id	sid	tid	token	lemma	pos
ejpam-4153	1	1	european	european	PROPN
ejpam-4153	1	2	journal	journal	PROPN
ejpam-4153	1	3	of	of	ADP
ejpam-4153	1	4	pure	pure	ADJ
ejpam-4153	1	5	and	and	CCONJ
ejpam-4153	1	6	applied	apply	VERB
ejpam-4153	1	7	mathematics	mathematic	NOUN
ejpam-4153	1	8	vol	vol	NOUN
ejpam-4153	1	9	.	.	PROPN
ejpam-4153	2	1	15	15	NUM
ejpam-4153	2	2	,	,	PUNCT
ejpam-4153	2	3	no	no	INTJ
ejpam-4153	2	4	.	.	NOUN
ejpam-4153	2	5	1	1	NUM
ejpam-4153	2	6	,	,	PUNCT
ejpam-4153	2	7	2022	2022	NUM
ejpam-4153	2	8	,	,	PUNCT
ejpam-4153	2	9	229	229	NUM
ejpam-4153	2	10	-	-	SYM
ejpam-4153	2	11	237	237	NUM
ejpam-4153	2	12	issn	issn	PROPN
ejpam-4153	2	13	1307	1307	NUM
ejpam-4153	2	14	-	-	SYM
ejpam-4153	2	15	5543	5543	NUM
ejpam-4153	2	16	–	–	PUNCT
ejpam-4153	2	17	ejpam.com	ejpam.com	X
ejpam-4153	2	18	published	publish	VERB
ejpam-4153	2	19	by	by	ADP
ejpam-4153	2	20	new	new	PROPN
ejpam-4153	2	21	york	york	PROPN
ejpam-4153	2	22	business	business	PROPN
ejpam-4153	2	23	global	global	ADJ
ejpam-4153	2	24	definite	definite	ADJ
ejpam-4153	2	25	integrals	integral	NOUN
ejpam-4153	2	26	involving	involve	VERB
ejpam-4153	2	27	logarithmic	logarithmic	ADJ
ejpam-4153	2	28	powers	power	NOUN
ejpam-4153	2	29	,	,	PUNCT
ejpam-4153	2	30	binomials	binomial	NOUN
ejpam-4153	2	31	and	and	CCONJ
ejpam-4153	2	32	polynomials	polynomial	NOUN
ejpam-4153	2	33	expressed	express	VERB
ejpam-4153	2	34	in	in	ADP
ejpam-4153	2	35	terms	term	NOUN
ejpam-4153	2	36	of	of	ADP
ejpam-4153	2	37	the	the	DET
ejpam-4153	2	38	lerch	lerch	PROPN
ejpam-4153	2	39	function	function	PROPN
ejpam-4153	2	40	robert	robert	PROPN
ejpam-4153	2	41	reynolds1,∗	reynolds1,∗	PROPN
ejpam-4153	2	42	,	,	PUNCT
ejpam-4153	2	43	allan	allan	PROPN
ejpam-4153	2	44	stauffer1	stauffer1	PROPN
ejpam-4153	2	45	1	1	NUM
ejpam-4153	2	46	department	department	NOUN
ejpam-4153	2	47	of	of	ADP
ejpam-4153	2	48	mathematics	mathematic	NOUN
ejpam-4153	2	49	and	and	CCONJ
ejpam-4153	2	50	statistics	statistic	NOUN
ejpam-4153	2	51	,	,	PUNCT
ejpam-4153	2	52	faculty	faculty	NOUN
ejpam-4153	2	53	of	of	ADP
ejpam-4153	2	54	science	science	PROPN
ejpam-4153	2	55	,	,	PUNCT
ejpam-4153	2	56	york	york	PROPN
ejpam-4153	2	57	university	university	PROPN
ejpam-4153	2	58	,	,	PUNCT
ejpam-4153	2	59	toronto	toronto	PROPN
ejpam-4153	2	60	,	,	PUNCT
ejpam-4153	2	61	ontario	ontario	PROPN
ejpam-4153	2	62	,	,	PUNCT
ejpam-4153	2	63	canada	canada	PROPN
ejpam-4153	2	64	,	,	PUNCT
ejpam-4153	2	65	m3j1p3	m3j1p3	PROPN
ejpam-4153	2	66	abstract	abstract	NOUN
ejpam-4153	2	67	.	.	PUNCT
ejpam-4153	3	1	closed	close	VERB
ejpam-4153	3	2	expressions	expression	NOUN
ejpam-4153	3	3	using	use	VERB
ejpam-4153	3	4	the	the	DET
ejpam-4153	3	5	lerch	lerch	PROPN
ejpam-4153	3	6	function	function	NOUN
ejpam-4153	3	7	for	for	ADP
ejpam-4153	3	8	a	a	DET
ejpam-4153	3	9	definite	definite	ADJ
ejpam-4153	3	10	integral	integral	NOUN
ejpam-4153	3	11	are	be	AUX
ejpam-4153	3	12	derived	derive	VERB
ejpam-4153	3	13	and	and	CCONJ
ejpam-4153	3	14	evaluated	evaluate	VERB
ejpam-4153	3	15	.	.	PUNCT
ejpam-4153	4	1	some	some	PRON
ejpam-4153	4	2	of	of	ADP
ejpam-4153	4	3	these	these	DET
ejpam-4153	4	4	closed	closed	ADJ
ejpam-4153	4	5	expressions	expression	NOUN
ejpam-4153	4	6	are	be	AUX
ejpam-4153	4	7	given	give	VERB
ejpam-4153	4	8	in	in	ADP
ejpam-4153	4	9	gradshteyn	gradshteyn	PROPN
ejpam-4153	4	10	and	and	CCONJ
ejpam-4153	4	11	ryzhik	ryzhik	ADJ
ejpam-4153	4	12	.	.	PUNCT
ejpam-4153	5	1	some	some	DET
ejpam-4153	5	2	special	special	ADJ
ejpam-4153	5	3	cases	case	NOUN
ejpam-4153	5	4	of	of	ADP
ejpam-4153	5	5	the	the	DET
ejpam-4153	5	6	integral	integral	ADJ
ejpam-4153	5	7	are	be	AUX
ejpam-4153	5	8	derived	derive	VERB
ejpam-4153	5	9	and	and	CCONJ
ejpam-4153	5	10	discussed	discuss	VERB
ejpam-4153	5	11	.	.	PUNCT
ejpam-4153	6	1	the	the	DET
ejpam-4153	6	2	majority	majority	NOUN
ejpam-4153	6	3	of	of	ADP
ejpam-4153	6	4	the	the	DET
ejpam-4153	6	5	results	result	NOUN
ejpam-4153	6	6	in	in	ADP
ejpam-4153	6	7	this	this	DET
ejpam-4153	6	8	work	work	NOUN
ejpam-4153	6	9	are	be	AUX
ejpam-4153	6	10	new	new	ADJ
ejpam-4153	6	11	.	.	PUNCT
ejpam-4153	7	1	2020	2020	NUM
ejpam-4153	7	2	mathematics	mathematic	NOUN
ejpam-4153	7	3	subject	subject	NOUN
ejpam-4153	7	4	classifications	classification	NOUN
ejpam-4153	7	5	:	:	PUNCT
ejpam-4153	7	6	30e20	30e20	NUM
ejpam-4153	7	7	,	,	PUNCT
ejpam-4153	7	8	33	33	NUM
ejpam-4153	7	9	-	-	SYM
ejpam-4153	7	10	01	01	NUM
ejpam-4153	7	11	,	,	PUNCT
ejpam-4153	7	12	33	33	NUM
ejpam-4153	7	13	-	-	SYM
ejpam-4153	7	14	03	03	NUM
ejpam-4153	7	15	,	,	PUNCT
ejpam-4153	7	16	33	33	NUM
ejpam-4153	7	17	-	-	PUNCT
ejpam-4153	7	18	04	04	NUM
ejpam-4153	7	19	,	,	PUNCT
ejpam-4153	7	20	33	33	NUM
ejpam-4153	7	21	-	-	PUNCT
ejpam-4153	7	22	33b	33b	NUM
ejpam-4153	7	23	key	key	ADJ
ejpam-4153	7	24	words	word	NOUN
ejpam-4153	7	25	and	and	CCONJ
ejpam-4153	7	26	phrases	phrase	NOUN
ejpam-4153	7	27	:	:	PUNCT
ejpam-4153	7	28	entries	entry	NOUN
ejpam-4153	7	29	of	of	ADP
ejpam-4153	7	30	gradshteyn	gradshteyn	PROPN
ejpam-4153	7	31	and	and	CCONJ
ejpam-4153	7	32	ryzhik	ryzhik	ADJ
ejpam-4153	7	33	;	;	PUNCT
ejpam-4153	7	34	lerch	lerch	PROPN
ejpam-4153	7	35	function	function	PROPN
ejpam-4153	7	36	;	;	PUNCT
ejpam-4153	8	1	analytic	analytic	ADJ
ejpam-4153	8	2	continuation	continuation	NOUN
ejpam-4153	8	3	1	1	NUM
ejpam-4153	8	4	.	.	PUNCT
ejpam-4153	8	5	introduction	introduction	NOUN
ejpam-4153	8	6	in	in	ADP
ejpam-4153	8	7	this	this	DET
ejpam-4153	8	8	manuscript	manuscript	NOUN
ejpam-4153	8	9	we	we	PRON
ejpam-4153	8	10	focus	focus	VERB
ejpam-4153	8	11	on	on	ADP
ejpam-4153	8	12	the	the	DET
ejpam-4153	8	13	derivation	derivation	NOUN
ejpam-4153	8	14	of	of	ADP
ejpam-4153	8	15	the	the	DET
ejpam-4153	8	16	definite	definite	ADJ
ejpam-4153	8	17	integral	integral	ADJ
ejpam-4153	8	18	given	give	VERB
ejpam-4153	8	19	by∫	by∫	PROPN
ejpam-4153	8	20	1	1	NUM
ejpam-4153	8	21	0	0	NUM
ejpam-4153	8	22	xm	xm	PROPN
ejpam-4153	9	1	logk(ax)−	logk(ax)−	PROPN
ejpam-4153	9	2	x−m	x−m	PROPN
ejpam-4153	9	3	logk	logk	PROPN
ejpam-4153	9	4	(	(	PUNCT
ejpam-4153	9	5	a	a	DET
ejpam-4153	9	6	x	x	X
ejpam-4153	9	7	)	)	PUNCT
ejpam-4153	10	1	x2	x2	NOUN
ejpam-4153	10	2	−	−	PROPN
ejpam-4153	10	3	1	1	NUM
ejpam-4153	10	4	dx	dx	PROPN
ejpam-4153	10	5	,	,	PUNCT
ejpam-4153	10	6	(	(	PUNCT
ejpam-4153	10	7	1	1	X
ejpam-4153	10	8	)	)	PUNCT
ejpam-4153	10	9	which	which	PRON
ejpam-4153	10	10	has	have	VERB
ejpam-4153	10	11	a	a	DET
ejpam-4153	10	12	closed	closed	ADJ
ejpam-4153	10	13	form	form	NOUN
ejpam-4153	10	14	solution	solution	NOUN
ejpam-4153	10	15	in	in	ADP
ejpam-4153	10	16	terms	term	NOUN
ejpam-4153	10	17	of	of	ADP
ejpam-4153	10	18	the	the	DET
ejpam-4153	10	19	lerch	lerch	PROPN
ejpam-4153	10	20	function	function	PROPN
ejpam-4153	10	21	.	.	PUNCT
ejpam-4153	11	1	in	in	ADP
ejpam-4153	11	2	our	our	PRON
ejpam-4153	11	3	case	case	NOUN
ejpam-4153	11	4	the	the	DET
ejpam-4153	11	5	parameters	parameter	NOUN
ejpam-4153	11	6	in	in	ADP
ejpam-4153	11	7	the	the	DET
ejpam-4153	11	8	formula	formula	NOUN
ejpam-4153	11	9	are	be	AUX
ejpam-4153	11	10	general	general	ADJ
ejpam-4153	11	11	complex	complex	ADJ
ejpam-4153	11	12	numbers	number	NOUN
ejpam-4153	11	13	subject	subject	ADJ
ejpam-4153	11	14	to	to	ADP
ejpam-4153	11	15	the	the	DET
ejpam-4153	11	16	restrictions	restriction	NOUN
ejpam-4153	11	17	given	give	VERB
ejpam-4153	11	18	below	below	ADV
ejpam-4153	11	19	.	.	PUNCT
ejpam-4153	12	1	this	this	DET
ejpam-4153	12	2	integral	integral	ADJ
ejpam-4153	12	3	and	and	CCONJ
ejpam-4153	12	4	its	its	PRON
ejpam-4153	12	5	closed	closed	ADJ
ejpam-4153	12	6	form	form	NOUN
ejpam-4153	12	7	solution	solution	NOUN
ejpam-4153	12	8	are	be	AUX
ejpam-4153	12	9	important	important	ADJ
ejpam-4153	12	10	because	because	SCONJ
ejpam-4153	12	11	it	it	PRON
ejpam-4153	12	12	allows	allow	VERB
ejpam-4153	12	13	us	we	PRON
ejpam-4153	12	14	to	to	PART
ejpam-4153	12	15	provide	provide	VERB
ejpam-4153	12	16	derivations	derivation	NOUN
ejpam-4153	12	17	for	for	ADP
ejpam-4153	12	18	integrals	integral	NOUN
ejpam-4153	12	19	in	in	ADP
ejpam-4153	12	20	the	the	DET
ejpam-4153	12	21	books	book	NOUN
ejpam-4153	12	22	of	of	ADP
ejpam-4153	12	23	gradshteyn	gradshteyn	NOUN
ejpam-4153	12	24	and	and	CCONJ
ejpam-4153	12	25	rhyzik	rhyzik	ADJ
ejpam-4153	12	26	[	[	X
ejpam-4153	12	27	6	6	NUM
ejpam-4153	12	28	]	]	PUNCT
ejpam-4153	12	29	and	and	CCONJ
ejpam-4153	12	30	birens	birens	PROPN
ejpam-4153	12	31	de	de	PROPN
ejpam-4153	12	32	haan	haan	PROPN
ejpam-4153	12	33	[	[	X
ejpam-4153	12	34	8	8	NUM
ejpam-4153	12	35	]	]	PUNCT
ejpam-4153	12	36	.	.	PUNCT
ejpam-4153	13	1	we	we	PRON
ejpam-4153	13	2	also	also	ADV
ejpam-4153	13	3	derive	derive	VERB
ejpam-4153	13	4	new	new	ADJ
ejpam-4153	13	5	forms	form	NOUN
ejpam-4153	13	6	of	of	ADP
ejpam-4153	13	7	definite	definite	ADJ
ejpam-4153	13	8	integrals	integral	NOUN
ejpam-4153	13	9	such	such	ADJ
ejpam-4153	13	10	as	as	ADP
ejpam-4153	13	11	tan−1(log(x	tan−1(log(x	NOUN
ejpam-4153	13	12	)	)	PUNCT
ejpam-4153	13	13	)	)	PUNCT
ejpam-4153	13	14	not	not	PART
ejpam-4153	13	15	available	available	ADJ
ejpam-4153	13	16	in	in	ADP
ejpam-4153	13	17	current	current	ADJ
ejpam-4153	13	18	literature	literature	NOUN
ejpam-4153	13	19	.	.	PUNCT
ejpam-4153	14	1	since	since	SCONJ
ejpam-4153	14	2	equation	equation	NOUN
ejpam-4153	14	3	(	(	PUNCT
ejpam-4153	14	4	1	1	X
ejpam-4153	14	5	)	)	PUNCT
ejpam-4153	14	6	is	be	AUX
ejpam-4153	14	7	expressed	express	VERB
ejpam-4153	14	8	in	in	ADP
ejpam-4153	14	9	terms	term	NOUN
ejpam-4153	14	10	of	of	ADP
ejpam-4153	14	11	the	the	DET
ejpam-4153	14	12	lerch	lerch	PROPN
ejpam-4153	14	13	function	function	PROPN
ejpam-4153	14	14	,	,	PUNCT
ejpam-4153	14	15	all	all	DET
ejpam-4153	14	16	solutions	solution	NOUN
ejpam-4153	14	17	of	of	ADP
ejpam-4153	14	18	the	the	DET
ejpam-4153	14	19	integrals	integral	NOUN
ejpam-4153	14	20	are	be	AUX
ejpam-4153	14	21	analytically	analytically	ADV
ejpam-4153	14	22	continued	continue	VERB
ejpam-4153	14	23	which	which	PRON
ejpam-4153	14	24	widens	widen	VERB
ejpam-4153	14	25	the	the	DET
ejpam-4153	14	26	range	range	NOUN
ejpam-4153	14	27	of	of	ADP
ejpam-4153	14	28	computation	computation	NOUN
ejpam-4153	14	29	.	.	PUNCT
ejpam-4153	15	1	the	the	DET
ejpam-4153	15	2	derivations	derivation	NOUN
ejpam-4153	15	3	follow	follow	VERB
ejpam-4153	15	4	the	the	DET
ejpam-4153	15	5	method	method	NOUN
ejpam-4153	15	6	used	use	VERB
ejpam-4153	15	7	by	by	ADP
ejpam-4153	15	8	us	we	PRON
ejpam-4153	15	9	in	in	ADP
ejpam-4153	15	10	[	[	X
ejpam-4153	15	11	10	10	NUM
ejpam-4153	15	12	]	]	PUNCT
ejpam-4153	15	13	.	.	PUNCT
ejpam-4153	16	1	this	this	DET
ejpam-4153	16	2	method	method	NOUN
ejpam-4153	16	3	involves	involve	VERB
ejpam-4153	16	4	using	use	VERB
ejpam-4153	16	5	a	a	DET
ejpam-4153	16	6	form	form	NOUN
ejpam-4153	16	7	of	of	ADP
ejpam-4153	16	8	the	the	DET
ejpam-4153	16	9	generalized	generalize	VERB
ejpam-4153	16	10	cauchy	cauchy	PROPN
ejpam-4153	16	11	’s	’s	PART
ejpam-4153	16	12	integral	integral	ADJ
ejpam-4153	16	13	formula	formula	NOUN
ejpam-4153	16	14	given	give	VERB
ejpam-4153	16	15	by	by	ADP
ejpam-4153	16	16	yk	yk	PROPN
ejpam-4153	16	17	γ(k	γ(k	PROPN
ejpam-4153	16	18	+	+	CCONJ
ejpam-4153	16	19	1	1	X
ejpam-4153	16	20	)	)	PUNCT
ejpam-4153	16	21	=	=	SYM
ejpam-4153	16	22	1	1	NUM
ejpam-4153	16	23	2πi	2πi	ADJ
ejpam-4153	16	24	∫	∫	PROPN
ejpam-4153	16	25	c	c	PROPN
ejpam-4153	16	26	ewy	ewy	PROPN
ejpam-4153	16	27	wk+1	wk+1	PROPN
ejpam-4153	16	28	dw	dw	PROPN
ejpam-4153	16	29	.	.	PUNCT
ejpam-4153	17	1	(	(	PUNCT
ejpam-4153	17	2	2	2	X
ejpam-4153	17	3	)	)	PUNCT
ejpam-4153	17	4	∗corresponding	∗corresponde	VERB
ejpam-4153	17	5	author	author	NOUN
ejpam-4153	17	6	.	.	PUNCT
ejpam-4153	18	1	doi	doi	NOUN
ejpam-4153	18	2	:	:	PUNCT
ejpam-4153	18	3	https://doi.org/10.29020/nybg.ejpam.v15i1.4153	https://doi.org/10.29020/nybg.ejpam.v15i1.4153	VERB
ejpam-4153	18	4	email	email	NOUN
ejpam-4153	18	5	addresses	address	NOUN
ejpam-4153	18	6	:	:	PUNCT
ejpam-4153	19	1	milver@my.yorku.ca	milver@my.yorku.ca	NOUN
ejpam-4153	19	2	(	(	PUNCT
ejpam-4153	19	3	r.	r.	PROPN
ejpam-4153	19	4	reynolds	reynolds	PROPN
ejpam-4153	19	5	)	)	PUNCT
ejpam-4153	19	6	,	,	PUNCT
ejpam-4153	19	7	stauffer@yorku.ca	stauffer@yorku.ca	NOUN
ejpam-4153	19	8	(	(	PUNCT
ejpam-4153	19	9	a.	a.	NOUN
ejpam-4153	19	10	stauffer	stauffer	PROPN
ejpam-4153	19	11	)	)	PUNCT
ejpam-4153	19	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4153	20	1	229	229	NUM
ejpam-4153	21	1	©	©	ADP
ejpam-4153	21	2	2022	2022	NUM
ejpam-4153	21	3	ejpam	ejpam	VERB
ejpam-4153	21	4	all	all	DET
ejpam-4153	21	5	rights	right	NOUN
ejpam-4153	21	6	reserved	reserve	VERB
ejpam-4153	21	7	.	.	PUNCT
ejpam-4153	22	1	r.	r.	PROPN
ejpam-4153	22	2	reynolds	reynolds	PROPN
ejpam-4153	22	3	,	,	PUNCT
ejpam-4153	22	4	a.	a.	PROPN
ejpam-4153	22	5	stauffer	stauffer	PROPN
ejpam-4153	22	6	/	/	SYM
ejpam-4153	22	7	eur	eur	PROPN
ejpam-4153	22	8	.	.	PUNCT
ejpam-4153	23	1	j.	j.	PROPN
ejpam-4153	23	2	pure	pure	PROPN
ejpam-4153	23	3	appl	appl	PROPN
ejpam-4153	23	4	.	.	PROPN
ejpam-4153	23	5	math	math	PROPN
ejpam-4153	23	6	,	,	PUNCT
ejpam-4153	23	7	15	15	NUM
ejpam-4153	23	8	(	(	PUNCT
ejpam-4153	23	9	1	1	NUM
ejpam-4153	23	10	)	)	PUNCT
ejpam-4153	23	11	(	(	PUNCT
ejpam-4153	23	12	2022	2022	NUM
ejpam-4153	23	13	)	)	PUNCT
ejpam-4153	23	14	,	,	PUNCT
ejpam-4153	23	15	229	229	NUM
ejpam-4153	23	16	-	-	SYM
ejpam-4153	23	17	237	237	NUM
ejpam-4153	23	18	230	230	NUM
ejpam-4153	23	19	where	where	SCONJ
ejpam-4153	23	20	c	c	NOUN
ejpam-4153	23	21	is	be	AUX
ejpam-4153	23	22	in	in	ADP
ejpam-4153	23	23	general	general	ADJ
ejpam-4153	23	24	an	an	DET
ejpam-4153	23	25	open	open	ADJ
ejpam-4153	23	26	contour	contour	NOUN
ejpam-4153	23	27	in	in	ADP
ejpam-4153	23	28	the	the	DET
ejpam-4153	23	29	complex	complex	ADJ
ejpam-4153	23	30	plane	plane	NOUN
ejpam-4153	23	31	where	where	SCONJ
ejpam-4153	23	32	the	the	DET
ejpam-4153	23	33	bilinear	bilinear	NOUN
ejpam-4153	23	34	concomitant	concomitant	NOUN
ejpam-4153	24	1	[	[	X
ejpam-4153	24	2	10	10	NUM
ejpam-4153	24	3	]	]	PUNCT
ejpam-4153	24	4	has	have	VERB
ejpam-4153	24	5	the	the	DET
ejpam-4153	24	6	same	same	ADJ
ejpam-4153	24	7	value	value	NOUN
ejpam-4153	24	8	at	at	ADP
ejpam-4153	24	9	the	the	DET
ejpam-4153	24	10	end	end	NOUN
ejpam-4153	24	11	points	point	NOUN
ejpam-4153	24	12	of	of	ADP
ejpam-4153	24	13	the	the	DET
ejpam-4153	24	14	contour	contour	NOUN
ejpam-4153	24	15	.	.	PUNCT
ejpam-4153	25	1	then	then	ADV
ejpam-4153	25	2	we	we	PRON
ejpam-4153	25	3	multiply	multiply	VERB
ejpam-4153	25	4	both	both	DET
ejpam-4153	25	5	sides	side	NOUN
ejpam-4153	25	6	by	by	ADP
ejpam-4153	25	7	a	a	DET
ejpam-4153	25	8	function	function	NOUN
ejpam-4153	25	9	and	and	CCONJ
ejpam-4153	25	10	take	take	VERB
ejpam-4153	25	11	a	a	DET
ejpam-4153	25	12	definite	definite	ADJ
ejpam-4153	25	13	integral	integral	NOUN
ejpam-4153	25	14	of	of	ADP
ejpam-4153	25	15	both	both	DET
ejpam-4153	25	16	sides	side	NOUN
ejpam-4153	25	17	.	.	PUNCT
ejpam-4153	26	1	this	this	PRON
ejpam-4153	26	2	yields	yield	VERB
ejpam-4153	26	3	a	a	DET
ejpam-4153	26	4	definite	definite	ADJ
ejpam-4153	26	5	integral	integral	ADJ
ejpam-4153	26	6	in	in	ADP
ejpam-4153	26	7	terms	term	NOUN
ejpam-4153	26	8	of	of	ADP
ejpam-4153	26	9	a	a	DET
ejpam-4153	26	10	contour	contour	NOUN
ejpam-4153	26	11	integral	integral	NOUN
ejpam-4153	26	12	.	.	PUNCT
ejpam-4153	27	1	then	then	ADV
ejpam-4153	27	2	we	we	PRON
ejpam-4153	27	3	multiply	multiply	VERB
ejpam-4153	27	4	both	both	DET
ejpam-4153	27	5	sides	side	NOUN
ejpam-4153	27	6	of	of	ADP
ejpam-4153	27	7	equation	equation	NOUN
ejpam-4153	27	8	(	(	PUNCT
ejpam-4153	27	9	2	2	NUM
ejpam-4153	27	10	)	)	PUNCT
ejpam-4153	27	11	by	by	ADP
ejpam-4153	27	12	another	another	DET
ejpam-4153	27	13	function	function	NOUN
ejpam-4153	27	14	and	and	CCONJ
ejpam-4153	27	15	take	take	VERB
ejpam-4153	27	16	the	the	DET
ejpam-4153	27	17	infinite	infinite	ADJ
ejpam-4153	27	18	sum	sum	NOUN
ejpam-4153	27	19	of	of	ADP
ejpam-4153	27	20	both	both	DET
ejpam-4153	27	21	sides	side	NOUN
ejpam-4153	27	22	such	such	ADJ
ejpam-4153	27	23	that	that	SCONJ
ejpam-4153	27	24	the	the	DET
ejpam-4153	27	25	contour	contour	NOUN
ejpam-4153	27	26	integral	integral	NOUN
ejpam-4153	27	27	of	of	ADP
ejpam-4153	27	28	both	both	DET
ejpam-4153	27	29	equations	equation	NOUN
ejpam-4153	27	30	are	be	AUX
ejpam-4153	27	31	the	the	DET
ejpam-4153	27	32	same	same	ADJ
ejpam-4153	27	33	.	.	PUNCT
ejpam-4153	28	1	2	2	X
ejpam-4153	28	2	.	.	X
ejpam-4153	28	3	definite	definite	ADJ
ejpam-4153	28	4	integral	integral	ADJ
ejpam-4153	28	5	of	of	ADP
ejpam-4153	28	6	the	the	DET
ejpam-4153	28	7	contour	contour	NOUN
ejpam-4153	28	8	integral	integral	NOUN
ejpam-4153	28	9	we	we	PRON
ejpam-4153	28	10	use	use	VERB
ejpam-4153	28	11	the	the	DET
ejpam-4153	28	12	method	method	NOUN
ejpam-4153	28	13	in	in	ADP
ejpam-4153	28	14	[	[	X
ejpam-4153	28	15	10	10	NUM
ejpam-4153	28	16	]	]	PUNCT
ejpam-4153	28	17	.	.	PUNCT
ejpam-4153	29	1	here	here	ADV
ejpam-4153	29	2	we	we	PRON
ejpam-4153	29	3	use	use	VERB
ejpam-4153	29	4	the	the	DET
ejpam-4153	29	5	contour	contour	NOUN
ejpam-4153	29	6	of	of	ADP
ejpam-4153	29	7	figure	figure	NOUN
ejpam-4153	29	8	2	2	NUM
ejpam-4153	29	9	in	in	ADP
ejpam-4153	29	10	[	[	X
ejpam-4153	29	11	10	10	NUM
ejpam-4153	29	12	]	]	PUNCT
ejpam-4153	29	13	but	but	CCONJ
ejpam-4153	29	14	for	for	ADP
ejpam-4153	29	15	the	the	DET
ejpam-4153	29	16	z	z	NOUN
ejpam-4153	29	17	-	-	NOUN
ejpam-4153	29	18	plane	plane	NOUN
ejpam-4153	29	19	where	where	SCONJ
ejpam-4153	29	20	z	z	NOUN
ejpam-4153	29	21	=	=	PUNCT
ejpam-4153	29	22	m+w	m+w	VERB
ejpam-4153	29	23	except	except	SCONJ
ejpam-4153	29	24	we	we	PRON
ejpam-4153	29	25	replace	replace	VERB
ejpam-4153	29	26	the	the	DET
ejpam-4153	29	27	vertical	vertical	ADJ
ejpam-4153	29	28	lines	line	NOUN
ejpam-4153	29	29	±0	±0	VERB
ejpam-4153	29	30	by	by	ADP
ejpam-4153	29	31	±ℜ(a	±ℜ(a	NOUN
ejpam-4153	29	32	)	)	PUNCT
ejpam-4153	29	33	.	.	PUNCT
ejpam-4153	30	1	note	note	VERB
ejpam-4153	30	2	figure	figure	NOUN
ejpam-4153	30	3	2	2	NUM
ejpam-4153	30	4	represents	represent	VERB
ejpam-4153	30	5	a	a	DET
ejpam-4153	30	6	hankel	hankel	NOUN
ejpam-4153	30	7	contour	contour	NOUN
ejpam-4153	30	8	which	which	PRON
ejpam-4153	30	9	is	be	AUX
ejpam-4153	30	10	in	in	ADP
ejpam-4153	30	11	the	the	DET
ejpam-4153	30	12	z	z	NOUN
ejpam-4153	30	13	-	-	NOUN
ejpam-4153	30	14	plane	plane	NOUN
ejpam-4153	30	15	,	,	PUNCT
ejpam-4153	30	16	with	with	ADP
ejpam-4153	30	17	the	the	DET
ejpam-4153	30	18	cut	cut	NOUN
ejpam-4153	30	19	along	along	ADP
ejpam-4153	30	20	the	the	DET
ejpam-4153	30	21	positive	positive	ADJ
ejpam-4153	30	22	y	y	NOUN
ejpam-4153	30	23	-	-	PUNCT
ejpam-4153	30	24	axis	axis	NOUN
ejpam-4153	30	25	and	and	CCONJ
ejpam-4153	30	26	the	the	DET
ejpam-4153	30	27	contour	contour	NOUN
ejpam-4153	30	28	on	on	ADP
ejpam-4153	30	29	opposite	opposite	ADJ
ejpam-4153	30	30	sides	side	NOUN
ejpam-4153	30	31	of	of	ADP
ejpam-4153	30	32	the	the	DET
ejpam-4153	30	33	cut	cut	NOUN
ejpam-4153	30	34	but	but	CCONJ
ejpam-4153	30	35	along	along	ADP
ejpam-4153	30	36	the	the	DET
ejpam-4153	30	37	y	y	NOUN
ejpam-4153	30	38	-	-	PUNCT
ejpam-4153	30	39	axis	axis	NOUN
ejpam-4153	30	40	.	.	PUNCT
ejpam-4153	31	1	using	use	VERB
ejpam-4153	31	2	a	a	DET
ejpam-4153	31	3	generalization	generalization	NOUN
ejpam-4153	31	4	of	of	ADP
ejpam-4153	31	5	cauchy	cauchy	PROPN
ejpam-4153	31	6	’s	’s	PART
ejpam-4153	31	7	integral	integral	ADJ
ejpam-4153	31	8	formula	formula	NOUN
ejpam-4153	31	9	we	we	PRON
ejpam-4153	31	10	first	first	ADV
ejpam-4153	31	11	replace	replace	VERB
ejpam-4153	31	12	y	y	PROPN
ejpam-4153	31	13	by	by	ADP
ejpam-4153	31	14	log(ax	log(ax	NOUN
ejpam-4153	31	15	)	)	PUNCT
ejpam-4153	31	16	then	then	ADV
ejpam-4153	31	17	y	y	PROPN
ejpam-4153	31	18	by	by	ADP
ejpam-4153	31	19	log(a	log(a	PROPN
ejpam-4153	31	20	/	/	SYM
ejpam-4153	31	21	x	x	NOUN
ejpam-4153	31	22	)	)	PUNCT
ejpam-4153	31	23	takig	takig	VERB
ejpam-4153	31	24	their	their	PRON
ejpam-4153	31	25	difference	difference	NOUN
ejpam-4153	31	26	followed	follow	VERB
ejpam-4153	31	27	by	by	ADP
ejpam-4153	31	28	multiplying	multiply	VERB
ejpam-4153	31	29	both	both	DET
ejpam-4153	31	30	sides	side	NOUN
ejpam-4153	31	31	by	by	ADP
ejpam-4153	31	32	1	1	NUM
ejpam-4153	31	33	x2−1	x2−1	NOUN
ejpam-4153	31	34	then	then	ADV
ejpam-4153	31	35	taking	take	VERB
ejpam-4153	31	36	the	the	DET
ejpam-4153	31	37	definite	definite	ADJ
ejpam-4153	31	38	integral	integral	ADJ
ejpam-4153	31	39	with	with	ADP
ejpam-4153	31	40	respect	respect	NOUN
ejpam-4153	31	41	x	x	X
ejpam-4153	31	42	∈	∈	PROPN
ejpam-4153	32	1	[	[	X
ejpam-4153	32	2	0	0	NUM
ejpam-4153	32	3	,	,	PUNCT
ejpam-4153	32	4	1	1	NUM
ejpam-4153	32	5	]	]	PUNCT
ejpam-4153	32	6	to	to	PART
ejpam-4153	32	7	get	get	VERB
ejpam-4153	32	8	(	(	PUNCT
ejpam-4153	32	9	3	3	NUM
ejpam-4153	32	10	)	)	PUNCT
ejpam-4153	32	11	∫	∫	NOUN
ejpam-4153	32	12	1	1	NUM
ejpam-4153	32	13	0	0	NUM
ejpam-4153	32	14	xm	xm	PROPN
ejpam-4153	33	1	logk(ax)−	logk(ax)−	PROPN
ejpam-4153	33	2	x−m	x−m	PROPN
ejpam-4153	33	3	logk	logk	PROPN
ejpam-4153	33	4	(	(	PUNCT
ejpam-4153	33	5	a	a	DET
ejpam-4153	33	6	x	x	X
ejpam-4153	33	7	)	)	PUNCT
ejpam-4153	34	1	x2	x2	NOUN
ejpam-4153	34	2	−	−	PROPN
ejpam-4153	34	3	1	1	NUM
ejpam-4153	34	4	dx	dx	NOUN
ejpam-4153	34	5	=	=	SYM
ejpam-4153	34	6	1	1	NUM
ejpam-4153	34	7	2πi	2πi	NOUN
ejpam-4153	34	8	∫	∫	NOUN
ejpam-4153	35	1	1	1	NUM
ejpam-4153	35	2	0	0	NUM
ejpam-4153	35	3	∫	∫	PROPN
ejpam-4153	35	4	c	c	PROPN
ejpam-4153	35	5	aww−k−1	aww−k−1	NOUN
ejpam-4153	35	6	(	(	PUNCT
ejpam-4153	35	7	xm+w	xm+w	PROPN
ejpam-4153	35	8	−	−	PROPN
ejpam-4153	35	9	x−m−w	x−m−w	PROPN
ejpam-4153	35	10	)	)	PUNCT
ejpam-4153	36	1	x2	x2	PRON
ejpam-4153	37	1	−	−	NOUN
ejpam-4153	37	2	1	1	NUM
ejpam-4153	37	3	dwdx	dwdx	VERB
ejpam-4153	37	4	=	=	SYM
ejpam-4153	37	5	1	1	NUM
ejpam-4153	37	6	2πi	2πi	NOUN
ejpam-4153	37	7	∫	∫	PROPN
ejpam-4153	38	1	c	c	NOUN
ejpam-4153	38	2	∫	∫	PROPN
ejpam-4153	38	3	1	1	NUM
ejpam-4153	38	4	0	0	NUM
ejpam-4153	38	5	aww−k−1	aww−k−1	NOUN
ejpam-4153	38	6	(	(	PUNCT
ejpam-4153	38	7	xm+w	xm+w	PROPN
ejpam-4153	38	8	−	−	PROPN
ejpam-4153	38	9	x−m−w	x−m−w	PROPN
ejpam-4153	38	10	)	)	PUNCT
ejpam-4153	39	1	x2	x2	PRON
ejpam-4153	40	1	−	−	PROPN
ejpam-4153	40	2	1	1	NUM
ejpam-4153	40	3	dxdw	dxdw	NOUN
ejpam-4153	40	4	=	=	SYM
ejpam-4153	40	5	1	1	NUM
ejpam-4153	40	6	2πi	2πi	ADJ
ejpam-4153	40	7	∫	∫	PROPN
ejpam-4153	40	8	c	c	NOUN
ejpam-4153	40	9	1	1	NUM
ejpam-4153	40	10	2	2	NUM
ejpam-4153	40	11	πaww−k−1	πaww−k−1	PROPN
ejpam-4153	40	12	tan	tan	PROPN
ejpam-4153	40	13	(	(	PUNCT
ejpam-4153	40	14	1	1	NUM
ejpam-4153	40	15	2	2	NUM
ejpam-4153	40	16	π(m+	π(m+	X
ejpam-4153	40	17	w	w	NOUN
ejpam-4153	40	18	)	)	PUNCT
ejpam-4153	40	19	)	)	PUNCT
ejpam-4153	40	20	dw	dw	PROPN
ejpam-4153	40	21	,	,	PUNCT
ejpam-4153	40	22	from	from	ADP
ejpam-4153	40	23	(	(	PUNCT
ejpam-4153	40	24	3.269.3	3.269.3	NUM
ejpam-4153	40	25	)	)	PUNCT
ejpam-4153	40	26	in	in	ADP
ejpam-4153	40	27	[	[	X
ejpam-4153	40	28	6	6	NUM
ejpam-4153	40	29	]	]	PUNCT
ejpam-4153	40	30	where	where	SCONJ
ejpam-4153	40	31	the	the	DET
ejpam-4153	40	32	digamma	digamma	PROPN
ejpam-4153	40	33	function	function	NOUN
ejpam-4153	40	34	ψ0(x	ψ0(x	PRON
ejpam-4153	40	35	)	)	PUNCT
ejpam-4153	40	36	can	can	AUX
ejpam-4153	40	37	be	be	AUX
ejpam-4153	40	38	written	write	VERB
ejpam-4153	40	39	out	out	ADP
ejpam-4153	40	40	using	use	VERB
ejpam-4153	40	41	equation	equation	NOUN
ejpam-4153	40	42	(	(	PUNCT
ejpam-4153	40	43	44:5:3	44:5:3	NUM
ejpam-4153	40	44	)	)	PUNCT
ejpam-4153	40	45	in	in	ADP
ejpam-4153	40	46	[	[	X
ejpam-4153	40	47	9	9	NUM
ejpam-4153	40	48	]	]	PUNCT
ejpam-4153	40	49	and	and	CCONJ
ejpam-4153	40	50	−1	−1	NOUN
ejpam-4153	40	51	<	<	X
ejpam-4153	40	52	ℜ(m+	ℜ(m+	PROPN
ejpam-4153	40	53	w	w	PROPN
ejpam-4153	40	54	)	)	PUNCT
ejpam-4153	40	55	<	<	X
ejpam-4153	40	56	1	1	X
ejpam-4153	40	57	.	.	PUNCT
ejpam-4153	41	1	the	the	DET
ejpam-4153	41	2	logarithmic	logarithmic	ADJ
ejpam-4153	41	3	function	function	NOUN
ejpam-4153	41	4	is	be	AUX
ejpam-4153	41	5	given	give	VERB
ejpam-4153	41	6	for	for	ADP
ejpam-4153	41	7	example	example	NOUN
ejpam-4153	41	8	in	in	ADP
ejpam-4153	41	9	section	section	NOUN
ejpam-4153	41	10	(	(	PUNCT
ejpam-4153	41	11	4.1	4.1	NUM
ejpam-4153	41	12	)	)	PUNCT
ejpam-4153	41	13	in	in	ADP
ejpam-4153	41	14	[	[	X
ejpam-4153	41	15	1	1	NUM
ejpam-4153	41	16	]	]	PUNCT
ejpam-4153	41	17	.	.	PUNCT
ejpam-4153	42	1	we	we	PRON
ejpam-4153	42	2	are	be	AUX
ejpam-4153	42	3	able	able	ADJ
ejpam-4153	42	4	to	to	PART
ejpam-4153	42	5	switch	switch	VERB
ejpam-4153	42	6	the	the	DET
ejpam-4153	42	7	order	order	NOUN
ejpam-4153	42	8	of	of	ADP
ejpam-4153	42	9	integration	integration	NOUN
ejpam-4153	42	10	over	over	ADP
ejpam-4153	42	11	z	z	NOUN
ejpam-4153	42	12	=	=	PUNCT
ejpam-4153	42	13	w	w	PROPN
ejpam-4153	43	1	+	+	NOUN
ejpam-4153	43	2	m	m	VERB
ejpam-4153	43	3	and	and	CCONJ
ejpam-4153	43	4	x	x	SYM
ejpam-4153	43	5	using	use	VERB
ejpam-4153	43	6	fubini	fubini	NOUN
ejpam-4153	43	7	’s	’s	PART
ejpam-4153	43	8	theorem	theorem	NOUN
ejpam-4153	43	9	since	since	SCONJ
ejpam-4153	43	10	the	the	DET
ejpam-4153	43	11	integrand	integrand	NOUN
ejpam-4153	43	12	is	be	AUX
ejpam-4153	43	13	of	of	ADP
ejpam-4153	43	14	bounded	bounded	ADJ
ejpam-4153	43	15	measure	measure	NOUN
ejpam-4153	43	16	over	over	ADP
ejpam-4153	43	17	the	the	DET
ejpam-4153	43	18	space	space	NOUN
ejpam-4153	43	19	c×	c×	PROPN
ejpam-4153	44	1	[	[	X
ejpam-4153	44	2	0	0	NUM
ejpam-4153	44	3	,	,	PUNCT
ejpam-4153	44	4	1	1	NUM
ejpam-4153	44	5	]	]	PUNCT
ejpam-4153	44	6	.	.	PUNCT
ejpam-4153	45	1	3	3	X
ejpam-4153	45	2	.	.	X
ejpam-4153	45	3	the	the	DET
ejpam-4153	45	4	lerch	lerch	PROPN
ejpam-4153	45	5	function	function	VERB
ejpam-4153	45	6	the	the	DET
ejpam-4153	45	7	lerch	lerch	PROPN
ejpam-4153	45	8	function	function	NOUN
ejpam-4153	46	1	[	[	X
ejpam-4153	46	2	3	3	X
ejpam-4153	46	3	]	]	PUNCT
ejpam-4153	46	4	has	have	VERB
ejpam-4153	46	5	a	a	DET
ejpam-4153	46	6	series	series	NOUN
ejpam-4153	46	7	representation	representation	NOUN
ejpam-4153	46	8	given	give	VERB
ejpam-4153	46	9	by	by	ADP
ejpam-4153	46	10	φ(z	φ(z	PROPN
ejpam-4153	46	11	,	,	PUNCT
ejpam-4153	46	12	s	s	NOUN
ejpam-4153	46	13	,	,	PUNCT
ejpam-4153	46	14	v	v	NOUN
ejpam-4153	46	15	)	)	PUNCT
ejpam-4153	46	16	=	=	PUNCT
ejpam-4153	47	1	∞∑	∞∑	NUM
ejpam-4153	47	2	n=0	n=0	NUM
ejpam-4153	47	3	(	(	PUNCT
ejpam-4153	47	4	v	v	NOUN
ejpam-4153	47	5	+	+	NUM
ejpam-4153	47	6	n)−szn	n)−szn	NUM
ejpam-4153	47	7	,	,	PUNCT
ejpam-4153	47	8	(	(	PUNCT
ejpam-4153	47	9	4	4	NUM
ejpam-4153	47	10	)	)	PUNCT
ejpam-4153	47	11	where	where	SCONJ
ejpam-4153	47	12	|z|	|z|	VERB
ejpam-4153	47	13	<	<	X
ejpam-4153	47	14	1	1	NUM
ejpam-4153	47	15	,	,	PUNCT
ejpam-4153	47	16	v	v	ADP
ejpam-4153	47	17	̸=	̸=	PROPN
ejpam-4153	47	18	0,−1	0,−1	PROPN
ejpam-4153	47	19	,	,	PUNCT
ejpam-4153	47	20	..	..	PUNCT
ejpam-4153	47	21	and	and	CCONJ
ejpam-4153	47	22	is	be	AUX
ejpam-4153	47	23	continued	continue	VERB
ejpam-4153	47	24	analytically	analytically	ADV
ejpam-4153	47	25	by	by	ADP
ejpam-4153	47	26	its	its	PRON
ejpam-4153	47	27	integral	integral	ADJ
ejpam-4153	47	28	representation	representation	NOUN
ejpam-4153	47	29	given	give	VERB
ejpam-4153	47	30	by	by	ADP
ejpam-4153	47	31	φ(z	φ(z	PROPN
ejpam-4153	47	32	,	,	PUNCT
ejpam-4153	47	33	s	s	NOUN
ejpam-4153	47	34	,	,	PUNCT
ejpam-4153	47	35	v	v	NOUN
ejpam-4153	47	36	)	)	PUNCT
ejpam-4153	47	37	=	=	SYM
ejpam-4153	47	38	1	1	NUM
ejpam-4153	47	39	γ(s	γ(	NOUN
ejpam-4153	47	40	)	)	PUNCT
ejpam-4153	47	41	∫	∫	PROPN
ejpam-4153	48	1	∞	∞	PROPN
ejpam-4153	48	2	0	0	NUM
ejpam-4153	49	1	ts−1e−vt	ts−1e−vt	PRON
ejpam-4153	50	1	1−	1−	NUM
ejpam-4153	50	2	ze−t	ze−t	NOUN
ejpam-4153	50	3	dt	dt	NOUN
ejpam-4153	51	1	=	=	SYM
ejpam-4153	51	2	1	1	NUM
ejpam-4153	51	3	γ(s	γ(s	PROPN
ejpam-4153	51	4	)	)	PUNCT
ejpam-4153	51	5	∫	∫	PROPN
ejpam-4153	52	1	∞	∞	NUM
ejpam-4153	52	2	0	0	NUM
ejpam-4153	53	1	ts−1e−(v−1)t	ts−1e−(v−1)t	PROPN
ejpam-4153	53	2	et	et	NOUN
ejpam-4153	53	3	−	−	NOUN
ejpam-4153	53	4	z	z	NOUN
ejpam-4153	53	5	dt	dt	X
ejpam-4153	53	6	(	(	PUNCT
ejpam-4153	53	7	5	5	NUM
ejpam-4153	53	8	)	)	PUNCT
ejpam-4153	53	9	where	where	SCONJ
ejpam-4153	53	10	ℜ(v	ℜ(v	X
ejpam-4153	53	11	)	)	PUNCT
ejpam-4153	53	12	>	>	X
ejpam-4153	53	13	0	0	NUM
ejpam-4153	53	14	,	,	PUNCT
ejpam-4153	53	15	and	and	CCONJ
ejpam-4153	53	16	either	either	ADV
ejpam-4153	53	17	|z|≤	|z|≤	SYM
ejpam-4153	53	18	1	1	NUM
ejpam-4153	53	19	,	,	PUNCT
ejpam-4153	53	20	z	z	PROPN
ejpam-4153	53	21	̸=	̸=	PROPN
ejpam-4153	53	22	1,ℜ(s	1,ℜ(s	NUM
ejpam-4153	53	23	)	)	PUNCT
ejpam-4153	53	24	>	>	X
ejpam-4153	53	25	0	0	NUM
ejpam-4153	53	26	,	,	PUNCT
ejpam-4153	53	27	or	or	CCONJ
ejpam-4153	53	28	z	z	NOUN
ejpam-4153	53	29	=	=	SYM
ejpam-4153	53	30	1,ℜ(s	1,ℜ(s	NUM
ejpam-4153	53	31	)	)	PUNCT
ejpam-4153	53	32	>	>	X
ejpam-4153	54	1	1	1	X
ejpam-4153	54	2	.	.	PUNCT
ejpam-4153	54	3	r.	r.	PROPN
ejpam-4153	54	4	reynolds	reynolds	PROPN
ejpam-4153	54	5	,	,	PUNCT
ejpam-4153	54	6	a.	a.	PROPN
ejpam-4153	54	7	stauffer	stauffer	PROPN
ejpam-4153	54	8	/	/	SYM
ejpam-4153	54	9	eur	eur	PROPN
ejpam-4153	54	10	.	.	PUNCT
ejpam-4153	55	1	j.	j.	PROPN
ejpam-4153	55	2	pure	pure	PROPN
ejpam-4153	55	3	appl	appl	PROPN
ejpam-4153	55	4	.	.	PROPN
ejpam-4153	55	5	math	math	PROPN
ejpam-4153	55	6	,	,	PUNCT
ejpam-4153	55	7	15	15	NUM
ejpam-4153	55	8	(	(	PUNCT
ejpam-4153	55	9	1	1	NUM
ejpam-4153	55	10	)	)	PUNCT
ejpam-4153	55	11	(	(	PUNCT
ejpam-4153	55	12	2022	2022	NUM
ejpam-4153	55	13	)	)	PUNCT
ejpam-4153	55	14	,	,	PUNCT
ejpam-4153	55	15	229	229	NUM
ejpam-4153	55	16	-	-	SYM
ejpam-4153	55	17	237	237	NUM
ejpam-4153	55	18	231	231	NUM
ejpam-4153	55	19	4	4	NUM
ejpam-4153	55	20	.	.	PUNCT
ejpam-4153	55	21	infinite	infinite	ADJ
ejpam-4153	55	22	sum	sum	NOUN
ejpam-4153	55	23	of	of	ADP
ejpam-4153	55	24	the	the	DET
ejpam-4153	55	25	contour	contour	NOUN
ejpam-4153	55	26	integral	integral	ADJ
ejpam-4153	55	27	using	use	VERB
ejpam-4153	55	28	equation	equation	NOUN
ejpam-4153	55	29	(	(	PUNCT
ejpam-4153	55	30	2	2	NUM
ejpam-4153	55	31	)	)	PUNCT
ejpam-4153	55	32	and	and	CCONJ
ejpam-4153	55	33	replace	replace	VERB
ejpam-4153	55	34	y	y	PROPN
ejpam-4153	55	35	by	by	ADP
ejpam-4153	55	36	log(a	log(a	PROPN
ejpam-4153	55	37	)	)	PUNCT
ejpam-4153	56	1	+	+	NUM
ejpam-4153	56	2	iπ(y	iπ(y	X
ejpam-4153	57	1	+	+	CCONJ
ejpam-4153	57	2	1	1	X
ejpam-4153	57	3	)	)	PUNCT
ejpam-4153	57	4	then	then	ADV
ejpam-4153	57	5	multiply	multiply	VERB
ejpam-4153	57	6	both	both	DET
ejpam-4153	57	7	sides	side	NOUN
ejpam-4153	57	8	by	by	ADP
ejpam-4153	57	9	−iπ(−1)yeiπm(y+1	−iπ(−1)yeiπm(y+1	PROPN
ejpam-4153	57	10	)	)	PUNCT
ejpam-4153	57	11	followed	follow	VERB
ejpam-4153	57	12	by	by	ADP
ejpam-4153	57	13	taking	take	VERB
ejpam-4153	57	14	the	the	DET
ejpam-4153	57	15	infinite	infinite	ADJ
ejpam-4153	57	16	sum	sum	NOUN
ejpam-4153	57	17	over	over	ADP
ejpam-4153	57	18	y	y	PROPN
ejpam-4153	57	19	∈	∈	PROPN
ejpam-4153	58	1	[	[	X
ejpam-4153	58	2	0,∞	0,∞	NOUN
ejpam-4153	58	3	)	)	PUNCT
ejpam-4153	58	4	,	,	PUNCT
ejpam-4153	58	5	simplify	simplify	VERB
ejpam-4153	58	6	to	to	PART
ejpam-4153	58	7	get	get	VERB
ejpam-4153	58	8	(	(	PUNCT
ejpam-4153	58	9	6	6	NUM
ejpam-4153	58	10	)	)	PUNCT
ejpam-4153	58	11	−	−	PROPN
ejpam-4153	59	1	(	(	PUNCT
ejpam-4153	59	2	iπ)k+1eiπmφ	iπ)k+1eiπmφ	NOUN
ejpam-4153	59	3	(	(	PUNCT
ejpam-4153	59	4	−eimπ,−k	−eimπ,−k	PROPN
ejpam-4153	59	5	,	,	PUNCT
ejpam-4153	59	6	1−	1−	NUM
ejpam-4153	59	7	i	i	NUM
ejpam-4153	59	8	log(a	log(a	PROPN
ejpam-4153	59	9	)	)	PUNCT
ejpam-4153	59	10	π	π	PROPN
ejpam-4153	59	11	)	)	PUNCT
ejpam-4153	60	1	γ(k	γ(k	NOUN
ejpam-4153	60	2	+	+	CCONJ
ejpam-4153	60	3	1	1	X
ejpam-4153	60	4	)	)	PUNCT
ejpam-4153	60	5	=	=	SYM
ejpam-4153	61	1	−	−	PROPN
ejpam-4153	61	2	1	1	NUM
ejpam-4153	61	3	2πi	2πi	NOUN
ejpam-4153	61	4	∞∑	∞∑	NUM
ejpam-4153	61	5	y=0	y=0	NUM
ejpam-4153	61	6	∫	∫	PROPN
ejpam-4153	61	7	c	c	PROPN
ejpam-4153	61	8	iπ(−1)yw−k−1	iπ(−1)yw−k−1	PROPN
ejpam-4153	61	9	exp(w(log(a	exp(w(log(a	NUM
ejpam-4153	61	10	)	)	PUNCT
ejpam-4153	62	1	+	+	CCONJ
ejpam-4153	62	2	iπ(y	iπ(y	X
ejpam-4153	63	1	+	+	CCONJ
ejpam-4153	63	2	1	1	NUM
ejpam-4153	63	3	)	)	PUNCT
ejpam-4153	63	4	)	)	PUNCT
ejpam-4153	64	1	+	+	CCONJ
ejpam-4153	64	2	iπm(y	iπm(y	X
ejpam-4153	65	1	+	+	NUM
ejpam-4153	65	2	1))dw	1))dw	PROPN
ejpam-4153	65	3	=	=	SYM
ejpam-4153	65	4	−	−	PROPN
ejpam-4153	65	5	1	1	NUM
ejpam-4153	65	6	2πi	2πi	NOUN
ejpam-4153	65	7	∫	∫	PROPN
ejpam-4153	65	8	c	c	NOUN
ejpam-4153	65	9	∞∑	∞∑	NUM
ejpam-4153	65	10	y=0	y=0	NOUN
ejpam-4153	65	11	iπ(−1)yw−k−1	iπ(−1)yw−k−1	PROPN
ejpam-4153	65	12	exp(w(log(a	exp(w(log(a	NUM
ejpam-4153	65	13	)	)	PUNCT
ejpam-4153	66	1	+	+	NUM
ejpam-4153	66	2	iπ(y	iπ(y	X
ejpam-4153	67	1	+	+	CCONJ
ejpam-4153	67	2	1	1	NUM
ejpam-4153	67	3	)	)	PUNCT
ejpam-4153	67	4	)	)	PUNCT
ejpam-4153	68	1	+	+	CCONJ
ejpam-4153	68	2	iπm(y	iπm(y	X
ejpam-4153	69	1	+	+	NUM
ejpam-4153	69	2	1))dw	1))dw	NOUN
ejpam-4153	69	3	=	=	SYM
ejpam-4153	69	4	1	1	NUM
ejpam-4153	69	5	2πi	2πi	NOUN
ejpam-4153	69	6	∫	∫	PROPN
ejpam-4153	69	7	c	c	NOUN
ejpam-4153	69	8	(	(	PUNCT
ejpam-4153	69	9	1	1	NUM
ejpam-4153	69	10	2	2	NUM
ejpam-4153	69	11	πaww−k−1	πaww−k−1	PROPN
ejpam-4153	69	12	tan	tan	PROPN
ejpam-4153	69	13	(	(	PUNCT
ejpam-4153	69	14	1	1	NUM
ejpam-4153	69	15	2	2	NUM
ejpam-4153	69	16	π(m+	π(m+	X
ejpam-4153	69	17	w	w	NOUN
ejpam-4153	69	18	)	)	PUNCT
ejpam-4153	69	19	)	)	PUNCT
ejpam-4153	70	1	−	−	NOUN
ejpam-4153	70	2	1	1	NUM
ejpam-4153	70	3	2	2	NUM
ejpam-4153	71	1	iπaww−k−1	iπaww−k−1	PROPN
ejpam-4153	71	2	)	)	PUNCT
ejpam-4153	71	3	dw	dw	PROPN
ejpam-4153	71	4	.	.	PROPN
ejpam-4153	71	5	from	from	ADP
ejpam-4153	71	6	equation	equation	NOUN
ejpam-4153	71	7	(	(	PUNCT
ejpam-4153	71	8	1.232.1	1.232.1	NUM
ejpam-4153	71	9	)	)	PUNCT
ejpam-4153	71	10	in	in	ADP
ejpam-4153	71	11	[	[	X
ejpam-4153	71	12	6	6	NUM
ejpam-4153	71	13	]	]	PUNCT
ejpam-4153	71	14	,	,	PUNCT
ejpam-4153	71	15	where	where	SCONJ
ejpam-4153	71	16	ℑ(m+	ℑ(m+	NUM
ejpam-4153	71	17	w	w	NOUN
ejpam-4153	71	18	)	)	PUNCT
ejpam-4153	71	19	>	>	X
ejpam-4153	71	20	0	0	PUNCT
ejpam-4153	72	1	in	in	ADP
ejpam-4153	72	2	order	order	NOUN
ejpam-4153	72	3	for	for	SCONJ
ejpam-4153	72	4	the	the	DET
ejpam-4153	72	5	sum	sum	NOUN
ejpam-4153	72	6	to	to	PART
ejpam-4153	72	7	converge	converge	VERB
ejpam-4153	72	8	.	.	PUNCT
ejpam-4153	73	1	5	5	X
ejpam-4153	73	2	.	.	X
ejpam-4153	73	3	the	the	DET
ejpam-4153	73	4	additional	additional	ADJ
ejpam-4153	73	5	contour	contour	NOUN
ejpam-4153	73	6	integral	integral	ADJ
ejpam-4153	73	7	using	use	VERB
ejpam-4153	73	8	equation	equation	NOUN
ejpam-4153	73	9	(	(	PUNCT
ejpam-4153	73	10	2	2	NUM
ejpam-4153	73	11	)	)	PUNCT
ejpam-4153	73	12	and	and	CCONJ
ejpam-4153	73	13	replace	replace	VERB
ejpam-4153	73	14	y	y	PROPN
ejpam-4153	73	15	by	by	ADP
ejpam-4153	73	16	log(a	log(a	PROPN
ejpam-4153	73	17	)	)	PUNCT
ejpam-4153	73	18	followed	follow	VERB
ejpam-4153	73	19	by	by	ADP
ejpam-4153	73	20	multiplying	multiply	VERB
ejpam-4153	73	21	both	both	DET
ejpam-4153	73	22	sides	side	NOUN
ejpam-4153	73	23	by	by	ADP
ejpam-4153	73	24	π	π	PROPN
ejpam-4153	73	25	2i	2i	NOUN
ejpam-4153	73	26	to	to	PART
ejpam-4153	73	27	get	get	VERB
ejpam-4153	73	28	−	−	PROPN
ejpam-4153	73	29	iπ	iπ	ADJ
ejpam-4153	73	30	log	log	NOUN
ejpam-4153	73	31	k(a	k(a	NOUN
ejpam-4153	73	32	)	)	PUNCT
ejpam-4153	73	33	2γ(k	2γ(k	NUM
ejpam-4153	73	34	+	+	CCONJ
ejpam-4153	73	35	1	1	X
ejpam-4153	73	36	)	)	PUNCT
ejpam-4153	73	37	=	=	SYM
ejpam-4153	74	1	−	−	PROPN
ejpam-4153	74	2	1	1	NUM
ejpam-4153	74	3	2πi	2πi	NOUN
ejpam-4153	74	4	∫	∫	PROPN
ejpam-4153	74	5	c	c	NOUN
ejpam-4153	74	6	1	1	NUM
ejpam-4153	74	7	2	2	NUM
ejpam-4153	74	8	iπaww−k−1dw	iπaww−k−1dw	NOUN
ejpam-4153	74	9	,	,	PUNCT
ejpam-4153	74	10	(	(	PUNCT
ejpam-4153	74	11	7	7	X
ejpam-4153	74	12	)	)	PUNCT
ejpam-4153	74	13	6	6	NUM
ejpam-4153	74	14	.	.	PUNCT
ejpam-4153	75	1	a	a	DET
ejpam-4153	75	2	note	note	NOUN
ejpam-4153	75	3	on	on	ADP
ejpam-4153	75	4	the	the	DET
ejpam-4153	75	5	hypergeometric	hypergeometric	ADJ
ejpam-4153	75	6	function	function	NOUN
ejpam-4153	75	7	in	in	ADP
ejpam-4153	75	8	this	this	DET
ejpam-4153	75	9	manuscript	manuscript	NOUN
ejpam-4153	75	10	we	we	PRON
ejpam-4153	75	11	will	will	AUX
ejpam-4153	75	12	derive	derive	VERB
ejpam-4153	75	13	definite	definite	ADJ
ejpam-4153	75	14	integrals	integral	NOUN
ejpam-4153	75	15	in	in	ADP
ejpam-4153	75	16	terms	term	NOUN
ejpam-4153	75	17	of	of	ADP
ejpam-4153	75	18	the	the	DET
ejpam-4153	75	19	lerch	lerch	PROPN
ejpam-4153	75	20	function	function	NOUN
ejpam-4153	75	21	which	which	PRON
ejpam-4153	75	22	simplify	simplify	VERB
ejpam-4153	75	23	to	to	ADP
ejpam-4153	75	24	the	the	DET
ejpam-4153	75	25	hypergeometric	hypergeometric	ADJ
ejpam-4153	75	26	function	function	NOUN
ejpam-4153	75	27	by	by	ADP
ejpam-4153	75	28	equation	equation	NOUN
ejpam-4153	75	29	(	(	PUNCT
ejpam-4153	75	30	1.11.10	1.11.10	NUM
ejpam-4153	75	31	)	)	PUNCT
ejpam-4153	75	32	in	in	ADP
ejpam-4153	75	33	[	[	X
ejpam-4153	75	34	4	4	NUM
ejpam-4153	75	35	]	]	PUNCT
ejpam-4153	75	36	.	.	PUNCT
ejpam-4153	76	1	φ(z	φ(z	PROPN
ejpam-4153	76	2	,	,	PUNCT
ejpam-4153	76	3	1	1	NUM
ejpam-4153	76	4	,	,	PUNCT
ejpam-4153	76	5	v	v	NOUN
ejpam-4153	76	6	)	)	PUNCT
ejpam-4153	76	7	=	=	PUNCT
ejpam-4153	77	1	∞∑	∞∑	NUM
ejpam-4153	77	2	n=0	n=0	NUM
ejpam-4153	77	3	zn	zn	PROPN
ejpam-4153	77	4	n+	n+	NOUN
ejpam-4153	77	5	v	v	NOUN
ejpam-4153	77	6	=	=	SYM
ejpam-4153	77	7	v−1	v−1	PROPN
ejpam-4153	77	8	2f1(1	2f1(1	NUM
ejpam-4153	77	9	,	,	PUNCT
ejpam-4153	77	10	v	v	NOUN
ejpam-4153	77	11	,	,	PUNCT
ejpam-4153	77	12	1	1	NUM
ejpam-4153	77	13	+	+	SYM
ejpam-4153	77	14	v	v	ADJ
ejpam-4153	77	15	;	;	PUNCT
ejpam-4153	77	16	z	z	NOUN
ejpam-4153	77	17	)	)	PUNCT
ejpam-4153	77	18	.	.	PUNCT
ejpam-4153	78	1	(	(	PUNCT
ejpam-4153	78	2	8)	8)	NUM
ejpam-4153	78	3	7	7	NUM
ejpam-4153	78	4	.	.	PUNCT
ejpam-4153	79	1	the	the	DET
ejpam-4153	79	2	definite	definite	ADJ
ejpam-4153	79	3	integral	integral	ADJ
ejpam-4153	79	4	in	in	ADP
ejpam-4153	79	5	terms	term	NOUN
ejpam-4153	79	6	of	of	ADP
ejpam-4153	79	7	the	the	DET
ejpam-4153	79	8	lerch	lerch	PROPN
ejpam-4153	79	9	function	function	PROPN
ejpam-4153	79	10	since	since	SCONJ
ejpam-4153	79	11	the	the	DET
ejpam-4153	79	12	right	right	ADJ
ejpam-4153	79	13	-	-	PUNCT
ejpam-4153	79	14	hand	hand	NOUN
ejpam-4153	79	15	sides	side	NOUN
ejpam-4153	79	16	of	of	ADP
ejpam-4153	79	17	equations	equation	NOUN
ejpam-4153	79	18	(	(	PUNCT
ejpam-4153	79	19	3	3	NUM
ejpam-4153	79	20	)	)	PUNCT
ejpam-4153	79	21	,	,	PUNCT
ejpam-4153	79	22	(	(	PUNCT
ejpam-4153	79	23	6	6	NUM
ejpam-4153	79	24	)	)	PUNCT
ejpam-4153	79	25	and	and	CCONJ
ejpam-4153	79	26	(	(	PUNCT
ejpam-4153	79	27	7	7	X
ejpam-4153	79	28	)	)	PUNCT
ejpam-4153	79	29	are	be	AUX
ejpam-4153	79	30	equal	equal	ADJ
ejpam-4153	79	31	we	we	PRON
ejpam-4153	79	32	may	may	AUX
ejpam-4153	79	33	equate	equate	VERB
ejpam-4153	79	34	the	the	DET
ejpam-4153	79	35	left	left	ADJ
ejpam-4153	79	36	hand	hand	NOUN
ejpam-4153	79	37	sides	side	NOUN
ejpam-4153	79	38	simplify	simplify	VERB
ejpam-4153	79	39	to	to	PART
ejpam-4153	79	40	get	get	VERB
ejpam-4153	79	41	r.	r.	PROPN
ejpam-4153	79	42	reynolds	reynolds	PROPN
ejpam-4153	79	43	,	,	PUNCT
ejpam-4153	79	44	a.	a.	PROPN
ejpam-4153	79	45	stauffer	stauffer	PROPN
ejpam-4153	79	46	/	/	SYM
ejpam-4153	79	47	eur	eur	PROPN
ejpam-4153	79	48	.	.	PUNCT
ejpam-4153	80	1	j.	j.	PROPN
ejpam-4153	80	2	pure	pure	PROPN
ejpam-4153	80	3	appl	appl	PROPN
ejpam-4153	80	4	.	.	PROPN
ejpam-4153	80	5	math	math	PROPN
ejpam-4153	80	6	,	,	PUNCT
ejpam-4153	80	7	15	15	NUM
ejpam-4153	80	8	(	(	PUNCT
ejpam-4153	80	9	1	1	NUM
ejpam-4153	80	10	)	)	PUNCT
ejpam-4153	80	11	(	(	PUNCT
ejpam-4153	80	12	2022	2022	NUM
ejpam-4153	80	13	)	)	PUNCT
ejpam-4153	80	14	,	,	PUNCT
ejpam-4153	80	15	229	229	NUM
ejpam-4153	80	16	-	-	SYM
ejpam-4153	80	17	237	237	NUM
ejpam-4153	80	18	232∫	232∫	NUM
ejpam-4153	80	19	1	1	NUM
ejpam-4153	80	20	0	0	NUM
ejpam-4153	80	21	xm	xm	PROPN
ejpam-4153	81	1	logk(ax)−	logk(ax)−	PROPN
ejpam-4153	81	2	x−m	x−m	PROPN
ejpam-4153	81	3	logk	logk	PROPN
ejpam-4153	81	4	(	(	PUNCT
ejpam-4153	81	5	a	a	DET
ejpam-4153	81	6	x	x	X
ejpam-4153	81	7	)	)	PUNCT
ejpam-4153	82	1	x2	x2	NOUN
ejpam-4153	82	2	−	−	PROPN
ejpam-4153	83	1	1	1	NUM
ejpam-4153	83	2	dx	dx	NOUN
ejpam-4153	83	3	=	=	SYM
ejpam-4153	83	4	1	1	NUM
ejpam-4153	83	5	2	2	NUM
ejpam-4153	83	6	iπ	iπ	NOUN
ejpam-4153	83	7	(	(	PUNCT
ejpam-4153	83	8	logk(a)−	logk(a)−	PROPN
ejpam-4153	83	9	2(iπ)keiπmφ	2(iπ)keiπmφ	PROPN
ejpam-4153	83	10	(	(	PUNCT
ejpam-4153	83	11	−eimπ,−k	−eimπ,−k	PROPN
ejpam-4153	83	12	,	,	PUNCT
ejpam-4153	83	13	1−	1−	NUM
ejpam-4153	83	14	i	i	NUM
ejpam-4153	83	15	log(a	log(a	PROPN
ejpam-4153	83	16	)	)	PUNCT
ejpam-4153	83	17	π	π	NOUN
ejpam-4153	83	18	)	)	PUNCT
ejpam-4153	83	19	)	)	PUNCT
ejpam-4153	83	20	,	,	PUNCT
ejpam-4153	83	21	(	(	PUNCT
ejpam-4153	83	22	9	9	X
ejpam-4153	83	23	)	)	PUNCT
ejpam-4153	83	24	where	where	SCONJ
ejpam-4153	83	25	−1	−1	NOUN
ejpam-4153	83	26	<	<	X
ejpam-4153	83	27	ℜ(m	ℜ(m	NOUN
ejpam-4153	83	28	)	)	PUNCT
ejpam-4153	83	29	<	<	X
ejpam-4153	83	30	1	1	NUM
ejpam-4153	83	31	.	.	NOUN
ejpam-4153	83	32	8	8	NUM
ejpam-4153	83	33	.	.	PUNCT
ejpam-4153	84	1	derivation	derivation	NOUN
ejpam-4153	84	2	of	of	ADP
ejpam-4153	84	3	entry	entry	NOUN
ejpam-4153	84	4	4.282.13	4.282.13	NUM
ejpam-4153	84	5	in	in	ADP
ejpam-4153	84	6	[	[	X
ejpam-4153	84	7	6	6	NUM
ejpam-4153	84	8	]	]	PUNCT
ejpam-4153	84	9	using	use	VERB
ejpam-4153	84	10	equation	equation	NOUN
ejpam-4153	84	11	(	(	PUNCT
ejpam-4153	84	12	9	9	NUM
ejpam-4153	84	13	)	)	PUNCT
ejpam-4153	84	14	first	first	ADV
ejpam-4153	84	15	replacing	replace	VERB
ejpam-4153	84	16	a	a	PRON
ejpam-4153	84	17	by	by	ADP
ejpam-4153	84	18	eqi	eqi	NOUN
ejpam-4153	84	19	then	then	ADV
ejpam-4153	84	20	setting	set	VERB
ejpam-4153	84	21	k	k	PROPN
ejpam-4153	84	22	=	=	PUNCT
ejpam-4153	84	23	−1	−1	NOUN
ejpam-4153	84	24	,	,	PUNCT
ejpam-4153	84	25	we	we	PRON
ejpam-4153	84	26	then	then	ADV
ejpam-4153	84	27	replace	replace	VERB
ejpam-4153	84	28	m	m	PRON
ejpam-4153	84	29	by	by	ADP
ejpam-4153	84	30	p	p	NOUN
ejpam-4153	84	31	and	and	CCONJ
ejpam-4153	84	32	−p	−p	ADJ
ejpam-4153	84	33	to	to	PART
ejpam-4153	84	34	get	get	VERB
ejpam-4153	84	35	a	a	DET
ejpam-4153	84	36	second	second	ADJ
ejpam-4153	84	37	equation	equation	NOUN
ejpam-4153	84	38	,	,	PUNCT
ejpam-4153	84	39	then	then	ADV
ejpam-4153	84	40	taking	take	VERB
ejpam-4153	84	41	the	the	DET
ejpam-4153	84	42	difference	difference	NOUN
ejpam-4153	84	43	of	of	ADP
ejpam-4153	84	44	these	these	DET
ejpam-4153	84	45	two	two	NUM
ejpam-4153	84	46	equations	equation	NOUN
ejpam-4153	84	47	simplify	simplify	VERB
ejpam-4153	84	48	we	we	PRON
ejpam-4153	84	49	get	get	VERB
ejpam-4153	84	50	∫	∫	PROPN
ejpam-4153	84	51	1	1	NUM
ejpam-4153	84	52	0	0	NUM
ejpam-4153	85	1	(	(	PUNCT
ejpam-4153	85	2	xp	xp	INTJ
ejpam-4153	85	3	−	−	PROPN
ejpam-4153	85	4	x−p	x−p	PROPN
ejpam-4153	85	5	)	)	PUNCT
ejpam-4153	85	6	(	(	PUNCT
ejpam-4153	85	7	x2	x2	INTJ
ejpam-4153	85	8	−	−	PROPN
ejpam-4153	85	9	1	1	NUM
ejpam-4153	85	10	)	)	PUNCT
ejpam-4153	85	11	(	(	PUNCT
ejpam-4153	85	12	q2	q2	NOUN
ejpam-4153	85	13	+	+	CCONJ
ejpam-4153	85	14	log2(x	log2(x	NOUN
ejpam-4153	85	15	)	)	PUNCT
ejpam-4153	85	16	)	)	PUNCT
ejpam-4153	85	17	dx	dx	PROPN
ejpam-4153	85	18	=	=	SYM
ejpam-4153	86	1	ie−iπp	ie−iπp	PROPN
ejpam-4153	86	2	2q	2q	NUM
ejpam-4153	86	3	(	(	PUNCT
ejpam-4153	86	4	φ	φ	PROPN
ejpam-4153	86	5	(	(	PUNCT
ejpam-4153	86	6	−e−ipπ	−e−ipπ	PROPN
ejpam-4153	86	7	,	,	PUNCT
ejpam-4153	86	8	1	1	NUM
ejpam-4153	86	9	,	,	PUNCT
ejpam-4153	86	10	q	q	NOUN
ejpam-4153	87	1	+	+	NUM
ejpam-4153	87	2	π	π	PROPN
ejpam-4153	87	3	π	π	PROPN
ejpam-4153	87	4	)	)	PUNCT
ejpam-4153	87	5	−	−	ADP
ejpam-4153	87	6	e2iπpφ	e2iπpφ	ADV
ejpam-4153	87	7	(	(	PUNCT
ejpam-4153	87	8	−eipπ	−eipπ	NOUN
ejpam-4153	87	9	,	,	PUNCT
ejpam-4153	87	10	1	1	NUM
ejpam-4153	87	11	,	,	PUNCT
ejpam-4153	87	12	q	q	NOUN
ejpam-4153	88	1	+	+	NUM
ejpam-4153	88	2	π	π	PROPN
ejpam-4153	88	3	π	π	NOUN
ejpam-4153	88	4	)	)	PUNCT
ejpam-4153	88	5	)	)	PUNCT
ejpam-4153	89	1	=	=	PUNCT
ejpam-4153	90	1	iπe−iπp	iπe−iπp	PRON
ejpam-4153	90	2	2q(q	2q(q	NUM
ejpam-4153	90	3	+	+	CCONJ
ejpam-4153	90	4	π	π	X
ejpam-4153	90	5	)	)	PUNCT
ejpam-4153	90	6	(	(	PUNCT
ejpam-4153	90	7	2f1	2f1	NUM
ejpam-4153	90	8	(	(	PUNCT
ejpam-4153	90	9	1	1	NUM
ejpam-4153	90	10	,	,	PUNCT
ejpam-4153	90	11	q	q	NOUN
ejpam-4153	91	1	+	+	NOUN
ejpam-4153	91	2	π	π	PROPN
ejpam-4153	91	3	π	π	X
ejpam-4153	91	4	;	;	PUNCT
ejpam-4153	91	5	q	q	PROPN
ejpam-4153	91	6	π	π	X
ejpam-4153	91	7	+	+	CCONJ
ejpam-4153	91	8	2;−e−ipπ	2;−e−ipπ	NUM
ejpam-4153	91	9	)	)	PUNCT
ejpam-4153	92	1	−	−	PROPN
ejpam-4153	92	2	e2iπp	e2iπp	NOUN
ejpam-4153	92	3	2f1	2f1	NUM
ejpam-4153	92	4	(	(	PUNCT
ejpam-4153	92	5	1	1	NUM
ejpam-4153	92	6	,	,	PUNCT
ejpam-4153	92	7	q	q	NOUN
ejpam-4153	93	1	+	+	NOUN
ejpam-4153	93	2	π	π	PROPN
ejpam-4153	93	3	π	π	X
ejpam-4153	93	4	;	;	PUNCT
ejpam-4153	93	5	q	q	PROPN
ejpam-4153	93	6	π	π	X
ejpam-4153	93	7	+	+	CCONJ
ejpam-4153	93	8	2;−eipπ	2;−eipπ	NUM
ejpam-4153	93	9	)	)	PUNCT
ejpam-4153	93	10	)	)	PUNCT
ejpam-4153	93	11	.	.	PUNCT
ejpam-4153	94	1	(	(	PUNCT
ejpam-4153	94	2	10	10	NUM
ejpam-4153	94	3	)	)	PUNCT
ejpam-4153	94	4	this	this	DET
ejpam-4153	94	5	solution	solution	NOUN
ejpam-4153	94	6	represents	represent	VERB
ejpam-4153	94	7	the	the	DET
ejpam-4153	94	8	analytic	analytic	ADJ
ejpam-4153	94	9	continuation	continuation	NOUN
ejpam-4153	94	10	of	of	ADP
ejpam-4153	94	11	the	the	DET
ejpam-4153	94	12	integral	integral	ADJ
ejpam-4153	94	13	in	in	ADP
ejpam-4153	94	14	[	[	X
ejpam-4153	94	15	6	6	NUM
ejpam-4153	94	16	]	]	PUNCT
ejpam-4153	94	17	.	.	PUNCT
ejpam-4153	95	1	the	the	DET
ejpam-4153	95	2	solution	solution	NOUN
ejpam-4153	95	3	listed	list	VERB
ejpam-4153	95	4	in	in	ADP
ejpam-4153	95	5	[	[	X
ejpam-4153	95	6	6	6	NUM
ejpam-4153	95	7	]	]	PUNCT
ejpam-4153	95	8	is	be	AUX
ejpam-4153	95	9	slowly	slowly	ADV
ejpam-4153	95	10	convergent	convergent	ADJ
ejpam-4153	95	11	and	and	CCONJ
ejpam-4153	95	12	limited	limit	VERB
ejpam-4153	95	13	in	in	ADP
ejpam-4153	95	14	the	the	DET
ejpam-4153	95	15	variable	variable	ADJ
ejpam-4153	95	16	domain	domain	NOUN
ejpam-4153	95	17	of	of	ADP
ejpam-4153	95	18	evaluation	evaluation	NOUN
ejpam-4153	95	19	.	.	PUNCT
ejpam-4153	96	1	9	9	X
ejpam-4153	96	2	.	.	X
ejpam-4153	96	3	derivation	derivation	NOUN
ejpam-4153	96	4	of	of	ADP
ejpam-4153	96	5	entry	entry	NOUN
ejpam-4153	96	6	4.282.4	4.282.4	NUM
ejpam-4153	96	7	in	in	ADP
ejpam-4153	96	8	[	[	X
ejpam-4153	96	9	6	6	NUM
ejpam-4153	96	10	]	]	PUNCT
ejpam-4153	96	11	in	in	ADP
ejpam-4153	96	12	this	this	DET
ejpam-4153	96	13	section	section	NOUN
ejpam-4153	96	14	we	we	PRON
ejpam-4153	96	15	will	will	AUX
ejpam-4153	96	16	use	use	VERB
ejpam-4153	96	17	the	the	DET
ejpam-4153	96	18	formula	formula	NOUN
ejpam-4153	96	19	2f1(1	2f1(1	NUM
ejpam-4153	96	20	,	,	PUNCT
ejpam-4153	96	21	2	2	NUM
ejpam-4153	96	22	;	;	PUNCT
ejpam-4153	96	23	3	3	NUM
ejpam-4153	96	24	;	;	PUNCT
ejpam-4153	96	25	z	z	X
ejpam-4153	96	26	)	)	PUNCT
ejpam-4153	96	27	=	=	SYM
ejpam-4153	96	28	−2(z+log(1−z	−2(z+log(1−z	NUM
ejpam-4153	96	29	)	)	PUNCT
ejpam-4153	96	30	)	)	PUNCT
ejpam-4153	97	1	z2	z2	NOUN
ejpam-4153	97	2	where	where	SCONJ
ejpam-4153	97	3	z	z	NOUN
ejpam-4153	97	4	=	=	SYM
ejpam-4153	97	5	−1	−1	NOUN
ejpam-4153	97	6	,	,	PUNCT
ejpam-4153	97	7	which	which	PRON
ejpam-4153	97	8	is	be	AUX
ejpam-4153	97	9	derived	derive	VERB
ejpam-4153	97	10	from	from	ADP
ejpam-4153	97	11	section	section	NOUN
ejpam-4153	97	12	(	(	PUNCT
ejpam-4153	97	13	15.2	15.2	NUM
ejpam-4153	97	14	)	)	PUNCT
ejpam-4153	97	15	(	(	PUNCT
ejpam-4153	97	16	relations	relation	NOUN
ejpam-4153	97	17	between	between	ADP
ejpam-4153	97	18	contiguous	contiguous	ADJ
ejpam-4153	97	19	functions	function	NOUN
ejpam-4153	97	20	)	)	PUNCT
ejpam-4153	97	21	in	in	ADP
ejpam-4153	97	22	[	[	X
ejpam-4153	97	23	1	1	NUM
ejpam-4153	97	24	]	]	PUNCT
ejpam-4153	97	25	.	.	PUNCT
ejpam-4153	98	1	using	use	VERB
ejpam-4153	98	2	equation	equation	NOUN
ejpam-4153	98	3	(	(	PUNCT
ejpam-4153	98	4	10	10	NUM
ejpam-4153	98	5	)	)	PUNCT
ejpam-4153	98	6	then	then	ADV
ejpam-4153	98	7	taking	take	VERB
ejpam-4153	98	8	the	the	DET
ejpam-4153	98	9	first	first	ADJ
ejpam-4153	98	10	partial	partial	ADJ
ejpam-4153	98	11	derivative	derivative	NOUN
ejpam-4153	98	12	with	with	ADP
ejpam-4153	98	13	respect	respect	NOUN
ejpam-4153	98	14	to	to	ADP
ejpam-4153	98	15	p	p	NOUN
ejpam-4153	98	16	followed	follow	VERB
ejpam-4153	98	17	by	by	ADP
ejpam-4153	98	18	setting	set	VERB
ejpam-4153	98	19	q	q	X
ejpam-4153	98	20	=	=	PUNCT
ejpam-4153	98	21	π	π	X
ejpam-4153	98	22	and	and	CCONJ
ejpam-4153	98	23	p	p	NOUN
ejpam-4153	98	24	=	=	NOUN
ejpam-4153	98	25	0	0	NUM
ejpam-4153	98	26	we	we	PRON
ejpam-4153	98	27	get∫	get∫	VERB
ejpam-4153	98	28	1	1	NUM
ejpam-4153	98	29	0	0	NUM
ejpam-4153	98	30	log(x	log(x	NUM
ejpam-4153	98	31	)	)	PUNCT
ejpam-4153	98	32	(	(	PUNCT
ejpam-4153	98	33	x2	x2	INTJ
ejpam-4153	98	34	−	−	PROPN
ejpam-4153	98	35	1	1	NUM
ejpam-4153	98	36	)	)	PUNCT
ejpam-4153	98	37	(	(	PUNCT
ejpam-4153	98	38	log2(x	log2(x	X
ejpam-4153	98	39	)	)	PUNCT
ejpam-4153	99	1	+	+	CCONJ
ejpam-4153	99	2	π2	π2	ADJ
ejpam-4153	99	3	)	)	PUNCT
ejpam-4153	99	4	dx	dx	PROPN
ejpam-4153	99	5	=	=	SYM
ejpam-4153	99	6	1	1	NUM
ejpam-4153	99	7	4	4	NUM
ejpam-4153	99	8	(	(	PUNCT
ejpam-4153	99	9	log(4)−	log(4)−	NOUN
ejpam-4153	99	10	1	1	NUM
ejpam-4153	99	11	)	)	PUNCT
ejpam-4153	99	12	.	.	PUNCT
ejpam-4153	100	1	(	(	PUNCT
ejpam-4153	100	2	11	11	NUM
ejpam-4153	100	3	)	)	PUNCT
ejpam-4153	100	4	10	10	NUM
ejpam-4153	100	5	.	.	PUNCT
ejpam-4153	101	1	derivation	derivation	NOUN
ejpam-4153	101	2	of	of	ADP
ejpam-4153	101	3	entry	entry	NOUN
ejpam-4153	101	4	4.282.8	4.282.8	NUM
ejpam-4153	101	5	in	in	ADP
ejpam-4153	101	6	[	[	X
ejpam-4153	101	7	6	6	NUM
ejpam-4153	101	8	]	]	PUNCT
ejpam-4153	101	9	in	in	ADP
ejpam-4153	101	10	this	this	DET
ejpam-4153	101	11	section	section	NOUN
ejpam-4153	101	12	we	we	PRON
ejpam-4153	101	13	will	will	AUX
ejpam-4153	101	14	use	use	VERB
ejpam-4153	101	15	the	the	DET
ejpam-4153	101	16	formula	formula	NOUN
ejpam-4153	101	17	2f1	2f1	NUM
ejpam-4153	101	18	(	(	PUNCT
ejpam-4153	101	19	1	1	NUM
ejpam-4153	101	20	,	,	PUNCT
ejpam-4153	101	21	32	32	NUM
ejpam-4153	101	22	;	;	PUNCT
ejpam-4153	101	23	5	5	NUM
ejpam-4153	101	24	2	2	NUM
ejpam-4153	101	25	;	;	PUNCT
ejpam-4153	101	26	z	z	X
ejpam-4153	101	27	)	)	PUNCT
ejpam-4153	102	1	=	=	PUNCT
ejpam-4153	102	2	−3	−3	PROPN
ejpam-4153	102	3	z+	z+	NUM
ejpam-4153	102	4	3	3	NUM
ejpam-4153	102	5	tanh−1	tanh−1	PROPN
ejpam-4153	102	6	(	(	PUNCT
ejpam-4153	102	7	√	√	PROPN
ejpam-4153	102	8	z	z	NOUN
ejpam-4153	102	9	)	)	PUNCT
ejpam-4153	102	10	z3/2	z3/2	NOUN
ejpam-4153	102	11	where	where	SCONJ
ejpam-4153	102	12	z	z	NOUN
ejpam-4153	102	13	=	=	SYM
ejpam-4153	102	14	−1	−1	NOUN
ejpam-4153	102	15	,	,	PUNCT
ejpam-4153	102	16	which	which	PRON
ejpam-4153	102	17	is	be	AUX
ejpam-4153	102	18	derived	derive	VERB
ejpam-4153	102	19	from	from	ADP
ejpam-4153	102	20	section	section	NOUN
ejpam-4153	102	21	(	(	PUNCT
ejpam-4153	102	22	15.2	15.2	NUM
ejpam-4153	102	23	)	)	PUNCT
ejpam-4153	102	24	(	(	PUNCT
ejpam-4153	102	25	relations	relation	NOUN
ejpam-4153	102	26	between	between	ADP
ejpam-4153	102	27	contiguous	contiguous	ADJ
ejpam-4153	102	28	functions	function	NOUN
ejpam-4153	102	29	)	)	PUNCT
ejpam-4153	102	30	in	in	ADP
ejpam-4153	102	31	[	[	X
ejpam-4153	102	32	1	1	NUM
ejpam-4153	102	33	]	]	PUNCT
ejpam-4153	102	34	.	.	PUNCT
ejpam-4153	103	1	using	use	VERB
ejpam-4153	103	2	equation	equation	NOUN
ejpam-4153	103	3	(	(	PUNCT
ejpam-4153	103	4	10	10	NUM
ejpam-4153	103	5	)	)	PUNCT
ejpam-4153	103	6	then	then	ADV
ejpam-4153	103	7	taking	take	VERB
ejpam-4153	103	8	the	the	DET
ejpam-4153	103	9	first	first	ADJ
ejpam-4153	103	10	partial	partial	ADJ
ejpam-4153	103	11	derivative	derivative	NOUN
ejpam-4153	103	12	with	with	ADP
ejpam-4153	103	13	respect	respect	NOUN
ejpam-4153	103	14	to	to	ADP
ejpam-4153	103	15	p	p	NOUN
ejpam-4153	103	16	followed	follow	VERB
ejpam-4153	103	17	by	by	ADP
ejpam-4153	103	18	setting	set	VERB
ejpam-4153	103	19	q	q	PROPN
ejpam-4153	103	20	=	=	PUNCT
ejpam-4153	103	21	π/2	π/2	NUM
ejpam-4153	103	22	and	and	CCONJ
ejpam-4153	103	23	p	p	X
ejpam-4153	104	1	=	=	NOUN
ejpam-4153	104	2	0	0	NUM
ejpam-4153	104	3	we	we	PRON
ejpam-4153	104	4	get∫	get∫	VERB
ejpam-4153	104	5	1	1	NUM
ejpam-4153	104	6	0	0	NUM
ejpam-4153	104	7	log(x	log(x	NUM
ejpam-4153	104	8	)	)	PUNCT
ejpam-4153	104	9	(	(	PUNCT
ejpam-4153	104	10	x2	x2	INTJ
ejpam-4153	104	11	−	−	PROPN
ejpam-4153	104	12	1	1	NUM
ejpam-4153	104	13	)	)	PUNCT
ejpam-4153	104	14	(	(	PUNCT
ejpam-4153	104	15	4	4	NUM
ejpam-4153	104	16	log2(x	log2(x	NOUN
ejpam-4153	104	17	)	)	PUNCT
ejpam-4153	105	1	+	+	CCONJ
ejpam-4153	105	2	π2	π2	ADJ
ejpam-4153	105	3	)	)	PUNCT
ejpam-4153	105	4	dx	dx	PROPN
ejpam-4153	106	1	=	=	SYM
ejpam-4153	106	2	1	1	NUM
ejpam-4153	106	3	16	16	NUM
ejpam-4153	106	4	(	(	PUNCT
ejpam-4153	106	5	π	π	PROPN
ejpam-4153	106	6	−	−	PROPN
ejpam-4153	106	7	2	2	NUM
ejpam-4153	106	8	)	)	PUNCT
ejpam-4153	106	9	.	.	PUNCT
ejpam-4153	107	1	(	(	PUNCT
ejpam-4153	107	2	12	12	NUM
ejpam-4153	107	3	)	)	PUNCT
ejpam-4153	107	4	r.	r.	PROPN
ejpam-4153	107	5	reynolds	reynolds	PROPN
ejpam-4153	107	6	,	,	PUNCT
ejpam-4153	107	7	a.	a.	PROPN
ejpam-4153	107	8	stauffer	stauffer	PROPN
ejpam-4153	107	9	/	/	SYM
ejpam-4153	107	10	eur	eur	PROPN
ejpam-4153	107	11	.	.	PUNCT
ejpam-4153	108	1	j.	j.	PROPN
ejpam-4153	108	2	pure	pure	PROPN
ejpam-4153	108	3	appl	appl	PROPN
ejpam-4153	108	4	.	.	PROPN
ejpam-4153	108	5	math	math	PROPN
ejpam-4153	108	6	,	,	PUNCT
ejpam-4153	108	7	15	15	NUM
ejpam-4153	108	8	(	(	PUNCT
ejpam-4153	108	9	1	1	NUM
ejpam-4153	108	10	)	)	PUNCT
ejpam-4153	108	11	(	(	PUNCT
ejpam-4153	108	12	2022	2022	NUM
ejpam-4153	108	13	)	)	PUNCT
ejpam-4153	108	14	,	,	PUNCT
ejpam-4153	108	15	229	229	NUM
ejpam-4153	108	16	-	-	SYM
ejpam-4153	108	17	237	237	NUM
ejpam-4153	108	18	233	233	NUM
ejpam-4153	108	19	11	11	NUM
ejpam-4153	108	20	.	.	PUNCT
ejpam-4153	109	1	derivation	derivation	NOUN
ejpam-4153	109	2	of	of	ADP
ejpam-4153	109	3	entry	entry	NOUN
ejpam-4153	109	4	4.282.10	4.282.10	NUM
ejpam-4153	109	5	in	in	ADP
ejpam-4153	109	6	[	[	X
ejpam-4153	109	7	6	6	NUM
ejpam-4153	109	8	]	]	PUNCT
ejpam-4153	109	9	in	in	ADP
ejpam-4153	109	10	this	this	DET
ejpam-4153	109	11	section	section	NOUN
ejpam-4153	109	12	we	we	PRON
ejpam-4153	109	13	will	will	AUX
ejpam-4153	109	14	use	use	VERB
ejpam-4153	109	15	the	the	DET
ejpam-4153	109	16	formula	formula	NOUN
ejpam-4153	109	17	2f1	2f1	NUM
ejpam-4153	109	18	(	(	PUNCT
ejpam-4153	109	19	1	1	NUM
ejpam-4153	109	20	,	,	PUNCT
ejpam-4153	109	21	54	54	NUM
ejpam-4153	109	22	;	;	PUNCT
ejpam-4153	109	23	7	7	NUM
ejpam-4153	109	24	4	4	NUM
ejpam-4153	109	25	;	;	PUNCT
ejpam-4153	109	26	z	z	X
ejpam-4153	109	27	)	)	PUNCT
ejpam-4153	110	1	=	=	PUNCT
ejpam-4153	110	2	3bz	3bz	ADJ
ejpam-4153	110	3	(	(	PUNCT
ejpam-4153	110	4	3	3	NUM
ejpam-4153	110	5	4	4	NUM
ejpam-4153	110	6	,	,	PUNCT
ejpam-4153	110	7	1	1	NUM
ejpam-4153	110	8	2	2	NUM
ejpam-4153	110	9	)	)	PUNCT
ejpam-4153	110	10	4	4	NUM
ejpam-4153	110	11	√	√	NOUN
ejpam-4153	110	12	1−zz3/4	1−zz3/4	NUM
ejpam-4153	111	1	where	where	SCONJ
ejpam-4153	111	2	z	z	NOUN
ejpam-4153	111	3	=	=	SYM
ejpam-4153	111	4	−1	−1	NOUN
ejpam-4153	111	5	,	,	PUNCT
ejpam-4153	111	6	which	which	PRON
ejpam-4153	111	7	is	be	AUX
ejpam-4153	111	8	derived	derive	VERB
ejpam-4153	111	9	from	from	ADP
ejpam-4153	111	10	section	section	NOUN
ejpam-4153	111	11	(	(	PUNCT
ejpam-4153	111	12	15.2	15.2	NUM
ejpam-4153	111	13	)	)	PUNCT
ejpam-4153	111	14	(	(	PUNCT
ejpam-4153	111	15	relations	relation	NOUN
ejpam-4153	111	16	between	between	ADP
ejpam-4153	111	17	contiguous	contiguous	ADJ
ejpam-4153	111	18	functions	function	NOUN
ejpam-4153	111	19	)	)	PUNCT
ejpam-4153	111	20	in	in	ADP
ejpam-4153	111	21	[	[	X
ejpam-4153	111	22	1	1	NUM
ejpam-4153	111	23	]	]	PUNCT
ejpam-4153	111	24	.	.	PUNCT
ejpam-4153	111	25	using	use	VERB
ejpam-4153	111	26	equation	equation	NOUN
ejpam-4153	111	27	(	(	PUNCT
ejpam-4153	111	28	10	10	NUM
ejpam-4153	111	29	)	)	PUNCT
ejpam-4153	111	30	then	then	ADV
ejpam-4153	111	31	taking	take	VERB
ejpam-4153	111	32	the	the	DET
ejpam-4153	111	33	first	first	ADJ
ejpam-4153	111	34	partial	partial	ADJ
ejpam-4153	111	35	derivative	derivative	NOUN
ejpam-4153	111	36	with	with	ADP
ejpam-4153	111	37	respect	respect	NOUN
ejpam-4153	111	38	to	to	ADP
ejpam-4153	111	39	p	p	NOUN
ejpam-4153	111	40	followed	follow	VERB
ejpam-4153	111	41	by	by	ADP
ejpam-4153	111	42	setting	set	VERB
ejpam-4153	111	43	q	q	X
ejpam-4153	111	44	=	=	PUNCT
ejpam-4153	111	45	π/4	π/4	PROPN
ejpam-4153	111	46	and	and	CCONJ
ejpam-4153	111	47	p	p	X
ejpam-4153	111	48	=	=	NOUN
ejpam-4153	111	49	0	0	NUM
ejpam-4153	111	50	we	we	PRON
ejpam-4153	111	51	get	get	VERB
ejpam-4153	111	52	∫	∫	PROPN
ejpam-4153	111	53	1	1	NUM
ejpam-4153	111	54	0	0	NUM
ejpam-4153	111	55	log(x	log(x	NUM
ejpam-4153	111	56	)	)	PUNCT
ejpam-4153	112	1	(	(	PUNCT
ejpam-4153	112	2	x2	x2	INTJ
ejpam-4153	112	3	−	−	PROPN
ejpam-4153	113	1	1	1	NUM
ejpam-4153	113	2	)	)	PUNCT
ejpam-4153	113	3	(	(	PUNCT
ejpam-4153	113	4	16	16	NUM
ejpam-4153	113	5	log2(x	log2(x	NOUN
ejpam-4153	113	6	)	)	PUNCT
ejpam-4153	113	7	+	+	CCONJ
ejpam-4153	113	8	π2	π2	ADJ
ejpam-4153	113	9	)	)	PUNCT
ejpam-4153	113	10	dx	dx	PROPN
ejpam-4153	114	1	=	=	SYM
ejpam-4153	114	2	1	1	NUM
ejpam-4153	114	3	64	64	NUM
ejpam-4153	114	4	(	(	PUNCT
ejpam-4153	114	5	−4	−4	X
ejpam-4153	114	6	+	+	CCONJ
ejpam-4153	114	7	√	√	VERB
ejpam-4153	114	8	2π	2π	NOUN
ejpam-4153	114	9	+	+	CCONJ
ejpam-4153	114	10	2	2	NUM
ejpam-4153	114	11	√	√	NUM
ejpam-4153	114	12	2	2	NUM
ejpam-4153	114	13	log	log	NOUN
ejpam-4153	114	14	(	(	PUNCT
ejpam-4153	114	15	cot	cot	NOUN
ejpam-4153	114	16	(	(	PUNCT
ejpam-4153	114	17	π	π	NOUN
ejpam-4153	114	18	8	8	NUM
ejpam-4153	114	19	)	)	PUNCT
ejpam-4153	114	20	)	)	PUNCT
ejpam-4153	114	21	)	)	PUNCT
ejpam-4153	114	22	.	.	PUNCT
ejpam-4153	115	1	(	(	PUNCT
ejpam-4153	115	2	13	13	NUM
ejpam-4153	115	3	)	)	PUNCT
ejpam-4153	115	4	12	12	NUM
ejpam-4153	115	5	.	.	PUNCT
ejpam-4153	116	1	a	a	DET
ejpam-4153	116	2	special	special	ADJ
ejpam-4153	116	3	case	case	NOUN
ejpam-4153	116	4	in	in	ADP
ejpam-4153	116	5	terms	term	NOUN
ejpam-4153	116	6	of	of	ADP
ejpam-4153	116	7	the	the	DET
ejpam-4153	116	8	hypergeometric	hypergeometric	ADJ
ejpam-4153	116	9	function	function	NOUN
ejpam-4153	116	10	using	use	VERB
ejpam-4153	116	11	equation	equation	NOUN
ejpam-4153	116	12	(	(	PUNCT
ejpam-4153	116	13	9	9	NUM
ejpam-4153	116	14	)	)	PUNCT
ejpam-4153	116	15	and	and	CCONJ
ejpam-4153	116	16	first	first	ADV
ejpam-4153	116	17	replacing	replace	VERB
ejpam-4153	116	18	a	a	PRON
ejpam-4153	116	19	and	and	CCONJ
ejpam-4153	116	20	eai	eai	PROPN
ejpam-4153	116	21	then	then	ADV
ejpam-4153	116	22	setting	set	VERB
ejpam-4153	116	23	k	k	PROPN
ejpam-4153	116	24	=	=	PUNCT
ejpam-4153	116	25	−1	−1	NOUN
ejpam-4153	116	26	,	,	PUNCT
ejpam-4153	116	27	and	and	CCONJ
ejpam-4153	116	28	replacing	replace	VERB
ejpam-4153	116	29	m	m	PRON
ejpam-4153	116	30	by	by	ADP
ejpam-4153	116	31	−m	−m	NOUN
ejpam-4153	116	32	to	to	PART
ejpam-4153	116	33	form	form	VERB
ejpam-4153	116	34	a	a	DET
ejpam-4153	116	35	second	second	ADJ
ejpam-4153	116	36	equation	equation	NOUN
ejpam-4153	116	37	and	and	CCONJ
ejpam-4153	116	38	adding	add	VERB
ejpam-4153	116	39	both	both	DET
ejpam-4153	116	40	simplify	simplify	ADJ
ejpam-4153	116	41	to	to	PART
ejpam-4153	116	42	get	get	VERB
ejpam-4153	116	43	∫	∫	PROPN
ejpam-4153	116	44	1	1	NUM
ejpam-4153	116	45	0	0	NUM
ejpam-4153	116	46	x−p	x−p	PROPN
ejpam-4153	116	47	(	(	PUNCT
ejpam-4153	116	48	x2p	x2p	PUNCT
ejpam-4153	116	49	+	+	CCONJ
ejpam-4153	116	50	1	1	X
ejpam-4153	116	51	)	)	PUNCT
ejpam-4153	116	52	log(x	log(x	PROPN
ejpam-4153	116	53	)	)	PUNCT
ejpam-4153	116	54	(	(	PUNCT
ejpam-4153	116	55	x2	x2	INTJ
ejpam-4153	116	56	−	−	PROPN
ejpam-4153	117	1	1	1	NUM
ejpam-4153	117	2	)	)	PUNCT
ejpam-4153	117	3	(	(	PUNCT
ejpam-4153	117	4	q2	q2	NOUN
ejpam-4153	117	5	+	+	CCONJ
ejpam-4153	117	6	log2(x	log2(x	NOUN
ejpam-4153	117	7	)	)	PUNCT
ejpam-4153	117	8	)	)	PUNCT
ejpam-4153	117	9	dx	dx	PROPN
ejpam-4153	118	1	=	=	SYM
ejpam-4153	118	2	1	1	NUM
ejpam-4153	118	3	2	2	NUM
ejpam-4153	118	4	π	π	NOUN
ejpam-4153	118	5	(	(	PUNCT
ejpam-4153	118	6	1	1	NUM
ejpam-4153	118	7	q	q	NOUN
ejpam-4153	118	8	−	−	PROPN
ejpam-4153	118	9	e−iπp	e−iπp	ADJ
ejpam-4153	118	10	q	q	NOUN
ejpam-4153	119	1	+	+	NUM
ejpam-4153	119	2	π	π	X
ejpam-4153	119	3	(	(	PUNCT
ejpam-4153	119	4	2f1	2f1	NUM
ejpam-4153	119	5	(	(	PUNCT
ejpam-4153	119	6	1	1	NUM
ejpam-4153	119	7	,	,	PUNCT
ejpam-4153	119	8	q	q	NOUN
ejpam-4153	120	1	+	+	NOUN
ejpam-4153	120	2	π	π	PROPN
ejpam-4153	120	3	π	π	X
ejpam-4153	120	4	;	;	PUNCT
ejpam-4153	120	5	q	q	PROPN
ejpam-4153	120	6	π	π	X
ejpam-4153	120	7	+	+	CCONJ
ejpam-4153	120	8	2;−e−ipπ	2;−e−ipπ	NUM
ejpam-4153	120	9	)	)	PUNCT
ejpam-4153	121	1	+	+	CCONJ
ejpam-4153	121	2	e2iπp	e2iπp	NOUN
ejpam-4153	121	3	2f1	2f1	NUM
ejpam-4153	121	4	(	(	PUNCT
ejpam-4153	121	5	1	1	NUM
ejpam-4153	121	6	,	,	PUNCT
ejpam-4153	121	7	q	q	NOUN
ejpam-4153	122	1	+	+	NOUN
ejpam-4153	122	2	π	π	PROPN
ejpam-4153	122	3	π	π	X
ejpam-4153	122	4	;	;	PUNCT
ejpam-4153	122	5	q	q	PROPN
ejpam-4153	122	6	π	π	X
ejpam-4153	122	7	+	+	CCONJ
ejpam-4153	122	8	2;−eipπ	2;−eipπ	NUM
ejpam-4153	122	9	)	)	PUNCT
ejpam-4153	122	10	)	)	PUNCT
ejpam-4153	122	11	)	)	PUNCT
ejpam-4153	122	12	.	.	PUNCT
ejpam-4153	123	1	(	(	PUNCT
ejpam-4153	123	2	14	14	NUM
ejpam-4153	123	3	)	)	PUNCT
ejpam-4153	123	4	13	13	NUM
ejpam-4153	123	5	.	.	PUNCT
ejpam-4153	124	1	a	a	DET
ejpam-4153	124	2	special	special	ADJ
ejpam-4153	124	3	case	case	NOUN
ejpam-4153	124	4	in	in	ADP
ejpam-4153	124	5	terms	term	NOUN
ejpam-4153	124	6	of	of	ADP
ejpam-4153	124	7	the	the	DET
ejpam-4153	124	8	polylogarithm	polylogarithm	PROPN
ejpam-4153	124	9	function	function	NOUN
ejpam-4153	124	10	using	use	VERB
ejpam-4153	124	11	equation	equation	NOUN
ejpam-4153	124	12	(	(	PUNCT
ejpam-4153	124	13	9	9	NUM
ejpam-4153	124	14	)	)	PUNCT
ejpam-4153	124	15	and	and	CCONJ
ejpam-4153	124	16	first	first	ADV
ejpam-4153	124	17	setting	set	VERB
ejpam-4153	124	18	a	a	DET
ejpam-4153	124	19	=	=	SYM
ejpam-4153	124	20	1	1	NUM
ejpam-4153	124	21	and	and	CCONJ
ejpam-4153	124	22	replacing	replace	VERB
ejpam-4153	124	23	m	m	PRON
ejpam-4153	124	24	by	by	ADP
ejpam-4153	124	25	−m	−m	NOUN
ejpam-4153	124	26	to	to	PART
ejpam-4153	124	27	form	form	VERB
ejpam-4153	124	28	a	a	DET
ejpam-4153	124	29	second	second	ADJ
ejpam-4153	124	30	equation	equation	NOUN
ejpam-4153	124	31	and	and	CCONJ
ejpam-4153	124	32	subtracting	subtract	VERB
ejpam-4153	124	33	both	both	CCONJ
ejpam-4153	124	34	simplify	simplify	ADJ
ejpam-4153	124	35	to	to	PART
ejpam-4153	124	36	get	get	VERB
ejpam-4153	124	37	∫	∫	PROPN
ejpam-4153	124	38	1	1	NUM
ejpam-4153	124	39	0	0	NUM
ejpam-4153	124	40	x−m	x−m	NOUN
ejpam-4153	124	41	(	(	PUNCT
ejpam-4153	124	42	x2	x2	PROPN
ejpam-4153	124	43	m	m	NOUN
ejpam-4153	124	44	−	−	NUM
ejpam-4153	124	45	1	1	NUM
ejpam-4153	124	46	)	)	PUNCT
ejpam-4153	124	47	logk(x	logk(x	PROPN
ejpam-4153	124	48	)	)	PUNCT
ejpam-4153	125	1	x2	x2	PROPN
ejpam-4153	126	1	−	−	PROPN
ejpam-4153	127	1	1	1	NUM
ejpam-4153	127	2	dx	dx	PROPN
ejpam-4153	127	3	=	=	SYM
ejpam-4153	127	4	−1	−1	NOUN
ejpam-4153	127	5	2	2	NUM
ejpam-4153	127	6	ieiπkπk+1	ieiπkπk+1	NOUN
ejpam-4153	127	7	sec	sec	PROPN
ejpam-4153	127	8	(	(	PUNCT
ejpam-4153	127	9	πk	πk	PROPN
ejpam-4153	127	10	2	2	NUM
ejpam-4153	127	11	)	)	PUNCT
ejpam-4153	127	12	(	(	PUNCT
ejpam-4153	127	13	li−k	li−k	VERB
ejpam-4153	127	14	(	(	PUNCT
ejpam-4153	127	15	−e−imπ	−e−imπ	PROPN
ejpam-4153	127	16	)	)	PUNCT
ejpam-4153	127	17	−	−	ADP
ejpam-4153	127	18	li−k	li−k	NOUN
ejpam-4153	127	19	(	(	PUNCT
ejpam-4153	127	20	−eimπ	−eimπ	X
ejpam-4153	127	21	)	)	PUNCT
ejpam-4153	127	22	)	)	PUNCT
ejpam-4153	127	23	,	,	PUNCT
ejpam-4153	127	24	(	(	PUNCT
ejpam-4153	127	25	15	15	NUM
ejpam-4153	127	26	)	)	PUNCT
ejpam-4153	127	27	from	from	ADP
ejpam-4153	127	28	equation	equation	NOUN
ejpam-4153	127	29	(	(	PUNCT
ejpam-4153	127	30	6	6	NUM
ejpam-4153	127	31	)	)	PUNCT
ejpam-4153	127	32	in	in	ADP
ejpam-4153	127	33	[	[	X
ejpam-4153	127	34	7	7	NUM
ejpam-4153	127	35	]	]	PUNCT
ejpam-4153	127	36	.	.	PUNCT
ejpam-4153	128	1	14	14	NUM
ejpam-4153	128	2	.	.	PUNCT
ejpam-4153	129	1	a	a	DET
ejpam-4153	129	2	special	special	ADJ
ejpam-4153	129	3	case	case	NOUN
ejpam-4153	129	4	in	in	ADP
ejpam-4153	129	5	terms	term	NOUN
ejpam-4153	129	6	of	of	ADP
ejpam-4153	129	7	the	the	DET
ejpam-4153	129	8	lerch	lerch	PROPN
ejpam-4153	129	9	function	function	NOUN
ejpam-4153	129	10	using	use	VERB
ejpam-4153	129	11	equation	equation	NOUN
ejpam-4153	129	12	(	(	PUNCT
ejpam-4153	129	13	9	9	NUM
ejpam-4153	129	14	)	)	PUNCT
ejpam-4153	129	15	and	and	CCONJ
ejpam-4153	129	16	first	first	ADV
ejpam-4153	129	17	setting	set	VERB
ejpam-4153	129	18	k	k	X
ejpam-4153	129	19	=	=	PUNCT
ejpam-4153	129	20	−2	−2	NOUN
ejpam-4153	129	21	and	and	CCONJ
ejpam-4153	129	22	replacing	replace	VERB
ejpam-4153	129	23	a	a	PRON
ejpam-4153	129	24	by	by	ADP
ejpam-4153	129	25	eqi	eqi	NOUN
ejpam-4153	129	26	then	then	ADV
ejpam-4153	129	27	replacing	replace	VERB
ejpam-4153	129	28	m	m	PRON
ejpam-4153	129	29	by	by	ADP
ejpam-4153	129	30	−m	−m	NOUN
ejpam-4153	129	31	to	to	PART
ejpam-4153	129	32	form	form	VERB
ejpam-4153	129	33	a	a	DET
ejpam-4153	129	34	second	second	ADJ
ejpam-4153	129	35	equation	equation	NOUN
ejpam-4153	129	36	and	and	CCONJ
ejpam-4153	129	37	subtracting	subtract	VERB
ejpam-4153	129	38	both	both	CCONJ
ejpam-4153	129	39	simplify	simplify	ADJ
ejpam-4153	129	40	to	to	PART
ejpam-4153	129	41	get	get	VERB
ejpam-4153	129	42	∫	∫	PROPN
ejpam-4153	129	43	1	1	NUM
ejpam-4153	129	44	0	0	NUM
ejpam-4153	129	45	x−m	x−m	NOUN
ejpam-4153	129	46	(	(	PUNCT
ejpam-4153	129	47	x2	x2	PROPN
ejpam-4153	129	48	m	m	NOUN
ejpam-4153	129	49	−	−	NOUN
ejpam-4153	129	50	1	1	NUM
ejpam-4153	129	51	)	)	PUNCT
ejpam-4153	129	52	(	(	PUNCT
ejpam-4153	129	53	q2	q2	NOUN
ejpam-4153	129	54	−	−	PROPN
ejpam-4153	129	55	log2(x	log2(x	NOUN
ejpam-4153	129	56	)	)	PUNCT
ejpam-4153	129	57	)	)	PUNCT
ejpam-4153	130	1	(	(	PUNCT
ejpam-4153	130	2	x2	x2	INTJ
ejpam-4153	130	3	−	−	PROPN
ejpam-4153	130	4	1	1	NUM
ejpam-4153	130	5	)	)	PUNCT
ejpam-4153	130	6	(	(	PUNCT
ejpam-4153	130	7	q2	q2	NOUN
ejpam-4153	130	8	+	+	CCONJ
ejpam-4153	130	9	log2(x	log2(x	NOUN
ejpam-4153	130	10	)	)	PUNCT
ejpam-4153	130	11	)	)	PUNCT
ejpam-4153	130	12	2	2	NUM
ejpam-4153	130	13	dx	dx	PROPN
ejpam-4153	130	14	r.	r.	PROPN
ejpam-4153	130	15	reynolds	reynolds	PROPN
ejpam-4153	130	16	,	,	PUNCT
ejpam-4153	130	17	a.	a.	PROPN
ejpam-4153	130	18	stauffer	stauffer	PROPN
ejpam-4153	130	19	/	/	SYM
ejpam-4153	130	20	eur	eur	PROPN
ejpam-4153	130	21	.	.	PUNCT
ejpam-4153	131	1	j.	j.	PROPN
ejpam-4153	131	2	pure	pure	PROPN
ejpam-4153	131	3	appl	appl	PROPN
ejpam-4153	131	4	.	.	PROPN
ejpam-4153	131	5	math	math	PROPN
ejpam-4153	131	6	,	,	PUNCT
ejpam-4153	131	7	15	15	NUM
ejpam-4153	131	8	(	(	PUNCT
ejpam-4153	131	9	1	1	NUM
ejpam-4153	131	10	)	)	PUNCT
ejpam-4153	131	11	(	(	PUNCT
ejpam-4153	131	12	2022	2022	NUM
ejpam-4153	131	13	)	)	PUNCT
ejpam-4153	131	14	,	,	PUNCT
ejpam-4153	131	15	229	229	NUM
ejpam-4153	131	16	-	-	SYM
ejpam-4153	131	17	237	237	NUM
ejpam-4153	131	18	234	234	NUM
ejpam-4153	131	19	=	=	SYM
ejpam-4153	131	20	ie−iπm	ie−iπm	PROPN
ejpam-4153	131	21	2π	2π	NOUN
ejpam-4153	131	22	(	(	PUNCT
ejpam-4153	131	23	φ	φ	PROPN
ejpam-4153	131	24	(	(	PUNCT
ejpam-4153	131	25	−e−imπ	−e−imπ	PROPN
ejpam-4153	131	26	,	,	PUNCT
ejpam-4153	131	27	2	2	NUM
ejpam-4153	131	28	,	,	PUNCT
ejpam-4153	131	29	q	q	NOUN
ejpam-4153	132	1	+	+	NUM
ejpam-4153	132	2	π	π	PROPN
ejpam-4153	132	3	π	π	PROPN
ejpam-4153	132	4	)	)	PUNCT
ejpam-4153	132	5	−	−	PROPN
ejpam-4153	132	6	e2iπmφ	e2iπmφ	PROPN
ejpam-4153	132	7	(	(	PUNCT
ejpam-4153	132	8	−eimπ	−eimπ	PUNCT
ejpam-4153	132	9	,	,	PUNCT
ejpam-4153	132	10	2	2	NUM
ejpam-4153	132	11	,	,	PUNCT
ejpam-4153	132	12	q	q	NOUN
ejpam-4153	133	1	+	+	NUM
ejpam-4153	133	2	π	π	PROPN
ejpam-4153	133	3	π	π	PROPN
ejpam-4153	133	4	)	)	PUNCT
ejpam-4153	133	5	)	)	PUNCT
ejpam-4153	133	6	.	.	PUNCT
ejpam-4153	134	1	(	(	PUNCT
ejpam-4153	134	2	16	16	NUM
ejpam-4153	134	3	)	)	PUNCT
ejpam-4153	134	4	15	15	NUM
ejpam-4153	134	5	.	.	PUNCT
ejpam-4153	135	1	definite	definite	ADJ
ejpam-4153	135	2	integral	integral	ADJ
ejpam-4153	135	3	of	of	ADP
ejpam-4153	135	4	nested	nested	ADJ
ejpam-4153	135	5	logarithm	logarithm	NOUN
ejpam-4153	135	6	function	function	NOUN
ejpam-4153	135	7	in	in	ADP
ejpam-4153	135	8	terms	term	NOUN
ejpam-4153	135	9	of	of	ADP
ejpam-4153	135	10	the	the	DET
ejpam-4153	135	11	derivative	derivative	NOUN
ejpam-4153	135	12	of	of	ADP
ejpam-4153	135	13	the	the	DET
ejpam-4153	135	14	polylogarithm	polylogarithm	PROPN
ejpam-4153	135	15	function	function	NOUN
ejpam-4153	135	16	using	use	VERB
ejpam-4153	135	17	equation	equation	NOUN
ejpam-4153	135	18	(	(	PUNCT
ejpam-4153	135	19	9	9	NUM
ejpam-4153	135	20	)	)	PUNCT
ejpam-4153	135	21	and	and	CCONJ
ejpam-4153	135	22	first	first	ADV
ejpam-4153	135	23	setting	set	VERB
ejpam-4153	135	24	k	k	X
ejpam-4153	135	25	=	=	PUNCT
ejpam-4153	135	26	−2	−2	NOUN
ejpam-4153	135	27	and	and	CCONJ
ejpam-4153	135	28	replacing	replace	VERB
ejpam-4153	135	29	a	a	PRON
ejpam-4153	135	30	by	by	ADP
ejpam-4153	135	31	eqi	eqi	NOUN
ejpam-4153	135	32	then	then	ADV
ejpam-4153	135	33	replacing	replace	VERB
ejpam-4153	135	34	m	m	PRON
ejpam-4153	135	35	by	by	ADP
ejpam-4153	135	36	−m	−m	NOUN
ejpam-4153	135	37	to	to	PART
ejpam-4153	135	38	form	form	VERB
ejpam-4153	135	39	a	a	DET
ejpam-4153	135	40	second	second	ADJ
ejpam-4153	135	41	equation	equation	NOUN
ejpam-4153	135	42	and	and	CCONJ
ejpam-4153	135	43	subtracting	subtract	VERB
ejpam-4153	135	44	both	both	CCONJ
ejpam-4153	135	45	simplify	simplify	ADJ
ejpam-4153	135	46	to	to	PART
ejpam-4153	135	47	get	get	VERB
ejpam-4153	135	48	(	(	PUNCT
ejpam-4153	135	49	17	17	NUM
ejpam-4153	135	50	)	)	PUNCT
ejpam-4153	135	51	∫	∫	NOUN
ejpam-4153	135	52	1	1	NUM
ejpam-4153	135	53	0	0	NUM
ejpam-4153	135	54	1	1	NUM
ejpam-4153	135	55	√	√	NUM
ejpam-4153	135	56	x(x+	x(x+	PROPN
ejpam-4153	135	57	1	1	NUM
ejpam-4153	135	58	)	)	PUNCT
ejpam-4153	135	59	(	(	PUNCT
ejpam-4153	135	60	log2(x	log2(x	X
ejpam-4153	135	61	)	)	PUNCT
ejpam-4153	135	62	+	+	CCONJ
ejpam-4153	135	63	π2	π2	ADJ
ejpam-4153	135	64	)	)	PUNCT
ejpam-4153	135	65	dx	dx	PROPN
ejpam-4153	135	66	=	=	PUNCT
ejpam-4153	135	67	log(2	log(2	PROPN
ejpam-4153	135	68	)	)	PUNCT
ejpam-4153	135	69	2π	2π	PROPN
ejpam-4153	135	70	and∫	and∫	VERB
ejpam-4153	135	71	1	1	NUM
ejpam-4153	135	72	0	0	NUM
ejpam-4153	136	1	iπ	iπ	PRON
ejpam-4153	136	2	log	log	NOUN
ejpam-4153	136	3	(	(	PUNCT
ejpam-4153	136	4	log2(x	log2(x	NOUN
ejpam-4153	136	5	)	)	PUNCT
ejpam-4153	136	6	+	+	CCONJ
ejpam-4153	136	7	π2	π2	ADJ
ejpam-4153	136	8	)	)	PUNCT
ejpam-4153	136	9	+	+	SYM
ejpam-4153	136	10	log(x	log(x	X
ejpam-4153	136	11	)	)	PUNCT
ejpam-4153	136	12	log	log	NOUN
ejpam-4153	136	13	(	(	PUNCT
ejpam-4153	136	14	π+i	π+i	X
ejpam-4153	136	15	log(x	log(x	NUM
ejpam-4153	136	16	)	)	PUNCT
ejpam-4153	136	17	π−i	π−i	PROPN
ejpam-4153	136	18	log(x	log(x	PROPN
ejpam-4153	136	19	)	)	PUNCT
ejpam-4153	136	20	)	)	PUNCT
ejpam-4153	137	1	√	√	ADP
ejpam-4153	138	1	x(x+	x(x+	NUM
ejpam-4153	138	2	1	1	NUM
ejpam-4153	138	3	)	)	PUNCT
ejpam-4153	138	4	(	(	PUNCT
ejpam-4153	138	5	log2(x	log2(x	X
ejpam-4153	138	6	)	)	PUNCT
ejpam-4153	138	7	+	+	CCONJ
ejpam-4153	138	8	π2	π2	ADJ
ejpam-4153	138	9	)	)	PUNCT
ejpam-4153	138	10	dx	dx	PROPN
ejpam-4153	138	11	=	=	SYM
ejpam-4153	138	12	ili′1(−i	ili′1(−i	PROPN
ejpam-4153	138	13	)	)	PUNCT
ejpam-4153	138	14	+	+	CCONJ
ejpam-4153	138	15	ili′1(i	ili′1(i	PROPN
ejpam-4153	138	16	)	)	PUNCT
ejpam-4153	139	1	+	+	CCONJ
ejpam-4153	139	2	i	i	PRON
ejpam-4153	139	3	log(2	log(2	NOUN
ejpam-4153	139	4	)	)	PUNCT
ejpam-4153	139	5	log(π	log(π	PROPN
ejpam-4153	139	6	)	)	PUNCT
ejpam-4153	139	7	,	,	PUNCT
ejpam-4153	139	8	(	(	PUNCT
ejpam-4153	139	9	18	18	NUM
ejpam-4153	139	10	)	)	PUNCT
ejpam-4153	139	11	from	from	ADP
ejpam-4153	139	12	equation	equation	NOUN
ejpam-4153	139	13	(	(	PUNCT
ejpam-4153	139	14	27	27	NUM
ejpam-4153	139	15	)	)	PUNCT
ejpam-4153	139	16	in	in	ADP
ejpam-4153	139	17	[	[	X
ejpam-4153	139	18	2	2	NUM
ejpam-4153	139	19	]	]	PUNCT
ejpam-4153	139	20	.	.	PUNCT
ejpam-4153	140	1	16	16	NUM
ejpam-4153	140	2	.	.	PUNCT
ejpam-4153	141	1	derivation	derivation	NOUN
ejpam-4153	141	2	of	of	ADP
ejpam-4153	141	3	entry	entry	NOUN
ejpam-4153	141	4	bi(131)(3	bi(131)(3	NOUN
ejpam-4153	141	5	)	)	PUNCT
ejpam-4153	141	6	in	in	ADP
ejpam-4153	141	7	[	[	X
ejpam-4153	141	8	8	8	NUM
ejpam-4153	141	9	]	]	PUNCT
ejpam-4153	141	10	in	in	ADP
ejpam-4153	141	11	this	this	DET
ejpam-4153	141	12	section	section	NOUN
ejpam-4153	141	13	we	we	PRON
ejpam-4153	141	14	will	will	AUX
ejpam-4153	141	15	use	use	VERB
ejpam-4153	141	16	the	the	DET
ejpam-4153	141	17	formula	formula	NOUN
ejpam-4153	141	18	2f1(1	2f1(1	NUM
ejpam-4153	141	19	,	,	PUNCT
ejpam-4153	141	20	2	2	NUM
ejpam-4153	141	21	;	;	PUNCT
ejpam-4153	141	22	3	3	NUM
ejpam-4153	141	23	;	;	PUNCT
ejpam-4153	141	24	z	z	X
ejpam-4153	141	25	)	)	PUNCT
ejpam-4153	141	26	=	=	SYM
ejpam-4153	141	27	−2(z+log(1−z	−2(z+log(1−z	NUM
ejpam-4153	141	28	)	)	PUNCT
ejpam-4153	141	29	)	)	PUNCT
ejpam-4153	142	1	z2	z2	NOUN
ejpam-4153	142	2	where	where	SCONJ
ejpam-4153	142	3	z	z	NOUN
ejpam-4153	142	4	=	=	SYM
ejpam-4153	142	5	−1	−1	NOUN
ejpam-4153	142	6	,	,	PUNCT
ejpam-4153	142	7	which	which	PRON
ejpam-4153	142	8	is	be	AUX
ejpam-4153	142	9	derived	derive	VERB
ejpam-4153	142	10	from	from	ADP
ejpam-4153	142	11	section	section	NOUN
ejpam-4153	142	12	(	(	PUNCT
ejpam-4153	142	13	15.2	15.2	NUM
ejpam-4153	142	14	)	)	PUNCT
ejpam-4153	142	15	(	(	PUNCT
ejpam-4153	142	16	relations	relation	NOUN
ejpam-4153	142	17	between	between	ADP
ejpam-4153	142	18	contiguous	contiguous	ADJ
ejpam-4153	142	19	functions	function	NOUN
ejpam-4153	142	20	)	)	PUNCT
ejpam-4153	142	21	in	in	ADP
ejpam-4153	142	22	[	[	X
ejpam-4153	142	23	1	1	NUM
ejpam-4153	142	24	]	]	PUNCT
ejpam-4153	142	25	.	.	PUNCT
ejpam-4153	143	1	using	use	VERB
ejpam-4153	143	2	equation	equation	NOUN
ejpam-4153	143	3	(	(	PUNCT
ejpam-4153	143	4	14	14	NUM
ejpam-4153	143	5	)	)	PUNCT
ejpam-4153	143	6	and	and	CCONJ
ejpam-4153	143	7	setting	set	VERB
ejpam-4153	143	8	q	q	X
ejpam-4153	143	9	=	=	PUNCT
ejpam-4153	143	10	π	π	NOUN
ejpam-4153	143	11	simplify	simplify	NOUN
ejpam-4153	143	12	we	we	PRON
ejpam-4153	143	13	get	get	VERB
ejpam-4153	143	14	∫	∫	PROPN
ejpam-4153	143	15	1	1	NUM
ejpam-4153	143	16	0	0	NUM
ejpam-4153	143	17	x−p	x−p	PROPN
ejpam-4153	143	18	(	(	PUNCT
ejpam-4153	143	19	x2p	x2p	PUNCT
ejpam-4153	143	20	+	+	CCONJ
ejpam-4153	143	21	1	1	X
ejpam-4153	143	22	)	)	PUNCT
ejpam-4153	143	23	log(x	log(x	PROPN
ejpam-4153	143	24	)	)	PUNCT
ejpam-4153	143	25	(	(	PUNCT
ejpam-4153	143	26	x2	x2	INTJ
ejpam-4153	143	27	−	−	PROPN
ejpam-4153	143	28	1	1	NUM
ejpam-4153	143	29	)	)	PUNCT
ejpam-4153	143	30	(	(	PUNCT
ejpam-4153	143	31	log2(x	log2(x	X
ejpam-4153	143	32	)	)	PUNCT
ejpam-4153	144	1	+	+	CCONJ
ejpam-4153	144	2	π2	π2	ADJ
ejpam-4153	144	3	)	)	PUNCT
ejpam-4153	144	4	dx	dx	PROPN
ejpam-4153	144	5	=	=	SYM
ejpam-4153	144	6	1	1	NUM
ejpam-4153	144	7	2	2	NUM
ejpam-4153	144	8	(	(	PUNCT
ejpam-4153	144	9	πp	πp	PRON
ejpam-4153	144	10	sin(πp	sin(πp	NOUN
ejpam-4153	144	11	)	)	PUNCT
ejpam-4153	144	12	+	+	CCONJ
ejpam-4153	144	13	cos(πp	cos(πp	NOUN
ejpam-4153	144	14	)	)	PUNCT
ejpam-4153	144	15	log(2(cos(πp	log(2(cos(πp	PUNCT
ejpam-4153	144	16	)	)	PUNCT
ejpam-4153	145	1	+	+	CCONJ
ejpam-4153	145	2	1))−	1))−	NUM
ejpam-4153	145	3	1	1	NUM
ejpam-4153	145	4	)	)	PUNCT
ejpam-4153	145	5	.	.	PUNCT
ejpam-4153	146	1	(	(	PUNCT
ejpam-4153	146	2	19	19	NUM
ejpam-4153	146	3	)	)	PUNCT
ejpam-4153	146	4	17	17	NUM
ejpam-4153	146	5	.	.	PUNCT
ejpam-4153	147	1	derivation	derivation	NOUN
ejpam-4153	147	2	of	of	ADP
ejpam-4153	147	3	entry	entry	NOUN
ejpam-4153	147	4	bi(131)(4	bi(131)(4	PROPN
ejpam-4153	147	5	)	)	PUNCT
ejpam-4153	147	6	in	in	ADP
ejpam-4153	147	7	[	[	X
ejpam-4153	147	8	8	8	NUM
ejpam-4153	147	9	]	]	PUNCT
ejpam-4153	147	10	in	in	ADP
ejpam-4153	147	11	this	this	DET
ejpam-4153	147	12	section	section	NOUN
ejpam-4153	147	13	we	we	PRON
ejpam-4153	147	14	will	will	AUX
ejpam-4153	147	15	use	use	VERB
ejpam-4153	147	16	the	the	DET
ejpam-4153	147	17	formula	formula	NOUN
ejpam-4153	147	18	2f1(1	2f1(1	NUM
ejpam-4153	147	19	,	,	PUNCT
ejpam-4153	147	20	1	1	NUM
ejpam-4153	147	21	;	;	PUNCT
ejpam-4153	147	22	2	2	NUM
ejpam-4153	147	23	;	;	PUNCT
ejpam-4153	147	24	z	z	X
ejpam-4153	147	25	)	)	PUNCT
ejpam-4153	147	26	=	=	SYM
ejpam-4153	147	27	−	−	PROPN
ejpam-4153	147	28	log(1−z	log(1−z	PROPN
ejpam-4153	147	29	)	)	PUNCT
ejpam-4153	147	30	z	z	NOUN
ejpam-4153	147	31	which	which	PRON
ejpam-4153	147	32	is	be	AUX
ejpam-4153	147	33	derived	derive	VERB
ejpam-4153	147	34	from	from	ADP
ejpam-4153	147	35	section	section	NOUN
ejpam-4153	147	36	(	(	PUNCT
ejpam-4153	147	37	15.2	15.2	NUM
ejpam-4153	147	38	)	)	PUNCT
ejpam-4153	147	39	(	(	PUNCT
ejpam-4153	147	40	relations	relation	NOUN
ejpam-4153	147	41	between	between	ADP
ejpam-4153	147	42	contiguous	contiguous	ADJ
ejpam-4153	147	43	functions	function	NOUN
ejpam-4153	147	44	)	)	PUNCT
ejpam-4153	147	45	in	in	ADP
ejpam-4153	147	46	[	[	X
ejpam-4153	147	47	1	1	NUM
ejpam-4153	147	48	]	]	PUNCT
ejpam-4153	147	49	.	.	PUNCT
ejpam-4153	148	1	using	use	VERB
ejpam-4153	148	2	equation	equation	NOUN
ejpam-4153	148	3	(	(	PUNCT
ejpam-4153	148	4	10	10	NUM
ejpam-4153	148	5	)	)	PUNCT
ejpam-4153	148	6	and	and	CCONJ
ejpam-4153	148	7	setting	set	VERB
ejpam-4153	148	8	q	q	NOUN
ejpam-4153	148	9	=	=	PUNCT
ejpam-4153	148	10	π	π	NOUN
ejpam-4153	148	11	simplify	simplify	NOUN
ejpam-4153	148	12	we	we	PRON
ejpam-4153	148	13	get	get	VERB
ejpam-4153	148	14	(	(	PUNCT
ejpam-4153	148	15	20	20	NUM
ejpam-4153	148	16	)	)	PUNCT
ejpam-4153	148	17	∫	∫	PROPN
ejpam-4153	148	18	1	1	NUM
ejpam-4153	148	19	0	0	NUM
ejpam-4153	148	20	x−p	x−p	PROPN
ejpam-4153	148	21	(	(	PUNCT
ejpam-4153	148	22	x2p	x2p	NUM
ejpam-4153	148	23	−	−	PROPN
ejpam-4153	148	24	1	1	NUM
ejpam-4153	148	25	)	)	PUNCT
ejpam-4153	148	26	(	(	PUNCT
ejpam-4153	148	27	x2	x2	INTJ
ejpam-4153	148	28	−	−	PROPN
ejpam-4153	148	29	1	1	NUM
ejpam-4153	148	30	)	)	PUNCT
ejpam-4153	148	31	(	(	PUNCT
ejpam-4153	148	32	log2(x	log2(x	X
ejpam-4153	148	33	)	)	PUNCT
ejpam-4153	149	1	+	+	CCONJ
ejpam-4153	149	2	π2	π2	ADJ
ejpam-4153	149	3	)	)	PUNCT
ejpam-4153	149	4	dx	dx	PROPN
ejpam-4153	150	1	=	=	SYM
ejpam-4153	150	2	i	i	PRON
ejpam-4153	150	3	(	(	PUNCT
ejpam-4153	150	4	e−iπp	e−iπp	ADJ
ejpam-4153	150	5	log	log	NOUN
ejpam-4153	150	6	(	(	PUNCT
ejpam-4153	150	7	1	1	NUM
ejpam-4153	150	8	+	+	CCONJ
ejpam-4153	150	9	eiπp	eiπp	ADJ
ejpam-4153	150	10	)	)	PUNCT
ejpam-4153	151	1	−	−	PROPN
ejpam-4153	151	2	eiπp	eiπp	PROPN
ejpam-4153	151	3	log	log	NOUN
ejpam-4153	151	4	(	(	PUNCT
ejpam-4153	151	5	1	1	NUM
ejpam-4153	151	6	+	+	CCONJ
ejpam-4153	151	7	e−iπp	e−iπp	NOUN
ejpam-4153	151	8	)	)	PUNCT
ejpam-4153	151	9	)	)	PUNCT
ejpam-4153	152	1	2π	2π	PROPN
ejpam-4153	152	2	=	=	SYM
ejpam-4153	152	3	sin(πp	sin(πp	X
ejpam-4153	152	4	)	)	PUNCT
ejpam-4153	152	5	log(2(cos(πp	log(2(cos(πp	PUNCT
ejpam-4153	152	6	)	)	PUNCT
ejpam-4153	153	1	+	+	CCONJ
ejpam-4153	153	2	1))−	1))−	NUM
ejpam-4153	153	3	πp	πp	ADP
ejpam-4153	153	4	cos(πp	cos(πp	PROPN
ejpam-4153	153	5	)	)	PUNCT
ejpam-4153	153	6	2π	2π	PROPN
ejpam-4153	153	7	.	.	PUNCT
ejpam-4153	154	1	r.	r.	PROPN
ejpam-4153	154	2	reynolds	reynolds	PROPN
ejpam-4153	154	3	,	,	PUNCT
ejpam-4153	154	4	a.	a.	PROPN
ejpam-4153	154	5	stauffer	stauffer	PROPN
ejpam-4153	154	6	/	/	SYM
ejpam-4153	154	7	eur	eur	PROPN
ejpam-4153	154	8	.	.	PUNCT
ejpam-4153	155	1	j.	j.	PROPN
ejpam-4153	155	2	pure	pure	PROPN
ejpam-4153	155	3	appl	appl	PROPN
ejpam-4153	155	4	.	.	PROPN
ejpam-4153	155	5	math	math	PROPN
ejpam-4153	155	6	,	,	PUNCT
ejpam-4153	155	7	15	15	NUM
ejpam-4153	155	8	(	(	PUNCT
ejpam-4153	155	9	1	1	NUM
ejpam-4153	155	10	)	)	PUNCT
ejpam-4153	155	11	(	(	PUNCT
ejpam-4153	155	12	2022	2022	NUM
ejpam-4153	155	13	)	)	PUNCT
ejpam-4153	155	14	,	,	PUNCT
ejpam-4153	155	15	229	229	NUM
ejpam-4153	155	16	-	-	SYM
ejpam-4153	155	17	237	237	NUM
ejpam-4153	155	18	235	235	NUM
ejpam-4153	155	19	18	18	NUM
ejpam-4153	155	20	.	.	PUNCT
ejpam-4153	156	1	derivation	derivation	NOUN
ejpam-4153	156	2	of	of	ADP
ejpam-4153	156	3	arctangent	arctangent	NOUN
ejpam-4153	156	4	logarithmic	logarithmic	ADJ
ejpam-4153	156	5	integrals	integral	NOUN
ejpam-4153	156	6	in	in	ADP
ejpam-4153	156	7	this	this	DET
ejpam-4153	156	8	section	section	NOUN
ejpam-4153	156	9	we	we	PRON
ejpam-4153	156	10	will	will	AUX
ejpam-4153	156	11	look	look	VERB
ejpam-4153	156	12	at	at	ADP
ejpam-4153	156	13	deriving	derive	VERB
ejpam-4153	156	14	definite	definite	ADJ
ejpam-4153	156	15	integrals	integral	NOUN
ejpam-4153	156	16	of	of	ADP
ejpam-4153	156	17	the	the	DET
ejpam-4153	156	18	arctangent	arctangent	NOUN
ejpam-4153	156	19	of	of	ADP
ejpam-4153	156	20	the	the	DET
ejpam-4153	156	21	logarithmic	logarithmic	ADJ
ejpam-4153	156	22	function	function	NOUN
ejpam-4153	156	23	.	.	PUNCT
ejpam-4153	157	1	we	we	PRON
ejpam-4153	157	2	will	will	AUX
ejpam-4153	157	3	also	also	ADV
ejpam-4153	157	4	derive	derive	VERB
ejpam-4153	157	5	integrals	integral	NOUN
ejpam-4153	157	6	in	in	ADP
ejpam-4153	157	7	terms	term	NOUN
ejpam-4153	157	8	of	of	ADP
ejpam-4153	157	9	π	π	PROPN
ejpam-4153	157	10	and	and	CCONJ
ejpam-4153	157	11	the	the	DET
ejpam-4153	157	12	loggmma	loggmma	PROPN
ejpam-4153	157	13	function	function	NOUN
ejpam-4153	157	14	.	.	PUNCT
ejpam-4153	158	1	using	use	VERB
ejpam-4153	158	2	(	(	PUNCT
ejpam-4153	158	3	9	9	NUM
ejpam-4153	158	4	)	)	PUNCT
ejpam-4153	158	5	and	and	CCONJ
ejpam-4153	158	6	setting	set	VERB
ejpam-4153	158	7	m	m	NOUN
ejpam-4153	158	8	=	=	SYM
ejpam-4153	158	9	0	0	NUM
ejpam-4153	158	10	simplifying	simplify	VERB
ejpam-4153	158	11	we	we	PRON
ejpam-4153	158	12	get	get	VERB
ejpam-4153	158	13	∫	∫	PROPN
ejpam-4153	158	14	1	1	NUM
ejpam-4153	158	15	0	0	NUM
ejpam-4153	158	16	logk(ax)−	logk(ax)−	PROPN
ejpam-4153	158	17	logk	logk	NOUN
ejpam-4153	158	18	(	(	PUNCT
ejpam-4153	158	19	a	a	DET
ejpam-4153	158	20	x	x	X
ejpam-4153	158	21	)	)	PUNCT
ejpam-4153	159	1	x2	x2	NOUN
ejpam-4153	159	2	−	−	PROPN
ejpam-4153	160	1	1	1	NUM
ejpam-4153	160	2	dx	dx	NOUN
ejpam-4153	160	3	=	=	SYM
ejpam-4153	160	4	1	1	NUM
ejpam-4153	160	5	2	2	NUM
ejpam-4153	160	6	(	(	PUNCT
ejpam-4153	160	7	(	(	PUNCT
ejpam-4153	160	8	2iπ)k+1	2iπ)k+1	NUM
ejpam-4153	160	9	(	(	PUNCT
ejpam-4153	160	10	ζ	ζ	X
ejpam-4153	160	11	(	(	PUNCT
ejpam-4153	160	12	−k	−k	PROPN
ejpam-4153	160	13	,	,	PUNCT
ejpam-4153	160	14	1−	1−	NUM
ejpam-4153	160	15	i	i	NUM
ejpam-4153	160	16	log(a	log(a	PROPN
ejpam-4153	160	17	)	)	PUNCT
ejpam-4153	160	18	2π	2π	PROPN
ejpam-4153	160	19	)	)	PUNCT
ejpam-4153	161	1	−	−	PROPN
ejpam-4153	161	2	ζ	ζ	NOUN
ejpam-4153	161	3	(	(	PUNCT
ejpam-4153	161	4	−k	−k	PROPN
ejpam-4153	161	5	,	,	PUNCT
ejpam-4153	161	6	π	π	PROPN
ejpam-4153	161	7	−	−	PROPN
ejpam-4153	161	8	i	i	PRON
ejpam-4153	161	9	log(a	log(a	PROPN
ejpam-4153	161	10	)	)	PUNCT
ejpam-4153	161	11	2π	2π	NOUN
ejpam-4153	161	12	)	)	PUNCT
ejpam-4153	161	13	)	)	PUNCT
ejpam-4153	162	1	+	+	CCONJ
ejpam-4153	162	2	iπ	iπ	DET
ejpam-4153	162	3	logk(a	logk(a	NOUN
ejpam-4153	162	4	)	)	PUNCT
ejpam-4153	162	5	)	)	PUNCT
ejpam-4153	162	6	,	,	PUNCT
ejpam-4153	162	7	(	(	PUNCT
ejpam-4153	162	8	21	21	NUM
ejpam-4153	162	9	)	)	PUNCT
ejpam-4153	162	10	from	from	ADP
ejpam-4153	162	11	equations	equation	NOUN
ejpam-4153	162	12	(	(	PUNCT
ejpam-4153	162	13	64:5:3	64:5:3	NUM
ejpam-4153	162	14	)	)	PUNCT
ejpam-4153	162	15	in	in	ADP
ejpam-4153	162	16	[	[	X
ejpam-4153	162	17	9	9	NUM
ejpam-4153	162	18	]	]	PUNCT
ejpam-4153	162	19	and	and	CCONJ
ejpam-4153	162	20	(	(	PUNCT
ejpam-4153	162	21	25.14.2	25.14.2	NUM
ejpam-4153	162	22	)	)	PUNCT
ejpam-4153	162	23	in	in	ADP
ejpam-4153	162	24	[	[	X
ejpam-4153	162	25	5	5	NUM
ejpam-4153	162	26	]	]	PUNCT
ejpam-4153	162	27	.	.	PUNCT
ejpam-4153	163	1	then	then	ADV
ejpam-4153	163	2	we	we	PRON
ejpam-4153	163	3	take	take	VERB
ejpam-4153	163	4	the	the	DET
ejpam-4153	163	5	first	first	ADJ
ejpam-4153	163	6	partial	partial	ADJ
ejpam-4153	163	7	derivative	derivative	NOUN
ejpam-4153	163	8	with	with	ADP
ejpam-4153	163	9	respect	respect	NOUN
ejpam-4153	163	10	to	to	ADP
ejpam-4153	163	11	k	k	PROPN
ejpam-4153	163	12	then	then	ADV
ejpam-4153	163	13	set	set	VERB
ejpam-4153	163	14	k	k	PROPN
ejpam-4153	163	15	=	=	PUNCT
ejpam-4153	163	16	0	0	PUNCT
ejpam-4153	163	17	and	and	CCONJ
ejpam-4153	163	18	replace	replace	VERB
ejpam-4153	163	19	a	a	DET
ejpam-4153	163	20	=	=	SYM
ejpam-4153	163	21	ea	ea	NOUN
ejpam-4153	163	22	simplifying	simplify	VERB
ejpam-4153	163	23	to	to	PART
ejpam-4153	163	24	get	get	VERB
ejpam-4153	163	25	∫	∫	PROPN
ejpam-4153	163	26	1	1	NUM
ejpam-4153	163	27	0	0	NUM
ejpam-4153	163	28	tanh−1	tanh−1	NOUN
ejpam-4153	163	29	(	(	PUNCT
ejpam-4153	163	30	log(x	log(x	PROPN
ejpam-4153	163	31	)	)	PUNCT
ejpam-4153	163	32	a	a	PRON
ejpam-4153	163	33	)	)	PUNCT
ejpam-4153	164	1	x2	x2	NOUN
ejpam-4153	164	2	−	−	PROPN
ejpam-4153	164	3	1	1	NUM
ejpam-4153	164	4	dx	dx	NOUN
ejpam-4153	164	5	=	=	SYM
ejpam-4153	164	6	1	1	NUM
ejpam-4153	164	7	8	8	NUM
ejpam-4153	164	8	π	π	NOUN
ejpam-4153	164	9	(	(	PUNCT
ejpam-4153	164	10	−4ilogγ	−4ilogγ	PROPN
ejpam-4153	164	11	(	(	PUNCT
ejpam-4153	164	12	−	−	PROPN
ejpam-4153	164	13	ia	ia	PROPN
ejpam-4153	164	14	2π	2π	PROPN
ejpam-4153	164	15	)	)	PUNCT
ejpam-4153	165	1	+	+	CCONJ
ejpam-4153	165	2	4ilogγ	4ilogγ	NUM
ejpam-4153	165	3	(	(	PUNCT
ejpam-4153	165	4	−	−	NUM
ejpam-4153	165	5	ia+	ia+	NOUN
ejpam-4153	165	6	π	π	PROPN
ejpam-4153	165	7	2π	2π	PROPN
ejpam-4153	165	8	)	)	PUNCT
ejpam-4153	165	9	−4i	−4i	PROPN
ejpam-4153	165	10	log(−ia	log(−ia	PROPN
ejpam-4153	165	11	)	)	PUNCT
ejpam-4153	166	1	+	+	CCONJ
ejpam-4153	166	2	2i	2i	NUM
ejpam-4153	166	3	log(a	log(a	PROPN
ejpam-4153	166	4	)	)	PUNCT
ejpam-4153	167	1	+	+	NUM
ejpam-4153	167	2	4i	4i	PROPN
ejpam-4153	167	3	log(−π	log(−π	PROPN
ejpam-4153	167	4	−	−	PROPN
ejpam-4153	167	5	ia	ia	PROPN
ejpam-4153	167	6	)	)	PUNCT
ejpam-4153	167	7	+	+	CCONJ
ejpam-4153	167	8	π	π	PROPN
ejpam-4153	167	9	−	−	PROPN
ejpam-4153	167	10	2i	2i	PROPN
ejpam-4153	167	11	log(2π	log(2π	NOUN
ejpam-4153	167	12	)	)	PUNCT
ejpam-4153	167	13	)	)	PUNCT
ejpam-4153	167	14	(	(	PUNCT
ejpam-4153	167	15	22	22	NUM
ejpam-4153	167	16	)	)	PUNCT
ejpam-4153	167	17	next	next	ADV
ejpam-4153	167	18	we	we	PRON
ejpam-4153	167	19	replace	replace	VERB
ejpam-4153	167	20	a	a	PRON
ejpam-4153	167	21	by	by	ADP
ejpam-4153	167	22	−	−	PROPN
ejpam-4153	167	23	1	1	NUM
ejpam-4153	167	24	ai	ai	AUX
ejpam-4153	167	25	simplifying	simplify	VERB
ejpam-4153	167	26	to	to	PART
ejpam-4153	167	27	get	get	VERB
ejpam-4153	167	28	∫	∫	PROPN
ejpam-4153	167	29	1	1	NUM
ejpam-4153	167	30	0	0	NUM
ejpam-4153	167	31	tan−1(a	tan−1(a	NOUN
ejpam-4153	167	32	log(x	log(x	NUM
ejpam-4153	167	33	)	)	PUNCT
ejpam-4153	167	34	)	)	PUNCT
ejpam-4153	168	1	x2	x2	PRON
ejpam-4153	169	1	−	−	PROPN
ejpam-4153	169	2	1	1	NUM
ejpam-4153	169	3	dx	dx	NOUN
ejpam-4153	169	4	=	=	SYM
ejpam-4153	169	5	1	1	NUM
ejpam-4153	169	6	8	8	NUM
ejpam-4153	169	7	iπ	iπ	NOUN
ejpam-4153	169	8	π	π	NOUN
ejpam-4153	169	9	+	+	PUNCT
ejpam-4153	169	10	4i	4i	NUM
ejpam-4153	169	11	log	log	NOUN
ejpam-4153	169	12			AUX
ejpam-4153	169	13	√	√	INTJ
ejpam-4153	170	1	i	i	PRON
ejpam-4153	170	2	aγ	aγ	INTJ
ejpam-4153	170	3	(	(	PUNCT
ejpam-4153	170	4	π+	π+	X
ejpam-4153	170	5	1	1	NUM
ejpam-4153	170	6	a	a	DET
ejpam-4153	170	7	2π	2π	NOUN
ejpam-4153	170	8	)	)	PUNCT
ejpam-4153	170	9	√	√	NUM
ejpam-4153	170	10	2πγ	2πγ	NOUN
ejpam-4153	170	11	(	(	PUNCT
ejpam-4153	170	12	1	1	NUM
ejpam-4153	170	13	+	+	SYM
ejpam-4153	170	14	1	1	NUM
ejpam-4153	170	15	2πa	2πa	NOUN
ejpam-4153	170	16	)	)	PUNCT
ejpam-4153	171	1			PROPN
ejpam-4153	171	2			PROPN
ejpam-4153	171	3	(	(	PUNCT
ejpam-4153	171	4	23	23	NUM
ejpam-4153	171	5	)	)	PUNCT
ejpam-4153	171	6	where	where	SCONJ
ejpam-4153	171	7	re(a	re(a	NOUN
ejpam-4153	171	8	)	)	PUNCT
ejpam-4153	171	9	>	>	X
ejpam-4153	171	10	0	0	X
ejpam-4153	171	11	.	.	PROPN
ejpam-4153	172	1	18.1	18.1	NUM
ejpam-4153	172	2	.	.	PUNCT
ejpam-4153	172	3	example	example	NOUN
ejpam-4153	172	4	1	1	NUM
ejpam-4153	172	5	using	use	VERB
ejpam-4153	172	6	equation	equation	NOUN
ejpam-4153	172	7	(	(	PUNCT
ejpam-4153	172	8	23	23	NUM
ejpam-4153	172	9	)	)	PUNCT
ejpam-4153	172	10	and	and	CCONJ
ejpam-4153	172	11	setting	set	VERB
ejpam-4153	172	12	a	a	DET
ejpam-4153	172	13	=	=	SYM
ejpam-4153	172	14	1	1	NUM
ejpam-4153	172	15	simplifying	simplify	VERB
ejpam-4153	172	16	we	we	PRON
ejpam-4153	172	17	get∫	get∫	NOUN
ejpam-4153	172	18	1	1	NUM
ejpam-4153	172	19	0	0	NUM
ejpam-4153	172	20	tan−1(log(x	tan−1(log(x	NOUN
ejpam-4153	172	21	)	)	PUNCT
ejpam-4153	172	22	)	)	PUNCT
ejpam-4153	173	1	x2	x2	PRON
ejpam-4153	174	1	−	−	PROPN
ejpam-4153	174	2	1	1	NUM
ejpam-4153	174	3	dx	dx	NOUN
ejpam-4153	174	4	=	=	NOUN
ejpam-4153	174	5	1	1	NUM
ejpam-4153	174	6	4	4	NUM
ejpam-4153	174	7	π	π	NOUN
ejpam-4153	174	8	log	log	NOUN
ejpam-4153	174	9	(	(	PUNCT
ejpam-4153	174	10	2πγ	2πγ	NOUN
ejpam-4153	174	11	(	(	PUNCT
ejpam-4153	174	12	1	1	NUM
ejpam-4153	174	13	+	+	SYM
ejpam-4153	174	14	1	1	NUM
ejpam-4153	174	15	2π	2π	NOUN
ejpam-4153	174	16	)	)	PUNCT
ejpam-4153	174	17	2	2	NUM
ejpam-4153	174	18	γ	γ	X
ejpam-4153	174	19	(	(	PUNCT
ejpam-4153	174	20	1+π	1+π	NUM
ejpam-4153	174	21	2π	2π	NOUN
ejpam-4153	174	22	)	)	PUNCT
ejpam-4153	174	23	2	2	X
ejpam-4153	174	24	)	)	PUNCT
ejpam-4153	174	25	(	(	PUNCT
ejpam-4153	174	26	24	24	NUM
ejpam-4153	174	27	)	)	PUNCT
ejpam-4153	174	28	18.2	18.2	NUM
ejpam-4153	174	29	.	.	PUNCT
ejpam-4153	174	30	example	example	NOUN
ejpam-4153	174	31	2	2	NUM
ejpam-4153	174	32	using	use	VERB
ejpam-4153	174	33	equation	equation	NOUN
ejpam-4153	174	34	(	(	PUNCT
ejpam-4153	174	35	23	23	NUM
ejpam-4153	174	36	)	)	PUNCT
ejpam-4153	174	37	and	and	CCONJ
ejpam-4153	174	38	setting	set	VERB
ejpam-4153	174	39	a	a	DET
ejpam-4153	174	40	=	=	ADJ
ejpam-4153	174	41	1	1	NUM
ejpam-4153	174	42	/	/	SYM
ejpam-4153	174	43	π	π	NOUN
ejpam-4153	174	44	simplifying	simplify	VERB
ejpam-4153	174	45	we	we	PRON
ejpam-4153	174	46	get	get	VERB
ejpam-4153	174	47	∫	∫	PROPN
ejpam-4153	174	48	1	1	NUM
ejpam-4153	174	49	0	0	NUM
ejpam-4153	174	50	tan−1	tan−1	PROPN
ejpam-4153	174	51	(	(	PUNCT
ejpam-4153	174	52	log(x	log(x	PROPN
ejpam-4153	174	53	)	)	PUNCT
ejpam-4153	174	54	π	π	NOUN
ejpam-4153	174	55	)	)	PUNCT
ejpam-4153	175	1	x2	x2	PROPN
ejpam-4153	175	2	−	−	PROPN
ejpam-4153	176	1	1	1	NUM
ejpam-4153	176	2	dx	dx	NOUN
ejpam-4153	176	3	=	=	NOUN
ejpam-4153	176	4	1	1	NUM
ejpam-4153	176	5	4	4	NUM
ejpam-4153	176	6	π	π	NOUN
ejpam-4153	176	7	log	log	NOUN
ejpam-4153	176	8	(	(	PUNCT
ejpam-4153	176	9	π	π	NOUN
ejpam-4153	176	10	2	2	NUM
ejpam-4153	176	11	)	)	PUNCT
ejpam-4153	176	12	(	(	PUNCT
ejpam-4153	176	13	25	25	NUM
ejpam-4153	176	14	)	)	PUNCT
ejpam-4153	176	15	references	reference	NOUN
ejpam-4153	176	16	236	236	NUM
ejpam-4153	176	17	18.3	18.3	NUM
ejpam-4153	176	18	.	.	PUNCT
ejpam-4153	176	19	example	example	NOUN
ejpam-4153	176	20	3	3	NUM
ejpam-4153	176	21	using	use	VERB
ejpam-4153	176	22	equation	equation	NOUN
ejpam-4153	176	23	(	(	PUNCT
ejpam-4153	176	24	23	23	NUM
ejpam-4153	176	25	)	)	PUNCT
ejpam-4153	176	26	and	and	CCONJ
ejpam-4153	176	27	setting	set	VERB
ejpam-4153	176	28	a	a	PRON
ejpam-4153	176	29	=	=	SYM
ejpam-4153	176	30	1/(2π	1/(2π	NUM
ejpam-4153	176	31	)	)	PUNCT
ejpam-4153	176	32	simplifying	simplify	VERB
ejpam-4153	176	33	we	we	PRON
ejpam-4153	176	34	get	get	VERB
ejpam-4153	176	35	∫	∫	PROPN
ejpam-4153	176	36	1	1	NUM
ejpam-4153	177	1	0	0	X
ejpam-4153	177	2	cot−1	cot−1	PROPN
ejpam-4153	177	3	(	(	PUNCT
ejpam-4153	177	4	2π	2π	PROPN
ejpam-4153	177	5	log(x	log(x	NUM
ejpam-4153	177	6	)	)	PUNCT
ejpam-4153	177	7	)	)	PUNCT
ejpam-4153	178	1	x2	x2	PRON
ejpam-4153	179	1	−	−	PROPN
ejpam-4153	179	2	1	1	NUM
ejpam-4153	179	3	dx	dx	NOUN
ejpam-4153	179	4	=	=	NOUN
ejpam-4153	179	5	1	1	NUM
ejpam-4153	179	6	4	4	NUM
ejpam-4153	179	7	π	π	NOUN
ejpam-4153	179	8	log	log	NOUN
ejpam-4153	179	9	(	(	PUNCT
ejpam-4153	179	10	4	4	NUM
ejpam-4153	179	11	π	π	NOUN
ejpam-4153	179	12	)	)	PUNCT
ejpam-4153	179	13	.	.	PUNCT
ejpam-4153	180	1	(	(	PUNCT
ejpam-4153	180	2	26	26	NUM
ejpam-4153	180	3	)	)	PUNCT
ejpam-4153	180	4	19	19	NUM
ejpam-4153	180	5	.	.	PUNCT
ejpam-4153	180	6	discussion	discussion	NOUN
ejpam-4153	180	7	in	in	ADP
ejpam-4153	180	8	comparing	compare	VERB
ejpam-4153	180	9	our	our	PRON
ejpam-4153	180	10	results	result	NOUN
ejpam-4153	180	11	with	with	ADP
ejpam-4153	180	12	table	table	NOUN
ejpam-4153	180	13	4.282	4.282	NUM
ejpam-4153	180	14	in	in	ADP
ejpam-4153	180	15	[	[	X
ejpam-4153	180	16	6	6	NUM
ejpam-4153	180	17	]	]	PUNCT
ejpam-4153	180	18	,	,	PUNCT
ejpam-4153	180	19	our	our	PRON
ejpam-4153	180	20	formulae	formulae	NOUN
ejpam-4153	180	21	have	have	VERB
ejpam-4153	180	22	a	a	DET
ejpam-4153	180	23	wider	wide	ADJ
ejpam-4153	180	24	range	range	NOUN
ejpam-4153	180	25	of	of	ADP
ejpam-4153	180	26	the	the	DET
ejpam-4153	180	27	parameters	parameter	NOUN
ejpam-4153	180	28	than	than	SCONJ
ejpam-4153	180	29	are	be	AUX
ejpam-4153	180	30	listed	list	VERB
ejpam-4153	180	31	in	in	ADP
ejpam-4153	180	32	the	the	DET
ejpam-4153	180	33	gradshteyn	gradshteyn	ADJ
ejpam-4153	180	34	and	and	CCONJ
ejpam-4153	180	35	ryzhik	ryzhik	ADJ
ejpam-4153	180	36	book	book	NOUN
ejpam-4153	181	1	[	[	X
ejpam-4153	181	2	6	6	NUM
ejpam-4153	181	3	]	]	PUNCT
ejpam-4153	181	4	due	due	ADP
ejpam-4153	181	5	to	to	ADP
ejpam-4153	181	6	the	the	DET
ejpam-4153	181	7	use	use	NOUN
ejpam-4153	181	8	of	of	ADP
ejpam-4153	181	9	the	the	DET
ejpam-4153	181	10	lerch	lerch	PROPN
ejpam-4153	181	11	function	function	NOUN
ejpam-4153	181	12	in	in	ADP
ejpam-4153	181	13	the	the	DET
ejpam-4153	181	14	derivation	derivation	NOUN
ejpam-4153	181	15	of	of	ADP
ejpam-4153	181	16	these	these	DET
ejpam-4153	181	17	integrals	integral	NOUN
ejpam-4153	181	18	.	.	PUNCT
ejpam-4153	182	1	we	we	PRON
ejpam-4153	182	2	also	also	ADV
ejpam-4153	182	3	provided	provide	VERB
ejpam-4153	182	4	correct	correct	ADJ
ejpam-4153	182	5	formula	formula	NOUN
ejpam-4153	182	6	for	for	ADP
ejpam-4153	182	7	an	an	DET
ejpam-4153	182	8	integral	integral	ADJ
ejpam-4153	182	9	supplied	supply	VERB
ejpam-4153	182	10	by	by	ADP
ejpam-4153	182	11	bierens	bieren	NOUN
ejpam-4153	182	12	de	de	X
ejpam-4153	182	13	haan	haan	PROPN
ejpam-4153	182	14	.	.	PUNCT
ejpam-4153	183	1	we	we	PRON
ejpam-4153	183	2	will	will	AUX
ejpam-4153	183	3	be	be	AUX
ejpam-4153	183	4	looking	look	VERB
ejpam-4153	183	5	at	at	ADP
ejpam-4153	183	6	other	other	ADJ
ejpam-4153	183	7	integrals	integral	NOUN
ejpam-4153	183	8	using	use	VERB
ejpam-4153	183	9	this	this	DET
ejpam-4153	183	10	contour	contour	ADJ
ejpam-4153	183	11	integral	integral	ADJ
ejpam-4153	183	12	method	method	NOUN
ejpam-4153	183	13	for	for	ADP
ejpam-4153	183	14	future	future	ADJ
ejpam-4153	183	15	work	work	NOUN
ejpam-4153	183	16	.	.	PUNCT
ejpam-4153	184	1	20	20	NUM
ejpam-4153	184	2	.	.	PUNCT
ejpam-4153	184	3	conclusion	conclusion	NOUN
ejpam-4153	184	4	in	in	ADP
ejpam-4153	184	5	this	this	DET
ejpam-4153	184	6	paper	paper	NOUN
ejpam-4153	184	7	,	,	PUNCT
ejpam-4153	184	8	we	we	PRON
ejpam-4153	184	9	have	have	AUX
ejpam-4153	184	10	presented	present	VERB
ejpam-4153	184	11	a	a	DET
ejpam-4153	184	12	novel	novel	ADJ
ejpam-4153	184	13	method	method	NOUN
ejpam-4153	184	14	for	for	ADP
ejpam-4153	184	15	deriving	derive	VERB
ejpam-4153	184	16	some	some	DET
ejpam-4153	184	17	interesting	interesting	ADJ
ejpam-4153	184	18	definite	definite	ADJ
ejpam-4153	184	19	integrals	integral	NOUN
ejpam-4153	184	20	not	not	PART
ejpam-4153	184	21	previously	previously	ADV
ejpam-4153	184	22	published	publish	VERB
ejpam-4153	184	23	in	in	ADP
ejpam-4153	184	24	literature	literature	NOUN
ejpam-4153	184	25	using	use	VERB
ejpam-4153	184	26	contour	contour	NOUN
ejpam-4153	184	27	integration	integration	NOUN
ejpam-4153	184	28	.	.	PUNCT
ejpam-4153	185	1	the	the	DET
ejpam-4153	185	2	results	result	NOUN
ejpam-4153	185	3	presented	present	VERB
ejpam-4153	185	4	were	be	AUX
ejpam-4153	185	5	numerically	numerically	ADV
ejpam-4153	185	6	verified	verify	VERB
ejpam-4153	185	7	for	for	ADP
ejpam-4153	185	8	both	both	CCONJ
ejpam-4153	185	9	real	real	ADJ
ejpam-4153	185	10	and	and	CCONJ
ejpam-4153	185	11	imaginary	imaginary	ADJ
ejpam-4153	185	12	and	and	CCONJ
ejpam-4153	185	13	complex	complex	ADJ
ejpam-4153	185	14	values	value	NOUN
ejpam-4153	185	15	of	of	ADP
ejpam-4153	185	16	the	the	DET
ejpam-4153	185	17	parameters	parameter	NOUN
ejpam-4153	185	18	in	in	ADP
ejpam-4153	185	19	the	the	DET
ejpam-4153	185	20	integrals	integral	NOUN
ejpam-4153	185	21	using	use	VERB
ejpam-4153	185	22	mathematica	mathematica	PROPN
ejpam-4153	185	23	by	by	ADP
ejpam-4153	185	24	wolfram	wolfram	PROPN
ejpam-4153	185	25	.	.	PUNCT
ejpam-4153	186	1	acknowledgements	acknowledgement	NOUN
ejpam-4153	186	2	this	this	DET
ejpam-4153	186	3	research	research	NOUN
ejpam-4153	186	4	is	be	AUX
ejpam-4153	186	5	supported	support	VERB
ejpam-4153	186	6	by	by	ADP
ejpam-4153	186	7	nserc	nserc	PROPN
ejpam-4153	186	8	canada	canada	PROPN
ejpam-4153	186	9	under	under	ADP
ejpam-4153	186	10	grant	grant	PROPN
ejpam-4153	186	11	504070	504070	NUM
ejpam-4153	186	12	.	.	PUNCT
ejpam-4153	187	1	references	reference	NOUN
ejpam-4153	187	2	[	[	X
ejpam-4153	187	3	1	1	X
ejpam-4153	187	4	]	]	X
ejpam-4153	187	5	milton	milton	PROPN
ejpam-4153	187	6	abramowitz	abramowitz	PROPN
ejpam-4153	187	7	and	and	CCONJ
ejpam-4153	187	8	irene	irene	PROPN
ejpam-4153	187	9	a.	a.	PROPN
ejpam-4153	187	10	stegun	stegun	PROPN
ejpam-4153	187	11	.	.	PUNCT
ejpam-4153	188	1	handbook	handbook	NOUN
ejpam-4153	188	2	of	of	ADP
ejpam-4153	188	3	mathematical	mathematical	ADJ
ejpam-4153	188	4	functions	function	NOUN
ejpam-4153	188	5	:	:	PUNCT
ejpam-4153	188	6	with	with	ADP
ejpam-4153	188	7	formulas	formula	NOUN
ejpam-4153	188	8	,	,	PUNCT
ejpam-4153	188	9	graphs	graph	NOUN
ejpam-4153	188	10	,	,	PUNCT
ejpam-4153	188	11	and	and	CCONJ
ejpam-4153	188	12	mathematical	mathematical	ADJ
ejpam-4153	188	13	tables	table	NOUN
ejpam-4153	188	14	.	.	PUNCT
ejpam-4153	189	1	courier	courier	NOUN
ejpam-4153	189	2	corporation	corporation	NOUN
ejpam-4153	189	3	,	,	PUNCT
ejpam-4153	189	4	01	01	NUM
ejpam-4153	189	5	1965	1965	NUM
ejpam-4153	189	6	.	.	PUNCT
ejpam-4153	190	1	[	[	X
ejpam-4153	190	2	2	2	NUM
ejpam-4153	190	3	]	]	X
ejpam-4153	190	4	d.h	d.h	PROPN
ejpam-4153	190	5	.	.	PROPN
ejpam-4153	190	6	bailey	bailey	PROPN
ejpam-4153	190	7	and	and	CCONJ
ejpam-4153	190	8	j.m	j.m	PROPN
ejpam-4153	190	9	.	.	PROPN
ejpam-4153	190	10	borwein	borwein	PROPN
ejpam-4153	190	11	.	.	PUNCT
ejpam-4153	191	1	crandall	crandall	PROPN
ejpam-4153	191	2	’s	’s	PART
ejpam-4153	191	3	computation	computation	NOUN
ejpam-4153	191	4	of	of	ADP
ejpam-4153	191	5	the	the	DET
ejpam-4153	191	6	incomplete	incomplete	ADJ
ejpam-4153	191	7	gamma	gamma	NOUN
ejpam-4153	191	8	function	function	NOUN
ejpam-4153	191	9	and	and	CCONJ
ejpam-4153	191	10	the	the	DET
ejpam-4153	191	11	hurwitz	hurwitz	PROPN
ejpam-4153	191	12	zeta	zeta	PROPN
ejpam-4153	191	13	function	function	PROPN
ejpam-4153	191	14	,	,	PUNCT
ejpam-4153	191	15	with	with	ADP
ejpam-4153	191	16	applications	application	NOUN
ejpam-4153	191	17	to	to	ADP
ejpam-4153	191	18	dirichlet	dirichlet	PROPN
ejpam-4153	191	19	l	l	PROPN
ejpam-4153	191	20	-	-	NOUN
ejpam-4153	191	21	series	series	NOUN
ejpam-4153	191	22	.	.	PUNCT
ejpam-4153	192	1	applied	apply	VERB
ejpam-4153	192	2	mathematics	mathematic	NOUN
ejpam-4153	192	3	and	and	CCONJ
ejpam-4153	192	4	computation	computation	NOUN
ejpam-4153	192	5	,	,	PUNCT
ejpam-4153	192	6	268:462–477	268:462–477	NUM
ejpam-4153	192	7	,	,	PUNCT
ejpam-4153	192	8	10	10	NUM
ejpam-4153	192	9	2015	2015	NUM
ejpam-4153	192	10	.	.	PUNCT
ejpam-4153	193	1	[	[	X
ejpam-4153	193	2	3	3	X
ejpam-4153	193	3	]	]	X
ejpam-4153	193	4	eugenio	eugenio	PROPN
ejpam-4153	193	5	balanzario	balanzario	PROPN
ejpam-4153	193	6	and	and	CCONJ
ejpam-4153	193	7	jorge	jorge	VERB
ejpam-4153	193	8	sánchez	sánchez	PROPN
ejpam-4153	193	9	-	-	PUNCT
ejpam-4153	193	10	ortiz	ortiz	PROPN
ejpam-4153	193	11	.	.	PUNCT
ejpam-4153	194	1	riemann	riemann	PROPN
ejpam-4153	194	2	-	-	PUNCT
ejpam-4153	194	3	siegel	siegel	PROPN
ejpam-4153	194	4	integral	integral	ADJ
ejpam-4153	194	5	formula	formula	NOUN
ejpam-4153	194	6	for	for	ADP
ejpam-4153	194	7	the	the	DET
ejpam-4153	194	8	lerch	lerch	PROPN
ejpam-4153	194	9	zeta	zeta	PROPN
ejpam-4153	194	10	function	function	PROPN
ejpam-4153	194	11	.	.	PUNCT
ejpam-4153	195	1	mathematics	mathematic	NOUN
ejpam-4153	195	2	of	of	ADP
ejpam-4153	195	3	computation	computation	NOUN
ejpam-4153	195	4	,	,	PUNCT
ejpam-4153	195	5	81:2319–2333	81:2319–2333	NUM
ejpam-4153	195	6	,	,	PUNCT
ejpam-4153	195	7	11	11	NUM
ejpam-4153	195	8	2011	2011	NUM
ejpam-4153	195	9	.	.	PUNCT
ejpam-4153	196	1	[	[	X
ejpam-4153	196	2	4	4	X
ejpam-4153	196	3	]	]	X
ejpam-4153	196	4	harry	harry	PROPN
ejpam-4153	196	5	bateman	bateman	PROPN
ejpam-4153	196	6	.	.	PUNCT
ejpam-4153	197	1	higher	high	ADJ
ejpam-4153	197	2	transcendental	transcendental	ADJ
ejpam-4153	197	3	functions	function	NOUN
ejpam-4153	197	4	v.1	v.1	PUNCT
ejpam-4153	197	5	.	.	PUNCT
ejpam-4153	198	1	mcgraw	mcgraw	PROPN
ejpam-4153	198	2	-	-	PUNCT
ejpam-4153	198	3	hill	hill	PROPN
ejpam-4153	198	4	,	,	PUNCT
ejpam-4153	198	5	1953	1953	NUM
ejpam-4153	198	6	.	.	PUNCT
ejpam-4153	199	1	[	[	X
ejpam-4153	199	2	5	5	NUM
ejpam-4153	199	3	]	]	PUNCT
ejpam-4153	199	4	nist	nist	NOUN
ejpam-4153	199	5	digital	digital	PROPN
ejpam-4153	199	6	library	library	NOUN
ejpam-4153	199	7	of	of	ADP
ejpam-4153	199	8	mathematical	mathematical	ADJ
ejpam-4153	199	9	functions	function	NOUN
ejpam-4153	199	10	.	.	PUNCT
ejpam-4153	200	1	f.	f.	PROPN
ejpam-4153	200	2	w.	w.	PROPN
ejpam-4153	200	3	j.	j.	PROPN
ejpam-4153	200	4	olver	olver	PROPN
ejpam-4153	200	5	,	,	PUNCT
ejpam-4153	200	6	a.	a.	PROPN
ejpam-4153	200	7	b.	b.	PROPN
ejpam-4153	200	8	olde	olde	PROPN
ejpam-4153	200	9	daalhuis	daalhuis	PROPN
ejpam-4153	200	10	,	,	PUNCT
ejpam-4153	200	11	d.	d.	PROPN
ejpam-4153	200	12	w.	w.	PROPN
ejpam-4153	200	13	lozier	lozier	PROPN
ejpam-4153	200	14	,	,	PUNCT
ejpam-4153	200	15	b.	b.	PROPN
ejpam-4153	200	16	i.	i.	PROPN
ejpam-4153	200	17	schneider	schneider	PROPN
ejpam-4153	200	18	,	,	PUNCT
ejpam-4153	200	19	r.	r.	PROPN
ejpam-4153	200	20	f.	f.	PROPN
ejpam-4153	200	21	boisvert	boisvert	PROPN
ejpam-4153	200	22	,	,	PUNCT
ejpam-4153	200	23	c.	c.	PROPN
ejpam-4153	200	24	w.	w.	PROPN
ejpam-4153	200	25	clark	clark	PROPN
ejpam-4153	200	26	,	,	PUNCT
ejpam-4153	200	27	b.	b.	PROPN
ejpam-4153	200	28	r.	r.	PROPN
ejpam-4153	200	29	miller	miller	PROPN
ejpam-4153	200	30	,	,	PUNCT
ejpam-4153	200	31	b.	b.	PROPN
ejpam-4153	201	1	v.	v.	PROPN
ejpam-4153	201	2	saunders	saunders	PROPN
ejpam-4153	201	3	,	,	PUNCT
ejpam-4153	201	4	h.	h.	PROPN
ejpam-4153	201	5	s.	s.	PROPN
ejpam-4153	201	6	cohl	cohl	PROPN
ejpam-4153	201	7	,	,	PUNCT
ejpam-4153	201	8	and	and	CCONJ
ejpam-4153	201	9	m.	m.	PROPN
ejpam-4153	201	10	a.	a.	PROPN
ejpam-4153	201	11	mcclain	mcclain	PROPN
ejpam-4153	201	12	,	,	PUNCT
ejpam-4153	201	13	eds	eds	PROPN
ejpam-4153	201	14	.	.	PUNCT
ejpam-4153	201	15	references	reference	NOUN
ejpam-4153	201	16	237	237	NUM
ejpam-4153	201	17	[	[	SYM
ejpam-4153	201	18	6	6	NUM
ejpam-4153	201	19	]	]	PUNCT
ejpam-4153	201	20	i.	i.	PROPN
ejpam-4153	201	21	s.	s.	PROPN
ejpam-4153	201	22	gradshteyn	gradshteyn	PROPN
ejpam-4153	201	23	and	and	CCONJ
ejpam-4153	201	24	i.	i.	PROPN
ejpam-4153	201	25	m.	m.	PROPN
ejpam-4153	201	26	ryzhik	ryzhik	PROPN
ejpam-4153	201	27	.	.	PUNCT
ejpam-4153	202	1	table	table	NOUN
ejpam-4153	202	2	of	of	ADP
ejpam-4153	202	3	integrals	integral	NOUN
ejpam-4153	202	4	,	,	PUNCT
ejpam-4153	202	5	series	series	NOUN
ejpam-4153	202	6	,	,	PUNCT
ejpam-4153	202	7	and	and	CCONJ
ejpam-4153	202	8	products	product	NOUN
ejpam-4153	202	9	.	.	PUNCT
ejpam-4153	203	1	elsevier	elsevier	NOUN
ejpam-4153	203	2	/	/	SYM
ejpam-4153	203	3	academic	academic	ADJ
ejpam-4153	203	4	press	press	NOUN
ejpam-4153	203	5	,	,	PUNCT
ejpam-4153	203	6	amsterdam	amsterdam	PROPN
ejpam-4153	203	7	,	,	PUNCT
ejpam-4153	203	8	seventh	seventh	ADJ
ejpam-4153	203	9	edition	edition	NOUN
ejpam-4153	203	10	,	,	PUNCT
ejpam-4153	203	11	2007	2007	NUM
ejpam-4153	203	12	.	.	PUNCT
ejpam-4153	204	1	[	[	X
ejpam-4153	204	2	7	7	X
ejpam-4153	204	3	]	]	X
ejpam-4153	204	4	jesús	jesús	PROPN
ejpam-4153	204	5	guillera	guillera	PROPN
ejpam-4153	204	6	and	and	CCONJ
ejpam-4153	204	7	jonathan	jonathan	PROPN
ejpam-4153	204	8	sondow	sondow	PROPN
ejpam-4153	204	9	.	.	PUNCT
ejpam-4153	205	1	double	double	ADJ
ejpam-4153	205	2	integrals	integral	NOUN
ejpam-4153	205	3	and	and	CCONJ
ejpam-4153	205	4	infinite	infinite	ADJ
ejpam-4153	205	5	products	product	NOUN
ejpam-4153	205	6	for	for	ADP
ejpam-4153	205	7	some	some	DET
ejpam-4153	205	8	classical	classical	ADJ
ejpam-4153	205	9	constants	constant	NOUN
ejpam-4153	205	10	via	via	ADP
ejpam-4153	205	11	analytic	analytic	ADJ
ejpam-4153	205	12	continuations	continuation	NOUN
ejpam-4153	205	13	of	of	ADP
ejpam-4153	205	14	lerch	lerch	PROPN
ejpam-4153	205	15	’s	’s	PART
ejpam-4153	205	16	transcendent	transcendent	NOUN
ejpam-4153	205	17	.	.	PUNCT
ejpam-4153	206	1	the	the	DET
ejpam-4153	206	2	ramanujan	ramanujan	PROPN
ejpam-4153	206	3	journal	journal	PROPN
ejpam-4153	206	4	,	,	PUNCT
ejpam-4153	206	5	16:247–270	16:247–270	NUM
ejpam-4153	206	6	,	,	PUNCT
ejpam-4153	206	7	07	07	NUM
ejpam-4153	206	8	2008	2008	NUM
ejpam-4153	206	9	.	.	PUNCT
ejpam-4153	207	1	[	[	X
ejpam-4153	207	2	8	8	NUM
ejpam-4153	207	3	]	]	X
ejpam-4153	207	4	d.	d.	PROPN
ejpam-4153	207	5	bierens	bierens	PROPN
ejpam-4153	207	6	de	de	PROPN
ejpam-4153	207	7	(	(	PUNCT
ejpam-4153	207	8	david	david	PROPN
ejpam-4153	207	9	bierens	bierens	PROPN
ejpam-4153	207	10	)	)	PUNCT
ejpam-4153	207	11	haan	haan	PROPN
ejpam-4153	207	12	.	.	PUNCT
ejpam-4153	208	1	nouvelles	nouvelles	PROPN
ejpam-4153	208	2	tables	table	NOUN
ejpam-4153	208	3	d’integrales	d’integrale	VERB
ejpam-4153	208	4	definies	definie	NOUN
ejpam-4153	208	5	.	.	PUNCT
ejpam-4153	209	1	jscholarship.library.jhu.edu	jscholarship.library.jhu.edu	PROPN
ejpam-4153	209	2	,	,	PUNCT
ejpam-4153	209	3	1867	1867	NUM
ejpam-4153	209	4	.	.	PUNCT
ejpam-4153	210	1	[	[	X
ejpam-4153	210	2	9	9	NUM
ejpam-4153	210	3	]	]	X
ejpam-4153	210	4	keith	keith	PROPN
ejpam-4153	210	5	b.	b.	PROPN
ejpam-4153	210	6	oldham	oldham	PROPN
ejpam-4153	210	7	,	,	PUNCT
ejpam-4153	210	8	jan	jan	PROPN
ejpam-4153	210	9	myland	myland	PROPN
ejpam-4153	210	10	,	,	PUNCT
ejpam-4153	210	11	and	and	CCONJ
ejpam-4153	210	12	jerome	jerome	PROPN
ejpam-4153	210	13	spanier	spanier	NOUN
ejpam-4153	210	14	.	.	PUNCT
ejpam-4153	211	1	an	an	DET
ejpam-4153	211	2	atlas	atlas	PROPN
ejpam-4153	211	3	of	of	ADP
ejpam-4153	211	4	functions	function	NOUN
ejpam-4153	211	5	:	:	PUNCT
ejpam-4153	211	6	with	with	ADP
ejpam-4153	211	7	equator	equator	NOUN
ejpam-4153	211	8	,	,	PUNCT
ejpam-4153	211	9	the	the	DET
ejpam-4153	211	10	atlas	atlas	PROPN
ejpam-4153	211	11	function	function	PROPN
ejpam-4153	211	12	calculator	calculator	NOUN
ejpam-4153	211	13	.	.	PUNCT
ejpam-4153	212	1	springer	springer	NOUN
ejpam-4153	212	2	science	science	PROPN
ejpam-4153	212	3	&	&	CCONJ
ejpam-4153	212	4	business	business	NOUN
ejpam-4153	212	5	media	medium	NOUN
ejpam-4153	212	6	,	,	PUNCT
ejpam-4153	212	7	07	07	NUM
ejpam-4153	212	8	2010	2010	NUM
ejpam-4153	212	9	.	.	PUNCT
ejpam-4153	213	1	[	[	X
ejpam-4153	213	2	10	10	NUM
ejpam-4153	213	3	]	]	X
ejpam-4153	213	4	robert	robert	PROPN
ejpam-4153	213	5	reynolds	reynolds	PROPN
ejpam-4153	213	6	and	and	CCONJ
ejpam-4153	213	7	allan	allan	PROPN
ejpam-4153	213	8	stauffer	stauffer	PROPN
ejpam-4153	213	9	.	.	PUNCT
ejpam-4153	214	1	a	a	DET
ejpam-4153	214	2	method	method	NOUN
ejpam-4153	214	3	for	for	ADP
ejpam-4153	214	4	evaluating	evaluate	VERB
ejpam-4153	214	5	definite	definite	ADJ
ejpam-4153	214	6	integrals	integral	NOUN
ejpam-4153	214	7	in	in	ADP
ejpam-4153	214	8	terms	term	NOUN
ejpam-4153	214	9	of	of	ADP
ejpam-4153	214	10	special	special	ADJ
ejpam-4153	214	11	functions	function	NOUN
ejpam-4153	214	12	with	with	ADP
ejpam-4153	214	13	examples	example	NOUN
ejpam-4153	214	14	.	.	PUNCT
ejpam-4153	215	1	international	international	ADJ
ejpam-4153	215	2	mathematical	mathematical	PROPN
ejpam-4153	215	3	forum	forum	PROPN
ejpam-4153	215	4	,	,	PUNCT
ejpam-4153	215	5	15:235	15:235	NUM
ejpam-4153	215	6	–	–	PUNCT
ejpam-4153	215	7	244	244	NUM
ejpam-4153	215	8	,	,	PUNCT
ejpam-4153	215	9	2020	2020	NUM
ejpam-4153	215	10	.	.	PUNCT