id	sid	tid	token	lemma	pos
ejpam-4137	1	1	european	european	PROPN
ejpam-4137	1	2	journal	journal	PROPN
ejpam-4137	1	3	of	of	ADP
ejpam-4137	1	4	pure	pure	ADJ
ejpam-4137	1	5	and	and	CCONJ
ejpam-4137	1	6	applied	apply	VERB
ejpam-4137	1	7	mathematics	mathematic	NOUN
ejpam-4137	1	8	vol	vol	NOUN
ejpam-4137	1	9	.	.	PROPN
ejpam-4137	2	1	15	15	NUM
ejpam-4137	2	2	,	,	PUNCT
ejpam-4137	2	3	no	no	INTJ
ejpam-4137	2	4	.	.	NOUN
ejpam-4137	2	5	1	1	NUM
ejpam-4137	2	6	,	,	PUNCT
ejpam-4137	2	7	2022	2022	NUM
ejpam-4137	2	8	,	,	PUNCT
ejpam-4137	2	9	158	158	NUM
ejpam-4137	2	10	-	-	SYM
ejpam-4137	2	11	168	168	NUM
ejpam-4137	2	12	issn	issn	PROPN
ejpam-4137	2	13	1307	1307	NUM
ejpam-4137	2	14	-	-	SYM
ejpam-4137	2	15	5543	5543	NUM
ejpam-4137	2	16	–	–	PUNCT
ejpam-4137	3	1	ejpam.com	ejpam.com	X
ejpam-4137	3	2	published	publish	VERB
ejpam-4137	3	3	by	by	ADP
ejpam-4137	3	4	new	new	PROPN
ejpam-4137	3	5	york	york	PROPN
ejpam-4137	3	6	business	business	PROPN
ejpam-4137	3	7	global	global	PROPN
ejpam-4137	3	8	a	a	DET
ejpam-4137	3	9	note	note	NOUN
ejpam-4137	3	10	on	on	ADP
ejpam-4137	3	11	the	the	DET
ejpam-4137	3	12	infinite	infinite	ADJ
ejpam-4137	3	13	sum	sum	NOUN
ejpam-4137	3	14	of	of	ADP
ejpam-4137	3	15	the	the	DET
ejpam-4137	3	16	lerch	lerch	PROPN
ejpam-4137	3	17	function	function	PROPN
ejpam-4137	3	18	robert	robert	PROPN
ejpam-4137	3	19	reynolds1,∗	reynolds1,∗	PROPN
ejpam-4137	3	20	,	,	PUNCT
ejpam-4137	3	21	allan	allan	PROPN
ejpam-4137	3	22	stauffer1	stauffer1	PROPN
ejpam-4137	3	23	1	1	NUM
ejpam-4137	3	24	department	department	NOUN
ejpam-4137	3	25	of	of	ADP
ejpam-4137	3	26	mathematics	mathematic	NOUN
ejpam-4137	3	27	and	and	CCONJ
ejpam-4137	3	28	statistics	statistic	NOUN
ejpam-4137	3	29	,	,	PUNCT
ejpam-4137	3	30	faculty	faculty	NOUN
ejpam-4137	3	31	of	of	ADP
ejpam-4137	3	32	science	science	PROPN
ejpam-4137	3	33	,	,	PUNCT
ejpam-4137	3	34	york	york	PROPN
ejpam-4137	3	35	university	university	PROPN
ejpam-4137	3	36	,	,	PUNCT
ejpam-4137	3	37	toronto	toronto	PROPN
ejpam-4137	3	38	,	,	PUNCT
ejpam-4137	3	39	ontario	ontario	PROPN
ejpam-4137	3	40	,	,	PUNCT
ejpam-4137	3	41	canada	canada	PROPN
ejpam-4137	3	42	,	,	PUNCT
ejpam-4137	3	43	m3j1p3	m3j1p3	PROPN
ejpam-4137	3	44	abstract	abstract	NOUN
ejpam-4137	3	45	.	.	PUNCT
ejpam-4137	4	1	we	we	PRON
ejpam-4137	4	2	derive	derive	VERB
ejpam-4137	4	3	the	the	DET
ejpam-4137	4	4	infinite	infinite	ADJ
ejpam-4137	4	5	sum	sum	NOUN
ejpam-4137	4	6	of	of	ADP
ejpam-4137	4	7	the	the	DET
ejpam-4137	4	8	lerch	lerch	PROPN
ejpam-4137	4	9	function	function	PROPN
ejpam-4137	4	10	in	in	ADP
ejpam-4137	4	11	terms	term	NOUN
ejpam-4137	4	12	of	of	ADP
ejpam-4137	4	13	the	the	DET
ejpam-4137	4	14	incomplete	incomplete	ADJ
ejpam-4137	4	15	gamma	gamma	NOUN
ejpam-4137	4	16	function	function	NOUN
ejpam-4137	4	17	and	and	CCONJ
ejpam-4137	4	18	the	the	DET
ejpam-4137	4	19	lerch	lerch	PROPN
ejpam-4137	4	20	function	function	PROPN
ejpam-4137	4	21	.	.	PUNCT
ejpam-4137	5	1	special	special	ADJ
ejpam-4137	5	2	cases	case	NOUN
ejpam-4137	5	3	are	be	AUX
ejpam-4137	5	4	evaluated	evaluate	VERB
ejpam-4137	5	5	in	in	ADP
ejpam-4137	5	6	terms	term	NOUN
ejpam-4137	5	7	of	of	ADP
ejpam-4137	5	8	fundamentals	fundamental	NOUN
ejpam-4137	5	9	constants	constant	NOUN
ejpam-4137	5	10	.	.	PUNCT
ejpam-4137	6	1	all	all	DET
ejpam-4137	6	2	the	the	DET
ejpam-4137	6	3	results	result	NOUN
ejpam-4137	6	4	in	in	ADP
ejpam-4137	6	5	this	this	DET
ejpam-4137	6	6	work	work	NOUN
ejpam-4137	6	7	are	be	AUX
ejpam-4137	6	8	new	new	ADJ
ejpam-4137	6	9	.	.	PUNCT
ejpam-4137	7	1	2020	2020	NUM
ejpam-4137	7	2	mathematics	mathematic	NOUN
ejpam-4137	7	3	subject	subject	NOUN
ejpam-4137	7	4	classifications	classification	NOUN
ejpam-4137	7	5	:	:	PUNCT
ejpam-4137	7	6	30e20	30e20	NUM
ejpam-4137	7	7	,	,	PUNCT
ejpam-4137	7	8	33	33	NUM
ejpam-4137	7	9	-	-	SYM
ejpam-4137	7	10	01	01	NUM
ejpam-4137	7	11	,	,	PUNCT
ejpam-4137	7	12	33	33	NUM
ejpam-4137	7	13	-	-	SYM
ejpam-4137	7	14	03	03	NUM
ejpam-4137	7	15	,	,	PUNCT
ejpam-4137	7	16	33	33	NUM
ejpam-4137	7	17	-	-	PUNCT
ejpam-4137	7	18	04	04	NUM
ejpam-4137	7	19	,	,	PUNCT
ejpam-4137	7	20	33	33	NUM
ejpam-4137	7	21	-	-	PUNCT
ejpam-4137	7	22	33b	33b	NUM
ejpam-4137	7	23	key	key	ADJ
ejpam-4137	7	24	words	word	NOUN
ejpam-4137	7	25	and	and	CCONJ
ejpam-4137	7	26	phrases	phrase	NOUN
ejpam-4137	7	27	:	:	PUNCT
ejpam-4137	7	28	lerch	lerch	PROPN
ejpam-4137	7	29	function	function	PROPN
ejpam-4137	7	30	,	,	PUNCT
ejpam-4137	7	31	incomplete	incomplete	ADJ
ejpam-4137	7	32	gamma	gamma	NOUN
ejpam-4137	7	33	function	function	PROPN
ejpam-4137	7	34	,	,	PUNCT
ejpam-4137	7	35	catalan	catalan	NOUN
ejpam-4137	7	36	’s	’s	PART
ejpam-4137	7	37	constant	constant	ADJ
ejpam-4137	7	38	,	,	PUNCT
ejpam-4137	7	39	apréy	apréy	PROPN
ejpam-4137	7	40	’s	’s	PART
ejpam-4137	7	41	constant	constant	ADJ
ejpam-4137	7	42	1	1	NUM
ejpam-4137	7	43	.	.	PUNCT
ejpam-4137	7	44	introduction	introduction	NOUN
ejpam-4137	7	45	infinite	infinite	NOUN
ejpam-4137	7	46	sums	sum	NOUN
ejpam-4137	7	47	of	of	ADP
ejpam-4137	7	48	special	special	ADJ
ejpam-4137	7	49	functions	function	NOUN
ejpam-4137	7	50	have	have	AUX
ejpam-4137	7	51	been	be	AUX
ejpam-4137	7	52	studied	study	VERB
ejpam-4137	7	53	in	in	ADP
ejpam-4137	7	54	the	the	DET
ejpam-4137	7	55	works	work	NOUN
ejpam-4137	7	56	of	of	ADP
ejpam-4137	7	57	[	[	X
ejpam-4137	7	58	1	1	NUM
ejpam-4137	7	59	,	,	PUNCT
ejpam-4137	7	60	5	5	NUM
ejpam-4137	7	61	,	,	PUNCT
ejpam-4137	7	62	6	6	NUM
ejpam-4137	7	63	,	,	PUNCT
ejpam-4137	7	64	10	10	NUM
ejpam-4137	7	65	,	,	PUNCT
ejpam-4137	7	66	13	13	NUM
ejpam-4137	7	67	]	]	PUNCT
ejpam-4137	7	68	.	.	PUNCT
ejpam-4137	8	1	in	in	ADP
ejpam-4137	8	2	this	this	DET
ejpam-4137	8	3	present	present	ADJ
ejpam-4137	8	4	work	work	NOUN
ejpam-4137	8	5	we	we	PRON
ejpam-4137	8	6	derive	derive	VERB
ejpam-4137	8	7	a	a	DET
ejpam-4137	8	8	new	new	ADJ
ejpam-4137	8	9	expression	expression	NOUN
ejpam-4137	8	10	for	for	ADP
ejpam-4137	8	11	the	the	DET
ejpam-4137	8	12	lerch	lerch	PROPN
ejpam-4137	8	13	function	function	PROPN
ejpam-4137	8	14	in	in	ADP
ejpam-4137	8	15	terms	term	NOUN
ejpam-4137	8	16	of	of	ADP
ejpam-4137	8	17	the	the	DET
ejpam-4137	8	18	infinite	infinite	ADJ
ejpam-4137	8	19	sum	sum	NOUN
ejpam-4137	8	20	of	of	ADP
ejpam-4137	8	21	the	the	DET
ejpam-4137	8	22	incomplete	incomplete	ADJ
ejpam-4137	8	23	gamma	gamma	NOUN
ejpam-4137	8	24	function	function	NOUN
ejpam-4137	8	25	given	give	VERB
ejpam-4137	8	26	by	by	ADP
ejpam-4137	8	27	(	(	PUNCT
ejpam-4137	8	28	1	1	X
ejpam-4137	8	29	)	)	PUNCT
ejpam-4137	8	30	∞∑	∞∑	NUM
ejpam-4137	8	31	n	n	NOUN
ejpam-4137	8	32	=	=	SYM
ejpam-4137	8	33	1	1	NUM
ejpam-4137	8	34	2k−n+1	2k−n+1	NUM
ejpam-4137	8	35	(	(	PUNCT
ejpam-4137	8	36	2−n	2−n	NUM
ejpam-4137	8	37	)	)	PUNCT
ejpam-4137	8	38	k	k	NOUN
ejpam-4137	8	39	em21−n	em21−n	PROPN
ejpam-4137	8	40	φ	φ	PROPN
ejpam-4137	8	41	(	(	PUNCT
ejpam-4137	8	42	−e2	−e2	PROPN
ejpam-4137	8	43	1−nm,−k	1−nm,−k	NOUN
ejpam-4137	8	44	,	,	PUNCT
ejpam-4137	8	45	2n−1	2n−1	PROPN
ejpam-4137	8	46	log(a	log(a	PROPN
ejpam-4137	8	47	)	)	PUNCT
ejpam-4137	9	1	+	+	CCONJ
ejpam-4137	9	2	1	1	X
ejpam-4137	9	3	)	)	PUNCT
ejpam-4137	9	4	=	=	PUNCT
ejpam-4137	9	5	−a−m(−m)−kγ(k	−a−m(−m)−kγ(k	NUM
ejpam-4137	9	6	+	+	CCONJ
ejpam-4137	9	7	1,−m	1,−m	NUM
ejpam-4137	9	8	log(a	log(a	PROPN
ejpam-4137	9	9	)	)	PUNCT
ejpam-4137	9	10	)	)	PUNCT
ejpam-4137	10	1	m	m	VERB
ejpam-4137	11	1	−	−	NOUN
ejpam-4137	11	2	2k+1e2mφ	2k+1e2mφ	NUM
ejpam-4137	11	3	(	(	PUNCT
ejpam-4137	11	4	e2m,−k	e2m,−k	PROPN
ejpam-4137	11	5	,	,	PUNCT
ejpam-4137	11	6	log(a	log(a	PROPN
ejpam-4137	11	7	)	)	PUNCT
ejpam-4137	11	8	2	2	NUM
ejpam-4137	12	1	+	+	CCONJ
ejpam-4137	12	2	1	1	NUM
ejpam-4137	12	3	)	)	PUNCT
ejpam-4137	13	1	where	where	SCONJ
ejpam-4137	13	2	the	the	DET
ejpam-4137	13	3	variables	variable	NOUN
ejpam-4137	13	4	k	k	PROPN
ejpam-4137	13	5	,	,	PUNCT
ejpam-4137	13	6	a	a	PRON
ejpam-4137	13	7	,	,	PUNCT
ejpam-4137	13	8	m	m	VERB
ejpam-4137	13	9	are	be	AUX
ejpam-4137	13	10	general	general	ADJ
ejpam-4137	13	11	complex	complex	ADJ
ejpam-4137	13	12	numbers	number	NOUN
ejpam-4137	13	13	.	.	PUNCT
ejpam-4137	14	1	this	this	DET
ejpam-4137	14	2	new	new	ADJ
ejpam-4137	14	3	expression	expression	NOUN
ejpam-4137	14	4	is	be	AUX
ejpam-4137	14	5	then	then	ADV
ejpam-4137	14	6	used	use	VERB
ejpam-4137	14	7	to	to	PART
ejpam-4137	14	8	derive	derive	VERB
ejpam-4137	14	9	special	special	ADJ
ejpam-4137	14	10	cases	case	NOUN
ejpam-4137	14	11	in	in	ADP
ejpam-4137	14	12	terms	term	NOUN
ejpam-4137	14	13	of	of	ADP
ejpam-4137	14	14	fundamental	fundamental	ADJ
ejpam-4137	14	15	constant	constant	ADJ
ejpam-4137	14	16	and	and	CCONJ
ejpam-4137	14	17	special	special	ADJ
ejpam-4137	14	18	functions	function	NOUN
ejpam-4137	14	19	.	.	PUNCT
ejpam-4137	15	1	the	the	DET
ejpam-4137	15	2	derivations	derivation	NOUN
ejpam-4137	15	3	follow	follow	VERB
ejpam-4137	15	4	the	the	DET
ejpam-4137	15	5	method	method	NOUN
ejpam-4137	15	6	used	use	VERB
ejpam-4137	15	7	by	by	ADP
ejpam-4137	15	8	us	we	PRON
ejpam-4137	15	9	in	in	ADP
ejpam-4137	15	10	[	[	X
ejpam-4137	15	11	12	12	NUM
ejpam-4137	15	12	]	]	PUNCT
ejpam-4137	15	13	.	.	PUNCT
ejpam-4137	16	1	this	this	DET
ejpam-4137	16	2	method	method	NOUN
ejpam-4137	16	3	involves	involve	VERB
ejpam-4137	16	4	using	use	VERB
ejpam-4137	16	5	a	a	DET
ejpam-4137	16	6	form	form	NOUN
ejpam-4137	16	7	of	of	ADP
ejpam-4137	16	8	the	the	DET
ejpam-4137	16	9	generalized	generalize	VERB
ejpam-4137	16	10	cauchy	cauchy	PROPN
ejpam-4137	16	11	’s	’s	PART
ejpam-4137	16	12	integral	integral	ADJ
ejpam-4137	16	13	formula	formula	NOUN
ejpam-4137	16	14	given	give	VERB
ejpam-4137	16	15	by	by	ADP
ejpam-4137	16	16	yk	yk	PROPN
ejpam-4137	16	17	γ(k	γ(k	PROPN
ejpam-4137	16	18	+	+	CCONJ
ejpam-4137	16	19	1	1	X
ejpam-4137	16	20	)	)	PUNCT
ejpam-4137	16	21	=	=	SYM
ejpam-4137	16	22	1	1	NUM
ejpam-4137	16	23	2πi	2πi	ADJ
ejpam-4137	16	24	∫	∫	PROPN
ejpam-4137	16	25	c	c	PROPN
ejpam-4137	16	26	ewy	ewy	PROPN
ejpam-4137	16	27	wk+1	wk+1	PROPN
ejpam-4137	16	28	dw	dw	PROPN
ejpam-4137	16	29	,	,	PUNCT
ejpam-4137	16	30	(	(	PUNCT
ejpam-4137	16	31	2	2	X
ejpam-4137	16	32	)	)	PUNCT
ejpam-4137	16	33	∗corresponding	∗corresponde	VERB
ejpam-4137	16	34	author	author	NOUN
ejpam-4137	16	35	.	.	PUNCT
ejpam-4137	17	1	doi	doi	NOUN
ejpam-4137	17	2	:	:	PUNCT
ejpam-4137	17	3	https://doi.org/10.29020/nybg.ejpam.v15i1.4137	https://doi.org/10.29020/nybg.ejpam.v15i1.4137	PROPN
ejpam-4137	17	4	email	email	NOUN
ejpam-4137	17	5	addresses	address	NOUN
ejpam-4137	17	6	:	:	PUNCT
ejpam-4137	18	1	milver@my.yorku.ca	milver@my.yorku.ca	NOUN
ejpam-4137	18	2	(	(	PUNCT
ejpam-4137	18	3	r.	r.	PROPN
ejpam-4137	18	4	reynolds	reynolds	PROPN
ejpam-4137	18	5	)	)	PUNCT
ejpam-4137	18	6	,	,	PUNCT
ejpam-4137	18	7	stauffer@yorku.ca	stauffer@yorku.ca	NOUN
ejpam-4137	18	8	(	(	PUNCT
ejpam-4137	18	9	a.	a.	NOUN
ejpam-4137	18	10	stauffer	stauffer	PROPN
ejpam-4137	18	11	)	)	PUNCT
ejpam-4137	18	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4137	19	1	158	158	NUM
ejpam-4137	20	1	©	©	PROPN
ejpam-4137	20	2	2022	2022	NUM
ejpam-4137	20	3	ejpam	ejpam	VERB
ejpam-4137	20	4	all	all	DET
ejpam-4137	20	5	rights	right	NOUN
ejpam-4137	20	6	reserved	reserve	VERB
ejpam-4137	20	7	.	.	PUNCT
ejpam-4137	21	1	r.	r.	PROPN
ejpam-4137	21	2	reynolds	reynolds	PROPN
ejpam-4137	21	3	,	,	PUNCT
ejpam-4137	21	4	a.	a.	PROPN
ejpam-4137	21	5	stauffer	stauffer	PROPN
ejpam-4137	21	6	/	/	SYM
ejpam-4137	21	7	eur	eur	PROPN
ejpam-4137	21	8	.	.	PUNCT
ejpam-4137	22	1	j.	j.	PROPN
ejpam-4137	22	2	pure	pure	PROPN
ejpam-4137	22	3	appl	appl	PROPN
ejpam-4137	22	4	.	.	PROPN
ejpam-4137	22	5	math	math	PROPN
ejpam-4137	22	6	,	,	PUNCT
ejpam-4137	22	7	15	15	NUM
ejpam-4137	22	8	(	(	PUNCT
ejpam-4137	22	9	1	1	NUM
ejpam-4137	22	10	)	)	PUNCT
ejpam-4137	22	11	(	(	PUNCT
ejpam-4137	22	12	2022	2022	NUM
ejpam-4137	22	13	)	)	PUNCT
ejpam-4137	22	14	,	,	PUNCT
ejpam-4137	22	15	158	158	NUM
ejpam-4137	22	16	-	-	SYM
ejpam-4137	22	17	168	168	NUM
ejpam-4137	22	18	159	159	NUM
ejpam-4137	22	19	where	where	SCONJ
ejpam-4137	22	20	y	y	PROPN
ejpam-4137	22	21	,	,	PUNCT
ejpam-4137	22	22	w	w	PROPN
ejpam-4137	22	23	∈	∈	PROPN
ejpam-4137	22	24	c	c	NOUN
ejpam-4137	22	25	and	and	CCONJ
ejpam-4137	22	26	c	c	PROPN
ejpam-4137	22	27	is	be	AUX
ejpam-4137	22	28	in	in	ADP
ejpam-4137	22	29	general	general	ADJ
ejpam-4137	22	30	an	an	DET
ejpam-4137	22	31	open	open	ADJ
ejpam-4137	22	32	contour	contour	NOUN
ejpam-4137	22	33	in	in	ADP
ejpam-4137	22	34	the	the	DET
ejpam-4137	22	35	complex	complex	ADJ
ejpam-4137	22	36	plane	plane	NOUN
ejpam-4137	22	37	where	where	SCONJ
ejpam-4137	22	38	the	the	DET
ejpam-4137	22	39	bilinear	bilinear	NOUN
ejpam-4137	22	40	concomitant	concomitant	NOUN
ejpam-4137	23	1	[	[	X
ejpam-4137	23	2	12	12	NUM
ejpam-4137	23	3	]	]	PUNCT
ejpam-4137	23	4	has	have	VERB
ejpam-4137	23	5	the	the	DET
ejpam-4137	23	6	same	same	ADJ
ejpam-4137	23	7	value	value	NOUN
ejpam-4137	23	8	at	at	ADP
ejpam-4137	23	9	the	the	DET
ejpam-4137	23	10	end	end	NOUN
ejpam-4137	23	11	points	point	NOUN
ejpam-4137	23	12	of	of	ADP
ejpam-4137	23	13	the	the	DET
ejpam-4137	23	14	contour	contour	NOUN
ejpam-4137	23	15	.	.	PUNCT
ejpam-4137	24	1	this	this	DET
ejpam-4137	24	2	method	method	NOUN
ejpam-4137	24	3	involves	involve	VERB
ejpam-4137	24	4	using	use	VERB
ejpam-4137	24	5	a	a	DET
ejpam-4137	24	6	form	form	NOUN
ejpam-4137	24	7	of	of	ADP
ejpam-4137	24	8	equation	equation	NOUN
ejpam-4137	24	9	(	(	PUNCT
ejpam-4137	24	10	2	2	NUM
ejpam-4137	24	11	)	)	PUNCT
ejpam-4137	24	12	then	then	ADV
ejpam-4137	24	13	multiplies	multiply	VERB
ejpam-4137	24	14	both	both	DET
ejpam-4137	24	15	sides	side	NOUN
ejpam-4137	24	16	by	by	ADP
ejpam-4137	24	17	a	a	DET
ejpam-4137	24	18	function	function	NOUN
ejpam-4137	24	19	,	,	PUNCT
ejpam-4137	24	20	then	then	ADV
ejpam-4137	24	21	takes	take	VERB
ejpam-4137	24	22	the	the	DET
ejpam-4137	24	23	definite	definite	ADJ
ejpam-4137	24	24	integral	integral	NOUN
ejpam-4137	24	25	of	of	ADP
ejpam-4137	24	26	both	both	DET
ejpam-4137	24	27	sides	side	NOUN
ejpam-4137	24	28	.	.	PUNCT
ejpam-4137	25	1	this	this	PRON
ejpam-4137	25	2	yields	yield	VERB
ejpam-4137	25	3	a	a	DET
ejpam-4137	25	4	definite	definite	ADJ
ejpam-4137	25	5	integral	integral	ADJ
ejpam-4137	25	6	in	in	ADP
ejpam-4137	25	7	terms	term	NOUN
ejpam-4137	25	8	of	of	ADP
ejpam-4137	25	9	a	a	DET
ejpam-4137	25	10	contour	contour	NOUN
ejpam-4137	25	11	integral	integral	NOUN
ejpam-4137	25	12	.	.	PUNCT
ejpam-4137	26	1	then	then	ADV
ejpam-4137	26	2	we	we	PRON
ejpam-4137	26	3	multiply	multiply	VERB
ejpam-4137	26	4	both	both	DET
ejpam-4137	26	5	sides	side	NOUN
ejpam-4137	26	6	of	of	ADP
ejpam-4137	26	7	equation	equation	NOUN
ejpam-4137	26	8	(	(	PUNCT
ejpam-4137	26	9	2	2	NUM
ejpam-4137	26	10	)	)	PUNCT
ejpam-4137	26	11	by	by	ADP
ejpam-4137	26	12	another	another	DET
ejpam-4137	26	13	function	function	NOUN
ejpam-4137	26	14	and	and	CCONJ
ejpam-4137	26	15	take	take	VERB
ejpam-4137	26	16	the	the	DET
ejpam-4137	26	17	infinite	infinite	ADJ
ejpam-4137	26	18	sum	sum	NOUN
ejpam-4137	26	19	of	of	ADP
ejpam-4137	26	20	both	both	DET
ejpam-4137	26	21	sides	side	NOUN
ejpam-4137	26	22	such	such	ADJ
ejpam-4137	26	23	that	that	SCONJ
ejpam-4137	26	24	the	the	DET
ejpam-4137	26	25	contour	contour	NOUN
ejpam-4137	26	26	integral	integral	NOUN
ejpam-4137	26	27	of	of	ADP
ejpam-4137	26	28	both	both	DET
ejpam-4137	26	29	equations	equation	NOUN
ejpam-4137	26	30	are	be	AUX
ejpam-4137	26	31	the	the	DET
ejpam-4137	26	32	same	same	ADJ
ejpam-4137	26	33	.	.	PUNCT
ejpam-4137	27	1	1.1	1.1	NUM
ejpam-4137	27	2	.	.	PUNCT
ejpam-4137	28	1	the	the	DET
ejpam-4137	28	2	incomplete	incomplete	ADJ
ejpam-4137	28	3	gamma	gamma	NOUN
ejpam-4137	28	4	function	function	VERB
ejpam-4137	28	5	the	the	DET
ejpam-4137	28	6	multivalued	multivalued	ADJ
ejpam-4137	28	7	incomplete	incomplete	ADJ
ejpam-4137	28	8	gamma	gamma	NOUN
ejpam-4137	28	9	functions	function	NOUN
ejpam-4137	28	10	[	[	X
ejpam-4137	28	11	3	3	NUM
ejpam-4137	28	12	]	]	PUNCT
ejpam-4137	28	13	,	,	PUNCT
ejpam-4137	28	14	γ(s	γ(s	PROPN
ejpam-4137	28	15	,	,	PUNCT
ejpam-4137	28	16	z	z	NOUN
ejpam-4137	28	17	)	)	PUNCT
ejpam-4137	28	18	and	and	CCONJ
ejpam-4137	28	19	γ(s	γ(s	PROPN
ejpam-4137	28	20	,	,	PUNCT
ejpam-4137	28	21	z	z	NOUN
ejpam-4137	28	22	)	)	PUNCT
ejpam-4137	28	23	,	,	PUNCT
ejpam-4137	28	24	are	be	AUX
ejpam-4137	28	25	defined	define	VERB
ejpam-4137	28	26	by	by	ADP
ejpam-4137	28	27	γ(s	γ(	NOUN
ejpam-4137	28	28	,	,	PUNCT
ejpam-4137	28	29	z	z	NOUN
ejpam-4137	28	30	)	)	PUNCT
ejpam-4137	28	31	=	=	SYM
ejpam-4137	29	1	∫	∫	PROPN
ejpam-4137	29	2	z	z	PROPN
ejpam-4137	29	3	0	0	PUNCT
ejpam-4137	29	4	ts−1e−tdt	ts−1e−tdt	PROPN
ejpam-4137	29	5	,	,	PUNCT
ejpam-4137	29	6	and	and	CCONJ
ejpam-4137	29	7	γ(s	γ(s	PROPN
ejpam-4137	29	8	,	,	PUNCT
ejpam-4137	29	9	z	z	NOUN
ejpam-4137	29	10	)	)	PUNCT
ejpam-4137	29	11	=	=	SYM
ejpam-4137	30	1	∫	∫	PROPN
ejpam-4137	30	2	∞	∞	PROPN
ejpam-4137	30	3	z	z	PROPN
ejpam-4137	30	4	ts−1e−tdt	ts−1e−tdt	PROPN
ejpam-4137	30	5	,	,	PUNCT
ejpam-4137	30	6	where	where	SCONJ
ejpam-4137	30	7	re(z	re(z	NOUN
ejpam-4137	30	8	)	)	PUNCT
ejpam-4137	30	9	>	>	X
ejpam-4137	31	1	0	0	X
ejpam-4137	31	2	.	.	PUNCT
ejpam-4137	32	1	the	the	DET
ejpam-4137	32	2	incomplete	incomplete	ADJ
ejpam-4137	32	3	gamma	gamma	NOUN
ejpam-4137	32	4	function	function	NOUN
ejpam-4137	32	5	has	have	VERB
ejpam-4137	32	6	a	a	DET
ejpam-4137	32	7	recurrence	recurrence	NOUN
ejpam-4137	32	8	relation	relation	NOUN
ejpam-4137	32	9	given	give	VERB
ejpam-4137	32	10	by	by	ADP
ejpam-4137	32	11	γ(s	γ(	NOUN
ejpam-4137	32	12	,	,	PUNCT
ejpam-4137	32	13	z	z	NOUN
ejpam-4137	32	14	)	)	PUNCT
ejpam-4137	33	1	+	+	CCONJ
ejpam-4137	33	2	γ(s	γ(	NOUN
ejpam-4137	33	3	,	,	PUNCT
ejpam-4137	33	4	z	z	NOUN
ejpam-4137	33	5	)	)	PUNCT
ejpam-4137	33	6	=	=	SYM
ejpam-4137	33	7	γ(s	γ(	NOUN
ejpam-4137	33	8	)	)	PUNCT
ejpam-4137	33	9	,	,	PUNCT
ejpam-4137	34	1	where	where	SCONJ
ejpam-4137	34	2	z	z	NOUN
ejpam-4137	34	3	̸=	̸=	PROPN
ejpam-4137	34	4	0,−1,−2	0,−1,−2	NUM
ejpam-4137	34	5	,	,	PUNCT
ejpam-4137	34	6	...	...	PUNCT
ejpam-4137	34	7	the	the	DET
ejpam-4137	34	8	incomplete	incomplete	ADJ
ejpam-4137	34	9	gamma	gamma	NOUN
ejpam-4137	34	10	function	function	NOUN
ejpam-4137	34	11	is	be	AUX
ejpam-4137	34	12	continued	continue	VERB
ejpam-4137	34	13	analytically	analytically	ADV
ejpam-4137	34	14	by	by	ADP
ejpam-4137	34	15	γ(a	γ(a	PROPN
ejpam-4137	34	16	,	,	PUNCT
ejpam-4137	34	17	ze2mπi	ze2mπi	PROPN
ejpam-4137	34	18	)	)	PUNCT
ejpam-4137	34	19	=	=	PUNCT
ejpam-4137	35	1	e2πmiaγ(a	e2πmiaγ(a	PROPN
ejpam-4137	35	2	,	,	PUNCT
ejpam-4137	35	3	z	z	NOUN
ejpam-4137	35	4	)	)	PUNCT
ejpam-4137	35	5	,	,	PUNCT
ejpam-4137	35	6	and	and	CCONJ
ejpam-4137	35	7	γ(s	γ(s	PROPN
ejpam-4137	35	8	,	,	PUNCT
ejpam-4137	35	9	ze2mπi	ze2mπi	PROPN
ejpam-4137	35	10	)	)	PUNCT
ejpam-4137	35	11	=	=	SYM
ejpam-4137	35	12	e2πmisγ(s	e2πmisγ(s	PROPN
ejpam-4137	35	13	,	,	PUNCT
ejpam-4137	35	14	z	z	NOUN
ejpam-4137	35	15	)	)	PUNCT
ejpam-4137	36	1	+	+	CCONJ
ejpam-4137	36	2	(	(	PUNCT
ejpam-4137	36	3	1−	1−	NUM
ejpam-4137	36	4	e2πmis)γ(s	e2πmis)γ(s	PROPN
ejpam-4137	36	5	)	)	PUNCT
ejpam-4137	36	6	,	,	PUNCT
ejpam-4137	36	7	where	where	SCONJ
ejpam-4137	36	8	m	m	VERB
ejpam-4137	36	9	∈	∈	PROPN
ejpam-4137	36	10	z.	z.	PROPN
ejpam-4137	36	11	when	when	SCONJ
ejpam-4137	36	12	z	z	PROPN
ejpam-4137	36	13	̸=	̸=	PROPN
ejpam-4137	36	14	0	0	NUM
ejpam-4137	36	15	,	,	PUNCT
ejpam-4137	36	16	γ(s	γ(s	PROPN
ejpam-4137	36	17	,	,	PUNCT
ejpam-4137	36	18	z	z	NOUN
ejpam-4137	36	19	)	)	PUNCT
ejpam-4137	36	20	is	be	AUX
ejpam-4137	36	21	an	an	DET
ejpam-4137	36	22	entire	entire	ADJ
ejpam-4137	36	23	function	function	NOUN
ejpam-4137	36	24	of	of	ADP
ejpam-4137	36	25	s	s	NOUN
ejpam-4137	36	26	and	and	CCONJ
ejpam-4137	36	27	γ(s	γ(s	PROPN
ejpam-4137	36	28	,	,	PUNCT
ejpam-4137	36	29	z	z	NOUN
ejpam-4137	36	30	)	)	PUNCT
ejpam-4137	36	31	is	be	AUX
ejpam-4137	36	32	meromorphic	meromorphic	ADJ
ejpam-4137	36	33	with	with	ADP
ejpam-4137	36	34	simple	simple	ADJ
ejpam-4137	36	35	poles	pole	NOUN
ejpam-4137	36	36	at	at	ADP
ejpam-4137	36	37	s	s	NOUN
ejpam-4137	36	38	=	=	NOUN
ejpam-4137	36	39	−n	−n	PROPN
ejpam-4137	36	40	for	for	ADP
ejpam-4137	36	41	n	n	NOUN
ejpam-4137	36	42	=	=	SYM
ejpam-4137	36	43	0	0	NUM
ejpam-4137	36	44	,	,	PUNCT
ejpam-4137	36	45	1	1	NUM
ejpam-4137	36	46	,	,	PUNCT
ejpam-4137	36	47	2	2	NUM
ejpam-4137	36	48	,	,	PUNCT
ejpam-4137	36	49	...	...	PUNCT
ejpam-4137	36	50	with	with	ADP
ejpam-4137	36	51	residue	residue	NOUN
ejpam-4137	36	52	(	(	PUNCT
ejpam-4137	36	53	−1)n	−1)n	NOUN
ejpam-4137	36	54	n	n	CCONJ
ejpam-4137	36	55	!	!	PUNCT
ejpam-4137	36	56	.	.	PUNCT
ejpam-4137	37	1	these	these	DET
ejpam-4137	37	2	definitions	definition	NOUN
ejpam-4137	37	3	are	be	AUX
ejpam-4137	37	4	listed	list	VERB
ejpam-4137	37	5	in	in	ADP
ejpam-4137	37	6	section	section	NOUN
ejpam-4137	37	7	8.2(i	8.2(i	NUM
ejpam-4137	37	8	)	)	PUNCT
ejpam-4137	37	9	and	and	CCONJ
ejpam-4137	37	10	(	(	PUNCT
ejpam-4137	37	11	ii	ii	NOUN
ejpam-4137	37	12	)	)	PUNCT
ejpam-4137	37	13	in	in	ADP
ejpam-4137	37	14	[	[	X
ejpam-4137	37	15	3	3	NUM
ejpam-4137	37	16	]	]	PUNCT
ejpam-4137	37	17	.	.	PUNCT
ejpam-4137	38	1	2	2	X
ejpam-4137	38	2	.	.	X
ejpam-4137	38	3	the	the	DET
ejpam-4137	38	4	lerch	lerch	PROPN
ejpam-4137	38	5	function	function	NOUN
ejpam-4137	38	6	we	we	PRON
ejpam-4137	38	7	use	use	VERB
ejpam-4137	38	8	equation	equation	NOUN
ejpam-4137	38	9	(	(	PUNCT
ejpam-4137	38	10	1.11.3	1.11.3	NUM
ejpam-4137	38	11	)	)	PUNCT
ejpam-4137	38	12	in	in	ADP
ejpam-4137	38	13	[	[	X
ejpam-4137	38	14	2	2	NUM
ejpam-4137	38	15	]	]	PUNCT
ejpam-4137	38	16	where	where	SCONJ
ejpam-4137	38	17	φ(z	φ(z	PROPN
ejpam-4137	38	18	,	,	PUNCT
ejpam-4137	38	19	s	s	NOUN
ejpam-4137	38	20	,	,	PUNCT
ejpam-4137	38	21	v	v	NOUN
ejpam-4137	38	22	)	)	PUNCT
ejpam-4137	38	23	is	be	AUX
ejpam-4137	38	24	the	the	DET
ejpam-4137	38	25	lerch	lerch	PROPN
ejpam-4137	38	26	function	function	NOUN
ejpam-4137	38	27	which	which	PRON
ejpam-4137	38	28	is	be	AUX
ejpam-4137	38	29	a	a	DET
ejpam-4137	38	30	generalization	generalization	NOUN
ejpam-4137	38	31	of	of	ADP
ejpam-4137	38	32	the	the	DET
ejpam-4137	38	33	hurwitz	hurwitz	PROPN
ejpam-4137	38	34	zeta	zeta	PROPN
ejpam-4137	38	35	ζ(s	ζ(s	PROPN
ejpam-4137	38	36	,	,	PUNCT
ejpam-4137	38	37	v	v	NOUN
ejpam-4137	38	38	)	)	PUNCT
ejpam-4137	38	39	and	and	CCONJ
ejpam-4137	38	40	polylogarithm	polylogarithm	PROPN
ejpam-4137	38	41	functions	function	NOUN
ejpam-4137	38	42	lin(z	lin(z	PROPN
ejpam-4137	38	43	)	)	PUNCT
ejpam-4137	38	44	.	.	PUNCT
ejpam-4137	39	1	the	the	DET
ejpam-4137	39	2	lerch	lerch	PROPN
ejpam-4137	39	3	function	function	PROPN
ejpam-4137	39	4	has	have	VERB
ejpam-4137	39	5	a	a	DET
ejpam-4137	39	6	series	series	NOUN
ejpam-4137	39	7	representation	representation	NOUN
ejpam-4137	39	8	given	give	VERB
ejpam-4137	39	9	by	by	ADP
ejpam-4137	39	10	φ(z	φ(z	PROPN
ejpam-4137	39	11	,	,	PUNCT
ejpam-4137	39	12	s	s	NOUN
ejpam-4137	39	13	,	,	PUNCT
ejpam-4137	39	14	v	v	NOUN
ejpam-4137	39	15	)	)	PUNCT
ejpam-4137	39	16	=	=	PUNCT
ejpam-4137	40	1	∞∑	∞∑	NUM
ejpam-4137	40	2	n=0	n=0	NUM
ejpam-4137	40	3	(	(	PUNCT
ejpam-4137	40	4	v	v	NOUN
ejpam-4137	40	5	+	+	NOUN
ejpam-4137	40	6	n)−szn	n)−szn	NUM
ejpam-4137	40	7	(	(	PUNCT
ejpam-4137	40	8	3	3	NUM
ejpam-4137	40	9	)	)	PUNCT
ejpam-4137	40	10	where	where	SCONJ
ejpam-4137	40	11	|z|	|z|	VERB
ejpam-4137	40	12	<	<	X
ejpam-4137	40	13	1	1	NUM
ejpam-4137	40	14	,	,	PUNCT
ejpam-4137	40	15	v	v	ADP
ejpam-4137	40	16	̸=	̸=	PROPN
ejpam-4137	40	17	0,−1,−2,−3	0,−1,−2,−3	NUM
ejpam-4137	40	18	,	,	PUNCT
ejpam-4137	40	19	..	..	PUNCT
ejpam-4137	40	20	,	,	PUNCT
ejpam-4137	40	21	and	and	CCONJ
ejpam-4137	40	22	is	be	AUX
ejpam-4137	40	23	continued	continue	VERB
ejpam-4137	40	24	analytically	analytically	ADV
ejpam-4137	40	25	by	by	ADP
ejpam-4137	40	26	its	its	PRON
ejpam-4137	40	27	integral	integral	ADJ
ejpam-4137	40	28	representation	representation	NOUN
ejpam-4137	40	29	given	give	VERB
ejpam-4137	40	30	by	by	ADP
ejpam-4137	40	31	φ(z	φ(z	PROPN
ejpam-4137	40	32	,	,	PUNCT
ejpam-4137	40	33	s	s	NOUN
ejpam-4137	40	34	,	,	PUNCT
ejpam-4137	40	35	v	v	NOUN
ejpam-4137	40	36	)	)	PUNCT
ejpam-4137	40	37	=	=	SYM
ejpam-4137	40	38	1	1	NUM
ejpam-4137	40	39	γ(s	γ(	NOUN
ejpam-4137	40	40	)	)	PUNCT
ejpam-4137	40	41	∫	∫	PROPN
ejpam-4137	41	1	∞	∞	PROPN
ejpam-4137	41	2	0	0	NUM
ejpam-4137	42	1	ts−1e−vt	ts−1e−vt	PRON
ejpam-4137	43	1	1−	1−	NUM
ejpam-4137	43	2	ze−t	ze−t	NOUN
ejpam-4137	43	3	dt	dt	NOUN
ejpam-4137	44	1	=	=	SYM
ejpam-4137	44	2	1	1	NUM
ejpam-4137	44	3	γ(s	γ(s	PROPN
ejpam-4137	44	4	)	)	PUNCT
ejpam-4137	44	5	∫	∫	PROPN
ejpam-4137	45	1	∞	∞	NUM
ejpam-4137	45	2	0	0	NUM
ejpam-4137	46	1	ts−1e−(v−1)t	ts−1e−(v−1)t	PROPN
ejpam-4137	46	2	et	et	NOUN
ejpam-4137	46	3	−	−	NOUN
ejpam-4137	46	4	z	z	NOUN
ejpam-4137	46	5	dt	dt	X
ejpam-4137	46	6	(	(	PUNCT
ejpam-4137	46	7	4	4	NUM
ejpam-4137	46	8	)	)	PUNCT
ejpam-4137	46	9	where	where	SCONJ
ejpam-4137	46	10	re(v	re(v	NOUN
ejpam-4137	46	11	)	)	PUNCT
ejpam-4137	46	12	>	>	X
ejpam-4137	46	13	0	0	NUM
ejpam-4137	46	14	,	,	PUNCT
ejpam-4137	46	15	and	and	CCONJ
ejpam-4137	46	16	either	either	ADV
ejpam-4137	46	17	|z|≤	|z|≤	SYM
ejpam-4137	46	18	1	1	NUM
ejpam-4137	46	19	,	,	PUNCT
ejpam-4137	46	20	z	z	NOUN
ejpam-4137	46	21	̸=	̸=	PROPN
ejpam-4137	46	22	1	1	NUM
ejpam-4137	46	23	,	,	PUNCT
ejpam-4137	46	24	re(s	re(s	ADJ
ejpam-4137	46	25	)	)	PUNCT
ejpam-4137	46	26	>	>	X
ejpam-4137	46	27	0	0	NUM
ejpam-4137	46	28	,	,	PUNCT
ejpam-4137	46	29	or	or	CCONJ
ejpam-4137	46	30	z	z	NOUN
ejpam-4137	46	31	=	=	SYM
ejpam-4137	46	32	1	1	NUM
ejpam-4137	46	33	,	,	PUNCT
ejpam-4137	46	34	re(s	re(s	ADJ
ejpam-4137	46	35	)	)	PUNCT
ejpam-4137	46	36	>	>	X
ejpam-4137	47	1	1	1	X
ejpam-4137	47	2	.	.	PUNCT
ejpam-4137	47	3	r.	r.	PROPN
ejpam-4137	47	4	reynolds	reynolds	PROPN
ejpam-4137	47	5	,	,	PUNCT
ejpam-4137	47	6	a.	a.	PROPN
ejpam-4137	47	7	stauffer	stauffer	PROPN
ejpam-4137	47	8	/	/	SYM
ejpam-4137	47	9	eur	eur	PROPN
ejpam-4137	47	10	.	.	PUNCT
ejpam-4137	48	1	j.	j.	PROPN
ejpam-4137	48	2	pure	pure	PROPN
ejpam-4137	48	3	appl	appl	PROPN
ejpam-4137	48	4	.	.	PROPN
ejpam-4137	48	5	math	math	PROPN
ejpam-4137	48	6	,	,	PUNCT
ejpam-4137	48	7	15	15	NUM
ejpam-4137	48	8	(	(	PUNCT
ejpam-4137	48	9	1	1	NUM
ejpam-4137	48	10	)	)	PUNCT
ejpam-4137	48	11	(	(	PUNCT
ejpam-4137	48	12	2022	2022	NUM
ejpam-4137	48	13	)	)	PUNCT
ejpam-4137	48	14	,	,	PUNCT
ejpam-4137	48	15	158	158	NUM
ejpam-4137	48	16	-	-	SYM
ejpam-4137	48	17	168	168	NUM
ejpam-4137	48	18	160	160	NUM
ejpam-4137	48	19	3	3	NUM
ejpam-4137	48	20	.	.	PUNCT
ejpam-4137	49	1	contour	contour	ADJ
ejpam-4137	49	2	integral	integral	ADJ
ejpam-4137	49	3	representation	representation	NOUN
ejpam-4137	49	4	for	for	ADP
ejpam-4137	49	5	the	the	DET
ejpam-4137	49	6	infinite	infinite	ADJ
ejpam-4137	49	7	sum	sum	NOUN
ejpam-4137	49	8	of	of	ADP
ejpam-4137	49	9	the	the	DET
ejpam-4137	49	10	lerch	lerch	PROPN
ejpam-4137	49	11	function	function	NOUN
ejpam-4137	49	12	we	we	PRON
ejpam-4137	49	13	use	use	VERB
ejpam-4137	49	14	the	the	DET
ejpam-4137	49	15	method	method	NOUN
ejpam-4137	49	16	in	in	ADP
ejpam-4137	49	17	[	[	X
ejpam-4137	49	18	12	12	NUM
ejpam-4137	49	19	]	]	PUNCT
ejpam-4137	49	20	.	.	PUNCT
ejpam-4137	50	1	the	the	DET
ejpam-4137	50	2	cut	cut	NOUN
ejpam-4137	50	3	and	and	CCONJ
ejpam-4137	50	4	contour	contour	NOUN
ejpam-4137	50	5	are	be	AUX
ejpam-4137	50	6	in	in	ADP
ejpam-4137	50	7	the	the	DET
ejpam-4137	50	8	first	first	ADJ
ejpam-4137	50	9	quadrant	quadrant	NOUN
ejpam-4137	50	10	of	of	ADP
ejpam-4137	50	11	the	the	DET
ejpam-4137	50	12	complex	complex	ADJ
ejpam-4137	50	13	w	w	NOUN
ejpam-4137	50	14	-	-	PUNCT
ejpam-4137	50	15	plane	plane	NOUN
ejpam-4137	50	16	with	with	ADP
ejpam-4137	50	17	0	0	NUM
ejpam-4137	50	18	<	<	X
ejpam-4137	50	19	re(w	re(w	ADV
ejpam-4137	50	20	+	+	NUM
ejpam-4137	50	21	m	m	NOUN
ejpam-4137	50	22	)	)	PUNCT
ejpam-4137	50	23	<	<	X
ejpam-4137	50	24	1	1	X
ejpam-4137	50	25	.	.	PUNCT
ejpam-4137	51	1	the	the	DET
ejpam-4137	51	2	cut	cut	NOUN
ejpam-4137	51	3	approaches	approach	VERB
ejpam-4137	51	4	the	the	DET
ejpam-4137	51	5	origin	origin	NOUN
ejpam-4137	51	6	from	from	ADP
ejpam-4137	51	7	the	the	DET
ejpam-4137	51	8	interior	interior	NOUN
ejpam-4137	51	9	of	of	ADP
ejpam-4137	51	10	the	the	DET
ejpam-4137	51	11	first	first	ADJ
ejpam-4137	51	12	quadrant	quadrant	NOUN
ejpam-4137	51	13	and	and	CCONJ
ejpam-4137	51	14	goes	go	VERB
ejpam-4137	51	15	to	to	PART
ejpam-4137	51	16	infinity	infinity	NOUN
ejpam-4137	51	17	vertically	vertically	ADV
ejpam-4137	51	18	and	and	CCONJ
ejpam-4137	51	19	the	the	DET
ejpam-4137	51	20	contour	contour	NOUN
ejpam-4137	51	21	goes	go	VERB
ejpam-4137	51	22	round	round	ADP
ejpam-4137	51	23	the	the	DET
ejpam-4137	51	24	origin	origin	NOUN
ejpam-4137	51	25	with	with	ADP
ejpam-4137	51	26	zero	zero	NUM
ejpam-4137	51	27	radius	radius	NOUN
ejpam-4137	51	28	and	and	CCONJ
ejpam-4137	51	29	is	be	AUX
ejpam-4137	51	30	on	on	ADP
ejpam-4137	51	31	opposite	opposite	ADJ
ejpam-4137	51	32	sides	side	NOUN
ejpam-4137	51	33	of	of	ADP
ejpam-4137	51	34	the	the	DET
ejpam-4137	51	35	cut	cut	NOUN
ejpam-4137	51	36	.	.	PUNCT
ejpam-4137	52	1	using	use	VERB
ejpam-4137	52	2	a	a	DET
ejpam-4137	52	3	generalization	generalization	NOUN
ejpam-4137	52	4	of	of	ADP
ejpam-4137	52	5	cauchy	cauchy	PROPN
ejpam-4137	52	6	’s	’s	PART
ejpam-4137	52	7	integral	integral	ADJ
ejpam-4137	52	8	formula	formula	NOUN
ejpam-4137	52	9	(	(	PUNCT
ejpam-4137	52	10	2	2	X
ejpam-4137	52	11	)	)	PUNCT
ejpam-4137	52	12	we	we	PRON
ejpam-4137	52	13	first	first	ADV
ejpam-4137	52	14	replace	replace	VERB
ejpam-4137	52	15	y	y	PROPN
ejpam-4137	52	16	→	→	SYM
ejpam-4137	52	17	log(a)+21−n(y+1	log(a)+21−n(y+1	PROPN
ejpam-4137	52	18	)	)	PUNCT
ejpam-4137	52	19	then	then	ADV
ejpam-4137	52	20	multiply	multiply	VERB
ejpam-4137	52	21	both	both	DET
ejpam-4137	52	22	sides	side	NOUN
ejpam-4137	52	23	by	by	ADP
ejpam-4137	52	24	(	(	PUNCT
ejpam-4137	52	25	−1)yem21−n(y+1	−1)yem21−n(y+1	PROPN
ejpam-4137	52	26	)	)	PUNCT
ejpam-4137	52	27	and	and	CCONJ
ejpam-4137	52	28	take	take	VERB
ejpam-4137	52	29	the	the	DET
ejpam-4137	52	30	infinite	infinite	ADJ
ejpam-4137	52	31	sums	sum	NOUN
ejpam-4137	52	32	over	over	ADP
ejpam-4137	52	33	y	y	PROPN
ejpam-4137	52	34	∈	∈	PROPN
ejpam-4137	53	1	[	[	X
ejpam-4137	53	2	0,∞	0,∞	NUM
ejpam-4137	53	3	)	)	PUNCT
ejpam-4137	53	4	and	and	CCONJ
ejpam-4137	53	5	n	n	PRON
ejpam-4137	53	6	∈	∈	PROPN
ejpam-4137	54	1	[	[	X
ejpam-4137	54	2	1,∞	1,∞	NUM
ejpam-4137	54	3	)	)	PUNCT
ejpam-4137	54	4	and	and	CCONJ
ejpam-4137	54	5	simplify	simplify	VERB
ejpam-4137	54	6	in	in	ADP
ejpam-4137	54	7	terms	term	NOUN
ejpam-4137	54	8	of	of	ADP
ejpam-4137	54	9	the	the	DET
ejpam-4137	54	10	lerch	lerch	PROPN
ejpam-4137	54	11	function	function	NOUN
ejpam-4137	54	12	to	to	PART
ejpam-4137	54	13	get	get	VERB
ejpam-4137	54	14	(	(	PUNCT
ejpam-4137	54	15	5	5	NUM
ejpam-4137	54	16	)	)	PUNCT
ejpam-4137	55	1	∞∑	∞∑	NUM
ejpam-4137	55	2	n	n	NOUN
ejpam-4137	55	3	=	=	SYM
ejpam-4137	55	4	1	1	NUM
ejpam-4137	55	5	2k−n+1	2k−n+1	NUM
ejpam-4137	55	6	(	(	PUNCT
ejpam-4137	55	7	2−n	2−n	NUM
ejpam-4137	55	8	)	)	PUNCT
ejpam-4137	55	9	k	k	NOUN
ejpam-4137	55	10	em21−n	em21−n	X
ejpam-4137	55	11	φ	φ	PROPN
ejpam-4137	55	12	(	(	PUNCT
ejpam-4137	55	13	−e2	−e2	PROPN
ejpam-4137	55	14	1−nm,−k	1−nm,−k	NOUN
ejpam-4137	55	15	,	,	PUNCT
ejpam-4137	55	16	2n−1	2n−1	PROPN
ejpam-4137	55	17	log(a	log(a	PROPN
ejpam-4137	55	18	)	)	PUNCT
ejpam-4137	56	1	+	+	CCONJ
ejpam-4137	56	2	1	1	X
ejpam-4137	56	3	)	)	PUNCT
ejpam-4137	56	4	γ(k	γ(k	NOUN
ejpam-4137	56	5	+	+	CCONJ
ejpam-4137	56	6	1	1	X
ejpam-4137	56	7	)	)	PUNCT
ejpam-4137	56	8	=	=	SYM
ejpam-4137	56	9	1	1	NUM
ejpam-4137	56	10	2πi	2πi	NOUN
ejpam-4137	56	11	∞∑	∞∑	NOUN
ejpam-4137	56	12	n=1	n=1	ADP
ejpam-4137	56	13	∞∑	∞∑	NUM
ejpam-4137	56	14	y=0	y=0	NUM
ejpam-4137	56	15	∫	∫	PROPN
ejpam-4137	56	16	c	c	PROPN
ejpam-4137	56	17	2(−1)yaww−k−1e2	2(−1)yaww−k−1e2	NUM
ejpam-4137	56	18	1−n(y+1)(m+w)dw	1−n(y+1)(m+w)dw	NOUN
ejpam-4137	56	19	=	=	SYM
ejpam-4137	56	20	1	1	NUM
ejpam-4137	56	21	2πi	2πi	NOUN
ejpam-4137	56	22	∫	∫	PROPN
ejpam-4137	56	23	c	c	PROPN
ejpam-4137	56	24	∞∑	∞∑	NUM
ejpam-4137	56	25	n=1	n=1	ADP
ejpam-4137	56	26	∞∑	∞∑	ADJ
ejpam-4137	56	27	y=0	y=0	NOUN
ejpam-4137	56	28	2(−1)yaww−k−1e2	2(−1)yaww−k−1e2	NUM
ejpam-4137	56	29	1−n(y+1)(m+w)dw	1−n(y+1)(m+w)dw	NOUN
ejpam-4137	56	30	=	=	SYM
ejpam-4137	56	31	1	1	NUM
ejpam-4137	56	32	2πi	2πi	NOUN
ejpam-4137	56	33	∫	∫	PROPN
ejpam-4137	57	1	c	c	NOUN
ejpam-4137	57	2	∞∑	∞∑	NUM
ejpam-4137	57	3	n=1	n=1	PROPN
ejpam-4137	57	4	(	(	PUNCT
ejpam-4137	57	5	2−naww−k−1	2−naww−k−1	NUM
ejpam-4137	57	6	tanh	tanh	NOUN
ejpam-4137	57	7	(	(	PUNCT
ejpam-4137	57	8	2−n(m+	2−n(m+	NOUN
ejpam-4137	57	9	w	w	NOUN
ejpam-4137	57	10	)	)	PUNCT
ejpam-4137	57	11	)	)	PUNCT
ejpam-4137	58	1	+	+	CCONJ
ejpam-4137	58	2	2−naww−k−1	2−naww−k−1	X
ejpam-4137	58	3	)	)	PUNCT
ejpam-4137	58	4	dw	dw	NOUN
ejpam-4137	58	5	=	=	SYM
ejpam-4137	58	6	1	1	NUM
ejpam-4137	58	7	2πi	2πi	NOUN
ejpam-4137	58	8	∫	∫	PROPN
ejpam-4137	58	9	c	c	PROPN
ejpam-4137	58	10	(	(	PUNCT
ejpam-4137	58	11	aww−k−1	aww−k−1	NOUN
ejpam-4137	58	12	coth(m+	coth(m+	X
ejpam-4137	58	13	w)−	w)−	PROPN
ejpam-4137	58	14	aww−k−1	aww−k−1	NOUN
ejpam-4137	58	15	m+	m+	NUM
ejpam-4137	58	16	w	w	NOUN
ejpam-4137	58	17	+	+	X
ejpam-4137	58	18	aww−k−1	aww−k−1	NOUN
ejpam-4137	58	19	)	)	PUNCT
ejpam-4137	59	1	dw	dw	PROPN
ejpam-4137	59	2	from	from	ADP
ejpam-4137	59	3	equations	equation	NOUN
ejpam-4137	59	4	(	(	PUNCT
ejpam-4137	59	5	5.3.8.4	5.3.8.4	NUM
ejpam-4137	59	6	)	)	PUNCT
ejpam-4137	59	7	in	in	ADP
ejpam-4137	59	8	[	[	X
ejpam-4137	59	9	11	11	NUM
ejpam-4137	59	10	]	]	PUNCT
ejpam-4137	59	11	and	and	CCONJ
ejpam-4137	59	12	(	(	PUNCT
ejpam-4137	59	13	1.232.1	1.232.1	NUM
ejpam-4137	59	14	)	)	PUNCT
ejpam-4137	59	15	in	in	ADP
ejpam-4137	59	16	[	[	X
ejpam-4137	59	17	4	4	X
ejpam-4137	59	18	]	]	PUNCT
ejpam-4137	59	19	where	where	SCONJ
ejpam-4137	59	20	re(w+m	re(w+m	NOUN
ejpam-4137	59	21	)	)	PUNCT
ejpam-4137	59	22	>	>	X
ejpam-4137	59	23	0	0	PUNCT
ejpam-4137	59	24	and	and	CCONJ
ejpam-4137	59	25	im(w+m	im(w+m	NOUN
ejpam-4137	59	26	)	)	PUNCT
ejpam-4137	59	27	>	>	X
ejpam-4137	59	28	0	0	PUNCT
ejpam-4137	60	1	in	in	ADP
ejpam-4137	60	2	order	order	NOUN
ejpam-4137	60	3	for	for	SCONJ
ejpam-4137	60	4	the	the	DET
ejpam-4137	60	5	sums	sum	NOUN
ejpam-4137	60	6	to	to	PART
ejpam-4137	60	7	converge	converge	VERB
ejpam-4137	60	8	.	.	PUNCT
ejpam-4137	60	9	3.1	3.1	NUM
ejpam-4137	60	10	.	.	PUNCT
ejpam-4137	61	1	additional	additional	ADJ
ejpam-4137	61	2	contour	contour	NOUN
ejpam-4137	61	3	integral	integral	ADJ
ejpam-4137	61	4	using	use	VERB
ejpam-4137	61	5	a	a	DET
ejpam-4137	61	6	generalization	generalization	NOUN
ejpam-4137	61	7	of	of	ADP
ejpam-4137	61	8	cauchy	cauchy	PROPN
ejpam-4137	61	9	’s	’s	PART
ejpam-4137	61	10	integral	integral	ADJ
ejpam-4137	61	11	formula	formula	NOUN
ejpam-4137	61	12	(	(	PUNCT
ejpam-4137	61	13	2	2	X
ejpam-4137	61	14	)	)	PUNCT
ejpam-4137	61	15	we	we	PRON
ejpam-4137	61	16	first	first	ADV
ejpam-4137	61	17	replace	replace	VERB
ejpam-4137	61	18	y	y	PROPN
ejpam-4137	61	19	→	→	SYM
ejpam-4137	61	20	log(a	log(a	PROPN
ejpam-4137	61	21	)	)	PUNCT
ejpam-4137	61	22	then	then	ADV
ejpam-4137	61	23	multiply	multiply	VERB
ejpam-4137	61	24	both	both	DET
ejpam-4137	61	25	sides	side	NOUN
ejpam-4137	61	26	by	by	ADP
ejpam-4137	61	27	2−n	2−n	NUM
ejpam-4137	61	28	and	and	CCONJ
ejpam-4137	61	29	take	take	VERB
ejpam-4137	61	30	the	the	DET
ejpam-4137	61	31	infinite	infinite	ADJ
ejpam-4137	61	32	sum	sum	NOUN
ejpam-4137	61	33	over	over	ADP
ejpam-4137	61	34	n	n	PRON
ejpam-4137	61	35	∈	∈	PROPN
ejpam-4137	62	1	[	[	X
ejpam-4137	62	2	1,∞	1,∞	NUM
ejpam-4137	62	3	)	)	PUNCT
ejpam-4137	62	4	to	to	PART
ejpam-4137	62	5	get	get	VERB
ejpam-4137	62	6	(	(	PUNCT
ejpam-4137	62	7	6	6	NUM
ejpam-4137	62	8	)	)	PUNCT
ejpam-4137	63	1	−	−	NOUN
ejpam-4137	63	2	∞∑	∞∑	NUM
ejpam-4137	63	3	n	n	NOUN
ejpam-4137	63	4	=	=	SYM
ejpam-4137	63	5	1	1	NUM
ejpam-4137	63	6	2−n	2−n	NUM
ejpam-4137	63	7	logk(a	logk(a	NOUN
ejpam-4137	63	8	)	)	PUNCT
ejpam-4137	64	1	γ(k	γ(k	NOUN
ejpam-4137	64	2	+	+	CCONJ
ejpam-4137	64	3	1	1	X
ejpam-4137	64	4	)	)	PUNCT
ejpam-4137	64	5	=	=	SYM
ejpam-4137	65	1	−	−	PROPN
ejpam-4137	65	2	1	1	NUM
ejpam-4137	65	3	2πi	2πi	NOUN
ejpam-4137	65	4	∞∑	∞∑	NUM
ejpam-4137	65	5	n=1	n=1	PROPN
ejpam-4137	65	6	∫	∫	PROPN
ejpam-4137	65	7	c	c	PROPN
ejpam-4137	65	8	2−naww−k−1dw	2−naww−k−1dw	NUM
ejpam-4137	65	9	=	=	SYM
ejpam-4137	65	10	−	−	PROPN
ejpam-4137	65	11	1	1	NUM
ejpam-4137	65	12	2πi	2πi	NOUN
ejpam-4137	65	13	∫	∫	PROPN
ejpam-4137	66	1	c	c	NOUN
ejpam-4137	67	1	∞∑	∞∑	NUM
ejpam-4137	67	2	n=1	n=1	PROPN
ejpam-4137	67	3	2−naww−k−1dw	2−naww−k−1dw	NUM
ejpam-4137	67	4	=	=	SYM
ejpam-4137	67	5	−	−	PROPN
ejpam-4137	67	6	1	1	NUM
ejpam-4137	67	7	2πi	2πi	NOUN
ejpam-4137	67	8	∫	∫	PROPN
ejpam-4137	68	1	c	c	PROPN
ejpam-4137	69	1	aww−k−1dw	aww−k−1dw	PROPN
ejpam-4137	70	1	r.	r.	PROPN
ejpam-4137	70	2	reynolds	reynolds	PROPN
ejpam-4137	70	3	,	,	PUNCT
ejpam-4137	70	4	a.	a.	PROPN
ejpam-4137	70	5	stauffer	stauffer	PROPN
ejpam-4137	70	6	/	/	SYM
ejpam-4137	70	7	eur	eur	PROPN
ejpam-4137	70	8	.	.	PUNCT
ejpam-4137	71	1	j.	j.	PROPN
ejpam-4137	71	2	pure	pure	PROPN
ejpam-4137	71	3	appl	appl	PROPN
ejpam-4137	71	4	.	.	PROPN
ejpam-4137	71	5	math	math	PROPN
ejpam-4137	71	6	,	,	PUNCT
ejpam-4137	71	7	15	15	NUM
ejpam-4137	71	8	(	(	PUNCT
ejpam-4137	71	9	1	1	NUM
ejpam-4137	71	10	)	)	PUNCT
ejpam-4137	71	11	(	(	PUNCT
ejpam-4137	71	12	2022	2022	NUM
ejpam-4137	71	13	)	)	PUNCT
ejpam-4137	71	14	,	,	PUNCT
ejpam-4137	71	15	158	158	NUM
ejpam-4137	71	16	-	-	SYM
ejpam-4137	71	17	168	168	NUM
ejpam-4137	71	18	161	161	NUM
ejpam-4137	71	19	4	4	NUM
ejpam-4137	71	20	.	.	PUNCT
ejpam-4137	72	1	contour	contour	ADJ
ejpam-4137	72	2	integral	integral	ADJ
ejpam-4137	72	3	representation	representation	NOUN
ejpam-4137	72	4	for	for	ADP
ejpam-4137	72	5	the	the	DET
ejpam-4137	72	6	lerch	lerch	PROPN
ejpam-4137	72	7	and	and	CCONJ
ejpam-4137	72	8	incomplete	incomplete	ADJ
ejpam-4137	72	9	gamma	gamma	NOUN
ejpam-4137	72	10	functions	function	NOUN
ejpam-4137	72	11	using	use	VERB
ejpam-4137	72	12	a	a	DET
ejpam-4137	72	13	generalization	generalization	NOUN
ejpam-4137	72	14	of	of	ADP
ejpam-4137	72	15	cauchy	cauchy	PROPN
ejpam-4137	72	16	’s	’s	PART
ejpam-4137	72	17	integral	integral	ADJ
ejpam-4137	72	18	formula	formula	NOUN
ejpam-4137	72	19	(	(	PUNCT
ejpam-4137	72	20	2	2	X
ejpam-4137	72	21	)	)	PUNCT
ejpam-4137	72	22	we	we	PRON
ejpam-4137	72	23	first	first	ADV
ejpam-4137	72	24	replace	replace	VERB
ejpam-4137	72	25	y	y	PROPN
ejpam-4137	72	26	→	→	SYM
ejpam-4137	72	27	log(a	log(a	PROPN
ejpam-4137	72	28	)	)	PUNCT
ejpam-4137	72	29	+	+	CCONJ
ejpam-4137	73	1	2(y	2(y	NUM
ejpam-4137	74	1	+	+	CCONJ
ejpam-4137	74	2	1	1	NUM
ejpam-4137	74	3	)	)	PUNCT
ejpam-4137	74	4	then	then	ADV
ejpam-4137	74	5	multiply	multiply	VERB
ejpam-4137	74	6	both	both	DET
ejpam-4137	74	7	sides	side	NOUN
ejpam-4137	74	8	by	by	ADP
ejpam-4137	74	9	e2m(y+1	e2m(y+1	NOUN
ejpam-4137	74	10	)	)	PUNCT
ejpam-4137	74	11	and	and	CCONJ
ejpam-4137	74	12	take	take	VERB
ejpam-4137	74	13	the	the	DET
ejpam-4137	74	14	infinite	infinite	ADJ
ejpam-4137	74	15	sum	sum	NOUN
ejpam-4137	74	16	over	over	ADP
ejpam-4137	74	17	y	y	PROPN
ejpam-4137	74	18	∈	∈	PROPN
ejpam-4137	75	1	[	[	X
ejpam-4137	75	2	0,∞	0,∞	NOUN
ejpam-4137	75	3	)	)	PUNCT
ejpam-4137	75	4	and	and	CCONJ
ejpam-4137	75	5	simplify	simplify	VERB
ejpam-4137	75	6	in	in	ADP
ejpam-4137	75	7	terms	term	NOUN
ejpam-4137	75	8	of	of	ADP
ejpam-4137	75	9	the	the	DET
ejpam-4137	75	10	lerch	lerch	PROPN
ejpam-4137	75	11	function	function	NOUN
ejpam-4137	75	12	to	to	PART
ejpam-4137	75	13	get	get	VERB
ejpam-4137	75	14	(	(	PUNCT
ejpam-4137	75	15	7)−	7)−	NUM
ejpam-4137	75	16	2k+1e2mφ	2k+1e2mφ	NUM
ejpam-4137	75	17	(	(	PUNCT
ejpam-4137	75	18	e2m,−k	e2m,−k	NOUN
ejpam-4137	75	19	,	,	PUNCT
ejpam-4137	75	20	log(a)2	log(a)2	NOUN
ejpam-4137	75	21	+	+	CCONJ
ejpam-4137	75	22	1	1	X
ejpam-4137	75	23	)	)	PUNCT
ejpam-4137	75	24	γ(k	γ(k	NOUN
ejpam-4137	75	25	+	+	CCONJ
ejpam-4137	76	1	1	1	X
ejpam-4137	76	2	)	)	PUNCT
ejpam-4137	76	3	=	=	SYM
ejpam-4137	76	4	1	1	NUM
ejpam-4137	76	5	2πi	2πi	ADJ
ejpam-4137	76	6	∫	∫	PROPN
ejpam-4137	76	7	c	c	PROPN
ejpam-4137	76	8	aww−k−1	aww−k−1	NOUN
ejpam-4137	76	9	coth(m+	coth(m+	X
ejpam-4137	76	10	w	w	NOUN
ejpam-4137	76	11	)	)	PUNCT
ejpam-4137	77	1	+	+	CCONJ
ejpam-4137	77	2	aww−k−1dw	aww−k−1dw	VERB
ejpam-4137	77	3	from	from	ADP
ejpam-4137	77	4	equation	equation	NOUN
ejpam-4137	77	5	(	(	PUNCT
ejpam-4137	77	6	1.232.1	1.232.1	NUM
ejpam-4137	77	7	)	)	PUNCT
ejpam-4137	77	8	in	in	ADP
ejpam-4137	77	9	[	[	X
ejpam-4137	77	10	4	4	X
ejpam-4137	77	11	]	]	PUNCT
ejpam-4137	77	12	where	where	SCONJ
ejpam-4137	77	13	im(w	im(w	PUNCT
ejpam-4137	77	14	+	+	NOUN
ejpam-4137	77	15	m	m	VERB
ejpam-4137	77	16	)	)	PUNCT
ejpam-4137	77	17	>	>	X
ejpam-4137	77	18	0	0	PUNCT
ejpam-4137	78	1	in	in	ADP
ejpam-4137	78	2	order	order	NOUN
ejpam-4137	78	3	for	for	SCONJ
ejpam-4137	78	4	the	the	DET
ejpam-4137	78	5	sum	sum	NOUN
ejpam-4137	78	6	to	to	PART
ejpam-4137	78	7	converge	converge	VERB
ejpam-4137	78	8	.	.	PUNCT
ejpam-4137	78	9	4.1	4.1	NUM
ejpam-4137	78	10	.	.	PUNCT
ejpam-4137	79	1	additional	additional	ADJ
ejpam-4137	79	2	contour	contour	NOUN
ejpam-4137	79	3	integral	integral	ADJ
ejpam-4137	79	4	using	use	VERB
ejpam-4137	79	5	a	a	DET
ejpam-4137	79	6	generalization	generalization	NOUN
ejpam-4137	79	7	of	of	ADP
ejpam-4137	79	8	cauchy	cauchy	PROPN
ejpam-4137	79	9	’s	’s	PART
ejpam-4137	79	10	integral	integral	ADJ
ejpam-4137	79	11	formula	formula	NOUN
ejpam-4137	79	12	(	(	PUNCT
ejpam-4137	79	13	2	2	X
ejpam-4137	79	14	)	)	PUNCT
ejpam-4137	79	15	we	we	PRON
ejpam-4137	79	16	first	first	ADV
ejpam-4137	79	17	replace	replace	VERB
ejpam-4137	79	18	y	y	PROPN
ejpam-4137	79	19	→	→	SYM
ejpam-4137	79	20	log(a	log(a	PROPN
ejpam-4137	79	21	)	)	PUNCT
ejpam-4137	79	22	and	and	CCONJ
ejpam-4137	79	23	simplify	simplify	VERB
ejpam-4137	79	24	to	to	PART
ejpam-4137	79	25	get	get	VERB
ejpam-4137	79	26	(	(	PUNCT
ejpam-4137	79	27	8)	8)	NUM
ejpam-4137	79	28	logk(a	logk(a	NOUN
ejpam-4137	79	29	)	)	PUNCT
ejpam-4137	79	30	γ(k	γ(k	NOUN
ejpam-4137	79	31	+	+	CCONJ
ejpam-4137	79	32	1	1	X
ejpam-4137	79	33	)	)	PUNCT
ejpam-4137	79	34	=	=	SYM
ejpam-4137	80	1	1	1	NUM
ejpam-4137	80	2	2πi	2πi	NOUN
ejpam-4137	80	3	∫	∫	PROPN
ejpam-4137	80	4	c	c	PROPN
ejpam-4137	80	5	aww−k−1dw	aww−k−1dw	PROPN
ejpam-4137	80	6	4.2	4.2	NUM
ejpam-4137	80	7	.	.	PUNCT
ejpam-4137	80	8	contour	contour	ADJ
ejpam-4137	80	9	integral	integral	ADJ
ejpam-4137	80	10	representation	representation	NOUN
ejpam-4137	80	11	for	for	ADP
ejpam-4137	80	12	the	the	DET
ejpam-4137	80	13	incomplete	incomplete	ADJ
ejpam-4137	80	14	gamma	gamma	NOUN
ejpam-4137	80	15	function	function	NOUN
ejpam-4137	80	16	using	use	VERB
ejpam-4137	80	17	a	a	DET
ejpam-4137	80	18	generalization	generalization	NOUN
ejpam-4137	80	19	of	of	ADP
ejpam-4137	80	20	cauchy	cauchy	PROPN
ejpam-4137	80	21	’s	’s	PART
ejpam-4137	80	22	integral	integral	ADJ
ejpam-4137	80	23	formula	formula	NOUN
ejpam-4137	80	24	(	(	PUNCT
ejpam-4137	80	25	2	2	X
ejpam-4137	80	26	)	)	PUNCT
ejpam-4137	80	27	we	we	PRON
ejpam-4137	80	28	first	first	ADV
ejpam-4137	80	29	replace	replace	VERB
ejpam-4137	80	30	y	y	PROPN
ejpam-4137	80	31	→	→	SYM
ejpam-4137	80	32	y+	y+	NUM
ejpam-4137	80	33	log(a	log(a	PROPN
ejpam-4137	80	34	)	)	PUNCT
ejpam-4137	80	35	then	then	ADV
ejpam-4137	80	36	multiply	multiply	VERB
ejpam-4137	80	37	both	both	DET
ejpam-4137	80	38	sides	side	NOUN
ejpam-4137	80	39	by	by	ADP
ejpam-4137	80	40	emy	emy	PROPN
ejpam-4137	80	41	and	and	CCONJ
ejpam-4137	80	42	take	take	VERB
ejpam-4137	80	43	the	the	DET
ejpam-4137	80	44	definite	definite	ADJ
ejpam-4137	80	45	integral	integral	ADJ
ejpam-4137	80	46	over	over	ADP
ejpam-4137	80	47	y	y	PROPN
ejpam-4137	80	48	∈	∈	PROPN
ejpam-4137	81	1	[	[	X
ejpam-4137	81	2	0,∞	0,∞	NOUN
ejpam-4137	81	3	)	)	PUNCT
ejpam-4137	81	4	to	to	PART
ejpam-4137	81	5	get	get	VERB
ejpam-4137	81	6	(	(	PUNCT
ejpam-4137	81	7	9	9	NUM
ejpam-4137	81	8	)	)	PUNCT
ejpam-4137	81	9	a−m(−m)−k−1γ(k	a−m(−m)−k−1γ(k	NOUN
ejpam-4137	81	10	+	+	CCONJ
ejpam-4137	81	11	1,−m	1,−m	NUM
ejpam-4137	81	12	log(a	log(a	PROPN
ejpam-4137	81	13	)	)	PUNCT
ejpam-4137	81	14	)	)	PUNCT
ejpam-4137	82	1	γ(k	γ(k	NOUN
ejpam-4137	82	2	+	+	CCONJ
ejpam-4137	82	3	1	1	X
ejpam-4137	82	4	)	)	PUNCT
ejpam-4137	82	5	=	=	SYM
ejpam-4137	83	1	−	−	PROPN
ejpam-4137	83	2	1	1	NUM
ejpam-4137	83	3	2πi	2πi	NOUN
ejpam-4137	83	4	∫	∫	PROPN
ejpam-4137	83	5	c	c	PROPN
ejpam-4137	83	6	aww−k−1	aww−k−1	PROPN
ejpam-4137	84	1	m+	m+	NUM
ejpam-4137	84	2	w	w	PROPN
ejpam-4137	84	3	dw	dw	PROPN
ejpam-4137	84	4	from	from	ADP
ejpam-4137	84	5	equation	equation	NOUN
ejpam-4137	84	6	(	(	PUNCT
ejpam-4137	84	7	3.383.4	3.383.4	NUM
ejpam-4137	84	8	)	)	PUNCT
ejpam-4137	84	9	in	in	ADP
ejpam-4137	84	10	[	[	X
ejpam-4137	84	11	4	4	X
ejpam-4137	84	12	]	]	PUNCT
ejpam-4137	84	13	where	where	SCONJ
ejpam-4137	84	14	0	0	NUM
ejpam-4137	84	15	<	<	X
ejpam-4137	84	16	re(w	re(w	X
ejpam-4137	84	17	+	+	NOUN
ejpam-4137	84	18	m	m	X
ejpam-4137	84	19	)	)	PUNCT
ejpam-4137	84	20	<	<	X
ejpam-4137	85	1	1	1	NUM
ejpam-4137	85	2	.	.	SYM
ejpam-4137	85	3	5	5	NUM
ejpam-4137	85	4	.	.	X
ejpam-4137	85	5	infinite	infinite	ADJ
ejpam-4137	85	6	sum	sum	NOUN
ejpam-4137	85	7	of	of	ADP
ejpam-4137	85	8	the	the	DET
ejpam-4137	85	9	lerch	lerch	PROPN
ejpam-4137	85	10	function	function	PROPN
ejpam-4137	85	11	in	in	ADP
ejpam-4137	85	12	terms	term	NOUN
ejpam-4137	85	13	of	of	ADP
ejpam-4137	85	14	the	the	DET
ejpam-4137	85	15	lerch	lerch	PROPN
ejpam-4137	85	16	function	function	PROPN
ejpam-4137	85	17	theorem	theorem	VERB
ejpam-4137	85	18	1	1	NUM
ejpam-4137	85	19	.	.	PUNCT
ejpam-4137	86	1	for	for	ADP
ejpam-4137	86	2	all	all	DET
ejpam-4137	86	3	k	k	PROPN
ejpam-4137	86	4	,	,	PUNCT
ejpam-4137	86	5	a	a	DET
ejpam-4137	86	6	,	,	PUNCT
ejpam-4137	86	7	m	m	VERB
ejpam-4137	86	8	∈	∈	PROPN
ejpam-4137	86	9	c	c	NOUN
ejpam-4137	86	10	,	,	PUNCT
ejpam-4137	86	11	∞∑	∞∑	PRON
ejpam-4137	86	12	n=1	n=1	PROPN
ejpam-4137	86	13	2k−n+1	2k−n+1	NUM
ejpam-4137	86	14	(	(	PUNCT
ejpam-4137	86	15	2−n	2−n	NUM
ejpam-4137	86	16	)	)	PUNCT
ejpam-4137	87	1	k	k	NOUN
ejpam-4137	87	2	em21−n	em21−n	PROPN
ejpam-4137	87	3	φ	φ	PROPN
ejpam-4137	87	4	(	(	PUNCT
ejpam-4137	87	5	−e2	−e2	PROPN
ejpam-4137	87	6	1−nm,−k	1−nm,−k	NOUN
ejpam-4137	87	7	,	,	PUNCT
ejpam-4137	87	8	2n−1	2n−1	PROPN
ejpam-4137	87	9	log(a	log(a	PROPN
ejpam-4137	87	10	)	)	PUNCT
ejpam-4137	88	1	+	+	CCONJ
ejpam-4137	88	2	1	1	X
ejpam-4137	88	3	)	)	PUNCT
ejpam-4137	88	4	=	=	PUNCT
ejpam-4137	88	5	−a−m(−m)−kγ(k	−a−m(−m)−kγ(k	NUM
ejpam-4137	88	6	+	+	CCONJ
ejpam-4137	88	7	1,−m	1,−m	NUM
ejpam-4137	88	8	log(a	log(a	PROPN
ejpam-4137	88	9	)	)	PUNCT
ejpam-4137	88	10	)	)	PUNCT
ejpam-4137	89	1	m	m	VERB
ejpam-4137	90	1	−	−	NOUN
ejpam-4137	90	2	2k+1e2mφ	2k+1e2mφ	NUM
ejpam-4137	90	3	(	(	PUNCT
ejpam-4137	90	4	e2m,−k	e2m,−k	PROPN
ejpam-4137	90	5	,	,	PUNCT
ejpam-4137	90	6	log(a	log(a	PROPN
ejpam-4137	90	7	)	)	PUNCT
ejpam-4137	90	8	2	2	NUM
ejpam-4137	91	1	+	+	CCONJ
ejpam-4137	91	2	1	1	NUM
ejpam-4137	91	3	)	)	PUNCT
ejpam-4137	91	4	(	(	PUNCT
ejpam-4137	91	5	10	10	NUM
ejpam-4137	91	6	)	)	PUNCT
ejpam-4137	91	7	or	or	CCONJ
ejpam-4137	91	8	∞∑	∞∑	NUM
ejpam-4137	91	9	n=1	n=1	PROPN
ejpam-4137	91	10	2k−n+1	2k−n+1	NUM
ejpam-4137	91	11	(	(	PUNCT
ejpam-4137	91	12	2−n	2−n	NUM
ejpam-4137	91	13	)	)	PUNCT
ejpam-4137	92	1	k	k	PROPN
ejpam-4137	92	2	m2−n	m2−n	PROPN
ejpam-4137	92	3	φ	φ	PROPN
ejpam-4137	92	4	(	(	PUNCT
ejpam-4137	92	5	−m2−n	−m2−n	PROPN
ejpam-4137	92	6	,	,	PUNCT
ejpam-4137	92	7	−k	−k	PROPN
ejpam-4137	92	8	,	,	PUNCT
ejpam-4137	92	9	2n(a−	2n(a−	NUM
ejpam-4137	92	10	1	1	NUM
ejpam-4137	92	11	)	)	PUNCT
ejpam-4137	92	12	+	+	CCONJ
ejpam-4137	92	13	1	1	X
ejpam-4137	92	14	)	)	PUNCT
ejpam-4137	92	15	=	=	SYM
ejpam-4137	92	16	−2k+1mφ(m,−k	−2k+1mφ(m,−k	NOUN
ejpam-4137	92	17	,	,	PUNCT
ejpam-4137	92	18	a)−	a)−	PROPN
ejpam-4137	92	19	2k+1	2k+1	PROPN
ejpam-4137	92	20	(	(	PUNCT
ejpam-4137	92	21	e2(a−1	e2(a−1	NOUN
ejpam-4137	92	22	)	)	PUNCT
ejpam-4137	92	23	)	)	PUNCT
ejpam-4137	93	1	−	−	PROPN
ejpam-4137	94	1	log(m	log(m	PROPN
ejpam-4137	94	2	)	)	PUNCT
ejpam-4137	94	3	2	2	NUM
ejpam-4137	94	4	(	(	PUNCT
ejpam-4137	94	5	−	−	PROPN
ejpam-4137	94	6	log(m))−kγ(k	log(m))−kγ(k	PROPN
ejpam-4137	94	7	+	+	NOUN
ejpam-4137	94	8	1	1	NUM
ejpam-4137	94	9	,	,	PUNCT
ejpam-4137	94	10	(	(	PUNCT
ejpam-4137	94	11	1−	1−	NUM
ejpam-4137	94	12	a	a	PRON
ejpam-4137	94	13	)	)	PUNCT
ejpam-4137	94	14	log(m	log(m	PROPN
ejpam-4137	94	15	)	)	PUNCT
ejpam-4137	94	16	)	)	PUNCT
ejpam-4137	95	1	log(m	log(m	PROPN
ejpam-4137	95	2	)	)	PUNCT
ejpam-4137	95	3	(	(	PUNCT
ejpam-4137	95	4	11	11	NUM
ejpam-4137	95	5	)	)	PUNCT
ejpam-4137	95	6	r.	r.	PROPN
ejpam-4137	95	7	reynolds	reynolds	PROPN
ejpam-4137	95	8	,	,	PUNCT
ejpam-4137	95	9	a.	a.	PROPN
ejpam-4137	95	10	stauffer	stauffer	PROPN
ejpam-4137	95	11	/	/	SYM
ejpam-4137	95	12	eur	eur	PROPN
ejpam-4137	95	13	.	.	PUNCT
ejpam-4137	96	1	j.	j.	PROPN
ejpam-4137	96	2	pure	pure	PROPN
ejpam-4137	96	3	appl	appl	PROPN
ejpam-4137	96	4	.	.	PROPN
ejpam-4137	96	5	math	math	PROPN
ejpam-4137	96	6	,	,	PUNCT
ejpam-4137	96	7	15	15	NUM
ejpam-4137	96	8	(	(	PUNCT
ejpam-4137	96	9	1	1	NUM
ejpam-4137	96	10	)	)	PUNCT
ejpam-4137	96	11	(	(	PUNCT
ejpam-4137	96	12	2022	2022	NUM
ejpam-4137	96	13	)	)	PUNCT
ejpam-4137	96	14	,	,	PUNCT
ejpam-4137	96	15	158	158	NUM
ejpam-4137	96	16	-	-	SYM
ejpam-4137	96	17	168	168	NUM
ejpam-4137	96	18	162	162	NUM
ejpam-4137	96	19	proof	proof	NOUN
ejpam-4137	96	20	.	.	PUNCT
ejpam-4137	97	1	observe	observe	VERB
ejpam-4137	97	2	that	that	SCONJ
ejpam-4137	97	3	the	the	DET
ejpam-4137	97	4	the	the	DET
ejpam-4137	97	5	addition	addition	NOUN
ejpam-4137	97	6	of	of	ADP
ejpam-4137	97	7	the	the	DET
ejpam-4137	97	8	right	right	ADJ
ejpam-4137	97	9	-	-	PUNCT
ejpam-4137	97	10	hand	hand	NOUN
ejpam-4137	97	11	sides	side	NOUN
ejpam-4137	97	12	of	of	ADP
ejpam-4137	97	13	equations	equation	NOUN
ejpam-4137	97	14	(	(	PUNCT
ejpam-4137	97	15	5	5	NUM
ejpam-4137	97	16	)	)	PUNCT
ejpam-4137	97	17	and	and	CCONJ
ejpam-4137	97	18	(	(	PUNCT
ejpam-4137	97	19	6	6	NUM
ejpam-4137	97	20	)	)	PUNCT
ejpam-4137	97	21	is	be	AUX
ejpam-4137	97	22	equal	equal	ADJ
ejpam-4137	97	23	to	to	ADP
ejpam-4137	97	24	the	the	DET
ejpam-4137	97	25	addition	addition	NOUN
ejpam-4137	97	26	of	of	ADP
ejpam-4137	97	27	the	the	DET
ejpam-4137	97	28	right	right	ADJ
ejpam-4137	97	29	-	-	PUNCT
ejpam-4137	97	30	hand	hand	NOUN
ejpam-4137	97	31	sides	side	NOUN
ejpam-4137	97	32	of	of	ADP
ejpam-4137	97	33	equation	equation	NOUN
ejpam-4137	97	34	(	(	PUNCT
ejpam-4137	97	35	7	7	NUM
ejpam-4137	97	36	)	)	PUNCT
ejpam-4137	97	37	,	,	PUNCT
ejpam-4137	97	38	(	(	PUNCT
ejpam-4137	97	39	8)	8)	NUM
ejpam-4137	97	40	and	and	CCONJ
ejpam-4137	97	41	(	(	PUNCT
ejpam-4137	97	42	9	9	NUM
ejpam-4137	97	43	)	)	PUNCT
ejpam-4137	97	44	so	so	SCONJ
ejpam-4137	97	45	we	we	PRON
ejpam-4137	97	46	may	may	AUX
ejpam-4137	97	47	equate	equate	VERB
ejpam-4137	97	48	the	the	DET
ejpam-4137	97	49	left	left	ADJ
ejpam-4137	97	50	-	-	PUNCT
ejpam-4137	97	51	hand	hand	NOUN
ejpam-4137	97	52	sides	side	NOUN
ejpam-4137	97	53	and	and	CCONJ
ejpam-4137	97	54	simplify	simplify	VERB
ejpam-4137	97	55	the	the	DET
ejpam-4137	97	56	the	the	DET
ejpam-4137	97	57	gamma	gamma	NOUN
ejpam-4137	97	58	function	function	NOUN
ejpam-4137	97	59	to	to	PART
ejpam-4137	97	60	yield	yield	VERB
ejpam-4137	97	61	the	the	DET
ejpam-4137	97	62	stated	state	VERB
ejpam-4137	97	63	result	result	NOUN
ejpam-4137	97	64	.	.	PUNCT
ejpam-4137	98	1	6	6	X
ejpam-4137	98	2	.	.	X
ejpam-4137	98	3	special	special	ADJ
ejpam-4137	98	4	cases	case	NOUN
ejpam-4137	98	5	in	in	ADP
ejpam-4137	98	6	this	this	DET
ejpam-4137	98	7	section	section	NOUN
ejpam-4137	98	8	we	we	PRON
ejpam-4137	98	9	will	will	AUX
ejpam-4137	98	10	evaluate	evaluate	VERB
ejpam-4137	98	11	equation	equation	NOUN
ejpam-4137	98	12	(	(	PUNCT
ejpam-4137	98	13	10	10	NUM
ejpam-4137	98	14	)	)	PUNCT
ejpam-4137	98	15	for	for	ADP
ejpam-4137	98	16	various	various	ADJ
ejpam-4137	98	17	parameter	parameter	NOUN
ejpam-4137	98	18	ranges	range	NOUN
ejpam-4137	98	19	.	.	PUNCT
ejpam-4137	99	1	we	we	PRON
ejpam-4137	99	2	will	will	AUX
ejpam-4137	99	3	use	use	VERB
ejpam-4137	99	4	the	the	DET
ejpam-4137	99	5	following	follow	VERB
ejpam-4137	99	6	functions	function	NOUN
ejpam-4137	99	7	for	for	ADP
ejpam-4137	99	8	simplification	simplification	NOUN
ejpam-4137	99	9	;	;	PUNCT
ejpam-4137	99	10	exponential	exponential	ADJ
ejpam-4137	99	11	integral	integral	ADJ
ejpam-4137	99	12	function	function	NOUN
ejpam-4137	99	13	en(z	en(z	NOUN
ejpam-4137	99	14	)	)	PUNCT
ejpam-4137	99	15	given	give	VERB
ejpam-4137	99	16	in	in	ADP
ejpam-4137	99	17	section	section	NOUN
ejpam-4137	99	18	(	(	PUNCT
ejpam-4137	99	19	8.19	8.19	NUM
ejpam-4137	99	20	)	)	PUNCT
ejpam-4137	99	21	in	in	ADP
ejpam-4137	99	22	[	[	X
ejpam-4137	99	23	3	3	NUM
ejpam-4137	99	24	]	]	PUNCT
ejpam-4137	99	25	,	,	PUNCT
ejpam-4137	99	26	and	and	CCONJ
ejpam-4137	99	27	the	the	DET
ejpam-4137	99	28	exponential	exponential	ADJ
ejpam-4137	99	29	integral	integral	ADJ
ejpam-4137	99	30	function	function	NOUN
ejpam-4137	99	31	ei(z	ei(z	ADV
ejpam-4137	99	32	)	)	PUNCT
ejpam-4137	99	33	given	give	VERB
ejpam-4137	99	34	in	in	ADP
ejpam-4137	99	35	equation	equation	NOUN
ejpam-4137	99	36	(	(	PUNCT
ejpam-4137	99	37	6.11.2	6.11.2	NUM
ejpam-4137	99	38	)	)	PUNCT
ejpam-4137	100	1	[	[	X
ejpam-4137	100	2	3	3	NUM
ejpam-4137	100	3	]	]	PUNCT
ejpam-4137	100	4	,	,	PUNCT
ejpam-4137	100	5	and	and	CCONJ
ejpam-4137	100	6	the	the	DET
ejpam-4137	100	7	riemann	riemann	PROPN
ejpam-4137	100	8	zeta	zeta	PROPN
ejpam-4137	100	9	function	function	NOUN
ejpam-4137	100	10	given	give	VERB
ejpam-4137	100	11	in	in	ADP
ejpam-4137	100	12	equation	equation	NOUN
ejpam-4137	100	13	(	(	PUNCT
ejpam-4137	100	14	25.2.1	25.2.1	NUM
ejpam-4137	100	15	)	)	PUNCT
ejpam-4137	100	16	in	in	ADP
ejpam-4137	100	17	[	[	X
ejpam-4137	100	18	3	3	NUM
ejpam-4137	100	19	]	]	PUNCT
ejpam-4137	100	20	.	.	PUNCT
ejpam-4137	100	21	example	example	NOUN
ejpam-4137	101	1	1	1	NUM
ejpam-4137	101	2	.	.	PUNCT
ejpam-4137	102	1	the	the	DET
ejpam-4137	102	2	degenerate	degenerate	ADJ
ejpam-4137	102	3	case	case	NOUN
ejpam-4137	102	4	.	.	PUNCT
ejpam-4137	103	1	∞∑	∞∑	NUM
ejpam-4137	103	2	n=1	n=1	NUM
ejpam-4137	103	3	21−n	21−n	NUM
ejpam-4137	103	4	(	(	PUNCT
ejpam-4137	103	5	1−	1−	NUM
ejpam-4137	103	6	1	1	NUM
ejpam-4137	103	7	em21−n	em21−n	NOUN
ejpam-4137	103	8	+	+	NOUN
ejpam-4137	103	9	1	1	NUM
ejpam-4137	103	10	)	)	PUNCT
ejpam-4137	103	11	=	=	NOUN
ejpam-4137	104	1	∞∑	∞∑	NUM
ejpam-4137	104	2	n=1	n=1	NUM
ejpam-4137	104	3	2−n	2−n	NUM
ejpam-4137	104	4	(	(	PUNCT
ejpam-4137	104	5	tanh	tanh	PROPN
ejpam-4137	104	6	(	(	PUNCT
ejpam-4137	104	7	m2−n	m2−n	PROPN
ejpam-4137	104	8	)	)	PUNCT
ejpam-4137	104	9	+	+	CCONJ
ejpam-4137	104	10	1	1	X
ejpam-4137	104	11	)	)	PUNCT
ejpam-4137	104	12	=	=	SYM
ejpam-4137	104	13	−	−	PROPN
ejpam-4137	104	14	1	1	NUM
ejpam-4137	104	15	m	m	NOUN
ejpam-4137	104	16	+	+	CCONJ
ejpam-4137	104	17	coth(m	coth(m	NOUN
ejpam-4137	104	18	)	)	PUNCT
ejpam-4137	104	19	+	+	CCONJ
ejpam-4137	104	20	1	1	NUM
ejpam-4137	104	21	(	(	PUNCT
ejpam-4137	104	22	12	12	NUM
ejpam-4137	104	23	)	)	PUNCT
ejpam-4137	104	24	proof	proof	NOUN
ejpam-4137	104	25	.	.	PUNCT
ejpam-4137	105	1	use	use	VERB
ejpam-4137	105	2	equation	equation	NOUN
ejpam-4137	105	3	(	(	PUNCT
ejpam-4137	105	4	10	10	NUM
ejpam-4137	105	5	)	)	PUNCT
ejpam-4137	105	6	and	and	CCONJ
ejpam-4137	105	7	set	set	VERB
ejpam-4137	105	8	k	k	PROPN
ejpam-4137	105	9	=	=	PUNCT
ejpam-4137	105	10	0	0	PUNCT
ejpam-4137	105	11	and	and	CCONJ
ejpam-4137	105	12	simplify	simplify	VERB
ejpam-4137	105	13	using	use	VERB
ejpam-4137	105	14	entry	entry	NOUN
ejpam-4137	105	15	(	(	PUNCT
ejpam-4137	105	16	4	4	NUM
ejpam-4137	105	17	)	)	PUNCT
ejpam-4137	105	18	in	in	ADP
ejpam-4137	105	19	table	table	NOUN
ejpam-4137	105	20	below	below	ADV
ejpam-4137	105	21	(	(	PUNCT
ejpam-4137	105	22	64:12:7	64:12:7	NUM
ejpam-4137	105	23	)	)	PUNCT
ejpam-4137	105	24	in	in	ADP
ejpam-4137	105	25	[	[	X
ejpam-4137	105	26	9	9	NUM
ejpam-4137	105	27	]	]	PUNCT
ejpam-4137	105	28	.	.	PUNCT
ejpam-4137	105	29	example	example	NOUN
ejpam-4137	106	1	2	2	NUM
ejpam-4137	106	2	.	.	X
ejpam-4137	106	3	apéry	apéry	PROPN
ejpam-4137	106	4	’s	’s	NOUN
ejpam-4137	106	5	constant	constant	ADJ
ejpam-4137	106	6	ζ(3	ζ(3	NOUN
ejpam-4137	106	7	)	)	PUNCT
ejpam-4137	106	8	(	(	PUNCT
ejpam-4137	106	9	13	13	NUM
ejpam-4137	106	10	)	)	PUNCT
ejpam-4137	106	11	∞∑	∞∑	NUM
ejpam-4137	106	12	n	n	NOUN
ejpam-4137	106	13	=	=	SYM
ejpam-4137	106	14	1	1	NUM
ejpam-4137	106	15	(	(	PUNCT
ejpam-4137	106	16	−1)2	−1)2	X
ejpam-4137	106	17	−n	−n	ADJ
ejpam-4137	106	18	4n−1φ	4n−1φ	NUM
ejpam-4137	106	19	(	(	PUNCT
ejpam-4137	106	20	(	(	PUNCT
ejpam-4137	106	21	−1)1	−1)1	PUNCT
ejpam-4137	106	22	+	+	NOUN
ejpam-4137	106	23	2−n	2−n	NUM
ejpam-4137	106	24	,	,	PUNCT
ejpam-4137	106	25	3	3	NUM
ejpam-4137	106	26	,	,	PUNCT
ejpam-4137	106	27	1	1	NUM
ejpam-4137	106	28	+	+	NUM
ejpam-4137	106	29	2n	2n	NUM
ejpam-4137	106	30	)	)	PUNCT
ejpam-4137	106	31	=	=	SYM
ejpam-4137	107	1	1	1	NUM
ejpam-4137	107	2	16	16	NUM
ejpam-4137	107	3	(	(	PUNCT
ejpam-4137	107	4	−4e3(−iπ)−	−4e3(−iπ)−	NOUN
ejpam-4137	107	5	3ζ(3	3ζ(3	NUM
ejpam-4137	107	6	)	)	PUNCT
ejpam-4137	108	1	+	+	CCONJ
ejpam-4137	108	2	4	4	X
ejpam-4137	108	3	)	)	PUNCT
ejpam-4137	108	4	proof	proof	NOUN
ejpam-4137	108	5	.	.	PUNCT
ejpam-4137	109	1	use	use	VERB
ejpam-4137	109	2	equation	equation	NOUN
ejpam-4137	109	3	(	(	PUNCT
ejpam-4137	109	4	11	11	NUM
ejpam-4137	109	5	)	)	PUNCT
ejpam-4137	109	6	and	and	CCONJ
ejpam-4137	109	7	set	set	VERB
ejpam-4137	109	8	m	m	PROPN
ejpam-4137	109	9	=	=	NOUN
ejpam-4137	109	10	−1	−1	NOUN
ejpam-4137	109	11	and	and	CCONJ
ejpam-4137	109	12	simplify	simplify	VERB
ejpam-4137	109	13	in	in	ADP
ejpam-4137	109	14	terms	term	NOUN
ejpam-4137	109	15	of	of	ADP
ejpam-4137	109	16	the	the	DET
ejpam-4137	109	17	hurwitz	hurwitz	PROPN
ejpam-4137	109	18	zeta	zeta	PROPN
ejpam-4137	109	19	function	function	PROPN
ejpam-4137	109	20	ζ(s	ζ(s	PROPN
ejpam-4137	109	21	,	,	PUNCT
ejpam-4137	109	22	a	a	PRON
ejpam-4137	109	23	)	)	PUNCT
ejpam-4137	109	24	using	use	VERB
ejpam-4137	109	25	entry	entry	NOUN
ejpam-4137	109	26	(	(	PUNCT
ejpam-4137	109	27	4	4	NUM
ejpam-4137	109	28	)	)	PUNCT
ejpam-4137	109	29	in	in	ADP
ejpam-4137	109	30	table	table	NOUN
ejpam-4137	109	31	below	below	ADV
ejpam-4137	109	32	(	(	PUNCT
ejpam-4137	109	33	64:12:7	64:12:7	NUM
ejpam-4137	109	34	)	)	PUNCT
ejpam-4137	109	35	in	in	ADP
ejpam-4137	109	36	[	[	X
ejpam-4137	109	37	9	9	NUM
ejpam-4137	109	38	]	]	PUNCT
ejpam-4137	109	39	.	.	PUNCT
ejpam-4137	110	1	next	next	ADJ
ejpam-4137	110	2	set	set	VERB
ejpam-4137	110	3	k	k	PROPN
ejpam-4137	110	4	=	=	PUNCT
ejpam-4137	110	5	−3	−3	PROPN
ejpam-4137	110	6	,	,	PUNCT
ejpam-4137	110	7	a	a	DET
ejpam-4137	110	8	=	=	SYM
ejpam-4137	110	9	2	2	NUM
ejpam-4137	110	10	and	and	CCONJ
ejpam-4137	110	11	simplify	simplify	VERB
ejpam-4137	110	12	using	use	VERB
ejpam-4137	110	13	equation	equation	NOUN
ejpam-4137	110	14	(	(	PUNCT
ejpam-4137	110	15	8.19.2	8.19.2	NUM
ejpam-4137	110	16	)	)	PUNCT
ejpam-4137	110	17	in	in	ADP
ejpam-4137	110	18	[	[	X
ejpam-4137	110	19	3	3	NUM
ejpam-4137	110	20	]	]	PUNCT
ejpam-4137	110	21	and	and	CCONJ
ejpam-4137	110	22	entry	entry	NOUN
ejpam-4137	110	23	(	(	PUNCT
ejpam-4137	110	24	2	2	NUM
ejpam-4137	110	25	)	)	PUNCT
ejpam-4137	110	26	in	in	ADP
ejpam-4137	110	27	table	table	NOUN
ejpam-4137	110	28	below	below	ADV
ejpam-4137	110	29	(	(	PUNCT
ejpam-4137	110	30	64:7	64:7	NUM
ejpam-4137	110	31	)	)	PUNCT
ejpam-4137	110	32	in	in	ADP
ejpam-4137	110	33	[	[	X
ejpam-4137	110	34	9	9	NUM
ejpam-4137	110	35	]	]	PUNCT
ejpam-4137	110	36	.	.	PUNCT
ejpam-4137	111	1	example	example	NOUN
ejpam-4137	112	1	3	3	NUM
ejpam-4137	112	2	.	.	PUNCT
ejpam-4137	112	3	fundamental	fundamental	ADJ
ejpam-4137	112	4	constant	constant	ADJ
ejpam-4137	112	5	ζ(5	ζ(5	PROPN
ejpam-4137	112	6	)	)	PUNCT
ejpam-4137	112	7	(	(	PUNCT
ejpam-4137	112	8	14	14	NUM
ejpam-4137	112	9	)	)	PUNCT
ejpam-4137	112	10	∞∑	∞∑	NUM
ejpam-4137	112	11	n	n	NOUN
ejpam-4137	112	12	=	=	SYM
ejpam-4137	112	13	1	1	NUM
ejpam-4137	112	14	(	(	PUNCT
ejpam-4137	112	15	−1)2	−1)2	X
ejpam-4137	112	16	−n	−n	ADJ
ejpam-4137	112	17	16n−1φ	16n−1φ	NOUN
ejpam-4137	112	18	(	(	PUNCT
ejpam-4137	112	19	(	(	PUNCT
ejpam-4137	112	20	−1)1	−1)1	PUNCT
ejpam-4137	112	21	+	+	NOUN
ejpam-4137	112	22	2−n	2−n	NUM
ejpam-4137	112	23	,	,	PUNCT
ejpam-4137	112	24	5	5	NUM
ejpam-4137	112	25	,	,	PUNCT
ejpam-4137	112	26	1	1	NUM
ejpam-4137	112	27	+	+	NUM
ejpam-4137	112	28	2n	2n	NUM
ejpam-4137	112	29	)	)	PUNCT
ejpam-4137	112	30	=	=	SYM
ejpam-4137	112	31	1	1	NUM
ejpam-4137	112	32	256	256	NUM
ejpam-4137	112	33	(	(	PUNCT
ejpam-4137	112	34	−16e5(−iπ)−	−16e5(−iπ)−	X
ejpam-4137	112	35	15ζ(5	15ζ(5	NUM
ejpam-4137	112	36	)	)	PUNCT
ejpam-4137	112	37	+	+	NUM
ejpam-4137	112	38	16	16	X
ejpam-4137	112	39	)	)	PUNCT
ejpam-4137	112	40	proof	proof	NOUN
ejpam-4137	112	41	.	.	PUNCT
ejpam-4137	113	1	use	use	VERB
ejpam-4137	113	2	equation	equation	NOUN
ejpam-4137	113	3	(	(	PUNCT
ejpam-4137	113	4	11	11	NUM
ejpam-4137	113	5	)	)	PUNCT
ejpam-4137	113	6	and	and	CCONJ
ejpam-4137	113	7	set	set	VERB
ejpam-4137	113	8	m	m	PROPN
ejpam-4137	113	9	=	=	NOUN
ejpam-4137	113	10	−1	−1	NOUN
ejpam-4137	113	11	and	and	CCONJ
ejpam-4137	113	12	simplify	simplify	VERB
ejpam-4137	113	13	in	in	ADP
ejpam-4137	113	14	terms	term	NOUN
ejpam-4137	113	15	of	of	ADP
ejpam-4137	113	16	the	the	DET
ejpam-4137	113	17	hurwitz	hurwitz	PROPN
ejpam-4137	113	18	zeta	zeta	PROPN
ejpam-4137	113	19	function	function	PROPN
ejpam-4137	113	20	ζ(s	ζ(s	PROPN
ejpam-4137	113	21	,	,	PUNCT
ejpam-4137	113	22	a	a	PRON
ejpam-4137	113	23	)	)	PUNCT
ejpam-4137	113	24	using	use	VERB
ejpam-4137	113	25	entry	entry	NOUN
ejpam-4137	113	26	(	(	PUNCT
ejpam-4137	113	27	4	4	NUM
ejpam-4137	113	28	)	)	PUNCT
ejpam-4137	113	29	in	in	ADP
ejpam-4137	113	30	table	table	NOUN
ejpam-4137	113	31	below	below	ADV
ejpam-4137	113	32	(	(	PUNCT
ejpam-4137	113	33	64:12:7	64:12:7	NUM
ejpam-4137	113	34	)	)	PUNCT
ejpam-4137	113	35	in	in	ADP
ejpam-4137	113	36	[	[	X
ejpam-4137	113	37	9	9	NUM
ejpam-4137	113	38	]	]	PUNCT
ejpam-4137	113	39	.	.	PUNCT
ejpam-4137	114	1	next	next	ADJ
ejpam-4137	114	2	set	set	VERB
ejpam-4137	114	3	k	k	PROPN
ejpam-4137	114	4	=	=	PUNCT
ejpam-4137	114	5	−5	−5	PROPN
ejpam-4137	114	6	,	,	PUNCT
ejpam-4137	114	7	a	a	DET
ejpam-4137	114	8	=	=	SYM
ejpam-4137	114	9	2	2	NUM
ejpam-4137	114	10	and	and	CCONJ
ejpam-4137	114	11	simplify	simplify	VERB
ejpam-4137	114	12	using	use	VERB
ejpam-4137	114	13	equation	equation	NOUN
ejpam-4137	114	14	(	(	PUNCT
ejpam-4137	114	15	8.19.2	8.19.2	NUM
ejpam-4137	114	16	)	)	PUNCT
ejpam-4137	114	17	in	in	ADP
ejpam-4137	114	18	[	[	X
ejpam-4137	114	19	3	3	NUM
ejpam-4137	114	20	]	]	PUNCT
ejpam-4137	114	21	and	and	CCONJ
ejpam-4137	114	22	entry	entry	NOUN
ejpam-4137	114	23	(	(	PUNCT
ejpam-4137	114	24	2	2	NUM
ejpam-4137	114	25	)	)	PUNCT
ejpam-4137	114	26	in	in	ADP
ejpam-4137	114	27	table	table	NOUN
ejpam-4137	114	28	below	below	ADV
ejpam-4137	114	29	(	(	PUNCT
ejpam-4137	114	30	64:7	64:7	NUM
ejpam-4137	114	31	)	)	PUNCT
ejpam-4137	114	32	in	in	ADP
ejpam-4137	114	33	[	[	X
ejpam-4137	114	34	9	9	NUM
ejpam-4137	114	35	]	]	PUNCT
ejpam-4137	114	36	.	.	PUNCT
ejpam-4137	115	1	example	example	NOUN
ejpam-4137	116	1	4	4	NUM
ejpam-4137	116	2	.	.	X
ejpam-4137	116	3	catalan	catalan	NOUN
ejpam-4137	116	4	’s	’s	PART
ejpam-4137	116	5	constant	constant	ADJ
ejpam-4137	116	6	c	c	NOUN
ejpam-4137	116	7	∞∑	∞∑	NUM
ejpam-4137	116	8	n=1	n=1	PROPN
ejpam-4137	116	9	(	(	PUNCT
ejpam-4137	116	10	−1)2	−1)2	X
ejpam-4137	116	11	−n	−n	ADJ
ejpam-4137	116	12	2n−1φ	2n−1φ	NUM
ejpam-4137	116	13	(	(	PUNCT
ejpam-4137	116	14	(	(	PUNCT
ejpam-4137	116	15	−1)1	−1)1	PUNCT
ejpam-4137	116	16	+	+	NOUN
ejpam-4137	116	17	2−n	2−n	NUM
ejpam-4137	116	18	,	,	PUNCT
ejpam-4137	116	19	2	2	NUM
ejpam-4137	116	20	,	,	PUNCT
ejpam-4137	116	21	1	1	NUM
ejpam-4137	116	22	+	+	CCONJ
ejpam-4137	116	23	2n−1	2n−1	NUM
ejpam-4137	116	24	)	)	PUNCT
ejpam-4137	117	1	=	=	PUNCT
ejpam-4137	118	1	−2c	−2c	ADJ
ejpam-4137	118	2	+	+	CCONJ
ejpam-4137	118	3	3	3	NUM
ejpam-4137	118	4	+	+	SYM
ejpam-4137	118	5	1	1	NUM
ejpam-4137	118	6	2	2	NUM
ejpam-4137	118	7	πγ	πγ	NOUN
ejpam-4137	118	8	(	(	PUNCT
ejpam-4137	118	9	0,−	0,−	NUM
ejpam-4137	118	10	iπ	iπ	PRON
ejpam-4137	118	11	2	2	NUM
ejpam-4137	118	12	)	)	PUNCT
ejpam-4137	118	13	(	(	PUNCT
ejpam-4137	118	14	15	15	X
ejpam-4137	118	15	)	)	PUNCT
ejpam-4137	118	16	r.	r.	PROPN
ejpam-4137	118	17	reynolds	reynolds	PROPN
ejpam-4137	118	18	,	,	PUNCT
ejpam-4137	118	19	a.	a.	PROPN
ejpam-4137	118	20	stauffer	stauffer	PROPN
ejpam-4137	118	21	/	/	SYM
ejpam-4137	118	22	eur	eur	PROPN
ejpam-4137	118	23	.	.	PUNCT
ejpam-4137	119	1	j.	j.	PROPN
ejpam-4137	119	2	pure	pure	PROPN
ejpam-4137	119	3	appl	appl	PROPN
ejpam-4137	119	4	.	.	PROPN
ejpam-4137	119	5	math	math	PROPN
ejpam-4137	119	6	,	,	PUNCT
ejpam-4137	119	7	15	15	NUM
ejpam-4137	119	8	(	(	PUNCT
ejpam-4137	119	9	1	1	NUM
ejpam-4137	119	10	)	)	PUNCT
ejpam-4137	119	11	(	(	PUNCT
ejpam-4137	119	12	2022	2022	NUM
ejpam-4137	119	13	)	)	PUNCT
ejpam-4137	119	14	,	,	PUNCT
ejpam-4137	119	15	158	158	NUM
ejpam-4137	119	16	-	-	SYM
ejpam-4137	119	17	168	168	NUM
ejpam-4137	119	18	163	163	NUM
ejpam-4137	119	19	proof	proof	NOUN
ejpam-4137	119	20	.	.	PUNCT
ejpam-4137	120	1	use	use	VERB
ejpam-4137	120	2	equation	equation	NOUN
ejpam-4137	120	3	(	(	PUNCT
ejpam-4137	120	4	11	11	NUM
ejpam-4137	120	5	)	)	PUNCT
ejpam-4137	120	6	and	and	CCONJ
ejpam-4137	120	7	set	set	VERB
ejpam-4137	120	8	m	m	PROPN
ejpam-4137	120	9	=	=	NOUN
ejpam-4137	120	10	−1	−1	NOUN
ejpam-4137	120	11	and	and	CCONJ
ejpam-4137	120	12	simplify	simplify	VERB
ejpam-4137	120	13	in	in	ADP
ejpam-4137	120	14	terms	term	NOUN
ejpam-4137	120	15	of	of	ADP
ejpam-4137	120	16	the	the	DET
ejpam-4137	120	17	hurwitz	hurwitz	PROPN
ejpam-4137	120	18	zeta	zeta	PROPN
ejpam-4137	120	19	function	function	PROPN
ejpam-4137	120	20	ζ(s	ζ(s	PROPN
ejpam-4137	120	21	,	,	PUNCT
ejpam-4137	120	22	a	a	PRON
ejpam-4137	120	23	)	)	PUNCT
ejpam-4137	120	24	using	use	VERB
ejpam-4137	120	25	entry	entry	NOUN
ejpam-4137	120	26	(	(	PUNCT
ejpam-4137	120	27	4	4	NUM
ejpam-4137	120	28	)	)	PUNCT
ejpam-4137	120	29	in	in	ADP
ejpam-4137	120	30	table	table	NOUN
ejpam-4137	120	31	below	below	ADV
ejpam-4137	120	32	(	(	PUNCT
ejpam-4137	120	33	64:12:7	64:12:7	NUM
ejpam-4137	120	34	)	)	PUNCT
ejpam-4137	120	35	in	in	ADP
ejpam-4137	120	36	[	[	X
ejpam-4137	120	37	9	9	NUM
ejpam-4137	120	38	]	]	PUNCT
ejpam-4137	120	39	.	.	PUNCT
ejpam-4137	121	1	next	next	ADJ
ejpam-4137	121	2	set	set	VERB
ejpam-4137	121	3	k	k	PROPN
ejpam-4137	121	4	=	=	SYM
ejpam-4137	121	5	−2	−2	PROPN
ejpam-4137	121	6	,	,	PUNCT
ejpam-4137	121	7	a	a	DET
ejpam-4137	121	8	=	=	SYM
ejpam-4137	121	9	3/2	3/2	NUM
ejpam-4137	121	10	and	and	CCONJ
ejpam-4137	121	11	simplify	simplify	VERB
ejpam-4137	121	12	using	use	VERB
ejpam-4137	121	13	equation	equation	NOUN
ejpam-4137	121	14	(	(	PUNCT
ejpam-4137	121	15	8.19.2	8.19.2	NUM
ejpam-4137	121	16	)	)	PUNCT
ejpam-4137	121	17	in	in	ADP
ejpam-4137	121	18	[	[	X
ejpam-4137	121	19	3	3	NUM
ejpam-4137	121	20	]	]	PUNCT
ejpam-4137	121	21	,	,	PUNCT
ejpam-4137	121	22	equation	equation	NOUN
ejpam-4137	121	23	(	(	PUNCT
ejpam-4137	121	24	64:4:1	64:4:1	NUM
ejpam-4137	121	25	)	)	PUNCT
ejpam-4137	121	26	in	in	ADP
ejpam-4137	121	27	[	[	X
ejpam-4137	121	28	9	9	NUM
ejpam-4137	121	29	]	]	PUNCT
ejpam-4137	121	30	and	and	CCONJ
ejpam-4137	121	31	equation	equation	NOUN
ejpam-4137	121	32	(	(	PUNCT
ejpam-4137	121	33	2.2.1.2.7	2.2.1.2.7	NUM
ejpam-4137	121	34	)	)	PUNCT
ejpam-4137	121	35	in	in	ADP
ejpam-4137	121	36	[	[	X
ejpam-4137	121	37	7	7	NUM
ejpam-4137	121	38	]	]	PUNCT
ejpam-4137	121	39	.	.	PUNCT
ejpam-4137	122	1	example	example	NOUN
ejpam-4137	122	2	5	5	NUM
ejpam-4137	122	3	.	.	PUNCT
ejpam-4137	123	1	the	the	DET
ejpam-4137	123	2	exponential	exponential	ADJ
ejpam-4137	123	3	integral	integral	ADJ
ejpam-4137	123	4	function	function	NOUN
ejpam-4137	123	5	en(z	en(z	NOUN
ejpam-4137	123	6	)	)	PUNCT
ejpam-4137	123	7	∞∑	∞∑	NUM
ejpam-4137	123	8	n=1	n=1	PROPN
ejpam-4137	123	9	(	(	PUNCT
ejpam-4137	123	10	−1)2	−1)2	X
ejpam-4137	123	11	−n	−n	ADV
ejpam-4137	123	12	φ	φ	PROPN
ejpam-4137	123	13	(	(	PUNCT
ejpam-4137	123	14	(	(	PUNCT
ejpam-4137	123	15	−1)1	−1)1	PUNCT
ejpam-4137	123	16	+	+	NOUN
ejpam-4137	123	17	2−n	2−n	NUM
ejpam-4137	123	18	,	,	PUNCT
ejpam-4137	123	19	1	1	NUM
ejpam-4137	123	20	,	,	PUNCT
ejpam-4137	123	21	1	1	NUM
ejpam-4137	123	22	+	+	CCONJ
ejpam-4137	123	23	2n−1	2n−1	NUM
ejpam-4137	123	24	)	)	PUNCT
ejpam-4137	123	25	=	=	SYM
ejpam-4137	123	26	1	1	NUM
ejpam-4137	123	27	2	2	NUM
ejpam-4137	123	28	(	(	PUNCT
ejpam-4137	123	29	2iei	2iei	NUM
ejpam-4137	123	30	(	(	PUNCT
ejpam-4137	123	31	iπ	iπ	ADV
ejpam-4137	123	32	2	2	X
ejpam-4137	123	33	)	)	PUNCT
ejpam-4137	123	34	+	+	CCONJ
ejpam-4137	123	35	4	4	NUM
ejpam-4137	123	36	+	+	NUM
ejpam-4137	123	37	π	π	NOUN
ejpam-4137	123	38	)	)	PUNCT
ejpam-4137	123	39	(	(	PUNCT
ejpam-4137	123	40	16	16	X
ejpam-4137	123	41	)	)	PUNCT
ejpam-4137	123	42	proof	proof	NOUN
ejpam-4137	123	43	.	.	PUNCT
ejpam-4137	124	1	use	use	VERB
ejpam-4137	124	2	equation	equation	NOUN
ejpam-4137	124	3	(	(	PUNCT
ejpam-4137	124	4	11	11	NUM
ejpam-4137	124	5	)	)	PUNCT
ejpam-4137	124	6	and	and	CCONJ
ejpam-4137	124	7	set	set	VERB
ejpam-4137	124	8	m	m	PROPN
ejpam-4137	124	9	=	=	NOUN
ejpam-4137	124	10	−1	−1	NOUN
ejpam-4137	124	11	and	and	CCONJ
ejpam-4137	124	12	simplify	simplify	VERB
ejpam-4137	124	13	in	in	ADP
ejpam-4137	124	14	terms	term	NOUN
ejpam-4137	124	15	of	of	ADP
ejpam-4137	124	16	the	the	DET
ejpam-4137	124	17	hurwitz	hurwitz	PROPN
ejpam-4137	124	18	zeta	zeta	PROPN
ejpam-4137	124	19	function	function	PROPN
ejpam-4137	124	20	ζ(s	ζ(s	PROPN
ejpam-4137	124	21	,	,	PUNCT
ejpam-4137	124	22	a	a	PRON
ejpam-4137	124	23	)	)	PUNCT
ejpam-4137	124	24	using	use	VERB
ejpam-4137	124	25	entry	entry	NOUN
ejpam-4137	124	26	(	(	PUNCT
ejpam-4137	124	27	4	4	NUM
ejpam-4137	124	28	)	)	PUNCT
ejpam-4137	124	29	in	in	ADP
ejpam-4137	124	30	table	table	NOUN
ejpam-4137	124	31	below	below	ADV
ejpam-4137	124	32	(	(	PUNCT
ejpam-4137	124	33	64:12:7	64:12:7	NUM
ejpam-4137	124	34	)	)	PUNCT
ejpam-4137	124	35	in	in	ADP
ejpam-4137	124	36	[	[	X
ejpam-4137	124	37	9	9	NUM
ejpam-4137	124	38	]	]	PUNCT
ejpam-4137	124	39	.	.	PUNCT
ejpam-4137	125	1	next	next	ADV
ejpam-4137	125	2	we	we	PRON
ejpam-4137	125	3	apply	apply	VERB
ejpam-4137	125	4	l’hopital	l’hopital	PROPN
ejpam-4137	125	5	’s	’s	PART
ejpam-4137	125	6	rule	rule	NOUN
ejpam-4137	125	7	as	as	ADP
ejpam-4137	125	8	k	k	PROPN
ejpam-4137	125	9	→	→	SYM
ejpam-4137	125	10	−1	−1	NOUN
ejpam-4137	125	11	and	and	CCONJ
ejpam-4137	125	12	simplify	simplify	VERB
ejpam-4137	125	13	using	use	VERB
ejpam-4137	125	14	equation	equation	NOUN
ejpam-4137	125	15	(	(	PUNCT
ejpam-4137	125	16	8.19.2	8.19.2	NUM
ejpam-4137	125	17	)	)	PUNCT
ejpam-4137	125	18	in	in	ADP
ejpam-4137	125	19	[	[	X
ejpam-4137	125	20	3	3	NUM
ejpam-4137	125	21	]	]	PUNCT
ejpam-4137	125	22	and	and	CCONJ
ejpam-4137	125	23	equation	equation	NOUN
ejpam-4137	125	24	(	(	PUNCT
ejpam-4137	125	25	64:4:1	64:4:1	NUM
ejpam-4137	125	26	)	)	PUNCT
ejpam-4137	125	27	in	in	ADP
ejpam-4137	125	28	[	[	X
ejpam-4137	125	29	9	9	NUM
ejpam-4137	125	30	]	]	PUNCT
ejpam-4137	125	31	.	.	PUNCT
ejpam-4137	126	1	example	example	NOUN
ejpam-4137	127	1	6	6	NUM
ejpam-4137	127	2	.	.	PUNCT
ejpam-4137	128	1	∞∑	∞∑	NUM
ejpam-4137	128	2	n=1	n=1	NUM
ejpam-4137	128	3	(	(	PUNCT
ejpam-4137	128	4	−1)2	−1)2	X
ejpam-4137	128	5	−n	−n	ADV
ejpam-4137	128	6	(	(	PUNCT
ejpam-4137	128	7	2−n	2−n	NUM
ejpam-4137	128	8	)	)	PUNCT
ejpam-4137	128	9	3/2	3/2	NUM
ejpam-4137	128	10	φ	φ	X
ejpam-4137	128	11	(	(	PUNCT
ejpam-4137	128	12	(	(	PUNCT
ejpam-4137	128	13	−1)1	−1)1	PUNCT
ejpam-4137	128	14	+	+	NOUN
ejpam-4137	128	15	2−n	2−n	NUM
ejpam-4137	128	16	,	,	PUNCT
ejpam-4137	128	17	−1	−1	NOUN
ejpam-4137	128	18	2	2	NUM
ejpam-4137	128	19	,	,	PUNCT
ejpam-4137	128	20	1	1	NUM
ejpam-4137	128	21	+	+	NUM
ejpam-4137	128	22	2n	2n	NUM
ejpam-4137	128	23	)	)	PUNCT
ejpam-4137	129	1	=	=	PRON
ejpam-4137	129	2	−e−	−e−	VERB
ejpam-4137	129	3	1	1	NUM
ejpam-4137	129	4	2	2	NUM
ejpam-4137	129	5	(	(	PUNCT
ejpam-4137	129	6	−iπ	−iπ	SYM
ejpam-4137	129	7	)	)	PUNCT
ejpam-4137	129	8	+	+	CCONJ
ejpam-4137	129	9	(	(	PUNCT
ejpam-4137	129	10	2	2	NUM
ejpam-4137	129	11	√	√	NUM
ejpam-4137	129	12	2−	2−	NUM
ejpam-4137	129	13	1	1	NUM
ejpam-4137	129	14	)	)	PUNCT
ejpam-4137	129	15	ζ	ζ	NOUN
ejpam-4137	129	16	(	(	PUNCT
ejpam-4137	129	17	−1	−1	NOUN
ejpam-4137	129	18	2	2	NUM
ejpam-4137	129	19	)	)	PUNCT
ejpam-4137	130	1	+	+	CCONJ
ejpam-4137	130	2	1	1	NUM
ejpam-4137	130	3	(	(	PUNCT
ejpam-4137	130	4	17	17	NUM
ejpam-4137	130	5	)	)	PUNCT
ejpam-4137	130	6	proof	proof	NOUN
ejpam-4137	130	7	.	.	PUNCT
ejpam-4137	131	1	use	use	VERB
ejpam-4137	131	2	equation	equation	NOUN
ejpam-4137	131	3	(	(	PUNCT
ejpam-4137	131	4	11	11	NUM
ejpam-4137	131	5	)	)	PUNCT
ejpam-4137	131	6	and	and	CCONJ
ejpam-4137	131	7	set	set	VERB
ejpam-4137	131	8	m	m	PROPN
ejpam-4137	131	9	=	=	NOUN
ejpam-4137	131	10	−1	−1	NOUN
ejpam-4137	131	11	and	and	CCONJ
ejpam-4137	131	12	simplify	simplify	VERB
ejpam-4137	131	13	in	in	ADP
ejpam-4137	131	14	terms	term	NOUN
ejpam-4137	131	15	of	of	ADP
ejpam-4137	131	16	the	the	DET
ejpam-4137	131	17	hurwitz	hurwitz	PROPN
ejpam-4137	131	18	zeta	zeta	PROPN
ejpam-4137	131	19	function	function	PROPN
ejpam-4137	131	20	ζ(s	ζ(s	PROPN
ejpam-4137	131	21	,	,	PUNCT
ejpam-4137	131	22	a	a	PRON
ejpam-4137	131	23	)	)	PUNCT
ejpam-4137	131	24	using	use	VERB
ejpam-4137	131	25	entry	entry	NOUN
ejpam-4137	131	26	(	(	PUNCT
ejpam-4137	131	27	4	4	NUM
ejpam-4137	131	28	)	)	PUNCT
ejpam-4137	131	29	in	in	ADP
ejpam-4137	131	30	table	table	NOUN
ejpam-4137	131	31	below	below	ADV
ejpam-4137	131	32	(	(	PUNCT
ejpam-4137	131	33	64:12:7	64:12:7	NUM
ejpam-4137	131	34	)	)	PUNCT
ejpam-4137	131	35	in	in	ADP
ejpam-4137	131	36	[	[	X
ejpam-4137	131	37	9	9	NUM
ejpam-4137	131	38	]	]	PUNCT
ejpam-4137	131	39	.	.	PUNCT
ejpam-4137	132	1	next	next	ADV
ejpam-4137	132	2	set	set	VERB
ejpam-4137	132	3	a	a	DET
ejpam-4137	132	4	=	=	SYM
ejpam-4137	132	5	2	2	NUM
ejpam-4137	132	6	and	and	CCONJ
ejpam-4137	132	7	simplify	simplify	VERB
ejpam-4137	132	8	in	in	ADP
ejpam-4137	132	9	terms	term	NOUN
ejpam-4137	132	10	of	of	ADP
ejpam-4137	132	11	the	the	DET
ejpam-4137	132	12	riemann	riemann	PROPN
ejpam-4137	132	13	zeta	zeta	PROPN
ejpam-4137	132	14	function	function	PROPN
ejpam-4137	132	15	ζ(s	ζ(s	PROPN
ejpam-4137	132	16	)	)	PUNCT
ejpam-4137	132	17	using	use	VERB
ejpam-4137	132	18	entry	entry	NOUN
ejpam-4137	132	19	(	(	PUNCT
ejpam-4137	132	20	2	2	NUM
ejpam-4137	132	21	)	)	PUNCT
ejpam-4137	132	22	in	in	ADP
ejpam-4137	132	23	table	table	NOUN
ejpam-4137	132	24	below	below	ADV
ejpam-4137	132	25	(	(	PUNCT
ejpam-4137	132	26	64:7	64:7	NUM
ejpam-4137	132	27	)	)	PUNCT
ejpam-4137	132	28	in	in	ADP
ejpam-4137	132	29	[	[	X
ejpam-4137	132	30	9	9	NUM
ejpam-4137	132	31	]	]	PUNCT
ejpam-4137	132	32	.	.	PUNCT
ejpam-4137	133	1	next	next	ADJ
ejpam-4137	133	2	set	set	VERB
ejpam-4137	133	3	k	k	PROPN
ejpam-4137	134	1	=	=	PUNCT
ejpam-4137	135	1	−1/2	−1/2	ADJ
ejpam-4137	135	2	and	and	CCONJ
ejpam-4137	135	3	simplify	simplify	NOUN
ejpam-4137	135	4	.	.	PUNCT
ejpam-4137	135	5	example	example	NOUN
ejpam-4137	135	6	7	7	NUM
ejpam-4137	135	7	.	.	PUNCT
ejpam-4137	136	1	∞∑	∞∑	NUM
ejpam-4137	136	2	n=1	n=1	NUM
ejpam-4137	136	3	(	(	PUNCT
ejpam-4137	136	4	−1)2	−1)2	X
ejpam-4137	136	5	−n√	−n√	PROPN
ejpam-4137	136	6	2−nφ	2−nφ	NUM
ejpam-4137	136	7	(	(	PUNCT
ejpam-4137	136	8	(	(	PUNCT
ejpam-4137	136	9	−1)1	−1)1	PUNCT
ejpam-4137	136	10	+	+	NOUN
ejpam-4137	136	11	2−n	2−n	NUM
ejpam-4137	136	12	,	,	PUNCT
ejpam-4137	136	13	1	1	NUM
ejpam-4137	136	14	2	2	NUM
ejpam-4137	136	15	,	,	PUNCT
ejpam-4137	136	16	1	1	NUM
ejpam-4137	136	17	+	+	NUM
ejpam-4137	136	18	2n	2n	NUM
ejpam-4137	136	19	)	)	PUNCT
ejpam-4137	136	20	=	=	PUNCT
ejpam-4137	136	21	−e	−e	NOUN
ejpam-4137	136	22	1	1	NUM
ejpam-4137	136	23	2	2	NUM
ejpam-4137	136	24	(	(	PUNCT
ejpam-4137	136	25	−iπ	−iπ	SYM
ejpam-4137	136	26	)	)	PUNCT
ejpam-4137	136	27	+	+	CCONJ
ejpam-4137	136	28	(	(	PUNCT
ejpam-4137	136	29	√	√	NUM
ejpam-4137	136	30	2−	2−	NUM
ejpam-4137	136	31	1	1	NUM
ejpam-4137	136	32	)	)	PUNCT
ejpam-4137	136	33	ζ	ζ	NOUN
ejpam-4137	136	34	(	(	PUNCT
ejpam-4137	136	35	1	1	NUM
ejpam-4137	136	36	2	2	NUM
ejpam-4137	136	37	)	)	PUNCT
ejpam-4137	136	38	+	+	CCONJ
ejpam-4137	136	39	1	1	NUM
ejpam-4137	136	40	(	(	PUNCT
ejpam-4137	136	41	18	18	NUM
ejpam-4137	136	42	)	)	PUNCT
ejpam-4137	136	43	proof	proof	NOUN
ejpam-4137	136	44	.	.	PUNCT
ejpam-4137	137	1	use	use	VERB
ejpam-4137	137	2	equation	equation	NOUN
ejpam-4137	137	3	(	(	PUNCT
ejpam-4137	137	4	11	11	NUM
ejpam-4137	137	5	)	)	PUNCT
ejpam-4137	137	6	and	and	CCONJ
ejpam-4137	137	7	set	set	VERB
ejpam-4137	137	8	m	m	PROPN
ejpam-4137	137	9	=	=	NOUN
ejpam-4137	137	10	−1	−1	NOUN
ejpam-4137	137	11	and	and	CCONJ
ejpam-4137	137	12	simplify	simplify	VERB
ejpam-4137	137	13	in	in	ADP
ejpam-4137	137	14	terms	term	NOUN
ejpam-4137	137	15	of	of	ADP
ejpam-4137	137	16	the	the	DET
ejpam-4137	137	17	hurwitz	hurwitz	PROPN
ejpam-4137	137	18	zeta	zeta	PROPN
ejpam-4137	137	19	function	function	PROPN
ejpam-4137	137	20	ζ(s	ζ(s	PROPN
ejpam-4137	137	21	,	,	PUNCT
ejpam-4137	137	22	a	a	PRON
ejpam-4137	137	23	)	)	PUNCT
ejpam-4137	137	24	using	use	VERB
ejpam-4137	137	25	entry	entry	NOUN
ejpam-4137	137	26	(	(	PUNCT
ejpam-4137	137	27	4	4	NUM
ejpam-4137	137	28	)	)	PUNCT
ejpam-4137	137	29	in	in	ADP
ejpam-4137	137	30	table	table	NOUN
ejpam-4137	137	31	below	below	ADV
ejpam-4137	137	32	(	(	PUNCT
ejpam-4137	137	33	64:12:7	64:12:7	NUM
ejpam-4137	137	34	)	)	PUNCT
ejpam-4137	137	35	in	in	ADP
ejpam-4137	137	36	[	[	X
ejpam-4137	137	37	9	9	NUM
ejpam-4137	137	38	]	]	PUNCT
ejpam-4137	137	39	.	.	PUNCT
ejpam-4137	138	1	next	next	ADV
ejpam-4137	138	2	set	set	VERB
ejpam-4137	138	3	a	a	DET
ejpam-4137	138	4	=	=	SYM
ejpam-4137	138	5	2	2	NUM
ejpam-4137	138	6	and	and	CCONJ
ejpam-4137	138	7	simplify	simplify	VERB
ejpam-4137	138	8	in	in	ADP
ejpam-4137	138	9	terms	term	NOUN
ejpam-4137	138	10	of	of	ADP
ejpam-4137	138	11	the	the	DET
ejpam-4137	138	12	riemann	riemann	PROPN
ejpam-4137	138	13	zeta	zeta	PROPN
ejpam-4137	138	14	function	function	PROPN
ejpam-4137	138	15	ζ(s	ζ(s	PROPN
ejpam-4137	138	16	)	)	PUNCT
ejpam-4137	138	17	using	use	VERB
ejpam-4137	138	18	entry	entry	NOUN
ejpam-4137	138	19	(	(	PUNCT
ejpam-4137	138	20	2	2	NUM
ejpam-4137	138	21	)	)	PUNCT
ejpam-4137	138	22	in	in	ADP
ejpam-4137	138	23	table	table	NOUN
ejpam-4137	138	24	below	below	ADV
ejpam-4137	138	25	(	(	PUNCT
ejpam-4137	138	26	64:7	64:7	NUM
ejpam-4137	138	27	)	)	PUNCT
ejpam-4137	138	28	in	in	ADP
ejpam-4137	138	29	[	[	X
ejpam-4137	138	30	9	9	NUM
ejpam-4137	138	31	]	]	PUNCT
ejpam-4137	138	32	.	.	PUNCT
ejpam-4137	139	1	next	next	ADJ
ejpam-4137	139	2	set	set	VERB
ejpam-4137	139	3	k	k	PROPN
ejpam-4137	139	4	=	=	SYM
ejpam-4137	139	5	1/2	1/2	NUM
ejpam-4137	139	6	and	and	CCONJ
ejpam-4137	139	7	simplify	simplify	NOUN
ejpam-4137	139	8	.	.	PUNCT
ejpam-4137	140	1	7	7	X
ejpam-4137	140	2	.	.	X
ejpam-4137	140	3	infinite	infinite	ADJ
ejpam-4137	140	4	sum	sum	NOUN
ejpam-4137	140	5	of	of	ADP
ejpam-4137	140	6	the	the	DET
ejpam-4137	140	7	lerch	lerch	PROPN
ejpam-4137	140	8	function	function	PROPN
ejpam-4137	140	9	in	in	ADP
ejpam-4137	140	10	terms	term	NOUN
ejpam-4137	140	11	of	of	ADP
ejpam-4137	140	12	the	the	DET
ejpam-4137	140	13	lerch	lerch	PROPN
ejpam-4137	140	14	transformation	transformation	NOUN
ejpam-4137	140	15	theorem	theorem	VERB
ejpam-4137	140	16	2	2	NUM
ejpam-4137	140	17	.	.	X
ejpam-4137	140	18	for	for	ADP
ejpam-4137	140	19	re(s	re(s	ADJ
ejpam-4137	140	20	)	)	PUNCT
ejpam-4137	140	21	<	<	X
ejpam-4137	140	22	0	0	NUM
ejpam-4137	140	23	,	,	PUNCT
ejpam-4137	140	24	0	0	NUM
ejpam-4137	140	25	<	<	X
ejpam-4137	140	26	v	v	X
ejpam-4137	140	27	≤	≤	NUM
ejpam-4137	140	28	1	1	NUM
ejpam-4137	140	29	,	,	PUNCT
ejpam-4137	140	30	0	0	NUM
ejpam-4137	140	31	≤	≤	NUM
ejpam-4137	140	32	im(α	im(α	NOUN
ejpam-4137	140	33	)	)	PUNCT
ejpam-4137	140	34	<	<	X
ejpam-4137	140	35	2π	2π	NOUN
ejpam-4137	140	36	,	,	PUNCT
ejpam-4137	140	37	∞∑	∞∑	NUM
ejpam-4137	140	38	n=1	n=1	ADP
ejpam-4137	140	39	eα(−2−n)2−n−s+1	eα(−2−n)2−n−s+1	PROPN
ejpam-4137	140	40	(	(	PUNCT
ejpam-4137	140	41	2−n	2−n	NUM
ejpam-4137	140	42	)	)	PUNCT
ejpam-4137	140	43	−s	−s	NOUN
ejpam-4137	140	44	φ	φ	PROPN
ejpam-4137	140	45	(	(	PUNCT
ejpam-4137	140	46	−e−2−nα	−e−2−nα	PROPN
ejpam-4137	140	47	,	,	PUNCT
ejpam-4137	140	48	s	s	X
ejpam-4137	140	49	,	,	PUNCT
ejpam-4137	140	50	2n(v	2n(v	NUM
ejpam-4137	140	51	−	−	NOUN
ejpam-4137	140	52	1	1	NUM
ejpam-4137	140	53	)	)	PUNCT
ejpam-4137	140	54	+	+	CCONJ
ejpam-4137	140	55	1	1	X
ejpam-4137	140	56	)	)	PUNCT
ejpam-4137	140	57	r.	r.	PROPN
ejpam-4137	140	58	reynolds	reynolds	PROPN
ejpam-4137	140	59	,	,	PUNCT
ejpam-4137	140	60	a.	a.	PROPN
ejpam-4137	140	61	stauffer	stauffer	PROPN
ejpam-4137	140	62	/	/	SYM
ejpam-4137	140	63	eur	eur	PROPN
ejpam-4137	140	64	.	.	PUNCT
ejpam-4137	141	1	j.	j.	PROPN
ejpam-4137	141	2	pure	pure	PROPN
ejpam-4137	141	3	appl	appl	PROPN
ejpam-4137	141	4	.	.	PROPN
ejpam-4137	141	5	math	math	PROPN
ejpam-4137	141	6	,	,	PUNCT
ejpam-4137	141	7	15	15	NUM
ejpam-4137	141	8	(	(	PUNCT
ejpam-4137	141	9	1	1	NUM
ejpam-4137	141	10	)	)	PUNCT
ejpam-4137	141	11	(	(	PUNCT
ejpam-4137	141	12	2022	2022	NUM
ejpam-4137	141	13	)	)	PUNCT
ejpam-4137	141	14	,	,	PUNCT
ejpam-4137	141	15	158	158	NUM
ejpam-4137	141	16	-	-	SYM
ejpam-4137	141	17	168	168	NUM
ejpam-4137	141	18	164	164	NUM
ejpam-4137	141	19	=	=	SYM
ejpam-4137	141	20	21−sαs−1	21−sαs−1	NUM
ejpam-4137	141	21	(	(	PUNCT
ejpam-4137	141	22	e2(v−1	e2(v−1	NOUN
ejpam-4137	141	23	)	)	PUNCT
ejpam-4137	141	24	)	)	PUNCT
ejpam-4137	141	25	α/2	α/2	NUM
ejpam-4137	141	26	γ(1−	γ(1−	PROPN
ejpam-4137	141	27	s	s	PART
ejpam-4137	141	28	,	,	PUNCT
ejpam-4137	141	29	(	(	PUNCT
ejpam-4137	141	30	v	v	NOUN
ejpam-4137	141	31	−	−	PROPN
ejpam-4137	141	32	1)α)−	1)α)−	PROPN
ejpam-4137	141	33	e−α21−s	e−α21−s	PROPN
ejpam-4137	141	34	(	(	PUNCT
ejpam-4137	141	35	αs−1γ(1−	αs−1γ(1−	PROPN
ejpam-4137	141	36	s)eαv	s)eαv	PROPN
ejpam-4137	141	37	−i(2π)s−1γ(1−	−i(2π)s−1γ(1−	PROPN
ejpam-4137	141	38	s)eαv	s)eαv	PROPN
ejpam-4137	141	39	(	(	PUNCT
ejpam-4137	141	40	ei	ei	PROPN
ejpam-4137	141	41	(	(	PUNCT
ejpam-4137	141	42	πs	πs	PROPN
ejpam-4137	141	43	2	2	NUM
ejpam-4137	141	44	+2πv)φ	+2πv)φ	NOUN
ejpam-4137	141	45	(	(	PUNCT
ejpam-4137	141	46	e2iπv	e2iπv	X
ejpam-4137	141	47	,	,	PUNCT
ejpam-4137	141	48	1−	1−	NUM
ejpam-4137	141	49	s	s	NUM
ejpam-4137	141	50	,	,	PUNCT
ejpam-4137	141	51	1−	1−	NUM
ejpam-4137	141	52	iα	iα	PROPN
ejpam-4137	141	53	2π	2π	PROPN
ejpam-4137	141	54	)	)	PUNCT
ejpam-4137	141	55	−	−	PROPN
ejpam-4137	142	1	e−i(πs	e−i(πs	PROPN
ejpam-4137	142	2	2	2	NUM
ejpam-4137	142	3	+2πv)φ	+2πv)φ	PROPN
ejpam-4137	142	4	(	(	PUNCT
ejpam-4137	142	5	e−2iπv	e−2iπv	PROPN
ejpam-4137	142	6	,	,	PUNCT
ejpam-4137	142	7	1−	1−	NUM
ejpam-4137	142	8	s	s	NUM
ejpam-4137	142	9	,	,	PUNCT
ejpam-4137	142	10	iα	iα	ADP
ejpam-4137	142	11	2π	2π	NOUN
ejpam-4137	142	12	+	+	CCONJ
ejpam-4137	142	13	1	1	NUM
ejpam-4137	142	14	)	)	PUNCT
ejpam-4137	142	15	)	)	PUNCT
ejpam-4137	142	16	)	)	PUNCT
ejpam-4137	143	1	(	(	PUNCT
ejpam-4137	143	2	19	19	NUM
ejpam-4137	143	3	)	)	PUNCT
ejpam-4137	143	4	proof	proof	NOUN
ejpam-4137	143	5	.	.	PUNCT
ejpam-4137	144	1	use	use	VERB
ejpam-4137	144	2	equation	equation	NOUN
ejpam-4137	144	3	(	(	PUNCT
ejpam-4137	144	4	12	12	NUM
ejpam-4137	144	5	)	)	PUNCT
ejpam-4137	144	6	in	in	ADP
ejpam-4137	144	7	[	[	X
ejpam-4137	144	8	8	8	NUM
ejpam-4137	144	9	]	]	PUNCT
ejpam-4137	144	10	and	and	CCONJ
ejpam-4137	144	11	substitute	substitute	NOUN
ejpam-4137	144	12	into	into	ADP
ejpam-4137	144	13	equation	equation	NOUN
ejpam-4137	144	14	(	(	PUNCT
ejpam-4137	144	15	11	11	NUM
ejpam-4137	144	16	)	)	PUNCT
ejpam-4137	144	17	and	and	CCONJ
ejpam-4137	144	18	simplify	simplify	NOUN
ejpam-4137	144	19	.	.	PUNCT
ejpam-4137	145	1	8	8	X
ejpam-4137	145	2	.	.	NUM
ejpam-4137	145	3	extended	extend	VERB
ejpam-4137	145	4	vălean	vălean	ADJ
ejpam-4137	145	5	infinite	infinite	NOUN
ejpam-4137	145	6	sums	sum	NOUN
ejpam-4137	145	7	and	and	CCONJ
ejpam-4137	145	8	infinite	infinite	ADJ
ejpam-4137	145	9	products	product	NOUN
ejpam-4137	145	10	in	in	ADP
ejpam-4137	145	11	the	the	DET
ejpam-4137	145	12	book	book	NOUN
ejpam-4137	145	13	of	of	ADP
ejpam-4137	145	14	vălean	vălean	PROPN
ejpam-4137	145	15	[	[	X
ejpam-4137	145	16	14	14	NUM
ejpam-4137	145	17	]	]	X
ejpam-4137	145	18	section	section	NOUN
ejpam-4137	145	19	(	(	PUNCT
ejpam-4137	145	20	3.59	3.59	NUM
ejpam-4137	145	21	)	)	PUNCT
ejpam-4137	145	22	has	have	VERB
ejpam-4137	145	23	some	some	DET
ejpam-4137	145	24	very	very	ADV
ejpam-4137	145	25	interesting	interesting	ADJ
ejpam-4137	145	26	infinite	infinite	ADJ
ejpam-4137	145	27	sums	sum	NOUN
ejpam-4137	145	28	of	of	ADP
ejpam-4137	145	29	trigonometric	trigonometric	ADJ
ejpam-4137	145	30	functions	function	NOUN
ejpam-4137	145	31	.	.	PUNCT
ejpam-4137	146	1	in	in	ADP
ejpam-4137	146	2	this	this	DET
ejpam-4137	146	3	section	section	NOUN
ejpam-4137	146	4	of	of	ADP
ejpam-4137	146	5	the	the	DET
ejpam-4137	146	6	present	present	ADJ
ejpam-4137	146	7	paper	paper	NOUN
ejpam-4137	146	8	we	we	PRON
ejpam-4137	146	9	will	will	AUX
ejpam-4137	146	10	expand	expand	VERB
ejpam-4137	146	11	on	on	ADP
ejpam-4137	146	12	the	the	DET
ejpam-4137	146	13	sums	sum	NOUN
ejpam-4137	146	14	published	publish	VERB
ejpam-4137	146	15	by	by	ADP
ejpam-4137	146	16	vălean	vălean	NOUN
ejpam-4137	146	17	using	use	VERB
ejpam-4137	146	18	a	a	DET
ejpam-4137	146	19	special	special	ADJ
ejpam-4137	146	20	case	case	NOUN
ejpam-4137	146	21	of	of	ADP
ejpam-4137	146	22	equation	equation	NOUN
ejpam-4137	146	23	(	(	PUNCT
ejpam-4137	146	24	11	11	NUM
ejpam-4137	146	25	)	)	PUNCT
ejpam-4137	146	26	for	for	ADP
ejpam-4137	146	27	various	various	ADJ
ejpam-4137	146	28	values	value	NOUN
ejpam-4137	146	29	of	of	ADP
ejpam-4137	146	30	the	the	DET
ejpam-4137	146	31	parameters	parameter	NOUN
ejpam-4137	146	32	involved	involve	VERB
ejpam-4137	146	33	.	.	PUNCT
ejpam-4137	147	1	lemma	lemma	PROPN
ejpam-4137	147	2	1	1	NUM
ejpam-4137	147	3	.	.	PUNCT
ejpam-4137	148	1	∞∑	∞∑	NUM
ejpam-4137	148	2	n=1	n=1	NUM
ejpam-4137	148	3	(	(	PUNCT
ejpam-4137	148	4	−1)2	−1)2	X
ejpam-4137	148	5	−n	−n	NOUN
ejpam-4137	148	6	2k−n+1	2k−n+1	NUM
ejpam-4137	148	7	(	(	PUNCT
ejpam-4137	148	8	2−n	2−n	NUM
ejpam-4137	148	9	)	)	PUNCT
ejpam-4137	149	1	k	k	PROPN
ejpam-4137	149	2	φ	φ	PROPN
ejpam-4137	149	3	(	(	PUNCT
ejpam-4137	149	4	(	(	PUNCT
ejpam-4137	149	5	−1)1	−1)1	PUNCT
ejpam-4137	149	6	+	+	NOUN
ejpam-4137	149	7	2−n	2−n	NUM
ejpam-4137	149	8	,	,	PUNCT
ejpam-4137	149	9	−k	−k	PROPN
ejpam-4137	149	10	,	,	PUNCT
ejpam-4137	149	11	2n(a−	2n(a−	NUM
ejpam-4137	149	12	1	1	NUM
ejpam-4137	149	13	)	)	PUNCT
ejpam-4137	149	14	+	+	CCONJ
ejpam-4137	149	15	1	1	X
ejpam-4137	149	16	)	)	PUNCT
ejpam-4137	149	17	=	=	SYM
ejpam-4137	149	18	2k+1	2k+1	NOUN
ejpam-4137	149	19	(	(	PUNCT
ejpam-4137	149	20	2kζ	2kζ	ADJ
ejpam-4137	149	21	(	(	PUNCT
ejpam-4137	149	22	−k	−k	PROPN
ejpam-4137	149	23	,	,	PUNCT
ejpam-4137	149	24	a	a	DET
ejpam-4137	149	25	2	2	NUM
ejpam-4137	149	26	)	)	PUNCT
ejpam-4137	149	27	−	−	PROPN
ejpam-4137	149	28	2kζ	2kζ	NOUN
ejpam-4137	149	29	(	(	PUNCT
ejpam-4137	149	30	−k	−k	PROPN
ejpam-4137	149	31	,	,	PUNCT
ejpam-4137	149	32	a+	a+	PUNCT
ejpam-4137	149	33	1	1	NUM
ejpam-4137	149	34	2	2	NUM
ejpam-4137	149	35	)	)	PUNCT
ejpam-4137	149	36	)	)	PUNCT
ejpam-4137	150	1	+	+	ADV
ejpam-4137	150	2	i	i	PRON
ejpam-4137	150	3	(	(	PUNCT
ejpam-4137	150	4	e2(a−1	e2(a−1	NOUN
ejpam-4137	150	5	)	)	PUNCT
ejpam-4137	150	6	)	)	PUNCT
ejpam-4137	150	7	−	−	NOUN
ejpam-4137	151	1	iπ	iπ	ADV
ejpam-4137	151	2	2	2	NUM
ejpam-4137	151	3	(	(	PUNCT
ejpam-4137	151	4	−i)−k2k+1π−k−1γ(k+1	−i)−k2k+1π−k−1γ(k+1	NUM
ejpam-4137	151	5	,	,	PUNCT
ejpam-4137	151	6	i(1−a)π	i(1−a)π	NOUN
ejpam-4137	151	7	)	)	PUNCT
ejpam-4137	151	8	(	(	PUNCT
ejpam-4137	151	9	20	20	X
ejpam-4137	151	10	)	)	PUNCT
ejpam-4137	151	11	proof	proof	NOUN
ejpam-4137	151	12	.	.	PUNCT
ejpam-4137	152	1	use	use	VERB
ejpam-4137	152	2	equation	equation	NOUN
ejpam-4137	152	3	(	(	PUNCT
ejpam-4137	152	4	11	11	NUM
ejpam-4137	152	5	)	)	PUNCT
ejpam-4137	152	6	and	and	CCONJ
ejpam-4137	152	7	set	set	VERB
ejpam-4137	152	8	m	m	PROPN
ejpam-4137	152	9	=	=	SYM
ejpam-4137	152	10	1	1	NUM
ejpam-4137	152	11	and	and	CCONJ
ejpam-4137	152	12	simplify	simplify	VERB
ejpam-4137	152	13	using	use	VERB
ejpam-4137	152	14	entry	entry	NOUN
ejpam-4137	152	15	(	(	PUNCT
ejpam-4137	152	16	5	5	NUM
ejpam-4137	152	17	)	)	PUNCT
ejpam-4137	152	18	in	in	ADP
ejpam-4137	152	19	table	table	NOUN
ejpam-4137	152	20	below	below	ADV
ejpam-4137	152	21	(	(	PUNCT
ejpam-4137	152	22	64:12:7	64:12:7	NUM
ejpam-4137	152	23	)	)	PUNCT
ejpam-4137	152	24	in	in	ADP
ejpam-4137	152	25	[	[	X
ejpam-4137	152	26	9	9	NUM
ejpam-4137	152	27	]	]	PUNCT
ejpam-4137	152	28	.	.	PUNCT
ejpam-4137	152	29	example	example	NOUN
ejpam-4137	153	1	8	8	NUM
ejpam-4137	153	2	.	.	PUNCT
ejpam-4137	154	1	∞∑	∞∑	NUM
ejpam-4137	154	2	n=1	n=1	ADP
ejpam-4137	154	3	21−2n	21−2n	NUM
ejpam-4137	154	4	(	(	PUNCT
ejpam-4137	154	5	1	1	NUM
ejpam-4137	154	6	+	+	X
ejpam-4137	154	7	α2n	α2n	PROPN
ejpam-4137	154	8	(	(	PUNCT
ejpam-4137	154	9	1	1	NUM
ejpam-4137	154	10	+	+	NUM
ejpam-4137	154	11	eiπ2	eiπ2	NOUN
ejpam-4137	154	12	−n	−n	ADJ
ejpam-4137	154	13	)	)	PUNCT
ejpam-4137	154	14	)	)	PUNCT
ejpam-4137	155	1	cos	cos	PROPN
ejpam-4137	155	2	(	(	PUNCT
ejpam-4137	155	3	π2−n	π2−n	PROPN
ejpam-4137	155	4	)	)	PUNCT
ejpam-4137	155	5	+	+	CCONJ
ejpam-4137	155	6	1	1	NUM
ejpam-4137	155	7	=	=	SYM
ejpam-4137	155	8	2α+	2α+	NUM
ejpam-4137	155	9	4α2	4α2	NUM
ejpam-4137	155	10	(	(	PUNCT
ejpam-4137	155	11	e2α	e2α	NOUN
ejpam-4137	155	12	)	)	PUNCT
ejpam-4137	155	13	−	−	PROPN
ejpam-4137	156	1	iπ	iπ	PRON
ejpam-4137	156	2	2	2	NUM
ejpam-4137	156	3	e−1(−iπα	e−1(−iπα	NOUN
ejpam-4137	156	4	)	)	PUNCT
ejpam-4137	156	5	+	+	CCONJ
ejpam-4137	156	6	1	1	NUM
ejpam-4137	156	7	(	(	PUNCT
ejpam-4137	156	8	21	21	NUM
ejpam-4137	156	9	)	)	PUNCT
ejpam-4137	156	10	proof	proof	NOUN
ejpam-4137	156	11	.	.	PUNCT
ejpam-4137	157	1	use	use	VERB
ejpam-4137	157	2	equation	equation	NOUN
ejpam-4137	157	3	(	(	PUNCT
ejpam-4137	157	4	20	20	NUM
ejpam-4137	157	5	)	)	PUNCT
ejpam-4137	157	6	and	and	CCONJ
ejpam-4137	157	7	set	set	VERB
ejpam-4137	157	8	k	k	PROPN
ejpam-4137	157	9	=	=	SYM
ejpam-4137	157	10	1	1	NUM
ejpam-4137	157	11	and	and	CCONJ
ejpam-4137	157	12	replace	replace	VERB
ejpam-4137	157	13	a	a	DET
ejpam-4137	157	14	→	→	SYM
ejpam-4137	157	15	α+	α+	SYM
ejpam-4137	157	16	1	1	NUM
ejpam-4137	157	17	and	and	CCONJ
ejpam-4137	157	18	simplify	simplify	NOUN
ejpam-4137	157	19	.	.	PUNCT
ejpam-4137	157	20	example	example	NOUN
ejpam-4137	158	1	9	9	NUM
ejpam-4137	158	2	.	.	PUNCT
ejpam-4137	159	1	∞∑	∞∑	NUM
ejpam-4137	159	2	n=1	n=1	NUM
ejpam-4137	159	3	8−n	8−n	NUM
ejpam-4137	159	4	sin4	sin4	NOUN
ejpam-4137	159	5	(	(	PUNCT
ejpam-4137	159	6	π2−n−1	π2−n−1	PROPN
ejpam-4137	159	7	)	)	PUNCT
ejpam-4137	159	8	csc3	csc3	PROPN
ejpam-4137	159	9	(	(	PUNCT
ejpam-4137	159	10	π2−n	π2−n	NOUN
ejpam-4137	159	11	)	)	PUNCT
ejpam-4137	159	12	=	=	SYM
ejpam-4137	159	13	1	1	NUM
ejpam-4137	159	14	π3	π3	NOUN
ejpam-4137	159	15	(	(	PUNCT
ejpam-4137	159	16	22	22	NUM
ejpam-4137	159	17	)	)	PUNCT
ejpam-4137	159	18	proof	proof	NOUN
ejpam-4137	159	19	.	.	PUNCT
ejpam-4137	160	1	use	use	VERB
ejpam-4137	160	2	equation	equation	NOUN
ejpam-4137	160	3	(	(	PUNCT
ejpam-4137	160	4	20	20	NUM
ejpam-4137	160	5	)	)	PUNCT
ejpam-4137	160	6	and	and	CCONJ
ejpam-4137	160	7	set	set	VERB
ejpam-4137	160	8	k	k	PROPN
ejpam-4137	160	9	=	=	SYM
ejpam-4137	160	10	2	2	NUM
ejpam-4137	160	11	,	,	PUNCT
ejpam-4137	160	12	a	a	DET
ejpam-4137	160	13	=	=	SYM
ejpam-4137	160	14	1	1	NUM
ejpam-4137	160	15	and	and	CCONJ
ejpam-4137	160	16	simplify	simplify	ADJ
ejpam-4137	160	17	.	.	PUNCT
ejpam-4137	160	18	example	example	NOUN
ejpam-4137	161	1	10	10	NUM
ejpam-4137	161	2	.	.	PUNCT
ejpam-4137	162	1	∞∑	∞∑	NUM
ejpam-4137	162	2	n=1	n=1	ADP
ejpam-4137	162	3	2−4n	2−4n	NUM
ejpam-4137	162	4	(	(	PUNCT
ejpam-4137	162	5	cos	cos	X
ejpam-4137	162	6	(	(	PUNCT
ejpam-4137	162	7	π2−n	π2−n	PROPN
ejpam-4137	162	8	)	)	PUNCT
ejpam-4137	162	9	−	−	PROPN
ejpam-4137	162	10	2	2	X
ejpam-4137	162	11	)	)	PUNCT
ejpam-4137	162	12	sec4	sec4	NOUN
ejpam-4137	162	13	(	(	PUNCT
ejpam-4137	162	14	π2−n−1	π2−n−1	PROPN
ejpam-4137	162	15	)	)	PUNCT
ejpam-4137	162	16	=	=	SYM
ejpam-4137	162	17	48	48	NUM
ejpam-4137	162	18	π4	π4	NOUN
ejpam-4137	162	19	−	−	PROPN
ejpam-4137	162	20	1	1	NUM
ejpam-4137	162	21	(	(	PUNCT
ejpam-4137	162	22	23	23	NUM
ejpam-4137	162	23	)	)	PUNCT
ejpam-4137	162	24	r.	r.	PROPN
ejpam-4137	162	25	reynolds	reynolds	PROPN
ejpam-4137	162	26	,	,	PUNCT
ejpam-4137	162	27	a.	a.	PROPN
ejpam-4137	162	28	stauffer	stauffer	PROPN
ejpam-4137	162	29	/	/	SYM
ejpam-4137	162	30	eur	eur	PROPN
ejpam-4137	162	31	.	.	PUNCT
ejpam-4137	163	1	j.	j.	PROPN
ejpam-4137	163	2	pure	pure	PROPN
ejpam-4137	163	3	appl	appl	PROPN
ejpam-4137	163	4	.	.	PROPN
ejpam-4137	163	5	math	math	PROPN
ejpam-4137	163	6	,	,	PUNCT
ejpam-4137	163	7	15	15	NUM
ejpam-4137	163	8	(	(	PUNCT
ejpam-4137	163	9	1	1	NUM
ejpam-4137	163	10	)	)	PUNCT
ejpam-4137	163	11	(	(	PUNCT
ejpam-4137	163	12	2022	2022	NUM
ejpam-4137	163	13	)	)	PUNCT
ejpam-4137	163	14	,	,	PUNCT
ejpam-4137	163	15	158	158	NUM
ejpam-4137	163	16	-	-	SYM
ejpam-4137	163	17	168	168	NUM
ejpam-4137	163	18	165	165	NUM
ejpam-4137	163	19	proof	proof	NOUN
ejpam-4137	163	20	.	.	PUNCT
ejpam-4137	164	1	use	use	VERB
ejpam-4137	164	2	equation	equation	NOUN
ejpam-4137	164	3	(	(	PUNCT
ejpam-4137	164	4	20	20	NUM
ejpam-4137	164	5	)	)	PUNCT
ejpam-4137	164	6	and	and	CCONJ
ejpam-4137	164	7	set	set	VERB
ejpam-4137	164	8	k	k	PROPN
ejpam-4137	164	9	=	=	SYM
ejpam-4137	164	10	3	3	NUM
ejpam-4137	164	11	,	,	PUNCT
ejpam-4137	164	12	a	a	DET
ejpam-4137	164	13	=	=	SYM
ejpam-4137	164	14	1	1	NUM
ejpam-4137	164	15	and	and	CCONJ
ejpam-4137	164	16	simplify	simplify	NOUN
ejpam-4137	164	17	.	.	PUNCT
ejpam-4137	164	18	example	example	NOUN
ejpam-4137	165	1	11	11	NUM
ejpam-4137	165	2	.	.	PUNCT
ejpam-4137	166	1	the	the	DET
ejpam-4137	166	2	polylogarithm	polylogarithm	PROPN
ejpam-4137	166	3	function	function	NOUN
ejpam-4137	166	4	lin(z	lin(z	PROPN
ejpam-4137	166	5	)	)	PUNCT
ejpam-4137	166	6	and	and	CCONJ
ejpam-4137	166	7	riemann	riemann	PROPN
ejpam-4137	166	8	zeta	zeta	PROPN
ejpam-4137	166	9	function	function	PROPN
ejpam-4137	166	10	ζ(s	ζ(s	PROPN
ejpam-4137	166	11	)	)	PUNCT
ejpam-4137	166	12	∞∑	∞∑	NUM
ejpam-4137	166	13	n=1	n=1	PROPN
ejpam-4137	166	14	−2k−n+1	−2k−n+1	PROPN
ejpam-4137	166	15	(	(	PUNCT
ejpam-4137	166	16	2−n	2−n	NUM
ejpam-4137	166	17	)	)	PUNCT
ejpam-4137	167	1	k	k	NOUN
ejpam-4137	167	2	li−k	li−k	NOUN
ejpam-4137	167	3	(	(	PUNCT
ejpam-4137	167	4	(	(	PUNCT
ejpam-4137	167	5	−1)1	−1)1	PUNCT
ejpam-4137	167	6	+	+	NOUN
ejpam-4137	167	7	2−n	2−n	NUM
ejpam-4137	167	8	)	)	PUNCT
ejpam-4137	168	1	=	=	SYM
ejpam-4137	168	2	2k+1	2k+1	NOUN
ejpam-4137	168	3	(	(	PUNCT
ejpam-4137	168	4	−	−	PROPN
ejpam-4137	168	5	(	(	PUNCT
ejpam-4137	168	6	2k+1	2k+1	NOUN
ejpam-4137	168	7	−	−	NOUN
ejpam-4137	168	8	1	1	NUM
ejpam-4137	168	9	)	)	PUNCT
ejpam-4137	168	10	ζ(−k	ζ(−k	NOUN
ejpam-4137	168	11	)	)	PUNCT
ejpam-4137	168	12	+	+	CCONJ
ejpam-4137	168	13	i(−i)−kπ−k−1γ(k	i(−i)−kπ−k−1γ(k	PRON
ejpam-4137	168	14	+	+	CCONJ
ejpam-4137	168	15	1	1	NUM
ejpam-4137	168	16	)	)	PUNCT
ejpam-4137	168	17	)	)	PUNCT
ejpam-4137	169	1	(	(	PUNCT
ejpam-4137	169	2	24	24	NUM
ejpam-4137	169	3	)	)	PUNCT
ejpam-4137	169	4	proof	proof	NOUN
ejpam-4137	169	5	.	.	PUNCT
ejpam-4137	170	1	use	use	VERB
ejpam-4137	170	2	equation	equation	NOUN
ejpam-4137	170	3	(	(	PUNCT
ejpam-4137	170	4	20	20	NUM
ejpam-4137	170	5	)	)	PUNCT
ejpam-4137	170	6	and	and	CCONJ
ejpam-4137	170	7	set	set	VERB
ejpam-4137	170	8	a	a	DET
ejpam-4137	170	9	=	=	SYM
ejpam-4137	170	10	1	1	NUM
ejpam-4137	170	11	and	and	CCONJ
ejpam-4137	170	12	simplify	simplify	VERB
ejpam-4137	170	13	using	use	VERB
ejpam-4137	170	14	entry	entry	NOUN
ejpam-4137	170	15	(	(	PUNCT
ejpam-4137	170	16	1	1	NUM
ejpam-4137	170	17	)	)	PUNCT
ejpam-4137	170	18	in	in	ADP
ejpam-4137	170	19	table	table	NOUN
ejpam-4137	170	20	below	below	ADV
ejpam-4137	170	21	(	(	PUNCT
ejpam-4137	170	22	64:7	64:7	NUM
ejpam-4137	170	23	)	)	PUNCT
ejpam-4137	170	24	in	in	ADP
ejpam-4137	170	25	[	[	X
ejpam-4137	170	26	9	9	NUM
ejpam-4137	170	27	]	]	PUNCT
ejpam-4137	170	28	.	.	PUNCT
ejpam-4137	170	29	example	example	NOUN
ejpam-4137	171	1	12	12	NUM
ejpam-4137	171	2	.	.	PUNCT
ejpam-4137	172	1	the	the	DET
ejpam-4137	172	2	polylogarithm	polylogarithm	PROPN
ejpam-4137	172	3	function	function	NOUN
ejpam-4137	172	4	lin(z	lin(z	X
ejpam-4137	172	5	)	)	PUNCT
ejpam-4137	172	6	∞∑	∞∑	NUM
ejpam-4137	172	7	n=1	n=1	ADJ
ejpam-4137	172	8	√	√	PROPN
ejpam-4137	172	9	21−nli	21−nli	NUM
ejpam-4137	172	10	1	1	NUM
ejpam-4137	172	11	2	2	NUM
ejpam-4137	172	12	(	(	PUNCT
ejpam-4137	172	13	(	(	PUNCT
ejpam-4137	172	14	−1)1	−1)1	PUNCT
ejpam-4137	172	15	+	+	NOUN
ejpam-4137	172	16	2−n	2−n	NUM
ejpam-4137	172	17	)	)	PUNCT
ejpam-4137	173	1	=	=	SYM
ejpam-4137	174	1	−	−	PROPN
ejpam-4137	174	2	(	(	PUNCT
ejpam-4137	174	3	√	√	NUM
ejpam-4137	174	4	2−	2−	NUM
ejpam-4137	174	5	2	2	NUM
ejpam-4137	174	6	)	)	PUNCT
ejpam-4137	174	7	ζ	ζ	NOUN
ejpam-4137	174	8	(	(	PUNCT
ejpam-4137	174	9	1	1	NUM
ejpam-4137	174	10	2	2	NUM
ejpam-4137	174	11	)	)	PUNCT
ejpam-4137	174	12	+	+	CCONJ
ejpam-4137	174	13	(	(	PUNCT
ejpam-4137	174	14	−1−	−1−	NOUN
ejpam-4137	174	15	i	i	PROPN
ejpam-4137	174	16	)	)	PUNCT
ejpam-4137	174	17	(	(	PUNCT
ejpam-4137	174	18	25	25	NUM
ejpam-4137	174	19	)	)	PUNCT
ejpam-4137	174	20	proof	proof	NOUN
ejpam-4137	174	21	.	.	PUNCT
ejpam-4137	175	1	use	use	VERB
ejpam-4137	175	2	equation	equation	NOUN
ejpam-4137	175	3	(	(	PUNCT
ejpam-4137	175	4	24	24	NUM
ejpam-4137	175	5	)	)	PUNCT
ejpam-4137	175	6	and	and	CCONJ
ejpam-4137	175	7	set	set	VERB
ejpam-4137	175	8	k	k	PROPN
ejpam-4137	175	9	=	=	PUNCT
ejpam-4137	175	10	−1/2	−1/2	ADJ
ejpam-4137	175	11	and	and	CCONJ
ejpam-4137	175	12	simplify	simplify	NOUN
ejpam-4137	175	13	.	.	PUNCT
ejpam-4137	175	14	example	example	NOUN
ejpam-4137	176	1	13	13	NUM
ejpam-4137	176	2	.	.	PUNCT
ejpam-4137	177	1	∞∑	∞∑	NUM
ejpam-4137	177	2	n=1	n=1	ADJ
ejpam-4137	177	3	4−n	4−n	PROPN
ejpam-4137	177	4	sec2	sec2	NOUN
ejpam-4137	177	5	(	(	PUNCT
ejpam-4137	177	6	π2−n−1	π2−n−1	PROPN
ejpam-4137	177	7	)	)	PUNCT
ejpam-4137	177	8	=	=	SYM
ejpam-4137	177	9	1−	1−	NUM
ejpam-4137	177	10	4	4	NUM
ejpam-4137	177	11	π2	π2	NOUN
ejpam-4137	177	12	(	(	PUNCT
ejpam-4137	177	13	26	26	NUM
ejpam-4137	177	14	)	)	PUNCT
ejpam-4137	177	15	proof	proof	NOUN
ejpam-4137	177	16	.	.	PUNCT
ejpam-4137	178	1	use	use	VERB
ejpam-4137	178	2	equation	equation	NOUN
ejpam-4137	178	3	(	(	PUNCT
ejpam-4137	178	4	10	10	NUM
ejpam-4137	178	5	)	)	PUNCT
ejpam-4137	178	6	and	and	CCONJ
ejpam-4137	178	7	set	set	VERB
ejpam-4137	178	8	k	k	PROPN
ejpam-4137	178	9	=	=	SYM
ejpam-4137	178	10	1	1	NUM
ejpam-4137	178	11	,	,	PUNCT
ejpam-4137	178	12	a	a	DET
ejpam-4137	178	13	=	=	X
ejpam-4137	178	14	1,m	1,m	NOUN
ejpam-4137	178	15	=	=	SYM
ejpam-4137	178	16	πi/2	πi/2	NOUN
ejpam-4137	178	17	and	and	CCONJ
ejpam-4137	178	18	simplify	simplify	VERB
ejpam-4137	178	19	using	use	VERB
ejpam-4137	178	20	entry	entry	NOUN
ejpam-4137	178	21	(	(	PUNCT
ejpam-4137	178	22	3	3	NUM
ejpam-4137	178	23	)	)	PUNCT
ejpam-4137	178	24	in	in	ADP
ejpam-4137	178	25	table	table	NOUN
ejpam-4137	178	26	below	below	ADV
ejpam-4137	178	27	(	(	PUNCT
ejpam-4137	178	28	64:12:7	64:12:7	NUM
ejpam-4137	178	29	)	)	PUNCT
ejpam-4137	178	30	in	in	ADP
ejpam-4137	178	31	[	[	X
ejpam-4137	178	32	9	9	NUM
ejpam-4137	178	33	]	]	PUNCT
ejpam-4137	178	34	.	.	PUNCT
ejpam-4137	179	1	8.1	8.1	NUM
ejpam-4137	179	2	.	.	PUNCT
ejpam-4137	180	1	definite	definite	ADJ
ejpam-4137	180	2	integral	integral	ADJ
ejpam-4137	180	3	of	of	ADP
ejpam-4137	180	4	infinite	infinite	ADJ
ejpam-4137	180	5	sum	sum	NOUN
ejpam-4137	180	6	in	in	ADP
ejpam-4137	180	7	this	this	DET
ejpam-4137	180	8	section	section	NOUN
ejpam-4137	180	9	we	we	PRON
ejpam-4137	180	10	extend	extend	VERB
ejpam-4137	180	11	upon	upon	SCONJ
ejpam-4137	180	12	the	the	DET
ejpam-4137	180	13	results	result	NOUN
ejpam-4137	180	14	in	in	ADP
ejpam-4137	180	15	[	[	X
ejpam-4137	180	16	14	14	NUM
ejpam-4137	180	17	]	]	PUNCT
ejpam-4137	180	18	.	.	PUNCT
ejpam-4137	181	1	we	we	PRON
ejpam-4137	181	2	take	take	VERB
ejpam-4137	181	3	the	the	DET
ejpam-4137	181	4	definite	definite	ADJ
ejpam-4137	181	5	integral	integral	NOUN
ejpam-4137	181	6	of	of	ADP
ejpam-4137	181	7	specific	specific	ADJ
ejpam-4137	181	8	infinite	infinite	ADJ
ejpam-4137	181	9	sums	sum	NOUN
ejpam-4137	181	10	in	in	ADP
ejpam-4137	181	11	terms	term	NOUN
ejpam-4137	181	12	of	of	ADP
ejpam-4137	181	13	hyperbolic	hyperbolic	ADJ
ejpam-4137	181	14	trigonometric	trigonometric	ADJ
ejpam-4137	181	15	functions	function	NOUN
ejpam-4137	181	16	.	.	PUNCT
ejpam-4137	182	1	these	these	DET
ejpam-4137	182	2	definite	definite	ADJ
ejpam-4137	182	3	integrals	integral	NOUN
ejpam-4137	182	4	result	result	VERB
ejpam-4137	182	5	in	in	ADP
ejpam-4137	182	6	the	the	DET
ejpam-4137	182	7	sum	sum	NOUN
ejpam-4137	182	8	of	of	ADP
ejpam-4137	182	9	the	the	DET
ejpam-4137	182	10	logarithm	logarithm	NOUN
ejpam-4137	182	11	of	of	ADP
ejpam-4137	182	12	hyperbolic	hyperbolic	ADJ
ejpam-4137	182	13	trigonometric	trigonometric	NOUN
ejpam-4137	182	14	functions	function	NOUN
ejpam-4137	182	15	which	which	PRON
ejpam-4137	182	16	is	be	AUX
ejpam-4137	182	17	equivalent	equivalent	ADJ
ejpam-4137	182	18	to	to	ADP
ejpam-4137	182	19	the	the	DET
ejpam-4137	182	20	infinite	infinite	ADJ
ejpam-4137	182	21	product	product	NOUN
ejpam-4137	182	22	of	of	ADP
ejpam-4137	182	23	the	the	DET
ejpam-4137	182	24	logarithm	logarithm	NOUN
ejpam-4137	182	25	of	of	ADP
ejpam-4137	182	26	hyperbolic	hyperbolic	ADJ
ejpam-4137	182	27	trigonometric	trigonometric	ADJ
ejpam-4137	182	28	functions	function	NOUN
ejpam-4137	182	29	.	.	PUNCT
ejpam-4137	183	1	example	example	NOUN
ejpam-4137	183	2	14	14	NUM
ejpam-4137	183	3	.	.	PUNCT
ejpam-4137	184	1	using	use	VERB
ejpam-4137	184	2	equation	equation	NOUN
ejpam-4137	184	3	(	(	PUNCT
ejpam-4137	184	4	10	10	NUM
ejpam-4137	184	5	)	)	PUNCT
ejpam-4137	184	6	and	and	CCONJ
ejpam-4137	184	7	setting	set	VERB
ejpam-4137	184	8	k	k	X
ejpam-4137	184	9	=	=	SYM
ejpam-4137	184	10	1	1	NUM
ejpam-4137	184	11	,	,	PUNCT
ejpam-4137	184	12	a	a	DET
ejpam-4137	184	13	=	=	X
ejpam-4137	184	14	1,m	1,m	NOUN
ejpam-4137	184	15	=	=	SYM
ejpam-4137	184	16	y	y	PROPN
ejpam-4137	184	17	and	and	CCONJ
ejpam-4137	184	18	simplifying	simplify	VERB
ejpam-4137	184	19	using	use	VERB
ejpam-4137	184	20	entry	entry	NOUN
ejpam-4137	184	21	(	(	PUNCT
ejpam-4137	184	22	3	3	NUM
ejpam-4137	184	23	)	)	PUNCT
ejpam-4137	184	24	in	in	ADP
ejpam-4137	184	25	table	table	NOUN
ejpam-4137	184	26	below	below	ADV
ejpam-4137	184	27	(	(	PUNCT
ejpam-4137	184	28	64:12:7	64:12:7	NUM
ejpam-4137	184	29	)	)	PUNCT
ejpam-4137	184	30	in	in	ADP
ejpam-4137	184	31	[	[	X
ejpam-4137	184	32	9	9	X
ejpam-4137	184	33	]	]	PUNCT
ejpam-4137	184	34	we	we	PRON
ejpam-4137	184	35	get	get	VERB
ejpam-4137	184	36	∞∑	∞∑	NUM
ejpam-4137	184	37	n=1	n=1	ADP
ejpam-4137	184	38	4−n	4−n	ADJ
ejpam-4137	184	39	sech2	sech2	NOUN
ejpam-4137	184	40	(	(	PUNCT
ejpam-4137	184	41	2−ny	2−ny	NUM
ejpam-4137	184	42	)	)	PUNCT
ejpam-4137	184	43	=	=	SYM
ejpam-4137	185	1	1	1	NUM
ejpam-4137	185	2	y2	y2	NOUN
ejpam-4137	185	3	−	−	PROPN
ejpam-4137	185	4	csch2(y	csch2(y	NOUN
ejpam-4137	185	5	)	)	PUNCT
ejpam-4137	186	1	next	next	ADV
ejpam-4137	186	2	we	we	PRON
ejpam-4137	186	3	take	take	VERB
ejpam-4137	186	4	the	the	DET
ejpam-4137	186	5	definite	definite	ADJ
ejpam-4137	186	6	integral	integral	ADJ
ejpam-4137	186	7	over	over	ADP
ejpam-4137	186	8	y	y	PROPN
ejpam-4137	186	9	∈	∈	PROPN
ejpam-4137	187	1	[	[	X
ejpam-4137	187	2	x	x	X
ejpam-4137	187	3	,	,	PUNCT
ejpam-4137	187	4	x/2	x/2	NUM
ejpam-4137	187	5	]	]	PUNCT
ejpam-4137	187	6	to	to	ADP
ejpam-4137	187	7	get∫	get∫	PROPN
ejpam-4137	187	8	x	x	X
ejpam-4137	187	9	x/2	x/2	X
ejpam-4137	187	10	(	(	PUNCT
ejpam-4137	187	11	∞∑	∞∑	NUM
ejpam-4137	187	12	n=1	n=1	ADP
ejpam-4137	187	13	4−n	4−n	ADJ
ejpam-4137	187	14	sech2	sech2	NOUN
ejpam-4137	187	15	(	(	PUNCT
ejpam-4137	187	16	2−ny	2−ny	NUM
ejpam-4137	187	17	)	)	PUNCT
ejpam-4137	187	18	=	=	SYM
ejpam-4137	188	1	1	1	NUM
ejpam-4137	188	2	y2	y2	NOUN
ejpam-4137	188	3	−	−	PROPN
ejpam-4137	188	4	csch2(y	csch2(y	NOUN
ejpam-4137	188	5	)	)	PUNCT
ejpam-4137	188	6	)	)	PUNCT
ejpam-4137	189	1	dy	dy	PROPN
ejpam-4137	189	2	r.	r.	PROPN
ejpam-4137	189	3	reynolds	reynolds	PROPN
ejpam-4137	189	4	,	,	PUNCT
ejpam-4137	189	5	a.	a.	PROPN
ejpam-4137	189	6	stauffer	stauffer	PROPN
ejpam-4137	189	7	/	/	SYM
ejpam-4137	189	8	eur	eur	PROPN
ejpam-4137	189	9	.	.	PUNCT
ejpam-4137	190	1	j.	j.	PROPN
ejpam-4137	190	2	pure	pure	PROPN
ejpam-4137	190	3	appl	appl	PROPN
ejpam-4137	190	4	.	.	PROPN
ejpam-4137	190	5	math	math	PROPN
ejpam-4137	190	6	,	,	PUNCT
ejpam-4137	190	7	15	15	NUM
ejpam-4137	190	8	(	(	PUNCT
ejpam-4137	190	9	1	1	NUM
ejpam-4137	190	10	)	)	PUNCT
ejpam-4137	190	11	(	(	PUNCT
ejpam-4137	190	12	2022	2022	NUM
ejpam-4137	190	13	)	)	PUNCT
ejpam-4137	190	14	,	,	PUNCT
ejpam-4137	190	15	158	158	NUM
ejpam-4137	190	16	-	-	SYM
ejpam-4137	190	17	168	168	NUM
ejpam-4137	190	18	166	166	NUM
ejpam-4137	190	19	we	we	PRON
ejpam-4137	190	20	reverse	reverse	VERB
ejpam-4137	190	21	the	the	DET
ejpam-4137	190	22	order	order	NOUN
ejpam-4137	190	23	of	of	ADP
ejpam-4137	190	24	integration	integration	NOUN
ejpam-4137	190	25	and	and	CCONJ
ejpam-4137	190	26	summation	summation	NOUN
ejpam-4137	190	27	and	and	CCONJ
ejpam-4137	190	28	again	again	ADV
ejpam-4137	190	29	take	take	VERB
ejpam-4137	190	30	the	the	DET
ejpam-4137	190	31	definite	definite	ADJ
ejpam-4137	190	32	integral	integral	ADJ
ejpam-4137	190	33	over	over	ADP
ejpam-4137	190	34	x	x	PUNCT
ejpam-4137	190	35	∈	∈	PROPN
ejpam-4137	191	1	[	[	X
ejpam-4137	191	2	z	z	NOUN
ejpam-4137	191	3	,	,	PUNCT
ejpam-4137	191	4	z/2	z/2	NUM
ejpam-4137	191	5	]	]	PUNCT
ejpam-4137	191	6	to	to	ADP
ejpam-4137	191	7	get∫	get∫	PROPN
ejpam-4137	191	8	z	z	PROPN
ejpam-4137	191	9	z/2	z/2	NUM
ejpam-4137	191	10	(	(	PUNCT
ejpam-4137	191	11	∞∑	∞∑	NUM
ejpam-4137	191	12	n=1	n=1	PROPN
ejpam-4137	191	13	−2−n	−2−n	PROPN
ejpam-4137	191	14	(	(	PUNCT
ejpam-4137	191	15	tanh	tanh	PROPN
ejpam-4137	191	16	(	(	PUNCT
ejpam-4137	191	17	2−n−1x	2−n−1x	NOUN
ejpam-4137	191	18	)	)	PUNCT
ejpam-4137	191	19	−	−	PROPN
ejpam-4137	191	20	tanh	tanh	NOUN
ejpam-4137	191	21	(	(	PUNCT
ejpam-4137	191	22	2−nx	2−nx	NUM
ejpam-4137	191	23	)	)	PUNCT
ejpam-4137	191	24	)	)	PUNCT
ejpam-4137	192	1	=	=	SYM
ejpam-4137	192	2	1	1	NUM
ejpam-4137	192	3	x	x	SYM
ejpam-4137	192	4	−	−	NOUN
ejpam-4137	192	5	coth	coth	NOUN
ejpam-4137	192	6	(	(	PUNCT
ejpam-4137	192	7	x	x	SYM
ejpam-4137	192	8	2	2	NUM
ejpam-4137	192	9	)	)	PUNCT
ejpam-4137	192	10	+	+	CCONJ
ejpam-4137	192	11	coth(x	coth(x	NOUN
ejpam-4137	192	12	)	)	PUNCT
ejpam-4137	192	13	)	)	PUNCT
ejpam-4137	193	1	dx	dx	PROPN
ejpam-4137	193	2	reversing	reverse	VERB
ejpam-4137	193	3	the	the	DET
ejpam-4137	193	4	order	order	NOUN
ejpam-4137	193	5	of	of	ADP
ejpam-4137	193	6	the	the	DET
ejpam-4137	193	7	sum	sum	NOUN
ejpam-4137	193	8	and	and	CCONJ
ejpam-4137	193	9	integral	integral	ADJ
ejpam-4137	193	10	and	and	CCONJ
ejpam-4137	193	11	simplifying	simplify	VERB
ejpam-4137	193	12	we	we	PRON
ejpam-4137	193	13	get	get	VERB
ejpam-4137	193	14	∞∑	∞∑	NUM
ejpam-4137	193	15	n=1	n=1	NUM
ejpam-4137	193	16	log	log	NOUN
ejpam-4137	193	17	(	(	PUNCT
ejpam-4137	193	18	cosh2	cosh2	X
ejpam-4137	193	19	(	(	PUNCT
ejpam-4137	193	20	2−n−2z	2−n−2z	NUM
ejpam-4137	193	21	)	)	PUNCT
ejpam-4137	193	22	cosh	cosh	NOUN
ejpam-4137	193	23	(	(	PUNCT
ejpam-4137	193	24	2−nz	2−nz	NUM
ejpam-4137	193	25	)	)	PUNCT
ejpam-4137	193	26	sech3	sech3	NOUN
ejpam-4137	193	27	(	(	PUNCT
ejpam-4137	193	28	2−n−1z	2−n−1z	NUM
ejpam-4137	193	29	)	)	PUNCT
ejpam-4137	193	30	)	)	PUNCT
ejpam-4137	194	1	=	=	PRON
ejpam-4137	194	2	log	log	NOUN
ejpam-4137	194	3	(	(	PUNCT
ejpam-4137	194	4	tanh2	tanh2	NOUN
ejpam-4137	194	5	(	(	PUNCT
ejpam-4137	194	6	z	z	NOUN
ejpam-4137	194	7	4	4	NUM
ejpam-4137	194	8	)	)	PUNCT
ejpam-4137	195	1	+	+	CCONJ
ejpam-4137	195	2	1	1	X
ejpam-4137	195	3	)	)	PUNCT
ejpam-4137	195	4	whence	whence	NOUN
ejpam-4137	195	5	upon	upon	SCONJ
ejpam-4137	195	6	replacing	replace	VERB
ejpam-4137	195	7	z	z	NOUN
ejpam-4137	195	8	→	→	PUNCT
ejpam-4137	195	9	x	x	SYM
ejpam-4137	195	10	we	we	PRON
ejpam-4137	195	11	obtain	obtain	VERB
ejpam-4137	195	12	that	that	DET
ejpam-4137	195	13	∞∏	∞∏	PROPN
ejpam-4137	195	14	n=1	n=1	PUNCT
ejpam-4137	195	15	cosh2	cosh2	PROPN
ejpam-4137	195	16	(	(	PUNCT
ejpam-4137	195	17	2−2−nx	2−2−nx	NUM
ejpam-4137	195	18	)	)	PUNCT
ejpam-4137	195	19	cosh	cosh	NOUN
ejpam-4137	195	20	(	(	PUNCT
ejpam-4137	195	21	2−nx	2−nx	NUM
ejpam-4137	195	22	)	)	PUNCT
ejpam-4137	195	23	cosh3	cosh3	NOUN
ejpam-4137	195	24	(	(	PUNCT
ejpam-4137	195	25	2−1−nx	2−1−nx	NUM
ejpam-4137	195	26	)	)	PUNCT
ejpam-4137	195	27	=	=	SYM
ejpam-4137	195	28	1	1	NUM
ejpam-4137	195	29	+	+	NUM
ejpam-4137	195	30	tanh2	tanh2	NOUN
ejpam-4137	195	31	(	(	PUNCT
ejpam-4137	195	32	x	x	SYM
ejpam-4137	195	33	4	4	X
ejpam-4137	195	34	)	)	PUNCT
ejpam-4137	195	35	example	example	NOUN
ejpam-4137	196	1	15	15	NUM
ejpam-4137	196	2	.	.	PUNCT
ejpam-4137	197	1	∞∏	∞∏	PROPN
ejpam-4137	197	2	n=1	n=1	PROPN
ejpam-4137	197	3	cosh	cosh	PROPN
ejpam-4137	197	4	(	(	PUNCT
ejpam-4137	197	5	2−nx	2−nx	NUM
ejpam-4137	197	6	)	)	PUNCT
ejpam-4137	197	7	(	(	PUNCT
ejpam-4137	197	8	tanh	tanh	PROPN
ejpam-4137	197	9	(	(	PUNCT
ejpam-4137	197	10	2−n−1x	2−n−1x	NOUN
ejpam-4137	197	11	)	)	PUNCT
ejpam-4137	198	1	+	+	CCONJ
ejpam-4137	198	2	1	1	X
ejpam-4137	198	3	)	)	PUNCT
ejpam-4137	198	4	e2	e2	PROPN
ejpam-4137	198	5	−n	−n	ADJ
ejpam-4137	198	6	tanh(2−n−1x	tanh(2−n−1x	NOUN
ejpam-4137	198	7	)	)	PUNCT
ejpam-4137	198	8	sech(2−nx	sech(2−nx	NOUN
ejpam-4137	198	9	)	)	PUNCT
ejpam-4137	198	10	=	=	SYM
ejpam-4137	198	11	1	1	NUM
ejpam-4137	198	12	2	2	NUM
ejpam-4137	198	13	(	(	PUNCT
ejpam-4137	198	14	ex	ex	X
ejpam-4137	198	15	+	+	NOUN
ejpam-4137	198	16	1	1	X
ejpam-4137	198	17	)	)	PUNCT
ejpam-4137	198	18	e	e	NOUN
ejpam-4137	198	19	1	1	NUM
ejpam-4137	198	20	x	x	SYM
ejpam-4137	198	21	−coth(x	−coth(x	PROPN
ejpam-4137	198	22	2	2	NUM
ejpam-4137	198	23	)	)	PUNCT
ejpam-4137	198	24	+	+	NOUN
ejpam-4137	198	25	coth(x	coth(x	X
ejpam-4137	198	26	)	)	PUNCT
ejpam-4137	198	27	(	(	PUNCT
ejpam-4137	198	28	27	27	NUM
ejpam-4137	198	29	)	)	PUNCT
ejpam-4137	198	30	proof	proof	NOUN
ejpam-4137	198	31	.	.	PUNCT
ejpam-4137	199	1	use	use	VERB
ejpam-4137	199	2	the	the	DET
ejpam-4137	199	3	process	process	NOUN
ejpam-4137	199	4	in	in	ADP
ejpam-4137	199	5	example	example	NOUN
ejpam-4137	199	6	(	(	PUNCT
ejpam-4137	199	7	14	14	NUM
ejpam-4137	199	8	)	)	PUNCT
ejpam-4137	199	9	with	with	ADP
ejpam-4137	199	10	k	k	PROPN
ejpam-4137	199	11	=	=	SYM
ejpam-4137	199	12	1	1	NUM
ejpam-4137	199	13	,	,	PUNCT
ejpam-4137	199	14	a	a	DET
ejpam-4137	199	15	=	=	SYM
ejpam-4137	199	16	e	e	NOUN
ejpam-4137	199	17	,	,	PUNCT
ejpam-4137	199	18	m	m	VERB
ejpam-4137	199	19	=	=	SYM
ejpam-4137	199	20	x	x	X
ejpam-4137	199	21	and	and	CCONJ
ejpam-4137	199	22	simplify	simplify	ADJ
ejpam-4137	199	23	.	.	PUNCT
ejpam-4137	199	24	example	example	NOUN
ejpam-4137	200	1	16	16	NUM
ejpam-4137	200	2	.	.	PUNCT
ejpam-4137	201	1	∞∏	∞∏	PROPN
ejpam-4137	201	2	n=1	n=1	X
ejpam-4137	201	3	cosh7	cosh7	NOUN
ejpam-4137	201	4	(	(	PUNCT
ejpam-4137	201	5	2−1−nx	2−1−nx	NUM
ejpam-4137	201	6	)	)	PUNCT
ejpam-4137	201	7	cosh8	cosh8	NOUN
ejpam-4137	201	8	(	(	PUNCT
ejpam-4137	201	9	2−3−nx	2−3−nx	NUM
ejpam-4137	201	10	)	)	PUNCT
ejpam-4137	201	11	cosh	cosh	NOUN
ejpam-4137	201	12	(	(	PUNCT
ejpam-4137	201	13	2−nx	2−nx	NOUN
ejpam-4137	201	14	)	)	PUNCT
ejpam-4137	201	15	cosh14	cosh14	NOUN
ejpam-4137	201	16	(	(	PUNCT
ejpam-4137	201	17	2−2−nx	2−2−nx	NUM
ejpam-4137	201	18	)	)	PUNCT
ejpam-4137	201	19	=	=	SYM
ejpam-4137	201	20	cosh6	cosh6	NOUN
ejpam-4137	201	21	(	(	PUNCT
ejpam-4137	201	22	x	x	SYM
ejpam-4137	201	23	4	4	X
ejpam-4137	201	24	)	)	PUNCT
ejpam-4137	201	25	cosh8	cosh8	NOUN
ejpam-4137	201	26	(	(	PUNCT
ejpam-4137	201	27	x	x	SYM
ejpam-4137	201	28	8	8	X
ejpam-4137	201	29	)	)	PUNCT
ejpam-4137	201	30	cosh	cosh	NOUN
ejpam-4137	201	31	(	(	PUNCT
ejpam-4137	201	32	x	x	SYM
ejpam-4137	201	33	2	2	X
ejpam-4137	201	34	)	)	PUNCT
ejpam-4137	201	35	(	(	PUNCT
ejpam-4137	201	36	28	28	NUM
ejpam-4137	201	37	)	)	PUNCT
ejpam-4137	201	38	proof	proof	NOUN
ejpam-4137	201	39	.	.	PUNCT
ejpam-4137	202	1	use	use	VERB
ejpam-4137	202	2	the	the	DET
ejpam-4137	202	3	process	process	NOUN
ejpam-4137	202	4	in	in	ADP
ejpam-4137	202	5	example	example	NOUN
ejpam-4137	202	6	(	(	PUNCT
ejpam-4137	202	7	14	14	NUM
ejpam-4137	202	8	)	)	PUNCT
ejpam-4137	202	9	with	with	ADP
ejpam-4137	202	10	k	k	PROPN
ejpam-4137	202	11	=	=	SYM
ejpam-4137	202	12	2	2	NUM
ejpam-4137	202	13	,	,	PUNCT
ejpam-4137	202	14	a	a	DET
ejpam-4137	202	15	=	=	X
ejpam-4137	202	16	1,m	1,m	NOUN
ejpam-4137	202	17	=	=	SYM
ejpam-4137	202	18	x	x	X
ejpam-4137	202	19	and	and	CCONJ
ejpam-4137	202	20	simplify	simplify	ADJ
ejpam-4137	202	21	.	.	PUNCT
ejpam-4137	202	22	example	example	NOUN
ejpam-4137	203	1	17	17	NUM
ejpam-4137	203	2	.	.	PUNCT
ejpam-4137	204	1	∞∏	∞∏	PROPN
ejpam-4137	204	2	n=1	n=1	PROPN
ejpam-4137	204	3	cosh	cosh	PROPN
ejpam-4137	204	4	(	(	PUNCT
ejpam-4137	204	5	2−nx	2−nx	NUM
ejpam-4137	204	6	)	)	PUNCT
ejpam-4137	204	7	(	(	PUNCT
ejpam-4137	204	8	tanh	tanh	PROPN
ejpam-4137	204	9	(	(	PUNCT
ejpam-4137	204	10	2−n−1x	2−n−1x	NOUN
ejpam-4137	204	11	)	)	PUNCT
ejpam-4137	205	1	+	+	CCONJ
ejpam-4137	205	2	1	1	X
ejpam-4137	205	3	)	)	PUNCT
ejpam-4137	205	4	=	=	SYM
ejpam-4137	205	5	1	1	NUM
ejpam-4137	205	6	2	2	NUM
ejpam-4137	205	7	ex/2	ex/2	NOUN
ejpam-4137	205	8	sinh(x	sinh(x	NOUN
ejpam-4137	205	9	)	)	PUNCT
ejpam-4137	205	10	csch	csch	NOUN
ejpam-4137	205	11	(	(	PUNCT
ejpam-4137	205	12	x	x	SYM
ejpam-4137	205	13	2	2	X
ejpam-4137	205	14	)	)	PUNCT
ejpam-4137	205	15	(	(	PUNCT
ejpam-4137	205	16	29	29	NUM
ejpam-4137	205	17	)	)	PUNCT
ejpam-4137	205	18	proof	proof	NOUN
ejpam-4137	205	19	.	.	PUNCT
ejpam-4137	206	1	use	use	VERB
ejpam-4137	206	2	the	the	DET
ejpam-4137	206	3	process	process	NOUN
ejpam-4137	206	4	in	in	ADP
ejpam-4137	206	5	example	example	NOUN
ejpam-4137	206	6	(	(	PUNCT
ejpam-4137	206	7	14	14	NUM
ejpam-4137	206	8	)	)	PUNCT
ejpam-4137	206	9	with	with	ADP
ejpam-4137	206	10	k	k	PROPN
ejpam-4137	206	11	=	=	SYM
ejpam-4137	206	12	1	1	NUM
ejpam-4137	206	13	,	,	PUNCT
ejpam-4137	206	14	a	a	DET
ejpam-4137	206	15	=	=	SYM
ejpam-4137	206	16	e2a	e2a	X
ejpam-4137	206	17	,	,	PUNCT
ejpam-4137	206	18	m	m	VERB
ejpam-4137	206	19	=	=	PUNCT
ejpam-4137	206	20	x	x	X
ejpam-4137	206	21	and	and	CCONJ
ejpam-4137	206	22	simplify	simplify	ADJ
ejpam-4137	206	23	.	.	PUNCT
ejpam-4137	206	24	example	example	NOUN
ejpam-4137	206	25	18	18	NUM
ejpam-4137	206	26	.	.	PUNCT
ejpam-4137	206	27	∞∏	∞∏	PROPN
ejpam-4137	206	28	n=1	n=1	PROPN
ejpam-4137	206	29	cosh	cosh	PROPN
ejpam-4137	206	30	(	(	PUNCT
ejpam-4137	206	31	2−nx	2−nx	NOUN
ejpam-4137	206	32	)	)	PUNCT
ejpam-4137	206	33	cosh	cosh	NOUN
ejpam-4137	206	34	(	(	PUNCT
ejpam-4137	206	35	2−1−nx	2−1−nx	NUM
ejpam-4137	206	36	)	)	PUNCT
ejpam-4137	206	37	=	=	SYM
ejpam-4137	206	38	sinh(x	sinh(x	PROPN
ejpam-4137	206	39	)	)	PUNCT
ejpam-4137	206	40	2	2	NUM
ejpam-4137	206	41	sinh	sinh	NOUN
ejpam-4137	206	42	(	(	PUNCT
ejpam-4137	206	43	x	x	SYM
ejpam-4137	206	44	2	2	X
ejpam-4137	206	45	)	)	PUNCT
ejpam-4137	206	46	(	(	PUNCT
ejpam-4137	206	47	30	30	X
ejpam-4137	206	48	)	)	PUNCT
ejpam-4137	206	49	proof	proof	NOUN
ejpam-4137	206	50	.	.	PUNCT
ejpam-4137	207	1	use	use	VERB
ejpam-4137	207	2	the	the	DET
ejpam-4137	207	3	process	process	NOUN
ejpam-4137	207	4	in	in	ADP
ejpam-4137	207	5	example	example	NOUN
ejpam-4137	207	6	(	(	PUNCT
ejpam-4137	207	7	14	14	NUM
ejpam-4137	207	8	)	)	PUNCT
ejpam-4137	207	9	with	with	ADP
ejpam-4137	207	10	k	k	PROPN
ejpam-4137	207	11	=	=	SYM
ejpam-4137	207	12	1	1	NUM
ejpam-4137	207	13	,	,	PUNCT
ejpam-4137	207	14	a	a	DET
ejpam-4137	207	15	=	=	SYM
ejpam-4137	207	16	ea	ea	PROPN
ejpam-4137	207	17	,	,	PUNCT
ejpam-4137	207	18	m	m	VERB
ejpam-4137	207	19	=	=	NOUN
ejpam-4137	207	20	x	x	X
ejpam-4137	207	21	and	and	CCONJ
ejpam-4137	207	22	simplify	simplify	ADJ
ejpam-4137	207	23	.	.	PUNCT
ejpam-4137	207	24	example	example	NOUN
ejpam-4137	208	1	19	19	NUM
ejpam-4137	208	2	.	.	PUNCT
ejpam-4137	208	3	∞∏	∞∏	PROPN
ejpam-4137	208	4	n=1	n=1	PROPN
ejpam-4137	208	5	cosh2	cosh2	PROPN
ejpam-4137	208	6	(	(	PUNCT
ejpam-4137	208	7	2−2−nx	2−2−nx	NUM
ejpam-4137	208	8	)	)	PUNCT
ejpam-4137	208	9	cosh	cosh	NOUN
ejpam-4137	208	10	(	(	PUNCT
ejpam-4137	208	11	2−nx	2−nx	NUM
ejpam-4137	208	12	)	)	PUNCT
ejpam-4137	208	13	cosh3	cosh3	NOUN
ejpam-4137	208	14	(	(	PUNCT
ejpam-4137	208	15	2−1−nx	2−1−nx	NUM
ejpam-4137	208	16	)	)	PUNCT
ejpam-4137	208	17	=	=	VERB
ejpam-4137	209	1	cosh	cosh	NOUN
ejpam-4137	209	2	(	(	PUNCT
ejpam-4137	209	3	x	x	SYM
ejpam-4137	209	4	2	2	X
ejpam-4137	209	5	)	)	PUNCT
ejpam-4137	209	6	cosh2	cosh2	NOUN
ejpam-4137	210	1	(	(	PUNCT
ejpam-4137	210	2	x	x	SYM
ejpam-4137	210	3	4	4	X
ejpam-4137	210	4	)	)	PUNCT
ejpam-4137	210	5	(	(	PUNCT
ejpam-4137	210	6	31	31	NUM
ejpam-4137	210	7	)	)	PUNCT
ejpam-4137	210	8	proof	proof	NOUN
ejpam-4137	210	9	.	.	PUNCT
ejpam-4137	211	1	use	use	VERB
ejpam-4137	211	2	the	the	DET
ejpam-4137	211	3	process	process	NOUN
ejpam-4137	211	4	in	in	ADP
ejpam-4137	211	5	example	example	NOUN
ejpam-4137	211	6	(	(	PUNCT
ejpam-4137	211	7	14	14	NUM
ejpam-4137	211	8	)	)	PUNCT
ejpam-4137	211	9	with	with	ADP
ejpam-4137	211	10	k	k	PROPN
ejpam-4137	211	11	=	=	SYM
ejpam-4137	211	12	1	1	NUM
ejpam-4137	211	13	,	,	PUNCT
ejpam-4137	211	14	a	a	DET
ejpam-4137	211	15	=	=	SYM
ejpam-4137	211	16	ea	ea	PROPN
ejpam-4137	211	17	,	,	PUNCT
ejpam-4137	211	18	m	m	VERB
ejpam-4137	211	19	=	=	PUNCT
ejpam-4137	211	20	x	x	PUNCT
ejpam-4137	211	21	by	by	ADP
ejpam-4137	211	22	forming	form	VERB
ejpam-4137	211	23	a	a	DET
ejpam-4137	211	24	second	second	ADJ
ejpam-4137	211	25	equation	equation	NOUN
ejpam-4137	211	26	with	with	ADP
ejpam-4137	211	27	replacing	replace	VERB
ejpam-4137	211	28	a	a	DET
ejpam-4137	211	29	→	→	SYM
ejpam-4137	211	30	−a	−a	NOUN
ejpam-4137	211	31	and	and	CCONJ
ejpam-4137	211	32	simplify	simplify	VERB
ejpam-4137	211	33	.	.	PUNCT
ejpam-4137	212	1	references	reference	NOUN
ejpam-4137	212	2	167	167	NUM
ejpam-4137	212	3	9	9	NUM
ejpam-4137	212	4	.	.	PUNCT
ejpam-4137	213	1	discussion	discussion	NOUN
ejpam-4137	213	2	the	the	DET
ejpam-4137	213	3	authors	author	NOUN
ejpam-4137	213	4	construct	construct	VERB
ejpam-4137	213	5	an	an	DET
ejpam-4137	213	6	infinite	infinite	ADJ
ejpam-4137	213	7	sum	sum	NOUN
ejpam-4137	213	8	of	of	ADP
ejpam-4137	213	9	the	the	DET
ejpam-4137	213	10	lerch	lerch	PROPN
ejpam-4137	213	11	function	function	PROPN
ejpam-4137	213	12	φ(k	φ(k	PROPN
ejpam-4137	213	13	,	,	PUNCT
ejpam-4137	213	14	a	a	DET
ejpam-4137	213	15	,	,	PUNCT
ejpam-4137	213	16	m	m	NOUN
ejpam-4137	213	17	)	)	PUNCT
ejpam-4137	213	18	in	in	ADP
ejpam-4137	213	19	terms	term	NOUN
ejpam-4137	213	20	of	of	ADP
ejpam-4137	213	21	the	the	DET
ejpam-4137	213	22	incomplete	incomplete	ADJ
ejpam-4137	213	23	gamma	gamma	NOUN
ejpam-4137	213	24	function	function	PROPN
ejpam-4137	213	25	γ(k	γ(k	PROPN
ejpam-4137	213	26	,	,	PUNCT
ejpam-4137	213	27	a	a	PRON
ejpam-4137	213	28	)	)	PUNCT
ejpam-4137	213	29	and	and	CCONJ
ejpam-4137	213	30	the	the	DET
ejpam-4137	213	31	lerch	lerch	PROPN
ejpam-4137	213	32	function	function	PROPN
ejpam-4137	213	33	,	,	PUNCT
ejpam-4137	213	34	where	where	SCONJ
ejpam-4137	213	35	the	the	DET
ejpam-4137	213	36	parameter	parameter	NOUN
ejpam-4137	213	37	constraints	constraint	NOUN
ejpam-4137	213	38	are	be	AUX
ejpam-4137	213	39	wide	wide	ADJ
ejpam-4137	213	40	.	.	PUNCT
ejpam-4137	214	1	the	the	DET
ejpam-4137	214	2	infinite	infinite	ADJ
ejpam-4137	214	3	sum	sum	NOUN
ejpam-4137	214	4	of	of	ADP
ejpam-4137	214	5	the	the	DET
ejpam-4137	214	6	lerch	lerch	PROPN
ejpam-4137	214	7	function	function	PROPN
ejpam-4137	214	8	in	in	ADP
ejpam-4137	214	9	terms	term	NOUN
ejpam-4137	214	10	of	of	ADP
ejpam-4137	214	11	the	the	DET
ejpam-4137	214	12	lerch	lerch	PROPN
ejpam-4137	214	13	transformation	transformation	NOUN
ejpam-4137	214	14	was	be	AUX
ejpam-4137	214	15	also	also	ADV
ejpam-4137	214	16	derived	derive	VERB
ejpam-4137	214	17	.	.	PUNCT
ejpam-4137	215	1	the	the	DET
ejpam-4137	215	2	derivations	derivation	NOUN
ejpam-4137	215	3	used	use	VERB
ejpam-4137	215	4	fundamental	fundamental	ADJ
ejpam-4137	215	5	constants	constant	NOUN
ejpam-4137	215	6	and	and	CCONJ
ejpam-4137	215	7	special	special	ADJ
ejpam-4137	215	8	functions	function	NOUN
ejpam-4137	215	9	,	,	PUNCT
ejpam-4137	215	10	and	and	CCONJ
ejpam-4137	215	11	the	the	DET
ejpam-4137	215	12	infinite	infinite	ADJ
ejpam-4137	215	13	sum	sum	NOUN
ejpam-4137	215	14	allowed	allow	VERB
ejpam-4137	215	15	for	for	ADP
ejpam-4137	215	16	a	a	DET
ejpam-4137	215	17	wide	wide	ADJ
ejpam-4137	215	18	range	range	NOUN
ejpam-4137	215	19	of	of	ADP
ejpam-4137	215	20	the	the	DET
ejpam-4137	215	21	parameters	parameter	NOUN
ejpam-4137	215	22	.	.	PUNCT
ejpam-4137	216	1	we	we	PRON
ejpam-4137	216	2	checked	check	VERB
ejpam-4137	216	3	the	the	DET
ejpam-4137	216	4	outcome	outcome	NOUN
ejpam-4137	216	5	numerically	numerically	ADV
ejpam-4137	216	6	using	use	VERB
ejpam-4137	216	7	wolfram	wolfram	PROPN
ejpam-4137	216	8	mathematica	mathematica	PROPN
ejpam-4137	216	9	.	.	PUNCT
ejpam-4137	217	1	references	reference	NOUN
ejpam-4137	217	2	[	[	X
ejpam-4137	217	3	1	1	NUM
ejpam-4137	217	4	]	]	X
ejpam-4137	217	5	d.h	d.h	PROPN
ejpam-4137	217	6	.	.	PROPN
ejpam-4137	217	7	bailey	bailey	PROPN
ejpam-4137	217	8	and	and	CCONJ
ejpam-4137	217	9	j.m	j.m	PROPN
ejpam-4137	217	10	.	.	PROPN
ejpam-4137	217	11	borwein	borwein	PROPN
ejpam-4137	217	12	.	.	PUNCT
ejpam-4137	218	1	crandall	crandall	PROPN
ejpam-4137	218	2	’s	’s	PART
ejpam-4137	218	3	computation	computation	NOUN
ejpam-4137	218	4	of	of	ADP
ejpam-4137	218	5	the	the	DET
ejpam-4137	218	6	incomplete	incomplete	ADJ
ejpam-4137	218	7	gamma	gamma	NOUN
ejpam-4137	218	8	function	function	NOUN
ejpam-4137	218	9	and	and	CCONJ
ejpam-4137	218	10	the	the	DET
ejpam-4137	218	11	hurwitz	hurwitz	PROPN
ejpam-4137	218	12	zeta	zeta	PROPN
ejpam-4137	218	13	function	function	PROPN
ejpam-4137	218	14	,	,	PUNCT
ejpam-4137	218	15	with	with	ADP
ejpam-4137	218	16	applications	application	NOUN
ejpam-4137	218	17	to	to	ADP
ejpam-4137	218	18	dirichlet	dirichlet	PROPN
ejpam-4137	218	19	l	l	PROPN
ejpam-4137	218	20	-	-	NOUN
ejpam-4137	218	21	series	series	NOUN
ejpam-4137	218	22	.	.	PUNCT
ejpam-4137	219	1	applied	apply	VERB
ejpam-4137	219	2	mathematics	mathematic	NOUN
ejpam-4137	219	3	and	and	CCONJ
ejpam-4137	219	4	computation	computation	NOUN
ejpam-4137	219	5	,	,	PUNCT
ejpam-4137	219	6	268:462–477	268:462–477	NUM
ejpam-4137	219	7	,	,	PUNCT
ejpam-4137	219	8	10	10	NUM
ejpam-4137	219	9	2015	2015	NUM
ejpam-4137	219	10	.	.	PUNCT
ejpam-4137	220	1	[	[	X
ejpam-4137	220	2	2	2	X
ejpam-4137	220	3	]	]	X
ejpam-4137	220	4	harry	harry	PROPN
ejpam-4137	220	5	bateman	bateman	PROPN
ejpam-4137	220	6	.	.	PUNCT
ejpam-4137	221	1	higher	high	ADJ
ejpam-4137	221	2	transcendental	transcendental	ADJ
ejpam-4137	221	3	functions	function	NOUN
ejpam-4137	221	4	v.1	v.1	PUNCT
ejpam-4137	221	5	.	.	PUNCT
ejpam-4137	222	1	mcgraw	mcgraw	PROPN
ejpam-4137	222	2	-	-	PUNCT
ejpam-4137	222	3	hill	hill	PROPN
ejpam-4137	222	4	,	,	PUNCT
ejpam-4137	222	5	1953	1953	NUM
ejpam-4137	222	6	.	.	PUNCT
ejpam-4137	223	1	[	[	X
ejpam-4137	223	2	3	3	X
ejpam-4137	223	3	]	]	PUNCT
ejpam-4137	223	4	nist	nist	NOUN
ejpam-4137	223	5	digital	digital	PROPN
ejpam-4137	223	6	library	library	NOUN
ejpam-4137	223	7	of	of	ADP
ejpam-4137	223	8	mathematical	mathematical	ADJ
ejpam-4137	223	9	functions	function	NOUN
ejpam-4137	223	10	.	.	PUNCT
ejpam-4137	224	1	f.	f.	PROPN
ejpam-4137	224	2	w.	w.	PROPN
ejpam-4137	224	3	j.	j.	PROPN
ejpam-4137	224	4	olver	olver	PROPN
ejpam-4137	224	5	,	,	PUNCT
ejpam-4137	224	6	a.	a.	PROPN
ejpam-4137	224	7	b.	b.	PROPN
ejpam-4137	224	8	olde	olde	PROPN
ejpam-4137	224	9	daalhuis	daalhuis	PROPN
ejpam-4137	224	10	,	,	PUNCT
ejpam-4137	224	11	d.	d.	PROPN
ejpam-4137	224	12	w.	w.	PROPN
ejpam-4137	224	13	lozier	lozier	PROPN
ejpam-4137	224	14	,	,	PUNCT
ejpam-4137	224	15	b.	b.	PROPN
ejpam-4137	224	16	i.	i.	PROPN
ejpam-4137	224	17	schneider	schneider	PROPN
ejpam-4137	224	18	,	,	PUNCT
ejpam-4137	224	19	r.	r.	PROPN
ejpam-4137	224	20	f.	f.	PROPN
ejpam-4137	224	21	boisvert	boisvert	PROPN
ejpam-4137	224	22	,	,	PUNCT
ejpam-4137	224	23	c.	c.	PROPN
ejpam-4137	224	24	w.	w.	PROPN
ejpam-4137	224	25	clark	clark	PROPN
ejpam-4137	224	26	,	,	PUNCT
ejpam-4137	224	27	b.	b.	PROPN
ejpam-4137	224	28	r.	r.	PROPN
ejpam-4137	224	29	miller	miller	PROPN
ejpam-4137	224	30	,	,	PUNCT
ejpam-4137	224	31	b.	b.	PROPN
ejpam-4137	225	1	v.	v.	PROPN
ejpam-4137	225	2	saunders	saunders	PROPN
ejpam-4137	225	3	,	,	PUNCT
ejpam-4137	225	4	h.	h.	PROPN
ejpam-4137	225	5	s.	s.	PROPN
ejpam-4137	225	6	cohl	cohl	PROPN
ejpam-4137	225	7	,	,	PUNCT
ejpam-4137	225	8	and	and	CCONJ
ejpam-4137	225	9	m.	m.	PROPN
ejpam-4137	225	10	a.	a.	PROPN
ejpam-4137	225	11	mcclain	mcclain	PROPN
ejpam-4137	225	12	,	,	PUNCT
ejpam-4137	225	13	eds	eds	PROPN
ejpam-4137	225	14	.	.	PUNCT
ejpam-4137	226	1	[	[	X
ejpam-4137	226	2	4	4	NUM
ejpam-4137	226	3	]	]	X
ejpam-4137	226	4	i.	i.	PROPN
ejpam-4137	226	5	s.	s.	PROPN
ejpam-4137	226	6	gradshteyn	gradshteyn	PROPN
ejpam-4137	226	7	and	and	CCONJ
ejpam-4137	226	8	i.	i.	PROPN
ejpam-4137	226	9	m.	m.	PROPN
ejpam-4137	226	10	ryzhik	ryzhik	PROPN
ejpam-4137	226	11	.	.	PUNCT
ejpam-4137	227	1	table	table	NOUN
ejpam-4137	227	2	of	of	ADP
ejpam-4137	227	3	integrals	integral	NOUN
ejpam-4137	227	4	,	,	PUNCT
ejpam-4137	227	5	series	series	NOUN
ejpam-4137	227	6	,	,	PUNCT
ejpam-4137	227	7	and	and	CCONJ
ejpam-4137	227	8	products	product	NOUN
ejpam-4137	227	9	.	.	PUNCT
ejpam-4137	228	1	elsevier	elsevier	NOUN
ejpam-4137	228	2	/	/	SYM
ejpam-4137	228	3	academic	academic	ADJ
ejpam-4137	228	4	press	press	NOUN
ejpam-4137	228	5	,	,	PUNCT
ejpam-4137	228	6	amsterdam	amsterdam	PROPN
ejpam-4137	228	7	,	,	PUNCT
ejpam-4137	228	8	seventh	seventh	ADJ
ejpam-4137	228	9	edition	edition	NOUN
ejpam-4137	228	10	,	,	PUNCT
ejpam-4137	228	11	2007	2007	NUM
ejpam-4137	228	12	.	.	PUNCT
ejpam-4137	229	1	[	[	X
ejpam-4137	229	2	5	5	X
ejpam-4137	229	3	]	]	PUNCT
ejpam-4137	229	4	s.	s.	PROPN
ejpam-4137	229	5	kanemitsu	kanemitsu	PROPN
ejpam-4137	229	6	,	,	PUNCT
ejpam-4137	229	7	h.	h.	PROPN
ejpam-4137	229	8	kumagai	kumagai	PROPN
ejpam-4137	229	9	,	,	PUNCT
ejpam-4137	229	10	h.m	h.m	PROPN
ejpam-4137	229	11	.	.	PROPN
ejpam-4137	229	12	srivastava	srivastava	PROPN
ejpam-4137	229	13	,	,	PUNCT
ejpam-4137	229	14	and	and	CCONJ
ejpam-4137	229	15	m.	m.	NOUN
ejpam-4137	229	16	yoshimoto	yoshimoto	PROPN
ejpam-4137	229	17	.	.	PUNCT
ejpam-4137	230	1	some	some	DET
ejpam-4137	230	2	integral	integral	ADJ
ejpam-4137	230	3	and	and	CCONJ
ejpam-4137	230	4	asymptotic	asymptotic	ADJ
ejpam-4137	230	5	formulas	formula	NOUN
ejpam-4137	230	6	associated	associate	VERB
ejpam-4137	230	7	with	with	ADP
ejpam-4137	230	8	the	the	DET
ejpam-4137	230	9	hurwitz	hurwitz	PROPN
ejpam-4137	230	10	zeta	zeta	PROPN
ejpam-4137	230	11	function	function	PROPN
ejpam-4137	230	12	.	.	PUNCT
ejpam-4137	231	1	applied	apply	VERB
ejpam-4137	231	2	mathematics	mathematic	NOUN
ejpam-4137	231	3	and	and	CCONJ
ejpam-4137	231	4	computation	computation	NOUN
ejpam-4137	231	5	,	,	PUNCT
ejpam-4137	231	6	154:641–664	154:641–664	NUM
ejpam-4137	231	7	,	,	PUNCT
ejpam-4137	231	8	07	07	NUM
ejpam-4137	231	9	2004	2004	NUM
ejpam-4137	231	10	.	.	PUNCT
ejpam-4137	232	1	[	[	X
ejpam-4137	232	2	6	6	NUM
ejpam-4137	232	3	]	]	PUNCT
ejpam-4137	232	4	s	s	VERB
ejpam-4137	232	5	kanemitsu	kanemitsu	NOUN
ejpam-4137	232	6	,	,	PUNCT
ejpam-4137	232	7	y	y	PROPN
ejpam-4137	232	8	tanigawa	tanigawa	PROPN
ejpam-4137	232	9	,	,	PUNCT
ejpam-4137	232	10	h	h	PROPN
ejpam-4137	232	11	tsukada	tsukada	PROPN
ejpam-4137	232	12	,	,	PUNCT
ejpam-4137	232	13	and	and	CCONJ
ejpam-4137	232	14	m	m	PROPN
ejpam-4137	232	15	yoshimoto	yoshimoto	NOUN
ejpam-4137	232	16	.	.	PUNCT
ejpam-4137	233	1	contributions	contribution	NOUN
ejpam-4137	233	2	to	to	ADP
ejpam-4137	233	3	the	the	DET
ejpam-4137	233	4	theory	theory	NOUN
ejpam-4137	233	5	of	of	ADP
ejpam-4137	233	6	the	the	DET
ejpam-4137	233	7	hurwitz	hurwitz	PROPN
ejpam-4137	233	8	zeta	zeta	PROPN
ejpam-4137	233	9	-	-	PUNCT
ejpam-4137	233	10	function	function	NOUN
ejpam-4137	233	11	.	.	PUNCT
ejpam-4137	234	1	hardy	hardy	ADJ
ejpam-4137	234	2	-	-	PUNCT
ejpam-4137	234	3	ramanujan	ramanujan	NOUN
ejpam-4137	234	4	journal	journal	NOUN
ejpam-4137	234	5	,	,	PUNCT
ejpam-4137	234	6	volume	volume	NOUN
ejpam-4137	234	7	30	30	NUM
ejpam-4137	234	8	,	,	PUNCT
ejpam-4137	234	9	01	01	NUM
ejpam-4137	234	10	2007	2007	NUM
ejpam-4137	234	11	.	.	PUNCT
ejpam-4137	235	1	[	[	X
ejpam-4137	235	2	7	7	X
ejpam-4137	235	3	]	]	X
ejpam-4137	235	4	leonard	leonard	PROPN
ejpam-4137	235	5	lewin	lewin	PROPN
ejpam-4137	235	6	.	.	PUNCT
ejpam-4137	236	1	polylogarithms	polylogarithm	NOUN
ejpam-4137	236	2	and	and	CCONJ
ejpam-4137	236	3	associated	associated	ADJ
ejpam-4137	236	4	functions	function	NOUN
ejpam-4137	236	5	.	.	PUNCT
ejpam-4137	237	1	north	north	NOUN
ejpam-4137	237	2	holland	holland	PROPN
ejpam-4137	237	3	,	,	PUNCT
ejpam-4137	237	4	1981	1981	NUM
ejpam-4137	237	5	.	.	PUNCT
ejpam-4137	238	1	[	[	X
ejpam-4137	238	2	8	8	NUM
ejpam-4137	238	3	]	]	X
ejpam-4137	238	4	f.	f.	PROPN
ejpam-4137	238	5	oberhettinger	oberhettinger	PROPN
ejpam-4137	238	6	.	.	PUNCT
ejpam-4137	239	1	note	note	NOUN
ejpam-4137	239	2	on	on	ADP
ejpam-4137	239	3	the	the	DET
ejpam-4137	239	4	lerch	lerch	PROPN
ejpam-4137	239	5	zeta	zeta	PROPN
ejpam-4137	239	6	function	function	PROPN
ejpam-4137	239	7	.	.	PUNCT
ejpam-4137	240	1	pacific	pacific	PROPN
ejpam-4137	240	2	journal	journal	PROPN
ejpam-4137	240	3	of	of	ADP
ejpam-4137	240	4	mathematics	mathematic	NOUN
ejpam-4137	240	5	,	,	PUNCT
ejpam-4137	240	6	6(1):117	6(1):117	NUM
ejpam-4137	240	7	–	–	PUNCT
ejpam-4137	240	8	120	120	NUM
ejpam-4137	240	9	,	,	PUNCT
ejpam-4137	240	10	1956	1956	NUM
ejpam-4137	240	11	.	.	PUNCT
ejpam-4137	241	1	[	[	X
ejpam-4137	241	2	9	9	NUM
ejpam-4137	241	3	]	]	X
ejpam-4137	241	4	keith	keith	PROPN
ejpam-4137	241	5	b.	b.	PROPN
ejpam-4137	241	6	oldham	oldham	PROPN
ejpam-4137	241	7	,	,	PUNCT
ejpam-4137	241	8	jan	jan	PROPN
ejpam-4137	241	9	myland	myland	PROPN
ejpam-4137	241	10	,	,	PUNCT
ejpam-4137	241	11	and	and	CCONJ
ejpam-4137	241	12	jerome	jerome	PROPN
ejpam-4137	241	13	spanier	spanier	NOUN
ejpam-4137	241	14	.	.	PUNCT
ejpam-4137	242	1	an	an	DET
ejpam-4137	242	2	atlas	atlas	PROPN
ejpam-4137	242	3	of	of	ADP
ejpam-4137	242	4	functions	function	NOUN
ejpam-4137	242	5	:	:	PUNCT
ejpam-4137	242	6	with	with	ADP
ejpam-4137	242	7	equator	equator	NOUN
ejpam-4137	242	8	,	,	PUNCT
ejpam-4137	242	9	the	the	DET
ejpam-4137	242	10	atlas	atlas	PROPN
ejpam-4137	242	11	function	function	PROPN
ejpam-4137	242	12	calculator	calculator	NOUN
ejpam-4137	242	13	.	.	PUNCT
ejpam-4137	243	1	springer	springer	NOUN
ejpam-4137	243	2	science	science	PROPN
ejpam-4137	243	3	&	&	CCONJ
ejpam-4137	243	4	business	business	NOUN
ejpam-4137	243	5	media	medium	NOUN
ejpam-4137	243	6	,	,	PUNCT
ejpam-4137	243	7	07	07	NUM
ejpam-4137	243	8	2010	2010	NUM
ejpam-4137	243	9	.	.	PUNCT
ejpam-4137	244	1	[	[	X
ejpam-4137	244	2	10	10	NUM
ejpam-4137	244	3	]	]	X
ejpam-4137	244	4	r.	r.	PROPN
ejpam-4137	244	5	b.	b.	PROPN
ejpam-4137	244	6	paris	paris	PROPN
ejpam-4137	244	7	.	.	PUNCT
ejpam-4137	245	1	the	the	DET
ejpam-4137	245	2	stokes	stokes	PROPN
ejpam-4137	245	3	phenomenon	phenomenon	NOUN
ejpam-4137	245	4	associated	associate	VERB
ejpam-4137	245	5	with	with	ADP
ejpam-4137	245	6	the	the	DET
ejpam-4137	245	7	hurwitz	hurwitz	PROPN
ejpam-4137	245	8	zeta	zeta	PROPN
ejpam-4137	245	9	function	function	PROPN
ejpam-4137	245	10	ζ(s	ζ(s	PROPN
ejpam-4137	245	11	,	,	PUNCT
ejpam-4137	245	12	a	a	PRON
ejpam-4137	245	13	)	)	PUNCT
ejpam-4137	245	14	.	.	PUNCT
ejpam-4137	246	1	proceedings	proceeding	NOUN
ejpam-4137	246	2	of	of	ADP
ejpam-4137	246	3	the	the	DET
ejpam-4137	246	4	royal	royal	ADJ
ejpam-4137	246	5	society	society	NOUN
ejpam-4137	246	6	a	a	DET
ejpam-4137	246	7	:	:	PUNCT
ejpam-4137	246	8	mathematical	mathematical	ADJ
ejpam-4137	246	9	,	,	PUNCT
ejpam-4137	246	10	physical	physical	ADJ
ejpam-4137	246	11	and	and	CCONJ
ejpam-4137	246	12	engineering	engineering	NOUN
ejpam-4137	246	13	sciences	science	NOUN
ejpam-4137	246	14	,	,	PUNCT
ejpam-4137	246	15	461:297–304	461:297–304	NUM
ejpam-4137	246	16	,	,	PUNCT
ejpam-4137	246	17	01	01	NUM
ejpam-4137	246	18	2005	2005	NUM
ejpam-4137	246	19	.	.	PUNCT
ejpam-4137	247	1	[	[	X
ejpam-4137	247	2	11	11	NUM
ejpam-4137	247	3	]	]	PUNCT
ejpam-4137	247	4	anatolĭı	anatolĭı	PROPN
ejpam-4137	247	5	platonovich	platonovich	PROPN
ejpam-4137	247	6	prudnikov	prudnikov	PROPN
ejpam-4137	247	7	,	,	PUNCT
ejpam-4137	247	8	yu	yu	PROPN
ejpam-4137	247	9	a.	a.	NOUN
ejpam-4137	247	10	brychkov	brychkov	PROPN
ejpam-4137	247	11	,	,	PUNCT
ejpam-4137	247	12	and	and	CCONJ
ejpam-4137	247	13	oleg	oleg	PROPN
ejpam-4137	247	14	igorevich	igorevich	PROPN
ejpam-4137	247	15	marichev	marichev	PROPN
ejpam-4137	247	16	.	.	PUNCT
ejpam-4137	248	1	integrals	integral	NOUN
ejpam-4137	248	2	and	and	CCONJ
ejpam-4137	248	3	series	series	NOUN
ejpam-4137	248	4	:	:	PUNCT
ejpam-4137	248	5	more	more	ADJ
ejpam-4137	248	6	special	special	ADJ
ejpam-4137	248	7	functions	function	NOUN
ejpam-4137	248	8	.	.	PUNCT
ejpam-4137	249	1	gordon	gordon	PROPN
ejpam-4137	249	2	and	and	CCONJ
ejpam-4137	249	3	breach	breach	VERB
ejpam-4137	249	4	science	science	NOUN
ejpam-4137	249	5	publishers	publisher	NOUN
ejpam-4137	249	6	,	,	PUNCT
ejpam-4137	249	7	1986	1986	NUM
ejpam-4137	249	8	.	.	PUNCT
ejpam-4137	250	1	references	reference	NOUN
ejpam-4137	250	2	168	168	NUM
ejpam-4137	251	1	[	[	X
ejpam-4137	251	2	12	12	NUM
ejpam-4137	251	3	]	]	X
ejpam-4137	251	4	robert	robert	PROPN
ejpam-4137	251	5	reynolds	reynolds	PROPN
ejpam-4137	251	6	and	and	CCONJ
ejpam-4137	251	7	allan	allan	PROPN
ejpam-4137	251	8	stauffer	stauffer	PROPN
ejpam-4137	251	9	.	.	PUNCT
ejpam-4137	252	1	a	a	DET
ejpam-4137	252	2	method	method	NOUN
ejpam-4137	252	3	for	for	ADP
ejpam-4137	252	4	evaluating	evaluate	VERB
ejpam-4137	252	5	definite	definite	ADJ
ejpam-4137	252	6	integrals	integral	NOUN
ejpam-4137	252	7	in	in	ADP
ejpam-4137	252	8	terms	term	NOUN
ejpam-4137	252	9	of	of	ADP
ejpam-4137	252	10	special	special	ADJ
ejpam-4137	252	11	functions	function	NOUN
ejpam-4137	252	12	with	with	ADP
ejpam-4137	252	13	examples	example	NOUN
ejpam-4137	252	14	.	.	PUNCT
ejpam-4137	253	1	international	international	ADJ
ejpam-4137	253	2	mathematical	mathematical	PROPN
ejpam-4137	253	3	forum	forum	PROPN
ejpam-4137	253	4	,	,	PUNCT
ejpam-4137	253	5	15:235	15:235	NUM
ejpam-4137	253	6	–	–	PUNCT
ejpam-4137	253	7	244	244	NUM
ejpam-4137	253	8	,	,	PUNCT
ejpam-4137	253	9	2020	2020	NUM
ejpam-4137	253	10	.	.	PUNCT
ejpam-4137	254	1	[	[	X
ejpam-4137	254	2	13	13	NUM
ejpam-4137	254	3	]	]	X
ejpam-4137	254	4	robert	robert	PROPN
ejpam-4137	254	5	reynolds	reynolds	PROPN
ejpam-4137	254	6	and	and	CCONJ
ejpam-4137	254	7	allan	allan	PROPN
ejpam-4137	254	8	stauffer	stauffer	PROPN
ejpam-4137	254	9	.	.	PUNCT
ejpam-4137	254	10	infinite	infinite	PROPN
ejpam-4137	254	11	sum	sum	NOUN
ejpam-4137	254	12	of	of	ADP
ejpam-4137	254	13	the	the	DET
ejpam-4137	254	14	incomplete	incomplete	ADJ
ejpam-4137	254	15	gamma	gamma	NOUN
ejpam-4137	254	16	function	function	NOUN
ejpam-4137	254	17	expressed	express	VERB
ejpam-4137	254	18	in	in	ADP
ejpam-4137	254	19	terms	term	NOUN
ejpam-4137	254	20	of	of	ADP
ejpam-4137	254	21	the	the	DET
ejpam-4137	254	22	hurwitz	hurwitz	PROPN
ejpam-4137	254	23	zeta	zeta	PROPN
ejpam-4137	254	24	function	function	NOUN
ejpam-4137	254	25	.	.	PUNCT
ejpam-4137	255	1	mathematics	mathematic	NOUN
ejpam-4137	255	2	,	,	PUNCT
ejpam-4137	255	3	9:1952	9:1952	NUM
ejpam-4137	255	4	,	,	PUNCT
ejpam-4137	255	5	08	08	NUM
ejpam-4137	255	6	2021	2021	NUM
ejpam-4137	255	7	.	.	PUNCT
ejpam-4137	256	1	[	[	X
ejpam-4137	256	2	14	14	NUM
ejpam-4137	256	3	]	]	X
ejpam-4137	256	4	cornel	cornel	PROPN
ejpam-4137	256	5	ioan	ioan	PROPN
ejpam-4137	256	6	vălean	vălean	PROPN
ejpam-4137	256	7	.	.	PUNCT
ejpam-4137	257	1	(	(	PUNCT
ejpam-4137	257	2	almost	almost	ADV
ejpam-4137	257	3	)	)	PUNCT
ejpam-4137	257	4	impossible	impossible	ADJ
ejpam-4137	257	5	integrals	integral	NOUN
ejpam-4137	257	6	,	,	PUNCT
ejpam-4137	257	7	sums	sum	NOUN
ejpam-4137	257	8	,	,	PUNCT
ejpam-4137	257	9	and	and	CCONJ
ejpam-4137	257	10	series	series	NOUN
ejpam-4137	257	11	.	.	PUNCT
ejpam-4137	258	1	springer	springer	PROPN
ejpam-4137	258	2	,	,	PUNCT
ejpam-4137	258	3	05	05	NUM
ejpam-4137	258	4	2019	2019	NUM
ejpam-4137	258	5	.	.	PUNCT