id	sid	tid	token	lemma	pos
ejpam-4030	1	1	european	european	PROPN
ejpam-4030	1	2	journal	journal	PROPN
ejpam-4030	1	3	of	of	ADP
ejpam-4030	1	4	pure	pure	ADJ
ejpam-4030	1	5	and	and	CCONJ
ejpam-4030	1	6	applied	apply	VERB
ejpam-4030	1	7	mathematics	mathematic	NOUN
ejpam-4030	1	8	vol	vol	NOUN
ejpam-4030	1	9	.	.	PUNCT
ejpam-4030	2	1	14	14	NUM
ejpam-4030	2	2	,	,	PUNCT
ejpam-4030	2	3	no	no	INTJ
ejpam-4030	2	4	.	.	NOUN
ejpam-4030	2	5	3	3	NUM
ejpam-4030	2	6	,	,	PUNCT
ejpam-4030	2	7	2021	2021	NUM
ejpam-4030	2	8	,	,	PUNCT
ejpam-4030	2	9	788	788	NUM
ejpam-4030	2	10	-	-	SYM
ejpam-4030	2	11	802	802	NUM
ejpam-4030	2	12	issn	issn	PROPN
ejpam-4030	2	13	1307	1307	NUM
ejpam-4030	2	14	-	-	SYM
ejpam-4030	2	15	5543	5543	NUM
ejpam-4030	2	16	–	–	PUNCT
ejpam-4030	2	17	ejpam.com	ejpam.com	X
ejpam-4030	2	18	published	publish	VERB
ejpam-4030	2	19	by	by	ADP
ejpam-4030	2	20	new	new	PROPN
ejpam-4030	2	21	york	york	PROPN
ejpam-4030	2	22	business	business	PROPN
ejpam-4030	3	1	global	global	PROPN
ejpam-4030	3	2	a	a	DET
ejpam-4030	3	3	note	note	NOUN
ejpam-4030	3	4	on	on	ADP
ejpam-4030	3	5	the	the	DET
ejpam-4030	3	6	definite	definite	ADJ
ejpam-4030	3	7	integral	integral	NOUN
ejpam-4030	3	8	of	of	ADP
ejpam-4030	3	9	the	the	DET
ejpam-4030	3	10	lerch	lerch	PROPN
ejpam-4030	3	11	function	function	PROPN
ejpam-4030	3	12	robert	robert	PROPN
ejpam-4030	3	13	reynolds1,∗	reynolds1,∗	PROPN
ejpam-4030	3	14	,	,	PUNCT
ejpam-4030	3	15	allan	allan	PROPN
ejpam-4030	3	16	stauffer1	stauffer1	PROPN
ejpam-4030	3	17	1	1	NUM
ejpam-4030	3	18	department	department	NOUN
ejpam-4030	3	19	of	of	ADP
ejpam-4030	3	20	mathematics	mathematic	NOUN
ejpam-4030	3	21	and	and	CCONJ
ejpam-4030	3	22	statistics	statistic	NOUN
ejpam-4030	3	23	,	,	PUNCT
ejpam-4030	3	24	faculty	faculty	NOUN
ejpam-4030	3	25	of	of	ADP
ejpam-4030	3	26	science	science	PROPN
ejpam-4030	3	27	,	,	PUNCT
ejpam-4030	3	28	york	york	PROPN
ejpam-4030	3	29	university	university	PROPN
ejpam-4030	3	30	,	,	PUNCT
ejpam-4030	3	31	toronto	toronto	PROPN
ejpam-4030	3	32	,	,	PUNCT
ejpam-4030	3	33	ontario	ontario	PROPN
ejpam-4030	3	34	,	,	PUNCT
ejpam-4030	3	35	canada	canada	PROPN
ejpam-4030	3	36	abstract	abstract	NOUN
ejpam-4030	3	37	.	.	PUNCT
ejpam-4030	4	1	in	in	ADP
ejpam-4030	4	2	this	this	DET
ejpam-4030	4	3	manuscript	manuscript	NOUN
ejpam-4030	4	4	,	,	PUNCT
ejpam-4030	4	5	the	the	DET
ejpam-4030	4	6	authors	author	NOUN
ejpam-4030	4	7	derive	derive	VERB
ejpam-4030	4	8	a	a	DET
ejpam-4030	4	9	formula	formula	NOUN
ejpam-4030	4	10	for	for	ADP
ejpam-4030	4	11	the	the	DET
ejpam-4030	4	12	double	double	ADJ
ejpam-4030	4	13	laplace	laplace	NOUN
ejpam-4030	4	14	transform	transform	NOUN
ejpam-4030	4	15	expressed	express	VERB
ejpam-4030	4	16	in	in	ADP
ejpam-4030	4	17	terms	term	NOUN
ejpam-4030	4	18	of	of	ADP
ejpam-4030	4	19	the	the	DET
ejpam-4030	4	20	lerch	lerch	PROPN
ejpam-4030	4	21	transcendent	transcendent	NOUN
ejpam-4030	4	22	.	.	PUNCT
ejpam-4030	5	1	the	the	DET
ejpam-4030	5	2	log	log	NOUN
ejpam-4030	5	3	term	term	NOUN
ejpam-4030	5	4	mixes	mix	VERB
ejpam-4030	5	5	the	the	DET
ejpam-4030	5	6	variables	variable	NOUN
ejpam-4030	5	7	so	so	SCONJ
ejpam-4030	5	8	that	that	SCONJ
ejpam-4030	5	9	the	the	DET
ejpam-4030	5	10	integral	integral	NOUN
ejpam-4030	5	11	is	be	AUX
ejpam-4030	5	12	not	not	PART
ejpam-4030	5	13	separable	separable	ADJ
ejpam-4030	5	14	except	except	SCONJ
ejpam-4030	5	15	for	for	ADP
ejpam-4030	5	16	special	special	ADJ
ejpam-4030	5	17	values	value	NOUN
ejpam-4030	5	18	of	of	ADP
ejpam-4030	5	19	k.	k.	PROPN
ejpam-4030	5	20	the	the	DET
ejpam-4030	5	21	method	method	NOUN
ejpam-4030	5	22	of	of	ADP
ejpam-4030	5	23	proof	proof	NOUN
ejpam-4030	5	24	follows	follow	VERB
ejpam-4030	5	25	the	the	DET
ejpam-4030	5	26	method	method	NOUN
ejpam-4030	5	27	used	use	VERB
ejpam-4030	5	28	by	by	ADP
ejpam-4030	5	29	us	we	PRON
ejpam-4030	5	30	to	to	PART
ejpam-4030	5	31	evaluate	evaluate	VERB
ejpam-4030	5	32	single	single	ADJ
ejpam-4030	5	33	integrals	integral	NOUN
ejpam-4030	5	34	.	.	PUNCT
ejpam-4030	6	1	this	this	DET
ejpam-4030	6	2	transform	transform	NOUN
ejpam-4030	6	3	is	be	AUX
ejpam-4030	6	4	then	then	ADV
ejpam-4030	6	5	used	use	VERB
ejpam-4030	6	6	to	to	PART
ejpam-4030	6	7	derive	derive	VERB
ejpam-4030	6	8	definite	definite	ADJ
ejpam-4030	6	9	integrals	integral	NOUN
ejpam-4030	6	10	in	in	ADP
ejpam-4030	6	11	terms	term	NOUN
ejpam-4030	6	12	of	of	ADP
ejpam-4030	6	13	fundamental	fundamental	ADJ
ejpam-4030	6	14	constants	constant	NOUN
ejpam-4030	6	15	,	,	PUNCT
ejpam-4030	6	16	elementary	elementary	ADJ
ejpam-4030	6	17	and	and	CCONJ
ejpam-4030	6	18	special	special	ADJ
ejpam-4030	6	19	functions	function	NOUN
ejpam-4030	6	20	.	.	PUNCT
ejpam-4030	7	1	a	a	DET
ejpam-4030	7	2	summary	summary	NOUN
ejpam-4030	7	3	of	of	ADP
ejpam-4030	7	4	the	the	DET
ejpam-4030	7	5	results	result	NOUN
ejpam-4030	7	6	is	be	AUX
ejpam-4030	7	7	produced	produce	VERB
ejpam-4030	7	8	in	in	ADP
ejpam-4030	7	9	the	the	DET
ejpam-4030	7	10	form	form	NOUN
ejpam-4030	7	11	of	of	ADP
ejpam-4030	7	12	a	a	DET
ejpam-4030	7	13	table	table	NOUN
ejpam-4030	7	14	of	of	ADP
ejpam-4030	7	15	definite	definite	ADJ
ejpam-4030	7	16	integrals	integral	NOUN
ejpam-4030	7	17	for	for	ADP
ejpam-4030	7	18	easy	easy	ADJ
ejpam-4030	7	19	referencing	referencing	NOUN
ejpam-4030	7	20	by	by	ADP
ejpam-4030	7	21	readers	reader	NOUN
ejpam-4030	7	22	.	.	PUNCT
ejpam-4030	8	1	the	the	DET
ejpam-4030	8	2	majority	majority	NOUN
ejpam-4030	8	3	of	of	ADP
ejpam-4030	8	4	the	the	DET
ejpam-4030	8	5	results	result	NOUN
ejpam-4030	8	6	in	in	ADP
ejpam-4030	8	7	the	the	DET
ejpam-4030	8	8	work	work	NOUN
ejpam-4030	8	9	are	be	AUX
ejpam-4030	8	10	new	new	ADJ
ejpam-4030	8	11	.	.	PUNCT
ejpam-4030	9	1	2020	2020	NUM
ejpam-4030	9	2	mathematics	mathematic	NOUN
ejpam-4030	9	3	subject	subject	NOUN
ejpam-4030	9	4	classifications	classification	NOUN
ejpam-4030	9	5	:	:	PUNCT
ejpam-4030	9	6	01a35	01a35	NOUN
ejpam-4030	9	7	,	,	PUNCT
ejpam-4030	9	8	11m06	11m06	NUM
ejpam-4030	9	9	,	,	PUNCT
ejpam-4030	9	10	11m35	11m35	NUM
ejpam-4030	9	11	,	,	PUNCT
ejpam-4030	9	12	30	30	NUM
ejpam-4030	9	13	-	-	SYM
ejpam-4030	9	14	02	02	NUM
ejpam-4030	9	15	,	,	PUNCT
ejpam-4030	9	16	30d10	30d10	NUM
ejpam-4030	9	17	,	,	PUNCT
ejpam-4030	9	18	30d30	30d30	NUM
ejpam-4030	9	19	,	,	PUNCT
ejpam-4030	9	20	30e20	30e20	NUM
ejpam-4030	9	21	key	key	ADJ
ejpam-4030	9	22	words	word	NOUN
ejpam-4030	9	23	and	and	CCONJ
ejpam-4030	9	24	phrases	phrase	NOUN
ejpam-4030	9	25	:	:	PUNCT
ejpam-4030	9	26	laplace	laplace	NOUN
ejpam-4030	9	27	transform	transform	NOUN
ejpam-4030	9	28	,	,	PUNCT
ejpam-4030	9	29	lerch	lerch	PROPN
ejpam-4030	9	30	transcendent	transcendent	NOUN
ejpam-4030	9	31	,	,	PUNCT
ejpam-4030	9	32	contour	contour	NOUN
ejpam-4030	9	33	integral	integral	ADJ
ejpam-4030	9	34	,	,	PUNCT
ejpam-4030	9	35	definite	definite	ADJ
ejpam-4030	9	36	integral	integral	ADJ
ejpam-4030	9	37	1	1	NUM
ejpam-4030	9	38	.	.	NOUN
ejpam-4030	9	39	significance	significance	NOUN
ejpam-4030	9	40	statement	statement	NOUN
ejpam-4030	9	41	definite	definite	ADJ
ejpam-4030	9	42	integrals	integral	NOUN
ejpam-4030	9	43	of	of	ADP
ejpam-4030	9	44	special	special	ADJ
ejpam-4030	9	45	functions	function	NOUN
ejpam-4030	9	46	occur	occur	VERB
ejpam-4030	9	47	in	in	ADP
ejpam-4030	9	48	a	a	DET
ejpam-4030	9	49	wide	wide	ADJ
ejpam-4030	9	50	range	range	NOUN
ejpam-4030	9	51	of	of	ADP
ejpam-4030	9	52	applications	application	NOUN
ejpam-4030	9	53	.	.	PUNCT
ejpam-4030	10	1	such	such	ADJ
ejpam-4030	10	2	applications	application	NOUN
ejpam-4030	10	3	of	of	ADP
ejpam-4030	10	4	these	these	DET
ejpam-4030	10	5	integrals	integral	NOUN
ejpam-4030	10	6	are	be	AUX
ejpam-4030	10	7	prominent	prominent	ADJ
ejpam-4030	10	8	in	in	ADP
ejpam-4030	10	9	diffusion	diffusion	NOUN
ejpam-4030	10	10	theory	theory	NOUN
ejpam-4030	10	11	[	[	X
ejpam-4030	10	12	8	8	NUM
ejpam-4030	10	13	]	]	PUNCT
ejpam-4030	10	14	,	,	PUNCT
ejpam-4030	10	15	transportation	transportation	NOUN
ejpam-4030	10	16	problems	problem	NOUN
ejpam-4030	10	17	[	[	X
ejpam-4030	10	18	8	8	NUM
ejpam-4030	10	19	]	]	PUNCT
ejpam-4030	10	20	,	,	PUNCT
ejpam-4030	10	21	the	the	DET
ejpam-4030	10	22	study	study	NOUN
ejpam-4030	10	23	of	of	ADP
ejpam-4030	10	24	the	the	DET
ejpam-4030	10	25	radiative	radiative	ADJ
ejpam-4030	10	26	equilibrium	equilibrium	NOUN
ejpam-4030	10	27	of	of	ADP
ejpam-4030	10	28	stellar	stellar	ADJ
ejpam-4030	10	29	atmospheres	atmosphere	NOUN
ejpam-4030	10	30	[	[	X
ejpam-4030	10	31	6	6	NUM
ejpam-4030	10	32	]	]	PUNCT
ejpam-4030	10	33	and	and	CCONJ
ejpam-4030	10	34	the	the	DET
ejpam-4030	10	35	evaluation	evaluation	NOUN
ejpam-4030	10	36	of	of	ADP
ejpam-4030	10	37	exchange	exchange	NOUN
ejpam-4030	10	38	integrals	integral	NOUN
ejpam-4030	10	39	in	in	ADP
ejpam-4030	10	40	quantum	quantum	ADJ
ejpam-4030	10	41	mechanics	mechanic	NOUN
ejpam-4030	10	42	[	[	X
ejpam-4030	10	43	7	7	NUM
ejpam-4030	10	44	]	]	PUNCT
ejpam-4030	10	45	.	.	PUNCT
ejpam-4030	11	1	this	this	DET
ejpam-4030	11	2	paper	paper	NOUN
ejpam-4030	11	3	is	be	AUX
ejpam-4030	11	4	an	an	DET
ejpam-4030	11	5	effort	effort	NOUN
ejpam-4030	11	6	to	to	PART
ejpam-4030	11	7	give	give	VERB
ejpam-4030	11	8	a	a	DET
ejpam-4030	11	9	tabulation	tabulation	NOUN
ejpam-4030	11	10	of	of	ADP
ejpam-4030	11	11	an	an	DET
ejpam-4030	11	12	integral	integral	NOUN
ejpam-4030	11	13	for	for	ADP
ejpam-4030	11	14	a	a	DET
ejpam-4030	11	15	particular	particular	ADJ
ejpam-4030	11	16	special	special	ADJ
ejpam-4030	11	17	function	function	NOUN
ejpam-4030	11	18	not	not	PART
ejpam-4030	11	19	present	present	ADJ
ejpam-4030	11	20	in	in	ADP
ejpam-4030	11	21	current	current	ADJ
ejpam-4030	11	22	literature	literature	NOUN
ejpam-4030	11	23	.	.	PUNCT
ejpam-4030	12	1	the	the	DET
ejpam-4030	12	2	special	special	ADJ
ejpam-4030	12	3	function	function	NOUN
ejpam-4030	12	4	researched	research	VERB
ejpam-4030	12	5	in	in	ADP
ejpam-4030	12	6	this	this	DET
ejpam-4030	12	7	work	work	NOUN
ejpam-4030	12	8	is	be	AUX
ejpam-4030	12	9	the	the	DET
ejpam-4030	12	10	lerch	lerch	PROPN
ejpam-4030	12	11	function	function	PROPN
ejpam-4030	12	12	.	.	PUNCT
ejpam-4030	13	1	in	in	ADP
ejpam-4030	13	2	1887	1887	NUM
ejpam-4030	13	3	mathias	mathias	PROPN
ejpam-4030	13	4	lerch	lerch	PROPN
ejpam-4030	14	1	[	[	X
ejpam-4030	14	2	9	9	NUM
ejpam-4030	14	3	]	]	PUNCT
ejpam-4030	14	4	produced	produce	VERB
ejpam-4030	14	5	his	his	PRON
ejpam-4030	14	6	famous	famous	ADJ
ejpam-4030	14	7	manuscript	manuscript	NOUN
ejpam-4030	14	8	on	on	ADP
ejpam-4030	14	9	the	the	DET
ejpam-4030	14	10	lerch	lerch	PROPN
ejpam-4030	14	11	function	function	PROPN
ejpam-4030	14	12	.	.	PUNCT
ejpam-4030	15	1	lerch	lerch	PROPN
ejpam-4030	15	2	’s	’s	PART
ejpam-4030	15	3	function	function	NOUN
ejpam-4030	15	4	has	have	AUX
ejpam-4030	15	5	been	be	AUX
ejpam-4030	15	6	extensively	extensively	ADV
ejpam-4030	15	7	in	in	ADP
ejpam-4030	15	8	studied	study	VERB
ejpam-4030	15	9	in	in	ADP
ejpam-4030	15	10	[	[	X
ejpam-4030	15	11	3–5	3–5	NOUN
ejpam-4030	15	12	,	,	PUNCT
ejpam-4030	15	13	9	9	NUM
ejpam-4030	15	14	,	,	PUNCT
ejpam-4030	15	15	10	10	NUM
ejpam-4030	15	16	,	,	PUNCT
ejpam-4030	15	17	13	13	NUM
ejpam-4030	15	18	]	]	PUNCT
ejpam-4030	15	19	.	.	PUNCT
ejpam-4030	16	1	the	the	DET
ejpam-4030	16	2	lerch	lerch	PROPN
ejpam-4030	16	3	function	function	PROPN
ejpam-4030	16	4	generalizes	generalize	VERB
ejpam-4030	16	5	the	the	DET
ejpam-4030	16	6	hurwitz	hurwitz	PROPN
ejpam-4030	16	7	zeta	zeta	PROPN
ejpam-4030	16	8	function	function	PROPN
ejpam-4030	16	9	,	,	PUNCT
ejpam-4030	16	10	the	the	DET
ejpam-4030	16	11	polylogarithms	polylogarithm	NOUN
ejpam-4030	16	12	,	,	PUNCT
ejpam-4030	16	13	and	and	CCONJ
ejpam-4030	16	14	many	many	ADJ
ejpam-4030	16	15	interesting	interesting	ADJ
ejpam-4030	16	16	and	and	CCONJ
ejpam-4030	16	17	important	important	ADJ
ejpam-4030	16	18	special	special	ADJ
ejpam-4030	16	19	functions	function	NOUN
ejpam-4030	16	20	.	.	PUNCT
ejpam-4030	17	1	definite	definite	ADJ
ejpam-4030	17	2	integrals	integral	NOUN
ejpam-4030	17	3	of	of	ADP
ejpam-4030	17	4	special	special	ADJ
ejpam-4030	17	5	functions	function	NOUN
ejpam-4030	17	6	such	such	ADJ
ejpam-4030	17	7	as	as	ADP
ejpam-4030	17	8	hurwitz	hurwitz	PROPN
ejpam-4030	17	9	zeta	zeta	PROPN
ejpam-4030	17	10	and	and	CCONJ
ejpam-4030	17	11	polylogarithm	polylogarithm	PROPN
ejpam-4030	17	12	have	have	AUX
ejpam-4030	17	13	been	be	AUX
ejpam-4030	17	14	studied	study	VERB
ejpam-4030	17	15	in	in	ADP
ejpam-4030	17	16	the	the	DET
ejpam-4030	17	17	works	work	NOUN
ejpam-4030	17	18	of	of	ADP
ejpam-4030	17	19	kurokawa	kurokawa	PROPN
ejpam-4030	17	20	et	et	PROPN
ejpam-4030	17	21	al	al	PROPN
ejpam-4030	17	22	and	and	CCONJ
ejpam-4030	17	23	reynolds	reynolds	PROPN
ejpam-4030	17	24	and	and	CCONJ
ejpam-4030	17	25	stauffer	stauffer	PROPN
ejpam-4030	18	1	[	[	X
ejpam-4030	18	2	8	8	NUM
ejpam-4030	18	3	,	,	PUNCT
ejpam-4030	18	4	14	14	NUM
ejpam-4030	18	5	]	]	PUNCT
ejpam-4030	18	6	.	.	PUNCT
ejpam-4030	19	1	relations	relation	NOUN
ejpam-4030	19	2	between	between	ADP
ejpam-4030	19	3	the	the	DET
ejpam-4030	19	4	hurwitz	hurwitz	PROPN
ejpam-4030	19	5	-	-	PUNCT
ejpam-4030	19	6	lerch	lerch	PROPN
ejpam-4030	19	7	zeta	zeta	PROPN
ejpam-4030	19	8	functions	function	NOUN
ejpam-4030	19	9	and	and	CCONJ
ejpam-4030	19	10	appel	appel	NOUN
ejpam-4030	19	11	functions	function	NOUN
ejpam-4030	19	12	as	as	ADP
ejpam-4030	19	13	∗corresponding	∗corresponde	VERB
ejpam-4030	19	14	author	author	NOUN
ejpam-4030	19	15	.	.	PUNCT
ejpam-4030	20	1	doi	doi	NOUN
ejpam-4030	20	2	:	:	PUNCT
ejpam-4030	20	3	https://doi.org/10.29020/nybg.ejpam.v14i3.4030	https://doi.org/10.29020/nybg.ejpam.v14i3.4030	PROPN
ejpam-4030	20	4	email	email	NOUN
ejpam-4030	20	5	addresses	address	NOUN
ejpam-4030	20	6	:	:	PUNCT
ejpam-4030	21	1	milver@my.yorku.ca	milver@my.yorku.ca	NOUN
ejpam-4030	21	2	(	(	PUNCT
ejpam-4030	21	3	r.	r.	PROPN
ejpam-4030	21	4	reynolds	reynolds	PROPN
ejpam-4030	21	5	)	)	PUNCT
ejpam-4030	21	6	,	,	PUNCT
ejpam-4030	21	7	stauffer@yorku.ca	stauffer@yorku.ca	NOUN
ejpam-4030	21	8	(	(	PUNCT
ejpam-4030	21	9	a.	a.	NOUN
ejpam-4030	21	10	stauffer	stauffer	PROPN
ejpam-4030	21	11	)	)	PUNCT
ejpam-4030	21	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4030	22	1	788	788	NUM
ejpam-4030	22	2	©	©	PROPN
ejpam-4030	22	3	2021	2021	NUM
ejpam-4030	22	4	ejpam	ejpam	VERB
ejpam-4030	22	5	all	all	DET
ejpam-4030	22	6	rights	right	NOUN
ejpam-4030	22	7	reserved	reserve	VERB
ejpam-4030	22	8	.	.	PUNCT
ejpam-4030	23	1	r.	r.	PROPN
ejpam-4030	23	2	reynolds	reynolds	PROPN
ejpam-4030	23	3	,	,	PUNCT
ejpam-4030	23	4	a.	a.	PROPN
ejpam-4030	23	5	stauffer	stauffer	PROPN
ejpam-4030	23	6	/	/	SYM
ejpam-4030	23	7	eur	eur	PROPN
ejpam-4030	23	8	.	.	PUNCT
ejpam-4030	24	1	j.	j.	PROPN
ejpam-4030	24	2	pure	pure	PROPN
ejpam-4030	24	3	appl	appl	PROPN
ejpam-4030	24	4	.	.	PROPN
ejpam-4030	24	5	math	math	PROPN
ejpam-4030	24	6	,	,	PUNCT
ejpam-4030	24	7	14	14	NUM
ejpam-4030	24	8	(	(	PUNCT
ejpam-4030	24	9	3	3	NUM
ejpam-4030	24	10	)	)	PUNCT
ejpam-4030	24	11	(	(	PUNCT
ejpam-4030	24	12	2021	2021	NUM
ejpam-4030	24	13	)	)	PUNCT
ejpam-4030	24	14	,	,	PUNCT
ejpam-4030	24	15	788	788	NUM
ejpam-4030	24	16	-	-	SYM
ejpam-4030	24	17	802	802	NUM
ejpam-4030	24	18	789	789	NUM
ejpam-4030	24	19	well	well	NOUN
ejpam-4030	24	20	as	as	SCONJ
ejpam-4030	24	21	humbert	humbert	X
ejpam-4030	24	22	hypergeometric	hypergeometric	ADJ
ejpam-4030	24	23	functions	function	NOUN
ejpam-4030	24	24	of	of	ADP
ejpam-4030	24	25	two	two	NUM
ejpam-4030	24	26	variables	variable	NOUN
ejpam-4030	24	27	are	be	AUX
ejpam-4030	24	28	found	find	VERB
ejpam-4030	24	29	in	in	ADP
ejpam-4030	24	30	the	the	DET
ejpam-4030	24	31	work	work	NOUN
ejpam-4030	24	32	of	of	ADP
ejpam-4030	24	33	[	[	X
ejpam-4030	24	34	2	2	NUM
ejpam-4030	24	35	]	]	PUNCT
ejpam-4030	24	36	.	.	PUNCT
ejpam-4030	25	1	in	in	ADP
ejpam-4030	25	2	this	this	DET
ejpam-4030	25	3	work	work	NOUN
ejpam-4030	25	4	our	our	PRON
ejpam-4030	25	5	goal	goal	NOUN
ejpam-4030	25	6	is	be	AUX
ejpam-4030	25	7	to	to	PART
ejpam-4030	25	8	expand	expand	VERB
ejpam-4030	25	9	upon	upon	SCONJ
ejpam-4030	25	10	the	the	DET
ejpam-4030	25	11	current	current	ADJ
ejpam-4030	25	12	literature	literature	NOUN
ejpam-4030	25	13	of	of	ADP
ejpam-4030	25	14	definite	definite	ADJ
ejpam-4030	25	15	integrals	integral	NOUN
ejpam-4030	25	16	of	of	ADP
ejpam-4030	25	17	special	special	ADJ
ejpam-4030	25	18	functions	function	NOUN
ejpam-4030	25	19	by	by	ADP
ejpam-4030	25	20	providing	provide	VERB
ejpam-4030	25	21	a	a	DET
ejpam-4030	25	22	formal	formal	ADJ
ejpam-4030	25	23	derivation	derivation	NOUN
ejpam-4030	25	24	of	of	ADP
ejpam-4030	25	25	the	the	DET
ejpam-4030	25	26	definite	definite	ADJ
ejpam-4030	25	27	integral	integral	NOUN
ejpam-4030	25	28	of	of	ADP
ejpam-4030	25	29	the	the	DET
ejpam-4030	25	30	lerch	lerch	PROPN
ejpam-4030	25	31	function	function	PROPN
ejpam-4030	25	32	and	and	CCONJ
ejpam-4030	25	33	express	express	VERB
ejpam-4030	25	34	this	this	DET
ejpam-4030	25	35	integral	integral	ADJ
ejpam-4030	25	36	in	in	ADP
ejpam-4030	25	37	terms	term	NOUN
ejpam-4030	25	38	of	of	ADP
ejpam-4030	25	39	the	the	DET
ejpam-4030	25	40	lerch	lerch	PROPN
ejpam-4030	25	41	function	function	PROPN
ejpam-4030	25	42	.	.	PUNCT
ejpam-4030	26	1	it	it	PRON
ejpam-4030	26	2	is	be	AUX
ejpam-4030	26	3	our	our	PRON
ejpam-4030	26	4	hope	hope	NOUN
ejpam-4030	26	5	that	that	SCONJ
ejpam-4030	26	6	researches	research	NOUN
ejpam-4030	26	7	will	will	AUX
ejpam-4030	26	8	find	find	VERB
ejpam-4030	26	9	this	this	DET
ejpam-4030	26	10	new	new	ADJ
ejpam-4030	26	11	integral	integral	ADJ
ejpam-4030	26	12	formula	formula	NOUN
ejpam-4030	26	13	useful	useful	ADJ
ejpam-4030	26	14	for	for	ADP
ejpam-4030	26	15	current	current	ADJ
ejpam-4030	26	16	and	and	CCONJ
ejpam-4030	26	17	future	future	ADJ
ejpam-4030	26	18	research	research	NOUN
ejpam-4030	26	19	work	work	NOUN
ejpam-4030	26	20	where	where	SCONJ
ejpam-4030	26	21	applicable	applicable	ADJ
ejpam-4030	26	22	.	.	PUNCT
ejpam-4030	27	1	consequently	consequently	ADV
ejpam-4030	27	2	,	,	PUNCT
ejpam-4030	27	3	any	any	DET
ejpam-4030	27	4	new	new	ADJ
ejpam-4030	27	5	result	result	NOUN
ejpam-4030	27	6	on	on	ADP
ejpam-4030	27	7	the	the	DET
ejpam-4030	27	8	lerch	lerch	PROPN
ejpam-4030	27	9	function	function	NOUN
ejpam-4030	27	10	is	be	AUX
ejpam-4030	27	11	important	important	ADJ
ejpam-4030	27	12	because	because	SCONJ
ejpam-4030	27	13	of	of	ADP
ejpam-4030	27	14	its	its	PRON
ejpam-4030	27	15	many	many	ADJ
ejpam-4030	27	16	applications	application	NOUN
ejpam-4030	27	17	in	in	ADP
ejpam-4030	27	18	applied	applied	ADJ
ejpam-4030	27	19	and	and	CCONJ
ejpam-4030	27	20	pure	pure	ADJ
ejpam-4030	27	21	mathematics	mathematic	NOUN
ejpam-4030	27	22	.	.	PUNCT
ejpam-4030	28	1	2	2	X
ejpam-4030	28	2	.	.	X
ejpam-4030	28	3	introduction	introduction	NOUN
ejpam-4030	28	4	in	in	ADP
ejpam-4030	28	5	the	the	DET
ejpam-4030	28	6	present	present	ADJ
ejpam-4030	28	7	work	work	NOUN
ejpam-4030	28	8	,	,	PUNCT
ejpam-4030	28	9	the	the	DET
ejpam-4030	28	10	authors	author	NOUN
ejpam-4030	28	11	used	use	VERB
ejpam-4030	28	12	their	their	PRON
ejpam-4030	28	13	contour	contour	NOUN
ejpam-4030	28	14	integral	integral	ADJ
ejpam-4030	28	15	method	method	NOUN
ejpam-4030	28	16	and	and	CCONJ
ejpam-4030	28	17	applied	apply	VERB
ejpam-4030	28	18	it	it	PRON
ejpam-4030	28	19	to	to	ADP
ejpam-4030	28	20	the	the	DET
ejpam-4030	28	21	lerch	lerch	PROPN
ejpam-4030	28	22	function	function	NOUN
ejpam-4030	28	23	to	to	PART
ejpam-4030	28	24	derive	derive	VERB
ejpam-4030	28	25	a	a	DET
ejpam-4030	28	26	definite	definite	ADJ
ejpam-4030	28	27	integral	integral	ADJ
ejpam-4030	28	28	and	and	CCONJ
ejpam-4030	28	29	expressed	express	VERB
ejpam-4030	28	30	its	its	PRON
ejpam-4030	28	31	closed	closed	ADJ
ejpam-4030	28	32	form	form	NOUN
ejpam-4030	28	33	in	in	ADP
ejpam-4030	28	34	terms	term	NOUN
ejpam-4030	28	35	of	of	ADP
ejpam-4030	28	36	a	a	DET
ejpam-4030	28	37	special	special	ADJ
ejpam-4030	28	38	function	function	NOUN
ejpam-4030	28	39	.	.	PUNCT
ejpam-4030	29	1	this	this	DET
ejpam-4030	29	2	derived	derive	VERB
ejpam-4030	29	3	integral	integral	ADJ
ejpam-4030	29	4	formula	formula	NOUN
ejpam-4030	29	5	was	be	AUX
ejpam-4030	29	6	then	then	ADV
ejpam-4030	29	7	used	use	VERB
ejpam-4030	29	8	to	to	PART
ejpam-4030	29	9	provide	provide	VERB
ejpam-4030	29	10	formal	formal	ADJ
ejpam-4030	29	11	derivations	derivation	NOUN
ejpam-4030	29	12	in	in	ADP
ejpam-4030	29	13	terms	term	NOUN
ejpam-4030	29	14	of	of	ADP
ejpam-4030	29	15	special	special	ADJ
ejpam-4030	29	16	functions	function	NOUN
ejpam-4030	29	17	and	and	CCONJ
ejpam-4030	29	18	fundamental	fundamental	ADJ
ejpam-4030	29	19	constants	constant	NOUN
ejpam-4030	29	20	.	.	PUNCT
ejpam-4030	30	1	the	the	DET
ejpam-4030	30	2	lerch	lerch	PROPN
ejpam-4030	30	3	function	function	PROPN
ejpam-4030	30	4	being	be	AUX
ejpam-4030	30	5	a	a	DET
ejpam-4030	30	6	special	special	ADJ
ejpam-4030	30	7	function	function	NOUN
ejpam-4030	30	8	has	have	VERB
ejpam-4030	30	9	the	the	DET
ejpam-4030	30	10	fundamental	fundamental	ADJ
ejpam-4030	30	11	property	property	NOUN
ejpam-4030	30	12	of	of	ADP
ejpam-4030	30	13	analytic	analytic	ADJ
ejpam-4030	30	14	continuation	continuation	NOUN
ejpam-4030	30	15	,	,	PUNCT
ejpam-4030	30	16	which	which	PRON
ejpam-4030	30	17	enables	enable	VERB
ejpam-4030	30	18	us	we	PRON
ejpam-4030	30	19	to	to	PART
ejpam-4030	30	20	widen	widen	VERB
ejpam-4030	30	21	the	the	DET
ejpam-4030	30	22	range	range	NOUN
ejpam-4030	30	23	of	of	ADP
ejpam-4030	30	24	evaluation	evaluation	NOUN
ejpam-4030	30	25	for	for	ADP
ejpam-4030	30	26	the	the	DET
ejpam-4030	30	27	parameters	parameter	NOUN
ejpam-4030	30	28	involved	involve	VERB
ejpam-4030	30	29	in	in	ADP
ejpam-4030	30	30	our	our	PRON
ejpam-4030	30	31	definite	definite	ADJ
ejpam-4030	30	32	integral	integral	ADJ
ejpam-4030	30	33	.	.	PUNCT
ejpam-4030	31	1	the	the	DET
ejpam-4030	31	2	lerch	lerch	PROPN
ejpam-4030	31	3	function	function	PROPN
ejpam-4030	31	4	is	be	AUX
ejpam-4030	31	5	a	a	DET
ejpam-4030	31	6	special	special	ADJ
ejpam-4030	31	7	function	function	NOUN
ejpam-4030	31	8	that	that	PRON
ejpam-4030	31	9	generalizes	generalize	VERB
ejpam-4030	31	10	the	the	DET
ejpam-4030	31	11	hurwitz	hurwitz	PROPN
ejpam-4030	31	12	zeta	zeta	PROPN
ejpam-4030	31	13	function	function	PROPN
ejpam-4030	31	14	,	,	PUNCT
ejpam-4030	31	15	the	the	DET
ejpam-4030	31	16	polylogarithms	polylogarithm	NOUN
ejpam-4030	31	17	,	,	PUNCT
ejpam-4030	31	18	and	and	CCONJ
ejpam-4030	31	19	so	so	ADV
ejpam-4030	31	20	many	many	ADJ
ejpam-4030	31	21	interesting	interesting	ADJ
ejpam-4030	31	22	and	and	CCONJ
ejpam-4030	31	23	important	important	ADJ
ejpam-4030	31	24	special	special	ADJ
ejpam-4030	31	25	functions	function	NOUN
ejpam-4030	31	26	.	.	PUNCT
ejpam-4030	32	1	the	the	DET
ejpam-4030	32	2	definite	definite	ADJ
ejpam-4030	32	3	integral	integral	ADJ
ejpam-4030	32	4	derived	derived	NOUN
ejpam-4030	32	5	in	in	ADP
ejpam-4030	32	6	this	this	DET
ejpam-4030	32	7	manuscript	manuscript	NOUN
ejpam-4030	32	8	is	be	AUX
ejpam-4030	32	9	given	give	VERB
ejpam-4030	32	10	by	by	ADP
ejpam-4030	32	11	∫	∫	PROPN
ejpam-4030	33	1	+	+	PROPN
ejpam-4030	33	2	∞	∞	PROPN
ejpam-4030	33	3	0	0	NUM
ejpam-4030	33	4	xa−1	xa−1	PROPN
ejpam-4030	33	5	logk	logk	PROPN
ejpam-4030	33	6	(	(	PUNCT
ejpam-4030	33	7	b	b	NOUN
ejpam-4030	33	8	x	x	X
ejpam-4030	33	9	)	)	PUNCT
ejpam-4030	33	10	φ(−cx	φ(−cx	ADJ
ejpam-4030	33	11	,	,	PUNCT
ejpam-4030	33	12	n	n	CCONJ
ejpam-4030	33	13	,	,	PUNCT
ejpam-4030	33	14	a)dx	a)dx	PROPN
ejpam-4030	33	15	=	=	PUNCT
ejpam-4030	33	16	eiπak!c−a(−2iπ)k+n+1φ	eiπak!c−a(−2iπ)k+n+1φ	PUNCT
ejpam-4030	33	17	(	(	PUNCT
ejpam-4030	33	18	e2iaπ,−k	e2iaπ,−k	NOUN
ejpam-4030	33	19	−	−	PROPN
ejpam-4030	33	20	n,−−i	n,−−i	NOUN
ejpam-4030	33	21	log(b)−i	log(b)−i	ADJ
ejpam-4030	33	22	log(c)−π2π	log(c)−π2π	NOUN
ejpam-4030	33	23	)	)	PUNCT
ejpam-4030	34	1	(	(	PUNCT
ejpam-4030	34	2	k	k	X
ejpam-4030	34	3	+	+	NOUN
ejpam-4030	34	4	n	n	CCONJ
ejpam-4030	34	5	)	)	PUNCT
ejpam-4030	34	6	!	!	PUNCT
ejpam-4030	35	1	(	(	PUNCT
ejpam-4030	35	2	1	1	X
ejpam-4030	35	3	)	)	PUNCT
ejpam-4030	35	4	where	where	SCONJ
ejpam-4030	35	5	the	the	DET
ejpam-4030	35	6	parameters	parameter	NOUN
ejpam-4030	35	7	k	k	PROPN
ejpam-4030	35	8	,	,	PUNCT
ejpam-4030	35	9	b	b	PROPN
ejpam-4030	35	10	and	and	CCONJ
ejpam-4030	35	11	a	a	PRON
ejpam-4030	35	12	are	be	AUX
ejpam-4030	35	13	general	general	ADJ
ejpam-4030	35	14	complex	complex	ADJ
ejpam-4030	35	15	numbers	number	NOUN
ejpam-4030	35	16	and	and	CCONJ
ejpam-4030	35	17	0	0	NUM
ejpam-4030	35	18	<	<	X
ejpam-4030	35	19	re(a	re(a	NOUN
ejpam-4030	35	20	)	)	PUNCT
ejpam-4030	35	21	<	<	X
ejpam-4030	35	22	1	1	NUM
ejpam-4030	35	23	,	,	PUNCT
ejpam-4030	35	24	c	c	PROPN
ejpam-4030	35	25	∈	∈	PROPN
ejpam-4030	35	26	r+	r+	NOUN
ejpam-4030	35	27	,	,	PUNCT
ejpam-4030	35	28	n	n	PROPN
ejpam-4030	35	29	∈	∈	PROPN
ejpam-4030	35	30	z−.	z−.	NOUN
ejpam-4030	35	31	this	this	DET
ejpam-4030	35	32	work	work	NOUN
ejpam-4030	35	33	is	be	AUX
ejpam-4030	35	34	important	important	ADJ
ejpam-4030	35	35	because	because	SCONJ
ejpam-4030	35	36	the	the	DET
ejpam-4030	35	37	authors	author	NOUN
ejpam-4030	35	38	were	be	AUX
ejpam-4030	35	39	unable	unable	ADJ
ejpam-4030	35	40	to	to	PART
ejpam-4030	35	41	find	find	VERB
ejpam-4030	35	42	similar	similar	ADJ
ejpam-4030	35	43	derivations	derivation	NOUN
ejpam-4030	35	44	in	in	ADP
ejpam-4030	35	45	the	the	DET
ejpam-4030	35	46	current	current	ADJ
ejpam-4030	35	47	literature	literature	NOUN
ejpam-4030	35	48	along	along	ADP
ejpam-4030	35	49	with	with	ADP
ejpam-4030	35	50	the	the	DET
ejpam-4030	35	51	many	many	ADJ
ejpam-4030	35	52	applications	application	NOUN
ejpam-4030	35	53	the	the	DET
ejpam-4030	35	54	lerch	lerch	PROPN
ejpam-4030	35	55	function	function	PROPN
ejpam-4030	35	56	has	have	VERB
ejpam-4030	35	57	in	in	ADP
ejpam-4030	35	58	applied	apply	VERB
ejpam-4030	35	59	and	and	CCONJ
ejpam-4030	35	60	pure	pure	ADJ
ejpam-4030	35	61	mathematics	mathematic	NOUN
ejpam-4030	35	62	.	.	PUNCT
ejpam-4030	36	1	the	the	DET
ejpam-4030	36	2	derivation	derivation	NOUN
ejpam-4030	36	3	of	of	ADP
ejpam-4030	36	4	the	the	DET
ejpam-4030	36	5	definite	definite	ADJ
ejpam-4030	36	6	integral	integral	NOUN
ejpam-4030	36	7	follows	follow	VERB
ejpam-4030	36	8	the	the	DET
ejpam-4030	36	9	method	method	NOUN
ejpam-4030	36	10	used	use	VERB
ejpam-4030	36	11	by	by	ADP
ejpam-4030	36	12	us	we	PRON
ejpam-4030	36	13	in	in	ADP
ejpam-4030	36	14	[	[	X
ejpam-4030	36	15	15	15	NUM
ejpam-4030	36	16	]	]	PUNCT
ejpam-4030	36	17	which	which	PRON
ejpam-4030	36	18	involves	involve	VERB
ejpam-4030	36	19	cauchy	cauchy	PROPN
ejpam-4030	36	20	’s	’s	PART
ejpam-4030	36	21	integral	integral	ADJ
ejpam-4030	36	22	formula	formula	NOUN
ejpam-4030	36	23	.	.	PUNCT
ejpam-4030	37	1	the	the	DET
ejpam-4030	37	2	generalized	generalized	ADJ
ejpam-4030	37	3	cauchy	cauchy	PROPN
ejpam-4030	37	4	’s	’s	PART
ejpam-4030	37	5	integral	integral	ADJ
ejpam-4030	37	6	formula	formula	NOUN
ejpam-4030	37	7	is	be	AUX
ejpam-4030	37	8	given	give	VERB
ejpam-4030	37	9	by	by	ADP
ejpam-4030	37	10	yk	yk	PROPN
ejpam-4030	37	11	k	k	PROPN
ejpam-4030	37	12	!	!	PUNCT
ejpam-4030	38	1	=	=	SYM
ejpam-4030	38	2	1	1	NUM
ejpam-4030	38	3	2πi	2πi	ADJ
ejpam-4030	38	4	∫	∫	PROPN
ejpam-4030	38	5	c	c	PROPN
ejpam-4030	38	6	ewy	ewy	PROPN
ejpam-4030	38	7	wk+1	wk+1	PROPN
ejpam-4030	38	8	dw	dw	PROPN
ejpam-4030	38	9	.	.	PUNCT
ejpam-4030	39	1	(	(	PUNCT
ejpam-4030	39	2	2	2	X
ejpam-4030	39	3	)	)	PUNCT
ejpam-4030	39	4	where	where	SCONJ
ejpam-4030	39	5	c	c	NOUN
ejpam-4030	39	6	is	be	AUX
ejpam-4030	39	7	in	in	ADP
ejpam-4030	39	8	general	general	ADJ
ejpam-4030	39	9	an	an	DET
ejpam-4030	39	10	open	open	ADJ
ejpam-4030	39	11	contour	contour	NOUN
ejpam-4030	39	12	in	in	ADP
ejpam-4030	39	13	the	the	DET
ejpam-4030	39	14	complex	complex	ADJ
ejpam-4030	39	15	plane	plane	NOUN
ejpam-4030	39	16	where	where	SCONJ
ejpam-4030	39	17	the	the	DET
ejpam-4030	39	18	bilinear	bilinear	NOUN
ejpam-4030	39	19	concomitant	concomitant	NOUN
ejpam-4030	40	1	[	[	X
ejpam-4030	40	2	15	15	NUM
ejpam-4030	40	3	]	]	PUNCT
ejpam-4030	40	4	.	.	PUNCT
ejpam-4030	41	1	this	this	DET
ejpam-4030	41	2	method	method	NOUN
ejpam-4030	41	3	involves	involve	VERB
ejpam-4030	41	4	using	use	VERB
ejpam-4030	41	5	a	a	DET
ejpam-4030	41	6	form	form	NOUN
ejpam-4030	41	7	of	of	ADP
ejpam-4030	41	8	equation	equation	NOUN
ejpam-4030	41	9	(	(	PUNCT
ejpam-4030	41	10	2	2	NUM
ejpam-4030	41	11	)	)	PUNCT
ejpam-4030	41	12	then	then	ADV
ejpam-4030	41	13	multiply	multiply	VERB
ejpam-4030	41	14	both	both	DET
ejpam-4030	41	15	sides	side	NOUN
ejpam-4030	41	16	by	by	ADP
ejpam-4030	41	17	a	a	DET
ejpam-4030	41	18	function	function	NOUN
ejpam-4030	41	19	,	,	PUNCT
ejpam-4030	41	20	then	then	ADV
ejpam-4030	41	21	take	take	VERB
ejpam-4030	41	22	a	a	DET
ejpam-4030	41	23	definite	definite	ADJ
ejpam-4030	41	24	integral	integral	NOUN
ejpam-4030	41	25	of	of	ADP
ejpam-4030	41	26	both	both	DET
ejpam-4030	41	27	sides	side	NOUN
ejpam-4030	41	28	.	.	PUNCT
ejpam-4030	42	1	this	this	PRON
ejpam-4030	42	2	yields	yield	VERB
ejpam-4030	42	3	a	a	DET
ejpam-4030	42	4	definite	definite	ADJ
ejpam-4030	42	5	integral	integral	ADJ
ejpam-4030	42	6	in	in	ADP
ejpam-4030	42	7	terms	term	NOUN
ejpam-4030	42	8	of	of	ADP
ejpam-4030	42	9	a	a	DET
ejpam-4030	42	10	contour	contour	NOUN
ejpam-4030	42	11	integral	integral	NOUN
ejpam-4030	42	12	.	.	PUNCT
ejpam-4030	43	1	a	a	DET
ejpam-4030	43	2	second	second	ADJ
ejpam-4030	43	3	contour	contour	NOUN
ejpam-4030	43	4	integral	integral	NOUN
ejpam-4030	43	5	is	be	AUX
ejpam-4030	43	6	derived	derive	VERB
ejpam-4030	43	7	by	by	ADP
ejpam-4030	43	8	multiplying	multiply	VERB
ejpam-4030	43	9	equation	equation	NOUN
ejpam-4030	43	10	(	(	PUNCT
ejpam-4030	43	11	2	2	NUM
ejpam-4030	43	12	)	)	PUNCT
ejpam-4030	43	13	by	by	ADP
ejpam-4030	43	14	a	a	DET
ejpam-4030	43	15	function	function	NOUN
ejpam-4030	43	16	and	and	CCONJ
ejpam-4030	43	17	performing	perform	VERB
ejpam-4030	43	18	some	some	DET
ejpam-4030	43	19	substitutions	substitution	NOUN
ejpam-4030	43	20	so	so	SCONJ
ejpam-4030	43	21	that	that	SCONJ
ejpam-4030	43	22	the	the	DET
ejpam-4030	43	23	contour	contour	NOUN
ejpam-4030	43	24	integrals	integral	NOUN
ejpam-4030	43	25	are	be	AUX
ejpam-4030	43	26	the	the	DET
ejpam-4030	43	27	same	same	ADJ
ejpam-4030	43	28	.	.	PUNCT
ejpam-4030	44	1	r.	r.	PROPN
ejpam-4030	44	2	reynolds	reynolds	PROPN
ejpam-4030	44	3	,	,	PUNCT
ejpam-4030	44	4	a.	a.	PROPN
ejpam-4030	44	5	stauffer	stauffer	PROPN
ejpam-4030	44	6	/	/	SYM
ejpam-4030	44	7	eur	eur	PROPN
ejpam-4030	44	8	.	.	PUNCT
ejpam-4030	45	1	j.	j.	PROPN
ejpam-4030	45	2	pure	pure	PROPN
ejpam-4030	45	3	appl	appl	PROPN
ejpam-4030	45	4	.	.	PROPN
ejpam-4030	45	5	math	math	PROPN
ejpam-4030	45	6	,	,	PUNCT
ejpam-4030	45	7	14	14	NUM
ejpam-4030	45	8	(	(	PUNCT
ejpam-4030	45	9	3	3	NUM
ejpam-4030	45	10	)	)	PUNCT
ejpam-4030	45	11	(	(	PUNCT
ejpam-4030	45	12	2021	2021	NUM
ejpam-4030	45	13	)	)	PUNCT
ejpam-4030	45	14	,	,	PUNCT
ejpam-4030	45	15	788	788	NUM
ejpam-4030	45	16	-	-	SYM
ejpam-4030	45	17	802	802	NUM
ejpam-4030	45	18	790	790	NUM
ejpam-4030	45	19	3	3	NUM
ejpam-4030	45	20	.	.	PUNCT
ejpam-4030	46	1	definite	definite	ADJ
ejpam-4030	46	2	integral	integral	ADJ
ejpam-4030	46	3	of	of	ADP
ejpam-4030	46	4	the	the	DET
ejpam-4030	46	5	contour	contour	NOUN
ejpam-4030	46	6	integral	integral	NOUN
ejpam-4030	46	7	we	we	PRON
ejpam-4030	46	8	use	use	VERB
ejpam-4030	46	9	the	the	DET
ejpam-4030	46	10	method	method	NOUN
ejpam-4030	46	11	in	in	ADP
ejpam-4030	46	12	[	[	X
ejpam-4030	46	13	15	15	NUM
ejpam-4030	46	14	]	]	PUNCT
ejpam-4030	46	15	.	.	PUNCT
ejpam-4030	47	1	the	the	DET
ejpam-4030	47	2	variable	variable	NOUN
ejpam-4030	47	3	of	of	ADP
ejpam-4030	47	4	integration	integration	NOUN
ejpam-4030	47	5	in	in	ADP
ejpam-4030	47	6	the	the	DET
ejpam-4030	47	7	contour	contour	NOUN
ejpam-4030	47	8	integral	integral	NOUN
ejpam-4030	47	9	is	be	AUX
ejpam-4030	47	10	t	t	NOUN
ejpam-4030	47	11	=	=	PUNCT
ejpam-4030	47	12	w	w	PROPN
ejpam-4030	47	13	−	−	PROPN
ejpam-4030	47	14	a.	a.	NOUN
ejpam-4030	47	15	the	the	DET
ejpam-4030	47	16	cut	cut	NOUN
ejpam-4030	47	17	and	and	CCONJ
ejpam-4030	47	18	contour	contour	NOUN
ejpam-4030	47	19	are	be	AUX
ejpam-4030	47	20	in	in	ADP
ejpam-4030	47	21	the	the	DET
ejpam-4030	47	22	second	second	ADJ
ejpam-4030	47	23	quadrant	quadrant	NOUN
ejpam-4030	47	24	of	of	ADP
ejpam-4030	47	25	the	the	DET
ejpam-4030	47	26	complex	complex	ADJ
ejpam-4030	47	27	z	z	NOUN
ejpam-4030	47	28	-	-	NOUN
ejpam-4030	47	29	plane	plane	NOUN
ejpam-4030	47	30	.	.	PUNCT
ejpam-4030	48	1	the	the	DET
ejpam-4030	48	2	cut	cut	NOUN
ejpam-4030	48	3	approaches	approach	VERB
ejpam-4030	48	4	the	the	DET
ejpam-4030	48	5	origin	origin	NOUN
ejpam-4030	48	6	from	from	ADP
ejpam-4030	48	7	the	the	DET
ejpam-4030	48	8	interior	interior	NOUN
ejpam-4030	48	9	of	of	ADP
ejpam-4030	48	10	the	the	DET
ejpam-4030	48	11	second	second	ADJ
ejpam-4030	48	12	quadrant	quadrant	NOUN
ejpam-4030	48	13	and	and	CCONJ
ejpam-4030	48	14	the	the	DET
ejpam-4030	48	15	contour	contour	NOUN
ejpam-4030	48	16	goes	go	VERB
ejpam-4030	48	17	round	round	ADP
ejpam-4030	48	18	the	the	DET
ejpam-4030	48	19	origin	origin	NOUN
ejpam-4030	48	20	with	with	ADP
ejpam-4030	48	21	zero	zero	NUM
ejpam-4030	48	22	radius	radius	NOUN
ejpam-4030	48	23	and	and	CCONJ
ejpam-4030	48	24	is	be	AUX
ejpam-4030	48	25	on	on	ADP
ejpam-4030	48	26	opposite	opposite	ADJ
ejpam-4030	48	27	sides	side	NOUN
ejpam-4030	48	28	of	of	ADP
ejpam-4030	48	29	the	the	DET
ejpam-4030	48	30	cut	cut	NOUN
ejpam-4030	48	31	.	.	PUNCT
ejpam-4030	49	1	using	use	VERB
ejpam-4030	49	2	equation	equation	NOUN
ejpam-4030	49	3	(	(	PUNCT
ejpam-4030	49	4	2	2	X
ejpam-4030	49	5	)	)	PUNCT
ejpam-4030	49	6	we	we	PRON
ejpam-4030	49	7	replace	replace	VERB
ejpam-4030	49	8	y	y	NOUN
ejpam-4030	49	9	by	by	ADP
ejpam-4030	49	10	1	1	NUM
ejpam-4030	49	11	/	/	SYM
ejpam-4030	49	12	x+	x+	ADJ
ejpam-4030	49	13	log(b	log(b	X
ejpam-4030	49	14	)	)	PUNCT
ejpam-4030	49	15	then	then	ADV
ejpam-4030	49	16	multiply	multiply	VERB
ejpam-4030	49	17	by	by	ADP
ejpam-4030	49	18	xa−1φ(−cx	xa−1φ(−cx	NUM
ejpam-4030	49	19	,	,	PUNCT
ejpam-4030	49	20	n	n	CCONJ
ejpam-4030	49	21	,	,	PUNCT
ejpam-4030	49	22	a	a	PRON
ejpam-4030	49	23	)	)	PUNCT
ejpam-4030	49	24	.	.	PUNCT
ejpam-4030	50	1	next	next	ADV
ejpam-4030	50	2	we	we	PRON
ejpam-4030	50	3	take	take	VERB
ejpam-4030	50	4	the	the	DET
ejpam-4030	50	5	infinite	infinite	ADJ
ejpam-4030	50	6	integral	integral	ADJ
ejpam-4030	50	7	over	over	ADP
ejpam-4030	50	8	x	x	PUNCT
ejpam-4030	50	9	∈	∈	PROPN
ejpam-4030	50	10	[	[	X
ejpam-4030	50	11	0,+∞	0,+∞	NUM
ejpam-4030	50	12	)	)	PUNCT
ejpam-4030	50	13	to	to	PART
ejpam-4030	50	14	get	get	VERB
ejpam-4030	50	15	1	1	NUM
ejpam-4030	50	16	k	k	NOUN
ejpam-4030	50	17	!	!	PUNCT
ejpam-4030	50	18	∫	∫	PROPN
ejpam-4030	51	1	+	+	CCONJ
ejpam-4030	51	2	∞	∞	PROPN
ejpam-4030	51	3	0	0	NUM
ejpam-4030	51	4	xa−1	xa−1	PROPN
ejpam-4030	51	5	logk	logk	PROPN
ejpam-4030	51	6	(	(	PUNCT
ejpam-4030	51	7	b	b	NOUN
ejpam-4030	51	8	x	x	X
ejpam-4030	51	9	)	)	PUNCT
ejpam-4030	51	10	φ(−cx	φ(−cx	ADJ
ejpam-4030	51	11	,	,	PUNCT
ejpam-4030	51	12	n	n	CCONJ
ejpam-4030	51	13	,	,	PUNCT
ejpam-4030	51	14	a)dx	a)dx	NOUN
ejpam-4030	51	15	=	=	SYM
ejpam-4030	51	16	1	1	NUM
ejpam-4030	51	17	2πi	2πi	NOUN
ejpam-4030	51	18	∫	∫	PROPN
ejpam-4030	52	1	+	+	NUM
ejpam-4030	52	2	∞	∞	PROPN
ejpam-4030	52	3	0	0	NUM
ejpam-4030	52	4	∫	∫	PROPN
ejpam-4030	52	5	c	c	PROPN
ejpam-4030	52	6	bww−k−1xa−w−1φ(−cx	bww−k−1xa−w−1φ(−cx	PROPN
ejpam-4030	52	7	,	,	PUNCT
ejpam-4030	52	8	n	n	CCONJ
ejpam-4030	52	9	,	,	PUNCT
ejpam-4030	52	10	a)dwdx	a)dwdx	X
ejpam-4030	52	11	=	=	SYM
ejpam-4030	53	1	1	1	NUM
ejpam-4030	53	2	2πi	2πi	NOUN
ejpam-4030	53	3	∫	∫	PROPN
ejpam-4030	53	4	c	c	PROPN
ejpam-4030	53	5	∫	∫	PROPN
ejpam-4030	54	1	+	+	NUM
ejpam-4030	54	2	∞	∞	PROPN
ejpam-4030	54	3	0	0	X
ejpam-4030	54	4	bww−k−1xa−w−1φ(−cx	bww−k−1xa−w−1φ(−cx	PROPN
ejpam-4030	54	5	,	,	PUNCT
ejpam-4030	54	6	n	n	CCONJ
ejpam-4030	54	7	,	,	PUNCT
ejpam-4030	54	8	a)dxdw	a)dxdw	PROPN
ejpam-4030	54	9	=	=	SYM
ejpam-4030	54	10	1	1	NUM
ejpam-4030	54	11	2πi	2πi	NOUN
ejpam-4030	54	12	∫	∫	PROPN
ejpam-4030	55	1	c	c	PROPN
ejpam-4030	55	2	πbwcw−a	πbwcw−a	NOUN
ejpam-4030	55	3	csc(π(a−	csc(π(a−	NOUN
ejpam-4030	55	4	w))w−k−n−1dw	w))w−k−n−1dw	NUM
ejpam-4030	55	5	(	(	PUNCT
ejpam-4030	55	6	3	3	NUM
ejpam-4030	55	7	)	)	PUNCT
ejpam-4030	55	8	where	where	SCONJ
ejpam-4030	55	9	−1	−1	NOUN
ejpam-4030	55	10	<	<	X
ejpam-4030	55	11	re(a	re(a	NUM
ejpam-4030	55	12	−	−	PROPN
ejpam-4030	55	13	w	w	NOUN
ejpam-4030	55	14	)	)	PUNCT
ejpam-4030	55	15	<	<	X
ejpam-4030	55	16	0	0	X
ejpam-4030	55	17	.	.	PUNCT
ejpam-4030	55	18	using	use	VERB
ejpam-4030	55	19	equation	equation	NOUN
ejpam-4030	55	20	(	(	PUNCT
ejpam-4030	55	21	9.550	9.550	NUM
ejpam-4030	55	22	)	)	PUNCT
ejpam-4030	55	23	we	we	PRON
ejpam-4030	55	24	multiply	multiply	VERB
ejpam-4030	55	25	both	both	DET
ejpam-4030	55	26	sides	side	NOUN
ejpam-4030	55	27	by	by	ADP
ejpam-4030	55	28	xb−1	xb−1	PROPN
ejpam-4030	55	29	and	and	CCONJ
ejpam-4030	55	30	integrate	integrate	VERB
ejpam-4030	55	31	over	over	ADP
ejpam-4030	55	32	x	x	PUNCT
ejpam-4030	55	33	∈	∈	PROPN
ejpam-4030	56	1	[	[	X
ejpam-4030	56	2	0,+∞	0,+∞	NUM
ejpam-4030	56	3	)	)	PUNCT
ejpam-4030	57	1	and	and	CCONJ
ejpam-4030	57	2	using	use	VERB
ejpam-4030	57	3	equation	equation	NOUN
ejpam-4030	57	4	(	(	PUNCT
ejpam-4030	57	5	3.194.4	3.194.4	NUM
ejpam-4030	57	6	)	)	PUNCT
ejpam-4030	57	7	in	in	ADP
ejpam-4030	57	8	[	[	X
ejpam-4030	57	9	17	17	NUM
ejpam-4030	57	10	]	]	PUNCT
ejpam-4030	57	11	.	.	PUNCT
ejpam-4030	58	1	we	we	PRON
ejpam-4030	58	2	are	be	AUX
ejpam-4030	58	3	able	able	ADJ
ejpam-4030	58	4	to	to	PART
ejpam-4030	58	5	switch	switch	VERB
ejpam-4030	58	6	the	the	DET
ejpam-4030	58	7	order	order	NOUN
ejpam-4030	58	8	of	of	ADP
ejpam-4030	58	9	integration	integration	NOUN
ejpam-4030	58	10	over	over	ADP
ejpam-4030	58	11	z	z	PROPN
ejpam-4030	58	12	,	,	PUNCT
ejpam-4030	58	13	x	x	PUNCT
ejpam-4030	58	14	and	and	CCONJ
ejpam-4030	58	15	y	y	PROPN
ejpam-4030	58	16	using	use	VERB
ejpam-4030	58	17	fubini	fubini	NOUN
ejpam-4030	58	18	’s	’s	PART
ejpam-4030	58	19	theorem	theorem	NOUN
ejpam-4030	58	20	since	since	SCONJ
ejpam-4030	58	21	the	the	DET
ejpam-4030	58	22	integrand	integrand	NOUN
ejpam-4030	58	23	is	be	AUX
ejpam-4030	58	24	of	of	ADP
ejpam-4030	58	25	bounded	bounded	ADJ
ejpam-4030	58	26	measure	measure	NOUN
ejpam-4030	58	27	over	over	ADP
ejpam-4030	58	28	the	the	DET
ejpam-4030	58	29	space	space	NOUN
ejpam-4030	58	30	c	c	NOUN
ejpam-4030	58	31	×	×	NOUN
ejpam-4030	59	1	[	[	X
ejpam-4030	59	2	0,+∞	0,+∞	NUM
ejpam-4030	59	3	)	)	PUNCT
ejpam-4030	59	4	.	.	PUNCT
ejpam-4030	60	1	4	4	X
ejpam-4030	60	2	.	.	X
ejpam-4030	60	3	the	the	DET
ejpam-4030	60	4	lerch	lerch	PROPN
ejpam-4030	60	5	function	function	NOUN
ejpam-4030	60	6	we	we	PRON
ejpam-4030	60	7	use	use	VERB
ejpam-4030	60	8	(	(	PUNCT
ejpam-4030	60	9	9.550	9.550	NUM
ejpam-4030	60	10	)	)	PUNCT
ejpam-4030	60	11	and	and	CCONJ
ejpam-4030	60	12	(	(	PUNCT
ejpam-4030	60	13	9.556	9.556	NUM
ejpam-4030	60	14	)	)	PUNCT
ejpam-4030	60	15	in	in	ADP
ejpam-4030	60	16	[	[	X
ejpam-4030	60	17	17	17	NUM
ejpam-4030	60	18	]	]	PUNCT
ejpam-4030	60	19	where	where	SCONJ
ejpam-4030	60	20	φ(z	φ(z	PROPN
ejpam-4030	60	21	,	,	PUNCT
ejpam-4030	60	22	s	s	NOUN
ejpam-4030	60	23	,	,	PUNCT
ejpam-4030	60	24	v	v	NOUN
ejpam-4030	60	25	)	)	PUNCT
ejpam-4030	60	26	is	be	AUX
ejpam-4030	60	27	the	the	DET
ejpam-4030	60	28	lerch	lerch	PROPN
ejpam-4030	60	29	function	function	NOUN
ejpam-4030	60	30	which	which	PRON
ejpam-4030	60	31	is	be	AUX
ejpam-4030	60	32	a	a	DET
ejpam-4030	60	33	generalization	generalization	NOUN
ejpam-4030	60	34	of	of	ADP
ejpam-4030	60	35	the	the	DET
ejpam-4030	60	36	hurwitz	hurwitz	PROPN
ejpam-4030	60	37	zeta	zeta	PROPN
ejpam-4030	60	38	ζ(s	ζ(s	PROPN
ejpam-4030	60	39	,	,	PUNCT
ejpam-4030	60	40	v	v	NOUN
ejpam-4030	60	41	)	)	PUNCT
ejpam-4030	60	42	and	and	CCONJ
ejpam-4030	60	43	polylogarithm	polylogarithm	PROPN
ejpam-4030	60	44	functions	function	NOUN
ejpam-4030	60	45	lin(z	lin(z	PROPN
ejpam-4030	60	46	)	)	PUNCT
ejpam-4030	60	47	.	.	PUNCT
ejpam-4030	61	1	the	the	DET
ejpam-4030	61	2	lerch	lerch	PROPN
ejpam-4030	61	3	function	function	PROPN
ejpam-4030	61	4	has	have	VERB
ejpam-4030	61	5	a	a	DET
ejpam-4030	61	6	series	series	NOUN
ejpam-4030	61	7	representation	representation	NOUN
ejpam-4030	61	8	given	give	VERB
ejpam-4030	61	9	by	by	ADP
ejpam-4030	61	10	φ(z	φ(z	PROPN
ejpam-4030	61	11	,	,	PUNCT
ejpam-4030	61	12	s	s	NOUN
ejpam-4030	61	13	,	,	PUNCT
ejpam-4030	61	14	v	v	NOUN
ejpam-4030	61	15	)	)	PUNCT
ejpam-4030	61	16	=	=	PUNCT
ejpam-4030	62	1	+	+	ADP
ejpam-4030	62	2	∞∑	∞∑	NUM
ejpam-4030	62	3	n=0	n=0	NUM
ejpam-4030	62	4	(	(	PUNCT
ejpam-4030	62	5	v	v	NOUN
ejpam-4030	62	6	+	+	PRON
ejpam-4030	62	7	n)−szn	n)−szn	NUM
ejpam-4030	62	8	(	(	PUNCT
ejpam-4030	62	9	4	4	NUM
ejpam-4030	62	10	)	)	PUNCT
ejpam-4030	62	11	where	where	SCONJ
ejpam-4030	62	12	|z|	|z|	NOUN
ejpam-4030	62	13	<	<	X
ejpam-4030	62	14	1	1	NUM
ejpam-4030	62	15	,	,	PUNCT
ejpam-4030	62	16	v	v	NOUN
ejpam-4030	62	17	6=	6=	ADP
ejpam-4030	62	18	0,−1	0,−1	PROPN
ejpam-4030	62	19	,	,	PUNCT
ejpam-4030	62	20	..	..	PUNCT
ejpam-4030	62	21	and	and	CCONJ
ejpam-4030	62	22	is	be	AUX
ejpam-4030	62	23	continued	continue	VERB
ejpam-4030	62	24	analytically	analytically	ADV
ejpam-4030	62	25	by	by	ADP
ejpam-4030	62	26	its	its	PRON
ejpam-4030	62	27	integral	integral	ADJ
ejpam-4030	62	28	representation	representation	NOUN
ejpam-4030	62	29	given	give	VERB
ejpam-4030	62	30	by	by	ADP
ejpam-4030	62	31	φ(z	φ(z	PROPN
ejpam-4030	62	32	,	,	PUNCT
ejpam-4030	62	33	s	s	NOUN
ejpam-4030	62	34	,	,	PUNCT
ejpam-4030	62	35	v	v	NOUN
ejpam-4030	62	36	)	)	PUNCT
ejpam-4030	62	37	=	=	SYM
ejpam-4030	62	38	1	1	NUM
ejpam-4030	62	39	γ(s	γ(	NOUN
ejpam-4030	62	40	)	)	PUNCT
ejpam-4030	62	41	∫	∫	PROPN
ejpam-4030	63	1	+	+	PROPN
ejpam-4030	63	2	∞	∞	PROPN
ejpam-4030	63	3	0	0	SYM
ejpam-4030	63	4	ts−1e−vt	ts−1e−vt	NOUN
ejpam-4030	63	5	1−	1−	NUM
ejpam-4030	64	1	ze−t	ze−t	NOUN
ejpam-4030	64	2	dt	dt	NOUN
ejpam-4030	65	1	=	=	SYM
ejpam-4030	65	2	1	1	NUM
ejpam-4030	65	3	γ(s	γ(s	PROPN
ejpam-4030	65	4	)	)	PUNCT
ejpam-4030	65	5	∫	∫	PROPN
ejpam-4030	66	1	+	+	PROPN
ejpam-4030	66	2	∞	∞	PROPN
ejpam-4030	66	3	0	0	NUM
ejpam-4030	67	1	ts−1e−(v−1)t	ts−1e−(v−1)t	PROPN
ejpam-4030	67	2	et	et	NOUN
ejpam-4030	67	3	−	−	NOUN
ejpam-4030	67	4	z	z	NOUN
ejpam-4030	67	5	dt	dt	X
ejpam-4030	67	6	(	(	PUNCT
ejpam-4030	67	7	5	5	NUM
ejpam-4030	67	8	)	)	PUNCT
ejpam-4030	67	9	where	where	SCONJ
ejpam-4030	67	10	re(v	re(v	NOUN
ejpam-4030	67	11	)	)	PUNCT
ejpam-4030	67	12	>	>	X
ejpam-4030	67	13	0	0	NUM
ejpam-4030	67	14	,	,	PUNCT
ejpam-4030	67	15	or	or	CCONJ
ejpam-4030	67	16	|z|	|z|	VERB
ejpam-4030	67	17	≤	≤	NUM
ejpam-4030	67	18	1	1	NUM
ejpam-4030	67	19	,	,	PUNCT
ejpam-4030	67	20	z	z	NOUN
ejpam-4030	67	21	6=	6=	NUM
ejpam-4030	67	22	1	1	NUM
ejpam-4030	67	23	,	,	PUNCT
ejpam-4030	67	24	re(s	re(s	ADJ
ejpam-4030	67	25	)	)	PUNCT
ejpam-4030	67	26	>	>	X
ejpam-4030	67	27	0	0	NUM
ejpam-4030	67	28	,	,	PUNCT
ejpam-4030	67	29	or	or	CCONJ
ejpam-4030	67	30	z	z	NOUN
ejpam-4030	67	31	=	=	SYM
ejpam-4030	67	32	1	1	NUM
ejpam-4030	67	33	,	,	PUNCT
ejpam-4030	67	34	re(s	re(s	ADJ
ejpam-4030	67	35	)	)	PUNCT
ejpam-4030	67	36	>	>	X
ejpam-4030	68	1	1	1	NUM
ejpam-4030	68	2	.	.	X
ejpam-4030	68	3	5	5	NUM
ejpam-4030	68	4	.	.	X
ejpam-4030	68	5	infinite	infinite	ADJ
ejpam-4030	68	6	sum	sum	NOUN
ejpam-4030	68	7	of	of	ADP
ejpam-4030	68	8	the	the	DET
ejpam-4030	68	9	contour	contour	NOUN
ejpam-4030	68	10	integral	integral	NOUN
ejpam-4030	68	11	in	in	ADP
ejpam-4030	68	12	this	this	DET
ejpam-4030	68	13	section	section	NOUN
ejpam-4030	68	14	we	we	PRON
ejpam-4030	68	15	will	will	AUX
ejpam-4030	68	16	again	again	ADV
ejpam-4030	68	17	use	use	VERB
ejpam-4030	68	18	cauchy	cauchy	NOUN
ejpam-4030	68	19	’s	’s	PART
ejpam-4030	68	20	integral	integral	ADJ
ejpam-4030	68	21	formula	formula	NOUN
ejpam-4030	68	22	(	(	PUNCT
ejpam-4030	68	23	2	2	NUM
ejpam-4030	68	24	)	)	PUNCT
ejpam-4030	68	25	and	and	CCONJ
ejpam-4030	68	26	take	take	VERB
ejpam-4030	68	27	the	the	DET
ejpam-4030	68	28	infinite	infinite	ADJ
ejpam-4030	68	29	sum	sum	NOUN
ejpam-4030	68	30	to	to	PART
ejpam-4030	68	31	derive	derive	VERB
ejpam-4030	68	32	equivalent	equivalent	ADJ
ejpam-4030	68	33	sum	sum	NOUN
ejpam-4030	68	34	representations	representation	NOUN
ejpam-4030	68	35	for	for	ADP
ejpam-4030	68	36	the	the	DET
ejpam-4030	68	37	contour	contour	NOUN
ejpam-4030	68	38	integrals	integral	NOUN
ejpam-4030	68	39	.	.	PUNCT
ejpam-4030	69	1	we	we	PRON
ejpam-4030	69	2	proceed	proceed	VERB
ejpam-4030	69	3	using	use	VERB
ejpam-4030	69	4	r.	r.	PROPN
ejpam-4030	69	5	reynolds	reynolds	PROPN
ejpam-4030	69	6	,	,	PUNCT
ejpam-4030	69	7	a.	a.	PROPN
ejpam-4030	69	8	stauffer	stauffer	PROPN
ejpam-4030	69	9	/	/	SYM
ejpam-4030	69	10	eur	eur	PROPN
ejpam-4030	69	11	.	.	PUNCT
ejpam-4030	70	1	j.	j.	PROPN
ejpam-4030	70	2	pure	pure	PROPN
ejpam-4030	70	3	appl	appl	PROPN
ejpam-4030	70	4	.	.	PROPN
ejpam-4030	70	5	math	math	PROPN
ejpam-4030	70	6	,	,	PUNCT
ejpam-4030	70	7	14	14	NUM
ejpam-4030	70	8	(	(	PUNCT
ejpam-4030	70	9	3	3	NUM
ejpam-4030	70	10	)	)	PUNCT
ejpam-4030	70	11	(	(	PUNCT
ejpam-4030	70	12	2021	2021	NUM
ejpam-4030	70	13	)	)	PUNCT
ejpam-4030	70	14	,	,	PUNCT
ejpam-4030	70	15	788	788	NUM
ejpam-4030	70	16	-	-	SYM
ejpam-4030	70	17	802	802	NUM
ejpam-4030	70	18	791	791	NUM
ejpam-4030	70	19	equation	equation	NOUN
ejpam-4030	70	20	(	(	PUNCT
ejpam-4030	70	21	2	2	NUM
ejpam-4030	70	22	)	)	PUNCT
ejpam-4030	70	23	and	and	CCONJ
ejpam-4030	70	24	replace	replace	VERB
ejpam-4030	70	25	y	y	PROPN
ejpam-4030	70	26	by	by	ADP
ejpam-4030	70	27	log(b	log(b	NOUN
ejpam-4030	70	28	)	)	PUNCT
ejpam-4030	70	29	+	+	SYM
ejpam-4030	70	30	log(c	log(c	PROPN
ejpam-4030	70	31	)	)	PUNCT
ejpam-4030	70	32	+	+	CCONJ
ejpam-4030	70	33	iπt(2y	iπt(2y	NOUN
ejpam-4030	70	34	+	+	CCONJ
ejpam-4030	70	35	1	1	X
ejpam-4030	70	36	)	)	PUNCT
ejpam-4030	70	37	and	and	CCONJ
ejpam-4030	70	38	multiply	multiply	VERB
ejpam-4030	70	39	both	both	DET
ejpam-4030	70	40	sides	side	NOUN
ejpam-4030	70	41	by	by	ADP
ejpam-4030	70	42	−2iπc−ae2iπay+iπa	−2iπc−ae2iπay+iπa	PUNCT
ejpam-4030	70	43	and	and	CCONJ
ejpam-4030	70	44	set	set	VERB
ejpam-4030	70	45	t	t	NOUN
ejpam-4030	70	46	=	=	SYM
ejpam-4030	70	47	−1	−1	NOUN
ejpam-4030	70	48	and	and	CCONJ
ejpam-4030	70	49	replace	replace	VERB
ejpam-4030	70	50	k	k	PROPN
ejpam-4030	70	51	by	by	ADP
ejpam-4030	70	52	k	k	PROPN
ejpam-4030	70	53	+	+	CCONJ
ejpam-4030	70	54	n	n	ADV
ejpam-4030	70	55	simplifying	simplify	VERB
ejpam-4030	70	56	to	to	PART
ejpam-4030	70	57	get	get	VERB
ejpam-4030	70	58	−	−	PROPN
ejpam-4030	70	59	2iπc−aeiπa(2y+1)(−i)k+n(i	2iπc−aeiπa(2y+1)(−i)k+n(i	PROPN
ejpam-4030	70	60	log(b	log(b	PROPN
ejpam-4030	70	61	)	)	PUNCT
ejpam-4030	71	1	+	+	CCONJ
ejpam-4030	71	2	i	i	PRON
ejpam-4030	71	3	log(c	log(c	VERB
ejpam-4030	71	4	)	)	PUNCT
ejpam-4030	72	1	+	+	NUM
ejpam-4030	72	2	2πy	2πy	NOUN
ejpam-4030	72	3	+	+	CCONJ
ejpam-4030	72	4	π)k+n	π)k+n	NOUN
ejpam-4030	72	5	(	(	PUNCT
ejpam-4030	72	6	k	k	NOUN
ejpam-4030	72	7	+	+	PROPN
ejpam-4030	72	8	n	n	CCONJ
ejpam-4030	72	9	)	)	PUNCT
ejpam-4030	72	10	!	!	PUNCT
ejpam-4030	73	1	=	=	PUNCT
ejpam-4030	74	1	−	−	PROPN
ejpam-4030	74	2	1	1	NUM
ejpam-4030	74	3	2πi	2πi	NOUN
ejpam-4030	74	4	∫	∫	PROPN
ejpam-4030	74	5	c	c	PROPN
ejpam-4030	74	6	2iπbwcw−aeiπ(2y+1)(a−w)w−k−n−1dw	2iπbwcw−aeiπ(2y+1)(a−w)w−k−n−1dw	PROPN
ejpam-4030	74	7	(	(	PUNCT
ejpam-4030	74	8	6	6	NUM
ejpam-4030	74	9	)	)	PUNCT
ejpam-4030	74	10	next	next	ADV
ejpam-4030	74	11	take	take	VERB
ejpam-4030	74	12	the	the	DET
ejpam-4030	74	13	infinite	infinite	NOUN
ejpam-4030	74	14	over	over	ADP
ejpam-4030	74	15	y	y	PROPN
ejpam-4030	74	16	∈	∈	PROPN
ejpam-4030	75	1	[	[	X
ejpam-4030	75	2	0,+∞	0,+∞	NUM
ejpam-4030	75	3	)	)	PUNCT
ejpam-4030	75	4	and	and	CCONJ
ejpam-4030	75	5	simplify	simplify	VERB
ejpam-4030	75	6	using	use	VERB
ejpam-4030	75	7	the	the	DET
ejpam-4030	75	8	lerch	lerch	PROPN
ejpam-4030	75	9	function	function	NOUN
ejpam-4030	75	10	to	to	PART
ejpam-4030	75	11	get	get	VERB
ejpam-4030	75	12	eiπac−a(−2iπ)k+n+1φ	eiπac−a(−2iπ)k+n+1φ	NOUN
ejpam-4030	75	13	(	(	PUNCT
ejpam-4030	75	14	e2iaπ,−k	e2iaπ,−k	NOUN
ejpam-4030	75	15	−	−	PROPN
ejpam-4030	75	16	n,−−i	n,−−i	NOUN
ejpam-4030	75	17	log(b)−i	log(b)−i	ADJ
ejpam-4030	75	18	log(c)−π2π	log(c)−π2π	NOUN
ejpam-4030	75	19	)	)	PUNCT
ejpam-4030	76	1	(	(	PUNCT
ejpam-4030	76	2	k	k	X
ejpam-4030	76	3	+	+	NOUN
ejpam-4030	76	4	n	n	CCONJ
ejpam-4030	76	5	)	)	PUNCT
ejpam-4030	76	6	!	!	PUNCT
ejpam-4030	77	1	=	=	PUNCT
ejpam-4030	78	1	−	−	NOUN
ejpam-4030	78	2	1	1	NUM
ejpam-4030	78	3	2πi	2πi	NOUN
ejpam-4030	79	1	+	+	ADP
ejpam-4030	79	2	∞∑	∞∑	NUM
ejpam-4030	79	3	y=0	y=0	NUM
ejpam-4030	79	4	∫	∫	PROPN
ejpam-4030	79	5	c	c	PROPN
ejpam-4030	79	6	2iπbwcw−aeiπ(2y+1)(a−w)w−k−n−1dw	2iπbwcw−aeiπ(2y+1)(a−w)w−k−n−1dw	PROPN
ejpam-4030	80	1	=	=	PUNCT
ejpam-4030	80	2	−	−	PROPN
ejpam-4030	80	3	1	1	NUM
ejpam-4030	80	4	2πi	2πi	NOUN
ejpam-4030	80	5	∫	∫	PROPN
ejpam-4030	81	1	c	c	X
ejpam-4030	82	1	+	+	NOUN
ejpam-4030	82	2	∞∑	∞∑	NUM
ejpam-4030	82	3	y=0	y=0	NOUN
ejpam-4030	82	4	2iπbwcw−aeiπ(2y+1)(a−w)w−k−n−1dw	2iπbwcw−aeiπ(2y+1)(a−w)w−k−n−1dw	PUNCT
ejpam-4030	82	5	=	=	SYM
ejpam-4030	82	6	1	1	NUM
ejpam-4030	82	7	2πi	2πi	NOUN
ejpam-4030	82	8	∫	∫	PROPN
ejpam-4030	83	1	c	c	PROPN
ejpam-4030	83	2	πbwcw−a	πbwcw−a	NOUN
ejpam-4030	83	3	csc(π(a−	csc(π(a−	NOUN
ejpam-4030	83	4	w))w−k−n−1dw	w))w−k−n−1dw	NUM
ejpam-4030	83	5	(	(	PUNCT
ejpam-4030	83	6	7	7	NUM
ejpam-4030	83	7	)	)	PUNCT
ejpam-4030	83	8	from	from	ADP
ejpam-4030	83	9	(	(	PUNCT
ejpam-4030	83	10	1.232.3	1.232.3	NUM
ejpam-4030	83	11	)	)	PUNCT
ejpam-4030	83	12	in	in	ADP
ejpam-4030	83	13	[	[	X
ejpam-4030	83	14	17	17	NUM
ejpam-4030	83	15	]	]	PUNCT
ejpam-4030	83	16	and	and	CCONJ
ejpam-4030	83	17	im(a−	im(a−	ADP
ejpam-4030	83	18	w	w	PROPN
ejpam-4030	83	19	)	)	PUNCT
ejpam-4030	83	20	>	>	X
ejpam-4030	83	21	0	0	PUNCT
ejpam-4030	84	1	for	for	ADP
ejpam-4030	84	2	convergence	convergence	NOUN
ejpam-4030	84	3	of	of	ADP
ejpam-4030	84	4	the	the	DET
ejpam-4030	84	5	sum	sum	NOUN
ejpam-4030	84	6	.	.	PUNCT
ejpam-4030	85	1	6	6	X
ejpam-4030	85	2	.	.	X
ejpam-4030	85	3	definite	definite	ADJ
ejpam-4030	85	4	integral	integral	ADJ
ejpam-4030	85	5	in	in	ADP
ejpam-4030	85	6	terms	term	NOUN
ejpam-4030	85	7	of	of	ADP
ejpam-4030	85	8	the	the	DET
ejpam-4030	85	9	lerch	lerch	PROPN
ejpam-4030	85	10	function	function	NOUN
ejpam-4030	85	11	in	in	ADP
ejpam-4030	85	12	this	this	DET
ejpam-4030	85	13	section	section	NOUN
ejpam-4030	85	14	we	we	PRON
ejpam-4030	85	15	derive	derive	VERB
ejpam-4030	85	16	the	the	DET
ejpam-4030	85	17	definite	definite	ADJ
ejpam-4030	85	18	integral	integral	NOUN
ejpam-4030	85	19	involving	involve	VERB
ejpam-4030	85	20	the	the	DET
ejpam-4030	85	21	lerch	lerch	PROPN
ejpam-4030	85	22	and	and	CCONJ
ejpam-4030	85	23	logarithmic	logarithmic	ADJ
ejpam-4030	85	24	functions	function	NOUN
ejpam-4030	85	25	expressed	express	VERB
ejpam-4030	85	26	in	in	ADP
ejpam-4030	85	27	terms	term	NOUN
ejpam-4030	85	28	of	of	ADP
ejpam-4030	85	29	the	the	DET
ejpam-4030	85	30	lerch	lerch	PROPN
ejpam-4030	85	31	function	function	PROPN
ejpam-4030	85	32	.	.	PUNCT
ejpam-4030	86	1	theorem	theorem	NOUN
ejpam-4030	86	2	1	1	NUM
ejpam-4030	86	3	.	.	PUNCT
ejpam-4030	87	1	for	for	ADP
ejpam-4030	87	2	k	k	PROPN
ejpam-4030	87	3	,	,	PUNCT
ejpam-4030	87	4	b	b	PROPN
ejpam-4030	87	5	∈	∈	PROPN
ejpam-4030	87	6	c	c	NOUN
ejpam-4030	87	7	,	,	PUNCT
ejpam-4030	87	8	0	0	PUNCT
ejpam-4030	87	9	<	<	X
ejpam-4030	87	10	re(a	re(a	NOUN
ejpam-4030	87	11	)	)	PUNCT
ejpam-4030	87	12	<	<	X
ejpam-4030	87	13	1	1	NUM
ejpam-4030	87	14	,	,	PUNCT
ejpam-4030	87	15	n	n	PRON
ejpam-4030	87	16	∈	∈	PROPN
ejpam-4030	87	17	z−	z−	PROPN
ejpam-4030	87	18	,	,	PUNCT
ejpam-4030	87	19	c	c	PROPN
ejpam-4030	87	20	∈	∈	PROPN
ejpam-4030	87	21	z,∫	z,∫	PROPN
ejpam-4030	88	1	+	+	NOUN
ejpam-4030	88	2	∞	∞	PROPN
ejpam-4030	88	3	0	0	NUM
ejpam-4030	88	4	xa−1	xa−1	PROPN
ejpam-4030	88	5	logk	logk	PROPN
ejpam-4030	88	6	(	(	PUNCT
ejpam-4030	88	7	b	b	NOUN
ejpam-4030	88	8	x	x	X
ejpam-4030	88	9	)	)	PUNCT
ejpam-4030	88	10	φ(−cx	φ(−cx	ADJ
ejpam-4030	88	11	,	,	PUNCT
ejpam-4030	88	12	n	n	CCONJ
ejpam-4030	88	13	,	,	PUNCT
ejpam-4030	88	14	a)dx	a)dx	PROPN
ejpam-4030	88	15	=	=	PUNCT
ejpam-4030	88	16	eiπak!c−a(−2iπ)k+n+1φ	eiπak!c−a(−2iπ)k+n+1φ	PUNCT
ejpam-4030	88	17	(	(	PUNCT
ejpam-4030	88	18	e2iaπ,−k	e2iaπ,−k	NOUN
ejpam-4030	88	19	−	−	PROPN
ejpam-4030	88	20	n,−−i	n,−−i	NOUN
ejpam-4030	88	21	log(b)−i	log(b)−i	ADJ
ejpam-4030	88	22	log(c)−π2π	log(c)−π2π	NOUN
ejpam-4030	88	23	)	)	PUNCT
ejpam-4030	89	1	(	(	PUNCT
ejpam-4030	89	2	k	k	X
ejpam-4030	89	3	+	+	NOUN
ejpam-4030	89	4	n	n	CCONJ
ejpam-4030	89	5	)	)	PUNCT
ejpam-4030	89	6	!	!	PUNCT
ejpam-4030	90	1	(	(	PUNCT
ejpam-4030	90	2	8)	8)	NUM
ejpam-4030	90	3	proof	proof	NOUN
ejpam-4030	90	4	.	.	PUNCT
ejpam-4030	91	1	since	since	SCONJ
ejpam-4030	91	2	the	the	DET
ejpam-4030	91	3	right	right	ADJ
ejpam-4030	91	4	-	-	PUNCT
ejpam-4030	91	5	hand	hand	NOUN
ejpam-4030	91	6	sides	side	NOUN
ejpam-4030	91	7	of	of	ADP
ejpam-4030	91	8	equations	equation	NOUN
ejpam-4030	91	9	(	(	PUNCT
ejpam-4030	91	10	3	3	NUM
ejpam-4030	91	11	)	)	PUNCT
ejpam-4030	91	12	and	and	CCONJ
ejpam-4030	91	13	(	(	PUNCT
ejpam-4030	91	14	7	7	X
ejpam-4030	91	15	)	)	PUNCT
ejpam-4030	91	16	are	be	AUX
ejpam-4030	91	17	the	the	DET
ejpam-4030	91	18	same	same	ADJ
ejpam-4030	91	19	we	we	PRON
ejpam-4030	91	20	can	can	AUX
ejpam-4030	91	21	equate	equate	VERB
ejpam-4030	91	22	the	the	DET
ejpam-4030	91	23	left	left	ADJ
ejpam-4030	91	24	-	-	PUNCT
ejpam-4030	91	25	hand	hand	NOUN
ejpam-4030	91	26	sides	side	NOUN
ejpam-4030	91	27	to	to	PART
ejpam-4030	91	28	yield	yield	VERB
ejpam-4030	91	29	the	the	DET
ejpam-4030	91	30	stated	state	VERB
ejpam-4030	91	31	result	result	NOUN
ejpam-4030	91	32	.	.	PUNCT
ejpam-4030	92	1	theorem	theorem	ADJ
ejpam-4030	92	2	2	2	NUM
ejpam-4030	92	3	.	.	PUNCT
ejpam-4030	92	4	b	b	PROPN
ejpam-4030	92	5	∈	∈	PROPN
ejpam-4030	92	6	c	c	NOUN
ejpam-4030	92	7	,	,	PUNCT
ejpam-4030	92	8	re(k	re(k	NOUN
ejpam-4030	92	9	)	)	PUNCT
ejpam-4030	92	10	<	<	X
ejpam-4030	92	11	−2	−2	NOUN
ejpam-4030	92	12	,	,	PUNCT
ejpam-4030	92	13	0	0	PUNCT
ejpam-4030	92	14	<	<	X
ejpam-4030	92	15	re(a	re(a	NOUN
ejpam-4030	92	16	)	)	PUNCT
ejpam-4030	92	17	<	<	X
ejpam-4030	92	18	1	1	NUM
ejpam-4030	92	19	,	,	PUNCT
ejpam-4030	92	20	c	c	PROPN
ejpam-4030	92	21	∈	∈	PROPN
ejpam-4030	92	22	z−∫	z−∫	PROPN
ejpam-4030	93	1	+	+	NOUN
ejpam-4030	93	2	∞	∞	PROPN
ejpam-4030	93	3	0	0	NUM
ejpam-4030	93	4	xa−1φ(−cx	xa−1φ(−cx	NUM
ejpam-4030	93	5	,	,	PUNCT
ejpam-4030	93	6	1	1	NUM
ejpam-4030	93	7	,	,	PUNCT
ejpam-4030	93	8	a	a	DET
ejpam-4030	93	9	)	)	PUNCT
ejpam-4030	93	10	logk	logk	NOUN
ejpam-4030	93	11	(	(	PUNCT
ejpam-4030	93	12	b	b	NOUN
ejpam-4030	93	13	x	x	X
ejpam-4030	93	14	)	)	PUNCT
ejpam-4030	93	15	dx	dx	PROPN
ejpam-4030	93	16	r.	r.	PROPN
ejpam-4030	93	17	reynolds	reynolds	PROPN
ejpam-4030	93	18	,	,	PUNCT
ejpam-4030	93	19	a.	a.	PROPN
ejpam-4030	93	20	stauffer	stauffer	PROPN
ejpam-4030	93	21	/	/	SYM
ejpam-4030	93	22	eur	eur	PROPN
ejpam-4030	93	23	.	.	PUNCT
ejpam-4030	94	1	j.	j.	PROPN
ejpam-4030	94	2	pure	pure	PROPN
ejpam-4030	94	3	appl	appl	PROPN
ejpam-4030	94	4	.	.	PROPN
ejpam-4030	94	5	math	math	PROPN
ejpam-4030	94	6	,	,	PUNCT
ejpam-4030	94	7	14	14	NUM
ejpam-4030	94	8	(	(	PUNCT
ejpam-4030	94	9	3	3	NUM
ejpam-4030	94	10	)	)	PUNCT
ejpam-4030	94	11	(	(	PUNCT
ejpam-4030	94	12	2021	2021	NUM
ejpam-4030	94	13	)	)	PUNCT
ejpam-4030	94	14	,	,	PUNCT
ejpam-4030	94	15	788	788	NUM
ejpam-4030	94	16	-	-	SYM
ejpam-4030	94	17	802	802	NUM
ejpam-4030	94	18	792	792	NUM
ejpam-4030	94	19	=	=	NOUN
ejpam-4030	94	20	eiπa(−2iπ)k+2k!c−aφ	eiπa(−2iπ)k+2k!c−aφ	PRON
ejpam-4030	94	21	(	(	PUNCT
ejpam-4030	94	22	e2iaπ,−k	e2iaπ,−k	NOUN
ejpam-4030	94	23	−	−	PROPN
ejpam-4030	94	24	1,−−i	1,−−i	NUM
ejpam-4030	94	25	log(b)−i	log(b)−i	X
ejpam-4030	94	26	log(c)−π2π	log(c)−π2π	NOUN
ejpam-4030	94	27	)	)	PUNCT
ejpam-4030	95	1	(	(	PUNCT
ejpam-4030	95	2	k	k	X
ejpam-4030	95	3	+	+	PROPN
ejpam-4030	95	4	1	1	NUM
ejpam-4030	95	5	)	)	PUNCT
ejpam-4030	95	6	!	!	PUNCT
ejpam-4030	96	1	(	(	PUNCT
ejpam-4030	96	2	9	9	X
ejpam-4030	96	3	)	)	PUNCT
ejpam-4030	96	4	proof	proof	NOUN
ejpam-4030	96	5	.	.	PUNCT
ejpam-4030	97	1	use	use	VERB
ejpam-4030	97	2	equation	equation	NOUN
ejpam-4030	97	3	(	(	PUNCT
ejpam-4030	97	4	8)	8)	NUM
ejpam-4030	97	5	set	set	VERB
ejpam-4030	97	6	n	n	NOUN
ejpam-4030	97	7	=	=	SYM
ejpam-4030	97	8	−1	−1	NOUN
ejpam-4030	97	9	and	and	CCONJ
ejpam-4030	97	10	simplify	simplify	NOUN
ejpam-4030	97	11	.	.	PUNCT
ejpam-4030	98	1	7	7	X
ejpam-4030	98	2	.	.	X
ejpam-4030	98	3	definite	definite	ADJ
ejpam-4030	98	4	integrals	integral	NOUN
ejpam-4030	98	5	in	in	ADP
ejpam-4030	98	6	terms	term	NOUN
ejpam-4030	98	7	of	of	ADP
ejpam-4030	98	8	the	the	DET
ejpam-4030	98	9	hurwitz	hurwitz	PROPN
ejpam-4030	98	10	zeta	zeta	PROPN
ejpam-4030	98	11	function	function	VERB
ejpam-4030	98	12	when	when	SCONJ
ejpam-4030	98	13	a	a	DET
ejpam-4030	98	14	=	=	NOUN
ejpam-4030	98	15	1/2	1/2	NUM
ejpam-4030	98	16	and	and	CCONJ
ejpam-4030	98	17	a	a	DET
ejpam-4030	98	18	=	=	SYM
ejpam-4030	98	19	1	1	NUM
ejpam-4030	98	20	theorem	theorem	NOUN
ejpam-4030	98	21	3	3	NUM
ejpam-4030	98	22	.	.	X
ejpam-4030	98	23	for	for	ADP
ejpam-4030	98	24	k	k	PROPN
ejpam-4030	98	25	,	,	PUNCT
ejpam-4030	98	26	b	b	NOUN
ejpam-4030	98	27	,	,	PUNCT
ejpam-4030	98	28	c	c	PROPN
ejpam-4030	98	29	∈	∈	PROPN
ejpam-4030	98	30	c	c	NOUN
ejpam-4030	98	31	,	,	PUNCT
ejpam-4030	98	32	n	n	PROPN
ejpam-4030	98	33	∈	∈	PROPN
ejpam-4030	98	34	z−	z−	X
ejpam-4030	98	35	∫	∫	PROPN
ejpam-4030	99	1	+	+	NUM
ejpam-4030	99	2	∞	∞	PROPN
ejpam-4030	99	3	0	0	NUM
ejpam-4030	99	4	logk	logk	NOUN
ejpam-4030	99	5	(	(	PUNCT
ejpam-4030	99	6	b	b	NOUN
ejpam-4030	99	7	x	x	X
ejpam-4030	99	8	)	)	PUNCT
ejpam-4030	99	9	lin(−cx	lin(−cx	PROPN
ejpam-4030	99	10	)	)	PUNCT
ejpam-4030	100	1	x	x	X
ejpam-4030	100	2	dx	dx	PROPN
ejpam-4030	100	3	=	=	SYM
ejpam-4030	100	4	k!(−2iπ)k+n+1ζ	k!(−2iπ)k+n+1ζ	PROPN
ejpam-4030	100	5	(	(	PUNCT
ejpam-4030	100	6	−k	−k	PROPN
ejpam-4030	100	7	−	−	NOUN
ejpam-4030	100	8	n,−−i	n,−−i	NOUN
ejpam-4030	100	9	log(b)−i	log(b)−i	X
ejpam-4030	100	10	log(c)−π2π	log(c)−π2π	NOUN
ejpam-4030	100	11	)	)	PUNCT
ejpam-4030	101	1	(	(	PUNCT
ejpam-4030	101	2	k	k	X
ejpam-4030	101	3	+	+	NOUN
ejpam-4030	101	4	n	n	CCONJ
ejpam-4030	101	5	)	)	PUNCT
ejpam-4030	101	6	!	!	PUNCT
ejpam-4030	102	1	(	(	PUNCT
ejpam-4030	102	2	10	10	X
ejpam-4030	102	3	)	)	PUNCT
ejpam-4030	102	4	proof	proof	NOUN
ejpam-4030	102	5	.	.	PUNCT
ejpam-4030	103	1	use	use	VERB
ejpam-4030	103	2	equation	equation	NOUN
ejpam-4030	103	3	(	(	PUNCT
ejpam-4030	103	4	8)	8)	NUM
ejpam-4030	103	5	and	and	CCONJ
ejpam-4030	103	6	set	set	VERB
ejpam-4030	103	7	a	a	DET
ejpam-4030	103	8	=	=	SYM
ejpam-4030	103	9	1	1	NUM
ejpam-4030	103	10	and	and	CCONJ
ejpam-4030	103	11	simplify	simplify	VERB
ejpam-4030	103	12	using	use	VERB
ejpam-4030	103	13	equations	equation	NOUN
ejpam-4030	103	14	(	(	PUNCT
ejpam-4030	103	15	64:12:1	64:12:1	NUM
ejpam-4030	103	16	)	)	PUNCT
ejpam-4030	103	17	and	and	CCONJ
ejpam-4030	103	18	(	(	PUNCT
ejpam-4030	103	19	64:12:2	64:12:2	NUM
ejpam-4030	103	20	)	)	PUNCT
ejpam-4030	103	21	in	in	ADP
ejpam-4030	103	22	[	[	X
ejpam-4030	103	23	11	11	NUM
ejpam-4030	103	24	]	]	PUNCT
ejpam-4030	103	25	.	.	PUNCT
ejpam-4030	104	1	proposition	proposition	NOUN
ejpam-4030	104	2	1	1	NUM
ejpam-4030	104	3	.	.	PUNCT
ejpam-4030	105	1	for	for	ADP
ejpam-4030	105	2	b	b	NOUN
ejpam-4030	105	3	,	,	PUNCT
ejpam-4030	105	4	c	c	PROPN
ejpam-4030	105	5	∈	∈	PROPN
ejpam-4030	105	6	c	c	NOUN
ejpam-4030	105	7	,	,	PUNCT
ejpam-4030	105	8	re(k	re(k	NOUN
ejpam-4030	105	9	)	)	PUNCT
ejpam-4030	105	10	<	<	X
ejpam-4030	106	1	0∫	0∫	PUNCT
ejpam-4030	106	2	+	+	ADJ
ejpam-4030	106	3	∞	∞	PROPN
ejpam-4030	106	4	0	0	NUM
ejpam-4030	106	5	tanh−1(cx	tanh−1(cx	ADJ
ejpam-4030	106	6	)	)	PUNCT
ejpam-4030	106	7	logk	logk	NOUN
ejpam-4030	106	8	(	(	PUNCT
ejpam-4030	106	9	b	b	NOUN
ejpam-4030	106	10	x	x	X
ejpam-4030	106	11	)	)	PUNCT
ejpam-4030	107	1	x	x	SYM
ejpam-4030	107	2	dx	dx	PROPN
ejpam-4030	107	3	=	=	PUNCT
ejpam-4030	107	4	(	(	PUNCT
ejpam-4030	107	5	−i)k2k+1πk+2	−i)k2k+1πk+2	NUM
ejpam-4030	107	6	(	(	PUNCT
ejpam-4030	107	7	ζ	ζ	NOUN
ejpam-4030	107	8	(	(	PUNCT
ejpam-4030	107	9	−k	−k	NOUN
ejpam-4030	107	10	−	−	NOUN
ejpam-4030	107	11	1	1	NUM
ejpam-4030	107	12	,	,	PUNCT
ejpam-4030	107	13	i	i	PRON
ejpam-4030	107	14	log(b)+i	log(b)+i	X
ejpam-4030	107	15	log(c)+π2π	log(c)+π2π	PROPN
ejpam-4030	107	16	)	)	PUNCT
ejpam-4030	108	1	−	−	PROPN
ejpam-4030	108	2	ζ	ζ	NOUN
ejpam-4030	108	3	(	(	PUNCT
ejpam-4030	108	4	−k	−k	NOUN
ejpam-4030	108	5	−	−	NOUN
ejpam-4030	108	6	1	1	NUM
ejpam-4030	108	7	,	,	PUNCT
ejpam-4030	108	8	i	i	PRON
ejpam-4030	108	9	log(b)+i	log(b)+i	X
ejpam-4030	108	10	log(−c)+π2π	log(−c)+π2π	NOUN
ejpam-4030	108	11	)	)	PUNCT
ejpam-4030	108	12	)	)	PUNCT
ejpam-4030	109	1	k	k	X
ejpam-4030	110	1	+	+	PUNCT
ejpam-4030	110	2	1	1	NUM
ejpam-4030	110	3	(	(	PUNCT
ejpam-4030	110	4	11	11	NUM
ejpam-4030	110	5	)	)	PUNCT
ejpam-4030	110	6	proof	proof	NOUN
ejpam-4030	110	7	.	.	PUNCT
ejpam-4030	111	1	use	use	VERB
ejpam-4030	111	2	equation	equation	NOUN
ejpam-4030	111	3	(	(	PUNCT
ejpam-4030	111	4	10	10	NUM
ejpam-4030	111	5	)	)	PUNCT
ejpam-4030	111	6	set	set	VERB
ejpam-4030	111	7	n	n	NOUN
ejpam-4030	111	8	=	=	SYM
ejpam-4030	111	9	1	1	NUM
ejpam-4030	111	10	,	,	PUNCT
ejpam-4030	111	11	simplify	simplify	VERB
ejpam-4030	111	12	the	the	DET
ejpam-4030	111	13	factorial	factorial	NOUN
ejpam-4030	111	14	and	and	CCONJ
ejpam-4030	111	15	form	form	VERB
ejpam-4030	111	16	a	a	DET
ejpam-4030	111	17	second	second	ADJ
ejpam-4030	111	18	equation	equation	NOUN
ejpam-4030	111	19	by	by	ADP
ejpam-4030	111	20	replacing	replace	VERB
ejpam-4030	111	21	c	c	NOUN
ejpam-4030	111	22	by	by	ADP
ejpam-4030	111	23	−c	−c	NOUN
ejpam-4030	111	24	and	and	CCONJ
ejpam-4030	111	25	taking	take	VERB
ejpam-4030	111	26	their	their	PRON
ejpam-4030	111	27	difference	difference	NOUN
ejpam-4030	111	28	and	and	CCONJ
ejpam-4030	111	29	simplify	simplify	NOUN
ejpam-4030	111	30	.	.	PUNCT
ejpam-4030	112	1	proposition	proposition	NOUN
ejpam-4030	112	2	2	2	NUM
ejpam-4030	112	3	.	.	PUNCT
ejpam-4030	112	4	for	for	ADP
ejpam-4030	112	5	α	α	NOUN
ejpam-4030	112	6	,	,	PUNCT
ejpam-4030	112	7	β	β	X
ejpam-4030	112	8	∈	∈	X
ejpam-4030	112	9	c∫	c∫	PROPN
ejpam-4030	113	1	+	+	NOUN
ejpam-4030	113	2	∞	∞	PROPN
ejpam-4030	113	3	0	0	NUM
ejpam-4030	113	4	tanh−1(αx	tanh−1(αx	NOUN
ejpam-4030	113	5	)	)	PUNCT
ejpam-4030	114	1	x(β	x(β	NOUN
ejpam-4030	115	1	+	+	CCONJ
ejpam-4030	115	2	log(x))2	log(x))2	VERB
ejpam-4030	115	3	dx	dx	NOUN
ejpam-4030	115	4	=	=	SYM
ejpam-4030	115	5	1	1	NUM
ejpam-4030	115	6	2	2	NUM
ejpam-4030	115	7	(	(	PUNCT
ejpam-4030	115	8	ψ(0	ψ(0	NOUN
ejpam-4030	115	9	)	)	PUNCT
ejpam-4030	115	10	(	(	PUNCT
ejpam-4030	115	11	−	−	PROPN
ejpam-4030	115	12	i(β	i(β	NOUN
ejpam-4030	115	13	−	−	PROPN
ejpam-4030	115	14	log(α	log(α	PROPN
ejpam-4030	115	15	)	)	PUNCT
ejpam-4030	115	16	)	)	PUNCT
ejpam-4030	115	17	2π	2π	NOUN
ejpam-4030	115	18	)	)	PUNCT
ejpam-4030	116	1	−	−	PROPN
ejpam-4030	116	2	ψ(0	ψ(0	NOUN
ejpam-4030	116	3	)	)	PUNCT
ejpam-4030	116	4	(	(	PUNCT
ejpam-4030	116	5	−iβ	−iβ	X
ejpam-4030	117	1	+	+	CCONJ
ejpam-4030	117	2	i	i	PRON
ejpam-4030	117	3	log(α	log(α	PROPN
ejpam-4030	117	4	)	)	PUNCT
ejpam-4030	117	5	+	+	NUM
ejpam-4030	117	6	π	π	PROPN
ejpam-4030	117	7	2π	2π	NOUN
ejpam-4030	117	8	)	)	PUNCT
ejpam-4030	117	9	)	)	PUNCT
ejpam-4030	118	1	(	(	PUNCT
ejpam-4030	118	2	12	12	X
ejpam-4030	118	3	)	)	PUNCT
ejpam-4030	118	4	proof	proof	NOUN
ejpam-4030	118	5	.	.	PUNCT
ejpam-4030	119	1	use	use	VERB
ejpam-4030	119	2	equation	equation	NOUN
ejpam-4030	119	3	(	(	PUNCT
ejpam-4030	119	4	11	11	NUM
ejpam-4030	119	5	)	)	PUNCT
ejpam-4030	119	6	set	set	VERB
ejpam-4030	119	7	k	k	NOUN
ejpam-4030	119	8	=	=	SYM
ejpam-4030	119	9	−2	−2	PROPN
ejpam-4030	119	10	,	,	PUNCT
ejpam-4030	119	11	b	b	X
ejpam-4030	119	12	=	=	SYM
ejpam-4030	119	13	e−iβ	e−iβ	NOUN
ejpam-4030	119	14	,	,	PUNCT
ejpam-4030	119	15	c	c	NOUN
ejpam-4030	119	16	=	=	SYM
ejpam-4030	119	17	α	α	PROPN
ejpam-4030	119	18	and	and	CCONJ
ejpam-4030	119	19	simplify	simplify	VERB
ejpam-4030	119	20	using	use	VERB
ejpam-4030	119	21	equation	equation	NOUN
ejpam-4030	119	22	(	(	PUNCT
ejpam-4030	119	23	64:4:1	64:4:1	NUM
ejpam-4030	119	24	)	)	PUNCT
ejpam-4030	119	25	in	in	ADP
ejpam-4030	119	26	[	[	X
ejpam-4030	119	27	11	11	NUM
ejpam-4030	119	28	]	]	PUNCT
ejpam-4030	119	29	.	.	PUNCT
ejpam-4030	120	1	note	note	VERB
ejpam-4030	120	2	the	the	DET
ejpam-4030	120	3	singularity	singularity	NOUN
ejpam-4030	120	4	at	at	ADP
ejpam-4030	120	5	x	x	X
ejpam-4030	120	6	=	=	SYM
ejpam-4030	120	7	1	1	NUM
ejpam-4030	120	8	/	/	SYM
ejpam-4030	120	9	α	α	NOUN
ejpam-4030	120	10	.	.	PUNCT
ejpam-4030	121	1	proposition	proposition	NOUN
ejpam-4030	121	2	3	3	NUM
ejpam-4030	121	3	.	.	PUNCT
ejpam-4030	121	4	∫	∫	PROPN
ejpam-4030	122	1	+	+	NUM
ejpam-4030	122	2	∞	∞	PROPN
ejpam-4030	122	3	0	0	NUM
ejpam-4030	122	4	tanh−1(x	tanh−1(x	NOUN
ejpam-4030	122	5	)	)	PUNCT
ejpam-4030	122	6	x(log(x	x(log(x	PUNCT
ejpam-4030	122	7	)	)	PUNCT
ejpam-4030	123	1	+	+	CCONJ
ejpam-4030	123	2	iπ)2	iπ)2	PROPN
ejpam-4030	123	3	dx	dx	PROPN
ejpam-4030	123	4	=	=	SYM
ejpam-4030	123	5	−	−	PROPN
ejpam-4030	123	6	log(2	log(2	NOUN
ejpam-4030	123	7	)	)	PUNCT
ejpam-4030	123	8	(	(	PUNCT
ejpam-4030	123	9	13	13	X
ejpam-4030	123	10	)	)	PUNCT
ejpam-4030	123	11	proof	proof	NOUN
ejpam-4030	123	12	.	.	PUNCT
ejpam-4030	124	1	use	use	VERB
ejpam-4030	124	2	equation	equation	NOUN
ejpam-4030	124	3	(	(	PUNCT
ejpam-4030	124	4	12	12	NUM
ejpam-4030	124	5	)	)	PUNCT
ejpam-4030	124	6	and	and	CCONJ
ejpam-4030	124	7	set	set	VERB
ejpam-4030	124	8	β	β	X
ejpam-4030	124	9	=	=	PUNCT
ejpam-4030	124	10	πi	πi	PROPN
ejpam-4030	124	11	,	,	PUNCT
ejpam-4030	124	12	α	α	NOUN
ejpam-4030	124	13	=	=	SYM
ejpam-4030	124	14	1	1	NUM
ejpam-4030	124	15	and	and	CCONJ
ejpam-4030	124	16	simplify	simplify	VERB
ejpam-4030	124	17	in	in	ADP
ejpam-4030	124	18	terms	term	NOUN
ejpam-4030	124	19	of	of	ADP
ejpam-4030	124	20	euler	euler	PROPN
ejpam-4030	124	21	’s	’s	PART
ejpam-4030	124	22	constant	constant	ADJ
ejpam-4030	124	23	,	,	PUNCT
ejpam-4030	124	24	γ	γ	X
ejpam-4030	124	25	using	use	VERB
ejpam-4030	124	26	equation	equation	NOUN
ejpam-4030	124	27	(	(	PUNCT
ejpam-4030	124	28	6.3.16	6.3.16	NUM
ejpam-4030	124	29	)	)	PUNCT
ejpam-4030	124	30	in	in	ADP
ejpam-4030	124	31	[	[	X
ejpam-4030	124	32	1	1	NUM
ejpam-4030	124	33	]	]	PUNCT
ejpam-4030	124	34	.	.	PUNCT
ejpam-4030	125	1	r.	r.	PROPN
ejpam-4030	125	2	reynolds	reynolds	PROPN
ejpam-4030	125	3	,	,	PUNCT
ejpam-4030	125	4	a.	a.	PROPN
ejpam-4030	125	5	stauffer	stauffer	PROPN
ejpam-4030	125	6	/	/	SYM
ejpam-4030	125	7	eur	eur	PROPN
ejpam-4030	125	8	.	.	PUNCT
ejpam-4030	126	1	j.	j.	PROPN
ejpam-4030	126	2	pure	pure	PROPN
ejpam-4030	126	3	appl	appl	PROPN
ejpam-4030	126	4	.	.	PROPN
ejpam-4030	126	5	math	math	PROPN
ejpam-4030	126	6	,	,	PUNCT
ejpam-4030	126	7	14	14	NUM
ejpam-4030	126	8	(	(	PUNCT
ejpam-4030	126	9	3	3	NUM
ejpam-4030	126	10	)	)	PUNCT
ejpam-4030	126	11	(	(	PUNCT
ejpam-4030	126	12	2021	2021	NUM
ejpam-4030	126	13	)	)	PUNCT
ejpam-4030	126	14	,	,	PUNCT
ejpam-4030	126	15	788	788	NUM
ejpam-4030	126	16	-	-	SYM
ejpam-4030	126	17	802	802	NUM
ejpam-4030	126	18	793	793	NUM
ejpam-4030	126	19	theorem	theorem	NOUN
ejpam-4030	126	20	4	4	NUM
ejpam-4030	126	21	.	.	PUNCT
ejpam-4030	126	22	for	for	ADP
ejpam-4030	126	23	k	k	PROPN
ejpam-4030	126	24	,	,	PUNCT
ejpam-4030	126	25	b	b	PROPN
ejpam-4030	126	26	,	,	PUNCT
ejpam-4030	126	27	c	c	PROPN
ejpam-4030	126	28	∈	∈	PROPN
ejpam-4030	126	29	c	c	X
ejpam-4030	126	30	∫	∫	PROPN
ejpam-4030	127	1	+	+	CCONJ
ejpam-4030	127	2	∞	∞	PROPN
ejpam-4030	127	3	0	0	NUM
ejpam-4030	127	4	logk	logk	NOUN
ejpam-4030	127	5	(	(	PUNCT
ejpam-4030	127	6	b	b	NOUN
ejpam-4030	127	7	x	x	X
ejpam-4030	127	8	)	)	PUNCT
ejpam-4030	127	9	(	(	PUNCT
ejpam-4030	127	10	tan−1	tan−1	PROPN
ejpam-4030	127	11	(	(	PUNCT
ejpam-4030	127	12	√	√	PROPN
ejpam-4030	127	13	d	d	NOUN
ejpam-4030	127	14	√	√	NUM
ejpam-4030	127	15	x	x	SYM
ejpam-4030	127	16	)	)	PUNCT
ejpam-4030	127	17	−	−	PROPN
ejpam-4030	128	1	tan−1	tan−1	PROPN
ejpam-4030	128	2	(	(	PUNCT
ejpam-4030	128	3	√	√	PROPN
ejpam-4030	128	4	c	c	NOUN
ejpam-4030	128	5	√	√	NUM
ejpam-4030	128	6	x	x	NOUN
ejpam-4030	128	7	)	)	PUNCT
ejpam-4030	128	8	)	)	PUNCT
ejpam-4030	129	1	x	x	X
ejpam-4030	129	2	dx	dx	PROPN
ejpam-4030	129	3	=	=	SYM
ejpam-4030	129	4	−	−	PROPN
ejpam-4030	129	5	(	(	PUNCT
ejpam-4030	129	6	−4i)k+1πk+2ζ	−4i)k+1πk+2ζ	PROPN
ejpam-4030	129	7	(	(	PUNCT
ejpam-4030	129	8	−k	−k	PROPN
ejpam-4030	129	9	−	−	PROPN
ejpam-4030	129	10	1	1	NUM
ejpam-4030	129	11	,	,	PUNCT
ejpam-4030	129	12	i	i	PRON
ejpam-4030	129	13	log(b)+i	log(b)+i	VERB
ejpam-4030	129	14	log(c)+π4π	log(c)+π4π	PROPN
ejpam-4030	129	15	)	)	PUNCT
ejpam-4030	130	1	k	k	X
ejpam-4030	131	1	+	+	PUNCT
ejpam-4030	131	2	1	1	NUM
ejpam-4030	131	3	+	+	CCONJ
ejpam-4030	131	4	(	(	PUNCT
ejpam-4030	131	5	−4i)k+1πk+2ζ	−4i)k+1πk+2ζ	PROPN
ejpam-4030	131	6	(	(	PUNCT
ejpam-4030	131	7	−k	−k	PROPN
ejpam-4030	131	8	−	−	PROPN
ejpam-4030	131	9	1	1	NUM
ejpam-4030	131	10	,	,	PUNCT
ejpam-4030	131	11	i	i	PRON
ejpam-4030	131	12	log(b)+i	log(b)+i	VERB
ejpam-4030	131	13	log(c)+3π	log(c)+3π	PROPN
ejpam-4030	131	14	4π	4π	NUM
ejpam-4030	131	15	)	)	PUNCT
ejpam-4030	132	1	k	k	PROPN
ejpam-4030	133	1	+	+	PUNCT
ejpam-4030	133	2	1	1	NUM
ejpam-4030	133	3	+	+	CCONJ
ejpam-4030	133	4	(	(	PUNCT
ejpam-4030	133	5	−4i)k+1πk+2ζ	−4i)k+1πk+2ζ	PROPN
ejpam-4030	133	6	(	(	PUNCT
ejpam-4030	133	7	−k	−k	PROPN
ejpam-4030	133	8	−	−	PROPN
ejpam-4030	133	9	1	1	NUM
ejpam-4030	133	10	,	,	PUNCT
ejpam-4030	133	11	i	i	PRON
ejpam-4030	133	12	log(b)+i	log(b)+i	VERB
ejpam-4030	133	13	log(d)+π4π	log(d)+π4π	PROPN
ejpam-4030	133	14	)	)	PUNCT
ejpam-4030	134	1	k	k	PROPN
ejpam-4030	135	1	+	+	CCONJ
ejpam-4030	135	2	1	1	NUM
ejpam-4030	135	3	−	−	NOUN
ejpam-4030	135	4	(	(	PUNCT
ejpam-4030	135	5	−4i)k+1πk+2ζ	−4i)k+1πk+2ζ	PROPN
ejpam-4030	135	6	(	(	PUNCT
ejpam-4030	135	7	−k	−k	PROPN
ejpam-4030	135	8	−	−	PROPN
ejpam-4030	135	9	1	1	NUM
ejpam-4030	135	10	,	,	PUNCT
ejpam-4030	135	11	i	i	PRON
ejpam-4030	135	12	log(b)+i	log(b)+i	X
ejpam-4030	135	13	log(d)+3π	log(d)+3π	NOUN
ejpam-4030	135	14	4π	4π	NUM
ejpam-4030	135	15	)	)	PUNCT
ejpam-4030	136	1	k	k	PROPN
ejpam-4030	137	1	+	+	PUNCT
ejpam-4030	137	2	1	1	NUM
ejpam-4030	137	3	(	(	PUNCT
ejpam-4030	137	4	14	14	NUM
ejpam-4030	137	5	)	)	PUNCT
ejpam-4030	137	6	proof	proof	NOUN
ejpam-4030	137	7	.	.	PUNCT
ejpam-4030	138	1	use	use	VERB
ejpam-4030	138	2	equation	equation	NOUN
ejpam-4030	138	3	(	(	PUNCT
ejpam-4030	138	4	8)	8)	NUM
ejpam-4030	138	5	and	and	CCONJ
ejpam-4030	138	6	set	set	VERB
ejpam-4030	138	7	a	a	DET
ejpam-4030	138	8	=	=	NOUN
ejpam-4030	138	9	1/2	1/2	NUM
ejpam-4030	138	10	,	,	PUNCT
ejpam-4030	138	11	n	n	NOUN
ejpam-4030	138	12	=	=	SYM
ejpam-4030	138	13	−1	−1	NOUN
ejpam-4030	138	14	then	then	ADV
ejpam-4030	138	15	take	take	VERB
ejpam-4030	138	16	the	the	DET
ejpam-4030	138	17	first	first	ADJ
ejpam-4030	138	18	partial	partial	ADJ
ejpam-4030	138	19	derivative	derivative	NOUN
ejpam-4030	138	20	with	with	ADP
ejpam-4030	138	21	respect	respect	NOUN
ejpam-4030	138	22	to	to	ADP
ejpam-4030	138	23	k	k	PROPN
ejpam-4030	138	24	then	then	ADV
ejpam-4030	138	25	set	set	VERB
ejpam-4030	138	26	k	k	PROPN
ejpam-4030	138	27	=	=	SYM
ejpam-4030	138	28	1	1	NUM
ejpam-4030	138	29	and	and	CCONJ
ejpam-4030	138	30	simplify	simplify	VERB
ejpam-4030	138	31	using	use	VERB
ejpam-4030	138	32	entry	entry	NOUN
ejpam-4030	138	33	(	(	PUNCT
ejpam-4030	138	34	4	4	NUM
ejpam-4030	138	35	)	)	PUNCT
ejpam-4030	138	36	in	in	ADP
ejpam-4030	138	37	table	table	NOUN
ejpam-4030	138	38	below	below	ADV
ejpam-4030	138	39	(	(	PUNCT
ejpam-4030	138	40	64:12:7	64:12:7	NUM
ejpam-4030	138	41	)	)	PUNCT
ejpam-4030	138	42	in	in	ADP
ejpam-4030	138	43	[	[	X
ejpam-4030	138	44	11	11	NUM
ejpam-4030	138	45	]	]	PUNCT
ejpam-4030	138	46	.	.	PUNCT
ejpam-4030	139	1	proposition	proposition	NOUN
ejpam-4030	139	2	4	4	NUM
ejpam-4030	139	3	.	.	PUNCT
ejpam-4030	140	1	for	for	ADP
ejpam-4030	140	2	d	d	PROPN
ejpam-4030	140	3	,	,	PUNCT
ejpam-4030	140	4	c	c	PROPN
ejpam-4030	140	5	∈	∈	PROPN
ejpam-4030	140	6	c,∫	c,∫	NOUN
ejpam-4030	141	1	+	+	NOUN
ejpam-4030	141	2	∞	∞	PROPN
ejpam-4030	141	3	0	0	NUM
ejpam-4030	141	4	tan−1(dx)−	tan−1(dx)−	PROPN
ejpam-4030	141	5	tan−1(cx	tan−1(cx	PROPN
ejpam-4030	141	6	)	)	PUNCT
ejpam-4030	142	1	x	x	SYM
ejpam-4030	142	2	dx	dx	PROPN
ejpam-4030	142	3	=	=	SYM
ejpam-4030	142	4	1	1	NUM
ejpam-4030	142	5	2	2	NUM
ejpam-4030	142	6	π	π	NOUN
ejpam-4030	142	7	log	log	NOUN
ejpam-4030	142	8	(	(	PUNCT
ejpam-4030	142	9	d	d	NOUN
ejpam-4030	142	10	c	c	NOUN
ejpam-4030	142	11	)	)	PUNCT
ejpam-4030	142	12	(	(	PUNCT
ejpam-4030	142	13	15	15	X
ejpam-4030	142	14	)	)	PUNCT
ejpam-4030	142	15	proof	proof	NOUN
ejpam-4030	142	16	.	.	PUNCT
ejpam-4030	143	1	use	use	VERB
ejpam-4030	143	2	equation	equation	NOUN
ejpam-4030	143	3	(	(	PUNCT
ejpam-4030	143	4	9	9	X
ejpam-4030	143	5	)	)	PUNCT
ejpam-4030	143	6	set	set	VERB
ejpam-4030	143	7	a	a	DET
ejpam-4030	143	8	=	=	NOUN
ejpam-4030	143	9	1/2	1/2	NUM
ejpam-4030	143	10	and	and	CCONJ
ejpam-4030	143	11	simplify	simplify	VERB
ejpam-4030	143	12	using	use	VERB
ejpam-4030	143	13	entry	entry	NOUN
ejpam-4030	143	14	(	(	PUNCT
ejpam-4030	143	15	4	4	NUM
ejpam-4030	143	16	)	)	PUNCT
ejpam-4030	143	17	in	in	ADP
ejpam-4030	143	18	table	table	NOUN
ejpam-4030	143	19	below	below	ADV
ejpam-4030	143	20	(	(	PUNCT
ejpam-4030	143	21	64:12:7	64:12:7	NUM
ejpam-4030	143	22	)	)	PUNCT
ejpam-4030	143	23	in	in	ADP
ejpam-4030	143	24	[	[	X
ejpam-4030	143	25	11	11	NUM
ejpam-4030	143	26	]	]	PUNCT
ejpam-4030	143	27	.	.	PUNCT
ejpam-4030	144	1	next	next	ADJ
ejpam-4030	144	2	form	form	NOUN
ejpam-4030	144	3	a	a	DET
ejpam-4030	144	4	second	second	ADJ
ejpam-4030	144	5	equation	equation	NOUN
ejpam-4030	144	6	by	by	ADP
ejpam-4030	144	7	replacing	replace	VERB
ejpam-4030	144	8	c	c	NOUN
ejpam-4030	144	9	by	by	ADP
ejpam-4030	144	10	d	d	NOUN
ejpam-4030	144	11	and	and	CCONJ
ejpam-4030	144	12	take	take	VERB
ejpam-4030	144	13	their	their	PRON
ejpam-4030	144	14	difference	difference	NOUN
ejpam-4030	144	15	,	,	PUNCT
ejpam-4030	144	16	and	and	CCONJ
ejpam-4030	144	17	setting	set	VERB
ejpam-4030	144	18	k	k	PROPN
ejpam-4030	144	19	=	=	PUNCT
ejpam-4030	144	20	0	0	PUNCT
ejpam-4030	144	21	and	and	CCONJ
ejpam-4030	144	22	simplify	simplify	VERB
ejpam-4030	144	23	the	the	DET
ejpam-4030	144	24	integral	integral	ADJ
ejpam-4030	144	25	where	where	SCONJ
ejpam-4030	144	26	d	d	NOUN
ejpam-4030	144	27	is	be	AUX
ejpam-4030	144	28	replaced	replace	VERB
ejpam-4030	144	29	by	by	ADP
ejpam-4030	144	30	d2	d2	PROPN
ejpam-4030	144	31	,	,	PUNCT
ejpam-4030	144	32	c	c	PROPN
ejpam-4030	144	33	is	be	AUX
ejpam-4030	144	34	replaced	replace	VERB
ejpam-4030	144	35	by	by	ADP
ejpam-4030	144	36	c2	c2	PROPN
ejpam-4030	144	37	and	and	CCONJ
ejpam-4030	144	38	replacing	replace	VERB
ejpam-4030	144	39	x	x	PUNCT
ejpam-4030	144	40	by	by	ADP
ejpam-4030	144	41	x2	x2	PRON
ejpam-4030	144	42	where	where	SCONJ
ejpam-4030	144	43	dx	dx	PROPN
ejpam-4030	144	44	=	=	SYM
ejpam-4030	144	45	2xdx	2xdx	PROPN
ejpam-4030	144	46	.	.	PUNCT
ejpam-4030	145	1	this	this	PRON
ejpam-4030	145	2	is	be	AUX
ejpam-4030	145	3	a	a	DET
ejpam-4030	145	4	particular	particular	ADJ
ejpam-4030	145	5	case	case	NOUN
ejpam-4030	145	6	of	of	ADP
ejpam-4030	145	7	the	the	DET
ejpam-4030	145	8	well	well	ADV
ejpam-4030	145	9	-	-	PUNCT
ejpam-4030	145	10	known	know	VERB
ejpam-4030	145	11	frullani	frullani	ADJ
ejpam-4030	145	12	integrals	integral	NOUN
ejpam-4030	145	13	in	in	ADP
ejpam-4030	145	14	section	section	NOUN
ejpam-4030	145	15	(	(	PUNCT
ejpam-4030	145	16	2.5	2.5	NUM
ejpam-4030	145	17	)	)	PUNCT
ejpam-4030	145	18	in	in	ADP
ejpam-4030	145	19	[	[	X
ejpam-4030	145	20	16	16	NUM
ejpam-4030	145	21	]	]	PUNCT
ejpam-4030	145	22	.	.	PUNCT
ejpam-4030	146	1	proposition	proposition	NOUN
ejpam-4030	146	2	5	5	NUM
ejpam-4030	146	3	.	.	PUNCT
ejpam-4030	146	4	for	for	ADP
ejpam-4030	146	5	b	b	PROPN
ejpam-4030	146	6	,	,	PUNCT
ejpam-4030	146	7	d	d	PROPN
ejpam-4030	146	8	,	,	PUNCT
ejpam-4030	146	9	c	c	PROPN
ejpam-4030	146	10	∈	∈	PROPN
ejpam-4030	146	11	c	c	PROPN
ejpam-4030	146	12	,	,	PUNCT
ejpam-4030	146	13	∫	∫	PROPN
ejpam-4030	147	1	+	+	PROPN
ejpam-4030	147	2	∞	∞	PROPN
ejpam-4030	147	3	0	0	NUM
ejpam-4030	147	4	log	log	NOUN
ejpam-4030	147	5	(	(	PUNCT
ejpam-4030	147	6	b	b	NOUN
ejpam-4030	147	7	x	x	X
ejpam-4030	147	8	)	)	PUNCT
ejpam-4030	147	9	(	(	PUNCT
ejpam-4030	147	10	tan−1	tan−1	PROPN
ejpam-4030	147	11	(	(	PUNCT
ejpam-4030	147	12	√	√	PROPN
ejpam-4030	147	13	d	d	NOUN
ejpam-4030	147	14	√	√	NUM
ejpam-4030	147	15	x	x	SYM
ejpam-4030	147	16	)	)	PUNCT
ejpam-4030	147	17	−	−	PROPN
ejpam-4030	148	1	tan−1	tan−1	PROPN
ejpam-4030	148	2	(	(	PUNCT
ejpam-4030	148	3	√	√	PROPN
ejpam-4030	148	4	c	c	NOUN
ejpam-4030	148	5	√	√	NUM
ejpam-4030	148	6	x	x	NOUN
ejpam-4030	148	7	)	)	PUNCT
ejpam-4030	148	8	)	)	PUNCT
ejpam-4030	149	1	x	x	SYM
ejpam-4030	149	2	dx	dx	PROPN
ejpam-4030	149	3	=	=	SYM
ejpam-4030	149	4	−1	−1	NOUN
ejpam-4030	149	5	4	4	NUM
ejpam-4030	149	6	π	π	NOUN
ejpam-4030	149	7	log	log	NOUN
ejpam-4030	149	8	(	(	PUNCT
ejpam-4030	149	9	c	c	NOUN
ejpam-4030	149	10	d	d	NOUN
ejpam-4030	149	11	)	)	PUNCT
ejpam-4030	149	12	log	log	NOUN
ejpam-4030	149	13	(	(	PUNCT
ejpam-4030	149	14	b2cd	b2cd	PUNCT
ejpam-4030	149	15	)	)	PUNCT
ejpam-4030	149	16	(	(	PUNCT
ejpam-4030	149	17	16	16	X
ejpam-4030	149	18	)	)	PUNCT
ejpam-4030	149	19	proof	proof	NOUN
ejpam-4030	149	20	.	.	PUNCT
ejpam-4030	150	1	use	use	VERB
ejpam-4030	150	2	equation	equation	NOUN
ejpam-4030	150	3	(	(	PUNCT
ejpam-4030	150	4	9	9	X
ejpam-4030	150	5	)	)	PUNCT
ejpam-4030	150	6	set	set	VERB
ejpam-4030	150	7	a	a	DET
ejpam-4030	150	8	=	=	NOUN
ejpam-4030	150	9	1/2	1/2	NUM
ejpam-4030	150	10	and	and	CCONJ
ejpam-4030	150	11	simplify	simplify	VERB
ejpam-4030	150	12	using	use	VERB
ejpam-4030	150	13	entry	entry	NOUN
ejpam-4030	150	14	(	(	PUNCT
ejpam-4030	150	15	4	4	NUM
ejpam-4030	150	16	)	)	PUNCT
ejpam-4030	150	17	in	in	ADP
ejpam-4030	150	18	table	table	NOUN
ejpam-4030	150	19	below	below	ADV
ejpam-4030	150	20	(	(	PUNCT
ejpam-4030	150	21	64:12:7	64:12:7	NUM
ejpam-4030	150	22	)	)	PUNCT
ejpam-4030	150	23	in	in	ADP
ejpam-4030	150	24	[	[	X
ejpam-4030	150	25	11	11	NUM
ejpam-4030	150	26	]	]	PUNCT
ejpam-4030	150	27	.	.	PUNCT
ejpam-4030	151	1	next	next	ADJ
ejpam-4030	151	2	form	form	NOUN
ejpam-4030	151	3	a	a	DET
ejpam-4030	151	4	second	second	ADJ
ejpam-4030	151	5	equation	equation	NOUN
ejpam-4030	151	6	by	by	ADP
ejpam-4030	151	7	replacing	replace	VERB
ejpam-4030	151	8	c	c	NOUN
ejpam-4030	151	9	by	by	ADP
ejpam-4030	151	10	d	d	NOUN
ejpam-4030	151	11	and	and	CCONJ
ejpam-4030	151	12	take	take	VERB
ejpam-4030	151	13	their	their	PRON
ejpam-4030	151	14	difference	difference	NOUN
ejpam-4030	151	15	,	,	PUNCT
ejpam-4030	151	16	and	and	CCONJ
ejpam-4030	151	17	setting	set	VERB
ejpam-4030	151	18	k	k	X
ejpam-4030	151	19	=	=	SYM
ejpam-4030	151	20	1	1	NUM
ejpam-4030	151	21	and	and	CCONJ
ejpam-4030	151	22	simplify	simplify	VERB
ejpam-4030	151	23	the	the	DET
ejpam-4030	151	24	integral	integral	ADJ
ejpam-4030	151	25	where	where	SCONJ
ejpam-4030	151	26	d	d	NOUN
ejpam-4030	151	27	is	be	AUX
ejpam-4030	151	28	replaced	replace	VERB
ejpam-4030	151	29	by	by	ADP
ejpam-4030	151	30	d2	d2	PROPN
ejpam-4030	151	31	,	,	PUNCT
ejpam-4030	151	32	c	c	PROPN
ejpam-4030	151	33	is	be	AUX
ejpam-4030	151	34	replaced	replace	VERB
ejpam-4030	151	35	by	by	ADP
ejpam-4030	151	36	c2	c2	PROPN
ejpam-4030	151	37	and	and	CCONJ
ejpam-4030	151	38	replacing	replace	VERB
ejpam-4030	151	39	x	x	PUNCT
ejpam-4030	151	40	by	by	ADP
ejpam-4030	151	41	x2	x2	PRON
ejpam-4030	151	42	where	where	SCONJ
ejpam-4030	151	43	dx	dx	PROPN
ejpam-4030	151	44	=	=	SYM
ejpam-4030	151	45	2xdx	2xdx	PROPN
ejpam-4030	151	46	.	.	PUNCT
ejpam-4030	152	1	proposition	proposition	NOUN
ejpam-4030	152	2	6	6	NUM
ejpam-4030	152	3	.	.	PUNCT
ejpam-4030	152	4	for	for	ADP
ejpam-4030	152	5	b	b	PROPN
ejpam-4030	152	6	,	,	PUNCT
ejpam-4030	152	7	d	d	PROPN
ejpam-4030	152	8	,	,	PUNCT
ejpam-4030	152	9	c	c	PROPN
ejpam-4030	152	10	∈	∈	PROPN
ejpam-4030	152	11	c	c	PROPN
ejpam-4030	152	12	,	,	PUNCT
ejpam-4030	152	13	r.	r.	PROPN
ejpam-4030	152	14	reynolds	reynolds	PROPN
ejpam-4030	152	15	,	,	PUNCT
ejpam-4030	152	16	a.	a.	PROPN
ejpam-4030	152	17	stauffer	stauffer	PROPN
ejpam-4030	152	18	/	/	SYM
ejpam-4030	152	19	eur	eur	PROPN
ejpam-4030	152	20	.	.	PUNCT
ejpam-4030	153	1	j.	j.	PROPN
ejpam-4030	153	2	pure	pure	PROPN
ejpam-4030	153	3	appl	appl	PROPN
ejpam-4030	153	4	.	.	PROPN
ejpam-4030	153	5	math	math	PROPN
ejpam-4030	153	6	,	,	PUNCT
ejpam-4030	153	7	14	14	NUM
ejpam-4030	153	8	(	(	PUNCT
ejpam-4030	153	9	3	3	NUM
ejpam-4030	153	10	)	)	PUNCT
ejpam-4030	153	11	(	(	PUNCT
ejpam-4030	153	12	2021	2021	NUM
ejpam-4030	153	13	)	)	PUNCT
ejpam-4030	153	14	,	,	PUNCT
ejpam-4030	153	15	788	788	NUM
ejpam-4030	153	16	-	-	SYM
ejpam-4030	153	17	802	802	NUM
ejpam-4030	153	18	794	794	NUM
ejpam-4030	153	19	∫	∫	NOUN
ejpam-4030	154	1	+	+	NUM
ejpam-4030	154	2	∞	∞	PROPN
ejpam-4030	154	3	0	0	NUM
ejpam-4030	154	4	log2	log2	PROPN
ejpam-4030	154	5	(	(	PUNCT
ejpam-4030	154	6	b	b	NOUN
ejpam-4030	154	7	x	x	X
ejpam-4030	154	8	)	)	PUNCT
ejpam-4030	154	9	(	(	PUNCT
ejpam-4030	154	10	tan−1	tan−1	PROPN
ejpam-4030	154	11	(	(	PUNCT
ejpam-4030	154	12	√	√	PROPN
ejpam-4030	154	13	d	d	NOUN
ejpam-4030	154	14	√	√	NUM
ejpam-4030	154	15	x	x	SYM
ejpam-4030	154	16	)	)	PUNCT
ejpam-4030	154	17	−	−	PROPN
ejpam-4030	155	1	tan−1	tan−1	PROPN
ejpam-4030	155	2	(	(	PUNCT
ejpam-4030	155	3	√	√	PROPN
ejpam-4030	155	4	c	c	NOUN
ejpam-4030	155	5	√	√	NUM
ejpam-4030	155	6	x	x	NOUN
ejpam-4030	155	7	)	)	PUNCT
ejpam-4030	155	8	)	)	PUNCT
ejpam-4030	156	1	x	x	SYM
ejpam-4030	156	2	dx	dx	PROPN
ejpam-4030	156	3	=	=	SYM
ejpam-4030	156	4	−1	−1	NOUN
ejpam-4030	156	5	2	2	NUM
ejpam-4030	156	6	π	π	X
ejpam-4030	156	7	log(b	log(b	PROPN
ejpam-4030	156	8	)	)	PUNCT
ejpam-4030	156	9	log2(c)−	log2(c)−	NOUN
ejpam-4030	156	10	1	1	NUM
ejpam-4030	156	11	2	2	NUM
ejpam-4030	156	12	π	π	NOUN
ejpam-4030	156	13	log2(b	log2(b	ADV
ejpam-4030	156	14	)	)	PUNCT
ejpam-4030	156	15	log(c	log(c	PROPN
ejpam-4030	156	16	)	)	PUNCT
ejpam-4030	157	1	+	+	CCONJ
ejpam-4030	157	2	1	1	NUM
ejpam-4030	157	3	2	2	NUM
ejpam-4030	157	4	π	π	X
ejpam-4030	157	5	log(b	log(b	PROPN
ejpam-4030	157	6	)	)	PUNCT
ejpam-4030	157	7	log2(d	log2(d	NUM
ejpam-4030	157	8	)	)	PUNCT
ejpam-4030	158	1	+	+	CCONJ
ejpam-4030	158	2	1	1	NUM
ejpam-4030	158	3	2	2	NUM
ejpam-4030	158	4	π	π	NOUN
ejpam-4030	158	5	log2(b	log2(b	ADV
ejpam-4030	158	6	)	)	PUNCT
ejpam-4030	158	7	log(d)−	log(d)−	VERB
ejpam-4030	158	8	1	1	NUM
ejpam-4030	158	9	6	6	NUM
ejpam-4030	158	10	π	π	NOUN
ejpam-4030	158	11	log3(c)−	log3(c)−	VERB
ejpam-4030	158	12	1	1	NUM
ejpam-4030	158	13	2	2	NUM
ejpam-4030	158	14	π3	π3	NOUN
ejpam-4030	158	15	log(c	log(c	NOUN
ejpam-4030	158	16	)	)	PUNCT
ejpam-4030	159	1	+	+	CCONJ
ejpam-4030	159	2	1	1	NUM
ejpam-4030	159	3	6	6	NUM
ejpam-4030	159	4	π	π	NOUN
ejpam-4030	159	5	log3(d	log3(d	NOUN
ejpam-4030	159	6	)	)	PUNCT
ejpam-4030	159	7	+	+	CCONJ
ejpam-4030	159	8	1	1	NUM
ejpam-4030	159	9	2	2	NUM
ejpam-4030	159	10	π3	π3	NOUN
ejpam-4030	159	11	log(d	log(d	PROPN
ejpam-4030	159	12	)	)	PUNCT
ejpam-4030	159	13	(	(	PUNCT
ejpam-4030	159	14	17	17	NUM
ejpam-4030	159	15	)	)	PUNCT
ejpam-4030	159	16	proof	proof	NOUN
ejpam-4030	159	17	.	.	PUNCT
ejpam-4030	160	1	use	use	VERB
ejpam-4030	160	2	equation	equation	NOUN
ejpam-4030	160	3	(	(	PUNCT
ejpam-4030	160	4	9	9	X
ejpam-4030	160	5	)	)	PUNCT
ejpam-4030	160	6	set	set	VERB
ejpam-4030	160	7	a	a	DET
ejpam-4030	160	8	=	=	NOUN
ejpam-4030	160	9	1/2	1/2	NUM
ejpam-4030	160	10	and	and	CCONJ
ejpam-4030	160	11	simplify	simplify	VERB
ejpam-4030	160	12	using	use	VERB
ejpam-4030	160	13	entry	entry	NOUN
ejpam-4030	160	14	(	(	PUNCT
ejpam-4030	160	15	4	4	NUM
ejpam-4030	160	16	)	)	PUNCT
ejpam-4030	160	17	in	in	ADP
ejpam-4030	160	18	table	table	NOUN
ejpam-4030	160	19	below	below	ADV
ejpam-4030	160	20	(	(	PUNCT
ejpam-4030	160	21	64:12:7	64:12:7	NUM
ejpam-4030	160	22	)	)	PUNCT
ejpam-4030	160	23	in	in	ADP
ejpam-4030	160	24	[	[	X
ejpam-4030	160	25	11	11	NUM
ejpam-4030	160	26	]	]	PUNCT
ejpam-4030	160	27	.	.	PUNCT
ejpam-4030	161	1	next	next	ADJ
ejpam-4030	161	2	form	form	NOUN
ejpam-4030	161	3	a	a	DET
ejpam-4030	161	4	second	second	ADJ
ejpam-4030	161	5	equation	equation	NOUN
ejpam-4030	161	6	by	by	ADP
ejpam-4030	161	7	replacing	replace	VERB
ejpam-4030	161	8	c	c	NOUN
ejpam-4030	161	9	by	by	ADP
ejpam-4030	161	10	d	d	NOUN
ejpam-4030	161	11	and	and	CCONJ
ejpam-4030	161	12	take	take	VERB
ejpam-4030	161	13	their	their	PRON
ejpam-4030	161	14	difference	difference	NOUN
ejpam-4030	161	15	,	,	PUNCT
ejpam-4030	161	16	and	and	CCONJ
ejpam-4030	161	17	setting	set	VERB
ejpam-4030	161	18	k	k	X
ejpam-4030	161	19	=	=	SYM
ejpam-4030	161	20	2	2	NUM
ejpam-4030	161	21	and	and	CCONJ
ejpam-4030	161	22	simplify	simplify	VERB
ejpam-4030	161	23	the	the	DET
ejpam-4030	161	24	integral	integral	ADJ
ejpam-4030	161	25	by	by	ADP
ejpam-4030	161	26	setting	set	VERB
ejpam-4030	161	27	d	d	X
ejpam-4030	161	28	=	=	SYM
ejpam-4030	161	29	d2	d2	PROPN
ejpam-4030	161	30	,	,	PUNCT
ejpam-4030	161	31	c	c	X
ejpam-4030	161	32	=	=	SYM
ejpam-4030	161	33	c2	c2	PROPN
ejpam-4030	161	34	and	and	CCONJ
ejpam-4030	161	35	replacing	replace	VERB
ejpam-4030	161	36	x	x	PUNCT
ejpam-4030	161	37	by	by	ADP
ejpam-4030	161	38	x2	x2	PRON
ejpam-4030	161	39	where	where	SCONJ
ejpam-4030	161	40	dx	dx	PROPN
ejpam-4030	161	41	=	=	SYM
ejpam-4030	161	42	2xdx	2xdx	PROPN
ejpam-4030	161	43	.	.	PUNCT
ejpam-4030	162	1	proposition	proposition	NOUN
ejpam-4030	162	2	7	7	NUM
ejpam-4030	162	3	.	.	PUNCT
ejpam-4030	162	4	using	use	VERB
ejpam-4030	162	5	equation	equation	NOUN
ejpam-4030	162	6	(	(	PUNCT
ejpam-4030	162	7	14	14	NUM
ejpam-4030	162	8	)	)	PUNCT
ejpam-4030	162	9	and	and	CCONJ
ejpam-4030	162	10	setting	set	VERB
ejpam-4030	162	11	k	k	X
ejpam-4030	162	12	=	=	SYM
ejpam-4030	162	13	1/2	1/2	NUM
ejpam-4030	162	14	,	,	PUNCT
ejpam-4030	162	15	b	b	NOUN
ejpam-4030	162	16	=	=	SYM
ejpam-4030	162	17	−i	−i	PROPN
ejpam-4030	162	18	,	,	PUNCT
ejpam-4030	162	19	c	c	NOUN
ejpam-4030	162	20	=	=	SYM
ejpam-4030	162	21	1	1	NUM
ejpam-4030	162	22	,	,	PUNCT
ejpam-4030	162	23	d	d	NOUN
ejpam-4030	162	24	=	=	SYM
ejpam-4030	162	25	−1	−1	NOUN
ejpam-4030	162	26	simplifying	simplify	VERB
ejpam-4030	162	27	to	to	PART
ejpam-4030	162	28	get	get	VERB
ejpam-4030	162	29	∫	∫	PROPN
ejpam-4030	163	1	+	+	PROPN
ejpam-4030	163	2	∞	∞	PROPN
ejpam-4030	163	3	0	0	NUM
ejpam-4030	164	1	−	−	NOUN
ejpam-4030	165	1	√	√	NUM
ejpam-4030	165	2	log	log	NOUN
ejpam-4030	165	3	(	(	PUNCT
ejpam-4030	165	4	−	−	PROPN
ejpam-4030	165	5	i	i	NOUN
ejpam-4030	165	6	x	x	PUNCT
ejpam-4030	165	7	)	)	PUNCT
ejpam-4030	165	8	(	(	PUNCT
ejpam-4030	165	9	tan−1	tan−1	PROPN
ejpam-4030	165	10	(	(	PUNCT
ejpam-4030	165	11	√	√	INTJ
ejpam-4030	165	12	x)−	x)−	PROPN
ejpam-4030	165	13	i	i	PRON
ejpam-4030	165	14	tanh−1	tanh−1	VERB
ejpam-4030	165	15	(	(	PUNCT
ejpam-4030	165	16	√	√	NUM
ejpam-4030	165	17	x	x	SYM
ejpam-4030	165	18	)	)	PUNCT
ejpam-4030	165	19	)	)	PUNCT
ejpam-4030	166	1	x	x	SYM
ejpam-4030	166	2	dx	dx	PROPN
ejpam-4030	166	3	=	=	SYM
ejpam-4030	166	4	−16	−16	PROPN
ejpam-4030	166	5	3	3	NUM
ejpam-4030	166	6	4	4	NUM
ejpam-4030	166	7	√	√	NOUN
ejpam-4030	167	1	−1π5/2	−1π5/2	PROPN
ejpam-4030	167	2	(	(	PUNCT
ejpam-4030	167	3	ζ	ζ	X
ejpam-4030	167	4	(	(	PUNCT
ejpam-4030	167	5	−3	−3	PROPN
ejpam-4030	167	6	2	2	NUM
ejpam-4030	167	7	,	,	PUNCT
ejpam-4030	167	8	1	1	NUM
ejpam-4030	167	9	8	8	NUM
ejpam-4030	167	10	)	)	PUNCT
ejpam-4030	167	11	−	−	PROPN
ejpam-4030	168	1	ζ	ζ	NOUN
ejpam-4030	168	2	(	(	PUNCT
ejpam-4030	168	3	−3	−3	PROPN
ejpam-4030	168	4	2	2	NUM
ejpam-4030	168	5	,	,	PUNCT
ejpam-4030	168	6	3	3	NUM
ejpam-4030	168	7	8	8	NUM
ejpam-4030	168	8	)	)	PUNCT
ejpam-4030	168	9	−	−	PROPN
ejpam-4030	168	10	ζ	ζ	NOUN
ejpam-4030	168	11	(	(	PUNCT
ejpam-4030	168	12	−3	−3	PROPN
ejpam-4030	168	13	2	2	NUM
ejpam-4030	168	14	,	,	PUNCT
ejpam-4030	168	15	5	5	NUM
ejpam-4030	168	16	8	8	NUM
ejpam-4030	168	17	)	)	PUNCT
ejpam-4030	168	18	+	+	CCONJ
ejpam-4030	168	19	ζ	ζ	X
ejpam-4030	168	20	(	(	PUNCT
ejpam-4030	168	21	−3	−3	PROPN
ejpam-4030	168	22	2	2	NUM
ejpam-4030	168	23	,	,	PUNCT
ejpam-4030	168	24	7	7	NUM
ejpam-4030	168	25	8	8	NUM
ejpam-4030	168	26	)	)	PUNCT
ejpam-4030	168	27	)	)	PUNCT
ejpam-4030	168	28	(	(	PUNCT
ejpam-4030	168	29	18	18	NUM
ejpam-4030	168	30	)	)	PUNCT
ejpam-4030	168	31	theorem	theorem	NOUN
ejpam-4030	168	32	5	5	NUM
ejpam-4030	168	33	.	.	PUNCT
ejpam-4030	168	34	for	for	ADP
ejpam-4030	168	35	k	k	PROPN
ejpam-4030	168	36	,	,	PUNCT
ejpam-4030	168	37	b	b	NOUN
ejpam-4030	168	38	,	,	PUNCT
ejpam-4030	169	1	c	c	PROPN
ejpam-4030	169	2	∈	∈	PROPN
ejpam-4030	169	3	c∫	c∫	PROPN
ejpam-4030	170	1	+	+	NOUN
ejpam-4030	170	2	∞	∞	PROPN
ejpam-4030	170	3	0	0	NUM
ejpam-4030	170	4	(	(	PUNCT
ejpam-4030	170	5	cx−	cx−	ADP
ejpam-4030	170	6	1	1	NUM
ejpam-4030	170	7	)	)	PUNCT
ejpam-4030	170	8	logk	logk	NOUN
ejpam-4030	170	9	(	(	PUNCT
ejpam-4030	170	10	b	b	NOUN
ejpam-4030	170	11	x	x	X
ejpam-4030	170	12	)	)	PUNCT
ejpam-4030	170	13	√	√	ADP
ejpam-4030	170	14	x(cx+	x(cx+	NOUN
ejpam-4030	171	1	1)2	1)2	NUM
ejpam-4030	171	2	dx	dx	NOUN
ejpam-4030	172	1	=	=	SYM
ejpam-4030	173	1	ie−	ie−	ADP
ejpam-4030	173	2	1	1	NUM
ejpam-4030	173	3	2	2	NUM
ejpam-4030	173	4	iπkk(4π)k	iπkk(4π)k	NOUN
ejpam-4030	173	5	(	(	PUNCT
ejpam-4030	173	6	ζ	ζ	NOUN
ejpam-4030	173	7	(	(	PUNCT
ejpam-4030	173	8	1−	1−	NUM
ejpam-4030	173	9	k	k	NOUN
ejpam-4030	173	10	,	,	PUNCT
ejpam-4030	173	11	i	i	PRON
ejpam-4030	173	12	log(b)+i	log(b)+i	VERB
ejpam-4030	173	13	log(c)+3π	log(c)+3π	PROPN
ejpam-4030	173	14	4π	4π	NUM
ejpam-4030	173	15	)	)	PUNCT
ejpam-4030	173	16	−	−	PROPN
ejpam-4030	173	17	ζ	ζ	NOUN
ejpam-4030	173	18	(	(	PUNCT
ejpam-4030	173	19	1−	1−	NUM
ejpam-4030	173	20	k	k	NOUN
ejpam-4030	173	21	,	,	PUNCT
ejpam-4030	173	22	i	i	PRON
ejpam-4030	173	23	log(b)+i	log(b)+i	VERB
ejpam-4030	173	24	log(c)+π4π	log(c)+π4π	PROPN
ejpam-4030	173	25	)	)	PUNCT
ejpam-4030	173	26	)	)	PUNCT
ejpam-4030	174	1	√	√	ADP
ejpam-4030	174	2	c	c	NOUN
ejpam-4030	174	3	(	(	PUNCT
ejpam-4030	174	4	19	19	NUM
ejpam-4030	174	5	)	)	PUNCT
ejpam-4030	174	6	proof	proof	NOUN
ejpam-4030	174	7	.	.	PUNCT
ejpam-4030	175	1	use	use	VERB
ejpam-4030	175	2	equation	equation	NOUN
ejpam-4030	175	3	(	(	PUNCT
ejpam-4030	175	4	8)	8)	NUM
ejpam-4030	175	5	and	and	CCONJ
ejpam-4030	175	6	set	set	VERB
ejpam-4030	175	7	a	a	DET
ejpam-4030	175	8	=	=	NOUN
ejpam-4030	175	9	1/2	1/2	NUM
ejpam-4030	175	10	,	,	PUNCT
ejpam-4030	175	11	n	n	NOUN
ejpam-4030	175	12	=	=	SYM
ejpam-4030	175	13	−1	−1	NOUN
ejpam-4030	175	14	then	then	ADV
ejpam-4030	175	15	take	take	VERB
ejpam-4030	175	16	the	the	DET
ejpam-4030	175	17	first	first	ADJ
ejpam-4030	175	18	partial	partial	ADJ
ejpam-4030	175	19	derivative	derivative	NOUN
ejpam-4030	175	20	with	with	ADP
ejpam-4030	175	21	respect	respect	NOUN
ejpam-4030	175	22	to	to	ADP
ejpam-4030	175	23	k	k	PROPN
ejpam-4030	175	24	then	then	ADV
ejpam-4030	175	25	set	set	VERB
ejpam-4030	175	26	k	k	PROPN
ejpam-4030	175	27	=	=	SYM
ejpam-4030	175	28	1	1	NUM
ejpam-4030	175	29	and	and	CCONJ
ejpam-4030	175	30	simplify	simplify	VERB
ejpam-4030	175	31	using	use	VERB
ejpam-4030	175	32	entry	entry	NOUN
ejpam-4030	175	33	(	(	PUNCT
ejpam-4030	175	34	4	4	NUM
ejpam-4030	175	35	)	)	PUNCT
ejpam-4030	175	36	in	in	ADP
ejpam-4030	175	37	table	table	NOUN
ejpam-4030	175	38	below	below	ADV
ejpam-4030	175	39	(	(	PUNCT
ejpam-4030	175	40	64:12:7	64:12:7	NUM
ejpam-4030	175	41	)	)	PUNCT
ejpam-4030	175	42	in	in	ADP
ejpam-4030	175	43	[	[	X
ejpam-4030	175	44	11	11	NUM
ejpam-4030	175	45	]	]	PUNCT
ejpam-4030	175	46	.	.	PUNCT
ejpam-4030	176	1	proposition	proposition	NOUN
ejpam-4030	176	2	8	8	NUM
ejpam-4030	176	3	.	.	PUNCT
ejpam-4030	176	4	using	use	VERB
ejpam-4030	176	5	equation	equation	NOUN
ejpam-4030	176	6	(	(	PUNCT
ejpam-4030	176	7	19	19	NUM
ejpam-4030	176	8	)	)	PUNCT
ejpam-4030	176	9	setting	set	VERB
ejpam-4030	176	10	k	k	PROPN
ejpam-4030	176	11	=	=	PUNCT
ejpam-4030	176	12	−1	−1	NOUN
ejpam-4030	176	13	,	,	PUNCT
ejpam-4030	176	14	b	b	NOUN
ejpam-4030	176	15	=	=	SYM
ejpam-4030	176	16	1	1	NUM
ejpam-4030	176	17	,	,	PUNCT
ejpam-4030	176	18	c	c	NOUN
ejpam-4030	176	19	=	=	SYM
ejpam-4030	176	20	1	1	NUM
ejpam-4030	176	21	and	and	CCONJ
ejpam-4030	176	22	simplifying	simplify	VERB
ejpam-4030	176	23	in	in	ADP
ejpam-4030	176	24	terms	term	NOUN
ejpam-4030	176	25	of	of	ADP
ejpam-4030	176	26	catalan	catalan	NOUN
ejpam-4030	176	27	’s	’s	PART
ejpam-4030	176	28	constant	constant	ADJ
ejpam-4030	176	29	,	,	PUNCT
ejpam-4030	176	30	c	c	NOUN
ejpam-4030	176	31	using	use	VERB
ejpam-4030	176	32	equations	equation	NOUN
ejpam-4030	176	33	(	(	PUNCT
ejpam-4030	176	34	25.11.35	25.11.35	NOUN
ejpam-4030	176	35	)	)	PUNCT
ejpam-4030	176	36	and	and	CCONJ
ejpam-4030	176	37	(	(	PUNCT
ejpam-4030	176	38	25.11.40	25.11.40	NOUN
ejpam-4030	176	39	)	)	PUNCT
ejpam-4030	176	40	in	in	ADP
ejpam-4030	176	41	[	[	X
ejpam-4030	176	42	12	12	NUM
ejpam-4030	176	43	]	]	PUNCT
ejpam-4030	176	44	to	to	ADP
ejpam-4030	176	45	get∫	get∫	PROPN
ejpam-4030	176	46	+	+	PROPN
ejpam-4030	176	47	∞	∞	PROPN
ejpam-4030	176	48	0	0	NUM
ejpam-4030	176	49	1−	1−	NUM
ejpam-4030	176	50	x√	x√	NUM
ejpam-4030	176	51	x(x+	x(x+	PROPN
ejpam-4030	177	1	1)2	1)2	NUM
ejpam-4030	177	2	log(x	log(x	NUM
ejpam-4030	177	3	)	)	PUNCT
ejpam-4030	177	4	dx	dx	PROPN
ejpam-4030	178	1	=	=	SYM
ejpam-4030	178	2	−4c	−4c	PROPN
ejpam-4030	178	3	π	π	X
ejpam-4030	178	4	(	(	PUNCT
ejpam-4030	178	5	20	20	NUM
ejpam-4030	178	6	)	)	PUNCT
ejpam-4030	178	7	proposition	proposition	NOUN
ejpam-4030	178	8	9	9	NUM
ejpam-4030	178	9	.	.	PUNCT
ejpam-4030	178	10	using	use	VERB
ejpam-4030	178	11	equation	equation	NOUN
ejpam-4030	178	12	(	(	PUNCT
ejpam-4030	178	13	19	19	NUM
ejpam-4030	178	14	)	)	PUNCT
ejpam-4030	178	15	setting	set	VERB
ejpam-4030	178	16	k	k	X
ejpam-4030	178	17	=	=	PUNCT
ejpam-4030	178	18	−1/2	−1/2	ADJ
ejpam-4030	178	19	,	,	PUNCT
ejpam-4030	178	20	b	b	X
ejpam-4030	178	21	=	=	SYM
ejpam-4030	178	22	−i	−i	PROPN
ejpam-4030	178	23	,	,	PUNCT
ejpam-4030	178	24	c	c	NOUN
ejpam-4030	178	25	=	=	SYM
ejpam-4030	178	26	1	1	NUM
ejpam-4030	178	27	and	and	CCONJ
ejpam-4030	178	28	simplifying	simplify	VERB
ejpam-4030	178	29	to	to	PART
ejpam-4030	178	30	get	get	VERB
ejpam-4030	178	31	∫	∫	PROPN
ejpam-4030	179	1	+	+	PROPN
ejpam-4030	179	2	∞	∞	PROPN
ejpam-4030	179	3	0	0	NUM
ejpam-4030	179	4	x−	x−	PROPN
ejpam-4030	179	5	1	1	NUM
ejpam-4030	179	6	√	√	NUM
ejpam-4030	179	7	x(x+	x(x+	PUNCT
ejpam-4030	180	1	1)2	1)2	NUM
ejpam-4030	180	2	√	√	NUM
ejpam-4030	180	3	log	log	NOUN
ejpam-4030	180	4	(	(	PUNCT
ejpam-4030	180	5	−	−	PROPN
ejpam-4030	180	6	i	i	NOUN
ejpam-4030	180	7	x	x	X
ejpam-4030	180	8	)	)	PUNCT
ejpam-4030	180	9	dx	dx	PROPN
ejpam-4030	180	10	=	=	SYM
ejpam-4030	180	11	(	(	PUNCT
ejpam-4030	180	12	−1)3/4	−1)3/4	INTJ
ejpam-4030	180	13	(	(	PUNCT
ejpam-4030	180	14	ζ	ζ	X
ejpam-4030	180	15	(	(	PUNCT
ejpam-4030	180	16	3	3	NUM
ejpam-4030	180	17	2	2	NUM
ejpam-4030	180	18	,	,	PUNCT
ejpam-4030	180	19	3	3	NUM
ejpam-4030	180	20	8	8	NUM
ejpam-4030	180	21	)	)	PUNCT
ejpam-4030	180	22	−	−	PROPN
ejpam-4030	181	1	ζ	ζ	NOUN
ejpam-4030	181	2	(	(	PUNCT
ejpam-4030	181	3	3	3	NUM
ejpam-4030	181	4	2	2	NUM
ejpam-4030	181	5	,	,	PUNCT
ejpam-4030	181	6	7	7	NUM
ejpam-4030	181	7	8	8	NUM
ejpam-4030	181	8	)	)	PUNCT
ejpam-4030	181	9	)	)	PUNCT
ejpam-4030	181	10	4	4	NUM
ejpam-4030	181	11	√	√	NUM
ejpam-4030	181	12	π	π	PROPN
ejpam-4030	181	13	(	(	PUNCT
ejpam-4030	181	14	21	21	NUM
ejpam-4030	181	15	)	)	PUNCT
ejpam-4030	181	16	r.	r.	PROPN
ejpam-4030	181	17	reynolds	reynolds	PROPN
ejpam-4030	181	18	,	,	PUNCT
ejpam-4030	181	19	a.	a.	PROPN
ejpam-4030	181	20	stauffer	stauffer	PROPN
ejpam-4030	181	21	/	/	SYM
ejpam-4030	181	22	eur	eur	PROPN
ejpam-4030	181	23	.	.	PUNCT
ejpam-4030	182	1	j.	j.	PROPN
ejpam-4030	182	2	pure	pure	PROPN
ejpam-4030	182	3	appl	appl	PROPN
ejpam-4030	182	4	.	.	PROPN
ejpam-4030	182	5	math	math	PROPN
ejpam-4030	182	6	,	,	PUNCT
ejpam-4030	182	7	14	14	NUM
ejpam-4030	182	8	(	(	PUNCT
ejpam-4030	182	9	3	3	NUM
ejpam-4030	182	10	)	)	PUNCT
ejpam-4030	182	11	(	(	PUNCT
ejpam-4030	182	12	2021	2021	NUM
ejpam-4030	182	13	)	)	PUNCT
ejpam-4030	182	14	,	,	PUNCT
ejpam-4030	182	15	788	788	NUM
ejpam-4030	182	16	-	-	SYM
ejpam-4030	182	17	802	802	NUM
ejpam-4030	182	18	795	795	NUM
ejpam-4030	182	19	proposition	proposition	NOUN
ejpam-4030	182	20	10	10	NUM
ejpam-4030	182	21	.	.	PUNCT
ejpam-4030	183	1	using	use	VERB
ejpam-4030	183	2	equation	equation	NOUN
ejpam-4030	183	3	(	(	PUNCT
ejpam-4030	183	4	19	19	NUM
ejpam-4030	183	5	)	)	PUNCT
ejpam-4030	183	6	setting	set	VERB
ejpam-4030	183	7	k	k	X
ejpam-4030	183	8	=	=	SYM
ejpam-4030	183	9	1/2	1/2	NUM
ejpam-4030	183	10	,	,	PUNCT
ejpam-4030	183	11	b	b	NOUN
ejpam-4030	183	12	=	=	SYM
ejpam-4030	183	13	−i	−i	PROPN
ejpam-4030	183	14	,	,	PUNCT
ejpam-4030	183	15	c	c	NOUN
ejpam-4030	183	16	=	=	SYM
ejpam-4030	183	17	1	1	NUM
ejpam-4030	183	18	and	and	CCONJ
ejpam-4030	183	19	simplifying	simplify	VERB
ejpam-4030	183	20	to	to	PART
ejpam-4030	183	21	get	get	VERB
ejpam-4030	183	22	∫	∫	PROPN
ejpam-4030	184	1	+	+	PROPN
ejpam-4030	184	2	∞	∞	PROPN
ejpam-4030	184	3	0	0	NUM
ejpam-4030	184	4	(	(	PUNCT
ejpam-4030	184	5	x−	x−	PROPN
ejpam-4030	184	6	1	1	NUM
ejpam-4030	184	7	)	)	PUNCT
ejpam-4030	184	8	√	√	NOUN
ejpam-4030	185	1	log	log	NOUN
ejpam-4030	185	2	(	(	PUNCT
ejpam-4030	185	3	−	−	PROPN
ejpam-4030	185	4	i	i	NOUN
ejpam-4030	185	5	x	x	PUNCT
ejpam-4030	185	6	)	)	PUNCT
ejpam-4030	186	1	√	√	ADP
ejpam-4030	186	2	x(x+	x(x+	PUNCT
ejpam-4030	187	1	1)2	1)2	NUM
ejpam-4030	187	2	dx	dx	X
ejpam-4030	187	3	=	=	SYM
ejpam-4030	187	4	4	4	NUM
ejpam-4030	187	5	√	√	NUM
ejpam-4030	187	6	−1	−1	NOUN
ejpam-4030	187	7	√	√	PROPN
ejpam-4030	187	8	π	π	PROPN
ejpam-4030	187	9	(	(	PUNCT
ejpam-4030	187	10	ζ	ζ	X
ejpam-4030	187	11	(	(	PUNCT
ejpam-4030	187	12	1	1	NUM
ejpam-4030	187	13	2	2	NUM
ejpam-4030	187	14	,	,	PUNCT
ejpam-4030	187	15	7	7	NUM
ejpam-4030	187	16	8	8	NUM
ejpam-4030	187	17	)	)	PUNCT
ejpam-4030	187	18	−	−	PROPN
ejpam-4030	188	1	ζ	ζ	NOUN
ejpam-4030	188	2	(	(	PUNCT
ejpam-4030	188	3	1	1	NUM
ejpam-4030	188	4	2	2	NUM
ejpam-4030	188	5	,	,	PUNCT
ejpam-4030	188	6	3	3	NUM
ejpam-4030	188	7	8	8	NUM
ejpam-4030	188	8	)	)	PUNCT
ejpam-4030	188	9	)	)	PUNCT
ejpam-4030	189	1	(	(	PUNCT
ejpam-4030	189	2	22	22	NUM
ejpam-4030	189	3	)	)	PUNCT
ejpam-4030	189	4	8	8	NUM
ejpam-4030	189	5	.	.	PUNCT
ejpam-4030	190	1	definite	definite	ADJ
ejpam-4030	190	2	integrals	integral	NOUN
ejpam-4030	190	3	in	in	ADP
ejpam-4030	190	4	terms	term	NOUN
ejpam-4030	190	5	of	of	ADP
ejpam-4030	190	6	the	the	DET
ejpam-4030	190	7	lerch	lerch	PROPN
ejpam-4030	190	8	function	function	PROPN
ejpam-4030	190	9	when	when	SCONJ
ejpam-4030	190	10	n	n	X
ejpam-4030	190	11	∈	∈	PROPN
ejpam-4030	190	12	z−	z−	ADJ
ejpam-4030	190	13	proposition	proposition	NOUN
ejpam-4030	190	14	11	11	NUM
ejpam-4030	190	15	.	.	PUNCT
ejpam-4030	191	1	for	for	ADP
ejpam-4030	191	2	k	k	PROPN
ejpam-4030	191	3	,	,	PUNCT
ejpam-4030	191	4	b	b	X
ejpam-4030	191	5	∈	∈	PROPN
ejpam-4030	191	6	c∫	c∫	NOUN
ejpam-4030	192	1	+	+	NOUN
ejpam-4030	192	2	∞	∞	PROPN
ejpam-4030	192	3	0	0	NUM
ejpam-4030	193	1	(	(	PUNCT
ejpam-4030	193	2	(	(	PUNCT
ejpam-4030	193	3	x−	x−	PROPN
ejpam-4030	193	4	6)x+	6)x+	NUM
ejpam-4030	193	5	1	1	NUM
ejpam-4030	193	6	)	)	PUNCT
ejpam-4030	193	7	logk	logk	NOUN
ejpam-4030	193	8	(	(	PUNCT
ejpam-4030	193	9	b	b	NOUN
ejpam-4030	193	10	x	x	X
ejpam-4030	193	11	)	)	PUNCT
ejpam-4030	193	12	4	4	NUM
ejpam-4030	193	13	√	√	NUM
ejpam-4030	193	14	x(x+	x(x+	PROPN
ejpam-4030	194	1	1)3	1)3	PROPN
ejpam-4030	194	2	dx	dx	PROPN
ejpam-4030	195	1	=	=	SYM
ejpam-4030	195	2	22k−3e−	22k−3e−	NUM
ejpam-4030	195	3	1	1	NUM
ejpam-4030	195	4	2	2	NUM
ejpam-4030	195	5	iπk(k	iπk(k	PROPN
ejpam-4030	195	6	−	−	PROPN
ejpam-4030	195	7	1)kπk−1	1)kπk−1	NUM
ejpam-4030	195	8	(	(	PUNCT
ejpam-4030	195	9	ζ	ζ	PROPN
ejpam-4030	195	10	(	(	PUNCT
ejpam-4030	195	11	2−	2−	NUM
ejpam-4030	195	12	k	k	NOUN
ejpam-4030	195	13	,	,	PUNCT
ejpam-4030	195	14	i	i	PRON
ejpam-4030	195	15	log(b	log(b	PROPN
ejpam-4030	195	16	)	)	PUNCT
ejpam-4030	195	17	4π	4π	PRON
ejpam-4030	195	18	+	+	CCONJ
ejpam-4030	195	19	3	3	NUM
ejpam-4030	195	20	4	4	NUM
ejpam-4030	195	21	)	)	PUNCT
ejpam-4030	195	22	−	−	PROPN
ejpam-4030	195	23	ζ	ζ	NOUN
ejpam-4030	195	24	(	(	PUNCT
ejpam-4030	195	25	2−	2−	NUM
ejpam-4030	195	26	k	k	NOUN
ejpam-4030	195	27	,	,	PUNCT
ejpam-4030	195	28	i	i	PRON
ejpam-4030	195	29	log(b	log(b	PROPN
ejpam-4030	195	30	)	)	PUNCT
ejpam-4030	195	31	+	+	NUM
ejpam-4030	195	32	π	π	NOUN
ejpam-4030	195	33	4π	4π	NUM
ejpam-4030	195	34	)	)	PUNCT
ejpam-4030	195	35	)	)	PUNCT
ejpam-4030	195	36	(	(	PUNCT
ejpam-4030	195	37	23	23	X
ejpam-4030	195	38	)	)	PUNCT
ejpam-4030	195	39	proof	proof	NOUN
ejpam-4030	195	40	.	.	PUNCT
ejpam-4030	196	1	use	use	VERB
ejpam-4030	196	2	equation	equation	NOUN
ejpam-4030	196	3	(	(	PUNCT
ejpam-4030	196	4	8)	8)	NUM
ejpam-4030	196	5	and	and	CCONJ
ejpam-4030	196	6	set	set	VERB
ejpam-4030	196	7	a	a	DET
ejpam-4030	196	8	=	=	NOUN
ejpam-4030	196	9	1/2	1/2	NUM
ejpam-4030	196	10	,	,	PUNCT
ejpam-4030	196	11	n	n	NOUN
ejpam-4030	196	12	=	=	SYM
ejpam-4030	196	13	−2	−2	NOUN
ejpam-4030	196	14	,	,	PUNCT
ejpam-4030	196	15	c	c	NOUN
ejpam-4030	196	16	=	=	SYM
ejpam-4030	196	17	1	1	NUM
ejpam-4030	196	18	then	then	ADV
ejpam-4030	196	19	simplify	simplify	VERB
ejpam-4030	196	20	using	use	VERB
ejpam-4030	196	21	entry	entry	NOUN
ejpam-4030	196	22	(	(	PUNCT
ejpam-4030	196	23	4	4	NUM
ejpam-4030	196	24	)	)	PUNCT
ejpam-4030	196	25	in	in	ADP
ejpam-4030	196	26	table	table	NOUN
ejpam-4030	196	27	below	below	ADV
ejpam-4030	196	28	(	(	PUNCT
ejpam-4030	196	29	64:12:7	64:12:7	NUM
ejpam-4030	196	30	)	)	PUNCT
ejpam-4030	196	31	in	in	ADP
ejpam-4030	196	32	[	[	X
ejpam-4030	196	33	11	11	NUM
ejpam-4030	196	34	]	]	PUNCT
ejpam-4030	196	35	.	.	PUNCT
ejpam-4030	197	1	proposition	proposition	NOUN
ejpam-4030	197	2	12	12	NUM
ejpam-4030	197	3	.	.	PUNCT
ejpam-4030	198	1	using	use	VERB
ejpam-4030	198	2	equation	equation	NOUN
ejpam-4030	198	3	(	(	PUNCT
ejpam-4030	198	4	23	23	NUM
ejpam-4030	198	5	)	)	PUNCT
ejpam-4030	198	6	and	and	CCONJ
ejpam-4030	198	7	setting	set	VERB
ejpam-4030	198	8	k	k	PROPN
ejpam-4030	198	9	=	=	PUNCT
ejpam-4030	198	10	−1	−1	NOUN
ejpam-4030	198	11	,	,	PUNCT
ejpam-4030	198	12	b	b	X
ejpam-4030	198	13	=	=	PUNCT
ejpam-4030	198	14	−i	−i	PROPN
ejpam-4030	198	15	and	and	CCONJ
ejpam-4030	198	16	simplifying	simplify	VERB
ejpam-4030	198	17	we	we	PRON
ejpam-4030	198	18	get∫	get∫	PROPN
ejpam-4030	199	1	+	+	PROPN
ejpam-4030	199	2	∞	∞	NOUN
ejpam-4030	199	3	0	0	NUM
ejpam-4030	200	1	(	(	PUNCT
ejpam-4030	200	2	x−	x−	PROPN
ejpam-4030	200	3	6)x+	6)x+	NUM
ejpam-4030	200	4	1	1	NUM
ejpam-4030	200	5	√	√	NUM
ejpam-4030	200	6	x(x+	x(x+	PROPN
ejpam-4030	201	1	1)3	1)3	PROPN
ejpam-4030	201	2	(	(	PUNCT
ejpam-4030	201	3	4	4	NUM
ejpam-4030	201	4	log2(x	log2(x	NOUN
ejpam-4030	201	5	)	)	PUNCT
ejpam-4030	202	1	+	+	CCONJ
ejpam-4030	202	2	π2	π2	ADJ
ejpam-4030	202	3	)	)	PUNCT
ejpam-4030	202	4	dx	dx	PROPN
ejpam-4030	202	5	=	=	SYM
ejpam-4030	202	6	ζ	ζ	PROPN
ejpam-4030	202	7	(	(	PUNCT
ejpam-4030	202	8	3	3	NUM
ejpam-4030	202	9	,	,	PUNCT
ejpam-4030	202	10	78	78	NUM
ejpam-4030	202	11	)	)	PUNCT
ejpam-4030	202	12	−	−	PROPN
ejpam-4030	202	13	ζ	ζ	NOUN
ejpam-4030	202	14	(	(	PUNCT
ejpam-4030	202	15	3	3	NUM
ejpam-4030	202	16	,	,	PUNCT
ejpam-4030	202	17	38	38	NUM
ejpam-4030	202	18	)	)	PUNCT
ejpam-4030	202	19	8π3	8π3	PROPN
ejpam-4030	202	20	(	(	PUNCT
ejpam-4030	202	21	24	24	NUM
ejpam-4030	202	22	)	)	PUNCT
ejpam-4030	202	23	theorem	theorem	VERB
ejpam-4030	202	24	6.∫	6.∫	NUM
ejpam-4030	203	1	+	+	NOUN
ejpam-4030	203	2	∞	∞	NOUN
ejpam-4030	203	3	0	0	NUM
ejpam-4030	203	4	(	(	PUNCT
ejpam-4030	203	5	(	(	PUNCT
ejpam-4030	203	6	x−	x−	PROPN
ejpam-4030	203	7	6)x+	6)x+	NUM
ejpam-4030	203	8	1	1	NUM
ejpam-4030	203	9	)	)	PUNCT
ejpam-4030	203	10	log	log	NOUN
ejpam-4030	203	11	(	(	PUNCT
ejpam-4030	203	12	−	−	PROPN
ejpam-4030	203	13	log(x	log(x	NUM
ejpam-4030	203	14	)	)	PUNCT
ejpam-4030	204	1	+	+	CCONJ
ejpam-4030	204	2	iπ	iπ	DET
ejpam-4030	204	3	2	2	X
ejpam-4030	204	4	)	)	PUNCT
ejpam-4030	204	5	√	√	ADP
ejpam-4030	204	6	x(x+	x(x+	PROPN
ejpam-4030	205	1	1)3	1)3	PROPN
ejpam-4030	205	2	dx	dx	PROPN
ejpam-4030	205	3	=	=	SYM
ejpam-4030	205	4	ψ(1	ψ(1	PROPN
ejpam-4030	205	5	)	)	PUNCT
ejpam-4030	205	6	(	(	PUNCT
ejpam-4030	205	7	3	3	NUM
ejpam-4030	205	8	8	8	NUM
ejpam-4030	205	9	)	)	PUNCT
ejpam-4030	205	10	−	−	PROPN
ejpam-4030	206	1	ψ(1	ψ(1	PROPN
ejpam-4030	206	2	)	)	PUNCT
ejpam-4030	206	3	(	(	PUNCT
ejpam-4030	206	4	7	7	NUM
ejpam-4030	206	5	8	8	NUM
ejpam-4030	206	6	)	)	PUNCT
ejpam-4030	206	7	2π	2π	NOUN
ejpam-4030	206	8	(	(	PUNCT
ejpam-4030	206	9	25	25	NUM
ejpam-4030	206	10	)	)	PUNCT
ejpam-4030	206	11	proof	proof	NOUN
ejpam-4030	206	12	.	.	PUNCT
ejpam-4030	207	1	use	use	VERB
ejpam-4030	207	2	equation	equation	NOUN
ejpam-4030	207	3	(	(	PUNCT
ejpam-4030	207	4	23	23	NUM
ejpam-4030	207	5	)	)	PUNCT
ejpam-4030	207	6	take	take	VERB
ejpam-4030	207	7	the	the	DET
ejpam-4030	207	8	first	first	ADJ
ejpam-4030	207	9	partial	partial	ADJ
ejpam-4030	207	10	derivative	derivative	NOUN
ejpam-4030	207	11	with	with	ADP
ejpam-4030	207	12	respect	respect	NOUN
ejpam-4030	207	13	to	to	ADP
ejpam-4030	207	14	k	k	PROPN
ejpam-4030	207	15	then	then	ADV
ejpam-4030	207	16	set	set	VERB
ejpam-4030	207	17	k	k	PROPN
ejpam-4030	207	18	=	=	SYM
ejpam-4030	207	19	0	0	NUM
ejpam-4030	207	20	,	,	PUNCT
ejpam-4030	207	21	b	b	X
ejpam-4030	207	22	=	=	PUNCT
ejpam-4030	207	23	−i	−i	PROPN
ejpam-4030	207	24	and	and	CCONJ
ejpam-4030	207	25	simplify	simplify	VERB
ejpam-4030	207	26	.	.	PUNCT
ejpam-4030	208	1	proposition	proposition	NOUN
ejpam-4030	208	2	13	13	NUM
ejpam-4030	208	3	.	.	PUNCT
ejpam-4030	209	1	for	for	ADP
ejpam-4030	209	2	k	k	PROPN
ejpam-4030	209	3	,	,	PUNCT
ejpam-4030	209	4	b	b	NOUN
ejpam-4030	209	5	,	,	PUNCT
ejpam-4030	209	6	c	c	PROPN
ejpam-4030	209	7	∈	∈	PROPN
ejpam-4030	209	8	c∫	c∫	PROPN
ejpam-4030	210	1	+	+	NOUN
ejpam-4030	210	2	∞	∞	PROPN
ejpam-4030	210	3	0	0	NUM
ejpam-4030	210	4	(	(	PUNCT
ejpam-4030	210	5	cx−	cx−	ADP
ejpam-4030	210	6	1	1	NUM
ejpam-4030	210	7	)	)	PUNCT
ejpam-4030	210	8	logk	logk	NOUN
ejpam-4030	210	9	(	(	PUNCT
ejpam-4030	210	10	b	b	NOUN
ejpam-4030	210	11	x	x	X
ejpam-4030	210	12	)	)	PUNCT
ejpam-4030	210	13	(	(	PUNCT
ejpam-4030	210	14	cx+	cx+	NOUN
ejpam-4030	210	15	1)3	1)3	PROPN
ejpam-4030	210	16	dx	dx	PROPN
ejpam-4030	210	17	=	=	PUNCT
ejpam-4030	211	1	ie−	ie−	SYM
ejpam-4030	211	2	1	1	NUM
ejpam-4030	211	3	2	2	NUM
ejpam-4030	211	4	iπk(k	iπk(k	NOUN
ejpam-4030	211	5	−	−	PROPN
ejpam-4030	211	6	1)k(2π)k−1ζ	1)k(2π)k−1ζ	NUM
ejpam-4030	211	7	(	(	PUNCT
ejpam-4030	211	8	2−	2−	NUM
ejpam-4030	211	9	k	k	NOUN
ejpam-4030	211	10	,	,	PUNCT
ejpam-4030	211	11	i	i	PRON
ejpam-4030	211	12	log(b)+i	log(b)+i	X
ejpam-4030	211	13	log(c)+π2π	log(c)+π2π	PROPN
ejpam-4030	211	14	)	)	PUNCT
ejpam-4030	212	1	c	c	NOUN
ejpam-4030	212	2	(	(	PUNCT
ejpam-4030	212	3	26	26	NUM
ejpam-4030	212	4	)	)	PUNCT
ejpam-4030	212	5	proof	proof	NOUN
ejpam-4030	212	6	.	.	PUNCT
ejpam-4030	213	1	use	use	VERB
ejpam-4030	213	2	equation	equation	NOUN
ejpam-4030	213	3	(	(	PUNCT
ejpam-4030	213	4	8)	8)	NUM
ejpam-4030	213	5	and	and	CCONJ
ejpam-4030	213	6	set	set	VERB
ejpam-4030	213	7	a	a	DET
ejpam-4030	213	8	=	=	SYM
ejpam-4030	213	9	1	1	NUM
ejpam-4030	213	10	,	,	PUNCT
ejpam-4030	213	11	n	n	NOUN
ejpam-4030	213	12	=	=	NOUN
ejpam-4030	213	13	−2	−2	NOUN
ejpam-4030	213	14	then	then	ADV
ejpam-4030	213	15	simplify	simplify	VERB
ejpam-4030	213	16	using	use	VERB
ejpam-4030	213	17	entry	entry	NOUN
ejpam-4030	213	18	(	(	PUNCT
ejpam-4030	213	19	4	4	NUM
ejpam-4030	213	20	)	)	PUNCT
ejpam-4030	213	21	in	in	ADP
ejpam-4030	213	22	table	table	NOUN
ejpam-4030	213	23	below	below	ADV
ejpam-4030	213	24	(	(	PUNCT
ejpam-4030	213	25	64:12:7	64:12:7	NUM
ejpam-4030	213	26	)	)	PUNCT
ejpam-4030	213	27	in	in	ADP
ejpam-4030	213	28	[	[	X
ejpam-4030	213	29	11	11	NUM
ejpam-4030	213	30	]	]	PUNCT
ejpam-4030	213	31	.	.	PUNCT
ejpam-4030	214	1	proposition	proposition	NOUN
ejpam-4030	214	2	14	14	NUM
ejpam-4030	214	3	.	.	PUNCT
ejpam-4030	215	1	using	use	VERB
ejpam-4030	215	2	equation	equation	NOUN
ejpam-4030	215	3	(	(	PUNCT
ejpam-4030	215	4	26	26	NUM
ejpam-4030	215	5	)	)	PUNCT
ejpam-4030	215	6	and	and	CCONJ
ejpam-4030	215	7	setting	set	VERB
ejpam-4030	215	8	k	k	PROPN
ejpam-4030	215	9	=	=	PUNCT
ejpam-4030	215	10	−1	−1	NOUN
ejpam-4030	215	11	,	,	PUNCT
ejpam-4030	215	12	b	b	X
ejpam-4030	216	1	=	=	SYM
ejpam-4030	216	2	−i	−i	PROPN
ejpam-4030	216	3	,	,	PUNCT
ejpam-4030	216	4	c	c	NOUN
ejpam-4030	216	5	=	=	SYM
ejpam-4030	216	6	1	1	NUM
ejpam-4030	216	7	,	,	PUNCT
ejpam-4030	216	8	rationalizing	rationalize	VERB
ejpam-4030	216	9	the	the	DET
ejpam-4030	216	10	denominator	denominator	NOUN
ejpam-4030	216	11	and	and	CCONJ
ejpam-4030	216	12	simplify	simplify	VERB
ejpam-4030	216	13	we	we	PRON
ejpam-4030	216	14	get∫	get∫	VERB
ejpam-4030	217	1	+	+	PROPN
ejpam-4030	217	2	∞	∞	NOUN
ejpam-4030	217	3	0	0	NUM
ejpam-4030	217	4	(	(	PUNCT
ejpam-4030	217	5	x−	x−	PROPN
ejpam-4030	217	6	1	1	NUM
ejpam-4030	217	7	)	)	PUNCT
ejpam-4030	217	8	log(x	log(x	NUM
ejpam-4030	217	9	)	)	PUNCT
ejpam-4030	218	1	(	(	PUNCT
ejpam-4030	218	2	x+	x+	PROPN
ejpam-4030	218	3	1)3	1)3	PROPN
ejpam-4030	218	4	(	(	PUNCT
ejpam-4030	218	5	4	4	NUM
ejpam-4030	218	6	log2(x	log2(x	NOUN
ejpam-4030	218	7	)	)	PUNCT
ejpam-4030	218	8	+	+	CCONJ
ejpam-4030	218	9	π2	π2	ADJ
ejpam-4030	218	10	)	)	PUNCT
ejpam-4030	218	11	dx	dx	PROPN
ejpam-4030	218	12	=	=	SYM
ejpam-4030	218	13	ζ	ζ	PROPN
ejpam-4030	218	14	(	(	PUNCT
ejpam-4030	218	15	3	3	NUM
ejpam-4030	218	16	,	,	PUNCT
ejpam-4030	218	17	34	34	NUM
ejpam-4030	218	18	)	)	PUNCT
ejpam-4030	218	19	8π2	8π2	NUM
ejpam-4030	218	20	(	(	PUNCT
ejpam-4030	218	21	27	27	NUM
ejpam-4030	218	22	)	)	PUNCT
ejpam-4030	218	23	and	and	CCONJ
ejpam-4030	218	24	∫	∫	PROPN
ejpam-4030	219	1	+	+	PROPN
ejpam-4030	219	2	∞	∞	PROPN
ejpam-4030	219	3	0	0	NUM
ejpam-4030	219	4	x−	x−	PROPN
ejpam-4030	219	5	1	1	NUM
ejpam-4030	219	6	(	(	PUNCT
ejpam-4030	219	7	x+	x+	PROPN
ejpam-4030	219	8	1)3	1)3	PROPN
ejpam-4030	219	9	(	(	PUNCT
ejpam-4030	219	10	4	4	NUM
ejpam-4030	219	11	log2(x	log2(x	NOUN
ejpam-4030	219	12	)	)	PUNCT
ejpam-4030	219	13	+	+	CCONJ
ejpam-4030	219	14	π2	π2	ADJ
ejpam-4030	219	15	)	)	PUNCT
ejpam-4030	219	16	dx	dx	PROPN
ejpam-4030	219	17	=	=	SYM
ejpam-4030	219	18	0	0	NUM
ejpam-4030	219	19	(	(	PUNCT
ejpam-4030	219	20	28	28	NUM
ejpam-4030	219	21	)	)	PUNCT
ejpam-4030	219	22	r.	r.	PROPN
ejpam-4030	219	23	reynolds	reynolds	PROPN
ejpam-4030	219	24	,	,	PUNCT
ejpam-4030	219	25	a.	a.	PROPN
ejpam-4030	219	26	stauffer	stauffer	PROPN
ejpam-4030	219	27	/	/	SYM
ejpam-4030	219	28	eur	eur	PROPN
ejpam-4030	219	29	.	.	PUNCT
ejpam-4030	220	1	j.	j.	PROPN
ejpam-4030	220	2	pure	pure	PROPN
ejpam-4030	220	3	appl	appl	PROPN
ejpam-4030	220	4	.	.	PROPN
ejpam-4030	220	5	math	math	PROPN
ejpam-4030	220	6	,	,	PUNCT
ejpam-4030	220	7	14	14	NUM
ejpam-4030	220	8	(	(	PUNCT
ejpam-4030	220	9	3	3	NUM
ejpam-4030	220	10	)	)	PUNCT
ejpam-4030	220	11	(	(	PUNCT
ejpam-4030	220	12	2021	2021	NUM
ejpam-4030	220	13	)	)	PUNCT
ejpam-4030	220	14	,	,	PUNCT
ejpam-4030	220	15	788	788	NUM
ejpam-4030	220	16	-	-	SYM
ejpam-4030	220	17	802	802	NUM
ejpam-4030	220	18	796	796	NUM
ejpam-4030	220	19	theorem	theorem	NOUN
ejpam-4030	220	20	7	7	NUM
ejpam-4030	220	21	.	.	X
ejpam-4030	220	22	for	for	ADP
ejpam-4030	220	23	k	k	PROPN
ejpam-4030	220	24	,	,	PUNCT
ejpam-4030	220	25	b	b	NOUN
ejpam-4030	220	26	,	,	PUNCT
ejpam-4030	220	27	c	c	PROPN
ejpam-4030	220	28	∈	∈	PROPN
ejpam-4030	220	29	c∫	c∫	PROPN
ejpam-4030	221	1	+	+	NOUN
ejpam-4030	221	2	∞	∞	PROPN
ejpam-4030	221	3	0	0	NUM
ejpam-4030	221	4	(	(	PUNCT
ejpam-4030	221	5	cx(cx−	cx(cx−	ADP
ejpam-4030	221	6	4	4	NUM
ejpam-4030	221	7	)	)	PUNCT
ejpam-4030	221	8	+	+	CCONJ
ejpam-4030	221	9	1	1	X
ejpam-4030	221	10	)	)	PUNCT
ejpam-4030	221	11	log	log	NOUN
ejpam-4030	221	12	(	(	PUNCT
ejpam-4030	221	13	log	log	PROPN
ejpam-4030	221	14	(	(	PUNCT
ejpam-4030	221	15	b	b	NOUN
ejpam-4030	221	16	x	x	NOUN
ejpam-4030	221	17	)	)	PUNCT
ejpam-4030	221	18	)	)	PUNCT
ejpam-4030	222	1	logk	logk	NOUN
ejpam-4030	222	2	(	(	PUNCT
ejpam-4030	222	3	b	b	NOUN
ejpam-4030	222	4	x	x	X
ejpam-4030	222	5	)	)	PUNCT
ejpam-4030	222	6	(	(	PUNCT
ejpam-4030	222	7	cx+	cx+	NOUN
ejpam-4030	222	8	1)4	1)4	NUM
ejpam-4030	222	9	dx	dx	NOUN
ejpam-4030	223	1	=	=	SYM
ejpam-4030	223	2	−	−	PROPN
ejpam-4030	223	3	i2k−3e−	i2k−3e−	NOUN
ejpam-4030	223	4	1	1	NUM
ejpam-4030	223	5	2	2	NUM
ejpam-4030	223	6	ikππk−1ζ	ikππk−1ζ	NUM
ejpam-4030	223	7	(	(	PUNCT
ejpam-4030	223	8	3−	3−	NUM
ejpam-4030	223	9	k	k	NOUN
ejpam-4030	223	10	,	,	PUNCT
ejpam-4030	223	11	i	i	PRON
ejpam-4030	223	12	log(b)+i	log(b)+i	X
ejpam-4030	223	13	log(c)+π2π	log(c)+π2π	PROPN
ejpam-4030	223	14	)	)	PUNCT
ejpam-4030	224	1	k3	k3	VERB
ejpam-4030	224	2	c	c	PROPN
ejpam-4030	224	3	−	−	NOUN
ejpam-4030	224	4	e−	e−	PROPN
ejpam-4030	224	5	1	1	NUM
ejpam-4030	224	6	2	2	NUM
ejpam-4030	224	7	ikπ(2π)k−2ζ	ikπ(2π)k−2ζ	NOUN
ejpam-4030	224	8	′	′	NUM
ejpam-4030	225	1	(	(	PUNCT
ejpam-4030	225	2	3−	3−	NUM
ejpam-4030	225	3	k	k	NOUN
ejpam-4030	225	4	,	,	PUNCT
ejpam-4030	225	5	i	i	PRON
ejpam-4030	225	6	log(b)+i	log(b)+i	X
ejpam-4030	225	7	log(c)+π2π	log(c)+π2π	PROPN
ejpam-4030	225	8	)	)	PUNCT
ejpam-4030	226	1	k3	k3	VERB
ejpam-4030	226	2	c	c	NOUN
ejpam-4030	227	1	+	+	CCONJ
ejpam-4030	227	2	e−	e−	PROPN
ejpam-4030	227	3	1	1	NUM
ejpam-4030	227	4	2	2	NUM
ejpam-4030	227	5	ikπ(2π)k−2ζ	ikπ(2π)k−2ζ	NOUN
ejpam-4030	227	6	(	(	PUNCT
ejpam-4030	227	7	3−	3−	NUM
ejpam-4030	227	8	k	k	NOUN
ejpam-4030	227	9	,	,	PUNCT
ejpam-4030	227	10	i	i	PRON
ejpam-4030	227	11	log(b)+i	log(b)+i	X
ejpam-4030	227	12	log(c)+π2π	log(c)+π2π	PROPN
ejpam-4030	227	13	)	)	PUNCT
ejpam-4030	227	14	log(2π)k3	log(2π)k3	NOUN
ejpam-4030	227	15	c	c	NOUN
ejpam-4030	228	1	+	+	NOUN
ejpam-4030	228	2	3e−	3e−	NUM
ejpam-4030	228	3	1	1	NUM
ejpam-4030	228	4	2	2	NUM
ejpam-4030	228	5	ikπ(2π)k−2ζ	ikπ(2π)k−2ζ	NOUN
ejpam-4030	228	6	(	(	PUNCT
ejpam-4030	228	7	3−	3−	NUM
ejpam-4030	228	8	k	k	NOUN
ejpam-4030	228	9	,	,	PUNCT
ejpam-4030	228	10	i	i	PRON
ejpam-4030	228	11	log(b)+i	log(b)+i	X
ejpam-4030	228	12	log(c)+π2π	log(c)+π2π	PROPN
ejpam-4030	228	13	)	)	PUNCT
ejpam-4030	229	1	k2	k2	PROPN
ejpam-4030	229	2	c	c	PROPN
ejpam-4030	230	1	+	+	CCONJ
ejpam-4030	230	2	3i2k−3e−	3i2k−3e−	NUM
ejpam-4030	230	3	1	1	NUM
ejpam-4030	230	4	2	2	NUM
ejpam-4030	230	5	ikππk−1ζ	ikππk−1ζ	NUM
ejpam-4030	230	6	(	(	PUNCT
ejpam-4030	230	7	3−	3−	NUM
ejpam-4030	230	8	k	k	NOUN
ejpam-4030	230	9	,	,	PUNCT
ejpam-4030	230	10	i	i	PRON
ejpam-4030	230	11	log(b)+i	log(b)+i	X
ejpam-4030	230	12	log(c)+π2π	log(c)+π2π	PROPN
ejpam-4030	230	13	)	)	PUNCT
ejpam-4030	230	14	k2	k2	PROPN
ejpam-4030	230	15	c	c	PROPN
ejpam-4030	231	1	+	+	CCONJ
ejpam-4030	231	2	2k−1e−	2k−1e−	NUM
ejpam-4030	231	3	1	1	NUM
ejpam-4030	231	4	2	2	NUM
ejpam-4030	231	5	ikππk−2ζ	ikππk−2ζ	NUM
ejpam-4030	231	6	′	′	NUM
ejpam-4030	231	7	(	(	PUNCT
ejpam-4030	231	8	3−	3−	NUM
ejpam-4030	231	9	k	k	NOUN
ejpam-4030	231	10	,	,	PUNCT
ejpam-4030	231	11	i	i	PRON
ejpam-4030	231	12	log(b)+i	log(b)+i	X
ejpam-4030	231	13	log(c)+π2π	log(c)+π2π	PROPN
ejpam-4030	231	14	)	)	PUNCT
ejpam-4030	231	15	k2	k2	PROPN
ejpam-4030	231	16	c	c	PROPN
ejpam-4030	232	1	+	+	CCONJ
ejpam-4030	232	2	e−	e−	PROPN
ejpam-4030	232	3	1	1	NUM
ejpam-4030	232	4	2	2	NUM
ejpam-4030	232	5	ikπ(2π)k−2ζ	ikπ(2π)k−2ζ	NOUN
ejpam-4030	232	6	′	′	NUM
ejpam-4030	233	1	(	(	PUNCT
ejpam-4030	233	2	3−	3−	NUM
ejpam-4030	233	3	k	k	NOUN
ejpam-4030	233	4	,	,	PUNCT
ejpam-4030	233	5	i	i	PRON
ejpam-4030	233	6	log(b)+i	log(b)+i	X
ejpam-4030	233	7	log(c)+π2π	log(c)+π2π	PROPN
ejpam-4030	233	8	)	)	PUNCT
ejpam-4030	233	9	k2	k2	PROPN
ejpam-4030	233	10	c	c	PROPN
ejpam-4030	234	1	−	−	PROPN
ejpam-4030	234	2	3e−	3e−	NUM
ejpam-4030	234	3	1	1	NUM
ejpam-4030	234	4	2	2	NUM
ejpam-4030	234	5	ikπ(2π)k−2ζ	ikπ(2π)k−2ζ	NOUN
ejpam-4030	234	6	(	(	PUNCT
ejpam-4030	234	7	3−	3−	NUM
ejpam-4030	234	8	k	k	NOUN
ejpam-4030	234	9	,	,	PUNCT
ejpam-4030	234	10	i	i	PRON
ejpam-4030	234	11	log(b)+i	log(b)+i	X
ejpam-4030	234	12	log(c)+π2π	log(c)+π2π	PROPN
ejpam-4030	234	13	)	)	PUNCT
ejpam-4030	234	14	log(2π)k2	log(2π)k2	NOUN
ejpam-4030	234	15	c	c	NOUN
ejpam-4030	234	16	−	−	PROPN
ejpam-4030	234	17	3	3	NUM
ejpam-4030	234	18	2k−1e−	2k−1e−	NUM
ejpam-4030	234	19	1	1	NUM
ejpam-4030	234	20	2	2	NUM
ejpam-4030	234	21	ikππk−2ζ	ikππk−2ζ	NUM
ejpam-4030	234	22	(	(	PUNCT
ejpam-4030	234	23	3−	3−	NUM
ejpam-4030	234	24	k	k	NOUN
ejpam-4030	234	25	,	,	PUNCT
ejpam-4030	234	26	i	i	PRON
ejpam-4030	234	27	log(b)+i	log(b)+i	X
ejpam-4030	234	28	log(c)+π2π	log(c)+π2π	PROPN
ejpam-4030	234	29	)	)	PUNCT
ejpam-4030	235	1	k	k	PROPN
ejpam-4030	236	1	c	c	NOUN
ejpam-4030	236	2	−	−	PROPN
ejpam-4030	237	1	i2k−2e−	i2k−2e−	PROPN
ejpam-4030	237	2	1	1	NUM
ejpam-4030	237	3	2	2	NUM
ejpam-4030	237	4	ikππk−1ζ	ikππk−1ζ	PROPN
ejpam-4030	237	5	(	(	PUNCT
ejpam-4030	237	6	3−	3−	NUM
ejpam-4030	237	7	k	k	NOUN
ejpam-4030	237	8	,	,	PUNCT
ejpam-4030	237	9	i	i	PRON
ejpam-4030	237	10	log(b)+i	log(b)+i	X
ejpam-4030	237	11	log(c)+π2π	log(c)+π2π	PROPN
ejpam-4030	237	12	)	)	PUNCT
ejpam-4030	238	1	k	k	PROPN
ejpam-4030	238	2	c	c	NOUN
ejpam-4030	239	1	−	−	PROPN
ejpam-4030	240	1	2k−1e−	2k−1e−	NUM
ejpam-4030	240	2	1	1	NUM
ejpam-4030	240	3	2	2	NUM
ejpam-4030	240	4	ikππk−2ζ	ikππk−2ζ	NUM
ejpam-4030	240	5	′	′	NUM
ejpam-4030	240	6	(	(	PUNCT
ejpam-4030	240	7	3−	3−	NUM
ejpam-4030	240	8	k	k	NOUN
ejpam-4030	240	9	,	,	PUNCT
ejpam-4030	240	10	i	i	PRON
ejpam-4030	240	11	log(b)+i	log(b)+i	X
ejpam-4030	240	12	log(c)+π2π	log(c)+π2π	PROPN
ejpam-4030	240	13	)	)	PUNCT
ejpam-4030	241	1	k	k	PROPN
ejpam-4030	241	2	c	c	NOUN
ejpam-4030	241	3	+	+	CCONJ
ejpam-4030	242	1	2k−1e−	2k−1e−	NUM
ejpam-4030	242	2	1	1	NUM
ejpam-4030	242	3	2	2	NUM
ejpam-4030	242	4	ikππk−2ζ	ikππk−2ζ	NUM
ejpam-4030	242	5	(	(	PUNCT
ejpam-4030	242	6	3−	3−	NUM
ejpam-4030	242	7	k	k	NOUN
ejpam-4030	242	8	,	,	PUNCT
ejpam-4030	242	9	i	i	PRON
ejpam-4030	242	10	log(b)+i	log(b)+i	X
ejpam-4030	242	11	log(c)+π2π	log(c)+π2π	PROPN
ejpam-4030	242	12	)	)	PUNCT
ejpam-4030	242	13	log(2π)k	log(2π)k	VERB
ejpam-4030	242	14	c	c	NOUN
ejpam-4030	243	1	+	+	CCONJ
ejpam-4030	243	2	2k−1e−	2k−1e−	NUM
ejpam-4030	243	3	1	1	NUM
ejpam-4030	243	4	2	2	NUM
ejpam-4030	243	5	ikππk−2ζ	ikππk−2ζ	NUM
ejpam-4030	243	6	(	(	PUNCT
ejpam-4030	243	7	3−	3−	NUM
ejpam-4030	243	8	k	k	NOUN
ejpam-4030	243	9	,	,	PUNCT
ejpam-4030	243	10	i	i	PRON
ejpam-4030	243	11	log(b)+i	log(b)+i	X
ejpam-4030	243	12	log(c)+π2π	log(c)+π2π	PROPN
ejpam-4030	243	13	)	)	PUNCT
ejpam-4030	244	1	c	c	NOUN
ejpam-4030	244	2	(	(	PUNCT
ejpam-4030	244	3	29	29	NUM
ejpam-4030	244	4	)	)	PUNCT
ejpam-4030	244	5	proof	proof	NOUN
ejpam-4030	244	6	.	.	PUNCT
ejpam-4030	245	1	use	use	VERB
ejpam-4030	245	2	equation	equation	NOUN
ejpam-4030	245	3	(	(	PUNCT
ejpam-4030	245	4	8)	8)	NUM
ejpam-4030	245	5	and	and	CCONJ
ejpam-4030	245	6	set	set	VERB
ejpam-4030	245	7	a	a	DET
ejpam-4030	245	8	=	=	SYM
ejpam-4030	245	9	1	1	NUM
ejpam-4030	245	10	,	,	PUNCT
ejpam-4030	245	11	n	n	NOUN
ejpam-4030	245	12	=	=	PRON
ejpam-4030	245	13	−3	−3	NOUN
ejpam-4030	245	14	then	then	ADV
ejpam-4030	245	15	simplify	simplify	VERB
ejpam-4030	245	16	using	use	VERB
ejpam-4030	245	17	entry	entry	NOUN
ejpam-4030	245	18	(	(	PUNCT
ejpam-4030	245	19	4	4	NUM
ejpam-4030	245	20	)	)	PUNCT
ejpam-4030	245	21	in	in	ADP
ejpam-4030	245	22	table	table	NOUN
ejpam-4030	245	23	below	below	ADV
ejpam-4030	245	24	(	(	PUNCT
ejpam-4030	245	25	64:12:7	64:12:7	NUM
ejpam-4030	245	26	)	)	PUNCT
ejpam-4030	245	27	in	in	ADP
ejpam-4030	245	28	[	[	X
ejpam-4030	245	29	11	11	NUM
ejpam-4030	245	30	]	]	PUNCT
ejpam-4030	245	31	.	.	PUNCT
ejpam-4030	246	1	then	then	ADV
ejpam-4030	246	2	we	we	PRON
ejpam-4030	246	3	take	take	VERB
ejpam-4030	246	4	the	the	DET
ejpam-4030	246	5	first	first	ADJ
ejpam-4030	246	6	partial	partial	ADJ
ejpam-4030	246	7	derivative	derivative	NOUN
ejpam-4030	246	8	with	with	ADP
ejpam-4030	246	9	respect	respect	NOUN
ejpam-4030	246	10	to	to	ADP
ejpam-4030	246	11	k	k	PROPN
ejpam-4030	246	12	and	and	CCONJ
ejpam-4030	246	13	set	set	VERB
ejpam-4030	246	14	k	k	PROPN
ejpam-4030	246	15	=	=	SYM
ejpam-4030	246	16	0	0	NUM
ejpam-4030	246	17	,	,	PUNCT
ejpam-4030	246	18	b	b	X
ejpam-4030	246	19	=	=	SYM
ejpam-4030	246	20	1	1	NUM
ejpam-4030	246	21	,	,	PUNCT
ejpam-4030	246	22	c	c	NOUN
ejpam-4030	246	23	=	=	SYM
ejpam-4030	246	24	1	1	NUM
ejpam-4030	246	25	and	and	CCONJ
ejpam-4030	246	26	simplify	simplify	NOUN
ejpam-4030	246	27	.	.	PUNCT
ejpam-4030	247	1	r.	r.	PROPN
ejpam-4030	247	2	reynolds	reynolds	PROPN
ejpam-4030	247	3	,	,	PUNCT
ejpam-4030	247	4	a.	a.	PROPN
ejpam-4030	247	5	stauffer	stauffer	PROPN
ejpam-4030	247	6	/	/	SYM
ejpam-4030	247	7	eur	eur	PROPN
ejpam-4030	247	8	.	.	PUNCT
ejpam-4030	248	1	j.	j.	PROPN
ejpam-4030	248	2	pure	pure	PROPN
ejpam-4030	248	3	appl	appl	PROPN
ejpam-4030	248	4	.	.	PROPN
ejpam-4030	248	5	math	math	PROPN
ejpam-4030	248	6	,	,	PUNCT
ejpam-4030	248	7	14	14	NUM
ejpam-4030	248	8	(	(	PUNCT
ejpam-4030	248	9	3	3	NUM
ejpam-4030	248	10	)	)	PUNCT
ejpam-4030	248	11	(	(	PUNCT
ejpam-4030	248	12	2021	2021	NUM
ejpam-4030	248	13	)	)	PUNCT
ejpam-4030	248	14	,	,	PUNCT
ejpam-4030	248	15	788	788	NUM
ejpam-4030	248	16	-	-	SYM
ejpam-4030	248	17	802	802	NUM
ejpam-4030	248	18	797	797	NUM
ejpam-4030	248	19	proposition	proposition	NOUN
ejpam-4030	248	20	15	15	NUM
ejpam-4030	248	21	.	.	PUNCT
ejpam-4030	249	1	using	use	VERB
ejpam-4030	249	2	equation	equation	NOUN
ejpam-4030	249	3	(	(	PUNCT
ejpam-4030	249	4	29	29	NUM
ejpam-4030	249	5	)	)	PUNCT
ejpam-4030	249	6	and	and	CCONJ
ejpam-4030	249	7	setting	set	VERB
ejpam-4030	249	8	k	k	PROPN
ejpam-4030	249	9	=	=	PUNCT
ejpam-4030	249	10	−1	−1	NOUN
ejpam-4030	249	11	,	,	PUNCT
ejpam-4030	249	12	b	b	X
ejpam-4030	250	1	=	=	SYM
ejpam-4030	250	2	−i	−i	PROPN
ejpam-4030	250	3	,	,	PUNCT
ejpam-4030	250	4	c	c	NOUN
ejpam-4030	250	5	=	=	SYM
ejpam-4030	250	6	1	1	NUM
ejpam-4030	250	7	and	and	CCONJ
ejpam-4030	250	8	simplifying	simplify	VERB
ejpam-4030	250	9	we	we	PRON
ejpam-4030	250	10	get	get	VERB
ejpam-4030	250	11	∫	∫	PROPN
ejpam-4030	251	1	+	+	PROPN
ejpam-4030	251	2	∞	∞	PROPN
ejpam-4030	251	3	0	0	NUM
ejpam-4030	252	1	(	(	PUNCT
ejpam-4030	252	2	(	(	PUNCT
ejpam-4030	252	3	x−	x−	PROPN
ejpam-4030	252	4	4)x+	4)x+	NUM
ejpam-4030	252	5	1	1	NUM
ejpam-4030	252	6	)	)	PUNCT
ejpam-4030	252	7	log	log	NOUN
ejpam-4030	252	8	(	(	PUNCT
ejpam-4030	252	9	log	log	NOUN
ejpam-4030	252	10	(	(	PUNCT
ejpam-4030	252	11	1	1	NUM
ejpam-4030	252	12	x	x	NOUN
ejpam-4030	252	13	)	)	PUNCT
ejpam-4030	252	14	)	)	PUNCT
ejpam-4030	253	1	(	(	PUNCT
ejpam-4030	253	2	x+	x+	PROPN
ejpam-4030	253	3	1)4	1)4	NUM
ejpam-4030	253	4	dx	dx	NOUN
ejpam-4030	253	5	=	=	SYM
ejpam-4030	253	6	7ζ(3	7ζ(3	NUM
ejpam-4030	253	7	)	)	PUNCT
ejpam-4030	253	8	2π2	2π2	NUM
ejpam-4030	253	9	(	(	PUNCT
ejpam-4030	253	10	30	30	NUM
ejpam-4030	253	11	)	)	PUNCT
ejpam-4030	253	12	note	note	NOUN
ejpam-4030	253	13	there	there	PRON
ejpam-4030	253	14	exists	exist	VERB
ejpam-4030	253	15	a	a	DET
ejpam-4030	253	16	singularity	singularity	NOUN
ejpam-4030	253	17	at	at	ADP
ejpam-4030	253	18	x	x	X
ejpam-4030	253	19	=	=	SYM
ejpam-4030	253	20	1	1	X
ejpam-4030	253	21	.	.	PUNCT
ejpam-4030	253	22	proposition	proposition	NOUN
ejpam-4030	253	23	16	16	NUM
ejpam-4030	253	24	.	.	PUNCT
ejpam-4030	254	1	for	for	ADP
ejpam-4030	254	2	k	k	PROPN
ejpam-4030	254	3	,	,	PUNCT
ejpam-4030	254	4	b	b	NOUN
ejpam-4030	254	5	,	,	PUNCT
ejpam-4030	254	6	c	c	PROPN
ejpam-4030	254	7	∈	∈	PROPN
ejpam-4030	254	8	c∫	c∫	PROPN
ejpam-4030	255	1	+	+	NOUN
ejpam-4030	255	2	∞	∞	PROPN
ejpam-4030	255	3	0	0	NUM
ejpam-4030	255	4	(	(	PUNCT
ejpam-4030	255	5	cx−	cx−	PROPN
ejpam-4030	255	6	1)(cx(cx−	1)(cx(cx−	NUM
ejpam-4030	255	7	10	10	NUM
ejpam-4030	255	8	)	)	PUNCT
ejpam-4030	255	9	+	+	CCONJ
ejpam-4030	255	10	1	1	X
ejpam-4030	255	11	)	)	PUNCT
ejpam-4030	255	12	logk	logk	NOUN
ejpam-4030	255	13	(	(	PUNCT
ejpam-4030	255	14	b	b	NOUN
ejpam-4030	255	15	x	x	X
ejpam-4030	255	16	)	)	PUNCT
ejpam-4030	255	17	(	(	PUNCT
ejpam-4030	255	18	cx+	cx+	NOUN
ejpam-4030	255	19	1)5	1)5	NUM
ejpam-4030	255	20	dx	dx	X
ejpam-4030	255	21	=	=	SYM
ejpam-4030	255	22	−	−	PROPN
ejpam-4030	255	23	ie−	ie−	NOUN
ejpam-4030	255	24	1	1	NUM
ejpam-4030	255	25	2	2	NUM
ejpam-4030	256	1	iπk(k	iπk(k	ADJ
ejpam-4030	256	2	−	−	PROPN
ejpam-4030	256	3	3)(k	3)(k	NUM
ejpam-4030	256	4	−	−	PROPN
ejpam-4030	256	5	2)(k	2)(k	NUM
ejpam-4030	257	1	−	−	PROPN
ejpam-4030	257	2	1)k(2π)k−3φ	1)k(2π)k−3φ	NUM
ejpam-4030	257	3	(	(	PUNCT
ejpam-4030	257	4	1	1	NUM
ejpam-4030	257	5	,	,	PUNCT
ejpam-4030	257	6	4−	4−	PROPN
ejpam-4030	258	1	k	k	NOUN
ejpam-4030	258	2	,	,	PUNCT
ejpam-4030	258	3	i	i	PRON
ejpam-4030	258	4	log(b)+i	log(b)+i	X
ejpam-4030	258	5	log(c)+π2π	log(c)+π2π	PROPN
ejpam-4030	258	6	)	)	PUNCT
ejpam-4030	259	1	c	c	NOUN
ejpam-4030	259	2	(	(	PUNCT
ejpam-4030	259	3	31	31	NUM
ejpam-4030	259	4	)	)	PUNCT
ejpam-4030	259	5	proof	proof	NOUN
ejpam-4030	259	6	.	.	PUNCT
ejpam-4030	260	1	use	use	VERB
ejpam-4030	260	2	equation	equation	NOUN
ejpam-4030	260	3	(	(	PUNCT
ejpam-4030	260	4	8)	8)	NUM
ejpam-4030	260	5	and	and	CCONJ
ejpam-4030	260	6	set	set	VERB
ejpam-4030	260	7	a	a	DET
ejpam-4030	260	8	=	=	SYM
ejpam-4030	260	9	1	1	NUM
ejpam-4030	260	10	,	,	PUNCT
ejpam-4030	260	11	n	n	NOUN
ejpam-4030	260	12	=	=	SYM
ejpam-4030	260	13	−4	−4	X
ejpam-4030	260	14	then	then	ADV
ejpam-4030	260	15	simplify	simplify	VERB
ejpam-4030	260	16	using	use	VERB
ejpam-4030	260	17	entry	entry	NOUN
ejpam-4030	260	18	(	(	PUNCT
ejpam-4030	260	19	4	4	NUM
ejpam-4030	260	20	)	)	PUNCT
ejpam-4030	260	21	in	in	ADP
ejpam-4030	260	22	table	table	NOUN
ejpam-4030	260	23	below	below	ADV
ejpam-4030	260	24	(	(	PUNCT
ejpam-4030	260	25	64:12:7	64:12:7	NUM
ejpam-4030	260	26	)	)	PUNCT
ejpam-4030	260	27	in	in	ADP
ejpam-4030	260	28	[	[	X
ejpam-4030	260	29	11	11	NUM
ejpam-4030	260	30	]	]	PUNCT
ejpam-4030	260	31	.	.	PUNCT
ejpam-4030	261	1	theorem	theorem	ADJ
ejpam-4030	261	2	8	8	NUM
ejpam-4030	261	3	.	.	PUNCT
ejpam-4030	261	4	∫	∫	PROPN
ejpam-4030	262	1	+	+	NUM
ejpam-4030	262	2	∞	∞	PROPN
ejpam-4030	262	3	0	0	NUM
ejpam-4030	262	4	(	(	PUNCT
ejpam-4030	262	5	x−	x−	PROPN
ejpam-4030	262	6	1)((x−	1)((x−	PROPN
ejpam-4030	262	7	10)x+	10)x+	PROPN
ejpam-4030	262	8	1	1	NUM
ejpam-4030	262	9	)	)	PUNCT
ejpam-4030	262	10	log	log	NOUN
ejpam-4030	262	11	(	(	PUNCT
ejpam-4030	262	12	1	1	NUM
ejpam-4030	262	13	x	x	X
ejpam-4030	262	14	)	)	PUNCT
ejpam-4030	262	15	log	log	NOUN
ejpam-4030	262	16	(	(	PUNCT
ejpam-4030	262	17	log	log	NOUN
ejpam-4030	262	18	(	(	PUNCT
ejpam-4030	262	19	1	1	NUM
ejpam-4030	262	20	x	x	NOUN
ejpam-4030	262	21	)	)	PUNCT
ejpam-4030	262	22	)	)	PUNCT
ejpam-4030	263	1	(	(	PUNCT
ejpam-4030	263	2	x+	x+	PROPN
ejpam-4030	263	3	1)5	1)5	NUM
ejpam-4030	263	4	dx	dx	PROPN
ejpam-4030	263	5	=	=	SYM
ejpam-4030	263	6	−7ζ(3	−7ζ(3	PROPN
ejpam-4030	263	7	)	)	PUNCT
ejpam-4030	263	8	2π2	2π2	NUM
ejpam-4030	263	9	(	(	PUNCT
ejpam-4030	263	10	32	32	NUM
ejpam-4030	263	11	)	)	PUNCT
ejpam-4030	263	12	proof	proof	NOUN
ejpam-4030	263	13	.	.	PUNCT
ejpam-4030	264	1	use	use	VERB
ejpam-4030	264	2	equation	equation	NOUN
ejpam-4030	264	3	(	(	PUNCT
ejpam-4030	264	4	31	31	NUM
ejpam-4030	264	5	)	)	PUNCT
ejpam-4030	264	6	setting	set	VERB
ejpam-4030	264	7	a	a	DET
ejpam-4030	264	8	=	=	SYM
ejpam-4030	264	9	1	1	NUM
ejpam-4030	264	10	and	and	CCONJ
ejpam-4030	264	11	simplify	simplify	VERB
ejpam-4030	264	12	,	,	PUNCT
ejpam-4030	264	13	next	next	ADV
ejpam-4030	264	14	take	take	VERB
ejpam-4030	264	15	the	the	DET
ejpam-4030	264	16	first	first	ADJ
ejpam-4030	264	17	partial	partial	ADJ
ejpam-4030	264	18	derivative	derivative	NOUN
ejpam-4030	264	19	with	with	ADP
ejpam-4030	264	20	respect	respect	NOUN
ejpam-4030	264	21	to	to	ADP
ejpam-4030	264	22	k	k	PROPN
ejpam-4030	264	23	and	and	CCONJ
ejpam-4030	264	24	set	set	VERB
ejpam-4030	264	25	k	k	PROPN
ejpam-4030	264	26	=	=	SYM
ejpam-4030	264	27	1	1	NUM
ejpam-4030	264	28	,	,	PUNCT
ejpam-4030	264	29	b	b	NOUN
ejpam-4030	264	30	=	=	SYM
ejpam-4030	264	31	1	1	NUM
ejpam-4030	264	32	,	,	PUNCT
ejpam-4030	264	33	c	c	NOUN
ejpam-4030	264	34	=	=	SYM
ejpam-4030	264	35	1	1	NUM
ejpam-4030	264	36	and	and	CCONJ
ejpam-4030	264	37	simplify	simplify	VERB
ejpam-4030	264	38	using	use	VERB
ejpam-4030	264	39	equation	equation	NOUN
ejpam-4030	264	40	(	(	PUNCT
ejpam-4030	264	41	64:12:1	64:12:1	NUM
ejpam-4030	264	42	)	)	PUNCT
ejpam-4030	264	43	and	and	CCONJ
ejpam-4030	264	44	entry	entry	NOUN
ejpam-4030	264	45	(	(	PUNCT
ejpam-4030	264	46	2	2	NUM
ejpam-4030	264	47	)	)	PUNCT
ejpam-4030	264	48	in	in	ADP
ejpam-4030	264	49	table	table	NOUN
ejpam-4030	264	50	below	below	ADV
ejpam-4030	264	51	(	(	PUNCT
ejpam-4030	264	52	64:7	64:7	NUM
ejpam-4030	264	53	)	)	PUNCT
ejpam-4030	264	54	in	in	ADP
ejpam-4030	264	55	[	[	X
ejpam-4030	264	56	11	11	NUM
ejpam-4030	264	57	]	]	PUNCT
ejpam-4030	264	58	.	.	PUNCT
ejpam-4030	265	1	proposition	proposition	NOUN
ejpam-4030	265	2	17	17	NUM
ejpam-4030	265	3	.	.	PUNCT
ejpam-4030	266	1	for	for	ADP
ejpam-4030	266	2	k	k	PROPN
ejpam-4030	266	3	∈	∈	PROPN
ejpam-4030	266	4	c∫	c∫	PROPN
ejpam-4030	267	1	+	+	PROPN
ejpam-4030	267	2	∞	∞	PROPN
ejpam-4030	267	3	0	0	NUM
ejpam-4030	267	4	(	(	PUNCT
ejpam-4030	267	5	x−	x−	PROPN
ejpam-4030	267	6	1)((x−	1)((x−	PROPN
ejpam-4030	267	7	22)x+	22)x+	NUM
ejpam-4030	267	8	1	1	NUM
ejpam-4030	267	9	)	)	PUNCT
ejpam-4030	267	10	logk	logk	NOUN
ejpam-4030	267	11	(	(	PUNCT
ejpam-4030	267	12	1	1	NUM
ejpam-4030	267	13	x	x	SYM
ejpam-4030	267	14	)	)	PUNCT
ejpam-4030	267	15	8	8	NUM
ejpam-4030	268	1	√	√	NUM
ejpam-4030	268	2	x(x+	x(x+	PUNCT
ejpam-4030	269	1	1)4	1)4	NUM
ejpam-4030	269	2	dx	dx	PROPN
ejpam-4030	269	3	=	=	SYM
ejpam-4030	269	4	i22k−5e−	i22k−5e−	NOUN
ejpam-4030	269	5	1	1	NUM
ejpam-4030	269	6	2	2	NUM
ejpam-4030	269	7	iπk(k	iπk(k	PROPN
ejpam-4030	269	8	−	−	PROPN
ejpam-4030	269	9	2)(k	2)(k	NUM
ejpam-4030	269	10	−	−	PROPN
ejpam-4030	270	1	1)kπk−2	1)kπk−2	NUM
ejpam-4030	270	2	(	(	PUNCT
ejpam-4030	270	3	ζ	ζ	NOUN
ejpam-4030	270	4	(	(	PUNCT
ejpam-4030	270	5	3−	3−	NUM
ejpam-4030	270	6	k	k	NOUN
ejpam-4030	270	7	,	,	PUNCT
ejpam-4030	270	8	1	1	NUM
ejpam-4030	270	9	4	4	NUM
ejpam-4030	270	10	)	)	PUNCT
ejpam-4030	270	11	−	−	NOUN
ejpam-4030	270	12	ζ	ζ	NOUN
ejpam-4030	270	13	(	(	PUNCT
ejpam-4030	270	14	3−	3−	NUM
ejpam-4030	270	15	k	k	NOUN
ejpam-4030	270	16	,	,	PUNCT
ejpam-4030	270	17	3	3	NUM
ejpam-4030	270	18	4	4	NUM
ejpam-4030	270	19	)	)	PUNCT
ejpam-4030	270	20	)	)	PUNCT
ejpam-4030	270	21	(	(	PUNCT
ejpam-4030	270	22	33	33	NUM
ejpam-4030	270	23	)	)	PUNCT
ejpam-4030	270	24	proof	proof	NOUN
ejpam-4030	270	25	.	.	PUNCT
ejpam-4030	271	1	use	use	VERB
ejpam-4030	271	2	equation	equation	NOUN
ejpam-4030	271	3	(	(	PUNCT
ejpam-4030	271	4	8)	8)	NUM
ejpam-4030	271	5	and	and	CCONJ
ejpam-4030	271	6	set	set	VERB
ejpam-4030	271	7	a	a	DET
ejpam-4030	271	8	=	=	SYM
ejpam-4030	271	9	1	1	NUM
ejpam-4030	271	10	,	,	PUNCT
ejpam-4030	271	11	n	n	NOUN
ejpam-4030	271	12	=	=	SYM
ejpam-4030	271	13	−4	−4	X
ejpam-4030	271	14	then	then	ADV
ejpam-4030	271	15	simplify	simplify	VERB
ejpam-4030	271	16	using	use	VERB
ejpam-4030	271	17	entry	entry	NOUN
ejpam-4030	271	18	(	(	PUNCT
ejpam-4030	271	19	4	4	NUM
ejpam-4030	271	20	)	)	PUNCT
ejpam-4030	271	21	in	in	ADP
ejpam-4030	271	22	table	table	NOUN
ejpam-4030	271	23	below	below	ADV
ejpam-4030	271	24	(	(	PUNCT
ejpam-4030	271	25	64:12:7	64:12:7	NUM
ejpam-4030	271	26	)	)	PUNCT
ejpam-4030	271	27	in	in	ADP
ejpam-4030	271	28	[	[	X
ejpam-4030	271	29	11	11	NUM
ejpam-4030	271	30	]	]	PUNCT
ejpam-4030	271	31	.	.	PUNCT
ejpam-4030	272	1	theorem	theorem	VERB
ejpam-4030	272	2	9	9	NUM
ejpam-4030	272	3	.	.	PUNCT
ejpam-4030	272	4	∫	∫	PROPN
ejpam-4030	273	1	+	+	NUM
ejpam-4030	273	2	∞	∞	PROPN
ejpam-4030	273	3	0	0	NUM
ejpam-4030	273	4	(	(	PUNCT
ejpam-4030	273	5	x−	x−	PROPN
ejpam-4030	273	6	1)((x−	1)((x−	PROPN
ejpam-4030	273	7	22)x+	22)x+	NUM
ejpam-4030	273	8	1	1	NUM
ejpam-4030	273	9	)	)	PUNCT
ejpam-4030	273	10	log	log	NOUN
ejpam-4030	273	11	(	(	PUNCT
ejpam-4030	273	12	1	1	NUM
ejpam-4030	273	13	x	x	X
ejpam-4030	273	14	)	)	PUNCT
ejpam-4030	273	15	log	log	NOUN
ejpam-4030	273	16	(	(	PUNCT
ejpam-4030	273	17	log	log	NOUN
ejpam-4030	273	18	(	(	PUNCT
ejpam-4030	273	19	1	1	NUM
ejpam-4030	273	20	x	x	NOUN
ejpam-4030	273	21	)	)	PUNCT
ejpam-4030	273	22	)	)	PUNCT
ejpam-4030	273	23	8	8	NUM
ejpam-4030	274	1	√	√	NUM
ejpam-4030	274	2	x(x+	x(x+	PUNCT
ejpam-4030	275	1	1)4	1)4	NUM
ejpam-4030	275	2	dx	dx	NOUN
ejpam-4030	276	1	=	=	PUNCT
ejpam-4030	277	1	−2c	−2c	PROPN
ejpam-4030	277	2	π	π	X
ejpam-4030	277	3	(	(	PUNCT
ejpam-4030	277	4	34	34	NUM
ejpam-4030	277	5	)	)	PUNCT
ejpam-4030	277	6	proof	proof	NOUN
ejpam-4030	277	7	.	.	PUNCT
ejpam-4030	278	1	use	use	VERB
ejpam-4030	278	2	equation	equation	NOUN
ejpam-4030	278	3	(	(	PUNCT
ejpam-4030	278	4	33	33	NUM
ejpam-4030	278	5	)	)	PUNCT
ejpam-4030	278	6	and	and	CCONJ
ejpam-4030	278	7	take	take	VERB
ejpam-4030	278	8	the	the	DET
ejpam-4030	278	9	first	first	ADJ
ejpam-4030	278	10	partial	partial	ADJ
ejpam-4030	278	11	derivative	derivative	NOUN
ejpam-4030	278	12	with	with	ADP
ejpam-4030	278	13	respect	respect	NOUN
ejpam-4030	278	14	to	to	ADP
ejpam-4030	278	15	k	k	PROPN
ejpam-4030	278	16	and	and	CCONJ
ejpam-4030	278	17	set	set	VERB
ejpam-4030	278	18	k	k	PROPN
ejpam-4030	278	19	=	=	SYM
ejpam-4030	278	20	1	1	NUM
ejpam-4030	278	21	,	,	PUNCT
ejpam-4030	278	22	b	b	X
ejpam-4030	278	23	=	=	SYM
ejpam-4030	278	24	1	1	NUM
ejpam-4030	278	25	and	and	CCONJ
ejpam-4030	278	26	simplify	simplify	VERB
ejpam-4030	278	27	using	use	VERB
ejpam-4030	278	28	equation	equation	NOUN
ejpam-4030	278	29	(	(	PUNCT
ejpam-4030	278	30	64:7:1	64:7:1	NOUN
ejpam-4030	278	31	)	)	PUNCT
ejpam-4030	278	32	in	in	ADP
ejpam-4030	278	33	[	[	X
ejpam-4030	278	34	11	11	NUM
ejpam-4030	278	35	]	]	PUNCT
ejpam-4030	278	36	and	and	CCONJ
ejpam-4030	278	37	equation	equation	NOUN
ejpam-4030	278	38	(	(	PUNCT
ejpam-4030	278	39	16	16	NUM
ejpam-4030	278	40	)	)	PUNCT
ejpam-4030	278	41	in	in	ADP
ejpam-4030	278	42	[	[	X
ejpam-4030	278	43	2	2	NUM
ejpam-4030	278	44	]	]	PUNCT
ejpam-4030	278	45	.	.	PUNCT
ejpam-4030	279	1	r.	r.	PROPN
ejpam-4030	279	2	reynolds	reynolds	PROPN
ejpam-4030	279	3	,	,	PUNCT
ejpam-4030	279	4	a.	a.	PROPN
ejpam-4030	279	5	stauffer	stauffer	PROPN
ejpam-4030	279	6	/	/	SYM
ejpam-4030	279	7	eur	eur	PROPN
ejpam-4030	279	8	.	.	PUNCT
ejpam-4030	280	1	j.	j.	PROPN
ejpam-4030	280	2	pure	pure	PROPN
ejpam-4030	280	3	appl	appl	PROPN
ejpam-4030	280	4	.	.	PROPN
ejpam-4030	280	5	math	math	PROPN
ejpam-4030	280	6	,	,	PUNCT
ejpam-4030	280	7	14	14	NUM
ejpam-4030	280	8	(	(	PUNCT
ejpam-4030	280	9	3	3	NUM
ejpam-4030	280	10	)	)	PUNCT
ejpam-4030	280	11	(	(	PUNCT
ejpam-4030	280	12	2021	2021	NUM
ejpam-4030	280	13	)	)	PUNCT
ejpam-4030	280	14	,	,	PUNCT
ejpam-4030	280	15	788	788	NUM
ejpam-4030	280	16	-	-	SYM
ejpam-4030	280	17	802	802	NUM
ejpam-4030	280	18	798	798	NUM
ejpam-4030	280	19	9	9	NUM
ejpam-4030	280	20	.	.	PUNCT
ejpam-4030	281	1	definite	definite	ADJ
ejpam-4030	281	2	integral	integral	ADJ
ejpam-4030	281	3	of	of	ADP
ejpam-4030	281	4	the	the	DET
ejpam-4030	281	5	lerch	lerch	PROPN
ejpam-4030	281	6	function	function	PROPN
ejpam-4030	281	7	in	in	ADP
ejpam-4030	281	8	terms	term	NOUN
ejpam-4030	281	9	of	of	ADP
ejpam-4030	281	10	the	the	DET
ejpam-4030	281	11	lerch	lerch	PROPN
ejpam-4030	281	12	transformation	transformation	NOUN
ejpam-4030	281	13	in	in	ADP
ejpam-4030	281	14	this	this	DET
ejpam-4030	281	15	section	section	NOUN
ejpam-4030	281	16	we	we	PRON
ejpam-4030	281	17	will	will	AUX
ejpam-4030	281	18	apply	apply	VERB
ejpam-4030	281	19	the	the	DET
ejpam-4030	281	20	lerch	lerch	PROPN
ejpam-4030	281	21	transformation	transformation	NOUN
ejpam-4030	281	22	derived	derive	VERB
ejpam-4030	281	23	by	by	ADP
ejpam-4030	281	24	oberhettinger	oberhettinger	NOUN
ejpam-4030	281	25	in	in	ADP
ejpam-4030	281	26	[	[	X
ejpam-4030	281	27	10	10	NUM
ejpam-4030	281	28	]	]	PUNCT
ejpam-4030	281	29	and	and	CCONJ
ejpam-4030	281	30	apply	apply	VERB
ejpam-4030	281	31	it	it	PRON
ejpam-4030	281	32	to	to	ADP
ejpam-4030	281	33	our	our	PRON
ejpam-4030	281	34	definite	definite	ADJ
ejpam-4030	281	35	integral	integral	NOUN
ejpam-4030	281	36	of	of	ADP
ejpam-4030	281	37	the	the	DET
ejpam-4030	281	38	lerch	lerch	PROPN
ejpam-4030	281	39	function	function	PROPN
ejpam-4030	281	40	and	and	CCONJ
ejpam-4030	281	41	evaluate	evaluate	VERB
ejpam-4030	281	42	a	a	DET
ejpam-4030	281	43	few	few	ADJ
ejpam-4030	281	44	examples	example	NOUN
ejpam-4030	281	45	.	.	PUNCT
ejpam-4030	282	1	theorem	theorem	ADJ
ejpam-4030	282	2	10	10	NUM
ejpam-4030	282	3	.	.	PUNCT
ejpam-4030	283	1	for	for	ADP
ejpam-4030	283	2	k	k	PROPN
ejpam-4030	283	3	,	,	PUNCT
ejpam-4030	283	4	b	b	PROPN
ejpam-4030	283	5	,	,	PUNCT
ejpam-4030	283	6	a	a	DET
ejpam-4030	283	7	∈	∈	PROPN
ejpam-4030	283	8	c	c	NOUN
ejpam-4030	283	9	,	,	PUNCT
ejpam-4030	283	10	n	n	PROPN
ejpam-4030	283	11	∈	∈	PROPN
ejpam-4030	283	12	z−	z−	PROPN
ejpam-4030	283	13	,	,	PUNCT
ejpam-4030	283	14	c	c	PROPN
ejpam-4030	283	15	∈	∈	PROPN
ejpam-4030	283	16	r+	r+	X
ejpam-4030	283	17	,	,	PUNCT
ejpam-4030	283	18	e−iπaca(−2iπ)−k−n−1(k	e−iπaca(−2iπ)−k−n−1(k	NOUN
ejpam-4030	283	19	+	+	NOUN
ejpam-4030	283	20	n	n	CCONJ
ejpam-4030	283	21	)	)	PUNCT
ejpam-4030	283	22	!	!	PUNCT
ejpam-4030	284	1	k	k	X
ejpam-4030	284	2	!	!	PUNCT
ejpam-4030	284	3	∫	∫	PROPN
ejpam-4030	285	1	+	+	CCONJ
ejpam-4030	285	2	∞	∞	PROPN
ejpam-4030	285	3	0	0	NUM
ejpam-4030	285	4	xa−1	xa−1	PROPN
ejpam-4030	285	5	logk	logk	PROPN
ejpam-4030	285	6	(	(	PUNCT
ejpam-4030	285	7	b	b	NOUN
ejpam-4030	285	8	x	x	X
ejpam-4030	285	9	)	)	PUNCT
ejpam-4030	285	10	φ(−cx	φ(−cx	ADJ
ejpam-4030	285	11	,	,	PUNCT
ejpam-4030	285	12	n	n	CCONJ
ejpam-4030	285	13	,	,	PUNCT
ejpam-4030	285	14	a)dx	a)dx	PROPN
ejpam-4030	285	15	=	=	SYM
ejpam-4030	285	16	iba−1ca−1(2π)−k−n−1e−	iba−1ca−1(2π)−k−n−1e−	NOUN
ejpam-4030	285	17	1	1	NUM
ejpam-4030	285	18	2	2	NUM
ejpam-4030	285	19	iπ(2a+k+n)γ(k	iπ(2a+k+n)γ(k	NOUN
ejpam-4030	285	20	+	+	ADJ
ejpam-4030	285	21	n+	n+	X
ejpam-4030	285	22	1)φ	1)φ	NUM
ejpam-4030	285	23	(	(	PUNCT
ejpam-4030	285	24	−	−	PROPN
ejpam-4030	285	25	1	1	NUM
ejpam-4030	285	26	bc	bc	PROPN
ejpam-4030	285	27	,	,	PUNCT
ejpam-4030	285	28	k	k	PROPN
ejpam-4030	285	29	+	+	CCONJ
ejpam-4030	285	30	n+	n+	NUM
ejpam-4030	285	31	1	1	NUM
ejpam-4030	285	32	,	,	PUNCT
ejpam-4030	285	33	1−	1−	NUM
ejpam-4030	285	34	a	a	PRON
ejpam-4030	285	35	)	)	PUNCT
ejpam-4030	285	36	−	−	NOUN
ejpam-4030	285	37	iba+1ca+1(2π)−k−n−1eiπ(k+n)−	iba+1ca+1(2π)−k−n−1eiπ(k+n)−	VERB
ejpam-4030	285	38	1	1	NUM
ejpam-4030	285	39	2	2	NUM
ejpam-4030	285	40	iπ(2a+k+n)γ(k	iπ(2a+k+n)γ(k	NOUN
ejpam-4030	285	41	+	+	CCONJ
ejpam-4030	285	42	n+	n+	PUNCT
ejpam-4030	285	43	1)φ(−bc	1)φ(−bc	NUM
ejpam-4030	285	44	,	,	PUNCT
ejpam-4030	285	45	k	k	PROPN
ejpam-4030	285	46	+	+	CCONJ
ejpam-4030	285	47	n+	n+	NUM
ejpam-4030	285	48	1	1	NUM
ejpam-4030	285	49	,	,	PUNCT
ejpam-4030	285	50	a+	a+	PUNCT
ejpam-4030	285	51	1	1	NUM
ejpam-4030	285	52	)	)	PUNCT
ejpam-4030	285	53	+	+	CCONJ
ejpam-4030	286	1	baca(2π)−k−n−1(−ia)−k−n−1e	baca(2π)−k−n−1(−ia)−k−n−1e	NOUN
ejpam-4030	286	2	1	1	NUM
ejpam-4030	286	3	2	2	NUM
ejpam-4030	286	4	iπ(k+n)−	iπ(k+n)−	NOUN
ejpam-4030	286	5	1	1	NUM
ejpam-4030	286	6	2	2	NUM
ejpam-4030	286	7	iπ(2a+k+n)γ(k	iπ(2a+k+n)γ(k	NOUN
ejpam-4030	286	8	+	+	CCONJ
ejpam-4030	286	9	n+	n+	PUNCT
ejpam-4030	286	10	1	1	X
ejpam-4030	286	11	)	)	PUNCT
ejpam-4030	286	12	(	(	PUNCT
ejpam-4030	286	13	35	35	NUM
ejpam-4030	286	14	)	)	PUNCT
ejpam-4030	286	15	proof	proof	NOUN
ejpam-4030	286	16	.	.	PUNCT
ejpam-4030	287	1	use	use	VERB
ejpam-4030	287	2	equation	equation	NOUN
ejpam-4030	287	3	(	(	PUNCT
ejpam-4030	287	4	12	12	NUM
ejpam-4030	287	5	)	)	PUNCT
ejpam-4030	287	6	in	in	ADP
ejpam-4030	287	7	[	[	X
ejpam-4030	287	8	10	10	NUM
ejpam-4030	287	9	]	]	PUNCT
ejpam-4030	287	10	and	and	CCONJ
ejpam-4030	287	11	simplify	simplify	NOUN
ejpam-4030	287	12	.	.	PUNCT
ejpam-4030	288	1	proposition	proposition	NOUN
ejpam-4030	288	2	18	18	NUM
ejpam-4030	288	3	.	.	PUNCT
ejpam-4030	289	1	using	use	VERB
ejpam-4030	289	2	equation	equation	NOUN
ejpam-4030	289	3	(	(	PUNCT
ejpam-4030	289	4	35	35	NUM
ejpam-4030	289	5	)	)	PUNCT
ejpam-4030	289	6	setting	set	VERB
ejpam-4030	289	7	n	n	NOUN
ejpam-4030	289	8	=	=	SYM
ejpam-4030	289	9	0	0	NUM
ejpam-4030	289	10	,	,	PUNCT
ejpam-4030	289	11	c	c	NOUN
ejpam-4030	289	12	=	=	SYM
ejpam-4030	289	13	1	1	NUM
ejpam-4030	289	14	,	,	PUNCT
ejpam-4030	289	15	b	b	X
ejpam-4030	289	16	=	=	SYM
ejpam-4030	289	17	−i	−i	PROPN
ejpam-4030	289	18	,	,	PUNCT
ejpam-4030	289	19	a	a	DET
ejpam-4030	289	20	=	=	SYM
ejpam-4030	289	21	1/3	1/3	NUM
ejpam-4030	289	22	,	,	PUNCT
ejpam-4030	289	23	k	k	NOUN
ejpam-4030	289	24	=	=	SYM
ejpam-4030	289	25	1/2	1/2	NUM
ejpam-4030	289	26	and	and	CCONJ
ejpam-4030	289	27	simplify	simplify	VERB
ejpam-4030	289	28	to	to	PART
ejpam-4030	289	29	get	get	VERB
ejpam-4030	289	30	∫	∫	PROPN
ejpam-4030	290	1	+	+	PROPN
ejpam-4030	290	2	∞	∞	PROPN
ejpam-4030	290	3	0	0	NUM
ejpam-4030	290	4	(	(	PUNCT
ejpam-4030	290	5	−1)5/12	−1)5/12	NOUN
ejpam-4030	290	6	√	√	NUM
ejpam-4030	290	7	log	log	NOUN
ejpam-4030	290	8	(	(	PUNCT
ejpam-4030	290	9	−	−	PROPN
ejpam-4030	290	10	i	i	NOUN
ejpam-4030	290	11	x	x	PUNCT
ejpam-4030	290	12	)	)	PUNCT
ejpam-4030	291	1	√	√	NUM
ejpam-4030	291	2	2π3/2x2/3(2x+	2π3/2x2/3(2x+	NUM
ejpam-4030	291	3	2	2	NUM
ejpam-4030	291	4	)	)	PUNCT
ejpam-4030	291	5	dx	dx	PROPN
ejpam-4030	292	1	=	=	PUNCT
ejpam-4030	292	2	(	(	PUNCT
ejpam-4030	292	3	1	1	NUM
ejpam-4030	292	4	8	8	NUM
ejpam-4030	292	5	+	+	CCONJ
ejpam-4030	292	6	i	i	PRON
ejpam-4030	292	7	8	8	NUM
ejpam-4030	292	8	)	)	PUNCT
ejpam-4030	292	9	(	(	PUNCT
ejpam-4030	292	10	φ	φ	PROPN
ejpam-4030	292	11	(	(	PUNCT
ejpam-4030	292	12	−i	−i	PROPN
ejpam-4030	292	13	,	,	PUNCT
ejpam-4030	292	14	32	32	NUM
ejpam-4030	292	15	,	,	PUNCT
ejpam-4030	292	16	2	2	NUM
ejpam-4030	292	17	3	3	NUM
ejpam-4030	292	18	)	)	PUNCT
ejpam-4030	293	1	+	+	CCONJ
ejpam-4030	293	2	iφ	iφ	NOUN
ejpam-4030	293	3	(	(	PUNCT
ejpam-4030	293	4	i	i	NOUN
ejpam-4030	293	5	,	,	PUNCT
ejpam-4030	293	6	32	32	NUM
ejpam-4030	293	7	,	,	PUNCT
ejpam-4030	293	8	4	4	NUM
ejpam-4030	293	9	3	3	NUM
ejpam-4030	293	10	)	)	PUNCT
ejpam-4030	293	11	+	+	CCONJ
ejpam-4030	293	12	3	3	NUM
ejpam-4030	293	13	√	√	NUM
ejpam-4030	293	14	3	3	NUM
ejpam-4030	293	15	)	)	PUNCT
ejpam-4030	293	16	π	π	PROPN
ejpam-4030	293	17	(	(	PUNCT
ejpam-4030	293	18	36	36	NUM
ejpam-4030	293	19	)	)	PUNCT
ejpam-4030	293	20	proposition	proposition	NOUN
ejpam-4030	293	21	19	19	NUM
ejpam-4030	293	22	.	.	PUNCT
ejpam-4030	293	23	using	use	VERB
ejpam-4030	293	24	equation	equation	NOUN
ejpam-4030	293	25	(	(	PUNCT
ejpam-4030	293	26	35	35	NUM
ejpam-4030	293	27	)	)	PUNCT
ejpam-4030	293	28	setting	set	VERB
ejpam-4030	293	29	n	n	NOUN
ejpam-4030	293	30	=	=	SYM
ejpam-4030	293	31	−1	−1	NOUN
ejpam-4030	293	32	,	,	PUNCT
ejpam-4030	293	33	c	c	NOUN
ejpam-4030	293	34	=	=	SYM
ejpam-4030	293	35	1/2	1/2	NUM
ejpam-4030	293	36	,	,	PUNCT
ejpam-4030	293	37	b	b	NOUN
ejpam-4030	294	1	=	=	SYM
ejpam-4030	294	2	−i	−i	PROPN
ejpam-4030	294	3	,	,	PUNCT
ejpam-4030	294	4	a	a	DET
ejpam-4030	294	5	=	=	SYM
ejpam-4030	294	6	1/4	1/4	NUM
ejpam-4030	294	7	,	,	PUNCT
ejpam-4030	294	8	k	k	NOUN
ejpam-4030	294	9	=	=	PUNCT
ejpam-4030	294	10	−1/2	−1/2	ADJ
ejpam-4030	294	11	and	and	CCONJ
ejpam-4030	294	12	simplify	simplify	VERB
ejpam-4030	294	13	to	to	PART
ejpam-4030	294	14	get	get	VERB
ejpam-4030	294	15	∫	∫	PROPN
ejpam-4030	295	1	+	+	PROPN
ejpam-4030	295	2	∞	∞	PROPN
ejpam-4030	295	3	0	0	NUM
ejpam-4030	295	4	4	4	NUM
ejpam-4030	295	5	√	√	NUM
ejpam-4030	295	6	2	2	NUM
ejpam-4030	295	7	√	√	NOUN
ejpam-4030	295	8	π(2−	π(2−	PROPN
ejpam-4030	295	9	3x	3x	NUM
ejpam-4030	295	10	)	)	PUNCT
ejpam-4030	295	11	x3/4(x+	x3/4(x+	ADP
ejpam-4030	295	12	2)2	2)2	NUM
ejpam-4030	295	13	√	√	NUM
ejpam-4030	295	14	log	log	NOUN
ejpam-4030	295	15	(	(	PUNCT
ejpam-4030	295	16	−	−	PROPN
ejpam-4030	295	17	i	i	NOUN
ejpam-4030	295	18	x	x	X
ejpam-4030	295	19	)	)	PUNCT
ejpam-4030	295	20	dx	dx	PROPN
ejpam-4030	295	21	=	=	SYM
ejpam-4030	295	22	√	√	NUM
ejpam-4030	295	23	−1	−1	NOUN
ejpam-4030	296	1	+	+	CCONJ
ejpam-4030	296	2	iπ	iπ	PRON
ejpam-4030	296	3	(	(	PUNCT
ejpam-4030	296	4	φ	φ	PROPN
ejpam-4030	296	5	(	(	PUNCT
ejpam-4030	296	6	i	i	NOUN
ejpam-4030	296	7	2	2	NUM
ejpam-4030	296	8	,	,	PUNCT
ejpam-4030	296	9	−1	−1	NOUN
ejpam-4030	296	10	2	2	NUM
ejpam-4030	296	11	,	,	PUNCT
ejpam-4030	296	12	5	5	NUM
ejpam-4030	296	13	4	4	NUM
ejpam-4030	296	14	)	)	PUNCT
ejpam-4030	296	15	−	−	PROPN
ejpam-4030	297	1	i	i	PRON
ejpam-4030	297	2	(	(	PUNCT
ejpam-4030	297	3	1	1	NUM
ejpam-4030	297	4	+	+	NUM
ejpam-4030	297	5	4φ	4φ	NOUN
ejpam-4030	297	6	(	(	PUNCT
ejpam-4030	297	7	−2i,−1	−2i,−1	PROPN
ejpam-4030	297	8	2	2	NUM
ejpam-4030	297	9	,	,	PUNCT
ejpam-4030	297	10	3	3	NUM
ejpam-4030	297	11	4	4	NUM
ejpam-4030	297	12	)	)	PUNCT
ejpam-4030	297	13	)	)	PUNCT
ejpam-4030	297	14	)	)	PUNCT
ejpam-4030	298	1	(	(	PUNCT
ejpam-4030	298	2	37	37	NUM
ejpam-4030	298	3	)	)	PUNCT
ejpam-4030	298	4	theorem	theorem	VERB
ejpam-4030	298	5	11.∫	11.∫	NUM
ejpam-4030	298	6	+	+	NOUN
ejpam-4030	298	7	∞	∞	NUM
ejpam-4030	298	8	0	0	NUM
ejpam-4030	299	1	(	(	PUNCT
ejpam-4030	299	2	3x−	3x−	PROPN
ejpam-4030	299	3	2	2	NUM
ejpam-4030	299	4	)	)	PUNCT
ejpam-4030	299	5	log	log	NOUN
ejpam-4030	299	6	(	(	PUNCT
ejpam-4030	299	7	−	−	PUNCT
ejpam-4030	299	8	i	i	NOUN
ejpam-4030	299	9	x	x	X
ejpam-4030	299	10	)	)	PUNCT
ejpam-4030	299	11	log	log	NOUN
ejpam-4030	299	12	(	(	PUNCT
ejpam-4030	299	13	log	log	NOUN
ejpam-4030	299	14	(	(	PUNCT
ejpam-4030	299	15	−	−	PROPN
ejpam-4030	299	16	i	i	NOUN
ejpam-4030	299	17	x	x	NOUN
ejpam-4030	299	18	)	)	PUNCT
ejpam-4030	299	19	)	)	PUNCT
ejpam-4030	300	1	x3/4(x+	x3/4(x+	PROPN
ejpam-4030	300	2	2)2	2)2	NUM
ejpam-4030	300	3	dx	dx	NOUN
ejpam-4030	300	4	=	=	SYM
ejpam-4030	301	1	−(−1)3/8φ′	−(−1)3/8φ′	PRON
ejpam-4030	301	2	(	(	PUNCT
ejpam-4030	301	3	i	i	NOUN
ejpam-4030	301	4	2	2	NUM
ejpam-4030	301	5	,	,	PUNCT
ejpam-4030	301	6	1	1	NUM
ejpam-4030	301	7	,	,	PUNCT
ejpam-4030	301	8	5	5	NUM
ejpam-4030	301	9	4	4	NUM
ejpam-4030	301	10	)	)	PUNCT
ejpam-4030	301	11	−	−	PROPN
ejpam-4030	302	1	4(−1)3/8φ′	4(−1)3/8φ′	INTJ
ejpam-4030	302	2	(	(	PUNCT
ejpam-4030	302	3	−2i	−2i	PROPN
ejpam-4030	302	4	,	,	PUNCT
ejpam-4030	302	5	1	1	NUM
ejpam-4030	302	6	,	,	PUNCT
ejpam-4030	302	7	3	3	NUM
ejpam-4030	302	8	4	4	NUM
ejpam-4030	302	9	)	)	PUNCT
ejpam-4030	302	10	+	+	CCONJ
ejpam-4030	303	1	8(−1)7/8	8(−1)7/8	PROPN
ejpam-4030	303	2	2f1	2f1	NUM
ejpam-4030	303	3	(	(	PUNCT
ejpam-4030	303	4	1	1	NUM
ejpam-4030	303	5	4	4	NUM
ejpam-4030	303	6	,	,	PUNCT
ejpam-4030	303	7	1	1	NUM
ejpam-4030	303	8	;	;	PUNCT
ejpam-4030	303	9	5	5	NUM
ejpam-4030	303	10	4	4	NUM
ejpam-4030	303	11	;	;	PUNCT
ejpam-4030	303	12	i	i	PRON
ejpam-4030	303	13	2	2	X
ejpam-4030	303	14	)	)	PUNCT
ejpam-4030	303	15	−	−	PROPN
ejpam-4030	303	16	8(−1)7/8γ	8(−1)7/8γ	NUM
ejpam-4030	303	17	2f1	2f1	NUM
ejpam-4030	303	18	(	(	PUNCT
ejpam-4030	303	19	1	1	NUM
ejpam-4030	303	20	4	4	NUM
ejpam-4030	303	21	,	,	PUNCT
ejpam-4030	303	22	1	1	NUM
ejpam-4030	303	23	;	;	PUNCT
ejpam-4030	303	24	5	5	NUM
ejpam-4030	303	25	4	4	NUM
ejpam-4030	303	26	;	;	PUNCT
ejpam-4030	303	27	i	i	PRON
ejpam-4030	303	28	2	2	X
ejpam-4030	303	29	)	)	PUNCT
ejpam-4030	303	30	−	−	PROPN
ejpam-4030	303	31	16	16	NUM
ejpam-4030	303	32	3	3	NUM
ejpam-4030	303	33	(	(	PUNCT
ejpam-4030	303	34	−1)3/8	−1)3/8	NOUN
ejpam-4030	303	35	2f1	2f1	NUM
ejpam-4030	303	36	(	(	PUNCT
ejpam-4030	303	37	3	3	NUM
ejpam-4030	303	38	4	4	NUM
ejpam-4030	303	39	,	,	PUNCT
ejpam-4030	303	40	1	1	NUM
ejpam-4030	303	41	;	;	PUNCT
ejpam-4030	303	42	7	7	NUM
ejpam-4030	303	43	4	4	NUM
ejpam-4030	303	44	;	;	PUNCT
ejpam-4030	303	45	−2i	−2i	PROPN
ejpam-4030	303	46	)	)	PUNCT
ejpam-4030	304	1	+	+	CCONJ
ejpam-4030	304	2	16	16	NUM
ejpam-4030	304	3	3	3	NUM
ejpam-4030	304	4	(	(	PUNCT
ejpam-4030	304	5	−1)3/8γ	−1)3/8γ	PROPN
ejpam-4030	304	6	2f1	2f1	NUM
ejpam-4030	304	7	(	(	PUNCT
ejpam-4030	304	8	3	3	NUM
ejpam-4030	304	9	4	4	NUM
ejpam-4030	304	10	,	,	PUNCT
ejpam-4030	304	11	1	1	NUM
ejpam-4030	304	12	;	;	PUNCT
ejpam-4030	304	13	7	7	NUM
ejpam-4030	304	14	4	4	NUM
ejpam-4030	304	15	;	;	PUNCT
ejpam-4030	304	16	−2i	−2i	PROPN
ejpam-4030	304	17	)	)	PUNCT
ejpam-4030	304	18	r.	r.	PROPN
ejpam-4030	304	19	reynolds	reynolds	PROPN
ejpam-4030	304	20	,	,	PUNCT
ejpam-4030	304	21	a.	a.	PROPN
ejpam-4030	304	22	stauffer	stauffer	PROPN
ejpam-4030	304	23	/	/	SYM
ejpam-4030	304	24	eur	eur	PROPN
ejpam-4030	304	25	.	.	PUNCT
ejpam-4030	305	1	j.	j.	PROPN
ejpam-4030	305	2	pure	pure	PROPN
ejpam-4030	305	3	appl	appl	PROPN
ejpam-4030	305	4	.	.	PROPN
ejpam-4030	305	5	math	math	PROPN
ejpam-4030	305	6	,	,	PUNCT
ejpam-4030	305	7	14	14	NUM
ejpam-4030	305	8	(	(	PUNCT
ejpam-4030	305	9	3	3	NUM
ejpam-4030	305	10	)	)	PUNCT
ejpam-4030	305	11	(	(	PUNCT
ejpam-4030	305	12	2021	2021	NUM
ejpam-4030	305	13	)	)	PUNCT
ejpam-4030	305	14	,	,	PUNCT
ejpam-4030	305	15	788	788	NUM
ejpam-4030	305	16	-	-	SYM
ejpam-4030	305	17	802	802	NUM
ejpam-4030	305	18	799	799	NUM
ejpam-4030	305	19	+	+	CCONJ
ejpam-4030	305	20	16	16	NUM
ejpam-4030	305	21	3	3	NUM
ejpam-4030	305	22	(	(	PUNCT
ejpam-4030	305	23	−1)7/8π	−1)7/8π	PROPN
ejpam-4030	305	24	2f1	2f1	NUM
ejpam-4030	305	25	(	(	PUNCT
ejpam-4030	305	26	3	3	NUM
ejpam-4030	305	27	4	4	NUM
ejpam-4030	305	28	,	,	PUNCT
ejpam-4030	305	29	1	1	NUM
ejpam-4030	305	30	;	;	PUNCT
ejpam-4030	305	31	7	7	NUM
ejpam-4030	305	32	4	4	NUM
ejpam-4030	305	33	;	;	PUNCT
ejpam-4030	305	34	−2i	−2i	PROPN
ejpam-4030	305	35	)	)	PUNCT
ejpam-4030	306	1	+	+	CCONJ
ejpam-4030	306	2	8(−1)7/8	8(−1)7/8	PROPN
ejpam-4030	306	3	log(4	log(4	X
ejpam-4030	306	4	)	)	PUNCT
ejpam-4030	306	5	(	(	PUNCT
ejpam-4030	306	6	38	38	NUM
ejpam-4030	306	7	)	)	PUNCT
ejpam-4030	306	8	proof	proof	NOUN
ejpam-4030	306	9	.	.	PUNCT
ejpam-4030	307	1	use	use	VERB
ejpam-4030	307	2	equation	equation	NOUN
ejpam-4030	307	3	(	(	PUNCT
ejpam-4030	307	4	35	35	NUM
ejpam-4030	307	5	)	)	PUNCT
ejpam-4030	307	6	set	set	VERB
ejpam-4030	307	7	n	n	NOUN
ejpam-4030	307	8	=	=	SYM
ejpam-4030	307	9	−1	−1	NOUN
ejpam-4030	307	10	,	,	PUNCT
ejpam-4030	307	11	c	c	NOUN
ejpam-4030	307	12	=	=	SYM
ejpam-4030	307	13	1/2	1/2	NUM
ejpam-4030	307	14	,	,	PUNCT
ejpam-4030	307	15	b	b	NOUN
ejpam-4030	308	1	=	=	SYM
ejpam-4030	308	2	−i	−i	PROPN
ejpam-4030	308	3	,	,	PUNCT
ejpam-4030	308	4	a	a	DET
ejpam-4030	308	5	=	=	NOUN
ejpam-4030	308	6	1/4	1/4	NUM
ejpam-4030	308	7	then	then	ADV
ejpam-4030	308	8	take	take	VERB
ejpam-4030	308	9	the	the	DET
ejpam-4030	308	10	first	first	ADJ
ejpam-4030	308	11	partial	partial	ADJ
ejpam-4030	308	12	derivative	derivative	NOUN
ejpam-4030	308	13	with	with	ADP
ejpam-4030	308	14	respect	respect	NOUN
ejpam-4030	308	15	to	to	ADP
ejpam-4030	308	16	k	k	PROPN
ejpam-4030	308	17	and	and	CCONJ
ejpam-4030	308	18	set	set	VERB
ejpam-4030	308	19	k	k	PROPN
ejpam-4030	308	20	=	=	PUNCT
ejpam-4030	308	21	0	0	NUM
ejpam-4030	308	22	and	and	CCONJ
ejpam-4030	308	23	simplify	simplify	VERB
ejpam-4030	308	24	.	.	PUNCT
ejpam-4030	309	1	proposition	proposition	NOUN
ejpam-4030	309	2	20	20	NUM
ejpam-4030	309	3	.	.	PUNCT
ejpam-4030	310	1	using	use	VERB
ejpam-4030	310	2	equation	equation	NOUN
ejpam-4030	310	3	(	(	PUNCT
ejpam-4030	310	4	35	35	NUM
ejpam-4030	310	5	)	)	PUNCT
ejpam-4030	310	6	setting	set	VERB
ejpam-4030	310	7	n	n	NOUN
ejpam-4030	310	8	=	=	SYM
ejpam-4030	310	9	−2	−2	NOUN
ejpam-4030	310	10	,	,	PUNCT
ejpam-4030	310	11	c	c	NOUN
ejpam-4030	310	12	=	=	SYM
ejpam-4030	310	13	1	1	NUM
ejpam-4030	310	14	,	,	PUNCT
ejpam-4030	310	15	b	b	X
ejpam-4030	310	16	=	=	SYM
ejpam-4030	310	17	−i	−i	PROPN
ejpam-4030	310	18	,	,	PUNCT
ejpam-4030	310	19	a	a	DET
ejpam-4030	310	20	=	=	SYM
ejpam-4030	310	21	1/2	1/2	NUM
ejpam-4030	310	22	,	,	PUNCT
ejpam-4030	310	23	k	k	NOUN
ejpam-4030	310	24	=	=	SYM
ejpam-4030	310	25	1/2	1/2	NUM
ejpam-4030	310	26	and	and	CCONJ
ejpam-4030	310	27	simplify	simplify	VERB
ejpam-4030	310	28	to	to	PART
ejpam-4030	310	29	get	get	VERB
ejpam-4030	310	30	∫	∫	PROPN
ejpam-4030	311	1	+	+	PROPN
ejpam-4030	311	2	∞	∞	PROPN
ejpam-4030	311	3	0	0	NUM
ejpam-4030	312	1	(	(	PUNCT
ejpam-4030	312	2	(	(	PUNCT
ejpam-4030	312	3	x−	x−	PROPN
ejpam-4030	312	4	6)x+	6)x+	NUM
ejpam-4030	312	5	1	1	NUM
ejpam-4030	312	6	)	)	PUNCT
ejpam-4030	312	7	√	√	NOUN
ejpam-4030	312	8	log	log	NOUN
ejpam-4030	312	9	(	(	PUNCT
ejpam-4030	312	10	−	−	PROPN
ejpam-4030	312	11	i	i	NOUN
ejpam-4030	312	12	x	x	PUNCT
ejpam-4030	312	13	)	)	PUNCT
ejpam-4030	313	1	√	√	ADP
ejpam-4030	313	2	x(x+	x(x+	PROPN
ejpam-4030	314	1	1)3	1)3	PROPN
ejpam-4030	314	2	dx	dx	PROPN
ejpam-4030	314	3	=	=	SYM
ejpam-4030	314	4	(	(	PUNCT
ejpam-4030	314	5	1−	1−	NUM
ejpam-4030	314	6	i	i	NOUN
ejpam-4030	314	7	)	)	PUNCT
ejpam-4030	315	1	√	√	PROPN
ejpam-4030	315	2	π	π	PROPN
ejpam-4030	315	3	(	(	PUNCT
ejpam-4030	315	4	√	√	NUM
ejpam-4030	315	5	2φ	2φ	NUM
ejpam-4030	315	6	(	(	PUNCT
ejpam-4030	315	7	−i,−1	−i,−1	ADV
ejpam-4030	315	8	2	2	NUM
ejpam-4030	315	9	dx	dx	NOUN
ejpam-4030	315	10	=	=	SYM
ejpam-4030	315	11	1	1	NUM
ejpam-4030	315	12	2	2	NUM
ejpam-4030	315	13	)	)	PUNCT
ejpam-4030	316	1	+	+	CCONJ
ejpam-4030	316	2	i	i	PRON
ejpam-4030	316	3	√	√	VERB
ejpam-4030	316	4	2φ	2φ	NUM
ejpam-4030	316	5	(	(	PUNCT
ejpam-4030	316	6	i,−1	i,−1	PROPN
ejpam-4030	316	7	2	2	NUM
ejpam-4030	316	8	,	,	PUNCT
ejpam-4030	316	9	3	3	NUM
ejpam-4030	316	10	2	2	NUM
ejpam-4030	316	11	)	)	PUNCT
ejpam-4030	317	1	+	+	CCONJ
ejpam-4030	317	2	1	1	X
ejpam-4030	317	3	)	)	PUNCT
ejpam-4030	317	4	(	(	PUNCT
ejpam-4030	317	5	39	39	NUM
ejpam-4030	317	6	)	)	PUNCT
ejpam-4030	317	7	proposition	proposition	NOUN
ejpam-4030	317	8	21	21	NUM
ejpam-4030	317	9	.	.	PUNCT
ejpam-4030	318	1	using	use	VERB
ejpam-4030	318	2	equation	equation	NOUN
ejpam-4030	318	3	(	(	PUNCT
ejpam-4030	318	4	35	35	NUM
ejpam-4030	318	5	)	)	PUNCT
ejpam-4030	318	6	setting	set	VERB
ejpam-4030	318	7	n	n	NOUN
ejpam-4030	318	8	=	=	SYM
ejpam-4030	318	9	−3	−3	PROPN
ejpam-4030	318	10	,	,	PUNCT
ejpam-4030	318	11	c	c	NOUN
ejpam-4030	318	12	=	=	SYM
ejpam-4030	318	13	1/2	1/2	NUM
ejpam-4030	318	14	,	,	PUNCT
ejpam-4030	318	15	b	b	NOUN
ejpam-4030	318	16	=	=	SYM
ejpam-4030	318	17	−i	−i	PROPN
ejpam-4030	318	18	,	,	PUNCT
ejpam-4030	318	19	a	a	DET
ejpam-4030	318	20	=	=	SYM
ejpam-4030	318	21	1/3	1/3	NUM
ejpam-4030	318	22	,	,	PUNCT
ejpam-4030	318	23	k	k	X
ejpam-4030	318	24	=	=	PUNCT
ejpam-4030	318	25	−1/2	−1/2	ADJ
ejpam-4030	318	26	and	and	CCONJ
ejpam-4030	318	27	simplify	simplify	VERB
ejpam-4030	318	28	to	to	PART
ejpam-4030	318	29	get	get	VERB
ejpam-4030	318	30	∫	∫	PROPN
ejpam-4030	319	1	+	+	PROPN
ejpam-4030	319	2	∞	∞	PROPN
ejpam-4030	319	3	0	0	NUM
ejpam-4030	319	4	x(x(4x−	x(x(4x−	PROPN
ejpam-4030	319	5	93	93	NUM
ejpam-4030	319	6	)	)	PUNCT
ejpam-4030	320	1	+	+	CCONJ
ejpam-4030	321	1	120)−	120)−	NUM
ejpam-4030	321	2	4	4	NUM
ejpam-4030	321	3	x2/3(x+	x2/3(x+	NOUN
ejpam-4030	321	4	2)4	2)4	NUM
ejpam-4030	321	5	√	√	NUM
ejpam-4030	321	6	log	log	NOUN
ejpam-4030	321	7	(	(	PUNCT
ejpam-4030	321	8	−	−	PROPN
ejpam-4030	321	9	i	i	NOUN
ejpam-4030	321	10	x	x	PUNCT
ejpam-4030	321	11	)	)	PUNCT
ejpam-4030	321	12	dx	dx	PROPN
ejpam-4030	321	13	=	=	NOUN
ejpam-4030	321	14	1	1	NUM
ejpam-4030	321	15	8	8	NUM
ejpam-4030	321	16	(	(	PUNCT
ejpam-4030	321	17	−1)5/6	−1)5/6	NOUN
ejpam-4030	321	18	√	√	PROPN
ejpam-4030	321	19	π	π	PROPN
ejpam-4030	321	20	(	(	PUNCT
ejpam-4030	321	21	27iφ	27iφ	PROPN
ejpam-4030	321	22	(	(	PUNCT
ejpam-4030	321	23	i	i	PRON
ejpam-4030	321	24	2	2	NUM
ejpam-4030	321	25	,	,	PUNCT
ejpam-4030	321	26	−5	−5	ADV
ejpam-4030	321	27	2	2	NUM
ejpam-4030	321	28	,	,	PUNCT
ejpam-4030	321	29	4	4	NUM
ejpam-4030	321	30	3	3	NUM
ejpam-4030	321	31	)	)	PUNCT
ejpam-4030	321	32	+	+	CCONJ
ejpam-4030	321	33	2	2	NUM
ejpam-4030	321	34	(	(	PUNCT
ejpam-4030	321	35	√	√	NUM
ejpam-4030	321	36	3	3	NUM
ejpam-4030	321	37	+	+	SYM
ejpam-4030	321	38	54φ	54φ	NUM
ejpam-4030	321	39	(	(	PUNCT
ejpam-4030	321	40	−2i,−5	−2i,−5	NUM
ejpam-4030	321	41	2	2	NUM
ejpam-4030	321	42	,	,	PUNCT
ejpam-4030	321	43	2	2	NUM
ejpam-4030	321	44	3	3	NUM
ejpam-4030	321	45	)	)	PUNCT
ejpam-4030	321	46	)	)	PUNCT
ejpam-4030	321	47	)	)	PUNCT
ejpam-4030	322	1	(	(	PUNCT
ejpam-4030	322	2	40	40	NUM
ejpam-4030	322	3	)	)	PUNCT
ejpam-4030	322	4	proposition	proposition	NOUN
ejpam-4030	322	5	22	22	NUM
ejpam-4030	322	6	.	.	PUNCT
ejpam-4030	323	1	using	use	VERB
ejpam-4030	323	2	equation	equation	NOUN
ejpam-4030	323	3	(	(	PUNCT
ejpam-4030	323	4	35	35	NUM
ejpam-4030	323	5	)	)	PUNCT
ejpam-4030	323	6	setting	set	VERB
ejpam-4030	323	7	n	n	NOUN
ejpam-4030	323	8	=	=	SYM
ejpam-4030	323	9	−1	−1	NOUN
ejpam-4030	323	10	,	,	PUNCT
ejpam-4030	323	11	c	c	NOUN
ejpam-4030	323	12	=	=	SYM
ejpam-4030	323	13	1	1	NUM
ejpam-4030	323	14	,	,	PUNCT
ejpam-4030	323	15	b	b	X
ejpam-4030	324	1	=	=	SYM
ejpam-4030	324	2	−i	−i	PROPN
ejpam-4030	324	3	,	,	PUNCT
ejpam-4030	324	4	a	a	DET
ejpam-4030	324	5	=	=	SYM
ejpam-4030	324	6	1/2	1/2	NUM
ejpam-4030	324	7	,	,	PUNCT
ejpam-4030	324	8	k	k	X
ejpam-4030	324	9	=	=	SYM
ejpam-4030	324	10	3/2	3/2	NUM
ejpam-4030	324	11	and	and	CCONJ
ejpam-4030	324	12	simplify	simplify	VERB
ejpam-4030	324	13	to	to	PART
ejpam-4030	324	14	get	get	VERB
ejpam-4030	324	15	∫	∫	PROPN
ejpam-4030	325	1	+	+	PROPN
ejpam-4030	325	2	∞	∞	PROPN
ejpam-4030	325	3	0	0	NUM
ejpam-4030	326	1	(	(	PUNCT
ejpam-4030	326	2	x−	x−	PROPN
ejpam-4030	326	3	1	1	NUM
ejpam-4030	326	4	)	)	PUNCT
ejpam-4030	326	5	log	log	VERB
ejpam-4030	326	6	3	3	NUM
ejpam-4030	326	7	2	2	NUM
ejpam-4030	326	8	(	(	PUNCT
ejpam-4030	326	9	−	−	PROPN
ejpam-4030	326	10	i	i	NOUN
ejpam-4030	326	11	x	x	PUNCT
ejpam-4030	326	12	)	)	PUNCT
ejpam-4030	327	1	√	√	ADP
ejpam-4030	327	2	x(x+	x(x+	PUNCT
ejpam-4030	328	1	1)2	1)2	NUM
ejpam-4030	328	2	dx	dx	X
ejpam-4030	328	3	=	=	SYM
ejpam-4030	328	4	(	(	PUNCT
ejpam-4030	328	5	−3	−3	NOUN
ejpam-4030	328	6	4	4	NUM
ejpam-4030	328	7	+	+	NUM
ejpam-4030	328	8	3i	3i	NUM
ejpam-4030	328	9	4	4	NUM
ejpam-4030	328	10	)	)	PUNCT
ejpam-4030	328	11	√	√	PROPN
ejpam-4030	328	12	π	π	PROPN
ejpam-4030	328	13	(	(	PUNCT
ejpam-4030	328	14	√	√	NUM
ejpam-4030	328	15	2φ	2φ	NUM
ejpam-4030	328	16	(	(	PUNCT
ejpam-4030	328	17	−i	−i	PROPN
ejpam-4030	328	18	,	,	PUNCT
ejpam-4030	328	19	3	3	NUM
ejpam-4030	328	20	2	2	NUM
ejpam-4030	328	21	,	,	PUNCT
ejpam-4030	328	22	1	1	NUM
ejpam-4030	328	23	2	2	NUM
ejpam-4030	328	24	)	)	PUNCT
ejpam-4030	329	1	+	+	CCONJ
ejpam-4030	329	2	i	i	PRON
ejpam-4030	329	3	√	√	VERB
ejpam-4030	329	4	2φ	2φ	NUM
ejpam-4030	329	5	(	(	PUNCT
ejpam-4030	329	6	i	i	PRON
ejpam-4030	329	7	,	,	PUNCT
ejpam-4030	329	8	3	3	NUM
ejpam-4030	329	9	2	2	NUM
ejpam-4030	329	10	,	,	PUNCT
ejpam-4030	329	11	3	3	NUM
ejpam-4030	329	12	2	2	NUM
ejpam-4030	329	13	)	)	PUNCT
ejpam-4030	329	14	+	+	CCONJ
ejpam-4030	329	15	4	4	X
ejpam-4030	329	16	)	)	PUNCT
ejpam-4030	329	17	(	(	PUNCT
ejpam-4030	329	18	41	41	NUM
ejpam-4030	329	19	)	)	PUNCT
ejpam-4030	329	20	10	10	NUM
ejpam-4030	329	21	.	.	PUNCT
ejpam-4030	329	22	table	table	NOUN
ejpam-4030	329	23	of	of	ADP
ejpam-4030	329	24	integrals	integral	NOUN
ejpam-4030	329	25	the	the	DET
ejpam-4030	329	26	examples	example	NOUN
ejpam-4030	329	27	displayed	display	VERB
ejpam-4030	329	28	in	in	ADP
ejpam-4030	329	29	this	this	DET
ejpam-4030	329	30	table	table	NOUN
ejpam-4030	329	31	correspond	correspond	NOUN
ejpam-4030	329	32	to	to	ADP
ejpam-4030	329	33	equations	equation	NOUN
ejpam-4030	329	34	(	(	PUNCT
ejpam-4030	329	35	12	12	NUM
ejpam-4030	329	36	)	)	PUNCT
ejpam-4030	329	37	,	,	PUNCT
ejpam-4030	329	38	(	(	PUNCT
ejpam-4030	329	39	13	13	NUM
ejpam-4030	329	40	)	)	PUNCT
ejpam-4030	329	41	,	,	PUNCT
ejpam-4030	329	42	(	(	PUNCT
ejpam-4030	329	43	15	15	NUM
ejpam-4030	329	44	)	)	PUNCT
ejpam-4030	329	45	,	,	PUNCT
ejpam-4030	329	46	(	(	PUNCT
ejpam-4030	329	47	16	16	NUM
ejpam-4030	329	48	)	)	PUNCT
ejpam-4030	329	49	,	,	PUNCT
ejpam-4030	329	50	(	(	PUNCT
ejpam-4030	329	51	20	20	NUM
ejpam-4030	329	52	)	)	PUNCT
ejpam-4030	329	53	,	,	PUNCT
ejpam-4030	329	54	(	(	PUNCT
ejpam-4030	329	55	21	21	NUM
ejpam-4030	329	56	)	)	PUNCT
ejpam-4030	329	57	,	,	PUNCT
ejpam-4030	329	58	(	(	PUNCT
ejpam-4030	329	59	22	22	NUM
ejpam-4030	329	60	)	)	PUNCT
ejpam-4030	329	61	,	,	PUNCT
ejpam-4030	329	62	(	(	PUNCT
ejpam-4030	329	63	26	26	NUM
ejpam-4030	329	64	)	)	PUNCT
ejpam-4030	329	65	,	,	PUNCT
ejpam-4030	329	66	(	(	PUNCT
ejpam-4030	329	67	27	27	NUM
ejpam-4030	329	68	)	)	PUNCT
ejpam-4030	329	69	,	,	PUNCT
ejpam-4030	329	70	(	(	PUNCT
ejpam-4030	329	71	30	30	NUM
ejpam-4030	329	72	)	)	PUNCT
ejpam-4030	329	73	,	,	PUNCT
ejpam-4030	329	74	(	(	PUNCT
ejpam-4030	329	75	32	32	NUM
ejpam-4030	329	76	)	)	PUNCT
ejpam-4030	329	77	,	,	PUNCT
ejpam-4030	329	78	and	and	CCONJ
ejpam-4030	329	79	(	(	PUNCT
ejpam-4030	329	80	34	34	NUM
ejpam-4030	329	81	)	)	PUNCT
ejpam-4030	329	82	.	.	PUNCT
ejpam-4030	330	1	r.	r.	PROPN
ejpam-4030	330	2	reynolds	reynolds	PROPN
ejpam-4030	330	3	,	,	PUNCT
ejpam-4030	330	4	a.	a.	PROPN
ejpam-4030	330	5	stauffer	stauffer	PROPN
ejpam-4030	330	6	/	/	SYM
ejpam-4030	330	7	eur	eur	PROPN
ejpam-4030	330	8	.	.	PUNCT
ejpam-4030	331	1	j.	j.	PROPN
ejpam-4030	331	2	pure	pure	PROPN
ejpam-4030	331	3	appl	appl	PROPN
ejpam-4030	331	4	.	.	PROPN
ejpam-4030	331	5	math	math	PROPN
ejpam-4030	331	6	,	,	PUNCT
ejpam-4030	331	7	14	14	NUM
ejpam-4030	331	8	(	(	PUNCT
ejpam-4030	331	9	3	3	NUM
ejpam-4030	331	10	)	)	PUNCT
ejpam-4030	331	11	(	(	PUNCT
ejpam-4030	331	12	2021	2021	NUM
ejpam-4030	331	13	)	)	PUNCT
ejpam-4030	331	14	,	,	PUNCT
ejpam-4030	331	15	788	788	NUM
ejpam-4030	331	16	-	-	SYM
ejpam-4030	331	17	802	802	NUM
ejpam-4030	331	18	800	800	NUM
ejpam-4030	331	19	table	table	NOUN
ejpam-4030	331	20	1	1	NUM
ejpam-4030	331	21	:	:	PUNCT
ejpam-4030	331	22	table	table	NOUN
ejpam-4030	331	23	of	of	ADP
ejpam-4030	331	24	definite	definite	ADJ
ejpam-4030	331	25	integrals	integral	NOUN
ejpam-4030	331	26	f(x	f(x	PROPN
ejpam-4030	331	27	)	)	PUNCT
ejpam-4030	331	28	∫	∫	PROPN
ejpam-4030	332	1	+	+	PROPN
ejpam-4030	332	2	∞	∞	PROPN
ejpam-4030	332	3	0	0	NUM
ejpam-4030	332	4	f(x)dx	f(x)dx	NUM
ejpam-4030	332	5	tanh−1(αx	tanh−1(αx	NOUN
ejpam-4030	332	6	)	)	PUNCT
ejpam-4030	332	7	x(β+log(x))2	x(β+log(x))2	NOUN
ejpam-4030	332	8	1	1	NUM
ejpam-4030	332	9	2	2	NUM
ejpam-4030	332	10	(	(	PUNCT
ejpam-4030	332	11	ψ(0	ψ(0	NOUN
ejpam-4030	332	12	)	)	PUNCT
ejpam-4030	332	13	(	(	PUNCT
ejpam-4030	332	14	−	−	NOUN
ejpam-4030	332	15	i(β−log(α	i(β−log(α	NUM
ejpam-4030	332	16	)	)	PUNCT
ejpam-4030	332	17	)	)	PUNCT
ejpam-4030	332	18	2π	2π	NOUN
ejpam-4030	332	19	)	)	PUNCT
ejpam-4030	333	1	−	−	PROPN
ejpam-4030	333	2	ψ(0	ψ(0	NOUN
ejpam-4030	333	3	)	)	PUNCT
ejpam-4030	333	4	(	(	PUNCT
ejpam-4030	333	5	−iβ+i	−iβ+i	PROPN
ejpam-4030	333	6	log(α)+π	log(α)+π	X
ejpam-4030	333	7	2π	2π	PROPN
ejpam-4030	333	8	)	)	PUNCT
ejpam-4030	333	9	)	)	PUNCT
ejpam-4030	333	10	tanh−1(x	tanh−1(x	NOUN
ejpam-4030	333	11	)	)	PUNCT
ejpam-4030	333	12	x(log(x)+iπ)2	x(log(x)+iπ)2	PUNCT
ejpam-4030	334	1	−	−	PROPN
ejpam-4030	334	2	log(2	log(2	NOUN
ejpam-4030	334	3	)	)	PUNCT
ejpam-4030	334	4	tan−1(dx)−tan−1(cx	tan−1(dx)−tan−1(cx	PROPN
ejpam-4030	334	5	)	)	PUNCT
ejpam-4030	334	6	x	x	SYM
ejpam-4030	334	7	1	1	NUM
ejpam-4030	334	8	2π	2π	NUM
ejpam-4030	334	9	log	log	VERB
ejpam-4030	334	10	(	(	PUNCT
ejpam-4030	334	11	d	d	PROPN
ejpam-4030	334	12	c	c	PROPN
ejpam-4030	334	13	)	)	PUNCT
ejpam-4030	334	14	log	log	NOUN
ejpam-4030	334	15	(	(	PUNCT
ejpam-4030	334	16	bx)(tan−1	bx)(tan−1	PROPN
ejpam-4030	334	17	(	(	PUNCT
ejpam-4030	334	18	√	√	NOUN
ejpam-4030	334	19	d	d	NOUN
ejpam-4030	334	20	√	√	PROPN
ejpam-4030	334	21	x)−tan−1	x)−tan−1	PROPN
ejpam-4030	334	22	(	(	PUNCT
ejpam-4030	335	1	√	√	PROPN
ejpam-4030	335	2	c	c	NOUN
ejpam-4030	335	3	√	√	NUM
ejpam-4030	335	4	x	x	NOUN
ejpam-4030	335	5	)	)	PUNCT
ejpam-4030	335	6	)	)	PUNCT
ejpam-4030	336	1	x	x	SYM
ejpam-4030	336	2	−1	−1	NOUN
ejpam-4030	336	3	4π	4π	NUM
ejpam-4030	336	4	log	log	VERB
ejpam-4030	336	5	(	(	PUNCT
ejpam-4030	336	6	c	c	NOUN
ejpam-4030	336	7	d	d	NOUN
ejpam-4030	336	8	)	)	PUNCT
ejpam-4030	336	9	log	log	NOUN
ejpam-4030	336	10	(	(	PUNCT
ejpam-4030	336	11	b2cd	b2cd	PUNCT
ejpam-4030	336	12	)	)	PUNCT
ejpam-4030	336	13	1−x√	1−x√	PROPN
ejpam-4030	336	14	x(x+1)2	x(x+1)2	NUM
ejpam-4030	336	15	log(x	log(x	PROPN
ejpam-4030	336	16	)	)	PUNCT
ejpam-4030	336	17	−4c	−4c	PROPN
ejpam-4030	337	1	π	π	PROPN
ejpam-4030	337	2	x−1	x−1	PROPN
ejpam-4030	337	3	√	√	PROPN
ejpam-4030	337	4	x(x+1)2	x(x+1)2	PROPN
ejpam-4030	338	1	√	√	NUM
ejpam-4030	338	2	log(−	log(−	PROPN
ejpam-4030	338	3	i	i	PROPN
ejpam-4030	338	4	x	x	PROPN
ejpam-4030	338	5	)	)	PUNCT
ejpam-4030	338	6	(	(	PUNCT
ejpam-4030	338	7	−1)3/4(ζ	−1)3/4(ζ	NOUN
ejpam-4030	338	8	(	(	PUNCT
ejpam-4030	338	9	3	3	NUM
ejpam-4030	338	10	2	2	NUM
ejpam-4030	338	11	,	,	PUNCT
ejpam-4030	338	12	3	3	NUM
ejpam-4030	338	13	8)−ζ	8)−ζ	NUM
ejpam-4030	338	14	(	(	PUNCT
ejpam-4030	338	15	3	3	NUM
ejpam-4030	338	16	2	2	NUM
ejpam-4030	338	17	,	,	PUNCT
ejpam-4030	338	18	7	7	NUM
ejpam-4030	338	19	8)	8)	NUM
ejpam-4030	338	20	)	)	PUNCT
ejpam-4030	338	21	4	4	NUM
ejpam-4030	338	22	√	√	PROPN
ejpam-4030	338	23	π	π	PROPN
ejpam-4030	338	24	(	(	PUNCT
ejpam-4030	338	25	x−1	x−1	PROPN
ejpam-4030	338	26	)	)	PUNCT
ejpam-4030	338	27	√	√	NOUN
ejpam-4030	338	28	log(−	log(−	PROPN
ejpam-4030	338	29	i	i	PROPN
ejpam-4030	338	30	x	x	PROPN
ejpam-4030	338	31	)	)	PUNCT
ejpam-4030	338	32	√	√	PROPN
ejpam-4030	338	33	x(x+1)2	x(x+1)2	PROPN
ejpam-4030	338	34	4	4	NUM
ejpam-4030	338	35	√	√	NUM
ejpam-4030	338	36	−1	−1	NOUN
ejpam-4030	338	37	√	√	PROPN
ejpam-4030	338	38	π	π	PROPN
ejpam-4030	338	39	(	(	PUNCT
ejpam-4030	338	40	ζ	ζ	X
ejpam-4030	338	41	(	(	PUNCT
ejpam-4030	338	42	1	1	NUM
ejpam-4030	338	43	2	2	NUM
ejpam-4030	338	44	,	,	PUNCT
ejpam-4030	338	45	7	7	NUM
ejpam-4030	338	46	8	8	NUM
ejpam-4030	338	47	)	)	PUNCT
ejpam-4030	338	48	−	−	PROPN
ejpam-4030	338	49	ζ	ζ	NOUN
ejpam-4030	338	50	(	(	PUNCT
ejpam-4030	338	51	1	1	NUM
ejpam-4030	338	52	2	2	NUM
ejpam-4030	338	53	,	,	PUNCT
ejpam-4030	338	54	3	3	NUM
ejpam-4030	338	55	8	8	NUM
ejpam-4030	338	56	)	)	PUNCT
ejpam-4030	338	57	)	)	PUNCT
ejpam-4030	338	58	(	(	PUNCT
ejpam-4030	338	59	cx−1	cx−1	NOUN
ejpam-4030	338	60	)	)	PUNCT
ejpam-4030	338	61	logk	logk	PROPN
ejpam-4030	338	62	(	(	PUNCT
ejpam-4030	338	63	bx	bx	NOUN
ejpam-4030	338	64	)	)	PUNCT
ejpam-4030	338	65	(	(	PUNCT
ejpam-4030	338	66	cx+1)3	cx+1)3	NOUN
ejpam-4030	338	67	ie−	ie−	NOUN
ejpam-4030	338	68	1	1	NUM
ejpam-4030	338	69	2	2	NUM
ejpam-4030	338	70	iπk(k−1)k(2π)k−1ζ	iπk(k−1)k(2π)k−1ζ	NUM
ejpam-4030	338	71	(	(	PUNCT
ejpam-4030	338	72	2−k	2−k	NUM
ejpam-4030	338	73	,	,	PUNCT
ejpam-4030	338	74	i	i	PRON
ejpam-4030	338	75	log(b)+i	log(b)+i	VERB
ejpam-4030	338	76	log(c)+π	log(c)+π	ADP
ejpam-4030	338	77	2π	2π	PROPN
ejpam-4030	338	78	)	)	PUNCT
ejpam-4030	339	1	c	c	NOUN
ejpam-4030	339	2	(	(	PUNCT
ejpam-4030	339	3	x−1	x−1	NOUN
ejpam-4030	339	4	)	)	PUNCT
ejpam-4030	339	5	log(x	log(x	NOUN
ejpam-4030	339	6	)	)	PUNCT
ejpam-4030	339	7	(	(	PUNCT
ejpam-4030	339	8	x+1)3(4	x+1)3(4	PROPN
ejpam-4030	339	9	log2(x)+π2	log2(x)+π2	PROPN
ejpam-4030	339	10	)	)	PUNCT
ejpam-4030	339	11	ζ(3	ζ(3	PROPN
ejpam-4030	339	12	,	,	PUNCT
ejpam-4030	339	13	34	34	NUM
ejpam-4030	339	14	)	)	PUNCT
ejpam-4030	339	15	8π2	8π2	NUM
ejpam-4030	339	16	(	(	PUNCT
ejpam-4030	339	17	(	(	PUNCT
ejpam-4030	339	18	x−4)x+1	x−4)x+1	PROPN
ejpam-4030	339	19	)	)	PUNCT
ejpam-4030	339	20	log(log	log(log	NOUN
ejpam-4030	339	21	(	(	PUNCT
ejpam-4030	339	22	1	1	NUM
ejpam-4030	339	23	x	x	NOUN
ejpam-4030	339	24	)	)	PUNCT
ejpam-4030	339	25	)	)	PUNCT
ejpam-4030	340	1	(	(	PUNCT
ejpam-4030	340	2	x+1)4	x+1)4	PROPN
ejpam-4030	340	3	7ζ(3	7ζ(3	NUM
ejpam-4030	340	4	)	)	PUNCT
ejpam-4030	340	5	2π2	2π2	NUM
ejpam-4030	340	6	(	(	PUNCT
ejpam-4030	340	7	x−1)((x−10)x+1	x−1)((x−10)x+1	NOUN
ejpam-4030	340	8	)	)	PUNCT
ejpam-4030	340	9	log	log	NOUN
ejpam-4030	340	10	(	(	PUNCT
ejpam-4030	340	11	1	1	NUM
ejpam-4030	340	12	x	x	NOUN
ejpam-4030	340	13	)	)	PUNCT
ejpam-4030	340	14	log(log	log(log	NOUN
ejpam-4030	340	15	(	(	PUNCT
ejpam-4030	340	16	1	1	NUM
ejpam-4030	340	17	x	x	NOUN
ejpam-4030	340	18	)	)	PUNCT
ejpam-4030	340	19	)	)	PUNCT
ejpam-4030	340	20	(	(	PUNCT
ejpam-4030	340	21	x+1)5	x+1)5	PROPN
ejpam-4030	340	22	−7ζ(3	−7ζ(3	PROPN
ejpam-4030	340	23	)	)	PUNCT
ejpam-4030	340	24	2π2	2π2	NUM
ejpam-4030	340	25	(	(	PUNCT
ejpam-4030	340	26	x−1)((x−22)x+1	x−1)((x−22)x+1	NUM
ejpam-4030	340	27	)	)	PUNCT
ejpam-4030	340	28	log	log	NOUN
ejpam-4030	340	29	(	(	PUNCT
ejpam-4030	340	30	1	1	NUM
ejpam-4030	340	31	x	x	NOUN
ejpam-4030	340	32	)	)	PUNCT
ejpam-4030	340	33	log(log	log(log	NOUN
ejpam-4030	340	34	(	(	PUNCT
ejpam-4030	340	35	1	1	NUM
ejpam-4030	340	36	x	x	NOUN
ejpam-4030	340	37	)	)	PUNCT
ejpam-4030	340	38	)	)	PUNCT
ejpam-4030	340	39	8	8	NUM
ejpam-4030	340	40	√	√	NUM
ejpam-4030	340	41	x(x+1)4	x(x+1)4	PROPN
ejpam-4030	340	42	−2c	−2c	PROPN
ejpam-4030	340	43	π	π	X
ejpam-4030	340	44	(	(	PUNCT
ejpam-4030	340	45	(	(	PUNCT
ejpam-4030	340	46	x−6)x+1	x−6)x+1	NUM
ejpam-4030	340	47	)	)	PUNCT
ejpam-4030	340	48	log(−	log(−	PROPN
ejpam-4030	340	49	log(x)+	log(x)+	PROPN
ejpam-4030	340	50	iπ	iπ	ADV
ejpam-4030	340	51	2	2	NUM
ejpam-4030	340	52	)	)	PUNCT
ejpam-4030	340	53	√	√	NOUN
ejpam-4030	340	54	x(x+1)3	x(x+1)3	PUNCT
ejpam-4030	341	1	ψ(1	ψ(1	PROPN
ejpam-4030	341	2	)	)	PUNCT
ejpam-4030	341	3	(	(	PUNCT
ejpam-4030	341	4	3	3	NUM
ejpam-4030	341	5	8)−ψ(1	8)−ψ(1	NUM
ejpam-4030	341	6	)	)	PUNCT
ejpam-4030	341	7	(	(	PUNCT
ejpam-4030	341	8	7	7	NUM
ejpam-4030	341	9	8)	8)	NUM
ejpam-4030	341	10	2π	2π	NOUN
ejpam-4030	341	11	references	reference	VERB
ejpam-4030	341	12	801	801	NUM
ejpam-4030	341	13	11	11	NUM
ejpam-4030	341	14	.	.	PUNCT
ejpam-4030	342	1	discussion	discussion	NOUN
ejpam-4030	342	2	in	in	ADP
ejpam-4030	342	3	this	this	DET
ejpam-4030	342	4	work	work	NOUN
ejpam-4030	342	5	the	the	DET
ejpam-4030	342	6	authors	author	NOUN
ejpam-4030	342	7	used	use	VERB
ejpam-4030	342	8	their	their	PRON
ejpam-4030	342	9	contour	contour	NOUN
ejpam-4030	342	10	integral	integral	ADJ
ejpam-4030	342	11	method	method	NOUN
ejpam-4030	342	12	and	and	CCONJ
ejpam-4030	342	13	derived	derive	VERB
ejpam-4030	342	14	a	a	DET
ejpam-4030	342	15	definite	definite	ADJ
ejpam-4030	342	16	integral	integral	ADJ
ejpam-4030	342	17	using	use	VERB
ejpam-4030	342	18	the	the	DET
ejpam-4030	342	19	lerch	lerch	PROPN
ejpam-4030	342	20	function	function	NOUN
ejpam-4030	342	21	in	in	ADP
ejpam-4030	342	22	terms	term	NOUN
ejpam-4030	342	23	of	of	ADP
ejpam-4030	342	24	the	the	DET
ejpam-4030	342	25	lerch	lerch	PROPN
ejpam-4030	342	26	function	function	NOUN
ejpam-4030	342	27	which	which	PRON
ejpam-4030	342	28	has	have	AUX
ejpam-4030	342	29	not	not	PART
ejpam-4030	342	30	been	be	AUX
ejpam-4030	342	31	given	give	VERB
ejpam-4030	342	32	before	before	ADV
ejpam-4030	342	33	.	.	PUNCT
ejpam-4030	343	1	a	a	DET
ejpam-4030	343	2	definite	definite	ADJ
ejpam-4030	343	3	integral	integral	ADJ
ejpam-4030	343	4	representation	representation	NOUN
ejpam-4030	343	5	involving	involve	VERB
ejpam-4030	343	6	the	the	DET
ejpam-4030	343	7	lerch	lerch	PROPN
ejpam-4030	343	8	function	function	NOUN
ejpam-4030	343	9	was	be	AUX
ejpam-4030	343	10	also	also	ADV
ejpam-4030	343	11	derived	derive	VERB
ejpam-4030	343	12	for	for	ADP
ejpam-4030	343	13	the	the	DET
ejpam-4030	343	14	lerch	lerch	PROPN
ejpam-4030	343	15	transformation	transformation	NOUN
ejpam-4030	343	16	.	.	PUNCT
ejpam-4030	344	1	a	a	DET
ejpam-4030	344	2	table	table	NOUN
ejpam-4030	344	3	of	of	ADP
ejpam-4030	344	4	integrals	integral	NOUN
ejpam-4030	344	5	was	be	AUX
ejpam-4030	344	6	produced	produce	VERB
ejpam-4030	344	7	for	for	ADP
ejpam-4030	344	8	easy	easy	ADJ
ejpam-4030	344	9	reading	reading	NOUN
ejpam-4030	344	10	by	by	ADP
ejpam-4030	344	11	interested	interested	ADJ
ejpam-4030	344	12	readers	reader	NOUN
ejpam-4030	344	13	.	.	PUNCT
ejpam-4030	345	1	we	we	PRON
ejpam-4030	345	2	will	will	AUX
ejpam-4030	345	3	be	be	AUX
ejpam-4030	345	4	using	use	VERB
ejpam-4030	345	5	our	our	PRON
ejpam-4030	345	6	contour	contour	NOUN
ejpam-4030	345	7	integral	integral	ADJ
ejpam-4030	345	8	method	method	NOUN
ejpam-4030	345	9	to	to	PART
ejpam-4030	345	10	derive	derive	VERB
ejpam-4030	345	11	other	other	ADJ
ejpam-4030	345	12	integrals	integral	NOUN
ejpam-4030	345	13	in	in	ADP
ejpam-4030	345	14	our	our	PRON
ejpam-4030	345	15	future	future	ADJ
ejpam-4030	345	16	work	work	NOUN
ejpam-4030	345	17	.	.	PUNCT
ejpam-4030	346	1	references	reference	NOUN
ejpam-4030	346	2	[	[	X
ejpam-4030	346	3	1	1	NUM
ejpam-4030	346	4	]	]	X
ejpam-4030	346	5	milton	milton	PROPN
ejpam-4030	346	6	abramowitz	abramowitz	PROPN
ejpam-4030	346	7	and	and	CCONJ
ejpam-4030	346	8	irene	irene	PROPN
ejpam-4030	346	9	a.	a.	PROPN
ejpam-4030	346	10	stegun	stegun	PROPN
ejpam-4030	346	11	.	.	PUNCT
ejpam-4030	347	1	handbook	handbook	NOUN
ejpam-4030	347	2	of	of	ADP
ejpam-4030	347	3	mathematical	mathematical	ADJ
ejpam-4030	347	4	functions	function	NOUN
ejpam-4030	347	5	with	with	ADP
ejpam-4030	347	6	formulas	formula	NOUN
ejpam-4030	347	7	,	,	PUNCT
ejpam-4030	347	8	graphs	graph	NOUN
ejpam-4030	347	9	,	,	PUNCT
ejpam-4030	347	10	and	and	CCONJ
ejpam-4030	347	11	mathematical	mathematical	ADJ
ejpam-4030	347	12	tables	table	NOUN
ejpam-4030	347	13	,	,	PUNCT
ejpam-4030	347	14	12	12	NUM
ejpam-4030	347	15	1972	1972	NUM
ejpam-4030	347	16	.	.	PUNCT
ejpam-4030	348	1	[	[	X
ejpam-4030	348	2	2	2	X
ejpam-4030	348	3	]	]	PUNCT
ejpam-4030	348	4	horst	horst	PROPN
ejpam-4030	348	5	alzer	alzer	PROPN
ejpam-4030	348	6	and	and	CCONJ
ejpam-4030	348	7	junesang	junesang	PROPN
ejpam-4030	348	8	choi	choi	PROPN
ejpam-4030	348	9	.	.	PUNCT
ejpam-4030	349	1	the	the	DET
ejpam-4030	349	2	riemann	riemann	PROPN
ejpam-4030	349	3	zeta	zeta	PROPN
ejpam-4030	349	4	function	function	PROPN
ejpam-4030	349	5	and	and	CCONJ
ejpam-4030	349	6	classes	class	NOUN
ejpam-4030	349	7	of	of	ADP
ejpam-4030	349	8	infinite	infinite	ADJ
ejpam-4030	349	9	series	series	NOUN
ejpam-4030	349	10	.	.	PUNCT
ejpam-4030	350	1	applicable	applicable	ADJ
ejpam-4030	350	2	analysis	analysis	NOUN
ejpam-4030	350	3	and	and	CCONJ
ejpam-4030	350	4	discrete	discrete	ADJ
ejpam-4030	350	5	mathematics	mathematic	NOUN
ejpam-4030	350	6	,	,	PUNCT
ejpam-4030	350	7	11:386–398	11:386–398	NUM
ejpam-4030	350	8	,	,	PUNCT
ejpam-4030	350	9	2017	2017	NUM
ejpam-4030	350	10	.	.	PUNCT
ejpam-4030	351	1	[	[	X
ejpam-4030	351	2	3	3	X
ejpam-4030	351	3	]	]	PUNCT
ejpam-4030	351	4	t.	t.	PROPN
ejpam-4030	351	5	m.	m.	NOUN
ejpam-4030	351	6	apostol	apostol	PROPN
ejpam-4030	351	7	.	.	PUNCT
ejpam-4030	352	1	on	on	ADP
ejpam-4030	352	2	the	the	DET
ejpam-4030	352	3	lerch	lerch	PROPN
ejpam-4030	352	4	zeta	zeta	PROPN
ejpam-4030	352	5	function	function	PROPN
ejpam-4030	352	6	.	.	PUNCT
ejpam-4030	353	1	pacific	pacific	PROPN
ejpam-4030	353	2	journal	journal	PROPN
ejpam-4030	353	3	of	of	ADP
ejpam-4030	353	4	mathematics	mathematic	NOUN
ejpam-4030	353	5	,	,	PUNCT
ejpam-4030	353	6	1:161–167	1:161–167	NUM
ejpam-4030	353	7	,	,	PUNCT
ejpam-4030	353	8	01	01	NUM
ejpam-4030	353	9	1951	1951	NUM
ejpam-4030	353	10	.	.	PUNCT
ejpam-4030	354	1	[	[	X
ejpam-4030	354	2	4	4	X
ejpam-4030	354	3	]	]	PUNCT
ejpam-4030	354	4	e.	e.	PROPN
ejpam-4030	354	5	w.	w.	PROPN
ejpam-4030	354	6	barnes	barnes	PROPN
ejpam-4030	354	7	.	.	PUNCT
ejpam-4030	355	1	on	on	ADP
ejpam-4030	355	2	certain	certain	ADJ
ejpam-4030	355	3	functions	function	NOUN
ejpam-4030	355	4	defined	define	VERB
ejpam-4030	355	5	by	by	ADP
ejpam-4030	355	6	taylor	taylor	PROPN
ejpam-4030	355	7	’s	’s	PART
ejpam-4030	355	8	series	series	PROPN
ejpam-4030	355	9	of	of	ADP
ejpam-4030	355	10	finite	finite	PROPN
ejpam-4030	355	11	radius	radius	NOUN
ejpam-4030	355	12	of	of	ADP
ejpam-4030	355	13	convergence	convergence	NOUN
ejpam-4030	355	14	.	.	PUNCT
ejpam-4030	356	1	proceedings	proceeding	NOUN
ejpam-4030	356	2	of	of	ADP
ejpam-4030	356	3	the	the	DET
ejpam-4030	356	4	london	london	PROPN
ejpam-4030	356	5	mathematical	mathematical	ADJ
ejpam-4030	356	6	society	society	NOUN
ejpam-4030	356	7	,	,	PUNCT
ejpam-4030	356	8	s2	s2	PROPN
ejpam-4030	356	9	-	-	PUNCT
ejpam-4030	356	10	4:284–316	4:284–316	ADJ
ejpam-4030	356	11	,	,	PUNCT
ejpam-4030	356	12	1907	1907	NUM
ejpam-4030	356	13	.	.	PUNCT
ejpam-4030	357	1	[	[	X
ejpam-4030	357	2	5	5	X
ejpam-4030	357	3	]	]	PUNCT
ejpam-4030	357	4	g.	g.	PROPN
ejpam-4030	357	5	h.	h.	PROPN
ejpam-4030	357	6	hardy	hardy	PROPN
ejpam-4030	357	7	.	.	PUNCT
ejpam-4030	358	1	a	a	DET
ejpam-4030	358	2	method	method	NOUN
ejpam-4030	358	3	for	for	ADP
ejpam-4030	358	4	determining	determine	VERB
ejpam-4030	358	5	a	a	DET
ejpam-4030	358	6	behaviour	behaviour	NOUN
ejpam-4030	358	7	of	of	ADP
ejpam-4030	358	8	certain	certain	ADJ
ejpam-4030	358	9	classes	class	NOUN
ejpam-4030	358	10	of	of	ADP
ejpam-4030	358	11	power	power	NOUN
ejpam-4030	358	12	series	series	NOUN
ejpam-4030	358	13	near	near	ADP
ejpam-4030	358	14	a	a	DET
ejpam-4030	358	15	singular	singular	ADJ
ejpam-4030	358	16	point	point	NOUN
ejpam-4030	358	17	on	on	ADP
ejpam-4030	358	18	the	the	DET
ejpam-4030	358	19	circle	circle	NOUN
ejpam-4030	358	20	of	of	ADP
ejpam-4030	358	21	convergence	convergence	NOUN
ejpam-4030	358	22	.	.	PUNCT
ejpam-4030	359	1	proceedings	proceeding	NOUN
ejpam-4030	359	2	of	of	ADP
ejpam-4030	359	3	the	the	DET
ejpam-4030	359	4	london	london	PROPN
ejpam-4030	359	5	mathematical	mathematical	ADJ
ejpam-4030	359	6	society	society	NOUN
ejpam-4030	359	7	,	,	PUNCT
ejpam-4030	359	8	s2	s2	NOUN
ejpam-4030	359	9	-	-	PUNCT
ejpam-4030	359	10	3:381–389	3:381–389	NUM
ejpam-4030	359	11	,	,	PUNCT
ejpam-4030	359	12	1905	1905	NUM
ejpam-4030	359	13	.	.	PUNCT
ejpam-4030	360	1	[	[	X
ejpam-4030	360	2	6	6	X
ejpam-4030	360	3	]	]	PUNCT
ejpam-4030	360	4	eberhard	eberhard	NOUN
ejpam-4030	360	5	hopf	hopf	ADJ
ejpam-4030	360	6	.	.	PUNCT
ejpam-4030	361	1	mathematical	mathematical	ADJ
ejpam-4030	361	2	problems	problem	NOUN
ejpam-4030	361	3	of	of	ADP
ejpam-4030	361	4	radiative	radiative	ADJ
ejpam-4030	361	5	equilibrium	equilibrium	NOUN
ejpam-4030	361	6	.	.	PUNCT
ejpam-4030	362	1	nature	nature	NOUN
ejpam-4030	362	2	,	,	PUNCT
ejpam-4030	362	3	135:51–51	135:51–51	NUM
ejpam-4030	362	4	,	,	PUNCT
ejpam-4030	362	5	01	01	NUM
ejpam-4030	362	6	1935	1935	NUM
ejpam-4030	362	7	.	.	PUNCT
ejpam-4030	363	1	[	[	X
ejpam-4030	363	2	7	7	X
ejpam-4030	363	3	]	]	X
ejpam-4030	363	4	masao	masao	PROPN
ejpam-4030	363	5	kotani	kotani	PROPN
ejpam-4030	363	6	and	and	CCONJ
ejpam-4030	363	7	ayao	ayao	ADJ
ejpam-4030	363	8	amemiya	amemiya	NOUN
ejpam-4030	363	9	.	.	PUNCT
ejpam-4030	364	1	table	table	NOUN
ejpam-4030	364	2	of	of	ADP
ejpam-4030	364	3	molecular	molecular	ADJ
ejpam-4030	364	4	integrals	integral	NOUN
ejpam-4030	364	5	.	.	PUNCT
ejpam-4030	365	1	maruzen	maruzen	NOUN
ejpam-4030	365	2	company	company	NOUN
ejpam-4030	365	3	,	,	PUNCT
ejpam-4030	365	4	1955	1955	NUM
ejpam-4030	365	5	.	.	PUNCT
ejpam-4030	366	1	[	[	X
ejpam-4030	366	2	8	8	NUM
ejpam-4030	366	3	]	]	X
ejpam-4030	366	4	nobushige	nobushige	PROPN
ejpam-4030	366	5	kurokawa	kurokawa	PROPN
ejpam-4030	366	6	,	,	PUNCT
ejpam-4030	366	7	katsuhisa	katsuhisa	NOUN
ejpam-4030	366	8	mimachi	mimachi	NOUN
ejpam-4030	366	9	,	,	PUNCT
ejpam-4030	366	10	and	and	CCONJ
ejpam-4030	366	11	masato	masato	PROPN
ejpam-4030	366	12	wakayama	wakayama	PROPN
ejpam-4030	366	13	.	.	PUNCT
ejpam-4030	367	1	jackson	jackson	PROPN
ejpam-4030	367	2	’s	’s	PROPN
ejpam-4030	367	3	integral	integral	ADJ
ejpam-4030	367	4	of	of	ADP
ejpam-4030	367	5	the	the	DET
ejpam-4030	367	6	hurwitz	hurwitz	PROPN
ejpam-4030	367	7	zeta	zeta	PROPN
ejpam-4030	367	8	function	function	PROPN
ejpam-4030	367	9	.	.	PUNCT
ejpam-4030	368	1	rendiconti	rendiconti	ADJ
ejpam-4030	368	2	del	del	PROPN
ejpam-4030	368	3	circolo	circolo	PROPN
ejpam-4030	368	4	matematico	matematico	NOUN
ejpam-4030	368	5	di	di	NOUN
ejpam-4030	368	6	palermo	palermo	NOUN
ejpam-4030	368	7	,	,	PUNCT
ejpam-4030	368	8	56:43–56	56:43–56	NUM
ejpam-4030	368	9	,	,	PUNCT
ejpam-4030	368	10	02	02	NUM
ejpam-4030	368	11	2007	2007	NUM
ejpam-4030	368	12	.	.	PUNCT
ejpam-4030	369	1	[	[	X
ejpam-4030	369	2	9	9	NUM
ejpam-4030	369	3	]	]	PUNCT
ejpam-4030	369	4	m.	m.	NOUN
ejpam-4030	369	5	lerch	lerch	PROPN
ejpam-4030	369	6	.	.	PUNCT
ejpam-4030	370	1	note	note	VERB
ejpam-4030	370	2	sur	sur	PROPN
ejpam-4030	370	3	la	la	PRON
ejpam-4030	370	4	fonction	fonction	PROPN
ejpam-4030	370	5	k(w	k(w	PROPN
ejpam-4030	370	6	,	,	PUNCT
ejpam-4030	370	7	x	x	X
ejpam-4030	370	8	,	,	PUNCT
ejpam-4030	370	9	s	s	PART
ejpam-4030	370	10	)	)	PUNCT
ejpam-4030	370	11	=	=	SYM
ejpam-4030	371	1	∞∑	∞∑	DET
ejpam-4030	371	2	k=0	k=0	PROPN
ejpam-4030	371	3	e2kπix	e2kπix	NOUN
ejpam-4030	371	4	(	(	PUNCT
ejpam-4030	371	5	w+k)3	w+k)3	PROPN
ejpam-4030	371	6	.	.	PUNCT
ejpam-4030	372	1	acta	acta	PROPN
ejpam-4030	372	2	mathematica	mathematica	PROPN
ejpam-4030	372	3	,	,	PUNCT
ejpam-4030	372	4	11:19–24	11:19–24	PROPN
ejpam-4030	372	5	,	,	PUNCT
ejpam-4030	372	6	1887	1887	NUM
ejpam-4030	372	7	.	.	PUNCT
ejpam-4030	373	1	[	[	X
ejpam-4030	373	2	10	10	NUM
ejpam-4030	373	3	]	]	X
ejpam-4030	373	4	f.	f.	PROPN
ejpam-4030	373	5	oberhettinger	oberhettinger	PROPN
ejpam-4030	373	6	.	.	PUNCT
ejpam-4030	374	1	note	note	NOUN
ejpam-4030	374	2	on	on	ADP
ejpam-4030	374	3	the	the	DET
ejpam-4030	374	4	lerch	lerch	PROPN
ejpam-4030	374	5	zeta	zeta	PROPN
ejpam-4030	374	6	function	function	PROPN
ejpam-4030	374	7	.	.	PUNCT
ejpam-4030	375	1	pacific	pacific	PROPN
ejpam-4030	375	2	journal	journal	PROPN
ejpam-4030	375	3	of	of	ADP
ejpam-4030	375	4	mathematics	mathematic	NOUN
ejpam-4030	375	5	,	,	PUNCT
ejpam-4030	375	6	6:117–120	6:117–120	PROPN
ejpam-4030	375	7	,	,	PUNCT
ejpam-4030	375	8	01	01	NUM
ejpam-4030	375	9	1956	1956	NUM
ejpam-4030	375	10	.	.	PUNCT
ejpam-4030	376	1	[	[	X
ejpam-4030	376	2	11	11	NUM
ejpam-4030	376	3	]	]	X
ejpam-4030	376	4	keit	keit	PROPN
ejpam-4030	376	5	oldham	oldham	PROPN
ejpam-4030	376	6	,	,	PUNCT
ejpam-4030	376	7	jan	jan	PROPN
ejpam-4030	376	8	myland	myland	PROPN
ejpam-4030	376	9	,	,	PUNCT
ejpam-4030	376	10	and	and	CCONJ
ejpam-4030	376	11	jerome	jerome	PROPN
ejpam-4030	376	12	spanier	spanier	NOUN
ejpam-4030	376	13	.	.	PUNCT
ejpam-4030	377	1	an	an	DET
ejpam-4030	377	2	atlas	atlas	PROPN
ejpam-4030	377	3	of	of	ADP
ejpam-4030	377	4	functions	function	NOUN
ejpam-4030	377	5	.	.	PUNCT
ejpam-4030	378	1	springer	springer	PROPN
ejpam-4030	378	2	us	we	PRON
ejpam-4030	378	3	,	,	PUNCT
ejpam-4030	378	4	2009	2009	NUM
ejpam-4030	378	5	.	.	PUNCT
ejpam-4030	379	1	references	reference	NOUN
ejpam-4030	379	2	802	802	NUM
ejpam-4030	379	3	[	[	X
ejpam-4030	379	4	12	12	NUM
ejpam-4030	379	5	]	]	X
ejpam-4030	379	6	f	f	PROPN
ejpam-4030	379	7	olver	olver	ADV
ejpam-4030	379	8	,	,	PUNCT
ejpam-4030	379	9	a.	a.	PROPN
ejpam-4030	379	10	b.	b.	PROPN
ejpam-4030	379	11	olde	olde	PROPN
ejpam-4030	379	12	daalhuis	daalhuis	PROPN
ejpam-4030	379	13	,	,	PUNCT
ejpam-4030	379	14	d.	d.	PROPN
ejpam-4030	379	15	w.	w.	PROPN
ejpam-4030	379	16	lozier	lozier	PROPN
ejpam-4030	379	17	,	,	PUNCT
ejpam-4030	379	18	b.	b.	PROPN
ejpam-4030	379	19	i.	i.	PROPN
ejpam-4030	379	20	schneider	schneider	PROPN
ejpam-4030	379	21	,	,	PUNCT
ejpam-4030	379	22	r.	r.	PROPN
ejpam-4030	379	23	f.	f.	PROPN
ejpam-4030	379	24	boisvert	boisvert	PROPN
ejpam-4030	379	25	,	,	PUNCT
ejpam-4030	379	26	c.	c.	PROPN
ejpam-4030	379	27	w.	w.	PROPN
ejpam-4030	379	28	clark	clark	PROPN
ejpam-4030	379	29	,	,	PUNCT
ejpam-4030	379	30	b.	b.	PROPN
ejpam-4030	379	31	r.	r.	PROPN
ejpam-4030	379	32	miller	miller	PROPN
ejpam-4030	379	33	,	,	PUNCT
ejpam-4030	379	34	b.	b.	PROPN
ejpam-4030	380	1	v.	v.	PROPN
ejpam-4030	380	2	saunders	saunders	PROPN
ejpam-4030	380	3	,	,	PUNCT
ejpam-4030	380	4	h.	h.	PROPN
ejpam-4030	380	5	s.	s.	PROPN
ejpam-4030	380	6	cohl	cohl	PROPN
ejpam-4030	380	7	,	,	PUNCT
ejpam-4030	380	8	and	and	CCONJ
ejpam-4030	380	9	m.	m.	PROPN
ejpam-4030	380	10	a.	a.	PROPN
ejpam-4030	380	11	mcclain	mcclain	PROPN
ejpam-4030	380	12	.	.	PUNCT
ejpam-4030	381	1	dlmf	dlmf	PROPN
ejpam-4030	381	2	:	:	PUNCT
ejpam-4030	381	3	nist	nist	PROPN
ejpam-4030	381	4	digital	digital	PROPN
ejpam-4030	381	5	library	library	NOUN
ejpam-4030	381	6	of	of	ADP
ejpam-4030	381	7	mathematical	mathematical	ADJ
ejpam-4030	381	8	functions	function	NOUN
ejpam-4030	381	9	,	,	PUNCT
ejpam-4030	381	10	01	01	NUM
ejpam-4030	381	11	2021	2021	NUM
ejpam-4030	381	12	.	.	PUNCT
ejpam-4030	382	1	[	[	X
ejpam-4030	382	2	13	13	NUM
ejpam-4030	382	3	]	]	PUNCT
ejpam-4030	382	4	bateman	bateman	PROPN
ejpam-4030	382	5	manuscript	manuscript	PROPN
ejpam-4030	382	6	project	project	PROPN
ejpam-4030	382	7	,	,	PUNCT
ejpam-4030	382	8	harry	harry	PROPN
ejpam-4030	382	9	bateman	bateman	PROPN
ejpam-4030	382	10	,	,	PUNCT
ejpam-4030	382	11	arthur	arthur	PROPN
ejpam-4030	382	12	erdèlyi	erdèlyi	PROPN
ejpam-4030	382	13	,	,	PUNCT
ejpam-4030	382	14	united	united	ADJ
ejpam-4030	382	15	states	states	PROPN
ejpam-4030	382	16	,	,	PUNCT
ejpam-4030	382	17	and	and	CCONJ
ejpam-4030	382	18	office	office	NOUN
ejpam-4030	382	19	of	of	ADP
ejpam-4030	382	20	naval	naval	ADJ
ejpam-4030	382	21	research	research	NOUN
ejpam-4030	382	22	.	.	PUNCT
ejpam-4030	383	1	higher	high	ADJ
ejpam-4030	383	2	transcendental	transcendental	ADJ
ejpam-4030	383	3	functions	function	NOUN
ejpam-4030	383	4	,	,	PUNCT
ejpam-4030	383	5	volume	volume	NOUN
ejpam-4030	383	6	1	1	NUM
ejpam-4030	383	7	.	.	PUNCT
ejpam-4030	384	1	mcgraw	mcgraw	PROPN
ejpam-4030	384	2	-	-	PUNCT
ejpam-4030	384	3	hill	hill	PROPN
ejpam-4030	384	4	,	,	PUNCT
ejpam-4030	384	5	1953	1953	NUM
ejpam-4030	384	6	.	.	PUNCT
ejpam-4030	385	1	[	[	X
ejpam-4030	385	2	14	14	NUM
ejpam-4030	385	3	]	]	X
ejpam-4030	385	4	robert	robert	PROPN
ejpam-4030	385	5	reynolds	reynolds	PROPN
ejpam-4030	385	6	and	and	CCONJ
ejpam-4030	385	7	allan	allan	PROPN
ejpam-4030	385	8	stauffer	stauffer	PROPN
ejpam-4030	385	9	.	.	PUNCT
ejpam-4030	386	1	definite	definite	ADJ
ejpam-4030	386	2	integral	integral	ADJ
ejpam-4030	386	3	of	of	ADP
ejpam-4030	386	4	arctangent	arctangent	NOUN
ejpam-4030	386	5	and	and	CCONJ
ejpam-4030	386	6	polylogarithmic	polylogarithmic	ADJ
ejpam-4030	386	7	functions	function	NOUN
ejpam-4030	386	8	expressed	express	VERB
ejpam-4030	386	9	as	as	ADP
ejpam-4030	386	10	a	a	DET
ejpam-4030	386	11	series	series	NOUN
ejpam-4030	386	12	.	.	PUNCT
ejpam-4030	387	1	mathematics	mathematic	NOUN
ejpam-4030	387	2	,	,	PUNCT
ejpam-4030	387	3	7:1099	7:1099	NUM
ejpam-4030	387	4	,	,	PUNCT
ejpam-4030	387	5	11	11	NUM
ejpam-4030	387	6	2019	2019	NUM
ejpam-4030	387	7	.	.	PUNCT
ejpam-4030	388	1	[	[	X
ejpam-4030	388	2	15	15	NUM
ejpam-4030	388	3	]	]	X
ejpam-4030	388	4	robert	robert	PROPN
ejpam-4030	388	5	reynolds	reynolds	PROPN
ejpam-4030	388	6	and	and	CCONJ
ejpam-4030	388	7	allan	allan	PROPN
ejpam-4030	388	8	stauffer	stauffer	PROPN
ejpam-4030	388	9	.	.	PUNCT
ejpam-4030	389	1	a	a	DET
ejpam-4030	389	2	method	method	NOUN
ejpam-4030	389	3	for	for	ADP
ejpam-4030	389	4	evaluating	evaluate	VERB
ejpam-4030	389	5	definite	definite	ADJ
ejpam-4030	389	6	integrals	integral	NOUN
ejpam-4030	389	7	in	in	ADP
ejpam-4030	389	8	terms	term	NOUN
ejpam-4030	389	9	of	of	ADP
ejpam-4030	389	10	special	special	ADJ
ejpam-4030	389	11	functions	function	NOUN
ejpam-4030	389	12	with	with	ADP
ejpam-4030	389	13	examples	example	NOUN
ejpam-4030	389	14	.	.	PUNCT
ejpam-4030	390	1	international	international	ADJ
ejpam-4030	390	2	mathematical	mathematical	PROPN
ejpam-4030	390	3	forum	forum	PROPN
ejpam-4030	390	4	,	,	PUNCT
ejpam-4030	390	5	15:235	15:235	NUM
ejpam-4030	390	6	–	–	PUNCT
ejpam-4030	390	7	244	244	NUM
ejpam-4030	390	8	,	,	PUNCT
ejpam-4030	390	9	2020	2020	NUM
ejpam-4030	390	10	.	.	PUNCT
ejpam-4030	391	1	[	[	X
ejpam-4030	391	2	16	16	NUM
ejpam-4030	391	3	]	]	PUNCT
ejpam-4030	391	4	ioannis	ioannis	PROPN
ejpam-4030	391	5	markos	markos	PROPN
ejpam-4030	391	6	roussos	roussos	PROPN
ejpam-4030	391	7	.	.	PUNCT
ejpam-4030	392	1	improper	improper	ADJ
ejpam-4030	392	2	riemann	riemann	PROPN
ejpam-4030	392	3	integrals	integral	NOUN
ejpam-4030	392	4	,	,	PUNCT
ejpam-4030	392	5	12	12	NUM
ejpam-4030	392	6	2013	2013	NUM
ejpam-4030	392	7	.	.	PUNCT
ejpam-4030	393	1	[	[	X
ejpam-4030	393	2	17	17	NUM
ejpam-4030	393	3	]	]	X
ejpam-4030	393	4	daniel	daniel	PROPN
ejpam-4030	393	5	zwillinger	zwillinger	PROPN
ejpam-4030	393	6	and	and	CCONJ
ejpam-4030	393	7	alan	alan	PROPN
ejpam-4030	393	8	jeffrey	jeffrey	PROPN
ejpam-4030	393	9	.	.	PUNCT
ejpam-4030	394	1	table	table	NOUN
ejpam-4030	394	2	of	of	ADP
ejpam-4030	394	3	integrals	integral	NOUN
ejpam-4030	394	4	,	,	PUNCT
ejpam-4030	394	5	series	series	NOUN
ejpam-4030	394	6	,	,	PUNCT
ejpam-4030	394	7	and	and	CCONJ
ejpam-4030	394	8	products	product	NOUN
ejpam-4030	394	9	.	.	PUNCT
ejpam-4030	395	1	academic	academic	ADJ
ejpam-4030	395	2	press	press	NOUN
ejpam-4030	395	3	,	,	PUNCT
ejpam-4030	395	4	08	08	NUM
ejpam-4030	395	5	2000	2000	NUM
ejpam-4030	395	6	.	.	PUNCT