id	sid	tid	token	lemma	pos
ejpam-4029	1	1	european	european	PROPN
ejpam-4029	1	2	journal	journal	PROPN
ejpam-4029	1	3	of	of	ADP
ejpam-4029	1	4	pure	pure	ADJ
ejpam-4029	1	5	and	and	CCONJ
ejpam-4029	1	6	applied	apply	VERB
ejpam-4029	1	7	mathematics	mathematic	NOUN
ejpam-4029	1	8	vol	vol	NOUN
ejpam-4029	1	9	.	.	PUNCT
ejpam-4029	2	1	14	14	NUM
ejpam-4029	2	2	,	,	PUNCT
ejpam-4029	2	3	no	no	INTJ
ejpam-4029	2	4	.	.	NOUN
ejpam-4029	2	5	4	4	NUM
ejpam-4029	2	6	,	,	PUNCT
ejpam-4029	2	7	2021	2021	NUM
ejpam-4029	2	8	,	,	PUNCT
ejpam-4029	2	9	1132	1132	NUM
ejpam-4029	2	10	-	-	SYM
ejpam-4029	2	11	1147	1147	NUM
ejpam-4029	2	12	issn	issn	PROPN
ejpam-4029	2	13	1307	1307	NUM
ejpam-4029	2	14	-	-	SYM
ejpam-4029	2	15	5543	5543	NUM
ejpam-4029	2	16	–	–	PUNCT
ejpam-4029	2	17	ejpam.com	ejpam.com	X
ejpam-4029	2	18	published	publish	VERB
ejpam-4029	2	19	by	by	ADP
ejpam-4029	2	20	new	new	PROPN
ejpam-4029	2	21	york	york	PROPN
ejpam-4029	2	22	business	business	PROPN
ejpam-4029	2	23	global	global	ADJ
ejpam-4029	2	24	definite	definite	ADJ
ejpam-4029	2	25	integral	integral	ADJ
ejpam-4029	2	26	of	of	ADP
ejpam-4029	2	27	a	a	DET
ejpam-4029	2	28	hyperbolic	hyperbolic	ADJ
ejpam-4029	2	29	quotient	quotient	NOUN
ejpam-4029	2	30	function	function	NOUN
ejpam-4029	2	31	expressed	express	VERB
ejpam-4029	2	32	in	in	ADP
ejpam-4029	2	33	terms	term	NOUN
ejpam-4029	2	34	of	of	ADP
ejpam-4029	2	35	the	the	DET
ejpam-4029	2	36	lerch	lerch	PROPN
ejpam-4029	2	37	function	function	PROPN
ejpam-4029	2	38	robert	robert	PROPN
ejpam-4029	2	39	reynolds1,∗	reynolds1,∗	PROPN
ejpam-4029	2	40	,	,	PUNCT
ejpam-4029	2	41	allan	allan	PROPN
ejpam-4029	2	42	stauffer1	stauffer1	PROPN
ejpam-4029	2	43	1	1	NUM
ejpam-4029	2	44	department	department	NOUN
ejpam-4029	2	45	of	of	ADP
ejpam-4029	2	46	mathematics	mathematic	NOUN
ejpam-4029	2	47	and	and	CCONJ
ejpam-4029	2	48	statistics	statistic	NOUN
ejpam-4029	2	49	,	,	PUNCT
ejpam-4029	2	50	faculty	faculty	NOUN
ejpam-4029	2	51	of	of	ADP
ejpam-4029	2	52	science	science	PROPN
ejpam-4029	2	53	,	,	PUNCT
ejpam-4029	2	54	york	york	PROPN
ejpam-4029	2	55	university	university	PROPN
ejpam-4029	2	56	,	,	PUNCT
ejpam-4029	2	57	toronto	toronto	PROPN
ejpam-4029	2	58	,	,	PUNCT
ejpam-4029	2	59	ontario	ontario	PROPN
ejpam-4029	2	60	,	,	PUNCT
ejpam-4029	2	61	canada	canada	PROPN
ejpam-4029	2	62	,	,	PUNCT
ejpam-4029	2	63	m3j1p3	m3j1p3	PROPN
ejpam-4029	2	64	abstract	abstract	NOUN
ejpam-4029	2	65	.	.	PUNCT
ejpam-4029	3	1	in	in	ADP
ejpam-4029	3	2	applied	applied	ADJ
ejpam-4029	3	3	sciences	science	NOUN
ejpam-4029	3	4	it	it	PRON
ejpam-4029	3	5	is	be	AUX
ejpam-4029	3	6	always	always	ADV
ejpam-4029	3	7	useful	useful	ADJ
ejpam-4029	3	8	to	to	PART
ejpam-4029	3	9	improve	improve	VERB
ejpam-4029	3	10	the	the	DET
ejpam-4029	3	11	catalogue	catalogue	NOUN
ejpam-4029	3	12	of	of	ADP
ejpam-4029	3	13	definite	definite	ADJ
ejpam-4029	3	14	integrals	integral	NOUN
ejpam-4029	3	15	available	available	ADJ
ejpam-4029	3	16	in	in	ADP
ejpam-4029	3	17	tables	table	NOUN
ejpam-4029	3	18	.	.	PUNCT
ejpam-4029	4	1	this	this	DET
ejpam-4029	4	2	present	present	ADJ
ejpam-4029	4	3	paper	paper	NOUN
ejpam-4029	4	4	is	be	AUX
ejpam-4029	4	5	a	a	DET
ejpam-4029	4	6	compendium	compendium	NOUN
ejpam-4029	4	7	of	of	ADP
ejpam-4029	4	8	definite	definite	ADJ
ejpam-4029	4	9	integrals	integral	NOUN
ejpam-4029	4	10	involving	involve	VERB
ejpam-4029	4	11	a	a	DET
ejpam-4029	4	12	hyperbolic	hyperbolic	ADJ
ejpam-4029	4	13	quotient	quotient	NOUN
ejpam-4029	4	14	function	function	NOUN
ejpam-4029	4	15	expressed	express	VERB
ejpam-4029	4	16	in	in	ADP
ejpam-4029	4	17	terms	term	NOUN
ejpam-4029	4	18	of	of	ADP
ejpam-4029	4	19	the	the	DET
ejpam-4029	4	20	lerch	lerch	PROPN
ejpam-4029	4	21	function	function	PROPN
ejpam-4029	4	22	.	.	PUNCT
ejpam-4029	5	1	a	a	DET
ejpam-4029	5	2	substantial	substantial	ADJ
ejpam-4029	5	3	portion	portion	NOUN
ejpam-4029	5	4	of	of	ADP
ejpam-4029	5	5	the	the	DET
ejpam-4029	5	6	results	result	NOUN
ejpam-4029	5	7	are	be	AUX
ejpam-4029	5	8	new	new	ADJ
ejpam-4029	5	9	.	.	PUNCT
ejpam-4029	6	1	2020	2020	NUM
ejpam-4029	6	2	mathematics	mathematic	NOUN
ejpam-4029	6	3	subject	subject	NOUN
ejpam-4029	6	4	classifications	classification	NOUN
ejpam-4029	6	5	:	:	PUNCT
ejpam-4029	6	6	30e20	30e20	NUM
ejpam-4029	6	7	,	,	PUNCT
ejpam-4029	6	8	33	33	NUM
ejpam-4029	6	9	-	-	SYM
ejpam-4029	6	10	01	01	NUM
ejpam-4029	6	11	,	,	PUNCT
ejpam-4029	6	12	33	33	NUM
ejpam-4029	6	13	-	-	SYM
ejpam-4029	6	14	03	03	NUM
ejpam-4029	6	15	,	,	PUNCT
ejpam-4029	6	16	33	33	NUM
ejpam-4029	6	17	-	-	PUNCT
ejpam-4029	6	18	04	04	NUM
ejpam-4029	6	19	,	,	PUNCT
ejpam-4029	6	20	33	33	NUM
ejpam-4029	6	21	-	-	PUNCT
ejpam-4029	6	22	33b	33b	NUM
ejpam-4029	6	23	,	,	PUNCT
ejpam-4029	6	24	33e20	33e20	NUM
ejpam-4029	6	25	,	,	PUNCT
ejpam-4029	6	26	33e33	33e33	NUM
ejpam-4029	6	27	key	key	ADJ
ejpam-4029	6	28	words	word	NOUN
ejpam-4029	6	29	and	and	CCONJ
ejpam-4029	6	30	phrases	phrase	NOUN
ejpam-4029	6	31	:	:	PUNCT
ejpam-4029	6	32	entries	entry	NOUN
ejpam-4029	6	33	in	in	ADP
ejpam-4029	6	34	gradshteyn	gradshteyn	PROPN
ejpam-4029	6	35	and	and	CCONJ
ejpam-4029	6	36	ryzhik	ryzhik	ADJ
ejpam-4029	6	37	,	,	PUNCT
ejpam-4029	6	38	mellin	mellin	NOUN
ejpam-4029	6	39	transform	transform	NOUN
ejpam-4029	6	40	,	,	PUNCT
ejpam-4029	6	41	hyperbolic	hyperbolic	ADJ
ejpam-4029	6	42	function	function	NOUN
ejpam-4029	6	43	,	,	PUNCT
ejpam-4029	6	44	definite	definite	ADJ
ejpam-4029	6	45	integral	integral	ADJ
ejpam-4029	6	46	,	,	PUNCT
ejpam-4029	6	47	catalan	catalan	NOUN
ejpam-4029	6	48	’s	’s	PART
ejpam-4029	6	49	constant	constant	ADJ
ejpam-4029	6	50	1	1	NUM
ejpam-4029	6	51	.	.	PUNCT
ejpam-4029	6	52	significance	significance	NOUN
ejpam-4029	6	53	statement	statement	NOUN
ejpam-4029	6	54	the	the	DET
ejpam-4029	6	55	works	work	NOUN
ejpam-4029	6	56	of	of	ADP
ejpam-4029	6	57	bonderson	bonderson	NOUN
ejpam-4029	6	58	and	and	CCONJ
ejpam-4029	6	59	gorda	gorda	NOUN
ejpam-4029	7	1	[	[	X
ejpam-4029	7	2	2	2	NUM
ejpam-4029	7	3	,	,	PUNCT
ejpam-4029	7	4	4	4	NUM
ejpam-4029	7	5	]	]	PUNCT
ejpam-4029	7	6	are	be	AUX
ejpam-4029	7	7	concerned	concern	VERB
ejpam-4029	7	8	with	with	ADP
ejpam-4029	7	9	some	some	DET
ejpam-4029	7	10	very	very	ADV
ejpam-4029	7	11	interesting	interesting	ADJ
ejpam-4029	7	12	topics	topic	NOUN
ejpam-4029	7	13	in	in	ADP
ejpam-4029	7	14	particle	particle	NOUN
ejpam-4029	7	15	and	and	CCONJ
ejpam-4029	7	16	plasma	plasma	NOUN
ejpam-4029	7	17	physics	physics	NOUN
ejpam-4029	7	18	.	.	PUNCT
ejpam-4029	8	1	within	within	ADP
ejpam-4029	8	2	these	these	DET
ejpam-4029	8	3	articles	article	NOUN
ejpam-4029	8	4	the	the	DET
ejpam-4029	8	5	authors	author	NOUN
ejpam-4029	8	6	used	use	VERB
ejpam-4029	8	7	some	some	DET
ejpam-4029	8	8	mathematical	mathematical	ADJ
ejpam-4029	8	9	formula	formula	NOUN
ejpam-4029	8	10	from	from	ADP
ejpam-4029	8	11	the	the	DET
ejpam-4029	8	12	book	book	NOUN
ejpam-4029	8	13	of	of	ADP
ejpam-4029	8	14	gradshteyn	gradshteyn	PROPN
ejpam-4029	8	15	and	and	CCONJ
ejpam-4029	8	16	ryzhik	ryzhik	ADJ
ejpam-4029	8	17	[	[	X
ejpam-4029	8	18	8	8	NUM
ejpam-4029	8	19	]	]	PUNCT
ejpam-4029	8	20	.	.	PUNCT
ejpam-4029	9	1	in	in	ADP
ejpam-4029	9	2	this	this	DET
ejpam-4029	9	3	paper	paper	NOUN
ejpam-4029	9	4	the	the	DET
ejpam-4029	9	5	authors	author	NOUN
ejpam-4029	9	6	provided	provide	VERB
ejpam-4029	9	7	a	a	DET
ejpam-4029	9	8	formal	formal	ADJ
ejpam-4029	9	9	derivation	derivation	NOUN
ejpam-4029	9	10	for	for	ADP
ejpam-4029	9	11	the	the	DET
ejpam-4029	9	12	formulae	formulae	NOUN
ejpam-4029	9	13	used	use	VERB
ejpam-4029	9	14	in	in	ADP
ejpam-4029	9	15	[	[	X
ejpam-4029	9	16	2	2	NUM
ejpam-4029	9	17	,	,	PUNCT
ejpam-4029	9	18	4	4	NUM
ejpam-4029	9	19	]	]	PUNCT
ejpam-4029	9	20	along	along	ADP
ejpam-4029	9	21	with	with	ADP
ejpam-4029	9	22	deriving	derive	VERB
ejpam-4029	9	23	generalized	generalized	ADJ
ejpam-4029	9	24	forms	form	NOUN
ejpam-4029	9	25	for	for	ADP
ejpam-4029	9	26	some	some	DET
ejpam-4029	9	27	known	know	VERB
ejpam-4029	9	28	and	and	CCONJ
ejpam-4029	9	29	new	new	ADJ
ejpam-4029	9	30	integrals	integral	NOUN
ejpam-4029	9	31	.	.	PUNCT
ejpam-4029	10	1	the	the	DET
ejpam-4029	10	2	definite	definite	ADJ
ejpam-4029	10	3	integrals	integral	NOUN
ejpam-4029	10	4	derived	derive	VERB
ejpam-4029	10	5	in	in	ADP
ejpam-4029	10	6	this	this	DET
ejpam-4029	10	7	work	work	NOUN
ejpam-4029	10	8	are	be	AUX
ejpam-4029	10	9	useful	useful	ADJ
ejpam-4029	10	10	in	in	ADP
ejpam-4029	10	11	applications	application	NOUN
ejpam-4029	10	12	,	,	PUNCT
ejpam-4029	10	13	in	in	ADP
ejpam-4029	10	14	particular	particular	ADJ
ejpam-4029	10	15	in	in	ADP
ejpam-4029	10	16	perturbation	perturbation	NOUN
ejpam-4029	10	17	analysis	analysis	NOUN
ejpam-4029	10	18	of	of	ADP
ejpam-4029	10	19	solitons	soliton	NOUN
ejpam-4029	10	20	and	and	CCONJ
ejpam-4029	10	21	plasma	plasma	NOUN
ejpam-4029	10	22	physics	physics	NOUN
ejpam-4029	10	23	[	[	X
ejpam-4029	10	24	1	1	NUM
ejpam-4029	10	25	,	,	PUNCT
ejpam-4029	10	26	3	3	NUM
ejpam-4029	10	27	,	,	PUNCT
ejpam-4029	10	28	5	5	NUM
ejpam-4029	10	29	,	,	PUNCT
ejpam-4029	10	30	6	6	NUM
ejpam-4029	10	31	,	,	PUNCT
ejpam-4029	10	32	9	9	NUM
ejpam-4029	10	33	,	,	PUNCT
ejpam-4029	10	34	14	14	NUM
ejpam-4029	10	35	]	]	PUNCT
ejpam-4029	10	36	.	.	PUNCT
ejpam-4029	11	1	the	the	DET
ejpam-4029	11	2	derived	derive	VERB
ejpam-4029	11	3	integral	integral	ADJ
ejpam-4029	11	4	formula	formula	NOUN
ejpam-4029	11	5	in	in	ADP
ejpam-4029	11	6	this	this	DET
ejpam-4029	11	7	present	present	ADJ
ejpam-4029	11	8	work	work	NOUN
ejpam-4029	11	9	is	be	AUX
ejpam-4029	11	10	expressed	express	VERB
ejpam-4029	11	11	in	in	ADP
ejpam-4029	11	12	terms	term	NOUN
ejpam-4029	11	13	of	of	ADP
ejpam-4029	11	14	lerch	lerch	PROPN
ejpam-4029	11	15	function	function	PROPN
ejpam-4029	11	16	.	.	PUNCT
ejpam-4029	12	1	the	the	DET
ejpam-4029	12	2	lerch	lerch	PROPN
ejpam-4029	12	3	function	function	PROPN
ejpam-4029	12	4	being	be	AUX
ejpam-4029	12	5	a	a	DET
ejpam-4029	12	6	special	special	ADJ
ejpam-4029	12	7	function	function	NOUN
ejpam-4029	12	8	has	have	VERB
ejpam-4029	12	9	the	the	DET
ejpam-4029	12	10	fundamental	fundamental	ADJ
ejpam-4029	12	11	property	property	NOUN
ejpam-4029	12	12	of	of	ADP
ejpam-4029	12	13	analytic	analytic	ADJ
ejpam-4029	12	14	continuation	continuation	NOUN
ejpam-4029	12	15	,	,	PUNCT
ejpam-4029	12	16	which	which	PRON
ejpam-4029	12	17	enables	enable	VERB
ejpam-4029	12	18	us	we	PRON
ejpam-4029	12	19	to	to	PART
ejpam-4029	12	20	widen	widen	VERB
ejpam-4029	12	21	the	the	DET
ejpam-4029	12	22	range	range	NOUN
ejpam-4029	12	23	of	of	ADP
ejpam-4029	12	24	evaluation	evaluation	NOUN
ejpam-4029	12	25	for	for	ADP
ejpam-4029	12	26	the	the	DET
ejpam-4029	12	27	parameters	parameter	NOUN
ejpam-4029	12	28	involved	involve	VERB
ejpam-4029	12	29	.	.	PUNCT
ejpam-4029	13	1	we	we	PRON
ejpam-4029	13	2	provide	provide	VERB
ejpam-4029	13	3	formal	formal	ADJ
ejpam-4029	13	4	derivations	derivation	NOUN
ejpam-4029	13	5	of	of	ADP
ejpam-4029	13	6	some	some	DET
ejpam-4029	13	7	formula	formula	NOUN
ejpam-4029	13	8	in	in	ADP
ejpam-4029	13	9	the	the	DET
ejpam-4029	13	10	books	book	NOUN
ejpam-4029	13	11	of	of	ADP
ejpam-4029	13	12	[	[	X
ejpam-4029	13	13	8	8	NUM
ejpam-4029	13	14	]	]	PUNCT
ejpam-4029	13	15	and	and	CCONJ
ejpam-4029	13	16	[	[	X
ejpam-4029	13	17	12	12	NUM
ejpam-4029	13	18	]	]	PUNCT
ejpam-4029	13	19	not	not	PART
ejpam-4029	13	20	previously	previously	ADV
ejpam-4029	13	21	published	publish	VERB
ejpam-4029	13	22	to	to	ADP
ejpam-4029	13	23	the	the	DET
ejpam-4029	13	24	best	good	ADJ
ejpam-4029	13	25	of	of	ADP
ejpam-4029	13	26	our	our	PRON
ejpam-4029	13	27	knowledge	knowledge	NOUN
ejpam-4029	13	28	.	.	PUNCT
ejpam-4029	14	1	∗corresponding	∗corresponde	VERB
ejpam-4029	14	2	author	author	NOUN
ejpam-4029	14	3	.	.	PUNCT
ejpam-4029	15	1	doi	doi	NOUN
ejpam-4029	15	2	:	:	PUNCT
ejpam-4029	15	3	https://doi.org/10.29020/nybg.ejpam.v14i4.4029	https://doi.org/10.29020/nybg.ejpam.v14i4.4029	PROPN
ejpam-4029	15	4	email	email	NOUN
ejpam-4029	15	5	addresses	address	NOUN
ejpam-4029	15	6	:	:	PUNCT
ejpam-4029	16	1	milver@my.yorku.ca	milver@my.yorku.ca	NOUN
ejpam-4029	16	2	(	(	PUNCT
ejpam-4029	16	3	r.	r.	PROPN
ejpam-4029	16	4	reynolds	reynolds	PROPN
ejpam-4029	16	5	)	)	PUNCT
ejpam-4029	16	6	,	,	PUNCT
ejpam-4029	16	7	stauffer@yorku.ca	stauffer@yorku.ca	NOUN
ejpam-4029	16	8	(	(	PUNCT
ejpam-4029	16	9	a.	a.	NOUN
ejpam-4029	16	10	stauffer	stauffer	PROPN
ejpam-4029	16	11	)	)	PUNCT
ejpam-4029	16	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4029	17	1	1132	1132	NUM
ejpam-4029	18	1	©	©	PROPN
ejpam-4029	18	2	2021	2021	NUM
ejpam-4029	18	3	ejpam	ejpam	VERB
ejpam-4029	18	4	all	all	DET
ejpam-4029	18	5	rights	right	NOUN
ejpam-4029	18	6	reserved	reserve	VERB
ejpam-4029	18	7	.	.	PUNCT
ejpam-4029	19	1	r.	r.	PROPN
ejpam-4029	19	2	reynolds	reynolds	PROPN
ejpam-4029	19	3	,	,	PUNCT
ejpam-4029	19	4	a.	a.	PROPN
ejpam-4029	19	5	stauffer	stauffer	PROPN
ejpam-4029	19	6	/	/	SYM
ejpam-4029	19	7	eur	eur	PROPN
ejpam-4029	19	8	.	.	PUNCT
ejpam-4029	20	1	j.	j.	PROPN
ejpam-4029	20	2	pure	pure	PROPN
ejpam-4029	20	3	appl	appl	PROPN
ejpam-4029	20	4	.	.	PROPN
ejpam-4029	20	5	math	math	PROPN
ejpam-4029	20	6	,	,	PUNCT
ejpam-4029	20	7	14	14	NUM
ejpam-4029	20	8	(	(	PUNCT
ejpam-4029	20	9	4	4	NUM
ejpam-4029	20	10	)	)	PUNCT
ejpam-4029	20	11	(	(	PUNCT
ejpam-4029	20	12	2021	2021	NUM
ejpam-4029	20	13	)	)	PUNCT
ejpam-4029	20	14	,	,	PUNCT
ejpam-4029	20	15	1132	1132	NUM
ejpam-4029	20	16	-	-	SYM
ejpam-4029	20	17	1147	1147	NUM
ejpam-4029	20	18	1133	1133	NUM
ejpam-4029	20	19	2	2	NUM
ejpam-4029	20	20	.	.	PUNCT
ejpam-4029	20	21	introduction	introduction	NOUN
ejpam-4029	20	22	the	the	DET
ejpam-4029	20	23	definite	definite	ADJ
ejpam-4029	20	24	integral	integral	ADJ
ejpam-4029	20	25	derived	derived	NOUN
ejpam-4029	20	26	in	in	ADP
ejpam-4029	20	27	this	this	DET
ejpam-4029	20	28	manuscript	manuscript	NOUN
ejpam-4029	20	29	is	be	AUX
ejpam-4029	20	30	given	give	VERB
ejpam-4029	20	31	by∫	by∫	PROPN
ejpam-4029	20	32	∞	∞	PROPN
ejpam-4029	20	33	0	0	PUNCT
ejpam-4029	21	1	csch2(cx	csch2(cx	NOUN
ejpam-4029	21	2	)	)	PUNCT
ejpam-4029	21	3	(	(	PUNCT
ejpam-4029	21	4	e−2mx(log(a)−	e−2mx(log(a)−	ADV
ejpam-4029	22	1	2x)k	2x)k	NUM
ejpam-4029	22	2	+	+	NUM
ejpam-4029	22	3	e2mx(log(a	e2mx(log(a	NOUN
ejpam-4029	22	4	)	)	PUNCT
ejpam-4029	23	1	+	+	CCONJ
ejpam-4029	23	2	2x)k	2x)k	NUM
ejpam-4029	23	3	−	−	NOUN
ejpam-4029	23	4	2	2	NUM
ejpam-4029	23	5	logk(a	logk(a	NOUN
ejpam-4029	23	6	)	)	PUNCT
ejpam-4029	23	7	)	)	PUNCT
ejpam-4029	24	1	dx	dx	PROPN
ejpam-4029	24	2	(	(	PUNCT
ejpam-4029	24	3	1	1	NUM
ejpam-4029	24	4	)	)	PUNCT
ejpam-4029	24	5	where	where	SCONJ
ejpam-4029	24	6	the	the	DET
ejpam-4029	24	7	parameters	parameter	NOUN
ejpam-4029	24	8	k	k	PROPN
ejpam-4029	24	9	,	,	PUNCT
ejpam-4029	24	10	a	a	PRON
ejpam-4029	24	11	are	be	AUX
ejpam-4029	24	12	general	general	ADJ
ejpam-4029	24	13	complex	complex	ADJ
ejpam-4029	24	14	numbers	number	NOUN
ejpam-4029	24	15	and	and	CCONJ
ejpam-4029	24	16	|re(c)|	|re(c)|	ADJ
ejpam-4029	24	17	>	>	X
ejpam-4029	24	18	m.	m.	NOUN
ejpam-4029	24	19	the	the	DET
ejpam-4029	24	20	derivation	derivation	NOUN
ejpam-4029	24	21	of	of	ADP
ejpam-4029	24	22	the	the	DET
ejpam-4029	24	23	definite	definite	ADJ
ejpam-4029	24	24	integral	integral	NOUN
ejpam-4029	24	25	follows	follow	VERB
ejpam-4029	24	26	the	the	DET
ejpam-4029	24	27	method	method	NOUN
ejpam-4029	24	28	used	use	VERB
ejpam-4029	24	29	by	by	ADP
ejpam-4029	24	30	us	we	PRON
ejpam-4029	24	31	in	in	ADP
ejpam-4029	24	32	[	[	X
ejpam-4029	24	33	13	13	NUM
ejpam-4029	24	34	]	]	PUNCT
ejpam-4029	24	35	which	which	PRON
ejpam-4029	24	36	involves	involve	VERB
ejpam-4029	24	37	cauchy	cauchy	PROPN
ejpam-4029	24	38	’s	’s	PART
ejpam-4029	24	39	integral	integral	ADJ
ejpam-4029	24	40	formula	formula	NOUN
ejpam-4029	24	41	.	.	PUNCT
ejpam-4029	25	1	the	the	DET
ejpam-4029	25	2	generalized	generalized	ADJ
ejpam-4029	25	3	cauchy	cauchy	PROPN
ejpam-4029	25	4	’s	’s	PART
ejpam-4029	25	5	integral	integral	ADJ
ejpam-4029	25	6	formula	formula	NOUN
ejpam-4029	25	7	is	be	AUX
ejpam-4029	25	8	given	give	VERB
ejpam-4029	25	9	by	by	ADP
ejpam-4029	25	10	yk	yk	PROPN
ejpam-4029	25	11	γ(k	γ(k	PROPN
ejpam-4029	25	12	+	+	CCONJ
ejpam-4029	25	13	1	1	X
ejpam-4029	25	14	)	)	PUNCT
ejpam-4029	25	15	=	=	SYM
ejpam-4029	25	16	1	1	NUM
ejpam-4029	25	17	2πi	2πi	ADJ
ejpam-4029	25	18	∫	∫	PROPN
ejpam-4029	25	19	c	c	PROPN
ejpam-4029	25	20	ewy	ewy	PROPN
ejpam-4029	25	21	wk+1	wk+1	PROPN
ejpam-4029	25	22	dw	dw	PROPN
ejpam-4029	25	23	.	.	PUNCT
ejpam-4029	26	1	(	(	PUNCT
ejpam-4029	26	2	2	2	X
ejpam-4029	26	3	)	)	PUNCT
ejpam-4029	26	4	where	where	SCONJ
ejpam-4029	26	5	c	c	NOUN
ejpam-4029	26	6	is	be	AUX
ejpam-4029	26	7	in	in	ADP
ejpam-4029	26	8	general	general	ADJ
ejpam-4029	26	9	an	an	DET
ejpam-4029	26	10	open	open	ADJ
ejpam-4029	26	11	contour	contour	NOUN
ejpam-4029	26	12	in	in	ADP
ejpam-4029	26	13	the	the	DET
ejpam-4029	26	14	complex	complex	ADJ
ejpam-4029	26	15	plane	plane	NOUN
ejpam-4029	26	16	where	where	SCONJ
ejpam-4029	26	17	the	the	DET
ejpam-4029	26	18	theorem	theorem	NOUN
ejpam-4029	26	19	in	in	ADP
ejpam-4029	26	20	[	[	X
ejpam-4029	26	21	13	13	NUM
ejpam-4029	26	22	]	]	PUNCT
ejpam-4029	26	23	gives	give	VERB
ejpam-4029	26	24	the	the	DET
ejpam-4029	26	25	result	result	NOUN
ejpam-4029	26	26	.	.	PUNCT
ejpam-4029	27	1	this	this	DET
ejpam-4029	27	2	method	method	NOUN
ejpam-4029	27	3	involves	involve	VERB
ejpam-4029	27	4	using	use	VERB
ejpam-4029	27	5	a	a	DET
ejpam-4029	27	6	form	form	NOUN
ejpam-4029	27	7	of	of	ADP
ejpam-4029	27	8	equation	equation	NOUN
ejpam-4029	27	9	(	(	PUNCT
ejpam-4029	27	10	2	2	NUM
ejpam-4029	27	11	)	)	PUNCT
ejpam-4029	27	12	then	then	ADV
ejpam-4029	27	13	multiply	multiply	VERB
ejpam-4029	27	14	both	both	DET
ejpam-4029	27	15	sides	side	NOUN
ejpam-4029	27	16	by	by	ADP
ejpam-4029	27	17	a	a	DET
ejpam-4029	27	18	different	different	ADJ
ejpam-4029	27	19	function	function	NOUN
ejpam-4029	27	20	,	,	PUNCT
ejpam-4029	27	21	then	then	ADV
ejpam-4029	27	22	take	take	VERB
ejpam-4029	27	23	a	a	DET
ejpam-4029	27	24	definite	definite	ADJ
ejpam-4029	27	25	integral	integral	NOUN
ejpam-4029	27	26	of	of	ADP
ejpam-4029	27	27	both	both	DET
ejpam-4029	27	28	sides	side	NOUN
ejpam-4029	27	29	.	.	PUNCT
ejpam-4029	28	1	this	this	PRON
ejpam-4029	28	2	yields	yield	VERB
ejpam-4029	28	3	a	a	DET
ejpam-4029	28	4	definite	definite	ADJ
ejpam-4029	28	5	integral	integral	ADJ
ejpam-4029	28	6	in	in	ADP
ejpam-4029	28	7	terms	term	NOUN
ejpam-4029	28	8	of	of	ADP
ejpam-4029	28	9	a	a	DET
ejpam-4029	28	10	contour	contour	NOUN
ejpam-4029	28	11	integral	integral	NOUN
ejpam-4029	28	12	.	.	PUNCT
ejpam-4029	29	1	a	a	DET
ejpam-4029	29	2	second	second	ADJ
ejpam-4029	29	3	contour	contour	NOUN
ejpam-4029	29	4	integral	integral	NOUN
ejpam-4029	29	5	is	be	AUX
ejpam-4029	29	6	derived	derive	VERB
ejpam-4029	29	7	by	by	ADP
ejpam-4029	29	8	multiplying	multiply	VERB
ejpam-4029	29	9	equation	equation	NOUN
ejpam-4029	29	10	(	(	PUNCT
ejpam-4029	29	11	2	2	NUM
ejpam-4029	29	12	)	)	PUNCT
ejpam-4029	29	13	by	by	ADP
ejpam-4029	29	14	a	a	DET
ejpam-4029	29	15	function	function	NOUN
ejpam-4029	29	16	and	and	CCONJ
ejpam-4029	29	17	performing	perform	VERB
ejpam-4029	29	18	some	some	DET
ejpam-4029	29	19	substitutions	substitution	NOUN
ejpam-4029	29	20	so	so	SCONJ
ejpam-4029	29	21	that	that	SCONJ
ejpam-4029	29	22	the	the	DET
ejpam-4029	29	23	contour	contour	NOUN
ejpam-4029	29	24	integrals	integral	NOUN
ejpam-4029	29	25	are	be	AUX
ejpam-4029	29	26	the	the	DET
ejpam-4029	29	27	same	same	ADJ
ejpam-4029	29	28	.	.	PUNCT
ejpam-4029	30	1	3	3	X
ejpam-4029	30	2	.	.	X
ejpam-4029	30	3	definite	definite	ADJ
ejpam-4029	30	4	integral	integral	ADJ
ejpam-4029	30	5	of	of	ADP
ejpam-4029	30	6	the	the	DET
ejpam-4029	30	7	contour	contour	NOUN
ejpam-4029	30	8	integral	integral	NOUN
ejpam-4029	30	9	we	we	PRON
ejpam-4029	30	10	use	use	VERB
ejpam-4029	30	11	the	the	DET
ejpam-4029	30	12	method	method	NOUN
ejpam-4029	30	13	in	in	ADP
ejpam-4029	30	14	[	[	X
ejpam-4029	30	15	13	13	NUM
ejpam-4029	30	16	]	]	PUNCT
ejpam-4029	30	17	.	.	PUNCT
ejpam-4029	31	1	we	we	PRON
ejpam-4029	31	2	will	will	AUX
ejpam-4029	31	3	derive	derive	VERB
ejpam-4029	31	4	three	three	NUM
ejpam-4029	31	5	contour	contour	ADJ
ejpam-4029	31	6	integral	integral	ADJ
ejpam-4029	31	7	representations	representation	NOUN
ejpam-4029	31	8	and	and	CCONJ
ejpam-4029	31	9	add	add	VERB
ejpam-4029	31	10	them	they	PRON
ejpam-4029	31	11	such	such	ADJ
ejpam-4029	31	12	that	that	SCONJ
ejpam-4029	31	13	we	we	PRON
ejpam-4029	31	14	get	get	VERB
ejpam-4029	31	15	an	an	DET
ejpam-4029	31	16	equivalent	equivalent	ADJ
ejpam-4029	31	17	form	form	NOUN
ejpam-4029	31	18	for	for	ADP
ejpam-4029	31	19	the	the	DET
ejpam-4029	31	20	infinite	infinite	ADJ
ejpam-4029	31	21	sum	sum	NOUN
ejpam-4029	31	22	.	.	PUNCT
ejpam-4029	32	1	deriving	derive	VERB
ejpam-4029	32	2	the	the	DET
ejpam-4029	32	3	first	first	ADJ
ejpam-4029	32	4	contour	contour	NOUN
ejpam-4029	32	5	we	we	PRON
ejpam-4029	32	6	use	use	VERB
ejpam-4029	32	7	equation	equation	NOUN
ejpam-4029	32	8	(	(	PUNCT
ejpam-4029	32	9	2	2	NUM
ejpam-4029	32	10	)	)	PUNCT
ejpam-4029	32	11	and	and	CCONJ
ejpam-4029	32	12	replace	replace	VERB
ejpam-4029	32	13	y	y	PROPN
ejpam-4029	32	14	by	by	ADP
ejpam-4029	32	15	log(a	log(a	PROPN
ejpam-4029	32	16	)	)	PUNCT
ejpam-4029	32	17	and	and	CCONJ
ejpam-4029	32	18	multiply	multiply	ADV
ejpam-4029	32	19	by	by	ADP
ejpam-4029	32	20	−1	−1	NOUN
ejpam-4029	32	21	2csch	2csch	NUM
ejpam-4029	32	22	2(cx	2(cx	NUM
ejpam-4029	32	23	)	)	PUNCT
ejpam-4029	32	24	to	to	PART
ejpam-4029	32	25	get	get	VERB
ejpam-4029	32	26	−	−	PROPN
ejpam-4029	32	27	logk(a)csch2(cx	logk(a)csch2(cx	NOUN
ejpam-4029	32	28	)	)	PUNCT
ejpam-4029	32	29	2γ(k	2γ(k	NUM
ejpam-4029	33	1	+	+	CCONJ
ejpam-4029	33	2	1	1	X
ejpam-4029	33	3	)	)	PUNCT
ejpam-4029	33	4	=	=	SYM
ejpam-4029	34	1	−	−	PROPN
ejpam-4029	34	2	1	1	NUM
ejpam-4029	34	3	4πi	4πi	NOUN
ejpam-4029	34	4	∫	∫	PROPN
ejpam-4029	34	5	c	c	NOUN
ejpam-4029	34	6	aww−k−1csch2(cx)dw	aww−k−1csch2(cx)dw	NOUN
ejpam-4029	34	7	(	(	PUNCT
ejpam-4029	34	8	3	3	X
ejpam-4029	34	9	)	)	PUNCT
ejpam-4029	34	10	deriving	derive	VERB
ejpam-4029	34	11	the	the	DET
ejpam-4029	34	12	second	second	ADJ
ejpam-4029	34	13	contour	contour	NOUN
ejpam-4029	34	14	we	we	PRON
ejpam-4029	34	15	use	use	VERB
ejpam-4029	34	16	equation	equation	NOUN
ejpam-4029	34	17	(	(	PUNCT
ejpam-4029	34	18	2	2	NUM
ejpam-4029	34	19	)	)	PUNCT
ejpam-4029	34	20	and	and	CCONJ
ejpam-4029	34	21	replace	replace	VERB
ejpam-4029	34	22	y	y	PROPN
ejpam-4029	34	23	by	by	ADP
ejpam-4029	34	24	log(a)−2x	log(a)−2x	NOUN
ejpam-4029	34	25	and	and	CCONJ
ejpam-4029	34	26	multiply	multiply	ADV
ejpam-4029	34	27	by	by	ADP
ejpam-4029	34	28	1	1	NUM
ejpam-4029	34	29	8e	8e	NUM
ejpam-4029	34	30	−2mxcsch2(cx	−2mxcsch2(cx	NUM
ejpam-4029	34	31	)	)	PUNCT
ejpam-4029	34	32	to	to	PART
ejpam-4029	34	33	get	get	VERB
ejpam-4029	34	34	e−2mxcsch2(cx)(log(a)−	e−2mxcsch2(cx)(log(a)−	ADJ
ejpam-4029	34	35	2x)k	2x)k	NUM
ejpam-4029	34	36	8γ(k	8γ(k	NOUN
ejpam-4029	34	37	+	+	CCONJ
ejpam-4029	34	38	1	1	X
ejpam-4029	34	39	)	)	PUNCT
ejpam-4029	34	40	=	=	SYM
ejpam-4029	34	41	1	1	NUM
ejpam-4029	34	42	16πi	16πi	NOUN
ejpam-4029	34	43	∫	∫	PROPN
ejpam-4029	34	44	c	c	PROPN
ejpam-4029	34	45	aww−k−1csch2(cx)e−2x(m+w)dw	aww−k−1csch2(cx)e−2x(m+w)dw	PROPN
ejpam-4029	34	46	(	(	PUNCT
ejpam-4029	34	47	4	4	X
ejpam-4029	34	48	)	)	PUNCT
ejpam-4029	34	49	deriving	derive	VERB
ejpam-4029	34	50	the	the	DET
ejpam-4029	34	51	third	third	ADJ
ejpam-4029	34	52	contour	contour	NOUN
ejpam-4029	34	53	we	we	PRON
ejpam-4029	34	54	use	use	VERB
ejpam-4029	34	55	equation	equation	NOUN
ejpam-4029	34	56	(	(	PUNCT
ejpam-4029	34	57	2	2	NUM
ejpam-4029	34	58	)	)	PUNCT
ejpam-4029	34	59	and	and	CCONJ
ejpam-4029	34	60	replace	replace	VERB
ejpam-4029	34	61	y	y	PROPN
ejpam-4029	34	62	by	by	ADP
ejpam-4029	34	63	log(a	log(a	PROPN
ejpam-4029	34	64	)	)	PUNCT
ejpam-4029	34	65	+	+	NUM
ejpam-4029	34	66	2x	2x	NUM
ejpam-4029	34	67	and	and	CCONJ
ejpam-4029	34	68	multiply	multiply	ADV
ejpam-4029	34	69	by	by	ADP
ejpam-4029	34	70	1	1	NUM
ejpam-4029	34	71	4e	4e	NOUN
ejpam-4029	34	72	2mxcsch2(cx	2mxcsch2(cx	NUM
ejpam-4029	34	73	)	)	PUNCT
ejpam-4029	34	74	to	to	PART
ejpam-4029	34	75	get	get	VERB
ejpam-4029	34	76	e2mxcsch2(cx)(log(a	e2mxcsch2(cx)(log(a	NOUN
ejpam-4029	34	77	)	)	PUNCT
ejpam-4029	35	1	+	+	NOUN
ejpam-4029	35	2	2x)k	2x)k	NUM
ejpam-4029	35	3	4γ(k	4γ(k	NOUN
ejpam-4029	36	1	+	+	CCONJ
ejpam-4029	37	1	1	1	X
ejpam-4029	37	2	)	)	PUNCT
ejpam-4029	37	3	=	=	SYM
ejpam-4029	37	4	1	1	NUM
ejpam-4029	37	5	8πi	8πi	ADJ
ejpam-4029	37	6	∫	∫	PROPN
ejpam-4029	37	7	c	c	PROPN
ejpam-4029	37	8	aww−k−1csch2(cx)e2x(m+w)dw	aww−k−1csch2(cx)e2x(m+w)dw	PROPN
ejpam-4029	37	9	(	(	PUNCT
ejpam-4029	37	10	5	5	NUM
ejpam-4029	37	11	)	)	PUNCT
ejpam-4029	37	12	next	next	ADV
ejpam-4029	37	13	we	we	PRON
ejpam-4029	37	14	add	add	VERB
ejpam-4029	37	15	equations	equation	NOUN
ejpam-4029	37	16	(	(	PUNCT
ejpam-4029	37	17	3	3	NUM
ejpam-4029	37	18	)	)	PUNCT
ejpam-4029	37	19	,	,	PUNCT
ejpam-4029	37	20	(	(	PUNCT
ejpam-4029	37	21	4	4	NUM
ejpam-4029	37	22	)	)	PUNCT
ejpam-4029	37	23	and	and	CCONJ
ejpam-4029	37	24	(	(	PUNCT
ejpam-4029	37	25	5	5	NUM
ejpam-4029	37	26	)	)	PUNCT
ejpam-4029	37	27	then	then	ADV
ejpam-4029	37	28	take	take	VERB
ejpam-4029	37	29	the	the	DET
ejpam-4029	37	30	infinite	infinite	ADJ
ejpam-4029	37	31	integral	integral	ADJ
ejpam-4029	37	32	over	over	ADP
ejpam-4029	37	33	x	x	PUNCT
ejpam-4029	37	34	∈	∈	PROPN
ejpam-4029	38	1	[	[	X
ejpam-4029	38	2	0,∞	0,∞	NOUN
ejpam-4029	38	3	)	)	PUNCT
ejpam-4029	38	4	to	to	PART
ejpam-4029	38	5	get	get	VERB
ejpam-4029	38	6	1	1	NUM
ejpam-4029	38	7	γ(k	γ(k	NOUN
ejpam-4029	38	8	+	+	CCONJ
ejpam-4029	38	9	1	1	X
ejpam-4029	38	10	)	)	PUNCT
ejpam-4029	38	11	∫	∫	PROPN
ejpam-4029	39	1	∞	∞	PROPN
ejpam-4029	39	2	0	0	NUM
ejpam-4029	39	3	csch2(cx	csch2(cx	NOUN
ejpam-4029	39	4	)	)	PUNCT
ejpam-4029	39	5	(	(	PUNCT
ejpam-4029	39	6	e−2mx(log(a)−	e−2mx(log(a)−	ADV
ejpam-4029	39	7	2x)k	2x)k	NUM
ejpam-4029	39	8	+	+	NUM
ejpam-4029	39	9	e2mx(log(a	e2mx(log(a	NOUN
ejpam-4029	39	10	)	)	PUNCT
ejpam-4029	40	1	+	+	CCONJ
ejpam-4029	40	2	2x)k	2x)k	NUM
ejpam-4029	40	3	−	−	NOUN
ejpam-4029	40	4	2	2	NUM
ejpam-4029	40	5	logk(a	logk(a	NOUN
ejpam-4029	40	6	)	)	PUNCT
ejpam-4029	40	7	)	)	PUNCT
ejpam-4029	41	1	dx	dx	PROPN
ejpam-4029	41	2	r.	r.	PROPN
ejpam-4029	41	3	reynolds	reynolds	PROPN
ejpam-4029	41	4	,	,	PUNCT
ejpam-4029	41	5	a.	a.	PROPN
ejpam-4029	41	6	stauffer	stauffer	PROPN
ejpam-4029	41	7	/	/	SYM
ejpam-4029	41	8	eur	eur	PROPN
ejpam-4029	41	9	.	.	PUNCT
ejpam-4029	42	1	j.	j.	PROPN
ejpam-4029	42	2	pure	pure	PROPN
ejpam-4029	42	3	appl	appl	PROPN
ejpam-4029	42	4	.	.	PROPN
ejpam-4029	42	5	math	math	PROPN
ejpam-4029	42	6	,	,	PUNCT
ejpam-4029	42	7	14	14	NUM
ejpam-4029	42	8	(	(	PUNCT
ejpam-4029	42	9	4	4	NUM
ejpam-4029	42	10	)	)	PUNCT
ejpam-4029	42	11	(	(	PUNCT
ejpam-4029	42	12	2021	2021	NUM
ejpam-4029	42	13	)	)	PUNCT
ejpam-4029	42	14	,	,	PUNCT
ejpam-4029	42	15	1132	1132	NUM
ejpam-4029	42	16	-	-	SYM
ejpam-4029	42	17	1147	1147	NUM
ejpam-4029	42	18	1134	1134	NUM
ejpam-4029	42	19	=	=	SYM
ejpam-4029	42	20	1	1	NUM
ejpam-4029	42	21	2πi	2πi	NOUN
ejpam-4029	42	22	∫	∫	PROPN
ejpam-4029	43	1	∞	∞	NUM
ejpam-4029	43	2	0	0	NUM
ejpam-4029	43	3	∫	∫	PROPN
ejpam-4029	43	4	c	c	PROPN
ejpam-4029	43	5	aww−k−1csch2(cx	aww−k−1csch2(cx	PROPN
ejpam-4029	43	6	)	)	PUNCT
ejpam-4029	43	7	sinh2(x(m+	sinh2(x(m+	NOUN
ejpam-4029	43	8	w))dwdx	w))dwdx	NOUN
ejpam-4029	43	9	=	=	SYM
ejpam-4029	43	10	1	1	NUM
ejpam-4029	43	11	2πi	2πi	NOUN
ejpam-4029	43	12	∫	∫	PROPN
ejpam-4029	44	1	c	c	PROPN
ejpam-4029	44	2	∫	∫	PROPN
ejpam-4029	45	1	∞	∞	PROPN
ejpam-4029	45	2	0	0	NUM
ejpam-4029	45	3	aww−k−1csch2(cx	aww−k−1csch2(cx	PROPN
ejpam-4029	45	4	)	)	PUNCT
ejpam-4029	45	5	sinh2(x(m+	sinh2(x(m+	NOUN
ejpam-4029	45	6	w))dxdw	w))dxdw	NOUN
ejpam-4029	45	7	=	=	SYM
ejpam-4029	45	8	1	1	NUM
ejpam-4029	45	9	2πi	2πi	NOUN
ejpam-4029	45	10	∫	∫	PROPN
ejpam-4029	45	11	c	c	PROPN
ejpam-4029	45	12	aww−k−1	aww−k−1	NOUN
ejpam-4029	45	13	(	(	PUNCT
ejpam-4029	45	14	c−	c−	NOUN
ejpam-4029	45	15	π(m+	π(m+	X
ejpam-4029	45	16	w	w	NOUN
ejpam-4029	45	17	)	)	PUNCT
ejpam-4029	45	18	cot	cot	NOUN
ejpam-4029	45	19	(	(	PUNCT
ejpam-4029	45	20	π(m+w	π(m+w	NOUN
ejpam-4029	45	21	)	)	PUNCT
ejpam-4029	45	22	c	c	NOUN
ejpam-4029	45	23	)	)	PUNCT
ejpam-4029	45	24	)	)	PUNCT
ejpam-4029	45	25	2c2	2c2	NUM
ejpam-4029	45	26	dw	dw	NOUN
ejpam-4029	45	27	(	(	PUNCT
ejpam-4029	45	28	6	6	NUM
ejpam-4029	45	29	)	)	PUNCT
ejpam-4029	45	30	from	from	ADP
ejpam-4029	45	31	equation	equation	NOUN
ejpam-4029	45	32	(	(	PUNCT
ejpam-4029	45	33	2.4.4.2	2.4.4.2	NUM
ejpam-4029	45	34	)	)	PUNCT
ejpam-4029	45	35	in	in	ADP
ejpam-4029	45	36	[	[	X
ejpam-4029	45	37	12	12	NUM
ejpam-4029	45	38	]	]	PUNCT
ejpam-4029	45	39	where	where	SCONJ
ejpam-4029	45	40	z	z	NOUN
ejpam-4029	45	41	=	=	SYM
ejpam-4029	45	42	m+w	m+w	NOUN
ejpam-4029	45	43	c	c	NOUN
ejpam-4029	45	44	,	,	PUNCT
ejpam-4029	45	45	−1	−1	NOUN
ejpam-4029	45	46	<	<	X
ejpam-4029	45	47	re(z	re(z	NOUN
ejpam-4029	45	48	)	)	PUNCT
ejpam-4029	45	49	<	<	X
ejpam-4029	45	50	1	1	NUM
ejpam-4029	45	51	and	and	CCONJ
ejpam-4029	45	52	im(z	im(z	NOUN
ejpam-4029	45	53	)	)	PUNCT
ejpam-4029	45	54	>	>	X
ejpam-4029	45	55	0	0	NUM
ejpam-4029	45	56	,	,	PUNCT
ejpam-4029	45	57	|re(c)|	|re(c)|	ADJ
ejpam-4029	45	58	>	>	X
ejpam-4029	45	59	m.	m.	NOUN
ejpam-4029	45	60	we	we	PRON
ejpam-4029	45	61	are	be	AUX
ejpam-4029	45	62	able	able	ADJ
ejpam-4029	45	63	to	to	PART
ejpam-4029	45	64	switch	switch	VERB
ejpam-4029	45	65	the	the	DET
ejpam-4029	45	66	order	order	NOUN
ejpam-4029	45	67	of	of	ADP
ejpam-4029	45	68	integration	integration	NOUN
ejpam-4029	45	69	over	over	ADP
ejpam-4029	45	70	w	w	PROPN
ejpam-4029	45	71	and	and	CCONJ
ejpam-4029	45	72	x	x	ADP
ejpam-4029	45	73	,	,	PUNCT
ejpam-4029	45	74	using	use	VERB
ejpam-4029	45	75	fubini	fubini	NOUN
ejpam-4029	45	76	’s	’s	PART
ejpam-4029	45	77	theorem	theorem	NOUN
ejpam-4029	45	78	since	since	SCONJ
ejpam-4029	45	79	the	the	DET
ejpam-4029	45	80	integrand	integrand	NOUN
ejpam-4029	45	81	is	be	AUX
ejpam-4029	45	82	of	of	ADP
ejpam-4029	45	83	bounded	bounded	ADJ
ejpam-4029	45	84	measure	measure	NOUN
ejpam-4029	45	85	over	over	ADP
ejpam-4029	45	86	the	the	DET
ejpam-4029	45	87	space	space	NOUN
ejpam-4029	45	88	c	c	NOUN
ejpam-4029	45	89	×	×	NOUN
ejpam-4029	45	90	[	[	X
ejpam-4029	45	91	0,∞	0,∞	NOUN
ejpam-4029	45	92	)	)	PUNCT
ejpam-4029	45	93	.	.	PUNCT
ejpam-4029	46	1	4	4	X
ejpam-4029	46	2	.	.	X
ejpam-4029	46	3	the	the	DET
ejpam-4029	46	4	lerch	lerch	PROPN
ejpam-4029	46	5	function	function	NOUN
ejpam-4029	46	6	we	we	PRON
ejpam-4029	46	7	use	use	VERB
ejpam-4029	46	8	(	(	PUNCT
ejpam-4029	46	9	9.550	9.550	NUM
ejpam-4029	46	10	)	)	PUNCT
ejpam-4029	46	11	and	and	CCONJ
ejpam-4029	46	12	(	(	PUNCT
ejpam-4029	46	13	9.556	9.556	NUM
ejpam-4029	46	14	)	)	PUNCT
ejpam-4029	46	15	in	in	ADP
ejpam-4029	46	16	[	[	X
ejpam-4029	46	17	8	8	NUM
ejpam-4029	46	18	]	]	PUNCT
ejpam-4029	46	19	where	where	SCONJ
ejpam-4029	46	20	φ(z	φ(z	PROPN
ejpam-4029	46	21	,	,	PUNCT
ejpam-4029	46	22	s	s	NOUN
ejpam-4029	46	23	,	,	PUNCT
ejpam-4029	46	24	v	v	NOUN
ejpam-4029	46	25	)	)	PUNCT
ejpam-4029	46	26	is	be	AUX
ejpam-4029	46	27	the	the	DET
ejpam-4029	46	28	lerch	lerch	PROPN
ejpam-4029	46	29	function	function	NOUN
ejpam-4029	46	30	which	which	PRON
ejpam-4029	46	31	is	be	AUX
ejpam-4029	46	32	a	a	DET
ejpam-4029	46	33	generalization	generalization	NOUN
ejpam-4029	46	34	of	of	ADP
ejpam-4029	46	35	the	the	DET
ejpam-4029	46	36	hurwitz	hurwitz	PROPN
ejpam-4029	46	37	zeta	zeta	PROPN
ejpam-4029	46	38	ζ(s	ζ(s	PROPN
ejpam-4029	46	39	,	,	PUNCT
ejpam-4029	46	40	v	v	NOUN
ejpam-4029	46	41	)	)	PUNCT
ejpam-4029	46	42	and	and	CCONJ
ejpam-4029	46	43	polylogarithm	polylogarithm	PROPN
ejpam-4029	46	44	functions	function	NOUN
ejpam-4029	46	45	lin(z	lin(z	PROPN
ejpam-4029	46	46	)	)	PUNCT
ejpam-4029	46	47	.	.	PUNCT
ejpam-4029	47	1	the	the	DET
ejpam-4029	47	2	lerch	lerch	PROPN
ejpam-4029	47	3	function	function	PROPN
ejpam-4029	47	4	has	have	VERB
ejpam-4029	47	5	a	a	DET
ejpam-4029	47	6	series	series	NOUN
ejpam-4029	47	7	representation	representation	NOUN
ejpam-4029	47	8	given	give	VERB
ejpam-4029	47	9	by	by	ADP
ejpam-4029	47	10	φ(z	φ(z	PROPN
ejpam-4029	47	11	,	,	PUNCT
ejpam-4029	47	12	s	s	NOUN
ejpam-4029	47	13	,	,	PUNCT
ejpam-4029	47	14	v	v	NOUN
ejpam-4029	47	15	)	)	PUNCT
ejpam-4029	47	16	=	=	PUNCT
ejpam-4029	48	1	∞∑	∞∑	NUM
ejpam-4029	48	2	n=0	n=0	NUM
ejpam-4029	48	3	(	(	PUNCT
ejpam-4029	48	4	v	v	NOUN
ejpam-4029	48	5	+	+	NOUN
ejpam-4029	48	6	n)−szn	n)−szn	NUM
ejpam-4029	48	7	(	(	PUNCT
ejpam-4029	48	8	7	7	NUM
ejpam-4029	48	9	)	)	PUNCT
ejpam-4029	48	10	where	where	SCONJ
ejpam-4029	48	11	|z|	|z|	VERB
ejpam-4029	48	12	<	<	X
ejpam-4029	48	13	1	1	NUM
ejpam-4029	48	14	,	,	PUNCT
ejpam-4029	48	15	v	v	ADP
ejpam-4029	48	16	̸=	̸=	PROPN
ejpam-4029	48	17	0,−1	0,−1	PROPN
ejpam-4029	48	18	,	,	PUNCT
ejpam-4029	48	19	..	..	PUNCT
ejpam-4029	48	20	and	and	CCONJ
ejpam-4029	48	21	is	be	AUX
ejpam-4029	48	22	continued	continue	VERB
ejpam-4029	48	23	analytically	analytically	ADV
ejpam-4029	48	24	by	by	ADP
ejpam-4029	48	25	its	its	PRON
ejpam-4029	48	26	integral	integral	ADJ
ejpam-4029	48	27	representation	representation	NOUN
ejpam-4029	48	28	given	give	VERB
ejpam-4029	48	29	by	by	ADP
ejpam-4029	48	30	φ(z	φ(z	PROPN
ejpam-4029	48	31	,	,	PUNCT
ejpam-4029	48	32	s	s	NOUN
ejpam-4029	48	33	,	,	PUNCT
ejpam-4029	48	34	v	v	NOUN
ejpam-4029	48	35	)	)	PUNCT
ejpam-4029	48	36	=	=	SYM
ejpam-4029	48	37	1	1	NUM
ejpam-4029	48	38	γ(s	γ(	NOUN
ejpam-4029	48	39	)	)	PUNCT
ejpam-4029	48	40	∫	∫	PROPN
ejpam-4029	49	1	∞	∞	PROPN
ejpam-4029	49	2	0	0	NUM
ejpam-4029	50	1	ts−1e−vt	ts−1e−vt	PRON
ejpam-4029	51	1	1−	1−	NUM
ejpam-4029	51	2	ze−t	ze−t	NOUN
ejpam-4029	51	3	dt	dt	NOUN
ejpam-4029	52	1	=	=	SYM
ejpam-4029	52	2	1	1	NUM
ejpam-4029	52	3	γ(s	γ(s	PROPN
ejpam-4029	52	4	)	)	PUNCT
ejpam-4029	52	5	∫	∫	PROPN
ejpam-4029	53	1	∞	∞	NUM
ejpam-4029	53	2	0	0	NUM
ejpam-4029	54	1	ts−1e−(v−1)t	ts−1e−(v−1)t	PROPN
ejpam-4029	54	2	et	et	NOUN
ejpam-4029	54	3	−	−	NOUN
ejpam-4029	54	4	z	z	NOUN
ejpam-4029	54	5	dt	dt	X
ejpam-4029	54	6	(	(	PUNCT
ejpam-4029	54	7	8)	8)	NUM
ejpam-4029	54	8	where	where	SCONJ
ejpam-4029	54	9	re(v	re(v	NOUN
ejpam-4029	54	10	)	)	PUNCT
ejpam-4029	54	11	>	>	X
ejpam-4029	54	12	0	0	NUM
ejpam-4029	54	13	,	,	PUNCT
ejpam-4029	54	14	and	and	CCONJ
ejpam-4029	54	15	either	either	ADV
ejpam-4029	54	16	|z|≤	|z|≤	SYM
ejpam-4029	54	17	1	1	NUM
ejpam-4029	54	18	,	,	PUNCT
ejpam-4029	54	19	z	z	NOUN
ejpam-4029	54	20	̸=	̸=	PROPN
ejpam-4029	54	21	1	1	NUM
ejpam-4029	54	22	,	,	PUNCT
ejpam-4029	54	23	re(s	re(s	ADJ
ejpam-4029	54	24	)	)	PUNCT
ejpam-4029	54	25	>	>	X
ejpam-4029	54	26	0	0	NUM
ejpam-4029	54	27	,	,	PUNCT
ejpam-4029	54	28	or	or	CCONJ
ejpam-4029	54	29	z	z	NOUN
ejpam-4029	54	30	=	=	SYM
ejpam-4029	54	31	1	1	NUM
ejpam-4029	54	32	,	,	PUNCT
ejpam-4029	54	33	re(s	re(s	ADJ
ejpam-4029	54	34	)	)	PUNCT
ejpam-4029	54	35	>	>	X
ejpam-4029	55	1	1	1	NUM
ejpam-4029	55	2	.	.	X
ejpam-4029	55	3	4.1	4.1	NUM
ejpam-4029	55	4	.	.	PUNCT
ejpam-4029	55	5	infinite	infinite	ADJ
ejpam-4029	55	6	sum	sum	NOUN
ejpam-4029	55	7	of	of	ADP
ejpam-4029	55	8	the	the	DET
ejpam-4029	55	9	first	first	ADJ
ejpam-4029	55	10	contour	contour	NOUN
ejpam-4029	55	11	integral	integral	ADJ
ejpam-4029	55	12	in	in	ADP
ejpam-4029	55	13	this	this	DET
ejpam-4029	55	14	section	section	NOUN
ejpam-4029	55	15	we	we	PRON
ejpam-4029	55	16	will	will	AUX
ejpam-4029	55	17	again	again	ADV
ejpam-4029	55	18	use	use	VERB
ejpam-4029	55	19	cauchy	cauchy	NOUN
ejpam-4029	55	20	’s	’s	PART
ejpam-4029	55	21	integral	integral	ADJ
ejpam-4029	55	22	formula	formula	NOUN
ejpam-4029	55	23	(	(	PUNCT
ejpam-4029	55	24	2	2	NUM
ejpam-4029	55	25	)	)	PUNCT
ejpam-4029	55	26	and	and	CCONJ
ejpam-4029	55	27	taking	take	VERB
ejpam-4029	55	28	the	the	DET
ejpam-4029	55	29	infinite	infinite	ADJ
ejpam-4029	55	30	sum	sum	NOUN
ejpam-4029	55	31	to	to	PART
ejpam-4029	55	32	derive	derive	VERB
ejpam-4029	55	33	equivalent	equivalent	ADJ
ejpam-4029	55	34	sum	sum	NOUN
ejpam-4029	55	35	representations	representation	NOUN
ejpam-4029	55	36	for	for	ADP
ejpam-4029	55	37	the	the	DET
ejpam-4029	55	38	contour	contour	NOUN
ejpam-4029	55	39	integrals	integral	NOUN
ejpam-4029	55	40	.	.	PUNCT
ejpam-4029	56	1	we	we	PRON
ejpam-4029	56	2	proceed	proceed	VERB
ejpam-4029	56	3	using	use	VERB
ejpam-4029	56	4	equation	equation	NOUN
ejpam-4029	56	5	(	(	PUNCT
ejpam-4029	56	6	2	2	NUM
ejpam-4029	56	7	)	)	PUNCT
ejpam-4029	56	8	and	and	CCONJ
ejpam-4029	56	9	replace	replace	VERB
ejpam-4029	56	10	y	y	PROPN
ejpam-4029	56	11	by	by	ADP
ejpam-4029	56	12	log(a	log(a	PROPN
ejpam-4029	56	13	)	)	PUNCT
ejpam-4029	57	1	+	+	NUM
ejpam-4029	57	2	2iπ(y+1	2iπ(y+1	X
ejpam-4029	57	3	)	)	PUNCT
ejpam-4029	57	4	c	c	NOUN
ejpam-4029	57	5	and	and	CCONJ
ejpam-4029	57	6	multiply	multiply	VERB
ejpam-4029	57	7	both	both	DET
ejpam-4029	57	8	sides	side	NOUN
ejpam-4029	57	9	by	by	ADP
ejpam-4029	57	10	iπm	iπm	PROPN
ejpam-4029	57	11	c2	c2	PROPN
ejpam-4029	57	12	e	e	PROPN
ejpam-4029	57	13	2iπm(y+1	2iπm(y+1	NUM
ejpam-4029	57	14	)	)	PUNCT
ejpam-4029	57	15	c	c	NOUN
ejpam-4029	57	16	and	and	CCONJ
ejpam-4029	57	17	simplifying	simplify	VERB
ejpam-4029	57	18	to	to	PART
ejpam-4029	57	19	get	get	VERB
ejpam-4029	57	20	πk+1	πk+1	NOUN
ejpam-4029	57	21	m	m	VERB
ejpam-4029	57	22	(	(	PUNCT
ejpam-4029	57	23	i	i	NOUN
ejpam-4029	57	24	c	c	NOUN
ejpam-4029	57	25	)	)	PUNCT
ejpam-4029	57	26	k+1	k+1	X
ejpam-4029	57	27	e	e	X
ejpam-4029	57	28	2iπm(y+1	2iπm(y+1	NUM
ejpam-4029	57	29	)	)	PUNCT
ejpam-4029	58	1	c	c	NOUN
ejpam-4029	58	2	(	(	PUNCT
ejpam-4029	58	3	−	−	PROPN
ejpam-4029	58	4	ic	ic	PROPN
ejpam-4029	58	5	log(a	log(a	PROPN
ejpam-4029	58	6	)	)	PUNCT
ejpam-4029	58	7	π	π	PROPN
ejpam-4029	59	1	+	+	CCONJ
ejpam-4029	59	2	2y	2y	PROPN
ejpam-4029	59	3	+	+	CCONJ
ejpam-4029	59	4	2	2	NUM
ejpam-4029	59	5	)	)	PUNCT
ejpam-4029	59	6	k	k	NOUN
ejpam-4029	59	7	cγ(k	cγ(k	X
ejpam-4029	59	8	+	+	CCONJ
ejpam-4029	59	9	1	1	X
ejpam-4029	59	10	)	)	PUNCT
ejpam-4029	59	11	=	=	SYM
ejpam-4029	60	1	1	1	NUM
ejpam-4029	60	2	2πi	2πi	NOUN
ejpam-4029	60	3	∫	∫	PROPN
ejpam-4029	60	4	c	c	PROPN
ejpam-4029	60	5	iπmaww−k−1e	iπmaww−k−1e	PROPN
ejpam-4029	60	6	2iπ(y+1)(m+w	2iπ(y+1)(m+w	PROPN
ejpam-4029	60	7	)	)	PUNCT
ejpam-4029	60	8	c	c	PROPN
ejpam-4029	60	9	c2	c2	PROPN
ejpam-4029	60	10	dw	dw	PROPN
ejpam-4029	60	11	(	(	PUNCT
ejpam-4029	60	12	9	9	NUM
ejpam-4029	60	13	)	)	PUNCT
ejpam-4029	60	14	next	next	ADV
ejpam-4029	60	15	we	we	PRON
ejpam-4029	60	16	take	take	VERB
ejpam-4029	60	17	the	the	DET
ejpam-4029	60	18	infinite	infinite	ADJ
ejpam-4029	60	19	sum	sum	NOUN
ejpam-4029	60	20	over	over	ADP
ejpam-4029	60	21	y	y	PROPN
ejpam-4029	60	22	∈	∈	PROPN
ejpam-4029	61	1	[	[	X
ejpam-4029	61	2	0,∞	0,∞	NOUN
ejpam-4029	61	3	)	)	PUNCT
ejpam-4029	61	4	and	and	CCONJ
ejpam-4029	61	5	simplify	simplify	VERB
ejpam-4029	61	6	using	use	VERB
ejpam-4029	61	7	the	the	DET
ejpam-4029	61	8	lerch	lerch	PROPN
ejpam-4029	61	9	function	function	NOUN
ejpam-4029	61	10	to	to	PART
ejpam-4029	61	11	get	get	VERB
ejpam-4029	61	12	r.	r.	PROPN
ejpam-4029	61	13	reynolds	reynolds	PROPN
ejpam-4029	61	14	,	,	PUNCT
ejpam-4029	61	15	a.	a.	PROPN
ejpam-4029	61	16	stauffer	stauffer	PROPN
ejpam-4029	61	17	/	/	SYM
ejpam-4029	61	18	eur	eur	PROPN
ejpam-4029	61	19	.	.	PUNCT
ejpam-4029	62	1	j.	j.	PROPN
ejpam-4029	62	2	pure	pure	PROPN
ejpam-4029	62	3	appl	appl	PROPN
ejpam-4029	62	4	.	.	PROPN
ejpam-4029	62	5	math	math	PROPN
ejpam-4029	62	6	,	,	PUNCT
ejpam-4029	62	7	14	14	NUM
ejpam-4029	62	8	(	(	PUNCT
ejpam-4029	62	9	4	4	NUM
ejpam-4029	62	10	)	)	PUNCT
ejpam-4029	62	11	(	(	PUNCT
ejpam-4029	62	12	2021	2021	NUM
ejpam-4029	62	13	)	)	PUNCT
ejpam-4029	62	14	,	,	PUNCT
ejpam-4029	62	15	1132	1132	NUM
ejpam-4029	62	16	-	-	SYM
ejpam-4029	62	17	1147	1147	NUM
ejpam-4029	62	18	1135	1135	NUM
ejpam-4029	62	19	2kπk+1	2kπk+1	NUM
ejpam-4029	62	20	m	m	NOUN
ejpam-4029	62	21	(	(	PUNCT
ejpam-4029	62	22	i	i	NOUN
ejpam-4029	62	23	c	c	NOUN
ejpam-4029	62	24	)	)	PUNCT
ejpam-4029	62	25	k+1	k+1	X
ejpam-4029	63	1	e	e	X
ejpam-4029	63	2	2iπm	2iπm	PROPN
ejpam-4029	63	3	c	c	PROPN
ejpam-4029	63	4	φ	φ	X
ejpam-4029	63	5	(	(	PUNCT
ejpam-4029	63	6	e	e	X
ejpam-4029	63	7	2imπ	2imπ	PROPN
ejpam-4029	63	8	c	c	NOUN
ejpam-4029	63	9	,	,	PUNCT
ejpam-4029	63	10	−k	−k	PROPN
ejpam-4029	63	11	,	,	PUNCT
ejpam-4029	63	12	1−	1−	NUM
ejpam-4029	63	13	ic	ic	PROPN
ejpam-4029	63	14	log(a	log(a	PROPN
ejpam-4029	63	15	)	)	PUNCT
ejpam-4029	63	16	2π	2π	PROPN
ejpam-4029	63	17	)	)	PUNCT
ejpam-4029	63	18	cγ(k	cγ(k	X
ejpam-4029	64	1	+	+	CCONJ
ejpam-4029	64	2	1	1	X
ejpam-4029	64	3	)	)	PUNCT
ejpam-4029	64	4	=	=	SYM
ejpam-4029	64	5	1	1	NUM
ejpam-4029	64	6	2πi	2πi	NOUN
ejpam-4029	64	7	∞∑	∞∑	NUM
ejpam-4029	64	8	y=0	y=0	NUM
ejpam-4029	64	9	∫	∫	PROPN
ejpam-4029	64	10	c	c	PROPN
ejpam-4029	64	11	iπmaww−k−1e	iπmaww−k−1e	PROPN
ejpam-4029	64	12	2iπ(y+1)(m+w	2iπ(y+1)(m+w	PROPN
ejpam-4029	64	13	)	)	PUNCT
ejpam-4029	64	14	c	c	PROPN
ejpam-4029	64	15	c2	c2	PROPN
ejpam-4029	64	16	dw	dw	PROPN
ejpam-4029	64	17	=	=	SYM
ejpam-4029	64	18	1	1	NUM
ejpam-4029	64	19	2πi	2πi	NOUN
ejpam-4029	64	20	∫	∫	PROPN
ejpam-4029	64	21	c	c	NOUN
ejpam-4029	65	1	∞∑	∞∑	NUM
ejpam-4029	65	2	y=0	y=0	NOUN
ejpam-4029	65	3	iπmaww−k−1e	iπmaww−k−1e	ADV
ejpam-4029	65	4	2iπ(y+1)(m+w	2iπ(y+1)(m+w	NOUN
ejpam-4029	65	5	)	)	PUNCT
ejpam-4029	65	6	c	c	PROPN
ejpam-4029	65	7	c2	c2	PROPN
ejpam-4029	65	8	dw	dw	PROPN
ejpam-4029	66	1	=	=	SYM
ejpam-4029	66	2	−	−	PROPN
ejpam-4029	66	3	1	1	NUM
ejpam-4029	66	4	2πi	2πi	NOUN
ejpam-4029	66	5	∫	∫	PROPN
ejpam-4029	67	1	c	c	PROPN
ejpam-4029	67	2	πmaww−k−1	πmaww−k−1	PROPN
ejpam-4029	67	3	(	(	PUNCT
ejpam-4029	67	4	cot	cot	NOUN
ejpam-4029	67	5	(	(	PUNCT
ejpam-4029	67	6	π(m+w	π(m+w	NOUN
ejpam-4029	67	7	)	)	PUNCT
ejpam-4029	67	8	c	c	NOUN
ejpam-4029	67	9	)	)	PUNCT
ejpam-4029	68	1	+	+	CCONJ
ejpam-4029	68	2	i	i	NOUN
ejpam-4029	68	3	)	)	PUNCT
ejpam-4029	68	4	2c2	2c2	NUM
ejpam-4029	69	1	dw	dw	NOUN
ejpam-4029	69	2	(	(	PUNCT
ejpam-4029	69	3	10	10	NUM
ejpam-4029	69	4	)	)	PUNCT
ejpam-4029	69	5	from	from	ADP
ejpam-4029	69	6	(	(	PUNCT
ejpam-4029	69	7	1.232.1	1.232.1	NUM
ejpam-4029	69	8	)	)	PUNCT
ejpam-4029	69	9	in	in	ADP
ejpam-4029	69	10	[	[	X
ejpam-4029	69	11	8	8	NUM
ejpam-4029	69	12	]	]	PUNCT
ejpam-4029	69	13	and	and	CCONJ
ejpam-4029	69	14	im(w	im(w	ADJ
ejpam-4029	69	15	+	+	NOUN
ejpam-4029	69	16	m	m	NOUN
ejpam-4029	69	17	)	)	PUNCT
ejpam-4029	69	18	>	>	X
ejpam-4029	69	19	0	0	PUNCT
ejpam-4029	70	1	for	for	ADP
ejpam-4029	70	2	convergence	convergence	NOUN
ejpam-4029	70	3	of	of	ADP
ejpam-4029	70	4	the	the	DET
ejpam-4029	70	5	sum	sum	NOUN
ejpam-4029	70	6	.	.	PUNCT
ejpam-4029	71	1	4.2	4.2	NUM
ejpam-4029	71	2	.	.	PUNCT
ejpam-4029	71	3	infinite	infinite	ADJ
ejpam-4029	71	4	sum	sum	NOUN
ejpam-4029	71	5	of	of	ADP
ejpam-4029	71	6	the	the	DET
ejpam-4029	71	7	second	second	ADJ
ejpam-4029	71	8	contour	contour	NOUN
ejpam-4029	71	9	integral	integral	ADJ
ejpam-4029	71	10	the	the	DET
ejpam-4029	71	11	derivation	derivation	NOUN
ejpam-4029	71	12	in	in	ADP
ejpam-4029	71	13	this	this	DET
ejpam-4029	71	14	section	section	NOUN
ejpam-4029	71	15	is	be	AUX
ejpam-4029	71	16	equivalent	equivalent	ADJ
ejpam-4029	71	17	to	to	ADP
ejpam-4029	71	18	section	section	NOUN
ejpam-4029	71	19	(	(	PUNCT
ejpam-4029	71	20	2.1	2.1	NUM
ejpam-4029	71	21	)	)	PUNCT
ejpam-4029	71	22	after	after	ADP
ejpam-4029	71	23	multiplication	multiplication	NOUN
ejpam-4029	71	24	by	by	ADP
ejpam-4029	71	25	m	m	NOUN
ejpam-4029	71	26	and	and	CCONJ
ejpam-4029	71	27	replacement	replacement	NOUN
ejpam-4029	71	28	of	of	ADP
ejpam-4029	71	29	k	k	PROPN
ejpam-4029	71	30	→	→	PUNCT
ejpam-4029	71	31	(	(	PUNCT
ejpam-4029	71	32	k	k	NOUN
ejpam-4029	71	33	−	−	PROPN
ejpam-4029	71	34	1	1	NUM
ejpam-4029	71	35	)	)	PUNCT
ejpam-4029	71	36	.	.	PUNCT
ejpam-4029	72	1	2k−1πk	2k−1πk	NUM
ejpam-4029	72	2	(	(	PUNCT
ejpam-4029	72	3	i	i	NOUN
ejpam-4029	72	4	c	c	NOUN
ejpam-4029	72	5	)	)	PUNCT
ejpam-4029	73	1	k	k	PROPN
ejpam-4029	74	1	e	e	X
ejpam-4029	74	2	2iπm	2iπm	PROPN
ejpam-4029	74	3	c	c	PROPN
ejpam-4029	74	4	φ	φ	X
ejpam-4029	74	5	(	(	PUNCT
ejpam-4029	74	6	e	e	X
ejpam-4029	74	7	2imπ	2imπ	NUM
ejpam-4029	74	8	c	c	PROPN
ejpam-4029	74	9	,	,	PUNCT
ejpam-4029	74	10	1−	1−	NUM
ejpam-4029	74	11	k	k	X
ejpam-4029	74	12	,	,	PUNCT
ejpam-4029	74	13	1−	1−	NUM
ejpam-4029	74	14	ic	ic	PROPN
ejpam-4029	74	15	log(a	log(a	PROPN
ejpam-4029	74	16	)	)	PUNCT
ejpam-4029	74	17	2π	2π	NOUN
ejpam-4029	74	18	)	)	PUNCT
ejpam-4029	75	1	c(k	c(k	NOUN
ejpam-4029	75	2	−	−	NOUN
ejpam-4029	75	3	1	1	NUM
ejpam-4029	75	4	)	)	PUNCT
ejpam-4029	75	5	!	!	PUNCT
ejpam-4029	76	1	=	=	PUNCT
ejpam-4029	77	1	−	−	PROPN
ejpam-4029	77	2	1	1	NUM
ejpam-4029	77	3	2πi	2πi	NOUN
ejpam-4029	77	4	∫	∫	PROPN
ejpam-4029	77	5	c	c	PROPN
ejpam-4029	77	6	πaww−k	πaww−k	PROPN
ejpam-4029	77	7	(	(	PUNCT
ejpam-4029	77	8	cot	cot	NOUN
ejpam-4029	77	9	(	(	PUNCT
ejpam-4029	77	10	π(m+w	π(m+w	NOUN
ejpam-4029	77	11	)	)	PUNCT
ejpam-4029	77	12	c	c	NOUN
ejpam-4029	77	13	)	)	PUNCT
ejpam-4029	78	1	+	+	CCONJ
ejpam-4029	78	2	i	i	NOUN
ejpam-4029	78	3	)	)	PUNCT
ejpam-4029	78	4	2c2	2c2	NUM
ejpam-4029	79	1	dw	dw	NOUN
ejpam-4029	79	2	(	(	PUNCT
ejpam-4029	79	3	11	11	NUM
ejpam-4029	79	4	)	)	PUNCT
ejpam-4029	79	5	from	from	ADP
ejpam-4029	79	6	(	(	PUNCT
ejpam-4029	79	7	1.232.1	1.232.1	NUM
ejpam-4029	79	8	)	)	PUNCT
ejpam-4029	79	9	in	in	ADP
ejpam-4029	79	10	[	[	X
ejpam-4029	79	11	8	8	NUM
ejpam-4029	79	12	]	]	PUNCT
ejpam-4029	79	13	and	and	CCONJ
ejpam-4029	79	14	im(w	im(w	ADJ
ejpam-4029	79	15	+	+	NOUN
ejpam-4029	79	16	m	m	NOUN
ejpam-4029	79	17	)	)	PUNCT
ejpam-4029	79	18	>	>	X
ejpam-4029	79	19	0	0	PUNCT
ejpam-4029	80	1	for	for	ADP
ejpam-4029	80	2	convergence	convergence	NOUN
ejpam-4029	80	3	of	of	ADP
ejpam-4029	80	4	the	the	DET
ejpam-4029	80	5	sum	sum	NOUN
ejpam-4029	80	6	.	.	PUNCT
ejpam-4029	81	1	4.3	4.3	NUM
ejpam-4029	81	2	.	.	PUNCT
ejpam-4029	81	3	additional	additional	ADJ
ejpam-4029	81	4	contours	contours	NOUN
ejpam-4029	81	5	in	in	ADP
ejpam-4029	81	6	this	this	DET
ejpam-4029	81	7	section	section	NOUN
ejpam-4029	81	8	we	we	PRON
ejpam-4029	81	9	will	will	AUX
ejpam-4029	81	10	derive	derive	VERB
ejpam-4029	81	11	the	the	DET
ejpam-4029	81	12	additional	additional	ADJ
ejpam-4029	81	13	contours	contours	NOUN
ejpam-4029	81	14	from	from	ADP
ejpam-4029	81	15	equations	equation	NOUN
ejpam-4029	81	16	(	(	PUNCT
ejpam-4029	81	17	6	6	NUM
ejpam-4029	81	18	)	)	PUNCT
ejpam-4029	81	19	,	,	PUNCT
ejpam-4029	81	20	(	(	PUNCT
ejpam-4029	81	21	10	10	NUM
ejpam-4029	81	22	)	)	PUNCT
ejpam-4029	81	23	and	and	CCONJ
ejpam-4029	81	24	(	(	PUNCT
ejpam-4029	81	25	11	11	NUM
ejpam-4029	81	26	)	)	PUNCT
ejpam-4029	81	27	.	.	PUNCT
ejpam-4029	82	1	we	we	PRON
ejpam-4029	82	2	proceed	proceed	VERB
ejpam-4029	82	3	using	use	VERB
ejpam-4029	82	4	equation	equation	NOUN
ejpam-4029	82	5	(	(	PUNCT
ejpam-4029	82	6	2	2	NUM
ejpam-4029	82	7	)	)	PUNCT
ejpam-4029	82	8	and	and	CCONJ
ejpam-4029	82	9	replace	replace	VERB
ejpam-4029	82	10	y	y	PROPN
ejpam-4029	82	11	by	by	ADP
ejpam-4029	82	12	log(a	log(a	PROPN
ejpam-4029	82	13	)	)	PUNCT
ejpam-4029	82	14	and	and	CCONJ
ejpam-4029	82	15	multiply	multiply	VERB
ejpam-4029	82	16	both	both	DET
ejpam-4029	82	17	sides	side	NOUN
ejpam-4029	82	18	by	by	ADP
ejpam-4029	82	19	1	1	NUM
ejpam-4029	82	20	2c	2c	NUM
ejpam-4029	82	21	and	and	CCONJ
ejpam-4029	82	22	simplifying	simplify	VERB
ejpam-4029	82	23	to	to	PART
ejpam-4029	82	24	get	get	VERB
ejpam-4029	82	25	logk(a	logk(a	NOUN
ejpam-4029	82	26	)	)	PUNCT
ejpam-4029	82	27	2cγ(k	2cγ(k	NUM
ejpam-4029	83	1	+	+	CCONJ
ejpam-4029	84	1	1	1	X
ejpam-4029	84	2	)	)	PUNCT
ejpam-4029	84	3	=	=	SYM
ejpam-4029	84	4	1	1	NUM
ejpam-4029	84	5	2πi	2πi	ADJ
ejpam-4029	84	6	∫	∫	PROPN
ejpam-4029	84	7	c	c	PROPN
ejpam-4029	84	8	aww−k−1	aww−k−1	PROPN
ejpam-4029	84	9	2c	2c	PROPN
ejpam-4029	84	10	dw	dw	PROPN
ejpam-4029	84	11	(	(	PUNCT
ejpam-4029	84	12	12	12	NUM
ejpam-4029	84	13	)	)	PUNCT
ejpam-4029	84	14	next	next	ADJ
ejpam-4029	84	15	using	use	VERB
ejpam-4029	84	16	equation	equation	NOUN
ejpam-4029	84	17	(	(	PUNCT
ejpam-4029	84	18	2	2	NUM
ejpam-4029	84	19	)	)	PUNCT
ejpam-4029	84	20	and	and	CCONJ
ejpam-4029	84	21	replace	replace	VERB
ejpam-4029	84	22	y	y	PROPN
ejpam-4029	84	23	by	by	ADP
ejpam-4029	84	24	log(a	log(a	PROPN
ejpam-4029	84	25	)	)	PUNCT
ejpam-4029	84	26	and	and	CCONJ
ejpam-4029	84	27	multiply	multiply	VERB
ejpam-4029	84	28	both	both	DET
ejpam-4029	84	29	sides	side	NOUN
ejpam-4029	84	30	by	by	ADP
ejpam-4029	84	31	−	−	PROPN
ejpam-4029	84	32	iπm	iπm	NOUN
ejpam-4029	84	33	2c2	2c2	NUM
ejpam-4029	84	34	and	and	CCONJ
ejpam-4029	84	35	simplifying	simplify	VERB
ejpam-4029	84	36	to	to	PART
ejpam-4029	84	37	get	get	VERB
ejpam-4029	84	38	iπm	iπm	NOUN
ejpam-4029	84	39	logk(a	logk(a	NOUN
ejpam-4029	84	40	)	)	PUNCT
ejpam-4029	84	41	2c2γ(k	2c2γ(k	NUM
ejpam-4029	84	42	+	+	NOUN
ejpam-4029	84	43	1	1	NUM
ejpam-4029	84	44	)	)	PUNCT
ejpam-4029	84	45	=	=	SYM
ejpam-4029	85	1	−	−	PROPN
ejpam-4029	85	2	1	1	NUM
ejpam-4029	85	3	2πi	2πi	NOUN
ejpam-4029	85	4	∫	∫	PROPN
ejpam-4029	85	5	c	c	PROPN
ejpam-4029	85	6	iπmaww−k−1	iπmaww−k−1	PROPN
ejpam-4029	85	7	2c2	2c2	NUM
ejpam-4029	85	8	dw	dw	NOUN
ejpam-4029	85	9	(	(	PUNCT
ejpam-4029	85	10	13	13	NUM
ejpam-4029	85	11	)	)	PUNCT
ejpam-4029	85	12	next	next	ADV
ejpam-4029	85	13	using	use	VERB
ejpam-4029	85	14	equation	equation	NOUN
ejpam-4029	85	15	(	(	PUNCT
ejpam-4029	85	16	2	2	NUM
ejpam-4029	85	17	)	)	PUNCT
ejpam-4029	85	18	and	and	CCONJ
ejpam-4029	85	19	replace	replace	VERB
ejpam-4029	85	20	y	y	PROPN
ejpam-4029	85	21	by	by	ADP
ejpam-4029	85	22	log(a	log(a	PROPN
ejpam-4029	85	23	)	)	PUNCT
ejpam-4029	85	24	,	,	PUNCT
ejpam-4029	85	25	k	k	PROPN
ejpam-4029	85	26	by	by	ADP
ejpam-4029	85	27	k	k	PROPN
ejpam-4029	85	28	−	−	PROPN
ejpam-4029	85	29	1	1	NUM
ejpam-4029	85	30	and	and	CCONJ
ejpam-4029	85	31	multiply	multiply	VERB
ejpam-4029	85	32	both	both	DET
ejpam-4029	85	33	sides	side	NOUN
ejpam-4029	85	34	by	by	ADP
ejpam-4029	85	35	−	−	PROPN
ejpam-4029	85	36	iπ	iπ	PRON
ejpam-4029	85	37	2c2	2c2	NUM
ejpam-4029	85	38	and	and	CCONJ
ejpam-4029	85	39	simplifying	simplify	VERB
ejpam-4029	85	40	to	to	PART
ejpam-4029	85	41	get	get	VERB
ejpam-4029	85	42	r.	r.	PROPN
ejpam-4029	85	43	reynolds	reynolds	PROPN
ejpam-4029	85	44	,	,	PUNCT
ejpam-4029	85	45	a.	a.	PROPN
ejpam-4029	85	46	stauffer	stauffer	PROPN
ejpam-4029	85	47	/	/	SYM
ejpam-4029	85	48	eur	eur	PROPN
ejpam-4029	85	49	.	.	PUNCT
ejpam-4029	86	1	j.	j.	PROPN
ejpam-4029	86	2	pure	pure	PROPN
ejpam-4029	86	3	appl	appl	PROPN
ejpam-4029	86	4	.	.	PROPN
ejpam-4029	86	5	math	math	PROPN
ejpam-4029	86	6	,	,	PUNCT
ejpam-4029	86	7	14	14	NUM
ejpam-4029	86	8	(	(	PUNCT
ejpam-4029	86	9	4	4	NUM
ejpam-4029	86	10	)	)	PUNCT
ejpam-4029	86	11	(	(	PUNCT
ejpam-4029	86	12	2021	2021	NUM
ejpam-4029	86	13	)	)	PUNCT
ejpam-4029	86	14	,	,	PUNCT
ejpam-4029	86	15	1132	1132	NUM
ejpam-4029	86	16	-	-	SYM
ejpam-4029	86	17	1147	1147	NUM
ejpam-4029	86	18	1136	1136	NUM
ejpam-4029	86	19	−	−	NOUN
ejpam-4029	86	20	iπ	iπ	DET
ejpam-4029	86	21	logk−1(a	logk−1(a	NOUN
ejpam-4029	86	22	)	)	PUNCT
ejpam-4029	86	23	2c2γ(k	2c2γ(k	NUM
ejpam-4029	86	24	)	)	PUNCT
ejpam-4029	87	1	=	=	SYM
ejpam-4029	87	2	−	−	PROPN
ejpam-4029	87	3	1	1	NUM
ejpam-4029	87	4	2πi	2πi	NOUN
ejpam-4029	87	5	∫	∫	PROPN
ejpam-4029	87	6	c	c	PROPN
ejpam-4029	87	7	iπaww−k	iπaww−k	PROPN
ejpam-4029	87	8	2c2	2c2	NUM
ejpam-4029	87	9	dw	dw	PROPN
ejpam-4029	87	10	(	(	PUNCT
ejpam-4029	87	11	14	14	NUM
ejpam-4029	87	12	)	)	PUNCT
ejpam-4029	87	13	note	note	NOUN
ejpam-4029	87	14	that	that	SCONJ
ejpam-4029	87	15	the	the	DET
ejpam-4029	87	16	equations	equation	NOUN
ejpam-4029	87	17	(	(	PUNCT
ejpam-4029	87	18	12	12	NUM
ejpam-4029	87	19	)	)	PUNCT
ejpam-4029	87	20	,	,	PUNCT
ejpam-4029	87	21	(	(	PUNCT
ejpam-4029	87	22	13	13	NUM
ejpam-4029	87	23	)	)	PUNCT
ejpam-4029	87	24	and	and	CCONJ
ejpam-4029	87	25	(	(	PUNCT
ejpam-4029	87	26	14	14	NUM
ejpam-4029	87	27	)	)	PUNCT
ejpam-4029	87	28	are	be	AUX
ejpam-4029	87	29	equivalent	equivalent	ADJ
ejpam-4029	87	30	to	to	ADP
ejpam-4029	87	31	(	(	PUNCT
ejpam-4029	87	32	3	3	NUM
ejpam-4029	87	33	)	)	PUNCT
ejpam-4029	87	34	with	with	ADP
ejpam-4029	87	35	csch(cx	csch(cx	NOUN
ejpam-4029	87	36	)	)	PUNCT
ejpam-4029	87	37	dropped	drop	VERB
ejpam-4029	87	38	and	and	CCONJ
ejpam-4029	87	39	different	different	ADJ
ejpam-4029	87	40	multipliers	multiplier	NOUN
ejpam-4029	87	41	.	.	PUNCT
ejpam-4029	88	1	5	5	X
ejpam-4029	88	2	.	.	X
ejpam-4029	88	3	definite	definite	ADJ
ejpam-4029	88	4	integral	integral	ADJ
ejpam-4029	88	5	in	in	ADP
ejpam-4029	88	6	terms	term	NOUN
ejpam-4029	88	7	of	of	ADP
ejpam-4029	88	8	the	the	DET
ejpam-4029	88	9	lerch	lerch	PROPN
ejpam-4029	88	10	function	function	PROPN
ejpam-4029	88	11	theorem	theorem	VERB
ejpam-4029	88	12	1	1	NUM
ejpam-4029	88	13	.	.	PUNCT
ejpam-4029	89	1	for	for	ADP
ejpam-4029	89	2	all	all	DET
ejpam-4029	89	3	k	k	NOUN
ejpam-4029	89	4	,	,	PUNCT
ejpam-4029	89	5	a	a	DET
ejpam-4029	89	6	∈	∈	PROPN
ejpam-4029	89	7	c	c	NOUN
ejpam-4029	89	8	,	,	PUNCT
ejpam-4029	89	9	|re(c)|	|re(c)|	ADJ
ejpam-4029	89	10	>	>	X
ejpam-4029	89	11	m,∫	m,∫	NOUN
ejpam-4029	90	1	∞	∞	NOUN
ejpam-4029	90	2	0	0	NUM
ejpam-4029	90	3	csch2(cx	csch2(cx	NOUN
ejpam-4029	90	4	)	)	PUNCT
ejpam-4029	90	5	(	(	PUNCT
ejpam-4029	90	6	e−2mx(log(a)−	e−2mx(log(a)−	ADV
ejpam-4029	91	1	2x)k	2x)k	NUM
ejpam-4029	91	2	+	+	NUM
ejpam-4029	91	3	e2mx(log(a	e2mx(log(a	NOUN
ejpam-4029	91	4	)	)	PUNCT
ejpam-4029	92	1	+	+	CCONJ
ejpam-4029	92	2	2x)k	2x)k	NUM
ejpam-4029	92	3	−	−	NOUN
ejpam-4029	92	4	2	2	NUM
ejpam-4029	92	5	logk(a	logk(a	NOUN
ejpam-4029	92	6	)	)	PUNCT
ejpam-4029	92	7	)	)	PUNCT
ejpam-4029	93	1	dx	dx	PROPN
ejpam-4029	93	2	=	=	PUNCT
ejpam-4029	94	1	i2k+2πk+1	i2k+2πk+1	PROPN
ejpam-4029	94	2	m	m	VERB
ejpam-4029	94	3	(	(	PUNCT
ejpam-4029	94	4	i	i	NOUN
ejpam-4029	94	5	c	c	NOUN
ejpam-4029	94	6	)	)	PUNCT
ejpam-4029	95	1	k	k	PROPN
ejpam-4029	95	2	e	e	X
ejpam-4029	95	3	2iπm	2iπm	PROPN
ejpam-4029	95	4	c	c	PROPN
ejpam-4029	95	5	φ	φ	X
ejpam-4029	95	6	(	(	PUNCT
ejpam-4029	95	7	e	e	X
ejpam-4029	95	8	2imπ	2imπ	PROPN
ejpam-4029	95	9	c	c	NOUN
ejpam-4029	95	10	,	,	PUNCT
ejpam-4029	95	11	−k	−k	PROPN
ejpam-4029	95	12	,	,	PUNCT
ejpam-4029	95	13	1−	1−	NUM
ejpam-4029	95	14	ic	ic	PROPN
ejpam-4029	95	15	log(a	log(a	PROPN
ejpam-4029	95	16	)	)	PUNCT
ejpam-4029	95	17	2π	2π	NOUN
ejpam-4029	95	18	)	)	PUNCT
ejpam-4029	96	1	c2	c2	PROPN
ejpam-4029	96	2	+	+	CCONJ
ejpam-4029	96	3	2iπm	2iπm	NUM
ejpam-4029	96	4	logk(a	logk(a	NOUN
ejpam-4029	96	5	)	)	PUNCT
ejpam-4029	96	6	c2	c2	PROPN
ejpam-4029	96	7	+	+	CCONJ
ejpam-4029	96	8	2iπk	2iπk	NUM
ejpam-4029	96	9	logk−1(a	logk−1(a	NOUN
ejpam-4029	96	10	)	)	PUNCT
ejpam-4029	96	11	c2	c2	PROPN
ejpam-4029	96	12	+	+	PROPN
ejpam-4029	96	13	2k+1kπk	2k+1kπk	NUM
ejpam-4029	96	14	(	(	PUNCT
ejpam-4029	96	15	i	i	NOUN
ejpam-4029	96	16	c	c	NOUN
ejpam-4029	96	17	)	)	PUNCT
ejpam-4029	97	1	k	k	PROPN
ejpam-4029	97	2	e	e	X
ejpam-4029	97	3	2iπm	2iπm	PROPN
ejpam-4029	97	4	c	c	PROPN
ejpam-4029	97	5	φ	φ	X
ejpam-4029	97	6	(	(	PUNCT
ejpam-4029	97	7	e	e	X
ejpam-4029	97	8	2imπ	2imπ	NUM
ejpam-4029	97	9	c	c	PROPN
ejpam-4029	97	10	,	,	PUNCT
ejpam-4029	97	11	1−	1−	NUM
ejpam-4029	97	12	k	k	X
ejpam-4029	97	13	,	,	PUNCT
ejpam-4029	97	14	1−	1−	NUM
ejpam-4029	97	15	ic	ic	PROPN
ejpam-4029	97	16	log(a	log(a	PROPN
ejpam-4029	97	17	)	)	PUNCT
ejpam-4029	97	18	2π	2π	NOUN
ejpam-4029	97	19	)	)	PUNCT
ejpam-4029	98	1	c	c	X
ejpam-4029	99	1	+	+	CCONJ
ejpam-4029	99	2	2	2	NUM
ejpam-4029	99	3	logk(a	logk(a	NOUN
ejpam-4029	99	4	)	)	PUNCT
ejpam-4029	99	5	c	c	NOUN
ejpam-4029	99	6	(	(	PUNCT
ejpam-4029	99	7	15	15	NUM
ejpam-4029	99	8	)	)	PUNCT
ejpam-4029	99	9	proof	proof	NOUN
ejpam-4029	99	10	.	.	PUNCT
ejpam-4029	100	1	since	since	SCONJ
ejpam-4029	100	2	the	the	DET
ejpam-4029	100	3	right	right	ADJ
ejpam-4029	100	4	-	-	PUNCT
ejpam-4029	100	5	hand	hand	NOUN
ejpam-4029	100	6	side	side	NOUN
ejpam-4029	100	7	of	of	ADP
ejpam-4029	100	8	equation	equation	NOUN
ejpam-4029	100	9	(	(	PUNCT
ejpam-4029	100	10	6	6	NUM
ejpam-4029	100	11	)	)	PUNCT
ejpam-4029	100	12	is	be	AUX
ejpam-4029	100	13	equal	equal	ADJ
ejpam-4029	100	14	to	to	ADP
ejpam-4029	100	15	the	the	DET
ejpam-4029	100	16	sum	sum	NOUN
ejpam-4029	100	17	of	of	ADP
ejpam-4029	100	18	the	the	DET
ejpam-4029	100	19	right	right	ADJ
ejpam-4029	100	20	-	-	PUNCT
ejpam-4029	100	21	hand	hand	NOUN
ejpam-4029	100	22	sides	side	NOUN
ejpam-4029	100	23	of	of	ADP
ejpam-4029	100	24	equations	equation	NOUN
ejpam-4029	100	25	(	(	PUNCT
ejpam-4029	100	26	10	10	NUM
ejpam-4029	100	27	)	)	PUNCT
ejpam-4029	100	28	,	,	PUNCT
ejpam-4029	100	29	(	(	PUNCT
ejpam-4029	100	30	11	11	NUM
ejpam-4029	100	31	)	)	PUNCT
ejpam-4029	100	32	,	,	PUNCT
ejpam-4029	100	33	(	(	PUNCT
ejpam-4029	100	34	12	12	NUM
ejpam-4029	100	35	)	)	PUNCT
ejpam-4029	100	36	,	,	PUNCT
ejpam-4029	100	37	(	(	PUNCT
ejpam-4029	100	38	13	13	NUM
ejpam-4029	100	39	)	)	PUNCT
ejpam-4029	100	40	and	and	CCONJ
ejpam-4029	100	41	(	(	PUNCT
ejpam-4029	100	42	14	14	NUM
ejpam-4029	100	43	)	)	PUNCT
ejpam-4029	100	44	,	,	PUNCT
ejpam-4029	100	45	we	we	PRON
ejpam-4029	100	46	can	can	AUX
ejpam-4029	100	47	equate	equate	VERB
ejpam-4029	100	48	the	the	DET
ejpam-4029	100	49	left	left	ADJ
ejpam-4029	100	50	-	-	PUNCT
ejpam-4029	100	51	hand	hand	NOUN
ejpam-4029	100	52	sides	side	NOUN
ejpam-4029	100	53	to	to	PART
ejpam-4029	100	54	achieve	achieve	VERB
ejpam-4029	100	55	the	the	DET
ejpam-4029	100	56	stated	state	VERB
ejpam-4029	100	57	result	result	NOUN
ejpam-4029	100	58	.	.	PUNCT
ejpam-4029	101	1	6	6	X
ejpam-4029	101	2	.	.	X
ejpam-4029	101	3	derivation	derivation	NOUN
ejpam-4029	101	4	of	of	ADP
ejpam-4029	101	5	entry	entry	NOUN
ejpam-4029	101	6	(	(	PUNCT
ejpam-4029	101	7	2.4.4.2	2.4.4.2	NUM
ejpam-4029	101	8	)	)	PUNCT
ejpam-4029	101	9	in	in	ADP
ejpam-4029	101	10	[	[	X
ejpam-4029	101	11	12	12	NUM
ejpam-4029	101	12	]	]	X
ejpam-4029	101	13	corollary	corollary	ADJ
ejpam-4029	101	14	1	1	NUM
ejpam-4029	101	15	.	.	PUNCT
ejpam-4029	101	16	for	for	ADP
ejpam-4029	101	17	|re(c)|	|re(c)|	PROPN
ejpam-4029	101	18	>	>	X
ejpam-4029	101	19	m,∫	m,∫	NOUN
ejpam-4029	102	1	∞	∞	NOUN
ejpam-4029	102	2	0	0	NUM
ejpam-4029	102	3	csch2(cx	csch2(cx	NOUN
ejpam-4029	102	4	)	)	PUNCT
ejpam-4029	102	5	sinh2(mx)dx	sinh2(mx)dx	NOUN
ejpam-4029	102	6	=	=	SYM
ejpam-4029	102	7	c−	c−	NOUN
ejpam-4029	102	8	πm	πm	PRON
ejpam-4029	102	9	cot	cot	NOUN
ejpam-4029	102	10	(	(	PUNCT
ejpam-4029	102	11	πm	πm	ADP
ejpam-4029	102	12	c	c	NOUN
ejpam-4029	102	13	)	)	PUNCT
ejpam-4029	102	14	2c2	2c2	NUM
ejpam-4029	102	15	(	(	PUNCT
ejpam-4029	102	16	16	16	NUM
ejpam-4029	102	17	)	)	PUNCT
ejpam-4029	102	18	proof	proof	NOUN
ejpam-4029	102	19	.	.	PUNCT
ejpam-4029	103	1	use	use	VERB
ejpam-4029	103	2	equation	equation	NOUN
ejpam-4029	103	3	(	(	PUNCT
ejpam-4029	103	4	15	15	NUM
ejpam-4029	103	5	)	)	PUNCT
ejpam-4029	103	6	and	and	CCONJ
ejpam-4029	103	7	set	set	VERB
ejpam-4029	103	8	k	k	PROPN
ejpam-4029	103	9	=	=	PUNCT
ejpam-4029	103	10	0	0	PUNCT
ejpam-4029	103	11	and	and	CCONJ
ejpam-4029	103	12	simplify	simplify	VERB
ejpam-4029	103	13	using	use	VERB
ejpam-4029	103	14	entry	entry	NOUN
ejpam-4029	103	15	(	(	PUNCT
ejpam-4029	103	16	2	2	NUM
ejpam-4029	103	17	)	)	PUNCT
ejpam-4029	103	18	in	in	ADP
ejpam-4029	103	19	table	table	NOUN
ejpam-4029	103	20	below	below	ADV
ejpam-4029	103	21	(	(	PUNCT
ejpam-4029	103	22	64:12:7	64:12:7	NUM
ejpam-4029	103	23	)	)	PUNCT
ejpam-4029	103	24	in	in	ADP
ejpam-4029	103	25	[	[	X
ejpam-4029	103	26	11	11	NUM
ejpam-4029	103	27	]	]	PUNCT
ejpam-4029	103	28	.	.	PUNCT
ejpam-4029	104	1	7	7	X
ejpam-4029	104	2	.	.	X
ejpam-4029	104	3	derivation	derivation	NOUN
ejpam-4029	104	4	of	of	ADP
ejpam-4029	104	5	new	new	ADJ
ejpam-4029	104	6	entry	entry	NOUN
ejpam-4029	104	7	for	for	ADP
ejpam-4029	104	8	table	table	NOUN
ejpam-4029	104	9	2.4.4	2.4.4	NUM
ejpam-4029	104	10	in	in	ADP
ejpam-4029	104	11	[	[	X
ejpam-4029	104	12	12	12	NUM
ejpam-4029	104	13	]	]	X
ejpam-4029	104	14	corollary	corollary	ADJ
ejpam-4029	104	15	2	2	NUM
ejpam-4029	104	16	.	.	PUNCT
ejpam-4029	104	17	for	for	ADP
ejpam-4029	104	18	all	all	DET
ejpam-4029	104	19	re(β	re(β	NOUN
ejpam-4029	104	20	)	)	PUNCT
ejpam-4029	104	21	>	>	X
ejpam-4029	104	22	|re(α)|/2	|re(α)|/2	PROPN
ejpam-4029	104	23	,	,	PUNCT
ejpam-4029	104	24	∫	∫	PROPN
ejpam-4029	104	25	∞	∞	NUM
ejpam-4029	104	26	0	0	NUM
ejpam-4029	104	27	x	x	SYM
ejpam-4029	104	28	sinh(αx	sinh(αx	NOUN
ejpam-4029	104	29	)	)	PUNCT
ejpam-4029	104	30	csch2(βx)dx	csch2(βx)dx	PROPN
ejpam-4029	104	31	=	=	SYM
ejpam-4029	104	32	π	π	X
ejpam-4029	104	33	(	(	PUNCT
ejpam-4029	104	34	πα−	πα−	PUNCT
ejpam-4029	104	35	β	β	X
ejpam-4029	104	36	sin	sin	NOUN
ejpam-4029	104	37	(	(	PUNCT
ejpam-4029	104	38	πα	πα	PROPN
ejpam-4029	104	39	β	β	X
ejpam-4029	104	40	)	)	PUNCT
ejpam-4029	104	41	)	)	PUNCT
ejpam-4029	105	1	csc2	csc2	NOUN
ejpam-4029	105	2	(	(	PUNCT
ejpam-4029	105	3	πα	πα	PROPN
ejpam-4029	105	4	2β	2β	NOUN
ejpam-4029	105	5	)	)	PUNCT
ejpam-4029	105	6	4β3	4β3	NUM
ejpam-4029	105	7	(	(	PUNCT
ejpam-4029	105	8	17	17	NUM
ejpam-4029	105	9	)	)	PUNCT
ejpam-4029	105	10	proof	proof	NOUN
ejpam-4029	105	11	.	.	PUNCT
ejpam-4029	106	1	use	use	VERB
ejpam-4029	106	2	equation	equation	NOUN
ejpam-4029	106	3	(	(	PUNCT
ejpam-4029	106	4	15	15	NUM
ejpam-4029	106	5	)	)	PUNCT
ejpam-4029	106	6	and	and	CCONJ
ejpam-4029	106	7	set	set	VERB
ejpam-4029	106	8	k	k	PROPN
ejpam-4029	106	9	=	=	SYM
ejpam-4029	106	10	1	1	NUM
ejpam-4029	106	11	,	,	PUNCT
ejpam-4029	106	12	a	a	DET
ejpam-4029	106	13	=	=	SYM
ejpam-4029	106	14	1,m	1,m	NOUN
ejpam-4029	106	15	=	=	SYM
ejpam-4029	106	16	α/2	α/2	NUM
ejpam-4029	106	17	,	,	PUNCT
ejpam-4029	106	18	c	c	PROPN
ejpam-4029	106	19	=	=	SYM
ejpam-4029	106	20	β	β	NOUN
ejpam-4029	106	21	and	and	CCONJ
ejpam-4029	106	22	simplify	simplify	VERB
ejpam-4029	106	23	using	use	VERB
ejpam-4029	106	24	entry	entry	NOUN
ejpam-4029	106	25	(	(	PUNCT
ejpam-4029	106	26	1	1	NUM
ejpam-4029	106	27	)	)	PUNCT
ejpam-4029	106	28	in	in	ADP
ejpam-4029	106	29	table	table	NOUN
ejpam-4029	106	30	below	below	ADV
ejpam-4029	106	31	(	(	PUNCT
ejpam-4029	106	32	64:12:7	64:12:7	NUM
ejpam-4029	106	33	)	)	PUNCT
ejpam-4029	106	34	in	in	ADP
ejpam-4029	106	35	[	[	X
ejpam-4029	106	36	11	11	NUM
ejpam-4029	106	37	]	]	PUNCT
ejpam-4029	106	38	.	.	PUNCT
ejpam-4029	107	1	r.	r.	PROPN
ejpam-4029	107	2	reynolds	reynolds	PROPN
ejpam-4029	107	3	,	,	PUNCT
ejpam-4029	107	4	a.	a.	PROPN
ejpam-4029	107	5	stauffer	stauffer	PROPN
ejpam-4029	107	6	/	/	SYM
ejpam-4029	107	7	eur	eur	PROPN
ejpam-4029	107	8	.	.	PUNCT
ejpam-4029	108	1	j.	j.	PROPN
ejpam-4029	108	2	pure	pure	PROPN
ejpam-4029	108	3	appl	appl	PROPN
ejpam-4029	108	4	.	.	PROPN
ejpam-4029	108	5	math	math	PROPN
ejpam-4029	108	6	,	,	PUNCT
ejpam-4029	108	7	14	14	NUM
ejpam-4029	108	8	(	(	PUNCT
ejpam-4029	108	9	4	4	NUM
ejpam-4029	108	10	)	)	PUNCT
ejpam-4029	108	11	(	(	PUNCT
ejpam-4029	108	12	2021	2021	NUM
ejpam-4029	108	13	)	)	PUNCT
ejpam-4029	108	14	,	,	PUNCT
ejpam-4029	108	15	1132	1132	NUM
ejpam-4029	108	16	-	-	SYM
ejpam-4029	108	17	1147	1147	NUM
ejpam-4029	108	18	1137	1137	NUM
ejpam-4029	108	19	8	8	NUM
ejpam-4029	108	20	.	.	PUNCT
ejpam-4029	109	1	derivation	derivation	NOUN
ejpam-4029	109	2	of	of	ADP
ejpam-4029	109	3	the	the	DET
ejpam-4029	109	4	mellin	mellin	PROPN
ejpam-4029	109	5	transform	transform	NOUN
ejpam-4029	109	6	in	in	ADP
ejpam-4029	109	7	this	this	DET
ejpam-4029	109	8	section	section	NOUN
ejpam-4029	109	9	we	we	PRON
ejpam-4029	109	10	will	will	AUX
ejpam-4029	109	11	derive	derive	VERB
ejpam-4029	109	12	a	a	DET
ejpam-4029	109	13	generalize	generalize	NOUN
ejpam-4029	109	14	mellin	mellin	PROPN
ejpam-4029	109	15	transform	transform	NOUN
ejpam-4029	109	16	of	of	ADP
ejpam-4029	109	17	equations	equation	NOUN
ejpam-4029	109	18	(	(	PUNCT
ejpam-4029	109	19	2.3.1.19	2.3.1.19	NOUN
ejpam-4029	109	20	)	)	PUNCT
ejpam-4029	109	21	in	in	ADP
ejpam-4029	109	22	[	[	X
ejpam-4029	109	23	7	7	NUM
ejpam-4029	109	24	]	]	PUNCT
ejpam-4029	109	25	,	,	PUNCT
ejpam-4029	109	26	(	(	PUNCT
ejpam-4029	109	27	3.527.8	3.527.8	NUM
ejpam-4029	109	28	)	)	PUNCT
ejpam-4029	109	29	and	and	CCONJ
ejpam-4029	109	30	(	(	PUNCT
ejpam-4029	109	31	3.527.9	3.527.9	NUM
ejpam-4029	109	32	)	)	PUNCT
ejpam-4029	109	33	in	in	ADP
ejpam-4029	109	34	[	[	X
ejpam-4029	109	35	8	8	NUM
ejpam-4029	109	36	]	]	PUNCT
ejpam-4029	109	37	.	.	PUNCT
ejpam-4029	110	1	theorem	theorem	NOUN
ejpam-4029	110	2	2	2	NUM
ejpam-4029	110	3	.	.	X
ejpam-4029	110	4	for	for	ADP
ejpam-4029	110	5	all	all	DET
ejpam-4029	110	6	re(s	re(s	ADJ
ejpam-4029	110	7	)	)	PUNCT
ejpam-4029	110	8	>	>	X
ejpam-4029	110	9	0	0	NUM
ejpam-4029	110	10	,	,	PUNCT
ejpam-4029	110	11	re(β	re(β	X
ejpam-4029	110	12	)	)	PUNCT
ejpam-4029	110	13	=	=	SYM
ejpam-4029	110	14	√	√	NUM
ejpam-4029	110	15	|re(α)|,∫	|re(α)|,∫	VERB
ejpam-4029	110	16	∞	∞	PROPN
ejpam-4029	110	17	0	0	NUM
ejpam-4029	111	1	xs−1	xs−1	PROPN
ejpam-4029	111	2	cosh(αx	cosh(αx	PROPN
ejpam-4029	111	3	)	)	PUNCT
ejpam-4029	111	4	csch2(βx)dx	csch2(βx)dx	PROPN
ejpam-4029	111	5	=	=	SYM
ejpam-4029	111	6	−1	−1	NOUN
ejpam-4029	111	7	2	2	NUM
ejpam-4029	111	8	πs−1	πs−1	NOUN
ejpam-4029	111	9	(	(	PUNCT
ejpam-4029	111	10	1	1	NUM
ejpam-4029	111	11	β	β	X
ejpam-4029	111	12	)	)	PUNCT
ejpam-4029	111	13	s	s	PART
ejpam-4029	112	1	csc	csc	PROPN
ejpam-4029	112	2	(	(	PUNCT
ejpam-4029	112	3	πs	πs	PROPN
ejpam-4029	112	4	2	2	NUM
ejpam-4029	112	5	)	)	PUNCT
ejpam-4029	112	6	li2−s	li2−s	PROPN
ejpam-4029	112	7	(	(	PUNCT
ejpam-4029	112	8	e	e	X
ejpam-4029	112	9	−	−	PROPN
ejpam-4029	112	10	iπα	iπα	PROPN
ejpam-4029	112	11	β	β	X
ejpam-4029	112	12	)	)	PUNCT
ejpam-4029	113	1	+	+	CCONJ
ejpam-4029	113	2	1	1	NUM
ejpam-4029	113	3	2	2	NUM
ejpam-4029	113	4	πs−1s	πs−1s	SYM
ejpam-4029	113	5	(	(	PUNCT
ejpam-4029	113	6	1	1	NUM
ejpam-4029	113	7	β	β	X
ejpam-4029	113	8	)	)	PUNCT
ejpam-4029	113	9	s	s	PART
ejpam-4029	113	10	csc	csc	PROPN
ejpam-4029	113	11	(	(	PUNCT
ejpam-4029	113	12	πs	πs	PROPN
ejpam-4029	113	13	2	2	NUM
ejpam-4029	113	14	)	)	PUNCT
ejpam-4029	113	15	li2−s	li2−s	PROPN
ejpam-4029	113	16	(	(	PUNCT
ejpam-4029	113	17	e	e	X
ejpam-4029	113	18	−	−	PROPN
ejpam-4029	113	19	iπα	iπα	PROPN
ejpam-4029	113	20	β	β	X
ejpam-4029	113	21	)	)	PUNCT
ejpam-4029	114	1	−	−	PROPN
ejpam-4029	114	2	1	1	NUM
ejpam-4029	114	3	2	2	NUM
ejpam-4029	114	4	πs−1	πs−1	NOUN
ejpam-4029	114	5	(	(	PUNCT
ejpam-4029	114	6	1	1	NUM
ejpam-4029	114	7	β	β	X
ejpam-4029	114	8	)	)	PUNCT
ejpam-4029	114	9	s	s	PART
ejpam-4029	114	10	csc	csc	PROPN
ejpam-4029	114	11	(	(	PUNCT
ejpam-4029	114	12	πs	πs	PROPN
ejpam-4029	114	13	2	2	NUM
ejpam-4029	114	14	)	)	PUNCT
ejpam-4029	114	15	li2−s	li2−s	PROPN
ejpam-4029	114	16	(	(	PUNCT
ejpam-4029	114	17	e	e	X
ejpam-4029	114	18	iπα	iπα	PROPN
ejpam-4029	114	19	β	β	X
ejpam-4029	114	20	)	)	PUNCT
ejpam-4029	115	1	+	+	CCONJ
ejpam-4029	115	2	1	1	NUM
ejpam-4029	115	3	2	2	NUM
ejpam-4029	115	4	πs−1s	πs−1s	SYM
ejpam-4029	115	5	(	(	PUNCT
ejpam-4029	115	6	1	1	NUM
ejpam-4029	115	7	β	β	X
ejpam-4029	115	8	)	)	PUNCT
ejpam-4029	115	9	s	s	PART
ejpam-4029	115	10	csc	csc	PROPN
ejpam-4029	115	11	(	(	PUNCT
ejpam-4029	115	12	πs	πs	PROPN
ejpam-4029	115	13	2	2	NUM
ejpam-4029	115	14	)	)	PUNCT
ejpam-4029	115	15	li2−s	li2−s	PROPN
ejpam-4029	115	16	(	(	PUNCT
ejpam-4029	115	17	e	e	X
ejpam-4029	115	18	iπα	iπα	PROPN
ejpam-4029	115	19	β	β	X
ejpam-4029	115	20	)	)	PUNCT
ejpam-4029	116	1	−	−	PROPN
ejpam-4029	116	2	1	1	NUM
ejpam-4029	116	3	2	2	NUM
ejpam-4029	116	4	iαπs	iαπs	NOUN
ejpam-4029	116	5	(	(	PUNCT
ejpam-4029	116	6	1	1	NUM
ejpam-4029	116	7	β	β	X
ejpam-4029	116	8	)	)	PUNCT
ejpam-4029	116	9	s+1	s+1	PROPN
ejpam-4029	116	10	csc	csc	PROPN
ejpam-4029	116	11	(	(	PUNCT
ejpam-4029	116	12	πs	πs	PROPN
ejpam-4029	116	13	2	2	X
ejpam-4029	116	14	)	)	PUNCT
ejpam-4029	116	15	li1−s	li1−s	PROPN
ejpam-4029	116	16	(	(	PUNCT
ejpam-4029	116	17	e	e	X
ejpam-4029	116	18	−	−	PROPN
ejpam-4029	116	19	iπα	iπα	PROPN
ejpam-4029	116	20	β	β	X
ejpam-4029	116	21	)	)	PUNCT
ejpam-4029	117	1	+	+	CCONJ
ejpam-4029	117	2	1	1	NUM
ejpam-4029	117	3	2	2	NUM
ejpam-4029	117	4	iαπs	iαπs	NOUN
ejpam-4029	117	5	(	(	PUNCT
ejpam-4029	117	6	1	1	NUM
ejpam-4029	117	7	β	β	X
ejpam-4029	117	8	)	)	PUNCT
ejpam-4029	117	9	s+1	s+1	PROPN
ejpam-4029	117	10	csc	csc	PROPN
ejpam-4029	117	11	(	(	PUNCT
ejpam-4029	117	12	πs	πs	PROPN
ejpam-4029	117	13	2	2	X
ejpam-4029	117	14	)	)	PUNCT
ejpam-4029	117	15	li1−s	li1−s	PROPN
ejpam-4029	117	16	(	(	PUNCT
ejpam-4029	117	17	e	e	X
ejpam-4029	117	18	iπα	iπα	PROPN
ejpam-4029	117	19	β	β	X
ejpam-4029	117	20	)	)	PUNCT
ejpam-4029	117	21	(	(	PUNCT
ejpam-4029	117	22	18	18	NUM
ejpam-4029	117	23	)	)	PUNCT
ejpam-4029	117	24	proof	proof	NOUN
ejpam-4029	117	25	.	.	PUNCT
ejpam-4029	118	1	use	use	VERB
ejpam-4029	118	2	equation	equation	NOUN
ejpam-4029	118	3	(	(	PUNCT
ejpam-4029	118	4	15	15	NUM
ejpam-4029	118	5	)	)	PUNCT
ejpam-4029	118	6	set	set	VERB
ejpam-4029	118	7	m	m	NOUN
ejpam-4029	118	8	=	=	SYM
ejpam-4029	118	9	m/2	m/2	NUM
ejpam-4029	118	10	,	,	PUNCT
ejpam-4029	118	11	a	a	PRON
ejpam-4029	118	12	=	=	PUNCT
ejpam-4029	118	13	e2a	e2a	X
ejpam-4029	118	14	and	and	CCONJ
ejpam-4029	118	15	replace	replace	VERB
ejpam-4029	118	16	m	m	NOUN
ejpam-4029	118	17	by	by	ADP
ejpam-4029	118	18	−m	−m	NOUN
ejpam-4029	118	19	to	to	PART
ejpam-4029	118	20	form	form	VERB
ejpam-4029	118	21	a	a	DET
ejpam-4029	118	22	second	second	ADJ
ejpam-4029	118	23	equation	equation	NOUN
ejpam-4029	118	24	and	and	CCONJ
ejpam-4029	118	25	take	take	VERB
ejpam-4029	118	26	their	their	PRON
ejpam-4029	118	27	difference	difference	NOUN
ejpam-4029	118	28	to	to	PART
ejpam-4029	118	29	get	get	VERB
ejpam-4029	118	30	∫	∫	PROPN
ejpam-4029	118	31	∞	∞	PROPN
ejpam-4029	118	32	0	0	PUNCT
ejpam-4029	119	1	(	(	PUNCT
ejpam-4029	119	2	(	(	PUNCT
ejpam-4029	119	3	a−	a−	PROPN
ejpam-4029	119	4	x)k	x)k	NOUN
ejpam-4029	120	1	−	−	PROPN
ejpam-4029	120	2	(	(	PUNCT
ejpam-4029	120	3	a+	a+	X
ejpam-4029	120	4	x)k	x)k	NOUN
ejpam-4029	120	5	)	)	PUNCT
ejpam-4029	121	1	csch2(cx	csch2(cx	NOUN
ejpam-4029	121	2	)	)	PUNCT
ejpam-4029	121	3	sinh(mx)dx	sinh(mx)dx	VERB
ejpam-4029	121	4	=	=	SYM
ejpam-4029	121	5	−	−	PROPN
ejpam-4029	121	6	iπmak	iπmak	NOUN
ejpam-4029	121	7	c2	c2	PROPN
ejpam-4029	121	8	−	−	PROPN
ejpam-4029	121	9	iπk+1	iπk+1	NOUN
ejpam-4029	121	10	m	m	VERB
ejpam-4029	121	11	(	(	PUNCT
ejpam-4029	121	12	i	i	NOUN
ejpam-4029	121	13	c	c	NOUN
ejpam-4029	121	14	)	)	PUNCT
ejpam-4029	122	1	k	k	NOUN
ejpam-4029	122	2	e−	e−	PROPN
ejpam-4029	122	3	iπm	iπm	VERB
ejpam-4029	122	4	c	c	PROPN
ejpam-4029	122	5	φ	φ	PROPN
ejpam-4029	122	6	(	(	PUNCT
ejpam-4029	122	7	e−	e−	X
ejpam-4029	122	8	imπ	imπ	VERB
ejpam-4029	123	1	c	c	PROPN
ejpam-4029	123	2	,	,	PUNCT
ejpam-4029	123	3	−k	−k	PROPN
ejpam-4029	123	4	,	,	PUNCT
ejpam-4029	123	5	1−	1−	NUM
ejpam-4029	123	6	iac	iac	NOUN
ejpam-4029	123	7	π	π	PROPN
ejpam-4029	123	8	)	)	PUNCT
ejpam-4029	123	9	c2	c2	PROPN
ejpam-4029	123	10	−	−	PROPN
ejpam-4029	123	11	iπk+1	iπk+1	NOUN
ejpam-4029	123	12	m	m	VERB
ejpam-4029	123	13	(	(	PUNCT
ejpam-4029	123	14	i	i	NOUN
ejpam-4029	123	15	c	c	NOUN
ejpam-4029	123	16	)	)	PUNCT
ejpam-4029	124	1	k	k	NOUN
ejpam-4029	124	2	e	e	X
ejpam-4029	124	3	iπm	iπm	PROPN
ejpam-4029	124	4	c	c	PROPN
ejpam-4029	124	5	φ	φ	PROPN
ejpam-4029	124	6	(	(	PUNCT
ejpam-4029	124	7	e	e	NOUN
ejpam-4029	124	8	imπ	imπ	VERB
ejpam-4029	124	9	c	c	PROPN
ejpam-4029	124	10	,	,	PUNCT
ejpam-4029	124	11	−k	−k	PROPN
ejpam-4029	124	12	,	,	PUNCT
ejpam-4029	124	13	1−	1−	NUM
ejpam-4029	124	14	iac	iac	NOUN
ejpam-4029	124	15	π	π	PROPN
ejpam-4029	124	16	)	)	PUNCT
ejpam-4029	125	1	c2	c2	PROPN
ejpam-4029	125	2	+	+	CCONJ
ejpam-4029	125	3	kπk	kπk	PROPN
ejpam-4029	125	4	(	(	PUNCT
ejpam-4029	125	5	i	i	NOUN
ejpam-4029	125	6	c	c	NOUN
ejpam-4029	125	7	)	)	PUNCT
ejpam-4029	126	1	k	k	NOUN
ejpam-4029	126	2	e−	e−	PROPN
ejpam-4029	126	3	iπm	iπm	VERB
ejpam-4029	126	4	c	c	PROPN
ejpam-4029	126	5	φ	φ	PROPN
ejpam-4029	126	6	(	(	PUNCT
ejpam-4029	126	7	e−	e−	X
ejpam-4029	126	8	imπ	imπ	VERB
ejpam-4029	126	9	c	c	PROPN
ejpam-4029	126	10	,	,	PUNCT
ejpam-4029	126	11	1−	1−	NUM
ejpam-4029	126	12	k	k	X
ejpam-4029	126	13	,	,	PUNCT
ejpam-4029	127	1	1−	1−	NUM
ejpam-4029	127	2	iac	iac	PROPN
ejpam-4029	127	3	π	π	PROPN
ejpam-4029	127	4	)	)	PUNCT
ejpam-4029	127	5	c	c	PROPN
ejpam-4029	128	1	−	−	PROPN
ejpam-4029	128	2	kπk	kπk	PROPN
ejpam-4029	128	3	(	(	PUNCT
ejpam-4029	128	4	i	i	NOUN
ejpam-4029	128	5	c	c	NOUN
ejpam-4029	128	6	)	)	PUNCT
ejpam-4029	129	1	k	k	NOUN
ejpam-4029	129	2	e	e	X
ejpam-4029	129	3	iπm	iπm	PROPN
ejpam-4029	129	4	c	c	PROPN
ejpam-4029	129	5	φ	φ	PROPN
ejpam-4029	129	6	(	(	PUNCT
ejpam-4029	129	7	e	e	NOUN
ejpam-4029	129	8	imπ	imπ	VERB
ejpam-4029	129	9	c	c	PROPN
ejpam-4029	129	10	,	,	PUNCT
ejpam-4029	129	11	1−	1−	NUM
ejpam-4029	129	12	k	k	X
ejpam-4029	129	13	,	,	PUNCT
ejpam-4029	129	14	1−	1−	NUM
ejpam-4029	129	15	iac	iac	PROPN
ejpam-4029	129	16	π	π	PROPN
ejpam-4029	129	17	)	)	PUNCT
ejpam-4029	129	18	c	c	PROPN
ejpam-4029	129	19	(	(	PUNCT
ejpam-4029	129	20	19	19	NUM
ejpam-4029	129	21	)	)	PUNCT
ejpam-4029	129	22	next	next	ADV
ejpam-4029	129	23	set	set	VERB
ejpam-4029	129	24	a	a	DET
ejpam-4029	129	25	=	=	X
ejpam-4029	129	26	0,m	0,m	NOUN
ejpam-4029	129	27	=	=	SYM
ejpam-4029	129	28	α	α	PROPN
ejpam-4029	129	29	,	,	PUNCT
ejpam-4029	129	30	c	c	NOUN
ejpam-4029	129	31	=	=	SYM
ejpam-4029	129	32	β	β	X
ejpam-4029	129	33	,	,	PUNCT
ejpam-4029	129	34	k	k	PROPN
ejpam-4029	129	35	=	=	PUNCT
ejpam-4029	129	36	s−	s−	PROPN
ejpam-4029	129	37	1	1	NUM
ejpam-4029	129	38	and	and	CCONJ
ejpam-4029	129	39	simplify	simplify	VERB
ejpam-4029	129	40	using	use	VERB
ejpam-4029	129	41	equation	equation	NOUN
ejpam-4029	129	42	(	(	PUNCT
ejpam-4029	129	43	64:12:2	64:12:2	NUM
ejpam-4029	129	44	)	)	PUNCT
ejpam-4029	129	45	in	in	ADP
ejpam-4029	129	46	[	[	X
ejpam-4029	129	47	11	11	NUM
ejpam-4029	129	48	]	]	SYM
ejpam-4029	129	49	.	.	PUNCT
ejpam-4029	130	1	9	9	X
ejpam-4029	130	2	.	.	X
ejpam-4029	130	3	derivation	derivation	NOUN
ejpam-4029	130	4	of	of	ADP
ejpam-4029	130	5	(	(	PUNCT
ejpam-4029	130	6	3.527.1	3.527.1	NUM
ejpam-4029	130	7	)	)	PUNCT
ejpam-4029	130	8	in	in	ADP
ejpam-4029	130	9	[	[	X
ejpam-4029	130	10	8	8	NUM
ejpam-4029	130	11	]	]	PUNCT
ejpam-4029	130	12	theorem	theorem	NOUN
ejpam-4029	130	13	3	3	NUM
ejpam-4029	130	14	.	.	PUNCT
ejpam-4029	130	15	for	for	ADP
ejpam-4029	130	16	all	all	DET
ejpam-4029	130	17	re(a	re(a	NOUN
ejpam-4029	130	18	)	)	PUNCT
ejpam-4029	130	19	>	>	X
ejpam-4029	130	20	0	0	NUM
ejpam-4029	130	21	,	,	PUNCT
ejpam-4029	130	22	re(µ	re(µ	X
ejpam-4029	130	23	)	)	PUNCT
ejpam-4029	130	24	>	>	X
ejpam-4029	131	1	2,∫	2,∫	NUM
ejpam-4029	131	2	∞	∞	NUM
ejpam-4029	131	3	0	0	PUNCT
ejpam-4029	132	1	xµ−1	xµ−1	PROPN
ejpam-4029	132	2	csch2(ax)dx	csch2(ax)dx	VERB
ejpam-4029	132	3	=	=	SYM
ejpam-4029	132	4	22−µ	22−µ	NUM
ejpam-4029	132	5	(	(	PUNCT
ejpam-4029	132	6	1	1	NUM
ejpam-4029	132	7	a	a	PRON
ejpam-4029	132	8	)	)	PUNCT
ejpam-4029	132	9	µ	µ	PROPN
ejpam-4029	132	10	γ(µ)ζ(µ−	γ(µ)ζ(µ−	NOUN
ejpam-4029	132	11	1	1	NUM
ejpam-4029	132	12	)	)	PUNCT
ejpam-4029	132	13	(	(	PUNCT
ejpam-4029	132	14	20	20	X
ejpam-4029	132	15	)	)	PUNCT
ejpam-4029	132	16	proof	proof	NOUN
ejpam-4029	132	17	.	.	PUNCT
ejpam-4029	133	1	use	use	VERB
ejpam-4029	133	2	equation	equation	NOUN
ejpam-4029	133	3	(	(	PUNCT
ejpam-4029	133	4	18	18	NUM
ejpam-4029	133	5	)	)	PUNCT
ejpam-4029	133	6	and	and	CCONJ
ejpam-4029	133	7	set	set	VERB
ejpam-4029	133	8	α	α	NOUN
ejpam-4029	133	9	=	=	SYM
ejpam-4029	133	10	0	0	NUM
ejpam-4029	133	11	,	,	PUNCT
ejpam-4029	133	12	s	s	PART
ejpam-4029	133	13	=	=	SYM
ejpam-4029	133	14	µ	µ	X
ejpam-4029	133	15	,	,	PUNCT
ejpam-4029	133	16	β	β	X
ejpam-4029	133	17	=	=	PUNCT
ejpam-4029	133	18	a	a	PRON
ejpam-4029	133	19	and	and	CCONJ
ejpam-4029	133	20	simplify	simplify	VERB
ejpam-4029	133	21	using	use	VERB
ejpam-4029	133	22	equation	equation	NOUN
ejpam-4029	133	23	(	(	PUNCT
ejpam-4029	133	24	25:12:5	25:12:5	NUM
ejpam-4029	133	25	)	)	PUNCT
ejpam-4029	133	26	in	in	ADP
ejpam-4029	133	27	[	[	X
ejpam-4029	133	28	11	11	NUM
ejpam-4029	133	29	]	]	PUNCT
ejpam-4029	133	30	.	.	PUNCT
ejpam-4029	134	1	r.	r.	PROPN
ejpam-4029	134	2	reynolds	reynolds	PROPN
ejpam-4029	134	3	,	,	PUNCT
ejpam-4029	134	4	a.	a.	PROPN
ejpam-4029	134	5	stauffer	stauffer	PROPN
ejpam-4029	134	6	/	/	SYM
ejpam-4029	134	7	eur	eur	PROPN
ejpam-4029	134	8	.	.	PUNCT
ejpam-4029	135	1	j.	j.	PROPN
ejpam-4029	135	2	pure	pure	PROPN
ejpam-4029	135	3	appl	appl	PROPN
ejpam-4029	135	4	.	.	PROPN
ejpam-4029	135	5	math	math	PROPN
ejpam-4029	135	6	,	,	PUNCT
ejpam-4029	135	7	14	14	NUM
ejpam-4029	135	8	(	(	PUNCT
ejpam-4029	135	9	4	4	NUM
ejpam-4029	135	10	)	)	PUNCT
ejpam-4029	135	11	(	(	PUNCT
ejpam-4029	135	12	2021	2021	NUM
ejpam-4029	135	13	)	)	PUNCT
ejpam-4029	135	14	,	,	PUNCT
ejpam-4029	135	15	1132	1132	NUM
ejpam-4029	135	16	-	-	SYM
ejpam-4029	135	17	1147	1147	NUM
ejpam-4029	135	18	1138	1138	NUM
ejpam-4029	135	19	10	10	NUM
ejpam-4029	135	20	.	.	PUNCT
ejpam-4029	136	1	derivation	derivation	NOUN
ejpam-4029	136	2	of	of	ADP
ejpam-4029	136	3	entry	entry	NOUN
ejpam-4029	136	4	(	(	PUNCT
ejpam-4029	136	5	3.527.2	3.527.2	NUM
ejpam-4029	136	6	)	)	PUNCT
ejpam-4029	136	7	in	in	ADP
ejpam-4029	136	8	[	[	X
ejpam-4029	136	9	8	8	NUM
ejpam-4029	136	10	]	]	PUNCT
ejpam-4029	136	11	theorem	theorem	NOUN
ejpam-4029	136	12	4	4	NUM
ejpam-4029	136	13	.	.	PUNCT
ejpam-4029	136	14	for	for	ADP
ejpam-4029	136	15	all	all	DET
ejpam-4029	136	16	re(β	re(β	NOUN
ejpam-4029	136	17	)	)	PUNCT
ejpam-4029	136	18	>	>	X
ejpam-4029	137	1	0,∫	0,∫	X
ejpam-4029	137	2	∞	∞	NUM
ejpam-4029	137	3	0	0	NUM
ejpam-4029	138	1	x2	x2	NUM
ejpam-4029	138	2	m	m	VERB
ejpam-4029	138	3	csch2(βx)dx	csch2(βx)dx	NOUN
ejpam-4029	138	4	=	=	SYM
ejpam-4029	139	1	π2	π2	NUM
ejpam-4029	139	2	m	m	NOUN
ejpam-4029	139	3	(	(	PUNCT
ejpam-4029	139	4	1	1	NUM
ejpam-4029	139	5	β	β	X
ejpam-4029	139	6	)	)	PUNCT
ejpam-4029	139	7	2m+1	2m+1	PROPN
ejpam-4029	139	8	|b2m|	|b2m|	NOUN
ejpam-4029	139	9	(	(	PUNCT
ejpam-4029	139	10	21	21	NUM
ejpam-4029	139	11	)	)	PUNCT
ejpam-4029	139	12	proof	proof	NOUN
ejpam-4029	139	13	.	.	PUNCT
ejpam-4029	140	1	use	use	VERB
ejpam-4029	140	2	equation	equation	NOUN
ejpam-4029	140	3	(	(	PUNCT
ejpam-4029	140	4	20	20	NUM
ejpam-4029	140	5	)	)	PUNCT
ejpam-4029	140	6	and	and	CCONJ
ejpam-4029	140	7	set	set	VERB
ejpam-4029	140	8	µ	µ	NOUN
ejpam-4029	140	9	=	=	SYM
ejpam-4029	140	10	2	2	NUM
ejpam-4029	140	11	m	m	NOUN
ejpam-4029	140	12	+	+	NUM
ejpam-4029	140	13	1	1	NUM
ejpam-4029	140	14	and	and	CCONJ
ejpam-4029	140	15	simplify	simplify	VERB
ejpam-4029	140	16	using	use	VERB
ejpam-4029	140	17	equation	equation	NOUN
ejpam-4029	140	18	(	(	PUNCT
ejpam-4029	140	19	3:13:1	3:13:1	NUM
ejpam-4029	140	20	)	)	PUNCT
ejpam-4029	140	21	in	in	ADP
ejpam-4029	140	22	[	[	X
ejpam-4029	140	23	11	11	NUM
ejpam-4029	140	24	]	]	SYM
ejpam-4029	140	25	.	.	PUNCT
ejpam-4029	141	1	11	11	NUM
ejpam-4029	141	2	.	.	PUNCT
ejpam-4029	142	1	derivation	derivation	NOUN
ejpam-4029	142	2	of	of	ADP
ejpam-4029	142	3	entry	entry	NOUN
ejpam-4029	142	4	(	(	PUNCT
ejpam-4029	142	5	3.527.9	3.527.9	NUM
ejpam-4029	142	6	)	)	PUNCT
ejpam-4029	142	7	in	in	ADP
ejpam-4029	142	8	[	[	X
ejpam-4029	142	9	8	8	NUM
ejpam-4029	142	10	]	]	PUNCT
ejpam-4029	142	11	theorem	theorem	NOUN
ejpam-4029	142	12	5	5	NUM
ejpam-4029	142	13	.	.	PUNCT
ejpam-4029	142	14	for	for	ADP
ejpam-4029	142	15	all	all	DET
ejpam-4029	142	16	re(m	re(m	NOUN
ejpam-4029	142	17	)	)	PUNCT
ejpam-4029	142	18	>	>	X
ejpam-4029	142	19	0	0	NUM
ejpam-4029	142	20	,	,	PUNCT
ejpam-4029	142	21	re(a	re(a	NOUN
ejpam-4029	142	22	)	)	PUNCT
ejpam-4029	142	23	>	>	X
ejpam-4029	143	1	0,∫	0,∫	X
ejpam-4029	143	2	∞	∞	NUM
ejpam-4029	143	3	0	0	NUM
ejpam-4029	144	1	x2m+1	x2m+1	PROPN
ejpam-4029	144	2	coth(ax	coth(ax	PROPN
ejpam-4029	144	3	)	)	PUNCT
ejpam-4029	144	4	csch(ax)dx	csch(ax)dx	NOUN
ejpam-4029	144	5	=	=	PUNCT
ejpam-4029	144	6	(	(	PUNCT
ejpam-4029	144	7	1−	1−	NUM
ejpam-4029	144	8	22m+1	22m+1	NUM
ejpam-4029	144	9	)	)	PUNCT
ejpam-4029	144	10	(	(	PUNCT
ejpam-4029	144	11	2m+	2m+	NUM
ejpam-4029	144	12	1)π2m+1	1)π2m+1	NUM
ejpam-4029	144	13	(	(	PUNCT
ejpam-4029	144	14	1	1	NUM
ejpam-4029	144	15	a	a	X
ejpam-4029	144	16	)	)	PUNCT
ejpam-4029	144	17	2m+2	2m+2	PROPN
ejpam-4029	144	18	ζ(−2	ζ(−2	NOUN
ejpam-4029	144	19	m	m	NOUN
ejpam-4029	144	20	)	)	PUNCT
ejpam-4029	144	21	csc(πm	csc(πm	NOUN
ejpam-4029	144	22	)	)	PUNCT
ejpam-4029	144	23	(	(	PUNCT
ejpam-4029	144	24	22	22	NUM
ejpam-4029	144	25	)	)	PUNCT
ejpam-4029	144	26	proof	proof	NOUN
ejpam-4029	144	27	.	.	PUNCT
ejpam-4029	145	1	use	use	VERB
ejpam-4029	145	2	equation	equation	NOUN
ejpam-4029	145	3	(	(	PUNCT
ejpam-4029	145	4	18	18	NUM
ejpam-4029	145	5	)	)	PUNCT
ejpam-4029	145	6	and	and	CCONJ
ejpam-4029	145	7	set	set	VERB
ejpam-4029	145	8	s	s	X
ejpam-4029	145	9	=	=	X
ejpam-4029	145	10	2m+	2m+	NUM
ejpam-4029	145	11	2	2	NUM
ejpam-4029	145	12	,	,	PUNCT
ejpam-4029	145	13	α	α	NOUN
ejpam-4029	145	14	=	=	PUNCT
ejpam-4029	145	15	β	β	X
ejpam-4029	145	16	=	=	PUNCT
ejpam-4029	145	17	a	a	PRON
ejpam-4029	145	18	and	and	CCONJ
ejpam-4029	145	19	simplify	simplify	VERB
ejpam-4029	145	20	using	use	VERB
ejpam-4029	145	21	entry	entry	NOUN
ejpam-4029	145	22	(	(	PUNCT
ejpam-4029	145	23	4	4	NUM
ejpam-4029	145	24	)	)	PUNCT
ejpam-4029	145	25	in	in	ADP
ejpam-4029	145	26	table	table	NOUN
ejpam-4029	145	27	below	below	ADV
ejpam-4029	145	28	(	(	PUNCT
ejpam-4029	145	29	25:12:5	25:12:5	NOUN
ejpam-4029	145	30	)	)	PUNCT
ejpam-4029	145	31	in	in	ADP
ejpam-4029	145	32	[	[	X
ejpam-4029	145	33	11	11	NUM
ejpam-4029	145	34	]	]	PUNCT
ejpam-4029	145	35	.	.	PUNCT
ejpam-4029	146	1	12	12	NUM
ejpam-4029	146	2	.	.	PUNCT
ejpam-4029	147	1	derivation	derivation	NOUN
ejpam-4029	147	2	of	of	ADP
ejpam-4029	147	3	entry	entry	NOUN
ejpam-4029	147	4	(	(	PUNCT
ejpam-4029	147	5	3.527.10	3.527.10	NUM
ejpam-4029	147	6	)	)	PUNCT
ejpam-4029	147	7	in	in	ADP
ejpam-4029	147	8	[	[	X
ejpam-4029	147	9	8	8	NUM
ejpam-4029	147	10	]	]	X
ejpam-4029	147	11	corollary	corollary	ADJ
ejpam-4029	147	12	3	3	X
ejpam-4029	147	13	.	.	PUNCT
ejpam-4029	147	14	for	for	ADP
ejpam-4029	147	15	all	all	DET
ejpam-4029	147	16	re(a	re(a	NOUN
ejpam-4029	147	17	)	)	PUNCT
ejpam-4029	147	18	>	>	X
ejpam-4029	147	19	0	0	NUM
ejpam-4029	147	20	,	,	PUNCT
ejpam-4029	147	21	re(m	re(m	PROPN
ejpam-4029	147	22	)	)	PUNCT
ejpam-4029	147	23	>	>	X
ejpam-4029	148	1	1/2,∫	1/2,∫	NUM
ejpam-4029	148	2	∞	∞	NUM
ejpam-4029	148	3	0	0	NUM
ejpam-4029	149	1	x2	x2	NUM
ejpam-4029	149	2	m	m	NOUN
ejpam-4029	149	3	coth(ax	coth(ax	NOUN
ejpam-4029	149	4	)	)	PUNCT
ejpam-4029	149	5	csch(ax)dx	csch(ax)dx	NOUN
ejpam-4029	149	6	=	=	SYM
ejpam-4029	149	7	41−m	41−m	NUM
ejpam-4029	149	8	(	(	PUNCT
ejpam-4029	149	9	4	4	NUM
ejpam-4029	149	10	m	m	NOUN
ejpam-4029	149	11	−	−	NOUN
ejpam-4029	149	12	1)m	1)m	NUM
ejpam-4029	149	13	(	(	PUNCT
ejpam-4029	149	14	1	1	NUM
ejpam-4029	149	15	a	a	PRON
ejpam-4029	149	16	)	)	PUNCT
ejpam-4029	149	17	2m+1	2m+1	PROPN
ejpam-4029	149	18	ζ(2m)γ(2	ζ(2m)γ(2	PROPN
ejpam-4029	149	19	m	m	PROPN
ejpam-4029	149	20	)	)	PUNCT
ejpam-4029	149	21	(	(	PUNCT
ejpam-4029	149	22	23	23	X
ejpam-4029	149	23	)	)	PUNCT
ejpam-4029	149	24	proof	proof	NOUN
ejpam-4029	149	25	.	.	PUNCT
ejpam-4029	150	1	use	use	VERB
ejpam-4029	150	2	equation	equation	NOUN
ejpam-4029	150	3	(	(	PUNCT
ejpam-4029	150	4	18	18	NUM
ejpam-4029	150	5	)	)	PUNCT
ejpam-4029	150	6	and	and	CCONJ
ejpam-4029	150	7	set	set	VERB
ejpam-4029	150	8	s	s	PART
ejpam-4029	150	9	=	=	SYM
ejpam-4029	150	10	2	2	NUM
ejpam-4029	150	11	m	m	NOUN
ejpam-4029	150	12	+	+	NOUN
ejpam-4029	150	13	1	1	NUM
ejpam-4029	150	14	,	,	PUNCT
ejpam-4029	150	15	α	α	NOUN
ejpam-4029	150	16	=	=	SYM
ejpam-4029	150	17	a	a	PROPN
ejpam-4029	150	18	,	,	PUNCT
ejpam-4029	150	19	β	β	X
ejpam-4029	150	20	=	=	PUNCT
ejpam-4029	150	21	a	a	PRON
ejpam-4029	150	22	and	and	CCONJ
ejpam-4029	150	23	simplify	simplify	VERB
ejpam-4029	150	24	using	use	VERB
ejpam-4029	150	25	entry	entry	NOUN
ejpam-4029	150	26	(	(	PUNCT
ejpam-4029	150	27	4	4	NUM
ejpam-4029	150	28	)	)	PUNCT
ejpam-4029	150	29	in	in	ADP
ejpam-4029	150	30	table	table	NOUN
ejpam-4029	150	31	below	below	ADV
ejpam-4029	150	32	(	(	PUNCT
ejpam-4029	150	33	3:13:1	3:13:1	NUM
ejpam-4029	150	34	)	)	PUNCT
ejpam-4029	150	35	in	in	ADP
ejpam-4029	150	36	[	[	X
ejpam-4029	150	37	11	11	NUM
ejpam-4029	150	38	]	]	SYM
ejpam-4029	150	39	.	.	PUNCT
ejpam-4029	151	1	13	13	NUM
ejpam-4029	151	2	.	.	PUNCT
ejpam-4029	152	1	derivation	derivation	NOUN
ejpam-4029	152	2	of	of	ADP
ejpam-4029	152	3	entry	entry	NOUN
ejpam-4029	152	4	(	(	PUNCT
ejpam-4029	152	5	3.527.12	3.527.12	NUM
ejpam-4029	152	6	)	)	PUNCT
ejpam-4029	152	7	in	in	ADP
ejpam-4029	152	8	[	[	X
ejpam-4029	152	9	8	8	NUM
ejpam-4029	152	10	]	]	X
ejpam-4029	152	11	corollary	corollary	ADJ
ejpam-4029	152	12	4	4	NUM
ejpam-4029	152	13	.	.	PUNCT
ejpam-4029	152	14	∫	∫	PROPN
ejpam-4029	153	1	∞	∞	PROPN
ejpam-4029	153	2	0	0	NUM
ejpam-4029	154	1	x2	x2	ADJ
ejpam-4029	154	2	csch2(x)dx	csch2(x)dx	NOUN
ejpam-4029	154	3	=	=	SYM
ejpam-4029	154	4	π2	π2	X
ejpam-4029	154	5	6	6	NUM
ejpam-4029	154	6	(	(	PUNCT
ejpam-4029	154	7	24	24	NUM
ejpam-4029	154	8	)	)	PUNCT
ejpam-4029	154	9	proof	proof	NOUN
ejpam-4029	154	10	.	.	PUNCT
ejpam-4029	155	1	use	use	VERB
ejpam-4029	155	2	equation	equation	NOUN
ejpam-4029	155	3	(	(	PUNCT
ejpam-4029	155	4	21	21	NUM
ejpam-4029	155	5	)	)	PUNCT
ejpam-4029	155	6	and	and	CCONJ
ejpam-4029	155	7	set	set	VERB
ejpam-4029	155	8	m	m	PROPN
ejpam-4029	155	9	=	=	SYM
ejpam-4029	155	10	β	β	SYM
ejpam-4029	155	11	=	=	SYM
ejpam-4029	155	12	1	1	NUM
ejpam-4029	155	13	and	and	CCONJ
ejpam-4029	155	14	simplify	simplify	NOUN
ejpam-4029	155	15	.	.	PUNCT
ejpam-4029	156	1	r.	r.	PROPN
ejpam-4029	156	2	reynolds	reynolds	PROPN
ejpam-4029	156	3	,	,	PUNCT
ejpam-4029	156	4	a.	a.	PROPN
ejpam-4029	156	5	stauffer	stauffer	PROPN
ejpam-4029	156	6	/	/	SYM
ejpam-4029	156	7	eur	eur	PROPN
ejpam-4029	156	8	.	.	PUNCT
ejpam-4029	157	1	j.	j.	PROPN
ejpam-4029	157	2	pure	pure	PROPN
ejpam-4029	157	3	appl	appl	PROPN
ejpam-4029	157	4	.	.	PROPN
ejpam-4029	157	5	math	math	PROPN
ejpam-4029	157	6	,	,	PUNCT
ejpam-4029	157	7	14	14	NUM
ejpam-4029	157	8	(	(	PUNCT
ejpam-4029	157	9	4	4	NUM
ejpam-4029	157	10	)	)	PUNCT
ejpam-4029	157	11	(	(	PUNCT
ejpam-4029	157	12	2021	2021	NUM
ejpam-4029	157	13	)	)	PUNCT
ejpam-4029	157	14	,	,	PUNCT
ejpam-4029	157	15	1132	1132	NUM
ejpam-4029	157	16	-	-	SYM
ejpam-4029	157	17	1147	1147	NUM
ejpam-4029	157	18	1139	1139	NUM
ejpam-4029	157	19	14	14	NUM
ejpam-4029	157	20	.	.	PUNCT
ejpam-4029	158	1	derivation	derivation	NOUN
ejpam-4029	158	2	of	of	ADP
ejpam-4029	158	3	entry	entry	NOUN
ejpam-4029	158	4	(	(	PUNCT
ejpam-4029	158	5	3.527.13	3.527.13	NOUN
ejpam-4029	158	6	)	)	PUNCT
ejpam-4029	158	7	in	in	ADP
ejpam-4029	158	8	[	[	X
ejpam-4029	158	9	8	8	NUM
ejpam-4029	158	10	]	]	X
ejpam-4029	158	11	corollary	corollary	ADJ
ejpam-4029	158	12	5	5	NUM
ejpam-4029	158	13	.	.	PUNCT
ejpam-4029	158	14	for	for	ADP
ejpam-4029	158	15	all	all	DET
ejpam-4029	158	16	re(a	re(a	NOUN
ejpam-4029	158	17	)	)	PUNCT
ejpam-4029	158	18	>	>	X
ejpam-4029	159	1	0∫	0∫	NUM
ejpam-4029	159	2	∞	∞	NUM
ejpam-4029	159	3	0	0	NUM
ejpam-4029	159	4	x2	x2	PROPN
ejpam-4029	159	5	coth(ax	coth(ax	NOUN
ejpam-4029	159	6	)	)	PUNCT
ejpam-4029	159	7	csch(ax)dx	csch(ax)dx	NOUN
ejpam-4029	159	8	=	=	PUNCT
ejpam-4029	160	1	π2	π2	NUM
ejpam-4029	160	2	2a3	2a3	NUM
ejpam-4029	160	3	(	(	PUNCT
ejpam-4029	160	4	25	25	NUM
ejpam-4029	160	5	)	)	PUNCT
ejpam-4029	160	6	proof	proof	NOUN
ejpam-4029	160	7	.	.	PUNCT
ejpam-4029	161	1	use	use	VERB
ejpam-4029	161	2	equation	equation	NOUN
ejpam-4029	161	3	(	(	PUNCT
ejpam-4029	161	4	18	18	NUM
ejpam-4029	161	5	)	)	PUNCT
ejpam-4029	161	6	and	and	CCONJ
ejpam-4029	161	7	set	set	VERB
ejpam-4029	161	8	s	s	PART
ejpam-4029	161	9	=	=	SYM
ejpam-4029	161	10	3	3	NUM
ejpam-4029	161	11	,	,	PUNCT
ejpam-4029	161	12	α	α	X
ejpam-4029	161	13	=	=	PUNCT
ejpam-4029	161	14	β	β	X
ejpam-4029	161	15	=	=	PUNCT
ejpam-4029	161	16	a	a	PRON
ejpam-4029	161	17	and	and	CCONJ
ejpam-4029	161	18	simplify	simplify	ADJ
ejpam-4029	161	19	.	.	PUNCT
ejpam-4029	162	1	15	15	X
ejpam-4029	162	2	.	.	PUNCT
ejpam-4029	163	1	derivation	derivation	NOUN
ejpam-4029	163	2	of	of	ADP
ejpam-4029	163	3	entry	entry	NOUN
ejpam-4029	163	4	(	(	PUNCT
ejpam-4029	163	5	3.527.16	3.527.16	NUM
ejpam-4029	163	6	)	)	PUNCT
ejpam-4029	163	7	in	in	ADP
ejpam-4029	163	8	[	[	X
ejpam-4029	163	9	8	8	NUM
ejpam-4029	163	10	]	]	PUNCT
ejpam-4029	163	11	and	and	CCONJ
ejpam-4029	163	12	(	(	PUNCT
ejpam-4029	163	13	2.4.5.12	2.4.5.12	X
ejpam-4029	163	14	)	)	PUNCT
ejpam-4029	163	15	in	in	ADP
ejpam-4029	163	16	[	[	X
ejpam-4029	163	17	12	12	NUM
ejpam-4029	163	18	]	]	PUNCT
ejpam-4029	163	19	theorem	theorem	NOUN
ejpam-4029	163	20	6	6	NUM
ejpam-4029	163	21	.	.	PUNCT
ejpam-4029	163	22	for	for	ADP
ejpam-4029	163	23	all	all	DET
ejpam-4029	163	24	re(a	re(a	NOUN
ejpam-4029	163	25	)	)	PUNCT
ejpam-4029	163	26	>	>	X
ejpam-4029	163	27	0	0	NUM
ejpam-4029	163	28	,	,	PUNCT
ejpam-4029	163	29	re(µ	re(µ	X
ejpam-4029	163	30	)	)	PUNCT
ejpam-4029	163	31	>	>	X
ejpam-4029	164	1	2∫	2∫	NUM
ejpam-4029	164	2	∞	∞	NOUN
ejpam-4029	164	3	0	0	NUM
ejpam-4029	165	1	xµ−1	xµ−1	PROPN
ejpam-4029	165	2	coth(ax	coth(ax	PROPN
ejpam-4029	165	3	)	)	PUNCT
ejpam-4029	165	4	csch(ax)dx	csch(ax)dx	NOUN
ejpam-4029	165	5	=	=	SYM
ejpam-4029	165	6	21−µ	21−µ	NUM
ejpam-4029	165	7	(	(	PUNCT
ejpam-4029	165	8	2µ	2µ	NUM
ejpam-4029	165	9	−	−	NOUN
ejpam-4029	165	10	2	2	NUM
ejpam-4029	165	11	)	)	PUNCT
ejpam-4029	165	12	(	(	PUNCT
ejpam-4029	165	13	1	1	NUM
ejpam-4029	165	14	a	a	PRON
ejpam-4029	165	15	)	)	PUNCT
ejpam-4029	165	16	µ	µ	PROPN
ejpam-4029	165	17	γ(µ)ζ(µ−	γ(µ)ζ(µ−	NOUN
ejpam-4029	165	18	1	1	NUM
ejpam-4029	165	19	)	)	PUNCT
ejpam-4029	165	20	(	(	PUNCT
ejpam-4029	165	21	26	26	NUM
ejpam-4029	165	22	)	)	PUNCT
ejpam-4029	165	23	proof	proof	NOUN
ejpam-4029	165	24	.	.	PUNCT
ejpam-4029	166	1	use	use	VERB
ejpam-4029	166	2	equation	equation	NOUN
ejpam-4029	166	3	(	(	PUNCT
ejpam-4029	166	4	18	18	NUM
ejpam-4029	166	5	)	)	PUNCT
ejpam-4029	166	6	and	and	CCONJ
ejpam-4029	166	7	set	set	VERB
ejpam-4029	166	8	s	s	PART
ejpam-4029	166	9	=	=	SYM
ejpam-4029	166	10	µ	µ	X
ejpam-4029	166	11	,	,	PUNCT
ejpam-4029	166	12	α	α	X
ejpam-4029	166	13	=	=	SYM
ejpam-4029	166	14	β	β	X
ejpam-4029	166	15	=	=	PUNCT
ejpam-4029	166	16	a	a	PRON
ejpam-4029	166	17	and	and	CCONJ
ejpam-4029	166	18	simplify	simplify	VERB
ejpam-4029	166	19	using	use	VERB
ejpam-4029	166	20	entry	entry	NOUN
ejpam-4029	166	21	(	(	PUNCT
ejpam-4029	166	22	4	4	NUM
ejpam-4029	166	23	)	)	PUNCT
ejpam-4029	166	24	in	in	ADP
ejpam-4029	166	25	table	table	NOUN
ejpam-4029	166	26	below	below	ADV
ejpam-4029	166	27	(	(	PUNCT
ejpam-4029	166	28	25:12:5	25:12:5	NOUN
ejpam-4029	166	29	)	)	PUNCT
ejpam-4029	166	30	in	in	ADP
ejpam-4029	166	31	[	[	X
ejpam-4029	166	32	11	11	NUM
ejpam-4029	166	33	]	]	PUNCT
ejpam-4029	166	34	.	.	PUNCT
ejpam-4029	167	1	16	16	NUM
ejpam-4029	167	2	.	.	PUNCT
ejpam-4029	168	1	derivation	derivation	NOUN
ejpam-4029	168	2	of	of	ADP
ejpam-4029	168	3	entry	entry	NOUN
ejpam-4029	168	4	(	(	PUNCT
ejpam-4029	168	5	2.3.1.9	2.3.1.9	NUM
ejpam-4029	168	6	)	)	PUNCT
ejpam-4029	168	7	in	in	ADP
ejpam-4029	168	8	brychkov	brychkov	NOUN
ejpam-4029	168	9	,	,	PUNCT
ejpam-4029	168	10	(	(	PUNCT
ejpam-4029	168	11	3.523.1	3.523.1	NUM
ejpam-4029	168	12	)	)	PUNCT
ejpam-4029	168	13	in	in	ADP
ejpam-4029	168	14	[	[	X
ejpam-4029	168	15	8	8	NUM
ejpam-4029	168	16	]	]	PUNCT
ejpam-4029	168	17	theorem	theorem	NOUN
ejpam-4029	168	18	7	7	NUM
ejpam-4029	168	19	.	.	PUNCT
ejpam-4029	168	20	for	for	ADP
ejpam-4029	168	21	all	all	DET
ejpam-4029	168	22	re(s	re(s	ADJ
ejpam-4029	168	23	)	)	PUNCT
ejpam-4029	168	24	>	>	X
ejpam-4029	168	25	1	1	NUM
ejpam-4029	168	26	,	,	PUNCT
ejpam-4029	168	27	re(α	re(α	NOUN
ejpam-4029	168	28	)	)	PUNCT
ejpam-4029	168	29	>	>	X
ejpam-4029	169	1	0∫	0∫	NUM
ejpam-4029	170	1	∞	∞	NOUN
ejpam-4029	170	2	0	0	PUNCT
ejpam-4029	171	1	xs−1	xs−1	NOUN
ejpam-4029	171	2	csch(αx)dx	csch(αx)dx	NOUN
ejpam-4029	171	3	=	=	SYM
ejpam-4029	171	4	21−s	21−s	NUM
ejpam-4029	171	5	(	(	PUNCT
ejpam-4029	171	6	2s	2s	NUM
ejpam-4029	171	7	−	−	NOUN
ejpam-4029	171	8	1	1	NUM
ejpam-4029	171	9	)	)	PUNCT
ejpam-4029	171	10	(	(	PUNCT
ejpam-4029	171	11	1	1	NUM
ejpam-4029	171	12	α	α	NOUN
ejpam-4029	171	13	)	)	PUNCT
ejpam-4029	171	14	s	s	PART
ejpam-4029	171	15	ζ(s)γ(s	ζ(s)γ(s	NOUN
ejpam-4029	171	16	)	)	PUNCT
ejpam-4029	171	17	(	(	PUNCT
ejpam-4029	171	18	27	27	NUM
ejpam-4029	171	19	)	)	PUNCT
ejpam-4029	171	20	proof	proof	NOUN
ejpam-4029	171	21	.	.	PUNCT
ejpam-4029	172	1	use	use	VERB
ejpam-4029	172	2	equation	equation	NOUN
ejpam-4029	172	3	(	(	PUNCT
ejpam-4029	172	4	18	18	NUM
ejpam-4029	172	5	)	)	PUNCT
ejpam-4029	172	6	and	and	CCONJ
ejpam-4029	172	7	take	take	VERB
ejpam-4029	172	8	the	the	DET
ejpam-4029	172	9	first	first	ADJ
ejpam-4029	172	10	partial	partial	ADJ
ejpam-4029	172	11	derivative	derivative	NOUN
ejpam-4029	172	12	with	with	ADP
ejpam-4029	172	13	respect	respect	NOUN
ejpam-4029	172	14	to	to	ADP
ejpam-4029	172	15	α	α	PRON
ejpam-4029	172	16	then	then	ADV
ejpam-4029	172	17	set	set	VERB
ejpam-4029	172	18	α	α	NOUN
ejpam-4029	172	19	=	=	SYM
ejpam-4029	172	20	β	β	X
ejpam-4029	172	21	,	,	PUNCT
ejpam-4029	172	22	s	s	PART
ejpam-4029	172	23	=	=	PUNCT
ejpam-4029	172	24	s−	s−	PROPN
ejpam-4029	172	25	1	1	NUM
ejpam-4029	172	26	and	and	CCONJ
ejpam-4029	172	27	simplify	simplify	VERB
ejpam-4029	172	28	using	use	VERB
ejpam-4029	172	29	entry	entry	NOUN
ejpam-4029	172	30	(	(	PUNCT
ejpam-4029	172	31	4	4	NUM
ejpam-4029	172	32	)	)	PUNCT
ejpam-4029	172	33	in	in	ADP
ejpam-4029	172	34	table	table	NOUN
ejpam-4029	172	35	below	below	ADV
ejpam-4029	172	36	(	(	PUNCT
ejpam-4029	172	37	25:12:5	25:12:5	NOUN
ejpam-4029	172	38	)	)	PUNCT
ejpam-4029	172	39	in	in	ADP
ejpam-4029	172	40	[	[	X
ejpam-4029	172	41	11	11	NUM
ejpam-4029	172	42	]	]	PUNCT
ejpam-4029	172	43	.	.	PUNCT
ejpam-4029	173	1	17	17	NUM
ejpam-4029	173	2	.	.	PUNCT
ejpam-4029	174	1	derivation	derivation	NOUN
ejpam-4029	174	2	of	of	ADP
ejpam-4029	174	3	entry	entry	NOUN
ejpam-4029	174	4	(	(	PUNCT
ejpam-4029	174	5	3.523.2	3.523.2	NUM
ejpam-4029	174	6	)	)	PUNCT
ejpam-4029	174	7	in	in	ADP
ejpam-4029	174	8	[	[	X
ejpam-4029	174	9	8	8	NUM
ejpam-4029	174	10	]	]	PUNCT
ejpam-4029	174	11	theorem	theorem	NOUN
ejpam-4029	174	12	8	8	NUM
ejpam-4029	174	13	.	.	PUNCT
ejpam-4029	174	14	for	for	ADP
ejpam-4029	174	15	all	all	DET
ejpam-4029	174	16	re(a	re(a	NOUN
ejpam-4029	174	17	)	)	PUNCT
ejpam-4029	174	18	>	>	X
ejpam-4029	174	19	0	0	NUM
ejpam-4029	174	20	,	,	PUNCT
ejpam-4029	174	21	n	n	NOUN
ejpam-4029	174	22	=	=	SYM
ejpam-4029	174	23	1	1	NUM
ejpam-4029	174	24	,	,	PUNCT
ejpam-4029	174	25	2	2	NUM
ejpam-4029	174	26	,	,	PUNCT
ejpam-4029	174	27	..	..	PUNCT
ejpam-4029	174	28	∫	∫	PROPN
ejpam-4029	175	1	∞	∞	NUM
ejpam-4029	175	2	0	0	NUM
ejpam-4029	176	1	x2n−1	x2n−1	PROPN
ejpam-4029	176	2	csch(αx)dx	csch(αx)dx	PROPN
ejpam-4029	176	3	=	=	PUNCT
ejpam-4029	176	4	(	(	PUNCT
ejpam-4029	176	5	4n	4n	X
ejpam-4029	176	6	−	−	PROPN
ejpam-4029	176	7	1)π2n	1)π2n	NUM
ejpam-4029	176	8	(	(	PUNCT
ejpam-4029	176	9	1	1	NUM
ejpam-4029	176	10	α	α	NOUN
ejpam-4029	176	11	)	)	PUNCT
ejpam-4029	176	12	2n	2n	NUM
ejpam-4029	176	13	|b2n|	|b2n|	NOUN
ejpam-4029	176	14	2n	2n	NUM
ejpam-4029	176	15	(	(	PUNCT
ejpam-4029	176	16	28	28	NUM
ejpam-4029	176	17	)	)	PUNCT
ejpam-4029	176	18	proof	proof	NOUN
ejpam-4029	176	19	.	.	PUNCT
ejpam-4029	177	1	use	use	VERB
ejpam-4029	177	2	equation	equation	NOUN
ejpam-4029	177	3	(	(	PUNCT
ejpam-4029	177	4	18	18	NUM
ejpam-4029	177	5	)	)	PUNCT
ejpam-4029	177	6	and	and	CCONJ
ejpam-4029	177	7	take	take	VERB
ejpam-4029	177	8	the	the	DET
ejpam-4029	177	9	first	first	ADJ
ejpam-4029	177	10	partial	partial	ADJ
ejpam-4029	177	11	derivative	derivative	NOUN
ejpam-4029	177	12	with	with	ADP
ejpam-4029	177	13	respect	respect	NOUN
ejpam-4029	177	14	to	to	ADP
ejpam-4029	177	15	α	α	PRON
ejpam-4029	177	16	then	then	ADV
ejpam-4029	177	17	set	set	VERB
ejpam-4029	177	18	α	α	NOUN
ejpam-4029	177	19	=	=	SYM
ejpam-4029	177	20	β	β	X
ejpam-4029	177	21	,	,	PUNCT
ejpam-4029	177	22	s	s	NOUN
ejpam-4029	177	23	=	=	X
ejpam-4029	177	24	2n	2n	NUM
ejpam-4029	177	25	and	and	CCONJ
ejpam-4029	177	26	simplify	simplify	VERB
ejpam-4029	177	27	using	use	VERB
ejpam-4029	177	28	equation	equation	NOUN
ejpam-4029	177	29	(	(	PUNCT
ejpam-4029	177	30	3:13:1	3:13:1	NUM
ejpam-4029	177	31	)	)	PUNCT
ejpam-4029	177	32	in	in	ADP
ejpam-4029	177	33	[	[	X
ejpam-4029	177	34	11	11	NUM
ejpam-4029	177	35	]	]	PUNCT
ejpam-4029	177	36	.	.	PUNCT
ejpam-4029	178	1	18	18	NUM
ejpam-4029	178	2	.	.	PUNCT
ejpam-4029	178	3	derivation	derivation	NOUN
ejpam-4029	178	4	of	of	ADP
ejpam-4029	178	5	entry	entry	NOUN
ejpam-4029	178	6	(	(	PUNCT
ejpam-4029	178	7	3.523.6	3.523.6	NUM
ejpam-4029	178	8	)	)	PUNCT
ejpam-4029	178	9	in	in	ADP
ejpam-4029	178	10	[	[	X
ejpam-4029	178	11	8	8	NUM
ejpam-4029	178	12	]	]	X
ejpam-4029	178	13	corollary	corollary	ADJ
ejpam-4029	178	14	6	6	NUM
ejpam-4029	178	15	.	.	PUNCT
ejpam-4029	178	16	∫	∫	PROPN
ejpam-4029	179	1	∞	∞	PROPN
ejpam-4029	179	2	0	0	NUM
ejpam-4029	179	3	x3	x3	ADJ
ejpam-4029	179	4	csch(x)dx	csch(x)dx	VERB
ejpam-4029	179	5	=	=	SYM
ejpam-4029	179	6	π4	π4	NUM
ejpam-4029	179	7	8	8	NUM
ejpam-4029	179	8	(	(	PUNCT
ejpam-4029	179	9	29	29	NUM
ejpam-4029	179	10	)	)	PUNCT
ejpam-4029	179	11	proof	proof	NOUN
ejpam-4029	179	12	.	.	PUNCT
ejpam-4029	180	1	use	use	VERB
ejpam-4029	180	2	equation	equation	NOUN
ejpam-4029	180	3	(	(	PUNCT
ejpam-4029	180	4	18	18	NUM
ejpam-4029	180	5	)	)	PUNCT
ejpam-4029	180	6	and	and	CCONJ
ejpam-4029	180	7	take	take	VERB
ejpam-4029	180	8	the	the	DET
ejpam-4029	180	9	first	first	ADJ
ejpam-4029	180	10	partial	partial	ADJ
ejpam-4029	180	11	derivative	derivative	NOUN
ejpam-4029	180	12	with	with	ADP
ejpam-4029	180	13	respect	respect	NOUN
ejpam-4029	180	14	to	to	ADP
ejpam-4029	180	15	α	α	PRON
ejpam-4029	180	16	then	then	ADV
ejpam-4029	180	17	set	set	VERB
ejpam-4029	180	18	α	α	NOUN
ejpam-4029	180	19	=	=	PUNCT
ejpam-4029	180	20	β	β	X
ejpam-4029	180	21	=	=	SYM
ejpam-4029	180	22	1	1	NUM
ejpam-4029	180	23	,	,	PUNCT
ejpam-4029	180	24	s	s	NOUN
ejpam-4029	180	25	=	=	NOUN
ejpam-4029	180	26	3	3	NUM
ejpam-4029	180	27	and	and	CCONJ
ejpam-4029	180	28	simplify	simplify	VERB
ejpam-4029	180	29	using	use	VERB
ejpam-4029	180	30	entry	entry	NOUN
ejpam-4029	180	31	(	(	PUNCT
ejpam-4029	180	32	2	2	NUM
ejpam-4029	180	33	)	)	PUNCT
ejpam-4029	180	34	in	in	ADP
ejpam-4029	180	35	table	table	NOUN
ejpam-4029	180	36	below	below	ADV
ejpam-4029	180	37	(	(	PUNCT
ejpam-4029	180	38	25:12:5	25:12:5	NOUN
ejpam-4029	180	39	)	)	PUNCT
ejpam-4029	180	40	in	in	ADP
ejpam-4029	180	41	[	[	X
ejpam-4029	180	42	11	11	NUM
ejpam-4029	180	43	]	]	PUNCT
ejpam-4029	180	44	.	.	PUNCT
ejpam-4029	181	1	r.	r.	PROPN
ejpam-4029	181	2	reynolds	reynolds	PROPN
ejpam-4029	181	3	,	,	PUNCT
ejpam-4029	181	4	a.	a.	PROPN
ejpam-4029	181	5	stauffer	stauffer	PROPN
ejpam-4029	181	6	/	/	SYM
ejpam-4029	181	7	eur	eur	PROPN
ejpam-4029	181	8	.	.	PUNCT
ejpam-4029	182	1	j.	j.	PROPN
ejpam-4029	182	2	pure	pure	PROPN
ejpam-4029	182	3	appl	appl	PROPN
ejpam-4029	182	4	.	.	PROPN
ejpam-4029	182	5	math	math	PROPN
ejpam-4029	182	6	,	,	PUNCT
ejpam-4029	182	7	14	14	NUM
ejpam-4029	182	8	(	(	PUNCT
ejpam-4029	182	9	4	4	NUM
ejpam-4029	182	10	)	)	PUNCT
ejpam-4029	182	11	(	(	PUNCT
ejpam-4029	182	12	2021	2021	NUM
ejpam-4029	182	13	)	)	PUNCT
ejpam-4029	182	14	,	,	PUNCT
ejpam-4029	182	15	1132	1132	NUM
ejpam-4029	182	16	-	-	SYM
ejpam-4029	182	17	1147	1147	NUM
ejpam-4029	182	18	1140	1140	NUM
ejpam-4029	182	19	19	19	NUM
ejpam-4029	182	20	.	.	PUNCT
ejpam-4029	183	1	derivation	derivation	NOUN
ejpam-4029	183	2	of	of	ADP
ejpam-4029	183	3	entry	entry	NOUN
ejpam-4029	183	4	(	(	PUNCT
ejpam-4029	183	5	3.523.8	3.523.8	NUM
ejpam-4029	183	6	)	)	PUNCT
ejpam-4029	183	7	in	in	ADP
ejpam-4029	183	8	[	[	X
ejpam-4029	183	9	8	8	NUM
ejpam-4029	183	10	]	]	X
ejpam-4029	183	11	corollary	corollary	ADJ
ejpam-4029	183	12	7	7	NUM
ejpam-4029	183	13	.	.	PUNCT
ejpam-4029	183	14	∫	∫	PROPN
ejpam-4029	184	1	∞	∞	PROPN
ejpam-4029	184	2	0	0	NUM
ejpam-4029	184	3	x5	x5	NOUN
ejpam-4029	184	4	csch(x)dx	csch(x)dx	VERB
ejpam-4029	184	5	=	=	NOUN
ejpam-4029	184	6	π6	π6	NOUN
ejpam-4029	184	7	4	4	NUM
ejpam-4029	184	8	(	(	PUNCT
ejpam-4029	184	9	30	30	NUM
ejpam-4029	184	10	)	)	PUNCT
ejpam-4029	184	11	proof	proof	NOUN
ejpam-4029	184	12	.	.	PUNCT
ejpam-4029	185	1	use	use	VERB
ejpam-4029	185	2	equation	equation	NOUN
ejpam-4029	185	3	(	(	PUNCT
ejpam-4029	185	4	18	18	NUM
ejpam-4029	185	5	)	)	PUNCT
ejpam-4029	185	6	and	and	CCONJ
ejpam-4029	185	7	take	take	VERB
ejpam-4029	185	8	the	the	DET
ejpam-4029	185	9	first	first	ADJ
ejpam-4029	185	10	partial	partial	ADJ
ejpam-4029	185	11	derivative	derivative	NOUN
ejpam-4029	185	12	with	with	ADP
ejpam-4029	185	13	respect	respect	NOUN
ejpam-4029	185	14	to	to	ADP
ejpam-4029	185	15	α	α	PRON
ejpam-4029	185	16	then	then	ADV
ejpam-4029	185	17	set	set	VERB
ejpam-4029	185	18	α	α	NOUN
ejpam-4029	185	19	=	=	PUNCT
ejpam-4029	185	20	β	β	X
ejpam-4029	185	21	=	=	SYM
ejpam-4029	185	22	1	1	NUM
ejpam-4029	185	23	,	,	PUNCT
ejpam-4029	185	24	s	s	NOUN
ejpam-4029	185	25	=	=	SYM
ejpam-4029	185	26	5	5	NUM
ejpam-4029	185	27	and	and	CCONJ
ejpam-4029	185	28	simplify	simplify	VERB
ejpam-4029	185	29	using	use	VERB
ejpam-4029	185	30	entry	entry	NOUN
ejpam-4029	185	31	(	(	PUNCT
ejpam-4029	185	32	2	2	NUM
ejpam-4029	185	33	)	)	PUNCT
ejpam-4029	185	34	in	in	ADP
ejpam-4029	185	35	table	table	NOUN
ejpam-4029	185	36	below	below	ADV
ejpam-4029	185	37	(	(	PUNCT
ejpam-4029	185	38	25:12:5	25:12:5	NOUN
ejpam-4029	185	39	)	)	PUNCT
ejpam-4029	185	40	in	in	ADP
ejpam-4029	185	41	[	[	X
ejpam-4029	185	42	11	11	NUM
ejpam-4029	185	43	]	]	SYM
ejpam-4029	185	44	.	.	PUNCT
ejpam-4029	186	1	20	20	NUM
ejpam-4029	186	2	.	.	PUNCT
ejpam-4029	187	1	derivation	derivation	NOUN
ejpam-4029	187	2	of	of	ADP
ejpam-4029	187	3	entry	entry	NOUN
ejpam-4029	187	4	(	(	PUNCT
ejpam-4029	187	5	3.523.10	3.523.10	NUM
ejpam-4029	187	6	)	)	PUNCT
ejpam-4029	187	7	in	in	ADP
ejpam-4029	187	8	[	[	X
ejpam-4029	187	9	8	8	NUM
ejpam-4029	187	10	]	]	X
ejpam-4029	187	11	corollary	corollary	ADJ
ejpam-4029	187	12	8	8	NUM
ejpam-4029	187	13	.	.	PUNCT
ejpam-4029	188	1	∫	∫	PROPN
ejpam-4029	189	1	∞	∞	PROPN
ejpam-4029	189	2	0	0	NUM
ejpam-4029	190	1	x7	x7	NOUN
ejpam-4029	190	2	csch(x)dx	csch(x)dx	VERB
ejpam-4029	190	3	=	=	SYM
ejpam-4029	190	4	17π8	17π8	NUM
ejpam-4029	190	5	16	16	NUM
ejpam-4029	190	6	(	(	PUNCT
ejpam-4029	190	7	31	31	NUM
ejpam-4029	190	8	)	)	PUNCT
ejpam-4029	190	9	proof	proof	NOUN
ejpam-4029	190	10	.	.	PUNCT
ejpam-4029	191	1	use	use	VERB
ejpam-4029	191	2	equation	equation	NOUN
ejpam-4029	191	3	(	(	PUNCT
ejpam-4029	191	4	18	18	NUM
ejpam-4029	191	5	)	)	PUNCT
ejpam-4029	191	6	and	and	CCONJ
ejpam-4029	191	7	take	take	VERB
ejpam-4029	191	8	the	the	DET
ejpam-4029	191	9	first	first	ADJ
ejpam-4029	191	10	partial	partial	ADJ
ejpam-4029	191	11	derivative	derivative	NOUN
ejpam-4029	191	12	with	with	ADP
ejpam-4029	191	13	respect	respect	NOUN
ejpam-4029	191	14	to	to	ADP
ejpam-4029	191	15	α	α	PRON
ejpam-4029	191	16	then	then	ADV
ejpam-4029	191	17	set	set	VERB
ejpam-4029	191	18	α	α	NOUN
ejpam-4029	191	19	=	=	PUNCT
ejpam-4029	191	20	β	β	X
ejpam-4029	191	21	=	=	SYM
ejpam-4029	191	22	1	1	NUM
ejpam-4029	191	23	,	,	PUNCT
ejpam-4029	191	24	s	s	PART
ejpam-4029	191	25	=	=	NOUN
ejpam-4029	191	26	7	7	NUM
ejpam-4029	191	27	and	and	CCONJ
ejpam-4029	191	28	simplify	simplify	VERB
ejpam-4029	191	29	using	use	VERB
ejpam-4029	191	30	entry	entry	NOUN
ejpam-4029	191	31	(	(	PUNCT
ejpam-4029	191	32	2	2	NUM
ejpam-4029	191	33	)	)	PUNCT
ejpam-4029	191	34	in	in	ADP
ejpam-4029	191	35	table	table	NOUN
ejpam-4029	191	36	below	below	ADV
ejpam-4029	191	37	(	(	PUNCT
ejpam-4029	191	38	25:12:5	25:12:5	NOUN
ejpam-4029	191	39	)	)	PUNCT
ejpam-4029	191	40	in	in	ADP
ejpam-4029	191	41	[	[	X
ejpam-4029	191	42	11	11	NUM
ejpam-4029	191	43	]	]	PUNCT
ejpam-4029	191	44	.	.	PUNCT
ejpam-4029	192	1	21	21	NUM
ejpam-4029	192	2	.	.	PUNCT
ejpam-4029	193	1	derivation	derivation	NOUN
ejpam-4029	193	2	of	of	ADP
ejpam-4029	193	3	entry	entry	NOUN
ejpam-4029	193	4	(	(	PUNCT
ejpam-4029	193	5	3.521.1	3.521.1	NUM
ejpam-4029	193	6	)	)	PUNCT
ejpam-4029	193	7	in	in	ADP
ejpam-4029	193	8	[	[	X
ejpam-4029	193	9	8	8	NUM
ejpam-4029	193	10	]	]	PUNCT
ejpam-4029	193	11	theorem	theorem	NOUN
ejpam-4029	193	12	9	9	NUM
ejpam-4029	193	13	.	.	PUNCT
ejpam-4029	193	14	for	for	ADP
ejpam-4029	193	15	α	α	PRON
ejpam-4029	193	16	∈	∈	PROPN
ejpam-4029	193	17	c	c	X
ejpam-4029	193	18	,	,	PUNCT
ejpam-4029	193	19	∫	∫	PROPN
ejpam-4029	193	20	∞	∞	NUM
ejpam-4029	193	21	0	0	NUM
ejpam-4029	194	1	x	x	SYM
ejpam-4029	194	2	csch(αx)dx	csch(αx)dx	PROPN
ejpam-4029	194	3	=	=	PUNCT
ejpam-4029	194	4			PUNCT
ejpam-4029	194	5	π2	π2	NOUN
ejpam-4029	194	6	4α2	4α2	NOUN
ejpam-4029	194	7	,	,	PUNCT
ejpam-4029	194	8	for	for	ADP
ejpam-4029	194	9	re(α	re(α	NOUN
ejpam-4029	194	10	)	)	PUNCT
ejpam-4029	194	11	>	>	X
ejpam-4029	194	12	0	0	PUNCT
ejpam-4029	195	1	−	−	X
ejpam-4029	195	2	π2	π2	PROPN
ejpam-4029	195	3	4α2	4α2	NOUN
ejpam-4029	195	4	,	,	PUNCT
ejpam-4029	195	5	for	for	ADP
ejpam-4029	195	6	re(α	re(α	NOUN
ejpam-4029	195	7	)	)	PUNCT
ejpam-4029	195	8	<	<	X
ejpam-4029	195	9	0	0	PUNCT
ejpam-4029	195	10	(	(	PUNCT
ejpam-4029	195	11	32	32	NUM
ejpam-4029	195	12	)	)	PUNCT
ejpam-4029	195	13	proof	proof	NOUN
ejpam-4029	195	14	.	.	PUNCT
ejpam-4029	196	1	use	use	VERB
ejpam-4029	196	2	equation	equation	NOUN
ejpam-4029	196	3	(	(	PUNCT
ejpam-4029	196	4	18	18	NUM
ejpam-4029	196	5	)	)	PUNCT
ejpam-4029	196	6	and	and	CCONJ
ejpam-4029	196	7	take	take	VERB
ejpam-4029	196	8	the	the	DET
ejpam-4029	196	9	first	first	ADJ
ejpam-4029	196	10	partial	partial	ADJ
ejpam-4029	196	11	derivative	derivative	NOUN
ejpam-4029	196	12	with	with	ADP
ejpam-4029	196	13	respect	respect	NOUN
ejpam-4029	196	14	to	to	ADP
ejpam-4029	196	15	α	α	PRON
ejpam-4029	196	16	then	then	ADV
ejpam-4029	196	17	set	set	VERB
ejpam-4029	196	18	α	α	NOUN
ejpam-4029	196	19	=	=	SYM
ejpam-4029	196	20	β	β	X
ejpam-4029	196	21	,	,	PUNCT
ejpam-4029	196	22	s	s	NOUN
ejpam-4029	196	23	=	=	SYM
ejpam-4029	196	24	1	1	NUM
ejpam-4029	196	25	and	and	CCONJ
ejpam-4029	196	26	simplify	simplify	VERB
ejpam-4029	196	27	using	use	VERB
ejpam-4029	196	28	entry	entry	NOUN
ejpam-4029	196	29	(	(	PUNCT
ejpam-4029	196	30	2	2	NUM
ejpam-4029	196	31	)	)	PUNCT
ejpam-4029	196	32	in	in	ADP
ejpam-4029	196	33	table	table	NOUN
ejpam-4029	196	34	below	below	ADV
ejpam-4029	196	35	(	(	PUNCT
ejpam-4029	196	36	25:12:5	25:12:5	NOUN
ejpam-4029	196	37	)	)	PUNCT
ejpam-4029	196	38	in	in	ADP
ejpam-4029	196	39	[	[	X
ejpam-4029	196	40	11	11	NUM
ejpam-4029	196	41	]	]	PUNCT
ejpam-4029	196	42	.	.	PUNCT
ejpam-4029	197	1	22	22	NUM
ejpam-4029	197	2	.	.	PUNCT
ejpam-4029	197	3	derivations	derivation	NOUN
ejpam-4029	197	4	in	in	ADP
ejpam-4029	197	5	terms	term	NOUN
ejpam-4029	197	6	of	of	ADP
ejpam-4029	197	7	catalan	catalan	NOUN
ejpam-4029	197	8	’s	’s	PART
ejpam-4029	197	9	constant	constant	ADJ
ejpam-4029	197	10	c	c	NOUN
ejpam-4029	197	11	and	and	CCONJ
ejpam-4029	197	12	π	π	PROPN
ejpam-4029	197	13	corollary	corollary	ADJ
ejpam-4029	197	14	9.∫	9.∫	NUM
ejpam-4029	197	15	∞	∞	NOUN
ejpam-4029	197	16	0	0	NUM
ejpam-4029	197	17	csch(x	csch(x	NOUN
ejpam-4029	197	18	)	)	PUNCT
ejpam-4029	197	19	(	(	PUNCT
ejpam-4029	197	20	−4x2	−4x2	PROPN
ejpam-4029	197	21	csch(x	csch(x	PROPN
ejpam-4029	197	22	)	)	PUNCT
ejpam-4029	198	1	+	+	CCONJ
ejpam-4029	198	2	π2	π2	ADJ
ejpam-4029	198	3	coth(x)−	coth(x)−	PROPN
ejpam-4029	198	4	π2	π2	PROPN
ejpam-4029	198	5	csch(x	csch(x	PROPN
ejpam-4029	198	6	)	)	PUNCT
ejpam-4029	198	7	)	)	PUNCT
ejpam-4029	198	8	4x2	4x2	NUM
ejpam-4029	199	1	+	+	CCONJ
ejpam-4029	199	2	π2	π2	ADJ
ejpam-4029	199	3	dx	dx	PROPN
ejpam-4029	199	4	=	=	PUNCT
ejpam-4029	199	5	−2(c	−2(c	PUNCT
ejpam-4029	199	6	−	−	PROPN
ejpam-4029	199	7	1	1	NUM
ejpam-4029	199	8	)	)	PUNCT
ejpam-4029	199	9	(	(	PUNCT
ejpam-4029	199	10	33	33	NUM
ejpam-4029	199	11	)	)	PUNCT
ejpam-4029	199	12	corollary	corollary	ADJ
ejpam-4029	199	13	10	10	NUM
ejpam-4029	199	14	.	.	PUNCT
ejpam-4029	200	1	∫	∫	PROPN
ejpam-4029	201	1	∞	∞	NUM
ejpam-4029	201	2	0	0	NUM
ejpam-4029	201	3	x	x	SYM
ejpam-4029	201	4	csch(x	csch(x	PROPN
ejpam-4029	201	5	)	)	PUNCT
ejpam-4029	201	6	4x2	4x2	NUM
ejpam-4029	202	1	+	+	CCONJ
ejpam-4029	203	1	π2	π2	ADJ
ejpam-4029	203	2	dx	dx	PROPN
ejpam-4029	203	3	=	=	SYM
ejpam-4029	203	4	1	1	NUM
ejpam-4029	203	5	8	8	NUM
ejpam-4029	203	6	(	(	PUNCT
ejpam-4029	203	7	π	π	NOUN
ejpam-4029	203	8	−	−	PROPN
ejpam-4029	203	9	2	2	NUM
ejpam-4029	203	10	)	)	PUNCT
ejpam-4029	203	11	(	(	PUNCT
ejpam-4029	203	12	34	34	NUM
ejpam-4029	203	13	)	)	PUNCT
ejpam-4029	203	14	proof	proof	NOUN
ejpam-4029	203	15	.	.	PUNCT
ejpam-4029	204	1	use	use	VERB
ejpam-4029	204	2	equation	equation	NOUN
ejpam-4029	204	3	(	(	PUNCT
ejpam-4029	204	4	15	15	NUM
ejpam-4029	204	5	)	)	PUNCT
ejpam-4029	204	6	and	and	CCONJ
ejpam-4029	204	7	set	set	VERB
ejpam-4029	204	8	k	k	PROPN
ejpam-4029	204	9	=	=	PUNCT
ejpam-4029	204	10	−1	−1	NOUN
ejpam-4029	204	11	,	,	PUNCT
ejpam-4029	204	12	a	a	DET
ejpam-4029	204	13	=	=	SYM
ejpam-4029	204	14	−1	−1	NOUN
ejpam-4029	204	15	,	,	PUNCT
ejpam-4029	204	16	c	c	NOUN
ejpam-4029	204	17	=	=	SYM
ejpam-4029	205	1	1,m	1,m	PROPN
ejpam-4029	205	2	=	=	SYM
ejpam-4029	205	3	1/2	1/2	NUM
ejpam-4029	205	4	and	and	CCONJ
ejpam-4029	205	5	simplify	simplify	VERB
ejpam-4029	205	6	in	in	ADP
ejpam-4029	205	7	terms	term	NOUN
ejpam-4029	205	8	of	of	ADP
ejpam-4029	205	9	catalan	catalan	NOUN
ejpam-4029	205	10	’s	’s	PART
ejpam-4029	205	11	constant	constant	ADJ
ejpam-4029	205	12	c	c	NOUN
ejpam-4029	205	13	,	,	PUNCT
ejpam-4029	205	14	using	use	VERB
ejpam-4029	205	15	entries	entry	NOUN
ejpam-4029	205	16	(	(	PUNCT
ejpam-4029	205	17	1	1	NUM
ejpam-4029	205	18	)	)	PUNCT
ejpam-4029	205	19	and	and	CCONJ
ejpam-4029	205	20	(	(	PUNCT
ejpam-4029	205	21	4	4	X
ejpam-4029	205	22	)	)	PUNCT
ejpam-4029	205	23	in	in	ADP
ejpam-4029	205	24	tables	table	NOUN
ejpam-4029	205	25	below	below	ADP
ejpam-4029	205	26	(	(	PUNCT
ejpam-4029	205	27	64:12:7	64:12:7	NUM
ejpam-4029	205	28	)	)	PUNCT
ejpam-4029	205	29	in	in	ADP
ejpam-4029	205	30	[	[	X
ejpam-4029	205	31	11	11	NUM
ejpam-4029	205	32	]	]	PUNCT
ejpam-4029	205	33	and	and	CCONJ
ejpam-4029	205	34	equations	equation	NOUN
ejpam-4029	205	35	(	(	PUNCT
ejpam-4029	205	36	2.3	2.3	NUM
ejpam-4029	205	37	)	)	PUNCT
ejpam-4029	205	38	and	and	CCONJ
ejpam-4029	205	39	(	(	PUNCT
ejpam-4029	205	40	2.7	2.7	NUM
ejpam-4029	205	41	)	)	PUNCT
ejpam-4029	205	42	in	in	ADP
ejpam-4029	205	43	[	[	X
ejpam-4029	205	44	10	10	NUM
ejpam-4029	205	45	]	]	PUNCT
ejpam-4029	205	46	and	and	CCONJ
ejpam-4029	205	47	equation	equation	NOUN
ejpam-4029	205	48	(	(	PUNCT
ejpam-4029	205	49	9.73	9.73	NUM
ejpam-4029	205	50	)	)	PUNCT
ejpam-4029	205	51	in	in	ADP
ejpam-4029	205	52	[	[	X
ejpam-4029	205	53	8	8	NUM
ejpam-4029	205	54	]	]	PUNCT
ejpam-4029	205	55	and	and	CCONJ
ejpam-4029	205	56	simplify	simplify	VERB
ejpam-4029	205	57	in	in	ADP
ejpam-4029	205	58	terms	term	NOUN
ejpam-4029	205	59	of	of	ADP
ejpam-4029	205	60	the	the	DET
ejpam-4029	205	61	real	real	ADJ
ejpam-4029	205	62	and	and	CCONJ
ejpam-4029	205	63	imaginary	imaginary	ADJ
ejpam-4029	205	64	parts	part	NOUN
ejpam-4029	205	65	.	.	PUNCT
ejpam-4029	206	1	r.	r.	PROPN
ejpam-4029	206	2	reynolds	reynolds	PROPN
ejpam-4029	206	3	,	,	PUNCT
ejpam-4029	206	4	a.	a.	PROPN
ejpam-4029	206	5	stauffer	stauffer	PROPN
ejpam-4029	206	6	/	/	SYM
ejpam-4029	206	7	eur	eur	PROPN
ejpam-4029	206	8	.	.	PUNCT
ejpam-4029	207	1	j.	j.	PROPN
ejpam-4029	207	2	pure	pure	PROPN
ejpam-4029	207	3	appl	appl	PROPN
ejpam-4029	207	4	.	.	PROPN
ejpam-4029	207	5	math	math	PROPN
ejpam-4029	207	6	,	,	PUNCT
ejpam-4029	207	7	14	14	NUM
ejpam-4029	207	8	(	(	PUNCT
ejpam-4029	207	9	4	4	NUM
ejpam-4029	207	10	)	)	PUNCT
ejpam-4029	207	11	(	(	PUNCT
ejpam-4029	207	12	2021	2021	NUM
ejpam-4029	207	13	)	)	PUNCT
ejpam-4029	207	14	,	,	PUNCT
ejpam-4029	207	15	1132	1132	NUM
ejpam-4029	207	16	-	-	SYM
ejpam-4029	207	17	1147	1147	NUM
ejpam-4029	207	18	1141	1141	NUM
ejpam-4029	207	19	corollary	corollary	ADJ
ejpam-4029	207	20	11	11	NUM
ejpam-4029	207	21	.	.	PUNCT
ejpam-4029	208	1	∫	∫	PROPN
ejpam-4029	209	1	∞	∞	NUM
ejpam-4029	209	2	0	0	NUM
ejpam-4029	209	3	x	x	SYM
ejpam-4029	209	4	csch(x	csch(x	PROPN
ejpam-4029	209	5	)	)	PUNCT
ejpam-4029	209	6	x2	x2	PROPN
ejpam-4029	210	1	+	+	CCONJ
ejpam-4029	210	2	π2	π2	ADJ
ejpam-4029	210	3	dx	dx	PROPN
ejpam-4029	210	4	=	=	SYM
ejpam-4029	210	5	log(2)−	log(2)−	VERB
ejpam-4029	210	6	1	1	NUM
ejpam-4029	210	7	2	2	NUM
ejpam-4029	210	8	(	(	PUNCT
ejpam-4029	210	9	35	35	NUM
ejpam-4029	210	10	)	)	PUNCT
ejpam-4029	210	11	corollary	corollary	NOUN
ejpam-4029	210	12	12	12	NUM
ejpam-4029	210	13	.	.	PUNCT
ejpam-4029	211	1	∫	∫	PROPN
ejpam-4029	212	1	∞	∞	NUM
ejpam-4029	212	2	0	0	NUM
ejpam-4029	212	3	x	x	SYM
ejpam-4029	212	4	sinh(x	sinh(x	PROPN
ejpam-4029	212	5	)	)	PUNCT
ejpam-4029	212	6	csch2(2x	csch2(2x	PROPN
ejpam-4029	212	7	)	)	PUNCT
ejpam-4029	213	1	x2	x2	PROPN
ejpam-4029	214	1	+	+	CCONJ
ejpam-4029	214	2	π2	π2	ADJ
ejpam-4029	214	3	dx	dx	PROPN
ejpam-4029	214	4	=	=	NOUN
ejpam-4029	214	5	8c	8c	NUM
ejpam-4029	214	6	−	−	ADP
ejpam-4029	214	7	8	8	NUM
ejpam-4029	215	1	+	+	CCONJ
ejpam-4029	215	2	π(log(4)−	π(log(4)−	NOUN
ejpam-4029	215	3	1	1	NUM
ejpam-4029	215	4	)	)	PUNCT
ejpam-4029	215	5	8π	8π	NUM
ejpam-4029	215	6	(	(	PUNCT
ejpam-4029	215	7	36	36	NUM
ejpam-4029	215	8	)	)	PUNCT
ejpam-4029	215	9	proof	proof	NOUN
ejpam-4029	215	10	.	.	PUNCT
ejpam-4029	216	1	use	use	VERB
ejpam-4029	216	2	equation	equation	NOUN
ejpam-4029	216	3	(	(	PUNCT
ejpam-4029	216	4	19	19	NUM
ejpam-4029	216	5	)	)	PUNCT
ejpam-4029	216	6	and	and	CCONJ
ejpam-4029	216	7	set	set	VERB
ejpam-4029	216	8	k	k	PROPN
ejpam-4029	216	9	=	=	PUNCT
ejpam-4029	216	10	−1	−1	NOUN
ejpam-4029	216	11	,	,	PUNCT
ejpam-4029	216	12	a	a	DET
ejpam-4029	216	13	=	=	X
ejpam-4029	216	14	πi	πi	PROPN
ejpam-4029	216	15	,	,	PUNCT
ejpam-4029	216	16	m	m	VERB
ejpam-4029	216	17	=	=	NOUN
ejpam-4029	216	18	1	1	NUM
ejpam-4029	216	19	,	,	PUNCT
ejpam-4029	216	20	c	c	NOUN
ejpam-4029	216	21	=	=	SYM
ejpam-4029	216	22	1	1	NUM
ejpam-4029	216	23	and	and	CCONJ
ejpam-4029	216	24	k	k	NOUN
ejpam-4029	216	25	=	=	SYM
ejpam-4029	216	26	−1	−1	PROPN
ejpam-4029	216	27	,	,	PUNCT
ejpam-4029	216	28	a	a	DET
ejpam-4029	216	29	=	=	X
ejpam-4029	216	30	πi	πi	PROPN
ejpam-4029	216	31	,	,	PUNCT
ejpam-4029	216	32	m	m	VERB
ejpam-4029	216	33	=	=	NOUN
ejpam-4029	216	34	1	1	NUM
ejpam-4029	216	35	,	,	PUNCT
ejpam-4029	216	36	c	c	NOUN
ejpam-4029	216	37	=	=	SYM
ejpam-4029	216	38	2	2	NUM
ejpam-4029	216	39	respectively	respectively	ADV
ejpam-4029	216	40	and	and	CCONJ
ejpam-4029	216	41	simplify	simplify	VERB
ejpam-4029	216	42	using	use	VERB
ejpam-4029	216	43	entries	entry	NOUN
ejpam-4029	216	44	(	(	PUNCT
ejpam-4029	216	45	1	1	NUM
ejpam-4029	216	46	)	)	PUNCT
ejpam-4029	216	47	and	and	CCONJ
ejpam-4029	216	48	(	(	PUNCT
ejpam-4029	216	49	4	4	X
ejpam-4029	216	50	)	)	PUNCT
ejpam-4029	216	51	in	in	ADP
ejpam-4029	216	52	tables	table	NOUN
ejpam-4029	216	53	below	below	ADP
ejpam-4029	216	54	(	(	PUNCT
ejpam-4029	216	55	64:12:7	64:12:7	NUM
ejpam-4029	216	56	)	)	PUNCT
ejpam-4029	216	57	in	in	ADP
ejpam-4029	216	58	[	[	X
ejpam-4029	216	59	11	11	NUM
ejpam-4029	216	60	]	]	PUNCT
ejpam-4029	216	61	and	and	CCONJ
ejpam-4029	216	62	equations	equation	NOUN
ejpam-4029	216	63	(	(	PUNCT
ejpam-4029	216	64	2.3	2.3	NUM
ejpam-4029	216	65	)	)	PUNCT
ejpam-4029	216	66	and	and	CCONJ
ejpam-4029	216	67	(	(	PUNCT
ejpam-4029	216	68	2.7	2.7	NUM
ejpam-4029	216	69	)	)	PUNCT
ejpam-4029	216	70	in	in	ADP
ejpam-4029	216	71	[	[	X
ejpam-4029	216	72	10	10	NUM
ejpam-4029	216	73	]	]	PUNCT
ejpam-4029	216	74	.	.	PUNCT
ejpam-4029	217	1	23	23	NUM
ejpam-4029	217	2	.	.	PUNCT
ejpam-4029	218	1	derivation	derivation	NOUN
ejpam-4029	218	2	of	of	ADP
ejpam-4029	218	3	a	a	DET
ejpam-4029	218	4	new	new	ADJ
ejpam-4029	218	5	entry	entry	NOUN
ejpam-4029	218	6	for	for	ADP
ejpam-4029	218	7	table	table	NOUN
ejpam-4029	218	8	2.4.5	2.4.5	NUM
ejpam-4029	218	9	in	in	ADP
ejpam-4029	218	10	[	[	X
ejpam-4029	218	11	12	12	NUM
ejpam-4029	218	12	]	]	PUNCT
ejpam-4029	218	13	theorem	theorem	NOUN
ejpam-4029	218	14	10	10	NUM
ejpam-4029	218	15	.	.	PUNCT
ejpam-4029	218	16	for	for	ADP
ejpam-4029	218	17	all	all	DET
ejpam-4029	218	18	re(c	re(c	NOUN
ejpam-4029	218	19	)	)	PUNCT
ejpam-4029	218	20	>	>	X
ejpam-4029	218	21	0	0	NUM
ejpam-4029	218	22	,	,	PUNCT
ejpam-4029	218	23	re(m	re(m	PROPN
ejpam-4029	218	24	)	)	PUNCT
ejpam-4029	218	25	>	>	X
ejpam-4029	218	26	0	0	NUM
ejpam-4029	218	27	,	,	PUNCT
ejpam-4029	218	28	z	z	NOUN
ejpam-4029	218	29	∈	∈	NOUN
ejpam-4029	218	30	c,∫	c,∫	NOUN
ejpam-4029	218	31	∞	∞	NOUN
ejpam-4029	218	32	0	0	NUM
ejpam-4029	219	1	x	x	SYM
ejpam-4029	219	2	csch2(cx	csch2(cx	NOUN
ejpam-4029	219	3	)	)	PUNCT
ejpam-4029	219	4	sinh(mx	sinh(mx	NOUN
ejpam-4029	219	5	)	)	PUNCT
ejpam-4029	219	6	x2	x2	PROPN
ejpam-4029	220	1	+	+	PUNCT
ejpam-4029	220	2	z2	z2	PROPN
ejpam-4029	220	3	dx	dx	PROPN
ejpam-4029	220	4	=	=	PUNCT
ejpam-4029	220	5	πm	πm	ADP
ejpam-4029	220	6	2c2z	2c2z	NOUN
ejpam-4029	220	7	+	+	CCONJ
ejpam-4029	220	8	me−	me−	PUNCT
ejpam-4029	220	9	iπm	iπm	PROPN
ejpam-4029	220	10	c	c	PROPN
ejpam-4029	220	11	φ	φ	PROPN
ejpam-4029	220	12	(	(	PUNCT
ejpam-4029	220	13	e−	e−	X
ejpam-4029	220	14	imπ	imπ	VERB
ejpam-4029	220	15	c	c	PROPN
ejpam-4029	220	16	,	,	PUNCT
ejpam-4029	220	17	1	1	NUM
ejpam-4029	220	18	,	,	PUNCT
ejpam-4029	220	19	czπ	czπ	VERB
ejpam-4029	220	20	+	+	CCONJ
ejpam-4029	220	21	1	1	NUM
ejpam-4029	220	22	)	)	PUNCT
ejpam-4029	220	23	2c	2c	NOUN
ejpam-4029	221	1	+	+	CCONJ
ejpam-4029	221	2	me	i	PRON
ejpam-4029	221	3	iπm	iπm	VERB
ejpam-4029	221	4	c	c	PROPN
ejpam-4029	221	5	φ	φ	PROPN
ejpam-4029	221	6	(	(	PUNCT
ejpam-4029	221	7	e	e	NOUN
ejpam-4029	221	8	imπ	imπ	VERB
ejpam-4029	221	9	c	c	PROPN
ejpam-4029	221	10	,	,	PUNCT
ejpam-4029	221	11	1	1	NUM
ejpam-4029	221	12	,	,	PUNCT
ejpam-4029	221	13	czπ	czπ	VERB
ejpam-4029	221	14	+	+	CCONJ
ejpam-4029	221	15	1	1	NUM
ejpam-4029	221	16	)	)	PUNCT
ejpam-4029	221	17	2c	2c	NOUN
ejpam-4029	221	18	−	−	NOUN
ejpam-4029	221	19	ie−	ie−	PUNCT
ejpam-4029	221	20	iπm	iπm	PROPN
ejpam-4029	221	21	c	c	PROPN
ejpam-4029	221	22	φ	φ	PROPN
ejpam-4029	221	23	(	(	PUNCT
ejpam-4029	221	24	e−	e−	X
ejpam-4029	221	25	imπ	imπ	VERB
ejpam-4029	221	26	c	c	PROPN
ejpam-4029	221	27	,	,	PUNCT
ejpam-4029	221	28	2	2	NUM
ejpam-4029	221	29	,	,	PUNCT
ejpam-4029	221	30	czπ	czπ	VERB
ejpam-4029	221	31	+	+	CCONJ
ejpam-4029	221	32	1	1	X
ejpam-4029	221	33	)	)	PUNCT
ejpam-4029	221	34	2π	2π	NOUN
ejpam-4029	221	35	+	+	CCONJ
ejpam-4029	221	36	ie	ie	X
ejpam-4029	221	37	iπm	iπm	PROPN
ejpam-4029	221	38	c	c	PROPN
ejpam-4029	221	39	φ	φ	PROPN
ejpam-4029	221	40	(	(	PUNCT
ejpam-4029	221	41	e	e	NOUN
ejpam-4029	221	42	imπ	imπ	VERB
ejpam-4029	221	43	c	c	PROPN
ejpam-4029	221	44	,	,	PUNCT
ejpam-4029	221	45	2	2	NUM
ejpam-4029	221	46	,	,	PUNCT
ejpam-4029	221	47	czπ	czπ	VERB
ejpam-4029	221	48	+	+	CCONJ
ejpam-4029	221	49	1	1	X
ejpam-4029	221	50	)	)	PUNCT
ejpam-4029	221	51	2π	2π	NOUN
ejpam-4029	221	52	(	(	PUNCT
ejpam-4029	221	53	37	37	NUM
ejpam-4029	221	54	)	)	PUNCT
ejpam-4029	221	55	proof	proof	NOUN
ejpam-4029	221	56	.	.	PUNCT
ejpam-4029	222	1	use	use	VERB
ejpam-4029	222	2	equation	equation	NOUN
ejpam-4029	222	3	(	(	PUNCT
ejpam-4029	222	4	19	19	NUM
ejpam-4029	222	5	)	)	PUNCT
ejpam-4029	222	6	and	and	CCONJ
ejpam-4029	222	7	set	set	VERB
ejpam-4029	222	8	k	k	PROPN
ejpam-4029	222	9	=	=	PUNCT
ejpam-4029	222	10	−1	−1	NOUN
ejpam-4029	222	11	,	,	PUNCT
ejpam-4029	222	12	a	a	DET
ejpam-4029	222	13	=	=	X
ejpam-4029	222	14	zi	zi	NOUN
ejpam-4029	222	15	and	and	CCONJ
ejpam-4029	222	16	simplify	simplify	VERB
ejpam-4029	222	17	.	.	PUNCT
ejpam-4029	223	1	24	24	NUM
ejpam-4029	223	2	.	.	PUNCT
ejpam-4029	223	3	derivations	derivation	NOUN
ejpam-4029	223	4	in	in	ADP
ejpam-4029	223	5	terms	term	NOUN
ejpam-4029	223	6	of	of	ADP
ejpam-4029	223	7	catalan	catalan	NOUN
ejpam-4029	223	8	’s	’s	PART
ejpam-4029	223	9	constant	constant	ADJ
ejpam-4029	223	10	c	c	NOUN
ejpam-4029	223	11	and	and	CCONJ
ejpam-4029	223	12	π	π	PROPN
ejpam-4029	223	13	theorem	theorem	VERB
ejpam-4029	223	14	11	11	NUM
ejpam-4029	223	15	.	.	PUNCT
ejpam-4029	224	1	for	for	ADP
ejpam-4029	224	2	all	all	DET
ejpam-4029	224	3	k	k	NOUN
ejpam-4029	224	4	,	,	PUNCT
ejpam-4029	224	5	a	a	DET
ejpam-4029	224	6	∈	∈	PROPN
ejpam-4029	224	7	c	c	NOUN
ejpam-4029	224	8	,	,	PUNCT
ejpam-4029	224	9	re(c	re(c	NUM
ejpam-4029	224	10	)	)	PUNCT
ejpam-4029	224	11	>	>	X
ejpam-4029	225	1	0,∫	0,∫	X
ejpam-4029	225	2	∞	∞	NUM
ejpam-4029	225	3	0	0	NUM
ejpam-4029	225	4	2	2	NUM
ejpam-4029	225	5	csch2(cx	csch2(cx	NOUN
ejpam-4029	225	6	)	)	PUNCT
ejpam-4029	225	7	(	(	PUNCT
ejpam-4029	225	8	cosh(2mx	cosh(2mx	PROPN
ejpam-4029	225	9	)	)	PUNCT
ejpam-4029	225	10	(	(	PUNCT
ejpam-4029	225	11	(	(	PUNCT
ejpam-4029	225	12	log(a)−	log(a)−	NOUN
ejpam-4029	225	13	2x)k	2x)k	NUM
ejpam-4029	225	14	+	+	CCONJ
ejpam-4029	225	15	(	(	PUNCT
ejpam-4029	225	16	log(a	log(a	PROPN
ejpam-4029	225	17	)	)	PUNCT
ejpam-4029	226	1	+	+	NUM
ejpam-4029	226	2	2x)k	2x)k	NUM
ejpam-4029	226	3	)	)	PUNCT
ejpam-4029	227	1	−	−	PROPN
ejpam-4029	227	2	2	2	NUM
ejpam-4029	227	3	logk(a	logk(a	NOUN
ejpam-4029	227	4	)	)	PUNCT
ejpam-4029	227	5	)	)	PUNCT
ejpam-4029	228	1	dx	dx	PROPN
ejpam-4029	229	1	=	=	SYM
ejpam-4029	229	2	−	−	PROPN
ejpam-4029	229	3	i2k+2πk+1	i2k+2πk+1	VERB
ejpam-4029	229	4	m	m	VERB
ejpam-4029	229	5	(	(	PUNCT
ejpam-4029	229	6	i	i	NOUN
ejpam-4029	229	7	c	c	NOUN
ejpam-4029	229	8	)	)	PUNCT
ejpam-4029	230	1	k	k	NOUN
ejpam-4029	230	2	e−	e−	PROPN
ejpam-4029	230	3	2iπm	2iπm	PROPN
ejpam-4029	230	4	c	c	PROPN
ejpam-4029	230	5	φ	φ	PROPN
ejpam-4029	230	6	(	(	PUNCT
ejpam-4029	230	7	e−	e−	PROPN
ejpam-4029	230	8	2imπ	2imπ	PROPN
ejpam-4029	230	9	c	c	NOUN
ejpam-4029	230	10	,	,	PUNCT
ejpam-4029	230	11	−k	−k	PROPN
ejpam-4029	230	12	,	,	PUNCT
ejpam-4029	230	13	1−	1−	NUM
ejpam-4029	230	14	ic	ic	PROPN
ejpam-4029	230	15	log(a	log(a	PROPN
ejpam-4029	230	16	)	)	PUNCT
ejpam-4029	230	17	2π	2π	NOUN
ejpam-4029	230	18	)	)	PUNCT
ejpam-4029	231	1	c2	c2	PROPN
ejpam-4029	231	2	+	+	CCONJ
ejpam-4029	231	3	i2k+2πk+1	i2k+2πk+1	NOUN
ejpam-4029	231	4	m	m	VERB
ejpam-4029	231	5	(	(	PUNCT
ejpam-4029	231	6	i	i	NOUN
ejpam-4029	231	7	c	c	NOUN
ejpam-4029	231	8	)	)	PUNCT
ejpam-4029	231	9	k	k	PROPN
ejpam-4029	232	1	e	e	X
ejpam-4029	232	2	2iπm	2iπm	PROPN
ejpam-4029	232	3	c	c	PROPN
ejpam-4029	232	4	φ	φ	X
ejpam-4029	232	5	(	(	PUNCT
ejpam-4029	232	6	e	e	X
ejpam-4029	232	7	2imπ	2imπ	PROPN
ejpam-4029	232	8	c	c	NOUN
ejpam-4029	232	9	,	,	PUNCT
ejpam-4029	232	10	−k	−k	PROPN
ejpam-4029	232	11	,	,	PUNCT
ejpam-4029	232	12	1−	1−	NUM
ejpam-4029	232	13	ic	ic	PROPN
ejpam-4029	232	14	log(a	log(a	PROPN
ejpam-4029	232	15	)	)	PUNCT
ejpam-4029	232	16	2π	2π	NOUN
ejpam-4029	232	17	)	)	PUNCT
ejpam-4029	233	1	c2	c2	PROPN
ejpam-4029	233	2	+	+	CCONJ
ejpam-4029	233	3	4iπk	4iπk	NUM
ejpam-4029	233	4	logk−1(a	logk−1(a	NOUN
ejpam-4029	233	5	)	)	PUNCT
ejpam-4029	233	6	c2	c2	PROPN
ejpam-4029	234	1	+	+	PROPN
ejpam-4029	234	2	2k+1kπk	2k+1kπk	NUM
ejpam-4029	235	1	(	(	PUNCT
ejpam-4029	235	2	i	i	NOUN
ejpam-4029	235	3	c	c	NOUN
ejpam-4029	235	4	)	)	PUNCT
ejpam-4029	236	1	k	k	NOUN
ejpam-4029	236	2	e−	e−	PROPN
ejpam-4029	236	3	2iπm	2iπm	PROPN
ejpam-4029	236	4	c	c	PROPN
ejpam-4029	236	5	φ	φ	PROPN
ejpam-4029	236	6	(	(	PUNCT
ejpam-4029	236	7	e−	e−	PROPN
ejpam-4029	236	8	2imπ	2imπ	PROPN
ejpam-4029	236	9	c	c	PROPN
ejpam-4029	236	10	,	,	PUNCT
ejpam-4029	236	11	1−	1−	NUM
ejpam-4029	236	12	k	k	X
ejpam-4029	236	13	,	,	PUNCT
ejpam-4029	236	14	1−	1−	NUM
ejpam-4029	236	15	ic	ic	PROPN
ejpam-4029	236	16	log(a	log(a	PROPN
ejpam-4029	236	17	)	)	PUNCT
ejpam-4029	236	18	2π	2π	NOUN
ejpam-4029	236	19	)	)	PUNCT
ejpam-4029	237	1	c	c	X
ejpam-4029	238	1	+	+	NOUN
ejpam-4029	238	2	2k+1kπk	2k+1kπk	NUM
ejpam-4029	239	1	(	(	PUNCT
ejpam-4029	239	2	i	i	NOUN
ejpam-4029	239	3	c	c	NOUN
ejpam-4029	239	4	)	)	PUNCT
ejpam-4029	240	1	k	k	PROPN
ejpam-4029	240	2	e	e	X
ejpam-4029	240	3	2iπm	2iπm	PROPN
ejpam-4029	240	4	c	c	PROPN
ejpam-4029	240	5	φ	φ	X
ejpam-4029	240	6	(	(	PUNCT
ejpam-4029	240	7	e	e	X
ejpam-4029	240	8	2imπ	2imπ	NUM
ejpam-4029	240	9	c	c	PROPN
ejpam-4029	240	10	,	,	PUNCT
ejpam-4029	240	11	1−	1−	NUM
ejpam-4029	240	12	k	k	X
ejpam-4029	240	13	,	,	PUNCT
ejpam-4029	240	14	1−	1−	NUM
ejpam-4029	240	15	ic	ic	PROPN
ejpam-4029	240	16	log(a	log(a	PROPN
ejpam-4029	240	17	)	)	PUNCT
ejpam-4029	240	18	2π	2π	NOUN
ejpam-4029	240	19	)	)	PUNCT
ejpam-4029	241	1	c	c	X
ejpam-4029	242	1	+	+	NOUN
ejpam-4029	242	2	4	4	NUM
ejpam-4029	242	3	logk(a	logk(a	NOUN
ejpam-4029	242	4	)	)	PUNCT
ejpam-4029	242	5	c	c	NOUN
ejpam-4029	242	6	(	(	PUNCT
ejpam-4029	242	7	38	38	NUM
ejpam-4029	242	8	)	)	PUNCT
ejpam-4029	242	9	r.	r.	PROPN
ejpam-4029	242	10	reynolds	reynolds	PROPN
ejpam-4029	242	11	,	,	PUNCT
ejpam-4029	242	12	a.	a.	PROPN
ejpam-4029	242	13	stauffer	stauffer	PROPN
ejpam-4029	242	14	/	/	SYM
ejpam-4029	242	15	eur	eur	PROPN
ejpam-4029	242	16	.	.	PUNCT
ejpam-4029	243	1	j.	j.	PROPN
ejpam-4029	243	2	pure	pure	PROPN
ejpam-4029	243	3	appl	appl	PROPN
ejpam-4029	243	4	.	.	PROPN
ejpam-4029	243	5	math	math	PROPN
ejpam-4029	243	6	,	,	PUNCT
ejpam-4029	243	7	14	14	NUM
ejpam-4029	243	8	(	(	PUNCT
ejpam-4029	243	9	4	4	NUM
ejpam-4029	243	10	)	)	PUNCT
ejpam-4029	243	11	(	(	PUNCT
ejpam-4029	243	12	2021	2021	NUM
ejpam-4029	243	13	)	)	PUNCT
ejpam-4029	243	14	,	,	PUNCT
ejpam-4029	243	15	1132	1132	NUM
ejpam-4029	243	16	-	-	SYM
ejpam-4029	243	17	1147	1147	NUM
ejpam-4029	243	18	1142	1142	NUM
ejpam-4029	243	19	proof	proof	NOUN
ejpam-4029	243	20	.	.	PUNCT
ejpam-4029	244	1	use	use	VERB
ejpam-4029	244	2	equation	equation	NOUN
ejpam-4029	244	3	(	(	PUNCT
ejpam-4029	244	4	18	18	NUM
ejpam-4029	244	5	)	)	PUNCT
ejpam-4029	244	6	and	and	CCONJ
ejpam-4029	244	7	form	form	VERB
ejpam-4029	244	8	a	a	DET
ejpam-4029	244	9	second	second	ADJ
ejpam-4029	244	10	equation	equation	NOUN
ejpam-4029	244	11	by	by	ADP
ejpam-4029	244	12	replacing	replace	VERB
ejpam-4029	244	13	m	m	PRON
ejpam-4029	244	14	by	by	ADP
ejpam-4029	244	15	−m	−m	NOUN
ejpam-4029	244	16	and	and	CCONJ
ejpam-4029	244	17	adding	add	VERB
ejpam-4029	244	18	both	both	PRON
ejpam-4029	244	19	and	and	CCONJ
ejpam-4029	244	20	simplify	simplify	ADJ
ejpam-4029	244	21	.	.	PUNCT
ejpam-4029	245	1	corollary	corollary	ADJ
ejpam-4029	245	2	13	13	NUM
ejpam-4029	245	3	.	.	PUNCT
ejpam-4029	246	1	∫	∫	PROPN
ejpam-4029	247	1	∞	∞	PROPN
ejpam-4029	247	2	0	0	NUM
ejpam-4029	248	1	(	(	PUNCT
ejpam-4029	248	2	−4x2	−4x2	PROPN
ejpam-4029	248	3	+	+	CCONJ
ejpam-4029	248	4	π2	π2	PROPN
ejpam-4029	248	5	cosh(x)−	cosh(x)−	PROPN
ejpam-4029	248	6	π2	π2	PROPN
ejpam-4029	248	7	)	)	PUNCT
ejpam-4029	248	8	csch2(x	csch2(x	NOUN
ejpam-4029	248	9	)	)	PUNCT
ejpam-4029	248	10	2	2	NUM
ejpam-4029	248	11	(	(	PUNCT
ejpam-4029	248	12	4x2	4x2	NUM
ejpam-4029	249	1	+	+	CCONJ
ejpam-4029	249	2	π2	π2	PROPN
ejpam-4029	249	3	)	)	PUNCT
ejpam-4029	249	4	dx	dx	PROPN
ejpam-4029	249	5	=	=	SYM
ejpam-4029	249	6	1−	1−	NUM
ejpam-4029	249	7	c	c	X
ejpam-4029	249	8	(	(	PUNCT
ejpam-4029	249	9	39	39	NUM
ejpam-4029	249	10	)	)	PUNCT
ejpam-4029	249	11	proof	proof	NOUN
ejpam-4029	249	12	.	.	PUNCT
ejpam-4029	250	1	use	use	VERB
ejpam-4029	250	2	equation	equation	NOUN
ejpam-4029	250	3	(	(	PUNCT
ejpam-4029	250	4	38	38	NUM
ejpam-4029	250	5	)	)	PUNCT
ejpam-4029	250	6	and	and	CCONJ
ejpam-4029	250	7	set	set	VERB
ejpam-4029	250	8	k	k	PROPN
ejpam-4029	250	9	=	=	PUNCT
ejpam-4029	250	10	−1	−1	NOUN
ejpam-4029	250	11	,	,	PUNCT
ejpam-4029	250	12	a	a	DET
ejpam-4029	250	13	=	=	X
ejpam-4029	250	14	−1,m	−1,m	PROPN
ejpam-4029	250	15	=	=	SYM
ejpam-4029	250	16	1/2	1/2	NUM
ejpam-4029	250	17	,	,	PUNCT
ejpam-4029	250	18	c	c	NOUN
ejpam-4029	250	19	=	=	SYM
ejpam-4029	250	20	1and	1and	NUM
ejpam-4029	250	21	simplify	simplify	NOUN
ejpam-4029	250	22	using	use	VERB
ejpam-4029	250	23	entries	entry	NOUN
ejpam-4029	250	24	(	(	PUNCT
ejpam-4029	250	25	1	1	NUM
ejpam-4029	250	26	)	)	PUNCT
ejpam-4029	250	27	and	and	CCONJ
ejpam-4029	250	28	(	(	PUNCT
ejpam-4029	250	29	4	4	X
ejpam-4029	250	30	)	)	PUNCT
ejpam-4029	250	31	in	in	ADP
ejpam-4029	250	32	tables	table	NOUN
ejpam-4029	250	33	below	below	ADP
ejpam-4029	250	34	(	(	PUNCT
ejpam-4029	250	35	64:12:7	64:12:7	NUM
ejpam-4029	250	36	)	)	PUNCT
ejpam-4029	250	37	in	in	ADP
ejpam-4029	250	38	[	[	X
ejpam-4029	250	39	11	11	NUM
ejpam-4029	250	40	]	]	PUNCT
ejpam-4029	250	41	and	and	CCONJ
ejpam-4029	250	42	equations	equation	NOUN
ejpam-4029	250	43	(	(	PUNCT
ejpam-4029	250	44	2.3	2.3	NUM
ejpam-4029	250	45	)	)	PUNCT
ejpam-4029	250	46	and	and	CCONJ
ejpam-4029	250	47	(	(	PUNCT
ejpam-4029	250	48	2.7	2.7	NUM
ejpam-4029	250	49	)	)	PUNCT
ejpam-4029	250	50	in	in	ADP
ejpam-4029	250	51	[	[	X
ejpam-4029	250	52	10	10	NUM
ejpam-4029	250	53	]	]	PUNCT
ejpam-4029	250	54	and	and	CCONJ
ejpam-4029	250	55	equation	equation	NOUN
ejpam-4029	250	56	(	(	PUNCT
ejpam-4029	250	57	9.73	9.73	NUM
ejpam-4029	250	58	)	)	PUNCT
ejpam-4029	250	59	in	in	ADP
ejpam-4029	250	60	[	[	X
ejpam-4029	250	61	8	8	NUM
ejpam-4029	250	62	]	]	PUNCT
ejpam-4029	250	63	.	.	PUNCT
ejpam-4029	251	1	corollary	corollary	ADJ
ejpam-4029	251	2	14.∫	14.∫	NUM
ejpam-4029	251	3	∞	∞	NOUN
ejpam-4029	251	4	0	0	NUM
ejpam-4029	252	1	(	(	PUNCT
ejpam-4029	252	2	−4x2	−4x2	PROPN
ejpam-4029	252	3	+	+	CCONJ
ejpam-4029	252	4	π2	π2	PROPN
ejpam-4029	252	5	cosh(x)−	cosh(x)−	PROPN
ejpam-4029	252	6	π2	π2	PROPN
ejpam-4029	252	7	)	)	PUNCT
ejpam-4029	252	8	csch2(2x	csch2(2x	VERB
ejpam-4029	252	9	)	)	PUNCT
ejpam-4029	252	10	4x2	4x2	NUM
ejpam-4029	253	1	+	+	CCONJ
ejpam-4029	253	2	π2	π2	ADJ
ejpam-4029	253	3	dx	dx	PROPN
ejpam-4029	253	4	=	=	SYM
ejpam-4029	253	5	1	1	NUM
ejpam-4029	253	6	8	8	NUM
ejpam-4029	253	7	(	(	PUNCT
ejpam-4029	253	8	−4c	−4c	PROPN
ejpam-4029	253	9	+	+	CCONJ
ejpam-4029	253	10	6−	6−	NUM
ejpam-4029	253	11	π	π	NOUN
ejpam-4029	253	12	log(2	log(2	NOUN
ejpam-4029	253	13	)	)	PUNCT
ejpam-4029	253	14	)	)	PUNCT
ejpam-4029	254	1	(	(	PUNCT
ejpam-4029	254	2	40	40	NUM
ejpam-4029	254	3	)	)	PUNCT
ejpam-4029	254	4	proof	proof	NOUN
ejpam-4029	254	5	.	.	PUNCT
ejpam-4029	255	1	use	use	VERB
ejpam-4029	255	2	equation	equation	NOUN
ejpam-4029	255	3	(	(	PUNCT
ejpam-4029	255	4	38	38	NUM
ejpam-4029	255	5	)	)	PUNCT
ejpam-4029	255	6	and	and	CCONJ
ejpam-4029	255	7	set	set	VERB
ejpam-4029	255	8	k	k	PROPN
ejpam-4029	255	9	=	=	PUNCT
ejpam-4029	255	10	−1	−1	NOUN
ejpam-4029	255	11	,	,	PUNCT
ejpam-4029	255	12	a	a	DET
ejpam-4029	255	13	=	=	X
ejpam-4029	255	14	−1,m	−1,m	PROPN
ejpam-4029	255	15	=	=	SYM
ejpam-4029	255	16	1/2	1/2	NUM
ejpam-4029	255	17	,	,	PUNCT
ejpam-4029	255	18	c	c	NOUN
ejpam-4029	255	19	=	=	SYM
ejpam-4029	255	20	2and	2and	NUM
ejpam-4029	255	21	simplify	simplify	NOUN
ejpam-4029	255	22	using	use	VERB
ejpam-4029	255	23	entries	entry	NOUN
ejpam-4029	255	24	(	(	PUNCT
ejpam-4029	255	25	1	1	NUM
ejpam-4029	255	26	)	)	PUNCT
ejpam-4029	255	27	and	and	CCONJ
ejpam-4029	255	28	(	(	PUNCT
ejpam-4029	255	29	4	4	X
ejpam-4029	255	30	)	)	PUNCT
ejpam-4029	255	31	in	in	ADP
ejpam-4029	255	32	tables	table	NOUN
ejpam-4029	255	33	below	below	ADP
ejpam-4029	255	34	(	(	PUNCT
ejpam-4029	255	35	64:12:7	64:12:7	NUM
ejpam-4029	255	36	)	)	PUNCT
ejpam-4029	255	37	in	in	ADP
ejpam-4029	255	38	[	[	X
ejpam-4029	255	39	11	11	NUM
ejpam-4029	255	40	]	]	PUNCT
ejpam-4029	255	41	and	and	CCONJ
ejpam-4029	255	42	equations	equation	NOUN
ejpam-4029	255	43	(	(	PUNCT
ejpam-4029	255	44	2.3	2.3	NUM
ejpam-4029	255	45	)	)	PUNCT
ejpam-4029	255	46	and	and	CCONJ
ejpam-4029	255	47	(	(	PUNCT
ejpam-4029	255	48	2.7	2.7	NUM
ejpam-4029	255	49	)	)	PUNCT
ejpam-4029	255	50	in	in	ADP
ejpam-4029	255	51	[	[	X
ejpam-4029	255	52	10	10	NUM
ejpam-4029	255	53	]	]	PUNCT
ejpam-4029	255	54	and	and	CCONJ
ejpam-4029	255	55	equation	equation	NOUN
ejpam-4029	255	56	(	(	PUNCT
ejpam-4029	255	57	9.73	9.73	NUM
ejpam-4029	255	58	)	)	PUNCT
ejpam-4029	255	59	in	in	ADP
ejpam-4029	255	60	[	[	X
ejpam-4029	255	61	8	8	NUM
ejpam-4029	255	62	]	]	PUNCT
ejpam-4029	255	63	.	.	PUNCT
ejpam-4029	256	1	25	25	NUM
ejpam-4029	256	2	.	.	PUNCT
ejpam-4029	257	1	definite	definite	ADJ
ejpam-4029	257	2	integral	integral	ADJ
ejpam-4029	257	3	involving	involve	VERB
ejpam-4029	257	4	the	the	DET
ejpam-4029	257	5	arctangent	arctangent	NOUN
ejpam-4029	257	6	function	function	NOUN
ejpam-4029	257	7	in	in	ADP
ejpam-4029	257	8	terms	term	NOUN
ejpam-4029	257	9	of	of	ADP
ejpam-4029	257	10	the	the	DET
ejpam-4029	257	11	log	log	NOUN
ejpam-4029	257	12	-	-	PUNCT
ejpam-4029	257	13	gamma	gamma	NOUN
ejpam-4029	257	14	and	and	CCONJ
ejpam-4029	257	15	harmonic	harmonic	ADJ
ejpam-4029	257	16	number	number	NOUN
ejpam-4029	257	17	functions	function	NOUN
ejpam-4029	257	18	theorem	theorem	VERB
ejpam-4029	257	19	12	12	NUM
ejpam-4029	257	20	.	.	PUNCT
ejpam-4029	258	1	for	for	ADP
ejpam-4029	258	2	all	all	DET
ejpam-4029	258	3	a	a	DET
ejpam-4029	258	4	∈	∈	PROPN
ejpam-4029	258	5	c	c	NOUN
ejpam-4029	258	6	,	,	PUNCT
ejpam-4029	258	7	re(c	re(c	NUM
ejpam-4029	258	8	)	)	PUNCT
ejpam-4029	258	9	>	>	X
ejpam-4029	258	10	0	0	NUM
ejpam-4029	258	11	,	,	PUNCT
ejpam-4029	258	12	(	(	PUNCT
ejpam-4029	258	13	41	41	NUM
ejpam-4029	258	14	)	)	PUNCT
ejpam-4029	258	15	∫	∫	PROPN
ejpam-4029	259	1	∞	∞	NUM
ejpam-4029	259	2	0	0	NUM
ejpam-4029	260	1	x	x	SYM
ejpam-4029	260	2	tanh−1	tanh−1	PROPN
ejpam-4029	260	3	(	(	PUNCT
ejpam-4029	260	4	x	x	NOUN
ejpam-4029	260	5	a	a	PRON
ejpam-4029	260	6	)	)	PUNCT
ejpam-4029	260	7	coth(cx	coth(cx	ADJ
ejpam-4029	260	8	)	)	PUNCT
ejpam-4029	260	9	csch(cx)dx	csch(cx)dx	PROPN
ejpam-4029	260	10	=	=	SYM
ejpam-4029	260	11	ac	ac	PROPN
ejpam-4029	260	12	(	(	PUNCT
ejpam-4029	260	13	h−	h−	PROPN
ejpam-4029	260	14	iac	iac	PROPN
ejpam-4029	260	15	2π	2π	PROPN
ejpam-4029	260	16	−h−	−h−	VERB
ejpam-4029	260	17	iac+π	iac+π	PROPN
ejpam-4029	260	18	2π	2π	PROPN
ejpam-4029	260	19	)	)	PUNCT
ejpam-4029	261	1	+	+	CCONJ
ejpam-4029	261	2	iπ	iπ	PRON
ejpam-4029	261	3	(	(	PUNCT
ejpam-4029	261	4	−1	−1	NOUN
ejpam-4029	261	5	+	+	CCONJ
ejpam-4029	261	6	2	2	NUM
ejpam-4029	261	7	log	log	NOUN
ejpam-4029	261	8	(	(	PUNCT
ejpam-4029	261	9	i(−π−iac)γ(−	i(−π−iac)γ(−	PROPN
ejpam-4029	261	10	iac+π	iac+π	PROPN
ejpam-4029	261	11	2π	2π	PROPN
ejpam-4029	261	12	)	)	PUNCT
ejpam-4029	261	13	√	√	VERB
ejpam-4029	261	14	2π	2π	NUM
ejpam-4029	261	15	√	√	NUM
ejpam-4029	261	16	a	a	PRON
ejpam-4029	261	17	√	√	NOUN
ejpam-4029	261	18	i	i	PRON
ejpam-4029	261	19	c	c	PROPN
ejpam-4029	261	20	cγ(−	cγ(−	PROPN
ejpam-4029	261	21	iac	iac	PROPN
ejpam-4029	261	22	2π	2π	PROPN
ejpam-4029	261	23	)	)	PUNCT
ejpam-4029	261	24	)	)	PUNCT
ejpam-4029	261	25	)	)	PUNCT
ejpam-4029	262	1	2c2	2c2	NUM
ejpam-4029	262	2	proof	proof	NOUN
ejpam-4029	262	3	.	.	PUNCT
ejpam-4029	263	1	use	use	VERB
ejpam-4029	263	2	equation	equation	NOUN
ejpam-4029	263	3	(	(	PUNCT
ejpam-4029	263	4	19	19	NUM
ejpam-4029	263	5	)	)	PUNCT
ejpam-4029	263	6	and	and	CCONJ
ejpam-4029	263	7	take	take	VERB
ejpam-4029	263	8	the	the	DET
ejpam-4029	263	9	first	first	ADJ
ejpam-4029	263	10	partial	partial	ADJ
ejpam-4029	263	11	derivative	derivative	NOUN
ejpam-4029	263	12	with	with	ADP
ejpam-4029	263	13	respect	respect	NOUN
ejpam-4029	263	14	to	to	ADP
ejpam-4029	263	15	m.	m.	NOUN
ejpam-4029	263	16	next	next	ADV
ejpam-4029	263	17	set	set	NOUN
ejpam-4029	263	18	m	m	PROPN
ejpam-4029	263	19	=	=	SYM
ejpam-4029	263	20	c	c	NOUN
ejpam-4029	263	21	,	,	PUNCT
ejpam-4029	263	22	followed	follow	VERB
ejpam-4029	263	23	by	by	ADP
ejpam-4029	263	24	taking	take	VERB
ejpam-4029	263	25	the	the	DET
ejpam-4029	263	26	first	first	ADJ
ejpam-4029	263	27	partial	partial	ADJ
ejpam-4029	263	28	derivative	derivative	NOUN
ejpam-4029	263	29	with	with	ADP
ejpam-4029	263	30	respect	respect	NOUN
ejpam-4029	263	31	to	to	ADP
ejpam-4029	263	32	k	k	PROPN
ejpam-4029	263	33	then	then	ADV
ejpam-4029	263	34	applying	apply	VERB
ejpam-4029	263	35	l’hopital	l’hopital	PROPN
ejpam-4029	263	36	’s	’s	PART
ejpam-4029	263	37	rule	rule	NOUN
ejpam-4029	263	38	as	as	ADP
ejpam-4029	263	39	k	k	PROPN
ejpam-4029	263	40	→	→	SYM
ejpam-4029	263	41	0	0	NUM
ejpam-4029	263	42	and	and	CCONJ
ejpam-4029	263	43	simplify	simplify	VERB
ejpam-4029	263	44	using	use	VERB
ejpam-4029	263	45	equations	equation	NOUN
ejpam-4029	263	46	(	(	PUNCT
ejpam-4029	263	47	64:10:2	64:10:2	NUM
ejpam-4029	263	48	)	)	PUNCT
ejpam-4029	263	49	,	,	PUNCT
ejpam-4029	263	50	(	(	PUNCT
ejpam-4029	263	51	64:4:1	64:4:1	NUM
ejpam-4029	263	52	)	)	PUNCT
ejpam-4029	263	53	,	,	PUNCT
ejpam-4029	263	54	(	(	PUNCT
ejpam-4029	263	55	44:1:1	44:1:1	NUM
ejpam-4029	263	56	)	)	PUNCT
ejpam-4029	263	57	and	and	CCONJ
ejpam-4029	263	58	entry	entry	NOUN
ejpam-4029	263	59	(	(	PUNCT
ejpam-4029	263	60	4	4	NUM
ejpam-4029	263	61	)	)	PUNCT
ejpam-4029	263	62	in	in	ADP
ejpam-4029	263	63	table	table	NOUN
ejpam-4029	263	64	below	below	ADV
ejpam-4029	263	65	(	(	PUNCT
ejpam-4029	263	66	64:12:7	64:12:7	NUM
ejpam-4029	263	67	)	)	PUNCT
ejpam-4029	263	68	in	in	ADP
ejpam-4029	263	69	[	[	X
ejpam-4029	263	70	11	11	NUM
ejpam-4029	263	71	]	]	PUNCT
ejpam-4029	263	72	.	.	PUNCT
ejpam-4029	264	1	corollary	corollary	ADJ
ejpam-4029	264	2	15.∫	15.∫	PROPN
ejpam-4029	264	3	∞	∞	NOUN
ejpam-4029	264	4	0	0	NUM
ejpam-4029	264	5	x	x	SYM
ejpam-4029	264	6	tanh−1(x	tanh−1(x	NOUN
ejpam-4029	264	7	)	)	PUNCT
ejpam-4029	264	8	coth(x	coth(x	NOUN
ejpam-4029	264	9	)	)	PUNCT
ejpam-4029	264	10	csch(x)dx	csch(x)dx	VERB
ejpam-4029	264	11	=	=	SYM
ejpam-4029	264	12	1	1	NUM
ejpam-4029	264	13	2	2	NUM
ejpam-4029	264	14	h−	h−	NOUN
ejpam-4029	264	15	i	i	PRON
ejpam-4029	264	16	2π	2π	VERB
ejpam-4029	264	17	−	−	NUM
ejpam-4029	264	18	1	1	NUM
ejpam-4029	264	19	2	2	NUM
ejpam-4029	264	20	h−	h−	NOUN
ejpam-4029	264	21	i+π	i+π	NOUN
ejpam-4029	264	22	2π	2π	NOUN
ejpam-4029	264	23	−	−	NOUN
ejpam-4029	264	24	iπ	iπ	ADV
ejpam-4029	264	25	2	2	NUM
ejpam-4029	264	26	+	+	CCONJ
ejpam-4029	264	27	3π2	3π2	NUM
ejpam-4029	264	28	4	4	NUM
ejpam-4029	264	29	−	−	NOUN
ejpam-4029	264	30	1	1	NUM
ejpam-4029	264	31	2	2	NUM
ejpam-4029	264	32	iπ	iπ	PRON
ejpam-4029	264	33	log	log	NOUN
ejpam-4029	264	34	(	(	PUNCT
ejpam-4029	264	35	2π	2π	NOUN
ejpam-4029	264	36	(	(	PUNCT
ejpam-4029	264	37	π	π	NOUN
ejpam-4029	264	38	+	+	CCONJ
ejpam-4029	264	39	i)2	i)2	ADJ
ejpam-4029	264	40	)	)	PUNCT
ejpam-4029	265	1	−	−	ADP
ejpam-4029	265	2	iπ	iπ	DET
ejpam-4029	265	3	log	log	NOUN
ejpam-4029	265	4	(	(	PUNCT
ejpam-4029	265	5	γ	γ	X
ejpam-4029	265	6	(	(	PUNCT
ejpam-4029	265	7	−	−	PROPN
ejpam-4029	265	8	i	i	PRON
ejpam-4029	265	9	2π	2π	NOUN
ejpam-4029	265	10	)	)	PUNCT
ejpam-4029	265	11	)	)	PUNCT
ejpam-4029	266	1	+	+	CCONJ
ejpam-4029	266	2	iπ	iπ	DET
ejpam-4029	266	3	log	log	NOUN
ejpam-4029	266	4	(	(	PUNCT
ejpam-4029	266	5	γ	γ	X
ejpam-4029	266	6	(	(	PUNCT
ejpam-4029	266	7	−	−	PROPN
ejpam-4029	266	8	i+	i+	NUM
ejpam-4029	266	9	π	π	PROPN
ejpam-4029	266	10	2π	2π	PROPN
ejpam-4029	266	11	)	)	PUNCT
ejpam-4029	266	12	)	)	PUNCT
ejpam-4029	266	13	(	(	PUNCT
ejpam-4029	266	14	42	42	X
ejpam-4029	266	15	)	)	PUNCT
ejpam-4029	266	16	r.	r.	PROPN
ejpam-4029	266	17	reynolds	reynolds	PROPN
ejpam-4029	266	18	,	,	PUNCT
ejpam-4029	266	19	a.	a.	PROPN
ejpam-4029	266	20	stauffer	stauffer	PROPN
ejpam-4029	266	21	/	/	SYM
ejpam-4029	266	22	eur	eur	PROPN
ejpam-4029	266	23	.	.	PUNCT
ejpam-4029	267	1	j.	j.	PROPN
ejpam-4029	267	2	pure	pure	PROPN
ejpam-4029	267	3	appl	appl	PROPN
ejpam-4029	267	4	.	.	PROPN
ejpam-4029	267	5	math	math	PROPN
ejpam-4029	267	6	,	,	PUNCT
ejpam-4029	267	7	14	14	NUM
ejpam-4029	267	8	(	(	PUNCT
ejpam-4029	267	9	4	4	NUM
ejpam-4029	267	10	)	)	PUNCT
ejpam-4029	267	11	(	(	PUNCT
ejpam-4029	267	12	2021	2021	NUM
ejpam-4029	267	13	)	)	PUNCT
ejpam-4029	267	14	,	,	PUNCT
ejpam-4029	267	15	1132	1132	NUM
ejpam-4029	267	16	-	-	SYM
ejpam-4029	267	17	1147	1147	NUM
ejpam-4029	267	18	1143	1143	NUM
ejpam-4029	267	19	proof	proof	NOUN
ejpam-4029	267	20	.	.	PUNCT
ejpam-4029	268	1	use	use	NOUN
ejpam-4029	268	2	equation	equation	NOUN
ejpam-4029	268	3	(	(	PUNCT
ejpam-4029	268	4	41	41	NUM
ejpam-4029	268	5	)	)	PUNCT
ejpam-4029	268	6	and	and	CCONJ
ejpam-4029	268	7	set	set	VERB
ejpam-4029	268	8	a	a	DET
ejpam-4029	268	9	=	=	SYM
ejpam-4029	268	10	c	c	NOUN
ejpam-4029	268	11	=	=	SYM
ejpam-4029	268	12	1	1	NUM
ejpam-4029	268	13	and	and	CCONJ
ejpam-4029	268	14	simplify	simplify	NOUN
ejpam-4029	268	15	.	.	PUNCT
ejpam-4029	269	1	note	note	NOUN
ejpam-4029	269	2	:	:	PUNCT
ejpam-4029	269	3	there	there	PRON
ejpam-4029	269	4	exists	exist	VERB
ejpam-4029	269	5	a	a	DET
ejpam-4029	269	6	singularity	singularity	NOUN
ejpam-4029	269	7	at	at	ADP
ejpam-4029	269	8	x	x	X
ejpam-4029	269	9	=	=	SYM
ejpam-4029	269	10	1	1	X
ejpam-4029	269	11	.	.	PUNCT
ejpam-4029	269	12	corollary	corollary	ADJ
ejpam-4029	269	13	16	16	NUM
ejpam-4029	269	14	.	.	PUNCT
ejpam-4029	270	1	for	for	ADP
ejpam-4029	270	2	a	a	DET
ejpam-4029	270	3	∈	∈	PROPN
ejpam-4029	270	4	c	c	NOUN
ejpam-4029	270	5	,	,	PUNCT
ejpam-4029	270	6	∫	∫	PROPN
ejpam-4029	270	7	∞	∞	NUM
ejpam-4029	270	8	0	0	PUNCT
ejpam-4029	270	9	x	x	SYM
ejpam-4029	270	10	cot	cot	NOUN
ejpam-4029	270	11	(	(	PUNCT
ejpam-4029	270	12	πx	πx	X
ejpam-4029	270	13	2a	2a	NUM
ejpam-4029	270	14	)	)	PUNCT
ejpam-4029	270	15	csc	csc	PROPN
ejpam-4029	270	16	(	(	PUNCT
ejpam-4029	270	17	πx	πx	X
ejpam-4029	270	18	2a	2a	NUM
ejpam-4029	270	19	)	)	PUNCT
ejpam-4029	270	20	tanh−1	tanh−1	VERB
ejpam-4029	270	21	(	(	PUNCT
ejpam-4029	270	22	x	x	NOUN
ejpam-4029	270	23	a	a	NOUN
ejpam-4029	270	24	)	)	PUNCT
ejpam-4029	270	25	dx	dx	PROPN
ejpam-4029	270	26	=	=	SYM
ejpam-4029	270	27			NUM
ejpam-4029	270	28	−	−	PROPN
ejpam-4029	270	29	ia2	ia2	NOUN
ejpam-4029	270	30	π	π	PROPN
ejpam-4029	270	31	(	(	PUNCT
ejpam-4029	270	32	−2	−2	NOUN
ejpam-4029	271	1	+	+	CCONJ
ejpam-4029	271	2	π	π	X
ejpam-4029	271	3	+	+	CCONJ
ejpam-4029	271	4	log	log	PROPN
ejpam-4029	271	5	(	(	PUNCT
ejpam-4029	271	6	16γ	16γ	NUM
ejpam-4029	271	7	(	(	PUNCT
ejpam-4029	271	8	1	1	NUM
ejpam-4029	271	9	4	4	NUM
ejpam-4029	271	10	)	)	SYM
ejpam-4029	271	11	4	4	NUM
ejpam-4029	271	12	γ	γ	X
ejpam-4029	271	13	(	(	PUNCT
ejpam-4029	271	14	−1	−1	NOUN
ejpam-4029	271	15	4	4	NUM
ejpam-4029	271	16	)	)	PUNCT
ejpam-4029	271	17	4	4	NUM
ejpam-4029	271	18	)	)	PUNCT
ejpam-4029	271	19	)	)	PUNCT
ejpam-4029	271	20	,	,	PUNCT
ejpam-4029	271	21	for	for	ADP
ejpam-4029	271	22	im(a	im(a	NOUN
ejpam-4029	271	23	)	)	PUNCT
ejpam-4029	271	24	>	>	X
ejpam-4029	271	25	0	0	NUM
ejpam-4029	272	1	ia2	ia2	PROPN
ejpam-4029	272	2	π	π	PROPN
ejpam-4029	272	3	(	(	PUNCT
ejpam-4029	272	4	−2	−2	NOUN
ejpam-4029	272	5	+	+	CCONJ
ejpam-4029	272	6	π	π	X
ejpam-4029	272	7	+	+	CCONJ
ejpam-4029	272	8	log	log	PROPN
ejpam-4029	272	9	(	(	PUNCT
ejpam-4029	272	10	16γ	16γ	NUM
ejpam-4029	272	11	(	(	PUNCT
ejpam-4029	272	12	1	1	NUM
ejpam-4029	272	13	4	4	NUM
ejpam-4029	272	14	)	)	SYM
ejpam-4029	272	15	4	4	NUM
ejpam-4029	272	16	γ	γ	X
ejpam-4029	272	17	(	(	PUNCT
ejpam-4029	272	18	−1	−1	NOUN
ejpam-4029	272	19	4	4	NUM
ejpam-4029	272	20	)	)	PUNCT
ejpam-4029	272	21	4	4	NUM
ejpam-4029	272	22	)	)	PUNCT
ejpam-4029	272	23	)	)	PUNCT
ejpam-4029	272	24	,	,	PUNCT
ejpam-4029	272	25	for	for	ADP
ejpam-4029	272	26	im(a	im(a	NOUN
ejpam-4029	272	27	)	)	PUNCT
ejpam-4029	272	28	<	<	X
ejpam-4029	272	29	0	0	PUNCT
ejpam-4029	272	30	(	(	PUNCT
ejpam-4029	272	31	43	43	NUM
ejpam-4029	272	32	)	)	PUNCT
ejpam-4029	272	33	proof	proof	NOUN
ejpam-4029	272	34	.	.	PUNCT
ejpam-4029	273	1	use	use	VERB
ejpam-4029	273	2	equation	equation	NOUN
ejpam-4029	273	3	(	(	PUNCT
ejpam-4029	273	4	41	41	NUM
ejpam-4029	273	5	)	)	PUNCT
ejpam-4029	273	6	and	and	CCONJ
ejpam-4029	273	7	set	set	VERB
ejpam-4029	273	8	c	c	NOUN
ejpam-4029	273	9	=	=	PUNCT
ejpam-4029	273	10	iπ	iπ	PRON
ejpam-4029	273	11	2a	2a	NUM
ejpam-4029	273	12	and	and	CCONJ
ejpam-4029	273	13	simplify	simplify	ADJ
ejpam-4029	273	14	.	.	PUNCT
ejpam-4029	274	1	corollary	corollary	ADJ
ejpam-4029	274	2	17	17	NUM
ejpam-4029	274	3	.	.	PUNCT
ejpam-4029	275	1	∫	∫	PROPN
ejpam-4029	276	1	∞	∞	NUM
ejpam-4029	276	2	0	0	NUM
ejpam-4029	276	3	x	x	SYM
ejpam-4029	276	4	tan−1(x	tan−1(x	NOUN
ejpam-4029	276	5	)	)	PUNCT
ejpam-4029	276	6	coth	coth	NOUN
ejpam-4029	276	7	(	(	PUNCT
ejpam-4029	276	8	πx	πx	NOUN
ejpam-4029	276	9	2	2	X
ejpam-4029	276	10	)	)	PUNCT
ejpam-4029	276	11	csch	csch	NOUN
ejpam-4029	276	12	(	(	PUNCT
ejpam-4029	276	13	πx	πx	X
ejpam-4029	276	14	2	2	NUM
ejpam-4029	276	15	)	)	PUNCT
ejpam-4029	276	16	dx	dx	PROPN
ejpam-4029	277	1	=	=	PUNCT
ejpam-4029	277	2	−2	−2	PROPN
ejpam-4029	278	1	+	+	NUM
ejpam-4029	278	2	π	π	X
ejpam-4029	278	3	+	+	CCONJ
ejpam-4029	278	4	log	log	NOUN
ejpam-4029	278	5	(	(	PUNCT
ejpam-4029	278	6	16γ	16γ	NUM
ejpam-4029	278	7	(	(	PUNCT
ejpam-4029	278	8	1	1	NUM
ejpam-4029	278	9	4	4	NUM
ejpam-4029	278	10	)	)	PUNCT
ejpam-4029	278	11	4	4	NUM
ejpam-4029	278	12	γ(−	γ(−	SYM
ejpam-4029	278	13	1	1	NUM
ejpam-4029	278	14	4	4	NUM
ejpam-4029	278	15	)	)	PUNCT
ejpam-4029	278	16	4	4	NUM
ejpam-4029	278	17	)	)	PUNCT
ejpam-4029	278	18	π	π	PROPN
ejpam-4029	278	19	(	(	PUNCT
ejpam-4029	278	20	44	44	NUM
ejpam-4029	278	21	)	)	PUNCT
ejpam-4029	278	22	proof	proof	NOUN
ejpam-4029	278	23	.	.	PUNCT
ejpam-4029	279	1	use	use	VERB
ejpam-4029	279	2	equation	equation	NOUN
ejpam-4029	279	3	(	(	PUNCT
ejpam-4029	279	4	43	43	NUM
ejpam-4029	279	5	)	)	PUNCT
ejpam-4029	279	6	and	and	CCONJ
ejpam-4029	279	7	set	set	VERB
ejpam-4029	279	8	a	a	DET
ejpam-4029	279	9	=	=	NOUN
ejpam-4029	279	10	i.	i.	NOUN
ejpam-4029	279	11	corollary	corollary	NOUN
ejpam-4029	279	12	18.∫	18.∫	PROPN
ejpam-4029	279	13	∞	∞	NUM
ejpam-4029	279	14	0	0	NUM
ejpam-4029	280	1	x	x	SYM
ejpam-4029	280	2	tan−1	tan−1	PROPN
ejpam-4029	280	3	(	(	PUNCT
ejpam-4029	280	4	x√	x√	X
ejpam-4029	280	5	π	π	PROPN
ejpam-4029	280	6	)	)	PUNCT
ejpam-4029	280	7	coth	coth	NOUN
ejpam-4029	280	8	(	(	PUNCT
ejpam-4029	280	9	√	√	NUM
ejpam-4029	280	10	πx	πx	PRON
ejpam-4029	280	11	2	2	NUM
ejpam-4029	280	12	)	)	PUNCT
ejpam-4029	280	13	csch	csch	NOUN
ejpam-4029	280	14	(	(	PUNCT
ejpam-4029	280	15	√	√	NUM
ejpam-4029	280	16	πx	πx	PRON
ejpam-4029	280	17	2	2	NUM
ejpam-4029	280	18	)	)	PUNCT
ejpam-4029	280	19	dx	dx	PROPN
ejpam-4029	281	1	=	=	PUNCT
ejpam-4029	281	2	−2	−2	PROPN
ejpam-4029	282	1	+	+	NUM
ejpam-4029	282	2	π	π	X
ejpam-4029	282	3	+	+	CCONJ
ejpam-4029	282	4	log	log	PROPN
ejpam-4029	282	5	(	(	PUNCT
ejpam-4029	282	6	16γ	16γ	NUM
ejpam-4029	282	7	(	(	PUNCT
ejpam-4029	282	8	1	1	NUM
ejpam-4029	282	9	4	4	NUM
ejpam-4029	282	10	)	)	SYM
ejpam-4029	282	11	4	4	NUM
ejpam-4029	282	12	γ	γ	X
ejpam-4029	282	13	(	(	PUNCT
ejpam-4029	282	14	−1	−1	NOUN
ejpam-4029	282	15	4	4	NUM
ejpam-4029	282	16	)	)	PUNCT
ejpam-4029	282	17	4	4	NUM
ejpam-4029	282	18	)	)	PUNCT
ejpam-4029	282	19	(	(	PUNCT
ejpam-4029	282	20	45	45	NUM
ejpam-4029	282	21	)	)	PUNCT
ejpam-4029	282	22	proof	proof	NOUN
ejpam-4029	282	23	.	.	PUNCT
ejpam-4029	283	1	use	use	VERB
ejpam-4029	283	2	equation	equation	NOUN
ejpam-4029	283	3	(	(	PUNCT
ejpam-4029	283	4	43	43	NUM
ejpam-4029	283	5	)	)	PUNCT
ejpam-4029	283	6	and	and	CCONJ
ejpam-4029	283	7	set	set	VERB
ejpam-4029	283	8	a	a	DET
ejpam-4029	283	9	=	=	NOUN
ejpam-4029	283	10	√	√	NOUN
ejpam-4029	283	11	2i	2i	NUM
ejpam-4029	283	12	.	.	PUNCT
ejpam-4029	284	1	corollary	corollary	ADJ
ejpam-4029	284	2	19	19	NUM
ejpam-4029	284	3	.	.	PUNCT
ejpam-4029	285	1	for	for	ADP
ejpam-4029	285	2	a	a	DET
ejpam-4029	285	3	∈	∈	PROPN
ejpam-4029	285	4	c	c	NOUN
ejpam-4029	285	5	,	,	PUNCT
ejpam-4029	285	6	(	(	PUNCT
ejpam-4029	285	7	46	46	NUM
ejpam-4029	285	8	)	)	PUNCT
ejpam-4029	285	9	∫	∫	PROPN
ejpam-4029	286	1	∞	∞	NUM
ejpam-4029	286	2	0	0	PUNCT
ejpam-4029	287	1	x	x	SYM
ejpam-4029	287	2	cot	cot	NOUN
ejpam-4029	287	3	(	(	PUNCT
ejpam-4029	287	4	πx	πx	X
ejpam-4029	287	5	a	a	PRON
ejpam-4029	287	6	)	)	PUNCT
ejpam-4029	287	7	csc	csc	PROPN
ejpam-4029	287	8	(	(	PUNCT
ejpam-4029	287	9	πx	πx	X
ejpam-4029	287	10	a	a	PRON
ejpam-4029	287	11	)	)	PUNCT
ejpam-4029	287	12	tanh−1	tanh−1	PROPN
ejpam-4029	287	13	(	(	PUNCT
ejpam-4029	287	14	x	x	NOUN
ejpam-4029	287	15	a	a	NOUN
ejpam-4029	287	16	)	)	PUNCT
ejpam-4029	287	17	dx	dx	PROPN
ejpam-4029	287	18	=	=	PRON
ejpam-4029	287	19	{	{	PUNCT
ejpam-4029	287	20	−	−	PROPN
ejpam-4029	287	21	ia2	ia2	ADJ
ejpam-4029	287	22	2π	2π	NOUN
ejpam-4029	287	23	(	(	PUNCT
ejpam-4029	287	24	−1	−1	NOUN
ejpam-4029	287	25	+	+	NUM
ejpam-4029	287	26	log(2	log(2	NOUN
ejpam-4029	287	27	)	)	PUNCT
ejpam-4029	288	1	+	+	CCONJ
ejpam-4029	288	2	log(π	log(π	NOUN
ejpam-4029	288	3	)	)	PUNCT
ejpam-4029	288	4	)	)	PUNCT
ejpam-4029	288	5	,	,	PUNCT
ejpam-4029	288	6	for	for	ADP
ejpam-4029	288	7	im(a	im(a	NOUN
ejpam-4029	288	8	)	)	PUNCT
ejpam-4029	288	9	>	>	X
ejpam-4029	288	10	0	0	NUM
ejpam-4029	289	1	ia2	ia2	PROPN
ejpam-4029	289	2	2π	2π	NOUN
ejpam-4029	289	3	(	(	PUNCT
ejpam-4029	289	4	−1	−1	NOUN
ejpam-4029	289	5	+	+	NUM
ejpam-4029	289	6	log(2	log(2	NOUN
ejpam-4029	289	7	)	)	PUNCT
ejpam-4029	290	1	+	+	CCONJ
ejpam-4029	290	2	log(π	log(π	NOUN
ejpam-4029	290	3	)	)	PUNCT
ejpam-4029	290	4	)	)	PUNCT
ejpam-4029	290	5	,	,	PUNCT
ejpam-4029	290	6	for	for	ADP
ejpam-4029	290	7	im(a	im(a	NOUN
ejpam-4029	290	8	)	)	PUNCT
ejpam-4029	290	9	<	<	X
ejpam-4029	290	10	0	0	NUM
ejpam-4029	290	11	proof	proof	NOUN
ejpam-4029	290	12	.	.	PUNCT
ejpam-4029	291	1	use	use	VERB
ejpam-4029	291	2	equation	equation	NOUN
ejpam-4029	291	3	(	(	PUNCT
ejpam-4029	291	4	41	41	NUM
ejpam-4029	291	5	)	)	PUNCT
ejpam-4029	291	6	and	and	CCONJ
ejpam-4029	291	7	apply	apply	VERB
ejpam-4029	291	8	l’hopital	l’hopital	PROPN
ejpam-4029	291	9	’s	’s	PART
ejpam-4029	291	10	rule	rule	NOUN
ejpam-4029	291	11	as	as	ADP
ejpam-4029	291	12	c	c	NOUN
ejpam-4029	291	13	→	→	PUNCT
ejpam-4029	291	14	iπ	iπ	NOUN
ejpam-4029	291	15	a	a	PRON
ejpam-4029	291	16	and	and	CCONJ
ejpam-4029	291	17	simplify	simplify	ADJ
ejpam-4029	291	18	.	.	PUNCT
ejpam-4029	292	1	corollary	corollary	ADJ
ejpam-4029	292	2	20	20	NUM
ejpam-4029	292	3	.	.	PUNCT
ejpam-4029	293	1	∫	∫	PROPN
ejpam-4029	294	1	∞	∞	NUM
ejpam-4029	294	2	0	0	NUM
ejpam-4029	294	3	x	x	SYM
ejpam-4029	294	4	tan−1(x	tan−1(x	NOUN
ejpam-4029	294	5	)	)	PUNCT
ejpam-4029	294	6	coth(πx	coth(πx	NOUN
ejpam-4029	294	7	)	)	PUNCT
ejpam-4029	294	8	csch(πx)dx	csch(πx)dx	NOUN
ejpam-4029	294	9	=	=	SYM
ejpam-4029	294	10	log(2π)−	log(2π)−	PART
ejpam-4029	294	11	1	1	NUM
ejpam-4029	294	12	2π	2π	NOUN
ejpam-4029	294	13	(	(	PUNCT
ejpam-4029	294	14	47	47	NUM
ejpam-4029	294	15	)	)	PUNCT
ejpam-4029	294	16	r.	r.	PROPN
ejpam-4029	294	17	reynolds	reynolds	PROPN
ejpam-4029	294	18	,	,	PUNCT
ejpam-4029	294	19	a.	a.	PROPN
ejpam-4029	294	20	stauffer	stauffer	PROPN
ejpam-4029	294	21	/	/	SYM
ejpam-4029	294	22	eur	eur	PROPN
ejpam-4029	294	23	.	.	PUNCT
ejpam-4029	295	1	j.	j.	PROPN
ejpam-4029	295	2	pure	pure	PROPN
ejpam-4029	295	3	appl	appl	PROPN
ejpam-4029	295	4	.	.	PROPN
ejpam-4029	295	5	math	math	PROPN
ejpam-4029	295	6	,	,	PUNCT
ejpam-4029	295	7	14	14	NUM
ejpam-4029	295	8	(	(	PUNCT
ejpam-4029	295	9	4	4	NUM
ejpam-4029	295	10	)	)	PUNCT
ejpam-4029	295	11	(	(	PUNCT
ejpam-4029	295	12	2021	2021	NUM
ejpam-4029	295	13	)	)	PUNCT
ejpam-4029	295	14	,	,	PUNCT
ejpam-4029	295	15	1132	1132	NUM
ejpam-4029	295	16	-	-	SYM
ejpam-4029	295	17	1147	1147	NUM
ejpam-4029	295	18	1144	1144	NUM
ejpam-4029	295	19	proof	proof	NOUN
ejpam-4029	295	20	.	.	PUNCT
ejpam-4029	296	1	use	use	VERB
ejpam-4029	296	2	equation	equation	NOUN
ejpam-4029	296	3	(	(	PUNCT
ejpam-4029	296	4	46	46	NUM
ejpam-4029	296	5	)	)	PUNCT
ejpam-4029	296	6	and	and	CCONJ
ejpam-4029	296	7	set	set	VERB
ejpam-4029	296	8	a	a	DET
ejpam-4029	296	9	=	=	NOUN
ejpam-4029	296	10	i.	i.	NOUN
ejpam-4029	296	11	corollary	corollary	NOUN
ejpam-4029	296	12	21.∫	21.∫	NOUN
ejpam-4029	296	13	∞	∞	NOUN
ejpam-4029	296	14	0	0	NUM
ejpam-4029	297	1	x	x	SYM
ejpam-4029	297	2	tan−1	tan−1	PROPN
ejpam-4029	297	3	(	(	PUNCT
ejpam-4029	297	4	x√	x√	X
ejpam-4029	297	5	2π	2π	NOUN
ejpam-4029	297	6	)	)	PUNCT
ejpam-4029	297	7	coth	coth	NOUN
ejpam-4029	297	8	(	(	PUNCT
ejpam-4029	297	9	√	√	PROPN
ejpam-4029	297	10	π	π	PROPN
ejpam-4029	297	11	2	2	NUM
ejpam-4029	297	12	x	x	SYM
ejpam-4029	297	13	)	)	PUNCT
ejpam-4029	297	14	csch	csch	NOUN
ejpam-4029	297	15	(	(	PUNCT
ejpam-4029	297	16	√	√	PROPN
ejpam-4029	297	17	π	π	PROPN
ejpam-4029	297	18	2	2	NUM
ejpam-4029	297	19	x	x	SYM
ejpam-4029	297	20	)	)	PUNCT
ejpam-4029	297	21	dx	dx	PROPN
ejpam-4029	298	1	=	=	SYM
ejpam-4029	298	2	log(2π)−	log(2π)−	SYM
ejpam-4029	298	3	1	1	NUM
ejpam-4029	298	4	(	(	PUNCT
ejpam-4029	298	5	48	48	NUM
ejpam-4029	298	6	)	)	PUNCT
ejpam-4029	298	7	proof	proof	NOUN
ejpam-4029	298	8	.	.	PUNCT
ejpam-4029	299	1	use	use	VERB
ejpam-4029	299	2	equation	equation	NOUN
ejpam-4029	299	3	(	(	PUNCT
ejpam-4029	299	4	46	46	NUM
ejpam-4029	299	5	)	)	PUNCT
ejpam-4029	299	6	and	and	CCONJ
ejpam-4029	299	7	set	set	VERB
ejpam-4029	299	8	a	a	DET
ejpam-4029	299	9	=	=	NOUN
ejpam-4029	299	10	√	√	NOUN
ejpam-4029	299	11	2πi	2πi	NOUN
ejpam-4029	299	12	.	.	PUNCT
ejpam-4029	300	1	r.	r.	PROPN
ejpam-4029	300	2	reynolds	reynolds	PROPN
ejpam-4029	300	3	,	,	PUNCT
ejpam-4029	300	4	a.	a.	PROPN
ejpam-4029	300	5	stauffer	stauffer	PROPN
ejpam-4029	300	6	/	/	SYM
ejpam-4029	300	7	eur	eur	PROPN
ejpam-4029	300	8	.	.	PUNCT
ejpam-4029	301	1	j.	j.	PROPN
ejpam-4029	301	2	pure	pure	PROPN
ejpam-4029	301	3	appl	appl	PROPN
ejpam-4029	301	4	.	.	PROPN
ejpam-4029	301	5	math	math	PROPN
ejpam-4029	301	6	,	,	PUNCT
ejpam-4029	301	7	14	14	NUM
ejpam-4029	301	8	(	(	PUNCT
ejpam-4029	301	9	4	4	NUM
ejpam-4029	301	10	)	)	PUNCT
ejpam-4029	301	11	(	(	PUNCT
ejpam-4029	301	12	2021	2021	NUM
ejpam-4029	301	13	)	)	PUNCT
ejpam-4029	301	14	,	,	PUNCT
ejpam-4029	301	15	1132	1132	NUM
ejpam-4029	301	16	-	-	SYM
ejpam-4029	301	17	1147	1147	NUM
ejpam-4029	301	18	1145	1145	NUM
ejpam-4029	301	19	26	26	NUM
ejpam-4029	301	20	.	.	PUNCT
ejpam-4029	302	1	tables	table	NOUN
ejpam-4029	302	2	of	of	ADP
ejpam-4029	302	3	results	result	NOUN
ejpam-4029	302	4	table	table	VERB
ejpam-4029	302	5	1	1	NUM
ejpam-4029	302	6	:	:	PUNCT
ejpam-4029	302	7	table	table	NOUN
ejpam-4029	302	8	of	of	ADP
ejpam-4029	302	9	definite	definite	ADJ
ejpam-4029	302	10	integrals	integral	NOUN
ejpam-4029	302	11	f(x	f(x	PROPN
ejpam-4029	302	12	)	)	PUNCT
ejpam-4029	302	13	∫∞	∫∞	NOUN
ejpam-4029	302	14	0	0	NUM
ejpam-4029	302	15	f(x)dx	f(x)dx	NUM
ejpam-4029	302	16	csch2(cx	csch2(cx	NOUN
ejpam-4029	302	17	)	)	PUNCT
ejpam-4029	302	18	sinh2(mx	sinh2(mx	ADV
ejpam-4029	302	19	)	)	PUNCT
ejpam-4029	302	20	c−πm	c−πm	PROPN
ejpam-4029	302	21	cot(πm	cot(πm	NOUN
ejpam-4029	302	22	c	c	NOUN
ejpam-4029	302	23	)	)	PUNCT
ejpam-4029	302	24	2c2	2c2	NUM
ejpam-4029	302	25	x	x	SYM
ejpam-4029	302	26	sinh(αx)csch2(βx	sinh(αx)csch2(βx	NOUN
ejpam-4029	302	27	)	)	PUNCT
ejpam-4029	302	28	π	π	PROPN
ejpam-4029	302	29	(	(	PUNCT
ejpam-4029	302	30	πα−β	πα−β	NOUN
ejpam-4029	302	31	sin	sin	NOUN
ejpam-4029	302	32	(	(	PUNCT
ejpam-4029	302	33	πα	πα	NOUN
ejpam-4029	302	34	β	β	X
ejpam-4029	302	35	)	)	PUNCT
ejpam-4029	302	36	)	)	PUNCT
ejpam-4029	303	1	csc2	csc2	NOUN
ejpam-4029	303	2	(	(	PUNCT
ejpam-4029	303	3	πα	πα	PROPN
ejpam-4029	303	4	2β	2β	NOUN
ejpam-4029	303	5	)	)	PUNCT
ejpam-4029	303	6	4β3	4β3	NUM
ejpam-4029	303	7	xµ−1csch2(ax	xµ−1csch2(ax	NOUN
ejpam-4029	303	8	)	)	PUNCT
ejpam-4029	303	9	22−µ	22−µ	NUM
ejpam-4029	303	10	(	(	PUNCT
ejpam-4029	303	11	1	1	NUM
ejpam-4029	303	12	a	a	PRON
ejpam-4029	303	13	)	)	PUNCT
ejpam-4029	303	14	µ	µ	PROPN
ejpam-4029	303	15	γ(µ)ζ(µ−	γ(µ)ζ(µ−	NOUN
ejpam-4029	303	16	1	1	NUM
ejpam-4029	303	17	)	)	PUNCT
ejpam-4029	303	18	x2mcsch2(βx	x2mcsch2(βx	NUM
ejpam-4029	303	19	)	)	PUNCT
ejpam-4029	304	1	π2	π2	ADV
ejpam-4029	304	2	m	m	PROPN
ejpam-4029	304	3	(	(	PUNCT
ejpam-4029	304	4	1	1	NUM
ejpam-4029	304	5	β	β	X
ejpam-4029	304	6	)	)	PUNCT
ejpam-4029	305	1	2m+1	2m+1	PROPN
ejpam-4029	305	2	|b2m|	|b2m|	NOUN
ejpam-4029	305	3	x2	x2	PROPN
ejpam-4029	305	4	m	m	PROPN
ejpam-4029	305	5	coth(ax)csch(ax	coth(ax)csch(ax	NOUN
ejpam-4029	305	6	)	)	PUNCT
ejpam-4029	305	7	41−m	41−m	NUM
ejpam-4029	305	8	(	(	PUNCT
ejpam-4029	305	9	4	4	NUM
ejpam-4029	305	10	m	m	NOUN
ejpam-4029	305	11	−	−	NOUN
ejpam-4029	306	1	1)m	1)m	NUM
ejpam-4029	306	2	(	(	PUNCT
ejpam-4029	306	3	1	1	NUM
ejpam-4029	306	4	a	a	PRON
ejpam-4029	306	5	)	)	PUNCT
ejpam-4029	306	6	2m+1	2m+1	PROPN
ejpam-4029	306	7	ζ(2m)γ(2	ζ(2m)γ(2	PROPN
ejpam-4029	306	8	m	m	PROPN
ejpam-4029	306	9	)	)	PUNCT
ejpam-4029	306	10	x2csch2(x	x2csch2(x	PROPN
ejpam-4029	306	11	)	)	PUNCT
ejpam-4029	307	1	π2	π2	ADP
ejpam-4029	307	2	6	6	NUM
ejpam-4029	307	3	x2	x2	PROPN
ejpam-4029	307	4	coth(ax)csch(ax	coth(ax)csch(ax	PROPN
ejpam-4029	307	5	)	)	PUNCT
ejpam-4029	307	6	π2	π2	NOUN
ejpam-4029	307	7	2a3	2a3	NUM
ejpam-4029	307	8	xµ−1	xµ−1	PROPN
ejpam-4029	307	9	coth(ax)csch(ax	coth(ax)csch(ax	PROPN
ejpam-4029	307	10	)	)	PUNCT
ejpam-4029	307	11	21−µ	21−µ	NUM
ejpam-4029	307	12	(	(	PUNCT
ejpam-4029	307	13	2µ	2µ	NUM
ejpam-4029	307	14	−	−	NOUN
ejpam-4029	307	15	2	2	NUM
ejpam-4029	307	16	)	)	PUNCT
ejpam-4029	307	17	(	(	PUNCT
ejpam-4029	307	18	1	1	NUM
ejpam-4029	307	19	a	a	PRON
ejpam-4029	307	20	)	)	PUNCT
ejpam-4029	307	21	µ	µ	PROPN
ejpam-4029	307	22	γ(µ)ζ(µ−	γ(µ)ζ(µ−	NOUN
ejpam-4029	307	23	1	1	NUM
ejpam-4029	307	24	)	)	PUNCT
ejpam-4029	307	25	xs−1csch(αx	xs−1csch(αx	NUM
ejpam-4029	307	26	)	)	PUNCT
ejpam-4029	307	27	21−s	21−s	NUM
ejpam-4029	308	1	(	(	PUNCT
ejpam-4029	308	2	2s	2s	NUM
ejpam-4029	308	3	−	−	NOUN
ejpam-4029	308	4	1	1	NUM
ejpam-4029	308	5	)	)	PUNCT
ejpam-4029	308	6	(	(	PUNCT
ejpam-4029	308	7	1	1	NUM
ejpam-4029	308	8	α	α	NOUN
ejpam-4029	308	9	)	)	PUNCT
ejpam-4029	308	10	s	s	PART
ejpam-4029	308	11	ζ(s)γ(s	ζ(s)γ(s	NOUN
ejpam-4029	308	12	)	)	PUNCT
ejpam-4029	308	13	x2n−1csch(αx	x2n−1csch(αx	PROPN
ejpam-4029	308	14	)	)	PUNCT
ejpam-4029	308	15	(	(	PUNCT
ejpam-4029	308	16	4n−1)π2n	4n−1)π2n	NUM
ejpam-4029	308	17	(	(	PUNCT
ejpam-4029	308	18	1	1	NUM
ejpam-4029	308	19	α	α	NOUN
ejpam-4029	308	20	)	)	PUNCT
ejpam-4029	308	21	2n|b2n|	2n|b2n|	NUM
ejpam-4029	308	22	2n	2n	NUM
ejpam-4029	308	23	x3csch(x	x3csch(x	PUNCT
ejpam-4029	308	24	)	)	PUNCT
ejpam-4029	309	1	π4	π4	ADP
ejpam-4029	309	2	8	8	NUM
ejpam-4029	309	3	x5csch(x	x5csch(x	NOUN
ejpam-4029	309	4	)	)	PUNCT
ejpam-4029	309	5	π6	π6	VERB
ejpam-4029	309	6	4	4	NUM
ejpam-4029	309	7	x7csch(x	x7csch(x	SYM
ejpam-4029	309	8	)	)	PUNCT
ejpam-4029	309	9	17π8	17π8	NUM
ejpam-4029	309	10	16	16	NUM
ejpam-4029	309	11	xcsch(αx	xcsch(αx	PROPN
ejpam-4029	309	12	)	)	PUNCT
ejpam-4029	309	13	π2	π2	ADP
ejpam-4029	309	14	4α2	4α2	NOUN
ejpam-4029	309	15	csch(x)(−4x2csch(x)+π2	csch(x)(−4x2csch(x)+π2	PROPN
ejpam-4029	309	16	coth(x)−π2csch(x	coth(x)−π2csch(x	PROPN
ejpam-4029	309	17	)	)	PUNCT
ejpam-4029	309	18	)	)	PUNCT
ejpam-4029	310	1	4x2+π2	4x2+π2	NUM
ejpam-4029	310	2	−2(c	−2(c	PUNCT
ejpam-4029	310	3	−	−	PROPN
ejpam-4029	310	4	1	1	NUM
ejpam-4029	310	5	)	)	PUNCT
ejpam-4029	310	6	r.	r.	PROPN
ejpam-4029	310	7	reynolds	reynolds	PROPN
ejpam-4029	310	8	,	,	PUNCT
ejpam-4029	310	9	a.	a.	PROPN
ejpam-4029	310	10	stauffer	stauffer	PROPN
ejpam-4029	310	11	/	/	SYM
ejpam-4029	310	12	eur	eur	PROPN
ejpam-4029	310	13	.	.	PUNCT
ejpam-4029	311	1	j.	j.	PROPN
ejpam-4029	311	2	pure	pure	PROPN
ejpam-4029	311	3	appl	appl	PROPN
ejpam-4029	311	4	.	.	PROPN
ejpam-4029	311	5	math	math	PROPN
ejpam-4029	311	6	,	,	PUNCT
ejpam-4029	311	7	14	14	NUM
ejpam-4029	311	8	(	(	PUNCT
ejpam-4029	311	9	4	4	NUM
ejpam-4029	311	10	)	)	PUNCT
ejpam-4029	311	11	(	(	PUNCT
ejpam-4029	311	12	2021	2021	NUM
ejpam-4029	311	13	)	)	PUNCT
ejpam-4029	311	14	,	,	PUNCT
ejpam-4029	311	15	1132	1132	NUM
ejpam-4029	311	16	-	-	SYM
ejpam-4029	311	17	1147	1147	NUM
ejpam-4029	311	18	1146	1146	NUM
ejpam-4029	311	19	table	table	NOUN
ejpam-4029	311	20	2	2	NUM
ejpam-4029	311	21	:	:	PUNCT
ejpam-4029	311	22	table	table	NOUN
ejpam-4029	311	23	of	of	ADP
ejpam-4029	311	24	definite	definite	ADJ
ejpam-4029	311	25	integrals	integral	NOUN
ejpam-4029	311	26	f(x	f(x	PROPN
ejpam-4029	311	27	)	)	PUNCT
ejpam-4029	311	28	∫∞	∫∞	NOUN
ejpam-4029	311	29	0	0	NUM
ejpam-4029	312	1	f(x)dx	f(x)dx	NUM
ejpam-4029	312	2	xcsch(x	xcsch(x	PROPN
ejpam-4029	312	3	)	)	PUNCT
ejpam-4029	313	1	4x2+π2	4x2+π2	NUM
ejpam-4029	313	2	1	1	NUM
ejpam-4029	313	3	8(π	8(π	NUM
ejpam-4029	313	4	−	−	NOUN
ejpam-4029	313	5	2	2	NUM
ejpam-4029	313	6	)	)	PUNCT
ejpam-4029	313	7	xcsch(x	xcsch(x	PROPN
ejpam-4029	313	8	)	)	PUNCT
ejpam-4029	313	9	x2+π2	x2+π2	PROPN
ejpam-4029	314	1	log(2)−	log(2)−	VERB
ejpam-4029	314	2	1	1	NUM
ejpam-4029	314	3	2	2	NUM
ejpam-4029	314	4	x	x	SYM
ejpam-4029	314	5	sinh(x)csch2	sinh(x)csch2	NOUN
ejpam-4029	314	6	(	(	PUNCT
ejpam-4029	314	7	2x	2x	NUM
ejpam-4029	314	8	)	)	PUNCT
ejpam-4029	314	9	x2+π2	x2+π2	PROPN
ejpam-4029	314	10	8c−8+π(log(4)−1	8c−8+π(log(4)−1	NUM
ejpam-4029	314	11	)	)	PUNCT
ejpam-4029	314	12	8π	8π	NOUN
ejpam-4029	314	13	(	(	PUNCT
ejpam-4029	314	14	−4x2+π2	−4x2+π2	NOUN
ejpam-4029	314	15	cosh(x)−π2)csch	cosh(x)−π2)csch	NOUN
ejpam-4029	314	16	2	2	NUM
ejpam-4029	314	17	(	(	PUNCT
ejpam-4029	314	18	x	x	NOUN
ejpam-4029	314	19	)	)	PUNCT
ejpam-4029	314	20	2(4x2+π2	2(4x2+π2	NUM
ejpam-4029	314	21	)	)	PUNCT
ejpam-4029	315	1	1−	1−	NUM
ejpam-4029	315	2	c	c	NOUN
ejpam-4029	315	3	(	(	PUNCT
ejpam-4029	315	4	−4x2+π2	−4x2+π2	NOUN
ejpam-4029	315	5	cosh(x)−π2)csch	cosh(x)−π2)csch	NOUN
ejpam-4029	315	6	2	2	NUM
ejpam-4029	315	7	(	(	PUNCT
ejpam-4029	315	8	2x	2x	NUM
ejpam-4029	315	9	)	)	PUNCT
ejpam-4029	315	10	4x2+π2	4x2+π2	NUM
ejpam-4029	315	11	1	1	NUM
ejpam-4029	315	12	8(−4c	8(−4c	NUM
ejpam-4029	315	13	+	+	CCONJ
ejpam-4029	315	14	6−	6−	NUM
ejpam-4029	315	15	π	π	NOUN
ejpam-4029	315	16	log(2	log(2	NOUN
ejpam-4029	315	17	)	)	PUNCT
ejpam-4029	315	18	)	)	PUNCT
ejpam-4029	315	19	x	x	X
ejpam-4029	315	20	tan−1(x	tan−1(x	NOUN
ejpam-4029	315	21	)	)	PUNCT
ejpam-4029	315	22	coth	coth	NOUN
ejpam-4029	315	23	(	(	PUNCT
ejpam-4029	315	24	πx	πx	NOUN
ejpam-4029	315	25	2	2	X
ejpam-4029	315	26	)	)	PUNCT
ejpam-4029	315	27	csch	csch	NOUN
ejpam-4029	315	28	(	(	PUNCT
ejpam-4029	315	29	πx	πx	X
ejpam-4029	315	30	2	2	NUM
ejpam-4029	315	31	)	)	PUNCT
ejpam-4029	315	32	−2+π+log	−2+π+log	NOUN
ejpam-4029	315	33	(	(	PUNCT
ejpam-4029	315	34	16γ	16γ	NUM
ejpam-4029	315	35	(	(	PUNCT
ejpam-4029	315	36	1	1	NUM
ejpam-4029	315	37	4	4	NUM
ejpam-4029	315	38	)	)	PUNCT
ejpam-4029	315	39	4	4	NUM
ejpam-4029	315	40	γ(−	γ(−	SYM
ejpam-4029	315	41	1	1	NUM
ejpam-4029	315	42	4	4	NUM
ejpam-4029	315	43	)	)	PUNCT
ejpam-4029	315	44	4	4	NUM
ejpam-4029	315	45	)	)	PUNCT
ejpam-4029	315	46	π	π	NOUN
ejpam-4029	315	47	x	x	SYM
ejpam-4029	315	48	tan−1(x	tan−1(x	NOUN
ejpam-4029	315	49	)	)	PUNCT
ejpam-4029	315	50	coth	coth	NOUN
ejpam-4029	315	51	(	(	PUNCT
ejpam-4029	315	52	πx	πx	NOUN
ejpam-4029	315	53	2	2	X
ejpam-4029	315	54	)	)	PUNCT
ejpam-4029	315	55	csch	csch	NOUN
ejpam-4029	315	56	(	(	PUNCT
ejpam-4029	315	57	πx	πx	X
ejpam-4029	315	58	2	2	NUM
ejpam-4029	315	59	)	)	PUNCT
ejpam-4029	315	60	−2+π+log	−2+π+log	NOUN
ejpam-4029	315	61	(	(	PUNCT
ejpam-4029	315	62	16γ	16γ	NUM
ejpam-4029	315	63	(	(	PUNCT
ejpam-4029	315	64	1	1	NUM
ejpam-4029	315	65	4	4	NUM
ejpam-4029	315	66	)	)	PUNCT
ejpam-4029	315	67	4	4	NUM
ejpam-4029	315	68	γ(−	γ(−	SYM
ejpam-4029	315	69	1	1	NUM
ejpam-4029	315	70	4	4	NUM
ejpam-4029	315	71	)	)	PUNCT
ejpam-4029	315	72	4	4	NUM
ejpam-4029	315	73	)	)	PUNCT
ejpam-4029	316	1	π	π	NOUN
ejpam-4029	316	2	x	x	PUNCT
ejpam-4029	316	3	tan−1	tan−1	PROPN
ejpam-4029	316	4	(	(	PUNCT
ejpam-4029	316	5	x√	x√	X
ejpam-4029	316	6	π	π	PROPN
ejpam-4029	316	7	)	)	PUNCT
ejpam-4029	316	8	coth	coth	NOUN
ejpam-4029	316	9	(	(	PUNCT
ejpam-4029	316	10	√	√	NUM
ejpam-4029	316	11	πx	πx	PRON
ejpam-4029	316	12	2	2	NUM
ejpam-4029	316	13	)	)	PUNCT
ejpam-4029	316	14	csch	csch	NOUN
ejpam-4029	316	15	(	(	PUNCT
ejpam-4029	316	16	√	√	NUM
ejpam-4029	316	17	πx	πx	VERB
ejpam-4029	316	18	2	2	NUM
ejpam-4029	316	19	)	)	PUNCT
ejpam-4029	316	20	−2	−2	NOUN
ejpam-4029	317	1	+	+	NUM
ejpam-4029	317	2	π	π	PROPN
ejpam-4029	317	3	+	+	CCONJ
ejpam-4029	317	4	log	log	NOUN
ejpam-4029	317	5	(	(	PUNCT
ejpam-4029	317	6	16γ	16γ	NUM
ejpam-4029	317	7	(	(	PUNCT
ejpam-4029	317	8	1	1	NUM
ejpam-4029	317	9	4	4	NUM
ejpam-4029	317	10	)	)	PUNCT
ejpam-4029	317	11	4	4	NUM
ejpam-4029	317	12	γ(−	γ(−	SYM
ejpam-4029	317	13	1	1	NUM
ejpam-4029	317	14	4	4	NUM
ejpam-4029	317	15	)	)	PUNCT
ejpam-4029	317	16	4	4	NUM
ejpam-4029	317	17	)	)	PUNCT
ejpam-4029	317	18	x	x	SYM
ejpam-4029	317	19	tan−1(x	tan−1(x	NOUN
ejpam-4029	317	20	)	)	PUNCT
ejpam-4029	317	21	coth(πx)csch(πx	coth(πx)csch(πx	NOUN
ejpam-4029	317	22	)	)	PUNCT
ejpam-4029	317	23	log(2π)−1	log(2π)−1	NOUN
ejpam-4029	317	24	2π	2π	NOUN
ejpam-4029	317	25	x	x	SYM
ejpam-4029	317	26	tan−1	tan−1	PROPN
ejpam-4029	317	27	(	(	PUNCT
ejpam-4029	317	28	x√	x√	X
ejpam-4029	317	29	2π	2π	NOUN
ejpam-4029	317	30	)	)	PUNCT
ejpam-4029	317	31	coth	coth	NOUN
ejpam-4029	317	32	(	(	PUNCT
ejpam-4029	317	33	√	√	PROPN
ejpam-4029	317	34	π	π	PROPN
ejpam-4029	317	35	2x	2x	NUM
ejpam-4029	317	36	)	)	PUNCT
ejpam-4029	317	37	csch	csch	NOUN
ejpam-4029	317	38	(	(	PUNCT
ejpam-4029	317	39	√	√	PROPN
ejpam-4029	317	40	π	π	PROPN
ejpam-4029	317	41	2x	2x	NUM
ejpam-4029	317	42	)	)	PUNCT
ejpam-4029	317	43	log(2π)−	log(2π)−	PART
ejpam-4029	317	44	1	1	NUM
ejpam-4029	317	45	27	27	NUM
ejpam-4029	317	46	.	.	PUNCT
ejpam-4029	318	1	discussion	discussion	NOUN
ejpam-4029	318	2	in	in	ADP
ejpam-4029	318	3	this	this	DET
ejpam-4029	318	4	work	work	NOUN
ejpam-4029	318	5	the	the	DET
ejpam-4029	318	6	authors	author	NOUN
ejpam-4029	318	7	derived	derive	VERB
ejpam-4029	318	8	definite	definite	ADJ
ejpam-4029	318	9	integrals	integral	NOUN
ejpam-4029	318	10	used	use	VERB
ejpam-4029	318	11	in	in	ADP
ejpam-4029	318	12	physics	physics	NOUN
ejpam-4029	318	13	along	along	ADP
ejpam-4029	318	14	with	with	ADP
ejpam-4029	318	15	some	some	DET
ejpam-4029	318	16	new	new	ADJ
ejpam-4029	318	17	forms	form	NOUN
ejpam-4029	318	18	not	not	PART
ejpam-4029	318	19	previously	previously	ADV
ejpam-4029	318	20	published	publish	VERB
ejpam-4029	318	21	.	.	PUNCT
ejpam-4029	319	1	some	some	PRON
ejpam-4029	319	2	of	of	ADP
ejpam-4029	319	3	the	the	DET
ejpam-4029	319	4	integral	integral	ADJ
ejpam-4029	319	5	forms	form	NOUN
ejpam-4029	319	6	were	be	AUX
ejpam-4029	319	7	expressed	express	VERB
ejpam-4029	319	8	in	in	ADP
ejpam-4029	319	9	terms	term	NOUN
ejpam-4029	319	10	of	of	ADP
ejpam-4029	319	11	fundamental	fundamental	ADJ
ejpam-4029	319	12	constants	constant	NOUN
ejpam-4029	319	13	such	such	ADJ
ejpam-4029	319	14	as	as	ADP
ejpam-4029	319	15	catalan	catalan	NOUN
ejpam-4029	319	16	’s	’s	PART
ejpam-4029	319	17	constant	constant	ADJ
ejpam-4029	319	18	and	and	CCONJ
ejpam-4029	319	19	π	π	NOUN
ejpam-4029	319	20	.	.	PUNCT
ejpam-4029	320	1	the	the	DET
ejpam-4029	320	2	integral	integral	ADJ
ejpam-4029	320	3	forms	form	NOUN
ejpam-4029	320	4	derived	derive	VERB
ejpam-4029	320	5	were	be	AUX
ejpam-4029	320	6	achieved	achieve	VERB
ejpam-4029	320	7	by	by	ADP
ejpam-4029	320	8	the	the	DET
ejpam-4029	320	9	use	use	NOUN
ejpam-4029	320	10	of	of	ADP
ejpam-4029	320	11	our	our	PRON
ejpam-4029	320	12	contour	contour	NOUN
ejpam-4029	320	13	integral	integral	ADJ
ejpam-4029	320	14	method	method	NOUN
ejpam-4029	320	15	[	[	X
ejpam-4029	320	16	13	13	NUM
ejpam-4029	320	17	]	]	PUNCT
ejpam-4029	320	18	and	and	CCONJ
ejpam-4029	320	19	the	the	DET
ejpam-4029	320	20	evaluation	evaluation	NOUN
ejpam-4029	320	21	of	of	ADP
ejpam-4029	320	22	integrals	integral	NOUN
ejpam-4029	320	23	using	use	VERB
ejpam-4029	320	24	the	the	DET
ejpam-4029	320	25	lerch	lerch	PROPN
ejpam-4029	320	26	function	function	PROPN
ejpam-4029	320	27	.	.	PUNCT
ejpam-4029	321	1	the	the	DET
ejpam-4029	321	2	lerch	lerch	PROPN
ejpam-4029	321	3	function	function	PROPN
ejpam-4029	321	4	being	be	AUX
ejpam-4029	321	5	multivariate	multivariate	NOUN
ejpam-4029	321	6	with	with	ADP
ejpam-4029	321	7	its	its	PRON
ejpam-4029	321	8	analytic	analytic	ADJ
ejpam-4029	321	9	continuation	continuation	NOUN
ejpam-4029	321	10	properties	property	NOUN
ejpam-4029	321	11	allowed	allow	VERB
ejpam-4029	321	12	the	the	DET
ejpam-4029	321	13	authors	author	NOUN
ejpam-4029	321	14	to	to	PART
ejpam-4029	321	15	widen	widen	VERB
ejpam-4029	321	16	the	the	DET
ejpam-4029	321	17	range	range	NOUN
ejpam-4029	321	18	of	of	ADP
ejpam-4029	321	19	computation	computation	NOUN
ejpam-4029	321	20	for	for	ADP
ejpam-4029	321	21	the	the	DET
ejpam-4029	321	22	formulae	formulae	NOUN
ejpam-4029	321	23	derived	derive	VERB
ejpam-4029	321	24	.	.	PUNCT
ejpam-4029	322	1	we	we	PRON
ejpam-4029	322	2	used	use	VERB
ejpam-4029	322	3	wolfram	wolfram	PROPN
ejpam-4029	322	4	’s	’s	PART
ejpam-4029	322	5	mathematica	mathematica	PROPN
ejpam-4029	322	6	software	software	PROPN
ejpam-4029	322	7	for	for	ADP
ejpam-4029	322	8	numerical	numerical	ADJ
ejpam-4029	322	9	evaluations	evaluation	NOUN
ejpam-4029	322	10	for	for	ADP
ejpam-4029	322	11	real	real	ADJ
ejpam-4029	322	12	and	and	CCONJ
ejpam-4029	322	13	imaginary	imaginary	ADJ
ejpam-4029	322	14	values	value	NOUN
ejpam-4029	322	15	of	of	ADP
ejpam-4029	322	16	the	the	DET
ejpam-4029	322	17	parameters	parameter	NOUN
ejpam-4029	322	18	involved	involve	VERB
ejpam-4029	322	19	.	.	PUNCT
ejpam-4029	323	1	derivations	derivation	NOUN
ejpam-4029	323	2	of	of	ADP
ejpam-4029	323	3	definite	definite	ADJ
ejpam-4029	323	4	integrals	integral	NOUN
ejpam-4029	323	5	in	in	ADP
ejpam-4029	323	6	[	[	X
ejpam-4029	323	7	7	7	NUM
ejpam-4029	323	8	,	,	PUNCT
ejpam-4029	323	9	8	8	NUM
ejpam-4029	323	10	,	,	PUNCT
ejpam-4029	323	11	12	12	NUM
ejpam-4029	323	12	]	]	PUNCT
ejpam-4029	323	13	are	be	AUX
ejpam-4029	323	14	useful	useful	ADJ
ejpam-4029	323	15	as	as	SCONJ
ejpam-4029	323	16	it	it	PRON
ejpam-4029	323	17	will	will	AUX
ejpam-4029	323	18	assist	assist	VERB
ejpam-4029	323	19	in	in	ADP
ejpam-4029	323	20	providing	provide	VERB
ejpam-4029	323	21	formal	formal	ADJ
ejpam-4029	323	22	proofs	proof	NOUN
ejpam-4029	323	23	and	and	CCONJ
ejpam-4029	323	24	verifying	verify	VERB
ejpam-4029	323	25	whether	whether	SCONJ
ejpam-4029	323	26	the	the	DET
ejpam-4029	323	27	formulae	formulae	NOUN
ejpam-4029	323	28	in	in	ADP
ejpam-4029	323	29	these	these	DET
ejpam-4029	323	30	books	book	NOUN
ejpam-4029	323	31	are	be	AUX
ejpam-4029	323	32	correct	correct	ADJ
ejpam-4029	323	33	.	.	PUNCT
ejpam-4029	324	1	we	we	PRON
ejpam-4029	324	2	will	will	AUX
ejpam-4029	324	3	be	be	AUX
ejpam-4029	324	4	using	use	VERB
ejpam-4029	324	5	our	our	PRON
ejpam-4029	324	6	method	method	NOUN
ejpam-4029	324	7	to	to	PART
ejpam-4029	324	8	produce	produce	VERB
ejpam-4029	324	9	more	more	ADJ
ejpam-4029	324	10	tables	table	NOUN
ejpam-4029	324	11	of	of	ADP
ejpam-4029	324	12	integrals	integral	NOUN
ejpam-4029	324	13	in	in	ADP
ejpam-4029	324	14	future	future	ADJ
ejpam-4029	324	15	work	work	NOUN
ejpam-4029	324	16	.	.	PUNCT
ejpam-4029	325	1	references	reference	NOUN
ejpam-4029	325	2	1147	1147	NUM
ejpam-4029	325	3	references	reference	NOUN
ejpam-4029	325	4	[	[	X
ejpam-4029	325	5	1	1	NUM
ejpam-4029	325	6	]	]	X
ejpam-4029	325	7	nail	nail	NOUN
ejpam-4029	325	8	akhmediev	akhmediev	PROPN
ejpam-4029	325	9	and	and	CCONJ
ejpam-4029	325	10	adrian	adrian	PROPN
ejpam-4029	325	11	ankiewicz	ankiewicz	NOUN
ejpam-4029	325	12	,	,	PUNCT
ejpam-4029	325	13	editors	editor	NOUN
ejpam-4029	325	14	.	.	PUNCT
ejpam-4029	326	1	dissipative	dissipative	ADJ
ejpam-4029	326	2	solitons	soliton	NOUN
ejpam-4029	326	3	.	.	PUNCT
ejpam-4029	327	1	springer	springer	PROPN
ejpam-4029	327	2	berlin	berlin	PROPN
ejpam-4029	327	3	heidelberg	heidelberg	PROPN
ejpam-4029	327	4	,	,	PUNCT
ejpam-4029	327	5	2005	2005	NUM
ejpam-4029	327	6	.	.	PUNCT
ejpam-4029	328	1	[	[	X
ejpam-4029	328	2	2	2	NUM
ejpam-4029	328	3	]	]	X
ejpam-4029	328	4	peter	peter	PROPN
ejpam-4029	328	5	arnold	arnold	PROPN
ejpam-4029	328	6	,	,	PUNCT
ejpam-4029	328	7	tyler	tyler	PROPN
ejpam-4029	328	8	gorda	gorda	PROPN
ejpam-4029	328	9	,	,	PUNCT
ejpam-4029	328	10	and	and	CCONJ
ejpam-4029	328	11	shahin	shahin	PROPN
ejpam-4029	328	12	iqbal	iqbal	PROPN
ejpam-4029	328	13	.	.	PUNCT
ejpam-4029	329	1	the	the	DET
ejpam-4029	329	2	lpm	lpm	NOUN
ejpam-4029	329	3	effect	effect	NOUN
ejpam-4029	329	4	in	in	ADP
ejpam-4029	329	5	sequential	sequential	ADJ
ejpam-4029	329	6	bremsstrahlung	bremsstrahlung	NOUN
ejpam-4029	329	7	:	:	PUNCT
ejpam-4029	329	8	nearly	nearly	ADV
ejpam-4029	329	9	complete	complete	ADJ
ejpam-4029	329	10	results	result	NOUN
ejpam-4029	329	11	for	for	ADP
ejpam-4029	329	12	qcd	qcd	PROPN
ejpam-4029	329	13	.	.	PUNCT
ejpam-4029	330	1	journal	journal	PROPN
ejpam-4029	330	2	of	of	ADP
ejpam-4029	330	3	high	high	ADJ
ejpam-4029	330	4	energy	energy	NOUN
ejpam-4029	330	5	physics	physics	NOUN
ejpam-4029	330	6	,	,	PUNCT
ejpam-4029	330	7	2020	2020	NUM
ejpam-4029	330	8	,	,	PUNCT
ejpam-4029	330	9	11	11	NUM
ejpam-4029	330	10	2020	2020	NUM
ejpam-4029	330	11	.	.	PUNCT
ejpam-4029	331	1	[	[	X
ejpam-4029	331	2	3	3	NUM
ejpam-4029	331	3	]	]	PUNCT
ejpam-4029	331	4	a.	a.	PROPN
ejpam-4029	331	5	d.	d.	PROPN
ejpam-4029	331	6	boardman	boardman	PROPN
ejpam-4029	331	7	and	and	CCONJ
ejpam-4029	331	8	a.	a.	PROPN
ejpam-4029	331	9	p.	p.	PROPN
ejpam-4029	331	10	sukhorukov	sukhorukov	PROPN
ejpam-4029	331	11	.	.	PUNCT
ejpam-4029	332	1	soliton	soliton	NOUN
ejpam-4029	332	2	-	-	PUNCT
ejpam-4029	332	3	driven	drive	VERB
ejpam-4029	332	4	photonics	photonic	NOUN
ejpam-4029	332	5	.	.	PUNCT
ejpam-4029	333	1	springer	springer	NOUN
ejpam-4029	333	2	science	science	PROPN
ejpam-4029	333	3	&	&	CCONJ
ejpam-4029	333	4	business	business	NOUN
ejpam-4029	333	5	media	medium	NOUN
ejpam-4029	333	6	,	,	PUNCT
ejpam-4029	333	7	08	08	NUM
ejpam-4029	333	8	2001	2001	NUM
ejpam-4029	333	9	.	.	PUNCT
ejpam-4029	334	1	[	[	X
ejpam-4029	334	2	4	4	NUM
ejpam-4029	334	3	]	]	X
ejpam-4029	334	4	anders	anders	PROPN
ejpam-4029	334	5	bondeson	bondeson	NOUN
ejpam-4029	334	6	.	.	PUNCT
ejpam-4029	335	1	perturbation	perturbation	NOUN
ejpam-4029	335	2	analysis	analysis	NOUN
ejpam-4029	335	3	of	of	ADP
ejpam-4029	335	4	single	single	ADJ
ejpam-4029	335	5	langmuir	langmuir	PROPN
ejpam-4029	335	6	solitons	soliton	NOUN
ejpam-4029	335	7	.	.	PUNCT
ejpam-4029	336	1	physics	physics	PROPN
ejpam-4029	336	2	of	of	ADP
ejpam-4029	336	3	fluids	fluid	NOUN
ejpam-4029	336	4	,	,	PUNCT
ejpam-4029	336	5	23:746	23:746	NUM
ejpam-4029	336	6	,	,	PUNCT
ejpam-4029	336	7	1980	1980	NUM
ejpam-4029	336	8	.	.	PUNCT
ejpam-4029	337	1	[	[	X
ejpam-4029	337	2	5	5	X
ejpam-4029	337	3	]	]	PUNCT
ejpam-4029	337	4	d.	d.	PROPN
ejpam-4029	337	5	i.	i.	PROPN
ejpam-4029	337	6	borisov	borisov	PROPN
ejpam-4029	337	7	,	,	PUNCT
ejpam-4029	337	8	g.	g.	PROPN
ejpam-4029	337	9	cardone	cardone	PROPN
ejpam-4029	337	10	,	,	PUNCT
ejpam-4029	337	11	g.	g.	PROPN
ejpam-4029	337	12	a.	a.	PROPN
ejpam-4029	337	13	chechkin	chechkin	PROPN
ejpam-4029	337	14	,	,	PUNCT
ejpam-4029	337	15	and	and	CCONJ
ejpam-4029	337	16	yu	yu	PROPN
ejpam-4029	337	17	.	.	PROPN
ejpam-4029	337	18	o.	o.	PROPN
ejpam-4029	337	19	koroleva	koroleva	PROPN
ejpam-4029	337	20	.	.	PUNCT
ejpam-4029	338	1	on	on	ADP
ejpam-4029	338	2	elliptic	elliptic	ADJ
ejpam-4029	338	3	operators	operator	NOUN
ejpam-4029	338	4	with	with	ADP
ejpam-4029	338	5	steklov	steklov	ADJ
ejpam-4029	338	6	condition	condition	NOUN
ejpam-4029	338	7	perturbed	perturb	VERB
ejpam-4029	338	8	by	by	ADP
ejpam-4029	338	9	dirichlet	dirichlet	PROPN
ejpam-4029	338	10	condition	condition	NOUN
ejpam-4029	338	11	on	on	ADP
ejpam-4029	338	12	a	a	DET
ejpam-4029	338	13	small	small	ADJ
ejpam-4029	338	14	part	part	NOUN
ejpam-4029	338	15	of	of	ADP
ejpam-4029	338	16	boundary	boundary	NOUN
ejpam-4029	338	17	.	.	PUNCT
ejpam-4029	339	1	calculus	calculus	NOUN
ejpam-4029	339	2	of	of	ADP
ejpam-4029	339	3	variations	variation	NOUN
ejpam-4029	339	4	and	and	CCONJ
ejpam-4029	339	5	partial	partial	ADJ
ejpam-4029	339	6	differential	differential	NOUN
ejpam-4029	339	7	equations	equation	NOUN
ejpam-4029	339	8	,	,	PUNCT
ejpam-4029	339	9	60	60	NUM
ejpam-4029	339	10	,	,	PUNCT
ejpam-4029	339	11	02	02	NUM
ejpam-4029	339	12	2021	2021	NUM
ejpam-4029	339	13	.	.	PUNCT
ejpam-4029	340	1	[	[	X
ejpam-4029	340	2	6	6	NUM
ejpam-4029	340	3	]	]	X
ejpam-4029	340	4	denis	denis	PROPN
ejpam-4029	340	5	borisov	borisov	PROPN
ejpam-4029	340	6	and	and	CCONJ
ejpam-4029	340	7	giuseppe	giuseppe	PROPN
ejpam-4029	340	8	cardone	cardone	PROPN
ejpam-4029	340	9	.	.	PUNCT
ejpam-4029	340	10	spectra	spectra	PROPN
ejpam-4029	340	11	of	of	ADP
ejpam-4029	340	12	operator	operator	NOUN
ejpam-4029	340	13	pencils	pencil	NOUN
ejpam-4029	340	14	with	with	ADP
ejpam-4029	340	15	small	small	ADJ
ejpam-4029	340	16	pjsymmetric	pjsymmetric	ADJ
ejpam-4029	340	17	periodic	periodic	ADJ
ejpam-4029	340	18	perturbation	perturbation	NOUN
ejpam-4029	340	19	.	.	PUNCT
ejpam-4029	341	1	esaim	esaim	NOUN
ejpam-4029	341	2	:	:	PUNCT
ejpam-4029	341	3	control	control	NOUN
ejpam-4029	341	4	,	,	PUNCT
ejpam-4029	341	5	optimisation	optimisation	NOUN
ejpam-4029	341	6	and	and	CCONJ
ejpam-4029	341	7	calculus	calculus	NOUN
ejpam-4029	341	8	of	of	ADP
ejpam-4029	341	9	variations	variation	NOUN
ejpam-4029	341	10	,	,	PUNCT
ejpam-4029	341	11	26:21	26:21	NUM
ejpam-4029	341	12	,	,	PUNCT
ejpam-4029	341	13	2020	2020	NUM
ejpam-4029	341	14	.	.	PUNCT
ejpam-4029	342	1	[	[	X
ejpam-4029	342	2	7	7	NUM
ejpam-4029	342	3	]	]	X
ejpam-4029	342	4	yu	yu	PROPN
ejpam-4029	342	5	a.	a.	NOUN
ejpam-4029	342	6	brychkov	brychkov	PROPN
ejpam-4029	342	7	,	,	PUNCT
ejpam-4029	342	8	o.	o.	PROPN
ejpam-4029	342	9	i.	i.	PROPN
ejpam-4029	342	10	marichev	marichev	PROPN
ejpam-4029	342	11	,	,	PUNCT
ejpam-4029	342	12	and	and	CCONJ
ejpam-4029	342	13	n.	n.	PROPN
ejpam-4029	342	14	v.	v.	PROPN
ejpam-4029	342	15	savischenko	savischenko	PROPN
ejpam-4029	342	16	.	.	PUNCT
ejpam-4029	343	1	handbook	handbook	NOUN
ejpam-4029	343	2	of	of	ADP
ejpam-4029	343	3	mellin	mellin	PROPN
ejpam-4029	343	4	transforms	transform	VERB
ejpam-4029	343	5	.	.	PUNCT
ejpam-4029	344	1	chapman	chapman	NOUN
ejpam-4029	344	2	and	and	CCONJ
ejpam-4029	344	3	hall	hall	PROPN
ejpam-4029	344	4	/	/	SYM
ejpam-4029	344	5	crc	crc	PROPN
ejpam-4029	344	6	;	;	PUNCT
ejpam-4029	344	7	1st	1st	PROPN
ejpam-4029	344	8	edition	edition	NOUN
ejpam-4029	344	9	(	(	PUNCT
ejpam-4029	344	10	oct	oct	PROPN
ejpam-4029	344	11	.	.	PROPN
ejpam-4029	344	12	10	10	NUM
ejpam-4029	344	13	2018	2018	NUM
ejpam-4029	344	14	)	)	PUNCT
ejpam-4029	344	15	,	,	PUNCT
ejpam-4029	344	16	10	10	NUM
ejpam-4029	344	17	2018	2018	NUM
ejpam-4029	344	18	.	.	PUNCT
ejpam-4029	345	1	[	[	X
ejpam-4029	345	2	8	8	NUM
ejpam-4029	345	3	]	]	X
ejpam-4029	345	4	i.	i.	PROPN
ejpam-4029	345	5	s.	s.	PROPN
ejpam-4029	345	6	gradshteyn	gradshteyn	PROPN
ejpam-4029	345	7	,	,	PUNCT
ejpam-4029	345	8	i.	i.	PROPN
ejpam-4029	345	9	m.	m.	PROPN
ejpam-4029	345	10	ryzhik	ryzhik	PROPN
ejpam-4029	345	11	,	,	PUNCT
ejpam-4029	345	12	alan	alan	PROPN
ejpam-4029	345	13	jeffrey	jeffrey	PROPN
ejpam-4029	345	14	,	,	PUNCT
ejpam-4029	345	15	and	and	CCONJ
ejpam-4029	345	16	daniel	daniel	PROPN
ejpam-4029	345	17	zwillinger	zwillinger	PROPN
ejpam-4029	345	18	.	.	PUNCT
ejpam-4029	345	19	table	table	NOUN
ejpam-4029	345	20	of	of	ADP
ejpam-4029	345	21	integrals	integral	NOUN
ejpam-4029	345	22	,	,	PUNCT
ejpam-4029	345	23	series	series	NOUN
ejpam-4029	345	24	,	,	PUNCT
ejpam-4029	345	25	and	and	CCONJ
ejpam-4029	345	26	products	product	NOUN
ejpam-4029	345	27	.	.	PUNCT
ejpam-4029	346	1	academic	academic	ADJ
ejpam-4029	346	2	press	press	NOUN
ejpam-4029	346	3	;	;	PUNCT
ejpam-4029	346	4	6th	6th	ADJ
ejpam-4029	346	5	edition	edition	NOUN
ejpam-4029	346	6	(	(	PUNCT
ejpam-4029	346	7	aug	aug	PROPN
ejpam-4029	346	8	.	.	PROPN
ejpam-4029	346	9	24	24	NUM
ejpam-4029	346	10	2000	2000	NUM
ejpam-4029	346	11	)	)	PUNCT
ejpam-4029	346	12	,	,	PUNCT
ejpam-4029	346	13	08	08	NUM
ejpam-4029	346	14	2000	2000	NUM
ejpam-4029	346	15	.	.	PUNCT
ejpam-4029	347	1	[	[	X
ejpam-4029	347	2	9	9	NUM
ejpam-4029	347	3	]	]	X
ejpam-4029	347	4	e.a	e.a	PROPN
ejpam-4029	347	5	.	.	PROPN
ejpam-4029	347	6	kuznetsov	kuznetsov	PROPN
ejpam-4029	347	7	,	,	PUNCT
ejpam-4029	347	8	a.m.	a.m.	NOUN
ejpam-4029	347	9	rubenchik	rubenchik	PROPN
ejpam-4029	347	10	,	,	PUNCT
ejpam-4029	347	11	and	and	CCONJ
ejpam-4029	347	12	v.e	v.e	PROPN
ejpam-4029	347	13	.	.	PROPN
ejpam-4029	348	1	zakharov	zakharov	PROPN
ejpam-4029	348	2	.	.	PUNCT
ejpam-4029	349	1	soliton	soliton	NOUN
ejpam-4029	349	2	stability	stability	NOUN
ejpam-4029	349	3	in	in	ADP
ejpam-4029	349	4	plasmas	plasma	NOUN
ejpam-4029	349	5	and	and	CCONJ
ejpam-4029	349	6	hydrodynamics	hydrodynamic	NOUN
ejpam-4029	349	7	.	.	PUNCT
ejpam-4029	350	1	physics	physics	NOUN
ejpam-4029	350	2	reports	report	NOUN
ejpam-4029	350	3	,	,	PUNCT
ejpam-4029	350	4	142:103–165	142:103–165	NUM
ejpam-4029	350	5	,	,	PUNCT
ejpam-4029	350	6	09	09	NUM
ejpam-4029	350	7	1986	1986	NUM
ejpam-4029	350	8	.	.	PUNCT
ejpam-4029	351	1	[	[	X
ejpam-4029	351	2	10	10	NUM
ejpam-4029	351	3	]	]	X
ejpam-4029	351	4	leonard	leonard	PROPN
ejpam-4029	351	5	lewin	lewin	PROPN
ejpam-4029	351	6	.	.	PUNCT
ejpam-4029	352	1	polylogarithms	polylogarithm	NOUN
ejpam-4029	352	2	and	and	CCONJ
ejpam-4029	352	3	associated	associated	ADJ
ejpam-4029	352	4	functions	function	NOUN
ejpam-4029	352	5	.	.	PUNCT
ejpam-4029	353	1	north	north	NOUN
ejpam-4029	353	2	holland	holland	PROPN
ejpam-4029	353	3	,	,	PUNCT
ejpam-4029	353	4	1981	1981	NUM
ejpam-4029	353	5	.	.	PUNCT
ejpam-4029	354	1	[	[	X
ejpam-4029	354	2	11	11	NUM
ejpam-4029	354	3	]	]	PUNCT
ejpam-4029	354	4	keith	keith	PROPN
ejpam-4029	354	5	b.	b.	PROPN
ejpam-4029	354	6	oldham	oldham	PROPN
ejpam-4029	354	7	,	,	PUNCT
ejpam-4029	354	8	jan	jan	PROPN
ejpam-4029	354	9	myland	myland	PROPN
ejpam-4029	354	10	,	,	PUNCT
ejpam-4029	354	11	and	and	CCONJ
ejpam-4029	354	12	jerome	jerome	PROPN
ejpam-4029	354	13	spanier	spanier	NOUN
ejpam-4029	354	14	.	.	PUNCT
ejpam-4029	355	1	an	an	DET
ejpam-4029	355	2	atlas	atlas	PROPN
ejpam-4029	355	3	of	of	ADP
ejpam-4029	355	4	functions	function	NOUN
ejpam-4029	355	5	:	:	PUNCT
ejpam-4029	355	6	with	with	ADP
ejpam-4029	355	7	equator	equator	NOUN
ejpam-4029	355	8	,	,	PUNCT
ejpam-4029	355	9	the	the	DET
ejpam-4029	355	10	atlas	atlas	PROPN
ejpam-4029	355	11	function	function	PROPN
ejpam-4029	355	12	calculator	calculator	NOUN
ejpam-4029	355	13	.	.	PUNCT
ejpam-4029	356	1	springer	springer	NOUN
ejpam-4029	356	2	science	science	PROPN
ejpam-4029	356	3	&	&	CCONJ
ejpam-4029	356	4	business	business	NOUN
ejpam-4029	356	5	media	medium	NOUN
ejpam-4029	356	6	,	,	PUNCT
ejpam-4029	356	7	07	07	NUM
ejpam-4029	356	8	2010	2010	NUM
ejpam-4029	356	9	.	.	PUNCT
ejpam-4029	357	1	[	[	X
ejpam-4029	357	2	12	12	NUM
ejpam-4029	357	3	]	]	PUNCT
ejpam-4029	357	4	anatolĭı	anatolĭı	PROPN
ejpam-4029	357	5	platonovich	platonovich	PROPN
ejpam-4029	357	6	prudnikov	prudnikov	PROPN
ejpam-4029	357	7	,	,	PUNCT
ejpam-4029	357	8	yu	yu	PROPN
ejpam-4029	357	9	a.	a.	NOUN
ejpam-4029	357	10	brychkov	brychkov	PROPN
ejpam-4029	357	11	,	,	PUNCT
ejpam-4029	357	12	and	and	CCONJ
ejpam-4029	357	13	oleg	oleg	PROPN
ejpam-4029	357	14	igorevich	igorevich	PROPN
ejpam-4029	357	15	marichev	marichev	PROPN
ejpam-4029	357	16	.	.	PUNCT
ejpam-4029	358	1	integrals	integral	NOUN
ejpam-4029	358	2	and	and	CCONJ
ejpam-4029	358	3	series	series	NOUN
ejpam-4029	358	4	:	:	PUNCT
ejpam-4029	358	5	more	more	ADJ
ejpam-4029	358	6	special	special	ADJ
ejpam-4029	358	7	functions	function	NOUN
ejpam-4029	358	8	.	.	PUNCT
ejpam-4029	359	1	gordon	gordon	PROPN
ejpam-4029	359	2	and	and	CCONJ
ejpam-4029	359	3	breach	breach	VERB
ejpam-4029	359	4	science	science	NOUN
ejpam-4029	359	5	publishers	publisher	NOUN
ejpam-4029	359	6	,	,	PUNCT
ejpam-4029	359	7	1986	1986	NUM
ejpam-4029	359	8	.	.	PUNCT
ejpam-4029	360	1	[	[	X
ejpam-4029	360	2	13	13	NUM
ejpam-4029	360	3	]	]	X
ejpam-4029	360	4	robert	robert	PROPN
ejpam-4029	360	5	reynolds	reynolds	PROPN
ejpam-4029	360	6	and	and	CCONJ
ejpam-4029	360	7	allan	allan	PROPN
ejpam-4029	360	8	stauffer	stauffer	PROPN
ejpam-4029	360	9	.	.	PUNCT
ejpam-4029	361	1	a	a	DET
ejpam-4029	361	2	method	method	NOUN
ejpam-4029	361	3	for	for	ADP
ejpam-4029	361	4	evaluating	evaluate	VERB
ejpam-4029	361	5	definite	definite	ADJ
ejpam-4029	361	6	integrals	integral	NOUN
ejpam-4029	361	7	in	in	ADP
ejpam-4029	361	8	terms	term	NOUN
ejpam-4029	361	9	of	of	ADP
ejpam-4029	361	10	special	special	ADJ
ejpam-4029	361	11	functions	function	NOUN
ejpam-4029	361	12	with	with	ADP
ejpam-4029	361	13	examples	example	NOUN
ejpam-4029	361	14	.	.	PUNCT
ejpam-4029	362	1	international	international	ADJ
ejpam-4029	362	2	mathematical	mathematical	PROPN
ejpam-4029	362	3	forum	forum	PROPN
ejpam-4029	362	4	,	,	PUNCT
ejpam-4029	362	5	15:235	15:235	NUM
ejpam-4029	362	6	–	–	PUNCT
ejpam-4029	362	7	244	244	NUM
ejpam-4029	362	8	,	,	PUNCT
ejpam-4029	362	9	2020	2020	NUM
ejpam-4029	362	10	.	.	PUNCT
ejpam-4029	363	1	[	[	X
ejpam-4029	363	2	14	14	NUM
ejpam-4029	363	3	]	]	X
ejpam-4029	363	4	ambaresh	ambaresh	NOUN
ejpam-4029	363	5	sahoo	sahoo	PROPN
ejpam-4029	363	6	and	and	CCONJ
ejpam-4029	363	7	samudra	samudra	PROPN
ejpam-4029	363	8	roy	roy	PROPN
ejpam-4029	363	9	.	.	PROPN
ejpam-4029	363	10	dissipative	dissipative	PROPN
ejpam-4029	363	11	soliton	soliton	NOUN
ejpam-4029	363	12	mediated	mediate	VERB
ejpam-4029	363	13	radiations	radiation	NOUN
ejpam-4029	363	14	in	in	ADP
ejpam-4029	363	15	active	active	ADJ
ejpam-4029	363	16	silicon	silicon	NOUN
ejpam-4029	363	17	-	-	PUNCT
ejpam-4029	363	18	based	base	VERB
ejpam-4029	363	19	waveguides	waveguide	NOUN
ejpam-4029	363	20	.	.	PUNCT
ejpam-4029	364	1	journal	journal	NOUN
ejpam-4029	364	2	of	of	ADP
ejpam-4029	364	3	the	the	DET
ejpam-4029	364	4	optical	optical	ADJ
ejpam-4029	364	5	society	society	NOUN
ejpam-4029	364	6	of	of	ADP
ejpam-4029	364	7	america	america	PROPN
ejpam-4029	364	8	b	b	PROPN
ejpam-4029	364	9	,	,	PUNCT
ejpam-4029	364	10	35:257	35:257	NUM
ejpam-4029	364	11	,	,	PUNCT
ejpam-4029	364	12	01	01	NUM
ejpam-4029	364	13	2018	2018	NUM
ejpam-4029	364	14	.	.	PUNCT