id	sid	tid	token	lemma	pos
ejpam-4065	1	1	european	european	PROPN
ejpam-4065	1	2	journal	journal	PROPN
ejpam-4065	1	3	of	of	ADP
ejpam-4065	1	4	pure	pure	ADJ
ejpam-4065	1	5	and	and	CCONJ
ejpam-4065	1	6	applied	apply	VERB
ejpam-4065	1	7	mathematics	mathematic	NOUN
ejpam-4065	1	8	vol	vol	NOUN
ejpam-4065	1	9	.	.	PUNCT
ejpam-4065	2	1	14	14	NUM
ejpam-4065	2	2	,	,	PUNCT
ejpam-4065	2	3	no	no	INTJ
ejpam-4065	2	4	.	.	NOUN
ejpam-4065	2	5	4	4	NUM
ejpam-4065	2	6	,	,	PUNCT
ejpam-4065	2	7	2021	2021	NUM
ejpam-4065	2	8	,	,	PUNCT
ejpam-4065	2	9	1379	1379	NUM
ejpam-4065	2	10	-	-	SYM
ejpam-4065	2	11	1387	1387	NUM
ejpam-4065	2	12	issn	issn	PROPN
ejpam-4065	2	13	1307	1307	NUM
ejpam-4065	2	14	-	-	SYM
ejpam-4065	2	15	5543	5543	NUM
ejpam-4065	2	16	–	–	PUNCT
ejpam-4065	2	17	ejpam.com	ejpam.com	X
ejpam-4065	2	18	published	publish	VERB
ejpam-4065	2	19	by	by	ADP
ejpam-4065	2	20	new	new	PROPN
ejpam-4065	2	21	york	york	PROPN
ejpam-4065	2	22	business	business	PROPN
ejpam-4065	2	23	global	global	ADJ
ejpam-4065	2	24	definite	definite	ADJ
ejpam-4065	2	25	integral	integral	ADJ
ejpam-4065	2	26	of	of	ADP
ejpam-4065	2	27	logarithmic	logarithmic	ADJ
ejpam-4065	2	28	power	power	NOUN
ejpam-4065	2	29	and	and	CCONJ
ejpam-4065	2	30	square	square	ADJ
ejpam-4065	2	31	root	root	NOUN
ejpam-4065	2	32	algebraic	algebraic	ADJ
ejpam-4065	2	33	functions	function	NOUN
ejpam-4065	2	34	expressed	express	VERB
ejpam-4065	2	35	in	in	ADP
ejpam-4065	2	36	terms	term	NOUN
ejpam-4065	2	37	of	of	ADP
ejpam-4065	2	38	the	the	DET
ejpam-4065	2	39	lerch	lerch	PROPN
ejpam-4065	2	40	function	function	PROPN
ejpam-4065	2	41	robert	robert	PROPN
ejpam-4065	2	42	reynolds1,∗	reynolds1,∗	PROPN
ejpam-4065	2	43	,	,	PUNCT
ejpam-4065	2	44	allan	allan	PROPN
ejpam-4065	2	45	stauffer2	stauffer2	PROPN
ejpam-4065	3	1	1	1	NUM
ejpam-4065	3	2	department	department	NOUN
ejpam-4065	3	3	of	of	ADP
ejpam-4065	3	4	mathematics	mathematic	NOUN
ejpam-4065	3	5	and	and	CCONJ
ejpam-4065	3	6	statistics	statistic	NOUN
ejpam-4065	3	7	,	,	PUNCT
ejpam-4065	3	8	faculty	faculty	NOUN
ejpam-4065	3	9	of	of	ADP
ejpam-4065	3	10	science	science	PROPN
ejpam-4065	3	11	,	,	PUNCT
ejpam-4065	3	12	york	york	PROPN
ejpam-4065	3	13	university	university	PROPN
ejpam-4065	3	14	,	,	PUNCT
ejpam-4065	3	15	toronto	toronto	PROPN
ejpam-4065	3	16	,	,	PUNCT
ejpam-4065	3	17	ontario	ontario	PROPN
ejpam-4065	3	18	,	,	PUNCT
ejpam-4065	3	19	canada	canada	PROPN
ejpam-4065	3	20	,	,	PUNCT
ejpam-4065	3	21	m3j1p3	m3j1p3	PROPN
ejpam-4065	3	22	abstract	abstract	NOUN
ejpam-4065	3	23	.	.	PUNCT
ejpam-4065	4	1	a	a	DET
ejpam-4065	4	2	definite	definite	ADJ
ejpam-4065	4	3	integral	integral	ADJ
ejpam-4065	4	4	involving	involve	VERB
ejpam-4065	4	5	the	the	DET
ejpam-4065	4	6	power	power	NOUN
ejpam-4065	4	7	square	square	ADJ
ejpam-4065	4	8	root	root	NOUN
ejpam-4065	4	9	of	of	ADP
ejpam-4065	4	10	an	an	DET
ejpam-4065	4	11	algebraic	algebraic	ADJ
ejpam-4065	4	12	function	function	NOUN
ejpam-4065	4	13	is	be	AUX
ejpam-4065	4	14	derived	derive	VERB
ejpam-4065	4	15	in	in	ADP
ejpam-4065	4	16	terms	term	NOUN
ejpam-4065	4	17	of	of	ADP
ejpam-4065	4	18	the	the	DET
ejpam-4065	4	19	lerch	lerch	PROPN
ejpam-4065	4	20	function	function	PROPN
ejpam-4065	4	21	.	.	PUNCT
ejpam-4065	5	1	a	a	DET
ejpam-4065	5	2	table	table	NOUN
ejpam-4065	5	3	consisting	consist	VERB
ejpam-4065	5	4	of	of	ADP
ejpam-4065	5	5	mostly	mostly	ADV
ejpam-4065	5	6	new	new	ADJ
ejpam-4065	5	7	results	result	NOUN
ejpam-4065	5	8	is	be	AUX
ejpam-4065	5	9	given	give	VERB
ejpam-4065	5	10	for	for	ADP
ejpam-4065	5	11	easy	easy	ADJ
ejpam-4065	5	12	reading	reading	NOUN
ejpam-4065	5	13	.	.	PUNCT
ejpam-4065	6	1	the	the	DET
ejpam-4065	6	2	majority	majority	NOUN
ejpam-4065	6	3	of	of	ADP
ejpam-4065	6	4	the	the	DET
ejpam-4065	6	5	results	result	NOUN
ejpam-4065	6	6	in	in	ADP
ejpam-4065	6	7	this	this	DET
ejpam-4065	6	8	work	work	NOUN
ejpam-4065	6	9	are	be	AUX
ejpam-4065	6	10	new	new	ADJ
ejpam-4065	6	11	.	.	PUNCT
ejpam-4065	7	1	2020	2020	NUM
ejpam-4065	7	2	mathematics	mathematic	NOUN
ejpam-4065	7	3	subject	subject	NOUN
ejpam-4065	7	4	classifications	classification	NOUN
ejpam-4065	7	5	:	:	PUNCT
ejpam-4065	7	6	primary	primary	ADJ
ejpam-4065	7	7	30e20,33	30e20,33	NUM
ejpam-4065	7	8	-	-	SYM
ejpam-4065	7	9	01	01	NUM
ejpam-4065	7	10	,	,	PUNCT
ejpam-4065	7	11	33	33	NUM
ejpam-4065	7	12	-	-	SYM
ejpam-4065	7	13	03	03	NUM
ejpam-4065	7	14	,	,	PUNCT
ejpam-4065	7	15	33	33	NUM
ejpam-4065	7	16	-	-	PUNCT
ejpam-4065	7	17	04	04	NUM
ejpam-4065	7	18	,	,	PUNCT
ejpam-4065	7	19	33	33	NUM
ejpam-4065	7	20	-	-	PUNCT
ejpam-4065	7	21	33b	33b	NUM
ejpam-4065	7	22	,	,	PUNCT
ejpam-4065	7	23	33e20	33e20	NUM
ejpam-4065	7	24	key	key	ADJ
ejpam-4065	7	25	words	word	NOUN
ejpam-4065	7	26	and	and	CCONJ
ejpam-4065	7	27	phrases	phrase	NOUN
ejpam-4065	7	28	:	:	PUNCT
ejpam-4065	7	29	definite	definite	ADJ
ejpam-4065	7	30	integral	integral	ADJ
ejpam-4065	7	31	,	,	PUNCT
ejpam-4065	7	32	square	square	ADJ
ejpam-4065	7	33	root	root	NOUN
ejpam-4065	7	34	function	function	NOUN
ejpam-4065	7	35	,	,	PUNCT
ejpam-4065	7	36	lerch	lerch	PROPN
ejpam-4065	7	37	function	function	PROPN
ejpam-4065	7	38	,	,	PUNCT
ejpam-4065	7	39	polylogarithm	polylogarithm	PROPN
ejpam-4065	7	40	function	function	PROPN
ejpam-4065	7	41	,	,	PUNCT
ejpam-4065	7	42	riemann	riemann	PROPN
ejpam-4065	7	43	zeta	zeta	PROPN
ejpam-4065	7	44	function	function	VERB
ejpam-4065	7	45	1	1	NUM
ejpam-4065	7	46	.	.	NOUN
ejpam-4065	7	47	significance	significance	NOUN
ejpam-4065	7	48	statement	statement	NOUN
ejpam-4065	7	49	definite	definite	ADJ
ejpam-4065	7	50	integrals	integral	NOUN
ejpam-4065	7	51	involving	involve	VERB
ejpam-4065	7	52	the	the	DET
ejpam-4065	7	53	nested	nested	ADJ
ejpam-4065	7	54	square	square	ADJ
ejpam-4065	7	55	root	root	NOUN
ejpam-4065	7	56	of	of	ADP
ejpam-4065	7	57	a	a	DET
ejpam-4065	7	58	function	function	NOUN
ejpam-4065	7	59	over	over	ADP
ejpam-4065	7	60	[	[	X
ejpam-4065	7	61	2,∞	2,∞	NUM
ejpam-4065	7	62	)	)	PUNCT
ejpam-4065	7	63	have	have	AUX
ejpam-4065	7	64	been	be	AUX
ejpam-4065	7	65	studied	study	VERB
ejpam-4065	7	66	by	by	ADP
ejpam-4065	7	67	nyblom	nyblom	PROPN
ejpam-4065	8	1	[	[	X
ejpam-4065	8	2	7	7	NUM
ejpam-4065	8	3	]	]	PUNCT
ejpam-4065	8	4	.	.	PUNCT
ejpam-4065	9	1	the	the	DET
ejpam-4065	9	2	authors	author	NOUN
ejpam-4065	9	3	studied	study	VERB
ejpam-4065	9	4	a	a	DET
ejpam-4065	9	5	definite	definite	ADJ
ejpam-4065	9	6	integral	integral	ADJ
ejpam-4065	9	7	with	with	ADP
ejpam-4065	9	8	a	a	DET
ejpam-4065	9	9	general	general	ADJ
ejpam-4065	9	10	root	root	NOUN
ejpam-4065	9	11	kernel	kernel	NOUN
ejpam-4065	9	12	in	in	ADP
ejpam-4065	9	13	[	[	X
ejpam-4065	9	14	9	9	NUM
ejpam-4065	9	15	]	]	PUNCT
ejpam-4065	9	16	.	.	PUNCT
ejpam-4065	10	1	in	in	ADP
ejpam-4065	10	2	this	this	DET
ejpam-4065	10	3	work	work	NOUN
ejpam-4065	10	4	we	we	PRON
ejpam-4065	10	5	will	will	AUX
ejpam-4065	10	6	derive	derive	VERB
ejpam-4065	10	7	and	and	CCONJ
ejpam-4065	10	8	evaluate	evaluate	VERB
ejpam-4065	10	9	integrals	integral	NOUN
ejpam-4065	10	10	involving	involve	VERB
ejpam-4065	10	11	a	a	DET
ejpam-4065	10	12	power	power	NOUN
ejpam-4065	10	13	square	square	ADJ
ejpam-4065	10	14	root	root	NOUN
ejpam-4065	10	15	and	and	CCONJ
ejpam-4065	10	16	algebraic	algebraic	ADJ
ejpam-4065	10	17	functions	function	NOUN
ejpam-4065	10	18	over	over	ADP
ejpam-4065	10	19	[	[	X
ejpam-4065	10	20	0,∞	0,∞	NOUN
ejpam-4065	10	21	)	)	PUNCT
ejpam-4065	10	22	.	.	PUNCT
ejpam-4065	11	1	this	this	DET
ejpam-4065	11	2	integral	integral	NOUN
ejpam-4065	11	3	is	be	AUX
ejpam-4065	11	4	also	also	ADV
ejpam-4065	11	5	derived	derive	VERB
ejpam-4065	11	6	in	in	ADP
ejpam-4065	11	7	terms	term	NOUN
ejpam-4065	11	8	of	of	ADP
ejpam-4065	11	9	the	the	DET
ejpam-4065	11	10	lerch	lerch	PROPN
ejpam-4065	11	11	function	function	NOUN
ejpam-4065	11	12	which	which	PRON
ejpam-4065	11	13	is	be	AUX
ejpam-4065	11	14	currently	currently	ADV
ejpam-4065	11	15	not	not	PART
ejpam-4065	11	16	present	present	ADJ
ejpam-4065	11	17	in	in	ADP
ejpam-4065	11	18	current	current	ADJ
ejpam-4065	11	19	literature	literature	NOUN
ejpam-4065	11	20	.	.	PUNCT
ejpam-4065	12	1	possible	possible	ADJ
ejpam-4065	12	2	applications	application	NOUN
ejpam-4065	12	3	of	of	ADP
ejpam-4065	12	4	these	these	DET
ejpam-4065	12	5	types	type	NOUN
ejpam-4065	12	6	integrals	integral	VERB
ejpam-4065	12	7	other	other	ADJ
ejpam-4065	12	8	than	than	ADP
ejpam-4065	12	9	those	those	PRON
ejpam-4065	12	10	met	meet	VERB
ejpam-4065	12	11	in	in	ADP
ejpam-4065	12	12	stochastic	stochastic	ADJ
ejpam-4065	12	13	problems	problem	NOUN
ejpam-4065	12	14	has	have	AUX
ejpam-4065	12	15	not	not	PART
ejpam-4065	12	16	yet	yet	ADV
ejpam-4065	12	17	been	be	AUX
ejpam-4065	12	18	explored	explore	VERB
ejpam-4065	12	19	.	.	PUNCT
ejpam-4065	13	1	2	2	X
ejpam-4065	13	2	.	.	X
ejpam-4065	13	3	introduction	introduction	NOUN
ejpam-4065	13	4	in	in	ADP
ejpam-4065	13	5	the	the	DET
ejpam-4065	13	6	present	present	ADJ
ejpam-4065	13	7	work	work	NOUN
ejpam-4065	13	8	,	,	PUNCT
ejpam-4065	13	9	the	the	DET
ejpam-4065	13	10	authors	author	NOUN
ejpam-4065	13	11	used	use	VERB
ejpam-4065	13	12	their	their	PRON
ejpam-4065	13	13	contour	contour	NOUN
ejpam-4065	13	14	integral	integral	ADJ
ejpam-4065	13	15	method	method	NOUN
ejpam-4065	13	16	and	and	CCONJ
ejpam-4065	13	17	applied	apply	VERB
ejpam-4065	13	18	it	it	PRON
ejpam-4065	13	19	to	to	ADP
ejpam-4065	13	20	the	the	DET
ejpam-4065	13	21	lerch	lerch	PROPN
ejpam-4065	13	22	function	function	NOUN
ejpam-4065	13	23	to	to	PART
ejpam-4065	13	24	derive	derive	VERB
ejpam-4065	13	25	a	a	DET
ejpam-4065	13	26	definite	definite	ADJ
ejpam-4065	13	27	integral	integral	ADJ
ejpam-4065	13	28	and	and	CCONJ
ejpam-4065	13	29	expressed	express	VERB
ejpam-4065	13	30	its	its	PRON
ejpam-4065	13	31	closed	closed	ADJ
ejpam-4065	13	32	form	form	NOUN
ejpam-4065	13	33	in	in	ADP
ejpam-4065	13	34	terms	term	NOUN
ejpam-4065	13	35	of	of	ADP
ejpam-4065	13	36	a	a	DET
ejpam-4065	13	37	special	special	ADJ
ejpam-4065	13	38	function	function	NOUN
ejpam-4065	13	39	.	.	PUNCT
ejpam-4065	14	1	this	this	DET
ejpam-4065	14	2	derived	derive	VERB
ejpam-4065	14	3	integral	integral	ADJ
ejpam-4065	14	4	formula	formula	NOUN
ejpam-4065	14	5	was	be	AUX
ejpam-4065	14	6	then	then	ADV
ejpam-4065	14	7	used	use	VERB
ejpam-4065	14	8	to	to	PART
ejpam-4065	14	9	provide	provide	VERB
ejpam-4065	14	10	formal	formal	ADJ
ejpam-4065	14	11	derivations	derivation	NOUN
ejpam-4065	14	12	in	in	ADP
ejpam-4065	14	13	terms	term	NOUN
ejpam-4065	14	14	of	of	ADP
ejpam-4065	14	15	special	special	ADJ
ejpam-4065	14	16	functions	function	NOUN
ejpam-4065	14	17	and	and	CCONJ
ejpam-4065	14	18	fundamental	fundamental	ADJ
ejpam-4065	14	19	constants	constant	NOUN
ejpam-4065	14	20	.	.	PUNCT
ejpam-4065	15	1	the	the	DET
ejpam-4065	15	2	lerch	lerch	PROPN
ejpam-4065	15	3	function	function	PROPN
ejpam-4065	15	4	being	be	AUX
ejpam-4065	15	5	a	a	DET
ejpam-4065	15	6	special	special	ADJ
ejpam-4065	15	7	function	function	NOUN
ejpam-4065	15	8	has	have	VERB
ejpam-4065	15	9	the	the	DET
ejpam-4065	15	10	fundamental	fundamental	ADJ
ejpam-4065	15	11	property	property	NOUN
ejpam-4065	15	12	of	of	ADP
ejpam-4065	15	13	analytic	analytic	ADJ
ejpam-4065	15	14	continuation	continuation	NOUN
ejpam-4065	15	15	,	,	PUNCT
ejpam-4065	15	16	which	which	PRON
ejpam-4065	15	17	enables	enable	VERB
ejpam-4065	15	18	us	we	PRON
ejpam-4065	15	19	to	to	PART
ejpam-4065	15	20	widen	widen	VERB
ejpam-4065	15	21	the	the	DET
ejpam-4065	15	22	range	range	NOUN
ejpam-4065	15	23	of	of	ADP
ejpam-4065	15	24	evaluation	evaluation	NOUN
ejpam-4065	15	25	for	for	ADP
ejpam-4065	15	26	the	the	DET
ejpam-4065	15	27	parameters	parameter	NOUN
ejpam-4065	15	28	involved	involve	VERB
ejpam-4065	15	29	in	in	ADP
ejpam-4065	15	30	our	our	PRON
ejpam-4065	15	31	definite	definite	ADJ
ejpam-4065	15	32	integral	integral	ADJ
ejpam-4065	15	33	.	.	PUNCT
ejpam-4065	16	1	∗corresponding	∗corresponde	VERB
ejpam-4065	16	2	author	author	NOUN
ejpam-4065	16	3	.	.	PUNCT
ejpam-4065	17	1	doi	doi	NOUN
ejpam-4065	17	2	:	:	PUNCT
ejpam-4065	17	3	https://doi.org/10.29020/nybg.ejpam.v14i4.4065	https://doi.org/10.29020/nybg.ejpam.v14i4.4065	PROPN
ejpam-4065	17	4	email	email	NOUN
ejpam-4065	17	5	addresses	address	NOUN
ejpam-4065	17	6	:	:	PUNCT
ejpam-4065	18	1	milver@my.yorku.ca	milver@my.yorku.ca	NOUN
ejpam-4065	18	2	(	(	PUNCT
ejpam-4065	18	3	r.	r.	PROPN
ejpam-4065	18	4	reynolds	reynolds	PROPN
ejpam-4065	18	5	)	)	PUNCT
ejpam-4065	18	6	,	,	PUNCT
ejpam-4065	18	7	stauffer@yorku.ca	stauffer@yorku.ca	NOUN
ejpam-4065	18	8	(	(	PUNCT
ejpam-4065	18	9	a.	a.	NOUN
ejpam-4065	18	10	stauffer	stauffer	PROPN
ejpam-4065	18	11	)	)	PUNCT
ejpam-4065	18	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4065	18	13	1379	1379	NUM
ejpam-4065	19	1	©	©	PROPN
ejpam-4065	19	2	2021	2021	NUM
ejpam-4065	19	3	ejpam	ejpam	VERB
ejpam-4065	19	4	all	all	DET
ejpam-4065	19	5	rights	right	NOUN
ejpam-4065	19	6	reserved	reserve	VERB
ejpam-4065	19	7	.	.	PUNCT
ejpam-4065	20	1	r.	r.	PROPN
ejpam-4065	20	2	reynolds	reynolds	PROPN
ejpam-4065	20	3	,	,	PUNCT
ejpam-4065	20	4	a.	a.	PROPN
ejpam-4065	20	5	stauffer	stauffer	PROPN
ejpam-4065	20	6	/	/	SYM
ejpam-4065	20	7	eur	eur	PROPN
ejpam-4065	20	8	.	.	PUNCT
ejpam-4065	21	1	j.	j.	PROPN
ejpam-4065	21	2	pure	pure	PROPN
ejpam-4065	21	3	appl	appl	PROPN
ejpam-4065	21	4	.	.	PROPN
ejpam-4065	21	5	math	math	PROPN
ejpam-4065	21	6	,	,	PUNCT
ejpam-4065	21	7	14	14	NUM
ejpam-4065	21	8	(	(	PUNCT
ejpam-4065	21	9	4	4	NUM
ejpam-4065	21	10	)	)	PUNCT
ejpam-4065	21	11	(	(	PUNCT
ejpam-4065	21	12	2021	2021	NUM
ejpam-4065	21	13	)	)	PUNCT
ejpam-4065	21	14	,	,	PUNCT
ejpam-4065	21	15	1379	1379	NUM
ejpam-4065	21	16	-	-	SYM
ejpam-4065	21	17	1387	1387	NUM
ejpam-4065	21	18	1380	1380	NUM
ejpam-4065	21	19	the	the	DET
ejpam-4065	21	20	lerch	lerch	PROPN
ejpam-4065	21	21	function	function	PROPN
ejpam-4065	21	22	is	be	AUX
ejpam-4065	21	23	a	a	DET
ejpam-4065	21	24	special	special	ADJ
ejpam-4065	21	25	function	function	NOUN
ejpam-4065	21	26	that	that	PRON
ejpam-4065	21	27	generalizes	generalize	VERB
ejpam-4065	21	28	the	the	DET
ejpam-4065	21	29	hurwitz	hurwitz	PROPN
ejpam-4065	21	30	zeta	zeta	PROPN
ejpam-4065	21	31	function	function	PROPN
ejpam-4065	21	32	,	,	PUNCT
ejpam-4065	21	33	the	the	DET
ejpam-4065	21	34	polylogarithms	polylogarithm	NOUN
ejpam-4065	21	35	,	,	PUNCT
ejpam-4065	21	36	and	and	CCONJ
ejpam-4065	21	37	so	so	ADV
ejpam-4065	21	38	many	many	ADJ
ejpam-4065	21	39	interesting	interesting	ADJ
ejpam-4065	21	40	and	and	CCONJ
ejpam-4065	21	41	important	important	ADJ
ejpam-4065	21	42	special	special	ADJ
ejpam-4065	21	43	functions	function	NOUN
ejpam-4065	21	44	.	.	PUNCT
ejpam-4065	22	1	the	the	DET
ejpam-4065	22	2	definite	definite	ADJ
ejpam-4065	22	3	integral	integral	ADJ
ejpam-4065	22	4	derived	derived	NOUN
ejpam-4065	22	5	in	in	ADP
ejpam-4065	22	6	this	this	DET
ejpam-4065	22	7	manuscript	manuscript	NOUN
ejpam-4065	22	8	is	be	AUX
ejpam-4065	22	9	given	give	VERB
ejpam-4065	22	10	by	by	ADP
ejpam-4065	22	11	∫	∫	PROPN
ejpam-4065	22	12	∞	∞	PROPN
ejpam-4065	22	13	0	0	NUM
ejpam-4065	22	14	(	(	PUNCT
ejpam-4065	22	15	√	√	NUM
ejpam-4065	22	16	b+	b+	NOUN
ejpam-4065	22	17	x−	x−	PROPN
ejpam-4065	22	18	√	√	PROPN
ejpam-4065	22	19	b	b	NOUN
ejpam-4065	22	20	)	)	PUNCT
ejpam-4065	22	21	−m	−m	NOUN
ejpam-4065	22	22	logk	logk	NOUN
ejpam-4065	22	23	(	(	PUNCT
ejpam-4065	22	24	a√	a√	PROPN
ejpam-4065	22	25	b+x−	b+x−	PROPN
ejpam-4065	22	26	√	√	PROPN
ejpam-4065	22	27	b	b	X
ejpam-4065	22	28	)	)	PUNCT
ejpam-4065	22	29	x	x	SYM
ejpam-4065	22	30	√	√	NUM
ejpam-4065	22	31	b+	b+	AUX
ejpam-4065	22	32	x	x	X
ejpam-4065	22	33	dx	dx	PROPN
ejpam-4065	22	34	(	(	PUNCT
ejpam-4065	22	35	1	1	NUM
ejpam-4065	22	36	)	)	PUNCT
ejpam-4065	22	37	where	where	SCONJ
ejpam-4065	22	38	the	the	DET
ejpam-4065	22	39	parameters	parameter	NOUN
ejpam-4065	22	40	k	k	PROPN
ejpam-4065	22	41	,	,	PUNCT
ejpam-4065	22	42	b	b	PROPN
ejpam-4065	22	43	and	and	CCONJ
ejpam-4065	22	44	a	a	PRON
ejpam-4065	22	45	are	be	AUX
ejpam-4065	22	46	general	general	ADJ
ejpam-4065	22	47	complex	complex	ADJ
ejpam-4065	22	48	numbers	number	NOUN
ejpam-4065	22	49	and	and	CCONJ
ejpam-4065	22	50	−1	−1	NOUN
ejpam-4065	22	51	<	<	X
ejpam-4065	22	52	re(m	re(m	PROPN
ejpam-4065	22	53	)	)	PUNCT
ejpam-4065	22	54	<	<	X
ejpam-4065	23	1	0	0	X
ejpam-4065	23	2	.	.	PUNCT
ejpam-4065	24	1	the	the	DET
ejpam-4065	24	2	derivation	derivation	NOUN
ejpam-4065	24	3	of	of	ADP
ejpam-4065	24	4	the	the	DET
ejpam-4065	24	5	definite	definite	ADJ
ejpam-4065	24	6	integral	integral	NOUN
ejpam-4065	24	7	follows	follow	VERB
ejpam-4065	24	8	the	the	DET
ejpam-4065	24	9	method	method	NOUN
ejpam-4065	24	10	used	use	VERB
ejpam-4065	24	11	by	by	ADP
ejpam-4065	24	12	us	we	PRON
ejpam-4065	24	13	in	in	ADP
ejpam-4065	24	14	[	[	X
ejpam-4065	24	15	10	10	NUM
ejpam-4065	24	16	]	]	PUNCT
ejpam-4065	24	17	which	which	PRON
ejpam-4065	24	18	involves	involve	VERB
ejpam-4065	24	19	cauchy	cauchy	PROPN
ejpam-4065	24	20	’s	’s	PART
ejpam-4065	24	21	integral	integral	ADJ
ejpam-4065	24	22	formula	formula	NOUN
ejpam-4065	24	23	.	.	PUNCT
ejpam-4065	25	1	the	the	DET
ejpam-4065	25	2	generalized	generalized	ADJ
ejpam-4065	25	3	cauchy	cauchy	PROPN
ejpam-4065	25	4	’s	’s	PART
ejpam-4065	25	5	integral	integral	ADJ
ejpam-4065	25	6	formula	formula	NOUN
ejpam-4065	25	7	is	be	AUX
ejpam-4065	25	8	given	give	VERB
ejpam-4065	25	9	by	by	ADP
ejpam-4065	25	10	yk	yk	PROPN
ejpam-4065	25	11	γ(k	γ(k	PROPN
ejpam-4065	25	12	+	+	CCONJ
ejpam-4065	25	13	1	1	X
ejpam-4065	25	14	)	)	PUNCT
ejpam-4065	25	15	=	=	SYM
ejpam-4065	25	16	1	1	NUM
ejpam-4065	25	17	2πi	2πi	ADJ
ejpam-4065	25	18	∫	∫	PROPN
ejpam-4065	25	19	c	c	PROPN
ejpam-4065	25	20	ewy	ewy	PROPN
ejpam-4065	25	21	wk+1	wk+1	PROPN
ejpam-4065	25	22	dw	dw	PROPN
ejpam-4065	25	23	.	.	PUNCT
ejpam-4065	26	1	(	(	PUNCT
ejpam-4065	26	2	2	2	X
ejpam-4065	26	3	)	)	PUNCT
ejpam-4065	26	4	where	where	SCONJ
ejpam-4065	26	5	c	c	NOUN
ejpam-4065	26	6	is	be	AUX
ejpam-4065	26	7	in	in	ADP
ejpam-4065	26	8	general	general	ADJ
ejpam-4065	26	9	an	an	DET
ejpam-4065	26	10	open	open	ADJ
ejpam-4065	26	11	contour	contour	NOUN
ejpam-4065	26	12	in	in	ADP
ejpam-4065	26	13	the	the	DET
ejpam-4065	26	14	complex	complex	ADJ
ejpam-4065	26	15	plane	plane	NOUN
ejpam-4065	26	16	where	where	SCONJ
ejpam-4065	26	17	the	the	DET
ejpam-4065	26	18	bilinear	bilinear	NOUN
ejpam-4065	26	19	concomitant	concomitant	NOUN
ejpam-4065	27	1	[	[	X
ejpam-4065	27	2	10	10	NUM
ejpam-4065	27	3	]	]	PUNCT
ejpam-4065	27	4	has	have	VERB
ejpam-4065	27	5	the	the	DET
ejpam-4065	27	6	same	same	ADJ
ejpam-4065	27	7	value	value	NOUN
ejpam-4065	27	8	at	at	ADP
ejpam-4065	27	9	the	the	DET
ejpam-4065	27	10	end	end	NOUN
ejpam-4065	27	11	points	point	NOUN
ejpam-4065	27	12	.	.	PUNCT
ejpam-4065	28	1	this	this	DET
ejpam-4065	28	2	method	method	NOUN
ejpam-4065	28	3	involves	involve	VERB
ejpam-4065	28	4	using	use	VERB
ejpam-4065	28	5	a	a	DET
ejpam-4065	28	6	form	form	NOUN
ejpam-4065	28	7	of	of	ADP
ejpam-4065	28	8	equation	equation	NOUN
ejpam-4065	28	9	(	(	PUNCT
ejpam-4065	28	10	2	2	NUM
ejpam-4065	28	11	)	)	PUNCT
ejpam-4065	28	12	then	then	ADV
ejpam-4065	28	13	multiply	multiply	VERB
ejpam-4065	28	14	both	both	DET
ejpam-4065	28	15	sides	side	NOUN
ejpam-4065	28	16	by	by	ADP
ejpam-4065	28	17	a	a	DET
ejpam-4065	28	18	function	function	NOUN
ejpam-4065	28	19	,	,	PUNCT
ejpam-4065	28	20	then	then	ADV
ejpam-4065	28	21	take	take	VERB
ejpam-4065	28	22	a	a	DET
ejpam-4065	28	23	definite	definite	ADJ
ejpam-4065	28	24	integral	integral	NOUN
ejpam-4065	28	25	of	of	ADP
ejpam-4065	28	26	both	both	DET
ejpam-4065	28	27	sides	side	NOUN
ejpam-4065	28	28	.	.	PUNCT
ejpam-4065	29	1	this	this	PRON
ejpam-4065	29	2	yields	yield	VERB
ejpam-4065	29	3	a	a	DET
ejpam-4065	29	4	definite	definite	ADJ
ejpam-4065	29	5	integral	integral	ADJ
ejpam-4065	29	6	in	in	ADP
ejpam-4065	29	7	terms	term	NOUN
ejpam-4065	29	8	of	of	ADP
ejpam-4065	29	9	a	a	DET
ejpam-4065	29	10	contour	contour	NOUN
ejpam-4065	29	11	integral	integral	NOUN
ejpam-4065	29	12	.	.	PUNCT
ejpam-4065	30	1	a	a	DET
ejpam-4065	30	2	second	second	ADJ
ejpam-4065	30	3	contour	contour	NOUN
ejpam-4065	30	4	integral	integral	NOUN
ejpam-4065	30	5	is	be	AUX
ejpam-4065	30	6	derived	derive	VERB
ejpam-4065	30	7	by	by	ADP
ejpam-4065	30	8	multiplying	multiply	VERB
ejpam-4065	30	9	equation	equation	NOUN
ejpam-4065	30	10	(	(	PUNCT
ejpam-4065	30	11	2	2	NUM
ejpam-4065	30	12	)	)	PUNCT
ejpam-4065	30	13	by	by	ADP
ejpam-4065	30	14	a	a	DET
ejpam-4065	30	15	function	function	NOUN
ejpam-4065	30	16	and	and	CCONJ
ejpam-4065	30	17	performing	perform	VERB
ejpam-4065	30	18	some	some	DET
ejpam-4065	30	19	substitutions	substitution	NOUN
ejpam-4065	30	20	so	so	SCONJ
ejpam-4065	30	21	that	that	SCONJ
ejpam-4065	30	22	the	the	DET
ejpam-4065	30	23	contour	contour	NOUN
ejpam-4065	30	24	integrals	integral	NOUN
ejpam-4065	30	25	are	be	AUX
ejpam-4065	30	26	the	the	DET
ejpam-4065	30	27	same	same	ADJ
ejpam-4065	30	28	.	.	PUNCT
ejpam-4065	31	1	3	3	X
ejpam-4065	31	2	.	.	X
ejpam-4065	31	3	definite	definite	ADJ
ejpam-4065	31	4	integral	integral	ADJ
ejpam-4065	31	5	of	of	ADP
ejpam-4065	31	6	contour	contour	NOUN
ejpam-4065	31	7	integral	integral	ADJ
ejpam-4065	31	8	we	we	PRON
ejpam-4065	31	9	use	use	VERB
ejpam-4065	31	10	the	the	DET
ejpam-4065	31	11	method	method	NOUN
ejpam-4065	31	12	in	in	ADP
ejpam-4065	31	13	[	[	X
ejpam-4065	31	14	10	10	NUM
ejpam-4065	31	15	]	]	PUNCT
ejpam-4065	31	16	.	.	PUNCT
ejpam-4065	32	1	the	the	DET
ejpam-4065	32	2	variable	variable	NOUN
ejpam-4065	32	3	of	of	ADP
ejpam-4065	32	4	integration	integration	NOUN
ejpam-4065	32	5	in	in	ADP
ejpam-4065	32	6	the	the	DET
ejpam-4065	32	7	contour	contour	NOUN
ejpam-4065	32	8	integral	integral	NOUN
ejpam-4065	32	9	is	be	AUX
ejpam-4065	32	10	z	z	NOUN
ejpam-4065	32	11	=	=	PUNCT
ejpam-4065	32	12	w+m	w+m	NUM
ejpam-4065	32	13	.	.	PUNCT
ejpam-4065	33	1	the	the	DET
ejpam-4065	33	2	cut	cut	NOUN
ejpam-4065	33	3	and	and	CCONJ
ejpam-4065	33	4	contour	contour	NOUN
ejpam-4065	33	5	are	be	AUX
ejpam-4065	33	6	in	in	ADP
ejpam-4065	33	7	the	the	DET
ejpam-4065	33	8	first	first	ADJ
ejpam-4065	33	9	quadrant	quadrant	NOUN
ejpam-4065	33	10	of	of	ADP
ejpam-4065	33	11	the	the	DET
ejpam-4065	33	12	complex	complex	ADJ
ejpam-4065	33	13	z	z	NOUN
ejpam-4065	33	14	-	-	NOUN
ejpam-4065	33	15	plane	plane	NOUN
ejpam-4065	33	16	.	.	PUNCT
ejpam-4065	34	1	the	the	DET
ejpam-4065	34	2	cut	cut	NOUN
ejpam-4065	34	3	approaches	approach	VERB
ejpam-4065	34	4	the	the	DET
ejpam-4065	34	5	origin	origin	NOUN
ejpam-4065	34	6	from	from	ADP
ejpam-4065	34	7	the	the	DET
ejpam-4065	34	8	interior	interior	NOUN
ejpam-4065	34	9	of	of	ADP
ejpam-4065	34	10	the	the	DET
ejpam-4065	34	11	first	first	ADJ
ejpam-4065	34	12	quadrant	quadrant	NOUN
ejpam-4065	34	13	and	and	CCONJ
ejpam-4065	34	14	the	the	DET
ejpam-4065	34	15	contour	contour	NOUN
ejpam-4065	34	16	goes	go	VERB
ejpam-4065	34	17	round	round	ADP
ejpam-4065	34	18	the	the	DET
ejpam-4065	34	19	origin	origin	NOUN
ejpam-4065	34	20	with	with	ADP
ejpam-4065	34	21	zero	zero	NUM
ejpam-4065	34	22	radius	radius	NOUN
ejpam-4065	34	23	and	and	CCONJ
ejpam-4065	34	24	is	be	AUX
ejpam-4065	34	25	on	on	ADP
ejpam-4065	34	26	opposite	opposite	ADJ
ejpam-4065	34	27	sides	side	NOUN
ejpam-4065	34	28	of	of	ADP
ejpam-4065	34	29	the	the	DET
ejpam-4065	34	30	cut	cut	NOUN
ejpam-4065	34	31	.	.	PUNCT
ejpam-4065	35	1	using	use	VERB
ejpam-4065	35	2	equation	equation	NOUN
ejpam-4065	35	3	(	(	PUNCT
ejpam-4065	35	4	2	2	X
ejpam-4065	35	5	)	)	PUNCT
ejpam-4065	35	6	we	we	PRON
ejpam-4065	35	7	replace	replace	VERB
ejpam-4065	35	8	y	y	PROPN
ejpam-4065	35	9	by	by	ADP
ejpam-4065	35	10	a√	a√	PROPN
ejpam-4065	35	11	b+x−	b+x−	PROPN
ejpam-4065	35	12	√	√	PROPN
ejpam-4065	35	13	b	b	PROPN
ejpam-4065	35	14	then	then	ADV
ejpam-4065	35	15	multiply	multiply	ADV
ejpam-4065	35	16	by	by	ADP
ejpam-4065	35	17	(	(	PUNCT
ejpam-4065	35	18	√	√	PROPN
ejpam-4065	35	19	b+x−	b+x−	PROPN
ejpam-4065	35	20	√	√	PROPN
ejpam-4065	35	21	b	b	NOUN
ejpam-4065	35	22	)	)	PUNCT
ejpam-4065	35	23	−m	−m	NOUN
ejpam-4065	35	24	x	x	PUNCT
ejpam-4065	35	25	√	√	NOUN
ejpam-4065	35	26	b+x	b+x	NUM
ejpam-4065	35	27	.	.	PUNCT
ejpam-4065	36	1	next	next	ADV
ejpam-4065	36	2	we	we	PRON
ejpam-4065	36	3	take	take	VERB
ejpam-4065	36	4	the	the	DET
ejpam-4065	36	5	infinite	infinite	ADJ
ejpam-4065	36	6	integral	integral	ADJ
ejpam-4065	36	7	over	over	ADP
ejpam-4065	36	8	x	x	PUNCT
ejpam-4065	36	9	∈	∈	PROPN
ejpam-4065	37	1	[	[	X
ejpam-4065	37	2	0,∞	0,∞	NOUN
ejpam-4065	37	3	)	)	PUNCT
ejpam-4065	37	4	to	to	PART
ejpam-4065	37	5	get	get	VERB
ejpam-4065	37	6	(	(	PUNCT
ejpam-4065	37	7	3	3	NUM
ejpam-4065	37	8	)	)	PUNCT
ejpam-4065	37	9	1	1	NUM
ejpam-4065	37	10	γ(k	γ(k	NOUN
ejpam-4065	37	11	+	+	CCONJ
ejpam-4065	37	12	1	1	X
ejpam-4065	37	13	)	)	PUNCT
ejpam-4065	37	14	∫	∫	PROPN
ejpam-4065	38	1	∞	∞	PROPN
ejpam-4065	38	2	0	0	NUM
ejpam-4065	38	3	(	(	PUNCT
ejpam-4065	38	4	√	√	NUM
ejpam-4065	38	5	b+	b+	NOUN
ejpam-4065	38	6	x−	x−	PROPN
ejpam-4065	38	7	√	√	PROPN
ejpam-4065	38	8	b	b	NOUN
ejpam-4065	38	9	)	)	PUNCT
ejpam-4065	38	10	−m	−m	NOUN
ejpam-4065	38	11	logk	logk	NOUN
ejpam-4065	38	12	(	(	PUNCT
ejpam-4065	38	13	a√	a√	PROPN
ejpam-4065	38	14	b+x−	b+x−	PROPN
ejpam-4065	38	15	√	√	PROPN
ejpam-4065	38	16	b	b	X
ejpam-4065	38	17	)	)	PUNCT
ejpam-4065	38	18	x	x	SYM
ejpam-4065	38	19	√	√	NUM
ejpam-4065	38	20	b+	b+	NOUN
ejpam-4065	38	21	x	x	X
ejpam-4065	38	22	dx	dx	PROPN
ejpam-4065	38	23	=	=	SYM
ejpam-4065	38	24	1	1	NUM
ejpam-4065	38	25	2πi	2πi	NOUN
ejpam-4065	38	26	∫	∫	PROPN
ejpam-4065	39	1	∞	∞	NUM
ejpam-4065	39	2	0	0	NUM
ejpam-4065	40	1	∫	∫	PROPN
ejpam-4065	40	2	c	c	PROPN
ejpam-4065	40	3	aww−k−1	aww−k−1	NOUN
ejpam-4065	40	4	(	(	PUNCT
ejpam-4065	40	5	√	√	NUM
ejpam-4065	40	6	b+	b+	NOUN
ejpam-4065	40	7	x−	x−	PROPN
ejpam-4065	40	8	√	√	PROPN
ejpam-4065	40	9	b	b	X
ejpam-4065	40	10	)	)	PUNCT
ejpam-4065	40	11	−m−w	−m−w	PROPN
ejpam-4065	40	12	x	x	PUNCT
ejpam-4065	40	13	√	√	NUM
ejpam-4065	40	14	b+	b+	NOUN
ejpam-4065	40	15	x	x	X
ejpam-4065	40	16	dwdx	dwdx	NOUN
ejpam-4065	40	17	=	=	SYM
ejpam-4065	40	18	1	1	NUM
ejpam-4065	40	19	2πi	2πi	NOUN
ejpam-4065	40	20	∫	∫	PROPN
ejpam-4065	41	1	c	c	PROPN
ejpam-4065	41	2	∫	∫	PROPN
ejpam-4065	41	3	∞	∞	NUM
ejpam-4065	41	4	0	0	NUM
ejpam-4065	41	5	aww−k−1	aww−k−1	NOUN
ejpam-4065	41	6	(	(	PUNCT
ejpam-4065	41	7	√	√	NUM
ejpam-4065	41	8	b+	b+	NOUN
ejpam-4065	41	9	x−	x−	PROPN
ejpam-4065	41	10	√	√	PROPN
ejpam-4065	41	11	b	b	X
ejpam-4065	41	12	)	)	PUNCT
ejpam-4065	41	13	−m−w	−m−w	PROPN
ejpam-4065	41	14	x	x	PUNCT
ejpam-4065	41	15	√	√	NUM
ejpam-4065	41	16	b+	b+	NOUN
ejpam-4065	41	17	x	x	X
ejpam-4065	41	18	dxdw	dxdw	NOUN
ejpam-4065	41	19	=	=	SYM
ejpam-4065	41	20	1	1	NUM
ejpam-4065	41	21	2πi	2πi	NOUN
ejpam-4065	41	22	∫	∫	PROPN
ejpam-4065	41	23	c	c	PROPN
ejpam-4065	42	1	πaww−k−1	πaww−k−1	PROPN
ejpam-4065	42	2	(	(	PUNCT
ejpam-4065	42	3	−2−m−w	−2−m−w	PROPN
ejpam-4065	42	4	)	)	PUNCT
ejpam-4065	42	5	b	b	NOUN
ejpam-4065	42	6	1	1	NUM
ejpam-4065	42	7	2	2	NUM
ejpam-4065	42	8	(	(	PUNCT
ejpam-4065	42	9	−m−w)−	−m−w)−	PROPN
ejpam-4065	42	10	1	1	NUM
ejpam-4065	42	11	2	2	NUM
ejpam-4065	42	12	csc(π(m+	csc(π(m+	NOUN
ejpam-4065	42	13	w))dw	w))dw	PROPN
ejpam-4065	42	14	r.	r.	PROPN
ejpam-4065	42	15	reynolds	reynolds	PROPN
ejpam-4065	42	16	,	,	PUNCT
ejpam-4065	42	17	a.	a.	PROPN
ejpam-4065	42	18	stauffer	stauffer	PROPN
ejpam-4065	42	19	/	/	SYM
ejpam-4065	42	20	eur	eur	PROPN
ejpam-4065	42	21	.	.	PUNCT
ejpam-4065	43	1	j.	j.	PROPN
ejpam-4065	43	2	pure	pure	PROPN
ejpam-4065	43	3	appl	appl	PROPN
ejpam-4065	43	4	.	.	PROPN
ejpam-4065	43	5	math	math	PROPN
ejpam-4065	43	6	,	,	PUNCT
ejpam-4065	43	7	14	14	NUM
ejpam-4065	43	8	(	(	PUNCT
ejpam-4065	43	9	4	4	NUM
ejpam-4065	43	10	)	)	PUNCT
ejpam-4065	43	11	(	(	PUNCT
ejpam-4065	43	12	2021	2021	NUM
ejpam-4065	43	13	)	)	PUNCT
ejpam-4065	43	14	,	,	PUNCT
ejpam-4065	43	15	1379	1379	NUM
ejpam-4065	43	16	-	-	SYM
ejpam-4065	43	17	1387	1387	NUM
ejpam-4065	43	18	1381	1381	NUM
ejpam-4065	43	19	from	from	ADP
ejpam-4065	43	20	equation	equation	NOUN
ejpam-4065	43	21	(	(	PUNCT
ejpam-4065	43	22	2.1.8.1	2.1.8.1	NUM
ejpam-4065	43	23	)	)	PUNCT
ejpam-4065	43	24	in	in	ADP
ejpam-4065	43	25	[	[	X
ejpam-4065	43	26	3	3	X
ejpam-4065	43	27	]	]	PUNCT
ejpam-4065	43	28	where	where	SCONJ
ejpam-4065	43	29	0	0	PUNCT
ejpam-4065	43	30	<	<	X
ejpam-4065	43	31	re(w+m	re(w+m	PROPN
ejpam-4065	43	32	2	2	NUM
ejpam-4065	43	33	)	)	PUNCT
ejpam-4065	43	34	<	<	X
ejpam-4065	43	35	1	1	NUM
ejpam-4065	43	36	,	,	PUNCT
ejpam-4065	43	37	|arg(b)|	|arg(b)|	VERB
ejpam-4065	43	38	<	<	X
ejpam-4065	43	39	π	π	X
ejpam-4065	43	40	.	.	PUNCT
ejpam-4065	44	1	we	we	PRON
ejpam-4065	44	2	are	be	AUX
ejpam-4065	44	3	able	able	ADJ
ejpam-4065	44	4	to	to	PART
ejpam-4065	44	5	switch	switch	VERB
ejpam-4065	44	6	the	the	DET
ejpam-4065	44	7	order	order	NOUN
ejpam-4065	44	8	of	of	ADP
ejpam-4065	44	9	integration	integration	NOUN
ejpam-4065	44	10	over	over	ADP
ejpam-4065	44	11	w+m	w+m	PROPN
ejpam-4065	44	12	and	and	CCONJ
ejpam-4065	44	13	x	x	SYM
ejpam-4065	44	14	using	use	VERB
ejpam-4065	44	15	fubini	fubini	NOUN
ejpam-4065	44	16	’s	’s	PART
ejpam-4065	44	17	theorem	theorem	NOUN
ejpam-4065	44	18	since	since	SCONJ
ejpam-4065	44	19	the	the	DET
ejpam-4065	44	20	integrand	integrand	NOUN
ejpam-4065	44	21	is	be	AUX
ejpam-4065	44	22	of	of	ADP
ejpam-4065	44	23	bounded	bounded	ADJ
ejpam-4065	44	24	measure	measure	NOUN
ejpam-4065	44	25	over	over	ADP
ejpam-4065	44	26	the	the	DET
ejpam-4065	44	27	space	space	NOUN
ejpam-4065	44	28	c×	c×	PROPN
ejpam-4065	45	1	[	[	X
ejpam-4065	45	2	0,∞	0,∞	NOUN
ejpam-4065	45	3	)	)	PUNCT
ejpam-4065	45	4	.	.	PUNCT
ejpam-4065	46	1	4	4	X
ejpam-4065	46	2	.	.	X
ejpam-4065	46	3	the	the	DET
ejpam-4065	46	4	lerch	lerch	PROPN
ejpam-4065	46	5	function	function	NOUN
ejpam-4065	46	6	we	we	PRON
ejpam-4065	46	7	use	use	VERB
ejpam-4065	46	8	equation	equation	NOUN
ejpam-4065	46	9	(	(	PUNCT
ejpam-4065	46	10	1.11.3	1.11.3	NUM
ejpam-4065	46	11	)	)	PUNCT
ejpam-4065	46	12	in	in	ADP
ejpam-4065	46	13	[	[	X
ejpam-4065	46	14	2	2	NUM
ejpam-4065	46	15	]	]	PUNCT
ejpam-4065	46	16	where	where	SCONJ
ejpam-4065	46	17	φ(z	φ(z	PROPN
ejpam-4065	46	18	,	,	PUNCT
ejpam-4065	46	19	s	s	NOUN
ejpam-4065	46	20	,	,	PUNCT
ejpam-4065	46	21	v	v	NOUN
ejpam-4065	46	22	)	)	PUNCT
ejpam-4065	46	23	is	be	AUX
ejpam-4065	46	24	the	the	DET
ejpam-4065	46	25	lerch	lerch	PROPN
ejpam-4065	46	26	function	function	NOUN
ejpam-4065	46	27	which	which	PRON
ejpam-4065	46	28	is	be	AUX
ejpam-4065	46	29	a	a	DET
ejpam-4065	46	30	generalization	generalization	NOUN
ejpam-4065	46	31	of	of	ADP
ejpam-4065	46	32	the	the	DET
ejpam-4065	46	33	hurwitz	hurwitz	PROPN
ejpam-4065	46	34	zeta	zeta	PROPN
ejpam-4065	46	35	ζ(s	ζ(s	PROPN
ejpam-4065	46	36	,	,	PUNCT
ejpam-4065	46	37	v	v	NOUN
ejpam-4065	46	38	)	)	PUNCT
ejpam-4065	46	39	and	and	CCONJ
ejpam-4065	46	40	polylogarithm	polylogarithm	PROPN
ejpam-4065	46	41	functions	function	NOUN
ejpam-4065	46	42	lin(z	lin(z	PROPN
ejpam-4065	46	43	)	)	PUNCT
ejpam-4065	46	44	.	.	PUNCT
ejpam-4065	47	1	the	the	DET
ejpam-4065	47	2	lerch	lerch	PROPN
ejpam-4065	47	3	function	function	PROPN
ejpam-4065	47	4	has	have	VERB
ejpam-4065	47	5	a	a	DET
ejpam-4065	47	6	series	series	NOUN
ejpam-4065	47	7	representation	representation	NOUN
ejpam-4065	47	8	given	give	VERB
ejpam-4065	47	9	by	by	ADP
ejpam-4065	47	10	φ(z	φ(z	PROPN
ejpam-4065	47	11	,	,	PUNCT
ejpam-4065	47	12	s	s	NOUN
ejpam-4065	47	13	,	,	PUNCT
ejpam-4065	47	14	v	v	NOUN
ejpam-4065	47	15	)	)	PUNCT
ejpam-4065	47	16	=	=	PUNCT
ejpam-4065	48	1	∞∑	∞∑	NUM
ejpam-4065	48	2	n=0	n=0	NUM
ejpam-4065	48	3	(	(	PUNCT
ejpam-4065	48	4	v	v	NOUN
ejpam-4065	48	5	+	+	PRON
ejpam-4065	48	6	n)−szn	n)−szn	NUM
ejpam-4065	48	7	(	(	PUNCT
ejpam-4065	48	8	4	4	NUM
ejpam-4065	48	9	)	)	PUNCT
ejpam-4065	48	10	where	where	SCONJ
ejpam-4065	48	11	|z|	|z|	VERB
ejpam-4065	48	12	<	<	X
ejpam-4065	48	13	1	1	NUM
ejpam-4065	48	14	,	,	PUNCT
ejpam-4065	48	15	v	v	ADP
ejpam-4065	48	16	̸=	̸=	PROPN
ejpam-4065	48	17	0,−1	0,−1	PROPN
ejpam-4065	48	18	,	,	PUNCT
ejpam-4065	48	19	..	..	PUNCT
ejpam-4065	48	20	and	and	CCONJ
ejpam-4065	48	21	is	be	AUX
ejpam-4065	48	22	continued	continue	VERB
ejpam-4065	48	23	analytically	analytically	ADV
ejpam-4065	48	24	by	by	ADP
ejpam-4065	48	25	its	its	PRON
ejpam-4065	48	26	integral	integral	ADJ
ejpam-4065	48	27	representation	representation	NOUN
ejpam-4065	48	28	given	give	VERB
ejpam-4065	48	29	by	by	ADP
ejpam-4065	48	30	φ(z	φ(z	PROPN
ejpam-4065	48	31	,	,	PUNCT
ejpam-4065	48	32	s	s	NOUN
ejpam-4065	48	33	,	,	PUNCT
ejpam-4065	48	34	v	v	NOUN
ejpam-4065	48	35	)	)	PUNCT
ejpam-4065	48	36	=	=	SYM
ejpam-4065	48	37	1	1	NUM
ejpam-4065	48	38	γ(s	γ(	NOUN
ejpam-4065	48	39	)	)	PUNCT
ejpam-4065	48	40	∫	∫	PROPN
ejpam-4065	49	1	∞	∞	PROPN
ejpam-4065	49	2	0	0	NUM
ejpam-4065	50	1	ts−1e−vt	ts−1e−vt	PRON
ejpam-4065	51	1	1−	1−	NUM
ejpam-4065	51	2	ze−t	ze−t	NOUN
ejpam-4065	51	3	dt	dt	NOUN
ejpam-4065	52	1	=	=	SYM
ejpam-4065	52	2	1	1	NUM
ejpam-4065	52	3	γ(s	γ(s	PROPN
ejpam-4065	52	4	)	)	PUNCT
ejpam-4065	52	5	∫	∫	PROPN
ejpam-4065	53	1	∞	∞	NUM
ejpam-4065	53	2	0	0	NUM
ejpam-4065	54	1	ts−1e−(v−1)t	ts−1e−(v−1)t	PROPN
ejpam-4065	54	2	et	et	NOUN
ejpam-4065	54	3	−	−	NOUN
ejpam-4065	54	4	z	z	NOUN
ejpam-4065	54	5	dt	dt	X
ejpam-4065	54	6	(	(	PUNCT
ejpam-4065	54	7	5	5	NUM
ejpam-4065	54	8	)	)	PUNCT
ejpam-4065	54	9	where	where	SCONJ
ejpam-4065	54	10	re(v	re(v	NOUN
ejpam-4065	54	11	)	)	PUNCT
ejpam-4065	54	12	>	>	X
ejpam-4065	54	13	0	0	NUM
ejpam-4065	54	14	,	,	PUNCT
ejpam-4065	54	15	and	and	CCONJ
ejpam-4065	54	16	either	either	ADV
ejpam-4065	54	17	|z|≤	|z|≤	SYM
ejpam-4065	54	18	1	1	NUM
ejpam-4065	54	19	,	,	PUNCT
ejpam-4065	54	20	z	z	NOUN
ejpam-4065	54	21	̸=	̸=	PROPN
ejpam-4065	54	22	1	1	NUM
ejpam-4065	54	23	,	,	PUNCT
ejpam-4065	54	24	re(s	re(s	ADJ
ejpam-4065	54	25	)	)	PUNCT
ejpam-4065	54	26	>	>	X
ejpam-4065	54	27	0	0	NUM
ejpam-4065	54	28	,	,	PUNCT
ejpam-4065	54	29	or	or	CCONJ
ejpam-4065	54	30	z	z	NOUN
ejpam-4065	54	31	=	=	SYM
ejpam-4065	54	32	1	1	NUM
ejpam-4065	54	33	,	,	PUNCT
ejpam-4065	54	34	re(s	re(s	ADJ
ejpam-4065	54	35	)	)	PUNCT
ejpam-4065	54	36	>	>	X
ejpam-4065	55	1	1	1	NUM
ejpam-4065	55	2	.	.	X
ejpam-4065	55	3	5	5	NUM
ejpam-4065	55	4	.	.	X
ejpam-4065	55	5	infinite	infinite	ADJ
ejpam-4065	55	6	sum	sum	NOUN
ejpam-4065	55	7	of	of	ADP
ejpam-4065	55	8	contour	contour	NOUN
ejpam-4065	55	9	integral	integral	ADJ
ejpam-4065	55	10	in	in	ADP
ejpam-4065	55	11	this	this	DET
ejpam-4065	55	12	section	section	NOUN
ejpam-4065	55	13	we	we	PRON
ejpam-4065	55	14	will	will	AUX
ejpam-4065	55	15	again	again	ADV
ejpam-4065	55	16	use	use	VERB
ejpam-4065	55	17	cauchy	cauchy	NOUN
ejpam-4065	55	18	’s	’s	PART
ejpam-4065	55	19	integral	integral	ADJ
ejpam-4065	55	20	formula	formula	NOUN
ejpam-4065	55	21	(	(	PUNCT
ejpam-4065	55	22	2	2	NUM
ejpam-4065	55	23	)	)	PUNCT
ejpam-4065	55	24	and	and	CCONJ
ejpam-4065	55	25	take	take	VERB
ejpam-4065	55	26	the	the	DET
ejpam-4065	55	27	infinite	infinite	ADJ
ejpam-4065	55	28	sum	sum	NOUN
ejpam-4065	55	29	to	to	PART
ejpam-4065	55	30	derive	derive	VERB
ejpam-4065	55	31	equivalent	equivalent	ADJ
ejpam-4065	55	32	sum	sum	NOUN
ejpam-4065	55	33	representations	representation	NOUN
ejpam-4065	55	34	for	for	ADP
ejpam-4065	55	35	the	the	DET
ejpam-4065	55	36	contour	contour	NOUN
ejpam-4065	55	37	integrals	integral	NOUN
ejpam-4065	55	38	.	.	PUNCT
ejpam-4065	56	1	we	we	PRON
ejpam-4065	56	2	proceed	proceed	VERB
ejpam-4065	56	3	using	use	VERB
ejpam-4065	56	4	equation	equation	NOUN
ejpam-4065	56	5	(	(	PUNCT
ejpam-4065	56	6	2	2	NUM
ejpam-4065	56	7	)	)	PUNCT
ejpam-4065	56	8	and	and	CCONJ
ejpam-4065	56	9	replace	replace	VERB
ejpam-4065	56	10	y	y	PROPN
ejpam-4065	56	11	by	by	ADP
ejpam-4065	56	12	log(a)−	log(a)−	PROPN
ejpam-4065	56	13	log(b	log(b	PROPN
ejpam-4065	56	14	)	)	PUNCT
ejpam-4065	56	15	2	2	NUM
ejpam-4065	57	1	+	+	ADV
ejpam-4065	57	2	iπ(2y+1)−	iπ(2y+1)−	PROPN
ejpam-4065	57	3	log(2	log(2	NOUN
ejpam-4065	57	4	)	)	PUNCT
ejpam-4065	58	1	and	and	CCONJ
ejpam-4065	58	2	multiply	multiply	VERB
ejpam-4065	58	3	both	both	DET
ejpam-4065	58	4	sides	side	NOUN
ejpam-4065	58	5	by	by	ADP
ejpam-4065	58	6	iπ21−mb	iπ21−mb	PROPN
ejpam-4065	58	7	1	1	NUM
ejpam-4065	58	8	2	2	NUM
ejpam-4065	58	9	(	(	PUNCT
ejpam-4065	58	10	−m−1)eiπm(2y+1	−m−1)eiπm(2y+1	ADJ
ejpam-4065	58	11	)	)	PUNCT
ejpam-4065	58	12	and	and	CCONJ
ejpam-4065	58	13	take	take	VERB
ejpam-4065	58	14	the	the	DET
ejpam-4065	58	15	infinite	infinite	ADJ
ejpam-4065	58	16	sum	sum	NOUN
ejpam-4065	58	17	over	over	ADP
ejpam-4065	58	18	y	y	PROPN
ejpam-4065	58	19	∈	∈	PROPN
ejpam-4065	59	1	[	[	X
ejpam-4065	59	2	0,∞	0,∞	NOUN
ejpam-4065	59	3	)	)	PUNCT
ejpam-4065	59	4	simplifying	simplify	VERB
ejpam-4065	59	5	in	in	ADP
ejpam-4065	59	6	terms	term	NOUN
ejpam-4065	59	7	of	of	ADP
ejpam-4065	59	8	the	the	DET
ejpam-4065	59	9	lerch	lerch	PROPN
ejpam-4065	59	10	function	function	NOUN
ejpam-4065	59	11	to	to	PART
ejpam-4065	59	12	get	get	VERB
ejpam-4065	59	13	(	(	PUNCT
ejpam-4065	59	14	6	6	NUM
ejpam-4065	59	15	)	)	PUNCT
ejpam-4065	59	16	(	(	PUNCT
ejpam-4065	59	17	iπ)k+1eiπmb−	iπ)k+1eiπmb−	NOUN
ejpam-4065	59	18	m	m	VERB
ejpam-4065	59	19	2	2	NUM
ejpam-4065	59	20	−	−	NOUN
ejpam-4065	59	21	1	1	NUM
ejpam-4065	59	22	2	2	NUM
ejpam-4065	59	23	2k−m+1φ	2k−m+1φ	NUM
ejpam-4065	59	24	(	(	PUNCT
ejpam-4065	59	25	e2imπ,−k	e2imπ,−k	NOUN
ejpam-4065	59	26	,	,	PUNCT
ejpam-4065	59	27	i(−2	i(−2	PROPN
ejpam-4065	59	28	log(a)+log(b)+log(4)−2iπ	log(a)+log(b)+log(4)−2iπ	PROPN
ejpam-4065	59	29	)	)	PUNCT
ejpam-4065	59	30	4π	4π	NUM
ejpam-4065	59	31	)	)	PUNCT
ejpam-4065	60	1	γ(k	γ(k	NOUN
ejpam-4065	60	2	+	+	CCONJ
ejpam-4065	60	3	1	1	X
ejpam-4065	60	4	)	)	PUNCT
ejpam-4065	60	5	=	=	SYM
ejpam-4065	60	6	1	1	NUM
ejpam-4065	60	7	2πi	2πi	NOUN
ejpam-4065	60	8	∞∑	∞∑	NUM
ejpam-4065	60	9	y=0	y=0	NUM
ejpam-4065	60	10	∫	∫	PROPN
ejpam-4065	60	11	c	c	PROPN
ejpam-4065	60	12	iπaww−k−12−m−w+1b	iπaww−k−12−m−w+1b	PROPN
ejpam-4065	60	13	1	1	NUM
ejpam-4065	60	14	2	2	NUM
ejpam-4065	60	15	(	(	PUNCT
ejpam-4065	60	16	−m−w−1)eiπ(2y+1)(m+w)dw	−m−w−1)eiπ(2y+1)(m+w)dw	NOUN
ejpam-4065	60	17	=	=	SYM
ejpam-4065	60	18	1	1	NUM
ejpam-4065	60	19	2πi	2πi	NOUN
ejpam-4065	60	20	∫	∫	PROPN
ejpam-4065	60	21	c	c	NOUN
ejpam-4065	61	1	∞∑	∞∑	NUM
ejpam-4065	61	2	y=0	y=0	NOUN
ejpam-4065	61	3	iπaww−k−12−m−w+1b	iπaww−k−12−m−w+1b	ADV
ejpam-4065	61	4	1	1	NUM
ejpam-4065	61	5	2	2	NUM
ejpam-4065	61	6	(	(	PUNCT
ejpam-4065	61	7	−m−w−1)eiπ(2y+1)(m+w)dw	−m−w−1)eiπ(2y+1)(m+w)dw	NOUN
ejpam-4065	61	8	=	=	SYM
ejpam-4065	61	9	1	1	NUM
ejpam-4065	61	10	2πi	2πi	NOUN
ejpam-4065	61	11	∫	∫	PROPN
ejpam-4065	61	12	c	c	PROPN
ejpam-4065	62	1	πaww−k−1	πaww−k−1	PROPN
ejpam-4065	62	2	(	(	PUNCT
ejpam-4065	62	3	−2−m−w	−2−m−w	PROPN
ejpam-4065	62	4	)	)	PUNCT
ejpam-4065	62	5	b	b	NOUN
ejpam-4065	62	6	1	1	NUM
ejpam-4065	62	7	2	2	NUM
ejpam-4065	62	8	(	(	PUNCT
ejpam-4065	62	9	−m−w−1	−m−w−1	NOUN
ejpam-4065	62	10	)	)	PUNCT
ejpam-4065	62	11	csc(π(m+	csc(π(m+	X
ejpam-4065	62	12	w))dw	w))dw	NOUN
ejpam-4065	62	13	from	from	ADP
ejpam-4065	62	14	equation	equation	NOUN
ejpam-4065	62	15	(	(	PUNCT
ejpam-4065	62	16	1.232.3	1.232.3	NUM
ejpam-4065	62	17	)	)	PUNCT
ejpam-4065	62	18	in	in	ADP
ejpam-4065	62	19	[	[	X
ejpam-4065	62	20	5	5	NUM
ejpam-4065	62	21	]	]	PUNCT
ejpam-4065	62	22	where	where	SCONJ
ejpam-4065	62	23	csch(ix	csch(ix	NOUN
ejpam-4065	62	24	)	)	PUNCT
ejpam-4065	62	25	=	=	SYM
ejpam-4065	62	26	−i	−i	ADJ
ejpam-4065	62	27	csc(x	csc(x	NOUN
ejpam-4065	62	28	)	)	PUNCT
ejpam-4065	62	29	from	from	ADP
ejpam-4065	62	30	equation	equation	NOUN
ejpam-4065	62	31	(	(	PUNCT
ejpam-4065	62	32	4.5.10	4.5.10	NUM
ejpam-4065	62	33	)	)	PUNCT
ejpam-4065	62	34	in	in	ADP
ejpam-4065	62	35	[	[	X
ejpam-4065	62	36	1	1	NUM
ejpam-4065	62	37	]	]	PUNCT
ejpam-4065	62	38	and	and	CCONJ
ejpam-4065	62	39	im(w	im(w	ADJ
ejpam-4065	62	40	+	+	NOUN
ejpam-4065	62	41	m	m	NOUN
ejpam-4065	62	42	)	)	PUNCT
ejpam-4065	62	43	>	>	X
ejpam-4065	62	44	0	0	PUNCT
ejpam-4065	63	1	for	for	SCONJ
ejpam-4065	63	2	the	the	DET
ejpam-4065	63	3	sum	sum	NOUN
ejpam-4065	63	4	to	to	PART
ejpam-4065	63	5	converge	converge	VERB
ejpam-4065	63	6	.	.	PUNCT
ejpam-4065	64	1	r.	r.	PROPN
ejpam-4065	64	2	reynolds	reynolds	PROPN
ejpam-4065	64	3	,	,	PUNCT
ejpam-4065	64	4	a.	a.	PROPN
ejpam-4065	64	5	stauffer	stauffer	PROPN
ejpam-4065	64	6	/	/	SYM
ejpam-4065	64	7	eur	eur	PROPN
ejpam-4065	64	8	.	.	PUNCT
ejpam-4065	65	1	j.	j.	PROPN
ejpam-4065	65	2	pure	pure	PROPN
ejpam-4065	65	3	appl	appl	PROPN
ejpam-4065	65	4	.	.	PROPN
ejpam-4065	65	5	math	math	PROPN
ejpam-4065	65	6	,	,	PUNCT
ejpam-4065	65	7	14	14	NUM
ejpam-4065	65	8	(	(	PUNCT
ejpam-4065	65	9	4	4	NUM
ejpam-4065	65	10	)	)	PUNCT
ejpam-4065	65	11	(	(	PUNCT
ejpam-4065	65	12	2021	2021	NUM
ejpam-4065	65	13	)	)	PUNCT
ejpam-4065	65	14	,	,	PUNCT
ejpam-4065	65	15	1379	1379	NUM
ejpam-4065	65	16	-	-	SYM
ejpam-4065	65	17	1387	1387	NUM
ejpam-4065	65	18	1382	1382	NUM
ejpam-4065	65	19	6	6	NUM
ejpam-4065	65	20	.	.	PUNCT
ejpam-4065	66	1	definite	definite	ADJ
ejpam-4065	66	2	integral	integral	ADJ
ejpam-4065	66	3	in	in	ADP
ejpam-4065	66	4	terms	term	NOUN
ejpam-4065	66	5	of	of	ADP
ejpam-4065	66	6	the	the	DET
ejpam-4065	66	7	lerch	lerch	PROPN
ejpam-4065	66	8	function	function	PROPN
ejpam-4065	66	9	theorem	theorem	VERB
ejpam-4065	66	10	1	1	NUM
ejpam-4065	66	11	.	.	X
ejpam-4065	67	1	for	for	ADP
ejpam-4065	67	2	k	k	PROPN
ejpam-4065	67	3	,	,	PUNCT
ejpam-4065	67	4	a	a	PRON
ejpam-4065	67	5	,	,	PUNCT
ejpam-4065	67	6	b	b	X
ejpam-4065	67	7	∈	∈	PROPN
ejpam-4065	67	8	c,−1	c,−1	NOUN
ejpam-4065	67	9	<	<	X
ejpam-4065	67	10	re(m	re(m	PROPN
ejpam-4065	67	11	)	)	PUNCT
ejpam-4065	67	12	<	<	X
ejpam-4065	68	1	−1/2	−1/2	ADJ
ejpam-4065	68	2	,	,	PUNCT
ejpam-4065	68	3	∫	∫	PROPN
ejpam-4065	68	4	∞	∞	PROPN
ejpam-4065	68	5	0	0	NUM
ejpam-4065	68	6	(	(	PUNCT
ejpam-4065	68	7	√	√	NUM
ejpam-4065	68	8	b+	b+	NOUN
ejpam-4065	68	9	x−	x−	PROPN
ejpam-4065	68	10	√	√	PROPN
ejpam-4065	68	11	b	b	NOUN
ejpam-4065	68	12	)	)	PUNCT
ejpam-4065	68	13	−m	−m	NOUN
ejpam-4065	68	14	logk	logk	NOUN
ejpam-4065	68	15	(	(	PUNCT
ejpam-4065	68	16	a√	a√	PROPN
ejpam-4065	68	17	b+x−	b+x−	PROPN
ejpam-4065	68	18	√	√	PROPN
ejpam-4065	68	19	b	b	X
ejpam-4065	68	20	)	)	PUNCT
ejpam-4065	68	21	x	x	SYM
ejpam-4065	68	22	√	√	NUM
ejpam-4065	68	23	b+	b+	NOUN
ejpam-4065	68	24	x	x	X
ejpam-4065	68	25	dx	dx	PROPN
ejpam-4065	68	26	=	=	SYM
ejpam-4065	68	27	(	(	PUNCT
ejpam-4065	68	28	iπ)k+1eiπmb−	iπ)k+1eiπmb−	PROPN
ejpam-4065	68	29	m	m	VERB
ejpam-4065	68	30	2	2	NUM
ejpam-4065	68	31	−	−	NOUN
ejpam-4065	68	32	1	1	NUM
ejpam-4065	68	33	2	2	NUM
ejpam-4065	68	34	2k−m+1φ	2k−m+1φ	NUM
ejpam-4065	68	35	(	(	PUNCT
ejpam-4065	68	36	e2imπ	e2imπ	PROPN
ejpam-4065	68	37	,	,	PUNCT
ejpam-4065	68	38	−k	−k	PROPN
ejpam-4065	68	39	,	,	PUNCT
ejpam-4065	68	40	i(−2	i(−2	PROPN
ejpam-4065	68	41	log(a	log(a	PROPN
ejpam-4065	68	42	)	)	PUNCT
ejpam-4065	68	43	+	+	SYM
ejpam-4065	68	44	log(b	log(b	PROPN
ejpam-4065	68	45	)	)	PUNCT
ejpam-4065	68	46	+	+	NUM
ejpam-4065	68	47	log(4)−	log(4)−	NOUN
ejpam-4065	68	48	2iπ	2iπ	NOUN
ejpam-4065	68	49	)	)	PUNCT
ejpam-4065	68	50	4π	4π	NUM
ejpam-4065	68	51	)	)	PUNCT
ejpam-4065	68	52	(	(	PUNCT
ejpam-4065	68	53	7	7	X
ejpam-4065	68	54	)	)	PUNCT
ejpam-4065	68	55	proof	proof	NOUN
ejpam-4065	68	56	.	.	PUNCT
ejpam-4065	69	1	since	since	SCONJ
ejpam-4065	69	2	the	the	DET
ejpam-4065	69	3	right	right	ADJ
ejpam-4065	69	4	-	-	PUNCT
ejpam-4065	69	5	hand	hand	NOUN
ejpam-4065	69	6	side	side	NOUN
ejpam-4065	69	7	of	of	ADP
ejpam-4065	69	8	equation	equation	NOUN
ejpam-4065	69	9	(	(	PUNCT
ejpam-4065	69	10	3	3	NUM
ejpam-4065	69	11	)	)	PUNCT
ejpam-4065	69	12	and	and	CCONJ
ejpam-4065	69	13	(	(	PUNCT
ejpam-4065	69	14	6	6	NUM
ejpam-4065	69	15	)	)	PUNCT
ejpam-4065	69	16	are	be	AUX
ejpam-4065	69	17	equal	equal	ADJ
ejpam-4065	69	18	we	we	PRON
ejpam-4065	69	19	can	can	AUX
ejpam-4065	69	20	equate	equate	VERB
ejpam-4065	69	21	the	the	DET
ejpam-4065	69	22	left	left	ADJ
ejpam-4065	69	23	-	-	PUNCT
ejpam-4065	69	24	hand	hand	NOUN
ejpam-4065	69	25	sides	side	NOUN
ejpam-4065	69	26	and	and	CCONJ
ejpam-4065	69	27	simplify	simplify	VERB
ejpam-4065	69	28	the	the	DET
ejpam-4065	69	29	factorials	factorial	NOUN
ejpam-4065	69	30	to	to	PART
ejpam-4065	69	31	get	get	VERB
ejpam-4065	69	32	the	the	DET
ejpam-4065	69	33	stated	state	VERB
ejpam-4065	69	34	result	result	NOUN
ejpam-4065	69	35	.	.	PUNCT
ejpam-4065	70	1	main	main	ADJ
ejpam-4065	70	2	results	result	NOUN
ejpam-4065	70	3	proposition	proposition	NOUN
ejpam-4065	70	4	1	1	NUM
ejpam-4065	70	5	.	.	PUNCT
ejpam-4065	71	1	for	for	ADP
ejpam-4065	71	2	−1	−1	NOUN
ejpam-4065	71	3	<	<	X
ejpam-4065	71	4	re(m	re(m	PROPN
ejpam-4065	71	5	)	)	PUNCT
ejpam-4065	71	6	<	<	X
ejpam-4065	71	7	−1/2	−1/2	ADJ
ejpam-4065	71	8	,	,	PUNCT
ejpam-4065	71	9	|arg(b)|	|arg(b)|	VERB
ejpam-4065	71	10	<	<	X
ejpam-4065	71	11	π	π	PROPN
ejpam-4065	71	12	,	,	PUNCT
ejpam-4065	71	13	(	(	PUNCT
ejpam-4065	71	14	8	8	NUM
ejpam-4065	71	15	)	)	PUNCT
ejpam-4065	71	16	∫	∫	PROPN
ejpam-4065	72	1	∞	∞	PROPN
ejpam-4065	72	2	0	0	NUM
ejpam-4065	72	3	(	(	PUNCT
ejpam-4065	72	4	√	√	NUM
ejpam-4065	72	5	b+	b+	NOUN
ejpam-4065	72	6	x−	x−	PROPN
ejpam-4065	72	7	√	√	PROPN
ejpam-4065	72	8	b	b	X
ejpam-4065	72	9	)	)	PUNCT
ejpam-4065	72	10	−m	−m	NOUN
ejpam-4065	72	11	x	x	PUNCT
ejpam-4065	72	12	√	√	NUM
ejpam-4065	72	13	b+	b+	NOUN
ejpam-4065	73	1	x	x	X
ejpam-4065	73	2	dx	dx	PROPN
ejpam-4065	73	3	=	=	PROPN
ejpam-4065	73	4	π	π	PROPN
ejpam-4065	73	5	(	(	PUNCT
ejpam-4065	73	6	−2−m	−2−m	NOUN
ejpam-4065	73	7	)	)	PUNCT
ejpam-4065	73	8	b−	b−	PROPN
ejpam-4065	73	9	m	m	VERB
ejpam-4065	73	10	2	2	NUM
ejpam-4065	73	11	−	−	NUM
ejpam-4065	73	12	1	1	NUM
ejpam-4065	73	13	2	2	NUM
ejpam-4065	73	14	csc(πm	csc(πm	NOUN
ejpam-4065	73	15	)	)	PUNCT
ejpam-4065	73	16	proof	proof	NOUN
ejpam-4065	73	17	.	.	PUNCT
ejpam-4065	74	1	use	use	VERB
ejpam-4065	74	2	equation	equation	NOUN
ejpam-4065	74	3	(	(	PUNCT
ejpam-4065	74	4	7	7	NUM
ejpam-4065	74	5	)	)	PUNCT
ejpam-4065	74	6	and	and	CCONJ
ejpam-4065	74	7	set	set	VERB
ejpam-4065	74	8	k	k	PROPN
ejpam-4065	74	9	=	=	PUNCT
ejpam-4065	74	10	0	0	PUNCT
ejpam-4065	74	11	and	and	CCONJ
ejpam-4065	74	12	simplify	simplify	VERB
ejpam-4065	74	13	using	use	VERB
ejpam-4065	74	14	entry	entry	NOUN
ejpam-4065	74	15	(	(	PUNCT
ejpam-4065	74	16	2	2	NUM
ejpam-4065	74	17	)	)	PUNCT
ejpam-4065	74	18	table	table	NOUN
ejpam-4065	74	19	below	below	ADP
ejpam-4065	74	20	(	(	PUNCT
ejpam-4065	74	21	64:12:7	64:12:7	NUM
ejpam-4065	74	22	)	)	PUNCT
ejpam-4065	74	23	in	in	ADP
ejpam-4065	74	24	[	[	X
ejpam-4065	74	25	8	8	NUM
ejpam-4065	74	26	]	]	PUNCT
ejpam-4065	74	27	.	.	PUNCT
ejpam-4065	75	1	proposition	proposition	NOUN
ejpam-4065	75	2	2	2	NUM
ejpam-4065	75	3	.	.	X
ejpam-4065	75	4	for	for	ADP
ejpam-4065	75	5	k	k	PROPN
ejpam-4065	75	6	∈	∈	PROPN
ejpam-4065	75	7	c,−1	c,−1	NOUN
ejpam-4065	75	8	<	<	X
ejpam-4065	75	9	re(m	re(m	PROPN
ejpam-4065	75	10	)	)	PUNCT
ejpam-4065	75	11	<	<	X
ejpam-4065	76	1	−1/2	−1/2	ADJ
ejpam-4065	76	2	,	,	PUNCT
ejpam-4065	76	3	(	(	PUNCT
ejpam-4065	76	4	9	9	NUM
ejpam-4065	76	5	)	)	PUNCT
ejpam-4065	76	6	∫	∫	PROPN
ejpam-4065	77	1	∞	∞	PROPN
ejpam-4065	77	2	0	0	PUNCT
ejpam-4065	77	3	(	(	PUNCT
ejpam-4065	77	4	√	√	NUM
ejpam-4065	77	5	x+	x+	NUM
ejpam-4065	77	6	1−	1−	NUM
ejpam-4065	77	7	1	1	NUM
ejpam-4065	77	8	)	)	PUNCT
ejpam-4065	77	9	−m	−m	NOUN
ejpam-4065	77	10	logk	logk	NOUN
ejpam-4065	77	11	(	(	PUNCT
ejpam-4065	77	12	2√	2√	PROPN
ejpam-4065	77	13	x+1−1	x+1−1	PROPN
ejpam-4065	77	14	)	)	PUNCT
ejpam-4065	77	15	x	x	SYM
ejpam-4065	77	16	√	√	ADV
ejpam-4065	77	17	x+	x+	NUM
ejpam-4065	77	18	1	1	NUM
ejpam-4065	77	19	dx	dx	NOUN
ejpam-4065	77	20	=	=	SYM
ejpam-4065	77	21	(	(	PUNCT
ejpam-4065	77	22	iπ)k+1eiπm2k−m+1φ	iπ)k+1eiπm2k−m+1φ	PROPN
ejpam-4065	77	23	(	(	PUNCT
ejpam-4065	77	24	e2imπ,−k	e2imπ,−k	NOUN
ejpam-4065	77	25	,	,	PUNCT
ejpam-4065	77	26	1	1	NUM
ejpam-4065	77	27	2	2	NUM
ejpam-4065	77	28	)	)	PUNCT
ejpam-4065	77	29	proof	proof	NOUN
ejpam-4065	77	30	.	.	PUNCT
ejpam-4065	78	1	use	use	VERB
ejpam-4065	78	2	equation	equation	NOUN
ejpam-4065	78	3	(	(	PUNCT
ejpam-4065	78	4	7	7	NUM
ejpam-4065	78	5	)	)	PUNCT
ejpam-4065	78	6	and	and	CCONJ
ejpam-4065	78	7	set	set	VERB
ejpam-4065	78	8	a	a	DET
ejpam-4065	78	9	=	=	SYM
ejpam-4065	78	10	2	2	NUM
ejpam-4065	78	11	,	,	PUNCT
ejpam-4065	78	12	b	b	NOUN
ejpam-4065	78	13	=	=	SYM
ejpam-4065	78	14	1	1	NUM
ejpam-4065	78	15	and	and	CCONJ
ejpam-4065	78	16	simplify	simplify	NOUN
ejpam-4065	78	17	.	.	PUNCT
ejpam-4065	79	1	proposition	proposition	NOUN
ejpam-4065	79	2	3	3	NUM
ejpam-4065	79	3	.	.	PUNCT
ejpam-4065	80	1	for	for	ADP
ejpam-4065	80	2	b	b	PROPN
ejpam-4065	80	3	∈	∈	PROPN
ejpam-4065	80	4	c,−1	c,−1	NOUN
ejpam-4065	80	5	<	<	X
ejpam-4065	80	6	re(m	re(m	PROPN
ejpam-4065	80	7	)	)	PUNCT
ejpam-4065	80	8	<	<	X
ejpam-4065	81	1	−1/2	−1/2	ADJ
ejpam-4065	81	2	,	,	PUNCT
ejpam-4065	81	3	∫	∫	PROPN
ejpam-4065	81	4	∞	∞	PROPN
ejpam-4065	81	5	0	0	NUM
ejpam-4065	82	1	(	(	PUNCT
ejpam-4065	82	2	√	√	NUM
ejpam-4065	82	3	b+	b+	NOUN
ejpam-4065	82	4	x−	x−	PROPN
ejpam-4065	82	5	√	√	PROPN
ejpam-4065	82	6	b	b	NOUN
ejpam-4065	82	7	)	)	PUNCT
ejpam-4065	82	8	−m	−m	NOUN
ejpam-4065	82	9	log	log	NOUN
ejpam-4065	82	10	(	(	PUNCT
ejpam-4065	82	11	√	√	NUM
ejpam-4065	82	12	b+x+	b+x+	NOUN
ejpam-4065	82	13	√	√	NUM
ejpam-4065	82	14	b	b	NOUN
ejpam-4065	82	15	x	x	X
ejpam-4065	82	16	)	)	PUNCT
ejpam-4065	82	17	x	x	SYM
ejpam-4065	82	18	√	√	NUM
ejpam-4065	82	19	b+	b+	NOUN
ejpam-4065	82	20	x	x	PART
ejpam-4065	82	21	dx=	dx=	PROPN
ejpam-4065	82	22	π2−m−1b−	π2−m−1b−	PROPN
ejpam-4065	82	23	m	m	VERB
ejpam-4065	82	24	2	2	NUM
ejpam-4065	82	25	−	−	NUM
ejpam-4065	82	26	1	1	NUM
ejpam-4065	82	27	2	2	NUM
ejpam-4065	82	28	csc(πm)(log(4b)+2π	csc(πm)(log(4b)+2π	NOUN
ejpam-4065	82	29	cot(πm	cot(πm	NOUN
ejpam-4065	82	30	)	)	PUNCT
ejpam-4065	82	31	)	)	PUNCT
ejpam-4065	82	32	(	(	PUNCT
ejpam-4065	82	33	10	10	NUM
ejpam-4065	82	34	)	)	PUNCT
ejpam-4065	82	35	r.	r.	PROPN
ejpam-4065	82	36	reynolds	reynolds	PROPN
ejpam-4065	82	37	,	,	PUNCT
ejpam-4065	82	38	a.	a.	PROPN
ejpam-4065	82	39	stauffer	stauffer	PROPN
ejpam-4065	82	40	/	/	SYM
ejpam-4065	82	41	eur	eur	PROPN
ejpam-4065	82	42	.	.	PUNCT
ejpam-4065	83	1	j.	j.	PROPN
ejpam-4065	83	2	pure	pure	PROPN
ejpam-4065	83	3	appl	appl	PROPN
ejpam-4065	83	4	.	.	PROPN
ejpam-4065	83	5	math	math	PROPN
ejpam-4065	83	6	,	,	PUNCT
ejpam-4065	83	7	14	14	NUM
ejpam-4065	83	8	(	(	PUNCT
ejpam-4065	83	9	4	4	NUM
ejpam-4065	83	10	)	)	PUNCT
ejpam-4065	83	11	(	(	PUNCT
ejpam-4065	83	12	2021	2021	NUM
ejpam-4065	83	13	)	)	PUNCT
ejpam-4065	83	14	,	,	PUNCT
ejpam-4065	83	15	1379	1379	NUM
ejpam-4065	83	16	-	-	SYM
ejpam-4065	83	17	1387	1387	NUM
ejpam-4065	83	18	1383	1383	NUM
ejpam-4065	83	19	proof	proof	NOUN
ejpam-4065	83	20	.	.	PUNCT
ejpam-4065	84	1	use	use	VERB
ejpam-4065	84	2	equation	equation	NOUN
ejpam-4065	84	3	(	(	PUNCT
ejpam-4065	84	4	7	7	NUM
ejpam-4065	84	5	)	)	PUNCT
ejpam-4065	84	6	and	and	CCONJ
ejpam-4065	84	7	set	set	VERB
ejpam-4065	84	8	k	k	PROPN
ejpam-4065	84	9	=	=	PUNCT
ejpam-4065	84	10	a	a	DET
ejpam-4065	84	11	=	=	SYM
ejpam-4065	84	12	1	1	NUM
ejpam-4065	84	13	and	and	CCONJ
ejpam-4065	84	14	simplify	simplify	VERB
ejpam-4065	84	15	using	use	VERB
ejpam-4065	84	16	entry	entry	NOUN
ejpam-4065	84	17	(	(	PUNCT
ejpam-4065	84	18	3	3	NUM
ejpam-4065	84	19	)	)	PUNCT
ejpam-4065	84	20	table	table	NOUN
ejpam-4065	84	21	below	below	ADP
ejpam-4065	84	22	(	(	PUNCT
ejpam-4065	84	23	64:12:7	64:12:7	NUM
ejpam-4065	84	24	)	)	PUNCT
ejpam-4065	84	25	in	in	ADP
ejpam-4065	84	26	[	[	X
ejpam-4065	84	27	8	8	NUM
ejpam-4065	84	28	]	]	PUNCT
ejpam-4065	84	29	.	.	PUNCT
ejpam-4065	85	1	proposition	proposition	NOUN
ejpam-4065	85	2	4	4	NUM
ejpam-4065	85	3	.	.	PUNCT
ejpam-4065	86	1	(	(	PUNCT
ejpam-4065	86	2	11	11	NUM
ejpam-4065	86	3	)	)	PUNCT
ejpam-4065	86	4	∫	∫	PROPN
ejpam-4065	87	1	∞	∞	NUM
ejpam-4065	87	2	0	0	NUM
ejpam-4065	87	3	3	3	NUM
ejpam-4065	87	4	√	√	NUM
ejpam-4065	87	5	2	2	NUM
ejpam-4065	87	6	(	(	PUNCT
ejpam-4065	87	7	√	√	ADP
ejpam-4065	87	8	4x+	4x+	NUM
ejpam-4065	87	9	1−	1−	NUM
ejpam-4065	87	10	1	1	NUM
ejpam-4065	87	11	)	)	PUNCT
ejpam-4065	87	12	2/3	2/3	NUM
ejpam-4065	87	13	−	−	PROPN
ejpam-4065	87	14	4	4	NUM
ejpam-4065	87	15	√	√	NOUN
ejpam-4065	87	16	2	2	NUM
ejpam-4065	87	17	(	(	PUNCT
ejpam-4065	87	18	√	√	ADP
ejpam-4065	87	19	4x+	4x+	NUM
ejpam-4065	87	20	1−	1−	NUM
ejpam-4065	87	21	1	1	NUM
ejpam-4065	87	22	)	)	PUNCT
ejpam-4065	87	23	3/4	3/4	NUM
ejpam-4065	87	24	x	x	SYM
ejpam-4065	87	25	√	√	NUM
ejpam-4065	87	26	4x+	4x+	NUM
ejpam-4065	87	27	1	1	NUM
ejpam-4065	87	28	log	log	NOUN
ejpam-4065	87	29	(	(	PUNCT
ejpam-4065	87	30	√	√	ADV
ejpam-4065	87	31	x+	x+	SYM
ejpam-4065	88	1	1	1	NUM
ejpam-4065	88	2	4	4	NUM
ejpam-4065	88	3	+	+	SYM
ejpam-4065	88	4	1	1	NUM
ejpam-4065	88	5	2	2	NUM
ejpam-4065	88	6	x	x	SYM
ejpam-4065	88	7	)	)	PUNCT
ejpam-4065	88	8	dx	dx	PROPN
ejpam-4065	88	9	=	=	SYM
ejpam-4065	89	1	1	1	NUM
ejpam-4065	89	2	12	12	NUM
ejpam-4065	89	3	log	log	NOUN
ejpam-4065	89	4	(	(	PUNCT
ejpam-4065	89	5	1	1	NUM
ejpam-4065	89	6	27	27	NUM
ejpam-4065	89	7	(	(	PUNCT
ejpam-4065	89	8	99	99	NUM
ejpam-4065	89	9	+	+	CCONJ
ejpam-4065	89	10	70	70	NUM
ejpam-4065	89	11	√	√	NUM
ejpam-4065	89	12	2	2	NUM
ejpam-4065	89	13	)	)	PUNCT
ejpam-4065	89	14	)	)	PUNCT
ejpam-4065	89	15	proof	proof	NOUN
ejpam-4065	89	16	.	.	PUNCT
ejpam-4065	90	1	use	use	VERB
ejpam-4065	90	2	equation	equation	NOUN
ejpam-4065	90	3	(	(	PUNCT
ejpam-4065	90	4	7	7	NUM
ejpam-4065	90	5	)	)	PUNCT
ejpam-4065	90	6	and	and	CCONJ
ejpam-4065	90	7	form	form	VERB
ejpam-4065	90	8	a	a	DET
ejpam-4065	90	9	second	second	ADJ
ejpam-4065	90	10	equation	equation	NOUN
ejpam-4065	90	11	by	by	ADP
ejpam-4065	90	12	setting	set	VERB
ejpam-4065	90	13	m	m	PRON
ejpam-4065	90	14	→	→	SYM
ejpam-4065	90	15	p	p	X
ejpam-4065	90	16	and	and	CCONJ
ejpam-4065	90	17	taking	take	VERB
ejpam-4065	90	18	their	their	PRON
ejpam-4065	90	19	difference	difference	NOUN
ejpam-4065	90	20	.	.	PUNCT
ejpam-4065	91	1	next	next	ADJ
ejpam-4065	91	2	set	set	VERB
ejpam-4065	91	3	k	k	PROPN
ejpam-4065	91	4	=	=	PUNCT
ejpam-4065	91	5	−1	−1	NOUN
ejpam-4065	91	6	,	,	PUNCT
ejpam-4065	91	7	a	a	PRON
ejpam-4065	91	8	=	=	SYM
ejpam-4065	91	9	1	1	NUM
ejpam-4065	91	10	,	,	PUNCT
ejpam-4065	91	11	b	b	X
ejpam-4065	91	12	=	=	SYM
ejpam-4065	91	13	1/4,m	1/4,m	NUM
ejpam-4065	91	14	=	=	NOUN
ejpam-4065	91	15	−3/4	−3/4	NOUN
ejpam-4065	91	16	,	,	PUNCT
ejpam-4065	91	17	p	p	NOUN
ejpam-4065	91	18	=	=	PUNCT
ejpam-4065	91	19	−2/3	−2/3	PROPN
ejpam-4065	91	20	and	and	CCONJ
ejpam-4065	91	21	simplify	simplify	VERB
ejpam-4065	91	22	using	use	VERB
ejpam-4065	91	23	entry	entry	NOUN
ejpam-4065	91	24	(	(	PUNCT
ejpam-4065	91	25	1	1	NUM
ejpam-4065	91	26	)	)	PUNCT
ejpam-4065	91	27	in	in	ADP
ejpam-4065	91	28	table	table	NOUN
ejpam-4065	91	29	below	below	ADV
ejpam-4065	91	30	(	(	PUNCT
ejpam-4065	91	31	64:12:7	64:12:7	NUM
ejpam-4065	91	32	)	)	PUNCT
ejpam-4065	91	33	in	in	ADP
ejpam-4065	91	34	[	[	X
ejpam-4065	91	35	8	8	NUM
ejpam-4065	91	36	]	]	PUNCT
ejpam-4065	91	37	.	.	PUNCT
ejpam-4065	92	1	proposition	proposition	NOUN
ejpam-4065	92	2	5	5	NUM
ejpam-4065	92	3	.	.	PUNCT
ejpam-4065	93	1	(	(	PUNCT
ejpam-4065	93	2	12	12	NUM
ejpam-4065	93	3	)	)	PUNCT
ejpam-4065	93	4	∫	∫	PROPN
ejpam-4065	94	1	∞	∞	NUM
ejpam-4065	94	2	0	0	NUM
ejpam-4065	94	3	3	3	NUM
ejpam-4065	94	4	√	√	NUM
ejpam-4065	94	5	2	2	NUM
ejpam-4065	94	6	√√	√√	ADV
ejpam-4065	94	7	4x+	4x+	NUM
ejpam-4065	94	8	1−	1−	NUM
ejpam-4065	94	9	1	1	NUM
ejpam-4065	94	10	(	(	PUNCT
ejpam-4065	94	11	6	6	NUM
ejpam-4065	94	12	√	√	NUM
ejpam-4065	94	13	2−	2−	NUM
ejpam-4065	94	14	6	6	NUM
ejpam-4065	94	15	√√	√√	ADV
ejpam-4065	94	16	4x+	4x+	NUM
ejpam-4065	94	17	1−	1−	NUM
ejpam-4065	94	18	1	1	NUM
ejpam-4065	94	19	)	)	PUNCT
ejpam-4065	94	20	x	x	SYM
ejpam-4065	95	1	√	√	NOUN
ejpam-4065	95	2	4x+	4x+	NUM
ejpam-4065	95	3	1	1	NUM
ejpam-4065	95	4	log	log	NOUN
ejpam-4065	95	5	(	(	PUNCT
ejpam-4065	95	6	√	√	NOUN
ejpam-4065	95	7	4x+1	4x+1	NOUN
ejpam-4065	95	8	+	+	PROPN
ejpam-4065	95	9	1	1	NUM
ejpam-4065	95	10	2x	2x	NOUN
ejpam-4065	95	11	)	)	PUNCT
ejpam-4065	95	12	dx	dx	PROPN
ejpam-4065	95	13	=	=	PUNCT
ejpam-4065	95	14	log(3	log(3	ADJ
ejpam-4065	95	15	)	)	PUNCT
ejpam-4065	95	16	proof	proof	NOUN
ejpam-4065	95	17	.	.	PUNCT
ejpam-4065	96	1	use	use	VERB
ejpam-4065	96	2	equation	equation	NOUN
ejpam-4065	96	3	(	(	PUNCT
ejpam-4065	96	4	7	7	NUM
ejpam-4065	96	5	)	)	PUNCT
ejpam-4065	96	6	and	and	CCONJ
ejpam-4065	96	7	form	form	VERB
ejpam-4065	96	8	a	a	DET
ejpam-4065	96	9	second	second	ADJ
ejpam-4065	96	10	equation	equation	NOUN
ejpam-4065	96	11	by	by	ADP
ejpam-4065	96	12	setting	set	VERB
ejpam-4065	96	13	m	m	PRON
ejpam-4065	96	14	→	→	SYM
ejpam-4065	96	15	p	p	X
ejpam-4065	96	16	and	and	CCONJ
ejpam-4065	96	17	taking	take	VERB
ejpam-4065	96	18	their	their	PRON
ejpam-4065	96	19	difference	difference	NOUN
ejpam-4065	96	20	.	.	PUNCT
ejpam-4065	97	1	next	next	ADJ
ejpam-4065	97	2	set	set	VERB
ejpam-4065	97	3	k	k	PROPN
ejpam-4065	97	4	=	=	PUNCT
ejpam-4065	97	5	−1	−1	NOUN
ejpam-4065	97	6	,	,	PUNCT
ejpam-4065	97	7	a	a	PRON
ejpam-4065	97	8	=	=	SYM
ejpam-4065	97	9	1	1	NUM
ejpam-4065	97	10	,	,	PUNCT
ejpam-4065	97	11	b	b	X
ejpam-4065	97	12	=	=	SYM
ejpam-4065	97	13	1/4,m	1/4,m	NUM
ejpam-4065	97	14	=	=	SYM
ejpam-4065	97	15	−1/2	−1/2	ADJ
ejpam-4065	97	16	,	,	PUNCT
ejpam-4065	97	17	p	p	NOUN
ejpam-4065	97	18	=	=	PUNCT
ejpam-4065	97	19	−2/3	−2/3	PROPN
ejpam-4065	97	20	and	and	CCONJ
ejpam-4065	97	21	simplify	simplify	VERB
ejpam-4065	97	22	using	use	VERB
ejpam-4065	97	23	entry	entry	NOUN
ejpam-4065	97	24	(	(	PUNCT
ejpam-4065	97	25	1	1	NUM
ejpam-4065	97	26	)	)	PUNCT
ejpam-4065	97	27	in	in	ADP
ejpam-4065	97	28	table	table	NOUN
ejpam-4065	97	29	below	below	ADV
ejpam-4065	97	30	(	(	PUNCT
ejpam-4065	97	31	64:12:7	64:12:7	NUM
ejpam-4065	97	32	)	)	PUNCT
ejpam-4065	97	33	in	in	ADP
ejpam-4065	97	34	[	[	X
ejpam-4065	97	35	8	8	NUM
ejpam-4065	97	36	]	]	PUNCT
ejpam-4065	97	37	.	.	PUNCT
ejpam-4065	98	1	theorem	theorem	NOUN
ejpam-4065	98	2	2	2	NUM
ejpam-4065	98	3	.	.	X
ejpam-4065	99	1	for	for	ADP
ejpam-4065	99	2	k	k	PROPN
ejpam-4065	99	3	∈	∈	PROPN
ejpam-4065	99	4	c,−1	c,−1	NOUN
ejpam-4065	99	5	<	<	X
ejpam-4065	99	6	re(m	re(m	PROPN
ejpam-4065	99	7	)	)	PUNCT
ejpam-4065	99	8	<	<	X
ejpam-4065	99	9	0	0	NUM
ejpam-4065	99	10	,	,	PUNCT
ejpam-4065	99	11	(	(	PUNCT
ejpam-4065	99	12	13	13	NUM
ejpam-4065	99	13	)	)	PUNCT
ejpam-4065	99	14	∫	∫	PROPN
ejpam-4065	100	1	∞	∞	PROPN
ejpam-4065	100	2	0	0	PUNCT
ejpam-4065	100	3	(	(	PUNCT
ejpam-4065	100	4	√	√	ADV
ejpam-4065	100	5	x+	x+	SYM
ejpam-4065	100	6	1	1	NUM
ejpam-4065	100	7	4	4	NUM
ejpam-4065	100	8	−	−	NUM
ejpam-4065	100	9	1	1	NUM
ejpam-4065	100	10	2	2	NUM
ejpam-4065	100	11	)	)	PUNCT
ejpam-4065	100	12	−m	−m	NOUN
ejpam-4065	100	13	logk	logk	NOUN
ejpam-4065	100	14	(	(	PUNCT
ejpam-4065	100	15	−	−	PROPN
ejpam-4065	100	16	2√	2√	NUM
ejpam-4065	100	17	4x+1−1	4x+1−1	NUM
ejpam-4065	100	18	)	)	PUNCT
ejpam-4065	100	19	x	x	SYM
ejpam-4065	100	20	√	√	ADV
ejpam-4065	100	21	x+	x+	SYM
ejpam-4065	100	22	1	1	NUM
ejpam-4065	100	23	4	4	NUM
ejpam-4065	100	24	dx	dx	NOUN
ejpam-4065	100	25	=	=	SYM
ejpam-4065	100	26	2k+2(iπ)k+1e−iπmli−k	2k+2(iπ)k+1e−iπmli−k	X
ejpam-4065	100	27	(	(	PUNCT
ejpam-4065	100	28	e2imπ	e2imπ	PROPN
ejpam-4065	100	29	)	)	PUNCT
ejpam-4065	100	30	proof	proof	NOUN
ejpam-4065	100	31	.	.	PUNCT
ejpam-4065	101	1	use	use	VERB
ejpam-4065	101	2	equation	equation	NOUN
ejpam-4065	101	3	(	(	PUNCT
ejpam-4065	101	4	7	7	NUM
ejpam-4065	101	5	)	)	PUNCT
ejpam-4065	101	6	and	and	CCONJ
ejpam-4065	101	7	set	set	VERB
ejpam-4065	101	8	a	a	DET
ejpam-4065	101	9	=	=	SYM
ejpam-4065	101	10	−1	−1	NOUN
ejpam-4065	101	11	,	,	PUNCT
ejpam-4065	101	12	b	b	NOUN
ejpam-4065	101	13	=	=	SYM
ejpam-4065	101	14	1/4	1/4	NUM
ejpam-4065	101	15	and	and	CCONJ
ejpam-4065	101	16	simplify	simplify	VERB
ejpam-4065	101	17	using	use	VERB
ejpam-4065	101	18	equation	equation	NOUN
ejpam-4065	101	19	(	(	PUNCT
ejpam-4065	101	20	64:12:2	64:12:2	NUM
ejpam-4065	101	21	)	)	PUNCT
ejpam-4065	101	22	in	in	ADP
ejpam-4065	101	23	[	[	X
ejpam-4065	101	24	8	8	NUM
ejpam-4065	101	25	]	]	PUNCT
ejpam-4065	101	26	.	.	PUNCT
ejpam-4065	102	1	theorem	theorem	NOUN
ejpam-4065	102	2	3	3	NUM
ejpam-4065	102	3	.	.	X
ejpam-4065	102	4	for	for	ADP
ejpam-4065	102	5	k	k	PROPN
ejpam-4065	102	6	∈	∈	PROPN
ejpam-4065	102	7	c	c	PROPN
ejpam-4065	102	8	,	,	PUNCT
ejpam-4065	102	9	(	(	PUNCT
ejpam-4065	102	10	14	14	NUM
ejpam-4065	102	11	)	)	PUNCT
ejpam-4065	102	12	∫	∫	PROPN
ejpam-4065	103	1	∞	∞	PROPN
ejpam-4065	103	2	0	0	NUM
ejpam-4065	104	1	√√	√√	ADV
ejpam-4065	104	2	x+	x+	PUNCT
ejpam-4065	104	3	1	1	NUM
ejpam-4065	104	4	4	4	NUM
ejpam-4065	104	5	−	−	NOUN
ejpam-4065	104	6	1	1	NUM
ejpam-4065	104	7	2	2	NUM
ejpam-4065	104	8	log	log	NOUN
ejpam-4065	104	9	k	k	PROPN
ejpam-4065	105	1	(	(	PUNCT
ejpam-4065	105	2	−	−	PROPN
ejpam-4065	105	3	2√	2√	PROPN
ejpam-4065	105	4	4x+1−1	4x+1−1	NUM
ejpam-4065	105	5	)	)	PUNCT
ejpam-4065	105	6	x	x	SYM
ejpam-4065	106	1	√	√	ADV
ejpam-4065	106	2	x+	x+	SYM
ejpam-4065	106	3	1	1	NUM
ejpam-4065	106	4	4	4	NUM
ejpam-4065	106	5	,	,	PUNCT
ejpam-4065	106	6	−ik2k+2	−ik2k+2	NUM
ejpam-4065	106	7	(	(	PUNCT
ejpam-4065	106	8	2k+1	2k+1	NOUN
ejpam-4065	106	9	−	−	NOUN
ejpam-4065	106	10	1	1	NUM
ejpam-4065	106	11	)	)	PUNCT
ejpam-4065	106	12	πk+1ζ(−k	πk+1ζ(−k	PROPN
ejpam-4065	106	13	)	)	PUNCT
ejpam-4065	106	14	r.	r.	PROPN
ejpam-4065	106	15	reynolds	reynolds	PROPN
ejpam-4065	106	16	,	,	PUNCT
ejpam-4065	106	17	a.	a.	PROPN
ejpam-4065	106	18	stauffer	stauffer	PROPN
ejpam-4065	106	19	/	/	SYM
ejpam-4065	106	20	eur	eur	PROPN
ejpam-4065	106	21	.	.	PUNCT
ejpam-4065	107	1	j.	j.	PROPN
ejpam-4065	107	2	pure	pure	PROPN
ejpam-4065	107	3	appl	appl	PROPN
ejpam-4065	107	4	.	.	PROPN
ejpam-4065	107	5	math	math	PROPN
ejpam-4065	107	6	,	,	PUNCT
ejpam-4065	107	7	14	14	NUM
ejpam-4065	107	8	(	(	PUNCT
ejpam-4065	107	9	4	4	NUM
ejpam-4065	107	10	)	)	PUNCT
ejpam-4065	107	11	(	(	PUNCT
ejpam-4065	107	12	2021	2021	NUM
ejpam-4065	107	13	)	)	PUNCT
ejpam-4065	107	14	,	,	PUNCT
ejpam-4065	107	15	1379	1379	NUM
ejpam-4065	107	16	-	-	SYM
ejpam-4065	107	17	1387	1387	NUM
ejpam-4065	107	18	1384	1384	NUM
ejpam-4065	107	19	proof	proof	NOUN
ejpam-4065	107	20	.	.	PUNCT
ejpam-4065	108	1	use	use	VERB
ejpam-4065	108	2	equation	equation	NOUN
ejpam-4065	108	3	(	(	PUNCT
ejpam-4065	108	4	7	7	NUM
ejpam-4065	108	5	)	)	PUNCT
ejpam-4065	108	6	and	and	CCONJ
ejpam-4065	108	7	set	set	VERB
ejpam-4065	108	8	a	a	DET
ejpam-4065	108	9	=	=	SYM
ejpam-4065	108	10	−1	−1	NOUN
ejpam-4065	108	11	,	,	PUNCT
ejpam-4065	108	12	b	b	X
ejpam-4065	109	1	=	=	SYM
ejpam-4065	109	2	1/4,m	1/4,m	NUM
ejpam-4065	109	3	=	=	SYM
ejpam-4065	109	4	−1/2	−1/2	VERB
ejpam-4065	109	5	and	and	CCONJ
ejpam-4065	109	6	simplify	simplify	VERB
ejpam-4065	109	7	using	use	VERB
ejpam-4065	109	8	entry	entry	NOUN
ejpam-4065	109	9	(	(	PUNCT
ejpam-4065	109	10	4	4	NUM
ejpam-4065	109	11	)	)	PUNCT
ejpam-4065	109	12	in	in	ADP
ejpam-4065	109	13	table	table	NOUN
ejpam-4065	109	14	below	below	ADV
ejpam-4065	109	15	(	(	PUNCT
ejpam-4065	109	16	64:12:7	64:12:7	NUM
ejpam-4065	109	17	)	)	PUNCT
ejpam-4065	109	18	and	and	CCONJ
ejpam-4065	109	19	equation	equation	NOUN
ejpam-4065	109	20	(	(	PUNCT
ejpam-4065	109	21	64:12:1	64:12:1	NUM
ejpam-4065	109	22	)	)	PUNCT
ejpam-4065	109	23	and	and	CCONJ
ejpam-4065	109	24	entry	entry	NOUN
ejpam-4065	109	25	(	(	PUNCT
ejpam-4065	109	26	2	2	NUM
ejpam-4065	109	27	)	)	PUNCT
ejpam-4065	109	28	in	in	ADP
ejpam-4065	109	29	table	table	NOUN
ejpam-4065	109	30	below	below	ADV
ejpam-4065	109	31	(	(	PUNCT
ejpam-4065	109	32	64:7	64:7	NUM
ejpam-4065	109	33	)	)	PUNCT
ejpam-4065	109	34	in	in	ADP
ejpam-4065	109	35	[	[	X
ejpam-4065	109	36	8	8	NUM
ejpam-4065	109	37	]	]	PUNCT
ejpam-4065	109	38	.	.	PUNCT
ejpam-4065	110	1	proposition	proposition	NOUN
ejpam-4065	110	2	6	6	NUM
ejpam-4065	110	3	.	.	PUNCT
ejpam-4065	111	1	(	(	PUNCT
ejpam-4065	111	2	15	15	NUM
ejpam-4065	111	3	)	)	PUNCT
ejpam-4065	111	4	∫	∫	PROPN
ejpam-4065	112	1	∞	∞	PROPN
ejpam-4065	112	2	0	0	PUNCT
ejpam-4065	113	1	(	(	PUNCT
ejpam-4065	113	2	√	√	ADV
ejpam-4065	113	3	x+	x+	SYM
ejpam-4065	113	4	1	1	NUM
ejpam-4065	113	5	4	4	NUM
ejpam-4065	113	6	−	−	NUM
ejpam-4065	113	7	1	1	NUM
ejpam-4065	113	8	2	2	NUM
ejpam-4065	113	9	)	)	PUNCT
ejpam-4065	113	10	3/4	3/4	NUM
ejpam-4065	113	11	x	x	SYM
ejpam-4065	113	12	√	√	NOUN
ejpam-4065	113	13	x+	x+	SYM
ejpam-4065	113	14	1	1	NUM
ejpam-4065	113	15	4	4	NUM
ejpam-4065	113	16	log	log	NOUN
ejpam-4065	113	17	2	2	NUM
ejpam-4065	113	18	(	(	PUNCT
ejpam-4065	113	19	−	−	PROPN
ejpam-4065	113	20	2√	2√	PROPN
ejpam-4065	113	21	4x+1−1	4x+1−1	NUM
ejpam-4065	113	22	)	)	PUNCT
ejpam-4065	113	23	dx	dx	PROPN
ejpam-4065	113	24	=	=	PUNCT
ejpam-4065	113	25	−(1−	−(1−	VERB
ejpam-4065	113	26	i)c√	i)c√	PROPN
ejpam-4065	113	27	2π	2π	NOUN
ejpam-4065	113	28	−	−	PROPN
ejpam-4065	113	29	(	(	PUNCT
ejpam-4065	113	30	1	1	NUM
ejpam-4065	113	31	48	48	NUM
ejpam-4065	113	32	+	+	CCONJ
ejpam-4065	113	33	i	i	PRON
ejpam-4065	113	34	48	48	NUM
ejpam-4065	113	35	)	)	PUNCT
ejpam-4065	114	1	π	π	X
ejpam-4065	114	2	√	√	ADP
ejpam-4065	114	3	2	2	NUM
ejpam-4065	114	4	proof	proof	NOUN
ejpam-4065	114	5	.	.	PUNCT
ejpam-4065	115	1	use	use	VERB
ejpam-4065	115	2	equation	equation	NOUN
ejpam-4065	115	3	(	(	PUNCT
ejpam-4065	115	4	13	13	NUM
ejpam-4065	115	5	)	)	PUNCT
ejpam-4065	115	6	and	and	CCONJ
ejpam-4065	115	7	set	set	VERB
ejpam-4065	115	8	k	k	PROPN
ejpam-4065	115	9	=	=	PUNCT
ejpam-4065	115	10	−2,m	−2,m	PROPN
ejpam-4065	115	11	=	=	SYM
ejpam-4065	115	12	−3/4	−3/4	NOUN
ejpam-4065	115	13	and	and	CCONJ
ejpam-4065	115	14	simplify	simplify	VERB
ejpam-4065	115	15	in	in	ADP
ejpam-4065	115	16	terms	term	NOUN
ejpam-4065	115	17	of	of	ADP
ejpam-4065	115	18	catalan	catalan	NOUN
ejpam-4065	115	19	’s	’s	PART
ejpam-4065	115	20	constant	constant	ADJ
ejpam-4065	115	21	(	(	PUNCT
ejpam-4065	115	22	c	c	NOUN
ejpam-4065	115	23	)	)	PUNCT
ejpam-4065	115	24	using	use	VERB
ejpam-4065	115	25	equation	equation	NOUN
ejpam-4065	115	26	(	(	PUNCT
ejpam-4065	115	27	2.3	2.3	NUM
ejpam-4065	115	28	)	)	PUNCT
ejpam-4065	115	29	in	in	ADP
ejpam-4065	115	30	[	[	X
ejpam-4065	115	31	6	6	NUM
ejpam-4065	115	32	]	]	PUNCT
ejpam-4065	115	33	and	and	CCONJ
ejpam-4065	115	34	section	section	NOUN
ejpam-4065	115	35	(	(	PUNCT
ejpam-4065	115	36	1.7.6	1.7.6	NUM
ejpam-4065	115	37	)	)	PUNCT
ejpam-4065	115	38	in	in	ADP
ejpam-4065	115	39	[	[	X
ejpam-4065	115	40	4	4	NUM
ejpam-4065	115	41	]	]	PUNCT
ejpam-4065	115	42	.	.	PUNCT
ejpam-4065	116	1	proposition	proposition	NOUN
ejpam-4065	116	2	7	7	NUM
ejpam-4065	116	3	.	.	PUNCT
ejpam-4065	117	1	(	(	PUNCT
ejpam-4065	117	2	16	16	NUM
ejpam-4065	117	3	)	)	PUNCT
ejpam-4065	117	4	∫	∫	PROPN
ejpam-4065	117	5	∞	∞	PROPN
ejpam-4065	117	6	0	0	NUM
ejpam-4065	118	1	√√	√√	ADV
ejpam-4065	118	2	x+	x+	PUNCT
ejpam-4065	118	3	1	1	NUM
ejpam-4065	118	4	4	4	NUM
ejpam-4065	118	5	−	−	NOUN
ejpam-4065	118	6	1	1	NUM
ejpam-4065	118	7	2	2	NUM
ejpam-4065	118	8	log	log	NOUN
ejpam-4065	118	9	(	(	PUNCT
ejpam-4065	118	10	log	log	NOUN
ejpam-4065	118	11	(	(	PUNCT
ejpam-4065	118	12	−	−	PROPN
ejpam-4065	118	13	2√	2√	PROPN
ejpam-4065	118	14	4x+1−1	4x+1−1	NUM
ejpam-4065	118	15	)	)	PUNCT
ejpam-4065	118	16	)	)	PUNCT
ejpam-4065	119	1	x	x	SYM
ejpam-4065	119	2	√	√	NOUN
ejpam-4065	119	3	x+	x+	SYM
ejpam-4065	119	4	1	1	NUM
ejpam-4065	119	5	4	4	NUM
ejpam-4065	119	6	log	log	NOUN
ejpam-4065	119	7	(	(	PUNCT
ejpam-4065	119	8	−	−	PROPN
ejpam-4065	119	9	2√	2√	PROPN
ejpam-4065	119	10	4x+1−1	4x+1−1	NUM
ejpam-4065	119	11	)	)	PUNCT
ejpam-4065	119	12	dx	dx	PROPN
ejpam-4065	119	13	=	=	PUNCT
ejpam-4065	119	14	log(2	log(2	PROPN
ejpam-4065	119	15	)	)	PUNCT
ejpam-4065	119	16	(	(	PUNCT
ejpam-4065	119	17	2iγ	2iγ	ADJ
ejpam-4065	120	1	+	+	CCONJ
ejpam-4065	120	2	π	π	PROPN
ejpam-4065	120	3	−	−	NOUN
ejpam-4065	121	1	i	i	PRON
ejpam-4065	121	2	log	log	VERB
ejpam-4065	121	3	(	(	PUNCT
ejpam-4065	121	4	8π2	8π2	NUM
ejpam-4065	121	5	)	)	PUNCT
ejpam-4065	121	6	)	)	PUNCT
ejpam-4065	122	1	proof	proof	NOUN
ejpam-4065	122	2	.	.	PUNCT
ejpam-4065	123	1	use	use	VERB
ejpam-4065	123	2	equation	equation	NOUN
ejpam-4065	123	3	14	14	NUM
ejpam-4065	123	4	and	and	CCONJ
ejpam-4065	123	5	take	take	VERB
ejpam-4065	123	6	the	the	DET
ejpam-4065	123	7	first	first	ADJ
ejpam-4065	123	8	partial	partial	ADJ
ejpam-4065	123	9	derivative	derivative	NOUN
ejpam-4065	123	10	with	with	ADP
ejpam-4065	123	11	respect	respect	NOUN
ejpam-4065	123	12	to	to	ADP
ejpam-4065	123	13	k	k	PROPN
ejpam-4065	123	14	then	then	ADV
ejpam-4065	123	15	apply	apply	VERB
ejpam-4065	123	16	l’hopital	l’hopital	PROPN
ejpam-4065	123	17	’s	’s	PART
ejpam-4065	123	18	rule	rule	NOUN
ejpam-4065	123	19	to	to	ADP
ejpam-4065	123	20	the	the	DET
ejpam-4065	123	21	right	right	ADJ
ejpam-4065	123	22	-	-	PUNCT
ejpam-4065	123	23	hand	hand	NOUN
ejpam-4065	123	24	side	side	NOUN
ejpam-4065	123	25	as	as	ADP
ejpam-4065	123	26	k	k	PROPN
ejpam-4065	123	27	→	→	SYM
ejpam-4065	123	28	−1	−1	NOUN
ejpam-4065	123	29	and	and	CCONJ
ejpam-4065	123	30	simplify	simplify	VERB
ejpam-4065	123	31	in	in	ADP
ejpam-4065	123	32	terms	term	NOUN
ejpam-4065	123	33	of	of	ADP
ejpam-4065	123	34	euler	euler	PROPN
ejpam-4065	123	35	’s	’s	PART
ejpam-4065	123	36	constant	constant	ADJ
ejpam-4065	123	37	(	(	PUNCT
ejpam-4065	123	38	γ	γ	NOUN
ejpam-4065	123	39	)	)	PUNCT
ejpam-4065	123	40	using	use	VERB
ejpam-4065	123	41	equation	equation	NOUN
ejpam-4065	123	42	(	(	PUNCT
ejpam-4065	123	43	3:10:1	3:10:1	NUM
ejpam-4065	123	44	)	)	PUNCT
ejpam-4065	123	45	in	in	ADP
ejpam-4065	123	46	[	[	X
ejpam-4065	123	47	8	8	NUM
ejpam-4065	123	48	]	]	PUNCT
ejpam-4065	123	49	and	and	CCONJ
ejpam-4065	123	50	(	(	PUNCT
ejpam-4065	123	51	2.15	2.15	NUM
ejpam-4065	123	52	)	)	PUNCT
ejpam-4065	123	53	in	in	ADP
ejpam-4065	123	54	[	[	X
ejpam-4065	123	55	4	4	NUM
ejpam-4065	123	56	]	]	PUNCT
ejpam-4065	123	57	.	.	PUNCT
ejpam-4065	124	1	proposition	proposition	NOUN
ejpam-4065	124	2	8	8	NUM
ejpam-4065	124	3	.	.	PUNCT
ejpam-4065	125	1	(	(	PUNCT
ejpam-4065	125	2	17	17	NUM
ejpam-4065	125	3	)	)	PUNCT
ejpam-4065	125	4	∫	∫	PROPN
ejpam-4065	126	1	∞	∞	PROPN
ejpam-4065	126	2	0	0	NUM
ejpam-4065	127	1	√√	√√	ADV
ejpam-4065	127	2	x+	x+	PUNCT
ejpam-4065	127	3	1	1	NUM
ejpam-4065	127	4	4	4	NUM
ejpam-4065	127	5	−	−	NOUN
ejpam-4065	127	6	1	1	NUM
ejpam-4065	127	7	2	2	NUM
ejpam-4065	127	8	log	log	NOUN
ejpam-4065	127	9	(	(	PUNCT
ejpam-4065	127	10	log	log	NOUN
ejpam-4065	127	11	(	(	PUNCT
ejpam-4065	127	12	−	−	PROPN
ejpam-4065	127	13	2√	2√	PROPN
ejpam-4065	127	14	4x+1−1	4x+1−1	NUM
ejpam-4065	127	15	)	)	PUNCT
ejpam-4065	127	16	)	)	PUNCT
ejpam-4065	128	1	x	x	SYM
ejpam-4065	128	2	√	√	NOUN
ejpam-4065	128	3	x+	x+	SYM
ejpam-4065	128	4	1	1	NUM
ejpam-4065	128	5	4	4	NUM
ejpam-4065	128	6	dx	dx	NOUN
ejpam-4065	128	7	=	=	SYM
ejpam-4065	128	8	π(log(16	π(log(16	X
ejpam-4065	128	9	)	)	PUNCT
ejpam-4065	129	1	+	+	CCONJ
ejpam-4065	129	2	iπ	iπ	X
ejpam-4065	129	3	)	)	PUNCT
ejpam-4065	129	4	proof	proof	NOUN
ejpam-4065	129	5	.	.	PUNCT
ejpam-4065	130	1	use	use	VERB
ejpam-4065	130	2	equation	equation	NOUN
ejpam-4065	130	3	(	(	PUNCT
ejpam-4065	130	4	14	14	NUM
ejpam-4065	130	5	)	)	PUNCT
ejpam-4065	130	6	and	and	CCONJ
ejpam-4065	130	7	take	take	VERB
ejpam-4065	130	8	the	the	DET
ejpam-4065	130	9	first	first	ADJ
ejpam-4065	130	10	partial	partial	ADJ
ejpam-4065	130	11	derivative	derivative	NOUN
ejpam-4065	130	12	with	with	ADP
ejpam-4065	130	13	respect	respect	NOUN
ejpam-4065	130	14	to	to	ADP
ejpam-4065	130	15	k	k	PROPN
ejpam-4065	130	16	and	and	CCONJ
ejpam-4065	130	17	set	set	VERB
ejpam-4065	130	18	k	k	PROPN
ejpam-4065	130	19	=	=	PUNCT
ejpam-4065	130	20	0	0	PUNCT
ejpam-4065	130	21	and	and	CCONJ
ejpam-4065	130	22	simplify	simplify	VERB
ejpam-4065	130	23	using	use	VERB
ejpam-4065	130	24	equation	equation	NOUN
ejpam-4065	130	25	(	(	PUNCT
ejpam-4065	130	26	3:10:1	3:10:1	NUM
ejpam-4065	130	27	)	)	PUNCT
ejpam-4065	130	28	in	in	ADP
ejpam-4065	130	29	[	[	X
ejpam-4065	130	30	8	8	NUM
ejpam-4065	130	31	]	]	PUNCT
ejpam-4065	130	32	and	and	CCONJ
ejpam-4065	130	33	(	(	PUNCT
ejpam-4065	130	34	2.15	2.15	NUM
ejpam-4065	130	35	)	)	PUNCT
ejpam-4065	130	36	in	in	ADP
ejpam-4065	130	37	[	[	X
ejpam-4065	130	38	4	4	NUM
ejpam-4065	130	39	]	]	PUNCT
ejpam-4065	130	40	.	.	PUNCT
ejpam-4065	131	1	proposition	proposition	NOUN
ejpam-4065	131	2	9	9	NUM
ejpam-4065	131	3	.	.	PUNCT
ejpam-4065	132	1	(	(	PUNCT
ejpam-4065	132	2	18	18	NUM
ejpam-4065	132	3	)	)	PUNCT
ejpam-4065	132	4	∫	∫	PROPN
ejpam-4065	132	5	∞	∞	PROPN
ejpam-4065	132	6	0	0	NUM
ejpam-4065	133	1	√√	√√	ADV
ejpam-4065	133	2	x+	x+	PUNCT
ejpam-4065	133	3	1	1	NUM
ejpam-4065	133	4	4	4	NUM
ejpam-4065	133	5	−	−	NOUN
ejpam-4065	133	6	1	1	NUM
ejpam-4065	133	7	2	2	NUM
ejpam-4065	133	8	log	log	NOUN
ejpam-4065	133	9	(	(	PUNCT
ejpam-4065	133	10	−	−	PROPN
ejpam-4065	133	11	2√	2√	PROPN
ejpam-4065	133	12	4x+1−1	4x+1−1	NUM
ejpam-4065	133	13	)	)	PUNCT
ejpam-4065	133	14	log	log	NOUN
ejpam-4065	133	15	(	(	PUNCT
ejpam-4065	133	16	log	log	NOUN
ejpam-4065	133	17	(	(	PUNCT
ejpam-4065	133	18	−	−	PROPN
ejpam-4065	133	19	2√	2√	PROPN
ejpam-4065	133	20	4x+1−1	4x+1−1	NUM
ejpam-4065	133	21	)	)	PUNCT
ejpam-4065	133	22	)	)	PUNCT
ejpam-4065	134	1	x	x	SYM
ejpam-4065	134	2	√	√	NOUN
ejpam-4065	134	3	x+	x+	SYM
ejpam-4065	134	4	1	1	NUM
ejpam-4065	134	5	4	4	NUM
ejpam-4065	134	6	dx	dx	NOUN
ejpam-4065	134	7	=	=	SYM
ejpam-4065	134	8	1	1	NUM
ejpam-4065	134	9	3	3	NUM
ejpam-4065	134	10	π2(−3π	π2(−3π	NOUN
ejpam-4065	134	11	+	+	CCONJ
ejpam-4065	134	12	2i(−36	2i(−36	NUM
ejpam-4065	134	13	log(a	log(a	PROPN
ejpam-4065	134	14	)	)	PUNCT
ejpam-4065	135	1	+	+	CCONJ
ejpam-4065	135	2	3	3	NUM
ejpam-4065	135	3	+	+	CCONJ
ejpam-4065	135	4	log(128	log(128	ADJ
ejpam-4065	135	5	)	)	PUNCT
ejpam-4065	135	6	+	+	CCONJ
ejpam-4065	135	7	3	3	NUM
ejpam-4065	135	8	log(π	log(π	NOUN
ejpam-4065	135	9	)	)	PUNCT
ejpam-4065	135	10	)	)	PUNCT
ejpam-4065	135	11	)	)	PUNCT
ejpam-4065	136	1	proof	proof	NOUN
ejpam-4065	136	2	.	.	PUNCT
ejpam-4065	137	1	use	use	VERB
ejpam-4065	137	2	equation	equation	NOUN
ejpam-4065	137	3	(	(	PUNCT
ejpam-4065	137	4	14	14	NUM
ejpam-4065	137	5	)	)	PUNCT
ejpam-4065	137	6	and	and	CCONJ
ejpam-4065	137	7	take	take	VERB
ejpam-4065	137	8	the	the	DET
ejpam-4065	137	9	first	first	ADJ
ejpam-4065	137	10	partial	partial	ADJ
ejpam-4065	137	11	derivative	derivative	NOUN
ejpam-4065	137	12	with	with	ADP
ejpam-4065	137	13	respect	respect	NOUN
ejpam-4065	137	14	to	to	ADP
ejpam-4065	137	15	k	k	PROPN
ejpam-4065	137	16	and	and	CCONJ
ejpam-4065	137	17	set	set	VERB
ejpam-4065	137	18	k	k	PROPN
ejpam-4065	137	19	=	=	SYM
ejpam-4065	137	20	1	1	NUM
ejpam-4065	137	21	and	and	CCONJ
ejpam-4065	137	22	simplify	simplify	VERB
ejpam-4065	137	23	in	in	ADP
ejpam-4065	137	24	terms	term	NOUN
ejpam-4065	137	25	of	of	ADP
ejpam-4065	137	26	glaisher	glaisher	PROPN
ejpam-4065	137	27	’s	’s	PART
ejpam-4065	137	28	constant	constant	ADJ
ejpam-4065	137	29	(	(	PUNCT
ejpam-4065	137	30	a	a	X
ejpam-4065	137	31	)	)	PUNCT
ejpam-4065	137	32	using	use	VERB
ejpam-4065	137	33	equation	equation	NOUN
ejpam-4065	137	34	(	(	PUNCT
ejpam-4065	137	35	3:10:1	3:10:1	NUM
ejpam-4065	137	36	)	)	PUNCT
ejpam-4065	137	37	in	in	ADP
ejpam-4065	137	38	[	[	X
ejpam-4065	137	39	8	8	NUM
ejpam-4065	137	40	]	]	PUNCT
ejpam-4065	137	41	and	and	CCONJ
ejpam-4065	137	42	(	(	PUNCT
ejpam-4065	137	43	2.15	2.15	NUM
ejpam-4065	137	44	)	)	PUNCT
ejpam-4065	137	45	in	in	ADP
ejpam-4065	137	46	[	[	X
ejpam-4065	137	47	4	4	NUM
ejpam-4065	137	48	]	]	PUNCT
ejpam-4065	137	49	.	.	PUNCT
ejpam-4065	138	1	r.	r.	PROPN
ejpam-4065	138	2	reynolds	reynolds	PROPN
ejpam-4065	138	3	,	,	PUNCT
ejpam-4065	138	4	a.	a.	PROPN
ejpam-4065	138	5	stauffer	stauffer	PROPN
ejpam-4065	138	6	/	/	SYM
ejpam-4065	138	7	eur	eur	PROPN
ejpam-4065	138	8	.	.	PUNCT
ejpam-4065	139	1	j.	j.	PROPN
ejpam-4065	139	2	pure	pure	PROPN
ejpam-4065	139	3	appl	appl	PROPN
ejpam-4065	139	4	.	.	PROPN
ejpam-4065	139	5	math	math	PROPN
ejpam-4065	139	6	,	,	PUNCT
ejpam-4065	139	7	14	14	NUM
ejpam-4065	139	8	(	(	PUNCT
ejpam-4065	139	9	4	4	NUM
ejpam-4065	139	10	)	)	PUNCT
ejpam-4065	139	11	(	(	PUNCT
ejpam-4065	139	12	2021	2021	NUM
ejpam-4065	139	13	)	)	PUNCT
ejpam-4065	139	14	,	,	PUNCT
ejpam-4065	139	15	1379	1379	NUM
ejpam-4065	139	16	-	-	SYM
ejpam-4065	139	17	1387	1387	NUM
ejpam-4065	139	18	1385	1385	NUM
ejpam-4065	139	19	7	7	NUM
ejpam-4065	139	20	.	.	PUNCT
ejpam-4065	139	21	table	table	NOUN
ejpam-4065	139	22	of	of	ADP
ejpam-4065	139	23	integrals	integral	NOUN
ejpam-4065	139	24	f(x	f(x	PROPN
ejpam-4065	139	25	)	)	PUNCT
ejpam-4065	139	26	∫∞	∫∞	NOUN
ejpam-4065	139	27	0	0	NUM
ejpam-4065	140	1	f(x)dx	f(x)dx	PART
ejpam-4065	140	2	(	(	PUNCT
ejpam-4065	140	3	√	√	PROPN
ejpam-4065	140	4	b+x−	b+x−	PROPN
ejpam-4065	140	5	√	√	PROPN
ejpam-4065	140	6	b	b	NOUN
ejpam-4065	140	7	)	)	PUNCT
ejpam-4065	140	8	−m	−m	NOUN
ejpam-4065	140	9	x	x	PUNCT
ejpam-4065	141	1	√	√	NOUN
ejpam-4065	141	2	b+x	b+x	NUM
ejpam-4065	142	1	π	π	PROPN
ejpam-4065	142	2	(	(	PUNCT
ejpam-4065	142	3	−2−m	−2−m	NOUN
ejpam-4065	142	4	)	)	PUNCT
ejpam-4065	142	5	b−	b−	PROPN
ejpam-4065	142	6	m	m	VERB
ejpam-4065	142	7	2	2	NUM
ejpam-4065	142	8	−	−	NUM
ejpam-4065	142	9	1	1	NUM
ejpam-4065	142	10	2	2	NUM
ejpam-4065	142	11	csc(πm	csc(πm	NOUN
ejpam-4065	142	12	)	)	PUNCT
ejpam-4065	142	13	(	(	PUNCT
ejpam-4065	142	14	√	√	NUM
ejpam-4065	142	15	b+x−	b+x−	PROPN
ejpam-4065	142	16	√	√	PROPN
ejpam-4065	142	17	b	b	NOUN
ejpam-4065	142	18	)	)	PUNCT
ejpam-4065	142	19	−m	−m	NOUN
ejpam-4065	142	20	log	log	NOUN
ejpam-4065	142	21	(	(	PUNCT
ejpam-4065	142	22	√	√	NUM
ejpam-4065	142	23	b+x+	b+x+	NOUN
ejpam-4065	142	24	√	√	NUM
ejpam-4065	142	25	b	b	NOUN
ejpam-4065	142	26	x	x	X
ejpam-4065	142	27	)	)	PUNCT
ejpam-4065	142	28	x	x	SYM
ejpam-4065	143	1	√	√	NOUN
ejpam-4065	143	2	b+x	b+x	NUM
ejpam-4065	143	3	π2−m−1b−	π2−m−1b−	NOUN
ejpam-4065	143	4	m	m	NOUN
ejpam-4065	143	5	2	2	NUM
ejpam-4065	143	6	−	−	NUM
ejpam-4065	143	7	1	1	NUM
ejpam-4065	143	8	2	2	NUM
ejpam-4065	143	9	csc(πm)(log(4b	csc(πm)(log(4b	NOUN
ejpam-4065	143	10	)	)	PUNCT
ejpam-4065	144	1	+	+	CCONJ
ejpam-4065	144	2	2π	2π	NOUN
ejpam-4065	144	3	cot(πm	cot(πm	NOUN
ejpam-4065	144	4	)	)	PUNCT
ejpam-4065	144	5	)	)	PUNCT
ejpam-4065	144	6	(	(	PUNCT
ejpam-4065	144	7	√	√	NUM
ejpam-4065	144	8	x+1−1	x+1−1	PROPN
ejpam-4065	144	9	)	)	PUNCT
ejpam-4065	144	10	−m	−m	ADJ
ejpam-4065	144	11	logk	logk	NOUN
ejpam-4065	144	12	(	(	PUNCT
ejpam-4065	144	13	2√	2√	PROPN
ejpam-4065	144	14	x+1−1	x+1−1	PROPN
ejpam-4065	144	15	)	)	PUNCT
ejpam-4065	144	16	x	x	SYM
ejpam-4065	145	1	√	√	PROPN
ejpam-4065	145	2	x+1	x+1	NUM
ejpam-4065	145	3	iπ)k+1eiπm2k−m+1φ	iπ)k+1eiπm2k−m+1φ	PROPN
ejpam-4065	145	4	(	(	PUNCT
ejpam-4065	145	5	e2imπ,−k	e2imπ,−k	NOUN
ejpam-4065	145	6	,	,	PUNCT
ejpam-4065	145	7	12	12	NUM
ejpam-4065	145	8	)	)	PUNCT
ejpam-4065	145	9	3	3	NUM
ejpam-4065	145	10	√	√	NUM
ejpam-4065	145	11	2	2	NUM
ejpam-4065	145	12	(	(	PUNCT
ejpam-4065	145	13	√	√	NUM
ejpam-4065	145	14	4x+1−1	4x+1−1	NUM
ejpam-4065	145	15	)	)	PUNCT
ejpam-4065	145	16	2/3−	2/3−	NUM
ejpam-4065	145	17	4	4	NUM
ejpam-4065	145	18	√	√	NUM
ejpam-4065	145	19	2	2	NUM
ejpam-4065	145	20	(	(	PUNCT
ejpam-4065	145	21	√	√	NUM
ejpam-4065	145	22	4x+1−1	4x+1−1	NUM
ejpam-4065	145	23	)	)	PUNCT
ejpam-4065	145	24	3/4	3/4	NUM
ejpam-4065	145	25	x	x	SYM
ejpam-4065	145	26	√	√	PROPN
ejpam-4065	145	27	4x+1	4x+1	NOUN
ejpam-4065	145	28	log	log	NOUN
ejpam-4065	145	29	(	(	PUNCT
ejpam-4065	145	30	√	√	PROPN
ejpam-4065	145	31	x+1	x+1	PROPN
ejpam-4065	145	32	4	4	NUM
ejpam-4065	145	33	+	+	NOUN
ejpam-4065	145	34	1	1	NUM
ejpam-4065	145	35	2	2	NUM
ejpam-4065	145	36	x	x	SYM
ejpam-4065	145	37	)	)	PUNCT
ejpam-4065	145	38	1	1	NUM
ejpam-4065	145	39	12	12	NUM
ejpam-4065	145	40	log	log	NOUN
ejpam-4065	145	41	(	(	PUNCT
ejpam-4065	145	42	1	1	NUM
ejpam-4065	145	43	27	27	NUM
ejpam-4065	145	44	(	(	PUNCT
ejpam-4065	145	45	99	99	NUM
ejpam-4065	146	1	+	+	CCONJ
ejpam-4065	146	2	70	70	NUM
ejpam-4065	146	3	√	√	NUM
ejpam-4065	146	4	2	2	NUM
ejpam-4065	146	5	)	)	PUNCT
ejpam-4065	146	6	)	)	PUNCT
ejpam-4065	146	7	3	3	NUM
ejpam-4065	146	8	√	√	NUM
ejpam-4065	146	9	2	2	NUM
ejpam-4065	146	10	√√	√√	ADV
ejpam-4065	146	11	4x+1−1	4x+1−1	NUM
ejpam-4065	146	12	(	(	PUNCT
ejpam-4065	146	13	6	6	NUM
ejpam-4065	146	14	√	√	NUM
ejpam-4065	146	15	2−	2−	NUM
ejpam-4065	146	16	6	6	NUM
ejpam-4065	146	17	√√	√√	ADV
ejpam-4065	146	18	4x+	4x+	NUM
ejpam-4065	146	19	1−	1−	NUM
ejpam-4065	146	20	1	1	NUM
ejpam-4065	146	21	)	)	PUNCT
ejpam-4065	146	22	x	x	SYM
ejpam-4065	147	1	√	√	NUM
ejpam-4065	147	2	4x+1	4x+1	NOUN
ejpam-4065	147	3	log	log	NOUN
ejpam-4065	147	4	(	(	PUNCT
ejpam-4065	147	5	√	√	NOUN
ejpam-4065	147	6	4x+1	4x+1	NOUN
ejpam-4065	147	7	+	+	PROPN
ejpam-4065	147	8	1	1	NUM
ejpam-4065	147	9	2x	2x	NUM
ejpam-4065	147	10	)	)	PUNCT
ejpam-4065	147	11	log(3	log(3	VERB
ejpam-4065	147	12	)	)	PUNCT
ejpam-4065	147	13	(	(	PUNCT
ejpam-4065	147	14	√	√	ADV
ejpam-4065	147	15	x+	x+	SYM
ejpam-4065	147	16	1	1	NUM
ejpam-4065	147	17	4	4	NUM
ejpam-4065	147	18	−	−	NUM
ejpam-4065	147	19	1	1	NUM
ejpam-4065	147	20	2	2	NUM
ejpam-4065	147	21	)	)	PUNCT
ejpam-4065	147	22	−m	−m	NOUN
ejpam-4065	147	23	logk	logk	NOUN
ejpam-4065	147	24	(	(	PUNCT
ejpam-4065	147	25	−	−	PROPN
ejpam-4065	147	26	2√	2√	NUM
ejpam-4065	147	27	4x+1−1	4x+1−1	NUM
ejpam-4065	147	28	)	)	PUNCT
ejpam-4065	147	29	x	x	SYM
ejpam-4065	147	30	√	√	ADV
ejpam-4065	147	31	x+	x+	SYM
ejpam-4065	147	32	1	1	NUM
ejpam-4065	147	33	4	4	NUM
ejpam-4065	147	34	2k+2(iπ)k+1e−iπmli−k	2k+2(iπ)k+1e−iπmli−k	NUM
ejpam-4065	147	35	(	(	PUNCT
ejpam-4065	147	36	e2imπ	e2imπ	PROPN
ejpam-4065	147	37	)	)	PUNCT
ejpam-4065	147	38	(	(	PUNCT
ejpam-4065	147	39	√	√	ADV
ejpam-4065	147	40	x+	x+	SYM
ejpam-4065	147	41	1	1	NUM
ejpam-4065	147	42	4	4	NUM
ejpam-4065	147	43	−	−	NUM
ejpam-4065	147	44	1	1	NUM
ejpam-4065	147	45	2	2	NUM
ejpam-4065	147	46	)	)	PUNCT
ejpam-4065	147	47	3/4	3/4	NUM
ejpam-4065	147	48	x	x	SYM
ejpam-4065	147	49	√	√	NUM
ejpam-4065	147	50	x+	x+	SYM
ejpam-4065	147	51	1	1	NUM
ejpam-4065	147	52	4	4	NUM
ejpam-4065	147	53	log2	log2	NOUN
ejpam-4065	147	54	(	(	PUNCT
ejpam-4065	147	55	−	−	PROPN
ejpam-4065	147	56	2√	2√	PROPN
ejpam-4065	147	57	4x+1−1	4x+1−1	NUM
ejpam-4065	147	58	)	)	PUNCT
ejpam-4065	147	59	−	−	PROPN
ejpam-4065	148	1	(	(	PUNCT
ejpam-4065	148	2	1−i)c√	1−i)c√	NUM
ejpam-4065	148	3	2π	2π	NOUN
ejpam-4065	148	4	−	−	PROPN
ejpam-4065	149	1	(	(	PUNCT
ejpam-4065	149	2	1	1	NUM
ejpam-4065	149	3	48	48	NUM
ejpam-4065	150	1	+	+	CCONJ
ejpam-4065	150	2	i	i	PRON
ejpam-4065	150	3	48)π√	48)π√	NOUN
ejpam-4065	151	1	2√√	2√√	NUM
ejpam-4065	151	2	x+	x+	SYM
ejpam-4065	151	3	1	1	NUM
ejpam-4065	151	4	4	4	NUM
ejpam-4065	151	5	−	−	NUM
ejpam-4065	151	6	1	1	NUM
ejpam-4065	151	7	2	2	NUM
ejpam-4065	151	8	logk	logk	NOUN
ejpam-4065	151	9	(	(	PUNCT
ejpam-4065	151	10	−	−	PROPN
ejpam-4065	151	11	2√	2√	PROPN
ejpam-4065	151	12	4x+1−1	4x+1−1	NUM
ejpam-4065	151	13	)	)	PUNCT
ejpam-4065	151	14	x	x	SYM
ejpam-4065	151	15	√	√	ADV
ejpam-4065	151	16	x+	x+	SYM
ejpam-4065	151	17	1	1	NUM
ejpam-4065	151	18	4	4	NUM
ejpam-4065	151	19	ik2k+2	ik2k+2	PROPN
ejpam-4065	151	20	(	(	PUNCT
ejpam-4065	151	21	2k+1	2k+1	NOUN
ejpam-4065	151	22	−	−	NOUN
ejpam-4065	151	23	1	1	NUM
ejpam-4065	151	24	)	)	PUNCT
ejpam-4065	151	25	πk+1ζ(−k	πk+1ζ(−k	PROPN
ejpam-4065	151	26	)	)	PUNCT
ejpam-4065	151	27	√√	√√	ADV
ejpam-4065	151	28	x+	x+	SYM
ejpam-4065	151	29	1	1	NUM
ejpam-4065	151	30	4	4	NUM
ejpam-4065	151	31	−	−	NOUN
ejpam-4065	151	32	1	1	NUM
ejpam-4065	151	33	2	2	NUM
ejpam-4065	151	34	log	log	NOUN
ejpam-4065	151	35	(	(	PUNCT
ejpam-4065	151	36	log	log	NOUN
ejpam-4065	151	37	(	(	PUNCT
ejpam-4065	151	38	−	−	PROPN
ejpam-4065	151	39	2√	2√	PROPN
ejpam-4065	151	40	4x+1−1	4x+1−1	NUM
ejpam-4065	151	41	)	)	PUNCT
ejpam-4065	151	42	)	)	PUNCT
ejpam-4065	151	43	x	x	SYM
ejpam-4065	152	1	√	√	NOUN
ejpam-4065	152	2	x+	x+	SYM
ejpam-4065	152	3	1	1	NUM
ejpam-4065	152	4	4	4	NUM
ejpam-4065	152	5	log	log	NOUN
ejpam-4065	152	6	(	(	PUNCT
ejpam-4065	152	7	−	−	PROPN
ejpam-4065	152	8	2√	2√	PROPN
ejpam-4065	152	9	4x+1−1	4x+1−1	NUM
ejpam-4065	152	10	)	)	PUNCT
ejpam-4065	152	11	log(2	log(2	NOUN
ejpam-4065	152	12	)	)	PUNCT
ejpam-4065	152	13	(	(	PUNCT
ejpam-4065	152	14	2iγ	2iγ	ADJ
ejpam-4065	153	1	+	+	CCONJ
ejpam-4065	153	2	π	π	PROPN
ejpam-4065	153	3	−	−	NOUN
ejpam-4065	154	1	i	i	PRON
ejpam-4065	154	2	log	log	VERB
ejpam-4065	154	3	(	(	PUNCT
ejpam-4065	154	4	8π2	8π2	NUM
ejpam-4065	154	5	)	)	PUNCT
ejpam-4065	154	6	)	)	PUNCT
ejpam-4065	155	1	√√	√√	ADV
ejpam-4065	155	2	x+	x+	SYM
ejpam-4065	155	3	1	1	NUM
ejpam-4065	155	4	4	4	NUM
ejpam-4065	155	5	−	−	NOUN
ejpam-4065	155	6	1	1	NUM
ejpam-4065	155	7	2	2	NUM
ejpam-4065	155	8	log	log	NOUN
ejpam-4065	155	9	(	(	PUNCT
ejpam-4065	155	10	log	log	NOUN
ejpam-4065	155	11	(	(	PUNCT
ejpam-4065	155	12	−	−	PROPN
ejpam-4065	155	13	2√	2√	PROPN
ejpam-4065	155	14	4x+1−1	4x+1−1	NUM
ejpam-4065	155	15	)	)	PUNCT
ejpam-4065	155	16	)	)	PUNCT
ejpam-4065	156	1	x	x	SYM
ejpam-4065	156	2	√	√	NOUN
ejpam-4065	156	3	x+	x+	SYM
ejpam-4065	156	4	1	1	NUM
ejpam-4065	156	5	4	4	NUM
ejpam-4065	156	6	π(log(16	π(log(16	NUM
ejpam-4065	156	7	)	)	PUNCT
ejpam-4065	157	1	+	+	CCONJ
ejpam-4065	157	2	iπ	iπ	X
ejpam-4065	157	3	)	)	PUNCT
ejpam-4065	157	4	√√	√√	ADV
ejpam-4065	157	5	x+	x+	SYM
ejpam-4065	157	6	1	1	NUM
ejpam-4065	157	7	4	4	NUM
ejpam-4065	157	8	−	−	NOUN
ejpam-4065	157	9	1	1	NUM
ejpam-4065	157	10	2	2	NUM
ejpam-4065	157	11	log	log	NOUN
ejpam-4065	157	12	(	(	PUNCT
ejpam-4065	157	13	−	−	PROPN
ejpam-4065	157	14	2√	2√	PROPN
ejpam-4065	157	15	4x+1−1	4x+1−1	NUM
ejpam-4065	157	16	)	)	PUNCT
ejpam-4065	157	17	log	log	NOUN
ejpam-4065	157	18	(	(	PUNCT
ejpam-4065	157	19	log	log	NOUN
ejpam-4065	157	20	(	(	PUNCT
ejpam-4065	157	21	−	−	PROPN
ejpam-4065	157	22	2√	2√	PROPN
ejpam-4065	157	23	4x+1−1	4x+1−1	NUM
ejpam-4065	157	24	)	)	PUNCT
ejpam-4065	157	25	)	)	PUNCT
ejpam-4065	158	1	x	x	SYM
ejpam-4065	158	2	√	√	NOUN
ejpam-4065	158	3	x+	x+	SYM
ejpam-4065	158	4	1	1	NUM
ejpam-4065	158	5	4	4	NUM
ejpam-4065	158	6	1	1	NUM
ejpam-4065	158	7	3π	3π	NOUN
ejpam-4065	158	8	2(−3π	2(−3π	PUNCT
ejpam-4065	159	1	+	+	CCONJ
ejpam-4065	159	2	2i(−36	2i(−36	NUM
ejpam-4065	159	3	log(a	log(a	PROPN
ejpam-4065	159	4	)	)	PUNCT
ejpam-4065	160	1	+	+	CCONJ
ejpam-4065	160	2	3	3	NUM
ejpam-4065	160	3	+	+	CCONJ
ejpam-4065	160	4	log(128	log(128	ADJ
ejpam-4065	160	5	)	)	PUNCT
ejpam-4065	160	6	+	+	CCONJ
ejpam-4065	160	7	3	3	NUM
ejpam-4065	160	8	log(π	log(π	NOUN
ejpam-4065	160	9	)	)	PUNCT
ejpam-4065	160	10	)	)	PUNCT
ejpam-4065	160	11	)	)	PUNCT
ejpam-4065	161	1	8	8	X
ejpam-4065	161	2	.	.	X
ejpam-4065	161	3	discussion	discussion	NOUN
ejpam-4065	161	4	in	in	ADP
ejpam-4065	161	5	this	this	DET
ejpam-4065	161	6	article	article	NOUN
ejpam-4065	161	7	we	we	PRON
ejpam-4065	161	8	derived	derive	VERB
ejpam-4065	161	9	the	the	DET
ejpam-4065	161	10	definite	definite	ADJ
ejpam-4065	161	11	integral	integral	NOUN
ejpam-4065	161	12	of	of	ADP
ejpam-4065	161	13	the	the	DET
ejpam-4065	161	14	logarithmic	logarithmic	ADJ
ejpam-4065	161	15	power	power	PROPN
ejpam-4065	161	16	square	square	PROPN
ejpam-4065	161	17	root	root	NOUN
ejpam-4065	161	18	of	of	ADP
ejpam-4065	161	19	an	an	DET
ejpam-4065	161	20	algebraic	algebraic	ADJ
ejpam-4065	161	21	function	function	NOUN
ejpam-4065	161	22	and	and	CCONJ
ejpam-4065	161	23	expressed	express	VERB
ejpam-4065	161	24	it	it	PRON
ejpam-4065	161	25	in	in	ADP
ejpam-4065	161	26	terms	term	NOUN
ejpam-4065	161	27	of	of	ADP
ejpam-4065	161	28	the	the	DET
ejpam-4065	161	29	lerch	lerch	PROPN
ejpam-4065	161	30	function	function	PROPN
ejpam-4065	161	31	.	.	PUNCT
ejpam-4065	162	1	we	we	PRON
ejpam-4065	162	2	then	then	ADV
ejpam-4065	162	3	used	use	VERB
ejpam-4065	162	4	this	this	DET
ejpam-4065	162	5	references	reference	NOUN
ejpam-4065	162	6	1386	1386	NUM
ejpam-4065	162	7	integral	integral	ADJ
ejpam-4065	162	8	transform	transform	NOUN
ejpam-4065	162	9	to	to	PART
ejpam-4065	162	10	derive	derive	VERB
ejpam-4065	162	11	a	a	DET
ejpam-4065	162	12	table	table	NOUN
ejpam-4065	162	13	of	of	ADP
ejpam-4065	162	14	integrals	integral	NOUN
ejpam-4065	162	15	consisting	consist	VERB
ejpam-4065	162	16	of	of	ADP
ejpam-4065	162	17	mostly	mostly	ADV
ejpam-4065	162	18	new	new	ADJ
ejpam-4065	162	19	formula	formula	NOUN
ejpam-4065	162	20	in	in	ADP
ejpam-4065	162	21	terms	term	NOUN
ejpam-4065	162	22	of	of	ADP
ejpam-4065	162	23	special	special	ADJ
ejpam-4065	162	24	constants	constant	NOUN
ejpam-4065	162	25	and	and	CCONJ
ejpam-4065	162	26	special	special	ADJ
ejpam-4065	162	27	functions	function	NOUN
ejpam-4065	162	28	.	.	PUNCT
ejpam-4065	163	1	the	the	DET
ejpam-4065	163	2	results	result	NOUN
ejpam-4065	163	3	presented	present	VERB
ejpam-4065	163	4	were	be	AUX
ejpam-4065	163	5	numerically	numerically	ADV
ejpam-4065	163	6	verified	verify	VERB
ejpam-4065	163	7	for	for	ADP
ejpam-4065	163	8	both	both	CCONJ
ejpam-4065	163	9	real	real	ADJ
ejpam-4065	163	10	and	and	CCONJ
ejpam-4065	163	11	imaginary	imaginary	ADJ
ejpam-4065	163	12	values	value	NOUN
ejpam-4065	163	13	of	of	ADP
ejpam-4065	163	14	the	the	DET
ejpam-4065	163	15	parameters	parameter	NOUN
ejpam-4065	163	16	in	in	ADP
ejpam-4065	163	17	the	the	DET
ejpam-4065	163	18	integrals	integral	NOUN
ejpam-4065	163	19	using	use	VERB
ejpam-4065	163	20	mathematica	mathematica	PROPN
ejpam-4065	163	21	by	by	ADP
ejpam-4065	163	22	wolfram	wolfram	PROPN
ejpam-4065	163	23	.	.	PUNCT
ejpam-4065	164	1	in	in	ADP
ejpam-4065	164	2	this	this	DET
ejpam-4065	164	3	work	work	NOUN
ejpam-4065	164	4	we	we	PRON
ejpam-4065	164	5	used	use	VERB
ejpam-4065	164	6	mathematica	mathematica	PROPN
ejpam-4065	164	7	software	software	PROPN
ejpam-4065	164	8	to	to	PART
ejpam-4065	164	9	numerically	numerically	ADV
ejpam-4065	164	10	evaluate	evaluate	VERB
ejpam-4065	164	11	both	both	CCONJ
ejpam-4065	164	12	the	the	DET
ejpam-4065	164	13	definite	definite	ADJ
ejpam-4065	164	14	integral	integral	ADJ
ejpam-4065	164	15	and	and	CCONJ
ejpam-4065	164	16	associated	associate	VERB
ejpam-4065	164	17	special	special	ADJ
ejpam-4065	164	18	function	function	NOUN
ejpam-4065	164	19	for	for	ADP
ejpam-4065	164	20	complex	complex	ADJ
ejpam-4065	164	21	values	value	NOUN
ejpam-4065	164	22	of	of	ADP
ejpam-4065	164	23	the	the	DET
ejpam-4065	164	24	parameters	parameter	NOUN
ejpam-4065	164	25	k	k	PROPN
ejpam-4065	164	26	,	,	PUNCT
ejpam-4065	164	27	a	a	PRON
ejpam-4065	164	28	,	,	PUNCT
ejpam-4065	164	29	b	b	NOUN
ejpam-4065	164	30	,	,	PUNCT
ejpam-4065	164	31	m.	m.	NOUN
ejpam-4065	164	32	we	we	PRON
ejpam-4065	164	33	considered	consider	VERB
ejpam-4065	164	34	various	various	ADJ
ejpam-4065	164	35	ranges	range	NOUN
ejpam-4065	164	36	of	of	ADP
ejpam-4065	164	37	these	these	DET
ejpam-4065	164	38	parameters	parameter	NOUN
ejpam-4065	164	39	for	for	ADP
ejpam-4065	164	40	real	real	ADJ
ejpam-4065	164	41	,	,	PUNCT
ejpam-4065	164	42	integer	integer	NOUN
ejpam-4065	164	43	,	,	PUNCT
ejpam-4065	164	44	negative	negative	ADJ
ejpam-4065	164	45	and	and	CCONJ
ejpam-4065	164	46	positive	positive	ADJ
ejpam-4065	164	47	values	value	NOUN
ejpam-4065	164	48	.	.	PUNCT
ejpam-4065	165	1	we	we	PRON
ejpam-4065	165	2	compared	compare	VERB
ejpam-4065	165	3	the	the	DET
ejpam-4065	165	4	evaluation	evaluation	NOUN
ejpam-4065	165	5	of	of	ADP
ejpam-4065	165	6	the	the	DET
ejpam-4065	165	7	definite	definite	ADJ
ejpam-4065	165	8	integral	integral	ADJ
ejpam-4065	165	9	to	to	ADP
ejpam-4065	165	10	the	the	DET
ejpam-4065	165	11	evaluated	evaluated	ADJ
ejpam-4065	165	12	special	special	ADJ
ejpam-4065	165	13	function	function	NOUN
ejpam-4065	165	14	and	and	CCONJ
ejpam-4065	165	15	ensured	ensure	VERB
ejpam-4065	165	16	agreement	agreement	NOUN
ejpam-4065	165	17	.	.	PUNCT
ejpam-4065	166	1	9	9	X
ejpam-4065	166	2	.	.	X
ejpam-4065	166	3	conclusion	conclusion	NOUN
ejpam-4065	166	4	in	in	ADP
ejpam-4065	166	5	this	this	DET
ejpam-4065	166	6	paper	paper	NOUN
ejpam-4065	166	7	,	,	PUNCT
ejpam-4065	166	8	we	we	PRON
ejpam-4065	166	9	have	have	AUX
ejpam-4065	166	10	derived	derive	VERB
ejpam-4065	166	11	a	a	DET
ejpam-4065	166	12	method	method	NOUN
ejpam-4065	166	13	for	for	ADP
ejpam-4065	166	14	expressing	express	VERB
ejpam-4065	166	15	definite	definite	ADJ
ejpam-4065	166	16	integrals	integral	NOUN
ejpam-4065	166	17	in	in	ADP
ejpam-4065	166	18	terms	term	NOUN
ejpam-4065	166	19	of	of	ADP
ejpam-4065	166	20	special	special	ADJ
ejpam-4065	166	21	functions	function	NOUN
ejpam-4065	166	22	using	use	VERB
ejpam-4065	166	23	our	our	PRON
ejpam-4065	166	24	contour	contour	NOUN
ejpam-4065	166	25	integration	integration	NOUN
ejpam-4065	166	26	method	method	NOUN
ejpam-4065	166	27	.	.	PUNCT
ejpam-4065	167	1	the	the	DET
ejpam-4065	167	2	contour	contour	NOUN
ejpam-4065	167	3	we	we	PRON
ejpam-4065	167	4	used	use	VERB
ejpam-4065	167	5	was	be	AUX
ejpam-4065	167	6	specific	specific	ADJ
ejpam-4065	167	7	to	to	ADP
ejpam-4065	167	8	solving	solve	VERB
ejpam-4065	167	9	integral	integral	ADJ
ejpam-4065	167	10	representations	representation	NOUN
ejpam-4065	167	11	in	in	ADP
ejpam-4065	167	12	terms	term	NOUN
ejpam-4065	167	13	of	of	ADP
ejpam-4065	167	14	the	the	DET
ejpam-4065	167	15	lerch	lerch	PROPN
ejpam-4065	167	16	function	function	PROPN
ejpam-4065	167	17	.	.	PUNCT
ejpam-4065	168	1	we	we	PRON
ejpam-4065	168	2	expect	expect	VERB
ejpam-4065	168	3	that	that	SCONJ
ejpam-4065	168	4	other	other	ADJ
ejpam-4065	168	5	contours	contours	NOUN
ejpam-4065	168	6	and	and	CCONJ
ejpam-4065	168	7	integrals	integral	NOUN
ejpam-4065	168	8	can	can	AUX
ejpam-4065	168	9	be	be	AUX
ejpam-4065	168	10	derived	derive	VERB
ejpam-4065	168	11	using	use	VERB
ejpam-4065	168	12	this	this	DET
ejpam-4065	168	13	method	method	NOUN
ejpam-4065	168	14	.	.	PUNCT
ejpam-4065	169	1	acknowledgements	acknowledgement	NOUN
ejpam-4065	169	2	this	this	DET
ejpam-4065	169	3	research	research	NOUN
ejpam-4065	169	4	is	be	AUX
ejpam-4065	169	5	supported	support	VERB
ejpam-4065	169	6	by	by	ADP
ejpam-4065	169	7	nserc	nserc	PROPN
ejpam-4065	169	8	canada	canada	PROPN
ejpam-4065	169	9	under	under	ADP
ejpam-4065	169	10	grant	grant	PROPN
ejpam-4065	169	11	504070	504070	NUM
ejpam-4065	169	12	.	.	PUNCT
ejpam-4065	170	1	references	reference	NOUN
ejpam-4065	170	2	[	[	X
ejpam-4065	170	3	1	1	X
ejpam-4065	170	4	]	]	X
ejpam-4065	170	5	milton	milton	PROPN
ejpam-4065	170	6	abramowitz	abramowitz	PROPN
ejpam-4065	170	7	and	and	CCONJ
ejpam-4065	170	8	irene	irene	PROPN
ejpam-4065	170	9	a.	a.	PROPN
ejpam-4065	170	10	stegun	stegun	PROPN
ejpam-4065	170	11	.	.	PUNCT
ejpam-4065	171	1	handbook	handbook	NOUN
ejpam-4065	171	2	of	of	ADP
ejpam-4065	171	3	mathematical	mathematical	ADJ
ejpam-4065	171	4	functions	function	NOUN
ejpam-4065	171	5	:	:	PUNCT
ejpam-4065	171	6	with	with	ADP
ejpam-4065	171	7	formulas	formula	NOUN
ejpam-4065	171	8	,	,	PUNCT
ejpam-4065	171	9	graphs	graph	NOUN
ejpam-4065	171	10	,	,	PUNCT
ejpam-4065	171	11	and	and	CCONJ
ejpam-4065	171	12	mathematical	mathematical	ADJ
ejpam-4065	171	13	tables	table	NOUN
ejpam-4065	171	14	.	.	PUNCT
ejpam-4065	172	1	courier	courier	NOUN
ejpam-4065	172	2	corporation	corporation	NOUN
ejpam-4065	172	3	,	,	PUNCT
ejpam-4065	172	4	01	01	NUM
ejpam-4065	172	5	1965	1965	NUM
ejpam-4065	172	6	.	.	PUNCT
ejpam-4065	173	1	[	[	X
ejpam-4065	173	2	2	2	X
ejpam-4065	173	3	]	]	X
ejpam-4065	173	4	harry	harry	PROPN
ejpam-4065	173	5	bateman	bateman	PROPN
ejpam-4065	173	6	.	.	PUNCT
ejpam-4065	174	1	higher	high	ADJ
ejpam-4065	174	2	transcendental	transcendental	ADJ
ejpam-4065	174	3	functions	function	NOUN
ejpam-4065	174	4	v.1	v.1	PUNCT
ejpam-4065	174	5	.	.	PUNCT
ejpam-4065	175	1	mcgraw	mcgraw	PROPN
ejpam-4065	175	2	-	-	PUNCT
ejpam-4065	175	3	hill	hill	PROPN
ejpam-4065	175	4	,	,	PUNCT
ejpam-4065	175	5	1953	1953	NUM
ejpam-4065	175	6	.	.	PUNCT
ejpam-4065	176	1	[	[	X
ejpam-4065	176	2	3	3	X
ejpam-4065	176	3	]	]	X
ejpam-4065	176	4	yu	yu	PROPN
ejpam-4065	176	5	a.	a.	NOUN
ejpam-4065	176	6	brychkov	brychkov	PROPN
ejpam-4065	176	7	,	,	PUNCT
ejpam-4065	176	8	o.	o.	PROPN
ejpam-4065	176	9	i.	i.	PROPN
ejpam-4065	176	10	marichev	marichev	PROPN
ejpam-4065	176	11	,	,	PUNCT
ejpam-4065	176	12	and	and	CCONJ
ejpam-4065	176	13	n.	n.	PROPN
ejpam-4065	176	14	v.	v.	PROPN
ejpam-4065	176	15	savischenko	savischenko	PROPN
ejpam-4065	176	16	.	.	PUNCT
ejpam-4065	177	1	handbook	handbook	NOUN
ejpam-4065	177	2	of	of	ADP
ejpam-4065	177	3	mellin	mellin	PROPN
ejpam-4065	177	4	transforms	transform	VERB
ejpam-4065	177	5	.	.	PUNCT
ejpam-4065	178	1	crc	crc	PROPN
ejpam-4065	178	2	press	press	PROPN
ejpam-4065	178	3	,	,	PUNCT
ejpam-4065	178	4	10	10	NUM
ejpam-4065	178	5	2018	2018	NUM
ejpam-4065	178	6	.	.	PUNCT
ejpam-4065	179	1	[	[	X
ejpam-4065	179	2	4	4	NUM
ejpam-4065	179	3	]	]	X
ejpam-4065	179	4	steven	steven	PROPN
ejpam-4065	179	5	r.	r.	PROPN
ejpam-4065	179	6	finch	finch	PROPN
ejpam-4065	179	7	.	.	PUNCT
ejpam-4065	180	1	mathematical	mathematical	ADJ
ejpam-4065	180	2	constants	constants	PROPN
ejpam-4065	180	3	icm	icm	PROPN
ejpam-4065	180	4	edition	edition	PROPN
ejpam-4065	180	5	.	.	PUNCT
ejpam-4065	181	1	cambridge	cambridge	PROPN
ejpam-4065	181	2	university	university	PROPN
ejpam-4065	181	3	press	press	NOUN
ejpam-4065	181	4	,	,	PUNCT
ejpam-4065	181	5	07	07	NUM
ejpam-4065	181	6	2010	2010	NUM
ejpam-4065	181	7	.	.	PUNCT
ejpam-4065	182	1	[	[	X
ejpam-4065	182	2	5	5	NUM
ejpam-4065	182	3	]	]	X
ejpam-4065	182	4	i.	i.	PROPN
ejpam-4065	182	5	s.	s.	PROPN
ejpam-4065	182	6	gradshteyn	gradshteyn	PROPN
ejpam-4065	182	7	and	and	CCONJ
ejpam-4065	182	8	i.	i.	PROPN
ejpam-4065	182	9	m.	m.	PROPN
ejpam-4065	182	10	ryzhik	ryzhik	PROPN
ejpam-4065	182	11	.	.	PUNCT
ejpam-4065	183	1	table	table	NOUN
ejpam-4065	183	2	of	of	ADP
ejpam-4065	183	3	integrals	integral	NOUN
ejpam-4065	183	4	,	,	PUNCT
ejpam-4065	183	5	series	series	NOUN
ejpam-4065	183	6	,	,	PUNCT
ejpam-4065	183	7	and	and	CCONJ
ejpam-4065	183	8	products	product	NOUN
ejpam-4065	183	9	.	.	PUNCT
ejpam-4065	184	1	academic	academic	ADJ
ejpam-4065	184	2	press	press	NOUN
ejpam-4065	184	3	,	,	PUNCT
ejpam-4065	184	4	05	05	NUM
ejpam-4065	184	5	2014	2014	NUM
ejpam-4065	184	6	.	.	PUNCT
ejpam-4065	185	1	[	[	X
ejpam-4065	185	2	6	6	NUM
ejpam-4065	185	3	]	]	PUNCT
ejpam-4065	185	4	leonard	leonard	PROPN
ejpam-4065	185	5	lewin	lewin	PROPN
ejpam-4065	185	6	.	.	PUNCT
ejpam-4065	186	1	polylogarithms	polylogarithm	NOUN
ejpam-4065	186	2	and	and	CCONJ
ejpam-4065	186	3	associated	associated	ADJ
ejpam-4065	186	4	functions	function	NOUN
ejpam-4065	186	5	.	.	PUNCT
ejpam-4065	187	1	north	north	NOUN
ejpam-4065	187	2	holland	holland	PROPN
ejpam-4065	187	3	,	,	PUNCT
ejpam-4065	187	4	1981	1981	NUM
ejpam-4065	187	5	.	.	PUNCT
ejpam-4065	188	1	[	[	X
ejpam-4065	188	2	7	7	X
ejpam-4065	188	3	]	]	X
ejpam-4065	188	4	m.a	m.a	PROPN
ejpam-4065	188	5	.	.	PROPN
ejpam-4065	188	6	nyblom	nyblom	PROPN
ejpam-4065	188	7	.	.	PUNCT
ejpam-4065	189	1	on	on	ADP
ejpam-4065	189	2	the	the	DET
ejpam-4065	189	3	evaluation	evaluation	NOUN
ejpam-4065	189	4	of	of	ADP
ejpam-4065	189	5	a	a	DET
ejpam-4065	189	6	definite	definite	ADJ
ejpam-4065	189	7	integral	integral	ADJ
ejpam-4065	189	8	involving	involve	VERB
ejpam-4065	189	9	nested	nest	VERB
ejpam-4065	189	10	square	square	ADJ
ejpam-4065	189	11	root	root	NOUN
ejpam-4065	189	12	functions	function	NOUN
ejpam-4065	189	13	.	.	PUNCT
ejpam-4065	190	1	rocky	rocky	ADJ
ejpam-4065	190	2	mountain	mountain	PROPN
ejpam-4065	190	3	journal	journal	NOUN
ejpam-4065	190	4	of	of	ADP
ejpam-4065	190	5	mathematics	mathematic	NOUN
ejpam-4065	190	6	,	,	PUNCT
ejpam-4065	190	7	37	37	NUM
ejpam-4065	190	8	,	,	PUNCT
ejpam-4065	190	9	08	08	NUM
ejpam-4065	190	10	2007	2007	NUM
ejpam-4065	190	11	.	.	PUNCT
ejpam-4065	191	1	[	[	X
ejpam-4065	191	2	8	8	X
ejpam-4065	191	3	]	]	X
ejpam-4065	191	4	keith	keith	PROPN
ejpam-4065	191	5	b.	b.	PROPN
ejpam-4065	191	6	oldham	oldham	PROPN
ejpam-4065	191	7	,	,	PUNCT
ejpam-4065	191	8	jan	jan	PROPN
ejpam-4065	191	9	myland	myland	PROPN
ejpam-4065	191	10	,	,	PUNCT
ejpam-4065	191	11	and	and	CCONJ
ejpam-4065	191	12	jerome	jerome	PROPN
ejpam-4065	191	13	spanier	spanier	NOUN
ejpam-4065	191	14	.	.	PUNCT
ejpam-4065	192	1	an	an	DET
ejpam-4065	192	2	atlas	atlas	PROPN
ejpam-4065	192	3	of	of	ADP
ejpam-4065	192	4	functions	function	NOUN
ejpam-4065	192	5	:	:	PUNCT
ejpam-4065	192	6	with	with	ADP
ejpam-4065	192	7	equator	equator	NOUN
ejpam-4065	192	8	,	,	PUNCT
ejpam-4065	192	9	the	the	DET
ejpam-4065	192	10	atlas	atlas	PROPN
ejpam-4065	192	11	function	function	PROPN
ejpam-4065	192	12	calculator	calculator	NOUN
ejpam-4065	192	13	.	.	PUNCT
ejpam-4065	193	1	springer	springer	NOUN
ejpam-4065	193	2	science	science	PROPN
ejpam-4065	193	3	&	&	CCONJ
ejpam-4065	193	4	business	business	NOUN
ejpam-4065	193	5	media	medium	NOUN
ejpam-4065	193	6	,	,	PUNCT
ejpam-4065	193	7	07	07	NUM
ejpam-4065	193	8	2010	2010	NUM
ejpam-4065	193	9	.	.	PUNCT
ejpam-4065	194	1	references	reference	NOUN
ejpam-4065	194	2	1387	1387	NUM
ejpam-4065	194	3	[	[	X
ejpam-4065	194	4	9	9	NUM
ejpam-4065	194	5	]	]	X
ejpam-4065	194	6	robert	robert	PROPN
ejpam-4065	194	7	reynolds	reynolds	PROPN
ejpam-4065	194	8	and	and	CCONJ
ejpam-4065	194	9	allan	allan	PROPN
ejpam-4065	194	10	stauffer	stauffer	PROPN
ejpam-4065	194	11	.	.	PUNCT
ejpam-4065	195	1	definite	definite	ADJ
ejpam-4065	195	2	integrals	integral	NOUN
ejpam-4065	195	3	involving	involve	VERB
ejpam-4065	195	4	product	product	NOUN
ejpam-4065	195	5	of	of	ADP
ejpam-4065	195	6	logarithmic	logarithmic	ADJ
ejpam-4065	195	7	functions	function	NOUN
ejpam-4065	195	8	and	and	CCONJ
ejpam-4065	195	9	logarithm	logarithm	NOUN
ejpam-4065	195	10	of	of	ADP
ejpam-4065	195	11	square	square	ADJ
ejpam-4065	195	12	root	root	NOUN
ejpam-4065	195	13	functions	function	NOUN
ejpam-4065	195	14	expressed	express	VERB
ejpam-4065	195	15	in	in	ADP
ejpam-4065	195	16	terms	term	NOUN
ejpam-4065	195	17	of	of	ADP
ejpam-4065	195	18	special	special	ADJ
ejpam-4065	195	19	functions	function	NOUN
ejpam-4065	195	20	.	.	PUNCT
ejpam-4065	196	1	aims	aim	VERB
ejpam-4065	196	2	mathematics	mathematic	NOUN
ejpam-4065	196	3	,	,	PUNCT
ejpam-4065	196	4	5:5724–5733	5:5724–5733	NUM
ejpam-4065	196	5	,	,	PUNCT
ejpam-4065	196	6	2020	2020	NUM
ejpam-4065	196	7	.	.	PUNCT
ejpam-4065	197	1	[	[	X
ejpam-4065	197	2	10	10	NUM
ejpam-4065	197	3	]	]	X
ejpam-4065	197	4	robert	robert	PROPN
ejpam-4065	197	5	reynolds	reynolds	PROPN
ejpam-4065	197	6	and	and	CCONJ
ejpam-4065	197	7	allan	allan	PROPN
ejpam-4065	197	8	stauffer	stauffer	PROPN
ejpam-4065	197	9	.	.	PUNCT
ejpam-4065	198	1	a	a	DET
ejpam-4065	198	2	method	method	NOUN
ejpam-4065	198	3	for	for	ADP
ejpam-4065	198	4	evaluating	evaluate	VERB
ejpam-4065	198	5	definite	definite	ADJ
ejpam-4065	198	6	integrals	integral	NOUN
ejpam-4065	198	7	in	in	ADP
ejpam-4065	198	8	terms	term	NOUN
ejpam-4065	198	9	of	of	ADP
ejpam-4065	198	10	special	special	ADJ
ejpam-4065	198	11	functions	function	NOUN
ejpam-4065	198	12	with	with	ADP
ejpam-4065	198	13	examples	example	NOUN
ejpam-4065	198	14	.	.	PUNCT
ejpam-4065	199	1	international	international	ADJ
ejpam-4065	199	2	mathematical	mathematical	PROPN
ejpam-4065	199	3	forum	forum	PROPN
ejpam-4065	199	4	,	,	PUNCT
ejpam-4065	199	5	15:235	15:235	NUM
ejpam-4065	199	6	–	–	PUNCT
ejpam-4065	199	7	244	244	NUM
ejpam-4065	199	8	,	,	PUNCT
ejpam-4065	199	9	2020	2020	NUM
ejpam-4065	199	10	.	.	PUNCT