id	sid	tid	token	lemma	pos
ejpam-4154	1	1	european	european	PROPN
ejpam-4154	1	2	journal	journal	PROPN
ejpam-4154	1	3	of	of	ADP
ejpam-4154	1	4	pure	pure	ADJ
ejpam-4154	1	5	and	and	CCONJ
ejpam-4154	1	6	applied	apply	VERB
ejpam-4154	1	7	mathematics	mathematic	NOUN
ejpam-4154	1	8	vol	vol	NOUN
ejpam-4154	1	9	.	.	PROPN
ejpam-4154	2	1	15	15	NUM
ejpam-4154	2	2	,	,	PUNCT
ejpam-4154	2	3	no	no	INTJ
ejpam-4154	2	4	.	.	NOUN
ejpam-4154	2	5	2	2	NUM
ejpam-4154	2	6	,	,	PUNCT
ejpam-4154	2	7	2022	2022	NUM
ejpam-4154	2	8	,	,	PUNCT
ejpam-4154	2	9	335	335	NUM
ejpam-4154	2	10	-	-	SYM
ejpam-4154	2	11	341	341	NUM
ejpam-4154	2	12	issn	issn	PROPN
ejpam-4154	2	13	1307	1307	NUM
ejpam-4154	2	14	-	-	SYM
ejpam-4154	2	15	5543	5543	NUM
ejpam-4154	2	16	–	–	PUNCT
ejpam-4154	2	17	ejpam.com	ejpam.com	X
ejpam-4154	2	18	published	publish	VERB
ejpam-4154	2	19	by	by	ADP
ejpam-4154	2	20	new	new	PROPN
ejpam-4154	2	21	york	york	PROPN
ejpam-4154	2	22	business	business	PROPN
ejpam-4154	2	23	global	global	PROPN
ejpam-4154	2	24	a	a	DET
ejpam-4154	2	25	note	note	NOUN
ejpam-4154	2	26	on	on	ADP
ejpam-4154	2	27	an	an	DET
ejpam-4154	2	28	octuple	octuple	NOUN
ejpam-4154	2	29	integral	integral	ADJ
ejpam-4154	2	30	in	in	ADP
ejpam-4154	2	31	terms	term	NOUN
ejpam-4154	2	32	of	of	ADP
ejpam-4154	2	33	the	the	DET
ejpam-4154	2	34	lerch	lerch	PROPN
ejpam-4154	2	35	function	function	PROPN
ejpam-4154	2	36	robert	robert	PROPN
ejpam-4154	2	37	reynolds1,∗	reynolds1,∗	PROPN
ejpam-4154	2	38	,	,	PUNCT
ejpam-4154	2	39	allan	allan	PROPN
ejpam-4154	2	40	stauffer1	stauffer1	PROPN
ejpam-4154	2	41	1	1	NUM
ejpam-4154	2	42	department	department	NOUN
ejpam-4154	2	43	of	of	ADP
ejpam-4154	2	44	mathematics	mathematic	NOUN
ejpam-4154	2	45	and	and	CCONJ
ejpam-4154	2	46	statistics	statistic	NOUN
ejpam-4154	2	47	,	,	PUNCT
ejpam-4154	2	48	faculty	faculty	NOUN
ejpam-4154	2	49	of	of	ADP
ejpam-4154	2	50	science	science	PROPN
ejpam-4154	2	51	,	,	PUNCT
ejpam-4154	2	52	york	york	PROPN
ejpam-4154	2	53	university	university	PROPN
ejpam-4154	2	54	,	,	PUNCT
ejpam-4154	2	55	toronto	toronto	PROPN
ejpam-4154	2	56	,	,	PUNCT
ejpam-4154	2	57	ontario	ontario	PROPN
ejpam-4154	2	58	,	,	PUNCT
ejpam-4154	2	59	canada	canada	PROPN
ejpam-4154	2	60	,	,	PUNCT
ejpam-4154	2	61	m3j1p3	m3j1p3	PROPN
ejpam-4154	2	62	abstract	abstract	NOUN
ejpam-4154	2	63	.	.	PUNCT
ejpam-4154	3	1	the	the	DET
ejpam-4154	3	2	known	know	VERB
ejpam-4154	3	3	exact	exact	ADJ
ejpam-4154	3	4	expression	expression	NOUN
ejpam-4154	3	5	for	for	ADP
ejpam-4154	3	6	an	an	DET
ejpam-4154	3	7	octuple	octuple	PROPN
ejpam-4154	3	8	integral	integral	ADJ
ejpam-4154	3	9	relating	relating	NOUN
ejpam-4154	3	10	to	to	ADP
ejpam-4154	3	11	research	research	NOUN
ejpam-4154	3	12	in	in	ADP
ejpam-4154	3	13	the	the	DET
ejpam-4154	3	14	fields	field	NOUN
ejpam-4154	3	15	of	of	ADP
ejpam-4154	3	16	mathematics	mathematic	NOUN
ejpam-4154	3	17	and	and	CCONJ
ejpam-4154	3	18	physics	physics	NOUN
ejpam-4154	3	19	is	be	AUX
ejpam-4154	3	20	summarized	summarize	VERB
ejpam-4154	3	21	.	.	PUNCT
ejpam-4154	4	1	a	a	DET
ejpam-4154	4	2	new	new	ADJ
ejpam-4154	4	3	closed	closed	ADJ
ejpam-4154	4	4	form	form	NOUN
ejpam-4154	4	5	expression	expression	NOUN
ejpam-4154	4	6	for	for	ADP
ejpam-4154	4	7	this	this	DET
ejpam-4154	4	8	integral	integral	NOUN
ejpam-4154	4	9	is	be	AUX
ejpam-4154	4	10	given	give	VERB
ejpam-4154	4	11	in	in	ADP
ejpam-4154	4	12	terms	term	NOUN
ejpam-4154	4	13	of	of	ADP
ejpam-4154	4	14	the	the	DET
ejpam-4154	4	15	lerch	lerch	PROPN
ejpam-4154	4	16	function	function	PROPN
ejpam-4154	4	17	.	.	PUNCT
ejpam-4154	5	1	2020	2020	NUM
ejpam-4154	5	2	mathematics	mathematic	NOUN
ejpam-4154	5	3	subject	subject	NOUN
ejpam-4154	5	4	classifications	classification	NOUN
ejpam-4154	5	5	:	:	PUNCT
ejpam-4154	5	6	primary	primary	ADJ
ejpam-4154	5	7	30e20	30e20	NOUN
ejpam-4154	5	8	,	,	PUNCT
ejpam-4154	5	9	33	33	NUM
ejpam-4154	5	10	-	-	SYM
ejpam-4154	5	11	01	01	NUM
ejpam-4154	5	12	,	,	PUNCT
ejpam-4154	5	13	33	33	NUM
ejpam-4154	5	14	-	-	SYM
ejpam-4154	5	15	03	03	NUM
ejpam-4154	5	16	,	,	PUNCT
ejpam-4154	5	17	33	33	NUM
ejpam-4154	5	18	-	-	PUNCT
ejpam-4154	5	19	04	04	NUM
ejpam-4154	5	20	,	,	PUNCT
ejpam-4154	5	21	33	33	NUM
ejpam-4154	5	22	-	-	PUNCT
ejpam-4154	5	23	33b	33b	NUM
ejpam-4154	5	24	key	key	ADJ
ejpam-4154	5	25	words	word	NOUN
ejpam-4154	5	26	and	and	CCONJ
ejpam-4154	5	27	phrases	phrase	NOUN
ejpam-4154	5	28	:	:	PUNCT
ejpam-4154	5	29	octuple	octuple	PROPN
ejpam-4154	5	30	integral	integral	PROPN
ejpam-4154	5	31	,	,	PUNCT
ejpam-4154	5	32	riemann	riemann	PROPN
ejpam-4154	5	33	zeta	zeta	PROPN
ejpam-4154	5	34	function	function	PROPN
ejpam-4154	5	35	,	,	PUNCT
ejpam-4154	5	36	cauchy	cauchy	PROPN
ejpam-4154	5	37	integral	integral	PROPN
ejpam-4154	5	38	,	,	PUNCT
ejpam-4154	5	39	lerch	lerch	PROPN
ejpam-4154	5	40	function	function	PROPN
ejpam-4154	5	41	1	1	NUM
ejpam-4154	5	42	.	.	PUNCT
ejpam-4154	5	43	significance	significance	NOUN
ejpam-4154	5	44	statement	statement	NOUN
ejpam-4154	5	45	octuple	octuple	PROPN
ejpam-4154	5	46	integrals	integral	NOUN
ejpam-4154	5	47	are	be	AUX
ejpam-4154	5	48	used	use	VERB
ejpam-4154	5	49	and	and	CCONJ
ejpam-4154	5	50	evaluated	evaluate	VERB
ejpam-4154	5	51	in	in	ADP
ejpam-4154	5	52	may	may	PROPN
ejpam-4154	5	53	areas	area	NOUN
ejpam-4154	5	54	of	of	ADP
ejpam-4154	5	55	mathematics	mathematic	NOUN
ejpam-4154	5	56	and	and	CCONJ
ejpam-4154	5	57	physics	physics	NOUN
ejpam-4154	5	58	.	.	PUNCT
ejpam-4154	6	1	some	some	DET
ejpam-4154	6	2	areas	area	NOUN
ejpam-4154	6	3	of	of	ADP
ejpam-4154	6	4	interest	interest	NOUN
ejpam-4154	6	5	where	where	SCONJ
ejpam-4154	6	6	these	these	DET
ejpam-4154	6	7	integrals	integral	NOUN
ejpam-4154	6	8	are	be	AUX
ejpam-4154	6	9	used	use	VERB
ejpam-4154	6	10	are	be	AUX
ejpam-4154	6	11	in	in	ADP
ejpam-4154	6	12	multipupil	multipupil	NOUN
ejpam-4154	6	13	in	in	ADP
ejpam-4154	6	14	phase	phase	NOUN
ejpam-4154	6	15	microscopy	microscopy	NOUN
ejpam-4154	6	16	,	,	PUNCT
ejpam-4154	6	17	where	where	SCONJ
ejpam-4154	6	18	pairs	pair	NOUN
ejpam-4154	6	19	of	of	ADP
ejpam-4154	6	20	fourier	fourier	NOUN
ejpam-4154	6	21	transforms	transform	NOUN
ejpam-4154	6	22	are	be	AUX
ejpam-4154	6	23	evaluated	evaluate	VERB
ejpam-4154	6	24	[	[	PUNCT
ejpam-4154	6	25	8	8	NUM
ejpam-4154	6	26	]	]	PUNCT
ejpam-4154	6	27	,	,	PUNCT
ejpam-4154	6	28	the	the	DET
ejpam-4154	6	29	kinetic	kinetic	ADJ
ejpam-4154	6	30	theory	theory	NOUN
ejpam-4154	6	31	of	of	ADP
ejpam-4154	6	32	simple	simple	ADJ
ejpam-4154	6	33	and	and	CCONJ
ejpam-4154	6	34	composite	composite	ADJ
ejpam-4154	6	35	monatomic	monatomic	ADJ
ejpam-4154	6	36	gases	gas	NOUN
ejpam-4154	6	37	:	:	PUNCT
ejpam-4154	6	38	viscosity	viscosity	NOUN
ejpam-4154	6	39	,	,	PUNCT
ejpam-4154	6	40	thermal	thermal	ADJ
ejpam-4154	6	41	conduction	conduction	NOUN
ejpam-4154	6	42	,	,	PUNCT
ejpam-4154	6	43	and	and	CCONJ
ejpam-4154	6	44	diffusion	diffusion	NOUN
ejpam-4154	7	1	[	[	X
ejpam-4154	7	2	1	1	NUM
ejpam-4154	7	3	]	]	PUNCT
ejpam-4154	7	4	,	,	PUNCT
ejpam-4154	7	5	statistical	statistical	ADJ
ejpam-4154	7	6	characteristics	characteristic	NOUN
ejpam-4154	7	7	of	of	ADP
ejpam-4154	7	8	the	the	DET
ejpam-4154	7	9	laser	laser	NOUN
ejpam-4154	7	10	-	-	PUNCT
ejpam-4154	7	11	radiation	radiation	NOUN
ejpam-4154	7	12	-	-	PUNCT
ejpam-4154	7	13	intensity	intensity	NOUN
ejpam-4154	7	14	fluctuations	fluctuation	NOUN
ejpam-4154	7	15	in	in	ADP
ejpam-4154	7	16	rainfall	rainfall	NOUN
ejpam-4154	7	17	[	[	X
ejpam-4154	7	18	6	6	NUM
ejpam-4154	7	19	]	]	PUNCT
ejpam-4154	7	20	,	,	PUNCT
ejpam-4154	7	21	the	the	DET
ejpam-4154	7	22	velocity	velocity	NOUN
ejpam-4154	7	23	distribution	distribution	NOUN
ejpam-4154	7	24	function	function	NOUN
ejpam-4154	7	25	,	,	PUNCT
ejpam-4154	7	26	and	and	CCONJ
ejpam-4154	7	27	on	on	ADP
ejpam-4154	7	28	the	the	DET
ejpam-4154	7	29	stresses	stress	NOUN
ejpam-4154	7	30	in	in	ADP
ejpam-4154	7	31	a	a	DET
ejpam-4154	7	32	non	non	ADJ
ejpam-4154	7	33	-	-	ADJ
ejpam-4154	7	34	uniform	uniform	ADJ
ejpam-4154	7	35	rarefied	rarefied	ADJ
ejpam-4154	7	36	monatomic	monatomic	ADJ
ejpam-4154	7	37	gas	gas	NOUN
ejpam-4154	8	1	[	[	X
ejpam-4154	8	2	5	5	NUM
ejpam-4154	8	3	]	]	PUNCT
ejpam-4154	8	4	,	,	PUNCT
ejpam-4154	8	5	and	and	CCONJ
ejpam-4154	8	6	some	some	DET
ejpam-4154	8	7	applications	application	NOUN
ejpam-4154	8	8	of	of	ADP
ejpam-4154	8	9	marcel	marcel	PROPN
ejpam-4154	8	10	riesz	riesz	PROPN
ejpam-4154	8	11	’s	’s	PART
ejpam-4154	8	12	integrals	integral	NOUN
ejpam-4154	8	13	of	of	ADP
ejpam-4154	8	14	fractional	fractional	ADJ
ejpam-4154	8	15	order	order	NOUN
ejpam-4154	8	16	[	[	X
ejpam-4154	8	17	2	2	NUM
ejpam-4154	8	18	]	]	PUNCT
ejpam-4154	8	19	.	.	PUNCT
ejpam-4154	9	1	in	in	ADP
ejpam-4154	9	2	current	current	ADJ
ejpam-4154	9	3	literature	literature	NOUN
ejpam-4154	9	4	octuple	octuple	PROPN
ejpam-4154	9	5	integrals	integral	NOUN
ejpam-4154	9	6	expressed	express	VERB
ejpam-4154	9	7	in	in	ADP
ejpam-4154	9	8	terms	term	NOUN
ejpam-4154	9	9	of	of	ADP
ejpam-4154	9	10	a	a	DET
ejpam-4154	9	11	closed	closed	ADJ
ejpam-4154	9	12	form	form	NOUN
ejpam-4154	9	13	solution	solution	NOUN
ejpam-4154	9	14	do	do	AUX
ejpam-4154	9	15	not	not	PART
ejpam-4154	9	16	appear	appear	VERB
ejpam-4154	9	17	to	to	PART
ejpam-4154	9	18	be	be	AUX
ejpam-4154	9	19	tabulated	tabulate	VERB
ejpam-4154	9	20	.	.	PUNCT
ejpam-4154	10	1	in	in	ADP
ejpam-4154	10	2	this	this	DET
ejpam-4154	10	3	work	work	NOUN
ejpam-4154	10	4	the	the	DET
ejpam-4154	10	5	authors	author	NOUN
ejpam-4154	10	6	derive	derive	VERB
ejpam-4154	10	7	and	and	CCONJ
ejpam-4154	10	8	evaluate	evaluate	VERB
ejpam-4154	10	9	a	a	DET
ejpam-4154	10	10	octuple	octuple	NOUN
ejpam-4154	10	11	integral	integral	ADJ
ejpam-4154	10	12	in	in	ADP
ejpam-4154	10	13	terms	term	NOUN
ejpam-4154	10	14	of	of	ADP
ejpam-4154	10	15	the	the	DET
ejpam-4154	10	16	lerch	lerch	PROPN
ejpam-4154	10	17	function	function	PROPN
ejpam-4154	10	18	and	and	CCONJ
ejpam-4154	10	19	derive	derive	VERB
ejpam-4154	10	20	special	special	ADJ
ejpam-4154	10	21	cases	case	NOUN
ejpam-4154	10	22	of	of	ADP
ejpam-4154	10	23	this	this	DET
ejpam-4154	10	24	integral	integral	ADJ
ejpam-4154	10	25	transform	transform	NOUN
ejpam-4154	10	26	in	in	ADP
ejpam-4154	10	27	terms	term	NOUN
ejpam-4154	10	28	of	of	ADP
ejpam-4154	10	29	special	special	ADJ
ejpam-4154	10	30	constants	constant	NOUN
ejpam-4154	10	31	.	.	PUNCT
ejpam-4154	11	1	it	it	PRON
ejpam-4154	11	2	is	be	AUX
ejpam-4154	11	3	our	our	PRON
ejpam-4154	11	4	hope	hope	NOUN
ejpam-4154	11	5	that	that	SCONJ
ejpam-4154	11	6	researchers	researcher	NOUN
ejpam-4154	11	7	will	will	AUX
ejpam-4154	11	8	find	find	VERB
ejpam-4154	11	9	such	such	ADJ
ejpam-4154	11	10	evaluations	evaluation	NOUN
ejpam-4154	11	11	useful	useful	ADJ
ejpam-4154	11	12	for	for	ADP
ejpam-4154	11	13	potential	potential	ADJ
ejpam-4154	11	14	research	research	NOUN
ejpam-4154	11	15	requiring	require	VERB
ejpam-4154	11	16	these	these	DET
ejpam-4154	11	17	formulae	formulae	NOUN
ejpam-4154	11	18	.	.	PUNCT
ejpam-4154	12	1	∗corresponding	∗corresponde	VERB
ejpam-4154	12	2	author	author	NOUN
ejpam-4154	12	3	.	.	PUNCT
ejpam-4154	13	1	doi	doi	NOUN
ejpam-4154	13	2	:	:	PUNCT
ejpam-4154	13	3	https://doi.org/10.29020/nybg.ejpam.v15i2.4154	https://doi.org/10.29020/nybg.ejpam.v15i2.4154	ADJ
ejpam-4154	13	4	email	email	NOUN
ejpam-4154	13	5	addresses	address	NOUN
ejpam-4154	13	6	:	:	PUNCT
ejpam-4154	14	1	milver@my.yorku.ca	milver@my.yorku.ca	NOUN
ejpam-4154	14	2	(	(	PUNCT
ejpam-4154	14	3	r.	r.	PROPN
ejpam-4154	14	4	reynolds	reynolds	PROPN
ejpam-4154	14	5	)	)	PUNCT
ejpam-4154	14	6	,	,	PUNCT
ejpam-4154	14	7	stauffer@yorku.ca	stauffer@yorku.ca	NOUN
ejpam-4154	14	8	(	(	PUNCT
ejpam-4154	14	9	a.	a.	NOUN
ejpam-4154	14	10	stauffer	stauffer	PROPN
ejpam-4154	14	11	)	)	PUNCT
ejpam-4154	14	12	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4154	15	1	335	335	NUM
ejpam-4154	16	1	©	©	NOUN
ejpam-4154	16	2	2022	2022	NUM
ejpam-4154	16	3	ejpam	ejpam	VERB
ejpam-4154	16	4	all	all	DET
ejpam-4154	16	5	rights	right	NOUN
ejpam-4154	16	6	reserved	reserve	VERB
ejpam-4154	16	7	.	.	PUNCT
ejpam-4154	17	1	r.	r.	PROPN
ejpam-4154	17	2	reynolds	reynolds	PROPN
ejpam-4154	17	3	,	,	PUNCT
ejpam-4154	17	4	a.	a.	PROPN
ejpam-4154	17	5	stauffer	stauffer	PROPN
ejpam-4154	17	6	/	/	SYM
ejpam-4154	17	7	eur	eur	PROPN
ejpam-4154	17	8	.	.	PUNCT
ejpam-4154	18	1	j.	j.	PROPN
ejpam-4154	18	2	pure	pure	PROPN
ejpam-4154	18	3	appl	appl	PROPN
ejpam-4154	18	4	.	.	PROPN
ejpam-4154	18	5	math	math	PROPN
ejpam-4154	18	6	,	,	PUNCT
ejpam-4154	18	7	15	15	NUM
ejpam-4154	18	8	(	(	PUNCT
ejpam-4154	18	9	2	2	NUM
ejpam-4154	18	10	)	)	PUNCT
ejpam-4154	18	11	(	(	PUNCT
ejpam-4154	18	12	2022	2022	NUM
ejpam-4154	18	13	)	)	PUNCT
ejpam-4154	18	14	,	,	PUNCT
ejpam-4154	18	15	335	335	NUM
ejpam-4154	18	16	-	-	SYM
ejpam-4154	18	17	341	341	NUM
ejpam-4154	18	18	336	336	NUM
ejpam-4154	18	19	2	2	NUM
ejpam-4154	18	20	.	.	PUNCT
ejpam-4154	19	1	introduction	introduction	NOUN
ejpam-4154	19	2	the	the	DET
ejpam-4154	19	3	octuple	octuple	PROPN
ejpam-4154	19	4	integral	integral	ADJ
ejpam-4154	19	5	derived	derive	VERB
ejpam-4154	19	6	in	in	ADP
ejpam-4154	19	7	this	this	DET
ejpam-4154	19	8	manuscript	manuscript	NOUN
ejpam-4154	19	9	is	be	AUX
ejpam-4154	19	10	given	give	VERB
ejpam-4154	19	11	by	by	ADP
ejpam-4154	19	12	∫	∫	PROPN
ejpam-4154	19	13	r8	r8	PROPN
ejpam-4154	20	1	+	+	CCONJ
ejpam-4154	20	2	(	(	PUNCT
ejpam-4154	20	3	rs	rs	NOUN
ejpam-4154	20	4	)	)	PUNCT
ejpam-4154	20	5	m−1	m−1	PROPN
ejpam-4154	20	6	2	2	NUM
ejpam-4154	20	7	(	(	PUNCT
ejpam-4154	20	8	r	r	NOUN
ejpam-4154	20	9	+	+	X
ejpam-4154	20	10	s)−m/2(tz)−	s)−m/2(tz)−	PROPN
ejpam-4154	20	11	m	m	PROPN
ejpam-4154	20	12	2	2	NUM
ejpam-4154	20	13	−1(t+	−1(t+	NOUN
ejpam-4154	20	14	z	z	NOUN
ejpam-4154	20	15	)	)	PUNCT
ejpam-4154	20	16	m+1	m+1	NUM
ejpam-4154	20	17	2	2	NUM
ejpam-4154	20	18	(	(	PUNCT
ejpam-4154	20	19	uv)−	uv)−	NOUN
ejpam-4154	20	20	m	m	NOUN
ejpam-4154	20	21	2	2	NUM
ejpam-4154	20	22	−	−	NOUN
ejpam-4154	20	23	1	1	NUM
ejpam-4154	20	24	2	2	NUM
ejpam-4154	20	25	(	(	PUNCT
ejpam-4154	20	26	u+	u+	NOUN
ejpam-4154	20	27	v)m/2(xy)m/2(x+	v)m/2(xy)m/2(x+	NOUN
ejpam-4154	20	28	y	y	NOUN
ejpam-4154	20	29	)	)	PUNCT
ejpam-4154	20	30	1	1	NUM
ejpam-4154	20	31	2	2	NUM
ejpam-4154	20	32	(	(	PUNCT
ejpam-4154	20	33	−m−1)e−p(r+u+x+z)−q(s+t+v+y	−m−1)e−p(r+u+x+z)−q(s+t+v+y	NOUN
ejpam-4154	20	34	)	)	PUNCT
ejpam-4154	20	35	logk	logk	NOUN
ejpam-4154	20	36	(	(	PUNCT
ejpam-4154	20	37	a	a	DET
ejpam-4154	20	38	√	√	NUM
ejpam-4154	20	39	rs	rs	NOUN
ejpam-4154	20	40	√	√	NUM
ejpam-4154	20	41	t+	t+	NOUN
ejpam-4154	20	42	z	z	NOUN
ejpam-4154	20	43	√	√	PROPN
ejpam-4154	20	44	u+	u+	NUM
ejpam-4154	20	45	v	v	ADP
ejpam-4154	20	46	√	√	PROPN
ejpam-4154	20	47	xy	xy	NOUN
ejpam-4154	20	48	√	√	PUNCT
ejpam-4154	21	1	r	r	NOUN
ejpam-4154	21	2	+	+	SYM
ejpam-4154	21	3	s	s	NOUN
ejpam-4154	21	4	√	√	NOUN
ejpam-4154	21	5	tz	tz	NOUN
ejpam-4154	21	6	√	√	NUM
ejpam-4154	21	7	uv	uv	NOUN
ejpam-4154	21	8	√	√	NOUN
ejpam-4154	21	9	x+	x+	PROPN
ejpam-4154	21	10	y	y	PROPN
ejpam-4154	21	11	)	)	PUNCT
ejpam-4154	21	12	dxdydzdrdsdtdudv	dxdydzdrdsdtdudv	PROPN
ejpam-4154	21	13	(	(	PUNCT
ejpam-4154	21	14	1	1	NUM
ejpam-4154	21	15	)	)	PUNCT
ejpam-4154	21	16	where	where	SCONJ
ejpam-4154	21	17	the	the	DET
ejpam-4154	21	18	parameters	parameter	NOUN
ejpam-4154	21	19	k	k	PROPN
ejpam-4154	21	20	,	,	PUNCT
ejpam-4154	21	21	a	a	DET
ejpam-4154	21	22	∈	∈	PROPN
ejpam-4154	21	23	c	c	NOUN
ejpam-4154	21	24	,	,	PUNCT
ejpam-4154	21	25	re(p	re(p	NOUN
ejpam-4154	21	26	,	,	PUNCT
ejpam-4154	21	27	q	q	X
ejpam-4154	21	28	)	)	PUNCT
ejpam-4154	21	29	>	>	X
ejpam-4154	21	30	0	0	PUNCT
ejpam-4154	21	31	are	be	AUX
ejpam-4154	21	32	general	general	ADJ
ejpam-4154	21	33	complex	complex	ADJ
ejpam-4154	21	34	numbers	number	NOUN
ejpam-4154	21	35	with	with	ADP
ejpam-4154	21	36	−1/2	−1/2	ADJ
ejpam-4154	21	37	≥	≥	NOUN
ejpam-4154	21	38	re(m	re(m	NUM
ejpam-4154	21	39	)	)	PUNCT
ejpam-4154	21	40	≥	≥	X
ejpam-4154	21	41	−1	−1	NOUN
ejpam-4154	21	42	.	.	PUNCT
ejpam-4154	22	1	the	the	DET
ejpam-4154	22	2	derivation	derivation	NOUN
ejpam-4154	22	3	of	of	ADP
ejpam-4154	22	4	the	the	DET
ejpam-4154	22	5	definite	definite	ADJ
ejpam-4154	22	6	integral	integral	NOUN
ejpam-4154	22	7	follows	follow	VERB
ejpam-4154	22	8	the	the	DET
ejpam-4154	22	9	method	method	NOUN
ejpam-4154	22	10	used	use	VERB
ejpam-4154	22	11	by	by	ADP
ejpam-4154	22	12	us	we	PRON
ejpam-4154	22	13	in	in	ADP
ejpam-4154	22	14	[	[	X
ejpam-4154	22	15	10	10	NUM
ejpam-4154	22	16	]	]	PUNCT
ejpam-4154	22	17	which	which	PRON
ejpam-4154	22	18	involves	involve	VERB
ejpam-4154	22	19	cauchy	cauchy	PROPN
ejpam-4154	22	20	’s	’s	PART
ejpam-4154	22	21	integral	integral	ADJ
ejpam-4154	22	22	formula	formula	NOUN
ejpam-4154	22	23	.	.	PUNCT
ejpam-4154	23	1	the	the	DET
ejpam-4154	23	2	generalized	generalized	ADJ
ejpam-4154	23	3	cauchy	cauchy	PROPN
ejpam-4154	23	4	’s	’s	PART
ejpam-4154	23	5	integral	integral	ADJ
ejpam-4154	23	6	formula	formula	NOUN
ejpam-4154	23	7	is	be	AUX
ejpam-4154	23	8	given	give	VERB
ejpam-4154	23	9	by	by	ADP
ejpam-4154	23	10	yk	yk	PROPN
ejpam-4154	23	11	γ(k	γ(k	PROPN
ejpam-4154	23	12	+	+	CCONJ
ejpam-4154	23	13	1	1	X
ejpam-4154	23	14	)	)	PUNCT
ejpam-4154	23	15	=	=	SYM
ejpam-4154	23	16	1	1	NUM
ejpam-4154	23	17	2πi	2πi	ADJ
ejpam-4154	23	18	∫	∫	PROPN
ejpam-4154	23	19	c	c	PROPN
ejpam-4154	23	20	ewy	ewy	PROPN
ejpam-4154	23	21	wk+1	wk+1	PROPN
ejpam-4154	23	22	dw	dw	PROPN
ejpam-4154	23	23	.	.	PUNCT
ejpam-4154	24	1	(	(	PUNCT
ejpam-4154	24	2	2	2	X
ejpam-4154	24	3	)	)	PUNCT
ejpam-4154	24	4	where	where	SCONJ
ejpam-4154	24	5	c	c	NOUN
ejpam-4154	24	6	is	be	AUX
ejpam-4154	24	7	in	in	ADP
ejpam-4154	24	8	general	general	ADJ
ejpam-4154	24	9	an	an	DET
ejpam-4154	24	10	open	open	ADJ
ejpam-4154	24	11	contour	contour	NOUN
ejpam-4154	24	12	in	in	ADP
ejpam-4154	24	13	the	the	DET
ejpam-4154	24	14	complex	complex	ADJ
ejpam-4154	24	15	plane	plane	NOUN
ejpam-4154	24	16	where	where	SCONJ
ejpam-4154	24	17	the	the	DET
ejpam-4154	24	18	bilinear	bilinear	NOUN
ejpam-4154	24	19	concomitant	concomitant	NOUN
ejpam-4154	25	1	[	[	X
ejpam-4154	25	2	10	10	NUM
ejpam-4154	25	3	]	]	PUNCT
ejpam-4154	25	4	has	have	VERB
ejpam-4154	25	5	the	the	DET
ejpam-4154	25	6	same	same	ADJ
ejpam-4154	25	7	value	value	NOUN
ejpam-4154	25	8	at	at	ADP
ejpam-4154	25	9	the	the	DET
ejpam-4154	25	10	end	end	NOUN
ejpam-4154	25	11	points	point	NOUN
ejpam-4154	25	12	of	of	ADP
ejpam-4154	25	13	the	the	DET
ejpam-4154	25	14	contour	contour	NOUN
ejpam-4154	25	15	.	.	PUNCT
ejpam-4154	26	1	the	the	DET
ejpam-4154	26	2	method	method	NOUN
ejpam-4154	26	3	in	in	ADP
ejpam-4154	26	4	[	[	X
ejpam-4154	26	5	10	10	NUM
ejpam-4154	26	6	]	]	PUNCT
ejpam-4154	26	7	involves	involve	VERB
ejpam-4154	26	8	using	use	VERB
ejpam-4154	26	9	a	a	DET
ejpam-4154	26	10	form	form	NOUN
ejpam-4154	26	11	of	of	ADP
ejpam-4154	26	12	equation	equation	NOUN
ejpam-4154	26	13	(	(	PUNCT
ejpam-4154	26	14	2	2	NUM
ejpam-4154	26	15	)	)	PUNCT
ejpam-4154	26	16	then	then	ADV
ejpam-4154	26	17	multiply	multiply	VERB
ejpam-4154	26	18	both	both	DET
ejpam-4154	26	19	sides	side	NOUN
ejpam-4154	26	20	by	by	ADP
ejpam-4154	26	21	a	a	DET
ejpam-4154	26	22	function	function	NOUN
ejpam-4154	26	23	,	,	PUNCT
ejpam-4154	26	24	then	then	ADV
ejpam-4154	26	25	take	take	VERB
ejpam-4154	26	26	a	a	DET
ejpam-4154	26	27	definite	definite	ADJ
ejpam-4154	26	28	integral	integral	NOUN
ejpam-4154	26	29	of	of	ADP
ejpam-4154	26	30	both	both	DET
ejpam-4154	26	31	sides	side	NOUN
ejpam-4154	26	32	.	.	PUNCT
ejpam-4154	27	1	this	this	PRON
ejpam-4154	27	2	yields	yield	VERB
ejpam-4154	27	3	a	a	DET
ejpam-4154	27	4	definite	definite	ADJ
ejpam-4154	27	5	integral	integral	ADJ
ejpam-4154	27	6	in	in	ADP
ejpam-4154	27	7	terms	term	NOUN
ejpam-4154	27	8	of	of	ADP
ejpam-4154	27	9	a	a	DET
ejpam-4154	27	10	contour	contour	NOUN
ejpam-4154	27	11	integral	integral	NOUN
ejpam-4154	27	12	.	.	PUNCT
ejpam-4154	28	1	a	a	DET
ejpam-4154	28	2	second	second	ADJ
ejpam-4154	28	3	contour	contour	NOUN
ejpam-4154	28	4	integral	integral	NOUN
ejpam-4154	28	5	is	be	AUX
ejpam-4154	28	6	derived	derive	VERB
ejpam-4154	28	7	by	by	ADP
ejpam-4154	28	8	multiplying	multiply	VERB
ejpam-4154	28	9	equation	equation	NOUN
ejpam-4154	28	10	(	(	PUNCT
ejpam-4154	28	11	2	2	NUM
ejpam-4154	28	12	)	)	PUNCT
ejpam-4154	28	13	by	by	ADP
ejpam-4154	28	14	a	a	DET
ejpam-4154	28	15	function	function	NOUN
ejpam-4154	28	16	and	and	CCONJ
ejpam-4154	28	17	performing	perform	VERB
ejpam-4154	28	18	some	some	DET
ejpam-4154	28	19	substitutions	substitution	NOUN
ejpam-4154	28	20	and	and	CCONJ
ejpam-4154	28	21	taking	take	VERB
ejpam-4154	28	22	the	the	DET
ejpam-4154	28	23	infinite	infinite	ADJ
ejpam-4154	28	24	sum	sum	NOUN
ejpam-4154	28	25	so	so	SCONJ
ejpam-4154	28	26	that	that	SCONJ
ejpam-4154	28	27	the	the	DET
ejpam-4154	28	28	contour	contour	NOUN
ejpam-4154	28	29	integrals	integral	NOUN
ejpam-4154	28	30	are	be	AUX
ejpam-4154	28	31	the	the	DET
ejpam-4154	28	32	same	same	ADJ
ejpam-4154	28	33	.	.	PUNCT
ejpam-4154	29	1	3	3	X
ejpam-4154	29	2	.	.	X
ejpam-4154	29	3	definite	definite	ADJ
ejpam-4154	29	4	integral	integral	ADJ
ejpam-4154	29	5	of	of	ADP
ejpam-4154	29	6	the	the	DET
ejpam-4154	29	7	contour	contour	NOUN
ejpam-4154	29	8	integral	integral	NOUN
ejpam-4154	29	9	we	we	PRON
ejpam-4154	29	10	use	use	VERB
ejpam-4154	29	11	the	the	DET
ejpam-4154	29	12	method	method	NOUN
ejpam-4154	29	13	in	in	ADP
ejpam-4154	29	14	[	[	X
ejpam-4154	29	15	10	10	NUM
ejpam-4154	29	16	]	]	PUNCT
ejpam-4154	29	17	.	.	PUNCT
ejpam-4154	30	1	the	the	DET
ejpam-4154	30	2	variable	variable	NOUN
ejpam-4154	30	3	of	of	ADP
ejpam-4154	30	4	integration	integration	NOUN
ejpam-4154	30	5	in	in	ADP
ejpam-4154	30	6	the	the	DET
ejpam-4154	30	7	contour	contour	NOUN
ejpam-4154	30	8	integral	integral	NOUN
ejpam-4154	30	9	is	be	AUX
ejpam-4154	30	10	z	z	NOUN
ejpam-4154	30	11	=	=	PUNCT
ejpam-4154	30	12	w+m	w+m	NUM
ejpam-4154	30	13	.	.	PUNCT
ejpam-4154	31	1	the	the	DET
ejpam-4154	31	2	cut	cut	NOUN
ejpam-4154	31	3	and	and	CCONJ
ejpam-4154	31	4	contour	contour	NOUN
ejpam-4154	31	5	are	be	AUX
ejpam-4154	31	6	in	in	ADP
ejpam-4154	31	7	the	the	DET
ejpam-4154	31	8	second	second	ADJ
ejpam-4154	31	9	quadrant	quadrant	NOUN
ejpam-4154	31	10	of	of	ADP
ejpam-4154	31	11	the	the	DET
ejpam-4154	31	12	complex	complex	ADJ
ejpam-4154	31	13	z	z	NOUN
ejpam-4154	31	14	-	-	NOUN
ejpam-4154	31	15	plane	plane	NOUN
ejpam-4154	31	16	.	.	PUNCT
ejpam-4154	32	1	the	the	DET
ejpam-4154	32	2	cut	cut	NOUN
ejpam-4154	32	3	approaches	approach	VERB
ejpam-4154	32	4	the	the	DET
ejpam-4154	32	5	origin	origin	NOUN
ejpam-4154	32	6	from	from	ADP
ejpam-4154	32	7	the	the	DET
ejpam-4154	32	8	interior	interior	NOUN
ejpam-4154	32	9	of	of	ADP
ejpam-4154	32	10	the	the	DET
ejpam-4154	32	11	first	first	ADJ
ejpam-4154	32	12	or	or	CCONJ
ejpam-4154	32	13	second	second	ADJ
ejpam-4154	32	14	quadrant	quadrant	NOUN
ejpam-4154	32	15	and	and	CCONJ
ejpam-4154	32	16	the	the	DET
ejpam-4154	32	17	contour	contour	NOUN
ejpam-4154	32	18	goes	go	VERB
ejpam-4154	32	19	round	round	ADP
ejpam-4154	32	20	the	the	DET
ejpam-4154	32	21	origin	origin	NOUN
ejpam-4154	32	22	with	with	ADP
ejpam-4154	32	23	zero	zero	NUM
ejpam-4154	32	24	radius	radius	NOUN
ejpam-4154	32	25	and	and	CCONJ
ejpam-4154	32	26	is	be	AUX
ejpam-4154	32	27	on	on	ADP
ejpam-4154	32	28	opposite	opposite	ADJ
ejpam-4154	32	29	sides	side	NOUN
ejpam-4154	32	30	of	of	ADP
ejpam-4154	32	31	the	the	DET
ejpam-4154	32	32	cut	cut	NOUN
ejpam-4154	32	33	.	.	PUNCT
ejpam-4154	33	1	using	use	VERB
ejpam-4154	33	2	equation	equation	NOUN
ejpam-4154	33	3	(	(	PUNCT
ejpam-4154	33	4	2	2	X
ejpam-4154	33	5	)	)	PUNCT
ejpam-4154	33	6	we	we	PRON
ejpam-4154	33	7	replace	replace	VERB
ejpam-4154	33	8	y	y	PRON
ejpam-4154	33	9	by	by	ADP
ejpam-4154	33	10	(	(	PUNCT
ejpam-4154	33	11	3)log	3)log	NUM
ejpam-4154	33	12	(	(	PUNCT
ejpam-4154	33	13	a	a	DET
ejpam-4154	33	14	√	√	NUM
ejpam-4154	33	15	rs	rs	NOUN
ejpam-4154	33	16	√	√	NUM
ejpam-4154	33	17	t+	t+	NOUN
ejpam-4154	33	18	z	z	NOUN
ejpam-4154	33	19	√	√	PROPN
ejpam-4154	33	20	u+	u+	NUM
ejpam-4154	33	21	v	v	ADP
ejpam-4154	33	22	√	√	PROPN
ejpam-4154	33	23	xy	xy	NOUN
ejpam-4154	34	1	√	√	PUNCT
ejpam-4154	35	1	r	r	NOUN
ejpam-4154	35	2	+	+	SYM
ejpam-4154	35	3	s	s	NOUN
ejpam-4154	35	4	√	√	NOUN
ejpam-4154	35	5	tz	tz	NOUN
ejpam-4154	35	6	√	√	NUM
ejpam-4154	35	7	uv	uv	NOUN
ejpam-4154	35	8	√	√	NOUN
ejpam-4154	35	9	x+	x+	PROPN
ejpam-4154	35	10	y	y	PROPN
ejpam-4154	35	11	)	)	PUNCT
ejpam-4154	35	12	then	then	ADV
ejpam-4154	35	13	multiply	multiply	VERB
ejpam-4154	35	14	by	by	ADP
ejpam-4154	35	15	both	both	DET
ejpam-4154	35	16	sides	side	NOUN
ejpam-4154	35	17	by	by	ADP
ejpam-4154	35	18	(	(	PUNCT
ejpam-4154	35	19	4)(rs	4)(rs	X
ejpam-4154	35	20	)	)	PUNCT
ejpam-4154	35	21	m−1	m−1	PROPN
ejpam-4154	35	22	2	2	NUM
ejpam-4154	35	23	(	(	PUNCT
ejpam-4154	35	24	r	r	NOUN
ejpam-4154	35	25	+	+	X
ejpam-4154	35	26	s)−m/2(tz)−	s)−m/2(tz)−	PROPN
ejpam-4154	35	27	m	m	PROPN
ejpam-4154	35	28	2	2	NUM
ejpam-4154	35	29	−1(t+	−1(t+	NOUN
ejpam-4154	35	30	z	z	NOUN
ejpam-4154	35	31	)	)	PUNCT
ejpam-4154	36	1	m+1	m+1	NUM
ejpam-4154	36	2	2	2	NUM
ejpam-4154	36	3	(	(	PUNCT
ejpam-4154	36	4	uv)−	uv)−	NOUN
ejpam-4154	36	5	m	m	NOUN
ejpam-4154	36	6	2	2	NUM
ejpam-4154	36	7	−	−	NOUN
ejpam-4154	36	8	1	1	NUM
ejpam-4154	36	9	2	2	NUM
ejpam-4154	36	10	(	(	PUNCT
ejpam-4154	36	11	u	u	NOUN
ejpam-4154	36	12	+	+	X
ejpam-4154	36	13	v)m/2(xy)m/2(x+	v)m/2(xy)m/2(x+	PROPN
ejpam-4154	36	14	y	y	ADJ
ejpam-4154	36	15	)	)	PUNCT
ejpam-4154	36	16	1	1	NUM
ejpam-4154	36	17	2	2	NUM
ejpam-4154	36	18	(	(	PUNCT
ejpam-4154	36	19	−m−1)e−p(r+u+x+z)−q(s+t+v+y	−m−1)e−p(r+u+x+z)−q(s+t+v+y	NOUN
ejpam-4154	36	20	)	)	PUNCT
ejpam-4154	36	21	and	and	CCONJ
ejpam-4154	36	22	take	take	VERB
ejpam-4154	36	23	the	the	DET
ejpam-4154	36	24	definite	definite	ADJ
ejpam-4154	36	25	octuple	octuple	NOUN
ejpam-4154	36	26	integral	integral	ADJ
ejpam-4154	36	27	over	over	ADP
ejpam-4154	36	28	x	x	PROPN
ejpam-4154	36	29	,	,	PUNCT
ejpam-4154	36	30	y	y	PROPN
ejpam-4154	36	31	,	,	PUNCT
ejpam-4154	36	32	z	z	PROPN
ejpam-4154	36	33	,	,	PUNCT
ejpam-4154	36	34	r	r	NOUN
ejpam-4154	36	35	,	,	PUNCT
ejpam-4154	36	36	s	s	PROPN
ejpam-4154	36	37	,	,	PUNCT
ejpam-4154	36	38	t	t	PROPN
ejpam-4154	36	39	,	,	PUNCT
ejpam-4154	36	40	u	u	NOUN
ejpam-4154	36	41	,	,	PUNCT
ejpam-4154	36	42	v	v	NOUN
ejpam-4154	36	43	∈	∈	PROPN
ejpam-4154	37	1	[	[	X
ejpam-4154	37	2	0,∞	0,∞	NOUN
ejpam-4154	37	3	)	)	PUNCT
ejpam-4154	37	4	to	to	PART
ejpam-4154	37	5	get	get	VERB
ejpam-4154	37	6	;	;	PUNCT
ejpam-4154	37	7	r.	r.	PROPN
ejpam-4154	37	8	reynolds	reynolds	PROPN
ejpam-4154	37	9	,	,	PUNCT
ejpam-4154	37	10	a.	a.	PROPN
ejpam-4154	37	11	stauffer	stauffer	PROPN
ejpam-4154	37	12	/	/	SYM
ejpam-4154	37	13	eur	eur	PROPN
ejpam-4154	37	14	.	.	PUNCT
ejpam-4154	38	1	j.	j.	PROPN
ejpam-4154	38	2	pure	pure	PROPN
ejpam-4154	38	3	appl	appl	PROPN
ejpam-4154	38	4	.	.	PROPN
ejpam-4154	38	5	math	math	PROPN
ejpam-4154	38	6	,	,	PUNCT
ejpam-4154	38	7	15	15	NUM
ejpam-4154	38	8	(	(	PUNCT
ejpam-4154	38	9	2	2	NUM
ejpam-4154	38	10	)	)	PUNCT
ejpam-4154	38	11	(	(	PUNCT
ejpam-4154	38	12	2022	2022	NUM
ejpam-4154	38	13	)	)	PUNCT
ejpam-4154	38	14	,	,	PUNCT
ejpam-4154	38	15	335	335	NUM
ejpam-4154	38	16	-	-	SYM
ejpam-4154	38	17	341	341	NUM
ejpam-4154	38	18	337∫	337∫	NUM
ejpam-4154	38	19	r8	r8	NOUN
ejpam-4154	38	20	+	+	CCONJ
ejpam-4154	38	21	(	(	PUNCT
ejpam-4154	38	22	rs	rs	NOUN
ejpam-4154	38	23	)	)	PUNCT
ejpam-4154	38	24	m−1	m−1	PROPN
ejpam-4154	38	25	2	2	NUM
ejpam-4154	38	26	(	(	PUNCT
ejpam-4154	38	27	r	r	NOUN
ejpam-4154	38	28	+	+	X
ejpam-4154	38	29	s)−m/2(tz)−	s)−m/2(tz)−	PROPN
ejpam-4154	38	30	m	m	PROPN
ejpam-4154	38	31	2	2	NUM
ejpam-4154	38	32	−1(t+	−1(t+	NOUN
ejpam-4154	38	33	z	z	NOUN
ejpam-4154	38	34	)	)	PUNCT
ejpam-4154	39	1	m+1	m+1	NUM
ejpam-4154	39	2	2	2	NUM
ejpam-4154	39	3	(	(	PUNCT
ejpam-4154	39	4	uv)−	uv)−	NOUN
ejpam-4154	39	5	m	m	NOUN
ejpam-4154	39	6	2	2	NUM
ejpam-4154	39	7	−	−	NOUN
ejpam-4154	39	8	1	1	NUM
ejpam-4154	39	9	2	2	NUM
ejpam-4154	39	10	(	(	PUNCT
ejpam-4154	39	11	u+	u+	NOUN
ejpam-4154	39	12	v)m/2(xy)m/2(x+	v)m/2(xy)m/2(x+	NOUN
ejpam-4154	39	13	y	y	NOUN
ejpam-4154	39	14	)	)	PUNCT
ejpam-4154	39	15	1	1	NUM
ejpam-4154	39	16	2	2	NUM
ejpam-4154	39	17	(	(	PUNCT
ejpam-4154	39	18	−m−1)e−p(r+u+x+z)−q(s+t+v+y	−m−1)e−p(r+u+x+z)−q(s+t+v+y	NOUN
ejpam-4154	39	19	)	)	PUNCT
ejpam-4154	39	20	logk	logk	NOUN
ejpam-4154	39	21	(	(	PUNCT
ejpam-4154	39	22	a	a	DET
ejpam-4154	39	23	√	√	NUM
ejpam-4154	39	24	rs	rs	NOUN
ejpam-4154	39	25	√	√	NUM
ejpam-4154	39	26	t+	t+	NOUN
ejpam-4154	39	27	z	z	NOUN
ejpam-4154	39	28	√	√	PROPN
ejpam-4154	39	29	u+	u+	NUM
ejpam-4154	39	30	v	v	ADP
ejpam-4154	39	31	√	√	PROPN
ejpam-4154	39	32	xy	xy	NOUN
ejpam-4154	39	33	√	√	PUNCT
ejpam-4154	40	1	r	r	NOUN
ejpam-4154	40	2	+	+	SYM
ejpam-4154	40	3	s	s	NOUN
ejpam-4154	40	4	√	√	NOUN
ejpam-4154	40	5	tz	tz	NOUN
ejpam-4154	40	6	√	√	NUM
ejpam-4154	40	7	uv	uv	NOUN
ejpam-4154	40	8	√	√	NOUN
ejpam-4154	40	9	x+	x+	PROPN
ejpam-4154	40	10	y	y	PROPN
ejpam-4154	40	11	)	)	PUNCT
ejpam-4154	40	12	dxdydzdrdsdtdudv	dxdydzdrdsdtdudv	PROPN
ejpam-4154	40	13	γ(k	γ(k	PROPN
ejpam-4154	40	14	+	+	CCONJ
ejpam-4154	40	15	1	1	X
ejpam-4154	40	16	)	)	PUNCT
ejpam-4154	40	17	=	=	SYM
ejpam-4154	40	18	1	1	NUM
ejpam-4154	40	19	2πi	2πi	ADJ
ejpam-4154	40	20	∫	∫	PROPN
ejpam-4154	40	21	c	c	PROPN
ejpam-4154	40	22	∫	∫	PROPN
ejpam-4154	40	23	r8	r8	PROPN
ejpam-4154	40	24	+	+	CCONJ
ejpam-4154	40	25	aww−k−1(rs	aww−k−1(rs	ADJ
ejpam-4154	40	26	)	)	PUNCT
ejpam-4154	40	27	1	1	NUM
ejpam-4154	40	28	2	2	NUM
ejpam-4154	40	29	(	(	PUNCT
ejpam-4154	40	30	m+w−1)(r	m+w−1)(r	NOUN
ejpam-4154	40	31	+	+	SYM
ejpam-4154	40	32	s	s	X
ejpam-4154	40	33	)	)	PUNCT
ejpam-4154	40	34	1	1	NUM
ejpam-4154	40	35	2	2	NUM
ejpam-4154	40	36	(	(	PUNCT
ejpam-4154	40	37	−m−w	−m−w	PROPN
ejpam-4154	40	38	)	)	PUNCT
ejpam-4154	40	39	(	(	PUNCT
ejpam-4154	40	40	tz	tz	NOUN
ejpam-4154	40	41	)	)	PUNCT
ejpam-4154	40	42	1	1	NUM
ejpam-4154	40	43	2	2	NUM
ejpam-4154	40	44	(	(	PUNCT
ejpam-4154	40	45	−m−w)−1(t+	−m−w)−1(t+	PROPN
ejpam-4154	40	46	z	z	NOUN
ejpam-4154	40	47	)	)	PUNCT
ejpam-4154	40	48	1	1	NUM
ejpam-4154	40	49	2	2	NUM
ejpam-4154	40	50	(	(	PUNCT
ejpam-4154	40	51	m+w+1)(uv	m+w+1)(uv	NOUN
ejpam-4154	40	52	)	)	PUNCT
ejpam-4154	40	53	1	1	NUM
ejpam-4154	40	54	2	2	NUM
ejpam-4154	40	55	(	(	PUNCT
ejpam-4154	40	56	−m−w)−	−m−w)−	PROPN
ejpam-4154	40	57	1	1	NUM
ejpam-4154	40	58	2	2	NUM
ejpam-4154	40	59	(	(	PUNCT
ejpam-4154	40	60	u+	u+	NOUN
ejpam-4154	40	61	v	v	NOUN
ejpam-4154	40	62	)	)	PUNCT
ejpam-4154	40	63	m+w	m+w	NUM
ejpam-4154	40	64	2	2	NUM
ejpam-4154	40	65	(	(	PUNCT
ejpam-4154	40	66	xy	xy	NOUN
ejpam-4154	40	67	)	)	PUNCT
ejpam-4154	40	68	m+w	m+w	NUM
ejpam-4154	40	69	2	2	NUM
ejpam-4154	40	70	(	(	PUNCT
ejpam-4154	40	71	x+	x+	PROPN
ejpam-4154	40	72	y	y	NOUN
ejpam-4154	40	73	)	)	PUNCT
ejpam-4154	40	74	1	1	NUM
ejpam-4154	40	75	2	2	NUM
ejpam-4154	40	76	(	(	PUNCT
ejpam-4154	40	77	−m−w−1)e−p(r+u+x+z)−q(s+t+v+y)dwdxdydzdrdsdtdudv	−m−w−1)e−p(r+u+x+z)−q(s+t+v+y)dwdxdydzdrdsdtdudv	NOUN
ejpam-4154	40	78	=	=	SYM
ejpam-4154	41	1	1	1	NUM
ejpam-4154	41	2	2πi	2πi	ADJ
ejpam-4154	41	3	∫	∫	PROPN
ejpam-4154	41	4	r8	r8	PROPN
ejpam-4154	41	5	+	+	CCONJ
ejpam-4154	41	6	∫	∫	PROPN
ejpam-4154	41	7	c	c	PROPN
ejpam-4154	41	8	aww−k−1(rs	aww−k−1(rs	PROPN
ejpam-4154	41	9	)	)	PUNCT
ejpam-4154	41	10	1	1	NUM
ejpam-4154	41	11	2	2	NUM
ejpam-4154	41	12	(	(	PUNCT
ejpam-4154	41	13	m+w−1)(r	m+w−1)(r	NOUN
ejpam-4154	41	14	+	+	SYM
ejpam-4154	41	15	s	s	X
ejpam-4154	41	16	)	)	PUNCT
ejpam-4154	41	17	1	1	NUM
ejpam-4154	41	18	2	2	NUM
ejpam-4154	41	19	(	(	PUNCT
ejpam-4154	41	20	−m−w	−m−w	PROPN
ejpam-4154	41	21	)	)	PUNCT
ejpam-4154	41	22	(	(	PUNCT
ejpam-4154	41	23	tz	tz	NOUN
ejpam-4154	41	24	)	)	PUNCT
ejpam-4154	41	25	1	1	NUM
ejpam-4154	41	26	2	2	NUM
ejpam-4154	41	27	(	(	PUNCT
ejpam-4154	41	28	−m−w)−1(t+	−m−w)−1(t+	PROPN
ejpam-4154	41	29	z	z	NOUN
ejpam-4154	41	30	)	)	PUNCT
ejpam-4154	41	31	1	1	NUM
ejpam-4154	41	32	2	2	NUM
ejpam-4154	41	33	(	(	PUNCT
ejpam-4154	41	34	m+w+1)(uv	m+w+1)(uv	NOUN
ejpam-4154	41	35	)	)	PUNCT
ejpam-4154	41	36	1	1	NUM
ejpam-4154	41	37	2	2	NUM
ejpam-4154	41	38	(	(	PUNCT
ejpam-4154	41	39	−m−w)−	−m−w)−	PROPN
ejpam-4154	41	40	1	1	NUM
ejpam-4154	41	41	2	2	NUM
ejpam-4154	41	42	(	(	PUNCT
ejpam-4154	41	43	u+	u+	NOUN
ejpam-4154	41	44	v	v	NOUN
ejpam-4154	41	45	)	)	PUNCT
ejpam-4154	41	46	m+w	m+w	NUM
ejpam-4154	41	47	2	2	NUM
ejpam-4154	41	48	(	(	PUNCT
ejpam-4154	41	49	xy	xy	NOUN
ejpam-4154	41	50	)	)	PUNCT
ejpam-4154	41	51	m+w	m+w	NUM
ejpam-4154	41	52	2	2	NUM
ejpam-4154	41	53	(	(	PUNCT
ejpam-4154	41	54	x+	x+	PROPN
ejpam-4154	41	55	y	y	NOUN
ejpam-4154	41	56	)	)	PUNCT
ejpam-4154	41	57	1	1	NUM
ejpam-4154	41	58	2	2	NUM
ejpam-4154	41	59	(	(	PUNCT
ejpam-4154	41	60	−m−w−1)e−p(r+u+x+z)−q(s+t+v+y)dxdydzdrdsdtdudvdw	−m−w−1)e−p(r+u+x+z)−q(s+t+v+y)dxdydzdrdsdtdudvdw	NOUN
ejpam-4154	41	61	=	=	SYM
ejpam-4154	41	62	−	−	PROPN
ejpam-4154	41	63	1	1	NUM
ejpam-4154	41	64	2πi	2πi	NOUN
ejpam-4154	41	65	∫	∫	PROPN
ejpam-4154	41	66	c	c	NOUN
ejpam-4154	41	67	2π4aww−k−1	2π4aww−k−1	NUM
ejpam-4154	41	68	csc(π(m+	csc(π(m+	NOUN
ejpam-4154	41	69	w	w	NOUN
ejpam-4154	41	70	)	)	PUNCT
ejpam-4154	41	71	)	)	PUNCT
ejpam-4154	42	1	p2q2	p2q2	ADP
ejpam-4154	42	2	dw	dw	NOUN
ejpam-4154	42	3	(	(	PUNCT
ejpam-4154	42	4	5	5	NUM
ejpam-4154	42	5	)	)	PUNCT
ejpam-4154	42	6	from	from	ADP
ejpam-4154	42	7	equation	equation	NOUN
ejpam-4154	42	8	(	(	PUNCT
ejpam-4154	42	9	3.1.3.9	3.1.3.9	NUM
ejpam-4154	42	10	)	)	PUNCT
ejpam-4154	42	11	in	in	ADP
ejpam-4154	42	12	[	[	X
ejpam-4154	42	13	9	9	NUM
ejpam-4154	42	14	]	]	PUNCT
ejpam-4154	42	15	where	where	SCONJ
ejpam-4154	42	16	−1	−1	NOUN
ejpam-4154	42	17	<	<	X
ejpam-4154	42	18	re(w+m	re(w+m	PROPN
ejpam-4154	42	19	)	)	PUNCT
ejpam-4154	42	20	<	<	X
ejpam-4154	42	21	1	1	NUM
ejpam-4154	42	22	and	and	CCONJ
ejpam-4154	42	23	using	use	VERB
ejpam-4154	42	24	the	the	DET
ejpam-4154	42	25	reflection	reflection	NOUN
ejpam-4154	42	26	formula	formula	NOUN
ejpam-4154	42	27	for	for	ADP
ejpam-4154	42	28	the	the	DET
ejpam-4154	42	29	gamma	gamma	PROPN
ejpam-4154	42	30	function	function	NOUN
ejpam-4154	42	31	.	.	PUNCT
ejpam-4154	43	1	the	the	DET
ejpam-4154	43	2	logarithmic	logarithmic	ADJ
ejpam-4154	43	3	function	function	NOUN
ejpam-4154	43	4	is	be	AUX
ejpam-4154	43	5	given	give	VERB
ejpam-4154	43	6	for	for	ADP
ejpam-4154	43	7	example	example	NOUN
ejpam-4154	43	8	in	in	ADP
ejpam-4154	43	9	section	section	NOUN
ejpam-4154	43	10	(	(	PUNCT
ejpam-4154	43	11	4.2	4.2	NUM
ejpam-4154	43	12	)	)	PUNCT
ejpam-4154	43	13	in	in	ADP
ejpam-4154	43	14	[	[	X
ejpam-4154	43	15	3	3	NUM
ejpam-4154	43	16	]	]	PUNCT
ejpam-4154	43	17	.	.	PUNCT
ejpam-4154	44	1	we	we	PRON
ejpam-4154	44	2	are	be	AUX
ejpam-4154	44	3	able	able	ADJ
ejpam-4154	44	4	to	to	PART
ejpam-4154	44	5	switch	switch	VERB
ejpam-4154	44	6	the	the	DET
ejpam-4154	44	7	order	order	NOUN
ejpam-4154	44	8	of	of	ADP
ejpam-4154	44	9	integration	integration	NOUN
ejpam-4154	44	10	over	over	ADP
ejpam-4154	44	11	w	w	PROPN
ejpam-4154	44	12	+	+	NOUN
ejpam-4154	44	13	m	m	VERB
ejpam-4154	44	14	and	and	CCONJ
ejpam-4154	44	15	x	x	NOUN
ejpam-4154	44	16	,	,	PUNCT
ejpam-4154	44	17	y	y	PROPN
ejpam-4154	44	18	,	,	PUNCT
ejpam-4154	44	19	z	z	PROPN
ejpam-4154	44	20	,	,	PUNCT
ejpam-4154	44	21	r	r	NOUN
ejpam-4154	44	22	,	,	PUNCT
ejpam-4154	44	23	s	s	PROPN
ejpam-4154	44	24	,	,	PUNCT
ejpam-4154	44	25	t	t	PROPN
ejpam-4154	44	26	,	,	PUNCT
ejpam-4154	44	27	u	u	NOUN
ejpam-4154	44	28	,	,	PUNCT
ejpam-4154	44	29	v	v	X
ejpam-4154	44	30	using	use	VERB
ejpam-4154	44	31	fubini	fubini	NOUN
ejpam-4154	44	32	’s	’s	PART
ejpam-4154	44	33	theorem	theorem	NOUN
ejpam-4154	44	34	since	since	SCONJ
ejpam-4154	44	35	the	the	DET
ejpam-4154	44	36	integrand	integrand	NOUN
ejpam-4154	44	37	is	be	AUX
ejpam-4154	44	38	of	of	ADP
ejpam-4154	44	39	bounded	bounded	ADJ
ejpam-4154	44	40	measure	measure	NOUN
ejpam-4154	44	41	over	over	ADP
ejpam-4154	44	42	the	the	DET
ejpam-4154	44	43	space	space	NOUN
ejpam-4154	44	44	c	c	NOUN
ejpam-4154	44	45	×	×	NOUN
ejpam-4154	45	1	[	[	X
ejpam-4154	45	2	0,∞	0,∞	NOUN
ejpam-4154	45	3	)	)	PUNCT
ejpam-4154	45	4	×	×	NOUN
ejpam-4154	46	1	[	[	X
ejpam-4154	46	2	0,∞)×	0,∞)×	NUM
ejpam-4154	46	3	[	[	X
ejpam-4154	46	4	0,∞)×	0,∞)×	NUM
ejpam-4154	47	1	[	[	X
ejpam-4154	47	2	0,∞)×	0,∞)×	NUM
ejpam-4154	47	3	[	[	X
ejpam-4154	47	4	0,∞)×	0,∞)×	NUM
ejpam-4154	47	5	[	[	X
ejpam-4154	47	6	0,∞)×	0,∞)×	NUM
ejpam-4154	47	7	[	[	X
ejpam-4154	47	8	0,∞)×	0,∞)×	NUM
ejpam-4154	47	9	[	[	X
ejpam-4154	47	10	0,∞	0,∞	NUM
ejpam-4154	47	11	)	)	PUNCT
ejpam-4154	47	12	.	.	PUNCT
ejpam-4154	48	1	4	4	X
ejpam-4154	48	2	.	.	X
ejpam-4154	48	3	the	the	DET
ejpam-4154	48	4	lerch	lerch	PROPN
ejpam-4154	48	5	function	function	NOUN
ejpam-4154	48	6	we	we	PRON
ejpam-4154	48	7	use	use	VERB
ejpam-4154	48	8	section	section	NOUN
ejpam-4154	48	9	(	(	PUNCT
ejpam-4154	48	10	25.14	25.14	NUM
ejpam-4154	48	11	)	)	PUNCT
ejpam-4154	48	12	in	in	ADP
ejpam-4154	48	13	[	[	X
ejpam-4154	48	14	3	3	X
ejpam-4154	48	15	]	]	PUNCT
ejpam-4154	48	16	where	where	SCONJ
ejpam-4154	48	17	φ(z	φ(z	PROPN
ejpam-4154	48	18	,	,	PUNCT
ejpam-4154	48	19	s	s	NOUN
ejpam-4154	48	20	,	,	PUNCT
ejpam-4154	48	21	v	v	NOUN
ejpam-4154	48	22	)	)	PUNCT
ejpam-4154	48	23	is	be	AUX
ejpam-4154	48	24	the	the	DET
ejpam-4154	48	25	lerch	lerch	PROPN
ejpam-4154	48	26	function	function	NOUN
ejpam-4154	48	27	which	which	PRON
ejpam-4154	48	28	is	be	AUX
ejpam-4154	48	29	a	a	DET
ejpam-4154	48	30	generalization	generalization	NOUN
ejpam-4154	48	31	of	of	ADP
ejpam-4154	48	32	the	the	DET
ejpam-4154	48	33	hurwitz	hurwitz	PROPN
ejpam-4154	48	34	zeta	zeta	PROPN
ejpam-4154	48	35	ζ(s	ζ(s	PROPN
ejpam-4154	48	36	,	,	PUNCT
ejpam-4154	48	37	v	v	NOUN
ejpam-4154	48	38	)	)	PUNCT
ejpam-4154	48	39	and	and	CCONJ
ejpam-4154	48	40	polylogarithm	polylogarithm	PROPN
ejpam-4154	48	41	functions	function	NOUN
ejpam-4154	48	42	lin(z	lin(z	PROPN
ejpam-4154	48	43	)	)	PUNCT
ejpam-4154	48	44	.	.	PUNCT
ejpam-4154	49	1	the	the	DET
ejpam-4154	49	2	lerch	lerch	PROPN
ejpam-4154	49	3	function	function	PROPN
ejpam-4154	49	4	has	have	VERB
ejpam-4154	49	5	a	a	DET
ejpam-4154	49	6	series	series	NOUN
ejpam-4154	49	7	representation	representation	NOUN
ejpam-4154	49	8	given	give	VERB
ejpam-4154	49	9	by	by	ADP
ejpam-4154	49	10	φ(z	φ(z	PROPN
ejpam-4154	49	11	,	,	PUNCT
ejpam-4154	49	12	s	s	NOUN
ejpam-4154	49	13	,	,	PUNCT
ejpam-4154	49	14	v	v	NOUN
ejpam-4154	49	15	)	)	PUNCT
ejpam-4154	49	16	=	=	PUNCT
ejpam-4154	50	1	∞∑	∞∑	NUM
ejpam-4154	50	2	n=0	n=0	NUM
ejpam-4154	50	3	(	(	PUNCT
ejpam-4154	50	4	v	v	NOUN
ejpam-4154	50	5	+	+	NOUN
ejpam-4154	50	6	n)−szn	n)−szn	NUM
ejpam-4154	50	7	(	(	PUNCT
ejpam-4154	50	8	6	6	NUM
ejpam-4154	50	9	)	)	PUNCT
ejpam-4154	50	10	where	where	SCONJ
ejpam-4154	50	11	|z|	|z|	VERB
ejpam-4154	50	12	<	<	X
ejpam-4154	50	13	1	1	NUM
ejpam-4154	50	14	,	,	PUNCT
ejpam-4154	50	15	v	v	ADP
ejpam-4154	50	16	̸=	̸=	PROPN
ejpam-4154	50	17	0,−1	0,−1	PROPN
ejpam-4154	50	18	,	,	PUNCT
ejpam-4154	50	19	..	..	PUNCT
ejpam-4154	50	20	and	and	CCONJ
ejpam-4154	50	21	is	be	AUX
ejpam-4154	50	22	continued	continue	VERB
ejpam-4154	50	23	analytically	analytically	ADV
ejpam-4154	50	24	by	by	ADP
ejpam-4154	50	25	its	its	PRON
ejpam-4154	50	26	integral	integral	ADJ
ejpam-4154	50	27	representation	representation	NOUN
ejpam-4154	50	28	given	give	VERB
ejpam-4154	50	29	by	by	ADP
ejpam-4154	50	30	φ(z	φ(z	PROPN
ejpam-4154	50	31	,	,	PUNCT
ejpam-4154	50	32	s	s	NOUN
ejpam-4154	50	33	,	,	PUNCT
ejpam-4154	50	34	v	v	NOUN
ejpam-4154	50	35	)	)	PUNCT
ejpam-4154	50	36	=	=	SYM
ejpam-4154	50	37	1	1	NUM
ejpam-4154	50	38	γ(s	γ(	NOUN
ejpam-4154	50	39	)	)	PUNCT
ejpam-4154	50	40	∫	∫	PROPN
ejpam-4154	51	1	∞	∞	PROPN
ejpam-4154	51	2	0	0	NUM
ejpam-4154	52	1	ts−1e−vt	ts−1e−vt	PRON
ejpam-4154	53	1	1−	1−	NUM
ejpam-4154	53	2	ze−t	ze−t	NOUN
ejpam-4154	53	3	dt	dt	NOUN
ejpam-4154	54	1	=	=	SYM
ejpam-4154	54	2	1	1	NUM
ejpam-4154	54	3	γ(s	γ(s	PROPN
ejpam-4154	54	4	)	)	PUNCT
ejpam-4154	54	5	∫	∫	PROPN
ejpam-4154	55	1	∞	∞	NUM
ejpam-4154	55	2	0	0	NUM
ejpam-4154	56	1	ts−1e−(v−1)t	ts−1e−(v−1)t	PROPN
ejpam-4154	56	2	et	et	NOUN
ejpam-4154	56	3	−	−	NOUN
ejpam-4154	56	4	z	z	SYM
ejpam-4154	56	5	dt	dt	NOUN
ejpam-4154	56	6	,	,	PUNCT
ejpam-4154	56	7	(	(	PUNCT
ejpam-4154	56	8	7	7	X
ejpam-4154	56	9	)	)	PUNCT
ejpam-4154	56	10	r.	r.	PROPN
ejpam-4154	56	11	reynolds	reynolds	PROPN
ejpam-4154	56	12	,	,	PUNCT
ejpam-4154	56	13	a.	a.	PROPN
ejpam-4154	56	14	stauffer	stauffer	PROPN
ejpam-4154	56	15	/	/	SYM
ejpam-4154	56	16	eur	eur	PROPN
ejpam-4154	56	17	.	.	PUNCT
ejpam-4154	57	1	j.	j.	PROPN
ejpam-4154	57	2	pure	pure	PROPN
ejpam-4154	57	3	appl	appl	PROPN
ejpam-4154	57	4	.	.	PROPN
ejpam-4154	57	5	math	math	PROPN
ejpam-4154	57	6	,	,	PUNCT
ejpam-4154	57	7	15	15	NUM
ejpam-4154	57	8	(	(	PUNCT
ejpam-4154	57	9	2	2	NUM
ejpam-4154	57	10	)	)	PUNCT
ejpam-4154	57	11	(	(	PUNCT
ejpam-4154	57	12	2022	2022	NUM
ejpam-4154	57	13	)	)	PUNCT
ejpam-4154	57	14	,	,	PUNCT
ejpam-4154	57	15	335	335	NUM
ejpam-4154	57	16	-	-	SYM
ejpam-4154	57	17	341	341	NUM
ejpam-4154	57	18	338	338	NUM
ejpam-4154	57	19	where	where	SCONJ
ejpam-4154	57	20	re(v	re(v	NOUN
ejpam-4154	57	21	)	)	PUNCT
ejpam-4154	57	22	>	>	X
ejpam-4154	57	23	0	0	NUM
ejpam-4154	57	24	,	,	PUNCT
ejpam-4154	57	25	and	and	CCONJ
ejpam-4154	57	26	either	either	ADV
ejpam-4154	57	27	|z|≤	|z|≤	SYM
ejpam-4154	57	28	1	1	NUM
ejpam-4154	57	29	,	,	PUNCT
ejpam-4154	57	30	z	z	NOUN
ejpam-4154	57	31	̸=	̸=	PROPN
ejpam-4154	57	32	1	1	NUM
ejpam-4154	57	33	,	,	PUNCT
ejpam-4154	57	34	re(s	re(s	ADJ
ejpam-4154	57	35	)	)	PUNCT
ejpam-4154	57	36	>	>	X
ejpam-4154	57	37	0	0	NUM
ejpam-4154	57	38	,	,	PUNCT
ejpam-4154	57	39	or	or	CCONJ
ejpam-4154	57	40	z	z	NOUN
ejpam-4154	57	41	=	=	SYM
ejpam-4154	57	42	1	1	NUM
ejpam-4154	57	43	,	,	PUNCT
ejpam-4154	57	44	re(s	re(s	ADJ
ejpam-4154	57	45	)	)	PUNCT
ejpam-4154	57	46	>	>	X
ejpam-4154	58	1	1	1	NUM
ejpam-4154	58	2	.	.	X
ejpam-4154	58	3	5	5	NUM
ejpam-4154	58	4	.	.	X
ejpam-4154	58	5	infinite	infinite	ADJ
ejpam-4154	58	6	sum	sum	NOUN
ejpam-4154	58	7	of	of	ADP
ejpam-4154	58	8	the	the	DET
ejpam-4154	58	9	contour	contour	NOUN
ejpam-4154	58	10	integral	integral	NOUN
ejpam-4154	58	11	in	in	ADP
ejpam-4154	58	12	this	this	DET
ejpam-4154	58	13	section	section	NOUN
ejpam-4154	58	14	we	we	PRON
ejpam-4154	58	15	will	will	AUX
ejpam-4154	58	16	again	again	ADV
ejpam-4154	58	17	use	use	VERB
ejpam-4154	58	18	cauchy	cauchy	NOUN
ejpam-4154	58	19	’s	’s	PART
ejpam-4154	58	20	integral	integral	ADJ
ejpam-4154	58	21	formula	formula	NOUN
ejpam-4154	58	22	(	(	PUNCT
ejpam-4154	58	23	2	2	NUM
ejpam-4154	58	24	)	)	PUNCT
ejpam-4154	58	25	and	and	CCONJ
ejpam-4154	58	26	take	take	VERB
ejpam-4154	58	27	the	the	DET
ejpam-4154	58	28	infinite	infinite	ADJ
ejpam-4154	58	29	sum	sum	NOUN
ejpam-4154	58	30	to	to	PART
ejpam-4154	58	31	derive	derive	VERB
ejpam-4154	58	32	equivalent	equivalent	ADJ
ejpam-4154	58	33	sum	sum	NOUN
ejpam-4154	58	34	representations	representation	NOUN
ejpam-4154	58	35	for	for	ADP
ejpam-4154	58	36	the	the	DET
ejpam-4154	58	37	contour	contour	NOUN
ejpam-4154	58	38	integrals	integral	NOUN
ejpam-4154	58	39	.	.	PUNCT
ejpam-4154	59	1	we	we	PRON
ejpam-4154	59	2	proceed	proceed	VERB
ejpam-4154	59	3	using	use	VERB
ejpam-4154	59	4	equation	equation	NOUN
ejpam-4154	59	5	(	(	PUNCT
ejpam-4154	59	6	2	2	NUM
ejpam-4154	59	7	)	)	PUNCT
ejpam-4154	59	8	and	and	CCONJ
ejpam-4154	59	9	replace	replace	VERB
ejpam-4154	59	10	y	y	PROPN
ejpam-4154	59	11	by	by	ADP
ejpam-4154	59	12	log(a	log(a	PROPN
ejpam-4154	59	13	)	)	PUNCT
ejpam-4154	60	1	+	+	CCONJ
ejpam-4154	60	2	iπ(2y	iπ(2y	PRON
ejpam-4154	60	3	+	+	NOUN
ejpam-4154	60	4	1	1	X
ejpam-4154	60	5	)	)	PUNCT
ejpam-4154	60	6	and	and	CCONJ
ejpam-4154	60	7	multiply	multiply	VERB
ejpam-4154	60	8	both	both	DET
ejpam-4154	60	9	sides	side	NOUN
ejpam-4154	60	10	by	by	ADP
ejpam-4154	60	11	4iπ4	4iπ4	PROPN
ejpam-4154	60	12	p2q2	p2q2	X
ejpam-4154	60	13	then	then	ADV
ejpam-4154	60	14	take	take	VERB
ejpam-4154	60	15	the	the	DET
ejpam-4154	60	16	infinite	infinite	ADJ
ejpam-4154	60	17	sum	sum	NOUN
ejpam-4154	60	18	over	over	ADP
ejpam-4154	60	19	y	y	PROPN
ejpam-4154	60	20	∈	∈	PROPN
ejpam-4154	61	1	[	[	X
ejpam-4154	61	2	0,∞	0,∞	NOUN
ejpam-4154	61	3	)	)	PUNCT
ejpam-4154	61	4	simplifying	simplify	VERB
ejpam-4154	61	5	in	in	ADP
ejpam-4154	61	6	terms	term	NOUN
ejpam-4154	61	7	of	of	ADP
ejpam-4154	61	8	the	the	DET
ejpam-4154	61	9	lerch	lerch	PROPN
ejpam-4154	61	10	function	function	NOUN
ejpam-4154	61	11	to	to	PART
ejpam-4154	61	12	get	get	VERB
ejpam-4154	61	13	ik+12k+2πk+4eiπmφ	ik+12k+2πk+4eiπmφ	PUNCT
ejpam-4154	61	14	(	(	PUNCT
ejpam-4154	61	15	e2imπ,−k	e2imπ,−k	NOUN
ejpam-4154	61	16	,	,	PUNCT
ejpam-4154	61	17	π−i	π−i	PROPN
ejpam-4154	61	18	log(a	log(a	PROPN
ejpam-4154	61	19	)	)	PUNCT
ejpam-4154	61	20	2π	2π	NOUN
ejpam-4154	61	21	)	)	PUNCT
ejpam-4154	62	1	p2q2γ(k	p2q2γ(k	NOUN
ejpam-4154	62	2	+	+	CCONJ
ejpam-4154	62	3	1	1	X
ejpam-4154	62	4	)	)	PUNCT
ejpam-4154	62	5	=	=	SYM
ejpam-4154	62	6	1	1	NUM
ejpam-4154	62	7	2πi	2πi	NOUN
ejpam-4154	62	8	∞∑	∞∑	NUM
ejpam-4154	62	9	y=0	y=0	NUM
ejpam-4154	62	10	∫	∫	PROPN
ejpam-4154	62	11	c	c	PROPN
ejpam-4154	62	12	4iπ4aww−k−1eiπ(2y+1)(m+w	4iπ4aww−k−1eiπ(2y+1)(m+w	PROPN
ejpam-4154	62	13	)	)	PUNCT
ejpam-4154	62	14	p2q2	p2q2	PUNCT
ejpam-4154	62	15	dw	dw	NOUN
ejpam-4154	62	16	=	=	SYM
ejpam-4154	62	17	1	1	NUM
ejpam-4154	62	18	2πi	2πi	NOUN
ejpam-4154	62	19	∫	∫	PROPN
ejpam-4154	62	20	c	c	NOUN
ejpam-4154	62	21	∞∑	∞∑	NUM
ejpam-4154	62	22	y=0	y=0	NOUN
ejpam-4154	62	23	4iπ4aww−k−1eiπ(2y+1)(m+w	4iπ4aww−k−1eiπ(2y+1)(m+w	NOUN
ejpam-4154	62	24	)	)	PUNCT
ejpam-4154	62	25	p2q2	p2q2	NUM
ejpam-4154	62	26	dw	dw	NOUN
ejpam-4154	62	27	=	=	SYM
ejpam-4154	62	28	−	−	PROPN
ejpam-4154	62	29	1	1	NUM
ejpam-4154	62	30	2πi	2πi	NOUN
ejpam-4154	62	31	∫	∫	PROPN
ejpam-4154	62	32	c	c	NOUN
ejpam-4154	62	33	2π4aww−k−1	2π4aww−k−1	NUM
ejpam-4154	62	34	csc(π(m+	csc(π(m+	NOUN
ejpam-4154	62	35	w	w	NOUN
ejpam-4154	62	36	)	)	PUNCT
ejpam-4154	62	37	)	)	PUNCT
ejpam-4154	63	1	p2q2	p2q2	ADP
ejpam-4154	63	2	dw	dw	PROPN
ejpam-4154	63	3	(	(	PUNCT
ejpam-4154	63	4	8)	8)	NUM
ejpam-4154	63	5	from	from	ADP
ejpam-4154	63	6	equation(1.232.3	equation(1.232.3	PROPN
ejpam-4154	63	7	)	)	PUNCT
ejpam-4154	63	8	in	in	ADP
ejpam-4154	63	9	[	[	X
ejpam-4154	63	10	4	4	X
ejpam-4154	63	11	]	]	PUNCT
ejpam-4154	63	12	where	where	SCONJ
ejpam-4154	63	13	im(w	im(w	PUNCT
ejpam-4154	63	14	+	+	NOUN
ejpam-4154	63	15	m	m	VERB
ejpam-4154	63	16	)	)	PUNCT
ejpam-4154	63	17	>	>	X
ejpam-4154	63	18	0	0	PUNCT
ejpam-4154	64	1	in	in	ADP
ejpam-4154	64	2	order	order	NOUN
ejpam-4154	64	3	for	for	SCONJ
ejpam-4154	64	4	the	the	DET
ejpam-4154	64	5	sum	sum	NOUN
ejpam-4154	64	6	to	to	PART
ejpam-4154	64	7	converge	converge	VERB
ejpam-4154	64	8	.	.	PUNCT
ejpam-4154	64	9	theorem	theorem	NOUN
ejpam-4154	64	10	1	1	NUM
ejpam-4154	64	11	.	.	PUNCT
ejpam-4154	65	1	for	for	ADP
ejpam-4154	65	2	all	all	DET
ejpam-4154	65	3	k	k	NOUN
ejpam-4154	65	4	,	,	PUNCT
ejpam-4154	65	5	a	a	DET
ejpam-4154	65	6	∈	∈	PROPN
ejpam-4154	65	7	c	c	NOUN
ejpam-4154	65	8	,	,	PUNCT
ejpam-4154	65	9	re(p	re(p	NOUN
ejpam-4154	65	10	,	,	PUNCT
ejpam-4154	65	11	q	q	NOUN
ejpam-4154	65	12	)	)	PUNCT
ejpam-4154	65	13	>	>	X
ejpam-4154	66	1	0,−1/2	0,−1/2	PROPN
ejpam-4154	66	2	<	<	X
ejpam-4154	66	3	re(m	re(m	PROPN
ejpam-4154	66	4	)	)	PUNCT
ejpam-4154	66	5	<	<	X
ejpam-4154	66	6	−1,∫	−1,∫	NUM
ejpam-4154	66	7	r8	r8	NOUN
ejpam-4154	66	8	+	+	CCONJ
ejpam-4154	66	9	(	(	PUNCT
ejpam-4154	66	10	rs	rs	NOUN
ejpam-4154	66	11	)	)	PUNCT
ejpam-4154	66	12	m−1	m−1	PROPN
ejpam-4154	66	13	2	2	NUM
ejpam-4154	66	14	(	(	PUNCT
ejpam-4154	66	15	r	r	NOUN
ejpam-4154	66	16	+	+	X
ejpam-4154	66	17	s)−m/2(tz)−	s)−m/2(tz)−	PROPN
ejpam-4154	66	18	m	m	PROPN
ejpam-4154	66	19	2	2	NUM
ejpam-4154	66	20	−1(t+	−1(t+	NOUN
ejpam-4154	66	21	z	z	NOUN
ejpam-4154	66	22	)	)	PUNCT
ejpam-4154	67	1	m+1	m+1	NUM
ejpam-4154	67	2	2	2	NUM
ejpam-4154	67	3	(	(	PUNCT
ejpam-4154	67	4	uv)−	uv)−	NOUN
ejpam-4154	67	5	m	m	NOUN
ejpam-4154	67	6	2	2	NUM
ejpam-4154	67	7	−	−	NOUN
ejpam-4154	67	8	1	1	NUM
ejpam-4154	67	9	2	2	NUM
ejpam-4154	67	10	(	(	PUNCT
ejpam-4154	67	11	u+	u+	NOUN
ejpam-4154	67	12	v)m/2(xy)m/2(x+	v)m/2(xy)m/2(x+	NOUN
ejpam-4154	67	13	y	y	NOUN
ejpam-4154	67	14	)	)	PUNCT
ejpam-4154	67	15	1	1	NUM
ejpam-4154	67	16	2	2	NUM
ejpam-4154	67	17	(	(	PUNCT
ejpam-4154	67	18	−m−1)e−p(r+u+x+z)−q(s+t+v+y	−m−1)e−p(r+u+x+z)−q(s+t+v+y	NOUN
ejpam-4154	67	19	)	)	PUNCT
ejpam-4154	67	20	logk	logk	NOUN
ejpam-4154	67	21	(	(	PUNCT
ejpam-4154	67	22	a	a	DET
ejpam-4154	67	23	√	√	NUM
ejpam-4154	67	24	rs	rs	NOUN
ejpam-4154	67	25	√	√	NUM
ejpam-4154	67	26	t+	t+	NOUN
ejpam-4154	67	27	z	z	NOUN
ejpam-4154	67	28	√	√	PROPN
ejpam-4154	67	29	u+	u+	NUM
ejpam-4154	67	30	v	v	ADP
ejpam-4154	67	31	√	√	PROPN
ejpam-4154	67	32	xy	xy	NOUN
ejpam-4154	67	33	√	√	PUNCT
ejpam-4154	68	1	r	r	NOUN
ejpam-4154	68	2	+	+	SYM
ejpam-4154	68	3	s	s	NOUN
ejpam-4154	68	4	√	√	NOUN
ejpam-4154	68	5	tz	tz	NOUN
ejpam-4154	68	6	√	√	NUM
ejpam-4154	68	7	uv	uv	NOUN
ejpam-4154	68	8	√	√	NOUN
ejpam-4154	68	9	x+	x+	PROPN
ejpam-4154	68	10	y	y	PROPN
ejpam-4154	68	11	)	)	PUNCT
ejpam-4154	68	12	dxdydzdrdsdtdudv	dxdydzdrdsdtdudv	PROPN
ejpam-4154	68	13	=	=	SYM
ejpam-4154	68	14	ik+12k+2πk+4eiπmφ	ik+12k+2πk+4eiπmφ	X
ejpam-4154	68	15	(	(	PUNCT
ejpam-4154	68	16	e2imπ,−k	e2imπ,−k	NOUN
ejpam-4154	68	17	,	,	PUNCT
ejpam-4154	68	18	π−i	π−i	PROPN
ejpam-4154	68	19	log(a	log(a	PROPN
ejpam-4154	68	20	)	)	PUNCT
ejpam-4154	68	21	2π	2π	NOUN
ejpam-4154	68	22	)	)	PUNCT
ejpam-4154	69	1	p2q2	p2q2	X
ejpam-4154	69	2	(	(	PUNCT
ejpam-4154	69	3	9	9	X
ejpam-4154	69	4	)	)	PUNCT
ejpam-4154	69	5	proof	proof	NOUN
ejpam-4154	69	6	.	.	PUNCT
ejpam-4154	70	1	observe	observe	VERB
ejpam-4154	70	2	the	the	DET
ejpam-4154	70	3	right	right	ADJ
ejpam-4154	70	4	-	-	PUNCT
ejpam-4154	70	5	hand	hand	NOUN
ejpam-4154	70	6	side	side	NOUN
ejpam-4154	70	7	of	of	ADP
ejpam-4154	70	8	equation	equation	NOUN
ejpam-4154	70	9	(	(	PUNCT
ejpam-4154	70	10	5	5	NUM
ejpam-4154	70	11	)	)	PUNCT
ejpam-4154	70	12	is	be	AUX
ejpam-4154	70	13	equal	equal	ADJ
ejpam-4154	70	14	to	to	ADP
ejpam-4154	70	15	the	the	DET
ejpam-4154	70	16	right	right	ADJ
ejpam-4154	70	17	-	-	PUNCT
ejpam-4154	70	18	hand	hand	NOUN
ejpam-4154	70	19	side	side	NOUN
ejpam-4154	70	20	of	of	ADP
ejpam-4154	70	21	equation	equation	NOUN
ejpam-4154	70	22	(	(	PUNCT
ejpam-4154	70	23	8)	8)	NUM
ejpam-4154	70	24	so	so	ADV
ejpam-4154	70	25	we	we	PRON
ejpam-4154	70	26	may	may	AUX
ejpam-4154	70	27	equate	equate	VERB
ejpam-4154	70	28	the	the	DET
ejpam-4154	70	29	left	left	ADJ
ejpam-4154	70	30	-	-	PUNCT
ejpam-4154	70	31	hand	hand	NOUN
ejpam-4154	70	32	sides	side	NOUN
ejpam-4154	70	33	and	and	CCONJ
ejpam-4154	70	34	simplify	simplify	VERB
ejpam-4154	70	35	the	the	DET
ejpam-4154	70	36	gamma	gamma	NOUN
ejpam-4154	70	37	function	function	NOUN
ejpam-4154	70	38	to	to	PART
ejpam-4154	70	39	yield	yield	VERB
ejpam-4154	70	40	the	the	DET
ejpam-4154	70	41	stated	state	VERB
ejpam-4154	70	42	result	result	NOUN
ejpam-4154	70	43	.	.	PUNCT
ejpam-4154	71	1	example	example	NOUN
ejpam-4154	72	1	1	1	NUM
ejpam-4154	72	2	.	.	PUNCT
ejpam-4154	73	1	the	the	DET
ejpam-4154	73	2	degenerate	degenerate	ADJ
ejpam-4154	73	3	case.∫	case.∫	NOUN
ejpam-4154	73	4	r8	r8	NOUN
ejpam-4154	73	5	+	+	CCONJ
ejpam-4154	73	6	(	(	PUNCT
ejpam-4154	73	7	rs	rs	NOUN
ejpam-4154	73	8	)	)	PUNCT
ejpam-4154	73	9	m−1	m−1	PROPN
ejpam-4154	73	10	2	2	NUM
ejpam-4154	73	11	(	(	PUNCT
ejpam-4154	73	12	r	r	NOUN
ejpam-4154	73	13	+	+	X
ejpam-4154	73	14	s)−m/2(tz)−	s)−m/2(tz)−	PROPN
ejpam-4154	73	15	m	m	PROPN
ejpam-4154	73	16	2	2	NUM
ejpam-4154	73	17	−1(t+	−1(t+	NOUN
ejpam-4154	73	18	z	z	NOUN
ejpam-4154	73	19	)	)	PUNCT
ejpam-4154	74	1	m+1	m+1	NUM
ejpam-4154	74	2	2	2	NUM
ejpam-4154	74	3	(	(	PUNCT
ejpam-4154	74	4	uv)−	uv)−	NOUN
ejpam-4154	74	5	m	m	NOUN
ejpam-4154	74	6	2	2	NUM
ejpam-4154	74	7	−	−	NOUN
ejpam-4154	74	8	1	1	NUM
ejpam-4154	74	9	2	2	NUM
ejpam-4154	74	10	(	(	PUNCT
ejpam-4154	74	11	u+	u+	NOUN
ejpam-4154	74	12	v)m/2(xy)m/2(x+	v)m/2(xy)m/2(x+	NOUN
ejpam-4154	74	13	y	y	NOUN
ejpam-4154	74	14	)	)	PUNCT
ejpam-4154	74	15	1	1	NUM
ejpam-4154	74	16	2	2	NUM
ejpam-4154	74	17	(	(	PUNCT
ejpam-4154	74	18	−m−1	−m−1	NUM
ejpam-4154	74	19	)	)	PUNCT
ejpam-4154	74	20	e−p(r+u+x+z)−q(s+t+v+y)dxdydzdrdsdtdudv	e−p(r+u+x+z)−q(s+t+v+y)dxdydzdrdsdtdudv	PROPN
ejpam-4154	74	21	r.	r.	PROPN
ejpam-4154	74	22	reynolds	reynolds	PROPN
ejpam-4154	74	23	,	,	PUNCT
ejpam-4154	74	24	a.	a.	PROPN
ejpam-4154	74	25	stauffer	stauffer	PROPN
ejpam-4154	74	26	/	/	SYM
ejpam-4154	74	27	eur	eur	PROPN
ejpam-4154	74	28	.	.	PUNCT
ejpam-4154	75	1	j.	j.	PROPN
ejpam-4154	75	2	pure	pure	PROPN
ejpam-4154	75	3	appl	appl	PROPN
ejpam-4154	75	4	.	.	PROPN
ejpam-4154	75	5	math	math	PROPN
ejpam-4154	75	6	,	,	PUNCT
ejpam-4154	75	7	15	15	NUM
ejpam-4154	75	8	(	(	PUNCT
ejpam-4154	75	9	2	2	NUM
ejpam-4154	75	10	)	)	PUNCT
ejpam-4154	75	11	(	(	PUNCT
ejpam-4154	75	12	2022	2022	NUM
ejpam-4154	75	13	)	)	PUNCT
ejpam-4154	75	14	,	,	PUNCT
ejpam-4154	75	15	335	335	NUM
ejpam-4154	75	16	-	-	SYM
ejpam-4154	75	17	341	341	NUM
ejpam-4154	75	18	339	339	NUM
ejpam-4154	75	19	=	=	NOUN
ejpam-4154	75	20	−2π4	−2π4	NUM
ejpam-4154	75	21	csc(πm	csc(πm	NOUN
ejpam-4154	75	22	)	)	PUNCT
ejpam-4154	75	23	p2q2	p2q2	X
ejpam-4154	75	24	(	(	PUNCT
ejpam-4154	75	25	10	10	NUM
ejpam-4154	75	26	)	)	PUNCT
ejpam-4154	75	27	proof	proof	NOUN
ejpam-4154	75	28	.	.	PUNCT
ejpam-4154	76	1	use	use	VERB
ejpam-4154	76	2	equation	equation	NOUN
ejpam-4154	76	3	(	(	PUNCT
ejpam-4154	76	4	9	9	NUM
ejpam-4154	76	5	)	)	PUNCT
ejpam-4154	76	6	and	and	CCONJ
ejpam-4154	76	7	set	set	VERB
ejpam-4154	76	8	k	k	PROPN
ejpam-4154	76	9	=	=	PUNCT
ejpam-4154	76	10	0	0	PUNCT
ejpam-4154	76	11	and	and	CCONJ
ejpam-4154	76	12	simplify	simplify	VERB
ejpam-4154	76	13	using	use	VERB
ejpam-4154	76	14	entry	entry	NOUN
ejpam-4154	76	15	(	(	PUNCT
ejpam-4154	76	16	2	2	NUM
ejpam-4154	76	17	)	)	PUNCT
ejpam-4154	76	18	in	in	ADP
ejpam-4154	76	19	table	table	NOUN
ejpam-4154	76	20	below	below	ADV
ejpam-4154	76	21	(	(	PUNCT
ejpam-4154	76	22	64:12:7	64:12:7	NUM
ejpam-4154	76	23	)	)	PUNCT
ejpam-4154	76	24	in	in	ADP
ejpam-4154	76	25	[	[	X
ejpam-4154	76	26	7	7	NUM
ejpam-4154	76	27	]	]	PUNCT
ejpam-4154	76	28	.	.	PUNCT
ejpam-4154	77	1	example	example	NOUN
ejpam-4154	77	2	2.∫	2.∫	NUM
ejpam-4154	77	3	r8	r8	NOUN
ejpam-4154	78	1	+	+	CCONJ
ejpam-4154	78	2	4	4	NUM
ejpam-4154	78	3	√	√	NOUN
ejpam-4154	79	1	r	r	NOUN
ejpam-4154	79	2	+	+	SYM
ejpam-4154	79	3	s	s	VERB
ejpam-4154	79	4	4	4	NUM
ejpam-4154	79	5	√	√	NOUN
ejpam-4154	79	6	t+	t+	NOUN
ejpam-4154	79	7	ze−r−2s−2t−u−2v−x−2y−z	ze−r−2s−2t−u−2v−x−2y−z	PROPN
ejpam-4154	79	8	(	(	PUNCT
ejpam-4154	79	9	rs)3/4(tz)3/4	rs)3/4(tz)3/4	NUM
ejpam-4154	79	10	4	4	NUM
ejpam-4154	79	11	√	√	NOUN
ejpam-4154	79	12	uv	uv	NOUN
ejpam-4154	79	13	4	4	NUM
ejpam-4154	79	14	√	√	PROPN
ejpam-4154	79	15	u+	u+	NUM
ejpam-4154	79	16	v	v	ADP
ejpam-4154	79	17	4	4	NUM
ejpam-4154	79	18	√	√	NOUN
ejpam-4154	79	19	xy	xy	PROPN
ejpam-4154	79	20	4	4	NUM
ejpam-4154	79	21	√	√	PROPN
ejpam-4154	79	22	x+	x+	PROPN
ejpam-4154	79	23	y	y	PROPN
ejpam-4154	79	24	(	(	PUNCT
ejpam-4154	79	25	log2	log2	PROPN
ejpam-4154	79	26	(	(	PUNCT
ejpam-4154	79	27	√	√	ADP
ejpam-4154	79	28	rs	rs	NOUN
ejpam-4154	79	29	√	√	PROPN
ejpam-4154	79	30	t+z	t+z	NUM
ejpam-4154	79	31	√	√	ADP
ejpam-4154	79	32	u+v	u+v	NUM
ejpam-4154	79	33	√	√	NUM
ejpam-4154	79	34	xy√	xy√	PUNCT
ejpam-4154	79	35	r+s	r+	NOUN
ejpam-4154	80	1	√	√	NUM
ejpam-4154	80	2	tz	tz	NOUN
ejpam-4154	80	3	√	√	NUM
ejpam-4154	80	4	uv	uv	NOUN
ejpam-4154	80	5	√	√	NOUN
ejpam-4154	80	6	x+y	x+y	NUM
ejpam-4154	80	7	)	)	PUNCT
ejpam-4154	81	1	+	+	CCONJ
ejpam-4154	81	2	π2	π2	ADJ
ejpam-4154	81	3	)	)	PUNCT
ejpam-4154	81	4	dxdydzdrdsdtdudv	dxdydzdrdsdtdudv	NOUN
ejpam-4154	81	5	=	=	SYM
ejpam-4154	81	6	1	1	NUM
ejpam-4154	81	7	2	2	NUM
ejpam-4154	81	8	π2	π2	NOUN
ejpam-4154	81	9	log(2	log(2	NOUN
ejpam-4154	81	10	)	)	PUNCT
ejpam-4154	81	11	(	(	PUNCT
ejpam-4154	81	12	11	11	NUM
ejpam-4154	81	13	)	)	PUNCT
ejpam-4154	81	14	and	and	CCONJ
ejpam-4154	81	15	(	(	PUNCT
ejpam-4154	81	16	12	12	NUM
ejpam-4154	81	17	)	)	PUNCT
ejpam-4154	81	18	∫	∫	PROPN
ejpam-4154	81	19	r8	r8	PROPN
ejpam-4154	81	20	+	+	CCONJ
ejpam-4154	82	1	4	4	NUM
ejpam-4154	82	2	√	√	NOUN
ejpam-4154	82	3	rs	rs	NOUN
ejpam-4154	82	4	4	4	NUM
ejpam-4154	82	5	√	√	NOUN
ejpam-4154	82	6	r	r	NOUN
ejpam-4154	83	1	+	+	SYM
ejpam-4154	83	2	s	s	NOUN
ejpam-4154	83	3	4	4	NUM
ejpam-4154	83	4	√	√	NOUN
ejpam-4154	83	5	tz	tz	PROPN
ejpam-4154	83	6	4	4	NUM
ejpam-4154	83	7	√	√	NOUN
ejpam-4154	83	8	t+	t+	PUNCT
ejpam-4154	83	9	z(uv)3/4(xy)3/4e−r−2s−2t−u−2v−x−2y−z	z(uv)3/4(xy)3/4e−r−2s−2t−u−2v−x−2y−z	PROPN
ejpam-4154	83	10	rstuvxyz	rstuvxyz	PROPN
ejpam-4154	83	11	4	4	NUM
ejpam-4154	83	12	√	√	NOUN
ejpam-4154	83	13	u+	u+	NUM
ejpam-4154	83	14	v	v	ADP
ejpam-4154	83	15	4	4	NUM
ejpam-4154	83	16	√	√	NOUN
ejpam-4154	83	17	x+	x+	PROPN
ejpam-4154	83	18	y	y	PROPN
ejpam-4154	83	19	(	(	PUNCT
ejpam-4154	83	20	log2	log2	PROPN
ejpam-4154	83	21	(	(	PUNCT
ejpam-4154	83	22	√	√	ADP
ejpam-4154	83	23	rs	rs	NOUN
ejpam-4154	83	24	√	√	PROPN
ejpam-4154	83	25	t+z	t+z	NUM
ejpam-4154	83	26	√	√	ADP
ejpam-4154	83	27	u+v	u+v	NUM
ejpam-4154	83	28	√	√	NUM
ejpam-4154	83	29	xy√	xy√	PUNCT
ejpam-4154	83	30	r+s	r+	NOUN
ejpam-4154	84	1	√	√	NUM
ejpam-4154	84	2	tz	tz	NOUN
ejpam-4154	84	3	√	√	NUM
ejpam-4154	84	4	uv	uv	NOUN
ejpam-4154	84	5	√	√	NOUN
ejpam-4154	84	6	x+y	x+y	NUM
ejpam-4154	84	7	)	)	PUNCT
ejpam-4154	85	1	+	+	CCONJ
ejpam-4154	85	2	π2	π2	ADJ
ejpam-4154	85	3	)	)	PUNCT
ejpam-4154	85	4	log	log	NOUN
ejpam-4154	85	5	(	(	PUNCT
ejpam-4154	85	6	√	√	NUM
ejpam-4154	85	7	rs	rs	NOUN
ejpam-4154	85	8	√	√	PROPN
ejpam-4154	85	9	t+	t+	NOUN
ejpam-4154	85	10	z	z	NOUN
ejpam-4154	85	11	√	√	PROPN
ejpam-4154	85	12	u+	u+	NUM
ejpam-4154	85	13	v	v	ADP
ejpam-4154	85	14	√	√	PROPN
ejpam-4154	85	15	xy	xy	NOUN
ejpam-4154	85	16	√	√	PUNCT
ejpam-4154	86	1	r	r	NOUN
ejpam-4154	86	2	+	+	SYM
ejpam-4154	86	3	s	s	NOUN
ejpam-4154	86	4	√	√	NOUN
ejpam-4154	86	5	tz	tz	NOUN
ejpam-4154	86	6	√	√	NUM
ejpam-4154	86	7	uv	uv	NOUN
ejpam-4154	86	8	√	√	NOUN
ejpam-4154	86	9	x+	x+	PROPN
ejpam-4154	86	10	y	y	PROPN
ejpam-4154	86	11	)	)	PUNCT
ejpam-4154	86	12	dxdydzdrdsdtdudv	dxdydzdrdsdtdudv	PROPN
ejpam-4154	86	13	=	=	SYM
ejpam-4154	86	14	0	0	NUM
ejpam-4154	86	15	proof	proof	NOUN
ejpam-4154	86	16	.	.	PUNCT
ejpam-4154	87	1	use	use	VERB
ejpam-4154	87	2	equation	equation	NOUN
ejpam-4154	87	3	(	(	PUNCT
ejpam-4154	87	4	9	9	NUM
ejpam-4154	87	5	)	)	PUNCT
ejpam-4154	87	6	and	and	CCONJ
ejpam-4154	87	7	set	set	VERB
ejpam-4154	87	8	a	a	DET
ejpam-4154	87	9	=	=	SYM
ejpam-4154	87	10	−1	−1	NOUN
ejpam-4154	87	11	,	,	PUNCT
ejpam-4154	87	12	p	p	NOUN
ejpam-4154	87	13	=	=	NOUN
ejpam-4154	87	14	1	1	NUM
ejpam-4154	87	15	,	,	PUNCT
ejpam-4154	87	16	q	q	NOUN
ejpam-4154	87	17	=	=	SYM
ejpam-4154	87	18	2,m	2,m	NOUN
ejpam-4154	87	19	=	=	SYM
ejpam-4154	87	20	−1/2	−1/2	VERB
ejpam-4154	87	21	and	and	CCONJ
ejpam-4154	87	22	simplify	simplify	VERB
ejpam-4154	87	23	in	in	ADP
ejpam-4154	87	24	terms	term	NOUN
ejpam-4154	87	25	of	of	ADP
ejpam-4154	87	26	the	the	DET
ejpam-4154	87	27	riemann	riemann	PROPN
ejpam-4154	87	28	zeta	zeta	PROPN
ejpam-4154	87	29	function	function	NOUN
ejpam-4154	87	30	using	use	VERB
ejpam-4154	87	31	entry	entry	NOUN
ejpam-4154	87	32	(	(	PUNCT
ejpam-4154	87	33	2	2	NUM
ejpam-4154	87	34	)	)	PUNCT
ejpam-4154	87	35	in	in	ADP
ejpam-4154	87	36	table	table	NOUN
ejpam-4154	87	37	below	below	ADV
ejpam-4154	87	38	(	(	PUNCT
ejpam-4154	87	39	64:7	64:7	NUM
ejpam-4154	87	40	)	)	PUNCT
ejpam-4154	87	41	and	and	CCONJ
ejpam-4154	87	42	entry	entry	NOUN
ejpam-4154	87	43	(	(	PUNCT
ejpam-4154	87	44	4	4	NUM
ejpam-4154	87	45	)	)	PUNCT
ejpam-4154	87	46	in	in	ADP
ejpam-4154	87	47	table	table	NOUN
ejpam-4154	87	48	below	below	ADV
ejpam-4154	87	49	(	(	PUNCT
ejpam-4154	87	50	64:12:7	64:12:7	NUM
ejpam-4154	87	51	)	)	PUNCT
ejpam-4154	87	52	in	in	ADP
ejpam-4154	87	53	[	[	X
ejpam-4154	87	54	7	7	NUM
ejpam-4154	87	55	]	]	PUNCT
ejpam-4154	87	56	.	.	PUNCT
ejpam-4154	88	1	next	next	ADJ
ejpam-4154	88	2	apply	apply	VERB
ejpam-4154	88	3	l’hopital	l’hopital	PROPN
ejpam-4154	88	4	’s	’s	PART
ejpam-4154	88	5	rule	rule	NOUN
ejpam-4154	88	6	to	to	ADP
ejpam-4154	88	7	the	the	DET
ejpam-4154	88	8	right	right	ADJ
ejpam-4154	88	9	-	-	PUNCT
ejpam-4154	88	10	hand	hand	NOUN
ejpam-4154	88	11	side	side	NOUN
ejpam-4154	88	12	as	as	SCONJ
ejpam-4154	88	13	k	k	PROPN
ejpam-4154	88	14	→	→	SYM
ejpam-4154	88	15	−1	−1	NOUN
ejpam-4154	88	16	rationalize	rationalize	VERB
ejpam-4154	88	17	the	the	DET
ejpam-4154	88	18	denominator	denominator	NOUN
ejpam-4154	88	19	equate	equate	VERB
ejpam-4154	88	20	real	real	ADJ
ejpam-4154	88	21	and	and	CCONJ
ejpam-4154	88	22	imaginary	imaginary	ADJ
ejpam-4154	88	23	parts	part	NOUN
ejpam-4154	88	24	and	and	CCONJ
ejpam-4154	88	25	simplify	simplify	NOUN
ejpam-4154	88	26	.	.	PUNCT
ejpam-4154	89	1	example	example	NOUN
ejpam-4154	90	1	3	3	NUM
ejpam-4154	90	2	.	.	PUNCT
ejpam-4154	90	3	(	(	PUNCT
ejpam-4154	90	4	13	13	NUM
ejpam-4154	90	5	)	)	PUNCT
ejpam-4154	90	6	∫	∫	PROPN
ejpam-4154	90	7	r8	r8	PROPN
ejpam-4154	90	8	+	+	CCONJ
ejpam-4154	90	9	(	(	PUNCT
ejpam-4154	90	10	r	r	NOUN
ejpam-4154	90	11	+	+	NUM
ejpam-4154	90	12	s)3/8	s)3/8	NOUN
ejpam-4154	90	13	8	8	NUM
ejpam-4154	90	14	√	√	NUM
ejpam-4154	90	15	t+	t+	PUNCT
ejpam-4154	90	16	ze−r−2s−2t−u−2v−x−2y−z	ze−r−2s−2t−u−2v−x−2y−z	PROPN
ejpam-4154	90	17	(	(	PUNCT
ejpam-4154	90	18	rs)7/8(tz)5/8	rs)7/8(tz)5/8	NUM
ejpam-4154	90	19	8	8	NUM
ejpam-4154	90	20	√	√	NOUN
ejpam-4154	90	21	uv(u+	uv(u+	PROPN
ejpam-4154	91	1	v)3/8(xy)3/8	v)3/8(xy)3/8	PROPN
ejpam-4154	91	2	8	8	NUM
ejpam-4154	91	3	√	√	NOUN
ejpam-4154	91	4	x+	x+	PROPN
ejpam-4154	91	5	y	y	PROPN
ejpam-4154	91	6	(	(	PUNCT
ejpam-4154	91	7	log2	log2	PROPN
ejpam-4154	91	8	(	(	PUNCT
ejpam-4154	91	9	−	−	PROPN
ejpam-4154	91	10	√	√	ADJ
ejpam-4154	91	11	rs	rs	NOUN
ejpam-4154	91	12	√	√	INTJ
ejpam-4154	91	13	t+z	t+z	NUM
ejpam-4154	91	14	√	√	ADP
ejpam-4154	91	15	u+v	u+v	NUM
ejpam-4154	91	16	√	√	NUM
ejpam-4154	91	17	xy√	xy√	PUNCT
ejpam-4154	91	18	r+s	r+	NOUN
ejpam-4154	92	1	√	√	NUM
ejpam-4154	92	2	tz	tz	NOUN
ejpam-4154	92	3	√	√	NUM
ejpam-4154	92	4	uv	uv	NOUN
ejpam-4154	92	5	√	√	NOUN
ejpam-4154	92	6	x+y	x+y	NUM
ejpam-4154	92	7	)	)	PUNCT
ejpam-4154	93	1	+	+	CCONJ
ejpam-4154	93	2	π2	π2	ADJ
ejpam-4154	93	3	)	)	PUNCT
ejpam-4154	93	4	dxdydzdrdsdtdudv	dxdydzdrdsdtdudv	NOUN
ejpam-4154	93	5	=	=	SYM
ejpam-4154	94	1	π2(π	π2(π	X
ejpam-4154	94	2	+	+	NUM
ejpam-4154	94	3	log(4	log(4	NOUN
ejpam-4154	94	4	)	)	PUNCT
ejpam-4154	94	5	)	)	PUNCT
ejpam-4154	94	6	8	8	NUM
ejpam-4154	94	7	√	√	NUM
ejpam-4154	94	8	2	2	NUM
ejpam-4154	94	9	and	and	CCONJ
ejpam-4154	94	10	(	(	PUNCT
ejpam-4154	94	11	14	14	NUM
ejpam-4154	94	12	)	)	PUNCT
ejpam-4154	94	13	∫	∫	PROPN
ejpam-4154	94	14	r8	r8	PROPN
ejpam-4154	94	15	+	+	CCONJ
ejpam-4154	94	16	(	(	PUNCT
ejpam-4154	94	17	r	r	NOUN
ejpam-4154	94	18	+	+	NUM
ejpam-4154	94	19	s)3/8	s)3/8	NOUN
ejpam-4154	94	20	8	8	NUM
ejpam-4154	94	21	√	√	NUM
ejpam-4154	94	22	t+	t+	NOUN
ejpam-4154	94	23	ze−r−2s−2t−u−2v−x−2y−z	ze−r−2s−2t−u−2v−x−2y−z	NOUN
ejpam-4154	94	24	log	log	NOUN
ejpam-4154	94	25	(	(	PUNCT
ejpam-4154	94	26	√	√	INTJ
ejpam-4154	94	27	rs	rs	NOUN
ejpam-4154	94	28	√	√	PROPN
ejpam-4154	94	29	t+z	t+z	NUM
ejpam-4154	94	30	√	√	ADP
ejpam-4154	94	31	u+v	u+v	NUM
ejpam-4154	94	32	√	√	NUM
ejpam-4154	94	33	xy√	xy√	PUNCT
ejpam-4154	95	1	r+s	r+	NOUN
ejpam-4154	96	1	√	√	NUM
ejpam-4154	96	2	tz	tz	NOUN
ejpam-4154	96	3	√	√	NUM
ejpam-4154	96	4	uv	uv	NOUN
ejpam-4154	96	5	√	√	NOUN
ejpam-4154	96	6	x+y	x+y	NUM
ejpam-4154	96	7	)	)	PUNCT
ejpam-4154	97	1	(	(	PUNCT
ejpam-4154	97	2	rs)7/8(tz)5/8	rs)7/8(tz)5/8	NUM
ejpam-4154	97	3	8	8	NUM
ejpam-4154	97	4	√	√	NOUN
ejpam-4154	97	5	uv(u+	uv(u+	PROPN
ejpam-4154	98	1	v)3/8(xy)3/8	v)3/8(xy)3/8	PROPN
ejpam-4154	98	2	8	8	NUM
ejpam-4154	98	3	√	√	NOUN
ejpam-4154	98	4	x+	x+	PROPN
ejpam-4154	98	5	y	y	PROPN
ejpam-4154	98	6	(	(	PUNCT
ejpam-4154	98	7	log2	log2	PROPN
ejpam-4154	98	8	(	(	PUNCT
ejpam-4154	98	9	√	√	ADP
ejpam-4154	98	10	rs	rs	NOUN
ejpam-4154	98	11	√	√	PROPN
ejpam-4154	98	12	t+z	t+z	NUM
ejpam-4154	98	13	√	√	ADP
ejpam-4154	98	14	u+v	u+v	NUM
ejpam-4154	98	15	√	√	NUM
ejpam-4154	98	16	xy√	xy√	PUNCT
ejpam-4154	98	17	r+s	r+	NOUN
ejpam-4154	99	1	√	√	NUM
ejpam-4154	99	2	tz	tz	NOUN
ejpam-4154	99	3	√	√	NUM
ejpam-4154	99	4	uv	uv	NOUN
ejpam-4154	99	5	√	√	NOUN
ejpam-4154	99	6	x+y	x+y	NUM
ejpam-4154	99	7	)	)	PUNCT
ejpam-4154	100	1	+	+	CCONJ
ejpam-4154	100	2	π2	π2	ADJ
ejpam-4154	100	3	)	)	PUNCT
ejpam-4154	100	4	dxdydzdrdsdtdudv	dxdydzdrdsdtdudv	NOUN
ejpam-4154	100	5	=	=	SYM
ejpam-4154	100	6	π3(log(4)−	π3(log(4)−	NOUN
ejpam-4154	100	7	π	π	NOUN
ejpam-4154	100	8	)	)	PUNCT
ejpam-4154	100	9	8	8	NUM
ejpam-4154	100	10	√	√	NUM
ejpam-4154	100	11	2	2	NUM
ejpam-4154	100	12	references	reference	NOUN
ejpam-4154	100	13	340	340	NUM
ejpam-4154	100	14	proof	proof	NOUN
ejpam-4154	100	15	.	.	PUNCT
ejpam-4154	101	1	use	use	VERB
ejpam-4154	101	2	equation	equation	NOUN
ejpam-4154	101	3	(	(	PUNCT
ejpam-4154	101	4	9	9	NUM
ejpam-4154	101	5	)	)	PUNCT
ejpam-4154	101	6	and	and	CCONJ
ejpam-4154	101	7	set	set	VERB
ejpam-4154	101	8	k	k	PROPN
ejpam-4154	101	9	=	=	PUNCT
ejpam-4154	101	10	−1	−1	NOUN
ejpam-4154	101	11	,	,	PUNCT
ejpam-4154	101	12	a	a	DET
ejpam-4154	101	13	=	=	SYM
ejpam-4154	101	14	−1	−1	NOUN
ejpam-4154	101	15	,	,	PUNCT
ejpam-4154	101	16	p	p	NOUN
ejpam-4154	101	17	=	=	NOUN
ejpam-4154	101	18	1	1	NUM
ejpam-4154	101	19	,	,	PUNCT
ejpam-4154	101	20	q	q	NOUN
ejpam-4154	101	21	=	=	SYM
ejpam-4154	101	22	2,m	2,m	NOUN
ejpam-4154	101	23	=	=	SYM
ejpam-4154	101	24	−1/2	−1/2	VERB
ejpam-4154	101	25	and	and	CCONJ
ejpam-4154	101	26	simplify	simplify	VERB
ejpam-4154	101	27	in	in	ADP
ejpam-4154	101	28	terms	term	NOUN
ejpam-4154	101	29	of	of	ADP
ejpam-4154	101	30	the	the	DET
ejpam-4154	101	31	polylogarithm	polylogarithm	PROPN
ejpam-4154	101	32	function	function	NOUN
ejpam-4154	101	33	lin(z	lin(z	PROPN
ejpam-4154	101	34	)	)	PUNCT
ejpam-4154	101	35	function	function	NOUN
ejpam-4154	101	36	using	use	VERB
ejpam-4154	101	37	entry	entry	NOUN
ejpam-4154	101	38	(	(	PUNCT
ejpam-4154	101	39	2	2	NUM
ejpam-4154	101	40	)	)	PUNCT
ejpam-4154	101	41	in	in	ADP
ejpam-4154	101	42	in	in	ADP
ejpam-4154	101	43	table	table	NOUN
ejpam-4154	101	44	below	below	ADP
ejpam-4154	101	45	(	(	PUNCT
ejpam-4154	101	46	64:12:7	64:12:7	NUM
ejpam-4154	101	47	)	)	PUNCT
ejpam-4154	101	48	in	in	ADP
ejpam-4154	101	49	[	[	X
ejpam-4154	101	50	7	7	NUM
ejpam-4154	101	51	]	]	PUNCT
ejpam-4154	101	52	and	and	CCONJ
ejpam-4154	101	53	equation	equation	NOUN
ejpam-4154	101	54	(	(	PUNCT
ejpam-4154	101	55	25.12.10	25.12.10	NUM
ejpam-4154	101	56	)	)	PUNCT
ejpam-4154	101	57	in	in	ADP
ejpam-4154	101	58	[	[	X
ejpam-4154	101	59	3	3	NUM
ejpam-4154	101	60	]	]	PUNCT
ejpam-4154	101	61	and	and	CCONJ
ejpam-4154	101	62	rationalize	rationalize	VERB
ejpam-4154	101	63	the	the	DET
ejpam-4154	101	64	denominator	denominator	NOUN
ejpam-4154	101	65	equate	equate	VERB
ejpam-4154	101	66	real	real	ADJ
ejpam-4154	101	67	and	and	CCONJ
ejpam-4154	101	68	imaginary	imaginary	ADJ
ejpam-4154	101	69	parts	part	NOUN
ejpam-4154	101	70	and	and	CCONJ
ejpam-4154	101	71	simplify	simplify	NOUN
ejpam-4154	101	72	.	.	PUNCT
ejpam-4154	102	1	example	example	NOUN
ejpam-4154	102	2	4.∫	4.∫	NUM
ejpam-4154	102	3	r8	r8	NOUN
ejpam-4154	103	1	+	+	CCONJ
ejpam-4154	103	2	(	(	PUNCT
ejpam-4154	103	3	r	r	NOUN
ejpam-4154	103	4	+	+	NUM
ejpam-4154	103	5	s)3/8	s)3/8	NOUN
ejpam-4154	103	6	8	8	NUM
ejpam-4154	103	7	√	√	NUM
ejpam-4154	103	8	t+	t+	PUNCT
ejpam-4154	103	9	ze−r−s−t−u−v−x−y−z	ze−r−s−t−u−v−x−y−z	PROPN
ejpam-4154	103	10	(	(	PUNCT
ejpam-4154	103	11	rs)7/8(tz)5/8	rs)7/8(tz)5/8	NUM
ejpam-4154	103	12	8	8	NUM
ejpam-4154	103	13	√	√	NOUN
ejpam-4154	103	14	uv(u+	uv(u+	PROPN
ejpam-4154	103	15	v)3/8(xy)3/8	v)3/8(xy)3/8	PROPN
ejpam-4154	103	16	8	8	NUM
ejpam-4154	103	17	√	√	ADV
ejpam-4154	103	18	x+	x+	NUM
ejpam-4154	103	19	y	y	PROPN
ejpam-4154	103	20	√	√	PROPN
ejpam-4154	103	21	log	log	NOUN
ejpam-4154	103	22	(	(	PUNCT
ejpam-4154	103	23	−	−	NOUN
ejpam-4154	103	24	√	√	NUM
ejpam-4154	103	25	rs	rs	NOUN
ejpam-4154	103	26	√	√	INTJ
ejpam-4154	103	27	t+z	t+z	NUM
ejpam-4154	103	28	√	√	ADP
ejpam-4154	103	29	u+v	u+v	NUM
ejpam-4154	103	30	√	√	NUM
ejpam-4154	103	31	xy√	xy√	PUNCT
ejpam-4154	103	32	r+s	r+	NOUN
ejpam-4154	104	1	√	√	NUM
ejpam-4154	104	2	tz	tz	NOUN
ejpam-4154	104	3	√	√	NUM
ejpam-4154	104	4	uv	uv	NOUN
ejpam-4154	104	5	√	√	PROPN
ejpam-4154	104	6	x+y	x+y	NUM
ejpam-4154	104	7	)	)	PUNCT
ejpam-4154	105	1	dxdydzdrdsdtdudv	dxdydzdrdsdtdudv	PROPN
ejpam-4154	105	2	=	=	SYM
ejpam-4154	105	3	(	(	PUNCT
ejpam-4154	105	4	−1−	−1−	PROPN
ejpam-4154	105	5	i	i	NOUN
ejpam-4154	105	6	)	)	PUNCT
ejpam-4154	105	7	√	√	PROPN
ejpam-4154	106	1	2π7/2	2π7/2	NUM
ejpam-4154	106	2	(	(	PUNCT
ejpam-4154	106	3	ζ	ζ	X
ejpam-4154	106	4	(	(	PUNCT
ejpam-4154	106	5	1	1	NUM
ejpam-4154	106	6	2	2	NUM
ejpam-4154	106	7	,	,	PUNCT
ejpam-4154	106	8	1	1	NUM
ejpam-4154	106	9	4	4	NUM
ejpam-4154	106	10	)	)	PUNCT
ejpam-4154	106	11	−	−	PROPN
ejpam-4154	107	1	iζ	iζ	NOUN
ejpam-4154	107	2	(	(	PUNCT
ejpam-4154	107	3	1	1	NUM
ejpam-4154	107	4	2	2	NUM
ejpam-4154	107	5	,	,	PUNCT
ejpam-4154	107	6	3	3	NUM
ejpam-4154	107	7	4	4	NUM
ejpam-4154	107	8	)	)	PUNCT
ejpam-4154	107	9	)	)	PUNCT
ejpam-4154	107	10	(	(	PUNCT
ejpam-4154	107	11	15	15	X
ejpam-4154	107	12	)	)	PUNCT
ejpam-4154	107	13	proof	proof	NOUN
ejpam-4154	107	14	.	.	PUNCT
ejpam-4154	108	1	use	use	VERB
ejpam-4154	108	2	equation	equation	NOUN
ejpam-4154	108	3	(	(	PUNCT
ejpam-4154	108	4	9	9	NUM
ejpam-4154	108	5	)	)	PUNCT
ejpam-4154	108	6	and	and	CCONJ
ejpam-4154	108	7	set	set	VERB
ejpam-4154	108	8	k	k	X
ejpam-4154	108	9	=	=	PUNCT
ejpam-4154	108	10	−1/2	−1/2	ADJ
ejpam-4154	108	11	,	,	PUNCT
ejpam-4154	108	12	a	a	DET
ejpam-4154	108	13	=	=	NOUN
ejpam-4154	108	14	−1	−1	NOUN
ejpam-4154	108	15	,	,	PUNCT
ejpam-4154	108	16	p	p	NOUN
ejpam-4154	108	17	=	=	X
ejpam-4154	108	18	q	q	NOUN
ejpam-4154	108	19	=	=	SYM
ejpam-4154	108	20	1,m	1,m	NOUN
ejpam-4154	108	21	=	=	SYM
ejpam-4154	108	22	−3/4	−3/4	NOUN
ejpam-4154	108	23	and	and	CCONJ
ejpam-4154	108	24	simplify	simplify	VERB
ejpam-4154	108	25	in	in	ADP
ejpam-4154	108	26	terms	term	NOUN
ejpam-4154	108	27	of	of	ADP
ejpam-4154	108	28	the	the	DET
ejpam-4154	108	29	hurwitz	hurwitz	PROPN
ejpam-4154	108	30	zeta	zeta	PROPN
ejpam-4154	108	31	function	function	NOUN
ejpam-4154	108	32	using	use	VERB
ejpam-4154	108	33	entry	entry	NOUN
ejpam-4154	108	34	(	(	PUNCT
ejpam-4154	108	35	4	4	NUM
ejpam-4154	108	36	)	)	PUNCT
ejpam-4154	108	37	in	in	ADP
ejpam-4154	108	38	table	table	NOUN
ejpam-4154	108	39	below	below	ADV
ejpam-4154	108	40	(	(	PUNCT
ejpam-4154	108	41	64:12:7	64:12:7	NUM
ejpam-4154	108	42	)	)	PUNCT
ejpam-4154	108	43	in	in	ADP
ejpam-4154	108	44	[	[	X
ejpam-4154	108	45	7	7	NUM
ejpam-4154	108	46	]	]	SYM
ejpam-4154	108	47	.	.	PUNCT
ejpam-4154	109	1	6	6	X
ejpam-4154	109	2	.	.	X
ejpam-4154	109	3	discussion	discussion	NOUN
ejpam-4154	109	4	in	in	ADP
ejpam-4154	109	5	this	this	DET
ejpam-4154	109	6	paper	paper	NOUN
ejpam-4154	109	7	,	,	PUNCT
ejpam-4154	109	8	we	we	PRON
ejpam-4154	109	9	have	have	AUX
ejpam-4154	109	10	presented	present	VERB
ejpam-4154	109	11	a	a	DET
ejpam-4154	109	12	novel	novel	ADJ
ejpam-4154	109	13	method	method	NOUN
ejpam-4154	109	14	for	for	ADP
ejpam-4154	109	15	deriving	derive	VERB
ejpam-4154	109	16	a	a	DET
ejpam-4154	109	17	new	new	ADJ
ejpam-4154	109	18	octuple	octuple	NOUN
ejpam-4154	109	19	integral	integral	ADJ
ejpam-4154	109	20	along	along	ADP
ejpam-4154	109	21	with	with	ADP
ejpam-4154	109	22	some	some	DET
ejpam-4154	109	23	interesting	interesting	ADJ
ejpam-4154	109	24	definite	definite	ADJ
ejpam-4154	109	25	integrals	integral	NOUN
ejpam-4154	109	26	using	use	VERB
ejpam-4154	109	27	contour	contour	NOUN
ejpam-4154	109	28	integration	integration	NOUN
ejpam-4154	109	29	.	.	PUNCT
ejpam-4154	110	1	the	the	DET
ejpam-4154	110	2	results	result	NOUN
ejpam-4154	110	3	presented	present	VERB
ejpam-4154	110	4	were	be	AUX
ejpam-4154	110	5	numerically	numerically	ADV
ejpam-4154	110	6	verified	verify	VERB
ejpam-4154	110	7	for	for	ADP
ejpam-4154	110	8	both	both	CCONJ
ejpam-4154	110	9	real	real	ADJ
ejpam-4154	110	10	and	and	CCONJ
ejpam-4154	110	11	imaginary	imaginary	ADJ
ejpam-4154	110	12	and	and	CCONJ
ejpam-4154	110	13	complex	complex	ADJ
ejpam-4154	110	14	values	value	NOUN
ejpam-4154	110	15	of	of	ADP
ejpam-4154	110	16	the	the	DET
ejpam-4154	110	17	parameters	parameter	NOUN
ejpam-4154	110	18	in	in	ADP
ejpam-4154	110	19	the	the	DET
ejpam-4154	110	20	integrals	integral	NOUN
ejpam-4154	110	21	using	use	VERB
ejpam-4154	110	22	mathematica	mathematica	PROPN
ejpam-4154	110	23	by	by	ADP
ejpam-4154	110	24	wolfram	wolfram	PROPN
ejpam-4154	110	25	.	.	PUNCT
ejpam-4154	111	1	some	some	PRON
ejpam-4154	111	2	of	of	ADP
ejpam-4154	111	3	the	the	DET
ejpam-4154	111	4	challenges	challenge	NOUN
ejpam-4154	111	5	encountered	encounter	VERB
ejpam-4154	111	6	were	be	AUX
ejpam-4154	111	7	in	in	ADP
ejpam-4154	111	8	the	the	DET
ejpam-4154	111	9	numerical	numerical	ADJ
ejpam-4154	111	10	evaluation	evaluation	NOUN
ejpam-4154	111	11	of	of	ADP
ejpam-4154	111	12	the	the	DET
ejpam-4154	111	13	integrals	integral	NOUN
ejpam-4154	111	14	.	.	PUNCT
ejpam-4154	112	1	we	we	PRON
ejpam-4154	112	2	know	know	VERB
ejpam-4154	112	3	from	from	ADP
ejpam-4154	112	4	our	our	PRON
ejpam-4154	112	5	method	method	NOUN
ejpam-4154	112	6	the	the	DET
ejpam-4154	112	7	definite	definite	ADJ
ejpam-4154	112	8	integral	integral	NOUN
ejpam-4154	112	9	is	be	AUX
ejpam-4154	112	10	equal	equal	ADJ
ejpam-4154	112	11	to	to	ADP
ejpam-4154	112	12	the	the	DET
ejpam-4154	112	13	lerch	lerch	PROPN
ejpam-4154	112	14	function	function	NOUN
ejpam-4154	112	15	so	so	SCONJ
ejpam-4154	112	16	this	this	PRON
ejpam-4154	112	17	is	be	AUX
ejpam-4154	112	18	a	a	DET
ejpam-4154	112	19	new	new	ADJ
ejpam-4154	112	20	way	way	NOUN
ejpam-4154	112	21	of	of	ADP
ejpam-4154	112	22	computing	compute	VERB
ejpam-4154	112	23	this	this	DET
ejpam-4154	112	24	octuple	octuple	PROPN
ejpam-4154	112	25	integral	integral	ADJ
ejpam-4154	112	26	.	.	PUNCT
ejpam-4154	113	1	we	we	PRON
ejpam-4154	113	2	tried	try	VERB
ejpam-4154	113	3	various	various	ADJ
ejpam-4154	113	4	numerical	numerical	ADJ
ejpam-4154	113	5	methods	method	NOUN
ejpam-4154	113	6	in	in	ADP
ejpam-4154	113	7	the	the	DET
ejpam-4154	113	8	mathematica	mathematica	PROPN
ejpam-4154	113	9	software	software	PROPN
ejpam-4154	113	10	to	to	PART
ejpam-4154	113	11	achieve	achieve	VERB
ejpam-4154	113	12	the	the	DET
ejpam-4154	113	13	best	good	ADJ
ejpam-4154	113	14	possible	possible	ADJ
ejpam-4154	113	15	result	result	NOUN
ejpam-4154	113	16	relative	relative	ADJ
ejpam-4154	113	17	to	to	ADP
ejpam-4154	113	18	the	the	DET
ejpam-4154	113	19	lerch	lerch	PROPN
ejpam-4154	113	20	function	function	PROPN
ejpam-4154	113	21	.	.	PUNCT
ejpam-4154	114	1	acknowledgements	acknowledgement	NOUN
ejpam-4154	114	2	this	this	DET
ejpam-4154	114	3	research	research	NOUN
ejpam-4154	114	4	is	be	AUX
ejpam-4154	114	5	supported	support	VERB
ejpam-4154	114	6	by	by	ADP
ejpam-4154	114	7	nserc	nserc	PROPN
ejpam-4154	114	8	canada	canada	PROPN
ejpam-4154	114	9	under	under	ADP
ejpam-4154	114	10	grant	grant	PROPN
ejpam-4154	114	11	504070	504070	NUM
ejpam-4154	114	12	.	.	PUNCT
ejpam-4154	115	1	references	reference	NOUN
ejpam-4154	115	2	[	[	X
ejpam-4154	115	3	1	1	NUM
ejpam-4154	115	4	]	]	X
ejpam-4154	115	5	s	s	PART
ejpam-4154	115	6	chapman	chapman	NOUN
ejpam-4154	115	7	.	.	PUNCT
ejpam-4154	116	1	the	the	DET
ejpam-4154	116	2	kinetic	kinetic	ADJ
ejpam-4154	116	3	theory	theory	NOUN
ejpam-4154	116	4	of	of	ADP
ejpam-4154	116	5	simple	simple	ADJ
ejpam-4154	116	6	and	and	CCONJ
ejpam-4154	116	7	composite	composite	ADJ
ejpam-4154	116	8	monatomic	monatomic	ADJ
ejpam-4154	116	9	gases	gas	NOUN
ejpam-4154	116	10	:	:	PUNCT
ejpam-4154	116	11	viscosity	viscosity	NOUN
ejpam-4154	116	12	,	,	PUNCT
ejpam-4154	116	13	thermal	thermal	ADJ
ejpam-4154	116	14	conduction	conduction	NOUN
ejpam-4154	116	15	,	,	PUNCT
ejpam-4154	116	16	and	and	CCONJ
ejpam-4154	116	17	diffusion	diffusion	NOUN
ejpam-4154	116	18	.	.	PUNCT
ejpam-4154	117	1	proceedings	proceeding	NOUN
ejpam-4154	117	2	of	of	ADP
ejpam-4154	117	3	the	the	DET
ejpam-4154	117	4	royal	royal	ADJ
ejpam-4154	117	5	society	society	NOUN
ejpam-4154	117	6	of	of	ADP
ejpam-4154	117	7	london	london	PROPN
ejpam-4154	117	8	.	.	PUNCT
ejpam-4154	118	1	series	series	PROPN
ejpam-4154	118	2	a	a	PROPN
ejpam-4154	118	3	,	,	PUNCT
ejpam-4154	118	4	containing	contain	VERB
ejpam-4154	118	5	papers	paper	NOUN
ejpam-4154	118	6	of	of	ADP
ejpam-4154	118	7	a	a	DET
ejpam-4154	118	8	mathematical	mathematical	ADJ
ejpam-4154	118	9	and	and	CCONJ
ejpam-4154	118	10	physical	physical	ADJ
ejpam-4154	118	11	character	character	NOUN
ejpam-4154	118	12	,	,	PUNCT
ejpam-4154	118	13	93:1–20	93:1–20	NUM
ejpam-4154	118	14	,	,	PUNCT
ejpam-4154	118	15	12	12	NUM
ejpam-4154	118	16	1916	1916	NUM
ejpam-4154	118	17	.	.	PUNCT
ejpam-4154	119	1	[	[	X
ejpam-4154	119	2	2	2	X
ejpam-4154	119	3	]	]	PUNCT
ejpam-4154	119	4	e.	e.	PROPN
ejpam-4154	119	5	t.	t.	PROPN
ejpam-4154	119	6	copson	copson	PROPN
ejpam-4154	119	7	.	.	PUNCT
ejpam-4154	120	1	xxii.—some	xxii.—some	PROPN
ejpam-4154	120	2	applications	application	NOUN
ejpam-4154	120	3	of	of	ADP
ejpam-4154	120	4	marcel	marcel	PROPN
ejpam-4154	120	5	riesz	riesz	PROPN
ejpam-4154	120	6	’s	’s	PART
ejpam-4154	120	7	integrals	integral	NOUN
ejpam-4154	120	8	of	of	ADP
ejpam-4154	120	9	fractional	fractional	ADJ
ejpam-4154	120	10	order	order	NOUN
ejpam-4154	120	11	.	.	PUNCT
ejpam-4154	121	1	proceedings	proceeding	NOUN
ejpam-4154	121	2	of	of	ADP
ejpam-4154	121	3	the	the	DET
ejpam-4154	121	4	royal	royal	ADJ
ejpam-4154	121	5	society	society	NOUN
ejpam-4154	121	6	of	of	ADP
ejpam-4154	121	7	edinburgh	edinburgh	PROPN
ejpam-4154	121	8	.	.	PUNCT
ejpam-4154	122	1	section	section	PROPN
ejpam-4154	122	2	a.	a.	PROPN
ejpam-4154	122	3	mathematical	mathematical	PROPN
ejpam-4154	122	4	and	and	CCONJ
ejpam-4154	122	5	physical	physical	ADJ
ejpam-4154	122	6	sciences	science	NOUN
ejpam-4154	122	7	,	,	PUNCT
ejpam-4154	122	8	61:260–272	61:260–272	PROPN
ejpam-4154	122	9	,	,	PUNCT
ejpam-4154	122	10	1943	1943	NUM
ejpam-4154	122	11	.	.	PUNCT
ejpam-4154	123	1	references	reference	NOUN
ejpam-4154	123	2	341	341	NUM
ejpam-4154	123	3	[	[	X
ejpam-4154	123	4	3	3	NUM
ejpam-4154	123	5	]	]	PUNCT
ejpam-4154	123	6	nist	nist	NOUN
ejpam-4154	123	7	digital	digital	PROPN
ejpam-4154	123	8	library	library	NOUN
ejpam-4154	123	9	of	of	ADP
ejpam-4154	123	10	mathematical	mathematical	ADJ
ejpam-4154	123	11	functions	function	NOUN
ejpam-4154	123	12	.	.	PUNCT
ejpam-4154	124	1	f.	f.	PROPN
ejpam-4154	124	2	w.	w.	PROPN
ejpam-4154	124	3	j.	j.	PROPN
ejpam-4154	124	4	olver	olver	PROPN
ejpam-4154	124	5	,	,	PUNCT
ejpam-4154	124	6	a.	a.	PROPN
ejpam-4154	124	7	b.	b.	PROPN
ejpam-4154	124	8	olde	olde	PROPN
ejpam-4154	124	9	daalhuis	daalhuis	PROPN
ejpam-4154	124	10	,	,	PUNCT
ejpam-4154	124	11	d.	d.	PROPN
ejpam-4154	124	12	w.	w.	PROPN
ejpam-4154	124	13	lozier	lozier	PROPN
ejpam-4154	124	14	,	,	PUNCT
ejpam-4154	124	15	b.	b.	PROPN
ejpam-4154	124	16	i.	i.	PROPN
ejpam-4154	124	17	schneider	schneider	PROPN
ejpam-4154	124	18	,	,	PUNCT
ejpam-4154	124	19	r.	r.	PROPN
ejpam-4154	124	20	f.	f.	PROPN
ejpam-4154	124	21	boisvert	boisvert	PROPN
ejpam-4154	124	22	,	,	PUNCT
ejpam-4154	124	23	c.	c.	PROPN
ejpam-4154	124	24	w.	w.	PROPN
ejpam-4154	124	25	clark	clark	PROPN
ejpam-4154	124	26	,	,	PUNCT
ejpam-4154	124	27	b.	b.	PROPN
ejpam-4154	124	28	r.	r.	PROPN
ejpam-4154	124	29	miller	miller	PROPN
ejpam-4154	124	30	,	,	PUNCT
ejpam-4154	124	31	b.	b.	PROPN
ejpam-4154	125	1	v.	v.	PROPN
ejpam-4154	125	2	saunders	saunders	PROPN
ejpam-4154	125	3	,	,	PUNCT
ejpam-4154	125	4	h.	h.	PROPN
ejpam-4154	125	5	s.	s.	PROPN
ejpam-4154	125	6	cohl	cohl	PROPN
ejpam-4154	125	7	,	,	PUNCT
ejpam-4154	125	8	and	and	CCONJ
ejpam-4154	125	9	m.	m.	PROPN
ejpam-4154	125	10	a.	a.	PROPN
ejpam-4154	125	11	mcclain	mcclain	PROPN
ejpam-4154	125	12	,	,	PUNCT
ejpam-4154	125	13	eds	eds	PROPN
ejpam-4154	125	14	.	.	PUNCT
ejpam-4154	126	1	[	[	X
ejpam-4154	126	2	4	4	NUM
ejpam-4154	126	3	]	]	X
ejpam-4154	126	4	i.	i.	PROPN
ejpam-4154	126	5	s.	s.	PROPN
ejpam-4154	126	6	gradshteyn	gradshteyn	PROPN
ejpam-4154	126	7	and	and	CCONJ
ejpam-4154	126	8	i.	i.	PROPN
ejpam-4154	126	9	m.	m.	PROPN
ejpam-4154	126	10	ryzhik	ryzhik	PROPN
ejpam-4154	126	11	.	.	PUNCT
ejpam-4154	127	1	table	table	NOUN
ejpam-4154	127	2	of	of	ADP
ejpam-4154	127	3	integrals	integral	NOUN
ejpam-4154	127	4	,	,	PUNCT
ejpam-4154	127	5	series	series	NOUN
ejpam-4154	127	6	,	,	PUNCT
ejpam-4154	127	7	and	and	CCONJ
ejpam-4154	127	8	products	product	NOUN
ejpam-4154	127	9	.	.	PUNCT
ejpam-4154	128	1	elsevier	elsevier	NOUN
ejpam-4154	128	2	/	/	SYM
ejpam-4154	128	3	academic	academic	ADJ
ejpam-4154	128	4	press	press	NOUN
ejpam-4154	128	5	,	,	PUNCT
ejpam-4154	128	6	amsterdam	amsterdam	PROPN
ejpam-4154	128	7	,	,	PUNCT
ejpam-4154	128	8	seventh	seventh	ADJ
ejpam-4154	128	9	edition	edition	NOUN
ejpam-4154	128	10	,	,	PUNCT
ejpam-4154	128	11	2007	2007	NUM
ejpam-4154	128	12	.	.	PUNCT
ejpam-4154	129	1	[	[	X
ejpam-4154	129	2	5	5	NUM
ejpam-4154	129	3	]	]	X
ejpam-4154	129	4	j.e	j.e	PROPN
ejpam-4154	129	5	.	.	PROPN
ejpam-4154	129	6	jones	jones	PROPN
ejpam-4154	129	7	.	.	PUNCT
ejpam-4154	129	8	i.	i.	PROPN
ejpam-4154	129	9	on	on	ADP
ejpam-4154	129	10	the	the	DET
ejpam-4154	129	11	velocity	velocity	NOUN
ejpam-4154	129	12	distribution	distribution	NOUN
ejpam-4154	129	13	function	function	NOUN
ejpam-4154	129	14	,	,	PUNCT
ejpam-4154	129	15	and	and	CCONJ
ejpam-4154	129	16	on	on	ADP
ejpam-4154	129	17	the	the	DET
ejpam-4154	129	18	stresses	stress	NOUN
ejpam-4154	129	19	in	in	ADP
ejpam-4154	129	20	a	a	DET
ejpam-4154	129	21	nonuniform	nonuniform	ADJ
ejpam-4154	129	22	rarefied	rarefy	VERB
ejpam-4154	129	23	monatomic	monatomic	ADJ
ejpam-4154	129	24	gas	gas	NOUN
ejpam-4154	129	25	.	.	PUNCT
ejpam-4154	130	1	philosophical	philosophical	ADJ
ejpam-4154	130	2	transactions	transaction	NOUN
ejpam-4154	130	3	of	of	ADP
ejpam-4154	130	4	the	the	DET
ejpam-4154	130	5	royal	royal	ADJ
ejpam-4154	130	6	society	society	NOUN
ejpam-4154	130	7	of	of	ADP
ejpam-4154	130	8	london	london	PROPN
ejpam-4154	130	9	.	.	PUNCT
ejpam-4154	131	1	series	series	PROPN
ejpam-4154	131	2	a	a	PROPN
ejpam-4154	131	3	,	,	PUNCT
ejpam-4154	131	4	containing	contain	VERB
ejpam-4154	131	5	papers	paper	NOUN
ejpam-4154	131	6	of	of	ADP
ejpam-4154	131	7	a	a	DET
ejpam-4154	131	8	mathematical	mathematical	ADJ
ejpam-4154	131	9	or	or	CCONJ
ejpam-4154	131	10	physical	physical	ADJ
ejpam-4154	131	11	character	character	NOUN
ejpam-4154	131	12	,	,	PUNCT
ejpam-4154	131	13	223:1–33	223:1–33	NUM
ejpam-4154	131	14	,	,	PUNCT
ejpam-4154	131	15	01	01	NUM
ejpam-4154	131	16	1923	1923	NUM
ejpam-4154	131	17	.	.	PUNCT
ejpam-4154	132	1	[	[	X
ejpam-4154	132	2	6	6	NUM
ejpam-4154	132	3	]	]	PUNCT
ejpam-4154	132	4	v.	v.	PROPN
ejpam-4154	132	5	l.	l.	PROPN
ejpam-4154	132	6	mironov	mironov	PROPN
ejpam-4154	132	7	and	and	CCONJ
ejpam-4154	132	8	s.	s.	PROPN
ejpam-4154	132	9	i.	i.	PROPN
ejpam-4154	132	10	tuzova	tuzova	PROPN
ejpam-4154	132	11	.	.	PUNCT
ejpam-4154	133	1	statistical	statistical	ADJ
ejpam-4154	133	2	characteristics	characteristic	NOUN
ejpam-4154	133	3	of	of	ADP
ejpam-4154	133	4	the	the	DET
ejpam-4154	133	5	laser	laser	NOUN
ejpam-4154	133	6	-	-	PUNCT
ejpam-4154	133	7	radiationintensity	radiationintensity	NOUN
ejpam-4154	133	8	fluctuations	fluctuation	NOUN
ejpam-4154	133	9	in	in	ADP
ejpam-4154	133	10	rainfall	rainfall	NOUN
ejpam-4154	133	11	.	.	PUNCT
ejpam-4154	134	1	optics	optic	NOUN
ejpam-4154	134	2	letters	letter	NOUN
ejpam-4154	134	3	,	,	PUNCT
ejpam-4154	134	4	5:362	5:362	NUM
ejpam-4154	134	5	,	,	PUNCT
ejpam-4154	134	6	08	08	NUM
ejpam-4154	134	7	1980	1980	NUM
ejpam-4154	134	8	.	.	PUNCT
ejpam-4154	135	1	[	[	X
ejpam-4154	135	2	7	7	X
ejpam-4154	135	3	]	]	X
ejpam-4154	135	4	keith	keith	PROPN
ejpam-4154	135	5	b.	b.	PROPN
ejpam-4154	135	6	oldham	oldham	PROPN
ejpam-4154	135	7	,	,	PUNCT
ejpam-4154	135	8	jan	jan	PROPN
ejpam-4154	135	9	myland	myland	PROPN
ejpam-4154	135	10	,	,	PUNCT
ejpam-4154	135	11	and	and	CCONJ
ejpam-4154	135	12	jerome	jerome	PROPN
ejpam-4154	135	13	spanier	spanier	NOUN
ejpam-4154	135	14	.	.	PUNCT
ejpam-4154	136	1	an	an	DET
ejpam-4154	136	2	atlas	atlas	PROPN
ejpam-4154	136	3	of	of	ADP
ejpam-4154	136	4	functions	function	NOUN
ejpam-4154	136	5	:	:	PUNCT
ejpam-4154	136	6	with	with	ADP
ejpam-4154	136	7	equator	equator	NOUN
ejpam-4154	136	8	,	,	PUNCT
ejpam-4154	136	9	the	the	DET
ejpam-4154	136	10	atlas	atlas	PROPN
ejpam-4154	136	11	function	function	PROPN
ejpam-4154	136	12	calculator	calculator	NOUN
ejpam-4154	136	13	.	.	PUNCT
ejpam-4154	137	1	springer	springer	NOUN
ejpam-4154	137	2	science	science	PROPN
ejpam-4154	137	3	&	&	CCONJ
ejpam-4154	137	4	business	business	NOUN
ejpam-4154	137	5	media	medium	NOUN
ejpam-4154	137	6	,	,	PUNCT
ejpam-4154	137	7	07	07	NUM
ejpam-4154	137	8	2010	2010	NUM
ejpam-4154	137	9	.	.	PUNCT
ejpam-4154	138	1	[	[	X
ejpam-4154	138	2	8	8	NUM
ejpam-4154	138	3	]	]	PUNCT
ejpam-4154	138	4	harold	harold	PROPN
ejpam-4154	138	5	osterberg	osterberg	PROPN
ejpam-4154	138	6	.	.	PUNCT
ejpam-4154	139	1	the	the	DET
ejpam-4154	139	2	multipupil	multipupil	NOUN
ejpam-4154	139	3	in	in	ADP
ejpam-4154	139	4	phase	phase	NOUN
ejpam-4154	139	5	microscopy	microscopy	NOUN
ejpam-4154	139	6	*	*	NOUN
ejpam-4154	139	7	.	.	PUNCT
ejpam-4154	139	8	journal	journal	PROPN
ejpam-4154	139	9	of	of	ADP
ejpam-4154	139	10	the	the	DET
ejpam-4154	139	11	optical	optical	ADJ
ejpam-4154	139	12	society	society	NOUN
ejpam-4154	139	13	of	of	ADP
ejpam-4154	139	14	america	america	PROPN
ejpam-4154	139	15	,	,	PUNCT
ejpam-4154	139	16	38:685	38:685	NUM
ejpam-4154	139	17	,	,	PUNCT
ejpam-4154	139	18	08	08	NUM
ejpam-4154	139	19	1948	1948	NUM
ejpam-4154	139	20	.	.	PUNCT
ejpam-4154	140	1	[	[	X
ejpam-4154	140	2	9	9	NUM
ejpam-4154	140	3	]	]	PUNCT
ejpam-4154	140	4	anatolĭı	anatolĭı	PROPN
ejpam-4154	140	5	platonovich	platonovich	PROPN
ejpam-4154	140	6	prudnikov	prudnikov	PROPN
ejpam-4154	140	7	,	,	PUNCT
ejpam-4154	140	8	yu	yu	PROPN
ejpam-4154	140	9	a.	a.	NOUN
ejpam-4154	140	10	brychkov	brychkov	PROPN
ejpam-4154	140	11	,	,	PUNCT
ejpam-4154	140	12	and	and	CCONJ
ejpam-4154	140	13	oleg	oleg	PROPN
ejpam-4154	140	14	igorevich	igorevich	PROPN
ejpam-4154	140	15	marichev	marichev	PROPN
ejpam-4154	140	16	.	.	PUNCT
ejpam-4154	140	17	integrals	integral	NOUN
ejpam-4154	140	18	and	and	CCONJ
ejpam-4154	140	19	series	series	NOUN
ejpam-4154	140	20	:	:	PUNCT
ejpam-4154	140	21	more	more	ADJ
ejpam-4154	140	22	special	special	ADJ
ejpam-4154	140	23	functions	function	NOUN
ejpam-4154	140	24	.	.	PUNCT
ejpam-4154	141	1	gordon	gordon	PROPN
ejpam-4154	141	2	and	and	CCONJ
ejpam-4154	141	3	breach	breach	VERB
ejpam-4154	141	4	science	science	NOUN
ejpam-4154	141	5	publishers	publisher	NOUN
ejpam-4154	141	6	,	,	PUNCT
ejpam-4154	141	7	1986	1986	NUM
ejpam-4154	141	8	.	.	PUNCT
ejpam-4154	142	1	[	[	X
ejpam-4154	142	2	10	10	NUM
ejpam-4154	142	3	]	]	X
ejpam-4154	142	4	robert	robert	PROPN
ejpam-4154	142	5	reynolds	reynolds	PROPN
ejpam-4154	142	6	and	and	CCONJ
ejpam-4154	142	7	allan	allan	PROPN
ejpam-4154	142	8	stauffer	stauffer	PROPN
ejpam-4154	142	9	.	.	PUNCT
ejpam-4154	143	1	a	a	DET
ejpam-4154	143	2	method	method	NOUN
ejpam-4154	143	3	for	for	ADP
ejpam-4154	143	4	evaluating	evaluate	VERB
ejpam-4154	143	5	definite	definite	ADJ
ejpam-4154	143	6	integrals	integral	NOUN
ejpam-4154	143	7	in	in	ADP
ejpam-4154	143	8	terms	term	NOUN
ejpam-4154	143	9	of	of	ADP
ejpam-4154	143	10	special	special	ADJ
ejpam-4154	143	11	functions	function	NOUN
ejpam-4154	143	12	with	with	ADP
ejpam-4154	143	13	examples	example	NOUN
ejpam-4154	143	14	.	.	PUNCT
ejpam-4154	144	1	international	international	ADJ
ejpam-4154	144	2	mathematical	mathematical	PROPN
ejpam-4154	144	3	forum	forum	PROPN
ejpam-4154	144	4	,	,	PUNCT
ejpam-4154	144	5	15:235	15:235	NUM
ejpam-4154	144	6	–	–	PUNCT
ejpam-4154	144	7	244	244	NUM
ejpam-4154	144	8	,	,	PUNCT
ejpam-4154	144	9	2020	2020	NUM
ejpam-4154	144	10	.	.	PUNCT