id	sid	tid	token	lemma	pos
ejpam-3987	1	1	european	european	PROPN
ejpam-3987	1	2	journal	journal	PROPN
ejpam-3987	1	3	of	of	ADP
ejpam-3987	1	4	pure	pure	ADJ
ejpam-3987	1	5	and	and	CCONJ
ejpam-3987	1	6	applied	apply	VERB
ejpam-3987	1	7	mathematics	mathematic	NOUN
ejpam-3987	1	8	vol	vol	NOUN
ejpam-3987	1	9	.	.	PUNCT
ejpam-3987	2	1	14	14	NUM
ejpam-3987	2	2	,	,	PUNCT
ejpam-3987	2	3	no	no	INTJ
ejpam-3987	2	4	.	.	NOUN
ejpam-3987	2	5	3	3	NUM
ejpam-3987	2	6	,	,	PUNCT
ejpam-3987	2	7	2021	2021	NUM
ejpam-3987	2	8	,	,	PUNCT
ejpam-3987	2	9	618	618	NUM
ejpam-3987	2	10	-	-	SYM
ejpam-3987	2	11	637	637	NUM
ejpam-3987	2	12	issn	issn	PROPN
ejpam-3987	2	13	1307	1307	NUM
ejpam-3987	2	14	-	-	SYM
ejpam-3987	2	15	5543	5543	NUM
ejpam-3987	2	16	–	–	PUNCT
ejpam-3987	2	17	ejpam.com	ejpam.com	X
ejpam-3987	2	18	published	publish	VERB
ejpam-3987	2	19	by	by	ADP
ejpam-3987	3	1	new	new	PROPN
ejpam-3987	3	2	york	york	PROPN
ejpam-3987	3	3	business	business	PROPN
ejpam-3987	3	4	global	global	PROPN
ejpam-3987	3	5	the	the	DET
ejpam-3987	3	6	double	double	ADJ
ejpam-3987	3	7	laplace	laplace	NOUN
ejpam-3987	3	8	transform	transform	NOUN
ejpam-3987	3	9	expressed	express	VERB
ejpam-3987	3	10	in	in	ADP
ejpam-3987	3	11	terms	term	NOUN
ejpam-3987	3	12	of	of	ADP
ejpam-3987	3	13	the	the	DET
ejpam-3987	3	14	lerch	lerch	PROPN
ejpam-3987	3	15	transcendent	transcendent	PROPN
ejpam-3987	3	16	robert	robert	PROPN
ejpam-3987	3	17	reynolds1,∗	reynolds1,∗	PROPN
ejpam-3987	3	18	,	,	PUNCT
ejpam-3987	3	19	allan	allan	PROPN
ejpam-3987	3	20	stauffer1	stauffer1	PROPN
ejpam-3987	3	21	1	1	NUM
ejpam-3987	3	22	department	department	NOUN
ejpam-3987	3	23	of	of	ADP
ejpam-3987	3	24	mathematics	mathematic	NOUN
ejpam-3987	3	25	and	and	CCONJ
ejpam-3987	3	26	statistics	statistic	NOUN
ejpam-3987	3	27	,	,	PUNCT
ejpam-3987	3	28	faculty	faculty	NOUN
ejpam-3987	3	29	of	of	ADP
ejpam-3987	3	30	science	science	PROPN
ejpam-3987	3	31	,	,	PUNCT
ejpam-3987	3	32	york	york	PROPN
ejpam-3987	3	33	university	university	PROPN
ejpam-3987	3	34	,	,	PUNCT
ejpam-3987	3	35	toronto	toronto	PROPN
ejpam-3987	3	36	,	,	PUNCT
ejpam-3987	3	37	ontario	ontario	PROPN
ejpam-3987	3	38	,	,	PUNCT
ejpam-3987	3	39	canada	canada	PROPN
ejpam-3987	3	40	abstract	abstract	NOUN
ejpam-3987	3	41	.	.	PUNCT
ejpam-3987	4	1	in	in	ADP
ejpam-3987	4	2	this	this	DET
ejpam-3987	4	3	paper	paper	NOUN
ejpam-3987	4	4	,	,	PUNCT
ejpam-3987	4	5	the	the	DET
ejpam-3987	4	6	authors	author	NOUN
ejpam-3987	4	7	derive	derive	VERB
ejpam-3987	4	8	a	a	DET
ejpam-3987	4	9	formula	formula	NOUN
ejpam-3987	4	10	for	for	ADP
ejpam-3987	4	11	the	the	DET
ejpam-3987	4	12	double	double	ADJ
ejpam-3987	4	13	laplace	laplace	NOUN
ejpam-3987	4	14	transform	transform	NOUN
ejpam-3987	4	15	expressed	express	VERB
ejpam-3987	4	16	in	in	ADP
ejpam-3987	4	17	terms	term	NOUN
ejpam-3987	4	18	of	of	ADP
ejpam-3987	4	19	the	the	DET
ejpam-3987	4	20	lerch	lerch	PROPN
ejpam-3987	4	21	transcendent	transcendent	NOUN
ejpam-3987	4	22	.	.	PUNCT
ejpam-3987	5	1	the	the	DET
ejpam-3987	5	2	log	log	NOUN
ejpam-3987	5	3	term	term	NOUN
ejpam-3987	5	4	mixes	mix	VERB
ejpam-3987	5	5	the	the	DET
ejpam-3987	5	6	variables	variable	NOUN
ejpam-3987	5	7	so	so	SCONJ
ejpam-3987	5	8	that	that	SCONJ
ejpam-3987	5	9	the	the	DET
ejpam-3987	5	10	integral	integral	NOUN
ejpam-3987	5	11	is	be	AUX
ejpam-3987	5	12	not	not	PART
ejpam-3987	5	13	separable	separable	ADJ
ejpam-3987	5	14	except	except	SCONJ
ejpam-3987	5	15	for	for	ADP
ejpam-3987	5	16	special	special	ADJ
ejpam-3987	5	17	values	value	NOUN
ejpam-3987	5	18	of	of	ADP
ejpam-3987	5	19	k.	k.	PROPN
ejpam-3987	5	20	the	the	DET
ejpam-3987	5	21	method	method	NOUN
ejpam-3987	5	22	of	of	ADP
ejpam-3987	5	23	proof	proof	NOUN
ejpam-3987	5	24	follows	follow	VERB
ejpam-3987	5	25	the	the	DET
ejpam-3987	5	26	method	method	NOUN
ejpam-3987	5	27	used	use	VERB
ejpam-3987	5	28	by	by	ADP
ejpam-3987	5	29	us	we	PRON
ejpam-3987	5	30	to	to	PART
ejpam-3987	5	31	evaluate	evaluate	VERB
ejpam-3987	5	32	single	single	ADJ
ejpam-3987	5	33	integrals	integral	NOUN
ejpam-3987	5	34	.	.	PUNCT
ejpam-3987	6	1	this	this	DET
ejpam-3987	6	2	transform	transform	NOUN
ejpam-3987	6	3	is	be	AUX
ejpam-3987	6	4	then	then	ADV
ejpam-3987	6	5	used	use	VERB
ejpam-3987	6	6	to	to	PART
ejpam-3987	6	7	derive	derive	VERB
ejpam-3987	6	8	definite	definite	ADJ
ejpam-3987	6	9	integrals	integral	NOUN
ejpam-3987	6	10	in	in	ADP
ejpam-3987	6	11	terms	term	NOUN
ejpam-3987	6	12	of	of	ADP
ejpam-3987	6	13	fundamental	fundamental	ADJ
ejpam-3987	6	14	constants	constant	NOUN
ejpam-3987	6	15	,	,	PUNCT
ejpam-3987	6	16	elementary	elementary	ADJ
ejpam-3987	6	17	and	and	CCONJ
ejpam-3987	6	18	special	special	ADJ
ejpam-3987	6	19	functions	function	NOUN
ejpam-3987	6	20	.	.	PUNCT
ejpam-3987	7	1	a	a	DET
ejpam-3987	7	2	summary	summary	NOUN
ejpam-3987	7	3	of	of	ADP
ejpam-3987	7	4	the	the	DET
ejpam-3987	7	5	results	result	NOUN
ejpam-3987	7	6	is	be	AUX
ejpam-3987	7	7	produced	produce	VERB
ejpam-3987	7	8	in	in	ADP
ejpam-3987	7	9	the	the	DET
ejpam-3987	7	10	form	form	NOUN
ejpam-3987	7	11	of	of	ADP
ejpam-3987	7	12	a	a	DET
ejpam-3987	7	13	table	table	NOUN
ejpam-3987	7	14	of	of	ADP
ejpam-3987	7	15	definite	definite	ADJ
ejpam-3987	7	16	integrals	integral	NOUN
ejpam-3987	7	17	for	for	ADP
ejpam-3987	7	18	easy	easy	ADJ
ejpam-3987	7	19	referencing	referencing	NOUN
ejpam-3987	7	20	by	by	ADP
ejpam-3987	7	21	readers	reader	NOUN
ejpam-3987	7	22	.	.	PUNCT
ejpam-3987	8	1	the	the	DET
ejpam-3987	8	2	majority	majority	NOUN
ejpam-3987	8	3	of	of	ADP
ejpam-3987	8	4	the	the	DET
ejpam-3987	8	5	results	result	NOUN
ejpam-3987	8	6	in	in	ADP
ejpam-3987	8	7	the	the	DET
ejpam-3987	8	8	work	work	NOUN
ejpam-3987	8	9	are	be	AUX
ejpam-3987	8	10	new	new	ADJ
ejpam-3987	8	11	.	.	PUNCT
ejpam-3987	9	1	2020	2020	NUM
ejpam-3987	9	2	mathematics	mathematic	NOUN
ejpam-3987	9	3	subject	subject	NOUN
ejpam-3987	9	4	classifications	classification	NOUN
ejpam-3987	9	5	:	:	PUNCT
ejpam-3987	9	6	01a35	01a35	NOUN
ejpam-3987	9	7	,	,	PUNCT
ejpam-3987	9	8	11m06	11m06	NUM
ejpam-3987	9	9	,	,	PUNCT
ejpam-3987	9	10	11m35	11m35	NUM
ejpam-3987	9	11	,	,	PUNCT
ejpam-3987	9	12	30	30	NUM
ejpam-3987	9	13	-	-	SYM
ejpam-3987	9	14	02	02	NUM
ejpam-3987	9	15	,	,	PUNCT
ejpam-3987	9	16	30d10	30d10	NUM
ejpam-3987	9	17	,	,	PUNCT
ejpam-3987	9	18	30d30	30d30	NUM
ejpam-3987	9	19	,	,	PUNCT
ejpam-3987	9	20	30e20	30e20	NUM
ejpam-3987	9	21	key	key	ADJ
ejpam-3987	9	22	words	word	NOUN
ejpam-3987	9	23	and	and	CCONJ
ejpam-3987	9	24	phrases	phrase	NOUN
ejpam-3987	9	25	:	:	PUNCT
ejpam-3987	9	26	laplace	laplace	NOUN
ejpam-3987	9	27	transform	transform	NOUN
ejpam-3987	9	28	,	,	PUNCT
ejpam-3987	9	29	lerch	lerch	PROPN
ejpam-3987	9	30	transcendent	transcendent	NOUN
ejpam-3987	9	31	,	,	PUNCT
ejpam-3987	9	32	contour	contour	NOUN
ejpam-3987	9	33	integral	integral	ADJ
ejpam-3987	9	34	,	,	PUNCT
ejpam-3987	9	35	definite	definite	ADJ
ejpam-3987	9	36	integral	integral	ADJ
ejpam-3987	9	37	1	1	NUM
ejpam-3987	9	38	.	.	PUNCT
ejpam-3987	9	39	introduction	introduction	NOUN
ejpam-3987	9	40	in	in	ADP
ejpam-3987	9	41	this	this	DET
ejpam-3987	9	42	paper	paper	NOUN
ejpam-3987	9	43	we	we	PRON
ejpam-3987	9	44	derive	derive	VERB
ejpam-3987	9	45	the	the	DET
ejpam-3987	9	46	double	double	ADJ
ejpam-3987	9	47	laplace	laplace	NOUN
ejpam-3987	9	48	transform	transform	NOUN
ejpam-3987	9	49	given	give	VERB
ejpam-3987	9	50	by	by	ADP
ejpam-3987	9	51	(	(	PUNCT
ejpam-3987	9	52	1	1	NUM
ejpam-3987	9	53	)	)	PUNCT
ejpam-3987	9	54	∫	∫	PROPN
ejpam-3987	9	55	∞	∞	PROPN
ejpam-3987	9	56	0	0	NUM
ejpam-3987	10	1	∫	∫	PROPN
ejpam-3987	10	2	∞	∞	NUM
ejpam-3987	10	3	0	0	NUM
ejpam-3987	11	1	xp−1yn−p−1	xp−1yn−p−1	NOUN
ejpam-3987	11	2	logk	logk	NOUN
ejpam-3987	11	3	(	(	PUNCT
ejpam-3987	11	4	bx	bx	NOUN
ejpam-3987	11	5	y	y	PROPN
ejpam-3987	11	6	)	)	PUNCT
ejpam-3987	11	7	e−(sx)n−(ty)ndxdy	e−(sx)n−(ty)ndxdy	PROPN
ejpam-3987	11	8	where	where	SCONJ
ejpam-3987	11	9	the	the	DET
ejpam-3987	11	10	parameters	parameter	NOUN
ejpam-3987	11	11	a	a	PRON
ejpam-3987	11	12	,	,	PUNCT
ejpam-3987	11	13	k	k	PROPN
ejpam-3987	11	14	s	s	PROPN
ejpam-3987	11	15	and	and	CCONJ
ejpam-3987	11	16	t	t	PROPN
ejpam-3987	11	17	are	be	AUX
ejpam-3987	11	18	general	general	ADJ
ejpam-3987	11	19	complex	complex	ADJ
ejpam-3987	11	20	numbers	number	NOUN
ejpam-3987	11	21	,	,	PUNCT
ejpam-3987	11	22	n	n	CCONJ
ejpam-3987	11	23	>	>	X
ejpam-3987	11	24	re(p	re(p	NOUN
ejpam-3987	11	25	)	)	PUNCT
ejpam-3987	11	26	and	and	CCONJ
ejpam-3987	11	27	re(p	re(p	NOUN
ejpam-3987	11	28	)	)	PUNCT
ejpam-3987	11	29	>	>	X
ejpam-3987	12	1	0	0	X
ejpam-3987	12	2	.	.	PUNCT
ejpam-3987	13	1	the	the	DET
ejpam-3987	13	2	transform	transform	NOUN
ejpam-3987	13	3	will	will	AUX
ejpam-3987	13	4	be	be	AUX
ejpam-3987	13	5	used	use	VERB
ejpam-3987	13	6	to	to	PART
ejpam-3987	13	7	derive	derive	VERB
ejpam-3987	13	8	special	special	ADJ
ejpam-3987	13	9	cases	case	NOUN
ejpam-3987	13	10	in	in	ADP
ejpam-3987	13	11	terms	term	NOUN
ejpam-3987	13	12	of	of	ADP
ejpam-3987	13	13	special	special	ADJ
ejpam-3987	13	14	functions	function	NOUN
ejpam-3987	13	15	and	and	CCONJ
ejpam-3987	13	16	fundamental	fundamental	ADJ
ejpam-3987	13	17	constants	constant	NOUN
ejpam-3987	13	18	.	.	PUNCT
ejpam-3987	14	1	we	we	PRON
ejpam-3987	14	2	then	then	ADV
ejpam-3987	14	3	tabulate	tabulate	VERB
ejpam-3987	14	4	our	our	PRON
ejpam-3987	14	5	results	result	NOUN
ejpam-3987	14	6	of	of	ADP
ejpam-3987	14	7	these	these	DET
ejpam-3987	14	8	new	new	ADJ
ejpam-3987	14	9	integral	integral	ADJ
ejpam-3987	14	10	formulae	formulae	NOUN
ejpam-3987	14	11	with	with	ADP
ejpam-3987	14	12	respect	respect	NOUN
ejpam-3987	14	13	the	the	DET
ejpam-3987	14	14	parameters	parameter	NOUN
ejpam-3987	14	15	of	of	ADP
ejpam-3987	14	16	the	the	DET
ejpam-3987	14	17	transform	transform	NOUN
ejpam-3987	14	18	.	.	PUNCT
ejpam-3987	15	1	the	the	DET
ejpam-3987	15	2	table	table	NOUN
ejpam-3987	15	3	of	of	ADP
ejpam-3987	15	4	results	result	NOUN
ejpam-3987	15	5	is	be	AUX
ejpam-3987	15	6	only	only	ADV
ejpam-3987	15	7	a	a	DET
ejpam-3987	15	8	subset	subset	NOUN
ejpam-3987	15	9	of	of	ADP
ejpam-3987	15	10	the	the	DET
ejpam-3987	15	11	actual	actual	ADJ
ejpam-3987	15	12	domain	domain	NOUN
ejpam-3987	15	13	and	and	CCONJ
ejpam-3987	15	14	range	range	NOUN
ejpam-3987	15	15	for	for	ADP
ejpam-3987	15	16	the	the	DET
ejpam-3987	15	17	transform	transform	NOUN
ejpam-3987	15	18	as	as	SCONJ
ejpam-3987	15	19	the	the	DET
ejpam-3987	15	20	number	number	NOUN
ejpam-3987	15	21	of	of	ADP
ejpam-3987	15	22	variables	variable	NOUN
ejpam-3987	15	23	are	be	AUX
ejpam-3987	15	24	too	too	ADV
ejpam-3987	15	25	many	many	ADJ
ejpam-3987	15	26	to	to	PART
ejpam-3987	15	27	compose	compose	VERB
ejpam-3987	15	28	a	a	DET
ejpam-3987	15	29	full	full	ADJ
ejpam-3987	15	30	table	table	NOUN
ejpam-3987	15	31	in	in	ADP
ejpam-3987	15	32	this	this	DET
ejpam-3987	15	33	work	work	NOUN
ejpam-3987	15	34	.	.	PUNCT
ejpam-3987	16	1	the	the	DET
ejpam-3987	16	2	authors	author	NOUN
ejpam-3987	16	3	however	however	ADV
ejpam-3987	16	4	,	,	PUNCT
ejpam-3987	16	5	used	use	VERB
ejpam-3987	16	6	their	their	PRON
ejpam-3987	16	7	transform	transform	NOUN
ejpam-3987	16	8	to	to	PART
ejpam-3987	16	9	tabulate	tabulate	VERB
ejpam-3987	16	10	in	in	ADP
ejpam-3987	16	11	their	their	PRON
ejpam-3987	16	12	opinion	opinion	NOUN
ejpam-3987	16	13	,	,	PUNCT
ejpam-3987	16	14	interesting	interesting	ADJ
ejpam-3987	16	15	integral	integral	ADJ
ejpam-3987	16	16	forms	form	NOUN
ejpam-3987	16	17	and	and	CCONJ
ejpam-3987	16	18	leave	leave	VERB
ejpam-3987	16	19	the	the	DET
ejpam-3987	16	20	readers	reader	NOUN
ejpam-3987	16	21	to	to	PART
ejpam-3987	16	22	derive	derive	VERB
ejpam-3987	16	23	other	other	ADJ
ejpam-3987	16	24	forms	form	NOUN
ejpam-3987	16	25	if	if	SCONJ
ejpam-3987	16	26	they	they	PRON
ejpam-3987	16	27	wish	wish	VERB
ejpam-3987	16	28	.	.	PUNCT
ejpam-3987	17	1	we	we	PRON
ejpam-3987	17	2	present	present	VERB
ejpam-3987	17	3	a	a	DET
ejpam-3987	17	4	formal	formal	ADJ
ejpam-3987	17	5	derivation	derivation	NOUN
ejpam-3987	17	6	for	for	ADP
ejpam-3987	17	7	a	a	DET
ejpam-3987	17	8	definite	definite	ADJ
ejpam-3987	17	9	integral	integral	NOUN
ejpam-3987	17	10	in	in	ADP
ejpam-3987	17	11	[	[	X
ejpam-3987	17	12	8	8	NUM
ejpam-3987	17	13	]	]	PUNCT
ejpam-3987	17	14	.	.	PUNCT
ejpam-3987	18	1	in	in	ADP
ejpam-3987	18	2	this	this	DET
ejpam-3987	18	3	work	work	NOUN
ejpam-3987	18	4	we	we	PRON
ejpam-3987	18	5	derive	derive	VERB
ejpam-3987	18	6	∗corresponding	∗corresponde	VERB
ejpam-3987	18	7	author	author	NOUN
ejpam-3987	18	8	.	.	PUNCT
ejpam-3987	19	1	doi	doi	NOUN
ejpam-3987	19	2	:	:	PUNCT
ejpam-3987	19	3	https://doi.org/10.29020/nybg.ejpam.v14i3.3987	https://doi.org/10.29020/nybg.ejpam.v14i3.3987	ADP
ejpam-3987	19	4	email	email	NOUN
ejpam-3987	19	5	addresses	address	NOUN
ejpam-3987	19	6	:	:	PUNCT
ejpam-3987	20	1	milver@my.yorku.ca	milver@my.yorku.ca	NOUN
ejpam-3987	20	2	(	(	PUNCT
ejpam-3987	20	3	r.	r.	PROPN
ejpam-3987	20	4	reynolds	reynolds	PROPN
ejpam-3987	20	5	)	)	PUNCT
ejpam-3987	20	6	,	,	PUNCT
ejpam-3987	20	7	stauffer@yorku.ca	stauffer@yorku.ca	NOUN
ejpam-3987	20	8	(	(	PUNCT
ejpam-3987	20	9	a.	a.	NOUN
ejpam-3987	20	10	stauffer	stauffer	PROPN
ejpam-3987	20	11	)	)	PUNCT
ejpam-3987	20	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3987	21	1	618	618	NUM
ejpam-3987	22	1	©	©	ADP
ejpam-3987	22	2	2021	2021	NUM
ejpam-3987	22	3	ejpam	ejpam	VERB
ejpam-3987	22	4	all	all	DET
ejpam-3987	22	5	rights	right	NOUN
ejpam-3987	22	6	reserved	reserve	VERB
ejpam-3987	22	7	.	.	PUNCT
ejpam-3987	23	1	r.	r.	PROPN
ejpam-3987	23	2	reynolds	reynolds	PROPN
ejpam-3987	23	3	,	,	PUNCT
ejpam-3987	23	4	a.	a.	PROPN
ejpam-3987	23	5	stauffer	stauffer	PROPN
ejpam-3987	23	6	/	/	SYM
ejpam-3987	23	7	eur	eur	PROPN
ejpam-3987	23	8	.	.	PUNCT
ejpam-3987	24	1	j.	j.	PROPN
ejpam-3987	24	2	pure	pure	PROPN
ejpam-3987	24	3	appl	appl	PROPN
ejpam-3987	24	4	.	.	PROPN
ejpam-3987	24	5	math	math	PROPN
ejpam-3987	24	6	,	,	PUNCT
ejpam-3987	24	7	14	14	NUM
ejpam-3987	24	8	(	(	PUNCT
ejpam-3987	24	9	3	3	NUM
ejpam-3987	24	10	)	)	PUNCT
ejpam-3987	24	11	(	(	PUNCT
ejpam-3987	24	12	2021	2021	NUM
ejpam-3987	24	13	)	)	PUNCT
ejpam-3987	24	14	,	,	PUNCT
ejpam-3987	24	15	618	618	NUM
ejpam-3987	24	16	-	-	SYM
ejpam-3987	24	17	637	637	NUM
ejpam-3987	24	18	619	619	NUM
ejpam-3987	24	19	the	the	DET
ejpam-3987	24	20	double	double	ADJ
ejpam-3987	24	21	laplace	laplace	NOUN
ejpam-3987	24	22	transform	transform	NOUN
ejpam-3987	24	23	in	in	ADP
ejpam-3987	24	24	terms	term	NOUN
ejpam-3987	24	25	of	of	ADP
ejpam-3987	24	26	the	the	DET
ejpam-3987	24	27	lerch	lerch	PROPN
ejpam-3987	24	28	transcendent	transcendent	NOUN
ejpam-3987	25	1	[	[	X
ejpam-3987	25	2	5	5	NUM
ejpam-3987	25	3	]	]	PUNCT
ejpam-3987	25	4	.	.	PUNCT
ejpam-3987	26	1	the	the	DET
ejpam-3987	26	2	derivations	derivation	NOUN
ejpam-3987	26	3	follow	follow	VERB
ejpam-3987	26	4	the	the	DET
ejpam-3987	26	5	method	method	NOUN
ejpam-3987	26	6	used	use	VERB
ejpam-3987	26	7	by	by	ADP
ejpam-3987	26	8	us	we	PRON
ejpam-3987	26	9	in	in	ADP
ejpam-3987	26	10	[	[	X
ejpam-3987	26	11	7	7	NUM
ejpam-3987	26	12	]	]	PUNCT
ejpam-3987	26	13	.	.	PUNCT
ejpam-3987	27	1	this	this	DET
ejpam-3987	27	2	method	method	NOUN
ejpam-3987	27	3	involves	involve	VERB
ejpam-3987	27	4	using	use	VERB
ejpam-3987	27	5	a	a	DET
ejpam-3987	27	6	form	form	NOUN
ejpam-3987	27	7	of	of	ADP
ejpam-3987	27	8	the	the	DET
ejpam-3987	27	9	generalized	generalize	VERB
ejpam-3987	27	10	cauchy	cauchy	PROPN
ejpam-3987	27	11	’s	’s	PART
ejpam-3987	27	12	integral	integral	ADJ
ejpam-3987	27	13	formula	formula	NOUN
ejpam-3987	27	14	given	give	VERB
ejpam-3987	27	15	by	by	ADP
ejpam-3987	27	16	yk	yk	PROPN
ejpam-3987	27	17	k	k	PROPN
ejpam-3987	27	18	!	!	PUNCT
ejpam-3987	28	1	=	=	SYM
ejpam-3987	28	2	1	1	NUM
ejpam-3987	28	3	2πi	2πi	ADJ
ejpam-3987	28	4	∫	∫	PROPN
ejpam-3987	28	5	c	c	PROPN
ejpam-3987	28	6	ewy	ewy	PROPN
ejpam-3987	28	7	wk+1	wk+1	PROPN
ejpam-3987	28	8	dw	dw	PROPN
ejpam-3987	28	9	.	.	PUNCT
ejpam-3987	29	1	(	(	PUNCT
ejpam-3987	29	2	2	2	X
ejpam-3987	29	3	)	)	PUNCT
ejpam-3987	29	4	we	we	PRON
ejpam-3987	29	5	then	then	ADV
ejpam-3987	29	6	multiply	multiply	VERB
ejpam-3987	29	7	both	both	DET
ejpam-3987	29	8	sides	side	NOUN
ejpam-3987	29	9	by	by	ADP
ejpam-3987	29	10	a	a	DET
ejpam-3987	29	11	function	function	NOUN
ejpam-3987	29	12	of	of	ADP
ejpam-3987	29	13	x	x	PUNCT
ejpam-3987	29	14	and	and	CCONJ
ejpam-3987	29	15	y	y	PROPN
ejpam-3987	29	16	,	,	PUNCT
ejpam-3987	29	17	then	then	ADV
ejpam-3987	29	18	take	take	VERB
ejpam-3987	29	19	a	a	DET
ejpam-3987	29	20	definite	definite	ADJ
ejpam-3987	29	21	double	double	ADJ
ejpam-3987	29	22	integral	integral	NOUN
ejpam-3987	29	23	of	of	ADP
ejpam-3987	29	24	both	both	DET
ejpam-3987	29	25	sides	side	NOUN
ejpam-3987	29	26	.	.	PUNCT
ejpam-3987	30	1	this	this	PRON
ejpam-3987	30	2	yields	yield	VERB
ejpam-3987	30	3	a	a	DET
ejpam-3987	30	4	definite	definite	ADJ
ejpam-3987	30	5	integral	integral	ADJ
ejpam-3987	30	6	in	in	ADP
ejpam-3987	30	7	terms	term	NOUN
ejpam-3987	30	8	of	of	ADP
ejpam-3987	30	9	a	a	DET
ejpam-3987	30	10	contour	contour	NOUN
ejpam-3987	30	11	integral	integral	NOUN
ejpam-3987	30	12	.	.	PUNCT
ejpam-3987	31	1	then	then	ADV
ejpam-3987	31	2	we	we	PRON
ejpam-3987	31	3	multiply	multiply	VERB
ejpam-3987	31	4	both	both	DET
ejpam-3987	31	5	sides	side	NOUN
ejpam-3987	31	6	of	of	ADP
ejpam-3987	31	7	equation	equation	NOUN
ejpam-3987	31	8	(	(	PUNCT
ejpam-3987	31	9	2	2	NUM
ejpam-3987	31	10	)	)	PUNCT
ejpam-3987	31	11	by	by	ADP
ejpam-3987	31	12	another	another	DET
ejpam-3987	31	13	function	function	NOUN
ejpam-3987	31	14	of	of	ADP
ejpam-3987	31	15	x	x	PUNCT
ejpam-3987	31	16	and	and	CCONJ
ejpam-3987	31	17	y	y	PROPN
ejpam-3987	31	18	and	and	CCONJ
ejpam-3987	31	19	take	take	VERB
ejpam-3987	31	20	the	the	DET
ejpam-3987	31	21	infinite	infinite	ADJ
ejpam-3987	31	22	sums	sum	NOUN
ejpam-3987	31	23	of	of	ADP
ejpam-3987	31	24	both	both	DET
ejpam-3987	31	25	sides	side	NOUN
ejpam-3987	31	26	such	such	ADJ
ejpam-3987	31	27	that	that	SCONJ
ejpam-3987	31	28	the	the	DET
ejpam-3987	31	29	contour	contour	NOUN
ejpam-3987	31	30	integral	integral	NOUN
ejpam-3987	31	31	of	of	ADP
ejpam-3987	31	32	both	both	DET
ejpam-3987	31	33	equations	equation	NOUN
ejpam-3987	31	34	are	be	AUX
ejpam-3987	31	35	the	the	DET
ejpam-3987	31	36	same	same	ADJ
ejpam-3987	31	37	.	.	PUNCT
ejpam-3987	32	1	2	2	X
ejpam-3987	32	2	.	.	X
ejpam-3987	32	3	definite	definite	ADJ
ejpam-3987	32	4	integral	integral	ADJ
ejpam-3987	32	5	of	of	ADP
ejpam-3987	32	6	the	the	DET
ejpam-3987	32	7	contour	contour	NOUN
ejpam-3987	32	8	integral	integral	NOUN
ejpam-3987	32	9	we	we	PRON
ejpam-3987	32	10	use	use	VERB
ejpam-3987	32	11	the	the	DET
ejpam-3987	32	12	method	method	NOUN
ejpam-3987	32	13	in	in	ADP
ejpam-3987	32	14	[	[	X
ejpam-3987	32	15	7	7	NUM
ejpam-3987	32	16	]	]	PUNCT
ejpam-3987	32	17	.	.	PUNCT
ejpam-3987	33	1	the	the	DET
ejpam-3987	33	2	variable	variable	NOUN
ejpam-3987	33	3	of	of	ADP
ejpam-3987	33	4	integration	integration	NOUN
ejpam-3987	33	5	in	in	ADP
ejpam-3987	33	6	the	the	DET
ejpam-3987	33	7	contour	contour	NOUN
ejpam-3987	33	8	integral	integral	NOUN
ejpam-3987	33	9	is	be	AUX
ejpam-3987	33	10	α	α	X
ejpam-3987	33	11	=	=	PUNCT
ejpam-3987	33	12	p	p	PROPN
ejpam-3987	34	1	+	+	CCONJ
ejpam-3987	34	2	w.	w.	NOUN
ejpam-3987	34	3	the	the	DET
ejpam-3987	34	4	cut	cut	NOUN
ejpam-3987	34	5	and	and	CCONJ
ejpam-3987	34	6	contour	contour	NOUN
ejpam-3987	34	7	are	be	AUX
ejpam-3987	34	8	in	in	ADP
ejpam-3987	34	9	the	the	DET
ejpam-3987	34	10	second	second	ADJ
ejpam-3987	34	11	quadrant	quadrant	NOUN
ejpam-3987	34	12	of	of	ADP
ejpam-3987	34	13	the	the	DET
ejpam-3987	34	14	complex	complex	ADJ
ejpam-3987	34	15	z	z	NOUN
ejpam-3987	34	16	-	-	NOUN
ejpam-3987	34	17	plane	plane	NOUN
ejpam-3987	34	18	.	.	PUNCT
ejpam-3987	35	1	the	the	DET
ejpam-3987	35	2	cut	cut	NOUN
ejpam-3987	35	3	approaches	approach	VERB
ejpam-3987	35	4	the	the	DET
ejpam-3987	35	5	origin	origin	NOUN
ejpam-3987	35	6	from	from	ADP
ejpam-3987	35	7	the	the	DET
ejpam-3987	35	8	interior	interior	NOUN
ejpam-3987	35	9	of	of	ADP
ejpam-3987	35	10	the	the	DET
ejpam-3987	35	11	second	second	ADJ
ejpam-3987	35	12	quadrant	quadrant	NOUN
ejpam-3987	35	13	and	and	CCONJ
ejpam-3987	35	14	the	the	DET
ejpam-3987	35	15	contour	contour	NOUN
ejpam-3987	35	16	goes	go	VERB
ejpam-3987	35	17	round	round	ADP
ejpam-3987	35	18	the	the	DET
ejpam-3987	35	19	origin	origin	NOUN
ejpam-3987	35	20	with	with	ADP
ejpam-3987	35	21	zero	zero	NUM
ejpam-3987	35	22	radius	radius	NOUN
ejpam-3987	35	23	and	and	CCONJ
ejpam-3987	35	24	is	be	AUX
ejpam-3987	35	25	on	on	ADP
ejpam-3987	35	26	opposite	opposite	ADJ
ejpam-3987	35	27	sides	side	NOUN
ejpam-3987	35	28	of	of	ADP
ejpam-3987	35	29	the	the	DET
ejpam-3987	35	30	cut	cut	NOUN
ejpam-3987	35	31	.	.	PUNCT
ejpam-3987	36	1	using	use	VERB
ejpam-3987	36	2	a	a	DET
ejpam-3987	36	3	generalization	generalization	NOUN
ejpam-3987	36	4	of	of	ADP
ejpam-3987	36	5	cauchy	cauchy	PROPN
ejpam-3987	36	6	’s	’s	PART
ejpam-3987	36	7	integral	integral	ADJ
ejpam-3987	36	8	formula	formula	NOUN
ejpam-3987	36	9	we	we	PRON
ejpam-3987	36	10	form	form	VERB
ejpam-3987	36	11	two	two	NUM
ejpam-3987	36	12	equations	equation	NOUN
ejpam-3987	36	13	by	by	ADP
ejpam-3987	36	14	replacing	replace	VERB
ejpam-3987	36	15	y	y	PRON
ejpam-3987	36	16	by	by	ADP
ejpam-3987	36	17	log	log	NOUN
ejpam-3987	36	18	(	(	PUNCT
ejpam-3987	36	19	ax	ax	NOUN
ejpam-3987	36	20	y	y	PROPN
ejpam-3987	36	21	)	)	PUNCT
ejpam-3987	36	22	and	and	CCONJ
ejpam-3987	36	23	multiplying	multiply	VERB
ejpam-3987	36	24	by	by	ADP
ejpam-3987	36	25	xp−1yn−p−1e−x	xp−1yn−p−1e−x	PROPN
ejpam-3987	36	26	n−yn	n−yn	PROPN
ejpam-3987	36	27	then	then	ADV
ejpam-3987	36	28	taking	take	VERB
ejpam-3987	36	29	the	the	DET
ejpam-3987	36	30	definite	definite	ADJ
ejpam-3987	36	31	integral	integral	ADJ
ejpam-3987	36	32	with	with	ADP
ejpam-3987	36	33	respect	respect	NOUN
ejpam-3987	36	34	x	x	X
ejpam-3987	36	35	∈	∈	NOUN
ejpam-3987	37	1	[	[	X
ejpam-3987	37	2	0,∞	0,∞	NOUN
ejpam-3987	37	3	)	)	PUNCT
ejpam-3987	37	4	and	and	CCONJ
ejpam-3987	37	5	y	y	PROPN
ejpam-3987	37	6	∈	∈	PROPN
ejpam-3987	38	1	[	[	X
ejpam-3987	38	2	0,∞	0,∞	NOUN
ejpam-3987	38	3	)	)	PUNCT
ejpam-3987	38	4	to	to	PART
ejpam-3987	38	5	get	get	VERB
ejpam-3987	38	6	(	(	PUNCT
ejpam-3987	38	7	3	3	NUM
ejpam-3987	38	8	)	)	PUNCT
ejpam-3987	38	9	1	1	NUM
ejpam-3987	39	1	k	k	X
ejpam-3987	39	2	!	!	PUNCT
ejpam-3987	39	3	∫	∫	PROPN
ejpam-3987	40	1	∞	∞	PROPN
ejpam-3987	40	2	0	0	NUM
ejpam-3987	41	1	∫	∫	PROPN
ejpam-3987	41	2	∞	∞	PROPN
ejpam-3987	41	3	0	0	NUM
ejpam-3987	42	1	xp−1yn−p−1e−x	xp−1yn−p−1e−x	PROPN
ejpam-3987	42	2	n−yn	n−yn	PROPN
ejpam-3987	42	3	logk	logk	NOUN
ejpam-3987	42	4	(	(	PUNCT
ejpam-3987	42	5	ax	ax	NOUN
ejpam-3987	42	6	y	y	PROPN
ejpam-3987	42	7	)	)	PUNCT
ejpam-3987	42	8	dxdy	dxdy	PROPN
ejpam-3987	42	9	=	=	SYM
ejpam-3987	42	10	1	1	NUM
ejpam-3987	42	11	2πi	2πi	NOUN
ejpam-3987	42	12	∫	∫	PROPN
ejpam-3987	43	1	∞	∞	PROPN
ejpam-3987	43	2	0	0	NUM
ejpam-3987	44	1	∫	∫	PROPN
ejpam-3987	44	2	∞	∞	NUM
ejpam-3987	44	3	0	0	NUM
ejpam-3987	45	1	∫	∫	PROPN
ejpam-3987	45	2	c	c	PROPN
ejpam-3987	45	3	w−k−1xp−1yn−p−1e−x	w−k−1xp−1yn−p−1e−x	NOUN
ejpam-3987	45	4	n−yn	n−yn	NOUN
ejpam-3987	45	5	(	(	PUNCT
ejpam-3987	45	6	ax	ax	NOUN
ejpam-3987	45	7	y	y	PROPN
ejpam-3987	45	8	)	)	PUNCT
ejpam-3987	45	9	w	w	PROPN
ejpam-3987	46	1	dwdxdy	dwdxdy	NOUN
ejpam-3987	46	2	=	=	SYM
ejpam-3987	46	3	1	1	NUM
ejpam-3987	46	4	2πi	2πi	NOUN
ejpam-3987	46	5	∫	∫	PROPN
ejpam-3987	46	6	c	c	PROPN
ejpam-3987	46	7	∫	∫	PROPN
ejpam-3987	47	1	∞	∞	NUM
ejpam-3987	47	2	0	0	NUM
ejpam-3987	48	1	∫	∫	PROPN
ejpam-3987	48	2	∞	∞	PROPN
ejpam-3987	48	3	0	0	PUNCT
ejpam-3987	49	1	w−k−1xp−1yn−p−1e−x	w−k−1xp−1yn−p−1e−x	NOUN
ejpam-3987	49	2	n−yn	n−yn	NOUN
ejpam-3987	49	3	(	(	PUNCT
ejpam-3987	49	4	ax	ax	NOUN
ejpam-3987	49	5	y	y	PROPN
ejpam-3987	49	6	)	)	PUNCT
ejpam-3987	49	7	w	w	PROPN
ejpam-3987	49	8	dxdydw	dxdydw	NOUN
ejpam-3987	49	9	=	=	SYM
ejpam-3987	49	10	1	1	NUM
ejpam-3987	49	11	2πi	2πi	NOUN
ejpam-3987	49	12	∫	∫	PROPN
ejpam-3987	49	13	c	c	PROPN
ejpam-3987	50	1	πaww−k−1	πaww−k−1	PROPN
ejpam-3987	50	2	csc	csc	PROPN
ejpam-3987	50	3	(	(	PUNCT
ejpam-3987	50	4	π(p+w	π(p+w	PROPN
ejpam-3987	50	5	)	)	PUNCT
ejpam-3987	50	6	n	n	CCONJ
ejpam-3987	50	7	)	)	PUNCT
ejpam-3987	50	8	n2	n2	PROPN
ejpam-3987	50	9	dw	dw	PROPN
ejpam-3987	50	10	from	from	ADP
ejpam-3987	50	11	equation	equation	NOUN
ejpam-3987	50	12	(	(	PUNCT
ejpam-3987	50	13	3.326.2	3.326.2	NOUN
ejpam-3987	50	14	)	)	PUNCT
ejpam-3987	50	15	in	in	ADP
ejpam-3987	50	16	[	[	X
ejpam-3987	50	17	9	9	NUM
ejpam-3987	50	18	]	]	PUNCT
ejpam-3987	50	19	and	and	CCONJ
ejpam-3987	50	20	using	use	VERB
ejpam-3987	50	21	the	the	DET
ejpam-3987	50	22	reflection	reflection	NOUN
ejpam-3987	50	23	formula	formula	NOUN
ejpam-3987	50	24	for	for	ADP
ejpam-3987	50	25	gamma	gamma	NOUN
ejpam-3987	50	26	functions	function	NOUN
ejpam-3987	50	27	.	.	PUNCT
ejpam-3987	51	1	the	the	DET
ejpam-3987	51	2	condition	condition	NOUN
ejpam-3987	51	3	on	on	ADP
ejpam-3987	51	4	the	the	DET
ejpam-3987	51	5	left	left	ADJ
ejpam-3987	51	6	-	-	PUNCT
ejpam-3987	51	7	hand	hand	NOUN
ejpam-3987	51	8	side	side	NOUN
ejpam-3987	51	9	of	of	ADP
ejpam-3987	51	10	equation	equation	NOUN
ejpam-3987	51	11	(	(	PUNCT
ejpam-3987	51	12	3	3	X
ejpam-3987	51	13	)	)	PUNCT
ejpam-3987	51	14	is	be	AUX
ejpam-3987	51	15	re(p	re(p	NOUN
ejpam-3987	51	16	)	)	PUNCT
ejpam-3987	51	17	>	>	X
ejpam-3987	51	18	0	0	PROPN
ejpam-3987	51	19	and	and	CCONJ
ejpam-3987	51	20	re(n	re(n	NUM
ejpam-3987	51	21	)	)	PUNCT
ejpam-3987	51	22	>	>	X
ejpam-3987	51	23	re(p	re(p	NOUN
ejpam-3987	51	24	)	)	PUNCT
ejpam-3987	51	25	.	.	PUNCT
ejpam-3987	52	1	we	we	PRON
ejpam-3987	52	2	are	be	AUX
ejpam-3987	52	3	able	able	ADJ
ejpam-3987	52	4	to	to	PART
ejpam-3987	52	5	switch	switch	VERB
ejpam-3987	52	6	the	the	DET
ejpam-3987	52	7	order	order	NOUN
ejpam-3987	52	8	of	of	ADP
ejpam-3987	52	9	integration	integration	NOUN
ejpam-3987	52	10	over	over	ADP
ejpam-3987	52	11	α	α	PROPN
ejpam-3987	52	12	,	,	PUNCT
ejpam-3987	52	13	x	x	PUNCT
ejpam-3987	52	14	and	and	CCONJ
ejpam-3987	52	15	y	y	PROPN
ejpam-3987	52	16	using	use	VERB
ejpam-3987	52	17	fubini	fubini	NOUN
ejpam-3987	52	18	’s	’s	PART
ejpam-3987	52	19	theorem	theorem	NOUN
ejpam-3987	52	20	since	since	SCONJ
ejpam-3987	52	21	the	the	DET
ejpam-3987	52	22	integrand	integrand	NOUN
ejpam-3987	52	23	is	be	AUX
ejpam-3987	52	24	of	of	ADP
ejpam-3987	52	25	bounded	bounded	ADJ
ejpam-3987	52	26	measure	measure	NOUN
ejpam-3987	52	27	over	over	ADP
ejpam-3987	52	28	the	the	DET
ejpam-3987	52	29	space	space	NOUN
ejpam-3987	52	30	c×	c×	NOUN
ejpam-3987	53	1	[	[	X
ejpam-3987	53	2	0,∞)×	0,∞)×	NUM
ejpam-3987	53	3	[	[	X
ejpam-3987	53	4	0,∞	0,∞	NUM
ejpam-3987	53	5	)	)	PUNCT
ejpam-3987	53	6	.	.	PUNCT
ejpam-3987	54	1	3	3	X
ejpam-3987	54	2	.	.	X
ejpam-3987	54	3	infinite	infinite	ADJ
ejpam-3987	54	4	sum	sum	NOUN
ejpam-3987	54	5	of	of	ADP
ejpam-3987	54	6	the	the	DET
ejpam-3987	54	7	contour	contour	NOUN
ejpam-3987	54	8	integral	integral	ADJ
ejpam-3987	54	9	using	use	VERB
ejpam-3987	54	10	equation	equation	NOUN
ejpam-3987	54	11	(	(	PUNCT
ejpam-3987	54	12	2	2	NUM
ejpam-3987	54	13	)	)	PUNCT
ejpam-3987	54	14	and	and	CCONJ
ejpam-3987	54	15	replacing	replace	VERB
ejpam-3987	54	16	y	y	PRON
ejpam-3987	54	17	by	by	ADP
ejpam-3987	54	18	log(a	log(a	PROPN
ejpam-3987	54	19	)	)	PUNCT
ejpam-3987	54	20	+	+	CCONJ
ejpam-3987	54	21	iπ(2y+1	iπ(2y+1	NOUN
ejpam-3987	54	22	)	)	PUNCT
ejpam-3987	54	23	n	n	CCONJ
ejpam-3987	54	24	then	then	ADV
ejpam-3987	54	25	multiplying	multiply	VERB
ejpam-3987	54	26	both	both	DET
ejpam-3987	54	27	sides	side	NOUN
ejpam-3987	54	28	by	by	ADP
ejpam-3987	54	29	−2iπe	−2iπe	NOUN
ejpam-3987	54	30	iπp(2y+1	iπp(2y+1	NOUN
ejpam-3987	54	31	)	)	PUNCT
ejpam-3987	54	32	n	n	NUM
ejpam-3987	55	1	n2	n2	NOUN
ejpam-3987	56	1	we	we	PRON
ejpam-3987	56	2	get	get	VERB
ejpam-3987	56	3	r.	r.	PROPN
ejpam-3987	56	4	reynolds	reynolds	PROPN
ejpam-3987	56	5	,	,	PUNCT
ejpam-3987	56	6	a.	a.	PROPN
ejpam-3987	56	7	stauffer	stauffer	PROPN
ejpam-3987	56	8	/	/	SYM
ejpam-3987	56	9	eur	eur	PROPN
ejpam-3987	56	10	.	.	PUNCT
ejpam-3987	57	1	j.	j.	PROPN
ejpam-3987	57	2	pure	pure	PROPN
ejpam-3987	57	3	appl	appl	PROPN
ejpam-3987	57	4	.	.	PROPN
ejpam-3987	57	5	math	math	PROPN
ejpam-3987	57	6	,	,	PUNCT
ejpam-3987	57	7	14	14	NUM
ejpam-3987	57	8	(	(	PUNCT
ejpam-3987	57	9	3	3	NUM
ejpam-3987	57	10	)	)	PUNCT
ejpam-3987	57	11	(	(	PUNCT
ejpam-3987	57	12	2021	2021	NUM
ejpam-3987	57	13	)	)	PUNCT
ejpam-3987	57	14	,	,	PUNCT
ejpam-3987	57	15	618	618	NUM
ejpam-3987	57	16	-	-	SYM
ejpam-3987	57	17	637	637	NUM
ejpam-3987	57	18	620	620	NUM
ejpam-3987	57	19	(	(	PUNCT
ejpam-3987	57	20	4	4	NUM
ejpam-3987	57	21	)	)	PUNCT
ejpam-3987	57	22	−	−	NOUN
ejpam-3987	58	1	i(2π)k+1	i(2π)k+1	NOUN
ejpam-3987	58	2	(	(	PUNCT
ejpam-3987	58	3	i	i	NOUN
ejpam-3987	58	4	n	n	PROPN
ejpam-3987	58	5	)	)	PUNCT
ejpam-3987	58	6	k	k	PROPN
ejpam-3987	58	7	e	e	PROPN
ejpam-3987	58	8	2iπpy	2iπpy	NUM
ejpam-3987	58	9	n	n	NOUN
ejpam-3987	58	10	+	+	CCONJ
ejpam-3987	58	11	iπp	iπp	NOUN
ejpam-3987	58	12	n	n	CCONJ
ejpam-3987	58	13	(	(	PUNCT
ejpam-3987	58	14	1	1	NUM
ejpam-3987	58	15	2(2y	2(2y	NUM
ejpam-3987	58	16	+	+	CCONJ
ejpam-3987	58	17	1)−	1)−	PROPN
ejpam-3987	58	18	in	in	ADP
ejpam-3987	58	19	log(a	log(a	PROPN
ejpam-3987	58	20	)	)	PUNCT
ejpam-3987	58	21	2π	2π	NOUN
ejpam-3987	58	22	)	)	PUNCT
ejpam-3987	59	1	k	k	PROPN
ejpam-3987	59	2	n2k	n2k	NOUN
ejpam-3987	59	3	!	!	PUNCT
ejpam-3987	60	1	=	=	PUNCT
ejpam-3987	61	1	−	−	PROPN
ejpam-3987	61	2	1	1	NUM
ejpam-3987	61	3	2πi	2πi	NOUN
ejpam-3987	61	4	∫	∫	PROPN
ejpam-3987	61	5	c	c	PROPN
ejpam-3987	61	6	2iπw−k−1	2iπw−k−1	NUM
ejpam-3987	61	7	exp	exp	NOUN
ejpam-3987	61	8	(	(	PUNCT
ejpam-3987	61	9	w	w	PROPN
ejpam-3987	61	10	(	(	PUNCT
ejpam-3987	61	11	log(a	log(a	PROPN
ejpam-3987	61	12	)	)	PUNCT
ejpam-3987	61	13	+	+	CCONJ
ejpam-3987	61	14	iπ(2y+1	iπ(2y+1	NOUN
ejpam-3987	61	15	)	)	PUNCT
ejpam-3987	61	16	n	n	NOUN
ejpam-3987	61	17	)	)	PUNCT
ejpam-3987	62	1	+	+	CCONJ
ejpam-3987	62	2	iπp(2y+1	iπp(2y+1	ADJ
ejpam-3987	62	3	)	)	PUNCT
ejpam-3987	62	4	n	n	CCONJ
ejpam-3987	62	5	)	)	PUNCT
ejpam-3987	62	6	n2	n2	PROPN
ejpam-3987	62	7	dw	dw	NOUN
ejpam-3987	63	1	we	we	PRON
ejpam-3987	63	2	then	then	ADV
ejpam-3987	63	3	take	take	VERB
ejpam-3987	63	4	the	the	DET
ejpam-3987	63	5	infinite	infinite	ADJ
ejpam-3987	63	6	sum	sum	NOUN
ejpam-3987	63	7	over	over	ADP
ejpam-3987	63	8	y	y	PROPN
ejpam-3987	63	9	∈	∈	PROPN
ejpam-3987	64	1	[	[	X
ejpam-3987	64	2	0,∞	0,∞	NOUN
ejpam-3987	64	3	)	)	PUNCT
ejpam-3987	64	4	to	to	PART
ejpam-3987	64	5	get	get	VERB
ejpam-3987	64	6	(	(	PUNCT
ejpam-3987	64	7	5	5	NUM
ejpam-3987	64	8	)	)	PUNCT
ejpam-3987	64	9	(	(	PUNCT
ejpam-3987	64	10	2π)k+1	2π)k+1	NUM
ejpam-3987	64	11	(	(	PUNCT
ejpam-3987	64	12	i	i	PRON
ejpam-3987	64	13	n	n	ADJ
ejpam-3987	64	14	)	)	PUNCT
ejpam-3987	64	15	k−1	k−1	PROPN
ejpam-3987	64	16	e	e	PROPN
ejpam-3987	64	17	iπp	iπp	PROPN
ejpam-3987	64	18	n	n	ADV
ejpam-3987	64	19	φ	φ	PROPN
ejpam-3987	64	20	(	(	PUNCT
ejpam-3987	64	21	e	e	X
ejpam-3987	64	22	2ipπ	2ipπ	NUM
ejpam-3987	64	23	n	n	DET
ejpam-3987	64	24	,	,	PUNCT
ejpam-3987	64	25	−k	−k	PROPN
ejpam-3987	64	26	,	,	PUNCT
ejpam-3987	64	27	π−in	π−in	NOUN
ejpam-3987	64	28	log(a	log(a	PROPN
ejpam-3987	64	29	)	)	PUNCT
ejpam-3987	64	30	2π	2π	NOUN
ejpam-3987	64	31	)	)	PUNCT
ejpam-3987	64	32	n3k	n3k	PROPN
ejpam-3987	64	33	!	!	PUNCT
ejpam-3987	65	1	=	=	PUNCT
ejpam-3987	65	2	−	−	PROPN
ejpam-3987	65	3	1	1	NUM
ejpam-3987	65	4	2πi	2πi	NOUN
ejpam-3987	65	5	∞∑	∞∑	NUM
ejpam-3987	65	6	y=0	y=0	NUM
ejpam-3987	65	7	∫	∫	PROPN
ejpam-3987	65	8	c	c	PROPN
ejpam-3987	65	9	2iπw−k−1	2iπw−k−1	NUM
ejpam-3987	65	10	exp	exp	NOUN
ejpam-3987	65	11	(	(	PUNCT
ejpam-3987	65	12	w	w	PROPN
ejpam-3987	65	13	(	(	PUNCT
ejpam-3987	65	14	log(a	log(a	PROPN
ejpam-3987	65	15	)	)	PUNCT
ejpam-3987	65	16	+	+	CCONJ
ejpam-3987	65	17	iπ(2y+1	iπ(2y+1	NOUN
ejpam-3987	65	18	)	)	PUNCT
ejpam-3987	65	19	n	n	NOUN
ejpam-3987	65	20	)	)	PUNCT
ejpam-3987	65	21	+	+	CCONJ
ejpam-3987	65	22	iπp(2y+1	iπp(2y+1	ADJ
ejpam-3987	65	23	)	)	PUNCT
ejpam-3987	65	24	n	n	CCONJ
ejpam-3987	65	25	)	)	PUNCT
ejpam-3987	65	26	n2	n2	PROPN
ejpam-3987	65	27	dw	dw	PROPN
ejpam-3987	65	28	=	=	SYM
ejpam-3987	66	1	−	−	PROPN
ejpam-3987	66	2	1	1	NUM
ejpam-3987	66	3	2πi	2πi	NOUN
ejpam-3987	66	4	∫	∫	PROPN
ejpam-3987	66	5	c	c	NOUN
ejpam-3987	66	6	∞∑	∞∑	NUM
ejpam-3987	66	7	y=0	y=0	NOUN
ejpam-3987	66	8	2iπw−k−1	2iπw−k−1	NUM
ejpam-3987	66	9	exp	exp	NOUN
ejpam-3987	66	10	(	(	PUNCT
ejpam-3987	66	11	w	w	PROPN
ejpam-3987	66	12	(	(	PUNCT
ejpam-3987	66	13	log(a	log(a	PROPN
ejpam-3987	66	14	)	)	PUNCT
ejpam-3987	66	15	+	+	CCONJ
ejpam-3987	66	16	iπ(2y+1	iπ(2y+1	NOUN
ejpam-3987	66	17	)	)	PUNCT
ejpam-3987	66	18	n	n	NOUN
ejpam-3987	66	19	)	)	PUNCT
ejpam-3987	66	20	+	+	CCONJ
ejpam-3987	66	21	iπp(2y+1	iπp(2y+1	ADJ
ejpam-3987	66	22	)	)	PUNCT
ejpam-3987	66	23	n	n	CCONJ
ejpam-3987	66	24	)	)	PUNCT
ejpam-3987	66	25	n2	n2	PROPN
ejpam-3987	66	26	dw	dw	NOUN
ejpam-3987	66	27	=	=	SYM
ejpam-3987	66	28	1	1	NUM
ejpam-3987	66	29	2πi	2πi	NOUN
ejpam-3987	66	30	∫	∫	PROPN
ejpam-3987	67	1	c	c	PROPN
ejpam-3987	68	1	πaww−k−1	πaww−k−1	PROPN
ejpam-3987	68	2	csc	csc	PROPN
ejpam-3987	68	3	(	(	PUNCT
ejpam-3987	68	4	π(p+w	π(p+w	PROPN
ejpam-3987	68	5	)	)	PUNCT
ejpam-3987	68	6	n	n	CCONJ
ejpam-3987	68	7	)	)	PUNCT
ejpam-3987	68	8	n2	n2	PROPN
ejpam-3987	68	9	dw	dw	PROPN
ejpam-3987	68	10	from	from	ADP
ejpam-3987	68	11	equation	equation	NOUN
ejpam-3987	68	12	(	(	PUNCT
ejpam-3987	68	13	1.232.3	1.232.3	NUM
ejpam-3987	68	14	)	)	PUNCT
ejpam-3987	68	15	in	in	ADP
ejpam-3987	68	16	[	[	X
ejpam-3987	68	17	9	9	NUM
ejpam-3987	68	18	]	]	PUNCT
ejpam-3987	68	19	and	and	CCONJ
ejpam-3987	68	20	im(p+	im(p+	PROPN
ejpam-3987	68	21	w	w	X
ejpam-3987	68	22	)	)	PUNCT
ejpam-3987	68	23	<	<	X
ejpam-3987	68	24	0	0	NUM
ejpam-3987	68	25	.	.	NOUN
ejpam-3987	68	26	4	4	NUM
ejpam-3987	68	27	.	.	X
ejpam-3987	69	1	the	the	DET
ejpam-3987	69	2	lerch	lerch	PROPN
ejpam-3987	69	3	function	function	NOUN
ejpam-3987	69	4	we	we	PRON
ejpam-3987	69	5	use	use	VERB
ejpam-3987	69	6	(	(	PUNCT
ejpam-3987	69	7	9.550	9.550	NUM
ejpam-3987	69	8	)	)	PUNCT
ejpam-3987	69	9	and	and	CCONJ
ejpam-3987	69	10	(	(	PUNCT
ejpam-3987	69	11	9.556	9.556	NUM
ejpam-3987	69	12	)	)	PUNCT
ejpam-3987	69	13	in	in	ADP
ejpam-3987	69	14	[	[	X
ejpam-3987	69	15	9	9	NUM
ejpam-3987	69	16	]	]	PUNCT
ejpam-3987	69	17	where	where	SCONJ
ejpam-3987	69	18	φ(z	φ(z	PROPN
ejpam-3987	69	19	,	,	PUNCT
ejpam-3987	69	20	s	s	NOUN
ejpam-3987	69	21	,	,	PUNCT
ejpam-3987	69	22	v	v	NOUN
ejpam-3987	69	23	)	)	PUNCT
ejpam-3987	69	24	is	be	AUX
ejpam-3987	69	25	the	the	DET
ejpam-3987	69	26	lerch	lerch	PROPN
ejpam-3987	69	27	function	function	NOUN
ejpam-3987	69	28	which	which	PRON
ejpam-3987	69	29	is	be	AUX
ejpam-3987	69	30	a	a	DET
ejpam-3987	69	31	generalization	generalization	NOUN
ejpam-3987	69	32	of	of	ADP
ejpam-3987	69	33	the	the	DET
ejpam-3987	69	34	hurwitz	hurwitz	PROPN
ejpam-3987	69	35	zeta	zeta	PROPN
ejpam-3987	69	36	and	and	CCONJ
ejpam-3987	69	37	polylogarithm	polylogarithm	PROPN
ejpam-3987	69	38	functions	function	NOUN
ejpam-3987	69	39	.	.	PUNCT
ejpam-3987	70	1	the	the	DET
ejpam-3987	70	2	lerch	lerch	PROPN
ejpam-3987	70	3	function	function	PROPN
ejpam-3987	70	4	has	have	VERB
ejpam-3987	70	5	a	a	DET
ejpam-3987	70	6	series	series	NOUN
ejpam-3987	70	7	representation	representation	NOUN
ejpam-3987	70	8	given	give	VERB
ejpam-3987	70	9	by	by	ADP
ejpam-3987	70	10	φ(z	φ(z	PROPN
ejpam-3987	70	11	,	,	PUNCT
ejpam-3987	70	12	s	s	NOUN
ejpam-3987	70	13	,	,	PUNCT
ejpam-3987	70	14	v	v	NOUN
ejpam-3987	70	15	)	)	PUNCT
ejpam-3987	70	16	=	=	PUNCT
ejpam-3987	71	1	∞∑	∞∑	NUM
ejpam-3987	71	2	n=0	n=0	NUM
ejpam-3987	71	3	(	(	PUNCT
ejpam-3987	71	4	v	v	NOUN
ejpam-3987	71	5	+	+	NOUN
ejpam-3987	71	6	n)−szn	n)−szn	NUM
ejpam-3987	71	7	(	(	PUNCT
ejpam-3987	71	8	6	6	NUM
ejpam-3987	71	9	)	)	PUNCT
ejpam-3987	71	10	where	where	SCONJ
ejpam-3987	71	11	|z|	|z|	VERB
ejpam-3987	71	12	<	<	X
ejpam-3987	71	13	1	1	NUM
ejpam-3987	71	14	,	,	PUNCT
ejpam-3987	71	15	v	v	NOUN
ejpam-3987	71	16	6=	6=	ADP
ejpam-3987	71	17	0,−1	0,−1	PROPN
ejpam-3987	71	18	,	,	PUNCT
ejpam-3987	71	19	..	..	PUNCT
ejpam-3987	71	20	and	and	CCONJ
ejpam-3987	71	21	is	be	AUX
ejpam-3987	71	22	continued	continue	VERB
ejpam-3987	71	23	analytically	analytically	ADV
ejpam-3987	71	24	by	by	ADP
ejpam-3987	71	25	its	its	PRON
ejpam-3987	71	26	integral	integral	ADJ
ejpam-3987	71	27	representation	representation	NOUN
ejpam-3987	71	28	given	give	VERB
ejpam-3987	71	29	by	by	ADP
ejpam-3987	71	30	φ(z	φ(z	PROPN
ejpam-3987	71	31	,	,	PUNCT
ejpam-3987	71	32	s	s	NOUN
ejpam-3987	71	33	,	,	PUNCT
ejpam-3987	71	34	v	v	NOUN
ejpam-3987	71	35	)	)	PUNCT
ejpam-3987	71	36	=	=	SYM
ejpam-3987	71	37	1	1	NUM
ejpam-3987	71	38	γ(s	γ(	NOUN
ejpam-3987	71	39	)	)	PUNCT
ejpam-3987	71	40	∫	∫	PROPN
ejpam-3987	72	1	∞	∞	PROPN
ejpam-3987	72	2	0	0	NUM
ejpam-3987	73	1	ts−1e−vt	ts−1e−vt	PRON
ejpam-3987	74	1	1−	1−	NUM
ejpam-3987	74	2	ze−t	ze−t	NOUN
ejpam-3987	74	3	dt	dt	NOUN
ejpam-3987	75	1	=	=	SYM
ejpam-3987	75	2	1	1	NUM
ejpam-3987	75	3	γ(s	γ(s	PROPN
ejpam-3987	75	4	)	)	PUNCT
ejpam-3987	75	5	∫	∫	PROPN
ejpam-3987	76	1	∞	∞	NUM
ejpam-3987	76	2	0	0	NUM
ejpam-3987	77	1	ts−1e−(v−1)t	ts−1e−(v−1)t	PROPN
ejpam-3987	77	2	et	et	NOUN
ejpam-3987	77	3	−	−	NOUN
ejpam-3987	77	4	z	z	NOUN
ejpam-3987	77	5	dt	dt	X
ejpam-3987	77	6	(	(	PUNCT
ejpam-3987	77	7	7	7	NUM
ejpam-3987	77	8	)	)	PUNCT
ejpam-3987	77	9	where	where	SCONJ
ejpam-3987	77	10	re(v	re(v	NOUN
ejpam-3987	77	11	)	)	PUNCT
ejpam-3987	77	12	>	>	X
ejpam-3987	77	13	0	0	NUM
ejpam-3987	77	14	,	,	PUNCT
ejpam-3987	77	15	or	or	CCONJ
ejpam-3987	77	16	|z|≤	|z|≤	SYM
ejpam-3987	77	17	1	1	NUM
ejpam-3987	77	18	,	,	PUNCT
ejpam-3987	77	19	z	z	NOUN
ejpam-3987	77	20	6=	6=	NUM
ejpam-3987	77	21	1	1	NUM
ejpam-3987	77	22	,	,	PUNCT
ejpam-3987	77	23	re(s	re(s	ADJ
ejpam-3987	77	24	)	)	PUNCT
ejpam-3987	77	25	>	>	X
ejpam-3987	77	26	0	0	NUM
ejpam-3987	77	27	,	,	PUNCT
ejpam-3987	77	28	or	or	CCONJ
ejpam-3987	77	29	z	z	NOUN
ejpam-3987	77	30	=	=	SYM
ejpam-3987	77	31	1	1	NUM
ejpam-3987	77	32	,	,	PUNCT
ejpam-3987	77	33	re(s	re(s	ADJ
ejpam-3987	77	34	)	)	PUNCT
ejpam-3987	77	35	>	>	PUNCT
ejpam-3987	77	36	1	1	NUM
ejpam-3987	77	37	5	5	NUM
ejpam-3987	77	38	.	.	PUNCT
ejpam-3987	77	39	definite	definite	ADJ
ejpam-3987	77	40	integral	integral	ADJ
ejpam-3987	77	41	in	in	ADP
ejpam-3987	77	42	terms	term	NOUN
ejpam-3987	77	43	of	of	ADP
ejpam-3987	77	44	the	the	DET
ejpam-3987	77	45	lerch	lerch	PROPN
ejpam-3987	77	46	transcendent	transcendent	NOUN
ejpam-3987	77	47	since	since	SCONJ
ejpam-3987	77	48	the	the	DET
ejpam-3987	77	49	right	right	ADJ
ejpam-3987	77	50	-	-	PUNCT
ejpam-3987	77	51	hand	hand	NOUN
ejpam-3987	77	52	side	side	NOUN
ejpam-3987	77	53	of	of	ADP
ejpam-3987	77	54	equation	equation	NOUN
ejpam-3987	77	55	(	(	PUNCT
ejpam-3987	77	56	3	3	X
ejpam-3987	77	57	)	)	PUNCT
ejpam-3987	77	58	is	be	AUX
ejpam-3987	77	59	equal	equal	ADJ
ejpam-3987	77	60	to	to	ADP
ejpam-3987	77	61	equation	equation	NOUN
ejpam-3987	77	62	(	(	PUNCT
ejpam-3987	77	63	5	5	X
ejpam-3987	77	64	)	)	PUNCT
ejpam-3987	77	65	we	we	PRON
ejpam-3987	77	66	may	may	AUX
ejpam-3987	77	67	equate	equate	VERB
ejpam-3987	77	68	the	the	DET
ejpam-3987	77	69	left	left	ADJ
ejpam-3987	77	70	hand	hand	NOUN
ejpam-3987	77	71	sides	side	NOUN
ejpam-3987	77	72	along	along	ADP
ejpam-3987	77	73	with	with	ADP
ejpam-3987	77	74	making	make	VERB
ejpam-3987	77	75	the	the	DET
ejpam-3987	77	76	the	the	DET
ejpam-3987	77	77	substitutions	substitution	NOUN
ejpam-3987	77	78	x	x	PUNCT
ejpam-3987	77	79	=	=	SYM
ejpam-3987	77	80	sx	sx	PROPN
ejpam-3987	77	81	,	,	PUNCT
ejpam-3987	77	82	y	y	PROPN
ejpam-3987	77	83	=	=	PUNCT
ejpam-3987	77	84	ty	ty	INTJ
ejpam-3987	77	85	and	and	CCONJ
ejpam-3987	77	86	a	a	DET
ejpam-3987	77	87	=	=	NOUN
ejpam-3987	77	88	bs	bs	PROPN
ejpam-3987	77	89	/	/	SYM
ejpam-3987	77	90	t	t	PROPN
ejpam-3987	77	91	and	and	CCONJ
ejpam-3987	77	92	simplifying	simplify	VERB
ejpam-3987	77	93	to	to	PART
ejpam-3987	77	94	get	get	VERB
ejpam-3987	77	95	r.	r.	PROPN
ejpam-3987	77	96	reynolds	reynolds	PROPN
ejpam-3987	77	97	,	,	PUNCT
ejpam-3987	77	98	a.	a.	PROPN
ejpam-3987	77	99	stauffer	stauffer	PROPN
ejpam-3987	77	100	/	/	SYM
ejpam-3987	77	101	eur	eur	PROPN
ejpam-3987	77	102	.	.	PUNCT
ejpam-3987	78	1	j.	j.	PROPN
ejpam-3987	78	2	pure	pure	PROPN
ejpam-3987	78	3	appl	appl	PROPN
ejpam-3987	78	4	.	.	PROPN
ejpam-3987	78	5	math	math	PROPN
ejpam-3987	78	6	,	,	PUNCT
ejpam-3987	78	7	14	14	NUM
ejpam-3987	78	8	(	(	PUNCT
ejpam-3987	78	9	3	3	NUM
ejpam-3987	78	10	)	)	PUNCT
ejpam-3987	78	11	(	(	PUNCT
ejpam-3987	78	12	2021	2021	NUM
ejpam-3987	78	13	)	)	PUNCT
ejpam-3987	78	14	,	,	PUNCT
ejpam-3987	78	15	618	618	NUM
ejpam-3987	78	16	-	-	SYM
ejpam-3987	78	17	637	637	NUM
ejpam-3987	78	18	621	621	NUM
ejpam-3987	78	19	(	(	PUNCT
ejpam-3987	78	20	8)	8)	NUM
ejpam-3987	78	21	∫	∫	NOUN
ejpam-3987	78	22	∞	∞	PROPN
ejpam-3987	78	23	0	0	NUM
ejpam-3987	79	1	∫	∫	PROPN
ejpam-3987	79	2	∞	∞	NUM
ejpam-3987	79	3	0	0	NUM
ejpam-3987	80	1	xp−1yn−p−1	xp−1yn−p−1	NOUN
ejpam-3987	80	2	logk	logk	NOUN
ejpam-3987	80	3	(	(	PUNCT
ejpam-3987	80	4	bx	bx	NOUN
ejpam-3987	80	5	y	y	PROPN
ejpam-3987	80	6	)	)	PUNCT
ejpam-3987	80	7	e−(sx)n−(ty)ndxdy	e−(sx)n−(ty)ndxdy	PROPN
ejpam-3987	80	8	=	=	SYM
ejpam-3987	80	9	(	(	PUNCT
ejpam-3987	80	10	2π)k+1	2π)k+1	NUM
ejpam-3987	80	11	(	(	PUNCT
ejpam-3987	80	12	i	i	PRON
ejpam-3987	80	13	n	n	ADJ
ejpam-3987	80	14	)	)	PUNCT
ejpam-3987	81	1	k−1	k−1	PROPN
ejpam-3987	81	2	e	e	PROPN
ejpam-3987	81	3	iπp	iπp	PROPN
ejpam-3987	81	4	n	n	PRON
ejpam-3987	81	5	s−ptp−n	s−ptp−n	PROPN
ejpam-3987	81	6	n3	n3	PROPN
ejpam-3987	81	7	φ	φ	PROPN
ejpam-3987	81	8	(	(	PUNCT
ejpam-3987	81	9	e	e	PROPN
ejpam-3987	81	10	2ipπ	2ipπ	NUM
ejpam-3987	81	11	n	n	DET
ejpam-3987	81	12	,	,	PUNCT
ejpam-3987	81	13	−k	−k	PROPN
ejpam-3987	81	14	,	,	PUNCT
ejpam-3987	81	15	π	π	PROPN
ejpam-3987	81	16	−	−	PROPN
ejpam-3987	81	17	in	in	ADP
ejpam-3987	81	18	log	log	PROPN
ejpam-3987	81	19	(	(	PUNCT
ejpam-3987	81	20	bt	bt	NOUN
ejpam-3987	81	21	s	s	X
ejpam-3987	81	22	)	)	PUNCT
ejpam-3987	81	23	2π	2π	NOUN
ejpam-3987	81	24	)	)	PUNCT
ejpam-3987	81	25	6	6	NUM
ejpam-3987	81	26	.	.	PUNCT
ejpam-3987	81	27	derivation	derivation	NOUN
ejpam-3987	81	28	of	of	ADP
ejpam-3987	81	29	definite	definite	ADJ
ejpam-3987	81	30	integrals	integral	NOUN
ejpam-3987	81	31	when	when	SCONJ
ejpam-3987	81	32	s	s	VERB
ejpam-3987	81	33	=	=	X
ejpam-3987	81	34	t	t	X
ejpam-3987	81	35	=	=	SYM
ejpam-3987	81	36	1	1	NUM
ejpam-3987	81	37	in	in	ADP
ejpam-3987	81	38	this	this	DET
ejpam-3987	81	39	section	section	NOUN
ejpam-3987	81	40	we	we	PRON
ejpam-3987	81	41	will	will	AUX
ejpam-3987	81	42	derive	derive	VERB
ejpam-3987	81	43	various	various	ADJ
ejpam-3987	81	44	definite	definite	ADJ
ejpam-3987	81	45	integrals	integral	NOUN
ejpam-3987	81	46	referred	refer	VERB
ejpam-3987	81	47	to	to	ADP
ejpam-3987	81	48	in	in	ADP
ejpam-3987	81	49	[	[	X
ejpam-3987	81	50	8	8	NUM
ejpam-3987	81	51	]	]	PUNCT
ejpam-3987	81	52	starting	start	VERB
ejpam-3987	81	53	with	with	ADP
ejpam-3987	81	54	(	(	PUNCT
ejpam-3987	81	55	45	45	NUM
ejpam-3987	81	56	)	)	PUNCT
ejpam-3987	81	57	on	on	ADP
ejpam-3987	81	58	p	p	NOUN
ejpam-3987	81	59	245	245	NUM
ejpam-3987	81	60	using	use	VERB
ejpam-3987	81	61	equation	equation	NOUN
ejpam-3987	81	62	(	(	PUNCT
ejpam-3987	81	63	8)	8)	NUM
ejpam-3987	81	64	in	in	ADP
ejpam-3987	81	65	terms	term	NOUN
ejpam-3987	81	66	of	of	ADP
ejpam-3987	81	67	special	special	ADJ
ejpam-3987	81	68	functions	function	NOUN
ejpam-3987	81	69	,	,	PUNCT
ejpam-3987	81	70	fundamental	fundamental	ADJ
ejpam-3987	81	71	constants	constant	NOUN
ejpam-3987	81	72	and	and	CCONJ
ejpam-3987	81	73	itemizing	itemize	VERB
ejpam-3987	81	74	each	each	PRON
ejpam-3987	81	75	as	as	ADP
ejpam-3987	81	76	entries	entry	NOUN
ejpam-3987	81	77	.	.	PUNCT
ejpam-3987	82	1	note	note	NOUN
ejpam-3987	82	2	in	in	ADP
ejpam-3987	82	3	this	this	DET
ejpam-3987	82	4	section	section	NOUN
ejpam-3987	82	5	a	a	DET
ejpam-3987	82	6	=	=	X
ejpam-3987	82	7	b.	b.	PROPN
ejpam-3987	82	8	6.1	6.1	NUM
ejpam-3987	82	9	.	.	PUNCT
ejpam-3987	83	1	derivation	derivation	NOUN
ejpam-3987	83	2	of	of	ADP
ejpam-3987	83	3	entry	entry	NOUN
ejpam-3987	83	4	45	45	NUM
ejpam-3987	83	5	using	use	VERB
ejpam-3987	83	6	equation	equation	NOUN
ejpam-3987	83	7	(	(	PUNCT
ejpam-3987	83	8	8)	8)	NUM
ejpam-3987	83	9	and	and	CCONJ
ejpam-3987	83	10	setting	set	VERB
ejpam-3987	83	11	a	a	DET
ejpam-3987	83	12	=	=	SYM
ejpam-3987	83	13	1	1	NUM
ejpam-3987	83	14	and	and	CCONJ
ejpam-3987	83	15	k	k	NOUN
ejpam-3987	83	16	=	=	SYM
ejpam-3987	83	17	0	0	PUNCT
ejpam-3987	83	18	and	and	CCONJ
ejpam-3987	83	19	simplifying	simplify	VERB
ejpam-3987	83	20	we	we	PRON
ejpam-3987	83	21	get	get	VERB
ejpam-3987	83	22	(	(	PUNCT
ejpam-3987	83	23	9	9	NUM
ejpam-3987	83	24	)	)	PUNCT
ejpam-3987	83	25	∫	∫	PROPN
ejpam-3987	84	1	∞	∞	PROPN
ejpam-3987	84	2	0	0	NUM
ejpam-3987	84	3	∫	∫	PROPN
ejpam-3987	85	1	∞	∞	PROPN
ejpam-3987	85	2	0	0	NUM
ejpam-3987	86	1	xp−1yn−p−1e−x	xp−1yn−p−1e−x	PROPN
ejpam-3987	86	2	n−yndxdy	n−yndxdy	X
ejpam-3987	87	1	=	=	PROPN
ejpam-3987	87	2	π	π	X
ejpam-3987	87	3	csc	csc	PROPN
ejpam-3987	87	4	(	(	PUNCT
ejpam-3987	87	5	πp	πp	ADP
ejpam-3987	87	6	n	n	NOUN
ejpam-3987	87	7	)	)	PUNCT
ejpam-3987	87	8	n2	n2	NOUN
ejpam-3987	87	9	from	from	ADP
ejpam-3987	87	10	entry	entry	NOUN
ejpam-3987	87	11	(	(	PUNCT
ejpam-3987	87	12	2	2	NUM
ejpam-3987	87	13	)	)	PUNCT
ejpam-3987	87	14	in	in	ADP
ejpam-3987	87	15	table	table	NOUN
ejpam-3987	87	16	below	below	ADV
ejpam-3987	87	17	(	(	PUNCT
ejpam-3987	87	18	64:12:7	64:12:7	NUM
ejpam-3987	87	19	)	)	PUNCT
ejpam-3987	87	20	in	in	ADP
ejpam-3987	87	21	[	[	X
ejpam-3987	87	22	6	6	NUM
ejpam-3987	87	23	]	]	PUNCT
ejpam-3987	87	24	.	.	PUNCT
ejpam-3987	88	1	6.2	6.2	NUM
ejpam-3987	88	2	.	.	PUNCT
ejpam-3987	89	1	derivation	derivation	NOUN
ejpam-3987	89	2	of	of	ADP
ejpam-3987	89	3	new	new	ADJ
ejpam-3987	89	4	entry	entry	NOUN
ejpam-3987	89	5	46	46	NUM
ejpam-3987	89	6	using	use	VERB
ejpam-3987	89	7	equation	equation	NOUN
ejpam-3987	89	8	(	(	PUNCT
ejpam-3987	89	9	8)	8)	NUM
ejpam-3987	89	10	and	and	CCONJ
ejpam-3987	89	11	setting	set	VERB
ejpam-3987	89	12	a	a	DET
ejpam-3987	89	13	=	=	SYM
ejpam-3987	89	14	1	1	NUM
ejpam-3987	89	15	and	and	CCONJ
ejpam-3987	89	16	k	k	NOUN
ejpam-3987	89	17	=	=	SYM
ejpam-3987	89	18	1	1	NUM
ejpam-3987	89	19	and	and	CCONJ
ejpam-3987	89	20	simplifying	simplify	VERB
ejpam-3987	89	21	we	we	PRON
ejpam-3987	89	22	get	get	VERB
ejpam-3987	89	23	(	(	PUNCT
ejpam-3987	89	24	10	10	NUM
ejpam-3987	89	25	)	)	PUNCT
ejpam-3987	89	26	∫	∫	PROPN
ejpam-3987	90	1	∞	∞	PROPN
ejpam-3987	90	2	0	0	NUM
ejpam-3987	91	1	∫	∫	PROPN
ejpam-3987	91	2	∞	∞	PROPN
ejpam-3987	91	3	0	0	NUM
ejpam-3987	92	1	xp−1yn−p−1e−x	xp−1yn−p−1e−x	PROPN
ejpam-3987	92	2	n−yn	n−yn	PROPN
ejpam-3987	92	3	log	log	NOUN
ejpam-3987	92	4	(	(	PUNCT
ejpam-3987	92	5	x	x	SYM
ejpam-3987	92	6	y	y	PROPN
ejpam-3987	92	7	)	)	PUNCT
ejpam-3987	92	8	dxdy	dxdy	PROPN
ejpam-3987	92	9	=	=	PUNCT
ejpam-3987	92	10	−	−	PROPN
ejpam-3987	92	11	π2	π2	ADJ
ejpam-3987	92	12	cot	cot	NOUN
ejpam-3987	92	13	(	(	PUNCT
ejpam-3987	92	14	πp	πp	ADP
ejpam-3987	92	15	n	n	NOUN
ejpam-3987	92	16	)	)	PUNCT
ejpam-3987	92	17	csc	csc	PROPN
ejpam-3987	92	18	(	(	PUNCT
ejpam-3987	92	19	πp	πp	ADP
ejpam-3987	92	20	n	n	NOUN
ejpam-3987	92	21	)	)	PUNCT
ejpam-3987	92	22	n3	n3	NOUN
ejpam-3987	92	23	from	from	ADP
ejpam-3987	92	24	entry	entry	NOUN
ejpam-3987	92	25	(	(	PUNCT
ejpam-3987	92	26	3	3	NUM
ejpam-3987	92	27	)	)	PUNCT
ejpam-3987	92	28	in	in	ADP
ejpam-3987	92	29	table	table	NOUN
ejpam-3987	92	30	below	below	ADV
ejpam-3987	92	31	(	(	PUNCT
ejpam-3987	92	32	64:12:7	64:12:7	NUM
ejpam-3987	92	33	)	)	PUNCT
ejpam-3987	92	34	in	in	ADP
ejpam-3987	92	35	[	[	X
ejpam-3987	92	36	6	6	NUM
ejpam-3987	92	37	]	]	PUNCT
ejpam-3987	92	38	.	.	PUNCT
ejpam-3987	93	1	6.3	6.3	NUM
ejpam-3987	93	2	.	.	PUNCT
ejpam-3987	94	1	derivation	derivation	NOUN
ejpam-3987	94	2	of	of	ADP
ejpam-3987	94	3	new	new	ADJ
ejpam-3987	94	4	entry	entry	NOUN
ejpam-3987	94	5	47	47	NUM
ejpam-3987	94	6	using	use	VERB
ejpam-3987	94	7	equation	equation	NOUN
ejpam-3987	94	8	(	(	PUNCT
ejpam-3987	94	9	8)	8)	NUM
ejpam-3987	94	10	and	and	CCONJ
ejpam-3987	94	11	setting	set	VERB
ejpam-3987	94	12	a	a	DET
ejpam-3987	94	13	=	=	SYM
ejpam-3987	94	14	1	1	NUM
ejpam-3987	94	15	and	and	CCONJ
ejpam-3987	94	16	k	k	NOUN
ejpam-3987	94	17	=	=	SYM
ejpam-3987	94	18	2	2	NUM
ejpam-3987	94	19	and	and	CCONJ
ejpam-3987	94	20	simplifying	simplify	VERB
ejpam-3987	94	21	we	we	PRON
ejpam-3987	94	22	get	get	VERB
ejpam-3987	94	23	(	(	PUNCT
ejpam-3987	94	24	11	11	NUM
ejpam-3987	94	25	)	)	PUNCT
ejpam-3987	94	26	∫	∫	PROPN
ejpam-3987	95	1	∞	∞	PROPN
ejpam-3987	95	2	0	0	NUM
ejpam-3987	95	3	∫	∫	PROPN
ejpam-3987	96	1	∞	∞	PROPN
ejpam-3987	96	2	0	0	NUM
ejpam-3987	97	1	xp−1yn−p−1e−x	xp−1yn−p−1e−x	PROPN
ejpam-3987	97	2	n−yn	n−yn	PROPN
ejpam-3987	97	3	log2	log2	PROPN
ejpam-3987	97	4	(	(	PUNCT
ejpam-3987	97	5	x	x	SYM
ejpam-3987	97	6	y	y	PROPN
ejpam-3987	97	7	)	)	PUNCT
ejpam-3987	97	8	dxdy	dxdy	PROPN
ejpam-3987	97	9	=	=	SYM
ejpam-3987	97	10	π3	π3	PROPN
ejpam-3987	97	11	(	(	PUNCT
ejpam-3987	97	12	cos	cos	X
ejpam-3987	97	13	(	(	PUNCT
ejpam-3987	97	14	2πp	2πp	NOUN
ejpam-3987	97	15	n	n	CCONJ
ejpam-3987	97	16	)	)	PUNCT
ejpam-3987	98	1	+	+	CCONJ
ejpam-3987	98	2	3	3	X
ejpam-3987	98	3	)	)	PUNCT
ejpam-3987	98	4	csc3	csc3	PROPN
ejpam-3987	98	5	(	(	PUNCT
ejpam-3987	98	6	πp	πp	ADP
ejpam-3987	98	7	n	n	X
ejpam-3987	98	8	)	)	PUNCT
ejpam-3987	98	9	2n4	2n4	NUM
ejpam-3987	98	10	from	from	ADP
ejpam-3987	98	11	entry	entry	NOUN
ejpam-3987	98	12	(	(	PUNCT
ejpam-3987	98	13	4	4	NUM
ejpam-3987	98	14	)	)	PUNCT
ejpam-3987	98	15	in	in	ADP
ejpam-3987	98	16	table	table	NOUN
ejpam-3987	98	17	below	below	ADV
ejpam-3987	98	18	(	(	PUNCT
ejpam-3987	98	19	64:12:7	64:12:7	NUM
ejpam-3987	98	20	)	)	PUNCT
ejpam-3987	98	21	in	in	ADP
ejpam-3987	98	22	[	[	X
ejpam-3987	98	23	6	6	NUM
ejpam-3987	98	24	]	]	PUNCT
ejpam-3987	98	25	.	.	PUNCT
ejpam-3987	99	1	6.4	6.4	NUM
ejpam-3987	99	2	.	.	PUNCT
ejpam-3987	99	3	derivation	derivation	NOUN
ejpam-3987	99	4	of	of	ADP
ejpam-3987	99	5	new	new	ADJ
ejpam-3987	99	6	entry	entry	NOUN
ejpam-3987	99	7	48	48	NUM
ejpam-3987	99	8	in	in	ADP
ejpam-3987	99	9	terms	term	NOUN
ejpam-3987	99	10	of	of	ADP
ejpam-3987	99	11	the	the	DET
ejpam-3987	99	12	hurwitz	hurwitz	PROPN
ejpam-3987	99	13	zeta	zeta	PROPN
ejpam-3987	99	14	function	function	NOUN
ejpam-3987	99	15	using	use	VERB
ejpam-3987	99	16	equation	equation	NOUN
ejpam-3987	99	17	(	(	PUNCT
ejpam-3987	99	18	8)	8)	NUM
ejpam-3987	99	19	and	and	CCONJ
ejpam-3987	99	20	setting	set	VERB
ejpam-3987	99	21	a	a	DET
ejpam-3987	99	22	=	=	NOUN
ejpam-3987	99	23	1	1	NUM
ejpam-3987	99	24	,	,	PUNCT
ejpam-3987	99	25	p	p	NOUN
ejpam-3987	99	26	=	=	SYM
ejpam-3987	99	27	1	1	NUM
ejpam-3987	99	28	and	and	CCONJ
ejpam-3987	99	29	n	n	CCONJ
ejpam-3987	99	30	=	=	SYM
ejpam-3987	99	31	2	2	NUM
ejpam-3987	99	32	and	and	CCONJ
ejpam-3987	99	33	simplifying	simplify	VERB
ejpam-3987	99	34	we	we	PRON
ejpam-3987	99	35	get	get	VERB
ejpam-3987	99	36	(	(	PUNCT
ejpam-3987	99	37	12	12	NUM
ejpam-3987	99	38	)	)	PUNCT
ejpam-3987	99	39	∫	∫	PROPN
ejpam-3987	99	40	∞	∞	PROPN
ejpam-3987	99	41	0	0	NUM
ejpam-3987	100	1	∫	∫	PROPN
ejpam-3987	100	2	∞	∞	PROPN
ejpam-3987	100	3	0	0	NUM
ejpam-3987	100	4	e−x	e−x	PROPN
ejpam-3987	100	5	2−y2	2−y2	NUM
ejpam-3987	100	6	logk	logk	NOUN
ejpam-3987	100	7	(	(	PUNCT
ejpam-3987	100	8	x	x	SYM
ejpam-3987	100	9	y	y	PROPN
ejpam-3987	100	10	)	)	PUNCT
ejpam-3987	100	11	dxdy	dxdy	PROPN
ejpam-3987	100	12	=	=	SYM
ejpam-3987	100	13	2k−1e	2k−1e	NUM
ejpam-3987	100	14	iπk	iπk	NOUN
ejpam-3987	100	15	2	2	NUM
ejpam-3987	100	16	πk+1	πk+1	NOUN
ejpam-3987	100	17	(	(	PUNCT
ejpam-3987	100	18	ζ	ζ	NOUN
ejpam-3987	100	19	(	(	PUNCT
ejpam-3987	100	20	−k	−k	PROPN
ejpam-3987	100	21	,	,	PUNCT
ejpam-3987	100	22	1	1	NUM
ejpam-3987	100	23	4	4	NUM
ejpam-3987	100	24	)	)	PUNCT
ejpam-3987	100	25	−	−	NOUN
ejpam-3987	101	1	ζ	ζ	NOUN
ejpam-3987	101	2	(	(	PUNCT
ejpam-3987	101	3	−k	−k	PROPN
ejpam-3987	101	4	,	,	PUNCT
ejpam-3987	101	5	3	3	NUM
ejpam-3987	101	6	4	4	NUM
ejpam-3987	101	7	)	)	PUNCT
ejpam-3987	101	8	)	)	PUNCT
ejpam-3987	101	9	from	from	ADP
ejpam-3987	101	10	equation	equation	NOUN
ejpam-3987	101	11	(	(	PUNCT
ejpam-3987	101	12	64:13:3)in	64:13:3)in	NUM
ejpam-3987	101	13	[	[	X
ejpam-3987	101	14	6	6	NUM
ejpam-3987	101	15	]	]	PUNCT
ejpam-3987	101	16	.	.	PUNCT
ejpam-3987	102	1	r.	r.	PROPN
ejpam-3987	102	2	reynolds	reynolds	PROPN
ejpam-3987	102	3	,	,	PUNCT
ejpam-3987	102	4	a.	a.	PROPN
ejpam-3987	102	5	stauffer	stauffer	PROPN
ejpam-3987	102	6	/	/	SYM
ejpam-3987	102	7	eur	eur	PROPN
ejpam-3987	102	8	.	.	PUNCT
ejpam-3987	103	1	j.	j.	PROPN
ejpam-3987	103	2	pure	pure	PROPN
ejpam-3987	103	3	appl	appl	PROPN
ejpam-3987	103	4	.	.	PROPN
ejpam-3987	103	5	math	math	PROPN
ejpam-3987	103	6	,	,	PUNCT
ejpam-3987	103	7	14	14	NUM
ejpam-3987	103	8	(	(	PUNCT
ejpam-3987	103	9	3	3	NUM
ejpam-3987	103	10	)	)	PUNCT
ejpam-3987	103	11	(	(	PUNCT
ejpam-3987	103	12	2021	2021	NUM
ejpam-3987	103	13	)	)	PUNCT
ejpam-3987	103	14	,	,	PUNCT
ejpam-3987	103	15	618	618	NUM
ejpam-3987	103	16	-	-	SYM
ejpam-3987	103	17	637	637	NUM
ejpam-3987	103	18	622	622	NUM
ejpam-3987	103	19	6.5	6.5	NUM
ejpam-3987	103	20	.	.	PUNCT
ejpam-3987	104	1	derivation	derivation	NOUN
ejpam-3987	104	2	of	of	ADP
ejpam-3987	104	3	new	new	ADJ
ejpam-3987	104	4	entry	entry	NOUN
ejpam-3987	104	5	49	49	NUM
ejpam-3987	104	6	using	use	VERB
ejpam-3987	104	7	equation	equation	NOUN
ejpam-3987	104	8	(	(	PUNCT
ejpam-3987	104	9	8)	8)	NUM
ejpam-3987	104	10	and	and	CCONJ
ejpam-3987	104	11	setting	set	VERB
ejpam-3987	104	12	k	k	PROPN
ejpam-3987	104	13	=	=	PUNCT
ejpam-3987	104	14	−1	−1	NOUN
ejpam-3987	104	15	,	,	PUNCT
ejpam-3987	104	16	n	n	NOUN
ejpam-3987	104	17	=	=	SYM
ejpam-3987	104	18	2	2	NUM
ejpam-3987	104	19	and	and	CCONJ
ejpam-3987	104	20	a	a	DET
ejpam-3987	104	21	=	=	NOUN
ejpam-3987	104	22	−1	−1	NOUN
ejpam-3987	104	23	rationalizing	rationalize	VERB
ejpam-3987	104	24	the	the	DET
ejpam-3987	104	25	denominator	denominator	NOUN
ejpam-3987	104	26	and	and	CCONJ
ejpam-3987	104	27	simplifying	simplify	VERB
ejpam-3987	104	28	we	we	PRON
ejpam-3987	104	29	get∫	get∫	PROPN
ejpam-3987	104	30	∞	∞	PROPN
ejpam-3987	104	31	0	0	NUM
ejpam-3987	105	1	∫	∫	PROPN
ejpam-3987	105	2	∞	∞	PROPN
ejpam-3987	105	3	0	0	PROPN
ejpam-3987	105	4	πxp−1y1−pe−x	πxp−1y1−pe−x	PROPN
ejpam-3987	105	5	2−y2	2−y2	NUM
ejpam-3987	105	6	log2	log2	NOUN
ejpam-3987	105	7	(	(	PUNCT
ejpam-3987	105	8	x	x	NOUN
ejpam-3987	105	9	y	y	PROPN
ejpam-3987	105	10	)	)	PUNCT
ejpam-3987	106	1	+	+	CCONJ
ejpam-3987	106	2	π2	π2	ADJ
ejpam-3987	106	3	dxdy	dxdy	NOUN
ejpam-3987	106	4	=	=	SYM
ejpam-3987	106	5	1	1	NUM
ejpam-3987	106	6	4	4	NUM
ejpam-3987	106	7	(	(	PUNCT
ejpam-3987	106	8	4	4	NUM
ejpam-3987	106	9	sin	sin	NOUN
ejpam-3987	106	10	(	(	PUNCT
ejpam-3987	106	11	πp	πp	ADP
ejpam-3987	106	12	2	2	NUM
ejpam-3987	106	13	)	)	PUNCT
ejpam-3987	107	1	+	+	ADP
ejpam-3987	107	2	π	π	PROPN
ejpam-3987	107	3	cos(πp)−	cos(πp)−	ADJ
ejpam-3987	107	4	2	2	NUM
ejpam-3987	107	5	sin(πp	sin(πp	NOUN
ejpam-3987	107	6	)	)	PUNCT
ejpam-3987	107	7	log	log	NOUN
ejpam-3987	107	8	(	(	PUNCT
ejpam-3987	107	9	cot	cot	NOUN
ejpam-3987	107	10	(	(	PUNCT
ejpam-3987	107	11	πp	πp	ADP
ejpam-3987	107	12	4	4	NUM
ejpam-3987	107	13	)	)	PUNCT
ejpam-3987	107	14	)	)	PUNCT
ejpam-3987	107	15	)	)	PUNCT
ejpam-3987	108	1	(	(	PUNCT
ejpam-3987	108	2	13	13	NUM
ejpam-3987	108	3	)	)	PUNCT
ejpam-3987	108	4	and	and	CCONJ
ejpam-3987	108	5	(	(	PUNCT
ejpam-3987	108	6	14	14	NUM
ejpam-3987	108	7	)	)	PUNCT
ejpam-3987	108	8	∫	∫	PROPN
ejpam-3987	109	1	∞	∞	PROPN
ejpam-3987	109	2	0	0	NUM
ejpam-3987	109	3	∫	∫	PROPN
ejpam-3987	109	4	∞	∞	NOUN
ejpam-3987	109	5	0	0	NUM
ejpam-3987	110	1	xp−1y1−pe−x	xp−1y1−pe−x	NUM
ejpam-3987	110	2	2−y2	2−y2	NUM
ejpam-3987	110	3	log	log	NOUN
ejpam-3987	110	4	(	(	PUNCT
ejpam-3987	110	5	x	x	NOUN
ejpam-3987	110	6	y	y	PROPN
ejpam-3987	110	7	)	)	PUNCT
ejpam-3987	110	8	log2	log2	PROPN
ejpam-3987	110	9	(	(	PUNCT
ejpam-3987	110	10	x	x	NOUN
ejpam-3987	110	11	y	y	PROPN
ejpam-3987	110	12	)	)	PUNCT
ejpam-3987	111	1	+	+	CCONJ
ejpam-3987	111	2	π2	π2	ADJ
ejpam-3987	111	3	dxdy	dxdy	NOUN
ejpam-3987	111	4	=	=	SYM
ejpam-3987	111	5	−1	−1	NOUN
ejpam-3987	111	6	4	4	NUM
ejpam-3987	111	7	π	π	NOUN
ejpam-3987	111	8	sin(πp	sin(πp	X
ejpam-3987	111	9	)	)	PUNCT
ejpam-3987	112	1	+	+	CCONJ
ejpam-3987	112	2	cos	cos	X
ejpam-3987	112	3	(	(	PUNCT
ejpam-3987	112	4	πp	πp	ADP
ejpam-3987	112	5	2	2	NUM
ejpam-3987	112	6	)	)	PUNCT
ejpam-3987	112	7	−	−	NOUN
ejpam-3987	112	8	1	1	NUM
ejpam-3987	112	9	2	2	NUM
ejpam-3987	112	10	cos(πp	cos(πp	PROPN
ejpam-3987	112	11	)	)	PUNCT
ejpam-3987	112	12	log	log	NOUN
ejpam-3987	112	13	(	(	PUNCT
ejpam-3987	112	14	cot	cot	NOUN
ejpam-3987	112	15	(	(	PUNCT
ejpam-3987	112	16	πp	πp	ADP
ejpam-3987	112	17	4	4	NUM
ejpam-3987	112	18	)	)	PUNCT
ejpam-3987	112	19	)	)	PUNCT
ejpam-3987	112	20	from	from	ADP
ejpam-3987	112	21	entry	entry	NOUN
ejpam-3987	112	22	(	(	PUNCT
ejpam-3987	112	23	1	1	NUM
ejpam-3987	112	24	)	)	PUNCT
ejpam-3987	112	25	in	in	ADP
ejpam-3987	112	26	table	table	NOUN
ejpam-3987	112	27	below	below	ADV
ejpam-3987	112	28	(	(	PUNCT
ejpam-3987	112	29	64:12:7	64:12:7	NUM
ejpam-3987	112	30	)	)	PUNCT
ejpam-3987	112	31	6.6	6.6	NUM
ejpam-3987	112	32	.	.	PUNCT
ejpam-3987	113	1	derivation	derivation	NOUN
ejpam-3987	113	2	of	of	ADP
ejpam-3987	113	3	new	new	ADJ
ejpam-3987	113	4	entry	entry	NOUN
ejpam-3987	113	5	50	50	NUM
ejpam-3987	113	6	in	in	ADP
ejpam-3987	113	7	terms	term	NOUN
ejpam-3987	113	8	of	of	ADP
ejpam-3987	113	9	the	the	DET
ejpam-3987	113	10	polylogarithm	polylogarithm	PROPN
ejpam-3987	113	11	function	function	NOUN
ejpam-3987	113	12	using	use	VERB
ejpam-3987	113	13	equation	equation	NOUN
ejpam-3987	113	14	(	(	PUNCT
ejpam-3987	113	15	8)	8)	NUM
ejpam-3987	113	16	and	and	CCONJ
ejpam-3987	113	17	replacing	replace	VERB
ejpam-3987	113	18	a	a	PRON
ejpam-3987	113	19	by	by	ADP
ejpam-3987	113	20	eπi	eπi	PROPN
ejpam-3987	113	21	/	/	SYM
ejpam-3987	113	22	n	n	PROPN
ejpam-3987	113	23	and	and	CCONJ
ejpam-3987	113	24	simplifying	simplify	VERB
ejpam-3987	113	25	we	we	PRON
ejpam-3987	113	26	get	get	VERB
ejpam-3987	113	27	∫	∫	PROPN
ejpam-3987	113	28	∞	∞	PROPN
ejpam-3987	113	29	0	0	NUM
ejpam-3987	114	1	∫	∫	PROPN
ejpam-3987	114	2	∞	∞	PROPN
ejpam-3987	114	3	0	0	NUM
ejpam-3987	115	1	xp−1yn−p−1e−x	xp−1yn−p−1e−x	PROPN
ejpam-3987	115	2	n−yn	n−yn	PROPN
ejpam-3987	115	3	logk	logk	NOUN
ejpam-3987	115	4	(	(	PUNCT
ejpam-3987	115	5	e	e	X
ejpam-3987	115	6	iπ	iπ	NOUN
ejpam-3987	115	7	n	n	PROPN
ejpam-3987	115	8	x	x	SYM
ejpam-3987	115	9	y	y	PROPN
ejpam-3987	115	10	)	)	PUNCT
ejpam-3987	115	11	dxdy	dxdy	PROPN
ejpam-3987	115	12	=	=	SYM
ejpam-3987	115	13	(	(	PUNCT
ejpam-3987	115	14	2π)k+1	2π)k+1	NUM
ejpam-3987	115	15	(	(	PUNCT
ejpam-3987	115	16	i	i	PRON
ejpam-3987	115	17	n	n	X
ejpam-3987	115	18	)	)	PUNCT
ejpam-3987	115	19	k−1	k−1	PROPN
ejpam-3987	115	20	e−	e−	PROPN
ejpam-3987	115	21	iπp	iπp	NOUN
ejpam-3987	115	22	n	n	ADP
ejpam-3987	115	23	li−k	li−k	VERB
ejpam-3987	115	24	(	(	PUNCT
ejpam-3987	115	25	e	e	X
ejpam-3987	115	26	2ipπ	2ipπ	NUM
ejpam-3987	115	27	n	n	NOUN
ejpam-3987	115	28	)	)	PUNCT
ejpam-3987	115	29	n3	n3	NOUN
ejpam-3987	115	30	(	(	PUNCT
ejpam-3987	115	31	15	15	NUM
ejpam-3987	115	32	)	)	PUNCT
ejpam-3987	115	33	from	from	ADP
ejpam-3987	115	34	equation	equation	NOUN
ejpam-3987	115	35	(	(	PUNCT
ejpam-3987	115	36	64:12:2	64:12:2	NUM
ejpam-3987	115	37	)	)	PUNCT
ejpam-3987	115	38	in	in	ADP
ejpam-3987	115	39	[	[	X
ejpam-3987	115	40	6	6	NUM
ejpam-3987	115	41	]	]	PUNCT
ejpam-3987	115	42	.	.	PUNCT
ejpam-3987	116	1	6.7	6.7	NUM
ejpam-3987	116	2	.	.	PUNCT
ejpam-3987	116	3	derivation	derivation	NOUN
ejpam-3987	116	4	of	of	ADP
ejpam-3987	116	5	new	new	ADJ
ejpam-3987	116	6	entry	entry	NOUN
ejpam-3987	116	7	51	51	NUM
ejpam-3987	116	8	in	in	ADP
ejpam-3987	116	9	terms	term	NOUN
ejpam-3987	116	10	of	of	ADP
ejpam-3987	116	11	catalan	catalan	NOUN
ejpam-3987	116	12	’s	’s	PART
ejpam-3987	116	13	constant	constant	ADJ
ejpam-3987	116	14	c	c	NOUN
ejpam-3987	116	15	using	use	VERB
ejpam-3987	116	16	equation	equation	NOUN
ejpam-3987	116	17	(	(	PUNCT
ejpam-3987	116	18	8)	8)	NUM
ejpam-3987	116	19	and	and	CCONJ
ejpam-3987	116	20	setting	set	VERB
ejpam-3987	116	21	a	a	DET
ejpam-3987	116	22	=	=	X
ejpam-3987	116	23	k	k	NOUN
ejpam-3987	116	24	=	=	SYM
ejpam-3987	116	25	1	1	NUM
ejpam-3987	116	26	and	and	CCONJ
ejpam-3987	116	27	replacing	replace	VERB
ejpam-3987	116	28	p	p	NOUN
ejpam-3987	116	29	by	by	ADP
ejpam-3987	116	30	n/2	n/2	NOUN
ejpam-3987	116	31	and	and	CCONJ
ejpam-3987	116	32	simplifying	simplify	VERB
ejpam-3987	116	33	we	we	PRON
ejpam-3987	116	34	get	get	VERB
ejpam-3987	116	35	(	(	PUNCT
ejpam-3987	116	36	16	16	NUM
ejpam-3987	116	37	)	)	PUNCT
ejpam-3987	116	38	∫	∫	PROPN
ejpam-3987	116	39	∞	∞	PROPN
ejpam-3987	116	40	0	0	NUM
ejpam-3987	117	1	∫	∫	PROPN
ejpam-3987	117	2	∞	∞	NUM
ejpam-3987	117	3	0	0	NUM
ejpam-3987	118	1	x	x	SYM
ejpam-3987	118	2	n	n	SYM
ejpam-3987	118	3	2	2	NUM
ejpam-3987	118	4	−1y	−1y	NOUN
ejpam-3987	118	5	n	n	DET
ejpam-3987	118	6	2	2	NUM
ejpam-3987	118	7	−1e−x	−1e−x	NOUN
ejpam-3987	118	8	n−yn	n−yn	NOUN
ejpam-3987	118	9	log	log	NOUN
ejpam-3987	118	10	(	(	PUNCT
ejpam-3987	118	11	x	x	NOUN
ejpam-3987	118	12	y	y	PROPN
ejpam-3987	118	13	)	)	PUNCT
ejpam-3987	118	14	log	log	NOUN
ejpam-3987	118	15	(	(	PUNCT
ejpam-3987	118	16	log	log	NOUN
ejpam-3987	118	17	(	(	PUNCT
ejpam-3987	118	18	x	x	NOUN
ejpam-3987	118	19	y	y	PROPN
ejpam-3987	118	20	)	)	PUNCT
ejpam-3987	118	21	)	)	PUNCT
ejpam-3987	119	1	dxdy	dxdy	PROPN
ejpam-3987	119	2	=	=	SYM
ejpam-3987	119	3	−4iπc	−4iπc	PROPN
ejpam-3987	120	1	n3	n3	NOUN
ejpam-3987	120	2	from	from	ADP
ejpam-3987	120	3	equation	equation	NOUN
ejpam-3987	120	4	(	(	PUNCT
ejpam-3987	120	5	9.73	9.73	NUM
ejpam-3987	120	6	)	)	PUNCT
ejpam-3987	120	7	in	in	ADP
ejpam-3987	120	8	[	[	X
ejpam-3987	120	9	9	9	NUM
ejpam-3987	120	10	]	]	PUNCT
ejpam-3987	120	11	.	.	PUNCT
ejpam-3987	121	1	6.8	6.8	NUM
ejpam-3987	121	2	.	.	PUNCT
ejpam-3987	122	1	derivation	derivation	NOUN
ejpam-3987	122	2	of	of	ADP
ejpam-3987	122	3	new	new	ADJ
ejpam-3987	122	4	entry	entry	NOUN
ejpam-3987	122	5	52	52	NUM
ejpam-3987	122	6	using	use	VERB
ejpam-3987	122	7	equation	equation	NOUN
ejpam-3987	122	8	(	(	PUNCT
ejpam-3987	122	9	8)	8)	NUM
ejpam-3987	122	10	and	and	CCONJ
ejpam-3987	122	11	setting	set	VERB
ejpam-3987	122	12	k	k	PROPN
ejpam-3987	122	13	=	=	SYM
ejpam-3987	122	14	3	3	NUM
ejpam-3987	122	15	and	and	CCONJ
ejpam-3987	122	16	a	a	DET
ejpam-3987	122	17	=	=	X
ejpam-3987	122	18	−1	−1	NOUN
ejpam-3987	122	19	and	and	CCONJ
ejpam-3987	122	20	simplifying	simplify	VERB
ejpam-3987	122	21	we	we	PRON
ejpam-3987	122	22	get	get	VERB
ejpam-3987	122	23	∫	∫	PROPN
ejpam-3987	122	24	∞	∞	PROPN
ejpam-3987	122	25	0	0	NUM
ejpam-3987	123	1	∫	∫	PROPN
ejpam-3987	124	1	∞	∞	PROPN
ejpam-3987	124	2	0	0	NUM
ejpam-3987	125	1	xp−1yn−p−1e−x	xp−1yn−p−1e−x	PROPN
ejpam-3987	125	2	n−yn	n−yn	PROPN
ejpam-3987	125	3	log3	log3	PROPN
ejpam-3987	125	4	(	(	PUNCT
ejpam-3987	125	5	x	x	SYM
ejpam-3987	125	6	y	y	PROPN
ejpam-3987	125	7	)	)	PUNCT
ejpam-3987	125	8	dxdy	dxdy	PROPN
ejpam-3987	125	9	=	=	SYM
ejpam-3987	126	1	−	−	PROPN
ejpam-3987	126	2	π4	π4	NOUN
ejpam-3987	126	3	(	(	PUNCT
ejpam-3987	126	4	23	23	NUM
ejpam-3987	126	5	cos	co	NOUN
ejpam-3987	126	6	(	(	PUNCT
ejpam-3987	126	7	πp	πp	ADP
ejpam-3987	126	8	n	n	X
ejpam-3987	126	9	)	)	PUNCT
ejpam-3987	127	1	+	+	CCONJ
ejpam-3987	127	2	cos	cos	X
ejpam-3987	127	3	(	(	PUNCT
ejpam-3987	127	4	3πp	3πp	ADJ
ejpam-3987	127	5	n	n	PRON
ejpam-3987	127	6	)	)	PUNCT
ejpam-3987	127	7	)	)	PUNCT
ejpam-3987	128	1	csc4	csc4	NOUN
ejpam-3987	128	2	(	(	PUNCT
ejpam-3987	128	3	πp	πp	ADP
ejpam-3987	128	4	n	n	NOUN
ejpam-3987	128	5	)	)	PUNCT
ejpam-3987	128	6	4n5	4n5	NUM
ejpam-3987	128	7	(	(	PUNCT
ejpam-3987	128	8	17	17	NUM
ejpam-3987	128	9	)	)	PUNCT
ejpam-3987	128	10	r.	r.	PROPN
ejpam-3987	128	11	reynolds	reynolds	PROPN
ejpam-3987	128	12	,	,	PUNCT
ejpam-3987	128	13	a.	a.	PROPN
ejpam-3987	128	14	stauffer	stauffer	PROPN
ejpam-3987	128	15	/	/	SYM
ejpam-3987	128	16	eur	eur	PROPN
ejpam-3987	128	17	.	.	PUNCT
ejpam-3987	129	1	j.	j.	PROPN
ejpam-3987	129	2	pure	pure	PROPN
ejpam-3987	129	3	appl	appl	PROPN
ejpam-3987	129	4	.	.	PROPN
ejpam-3987	129	5	math	math	PROPN
ejpam-3987	129	6	,	,	PUNCT
ejpam-3987	129	7	14	14	NUM
ejpam-3987	129	8	(	(	PUNCT
ejpam-3987	129	9	3	3	NUM
ejpam-3987	129	10	)	)	PUNCT
ejpam-3987	129	11	(	(	PUNCT
ejpam-3987	129	12	2021	2021	NUM
ejpam-3987	129	13	)	)	PUNCT
ejpam-3987	129	14	,	,	PUNCT
ejpam-3987	129	15	618	618	NUM
ejpam-3987	129	16	-	-	SYM
ejpam-3987	129	17	637	637	NUM
ejpam-3987	129	18	623	623	NUM
ejpam-3987	129	19	6.9	6.9	NUM
ejpam-3987	129	20	.	.	PUNCT
ejpam-3987	130	1	derivation	derivation	NOUN
ejpam-3987	130	2	of	of	ADP
ejpam-3987	130	3	new	new	ADJ
ejpam-3987	130	4	entry	entry	NOUN
ejpam-3987	130	5	53	53	NUM
ejpam-3987	130	6	in	in	ADP
ejpam-3987	130	7	terms	term	NOUN
ejpam-3987	130	8	of	of	ADP
ejpam-3987	130	9	the	the	DET
ejpam-3987	130	10	log	log	NOUN
ejpam-3987	130	11	-	-	PUNCT
ejpam-3987	130	12	gamma	gamma	NOUN
ejpam-3987	130	13	function	function	NOUN
ejpam-3987	130	14	using	use	VERB
ejpam-3987	130	15	equation	equation	NOUN
ejpam-3987	130	16	(	(	PUNCT
ejpam-3987	130	17	8)	8)	NUM
ejpam-3987	130	18	and	and	CCONJ
ejpam-3987	130	19	first	first	ADV
ejpam-3987	130	20	replacing	replace	VERB
ejpam-3987	130	21	p	p	NOUN
ejpam-3987	130	22	by	by	ADP
ejpam-3987	130	23	n/2	n/2	NOUN
ejpam-3987	130	24	followed	follow	VERB
ejpam-3987	130	25	by	by	ADP
ejpam-3987	130	26	taking	take	VERB
ejpam-3987	130	27	the	the	DET
ejpam-3987	130	28	first	first	ADJ
ejpam-3987	130	29	partial	partial	ADJ
ejpam-3987	130	30	derivative	derivative	NOUN
ejpam-3987	130	31	with	with	ADP
ejpam-3987	130	32	respect	respect	NOUN
ejpam-3987	130	33	to	to	ADP
ejpam-3987	130	34	k	k	PROPN
ejpam-3987	130	35	and	and	CCONJ
ejpam-3987	130	36	then	then	ADV
ejpam-3987	130	37	setting	set	VERB
ejpam-3987	130	38	k	k	PROPN
ejpam-3987	130	39	=	=	PUNCT
ejpam-3987	130	40	0	0	PUNCT
ejpam-3987	130	41	and	and	CCONJ
ejpam-3987	130	42	simplifying	simplify	VERB
ejpam-3987	130	43	we	we	PRON
ejpam-3987	130	44	get	get	VERB
ejpam-3987	130	45	(	(	PUNCT
ejpam-3987	130	46	18	18	NUM
ejpam-3987	130	47	)	)	PUNCT
ejpam-3987	130	48	∫	∫	PROPN
ejpam-3987	131	1	∞	∞	PROPN
ejpam-3987	131	2	0	0	NUM
ejpam-3987	132	1	∫	∫	PROPN
ejpam-3987	132	2	∞	∞	NUM
ejpam-3987	132	3	0	0	NUM
ejpam-3987	133	1	x	x	SYM
ejpam-3987	133	2	n	n	SYM
ejpam-3987	133	3	2	2	NUM
ejpam-3987	133	4	−1y	−1y	NOUN
ejpam-3987	133	5	n	n	DET
ejpam-3987	133	6	2	2	NUM
ejpam-3987	133	7	−1e−x	−1e−x	NOUN
ejpam-3987	133	8	n−yn	n−yn	NOUN
ejpam-3987	133	9	log	log	NOUN
ejpam-3987	133	10	(	(	PUNCT
ejpam-3987	133	11	log	log	NOUN
ejpam-3987	133	12	(	(	PUNCT
ejpam-3987	133	13	ax	ax	NOUN
ejpam-3987	133	14	y	y	PROPN
ejpam-3987	133	15	)	)	PUNCT
ejpam-3987	133	16	)	)	PUNCT
ejpam-3987	134	1	dxdy	dxdy	PROPN
ejpam-3987	134	2	=	=	SYM
ejpam-3987	134	3	2π	2π	NOUN
ejpam-3987	134	4	log	log	VERB
ejpam-3987	134	5	(	(	PUNCT
ejpam-3987	134	6	2	2	NUM
ejpam-3987	134	7	√	√	PROPN
ejpam-3987	134	8	π	π	PUNCT
ejpam-3987	134	9	√	√	VERB
ejpam-3987	135	1	i	i	PRON
ejpam-3987	135	2	n	n	VERB
ejpam-3987	135	3	γ	γ	X
ejpam-3987	135	4	(	(	PUNCT
ejpam-3987	135	5	3	3	NUM
ejpam-3987	135	6	4	4	NUM
ejpam-3987	135	7	−	−	NOUN
ejpam-3987	135	8	in	in	ADP
ejpam-3987	135	9	log(a	log(a	PROPN
ejpam-3987	135	10	)	)	PUNCT
ejpam-3987	135	11	4π	4π	NUM
ejpam-3987	135	12	)	)	PUNCT
ejpam-3987	135	13	γ	γ	PROPN
ejpam-3987	135	14	(	(	PUNCT
ejpam-3987	135	15	π−in	π−in	PROPN
ejpam-3987	135	16	log(a	log(a	PROPN
ejpam-3987	135	17	)	)	PUNCT
ejpam-3987	135	18	4π	4π	NUM
ejpam-3987	135	19	)	)	PUNCT
ejpam-3987	135	20	)	)	PUNCT
ejpam-3987	136	1	n2	n2	NOUN
ejpam-3987	136	2	from	from	ADP
ejpam-3987	136	3	equation	equation	NOUN
ejpam-3987	136	4	(	(	PUNCT
ejpam-3987	136	5	1.10.10	1.10.10	NUM
ejpam-3987	136	6	)	)	PUNCT
ejpam-3987	136	7	in	in	ADP
ejpam-3987	136	8	[	[	X
ejpam-3987	136	9	2	2	NUM
ejpam-3987	136	10	]	]	PUNCT
ejpam-3987	136	11	.	.	PUNCT
ejpam-3987	137	1	6.10	6.10	NUM
ejpam-3987	137	2	.	.	PUNCT
ejpam-3987	138	1	derivation	derivation	NOUN
ejpam-3987	138	2	of	of	ADP
ejpam-3987	138	3	new	new	ADJ
ejpam-3987	138	4	entry	entry	NOUN
ejpam-3987	138	5	54	54	NUM
ejpam-3987	138	6	using	use	VERB
ejpam-3987	138	7	equation	equation	NOUN
ejpam-3987	138	8	(	(	PUNCT
ejpam-3987	138	9	8)	8)	NUM
ejpam-3987	138	10	and	and	CCONJ
ejpam-3987	138	11	first	first	ADV
ejpam-3987	138	12	replacing	replace	VERB
ejpam-3987	138	13	p	p	NOUN
ejpam-3987	138	14	by	by	ADP
ejpam-3987	138	15	n/2	n/2	NOUN
ejpam-3987	138	16	followed	follow	VERB
ejpam-3987	138	17	by	by	ADP
ejpam-3987	138	18	taking	take	VERB
ejpam-3987	138	19	the	the	DET
ejpam-3987	138	20	first	first	ADJ
ejpam-3987	138	21	partial	partial	ADJ
ejpam-3987	138	22	derivative	derivative	NOUN
ejpam-3987	138	23	with	with	ADP
ejpam-3987	138	24	respect	respect	NOUN
ejpam-3987	138	25	to	to	ADP
ejpam-3987	138	26	a	a	PRON
ejpam-3987	138	27	and	and	CCONJ
ejpam-3987	138	28	then	then	ADV
ejpam-3987	138	29	setting	set	VERB
ejpam-3987	138	30	k	k	PROPN
ejpam-3987	138	31	=	=	SYM
ejpam-3987	138	32	2	2	NUM
ejpam-3987	138	33	and	and	CCONJ
ejpam-3987	138	34	a	a	DET
ejpam-3987	138	35	=	=	SYM
ejpam-3987	138	36	1	1	NUM
ejpam-3987	138	37	and	and	CCONJ
ejpam-3987	138	38	simplifying	simplify	VERB
ejpam-3987	138	39	we	we	PRON
ejpam-3987	138	40	get	get	VERB
ejpam-3987	138	41	(	(	PUNCT
ejpam-3987	138	42	19	19	NUM
ejpam-3987	138	43	)	)	PUNCT
ejpam-3987	138	44	∫	∫	PROPN
ejpam-3987	139	1	∞	∞	PROPN
ejpam-3987	139	2	0	0	NUM
ejpam-3987	140	1	∫	∫	PROPN
ejpam-3987	140	2	∞	∞	NUM
ejpam-3987	140	3	0	0	NUM
ejpam-3987	141	1	x	x	SYM
ejpam-3987	141	2	n	n	SYM
ejpam-3987	141	3	2	2	NUM
ejpam-3987	141	4	−1y	−1y	NOUN
ejpam-3987	141	5	n	n	DET
ejpam-3987	141	6	2	2	NUM
ejpam-3987	141	7	−1e−x	−1e−x	NOUN
ejpam-3987	141	8	n−yn	n−yn	NOUN
ejpam-3987	141	9	log	log	NOUN
ejpam-3987	141	10	(	(	PUNCT
ejpam-3987	141	11	x	x	SYM
ejpam-3987	141	12	y	y	PROPN
ejpam-3987	141	13	)	)	PUNCT
ejpam-3987	141	14	dxdy	dxdy	PROPN
ejpam-3987	141	15	=	=	PUNCT
ejpam-3987	141	16	0	0	NUM
ejpam-3987	141	17	where	where	SCONJ
ejpam-3987	141	18	n	n	X
ejpam-3987	141	19	∈	∈	PROPN
ejpam-3987	141	20	c.	c.	PROPN
ejpam-3987	141	21	6.11	6.11	NUM
ejpam-3987	141	22	.	.	PUNCT
ejpam-3987	142	1	derivation	derivation	NOUN
ejpam-3987	142	2	of	of	ADP
ejpam-3987	142	3	new	new	ADJ
ejpam-3987	142	4	entry	entry	NOUN
ejpam-3987	142	5	55	55	NUM
ejpam-3987	142	6	in	in	ADP
ejpam-3987	142	7	terms	term	NOUN
ejpam-3987	142	8	of	of	ADP
ejpam-3987	142	9	euler	euler	PROPN
ejpam-3987	142	10	’s	’s	PART
ejpam-3987	142	11	constant	constant	ADJ
ejpam-3987	142	12	using	use	VERB
ejpam-3987	142	13	equation	equation	NOUN
ejpam-3987	142	14	(	(	PUNCT
ejpam-3987	142	15	8)	8)	NUM
ejpam-3987	142	16	and	and	CCONJ
ejpam-3987	142	17	setting	set	VERB
ejpam-3987	142	18	p	p	X
ejpam-3987	142	19	=	=	SYM
ejpam-3987	142	20	1/2	1/2	NUM
ejpam-3987	142	21	,	,	PUNCT
ejpam-3987	142	22	a	a	DET
ejpam-3987	142	23	=	=	X
ejpam-3987	142	24	−1	−1	NOUN
ejpam-3987	142	25	and	and	CCONJ
ejpam-3987	142	26	n	n	NOUN
ejpam-3987	142	27	=	=	SYM
ejpam-3987	142	28	1	1	NUM
ejpam-3987	142	29	followed	follow	VERB
ejpam-3987	142	30	by	by	ADP
ejpam-3987	142	31	taking	take	VERB
ejpam-3987	142	32	the	the	DET
ejpam-3987	142	33	first	first	ADJ
ejpam-3987	142	34	partial	partial	ADJ
ejpam-3987	142	35	derivative	derivative	NOUN
ejpam-3987	142	36	with	with	ADP
ejpam-3987	142	37	respect	respect	NOUN
ejpam-3987	142	38	to	to	ADP
ejpam-3987	142	39	k	k	PROPN
ejpam-3987	142	40	and	and	CCONJ
ejpam-3987	142	41	then	then	ADV
ejpam-3987	142	42	setting	set	VERB
ejpam-3987	142	43	k	k	PROPN
ejpam-3987	142	44	=	=	PUNCT
ejpam-3987	142	45	−1	−1	NOUN
ejpam-3987	142	46	and	and	CCONJ
ejpam-3987	142	47	simplifying	simplify	VERB
ejpam-3987	142	48	we	we	PRON
ejpam-3987	142	49	get	get	VERB
ejpam-3987	142	50	(	(	PUNCT
ejpam-3987	142	51	20	20	NUM
ejpam-3987	142	52	)	)	PUNCT
ejpam-3987	142	53	∫	∫	PROPN
ejpam-3987	142	54	∞	∞	PROPN
ejpam-3987	142	55	0	0	NUM
ejpam-3987	143	1	∫	∫	PROPN
ejpam-3987	143	2	∞	∞	PROPN
ejpam-3987	143	3	0	0	NUM
ejpam-3987	144	1	e−x−y	e−x−y	NOUN
ejpam-3987	144	2	log	log	NOUN
ejpam-3987	144	3	(	(	PUNCT
ejpam-3987	144	4	log	log	NOUN
ejpam-3987	144	5	(	(	PUNCT
ejpam-3987	144	6	−x	−x	NOUN
ejpam-3987	144	7	y	y	PROPN
ejpam-3987	144	8	)	)	PUNCT
ejpam-3987	144	9	)	)	PUNCT
ejpam-3987	145	1	√	√	NUM
ejpam-3987	145	2	x	x	SYM
ejpam-3987	145	3	√	√	PROPN
ejpam-3987	145	4	y	y	PROPN
ejpam-3987	145	5	log	log	NOUN
ejpam-3987	145	6	(	(	PUNCT
ejpam-3987	145	7	−x	−x	NOUN
ejpam-3987	145	8	y	y	PROPN
ejpam-3987	145	9	)	)	PUNCT
ejpam-3987	145	10	dxdy	dxdy	PROPN
ejpam-3987	145	11	=	=	NOUN
ejpam-3987	145	12	1	1	NUM
ejpam-3987	145	13	2	2	NUM
ejpam-3987	145	14	log(2	log(2	NOUN
ejpam-3987	145	15	)	)	PUNCT
ejpam-3987	145	16	(	(	PUNCT
ejpam-3987	145	17	2iγ	2iγ	ADJ
ejpam-3987	146	1	+	+	CCONJ
ejpam-3987	146	2	π	π	PROPN
ejpam-3987	146	3	−	−	NOUN
ejpam-3987	147	1	i	i	PRON
ejpam-3987	147	2	log	log	VERB
ejpam-3987	147	3	(	(	PUNCT
ejpam-3987	147	4	8π2	8π2	NUM
ejpam-3987	147	5	)	)	PUNCT
ejpam-3987	147	6	)	)	PUNCT
ejpam-3987	147	7	from	from	ADP
ejpam-3987	147	8	equation	equation	NOUN
ejpam-3987	147	9	(	(	PUNCT
ejpam-3987	147	10	9.73	9.73	NUM
ejpam-3987	147	11	)	)	PUNCT
ejpam-3987	147	12	in	in	ADP
ejpam-3987	147	13	[	[	X
ejpam-3987	147	14	9	9	NUM
ejpam-3987	147	15	]	]	SYM
ejpam-3987	147	16	.	.	PUNCT
ejpam-3987	148	1	6.12	6.12	NUM
ejpam-3987	148	2	.	.	PUNCT
ejpam-3987	148	3	derivation	derivation	NOUN
ejpam-3987	148	4	of	of	ADP
ejpam-3987	148	5	new	new	ADJ
ejpam-3987	148	6	entry	entry	NOUN
ejpam-3987	148	7	56	56	NUM
ejpam-3987	148	8	in	in	ADP
ejpam-3987	148	9	terms	term	NOUN
ejpam-3987	148	10	of	of	ADP
ejpam-3987	148	11	the	the	DET
ejpam-3987	148	12	derivative	derivative	NOUN
ejpam-3987	148	13	of	of	ADP
ejpam-3987	148	14	the	the	DET
ejpam-3987	148	15	hurwitz	hurwitz	PROPN
ejpam-3987	148	16	zeta	zeta	PROPN
ejpam-3987	148	17	function	function	NOUN
ejpam-3987	148	18	using	use	VERB
ejpam-3987	148	19	equation	equation	NOUN
ejpam-3987	148	20	(	(	PUNCT
ejpam-3987	148	21	8)	8)	NUM
ejpam-3987	148	22	and	and	CCONJ
ejpam-3987	148	23	setting	set	VERB
ejpam-3987	148	24	p	p	NOUN
ejpam-3987	148	25	=	=	NOUN
ejpam-3987	148	26	1	1	NUM
ejpam-3987	148	27	,	,	PUNCT
ejpam-3987	148	28	a	a	DET
ejpam-3987	148	29	=	=	SYM
ejpam-3987	148	30	1	1	NUM
ejpam-3987	148	31	and	and	CCONJ
ejpam-3987	148	32	n	n	CCONJ
ejpam-3987	148	33	=	=	SYM
ejpam-3987	148	34	2	2	NUM
ejpam-3987	148	35	followed	follow	VERB
ejpam-3987	148	36	by	by	ADP
ejpam-3987	148	37	taking	take	VERB
ejpam-3987	148	38	the	the	DET
ejpam-3987	148	39	first	first	ADJ
ejpam-3987	148	40	partial	partial	ADJ
ejpam-3987	148	41	derivative	derivative	NOUN
ejpam-3987	148	42	with	with	ADP
ejpam-3987	148	43	respect	respect	NOUN
ejpam-3987	148	44	to	to	ADP
ejpam-3987	148	45	k	k	PROPN
ejpam-3987	148	46	and	and	CCONJ
ejpam-3987	148	47	then	then	ADV
ejpam-3987	148	48	setting	set	VERB
ejpam-3987	148	49	k	k	PROPN
ejpam-3987	148	50	=	=	SYM
ejpam-3987	148	51	2	2	NUM
ejpam-3987	148	52	and	and	CCONJ
ejpam-3987	148	53	simplifying	simplify	VERB
ejpam-3987	148	54	we	we	PRON
ejpam-3987	148	55	get	get	VERB
ejpam-3987	148	56	(	(	PUNCT
ejpam-3987	148	57	21	21	NUM
ejpam-3987	148	58	)	)	PUNCT
ejpam-3987	148	59	∫	∫	PROPN
ejpam-3987	149	1	∞	∞	PROPN
ejpam-3987	149	2	0	0	NUM
ejpam-3987	150	1	∫	∫	PROPN
ejpam-3987	150	2	∞	∞	PROPN
ejpam-3987	150	3	0	0	NUM
ejpam-3987	151	1	e−x	e−x	PROPN
ejpam-3987	151	2	2−y2	2−y2	NUM
ejpam-3987	151	3	log2	log2	NOUN
ejpam-3987	151	4	(	(	PUNCT
ejpam-3987	151	5	x	x	SYM
ejpam-3987	151	6	y	y	PROPN
ejpam-3987	151	7	)	)	PUNCT
ejpam-3987	151	8	log	log	NOUN
ejpam-3987	151	9	(	(	PUNCT
ejpam-3987	151	10	log	log	NOUN
ejpam-3987	151	11	(	(	PUNCT
ejpam-3987	151	12	x	x	NOUN
ejpam-3987	151	13	y	y	PROPN
ejpam-3987	151	14	)	)	PUNCT
ejpam-3987	151	15	)	)	PUNCT
ejpam-3987	151	16	dxdy	dxdy	NOUN
ejpam-3987	151	17	=	=	NOUN
ejpam-3987	151	18	1	1	NUM
ejpam-3987	151	19	32	32	NUM
ejpam-3987	151	20	π3	π3	NOUN
ejpam-3987	151	21	(	(	PUNCT
ejpam-3987	151	22	64	64	NUM
ejpam-3987	151	23	(	(	PUNCT
ejpam-3987	151	24	ζ	ζ	NOUN
ejpam-3987	151	25	′	′	NUM
ejpam-3987	151	26	(	(	PUNCT
ejpam-3987	151	27	−2	−2	NOUN
ejpam-3987	151	28	,	,	PUNCT
ejpam-3987	151	29	1	1	NUM
ejpam-3987	151	30	4	4	NUM
ejpam-3987	151	31	)	)	PUNCT
ejpam-3987	151	32	−	−	NOUN
ejpam-3987	152	1	ζ	ζ	NOUN
ejpam-3987	152	2	′	′	NOUN
ejpam-3987	152	3	(	(	PUNCT
ejpam-3987	152	4	−2	−2	NOUN
ejpam-3987	152	5	,	,	PUNCT
ejpam-3987	152	6	3	3	NUM
ejpam-3987	152	7	4	4	NUM
ejpam-3987	152	8	)	)	PUNCT
ejpam-3987	152	9	)	)	PUNCT
ejpam-3987	153	1	+	+	CCONJ
ejpam-3987	153	2	iπ	iπ	PRON
ejpam-3987	153	3	+	+	NUM
ejpam-3987	153	4	log	log	NOUN
ejpam-3987	153	5	(	(	PUNCT
ejpam-3987	153	6	4π2	4π2	NUM
ejpam-3987	153	7	)	)	PUNCT
ejpam-3987	153	8	)	)	PUNCT
ejpam-3987	153	9	from	from	ADP
ejpam-3987	153	10	equation	equation	NOUN
ejpam-3987	153	11	(	(	PUNCT
ejpam-3987	153	12	64:10:1	64:10:1	NUM
ejpam-3987	153	13	)	)	PUNCT
ejpam-3987	153	14	in	in	ADP
ejpam-3987	153	15	[	[	X
ejpam-3987	153	16	6	6	NUM
ejpam-3987	153	17	]	]	PUNCT
ejpam-3987	153	18	.	.	PUNCT
ejpam-3987	154	1	r.	r.	PROPN
ejpam-3987	154	2	reynolds	reynolds	PROPN
ejpam-3987	154	3	,	,	PUNCT
ejpam-3987	154	4	a.	a.	PROPN
ejpam-3987	154	5	stauffer	stauffer	PROPN
ejpam-3987	154	6	/	/	SYM
ejpam-3987	154	7	eur	eur	PROPN
ejpam-3987	154	8	.	.	PUNCT
ejpam-3987	155	1	j.	j.	PROPN
ejpam-3987	155	2	pure	pure	PROPN
ejpam-3987	155	3	appl	appl	PROPN
ejpam-3987	155	4	.	.	PROPN
ejpam-3987	155	5	math	math	PROPN
ejpam-3987	155	6	,	,	PUNCT
ejpam-3987	155	7	14	14	NUM
ejpam-3987	155	8	(	(	PUNCT
ejpam-3987	155	9	3	3	NUM
ejpam-3987	155	10	)	)	PUNCT
ejpam-3987	155	11	(	(	PUNCT
ejpam-3987	155	12	2021	2021	NUM
ejpam-3987	155	13	)	)	PUNCT
ejpam-3987	155	14	,	,	PUNCT
ejpam-3987	155	15	618	618	NUM
ejpam-3987	155	16	-	-	SYM
ejpam-3987	155	17	637	637	NUM
ejpam-3987	155	18	624	624	NUM
ejpam-3987	155	19	6.13	6.13	NUM
ejpam-3987	155	20	.	.	PUNCT
ejpam-3987	156	1	derivation	derivation	NOUN
ejpam-3987	156	2	of	of	ADP
ejpam-3987	156	3	new	new	ADJ
ejpam-3987	156	4	entry	entry	NOUN
ejpam-3987	156	5	57	57	NUM
ejpam-3987	156	6	in	in	ADP
ejpam-3987	156	7	terms	term	NOUN
ejpam-3987	156	8	of	of	ADP
ejpam-3987	156	9	the	the	DET
ejpam-3987	156	10	hurwitz	hurwitz	PROPN
ejpam-3987	156	11	zeta	zeta	PROPN
ejpam-3987	156	12	function	function	NOUN
ejpam-3987	156	13	using	use	VERB
ejpam-3987	156	14	equation	equation	NOUN
ejpam-3987	156	15	(	(	PUNCT
ejpam-3987	156	16	8)	8)	NUM
ejpam-3987	156	17	and	and	CCONJ
ejpam-3987	156	18	setting	set	VERB
ejpam-3987	156	19	k	k	X
ejpam-3987	156	20	=	=	SYM
ejpam-3987	156	21	1/2	1/2	NUM
ejpam-3987	156	22	,	,	PUNCT
ejpam-3987	156	23	a	a	DET
ejpam-3987	156	24	=	=	X
ejpam-3987	156	25	p	p	NOUN
ejpam-3987	156	26	=	=	SYM
ejpam-3987	156	27	1	1	NUM
ejpam-3987	156	28	and	and	CCONJ
ejpam-3987	156	29	n	n	CCONJ
ejpam-3987	156	30	=	=	SYM
ejpam-3987	156	31	2	2	NUM
ejpam-3987	156	32	and	and	CCONJ
ejpam-3987	156	33	simplifying	simplify	VERB
ejpam-3987	156	34	we	we	PRON
ejpam-3987	156	35	get	get	VERB
ejpam-3987	156	36	(	(	PUNCT
ejpam-3987	156	37	22	22	NUM
ejpam-3987	156	38	)	)	PUNCT
ejpam-3987	156	39	∫	∫	PROPN
ejpam-3987	157	1	∞	∞	PROPN
ejpam-3987	157	2	0	0	NUM
ejpam-3987	158	1	∫	∫	PROPN
ejpam-3987	158	2	∞	∞	NOUN
ejpam-3987	158	3	0	0	NUM
ejpam-3987	159	1	e−x	e−x	PROPN
ejpam-3987	159	2	2−y2	2−y2	NUM
ejpam-3987	159	3	√	√	NUM
ejpam-3987	159	4	log	log	NOUN
ejpam-3987	159	5	(	(	PUNCT
ejpam-3987	159	6	x	x	SYM
ejpam-3987	159	7	y	y	PROPN
ejpam-3987	159	8	)	)	PUNCT
ejpam-3987	159	9	dxdy	dxdy	PROPN
ejpam-3987	159	10	=	=	PUNCT
ejpam-3987	160	1	(	(	PUNCT
ejpam-3987	160	2	1	1	NUM
ejpam-3987	160	3	2	2	NUM
ejpam-3987	160	4	+	+	CCONJ
ejpam-3987	160	5	i	i	PROPN
ejpam-3987	160	6	2	2	X
ejpam-3987	160	7	)	)	PUNCT
ejpam-3987	160	8	π3/2	π3/2	NOUN
ejpam-3987	160	9	(	(	PUNCT
ejpam-3987	160	10	ζ	ζ	X
ejpam-3987	160	11	(	(	PUNCT
ejpam-3987	160	12	−1	−1	NOUN
ejpam-3987	160	13	2	2	NUM
ejpam-3987	160	14	1	1	NUM
ejpam-3987	160	15	4	4	NUM
ejpam-3987	160	16	)	)	PUNCT
ejpam-3987	160	17	−	−	PROPN
ejpam-3987	161	1	ζ	ζ	NOUN
ejpam-3987	161	2	(	(	PUNCT
ejpam-3987	161	3	−1	−1	NOUN
ejpam-3987	161	4	2	2	NUM
ejpam-3987	161	5	,	,	PUNCT
ejpam-3987	161	6	3	3	NUM
ejpam-3987	161	7	4	4	NUM
ejpam-3987	161	8	)	)	PUNCT
ejpam-3987	161	9	)	)	PUNCT
ejpam-3987	161	10	from	from	ADP
ejpam-3987	161	11	equation	equation	NOUN
ejpam-3987	161	12	(	(	PUNCT
ejpam-3987	161	13	64:13:3	64:13:3	NUM
ejpam-3987	161	14	)	)	PUNCT
ejpam-3987	161	15	in	in	ADP
ejpam-3987	161	16	[	[	X
ejpam-3987	161	17	6	6	NUM
ejpam-3987	161	18	]	]	PUNCT
ejpam-3987	161	19	.	.	PUNCT
ejpam-3987	162	1	6.14	6.14	NUM
ejpam-3987	162	2	.	.	PUNCT
ejpam-3987	163	1	derivation	derivation	NOUN
ejpam-3987	163	2	of	of	ADP
ejpam-3987	163	3	new	new	ADJ
ejpam-3987	163	4	entry	entry	NOUN
ejpam-3987	163	5	58	58	NUM
ejpam-3987	163	6	in	in	ADP
ejpam-3987	163	7	terms	term	NOUN
ejpam-3987	163	8	of	of	ADP
ejpam-3987	163	9	log(2	log(2	NOUN
ejpam-3987	163	10	)	)	PUNCT
ejpam-3987	163	11	,	,	PUNCT
ejpam-3987	163	12	ζ(3	ζ(3	PROPN
ejpam-3987	163	13	)	)	PUNCT
ejpam-3987	163	14	,	,	PUNCT
ejpam-3987	163	15	glaisher	glaisher	PROPN
ejpam-3987	163	16	’s	’s	PROPN
ejpam-3987	163	17	constant	constant	ADJ
ejpam-3987	163	18	a	a	PRON
ejpam-3987	163	19	and	and	CCONJ
ejpam-3987	163	20	π	π	NOUN
ejpam-3987	163	21	using	use	VERB
ejpam-3987	163	22	equation	equation	NOUN
ejpam-3987	163	23	(	(	PUNCT
ejpam-3987	163	24	8)	8)	NUM
ejpam-3987	163	25	and	and	CCONJ
ejpam-3987	163	26	setting	set	VERB
ejpam-3987	163	27	p	p	NOUN
ejpam-3987	163	28	=	=	SYM
ejpam-3987	163	29	1/2	1/2	NUM
ejpam-3987	163	30	,	,	PUNCT
ejpam-3987	163	31	n	n	NOUN
ejpam-3987	163	32	=	=	SYM
ejpam-3987	163	33	1	1	NUM
ejpam-3987	163	34	and	and	CCONJ
ejpam-3987	163	35	a	a	DET
ejpam-3987	163	36	=	=	X
ejpam-3987	163	37	−1	−1	NOUN
ejpam-3987	163	38	and	and	CCONJ
ejpam-3987	163	39	simplifying	simplify	VERB
ejpam-3987	163	40	we	we	PRON
ejpam-3987	163	41	get	get	VERB
ejpam-3987	163	42	(	(	PUNCT
ejpam-3987	163	43	23	23	NUM
ejpam-3987	163	44	)	)	PUNCT
ejpam-3987	163	45	∫	∫	PROPN
ejpam-3987	164	1	∞	∞	PROPN
ejpam-3987	164	2	0	0	NUM
ejpam-3987	165	1	∫	∫	PROPN
ejpam-3987	165	2	∞	∞	PROPN
ejpam-3987	165	3	0	0	PROPN
ejpam-3987	166	1	e−x−y	e−x−y	NOUN
ejpam-3987	166	2	logk	logk	NOUN
ejpam-3987	166	3	(	(	PUNCT
ejpam-3987	166	4	−x	−x	NOUN
ejpam-3987	166	5	y	y	PROPN
ejpam-3987	166	6	)	)	PUNCT
ejpam-3987	167	1	√	√	PROPN
ejpam-3987	167	2	x	x	SYM
ejpam-3987	167	3	√	√	NUM
ejpam-3987	167	4	y	y	PROPN
ejpam-3987	167	5	dxdy	dxdy	PROPN
ejpam-3987	167	6	=	=	SYM
ejpam-3987	167	7	−ik	−ik	NOUN
ejpam-3987	167	8	(	(	PUNCT
ejpam-3987	167	9	2k+1	2k+1	NOUN
ejpam-3987	167	10	−	−	NOUN
ejpam-3987	167	11	1	1	NUM
ejpam-3987	167	12	)	)	PUNCT
ejpam-3987	167	13	(	(	PUNCT
ejpam-3987	167	14	2π)k+1ζ(−k	2π)k+1ζ(−k	NOUN
ejpam-3987	167	15	)	)	PUNCT
ejpam-3987	167	16	from	from	ADP
ejpam-3987	167	17	entry	entry	NOUN
ejpam-3987	167	18	(	(	PUNCT
ejpam-3987	167	19	3	3	NUM
ejpam-3987	167	20	)	)	PUNCT
ejpam-3987	167	21	in	in	ADP
ejpam-3987	167	22	table	table	NOUN
ejpam-3987	167	23	below	below	ADV
ejpam-3987	167	24	(	(	PUNCT
ejpam-3987	167	25	64:12:7	64:12:7	NUM
ejpam-3987	167	26	)	)	PUNCT
ejpam-3987	167	27	,	,	PUNCT
ejpam-3987	167	28	equation	equation	NOUN
ejpam-3987	167	29	(	(	PUNCT
ejpam-3987	167	30	64:13:4	64:13:4	NUM
ejpam-3987	167	31	)	)	PUNCT
ejpam-3987	167	32	and	and	CCONJ
ejpam-3987	167	33	entry	entry	NOUN
ejpam-3987	167	34	(	(	PUNCT
ejpam-3987	167	35	2	2	NUM
ejpam-3987	167	36	)	)	PUNCT
ejpam-3987	167	37	in	in	ADP
ejpam-3987	167	38	table	table	NOUN
ejpam-3987	167	39	below	below	ADV
ejpam-3987	167	40	(	(	PUNCT
ejpam-3987	167	41	64:7	64:7	NUM
ejpam-3987	167	42	)	)	PUNCT
ejpam-3987	167	43	in	in	ADP
ejpam-3987	167	44	[	[	X
ejpam-3987	167	45	6	6	NUM
ejpam-3987	167	46	]	]	PUNCT
ejpam-3987	167	47	.	.	PUNCT
ejpam-3987	168	1	next	next	ADV
ejpam-3987	168	2	we	we	PRON
ejpam-3987	168	3	apply	apply	VERB
ejpam-3987	168	4	l’hopital	l’hopital	PROPN
ejpam-3987	168	5	’s	’s	PART
ejpam-3987	168	6	rule	rule	NOUN
ejpam-3987	168	7	to	to	ADP
ejpam-3987	168	8	the	the	DET
ejpam-3987	168	9	right	right	ADJ
ejpam-3987	168	10	-	-	PUNCT
ejpam-3987	168	11	hand	hand	NOUN
ejpam-3987	168	12	side	side	NOUN
ejpam-3987	168	13	of	of	ADP
ejpam-3987	168	14	equation	equation	NOUN
ejpam-3987	168	15	(	(	PUNCT
ejpam-3987	168	16	23	23	NUM
ejpam-3987	168	17	)	)	PUNCT
ejpam-3987	168	18	as	as	ADP
ejpam-3987	168	19	k	k	PROPN
ejpam-3987	168	20	→	→	SYM
ejpam-3987	168	21	−1	−1	NOUN
ejpam-3987	168	22	and	and	CCONJ
ejpam-3987	168	23	simplifying	simplify	VERB
ejpam-3987	168	24	we	we	PRON
ejpam-3987	168	25	get	get	VERB
ejpam-3987	168	26	(	(	PUNCT
ejpam-3987	168	27	24	24	NUM
ejpam-3987	168	28	)	)	PUNCT
ejpam-3987	168	29	∫	∫	PROPN
ejpam-3987	169	1	∞	∞	PROPN
ejpam-3987	169	2	0	0	NUM
ejpam-3987	170	1	∫	∫	PROPN
ejpam-3987	170	2	∞	∞	PROPN
ejpam-3987	170	3	0	0	NUM
ejpam-3987	171	1	e−x−y	e−x−y	NOUN
ejpam-3987	171	2	√	√	NUM
ejpam-3987	171	3	x	x	SYM
ejpam-3987	171	4	√	√	VERB
ejpam-3987	171	5	y	y	PROPN
ejpam-3987	171	6	(	(	PUNCT
ejpam-3987	171	7	log2	log2	PROPN
ejpam-3987	171	8	(	(	PUNCT
ejpam-3987	171	9	x	x	NOUN
ejpam-3987	171	10	y	y	PROPN
ejpam-3987	171	11	)	)	PUNCT
ejpam-3987	172	1	+	+	CCONJ
ejpam-3987	172	2	π2	π2	ADJ
ejpam-3987	172	3	)	)	PUNCT
ejpam-3987	172	4	dxdy	dxdy	NOUN
ejpam-3987	172	5	=	=	SYM
ejpam-3987	172	6	log(2	log(2	PROPN
ejpam-3987	172	7	)	)	PUNCT
ejpam-3987	173	1	π	π	NOUN
ejpam-3987	173	2	next	next	ADV
ejpam-3987	173	3	using	use	VERB
ejpam-3987	173	4	equation	equation	NOUN
ejpam-3987	173	5	(	(	PUNCT
ejpam-3987	173	6	23	23	NUM
ejpam-3987	173	7	)	)	PUNCT
ejpam-3987	173	8	and	and	CCONJ
ejpam-3987	173	9	taking	take	VERB
ejpam-3987	173	10	the	the	DET
ejpam-3987	173	11	first	first	ADJ
ejpam-3987	173	12	partial	partial	ADJ
ejpam-3987	173	13	derivative	derivative	NOUN
ejpam-3987	173	14	with	with	ADP
ejpam-3987	173	15	respect	respect	NOUN
ejpam-3987	173	16	to	to	ADP
ejpam-3987	173	17	k	k	PROPN
ejpam-3987	173	18	and	and	CCONJ
ejpam-3987	173	19	setting	set	VERB
ejpam-3987	173	20	k	k	PROPN
ejpam-3987	173	21	=	=	SYM
ejpam-3987	173	22	2	2	NUM
ejpam-3987	173	23	and	and	CCONJ
ejpam-3987	173	24	simplifying	simplify	VERB
ejpam-3987	173	25	we	we	PRON
ejpam-3987	173	26	get	get	VERB
ejpam-3987	173	27	(	(	PUNCT
ejpam-3987	173	28	25	25	NUM
ejpam-3987	173	29	)	)	PUNCT
ejpam-3987	173	30	∫	∫	PROPN
ejpam-3987	174	1	∞	∞	PROPN
ejpam-3987	174	2	0	0	NUM
ejpam-3987	175	1	∫	∫	PROPN
ejpam-3987	175	2	∞	∞	PROPN
ejpam-3987	175	3	0	0	PROPN
ejpam-3987	175	4	e−x−y	e−x−y	NOUN
ejpam-3987	175	5	log2	log2	PROPN
ejpam-3987	175	6	(	(	PUNCT
ejpam-3987	175	7	−x	−x	NOUN
ejpam-3987	175	8	y	y	PROPN
ejpam-3987	175	9	)	)	PUNCT
ejpam-3987	175	10	log	log	NOUN
ejpam-3987	175	11	(	(	PUNCT
ejpam-3987	175	12	log	log	PROPN
ejpam-3987	175	13	(	(	PUNCT
ejpam-3987	175	14	−x	−x	NOUN
ejpam-3987	175	15	y	y	PROPN
ejpam-3987	175	16	)	)	PUNCT
ejpam-3987	175	17	)	)	PUNCT
ejpam-3987	176	1	√	√	NUM
ejpam-3987	176	2	x	x	SYM
ejpam-3987	176	3	√	√	NUM
ejpam-3987	176	4	y	y	PROPN
ejpam-3987	176	5	dxdy	dxdy	PROPN
ejpam-3987	176	6	=	=	PUNCT
ejpam-3987	176	7	14πζ(3	14πζ(3	ADJ
ejpam-3987	176	8	)	)	PUNCT
ejpam-3987	176	9	next	next	ADV
ejpam-3987	176	10	using	use	VERB
ejpam-3987	176	11	equation	equation	NOUN
ejpam-3987	176	12	(	(	PUNCT
ejpam-3987	176	13	23	23	NUM
ejpam-3987	176	14	)	)	PUNCT
ejpam-3987	176	15	and	and	CCONJ
ejpam-3987	176	16	taking	take	VERB
ejpam-3987	176	17	the	the	DET
ejpam-3987	176	18	first	first	ADJ
ejpam-3987	176	19	partial	partial	ADJ
ejpam-3987	176	20	derivative	derivative	NOUN
ejpam-3987	176	21	with	with	ADP
ejpam-3987	176	22	respect	respect	NOUN
ejpam-3987	176	23	to	to	ADP
ejpam-3987	176	24	k	k	PROPN
ejpam-3987	176	25	and	and	CCONJ
ejpam-3987	176	26	setting	set	VERB
ejpam-3987	176	27	k	k	X
ejpam-3987	176	28	=	=	SYM
ejpam-3987	176	29	1	1	NUM
ejpam-3987	176	30	and	and	CCONJ
ejpam-3987	176	31	simplifying	simplify	VERB
ejpam-3987	176	32	we	we	PRON
ejpam-3987	176	33	get	get	VERB
ejpam-3987	176	34	(	(	PUNCT
ejpam-3987	176	35	26	26	NUM
ejpam-3987	176	36	)	)	PUNCT
ejpam-3987	176	37	∫	∫	PROPN
ejpam-3987	177	1	∞	∞	PROPN
ejpam-3987	177	2	0	0	NUM
ejpam-3987	178	1	∫	∫	PROPN
ejpam-3987	178	2	∞	∞	PROPN
ejpam-3987	178	3	0	0	NUM
ejpam-3987	179	1	e−x−y	e−x−y	NOUN
ejpam-3987	179	2	log	log	NOUN
ejpam-3987	179	3	(	(	PUNCT
ejpam-3987	179	4	−x	−x	NOUN
ejpam-3987	179	5	y	y	PROPN
ejpam-3987	179	6	)	)	PUNCT
ejpam-3987	179	7	log	log	NOUN
ejpam-3987	179	8	(	(	PUNCT
ejpam-3987	179	9	log	log	PROPN
ejpam-3987	179	10	(	(	PUNCT
ejpam-3987	179	11	−x	−x	NOUN
ejpam-3987	179	12	y	y	PROPN
ejpam-3987	179	13	)	)	PUNCT
ejpam-3987	179	14	)	)	PUNCT
ejpam-3987	180	1	√	√	NUM
ejpam-3987	180	2	x	x	SYM
ejpam-3987	180	3	√	√	NUM
ejpam-3987	180	4	y	y	PROPN
ejpam-3987	180	5	dxdy	dxdy	PROPN
ejpam-3987	180	6	=	=	PROPN
ejpam-3987	180	7	iπ2	iπ2	NOUN
ejpam-3987	180	8	log	log	NOUN
ejpam-3987	180	9	(	(	PUNCT
ejpam-3987	180	10	4i	4i	NUM
ejpam-3987	180	11	3	3	NUM
ejpam-3987	180	12	√	√	NUM
ejpam-3987	180	13	2eπ	2eπ	ADJ
ejpam-3987	180	14	a12	a12	NOUN
ejpam-3987	180	15	)	)	PUNCT
ejpam-3987	180	16	6.15	6.15	NUM
ejpam-3987	180	17	.	.	PUNCT
ejpam-3987	181	1	derivation	derivation	NOUN
ejpam-3987	181	2	of	of	ADP
ejpam-3987	181	3	new	new	ADJ
ejpam-3987	181	4	entry	entry	NOUN
ejpam-3987	181	5	59	59	NUM
ejpam-3987	181	6	in	in	ADP
ejpam-3987	181	7	terms	term	NOUN
ejpam-3987	181	8	of	of	ADP
ejpam-3987	181	9	digamma	digamma	PROPN
ejpam-3987	181	10	function	function	NOUN
ejpam-3987	181	11	using	use	VERB
ejpam-3987	181	12	equation	equation	NOUN
ejpam-3987	181	13	(	(	PUNCT
ejpam-3987	181	14	8)	8)	NUM
ejpam-3987	181	15	and	and	CCONJ
ejpam-3987	181	16	setting	set	VERB
ejpam-3987	181	17	p	p	X
ejpam-3987	181	18	=	=	PUNCT
ejpam-3987	181	19	n/2	n/2	NOUN
ejpam-3987	181	20	,	,	PUNCT
ejpam-3987	181	21	k	k	NOUN
ejpam-3987	181	22	=	=	PUNCT
ejpam-3987	181	23	−1	−1	NOUN
ejpam-3987	181	24	and	and	CCONJ
ejpam-3987	181	25	a	a	DET
ejpam-3987	181	26	=	=	SYM
ejpam-3987	181	27	eai	eai	NOUN
ejpam-3987	181	28	and	and	CCONJ
ejpam-3987	181	29	simplifying	simplify	VERB
ejpam-3987	181	30	we	we	PRON
ejpam-3987	181	31	get	get	VERB
ejpam-3987	181	32	(	(	PUNCT
ejpam-3987	181	33	27	27	NUM
ejpam-3987	181	34	)	)	PUNCT
ejpam-3987	181	35	∫	∫	PROPN
ejpam-3987	182	1	∞	∞	PROPN
ejpam-3987	182	2	0	0	NUM
ejpam-3987	183	1	∫	∫	PROPN
ejpam-3987	183	2	∞	∞	NUM
ejpam-3987	183	3	0	0	NUM
ejpam-3987	184	1	x	x	SYM
ejpam-3987	184	2	n	n	SYM
ejpam-3987	184	3	2	2	NUM
ejpam-3987	184	4	−1y	−1y	NOUN
ejpam-3987	184	5	n	n	DET
ejpam-3987	184	6	2	2	NUM
ejpam-3987	184	7	−1e−x	−1e−x	NOUN
ejpam-3987	184	8	n−yn	n−yn	NOUN
ejpam-3987	184	9	a2	a2	PROPN
ejpam-3987	184	10	+	+	CCONJ
ejpam-3987	184	11	log2	log2	PROPN
ejpam-3987	184	12	(	(	PUNCT
ejpam-3987	184	13	x	x	SYM
ejpam-3987	184	14	y	y	PROPN
ejpam-3987	184	15	)	)	PUNCT
ejpam-3987	184	16	dxdy	dxdy	PROPN
ejpam-3987	184	17	=	=	SYM
ejpam-3987	184	18	ψ(0	ψ(0	PROPN
ejpam-3987	184	19	)	)	PUNCT
ejpam-3987	184	20	(	(	PUNCT
ejpam-3987	184	21	an+3π	an+3π	NOUN
ejpam-3987	184	22	4π	4π	NUM
ejpam-3987	184	23	)	)	PUNCT
ejpam-3987	185	1	−	−	PROPN
ejpam-3987	185	2	ψ(0	ψ(0	NOUN
ejpam-3987	185	3	)	)	PUNCT
ejpam-3987	185	4	(	(	PUNCT
ejpam-3987	185	5	an+π	an+π	NUM
ejpam-3987	185	6	4π	4π	NUM
ejpam-3987	185	7	)	)	PUNCT
ejpam-3987	186	1	2an	2an	PROPN
ejpam-3987	186	2	r.	r.	PROPN
ejpam-3987	186	3	reynolds	reynolds	PROPN
ejpam-3987	186	4	,	,	PUNCT
ejpam-3987	186	5	a.	a.	PROPN
ejpam-3987	186	6	stauffer	stauffer	PROPN
ejpam-3987	186	7	/	/	SYM
ejpam-3987	186	8	eur	eur	PROPN
ejpam-3987	186	9	.	.	PUNCT
ejpam-3987	187	1	j.	j.	PROPN
ejpam-3987	187	2	pure	pure	PROPN
ejpam-3987	187	3	appl	appl	PROPN
ejpam-3987	187	4	.	.	PROPN
ejpam-3987	187	5	math	math	PROPN
ejpam-3987	187	6	,	,	PUNCT
ejpam-3987	187	7	14	14	NUM
ejpam-3987	187	8	(	(	PUNCT
ejpam-3987	187	9	3	3	NUM
ejpam-3987	187	10	)	)	PUNCT
ejpam-3987	187	11	(	(	PUNCT
ejpam-3987	187	12	2021	2021	NUM
ejpam-3987	187	13	)	)	PUNCT
ejpam-3987	187	14	,	,	PUNCT
ejpam-3987	187	15	618	618	NUM
ejpam-3987	187	16	-	-	SYM
ejpam-3987	187	17	637	637	NUM
ejpam-3987	187	18	625	625	NUM
ejpam-3987	187	19	7	7	NUM
ejpam-3987	187	20	.	.	PUNCT
ejpam-3987	188	1	derivation	derivation	NOUN
ejpam-3987	188	2	of	of	ADP
ejpam-3987	188	3	definite	definite	ADJ
ejpam-3987	188	4	integrals	integral	NOUN
ejpam-3987	188	5	when	when	SCONJ
ejpam-3987	188	6	s	s	AUX
ejpam-3987	188	7	6=	6=	PROPN
ejpam-3987	188	8	t	t	NOUN
ejpam-3987	188	9	the	the	DET
ejpam-3987	188	10	main	main	ADJ
ejpam-3987	188	11	related	relate	VERB
ejpam-3987	188	12	functions	function	NOUN
ejpam-3987	188	13	of	of	ADP
ejpam-3987	188	14	the	the	DET
ejpam-3987	188	15	lerch	lerch	PROPN
ejpam-3987	188	16	function	function	PROPN
ejpam-3987	188	17	and	and	CCONJ
ejpam-3987	188	18	transcendent	transcendent	NOUN
ejpam-3987	188	19	are	be	AUX
ejpam-3987	188	20	the	the	DET
ejpam-3987	188	21	hurwitz	hurwitz	PROPN
ejpam-3987	188	22	zeta	zeta	PROPN
ejpam-3987	188	23	function	function	PROPN
ejpam-3987	188	24	ζ(s	ζ(s	PROPN
ejpam-3987	188	25	,	,	PUNCT
ejpam-3987	188	26	a	a	PRON
ejpam-3987	188	27	)	)	PUNCT
ejpam-3987	188	28	from	from	ADP
ejpam-3987	188	29	equation	equation	NOUN
ejpam-3987	188	30	(	(	PUNCT
ejpam-3987	188	31	64:12:1	64:12:1	NOUN
ejpam-3987	188	32	)	)	PUNCT
ejpam-3987	188	33	in	in	ADP
ejpam-3987	188	34	[	[	X
ejpam-3987	188	35	6	6	NUM
ejpam-3987	188	36	]	]	PUNCT
ejpam-3987	188	37	,	,	PUNCT
ejpam-3987	188	38	jonquiére	jonquiére	PROPN
ejpam-3987	188	39	’s	’s	PART
ejpam-3987	188	40	function	function	NOUN
ejpam-3987	188	41	φ(z	φ(z	PROPN
ejpam-3987	188	42	,	,	PUNCT
ejpam-3987	188	43	s	s	PART
ejpam-3987	188	44	)	)	PUNCT
ejpam-3987	188	45	from	from	ADP
ejpam-3987	188	46	equation	equation	NOUN
ejpam-3987	188	47	(	(	PUNCT
ejpam-3987	188	48	64:12:2	64:12:2	NUM
ejpam-3987	188	49	)	)	PUNCT
ejpam-3987	188	50	in	in	ADP
ejpam-3987	188	51	[	[	X
ejpam-3987	188	52	6	6	NUM
ejpam-3987	188	53	]	]	PUNCT
ejpam-3987	188	54	,	,	PUNCT
ejpam-3987	188	55	and	and	CCONJ
ejpam-3987	188	56	the	the	DET
ejpam-3987	188	57	dirichlet	dirichlet	PROPN
ejpam-3987	188	58	l	l	PROPN
ejpam-3987	188	59	-	-	PUNCT
ejpam-3987	188	60	functions	function	NOUN
ejpam-3987	188	61	l(s	l(s	PROPN
ejpam-3987	188	62	,	,	PUNCT
ejpam-3987	188	63	χ	χ	X
ejpam-3987	188	64	)	)	PUNCT
ejpam-3987	188	65	from	from	ADP
ejpam-3987	188	66	entry	entry	NOUN
ejpam-3987	188	67	(	(	PUNCT
ejpam-3987	188	68	3	3	NUM
ejpam-3987	188	69	)	)	PUNCT
ejpam-3987	188	70	in	in	ADP
ejpam-3987	188	71	table	table	NOUN
ejpam-3987	188	72	below	below	ADV
ejpam-3987	188	73	(	(	PUNCT
ejpam-3987	188	74	64:12:7	64:12:7	NUM
ejpam-3987	188	75	)	)	PUNCT
ejpam-3987	188	76	in	in	ADP
ejpam-3987	188	77	[	[	X
ejpam-3987	188	78	6	6	NUM
ejpam-3987	188	79	]	]	PUNCT
ejpam-3987	188	80	.	.	PUNCT
ejpam-3987	189	1	in	in	ADP
ejpam-3987	189	2	this	this	DET
ejpam-3987	189	3	section	section	NOUN
ejpam-3987	189	4	we	we	PRON
ejpam-3987	189	5	will	will	AUX
ejpam-3987	189	6	derive	derive	VERB
ejpam-3987	189	7	definite	definite	ADJ
ejpam-3987	189	8	integrals	integral	NOUN
ejpam-3987	189	9	in	in	ADP
ejpam-3987	189	10	terms	term	NOUN
ejpam-3987	189	11	of	of	ADP
ejpam-3987	189	12	these	these	DET
ejpam-3987	189	13	special	special	ADJ
ejpam-3987	189	14	functions	function	NOUN
ejpam-3987	189	15	along	along	ADP
ejpam-3987	189	16	with	with	ADP
ejpam-3987	189	17	a	a	DET
ejpam-3987	189	18	few	few	ADJ
ejpam-3987	189	19	other	other	ADJ
ejpam-3987	189	20	examples	example	NOUN
ejpam-3987	189	21	.	.	PUNCT
ejpam-3987	190	1	7.1	7.1	NUM
ejpam-3987	190	2	.	.	PUNCT
ejpam-3987	191	1	derivation	derivation	NOUN
ejpam-3987	191	2	entry	entry	NOUN
ejpam-3987	191	3	60	60	NUM
ejpam-3987	191	4	in	in	ADP
ejpam-3987	191	5	terms	term	NOUN
ejpam-3987	191	6	of	of	ADP
ejpam-3987	191	7	the	the	DET
ejpam-3987	191	8	hurwitz	hurwitz	PROPN
ejpam-3987	191	9	zeta	zeta	PROPN
ejpam-3987	191	10	function	function	VERB
ejpam-3987	191	11	ζ(k	ζ(k	PROPN
ejpam-3987	191	12	,	,	PUNCT
ejpam-3987	191	13	z	z	NOUN
ejpam-3987	191	14	)	)	PUNCT
ejpam-3987	191	15	using	use	VERB
ejpam-3987	191	16	equation	equation	NOUN
ejpam-3987	191	17	(	(	PUNCT
ejpam-3987	191	18	8)	8)	NUM
ejpam-3987	191	19	and	and	CCONJ
ejpam-3987	191	20	replacing	replace	VERB
ejpam-3987	191	21	n	n	ADV
ejpam-3987	191	22	by	by	ADP
ejpam-3987	191	23	2p	2p	NUM
ejpam-3987	191	24	and	and	CCONJ
ejpam-3987	191	25	simplifying	simplify	VERB
ejpam-3987	191	26	we	we	PRON
ejpam-3987	191	27	get	get	VERB
ejpam-3987	191	28	(	(	PUNCT
ejpam-3987	191	29	28	28	NUM
ejpam-3987	191	30	)	)	PUNCT
ejpam-3987	191	31	∫	∫	PROPN
ejpam-3987	192	1	∞	∞	PROPN
ejpam-3987	192	2	0	0	NUM
ejpam-3987	193	1	∫	∫	PROPN
ejpam-3987	193	2	∞	∞	NUM
ejpam-3987	193	3	0	0	NUM
ejpam-3987	194	1	xp−1yp−1	xp−1yp−1	SYM
ejpam-3987	194	2	logk	logk	NOUN
ejpam-3987	194	3	(	(	PUNCT
ejpam-3987	194	4	bx	bx	NOUN
ejpam-3987	194	5	y	y	PROPN
ejpam-3987	194	6	)	)	PUNCT
ejpam-3987	194	7	e−(sx)2p−(ty)2p	e−(sx)2p−(ty)2p	X
ejpam-3987	195	1	dxdy	dxdy	PROPN
ejpam-3987	195	2	=	=	PUNCT
ejpam-3987	195	3	2k−1πk+1	2k−1πk+1	NUM
ejpam-3987	195	4	(	(	PUNCT
ejpam-3987	195	5	i	i	PRON
ejpam-3987	195	6	p	p	NOUN
ejpam-3987	195	7	)	)	PUNCT
ejpam-3987	196	1	k	k	PROPN
ejpam-3987	196	2	s−pt−p	s−pt−p	PROPN
ejpam-3987	196	3	(	(	PUNCT
ejpam-3987	196	4	ζ	ζ	X
ejpam-3987	196	5	(	(	PUNCT
ejpam-3987	196	6	−k	−k	PROPN
ejpam-3987	196	7	,	,	PUNCT
ejpam-3987	196	8	π−2ip	π−2ip	NOUN
ejpam-3987	196	9	log	log	NOUN
ejpam-3987	196	10	(	(	PUNCT
ejpam-3987	196	11	bts	bts	PROPN
ejpam-3987	196	12	)	)	PUNCT
ejpam-3987	196	13	4π	4π	NUM
ejpam-3987	196	14	)	)	PUNCT
ejpam-3987	196	15	−	−	PROPN
ejpam-3987	197	1	ζ	ζ	NOUN
ejpam-3987	197	2	(	(	PUNCT
ejpam-3987	197	3	−k	−k	PROPN
ejpam-3987	197	4	,	,	PUNCT
ejpam-3987	197	5	3	3	NUM
ejpam-3987	197	6	4	4	NUM
ejpam-3987	197	7	−	−	NOUN
ejpam-3987	197	8	ip	ip	NOUN
ejpam-3987	197	9	log	log	NOUN
ejpam-3987	197	10	(	(	PUNCT
ejpam-3987	197	11	bts	bt	NOUN
ejpam-3987	197	12	)	)	PUNCT
ejpam-3987	197	13	2π	2π	NOUN
ejpam-3987	197	14	)	)	PUNCT
ejpam-3987	197	15	)	)	PUNCT
ejpam-3987	197	16	p2	p2	PROPN
ejpam-3987	197	17	from	from	ADP
ejpam-3987	197	18	equation	equation	NOUN
ejpam-3987	197	19	(	(	PUNCT
ejpam-3987	197	20	64:13:3	64:13:3	NUM
ejpam-3987	197	21	)	)	PUNCT
ejpam-3987	197	22	in	in	ADP
ejpam-3987	197	23	[	[	X
ejpam-3987	197	24	6	6	NUM
ejpam-3987	197	25	]	]	PUNCT
ejpam-3987	197	26	.	.	PUNCT
ejpam-3987	198	1	7.2	7.2	NUM
ejpam-3987	198	2	.	.	PUNCT
ejpam-3987	198	3	derivation	derivation	NOUN
ejpam-3987	198	4	of	of	ADP
ejpam-3987	198	5	entry	entry	NOUN
ejpam-3987	198	6	61	61	NUM
ejpam-3987	198	7	in	in	ADP
ejpam-3987	198	8	terms	term	NOUN
ejpam-3987	198	9	of	of	ADP
ejpam-3987	198	10	the	the	DET
ejpam-3987	198	11	polylogarithm	polylogarithm	PROPN
ejpam-3987	198	12	function	function	PROPN
ejpam-3987	198	13	li−k	li−k	VERB
ejpam-3987	198	14	using	use	VERB
ejpam-3987	198	15	equation	equation	NOUN
ejpam-3987	198	16	(	(	PUNCT
ejpam-3987	198	17	8)	8)	NUM
ejpam-3987	198	18	and	and	CCONJ
ejpam-3987	198	19	replacing	replace	VERB
ejpam-3987	198	20	b	b	NOUN
ejpam-3987	198	21	by	by	ADP
ejpam-3987	198	22	e	e	PROPN
ejpam-3987	198	23	iπ	iπ	NOUN
ejpam-3987	198	24	n	n	PROPN
ejpam-3987	198	25	s	s	PROPN
ejpam-3987	198	26	t	t	NOUN
ejpam-3987	198	27	and	and	CCONJ
ejpam-3987	198	28	simplifying	simplify	VERB
ejpam-3987	198	29	we	we	PRON
ejpam-3987	198	30	get	get	VERB
ejpam-3987	198	31	(	(	PUNCT
ejpam-3987	198	32	29	29	NUM
ejpam-3987	198	33	)	)	PUNCT
ejpam-3987	198	34	∫	∫	PROPN
ejpam-3987	199	1	∞	∞	PROPN
ejpam-3987	199	2	0	0	NUM
ejpam-3987	200	1	∫	∫	PROPN
ejpam-3987	200	2	∞	∞	PROPN
ejpam-3987	200	3	0	0	NUM
ejpam-3987	201	1	xp−1yn−p−1e−(sx)n−(ty)n	xp−1yn−p−1e−(sx)n−(ty)n	PROPN
ejpam-3987	201	2	logk	logk	NOUN
ejpam-3987	201	3	(	(	PUNCT
ejpam-3987	201	4	e	e	X
ejpam-3987	201	5	iπ	iπ	NOUN
ejpam-3987	201	6	n	n	PRON
ejpam-3987	201	7	sx	sx	VERB
ejpam-3987	201	8	ty	ty	INTJ
ejpam-3987	201	9	)	)	PUNCT
ejpam-3987	201	10	dxdy	dxdy	PROPN
ejpam-3987	201	11	=	=	SYM
ejpam-3987	201	12	(	(	PUNCT
ejpam-3987	201	13	2π)k+1	2π)k+1	NUM
ejpam-3987	201	14	(	(	PUNCT
ejpam-3987	201	15	i	i	PRON
ejpam-3987	201	16	n	n	X
ejpam-3987	201	17	)	)	PUNCT
ejpam-3987	201	18	k−1	k−1	PROPN
ejpam-3987	201	19	e−	e−	PROPN
ejpam-3987	201	20	iπp	iπp	PROPN
ejpam-3987	201	21	n	n	NOUN
ejpam-3987	201	22	s−ptp−nli−k	s−ptp−nli−k	NOUN
ejpam-3987	201	23	(	(	PUNCT
ejpam-3987	201	24	e	e	X
ejpam-3987	201	25	2ipπ	2ipπ	NUM
ejpam-3987	201	26	n	n	NOUN
ejpam-3987	201	27	)	)	PUNCT
ejpam-3987	201	28	n3	n3	NOUN
ejpam-3987	201	29	from	from	ADP
ejpam-3987	201	30	equation	equation	NOUN
ejpam-3987	201	31	(	(	PUNCT
ejpam-3987	201	32	64:12:2	64:12:2	NUM
ejpam-3987	201	33	)	)	PUNCT
ejpam-3987	201	34	in	in	ADP
ejpam-3987	201	35	[	[	X
ejpam-3987	201	36	6	6	NUM
ejpam-3987	201	37	]	]	PUNCT
ejpam-3987	201	38	.	.	PUNCT
ejpam-3987	202	1	7.3	7.3	NUM
ejpam-3987	202	2	.	.	PUNCT
ejpam-3987	203	1	derivation	derivation	NOUN
ejpam-3987	203	2	of	of	ADP
ejpam-3987	203	3	entry	entry	NOUN
ejpam-3987	203	4	62	62	NUM
ejpam-3987	203	5	in	in	ADP
ejpam-3987	203	6	terms	term	NOUN
ejpam-3987	203	7	of	of	ADP
ejpam-3987	203	8	the	the	DET
ejpam-3987	203	9	hypergeometric	hypergeometric	ADJ
ejpam-3987	203	10	function	function	NOUN
ejpam-3987	203	11	2f1(1	2f1(1	NUM
ejpam-3987	203	12	,	,	PUNCT
ejpam-3987	203	13	v	v	NOUN
ejpam-3987	203	14	;	;	PUNCT
ejpam-3987	203	15	v	v	NOUN
ejpam-3987	203	16	+	+	NOUN
ejpam-3987	203	17	1	1	NUM
ejpam-3987	203	18	;	;	PUNCT
ejpam-3987	203	19	z	z	X
ejpam-3987	203	20	)	)	PUNCT
ejpam-3987	203	21	the	the	DET
ejpam-3987	203	22	relationship	relationship	NOUN
ejpam-3987	203	23	between	between	ADP
ejpam-3987	203	24	the	the	DET
ejpam-3987	203	25	lerch	lerch	PROPN
ejpam-3987	203	26	function	function	PROPN
ejpam-3987	203	27	and	and	CCONJ
ejpam-3987	203	28	the	the	DET
ejpam-3987	203	29	hypergeometric	hypergeometric	ADJ
ejpam-3987	203	30	function	function	NOUN
ejpam-3987	203	31	is	be	AUX
ejpam-3987	203	32	given	give	VERB
ejpam-3987	203	33	by	by	ADP
ejpam-3987	203	34	(	(	PUNCT
ejpam-3987	203	35	30)φ(z	30)φ(z	PROPN
ejpam-3987	203	36	,	,	PUNCT
ejpam-3987	203	37	1	1	NUM
ejpam-3987	203	38	,	,	PUNCT
ejpam-3987	203	39	v	v	NOUN
ejpam-3987	203	40	)	)	PUNCT
ejpam-3987	203	41	=	=	SYM
ejpam-3987	203	42	2f1(1	2f1(1	NUM
ejpam-3987	203	43	,	,	PUNCT
ejpam-3987	203	44	v	v	NOUN
ejpam-3987	203	45	;	;	PUNCT
ejpam-3987	203	46	v	v	NOUN
ejpam-3987	203	47	+	+	NOUN
ejpam-3987	203	48	1	1	NUM
ejpam-3987	203	49	;	;	PUNCT
ejpam-3987	203	50	z	z	X
ejpam-3987	203	51	)	)	PUNCT
ejpam-3987	203	52	v	v	NOUN
ejpam-3987	203	53	,	,	PUNCT
ejpam-3987	203	54	|z|	|z|	VERB
ejpam-3987	203	55	<	<	X
ejpam-3987	203	56	1	1	NUM
ejpam-3987	203	57	using	use	VERB
ejpam-3987	203	58	equation	equation	NOUN
ejpam-3987	203	59	(	(	PUNCT
ejpam-3987	203	60	8)	8)	NUM
ejpam-3987	203	61	and	and	CCONJ
ejpam-3987	203	62	setting	set	VERB
ejpam-3987	203	63	k	k	PROPN
ejpam-3987	203	64	=	=	PUNCT
ejpam-3987	203	65	−1	−1	NOUN
ejpam-3987	203	66	and	and	CCONJ
ejpam-3987	203	67	simplifying	simplify	VERB
ejpam-3987	203	68	we	we	PRON
ejpam-3987	203	69	get	get	VERB
ejpam-3987	203	70	r.	r.	PROPN
ejpam-3987	203	71	reynolds	reynolds	PROPN
ejpam-3987	203	72	,	,	PUNCT
ejpam-3987	203	73	a.	a.	PROPN
ejpam-3987	203	74	stauffer	stauffer	PROPN
ejpam-3987	203	75	/	/	SYM
ejpam-3987	203	76	eur	eur	PROPN
ejpam-3987	203	77	.	.	PUNCT
ejpam-3987	204	1	j.	j.	PROPN
ejpam-3987	204	2	pure	pure	PROPN
ejpam-3987	204	3	appl	appl	PROPN
ejpam-3987	204	4	.	.	PROPN
ejpam-3987	204	5	math	math	PROPN
ejpam-3987	204	6	,	,	PUNCT
ejpam-3987	204	7	14	14	NUM
ejpam-3987	204	8	(	(	PUNCT
ejpam-3987	204	9	3	3	NUM
ejpam-3987	204	10	)	)	PUNCT
ejpam-3987	204	11	(	(	PUNCT
ejpam-3987	204	12	2021	2021	NUM
ejpam-3987	204	13	)	)	PUNCT
ejpam-3987	204	14	,	,	PUNCT
ejpam-3987	204	15	618	618	NUM
ejpam-3987	204	16	-	-	SYM
ejpam-3987	204	17	637	637	NUM
ejpam-3987	204	18	626	626	NUM
ejpam-3987	204	19	(	(	PUNCT
ejpam-3987	204	20	31	31	NUM
ejpam-3987	204	21	)	)	PUNCT
ejpam-3987	204	22	∫	∫	PROPN
ejpam-3987	205	1	∞	∞	PROPN
ejpam-3987	205	2	0	0	NUM
ejpam-3987	206	1	∫	∫	PROPN
ejpam-3987	207	1	∞	∞	PROPN
ejpam-3987	207	2	0	0	NUM
ejpam-3987	208	1	xp−1yn−p−1e−(sx)n−(ty)n	xp−1yn−p−1e−(sx)n−(ty)n	PROPN
ejpam-3987	208	2	log	log	NOUN
ejpam-3987	208	3	(	(	PUNCT
ejpam-3987	208	4	bx	bx	NOUN
ejpam-3987	208	5	y	y	PROPN
ejpam-3987	208	6	)	)	PUNCT
ejpam-3987	208	7	dxdy	dxdy	PROPN
ejpam-3987	208	8	=	=	PUNCT
ejpam-3987	209	1	−	−	PROPN
ejpam-3987	209	2	e	e	X
ejpam-3987	209	3	iπp	iπp	NOUN
ejpam-3987	209	4	n	n	PRON
ejpam-3987	209	5	s−ptp−nφ	s−ptp−nφ	NOUN
ejpam-3987	209	6	(	(	PUNCT
ejpam-3987	209	7	e	e	NOUN
ejpam-3987	209	8	2ipπ	2ipπ	NUM
ejpam-3987	209	9	n	n	NUM
ejpam-3987	209	10	,	,	PUNCT
ejpam-3987	209	11	1	1	NUM
ejpam-3987	209	12	,	,	PUNCT
ejpam-3987	209	13	π−in	π−in	NOUN
ejpam-3987	209	14	log	log	NOUN
ejpam-3987	209	15	(	(	PUNCT
ejpam-3987	209	16	bts	bt	NOUN
ejpam-3987	209	17	)	)	PUNCT
ejpam-3987	209	18	2π	2π	NOUN
ejpam-3987	209	19	)	)	PUNCT
ejpam-3987	210	1	n	n	PROPN
ejpam-3987	210	2	=	=	SYM
ejpam-3987	210	3	−	−	PROPN
ejpam-3987	210	4	2πe	2πe	ADJ
ejpam-3987	210	5	iπp	iπp	NOUN
ejpam-3987	211	1	n	n	PRON
ejpam-3987	211	2	s−ptp−n	s−ptp−n	NOUN
ejpam-3987	211	3	2f1	2f1	NUM
ejpam-3987	211	4	(	(	PUNCT
ejpam-3987	211	5	1	1	NUM
ejpam-3987	211	6	,	,	PUNCT
ejpam-3987	211	7	π−in	π−in	NOUN
ejpam-3987	211	8	log	log	NOUN
ejpam-3987	211	9	(	(	PUNCT
ejpam-3987	211	10	bts	bt	NOUN
ejpam-3987	211	11	)	)	PUNCT
ejpam-3987	211	12	2π	2π	NOUN
ejpam-3987	211	13	;	;	PUNCT
ejpam-3987	211	14	3	3	NUM
ejpam-3987	211	15	2	2	NUM
ejpam-3987	211	16	−	−	NOUN
ejpam-3987	211	17	in	in	ADP
ejpam-3987	211	18	log	log	NOUN
ejpam-3987	211	19	(	(	PUNCT
ejpam-3987	211	20	bts	bt	NOUN
ejpam-3987	211	21	)	)	PUNCT
ejpam-3987	211	22	2π	2π	NOUN
ejpam-3987	211	23	;	;	PUNCT
ejpam-3987	211	24	e	e	X
ejpam-3987	211	25	2ipπ	2ipπ	NUM
ejpam-3987	211	26	n	n	NOUN
ejpam-3987	211	27	)	)	PUNCT
ejpam-3987	211	28	n	n	PROPN
ejpam-3987	211	29	(	(	PUNCT
ejpam-3987	211	30	π	π	PROPN
ejpam-3987	211	31	−	−	PROPN
ejpam-3987	212	1	in	in	ADP
ejpam-3987	212	2	log	log	PROPN
ejpam-3987	212	3	(	(	PUNCT
ejpam-3987	212	4	bt	bt	NOUN
ejpam-3987	212	5	s	s	NOUN
ejpam-3987	212	6	)	)	PUNCT
ejpam-3987	212	7	)	)	PUNCT
ejpam-3987	213	1	from	from	ADP
ejpam-3987	213	2	equation	equation	NOUN
ejpam-3987	213	3	(	(	PUNCT
ejpam-3987	213	4	1.11.10	1.11.10	NUM
ejpam-3987	213	5	)	)	PUNCT
ejpam-3987	213	6	in	in	ADP
ejpam-3987	213	7	[	[	X
ejpam-3987	213	8	2	2	NUM
ejpam-3987	213	9	]	]	PUNCT
ejpam-3987	213	10	,	,	PUNCT
ejpam-3987	213	11	where	where	SCONJ
ejpam-3987	213	12	im(p	im(p	NUM
ejpam-3987	213	13	/	/	SYM
ejpam-3987	213	14	n	n	CCONJ
ejpam-3987	213	15	)	)	PUNCT
ejpam-3987	213	16	>	>	X
ejpam-3987	213	17	0	0	X
ejpam-3987	213	18	.	.	X
ejpam-3987	213	19	7.4	7.4	NUM
ejpam-3987	213	20	.	.	PUNCT
ejpam-3987	213	21	derivation	derivation	NOUN
ejpam-3987	213	22	of	of	ADP
ejpam-3987	213	23	entry	entry	NOUN
ejpam-3987	213	24	63	63	NUM
ejpam-3987	213	25	in	in	ADP
ejpam-3987	213	26	terms	term	NOUN
ejpam-3987	213	27	of	of	ADP
ejpam-3987	213	28	the	the	DET
ejpam-3987	213	29	harmonic	harmonic	ADJ
ejpam-3987	213	30	number	number	NOUN
ejpam-3987	213	31	function	function	NOUN
ejpam-3987	213	32	hn	hn	NOUN
ejpam-3987	213	33	using	use	VERB
ejpam-3987	213	34	equation	equation	NOUN
ejpam-3987	213	35	(	(	PUNCT
ejpam-3987	213	36	8)	8)	NUM
ejpam-3987	213	37	and	and	CCONJ
ejpam-3987	213	38	replacing	replace	VERB
ejpam-3987	213	39	n	n	ADV
ejpam-3987	213	40	by	by	ADP
ejpam-3987	213	41	2p	2p	NUM
ejpam-3987	213	42	and	and	CCONJ
ejpam-3987	213	43	setting	set	VERB
ejpam-3987	213	44	k	k	PROPN
ejpam-3987	213	45	=	=	PUNCT
ejpam-3987	213	46	−1	−1	NOUN
ejpam-3987	213	47	and	and	CCONJ
ejpam-3987	213	48	simplifying	simplify	VERB
ejpam-3987	213	49	we	we	PRON
ejpam-3987	213	50	get	get	VERB
ejpam-3987	213	51	(	(	PUNCT
ejpam-3987	213	52	32	32	NUM
ejpam-3987	213	53	)	)	PUNCT
ejpam-3987	213	54	∫	∫	PROPN
ejpam-3987	214	1	∞	∞	PROPN
ejpam-3987	214	2	0	0	NUM
ejpam-3987	215	1	∫	∫	PROPN
ejpam-3987	215	2	∞	∞	PROPN
ejpam-3987	215	3	0	0	NUM
ejpam-3987	216	1	xp−1yp−1e−(sx)2p−(ty)2p	xp−1yp−1e−(sx)2p−(ty)2p	ADP
ejpam-3987	216	2	log	log	PROPN
ejpam-3987	216	3	(	(	PUNCT
ejpam-3987	216	4	bx	bx	NOUN
ejpam-3987	216	5	y	y	PROPN
ejpam-3987	216	6	)	)	PUNCT
ejpam-3987	216	7	dxdy	dxdy	PROPN
ejpam-3987	216	8	=	=	SYM
ejpam-3987	216	9	is−pt−p	is−pt−p	PROPN
ejpam-3987	216	10	(	(	PUNCT
ejpam-3987	216	11	h−2ip	h−2ip	NOUN
ejpam-3987	216	12	log	log	NOUN
ejpam-3987	216	13	(	(	PUNCT
ejpam-3987	216	14	bts	bts	NOUN
ejpam-3987	216	15	)	)	PUNCT
ejpam-3987	216	16	−3π	−3π	NOUN
ejpam-3987	216	17	4π	4π	PRON
ejpam-3987	216	18	−h	−h	VERB
ejpam-3987	216	19	−	−	PROPN
ejpam-3987	216	20	2ip	2ip	ADJ
ejpam-3987	216	21	log	log	NOUN
ejpam-3987	216	22	(	(	PUNCT
ejpam-3987	216	23	bts	bt	NOUN
ejpam-3987	216	24	)	)	PUNCT
ejpam-3987	217	1	+	+	NOUN
ejpam-3987	217	2	π	π	PROPN
ejpam-3987	217	3	4π	4π	NUM
ejpam-3987	217	4	)	)	PUNCT
ejpam-3987	217	5	4p	4p	NOUN
ejpam-3987	217	6	from	from	ADP
ejpam-3987	217	7	equations	equation	NOUN
ejpam-3987	217	8	(	(	PUNCT
ejpam-3987	217	9	1.8.6	1.8.6	NUM
ejpam-3987	217	10	)	)	PUNCT
ejpam-3987	217	11	and	and	CCONJ
ejpam-3987	217	12	(	(	PUNCT
ejpam-3987	217	13	1.11.10	1.11.10	NUM
ejpam-3987	217	14	)	)	PUNCT
ejpam-3987	217	15	in	in	ADP
ejpam-3987	217	16	[	[	X
ejpam-3987	217	17	2	2	NUM
ejpam-3987	217	18	]	]	PUNCT
ejpam-3987	217	19	.	.	PUNCT
ejpam-3987	218	1	7.5	7.5	NUM
ejpam-3987	218	2	.	.	PUNCT
ejpam-3987	219	1	derivation	derivation	NOUN
ejpam-3987	219	2	of	of	ADP
ejpam-3987	219	3	entry	entry	NOUN
ejpam-3987	219	4	64	64	NUM
ejpam-3987	219	5	in	in	ADP
ejpam-3987	219	6	terms	term	NOUN
ejpam-3987	219	7	of	of	ADP
ejpam-3987	219	8	the	the	DET
ejpam-3987	219	9	zeta	zeta	NOUN
ejpam-3987	219	10	function	function	NOUN
ejpam-3987	219	11	of	of	ADP
ejpam-3987	219	12	riemann	riemann	PROPN
ejpam-3987	219	13	ζ(s	ζ(s	PROPN
ejpam-3987	219	14	)	)	PUNCT
ejpam-3987	219	15	and	and	CCONJ
ejpam-3987	219	16	hurwitz	hurwitz	PROPN
ejpam-3987	219	17	zeta	zeta	PROPN
ejpam-3987	219	18	ζ(s	ζ(s	PROPN
ejpam-3987	219	19	,	,	PUNCT
ejpam-3987	219	20	a	a	PRON
ejpam-3987	219	21	)	)	PUNCT
ejpam-3987	219	22	using	use	VERB
ejpam-3987	219	23	equation	equation	NOUN
ejpam-3987	219	24	(	(	PUNCT
ejpam-3987	219	25	28	28	NUM
ejpam-3987	219	26	)	)	PUNCT
ejpam-3987	219	27	and	and	CCONJ
ejpam-3987	219	28	replacing	replace	VERB
ejpam-3987	219	29	b	b	NUM
ejpam-3987	219	30	by	by	ADP
ejpam-3987	219	31	e	e	PROPN
ejpam-3987	219	32	3iπ	3iπ	ADJ
ejpam-3987	219	33	2p	2p	NOUN
ejpam-3987	219	34	s	s	PART
ejpam-3987	219	35	t	t	NOUN
ejpam-3987	219	36	and	and	CCONJ
ejpam-3987	219	37	simplifying	simplify	VERB
ejpam-3987	219	38	we	we	PRON
ejpam-3987	219	39	get	get	VERB
ejpam-3987	219	40	(	(	PUNCT
ejpam-3987	219	41	33	33	NUM
ejpam-3987	219	42	)	)	PUNCT
ejpam-3987	219	43	∫	∫	PROPN
ejpam-3987	220	1	∞	∞	PROPN
ejpam-3987	220	2	0	0	NUM
ejpam-3987	221	1	∫	∫	PROPN
ejpam-3987	221	2	∞	∞	PROPN
ejpam-3987	221	3	0	0	NUM
ejpam-3987	222	1	xp−1yp−1e−(sx)2p−(ty)2p	xp−1yp−1e−(sx)2p−(ty)2p	PUNCT
ejpam-3987	222	2	logk	logk	PROPN
ejpam-3987	222	3	(	(	PUNCT
ejpam-3987	222	4	e	e	PROPN
ejpam-3987	222	5	3iπ	3iπ	ADJ
ejpam-3987	222	6	2p	2p	NUM
ejpam-3987	222	7	sx	sx	NOUN
ejpam-3987	222	8	ty	ty	INTJ
ejpam-3987	222	9	)	)	PUNCT
ejpam-3987	222	10	dxdy	dxdy	NOUN
ejpam-3987	222	11	=	=	PUNCT
ejpam-3987	223	1	2k−1πk+1	2k−1πk+1	NUM
ejpam-3987	223	2	(	(	PUNCT
ejpam-3987	223	3	i	i	PRON
ejpam-3987	223	4	p	p	NOUN
ejpam-3987	223	5	)	)	PUNCT
ejpam-3987	224	1	k	k	PROPN
ejpam-3987	224	2	s−pt−p	s−pt−p	PROPN
ejpam-3987	224	3	(	(	PUNCT
ejpam-3987	224	4	ζ(−k)−	ζ(−k)−	PROPN
ejpam-3987	224	5	ζ	ζ	NOUN
ejpam-3987	224	6	(	(	PUNCT
ejpam-3987	224	7	−k	−k	PROPN
ejpam-3987	224	8	,	,	PUNCT
ejpam-3987	224	9	3	3	NUM
ejpam-3987	224	10	2	2	NUM
ejpam-3987	224	11	)	)	PUNCT
ejpam-3987	224	12	)	)	PUNCT
ejpam-3987	224	13	p2	p2	PROPN
ejpam-3987	224	14	from	from	ADP
ejpam-3987	224	15	equations	equation	NOUN
ejpam-3987	224	16	(	(	PUNCT
ejpam-3987	224	17	1.10.1	1.10.1	NUM
ejpam-3987	224	18	)	)	PUNCT
ejpam-3987	224	19	and	and	CCONJ
ejpam-3987	224	20	(	(	PUNCT
ejpam-3987	224	21	1.12.1	1.12.1	NUM
ejpam-3987	224	22	)	)	PUNCT
ejpam-3987	224	23	in	in	ADP
ejpam-3987	224	24	[	[	X
ejpam-3987	224	25	2	2	NUM
ejpam-3987	224	26	]	]	PUNCT
ejpam-3987	224	27	.	.	PUNCT
ejpam-3987	225	1	7.6	7.6	NUM
ejpam-3987	225	2	.	.	PUNCT
ejpam-3987	225	3	derivation	derivation	NOUN
ejpam-3987	225	4	of	of	ADP
ejpam-3987	225	5	entry	entry	NOUN
ejpam-3987	225	6	65	65	NUM
ejpam-3987	225	7	in	in	ADP
ejpam-3987	225	8	terms	term	NOUN
ejpam-3987	225	9	of	of	ADP
ejpam-3987	225	10	the	the	DET
ejpam-3987	225	11	zeta	zeta	NOUN
ejpam-3987	225	12	function	function	NOUN
ejpam-3987	225	13	of	of	ADP
ejpam-3987	225	14	riemann	riemann	PROPN
ejpam-3987	225	15	ζ(s	ζ(s	PROPN
ejpam-3987	225	16	)	)	PUNCT
ejpam-3987	225	17	using	use	VERB
ejpam-3987	225	18	equation	equation	NOUN
ejpam-3987	225	19	(	(	PUNCT
ejpam-3987	225	20	28	28	NUM
ejpam-3987	225	21	)	)	PUNCT
ejpam-3987	225	22	and	and	CCONJ
ejpam-3987	225	23	replacing	replace	VERB
ejpam-3987	225	24	n	n	PRON
ejpam-3987	225	25	by	by	ADP
ejpam-3987	225	26	2p	2p	NUM
ejpam-3987	225	27	and	and	CCONJ
ejpam-3987	225	28	b	b	NOUN
ejpam-3987	225	29	by	by	ADP
ejpam-3987	225	30	e	e	X
ejpam-3987	226	1	iπ	iπ	ADV
ejpam-3987	226	2	2p	2p	PROPN
ejpam-3987	226	3	s	s	PART
ejpam-3987	226	4	t	t	NOUN
ejpam-3987	226	5	and	and	CCONJ
ejpam-3987	226	6	simplifying	simplify	VERB
ejpam-3987	226	7	we	we	PRON
ejpam-3987	226	8	get	get	VERB
ejpam-3987	226	9	(	(	PUNCT
ejpam-3987	226	10	34	34	NUM
ejpam-3987	226	11	)	)	PUNCT
ejpam-3987	226	12	∫	∫	PROPN
ejpam-3987	226	13	∞	∞	PROPN
ejpam-3987	226	14	0	0	NUM
ejpam-3987	226	15	∫	∫	PROPN
ejpam-3987	226	16	∞	∞	PROPN
ejpam-3987	226	17	0	0	NUM
ejpam-3987	227	1	xp−1yp−1e−(sx)2p−(ty)2p	xp−1yp−1e−(sx)2p−(ty)2p	PUNCT
ejpam-3987	227	2	logk	logk	PROPN
ejpam-3987	227	3	(	(	PUNCT
ejpam-3987	227	4	e	e	X
ejpam-3987	227	5	iπ	iπ	ADV
ejpam-3987	227	6	2p	2p	NUM
ejpam-3987	227	7	sx	sx	PROPN
ejpam-3987	227	8	ty	ty	INTJ
ejpam-3987	227	9	)	)	PUNCT
ejpam-3987	227	10	dxdy	dxdy	PROPN
ejpam-3987	227	11	=	=	PUNCT
ejpam-3987	228	1	−	−	PROPN
ejpam-3987	228	2	1	1	NUM
ejpam-3987	228	3	2p2	2p2	NUM
ejpam-3987	228	4	(	(	PUNCT
ejpam-3987	228	5	2k+1	2k+1	NOUN
ejpam-3987	228	6	−	−	NOUN
ejpam-3987	228	7	1	1	NUM
ejpam-3987	228	8	)	)	PUNCT
ejpam-3987	229	1	πk+1	πk+1	NOUN
ejpam-3987	229	2	(	(	PUNCT
ejpam-3987	229	3	i	i	PRON
ejpam-3987	229	4	p	p	NOUN
ejpam-3987	229	5	)	)	PUNCT
ejpam-3987	230	1	k	k	PROPN
ejpam-3987	230	2	ζ(−k)s−pt−p	ζ(−k)s−pt−p	PROPN
ejpam-3987	230	3	r.	r.	PROPN
ejpam-3987	230	4	reynolds	reynolds	PROPN
ejpam-3987	230	5	,	,	PUNCT
ejpam-3987	230	6	a.	a.	PROPN
ejpam-3987	230	7	stauffer	stauffer	PROPN
ejpam-3987	230	8	/	/	SYM
ejpam-3987	230	9	eur	eur	PROPN
ejpam-3987	230	10	.	.	PUNCT
ejpam-3987	231	1	j.	j.	PROPN
ejpam-3987	231	2	pure	pure	PROPN
ejpam-3987	231	3	appl	appl	PROPN
ejpam-3987	231	4	.	.	PROPN
ejpam-3987	231	5	math	math	PROPN
ejpam-3987	231	6	,	,	PUNCT
ejpam-3987	231	7	14	14	NUM
ejpam-3987	231	8	(	(	PUNCT
ejpam-3987	231	9	3	3	NUM
ejpam-3987	231	10	)	)	PUNCT
ejpam-3987	231	11	(	(	PUNCT
ejpam-3987	231	12	2021	2021	NUM
ejpam-3987	231	13	)	)	PUNCT
ejpam-3987	231	14	,	,	PUNCT
ejpam-3987	231	15	618	618	NUM
ejpam-3987	231	16	-	-	SYM
ejpam-3987	231	17	637	637	NUM
ejpam-3987	231	18	627	627	NUM
ejpam-3987	231	19	from	from	ADP
ejpam-3987	231	20	equations	equation	NOUN
ejpam-3987	231	21	(	(	PUNCT
ejpam-3987	231	22	1.12.1	1.12.1	NUM
ejpam-3987	231	23	)	)	PUNCT
ejpam-3987	231	24	in	in	ADP
ejpam-3987	231	25	[	[	X
ejpam-3987	231	26	2	2	NUM
ejpam-3987	231	27	]	]	PUNCT
ejpam-3987	231	28	.	.	PUNCT
ejpam-3987	232	1	8	8	X
ejpam-3987	232	2	.	.	PUNCT
ejpam-3987	233	1	derivation	derivation	NOUN
ejpam-3987	233	2	of	of	ADP
ejpam-3987	233	3	definite	definite	ADJ
ejpam-3987	233	4	integrals	integral	NOUN
ejpam-3987	233	5	with	with	ADP
ejpam-3987	233	6	log	log	NOUN
ejpam-3987	233	7	(	(	PUNCT
ejpam-3987	233	8	x	x	NOUN
ejpam-3987	233	9	y	y	PROPN
ejpam-3987	233	10	)	)	PUNCT
ejpam-3987	233	11	in	in	ADP
ejpam-3987	233	12	the	the	DET
ejpam-3987	233	13	denominator	denominator	NOUN
ejpam-3987	233	14	we	we	PRON
ejpam-3987	233	15	will	will	AUX
ejpam-3987	233	16	form	form	VERB
ejpam-3987	233	17	two	two	NUM
ejpam-3987	233	18	equations	equation	NOUN
ejpam-3987	233	19	and	and	CCONJ
ejpam-3987	233	20	take	take	VERB
ejpam-3987	233	21	their	their	PRON
ejpam-3987	233	22	difference	difference	NOUN
ejpam-3987	233	23	.	.	PUNCT
ejpam-3987	234	1	firstly	firstly	ADV
ejpam-3987	234	2	,	,	PUNCT
ejpam-3987	234	3	using	use	VERB
ejpam-3987	234	4	equation	equation	NOUN
ejpam-3987	234	5	(	(	PUNCT
ejpam-3987	234	6	8)	8)	NUM
ejpam-3987	234	7	we	we	PRON
ejpam-3987	234	8	replace	replace	VERB
ejpam-3987	234	9	p	p	NOUN
ejpam-3987	234	10	by	by	ADP
ejpam-3987	234	11	p+	p+	NOUN
ejpam-3987	234	12	q	q	NOUN
ejpam-3987	234	13	to	to	PART
ejpam-3987	234	14	form	form	VERB
ejpam-3987	234	15	the	the	DET
ejpam-3987	234	16	first	first	ADJ
ejpam-3987	234	17	equation	equation	NOUN
ejpam-3987	234	18	.	.	PUNCT
ejpam-3987	235	1	for	for	ADP
ejpam-3987	235	2	the	the	DET
ejpam-3987	235	3	second	second	ADJ
ejpam-3987	235	4	,	,	PUNCT
ejpam-3987	235	5	again	again	ADV
ejpam-3987	235	6	using	use	VERB
ejpam-3987	235	7	equation	equation	NOUN
ejpam-3987	235	8	(	(	PUNCT
ejpam-3987	235	9	8)	8)	NUM
ejpam-3987	235	10	we	we	PRON
ejpam-3987	235	11	replace	replace	VERB
ejpam-3987	235	12	p	p	NOUN
ejpam-3987	235	13	by	by	ADP
ejpam-3987	235	14	p	p	NOUN
ejpam-3987	235	15	−	−	PROPN
ejpam-3987	235	16	q.	q.	NOUN
ejpam-3987	235	17	next	next	ADV
ejpam-3987	235	18	we	we	PRON
ejpam-3987	235	19	take	take	VERB
ejpam-3987	235	20	the	the	DET
ejpam-3987	235	21	difference	difference	NOUN
ejpam-3987	235	22	of	of	ADP
ejpam-3987	235	23	these	these	DET
ejpam-3987	235	24	two	two	NUM
ejpam-3987	235	25	equations	equation	NOUN
ejpam-3987	235	26	setting	set	VERB
ejpam-3987	235	27	k	k	PROPN
ejpam-3987	235	28	=	=	PUNCT
ejpam-3987	235	29	−1	−1	NOUN
ejpam-3987	235	30	,	,	PUNCT
ejpam-3987	235	31	b	b	NOUN
ejpam-3987	235	32	=	=	SYM
ejpam-3987	235	33	1	1	NUM
ejpam-3987	235	34	and	and	CCONJ
ejpam-3987	235	35	simplifying	simplify	VERB
ejpam-3987	235	36	to	to	PART
ejpam-3987	235	37	get	get	VERB
ejpam-3987	235	38	(	(	PUNCT
ejpam-3987	235	39	35	35	NUM
ejpam-3987	235	40	)	)	PUNCT
ejpam-3987	235	41	∫	∫	PROPN
ejpam-3987	236	1	∞	∞	PROPN
ejpam-3987	236	2	0	0	NUM
ejpam-3987	236	3	∫	∫	PROPN
ejpam-3987	236	4	∞	∞	PROPN
ejpam-3987	236	5	0	0	NUM
ejpam-3987	237	1	xp−q−1	xp−q−1	PROPN
ejpam-3987	237	2	(	(	PUNCT
ejpam-3987	237	3	y2q	y2q	X
ejpam-3987	237	4	−	−	PROPN
ejpam-3987	237	5	x2q	x2q	NUM
ejpam-3987	237	6	)	)	PUNCT
ejpam-3987	238	1	yn−p−q−1e−(sx)n−(ty)n	yn−p−q−1e−(sx)n−(ty)n	PROPN
ejpam-3987	238	2	log	log	NOUN
ejpam-3987	238	3	(	(	PUNCT
ejpam-3987	238	4	x	x	SYM
ejpam-3987	238	5	y	y	PROPN
ejpam-3987	238	6	)	)	PUNCT
ejpam-3987	238	7	dxdy	dxdy	PROPN
ejpam-3987	238	8	=	=	PUNCT
ejpam-3987	238	9	s−p−qt−n+p−q	s−p−qt−n+p−q	ADJ
ejpam-3987	238	10	n	n	PROPN
ejpam-3987	238	11	(	(	PUNCT
ejpam-3987	238	12	t2qe	t2qe	X
ejpam-3987	238	13	iπ(p+q	iπ(p+q	X
ejpam-3987	238	14	)	)	PUNCT
ejpam-3987	238	15	n	n	CCONJ
ejpam-3987	238	16	φ	φ	PROPN
ejpam-3987	238	17	(	(	PUNCT
ejpam-3987	238	18	e	e	NOUN
ejpam-3987	238	19	2iπ(p+q	2iπ(p+q	NOUN
ejpam-3987	238	20	)	)	PUNCT
ejpam-3987	238	21	n	n	CCONJ
ejpam-3987	238	22	,	,	PUNCT
ejpam-3987	238	23	1	1	X
ejpam-3987	238	24	,	,	PUNCT
ejpam-3987	238	25	π	π	PROPN
ejpam-3987	238	26	−	−	PROPN
ejpam-3987	238	27	in	in	ADP
ejpam-3987	238	28	log	log	PROPN
ejpam-3987	238	29	(	(	PUNCT
ejpam-3987	238	30	t	t	PROPN
ejpam-3987	238	31	s	s	PART
ejpam-3987	238	32	)	)	PUNCT
ejpam-3987	238	33	2π	2π	PROPN
ejpam-3987	238	34	)	)	PUNCT
ejpam-3987	238	35	−	−	PROPN
ejpam-3987	238	36	s2qe	s2qe	X
ejpam-3987	238	37	iπ(p−q	iπ(p−q	X
ejpam-3987	238	38	)	)	PUNCT
ejpam-3987	238	39	n	n	CCONJ
ejpam-3987	238	40	φ	φ	PROPN
ejpam-3987	238	41	(	(	PUNCT
ejpam-3987	238	42	e	e	PROPN
ejpam-3987	238	43	2iπ(p−q	2iπ(p−q	NUM
ejpam-3987	238	44	)	)	PUNCT
ejpam-3987	238	45	n	n	CCONJ
ejpam-3987	238	46	,	,	PUNCT
ejpam-3987	238	47	1	1	X
ejpam-3987	238	48	,	,	PUNCT
ejpam-3987	238	49	π	π	PROPN
ejpam-3987	238	50	−	−	PROPN
ejpam-3987	238	51	in	in	ADP
ejpam-3987	238	52	log	log	PROPN
ejpam-3987	238	53	(	(	PUNCT
ejpam-3987	238	54	t	t	PROPN
ejpam-3987	238	55	s	s	PART
ejpam-3987	238	56	)	)	PUNCT
ejpam-3987	238	57	2π	2π	NOUN
ejpam-3987	238	58	)	)	PUNCT
ejpam-3987	238	59	)	)	PUNCT
ejpam-3987	238	60	from	from	ADP
ejpam-3987	238	61	entry	entry	NOUN
ejpam-3987	238	62	(	(	PUNCT
ejpam-3987	238	63	1	1	NUM
ejpam-3987	238	64	)	)	PUNCT
ejpam-3987	238	65	in	in	ADP
ejpam-3987	238	66	table	table	NOUN
ejpam-3987	238	67	below	below	ADV
ejpam-3987	238	68	(	(	PUNCT
ejpam-3987	238	69	64:12:7	64:12:7	NUM
ejpam-3987	238	70	)	)	PUNCT
ejpam-3987	238	71	and	and	CCONJ
ejpam-3987	238	72	equations	equation	NOUN
ejpam-3987	238	73	(	(	PUNCT
ejpam-3987	238	74	58:4:4	58:4:4	NOUN
ejpam-3987	238	75	)	)	PUNCT
ejpam-3987	238	76	and	and	CCONJ
ejpam-3987	238	77	(	(	PUNCT
ejpam-3987	238	78	58:12:2	58:12:2	NUM
ejpam-3987	238	79	)	)	PUNCT
ejpam-3987	238	80	in	in	ADP
ejpam-3987	238	81	[	[	X
ejpam-3987	238	82	6	6	NUM
ejpam-3987	238	83	]	]	PUNCT
ejpam-3987	238	84	.	.	PUNCT
ejpam-3987	239	1	8.1	8.1	NUM
ejpam-3987	239	2	.	.	PUNCT
ejpam-3987	240	1	derivation	derivation	NOUN
ejpam-3987	240	2	of	of	ADP
ejpam-3987	240	3	entry	entry	NOUN
ejpam-3987	240	4	66	66	NUM
ejpam-3987	240	5	in	in	ADP
ejpam-3987	240	6	terms	term	NOUN
ejpam-3987	240	7	of	of	ADP
ejpam-3987	240	8	the	the	DET
ejpam-3987	240	9	logarithmic	logarithmic	ADJ
ejpam-3987	240	10	function	function	NOUN
ejpam-3987	240	11	using	use	VERB
ejpam-3987	240	12	equation	equation	NOUN
ejpam-3987	240	13	(	(	PUNCT
ejpam-3987	240	14	35	35	NUM
ejpam-3987	240	15	)	)	PUNCT
ejpam-3987	240	16	and	and	CCONJ
ejpam-3987	240	17	setting	set	VERB
ejpam-3987	240	18	s	s	X
ejpam-3987	240	19	=	=	SYM
ejpam-3987	240	20	1	1	NUM
ejpam-3987	240	21	,	,	PUNCT
ejpam-3987	240	22	t	t	NOUN
ejpam-3987	240	23	=	=	SYM
ejpam-3987	240	24	1	1	NUM
ejpam-3987	240	25	,	,	PUNCT
ejpam-3987	240	26	p	p	NOUN
ejpam-3987	240	27	=	=	SYM
ejpam-3987	240	28	1/2	1/2	NUM
ejpam-3987	240	29	,	,	PUNCT
ejpam-3987	240	30	q	q	NOUN
ejpam-3987	240	31	=	=	SYM
ejpam-3987	240	32	1/3	1/3	NUM
ejpam-3987	240	33	,	,	PUNCT
ejpam-3987	240	34	n	n	NOUN
ejpam-3987	240	35	=	=	SYM
ejpam-3987	240	36	1	1	NUM
ejpam-3987	240	37	and	and	CCONJ
ejpam-3987	240	38	simplifying	simplify	VERB
ejpam-3987	240	39	we	we	PRON
ejpam-3987	240	40	get	get	VERB
ejpam-3987	240	41	(	(	PUNCT
ejpam-3987	240	42	36	36	NUM
ejpam-3987	240	43	)	)	PUNCT
ejpam-3987	240	44	∫	∫	PROPN
ejpam-3987	241	1	∞	∞	PROPN
ejpam-3987	241	2	0	0	NUM
ejpam-3987	242	1	∫	∫	PROPN
ejpam-3987	242	2	∞	∞	PROPN
ejpam-3987	242	3	0	0	PROPN
ejpam-3987	243	1	e−x−y	e−x−y	NOUN
ejpam-3987	243	2	(	(	PUNCT
ejpam-3987	243	3	x2/3	x2/3	PROPN
ejpam-3987	243	4	−	−	PROPN
ejpam-3987	243	5	y2/3	y2/3	PROPN
ejpam-3987	243	6	)	)	PUNCT
ejpam-3987	244	1	x5/6y5/6	x5/6y5/6	PROPN
ejpam-3987	244	2	log	log	VERB
ejpam-3987	244	3	(	(	PUNCT
ejpam-3987	244	4	x	x	SYM
ejpam-3987	244	5	y	y	PROPN
ejpam-3987	244	6	)	)	PUNCT
ejpam-3987	244	7	dxdy	dxdy	PROPN
ejpam-3987	244	8	=	=	SYM
ejpam-3987	244	9	log	log	PROPN
ejpam-3987	244	10	(	(	PUNCT
ejpam-3987	244	11	7	7	NUM
ejpam-3987	244	12	+	+	CCONJ
ejpam-3987	244	13	4	4	NUM
ejpam-3987	244	14	√	√	NUM
ejpam-3987	244	15	3	3	NUM
ejpam-3987	244	16	)	)	PUNCT
ejpam-3987	244	17	from	from	ADP
ejpam-3987	244	18	table	table	NOUN
ejpam-3987	244	19	(	(	PUNCT
ejpam-3987	244	20	18	18	NUM
ejpam-3987	244	21	-	-	SYM
ejpam-3987	244	22	1	1	NUM
ejpam-3987	244	23	)	)	PUNCT
ejpam-3987	244	24	in	in	ADP
ejpam-3987	244	25	[	[	X
ejpam-3987	244	26	6	6	NUM
ejpam-3987	244	27	]	]	PUNCT
ejpam-3987	244	28	.	.	PUNCT
ejpam-3987	245	1	8.2	8.2	NUM
ejpam-3987	245	2	.	.	PUNCT
ejpam-3987	245	3	derivation	derivation	NOUN
ejpam-3987	245	4	of	of	ADP
ejpam-3987	245	5	entry	entry	NOUN
ejpam-3987	245	6	67	67	NUM
ejpam-3987	245	7	in	in	ADP
ejpam-3987	245	8	terms	term	NOUN
ejpam-3987	245	9	of	of	ADP
ejpam-3987	245	10	the	the	DET
ejpam-3987	245	11	hyperbolic	hyperbolic	ADJ
ejpam-3987	245	12	cotangent	cotangent	NOUN
ejpam-3987	245	13	function	function	NOUN
ejpam-3987	245	14	using	use	VERB
ejpam-3987	245	15	equation	equation	NOUN
ejpam-3987	245	16	(	(	PUNCT
ejpam-3987	245	17	35	35	NUM
ejpam-3987	245	18	)	)	PUNCT
ejpam-3987	245	19	and	and	CCONJ
ejpam-3987	245	20	setting	set	VERB
ejpam-3987	245	21	s	s	X
ejpam-3987	245	22	=	=	SYM
ejpam-3987	245	23	1	1	NUM
ejpam-3987	245	24	,	,	PUNCT
ejpam-3987	245	25	t	t	NOUN
ejpam-3987	245	26	=	=	SYM
ejpam-3987	245	27	1	1	NUM
ejpam-3987	245	28	,	,	PUNCT
ejpam-3987	245	29	p	p	NOUN
ejpam-3987	245	30	=	=	SYM
ejpam-3987	245	31	1/2	1/2	NUM
ejpam-3987	245	32	,	,	PUNCT
ejpam-3987	245	33	q	q	NOUN
ejpam-3987	245	34	=	=	SYM
ejpam-3987	245	35	1/3	1/3	NUM
ejpam-3987	245	36	,	,	PUNCT
ejpam-3987	245	37	n	n	NOUN
ejpam-3987	245	38	=	=	SYM
ejpam-3987	245	39	2	2	NUM
ejpam-3987	245	40	and	and	CCONJ
ejpam-3987	245	41	simplifying	simplify	VERB
ejpam-3987	245	42	we	we	PRON
ejpam-3987	245	43	get	get	VERB
ejpam-3987	245	44	(	(	PUNCT
ejpam-3987	245	45	37	37	NUM
ejpam-3987	245	46	)	)	PUNCT
ejpam-3987	245	47	∫	∫	PROPN
ejpam-3987	246	1	∞	∞	PROPN
ejpam-3987	246	2	0	0	NUM
ejpam-3987	247	1	∫	∫	PROPN
ejpam-3987	247	2	∞	∞	NUM
ejpam-3987	247	3	0	0	NUM
ejpam-3987	247	4	6	6	NUM
ejpam-3987	247	5	√	√	PROPN
ejpam-3987	247	6	ye−x	ye−x	PROPN
ejpam-3987	247	7	2−y2	2−y2	NUM
ejpam-3987	247	8	(	(	PUNCT
ejpam-3987	247	9	x2/3	x2/3	PROPN
ejpam-3987	247	10	−	−	NUM
ejpam-3987	247	11	y2/3	y2/3	PROPN
ejpam-3987	247	12	)	)	PUNCT
ejpam-3987	248	1	x5/6	x5/6	PROPN
ejpam-3987	249	1	log	log	NOUN
ejpam-3987	249	2	(	(	PUNCT
ejpam-3987	249	3	x	x	SYM
ejpam-3987	249	4	y	y	PROPN
ejpam-3987	249	5	)	)	PUNCT
ejpam-3987	249	6	dxdy	dxdy	PROPN
ejpam-3987	249	7	=	=	PUNCT
ejpam-3987	250	1	coth−1	coth−1	NOUN
ejpam-3987	250	2	(	(	PUNCT
ejpam-3987	250	3	√	√	ADP
ejpam-3987	250	4	2	2	NUM
ejpam-3987	250	5	)	)	PUNCT
ejpam-3987	250	6	from	from	ADP
ejpam-3987	250	7	table	table	NOUN
ejpam-3987	250	8	(	(	PUNCT
ejpam-3987	250	9	18	18	NUM
ejpam-3987	250	10	-	-	SYM
ejpam-3987	250	11	1	1	NUM
ejpam-3987	250	12	)	)	PUNCT
ejpam-3987	250	13	in	in	ADP
ejpam-3987	250	14	[	[	X
ejpam-3987	250	15	6	6	NUM
ejpam-3987	250	16	]	]	PUNCT
ejpam-3987	250	17	.	.	PUNCT
ejpam-3987	251	1	r.	r.	PROPN
ejpam-3987	251	2	reynolds	reynolds	PROPN
ejpam-3987	251	3	,	,	PUNCT
ejpam-3987	251	4	a.	a.	PROPN
ejpam-3987	251	5	stauffer	stauffer	PROPN
ejpam-3987	251	6	/	/	SYM
ejpam-3987	251	7	eur	eur	PROPN
ejpam-3987	251	8	.	.	PUNCT
ejpam-3987	252	1	j.	j.	PROPN
ejpam-3987	252	2	pure	pure	PROPN
ejpam-3987	252	3	appl	appl	PROPN
ejpam-3987	252	4	.	.	PROPN
ejpam-3987	252	5	math	math	PROPN
ejpam-3987	252	6	,	,	PUNCT
ejpam-3987	252	7	14	14	NUM
ejpam-3987	252	8	(	(	PUNCT
ejpam-3987	252	9	3	3	NUM
ejpam-3987	252	10	)	)	PUNCT
ejpam-3987	252	11	(	(	PUNCT
ejpam-3987	252	12	2021	2021	NUM
ejpam-3987	252	13	)	)	PUNCT
ejpam-3987	252	14	,	,	PUNCT
ejpam-3987	252	15	618	618	NUM
ejpam-3987	252	16	-	-	SYM
ejpam-3987	252	17	637	637	NUM
ejpam-3987	252	18	628	628	NUM
ejpam-3987	252	19	8.3	8.3	NUM
ejpam-3987	252	20	.	.	PUNCT
ejpam-3987	253	1	derivation	derivation	NOUN
ejpam-3987	253	2	of	of	ADP
ejpam-3987	253	3	entry	entry	NOUN
ejpam-3987	253	4	68	68	NUM
ejpam-3987	253	5	in	in	ADP
ejpam-3987	253	6	terms	term	NOUN
ejpam-3987	253	7	of	of	ADP
ejpam-3987	253	8	the	the	DET
ejpam-3987	253	9	hyperbolic	hyperbolic	ADJ
ejpam-3987	253	10	cotangent	cotangent	NOUN
ejpam-3987	253	11	function	function	NOUN
ejpam-3987	253	12	using	use	VERB
ejpam-3987	253	13	equation	equation	NOUN
ejpam-3987	253	14	(	(	PUNCT
ejpam-3987	253	15	35	35	NUM
ejpam-3987	253	16	)	)	PUNCT
ejpam-3987	253	17	and	and	CCONJ
ejpam-3987	253	18	setting	set	VERB
ejpam-3987	253	19	s	s	X
ejpam-3987	253	20	=	=	SYM
ejpam-3987	253	21	1	1	NUM
ejpam-3987	253	22	,	,	PUNCT
ejpam-3987	253	23	t	t	NOUN
ejpam-3987	253	24	=	=	SYM
ejpam-3987	253	25	1	1	NUM
ejpam-3987	253	26	,	,	PUNCT
ejpam-3987	253	27	p	p	NOUN
ejpam-3987	253	28	=	=	SYM
ejpam-3987	253	29	1/2	1/2	NUM
ejpam-3987	253	30	,	,	PUNCT
ejpam-3987	253	31	q	q	NOUN
ejpam-3987	253	32	=	=	SYM
ejpam-3987	253	33	1/4	1/4	NUM
ejpam-3987	253	34	,	,	PUNCT
ejpam-3987	253	35	n	n	NOUN
ejpam-3987	253	36	=	=	SYM
ejpam-3987	253	37	1	1	NUM
ejpam-3987	253	38	and	and	CCONJ
ejpam-3987	253	39	simplifying	simplify	VERB
ejpam-3987	253	40	we	we	PRON
ejpam-3987	253	41	get	get	VERB
ejpam-3987	253	42	(	(	PUNCT
ejpam-3987	253	43	38	38	NUM
ejpam-3987	253	44	)	)	PUNCT
ejpam-3987	253	45	∫	∫	PROPN
ejpam-3987	254	1	∞	∞	PROPN
ejpam-3987	254	2	0	0	NUM
ejpam-3987	255	1	∫	∫	PROPN
ejpam-3987	255	2	∞	∞	PROPN
ejpam-3987	255	3	0	0	NUM
ejpam-3987	256	1	e−x−y	e−x−y	NOUN
ejpam-3987	256	2	(	(	PUNCT
ejpam-3987	256	3	√	√	PROPN
ejpam-3987	256	4	x−√y	x−√y	PUNCT
ejpam-3987	256	5	)	)	PUNCT
ejpam-3987	257	1	x3/4y3/4	x3/4y3/4	PROPN
ejpam-3987	257	2	log	log	VERB
ejpam-3987	257	3	(	(	PUNCT
ejpam-3987	257	4	x	x	SYM
ejpam-3987	257	5	y	y	PROPN
ejpam-3987	257	6	)	)	PUNCT
ejpam-3987	257	7	dxdy	dxdy	NOUN
ejpam-3987	257	8	=	=	SYM
ejpam-3987	257	9	2	2	NUM
ejpam-3987	257	10	coth−1	coth−1	NOUN
ejpam-3987	257	11	(	(	PUNCT
ejpam-3987	257	12	√	√	ADP
ejpam-3987	257	13	2	2	NUM
ejpam-3987	257	14	)	)	PUNCT
ejpam-3987	257	15	from	from	ADP
ejpam-3987	257	16	table	table	NOUN
ejpam-3987	257	17	(	(	PUNCT
ejpam-3987	257	18	18	18	NUM
ejpam-3987	257	19	-	-	SYM
ejpam-3987	257	20	1	1	NUM
ejpam-3987	257	21	)	)	PUNCT
ejpam-3987	257	22	in	in	ADP
ejpam-3987	257	23	[	[	X
ejpam-3987	257	24	6	6	NUM
ejpam-3987	257	25	]	]	PUNCT
ejpam-3987	257	26	.	.	PUNCT
ejpam-3987	258	1	8.4	8.4	NUM
ejpam-3987	258	2	.	.	PUNCT
ejpam-3987	259	1	derivation	derivation	NOUN
ejpam-3987	259	2	of	of	ADP
ejpam-3987	259	3	entry	entry	NOUN
ejpam-3987	259	4	69	69	NUM
ejpam-3987	259	5	in	in	ADP
ejpam-3987	259	6	terms	term	NOUN
ejpam-3987	259	7	of	of	ADP
ejpam-3987	259	8	the	the	DET
ejpam-3987	259	9	logarithmic	logarithmic	ADJ
ejpam-3987	259	10	function	function	NOUN
ejpam-3987	259	11	using	use	VERB
ejpam-3987	259	12	equation	equation	NOUN
ejpam-3987	259	13	(	(	PUNCT
ejpam-3987	259	14	35	35	NUM
ejpam-3987	259	15	)	)	PUNCT
ejpam-3987	259	16	and	and	CCONJ
ejpam-3987	259	17	setting	set	VERB
ejpam-3987	259	18	s	s	X
ejpam-3987	259	19	=	=	SYM
ejpam-3987	259	20	1	1	NUM
ejpam-3987	259	21	,	,	PUNCT
ejpam-3987	259	22	t	t	NOUN
ejpam-3987	259	23	=	=	SYM
ejpam-3987	259	24	1	1	NUM
ejpam-3987	259	25	,	,	PUNCT
ejpam-3987	259	26	p	p	NOUN
ejpam-3987	259	27	=	=	SYM
ejpam-3987	259	28	1/2	1/2	NUM
ejpam-3987	259	29	,	,	PUNCT
ejpam-3987	259	30	q	q	NOUN
ejpam-3987	259	31	=	=	SYM
ejpam-3987	259	32	−1/3	−1/3	ADJ
ejpam-3987	259	33	,	,	PUNCT
ejpam-3987	259	34	n	n	NOUN
ejpam-3987	259	35	=	=	SYM
ejpam-3987	259	36	1	1	NUM
ejpam-3987	259	37	and	and	CCONJ
ejpam-3987	259	38	simplifying	simplify	VERB
ejpam-3987	259	39	we	we	PRON
ejpam-3987	259	40	get	get	VERB
ejpam-3987	259	41	(	(	PUNCT
ejpam-3987	259	42	39	39	NUM
ejpam-3987	259	43	)	)	PUNCT
ejpam-3987	259	44	∫	∫	PROPN
ejpam-3987	260	1	∞	∞	PROPN
ejpam-3987	260	2	0	0	NUM
ejpam-3987	261	1	∫	∫	PROPN
ejpam-3987	261	2	∞	∞	PROPN
ejpam-3987	261	3	0	0	PROPN
ejpam-3987	262	1	e−x−y	e−x−y	NOUN
ejpam-3987	262	2	(	(	PUNCT
ejpam-3987	262	3	y2/3	y2/3	NOUN
ejpam-3987	262	4	−	−	PROPN
ejpam-3987	262	5	x2/3	x2/3	PROPN
ejpam-3987	262	6	)	)	PUNCT
ejpam-3987	263	1	x5/6y5/6	x5/6y5/6	PROPN
ejpam-3987	263	2	log	log	VERB
ejpam-3987	263	3	(	(	PUNCT
ejpam-3987	263	4	x	x	SYM
ejpam-3987	263	5	y	y	PROPN
ejpam-3987	263	6	)	)	PUNCT
ejpam-3987	263	7	dxdy	dxdy	PROPN
ejpam-3987	263	8	=	=	PUNCT
ejpam-3987	263	9	−2	−2	PROPN
ejpam-3987	264	1	log	log	NOUN
ejpam-3987	264	2	(	(	PUNCT
ejpam-3987	264	3	2	2	NUM
ejpam-3987	264	4	+	+	CCONJ
ejpam-3987	264	5	√	√	NUM
ejpam-3987	264	6	3	3	NUM
ejpam-3987	264	7	)	)	PUNCT
ejpam-3987	264	8	from	from	ADP
ejpam-3987	264	9	table	table	NOUN
ejpam-3987	264	10	(	(	PUNCT
ejpam-3987	264	11	18	18	NUM
ejpam-3987	264	12	-	-	SYM
ejpam-3987	264	13	1	1	NUM
ejpam-3987	264	14	)	)	PUNCT
ejpam-3987	264	15	in	in	ADP
ejpam-3987	264	16	[	[	X
ejpam-3987	264	17	6	6	NUM
ejpam-3987	264	18	]	]	PUNCT
ejpam-3987	264	19	.	.	PUNCT
ejpam-3987	265	1	8.5	8.5	NUM
ejpam-3987	265	2	.	.	PUNCT
ejpam-3987	266	1	derivation	derivation	NOUN
ejpam-3987	266	2	of	of	ADP
ejpam-3987	266	3	entry	entry	NOUN
ejpam-3987	266	4	70	70	NUM
ejpam-3987	266	5	in	in	ADP
ejpam-3987	266	6	terms	term	NOUN
ejpam-3987	266	7	of	of	ADP
ejpam-3987	266	8	the	the	DET
ejpam-3987	266	9	logarithmic	logarithmic	ADJ
ejpam-3987	266	10	function	function	NOUN
ejpam-3987	266	11	using	use	VERB
ejpam-3987	266	12	equation	equation	NOUN
ejpam-3987	266	13	(	(	PUNCT
ejpam-3987	266	14	35	35	NUM
ejpam-3987	266	15	)	)	PUNCT
ejpam-3987	266	16	and	and	CCONJ
ejpam-3987	266	17	setting	set	VERB
ejpam-3987	266	18	s	s	X
ejpam-3987	266	19	=	=	SYM
ejpam-3987	266	20	1	1	NUM
ejpam-3987	266	21	,	,	PUNCT
ejpam-3987	266	22	t	t	NOUN
ejpam-3987	266	23	=	=	SYM
ejpam-3987	266	24	1	1	NUM
ejpam-3987	266	25	,	,	PUNCT
ejpam-3987	266	26	p	p	NOUN
ejpam-3987	266	27	=	=	SYM
ejpam-3987	266	28	1/2	1/2	NUM
ejpam-3987	266	29	,	,	PUNCT
ejpam-3987	266	30	q	q	NOUN
ejpam-3987	266	31	=	=	SYM
ejpam-3987	266	32	1/4	1/4	NUM
ejpam-3987	266	33	,	,	PUNCT
ejpam-3987	266	34	n	n	NOUN
ejpam-3987	266	35	=	=	SYM
ejpam-3987	266	36	3	3	NUM
ejpam-3987	266	37	and	and	CCONJ
ejpam-3987	266	38	simplifying	simplify	VERB
ejpam-3987	266	39	we	we	PRON
ejpam-3987	266	40	get	get	VERB
ejpam-3987	266	41	(	(	PUNCT
ejpam-3987	266	42	40	40	NUM
ejpam-3987	266	43	)	)	PUNCT
ejpam-3987	266	44	∫	∫	PROPN
ejpam-3987	267	1	∞	∞	PROPN
ejpam-3987	267	2	0	0	NUM
ejpam-3987	267	3	∫	∫	PROPN
ejpam-3987	267	4	∞	∞	PROPN
ejpam-3987	267	5	0	0	NUM
ejpam-3987	268	1	y5/4e−x	y5/4e−x	PROPN
ejpam-3987	268	2	3−y3	3−y3	NUM
ejpam-3987	268	3	(	(	PUNCT
ejpam-3987	268	4	√	√	NUM
ejpam-3987	268	5	x−√y	x−√y	PUNCT
ejpam-3987	268	6	)	)	PUNCT
ejpam-3987	269	1	x3/4	x3/4	PROPN
ejpam-3987	269	2	log	log	NOUN
ejpam-3987	269	3	(	(	PUNCT
ejpam-3987	269	4	x	x	SYM
ejpam-3987	269	5	y	y	PROPN
ejpam-3987	269	6	)	)	PUNCT
ejpam-3987	269	7	dxdy	dxdy	PROPN
ejpam-3987	269	8	=	=	SYM
ejpam-3987	269	9	−1	−1	NOUN
ejpam-3987	269	10	6	6	NUM
ejpam-3987	269	11	log	log	NOUN
ejpam-3987	269	12	(	(	PUNCT
ejpam-3987	269	13	5−	5−	NUM
ejpam-3987	269	14	2	2	NUM
ejpam-3987	269	15	√	√	NUM
ejpam-3987	269	16	6	6	NUM
ejpam-3987	269	17	)	)	PUNCT
ejpam-3987	269	18	8.6	8.6	NUM
ejpam-3987	269	19	.	.	PUNCT
ejpam-3987	270	1	derivation	derivation	NOUN
ejpam-3987	270	2	of	of	ADP
ejpam-3987	270	3	entry	entry	NOUN
ejpam-3987	270	4	71	71	NUM
ejpam-3987	270	5	in	in	ADP
ejpam-3987	270	6	terms	term	NOUN
ejpam-3987	270	7	of	of	ADP
ejpam-3987	270	8	the	the	DET
ejpam-3987	270	9	hyperbolic	hyperbolic	ADJ
ejpam-3987	270	10	tangent	tangent	NOUN
ejpam-3987	270	11	function	function	NOUN
ejpam-3987	270	12	using	use	VERB
ejpam-3987	270	13	equation	equation	NOUN
ejpam-3987	270	14	(	(	PUNCT
ejpam-3987	270	15	35	35	NUM
ejpam-3987	270	16	)	)	PUNCT
ejpam-3987	270	17	and	and	CCONJ
ejpam-3987	270	18	setting	set	VERB
ejpam-3987	270	19	s	s	X
ejpam-3987	270	20	=	=	SYM
ejpam-3987	270	21	1	1	NUM
ejpam-3987	270	22	,	,	PUNCT
ejpam-3987	270	23	t	t	NOUN
ejpam-3987	270	24	=	=	SYM
ejpam-3987	270	25	1	1	NUM
ejpam-3987	270	26	,	,	PUNCT
ejpam-3987	270	27	p	p	NOUN
ejpam-3987	270	28	=	=	NOUN
ejpam-3987	270	29	1/4	1/4	NUM
ejpam-3987	270	30	,	,	PUNCT
ejpam-3987	270	31	q	q	NOUN
ejpam-3987	270	32	=	=	PUNCT
ejpam-3987	270	33	i/3	i/3	PROPN
ejpam-3987	270	34	,	,	PUNCT
ejpam-3987	270	35	n	n	NOUN
ejpam-3987	270	36	=	=	SYM
ejpam-3987	270	37	1	1	NUM
ejpam-3987	270	38	and	and	CCONJ
ejpam-3987	270	39	simplifying	simplify	VERB
ejpam-3987	270	40	we	we	PRON
ejpam-3987	270	41	get	get	VERB
ejpam-3987	270	42	(	(	PUNCT
ejpam-3987	270	43	41	41	NUM
ejpam-3987	270	44	)	)	PUNCT
ejpam-3987	270	45	∫	∫	PROPN
ejpam-3987	271	1	∞	∞	PROPN
ejpam-3987	271	2	0	0	NUM
ejpam-3987	272	1	∫	∫	PROPN
ejpam-3987	272	2	∞	∞	PROPN
ejpam-3987	272	3	0	0	PROPN
ejpam-3987	273	1	e−x−y	e−x−y	NOUN
ejpam-3987	273	2	(	(	PUNCT
ejpam-3987	273	3	x2/3	x2/3	PROPN
ejpam-3987	273	4	−	−	NUM
ejpam-3987	273	5	y2/3	y2/3	PROPN
ejpam-3987	273	6	)	)	PUNCT
ejpam-3987	273	7	x13/12y7/12	x13/12y7/12	PUNCT
ejpam-3987	274	1	log	log	VERB
ejpam-3987	274	2	(	(	PUNCT
ejpam-3987	274	3	x	x	SYM
ejpam-3987	274	4	y	y	PROPN
ejpam-3987	274	5	)	)	PUNCT
ejpam-3987	274	6	dxdy	dxdy	NOUN
ejpam-3987	274	7	=	=	SYM
ejpam-3987	274	8	2	2	NUM
ejpam-3987	274	9	tanh−1	tanh−1	NOUN
ejpam-3987	274	10	(	(	PUNCT
ejpam-3987	274	11	√	√	NUM
ejpam-3987	274	12	3	3	NUM
ejpam-3987	274	13	2	2	NUM
ejpam-3987	274	14	)	)	PUNCT
ejpam-3987	274	15	from	from	ADP
ejpam-3987	274	16	table	table	NOUN
ejpam-3987	274	17	(	(	PUNCT
ejpam-3987	274	18	18	18	NUM
ejpam-3987	274	19	-	-	SYM
ejpam-3987	274	20	1	1	NUM
ejpam-3987	274	21	)	)	PUNCT
ejpam-3987	274	22	in	in	ADP
ejpam-3987	274	23	[	[	X
ejpam-3987	274	24	6	6	NUM
ejpam-3987	274	25	]	]	PUNCT
ejpam-3987	274	26	.	.	PUNCT
ejpam-3987	275	1	8.7	8.7	NUM
ejpam-3987	275	2	.	.	PUNCT
ejpam-3987	275	3	derivation	derivation	NOUN
ejpam-3987	275	4	of	of	ADP
ejpam-3987	275	5	entry	entry	NOUN
ejpam-3987	275	6	72	72	NUM
ejpam-3987	275	7	in	in	ADP
ejpam-3987	275	8	terms	term	NOUN
ejpam-3987	275	9	of	of	ADP
ejpam-3987	275	10	the	the	DET
ejpam-3987	275	11	hypergeometric	hypergeometric	ADJ
ejpam-3987	275	12	function	function	NOUN
ejpam-3987	275	13	using	use	VERB
ejpam-3987	275	14	equation	equation	NOUN
ejpam-3987	275	15	(	(	PUNCT
ejpam-3987	275	16	35	35	NUM
ejpam-3987	275	17	)	)	PUNCT
ejpam-3987	275	18	and	and	CCONJ
ejpam-3987	275	19	setting	set	VERB
ejpam-3987	275	20	s	s	X
ejpam-3987	275	21	=	=	SYM
ejpam-3987	275	22	1	1	NUM
ejpam-3987	275	23	,	,	PUNCT
ejpam-3987	275	24	t	t	NOUN
ejpam-3987	275	25	=	=	SYM
ejpam-3987	275	26	1	1	NUM
ejpam-3987	275	27	,	,	PUNCT
ejpam-3987	275	28	p	p	NOUN
ejpam-3987	275	29	=	=	NOUN
ejpam-3987	275	30	1/4	1/4	NUM
ejpam-3987	275	31	,	,	PUNCT
ejpam-3987	275	32	q	q	NOUN
ejpam-3987	275	33	=	=	SYM
ejpam-3987	275	34	1/3	1/3	NUM
ejpam-3987	275	35	,	,	PUNCT
ejpam-3987	275	36	n	n	NOUN
ejpam-3987	275	37	=	=	SYM
ejpam-3987	275	38	3/2	3/2	NUM
ejpam-3987	275	39	and	and	CCONJ
ejpam-3987	275	40	simplifying	simplify	VERB
ejpam-3987	275	41	we	we	PRON
ejpam-3987	275	42	get	get	VERB
ejpam-3987	275	43	r.	r.	PROPN
ejpam-3987	275	44	reynolds	reynolds	PROPN
ejpam-3987	275	45	,	,	PUNCT
ejpam-3987	275	46	a.	a.	PROPN
ejpam-3987	275	47	stauffer	stauffer	PROPN
ejpam-3987	275	48	/	/	SYM
ejpam-3987	275	49	eur	eur	PROPN
ejpam-3987	275	50	.	.	PUNCT
ejpam-3987	276	1	j.	j.	PROPN
ejpam-3987	276	2	pure	pure	PROPN
ejpam-3987	276	3	appl	appl	PROPN
ejpam-3987	276	4	.	.	PROPN
ejpam-3987	276	5	math	math	PROPN
ejpam-3987	276	6	,	,	PUNCT
ejpam-3987	276	7	14	14	NUM
ejpam-3987	276	8	(	(	PUNCT
ejpam-3987	276	9	3	3	NUM
ejpam-3987	276	10	)	)	PUNCT
ejpam-3987	276	11	(	(	PUNCT
ejpam-3987	276	12	2021	2021	NUM
ejpam-3987	276	13	)	)	PUNCT
ejpam-3987	276	14	,	,	PUNCT
ejpam-3987	276	15	618	618	NUM
ejpam-3987	276	16	-	-	SYM
ejpam-3987	276	17	637	637	NUM
ejpam-3987	276	18	629	629	NUM
ejpam-3987	276	19	(	(	PUNCT
ejpam-3987	276	20	42	42	NUM
ejpam-3987	276	21	)	)	PUNCT
ejpam-3987	276	22	∫	∫	PROPN
ejpam-3987	277	1	∞	∞	PROPN
ejpam-3987	277	2	0	0	NUM
ejpam-3987	278	1	∫	∫	PROPN
ejpam-3987	278	2	∞	∞	NOUN
ejpam-3987	278	3	0	0	NUM
ejpam-3987	279	1	e−x	e−x	PROPN
ejpam-3987	279	2	3/2−y3/2	3/2−y3/2	PROPN
ejpam-3987	279	3	(	(	PUNCT
ejpam-3987	279	4	x2/3	x2/3	PROPN
ejpam-3987	279	5	−	−	NUM
ejpam-3987	279	6	y2/3	y2/3	PROPN
ejpam-3987	279	7	)	)	PUNCT
ejpam-3987	279	8	x5/6	x5/6	PROPN
ejpam-3987	280	1	3	3	NUM
ejpam-3987	280	2	√	√	NUM
ejpam-3987	280	3	y	y	PROPN
ejpam-3987	280	4	log	log	NOUN
ejpam-3987	280	5	(	(	PUNCT
ejpam-3987	280	6	x	x	NOUN
ejpam-3987	280	7	y	y	PROPN
ejpam-3987	280	8	)	)	PUNCT
ejpam-3987	280	9	dxdy	dxdy	PROPN
ejpam-3987	280	10	=	=	PUNCT
ejpam-3987	280	11	−4	−4	PROPN
ejpam-3987	280	12	3	3	NUM
ejpam-3987	280	13	(	(	PUNCT
ejpam-3987	280	14	(	(	PUNCT
ejpam-3987	280	15	−1)5/9	−1)5/9	PROPN
ejpam-3987	280	16	2f1	2f1	NUM
ejpam-3987	280	17	(	(	PUNCT
ejpam-3987	280	18	1	1	NUM
ejpam-3987	280	19	2	2	NUM
ejpam-3987	280	20	,	,	PUNCT
ejpam-3987	280	21	1	1	NUM
ejpam-3987	280	22	;	;	PUNCT
ejpam-3987	280	23	3	3	NUM
ejpam-3987	280	24	2	2	NUM
ejpam-3987	280	25	;	;	PUNCT
ejpam-3987	280	26	e−	e−	PROPN
ejpam-3987	280	27	8iπ	8iπ	NOUN
ejpam-3987	280	28	9	9	NUM
ejpam-3987	280	29	)	)	PUNCT
ejpam-3987	280	30	−	−	PROPN
ejpam-3987	280	31	9	9	NUM
ejpam-3987	280	32	√	√	NUM
ejpam-3987	280	33	−1	−1	NOUN
ejpam-3987	280	34	2f1	2f1	NUM
ejpam-3987	280	35	(	(	PUNCT
ejpam-3987	280	36	1	1	NUM
ejpam-3987	280	37	2	2	NUM
ejpam-3987	280	38	,	,	PUNCT
ejpam-3987	280	39	1	1	NUM
ejpam-3987	280	40	;	;	PUNCT
ejpam-3987	280	41	3	3	NUM
ejpam-3987	280	42	2	2	NUM
ejpam-3987	280	43	;	;	PUNCT
ejpam-3987	280	44	e	e	X
ejpam-3987	280	45	2iπ	2iπ	NOUN
ejpam-3987	280	46	9	9	NUM
ejpam-3987	280	47	)	)	PUNCT
ejpam-3987	280	48	)	)	PUNCT
ejpam-3987	280	49	from	from	ADP
ejpam-3987	280	50	equations	equation	NOUN
ejpam-3987	280	51	(	(	PUNCT
ejpam-3987	280	52	58:4:4	58:4:4	NOUN
ejpam-3987	280	53	)	)	PUNCT
ejpam-3987	280	54	and	and	CCONJ
ejpam-3987	280	55	(	(	PUNCT
ejpam-3987	280	56	58:12:2	58:12:2	NUM
ejpam-3987	280	57	)	)	PUNCT
ejpam-3987	280	58	in	in	ADP
ejpam-3987	280	59	[	[	X
ejpam-3987	280	60	6	6	NUM
ejpam-3987	280	61	]	]	PUNCT
ejpam-3987	280	62	.	.	PUNCT
ejpam-3987	281	1	9	9	X
ejpam-3987	281	2	.	.	X
ejpam-3987	282	1	the	the	DET
ejpam-3987	282	2	general	general	ADJ
ejpam-3987	282	3	case	case	NOUN
ejpam-3987	282	4	of	of	ADP
ejpam-3987	282	5	the	the	DET
ejpam-3987	282	6	difference	difference	NOUN
ejpam-3987	282	7	of	of	ADP
ejpam-3987	282	8	the	the	DET
ejpam-3987	282	9	double	double	ADJ
ejpam-3987	282	10	laplace	laplace	NOUN
ejpam-3987	282	11	transform	transform	NOUN
ejpam-3987	282	12	we	we	PRON
ejpam-3987	282	13	will	will	AUX
ejpam-3987	282	14	form	form	VERB
ejpam-3987	282	15	two	two	NUM
ejpam-3987	282	16	equations	equation	NOUN
ejpam-3987	282	17	and	and	CCONJ
ejpam-3987	282	18	take	take	VERB
ejpam-3987	282	19	their	their	PRON
ejpam-3987	282	20	difference	difference	NOUN
ejpam-3987	282	21	.	.	PUNCT
ejpam-3987	283	1	firstly	firstly	ADV
ejpam-3987	283	2	,	,	PUNCT
ejpam-3987	283	3	using	use	VERB
ejpam-3987	283	4	equation	equation	NOUN
ejpam-3987	283	5	(	(	PUNCT
ejpam-3987	283	6	8)	8)	NUM
ejpam-3987	283	7	we	we	PRON
ejpam-3987	283	8	replace	replace	VERB
ejpam-3987	283	9	p	p	NOUN
ejpam-3987	283	10	by	by	ADP
ejpam-3987	283	11	p+	p+	NOUN
ejpam-3987	283	12	q	q	NOUN
ejpam-3987	283	13	to	to	PART
ejpam-3987	283	14	form	form	VERB
ejpam-3987	283	15	the	the	DET
ejpam-3987	283	16	first	first	ADJ
ejpam-3987	283	17	equation	equation	NOUN
ejpam-3987	283	18	.	.	PUNCT
ejpam-3987	284	1	for	for	ADP
ejpam-3987	284	2	the	the	DET
ejpam-3987	284	3	second	second	ADJ
ejpam-3987	284	4	,	,	PUNCT
ejpam-3987	284	5	again	again	ADV
ejpam-3987	284	6	using	use	VERB
ejpam-3987	284	7	equation	equation	NOUN
ejpam-3987	284	8	(	(	PUNCT
ejpam-3987	284	9	8)	8)	NUM
ejpam-3987	284	10	we	we	PRON
ejpam-3987	284	11	replace	replace	VERB
ejpam-3987	284	12	p	p	NOUN
ejpam-3987	284	13	by	by	ADP
ejpam-3987	284	14	p−	p−	NOUN
ejpam-3987	284	15	q.	q.	NOUN
ejpam-3987	284	16	next	next	ADV
ejpam-3987	284	17	we	we	PRON
ejpam-3987	284	18	take	take	VERB
ejpam-3987	284	19	the	the	DET
ejpam-3987	284	20	difference	difference	NOUN
ejpam-3987	284	21	of	of	ADP
ejpam-3987	284	22	these	these	DET
ejpam-3987	284	23	two	two	NUM
ejpam-3987	284	24	equations	equation	NOUN
ejpam-3987	284	25	and	and	CCONJ
ejpam-3987	284	26	simplifying	simplify	VERB
ejpam-3987	284	27	to	to	PART
ejpam-3987	284	28	get	get	VERB
ejpam-3987	284	29	(	(	PUNCT
ejpam-3987	284	30	43	43	NUM
ejpam-3987	284	31	)	)	PUNCT
ejpam-3987	284	32	∫	∫	PROPN
ejpam-3987	285	1	∞	∞	PROPN
ejpam-3987	285	2	0	0	NUM
ejpam-3987	285	3	∫	∫	PROPN
ejpam-3987	285	4	∞	∞	PROPN
ejpam-3987	285	5	0	0	NUM
ejpam-3987	286	1	xp−q−1	xp−q−1	PROPN
ejpam-3987	286	2	(	(	PUNCT
ejpam-3987	286	3	y2q	y2q	X
ejpam-3987	286	4	−	−	PROPN
ejpam-3987	286	5	x2q	x2q	NUM
ejpam-3987	286	6	)	)	PUNCT
ejpam-3987	287	1	yn−p−q−1	yn−p−q−1	NOUN
ejpam-3987	287	2	logk	logk	NOUN
ejpam-3987	287	3	(	(	PUNCT
ejpam-3987	287	4	bx	bx	NOUN
ejpam-3987	287	5	y	y	PROPN
ejpam-3987	287	6	)	)	PUNCT
ejpam-3987	287	7	e−(sx)n−(ty)ndxdy	e−(sx)n−(ty)ndxdy	PROPN
ejpam-3987	287	8	=	=	SYM
ejpam-3987	287	9	(	(	PUNCT
ejpam-3987	287	10	2π)k+1	2π)k+1	NUM
ejpam-3987	287	11	(	(	PUNCT
ejpam-3987	287	12	i	i	PRON
ejpam-3987	287	13	n	n	ADJ
ejpam-3987	287	14	)	)	PUNCT
ejpam-3987	287	15	k−1	k−1	PROPN
ejpam-3987	287	16	s−p−qt−n+p−q	s−p−qt−n+p−q	ADJ
ejpam-3987	287	17	n3	n3	NOUN
ejpam-3987	287	18	(	(	PUNCT
ejpam-3987	287	19	s2qe	s2qe	X
ejpam-3987	287	20	iπ(p−q	iπ(p−q	X
ejpam-3987	287	21	)	)	PUNCT
ejpam-3987	287	22	n	n	CCONJ
ejpam-3987	287	23	φ	φ	PROPN
ejpam-3987	287	24	(	(	PUNCT
ejpam-3987	287	25	e	e	PROPN
ejpam-3987	287	26	2iπ(p−q	2iπ(p−q	NUM
ejpam-3987	287	27	)	)	PUNCT
ejpam-3987	287	28	n	n	CCONJ
ejpam-3987	287	29	,	,	PUNCT
ejpam-3987	287	30	−k	−k	PROPN
ejpam-3987	287	31	,	,	PUNCT
ejpam-3987	287	32	π	π	PROPN
ejpam-3987	287	33	−	−	PROPN
ejpam-3987	287	34	in	in	ADP
ejpam-3987	287	35	log	log	PROPN
ejpam-3987	287	36	(	(	PUNCT
ejpam-3987	287	37	bt	bt	NOUN
ejpam-3987	287	38	s	s	X
ejpam-3987	287	39	)	)	PUNCT
ejpam-3987	287	40	2π	2π	NOUN
ejpam-3987	287	41	)	)	PUNCT
ejpam-3987	287	42	−	−	PROPN
ejpam-3987	287	43	t2qe	t2qe	X
ejpam-3987	287	44	iπ(p+q	iπ(p+q	NOUN
ejpam-3987	287	45	)	)	PUNCT
ejpam-3987	287	46	n	n	CCONJ
ejpam-3987	287	47	φ	φ	PROPN
ejpam-3987	287	48	(	(	PUNCT
ejpam-3987	287	49	e	e	NOUN
ejpam-3987	287	50	2iπ(p+q	2iπ(p+q	NOUN
ejpam-3987	287	51	)	)	PUNCT
ejpam-3987	287	52	n	n	CCONJ
ejpam-3987	287	53	,	,	PUNCT
ejpam-3987	287	54	−k	−k	PROPN
ejpam-3987	287	55	,	,	PUNCT
ejpam-3987	287	56	π	π	PROPN
ejpam-3987	287	57	−	−	PROPN
ejpam-3987	287	58	in	in	ADP
ejpam-3987	287	59	log	log	PROPN
ejpam-3987	287	60	(	(	PUNCT
ejpam-3987	287	61	bt	bt	NOUN
ejpam-3987	287	62	s	s	X
ejpam-3987	287	63	)	)	PUNCT
ejpam-3987	287	64	2π	2π	NOUN
ejpam-3987	287	65	)	)	PUNCT
ejpam-3987	287	66	)	)	PUNCT
ejpam-3987	287	67	9.1	9.1	NUM
ejpam-3987	287	68	.	.	PUNCT
ejpam-3987	288	1	derivation	derivation	NOUN
ejpam-3987	288	2	of	of	ADP
ejpam-3987	288	3	entry	entry	NOUN
ejpam-3987	288	4	73	73	NUM
ejpam-3987	288	5	in	in	ADP
ejpam-3987	288	6	terms	term	NOUN
ejpam-3987	288	7	of	of	ADP
ejpam-3987	288	8	the	the	DET
ejpam-3987	288	9	lerch	lerch	PROPN
ejpam-3987	288	10	transcendent	transcendent	NOUN
ejpam-3987	288	11	using	use	VERB
ejpam-3987	288	12	equation	equation	NOUN
ejpam-3987	288	13	(	(	PUNCT
ejpam-3987	288	14	43	43	NUM
ejpam-3987	288	15	)	)	PUNCT
ejpam-3987	288	16	and	and	CCONJ
ejpam-3987	288	17	setting	set	VERB
ejpam-3987	288	18	s	s	X
ejpam-3987	288	19	=	=	SYM
ejpam-3987	288	20	1	1	NUM
ejpam-3987	288	21	,	,	PUNCT
ejpam-3987	288	22	t	t	NOUN
ejpam-3987	288	23	=	=	SYM
ejpam-3987	288	24	1	1	NUM
ejpam-3987	288	25	,	,	PUNCT
ejpam-3987	288	26	n	n	NOUN
ejpam-3987	288	27	=	=	SYM
ejpam-3987	288	28	1	1	NUM
ejpam-3987	288	29	,	,	PUNCT
ejpam-3987	288	30	p	p	NOUN
ejpam-3987	288	31	=	=	SYM
ejpam-3987	288	32	1/2	1/2	NUM
ejpam-3987	288	33	,	,	PUNCT
ejpam-3987	288	34	q	q	NOUN
ejpam-3987	288	35	=	=	SYM
ejpam-3987	288	36	1/3	1/3	NUM
ejpam-3987	288	37	,	,	PUNCT
ejpam-3987	288	38	b	b	NOUN
ejpam-3987	288	39	=	=	SYM
ejpam-3987	288	40	1	1	NUM
ejpam-3987	288	41	,	,	PUNCT
ejpam-3987	288	42	k	k	NOUN
ejpam-3987	288	43	=	=	PUNCT
ejpam-3987	288	44	−1/2	−1/2	ADJ
ejpam-3987	288	45	and	and	CCONJ
ejpam-3987	288	46	simplifying	simplify	VERB
ejpam-3987	288	47	we	we	PRON
ejpam-3987	288	48	get	get	VERB
ejpam-3987	288	49	(	(	PUNCT
ejpam-3987	288	50	44	44	NUM
ejpam-3987	288	51	)	)	PUNCT
ejpam-3987	288	52	∫	∫	PROPN
ejpam-3987	289	1	∞	∞	PROPN
ejpam-3987	289	2	0	0	NUM
ejpam-3987	290	1	∫	∫	PROPN
ejpam-3987	290	2	∞	∞	PROPN
ejpam-3987	290	3	0	0	PROPN
ejpam-3987	291	1	e−x−y	e−x−y	NOUN
ejpam-3987	291	2	(	(	PUNCT
ejpam-3987	291	3	x2/3	x2/3	PROPN
ejpam-3987	291	4	−	−	NUM
ejpam-3987	291	5	y2/3	y2/3	PROPN
ejpam-3987	291	6	)	)	PUNCT
ejpam-3987	292	1	x5/6y5/6	x5/6y5/6	PROPN
ejpam-3987	292	2	√	√	PROPN
ejpam-3987	293	1	log	log	NOUN
ejpam-3987	293	2	(	(	PUNCT
ejpam-3987	293	3	x	x	SYM
ejpam-3987	293	4	y	y	PROPN
ejpam-3987	293	5	)	)	PUNCT
ejpam-3987	293	6	dxdy	dxdy	PROPN
ejpam-3987	293	7	=	=	PUNCT
ejpam-3987	293	8	(	(	PUNCT
ejpam-3987	293	9	1	1	NUM
ejpam-3987	293	10	2	2	NUM
ejpam-3987	293	11	+	+	CCONJ
ejpam-3987	293	12	i	i	NOUN
ejpam-3987	293	13	2	2	NUM
ejpam-3987	293	14	)	)	PUNCT
ejpam-3987	293	15	√	√	PROPN
ejpam-3987	293	16	π	π	PROPN
ejpam-3987	293	17	(	(	PUNCT
ejpam-3987	293	18	(	(	PUNCT
ejpam-3987	293	19	√	√	ADP
ejpam-3987	293	20	3−	3−	NUM
ejpam-3987	293	21	i	i	NOUN
ejpam-3987	293	22	)	)	PUNCT
ejpam-3987	293	23	φ	φ	PROPN
ejpam-3987	293	24	(	(	PUNCT
ejpam-3987	293	25	1	1	NUM
ejpam-3987	293	26	2	2	NUM
ejpam-3987	293	27	−	−	NOUN
ejpam-3987	294	1	i	i	PRON
ejpam-3987	294	2	√	√	VERB
ejpam-3987	294	3	3	3	NUM
ejpam-3987	294	4	2	2	NUM
ejpam-3987	294	5	,	,	PUNCT
ejpam-3987	294	6	1	1	NUM
ejpam-3987	294	7	2	2	NUM
ejpam-3987	294	8	,	,	PUNCT
ejpam-3987	294	9	1	1	NUM
ejpam-3987	294	10	2	2	NUM
ejpam-3987	294	11	)	)	PUNCT
ejpam-3987	295	1	+	+	CCONJ
ejpam-3987	295	2	(	(	PUNCT
ejpam-3987	295	3	√	√	NUM
ejpam-3987	295	4	3	3	NUM
ejpam-3987	295	5	+	+	NUM
ejpam-3987	295	6	i	i	NOUN
ejpam-3987	295	7	)	)	PUNCT
ejpam-3987	295	8	φ	φ	PROPN
ejpam-3987	295	9	(	(	PUNCT
ejpam-3987	295	10	1	1	NUM
ejpam-3987	295	11	2	2	NUM
ejpam-3987	295	12	+	+	CCONJ
ejpam-3987	295	13	i	i	PRON
ejpam-3987	295	14	√	√	VERB
ejpam-3987	295	15	3	3	NUM
ejpam-3987	295	16	2	2	NUM
ejpam-3987	295	17	,	,	PUNCT
ejpam-3987	295	18	1	1	NUM
ejpam-3987	295	19	2	2	NUM
ejpam-3987	295	20	,	,	PUNCT
ejpam-3987	295	21	1	1	NUM
ejpam-3987	295	22	2	2	NUM
ejpam-3987	295	23	)	)	PUNCT
ejpam-3987	295	24	)	)	PUNCT
ejpam-3987	295	25	9.2	9.2	NUM
ejpam-3987	295	26	.	.	PUNCT
ejpam-3987	296	1	derivation	derivation	NOUN
ejpam-3987	296	2	of	of	ADP
ejpam-3987	296	3	entry	entry	NOUN
ejpam-3987	296	4	74	74	NUM
ejpam-3987	296	5	in	in	ADP
ejpam-3987	296	6	terms	term	NOUN
ejpam-3987	296	7	of	of	ADP
ejpam-3987	296	8	the	the	DET
ejpam-3987	296	9	lerch	lerch	PROPN
ejpam-3987	296	10	transcendent	transcendent	NOUN
ejpam-3987	296	11	using	use	VERB
ejpam-3987	296	12	equation	equation	NOUN
ejpam-3987	296	13	(	(	PUNCT
ejpam-3987	296	14	43	43	NUM
ejpam-3987	296	15	)	)	PUNCT
ejpam-3987	296	16	and	and	CCONJ
ejpam-3987	296	17	setting	set	VERB
ejpam-3987	296	18	s	s	X
ejpam-3987	296	19	=	=	SYM
ejpam-3987	296	20	1	1	NUM
ejpam-3987	296	21	,	,	PUNCT
ejpam-3987	296	22	t	t	NOUN
ejpam-3987	296	23	=	=	SYM
ejpam-3987	296	24	1	1	NUM
ejpam-3987	296	25	,	,	PUNCT
ejpam-3987	296	26	p	p	NOUN
ejpam-3987	296	27	=	=	SYM
ejpam-3987	296	28	1/2	1/2	NUM
ejpam-3987	296	29	,	,	PUNCT
ejpam-3987	296	30	q	q	NOUN
ejpam-3987	296	31	=	=	SYM
ejpam-3987	296	32	1/3	1/3	NUM
ejpam-3987	296	33	,	,	PUNCT
ejpam-3987	296	34	n	n	NOUN
ejpam-3987	296	35	=	=	SYM
ejpam-3987	296	36	1	1	NUM
ejpam-3987	296	37	,	,	PUNCT
ejpam-3987	296	38	k	k	NOUN
ejpam-3987	296	39	=	=	SYM
ejpam-3987	296	40	1/2	1/2	NUM
ejpam-3987	296	41	,	,	PUNCT
ejpam-3987	296	42	b	b	NOUN
ejpam-3987	296	43	=	=	SYM
ejpam-3987	296	44	1	1	NUM
ejpam-3987	296	45	and	and	CCONJ
ejpam-3987	296	46	simplifying	simplify	VERB
ejpam-3987	296	47	we	we	PRON
ejpam-3987	296	48	get	get	VERB
ejpam-3987	296	49	r.	r.	PROPN
ejpam-3987	296	50	reynolds	reynolds	PROPN
ejpam-3987	296	51	,	,	PUNCT
ejpam-3987	296	52	a.	a.	PROPN
ejpam-3987	296	53	stauffer	stauffer	PROPN
ejpam-3987	296	54	/	/	SYM
ejpam-3987	296	55	eur	eur	PROPN
ejpam-3987	296	56	.	.	PUNCT
ejpam-3987	297	1	j.	j.	PROPN
ejpam-3987	297	2	pure	pure	PROPN
ejpam-3987	297	3	appl	appl	PROPN
ejpam-3987	297	4	.	.	PROPN
ejpam-3987	297	5	math	math	PROPN
ejpam-3987	297	6	,	,	PUNCT
ejpam-3987	297	7	14	14	NUM
ejpam-3987	297	8	(	(	PUNCT
ejpam-3987	297	9	3	3	NUM
ejpam-3987	297	10	)	)	PUNCT
ejpam-3987	297	11	(	(	PUNCT
ejpam-3987	297	12	2021	2021	NUM
ejpam-3987	297	13	)	)	PUNCT
ejpam-3987	297	14	,	,	PUNCT
ejpam-3987	297	15	618	618	NUM
ejpam-3987	297	16	-	-	SYM
ejpam-3987	297	17	637	637	NUM
ejpam-3987	297	18	630	630	NUM
ejpam-3987	297	19	∫	∫	NOUN
ejpam-3987	297	20	∞	∞	NUM
ejpam-3987	297	21	0	0	NUM
ejpam-3987	298	1	∫	∫	PROPN
ejpam-3987	298	2	∞	∞	PROPN
ejpam-3987	298	3	0	0	PROPN
ejpam-3987	299	1	e−x−y	e−x−y	NOUN
ejpam-3987	299	2	(	(	PUNCT
ejpam-3987	299	3	x2/3	x2/3	PROPN
ejpam-3987	299	4	−	−	NUM
ejpam-3987	299	5	y2/3	y2/3	PROPN
ejpam-3987	299	6	)	)	PUNCT
ejpam-3987	299	7	√	√	PROPN
ejpam-3987	299	8	log	log	NOUN
ejpam-3987	299	9	(	(	PUNCT
ejpam-3987	299	10	x	x	NOUN
ejpam-3987	299	11	y	y	PROPN
ejpam-3987	299	12	)	)	PUNCT
ejpam-3987	299	13	x5/6y5/6	x5/6y5/6	PROPN
ejpam-3987	299	14	dxdy	dxdy	PROPN
ejpam-3987	299	15	=	=	SYM
ejpam-3987	299	16	(	(	PUNCT
ejpam-3987	299	17	1	1	NUM
ejpam-3987	299	18	+	+	NUM
ejpam-3987	299	19	i)π3/2	i)π3/2	NOUN
ejpam-3987	299	20	(	(	PUNCT
ejpam-3987	300	1	(	(	PUNCT
ejpam-3987	300	2	1	1	X
ejpam-3987	300	3	+	+	CCONJ
ejpam-3987	300	4	i	i	PRON
ejpam-3987	300	5	√	√	VERB
ejpam-3987	300	6	3	3	NUM
ejpam-3987	300	7	)	)	PUNCT
ejpam-3987	300	8	φ	φ	PROPN
ejpam-3987	300	9	(	(	PUNCT
ejpam-3987	300	10	1	1	NUM
ejpam-3987	300	11	2	2	NUM
ejpam-3987	300	12	−	−	NOUN
ejpam-3987	301	1	i	i	PRON
ejpam-3987	301	2	√	√	VERB
ejpam-3987	301	3	3	3	NUM
ejpam-3987	301	4	2	2	NUM
ejpam-3987	301	5	,	,	PUNCT
ejpam-3987	301	6	−1	−1	NOUN
ejpam-3987	301	7	2	2	NUM
ejpam-3987	301	8	,	,	PUNCT
ejpam-3987	301	9	1	1	NUM
ejpam-3987	301	10	2	2	NUM
ejpam-3987	301	11	)	)	PUNCT
ejpam-3987	302	1	+	+	CCONJ
ejpam-3987	302	2	i	i	PRON
ejpam-3987	302	3	(	(	PUNCT
ejpam-3987	302	4	√	√	ADP
ejpam-3987	302	5	3	3	NUM
ejpam-3987	302	6	+	+	CCONJ
ejpam-3987	302	7	i	i	PRON
ejpam-3987	302	8	)	)	PUNCT
ejpam-3987	302	9	φ	φ	PROPN
ejpam-3987	302	10	(	(	PUNCT
ejpam-3987	302	11	1	1	NUM
ejpam-3987	302	12	2	2	NUM
ejpam-3987	302	13	+	+	CCONJ
ejpam-3987	302	14	i	i	PRON
ejpam-3987	302	15	√	√	VERB
ejpam-3987	302	16	3	3	NUM
ejpam-3987	302	17	2	2	NUM
ejpam-3987	302	18	,	,	PUNCT
ejpam-3987	302	19	−1	−1	NOUN
ejpam-3987	302	20	2	2	NUM
ejpam-3987	302	21	,	,	PUNCT
ejpam-3987	302	22	1	1	NUM
ejpam-3987	302	23	2	2	NUM
ejpam-3987	302	24	)	)	PUNCT
ejpam-3987	302	25	)	)	PUNCT
ejpam-3987	302	26	(	(	PUNCT
ejpam-3987	302	27	45	45	NUM
ejpam-3987	302	28	)	)	PUNCT
ejpam-3987	302	29	9.3	9.3	NUM
ejpam-3987	302	30	.	.	PUNCT
ejpam-3987	303	1	derivation	derivation	NOUN
ejpam-3987	303	2	of	of	ADP
ejpam-3987	303	3	entry	entry	NOUN
ejpam-3987	303	4	75	75	NUM
ejpam-3987	303	5	in	in	ADP
ejpam-3987	303	6	terms	term	NOUN
ejpam-3987	303	7	of	of	ADP
ejpam-3987	303	8	the	the	DET
ejpam-3987	303	9	lerch	lerch	PROPN
ejpam-3987	303	10	transcendent	transcendent	NOUN
ejpam-3987	303	11	using	use	VERB
ejpam-3987	303	12	equation	equation	NOUN
ejpam-3987	303	13	(	(	PUNCT
ejpam-3987	303	14	43	43	NUM
ejpam-3987	303	15	)	)	PUNCT
ejpam-3987	303	16	and	and	CCONJ
ejpam-3987	303	17	setting	set	VERB
ejpam-3987	303	18	s	s	X
ejpam-3987	303	19	=	=	SYM
ejpam-3987	303	20	1	1	NUM
ejpam-3987	303	21	,	,	PUNCT
ejpam-3987	303	22	t	t	NOUN
ejpam-3987	303	23	=	=	SYM
ejpam-3987	303	24	1	1	NUM
ejpam-3987	303	25	,	,	PUNCT
ejpam-3987	303	26	p	p	NOUN
ejpam-3987	303	27	=	=	SYM
ejpam-3987	303	28	1/2	1/2	NUM
ejpam-3987	303	29	,	,	PUNCT
ejpam-3987	303	30	q	q	NOUN
ejpam-3987	303	31	=	=	SYM
ejpam-3987	303	32	1/3	1/3	NUM
ejpam-3987	303	33	,	,	PUNCT
ejpam-3987	303	34	n	n	NOUN
ejpam-3987	303	35	=	=	SYM
ejpam-3987	303	36	2	2	NUM
ejpam-3987	303	37	,	,	PUNCT
ejpam-3987	303	38	k	k	NOUN
ejpam-3987	303	39	=	=	SYM
ejpam-3987	303	40	2	2	NUM
ejpam-3987	303	41	,	,	PUNCT
ejpam-3987	303	42	b	b	NOUN
ejpam-3987	303	43	=	=	SYM
ejpam-3987	303	44	2	2	NUM
ejpam-3987	303	45	and	and	CCONJ
ejpam-3987	303	46	simplifying	simplify	VERB
ejpam-3987	303	47	we	we	PRON
ejpam-3987	303	48	get∫	get∫	PROPN
ejpam-3987	303	49	∞	∞	PROPN
ejpam-3987	303	50	0	0	NUM
ejpam-3987	304	1	∫	∫	PROPN
ejpam-3987	304	2	∞	∞	NUM
ejpam-3987	304	3	0	0	NUM
ejpam-3987	304	4	6	6	NUM
ejpam-3987	304	5	√	√	PROPN
ejpam-3987	304	6	ye−x	ye−x	PROPN
ejpam-3987	304	7	2−y2	2−y2	NUM
ejpam-3987	304	8	(	(	PUNCT
ejpam-3987	304	9	x2/3	x2/3	PROPN
ejpam-3987	304	10	−	−	PROPN
ejpam-3987	304	11	y2/3	y2/3	PROPN
ejpam-3987	304	12	)	)	PUNCT
ejpam-3987	305	1	log2	log2	PROPN
ejpam-3987	305	2	(	(	PUNCT
ejpam-3987	305	3	2x	2x	NUM
ejpam-3987	305	4	y	y	PROPN
ejpam-3987	305	5	)	)	PUNCT
ejpam-3987	305	6	x5/6	x5/6	PROPN
ejpam-3987	306	1	dxdy	dxdy	PROPN
ejpam-3987	306	2	=	=	PUNCT
ejpam-3987	307	1	−	−	PROPN
ejpam-3987	307	2	π	π	X
ejpam-3987	307	3	(	(	PUNCT
ejpam-3987	307	4	39π2	39π2	NUM
ejpam-3987	307	5	+	+	CCONJ
ejpam-3987	307	6	4	4	NUM
ejpam-3987	307	7	log2(2)−	log2(2)−	ADJ
ejpam-3987	307	8	20π	20π	NUM
ejpam-3987	307	9	log(2	log(2	NOUN
ejpam-3987	307	10	)	)	PUNCT
ejpam-3987	307	11	)	)	PUNCT
ejpam-3987	307	12	4	4	NUM
ejpam-3987	307	13	√	√	NUM
ejpam-3987	307	14	2	2	NUM
ejpam-3987	307	15	(	(	PUNCT
ejpam-3987	307	16	46	46	NUM
ejpam-3987	307	17	)	)	PUNCT
ejpam-3987	307	18	from	from	ADP
ejpam-3987	307	19	(	(	PUNCT
ejpam-3987	307	20	64:12:4	64:12:4	NUM
ejpam-3987	307	21	)	)	PUNCT
ejpam-3987	307	22	in	in	ADP
ejpam-3987	307	23	[	[	X
ejpam-3987	307	24	6	6	NUM
ejpam-3987	307	25	]	]	PUNCT
ejpam-3987	307	26	.	.	PUNCT
ejpam-3987	308	1	9.4	9.4	NUM
ejpam-3987	308	2	.	.	PUNCT
ejpam-3987	308	3	derivation	derivation	NOUN
ejpam-3987	308	4	of	of	ADP
ejpam-3987	308	5	entry	entry	NOUN
ejpam-3987	308	6	76	76	NUM
ejpam-3987	308	7	in	in	ADP
ejpam-3987	308	8	terms	term	NOUN
ejpam-3987	308	9	of	of	ADP
ejpam-3987	308	10	the	the	DET
ejpam-3987	308	11	lerch	lerch	PROPN
ejpam-3987	308	12	transcendent	transcendent	NOUN
ejpam-3987	308	13	using	use	VERB
ejpam-3987	308	14	equation	equation	NOUN
ejpam-3987	308	15	(	(	PUNCT
ejpam-3987	308	16	43	43	NUM
ejpam-3987	308	17	)	)	PUNCT
ejpam-3987	308	18	and	and	CCONJ
ejpam-3987	308	19	setting	set	VERB
ejpam-3987	308	20	s	s	X
ejpam-3987	308	21	=	=	SYM
ejpam-3987	308	22	1	1	NUM
ejpam-3987	308	23	,	,	PUNCT
ejpam-3987	308	24	t	t	NOUN
ejpam-3987	308	25	=	=	SYM
ejpam-3987	308	26	1	1	NUM
ejpam-3987	308	27	,	,	PUNCT
ejpam-3987	308	28	p	p	NOUN
ejpam-3987	308	29	=	=	SYM
ejpam-3987	308	30	1/2	1/2	NUM
ejpam-3987	308	31	,	,	PUNCT
ejpam-3987	308	32	q	q	NOUN
ejpam-3987	308	33	=	=	SYM
ejpam-3987	308	34	1/3	1/3	NUM
ejpam-3987	308	35	,	,	PUNCT
ejpam-3987	308	36	n	n	NOUN
ejpam-3987	308	37	=	=	SYM
ejpam-3987	308	38	1	1	NUM
ejpam-3987	308	39	,	,	PUNCT
ejpam-3987	308	40	b	b	X
ejpam-3987	308	41	=	=	SYM
ejpam-3987	308	42	1	1	NUM
ejpam-3987	308	43	followed	follow	VERB
ejpam-3987	308	44	by	by	ADP
ejpam-3987	308	45	taking	take	VERB
ejpam-3987	308	46	the	the	DET
ejpam-3987	308	47	first	first	ADJ
ejpam-3987	308	48	partial	partial	ADJ
ejpam-3987	308	49	derivative	derivative	NOUN
ejpam-3987	308	50	with	with	ADP
ejpam-3987	308	51	respect	respect	NOUN
ejpam-3987	308	52	to	to	ADP
ejpam-3987	308	53	k	k	PROPN
ejpam-3987	308	54	then	then	ADV
ejpam-3987	308	55	setting	set	VERB
ejpam-3987	308	56	k	k	PROPN
ejpam-3987	308	57	=	=	PUNCT
ejpam-3987	308	58	0	0	PUNCT
ejpam-3987	308	59	and	and	CCONJ
ejpam-3987	308	60	simplifying	simplify	VERB
ejpam-3987	308	61	we	we	PRON
ejpam-3987	308	62	get	get	VERB
ejpam-3987	308	63	(	(	PUNCT
ejpam-3987	308	64	47	47	NUM
ejpam-3987	308	65	)	)	PUNCT
ejpam-3987	308	66	∫	∫	PROPN
ejpam-3987	309	1	∞	∞	PROPN
ejpam-3987	309	2	0	0	NUM
ejpam-3987	310	1	∫	∫	PROPN
ejpam-3987	310	2	∞	∞	PROPN
ejpam-3987	310	3	0	0	PROPN
ejpam-3987	311	1	e−x−y	e−x−y	NOUN
ejpam-3987	311	2	(	(	PUNCT
ejpam-3987	311	3	x2/3	x2/3	PROPN
ejpam-3987	311	4	−	−	NUM
ejpam-3987	311	5	y2/3	y2/3	PROPN
ejpam-3987	311	6	)	)	PUNCT
ejpam-3987	311	7	log	log	NOUN
ejpam-3987	311	8	(	(	PUNCT
ejpam-3987	311	9	log	log	NOUN
ejpam-3987	311	10	(	(	PUNCT
ejpam-3987	311	11	x	x	NOUN
ejpam-3987	311	12	y	y	PROPN
ejpam-3987	311	13	)	)	PUNCT
ejpam-3987	311	14	)	)	PUNCT
ejpam-3987	312	1	x5/6y5/6	x5/6y5/6	PROPN
ejpam-3987	312	2	dxdy	dxdy	PROPN
ejpam-3987	312	3	=	=	PROPN
ejpam-3987	312	4	π	π	PROPN
ejpam-3987	312	5	(	(	PUNCT
ejpam-3987	312	6	(	(	PUNCT
ejpam-3987	312	7	−1−	−1−	NOUN
ejpam-3987	312	8	i	i	PRON
ejpam-3987	312	9	√	√	VERB
ejpam-3987	312	10	3	3	NUM
ejpam-3987	312	11	)	)	PUNCT
ejpam-3987	312	12	φ′	φ′	NUM
ejpam-3987	312	13	(	(	PUNCT
ejpam-3987	312	14	1	1	NUM
ejpam-3987	312	15	2	2	NUM
ejpam-3987	312	16	−	−	NOUN
ejpam-3987	313	1	i	i	PRON
ejpam-3987	313	2	√	√	VERB
ejpam-3987	313	3	3	3	NUM
ejpam-3987	313	4	2	2	NUM
ejpam-3987	313	5	,	,	PUNCT
ejpam-3987	313	6	0	0	NUM
ejpam-3987	313	7	,	,	PUNCT
ejpam-3987	313	8	1	1	NUM
ejpam-3987	313	9	2	2	NUM
ejpam-3987	313	10	)	)	PUNCT
ejpam-3987	314	1	+	+	CCONJ
ejpam-3987	314	2	(	(	PUNCT
ejpam-3987	314	3	1−	1−	NUM
ejpam-3987	314	4	i	i	PRON
ejpam-3987	314	5	√	√	VERB
ejpam-3987	314	6	3	3	NUM
ejpam-3987	314	7	)	)	PUNCT
ejpam-3987	314	8	φ′	φ′	NUM
ejpam-3987	314	9	(	(	PUNCT
ejpam-3987	314	10	1	1	NUM
ejpam-3987	314	11	2	2	NUM
ejpam-3987	315	1	+	+	CCONJ
ejpam-3987	315	2	i	i	PRON
ejpam-3987	315	3	√	√	VERB
ejpam-3987	315	4	3	3	NUM
ejpam-3987	315	5	2	2	NUM
ejpam-3987	315	6	,	,	PUNCT
ejpam-3987	315	7	0	0	NUM
ejpam-3987	315	8	,	,	PUNCT
ejpam-3987	315	9	1	1	NUM
ejpam-3987	315	10	2	2	NUM
ejpam-3987	315	11	)	)	PUNCT
ejpam-3987	315	12	)	)	PUNCT
ejpam-3987	315	13	9.5	9.5	NUM
ejpam-3987	315	14	.	.	PUNCT
ejpam-3987	316	1	derivation	derivation	NOUN
ejpam-3987	316	2	of	of	ADP
ejpam-3987	316	3	entry	entry	NOUN
ejpam-3987	316	4	77	77	NUM
ejpam-3987	316	5	in	in	ADP
ejpam-3987	316	6	terms	term	NOUN
ejpam-3987	316	7	of	of	ADP
ejpam-3987	316	8	the	the	DET
ejpam-3987	316	9	lerch	lerch	PROPN
ejpam-3987	316	10	transcendent	transcendent	NOUN
ejpam-3987	316	11	using	use	VERB
ejpam-3987	316	12	equation	equation	NOUN
ejpam-3987	316	13	(	(	PUNCT
ejpam-3987	316	14	43	43	NUM
ejpam-3987	316	15	)	)	PUNCT
ejpam-3987	316	16	and	and	CCONJ
ejpam-3987	316	17	setting	set	VERB
ejpam-3987	316	18	s	s	X
ejpam-3987	316	19	=	=	SYM
ejpam-3987	316	20	1	1	NUM
ejpam-3987	316	21	,	,	PUNCT
ejpam-3987	316	22	t	t	NOUN
ejpam-3987	316	23	=	=	SYM
ejpam-3987	316	24	1	1	NUM
ejpam-3987	316	25	,	,	PUNCT
ejpam-3987	316	26	p	p	NOUN
ejpam-3987	316	27	=	=	SYM
ejpam-3987	316	28	1/2	1/2	NUM
ejpam-3987	316	29	,	,	PUNCT
ejpam-3987	316	30	q	q	NOUN
ejpam-3987	316	31	=	=	SYM
ejpam-3987	316	32	1/3	1/3	NUM
ejpam-3987	316	33	,	,	PUNCT
ejpam-3987	316	34	n	n	NOUN
ejpam-3987	316	35	=	=	SYM
ejpam-3987	316	36	1	1	NUM
ejpam-3987	316	37	,	,	PUNCT
ejpam-3987	316	38	b	b	X
ejpam-3987	316	39	=	=	SYM
ejpam-3987	316	40	1	1	NUM
ejpam-3987	316	41	followed	follow	VERB
ejpam-3987	316	42	by	by	ADP
ejpam-3987	316	43	taking	take	VERB
ejpam-3987	316	44	the	the	DET
ejpam-3987	316	45	first	first	ADJ
ejpam-3987	316	46	partial	partial	ADJ
ejpam-3987	316	47	derivative	derivative	NOUN
ejpam-3987	316	48	with	with	ADP
ejpam-3987	316	49	respect	respect	NOUN
ejpam-3987	316	50	to	to	ADP
ejpam-3987	316	51	k	k	PROPN
ejpam-3987	316	52	then	then	ADV
ejpam-3987	316	53	setting	set	VERB
ejpam-3987	316	54	k	k	PROPN
ejpam-3987	316	55	=	=	PUNCT
ejpam-3987	316	56	1	1	NUM
ejpam-3987	316	57	and	and	CCONJ
ejpam-3987	316	58	simplifying	simplify	VERB
ejpam-3987	316	59	we	we	PRON
ejpam-3987	316	60	get	get	VERB
ejpam-3987	316	61	(	(	PUNCT
ejpam-3987	316	62	48	48	NUM
ejpam-3987	316	63	)	)	PUNCT
ejpam-3987	316	64	∫	∫	PROPN
ejpam-3987	317	1	∞	∞	PROPN
ejpam-3987	317	2	0	0	NUM
ejpam-3987	318	1	∫	∫	PROPN
ejpam-3987	318	2	∞	∞	PROPN
ejpam-3987	318	3	0	0	PROPN
ejpam-3987	319	1	e−x−y	e−x−y	NOUN
ejpam-3987	319	2	(	(	PUNCT
ejpam-3987	319	3	x2/3	x2/3	PROPN
ejpam-3987	319	4	−	−	NUM
ejpam-3987	319	5	y2/3	y2/3	PROPN
ejpam-3987	319	6	)	)	PUNCT
ejpam-3987	319	7	log	log	NOUN
ejpam-3987	319	8	(	(	PUNCT
ejpam-3987	319	9	x	x	NOUN
ejpam-3987	319	10	y	y	PROPN
ejpam-3987	319	11	)	)	PUNCT
ejpam-3987	319	12	log	log	NOUN
ejpam-3987	319	13	(	(	PUNCT
ejpam-3987	319	14	log	log	NOUN
ejpam-3987	319	15	(	(	PUNCT
ejpam-3987	319	16	x	x	NOUN
ejpam-3987	319	17	y	y	PROPN
ejpam-3987	319	18	)	)	PUNCT
ejpam-3987	319	19	)	)	PUNCT
ejpam-3987	320	1	x5/6y5/6	x5/6y5/6	PROPN
ejpam-3987	320	2	dxdy	dxdy	PROPN
ejpam-3987	320	3	=	=	PUNCT
ejpam-3987	320	4	2π2	2π2	NUM
ejpam-3987	320	5	(	(	PUNCT
ejpam-3987	320	6	(	(	PUNCT
ejpam-3987	320	7	√	√	ADP
ejpam-3987	320	8	3−	3−	NUM
ejpam-3987	320	9	i	i	NOUN
ejpam-3987	320	10	)	)	PUNCT
ejpam-3987	320	11	φ′	φ′	NUM
ejpam-3987	320	12	(	(	PUNCT
ejpam-3987	320	13	1	1	NUM
ejpam-3987	320	14	2	2	NUM
ejpam-3987	320	15	−	−	NOUN
ejpam-3987	321	1	i	i	PRON
ejpam-3987	321	2	√	√	VERB
ejpam-3987	321	3	3	3	NUM
ejpam-3987	321	4	2	2	NUM
ejpam-3987	321	5	,	,	PUNCT
ejpam-3987	321	6	−1	−1	NOUN
ejpam-3987	321	7	,	,	PUNCT
ejpam-3987	321	8	1	1	NUM
ejpam-3987	321	9	2	2	NUM
ejpam-3987	321	10	)	)	PUNCT
ejpam-3987	322	1	+	+	CCONJ
ejpam-3987	322	2	(	(	PUNCT
ejpam-3987	322	3	√	√	NUM
ejpam-3987	322	4	3	3	NUM
ejpam-3987	322	5	+	+	CCONJ
ejpam-3987	322	6	i	i	NOUN
ejpam-3987	322	7	)	)	PUNCT
ejpam-3987	322	8	φ′	φ′	NUM
ejpam-3987	322	9	(	(	PUNCT
ejpam-3987	322	10	1	1	NUM
ejpam-3987	322	11	2	2	NUM
ejpam-3987	323	1	+	+	CCONJ
ejpam-3987	323	2	i	i	PRON
ejpam-3987	323	3	√	√	VERB
ejpam-3987	323	4	3	3	NUM
ejpam-3987	323	5	2	2	NUM
ejpam-3987	323	6	,	,	PUNCT
ejpam-3987	323	7	−1	−1	NOUN
ejpam-3987	323	8	,	,	PUNCT
ejpam-3987	323	9	1	1	NUM
ejpam-3987	323	10	2	2	NUM
ejpam-3987	323	11	)	)	PUNCT
ejpam-3987	324	1	+	+	CCONJ
ejpam-3987	324	2	√	√	NUM
ejpam-3987	324	3	3	3	NUM
ejpam-3987	324	4	log(4	log(4	NOUN
ejpam-3987	324	5	)	)	PUNCT
ejpam-3987	325	1	+	+	CCONJ
ejpam-3987	325	2	2	2	NUM
ejpam-3987	325	3	√	√	NUM
ejpam-3987	325	4	3	3	NUM
ejpam-3987	325	5	log(iπ	log(iπ	NOUN
ejpam-3987	325	6	)	)	PUNCT
ejpam-3987	325	7	)	)	PUNCT
ejpam-3987	326	1	r.	r.	PROPN
ejpam-3987	326	2	reynolds	reynolds	PROPN
ejpam-3987	326	3	,	,	PUNCT
ejpam-3987	326	4	a.	a.	PROPN
ejpam-3987	326	5	stauffer	stauffer	PROPN
ejpam-3987	326	6	/	/	SYM
ejpam-3987	326	7	eur	eur	PROPN
ejpam-3987	326	8	.	.	PUNCT
ejpam-3987	327	1	j.	j.	PROPN
ejpam-3987	327	2	pure	pure	PROPN
ejpam-3987	327	3	appl	appl	PROPN
ejpam-3987	327	4	.	.	PROPN
ejpam-3987	327	5	math	math	PROPN
ejpam-3987	327	6	,	,	PUNCT
ejpam-3987	327	7	14	14	NUM
ejpam-3987	327	8	(	(	PUNCT
ejpam-3987	327	9	3	3	NUM
ejpam-3987	327	10	)	)	PUNCT
ejpam-3987	327	11	(	(	PUNCT
ejpam-3987	327	12	2021	2021	NUM
ejpam-3987	327	13	)	)	PUNCT
ejpam-3987	327	14	,	,	PUNCT
ejpam-3987	327	15	618	618	NUM
ejpam-3987	327	16	-	-	SYM
ejpam-3987	327	17	637	637	NUM
ejpam-3987	327	18	631	631	NUM
ejpam-3987	327	19	9.6	9.6	NUM
ejpam-3987	327	20	.	.	PUNCT
ejpam-3987	328	1	derivation	derivation	NOUN
ejpam-3987	328	2	of	of	ADP
ejpam-3987	328	3	entry	entry	NOUN
ejpam-3987	328	4	78	78	NUM
ejpam-3987	328	5	in	in	ADP
ejpam-3987	328	6	terms	term	NOUN
ejpam-3987	328	7	of	of	ADP
ejpam-3987	328	8	the	the	DET
ejpam-3987	328	9	lerch	lerch	PROPN
ejpam-3987	328	10	transcendent	transcendent	NOUN
ejpam-3987	328	11	using	use	VERB
ejpam-3987	328	12	equation	equation	NOUN
ejpam-3987	328	13	(	(	PUNCT
ejpam-3987	328	14	43	43	NUM
ejpam-3987	328	15	)	)	PUNCT
ejpam-3987	328	16	and	and	CCONJ
ejpam-3987	328	17	setting	set	VERB
ejpam-3987	328	18	s	s	PART
ejpam-3987	328	19	=	=	X
ejpam-3987	328	20	t	t	PROPN
ejpam-3987	328	21	,	,	PUNCT
ejpam-3987	328	22	p	p	NOUN
ejpam-3987	328	23	=	=	PROPN
ejpam-3987	328	24	1/2	1/2	NUM
ejpam-3987	328	25	,	,	PUNCT
ejpam-3987	328	26	q	q	NOUN
ejpam-3987	328	27	=	=	SYM
ejpam-3987	328	28	1/3	1/3	NUM
ejpam-3987	328	29	,	,	PUNCT
ejpam-3987	328	30	n	n	NOUN
ejpam-3987	328	31	=	=	SYM
ejpam-3987	328	32	1	1	NUM
ejpam-3987	328	33	,	,	PUNCT
ejpam-3987	328	34	b	b	NOUN
ejpam-3987	328	35	=	=	SYM
ejpam-3987	328	36	1	1	NUM
ejpam-3987	328	37	,	,	PUNCT
ejpam-3987	328	38	k	k	NOUN
ejpam-3987	328	39	=	=	SYM
ejpam-3987	328	40	1	1	NUM
ejpam-3987	328	41	followed	follow	VERB
ejpam-3987	328	42	by	by	ADP
ejpam-3987	328	43	taking	take	VERB
ejpam-3987	328	44	the	the	DET
ejpam-3987	328	45	integral	integral	ADJ
ejpam-3987	328	46	with	with	ADP
ejpam-3987	328	47	respect	respect	NOUN
ejpam-3987	328	48	to	to	ADP
ejpam-3987	328	49	t	t	PROPN
ejpam-3987	328	50	∈	∈	PROPN
ejpam-3987	329	1	[	[	X
ejpam-3987	329	2	1	1	NUM
ejpam-3987	329	3	,	,	PUNCT
ejpam-3987	329	4	2	2	NUM
ejpam-3987	329	5	]	]	PUNCT
ejpam-3987	329	6	and	and	CCONJ
ejpam-3987	329	7	simplifying	simplify	VERB
ejpam-3987	329	8	we	we	PRON
ejpam-3987	329	9	get	get	VERB
ejpam-3987	329	10	(	(	PUNCT
ejpam-3987	329	11	49	49	NUM
ejpam-3987	329	12	)	)	PUNCT
ejpam-3987	329	13	∫	∫	PROPN
ejpam-3987	330	1	∞	∞	PROPN
ejpam-3987	330	2	0	0	NUM
ejpam-3987	330	3	∫	∫	PROPN
ejpam-3987	330	4	∞	∞	PROPN
ejpam-3987	330	5	0	0	PUNCT
ejpam-3987	330	6	e−2(x+y	e−2(x+y	PRON
ejpam-3987	330	7	)	)	PUNCT
ejpam-3987	330	8	(	(	PUNCT
ejpam-3987	330	9	ex+y	ex+y	PROPN
ejpam-3987	330	10	−	−	PROPN
ejpam-3987	330	11	1	1	NUM
ejpam-3987	330	12	)	)	PUNCT
ejpam-3987	330	13	(	(	PUNCT
ejpam-3987	330	14	3	3	NUM
ejpam-3987	330	15	√	√	NUM
ejpam-3987	330	16	x−	x−	PROPN
ejpam-3987	330	17	3	3	NUM
ejpam-3987	330	18	√	√	PROPN
ejpam-3987	330	19	y	y	PROPN
ejpam-3987	330	20	)	)	PUNCT
ejpam-3987	330	21	log	log	NOUN
ejpam-3987	330	22	(	(	PUNCT
ejpam-3987	330	23	x	x	NOUN
ejpam-3987	330	24	y	y	PROPN
ejpam-3987	330	25	)	)	PUNCT
ejpam-3987	330	26	x5/6y5/6	x5/6y5/6	PROPN
ejpam-3987	330	27	(	(	PUNCT
ejpam-3987	330	28	x2/3	x2/3	PROPN
ejpam-3987	330	29	−	−	NOUN
ejpam-3987	330	30	3	3	NUM
ejpam-3987	330	31	√	√	NUM
ejpam-3987	330	32	x	x	SYM
ejpam-3987	330	33	3	3	NUM
ejpam-3987	330	34	√	√	PROPN
ejpam-3987	330	35	y	y	PROPN
ejpam-3987	330	36	+	+	CCONJ
ejpam-3987	330	37	y2/3	y2/3	PROPN
ejpam-3987	330	38	)	)	PUNCT
ejpam-3987	330	39	dxdy	dxdy	PROPN
ejpam-3987	330	40	=	=	PUNCT
ejpam-3987	330	41	√	√	PROPN
ejpam-3987	330	42	3π2	3π2	NUM
ejpam-3987	330	43	log(16	log(16	NOUN
ejpam-3987	330	44	)	)	PUNCT
ejpam-3987	330	45	from	from	ADP
ejpam-3987	330	46	entry	entry	NOUN
ejpam-3987	330	47	(	(	PUNCT
ejpam-3987	330	48	3	3	NUM
ejpam-3987	330	49	)	)	PUNCT
ejpam-3987	330	50	in	in	ADP
ejpam-3987	330	51	table	table	NOUN
ejpam-3987	330	52	below	below	ADV
ejpam-3987	330	53	(	(	PUNCT
ejpam-3987	330	54	64:12:7	64:12:7	NUM
ejpam-3987	330	55	)	)	PUNCT
ejpam-3987	330	56	in	in	ADP
ejpam-3987	330	57	[	[	X
ejpam-3987	330	58	6	6	NUM
ejpam-3987	330	59	]	]	PUNCT
ejpam-3987	330	60	.	.	PUNCT
ejpam-3987	331	1	9.7	9.7	NUM
ejpam-3987	331	2	.	.	PUNCT
ejpam-3987	331	3	derivation	derivation	NOUN
ejpam-3987	331	4	of	of	ADP
ejpam-3987	331	5	entry	entry	NOUN
ejpam-3987	331	6	79	79	NUM
ejpam-3987	331	7	in	in	ADP
ejpam-3987	331	8	terms	term	NOUN
ejpam-3987	331	9	of	of	ADP
ejpam-3987	331	10	the	the	DET
ejpam-3987	331	11	lerch	lerch	PROPN
ejpam-3987	331	12	transcendent	transcendent	NOUN
ejpam-3987	331	13	using	use	VERB
ejpam-3987	331	14	equation	equation	NOUN
ejpam-3987	331	15	(	(	PUNCT
ejpam-3987	331	16	43	43	NUM
ejpam-3987	331	17	)	)	PUNCT
ejpam-3987	331	18	and	and	CCONJ
ejpam-3987	331	19	setting	set	VERB
ejpam-3987	331	20	s	s	X
ejpam-3987	331	21	=	=	SYM
ejpam-3987	331	22	1/3	1/3	NUM
ejpam-3987	331	23	,	,	PUNCT
ejpam-3987	331	24	t	t	NOUN
ejpam-3987	331	25	=	=	SYM
ejpam-3987	331	26	1/2	1/2	NUM
ejpam-3987	331	27	,	,	PUNCT
ejpam-3987	331	28	p	p	NOUN
ejpam-3987	331	29	=	=	SYM
ejpam-3987	331	30	1/2	1/2	NUM
ejpam-3987	331	31	,	,	PUNCT
ejpam-3987	331	32	q	q	NOUN
ejpam-3987	331	33	=	=	SYM
ejpam-3987	331	34	1/3	1/3	NUM
ejpam-3987	331	35	,	,	PUNCT
ejpam-3987	331	36	n	n	NOUN
ejpam-3987	331	37	=	=	SYM
ejpam-3987	331	38	1	1	NUM
ejpam-3987	331	39	,	,	PUNCT
ejpam-3987	331	40	b	b	NOUN
ejpam-3987	331	41	=	=	SYM
ejpam-3987	331	42	1	1	NUM
ejpam-3987	331	43	,	,	PUNCT
ejpam-3987	331	44	k	k	NOUN
ejpam-3987	331	45	=	=	SYM
ejpam-3987	331	46	1/2	1/2	NUM
ejpam-3987	331	47	and	and	CCONJ
ejpam-3987	331	48	simplifying	simplify	VERB
ejpam-3987	331	49	we	we	PRON
ejpam-3987	331	50	get	get	VERB
ejpam-3987	331	51	(	(	PUNCT
ejpam-3987	331	52	50	50	NUM
ejpam-3987	331	53	)	)	PUNCT
ejpam-3987	331	54	∫	∫	PROPN
ejpam-3987	331	55	∞	∞	PROPN
ejpam-3987	331	56	0	0	NUM
ejpam-3987	332	1	∫	∫	PROPN
ejpam-3987	332	2	∞	∞	NOUN
ejpam-3987	332	3	0	0	PUNCT
ejpam-3987	333	1	e	e	NOUN
ejpam-3987	333	2	1	1	NUM
ejpam-3987	333	3	6	6	NUM
ejpam-3987	333	4	(	(	PUNCT
ejpam-3987	333	5	−2x−3y	−2x−3y	ADV
ejpam-3987	333	6	)	)	PUNCT
ejpam-3987	333	7	(	(	PUNCT
ejpam-3987	333	8	x2/3	x2/3	PROPN
ejpam-3987	333	9	−	−	NUM
ejpam-3987	333	10	y2/3	y2/3	PROPN
ejpam-3987	333	11	)	)	PUNCT
ejpam-3987	333	12	√	√	PROPN
ejpam-3987	333	13	log	log	NOUN
ejpam-3987	333	14	(	(	PUNCT
ejpam-3987	333	15	x	x	NOUN
ejpam-3987	333	16	y	y	PROPN
ejpam-3987	333	17	)	)	PUNCT
ejpam-3987	333	18	x5/6y5/6	x5/6y5/6	PROPN
ejpam-3987	333	19	dxdy	dxdy	PROPN
ejpam-3987	333	20	=	=	SYM
ejpam-3987	333	21	(	(	PUNCT
ejpam-3987	333	22	2−2i	2−2i	NUM
ejpam-3987	333	23	)	)	PUNCT
ejpam-3987	333	24	6	6	NUM
ejpam-3987	333	25	√	√	NOUN
ejpam-3987	334	1	−6π3/2	−6π3/2	PROPN
ejpam-3987	334	2	(	(	PUNCT
ejpam-3987	334	3	(	(	PUNCT
ejpam-3987	334	4	−3)2/3φ	−3)2/3φ	NUM
ejpam-3987	334	5	(	(	PUNCT
ejpam-3987	334	6	1	1	NUM
ejpam-3987	334	7	2	2	NUM
ejpam-3987	334	8	−	−	NOUN
ejpam-3987	335	1	i	i	PRON
ejpam-3987	335	2	√	√	VERB
ejpam-3987	335	3	3	3	NUM
ejpam-3987	335	4	2	2	NUM
ejpam-3987	335	5	,	,	PUNCT
ejpam-3987	335	6	−1	−1	NOUN
ejpam-3987	335	7	2	2	NUM
ejpam-3987	335	8	,	,	PUNCT
ejpam-3987	335	9	π	π	PROPN
ejpam-3987	335	10	−	−	PROPN
ejpam-3987	336	1	i	i	PRON
ejpam-3987	336	2	log	log	VERB
ejpam-3987	336	3	(	(	PUNCT
ejpam-3987	336	4	3	3	NUM
ejpam-3987	336	5	2	2	NUM
ejpam-3987	336	6	)	)	PUNCT
ejpam-3987	336	7	2π	2π	NOUN
ejpam-3987	336	8	)	)	PUNCT
ejpam-3987	336	9	−22/3φ	−22/3φ	PROPN
ejpam-3987	336	10	(	(	PUNCT
ejpam-3987	336	11	1	1	NUM
ejpam-3987	336	12	2	2	NUM
ejpam-3987	337	1	+	+	CCONJ
ejpam-3987	337	2	i	i	PRON
ejpam-3987	337	3	√	√	VERB
ejpam-3987	337	4	3	3	NUM
ejpam-3987	337	5	2	2	NUM
ejpam-3987	337	6	,	,	PUNCT
ejpam-3987	337	7	−1	−1	NOUN
ejpam-3987	337	8	2	2	NUM
ejpam-3987	337	9	,	,	PUNCT
ejpam-3987	337	10	π	π	PROPN
ejpam-3987	337	11	−	−	PROPN
ejpam-3987	338	1	i	i	PRON
ejpam-3987	338	2	log	log	VERB
ejpam-3987	338	3	(	(	PUNCT
ejpam-3987	338	4	3	3	NUM
ejpam-3987	338	5	2	2	NUM
ejpam-3987	338	6	)	)	PUNCT
ejpam-3987	338	7	2π	2π	NOUN
ejpam-3987	338	8	)	)	PUNCT
ejpam-3987	338	9	)	)	PUNCT
ejpam-3987	339	1	9.8	9.8	NUM
ejpam-3987	339	2	.	.	PUNCT
ejpam-3987	339	3	derivation	derivation	NOUN
ejpam-3987	339	4	of	of	ADP
ejpam-3987	339	5	entry	entry	NOUN
ejpam-3987	339	6	80	80	NUM
ejpam-3987	339	7	in	in	ADP
ejpam-3987	339	8	terms	term	NOUN
ejpam-3987	339	9	of	of	ADP
ejpam-3987	339	10	the	the	DET
ejpam-3987	339	11	lerch	lerch	PROPN
ejpam-3987	339	12	transcendent	transcendent	NOUN
ejpam-3987	339	13	using	use	VERB
ejpam-3987	339	14	equation	equation	NOUN
ejpam-3987	339	15	(	(	PUNCT
ejpam-3987	339	16	43	43	NUM
ejpam-3987	339	17	)	)	PUNCT
ejpam-3987	339	18	and	and	CCONJ
ejpam-3987	339	19	setting	set	VERB
ejpam-3987	339	20	s	s	X
ejpam-3987	339	21	=	=	SYM
ejpam-3987	339	22	1/3	1/3	NUM
ejpam-3987	339	23	,	,	PUNCT
ejpam-3987	339	24	t	t	NOUN
ejpam-3987	339	25	=	=	SYM
ejpam-3987	339	26	1/2	1/2	NUM
ejpam-3987	339	27	,	,	PUNCT
ejpam-3987	339	28	p	p	NOUN
ejpam-3987	339	29	=	=	SYM
ejpam-3987	339	30	1/2	1/2	NUM
ejpam-3987	339	31	,	,	PUNCT
ejpam-3987	339	32	q	q	NOUN
ejpam-3987	339	33	=	=	SYM
ejpam-3987	339	34	1/3	1/3	NUM
ejpam-3987	339	35	,	,	PUNCT
ejpam-3987	339	36	n	n	NOUN
ejpam-3987	339	37	=	=	SYM
ejpam-3987	339	38	1	1	NUM
ejpam-3987	339	39	,	,	PUNCT
ejpam-3987	339	40	b	b	NOUN
ejpam-3987	339	41	=	=	SYM
ejpam-3987	339	42	1	1	NUM
ejpam-3987	339	43	,	,	PUNCT
ejpam-3987	339	44	k	k	NOUN
ejpam-3987	339	45	=	=	PUNCT
ejpam-3987	339	46	−1/2	−1/2	ADJ
ejpam-3987	339	47	and	and	CCONJ
ejpam-3987	339	48	simplifying	simplify	VERB
ejpam-3987	339	49	we	we	PRON
ejpam-3987	339	50	get	get	VERB
ejpam-3987	339	51	(	(	PUNCT
ejpam-3987	339	52	51	51	NUM
ejpam-3987	339	53	)	)	PUNCT
ejpam-3987	339	54	∫	∫	PROPN
ejpam-3987	340	1	∞	∞	PROPN
ejpam-3987	340	2	0	0	NUM
ejpam-3987	341	1	∫	∫	PROPN
ejpam-3987	341	2	∞	∞	NOUN
ejpam-3987	341	3	0	0	PUNCT
ejpam-3987	342	1	e	e	NOUN
ejpam-3987	342	2	1	1	NUM
ejpam-3987	342	3	6	6	NUM
ejpam-3987	342	4	(	(	PUNCT
ejpam-3987	342	5	−2x−3y	−2x−3y	ADV
ejpam-3987	342	6	)	)	PUNCT
ejpam-3987	342	7	(	(	PUNCT
ejpam-3987	342	8	x2/3	x2/3	PROPN
ejpam-3987	342	9	−	−	NUM
ejpam-3987	342	10	y2/3	y2/3	PROPN
ejpam-3987	342	11	)	)	PUNCT
ejpam-3987	343	1	x5/6y5/6	x5/6y5/6	PROPN
ejpam-3987	343	2	√	√	PROPN
ejpam-3987	344	1	log	log	NOUN
ejpam-3987	344	2	(	(	PUNCT
ejpam-3987	344	3	x	x	SYM
ejpam-3987	344	4	y	y	PROPN
ejpam-3987	344	5	)	)	PUNCT
ejpam-3987	344	6	dxdy	dxdy	PROPN
ejpam-3987	344	7	=	=	SYM
ejpam-3987	344	8	(	(	PUNCT
ejpam-3987	344	9	1+i	1+i	NUM
ejpam-3987	344	10	)	)	PUNCT
ejpam-3987	344	11	6	6	NUM
ejpam-3987	344	12	√	√	NUM
ejpam-3987	344	13	−6	−6	NOUN
ejpam-3987	344	14	√	√	NUM
ejpam-3987	344	15	π	π	PROPN
ejpam-3987	344	16	(	(	PUNCT
ejpam-3987	344	17	22/3φ	22/3φ	NUM
ejpam-3987	344	18	(	(	PUNCT
ejpam-3987	344	19	1	1	NUM
ejpam-3987	344	20	2	2	NUM
ejpam-3987	345	1	+	+	CCONJ
ejpam-3987	345	2	i	i	PRON
ejpam-3987	345	3	√	√	VERB
ejpam-3987	345	4	3	3	NUM
ejpam-3987	345	5	2	2	NUM
ejpam-3987	345	6	,	,	PUNCT
ejpam-3987	345	7	1	1	NUM
ejpam-3987	345	8	2	2	NUM
ejpam-3987	345	9	,	,	PUNCT
ejpam-3987	345	10	π	π	PROPN
ejpam-3987	345	11	−	−	PROPN
ejpam-3987	346	1	i	i	PRON
ejpam-3987	346	2	log	log	VERB
ejpam-3987	346	3	(	(	PUNCT
ejpam-3987	346	4	3	3	NUM
ejpam-3987	346	5	2	2	NUM
ejpam-3987	346	6	)	)	PUNCT
ejpam-3987	346	7	2π	2π	NOUN
ejpam-3987	346	8	)	)	PUNCT
ejpam-3987	346	9	−(−3)2/3φ	−(−3)2/3φ	PROPN
ejpam-3987	346	10	(	(	PUNCT
ejpam-3987	346	11	1	1	NUM
ejpam-3987	346	12	2	2	NUM
ejpam-3987	346	13	−	−	NOUN
ejpam-3987	347	1	i	i	PRON
ejpam-3987	347	2	√	√	VERB
ejpam-3987	347	3	3	3	NUM
ejpam-3987	347	4	2	2	NUM
ejpam-3987	347	5	,	,	PUNCT
ejpam-3987	347	6	1	1	NUM
ejpam-3987	347	7	2	2	NUM
ejpam-3987	347	8	,	,	PUNCT
ejpam-3987	347	9	π	π	PROPN
ejpam-3987	347	10	−	−	PROPN
ejpam-3987	348	1	i	i	PRON
ejpam-3987	348	2	log	log	VERB
ejpam-3987	348	3	(	(	PUNCT
ejpam-3987	348	4	3	3	NUM
ejpam-3987	348	5	2	2	NUM
ejpam-3987	348	6	)	)	PUNCT
ejpam-3987	348	7	2π	2π	NOUN
ejpam-3987	348	8	)	)	PUNCT
ejpam-3987	348	9	)	)	PUNCT
ejpam-3987	348	10	10	10	NUM
ejpam-3987	348	11	.	.	PUNCT
ejpam-3987	349	1	some	some	DET
ejpam-3987	349	2	special	special	ADJ
ejpam-3987	349	3	cases	case	NOUN
ejpam-3987	349	4	of	of	ADP
ejpam-3987	349	5	the	the	DET
ejpam-3987	349	6	double	double	ADJ
ejpam-3987	349	7	laplace	laplace	NOUN
ejpam-3987	349	8	transform	transform	NOUN
ejpam-3987	349	9	involving	involve	VERB
ejpam-3987	349	10	the	the	DET
ejpam-3987	349	11	nested	nested	ADJ
ejpam-3987	349	12	logarithm	logarithm	NOUN
ejpam-3987	349	13	function	function	NOUN
ejpam-3987	349	14	in	in	ADP
ejpam-3987	349	15	this	this	DET
ejpam-3987	349	16	section	section	NOUN
ejpam-3987	349	17	we	we	PRON
ejpam-3987	349	18	will	will	AUX
ejpam-3987	349	19	use	use	VERB
ejpam-3987	349	20	a	a	DET
ejpam-3987	349	21	special	special	ADJ
ejpam-3987	349	22	case	case	NOUN
ejpam-3987	349	23	the	the	DET
ejpam-3987	349	24	double	double	ADJ
ejpam-3987	349	25	laplace	laplace	NOUN
ejpam-3987	349	26	transform	transform	NOUN
ejpam-3987	349	27	to	to	PART
ejpam-3987	349	28	derive	derive	VERB
ejpam-3987	349	29	definite	definite	ADJ
ejpam-3987	349	30	integrals	integral	NOUN
ejpam-3987	349	31	involving	involve	VERB
ejpam-3987	349	32	the	the	DET
ejpam-3987	349	33	special	special	ADJ
ejpam-3987	349	34	functions	function	NOUN
ejpam-3987	349	35	.	.	PUNCT
ejpam-3987	350	1	we	we	PRON
ejpam-3987	350	2	proceed	proceed	VERB
ejpam-3987	350	3	by	by	ADP
ejpam-3987	350	4	using	use	VERB
ejpam-3987	350	5	equation	equation	NOUN
ejpam-3987	350	6	(	(	PUNCT
ejpam-3987	350	7	43	43	NUM
ejpam-3987	350	8	)	)	PUNCT
ejpam-3987	350	9	and	and	CCONJ
ejpam-3987	350	10	replacing	replace	VERB
ejpam-3987	350	11	p	p	NOUN
ejpam-3987	350	12	by	by	ADP
ejpam-3987	350	13	2q	2q	NUM
ejpam-3987	350	14	and	and	CCONJ
ejpam-3987	350	15	setting	set	VERB
ejpam-3987	350	16	n	n	X
ejpam-3987	350	17	=	=	SYM
ejpam-3987	350	18	s	s	NOUN
ejpam-3987	350	19	=	=	X
ejpam-3987	350	20	t	t	X
ejpam-3987	350	21	=	=	SYM
ejpam-3987	350	22	1	1	NUM
ejpam-3987	350	23	and	and	CCONJ
ejpam-3987	350	24	simplifying	simplify	VERB
ejpam-3987	350	25	to	to	PART
ejpam-3987	350	26	get	get	VERB
ejpam-3987	350	27	(	(	PUNCT
ejpam-3987	350	28	52	52	NUM
ejpam-3987	350	29	)	)	PUNCT
ejpam-3987	350	30	∫	∫	PROPN
ejpam-3987	351	1	∞	∞	PROPN
ejpam-3987	351	2	0	0	NUM
ejpam-3987	352	1	∫	∫	PROPN
ejpam-3987	352	2	∞	∞	PROPN
ejpam-3987	352	3	0	0	NUM
ejpam-3987	353	1	xq−1y−3qe−x−y	xq−1y−3qe−x−y	PROPN
ejpam-3987	353	2	(	(	PUNCT
ejpam-3987	353	3	y2q	y2q	X
ejpam-3987	353	4	−	−	PROPN
ejpam-3987	353	5	x2q	x2q	NUM
ejpam-3987	353	6	)	)	PUNCT
ejpam-3987	354	1	logk	logk	NOUN
ejpam-3987	354	2	(	(	PUNCT
ejpam-3987	354	3	bx	bx	NOUN
ejpam-3987	354	4	y	y	PROPN
ejpam-3987	354	5	)	)	PUNCT
ejpam-3987	354	6	dxdy	dxdy	PROPN
ejpam-3987	354	7	=	=	SYM
ejpam-3987	355	1	(	(	PUNCT
ejpam-3987	355	2	2iπ)k+1eiπq	2iπ)k+1eiπq	NUM
ejpam-3987	355	3	(	(	PUNCT
ejpam-3987	355	4	e2iπqφ	e2iπqφ	PROPN
ejpam-3987	355	5	(	(	PUNCT
ejpam-3987	355	6	e6iπq,−k	e6iπq,−k	PROPN
ejpam-3987	355	7	,	,	PUNCT
ejpam-3987	355	8	π	π	PROPN
ejpam-3987	355	9	−	−	PROPN
ejpam-3987	355	10	i	i	PRON
ejpam-3987	355	11	log(b	log(b	PROPN
ejpam-3987	355	12	)	)	PUNCT
ejpam-3987	355	13	2π	2π	PROPN
ejpam-3987	355	14	)	)	PUNCT
ejpam-3987	356	1	−	−	PROPN
ejpam-3987	356	2	φ	φ	PROPN
ejpam-3987	356	3	(	(	PUNCT
ejpam-3987	356	4	e2iπq,−k	e2iπq,−k	PROPN
ejpam-3987	356	5	,	,	PUNCT
ejpam-3987	356	6	π	π	PROPN
ejpam-3987	356	7	−	−	PROPN
ejpam-3987	356	8	i	i	PRON
ejpam-3987	356	9	log(b	log(b	PROPN
ejpam-3987	356	10	)	)	PUNCT
ejpam-3987	356	11	2π	2π	NOUN
ejpam-3987	356	12	)	)	PUNCT
ejpam-3987	356	13	)	)	PUNCT
ejpam-3987	357	1	r.	r.	PROPN
ejpam-3987	357	2	reynolds	reynolds	PROPN
ejpam-3987	357	3	,	,	PUNCT
ejpam-3987	357	4	a.	a.	PROPN
ejpam-3987	357	5	stauffer	stauffer	PROPN
ejpam-3987	357	6	/	/	SYM
ejpam-3987	357	7	eur	eur	PROPN
ejpam-3987	357	8	.	.	PUNCT
ejpam-3987	358	1	j.	j.	PROPN
ejpam-3987	358	2	pure	pure	PROPN
ejpam-3987	358	3	appl	appl	PROPN
ejpam-3987	358	4	.	.	PROPN
ejpam-3987	358	5	math	math	PROPN
ejpam-3987	358	6	,	,	PUNCT
ejpam-3987	358	7	14	14	NUM
ejpam-3987	358	8	(	(	PUNCT
ejpam-3987	358	9	3	3	NUM
ejpam-3987	358	10	)	)	PUNCT
ejpam-3987	358	11	(	(	PUNCT
ejpam-3987	358	12	2021	2021	NUM
ejpam-3987	358	13	)	)	PUNCT
ejpam-3987	358	14	,	,	PUNCT
ejpam-3987	358	15	618	618	NUM
ejpam-3987	358	16	-	-	SYM
ejpam-3987	358	17	637	637	NUM
ejpam-3987	358	18	632	632	NUM
ejpam-3987	358	19	10.1	10.1	NUM
ejpam-3987	358	20	.	.	PUNCT
ejpam-3987	359	1	derivation	derivation	NOUN
ejpam-3987	359	2	of	of	ADP
ejpam-3987	359	3	entry	entry	NOUN
ejpam-3987	359	4	81	81	NUM
ejpam-3987	359	5	involving	involve	VERB
ejpam-3987	359	6	the	the	DET
ejpam-3987	359	7	log	log	NOUN
ejpam-3987	359	8	-	-	PUNCT
ejpam-3987	359	9	gamma	gamma	NOUN
ejpam-3987	359	10	function	function	NOUN
ejpam-3987	359	11	using	use	VERB
ejpam-3987	359	12	equation	equation	NOUN
ejpam-3987	359	13	(	(	PUNCT
ejpam-3987	359	14	52	52	NUM
ejpam-3987	359	15	)	)	PUNCT
ejpam-3987	359	16	setting	set	VERB
ejpam-3987	359	17	b	b	NOUN
ejpam-3987	359	18	=	=	SYM
ejpam-3987	359	19	1	1	NUM
ejpam-3987	359	20	and	and	CCONJ
ejpam-3987	359	21	q	q	NOUN
ejpam-3987	359	22	=	=	SYM
ejpam-3987	359	23	1/6	1/6	NUM
ejpam-3987	359	24	followed	follow	VERB
ejpam-3987	359	25	by	by	ADP
ejpam-3987	359	26	taking	take	VERB
ejpam-3987	359	27	the	the	DET
ejpam-3987	359	28	first	first	ADJ
ejpam-3987	359	29	partial	partial	ADJ
ejpam-3987	359	30	derivative	derivative	NOUN
ejpam-3987	359	31	by	by	ADP
ejpam-3987	359	32	k	k	PROPN
ejpam-3987	359	33	then	then	ADV
ejpam-3987	359	34	setting	set	VERB
ejpam-3987	359	35	k	k	PROPN
ejpam-3987	359	36	=	=	PUNCT
ejpam-3987	359	37	0	0	PUNCT
ejpam-3987	359	38	and	and	CCONJ
ejpam-3987	359	39	simplifying	simplify	VERB
ejpam-3987	359	40	to	to	PART
ejpam-3987	359	41	get	get	VERB
ejpam-3987	359	42	(	(	PUNCT
ejpam-3987	359	43	53	53	NUM
ejpam-3987	359	44	)	)	PUNCT
ejpam-3987	359	45	∫	∫	PROPN
ejpam-3987	360	1	∞	∞	PROPN
ejpam-3987	360	2	0	0	NUM
ejpam-3987	361	1	∫	∫	PROPN
ejpam-3987	361	2	∞	∞	PROPN
ejpam-3987	361	3	0	0	PROPN
ejpam-3987	362	1	e−x−y	e−x−y	NOUN
ejpam-3987	362	2	(	(	PUNCT
ejpam-3987	362	3	3	3	NUM
ejpam-3987	362	4	√	√	NUM
ejpam-3987	362	5	y	y	NUM
ejpam-3987	362	6	−	−	PROPN
ejpam-3987	362	7	3	3	NUM
ejpam-3987	362	8	√	√	PROPN
ejpam-3987	362	9	x	x	SYM
ejpam-3987	362	10	)	)	PUNCT
ejpam-3987	362	11	log	log	NOUN
ejpam-3987	362	12	(	(	PUNCT
ejpam-3987	362	13	log	log	NOUN
ejpam-3987	362	14	(	(	PUNCT
ejpam-3987	362	15	x	x	NOUN
ejpam-3987	362	16	y	y	PROPN
ejpam-3987	362	17	)	)	PUNCT
ejpam-3987	362	18	)	)	PUNCT
ejpam-3987	362	19	x5/6√y	x5/6√y	PUNCT
ejpam-3987	363	1	dxdy	dxdy	PROPN
ejpam-3987	363	2	=	=	PUNCT
ejpam-3987	363	3	1	1	NUM
ejpam-3987	363	4	2	2	NUM
ejpam-3987	363	5	π	π	NOUN
ejpam-3987	363	6	(	(	PUNCT
ejpam-3987	363	7	4(−1)2/3φ′	4(−1)2/3φ′	X
ejpam-3987	363	8	(	(	PUNCT
ejpam-3987	363	9	3	3	NUM
ejpam-3987	363	10	√	√	NUM
ejpam-3987	363	11	−1	−1	NOUN
ejpam-3987	363	12	,	,	PUNCT
ejpam-3987	363	13	0	0	NUM
ejpam-3987	363	14	,	,	PUNCT
ejpam-3987	363	15	1	1	NUM
ejpam-3987	363	16	2	2	NUM
ejpam-3987	363	17	)	)	PUNCT
ejpam-3987	364	1	+	+	CCONJ
ejpam-3987	364	2	iπ	iπ	PRON
ejpam-3987	364	3	+	+	NUM
ejpam-3987	364	4	log	log	NOUN
ejpam-3987	364	5	(	(	PUNCT
ejpam-3987	364	6	81π2γ	81π2γ	PROPN
ejpam-3987	364	7	(	(	PUNCT
ejpam-3987	364	8	−3	−3	PROPN
ejpam-3987	364	9	4	4	NUM
ejpam-3987	364	10	)	)	SYM
ejpam-3987	364	11	4	4	NUM
ejpam-3987	364	12	γ	γ	X
ejpam-3987	364	13	(	(	PUNCT
ejpam-3987	364	14	−1	−1	NOUN
ejpam-3987	364	15	4	4	NUM
ejpam-3987	364	16	)	)	PUNCT
ejpam-3987	364	17	4	4	NUM
ejpam-3987	364	18	)	)	PUNCT
ejpam-3987	364	19	)	)	PUNCT
ejpam-3987	364	20	from	from	ADP
ejpam-3987	364	21	equation	equation	NOUN
ejpam-3987	364	22	(	(	PUNCT
ejpam-3987	364	23	1.10.10	1.10.10	NUM
ejpam-3987	364	24	)	)	PUNCT
ejpam-3987	364	25	in	in	ADP
ejpam-3987	364	26	[	[	X
ejpam-3987	364	27	2	2	NUM
ejpam-3987	364	28	]	]	PUNCT
ejpam-3987	364	29	.	.	PUNCT
ejpam-3987	365	1	10.2	10.2	NUM
ejpam-3987	365	2	.	.	PUNCT
ejpam-3987	366	1	derivation	derivation	NOUN
ejpam-3987	366	2	of	of	ADP
ejpam-3987	366	3	entry	entry	NOUN
ejpam-3987	366	4	82	82	NUM
ejpam-3987	366	5	involving	involve	VERB
ejpam-3987	366	6	the	the	DET
ejpam-3987	366	7	stieltjes	stieltjes	NOUN
ejpam-3987	366	8	constant	constant	ADJ
ejpam-3987	366	9	(	(	PUNCT
ejpam-3987	366	10	γn	γn	NOUN
ejpam-3987	366	11	)	)	PUNCT
ejpam-3987	366	12	using	use	VERB
ejpam-3987	366	13	equation	equation	NOUN
ejpam-3987	366	14	(	(	PUNCT
ejpam-3987	366	15	52	52	NUM
ejpam-3987	366	16	)	)	PUNCT
ejpam-3987	366	17	setting	set	VERB
ejpam-3987	366	18	b	b	NOUN
ejpam-3987	366	19	=	=	SYM
ejpam-3987	366	20	1	1	NUM
ejpam-3987	366	21	and	and	CCONJ
ejpam-3987	366	22	q	q	NOUN
ejpam-3987	366	23	=	=	SYM
ejpam-3987	366	24	1/6	1/6	NUM
ejpam-3987	366	25	followed	follow	VERB
ejpam-3987	366	26	by	by	ADP
ejpam-3987	366	27	taking	take	VERB
ejpam-3987	366	28	the	the	DET
ejpam-3987	366	29	first	first	ADJ
ejpam-3987	366	30	partial	partial	ADJ
ejpam-3987	366	31	derivative	derivative	NOUN
ejpam-3987	366	32	by	by	ADP
ejpam-3987	366	33	k	k	PROPN
ejpam-3987	366	34	and	and	CCONJ
ejpam-3987	366	35	simplifying	simplify	VERB
ejpam-3987	366	36	to	to	PART
ejpam-3987	366	37	get	get	VERB
ejpam-3987	366	38	∫	∫	PROPN
ejpam-3987	366	39	∞	∞	PROPN
ejpam-3987	366	40	0	0	NUM
ejpam-3987	367	1	∫	∫	PROPN
ejpam-3987	367	2	∞	∞	PROPN
ejpam-3987	367	3	0	0	PROPN
ejpam-3987	368	1	e−x−y	e−x−y	NOUN
ejpam-3987	368	2	(	(	PUNCT
ejpam-3987	368	3	3	3	NUM
ejpam-3987	368	4	√	√	NUM
ejpam-3987	368	5	y	y	NUM
ejpam-3987	368	6	−	−	PROPN
ejpam-3987	368	7	3	3	NUM
ejpam-3987	368	8	√	√	PROPN
ejpam-3987	368	9	x	x	SYM
ejpam-3987	368	10	)	)	PUNCT
ejpam-3987	368	11	log	log	NOUN
ejpam-3987	368	12	(	(	PUNCT
ejpam-3987	368	13	log	log	NOUN
ejpam-3987	368	14	(	(	PUNCT
ejpam-3987	368	15	x	x	NOUN
ejpam-3987	368	16	y	y	PROPN
ejpam-3987	368	17	)	)	PUNCT
ejpam-3987	368	18	)	)	PUNCT
ejpam-3987	369	1	logk	logk	NOUN
ejpam-3987	369	2	(	(	PUNCT
ejpam-3987	369	3	x	x	NOUN
ejpam-3987	369	4	y	y	PROPN
ejpam-3987	369	5	)	)	PUNCT
ejpam-3987	369	6	x5/6√y	x5/6√y	PUNCT
ejpam-3987	370	1	dxdy	dxdy	PROPN
ejpam-3987	371	1	=	=	PUNCT
ejpam-3987	371	2	2ke	2ke	ADJ
ejpam-3987	371	3	iπk	iπk	NOUN
ejpam-3987	371	4	2	2	NUM
ejpam-3987	371	5	πk+1	πk+1	NOUN
ejpam-3987	371	6	(	(	PUNCT
ejpam-3987	371	7	2	2	NUM
ejpam-3987	371	8	(	(	PUNCT
ejpam-3987	371	9	(	(	PUNCT
ejpam-3987	371	10	−1)2/3φ′	−1)2/3φ′	PROPN
ejpam-3987	371	11	(	(	PUNCT
ejpam-3987	371	12	3	3	NUM
ejpam-3987	371	13	√	√	PROPN
ejpam-3987	371	14	−1,−k	−1,−k	NOUN
ejpam-3987	371	15	,	,	PUNCT
ejpam-3987	371	16	1	1	NUM
ejpam-3987	371	17	2	2	NUM
ejpam-3987	371	18	)	)	PUNCT
ejpam-3987	372	1	+	+	CCONJ
ejpam-3987	372	2	2k	2k	NUM
ejpam-3987	372	3	(	(	PUNCT
ejpam-3987	372	4	ζ	ζ	NOUN
ejpam-3987	372	5	′	′	NUM
ejpam-3987	372	6	(	(	PUNCT
ejpam-3987	372	7	−k	−k	PROPN
ejpam-3987	372	8	,	,	PUNCT
ejpam-3987	372	9	1	1	NUM
ejpam-3987	372	10	4	4	NUM
ejpam-3987	372	11	)	)	PUNCT
ejpam-3987	372	12	−	−	NOUN
ejpam-3987	373	1	ζ	ζ	NOUN
ejpam-3987	373	2	′	′	NOUN
ejpam-3987	373	3	(	(	PUNCT
ejpam-3987	373	4	−k	−k	PROPN
ejpam-3987	373	5	,	,	PUNCT
ejpam-3987	373	6	3	3	NUM
ejpam-3987	373	7	4	4	NUM
ejpam-3987	373	8	)	)	PUNCT
ejpam-3987	373	9	)	)	PUNCT
ejpam-3987	373	10	)	)	PUNCT
ejpam-3987	374	1	+	+	CCONJ
ejpam-3987	374	2	6	6	NUM
ejpam-3987	374	3	√	√	NUM
ejpam-3987	374	4	−1(π−2i	−1(π−2i	X
ejpam-3987	374	5	log(2π))φ	log(2π))φ	PROPN
ejpam-3987	374	6	(	(	PUNCT
ejpam-3987	374	7	3	3	NUM
ejpam-3987	374	8	√	√	NOUN
ejpam-3987	374	9	−1,−k	−1,−k	NOUN
ejpam-3987	374	10	,	,	PUNCT
ejpam-3987	374	11	1	1	NUM
ejpam-3987	374	12	2	2	NUM
ejpam-3987	374	13	)	)	PUNCT
ejpam-3987	375	1	−	−	PROPN
ejpam-3987	375	2	i2k(π−2i	i2k(π−2i	PROPN
ejpam-3987	375	3	log(4π	log(4π	NOUN
ejpam-3987	375	4	)	)	PUNCT
ejpam-3987	375	5	)	)	PUNCT
ejpam-3987	376	1	(	(	PUNCT
ejpam-3987	376	2	ζ	ζ	NOUN
ejpam-3987	376	3	(	(	PUNCT
ejpam-3987	376	4	−k	−k	PROPN
ejpam-3987	376	5	,	,	PUNCT
ejpam-3987	376	6	1	1	NUM
ejpam-3987	376	7	4	4	NUM
ejpam-3987	376	8	)	)	PUNCT
ejpam-3987	376	9	−	−	NOUN
ejpam-3987	376	10	ζ	ζ	NOUN
ejpam-3987	376	11	(	(	PUNCT
ejpam-3987	376	12	−k	−k	PROPN
ejpam-3987	376	13	,	,	PUNCT
ejpam-3987	376	14	3	3	NUM
ejpam-3987	376	15	4	4	NUM
ejpam-3987	376	16	)	)	PUNCT
ejpam-3987	376	17	)	)	PUNCT
ejpam-3987	376	18	)	)	PUNCT
ejpam-3987	376	19	(	(	PUNCT
ejpam-3987	376	20	54	54	NUM
ejpam-3987	376	21	)	)	PUNCT
ejpam-3987	376	22	next	next	ADV
ejpam-3987	376	23	we	we	PRON
ejpam-3987	376	24	apply	apply	VERB
ejpam-3987	376	25	l’hopitals	l’hopital	NOUN
ejpam-3987	376	26	rule	rule	NOUN
ejpam-3987	376	27	to	to	ADP
ejpam-3987	376	28	the	the	DET
ejpam-3987	376	29	right	right	ADJ
ejpam-3987	376	30	-	-	PUNCT
ejpam-3987	376	31	hand	hand	NOUN
ejpam-3987	376	32	side	side	NOUN
ejpam-3987	376	33	as	as	ADP
ejpam-3987	376	34	k	k	PROPN
ejpam-3987	376	35	→	→	SYM
ejpam-3987	376	36	−1	−1	NOUN
ejpam-3987	376	37	and	and	CCONJ
ejpam-3987	376	38	simplifying	simplify	VERB
ejpam-3987	376	39	to	to	PART
ejpam-3987	376	40	get	get	VERB
ejpam-3987	376	41	(	(	PUNCT
ejpam-3987	376	42	55	55	NUM
ejpam-3987	376	43	)	)	PUNCT
ejpam-3987	376	44	∫	∫	PROPN
ejpam-3987	377	1	∞	∞	PROPN
ejpam-3987	377	2	0	0	NUM
ejpam-3987	378	1	∫	∫	PROPN
ejpam-3987	378	2	∞	∞	PROPN
ejpam-3987	378	3	0	0	PROPN
ejpam-3987	379	1	e−x−y	e−x−y	NOUN
ejpam-3987	379	2	(	(	PUNCT
ejpam-3987	379	3	3	3	NUM
ejpam-3987	379	4	√	√	NUM
ejpam-3987	379	5	y	y	NUM
ejpam-3987	379	6	−	−	PROPN
ejpam-3987	379	7	3	3	NUM
ejpam-3987	379	8	√	√	PROPN
ejpam-3987	379	9	x	x	SYM
ejpam-3987	379	10	)	)	PUNCT
ejpam-3987	379	11	log	log	NOUN
ejpam-3987	379	12	(	(	PUNCT
ejpam-3987	379	13	log	log	NOUN
ejpam-3987	379	14	(	(	PUNCT
ejpam-3987	379	15	x	x	NOUN
ejpam-3987	379	16	y	y	PROPN
ejpam-3987	379	17	)	)	PUNCT
ejpam-3987	379	18	)	)	PUNCT
ejpam-3987	379	19	x5/6√y	x5/6√y	PUNCT
ejpam-3987	380	1	log	log	NOUN
ejpam-3987	380	2	(	(	PUNCT
ejpam-3987	380	3	x	x	SYM
ejpam-3987	380	4	y	y	PROPN
ejpam-3987	380	5	)	)	PUNCT
ejpam-3987	380	6	dxdy	dxdy	PROPN
ejpam-3987	381	1	=	=	SYM
ejpam-3987	381	2	−1	−1	NOUN
ejpam-3987	381	3	2	2	NUM
ejpam-3987	381	4	i	i	NOUN
ejpam-3987	381	5	(	(	PUNCT
ejpam-3987	381	6	2(−1)2/3φ′	2(−1)2/3φ′	NUM
ejpam-3987	381	7	(	(	PUNCT
ejpam-3987	381	8	3	3	NUM
ejpam-3987	381	9	√	√	NUM
ejpam-3987	381	10	−1	−1	NOUN
ejpam-3987	381	11	,	,	PUNCT
ejpam-3987	381	12	1	1	NUM
ejpam-3987	381	13	,	,	PUNCT
ejpam-3987	381	14	1	1	NUM
ejpam-3987	381	15	2	2	NUM
ejpam-3987	381	16	)	)	PUNCT
ejpam-3987	381	17	+2	+2	ADV
ejpam-3987	381	18	6	6	NUM
ejpam-3987	381	19	√	√	NUM
ejpam-3987	381	20	−1	−1	NOUN
ejpam-3987	381	21	2f1	2f1	NUM
ejpam-3987	381	22	(	(	PUNCT
ejpam-3987	381	23	1	1	NUM
ejpam-3987	381	24	2	2	NUM
ejpam-3987	381	25	,	,	PUNCT
ejpam-3987	381	26	1	1	NUM
ejpam-3987	381	27	;	;	PUNCT
ejpam-3987	381	28	3	3	NUM
ejpam-3987	381	29	2	2	NUM
ejpam-3987	381	30	;	;	PUNCT
ejpam-3987	381	31	3	3	NUM
ejpam-3987	381	32	√	√	NUM
ejpam-3987	381	33	−1	−1	NOUN
ejpam-3987	381	34	)	)	PUNCT
ejpam-3987	381	35	(	(	PUNCT
ejpam-3987	381	36	π−2i	π−2i	X
ejpam-3987	381	37	log(2π	log(2π	PROPN
ejpam-3987	381	38	)	)	PUNCT
ejpam-3987	381	39	)	)	PUNCT
ejpam-3987	382	1	−	−	PROPN
ejpam-3987	382	2	γ1	γ1	NOUN
ejpam-3987	382	3	(	(	PUNCT
ejpam-3987	382	4	1	1	NUM
ejpam-3987	382	5	4	4	NUM
ejpam-3987	382	6	)	)	PUNCT
ejpam-3987	382	7	+	+	CCONJ
ejpam-3987	382	8	γ1	γ1	NOUN
ejpam-3987	382	9	(	(	PUNCT
ejpam-3987	382	10	3	3	NUM
ejpam-3987	382	11	4	4	NUM
ejpam-3987	382	12	)	)	PUNCT
ejpam-3987	382	13	+	+	CCONJ
ejpam-3987	382	14	1	1	NUM
ejpam-3987	382	15	2	2	NUM
ejpam-3987	382	16	(	(	PUNCT
ejpam-3987	382	17	2	2	NUM
ejpam-3987	382	18	log(4π	log(4π	NOUN
ejpam-3987	382	19	)	)	PUNCT
ejpam-3987	383	1	+	+	CCONJ
ejpam-3987	383	2	iπ	iπ	NOUN
ejpam-3987	383	3	)	)	PUNCT
ejpam-3987	383	4	(	(	PUNCT
ejpam-3987	383	5	ψ(0	ψ(0	NOUN
ejpam-3987	383	6	)	)	PUNCT
ejpam-3987	383	7	(	(	PUNCT
ejpam-3987	383	8	1	1	NUM
ejpam-3987	383	9	4	4	NUM
ejpam-3987	383	10	)	)	PUNCT
ejpam-3987	383	11	−	−	PROPN
ejpam-3987	384	1	ψ(0	ψ(0	NOUN
ejpam-3987	384	2	)	)	PUNCT
ejpam-3987	384	3	(	(	PUNCT
ejpam-3987	384	4	3	3	NUM
ejpam-3987	384	5	4	4	NUM
ejpam-3987	384	6	)	)	PUNCT
ejpam-3987	384	7	)	)	PUNCT
ejpam-3987	384	8	)	)	PUNCT
ejpam-3987	385	1	next	next	ADV
ejpam-3987	385	2	we	we	PRON
ejpam-3987	385	3	simplify	simplify	VERB
ejpam-3987	385	4	the	the	DET
ejpam-3987	385	5	right	right	ADJ
ejpam-3987	385	6	-	-	PUNCT
ejpam-3987	385	7	hand	hand	NOUN
ejpam-3987	385	8	side	side	NOUN
ejpam-3987	385	9	in	in	ADP
ejpam-3987	385	10	terms	term	NOUN
ejpam-3987	385	11	of	of	ADP
ejpam-3987	385	12	the	the	DET
ejpam-3987	385	13	stieltjes	stieltjes	NOUN
ejpam-3987	385	14	constant	constant	ADJ
ejpam-3987	385	15	(	(	PUNCT
ejpam-3987	385	16	γn	γn	NOUN
ejpam-3987	385	17	)	)	PUNCT
ejpam-3987	385	18	and	and	CCONJ
ejpam-3987	385	19	simplifying	simplify	VERB
ejpam-3987	385	20	to	to	PART
ejpam-3987	385	21	get	get	VERB
ejpam-3987	385	22	r.	r.	PROPN
ejpam-3987	385	23	reynolds	reynolds	PROPN
ejpam-3987	385	24	,	,	PUNCT
ejpam-3987	385	25	a.	a.	PROPN
ejpam-3987	385	26	stauffer	stauffer	PROPN
ejpam-3987	385	27	/	/	SYM
ejpam-3987	385	28	eur	eur	PROPN
ejpam-3987	385	29	.	.	PUNCT
ejpam-3987	386	1	j.	j.	PROPN
ejpam-3987	386	2	pure	pure	PROPN
ejpam-3987	386	3	appl	appl	PROPN
ejpam-3987	386	4	.	.	PROPN
ejpam-3987	386	5	math	math	PROPN
ejpam-3987	386	6	,	,	PUNCT
ejpam-3987	386	7	14	14	NUM
ejpam-3987	386	8	(	(	PUNCT
ejpam-3987	386	9	3	3	NUM
ejpam-3987	386	10	)	)	PUNCT
ejpam-3987	386	11	(	(	PUNCT
ejpam-3987	386	12	2021	2021	NUM
ejpam-3987	386	13	)	)	PUNCT
ejpam-3987	386	14	,	,	PUNCT
ejpam-3987	386	15	618	618	NUM
ejpam-3987	386	16	-	-	SYM
ejpam-3987	386	17	637	637	NUM
ejpam-3987	386	18	633	633	NUM
ejpam-3987	386	19	(	(	PUNCT
ejpam-3987	386	20	56	56	NUM
ejpam-3987	386	21	)	)	PUNCT
ejpam-3987	386	22	∫	∫	PROPN
ejpam-3987	387	1	∞	∞	PROPN
ejpam-3987	387	2	0	0	NUM
ejpam-3987	388	1	∫	∫	PROPN
ejpam-3987	388	2	∞	∞	PROPN
ejpam-3987	388	3	0	0	PROPN
ejpam-3987	389	1	e−x−y	e−x−y	NOUN
ejpam-3987	389	2	(	(	PUNCT
ejpam-3987	389	3	3	3	NUM
ejpam-3987	389	4	√	√	NUM
ejpam-3987	389	5	y	y	NUM
ejpam-3987	389	6	−	−	PROPN
ejpam-3987	389	7	3	3	NUM
ejpam-3987	389	8	√	√	PROPN
ejpam-3987	389	9	x	x	SYM
ejpam-3987	389	10	)	)	PUNCT
ejpam-3987	389	11	log	log	NOUN
ejpam-3987	389	12	(	(	PUNCT
ejpam-3987	389	13	log	log	NOUN
ejpam-3987	389	14	(	(	PUNCT
ejpam-3987	389	15	x	x	NOUN
ejpam-3987	389	16	y	y	PROPN
ejpam-3987	389	17	)	)	PUNCT
ejpam-3987	389	18	)	)	PUNCT
ejpam-3987	389	19	x5/6√y	x5/6√y	PUNCT
ejpam-3987	390	1	log	log	NOUN
ejpam-3987	390	2	(	(	PUNCT
ejpam-3987	390	3	x	x	SYM
ejpam-3987	390	4	y	y	PROPN
ejpam-3987	390	5	)	)	PUNCT
ejpam-3987	390	6	dxdy	dxdy	PROPN
ejpam-3987	390	7	=	=	NOUN
ejpam-3987	390	8	1	1	NUM
ejpam-3987	390	9	4	4	NUM
ejpam-3987	390	10	(	(	PUNCT
ejpam-3987	390	11	4	4	NUM
ejpam-3987	390	12	6	6	NUM
ejpam-3987	390	13	√	√	NOUN
ejpam-3987	390	14	−1φ′	−1φ′	PROPN
ejpam-3987	390	15	(	(	PUNCT
ejpam-3987	390	16	3	3	NUM
ejpam-3987	390	17	√	√	NUM
ejpam-3987	390	18	−1	−1	NOUN
ejpam-3987	390	19	,	,	PUNCT
ejpam-3987	390	20	1	1	NUM
ejpam-3987	390	21	,	,	PUNCT
ejpam-3987	390	22	1	1	NUM
ejpam-3987	390	23	2	2	NUM
ejpam-3987	390	24	)	)	PUNCT
ejpam-3987	390	25	+	+	CCONJ
ejpam-3987	390	26	2iγ1	2iγ1	NUM
ejpam-3987	390	27	(	(	PUNCT
ejpam-3987	390	28	1	1	NUM
ejpam-3987	390	29	4	4	NUM
ejpam-3987	390	30	)	)	PUNCT
ejpam-3987	390	31	−	−	PROPN
ejpam-3987	390	32	2iγ1	2iγ1	NUM
ejpam-3987	390	33	(	(	PUNCT
ejpam-3987	390	34	3	3	NUM
ejpam-3987	390	35	4	4	NUM
ejpam-3987	390	36	)	)	PUNCT
ejpam-3987	390	37	−	−	PROPN
ejpam-3987	391	1	π2	π2	ADJ
ejpam-3987	391	2	+	+	CCONJ
ejpam-3987	391	3	2iπ	2iπ	ADJ
ejpam-3987	391	4	log(4π)−	log(4π)−	NOUN
ejpam-3987	391	5	4iπ	4iπ	NOUN
ejpam-3987	391	6	tanh−1	tanh−1	PROPN
ejpam-3987	391	7	(	(	PUNCT
ejpam-3987	391	8	6	6	NUM
ejpam-3987	391	9	√	√	NUM
ejpam-3987	391	10	−1	−1	NOUN
ejpam-3987	391	11	)	)	PUNCT
ejpam-3987	391	12	−	−	PROPN
ejpam-3987	391	13	8	8	NUM
ejpam-3987	391	14	log(2π	log(2π	NOUN
ejpam-3987	391	15	)	)	PUNCT
ejpam-3987	391	16	tanh−1	tanh−1	VERB
ejpam-3987	391	17	(	(	PUNCT
ejpam-3987	391	18	6	6	NUM
ejpam-3987	391	19	√	√	NUM
ejpam-3987	391	20	−1	−1	NOUN
ejpam-3987	391	21	)	)	PUNCT
ejpam-3987	391	22	)	)	PUNCT
ejpam-3987	391	23	from	from	ADP
ejpam-3987	391	24	equation	equation	NOUN
ejpam-3987	391	25	(	(	PUNCT
ejpam-3987	391	26	7.6	7.6	NUM
ejpam-3987	391	27	)	)	PUNCT
ejpam-3987	391	28	in	in	ADP
ejpam-3987	391	29	[	[	X
ejpam-3987	391	30	1	1	NUM
ejpam-3987	391	31	]	]	PUNCT
ejpam-3987	391	32	.	.	PUNCT
ejpam-3987	392	1	10.3	10.3	NUM
ejpam-3987	392	2	.	.	PUNCT
ejpam-3987	393	1	derivation	derivation	NOUN
ejpam-3987	393	2	of	of	ADP
ejpam-3987	393	3	entry	entry	NOUN
ejpam-3987	393	4	83	83	NUM
ejpam-3987	393	5	involving	involve	VERB
ejpam-3987	393	6	the	the	DET
ejpam-3987	393	7	catalan	catalan	NOUN
ejpam-3987	393	8	’s	’s	PART
ejpam-3987	393	9	constant	constant	ADJ
ejpam-3987	393	10	(	(	PUNCT
ejpam-3987	393	11	c	c	NOUN
ejpam-3987	393	12	)	)	PUNCT
ejpam-3987	393	13	using	use	VERB
ejpam-3987	393	14	equation	equation	NOUN
ejpam-3987	393	15	(	(	PUNCT
ejpam-3987	393	16	52	52	NUM
ejpam-3987	393	17	)	)	PUNCT
ejpam-3987	393	18	setting	set	VERB
ejpam-3987	393	19	b	b	NOUN
ejpam-3987	393	20	=	=	SYM
ejpam-3987	393	21	1	1	NUM
ejpam-3987	393	22	and	and	CCONJ
ejpam-3987	393	23	q	q	NOUN
ejpam-3987	393	24	=	=	SYM
ejpam-3987	393	25	1/6	1/6	NUM
ejpam-3987	393	26	followed	follow	VERB
ejpam-3987	393	27	by	by	ADP
ejpam-3987	393	28	taking	take	VERB
ejpam-3987	393	29	the	the	DET
ejpam-3987	393	30	first	first	ADJ
ejpam-3987	393	31	partial	partial	ADJ
ejpam-3987	393	32	derivative	derivative	NOUN
ejpam-3987	393	33	by	by	ADP
ejpam-3987	393	34	k	k	PROPN
ejpam-3987	393	35	and	and	CCONJ
ejpam-3987	393	36	setting	set	VERB
ejpam-3987	393	37	k	k	X
ejpam-3987	393	38	=	=	SYM
ejpam-3987	393	39	1	1	NUM
ejpam-3987	393	40	and	and	CCONJ
ejpam-3987	393	41	simplifying	simplify	VERB
ejpam-3987	393	42	to	to	PART
ejpam-3987	393	43	get	get	VERB
ejpam-3987	393	44	(	(	PUNCT
ejpam-3987	393	45	57	57	NUM
ejpam-3987	393	46	)	)	PUNCT
ejpam-3987	393	47	∫	∫	PROPN
ejpam-3987	394	1	∞	∞	PROPN
ejpam-3987	394	2	0	0	NUM
ejpam-3987	395	1	∫	∫	PROPN
ejpam-3987	395	2	∞	∞	PROPN
ejpam-3987	395	3	0	0	PROPN
ejpam-3987	396	1	e−x−y	e−x−y	NOUN
ejpam-3987	396	2	(	(	PUNCT
ejpam-3987	396	3	3	3	NUM
ejpam-3987	396	4	√	√	NUM
ejpam-3987	396	5	y	y	NUM
ejpam-3987	396	6	−	−	PROPN
ejpam-3987	396	7	3	3	NUM
ejpam-3987	396	8	√	√	PROPN
ejpam-3987	396	9	x	x	SYM
ejpam-3987	396	10	)	)	PUNCT
ejpam-3987	396	11	log	log	NOUN
ejpam-3987	396	12	(	(	PUNCT
ejpam-3987	396	13	x	x	NOUN
ejpam-3987	396	14	y	y	PROPN
ejpam-3987	396	15	)	)	PUNCT
ejpam-3987	396	16	log	log	NOUN
ejpam-3987	396	17	(	(	PUNCT
ejpam-3987	396	18	log	log	NOUN
ejpam-3987	396	19	(	(	PUNCT
ejpam-3987	396	20	x	x	NOUN
ejpam-3987	396	21	y	y	PROPN
ejpam-3987	396	22	)	)	PUNCT
ejpam-3987	396	23	)	)	PUNCT
ejpam-3987	396	24	x5/6√y	x5/6√y	PUNCT
ejpam-3987	397	1	dxdy	dxdy	PROPN
ejpam-3987	397	2	=	=	PUNCT
ejpam-3987	397	3	π	π	PROPN
ejpam-3987	397	4	(	(	PUNCT
ejpam-3987	397	5	π	π	PROPN
ejpam-3987	397	6	(	(	PUNCT
ejpam-3987	397	7	−2	−2	X
ejpam-3987	397	8	(	(	PUNCT
ejpam-3987	397	9	√	√	ADP
ejpam-3987	397	10	3	3	NUM
ejpam-3987	397	11	+	+	CCONJ
ejpam-3987	397	12	i	i	NOUN
ejpam-3987	397	13	)	)	PUNCT
ejpam-3987	397	14	φ′	φ′	NUM
ejpam-3987	397	15	(	(	PUNCT
ejpam-3987	397	16	3	3	NUM
ejpam-3987	397	17	√	√	NOUN
ejpam-3987	397	18	−1,−1	−1,−1	NOUN
ejpam-3987	397	19	,	,	PUNCT
ejpam-3987	397	20	1	1	NUM
ejpam-3987	397	21	2	2	NUM
ejpam-3987	397	22	)	)	PUNCT
ejpam-3987	397	23	−	−	PROPN
ejpam-3987	398	1	i	i	PRON
ejpam-3987	398	2	√	√	VERB
ejpam-3987	398	3	3π	3π	NUM
ejpam-3987	398	4	−	−	PROPN
ejpam-3987	398	5	2	2	NUM
ejpam-3987	398	6	√	√	NUM
ejpam-3987	398	7	3	3	NUM
ejpam-3987	398	8	log(2π	log(2π	NOUN
ejpam-3987	398	9	)	)	PUNCT
ejpam-3987	398	10	)	)	PUNCT
ejpam-3987	399	1	+	+	CCONJ
ejpam-3987	399	2	4ic	4ic	X
ejpam-3987	399	3	)	)	PUNCT
ejpam-3987	399	4	from	from	ADP
ejpam-3987	399	5	(	(	PUNCT
ejpam-3987	399	6	9.73	9.73	NUM
ejpam-3987	399	7	)	)	PUNCT
ejpam-3987	399	8	in	in	ADP
ejpam-3987	399	9	[	[	X
ejpam-3987	399	10	9	9	NUM
ejpam-3987	399	11	]	]	PUNCT
ejpam-3987	399	12	.	.	PUNCT
ejpam-3987	400	1	10.4	10.4	NUM
ejpam-3987	400	2	.	.	PUNCT
ejpam-3987	401	1	derivation	derivation	NOUN
ejpam-3987	401	2	of	of	ADP
ejpam-3987	401	3	entry	entry	NOUN
ejpam-3987	401	4	84	84	NUM
ejpam-3987	401	5	involving	involve	VERB
ejpam-3987	401	6	the	the	DET
ejpam-3987	401	7	polylogarithm	polylogarithm	PROPN
ejpam-3987	401	8	function	function	NOUN
ejpam-3987	401	9	using	use	VERB
ejpam-3987	401	10	equation	equation	NOUN
ejpam-3987	401	11	(	(	PUNCT
ejpam-3987	401	12	52	52	NUM
ejpam-3987	401	13	)	)	PUNCT
ejpam-3987	401	14	setting	set	VERB
ejpam-3987	401	15	b	b	NOUN
ejpam-3987	401	16	=	=	PUNCT
ejpam-3987	401	17	−1	−1	NOUN
ejpam-3987	401	18	and	and	CCONJ
ejpam-3987	401	19	q	q	NOUN
ejpam-3987	401	20	=	=	SYM
ejpam-3987	401	21	1/6	1/6	NUM
ejpam-3987	401	22	followed	follow	VERB
ejpam-3987	401	23	by	by	ADP
ejpam-3987	401	24	taking	take	VERB
ejpam-3987	401	25	the	the	DET
ejpam-3987	401	26	first	first	ADJ
ejpam-3987	401	27	partial	partial	ADJ
ejpam-3987	401	28	derivative	derivative	NOUN
ejpam-3987	401	29	by	by	ADP
ejpam-3987	401	30	k	k	PROPN
ejpam-3987	401	31	and	and	CCONJ
ejpam-3987	401	32	setting	set	VERB
ejpam-3987	401	33	k	k	X
ejpam-3987	401	34	=	=	SYM
ejpam-3987	401	35	1	1	NUM
ejpam-3987	401	36	and	and	CCONJ
ejpam-3987	401	37	simplifying	simplify	VERB
ejpam-3987	401	38	to	to	PART
ejpam-3987	401	39	get	get	VERB
ejpam-3987	401	40	(	(	PUNCT
ejpam-3987	401	41	58	58	NUM
ejpam-3987	401	42	)	)	PUNCT
ejpam-3987	401	43	∫	∫	PROPN
ejpam-3987	402	1	∞	∞	PROPN
ejpam-3987	402	2	0	0	NUM
ejpam-3987	403	1	∫	∫	PROPN
ejpam-3987	403	2	∞	∞	PROPN
ejpam-3987	403	3	0	0	PROPN
ejpam-3987	404	1	e−x−y	e−x−y	NOUN
ejpam-3987	404	2	(	(	PUNCT
ejpam-3987	404	3	3	3	NUM
ejpam-3987	404	4	√	√	NUM
ejpam-3987	404	5	y	y	NUM
ejpam-3987	404	6	−	−	PROPN
ejpam-3987	404	7	3	3	NUM
ejpam-3987	404	8	√	√	PROPN
ejpam-3987	404	9	x	x	SYM
ejpam-3987	404	10	)	)	PUNCT
ejpam-3987	404	11	logk	logk	NOUN
ejpam-3987	404	12	(	(	PUNCT
ejpam-3987	404	13	−x	−x	NOUN
ejpam-3987	404	14	y	y	PROPN
ejpam-3987	404	15	)	)	PUNCT
ejpam-3987	404	16	x5/6√y	x5/6√y	PUNCT
ejpam-3987	405	1	dxdy	dxdy	PROPN
ejpam-3987	405	2	=	=	SYM
ejpam-3987	405	3	ik+2(2π)k+1	ik+2(2π)k+1	PROPN
ejpam-3987	405	4	(	(	PUNCT
ejpam-3987	405	5	(	(	PUNCT
ejpam-3987	405	6	1−	1−	NUM
ejpam-3987	405	7	2k+1	2k+1	NOUN
ejpam-3987	405	8	)	)	PUNCT
ejpam-3987	405	9	ζ(−k)−	ζ(−k)−	VERB
ejpam-3987	405	10	e−	e−	PROPN
ejpam-3987	405	11	2iπ	2iπ	NOUN
ejpam-3987	405	12	3	3	NUM
ejpam-3987	405	13	li−k	li−k	NOUN
ejpam-3987	405	14	(	(	PUNCT
ejpam-3987	405	15	e	e	X
ejpam-3987	405	16	iπ	iπ	ADV
ejpam-3987	405	17	3	3	NUM
ejpam-3987	405	18	)	)	PUNCT
ejpam-3987	405	19	)	)	PUNCT
ejpam-3987	406	1	next	next	ADV
ejpam-3987	406	2	we	we	PRON
ejpam-3987	406	3	use	use	VERB
ejpam-3987	406	4	l’hopital	l’hopital	PROPN
ejpam-3987	406	5	’s	’s	PART
ejpam-3987	406	6	rule	rule	NOUN
ejpam-3987	406	7	on	on	ADP
ejpam-3987	406	8	the	the	DET
ejpam-3987	406	9	right	right	ADJ
ejpam-3987	406	10	hand	hand	NOUN
ejpam-3987	406	11	-	-	PUNCT
ejpam-3987	406	12	side	side	NOUN
ejpam-3987	406	13	as	as	ADP
ejpam-3987	406	14	k	k	PROPN
ejpam-3987	406	15	→	→	SYM
ejpam-3987	406	16	−1	−1	NOUN
ejpam-3987	406	17	and	and	CCONJ
ejpam-3987	406	18	simplifying	simplify	VERB
ejpam-3987	406	19	to	to	PART
ejpam-3987	406	20	get	get	VERB
ejpam-3987	406	21	(	(	PUNCT
ejpam-3987	406	22	59	59	NUM
ejpam-3987	406	23	)	)	PUNCT
ejpam-3987	406	24	∫	∫	PROPN
ejpam-3987	407	1	∞	∞	PROPN
ejpam-3987	407	2	0	0	NUM
ejpam-3987	408	1	∫	∫	PROPN
ejpam-3987	408	2	∞	∞	PROPN
ejpam-3987	408	3	0	0	PROPN
ejpam-3987	409	1	e−x−y	e−x−y	NOUN
ejpam-3987	409	2	(	(	PUNCT
ejpam-3987	409	3	3	3	NUM
ejpam-3987	409	4	√	√	NUM
ejpam-3987	409	5	y	y	NUM
ejpam-3987	409	6	−	−	PROPN
ejpam-3987	409	7	3	3	NUM
ejpam-3987	409	8	√	√	PROPN
ejpam-3987	409	9	x	x	SYM
ejpam-3987	409	10	)	)	PUNCT
ejpam-3987	409	11	x5/6√y	x5/6√y	PUNCT
ejpam-3987	410	1	log	log	NOUN
ejpam-3987	410	2	(	(	PUNCT
ejpam-3987	410	3	x	x	SYM
ejpam-3987	410	4	y	y	PROPN
ejpam-3987	410	5	)	)	PUNCT
ejpam-3987	410	6	dxdy	dxdy	PROPN
ejpam-3987	410	7	=	=	NOUN
ejpam-3987	410	8	1	1	NUM
ejpam-3987	410	9	2	2	NUM
ejpam-3987	410	10	i	i	NOUN
ejpam-3987	410	11	(	(	PUNCT
ejpam-3987	410	12	π	π	NOUN
ejpam-3987	410	13	−	−	PROPN
ejpam-3987	410	14	4	4	NUM
ejpam-3987	410	15	tan−1	tan−1	PROPN
ejpam-3987	410	16	(	(	PUNCT
ejpam-3987	410	17	1	1	NUM
ejpam-3987	410	18	2	2	NUM
ejpam-3987	410	19	−	−	NOUN
ejpam-3987	411	1	i	i	PRON
ejpam-3987	411	2	√	√	VERB
ejpam-3987	411	3	3	3	NUM
ejpam-3987	411	4	2	2	NUM
ejpam-3987	411	5	)	)	PUNCT
ejpam-3987	411	6	)	)	PUNCT
ejpam-3987	412	1	r.	r.	PROPN
ejpam-3987	412	2	reynolds	reynolds	PROPN
ejpam-3987	412	3	,	,	PUNCT
ejpam-3987	412	4	a.	a.	PROPN
ejpam-3987	412	5	stauffer	stauffer	PROPN
ejpam-3987	412	6	/	/	SYM
ejpam-3987	412	7	eur	eur	PROPN
ejpam-3987	412	8	.	.	PUNCT
ejpam-3987	413	1	j.	j.	PROPN
ejpam-3987	413	2	pure	pure	PROPN
ejpam-3987	413	3	appl	appl	PROPN
ejpam-3987	413	4	.	.	PROPN
ejpam-3987	413	5	math	math	PROPN
ejpam-3987	413	6	,	,	PUNCT
ejpam-3987	413	7	14	14	NUM
ejpam-3987	413	8	(	(	PUNCT
ejpam-3987	413	9	3	3	NUM
ejpam-3987	413	10	)	)	PUNCT
ejpam-3987	413	11	(	(	PUNCT
ejpam-3987	413	12	2021	2021	NUM
ejpam-3987	413	13	)	)	PUNCT
ejpam-3987	413	14	,	,	PUNCT
ejpam-3987	413	15	618	618	NUM
ejpam-3987	413	16	-	-	SYM
ejpam-3987	413	17	637	637	NUM
ejpam-3987	413	18	634	634	NUM
ejpam-3987	413	19	11	11	NUM
ejpam-3987	413	20	.	.	PUNCT
ejpam-3987	414	1	a	a	DET
ejpam-3987	414	2	general	general	ADJ
ejpam-3987	414	3	case	case	NOUN
ejpam-3987	414	4	of	of	ADP
ejpam-3987	414	5	definite	definite	ADJ
ejpam-3987	414	6	integrals	integral	NOUN
ejpam-3987	414	7	involving	involve	VERB
ejpam-3987	414	8	log	log	NOUN
ejpam-3987	414	9	(	(	PUNCT
ejpam-3987	414	10	x	x	NOUN
ejpam-3987	414	11	y	y	PROPN
ejpam-3987	414	12	)	)	PUNCT
ejpam-3987	414	13	in	in	ADP
ejpam-3987	414	14	the	the	DET
ejpam-3987	414	15	denominator	denominator	NOUN
ejpam-3987	414	16	in	in	ADP
ejpam-3987	414	17	this	this	DET
ejpam-3987	414	18	section	section	NOUN
ejpam-3987	414	19	we	we	PRON
ejpam-3987	414	20	will	will	AUX
ejpam-3987	414	21	derive	derive	VERB
ejpam-3987	414	22	the	the	DET
ejpam-3987	414	23	double	double	ADJ
ejpam-3987	414	24	laplace	laplace	NOUN
ejpam-3987	414	25	transform	transform	NOUN
ejpam-3987	414	26	and	and	CCONJ
ejpam-3987	414	27	derive	derive	VERB
ejpam-3987	414	28	a	a	DET
ejpam-3987	414	29	few	few	ADJ
ejpam-3987	414	30	examples	example	NOUN
ejpam-3987	414	31	illustrating	illustrate	VERB
ejpam-3987	414	32	this	this	DET
ejpam-3987	414	33	form	form	NOUN
ejpam-3987	414	34	.	.	PUNCT
ejpam-3987	415	1	this	this	DET
ejpam-3987	415	2	form	form	NOUN
ejpam-3987	415	3	was	be	AUX
ejpam-3987	415	4	derived	derive	VERB
ejpam-3987	415	5	by	by	ADP
ejpam-3987	415	6	gröbner	gröbner	NOUN
ejpam-3987	415	7	and	and	CCONJ
ejpam-3987	415	8	hofreiter	hofreiter	NOUN
ejpam-3987	415	9	[	[	X
ejpam-3987	415	10	3	3	NUM
ejpam-3987	415	11	]	]	PUNCT
ejpam-3987	415	12	and	and	CCONJ
ejpam-3987	415	13	bierens	bierens	PROPN
ejpam-3987	415	14	de	de	X
ejpam-3987	415	15	haan	haan	X
ejpam-3987	415	16	[	[	X
ejpam-3987	415	17	4	4	NUM
ejpam-3987	415	18	]	]	PUNCT
ejpam-3987	415	19	.	.	PUNCT
ejpam-3987	416	1	using	use	VERB
ejpam-3987	416	2	equation	equation	NOUN
ejpam-3987	416	3	(	(	PUNCT
ejpam-3987	416	4	52	52	NUM
ejpam-3987	416	5	)	)	PUNCT
ejpam-3987	416	6	and	and	CCONJ
ejpam-3987	416	7	setting	set	VERB
ejpam-3987	416	8	k	k	PROPN
ejpam-3987	416	9	=	=	PUNCT
ejpam-3987	416	10	−1	−1	NOUN
ejpam-3987	416	11	,	,	PUNCT
ejpam-3987	416	12	b	b	X
ejpam-3987	416	13	=	=	SYM
ejpam-3987	416	14	s	s	PART
ejpam-3987	416	15	=	=	X
ejpam-3987	416	16	t	t	X
ejpam-3987	416	17	=	=	SYM
ejpam-3987	416	18	1	1	NUM
ejpam-3987	416	19	and	and	CCONJ
ejpam-3987	416	20	simplifying	simplify	VERB
ejpam-3987	416	21	we	we	PRON
ejpam-3987	416	22	get	get	VERB
ejpam-3987	416	23	(	(	PUNCT
ejpam-3987	416	24	60	60	NUM
ejpam-3987	416	25	)	)	PUNCT
ejpam-3987	416	26	∫	∫	PROPN
ejpam-3987	417	1	∞	∞	PROPN
ejpam-3987	417	2	0	0	NUM
ejpam-3987	418	1	∫	∫	PROPN
ejpam-3987	418	2	∞	∞	PROPN
ejpam-3987	418	3	0	0	NUM
ejpam-3987	419	1	e−x	e−x	PROPN
ejpam-3987	419	2	n−ynxp−q−1	n−ynxp−q−1	PROPN
ejpam-3987	419	3	(	(	PUNCT
ejpam-3987	419	4	y2q	y2q	X
ejpam-3987	419	5	−	−	PROPN
ejpam-3987	419	6	x2q	x2q	NUM
ejpam-3987	419	7	)	)	PUNCT
ejpam-3987	419	8	yn−p−q−1	yn−p−q−1	NOUN
ejpam-3987	419	9	log	log	NOUN
ejpam-3987	419	10	(	(	PUNCT
ejpam-3987	419	11	x	x	SYM
ejpam-3987	419	12	y	y	PROPN
ejpam-3987	419	13	)	)	PUNCT
ejpam-3987	419	14	dxdy	dxdy	NOUN
ejpam-3987	419	15	=	=	SYM
ejpam-3987	419	16	2	2	NUM
ejpam-3987	419	17	n	n	NOUN
ejpam-3987	419	18	(	(	PUNCT
ejpam-3987	419	19	tanh−1	tanh−1	PROPN
ejpam-3987	419	20	(	(	PUNCT
ejpam-3987	419	21	e	e	NOUN
ejpam-3987	419	22	iπ(p−iq	iπ(p−iq	NOUN
ejpam-3987	419	23	)	)	PUNCT
ejpam-3987	419	24	n	n	CCONJ
ejpam-3987	419	25	)	)	PUNCT
ejpam-3987	419	26	−	−	PROPN
ejpam-3987	420	1	tanh−1	tanh−1	NOUN
ejpam-3987	420	2	(	(	PUNCT
ejpam-3987	420	3	e	e	NOUN
ejpam-3987	420	4	iπ(p+iq	iπ(p+iq	PROPN
ejpam-3987	420	5	)	)	PUNCT
ejpam-3987	420	6	n	n	CCONJ
ejpam-3987	420	7	)	)	PUNCT
ejpam-3987	420	8	)	)	PUNCT
ejpam-3987	421	1	=	=	SYM
ejpam-3987	421	2	1	1	NUM
ejpam-3987	421	3	n	n	NUM
ejpam-3987	421	4	log	log	NOUN
ejpam-3987	421	5	(	(	PUNCT
ejpam-3987	421	6	tan	tan	PROPN
ejpam-3987	421	7	(	(	PUNCT
ejpam-3987	421	8	πp	πp	ADP
ejpam-3987	421	9	2n	2n	NUM
ejpam-3987	421	10	−	−	PROPN
ejpam-3987	421	11	πq	πq	PROPN
ejpam-3987	421	12	2n	2n	PROPN
ejpam-3987	421	13	)	)	PUNCT
ejpam-3987	421	14	cot	cot	NOUN
ejpam-3987	421	15	(	(	PUNCT
ejpam-3987	421	16	πp	πp	PRON
ejpam-3987	421	17	2n	2n	NUM
ejpam-3987	421	18	+	+	CCONJ
ejpam-3987	421	19	πq	πq	PRON
ejpam-3987	421	20	2n	2n	NUM
ejpam-3987	421	21	)	)	PUNCT
ejpam-3987	421	22	)	)	PUNCT
ejpam-3987	422	1	11.1	11.1	NUM
ejpam-3987	422	2	.	.	PUNCT
ejpam-3987	423	1	derivation	derivation	NOUN
ejpam-3987	423	2	of	of	ADP
ejpam-3987	423	3	entry	entry	NOUN
ejpam-3987	423	4	85	85	NUM
ejpam-3987	423	5	involving	involve	VERB
ejpam-3987	423	6	the	the	DET
ejpam-3987	423	7	logarithm	logarithm	NOUN
ejpam-3987	423	8	,	,	PUNCT
ejpam-3987	423	9	cotangent	cotangent	NOUN
ejpam-3987	423	10	and	and	CCONJ
ejpam-3987	423	11	tangent	tangent	NOUN
ejpam-3987	423	12	functions	function	NOUN
ejpam-3987	423	13	using	use	VERB
ejpam-3987	423	14	equation	equation	NOUN
ejpam-3987	423	15	(	(	PUNCT
ejpam-3987	423	16	60	60	NUM
ejpam-3987	423	17	)	)	PUNCT
ejpam-3987	423	18	setting	set	VERB
ejpam-3987	423	19	p	p	NOUN
ejpam-3987	423	20	=	=	NOUN
ejpam-3987	423	21	1	1	NUM
ejpam-3987	423	22	,	,	PUNCT
ejpam-3987	423	23	q	q	NOUN
ejpam-3987	423	24	=	=	SYM
ejpam-3987	423	25	1/2	1/2	NUM
ejpam-3987	423	26	,	,	PUNCT
ejpam-3987	423	27	n	n	NOUN
ejpam-3987	423	28	=	=	SYM
ejpam-3987	423	29	2	2	NUM
ejpam-3987	423	30	and	and	CCONJ
ejpam-3987	423	31	simplifying	simplify	VERB
ejpam-3987	423	32	to	to	PART
ejpam-3987	423	33	get	get	VERB
ejpam-3987	423	34	(	(	PUNCT
ejpam-3987	423	35	61	61	NUM
ejpam-3987	423	36	)	)	PUNCT
ejpam-3987	423	37	∫	∫	PROPN
ejpam-3987	424	1	∞	∞	PROPN
ejpam-3987	424	2	0	0	NUM
ejpam-3987	425	1	∫	∫	PROPN
ejpam-3987	425	2	∞	∞	NOUN
ejpam-3987	425	3	0	0	NUM
ejpam-3987	426	1	e−x	e−x	NUM
ejpam-3987	426	2	2−y2	2−y2	NUM
ejpam-3987	426	3	(	(	PUNCT
ejpam-3987	426	4	x−	x−	PROPN
ejpam-3987	426	5	y	y	PROPN
ejpam-3987	426	6	)	)	PUNCT
ejpam-3987	426	7	√	√	PROPN
ejpam-3987	426	8	x	x	SYM
ejpam-3987	426	9	√	√	PROPN
ejpam-3987	426	10	y	y	PROPN
ejpam-3987	426	11	log	log	NOUN
ejpam-3987	426	12	(	(	PUNCT
ejpam-3987	426	13	x	x	NOUN
ejpam-3987	426	14	y	y	PROPN
ejpam-3987	426	15	)	)	PUNCT
ejpam-3987	426	16	dxdy	dxdy	PROPN
ejpam-3987	426	17	=	=	SYM
ejpam-3987	426	18	log	log	PROPN
ejpam-3987	426	19	(	(	PUNCT
ejpam-3987	426	20	cot	cot	NOUN
ejpam-3987	426	21	(	(	PUNCT
ejpam-3987	426	22	π	π	NOUN
ejpam-3987	426	23	8	8	NUM
ejpam-3987	426	24	)	)	PUNCT
ejpam-3987	426	25	)	)	PUNCT
ejpam-3987	427	1	11.2	11.2	NUM
ejpam-3987	427	2	.	.	PUNCT
ejpam-3987	428	1	derivation	derivation	NOUN
ejpam-3987	428	2	of	of	ADP
ejpam-3987	428	3	entry	entry	NOUN
ejpam-3987	428	4	86	86	NUM
ejpam-3987	428	5	involving	involve	VERB
ejpam-3987	428	6	the	the	DET
ejpam-3987	428	7	logarithm	logarithm	NOUN
ejpam-3987	428	8	,	,	PUNCT
ejpam-3987	428	9	cotangent	cotangent	NOUN
ejpam-3987	428	10	and	and	CCONJ
ejpam-3987	428	11	tangent	tangent	NOUN
ejpam-3987	428	12	functions	function	NOUN
ejpam-3987	428	13	using	use	VERB
ejpam-3987	428	14	equation	equation	NOUN
ejpam-3987	428	15	(	(	PUNCT
ejpam-3987	428	16	60	60	NUM
ejpam-3987	428	17	)	)	PUNCT
ejpam-3987	428	18	setting	set	VERB
ejpam-3987	428	19	p	p	NOUN
ejpam-3987	428	20	=	=	NOUN
ejpam-3987	428	21	1	1	NUM
ejpam-3987	428	22	,	,	PUNCT
ejpam-3987	428	23	q	q	NOUN
ejpam-3987	428	24	=	=	SYM
ejpam-3987	428	25	1/3	1/3	NUM
ejpam-3987	428	26	,	,	PUNCT
ejpam-3987	428	27	n	n	NOUN
ejpam-3987	428	28	=	=	SYM
ejpam-3987	428	29	2	2	NUM
ejpam-3987	428	30	and	and	CCONJ
ejpam-3987	428	31	simplifying	simplify	VERB
ejpam-3987	428	32	to	to	PART
ejpam-3987	428	33	get	get	VERB
ejpam-3987	428	34	(	(	PUNCT
ejpam-3987	428	35	62	62	NUM
ejpam-3987	428	36	)	)	PUNCT
ejpam-3987	428	37	∫	∫	PROPN
ejpam-3987	429	1	∞	∞	PROPN
ejpam-3987	429	2	0	0	NUM
ejpam-3987	430	1	∫	∫	PROPN
ejpam-3987	430	2	∞	∞	NOUN
ejpam-3987	430	3	0	0	NUM
ejpam-3987	431	1	e−x	e−x	NUM
ejpam-3987	431	2	2−y2	2−y2	NUM
ejpam-3987	431	3	(	(	PUNCT
ejpam-3987	431	4	x2/3	x2/3	PROPN
ejpam-3987	431	5	−	−	NUM
ejpam-3987	431	6	y2/3	y2/3	PROPN
ejpam-3987	431	7	)	)	PUNCT
ejpam-3987	431	8	3	3	NUM
ejpam-3987	431	9	√	√	NUM
ejpam-3987	431	10	x	x	SYM
ejpam-3987	431	11	3	3	NUM
ejpam-3987	431	12	√	√	PROPN
ejpam-3987	431	13	y	y	PROPN
ejpam-3987	431	14	log	log	NOUN
ejpam-3987	431	15	(	(	PUNCT
ejpam-3987	431	16	x	x	NOUN
ejpam-3987	431	17	y	y	PROPN
ejpam-3987	431	18	)	)	PUNCT
ejpam-3987	431	19	dxdy	dxdy	PROPN
ejpam-3987	431	20	=	=	SYM
ejpam-3987	431	21	log(3	log(3	PROPN
ejpam-3987	431	22	)	)	PUNCT
ejpam-3987	431	23	2	2	NUM
ejpam-3987	431	24	11.3	11.3	NUM
ejpam-3987	431	25	.	.	PUNCT
ejpam-3987	432	1	derivation	derivation	NOUN
ejpam-3987	432	2	of	of	ADP
ejpam-3987	432	3	entry	entry	NOUN
ejpam-3987	432	4	87	87	NUM
ejpam-3987	432	5	involving	involve	VERB
ejpam-3987	432	6	the	the	DET
ejpam-3987	432	7	logarithm	logarithm	NOUN
ejpam-3987	432	8	,	,	PUNCT
ejpam-3987	432	9	cotangent	cotangent	NOUN
ejpam-3987	432	10	and	and	CCONJ
ejpam-3987	432	11	tangent	tangent	NOUN
ejpam-3987	432	12	functions	function	NOUN
ejpam-3987	432	13	using	use	VERB
ejpam-3987	432	14	equation	equation	NOUN
ejpam-3987	432	15	(	(	PUNCT
ejpam-3987	432	16	60	60	NUM
ejpam-3987	432	17	)	)	PUNCT
ejpam-3987	432	18	setting	set	VERB
ejpam-3987	432	19	p	p	NOUN
ejpam-3987	432	20	=	=	SYM
ejpam-3987	432	21	1/2	1/2	NUM
ejpam-3987	432	22	,	,	PUNCT
ejpam-3987	432	23	q	q	NOUN
ejpam-3987	432	24	=	=	SYM
ejpam-3987	432	25	1/6	1/6	NUM
ejpam-3987	432	26	,	,	PUNCT
ejpam-3987	432	27	n	n	NOUN
ejpam-3987	432	28	=	=	SYM
ejpam-3987	432	29	3	3	NUM
ejpam-3987	432	30	and	and	CCONJ
ejpam-3987	432	31	simplifying	simplify	VERB
ejpam-3987	432	32	to	to	PART
ejpam-3987	432	33	get	get	VERB
ejpam-3987	432	34	(	(	PUNCT
ejpam-3987	432	35	63	63	NUM
ejpam-3987	432	36	)	)	PUNCT
ejpam-3987	432	37	∫	∫	PROPN
ejpam-3987	433	1	∞	∞	PROPN
ejpam-3987	433	2	0	0	NUM
ejpam-3987	434	1	∫	∫	PROPN
ejpam-3987	434	2	∞	∞	PROPN
ejpam-3987	434	3	0	0	NUM
ejpam-3987	435	1	y4/3e−x	y4/3e−x	PROPN
ejpam-3987	435	2	3−y3	3−y3	NUM
ejpam-3987	435	3	(	(	PUNCT
ejpam-3987	435	4	3	3	NUM
ejpam-3987	435	5	√	√	NUM
ejpam-3987	435	6	x−	x−	PROPN
ejpam-3987	435	7	3	3	NUM
ejpam-3987	435	8	√	√	PROPN
ejpam-3987	435	9	y	y	PROPN
ejpam-3987	435	10	)	)	PUNCT
ejpam-3987	435	11	x2/3	x2/3	PROPN
ejpam-3987	436	1	log	log	NOUN
ejpam-3987	436	2	(	(	PUNCT
ejpam-3987	436	3	x	x	SYM
ejpam-3987	436	4	y	y	PROPN
ejpam-3987	436	5	)	)	PUNCT
ejpam-3987	436	6	dxdy	dxdy	PROPN
ejpam-3987	436	7	=	=	NOUN
ejpam-3987	436	8	1	1	NUM
ejpam-3987	436	9	3	3	NUM
ejpam-3987	436	10	log	log	NOUN
ejpam-3987	436	11	(	(	PUNCT
ejpam-3987	436	12	tan	tan	PROPN
ejpam-3987	436	13	(	(	PUNCT
ejpam-3987	436	14	π	π	PROPN
ejpam-3987	436	15	9	9	NUM
ejpam-3987	436	16	)	)	PUNCT
ejpam-3987	436	17	cot	cot	NOUN
ejpam-3987	436	18	(	(	PUNCT
ejpam-3987	436	19	π	π	PROPN
ejpam-3987	436	20	18	18	NUM
ejpam-3987	436	21	)	)	PUNCT
ejpam-3987	436	22	)	)	PUNCT
ejpam-3987	436	23	11.4	11.4	NUM
ejpam-3987	436	24	.	.	PUNCT
ejpam-3987	437	1	derivation	derivation	NOUN
ejpam-3987	437	2	of	of	ADP
ejpam-3987	437	3	entry	entry	NOUN
ejpam-3987	437	4	88	88	NUM
ejpam-3987	437	5	involving	involve	VERB
ejpam-3987	437	6	the	the	DET
ejpam-3987	437	7	hyperbolic	hyperbolic	ADJ
ejpam-3987	437	8	,	,	PUNCT
ejpam-3987	437	9	cotangent	cotangent	NOUN
ejpam-3987	437	10	and	and	CCONJ
ejpam-3987	437	11	tangent	tangent	NOUN
ejpam-3987	437	12	functions	function	NOUN
ejpam-3987	437	13	using	use	VERB
ejpam-3987	437	14	equation	equation	NOUN
ejpam-3987	437	15	(	(	PUNCT
ejpam-3987	437	16	52	52	NUM
ejpam-3987	437	17	)	)	PUNCT
ejpam-3987	437	18	setting	set	VERB
ejpam-3987	437	19	k	k	PROPN
ejpam-3987	437	20	=	=	PUNCT
ejpam-3987	437	21	−1	−1	NOUN
ejpam-3987	437	22	,	,	PUNCT
ejpam-3987	437	23	b	b	NOUN
ejpam-3987	437	24	=	=	SYM
ejpam-3987	437	25	1	1	NUM
ejpam-3987	437	26	,	,	PUNCT
ejpam-3987	437	27	replacing	replace	VERB
ejpam-3987	437	28	s	s	PRON
ejpam-3987	437	29	by	by	ADP
ejpam-3987	437	30	t	t	NOUN
ejpam-3987	437	31	and	and	CCONJ
ejpam-3987	437	32	simplifying	simplify	VERB
ejpam-3987	437	33	to	to	PART
ejpam-3987	437	34	get	get	VERB
ejpam-3987	437	35	r.	r.	PROPN
ejpam-3987	437	36	reynolds	reynolds	PROPN
ejpam-3987	437	37	,	,	PUNCT
ejpam-3987	437	38	a.	a.	PROPN
ejpam-3987	437	39	stauffer	stauffer	PROPN
ejpam-3987	437	40	/	/	SYM
ejpam-3987	437	41	eur	eur	PROPN
ejpam-3987	437	42	.	.	PUNCT
ejpam-3987	438	1	j.	j.	PROPN
ejpam-3987	438	2	pure	pure	PROPN
ejpam-3987	438	3	appl	appl	PROPN
ejpam-3987	438	4	.	.	PROPN
ejpam-3987	438	5	math	math	PROPN
ejpam-3987	438	6	,	,	PUNCT
ejpam-3987	438	7	14	14	NUM
ejpam-3987	438	8	(	(	PUNCT
ejpam-3987	438	9	3	3	NUM
ejpam-3987	438	10	)	)	PUNCT
ejpam-3987	438	11	(	(	PUNCT
ejpam-3987	438	12	2021	2021	NUM
ejpam-3987	438	13	)	)	PUNCT
ejpam-3987	438	14	,	,	PUNCT
ejpam-3987	438	15	618	618	NUM
ejpam-3987	438	16	-	-	SYM
ejpam-3987	438	17	637	637	NUM
ejpam-3987	438	18	635	635	NUM
ejpam-3987	438	19	(	(	PUNCT
ejpam-3987	438	20	64	64	NUM
ejpam-3987	438	21	)	)	PUNCT
ejpam-3987	438	22	∫	∫	PROPN
ejpam-3987	439	1	∞	∞	PROPN
ejpam-3987	439	2	0	0	NUM
ejpam-3987	440	1	∫	∫	PROPN
ejpam-3987	440	2	∞	∞	NOUN
ejpam-3987	440	3	0	0	NUM
ejpam-3987	441	1	xq−1yn−3q−1	xq−1yn−3q−1	PRON
ejpam-3987	441	2	(	(	PUNCT
ejpam-3987	441	3	y2q	y2q	X
ejpam-3987	441	4	−	−	PROPN
ejpam-3987	441	5	x2q	x2q	NUM
ejpam-3987	441	6	)	)	PUNCT
ejpam-3987	441	7	e−(tx)n−(ty)n	e−(tx)n−(ty)n	X
ejpam-3987	441	8	log	log	NOUN
ejpam-3987	441	9	(	(	PUNCT
ejpam-3987	441	10	x	x	SYM
ejpam-3987	441	11	y	y	PROPN
ejpam-3987	441	12	)	)	PUNCT
ejpam-3987	441	13	dxdy	dxdy	PROPN
ejpam-3987	441	14	=	=	PUNCT
ejpam-3987	441	15	−2t−n	−2t−n	PROPN
ejpam-3987	441	16	n	n	CCONJ
ejpam-3987	441	17	(	(	PUNCT
ejpam-3987	441	18	tanh−1	tanh−1	X
ejpam-3987	441	19	(	(	PUNCT
ejpam-3987	441	20	e	e	X
ejpam-3987	441	21	iπq	iπq	PROPN
ejpam-3987	441	22	n	n	ADV
ejpam-3987	441	23	)	)	PUNCT
ejpam-3987	441	24	−	−	PROPN
ejpam-3987	442	1	tanh−1	tanh−1	ADJ
ejpam-3987	442	2	(	(	PUNCT
ejpam-3987	442	3	e	e	X
ejpam-3987	442	4	3iπq	3iπq	PROPN
ejpam-3987	442	5	n	n	NUM
ejpam-3987	442	6	)	)	PUNCT
ejpam-3987	442	7	)	)	PUNCT
ejpam-3987	443	1	next	next	ADV
ejpam-3987	443	2	setting	set	VERB
ejpam-3987	443	3	t	t	PROPN
ejpam-3987	443	4	=	=	SYM
ejpam-3987	443	5	8	8	NUM
ejpam-3987	443	6	,	,	PUNCT
ejpam-3987	443	7	n	n	NOUN
ejpam-3987	443	8	=	=	SYM
ejpam-3987	443	9	3/2	3/2	NUM
ejpam-3987	443	10	,	,	PUNCT
ejpam-3987	443	11	q	q	NOUN
ejpam-3987	443	12	=	=	SYM
ejpam-3987	443	13	1/4	1/4	NUM
ejpam-3987	443	14	,	,	PUNCT
ejpam-3987	443	15	comparing	compare	VERB
ejpam-3987	443	16	real	real	ADJ
ejpam-3987	443	17	and	and	CCONJ
ejpam-3987	443	18	imaginary	imaginary	ADJ
ejpam-3987	443	19	parts	part	NOUN
ejpam-3987	443	20	simplifying	simplify	VERB
ejpam-3987	443	21	we	we	PRON
ejpam-3987	443	22	get	get	VERB
ejpam-3987	443	23	(	(	PUNCT
ejpam-3987	443	24	65	65	NUM
ejpam-3987	443	25	)	)	PUNCT
ejpam-3987	443	26	∫	∫	PROPN
ejpam-3987	444	1	∞	∞	PROPN
ejpam-3987	444	2	0	0	NUM
ejpam-3987	444	3	∫	∫	PROPN
ejpam-3987	444	4	∞	∞	PROPN
ejpam-3987	444	5	0	0	NUM
ejpam-3987	445	1	e−16	e−16	NOUN
ejpam-3987	445	2	√	√	NUM
ejpam-3987	445	3	2(x3/2+y3/2	2(x3/2+y3/2	NUM
ejpam-3987	445	4	)	)	PUNCT
ejpam-3987	445	5	(	(	PUNCT
ejpam-3987	445	6	√y	√y	ADP
ejpam-3987	445	7	−√x	−√x	NOUN
ejpam-3987	445	8	)	)	PUNCT
ejpam-3987	445	9	x3/4	x3/4	PROPN
ejpam-3987	445	10	4	4	NUM
ejpam-3987	445	11	√	√	PROPN
ejpam-3987	445	12	y	y	PROPN
ejpam-3987	445	13	log	log	NOUN
ejpam-3987	445	14	(	(	PUNCT
ejpam-3987	445	15	x	x	NOUN
ejpam-3987	445	16	y	y	PROPN
ejpam-3987	445	17	)	)	PUNCT
ejpam-3987	445	18	dxdy	dxdy	PROPN
ejpam-3987	446	1	=	=	PUNCT
ejpam-3987	447	1	i	i	PROPN
ejpam-3987	447	2	(	(	PUNCT
ejpam-3987	447	3	π	π	PROPN
ejpam-3987	447	4	−	−	PROPN
ejpam-3987	447	5	4	4	NUM
ejpam-3987	447	6	cot−1	cot−1	NOUN
ejpam-3987	447	7	(	(	PUNCT
ejpam-3987	447	8	1	1	NUM
ejpam-3987	447	9	2	2	NUM
ejpam-3987	447	10	+	+	CCONJ
ejpam-3987	447	11	i	i	PRON
ejpam-3987	447	12	√	√	VERB
ejpam-3987	447	13	3	3	NUM
ejpam-3987	447	14	2	2	NUM
ejpam-3987	447	15	)	)	PUNCT
ejpam-3987	447	16	)	)	PUNCT
ejpam-3987	447	17	48	48	NUM
ejpam-3987	447	18	√	√	NUM
ejpam-3987	447	19	2	2	NUM
ejpam-3987	447	20	=	=	SYM
ejpam-3987	447	21	−	−	NOUN
ejpam-3987	447	22	log	log	NOUN
ejpam-3987	447	23	(	(	PUNCT
ejpam-3987	447	24	2	2	NUM
ejpam-3987	447	25	+	+	CCONJ
ejpam-3987	447	26	√	√	NUM
ejpam-3987	447	27	3	3	NUM
ejpam-3987	447	28	)	)	PUNCT
ejpam-3987	447	29	24	24	NUM
ejpam-3987	447	30	√	√	NUM
ejpam-3987	447	31	2	2	NUM
ejpam-3987	447	32	r.	r.	PROPN
ejpam-3987	447	33	reynolds	reynolds	PROPN
ejpam-3987	447	34	,	,	PUNCT
ejpam-3987	447	35	a.	a.	PROPN
ejpam-3987	447	36	stauffer	stauffer	PROPN
ejpam-3987	447	37	/	/	SYM
ejpam-3987	447	38	eur	eur	PROPN
ejpam-3987	447	39	.	.	PUNCT
ejpam-3987	448	1	j.	j.	PROPN
ejpam-3987	448	2	pure	pure	PROPN
ejpam-3987	448	3	appl	appl	PROPN
ejpam-3987	448	4	.	.	PROPN
ejpam-3987	448	5	math	math	PROPN
ejpam-3987	448	6	,	,	PUNCT
ejpam-3987	448	7	14	14	NUM
ejpam-3987	448	8	(	(	PUNCT
ejpam-3987	448	9	3	3	NUM
ejpam-3987	448	10	)	)	PUNCT
ejpam-3987	448	11	(	(	PUNCT
ejpam-3987	448	12	2021	2021	NUM
ejpam-3987	448	13	)	)	PUNCT
ejpam-3987	448	14	,	,	PUNCT
ejpam-3987	448	15	618	618	NUM
ejpam-3987	448	16	-	-	SYM
ejpam-3987	448	17	637	637	NUM
ejpam-3987	448	18	636	636	NUM
ejpam-3987	448	19	12	12	NUM
ejpam-3987	448	20	.	.	PUNCT
ejpam-3987	449	1	table	table	NOUN
ejpam-3987	449	2	of	of	ADP
ejpam-3987	449	3	definite	definite	ADJ
ejpam-3987	449	4	integrals	integral	NOUN
ejpam-3987	449	5	in	in	ADP
ejpam-3987	449	6	this	this	DET
ejpam-3987	449	7	section	section	NOUN
ejpam-3987	449	8	we	we	PRON
ejpam-3987	449	9	create	create	VERB
ejpam-3987	449	10	a	a	DET
ejpam-3987	449	11	table	table	NOUN
ejpam-3987	449	12	to	to	PART
ejpam-3987	449	13	summarize	summarize	VERB
ejpam-3987	449	14	our	our	PRON
ejpam-3987	449	15	results	result	NOUN
ejpam-3987	449	16	in	in	ADP
ejpam-3987	449	17	sections	section	NOUN
ejpam-3987	449	18	(	(	PUNCT
ejpam-3987	449	19	6	6	NUM
ejpam-3987	449	20	)	)	PUNCT
ejpam-3987	449	21	,	,	PUNCT
ejpam-3987	449	22	(	(	PUNCT
ejpam-3987	449	23	7	7	X
ejpam-3987	449	24	)	)	PUNCT
ejpam-3987	449	25	and	and	CCONJ
ejpam-3987	449	26	(	(	PUNCT
ejpam-3987	449	27	8)	8)	NUM
ejpam-3987	449	28	.	.	PUNCT
ejpam-3987	450	1	a	a	DET
ejpam-3987	450	2	table	table	NOUN
ejpam-3987	450	3	of	of	ADP
ejpam-3987	450	4	integrals	integral	NOUN
ejpam-3987	450	5	is	be	AUX
ejpam-3987	450	6	a	a	DET
ejpam-3987	450	7	more	more	ADV
ejpam-3987	450	8	compact	compact	ADJ
ejpam-3987	450	9	way	way	NOUN
ejpam-3987	450	10	of	of	ADP
ejpam-3987	450	11	showcasing	showcase	VERB
ejpam-3987	450	12	our	our	PRON
ejpam-3987	450	13	results	result	NOUN
ejpam-3987	450	14	and	and	CCONJ
ejpam-3987	450	15	makes	make	VERB
ejpam-3987	450	16	the	the	DET
ejpam-3987	450	17	list	list	NOUN
ejpam-3987	450	18	of	of	ADP
ejpam-3987	450	19	integral	integral	ADJ
ejpam-3987	450	20	formulae	formulae	NOUN
ejpam-3987	450	21	easier	easy	ADJ
ejpam-3987	450	22	to	to	PART
ejpam-3987	450	23	digest	digest	VERB
ejpam-3987	450	24	from	from	ADP
ejpam-3987	450	25	the	the	DET
ejpam-3987	450	26	readers	reader	NOUN
ejpam-3987	450	27	’	’	PART
ejpam-3987	450	28	perspective	perspective	NOUN
ejpam-3987	450	29	.	.	PUNCT
ejpam-3987	451	1	table	table	NOUN
ejpam-3987	451	2	1	1	NUM
ejpam-3987	451	3	:	:	PUNCT
ejpam-3987	451	4	table	table	NOUN
ejpam-3987	451	5	of	of	ADP
ejpam-3987	451	6	definite	definite	ADJ
ejpam-3987	451	7	integrals	integral	NOUN
ejpam-3987	451	8	f(x	f(x	PROPN
ejpam-3987	451	9	,	,	PUNCT
ejpam-3987	451	10	y	y	NOUN
ejpam-3987	451	11	)	)	PUNCT
ejpam-3987	451	12	∫∞	∫∞	NOUN
ejpam-3987	451	13	0	0	NUM
ejpam-3987	451	14	∫∞	∫∞	NOUN
ejpam-3987	451	15	0	0	NUM
ejpam-3987	451	16	f(x	f(x	PROPN
ejpam-3987	451	17	,	,	PUNCT
ejpam-3987	451	18	y)dxdy	y)dxdy	X
ejpam-3987	452	1	xp−1yn−p−1e−x	xp−1yn−p−1e−x	PROPN
ejpam-3987	452	2	n−yn	n−yn	PROPN
ejpam-3987	452	3	π	π	PROPN
ejpam-3987	452	4	csc(πpn	csc(πpn	NOUN
ejpam-3987	452	5	)	)	PUNCT
ejpam-3987	452	6	n2	n2	PROPN
ejpam-3987	452	7	xp−1yn−p−1e−x	xp−1yn−p−1e−x	PROPN
ejpam-3987	452	8	n−yn	n−yn	PROPN
ejpam-3987	452	9	log	log	NOUN
ejpam-3987	452	10	(	(	PUNCT
ejpam-3987	452	11	x	x	SYM
ejpam-3987	452	12	y	y	PROPN
ejpam-3987	452	13	)	)	PUNCT
ejpam-3987	452	14	−π2	−π2	PROPN
ejpam-3987	452	15	cot(πpn	cot(πpn	X
ejpam-3987	452	16	)	)	PUNCT
ejpam-3987	452	17	csc(πpn	csc(πpn	PROPN
ejpam-3987	452	18	)	)	PUNCT
ejpam-3987	453	1	n3	n3	PROPN
ejpam-3987	453	2	xp−1yn−p−1e−x	xp−1yn−p−1e−x	PROPN
ejpam-3987	453	3	n−yn	n−yn	PROPN
ejpam-3987	453	4	log2	log2	PROPN
ejpam-3987	453	5	(	(	PUNCT
ejpam-3987	453	6	x	x	SYM
ejpam-3987	453	7	y	y	PROPN
ejpam-3987	453	8	)	)	PUNCT
ejpam-3987	453	9	π3(cos	π3(cos	PROPN
ejpam-3987	453	10	(	(	PUNCT
ejpam-3987	453	11	2πp	2πp	NOUN
ejpam-3987	453	12	n	n	CCONJ
ejpam-3987	453	13	)	)	PUNCT
ejpam-3987	453	14	+3	+3	PROPN
ejpam-3987	453	15	)	)	PUNCT
ejpam-3987	453	16	csc3(πpn	csc3(πpn	VERB
ejpam-3987	453	17	)	)	PUNCT
ejpam-3987	453	18	2n4	2n4	NUM
ejpam-3987	453	19	e−x	e−x	NOUN
ejpam-3987	453	20	2−y2	2−y2	NUM
ejpam-3987	453	21	logk	logk	NOUN
ejpam-3987	453	22	(	(	PUNCT
ejpam-3987	453	23	x	x	NOUN
ejpam-3987	453	24	y	y	PROPN
ejpam-3987	453	25	)	)	PUNCT
ejpam-3987	453	26	2k−1e	2k−1e	NOUN
ejpam-3987	454	1	iπk	iπk	NOUN
ejpam-3987	454	2	2	2	NUM
ejpam-3987	454	3	πk+1	πk+1	NOUN
ejpam-3987	454	4	(	(	PUNCT
ejpam-3987	454	5	ζ	ζ	NOUN
ejpam-3987	454	6	(	(	PUNCT
ejpam-3987	454	7	−k	−k	PROPN
ejpam-3987	454	8	,	,	PUNCT
ejpam-3987	454	9	1	1	NUM
ejpam-3987	454	10	4	4	NUM
ejpam-3987	454	11	)	)	PUNCT
ejpam-3987	454	12	−	−	NOUN
ejpam-3987	454	13	ζ	ζ	NOUN
ejpam-3987	454	14	(	(	PUNCT
ejpam-3987	454	15	−k	−k	PROPN
ejpam-3987	454	16	,	,	PUNCT
ejpam-3987	454	17	3	3	NUM
ejpam-3987	454	18	4	4	NUM
ejpam-3987	454	19	)	)	PUNCT
ejpam-3987	454	20	)	)	PUNCT
ejpam-3987	454	21	πxp−1y1−pe−x	πxp−1y1−pe−x	PROPN
ejpam-3987	454	22	2−y2	2−y2	NUM
ejpam-3987	454	23	log2	log2	NOUN
ejpam-3987	454	24	(	(	PUNCT
ejpam-3987	454	25	x	x	NOUN
ejpam-3987	454	26	y	y	PROPN
ejpam-3987	454	27	)	)	PUNCT
ejpam-3987	455	1	+	+	VERB
ejpam-3987	455	2	π2	π2	ADJ
ejpam-3987	455	3	1	1	NUM
ejpam-3987	455	4	4	4	NUM
ejpam-3987	455	5	(	(	PUNCT
ejpam-3987	455	6	4	4	NUM
ejpam-3987	455	7	sin	sin	NOUN
ejpam-3987	455	8	(	(	PUNCT
ejpam-3987	455	9	πp	πp	ADP
ejpam-3987	455	10	2	2	NUM
ejpam-3987	455	11	)	)	PUNCT
ejpam-3987	456	1	+	+	CCONJ
ejpam-3987	456	2	π	π	PROPN
ejpam-3987	456	3	cos(πp)−	cos(πp)−	ADJ
ejpam-3987	456	4	2	2	NUM
ejpam-3987	456	5	sin(πp	sin(πp	NOUN
ejpam-3987	456	6	)	)	PUNCT
ejpam-3987	456	7	log	log	NOUN
ejpam-3987	456	8	(	(	PUNCT
ejpam-3987	456	9	cot	cot	NOUN
ejpam-3987	456	10	(	(	PUNCT
ejpam-3987	456	11	πp	πp	ADP
ejpam-3987	456	12	4	4	NUM
ejpam-3987	456	13	)	)	PUNCT
ejpam-3987	456	14	)	)	PUNCT
ejpam-3987	456	15	)	)	PUNCT
ejpam-3987	457	1	xp−1y1−pe−x	xp−1y1−pe−x	PUNCT
ejpam-3987	458	1	2−y2	2−y2	NUM
ejpam-3987	458	2	log	log	NOUN
ejpam-3987	458	3	(	(	PUNCT
ejpam-3987	458	4	x	x	NOUN
ejpam-3987	458	5	y	y	PROPN
ejpam-3987	458	6	)	)	PUNCT
ejpam-3987	458	7	log2	log2	PROPN
ejpam-3987	458	8	(	(	PUNCT
ejpam-3987	458	9	x	x	NOUN
ejpam-3987	458	10	y	y	PROPN
ejpam-3987	458	11	)	)	PUNCT
ejpam-3987	459	1	+	+	ADP
ejpam-3987	459	2	π2	π2	ADJ
ejpam-3987	459	3	−1	−1	NOUN
ejpam-3987	459	4	4π	4π	NUM
ejpam-3987	459	5	sin(πp	sin(πp	ADJ
ejpam-3987	459	6	)	)	PUNCT
ejpam-3987	460	1	+	+	CCONJ
ejpam-3987	460	2	cos	cos	X
ejpam-3987	460	3	(	(	PUNCT
ejpam-3987	460	4	πp	πp	ADP
ejpam-3987	460	5	2	2	NUM
ejpam-3987	460	6	)	)	PUNCT
ejpam-3987	460	7	−	−	NOUN
ejpam-3987	460	8	1	1	NUM
ejpam-3987	460	9	2	2	NUM
ejpam-3987	460	10	cos(πp	cos(πp	PROPN
ejpam-3987	460	11	)	)	PUNCT
ejpam-3987	460	12	log	log	NOUN
ejpam-3987	460	13	(	(	PUNCT
ejpam-3987	460	14	cot	cot	NOUN
ejpam-3987	460	15	(	(	PUNCT
ejpam-3987	460	16	πp	πp	ADP
ejpam-3987	460	17	4	4	NUM
ejpam-3987	460	18	)	)	PUNCT
ejpam-3987	460	19	)	)	PUNCT
ejpam-3987	461	1	xp−1yn−p−1e−x	xp−1yn−p−1e−x	PROPN
ejpam-3987	461	2	n−yn	n−yn	PROPN
ejpam-3987	461	3	logk	logk	NOUN
ejpam-3987	461	4	(	(	PUNCT
ejpam-3987	461	5	e	e	X
ejpam-3987	461	6	iπ	iπ	NOUN
ejpam-3987	461	7	n	n	NOUN
ejpam-3987	461	8	x	x	SYM
ejpam-3987	461	9	y	y	PROPN
ejpam-3987	461	10	)	)	PUNCT
ejpam-3987	461	11	(	(	PUNCT
ejpam-3987	461	12	2π)k+1	2π)k+1	NUM
ejpam-3987	461	13	(	(	PUNCT
ejpam-3987	461	14	in	in	ADP
ejpam-3987	461	15	)	)	PUNCT
ejpam-3987	461	16	k−1	k−1	PROPN
ejpam-3987	461	17	e−	e−	X
ejpam-3987	461	18	iπp	iπp	NOUN
ejpam-3987	462	1	n	n	ADP
ejpam-3987	462	2	li−k	li−k	VERB
ejpam-3987	462	3	(	(	PUNCT
ejpam-3987	462	4	e	e	X
ejpam-3987	462	5	2ipπ	2ipπ	NUM
ejpam-3987	462	6	n	n	NOUN
ejpam-3987	462	7	)	)	PUNCT
ejpam-3987	462	8	n3	n3	NOUN
ejpam-3987	462	9	x	x	SYM
ejpam-3987	462	10	n	n	CCONJ
ejpam-3987	462	11	2	2	NUM
ejpam-3987	462	12	−1y	−1y	NOUN
ejpam-3987	462	13	n	n	DET
ejpam-3987	462	14	2	2	NUM
ejpam-3987	462	15	−1e−x	−1e−x	NOUN
ejpam-3987	462	16	n−yn	n−yn	NOUN
ejpam-3987	462	17	log	log	NOUN
ejpam-3987	462	18	(	(	PUNCT
ejpam-3987	462	19	x	x	NOUN
ejpam-3987	462	20	y	y	PROPN
ejpam-3987	462	21	)	)	PUNCT
ejpam-3987	462	22	log	log	NOUN
ejpam-3987	462	23	(	(	PUNCT
ejpam-3987	462	24	log	log	NOUN
ejpam-3987	462	25	(	(	PUNCT
ejpam-3987	462	26	x	x	NOUN
ejpam-3987	462	27	y	y	PROPN
ejpam-3987	462	28	)	)	PUNCT
ejpam-3987	462	29	)	)	PUNCT
ejpam-3987	463	1	−4iπc	−4iπc	PROPN
ejpam-3987	463	2	n3	n3	PROPN
ejpam-3987	463	3	xp−1yn−p−1e−x	xp−1yn−p−1e−x	PROPN
ejpam-3987	463	4	n−yn	n−yn	PROPN
ejpam-3987	463	5	log3	log3	PROPN
ejpam-3987	463	6	(	(	PUNCT
ejpam-3987	463	7	x	x	NOUN
ejpam-3987	463	8	y	y	PROPN
ejpam-3987	463	9	)	)	PUNCT
ejpam-3987	463	10	−π4(23	−π4(23	VERB
ejpam-3987	463	11	cos(πpn	cos(πpn	PROPN
ejpam-3987	463	12	)	)	PUNCT
ejpam-3987	464	1	+	+	X
ejpam-3987	464	2	cos	cos	PROPN
ejpam-3987	464	3	(	(	PUNCT
ejpam-3987	464	4	3πp	3πp	ADJ
ejpam-3987	464	5	n	n	PRON
ejpam-3987	464	6	)	)	PUNCT
ejpam-3987	464	7	)	)	PUNCT
ejpam-3987	464	8	csc4(πpn	csc4(πpn	NOUN
ejpam-3987	464	9	)	)	PUNCT
ejpam-3987	464	10	4n5	4n5	NUM
ejpam-3987	464	11	x	x	SYM
ejpam-3987	464	12	n	n	SYM
ejpam-3987	464	13	2	2	NUM
ejpam-3987	464	14	−1y	−1y	NOUN
ejpam-3987	464	15	n	n	PRON
ejpam-3987	464	16	2	2	NUM
ejpam-3987	464	17	−1e−x	−1e−x	NOUN
ejpam-3987	464	18	n−yn	n−yn	NOUN
ejpam-3987	464	19	log	log	NOUN
ejpam-3987	464	20	(	(	PUNCT
ejpam-3987	464	21	log	log	NOUN
ejpam-3987	464	22	(	(	PUNCT
ejpam-3987	464	23	ax	ax	NOUN
ejpam-3987	464	24	y	y	PROPN
ejpam-3987	464	25	)	)	PUNCT
ejpam-3987	464	26	)	)	PUNCT
ejpam-3987	465	1	2π	2π	NOUN
ejpam-3987	465	2	log	log	VERB
ejpam-3987	465	3			PROPN
ejpam-3987	465	4	2	2	NUM
ejpam-3987	465	5	√	√	PROPN
ejpam-3987	465	6	π	π	NOUN
ejpam-3987	465	7	√	√	VERB
ejpam-3987	466	1	i	i	PRON
ejpam-3987	466	2	nγ	nγ	NOUN
ejpam-3987	466	3	(	(	PUNCT
ejpam-3987	466	4	3	3	NUM
ejpam-3987	466	5	4−	4−	PROPN
ejpam-3987	466	6	in	in	ADP
ejpam-3987	466	7	log(a	log(a	PROPN
ejpam-3987	466	8	)	)	PUNCT
ejpam-3987	466	9	4π	4π	NUM
ejpam-3987	466	10	)	)	PUNCT
ejpam-3987	466	11	γ	γ	PROPN
ejpam-3987	466	12	(	(	PUNCT
ejpam-3987	466	13	π−in	π−in	PROPN
ejpam-3987	466	14	log(a	log(a	PROPN
ejpam-3987	466	15	)	)	PUNCT
ejpam-3987	466	16	4π	4π	NUM
ejpam-3987	466	17	)	)	PUNCT
ejpam-3987	467	1			PROPN
ejpam-3987	467	2	n2	n2	NOUN
ejpam-3987	467	3	x	x	PUNCT
ejpam-3987	467	4	n	n	CCONJ
ejpam-3987	467	5	2	2	NUM
ejpam-3987	467	6	−1y	−1y	NOUN
ejpam-3987	467	7	n	n	DET
ejpam-3987	467	8	2	2	NUM
ejpam-3987	467	9	−1e−x	−1e−x	NOUN
ejpam-3987	467	10	n−yn	n−yn	NOUN
ejpam-3987	467	11	log	log	NOUN
ejpam-3987	467	12	(	(	PUNCT
ejpam-3987	467	13	x	x	NOUN
ejpam-3987	467	14	y	y	PROPN
ejpam-3987	467	15	)	)	PUNCT
ejpam-3987	467	16	0	0	NUM
ejpam-3987	468	1	e−x−y	e−x−y	NOUN
ejpam-3987	468	2	log	log	NOUN
ejpam-3987	468	3	(	(	PUNCT
ejpam-3987	468	4	log	log	NOUN
ejpam-3987	468	5	(	(	PUNCT
ejpam-3987	468	6	−x	−x	NOUN
ejpam-3987	468	7	y	y	PROPN
ejpam-3987	468	8	)	)	PUNCT
ejpam-3987	468	9	)	)	PUNCT
ejpam-3987	469	1	√	√	NUM
ejpam-3987	469	2	x	x	SYM
ejpam-3987	469	3	√	√	PROPN
ejpam-3987	469	4	y	y	PROPN
ejpam-3987	469	5	log	log	NOUN
ejpam-3987	469	6	(	(	PUNCT
ejpam-3987	469	7	−x	−x	NOUN
ejpam-3987	469	8	y	y	PROPN
ejpam-3987	469	9	)	)	PUNCT
ejpam-3987	469	10	1	1	NUM
ejpam-3987	469	11	2	2	NUM
ejpam-3987	469	12	log(2	log(2	NOUN
ejpam-3987	469	13	)	)	PUNCT
ejpam-3987	469	14	(	(	PUNCT
ejpam-3987	469	15	2iγ	2iγ	ADJ
ejpam-3987	470	1	+	+	CCONJ
ejpam-3987	470	2	π	π	PROPN
ejpam-3987	470	3	−	−	NOUN
ejpam-3987	471	1	i	i	PRON
ejpam-3987	471	2	log	log	VERB
ejpam-3987	471	3	(	(	PUNCT
ejpam-3987	471	4	8π2	8π2	NUM
ejpam-3987	471	5	)	)	PUNCT
ejpam-3987	471	6	)	)	PUNCT
ejpam-3987	472	1	e−x	e−x	PROPN
ejpam-3987	472	2	2−y2	2−y2	NUM
ejpam-3987	472	3	log2	log2	NOUN
ejpam-3987	472	4	(	(	PUNCT
ejpam-3987	472	5	x	x	SYM
ejpam-3987	472	6	y	y	PROPN
ejpam-3987	472	7	)	)	PUNCT
ejpam-3987	472	8	log	log	NOUN
ejpam-3987	472	9	(	(	PUNCT
ejpam-3987	472	10	log	log	NOUN
ejpam-3987	472	11	(	(	PUNCT
ejpam-3987	472	12	x	x	NOUN
ejpam-3987	472	13	y	y	PROPN
ejpam-3987	472	14	)	)	PUNCT
ejpam-3987	472	15	)	)	PUNCT
ejpam-3987	473	1	1	1	NUM
ejpam-3987	473	2	32π	32π	NUM
ejpam-3987	473	3	3	3	NUM
ejpam-3987	473	4	(	(	PUNCT
ejpam-3987	473	5	64	64	NUM
ejpam-3987	473	6	(	(	PUNCT
ejpam-3987	473	7	ζ	ζ	NOUN
ejpam-3987	473	8	′	′	NUM
ejpam-3987	473	9	(	(	PUNCT
ejpam-3987	473	10	−2	−2	NOUN
ejpam-3987	473	11	,	,	PUNCT
ejpam-3987	473	12	1	1	NUM
ejpam-3987	473	13	4	4	NUM
ejpam-3987	473	14	)	)	PUNCT
ejpam-3987	473	15	−	−	NOUN
ejpam-3987	473	16	ζ	ζ	NOUN
ejpam-3987	473	17	′	′	NOUN
ejpam-3987	473	18	(	(	PUNCT
ejpam-3987	473	19	−2	−2	NOUN
ejpam-3987	473	20	,	,	PUNCT
ejpam-3987	473	21	3	3	NUM
ejpam-3987	473	22	4	4	NUM
ejpam-3987	473	23	)	)	PUNCT
ejpam-3987	473	24	)	)	PUNCT
ejpam-3987	474	1	+	+	CCONJ
ejpam-3987	474	2	iπ	iπ	PRON
ejpam-3987	474	3	+	+	NUM
ejpam-3987	474	4	log	log	NOUN
ejpam-3987	474	5	(	(	PUNCT
ejpam-3987	474	6	4π2	4π2	NUM
ejpam-3987	474	7	)	)	PUNCT
ejpam-3987	474	8	)	)	PUNCT
ejpam-3987	475	1	e−x−y	e−x−y	NOUN
ejpam-3987	475	2	logk	logk	NOUN
ejpam-3987	475	3	(	(	PUNCT
ejpam-3987	475	4	−x	−x	NOUN
ejpam-3987	475	5	y	y	PROPN
ejpam-3987	475	6	)	)	PUNCT
ejpam-3987	476	1	√	√	PROPN
ejpam-3987	476	2	x	x	SYM
ejpam-3987	476	3	√	√	PUNCT
ejpam-3987	476	4	y	y	NOUN
ejpam-3987	476	5	−ik	−ik	NOUN
ejpam-3987	476	6	(	(	PUNCT
ejpam-3987	476	7	2k+1	2k+1	NOUN
ejpam-3987	476	8	−	−	NOUN
ejpam-3987	476	9	1	1	NUM
ejpam-3987	476	10	)	)	PUNCT
ejpam-3987	476	11	(	(	PUNCT
ejpam-3987	476	12	2π)k+1ζ(−k	2π)k+1ζ(−k	NOUN
ejpam-3987	476	13	)	)	PUNCT
ejpam-3987	476	14	e−x−y	e−x−y	NOUN
ejpam-3987	476	15	√	√	NUM
ejpam-3987	476	16	x	x	SYM
ejpam-3987	477	1	√	√	VERB
ejpam-3987	477	2	y	y	PROPN
ejpam-3987	477	3	(	(	PUNCT
ejpam-3987	477	4	log2	log2	PROPN
ejpam-3987	477	5	(	(	PUNCT
ejpam-3987	477	6	x	x	NOUN
ejpam-3987	477	7	y	y	PROPN
ejpam-3987	477	8	)	)	PUNCT
ejpam-3987	478	1	+	+	ADP
ejpam-3987	478	2	π2	π2	ADJ
ejpam-3987	478	3	)	)	PUNCT
ejpam-3987	478	4	log(2	log(2	NOUN
ejpam-3987	478	5	)	)	PUNCT
ejpam-3987	479	1	π	π	PROPN
ejpam-3987	479	2	e−x−y(x2/3−y2/3	e−x−y(x2/3−y2/3	PROPN
ejpam-3987	479	3	)	)	PUNCT
ejpam-3987	479	4	x5/6y5/6	x5/6y5/6	PROPN
ejpam-3987	479	5	log	log	NOUN
ejpam-3987	479	6	(	(	PUNCT
ejpam-3987	479	7	x	x	SYM
ejpam-3987	479	8	y	y	PROPN
ejpam-3987	479	9	)	)	PUNCT
ejpam-3987	479	10	log	log	NOUN
ejpam-3987	479	11	(	(	PUNCT
ejpam-3987	479	12	7	7	NUM
ejpam-3987	479	13	+	+	CCONJ
ejpam-3987	479	14	4	4	NUM
ejpam-3987	479	15	√	√	NUM
ejpam-3987	479	16	3	3	NUM
ejpam-3987	479	17	)	)	PUNCT
ejpam-3987	479	18	6	6	NUM
ejpam-3987	479	19	√	√	NUM
ejpam-3987	479	20	ye−x2−y2	ye−x2−y2	NOUN
ejpam-3987	479	21	(	(	PUNCT
ejpam-3987	479	22	x2/3−y2/3	x2/3−y2/3	NUM
ejpam-3987	479	23	)	)	PUNCT
ejpam-3987	479	24	x5/6	x5/6	PROPN
ejpam-3987	480	1	log	log	NOUN
ejpam-3987	480	2	(	(	PUNCT
ejpam-3987	480	3	x	x	NOUN
ejpam-3987	480	4	y	y	PROPN
ejpam-3987	480	5	)	)	PUNCT
ejpam-3987	480	6	coth−1	coth−1	NOUN
ejpam-3987	480	7	(	(	PUNCT
ejpam-3987	480	8	√	√	NUM
ejpam-3987	480	9	2	2	NUM
ejpam-3987	480	10	)	)	PUNCT
ejpam-3987	480	11	references	reference	VERB
ejpam-3987	480	12	637	637	NUM
ejpam-3987	480	13	13	13	NUM
ejpam-3987	480	14	.	.	PUNCT
ejpam-3987	481	1	conclusion	conclusion	NOUN
ejpam-3987	481	2	in	in	ADP
ejpam-3987	481	3	this	this	DET
ejpam-3987	481	4	work	work	NOUN
ejpam-3987	481	5	the	the	DET
ejpam-3987	481	6	authors	author	NOUN
ejpam-3987	481	7	used	use	VERB
ejpam-3987	481	8	their	their	PRON
ejpam-3987	481	9	contour	contour	NOUN
ejpam-3987	481	10	integral	integral	ADJ
ejpam-3987	481	11	method	method	NOUN
ejpam-3987	481	12	to	to	PART
ejpam-3987	481	13	derive	derive	VERB
ejpam-3987	481	14	a	a	DET
ejpam-3987	481	15	double	double	ADJ
ejpam-3987	481	16	integral	integral	ADJ
ejpam-3987	481	17	in	in	ADP
ejpam-3987	481	18	terms	term	NOUN
ejpam-3987	481	19	of	of	ADP
ejpam-3987	481	20	the	the	DET
ejpam-3987	481	21	lerch	lerch	PROPN
ejpam-3987	481	22	function	function	PROPN
ejpam-3987	481	23	.	.	PUNCT
ejpam-3987	482	1	by	by	ADP
ejpam-3987	482	2	deriving	derive	VERB
ejpam-3987	482	3	such	such	DET
ejpam-3987	482	4	an	an	DET
ejpam-3987	482	5	integral	integral	ADJ
ejpam-3987	482	6	transform	transform	NOUN
ejpam-3987	482	7	the	the	DET
ejpam-3987	482	8	authors	author	NOUN
ejpam-3987	482	9	produced	produce	VERB
ejpam-3987	482	10	new	new	ADJ
ejpam-3987	482	11	closed	closed	ADJ
ejpam-3987	482	12	form	form	NOUN
ejpam-3987	482	13	solutions	solution	NOUN
ejpam-3987	482	14	for	for	ADP
ejpam-3987	482	15	double	double	ADJ
ejpam-3987	482	16	integral	integral	ADJ
ejpam-3987	482	17	formula	formula	NOUN
ejpam-3987	482	18	not	not	PART
ejpam-3987	482	19	present	present	ADJ
ejpam-3987	482	20	in	in	ADP
ejpam-3987	482	21	current	current	ADJ
ejpam-3987	482	22	literature	literature	NOUN
ejpam-3987	482	23	.	.	PUNCT
ejpam-3987	483	1	this	this	DET
ejpam-3987	483	2	formulae	formulae	NOUN
ejpam-3987	483	3	derived	derive	VERB
ejpam-3987	483	4	in	in	ADP
ejpam-3987	483	5	this	this	DET
ejpam-3987	483	6	work	work	NOUN
ejpam-3987	483	7	showcases	showcase	VERB
ejpam-3987	483	8	a	a	DET
ejpam-3987	483	9	new	new	ADJ
ejpam-3987	483	10	mathematical	mathematical	ADJ
ejpam-3987	483	11	method	method	NOUN
ejpam-3987	483	12	which	which	PRON
ejpam-3987	483	13	could	could	AUX
ejpam-3987	483	14	be	be	AUX
ejpam-3987	483	15	used	use	VERB
ejpam-3987	483	16	derive	derive	ADJ
ejpam-3987	483	17	other	other	ADJ
ejpam-3987	483	18	integral	integral	ADJ
ejpam-3987	483	19	formulae	formulae	NOUN
ejpam-3987	483	20	.	.	PUNCT
ejpam-3987	484	1	the	the	DET
ejpam-3987	484	2	authors	author	NOUN
ejpam-3987	484	3	will	will	AUX
ejpam-3987	484	4	be	be	AUX
ejpam-3987	484	5	using	use	VERB
ejpam-3987	484	6	this	this	DET
ejpam-3987	484	7	method	method	NOUN
ejpam-3987	484	8	for	for	ADP
ejpam-3987	484	9	future	future	ADJ
ejpam-3987	484	10	work	work	NOUN
ejpam-3987	484	11	to	to	PART
ejpam-3987	484	12	produce	produce	VERB
ejpam-3987	484	13	more	more	ADJ
ejpam-3987	484	14	tables	table	NOUN
ejpam-3987	484	15	of	of	ADP
ejpam-3987	484	16	definite	definite	ADJ
ejpam-3987	484	17	integrals	integral	NOUN
ejpam-3987	484	18	.	.	PUNCT
ejpam-3987	485	1	references	reference	NOUN
ejpam-3987	485	2	[	[	X
ejpam-3987	485	3	1	1	NUM
ejpam-3987	485	4	]	]	PUNCT
ejpam-3987	485	5	mark	mark	PROPN
ejpam-3987	485	6	w	w	PROPN
ejpam-3987	485	7	coffey	coffey	PROPN
ejpam-3987	485	8	.	.	PUNCT
ejpam-3987	486	1	new	new	ADJ
ejpam-3987	486	2	summation	summation	NOUN
ejpam-3987	486	3	relations	relation	NOUN
ejpam-3987	486	4	for	for	ADP
ejpam-3987	486	5	the	the	DET
ejpam-3987	486	6	stieltjes	stieltjes	PROPN
ejpam-3987	486	7	constants	constant	NOUN
ejpam-3987	486	8	.	.	PUNCT
ejpam-3987	487	1	proceedings	proceeding	NOUN
ejpam-3987	487	2	of	of	ADP
ejpam-3987	487	3	the	the	DET
ejpam-3987	487	4	royal	royal	ADJ
ejpam-3987	487	5	society	society	NOUN
ejpam-3987	487	6	a	a	DET
ejpam-3987	487	7	:	:	PUNCT
ejpam-3987	487	8	mathematical	mathematical	ADJ
ejpam-3987	487	9	,	,	PUNCT
ejpam-3987	487	10	physical	physical	ADJ
ejpam-3987	487	11	and	and	CCONJ
ejpam-3987	487	12	engineering	engineering	NOUN
ejpam-3987	487	13	sciences	science	NOUN
ejpam-3987	487	14	,	,	PUNCT
ejpam-3987	487	15	462:2563–2573	462:2563–2573	NOUN
ejpam-3987	487	16	,	,	PUNCT
ejpam-3987	487	17	03	03	NUM
ejpam-3987	487	18	2006	2006	NUM
ejpam-3987	487	19	.	.	PUNCT
ejpam-3987	488	1	[	[	X
ejpam-3987	488	2	2	2	NUM
ejpam-3987	488	3	]	]	PUNCT
ejpam-3987	488	4	a.	a.	NOUN
ejpam-3987	488	5	;	;	PUNCT
ejpam-3987	488	6	magnus	magnus	PROPN
ejpam-3987	488	7	f.	f.	PROPN
ejpam-3987	488	8	g.	g.	PROPN
ejpam-3987	488	9	;	;	PUNCT
ejpam-3987	488	10	harry	harry	PROPN
ejpam-3987	488	11	bateman	bateman	PROPN
ejpam-3987	488	12	erdelyi	erdelyi	PROPN
ejpam-3987	488	13	.	.	PUNCT
ejpam-3987	489	1	higher	high	ADJ
ejpam-3987	489	2	transcendental	transcendental	ADJ
ejpam-3987	489	3	functions	function	NOUN
ejpam-3987	489	4	volume	volume	PROPN
ejpam-3987	489	5	i.	i.	PROPN
ejpam-3987	489	6	mcgraw	mcgraw	PROPN
ejpam-3987	489	7	-	-	PUNCT
ejpam-3987	489	8	hill	hill	NOUN
ejpam-3987	489	9	book	book	NOUN
ejpam-3987	489	10	company	company	NOUN
ejpam-3987	489	11	;	;	PUNCT
ejpam-3987	489	12	1st	1st	ADJ
ejpam-3987	489	13	edition	edition	NOUN
ejpam-3987	489	14	,	,	PUNCT
ejpam-3987	489	15	11	11	NUM
ejpam-3987	489	16	1953	1953	NUM
ejpam-3987	489	17	.	.	PUNCT
ejpam-3987	490	1	[	[	X
ejpam-3987	490	2	3	3	X
ejpam-3987	490	3	]	]	X
ejpam-3987	490	4	wolfgang	wolfgang	PROPN
ejpam-3987	490	5	gröbner	gröbner	PROPN
ejpam-3987	490	6	and	and	CCONJ
ejpam-3987	490	7	nikolaus	nikolaus	PROPN
ejpam-3987	490	8	hofreiter	hofreiter	PROPN
ejpam-3987	490	9	.	.	PUNCT
ejpam-3987	491	1	integraltafel	integraltafel	NOUN
ejpam-3987	491	2	:	:	PUNCT
ejpam-3987	491	3	teil	teil	PROPN
ejpam-3987	491	4	2	2	NUM
ejpam-3987	491	5	:	:	PUNCT
ejpam-3987	491	6	bestimmte	bestimmte	PROPN
ejpam-3987	491	7	integrale	integrale	NOUN
ejpam-3987	491	8	.	.	PUNCT
ejpam-3987	492	1	springer	springer	NOUN
ejpam-3987	492	2	-	-	PUNCT
ejpam-3987	492	3	verlag	verlag	PROPN
ejpam-3987	492	4	,	,	PUNCT
ejpam-3987	492	5	12	12	NUM
ejpam-3987	492	6	2013	2013	NUM
ejpam-3987	492	7	.	.	PUNCT
ejpam-3987	493	1	[	[	X
ejpam-3987	493	2	4	4	X
ejpam-3987	493	3	]	]	X
ejpam-3987	493	4	david	david	PROPN
ejpam-3987	493	5	bierens	bierens	PROPN
ejpam-3987	493	6	de	de	PROPN
ejpam-3987	493	7	haan	haan	PROPN
ejpam-3987	493	8	.	.	PUNCT
ejpam-3987	494	1	nouvelles	nouvelles	PROPN
ejpam-3987	494	2	tables	table	NOUN
ejpam-3987	494	3	d’intégrales	d’intégrales	PROPN
ejpam-3987	494	4	définies	définies	PROPN
ejpam-3987	494	5	.	.	PUNCT
ejpam-3987	495	1	p.	p.	NOUN
ejpam-3987	495	2	engels	engels	PROPN
ejpam-3987	495	3	,	,	PUNCT
ejpam-3987	495	4	1867	1867	NUM
ejpam-3987	495	5	.	.	PUNCT
ejpam-3987	496	1	[	[	X
ejpam-3987	496	2	5	5	NUM
ejpam-3987	496	3	]	]	PUNCT
ejpam-3987	496	4	m.	m.	NOUN
ejpam-3987	496	5	lerch	lerch	PROPN
ejpam-3987	496	6	.	.	PUNCT
ejpam-3987	497	1	note	note	VERB
ejpam-3987	497	2	sur	sur	PROPN
ejpam-3987	497	3	la	la	PRON
ejpam-3987	497	4	fonction	fonction	PROPN
ejpam-3987	497	5	k(w	k(w	PROPN
ejpam-3987	497	6	,	,	PUNCT
ejpam-3987	497	7	x	x	X
ejpam-3987	497	8	,	,	PUNCT
ejpam-3987	497	9	s	s	PART
ejpam-3987	497	10	)	)	PUNCT
ejpam-3987	497	11	=	=	SYM
ejpam-3987	498	1	∞∑	∞∑	DET
ejpam-3987	498	2	k=0	k=0	PROPN
ejpam-3987	498	3	e2kπix	e2kπix	NOUN
ejpam-3987	498	4	(	(	PUNCT
ejpam-3987	498	5	w+k)3	w+k)3	PROPN
ejpam-3987	498	6	.	.	PUNCT
ejpam-3987	499	1	acta	acta	PROPN
ejpam-3987	499	2	mathematica	mathematica	PROPN
ejpam-3987	499	3	,	,	PUNCT
ejpam-3987	499	4	11:19–24	11:19–24	PROPN
ejpam-3987	499	5	,	,	PUNCT
ejpam-3987	499	6	1887	1887	NUM
ejpam-3987	499	7	.	.	PUNCT
ejpam-3987	500	1	[	[	X
ejpam-3987	500	2	6	6	NUM
ejpam-3987	500	3	]	]	PUNCT
ejpam-3987	500	4	keith	keith	PROPN
ejpam-3987	500	5	b.	b.	PROPN
ejpam-3987	500	6	oldham	oldham	PROPN
ejpam-3987	500	7	,	,	PUNCT
ejpam-3987	500	8	jan	jan	PROPN
ejpam-3987	500	9	myland	myland	PROPN
ejpam-3987	500	10	,	,	PUNCT
ejpam-3987	500	11	and	and	CCONJ
ejpam-3987	500	12	jerome	jerome	PROPN
ejpam-3987	500	13	spanier	spanier	NOUN
ejpam-3987	500	14	.	.	PUNCT
ejpam-3987	501	1	an	an	DET
ejpam-3987	501	2	atlas	atlas	PROPN
ejpam-3987	501	3	of	of	ADP
ejpam-3987	501	4	functions	function	NOUN
ejpam-3987	501	5	:	:	PUNCT
ejpam-3987	501	6	with	with	ADP
ejpam-3987	501	7	equator	equator	NOUN
ejpam-3987	501	8	,	,	PUNCT
ejpam-3987	501	9	the	the	DET
ejpam-3987	501	10	atlas	atlas	PROPN
ejpam-3987	501	11	function	function	PROPN
ejpam-3987	501	12	calculator	calculator	NOUN
ejpam-3987	501	13	.	.	PUNCT
ejpam-3987	502	1	springer	springer	NOUN
ejpam-3987	502	2	science	science	PROPN
ejpam-3987	502	3	&	&	CCONJ
ejpam-3987	502	4	business	business	NOUN
ejpam-3987	502	5	media	medium	NOUN
ejpam-3987	502	6	,	,	PUNCT
ejpam-3987	502	7	07	07	NUM
ejpam-3987	502	8	2010	2010	NUM
ejpam-3987	502	9	.	.	PUNCT
ejpam-3987	503	1	[	[	X
ejpam-3987	503	2	7	7	X
ejpam-3987	503	3	]	]	X
ejpam-3987	503	4	robert	robert	PROPN
ejpam-3987	503	5	reynolds	reynolds	PROPN
ejpam-3987	503	6	and	and	CCONJ
ejpam-3987	503	7	allan	allan	PROPN
ejpam-3987	503	8	stauffer	stauffer	PROPN
ejpam-3987	503	9	.	.	PUNCT
ejpam-3987	504	1	a	a	DET
ejpam-3987	504	2	method	method	NOUN
ejpam-3987	504	3	for	for	ADP
ejpam-3987	504	4	evaluating	evaluate	VERB
ejpam-3987	504	5	definite	definite	ADJ
ejpam-3987	504	6	integrals	integral	NOUN
ejpam-3987	504	7	in	in	ADP
ejpam-3987	504	8	terms	term	NOUN
ejpam-3987	504	9	of	of	ADP
ejpam-3987	504	10	special	special	ADJ
ejpam-3987	504	11	functions	function	NOUN
ejpam-3987	504	12	with	with	ADP
ejpam-3987	504	13	examples	example	NOUN
ejpam-3987	504	14	.	.	PUNCT
ejpam-3987	505	1	international	international	ADJ
ejpam-3987	505	2	mathematical	mathematical	PROPN
ejpam-3987	505	3	forum	forum	PROPN
ejpam-3987	505	4	,	,	PUNCT
ejpam-3987	505	5	15:235	15:235	NUM
ejpam-3987	505	6	–	–	PUNCT
ejpam-3987	505	7	244	244	NUM
ejpam-3987	505	8	,	,	PUNCT
ejpam-3987	505	9	2020	2020	NUM
ejpam-3987	505	10	.	.	PUNCT
ejpam-3987	506	1	[	[	X
ejpam-3987	506	2	8	8	NUM
ejpam-3987	506	3	]	]	X
ejpam-3987	506	4	isaac	isaac	PROPN
ejpam-3987	506	5	todhunter	todhunter	PROPN
ejpam-3987	506	6	.	.	PUNCT
ejpam-3987	507	1	a	a	DET
ejpam-3987	507	2	treatise	treatise	NOUN
ejpam-3987	507	3	on	on	ADP
ejpam-3987	507	4	the	the	DET
ejpam-3987	507	5	integral	integral	ADJ
ejpam-3987	507	6	calculus	calculus	NOUN
ejpam-3987	507	7	and	and	CCONJ
ejpam-3987	507	8	its	its	PRON
ejpam-3987	507	9	applications	application	NOUN
ejpam-3987	507	10	with	with	ADP
ejpam-3987	507	11	numerous	numerous	ADJ
ejpam-3987	507	12	examples	example	NOUN
ejpam-3987	507	13	.	.	PUNCT
ejpam-3987	508	1	sagwan	sagwan	PROPN
ejpam-3987	508	2	press	press	PROPN
ejpam-3987	508	3	,	,	PUNCT
ejpam-3987	508	4	08	08	NUM
ejpam-3987	508	5	2015	2015	NUM
ejpam-3987	508	6	.	.	PUNCT
ejpam-3987	509	1	[	[	X
ejpam-3987	509	2	9	9	NUM
ejpam-3987	509	3	]	]	X
ejpam-3987	509	4	daniel	daniel	PROPN
ejpam-3987	509	5	zwillinger	zwillinger	PROPN
ejpam-3987	509	6	and	and	CCONJ
ejpam-3987	509	7	alan	alan	PROPN
ejpam-3987	509	8	jeffrey	jeffrey	PROPN
ejpam-3987	509	9	.	.	PUNCT
ejpam-3987	509	10	table	table	NOUN
ejpam-3987	509	11	of	of	ADP
ejpam-3987	509	12	integrals	integral	NOUN
ejpam-3987	509	13	,	,	PUNCT
ejpam-3987	509	14	series	series	NOUN
ejpam-3987	509	15	,	,	PUNCT
ejpam-3987	509	16	and	and	CCONJ
ejpam-3987	509	17	products	product	NOUN
ejpam-3987	509	18	.	.	PUNCT
ejpam-3987	510	1	academic	academic	ADJ
ejpam-3987	510	2	press	press	NOUN
ejpam-3987	510	3	,	,	PUNCT
ejpam-3987	510	4	08	08	NUM
ejpam-3987	510	5	2000	2000	NUM
ejpam-3987	510	6	.	.	PUNCT