	NUM
ejpam-4181	69	1	ts−1e−(v−1)t	ts−1e−(v−1)t	PROPN
ejpam-4181	69	2	et	et	NOUN
ejpam-4181	69	3	−	−	NOUN
ejpam-4181	69	4	z	z	NOUN
ejpam-4181	69	5	dt	dt	X
ejpam-4181	69	6	(	(	PUNCT
ejpam-4181	69	7	5	5	NUM
ejpam-4181	69	8	)	)	PUNCT
ejpam-4181	69	9	where	where	SCONJ
ejpam-4181	69	10	re(v	re(v	NOUN
ejpam-4181	69	11	)	)	PUNCT
ejpam-4181	69	12	>	>	X
ejpam-4181	69	13	0	0	NUM
ejpam-4181	69	14	,	,	PUNCT
ejpam-4181	69	15	and	and	CCONJ
ejpam-4181	69	16	either	either	ADV
ejpam-4181	69	17	|z|≤	|z|≤	SYM
ejpam-4181	69	18	1	1	NUM
ejpam-4181	69	19	,	,	PUNCT
ejpam-4181	69	20	z	z	NOUN
ejpam-4181	69	21	̸=	̸=	PROPN
ejpam-4181	69	22	1	1	NUM
ejpam-4181	69	23	,	,	PUNCT
ejpam-4181	69	24	re(s	re(s	ADJ
ejpam-4181	69	25	)	)	PUNCT
ejpam-4181	69	26	>	>	X
ejpam-4181	69	27	0	0	NUM
ejpam-4181	69	28	,	,	PUNCT
ejpam-4181	69	29	or	or	CCONJ
ejpam-4181	69	30	z	z	NOUN
ejpam-4181	69	31	=	=	SYM
ejpam-4181	69	32	1	1	NUM
ejpam-4181	69	33	,	,	PUNCT
ejpam-4181	69	34	re(s	re(s	ADJ
ejpam-4181	69	35	)	)	PUNCT
ejpam-4181	69	36	>	>	X
ejpam-4181	70	1	1	1	NUM
ejpam-4181	70	2	.	.	X
ejpam-4181	70	3	4.2	4.2	NUM
ejpam-4181	70	4	.	.	PUNCT
ejpam-4181	70	5	infinite	infinite	ADJ
ejpam-4181	70	6	sum	sum	NOUN
ejpam-4181	70	7	of	of	ADP
ejpam-4181	70	8	the	the	DET
ejpam-4181	70	9	contour	contour	NOUN
ejpam-4181	70	10	integral	integral	ADJ
ejpam-4181	70	11	using	use	VERB
ejpam-4181	70	12	equation	equation	NOUN
ejpam-4181	70	13	(	(	PUNCT
ejpam-4181	70	14	2	2	NUM
ejpam-4181	70	15	)	)	PUNCT
ejpam-4181	70	16	and	and	CCONJ
ejpam-4181	70	17	replacing	replace	VERB
ejpam-4181	70	18	y	y	PRON
ejpam-4181	70	19	by	by	ADP
ejpam-4181	70	20	log(a	log(a	PROPN
ejpam-4181	70	21	)	)	PUNCT
ejpam-4181	70	22	+	+	CCONJ
ejpam-4181	70	23	log(b)−	log(b)−	PROPN
ejpam-4181	70	24	log(log(p	log(log(p	PROPN
ejpam-4181	70	25	)	)	PUNCT
ejpam-4181	70	26	)	)	PUNCT
ejpam-4181	71	1	+	+	CCONJ
ejpam-4181	71	2	iπ(2y	iπ(2y	PRON
ejpam-4181	71	3	+	+	NOUN
ejpam-4181	71	4	1	1	X
ejpam-4181	71	5	)	)	PUNCT
ejpam-4181	71	6	then	then	ADV
ejpam-4181	71	7	multiplying	multiply	VERB
ejpam-4181	71	8	both	both	DET
ejpam-4181	71	9	sides	side	NOUN
ejpam-4181	71	10	by	by	ADP
ejpam-4181	71	11	−2iπbm−1p−α−1	−2iπbm−1p−α−1	PROPN
ejpam-4181	71	12	log−m−1(p	log−m−1(p	X
ejpam-4181	71	13	)	)	PUNCT
ejpam-4181	71	14	taking	take	VERB
ejpam-4181	71	15	the	the	DET
ejpam-4181	71	16	infinite	infinite	ADJ
ejpam-4181	71	17	sum	sum	NOUN
ejpam-4181	71	18	over	over	ADP
ejpam-4181	71	19	y	y	PROPN
ejpam-4181	71	20	∈	∈	PROPN
ejpam-4181	72	1	[	[	X
ejpam-4181	72	2	0,∞	0,∞	NOUN
ejpam-4181	72	3	)	)	PUNCT
ejpam-4181	72	4	and	and	CCONJ
ejpam-4181	72	5	simplifying	simplify	VERB
ejpam-4181	72	6	in	in	ADP
ejpam-4181	72	7	terms	term	NOUN
ejpam-4181	72	8	of	of	ADP
ejpam-4181	72	9	the	the	DET
ejpam-4181	72	10	hurwitz	hurwitz	PROPN
ejpam-4181	72	11	-	-	PUNCT
ejpam-4181	72	12	lerch	lerch	PROPN
ejpam-4181	72	13	zeta	zeta	PROPN
ejpam-4181	72	14	function	function	VERB
ejpam-4181	72	15	we	we	PRON
ejpam-4181	72	16	obtain	obtain	VERB
ejpam-4181	72	17	(	(	PUNCT
ejpam-4181	72	18	6	6	NUM
ejpam-4181	72	19	)	)	PUNCT
ejpam-4181	72	20	−	−	PROPN
ejpam-4181	72	21	1	1	NUM
ejpam-4181	73	1	γ(k	γ(k	NOUN
ejpam-4181	73	2	+	+	CCONJ
ejpam-4181	73	3	1	1	X
ejpam-4181	73	4	)	)	PUNCT
ejpam-4181	73	5	(	(	PUNCT
ejpam-4181	73	6	2iπ)k+1eiπmbm−1p−α−1	2iπ)k+1eiπmbm−1p−α−1	NUM
ejpam-4181	73	7	log−m−1(p	log−m−1(p	X
ejpam-4181	73	8	)	)	PUNCT
ejpam-4181	73	9	φ	φ	PROPN
ejpam-4181	73	10	(	(	PUNCT
ejpam-4181	73	11	e2imπ,−k	e2imπ,−k	PROPN
ejpam-4181	73	12	,	,	PUNCT
ejpam-4181	73	13	−i	−i	PROPN
ejpam-4181	73	14	log(a)−	log(a)−	PROPN
ejpam-4181	73	15	i	i	PRON
ejpam-4181	73	16	log(b	log(b	PROPN
ejpam-4181	73	17	)	)	PUNCT
ejpam-4181	74	1	+	+	CCONJ
ejpam-4181	74	2	i	i	PROPN
ejpam-4181	74	3	log(log(p	log(log(p	PROPN
ejpam-4181	74	4	)	)	PUNCT
ejpam-4181	74	5	)	)	PUNCT
ejpam-4181	75	1	+	+	CCONJ
ejpam-4181	75	2	π	π	PROPN
ejpam-4181	75	3	2π	2π	NOUN
ejpam-4181	75	4	)	)	PUNCT
ejpam-4181	76	1	=	=	PUNCT
ejpam-4181	76	2	−	−	PROPN
ejpam-4181	76	3	1	1	NUM
ejpam-4181	76	4	2πi	2πi	NOUN
ejpam-4181	76	5	∞∑	∞∑	NUM
ejpam-4181	76	6	y=0	y=0	NUM
ejpam-4181	76	7	∫	∫	PROPN
ejpam-4181	76	8	c	c	PROPN
ejpam-4181	76	9	2iπaww−k−1p−α−1bm+w−1eiπ(2y+1)(m+w	2iπaww−k−1p−α−1bm+w−1eiπ(2y+1)(m+w	NUM
ejpam-4181	76	10	)	)	PUNCT
ejpam-4181	76	11	log−m−w−1(p)dw	log−m−w−1(p)dw	PROPN
ejpam-4181	76	12	=	=	SYM
ejpam-4181	76	13	−	−	PROPN
ejpam-4181	76	14	1	1	NUM
ejpam-4181	76	15	2πi	2πi	NOUN
ejpam-4181	76	16	∫	∫	PROPN
ejpam-4181	76	17	c	c	NOUN
ejpam-4181	77	1	∞∑	∞∑	NUM
ejpam-4181	77	2	y=0	y=0	NOUN
ejpam-4181	77	3	2iπaww−k−1p−α−1bm+w−1eiπ(2y+1)(m+w	2iπaww−k−1p−α−1bm+w−1eiπ(2y+1)(m+w	NUM
ejpam-4181	77	4	)	)	PUNCT
ejpam-4181	77	5	log−m−w−1(p)dw	log−m−w−1(p)dw	NOUN
ejpam-4181	77	6	=	=	SYM
ejpam-4181	77	7	1	1	NUM
ejpam-4181	77	8	2πi	2πi	ADJ
ejpam-4181	77	9	∫	∫	PROPN
ejpam-4181	77	10	c	c	PROPN
ejpam-4181	77	11	πaww−k−1p−α−1bm+w−1	πaww−k−1p−α−1bm+w−1	X
ejpam-4181	77	12	csc(π(m+	csc(π(m+	PROPN
ejpam-4181	77	13	w	w	NOUN
ejpam-4181	77	14	)	)	PUNCT
ejpam-4181	77	15	)	)	PUNCT
ejpam-4181	78	1	log−m−w−1(p)dw	log−m−w−1(p)dw	PROPN
ejpam-4181	78	2	from	from	ADP
ejpam-4181	78	3	equation	equation	NOUN
ejpam-4181	78	4	(	(	PUNCT
ejpam-4181	78	5	1.232.2	1.232.2	NUM
ejpam-4181	78	6	)	)	PUNCT
ejpam-4181	78	7	in	in	ADP
ejpam-4181	78	8	[	[	X
ejpam-4181	78	9	3	3	X
ejpam-4181	78	10	]	]	PUNCT
ejpam-4181	78	11	where	where	SCONJ
ejpam-4181	78	12	im(w	im(w	PUNCT
ejpam-4181	78	13	+	+	NOUN
ejpam-4181	78	14	m	m	VERB
ejpam-4181	78	15	)	)	PUNCT
ejpam-4181	78	16	>	>	X
ejpam-4181	78	17	0	0	PUNCT
ejpam-4181	79	1	in	in	ADP
ejpam-4181	79	2	order	order	NOUN
ejpam-4181	79	3	for	for	SCONJ
ejpam-4181	79	4	the	the	DET
ejpam-4181	79	5	sum	sum	NOUN
ejpam-4181	79	6	to	to	PART
ejpam-4181	79	7	converge	converge	VERB
ejpam-4181	79	8	.	.	PUNCT
ejpam-4181	80	1	5	5	X
ejpam-4181	80	2	.	.	X
ejpam-4181	80	3	definite	definite	ADJ
ejpam-4181	80	4	integral	integral	ADJ
ejpam-4181	80	5	in	in	ADP
ejpam-4181	80	6	terms	term	NOUN
ejpam-4181	80	7	of	of	ADP
ejpam-4181	80	8	the	the	DET
ejpam-4181	80	9	hurwitz	hurwitz	PROPN
ejpam-4181	80	10	-	-	PUNCT
ejpam-4181	80	11	lerch	lerch	PROPN
ejpam-4181	80	12	zeta	zeta	PROPN
ejpam-4181	80	13	function	function	PROPN
ejpam-4181	80	14	theorem	theorem	VERB
ejpam-4181	80	15	1	1	NUM
ejpam-4181	80	16	.	.	PUNCT
ejpam-4181	81	1	for	for	ADP
ejpam-4181	81	2	all	all	DET
ejpam-4181	81	3	k	k	NOUN
ejpam-4181	81	4	,	,	PUNCT
ejpam-4181	81	5	a	a	DET
ejpam-4181	81	6	∈	∈	PROPN
ejpam-4181	81	7	c	c	NOUN
ejpam-4181	81	8	,	,	PUNCT
ejpam-4181	81	9	re(p	re(p	PROPN
ejpam-4181	81	10	)	)	PUNCT
ejpam-4181	81	11	>	>	X
ejpam-4181	81	12	1	1	NUM
ejpam-4181	81	13	,	,	PUNCT
ejpam-4181	81	14	re(b	re(b	X
ejpam-4181	81	15	)	)	PUNCT
ejpam-4181	81	16	>	>	X
ejpam-4181	81	17	0	0	NUM
ejpam-4181	81	18	,	,	PUNCT
ejpam-4181	81	19	re(α	re(α	NOUN
ejpam-4181	81	20	)	)	PUNCT
ejpam-4181	81	21	>	>	X
ejpam-4181	81	22	−1	−1	NOUN
ejpam-4181	81	23	,	,	PUNCT
ejpam-4181	81	24	1/2	1/2	NUM
ejpam-4181	81	25	<	<	X
ejpam-4181	81	26	re(m	re(m	PROPN
ejpam-4181	81	27	)	)	PUNCT
ejpam-4181	81	28	>	>	X
ejpam-4181	81	29	1	1	NUM
ejpam-4181	81	30	,	,	PUNCT
ejpam-4181	81	31	(	(	PUNCT
ejpam-4181	81	32	7	7	X
ejpam-4181	81	33	)	)	PUNCT
ejpam-4181	81	34	∫	∫	PROPN
ejpam-4181	82	1	∞	∞	PROPN
ejpam-4181	82	2	0	0	NUM
ejpam-4181	82	3	∫	∫	PROPN
ejpam-4181	82	4	∞	∞	PROPN
ejpam-4181	82	5	0	0	NUM
ejpam-4181	83	1	∫	∫	PROPN
ejpam-4181	83	2	∞	∞	PROPN
ejpam-4181	83	3	0	0	NUM
ejpam-4181	84	1	∫	∫	PROPN
ejpam-4181	85	1	∞	∞	PROPN
ejpam-4181	85	2	0	0	NUM
ejpam-4181	85	3	ym−1z−me−bz−pxxα+u+y	ym−1z−me−bz−pxxα+u+y	PROPN
ejpam-4181	85	4	logk	logk	NOUN
ejpam-4181	85	5	(	(	PUNCT
ejpam-4181	85	6	ay	ay	NOUN
ejpam-4181	85	7	z	z	NOUN
ejpam-4181	85	8	)	)	PUNCT
ejpam-4181	85	9	γ(u+	γ(u+	PROPN
ejpam-4181	86	1	y	y	PROPN
ejpam-4181	86	2	+	+	CCONJ
ejpam-4181	86	3	α+	α+	PUNCT
ejpam-4181	86	4	1	1	X
ejpam-4181	86	5	)	)	PUNCT
ejpam-4181	86	6	dxdydudz	dxdydudz	NOUN
ejpam-4181	86	7	=	=	SYM
ejpam-4181	86	8	(	(	PUNCT
ejpam-4181	86	9	2iπ)k+1eiπm	2iπ)k+1eiπm	NUM
ejpam-4181	86	10	(	(	PUNCT
ejpam-4181	86	11	−bm−1	−bm−1	NOUN
ejpam-4181	86	12	)	)	PUNCT
ejpam-4181	86	13	p−α−1	p−α−1	PROPN
ejpam-4181	86	14	log−m−1(p	log−m−1(p	X
ejpam-4181	86	15	)	)	PUNCT
ejpam-4181	86	16	φ	φ	PROPN
ejpam-4181	86	17	(	(	PUNCT
ejpam-4181	86	18	e2imπ,−k	e2imπ,−k	PROPN
ejpam-4181	86	19	,	,	PUNCT
ejpam-4181	86	20	−i	−i	PROPN
ejpam-4181	86	21	log(a)−	log(a)−	PROPN
ejpam-4181	86	22	i	i	PRON
ejpam-4181	86	23	log(b	log(b	PROPN
ejpam-4181	86	24	)	)	PUNCT
ejpam-4181	87	1	+	+	CCONJ
ejpam-4181	87	2	i	i	PROPN
ejpam-4181	87	3	log(log(p	log(log(p	PROPN
ejpam-4181	87	4	)	)	PUNCT
ejpam-4181	87	5	)	)	PUNCT
ejpam-4181	88	1	+	+	CCONJ
ejpam-4181	88	2	π	π	PROPN
ejpam-4181	88	3	2π	2π	PROPN
ejpam-4181	88	4	)	)	PUNCT
ejpam-4181	88	5	r.	r.	PROPN
ejpam-4181	88	6	reynolds	reynolds	PROPN
ejpam-4181	88	7	,	,	PUNCT
ejpam-4181	88	8	a.	a.	PROPN
ejpam-4181	88	9	stauffer	stauffer	PROPN
ejpam-4181	88	10	/	/	SYM
ejpam-4181	88	11	eur	eur	PROPN
ejpam-4181	88	12	.	.	PUNCT
ejpam-4181	89	1	j.	j.	PROPN
ejpam-4181	89	2	pure	pure	PROPN
ejpam-4181	89	3	appl	appl	PROPN
ejpam-4181	89	4	.	.	PROPN
ejpam-4181	89	5	math	math	PROPN
ejpam-4181	89	6	,	,	PUNCT
ejpam-4181	89	7	15	15	NUM
ejpam-4181	89	8	(	(	PUNCT
ejpam-4181	89	9	1	1	NUM
ejpam-4181	89	10	)	)	PUNCT
ejpam-4181	89	11	(	(	PUNCT
ejpam-4181	89	12	2022	2022	NUM
ejpam-4181	89	13	)	)	PUNCT
ejpam-4181	89	14	,	,	PUNCT
ejpam-4181	89	15	30	30	NUM
ejpam-4181	89	16	-	-	SYM
ejpam-4181	89	17	35	35	NUM
ejpam-4181	89	18	33	33	NUM
ejpam-4181	89	19	proof	proof	NOUN
ejpam-4181	89	20	.	.	PUNCT
ejpam-4181	90	1	observe	observe	VERB
ejpam-4181	90	2	the	the	DET
ejpam-4181	90	3	right	right	ADJ
ejpam-4181	90	4	-	-	PUNCT
ejpam-4181	90	5	hand	hand	NOUN
ejpam-4181	90	6	side	side	NOUN
ejpam-4181	90	7	of	of	ADP
ejpam-4181	90	8	equation	equation	NOUN
ejpam-4181	90	9	(	(	PUNCT
ejpam-4181	90	10	3	3	X
ejpam-4181	90	11	)	)	PUNCT
ejpam-4181	90	12	is	be	AUX
ejpam-4181	90	13	equal	equal	ADJ
ejpam-4181	90	14	to	to	ADP
ejpam-4181	90	15	the	the	DET
ejpam-4181	90	16	right	right	ADJ
ejpam-4181	90	17	-	-	PUNCT
ejpam-4181	90	18	hand	hand	NOUN
ejpam-4181	90	19	side	side	NOUN
ejpam-4181	90	20	of	of	ADP
ejpam-4181	90	21	equation	equation	NOUN
ejpam-4181	90	22	(	(	PUNCT
ejpam-4181	90	23	6	6	NUM
ejpam-4181	90	24	)	)	PUNCT
ejpam-4181	90	25	so	so	SCONJ
ejpam-4181	90	26	we	we	PRON
ejpam-4181	90	27	may	may	AUX
ejpam-4181	90	28	equate	equate	VERB
ejpam-4181	90	29	the	the	DET
ejpam-4181	90	30	left	left	ADJ
ejpam-4181	90	31	-	-	PUNCT
ejpam-4181	90	32	hand	hand	NOUN
ejpam-4181	90	33	sides	side	NOUN
ejpam-4181	90	34	to	to	PART
ejpam-4181	90	35	yield	yield	VERB
ejpam-4181	90	36	the	the	DET
ejpam-4181	90	37	stated	state	VERB
ejpam-4181	90	38	result	result	NOUN
ejpam-4181	90	39	.	.	PUNCT
ejpam-4181	91	1	6	6	X
ejpam-4181	91	2	.	.	X
ejpam-4181	91	3	special	special	ADJ
ejpam-4181	91	4	cases	case	NOUN
ejpam-4181	91	5	in	in	ADP
ejpam-4181	91	6	this	this	DET
ejpam-4181	91	7	section	section	NOUN
ejpam-4181	91	8	we	we	PRON
ejpam-4181	91	9	will	will	AUX
ejpam-4181	91	10	evaluate	evaluate	VERB
ejpam-4181	91	11	equation	equation	NOUN
ejpam-4181	91	12	(	(	PUNCT
ejpam-4181	91	13	7	7	NUM
ejpam-4181	91	14	)	)	PUNCT
ejpam-4181	91	15	for	for	ADP
ejpam-4181	91	16	various	various	ADJ
ejpam-4181	91	17	parameter	parameter	NOUN
ejpam-4181	91	18	values	value	NOUN
ejpam-4181	91	19	in	in	ADP
ejpam-4181	91	20	terms	term	NOUN
ejpam-4181	91	21	of	of	ADP
ejpam-4181	91	22	the	the	DET
ejpam-4181	91	23	riemann	riemann	PROPN
ejpam-4181	91	24	zeta	zeta	PROPN
ejpam-4181	91	25	function	function	PROPN
ejpam-4181	91	26	ζ(s	ζ(s	PROPN
ejpam-4181	91	27	)	)	PUNCT
ejpam-4181	91	28	,	,	PUNCT
ejpam-4181	91	29	equation	equation	NOUN
ejpam-4181	91	30	(	(	PUNCT
ejpam-4181	91	31	25.2.1	25.2.1	NUM
ejpam-4181	91	32	)	)	PUNCT
ejpam-4181	91	33	in	in	ADP
ejpam-4181	91	34	[	[	X
ejpam-4181	91	35	2	2	NUM
ejpam-4181	91	36	]	]	PUNCT
ejpam-4181	91	37	,	,	PUNCT
ejpam-4181	91	38	aprey	aprey	PROPN
ejpam-4181	91	39	’s	’s	PART
ejpam-4181	91	40	constant	constant	ADJ
ejpam-4181	91	41	ζ(3	ζ(3	PROPN
ejpam-4181	91	42	)	)	PUNCT
ejpam-4181	91	43	,	,	PUNCT
ejpam-4181	91	44	equation	equation	NOUN
ejpam-4181	91	45	(	(	PUNCT
ejpam-4181	91	46	25.6.9	25.6.9	NUM
ejpam-4181	91	47	)	)	PUNCT
ejpam-4181	91	48	in	in	ADP
ejpam-4181	91	49	[	[	X
ejpam-4181	91	50	2	2	NUM
ejpam-4181	91	51	]	]	PUNCT
ejpam-4181	91	52	,	,	PUNCT
ejpam-4181	91	53	log(2	log(2	NOUN
ejpam-4181	91	54	)	)	PUNCT
ejpam-4181	91	55	and	and	CCONJ
ejpam-4181	91	56	π	π	X
ejpam-4181	91	57	.	.	PROPN
ejpam-4181	91	58	example	example	NOUN
ejpam-4181	92	1	1	1	NUM
ejpam-4181	92	2	.	.	PUNCT
ejpam-4181	93	1	the	the	DET
ejpam-4181	93	2	degenerate	degenerate	ADJ
ejpam-4181	93	3	case	case	NOUN
ejpam-4181	93	4	.	.	PUNCT
ejpam-4181	94	1	(	(	PUNCT
ejpam-4181	94	2	8	8	X
ejpam-4181	94	3	)	)	PUNCT
ejpam-4181	94	4	∫	∫	PROPN
ejpam-4181	95	1	∞	∞	PROPN
ejpam-4181	95	2	0	0	NUM
ejpam-4181	95	3	∫	∫	PROPN
ejpam-4181	95	4	∞	∞	PROPN
ejpam-4181	95	5	0	0	NUM
ejpam-4181	96	1	∫	∫	PROPN
ejpam-4181	96	2	∞	∞	PROPN
ejpam-4181	96	3	0	0	NUM
ejpam-4181	97	1	∫	∫	PROPN
ejpam-4181	97	2	∞	∞	NOUN
ejpam-4181	97	3	0	0	NUM
ejpam-4181	98	1	ym−1z−me−bz−pxxα+u+y	ym−1z−me−bz−pxxα+u+y	PROPN
ejpam-4181	98	2	γ(u+	γ(u+	PROPN
ejpam-4181	99	1	y	y	PROPN
ejpam-4181	99	2	+	+	CCONJ
ejpam-4181	99	3	α+	α+	PUNCT
ejpam-4181	99	4	1	1	X
ejpam-4181	99	5	)	)	PUNCT
ejpam-4181	99	6	dxdydudz	dxdydudz	NOUN
ejpam-4181	99	7	=	=	SYM
ejpam-4181	99	8	πbm−1	πbm−1	PROPN
ejpam-4181	99	9	csc(πm)p−α−1	csc(πm)p−α−1	NOUN
ejpam-4181	99	10	log−m−1(p	log−m−1(p	X
ejpam-4181	99	11	)	)	PUNCT
ejpam-4181	99	12	proof	proof	NOUN
ejpam-4181	99	13	.	.	PUNCT
ejpam-4181	100	1	use	use	VERB
ejpam-4181	100	2	equation	equation	NOUN
ejpam-4181	100	3	(	(	PUNCT
ejpam-4181	100	4	7	7	NUM
ejpam-4181	100	5	)	)	PUNCT
ejpam-4181	100	6	and	and	CCONJ
ejpam-4181	100	7	set	set	VERB
ejpam-4181	100	8	k	k	PROPN
ejpam-4181	100	9	=	=	PUNCT
ejpam-4181	100	10	0	0	PUNCT
ejpam-4181	100	11	and	and	CCONJ
ejpam-4181	100	12	simplify	simplify	VERB
ejpam-4181	100	13	using	use	VERB
ejpam-4181	100	14	entry	entry	NOUN
ejpam-4181	100	15	(	(	PUNCT
ejpam-4181	100	16	2	2	NUM
ejpam-4181	100	17	)	)	PUNCT
ejpam-4181	100	18	in	in	ADP
ejpam-4181	100	19	table	table	NOUN
ejpam-4181	100	20	below	below	ADV
ejpam-4181	100	21	(	(	PUNCT
ejpam-4181	100	22	64:12:7	64:12:7	NUM
ejpam-4181	100	23	)	)	PUNCT
ejpam-4181	100	24	in	in	ADP
ejpam-4181	100	25	[	[	X
ejpam-4181	100	26	4	4	NUM
ejpam-4181	100	27	]	]	PUNCT
ejpam-4181	100	28	.	.	PUNCT
ejpam-4181	100	29	example	example	NOUN
ejpam-4181	101	1	2	2	NUM
ejpam-4181	101	2	.	.	PUNCT
ejpam-4181	101	3	(	(	PUNCT
ejpam-4181	101	4	9	9	NUM
ejpam-4181	101	5	)	)	PUNCT
ejpam-4181	101	6	∫	∫	PROPN
ejpam-4181	101	7	∞	∞	PROPN
ejpam-4181	101	8	0	0	NUM
ejpam-4181	102	1	∫	∫	PROPN
ejpam-4181	102	2	∞	∞	PROPN
ejpam-4181	102	3	0	0	NUM
ejpam-4181	103	1	∫	∫	PROPN
ejpam-4181	103	2	∞	∞	PROPN
ejpam-4181	103	3	0	0	NUM
ejpam-4181	104	1	∫	∫	PROPN
ejpam-4181	104	2	∞	∞	PROPN
ejpam-4181	104	3	0	0	NUM
ejpam-4181	104	4	e−ex−zxu+y+1	e−ex−zxu+y+1	VERB
ejpam-4181	104	5	logk	logk	NOUN
ejpam-4181	104	6	(	(	PUNCT
ejpam-4181	104	7	−y	−y	NOUN
ejpam-4181	104	8	z	z	NOUN
ejpam-4181	104	9	)	)	PUNCT
ejpam-4181	104	10	√	√	PROPN
ejpam-4181	105	1	y	y	NOUN
ejpam-4181	106	1	√	√	PROPN
ejpam-4181	106	2	zγ(u+	zγ(u+	PROPN
ejpam-4181	106	3	y	y	PROPN
ejpam-4181	106	4	+	+	CCONJ
ejpam-4181	106	5	2	2	X
ejpam-4181	106	6	)	)	PUNCT
ejpam-4181	106	7	dxdydudz	dxdydudz	NOUN
ejpam-4181	106	8	=	=	PUNCT
ejpam-4181	106	9	−	−	PROPN
ejpam-4181	106	10	ik+2	ik+2	PROPN
ejpam-4181	106	11	(	(	PUNCT
ejpam-4181	106	12	1−	1−	NUM
ejpam-4181	106	13	2k+1	2k+1	NOUN
ejpam-4181	106	14	)	)	PUNCT
ejpam-4181	106	15	(	(	PUNCT
ejpam-4181	106	16	2π)k+1ζ(−k	2π)k+1ζ(−k	NOUN
ejpam-4181	106	17	)	)	PUNCT
ejpam-4181	106	18	e2	e2	NOUN
ejpam-4181	106	19	proof	proof	NOUN
ejpam-4181	106	20	.	.	PUNCT
ejpam-4181	107	1	use	use	VERB
ejpam-4181	107	2	equation	equation	NOUN
ejpam-4181	107	3	(	(	PUNCT
ejpam-4181	107	4	7	7	NUM
ejpam-4181	107	5	)	)	PUNCT
ejpam-4181	107	6	and	and	CCONJ
ejpam-4181	107	7	set	set	VERB
ejpam-4181	107	8	a	a	DET
ejpam-4181	107	9	=	=	SYM
ejpam-4181	107	10	−1	−1	NOUN
ejpam-4181	107	11	,	,	PUNCT
ejpam-4181	107	12	p	p	X
ejpam-4181	107	13	=	=	SYM
ejpam-4181	107	14	e	e	PROPN
ejpam-4181	107	15	,	,	PUNCT
ejpam-4181	107	16	b	b	X
ejpam-4181	107	17	=	=	SYM
ejpam-4181	107	18	1,m	1,m	PROPN
ejpam-4181	107	19	=	=	SYM
ejpam-4181	107	20	1/2	1/2	NUM
ejpam-4181	107	21	,	,	PUNCT
ejpam-4181	107	22	α	α	NOUN
ejpam-4181	107	23	=	=	SYM
ejpam-4181	107	24	1	1	NUM
ejpam-4181	107	25	and	and	CCONJ
ejpam-4181	107	26	simplify	simplify	VERB
ejpam-4181	107	27	using	use	VERB
ejpam-4181	107	28	entry	entry	NOUN
ejpam-4181	107	29	(	(	PUNCT
ejpam-4181	107	30	2	2	NUM
ejpam-4181	107	31	)	)	PUNCT
ejpam-4181	107	32	in	in	ADP
ejpam-4181	107	33	table	table	NOUN
ejpam-4181	107	34	below	below	ADV
ejpam-4181	107	35	(	(	PUNCT
ejpam-4181	107	36	64:7	64:7	NUM
ejpam-4181	107	37	)	)	PUNCT
ejpam-4181	107	38	and	and	CCONJ
ejpam-4181	107	39	entry	entry	NOUN
ejpam-4181	107	40	(	(	PUNCT
ejpam-4181	107	41	4	4	NUM
ejpam-4181	107	42	)	)	PUNCT
ejpam-4181	107	43	in	in	ADP
ejpam-4181	107	44	table	table	NOUN
ejpam-4181	107	45	below	below	ADV
ejpam-4181	107	46	(	(	PUNCT
ejpam-4181	107	47	64:12:7	64:12:7	NUM
ejpam-4181	107	48	)	)	PUNCT
ejpam-4181	107	49	in	in	ADP
ejpam-4181	107	50	[	[	X
ejpam-4181	107	51	4	4	NUM
ejpam-4181	107	52	]	]	PUNCT
ejpam-4181	107	53	.	.	PUNCT
ejpam-4181	107	54	example	example	NOUN
ejpam-4181	108	1	3	3	NUM
ejpam-4181	108	2	.	.	PUNCT
ejpam-4181	108	3	(	(	PUNCT
ejpam-4181	108	4	10	10	NUM
ejpam-4181	108	5	)	)	PUNCT
ejpam-4181	108	6	∫	∫	PROPN
ejpam-4181	109	1	∞	∞	PROPN
ejpam-4181	109	2	0	0	NUM
ejpam-4181	109	3	∫	∫	PROPN
ejpam-4181	109	4	∞	∞	PROPN
ejpam-4181	109	5	0	0	NUM
ejpam-4181	110	1	∫	∫	PROPN
ejpam-4181	110	2	∞	∞	PROPN
ejpam-4181	110	3	0	0	NUM
ejpam-4181	111	1	∫	∫	PROPN
ejpam-4181	111	2	∞	∞	PROPN
ejpam-4181	111	3	0	0	NUM
ejpam-4181	111	4	e−ex−zxu+y+1	e−ex−zxu+y+1	NOUN
ejpam-4181	111	5	√	√	NUM
ejpam-4181	111	6	y	y	NUM
ejpam-4181	111	7	√	√	PROPN
ejpam-4181	111	8	zγ(u+	zγ(u+	PROPN
ejpam-4181	111	9	y	y	PROPN
ejpam-4181	112	1	+	+	NOUN
ejpam-4181	112	2	2	2	NUM
ejpam-4181	112	3	)	)	PUNCT
ejpam-4181	112	4	(	(	PUNCT
ejpam-4181	112	5	log2	log2	PROPN
ejpam-4181	112	6	(	(	PUNCT
ejpam-4181	112	7	y	y	PROPN
ejpam-4181	112	8	z	z	PROPN
ejpam-4181	112	9	)	)	PUNCT
ejpam-4181	113	1	+	+	CCONJ
ejpam-4181	113	2	π2	π2	ADJ
ejpam-4181	113	3	)	)	PUNCT
ejpam-4181	113	4	dxdydudz	dxdydudz	NOUN
ejpam-4181	113	5	=	=	PUNCT
ejpam-4181	113	6	log(2	log(2	ADJ
ejpam-4181	113	7	)	)	PUNCT
ejpam-4181	113	8	e2π	e2π	NOUN
ejpam-4181	113	9	and	and	CCONJ
ejpam-4181	113	10	(	(	PUNCT
ejpam-4181	113	11	11	11	NUM
ejpam-4181	113	12	)	)	PUNCT
ejpam-4181	113	13	∫	∫	PROPN
ejpam-4181	114	1	∞	∞	PROPN
ejpam-4181	114	2	0	0	NUM
ejpam-4181	114	3	∫	∫	PROPN
ejpam-4181	114	4	∞	∞	PROPN
ejpam-4181	114	5	0	0	NUM
ejpam-4181	115	1	∫	∫	PROPN
ejpam-4181	115	2	∞	∞	PROPN
ejpam-4181	115	3	0	0	NUM
ejpam-4181	116	1	∫	∫	PROPN
ejpam-4181	116	2	∞	∞	PROPN
ejpam-4181	116	3	0	0	NUM
ejpam-4181	116	4	e−ex−zxu+y+1	e−ex−zxu+y+1	NOUN
ejpam-4181	116	5	log	log	NOUN
ejpam-4181	116	6	(	(	PUNCT
ejpam-4181	116	7	y	y	PROPN
ejpam-4181	116	8	z	z	PROPN
ejpam-4181	116	9	)	)	PUNCT
ejpam-4181	117	1	√	√	PROPN
ejpam-4181	117	2	y	y	NOUN
ejpam-4181	118	1	√	√	PROPN
ejpam-4181	118	2	zγ(u+	zγ(u+	PROPN
ejpam-4181	118	3	y	y	PROPN
ejpam-4181	118	4	+	+	NOUN
ejpam-4181	118	5	2	2	NUM
ejpam-4181	118	6	)	)	PUNCT
ejpam-4181	118	7	(	(	PUNCT
ejpam-4181	118	8	log2	log2	PROPN
ejpam-4181	118	9	(	(	PUNCT
ejpam-4181	118	10	y	y	PROPN
ejpam-4181	118	11	z	z	PROPN
ejpam-4181	118	12	)	)	PUNCT
ejpam-4181	119	1	+	+	CCONJ
ejpam-4181	119	2	π2	π2	ADJ
ejpam-4181	119	3	)	)	PUNCT
ejpam-4181	119	4	dxdydudz	dxdydudz	NOUN
ejpam-4181	119	5	=	=	SYM
ejpam-4181	119	6	0	0	NUM
ejpam-4181	119	7	proof	proof	NOUN
ejpam-4181	119	8	.	.	PUNCT
ejpam-4181	120	1	use	use	VERB
ejpam-4181	120	2	equation	equation	NOUN
ejpam-4181	120	3	(	(	PUNCT
ejpam-4181	120	4	9	9	NUM
ejpam-4181	120	5	)	)	PUNCT
ejpam-4181	120	6	and	and	CCONJ
ejpam-4181	120	7	apply	apply	VERB
ejpam-4181	120	8	l’hopital	l’hopital	PROPN
ejpam-4181	120	9	’s	’s	PART
ejpam-4181	120	10	rule	rule	NOUN
ejpam-4181	120	11	to	to	ADP
ejpam-4181	120	12	the	the	DET
ejpam-4181	120	13	right	right	ADJ
ejpam-4181	120	14	-	-	PUNCT
ejpam-4181	120	15	hand	hand	NOUN
ejpam-4181	120	16	side	side	NOUN
ejpam-4181	120	17	as	as	ADP
ejpam-4181	120	18	k	k	PROPN
ejpam-4181	120	19	→	→	SYM
ejpam-4181	120	20	−1	−1	NOUN
ejpam-4181	120	21	simplify	simplify	NOUN
ejpam-4181	120	22	using	use	VERB
ejpam-4181	120	23	equation	equation	NOUN
ejpam-4181	120	24	(	(	PUNCT
ejpam-4181	120	25	25.6.11	25.6.11	X
ejpam-4181	120	26	)	)	PUNCT
ejpam-4181	120	27	in	in	ADP
ejpam-4181	120	28	[	[	X
ejpam-4181	120	29	2	2	NUM
ejpam-4181	120	30	]	]	PUNCT
ejpam-4181	120	31	and	and	CCONJ
ejpam-4181	120	32	rationalize	rationalize	VERB
ejpam-4181	120	33	the	the	DET
ejpam-4181	120	34	denominator	denominator	NOUN
ejpam-4181	120	35	and	and	CCONJ
ejpam-4181	120	36	equate	equate	VERB
ejpam-4181	120	37	real	real	ADJ
ejpam-4181	120	38	and	and	CCONJ
ejpam-4181	120	39	imaginary	imaginary	ADJ
ejpam-4181	120	40	parts	part	NOUN
ejpam-4181	120	41	.	.	PUNCT
ejpam-4181	121	1	r.	r.	PROPN
ejpam-4181	121	2	reynolds	reynolds	PROPN
ejpam-4181	121	3	,	,	PUNCT
ejpam-4181	121	4	a.	a.	PROPN
ejpam-4181	121	5	stauffer	stauffer	PROPN
ejpam-4181	121	6	/	/	SYM
ejpam-4181	121	7	eur	eur	PROPN
ejpam-4181	121	8	.	.	PUNCT
ejpam-4181	122	1	j.	j.	PROPN
ejpam-4181	122	2	pure	pure	PROPN
ejpam-4181	122	3	appl	appl	PROPN
ejpam-4181	122	4	.	.	PROPN
ejpam-4181	122	5	math	math	PROPN
ejpam-4181	122	6	,	,	PUNCT
ejpam-4181	122	7	15	15	NUM
ejpam-4181	122	8	(	(	PUNCT
ejpam-4181	122	9	1	1	NUM
ejpam-4181	122	10	)	)	PUNCT
ejpam-4181	122	11	(	(	PUNCT
ejpam-4181	122	12	2022	2022	NUM
ejpam-4181	122	13	)	)	PUNCT
ejpam-4181	122	14	,	,	PUNCT
ejpam-4181	122	15	30	30	NUM
ejpam-4181	122	16	-	-	SYM
ejpam-4181	122	17	35	35	NUM
ejpam-4181	122	18	34	34	NUM
ejpam-4181	122	19	example	example	NOUN
ejpam-4181	122	20	4	4	NUM
ejpam-4181	122	21	.	.	PUNCT
ejpam-4181	123	1	(	(	PUNCT
ejpam-4181	123	2	12	12	NUM
ejpam-4181	123	3	)	)	PUNCT
ejpam-4181	123	4	∫	∫	PROPN
ejpam-4181	124	1	∞	∞	PROPN
ejpam-4181	124	2	0	0	NUM
ejpam-4181	124	3	∫	∫	PROPN
ejpam-4181	124	4	∞	∞	PROPN
ejpam-4181	124	5	0	0	NUM
ejpam-4181	124	6	∫	∫	PROPN
ejpam-4181	124	7	∞	∞	PROPN
ejpam-4181	124	8	0	0	NUM
ejpam-4181	125	1	∫	∫	PROPN
ejpam-4181	125	2	∞	∞	PROPN
ejpam-4181	125	3	0	0	NUM
ejpam-4181	125	4	e−ex−zxu+y+1	e−ex−zxu+y+1	NOUN
ejpam-4181	126	1	(	(	PUNCT
ejpam-4181	126	2	π2	π2	ADV
ejpam-4181	126	3	−	−	PROPN
ejpam-4181	126	4	3	3	NUM
ejpam-4181	126	5	log2	log2	NOUN
ejpam-4181	126	6	(	(	PUNCT
ejpam-4181	126	7	y	y	PROPN
ejpam-4181	126	8	z	z	PROPN
ejpam-4181	126	9	)	)	PUNCT
ejpam-4181	126	10	)	)	PUNCT
ejpam-4181	127	1	√	√	PROPN
ejpam-4181	128	1	y	y	NOUN
ejpam-4181	128	2	√	√	PROPN
ejpam-4181	128	3	zγ(u+	zγ(u+	PROPN
ejpam-4181	128	4	y	y	PROPN
ejpam-4181	128	5	+	+	NOUN
ejpam-4181	128	6	2	2	NUM
ejpam-4181	128	7	)	)	PUNCT
ejpam-4181	128	8	(	(	PUNCT
ejpam-4181	128	9	log2	log2	PROPN
ejpam-4181	128	10	(	(	PUNCT
ejpam-4181	128	11	y	y	PROPN
ejpam-4181	128	12	z	z	PROPN
ejpam-4181	128	13	)	)	PUNCT
ejpam-4181	129	1	+	+	CCONJ
ejpam-4181	129	2	π2	π2	ADJ
ejpam-4181	129	3	)	)	PUNCT
ejpam-4181	129	4	3dxdydudz	3dxdydudz	NUM
ejpam-4181	129	5	=	=	SYM
ejpam-4181	129	6	3ζ(3	3ζ(3	NUM
ejpam-4181	129	7	)	)	PUNCT
ejpam-4181	129	8	16e2π3	16e2π3	PROPN
ejpam-4181	129	9	and	and	CCONJ
ejpam-4181	129	10	(	(	PUNCT
ejpam-4181	129	11	13	13	NUM
ejpam-4181	129	12	)	)	PUNCT
ejpam-4181	129	13	∫	∫	PROPN
ejpam-4181	130	1	∞	∞	PROPN
ejpam-4181	130	2	0	0	NUM
ejpam-4181	131	1	∫	∫	PROPN
ejpam-4181	131	2	∞	∞	PROPN
ejpam-4181	131	3	0	0	NUM
ejpam-4181	132	1	∫	∫	PROPN
ejpam-4181	132	2	∞	∞	PROPN
ejpam-4181	132	3	0	0	NUM
ejpam-4181	133	1	∫	∫	PROPN
ejpam-4181	133	2	∞	∞	PROPN
ejpam-4181	133	3	0	0	NUM
ejpam-4181	133	4	e−ex−zxu+y+1	e−ex−zxu+y+1	NOUN
ejpam-4181	133	5	log	log	NOUN
ejpam-4181	133	6	(	(	PUNCT
ejpam-4181	133	7	y	y	PROPN
ejpam-4181	133	8	z	z	PROPN
ejpam-4181	133	9	)	)	PUNCT
ejpam-4181	133	10	(	(	PUNCT
ejpam-4181	133	11	log2	log2	PROPN
ejpam-4181	133	12	(	(	PUNCT
ejpam-4181	133	13	y	y	PROPN
ejpam-4181	133	14	z	z	PROPN
ejpam-4181	133	15	)	)	PUNCT
ejpam-4181	134	1	−	−	ADP
ejpam-4181	134	2	3π2	3π2	NUM
ejpam-4181	134	3	)	)	PUNCT
ejpam-4181	135	1	√	√	PROPN
ejpam-4181	136	1	y	y	NOUN
ejpam-4181	136	2	√	√	PROPN
ejpam-4181	136	3	zγ(u+	zγ(u+	PROPN
ejpam-4181	136	4	y	y	PROPN
ejpam-4181	136	5	+	+	NOUN
ejpam-4181	136	6	2	2	NUM
ejpam-4181	136	7	)	)	PUNCT
ejpam-4181	136	8	(	(	PUNCT
ejpam-4181	136	9	log2	log2	PROPN
ejpam-4181	136	10	(	(	PUNCT
ejpam-4181	136	11	y	y	PROPN
ejpam-4181	136	12	z	z	PROPN
ejpam-4181	136	13	)	)	PUNCT
ejpam-4181	137	1	+	+	CCONJ
ejpam-4181	137	2	π2	π2	ADJ
ejpam-4181	137	3	)	)	PUNCT
ejpam-4181	137	4	3	3	NUM
ejpam-4181	137	5	dxdydudz	dxdydudz	NOUN
ejpam-4181	137	6	=	=	SYM
ejpam-4181	137	7	0	0	NUM
ejpam-4181	137	8	proof	proof	NOUN
ejpam-4181	137	9	.	.	PUNCT
ejpam-4181	138	1	use	use	VERB
ejpam-4181	138	2	equation	equation	NOUN
ejpam-4181	138	3	(	(	PUNCT
ejpam-4181	138	4	9	9	NUM
ejpam-4181	138	5	)	)	PUNCT
ejpam-4181	138	6	and	and	CCONJ
ejpam-4181	138	7	set	set	VERB
ejpam-4181	138	8	k	k	PROPN
ejpam-4181	138	9	=	=	PUNCT
ejpam-4181	138	10	−3	−3	PROPN
ejpam-4181	138	11	using	use	VERB
ejpam-4181	138	12	entry	entry	NOUN
ejpam-4181	138	13	(	(	PUNCT
ejpam-4181	138	14	2	2	NUM
ejpam-4181	138	15	)	)	PUNCT
ejpam-4181	138	16	in	in	ADP
ejpam-4181	138	17	table	table	NOUN
ejpam-4181	138	18	below	below	ADV
ejpam-4181	138	19	(	(	PUNCT
ejpam-4181	138	20	64:7	64:7	NUM
ejpam-4181	138	21	)	)	PUNCT
ejpam-4181	138	22	and	and	CCONJ
ejpam-4181	138	23	rationalize	rationalize	VERB
ejpam-4181	138	24	the	the	DET
ejpam-4181	138	25	denominator	denominator	NOUN
ejpam-4181	138	26	and	and	CCONJ
ejpam-4181	138	27	simplify	simplify	VERB
ejpam-4181	138	28	into	into	ADP
ejpam-4181	138	29	real	real	ADJ
ejpam-4181	138	30	and	and	CCONJ
ejpam-4181	138	31	imaginary	imaginary	ADJ
ejpam-4181	138	32	parts	part	NOUN
ejpam-4181	138	33	.	.	PUNCT
ejpam-4181	138	34	example	example	NOUN
ejpam-4181	139	1	5	5	NUM
ejpam-4181	139	2	.	.	PUNCT
ejpam-4181	140	1	(	(	PUNCT
ejpam-4181	140	2	14	14	NUM
ejpam-4181	140	3	)	)	PUNCT
ejpam-4181	140	4	∫	∫	PROPN
ejpam-4181	141	1	∞	∞	PROPN
ejpam-4181	141	2	0	0	NUM
ejpam-4181	141	3	∫	∫	PROPN
ejpam-4181	141	4	∞	∞	PROPN
ejpam-4181	141	5	0	0	NUM
ejpam-4181	142	1	∫	∫	PROPN
ejpam-4181	142	2	∞	∞	PROPN
ejpam-4181	142	3	0	0	NUM
ejpam-4181	143	1	∫	∫	PROPN
ejpam-4181	144	1	∞	∞	NUM
ejpam-4181	144	2	0	0	NUM
ejpam-4181	144	3	e−pxp−zxu+y+1	e−pxp−zxu+y+1	NUM
ejpam-4181	144	4	logk	logk	NOUN
ejpam-4181	144	5	(	(	PUNCT
ejpam-4181	144	6	−y	−y	NOUN
ejpam-4181	144	7	z	z	NOUN
ejpam-4181	144	8	)	)	PUNCT
ejpam-4181	145	1	√	√	PROPN
ejpam-4181	145	2	y	y	NOUN
ejpam-4181	146	1	√	√	PROPN
ejpam-4181	146	2	zγ(u+	zγ(u+	PROPN
ejpam-4181	146	3	y	y	PROPN
ejpam-4181	146	4	+	+	CCONJ
ejpam-4181	146	5	2	2	X
ejpam-4181	146	6	)	)	PUNCT
ejpam-4181	146	7	dxdydudz	dxdydudz	NOUN
ejpam-4181	146	8	=	=	PUNCT
ejpam-4181	146	9	−	−	PROPN
ejpam-4181	146	10	ik	ik	PROPN
ejpam-4181	146	11	(	(	PUNCT
ejpam-4181	146	12	2k+1	2k+1	NOUN
ejpam-4181	146	13	−	−	NOUN
ejpam-4181	146	14	1	1	NUM
ejpam-4181	146	15	)	)	PUNCT
ejpam-4181	146	16	(	(	PUNCT
ejpam-4181	146	17	2π)k+1ζ(−k	2π)k+1ζ(−k	NOUN
ejpam-4181	146	18	)	)	PUNCT
ejpam-4181	146	19	p2	p2	NOUN
ejpam-4181	146	20	log2(p	log2(p	NOUN
ejpam-4181	146	21	)	)	PUNCT
ejpam-4181	146	22	proof	proof	NOUN
ejpam-4181	146	23	.	.	PUNCT
ejpam-4181	147	1	use	use	VERB
ejpam-4181	147	2	equation	equation	NOUN
ejpam-4181	147	3	(	(	PUNCT
ejpam-4181	147	4	7	7	NUM
ejpam-4181	147	5	)	)	PUNCT
ejpam-4181	147	6	and	and	CCONJ
ejpam-4181	147	7	set	set	VERB
ejpam-4181	147	8	a	a	DET
ejpam-4181	147	9	=	=	SYM
ejpam-4181	147	10	−1	−1	NOUN
ejpam-4181	147	11	,	,	PUNCT
ejpam-4181	147	12	b	b	X
ejpam-4181	147	13	=	=	SYM
ejpam-4181	147	14	log(p),m	log(p),m	PROPN
ejpam-4181	147	15	=	=	SYM
ejpam-4181	147	16	1/2	1/2	NUM
ejpam-4181	147	17	,	,	PUNCT
ejpam-4181	147	18	α	α	NOUN
ejpam-4181	147	19	=	=	SYM
ejpam-4181	147	20	1	1	NUM
ejpam-4181	147	21	and	and	CCONJ
ejpam-4181	147	22	simplify	simplify	VERB
ejpam-4181	147	23	using	use	VERB
ejpam-4181	147	24	entry	entry	NOUN
ejpam-4181	147	25	(	(	PUNCT
ejpam-4181	147	26	2	2	NUM
ejpam-4181	147	27	)	)	PUNCT
ejpam-4181	147	28	in	in	ADP
ejpam-4181	147	29	table	table	NOUN
ejpam-4181	147	30	below	below	ADV
ejpam-4181	147	31	(	(	PUNCT
ejpam-4181	147	32	64:7	64:7	NUM
ejpam-4181	147	33	)	)	PUNCT
ejpam-4181	147	34	and	and	CCONJ
ejpam-4181	147	35	entry	entry	NOUN
ejpam-4181	147	36	(	(	PUNCT
ejpam-4181	147	37	4	4	NUM
ejpam-4181	147	38	)	)	PUNCT
ejpam-4181	147	39	in	in	ADP
ejpam-4181	147	40	table	table	NOUN
ejpam-4181	147	41	below	below	ADV
ejpam-4181	147	42	(	(	PUNCT
ejpam-4181	147	43	64:12:7	64:12:7	NUM
ejpam-4181	147	44	)	)	PUNCT
ejpam-4181	147	45	in	in	ADP
ejpam-4181	147	46	[	[	X
ejpam-4181	147	47	4	4	NUM
ejpam-4181	147	48	]	]	PUNCT
ejpam-4181	147	49	.	.	PUNCT
ejpam-4181	147	50	example	example	NOUN
ejpam-4181	148	1	6	6	NUM
ejpam-4181	148	2	.	.	PUNCT
ejpam-4181	148	3	(	(	PUNCT
ejpam-4181	148	4	15	15	NUM
ejpam-4181	148	5	)	)	PUNCT
ejpam-4181	148	6	∫	∫	PROPN
ejpam-4181	148	7	∞	∞	PROPN
ejpam-4181	148	8	0	0	NUM
ejpam-4181	149	1	∫	∫	PROPN
ejpam-4181	149	2	∞	∞	PROPN
ejpam-4181	149	3	0	0	NUM
ejpam-4181	150	1	∫	∫	PROPN
ejpam-4181	150	2	∞	∞	PROPN
ejpam-4181	150	3	0	0	NUM
ejpam-4181	151	1	∫	∫	PROPN
ejpam-4181	151	2	∞	∞	NUM
ejpam-4181	151	3	0	0	NUM
ejpam-4181	152	1	e−2x2−zxu+y+1	e−2x2−zxu+y+1	NOUN
ejpam-4181	152	2	√	√	NUM
ejpam-4181	152	3	y	y	NOUN
ejpam-4181	152	4	√	√	PROPN
ejpam-4181	152	5	zγ(u+	zγ(u+	PROPN
ejpam-4181	152	6	y	y	PROPN
ejpam-4181	153	1	+	+	NOUN
ejpam-4181	153	2	2	2	NUM
ejpam-4181	153	3	)	)	PUNCT
ejpam-4181	153	4	(	(	PUNCT
ejpam-4181	153	5	log2	log2	PROPN
ejpam-4181	153	6	(	(	PUNCT
ejpam-4181	153	7	y	y	PROPN
ejpam-4181	153	8	z	z	PROPN
ejpam-4181	153	9	)	)	PUNCT
ejpam-4181	154	1	+	+	CCONJ
ejpam-4181	154	2	π2	π2	ADJ
ejpam-4181	154	3	)	)	PUNCT
ejpam-4181	154	4	dxdydudz	dxdydudz	NOUN
ejpam-4181	154	5	=	=	SYM
ejpam-4181	154	6	1	1	NUM
ejpam-4181	154	7	4π	4π	NUM
ejpam-4181	154	8	log(2	log(2	NOUN
ejpam-4181	154	9	)	)	PUNCT
ejpam-4181	154	10	and	and	CCONJ
ejpam-4181	154	11	(	(	PUNCT
ejpam-4181	154	12	16	16	NUM
ejpam-4181	154	13	)	)	PUNCT
ejpam-4181	154	14	∫	∫	PROPN
ejpam-4181	155	1	∞	∞	PROPN
ejpam-4181	155	2	0	0	NUM
ejpam-4181	155	3	∫	∫	PROPN
ejpam-4181	155	4	∞	∞	PROPN
ejpam-4181	155	5	0	0	NUM
ejpam-4181	156	1	∫	∫	PROPN
ejpam-4181	156	2	∞	∞	PROPN
ejpam-4181	156	3	0	0	NUM
ejpam-4181	157	1	∫	∫	PROPN
ejpam-4181	157	2	∞	∞	NUM
ejpam-4181	157	3	0	0	NUM
ejpam-4181	157	4	e−2x2−zxu+y+1	e−2x2−zxu+y+1	NOUN
ejpam-4181	157	5	log	log	NOUN
ejpam-4181	157	6	(	(	PUNCT
ejpam-4181	157	7	y	y	PROPN
ejpam-4181	157	8	z	z	PROPN
ejpam-4181	157	9	)	)	PUNCT
ejpam-4181	158	1	√	√	PROPN
ejpam-4181	158	2	y	y	NOUN
ejpam-4181	159	1	√	√	PROPN
ejpam-4181	159	2	zγ(u+	zγ(u+	PROPN
ejpam-4181	159	3	y	y	PROPN
ejpam-4181	159	4	+	+	NOUN
ejpam-4181	159	5	2	2	NUM
ejpam-4181	159	6	)	)	PUNCT
ejpam-4181	159	7	(	(	PUNCT
ejpam-4181	159	8	log2	log2	PROPN
ejpam-4181	159	9	(	(	PUNCT
ejpam-4181	159	10	y	y	PROPN
ejpam-4181	159	11	z	z	PROPN
ejpam-4181	159	12	)	)	PUNCT
ejpam-4181	160	1	+	+	CCONJ
ejpam-4181	160	2	π2	π2	ADJ
ejpam-4181	160	3	)	)	PUNCT
ejpam-4181	160	4	dxdydudz	dxdydudz	NOUN
ejpam-4181	160	5	=	=	SYM
ejpam-4181	160	6	0	0	NUM
ejpam-4181	160	7	proof	proof	NOUN
ejpam-4181	160	8	.	.	PUNCT
ejpam-4181	161	1	use	use	VERB
ejpam-4181	161	2	equation	equation	NOUN
ejpam-4181	161	3	(	(	PUNCT
ejpam-4181	161	4	14	14	NUM
ejpam-4181	161	5	)	)	PUNCT
ejpam-4181	161	6	and	and	CCONJ
ejpam-4181	161	7	apply	apply	VERB
ejpam-4181	161	8	l’hopital	l’hopital	PROPN
ejpam-4181	161	9	’s	’s	PART
ejpam-4181	161	10	rule	rule	NOUN
ejpam-4181	161	11	to	to	ADP
ejpam-4181	161	12	the	the	DET
ejpam-4181	161	13	right	right	ADJ
ejpam-4181	161	14	-	-	PUNCT
ejpam-4181	161	15	hand	hand	NOUN
ejpam-4181	161	16	side	side	NOUN
ejpam-4181	161	17	as	as	ADP
ejpam-4181	161	18	k	k	PROPN
ejpam-4181	161	19	→	→	SYM
ejpam-4181	161	20	−1	−1	NOUN
ejpam-4181	161	21	and	and	CCONJ
ejpam-4181	161	22	set	set	VERB
ejpam-4181	161	23	p	p	NOUN
ejpam-4181	161	24	=	=	SYM
ejpam-4181	161	25	2	2	NUM
ejpam-4181	161	26	and	and	CCONJ
ejpam-4181	161	27	rationalize	rationalize	VERB
ejpam-4181	161	28	the	the	DET
ejpam-4181	161	29	denominator	denominator	NOUN
ejpam-4181	161	30	and	and	CCONJ
ejpam-4181	161	31	simplify	simplify	VERB
ejpam-4181	161	32	into	into	ADP
ejpam-4181	161	33	real	real	ADJ
ejpam-4181	161	34	and	and	CCONJ
ejpam-4181	161	35	imaginary	imaginary	ADJ
ejpam-4181	161	36	parts	part	NOUN
ejpam-4181	161	37	.	.	PUNCT
ejpam-4181	161	38	example	example	NOUN
ejpam-4181	162	1	7.∫	7.∫	NUM
ejpam-4181	162	2	∞	∞	NUM
ejpam-4181	162	3	0	0	NUM
ejpam-4181	162	4	∫	∫	PROPN
ejpam-4181	162	5	∞	∞	PROPN
ejpam-4181	162	6	0	0	NUM
ejpam-4181	162	7	∫	∫	PROPN
ejpam-4181	162	8	∞	∞	PROPN
ejpam-4181	162	9	0	0	NUM
ejpam-4181	162	10	∫	∫	PROPN
ejpam-4181	162	11	∞	∞	PROPN
ejpam-4181	162	12	0	0	PROPN
ejpam-4181	162	13	z−m−ne−bx−z	z−m−ne−bx−z	PROPN
ejpam-4181	162	14	log(b	log(b	PROPN
ejpam-4181	162	15	)	)	PUNCT
ejpam-4181	162	16	(	(	PUNCT
ejpam-4181	162	17	zmyn	zmyn	PROPN
ejpam-4181	162	18	−	−	PROPN
ejpam-4181	163	1	ymzn)xα+u+y	ymzn)xα+u+y	PROPN
ejpam-4181	163	2	y	y	PROPN
ejpam-4181	163	3	log	log	NOUN
ejpam-4181	163	4	(	(	PUNCT
ejpam-4181	163	5	y	y	PROPN
ejpam-4181	163	6	z	z	PROPN
ejpam-4181	163	7	)	)	PUNCT
ejpam-4181	163	8	γ(u+	γ(u+	PROPN
ejpam-4181	164	1	y	y	PROPN
ejpam-4181	164	2	+	+	CCONJ
ejpam-4181	164	3	α+	α+	PUNCT
ejpam-4181	164	4	1	1	X
ejpam-4181	164	5	)	)	PUNCT
ejpam-4181	164	6	dxdydudz	dxdydudz	NOUN
ejpam-4181	164	7	=	=	SYM
ejpam-4181	164	8	b−α−1	b−α−1	NOUN
ejpam-4181	164	9	log−m−n−2(b	log−m−n−2(b	ADJ
ejpam-4181	164	10	)	)	PUNCT
ejpam-4181	164	11	(	(	PUNCT
ejpam-4181	164	12	2	2	NUM
ejpam-4181	164	13	tanh−1	tanh−1	PROPN
ejpam-4181	164	14	(	(	PUNCT
ejpam-4181	164	15	eiπm	eiπm	PROPN
ejpam-4181	164	16	)	)	PUNCT
ejpam-4181	164	17	logm+n(b)−	logm+n(b)−	PROPN
ejpam-4181	164	18	2	2	NUM
ejpam-4181	164	19	tanh−1	tanh−1	PROPN
ejpam-4181	164	20	(	(	PUNCT
ejpam-4181	164	21	eiπn	eiπn	ADJ
ejpam-4181	164	22	)	)	PUNCT
ejpam-4181	164	23	logm+n(b	logm+n(b	PROPN
ejpam-4181	164	24	)	)	PUNCT
ejpam-4181	164	25	)	)	PUNCT
ejpam-4181	165	1	(	(	PUNCT
ejpam-4181	165	2	17	17	X
ejpam-4181	165	3	)	)	PUNCT
ejpam-4181	165	4	proof	proof	NOUN
ejpam-4181	165	5	.	.	PUNCT
ejpam-4181	166	1	use	use	VERB
ejpam-4181	166	2	equation(7	equation(7	PROPN
ejpam-4181	166	3	)	)	PUNCT
ejpam-4181	166	4	and	and	CCONJ
ejpam-4181	166	5	form	form	VERB
ejpam-4181	166	6	a	a	DET
ejpam-4181	166	7	second	second	ADJ
ejpam-4181	166	8	equation	equation	NOUN
ejpam-4181	166	9	by	by	ADP
ejpam-4181	166	10	replacing	replace	VERB
ejpam-4181	166	11	m	m	PRON
ejpam-4181	166	12	→	→	SYM
ejpam-4181	166	13	n	n	CCONJ
ejpam-4181	166	14	and	and	CCONJ
ejpam-4181	166	15	taking	take	VERB
ejpam-4181	166	16	their	their	PRON
ejpam-4181	166	17	difference	difference	NOUN
ejpam-4181	166	18	.	.	PUNCT
ejpam-4181	167	1	next	next	ADJ
ejpam-4181	167	2	set	set	VERB
ejpam-4181	167	3	k	k	PROPN
ejpam-4181	167	4	=	=	PUNCT
ejpam-4181	167	5	−1	−1	NOUN
ejpam-4181	167	6	,	,	PUNCT
ejpam-4181	167	7	a	a	DET
ejpam-4181	167	8	=	=	SYM
ejpam-4181	167	9	1	1	NUM
ejpam-4181	167	10	,	,	PUNCT
ejpam-4181	167	11	b	b	NOUN
ejpam-4181	167	12	=	=	SYM
ejpam-4181	167	13	log(b	log(b	PROPN
ejpam-4181	167	14	)	)	PUNCT
ejpam-4181	167	15	,	,	PUNCT
ejpam-4181	167	16	p	p	NOUN
ejpam-4181	167	17	=	=	SYM
ejpam-4181	167	18	b	b	PROPN
ejpam-4181	167	19	and	and	CCONJ
ejpam-4181	167	20	simplify	simplify	VERB
ejpam-4181	167	21	using	use	VERB
ejpam-4181	167	22	entry	entry	NOUN
ejpam-4181	167	23	(	(	PUNCT
ejpam-4181	167	24	3	3	NUM
ejpam-4181	167	25	)	)	PUNCT
ejpam-4181	167	26	in	in	ADP
ejpam-4181	167	27	table	table	NOUN
ejpam-4181	167	28	below	below	ADV
ejpam-4181	167	29	(	(	PUNCT
ejpam-4181	167	30	64:12:7	64:12:7	NUM
ejpam-4181	167	31	)	)	PUNCT
ejpam-4181	167	32	in	in	ADP
ejpam-4181	167	33	[	[	X
ejpam-4181	167	34	4	4	NUM
ejpam-4181	167	35	]	]	PUNCT
ejpam-4181	167	36	.	.	PUNCT
ejpam-4181	168	1	references	reference	NOUN
ejpam-4181	168	2	35	35	NUM
ejpam-4181	168	3	example	example	NOUN
ejpam-4181	168	4	8	8	NUM
ejpam-4181	168	5	.	.	PUNCT
ejpam-4181	169	1	(	(	PUNCT
ejpam-4181	169	2	18	18	NUM
ejpam-4181	169	3	)	)	PUNCT
ejpam-4181	169	4	∫	∫	PROPN
ejpam-4181	170	1	∞	∞	PROPN
ejpam-4181	170	2	0	0	NUM
ejpam-4181	170	3	∫	∫	PROPN
ejpam-4181	170	4	∞	∞	PROPN
ejpam-4181	170	5	0	0	NUM
ejpam-4181	171	1	∫	∫	PROPN
ejpam-4181	171	2	∞	∞	PROPN
ejpam-4181	171	3	0	0	NUM
ejpam-4181	172	1	∫	∫	PROPN
ejpam-4181	172	2	∞	∞	PROPN
ejpam-4181	172	3	0	0	NUM
ejpam-4181	173	1	e−2x2−z	e−2x2−z	NOUN
ejpam-4181	173	2	(	(	PUNCT
ejpam-4181	173	3	12	12	NUM
ejpam-4181	173	4	√	√	PROPN
ejpam-4181	173	5	z	z	NOUN
ejpam-4181	173	6	−	−	PROPN
ejpam-4181	174	1	12	12	NUM
ejpam-4181	174	2	√	√	PROPN
ejpam-4181	174	3	y	y	PROPN
ejpam-4181	174	4	)	)	PUNCT
ejpam-4181	174	5	xu+y+2	xu+y+2	NUM
ejpam-4181	174	6	3	3	NUM
ejpam-4181	175	1	√	√	PROPN
ejpam-4181	175	2	yz3/4γ(u+	yz3/4γ(u+	PROPN
ejpam-4181	175	3	y	y	PROPN
ejpam-4181	175	4	+	+	CCONJ
ejpam-4181	175	5	3	3	X
ejpam-4181	175	6	)	)	PUNCT
ejpam-4181	175	7	log	log	NOUN
ejpam-4181	175	8	(	(	PUNCT
ejpam-4181	175	9	y	y	PROPN
ejpam-4181	175	10	z	z	PROPN
ejpam-4181	175	11	)	)	PUNCT
ejpam-4181	176	1	dxdydudz	dxdydudz	NOUN
ejpam-4181	176	2	=	=	PUNCT
ejpam-4181	176	3	log	log	NOUN
ejpam-4181	176	4	(	(	PUNCT
ejpam-4181	176	5	9−	9−	NUM
ejpam-4181	176	6	6	6	NUM
ejpam-4181	176	7	√	√	NUM
ejpam-4181	176	8	2	2	NUM
ejpam-4181	176	9	)	)	PUNCT
ejpam-4181	176	10	16	16	NUM
ejpam-4181	176	11	log2(2	log2(2	ADJ
ejpam-4181	176	12	)	)	PUNCT
ejpam-4181	176	13	proof	proof	NOUN
ejpam-4181	176	14	.	.	PUNCT
ejpam-4181	177	1	use	use	VERB
ejpam-4181	177	2	equation	equation	NOUN
ejpam-4181	177	3	(	(	PUNCT
ejpam-4181	177	4	17	17	NUM
ejpam-4181	177	5	)	)	PUNCT
ejpam-4181	177	6	and	and	CCONJ
ejpam-4181	177	7	set	set	VERB
ejpam-4181	177	8	b	b	NOUN
ejpam-4181	177	9	=	=	SYM
ejpam-4181	177	10	2	2	NUM
ejpam-4181	177	11	,	,	PUNCT
ejpam-4181	177	12	α	α	NOUN
ejpam-4181	177	13	=	=	SYM
ejpam-4181	177	14	2	2	NUM
ejpam-4181	177	15	,	,	PUNCT
ejpam-4181	177	16	n	n	NOUN
ejpam-4181	177	17	=	=	SYM
ejpam-4181	177	18	2/3,m	2/3,m	NUM
ejpam-4181	177	19	=	=	SYM
ejpam-4181	177	20	3/4	3/4	NUM
ejpam-4181	177	21	and	and	CCONJ
ejpam-4181	177	22	simplify	simplify	NOUN
ejpam-4181	177	23	.	.	PUNCT
ejpam-4181	177	24	example	example	NOUN
ejpam-4181	178	1	9	9	NUM
ejpam-4181	178	2	.	.	PUNCT
ejpam-4181	179	1	(	(	PUNCT
ejpam-4181	179	2	19	19	NUM
ejpam-4181	179	3	)	)	PUNCT
ejpam-4181	179	4	∫	∫	PROPN
ejpam-4181	180	1	∞	∞	PROPN
ejpam-4181	180	2	0	0	NUM
ejpam-4181	181	1	∫	∫	PROPN
ejpam-4181	181	2	∞	∞	PROPN
ejpam-4181	181	3	0	0	NUM
ejpam-4181	182	1	∫	∫	PROPN
ejpam-4181	182	2	∞	∞	PROPN
ejpam-4181	182	3	0	0	NUM
ejpam-4181	183	1	∫	∫	PROPN
ejpam-4181	183	2	∞	∞	PROPN
ejpam-4181	183	3	0	0	NUM
ejpam-4181	184	1	e−2x2−z	e−2x2−z	NOUN
ejpam-4181	184	2	(	(	PUNCT
ejpam-4181	184	3	4	4	NUM
ejpam-4181	184	4	√	√	NOUN
ejpam-4181	184	5	y	y	NUM
ejpam-4181	184	6	−	−	PROPN
ejpam-4181	184	7	4	4	NUM
ejpam-4181	184	8	√	√	PROPN
ejpam-4181	184	9	z	z	NOUN
ejpam-4181	184	10	)	)	PUNCT
ejpam-4181	184	11	xu+y+1	xu+y+1	X
ejpam-4181	185	1	√	√	NUM
ejpam-4181	185	2	yz3/4γ(u+	yz3/4γ(u+	PROPN
ejpam-4181	185	3	y	y	PROPN
ejpam-4181	185	4	+	+	PROPN
ejpam-4181	185	5	2	2	X
ejpam-4181	185	6	)	)	PUNCT
ejpam-4181	185	7	log	log	NOUN
ejpam-4181	185	8	(	(	PUNCT
ejpam-4181	185	9	y	y	PROPN
ejpam-4181	185	10	z	z	PROPN
ejpam-4181	185	11	)	)	PUNCT
ejpam-4181	186	1	dxdydudz	dxdydudz	NOUN
ejpam-4181	186	2	=	=	PUNCT
ejpam-4181	187	1	coth−1	coth−1	NOUN
ejpam-4181	187	2	(	(	PUNCT
ejpam-4181	187	3	√	√	ADP
ejpam-4181	187	4	2	2	NUM
ejpam-4181	187	5	)	)	PUNCT
ejpam-4181	187	6	4	4	NUM
ejpam-4181	187	7	log2(2	log2(2	ADJ
ejpam-4181	187	8	)	)	PUNCT
ejpam-4181	187	9	proof	proof	NOUN
ejpam-4181	187	10	.	.	PUNCT
ejpam-4181	188	1	use	use	VERB
ejpam-4181	188	2	equation	equation	NOUN
ejpam-4181	188	3	(	(	PUNCT
ejpam-4181	188	4	17	17	NUM
ejpam-4181	188	5	)	)	PUNCT
ejpam-4181	188	6	and	and	CCONJ
ejpam-4181	188	7	set	set	VERB
ejpam-4181	188	8	b	b	NOUN
ejpam-4181	188	9	=	=	SYM
ejpam-4181	188	10	2	2	NUM
ejpam-4181	188	11	,	,	PUNCT
ejpam-4181	188	12	α	α	NOUN
ejpam-4181	188	13	=	=	SYM
ejpam-4181	188	14	1	1	NUM
ejpam-4181	188	15	,	,	PUNCT
ejpam-4181	188	16	n	n	NOUN
ejpam-4181	188	17	=	=	SYM
ejpam-4181	188	18	1/2,m	1/2,m	NUM
ejpam-4181	188	19	=	=	SYM
ejpam-4181	188	20	3/4	3/4	NUM
ejpam-4181	188	21	and	and	CCONJ
ejpam-4181	188	22	simplify	simplify	NOUN
ejpam-4181	188	23	.	.	PUNCT
ejpam-4181	189	1	7	7	X
ejpam-4181	189	2	.	.	X
ejpam-4181	189	3	discussion	discussion	NOUN
ejpam-4181	189	4	in	in	ADP
ejpam-4181	189	5	this	this	DET
ejpam-4181	189	6	paper	paper	NOUN
ejpam-4181	189	7	,	,	PUNCT
ejpam-4181	189	8	we	we	PRON
ejpam-4181	189	9	have	have	AUX
ejpam-4181	189	10	presented	present	VERB
ejpam-4181	189	11	a	a	DET
ejpam-4181	189	12	novel	novel	ADJ
ejpam-4181	189	13	method	method	NOUN
ejpam-4181	189	14	for	for	ADP
ejpam-4181	189	15	deriving	derive	VERB
ejpam-4181	189	16	a	a	DET
ejpam-4181	189	17	quadruple	quadruple	NOUN
ejpam-4181	189	18	integral	integral	ADJ
ejpam-4181	189	19	involving	involve	VERB
ejpam-4181	189	20	the	the	DET
ejpam-4181	189	21	volterra	volterra	NOUN
ejpam-4181	189	22	function	function	NOUN
ejpam-4181	189	23	along	along	ADP
ejpam-4181	189	24	with	with	ADP
ejpam-4181	189	25	some	some	DET
ejpam-4181	189	26	interesting	interesting	ADJ
ejpam-4181	189	27	definite	definite	ADJ
ejpam-4181	189	28	integrals	integral	NOUN
ejpam-4181	189	29	using	use	VERB
ejpam-4181	189	30	our	our	PRON
ejpam-4181	189	31	contour	contour	NOUN
ejpam-4181	189	32	integration	integration	NOUN
ejpam-4181	189	33	method	method	NOUN
ejpam-4181	189	34	.	.	PUNCT
ejpam-4181	190	1	the	the	DET
ejpam-4181	190	2	results	result	NOUN
ejpam-4181	190	3	presented	present	VERB
ejpam-4181	190	4	were	be	AUX
ejpam-4181	190	5	numerically	numerically	ADV
ejpam-4181	190	6	verified	verify	VERB
ejpam-4181	190	7	for	for	ADP
ejpam-4181	190	8	both	both	CCONJ
ejpam-4181	190	9	real	real	ADJ
ejpam-4181	190	10	and	and	CCONJ
ejpam-4181	190	11	imaginary	imaginary	ADJ
ejpam-4181	190	12	complex	complex	ADJ
ejpam-4181	190	13	values	value	NOUN
ejpam-4181	190	14	of	of	ADP
ejpam-4181	190	15	the	the	DET
ejpam-4181	190	16	parameters	parameter	NOUN
ejpam-4181	190	17	in	in	ADP
ejpam-4181	190	18	the	the	DET
ejpam-4181	190	19	integrals	integral	NOUN
ejpam-4181	190	20	using	use	VERB
ejpam-4181	190	21	mathematica	mathematica	PROPN
ejpam-4181	190	22	by	by	ADP
ejpam-4181	190	23	wolfram	wolfram	PROPN
ejpam-4181	190	24	.	.	PUNCT
ejpam-4181	191	1	acknowledgements	acknowledgement	NOUN
ejpam-4181	191	2	this	this	DET
ejpam-4181	191	3	research	research	NOUN
ejpam-4181	191	4	is	be	AUX
ejpam-4181	191	5	supported	support	VERB
ejpam-4181	191	6	by	by	ADP
ejpam-4181	191	7	nserc	nserc	PROPN
ejpam-4181	191	8	canada	canada	PROPN
ejpam-4181	191	9	under	under	ADP
ejpam-4181	191	10	grant	grant	PROPN
ejpam-4181	191	11	504070	504070	NUM
ejpam-4181	191	12	.	.	PUNCT
ejpam-4181	192	1	references	reference	NOUN
ejpam-4181	192	2	[	[	X
ejpam-4181	192	3	1	1	NUM
ejpam-4181	192	4	]	]	X
ejpam-4181	192	5	alexander	alexander	PROPN
ejpam-4181	192	6	apelblat	apelblat	PROPN
ejpam-4181	192	7	.	.	PUNCT
ejpam-4181	193	1	integral	integral	ADJ
ejpam-4181	193	2	transforms	transform	NOUN
ejpam-4181	193	3	and	and	CCONJ
ejpam-4181	193	4	volterra	volterra	NOUN
ejpam-4181	193	5	functions	function	NOUN
ejpam-4181	193	6	.	.	PUNCT
ejpam-4181	194	1	nova	nova	PROPN
ejpam-4181	194	2	science	science	NOUN
ejpam-4181	194	3	publishers	publisher	NOUN
ejpam-4181	194	4	,	,	PUNCT
ejpam-4181	194	5	inc	inc	PROPN
ejpam-4181	194	6	.	.	PROPN
ejpam-4181	194	7	,	,	PUNCT
ejpam-4181	194	8	12	12	NUM
ejpam-4181	194	9	2010	2010	NUM
ejpam-4181	194	10	.	.	PUNCT
ejpam-4181	195	1	[	[	X
ejpam-4181	195	2	2	2	NUM
ejpam-4181	195	3	]	]	PUNCT
ejpam-4181	195	4	nist	nist	NOUN
ejpam-4181	195	5	digital	digital	PROPN
ejpam-4181	195	6	library	library	NOUN
ejpam-4181	195	7	of	of	ADP
ejpam-4181	195	8	mathematical	mathematical	ADJ
ejpam-4181	195	9	functions	function	NOUN
ejpam-4181	195	10	.	.	PUNCT
ejpam-4181	196	1	f.	f.	PROPN
ejpam-4181	196	2	w.	w.	PROPN
ejpam-4181	196	3	j.	j.	PROPN
ejpam-4181	196	4	olver	olver	PROPN
ejpam-4181	196	5	,	,	PUNCT
ejpam-4181	196	6	a.	a.	PROPN
ejpam-4181	196	7	b.	b.	PROPN
ejpam-4181	196	8	olde	olde	PROPN
ejpam-4181	196	9	daalhuis	daalhuis	PROPN
ejpam-4181	196	10	,	,	PUNCT
ejpam-4181	196	11	d.	d.	PROPN
ejpam-4181	196	12	w.	w.	PROPN
ejpam-4181	196	13	lozier	lozier	PROPN
ejpam-4181	196	14	,	,	PUNCT
ejpam-4181	196	15	b.	b.	PROPN
ejpam-4181	196	16	i.	i.	PROPN
ejpam-4181	196	17	schneider	schneider	PROPN
ejpam-4181	196	18	,	,	PUNCT
ejpam-4181	196	19	r.	r.	PROPN
ejpam-4181	196	20	f.	f.	PROPN
ejpam-4181	196	21	boisvert	boisvert	PROPN
ejpam-4181	196	22	,	,	PUNCT
ejpam-4181	196	23	c.	c.	PROPN
ejpam-4181	196	24	w.	w.	PROPN
ejpam-4181	196	25	clark	clark	PROPN
ejpam-4181	196	26	,	,	PUNCT
ejpam-4181	196	27	b.	b.	PROPN
ejpam-4181	196	28	r.	r.	PROPN
ejpam-4181	196	29	miller	miller	PROPN
ejpam-4181	196	30	,	,	PUNCT
ejpam-4181	196	31	b.	b.	PROPN
ejpam-4181	197	1	v.	v.	PROPN
ejpam-4181	197	2	saunders	saunders	PROPN
ejpam-4181	197	3	,	,	PUNCT
ejpam-4181	197	4	h.	h.	PROPN
ejpam-4181	197	5	s.	s.	PROPN
ejpam-4181	197	6	cohl	cohl	PROPN
ejpam-4181	197	7	,	,	PUNCT
ejpam-4181	197	8	and	and	CCONJ
ejpam-4181	197	9	m.	m.	PROPN
ejpam-4181	197	10	a.	a.	PROPN
ejpam-4181	197	11	mcclain	mcclain	PROPN
ejpam-4181	197	12	,	,	PUNCT
ejpam-4181	197	13	eds	eds	PROPN
ejpam-4181	197	14	.	.	PUNCT
ejpam-4181	198	1	[	[	X
ejpam-4181	198	2	3	3	NUM
ejpam-4181	198	3	]	]	X
ejpam-4181	198	4	i.	i.	PROPN
ejpam-4181	198	5	s.	s.	PROPN
ejpam-4181	198	6	gradshteyn	gradshteyn	PROPN
ejpam-4181	198	7	and	and	CCONJ
ejpam-4181	198	8	i.	i.	PROPN
ejpam-4181	198	9	m.	m.	PROPN
ejpam-4181	198	10	ryzhik	ryzhik	PROPN
ejpam-4181	198	11	.	.	PUNCT
ejpam-4181	199	1	table	table	NOUN
ejpam-4181	199	2	of	of	ADP
ejpam-4181	199	3	integrals	integral	NOUN
ejpam-4181	199	4	,	,	PUNCT
ejpam-4181	199	5	series	series	NOUN
ejpam-4181	199	6	,	,	PUNCT
ejpam-4181	199	7	and	and	CCONJ
ejpam-4181	199	8	products	product	NOUN
ejpam-4181	199	9	.	.	PUNCT
ejpam-4181	200	1	elsevier	elsevier	NOUN
ejpam-4181	200	2	/	/	SYM
ejpam-4181	200	3	academic	academic	ADJ
ejpam-4181	200	4	press	press	NOUN
ejpam-4181	200	5	,	,	PUNCT
ejpam-4181	200	6	amsterdam	amsterdam	PROPN
ejpam-4181	200	7	,	,	PUNCT
ejpam-4181	200	8	seventh	seventh	ADJ
ejpam-4181	200	9	edition	edition	NOUN
ejpam-4181	200	10	,	,	PUNCT
ejpam-4181	200	11	2007	2007	NUM
ejpam-4181	200	12	.	.	PUNCT
ejpam-4181	201	1	[	[	X
ejpam-4181	201	2	4	4	X
ejpam-4181	201	3	]	]	PUNCT
ejpam-4181	201	4	keith	keith	PROPN
ejpam-4181	201	5	b.	b.	PROPN
ejpam-4181	201	6	oldham	oldham	PROPN
ejpam-4181	201	7	,	,	PUNCT
ejpam-4181	201	8	jan	jan	PROPN
ejpam-4181	201	9	myland	myland	PROPN
ejpam-4181	201	10	,	,	PUNCT
ejpam-4181	201	11	and	and	CCONJ
ejpam-4181	201	12	jerome	jerome	PROPN
ejpam-4181	201	13	spanier	spanier	NOUN
ejpam-4181	201	14	.	.	PUNCT
ejpam-4181	202	1	an	an	DET
ejpam-4181	202	2	atlas	atlas	PROPN
ejpam-4181	202	3	of	of	ADP
ejpam-4181	202	4	functions	function	NOUN
ejpam-4181	202	5	:	:	PUNCT
ejpam-4181	202	6	with	with	ADP
ejpam-4181	202	7	equator	equator	NOUN
ejpam-4181	202	8	,	,	PUNCT
ejpam-4181	202	9	the	the	DET
ejpam-4181	202	10	atlas	atlas	PROPN
ejpam-4181	202	11	function	function	PROPN
ejpam-4181	202	12	calculator	calculator	NOUN
ejpam-4181	202	13	.	.	PUNCT
ejpam-4181	203	1	springer	springer	NOUN
ejpam-4181	203	2	science	science	PROPN
ejpam-4181	203	3	&	&	CCONJ
ejpam-4181	203	4	business	business	NOUN
ejpam-4181	203	5	media	medium	NOUN
ejpam-4181	203	6	,	,	PUNCT
ejpam-4181	203	7	07	07	NUM
ejpam-4181	203	8	2010	2010	NUM
ejpam-4181	203	9	.	.	PUNCT
ejpam-4181	204	1	[	[	X
ejpam-4181	204	2	5	5	X
ejpam-4181	204	3	]	]	X
ejpam-4181	204	4	robert	robert	PROPN
ejpam-4181	204	5	reynolds	reynolds	PROPN
ejpam-4181	204	6	and	and	CCONJ
ejpam-4181	204	7	allan	allan	PROPN
ejpam-4181	204	8	stauffer	stauffer	PROPN
ejpam-4181	204	9	.	.	PUNCT
ejpam-4181	205	1	a	a	DET
ejpam-4181	205	2	method	method	NOUN
ejpam-4181	205	3	for	for	ADP
ejpam-4181	205	4	evaluating	evaluate	VERB
ejpam-4181	205	5	definite	definite	ADJ
ejpam-4181	205	6	integrals	integral	NOUN
ejpam-4181	205	7	in	in	ADP
ejpam-4181	205	8	terms	term	NOUN
ejpam-4181	205	9	of	of	ADP
ejpam-4181	205	10	special	special	ADJ
ejpam-4181	205	11	functions	function	NOUN
ejpam-4181	205	12	with	with	ADP
ejpam-4181	205	13	examples	example	NOUN
ejpam-4181	205	14	.	.	PUNCT
ejpam-4181	206	1	international	international	ADJ
ejpam-4181	206	2	mathematical	mathematical	PROPN
ejpam-4181	206	3	forum	forum	PROPN
ejpam-4181	206	4	,	,	PUNCT
ejpam-4181	206	5	15:235	15:235	NUM
ejpam-4181	206	6	–	–	PUNCT
ejpam-4181	206	7	244	244	NUM
ejpam-4181	206	8	,	,	PUNCT
ejpam-4181	206	9	2020	2020	NUM
ejpam-4181	206	10	.	.	PUNCT