id	sid	tid	token	lemma	pos
ejpam-3991	1	1	european	european	PROPN
ejpam-3991	1	2	journal	journal	PROPN
ejpam-3991	1	3	of	of	ADP
ejpam-3991	1	4	pure	pure	ADJ
ejpam-3991	1	5	and	and	CCONJ
ejpam-3991	1	6	applied	apply	VERB
ejpam-3991	1	7	mathematics	mathematic	NOUN
ejpam-3991	1	8	vol	vol	NOUN
ejpam-3991	1	9	.	.	PUNCT
ejpam-3991	2	1	14	14	NUM
ejpam-3991	2	2	,	,	PUNCT
ejpam-3991	2	3	no	no	INTJ
ejpam-3991	2	4	.	.	NOUN
ejpam-3991	2	5	3	3	NUM
ejpam-3991	2	6	,	,	PUNCT
ejpam-3991	2	7	2021	2021	NUM
ejpam-3991	2	8	,	,	PUNCT
ejpam-3991	2	9	723	723	NUM
ejpam-3991	2	10	-	-	SYM
ejpam-3991	2	11	736	736	NUM
ejpam-3991	2	12	issn	issn	PROPN
ejpam-3991	2	13	1307	1307	NUM
ejpam-3991	2	14	-	-	SYM
ejpam-3991	2	15	5543	5543	NUM
ejpam-3991	2	16	–	–	PUNCT
ejpam-3991	2	17	ejpam.com	ejpam.com	X
ejpam-3991	2	18	published	publish	VERB
ejpam-3991	2	19	by	by	ADP
ejpam-3991	2	20	new	new	PROPN
ejpam-3991	2	21	york	york	PROPN
ejpam-3991	2	22	business	business	PROPN
ejpam-3991	2	23	global	global	ADJ
ejpam-3991	2	24	note	note	NOUN
ejpam-3991	2	25	on	on	ADP
ejpam-3991	2	26	a	a	DET
ejpam-3991	2	27	stieltjes	stieltjes	NOUN
ejpam-3991	2	28	transform	transform	NOUN
ejpam-3991	2	29	in	in	ADP
ejpam-3991	2	30	terms	term	NOUN
ejpam-3991	2	31	of	of	ADP
ejpam-3991	2	32	the	the	DET
ejpam-3991	2	33	lerch	lerch	PROPN
ejpam-3991	2	34	function	function	PROPN
ejpam-3991	2	35	robert	robert	PROPN
ejpam-3991	2	36	reynolds1,∗	reynolds1,∗	PROPN
ejpam-3991	2	37	,	,	PUNCT
ejpam-3991	2	38	allan	allan	PROPN
ejpam-3991	2	39	stauffer1	stauffer1	PROPN
ejpam-3991	2	40	1	1	NUM
ejpam-3991	2	41	department	department	NOUN
ejpam-3991	2	42	of	of	ADP
ejpam-3991	2	43	mathematics	mathematic	NOUN
ejpam-3991	2	44	and	and	CCONJ
ejpam-3991	2	45	statistics	statistic	NOUN
ejpam-3991	2	46	,	,	PUNCT
ejpam-3991	2	47	faculty	faculty	NOUN
ejpam-3991	2	48	of	of	ADP
ejpam-3991	2	49	science	science	PROPN
ejpam-3991	2	50	,	,	PUNCT
ejpam-3991	2	51	york	york	PROPN
ejpam-3991	2	52	university	university	PROPN
ejpam-3991	2	53	,	,	PUNCT
ejpam-3991	2	54	toronto	toronto	PROPN
ejpam-3991	2	55	,	,	PUNCT
ejpam-3991	2	56	ontario	ontario	PROPN
ejpam-3991	2	57	,	,	PUNCT
ejpam-3991	2	58	canada	canada	PROPN
ejpam-3991	2	59	abstract	abstract	NOUN
ejpam-3991	2	60	.	.	PUNCT
ejpam-3991	3	1	in	in	ADP
ejpam-3991	3	2	this	this	DET
ejpam-3991	3	3	work	work	NOUN
ejpam-3991	3	4	the	the	DET
ejpam-3991	3	5	authors	author	NOUN
ejpam-3991	3	6	derive	derive	VERB
ejpam-3991	3	7	the	the	DET
ejpam-3991	3	8	stieltjes	stieltjes	PROPN
ejpam-3991	3	9	transform	transform	NOUN
ejpam-3991	3	10	of	of	ADP
ejpam-3991	3	11	the	the	DET
ejpam-3991	3	12	logarithmic	logarithmic	ADJ
ejpam-3991	3	13	function	function	NOUN
ejpam-3991	3	14	in	in	ADP
ejpam-3991	3	15	terms	term	NOUN
ejpam-3991	3	16	of	of	ADP
ejpam-3991	3	17	the	the	DET
ejpam-3991	3	18	lerch	lerch	PROPN
ejpam-3991	3	19	function	function	PROPN
ejpam-3991	3	20	.	.	PUNCT
ejpam-3991	4	1	this	this	DET
ejpam-3991	4	2	transform	transform	NOUN
ejpam-3991	4	3	is	be	AUX
ejpam-3991	4	4	used	use	VERB
ejpam-3991	4	5	to	to	PART
ejpam-3991	4	6	derive	derive	VERB
ejpam-3991	4	7	closed	closed	ADJ
ejpam-3991	4	8	form	form	NOUN
ejpam-3991	4	9	solutions	solution	NOUN
ejpam-3991	4	10	involving	involve	VERB
ejpam-3991	4	11	fundamental	fundamental	ADJ
ejpam-3991	4	12	constants	constant	NOUN
ejpam-3991	4	13	and	and	CCONJ
ejpam-3991	4	14	special	special	ADJ
ejpam-3991	4	15	functions	function	NOUN
ejpam-3991	4	16	.	.	PUNCT
ejpam-3991	5	1	specifically	specifically	ADV
ejpam-3991	5	2	we	we	PRON
ejpam-3991	5	3	derive	derive	VERB
ejpam-3991	5	4	the	the	DET
ejpam-3991	5	5	definite	definite	ADJ
ejpam-3991	5	6	integral	integral	ADJ
ejpam-3991	5	7	given	give	VERB
ejpam-3991	5	8	by∫	by∫	PROPN
ejpam-3991	5	9	∞	∞	PROPN
ejpam-3991	5	10	0	0	NUM
ejpam-3991	6	1	(	(	PUNCT
ejpam-3991	6	2	1−	1−	NUM
ejpam-3991	6	3	bx)m	bx)m	PROPN
ejpam-3991	6	4	logk(c(1−	logk(c(1−	PROPN
ejpam-3991	6	5	bx	bx	PROPN
ejpam-3991	6	6	)	)	PUNCT
ejpam-3991	6	7	)	)	PUNCT
ejpam-3991	7	1	+	+	CCONJ
ejpam-3991	7	2	(	(	PUNCT
ejpam-3991	7	3	bx+	bx+	PROPN
ejpam-3991	7	4	1)m	1)m	NUM
ejpam-3991	7	5	logk(c(bx+	logk(c(bx+	NUM
ejpam-3991	7	6	1	1	NUM
ejpam-3991	7	7	)	)	PUNCT
ejpam-3991	7	8	)	)	PUNCT
ejpam-3991	7	9	a+	a+	PUNCT
ejpam-3991	8	1	x2	x2	PROPN
ejpam-3991	8	2	dx	dx	PROPN
ejpam-3991	8	3	where	where	SCONJ
ejpam-3991	8	4	a	a	DET
ejpam-3991	8	5	,	,	PUNCT
ejpam-3991	8	6	b	b	NOUN
ejpam-3991	8	7	,	,	PUNCT
ejpam-3991	8	8	c	c	NOUN
ejpam-3991	8	9	,	,	PUNCT
ejpam-3991	8	10	m	m	VERB
ejpam-3991	8	11	and	and	CCONJ
ejpam-3991	8	12	k	k	PROPN
ejpam-3991	8	13	are	be	AUX
ejpam-3991	8	14	general	general	ADJ
ejpam-3991	8	15	complex	complex	ADJ
ejpam-3991	8	16	numbers	number	NOUN
ejpam-3991	8	17	subject	subject	ADJ
ejpam-3991	8	18	to	to	ADP
ejpam-3991	8	19	the	the	DET
ejpam-3991	8	20	restrictions	restriction	NOUN
ejpam-3991	8	21	given	give	VERB
ejpam-3991	8	22	in	in	ADP
ejpam-3991	8	23	connection	connection	NOUN
ejpam-3991	8	24	with	with	ADP
ejpam-3991	8	25	the	the	DET
ejpam-3991	8	26	formulas	formula	NOUN
ejpam-3991	8	27	.	.	PUNCT
ejpam-3991	9	1	2020	2020	NUM
ejpam-3991	9	2	mathematics	mathematic	NOUN
ejpam-3991	9	3	subject	subject	NOUN
ejpam-3991	9	4	classifications	classification	NOUN
ejpam-3991	9	5	:	:	PUNCT
ejpam-3991	9	6	01a55	01a55	NOUN
ejpam-3991	9	7	,	,	PUNCT
ejpam-3991	9	8	11m06	11m06	NUM
ejpam-3991	9	9	,	,	PUNCT
ejpam-3991	9	10	11m35	11m35	NUM
ejpam-3991	9	11	,	,	PUNCT
ejpam-3991	9	12	30	30	NUM
ejpam-3991	9	13	-	-	SYM
ejpam-3991	9	14	02	02	NUM
ejpam-3991	9	15	,	,	PUNCT
ejpam-3991	9	16	30d10	30d10	NUM
ejpam-3991	9	17	,	,	PUNCT
ejpam-3991	9	18	30d30	30d30	NUM
ejpam-3991	9	19	,	,	PUNCT
ejpam-3991	9	20	30e20	30e20	NUM
ejpam-3991	9	21	key	key	ADJ
ejpam-3991	9	22	words	word	NOUN
ejpam-3991	9	23	and	and	CCONJ
ejpam-3991	9	24	phrases	phrase	NOUN
ejpam-3991	9	25	:	:	PUNCT
ejpam-3991	9	26	stieltjes	stieltjes	PROPN
ejpam-3991	9	27	transform	transform	VERB
ejpam-3991	9	28	|	|	ADV
ejpam-3991	9	29	lerch	lerch	NOUN
ejpam-3991	9	30	|	|	ADV
ejpam-3991	9	31	definite	definite	ADJ
ejpam-3991	9	32	integral	integral	ADJ
ejpam-3991	9	33	|	|	NOUN
ejpam-3991	9	34	entries	entry	NOUN
ejpam-3991	9	35	in	in	ADP
ejpam-3991	9	36	gradshteyn	gradshteyn	PROPN
ejpam-3991	9	37	and	and	CCONJ
ejpam-3991	9	38	rhyzik	rhyzik	ADJ
ejpam-3991	9	39	1	1	NUM
ejpam-3991	9	40	.	.	PUNCT
ejpam-3991	9	41	significance	significance	NOUN
ejpam-3991	9	42	statement	statement	NOUN
ejpam-3991	9	43	the	the	DET
ejpam-3991	9	44	stieltjes	stieltjes	PROPN
ejpam-3991	9	45	transform	transform	VERB
ejpam-3991	9	46	and	and	CCONJ
ejpam-3991	9	47	lerch	lerch	PROPN
ejpam-3991	9	48	function	function	PROPN
ejpam-3991	9	49	were	be	AUX
ejpam-3991	9	50	both	both	PRON
ejpam-3991	9	51	developed	develop	VERB
ejpam-3991	9	52	between	between	ADP
ejpam-3991	9	53	1856	1856	NUM
ejpam-3991	9	54	-	-	SYM
ejpam-3991	9	55	1922	1922	NUM
ejpam-3991	9	56	,	,	PUNCT
ejpam-3991	9	57	by	by	ADP
ejpam-3991	9	58	famous	famous	ADJ
ejpam-3991	9	59	mathematicians	mathematician	NOUN
ejpam-3991	9	60	thomas	thomas	PROPN
ejpam-3991	9	61	joannes	joannes	PROPN
ejpam-3991	9	62	stieltjes	stieltjes	PROPN
ejpam-3991	9	63	and	and	CCONJ
ejpam-3991	9	64	mathias	mathias	PROPN
ejpam-3991	9	65	lerch	lerch	PROPN
ejpam-3991	9	66	respectively	respectively	ADV
ejpam-3991	9	67	.	.	PUNCT
ejpam-3991	10	1	the	the	DET
ejpam-3991	10	2	two	two	NUM
ejpam-3991	10	3	functions	function	NOUN
ejpam-3991	10	4	are	be	AUX
ejpam-3991	10	5	not	not	PART
ejpam-3991	10	6	well	well	ADV
ejpam-3991	10	7	documented	document	VERB
ejpam-3991	10	8	in	in	ADP
ejpam-3991	10	9	current	current	ADJ
ejpam-3991	10	10	literature	literature	NOUN
ejpam-3991	10	11	.	.	PUNCT
ejpam-3991	11	1	the	the	DET
ejpam-3991	11	2	stieltjes	stieltjes	PROPN
ejpam-3991	11	3	transform	transform	VERB
ejpam-3991	11	4	has	have	VERB
ejpam-3991	11	5	many	many	ADJ
ejpam-3991	11	6	real	real	ADJ
ejpam-3991	11	7	world	world	NOUN
ejpam-3991	11	8	applications	application	NOUN
ejpam-3991	11	9	such	such	ADJ
ejpam-3991	11	10	as	as	ADP
ejpam-3991	11	11	in	in	ADP
ejpam-3991	11	12	cognitive	cognitive	ADJ
ejpam-3991	11	13	radio	radio	NOUN
ejpam-3991	11	14	communication	communication	NOUN
ejpam-3991	11	15	and	and	CCONJ
ejpam-3991	11	16	networking	networking	NOUN
ejpam-3991	11	17	and	and	CCONJ
ejpam-3991	11	18	the	the	DET
ejpam-3991	11	19	lerch	lerch	PROPN
ejpam-3991	11	20	function	function	NOUN
ejpam-3991	11	21	is	be	AUX
ejpam-3991	11	22	closely	closely	ADV
ejpam-3991	11	23	related	relate	VERB
ejpam-3991	11	24	to	to	ADP
ejpam-3991	11	25	poisson	poisson	PROPN
ejpam-3991	11	26	’s	’s	PART
ejpam-3991	11	27	summation	summation	NOUN
ejpam-3991	11	28	formula	formula	NOUN
ejpam-3991	11	29	.	.	PUNCT
ejpam-3991	12	1	in	in	ADP
ejpam-3991	12	2	this	this	DET
ejpam-3991	12	3	article	article	NOUN
ejpam-3991	12	4	we	we	PRON
ejpam-3991	12	5	generate	generate	VERB
ejpam-3991	12	6	a	a	DET
ejpam-3991	12	7	new	new	ADJ
ejpam-3991	12	8	table	table	NOUN
ejpam-3991	12	9	of	of	ADP
ejpam-3991	12	10	definite	definite	ADJ
ejpam-3991	12	11	integral	integral	ADJ
ejpam-3991	12	12	formulas	formula	NOUN
ejpam-3991	12	13	which	which	PRON
ejpam-3991	12	14	can	can	AUX
ejpam-3991	12	15	be	be	AUX
ejpam-3991	12	16	used	use	VERB
ejpam-3991	12	17	as	as	ADP
ejpam-3991	12	18	reference	reference	NOUN
ejpam-3991	12	19	similar	similar	ADJ
ejpam-3991	12	20	to	to	ADP
ejpam-3991	12	21	current	current	ADJ
ejpam-3991	12	22	table	table	NOUN
ejpam-3991	12	23	of	of	ADP
ejpam-3991	12	24	definite	definite	ADJ
ejpam-3991	12	25	integrals	integral	NOUN
ejpam-3991	12	26	.	.	PUNCT
ejpam-3991	13	1	∗corresponding	∗corresponde	VERB
ejpam-3991	13	2	author	author	NOUN
ejpam-3991	13	3	.	.	PUNCT
ejpam-3991	14	1	doi	doi	NOUN
ejpam-3991	14	2	:	:	PUNCT
ejpam-3991	14	3	https://doi.org/10.29020/nybg.ejpam.v14i3.3991	https://doi.org/10.29020/nybg.ejpam.v14i3.3991	PROPN
ejpam-3991	14	4	email	email	NOUN
ejpam-3991	14	5	addresses	address	NOUN
ejpam-3991	14	6	:	:	PUNCT
ejpam-3991	15	1	milver@my.yorku.ca	milver@my.yorku.ca	NOUN
ejpam-3991	15	2	(	(	PUNCT
ejpam-3991	15	3	r.	r.	PROPN
ejpam-3991	15	4	reynolds	reynolds	PROPN
ejpam-3991	15	5	)	)	PUNCT
ejpam-3991	15	6	,	,	PUNCT
ejpam-3991	15	7	stauffer@yorku.ca	stauffer@yorku.ca	NOUN
ejpam-3991	15	8	(	(	PUNCT
ejpam-3991	15	9	a.	a.	NOUN
ejpam-3991	15	10	stauffer	stauffer	PROPN
ejpam-3991	15	11	)	)	PUNCT
ejpam-3991	15	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3991	16	1	723	723	NUM
ejpam-3991	16	2	©	©	PROPN
ejpam-3991	16	3	2021	2021	NUM
ejpam-3991	16	4	ejpam	ejpam	VERB
ejpam-3991	16	5	all	all	DET
ejpam-3991	16	6	rights	right	NOUN
ejpam-3991	16	7	reserved	reserve	VERB
ejpam-3991	16	8	.	.	PUNCT
ejpam-3991	17	1	r.	r.	PROPN
ejpam-3991	17	2	reynolds	reynolds	PROPN
ejpam-3991	17	3	,	,	PUNCT
ejpam-3991	17	4	a.	a.	PROPN
ejpam-3991	17	5	stauffer	stauffer	PROPN
ejpam-3991	17	6	/	/	SYM
ejpam-3991	17	7	eur	eur	PROPN
ejpam-3991	17	8	.	.	PUNCT
ejpam-3991	18	1	j.	j.	PROPN
ejpam-3991	18	2	pure	pure	PROPN
ejpam-3991	18	3	appl	appl	PROPN
ejpam-3991	18	4	.	.	PROPN
ejpam-3991	18	5	math	math	PROPN
ejpam-3991	18	6	,	,	PUNCT
ejpam-3991	18	7	14	14	NUM
ejpam-3991	18	8	(	(	PUNCT
ejpam-3991	18	9	3	3	NUM
ejpam-3991	18	10	)	)	PUNCT
ejpam-3991	18	11	(	(	PUNCT
ejpam-3991	18	12	2021	2021	NUM
ejpam-3991	18	13	)	)	PUNCT
ejpam-3991	18	14	,	,	PUNCT
ejpam-3991	18	15	723	723	NUM
ejpam-3991	18	16	-	-	SYM
ejpam-3991	18	17	736	736	NUM
ejpam-3991	18	18	724	724	NUM
ejpam-3991	18	19	2	2	NUM
ejpam-3991	18	20	.	.	PUNCT
ejpam-3991	19	1	introduction	introduction	NOUN
ejpam-3991	19	2	n	n	ADP
ejpam-3991	19	3	the	the	DET
ejpam-3991	19	4	late	late	ADJ
ejpam-3991	19	5	1800	1800	NUM
ejpam-3991	19	6	’s	’s	PART
ejpam-3991	19	7	thomas	thomas	PROPN
ejpam-3991	19	8	joannes	joannes	PROPN
ejpam-3991	19	9	stieltjes	stieltjes	PROPN
ejpam-3991	19	10	,	,	PUNCT
ejpam-3991	19	11	a	a	DET
ejpam-3991	19	12	dutch	dutch	ADJ
ejpam-3991	19	13	mathematician	mathematician	NOUN
ejpam-3991	19	14	found	find	VERB
ejpam-3991	19	15	the	the	DET
ejpam-3991	19	16	stieltjes	stieltjes	NOUN
ejpam-3991	19	17	transform	transform	VERB
ejpam-3991	19	18	.	.	PUNCT
ejpam-3991	20	1	in	in	ADP
ejpam-3991	20	2	this	this	DET
ejpam-3991	20	3	work	work	NOUN
ejpam-3991	20	4	we	we	PRON
ejpam-3991	20	5	will	will	AUX
ejpam-3991	20	6	derive	derive	VERB
ejpam-3991	20	7	this	this	DET
ejpam-3991	20	8	formula	formula	NOUN
ejpam-3991	20	9	as	as	SCONJ
ejpam-3991	20	10	shown	show	VERB
ejpam-3991	20	11	in	in	ADP
ejpam-3991	20	12	the	the	DET
ejpam-3991	20	13	abstract	abstract	ADJ
ejpam-3991	20	14	which	which	PRON
ejpam-3991	20	15	does	do	AUX
ejpam-3991	20	16	not	not	PART
ejpam-3991	20	17	exist	exist	VERB
ejpam-3991	20	18	in	in	ADP
ejpam-3991	20	19	current	current	ADJ
ejpam-3991	20	20	literature	literature	NOUN
ejpam-3991	20	21	.	.	PUNCT
ejpam-3991	21	1	we	we	PRON
ejpam-3991	21	2	will	will	AUX
ejpam-3991	21	3	use	use	VERB
ejpam-3991	21	4	this	this	DET
ejpam-3991	21	5	definite	definite	ADJ
ejpam-3991	21	6	integral	integral	ADJ
ejpam-3991	21	7	to	to	PART
ejpam-3991	21	8	produce	produce	VERB
ejpam-3991	21	9	formal	formal	ADJ
ejpam-3991	21	10	derivations	derivation	NOUN
ejpam-3991	21	11	of	of	ADP
ejpam-3991	21	12	known	know	VERB
ejpam-3991	21	13	integral	integral	ADJ
ejpam-3991	21	14	formulas	formula	NOUN
ejpam-3991	21	15	in	in	ADP
ejpam-3991	21	16	[	[	X
ejpam-3991	21	17	1	1	NUM
ejpam-3991	21	18	]	]	PUNCT
ejpam-3991	21	19	and	and	CCONJ
ejpam-3991	21	20	[	[	X
ejpam-3991	21	21	2	2	NUM
ejpam-3991	21	22	]	]	PUNCT
ejpam-3991	21	23	.	.	PUNCT
ejpam-3991	22	1	we	we	PRON
ejpam-3991	22	2	will	will	AUX
ejpam-3991	22	3	also	also	ADV
ejpam-3991	22	4	derive	derive	VERB
ejpam-3991	22	5	new	new	ADJ
ejpam-3991	22	6	formula	formula	NOUN
ejpam-3991	22	7	which	which	PRON
ejpam-3991	22	8	can	can	AUX
ejpam-3991	22	9	be	be	AUX
ejpam-3991	22	10	considered	consider	VERB
ejpam-3991	22	11	an	an	DET
ejpam-3991	22	12	extension	extension	NOUN
ejpam-3991	22	13	to	to	PART
ejpam-3991	22	14	erdeyli	erdeyli	VERB
ejpam-3991	22	15	’s	’s	PART
ejpam-3991	22	16	extensive	extensive	ADJ
ejpam-3991	22	17	table	table	NOUN
ejpam-3991	22	18	of	of	ADP
ejpam-3991	22	19	transforms	transform	NOUN
ejpam-3991	22	20	.	.	PUNCT
ejpam-3991	23	1	the	the	DET
ejpam-3991	23	2	derivations	derivation	NOUN
ejpam-3991	23	3	follow	follow	VERB
ejpam-3991	23	4	the	the	DET
ejpam-3991	23	5	method	method	NOUN
ejpam-3991	23	6	used	use	VERB
ejpam-3991	23	7	by	by	ADP
ejpam-3991	23	8	us	we	PRON
ejpam-3991	23	9	in	in	ADP
ejpam-3991	23	10	[	[	X
ejpam-3991	23	11	5	5	NUM
ejpam-3991	23	12	]	]	PUNCT
ejpam-3991	23	13	,	,	PUNCT
ejpam-3991	23	14	[	[	X
ejpam-3991	23	15	4	4	NUM
ejpam-3991	23	16	]	]	PUNCT
ejpam-3991	23	17	,	,	PUNCT
ejpam-3991	23	18	[	[	X
ejpam-3991	23	19	6	6	NUM
ejpam-3991	23	20	]	]	PUNCT
ejpam-3991	23	21	,	,	PUNCT
ejpam-3991	23	22	[	[	X
ejpam-3991	23	23	7	7	NUM
ejpam-3991	23	24	]	]	PUNCT
ejpam-3991	23	25	,	,	PUNCT
ejpam-3991	23	26	[	[	X
ejpam-3991	23	27	9	9	NUM
ejpam-3991	23	28	]	]	PUNCT
ejpam-3991	23	29	and	and	CCONJ
ejpam-3991	23	30	[	[	X
ejpam-3991	23	31	8	8	NUM
ejpam-3991	23	32	]	]	PUNCT
ejpam-3991	23	33	.	.	PUNCT
ejpam-3991	24	1	this	this	DET
ejpam-3991	24	2	method	method	NOUN
ejpam-3991	24	3	involves	involve	VERB
ejpam-3991	24	4	using	use	VERB
ejpam-3991	24	5	a	a	DET
ejpam-3991	24	6	form	form	NOUN
ejpam-3991	24	7	of	of	ADP
ejpam-3991	24	8	the	the	DET
ejpam-3991	24	9	generalized	generalize	VERB
ejpam-3991	24	10	cauchy	cauchy	PROPN
ejpam-3991	24	11	’s	’s	PART
ejpam-3991	24	12	integral	integral	ADJ
ejpam-3991	24	13	formula	formula	NOUN
ejpam-3991	24	14	given	give	VERB
ejpam-3991	24	15	by	by	ADP
ejpam-3991	24	16	(	(	PUNCT
ejpam-3991	24	17	1	1	X
ejpam-3991	24	18	)	)	PUNCT
ejpam-3991	24	19	yk	yk	PROPN
ejpam-3991	24	20	k	k	PROPN
ejpam-3991	24	21	!	!	PUNCT
ejpam-3991	25	1	=	=	SYM
ejpam-3991	25	2	1	1	NUM
ejpam-3991	25	3	2πi	2πi	ADJ
ejpam-3991	25	4	∫	∫	PROPN
ejpam-3991	25	5	c	c	PROPN
ejpam-3991	25	6	ewy	ewy	PROPN
ejpam-3991	25	7	wk+1	wk+1	X
ejpam-3991	25	8	dy	dy	NOUN
ejpam-3991	25	9	.	.	PUNCT
ejpam-3991	26	1	where	where	SCONJ
ejpam-3991	26	2	c	c	NOUN
ejpam-3991	26	3	is	be	AUX
ejpam-3991	26	4	in	in	ADP
ejpam-3991	26	5	general	general	ADJ
ejpam-3991	26	6	,	,	PUNCT
ejpam-3991	26	7	an	an	DET
ejpam-3991	26	8	open	open	ADJ
ejpam-3991	26	9	contour	contour	NOUN
ejpam-3991	26	10	in	in	ADP
ejpam-3991	26	11	the	the	DET
ejpam-3991	26	12	complex	complex	ADJ
ejpam-3991	26	13	plane	plane	NOUN
ejpam-3991	26	14	where	where	SCONJ
ejpam-3991	26	15	the	the	DET
ejpam-3991	26	16	bilinear	bilinear	NOUN
ejpam-3991	26	17	concomitant	concomitant	NOUN
ejpam-3991	26	18	has	have	VERB
ejpam-3991	26	19	the	the	DET
ejpam-3991	26	20	same	same	ADJ
ejpam-3991	26	21	value	value	NOUN
ejpam-3991	26	22	at	at	ADP
ejpam-3991	26	23	the	the	DET
ejpam-3991	26	24	end	end	NOUN
ejpam-3991	26	25	points	point	NOUN
ejpam-3991	26	26	of	of	ADP
ejpam-3991	26	27	the	the	DET
ejpam-3991	26	28	contour	contour	NOUN
ejpam-3991	26	29	.	.	PUNCT
ejpam-3991	27	1	then	then	ADV
ejpam-3991	27	2	multiply	multiply	VERB
ejpam-3991	27	3	both	both	DET
ejpam-3991	27	4	sides	side	NOUN
ejpam-3991	27	5	by	by	ADP
ejpam-3991	27	6	a	a	DET
ejpam-3991	27	7	function	function	NOUN
ejpam-3991	27	8	,	,	PUNCT
ejpam-3991	27	9	then	then	ADV
ejpam-3991	27	10	takes	take	VERB
ejpam-3991	27	11	a	a	DET
ejpam-3991	27	12	definite	definite	ADJ
ejpam-3991	27	13	integral	integral	NOUN
ejpam-3991	27	14	of	of	ADP
ejpam-3991	27	15	both	both	DET
ejpam-3991	27	16	sides	side	NOUN
ejpam-3991	27	17	.	.	PUNCT
ejpam-3991	28	1	this	this	PRON
ejpam-3991	28	2	yields	yield	VERB
ejpam-3991	28	3	a	a	DET
ejpam-3991	28	4	definite	definite	ADJ
ejpam-3991	28	5	integral	integral	ADJ
ejpam-3991	28	6	in	in	ADP
ejpam-3991	28	7	terms	term	NOUN
ejpam-3991	28	8	of	of	ADP
ejpam-3991	28	9	a	a	DET
ejpam-3991	28	10	contour	contour	NOUN
ejpam-3991	28	11	integral	integral	NOUN
ejpam-3991	28	12	.	.	PUNCT
ejpam-3991	29	1	then	then	ADV
ejpam-3991	29	2	we	we	PRON
ejpam-3991	29	3	multiply	multiply	VERB
ejpam-3991	29	4	both	both	DET
ejpam-3991	29	5	sides	side	NOUN
ejpam-3991	29	6	of	of	ADP
ejpam-3991	29	7	equation	equation	NOUN
ejpam-3991	29	8	(	(	PUNCT
ejpam-3991	29	9	1	1	NUM
ejpam-3991	29	10	)	)	PUNCT
ejpam-3991	29	11	by	by	ADP
ejpam-3991	29	12	another	another	DET
ejpam-3991	29	13	function	function	NOUN
ejpam-3991	29	14	and	and	CCONJ
ejpam-3991	29	15	take	take	VERB
ejpam-3991	29	16	the	the	DET
ejpam-3991	29	17	infinite	infinite	ADJ
ejpam-3991	29	18	sum	sum	NOUN
ejpam-3991	29	19	of	of	ADP
ejpam-3991	29	20	both	both	DET
ejpam-3991	29	21	sides	side	NOUN
ejpam-3991	29	22	such	such	ADJ
ejpam-3991	29	23	that	that	SCONJ
ejpam-3991	29	24	the	the	DET
ejpam-3991	29	25	contour	contour	NOUN
ejpam-3991	29	26	integral	integral	NOUN
ejpam-3991	29	27	of	of	ADP
ejpam-3991	29	28	both	both	DET
ejpam-3991	29	29	equations	equation	NOUN
ejpam-3991	29	30	are	be	AUX
ejpam-3991	29	31	the	the	DET
ejpam-3991	29	32	same	same	ADJ
ejpam-3991	29	33	.	.	PUNCT
ejpam-3991	30	1	3	3	X
ejpam-3991	30	2	.	.	X
ejpam-3991	30	3	definite	definite	ADJ
ejpam-3991	30	4	integral	integral	ADJ
ejpam-3991	30	5	of	of	ADP
ejpam-3991	30	6	the	the	DET
ejpam-3991	30	7	contour	contour	NOUN
ejpam-3991	30	8	integral	integral	NOUN
ejpam-3991	30	9	we	we	PRON
ejpam-3991	30	10	use	use	VERB
ejpam-3991	30	11	the	the	DET
ejpam-3991	30	12	method	method	NOUN
ejpam-3991	30	13	in	in	ADP
ejpam-3991	30	14	[	[	X
ejpam-3991	30	15	9	9	NUM
ejpam-3991	30	16	]	]	PUNCT
ejpam-3991	30	17	.	.	PUNCT
ejpam-3991	31	1	the	the	DET
ejpam-3991	31	2	variable	variable	NOUN
ejpam-3991	31	3	of	of	ADP
ejpam-3991	31	4	integration	integration	NOUN
ejpam-3991	31	5	in	in	ADP
ejpam-3991	31	6	the	the	DET
ejpam-3991	31	7	contour	contour	NOUN
ejpam-3991	31	8	integral	integral	NOUN
ejpam-3991	31	9	is	be	AUX
ejpam-3991	31	10	z	z	NOUN
ejpam-3991	31	11	=	=	SYM
ejpam-3991	31	12	m	m	VERB
ejpam-3991	31	13	+	+	X
ejpam-3991	31	14	w.	w.	NOUN
ejpam-3991	31	15	the	the	DET
ejpam-3991	31	16	cut	cut	NOUN
ejpam-3991	31	17	and	and	CCONJ
ejpam-3991	31	18	contour	contour	NOUN
ejpam-3991	31	19	are	be	AUX
ejpam-3991	31	20	in	in	ADP
ejpam-3991	31	21	the	the	DET
ejpam-3991	31	22	second	second	ADJ
ejpam-3991	31	23	quadrant	quadrant	NOUN
ejpam-3991	31	24	of	of	ADP
ejpam-3991	31	25	the	the	DET
ejpam-3991	31	26	complex	complex	ADJ
ejpam-3991	31	27	z	z	NOUN
ejpam-3991	31	28	-	-	NOUN
ejpam-3991	31	29	plane	plane	NOUN
ejpam-3991	31	30	.	.	PUNCT
ejpam-3991	32	1	the	the	DET
ejpam-3991	32	2	cut	cut	NOUN
ejpam-3991	32	3	approaches	approach	VERB
ejpam-3991	32	4	the	the	DET
ejpam-3991	32	5	origin	origin	NOUN
ejpam-3991	32	6	from	from	ADP
ejpam-3991	32	7	the	the	DET
ejpam-3991	32	8	interior	interior	NOUN
ejpam-3991	32	9	of	of	ADP
ejpam-3991	32	10	the	the	DET
ejpam-3991	32	11	second	second	ADJ
ejpam-3991	32	12	quadrant	quadrant	NOUN
ejpam-3991	32	13	and	and	CCONJ
ejpam-3991	32	14	the	the	DET
ejpam-3991	32	15	contour	contour	NOUN
ejpam-3991	32	16	goes	go	VERB
ejpam-3991	32	17	round	round	ADP
ejpam-3991	32	18	the	the	DET
ejpam-3991	32	19	origin	origin	NOUN
ejpam-3991	32	20	with	with	ADP
ejpam-3991	32	21	zero	zero	NUM
ejpam-3991	32	22	radius	radius	NOUN
ejpam-3991	32	23	and	and	CCONJ
ejpam-3991	32	24	is	be	AUX
ejpam-3991	32	25	on	on	ADP
ejpam-3991	32	26	opposite	opposite	ADJ
ejpam-3991	32	27	sides	side	NOUN
ejpam-3991	32	28	of	of	ADP
ejpam-3991	32	29	the	the	DET
ejpam-3991	32	30	cut	cut	NOUN
ejpam-3991	32	31	.	.	PUNCT
ejpam-3991	33	1	we	we	PRON
ejpam-3991	33	2	replace	replace	VERB
ejpam-3991	33	3	y	y	PROPN
ejpam-3991	33	4	in	in	ADP
ejpam-3991	33	5	1	1	NUM
ejpam-3991	33	6	by	by	ADP
ejpam-3991	33	7	logk(c(1	logk(c(1	VERB
ejpam-3991	33	8	−	−	PROPN
ejpam-3991	33	9	bx	bx	NOUN
ejpam-3991	33	10	)	)	PUNCT
ejpam-3991	33	11	)	)	PUNCT
ejpam-3991	33	12	and	and	CCONJ
ejpam-3991	33	13	multiply	multiply	ADV
ejpam-3991	33	14	by	by	ADP
ejpam-3991	33	15	(	(	PUNCT
ejpam-3991	33	16	1	1	NUM
ejpam-3991	33	17	−	−	PROPN
ejpam-3991	33	18	bx)m/(a2	bx)m/(a2	NOUN
ejpam-3991	34	1	+	+	CCONJ
ejpam-3991	34	2	x2	x2	NOUN
ejpam-3991	34	3	)	)	PUNCT
ejpam-3991	34	4	in	in	ADP
ejpam-3991	34	5	the	the	DET
ejpam-3991	34	6	first	first	ADJ
ejpam-3991	34	7	case	case	NOUN
ejpam-3991	34	8	and	and	CCONJ
ejpam-3991	34	9	by	by	ADP
ejpam-3991	34	10	logk(c(1	logk(c(1	NOUN
ejpam-3991	34	11	+	+	PROPN
ejpam-3991	34	12	bx	bx	NOUN
ejpam-3991	34	13	)	)	PUNCT
ejpam-3991	34	14	)	)	PUNCT
ejpam-3991	34	15	and	and	CCONJ
ejpam-3991	34	16	multiply	multiply	ADV
ejpam-3991	34	17	by	by	ADP
ejpam-3991	34	18	(	(	PUNCT
ejpam-3991	34	19	1	1	NUM
ejpam-3991	34	20	+	+	NUM
ejpam-3991	34	21	bx)m/(a2	bx)m/(a2	NOUN
ejpam-3991	34	22	+	+	CCONJ
ejpam-3991	34	23	x2	x2	NOUN
ejpam-3991	34	24	)	)	PUNCT
ejpam-3991	34	25	in	in	ADP
ejpam-3991	34	26	the	the	DET
ejpam-3991	34	27	second	second	ADJ
ejpam-3991	34	28	case	case	NOUN
ejpam-3991	34	29	and	and	CCONJ
ejpam-3991	34	30	add	add	VERB
ejpam-3991	34	31	them	they	PRON
ejpam-3991	34	32	.	.	PUNCT
ejpam-3991	35	1	the	the	DET
ejpam-3991	35	2	integration	integration	NOUN
ejpam-3991	35	3	is	be	AUX
ejpam-3991	35	4	over	over	ADV
ejpam-3991	35	5	x	x	PUNCT
ejpam-3991	35	6	now	now	ADV
ejpam-3991	35	7	instead	instead	ADV
ejpam-3991	35	8	of	of	ADP
ejpam-3991	35	9	y.	y.	NOUN
ejpam-3991	35	10	(	(	PUNCT
ejpam-3991	35	11	2	2	NUM
ejpam-3991	35	12	)	)	PUNCT
ejpam-3991	35	13	1	1	NUM
ejpam-3991	36	1	k	k	X
ejpam-3991	36	2	!	!	PUNCT
ejpam-3991	36	3	∫	∫	PROPN
ejpam-3991	37	1	∞	∞	PROPN
ejpam-3991	37	2	0	0	NUM
ejpam-3991	37	3	(	(	PUNCT
ejpam-3991	37	4	1−	1−	NUM
ejpam-3991	37	5	bx)m	bx)m	PROPN
ejpam-3991	37	6	logk(c(1−	logk(c(1−	PROPN
ejpam-3991	37	7	bx	bx	PROPN
ejpam-3991	37	8	)	)	PUNCT
ejpam-3991	37	9	)	)	PUNCT
ejpam-3991	38	1	+	+	CCONJ
ejpam-3991	38	2	(	(	PUNCT
ejpam-3991	38	3	bx+	bx+	PROPN
ejpam-3991	38	4	1)m	1)m	NUM
ejpam-3991	38	5	logk(c(bx+	logk(c(bx+	NUM
ejpam-3991	38	6	1	1	NUM
ejpam-3991	38	7	)	)	PUNCT
ejpam-3991	38	8	)	)	PUNCT
ejpam-3991	38	9	a+	a+	PUNCT
ejpam-3991	39	1	x2	x2	PROPN
ejpam-3991	39	2	dx	dx	PROPN
ejpam-3991	39	3	=	=	SYM
ejpam-3991	39	4	1	1	NUM
ejpam-3991	39	5	2πi	2πi	NOUN
ejpam-3991	39	6	∫	∫	PROPN
ejpam-3991	40	1	∞	∞	NUM
ejpam-3991	40	2	0	0	NUM
ejpam-3991	40	3	∫	∫	PROPN
ejpam-3991	40	4	c	c	PROPN
ejpam-3991	40	5	cww−k−1	cww−k−1	NOUN
ejpam-3991	40	6	(	(	PUNCT
ejpam-3991	40	7	(	(	PUNCT
ejpam-3991	40	8	1−	1−	NUM
ejpam-3991	40	9	bx)m+w	bx)m+w	NOUN
ejpam-3991	40	10	+	+	CCONJ
ejpam-3991	40	11	(	(	PUNCT
ejpam-3991	40	12	bx+	bx+	NOUN
ejpam-3991	40	13	1)m+w	1)m+w	NUM
ejpam-3991	40	14	)	)	PUNCT
ejpam-3991	40	15	a+	a+	PUNCT
ejpam-3991	41	1	x2	x2	PROPN
ejpam-3991	41	2	dwdx	dwdx	VERB
ejpam-3991	41	3	=	=	SYM
ejpam-3991	41	4	1	1	NUM
ejpam-3991	41	5	2πi	2πi	NOUN
ejpam-3991	41	6	∫	∫	PROPN
ejpam-3991	41	7	c	c	PROPN
ejpam-3991	41	8	∫	∫	PROPN
ejpam-3991	42	1	∞	∞	PROPN
ejpam-3991	42	2	0	0	NUM
ejpam-3991	42	3	cww−k−1	cww−k−1	NOUN
ejpam-3991	42	4	(	(	PUNCT
ejpam-3991	42	5	(	(	PUNCT
ejpam-3991	42	6	1−	1−	NUM
ejpam-3991	42	7	bx)m+w	bx)m+w	NOUN
ejpam-3991	42	8	+	+	CCONJ
ejpam-3991	42	9	(	(	PUNCT
ejpam-3991	42	10	bx+	bx+	NOUN
ejpam-3991	42	11	1)m+w	1)m+w	NUM
ejpam-3991	42	12	)	)	PUNCT
ejpam-3991	42	13	a+	a+	PUNCT
ejpam-3991	42	14	x2	x2	PROPN
ejpam-3991	42	15	dxdw	dxdw	NOUN
ejpam-3991	42	16	=	=	SYM
ejpam-3991	42	17	1	1	NUM
ejpam-3991	42	18	2πi	2πi	NOUN
ejpam-3991	42	19	∫	∫	PROPN
ejpam-3991	43	1	c	c	NOUN
ejpam-3991	44	1	πcww−k−1a	πcww−k−1a	INTJ
ejpam-3991	45	1	1	1	NUM
ejpam-3991	45	2	2	2	NUM
ejpam-3991	45	3	(	(	PUNCT
ejpam-3991	45	4	m+w−1)(−b)m+w	m+w−1)(−b)m+w	NOUN
ejpam-3991	45	5	csc(π(m+	csc(π(m+	NOUN
ejpam-3991	45	6	w	w	NOUN
ejpam-3991	45	7	)	)	PUNCT
ejpam-3991	45	8	)	)	PUNCT
ejpam-3991	46	1	(	(	PUNCT
ejpam-3991	46	2	1	1	NUM
ejpam-3991	46	3	ab2	ab2	ADJ
ejpam-3991	46	4	+	+	CCONJ
ejpam-3991	46	5	1	1	NUM
ejpam-3991	46	6	)	)	PUNCT
ejpam-3991	46	7	m+w	m+w	NUM
ejpam-3991	46	8	2	2	NUM
ejpam-3991	46	9	sin	sin	NOUN
ejpam-3991	46	10	(	(	PUNCT
ejpam-3991	46	11	1	1	NUM
ejpam-3991	46	12	2	2	NUM
ejpam-3991	46	13	(	(	PUNCT
ejpam-3991	46	14	m+	m+	NUM
ejpam-3991	46	15	w	w	NOUN
ejpam-3991	46	16	)	)	PUNCT
ejpam-3991	46	17	(	(	PUNCT
ejpam-3991	46	18	π	π	NOUN
ejpam-3991	46	19	−	−	PROPN
ejpam-3991	46	20	2	2	NUM
ejpam-3991	46	21	cot−1	cot−1	PROPN
ejpam-3991	46	22	(	(	PUNCT
ejpam-3991	46	23	√	√	PROPN
ejpam-3991	46	24	ab	ab	PROPN
ejpam-3991	46	25	)	)	PUNCT
ejpam-3991	46	26	)	)	PUNCT
ejpam-3991	46	27	)	)	PUNCT
ejpam-3991	47	1	+	+	CCONJ
ejpam-3991	47	2	πcww−k−1a	πcww−k−1a	INTJ
ejpam-3991	47	3	1	1	NUM
ejpam-3991	47	4	2	2	NUM
ejpam-3991	47	5	(	(	PUNCT
ejpam-3991	47	6	m+w−1)bm+w	m+w−1)bm+w	PROPN
ejpam-3991	47	7	csc(π(m+	csc(π(m+	PROPN
ejpam-3991	47	8	w	w	NOUN
ejpam-3991	47	9	)	)	PUNCT
ejpam-3991	47	10	)	)	PUNCT
ejpam-3991	47	11	(	(	PUNCT
ejpam-3991	47	12	1	1	NUM
ejpam-3991	47	13	ab2	ab2	ADJ
ejpam-3991	47	14	+	+	CCONJ
ejpam-3991	47	15	1	1	NUM
ejpam-3991	47	16	)	)	PUNCT
ejpam-3991	47	17	m+w	m+w	NUM
ejpam-3991	47	18	2	2	NUM
ejpam-3991	47	19	sin	sin	NOUN
ejpam-3991	47	20	(	(	PUNCT
ejpam-3991	47	21	1	1	NUM
ejpam-3991	47	22	2	2	NUM
ejpam-3991	47	23	(	(	PUNCT
ejpam-3991	47	24	m+	m+	NUM
ejpam-3991	47	25	w	w	NOUN
ejpam-3991	47	26	)	)	PUNCT
ejpam-3991	47	27	(	(	PUNCT
ejpam-3991	47	28	2	2	NUM
ejpam-3991	47	29	cot−1	cot−1	PROPN
ejpam-3991	47	30	(	(	PUNCT
ejpam-3991	47	31	√	√	PROPN
ejpam-3991	47	32	ab	ab	PROPN
ejpam-3991	47	33	)	)	PUNCT
ejpam-3991	48	1	+	+	CCONJ
ejpam-3991	48	2	π	π	NOUN
ejpam-3991	48	3	)	)	PUNCT
ejpam-3991	48	4	)	)	PUNCT
ejpam-3991	48	5	dw	dw	PROPN
ejpam-3991	48	6	r.	r.	PROPN
ejpam-3991	48	7	reynolds	reynolds	PROPN
ejpam-3991	48	8	,	,	PUNCT
ejpam-3991	48	9	a.	a.	PROPN
ejpam-3991	48	10	stauffer	stauffer	PROPN
ejpam-3991	48	11	/	/	SYM
ejpam-3991	48	12	eur	eur	PROPN
ejpam-3991	48	13	.	.	PUNCT
ejpam-3991	49	1	j.	j.	PROPN
ejpam-3991	49	2	pure	pure	PROPN
ejpam-3991	49	3	appl	appl	PROPN
ejpam-3991	49	4	.	.	PROPN
ejpam-3991	49	5	math	math	PROPN
ejpam-3991	49	6	,	,	PUNCT
ejpam-3991	49	7	14	14	NUM
ejpam-3991	49	8	(	(	PUNCT
ejpam-3991	49	9	3	3	NUM
ejpam-3991	49	10	)	)	PUNCT
ejpam-3991	49	11	(	(	PUNCT
ejpam-3991	49	12	2021	2021	NUM
ejpam-3991	49	13	)	)	PUNCT
ejpam-3991	49	14	,	,	PUNCT
ejpam-3991	49	15	723	723	NUM
ejpam-3991	49	16	-	-	SYM
ejpam-3991	49	17	736	736	NUM
ejpam-3991	49	18	725	725	NUM
ejpam-3991	49	19	from	from	ADP
ejpam-3991	49	20	equations	equation	NOUN
ejpam-3991	49	21	(	(	PUNCT
ejpam-3991	49	22	3.227.1	3.227.1	NUM
ejpam-3991	49	23	)	)	PUNCT
ejpam-3991	49	24	and	and	CCONJ
ejpam-3991	49	25	(	(	PUNCT
ejpam-3991	49	26	3.227.2	3.227.2	NUM
ejpam-3991	49	27	)	)	PUNCT
ejpam-3991	49	28	in	in	ADP
ejpam-3991	49	29	[	[	X
ejpam-3991	49	30	3	3	NUM
ejpam-3991	49	31	]	]	PUNCT
ejpam-3991	49	32	,	,	PUNCT
ejpam-3991	49	33	using	use	VERB
ejpam-3991	49	34	partial	partial	ADJ
ejpam-3991	49	35	fractions	fraction	NOUN
ejpam-3991	49	36	,	,	PUNCT
ejpam-3991	49	37	where	where	SCONJ
ejpam-3991	49	38	re(a	re(a	PUNCT
ejpam-3991	49	39	)	)	PUNCT
ejpam-3991	49	40	≥	≥	NOUN
ejpam-3991	49	41	0	0	NUM
ejpam-3991	49	42	and	and	CCONJ
ejpam-3991	49	43	re(m+	re(m+	NOUN
ejpam-3991	49	44	w	w	NOUN
ejpam-3991	49	45	)	)	PUNCT
ejpam-3991	49	46	<	<	X
ejpam-3991	49	47	1	1	NUM
ejpam-3991	49	48	.	.	NOUN
ejpam-3991	49	49	4	4	NUM
ejpam-3991	49	50	.	.	PUNCT
ejpam-3991	50	1	the	the	DET
ejpam-3991	50	2	lerch	lerch	PROPN
ejpam-3991	50	3	function	function	VERB
ejpam-3991	50	4	the	the	DET
ejpam-3991	50	5	lerch	lerch	PROPN
ejpam-3991	50	6	function	function	PROPN
ejpam-3991	50	7	has	have	VERB
ejpam-3991	50	8	a	a	DET
ejpam-3991	50	9	series	series	NOUN
ejpam-3991	50	10	representation	representation	NOUN
ejpam-3991	50	11	given	give	VERB
ejpam-3991	50	12	by	by	ADP
ejpam-3991	50	13	(	(	PUNCT
ejpam-3991	50	14	3)φ(z	3)φ(z	PROPN
ejpam-3991	50	15	,	,	PUNCT
ejpam-3991	50	16	s	s	X
ejpam-3991	50	17	,	,	PUNCT
ejpam-3991	50	18	v	v	NOUN
ejpam-3991	50	19	)	)	PUNCT
ejpam-3991	50	20	=	=	PUNCT
ejpam-3991	51	1	∞∑	∞∑	NUM
ejpam-3991	51	2	n=0	n=0	NUM
ejpam-3991	51	3	(	(	PUNCT
ejpam-3991	51	4	v	v	NOUN
ejpam-3991	51	5	+	+	PRON
ejpam-3991	51	6	n)−szn	n)−szn	NUM
ejpam-3991	51	7	where	where	SCONJ
ejpam-3991	51	8	|z|	|z|	VERB
ejpam-3991	51	9	<	<	X
ejpam-3991	51	10	1	1	NUM
ejpam-3991	51	11	,	,	PUNCT
ejpam-3991	51	12	v	v	NOUN
ejpam-3991	51	13	6=	6=	ADP
ejpam-3991	51	14	0,−1	0,−1	PROPN
ejpam-3991	51	15	,	,	PUNCT
ejpam-3991	51	16	..	..	PUNCT
ejpam-3991	51	17	and	and	CCONJ
ejpam-3991	51	18	is	be	AUX
ejpam-3991	51	19	continued	continue	VERB
ejpam-3991	51	20	analytically	analytically	ADV
ejpam-3991	51	21	by	by	ADP
ejpam-3991	51	22	its	its	PRON
ejpam-3991	51	23	integral	integral	ADJ
ejpam-3991	51	24	representation	representation	NOUN
ejpam-3991	51	25	given	give	VERB
ejpam-3991	51	26	by	by	ADP
ejpam-3991	51	27	(	(	PUNCT
ejpam-3991	51	28	4	4	NUM
ejpam-3991	51	29	)	)	PUNCT
ejpam-3991	51	30	φ(z	φ(z	PROPN
ejpam-3991	51	31	,	,	PUNCT
ejpam-3991	51	32	s	s	NOUN
ejpam-3991	51	33	,	,	PUNCT
ejpam-3991	51	34	v	v	NOUN
ejpam-3991	51	35	)	)	PUNCT
ejpam-3991	51	36	=	=	SYM
ejpam-3991	51	37	1	1	NUM
ejpam-3991	51	38	γ(s	γ(	NOUN
ejpam-3991	51	39	)	)	PUNCT
ejpam-3991	51	40	∫	∫	PROPN
ejpam-3991	51	41	∞	∞	PROPN
ejpam-3991	51	42	0	0	NUM
ejpam-3991	52	1	ts−1e−vt	ts−1e−vt	PRON
ejpam-3991	53	1	1−	1−	NUM
ejpam-3991	53	2	ze−t	ze−t	NOUN
ejpam-3991	53	3	dt	dt	NOUN
ejpam-3991	54	1	=	=	SYM
ejpam-3991	54	2	1	1	NUM
ejpam-3991	54	3	γ(s	γ(s	PROPN
ejpam-3991	54	4	)	)	PUNCT
ejpam-3991	54	5	∫	∫	PROPN
ejpam-3991	55	1	∞	∞	NUM
ejpam-3991	55	2	0	0	NUM
ejpam-3991	56	1	ts−1e−(v−1)t	ts−1e−(v−1)t	PROPN
ejpam-3991	56	2	et	et	NOUN
ejpam-3991	56	3	−	−	NOUN
ejpam-3991	56	4	z	z	NOUN
ejpam-3991	56	5	dt	dt	NOUN
ejpam-3991	56	6	where	where	SCONJ
ejpam-3991	56	7	re(v	re(v	NOUN
ejpam-3991	56	8	)	)	PUNCT
ejpam-3991	56	9	>	>	X
ejpam-3991	56	10	0	0	NUM
ejpam-3991	56	11	,	,	PUNCT
ejpam-3991	56	12	or	or	CCONJ
ejpam-3991	56	13	|z|≤	|z|≤	SYM
ejpam-3991	56	14	1	1	NUM
ejpam-3991	56	15	,	,	PUNCT
ejpam-3991	56	16	z	z	NOUN
ejpam-3991	56	17	6=	6=	NUM
ejpam-3991	56	18	1	1	NUM
ejpam-3991	56	19	,	,	PUNCT
ejpam-3991	56	20	re(s	re(s	ADJ
ejpam-3991	56	21	)	)	PUNCT
ejpam-3991	56	22	>	>	X
ejpam-3991	56	23	0	0	NUM
ejpam-3991	56	24	,	,	PUNCT
ejpam-3991	56	25	or	or	CCONJ
ejpam-3991	56	26	z	z	NOUN
ejpam-3991	56	27	=	=	SYM
ejpam-3991	56	28	1	1	NUM
ejpam-3991	56	29	,	,	PUNCT
ejpam-3991	56	30	re(s	re(s	ADJ
ejpam-3991	56	31	)	)	PUNCT
ejpam-3991	56	32	>	>	X
ejpam-3991	57	1	1	1	NUM
ejpam-3991	57	2	.	.	X
ejpam-3991	57	3	5	5	NUM
ejpam-3991	57	4	.	.	X
ejpam-3991	57	5	infinite	infinite	ADJ
ejpam-3991	57	6	sum	sum	NOUN
ejpam-3991	57	7	of	of	ADP
ejpam-3991	57	8	the	the	DET
ejpam-3991	57	9	contour	contour	NOUN
ejpam-3991	57	10	integral	integral	NOUN
ejpam-3991	57	11	in	in	ADP
ejpam-3991	57	12	this	this	DET
ejpam-3991	57	13	section	section	NOUN
ejpam-3991	57	14	we	we	PRON
ejpam-3991	57	15	will	will	AUX
ejpam-3991	57	16	again	again	ADV
ejpam-3991	57	17	use	use	VERB
ejpam-3991	57	18	cauchy	cauchy	NOUN
ejpam-3991	57	19	’s	’s	PART
ejpam-3991	57	20	integral	integral	ADJ
ejpam-3991	57	21	formula	formula	NOUN
ejpam-3991	57	22	(	(	PUNCT
ejpam-3991	57	23	1	1	NUM
ejpam-3991	57	24	)	)	PUNCT
ejpam-3991	57	25	and	and	CCONJ
ejpam-3991	57	26	taking	take	VERB
ejpam-3991	57	27	the	the	DET
ejpam-3991	57	28	infinite	infinite	ADJ
ejpam-3991	57	29	sum	sum	NOUN
ejpam-3991	57	30	to	to	PART
ejpam-3991	57	31	derive	derive	VERB
ejpam-3991	57	32	equivalent	equivalent	ADJ
ejpam-3991	57	33	sum	sum	NOUN
ejpam-3991	57	34	representations	representation	NOUN
ejpam-3991	57	35	for	for	ADP
ejpam-3991	57	36	the	the	DET
ejpam-3991	57	37	contour	contour	NOUN
ejpam-3991	57	38	integrals	integral	NOUN
ejpam-3991	57	39	.	.	PUNCT
ejpam-3991	58	1	5.1	5.1	NUM
ejpam-3991	58	2	.	.	PUNCT
ejpam-3991	59	1	derivation	derivation	NOUN
ejpam-3991	59	2	of	of	ADP
ejpam-3991	59	3	the	the	DET
ejpam-3991	59	4	general	general	ADJ
ejpam-3991	59	5	sine	sine	VERB
ejpam-3991	59	6	contour	contour	NOUN
ejpam-3991	59	7	integral	integral	ADJ
ejpam-3991	59	8	use	use	NOUN
ejpam-3991	59	9	equation	equation	NOUN
ejpam-3991	59	10	(	(	PUNCT
ejpam-3991	59	11	1	1	NUM
ejpam-3991	59	12	)	)	PUNCT
ejpam-3991	59	13	and	and	CCONJ
ejpam-3991	59	14	replace	replace	VERB
ejpam-3991	59	15	y	y	PROPN
ejpam-3991	59	16	by	by	ADP
ejpam-3991	59	17	y	y	PROPN
ejpam-3991	60	1	+	+	CCONJ
ejpam-3991	60	2	it	it	PRON
ejpam-3991	60	3	and	and	CCONJ
ejpam-3991	60	4	multiply	multiply	ADV
ejpam-3991	60	5	by	by	ADP
ejpam-3991	60	6	emit	emit	NOUN
ejpam-3991	60	7	for	for	ADP
ejpam-3991	60	8	the	the	DET
ejpam-3991	60	9	first	first	ADJ
ejpam-3991	60	10	equation	equation	NOUN
ejpam-3991	60	11	.	.	PUNCT
ejpam-3991	61	1	next	next	ADV
ejpam-3991	61	2	we	we	PRON
ejpam-3991	61	3	form	form	VERB
ejpam-3991	61	4	the	the	DET
ejpam-3991	61	5	second	second	ADJ
ejpam-3991	61	6	equation	equation	NOUN
ejpam-3991	61	7	by	by	ADP
ejpam-3991	61	8	replacing	replace	VERB
ejpam-3991	61	9	t	t	PROPN
ejpam-3991	61	10	by	by	ADP
ejpam-3991	61	11	−t	−t	NOUN
ejpam-3991	61	12	and	and	CCONJ
ejpam-3991	61	13	taking	take	VERB
ejpam-3991	61	14	their	their	PRON
ejpam-3991	61	15	difference	difference	NOUN
ejpam-3991	61	16	to	to	PART
ejpam-3991	61	17	get	get	VERB
ejpam-3991	61	18	(	(	PUNCT
ejpam-3991	61	19	5	5	NUM
ejpam-3991	61	20	)	)	PUNCT
ejpam-3991	61	21	ie−imt	ie−imt	X
ejpam-3991	61	22	(	(	PUNCT
ejpam-3991	61	23	(	(	PUNCT
ejpam-3991	61	24	y	y	PROPN
ejpam-3991	61	25	−	−	PROPN
ejpam-3991	61	26	it)k	it)k	PROPN
ejpam-3991	61	27	−	−	NOUN
ejpam-3991	61	28	e2imt(y	e2imt(y	X
ejpam-3991	61	29	+	+	CCONJ
ejpam-3991	61	30	it)k	it)k	ADJ
ejpam-3991	61	31	)	)	PUNCT
ejpam-3991	61	32	2k	2k	NOUN
ejpam-3991	61	33	!	!	PUNCT
ejpam-3991	62	1	=	=	SYM
ejpam-3991	62	2	1	1	NUM
ejpam-3991	62	3	2πi	2πi	ADJ
ejpam-3991	62	4	∫	∫	PROPN
ejpam-3991	62	5	c	c	PROPN
ejpam-3991	62	6	w−k−1ewy	w−k−1ewy	PROPN
ejpam-3991	62	7	sin(t(m+	sin(t(m+	VERB
ejpam-3991	62	8	w))dw	w))dw	NOUN
ejpam-3991	62	9	5.2	5.2	NUM
ejpam-3991	62	10	.	.	PUNCT
ejpam-3991	63	1	derivation	derivation	NOUN
ejpam-3991	63	2	of	of	ADP
ejpam-3991	63	3	the	the	DET
ejpam-3991	63	4	contour	contour	NOUN
ejpam-3991	63	5	integral	integral	NOUN
ejpam-3991	63	6	in	in	ADP
ejpam-3991	63	7	this	this	DET
ejpam-3991	63	8	section	section	NOUN
ejpam-3991	63	9	we	we	PRON
ejpam-3991	63	10	will	will	AUX
ejpam-3991	63	11	derive	derive	VERB
ejpam-3991	63	12	the	the	DET
ejpam-3991	63	13	contour	contour	NOUN
ejpam-3991	63	14	integral	integral	ADJ
ejpam-3991	63	15	given	give	VERB
ejpam-3991	63	16	by∫	by∫	PROPN
ejpam-3991	63	17	c	c	NOUN
ejpam-3991	63	18	πcww−k−1a	πcww−k−1a	INTJ
ejpam-3991	63	19	1	1	NUM
ejpam-3991	63	20	2	2	NUM
ejpam-3991	63	21	(	(	PUNCT
ejpam-3991	63	22	m+w−1)(−b)m+w	m+w−1)(−b)m+w	NOUN
ejpam-3991	63	23	csc(π(m+	csc(π(m+	NOUN
ejpam-3991	63	24	w	w	NOUN
ejpam-3991	63	25	)	)	PUNCT
ejpam-3991	63	26	)	)	PUNCT
ejpam-3991	64	1	(	(	PUNCT
ejpam-3991	64	2	1	1	NUM
ejpam-3991	64	3	ab2	ab2	ADJ
ejpam-3991	64	4	+	+	CCONJ
ejpam-3991	64	5	1	1	NUM
ejpam-3991	64	6	)	)	PUNCT
ejpam-3991	64	7	m+w	m+w	NUM
ejpam-3991	64	8	2	2	NUM
ejpam-3991	64	9	sin	sin	NOUN
ejpam-3991	64	10	(	(	PUNCT
ejpam-3991	64	11	1	1	NUM
ejpam-3991	64	12	2	2	NUM
ejpam-3991	64	13	(	(	PUNCT
ejpam-3991	64	14	m+	m+	NUM
ejpam-3991	64	15	w	w	NOUN
ejpam-3991	64	16	)	)	PUNCT
ejpam-3991	64	17	(	(	PUNCT
ejpam-3991	64	18	π	π	NOUN
ejpam-3991	64	19	−	−	PROPN
ejpam-3991	64	20	2	2	NUM
ejpam-3991	64	21	cot−1	cot−1	PROPN
ejpam-3991	64	22	(	(	PUNCT
ejpam-3991	64	23	√	√	PROPN
ejpam-3991	64	24	ab	ab	PROPN
ejpam-3991	64	25	)	)	PUNCT
ejpam-3991	64	26	)	)	PUNCT
ejpam-3991	64	27	)	)	PUNCT
ejpam-3991	65	1	dw	dw	NOUN
ejpam-3991	65	2	using	use	VERB
ejpam-3991	65	3	equation	equation	NOUN
ejpam-3991	65	4	(	(	PUNCT
ejpam-3991	65	5	5	5	NUM
ejpam-3991	65	6	)	)	PUNCT
ejpam-3991	65	7	and	and	CCONJ
ejpam-3991	65	8	substituting	substitute	VERB
ejpam-3991	65	9	y	y	NOUN
ejpam-3991	65	10	by	by	ADP
ejpam-3991	65	11	1	1	NUM
ejpam-3991	65	12	2	2	NUM
ejpam-3991	65	13	log	log	NOUN
ejpam-3991	65	14	(	(	PUNCT
ejpam-3991	65	15	1	1	NUM
ejpam-3991	65	16	ab2	ab2	ADJ
ejpam-3991	65	17	+	+	CCONJ
ejpam-3991	65	18	1	1	NUM
ejpam-3991	65	19	)	)	PUNCT
ejpam-3991	65	20	+	+	CCONJ
ejpam-3991	65	21	log(a	log(a	PROPN
ejpam-3991	65	22	)	)	PUNCT
ejpam-3991	65	23	2	2	NUM
ejpam-3991	65	24	+	+	CCONJ
ejpam-3991	65	25	log(−b	log(−b	PROPN
ejpam-3991	65	26	)	)	PUNCT
ejpam-3991	66	1	+	+	CCONJ
ejpam-3991	66	2	log(c	log(c	X
ejpam-3991	66	3	)	)	PUNCT
ejpam-3991	67	1	+	+	CCONJ
ejpam-3991	67	2	iπ(2y	iπ(2y	PRON
ejpam-3991	67	3	+	+	NOUN
ejpam-3991	67	4	1	1	X
ejpam-3991	67	5	)	)	PUNCT
ejpam-3991	67	6	and	and	CCONJ
ejpam-3991	67	7	multiplying	multiply	VERB
ejpam-3991	67	8	both	both	DET
ejpam-3991	67	9	sides	side	NOUN
ejpam-3991	67	10	by	by	ADP
ejpam-3991	67	11	e2iπmy+iπm	e2iπmy+iπm	PROPN
ejpam-3991	67	12	,	,	PUNCT
ejpam-3991	67	13	simplifying	simplify	VERB
ejpam-3991	67	14	we	we	PRON
ejpam-3991	67	15	get	get	VERB
ejpam-3991	67	16	r.	r.	PROPN
ejpam-3991	67	17	reynolds	reynolds	PROPN
ejpam-3991	67	18	,	,	PUNCT
ejpam-3991	67	19	a.	a.	PROPN
ejpam-3991	67	20	stauffer	stauffer	PROPN
ejpam-3991	67	21	/	/	SYM
ejpam-3991	67	22	eur	eur	PROPN
ejpam-3991	67	23	.	.	PUNCT
ejpam-3991	68	1	j.	j.	PROPN
ejpam-3991	68	2	pure	pure	PROPN
ejpam-3991	68	3	appl	appl	PROPN
ejpam-3991	68	4	.	.	PROPN
ejpam-3991	68	5	math	math	PROPN
ejpam-3991	68	6	,	,	PUNCT
ejpam-3991	68	7	14	14	NUM
ejpam-3991	68	8	(	(	PUNCT
ejpam-3991	68	9	3	3	NUM
ejpam-3991	68	10	)	)	PUNCT
ejpam-3991	68	11	(	(	PUNCT
ejpam-3991	68	12	2021	2021	NUM
ejpam-3991	68	13	)	)	PUNCT
ejpam-3991	68	14	,	,	PUNCT
ejpam-3991	68	15	723	723	NUM
ejpam-3991	68	16	-	-	SYM
ejpam-3991	68	17	736	736	NUM
ejpam-3991	68	18	726	726	NUM
ejpam-3991	68	19	ie−imt+2iπmy+iπm	ie−imt+2iπmy+iπm	NOUN
ejpam-3991	68	20	2k	2k	NUM
ejpam-3991	68	21	!	!	PUNCT
ejpam-3991	69	1	(2iπ)k	(2iπ)k	NOUN
ejpam-3991	69	2	(	(	PUNCT
ejpam-3991	69	3	−	−	PUNCT
ejpam-3991	69	4	i	i	PRON
ejpam-3991	69	5	log	log	VERB
ejpam-3991	69	6	(	(	PUNCT
ejpam-3991	69	7	1	1	NUM
ejpam-3991	69	8	ab2	ab2	ADJ
ejpam-3991	69	9	+	+	CCONJ
ejpam-3991	69	10	1	1	X
ejpam-3991	69	11	)	)	PUNCT
ejpam-3991	69	12	4π	4π	NUM
ejpam-3991	69	13	−	−	PROPN
ejpam-3991	70	1	i	i	PRON
ejpam-3991	70	2	log(a	log(a	PROPN
ejpam-3991	70	3	)	)	PUNCT
ejpam-3991	70	4	4π	4π	NUM
ejpam-3991	70	5	−	−	PROPN
ejpam-3991	71	1	i	i	PRON
ejpam-3991	71	2	log(−b	log(−b	PROPN
ejpam-3991	71	3	)	)	PUNCT
ejpam-3991	71	4	2π	2π	PROPN
ejpam-3991	72	1	−	−	PROPN
ejpam-3991	73	1	i	i	PRON
ejpam-3991	73	2	log(c	log(c	VERB
ejpam-3991	73	3	)	)	PUNCT
ejpam-3991	73	4	2π	2π	PROPN
ejpam-3991	73	5	−	−	PROPN
ejpam-3991	74	1	t	t	NOUN
ejpam-3991	74	2	2π	2π	NOUN
ejpam-3991	74	3	+	+	CCONJ
ejpam-3991	74	4	1	1	NUM
ejpam-3991	74	5	2	2	NUM
ejpam-3991	74	6	(	(	PUNCT
ejpam-3991	74	7	2y	2y	PROPN
ejpam-3991	74	8	+	+	NOUN
ejpam-3991	74	9	1	1	NUM
ejpam-3991	74	10	)	)	PUNCT
ejpam-3991	74	11	)	)	PUNCT
ejpam-3991	75	1	k	k	X
ejpam-3991	75	2	−	−	PROPN
ejpam-3991	75	3	(	(	PUNCT
ejpam-3991	75	4	2iπ)ke2imt	2iπ)ke2imt	NOUN
ejpam-3991	75	5	(	(	PUNCT
ejpam-3991	75	6	−	−	PROPN
ejpam-3991	75	7	i	i	PRON
ejpam-3991	75	8	log	log	VERB
ejpam-3991	75	9	(	(	PUNCT
ejpam-3991	75	10	1	1	NUM
ejpam-3991	75	11	ab2	ab2	ADJ
ejpam-3991	75	12	+	+	CCONJ
ejpam-3991	75	13	1	1	X
ejpam-3991	75	14	)	)	PUNCT
ejpam-3991	75	15	4π	4π	NUM
ejpam-3991	75	16	−	−	PROPN
ejpam-3991	75	17	i	i	PRON
ejpam-3991	75	18	log(a	log(a	PROPN
ejpam-3991	75	19	)	)	PUNCT
ejpam-3991	75	20	4π	4π	NUM
ejpam-3991	75	21	−	−	PROPN
ejpam-3991	76	1	i	i	PRON
ejpam-3991	76	2	log(−b	log(−b	PROPN
ejpam-3991	76	3	)	)	PUNCT
ejpam-3991	76	4	2π	2π	PROPN
ejpam-3991	77	1	−	−	PROPN
ejpam-3991	78	1	i	i	PRON
ejpam-3991	78	2	log(c	log(c	VERB
ejpam-3991	78	3	)	)	PUNCT
ejpam-3991	78	4	2π	2π	PROPN
ejpam-3991	79	1	+	+	CCONJ
ejpam-3991	79	2	t	t	X
ejpam-3991	79	3	2π	2π	NOUN
ejpam-3991	79	4	+	+	CCONJ
ejpam-3991	79	5	1	1	NUM
ejpam-3991	79	6	2	2	NUM
ejpam-3991	79	7	(	(	PUNCT
ejpam-3991	79	8	2y+	2y+	NUM
ejpam-3991	79	9	1	1	NUM
ejpam-3991	79	10	)	)	PUNCT
ejpam-3991	79	11	)	)	PUNCT
ejpam-3991	80	1	k	k	PROPN
ejpam-3991	80	2	=	=	SYM
ejpam-3991	81	1	1	1	NUM
ejpam-3991	81	2	2πi	2πi	NOUN
ejpam-3991	81	3	∫	∫	PROPN
ejpam-3991	81	4	c	c	X
ejpam-3991	81	5	w−k−1	w−k−1	PROPN
ejpam-3991	81	6	sin(t(m+w	sin(t(m+w	NOUN
ejpam-3991	81	7	)	)	PUNCT
ejpam-3991	81	8	)	)	PUNCT
ejpam-3991	81	9	exp	exp	NOUN
ejpam-3991	81	10	(	(	PUNCT
ejpam-3991	81	11	w	w	NOUN
ejpam-3991	81	12	(	(	PUNCT
ejpam-3991	81	13	1	1	NUM
ejpam-3991	81	14	2	2	NUM
ejpam-3991	81	15	log	log	NOUN
ejpam-3991	81	16	(	(	PUNCT
ejpam-3991	81	17	1	1	NUM
ejpam-3991	81	18	ab2	ab2	ADJ
ejpam-3991	81	19	+	+	CCONJ
ejpam-3991	81	20	1	1	NUM
ejpam-3991	81	21	)	)	PUNCT
ejpam-3991	81	22	+	+	CCONJ
ejpam-3991	81	23	log(a	log(a	PROPN
ejpam-3991	81	24	)	)	PUNCT
ejpam-3991	81	25	2	2	NUM
ejpam-3991	81	26	+	+	CCONJ
ejpam-3991	81	27	log(−b	log(−b	PROPN
ejpam-3991	81	28	)	)	PUNCT
ejpam-3991	82	1	+	+	CCONJ
ejpam-3991	82	2	log(c	log(c	X
ejpam-3991	82	3	)	)	PUNCT
ejpam-3991	83	1	+	+	CCONJ
ejpam-3991	83	2	iπ(2y	iπ(2y	PRON
ejpam-3991	83	3	+	+	NOUN
ejpam-3991	83	4	1	1	NUM
ejpam-3991	83	5	)	)	PUNCT
ejpam-3991	83	6	)	)	PUNCT
ejpam-3991	84	1	+	+	CCONJ
ejpam-3991	84	2	2iπmy	2iπmy	NUM
ejpam-3991	84	3	+	+	CCONJ
ejpam-3991	84	4	iπm	iπm	X
ejpam-3991	84	5	)	)	PUNCT
ejpam-3991	84	6	dw	dw	PROPN
ejpam-3991	84	7	(	(	PUNCT
ejpam-3991	84	8	6	6	NUM
ejpam-3991	84	9	)	)	PUNCT
ejpam-3991	84	10	next	next	ADV
ejpam-3991	84	11	we	we	PRON
ejpam-3991	84	12	take	take	VERB
ejpam-3991	84	13	the	the	DET
ejpam-3991	84	14	infinite	infinite	ADJ
ejpam-3991	84	15	sum	sum	NOUN
ejpam-3991	84	16	over	over	ADP
ejpam-3991	84	17	y	y	PROPN
ejpam-3991	84	18	∈	∈	PROPN
ejpam-3991	85	1	[	[	X
ejpam-3991	85	2	0,∞	0,∞	NOUN
ejpam-3991	85	3	)	)	PUNCT
ejpam-3991	85	4	and	and	CCONJ
ejpam-3991	85	5	replace	replace	VERB
ejpam-3991	85	6	t	t	NOUN
ejpam-3991	85	7	by	by	ADP
ejpam-3991	85	8	1	1	NUM
ejpam-3991	85	9	2	2	NUM
ejpam-3991	85	10	(	(	PUNCT
ejpam-3991	85	11	π	π	PROPN
ejpam-3991	85	12	−	−	PROPN
ejpam-3991	85	13	2	2	NUM
ejpam-3991	85	14	cot−1	cot−1	PROPN
ejpam-3991	85	15	(	(	PUNCT
ejpam-3991	85	16	√	√	PROPN
ejpam-3991	85	17	ab	ab	NUM
ejpam-3991	85	18	)	)	PUNCT
ejpam-3991	85	19	)	)	PUNCT
ejpam-3991	86	1	and	and	CCONJ
ejpam-3991	86	2	multiply	multiply	VERB
ejpam-3991	86	3	both	both	DET
ejpam-3991	86	4	sides	side	NOUN
ejpam-3991	86	5	by	by	ADP
ejpam-3991	86	6	−2iπa	−2iπa	PROPN
ejpam-3991	86	7	m−1	m−1	PROPN
ejpam-3991	86	8	2	2	NUM
ejpam-3991	86	9	(	(	PUNCT
ejpam-3991	86	10	−b)m	−b)m	NOUN
ejpam-3991	86	11	(	(	PUNCT
ejpam-3991	86	12	1	1	NUM
ejpam-3991	86	13	ab2	ab2	ADJ
ejpam-3991	86	14	+	+	CCONJ
ejpam-3991	86	15	1	1	NUM
ejpam-3991	86	16	)	)	PUNCT
ejpam-3991	86	17	m/2	m/2	X
ejpam-3991	86	18	simplifying	simplify	VERB
ejpam-3991	86	19	to	to	PART
ejpam-3991	86	20	get	get	VERB
ejpam-3991	86	21	r.	r.	PROPN
ejpam-3991	86	22	reynolds	reynolds	PROPN
ejpam-3991	86	23	,	,	PUNCT
ejpam-3991	86	24	a.	a.	PROPN
ejpam-3991	86	25	stauffer	stauffer	PROPN
ejpam-3991	86	26	/	/	SYM
ejpam-3991	86	27	eur	eur	PROPN
ejpam-3991	86	28	.	.	PUNCT
ejpam-3991	87	1	j.	j.	PROPN
ejpam-3991	87	2	pure	pure	PROPN
ejpam-3991	87	3	appl	appl	PROPN
ejpam-3991	87	4	.	.	PROPN
ejpam-3991	87	5	math	math	PROPN
ejpam-3991	87	6	,	,	PUNCT
ejpam-3991	87	7	14	14	NUM
ejpam-3991	87	8	(	(	PUNCT
ejpam-3991	87	9	3	3	NUM
ejpam-3991	87	10	)	)	PUNCT
ejpam-3991	87	11	(	(	PUNCT
ejpam-3991	87	12	2021	2021	NUM
ejpam-3991	87	13	)	)	PUNCT
ejpam-3991	87	14	,	,	PUNCT
ejpam-3991	87	15	723	723	NUM
ejpam-3991	87	16	-	-	SYM
ejpam-3991	87	17	736	736	NUM
ejpam-3991	87	18	727	727	NUM
ejpam-3991	87	19	(	(	PUNCT
ejpam-3991	87	20	7	7	NUM
ejpam-3991	87	21	)	)	PUNCT
ejpam-3991	87	22	2ke	2ke	ADJ
ejpam-3991	87	23	iπk	iπk	NOUN
ejpam-3991	87	24	2	2	NUM
ejpam-3991	87	25	πk+1a	πk+1a	VERB
ejpam-3991	87	26	m−1	m−1	PROPN
ejpam-3991	87	27	2	2	NUM
ejpam-3991	87	28	(	(	PUNCT
ejpam-3991	87	29	−b)m	−b)m	NOUN
ejpam-3991	87	30	k	k	X
ejpam-3991	87	31	!	!	PUNCT
ejpam-3991	88	1	(	(	PUNCT
ejpam-3991	88	2	1	1	NUM
ejpam-3991	88	3	ab2	ab2	ADJ
ejpam-3991	88	4	+	+	CCONJ
ejpam-3991	88	5	1	1	NUM
ejpam-3991	88	6	)	)	PUNCT
ejpam-3991	88	7	m/2	m/2	NUM
ejpam-3991	88	8	(	(	PUNCT
ejpam-3991	88	9	e	e	NOUN
ejpam-3991	88	10	1	1	NUM
ejpam-3991	88	11	2	2	NUM
ejpam-3991	88	12	im(2	im(2	PROPN
ejpam-3991	88	13	cot−1	cot−1	PROPN
ejpam-3991	88	14	(	(	PUNCT
ejpam-3991	88	15	√	√	ADP
ejpam-3991	88	16	ab)+π	ab)+π	NOUN
ejpam-3991	88	17	)	)	PUNCT
ejpam-3991	88	18	φ	φ	PROPN
ejpam-3991	88	19	(	(	PUNCT
ejpam-3991	88	20	e2imπ,−k,−	e2imπ,−k,−	PROPN
ejpam-3991	88	21	i	i	PRON
ejpam-3991	88	22	(	(	PUNCT
ejpam-3991	88	23	2i	2i	NOUN
ejpam-3991	88	24	cot−1	cot−1	PROPN
ejpam-3991	88	25	(	(	PUNCT
ejpam-3991	88	26	√	√	PROPN
ejpam-3991	88	27	ab	ab	NUM
ejpam-3991	88	28	)	)	PUNCT
ejpam-3991	89	1	+	+	X
ejpam-3991	89	2	log(a	log(a	PROPN
ejpam-3991	89	3	)	)	PUNCT
ejpam-3991	90	1	+	+	NUM
ejpam-3991	90	2	log	log	NOUN
ejpam-3991	90	3	(	(	PUNCT
ejpam-3991	90	4	1	1	NUM
ejpam-3991	90	5	+	+	NUM
ejpam-3991	90	6	1	1	NUM
ejpam-3991	90	7	b2a	b2a	NOUN
ejpam-3991	90	8	)	)	PUNCT
ejpam-3991	91	1	+	+	CCONJ
ejpam-3991	91	2	2	2	NUM
ejpam-3991	91	3	log(−b	log(−b	PROPN
ejpam-3991	91	4	)	)	PUNCT
ejpam-3991	92	1	+	+	CCONJ
ejpam-3991	92	2	2	2	NUM
ejpam-3991	92	3	log(c	log(c	NOUN
ejpam-3991	92	4	)	)	PUNCT
ejpam-3991	93	1	+	+	CCONJ
ejpam-3991	93	2	iπ	iπ	X
ejpam-3991	93	3	)	)	PUNCT
ejpam-3991	93	4	4π	4π	NUM
ejpam-3991	93	5	)	)	PUNCT
ejpam-3991	94	1	−	−	PUNCT
ejpam-3991	94	2	e	e	NOUN
ejpam-3991	94	3	1	1	NUM
ejpam-3991	94	4	2	2	NUM
ejpam-3991	94	5	im(3π−2	im(3π−2	PROPN
ejpam-3991	94	6	cot−1	cot−1	PROPN
ejpam-3991	94	7	(	(	PUNCT
ejpam-3991	94	8	√	√	PROPN
ejpam-3991	94	9	ab	ab	NUM
ejpam-3991	94	10	)	)	PUNCT
ejpam-3991	94	11	)	)	PUNCT
ejpam-3991	95	1	φ	φ	PROPN
ejpam-3991	95	2	(	(	PUNCT
ejpam-3991	95	3	e2imπ,−k,−	e2imπ,−k,−	PROPN
ejpam-3991	95	4	i	i	PRON
ejpam-3991	95	5	(	(	PUNCT
ejpam-3991	95	6	−2i	−2i	PROPN
ejpam-3991	95	7	cot−1	cot−1	PROPN
ejpam-3991	95	8	(	(	PUNCT
ejpam-3991	95	9	√	√	PROPN
ejpam-3991	95	10	ab	ab	NUM
ejpam-3991	95	11	)	)	PUNCT
ejpam-3991	95	12	+	+	X
ejpam-3991	95	13	log(a	log(a	PROPN
ejpam-3991	95	14	)	)	PUNCT
ejpam-3991	96	1	+	+	NUM
ejpam-3991	96	2	log	log	NOUN
ejpam-3991	96	3	(	(	PUNCT
ejpam-3991	96	4	1	1	NUM
ejpam-3991	96	5	+	+	NUM
ejpam-3991	96	6	1	1	NUM
ejpam-3991	96	7	b2a	b2a	NOUN
ejpam-3991	96	8	)	)	PUNCT
ejpam-3991	97	1	+	+	CCONJ
ejpam-3991	97	2	2	2	NUM
ejpam-3991	97	3	log(−b	log(−b	PROPN
ejpam-3991	97	4	)	)	PUNCT
ejpam-3991	98	1	+	+	CCONJ
ejpam-3991	98	2	2	2	NUM
ejpam-3991	98	3	log(c	log(c	NOUN
ejpam-3991	98	4	)	)	PUNCT
ejpam-3991	99	1	+	+	CCONJ
ejpam-3991	99	2	3iπ	3iπ	ADJ
ejpam-3991	99	3	)	)	PUNCT
ejpam-3991	99	4	4π	4π	NUM
ejpam-3991	99	5	)	)	PUNCT
ejpam-3991	99	6	)	)	PUNCT
ejpam-3991	100	1	=	=	SYM
ejpam-3991	100	2	1	1	NUM
ejpam-3991	100	3	2πi	2πi	NOUN
ejpam-3991	100	4	∞∑	∞∑	NUM
ejpam-3991	100	5	y=0	y=0	SYM
ejpam-3991	100	6	∫	∫	X
ejpam-3991	100	7	c	c	X
ejpam-3991	100	8	w−k−1	w−k−1	PROPN
ejpam-3991	100	9	sin(t(m+	sin(t(m+	PROPN
ejpam-3991	100	10	w	w	NOUN
ejpam-3991	100	11	)	)	PUNCT
ejpam-3991	100	12	)	)	PUNCT
ejpam-3991	100	13	exp	exp	NOUN
ejpam-3991	100	14	(	(	PUNCT
ejpam-3991	100	15	w	w	NOUN
ejpam-3991	100	16	(	(	PUNCT
ejpam-3991	100	17	1	1	NUM
ejpam-3991	100	18	2	2	NUM
ejpam-3991	100	19	log	log	NOUN
ejpam-3991	100	20	(	(	PUNCT
ejpam-3991	100	21	1	1	NUM
ejpam-3991	100	22	ab2	ab2	ADJ
ejpam-3991	100	23	+	+	CCONJ
ejpam-3991	100	24	1	1	NUM
ejpam-3991	100	25	)	)	PUNCT
ejpam-3991	100	26	+	+	CCONJ
ejpam-3991	100	27	log(a	log(a	PROPN
ejpam-3991	100	28	)	)	PUNCT
ejpam-3991	100	29	2	2	NUM
ejpam-3991	100	30	+	+	CCONJ
ejpam-3991	100	31	log(−b	log(−b	PROPN
ejpam-3991	100	32	)	)	PUNCT
ejpam-3991	101	1	+	+	CCONJ
ejpam-3991	101	2	log(c	log(c	X
ejpam-3991	101	3	)	)	PUNCT
ejpam-3991	102	1	+	+	CCONJ
ejpam-3991	102	2	iπ(2y	iπ(2y	PRON
ejpam-3991	102	3	+	+	NOUN
ejpam-3991	102	4	1	1	NUM
ejpam-3991	102	5	)	)	PUNCT
ejpam-3991	102	6	)	)	PUNCT
ejpam-3991	103	1	+	+	CCONJ
ejpam-3991	103	2	2iπmy	2iπmy	NUM
ejpam-3991	103	3	+	+	CCONJ
ejpam-3991	103	4	iπm	iπm	X
ejpam-3991	103	5	)	)	PUNCT
ejpam-3991	103	6	dw	dw	NOUN
ejpam-3991	103	7	=	=	NOUN
ejpam-3991	103	8	1	1	NUM
ejpam-3991	103	9	2πi	2πi	NOUN
ejpam-3991	103	10	∫	∫	PROPN
ejpam-3991	104	1	c	c	NOUN
ejpam-3991	105	1	∞∑	∞∑	NUM
ejpam-3991	105	2	y=0	y=0	NOUN
ejpam-3991	105	3	w−k−1	w−k−1	PROPN
ejpam-3991	105	4	sin(t(m+	sin(t(m+	PROPN
ejpam-3991	105	5	w	w	NOUN
ejpam-3991	105	6	)	)	PUNCT
ejpam-3991	105	7	)	)	PUNCT
ejpam-3991	105	8	exp	exp	NOUN
ejpam-3991	105	9	(	(	PUNCT
ejpam-3991	105	10	w	w	NOUN
ejpam-3991	105	11	(	(	PUNCT
ejpam-3991	105	12	1	1	NUM
ejpam-3991	105	13	2	2	NUM
ejpam-3991	105	14	log	log	NOUN
ejpam-3991	105	15	(	(	PUNCT
ejpam-3991	105	16	1	1	NUM
ejpam-3991	105	17	ab2	ab2	ADJ
ejpam-3991	105	18	+	+	CCONJ
ejpam-3991	105	19	1	1	NUM
ejpam-3991	105	20	)	)	PUNCT
ejpam-3991	105	21	+	+	CCONJ
ejpam-3991	105	22	log(a	log(a	PROPN
ejpam-3991	105	23	)	)	PUNCT
ejpam-3991	105	24	2	2	NUM
ejpam-3991	105	25	+	+	CCONJ
ejpam-3991	105	26	log(−b	log(−b	PROPN
ejpam-3991	105	27	)	)	PUNCT
ejpam-3991	106	1	+	+	CCONJ
ejpam-3991	106	2	log(c	log(c	X
ejpam-3991	106	3	)	)	PUNCT
ejpam-3991	107	1	+	+	CCONJ
ejpam-3991	107	2	iπ(2y	iπ(2y	PRON
ejpam-3991	107	3	+	+	NOUN
ejpam-3991	107	4	1	1	NUM
ejpam-3991	107	5	)	)	PUNCT
ejpam-3991	107	6	)	)	PUNCT
ejpam-3991	108	1	+	+	CCONJ
ejpam-3991	108	2	2iπmy	2iπmy	NUM
ejpam-3991	108	3	+	+	CCONJ
ejpam-3991	108	4	iπm	iπm	X
ejpam-3991	108	5	)	)	PUNCT
ejpam-3991	108	6	dw	dw	NOUN
ejpam-3991	108	7	=	=	NOUN
ejpam-3991	108	8	1	1	NUM
ejpam-3991	108	9	2πi	2πi	NOUN
ejpam-3991	108	10	∫	∫	PROPN
ejpam-3991	109	1	c	c	NOUN
ejpam-3991	109	2	πcww−k−1a	πcww−k−1a	INTJ
ejpam-3991	109	3	1	1	NUM
ejpam-3991	109	4	2	2	NUM
ejpam-3991	109	5	(	(	PUNCT
ejpam-3991	109	6	m+w−1)(−b)m+w	m+w−1)(−b)m+w	NOUN
ejpam-3991	109	7	csc(π(m+	csc(π(m+	NOUN
ejpam-3991	109	8	w	w	NOUN
ejpam-3991	109	9	)	)	PUNCT
ejpam-3991	109	10	)	)	PUNCT
ejpam-3991	110	1	(	(	PUNCT
ejpam-3991	110	2	1	1	NUM
ejpam-3991	110	3	ab2	ab2	ADJ
ejpam-3991	110	4	+	+	CCONJ
ejpam-3991	110	5	1	1	NUM
ejpam-3991	110	6	)	)	PUNCT
ejpam-3991	110	7	m+w	m+w	NUM
ejpam-3991	110	8	2	2	NUM
ejpam-3991	110	9	sin	sin	NOUN
ejpam-3991	110	10	(	(	PUNCT
ejpam-3991	110	11	1	1	NUM
ejpam-3991	110	12	2	2	NUM
ejpam-3991	110	13	(	(	PUNCT
ejpam-3991	110	14	m+	m+	NUM
ejpam-3991	110	15	w	w	NOUN
ejpam-3991	110	16	)	)	PUNCT
ejpam-3991	110	17	(	(	PUNCT
ejpam-3991	110	18	π	π	NOUN
ejpam-3991	110	19	−	−	PROPN
ejpam-3991	110	20	2	2	NUM
ejpam-3991	110	21	cot−1	cot−1	PROPN
ejpam-3991	110	22	(	(	PUNCT
ejpam-3991	110	23	√	√	PROPN
ejpam-3991	110	24	ab	ab	PROPN
ejpam-3991	110	25	)	)	PUNCT
ejpam-3991	110	26	)	)	PUNCT
ejpam-3991	110	27	)	)	PUNCT
ejpam-3991	111	1	dw	dw	NOUN
ejpam-3991	111	2	from	from	ADP
ejpam-3991	111	3	equation	equation	NOUN
ejpam-3991	111	4	(	(	PUNCT
ejpam-3991	111	5	1.232.3	1.232.3	NUM
ejpam-3991	111	6	)	)	PUNCT
ejpam-3991	111	7	in	in	ADP
ejpam-3991	111	8	[	[	X
ejpam-3991	111	9	3	3	X
ejpam-3991	111	10	]	]	PUNCT
ejpam-3991	111	11	where	where	SCONJ
ejpam-3991	111	12	im(m+w	im(m+w	NOUN
ejpam-3991	111	13	)	)	PUNCT
ejpam-3991	111	14	>	>	X
ejpam-3991	111	15	0	0	PUNCT
ejpam-3991	112	1	in	in	ADP
ejpam-3991	112	2	order	order	NOUN
ejpam-3991	112	3	for	for	SCONJ
ejpam-3991	112	4	the	the	DET
ejpam-3991	112	5	sum	sum	NOUN
ejpam-3991	112	6	to	to	PART
ejpam-3991	112	7	converge	converge	VERB
ejpam-3991	112	8	.	.	PUNCT
ejpam-3991	113	1	5.3	5.3	NUM
ejpam-3991	113	2	.	.	PUNCT
ejpam-3991	113	3	derivation	derivation	NOUN
ejpam-3991	113	4	of	of	ADP
ejpam-3991	113	5	the	the	DET
ejpam-3991	113	6	second	second	ADJ
ejpam-3991	113	7	contour	contour	NOUN
ejpam-3991	113	8	integral	integral	ADJ
ejpam-3991	113	9	in	in	ADP
ejpam-3991	113	10	this	this	DET
ejpam-3991	113	11	section	section	NOUN
ejpam-3991	113	12	we	we	PRON
ejpam-3991	113	13	derive	derive	VERB
ejpam-3991	113	14	the	the	DET
ejpam-3991	113	15	second	second	ADJ
ejpam-3991	113	16	contour	contour	NOUN
ejpam-3991	113	17	integral	integral	ADJ
ejpam-3991	113	18	given	give	VERB
ejpam-3991	113	19	by	by	ADP
ejpam-3991	113	20	(	(	PUNCT
ejpam-3991	113	21	8)	8)	NUM
ejpam-3991	113	22	1	1	NUM
ejpam-3991	113	23	2πi	2πi	NOUN
ejpam-3991	113	24	∫	∫	PROPN
ejpam-3991	114	1	c	c	NOUN
ejpam-3991	114	2	πcww−k−1a	πcww−k−1a	INTJ
ejpam-3991	114	3	1	1	NUM
ejpam-3991	114	4	2	2	NUM
ejpam-3991	114	5	(	(	PUNCT
ejpam-3991	114	6	m+w−1)bm+w	m+w−1)bm+w	PROPN
ejpam-3991	114	7	csc(π(m+	csc(π(m+	PROPN
ejpam-3991	114	8	w	w	NOUN
ejpam-3991	114	9	)	)	PUNCT
ejpam-3991	114	10	)	)	PUNCT
ejpam-3991	115	1	(	(	PUNCT
ejpam-3991	115	2	1	1	NUM
ejpam-3991	115	3	ab2	ab2	ADJ
ejpam-3991	115	4	+	+	CCONJ
ejpam-3991	115	5	1	1	NUM
ejpam-3991	115	6	)	)	PUNCT
ejpam-3991	115	7	m+w	m+w	NUM
ejpam-3991	115	8	2	2	NUM
ejpam-3991	115	9	sin	sin	NOUN
ejpam-3991	115	10	(	(	PUNCT
ejpam-3991	115	11	1	1	NUM
ejpam-3991	115	12	2	2	NUM
ejpam-3991	115	13	(	(	PUNCT
ejpam-3991	115	14	m+	m+	NUM
ejpam-3991	115	15	w	w	NOUN
ejpam-3991	115	16	)	)	PUNCT
ejpam-3991	115	17	(	(	PUNCT
ejpam-3991	115	18	2	2	NUM
ejpam-3991	115	19	cot−1	cot−1	PROPN
ejpam-3991	115	20	(	(	PUNCT
ejpam-3991	115	21	√	√	PROPN
ejpam-3991	115	22	ab	ab	PROPN
ejpam-3991	115	23	)	)	PUNCT
ejpam-3991	116	1	+	+	CCONJ
ejpam-3991	116	2	π	π	NOUN
ejpam-3991	116	3	)	)	PUNCT
ejpam-3991	116	4	)	)	PUNCT
ejpam-3991	117	1	dw	dw	NOUN
ejpam-3991	117	2	in	in	ADP
ejpam-3991	117	3	this	this	DET
ejpam-3991	117	4	derivation	derivation	NOUN
ejpam-3991	117	5	we	we	PRON
ejpam-3991	117	6	proceed	proceed	VERB
ejpam-3991	117	7	as	as	ADP
ejpam-3991	117	8	above	above	ADV
ejpam-3991	117	9	but	but	CCONJ
ejpam-3991	117	10	multiply	multiply	ADV
ejpam-3991	117	11	by	by	ADP
ejpam-3991	117	12	−2iπa	−2iπa	PROPN
ejpam-3991	117	13	m−1	m−1	PROPN
ejpam-3991	117	14	2	2	NUM
ejpam-3991	117	15	bm	bm	X
ejpam-3991	117	16	(	(	PUNCT
ejpam-3991	117	17	1	1	NUM
ejpam-3991	117	18	ab2	ab2	ADJ
ejpam-3991	117	19	+	+	CCONJ
ejpam-3991	117	20	1	1	NUM
ejpam-3991	117	21	)	)	PUNCT
ejpam-3991	117	22	m/2	m/2	NUM
ejpam-3991	117	23	and	and	CCONJ
ejpam-3991	117	24	replace	replace	VERB
ejpam-3991	117	25	t	t	NOUN
ejpam-3991	117	26	by	by	ADP
ejpam-3991	117	27	1	1	NUM
ejpam-3991	117	28	2	2	NUM
ejpam-3991	117	29	(	(	PUNCT
ejpam-3991	117	30	2	2	NUM
ejpam-3991	117	31	cot−1	cot−1	PROPN
ejpam-3991	117	32	(	(	PUNCT
ejpam-3991	117	33	√	√	PROPN
ejpam-3991	117	34	ab	ab	NUM
ejpam-3991	117	35	)	)	PUNCT
ejpam-3991	118	1	+	+	CCONJ
ejpam-3991	118	2	π	π	X
ejpam-3991	118	3	)	)	PUNCT
ejpam-3991	118	4	and	and	CCONJ
ejpam-3991	118	5	simplifying	simplify	VERB
ejpam-3991	118	6	to	to	PART
ejpam-3991	118	7	get	get	VERB
ejpam-3991	118	8	r.	r.	PROPN
ejpam-3991	118	9	reynolds	reynolds	PROPN
ejpam-3991	118	10	,	,	PUNCT
ejpam-3991	118	11	a.	a.	PROPN
ejpam-3991	118	12	stauffer	stauffer	PROPN
ejpam-3991	118	13	/	/	SYM
ejpam-3991	118	14	eur	eur	PROPN
ejpam-3991	118	15	.	.	PUNCT
ejpam-3991	119	1	j.	j.	PROPN
ejpam-3991	119	2	pure	pure	PROPN
ejpam-3991	119	3	appl	appl	PROPN
ejpam-3991	119	4	.	.	PROPN
ejpam-3991	119	5	math	math	PROPN
ejpam-3991	119	6	,	,	PUNCT
ejpam-3991	119	7	14	14	NUM
ejpam-3991	119	8	(	(	PUNCT
ejpam-3991	119	9	3	3	NUM
ejpam-3991	119	10	)	)	PUNCT
ejpam-3991	119	11	(	(	PUNCT
ejpam-3991	119	12	2021	2021	NUM
ejpam-3991	119	13	)	)	PUNCT
ejpam-3991	119	14	,	,	PUNCT
ejpam-3991	119	15	723	723	NUM
ejpam-3991	119	16	-	-	SYM
ejpam-3991	119	17	736	736	NUM
ejpam-3991	119	18	728	728	NUM
ejpam-3991	119	19	2ke	2ke	ADJ
ejpam-3991	119	20	iπk	iπk	NOUN
ejpam-3991	119	21	2	2	NUM
ejpam-3991	119	22	πk+1a	πk+1a	VERB
ejpam-3991	119	23	m−1	m−1	PROPN
ejpam-3991	119	24	2	2	NUM
ejpam-3991	119	25	bm	bm	PROPN
ejpam-3991	119	26	k	k	PROPN
ejpam-3991	119	27	!	!	PUNCT
ejpam-3991	120	1	(	(	PUNCT
ejpam-3991	120	2	1	1	NUM
ejpam-3991	120	3	ab2	ab2	ADJ
ejpam-3991	120	4	+	+	CCONJ
ejpam-3991	120	5	1	1	NUM
ejpam-3991	120	6	)	)	PUNCT
ejpam-3991	120	7	m/2	m/2	NUM
ejpam-3991	120	8	(	(	PUNCT
ejpam-3991	120	9	e	e	NOUN
ejpam-3991	120	10	1	1	NUM
ejpam-3991	120	11	2	2	NUM
ejpam-3991	120	12	im(π−2	im(π−2	PROPN
ejpam-3991	120	13	cot−1	cot−1	PROPN
ejpam-3991	120	14	(	(	PUNCT
ejpam-3991	120	15	√	√	PROPN
ejpam-3991	120	16	ab	ab	NUM
ejpam-3991	120	17	)	)	PUNCT
ejpam-3991	120	18	)	)	PUNCT
ejpam-3991	120	19	φ	φ	PROPN
ejpam-3991	120	20	(	(	PUNCT
ejpam-3991	120	21	e2imπ,−k,−	e2imπ,−k,−	PROPN
ejpam-3991	120	22	i	i	PRON
ejpam-3991	120	23	(	(	PUNCT
ejpam-3991	120	24	−2i	−2i	PROPN
ejpam-3991	120	25	cot−1	cot−1	PROPN
ejpam-3991	120	26	(	(	PUNCT
ejpam-3991	120	27	√	√	PROPN
ejpam-3991	120	28	ab	ab	NUM
ejpam-3991	120	29	)	)	PUNCT
ejpam-3991	120	30	+	+	X
ejpam-3991	120	31	log(a	log(a	PROPN
ejpam-3991	120	32	)	)	PUNCT
ejpam-3991	121	1	+	+	NUM
ejpam-3991	121	2	log	log	NOUN
ejpam-3991	121	3	(	(	PUNCT
ejpam-3991	121	4	1	1	NUM
ejpam-3991	121	5	+	+	NUM
ejpam-3991	121	6	1	1	NUM
ejpam-3991	121	7	b2a	b2a	NOUN
ejpam-3991	121	8	)	)	PUNCT
ejpam-3991	122	1	+	+	CCONJ
ejpam-3991	122	2	2	2	NUM
ejpam-3991	122	3	log(b	log(b	NOUN
ejpam-3991	122	4	)	)	PUNCT
ejpam-3991	122	5	+	+	CCONJ
ejpam-3991	122	6	2	2	NUM
ejpam-3991	122	7	log(c	log(c	NOUN
ejpam-3991	122	8	)	)	PUNCT
ejpam-3991	123	1	+	+	CCONJ
ejpam-3991	123	2	iπ	iπ	X
ejpam-3991	123	3	)	)	PUNCT
ejpam-3991	123	4	4π	4π	NUM
ejpam-3991	123	5	)	)	PUNCT
ejpam-3991	124	1	−	−	PUNCT
ejpam-3991	124	2	e	e	NOUN
ejpam-3991	124	3	1	1	NUM
ejpam-3991	124	4	2	2	NUM
ejpam-3991	124	5	im(2	im(2	PROPN
ejpam-3991	124	6	cot−1	cot−1	PROPN
ejpam-3991	124	7	(	(	PUNCT
ejpam-3991	124	8	√	√	NUM
ejpam-3991	124	9	ab)+3π	ab)+3π	ADP
ejpam-3991	124	10	)	)	PUNCT
ejpam-3991	124	11	φ	φ	PROPN
ejpam-3991	124	12	(	(	PUNCT
ejpam-3991	124	13	e2imπ,−k,−	e2imπ,−k,−	PROPN
ejpam-3991	124	14	i	i	PRON
ejpam-3991	124	15	(	(	PUNCT
ejpam-3991	124	16	2i	2i	NOUN
ejpam-3991	124	17	cot−1	cot−1	PROPN
ejpam-3991	124	18	(	(	PUNCT
ejpam-3991	124	19	√	√	PROPN
ejpam-3991	124	20	ab	ab	NUM
ejpam-3991	124	21	)	)	PUNCT
ejpam-3991	125	1	+	+	X
ejpam-3991	125	2	log(a	log(a	PROPN
ejpam-3991	125	3	)	)	PUNCT
ejpam-3991	126	1	+	+	NUM
ejpam-3991	126	2	log	log	NOUN
ejpam-3991	126	3	(	(	PUNCT
ejpam-3991	126	4	1	1	NUM
ejpam-3991	126	5	+	+	NUM
ejpam-3991	126	6	1	1	NUM
ejpam-3991	126	7	b2a	b2a	NOUN
ejpam-3991	126	8	)	)	PUNCT
ejpam-3991	127	1	+	+	CCONJ
ejpam-3991	127	2	2	2	NUM
ejpam-3991	127	3	log(b	log(b	NOUN
ejpam-3991	127	4	)	)	PUNCT
ejpam-3991	127	5	+	+	CCONJ
ejpam-3991	127	6	2	2	NUM
ejpam-3991	127	7	log(c	log(c	NOUN
ejpam-3991	127	8	)	)	PUNCT
ejpam-3991	128	1	+	+	CCONJ
ejpam-3991	128	2	3iπ	3iπ	ADJ
ejpam-3991	128	3	)	)	PUNCT
ejpam-3991	128	4	4π	4π	NUM
ejpam-3991	128	5	)	)	PUNCT
ejpam-3991	128	6	)	)	PUNCT
ejpam-3991	129	1	=	=	SYM
ejpam-3991	129	2	1	1	NUM
ejpam-3991	129	3	2πi	2πi	NOUN
ejpam-3991	129	4	∫	∫	PROPN
ejpam-3991	130	1	c	c	NOUN
ejpam-3991	130	2	πcww−k−1a	πcww−k−1a	INTJ
ejpam-3991	130	3	1	1	NUM
ejpam-3991	130	4	2	2	NUM
ejpam-3991	130	5	(	(	PUNCT
ejpam-3991	130	6	m+w−1)bm+w	m+w−1)bm+w	PROPN
ejpam-3991	130	7	csc(π(m+	csc(π(m+	PROPN
ejpam-3991	130	8	w	w	NOUN
ejpam-3991	130	9	)	)	PUNCT
ejpam-3991	130	10	)	)	PUNCT
ejpam-3991	131	1	(	(	PUNCT
ejpam-3991	131	2	1	1	NUM
ejpam-3991	131	3	ab2	ab2	ADJ
ejpam-3991	131	4	+	+	CCONJ
ejpam-3991	131	5	1	1	NUM
ejpam-3991	131	6	)	)	PUNCT
ejpam-3991	131	7	m+w	m+w	NUM
ejpam-3991	131	8	2	2	NUM
ejpam-3991	131	9	sin	sin	NOUN
ejpam-3991	131	10	(	(	PUNCT
ejpam-3991	131	11	1	1	NUM
ejpam-3991	131	12	2	2	NUM
ejpam-3991	131	13	(	(	PUNCT
ejpam-3991	131	14	m+	m+	NUM
ejpam-3991	131	15	w	w	NOUN
ejpam-3991	131	16	)	)	PUNCT
ejpam-3991	131	17	(	(	PUNCT
ejpam-3991	131	18	2	2	NUM
ejpam-3991	131	19	cot−1	cot−1	PROPN
ejpam-3991	131	20	(	(	PUNCT
ejpam-3991	131	21	√	√	PROPN
ejpam-3991	131	22	ab	ab	PROPN
ejpam-3991	131	23	)	)	PUNCT
ejpam-3991	132	1	+	+	CCONJ
ejpam-3991	132	2	π	π	NOUN
ejpam-3991	132	3	)	)	PUNCT
ejpam-3991	132	4	)	)	PUNCT
ejpam-3991	132	5	dw	dw	NOUN
ejpam-3991	132	6	(	(	PUNCT
ejpam-3991	132	7	9	9	NUM
ejpam-3991	132	8	)	)	PUNCT
ejpam-3991	132	9	from	from	ADP
ejpam-3991	132	10	equation	equation	NOUN
ejpam-3991	132	11	(	(	PUNCT
ejpam-3991	132	12	1.232.3	1.232.3	NUM
ejpam-3991	132	13	)	)	PUNCT
ejpam-3991	132	14	in	in	ADP
ejpam-3991	132	15	[	[	X
ejpam-3991	132	16	3	3	X
ejpam-3991	132	17	]	]	PUNCT
ejpam-3991	132	18	where	where	SCONJ
ejpam-3991	132	19	im(m+w	im(m+w	NOUN
ejpam-3991	132	20	)	)	PUNCT
ejpam-3991	132	21	>	>	X
ejpam-3991	132	22	0	0	PUNCT
ejpam-3991	133	1	in	in	ADP
ejpam-3991	133	2	order	order	NOUN
ejpam-3991	133	3	for	for	SCONJ
ejpam-3991	133	4	the	the	DET
ejpam-3991	133	5	sum	sum	NOUN
ejpam-3991	133	6	to	to	PART
ejpam-3991	133	7	converge	converge	VERB
ejpam-3991	133	8	.	.	PUNCT
ejpam-3991	134	1	6	6	X
ejpam-3991	134	2	.	.	PUNCT
ejpam-3991	134	3	the	the	DET
ejpam-3991	134	4	stieltjes	stieltjes	PROPN
ejpam-3991	134	5	transform	transform	VERB
ejpam-3991	134	6	in	in	ADP
ejpam-3991	134	7	terms	term	NOUN
ejpam-3991	134	8	of	of	ADP
ejpam-3991	134	9	the	the	DET
ejpam-3991	134	10	lerch	lerch	PROPN
ejpam-3991	134	11	function	function	PROPN
ejpam-3991	134	12	since	since	SCONJ
ejpam-3991	134	13	the	the	DET
ejpam-3991	134	14	right	right	ADJ
ejpam-3991	134	15	-	-	PUNCT
ejpam-3991	134	16	hand	hand	NOUN
ejpam-3991	134	17	side	side	NOUN
ejpam-3991	134	18	of	of	ADP
ejpam-3991	134	19	equation	equation	NOUN
ejpam-3991	134	20	(	(	PUNCT
ejpam-3991	134	21	2	2	X
ejpam-3991	134	22	)	)	PUNCT
ejpam-3991	134	23	is	be	AUX
ejpam-3991	134	24	equal	equal	ADJ
ejpam-3991	134	25	to	to	ADP
ejpam-3991	134	26	the	the	DET
ejpam-3991	134	27	sum	sum	NOUN
ejpam-3991	134	28	of	of	ADP
ejpam-3991	134	29	the	the	DET
ejpam-3991	134	30	right	right	ADJ
ejpam-3991	134	31	-	-	PUNCT
ejpam-3991	134	32	hand	hand	NOUN
ejpam-3991	134	33	sides	side	NOUN
ejpam-3991	134	34	of	of	ADP
ejpam-3991	134	35	equations	equation	NOUN
ejpam-3991	134	36	(	(	PUNCT
ejpam-3991	134	37	8)	8)	NUM
ejpam-3991	134	38	and	and	CCONJ
ejpam-3991	134	39	(	(	PUNCT
ejpam-3991	134	40	9	9	X
ejpam-3991	134	41	)	)	PUNCT
ejpam-3991	134	42	we	we	PRON
ejpam-3991	134	43	can	can	AUX
ejpam-3991	134	44	equate	equate	VERB
ejpam-3991	134	45	the	the	DET
ejpam-3991	134	46	left	left	ADJ
ejpam-3991	134	47	-	-	PUNCT
ejpam-3991	134	48	hand	hand	NOUN
ejpam-3991	134	49	sides	side	NOUN
ejpam-3991	134	50	and	and	CCONJ
ejpam-3991	134	51	simplifying	simplify	VERB
ejpam-3991	134	52	the	the	DET
ejpam-3991	134	53	factorial	factorial	NOUN
ejpam-3991	134	54	to	to	PART
ejpam-3991	134	55	get	get	VERB
ejpam-3991	134	56	(	(	PUNCT
ejpam-3991	134	57	10	10	NUM
ejpam-3991	134	58	)	)	PUNCT
ejpam-3991	134	59	∫	∫	PROPN
ejpam-3991	134	60	∞	∞	PROPN
ejpam-3991	134	61	0	0	NUM
ejpam-3991	135	1	(	(	PUNCT
ejpam-3991	135	2	1−	1−	NUM
ejpam-3991	135	3	bx)m	bx)m	PROPN
ejpam-3991	135	4	logk(c(1−	logk(c(1−	PROPN
ejpam-3991	135	5	bx	bx	PROPN
ejpam-3991	135	6	)	)	PUNCT
ejpam-3991	135	7	)	)	PUNCT
ejpam-3991	136	1	+	+	CCONJ
ejpam-3991	136	2	(	(	PUNCT
ejpam-3991	136	3	bx+	bx+	PROPN
ejpam-3991	136	4	1)m	1)m	NUM
ejpam-3991	136	5	logk(c(bx+	logk(c(bx+	NUM
ejpam-3991	136	6	1	1	NUM
ejpam-3991	136	7	)	)	PUNCT
ejpam-3991	136	8	)	)	PUNCT
ejpam-3991	136	9	a2	a2	PROPN
ejpam-3991	136	10	+	+	CCONJ
ejpam-3991	137	1	x2	x2	PROPN
ejpam-3991	137	2	dx	dx	PROPN
ejpam-3991	137	3	=	=	SYM
ejpam-3991	138	1	2ke	2ke	ADJ
ejpam-3991	138	2	iπk	iπk	VERB
ejpam-3991	138	3	2	2	NUM
ejpam-3991	138	4	πk+1am−1(−b)m	πk+1am−1(−b)m	NOUN
ejpam-3991	138	5	(	(	PUNCT
ejpam-3991	138	6	1	1	NUM
ejpam-3991	138	7	a2b2	a2b2	SYM
ejpam-3991	138	8	+	+	NOUN
ejpam-3991	138	9	1	1	NUM
ejpam-3991	138	10	)	)	PUNCT
ejpam-3991	138	11	m/2	m/2	NUM
ejpam-3991	138	12	(	(	PUNCT
ejpam-3991	138	13	e	e	NOUN
ejpam-3991	138	14	1	1	NUM
ejpam-3991	138	15	2	2	NUM
ejpam-3991	138	16	im(2	im(2	PROPN
ejpam-3991	138	17	cot−1(ab)+π	cot−1(ab)+π	PROPN
ejpam-3991	138	18	)	)	PUNCT
ejpam-3991	138	19	φ	φ	PROPN
ejpam-3991	138	20	(	(	PUNCT
ejpam-3991	138	21	e2imπ,−k,−	e2imπ,−k,−	PROPN
ejpam-3991	138	22	i	i	PRON
ejpam-3991	138	23	(	(	PUNCT
ejpam-3991	138	24	2i	2i	NUM
ejpam-3991	138	25	cot−1(ab	cot−1(ab	NOUN
ejpam-3991	138	26	)	)	PUNCT
ejpam-3991	138	27	+	+	NUM
ejpam-3991	138	28	log	log	NOUN
ejpam-3991	138	29	(	(	PUNCT
ejpam-3991	138	30	a2	a2	PROPN
ejpam-3991	138	31	)	)	PUNCT
ejpam-3991	139	1	+	+	CCONJ
ejpam-3991	139	2	log	log	NOUN
ejpam-3991	139	3	(	(	PUNCT
ejpam-3991	139	4	1	1	NUM
ejpam-3991	139	5	+	+	NUM
ejpam-3991	139	6	1	1	NUM
ejpam-3991	139	7	a2b2	a2b2	PUNCT
ejpam-3991	139	8	)	)	PUNCT
ejpam-3991	140	1	+	+	CCONJ
ejpam-3991	140	2	2	2	NUM
ejpam-3991	140	3	log(−b	log(−b	PROPN
ejpam-3991	140	4	)	)	PUNCT
ejpam-3991	140	5	+	+	CCONJ
ejpam-3991	140	6	2	2	NUM
ejpam-3991	140	7	log(c	log(c	NOUN
ejpam-3991	140	8	)	)	PUNCT
ejpam-3991	141	1	+	+	CCONJ
ejpam-3991	141	2	iπ	iπ	X
ejpam-3991	141	3	)	)	PUNCT
ejpam-3991	141	4	4π	4π	NUM
ejpam-3991	141	5	)	)	PUNCT
ejpam-3991	142	1	−	−	PUNCT
ejpam-3991	142	2	e	e	NOUN
ejpam-3991	142	3	1	1	NUM
ejpam-3991	142	4	2	2	NUM
ejpam-3991	142	5	im(3π−2	im(3π−2	PROPN
ejpam-3991	142	6	cot−1(ab	cot−1(ab	NOUN
ejpam-3991	142	7	)	)	PUNCT
ejpam-3991	142	8	)	)	PUNCT
ejpam-3991	143	1	φ	φ	PROPN
ejpam-3991	143	2	(	(	PUNCT
ejpam-3991	143	3	e2imπ,−k,−	e2imπ,−k,−	PROPN
ejpam-3991	143	4	i	i	PRON
ejpam-3991	143	5	(	(	PUNCT
ejpam-3991	143	6	−2i	−2i	PROPN
ejpam-3991	143	7	cot−1(ab	cot−1(ab	NOUN
ejpam-3991	143	8	)	)	PUNCT
ejpam-3991	143	9	+	+	NUM
ejpam-3991	143	10	log	log	NOUN
ejpam-3991	143	11	(	(	PUNCT
ejpam-3991	143	12	a2	a2	PROPN
ejpam-3991	143	13	)	)	PUNCT
ejpam-3991	144	1	+	+	CCONJ
ejpam-3991	144	2	log	log	NOUN
ejpam-3991	144	3	(	(	PUNCT
ejpam-3991	144	4	1	1	NUM
ejpam-3991	144	5	+	+	NUM
ejpam-3991	144	6	1	1	NUM
ejpam-3991	144	7	a2b2	a2b2	PUNCT
ejpam-3991	144	8	)	)	PUNCT
ejpam-3991	145	1	+	+	CCONJ
ejpam-3991	145	2	2	2	NUM
ejpam-3991	145	3	log(−b	log(−b	PROPN
ejpam-3991	145	4	)	)	PUNCT
ejpam-3991	145	5	+	+	CCONJ
ejpam-3991	145	6	2	2	NUM
ejpam-3991	145	7	log(c	log(c	NOUN
ejpam-3991	145	8	)	)	PUNCT
ejpam-3991	145	9	+	+	CCONJ
ejpam-3991	145	10	3iπ	3iπ	ADJ
ejpam-3991	145	11	)	)	PUNCT
ejpam-3991	145	12	4π	4π	NUM
ejpam-3991	145	13	)	)	PUNCT
ejpam-3991	145	14	)	)	PUNCT
ejpam-3991	146	1	+	+	CCONJ
ejpam-3991	146	2	2ke	2ke	ADJ
ejpam-3991	146	3	iπk	iπk	NOUN
ejpam-3991	146	4	2	2	NUM
ejpam-3991	146	5	πk+1am−1bm	πk+1am−1bm	NOUN
ejpam-3991	146	6	(	(	PUNCT
ejpam-3991	146	7	1	1	NUM
ejpam-3991	146	8	a2b2	a2b2	SYM
ejpam-3991	146	9	+	+	NOUN
ejpam-3991	146	10	1	1	NUM
ejpam-3991	146	11	)	)	PUNCT
ejpam-3991	146	12	m/2	m/2	NUM
ejpam-3991	146	13	(	(	PUNCT
ejpam-3991	146	14	e	e	NOUN
ejpam-3991	146	15	1	1	NUM
ejpam-3991	146	16	2	2	NUM
ejpam-3991	146	17	im(π−2	im(π−2	PROPN
ejpam-3991	146	18	cot−1(ab	cot−1(ab	NOUN
ejpam-3991	146	19	)	)	PUNCT
ejpam-3991	146	20	)	)	PUNCT
ejpam-3991	146	21	φ	φ	PROPN
ejpam-3991	146	22	(	(	PUNCT
ejpam-3991	146	23	e2imπ,−k,−	e2imπ,−k,−	PROPN
ejpam-3991	147	1	i	i	PRON
ejpam-3991	147	2	(	(	PUNCT
ejpam-3991	147	3	−2i	−2i	PROPN
ejpam-3991	147	4	cot−1(ab	cot−1(ab	NOUN
ejpam-3991	147	5	)	)	PUNCT
ejpam-3991	147	6	+	+	NUM
ejpam-3991	147	7	log	log	NOUN
ejpam-3991	147	8	(	(	PUNCT
ejpam-3991	147	9	a2	a2	PROPN
ejpam-3991	147	10	)	)	PUNCT
ejpam-3991	147	11	+	+	CCONJ
ejpam-3991	147	12	log	log	NOUN
ejpam-3991	147	13	(	(	PUNCT
ejpam-3991	147	14	1	1	NUM
ejpam-3991	147	15	+	+	NUM
ejpam-3991	147	16	1	1	NUM
ejpam-3991	147	17	a2b2	a2b2	PUNCT
ejpam-3991	147	18	)	)	PUNCT
ejpam-3991	148	1	+	+	CCONJ
ejpam-3991	148	2	2	2	NUM
ejpam-3991	148	3	log(b	log(b	NOUN
ejpam-3991	148	4	)	)	PUNCT
ejpam-3991	148	5	+	+	CCONJ
ejpam-3991	148	6	2	2	NUM
ejpam-3991	148	7	log(c	log(c	NOUN
ejpam-3991	148	8	)	)	PUNCT
ejpam-3991	149	1	+	+	CCONJ
ejpam-3991	149	2	iπ	iπ	X
ejpam-3991	149	3	)	)	PUNCT
ejpam-3991	149	4	4π	4π	NUM
ejpam-3991	149	5	)	)	PUNCT
ejpam-3991	150	1	−	−	PUNCT
ejpam-3991	150	2	e	e	NOUN
ejpam-3991	150	3	1	1	NUM
ejpam-3991	150	4	2	2	NUM
ejpam-3991	150	5	im(2	im(2	PROPN
ejpam-3991	150	6	cot−1(ab)+3π	cot−1(ab)+3π	PROPN
ejpam-3991	150	7	)	)	PUNCT
ejpam-3991	150	8	φ	φ	PROPN
ejpam-3991	150	9	(	(	PUNCT
ejpam-3991	150	10	e2imπ,−k,−	e2imπ,−k,−	PROPN
ejpam-3991	150	11	i	i	PRON
ejpam-3991	150	12	(	(	PUNCT
ejpam-3991	150	13	2i	2i	NUM
ejpam-3991	150	14	cot−1(ab	cot−1(ab	NOUN
ejpam-3991	150	15	)	)	PUNCT
ejpam-3991	150	16	+	+	NUM
ejpam-3991	150	17	log	log	NOUN
ejpam-3991	150	18	(	(	PUNCT
ejpam-3991	150	19	a2	a2	PROPN
ejpam-3991	150	20	)	)	PUNCT
ejpam-3991	151	1	+	+	CCONJ
ejpam-3991	151	2	log	log	NOUN
ejpam-3991	151	3	(	(	PUNCT
ejpam-3991	151	4	1	1	NUM
ejpam-3991	151	5	+	+	NUM
ejpam-3991	151	6	1	1	NUM
ejpam-3991	151	7	a2b2	a2b2	PUNCT
ejpam-3991	151	8	)	)	PUNCT
ejpam-3991	152	1	+	+	CCONJ
ejpam-3991	152	2	2	2	NUM
ejpam-3991	152	3	log(b	log(b	NOUN
ejpam-3991	152	4	)	)	PUNCT
ejpam-3991	152	5	+	+	CCONJ
ejpam-3991	152	6	2	2	NUM
ejpam-3991	152	7	log(c	log(c	NOUN
ejpam-3991	152	8	)	)	PUNCT
ejpam-3991	153	1	+	+	CCONJ
ejpam-3991	153	2	3iπ	3iπ	ADJ
ejpam-3991	153	3	)	)	PUNCT
ejpam-3991	153	4	4π	4π	NUM
ejpam-3991	153	5	)	)	PUNCT
ejpam-3991	153	6	)	)	PUNCT
ejpam-3991	154	1	r.	r.	PROPN
ejpam-3991	154	2	reynolds	reynolds	PROPN
ejpam-3991	154	3	,	,	PUNCT
ejpam-3991	154	4	a.	a.	PROPN
ejpam-3991	154	5	stauffer	stauffer	PROPN
ejpam-3991	154	6	/	/	SYM
ejpam-3991	154	7	eur	eur	PROPN
ejpam-3991	154	8	.	.	PUNCT
ejpam-3991	155	1	j.	j.	PROPN
ejpam-3991	155	2	pure	pure	PROPN
ejpam-3991	155	3	appl	appl	PROPN
ejpam-3991	155	4	.	.	PROPN
ejpam-3991	155	5	math	math	PROPN
ejpam-3991	155	6	,	,	PUNCT
ejpam-3991	155	7	14	14	NUM
ejpam-3991	155	8	(	(	PUNCT
ejpam-3991	155	9	3	3	NUM
ejpam-3991	155	10	)	)	PUNCT
ejpam-3991	155	11	(	(	PUNCT
ejpam-3991	155	12	2021	2021	NUM
ejpam-3991	155	13	)	)	PUNCT
ejpam-3991	155	14	,	,	PUNCT
ejpam-3991	155	15	723	723	NUM
ejpam-3991	155	16	-	-	SYM
ejpam-3991	155	17	736	736	NUM
ejpam-3991	155	18	729	729	NUM
ejpam-3991	155	19	7	7	NUM
ejpam-3991	155	20	.	.	PUNCT
ejpam-3991	155	21	definite	definite	ADJ
ejpam-3991	155	22	integrals	integral	NOUN
ejpam-3991	155	23	in	in	ADP
ejpam-3991	155	24	terms	term	NOUN
ejpam-3991	155	25	of	of	ADP
ejpam-3991	155	26	the	the	DET
ejpam-3991	155	27	hurwitz	hurwitz	PROPN
ejpam-3991	155	28	zeta	zeta	PROPN
ejpam-3991	155	29	function	function	NOUN
ejpam-3991	155	30	using	use	VERB
ejpam-3991	155	31	equation	equation	NOUN
ejpam-3991	155	32	(	(	PUNCT
ejpam-3991	155	33	10	10	NUM
ejpam-3991	155	34	)	)	PUNCT
ejpam-3991	155	35	replacing	replace	VERB
ejpam-3991	155	36	b	b	NUM
ejpam-3991	155	37	by	by	ADP
ejpam-3991	155	38	β	β	X
ejpam-3991	155	39	,	,	PUNCT
ejpam-3991	155	40	a	a	PRON
ejpam-3991	155	41	by	by	ADP
ejpam-3991	155	42	α	α	NOUN
ejpam-3991	155	43	and	and	CCONJ
ejpam-3991	155	44	setting	set	VERB
ejpam-3991	155	45	c	c	NOUN
ejpam-3991	155	46	=	=	SYM
ejpam-3991	155	47	1	1	NUM
ejpam-3991	155	48	followed	follow	VERB
ejpam-3991	155	49	by	by	ADP
ejpam-3991	155	50	taking	take	VERB
ejpam-3991	155	51	the	the	DET
ejpam-3991	155	52	sum	sum	NOUN
ejpam-3991	155	53	over	over	ADP
ejpam-3991	155	54	m	m	NOUN
ejpam-3991	155	55	∈	∈	NOUN
ejpam-3991	156	1	[	[	X
ejpam-3991	156	2	0,∞	0,∞	NOUN
ejpam-3991	156	3	)	)	PUNCT
ejpam-3991	156	4	and	and	CCONJ
ejpam-3991	156	5	simplifying	simplify	VERB
ejpam-3991	156	6	in	in	ADP
ejpam-3991	156	7	terms	term	NOUN
ejpam-3991	156	8	of	of	ADP
ejpam-3991	156	9	the	the	DET
ejpam-3991	156	10	hurwitz	hurwitz	PROPN
ejpam-3991	156	11	zeta	zeta	PROPN
ejpam-3991	156	12	function	function	VERB
ejpam-3991	156	13	we	we	PRON
ejpam-3991	156	14	get∫	get∫	VERB
ejpam-3991	157	1	∞	∞	NOUN
ejpam-3991	157	2	0	0	NUM
ejpam-3991	158	1	logk(1−	logk(1−	PROPN
ejpam-3991	158	2	βx)−	βx)−	PROPN
ejpam-3991	158	3	logk(βx+	logk(βx+	PROPN
ejpam-3991	158	4	1	1	NUM
ejpam-3991	158	5	)	)	PUNCT
ejpam-3991	158	6	x	x	NOUN
ejpam-3991	158	7	(	(	PUNCT
ejpam-3991	158	8	α2	α2	ADJ
ejpam-3991	158	9	+	+	CCONJ
ejpam-3991	158	10	x2	x2	ADJ
ejpam-3991	158	11	)	)	PUNCT
ejpam-3991	158	12	dx	dx	PROPN
ejpam-3991	159	1	=	=	SYM
ejpam-3991	159	2	−	−	PROPN
ejpam-3991	159	3	i2	i2	PROPN
ejpam-3991	159	4	ke	ke	NOUN
ejpam-3991	159	5	iπk	iπk	NOUN
ejpam-3991	159	6	2	2	NUM
ejpam-3991	159	7	πk+1	πk+1	NOUN
ejpam-3991	159	8	α2	α2	ADJ
ejpam-3991	159	9	(	(	PUNCT
ejpam-3991	159	10	ζ	ζ	NOUN
ejpam-3991	159	11	(	(	PUNCT
ejpam-3991	159	12	−k	−k	PROPN
ejpam-3991	159	13	,	,	PUNCT
ejpam-3991	159	14	i(−2	i(−2	PROPN
ejpam-3991	159	15	log(i−	log(i−	X
ejpam-3991	159	16	αβ)−	αβ)−	NUM
ejpam-3991	159	17	3iπ	3iπ	NOUN
ejpam-3991	159	18	)	)	PUNCT
ejpam-3991	159	19	4π	4π	NUM
ejpam-3991	159	20	)	)	PUNCT
ejpam-3991	160	1	−	−	PROPN
ejpam-3991	160	2	ζ	ζ	NOUN
ejpam-3991	160	3	(	(	PUNCT
ejpam-3991	160	4	−k,−	−k,−	VERB
ejpam-3991	160	5	i(2	i(2	PROPN
ejpam-3991	160	6	log(αβ	log(αβ	NOUN
ejpam-3991	160	7	−	−	PROPN
ejpam-3991	160	8	i	i	NOUN
ejpam-3991	160	9	)	)	PUNCT
ejpam-3991	161	1	+	+	CCONJ
ejpam-3991	161	2	iπ	iπ	X
ejpam-3991	161	3	)	)	PUNCT
ejpam-3991	161	4	4π	4π	NUM
ejpam-3991	161	5	)	)	PUNCT
ejpam-3991	161	6	)	)	PUNCT
ejpam-3991	162	1	(	(	PUNCT
ejpam-3991	162	2	11	11	X
ejpam-3991	162	3	)	)	PUNCT
ejpam-3991	162	4	using	use	VERB
ejpam-3991	162	5	equation	equation	NOUN
ejpam-3991	162	6	(	(	PUNCT
ejpam-3991	162	7	10	10	NUM
ejpam-3991	162	8	)	)	PUNCT
ejpam-3991	162	9	and	and	CCONJ
ejpam-3991	162	10	setting	set	VERB
ejpam-3991	162	11	m	m	NOUN
ejpam-3991	162	12	=	=	SYM
ejpam-3991	162	13	0	0	PUNCT
ejpam-3991	162	14	and	and	CCONJ
ejpam-3991	162	15	replacing	replace	VERB
ejpam-3991	162	16	a	a	PRON
ejpam-3991	162	17	by	by	ADP
ejpam-3991	162	18	√	√	PROPN
ejpam-3991	162	19	a	a	PRON
ejpam-3991	162	20	and	and	CCONJ
ejpam-3991	162	21	simplifying	simplify	VERB
ejpam-3991	162	22	in	in	ADP
ejpam-3991	162	23	terms	term	NOUN
ejpam-3991	162	24	of	of	ADP
ejpam-3991	162	25	the	the	DET
ejpam-3991	162	26	hurwitz	hurwitz	PROPN
ejpam-3991	162	27	zeta	zeta	PROPN
ejpam-3991	162	28	function	function	VERB
ejpam-3991	162	29	ζ(s	ζ(s	PROPN
ejpam-3991	162	30	,	,	PUNCT
ejpam-3991	162	31	v	v	NOUN
ejpam-3991	162	32	)	)	PUNCT
ejpam-3991	162	33	we	we	PRON
ejpam-3991	162	34	get∫	get∫	VERB
ejpam-3991	162	35	∞	∞	PROPN
ejpam-3991	162	36	0	0	NUM
ejpam-3991	162	37	logk(c−	logk(c−	PROPN
ejpam-3991	162	38	bcx	bcx	NOUN
ejpam-3991	162	39	)	)	PUNCT
ejpam-3991	163	1	+	+	CCONJ
ejpam-3991	163	2	logk(bcx+	logk(bcx+	PROPN
ejpam-3991	163	3	c	c	NOUN
ejpam-3991	163	4	)	)	PUNCT
ejpam-3991	163	5	a+	a+	PUNCT
ejpam-3991	164	1	x2	x2	PROPN
ejpam-3991	164	2	dx	dx	PROPN
ejpam-3991	164	3	=	=	PUNCT
ejpam-3991	164	4	(	(	PUNCT
ejpam-3991	164	5	2i)kπk+1	2i)kπk+1	NUM
ejpam-3991	164	6	√	√	PROPN
ejpam-3991	164	7	a	a	DET
ejpam-3991	164	8	(	(	PUNCT
ejpam-3991	164	9	ζ	ζ	X
ejpam-3991	164	10	(	(	PUNCT
ejpam-3991	164	11	−k	−k	PROPN
ejpam-3991	164	12	,	,	PUNCT
ejpam-3991	164	13	−	−	PROPN
ejpam-3991	164	14	i	i	PRON
ejpam-3991	164	15	(	(	PUNCT
ejpam-3991	164	16	−2i	−2i	PROPN
ejpam-3991	164	17	cot−1	cot−1	PROPN
ejpam-3991	164	18	(	(	PUNCT
ejpam-3991	164	19	√	√	PROPN
ejpam-3991	164	20	ab	ab	NUM
ejpam-3991	164	21	)	)	PUNCT
ejpam-3991	164	22	+	+	X
ejpam-3991	164	23	log(a	log(a	PROPN
ejpam-3991	164	24	)	)	PUNCT
ejpam-3991	165	1	+	+	NUM
ejpam-3991	165	2	log	log	NOUN
ejpam-3991	165	3	(	(	PUNCT
ejpam-3991	165	4	1	1	NUM
ejpam-3991	165	5	+	+	NUM
ejpam-3991	165	6	1	1	NUM
ejpam-3991	165	7	b2a	b2a	NOUN
ejpam-3991	165	8	)	)	PUNCT
ejpam-3991	166	1	+	+	CCONJ
ejpam-3991	166	2	2	2	NUM
ejpam-3991	166	3	log(b	log(b	NOUN
ejpam-3991	166	4	)	)	PUNCT
ejpam-3991	166	5	+	+	CCONJ
ejpam-3991	166	6	2	2	NUM
ejpam-3991	166	7	log(c	log(c	NOUN
ejpam-3991	166	8	)	)	PUNCT
ejpam-3991	167	1	+	+	CCONJ
ejpam-3991	167	2	iπ	iπ	X
ejpam-3991	167	3	)	)	PUNCT
ejpam-3991	167	4	4π	4π	NUM
ejpam-3991	167	5	)	)	PUNCT
ejpam-3991	168	1	−	−	PROPN
ejpam-3991	168	2	ζ	ζ	NOUN
ejpam-3991	168	3	(	(	PUNCT
ejpam-3991	168	4	−k	−k	PROPN
ejpam-3991	168	5	,	,	PUNCT
ejpam-3991	168	6	−	−	PROPN
ejpam-3991	168	7	i	i	PRON
ejpam-3991	168	8	(	(	PUNCT
ejpam-3991	168	9	−2i	−2i	PROPN
ejpam-3991	168	10	cot−1	cot−1	PROPN
ejpam-3991	168	11	(	(	PUNCT
ejpam-3991	168	12	√	√	PROPN
ejpam-3991	168	13	ab	ab	NUM
ejpam-3991	168	14	)	)	PUNCT
ejpam-3991	168	15	+	+	X
ejpam-3991	168	16	log(a	log(a	PROPN
ejpam-3991	168	17	)	)	PUNCT
ejpam-3991	169	1	+	+	NUM
ejpam-3991	169	2	log	log	NOUN
ejpam-3991	169	3	(	(	PUNCT
ejpam-3991	169	4	1	1	NUM
ejpam-3991	169	5	+	+	NUM
ejpam-3991	169	6	1	1	NUM
ejpam-3991	169	7	b2a	b2a	NOUN
ejpam-3991	169	8	)	)	PUNCT
ejpam-3991	170	1	+	+	CCONJ
ejpam-3991	170	2	2	2	NUM
ejpam-3991	170	3	log(b	log(b	NOUN
ejpam-3991	170	4	)	)	PUNCT
ejpam-3991	170	5	+	+	CCONJ
ejpam-3991	170	6	2	2	NUM
ejpam-3991	170	7	log(c	log(c	NOUN
ejpam-3991	170	8	)	)	PUNCT
ejpam-3991	171	1	+	+	CCONJ
ejpam-3991	171	2	5iπ	5iπ	ADJ
ejpam-3991	171	3	)	)	PUNCT
ejpam-3991	171	4	4π	4π	NUM
ejpam-3991	171	5	)	)	PUNCT
ejpam-3991	171	6	)	)	PUNCT
ejpam-3991	172	1	(	(	PUNCT
ejpam-3991	172	2	12	12	NUM
ejpam-3991	172	3	)	)	PUNCT
ejpam-3991	172	4	8	8	NUM
ejpam-3991	172	5	.	.	PUNCT
ejpam-3991	173	1	derivation	derivation	NOUN
ejpam-3991	173	2	of	of	ADP
ejpam-3991	173	3	entry	entry	NOUN
ejpam-3991	173	4	4.535.7	4.535.7	NUM
ejpam-3991	173	5	in	in	ADP
ejpam-3991	173	6	[	[	X
ejpam-3991	173	7	3	3	NUM
ejpam-3991	173	8	]	]	PUNCT
ejpam-3991	173	9	using	use	VERB
ejpam-3991	173	10	(	(	PUNCT
ejpam-3991	173	11	11	11	NUM
ejpam-3991	173	12	)	)	PUNCT
ejpam-3991	173	13	and	and	CCONJ
ejpam-3991	173	14	setting	set	VERB
ejpam-3991	173	15	k	k	X
ejpam-3991	173	16	=	=	PUNCT
ejpam-3991	173	17	α	α	NOUN
ejpam-3991	173	18	=	=	SYM
ejpam-3991	173	19	1	1	NUM
ejpam-3991	173	20	and	and	CCONJ
ejpam-3991	173	21	replacing	replace	VERB
ejpam-3991	173	22	β	β	VERB
ejpam-3991	173	23	by	by	ADP
ejpam-3991	173	24	−ip	−ip	ADV
ejpam-3991	173	25	and	and	CCONJ
ejpam-3991	173	26	simplifying	simplify	VERB
ejpam-3991	173	27	we	we	PRON
ejpam-3991	173	28	get	get	VERB
ejpam-3991	173	29	(	(	PUNCT
ejpam-3991	173	30	13	13	NUM
ejpam-3991	173	31	)	)	PUNCT
ejpam-3991	173	32	∫	∫	PROPN
ejpam-3991	174	1	∞	∞	NOUN
ejpam-3991	174	2	0	0	NUM
ejpam-3991	174	3	tan−1(px	tan−1(px	NOUN
ejpam-3991	174	4	)	)	PUNCT
ejpam-3991	174	5	x3	x3	VERB
ejpam-3991	174	6	+	+	CCONJ
ejpam-3991	174	7	x	x	PUNCT
ejpam-3991	174	8	dx	dx	PROPN
ejpam-3991	174	9	=	=	SYM
ejpam-3991	174	10	1	1	NUM
ejpam-3991	174	11	2	2	NUM
ejpam-3991	174	12	π	π	X
ejpam-3991	174	13	log(p+	log(p+	PROPN
ejpam-3991	174	14	1	1	NUM
ejpam-3991	174	15	)	)	PUNCT
ejpam-3991	174	16	9	9	NUM
ejpam-3991	174	17	.	.	PUNCT
ejpam-3991	175	1	derivation	derivation	NOUN
ejpam-3991	175	2	of	of	ADP
ejpam-3991	175	3	entry	entry	NOUN
ejpam-3991	175	4	4.535.8	4.535.8	NUM
ejpam-3991	175	5	in	in	ADP
ejpam-3991	175	6	[	[	X
ejpam-3991	175	7	3	3	X
ejpam-3991	175	8	]	]	PUNCT
ejpam-3991	175	9	using	use	VERB
ejpam-3991	175	10	(	(	PUNCT
ejpam-3991	175	11	11	11	NUM
ejpam-3991	175	12	)	)	PUNCT
ejpam-3991	175	13	and	and	CCONJ
ejpam-3991	175	14	setting	set	VERB
ejpam-3991	175	15	k	k	X
ejpam-3991	175	16	=	=	SYM
ejpam-3991	175	17	1	1	NUM
ejpam-3991	175	18	,	,	PUNCT
ejpam-3991	175	19	β	β	NOUN
ejpam-3991	175	20	=	=	SYM
ejpam-3991	175	21	−p	−p	NOUN
ejpam-3991	175	22	,	,	PUNCT
ejpam-3991	175	23	α	α	X
ejpam-3991	175	24	=	=	VERB
ejpam-3991	175	25	i	i	PRON
ejpam-3991	175	26	and	and	CCONJ
ejpam-3991	175	27	simplifying	simplify	VERB
ejpam-3991	175	28	we	we	PRON
ejpam-3991	175	29	get	get	VERB
ejpam-3991	175	30	(	(	PUNCT
ejpam-3991	175	31	14	14	NUM
ejpam-3991	175	32	)	)	PUNCT
ejpam-3991	175	33	∫	∫	PROPN
ejpam-3991	176	1	∞	∞	PROPN
ejpam-3991	176	2	0	0	NUM
ejpam-3991	176	3	tan−1(px	tan−1(px	NOUN
ejpam-3991	176	4	)	)	PUNCT
ejpam-3991	177	1	x−	x−	PROPN
ejpam-3991	177	2	x3	x3	PROPN
ejpam-3991	177	3	dx	dx	PROPN
ejpam-3991	178	1	=	=	NOUN
ejpam-3991	178	2	1	1	NUM
ejpam-3991	178	3	4	4	NUM
ejpam-3991	178	4	π(2	π(2	PROPN
ejpam-3991	178	5	log(p+	log(p+	PROPN
ejpam-3991	178	6	i)−	i)−	PROPN
ejpam-3991	178	7	iπ	iπ	NOUN
ejpam-3991	178	8	)	)	PUNCT
ejpam-3991	178	9	10	10	NUM
ejpam-3991	178	10	.	.	PUNCT
ejpam-3991	179	1	derivation	derivation	NOUN
ejpam-3991	179	2	of	of	ADP
ejpam-3991	179	3	entry	entry	NOUN
ejpam-3991	179	4	4.535.9	4.535.9	NUM
ejpam-3991	179	5	in	in	ADP
ejpam-3991	179	6	[	[	X
ejpam-3991	179	7	3	3	NUM
ejpam-3991	179	8	]	]	PUNCT
ejpam-3991	179	9	using	use	VERB
ejpam-3991	179	10	(	(	PUNCT
ejpam-3991	179	11	11	11	NUM
ejpam-3991	179	12	)	)	PUNCT
ejpam-3991	179	13	and	and	CCONJ
ejpam-3991	179	14	setting	set	VERB
ejpam-3991	179	15	k	k	X
ejpam-3991	179	16	=	=	SYM
ejpam-3991	179	17	1	1	NUM
ejpam-3991	179	18	and	and	CCONJ
ejpam-3991	179	19	replacing	replace	VERB
ejpam-3991	179	20	β	β	NOUN
ejpam-3991	179	21	by	by	ADP
ejpam-3991	179	22	−iq	−iq	PROPN
ejpam-3991	179	23	and	and	CCONJ
ejpam-3991	179	24	α	α	NOUN
ejpam-3991	179	25	by	by	ADP
ejpam-3991	179	26	p	p	NOUN
ejpam-3991	179	27	and	and	CCONJ
ejpam-3991	179	28	simplifying	simplify	VERB
ejpam-3991	179	29	we	we	PRON
ejpam-3991	179	30	get	get	VERB
ejpam-3991	179	31	(	(	PUNCT
ejpam-3991	179	32	15	15	NUM
ejpam-3991	179	33	)	)	PUNCT
ejpam-3991	179	34	∫	∫	PROPN
ejpam-3991	180	1	∞	∞	PROPN
ejpam-3991	180	2	0	0	NUM
ejpam-3991	180	3	tan−1(qx	tan−1(qx	NOUN
ejpam-3991	180	4	)	)	PUNCT
ejpam-3991	181	1	p2x+	p2x+	NOUN
ejpam-3991	181	2	x3	x3	VERB
ejpam-3991	181	3	dx	dx	PROPN
ejpam-3991	182	1	=	=	SYM
ejpam-3991	182	2	π	π	NOUN
ejpam-3991	182	3	log(pq	log(pq	VERB
ejpam-3991	182	4	+	+	CCONJ
ejpam-3991	182	5	1	1	X
ejpam-3991	182	6	)	)	PUNCT
ejpam-3991	182	7	2p2	2p2	PROPN
ejpam-3991	182	8	r.	r.	PROPN
ejpam-3991	182	9	reynolds	reynolds	PROPN
ejpam-3991	182	10	,	,	PUNCT
ejpam-3991	182	11	a.	a.	PROPN
ejpam-3991	182	12	stauffer	stauffer	PROPN
ejpam-3991	182	13	/	/	SYM
ejpam-3991	182	14	eur	eur	PROPN
ejpam-3991	182	15	.	.	PUNCT
ejpam-3991	183	1	j.	j.	PROPN
ejpam-3991	183	2	pure	pure	PROPN
ejpam-3991	183	3	appl	appl	PROPN
ejpam-3991	183	4	.	.	PROPN
ejpam-3991	183	5	math	math	PROPN
ejpam-3991	183	6	,	,	PUNCT
ejpam-3991	183	7	14	14	NUM
ejpam-3991	183	8	(	(	PUNCT
ejpam-3991	183	9	3	3	NUM
ejpam-3991	183	10	)	)	PUNCT
ejpam-3991	183	11	(	(	PUNCT
ejpam-3991	183	12	2021	2021	NUM
ejpam-3991	183	13	)	)	PUNCT
ejpam-3991	183	14	,	,	PUNCT
ejpam-3991	183	15	723	723	NUM
ejpam-3991	183	16	-	-	SYM
ejpam-3991	183	17	736	736	NUM
ejpam-3991	183	18	730	730	NUM
ejpam-3991	183	19	11	11	NUM
ejpam-3991	183	20	.	.	PUNCT
ejpam-3991	184	1	derivation	derivation	NOUN
ejpam-3991	184	2	of	of	ADP
ejpam-3991	184	3	entry	entry	NOUN
ejpam-3991	184	4	4.535.10	4.535.10	NUM
ejpam-3991	184	5	in	in	ADP
ejpam-3991	184	6	[	[	X
ejpam-3991	184	7	3	3	X
ejpam-3991	184	8	]	]	PUNCT
ejpam-3991	184	9	in	in	ADP
ejpam-3991	184	10	this	this	DET
ejpam-3991	184	11	evaluation	evaluation	NOUN
ejpam-3991	184	12	we	we	PRON
ejpam-3991	184	13	will	will	AUX
ejpam-3991	184	14	derive	derive	VERB
ejpam-3991	184	15	the	the	DET
ejpam-3991	184	16	definite	definite	ADJ
ejpam-3991	184	17	integrals	integral	NOUN
ejpam-3991	184	18	for	for	ADP
ejpam-3991	184	19	both	both	CCONJ
ejpam-3991	184	20	the	the	DET
ejpam-3991	184	21	arctangent	arctangent	NOUN
ejpam-3991	184	22	and	and	CCONJ
ejpam-3991	184	23	hyperbolic	hyperbolic	ADJ
ejpam-3991	184	24	tangent	tangent	NOUN
ejpam-3991	184	25	functions	function	NOUN
ejpam-3991	184	26	.	.	PUNCT
ejpam-3991	185	1	using	use	VERB
ejpam-3991	185	2	(	(	PUNCT
ejpam-3991	185	3	11	11	NUM
ejpam-3991	185	4	)	)	PUNCT
ejpam-3991	185	5	and	and	CCONJ
ejpam-3991	185	6	setting	set	VERB
ejpam-3991	185	7	k	k	X
ejpam-3991	185	8	=	=	SYM
ejpam-3991	185	9	1	1	NUM
ejpam-3991	185	10	and	and	CCONJ
ejpam-3991	185	11	replacing	replace	VERB
ejpam-3991	185	12	β	β	PRON
ejpam-3991	185	13	by	by	ADP
ejpam-3991	185	14	q	q	PROPN
ejpam-3991	185	15	and	and	CCONJ
ejpam-3991	185	16	α	α	NOUN
ejpam-3991	185	17	by	by	ADP
ejpam-3991	185	18	1	1	NUM
ejpam-3991	185	19	/	/	SYM
ejpam-3991	185	20	p	p	NOUN
ejpam-3991	185	21	simplifying	simplify	VERB
ejpam-3991	185	22	we	we	PRON
ejpam-3991	185	23	get	get	VERB
ejpam-3991	185	24	(	(	PUNCT
ejpam-3991	185	25	16	16	NUM
ejpam-3991	185	26	)	)	PUNCT
ejpam-3991	185	27	∫	∫	PROPN
ejpam-3991	186	1	∞	∞	PROPN
ejpam-3991	186	2	0	0	NUM
ejpam-3991	186	3	tanh−1(qx	tanh−1(qx	PROPN
ejpam-3991	186	4	)	)	PUNCT
ejpam-3991	186	5	p2x3	p2x3	VERB
ejpam-3991	187	1	+	+	CCONJ
ejpam-3991	187	2	x	x	SYM
ejpam-3991	187	3	dx	dx	PROPN
ejpam-3991	187	4	=	=	SYM
ejpam-3991	187	5	1	1	NUM
ejpam-3991	187	6	8	8	NUM
ejpam-3991	187	7	(	(	PUNCT
ejpam-3991	187	8	−	−	PROPN
ejpam-3991	187	9	log	log	NOUN
ejpam-3991	187	10	(	(	PUNCT
ejpam-3991	187	11	−q	−q	NOUN
ejpam-3991	187	12	p	p	X
ejpam-3991	188	1	+	+	PROPN
ejpam-3991	188	2	i	i	NOUN
ejpam-3991	188	3	)	)	PUNCT
ejpam-3991	189	1	+	+	CCONJ
ejpam-3991	189	2	log	log	NOUN
ejpam-3991	189	3	(	(	PUNCT
ejpam-3991	189	4	q	q	NOUN
ejpam-3991	189	5	p	p	X
ejpam-3991	189	6	−	−	PROPN
ejpam-3991	189	7	i	i	INTJ
ejpam-3991	189	8	)	)	PUNCT
ejpam-3991	189	9	−	−	ADP
ejpam-3991	190	1	iπ	iπ	INTJ
ejpam-3991	190	2	)	)	PUNCT
ejpam-3991	190	3	(	(	PUNCT
ejpam-3991	190	4	log	log	NOUN
ejpam-3991	190	5	(	(	PUNCT
ejpam-3991	190	6	−q	−q	NOUN
ejpam-3991	190	7	p	p	X
ejpam-3991	191	1	+	+	PROPN
ejpam-3991	191	2	i	i	NOUN
ejpam-3991	191	3	)	)	PUNCT
ejpam-3991	192	1	+	+	CCONJ
ejpam-3991	192	2	log	log	NOUN
ejpam-3991	192	3	(	(	PUNCT
ejpam-3991	192	4	q	q	NOUN
ejpam-3991	192	5	p	p	NOUN
ejpam-3991	192	6	−	−	PROPN
ejpam-3991	192	7	i	i	NOUN
ejpam-3991	192	8	)	)	PUNCT
ejpam-3991	192	9	)	)	PUNCT
ejpam-3991	193	1	next	next	ADV
ejpam-3991	193	2	we	we	PRON
ejpam-3991	193	3	multiply	multiply	VERB
ejpam-3991	193	4	by	by	ADP
ejpam-3991	193	5	−1	−1	NOUN
ejpam-3991	193	6	/	/	SYM
ejpam-3991	193	7	i	i	PROPN
ejpam-3991	193	8	,	,	PUNCT
ejpam-3991	193	9	replace	replace	VERB
ejpam-3991	193	10	p	p	NOUN
ejpam-3991	193	11	by	by	ADP
ejpam-3991	193	12	−ip	−ip	NOUN
ejpam-3991	193	13	and	and	CCONJ
ejpam-3991	193	14	q	q	NOUN
ejpam-3991	193	15	by	by	ADP
ejpam-3991	193	16	−iq	−iq	PROPN
ejpam-3991	193	17	simplifying	simplify	VERB
ejpam-3991	193	18	to	to	PART
ejpam-3991	193	19	get	get	VERB
ejpam-3991	193	20	(	(	PUNCT
ejpam-3991	193	21	17	17	NUM
ejpam-3991	193	22	)	)	PUNCT
ejpam-3991	193	23	∫	∫	PROPN
ejpam-3991	194	1	∞	∞	PROPN
ejpam-3991	194	2	0	0	NUM
ejpam-3991	194	3	tan−1(qx	tan−1(qx	PROPN
ejpam-3991	194	4	)	)	PUNCT
ejpam-3991	194	5	x−	x−	PROPN
ejpam-3991	195	1	p2x3	p2x3	PROPN
ejpam-3991	195	2	dx	dx	PROPN
ejpam-3991	195	3	=	=	SYM
ejpam-3991	195	4	1	1	NUM
ejpam-3991	195	5	2	2	NUM
ejpam-3991	195	6	π	π	NOUN
ejpam-3991	195	7	log	log	NOUN
ejpam-3991	195	8	(	(	PUNCT
ejpam-3991	195	9	1	1	NUM
ejpam-3991	195	10	+	+	CCONJ
ejpam-3991	195	11	iq	iq	PROPN
ejpam-3991	195	12	p	p	NOUN
ejpam-3991	195	13	)	)	PUNCT
ejpam-3991	195	14	the	the	DET
ejpam-3991	195	15	formula	formula	NOUN
ejpam-3991	195	16	given	give	VERB
ejpam-3991	195	17	in	in	ADP
ejpam-3991	195	18	[	[	NOUN
ejpam-3991	195	19	3	3	NUM
ejpam-3991	195	20	]	]	PUNCT
ejpam-3991	195	21	is	be	AUX
ejpam-3991	195	22	in	in	ADP
ejpam-3991	195	23	error	error	NOUN
ejpam-3991	195	24	.	.	PUNCT
ejpam-3991	196	1	12	12	NUM
ejpam-3991	196	2	.	.	PUNCT
ejpam-3991	197	1	derivation	derivation	NOUN
ejpam-3991	197	2	of	of	ADP
ejpam-3991	197	3	entry	entry	NOUN
ejpam-3991	197	4	4.535.11	4.535.11	NUM
ejpam-3991	197	5	in	in	ADP
ejpam-3991	197	6	[	[	X
ejpam-3991	197	7	3	3	NUM
ejpam-3991	197	8	]	]	PUNCT
ejpam-3991	197	9	in	in	ADP
ejpam-3991	197	10	this	this	DET
ejpam-3991	197	11	evaluation	evaluation	NOUN
ejpam-3991	197	12	we	we	PRON
ejpam-3991	197	13	will	will	AUX
ejpam-3991	197	14	derive	derive	VERB
ejpam-3991	197	15	the	the	DET
ejpam-3991	197	16	definite	definite	ADJ
ejpam-3991	197	17	integrals	integral	NOUN
ejpam-3991	197	18	for	for	ADP
ejpam-3991	197	19	both	both	CCONJ
ejpam-3991	197	20	the	the	DET
ejpam-3991	197	21	arctangent	arctangent	NOUN
ejpam-3991	197	22	and	and	CCONJ
ejpam-3991	197	23	hyperbolic	hyperbolic	ADJ
ejpam-3991	197	24	tangent	tangent	NOUN
ejpam-3991	197	25	functions	function	NOUN
ejpam-3991	197	26	.	.	PUNCT
ejpam-3991	198	1	using	use	VERB
ejpam-3991	198	2	(	(	PUNCT
ejpam-3991	198	3	10	10	NUM
ejpam-3991	198	4	)	)	PUNCT
ejpam-3991	198	5	and	and	CCONJ
ejpam-3991	198	6	setting	set	VERB
ejpam-3991	198	7	m	m	PROPN
ejpam-3991	198	8	=	=	SYM
ejpam-3991	198	9	0	0	NUM
ejpam-3991	198	10	,	,	PUNCT
ejpam-3991	198	11	k	k	NOUN
ejpam-3991	198	12	=	=	SYM
ejpam-3991	198	13	1	1	NUM
ejpam-3991	198	14	and	and	CCONJ
ejpam-3991	198	15	replacing	replace	VERB
ejpam-3991	198	16	β	β	PRON
ejpam-3991	198	17	by	by	ADP
ejpam-3991	198	18	q	q	PROPN
ejpam-3991	198	19	and	and	CCONJ
ejpam-3991	198	20	α	α	NOUN
ejpam-3991	198	21	by	by	ADP
ejpam-3991	198	22	1	1	NUM
ejpam-3991	198	23	/	/	SYM
ejpam-3991	198	24	p	p	NOUN
ejpam-3991	198	25	and	and	CCONJ
ejpam-3991	198	26	simplifying	simplify	VERB
ejpam-3991	198	27	we	we	PRON
ejpam-3991	198	28	get∫	get∫	PROPN
ejpam-3991	198	29	∞	∞	PROPN
ejpam-3991	198	30	0	0	NUM
ejpam-3991	198	31	tanh−1(bx	tanh−1(bx	NOUN
ejpam-3991	198	32	)	)	PUNCT
ejpam-3991	198	33	ax+	ax+	NOUN
ejpam-3991	199	1	x3	x3	ADJ
ejpam-3991	199	2	dx	dx	PROPN
ejpam-3991	200	1	=	=	SYM
ejpam-3991	200	2	−	−	PROPN
ejpam-3991	200	3	(	(	PUNCT
ejpam-3991	200	4	log(−b)−	log(−b)−	PROPN
ejpam-3991	200	5	log(b	log(b	PROPN
ejpam-3991	200	6	)	)	PUNCT
ejpam-3991	200	7	)	)	PUNCT
ejpam-3991	201	1	(	(	PUNCT
ejpam-3991	201	2	log	log	NOUN
ejpam-3991	201	3	(	(	PUNCT
ejpam-3991	201	4	1	1	NUM
ejpam-3991	201	5	ab2	ab2	ADJ
ejpam-3991	201	6	+	+	CCONJ
ejpam-3991	201	7	1	1	NUM
ejpam-3991	201	8	)	)	PUNCT
ejpam-3991	201	9	+	+	X
ejpam-3991	201	10	log(a	log(a	PROPN
ejpam-3991	201	11	)	)	PUNCT
ejpam-3991	201	12	+	+	NUM
ejpam-3991	201	13	log(−b	log(−b	PROPN
ejpam-3991	201	14	)	)	PUNCT
ejpam-3991	202	1	+	+	X
ejpam-3991	202	2	log(b	log(b	PROPN
ejpam-3991	202	3	)	)	PUNCT
ejpam-3991	202	4	)	)	PUNCT
ejpam-3991	203	1	+	+	CCONJ
ejpam-3991	203	2	2π	2π	NUM
ejpam-3991	203	3	cot−1	cot−1	PROPN
ejpam-3991	203	4	(	(	PUNCT
ejpam-3991	203	5	√	√	NUM
ejpam-3991	203	6	ab	ab	NUM
ejpam-3991	203	7	)	)	PUNCT
ejpam-3991	203	8	4a	4a	NOUN
ejpam-3991	203	9	(	(	PUNCT
ejpam-3991	203	10	18	18	NUM
ejpam-3991	203	11	)	)	PUNCT
ejpam-3991	203	12	next	next	ADV
ejpam-3991	203	13	we	we	PRON
ejpam-3991	203	14	split	split	VERB
ejpam-3991	203	15	the	the	DET
ejpam-3991	203	16	left	left	ADJ
ejpam-3991	203	17	-	-	PUNCT
ejpam-3991	203	18	hand	hand	NOUN
ejpam-3991	203	19	side	side	NOUN
ejpam-3991	203	20	to	to	ADP
ejpam-3991	203	21	get∫	get∫	PROPN
ejpam-3991	203	22	∞	∞	PROPN
ejpam-3991	203	23	0	0	NUM
ejpam-3991	204	1	(	(	PUNCT
ejpam-3991	204	2	tanh−1(bx	tanh−1(bx	PROPN
ejpam-3991	204	3	)	)	PUNCT
ejpam-3991	204	4	x	x	SYM
ejpam-3991	205	1	−	−	NOUN
ejpam-3991	205	2	x	x	SYM
ejpam-3991	205	3	tanh−1(bx	tanh−1(bx	NOUN
ejpam-3991	205	4	)	)	PUNCT
ejpam-3991	205	5	a+	a+	PUNCT
ejpam-3991	205	6	x2	x2	PROPN
ejpam-3991	205	7	)	)	PUNCT
ejpam-3991	205	8	dx=	dx=	VERB
ejpam-3991	205	9	1	1	NUM
ejpam-3991	205	10	4	4	NUM
ejpam-3991	205	11	(	(	PUNCT
ejpam-3991	205	12	−(log(−b)−	−(log(−b)−	PROPN
ejpam-3991	205	13	log(b	log(b	PROPN
ejpam-3991	205	14	)	)	PUNCT
ejpam-3991	205	15	)	)	PUNCT
ejpam-3991	206	1	(	(	PUNCT
ejpam-3991	206	2	log	log	NOUN
ejpam-3991	206	3	(	(	PUNCT
ejpam-3991	206	4	1	1	NUM
ejpam-3991	206	5	ab2	ab2	NOUN
ejpam-3991	206	6	+1	+1	NOUN
ejpam-3991	206	7	)	)	PUNCT
ejpam-3991	207	1	+	+	ADJ
ejpam-3991	207	2	log(a	log(a	X
ejpam-3991	207	3	)	)	PUNCT
ejpam-3991	208	1	+	+	NUM
ejpam-3991	208	2	log(−b	log(−b	PROPN
ejpam-3991	208	3	)	)	PUNCT
ejpam-3991	209	1	+	+	CCONJ
ejpam-3991	209	2	log(b	log(b	PROPN
ejpam-3991	209	3	)	)	PUNCT
ejpam-3991	209	4	)	)	PUNCT
ejpam-3991	210	1	−	−	PROPN
ejpam-3991	211	1	2π	2π	PROPN
ejpam-3991	211	2	cot−1	cot−1	PROPN
ejpam-3991	211	3	(	(	PUNCT
ejpam-3991	211	4	√	√	PROPN
ejpam-3991	211	5	ab	ab	PROPN
ejpam-3991	211	6	)	)	PUNCT
ejpam-3991	211	7	)	)	PUNCT
ejpam-3991	212	1	(	(	PUNCT
ejpam-3991	212	2	19	19	NUM
ejpam-3991	212	3	)	)	PUNCT
ejpam-3991	212	4	next	next	ADV
ejpam-3991	212	5	we	we	PRON
ejpam-3991	212	6	take	take	VERB
ejpam-3991	212	7	the	the	DET
ejpam-3991	212	8	first	first	ADJ
ejpam-3991	212	9	partial	partial	ADJ
ejpam-3991	212	10	derivative	derivative	NOUN
ejpam-3991	212	11	with	with	ADP
ejpam-3991	212	12	respect	respect	NOUN
ejpam-3991	212	13	to	to	ADP
ejpam-3991	212	14	a	a	DET
ejpam-3991	212	15	simplifying	simplifying	NOUN
ejpam-3991	212	16	to	to	PART
ejpam-3991	212	17	get	get	VERB
ejpam-3991	212	18	(	(	PUNCT
ejpam-3991	212	19	20	20	NUM
ejpam-3991	212	20	)	)	PUNCT
ejpam-3991	212	21	∫	∫	PROPN
ejpam-3991	213	1	∞	∞	NUM
ejpam-3991	213	2	0	0	NUM
ejpam-3991	213	3	x	x	SYM
ejpam-3991	213	4	tanh−1(bx	tanh−1(bx	PROPN
ejpam-3991	213	5	)	)	PUNCT
ejpam-3991	213	6	(	(	PUNCT
ejpam-3991	213	7	a2	a2	PROPN
ejpam-3991	213	8	+	+	CCONJ
ejpam-3991	213	9	x2)2	x2)2	NUM
ejpam-3991	213	10	dx	dx	PROPN
ejpam-3991	213	11	=	=	SYM
ejpam-3991	213	12	b	b	PROPN
ejpam-3991	213	13	(	(	PUNCT
ejpam-3991	213	14	π√	π√	PROPN
ejpam-3991	213	15	a2	a2	PROPN
ejpam-3991	213	16	−	−	PROPN
ejpam-3991	213	17	b	b	PROPN
ejpam-3991	213	18	log(−b	log(−b	PROPN
ejpam-3991	213	19	)	)	PUNCT
ejpam-3991	214	1	+	+	CCONJ
ejpam-3991	214	2	b	b	X
ejpam-3991	214	3	log(b	log(b	X
ejpam-3991	214	4	)	)	PUNCT
ejpam-3991	214	5	)	)	PUNCT
ejpam-3991	215	1	4a2b2	4a2b2	NUM
ejpam-3991	216	1	+	+	CCONJ
ejpam-3991	216	2	4	4	NUM
ejpam-3991	216	3	next	next	ADV
ejpam-3991	216	4	replacing	replace	VERB
ejpam-3991	216	5	b	b	NUM
ejpam-3991	216	6	by	by	ADP
ejpam-3991	216	7	ib	ib	NOUN
ejpam-3991	216	8	and	and	CCONJ
ejpam-3991	216	9	simplifying	simplify	VERB
ejpam-3991	216	10	we	we	PRON
ejpam-3991	216	11	get	get	VERB
ejpam-3991	216	12	(	(	PUNCT
ejpam-3991	216	13	21	21	NUM
ejpam-3991	216	14	)	)	PUNCT
ejpam-3991	216	15	∫	∫	PROPN
ejpam-3991	216	16	∞	∞	NOUN
ejpam-3991	216	17	0	0	NUM
ejpam-3991	217	1	x	x	SYM
ejpam-3991	217	2	tan−1(bx	tan−1(bx	PROPN
ejpam-3991	217	3	)	)	PUNCT
ejpam-3991	217	4	(	(	PUNCT
ejpam-3991	217	5	a2	a2	PROPN
ejpam-3991	217	6	+	+	CCONJ
ejpam-3991	217	7	x2)2	x2)2	NUM
ejpam-3991	217	8	dx	dx	PROPN
ejpam-3991	218	1	=	=	PRON
ejpam-3991	218	2	πb	πb	VERB
ejpam-3991	218	3	4a(ab+	4a(ab+	NUM
ejpam-3991	218	4	1	1	NUM
ejpam-3991	218	5	)	)	PUNCT
ejpam-3991	218	6	r.	r.	PROPN
ejpam-3991	218	7	reynolds	reynolds	PROPN
ejpam-3991	218	8	,	,	PUNCT
ejpam-3991	218	9	a.	a.	PROPN
ejpam-3991	218	10	stauffer	stauffer	PROPN
ejpam-3991	218	11	/	/	SYM
ejpam-3991	218	12	eur	eur	PROPN
ejpam-3991	218	13	.	.	PUNCT
ejpam-3991	219	1	j.	j.	PROPN
ejpam-3991	219	2	pure	pure	PROPN
ejpam-3991	219	3	appl	appl	PROPN
ejpam-3991	219	4	.	.	PROPN
ejpam-3991	219	5	math	math	PROPN
ejpam-3991	219	6	,	,	PUNCT
ejpam-3991	219	7	14	14	NUM
ejpam-3991	219	8	(	(	PUNCT
ejpam-3991	219	9	3	3	NUM
ejpam-3991	219	10	)	)	PUNCT
ejpam-3991	219	11	(	(	PUNCT
ejpam-3991	219	12	2021	2021	NUM
ejpam-3991	219	13	)	)	PUNCT
ejpam-3991	219	14	,	,	PUNCT
ejpam-3991	219	15	723	723	NUM
ejpam-3991	219	16	-	-	SYM
ejpam-3991	219	17	736	736	NUM
ejpam-3991	219	18	731	731	NUM
ejpam-3991	219	19	13	13	NUM
ejpam-3991	219	20	.	.	PUNCT
ejpam-3991	220	1	derivation	derivation	NOUN
ejpam-3991	220	2	of	of	ADP
ejpam-3991	220	3	entry	entry	NOUN
ejpam-3991	220	4	4.295.1	4.295.1	NUM
ejpam-3991	220	5	in	in	ADP
ejpam-3991	220	6	[	[	X
ejpam-3991	220	7	3	3	NUM
ejpam-3991	220	8	]	]	PUNCT
ejpam-3991	220	9	using	use	VERB
ejpam-3991	220	10	(	(	PUNCT
ejpam-3991	220	11	12	12	NUM
ejpam-3991	220	12	)	)	PUNCT
ejpam-3991	220	13	and	and	CCONJ
ejpam-3991	220	14	setting	set	VERB
ejpam-3991	220	15	k	k	X
ejpam-3991	220	16	=	=	PUNCT
ejpam-3991	220	17	c	c	NOUN
ejpam-3991	220	18	=	=	SYM
ejpam-3991	220	19	1	1	NUM
ejpam-3991	220	20	and	and	CCONJ
ejpam-3991	220	21	simplifying	simplify	VERB
ejpam-3991	220	22	we	we	PRON
ejpam-3991	220	23	get∫	get∫	PROPN
ejpam-3991	220	24	∞	∞	PROPN
ejpam-3991	220	25	0	0	NUM
ejpam-3991	220	26	log	log	NOUN
ejpam-3991	220	27	(	(	PUNCT
ejpam-3991	220	28	1−	1−	NUM
ejpam-3991	220	29	b2x2	b2x2	NOUN
ejpam-3991	220	30	)	)	PUNCT
ejpam-3991	220	31	a+	a+	PUNCT
ejpam-3991	221	1	x2	x2	PROPN
ejpam-3991	221	2	dx	dx	PROPN
ejpam-3991	221	3	=	=	SYM
ejpam-3991	221	4	1	1	NUM
ejpam-3991	221	5	2π	2π	NOUN
ejpam-3991	221	6	(	(	PUNCT
ejpam-3991	221	7	log	log	NOUN
ejpam-3991	221	8	(	(	PUNCT
ejpam-3991	221	9	1	1	NUM
ejpam-3991	221	10	ab2	ab2	ADJ
ejpam-3991	221	11	+	+	CCONJ
ejpam-3991	221	12	1	1	NUM
ejpam-3991	221	13	)	)	PUNCT
ejpam-3991	221	14	+	+	X
ejpam-3991	221	15	log(a	log(a	PROPN
ejpam-3991	221	16	)	)	PUNCT
ejpam-3991	221	17	+	+	NUM
ejpam-3991	221	18	log(−b	log(−b	PROPN
ejpam-3991	221	19	)	)	PUNCT
ejpam-3991	222	1	+	+	X
ejpam-3991	222	2	log(b	log(b	PROPN
ejpam-3991	222	3	)	)	PUNCT
ejpam-3991	222	4	)	)	PUNCT
ejpam-3991	223	1	+	+	CCONJ
ejpam-3991	223	2	(	(	PUNCT
ejpam-3991	223	3	log(b)−	log(b)−	NOUN
ejpam-3991	223	4	log(−b	log(−b	PROPN
ejpam-3991	223	5	)	)	PUNCT
ejpam-3991	223	6	)	)	PUNCT
ejpam-3991	224	1	cot−1	cot−1	PROPN
ejpam-3991	224	2	(	(	PUNCT
ejpam-3991	224	3	√	√	NUM
ejpam-3991	224	4	ab	ab	NUM
ejpam-3991	224	5	)	)	PUNCT
ejpam-3991	224	6	√	√	ADP
ejpam-3991	224	7	a	a	DET
ejpam-3991	224	8	(	(	PUNCT
ejpam-3991	224	9	22	22	NUM
ejpam-3991	224	10	)	)	PUNCT
ejpam-3991	224	11	next	next	ADV
ejpam-3991	224	12	we	we	PRON
ejpam-3991	224	13	replace	replace	VERB
ejpam-3991	224	14	b	b	NOUN
ejpam-3991	224	15	by	by	ADP
ejpam-3991	224	16	i	i	PRON
ejpam-3991	224	17	√	√	ADP
ejpam-3991	224	18	µ√	µ√	VERB
ejpam-3991	224	19	β	β	X
ejpam-3991	224	20	and	and	CCONJ
ejpam-3991	224	21	a	a	PRON
ejpam-3991	224	22	by	by	ADP
ejpam-3991	224	23	γ	γ	NOUN
ejpam-3991	224	24	simplifying	simplify	VERB
ejpam-3991	224	25	to	to	PART
ejpam-3991	224	26	get	get	VERB
ejpam-3991	224	27	(	(	PUNCT
ejpam-3991	224	28	23	23	NUM
ejpam-3991	224	29	)	)	PUNCT
ejpam-3991	224	30	∫	∫	PROPN
ejpam-3991	225	1	∞	∞	PROPN
ejpam-3991	225	2	0	0	NUM
ejpam-3991	225	3	log	log	NOUN
ejpam-3991	225	4	(	(	PUNCT
ejpam-3991	225	5	β	β	X
ejpam-3991	225	6	+	+	X
ejpam-3991	225	7	µx2	µx2	PROPN
ejpam-3991	225	8	)	)	PUNCT
ejpam-3991	225	9	γ	γ	PROPN
ejpam-3991	226	1	+	+	PROPN
ejpam-3991	226	2	x2	x2	PROPN
ejpam-3991	226	3	dx	dx	PROPN
ejpam-3991	226	4	=	=	PROPN
ejpam-3991	227	1	π	π	X
ejpam-3991	227	2	log	log	VERB
ejpam-3991	227	3	(	(	PUNCT
ejpam-3991	227	4	√	√	NUM
ejpam-3991	227	5	β	β	NOUN
ejpam-3991	227	6	+	+	CCONJ
ejpam-3991	227	7	√	√	ADP
ejpam-3991	227	8	γ	γ	PROPN
ejpam-3991	227	9	√	√	PROPN
ejpam-3991	227	10	µ	µ	X
ejpam-3991	227	11	)	)	PUNCT
ejpam-3991	227	12	√	√	ADP
ejpam-3991	227	13	γ	γ	NOUN
ejpam-3991	227	14	the	the	DET
ejpam-3991	227	15	equation	equation	NOUN
ejpam-3991	227	16	quoted	quote	VERB
ejpam-3991	227	17	in	in	ADP
ejpam-3991	227	18	[	[	X
ejpam-3991	227	19	3	3	NUM
ejpam-3991	227	20	]	]	PUNCT
ejpam-3991	227	21	is	be	AUX
ejpam-3991	227	22	not	not	PART
ejpam-3991	227	23	valid	valid	ADJ
ejpam-3991	227	24	for	for	ADP
ejpam-3991	227	25	general	general	ADJ
ejpam-3991	227	26	complex	complex	ADJ
ejpam-3991	227	27	numbers	number	NOUN
ejpam-3991	227	28	,	,	PUNCT
ejpam-3991	227	29	for	for	ADP
ejpam-3991	227	30	example	example	NOUN
ejpam-3991	227	31	when	when	SCONJ
ejpam-3991	227	32	re(γ	re(γ	NOUN
ejpam-3991	227	33	)	)	PUNCT
ejpam-3991	227	34	<	<	X
ejpam-3991	227	35	0	0	NUM
ejpam-3991	227	36	.	.	PROPN
ejpam-3991	227	37	14	14	NUM
ejpam-3991	227	38	.	.	PUNCT
ejpam-3991	228	1	derivation	derivation	NOUN
ejpam-3991	228	2	of	of	ADP
ejpam-3991	228	3	entry	entry	NOUN
ejpam-3991	228	4	4.295.7	4.295.7	NUM
ejpam-3991	228	5	in	in	ADP
ejpam-3991	228	6	[	[	X
ejpam-3991	228	7	3	3	NUM
ejpam-3991	228	8	]	]	PUNCT
ejpam-3991	228	9	using	use	VERB
ejpam-3991	228	10	(	(	PUNCT
ejpam-3991	228	11	23	23	NUM
ejpam-3991	228	12	)	)	PUNCT
ejpam-3991	228	13	and	and	CCONJ
ejpam-3991	228	14	replacing	replace	VERB
ejpam-3991	228	15	β	β	PRON
ejpam-3991	228	16	by	by	ADP
ejpam-3991	228	17	a2	a2	PROPN
ejpam-3991	228	18	,	,	PUNCT
ejpam-3991	228	19	µ	µ	NOUN
ejpam-3991	228	20	by	by	ADP
ejpam-3991	228	21	b2	b2	NOUN
ejpam-3991	228	22	and	and	CCONJ
ejpam-3991	228	23	γ	γ	X
ejpam-3991	228	24	by	by	X
ejpam-3991	228	25	(	(	PUNCT
ejpam-3991	228	26	c	c	NOUN
ejpam-3991	228	27	g	g	NOUN
ejpam-3991	228	28	)	)	PUNCT
ejpam-3991	228	29	2	2	NUM
ejpam-3991	228	30	and	and	CCONJ
ejpam-3991	228	31	simplifying	simplify	VERB
ejpam-3991	228	32	we	we	PRON
ejpam-3991	228	33	get	get	VERB
ejpam-3991	228	34	(	(	PUNCT
ejpam-3991	228	35	24	24	NUM
ejpam-3991	228	36	)	)	PUNCT
ejpam-3991	228	37	∫	∫	PROPN
ejpam-3991	229	1	∞	∞	PROPN
ejpam-3991	229	2	0	0	NUM
ejpam-3991	229	3	log	log	NOUN
ejpam-3991	229	4	(	(	PUNCT
ejpam-3991	229	5	a2	a2	PROPN
ejpam-3991	229	6	+	+	CCONJ
ejpam-3991	229	7	b2x2	b2x2	NOUN
ejpam-3991	229	8	)	)	PUNCT
ejpam-3991	229	9	c2	c2	PROPN
ejpam-3991	229	10	+	+	CCONJ
ejpam-3991	229	11	g2x2	g2x2	PROPN
ejpam-3991	229	12	dx	dx	PROPN
ejpam-3991	229	13	=	=	PROPN
ejpam-3991	230	1	π	π	X
ejpam-3991	230	2	log	log	NOUN
ejpam-3991	230	3	(	(	PUNCT
ejpam-3991	230	4	ag+bc	ag+bc	NOUN
ejpam-3991	230	5	g	g	NOUN
ejpam-3991	230	6	)	)	PUNCT
ejpam-3991	230	7	cg	cg	NOUN
ejpam-3991	230	8	15	15	NUM
ejpam-3991	230	9	.	.	PUNCT
ejpam-3991	230	10	derivation	derivation	NOUN
ejpam-3991	230	11	of	of	ADP
ejpam-3991	230	12	entry	entry	NOUN
ejpam-3991	230	13	4.295.8	4.295.8	NUM
ejpam-3991	230	14	in	in	ADP
ejpam-3991	230	15	[	[	X
ejpam-3991	230	16	3	3	NUM
ejpam-3991	230	17	]	]	PUNCT
ejpam-3991	230	18	using	use	VERB
ejpam-3991	230	19	(	(	PUNCT
ejpam-3991	230	20	24	24	NUM
ejpam-3991	230	21	)	)	PUNCT
ejpam-3991	230	22	and	and	CCONJ
ejpam-3991	230	23	replacing	replace	VERB
ejpam-3991	230	24	g	g	NOUN
ejpam-3991	230	25	by	by	ADP
ejpam-3991	230	26	ig	ig	PROPN
ejpam-3991	230	27	and	and	CCONJ
ejpam-3991	230	28	simplifying	simplify	VERB
ejpam-3991	230	29	we	we	PRON
ejpam-3991	230	30	get	get	VERB
ejpam-3991	230	31	(	(	PUNCT
ejpam-3991	230	32	25	25	NUM
ejpam-3991	230	33	)	)	PUNCT
ejpam-3991	230	34	∫	∫	PROPN
ejpam-3991	231	1	∞	∞	PROPN
ejpam-3991	231	2	0	0	NUM
ejpam-3991	231	3	log	log	NOUN
ejpam-3991	231	4	(	(	PUNCT
ejpam-3991	231	5	a2	a2	PROPN
ejpam-3991	231	6	+	+	CCONJ
ejpam-3991	231	7	b2x2	b2x2	NOUN
ejpam-3991	231	8	)	)	PUNCT
ejpam-3991	231	9	c2	c2	PROPN
ejpam-3991	231	10	−	−	PROPN
ejpam-3991	232	1	g2x2	g2x2	VERB
ejpam-3991	232	2	dx	dx	PROPN
ejpam-3991	233	1	=	=	PUNCT
ejpam-3991	233	2	−	−	PROPN
ejpam-3991	234	1	iπ	iπ	PRON
ejpam-3991	234	2	log	log	NOUN
ejpam-3991	234	3	(	(	PUNCT
ejpam-3991	234	4	−	−	PROPN
ejpam-3991	234	5	i(bc+iag	i(bc+iag	ADJ
ejpam-3991	234	6	)	)	PUNCT
ejpam-3991	234	7	g	g	NOUN
ejpam-3991	234	8	)	)	PUNCT
ejpam-3991	234	9	cg	cg	NOUN
ejpam-3991	234	10	16	16	NUM
ejpam-3991	234	11	.	.	PUNCT
ejpam-3991	235	1	derivation	derivation	NOUN
ejpam-3991	235	2	of	of	ADP
ejpam-3991	235	3	entry	entry	NOUN
ejpam-3991	235	4	4.295.9	4.295.9	NUM
ejpam-3991	235	5	in	in	ADP
ejpam-3991	235	6	[	[	X
ejpam-3991	235	7	3	3	X
ejpam-3991	235	8	]	]	PUNCT
ejpam-3991	235	9	we	we	PRON
ejpam-3991	235	10	will	will	AUX
ejpam-3991	235	11	form	form	VERB
ejpam-3991	235	12	two	two	NUM
ejpam-3991	235	13	equations	equation	NOUN
ejpam-3991	235	14	by	by	ADP
ejpam-3991	235	15	using	use	VERB
ejpam-3991	235	16	(	(	PUNCT
ejpam-3991	235	17	24	24	NUM
ejpam-3991	235	18	)	)	PUNCT
ejpam-3991	235	19	and	and	CCONJ
ejpam-3991	235	20	setting	set	VERB
ejpam-3991	235	21	β	β	NOUN
ejpam-3991	235	22	=	=	SYM
ejpam-3991	235	23	1	1	NUM
ejpam-3991	235	24	and	and	CCONJ
ejpam-3991	235	25	replacing	replace	VERB
ejpam-3991	235	26	µ	µ	NOUN
ejpam-3991	235	27	by	by	ADP
ejpam-3991	235	28	p2	p2	PROPN
ejpam-3991	235	29	for	for	ADP
ejpam-3991	235	30	the	the	DET
ejpam-3991	235	31	first	first	ADJ
ejpam-3991	235	32	equation	equation	NOUN
ejpam-3991	235	33	and	and	CCONJ
ejpam-3991	235	34	then	then	ADV
ejpam-3991	235	35	replacing	replace	VERB
ejpam-3991	235	36	p	p	NOUN
ejpam-3991	235	37	by	by	ADP
ejpam-3991	235	38	q	q	NOUN
ejpam-3991	235	39	for	for	ADP
ejpam-3991	235	40	the	the	DET
ejpam-3991	235	41	second	second	ADJ
ejpam-3991	235	42	,	,	PUNCT
ejpam-3991	235	43	subtracting	subtract	VERB
ejpam-3991	235	44	and	and	CCONJ
ejpam-3991	235	45	simplifying	simplify	VERB
ejpam-3991	235	46	we	we	PRON
ejpam-3991	235	47	get	get	VERB
ejpam-3991	235	48	(	(	PUNCT
ejpam-3991	235	49	26	26	NUM
ejpam-3991	235	50	)	)	PUNCT
ejpam-3991	235	51	∫	∫	PROPN
ejpam-3991	236	1	∞	∞	PROPN
ejpam-3991	236	2	0	0	NUM
ejpam-3991	236	3	log	log	NOUN
ejpam-3991	236	4	(	(	PUNCT
ejpam-3991	236	5	p2x2	p2x2	X
ejpam-3991	236	6	+	+	CCONJ
ejpam-3991	236	7	1	1	NUM
ejpam-3991	236	8	)	)	PUNCT
ejpam-3991	236	9	−	−	NOUN
ejpam-3991	237	1	log	log	NOUN
ejpam-3991	237	2	(	(	PUNCT
ejpam-3991	237	3	q2x2	q2x2	X
ejpam-3991	237	4	+	+	CCONJ
ejpam-3991	237	5	1	1	X
ejpam-3991	237	6	)	)	PUNCT
ejpam-3991	237	7	γ	γ	PROPN
ejpam-3991	237	8	+	+	PROPN
ejpam-3991	237	9	x2	x2	PROPN
ejpam-3991	237	10	dx	dx	PROPN
ejpam-3991	238	1	=	=	PROPN
ejpam-3991	238	2	π	π	X
ejpam-3991	238	3	log	log	NOUN
ejpam-3991	238	4	(	(	PUNCT
ejpam-3991	238	5	√	√	NUM
ejpam-3991	238	6	γp+1√	γp+1√	NOUN
ejpam-3991	238	7	γq+1	γq+1	NUM
ejpam-3991	238	8	)	)	PUNCT
ejpam-3991	238	9	√	√	ADP
ejpam-3991	238	10	γ	γ	PROPN
ejpam-3991	238	11	next	next	ADV
ejpam-3991	238	12	we	we	PRON
ejpam-3991	238	13	apply	apply	VERB
ejpam-3991	238	14	l’hopital	l’hopital	PROPN
ejpam-3991	238	15	’s	’s	PART
ejpam-3991	238	16	rule	rule	NOUN
ejpam-3991	238	17	as	as	ADP
ejpam-3991	238	18	γ	γ	X
ejpam-3991	238	19	→	→	SYM
ejpam-3991	238	20	0	0	NUM
ejpam-3991	238	21	to	to	ADP
ejpam-3991	238	22	the	the	DET
ejpam-3991	238	23	right	right	ADJ
ejpam-3991	238	24	-	-	PUNCT
ejpam-3991	238	25	hand	hand	NOUN
ejpam-3991	238	26	side	side	NOUN
ejpam-3991	238	27	simplifying	simplify	VERB
ejpam-3991	238	28	to	to	PART
ejpam-3991	238	29	get	get	VERB
ejpam-3991	238	30	(	(	PUNCT
ejpam-3991	238	31	27	27	NUM
ejpam-3991	238	32	)	)	PUNCT
ejpam-3991	238	33	∫	∫	PROPN
ejpam-3991	239	1	∞	∞	PROPN
ejpam-3991	239	2	0	0	NUM
ejpam-3991	239	3	log	log	NOUN
ejpam-3991	239	4	(	(	PUNCT
ejpam-3991	239	5	p2x2	p2x2	X
ejpam-3991	239	6	+	+	CCONJ
ejpam-3991	239	7	1	1	NUM
ejpam-3991	239	8	)	)	PUNCT
ejpam-3991	239	9	−	−	NOUN
ejpam-3991	240	1	log	log	NOUN
ejpam-3991	240	2	(	(	PUNCT
ejpam-3991	240	3	q2x2	q2x2	X
ejpam-3991	240	4	+	+	CCONJ
ejpam-3991	240	5	1	1	X
ejpam-3991	240	6	)	)	PUNCT
ejpam-3991	241	1	x2	x2	PRON
ejpam-3991	241	2	dx	dx	NOUN
ejpam-3991	242	1	=	=	PUNCT
ejpam-3991	242	2	π(p−	π(p−	VERB
ejpam-3991	242	3	q	q	NOUN
ejpam-3991	242	4	)	)	PUNCT
ejpam-3991	242	5	r.	r.	PROPN
ejpam-3991	242	6	reynolds	reynolds	PROPN
ejpam-3991	242	7	,	,	PUNCT
ejpam-3991	242	8	a.	a.	PROPN
ejpam-3991	242	9	stauffer	stauffer	PROPN
ejpam-3991	242	10	/	/	SYM
ejpam-3991	242	11	eur	eur	PROPN
ejpam-3991	242	12	.	.	PUNCT
ejpam-3991	243	1	j.	j.	PROPN
ejpam-3991	243	2	pure	pure	PROPN
ejpam-3991	243	3	appl	appl	PROPN
ejpam-3991	243	4	.	.	PROPN
ejpam-3991	243	5	math	math	PROPN
ejpam-3991	243	6	,	,	PUNCT
ejpam-3991	243	7	14	14	NUM
ejpam-3991	243	8	(	(	PUNCT
ejpam-3991	243	9	3	3	NUM
ejpam-3991	243	10	)	)	PUNCT
ejpam-3991	243	11	(	(	PUNCT
ejpam-3991	243	12	2021	2021	NUM
ejpam-3991	243	13	)	)	PUNCT
ejpam-3991	243	14	,	,	PUNCT
ejpam-3991	243	15	723	723	NUM
ejpam-3991	243	16	-	-	SYM
ejpam-3991	243	17	736	736	NUM
ejpam-3991	243	18	732	732	NUM
ejpam-3991	243	19	17	17	NUM
ejpam-3991	243	20	.	.	PUNCT
ejpam-3991	244	1	derivation	derivation	NOUN
ejpam-3991	244	2	of	of	ADP
ejpam-3991	244	3	entry	entry	NOUN
ejpam-3991	244	4	4.295.22	4.295.22	NUM
ejpam-3991	244	5	in	in	ADP
ejpam-3991	244	6	[	[	X
ejpam-3991	244	7	3	3	NUM
ejpam-3991	244	8	]	]	PUNCT
ejpam-3991	244	9	using	use	VERB
ejpam-3991	244	10	(	(	PUNCT
ejpam-3991	244	11	24	24	NUM
ejpam-3991	244	12	)	)	PUNCT
ejpam-3991	244	13	setting	set	VERB
ejpam-3991	244	14	a	a	DET
ejpam-3991	244	15	=	=	SYM
ejpam-3991	244	16	1	1	NUM
ejpam-3991	244	17	and	and	CCONJ
ejpam-3991	244	18	replacing	replace	VERB
ejpam-3991	244	19	c	c	NOUN
ejpam-3991	244	20	by	by	ADP
ejpam-3991	244	21	r	r	NOUN
ejpam-3991	244	22	,	,	PUNCT
ejpam-3991	244	23	g	g	NOUN
ejpam-3991	244	24	by	by	ADP
ejpam-3991	244	25	q	q	PROPN
ejpam-3991	244	26	,	,	PUNCT
ejpam-3991	244	27	b	b	NOUN
ejpam-3991	244	28	by	by	ADP
ejpam-3991	244	29	p	p	NOUN
ejpam-3991	244	30	and	and	CCONJ
ejpam-3991	244	31	simplifying	simplify	VERB
ejpam-3991	244	32	we	we	PRON
ejpam-3991	244	33	get	get	VERB
ejpam-3991	244	34	(	(	PUNCT
ejpam-3991	244	35	28	28	NUM
ejpam-3991	244	36	)	)	PUNCT
ejpam-3991	244	37	∫	∫	PROPN
ejpam-3991	245	1	∞	∞	PROPN
ejpam-3991	245	2	0	0	NUM
ejpam-3991	245	3	log	log	NOUN
ejpam-3991	245	4	(	(	PUNCT
ejpam-3991	245	5	p2x2	p2x2	X
ejpam-3991	245	6	+	+	CCONJ
ejpam-3991	245	7	1	1	NUM
ejpam-3991	245	8	)	)	PUNCT
ejpam-3991	246	1	q2x2	q2x2	NOUN
ejpam-3991	247	1	+	+	NUM
ejpam-3991	247	2	r2	r2	PROPN
ejpam-3991	247	3	dx	dx	PROPN
ejpam-3991	248	1	=	=	PUNCT
ejpam-3991	249	1	π	π	X
ejpam-3991	249	2	log	log	VERB
ejpam-3991	249	3	(	(	PUNCT
ejpam-3991	249	4	pr+q	pr+q	PROPN
ejpam-3991	249	5	q	q	NOUN
ejpam-3991	249	6	)	)	PUNCT
ejpam-3991	249	7	qr	qr	NOUN
ejpam-3991	249	8	18	18	NUM
ejpam-3991	249	9	.	.	PUNCT
ejpam-3991	249	10	derivation	derivation	NOUN
ejpam-3991	249	11	of	of	ADP
ejpam-3991	249	12	entry	entry	NOUN
ejpam-3991	249	13	4.295.25	4.295.25	NUM
ejpam-3991	249	14	in	in	ADP
ejpam-3991	249	15	[	[	X
ejpam-3991	249	16	3	3	NUM
ejpam-3991	249	17	]	]	PUNCT
ejpam-3991	249	18	using	use	VERB
ejpam-3991	249	19	(	(	PUNCT
ejpam-3991	249	20	24	24	NUM
ejpam-3991	249	21	)	)	PUNCT
ejpam-3991	249	22	and	and	CCONJ
ejpam-3991	249	23	taking	take	VERB
ejpam-3991	249	24	the	the	DET
ejpam-3991	249	25	first	first	ADJ
ejpam-3991	249	26	partial	partial	ADJ
ejpam-3991	249	27	derivative	derivative	NOUN
ejpam-3991	249	28	with	with	ADP
ejpam-3991	249	29	respect	respect	NOUN
ejpam-3991	249	30	to	to	ADP
ejpam-3991	249	31	c	c	NOUN
ejpam-3991	249	32	and	and	CCONJ
ejpam-3991	249	33	simplifying	simplify	VERB
ejpam-3991	249	34	we	we	PRON
ejpam-3991	249	35	get	get	VERB
ejpam-3991	249	36	(	(	PUNCT
ejpam-3991	249	37	29	29	NUM
ejpam-3991	249	38	)	)	PUNCT
ejpam-3991	249	39	∫	∫	PROPN
ejpam-3991	250	1	∞	∞	PROPN
ejpam-3991	250	2	0	0	NUM
ejpam-3991	250	3	log	log	NOUN
ejpam-3991	250	4	(	(	PUNCT
ejpam-3991	250	5	a2	a2	PROPN
ejpam-3991	250	6	+	+	CCONJ
ejpam-3991	250	7	b2x2	b2x2	INTJ
ejpam-3991	250	8	)	)	PUNCT
ejpam-3991	250	9	(	(	PUNCT
ejpam-3991	250	10	c2	c2	PROPN
ejpam-3991	250	11	+	+	NUM
ejpam-3991	250	12	g2x2)2	g2x2)2	NOUN
ejpam-3991	250	13	dx	dx	PROPN
ejpam-3991	250	14	=	=	PROPN
ejpam-3991	251	1	π	π	X
ejpam-3991	251	2	log	log	NOUN
ejpam-3991	251	3	(	(	PUNCT
ejpam-3991	251	4	ag+bc	ag+bc	NOUN
ejpam-3991	251	5	g	g	NOUN
ejpam-3991	251	6	)	)	PUNCT
ejpam-3991	251	7	2c3	2c3	NUM
ejpam-3991	251	8	g	g	NOUN
ejpam-3991	251	9	−	−	NOUN
ejpam-3991	251	10	πb	πb	PRON
ejpam-3991	251	11	2c2g(ag	2c2g(ag	NUM
ejpam-3991	251	12	+	+	CCONJ
ejpam-3991	251	13	bc	bc	PROPN
ejpam-3991	251	14	)	)	PUNCT
ejpam-3991	251	15	19	19	NUM
ejpam-3991	251	16	.	.	PUNCT
ejpam-3991	251	17	derivation	derivation	NOUN
ejpam-3991	251	18	of	of	ADP
ejpam-3991	251	19	entry	entry	NOUN
ejpam-3991	251	20	4.295.26	4.295.26	NUM
ejpam-3991	251	21	in	in	ADP
ejpam-3991	251	22	[	[	X
ejpam-3991	251	23	3	3	X
ejpam-3991	251	24	]	]	PUNCT
ejpam-3991	251	25	using	use	VERB
ejpam-3991	251	26	(	(	PUNCT
ejpam-3991	251	27	24	24	NUM
ejpam-3991	251	28	)	)	PUNCT
ejpam-3991	251	29	and	and	CCONJ
ejpam-3991	251	30	taking	take	VERB
ejpam-3991	251	31	the	the	DET
ejpam-3991	251	32	first	first	ADJ
ejpam-3991	251	33	partial	partial	ADJ
ejpam-3991	251	34	derivative	derivative	NOUN
ejpam-3991	251	35	with	with	ADP
ejpam-3991	251	36	respect	respect	NOUN
ejpam-3991	251	37	to	to	ADP
ejpam-3991	251	38	g	g	NOUN
ejpam-3991	251	39	and	and	CCONJ
ejpam-3991	251	40	simplifying	simplify	VERB
ejpam-3991	251	41	we	we	PRON
ejpam-3991	251	42	get	get	VERB
ejpam-3991	251	43	(	(	PUNCT
ejpam-3991	251	44	30	30	NUM
ejpam-3991	251	45	)	)	PUNCT
ejpam-3991	251	46	∫	∫	PROPN
ejpam-3991	252	1	∞	∞	NOUN
ejpam-3991	252	2	0	0	NUM
ejpam-3991	253	1	x2	x2	PRON
ejpam-3991	253	2	log	log	NOUN
ejpam-3991	253	3	(	(	PUNCT
ejpam-3991	253	4	a2	a2	PROPN
ejpam-3991	253	5	+	+	CCONJ
ejpam-3991	253	6	b2x2	b2x2	INTJ
ejpam-3991	253	7	)	)	PUNCT
ejpam-3991	253	8	(	(	PUNCT
ejpam-3991	253	9	c2	c2	PROPN
ejpam-3991	253	10	+	+	NUM
ejpam-3991	253	11	g2x2)2	g2x2)2	NOUN
ejpam-3991	253	12	dx	dx	PROPN
ejpam-3991	253	13	=	=	PUNCT
ejpam-3991	253	14	πb	πb	NUM
ejpam-3991	253	15	2g3(ag	2g3(ag	NUM
ejpam-3991	253	16	+	+	CCONJ
ejpam-3991	253	17	bc	bc	PROPN
ejpam-3991	253	18	)	)	PUNCT
ejpam-3991	253	19	+	+	CCONJ
ejpam-3991	253	20	π	π	PROPN
ejpam-3991	253	21	log	log	NOUN
ejpam-3991	253	22	(	(	PUNCT
ejpam-3991	253	23	ag+bc	ag+bc	NOUN
ejpam-3991	253	24	g	g	NOUN
ejpam-3991	253	25	)	)	PUNCT
ejpam-3991	253	26	2cg3	2cg3	NUM
ejpam-3991	253	27	20	20	NUM
ejpam-3991	253	28	.	.	PUNCT
ejpam-3991	254	1	definite	definite	ADJ
ejpam-3991	254	2	logarithmic	logarithmic	ADJ
ejpam-3991	254	3	integral	integral	ADJ
ejpam-3991	254	4	in	in	ADP
ejpam-3991	254	5	terms	term	NOUN
ejpam-3991	254	6	π	π	PROPN
ejpam-3991	254	7	using	use	VERB
ejpam-3991	254	8	(	(	PUNCT
ejpam-3991	254	9	12	12	NUM
ejpam-3991	254	10	)	)	PUNCT
ejpam-3991	254	11	and	and	CCONJ
ejpam-3991	254	12	setting	set	VERB
ejpam-3991	254	13	c	c	NOUN
ejpam-3991	254	14	=	=	SYM
ejpam-3991	254	15	1	1	NUM
ejpam-3991	254	16	,	,	PUNCT
ejpam-3991	254	17	b	b	X
ejpam-3991	254	18	=	=	SYM
ejpam-3991	254	19	1	1	NUM
ejpam-3991	254	20	and	and	CCONJ
ejpam-3991	254	21	a	a	DET
ejpam-3991	254	22	=	=	NOUN
ejpam-3991	254	23	1	1	NUM
ejpam-3991	254	24	simplifying	simplify	VERB
ejpam-3991	254	25	we	we	PRON
ejpam-3991	254	26	get	get	VERB
ejpam-3991	254	27	(	(	PUNCT
ejpam-3991	254	28	31	31	NUM
ejpam-3991	254	29	)	)	PUNCT
ejpam-3991	254	30	∫	∫	PROPN
ejpam-3991	255	1	∞	∞	NOUN
ejpam-3991	255	2	0	0	NUM
ejpam-3991	255	3	logk(1−	logk(1−	PROPN
ejpam-3991	255	4	x	x	X
ejpam-3991	255	5	)	)	PUNCT
ejpam-3991	255	6	+	+	CCONJ
ejpam-3991	255	7	logk(x+	logk(x+	NUM
ejpam-3991	255	8	1	1	NUM
ejpam-3991	255	9	)	)	PUNCT
ejpam-3991	255	10	x2	x2	NOUN
ejpam-3991	256	1	+	+	CCONJ
ejpam-3991	256	2	1	1	NUM
ejpam-3991	256	3	dx	dx	NOUN
ejpam-3991	256	4	=	=	SYM
ejpam-3991	256	5	(	(	PUNCT
ejpam-3991	256	6	2i)kπk+1	2i)kπk+1	NUM
ejpam-3991	256	7	(	(	PUNCT
ejpam-3991	256	8	ζ	ζ	NOUN
ejpam-3991	256	9	(	(	PUNCT
ejpam-3991	256	10	−k,−	−k,−	PROPN
ejpam-3991	256	11	−7π	−7π	PROPN
ejpam-3991	256	12	2	2	NUM
ejpam-3991	257	1	+	+	CCONJ
ejpam-3991	257	2	i	i	PRON
ejpam-3991	257	3	log(2	log(2	NOUN
ejpam-3991	257	4	)	)	PUNCT
ejpam-3991	257	5	4π	4π	NUM
ejpam-3991	257	6	)	)	PUNCT
ejpam-3991	258	1	−	−	PROPN
ejpam-3991	258	2	ζ	ζ	NOUN
ejpam-3991	258	3	(	(	PUNCT
ejpam-3991	258	4	−k	−k	ADJ
ejpam-3991	258	5	,	,	PUNCT
ejpam-3991	258	6	9π	9π	NUM
ejpam-3991	258	7	2	2	NUM
ejpam-3991	258	8	−	−	NOUN
ejpam-3991	258	9	i	i	PRON
ejpam-3991	258	10	log(2	log(2	VERB
ejpam-3991	258	11	)	)	PUNCT
ejpam-3991	258	12	4π	4π	NUM
ejpam-3991	258	13	)	)	PUNCT
ejpam-3991	258	14	)	)	PUNCT
ejpam-3991	259	1	+	+	CCONJ
ejpam-3991	259	2	(	(	PUNCT
ejpam-3991	259	3	2i)kπk+1	2i)kπk+1	NUM
ejpam-3991	259	4	(	(	PUNCT
ejpam-3991	259	5	ζ	ζ	NOUN
ejpam-3991	259	6	(	(	PUNCT
ejpam-3991	259	7	−k,−	−k,−	NOUN
ejpam-3991	259	8	−π	−π	ADP
ejpam-3991	259	9	2	2	NUM
ejpam-3991	260	1	+	+	CCONJ
ejpam-3991	260	2	i	i	PRON
ejpam-3991	260	3	log(2	log(2	NOUN
ejpam-3991	260	4	)	)	PUNCT
ejpam-3991	260	5	4π	4π	NUM
ejpam-3991	260	6	)	)	PUNCT
ejpam-3991	261	1	−	−	PROPN
ejpam-3991	261	2	ζ	ζ	NOUN
ejpam-3991	261	3	(	(	PUNCT
ejpam-3991	261	4	−k	−k	PROPN
ejpam-3991	261	5	,	,	PUNCT
ejpam-3991	261	6	7π	7π	NUM
ejpam-3991	261	7	2	2	NUM
ejpam-3991	261	8	−	−	NOUN
ejpam-3991	261	9	i	i	PRON
ejpam-3991	261	10	log(2	log(2	VERB
ejpam-3991	261	11	)	)	PUNCT
ejpam-3991	261	12	4π	4π	NUM
ejpam-3991	261	13	)	)	PUNCT
ejpam-3991	261	14	)	)	PUNCT
ejpam-3991	262	1	next	next	ADV
ejpam-3991	262	2	we	we	PRON
ejpam-3991	262	3	apply	apply	VERB
ejpam-3991	262	4	l’hopital	l’hopital	PROPN
ejpam-3991	262	5	’s	’s	PART
ejpam-3991	262	6	rule	rule	NOUN
ejpam-3991	262	7	as	as	ADP
ejpam-3991	262	8	k	k	PROPN
ejpam-3991	262	9	→	→	SYM
ejpam-3991	262	10	−1	−1	NOUN
ejpam-3991	262	11	and	and	CCONJ
ejpam-3991	262	12	simplifying	simplify	VERB
ejpam-3991	262	13	to	to	PART
ejpam-3991	262	14	get	get	VERB
ejpam-3991	262	15	(	(	PUNCT
ejpam-3991	262	16	32	32	NUM
ejpam-3991	262	17	)	)	PUNCT
ejpam-3991	262	18	∫	∫	PROPN
ejpam-3991	263	1	∞	∞	PROPN
ejpam-3991	263	2	0	0	NUM
ejpam-3991	263	3	log	log	NOUN
ejpam-3991	263	4	(	(	PUNCT
ejpam-3991	263	5	1−	1−	NUM
ejpam-3991	263	6	x2	x2	NOUN
ejpam-3991	263	7	)	)	PUNCT
ejpam-3991	263	8	(	(	PUNCT
ejpam-3991	264	1	x2	x2	NOUN
ejpam-3991	264	2	+	+	CCONJ
ejpam-3991	264	3	1	1	X
ejpam-3991	264	4	)	)	PUNCT
ejpam-3991	264	5	log(1−	log(1−	PROPN
ejpam-3991	264	6	x	x	X
ejpam-3991	264	7	)	)	PUNCT
ejpam-3991	264	8	log(x+	log(x+	ADV
ejpam-3991	264	9	1	1	NUM
ejpam-3991	264	10	)	)	PUNCT
ejpam-3991	264	11	dx	dx	PROPN
ejpam-3991	265	1	=	=	SYM
ejpam-3991	265	2	4π	4π	PRON
ejpam-3991	265	3	log(4	log(4	PRON
ejpam-3991	265	4	)	)	PUNCT
ejpam-3991	266	1	+	+	CCONJ
ejpam-3991	266	2	iπ	iπ	PRON
ejpam-3991	266	3	r.	r.	PROPN
ejpam-3991	266	4	reynolds	reynolds	PROPN
ejpam-3991	266	5	,	,	PUNCT
ejpam-3991	266	6	a.	a.	PROPN
ejpam-3991	266	7	stauffer	stauffer	PROPN
ejpam-3991	266	8	/	/	SYM
ejpam-3991	266	9	eur	eur	PROPN
ejpam-3991	266	10	.	.	PUNCT
ejpam-3991	267	1	j.	j.	PROPN
ejpam-3991	267	2	pure	pure	PROPN
ejpam-3991	267	3	appl	appl	PROPN
ejpam-3991	267	4	.	.	PROPN
ejpam-3991	267	5	math	math	PROPN
ejpam-3991	267	6	,	,	PUNCT
ejpam-3991	267	7	14	14	NUM
ejpam-3991	267	8	(	(	PUNCT
ejpam-3991	267	9	3	3	NUM
ejpam-3991	267	10	)	)	PUNCT
ejpam-3991	267	11	(	(	PUNCT
ejpam-3991	267	12	2021	2021	NUM
ejpam-3991	267	13	)	)	PUNCT
ejpam-3991	267	14	,	,	PUNCT
ejpam-3991	267	15	723	723	NUM
ejpam-3991	267	16	-	-	SYM
ejpam-3991	267	17	736	736	NUM
ejpam-3991	267	18	733	733	NUM
ejpam-3991	267	19	21	21	NUM
ejpam-3991	267	20	.	.	PUNCT
ejpam-3991	268	1	definite	definite	ADJ
ejpam-3991	268	2	nested	nest	VERB
ejpam-3991	268	3	logarithmic	logarithmic	ADJ
ejpam-3991	268	4	integral	integral	ADJ
ejpam-3991	268	5	in	in	ADP
ejpam-3991	268	6	terms	term	NOUN
ejpam-3991	268	7	π	π	PROPN
ejpam-3991	268	8	using	use	VERB
ejpam-3991	268	9	(	(	PUNCT
ejpam-3991	268	10	12	12	NUM
ejpam-3991	268	11	)	)	PUNCT
ejpam-3991	268	12	and	and	CCONJ
ejpam-3991	268	13	taking	take	VERB
ejpam-3991	268	14	the	the	DET
ejpam-3991	268	15	first	first	ADJ
ejpam-3991	268	16	partial	partial	ADJ
ejpam-3991	268	17	derivative	derivative	NOUN
ejpam-3991	268	18	with	with	ADP
ejpam-3991	268	19	respect	respect	NOUN
ejpam-3991	268	20	to	to	ADP
ejpam-3991	268	21	k	k	PROPN
ejpam-3991	268	22	setting	set	VERB
ejpam-3991	268	23	k	k	PROPN
ejpam-3991	268	24	=	=	SYM
ejpam-3991	268	25	0	0	NUM
ejpam-3991	268	26	,	,	PUNCT
ejpam-3991	268	27	c	c	NOUN
ejpam-3991	268	28	=	=	SYM
ejpam-3991	268	29	1	1	NUM
ejpam-3991	268	30	,	,	PUNCT
ejpam-3991	268	31	b	b	X
ejpam-3991	268	32	=	=	SYM
ejpam-3991	268	33	1	1	NUM
ejpam-3991	268	34	and	and	CCONJ
ejpam-3991	268	35	a	a	DET
ejpam-3991	268	36	=	=	SYM
ejpam-3991	268	37	1	1	NUM
ejpam-3991	268	38	and	and	CCONJ
ejpam-3991	268	39	simplifying	simplify	VERB
ejpam-3991	268	40	we	we	PRON
ejpam-3991	268	41	get	get	VERB
ejpam-3991	268	42	(	(	PUNCT
ejpam-3991	268	43	33	33	NUM
ejpam-3991	268	44	)	)	PUNCT
ejpam-3991	268	45	∫	∫	PROPN
ejpam-3991	269	1	∞	∞	NOUN
ejpam-3991	269	2	0	0	PUNCT
ejpam-3991	270	1	log(log(1−	log(log(1−	PROPN
ejpam-3991	270	2	x	x	NOUN
ejpam-3991	270	3	)	)	PUNCT
ejpam-3991	270	4	)	)	PUNCT
ejpam-3991	271	1	+	+	CCONJ
ejpam-3991	271	2	log(log(x+	log(log(x+	ADJ
ejpam-3991	271	3	1	1	NUM
ejpam-3991	271	4	)	)	PUNCT
ejpam-3991	271	5	)	)	PUNCT
ejpam-3991	271	6	x2	x2	PROPN
ejpam-3991	272	1	+	+	CCONJ
ejpam-3991	272	2	1	1	NUM
ejpam-3991	272	3	dx	dx	NOUN
ejpam-3991	272	4	=	=	SYM
ejpam-3991	272	5	1	1	NUM
ejpam-3991	272	6	2	2	NUM
ejpam-3991	272	7	π	π	NOUN
ejpam-3991	272	8	(	(	PUNCT
ejpam-3991	272	9	2logγ	2logγ	NUM
ejpam-3991	272	10	(	(	PUNCT
ejpam-3991	272	11	π	π	PROPN
ejpam-3991	272	12	−	−	PROPN
ejpam-3991	272	13	2i	2i	NUM
ejpam-3991	272	14	log(2	log(2	NOUN
ejpam-3991	272	15	)	)	PUNCT
ejpam-3991	272	16	8π	8π	NUM
ejpam-3991	272	17	)	)	PUNCT
ejpam-3991	273	1	−	−	PROPN
ejpam-3991	273	2	2logγ	2logγ	NUM
ejpam-3991	273	3	(	(	PUNCT
ejpam-3991	273	4	−7	−7	PROPN
ejpam-3991	273	5	8	8	NUM
ejpam-3991	273	6	−	−	NOUN
ejpam-3991	273	7	i	i	PRON
ejpam-3991	273	8	log(2	log(2	VERB
ejpam-3991	273	9	)	)	PUNCT
ejpam-3991	273	10	4π	4π	NUM
ejpam-3991	273	11	)	)	PUNCT
ejpam-3991	274	1	+	+	CCONJ
ejpam-3991	274	2	3iπ	3iπ	ADJ
ejpam-3991	274	3	+	+	CCONJ
ejpam-3991	274	4	log	log	NOUN
ejpam-3991	274	5	(	(	PUNCT
ejpam-3991	274	6	4π2(π	4π2(π	NOUN
ejpam-3991	274	7	−	−	PROPN
ejpam-3991	274	8	2i	2i	NOUN
ejpam-3991	274	9	log(2))2	log(2))2	NOUN
ejpam-3991	274	10	(	(	PUNCT
ejpam-3991	274	11	7π	7π	ADJ
ejpam-3991	274	12	+	+	CCONJ
ejpam-3991	274	13	2i	2i	NUM
ejpam-3991	274	14	log(2))2	log(2))2	NOUN
ejpam-3991	274	15	)	)	PUNCT
ejpam-3991	274	16	)	)	PUNCT
ejpam-3991	275	1	next	next	ADV
ejpam-3991	275	2	simplifying	simplify	VERB
ejpam-3991	275	3	the	the	DET
ejpam-3991	275	4	right	right	ADJ
ejpam-3991	275	5	-	-	PUNCT
ejpam-3991	275	6	hand	hand	NOUN
ejpam-3991	275	7	side	side	NOUN
ejpam-3991	275	8	we	we	PRON
ejpam-3991	275	9	get	get	VERB
ejpam-3991	275	10	(	(	PUNCT
ejpam-3991	275	11	34	34	NUM
ejpam-3991	275	12	)	)	PUNCT
ejpam-3991	275	13	∫	∫	PROPN
ejpam-3991	275	14	∞	∞	NOUN
ejpam-3991	275	15	0	0	PUNCT
ejpam-3991	276	1	log(log(1−	log(log(1−	PROPN
ejpam-3991	276	2	x	x	SYM
ejpam-3991	276	3	)	)	PUNCT
ejpam-3991	276	4	log(x+	log(x+	ADV
ejpam-3991	276	5	1	1	NUM
ejpam-3991	276	6	)	)	PUNCT
ejpam-3991	276	7	)	)	PUNCT
ejpam-3991	277	1	x2	x2	PROPN
ejpam-3991	278	1	+	+	CCONJ
ejpam-3991	278	2	1	1	NUM
ejpam-3991	278	3	dx	dx	NOUN
ejpam-3991	278	4	=	=	SYM
ejpam-3991	278	5	π	π	X
ejpam-3991	278	6	log	log	NOUN
ejpam-3991	278	7	(	(	PUNCT
ejpam-3991	278	8	1	1	NUM
ejpam-3991	278	9	4	4	NUM
ejpam-3991	278	10	i(π	i(π	NOUN
ejpam-3991	278	11	−	−	NOUN
ejpam-3991	278	12	2i	2i	NOUN
ejpam-3991	278	13	log(2	log(2	NOUN
ejpam-3991	278	14	)	)	PUNCT
ejpam-3991	278	15	)	)	PUNCT
ejpam-3991	278	16	)	)	PUNCT
ejpam-3991	279	1	22	22	NUM
ejpam-3991	279	2	.	.	PUNCT
ejpam-3991	280	1	definite	definite	ADJ
ejpam-3991	280	2	integral	integral	ADJ
ejpam-3991	280	3	of	of	ADP
ejpam-3991	280	4	the	the	DET
ejpam-3991	280	5	hyperbolic	hyperbolic	ADJ
ejpam-3991	280	6	tangent	tangent	NOUN
ejpam-3991	280	7	and	and	CCONJ
ejpam-3991	280	8	logarithmic	logarithmic	ADJ
ejpam-3991	280	9	functions	function	NOUN
ejpam-3991	280	10	using	use	VERB
ejpam-3991	280	11	(	(	PUNCT
ejpam-3991	280	12	11	11	NUM
ejpam-3991	280	13	)	)	PUNCT
ejpam-3991	280	14	and	and	CCONJ
ejpam-3991	280	15	setting	set	VERB
ejpam-3991	280	16	k	k	PROPN
ejpam-3991	280	17	=	=	SYM
ejpam-3991	280	18	2	2	NUM
ejpam-3991	280	19	and	and	CCONJ
ejpam-3991	280	20	simplifying	simplify	VERB
ejpam-3991	280	21	we	we	PRON
ejpam-3991	280	22	get∫	get∫	PROPN
ejpam-3991	280	23	∞	∞	PROPN
ejpam-3991	280	24	0	0	NUM
ejpam-3991	280	25	log	log	NOUN
ejpam-3991	280	26	(	(	PUNCT
ejpam-3991	280	27	1−	1−	NUM
ejpam-3991	280	28	β2x2	β2x2	NUM
ejpam-3991	280	29	)	)	PUNCT
ejpam-3991	280	30	tanh−1(βx	tanh−1(βx	NOUN
ejpam-3991	280	31	)	)	PUNCT
ejpam-3991	281	1	x3	x3	PROPN
ejpam-3991	282	1	+	+	CCONJ
ejpam-3991	282	2	α2x	α2x	NUM
ejpam-3991	282	3	dx	dx	PROPN
ejpam-3991	282	4	=	=	SYM
ejpam-3991	283	1	−4	−4	X
ejpam-3991	283	2	log3(−αβ	log3(−αβ	PROPN
ejpam-3991	284	1	+	+	CCONJ
ejpam-3991	284	2	i	i	NOUN
ejpam-3991	284	3	)	)	PUNCT
ejpam-3991	285	1	+	+	CCONJ
ejpam-3991	286	1	6iπ	6iπ	ADJ
ejpam-3991	286	2	log2(−αβ	log2(−αβ	PROPN
ejpam-3991	287	1	+	+	CCONJ
ejpam-3991	287	2	i)−	i)−	PROPN
ejpam-3991	287	3	4	4	NUM
ejpam-3991	287	4	log3(αβ	log3(αβ	NOUN
ejpam-3991	287	5	−	−	PROPN
ejpam-3991	287	6	i	i	NOUN
ejpam-3991	287	7	)	)	PUNCT
ejpam-3991	288	1	+	+	CCONJ
ejpam-3991	288	2	6iπ	6iπ	ADJ
ejpam-3991	288	3	log2(αβ	log2(αβ	PROPN
ejpam-3991	288	4	−	−	PROPN
ejpam-3991	289	1	i	i	NOUN
ejpam-3991	289	2	)	)	PUNCT
ejpam-3991	290	1	+	+	CCONJ
ejpam-3991	290	2	4iπ3	4iπ3	NUM
ejpam-3991	290	3	48α2	48α2	NUM
ejpam-3991	290	4	(	(	PUNCT
ejpam-3991	290	5	35	35	NUM
ejpam-3991	290	6	)	)	PUNCT
ejpam-3991	290	7	next	next	ADV
ejpam-3991	290	8	we	we	PRON
ejpam-3991	290	9	apply	apply	VERB
ejpam-3991	290	10	l’hopital	l’hopital	PROPN
ejpam-3991	290	11	’s	’s	PART
ejpam-3991	290	12	rule	rule	NOUN
ejpam-3991	290	13	to	to	ADP
ejpam-3991	290	14	the	the	DET
ejpam-3991	290	15	right	right	ADJ
ejpam-3991	290	16	-	-	PUNCT
ejpam-3991	290	17	hand	hand	NOUN
ejpam-3991	290	18	side	side	NOUN
ejpam-3991	290	19	as	as	ADP
ejpam-3991	290	20	α→	α→	PROPN
ejpam-3991	290	21	0	0	NUM
ejpam-3991	290	22	and	and	CCONJ
ejpam-3991	290	23	upon	upon	SCONJ
ejpam-3991	290	24	inspection	inspection	NOUN
ejpam-3991	290	25	of	of	ADP
ejpam-3991	290	26	this	this	DET
ejpam-3991	290	27	closed	close	VERB
ejpam-3991	290	28	form	form	NOUN
ejpam-3991	290	29	solution	solution	NOUN
ejpam-3991	290	30	we	we	PRON
ejpam-3991	290	31	are	be	AUX
ejpam-3991	290	32	able	able	ADJ
ejpam-3991	290	33	to	to	PART
ejpam-3991	290	34	write	write	VERB
ejpam-3991	290	35	down	down	ADP
ejpam-3991	290	36	the	the	DET
ejpam-3991	290	37	conditional	conditional	ADJ
ejpam-3991	290	38	form	form	NOUN
ejpam-3991	290	39	given	give	VERB
ejpam-3991	290	40	by	by	ADP
ejpam-3991	290	41	∫	∫	PROPN
ejpam-3991	290	42	∞	∞	PROPN
ejpam-3991	290	43	0	0	NUM
ejpam-3991	290	44	log	log	NOUN
ejpam-3991	290	45	(	(	PUNCT
ejpam-3991	290	46	1−	1−	NUM
ejpam-3991	290	47	β2x2	β2x2	NUM
ejpam-3991	290	48	)	)	PUNCT
ejpam-3991	290	49	tanh−1(βx	tanh−1(βx	NOUN
ejpam-3991	290	50	)	)	PUNCT
ejpam-3991	291	1	x3	x3	ADJ
ejpam-3991	291	2	dx	dx	X
ejpam-3991	292	1	=	=	SYM
ejpam-3991	292	2			NOUN
ejpam-3991	292	3	1	1	NUM
ejpam-3991	292	4	2	2	NUM
ejpam-3991	292	5	iπβ	iπβ	NOUN
ejpam-3991	292	6	2	2	NUM
ejpam-3991	292	7	if	if	SCONJ
ejpam-3991	292	8	im(β	im(β	NUM
ejpam-3991	292	9	)	)	PUNCT
ejpam-3991	292	10	<	<	X
ejpam-3991	292	11	0	0	NUM
ejpam-3991	292	12	,	,	PUNCT
ejpam-3991	292	13	1	1	NUM
ejpam-3991	292	14	2	2	NUM
ejpam-3991	292	15	iπβ|β|	iπβ|β|	NOUN
ejpam-3991	292	16	if	if	SCONJ
ejpam-3991	292	17	im(β	im(β	NUM
ejpam-3991	292	18	)	)	PUNCT
ejpam-3991	292	19	=	=	SYM
ejpam-3991	292	20	0	0	NUM
ejpam-3991	292	21	,	,	PUNCT
ejpam-3991	292	22	−1	−1	NOUN
ejpam-3991	292	23	2	2	NUM
ejpam-3991	292	24	iπβ|β|	iπβ|β|	NOUN
ejpam-3991	292	25	if	if	SCONJ
ejpam-3991	292	26	im(β	im(β	NOUN
ejpam-3991	292	27	)	)	PUNCT
ejpam-3991	292	28	>	>	X
ejpam-3991	292	29	0	0	X
ejpam-3991	292	30	.	.	PUNCT
ejpam-3991	293	1	(	(	PUNCT
ejpam-3991	293	2	36	36	NUM
ejpam-3991	293	3	)	)	PUNCT
ejpam-3991	293	4	we	we	PRON
ejpam-3991	293	5	can	can	AUX
ejpam-3991	293	6	also	also	ADV
ejpam-3991	293	7	expand	expand	VERB
ejpam-3991	293	8	the	the	DET
ejpam-3991	293	9	left	left	ADJ
ejpam-3991	293	10	-	-	PUNCT
ejpam-3991	293	11	hand	hand	NOUN
ejpam-3991	293	12	side	side	NOUN
ejpam-3991	293	13	of	of	ADP
ejpam-3991	293	14	equation	equation	NOUN
ejpam-3991	293	15	(	(	PUNCT
ejpam-3991	293	16	35	35	NUM
ejpam-3991	293	17	)	)	PUNCT
ejpam-3991	293	18	to	to	PART
ejpam-3991	293	19	get	get	VERB
ejpam-3991	293	20	(	(	PUNCT
ejpam-3991	293	21	37	37	NUM
ejpam-3991	293	22	)	)	PUNCT
ejpam-3991	293	23	∫	∫	PROPN
ejpam-3991	294	1	∞	∞	PROPN
ejpam-3991	294	2	0	0	NUM
ejpam-3991	294	3	(	(	PUNCT
ejpam-3991	294	4	log	log	NOUN
ejpam-3991	294	5	(	(	PUNCT
ejpam-3991	294	6	1−	1−	NUM
ejpam-3991	294	7	β2x2	β2x2	NUM
ejpam-3991	294	8	)	)	PUNCT
ejpam-3991	294	9	tanh−1(βx	tanh−1(βx	NOUN
ejpam-3991	294	10	)	)	PUNCT
ejpam-3991	294	11	x	x	X
ejpam-3991	295	1	−	−	NOUN
ejpam-3991	295	2	x	x	SYM
ejpam-3991	295	3	log	log	NOUN
ejpam-3991	295	4	(	(	PUNCT
ejpam-3991	295	5	1−	1−	NUM
ejpam-3991	295	6	β2x2	β2x2	NUM
ejpam-3991	295	7	)	)	PUNCT
ejpam-3991	295	8	tanh−1(βx	tanh−1(βx	NOUN
ejpam-3991	295	9	)	)	PUNCT
ejpam-3991	295	10	α2	α2	PROPN
ejpam-3991	296	1	+	+	CCONJ
ejpam-3991	296	2	x2	x2	ADJ
ejpam-3991	296	3	)	)	PUNCT
ejpam-3991	296	4	dx	dx	PROPN
ejpam-3991	297	1	=	=	NOUN
ejpam-3991	297	2	1	1	NUM
ejpam-3991	297	3	48	48	NUM
ejpam-3991	297	4	(	(	PUNCT
ejpam-3991	297	5	−4	−4	PROPN
ejpam-3991	297	6	log3(−αβ	log3(−αβ	PROPN
ejpam-3991	297	7	+	+	PUNCT
ejpam-3991	297	8	i)−	i)−	PROPN
ejpam-3991	297	9	6iπ	6iπ	NOUN
ejpam-3991	297	10	log2(−αβ	log2(−αβ	PROPN
ejpam-3991	298	1	+	+	CCONJ
ejpam-3991	298	2	i)−	i)−	PROPN
ejpam-3991	298	3	π2	π2	PROPN
ejpam-3991	298	4	log(−αβ	log(−αβ	PROPN
ejpam-3991	299	1	+	+	CCONJ
ejpam-3991	299	2	i	i	NOUN
ejpam-3991	299	3	)	)	PUNCT
ejpam-3991	300	1	−	−	PROPN
ejpam-3991	301	1	(	(	PUNCT
ejpam-3991	301	2	π	π	X
ejpam-3991	301	3	+	+	CCONJ
ejpam-3991	301	4	i	i	PRON
ejpam-3991	301	5	log(αβ	log(αβ	NOUN
ejpam-3991	301	6	−	−	PROPN
ejpam-3991	301	7	i	i	NOUN
ejpam-3991	301	8	)	)	PUNCT
ejpam-3991	301	9	)	)	PUNCT
ejpam-3991	302	1	(	(	PUNCT
ejpam-3991	302	2	2(π	2(π	NUM
ejpam-3991	302	3	+	+	CCONJ
ejpam-3991	302	4	2i	2i	NUM
ejpam-3991	302	5	log(αβ	log(αβ	NOUN
ejpam-3991	302	6	−	−	PROPN
ejpam-3991	302	7	i	i	NOUN
ejpam-3991	302	8	)	)	PUNCT
ejpam-3991	302	9	)	)	PUNCT
ejpam-3991	302	10	log(αβ	log(αβ	NOUN
ejpam-3991	302	11	−	−	PROPN
ejpam-3991	303	1	i	i	NOUN
ejpam-3991	303	2	)	)	PUNCT
ejpam-3991	304	1	+	+	CCONJ
ejpam-3991	304	2	3iπ2	3iπ2	NUM
ejpam-3991	304	3	)	)	PUNCT
ejpam-3991	304	4	)	)	PUNCT
ejpam-3991	305	1	and	and	CCONJ
ejpam-3991	305	2	take	take	VERB
ejpam-3991	305	3	the	the	DET
ejpam-3991	305	4	first	first	ADJ
ejpam-3991	305	5	partial	partial	ADJ
ejpam-3991	305	6	derivative	derivative	NOUN
ejpam-3991	305	7	with	with	ADP
ejpam-3991	305	8	respect	respect	NOUN
ejpam-3991	305	9	to	to	ADP
ejpam-3991	305	10	α	α	PRON
ejpam-3991	305	11	,	,	PUNCT
ejpam-3991	305	12	replacing	replace	VERB
ejpam-3991	305	13	β	β	X
ejpam-3991	305	14	by	by	ADP
ejpam-3991	305	15	−iβ	−iβ	NOUN
ejpam-3991	305	16	simplifying	simplify	VERB
ejpam-3991	305	17	to	to	PART
ejpam-3991	305	18	get	get	VERB
ejpam-3991	305	19	(	(	PUNCT
ejpam-3991	305	20	38	38	NUM
ejpam-3991	305	21	)	)	PUNCT
ejpam-3991	305	22	∫	∫	PROPN
ejpam-3991	306	1	∞	∞	NOUN
ejpam-3991	306	2	0	0	NUM
ejpam-3991	307	1	x	x	SYM
ejpam-3991	307	2	log	log	NOUN
ejpam-3991	307	3	(	(	PUNCT
ejpam-3991	307	4	β2x2	β2x2	PUNCT
ejpam-3991	307	5	+	+	NUM
ejpam-3991	307	6	1	1	X
ejpam-3991	307	7	)	)	PUNCT
ejpam-3991	307	8	tan−1(βx	tan−1(βx	CCONJ
ejpam-3991	307	9	)	)	PUNCT
ejpam-3991	307	10	(	(	PUNCT
ejpam-3991	307	11	α2	α2	ADJ
ejpam-3991	307	12	+	+	CCONJ
ejpam-3991	307	13	x2)2	x2)2	NUM
ejpam-3991	307	14	dx	dx	PROPN
ejpam-3991	308	1	=	=	SYM
ejpam-3991	308	2	πβ	πβ	PROPN
ejpam-3991	308	3	log	log	NOUN
ejpam-3991	308	4	(	(	PUNCT
ejpam-3991	308	5	(	(	PUNCT
ejpam-3991	308	6	αβ	αβ	INTJ
ejpam-3991	308	7	+	+	CCONJ
ejpam-3991	308	8	1)2	1)2	NUM
ejpam-3991	308	9	)	)	PUNCT
ejpam-3991	308	10	4α(αβ	4α(αβ	NUM
ejpam-3991	309	1	+	+	CCONJ
ejpam-3991	309	2	1	1	X
ejpam-3991	309	3	)	)	PUNCT
ejpam-3991	309	4	r.	r.	PROPN
ejpam-3991	309	5	reynolds	reynolds	PROPN
ejpam-3991	309	6	,	,	PUNCT
ejpam-3991	309	7	a.	a.	PROPN
ejpam-3991	309	8	stauffer	stauffer	PROPN
ejpam-3991	309	9	/	/	SYM
ejpam-3991	309	10	eur	eur	PROPN
ejpam-3991	309	11	.	.	PUNCT
ejpam-3991	310	1	j.	j.	PROPN
ejpam-3991	310	2	pure	pure	PROPN
ejpam-3991	310	3	appl	appl	PROPN
ejpam-3991	310	4	.	.	PROPN
ejpam-3991	310	5	math	math	PROPN
ejpam-3991	310	6	,	,	PUNCT
ejpam-3991	310	7	14	14	NUM
ejpam-3991	310	8	(	(	PUNCT
ejpam-3991	310	9	3	3	NUM
ejpam-3991	310	10	)	)	PUNCT
ejpam-3991	310	11	(	(	PUNCT
ejpam-3991	310	12	2021	2021	NUM
ejpam-3991	310	13	)	)	PUNCT
ejpam-3991	310	14	,	,	PUNCT
ejpam-3991	310	15	723	723	NUM
ejpam-3991	310	16	-	-	SYM
ejpam-3991	310	17	736	736	NUM
ejpam-3991	310	18	734	734	NUM
ejpam-3991	310	19	23	23	NUM
ejpam-3991	310	20	.	.	PUNCT
ejpam-3991	311	1	definite	definite	ADJ
ejpam-3991	311	2	integral	integral	ADJ
ejpam-3991	311	3	representation	representation	NOUN
ejpam-3991	311	4	for	for	ADP
ejpam-3991	311	5	π	π	PROPN
ejpam-3991	311	6	using	use	VERB
ejpam-3991	311	7	(	(	PUNCT
ejpam-3991	311	8	10	10	NUM
ejpam-3991	311	9	)	)	PUNCT
ejpam-3991	311	10	and	and	CCONJ
ejpam-3991	311	11	setting	set	VERB
ejpam-3991	311	12	b	b	NOUN
ejpam-3991	312	1	=	=	SYM
ejpam-3991	312	2	c	c	NOUN
ejpam-3991	312	3	=	=	PUNCT
ejpam-3991	312	4	k	k	PROPN
ejpam-3991	312	5	=	=	SYM
ejpam-3991	312	6	1	1	NUM
ejpam-3991	312	7	and	and	CCONJ
ejpam-3991	312	8	simplifying	simplify	VERB
ejpam-3991	312	9	we	we	PRON
ejpam-3991	312	10	get	get	VERB
ejpam-3991	312	11	∫	∫	PROPN
ejpam-3991	312	12	∞	∞	PROPN
ejpam-3991	312	13	0	0	NUM
ejpam-3991	313	1	(	(	PUNCT
ejpam-3991	313	2	1−	1−	NUM
ejpam-3991	313	3	x)m	x)m	X
ejpam-3991	313	4	log(1−	log(1−	PROPN
ejpam-3991	313	5	x	x	PRON
ejpam-3991	313	6	)	)	PUNCT
ejpam-3991	314	1	+	+	CCONJ
ejpam-3991	314	2	(	(	PUNCT
ejpam-3991	314	3	x+	x+	ADJ
ejpam-3991	314	4	1)m	1)m	PROPN
ejpam-3991	314	5	log(x+	log(x+	NOUN
ejpam-3991	314	6	1	1	NUM
ejpam-3991	314	7	)	)	PUNCT
ejpam-3991	314	8	a+	a+	PUNCT
ejpam-3991	315	1	x2	x2	PROPN
ejpam-3991	315	2	dx	dx	PROPN
ejpam-3991	315	3	=	=	NOUN
ejpam-3991	315	4	πe	πe	PROPN
ejpam-3991	315	5	iπm	iπm	NOUN
ejpam-3991	315	6	2	2	NUM
ejpam-3991	315	7	(	(	PUNCT
ejpam-3991	315	8	√	√	NUM
ejpam-3991	315	9	a−	a−	PROPN
ejpam-3991	315	10	i)m	i)m	NOUN
ejpam-3991	315	11	log	log	NOUN
ejpam-3991	315	12	(	(	PUNCT
ejpam-3991	315	13	−	−	PROPN
ejpam-3991	315	14	(	(	PUNCT
ejpam-3991	315	15	√	√	PUNCT
ejpam-3991	315	16	a−	a−	PROPN
ejpam-3991	315	17	i)2	i)2	PROPN
ejpam-3991	315	18	)	)	PUNCT
ejpam-3991	315	19	2	2	NUM
ejpam-3991	315	20	√	√	NUM
ejpam-3991	315	21	a	a	DET
ejpam-3991	315	22	(	(	PUNCT
ejpam-3991	315	23	39	39	NUM
ejpam-3991	315	24	)	)	PUNCT
ejpam-3991	316	1	next	next	ADV
ejpam-3991	316	2	we	we	PRON
ejpam-3991	316	3	apply	apply	VERB
ejpam-3991	316	4	l’hopital	l’hopital	PROPN
ejpam-3991	316	5	’s	’s	PART
ejpam-3991	316	6	rule	rule	NOUN
ejpam-3991	316	7	as	as	ADP
ejpam-3991	316	8	a→	a→	X
ejpam-3991	316	9	0	0	NUM
ejpam-3991	316	10	to	to	ADP
ejpam-3991	316	11	the	the	DET
ejpam-3991	316	12	right	right	ADJ
ejpam-3991	316	13	-	-	PUNCT
ejpam-3991	316	14	hand	hand	NOUN
ejpam-3991	316	15	side	side	NOUN
ejpam-3991	316	16	to	to	PART
ejpam-3991	316	17	get	get	VERB
ejpam-3991	316	18	(	(	PUNCT
ejpam-3991	316	19	40	40	NUM
ejpam-3991	316	20	)	)	PUNCT
ejpam-3991	316	21	∫	∫	PROPN
ejpam-3991	317	1	∞	∞	PROPN
ejpam-3991	317	2	0	0	NUM
ejpam-3991	317	3	(	(	PUNCT
ejpam-3991	317	4	1−	1−	NUM
ejpam-3991	317	5	x)m	x)m	X
ejpam-3991	317	6	log(1−	log(1−	PROPN
ejpam-3991	317	7	x	x	PRON
ejpam-3991	317	8	)	)	PUNCT
ejpam-3991	318	1	+	+	CCONJ
ejpam-3991	318	2	(	(	PUNCT
ejpam-3991	318	3	x+	x+	ADJ
ejpam-3991	318	4	1)m	1)m	PROPN
ejpam-3991	318	5	log(x+	log(x+	NOUN
ejpam-3991	318	6	1	1	NUM
ejpam-3991	318	7	)	)	PUNCT
ejpam-3991	319	1	x2	x2	PRON
ejpam-3991	319	2	dx	dx	PROPN
ejpam-3991	320	1	=	=	NOUN
ejpam-3991	320	2	iπ	iπ	PRON
ejpam-3991	320	3	next	next	ADV
ejpam-3991	320	4	we	we	PRON
ejpam-3991	320	5	take	take	VERB
ejpam-3991	320	6	the	the	DET
ejpam-3991	320	7	definite	definite	ADJ
ejpam-3991	320	8	integral	integral	ADJ
ejpam-3991	320	9	over	over	ADP
ejpam-3991	320	10	m	m	PROPN
ejpam-3991	320	11	∈	∈	NOUN
ejpam-3991	321	1	[	[	X
ejpam-3991	321	2	0,m	0,m	X
ejpam-3991	321	3	]	]	X
ejpam-3991	321	4	to	to	PART
ejpam-3991	321	5	get	get	VERB
ejpam-3991	321	6	(	(	PUNCT
ejpam-3991	321	7	41	41	NUM
ejpam-3991	321	8	)	)	PUNCT
ejpam-3991	321	9	∫	∫	PROPN
ejpam-3991	321	10	∞	∞	PROPN
ejpam-3991	321	11	0	0	NUM
ejpam-3991	322	1	(	(	PUNCT
ejpam-3991	322	2	1−	1−	NUM
ejpam-3991	322	3	x)m	x)m	X
ejpam-3991	323	1	+	+	CCONJ
ejpam-3991	323	2	(	(	PUNCT
ejpam-3991	323	3	x+	x+	ADJ
ejpam-3991	323	4	1)m	1)m	NUM
ejpam-3991	323	5	−	−	PROPN
ejpam-3991	323	6	2	2	NUM
ejpam-3991	323	7	x2	x2	NOUN
ejpam-3991	323	8	dx	dx	PROPN
ejpam-3991	323	9	=	=	PRON
ejpam-3991	323	10	iπm	iπm	VERB
ejpam-3991	323	11	where	where	SCONJ
ejpam-3991	323	12	−1	−1	NOUN
ejpam-3991	323	13	<	<	X
ejpam-3991	323	14	re(m	re(m	PROPN
ejpam-3991	323	15	)	)	PUNCT
ejpam-3991	323	16	<	<	X
ejpam-3991	324	1	1	1	X
ejpam-3991	324	2	.	.	PUNCT
ejpam-3991	324	3	references	reference	NOUN
ejpam-3991	324	4	735	735	NUM
ejpam-3991	324	5	24	24	NUM
ejpam-3991	324	6	.	.	PUNCT
ejpam-3991	324	7	table	table	NOUN
ejpam-3991	324	8	of	of	ADP
ejpam-3991	324	9	integrals	integral	NOUN
ejpam-3991	324	10	f(x	f(x	PROPN
ejpam-3991	324	11	)	)	PUNCT
ejpam-3991	324	12	∫∞	∫∞	NOUN
ejpam-3991	324	13	0	0	NUM
ejpam-3991	324	14	f(x)dx	f(x)dx	NUM
ejpam-3991	324	15	tan−1(px	tan−1(px	NOUN
ejpam-3991	324	16	)	)	PUNCT
ejpam-3991	325	1	x3+x	x3+x	PROPN
ejpam-3991	325	2	1	1	NUM
ejpam-3991	325	3	2π	2π	NUM
ejpam-3991	325	4	log(p+	log(p+	PROPN
ejpam-3991	325	5	1	1	NUM
ejpam-3991	325	6	)	)	PUNCT
ejpam-3991	325	7	tan−1(px	tan−1(px	NOUN
ejpam-3991	325	8	)	)	PUNCT
ejpam-3991	325	9	x−x3	x−x3	X
ejpam-3991	325	10	1	1	NUM
ejpam-3991	325	11	4π(2	4π(2	NUM
ejpam-3991	325	12	log(p+	log(p+	PROPN
ejpam-3991	325	13	i)−	i)−	PROPN
ejpam-3991	325	14	iπ	iπ	NOUN
ejpam-3991	325	15	)	)	PUNCT
ejpam-3991	325	16	tan−1(qx	tan−1(qx	NOUN
ejpam-3991	325	17	)	)	PUNCT
ejpam-3991	325	18	p2x+x3	p2x+x3	NOUN
ejpam-3991	325	19	π	π	PROPN
ejpam-3991	325	20	log(pq+1	log(pq+1	PROPN
ejpam-3991	325	21	)	)	PUNCT
ejpam-3991	325	22	2p2	2p2	NUM
ejpam-3991	325	23	tan−1(qx	tan−1(qx	NOUN
ejpam-3991	325	24	)	)	PUNCT
ejpam-3991	325	25	x−p2x3	x−p2x3	PROPN
ejpam-3991	325	26	1	1	NUM
ejpam-3991	325	27	4π	4π	NUM
ejpam-3991	325	28	log	log	NOUN
ejpam-3991	325	29	(	(	PUNCT
ejpam-3991	325	30	p2+q2	p2+q2	PROPN
ejpam-3991	325	31	p2	p2	PROPN
ejpam-3991	325	32	)	)	PUNCT
ejpam-3991	326	1	x	x	SYM
ejpam-3991	326	2	tan−1(bx	tan−1(bx	NOUN
ejpam-3991	326	3	)	)	PUNCT
ejpam-3991	326	4	(	(	PUNCT
ejpam-3991	326	5	a2+x2)2	a2+x2)2	X
ejpam-3991	326	6	πb	πb	NUM
ejpam-3991	326	7	4a(ab+1	4a(ab+1	NUM
ejpam-3991	326	8	)	)	PUNCT
ejpam-3991	326	9	log(β+µx2	log(β+µx2	PROPN
ejpam-3991	326	10	)	)	PUNCT
ejpam-3991	326	11	γ+x2	γ+x2	PROPN
ejpam-3991	326	12	π	π	PROPN
ejpam-3991	326	13	log	log	NOUN
ejpam-3991	326	14	(	(	PUNCT
ejpam-3991	326	15	√	√	NUM
ejpam-3991	326	16	β+	β+	PUNCT
ejpam-3991	327	1	√	√	NUM
ejpam-3991	327	2	γ	γ	PROPN
ejpam-3991	327	3	√	√	PROPN
ejpam-3991	327	4	µ)√	µ)√	ADV
ejpam-3991	327	5	γ	γ	NOUN
ejpam-3991	327	6	log(a2+b2x2	log(a2+b2x2	PROPN
ejpam-3991	327	7	)	)	PUNCT
ejpam-3991	327	8	c2+g2x2	c2+g2x2	NOUN
ejpam-3991	327	9	π	π	X
ejpam-3991	327	10	log	log	NOUN
ejpam-3991	327	11	(	(	PUNCT
ejpam-3991	327	12	ag+bc	ag+bc	NOUN
ejpam-3991	327	13	g	g	NOUN
ejpam-3991	327	14	)	)	PUNCT
ejpam-3991	327	15	cg	cg	NOUN
ejpam-3991	327	16	log(a2+b2x2	log(a2+b2x2	PROPN
ejpam-3991	327	17	)	)	PUNCT
ejpam-3991	327	18	c2−g2x2	c2−g2x2	NOUN
ejpam-3991	327	19	−	−	PROPN
ejpam-3991	327	20	iπ	iπ	PRON
ejpam-3991	327	21	log	log	NOUN
ejpam-3991	327	22	(	(	PUNCT
ejpam-3991	327	23	−	−	PROPN
ejpam-3991	327	24	i(bc+iag	i(bc+iag	ADJ
ejpam-3991	327	25	)	)	PUNCT
ejpam-3991	327	26	g	g	NOUN
ejpam-3991	327	27	)	)	PUNCT
ejpam-3991	327	28	cg	cg	NOUN
ejpam-3991	327	29	log(p2x2	log(p2x2	NOUN
ejpam-3991	327	30	+	+	NOUN
ejpam-3991	327	31	1)−log(q2x2	1)−log(q2x2	NUM
ejpam-3991	327	32	+	+	SYM
ejpam-3991	327	33	1	1	NUM
ejpam-3991	327	34	)	)	PUNCT
ejpam-3991	327	35	x2	x2	NOUN
ejpam-3991	327	36	π(p−	π(p−	VERB
ejpam-3991	327	37	q	q	NOUN
ejpam-3991	327	38	)	)	PUNCT
ejpam-3991	327	39	log(p2x2	log(p2x2	NOUN
ejpam-3991	327	40	+	+	NOUN
ejpam-3991	327	41	1	1	NUM
ejpam-3991	327	42	)	)	PUNCT
ejpam-3991	327	43	q2x2+r2	q2x2+r2	NOUN
ejpam-3991	327	44	π	π	PROPN
ejpam-3991	327	45	log	log	NOUN
ejpam-3991	327	46	(	(	PUNCT
ejpam-3991	327	47	pr+q	pr+q	PROPN
ejpam-3991	327	48	q	q	NOUN
ejpam-3991	327	49	)	)	PUNCT
ejpam-3991	327	50	qr	qr	PROPN
ejpam-3991	327	51	log(a2+b2x2	log(a2+b2x2	PROPN
ejpam-3991	327	52	)	)	PUNCT
ejpam-3991	327	53	(	(	PUNCT
ejpam-3991	327	54	c2+g2x2)2	c2+g2x2)2	NOUN
ejpam-3991	327	55	π	π	PROPN
ejpam-3991	327	56	log	log	NOUN
ejpam-3991	327	57	(	(	PUNCT
ejpam-3991	327	58	ag+bc	ag+bc	NOUN
ejpam-3991	327	59	g	g	NOUN
ejpam-3991	327	60	)	)	PUNCT
ejpam-3991	327	61	2c3	2c3	NUM
ejpam-3991	327	62	g	g	NOUN
ejpam-3991	327	63	−	−	NOUN
ejpam-3991	327	64	πb	πb	NUM
ejpam-3991	327	65	2c2g(ag+bc	2c2g(ag+bc	NUM
ejpam-3991	327	66	)	)	PUNCT
ejpam-3991	327	67	x2	x2	PROPN
ejpam-3991	327	68	log(a2+b2x2	log(a2+b2x2	PROPN
ejpam-3991	327	69	)	)	PUNCT
ejpam-3991	327	70	(	(	PUNCT
ejpam-3991	327	71	c2+g2x2)2	c2+g2x2)2	NOUN
ejpam-3991	327	72	πb	πb	PRON
ejpam-3991	327	73	2g3(ag+bc	2g3(ag+bc	NUM
ejpam-3991	327	74	)	)	PUNCT
ejpam-3991	328	1	+	+	CCONJ
ejpam-3991	328	2	π	π	X
ejpam-3991	328	3	log	log	NOUN
ejpam-3991	328	4	(	(	PUNCT
ejpam-3991	328	5	ag+bc	ag+bc	NOUN
ejpam-3991	328	6	g	g	NOUN
ejpam-3991	328	7	)	)	PUNCT
ejpam-3991	328	8	2cg3	2cg3	PUNCT
ejpam-3991	328	9	log(1−x2	log(1−x2	X
ejpam-3991	328	10	)	)	PUNCT
ejpam-3991	328	11	(	(	PUNCT
ejpam-3991	328	12	x2	x2	PROPN
ejpam-3991	328	13	+	+	ADJ
ejpam-3991	328	14	1	1	NUM
ejpam-3991	328	15	)	)	PUNCT
ejpam-3991	328	16	log(1−x	log(1−x	PROPN
ejpam-3991	328	17	)	)	PUNCT
ejpam-3991	328	18	log(x+1	log(x+1	PROPN
ejpam-3991	328	19	)	)	PUNCT
ejpam-3991	328	20	4π	4π	NOUN
ejpam-3991	328	21	log(4)+iπ	log(4)+iπ	ADJ
ejpam-3991	328	22	log(log(1−x	log(log(1−x	NOUN
ejpam-3991	328	23	)	)	PUNCT
ejpam-3991	328	24	log(x+1	log(x+1	PROPN
ejpam-3991	328	25	)	)	PUNCT
ejpam-3991	328	26	)	)	PUNCT
ejpam-3991	329	1	x2	x2	PROPN
ejpam-3991	330	1	+	+	NOUN
ejpam-3991	330	2	1	1	NUM
ejpam-3991	330	3	π	π	NOUN
ejpam-3991	330	4	log	log	NOUN
ejpam-3991	330	5	(	(	PUNCT
ejpam-3991	330	6	1	1	NUM
ejpam-3991	330	7	4	4	NUM
ejpam-3991	330	8	i(π	i(π	NOUN
ejpam-3991	330	9	−	−	NOUN
ejpam-3991	330	10	2i	2i	NOUN
ejpam-3991	330	11	log(2	log(2	NOUN
ejpam-3991	330	12	)	)	PUNCT
ejpam-3991	330	13	)	)	PUNCT
ejpam-3991	330	14	)	)	PUNCT
ejpam-3991	331	1	(	(	PUNCT
ejpam-3991	331	2	1−x)m	1−x)m	PROPN
ejpam-3991	331	3	log(1−x)+(x+1)m	log(1−x)+(x+1)m	PROPN
ejpam-3991	331	4	log(x+1	log(x+1	PROPN
ejpam-3991	331	5	)	)	PUNCT
ejpam-3991	331	6	x2	x2	NOUN
ejpam-3991	331	7	iπ	iπ	PRON
ejpam-3991	331	8	table	table	VERB
ejpam-3991	331	9	1	1	NUM
ejpam-3991	331	10	:	:	PUNCT
ejpam-3991	331	11	table	table	NOUN
ejpam-3991	331	12	of	of	ADP
ejpam-3991	331	13	definite	definite	ADJ
ejpam-3991	331	14	integrals	integral	NOUN
ejpam-3991	331	15	acknowledgements	acknowledgement	NOUN
ejpam-3991	331	16	supported	support	VERB
ejpam-3991	331	17	by	by	ADP
ejpam-3991	331	18	the	the	DET
ejpam-3991	331	19	natural	natural	ADJ
ejpam-3991	331	20	sciences	sciences	PROPN
ejpam-3991	331	21	and	and	CCONJ
ejpam-3991	331	22	engineering	engineering	NOUN
ejpam-3991	331	23	research	research	NOUN
ejpam-3991	331	24	council	council	PROPN
ejpam-3991	331	25	of	of	ADP
ejpam-3991	331	26	canada	canada	PROPN
ejpam-3991	331	27	(	(	PUNCT
ejpam-3991	331	28	nserc	nserc	PROPN
ejpam-3991	331	29	)	)	PUNCT
ejpam-3991	331	30	,	,	PUNCT
ejpam-3991	331	31	grant	grant	VERB
ejpam-3991	331	32	number	number	NOUN
ejpam-3991	331	33	504070	504070	NUM
ejpam-3991	331	34	.	.	PUNCT
ejpam-3991	332	1	references	reference	NOUN
ejpam-3991	332	2	[	[	X
ejpam-3991	332	3	1	1	X
ejpam-3991	332	4	]	]	PUNCT
ejpam-3991	332	5	d.	d.	PROPN
ejpam-3991	332	6	bierens	bierens	PROPN
ejpam-3991	332	7	de	de	PROPN
ejpam-3991	332	8	haan	haan	PROPN
ejpam-3991	332	9	.	.	PUNCT
ejpam-3991	333	1	nouvelles	nouvelles	PROPN
ejpam-3991	333	2	tables	table	NOUN
ejpam-3991	333	3	d’intégrales	d’intégrales	PROPN
ejpam-3991	333	4	définies	définies	PROPN
ejpam-3991	333	5	.	.	PUNCT
ejpam-3991	334	1	p.	p.	NOUN
ejpam-3991	334	2	engels	engels	PROPN
ejpam-3991	334	3	,	,	PUNCT
ejpam-3991	334	4	leiden	leiden	PROPN
ejpam-3991	334	5	,	,	PUNCT
ejpam-3991	334	6	1867	1867	NUM
ejpam-3991	334	7	.	.	PUNCT
ejpam-3991	335	1	[	[	X
ejpam-3991	335	2	2	2	NUM
ejpam-3991	335	3	]	]	PUNCT
ejpam-3991	335	4	a.	a.	NOUN
ejpam-3991	335	5	erdélyi	erdélyi	PROPN
ejpam-3991	335	6	.	.	PUNCT
ejpam-3991	335	7	tables	table	NOUN
ejpam-3991	335	8	of	of	ADP
ejpam-3991	335	9	integral	integral	ADJ
ejpam-3991	335	10	transforms	transform	NOUN
ejpam-3991	335	11	.	.	PUNCT
ejpam-3991	336	1	mcgraw	mcgraw	PROPN
ejpam-3991	336	2	-	-	PUNCT
ejpam-3991	336	3	hill	hill	PROPN
ejpam-3991	336	4	,	,	PUNCT
ejpam-3991	336	5	new	new	PROPN
ejpam-3991	336	6	york	york	PROPN
ejpam-3991	336	7	,	,	PUNCT
ejpam-3991	336	8	1954	1954	NUM
ejpam-3991	336	9	.	.	PUNCT
ejpam-3991	337	1	references	reference	NOUN
ejpam-3991	337	2	736	736	NUM
ejpam-3991	338	1	[	[	X
ejpam-3991	338	2	3	3	NUM
ejpam-3991	338	3	]	]	X
ejpam-3991	338	4	i.	i.	PROPN
ejpam-3991	338	5	s.	s.	PROPN
ejpam-3991	338	6	gradshteyn	gradshteyn	PROPN
ejpam-3991	338	7	and	and	CCONJ
ejpam-3991	338	8	i.	i.	PROPN
ejpam-3991	338	9	m.	m.	PROPN
ejpam-3991	338	10	ryzhik	ryzhik	PROPN
ejpam-3991	338	11	.	.	PUNCT
ejpam-3991	339	1	table	table	NOUN
ejpam-3991	339	2	of	of	ADP
ejpam-3991	339	3	integrals	integral	NOUN
ejpam-3991	339	4	,	,	PUNCT
ejpam-3991	339	5	series	series	NOUN
ejpam-3991	339	6	,	,	PUNCT
ejpam-3991	339	7	and	and	CCONJ
ejpam-3991	339	8	products	product	NOUN
ejpam-3991	339	9	.	.	PUNCT
ejpam-3991	340	1	elsevier	elsevier	NOUN
ejpam-3991	340	2	/	/	SYM
ejpam-3991	340	3	academic	academic	ADJ
ejpam-3991	340	4	press	press	NOUN
ejpam-3991	340	5	,	,	PUNCT
ejpam-3991	340	6	amsterdam	amsterdam	PROPN
ejpam-3991	340	7	,	,	PUNCT
ejpam-3991	340	8	seventh	seventh	ADJ
ejpam-3991	340	9	edition	edition	NOUN
ejpam-3991	340	10	,	,	PUNCT
ejpam-3991	340	11	2007	2007	NUM
ejpam-3991	340	12	.	.	PUNCT
ejpam-3991	341	1	translated	translate	VERB
ejpam-3991	341	2	from	from	ADP
ejpam-3991	341	3	the	the	DET
ejpam-3991	341	4	russian	russian	NOUN
ejpam-3991	341	5	,	,	PUNCT
ejpam-3991	341	6	translation	translation	NOUN
ejpam-3991	341	7	edited	edit	VERB
ejpam-3991	341	8	and	and	CCONJ
ejpam-3991	341	9	with	with	ADP
ejpam-3991	341	10	a	a	DET
ejpam-3991	341	11	preface	preface	NOUN
ejpam-3991	341	12	by	by	ADP
ejpam-3991	341	13	alan	alan	PROPN
ejpam-3991	341	14	jeffrey	jeffrey	PROPN
ejpam-3991	341	15	and	and	CCONJ
ejpam-3991	341	16	daniel	daniel	PROPN
ejpam-3991	341	17	zwillinger	zwillinger	PROPN
ejpam-3991	341	18	,	,	PUNCT
ejpam-3991	341	19	with	with	ADP
ejpam-3991	341	20	one	one	NUM
ejpam-3991	341	21	cd	cd	PROPN
ejpam-3991	341	22	-	-	PUNCT
ejpam-3991	341	23	rom	rom	PROPN
ejpam-3991	341	24	(	(	PUNCT
ejpam-3991	341	25	windows	window	NOUN
ejpam-3991	341	26	,	,	PUNCT
ejpam-3991	341	27	macintosh	macintosh	PROPN
ejpam-3991	341	28	and	and	CCONJ
ejpam-3991	341	29	unix	unix	NOUN
ejpam-3991	341	30	)	)	PUNCT
ejpam-3991	341	31	.	.	PUNCT
ejpam-3991	342	1	[	[	X
ejpam-3991	342	2	4	4	X
ejpam-3991	342	3	]	]	X
ejpam-3991	342	4	a	a	DET
ejpam-3991	342	5	reynolds	reynolds	PROPN
ejpam-3991	342	6	,	,	PUNCT
ejpam-3991	342	7	r.	r.	PROPN
ejpam-3991	342	8	;	;	PUNCT
ejpam-3991	342	9	stauffer	stauffer	PROPN
ejpam-3991	342	10	.	.	PUNCT
ejpam-3991	343	1	a	a	DET
ejpam-3991	343	2	definite	definite	ADJ
ejpam-3991	343	3	integral	integral	ADJ
ejpam-3991	343	4	involving	involve	VERB
ejpam-3991	343	5	the	the	DET
ejpam-3991	343	6	logarithmic	logarithmic	ADJ
ejpam-3991	343	7	function	function	NOUN
ejpam-3991	343	8	in	in	ADP
ejpam-3991	343	9	terms	term	NOUN
ejpam-3991	343	10	of	of	ADP
ejpam-3991	343	11	the	the	DET
ejpam-3991	343	12	lerch	lerch	PROPN
ejpam-3991	343	13	function	function	PROPN
ejpam-3991	343	14	.	.	PUNCT
ejpam-3991	344	1	mathematics	mathematic	NOUN
ejpam-3991	344	2	,	,	PUNCT
ejpam-3991	344	3	1148(7	1148(7	NUM
ejpam-3991	344	4	)	)	PUNCT
ejpam-3991	344	5	,	,	PUNCT
ejpam-3991	344	6	2019	2019	NUM
ejpam-3991	344	7	.	.	PUNCT
ejpam-3991	345	1	[	[	X
ejpam-3991	345	2	5	5	NUM
ejpam-3991	345	3	]	]	PUNCT
ejpam-3991	345	4	a	a	DET
ejpam-3991	345	5	reynolds	reynolds	PROPN
ejpam-3991	345	6	,	,	PUNCT
ejpam-3991	345	7	r.	r.	PROPN
ejpam-3991	345	8	;	;	PUNCT
ejpam-3991	345	9	stauffer	stauffer	PROPN
ejpam-3991	345	10	.	.	PUNCT
ejpam-3991	346	1	definite	definite	ADJ
ejpam-3991	346	2	integral	integral	ADJ
ejpam-3991	346	3	of	of	ADP
ejpam-3991	346	4	arctangent	arctangent	NOUN
ejpam-3991	346	5	and	and	CCONJ
ejpam-3991	346	6	polylogarithmic	polylogarithmic	ADJ
ejpam-3991	346	7	functions	function	NOUN
ejpam-3991	346	8	expressed	express	VERB
ejpam-3991	346	9	as	as	ADP
ejpam-3991	346	10	a	a	DET
ejpam-3991	346	11	series	series	NOUN
ejpam-3991	346	12	.	.	PUNCT
ejpam-3991	347	1	mathematics	mathematic	NOUN
ejpam-3991	347	2	,	,	PUNCT
ejpam-3991	347	3	1099(7	1099(7	NUM
ejpam-3991	347	4	)	)	PUNCT
ejpam-3991	347	5	,	,	PUNCT
ejpam-3991	347	6	2019	2019	NUM
ejpam-3991	347	7	.	.	PUNCT
ejpam-3991	348	1	[	[	X
ejpam-3991	348	2	6	6	NUM
ejpam-3991	348	3	]	]	PUNCT
ejpam-3991	348	4	a	a	DET
ejpam-3991	348	5	reynolds	reynolds	PROPN
ejpam-3991	348	6	,	,	PUNCT
ejpam-3991	348	7	r.	r.	PROPN
ejpam-3991	348	8	;	;	PUNCT
ejpam-3991	348	9	stauffer	stauffer	PROPN
ejpam-3991	348	10	.	.	PUNCT
ejpam-3991	349	1	a	a	DET
ejpam-3991	349	2	definite	definite	ADJ
ejpam-3991	349	3	integral	integral	ADJ
ejpam-3991	349	4	involving	involve	VERB
ejpam-3991	349	5	the	the	DET
ejpam-3991	349	6	logarithmic	logarithmic	ADJ
ejpam-3991	349	7	function	function	NOUN
ejpam-3991	349	8	in	in	ADP
ejpam-3991	349	9	terms	term	NOUN
ejpam-3991	349	10	of	of	ADP
ejpam-3991	349	11	the	the	DET
ejpam-3991	349	12	lerch	lerch	PROPN
ejpam-3991	349	13	function	function	PROPN
ejpam-3991	349	14	.	.	PUNCT
ejpam-3991	350	1	mathematics	mathematic	NOUN
ejpam-3991	350	2	,	,	PUNCT
ejpam-3991	350	3	687(7	687(7	NUM
ejpam-3991	350	4	)	)	PUNCT
ejpam-3991	350	5	,	,	PUNCT
ejpam-3991	350	6	2020	2020	NUM
ejpam-3991	350	7	.	.	PUNCT
ejpam-3991	351	1	[	[	X
ejpam-3991	351	2	7	7	X
ejpam-3991	351	3	]	]	X
ejpam-3991	351	4	a	a	DET
ejpam-3991	351	5	reynolds	reynolds	PROPN
ejpam-3991	351	6	,	,	PUNCT
ejpam-3991	351	7	r.	r.	PROPN
ejpam-3991	351	8	;	;	PUNCT
ejpam-3991	351	9	stauffer	stauffer	PROPN
ejpam-3991	351	10	.	.	PUNCT
ejpam-3991	352	1	definite	definite	ADJ
ejpam-3991	352	2	integrals	integral	NOUN
ejpam-3991	352	3	involving	involve	VERB
ejpam-3991	352	4	product	product	NOUN
ejpam-3991	352	5	of	of	ADP
ejpam-3991	352	6	logarithmic	logarithmic	ADJ
ejpam-3991	352	7	functions	function	NOUN
ejpam-3991	352	8	and	and	CCONJ
ejpam-3991	352	9	logarithm	logarithm	NOUN
ejpam-3991	352	10	of	of	ADP
ejpam-3991	352	11	square	square	ADJ
ejpam-3991	352	12	root	root	NOUN
ejpam-3991	352	13	functions	function	NOUN
ejpam-3991	352	14	expressed	express	VERB
ejpam-3991	352	15	in	in	ADP
ejpam-3991	352	16	terms	term	NOUN
ejpam-3991	352	17	of	of	ADP
ejpam-3991	352	18	special	special	ADJ
ejpam-3991	352	19	functions	function	NOUN
ejpam-3991	352	20	.	.	PUNCT
ejpam-3991	353	1	aims	aim	VERB
ejpam-3991	353	2	mathematics	mathematic	NOUN
ejpam-3991	353	3	,	,	PUNCT
ejpam-3991	353	4	(	(	PUNCT
ejpam-3991	353	5	5	5	NUM
ejpam-3991	353	6	)	)	PUNCT
ejpam-3991	353	7	,	,	PUNCT
ejpam-3991	353	8	2020	2020	NUM
ejpam-3991	353	9	.	.	PUNCT
ejpam-3991	354	1	[	[	X
ejpam-3991	354	2	8	8	NUM
ejpam-3991	354	3	]	]	X
ejpam-3991	354	4	a	a	DET
ejpam-3991	354	5	reynolds	reynolds	PROPN
ejpam-3991	354	6	,	,	PUNCT
ejpam-3991	354	7	r.	r.	PROPN
ejpam-3991	354	8	;	;	PUNCT
ejpam-3991	354	9	stauffer	stauffer	PROPN
ejpam-3991	354	10	.	.	PUNCT
ejpam-3991	354	11	integrals	integral	NOUN
ejpam-3991	354	12	in	in	ADP
ejpam-3991	354	13	gradshteyn	gradshteyn	PROPN
ejpam-3991	354	14	and	and	CCONJ
ejpam-3991	354	15	ryzhik	ryzhik	ADJ
ejpam-3991	354	16	:	:	PUNCT
ejpam-3991	354	17	hyperbolic	hyperbolic	ADJ
ejpam-3991	354	18	and	and	CCONJ
ejpam-3991	354	19	algebraic	algebraic	ADJ
ejpam-3991	354	20	functions	function	NOUN
ejpam-3991	354	21	.	.	PUNCT
ejpam-3991	355	1	international	international	ADJ
ejpam-3991	355	2	mathematical	mathematical	PROPN
ejpam-3991	355	3	forum	forum	PROPN
ejpam-3991	355	4	,	,	PUNCT
ejpam-3991	355	5	15(6):255–263	15(6):255–263	NUM
ejpam-3991	355	6	,	,	PUNCT
ejpam-3991	355	7	2020	2020	NUM
ejpam-3991	355	8	.	.	PUNCT
ejpam-3991	356	1	[	[	X
ejpam-3991	356	2	9	9	NUM
ejpam-3991	356	3	]	]	X
ejpam-3991	356	4	a	a	DET
ejpam-3991	356	5	reynolds	reynolds	PROPN
ejpam-3991	356	6	,	,	PUNCT
ejpam-3991	356	7	r.	r.	PROPN
ejpam-3991	356	8	;	;	PUNCT
ejpam-3991	356	9	stauffer	stauffer	PROPN
ejpam-3991	356	10	.	.	PUNCT
ejpam-3991	357	1	a	a	DET
ejpam-3991	357	2	method	method	NOUN
ejpam-3991	357	3	for	for	ADP
ejpam-3991	357	4	evaluating	evaluate	VERB
ejpam-3991	357	5	definite	definite	ADJ
ejpam-3991	357	6	integrals	integral	NOUN
ejpam-3991	357	7	in	in	ADP
ejpam-3991	357	8	terms	term	NOUN
ejpam-3991	357	9	of	of	ADP
ejpam-3991	357	10	special	special	ADJ
ejpam-3991	357	11	functions	function	NOUN
ejpam-3991	357	12	with	with	ADP
ejpam-3991	357	13	examples	example	NOUN
ejpam-3991	357	14	.	.	PUNCT
ejpam-3991	358	1	international	international	ADJ
ejpam-3991	358	2	mathematical	mathematical	PROPN
ejpam-3991	358	3	forum	forum	PROPN
ejpam-3991	358	4	,	,	PUNCT
ejpam-3991	358	5	15(5):235–244	15(5):235–244	PROPN
ejpam-3991	358	6	,	,	PUNCT
ejpam-3991	358	7	2020	2020	NUM
ejpam-3991	358	8	.	.	PUNCT