id	sid	tid	token	lemma	pos
ejpam-4063	1	1	european	european	PROPN
ejpam-4063	1	2	journal	journal	PROPN
ejpam-4063	1	3	of	of	ADP
ejpam-4063	1	4	pure	pure	ADJ
ejpam-4063	1	5	and	and	CCONJ
ejpam-4063	1	6	applied	apply	VERB
ejpam-4063	1	7	mathematics	mathematic	NOUN
ejpam-4063	1	8	vol	vol	NOUN
ejpam-4063	1	9	.	.	PUNCT
ejpam-4063	2	1	14	14	NUM
ejpam-4063	2	2	,	,	PUNCT
ejpam-4063	2	3	no	no	INTJ
ejpam-4063	2	4	.	.	NOUN
ejpam-4063	2	5	4	4	NUM
ejpam-4063	2	6	,	,	PUNCT
ejpam-4063	2	7	2021	2021	NUM
ejpam-4063	2	8	,	,	PUNCT
ejpam-4063	2	9	1249	1249	NUM
ejpam-4063	2	10	-	-	SYM
ejpam-4063	2	11	1265	1265	NUM
ejpam-4063	2	12	issn	issn	PROPN
ejpam-4063	2	13	1307	1307	NUM
ejpam-4063	2	14	-	-	SYM
ejpam-4063	2	15	5543	5543	NUM
ejpam-4063	2	16	–	–	PUNCT
ejpam-4063	2	17	ejpam.com	ejpam.com	X
ejpam-4063	2	18	published	publish	VERB
ejpam-4063	2	19	by	by	ADP
ejpam-4063	2	20	new	new	PROPN
ejpam-4063	2	21	york	york	PROPN
ejpam-4063	2	22	business	business	PROPN
ejpam-4063	2	23	global	global	ADJ
ejpam-4063	2	24	definite	definite	ADJ
ejpam-4063	2	25	integral	integral	ADJ
ejpam-4063	2	26	of	of	ADP
ejpam-4063	2	27	logarithmic	logarithmic	ADJ
ejpam-4063	2	28	trigonometric	trigonometric	ADJ
ejpam-4063	2	29	functions	function	NOUN
ejpam-4063	2	30	expressed	express	VERB
ejpam-4063	2	31	in	in	ADP
ejpam-4063	2	32	terms	term	NOUN
ejpam-4063	2	33	of	of	ADP
ejpam-4063	2	34	the	the	DET
ejpam-4063	2	35	incomplete	incomplete	ADJ
ejpam-4063	2	36	gamma	gamma	PROPN
ejpam-4063	2	37	function	function	PROPN
ejpam-4063	2	38	robert	robert	PROPN
ejpam-4063	2	39	reynolds1,∗	reynolds1,∗	PROPN
ejpam-4063	2	40	,	,	PUNCT
ejpam-4063	2	41	allan	allan	PROPN
ejpam-4063	2	42	stauffer1	stauffer1	PROPN
ejpam-4063	2	43	1	1	NUM
ejpam-4063	2	44	department	department	NOUN
ejpam-4063	2	45	of	of	ADP
ejpam-4063	2	46	mathematics	mathematic	NOUN
ejpam-4063	2	47	and	and	CCONJ
ejpam-4063	2	48	statistics	statistic	NOUN
ejpam-4063	2	49	,	,	PUNCT
ejpam-4063	2	50	faculty	faculty	NOUN
ejpam-4063	2	51	of	of	ADP
ejpam-4063	2	52	science	science	PROPN
ejpam-4063	2	53	,	,	PUNCT
ejpam-4063	2	54	york	york	PROPN
ejpam-4063	2	55	university	university	PROPN
ejpam-4063	2	56	,	,	PUNCT
ejpam-4063	2	57	toronto	toronto	PROPN
ejpam-4063	2	58	,	,	PUNCT
ejpam-4063	2	59	ontario	ontario	PROPN
ejpam-4063	2	60	,	,	PUNCT
ejpam-4063	2	61	canada	canada	PROPN
ejpam-4063	2	62	,	,	PUNCT
ejpam-4063	2	63	m3j1p3	m3j1p3	PROPN
ejpam-4063	2	64	abstract	abstract	NOUN
ejpam-4063	2	65	.	.	PUNCT
ejpam-4063	3	1	we	we	PRON
ejpam-4063	3	2	present	present	VERB
ejpam-4063	3	3	a	a	DET
ejpam-4063	3	4	method	method	NOUN
ejpam-4063	3	5	using	use	VERB
ejpam-4063	3	6	contour	contour	NOUN
ejpam-4063	3	7	integration	integration	NOUN
ejpam-4063	3	8	to	to	PART
ejpam-4063	3	9	derive	derive	VERB
ejpam-4063	3	10	definite	definite	ADJ
ejpam-4063	3	11	integrals	integral	NOUN
ejpam-4063	3	12	and	and	CCONJ
ejpam-4063	3	13	their	their	PRON
ejpam-4063	3	14	associated	associate	VERB
ejpam-4063	3	15	infinite	infinite	NOUN
ejpam-4063	3	16	sums	sum	NOUN
ejpam-4063	3	17	which	which	PRON
ejpam-4063	3	18	can	can	AUX
ejpam-4063	3	19	be	be	AUX
ejpam-4063	3	20	expressed	express	VERB
ejpam-4063	3	21	as	as	ADP
ejpam-4063	3	22	a	a	DET
ejpam-4063	3	23	special	special	ADJ
ejpam-4063	3	24	function	function	NOUN
ejpam-4063	3	25	.	.	PUNCT
ejpam-4063	4	1	we	we	PRON
ejpam-4063	4	2	give	give	VERB
ejpam-4063	4	3	a	a	DET
ejpam-4063	4	4	proof	proof	NOUN
ejpam-4063	4	5	of	of	ADP
ejpam-4063	4	6	the	the	DET
ejpam-4063	4	7	basic	basic	ADJ
ejpam-4063	4	8	equation	equation	NOUN
ejpam-4063	4	9	and	and	CCONJ
ejpam-4063	4	10	some	some	DET
ejpam-4063	4	11	examples	example	NOUN
ejpam-4063	4	12	of	of	ADP
ejpam-4063	4	13	the	the	DET
ejpam-4063	4	14	method	method	NOUN
ejpam-4063	4	15	.	.	PUNCT
ejpam-4063	5	1	the	the	DET
ejpam-4063	5	2	advantage	advantage	NOUN
ejpam-4063	5	3	of	of	ADP
ejpam-4063	5	4	using	use	VERB
ejpam-4063	5	5	special	special	ADJ
ejpam-4063	5	6	functions	function	NOUN
ejpam-4063	5	7	is	be	AUX
ejpam-4063	5	8	their	their	PRON
ejpam-4063	5	9	analytic	analytic	ADJ
ejpam-4063	5	10	continuation	continuation	NOUN
ejpam-4063	5	11	which	which	PRON
ejpam-4063	5	12	widens	widen	VERB
ejpam-4063	5	13	the	the	DET
ejpam-4063	5	14	range	range	NOUN
ejpam-4063	5	15	of	of	ADP
ejpam-4063	5	16	the	the	DET
ejpam-4063	5	17	parameters	parameter	NOUN
ejpam-4063	5	18	of	of	ADP
ejpam-4063	5	19	the	the	DET
ejpam-4063	5	20	definite	definite	ADJ
ejpam-4063	5	21	integral	integral	NOUN
ejpam-4063	5	22	over	over	ADP
ejpam-4063	5	23	which	which	PRON
ejpam-4063	5	24	the	the	DET
ejpam-4063	5	25	formula	formula	NOUN
ejpam-4063	5	26	is	be	AUX
ejpam-4063	5	27	valid	valid	ADJ
ejpam-4063	5	28	.	.	PUNCT
ejpam-4063	6	1	we	we	PRON
ejpam-4063	6	2	give	give	VERB
ejpam-4063	6	3	as	as	ADP
ejpam-4063	6	4	examples	example	NOUN
ejpam-4063	6	5	definite	definite	ADJ
ejpam-4063	6	6	integrals	integral	NOUN
ejpam-4063	6	7	of	of	ADP
ejpam-4063	6	8	logarithmic	logarithmic	ADJ
ejpam-4063	6	9	functions	function	NOUN
ejpam-4063	6	10	times	time	NOUN
ejpam-4063	6	11	a	a	DET
ejpam-4063	6	12	trigonometric	trigonometric	ADJ
ejpam-4063	6	13	function	function	NOUN
ejpam-4063	6	14	.	.	PUNCT
ejpam-4063	7	1	in	in	ADP
ejpam-4063	7	2	various	various	ADJ
ejpam-4063	7	3	cases	case	NOUN
ejpam-4063	7	4	these	these	DET
ejpam-4063	7	5	generalizations	generalization	NOUN
ejpam-4063	7	6	evaluate	evaluate	VERB
ejpam-4063	7	7	to	to	ADP
ejpam-4063	7	8	known	know	VERB
ejpam-4063	7	9	mathematical	mathematical	ADJ
ejpam-4063	7	10	constants	constant	NOUN
ejpam-4063	7	11	such	such	ADJ
ejpam-4063	7	12	as	as	ADP
ejpam-4063	7	13	catalan	catalan	NOUN
ejpam-4063	7	14	’s	’s	PART
ejpam-4063	7	15	constant	constant	ADJ
ejpam-4063	7	16	and	and	CCONJ
ejpam-4063	7	17	π	π	PROPN
ejpam-4063	7	18	.	.	PROPN
ejpam-4063	7	19	2020	2020	NUM
ejpam-4063	7	20	mathematics	mathematic	NOUN
ejpam-4063	7	21	subject	subject	NOUN
ejpam-4063	7	22	classifications	classification	NOUN
ejpam-4063	7	23	:	:	PUNCT
ejpam-4063	7	24	30	30	NUM
ejpam-4063	7	25	-	-	SYM
ejpam-4063	7	26	02	02	NUM
ejpam-4063	7	27	,	,	PUNCT
ejpam-4063	7	28	30d10	30d10	NUM
ejpam-4063	7	29	,	,	PUNCT
ejpam-4063	7	30	30d30	30d30	NUM
ejpam-4063	7	31	,	,	PUNCT
ejpam-4063	7	32	30e20	30e20	NUM
ejpam-4063	7	33	,	,	PUNCT
ejpam-4063	7	34	11m35	11m35	NUM
ejpam-4063	7	35	,	,	PUNCT
ejpam-4063	7	36	11m06	11m06	NUM
ejpam-4063	7	37	,	,	PUNCT
ejpam-4063	7	38	01a55	01a55	NOUN
ejpam-4063	7	39	key	key	ADJ
ejpam-4063	7	40	words	word	NOUN
ejpam-4063	7	41	and	and	CCONJ
ejpam-4063	7	42	phrases	phrase	NOUN
ejpam-4063	7	43	:	:	PUNCT
ejpam-4063	7	44	entries	entry	NOUN
ejpam-4063	7	45	in	in	ADP
ejpam-4063	7	46	gradshteyn	gradshteyn	PROPN
ejpam-4063	7	47	and	and	CCONJ
ejpam-4063	7	48	rhyzik	rhyzik	ADJ
ejpam-4063	7	49	,	,	PUNCT
ejpam-4063	7	50	lerch	lerch	PROPN
ejpam-4063	7	51	function	function	PROPN
ejpam-4063	7	52	,	,	PUNCT
ejpam-4063	7	53	logarithm	logarithm	NOUN
ejpam-4063	7	54	function	function	NOUN
ejpam-4063	7	55	,	,	PUNCT
ejpam-4063	7	56	contour	contour	NOUN
ejpam-4063	7	57	integral	integral	ADJ
ejpam-4063	7	58	,	,	PUNCT
ejpam-4063	7	59	cauchy	cauchy	PROPN
ejpam-4063	7	60	,	,	PUNCT
ejpam-4063	7	61	infinite	infinite	ADJ
ejpam-4063	7	62	integral	integral	ADJ
ejpam-4063	7	63	1	1	NUM
ejpam-4063	7	64	.	.	PUNCT
ejpam-4063	7	65	introduction	introduction	NOUN
ejpam-4063	7	66	we	we	PRON
ejpam-4063	7	67	will	will	AUX
ejpam-4063	7	68	derive	derive	VERB
ejpam-4063	7	69	integrals	integral	NOUN
ejpam-4063	7	70	as	as	SCONJ
ejpam-4063	7	71	indicated	indicate	VERB
ejpam-4063	7	72	in	in	ADP
ejpam-4063	7	73	the	the	DET
ejpam-4063	7	74	abstract	abstract	NOUN
ejpam-4063	7	75	in	in	ADP
ejpam-4063	7	76	terms	term	NOUN
ejpam-4063	7	77	of	of	ADP
ejpam-4063	7	78	special	special	ADJ
ejpam-4063	7	79	functions	function	NOUN
ejpam-4063	7	80	.	.	PUNCT
ejpam-4063	8	1	some	some	DET
ejpam-4063	8	2	special	special	ADJ
ejpam-4063	8	3	cases	case	NOUN
ejpam-4063	8	4	of	of	ADP
ejpam-4063	8	5	these	these	DET
ejpam-4063	8	6	integrals	integral	NOUN
ejpam-4063	8	7	have	have	AUX
ejpam-4063	8	8	been	be	AUX
ejpam-4063	8	9	reported	report	VERB
ejpam-4063	8	10	in	in	ADP
ejpam-4063	8	11	gradshteyn	gradshteyn	PROPN
ejpam-4063	8	12	and	and	CCONJ
ejpam-4063	8	13	ryzhik	ryzhik	ADJ
ejpam-4063	8	14	[	[	X
ejpam-4063	8	15	3	3	NUM
ejpam-4063	8	16	]	]	PUNCT
ejpam-4063	8	17	.	.	PUNCT
ejpam-4063	9	1	in	in	ADP
ejpam-4063	9	2	1867	1867	NUM
ejpam-4063	9	3	david	david	PROPN
ejpam-4063	9	4	bierens	bierens	PROPN
ejpam-4063	9	5	de	de	PROPN
ejpam-4063	9	6	haan	haan	X
ejpam-4063	9	7	[	[	X
ejpam-4063	9	8	4	4	NUM
ejpam-4063	9	9	]	]	PUNCT
ejpam-4063	9	10	derived	derive	VERB
ejpam-4063	9	11	hyperbolic	hyperbolic	ADJ
ejpam-4063	9	12	integrals	integral	NOUN
ejpam-4063	9	13	of	of	ADP
ejpam-4063	9	14	the	the	DET
ejpam-4063	9	15	form∫	form∫	ADJ
ejpam-4063	9	16	∞	∞	PROPN
ejpam-4063	9	17	0	0	NUM
ejpam-4063	9	18	sinh(ax	sinh(ax	NOUN
ejpam-4063	9	19	)	)	PUNCT
ejpam-4063	9	20	(	(	PUNCT
ejpam-4063	9	21	e−mx(log(α)−	e−mx(log(α)−	PROPN
ejpam-4063	9	22	x)k	x)k	NOUN
ejpam-4063	10	1	−	−	PROPN
ejpam-4063	10	2	emx(log(α	emx(log(α	PROPN
ejpam-4063	10	3	)	)	PUNCT
ejpam-4063	10	4	+	+	NUM
ejpam-4063	10	5	x)k	x)k	X
ejpam-4063	10	6	)	)	PUNCT
ejpam-4063	11	1	(	(	PUNCT
ejpam-4063	11	2	cosh(ax	cosh(ax	NOUN
ejpam-4063	11	3	)	)	PUNCT
ejpam-4063	12	1	+	+	CCONJ
ejpam-4063	12	2	cos(t))2	cos(t))2	VERB
ejpam-4063	12	3	dx	dx	PROPN
ejpam-4063	12	4	in	in	ADP
ejpam-4063	12	5	our	our	PRON
ejpam-4063	12	6	case	case	NOUN
ejpam-4063	12	7	the	the	DET
ejpam-4063	12	8	constants	constant	NOUN
ejpam-4063	12	9	in	in	ADP
ejpam-4063	12	10	the	the	DET
ejpam-4063	12	11	formulas	formula	NOUN
ejpam-4063	12	12	are	be	AUX
ejpam-4063	12	13	general	general	ADJ
ejpam-4063	12	14	complex	complex	ADJ
ejpam-4063	12	15	numbers	number	NOUN
ejpam-4063	12	16	subject	subject	ADJ
ejpam-4063	12	17	to	to	ADP
ejpam-4063	12	18	the	the	DET
ejpam-4063	12	19	restrictions	restriction	NOUN
ejpam-4063	12	20	given	give	VERB
ejpam-4063	12	21	below	below	ADV
ejpam-4063	12	22	.	.	PUNCT
ejpam-4063	13	1	the	the	DET
ejpam-4063	13	2	derivations	derivation	NOUN
ejpam-4063	13	3	follow	follow	VERB
ejpam-4063	13	4	the	the	DET
ejpam-4063	13	5	method	method	NOUN
ejpam-4063	13	6	used	use	VERB
ejpam-4063	13	7	by	by	ADP
ejpam-4063	13	8	us	we	PRON
ejpam-4063	13	9	in	in	ADP
ejpam-4063	13	10	[	[	X
ejpam-4063	13	11	8	8	NUM
ejpam-4063	13	12	]	]	PUNCT
ejpam-4063	13	13	.	.	PUNCT
ejpam-4063	14	1	the	the	DET
ejpam-4063	14	2	generalized	generalized	ADJ
ejpam-4063	14	3	cauchy	cauchy	PROPN
ejpam-4063	14	4	’s	’s	PART
ejpam-4063	14	5	integral	integral	ADJ
ejpam-4063	14	6	formula	formula	NOUN
ejpam-4063	14	7	is	be	AUX
ejpam-4063	14	8	given	give	VERB
ejpam-4063	14	9	by	by	ADP
ejpam-4063	14	10	xk	xk	PROPN
ejpam-4063	14	11	γ(k	γ(k	PROPN
ejpam-4063	14	12	+	+	CCONJ
ejpam-4063	14	13	1	1	X
ejpam-4063	14	14	)	)	PUNCT
ejpam-4063	14	15	=	=	SYM
ejpam-4063	14	16	1	1	NUM
ejpam-4063	14	17	2πi	2πi	ADJ
ejpam-4063	14	18	∫	∫	PROPN
ejpam-4063	14	19	c	c	PROPN
ejpam-4063	14	20	ewx	ewx	PROPN
ejpam-4063	14	21	wk+1	wk+1	PUNCT
ejpam-4063	14	22	dw	dw	PROPN
ejpam-4063	14	23	.	.	PUNCT
ejpam-4063	15	1	(	(	PUNCT
ejpam-4063	15	2	1	1	X
ejpam-4063	15	3	)	)	PUNCT
ejpam-4063	15	4	∗corresponding	∗corresponde	VERB
ejpam-4063	15	5	author	author	NOUN
ejpam-4063	15	6	.	.	PUNCT
ejpam-4063	16	1	doi	doi	NOUN
ejpam-4063	16	2	:	:	PUNCT
ejpam-4063	16	3	https://doi.org/10.29020/nybg.ejpam.v14i4.4063	https://doi.org/10.29020/nybg.ejpam.v14i4.4063	PROPN
ejpam-4063	16	4	email	email	NOUN
ejpam-4063	16	5	addresses	address	NOUN
ejpam-4063	16	6	:	:	PUNCT
ejpam-4063	17	1	milver@my.yorku.ca	milver@my.yorku.ca	NOUN
ejpam-4063	17	2	(	(	PUNCT
ejpam-4063	17	3	r.	r.	PROPN
ejpam-4063	17	4	reynolds	reynolds	PROPN
ejpam-4063	17	5	)	)	PUNCT
ejpam-4063	17	6	,	,	PUNCT
ejpam-4063	17	7	stauffer@yorku.ca	stauffer@yorku.ca	NOUN
ejpam-4063	17	8	(	(	PUNCT
ejpam-4063	17	9	a.	a.	NOUN
ejpam-4063	17	10	stauffer	stauffer	PROPN
ejpam-4063	17	11	)	)	PUNCT
ejpam-4063	17	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4063	18	1	1249	1249	NUM
ejpam-4063	19	1	©	©	ADP
ejpam-4063	19	2	2021	2021	NUM
ejpam-4063	19	3	ejpam	ejpam	VERB
ejpam-4063	19	4	all	all	DET
ejpam-4063	19	5	rights	right	NOUN
ejpam-4063	19	6	reserved	reserve	VERB
ejpam-4063	19	7	.	.	PUNCT
ejpam-4063	20	1	r.	r.	PROPN
ejpam-4063	20	2	reynolds	reynolds	PROPN
ejpam-4063	20	3	,	,	PUNCT
ejpam-4063	20	4	a.	a.	PROPN
ejpam-4063	20	5	stauffer	stauffer	PROPN
ejpam-4063	20	6	/	/	SYM
ejpam-4063	20	7	eur	eur	PROPN
ejpam-4063	20	8	.	.	PUNCT
ejpam-4063	21	1	j.	j.	PROPN
ejpam-4063	21	2	pure	pure	PROPN
ejpam-4063	21	3	appl	appl	PROPN
ejpam-4063	21	4	.	.	PROPN
ejpam-4063	21	5	math	math	PROPN
ejpam-4063	21	6	,	,	PUNCT
ejpam-4063	21	7	14	14	NUM
ejpam-4063	21	8	(	(	PUNCT
ejpam-4063	21	9	4	4	NUM
ejpam-4063	21	10	)	)	PUNCT
ejpam-4063	21	11	(	(	PUNCT
ejpam-4063	21	12	2021	2021	NUM
ejpam-4063	21	13	)	)	PUNCT
ejpam-4063	21	14	,	,	PUNCT
ejpam-4063	21	15	1249	1249	NUM
ejpam-4063	21	16	-	-	SYM
ejpam-4063	21	17	1265	1265	NUM
ejpam-4063	21	18	1250	1250	NUM
ejpam-4063	21	19	this	this	DET
ejpam-4063	21	20	method	method	NOUN
ejpam-4063	21	21	involves	involve	VERB
ejpam-4063	21	22	using	use	VERB
ejpam-4063	21	23	a	a	DET
ejpam-4063	21	24	form	form	NOUN
ejpam-4063	21	25	of	of	ADP
ejpam-4063	21	26	equation	equation	NOUN
ejpam-4063	21	27	(	(	PUNCT
ejpam-4063	21	28	1	1	NUM
ejpam-4063	21	29	)	)	PUNCT
ejpam-4063	21	30	then	then	ADV
ejpam-4063	21	31	multiplys	multiplys	VERB
ejpam-4063	21	32	both	both	DET
ejpam-4063	21	33	sides	side	NOUN
ejpam-4063	21	34	by	by	ADP
ejpam-4063	21	35	a	a	DET
ejpam-4063	21	36	function	function	NOUN
ejpam-4063	21	37	,	,	PUNCT
ejpam-4063	21	38	then	then	ADV
ejpam-4063	21	39	takes	take	VERB
ejpam-4063	21	40	a	a	DET
ejpam-4063	21	41	definite	definite	ADJ
ejpam-4063	21	42	integral	integral	NOUN
ejpam-4063	21	43	of	of	ADP
ejpam-4063	21	44	both	both	DET
ejpam-4063	21	45	sides	side	NOUN
ejpam-4063	21	46	.	.	PUNCT
ejpam-4063	22	1	this	this	PRON
ejpam-4063	22	2	yields	yield	VERB
ejpam-4063	22	3	a	a	DET
ejpam-4063	22	4	definite	definite	ADJ
ejpam-4063	22	5	integral	integral	ADJ
ejpam-4063	22	6	in	in	ADP
ejpam-4063	22	7	terms	term	NOUN
ejpam-4063	22	8	of	of	ADP
ejpam-4063	22	9	a	a	DET
ejpam-4063	22	10	contour	contour	NOUN
ejpam-4063	22	11	integral	integral	NOUN
ejpam-4063	22	12	.	.	PUNCT
ejpam-4063	23	1	then	then	ADV
ejpam-4063	23	2	we	we	PRON
ejpam-4063	23	3	multiply	multiply	VERB
ejpam-4063	23	4	both	both	DET
ejpam-4063	23	5	sides	side	NOUN
ejpam-4063	23	6	of	of	ADP
ejpam-4063	23	7	equation	equation	NOUN
ejpam-4063	23	8	(	(	PUNCT
ejpam-4063	23	9	1	1	NUM
ejpam-4063	23	10	)	)	PUNCT
ejpam-4063	23	11	by	by	ADP
ejpam-4063	23	12	another	another	DET
ejpam-4063	23	13	function	function	NOUN
ejpam-4063	23	14	and	and	CCONJ
ejpam-4063	23	15	take	take	VERB
ejpam-4063	23	16	the	the	DET
ejpam-4063	23	17	infinite	infinite	ADJ
ejpam-4063	23	18	sum	sum	NOUN
ejpam-4063	23	19	of	of	ADP
ejpam-4063	23	20	both	both	DET
ejpam-4063	23	21	sides	side	NOUN
ejpam-4063	23	22	such	such	ADJ
ejpam-4063	23	23	that	that	SCONJ
ejpam-4063	23	24	the	the	DET
ejpam-4063	23	25	contour	contour	NOUN
ejpam-4063	23	26	integral	integral	NOUN
ejpam-4063	23	27	of	of	ADP
ejpam-4063	23	28	both	both	DET
ejpam-4063	23	29	equations	equation	NOUN
ejpam-4063	23	30	are	be	AUX
ejpam-4063	23	31	the	the	DET
ejpam-4063	23	32	same	same	ADJ
ejpam-4063	23	33	.	.	PUNCT
ejpam-4063	24	1	2	2	X
ejpam-4063	24	2	.	.	X
ejpam-4063	24	3	derivation	derivation	NOUN
ejpam-4063	24	4	of	of	ADP
ejpam-4063	24	5	the	the	DET
ejpam-4063	24	6	definite	definite	ADJ
ejpam-4063	24	7	integral	integral	NOUN
ejpam-4063	24	8	of	of	ADP
ejpam-4063	24	9	the	the	DET
ejpam-4063	24	10	contour	contour	NOUN
ejpam-4063	24	11	integral	integral	NOUN
ejpam-4063	24	12	we	we	PRON
ejpam-4063	24	13	use	use	VERB
ejpam-4063	24	14	the	the	DET
ejpam-4063	24	15	method	method	NOUN
ejpam-4063	24	16	in	in	ADP
ejpam-4063	24	17	[	[	X
ejpam-4063	24	18	8	8	NUM
ejpam-4063	24	19	]	]	PUNCT
ejpam-4063	24	20	.	.	PUNCT
ejpam-4063	25	1	here	here	ADV
ejpam-4063	25	2	the	the	DET
ejpam-4063	25	3	contour	contour	NOUN
ejpam-4063	25	4	is	be	AUX
ejpam-4063	25	5	similar	similar	ADJ
ejpam-4063	25	6	to	to	PART
ejpam-4063	25	7	figure	figure	VERB
ejpam-4063	25	8	2	2	NUM
ejpam-4063	25	9	in	in	ADP
ejpam-4063	25	10	[	[	X
ejpam-4063	25	11	8	8	NUM
ejpam-4063	25	12	]	]	PUNCT
ejpam-4063	25	13	.	.	PUNCT
ejpam-4063	26	1	using	use	VERB
ejpam-4063	26	2	a	a	DET
ejpam-4063	26	3	generalization	generalization	NOUN
ejpam-4063	26	4	of	of	ADP
ejpam-4063	26	5	cauchy	cauchy	PROPN
ejpam-4063	26	6	’s	’s	PART
ejpam-4063	26	7	integral	integral	ADJ
ejpam-4063	26	8	formula	formula	NOUN
ejpam-4063	26	9	we	we	PRON
ejpam-4063	26	10	first	first	ADV
ejpam-4063	26	11	replace	replace	VERB
ejpam-4063	26	12	x	x	PUNCT
ejpam-4063	26	13	by	by	ADP
ejpam-4063	26	14	ix+	ix+	PROPN
ejpam-4063	26	15	log(a	log(a	PROPN
ejpam-4063	26	16	)	)	PUNCT
ejpam-4063	26	17	then	then	ADV
ejpam-4063	26	18	multiply	multiply	VERB
ejpam-4063	26	19	both	both	DET
ejpam-4063	26	20	sides	side	NOUN
ejpam-4063	26	21	by	by	ADP
ejpam-4063	26	22	emx	emx	NOUN
ejpam-4063	26	23	for	for	ADP
ejpam-4063	26	24	the	the	DET
ejpam-4063	26	25	first	first	ADJ
ejpam-4063	26	26	equation	equation	NOUN
ejpam-4063	26	27	and	and	CCONJ
ejpam-4063	26	28	the	the	DET
ejpam-4063	26	29	replace	replace	NOUN
ejpam-4063	26	30	x	x	PUNCT
ejpam-4063	26	31	with	with	ADP
ejpam-4063	26	32	−x	−x	NOUN
ejpam-4063	26	33	and	and	CCONJ
ejpam-4063	26	34	multiplying	multiply	VERB
ejpam-4063	26	35	both	both	DET
ejpam-4063	26	36	sides	side	NOUN
ejpam-4063	26	37	by	by	ADP
ejpam-4063	26	38	e−mx	e−mx	NOUN
ejpam-4063	26	39	to	to	PART
ejpam-4063	26	40	get	get	VERB
ejpam-4063	26	41	the	the	DET
ejpam-4063	26	42	second	second	ADJ
ejpam-4063	26	43	equation	equation	NOUN
ejpam-4063	26	44	.	.	PUNCT
ejpam-4063	27	1	then	then	ADV
ejpam-4063	27	2	we	we	PRON
ejpam-4063	27	3	subtract	subtract	VERB
ejpam-4063	27	4	these	these	DET
ejpam-4063	27	5	two	two	NUM
ejpam-4063	27	6	equations	equation	NOUN
ejpam-4063	27	7	,	,	PUNCT
ejpam-4063	27	8	followed	follow	VERB
ejpam-4063	27	9	by	by	ADP
ejpam-4063	27	10	multiplying	multiply	VERB
ejpam-4063	27	11	both	both	DET
ejpam-4063	27	12	sides	side	NOUN
ejpam-4063	27	13	by	by	ADP
ejpam-4063	27	14	−	−	PROPN
ejpam-4063	27	15	sinh(ax	sinh(ax	NOUN
ejpam-4063	27	16	)	)	PUNCT
ejpam-4063	27	17	2(cosh(ax)+cos(t))2	2(cosh(ax)+cos(t))2	NOUN
ejpam-4063	27	18	to	to	PART
ejpam-4063	27	19	get	get	VERB
ejpam-4063	27	20	−	−	PROPN
ejpam-4063	27	21	sinh(ax	sinh(ax	NOUN
ejpam-4063	27	22	)	)	PUNCT
ejpam-4063	27	23	(	(	PUNCT
ejpam-4063	27	24	e−mx(log(α)−	e−mx(log(α)−	PROPN
ejpam-4063	27	25	x)k	x)k	NOUN
ejpam-4063	27	26	−	−	PROPN
ejpam-4063	27	27	emx(log(α	emx(log(α	PROPN
ejpam-4063	27	28	)	)	PUNCT
ejpam-4063	27	29	+	+	NUM
ejpam-4063	27	30	x)k	x)k	X
ejpam-4063	27	31	)	)	PUNCT
ejpam-4063	27	32	2γ(k	2γ(k	NUM
ejpam-4063	28	1	+	+	CCONJ
ejpam-4063	28	2	1)(cosh(ax	1)(cosh(ax	NUM
ejpam-4063	28	3	)	)	PUNCT
ejpam-4063	29	1	+	+	CCONJ
ejpam-4063	29	2	cos(t))2	cos(t))2	NOUN
ejpam-4063	29	3	=	=	SYM
ejpam-4063	29	4	1	1	NUM
ejpam-4063	29	5	2πi	2πi	ADJ
ejpam-4063	29	6	∫	∫	PROPN
ejpam-4063	29	7	c	c	NOUN
ejpam-4063	29	8	w−k−1αw	w−k−1αw	NOUN
ejpam-4063	29	9	sinh(ax	sinh(ax	NOUN
ejpam-4063	29	10	)	)	PUNCT
ejpam-4063	29	11	sinh(x(m+	sinh(x(m+	NOUN
ejpam-4063	29	12	w	w	NOUN
ejpam-4063	29	13	)	)	PUNCT
ejpam-4063	29	14	)	)	PUNCT
ejpam-4063	30	1	(	(	PUNCT
ejpam-4063	30	2	cosh(ax	cosh(ax	NOUN
ejpam-4063	30	3	)	)	PUNCT
ejpam-4063	31	1	+	+	CCONJ
ejpam-4063	31	2	cos(t))2	cos(t))2	PROPN
ejpam-4063	31	3	dw	dw	PROPN
ejpam-4063	31	4	(	(	PUNCT
ejpam-4063	31	5	2	2	NUM
ejpam-4063	31	6	)	)	PUNCT
ejpam-4063	31	7	where	where	SCONJ
ejpam-4063	31	8	the	the	DET
ejpam-4063	31	9	logarithmic	logarithmic	ADJ
ejpam-4063	31	10	function	function	NOUN
ejpam-4063	31	11	is	be	AUX
ejpam-4063	31	12	defined	define	VERB
ejpam-4063	31	13	in	in	ADP
ejpam-4063	31	14	equation	equation	NOUN
ejpam-4063	31	15	(	(	PUNCT
ejpam-4063	31	16	4.1.2	4.1.2	NUM
ejpam-4063	31	17	)	)	PUNCT
ejpam-4063	31	18	in	in	ADP
ejpam-4063	31	19	[	[	X
ejpam-4063	31	20	1	1	NUM
ejpam-4063	31	21	]	]	PUNCT
ejpam-4063	31	22	.	.	PUNCT
ejpam-4063	32	1	we	we	PRON
ejpam-4063	32	2	then	then	ADV
ejpam-4063	32	3	take	take	VERB
ejpam-4063	32	4	the	the	DET
ejpam-4063	32	5	definite	definite	ADJ
ejpam-4063	32	6	integral	integral	ADJ
ejpam-4063	32	7	over	over	ADP
ejpam-4063	32	8	x	x	PUNCT
ejpam-4063	32	9	∈	∈	PROPN
ejpam-4063	33	1	[	[	X
ejpam-4063	33	2	0,∞	0,∞	NOUN
ejpam-4063	33	3	)	)	PUNCT
ejpam-4063	33	4	of	of	ADP
ejpam-4063	33	5	both	both	DET
ejpam-4063	33	6	sides	side	NOUN
ejpam-4063	33	7	to	to	PART
ejpam-4063	33	8	get	get	VERB
ejpam-4063	33	9	(	(	PUNCT
ejpam-4063	33	10	3	3	NUM
ejpam-4063	33	11	)	)	PUNCT
ejpam-4063	33	12	−	−	NOUN
ejpam-4063	34	1	∫	∫	PROPN
ejpam-4063	34	2	∞	∞	PROPN
ejpam-4063	34	3	0	0	NUM
ejpam-4063	34	4	sinh(ax	sinh(ax	NOUN
ejpam-4063	34	5	)	)	PUNCT
ejpam-4063	34	6	(	(	PUNCT
ejpam-4063	34	7	e−mx(log(α)−	e−mx(log(α)−	PROPN
ejpam-4063	34	8	x)k	x)k	NOUN
ejpam-4063	34	9	−	−	PROPN
ejpam-4063	34	10	emx(log(α	emx(log(α	PROPN
ejpam-4063	34	11	)	)	PUNCT
ejpam-4063	35	1	+	+	NUM
ejpam-4063	35	2	x)k	x)k	X
ejpam-4063	35	3	)	)	PUNCT
ejpam-4063	35	4	2γ(k	2γ(k	NUM
ejpam-4063	35	5	+	+	CCONJ
ejpam-4063	35	6	1)(cosh(ax	1)(cosh(ax	NUM
ejpam-4063	35	7	)	)	PUNCT
ejpam-4063	36	1	+	+	CCONJ
ejpam-4063	36	2	cos(t))2	cos(t))2	ADP
ejpam-4063	36	3	dx	dx	X
ejpam-4063	36	4	=	=	SYM
ejpam-4063	36	5	1	1	NUM
ejpam-4063	36	6	2πi	2πi	NOUN
ejpam-4063	36	7	∫	∫	PROPN
ejpam-4063	37	1	∞	∞	NUM
ejpam-4063	37	2	0	0	NUM
ejpam-4063	37	3	∫	∫	PROPN
ejpam-4063	37	4	c	c	PROPN
ejpam-4063	37	5	w−k−1αw	w−k−1αw	NOUN
ejpam-4063	37	6	sinh(ax	sinh(ax	NOUN
ejpam-4063	37	7	)	)	PUNCT
ejpam-4063	37	8	sinh(x(m+	sinh(x(m+	NOUN
ejpam-4063	37	9	w	w	NOUN
ejpam-4063	37	10	)	)	PUNCT
ejpam-4063	37	11	)	)	PUNCT
ejpam-4063	38	1	(	(	PUNCT
ejpam-4063	38	2	cosh(ax	cosh(ax	NOUN
ejpam-4063	38	3	)	)	PUNCT
ejpam-4063	39	1	+	+	CCONJ
ejpam-4063	39	2	cos(t))2	cos(t))2	ADP
ejpam-4063	39	3	dwdx	dwdx	NOUN
ejpam-4063	39	4	=	=	SYM
ejpam-4063	39	5	1	1	NUM
ejpam-4063	39	6	2πi	2πi	NOUN
ejpam-4063	39	7	∫	∫	PROPN
ejpam-4063	40	1	c	c	PROPN
ejpam-4063	40	2	∫	∫	PROPN
ejpam-4063	40	3	∞	∞	NUM
ejpam-4063	40	4	0	0	NUM
ejpam-4063	40	5	w−k−1αw	w−k−1αw	NOUN
ejpam-4063	40	6	sinh(ax	sinh(ax	NOUN
ejpam-4063	40	7	)	)	PUNCT
ejpam-4063	40	8	sinh(x(m+	sinh(x(m+	NOUN
ejpam-4063	40	9	w	w	NOUN
ejpam-4063	40	10	)	)	PUNCT
ejpam-4063	40	11	)	)	PUNCT
ejpam-4063	41	1	(	(	PUNCT
ejpam-4063	41	2	cosh(ax	cosh(ax	NOUN
ejpam-4063	41	3	)	)	PUNCT
ejpam-4063	42	1	+	+	CCONJ
ejpam-4063	42	2	cos(t))2	cos(t))2	X
ejpam-4063	42	3	dxdw	dxdw	NOUN
ejpam-4063	42	4	=	=	SYM
ejpam-4063	42	5	1	1	NUM
ejpam-4063	42	6	2πi	2πi	ADJ
ejpam-4063	42	7	∫	∫	PROPN
ejpam-4063	42	8	c	c	PROPN
ejpam-4063	42	9	πmw−k−1	πmw−k−1	PROPN
ejpam-4063	42	10	csc(t)αw	csc(t)αw	PROPN
ejpam-4063	42	11	csc	csc	PROPN
ejpam-4063	42	12	(	(	PUNCT
ejpam-4063	42	13	π(m+w	π(m+w	PROPN
ejpam-4063	42	14	)	)	PUNCT
ejpam-4063	42	15	a	a	PRON
ejpam-4063	42	16	)	)	PUNCT
ejpam-4063	42	17	sin	sin	NOUN
ejpam-4063	42	18	(	(	PUNCT
ejpam-4063	42	19	t(m+w	t(m+w	NOUN
ejpam-4063	42	20	)	)	PUNCT
ejpam-4063	42	21	a	a	DET
ejpam-4063	42	22	)	)	PUNCT
ejpam-4063	42	23	a2	a2	PROPN
ejpam-4063	42	24	dw	dw	NOUN
ejpam-4063	42	25	+	+	CCONJ
ejpam-4063	42	26	1	1	NUM
ejpam-4063	42	27	2πi	2πi	ADJ
ejpam-4063	42	28	∫	∫	PROPN
ejpam-4063	42	29	c	c	PROPN
ejpam-4063	42	30	πw−k	πw−k	PROPN
ejpam-4063	42	31	csc(t)αw	csc(t)αw	PROPN
ejpam-4063	42	32	csc	csc	PROPN
ejpam-4063	42	33	(	(	PUNCT
ejpam-4063	42	34	π(m+w	π(m+w	PROPN
ejpam-4063	42	35	)	)	PUNCT
ejpam-4063	42	36	a	a	PRON
ejpam-4063	42	37	)	)	PUNCT
ejpam-4063	42	38	sin	sin	NOUN
ejpam-4063	42	39	(	(	PUNCT
ejpam-4063	42	40	t(m+w	t(m+w	NOUN
ejpam-4063	42	41	)	)	PUNCT
ejpam-4063	42	42	a	a	DET
ejpam-4063	42	43	)	)	PUNCT
ejpam-4063	42	44	a2	a2	PROPN
ejpam-4063	42	45	dw	dw	PROPN
ejpam-4063	42	46	from	from	ADP
ejpam-4063	42	47	equation	equation	NOUN
ejpam-4063	42	48	(	(	PUNCT
ejpam-4063	42	49	2.5.48.18	2.5.48.18	NUM
ejpam-4063	42	50	)	)	PUNCT
ejpam-4063	42	51	in	in	ADP
ejpam-4063	42	52	[	[	X
ejpam-4063	42	53	7	7	NUM
ejpam-4063	42	54	]	]	PUNCT
ejpam-4063	42	55	and	and	CCONJ
ejpam-4063	42	56	the	the	DET
ejpam-4063	42	57	integrals	integral	NOUN
ejpam-4063	42	58	are	be	AUX
ejpam-4063	42	59	valid	valid	ADJ
ejpam-4063	42	60	for	for	ADP
ejpam-4063	42	61	a	a	DET
ejpam-4063	42	62	,	,	PUNCT
ejpam-4063	42	63	m	m	PROPN
ejpam-4063	42	64	,	,	PUNCT
ejpam-4063	42	65	k	k	PROPN
ejpam-4063	42	66	,	,	PUNCT
ejpam-4063	42	67	t	t	PROPN
ejpam-4063	42	68	and	and	CCONJ
ejpam-4063	42	69	α	α	DET
ejpam-4063	42	70	complex	complex	NOUN
ejpam-4063	42	71	and	and	CCONJ
ejpam-4063	42	72	−1	−1	NOUN
ejpam-4063	42	73	<	<	X
ejpam-4063	42	74	re(w	re(w	X
ejpam-4063	42	75	+	+	NOUN
ejpam-4063	42	76	m	m	X
ejpam-4063	42	77	)	)	PUNCT
ejpam-4063	42	78	<	<	X
ejpam-4063	42	79	0	0	NUM
ejpam-4063	42	80	and	and	CCONJ
ejpam-4063	42	81	re(α	re(α	NOUN
ejpam-4063	42	82	)	)	PUNCT
ejpam-4063	42	83	̸=	̸=	PROPN
ejpam-4063	42	84	0	0	NUM
ejpam-4063	42	85	.	.	PUNCT
ejpam-4063	43	1	we	we	PRON
ejpam-4063	43	2	are	be	AUX
ejpam-4063	43	3	able	able	ADJ
ejpam-4063	43	4	to	to	PART
ejpam-4063	43	5	switch	switch	VERB
ejpam-4063	43	6	the	the	DET
ejpam-4063	43	7	order	order	NOUN
ejpam-4063	43	8	of	of	ADP
ejpam-4063	43	9	integration	integration	NOUN
ejpam-4063	43	10	over	over	ADP
ejpam-4063	43	11	w	w	PROPN
ejpam-4063	43	12	and	and	CCONJ
ejpam-4063	43	13	x	x	SYM
ejpam-4063	43	14	using	use	VERB
ejpam-4063	43	15	fubini	fubini	NOUN
ejpam-4063	43	16	’s	’s	PART
ejpam-4063	43	17	theorem	theorem	NOUN
ejpam-4063	43	18	since	since	SCONJ
ejpam-4063	43	19	the	the	DET
ejpam-4063	43	20	integrand	integrand	NOUN
ejpam-4063	43	21	is	be	AUX
ejpam-4063	43	22	of	of	ADP
ejpam-4063	43	23	bounded	bounded	ADJ
ejpam-4063	43	24	measure	measure	NOUN
ejpam-4063	43	25	over	over	ADP
ejpam-4063	43	26	the	the	DET
ejpam-4063	43	27	space	space	NOUN
ejpam-4063	43	28	c×	c×	PROPN
ejpam-4063	44	1	[	[	X
ejpam-4063	44	2	0,∞	0,∞	NOUN
ejpam-4063	44	3	)	)	PUNCT
ejpam-4063	44	4	.	.	PUNCT
ejpam-4063	45	1	r.	r.	PROPN
ejpam-4063	45	2	reynolds	reynolds	PROPN
ejpam-4063	45	3	,	,	PUNCT
ejpam-4063	45	4	a.	a.	PROPN
ejpam-4063	45	5	stauffer	stauffer	PROPN
ejpam-4063	45	6	/	/	SYM
ejpam-4063	45	7	eur	eur	PROPN
ejpam-4063	45	8	.	.	PUNCT
ejpam-4063	46	1	j.	j.	PROPN
ejpam-4063	46	2	pure	pure	PROPN
ejpam-4063	46	3	appl	appl	PROPN
ejpam-4063	46	4	.	.	PROPN
ejpam-4063	46	5	math	math	PROPN
ejpam-4063	46	6	,	,	PUNCT
ejpam-4063	46	7	14	14	NUM
ejpam-4063	46	8	(	(	PUNCT
ejpam-4063	46	9	4	4	NUM
ejpam-4063	46	10	)	)	PUNCT
ejpam-4063	46	11	(	(	PUNCT
ejpam-4063	46	12	2021	2021	NUM
ejpam-4063	46	13	)	)	PUNCT
ejpam-4063	46	14	,	,	PUNCT
ejpam-4063	46	15	1249	1249	NUM
ejpam-4063	46	16	-	-	SYM
ejpam-4063	46	17	1265	1265	NUM
ejpam-4063	46	18	1251	1251	NUM
ejpam-4063	46	19	3	3	NUM
ejpam-4063	46	20	.	.	PUNCT
ejpam-4063	47	1	derivation	derivation	NOUN
ejpam-4063	47	2	of	of	ADP
ejpam-4063	47	3	the	the	DET
ejpam-4063	47	4	infinite	infinite	ADJ
ejpam-4063	47	5	sum	sum	NOUN
ejpam-4063	47	6	of	of	ADP
ejpam-4063	47	7	the	the	DET
ejpam-4063	47	8	contour	contour	NOUN
ejpam-4063	47	9	integral	integral	ADJ
ejpam-4063	47	10	3.1	3.1	NUM
ejpam-4063	47	11	.	.	PUNCT
ejpam-4063	48	1	derivation	derivation	NOUN
ejpam-4063	48	2	of	of	ADP
ejpam-4063	48	3	the	the	DET
ejpam-4063	48	4	first	first	ADJ
ejpam-4063	48	5	contour	contour	NOUN
ejpam-4063	48	6	integral	integral	ADJ
ejpam-4063	48	7	in	in	ADP
ejpam-4063	48	8	this	this	DET
ejpam-4063	48	9	section	section	NOUN
ejpam-4063	48	10	we	we	PRON
ejpam-4063	48	11	will	will	AUX
ejpam-4063	48	12	again	again	ADV
ejpam-4063	48	13	use	use	VERB
ejpam-4063	48	14	the	the	DET
ejpam-4063	48	15	generalized	generalize	VERB
ejpam-4063	48	16	cauchy	cauchy	NOUN
ejpam-4063	48	17	’s	’s	PART
ejpam-4063	48	18	integral	integral	ADJ
ejpam-4063	48	19	formula	formula	NOUN
ejpam-4063	48	20	to	to	PART
ejpam-4063	48	21	derive	derive	VERB
ejpam-4063	48	22	equivalent	equivalent	ADJ
ejpam-4063	48	23	contour	contour	NOUN
ejpam-4063	48	24	integrals	integral	NOUN
ejpam-4063	48	25	.	.	PUNCT
ejpam-4063	49	1	first	first	ADV
ejpam-4063	49	2	we	we	PRON
ejpam-4063	49	3	multiply	multiply	VERB
ejpam-4063	49	4	equation	equation	NOUN
ejpam-4063	49	5	(	(	PUNCT
ejpam-4063	49	6	1	1	NUM
ejpam-4063	49	7	)	)	PUNCT
ejpam-4063	49	8	by	by	ADP
ejpam-4063	49	9	eimt	eimt	VERB
ejpam-4063	49	10	/	/	SYM
ejpam-4063	49	11	α/2i	α/2i	NUM
ejpam-4063	49	12	then	then	ADV
ejpam-4063	49	13	replace	replace	VERB
ejpam-4063	49	14	by	by	ADP
ejpam-4063	49	15	x	x	PUNCT
ejpam-4063	49	16	by	by	ADP
ejpam-4063	49	17	p+	p+	NOUN
ejpam-4063	49	18	it	it	PRON
ejpam-4063	49	19	/	/	SYM
ejpam-4063	49	20	α	α	NOUN
ejpam-4063	49	21	for	for	ADP
ejpam-4063	49	22	the	the	DET
ejpam-4063	49	23	first	first	ADJ
ejpam-4063	49	24	equation	equation	NOUN
ejpam-4063	49	25	and	and	CCONJ
ejpam-4063	49	26	then	then	ADV
ejpam-4063	49	27	p−	p−	VERB
ejpam-4063	49	28	it	it	PRON
ejpam-4063	49	29	/	/	SYM
ejpam-4063	49	30	α	α	NOUN
ejpam-4063	49	31	for	for	ADP
ejpam-4063	49	32	the	the	DET
ejpam-4063	49	33	second	second	ADJ
ejpam-4063	49	34	equation	equation	NOUN
ejpam-4063	49	35	to	to	PART
ejpam-4063	49	36	get	get	VERB
ejpam-4063	49	37	ie−	ie−	ADJ
ejpam-4063	49	38	imt	imt	X
ejpam-4063	49	39	a	a	X
ejpam-4063	49	40	(	(	PUNCT
ejpam-4063	49	41	(	(	PUNCT
ejpam-4063	49	42	p−	p−	VERB
ejpam-4063	49	43	it	it	PRON
ejpam-4063	49	44	a	a	PRON
ejpam-4063	49	45	)	)	PUNCT
ejpam-4063	50	1	k	k	NOUN
ejpam-4063	50	2	−	−	PROPN
ejpam-4063	50	3	e	e	X
ejpam-4063	50	4	2imt	2imt	NUM
ejpam-4063	50	5	a	a	PRON
ejpam-4063	50	6	(	(	PUNCT
ejpam-4063	50	7	p+	p+	VERB
ejpam-4063	50	8	it	it	PRON
ejpam-4063	50	9	a	a	DET
ejpam-4063	50	10	)	)	PUNCT
ejpam-4063	50	11	k	k	NOUN
ejpam-4063	50	12	)	)	PUNCT
ejpam-4063	50	13	2γ(k	2γ(k	NUM
ejpam-4063	50	14	+	+	CCONJ
ejpam-4063	50	15	1	1	X
ejpam-4063	50	16	)	)	PUNCT
ejpam-4063	50	17	=	=	SYM
ejpam-4063	51	1	1	1	NUM
ejpam-4063	51	2	2π	2π	NUM
ejpam-4063	51	3	∫	∫	PROPN
ejpam-4063	51	4	c	c	PROPN
ejpam-4063	51	5	w−k−1ewp	w−k−1ewp	VERB
ejpam-4063	51	6	sin	sin	NOUN
ejpam-4063	51	7	(	(	PUNCT
ejpam-4063	51	8	t(m+	t(m+	NOUN
ejpam-4063	51	9	w	w	NOUN
ejpam-4063	51	10	)	)	PUNCT
ejpam-4063	51	11	a	a	DET
ejpam-4063	51	12	)	)	PUNCT
ejpam-4063	51	13	dw	dw	NOUN
ejpam-4063	51	14	(	(	PUNCT
ejpam-4063	51	15	4	4	NUM
ejpam-4063	51	16	)	)	PUNCT
ejpam-4063	51	17	then	then	ADV
ejpam-4063	51	18	we	we	PRON
ejpam-4063	51	19	replace	replace	VERB
ejpam-4063	51	20	p	p	NOUN
ejpam-4063	51	21	with	with	ADP
ejpam-4063	51	22	πi(2p+	πi(2p+	PRON
ejpam-4063	51	23	1)/a+	1)/a+	NUM
ejpam-4063	51	24	log(α	log(α	NUM
ejpam-4063	51	25	)	)	PUNCT
ejpam-4063	51	26	and	and	CCONJ
ejpam-4063	51	27	multiply	multiply	VERB
ejpam-4063	51	28	both	both	DET
ejpam-4063	51	29	sides	side	NOUN
ejpam-4063	51	30	by	by	ADP
ejpam-4063	51	31	−2π	−2π	PROPN
ejpam-4063	51	32	a1	a1	NOUN
ejpam-4063	51	33	to	to	PART
ejpam-4063	51	34	get	get	VERB
ejpam-4063	51	35	ie−	ie−	ADJ
ejpam-4063	51	36	imt	imt	X
ejpam-4063	51	37	a	a	PRON
ejpam-4063	51	38	(	(	PUNCT
ejpam-4063	51	39	(	(	PUNCT
ejpam-4063	51	40	iπ(2p+1	iπ(2p+1	INTJ
ejpam-4063	51	41	)	)	PUNCT
ejpam-4063	51	42	a	a	DET
ejpam-4063	51	43	−	−	X
ejpam-4063	51	44	it	it	PRON
ejpam-4063	51	45	a	a	DET
ejpam-4063	51	46	+	+	X
ejpam-4063	51	47	log(α	log(α	NOUN
ejpam-4063	51	48	)	)	PUNCT
ejpam-4063	51	49	)	)	PUNCT
ejpam-4063	52	1	k	k	X
ejpam-4063	53	1	−	−	PUNCT
ejpam-4063	53	2	e	e	X
ejpam-4063	53	3	2imt	2imt	NUM
ejpam-4063	53	4	a	a	DET
ejpam-4063	53	5	(	(	PUNCT
ejpam-4063	53	6	iπ(2p+1	iπ(2p+1	NOUN
ejpam-4063	53	7	)	)	PUNCT
ejpam-4063	53	8	a	a	PRON
ejpam-4063	54	1	+	+	X
ejpam-4063	54	2	it	it	PRON
ejpam-4063	54	3	a	a	DET
ejpam-4063	54	4	+	+	CCONJ
ejpam-4063	54	5	log(α	log(α	PROPN
ejpam-4063	54	6	)	)	PUNCT
ejpam-4063	54	7	)	)	PUNCT
ejpam-4063	55	1	k	k	X
ejpam-4063	55	2	)	)	PUNCT
ejpam-4063	55	3	2γ(k	2γ(k	NUM
ejpam-4063	56	1	+	+	CCONJ
ejpam-4063	56	2	1	1	X
ejpam-4063	56	3	)	)	PUNCT
ejpam-4063	56	4	=	=	SYM
ejpam-4063	56	5	1	1	NUM
ejpam-4063	56	6	2πi	2πi	NOUN
ejpam-4063	56	7	∫	∫	PROPN
ejpam-4063	56	8	c	c	X
ejpam-4063	56	9	w−k−1	w−k−1	PRON
ejpam-4063	56	10	sin	sin	NOUN
ejpam-4063	56	11	(	(	PUNCT
ejpam-4063	56	12	t(m+	t(m+	NOUN
ejpam-4063	56	13	w	w	NOUN
ejpam-4063	56	14	)	)	PUNCT
ejpam-4063	56	15	a	a	PRON
ejpam-4063	56	16	)	)	PUNCT
ejpam-4063	56	17	e	e	X
ejpam-4063	56	18	w	w	PROPN
ejpam-4063	56	19	(	(	PUNCT
ejpam-4063	56	20	log(α)+	log(α)+	PROPN
ejpam-4063	56	21	iπ(2p+1	iπ(2p+1	NOUN
ejpam-4063	56	22	)	)	PUNCT
ejpam-4063	56	23	a	a	DET
ejpam-4063	56	24	)	)	PUNCT
ejpam-4063	56	25	dw	dw	NOUN
ejpam-4063	56	26	(	(	PUNCT
ejpam-4063	56	27	5	5	NUM
ejpam-4063	56	28	)	)	PUNCT
ejpam-4063	56	29	then	then	ADV
ejpam-4063	56	30	we	we	PRON
ejpam-4063	56	31	multiply	multiply	VERB
ejpam-4063	56	32	both	both	DET
ejpam-4063	56	33	sides	side	NOUN
ejpam-4063	56	34	by	by	ADP
ejpam-4063	56	35	−2iπ	−2iπ	PROPN
ejpam-4063	56	36	a2	a2	PROPN
ejpam-4063	56	37	e	e	NOUN
ejpam-4063	56	38	iπm(2y+1	iπm(2y+1	NOUN
ejpam-4063	56	39	)	)	PUNCT
ejpam-4063	56	40	a	a	PRON
ejpam-4063	56	41	and	and	CCONJ
ejpam-4063	56	42	take	take	VERB
ejpam-4063	56	43	the	the	DET
ejpam-4063	56	44	sum	sum	NOUN
ejpam-4063	56	45	over	over	ADP
ejpam-4063	56	46	p	p	X
ejpam-4063	56	47	∈	∈	PROPN
ejpam-4063	57	1	[	[	X
ejpam-4063	57	2	0,∞	0,∞	NOUN
ejpam-4063	57	3	)	)	PUNCT
ejpam-4063	58	1	and	and	CCONJ
ejpam-4063	58	2	simplify	simplify	VERB
ejpam-4063	58	3	the	the	DET
ejpam-4063	58	4	left	left	ADJ
ejpam-4063	58	5	-	-	PUNCT
ejpam-4063	58	6	hand	hand	NOUN
ejpam-4063	58	7	side	side	NOUN
ejpam-4063	58	8	in	in	ADP
ejpam-4063	58	9	terms	term	NOUN
ejpam-4063	58	10	of	of	ADP
ejpam-4063	58	11	the	the	DET
ejpam-4063	58	12	lerch	lerch	PROPN
ejpam-4063	58	13	function	function	NOUN
ejpam-4063	58	14	to	to	PART
ejpam-4063	58	15	get	get	VERB
ejpam-4063	58	16	2kπk+1	2kπk+1	NUM
ejpam-4063	58	17	(	(	PUNCT
ejpam-4063	58	18	i	i	PRON
ejpam-4063	58	19	a	a	X
ejpam-4063	58	20	)	)	PUNCT
ejpam-4063	58	21	k	k	PROPN
ejpam-4063	58	22	e	e	PROPN
ejpam-4063	58	23	im(π−t	im(π−t	PROPN
ejpam-4063	58	24	)	)	PUNCT
ejpam-4063	59	1	a	a	DET
ejpam-4063	59	2	(	(	PUNCT
ejpam-4063	59	3	φ	φ	X
ejpam-4063	59	4	(	(	PUNCT
ejpam-4063	59	5	e	e	X
ejpam-4063	59	6	2imπ	2imπ	NUM
ejpam-4063	59	7	a	a	DET
ejpam-4063	59	8	,	,	PUNCT
ejpam-4063	59	9	−k	−k	PROPN
ejpam-4063	59	10	,	,	PUNCT
ejpam-4063	59	11	−t−ia	−t−ia	X
ejpam-4063	59	12	log(α)+π	log(α)+π	X
ejpam-4063	59	13	2π	2π	PROPN
ejpam-4063	59	14	)	)	PUNCT
ejpam-4063	60	1	−	−	PUNCT
ejpam-4063	61	1	e	e	X
ejpam-4063	61	2	2imt	2imt	NUM
ejpam-4063	61	3	a	a	DET
ejpam-4063	61	4	φ	φ	NOUN
ejpam-4063	61	5	(	(	PUNCT
ejpam-4063	61	6	e	e	X
ejpam-4063	61	7	2imπ	2imπ	NUM
ejpam-4063	61	8	a	a	DET
ejpam-4063	61	9	,	,	PUNCT
ejpam-4063	61	10	−k	−k	PROPN
ejpam-4063	61	11	,	,	PUNCT
ejpam-4063	61	12	t−ia	t−ia	X
ejpam-4063	61	13	log(α)+π	log(α)+π	PRON
ejpam-4063	61	14	2π	2π	NOUN
ejpam-4063	61	15	)	)	PUNCT
ejpam-4063	61	16	)	)	PUNCT
ejpam-4063	62	1	a2γ(k	a2γ(k	PROPN
ejpam-4063	62	2	+	+	CCONJ
ejpam-4063	62	3	1	1	X
ejpam-4063	62	4	)	)	PUNCT
ejpam-4063	62	5	=	=	SYM
ejpam-4063	62	6	1	1	NUM
ejpam-4063	62	7	2πi	2πi	NOUN
ejpam-4063	62	8	∞∑	∞∑	ADJ
ejpam-4063	62	9	p=0	p=0	PROPN
ejpam-4063	62	10	∫	∫	PROPN
ejpam-4063	63	1	c	c	PROPN
ejpam-4063	63	2	w−k−1	w−k−1	PROPN
ejpam-4063	63	3	sin	sin	NOUN
ejpam-4063	63	4	(	(	PUNCT
ejpam-4063	63	5	t(m+	t(m+	NOUN
ejpam-4063	63	6	w	w	NOUN
ejpam-4063	63	7	)	)	PUNCT
ejpam-4063	63	8	a	a	PRON
ejpam-4063	63	9	)	)	PUNCT
ejpam-4063	63	10	e	e	X
ejpam-4063	63	11	w	w	PROPN
ejpam-4063	63	12	(	(	PUNCT
ejpam-4063	63	13	log(α)+	log(α)+	PROPN
ejpam-4063	63	14	iπ(2p+1	iπ(2p+1	NOUN
ejpam-4063	63	15	)	)	PUNCT
ejpam-4063	63	16	a	a	PRON
ejpam-4063	63	17	)	)	PUNCT
ejpam-4063	63	18	dw	dw	NOUN
ejpam-4063	63	19	=	=	SYM
ejpam-4063	64	1	1	1	NUM
ejpam-4063	64	2	2πi	2πi	NOUN
ejpam-4063	64	3	∫	∫	PROPN
ejpam-4063	64	4	c	c	PROPN
ejpam-4063	65	1	∞∑	∞∑	PROPN
ejpam-4063	65	2	p=0	p=0	PROPN
ejpam-4063	65	3	w−k−1	w−k−1	PRON
ejpam-4063	65	4	sin	sin	NOUN
ejpam-4063	65	5	(	(	PUNCT
ejpam-4063	65	6	t(m+	t(m+	NOUN
ejpam-4063	65	7	w	w	NOUN
ejpam-4063	65	8	)	)	PUNCT
ejpam-4063	65	9	a	a	PRON
ejpam-4063	65	10	)	)	PUNCT
ejpam-4063	65	11	e	e	X
ejpam-4063	65	12	w	w	PROPN
ejpam-4063	65	13	(	(	PUNCT
ejpam-4063	65	14	log(α)+	log(α)+	PROPN
ejpam-4063	65	15	iπ(2p+1	iπ(2p+1	NOUN
ejpam-4063	65	16	)	)	PUNCT
ejpam-4063	65	17	a	a	PRON
ejpam-4063	65	18	)	)	PUNCT
ejpam-4063	65	19	dw	dw	NOUN
ejpam-4063	65	20	=	=	SYM
ejpam-4063	65	21	1	1	NUM
ejpam-4063	65	22	2π	2π	NUM
ejpam-4063	65	23	∫	∫	PROPN
ejpam-4063	66	1	c	c	PROPN
ejpam-4063	66	2	πw−k−1αw	πw−k−1αw	PROPN
ejpam-4063	66	3	csc	csc	PROPN
ejpam-4063	66	4	(	(	PUNCT
ejpam-4063	66	5	π(m+w	π(m+w	PROPN
ejpam-4063	66	6	)	)	PUNCT
ejpam-4063	66	7	a	a	DET
ejpam-4063	66	8	)	)	PUNCT
ejpam-4063	66	9	sin	sin	NOUN
ejpam-4063	66	10	(	(	PUNCT
ejpam-4063	66	11	t(m+w	t(m+w	NOUN
ejpam-4063	66	12	)	)	PUNCT
ejpam-4063	66	13	a	a	DET
ejpam-4063	66	14	)	)	PUNCT
ejpam-4063	66	15	a2	a2	PROPN
ejpam-4063	66	16	dw	dw	PROPN
ejpam-4063	66	17	(	(	PUNCT
ejpam-4063	66	18	6	6	NUM
ejpam-4063	66	19	)	)	PUNCT
ejpam-4063	66	20	from	from	ADP
ejpam-4063	66	21	equation	equation	NOUN
ejpam-4063	66	22	(	(	PUNCT
ejpam-4063	66	23	1.232.3	1.232.3	NUM
ejpam-4063	66	24	)	)	PUNCT
ejpam-4063	66	25	in	in	ADP
ejpam-4063	66	26	[	[	X
ejpam-4063	66	27	3	3	X
ejpam-4063	66	28	]	]	PUNCT
ejpam-4063	66	29	where	where	SCONJ
ejpam-4063	66	30	csch(ix	csch(ix	NOUN
ejpam-4063	66	31	)	)	PUNCT
ejpam-4063	66	32	=	=	SYM
ejpam-4063	66	33	−i	−i	ADJ
ejpam-4063	66	34	csc(x	csc(x	NOUN
ejpam-4063	66	35	)	)	PUNCT
ejpam-4063	66	36	from	from	ADP
ejpam-4063	66	37	equation	equation	NOUN
ejpam-4063	66	38	(	(	PUNCT
ejpam-4063	66	39	4.5.10	4.5.10	NUM
ejpam-4063	66	40	)	)	PUNCT
ejpam-4063	66	41	in	in	ADP
ejpam-4063	66	42	[	[	X
ejpam-4063	66	43	1	1	NUM
ejpam-4063	66	44	]	]	PUNCT
ejpam-4063	66	45	and	and	CCONJ
ejpam-4063	66	46	im(w	im(w	NOUN
ejpam-4063	66	47	)	)	PUNCT
ejpam-4063	66	48	>	>	X
ejpam-4063	66	49	0	0	PUNCT
ejpam-4063	67	1	for	for	SCONJ
ejpam-4063	67	2	the	the	DET
ejpam-4063	67	3	sum	sum	NOUN
ejpam-4063	67	4	to	to	PART
ejpam-4063	67	5	converge	converge	VERB
ejpam-4063	67	6	.	.	PUNCT
ejpam-4063	68	1	the	the	DET
ejpam-4063	68	2	log	log	NOUN
ejpam-4063	68	3	terms	term	NOUN
ejpam-4063	68	4	can	can	AUX
ejpam-4063	68	5	not	not	PART
ejpam-4063	68	6	be	be	AUX
ejpam-4063	68	7	combined	combine	VERB
ejpam-4063	68	8	in	in	ADP
ejpam-4063	68	9	general	general	ADJ
ejpam-4063	68	10	.	.	PUNCT
ejpam-4063	69	1	3.2	3.2	NUM
ejpam-4063	69	2	.	.	PUNCT
ejpam-4063	70	1	derivation	derivation	NOUN
ejpam-4063	70	2	of	of	ADP
ejpam-4063	70	3	the	the	DET
ejpam-4063	70	4	second	second	ADJ
ejpam-4063	70	5	contour	contour	NOUN
ejpam-4063	70	6	integral	integral	ADJ
ejpam-4063	70	7	next	next	ADV
ejpam-4063	70	8	we	we	PRON
ejpam-4063	70	9	will	will	AUX
ejpam-4063	70	10	derive	derive	VERB
ejpam-4063	70	11	the	the	DET
ejpam-4063	70	12	second	second	ADJ
ejpam-4063	70	13	equation	equation	NOUN
ejpam-4063	70	14	by	by	ADP
ejpam-4063	70	15	using	use	VERB
ejpam-4063	70	16	equation	equation	NOUN
ejpam-4063	70	17	(	(	PUNCT
ejpam-4063	70	18	6	6	NUM
ejpam-4063	70	19	)	)	PUNCT
ejpam-4063	70	20	,	,	PUNCT
ejpam-4063	70	21	multiplying	multiply	VERB
ejpam-4063	70	22	by	by	ADP
ejpam-4063	70	23	m	m	PROPN
ejpam-4063	70	24	csc(t	csc(t	PROPN
ejpam-4063	70	25	)	)	PUNCT
ejpam-4063	70	26	and	and	CCONJ
ejpam-4063	70	27	taking	take	VERB
ejpam-4063	70	28	the	the	DET
ejpam-4063	70	29	infinite	infinite	ADJ
ejpam-4063	70	30	sum	sum	NOUN
ejpam-4063	70	31	over	over	ADP
ejpam-4063	70	32	p	p	X
ejpam-4063	70	33	∈	∈	PROPN
ejpam-4063	71	1	[	[	X
ejpam-4063	71	2	0,∞	0,∞	NOUN
ejpam-4063	71	3	)	)	PUNCT
ejpam-4063	71	4	to	to	PART
ejpam-4063	71	5	get	get	VERB
ejpam-4063	71	6	r.	r.	PROPN
ejpam-4063	71	7	reynolds	reynolds	PROPN
ejpam-4063	71	8	,	,	PUNCT
ejpam-4063	71	9	a.	a.	PROPN
ejpam-4063	71	10	stauffer	stauffer	PROPN
ejpam-4063	71	11	/	/	SYM
ejpam-4063	71	12	eur	eur	PROPN
ejpam-4063	71	13	.	.	PUNCT
ejpam-4063	72	1	j.	j.	PROPN
ejpam-4063	72	2	pure	pure	PROPN
ejpam-4063	72	3	appl	appl	PROPN
ejpam-4063	72	4	.	.	PROPN
ejpam-4063	72	5	math	math	PROPN
ejpam-4063	72	6	,	,	PUNCT
ejpam-4063	72	7	14	14	NUM
ejpam-4063	72	8	(	(	PUNCT
ejpam-4063	72	9	4	4	NUM
ejpam-4063	72	10	)	)	PUNCT
ejpam-4063	72	11	(	(	PUNCT
ejpam-4063	72	12	2021	2021	NUM
ejpam-4063	72	13	)	)	PUNCT
ejpam-4063	72	14	,	,	PUNCT
ejpam-4063	72	15	1249	1249	NUM
ejpam-4063	72	16	-	-	SYM
ejpam-4063	72	17	1265	1265	NUM
ejpam-4063	72	18	1252	1252	NUM
ejpam-4063	72	19	2kπk+1	2kπk+1	NUM
ejpam-4063	72	20	m	m	NOUN
ejpam-4063	72	21	(	(	PUNCT
ejpam-4063	72	22	i	i	PRON
ejpam-4063	72	23	a	a	X
ejpam-4063	72	24	)	)	PUNCT
ejpam-4063	72	25	k	k	PROPN
ejpam-4063	72	26	csc(t)e	csc(t)e	PROPN
ejpam-4063	72	27	im(π−t	im(π−t	PROPN
ejpam-4063	72	28	)	)	PUNCT
ejpam-4063	72	29	a	a	PRON
ejpam-4063	72	30	(	(	PUNCT
ejpam-4063	72	31	φ	φ	X
ejpam-4063	72	32	(	(	PUNCT
ejpam-4063	72	33	e	e	X
ejpam-4063	72	34	2imπ	2imπ	NUM
ejpam-4063	72	35	a	a	DET
ejpam-4063	72	36	,	,	PUNCT
ejpam-4063	72	37	−k	−k	PROPN
ejpam-4063	72	38	,	,	PUNCT
ejpam-4063	72	39	−t−ia	−t−ia	X
ejpam-4063	72	40	log(α)+π	log(α)+π	X
ejpam-4063	72	41	2π	2π	PROPN
ejpam-4063	72	42	)	)	PUNCT
ejpam-4063	73	1	−	−	PUNCT
ejpam-4063	74	1	e	e	X
ejpam-4063	74	2	2imt	2imt	NUM
ejpam-4063	74	3	a	a	DET
ejpam-4063	74	4	φ	φ	NOUN
ejpam-4063	74	5	(	(	PUNCT
ejpam-4063	74	6	e	e	X
ejpam-4063	74	7	2imπ	2imπ	NUM
ejpam-4063	74	8	a	a	DET
ejpam-4063	74	9	,	,	PUNCT
ejpam-4063	74	10	−k	−k	PROPN
ejpam-4063	74	11	,	,	PUNCT
ejpam-4063	74	12	t−ia	t−ia	X
ejpam-4063	74	13	log(α)+π	log(α)+π	PRON
ejpam-4063	74	14	2π	2π	NOUN
ejpam-4063	74	15	)	)	PUNCT
ejpam-4063	74	16	)	)	PUNCT
ejpam-4063	75	1	a2γ(k	a2γ(k	PROPN
ejpam-4063	75	2	+	+	CCONJ
ejpam-4063	75	3	1	1	X
ejpam-4063	75	4	)	)	PUNCT
ejpam-4063	75	5	=	=	SYM
ejpam-4063	75	6	1	1	NUM
ejpam-4063	75	7	2πi	2πi	ADJ
ejpam-4063	75	8	∫	∫	PROPN
ejpam-4063	75	9	c	c	PROPN
ejpam-4063	75	10	πmw−k−1	πmw−k−1	PROPN
ejpam-4063	75	11	csc(t)αw	csc(t)αw	PROPN
ejpam-4063	75	12	csc	csc	PROPN
ejpam-4063	75	13	(	(	PUNCT
ejpam-4063	75	14	π(m+w	π(m+w	PROPN
ejpam-4063	75	15	)	)	PUNCT
ejpam-4063	75	16	a	a	PRON
ejpam-4063	75	17	)	)	PUNCT
ejpam-4063	75	18	sin	sin	NOUN
ejpam-4063	75	19	(	(	PUNCT
ejpam-4063	75	20	t(m+w	t(m+w	NOUN
ejpam-4063	75	21	)	)	PUNCT
ejpam-4063	75	22	a	a	DET
ejpam-4063	75	23	)	)	PUNCT
ejpam-4063	75	24	a2	a2	PROPN
ejpam-4063	75	25	dw	dw	PROPN
ejpam-4063	75	26	(	(	PUNCT
ejpam-4063	75	27	7	7	NUM
ejpam-4063	75	28	)	)	PUNCT
ejpam-4063	75	29	then	then	ADV
ejpam-4063	75	30	we	we	PRON
ejpam-4063	75	31	replace	replace	VERB
ejpam-4063	75	32	k	k	PROPN
ejpam-4063	75	33	with	with	ADP
ejpam-4063	75	34	k	k	PROPN
ejpam-4063	75	35	−	−	PROPN
ejpam-4063	75	36	1	1	NUM
ejpam-4063	75	37	to	to	PART
ejpam-4063	75	38	get	get	VERB
ejpam-4063	75	39	2k−1πk	2k−1πk	NUM
ejpam-4063	75	40	(	(	PUNCT
ejpam-4063	75	41	i	i	PRON
ejpam-4063	75	42	a	a	X
ejpam-4063	75	43	)	)	PUNCT
ejpam-4063	75	44	k−1	k−1	PROPN
ejpam-4063	75	45	csc(t)e	csc(t)e	NOUN
ejpam-4063	75	46	im(π−t	im(π−t	PROPN
ejpam-4063	75	47	)	)	PUNCT
ejpam-4063	76	1	a	a	PRON
ejpam-4063	76	2	(	(	PUNCT
ejpam-4063	76	3	φ	φ	X
ejpam-4063	76	4	(	(	PUNCT
ejpam-4063	76	5	e	e	X
ejpam-4063	76	6	2imπ	2imπ	NUM
ejpam-4063	76	7	a	a	DET
ejpam-4063	76	8	,	,	PUNCT
ejpam-4063	76	9	1−	1−	NUM
ejpam-4063	76	10	k	k	X
ejpam-4063	76	11	,	,	PUNCT
ejpam-4063	76	12	−t−ia	−t−ia	X
ejpam-4063	76	13	log(α)+π	log(α)+π	X
ejpam-4063	76	14	2π	2π	PROPN
ejpam-4063	76	15	)	)	PUNCT
ejpam-4063	76	16	−	−	PUNCT
ejpam-4063	77	1	e	e	X
ejpam-4063	77	2	2imt	2imt	NUM
ejpam-4063	77	3	a	a	DET
ejpam-4063	77	4	φ	φ	NOUN
ejpam-4063	77	5	(	(	PUNCT
ejpam-4063	77	6	e	e	X
ejpam-4063	77	7	2imπ	2imπ	NUM
ejpam-4063	77	8	a	a	DET
ejpam-4063	77	9	,	,	PUNCT
ejpam-4063	77	10	1−	1−	NUM
ejpam-4063	77	11	k	k	X
ejpam-4063	77	12	,	,	PUNCT
ejpam-4063	77	13	t−ia	t−ia	VERB
ejpam-4063	77	14	log(α)+π	log(α)+π	PRON
ejpam-4063	77	15	2π	2π	PROPN
ejpam-4063	77	16	)	)	PUNCT
ejpam-4063	77	17	)	)	PUNCT
ejpam-4063	78	1	a2(k	a2(k	ADP
ejpam-4063	78	2	−	−	NOUN
ejpam-4063	78	3	1	1	NUM
ejpam-4063	78	4	)	)	PUNCT
ejpam-4063	78	5	!	!	PUNCT
ejpam-4063	79	1	=	=	SYM
ejpam-4063	79	2	1	1	NUM
ejpam-4063	79	3	2πi	2πi	NOUN
ejpam-4063	79	4	∫	∫	PROPN
ejpam-4063	79	5	c	c	PROPN
ejpam-4063	79	6	πw−k	πw−k	PROPN
ejpam-4063	79	7	csc(t)αw	csc(t)αw	PROPN
ejpam-4063	79	8	csc	csc	PROPN
ejpam-4063	79	9	(	(	PUNCT
ejpam-4063	79	10	π(m+w	π(m+w	PROPN
ejpam-4063	79	11	)	)	PUNCT
ejpam-4063	79	12	a	a	PRON
ejpam-4063	79	13	)	)	PUNCT
ejpam-4063	79	14	sin	sin	NOUN
ejpam-4063	79	15	(	(	PUNCT
ejpam-4063	79	16	t(m+w	t(m+w	NOUN
ejpam-4063	79	17	)	)	PUNCT
ejpam-4063	79	18	a	a	DET
ejpam-4063	79	19	)	)	PUNCT
ejpam-4063	79	20	a2	a2	PROPN
ejpam-4063	79	21	dw	dw	PROPN
ejpam-4063	79	22	(	(	PUNCT
ejpam-4063	79	23	8)	8)	NUM
ejpam-4063	79	24	from	from	ADP
ejpam-4063	79	25	equation	equation	NOUN
ejpam-4063	79	26	(	(	PUNCT
ejpam-4063	79	27	1.232.3	1.232.3	NUM
ejpam-4063	79	28	)	)	PUNCT
ejpam-4063	79	29	in	in	ADP
ejpam-4063	79	30	[	[	X
ejpam-4063	79	31	3	3	X
ejpam-4063	79	32	]	]	PUNCT
ejpam-4063	79	33	where	where	SCONJ
ejpam-4063	79	34	csch(ix	csch(ix	NOUN
ejpam-4063	79	35	)	)	PUNCT
ejpam-4063	79	36	=	=	SYM
ejpam-4063	79	37	−i	−i	ADJ
ejpam-4063	79	38	csc(x	csc(x	NOUN
ejpam-4063	79	39	)	)	PUNCT
ejpam-4063	79	40	from	from	ADP
ejpam-4063	79	41	equation	equation	NOUN
ejpam-4063	79	42	(	(	PUNCT
ejpam-4063	79	43	4.5.10	4.5.10	NUM
ejpam-4063	79	44	)	)	PUNCT
ejpam-4063	79	45	in	in	ADP
ejpam-4063	79	46	[	[	X
ejpam-4063	79	47	1	1	NUM
ejpam-4063	79	48	]	]	PUNCT
ejpam-4063	79	49	and	and	CCONJ
ejpam-4063	79	50	im(w	im(w	NOUN
ejpam-4063	79	51	)	)	PUNCT
ejpam-4063	79	52	>	>	X
ejpam-4063	79	53	0	0	PUNCT
ejpam-4063	80	1	for	for	SCONJ
ejpam-4063	80	2	the	the	DET
ejpam-4063	80	3	sum	sum	NOUN
ejpam-4063	80	4	to	to	PART
ejpam-4063	80	5	converge	converge	VERB
ejpam-4063	80	6	.	.	PUNCT
ejpam-4063	81	1	4	4	X
ejpam-4063	81	2	.	.	X
ejpam-4063	81	3	the	the	DET
ejpam-4063	81	4	lerch	lerch	PROPN
ejpam-4063	81	5	function	function	VERB
ejpam-4063	81	6	the	the	DET
ejpam-4063	81	7	lerch	lerch	PROPN
ejpam-4063	81	8	function	function	PROPN
ejpam-4063	81	9	see	see	VERB
ejpam-4063	81	10	section	section	NOUN
ejpam-4063	81	11	(	(	PUNCT
ejpam-4063	81	12	24.14	24.14	NUM
ejpam-4063	81	13	)	)	PUNCT
ejpam-4063	81	14	in	in	ADP
ejpam-4063	81	15	[	[	X
ejpam-4063	81	16	6	6	NUM
ejpam-4063	81	17	]	]	PUNCT
ejpam-4063	81	18	has	have	VERB
ejpam-4063	81	19	a	a	DET
ejpam-4063	81	20	series	series	NOUN
ejpam-4063	81	21	representation	representation	NOUN
ejpam-4063	81	22	given	give	VERB
ejpam-4063	81	23	by	by	ADP
ejpam-4063	81	24	φ(z	φ(z	PROPN
ejpam-4063	81	25	,	,	PUNCT
ejpam-4063	81	26	s	s	NOUN
ejpam-4063	81	27	,	,	PUNCT
ejpam-4063	81	28	v	v	NOUN
ejpam-4063	81	29	)	)	PUNCT
ejpam-4063	81	30	=	=	PUNCT
ejpam-4063	82	1	∞∑	∞∑	NUM
ejpam-4063	82	2	n=0	n=0	NUM
ejpam-4063	82	3	(	(	PUNCT
ejpam-4063	82	4	v	v	NOUN
ejpam-4063	82	5	+	+	PRON
ejpam-4063	82	6	n)−szn	n)−szn	NUM
ejpam-4063	82	7	(	(	PUNCT
ejpam-4063	82	8	9	9	NUM
ejpam-4063	82	9	)	)	PUNCT
ejpam-4063	82	10	where	where	SCONJ
ejpam-4063	82	11	|z|	|z|	VERB
ejpam-4063	82	12	<	<	X
ejpam-4063	82	13	1	1	NUM
ejpam-4063	82	14	,	,	PUNCT
ejpam-4063	82	15	v	v	ADP
ejpam-4063	82	16	̸=	̸=	PROPN
ejpam-4063	82	17	0,−1	0,−1	PROPN
ejpam-4063	82	18	,	,	PUNCT
ejpam-4063	82	19	..	..	PUNCT
ejpam-4063	82	20	and	and	CCONJ
ejpam-4063	82	21	is	be	AUX
ejpam-4063	82	22	continued	continue	VERB
ejpam-4063	82	23	analytically	analytically	ADV
ejpam-4063	82	24	by	by	ADP
ejpam-4063	82	25	its	its	PRON
ejpam-4063	82	26	integral	integral	ADJ
ejpam-4063	82	27	representation	representation	NOUN
ejpam-4063	82	28	given	give	VERB
ejpam-4063	82	29	by	by	ADP
ejpam-4063	82	30	φ(z	φ(z	PROPN
ejpam-4063	82	31	,	,	PUNCT
ejpam-4063	82	32	s	s	NOUN
ejpam-4063	82	33	,	,	PUNCT
ejpam-4063	82	34	v	v	NOUN
ejpam-4063	82	35	)	)	PUNCT
ejpam-4063	82	36	=	=	SYM
ejpam-4063	82	37	1	1	NUM
ejpam-4063	82	38	γ(s	γ(	NOUN
ejpam-4063	82	39	)	)	PUNCT
ejpam-4063	82	40	∫	∫	PROPN
ejpam-4063	83	1	∞	∞	PROPN
ejpam-4063	83	2	0	0	NUM
ejpam-4063	84	1	ts−1e−vt	ts−1e−vt	PRON
ejpam-4063	85	1	1−	1−	NUM
ejpam-4063	85	2	ze−t	ze−t	NOUN
ejpam-4063	85	3	dt	dt	NOUN
ejpam-4063	86	1	=	=	SYM
ejpam-4063	86	2	1	1	NUM
ejpam-4063	86	3	γ(s	γ(s	PROPN
ejpam-4063	86	4	)	)	PUNCT
ejpam-4063	86	5	∫	∫	PROPN
ejpam-4063	87	1	∞	∞	NUM
ejpam-4063	87	2	0	0	NUM
ejpam-4063	88	1	ts−1e−(v−1)t	ts−1e−(v−1)t	PROPN
ejpam-4063	88	2	et	et	NOUN
ejpam-4063	88	3	−	−	NOUN
ejpam-4063	88	4	z	z	NOUN
ejpam-4063	88	5	dt	dt	X
ejpam-4063	88	6	(	(	PUNCT
ejpam-4063	88	7	10	10	NUM
ejpam-4063	88	8	)	)	PUNCT
ejpam-4063	88	9	where	where	SCONJ
ejpam-4063	88	10	re(v	re(v	NOUN
ejpam-4063	88	11	)	)	PUNCT
ejpam-4063	88	12	>	>	X
ejpam-4063	88	13	0	0	NUM
ejpam-4063	88	14	,	,	PUNCT
ejpam-4063	88	15	or	or	CCONJ
ejpam-4063	88	16	|z|≤	|z|≤	SYM
ejpam-4063	88	17	1	1	NUM
ejpam-4063	88	18	,	,	PUNCT
ejpam-4063	88	19	z	z	NOUN
ejpam-4063	88	20	̸=	̸=	PROPN
ejpam-4063	88	21	1	1	NUM
ejpam-4063	88	22	,	,	PUNCT
ejpam-4063	88	23	re(s	re(s	ADJ
ejpam-4063	88	24	)	)	PUNCT
ejpam-4063	88	25	>	>	X
ejpam-4063	88	26	0	0	NUM
ejpam-4063	88	27	,	,	PUNCT
ejpam-4063	88	28	or	or	CCONJ
ejpam-4063	88	29	z	z	NOUN
ejpam-4063	88	30	=	=	SYM
ejpam-4063	88	31	1	1	NUM
ejpam-4063	88	32	,	,	PUNCT
ejpam-4063	88	33	re(s	re(s	ADJ
ejpam-4063	88	34	)	)	PUNCT
ejpam-4063	88	35	>	>	X
ejpam-4063	89	1	1	1	NUM
ejpam-4063	89	2	.	.	X
ejpam-4063	89	3	5	5	NUM
ejpam-4063	89	4	.	.	X
ejpam-4063	89	5	definite	definite	ADJ
ejpam-4063	89	6	integral	integral	ADJ
ejpam-4063	89	7	in	in	ADP
ejpam-4063	89	8	terms	term	NOUN
ejpam-4063	89	9	of	of	ADP
ejpam-4063	89	10	the	the	DET
ejpam-4063	89	11	lerch	lerch	PROPN
ejpam-4063	89	12	function	function	PROPN
ejpam-4063	89	13	since	since	SCONJ
ejpam-4063	89	14	the	the	DET
ejpam-4063	89	15	right	right	ADJ
ejpam-4063	89	16	-	-	PUNCT
ejpam-4063	89	17	hand	hand	NOUN
ejpam-4063	89	18	sides	side	NOUN
ejpam-4063	89	19	of	of	ADP
ejpam-4063	89	20	equation	equation	NOUN
ejpam-4063	89	21	(	(	PUNCT
ejpam-4063	89	22	3	3	NUM
ejpam-4063	89	23	)	)	PUNCT
ejpam-4063	89	24	,	,	PUNCT
ejpam-4063	89	25	(	(	PUNCT
ejpam-4063	89	26	6	6	NUM
ejpam-4063	89	27	)	)	PUNCT
ejpam-4063	89	28	and	and	CCONJ
ejpam-4063	89	29	(	(	PUNCT
ejpam-4063	89	30	8)	8)	NUM
ejpam-4063	89	31	are	be	AUX
ejpam-4063	89	32	equivalent	equivalent	ADJ
ejpam-4063	89	33	we	we	PRON
ejpam-4063	89	34	can	can	AUX
ejpam-4063	89	35	equate	equate	VERB
ejpam-4063	89	36	the	the	DET
ejpam-4063	89	37	left	left	ADJ
ejpam-4063	89	38	-	-	PUNCT
ejpam-4063	89	39	hand	hand	NOUN
ejpam-4063	89	40	sides	side	NOUN
ejpam-4063	89	41	simplify	simplify	VERB
ejpam-4063	89	42	the	the	DET
ejpam-4063	89	43	factorial	factorial	NOUN
ejpam-4063	89	44	to	to	PART
ejpam-4063	89	45	get	get	VERB
ejpam-4063	89	46	r.	r.	PROPN
ejpam-4063	89	47	reynolds	reynolds	PROPN
ejpam-4063	89	48	,	,	PUNCT
ejpam-4063	89	49	a.	a.	PROPN
ejpam-4063	89	50	stauffer	stauffer	PROPN
ejpam-4063	89	51	/	/	SYM
ejpam-4063	89	52	eur	eur	PROPN
ejpam-4063	89	53	.	.	PUNCT
ejpam-4063	90	1	j.	j.	PROPN
ejpam-4063	90	2	pure	pure	PROPN
ejpam-4063	90	3	appl	appl	PROPN
ejpam-4063	90	4	.	.	PROPN
ejpam-4063	90	5	math	math	PROPN
ejpam-4063	90	6	,	,	PUNCT
ejpam-4063	90	7	14	14	NUM
ejpam-4063	90	8	(	(	PUNCT
ejpam-4063	90	9	4	4	NUM
ejpam-4063	90	10	)	)	PUNCT
ejpam-4063	90	11	(	(	PUNCT
ejpam-4063	90	12	2021	2021	NUM
ejpam-4063	90	13	)	)	PUNCT
ejpam-4063	90	14	,	,	PUNCT
ejpam-4063	90	15	1249	1249	NUM
ejpam-4063	90	16	-	-	SYM
ejpam-4063	90	17	1265	1265	NUM
ejpam-4063	90	18	1253	1253	NUM
ejpam-4063	90	19	(	(	PUNCT
ejpam-4063	90	20	11	11	NUM
ejpam-4063	90	21	)	)	PUNCT
ejpam-4063	90	22	∫	∫	PROPN
ejpam-4063	91	1	∞	∞	PROPN
ejpam-4063	91	2	0	0	NUM
ejpam-4063	91	3	sinh(ax	sinh(ax	NOUN
ejpam-4063	91	4	)	)	PUNCT
ejpam-4063	91	5	(	(	PUNCT
ejpam-4063	91	6	e−mx(log(α)−	e−mx(log(α)−	PROPN
ejpam-4063	91	7	x)k	x)k	NOUN
ejpam-4063	91	8	−	−	PROPN
ejpam-4063	91	9	emx(log(α	emx(log(α	PROPN
ejpam-4063	91	10	)	)	PUNCT
ejpam-4063	92	1	+	+	NUM
ejpam-4063	92	2	x)k	x)k	X
ejpam-4063	92	3	)	)	PUNCT
ejpam-4063	92	4	(	(	PUNCT
ejpam-4063	92	5	cosh(ax	cosh(ax	NOUN
ejpam-4063	92	6	)	)	PUNCT
ejpam-4063	92	7	+	+	CCONJ
ejpam-4063	93	1	cos(t))2	cos(t))2	ADP
ejpam-4063	93	2	dx	dx	PROPN
ejpam-4063	93	3	=	=	SYM
ejpam-4063	94	1	−	−	PROPN
ejpam-4063	94	2	k(2π)k	k(2π)k	PROPN
ejpam-4063	94	3	(	(	PUNCT
ejpam-4063	94	4	i	i	PRON
ejpam-4063	94	5	a	a	X
ejpam-4063	94	6	)	)	PUNCT
ejpam-4063	94	7	k−1	k−1	PROPN
ejpam-4063	94	8	csc(t)e	csc(t)e	NOUN
ejpam-4063	94	9	im(π−t	im(π−t	PROPN
ejpam-4063	94	10	)	)	PUNCT
ejpam-4063	94	11	a	a	DET
ejpam-4063	94	12	φ	φ	NOUN
ejpam-4063	94	13	(	(	PUNCT
ejpam-4063	94	14	e	e	X
ejpam-4063	94	15	2imπ	2imπ	NUM
ejpam-4063	94	16	a	a	DET
ejpam-4063	94	17	,	,	PUNCT
ejpam-4063	94	18	1−	1−	NUM
ejpam-4063	94	19	k	k	X
ejpam-4063	94	20	,	,	PUNCT
ejpam-4063	94	21	−t−ia	−t−ia	X
ejpam-4063	94	22	log(α)+π	log(α)+π	X
ejpam-4063	94	23	2π	2π	PROPN
ejpam-4063	94	24	)	)	PUNCT
ejpam-4063	94	25	a2	a2	PROPN
ejpam-4063	94	26	+	+	CCONJ
ejpam-4063	95	1	k(2π)k	k(2π)k	PROPN
ejpam-4063	95	2	(	(	PUNCT
ejpam-4063	95	3	i	i	PRON
ejpam-4063	95	4	a	a	X
ejpam-4063	95	5	)	)	PUNCT
ejpam-4063	95	6	k−1	k−1	PROPN
ejpam-4063	95	7	csc(t)e	csc(t)e	NOUN
ejpam-4063	95	8	im(π−t	im(π−t	PROPN
ejpam-4063	95	9	)	)	PUNCT
ejpam-4063	96	1	a	a	PRON
ejpam-4063	96	2	+	+	NUM
ejpam-4063	96	3	2imt	2imt	NUM
ejpam-4063	96	4	a	a	DET
ejpam-4063	96	5	φ	φ	NOUN
ejpam-4063	96	6	(	(	PUNCT
ejpam-4063	96	7	e	e	X
ejpam-4063	96	8	2imπ	2imπ	NUM
ejpam-4063	96	9	a	a	DET
ejpam-4063	96	10	,	,	PUNCT
ejpam-4063	96	11	1−	1−	NUM
ejpam-4063	96	12	k	k	X
ejpam-4063	96	13	,	,	PUNCT
ejpam-4063	96	14	t−ia	t−ia	VERB
ejpam-4063	96	15	log(α)+π	log(α)+π	PRON
ejpam-4063	96	16	2π	2π	PROPN
ejpam-4063	96	17	)	)	PUNCT
ejpam-4063	96	18	a2	a2	PROPN
ejpam-4063	96	19	−	−	PROPN
ejpam-4063	97	1	(	(	PUNCT
ejpam-4063	97	2	2π)k+1	2π)k+1	NUM
ejpam-4063	97	3	m	m	NOUN
ejpam-4063	97	4	(	(	PUNCT
ejpam-4063	97	5	i	i	PRON
ejpam-4063	97	6	a	a	X
ejpam-4063	97	7	)	)	PUNCT
ejpam-4063	97	8	k	k	PROPN
ejpam-4063	97	9	csc(t)e	csc(t)e	PROPN
ejpam-4063	97	10	im(π−t	im(π−t	PROPN
ejpam-4063	97	11	)	)	PUNCT
ejpam-4063	98	1	a	a	DET
ejpam-4063	98	2	φ	φ	NOUN
ejpam-4063	98	3	(	(	PUNCT
ejpam-4063	98	4	e	e	X
ejpam-4063	98	5	2imπ	2imπ	NUM
ejpam-4063	98	6	a	a	DET
ejpam-4063	98	7	,	,	PUNCT
ejpam-4063	98	8	−k	−k	PROPN
ejpam-4063	98	9	,	,	PUNCT
ejpam-4063	98	10	−t−ia	−t−ia	X
ejpam-4063	98	11	log(α)+π	log(α)+π	X
ejpam-4063	98	12	2π	2π	PROPN
ejpam-4063	98	13	)	)	PUNCT
ejpam-4063	98	14	a2	a2	PROPN
ejpam-4063	98	15	+	+	CCONJ
ejpam-4063	98	16	(	(	PUNCT
ejpam-4063	98	17	2π)k+1	2π)k+1	NUM
ejpam-4063	98	18	m	m	NOUN
ejpam-4063	98	19	(	(	PUNCT
ejpam-4063	98	20	i	i	PRON
ejpam-4063	98	21	a	a	X
ejpam-4063	98	22	)	)	PUNCT
ejpam-4063	98	23	k	k	PROPN
ejpam-4063	98	24	csc(t)e	csc(t)e	PROPN
ejpam-4063	98	25	im(π−t	im(π−t	PROPN
ejpam-4063	98	26	)	)	PUNCT
ejpam-4063	98	27	a	a	PRON
ejpam-4063	99	1	+	+	NUM
ejpam-4063	99	2	2imt	2imt	NUM
ejpam-4063	99	3	a	a	DET
ejpam-4063	99	4	φ	φ	NOUN
ejpam-4063	99	5	(	(	PUNCT
ejpam-4063	99	6	e	e	X
ejpam-4063	99	7	2imπ	2imπ	NUM
ejpam-4063	99	8	a	a	DET
ejpam-4063	99	9	,	,	PUNCT
ejpam-4063	99	10	−k	−k	PROPN
ejpam-4063	99	11	,	,	PUNCT
ejpam-4063	99	12	t−ia	t−ia	X
ejpam-4063	99	13	log(α)+π	log(α)+π	PRON
ejpam-4063	99	14	2π	2π	PROPN
ejpam-4063	99	15	)	)	PUNCT
ejpam-4063	100	1	a2	a2	VERB
ejpam-4063	100	2	the	the	DET
ejpam-4063	100	3	integral	integral	ADJ
ejpam-4063	100	4	in	in	ADP
ejpam-4063	100	5	equation	equation	NOUN
ejpam-4063	100	6	(	(	PUNCT
ejpam-4063	100	7	11	11	NUM
ejpam-4063	100	8	)	)	PUNCT
ejpam-4063	100	9	can	can	AUX
ejpam-4063	100	10	be	be	AUX
ejpam-4063	100	11	used	use	VERB
ejpam-4063	100	12	as	as	ADP
ejpam-4063	100	13	an	an	DET
ejpam-4063	100	14	alternative	alternative	ADJ
ejpam-4063	100	15	method	method	NOUN
ejpam-4063	100	16	to	to	ADP
ejpam-4063	100	17	evaluating	evaluate	VERB
ejpam-4063	100	18	the	the	DET
ejpam-4063	100	19	lerch	lerch	PROPN
ejpam-4063	100	20	function	function	PROPN
ejpam-4063	100	21	.	.	PUNCT
ejpam-4063	101	1	6	6	X
ejpam-4063	101	2	.	.	X
ejpam-4063	101	3	evaluation	evaluation	NOUN
ejpam-4063	101	4	of	of	ADP
ejpam-4063	101	5	special	special	ADJ
ejpam-4063	101	6	cases	case	NOUN
ejpam-4063	101	7	of	of	ADP
ejpam-4063	101	8	definite	definite	ADJ
ejpam-4063	101	9	integrals	integral	NOUN
ejpam-4063	101	10	6.1	6.1	NUM
ejpam-4063	101	11	.	.	PUNCT
ejpam-4063	101	12	special	special	ADJ
ejpam-4063	101	13	case	case	NOUN
ejpam-4063	101	14	1	1	NUM
ejpam-4063	101	15	for	for	ADP
ejpam-4063	101	16	this	this	DET
ejpam-4063	101	17	special	special	ADJ
ejpam-4063	101	18	case	case	NOUN
ejpam-4063	101	19	we	we	PRON
ejpam-4063	101	20	will	will	AUX
ejpam-4063	101	21	form	form	VERB
ejpam-4063	101	22	a	a	DET
ejpam-4063	101	23	second	second	ADJ
ejpam-4063	101	24	equation	equation	NOUN
ejpam-4063	101	25	using	use	VERB
ejpam-4063	101	26	(	(	PUNCT
ejpam-4063	101	27	11	11	NUM
ejpam-4063	101	28	)	)	PUNCT
ejpam-4063	101	29	by	by	ADP
ejpam-4063	101	30	replacing	replace	VERB
ejpam-4063	101	31	m	m	PRON
ejpam-4063	101	32	by	by	ADP
ejpam-4063	101	33	−m	−m	NOUN
ejpam-4063	101	34	taking	take	VERB
ejpam-4063	101	35	the	the	DET
ejpam-4063	101	36	difference	difference	NOUN
ejpam-4063	101	37	from	from	ADP
ejpam-4063	101	38	the	the	DET
ejpam-4063	101	39	original	original	ADJ
ejpam-4063	101	40	equation	equation	NOUN
ejpam-4063	101	41	and	and	CCONJ
ejpam-4063	101	42	simplifying	simplify	VERB
ejpam-4063	101	43	to	to	PART
ejpam-4063	101	44	get	get	VERB
ejpam-4063	101	45	r.	r.	PROPN
ejpam-4063	101	46	reynolds	reynolds	PROPN
ejpam-4063	101	47	,	,	PUNCT
ejpam-4063	101	48	a.	a.	PROPN
ejpam-4063	101	49	stauffer	stauffer	PROPN
ejpam-4063	101	50	/	/	SYM
ejpam-4063	101	51	eur	eur	PROPN
ejpam-4063	101	52	.	.	PUNCT
ejpam-4063	102	1	j.	j.	PROPN
ejpam-4063	102	2	pure	pure	PROPN
ejpam-4063	102	3	appl	appl	PROPN
ejpam-4063	102	4	.	.	PROPN
ejpam-4063	102	5	math	math	PROPN
ejpam-4063	102	6	,	,	PUNCT
ejpam-4063	102	7	14	14	NUM
ejpam-4063	102	8	(	(	PUNCT
ejpam-4063	102	9	4	4	NUM
ejpam-4063	102	10	)	)	PUNCT
ejpam-4063	102	11	(	(	PUNCT
ejpam-4063	102	12	2021	2021	NUM
ejpam-4063	102	13	)	)	PUNCT
ejpam-4063	102	14	,	,	PUNCT
ejpam-4063	102	15	1249	1249	NUM
ejpam-4063	102	16	-	-	SYM
ejpam-4063	102	17	1265	1265	NUM
ejpam-4063	102	18	1254	1254	NUM
ejpam-4063	102	19	(	(	PUNCT
ejpam-4063	102	20	12	12	NUM
ejpam-4063	102	21	)	)	PUNCT
ejpam-4063	102	22	−	−	NOUN
ejpam-4063	103	1	∫	∫	PROPN
ejpam-4063	103	2	∞	∞	NUM
ejpam-4063	103	3	0	0	NUM
ejpam-4063	103	4	2	2	NUM
ejpam-4063	103	5	sinh(ax	sinh(ax	NOUN
ejpam-4063	103	6	)	)	PUNCT
ejpam-4063	103	7	sinh(mx	sinh(mx	NOUN
ejpam-4063	103	8	)	)	PUNCT
ejpam-4063	103	9	(	(	PUNCT
ejpam-4063	103	10	(	(	PUNCT
ejpam-4063	103	11	log(α)−	log(α)−	INTJ
ejpam-4063	103	12	x)k	x)k	PUNCT
ejpam-4063	104	1	+	+	CCONJ
ejpam-4063	104	2	(	(	PUNCT
ejpam-4063	104	3	log(α	log(α	PROPN
ejpam-4063	104	4	)	)	PUNCT
ejpam-4063	104	5	+	+	NUM
ejpam-4063	104	6	x)k	x)k	X
ejpam-4063	104	7	)	)	PUNCT
ejpam-4063	105	1	(	(	PUNCT
ejpam-4063	105	2	cosh(ax	cosh(ax	NOUN
ejpam-4063	105	3	)	)	PUNCT
ejpam-4063	105	4	+	+	CCONJ
ejpam-4063	105	5	cos(t))2	cos(t))2	NUM
ejpam-4063	105	6	dx	dx	PROPN
ejpam-4063	106	1	=	=	SYM
ejpam-4063	107	1	k(2π)k	k(2π)k	PROPN
ejpam-4063	108	1	(	(	PUNCT
ejpam-4063	108	2	i	i	PRON
ejpam-4063	108	3	a	a	X
ejpam-4063	108	4	)	)	PUNCT
ejpam-4063	108	5	k−1	k−1	PROPN
ejpam-4063	108	6	csc(t)e−	csc(t)e−	PROPN
ejpam-4063	109	1	im(π−t	im(π−t	PRON
ejpam-4063	109	2	)	)	PUNCT
ejpam-4063	109	3	a	a	DET
ejpam-4063	109	4	φ	φ	X
ejpam-4063	109	5	(	(	PUNCT
ejpam-4063	109	6	e−	e−	PROPN
ejpam-4063	109	7	2imπ	2imπ	PROPN
ejpam-4063	109	8	a	a	DET
ejpam-4063	109	9	,	,	PUNCT
ejpam-4063	109	10	1−	1−	NUM
ejpam-4063	109	11	k	k	X
ejpam-4063	109	12	,	,	PUNCT
ejpam-4063	109	13	−t−ia	−t−ia	X
ejpam-4063	109	14	log(α)+π	log(α)+π	X
ejpam-4063	109	15	2π	2π	PROPN
ejpam-4063	109	16	)	)	PUNCT
ejpam-4063	109	17	a2	a2	PROPN
ejpam-4063	109	18	−	−	PROPN
ejpam-4063	110	1	k(2π)k	k(2π)k	PROPN
ejpam-4063	110	2	(	(	PUNCT
ejpam-4063	110	3	i	i	PRON
ejpam-4063	110	4	a	a	X
ejpam-4063	110	5	)	)	PUNCT
ejpam-4063	110	6	k−1	k−1	PROPN
ejpam-4063	110	7	csc(t)e−	csc(t)e−	PROPN
ejpam-4063	110	8	im(π−t	im(π−t	PRON
ejpam-4063	110	9	)	)	PUNCT
ejpam-4063	110	10	a	a	DET
ejpam-4063	110	11	−	−	PROPN
ejpam-4063	110	12	2imt	2imt	NUM
ejpam-4063	110	13	a	a	DET
ejpam-4063	110	14	φ	φ	NOUN
ejpam-4063	110	15	(	(	PUNCT
ejpam-4063	110	16	e−	e−	PROPN
ejpam-4063	110	17	2imπ	2imπ	PROPN
ejpam-4063	110	18	a	a	DET
ejpam-4063	110	19	,	,	PUNCT
ejpam-4063	110	20	1−	1−	NUM
ejpam-4063	110	21	k	k	X
ejpam-4063	110	22	,	,	PUNCT
ejpam-4063	110	23	t−ia	t−ia	VERB
ejpam-4063	110	24	log(α)+π	log(α)+π	PRON
ejpam-4063	110	25	2π	2π	PROPN
ejpam-4063	110	26	)	)	PUNCT
ejpam-4063	110	27	a2	a2	PROPN
ejpam-4063	110	28	−	−	PROPN
ejpam-4063	111	1	k(2π)k	k(2π)k	PROPN
ejpam-4063	111	2	(	(	PUNCT
ejpam-4063	111	3	i	i	PRON
ejpam-4063	111	4	a	a	X
ejpam-4063	111	5	)	)	PUNCT
ejpam-4063	111	6	k−1	k−1	PROPN
ejpam-4063	111	7	csc(t)e	csc(t)e	NOUN
ejpam-4063	111	8	im(π−t	im(π−t	PROPN
ejpam-4063	111	9	)	)	PUNCT
ejpam-4063	111	10	a	a	DET
ejpam-4063	111	11	φ	φ	NOUN
ejpam-4063	111	12	(	(	PUNCT
ejpam-4063	111	13	e	e	X
ejpam-4063	111	14	2imπ	2imπ	NUM
ejpam-4063	111	15	a	a	DET
ejpam-4063	111	16	,	,	PUNCT
ejpam-4063	111	17	1−	1−	NUM
ejpam-4063	111	18	k	k	X
ejpam-4063	111	19	,	,	PUNCT
ejpam-4063	111	20	−t−ia	−t−ia	X
ejpam-4063	111	21	log(α)+π	log(α)+π	X
ejpam-4063	111	22	2π	2π	PROPN
ejpam-4063	111	23	)	)	PUNCT
ejpam-4063	111	24	a2	a2	PROPN
ejpam-4063	111	25	+	+	CCONJ
ejpam-4063	112	1	k(2π)k	k(2π)k	PROPN
ejpam-4063	112	2	(	(	PUNCT
ejpam-4063	112	3	i	i	PRON
ejpam-4063	112	4	a	a	X
ejpam-4063	112	5	)	)	PUNCT
ejpam-4063	112	6	k−1	k−1	PROPN
ejpam-4063	112	7	csc(t)e	csc(t)e	NOUN
ejpam-4063	112	8	im(π−t	im(π−t	PROPN
ejpam-4063	112	9	)	)	PUNCT
ejpam-4063	113	1	a	a	PRON
ejpam-4063	113	2	+	+	NUM
ejpam-4063	113	3	2imt	2imt	NUM
ejpam-4063	113	4	a	a	DET
ejpam-4063	113	5	φ	φ	NOUN
ejpam-4063	113	6	(	(	PUNCT
ejpam-4063	113	7	e	e	X
ejpam-4063	113	8	2imπ	2imπ	NUM
ejpam-4063	113	9	a	a	DET
ejpam-4063	113	10	,	,	PUNCT
ejpam-4063	113	11	1−	1−	NUM
ejpam-4063	113	12	k	k	X
ejpam-4063	113	13	,	,	PUNCT
ejpam-4063	113	14	t−ia	t−ia	VERB
ejpam-4063	113	15	log(α)+π	log(α)+π	PRON
ejpam-4063	113	16	2π	2π	PROPN
ejpam-4063	113	17	)	)	PUNCT
ejpam-4063	113	18	a2	a2	PROPN
ejpam-4063	113	19	−	−	PROPN
ejpam-4063	114	1	(	(	PUNCT
ejpam-4063	114	2	2π)k+1	2π)k+1	NUM
ejpam-4063	114	3	m	m	NOUN
ejpam-4063	114	4	(	(	PUNCT
ejpam-4063	114	5	i	i	PRON
ejpam-4063	114	6	a	a	X
ejpam-4063	114	7	)	)	PUNCT
ejpam-4063	114	8	k	k	PROPN
ejpam-4063	114	9	csc(t)e−	csc(t)e−	PROPN
ejpam-4063	115	1	im(π−t	im(π−t	PROPN
ejpam-4063	115	2	)	)	PUNCT
ejpam-4063	116	1	a	a	DET
ejpam-4063	116	2	φ	φ	X
ejpam-4063	116	3	(	(	PUNCT
ejpam-4063	116	4	e−	e−	PROPN
ejpam-4063	116	5	2imπ	2imπ	PROPN
ejpam-4063	116	6	a	a	DET
ejpam-4063	116	7	,	,	PUNCT
ejpam-4063	116	8	−k	−k	PROPN
ejpam-4063	116	9	,	,	PUNCT
ejpam-4063	116	10	−t−ia	−t−ia	X
ejpam-4063	116	11	log(α)+π	log(α)+π	X
ejpam-4063	116	12	2π	2π	PROPN
ejpam-4063	116	13	)	)	PUNCT
ejpam-4063	116	14	a2	a2	PROPN
ejpam-4063	116	15	+	+	CCONJ
ejpam-4063	116	16	(	(	PUNCT
ejpam-4063	116	17	2π)k+1	2π)k+1	NUM
ejpam-4063	116	18	m	m	NOUN
ejpam-4063	116	19	(	(	PUNCT
ejpam-4063	116	20	i	i	PRON
ejpam-4063	116	21	a	a	X
ejpam-4063	116	22	)	)	PUNCT
ejpam-4063	116	23	k	k	PROPN
ejpam-4063	116	24	csc(t)e−	csc(t)e−	PROPN
ejpam-4063	116	25	im(π−t	im(π−t	PROPN
ejpam-4063	116	26	)	)	PUNCT
ejpam-4063	116	27	a	a	DET
ejpam-4063	116	28	−	−	PROPN
ejpam-4063	116	29	2imt	2imt	NUM
ejpam-4063	116	30	a	a	DET
ejpam-4063	116	31	φ	φ	NOUN
ejpam-4063	116	32	(	(	PUNCT
ejpam-4063	116	33	e−	e−	PROPN
ejpam-4063	116	34	2imπ	2imπ	PROPN
ejpam-4063	116	35	a	a	DET
ejpam-4063	116	36	,	,	PUNCT
ejpam-4063	116	37	−k	−k	PROPN
ejpam-4063	116	38	,	,	PUNCT
ejpam-4063	116	39	t−ia	t−ia	X
ejpam-4063	116	40	log(α)+π	log(α)+π	PRON
ejpam-4063	116	41	2π	2π	PROPN
ejpam-4063	116	42	)	)	PUNCT
ejpam-4063	116	43	a2	a2	PROPN
ejpam-4063	116	44	−	−	PROPN
ejpam-4063	116	45	(	(	PUNCT
ejpam-4063	116	46	2π)k+1	2π)k+1	NUM
ejpam-4063	116	47	m	m	NOUN
ejpam-4063	116	48	(	(	PUNCT
ejpam-4063	116	49	i	i	PRON
ejpam-4063	116	50	a	a	X
ejpam-4063	116	51	)	)	PUNCT
ejpam-4063	116	52	k	k	PROPN
ejpam-4063	116	53	csc(t)e	csc(t)e	PROPN
ejpam-4063	116	54	im(π−t	im(π−t	PROPN
ejpam-4063	116	55	)	)	PUNCT
ejpam-4063	116	56	a	a	DET
ejpam-4063	116	57	φ	φ	NOUN
ejpam-4063	116	58	(	(	PUNCT
ejpam-4063	116	59	e	e	X
ejpam-4063	116	60	2imπ	2imπ	NUM
ejpam-4063	116	61	a	a	DET
ejpam-4063	116	62	,	,	PUNCT
ejpam-4063	116	63	−k	−k	PROPN
ejpam-4063	116	64	,	,	PUNCT
ejpam-4063	116	65	−t−ia	−t−ia	X
ejpam-4063	116	66	log(α)+π	log(α)+π	X
ejpam-4063	116	67	2π	2π	PROPN
ejpam-4063	116	68	)	)	PUNCT
ejpam-4063	116	69	a2	a2	PROPN
ejpam-4063	116	70	+	+	CCONJ
ejpam-4063	116	71	(	(	PUNCT
ejpam-4063	116	72	2π)k+1	2π)k+1	NUM
ejpam-4063	116	73	m	m	NOUN
ejpam-4063	116	74	(	(	PUNCT
ejpam-4063	116	75	i	i	PRON
ejpam-4063	116	76	a	a	X
ejpam-4063	116	77	)	)	PUNCT
ejpam-4063	116	78	k	k	PROPN
ejpam-4063	116	79	csc(t)e	csc(t)e	PROPN
ejpam-4063	116	80	im(π−t	im(π−t	PROPN
ejpam-4063	116	81	)	)	PUNCT
ejpam-4063	116	82	a	a	PRON
ejpam-4063	117	1	+	+	NUM
ejpam-4063	117	2	2imt	2imt	NUM
ejpam-4063	117	3	a	a	DET
ejpam-4063	117	4	φ	φ	NOUN
ejpam-4063	117	5	(	(	PUNCT
ejpam-4063	117	6	e	e	X
ejpam-4063	117	7	2imπ	2imπ	NUM
ejpam-4063	117	8	a	a	DET
ejpam-4063	117	9	,	,	PUNCT
ejpam-4063	117	10	−k	−k	PROPN
ejpam-4063	117	11	,	,	PUNCT
ejpam-4063	117	12	t−ia	t−ia	X
ejpam-4063	117	13	log(α)+π	log(α)+π	PRON
ejpam-4063	117	14	2π	2π	PROPN
ejpam-4063	117	15	)	)	PUNCT
ejpam-4063	118	1	a2	a2	PROPN
ejpam-4063	118	2	6.2	6.2	NUM
ejpam-4063	118	3	.	.	PUNCT
ejpam-4063	119	1	special	special	ADJ
ejpam-4063	119	2	case	case	NOUN
ejpam-4063	119	3	2	2	NUM
ejpam-4063	119	4	for	for	ADP
ejpam-4063	119	5	this	this	DET
ejpam-4063	119	6	special	special	ADJ
ejpam-4063	119	7	case	case	NOUN
ejpam-4063	119	8	we	we	PRON
ejpam-4063	119	9	use	use	VERB
ejpam-4063	119	10	equation	equation	NOUN
ejpam-4063	119	11	(	(	PUNCT
ejpam-4063	119	12	12	12	NUM
ejpam-4063	119	13	)	)	PUNCT
ejpam-4063	119	14	setting	set	VERB
ejpam-4063	119	15	α	α	NOUN
ejpam-4063	119	16	=	=	SYM
ejpam-4063	119	17	1	1	NUM
ejpam-4063	119	18	and	and	CCONJ
ejpam-4063	119	19	taking	take	VERB
ejpam-4063	119	20	the	the	DET
ejpam-4063	119	21	first	first	ADJ
ejpam-4063	119	22	partial	partial	ADJ
ejpam-4063	119	23	derivative	derivative	NOUN
ejpam-4063	119	24	with	with	ADP
ejpam-4063	119	25	respect	respect	NOUN
ejpam-4063	119	26	to	to	ADP
ejpam-4063	119	27	m	m	AUX
ejpam-4063	119	28	simplifying	simplify	VERB
ejpam-4063	119	29	to	to	PART
ejpam-4063	119	30	get	get	VERB
ejpam-4063	119	31	r.	r.	PROPN
ejpam-4063	119	32	reynolds	reynolds	PROPN
ejpam-4063	119	33	,	,	PUNCT
ejpam-4063	119	34	a.	a.	PROPN
ejpam-4063	119	35	stauffer	stauffer	PROPN
ejpam-4063	119	36	/	/	SYM
ejpam-4063	119	37	eur	eur	PROPN
ejpam-4063	119	38	.	.	PUNCT
ejpam-4063	120	1	j.	j.	PROPN
ejpam-4063	120	2	pure	pure	PROPN
ejpam-4063	120	3	appl	appl	PROPN
ejpam-4063	120	4	.	.	PROPN
ejpam-4063	120	5	math	math	PROPN
ejpam-4063	120	6	,	,	PUNCT
ejpam-4063	120	7	14	14	NUM
ejpam-4063	120	8	(	(	PUNCT
ejpam-4063	120	9	4	4	NUM
ejpam-4063	120	10	)	)	PUNCT
ejpam-4063	120	11	(	(	PUNCT
ejpam-4063	120	12	2021	2021	NUM
ejpam-4063	120	13	)	)	PUNCT
ejpam-4063	120	14	,	,	PUNCT
ejpam-4063	120	15	1249	1249	NUM
ejpam-4063	120	16	-	-	SYM
ejpam-4063	120	17	1265	1265	NUM
ejpam-4063	120	18	1255∫	1255∫	NUM
ejpam-4063	120	19	∞	∞	PROPN
ejpam-4063	120	20	0	0	NUM
ejpam-4063	120	21	xk	xk	PROPN
ejpam-4063	120	22	sinh(ax	sinh(ax	PROPN
ejpam-4063	120	23	)	)	PUNCT
ejpam-4063	120	24	cosh(mx	cosh(mx	PROPN
ejpam-4063	120	25	)	)	PUNCT
ejpam-4063	120	26	(	(	PUNCT
ejpam-4063	120	27	cosh(ax	cosh(ax	NOUN
ejpam-4063	120	28	)	)	PUNCT
ejpam-4063	120	29	+	+	CCONJ
ejpam-4063	121	1	cos(t))2	cos(t))2	NUM
ejpam-4063	121	2	dx	dx	PROPN
ejpam-4063	121	3	=	=	SYM
ejpam-4063	121	4	2k−1πk	2k−1πk	PROPN
ejpam-4063	121	5	(	(	PUNCT
ejpam-4063	121	6	i	i	PRON
ejpam-4063	121	7	a	a	X
ejpam-4063	121	8	)	)	PUNCT
ejpam-4063	122	1	k+1	k+1	PROPN
ejpam-4063	122	2	csc(t)e−	csc(t)e−	PROPN
ejpam-4063	122	3	im(t+π	im(t+π	PROPN
ejpam-4063	122	4	)	)	PUNCT
ejpam-4063	122	5	a	a	DET
ejpam-4063	122	6	a	a	DET
ejpam-4063	122	7	(	(	PUNCT
ejpam-4063	122	8	−1	−1	NOUN
ejpam-4063	122	9	+	+	CCONJ
ejpam-4063	122	10	eiπk	eiπk	ADJ
ejpam-4063	122	11	)	)	PUNCT
ejpam-4063	122	12	(	(	PUNCT
ejpam-4063	122	13	ake	ake	NOUN
ejpam-4063	122	14	2imt	2imt	NUM
ejpam-4063	122	15	a	a	DET
ejpam-4063	122	16	φ	φ	NOUN
ejpam-4063	122	17	(	(	PUNCT
ejpam-4063	122	18	e−	e−	PROPN
ejpam-4063	122	19	2imπ	2imπ	PROPN
ejpam-4063	122	20	a	a	DET
ejpam-4063	122	21	,	,	PUNCT
ejpam-4063	122	22	1	1	NUM
ejpam-4063	122	23	−	−	NOUN
ejpam-4063	123	1	k	k	NOUN
ejpam-4063	123	2	,	,	PUNCT
ejpam-4063	123	3	π	π	PROPN
ejpam-4063	123	4	−	−	PROPN
ejpam-4063	123	5	t	t	PROPN
ejpam-4063	123	6	2π	2π	NOUN
ejpam-4063	123	7	)	)	PUNCT
ejpam-4063	124	1	−	−	PROPN
ejpam-4063	124	2	akφ	akφ	PROPN
ejpam-4063	124	3	(	(	PUNCT
ejpam-4063	124	4	e−	e−	PROPN
ejpam-4063	124	5	2imπ	2imπ	PROPN
ejpam-4063	124	6	a	a	DET
ejpam-4063	124	7	,	,	PUNCT
ejpam-4063	124	8	1−	1−	NUM
ejpam-4063	124	9	k	k	NOUN
ejpam-4063	124	10	,	,	PUNCT
ejpam-4063	124	11	t+	t+	PUNCT
ejpam-4063	124	12	π	π	PROPN
ejpam-4063	124	13	2π	2π	PROPN
ejpam-4063	124	14	)	)	PUNCT
ejpam-4063	125	1	−	−	PROPN
ejpam-4063	126	1	2iπm	2iπm	NUM
ejpam-4063	126	2	(	(	PUNCT
ejpam-4063	126	3	e	e	PROPN
ejpam-4063	126	4	2imt	2imt	NUM
ejpam-4063	126	5	a	a	DET
ejpam-4063	126	6	φ	φ	NOUN
ejpam-4063	126	7	(	(	PUNCT
ejpam-4063	126	8	e−	e−	PROPN
ejpam-4063	126	9	2imπ	2imπ	PROPN
ejpam-4063	126	10	a	a	PRON
ejpam-4063	126	11	,	,	PUNCT
ejpam-4063	126	12	−k	−k	PROPN
ejpam-4063	126	13	,	,	PUNCT
ejpam-4063	126	14	π	π	PROPN
ejpam-4063	126	15	−	−	PROPN
ejpam-4063	126	16	t	t	PROPN
ejpam-4063	126	17	2π	2π	NOUN
ejpam-4063	126	18	)	)	PUNCT
ejpam-4063	127	1	−	−	PROPN
ejpam-4063	127	2	φ	φ	PROPN
ejpam-4063	127	3	(	(	PUNCT
ejpam-4063	127	4	e−	e−	PROPN
ejpam-4063	127	5	2imπ	2imπ	PROPN
ejpam-4063	127	6	a	a	PRON
ejpam-4063	127	7	,	,	PUNCT
ejpam-4063	127	8	−k	−k	PROPN
ejpam-4063	127	9	,	,	PUNCT
ejpam-4063	127	10	t+	t+	PUNCT
ejpam-4063	127	11	π	π	PROPN
ejpam-4063	127	12	2π	2π	NOUN
ejpam-4063	127	13	)	)	PUNCT
ejpam-4063	127	14	)	)	PUNCT
ejpam-4063	128	1	+	+	CCONJ
ejpam-4063	128	2	e	e	X
ejpam-4063	128	3	2iπm	2iπm	NUM
ejpam-4063	128	4	a	a	DET
ejpam-4063	128	5	(	(	PUNCT
ejpam-4063	128	6	akφ	akφ	PROPN
ejpam-4063	128	7	(	(	PUNCT
ejpam-4063	128	8	e	e	X
ejpam-4063	128	9	2imπ	2imπ	NUM
ejpam-4063	128	10	a	a	DET
ejpam-4063	128	11	,	,	PUNCT
ejpam-4063	128	12	1−	1−	NUM
ejpam-4063	128	13	k	k	NOUN
ejpam-4063	128	14	,	,	PUNCT
ejpam-4063	128	15	π	π	PROPN
ejpam-4063	128	16	−	−	PROPN
ejpam-4063	128	17	t	t	PROPN
ejpam-4063	128	18	2π	2π	NOUN
ejpam-4063	128	19	)	)	PUNCT
ejpam-4063	129	1	+	+	CCONJ
ejpam-4063	129	2	2iπmφ	2iπmφ	NUM
ejpam-4063	129	3	(	(	PUNCT
ejpam-4063	129	4	e	e	X
ejpam-4063	129	5	2imπ	2imπ	NUM
ejpam-4063	129	6	a	a	DET
ejpam-4063	129	7	,	,	PUNCT
ejpam-4063	129	8	−k	−k	PROPN
ejpam-4063	129	9	,	,	PUNCT
ejpam-4063	129	10	π	π	PROPN
ejpam-4063	129	11	−	−	PROPN
ejpam-4063	129	12	t	t	PROPN
ejpam-4063	129	13	2π	2π	NOUN
ejpam-4063	129	14	)	)	PUNCT
ejpam-4063	129	15	)	)	PUNCT
ejpam-4063	130	1	−	−	PROPN
ejpam-4063	130	2	e	e	X
ejpam-4063	130	3	2im(t+π	2im(t+π	NOUN
ejpam-4063	130	4	)	)	PUNCT
ejpam-4063	130	5	a	a	DET
ejpam-4063	130	6	(	(	PUNCT
ejpam-4063	130	7	akφ	akφ	INTJ
ejpam-4063	130	8	(	(	PUNCT
ejpam-4063	130	9	e	e	X
ejpam-4063	130	10	2imπ	2imπ	NUM
ejpam-4063	130	11	a	a	DET
ejpam-4063	130	12	,	,	PUNCT
ejpam-4063	130	13	1−	1−	NUM
ejpam-4063	130	14	k	k	NOUN
ejpam-4063	130	15	,	,	PUNCT
ejpam-4063	130	16	t+	t+	PUNCT
ejpam-4063	130	17	π	π	PROPN
ejpam-4063	130	18	2π	2π	NOUN
ejpam-4063	130	19	)	)	PUNCT
ejpam-4063	131	1	+	+	CCONJ
ejpam-4063	131	2	2iπmφ	2iπmφ	NUM
ejpam-4063	131	3	(	(	PUNCT
ejpam-4063	131	4	e	e	X
ejpam-4063	131	5	2imπ	2imπ	NUM
ejpam-4063	131	6	a	a	DET
ejpam-4063	131	7	,	,	PUNCT
ejpam-4063	131	8	−k	−k	PROPN
ejpam-4063	131	9	,	,	PUNCT
ejpam-4063	131	10	t+	t+	PUNCT
ejpam-4063	131	11	π	π	PROPN
ejpam-4063	131	12	2π	2π	PROPN
ejpam-4063	131	13	)	)	PUNCT
ejpam-4063	131	14	)	)	PUNCT
ejpam-4063	131	15	)	)	PUNCT
ejpam-4063	131	16	(	(	PUNCT
ejpam-4063	131	17	13	13	NUM
ejpam-4063	131	18	)	)	PUNCT
ejpam-4063	131	19	7	7	NUM
ejpam-4063	131	20	.	.	PUNCT
ejpam-4063	131	21	derivation	derivation	NOUN
ejpam-4063	131	22	of	of	ADP
ejpam-4063	131	23	entry	entry	NOUN
ejpam-4063	131	24	3.514.4	3.514.4	NUM
ejpam-4063	131	25	in	in	ADP
ejpam-4063	131	26	[	[	X
ejpam-4063	131	27	3	3	NUM
ejpam-4063	131	28	]	]	PUNCT
ejpam-4063	131	29	using	use	VERB
ejpam-4063	131	30	equation	equation	NOUN
ejpam-4063	131	31	(	(	PUNCT
ejpam-4063	131	32	12	12	NUM
ejpam-4063	131	33	)	)	PUNCT
ejpam-4063	131	34	we	we	PRON
ejpam-4063	131	35	proceed	proceed	VERB
ejpam-4063	131	36	by	by	ADP
ejpam-4063	131	37	setting	set	VERB
ejpam-4063	131	38	α	α	NOUN
ejpam-4063	131	39	=	=	SYM
ejpam-4063	131	40	1	1	NUM
ejpam-4063	131	41	and	and	CCONJ
ejpam-4063	131	42	simplifying	simplify	VERB
ejpam-4063	131	43	to	to	PART
ejpam-4063	131	44	get	get	VERB
ejpam-4063	131	45	r.	r.	PROPN
ejpam-4063	131	46	reynolds	reynolds	PROPN
ejpam-4063	131	47	,	,	PUNCT
ejpam-4063	131	48	a.	a.	PROPN
ejpam-4063	131	49	stauffer	stauffer	PROPN
ejpam-4063	131	50	/	/	SYM
ejpam-4063	131	51	eur	eur	PROPN
ejpam-4063	131	52	.	.	PUNCT
ejpam-4063	132	1	j.	j.	PROPN
ejpam-4063	132	2	pure	pure	PROPN
ejpam-4063	132	3	appl	appl	PROPN
ejpam-4063	132	4	.	.	PROPN
ejpam-4063	132	5	math	math	PROPN
ejpam-4063	132	6	,	,	PUNCT
ejpam-4063	132	7	14	14	NUM
ejpam-4063	132	8	(	(	PUNCT
ejpam-4063	132	9	4	4	NUM
ejpam-4063	132	10	)	)	PUNCT
ejpam-4063	132	11	(	(	PUNCT
ejpam-4063	132	12	2021	2021	NUM
ejpam-4063	132	13	)	)	PUNCT
ejpam-4063	132	14	,	,	PUNCT
ejpam-4063	132	15	1249	1249	NUM
ejpam-4063	132	16	-	-	SYM
ejpam-4063	132	17	1265	1265	NUM
ejpam-4063	132	18	1256	1256	NUM
ejpam-4063	132	19	∫	∫	PROPN
ejpam-4063	132	20	∞	∞	PROPN
ejpam-4063	132	21	0	0	NUM
ejpam-4063	132	22	xk	xk	PROPN
ejpam-4063	132	23	sinh(ax	sinh(ax	PROPN
ejpam-4063	132	24	)	)	PUNCT
ejpam-4063	132	25	sinh(mx	sinh(mx	PROPN
ejpam-4063	132	26	)	)	PUNCT
ejpam-4063	132	27	(	(	PUNCT
ejpam-4063	132	28	cosh(ax	cosh(ax	NOUN
ejpam-4063	132	29	)	)	PUNCT
ejpam-4063	132	30	+	+	CCONJ
ejpam-4063	132	31	cos(t))2	cos(t))2	NUM
ejpam-4063	132	32	dx	dx	X
ejpam-4063	132	33	=	=	SYM
ejpam-4063	132	34	2kπk+1	2kπk+1	NUM
ejpam-4063	132	35	m	m	NOUN
ejpam-4063	132	36	(	(	PUNCT
ejpam-4063	132	37	i	i	PRON
ejpam-4063	132	38	a	a	X
ejpam-4063	132	39	)	)	PUNCT
ejpam-4063	132	40	k	k	PROPN
ejpam-4063	132	41	csc(t)e	csc(t)e	NOUN
ejpam-4063	132	42	2imt	2imt	NUM
ejpam-4063	132	43	a	a	DET
ejpam-4063	132	44	−	−	PROPN
ejpam-4063	132	45	im(t+π	im(t+π	PROPN
ejpam-4063	132	46	)	)	PUNCT
ejpam-4063	132	47	a	a	DET
ejpam-4063	132	48	φ	φ	X
ejpam-4063	132	49	(	(	PUNCT
ejpam-4063	132	50	e−	e−	PROPN
ejpam-4063	132	51	2imπ	2imπ	PROPN
ejpam-4063	132	52	a	a	DET
ejpam-4063	132	53	,	,	PUNCT
ejpam-4063	132	54	−k	−k	PROPN
ejpam-4063	132	55	,	,	PUNCT
ejpam-4063	132	56	π−t	π−t	X
ejpam-4063	132	57	2π	2π	NOUN
ejpam-4063	132	58	)	)	PUNCT
ejpam-4063	132	59	a2	a2	PROPN
ejpam-4063	132	60	(	(	PUNCT
ejpam-4063	132	61	(	(	PUNCT
ejpam-4063	132	62	−1)k	−1)k	PROPN
ejpam-4063	132	63	+	+	NUM
ejpam-4063	132	64	1	1	X
ejpam-4063	132	65	)	)	PUNCT
ejpam-4063	132	66	−	−	NOUN
ejpam-4063	132	67	2kπk+1	2kπk+1	NUM
ejpam-4063	132	68	m	m	VERB
ejpam-4063	132	69	(	(	PUNCT
ejpam-4063	132	70	i	i	PRON
ejpam-4063	132	71	a	a	X
ejpam-4063	132	72	)	)	PUNCT
ejpam-4063	133	1	k	k	PROPN
ejpam-4063	133	2	csc(t)e−	csc(t)e−	PROPN
ejpam-4063	133	3	im(t+π	im(t+π	PROPN
ejpam-4063	133	4	)	)	PUNCT
ejpam-4063	133	5	a	a	DET
ejpam-4063	133	6	φ	φ	X
ejpam-4063	133	7	(	(	PUNCT
ejpam-4063	133	8	e−	e−	PROPN
ejpam-4063	133	9	2imπ	2imπ	PROPN
ejpam-4063	133	10	a	a	DET
ejpam-4063	133	11	,	,	PUNCT
ejpam-4063	133	12	−k	−k	PROPN
ejpam-4063	133	13	,	,	PUNCT
ejpam-4063	133	14	t+π	t+π	CCONJ
ejpam-4063	133	15	2π	2π	NOUN
ejpam-4063	133	16	)	)	PUNCT
ejpam-4063	133	17	a2	a2	PROPN
ejpam-4063	133	18	(	(	PUNCT
ejpam-4063	133	19	(	(	PUNCT
ejpam-4063	133	20	−1)k	−1)k	PROPN
ejpam-4063	133	21	+	+	NUM
ejpam-4063	133	22	1	1	X
ejpam-4063	133	23	)	)	PUNCT
ejpam-4063	133	24	+	+	CCONJ
ejpam-4063	133	25	2kπk+1	2kπk+1	NUM
ejpam-4063	133	26	m	m	NOUN
ejpam-4063	133	27	(	(	PUNCT
ejpam-4063	133	28	i	i	PRON
ejpam-4063	133	29	a	a	X
ejpam-4063	133	30	)	)	PUNCT
ejpam-4063	133	31	k	k	NOUN
ejpam-4063	133	32	csc(t)e	csc(t)e	NOUN
ejpam-4063	133	33	2iπm	2iπm	PROPN
ejpam-4063	133	34	a	a	DET
ejpam-4063	133	35	−	−	PROPN
ejpam-4063	133	36	im(t+π	im(t+π	PROPN
ejpam-4063	133	37	)	)	PUNCT
ejpam-4063	133	38	a	a	DET
ejpam-4063	133	39	φ	φ	NOUN
ejpam-4063	133	40	(	(	PUNCT
ejpam-4063	133	41	e	e	X
ejpam-4063	133	42	2imπ	2imπ	NUM
ejpam-4063	133	43	a	a	DET
ejpam-4063	133	44	,	,	PUNCT
ejpam-4063	133	45	−k	−k	PROPN
ejpam-4063	133	46	,	,	PUNCT
ejpam-4063	133	47	π−t	π−t	X
ejpam-4063	133	48	2π	2π	NOUN
ejpam-4063	133	49	)	)	PUNCT
ejpam-4063	133	50	a2	a2	PROPN
ejpam-4063	133	51	(	(	PUNCT
ejpam-4063	133	52	(	(	PUNCT
ejpam-4063	133	53	−1)k	−1)k	PROPN
ejpam-4063	133	54	+	+	NUM
ejpam-4063	133	55	1	1	X
ejpam-4063	133	56	)	)	PUNCT
ejpam-4063	133	57	−	−	NOUN
ejpam-4063	134	1	2kπk+1	2kπk+1	NUM
ejpam-4063	134	2	m	m	VERB
ejpam-4063	134	3	(	(	PUNCT
ejpam-4063	134	4	i	i	PRON
ejpam-4063	134	5	a	a	X
ejpam-4063	134	6	)	)	PUNCT
ejpam-4063	134	7	k	k	PROPN
ejpam-4063	134	8	csc(t)e	csc(t)e	PROPN
ejpam-4063	134	9	im(t+π	im(t+π	PROPN
ejpam-4063	134	10	)	)	PUNCT
ejpam-4063	134	11	a	a	DET
ejpam-4063	134	12	φ	φ	NOUN
ejpam-4063	134	13	(	(	PUNCT
ejpam-4063	134	14	e	e	X
ejpam-4063	134	15	2imπ	2imπ	NUM
ejpam-4063	134	16	a	a	PRON
ejpam-4063	134	17	,	,	PUNCT
ejpam-4063	134	18	−k	−k	PROPN
ejpam-4063	134	19	,	,	PUNCT
ejpam-4063	134	20	t+π	t+π	CCONJ
ejpam-4063	134	21	2π	2π	NOUN
ejpam-4063	134	22	)	)	PUNCT
ejpam-4063	134	23	a2	a2	PROPN
ejpam-4063	134	24	(	(	PUNCT
ejpam-4063	134	25	(	(	PUNCT
ejpam-4063	134	26	−1)k	−1)k	PROPN
ejpam-4063	134	27	+	+	NUM
ejpam-4063	134	28	1	1	X
ejpam-4063	134	29	)	)	PUNCT
ejpam-4063	135	1	+	+	CCONJ
ejpam-4063	135	2	i2k−1kπk	i2k−1kπk	NOUN
ejpam-4063	135	3	(	(	PUNCT
ejpam-4063	135	4	i	i	PRON
ejpam-4063	135	5	a	a	X
ejpam-4063	135	6	)	)	PUNCT
ejpam-4063	135	7	k	k	PROPN
ejpam-4063	135	8	csc(t)e	csc(t)e	NOUN
ejpam-4063	135	9	2imt	2imt	NUM
ejpam-4063	135	10	a	a	DET
ejpam-4063	135	11	−	−	PROPN
ejpam-4063	135	12	im(t+π	im(t+π	PROPN
ejpam-4063	135	13	)	)	PUNCT
ejpam-4063	135	14	a	a	DET
ejpam-4063	135	15	φ	φ	X
ejpam-4063	135	16	(	(	PUNCT
ejpam-4063	135	17	e−	e−	PROPN
ejpam-4063	135	18	2imπ	2imπ	PROPN
ejpam-4063	135	19	a	a	DET
ejpam-4063	135	20	,	,	PUNCT
ejpam-4063	135	21	1−	1−	NUM
ejpam-4063	135	22	k	k	X
ejpam-4063	135	23	,	,	PUNCT
ejpam-4063	135	24	π−t	π−t	X
ejpam-4063	135	25	2π	2π	PROPN
ejpam-4063	135	26	)	)	PUNCT
ejpam-4063	136	1	a	a	DET
ejpam-4063	136	2	(	(	PUNCT
ejpam-4063	136	3	(	(	PUNCT
ejpam-4063	136	4	−1)k	−1)k	PROPN
ejpam-4063	136	5	+	+	NUM
ejpam-4063	136	6	1	1	X
ejpam-4063	136	7	)	)	PUNCT
ejpam-4063	136	8	−	−	PROPN
ejpam-4063	136	9	i2k−1kπk	i2k−1kπk	NOUN
ejpam-4063	136	10	(	(	PUNCT
ejpam-4063	136	11	i	i	PRON
ejpam-4063	136	12	a	a	X
ejpam-4063	136	13	)	)	PUNCT
ejpam-4063	136	14	k	k	PROPN
ejpam-4063	136	15	csc(t)e−	csc(t)e−	PROPN
ejpam-4063	136	16	im(t+π	im(t+π	PROPN
ejpam-4063	136	17	)	)	PUNCT
ejpam-4063	136	18	a	a	DET
ejpam-4063	136	19	φ	φ	X
ejpam-4063	136	20	(	(	PUNCT
ejpam-4063	136	21	e−	e−	PROPN
ejpam-4063	136	22	2imπ	2imπ	PROPN
ejpam-4063	136	23	a	a	DET
ejpam-4063	136	24	,	,	PUNCT
ejpam-4063	136	25	1−	1−	NUM
ejpam-4063	136	26	k	k	NOUN
ejpam-4063	136	27	,	,	PUNCT
ejpam-4063	136	28	t+π	t+π	NUM
ejpam-4063	136	29	2π	2π	NOUN
ejpam-4063	136	30	)	)	PUNCT
ejpam-4063	136	31	a	a	PRON
ejpam-4063	136	32	(	(	PUNCT
ejpam-4063	136	33	(	(	PUNCT
ejpam-4063	136	34	−1)k	−1)k	PROPN
ejpam-4063	136	35	+	+	NUM
ejpam-4063	136	36	1	1	X
ejpam-4063	136	37	)	)	PUNCT
ejpam-4063	136	38	−	−	PROPN
ejpam-4063	136	39	i2k−1kπk	i2k−1kπk	NOUN
ejpam-4063	136	40	(	(	PUNCT
ejpam-4063	136	41	i	i	PRON
ejpam-4063	136	42	a	a	X
ejpam-4063	136	43	)	)	PUNCT
ejpam-4063	136	44	k	k	NOUN
ejpam-4063	136	45	csc(t)e	csc(t)e	NOUN
ejpam-4063	136	46	2iπm	2iπm	PROPN
ejpam-4063	136	47	a	a	DET
ejpam-4063	136	48	−	−	PROPN
ejpam-4063	136	49	im(t+π	im(t+π	PROPN
ejpam-4063	136	50	)	)	PUNCT
ejpam-4063	136	51	a	a	DET
ejpam-4063	136	52	φ	φ	NOUN
ejpam-4063	136	53	(	(	PUNCT
ejpam-4063	136	54	e	e	X
ejpam-4063	136	55	2imπ	2imπ	NUM
ejpam-4063	136	56	a	a	DET
ejpam-4063	136	57	,	,	PUNCT
ejpam-4063	136	58	1−	1−	NUM
ejpam-4063	136	59	k	k	X
ejpam-4063	136	60	,	,	PUNCT
ejpam-4063	136	61	π−t	π−t	X
ejpam-4063	136	62	2π	2π	PROPN
ejpam-4063	136	63	)	)	PUNCT
ejpam-4063	136	64	a	a	PRON
ejpam-4063	136	65	(	(	PUNCT
ejpam-4063	136	66	(	(	PUNCT
ejpam-4063	136	67	−1)k	−1)k	PROPN
ejpam-4063	136	68	+	+	NUM
ejpam-4063	136	69	1	1	X
ejpam-4063	136	70	)	)	PUNCT
ejpam-4063	136	71	+	+	CCONJ
ejpam-4063	136	72	i2k−1kπk	i2k−1kπk	NOUN
ejpam-4063	136	73	(	(	PUNCT
ejpam-4063	136	74	i	i	PRON
ejpam-4063	136	75	a	a	X
ejpam-4063	136	76	)	)	PUNCT
ejpam-4063	136	77	k	k	PROPN
ejpam-4063	136	78	csc(t)e	csc(t)e	PROPN
ejpam-4063	136	79	im(t+π	im(t+π	PROPN
ejpam-4063	136	80	)	)	PUNCT
ejpam-4063	136	81	a	a	DET
ejpam-4063	136	82	φ	φ	NOUN
ejpam-4063	136	83	(	(	PUNCT
ejpam-4063	136	84	e	e	X
ejpam-4063	136	85	2imπ	2imπ	NUM
ejpam-4063	136	86	a	a	DET
ejpam-4063	136	87	,	,	PUNCT
ejpam-4063	136	88	1−	1−	NUM
ejpam-4063	136	89	k	k	NOUN
ejpam-4063	136	90	,	,	PUNCT
ejpam-4063	136	91	t+π	t+π	NUM
ejpam-4063	136	92	2π	2π	NOUN
ejpam-4063	136	93	)	)	PUNCT
ejpam-4063	136	94	a	a	DET
ejpam-4063	136	95	(	(	PUNCT
ejpam-4063	136	96	(	(	PUNCT
ejpam-4063	136	97	−1)k	−1)k	PROPN
ejpam-4063	136	98	+	+	NUM
ejpam-4063	136	99	1	1	X
ejpam-4063	136	100	)	)	PUNCT
ejpam-4063	136	101	(	(	PUNCT
ejpam-4063	136	102	14	14	NUM
ejpam-4063	136	103	)	)	PUNCT
ejpam-4063	136	104	note	note	NOUN
ejpam-4063	136	105	:	:	PUNCT
ejpam-4063	136	106	when	when	SCONJ
ejpam-4063	136	107	we	we	PRON
ejpam-4063	136	108	replace	replace	VERB
ejpam-4063	136	109	k	k	PROPN
ejpam-4063	136	110	by	by	ADP
ejpam-4063	136	111	k	k	PROPN
ejpam-4063	136	112	−	−	PROPN
ejpam-4063	136	113	1	1	NUM
ejpam-4063	136	114	we	we	PRON
ejpam-4063	136	115	get	get	VERB
ejpam-4063	136	116	the	the	DET
ejpam-4063	136	117	mellin	mellin	NOUN
ejpam-4063	136	118	transform	transform	NOUN
ejpam-4063	136	119	.	.	PUNCT
ejpam-4063	137	1	next	next	ADV
ejpam-4063	137	2	we	we	PRON
ejpam-4063	137	3	set	set	VERB
ejpam-4063	137	4	k	k	PROPN
ejpam-4063	137	5	=	=	PUNCT
ejpam-4063	137	6	0	0	PROPN
ejpam-4063	137	7	and	and	CCONJ
ejpam-4063	137	8	m	m	PROPN
ejpam-4063	137	9	=	=	SYM
ejpam-4063	137	10	b	b	NOUN
ejpam-4063	137	11	simplify	simplify	NOUN
ejpam-4063	137	12	to	to	PART
ejpam-4063	137	13	get	get	VERB
ejpam-4063	137	14	(	(	PUNCT
ejpam-4063	137	15	15	15	NUM
ejpam-4063	137	16	)	)	PUNCT
ejpam-4063	137	17	∫	∫	PROPN
ejpam-4063	138	1	∞	∞	PROPN
ejpam-4063	138	2	0	0	NUM
ejpam-4063	138	3	sinh(ax	sinh(ax	NOUN
ejpam-4063	138	4	)	)	PUNCT
ejpam-4063	138	5	sinh(bx	sinh(bx	PROPN
ejpam-4063	138	6	)	)	PUNCT
ejpam-4063	138	7	(	(	PUNCT
ejpam-4063	138	8	cosh(ax	cosh(ax	NOUN
ejpam-4063	138	9	)	)	PUNCT
ejpam-4063	138	10	+	+	CCONJ
ejpam-4063	139	1	cos(t))2	cos(t))2	ADP
ejpam-4063	139	2	dx	dx	PROPN
ejpam-4063	139	3	=	=	NOUN
ejpam-4063	139	4	πb	πb	PROPN
ejpam-4063	139	5	csc(t	csc(t	PROPN
ejpam-4063	139	6	)	)	PUNCT
ejpam-4063	139	7	csc	csc	PROPN
ejpam-4063	139	8	(	(	PUNCT
ejpam-4063	139	9	πb	πb	INTJ
ejpam-4063	139	10	a	a	PRON
ejpam-4063	139	11	)	)	PUNCT
ejpam-4063	139	12	sin	sin	NOUN
ejpam-4063	139	13	(	(	PUNCT
ejpam-4063	139	14	bt	bt	NOUN
ejpam-4063	139	15	a	a	PRON
ejpam-4063	139	16	)	)	PUNCT
ejpam-4063	139	17	a2	a2	PROPN
ejpam-4063	139	18	from	from	ADP
ejpam-4063	139	19	entry	entry	NOUN
ejpam-4063	139	20	(	(	PUNCT
ejpam-4063	139	21	2	2	NUM
ejpam-4063	139	22	)	)	PUNCT
ejpam-4063	139	23	in	in	ADP
ejpam-4063	139	24	table	table	NOUN
ejpam-4063	139	25	(	(	PUNCT
ejpam-4063	139	26	64:12:7	64:12:7	NUM
ejpam-4063	139	27	)	)	PUNCT
ejpam-4063	139	28	in	in	ADP
ejpam-4063	139	29	[	[	X
ejpam-4063	139	30	5	5	NUM
ejpam-4063	139	31	]	]	PUNCT
ejpam-4063	139	32	,	,	PUNCT
ejpam-4063	139	33	where	where	SCONJ
ejpam-4063	139	34	−π	−π	ADV
ejpam-4063	139	35	<	<	X
ejpam-4063	139	36	re(t	re(t	PUNCT
ejpam-4063	139	37	)	)	PUNCT
ejpam-4063	139	38	<	<	X
ejpam-4063	139	39	π	π	X
ejpam-4063	139	40	and	and	CCONJ
ejpam-4063	139	41	0	0	NUM
ejpam-4063	139	42	<	<	X
ejpam-4063	139	43	|b|	|b|	PROPN
ejpam-4063	139	44	<	<	X
ejpam-4063	139	45	a.	a.	NOUN
ejpam-4063	139	46	8	8	NUM
ejpam-4063	139	47	.	.	PUNCT
ejpam-4063	140	1	derivation	derivation	NOUN
ejpam-4063	140	2	of	of	ADP
ejpam-4063	140	3	entry	entry	NOUN
ejpam-4063	140	4	(	(	PUNCT
ejpam-4063	140	5	2.3.1.19	2.3.1.19	NOUN
ejpam-4063	140	6	)	)	PUNCT
ejpam-4063	140	7	in	in	ADP
ejpam-4063	140	8	[	[	X
ejpam-4063	140	9	2	2	X
ejpam-4063	140	10	]	]	PUNCT
ejpam-4063	140	11	using	use	VERB
ejpam-4063	140	12	equation	equation	NOUN
ejpam-4063	140	13	(	(	PUNCT
ejpam-4063	140	14	13	13	NUM
ejpam-4063	140	15	)	)	PUNCT
ejpam-4063	140	16	and	and	CCONJ
ejpam-4063	140	17	setting	set	VERB
ejpam-4063	140	18	m	m	NOUN
ejpam-4063	140	19	=	=	SYM
ejpam-4063	140	20	0	0	NUM
ejpam-4063	140	21	simplifying	simplify	VERB
ejpam-4063	140	22	we	we	PRON
ejpam-4063	140	23	get	get	VERB
ejpam-4063	140	24	r.	r.	PROPN
ejpam-4063	140	25	reynolds	reynolds	PROPN
ejpam-4063	140	26	,	,	PUNCT
ejpam-4063	140	27	a.	a.	PROPN
ejpam-4063	140	28	stauffer	stauffer	PROPN
ejpam-4063	140	29	/	/	SYM
ejpam-4063	140	30	eur	eur	PROPN
ejpam-4063	140	31	.	.	PUNCT
ejpam-4063	141	1	j.	j.	PROPN
ejpam-4063	141	2	pure	pure	PROPN
ejpam-4063	141	3	appl	appl	PROPN
ejpam-4063	141	4	.	.	PROPN
ejpam-4063	141	5	math	math	PROPN
ejpam-4063	141	6	,	,	PUNCT
ejpam-4063	141	7	14	14	NUM
ejpam-4063	141	8	(	(	PUNCT
ejpam-4063	141	9	4	4	NUM
ejpam-4063	141	10	)	)	PUNCT
ejpam-4063	141	11	(	(	PUNCT
ejpam-4063	141	12	2021	2021	NUM
ejpam-4063	141	13	)	)	PUNCT
ejpam-4063	141	14	,	,	PUNCT
ejpam-4063	141	15	1249	1249	NUM
ejpam-4063	141	16	-	-	SYM
ejpam-4063	141	17	1265	1265	NUM
ejpam-4063	141	18	1257	1257	NUM
ejpam-4063	141	19	(	(	PUNCT
ejpam-4063	141	20	16	16	NUM
ejpam-4063	141	21	)	)	PUNCT
ejpam-4063	141	22	∫	∫	PROPN
ejpam-4063	142	1	∞	∞	PROPN
ejpam-4063	142	2	0	0	NUM
ejpam-4063	142	3	xk	xk	PROPN
ejpam-4063	142	4	sinh(ax	sinh(ax	PROPN
ejpam-4063	142	5	)	)	PUNCT
ejpam-4063	142	6	(	(	PUNCT
ejpam-4063	142	7	cosh(ax	cosh(ax	NOUN
ejpam-4063	142	8	)	)	PUNCT
ejpam-4063	142	9	+	+	CCONJ
ejpam-4063	143	1	cos(t))2	cos(t))2	ADP
ejpam-4063	143	2	dx	dx	PROPN
ejpam-4063	143	3	=	=	SYM
ejpam-4063	143	4	2k−1kπk	2k−1kπk	NUM
ejpam-4063	143	5	(	(	PUNCT
ejpam-4063	143	6	1	1	NUM
ejpam-4063	143	7	a	a	X
ejpam-4063	143	8	)	)	PUNCT
ejpam-4063	144	1	k+1	k+1	PROPN
ejpam-4063	144	2	csc	csc	PROPN
ejpam-4063	144	3	(	(	PUNCT
ejpam-4063	144	4	πk	πk	PROPN
ejpam-4063	144	5	2	2	NUM
ejpam-4063	144	6	)	)	PUNCT
ejpam-4063	144	7	csc(t	csc(t	PROPN
ejpam-4063	144	8	)	)	PUNCT
ejpam-4063	144	9	(	(	PUNCT
ejpam-4063	144	10	ζ	ζ	X
ejpam-4063	144	11	(	(	PUNCT
ejpam-4063	144	12	1−	1−	NUM
ejpam-4063	144	13	k	k	NOUN
ejpam-4063	144	14	,	,	PUNCT
ejpam-4063	144	15	π	π	PROPN
ejpam-4063	144	16	−	−	PROPN
ejpam-4063	144	17	t	t	PROPN
ejpam-4063	144	18	2π	2π	NOUN
ejpam-4063	144	19	)	)	PUNCT
ejpam-4063	145	1	−	−	PROPN
ejpam-4063	145	2	ζ	ζ	NOUN
ejpam-4063	145	3	(	(	PUNCT
ejpam-4063	145	4	1−	1−	NUM
ejpam-4063	145	5	k	k	NOUN
ejpam-4063	145	6	,	,	PUNCT
ejpam-4063	145	7	t+	t+	PUNCT
ejpam-4063	145	8	π	π	PROPN
ejpam-4063	145	9	2π	2π	PROPN
ejpam-4063	145	10	)	)	PUNCT
ejpam-4063	145	11	)	)	PUNCT
ejpam-4063	146	1	next	next	ADV
ejpam-4063	146	2	we	we	PRON
ejpam-4063	146	3	set	set	VERB
ejpam-4063	146	4	t	t	PROPN
ejpam-4063	146	5	=	=	PUNCT
ejpam-4063	146	6	π/2	π/2	NUM
ejpam-4063	146	7	simplify	simplify	VERB
ejpam-4063	146	8	to	to	PART
ejpam-4063	146	9	get	get	VERB
ejpam-4063	146	10	(	(	PUNCT
ejpam-4063	146	11	17	17	NUM
ejpam-4063	146	12	)	)	PUNCT
ejpam-4063	146	13	∫	∫	PROPN
ejpam-4063	146	14	∞	∞	PROPN
ejpam-4063	146	15	0	0	NUM
ejpam-4063	147	1	xs−1	xs−1	PROPN
ejpam-4063	147	2	tanh(ax)sech(ax)dx	tanh(ax)sech(ax)dx	PROPN
ejpam-4063	147	3	=	=	PUNCT
ejpam-4063	147	4	−2s−2πs−1(s−	−2s−2πs−1(s−	NOUN
ejpam-4063	147	5	1	1	NUM
ejpam-4063	147	6	)	)	PUNCT
ejpam-4063	147	7	(	(	PUNCT
ejpam-4063	147	8	1	1	NUM
ejpam-4063	147	9	a	a	X
ejpam-4063	147	10	)	)	PUNCT
ejpam-4063	147	11	s	s	NOUN
ejpam-4063	147	12	(	(	PUNCT
ejpam-4063	147	13	ζ	ζ	NOUN
ejpam-4063	147	14	(	(	PUNCT
ejpam-4063	147	15	2−	2−	NUM
ejpam-4063	147	16	s	s	NOUN
ejpam-4063	147	17	,	,	PUNCT
ejpam-4063	147	18	1	1	NUM
ejpam-4063	147	19	4	4	NUM
ejpam-4063	147	20	)	)	PUNCT
ejpam-4063	147	21	−	−	PROPN
ejpam-4063	148	1	ζ	ζ	NOUN
ejpam-4063	148	2	(	(	PUNCT
ejpam-4063	148	3	2−	2−	NUM
ejpam-4063	148	4	s	s	NOUN
ejpam-4063	148	5	,	,	PUNCT
ejpam-4063	148	6	3	3	NUM
ejpam-4063	148	7	4	4	NUM
ejpam-4063	148	8	)	)	PUNCT
ejpam-4063	148	9	)	)	PUNCT
ejpam-4063	148	10	sec	sec	PROPN
ejpam-4063	149	1	(	(	PUNCT
ejpam-4063	149	2	πs	πs	PROPN
ejpam-4063	149	3	2	2	NUM
ejpam-4063	149	4	)	)	PUNCT
ejpam-4063	149	5	from	from	ADP
ejpam-4063	149	6	entries	entry	NOUN
ejpam-4063	149	7	(	(	PUNCT
ejpam-4063	149	8	2	2	NUM
ejpam-4063	149	9	)	)	PUNCT
ejpam-4063	149	10	and	and	CCONJ
ejpam-4063	149	11	(	(	PUNCT
ejpam-4063	149	12	3	3	X
ejpam-4063	149	13	)	)	PUNCT
ejpam-4063	149	14	in	in	ADP
ejpam-4063	149	15	table	table	NOUN
ejpam-4063	149	16	(	(	PUNCT
ejpam-4063	149	17	64:12:7	64:12:7	NUM
ejpam-4063	149	18	)	)	PUNCT
ejpam-4063	149	19	in	in	ADP
ejpam-4063	149	20	[	[	X
ejpam-4063	149	21	5	5	NUM
ejpam-4063	149	22	]	]	PUNCT
ejpam-4063	149	23	.	.	PUNCT
ejpam-4063	150	1	9	9	X
ejpam-4063	150	2	.	.	X
ejpam-4063	150	3	derivation	derivation	NOUN
ejpam-4063	150	4	of	of	ADP
ejpam-4063	150	5	a	a	DET
ejpam-4063	150	6	new	new	ADJ
ejpam-4063	150	7	entry	entry	NOUN
ejpam-4063	150	8	for	for	ADP
ejpam-4063	150	9	table	table	NOUN
ejpam-4063	150	10	3.514	3.514	NUM
ejpam-4063	150	11	in	in	ADP
ejpam-4063	150	12	[	[	X
ejpam-4063	150	13	3	3	NUM
ejpam-4063	150	14	]	]	PUNCT
ejpam-4063	150	15	using	use	VERB
ejpam-4063	150	16	equation	equation	NOUN
ejpam-4063	150	17	(	(	PUNCT
ejpam-4063	150	18	12	12	NUM
ejpam-4063	150	19	)	)	PUNCT
ejpam-4063	150	20	and	and	CCONJ
ejpam-4063	150	21	setting	set	VERB
ejpam-4063	150	22	k	k	PROPN
ejpam-4063	150	23	=	=	PUNCT
ejpam-4063	150	24	−1	−1	NOUN
ejpam-4063	150	25	,	,	PUNCT
ejpam-4063	150	26	α	α	NOUN
ejpam-4063	150	27	=	=	SYM
ejpam-4063	150	28	−1	−1	NOUN
ejpam-4063	150	29	,	,	PUNCT
ejpam-4063	150	30	a	a	DET
ejpam-4063	150	31	=	=	SYM
ejpam-4063	150	32	1	1	NUM
ejpam-4063	150	33	,	,	PUNCT
ejpam-4063	150	34	t	t	NOUN
ejpam-4063	150	35	=	=	SYM
ejpam-4063	150	36	π/2,m	π/2,m	NOUN
ejpam-4063	150	37	=	=	NOUN
ejpam-4063	150	38	1/2	1/2	NUM
ejpam-4063	150	39	and	and	CCONJ
ejpam-4063	150	40	simplifying	simplify	VERB
ejpam-4063	150	41	we	we	PRON
ejpam-4063	150	42	get	get	VERB
ejpam-4063	150	43	r.	r.	PROPN
ejpam-4063	150	44	reynolds	reynolds	PROPN
ejpam-4063	150	45	,	,	PUNCT
ejpam-4063	150	46	a.	a.	PROPN
ejpam-4063	150	47	stauffer	stauffer	PROPN
ejpam-4063	150	48	/	/	SYM
ejpam-4063	150	49	eur	eur	PROPN
ejpam-4063	150	50	.	.	PUNCT
ejpam-4063	151	1	j.	j.	PROPN
ejpam-4063	151	2	pure	pure	PROPN
ejpam-4063	151	3	appl	appl	PROPN
ejpam-4063	151	4	.	.	PROPN
ejpam-4063	151	5	math	math	PROPN
ejpam-4063	151	6	,	,	PUNCT
ejpam-4063	151	7	14	14	NUM
ejpam-4063	151	8	(	(	PUNCT
ejpam-4063	151	9	4	4	NUM
ejpam-4063	151	10	)	)	PUNCT
ejpam-4063	151	11	(	(	PUNCT
ejpam-4063	151	12	2021	2021	NUM
ejpam-4063	151	13	)	)	PUNCT
ejpam-4063	151	14	,	,	PUNCT
ejpam-4063	151	15	1249	1249	NUM
ejpam-4063	151	16	-	-	SYM
ejpam-4063	151	17	1265	1265	NUM
ejpam-4063	151	18	1258	1258	NUM
ejpam-4063	151	19	(	(	PUNCT
ejpam-4063	151	20	18	18	NUM
ejpam-4063	151	21	)	)	PUNCT
ejpam-4063	151	22	∫	∫	PROPN
ejpam-4063	152	1	∞	∞	PROPN
ejpam-4063	152	2	0	0	NUM
ejpam-4063	152	3	sinh	sinh	NOUN
ejpam-4063	152	4	(	(	PUNCT
ejpam-4063	152	5	x	x	SYM
ejpam-4063	152	6	2	2	X
ejpam-4063	152	7	)	)	PUNCT
ejpam-4063	152	8	tanh(x)sech(x	tanh(x)sech(x	NOUN
ejpam-4063	152	9	)	)	PUNCT
ejpam-4063	153	1	x2	x2	PROPN
ejpam-4063	154	1	+	+	CCONJ
ejpam-4063	154	2	π2	π2	ADJ
ejpam-4063	154	3	dx	dx	PROPN
ejpam-4063	155	1	=	=	SYM
ejpam-4063	155	2	√	√	PROPN
ejpam-4063	155	3	2	2	NUM
ejpam-4063	155	4	32π2	32π2	NUM
ejpam-4063	155	5	(	(	PUNCT
ejpam-4063	155	6	−ψ(1	−ψ(1	PROPN
ejpam-4063	155	7	)	)	PUNCT
ejpam-4063	155	8	(	(	PUNCT
ejpam-4063	155	9	3	3	NUM
ejpam-4063	155	10	8	8	NUM
ejpam-4063	155	11	)	)	PUNCT
ejpam-4063	155	12	+	+	CCONJ
ejpam-4063	155	13	ψ(1	ψ(1	X
ejpam-4063	155	14	)	)	PUNCT
ejpam-4063	155	15	(	(	PUNCT
ejpam-4063	155	16	5	5	NUM
ejpam-4063	155	17	8	8	NUM
ejpam-4063	155	18	)	)	PUNCT
ejpam-4063	155	19	+	+	CCONJ
ejpam-4063	155	20	ψ(1	ψ(1	X
ejpam-4063	155	21	)	)	PUNCT
ejpam-4063	155	22	(	(	PUNCT
ejpam-4063	155	23	7	7	NUM
ejpam-4063	155	24	8	8	NUM
ejpam-4063	155	25	)	)	PUNCT
ejpam-4063	155	26	−	−	NOUN
ejpam-4063	155	27	ψ(1	ψ(1	PROPN
ejpam-4063	155	28	)	)	PUNCT
ejpam-4063	155	29	(	(	PUNCT
ejpam-4063	155	30	9	9	NUM
ejpam-4063	155	31	8	8	NUM
ejpam-4063	155	32	)	)	PUNCT
ejpam-4063	155	33	)	)	PUNCT
ejpam-4063	156	1	+	+	CCONJ
ejpam-4063	156	2	16π	16π	X
ejpam-4063	156	3	(	(	PUNCT
ejpam-4063	156	4	√	√	ADP
ejpam-4063	156	5	2	2	NUM
ejpam-4063	156	6	+	+	CCONJ
ejpam-4063	156	7	log	log	NOUN
ejpam-4063	156	8	(	(	PUNCT
ejpam-4063	156	9	tan	tan	PROPN
ejpam-4063	156	10	(	(	PUNCT
ejpam-4063	156	11	π	π	PROPN
ejpam-4063	156	12	8	8	NUM
ejpam-4063	156	13	)	)	PUNCT
ejpam-4063	156	14	)	)	PUNCT
ejpam-4063	156	15	)	)	PUNCT
ejpam-4063	156	16	from	from	ADP
ejpam-4063	156	17	entry	entry	NOUN
ejpam-4063	156	18	(	(	PUNCT
ejpam-4063	156	19	3	3	NUM
ejpam-4063	156	20	)	)	PUNCT
ejpam-4063	156	21	table	table	NOUN
ejpam-4063	156	22	(	(	PUNCT
ejpam-4063	156	23	64:12:7:2	64:12:7:2	NOUN
ejpam-4063	156	24	)	)	PUNCT
ejpam-4063	156	25	and	and	CCONJ
ejpam-4063	156	26	entry	entry	NOUN
ejpam-4063	156	27	(	(	PUNCT
ejpam-4063	156	28	4	4	NUM
ejpam-4063	156	29	)	)	PUNCT
ejpam-4063	156	30	table	table	NOUN
ejpam-4063	156	31	(	(	PUNCT
ejpam-4063	156	32	64:12:7:3	64:12:7:3	NOUN
ejpam-4063	156	33	)	)	PUNCT
ejpam-4063	156	34	.	.	PUNCT
ejpam-4063	157	1	10	10	NUM
ejpam-4063	157	2	.	.	PUNCT
ejpam-4063	158	1	definite	definite	ADJ
ejpam-4063	158	2	integral	integral	ADJ
ejpam-4063	158	3	in	in	ADP
ejpam-4063	158	4	terms	term	NOUN
ejpam-4063	158	5	of	of	ADP
ejpam-4063	158	6	the	the	DET
ejpam-4063	158	7	hurwitz	hurwitz	PROPN
ejpam-4063	158	8	zeta	zeta	PROPN
ejpam-4063	158	9	function	function	NOUN
ejpam-4063	158	10	using	use	VERB
ejpam-4063	158	11	equation	equation	NOUN
ejpam-4063	158	12	(	(	PUNCT
ejpam-4063	158	13	14	14	NUM
ejpam-4063	158	14	)	)	PUNCT
ejpam-4063	158	15	and	and	CCONJ
ejpam-4063	158	16	setting	set	VERB
ejpam-4063	158	17	m	m	NOUN
ejpam-4063	158	18	=	=	SYM
ejpam-4063	158	19	1	1	NUM
ejpam-4063	158	20	and	and	CCONJ
ejpam-4063	158	21	a	a	DET
ejpam-4063	158	22	=	=	SYM
ejpam-4063	158	23	2	2	NUM
ejpam-4063	158	24	to	to	PART
ejpam-4063	158	25	get	get	VERB
ejpam-4063	158	26	(	(	PUNCT
ejpam-4063	158	27	19	19	NUM
ejpam-4063	158	28	)	)	PUNCT
ejpam-4063	158	29	∫	∫	PROPN
ejpam-4063	159	1	∞	∞	PROPN
ejpam-4063	159	2	0	0	NUM
ejpam-4063	159	3	xk	xk	PROPN
ejpam-4063	159	4	sinh(x	sinh(x	PROPN
ejpam-4063	159	5	)	)	PUNCT
ejpam-4063	159	6	sinh(2x	sinh(2x	PROPN
ejpam-4063	159	7	)	)	PUNCT
ejpam-4063	159	8	(	(	PUNCT
ejpam-4063	159	9	cos(t	cos(t	PROPN
ejpam-4063	159	10	)	)	PUNCT
ejpam-4063	159	11	+	+	NUM
ejpam-4063	159	12	cosh(2x))2	cosh(2x))2	NOUN
ejpam-4063	159	13	=	=	PUNCT
ejpam-4063	160	1	2k−3e	2k−3e	NUM
ejpam-4063	160	2	iπk	iπk	NOUN
ejpam-4063	160	3	2	2	NUM
ejpam-4063	160	4	kπk	kπk	PROPN
ejpam-4063	160	5	csc	csc	PROPN
ejpam-4063	160	6	(	(	PUNCT
ejpam-4063	160	7	t	t	PROPN
ejpam-4063	160	8	2	2	NUM
ejpam-4063	160	9	)	)	PUNCT
ejpam-4063	160	10	ζ	ζ	NOUN
ejpam-4063	160	11	(	(	PUNCT
ejpam-4063	160	12	1−	1−	NUM
ejpam-4063	160	13	k	k	NOUN
ejpam-4063	160	14	,	,	PUNCT
ejpam-4063	160	15	π−t	π−t	NOUN
ejpam-4063	160	16	4π	4π	NUM
ejpam-4063	160	17	)	)	PUNCT
ejpam-4063	160	18	(	(	PUNCT
ejpam-4063	160	19	−1)k	−1)k	PROPN
ejpam-4063	160	20	+	+	CCONJ
ejpam-4063	160	21	1	1	NUM
ejpam-4063	160	22	−	−	NOUN
ejpam-4063	160	23	2k−3e	2k−3e	NUM
ejpam-4063	160	24	iπk	iπk	NOUN
ejpam-4063	160	25	2	2	NUM
ejpam-4063	160	26	kπk	kπk	PROPN
ejpam-4063	160	27	csc	csc	PROPN
ejpam-4063	160	28	(	(	PUNCT
ejpam-4063	160	29	t	t	PROPN
ejpam-4063	160	30	2	2	NUM
ejpam-4063	160	31	)	)	PUNCT
ejpam-4063	160	32	ζ	ζ	NOUN
ejpam-4063	160	33	(	(	PUNCT
ejpam-4063	160	34	1−	1−	NUM
ejpam-4063	160	35	k	k	NOUN
ejpam-4063	160	36	,	,	PUNCT
ejpam-4063	160	37	t+π	t+π	NOUN
ejpam-4063	160	38	4π	4π	NUM
ejpam-4063	160	39	)	)	PUNCT
ejpam-4063	160	40	(	(	PUNCT
ejpam-4063	160	41	−1)k	−1)k	PROPN
ejpam-4063	160	42	+	+	CCONJ
ejpam-4063	160	43	1	1	NUM
ejpam-4063	160	44	−	−	NOUN
ejpam-4063	160	45	2k−3e	2k−3e	NUM
ejpam-4063	160	46	iπk	iπk	NOUN
ejpam-4063	160	47	2	2	NUM
ejpam-4063	160	48	kπk	kπk	PROPN
ejpam-4063	160	49	csc	csc	PROPN
ejpam-4063	160	50	(	(	PUNCT
ejpam-4063	160	51	t	t	PROPN
ejpam-4063	160	52	2	2	NUM
ejpam-4063	160	53	)	)	PUNCT
ejpam-4063	160	54	ζ	ζ	NOUN
ejpam-4063	160	55	(	(	PUNCT
ejpam-4063	160	56	1−	1−	NUM
ejpam-4063	160	57	k	k	NOUN
ejpam-4063	160	58	,	,	PUNCT
ejpam-4063	160	59	34	34	NUM
ejpam-4063	160	60	−	−	NOUN
ejpam-4063	160	61	t	t	NOUN
ejpam-4063	160	62	4π	4π	NUM
ejpam-4063	160	63	)	)	PUNCT
ejpam-4063	160	64	(	(	PUNCT
ejpam-4063	160	65	−1)k	−1)k	PROPN
ejpam-4063	160	66	+	+	CCONJ
ejpam-4063	160	67	1	1	NUM
ejpam-4063	160	68	+	+	NUM
ejpam-4063	160	69	2k−3e	2k−3e	NUM
ejpam-4063	160	70	iπk	iπk	NOUN
ejpam-4063	160	71	2	2	NUM
ejpam-4063	160	72	kπk	kπk	PROPN
ejpam-4063	160	73	csc	csc	PROPN
ejpam-4063	160	74	(	(	PUNCT
ejpam-4063	160	75	t	t	PROPN
ejpam-4063	160	76	2	2	NUM
ejpam-4063	160	77	)	)	PUNCT
ejpam-4063	160	78	ζ	ζ	NOUN
ejpam-4063	160	79	(	(	PUNCT
ejpam-4063	160	80	1−	1−	NUM
ejpam-4063	160	81	k	k	NOUN
ejpam-4063	160	82	,	,	PUNCT
ejpam-4063	160	83	14	14	NUM
ejpam-4063	160	84	(	(	PUNCT
ejpam-4063	160	85	t	t	PROPN
ejpam-4063	160	86	π	π	PROPN
ejpam-4063	160	87	+	+	CCONJ
ejpam-4063	160	88	3	3	NUM
ejpam-4063	160	89	)	)	PUNCT
ejpam-4063	160	90	)	)	PUNCT
ejpam-4063	161	1	(	(	PUNCT
ejpam-4063	161	2	−1)k	−1)k	PROPN
ejpam-4063	161	3	+	+	CCONJ
ejpam-4063	161	4	1	1	NUM
ejpam-4063	161	5	+	+	SYM
ejpam-4063	161	6	2k−2e	2k−2e	NUM
ejpam-4063	161	7	iπk	iπk	NOUN
ejpam-4063	161	8	2	2	NUM
ejpam-4063	161	9	πk+1	πk+1	NOUN
ejpam-4063	161	10	sec	sec	PROPN
ejpam-4063	161	11	(	(	PUNCT
ejpam-4063	161	12	t	t	PROPN
ejpam-4063	161	13	2	2	NUM
ejpam-4063	161	14	)	)	PUNCT
ejpam-4063	161	15	ζ	ζ	NOUN
ejpam-4063	161	16	(	(	PUNCT
ejpam-4063	161	17	−k	−k	PROPN
ejpam-4063	161	18	,	,	PUNCT
ejpam-4063	161	19	π−t	π−t	NOUN
ejpam-4063	161	20	4π	4π	NUM
ejpam-4063	161	21	)	)	PUNCT
ejpam-4063	161	22	(	(	PUNCT
ejpam-4063	161	23	−1)k	−1)k	PROPN
ejpam-4063	161	24	+	+	CCONJ
ejpam-4063	161	25	1	1	NUM
ejpam-4063	161	26	+	+	SYM
ejpam-4063	161	27	2k−2e	2k−2e	NUM
ejpam-4063	161	28	iπk	iπk	NOUN
ejpam-4063	161	29	2	2	NUM
ejpam-4063	161	30	πk+1	πk+1	NOUN
ejpam-4063	161	31	sec	sec	PROPN
ejpam-4063	161	32	(	(	PUNCT
ejpam-4063	161	33	t	t	PROPN
ejpam-4063	161	34	2	2	NUM
ejpam-4063	161	35	)	)	PUNCT
ejpam-4063	161	36	ζ	ζ	NOUN
ejpam-4063	161	37	(	(	PUNCT
ejpam-4063	161	38	−k	−k	PROPN
ejpam-4063	161	39	,	,	PUNCT
ejpam-4063	161	40	t+π	t+π	NOUN
ejpam-4063	161	41	4π	4π	NUM
ejpam-4063	161	42	)	)	PUNCT
ejpam-4063	161	43	(	(	PUNCT
ejpam-4063	161	44	−1)k	−1)k	PROPN
ejpam-4063	161	45	+	+	CCONJ
ejpam-4063	161	46	1	1	NUM
ejpam-4063	161	47	−	−	PROPN
ejpam-4063	161	48	2k−2e	2k−2e	NUM
ejpam-4063	161	49	iπk	iπk	NOUN
ejpam-4063	161	50	2	2	NUM
ejpam-4063	161	51	πk+1	πk+1	NOUN
ejpam-4063	161	52	sec	sec	PROPN
ejpam-4063	161	53	(	(	PUNCT
ejpam-4063	161	54	t	t	PROPN
ejpam-4063	161	55	2	2	NUM
ejpam-4063	161	56	)	)	PUNCT
ejpam-4063	161	57	ζ	ζ	NOUN
ejpam-4063	161	58	(	(	PUNCT
ejpam-4063	161	59	−k	−k	PROPN
ejpam-4063	161	60	,	,	PUNCT
ejpam-4063	161	61	34	34	NUM
ejpam-4063	161	62	−	−	NOUN
ejpam-4063	161	63	t	t	NOUN
ejpam-4063	161	64	4π	4π	NUM
ejpam-4063	161	65	)	)	PUNCT
ejpam-4063	161	66	(	(	PUNCT
ejpam-4063	161	67	−1)k	−1)k	PROPN
ejpam-4063	161	68	+	+	CCONJ
ejpam-4063	161	69	1	1	NUM
ejpam-4063	161	70	−	−	PROPN
ejpam-4063	161	71	2k−2e	2k−2e	NUM
ejpam-4063	161	72	iπk	iπk	NOUN
ejpam-4063	161	73	2	2	NUM
ejpam-4063	161	74	πk+1	πk+1	NOUN
ejpam-4063	161	75	sec	sec	PROPN
ejpam-4063	161	76	(	(	PUNCT
ejpam-4063	161	77	t	t	PROPN
ejpam-4063	161	78	2	2	NUM
ejpam-4063	161	79	)	)	PUNCT
ejpam-4063	161	80	ζ	ζ	NOUN
ejpam-4063	161	81	(	(	PUNCT
ejpam-4063	161	82	−k	−k	PROPN
ejpam-4063	161	83	,	,	PUNCT
ejpam-4063	161	84	14	14	NUM
ejpam-4063	161	85	(	(	PUNCT
ejpam-4063	161	86	t	t	PROPN
ejpam-4063	161	87	π	π	PROPN
ejpam-4063	161	88	+	+	CCONJ
ejpam-4063	161	89	3	3	NUM
ejpam-4063	161	90	)	)	PUNCT
ejpam-4063	161	91	)	)	PUNCT
ejpam-4063	162	1	(	(	PUNCT
ejpam-4063	162	2	−1)k	−1)k	PROPN
ejpam-4063	162	3	+	+	CCONJ
ejpam-4063	162	4	1	1	NUM
ejpam-4063	162	5	next	next	ADV
ejpam-4063	162	6	we	we	PRON
ejpam-4063	162	7	apply	apply	VERB
ejpam-4063	162	8	l’hôpital	l’hôpital	ADJ
ejpam-4063	162	9	’s	’s	PART
ejpam-4063	162	10	rule	rule	NOUN
ejpam-4063	162	11	to	to	ADP
ejpam-4063	162	12	the	the	DET
ejpam-4063	162	13	right	right	ADJ
ejpam-4063	162	14	-	-	PUNCT
ejpam-4063	162	15	hand	hand	NOUN
ejpam-4063	162	16	side	side	NOUN
ejpam-4063	162	17	as	as	ADP
ejpam-4063	162	18	k	k	PROPN
ejpam-4063	162	19	→	→	SYM
ejpam-4063	162	20	0	0	NUM
ejpam-4063	162	21	to	to	PART
ejpam-4063	162	22	get	get	VERB
ejpam-4063	162	23	r.	r.	PROPN
ejpam-4063	162	24	reynolds	reynolds	PROPN
ejpam-4063	162	25	,	,	PUNCT
ejpam-4063	162	26	a.	a.	PROPN
ejpam-4063	162	27	stauffer	stauffer	PROPN
ejpam-4063	162	28	/	/	SYM
ejpam-4063	162	29	eur	eur	PROPN
ejpam-4063	162	30	.	.	PUNCT
ejpam-4063	163	1	j.	j.	PROPN
ejpam-4063	163	2	pure	pure	PROPN
ejpam-4063	163	3	appl	appl	PROPN
ejpam-4063	163	4	.	.	PROPN
ejpam-4063	163	5	math	math	PROPN
ejpam-4063	163	6	,	,	PUNCT
ejpam-4063	163	7	14	14	NUM
ejpam-4063	163	8	(	(	PUNCT
ejpam-4063	163	9	4	4	NUM
ejpam-4063	163	10	)	)	PUNCT
ejpam-4063	163	11	(	(	PUNCT
ejpam-4063	163	12	2021	2021	NUM
ejpam-4063	163	13	)	)	PUNCT
ejpam-4063	163	14	,	,	PUNCT
ejpam-4063	163	15	1249	1249	NUM
ejpam-4063	163	16	-	-	SYM
ejpam-4063	163	17	1265	1265	NUM
ejpam-4063	163	18	1259	1259	NUM
ejpam-4063	163	19	(	(	PUNCT
ejpam-4063	163	20	20	20	NUM
ejpam-4063	163	21	)	)	PUNCT
ejpam-4063	163	22	∫	∫	PROPN
ejpam-4063	164	1	∞	∞	NUM
ejpam-4063	164	2	0	0	NUM
ejpam-4063	164	3	x	x	SYM
ejpam-4063	164	4	sinh(x	sinh(x	PROPN
ejpam-4063	164	5	)	)	PUNCT
ejpam-4063	164	6	sinh(2x	sinh(2x	PROPN
ejpam-4063	164	7	)	)	PUNCT
ejpam-4063	164	8	(	(	PUNCT
ejpam-4063	164	9	cos(t	cos(t	PROPN
ejpam-4063	164	10	)	)	PUNCT
ejpam-4063	165	1	+	+	NUM
ejpam-4063	165	2	cosh(2x))2	cosh(2x))2	NOUN
ejpam-4063	165	3	dx	dx	PROPN
ejpam-4063	165	4	=	=	SYM
ejpam-4063	165	5	1	1	NUM
ejpam-4063	165	6	2	2	NUM
ejpam-4063	165	7	π	π	PROPN
ejpam-4063	165	8	sec	sec	PROPN
ejpam-4063	165	9	(	(	PUNCT
ejpam-4063	165	10	t	t	PROPN
ejpam-4063	165	11	2	2	NUM
ejpam-4063	165	12	)	)	PUNCT
ejpam-4063	165	13	ζ	ζ	NOUN
ejpam-4063	165	14	(	(	PUNCT
ejpam-4063	165	15	−1	−1	NOUN
ejpam-4063	165	16	,	,	PUNCT
ejpam-4063	165	17	π	π	PROPN
ejpam-4063	165	18	−	−	PROPN
ejpam-4063	165	19	t	t	PROPN
ejpam-4063	165	20	4π	4π	NUM
ejpam-4063	165	21	)	)	PUNCT
ejpam-4063	166	1	+	+	CCONJ
ejpam-4063	166	2	1	1	NUM
ejpam-4063	166	3	2	2	NUM
ejpam-4063	166	4	π	π	PROPN
ejpam-4063	166	5	sec	sec	PROPN
ejpam-4063	166	6	(	(	PUNCT
ejpam-4063	166	7	t	t	PROPN
ejpam-4063	166	8	2	2	NUM
ejpam-4063	166	9	)	)	PUNCT
ejpam-4063	166	10	ζ	ζ	NOUN
ejpam-4063	166	11	(	(	PUNCT
ejpam-4063	166	12	−1	−1	NOUN
ejpam-4063	166	13	,	,	PUNCT
ejpam-4063	166	14	t+	t+	PUNCT
ejpam-4063	166	15	π	π	PROPN
ejpam-4063	166	16	4π	4π	NUM
ejpam-4063	166	17	)	)	PUNCT
ejpam-4063	167	1	−	−	PROPN
ejpam-4063	167	2	1	1	NUM
ejpam-4063	167	3	2	2	NUM
ejpam-4063	167	4	π	π	PROPN
ejpam-4063	167	5	sec	sec	PROPN
ejpam-4063	167	6	(	(	PUNCT
ejpam-4063	167	7	t	t	PROPN
ejpam-4063	167	8	2	2	NUM
ejpam-4063	167	9	)	)	PUNCT
ejpam-4063	167	10	ζ	ζ	NOUN
ejpam-4063	167	11	(	(	PUNCT
ejpam-4063	167	12	−1	−1	NOUN
ejpam-4063	167	13	,	,	PUNCT
ejpam-4063	167	14	3	3	NUM
ejpam-4063	167	15	4	4	NUM
ejpam-4063	167	16	−	−	NOUN
ejpam-4063	167	17	t	t	NOUN
ejpam-4063	167	18	4π	4π	NUM
ejpam-4063	167	19	)	)	PUNCT
ejpam-4063	168	1	−	−	PROPN
ejpam-4063	168	2	1	1	NUM
ejpam-4063	168	3	2	2	NUM
ejpam-4063	168	4	π	π	PROPN
ejpam-4063	168	5	sec	sec	PROPN
ejpam-4063	168	6	(	(	PUNCT
ejpam-4063	168	7	t	t	PROPN
ejpam-4063	168	8	2	2	NUM
ejpam-4063	168	9	)	)	PUNCT
ejpam-4063	168	10	ζ	ζ	NOUN
ejpam-4063	168	11	(	(	PUNCT
ejpam-4063	168	12	−1	−1	NOUN
ejpam-4063	168	13	,	,	PUNCT
ejpam-4063	168	14	1	1	NUM
ejpam-4063	168	15	4	4	NUM
ejpam-4063	168	16	(	(	PUNCT
ejpam-4063	168	17	t	t	PROPN
ejpam-4063	168	18	π	π	PROPN
ejpam-4063	168	19	+	+	CCONJ
ejpam-4063	168	20	3	3	NUM
ejpam-4063	168	21	)	)	PUNCT
ejpam-4063	168	22	)	)	PUNCT
ejpam-4063	169	1	+	+	CCONJ
ejpam-4063	169	2	1	1	NUM
ejpam-4063	169	3	4	4	NUM
ejpam-4063	169	4	csc	csc	PROPN
ejpam-4063	169	5	(	(	PUNCT
ejpam-4063	169	6	t	t	PROPN
ejpam-4063	169	7	2	2	NUM
ejpam-4063	169	8	)	)	PUNCT
ejpam-4063	169	9	log	log	NOUN
ejpam-4063	169	10	(	(	PUNCT
ejpam-4063	169	11	tan	tan	PROPN
ejpam-4063	169	12	(	(	PUNCT
ejpam-4063	169	13	t+	t+	NOUN
ejpam-4063	169	14	π	π	PROPN
ejpam-4063	169	15	4	4	NUM
ejpam-4063	169	16	)	)	PUNCT
ejpam-4063	169	17	)	)	PUNCT
ejpam-4063	169	18	from	from	ADP
ejpam-4063	169	19	entry	entry	NOUN
ejpam-4063	169	20	(	(	PUNCT
ejpam-4063	169	21	1	1	NUM
ejpam-4063	169	22	)	)	PUNCT
ejpam-4063	169	23	in	in	ADP
ejpam-4063	169	24	table	table	NOUN
ejpam-4063	169	25	(	(	PUNCT
ejpam-4063	169	26	64:4:2	64:4:2	NUM
ejpam-4063	169	27	)	)	PUNCT
ejpam-4063	169	28	in	in	ADP
ejpam-4063	169	29	[	[	X
ejpam-4063	169	30	5	5	NUM
ejpam-4063	169	31	]	]	PUNCT
ejpam-4063	169	32	,	,	PUNCT
ejpam-4063	169	33	where	where	SCONJ
ejpam-4063	169	34	−π	−π	ADV
ejpam-4063	169	35	<	<	X
ejpam-4063	169	36	re(t	re(t	PUNCT
ejpam-4063	169	37	)	)	PUNCT
ejpam-4063	169	38	<	<	X
ejpam-4063	169	39	π	π	X
ejpam-4063	169	40	.	.	PROPN
ejpam-4063	169	41	11	11	NUM
ejpam-4063	169	42	.	.	PUNCT
ejpam-4063	170	1	definite	definite	ADJ
ejpam-4063	170	2	integral	integral	ADJ
ejpam-4063	170	3	in	in	ADP
ejpam-4063	170	4	terms	term	NOUN
ejpam-4063	170	5	of	of	ADP
ejpam-4063	170	6	the	the	DET
ejpam-4063	170	7	log	log	NOUN
ejpam-4063	170	8	-	-	PUNCT
ejpam-4063	170	9	gamma	gamma	NOUN
ejpam-4063	170	10	log(γ(x	log(γ(x	NOUN
ejpam-4063	170	11	)	)	PUNCT
ejpam-4063	170	12	)	)	PUNCT
ejpam-4063	171	1	and	and	CCONJ
ejpam-4063	171	2	harmonic	harmonic	ADJ
ejpam-4063	171	3	number	number	NOUN
ejpam-4063	171	4	hk	hk	PROPN
ejpam-4063	171	5	functions	function	NOUN
ejpam-4063	171	6	using	use	VERB
ejpam-4063	171	7	equation	equation	NOUN
ejpam-4063	171	8	(	(	PUNCT
ejpam-4063	171	9	19	19	NUM
ejpam-4063	171	10	)	)	PUNCT
ejpam-4063	171	11	taking	take	VERB
ejpam-4063	171	12	the	the	DET
ejpam-4063	171	13	first	first	ADJ
ejpam-4063	171	14	partial	partial	ADJ
ejpam-4063	171	15	derivative	derivative	NOUN
ejpam-4063	171	16	with	with	ADP
ejpam-4063	171	17	respect	respect	NOUN
ejpam-4063	171	18	to	to	ADP
ejpam-4063	171	19	k	k	PROPN
ejpam-4063	171	20	and	and	CCONJ
ejpam-4063	171	21	applying	apply	VERB
ejpam-4063	171	22	l’hopitals	l’hopital	NOUN
ejpam-4063	171	23	’	'	PUNCT
ejpam-4063	171	24	rule	rule	NOUN
ejpam-4063	171	25	as	as	ADP
ejpam-4063	171	26	k	k	PROPN
ejpam-4063	171	27	→	→	SYM
ejpam-4063	171	28	0	0	NUM
ejpam-4063	171	29	and	and	CCONJ
ejpam-4063	171	30	simplifying	simplify	VERB
ejpam-4063	171	31	to	to	PART
ejpam-4063	171	32	get	get	VERB
ejpam-4063	171	33	r.	r.	PROPN
ejpam-4063	171	34	reynolds	reynolds	PROPN
ejpam-4063	171	35	,	,	PUNCT
ejpam-4063	171	36	a.	a.	PROPN
ejpam-4063	171	37	stauffer	stauffer	PROPN
ejpam-4063	171	38	/	/	SYM
ejpam-4063	171	39	eur	eur	PROPN
ejpam-4063	171	40	.	.	PUNCT
ejpam-4063	172	1	j.	j.	PROPN
ejpam-4063	172	2	pure	pure	PROPN
ejpam-4063	172	3	appl	appl	PROPN
ejpam-4063	172	4	.	.	PROPN
ejpam-4063	172	5	math	math	PROPN
ejpam-4063	172	6	,	,	PUNCT
ejpam-4063	172	7	14	14	NUM
ejpam-4063	172	8	(	(	PUNCT
ejpam-4063	172	9	4	4	NUM
ejpam-4063	172	10	)	)	PUNCT
ejpam-4063	172	11	(	(	PUNCT
ejpam-4063	172	12	2021	2021	NUM
ejpam-4063	172	13	)	)	PUNCT
ejpam-4063	172	14	,	,	PUNCT
ejpam-4063	172	15	1249	1249	NUM
ejpam-4063	172	16	-	-	SYM
ejpam-4063	172	17	1265	1265	NUM
ejpam-4063	172	18	1260	1260	NUM
ejpam-4063	172	19	(	(	PUNCT
ejpam-4063	172	20	21	21	NUM
ejpam-4063	172	21	)	)	PUNCT
ejpam-4063	172	22	∫	∫	PROPN
ejpam-4063	173	1	∞	∞	PROPN
ejpam-4063	173	2	0	0	NUM
ejpam-4063	173	3	log(x	log(x	NUM
ejpam-4063	173	4	)	)	PUNCT
ejpam-4063	173	5	sinh(x	sinh(x	PROPN
ejpam-4063	173	6	)	)	PUNCT
ejpam-4063	173	7	sinh(2x	sinh(2x	PROPN
ejpam-4063	173	8	)	)	PUNCT
ejpam-4063	173	9	(	(	PUNCT
ejpam-4063	173	10	cos(t	cos(t	PROPN
ejpam-4063	173	11	)	)	PUNCT
ejpam-4063	174	1	+	+	NUM
ejpam-4063	174	2	cosh(2x))2	cosh(2x))2	NOUN
ejpam-4063	174	3	dx	dx	PROPN
ejpam-4063	174	4	=	=	SYM
ejpam-4063	174	5	1	1	NUM
ejpam-4063	174	6	16	16	NUM
ejpam-4063	174	7	(	(	PUNCT
ejpam-4063	174	8	csc	csc	PROPN
ejpam-4063	174	9	(	(	PUNCT
ejpam-4063	174	10	t	t	PROPN
ejpam-4063	174	11	2	2	NUM
ejpam-4063	174	12	)	)	PUNCT
ejpam-4063	174	13	(	(	PUNCT
ejpam-4063	174	14	h−	h−	PROPN
ejpam-4063	174	15	t+π	t+π	NOUN
ejpam-4063	174	16	4π	4π	PRON
ejpam-4063	174	17	−h−	−h−	VERB
ejpam-4063	174	18	t+3π	t+3π	PROPN
ejpam-4063	174	19	4π	4π	PROPN
ejpam-4063	174	20	+	+	CCONJ
ejpam-4063	174	21	ψ(0	ψ(0	NOUN
ejpam-4063	174	22	)	)	PUNCT
ejpam-4063	174	23	(	(	PUNCT
ejpam-4063	174	24	t+	t+	PUNCT
ejpam-4063	174	25	π	π	PROPN
ejpam-4063	174	26	4π	4π	NUM
ejpam-4063	174	27	)	)	PUNCT
ejpam-4063	174	28	−	−	PROPN
ejpam-4063	175	1	ψ(0	ψ(0	NOUN
ejpam-4063	175	2	)	)	PUNCT
ejpam-4063	175	3	(	(	PUNCT
ejpam-4063	175	4	1	1	NUM
ejpam-4063	175	5	4	4	NUM
ejpam-4063	175	6	(	(	PUNCT
ejpam-4063	175	7	t	t	NOUN
ejpam-4063	175	8	π	π	PROPN
ejpam-4063	175	9	+	+	CCONJ
ejpam-4063	175	10	3	3	NUM
ejpam-4063	175	11	)	)	PUNCT
ejpam-4063	175	12	)	)	PUNCT
ejpam-4063	175	13	)	)	PUNCT
ejpam-4063	176	1	+	+	CCONJ
ejpam-4063	176	2	2π	2π	PROPN
ejpam-4063	176	3	sec	sec	PROPN
ejpam-4063	176	4	(	(	PUNCT
ejpam-4063	176	5	t	t	PROPN
ejpam-4063	176	6	2	2	NUM
ejpam-4063	176	7	)	)	PUNCT
ejpam-4063	176	8	log	log	NOUN
ejpam-4063	176	9	(	(	PUNCT
ejpam-4063	176	10	2πγ	2πγ	NOUN
ejpam-4063	176	11	(	(	PUNCT
ejpam-4063	176	12	3	3	NUM
ejpam-4063	176	13	4	4	NUM
ejpam-4063	176	14	−	−	NOUN
ejpam-4063	176	15	t	t	NOUN
ejpam-4063	176	16	4π	4π	NUM
ejpam-4063	176	17	)	)	PUNCT
ejpam-4063	176	18	γ	γ	PROPN
ejpam-4063	176	19	(	(	PUNCT
ejpam-4063	176	20	1	1	NUM
ejpam-4063	176	21	4	4	NUM
ejpam-4063	176	22	(	(	PUNCT
ejpam-4063	176	23	t	t	NOUN
ejpam-4063	176	24	π	π	PROPN
ejpam-4063	176	25	+	+	CCONJ
ejpam-4063	176	26	3	3	NUM
ejpam-4063	176	27	)	)	PUNCT
ejpam-4063	176	28	)	)	PUNCT
ejpam-4063	177	1	γ	γ	PROPN
ejpam-4063	177	2	(	(	PUNCT
ejpam-4063	177	3	π−t	π−t	X
ejpam-4063	177	4	4π	4π	NUM
ejpam-4063	177	5	)	)	PUNCT
ejpam-4063	177	6	γ	γ	PROPN
ejpam-4063	177	7	(	(	PUNCT
ejpam-4063	177	8	t+π	t+π	VERB
ejpam-4063	177	9	4π	4π	NUM
ejpam-4063	177	10	)	)	PUNCT
ejpam-4063	177	11	)	)	PUNCT
ejpam-4063	177	12	)	)	PUNCT
ejpam-4063	177	13	from	from	ADP
ejpam-4063	177	14	equations	equation	NOUN
ejpam-4063	177	15	(	(	PUNCT
ejpam-4063	177	16	64:4:1	64:4:1	NUM
ejpam-4063	177	17	)	)	PUNCT
ejpam-4063	177	18	,	,	PUNCT
ejpam-4063	177	19	(	(	PUNCT
ejpam-4063	177	20	64:9:2	64:9:2	NOUN
ejpam-4063	177	21	)	)	PUNCT
ejpam-4063	177	22	,	,	PUNCT
ejpam-4063	177	23	and	and	CCONJ
ejpam-4063	177	24	(	(	PUNCT
ejpam-4063	177	25	64:10:2	64:10:2	NUM
ejpam-4063	177	26	)	)	PUNCT
ejpam-4063	177	27	in	in	ADP
ejpam-4063	177	28	[	[	X
ejpam-4063	177	29	5	5	NUM
ejpam-4063	177	30	]	]	PUNCT
ejpam-4063	177	31	.	.	PUNCT
ejpam-4063	178	1	11.1	11.1	NUM
ejpam-4063	178	2	.	.	PUNCT
ejpam-4063	178	3	example	example	NOUN
ejpam-4063	178	4	1	1	NUM
ejpam-4063	178	5	using	use	VERB
ejpam-4063	178	6	equation	equation	NOUN
ejpam-4063	178	7	(	(	PUNCT
ejpam-4063	178	8	21	21	NUM
ejpam-4063	178	9	)	)	PUNCT
ejpam-4063	178	10	and	and	CCONJ
ejpam-4063	178	11	setting	set	VERB
ejpam-4063	178	12	t	t	X
ejpam-4063	178	13	=	=	PUNCT
ejpam-4063	178	14	π/2	π/2	NUM
ejpam-4063	178	15	simplifying	simplify	VERB
ejpam-4063	178	16	to	to	PART
ejpam-4063	178	17	get	get	VERB
ejpam-4063	178	18	(	(	PUNCT
ejpam-4063	178	19	22	22	NUM
ejpam-4063	178	20	)	)	PUNCT
ejpam-4063	178	21	∫	∫	PROPN
ejpam-4063	179	1	∞	∞	PROPN
ejpam-4063	179	2	0	0	NUM
ejpam-4063	179	3	log(x	log(x	NUM
ejpam-4063	179	4	)	)	PUNCT
ejpam-4063	179	5	sinh(x	sinh(x	PROPN
ejpam-4063	179	6	)	)	PUNCT
ejpam-4063	179	7	tanh(2x)sech(2x)dx	tanh(2x)sech(2x)dx	NOUN
ejpam-4063	179	8	=	=	SYM
ejpam-4063	179	9	1	1	NUM
ejpam-4063	179	10	8	8	NUM
ejpam-4063	179	11	(	(	PUNCT
ejpam-4063	179	12	4	4	NUM
ejpam-4063	179	13	sinh−1(1	sinh−1(1	NOUN
ejpam-4063	179	14	)	)	PUNCT
ejpam-4063	179	15	+	+	NUM
ejpam-4063	180	1	√	√	ADJ
ejpam-4063	180	2	2π	2π	NUM
ejpam-4063	180	3	log	log	VERB
ejpam-4063	180	4	(	(	PUNCT
ejpam-4063	180	5	2πγ	2πγ	NOUN
ejpam-4063	180	6	(	(	PUNCT
ejpam-4063	180	7	5	5	NUM
ejpam-4063	180	8	8	8	NUM
ejpam-4063	180	9	)	)	PUNCT
ejpam-4063	180	10	γ	γ	X
ejpam-4063	180	11	(	(	PUNCT
ejpam-4063	180	12	7	7	NUM
ejpam-4063	180	13	8	8	NUM
ejpam-4063	180	14	)	)	PUNCT
ejpam-4063	180	15	γ	γ	X
ejpam-4063	180	16	(	(	PUNCT
ejpam-4063	180	17	1	1	NUM
ejpam-4063	180	18	8	8	NUM
ejpam-4063	180	19	)	)	PUNCT
ejpam-4063	180	20	γ	γ	X
ejpam-4063	180	21	(	(	PUNCT
ejpam-4063	180	22	3	3	NUM
ejpam-4063	180	23	8	8	NUM
ejpam-4063	180	24	)	)	PUNCT
ejpam-4063	180	25	)	)	PUNCT
ejpam-4063	180	26	)	)	PUNCT
ejpam-4063	181	1	11.2	11.2	NUM
ejpam-4063	181	2	.	.	PUNCT
ejpam-4063	181	3	example	example	NOUN
ejpam-4063	181	4	2	2	NUM
ejpam-4063	181	5	using	use	VERB
ejpam-4063	181	6	equation	equation	NOUN
ejpam-4063	181	7	(	(	PUNCT
ejpam-4063	181	8	21	21	NUM
ejpam-4063	181	9	)	)	PUNCT
ejpam-4063	181	10	and	and	CCONJ
ejpam-4063	181	11	setting	set	VERB
ejpam-4063	181	12	t	t	NOUN
ejpam-4063	181	13	=	=	PUNCT
ejpam-4063	181	14	π/3	π/3	PUNCT
ejpam-4063	181	15	simplifying	simplify	VERB
ejpam-4063	181	16	to	to	PART
ejpam-4063	181	17	get	get	VERB
ejpam-4063	181	18	(	(	PUNCT
ejpam-4063	181	19	23	23	NUM
ejpam-4063	181	20	)	)	PUNCT
ejpam-4063	181	21	∫	∫	PROPN
ejpam-4063	182	1	∞	∞	PROPN
ejpam-4063	182	2	0	0	NUM
ejpam-4063	182	3	log(x	log(x	NUM
ejpam-4063	182	4	)	)	PUNCT
ejpam-4063	182	5	sinh(x	sinh(x	PROPN
ejpam-4063	182	6	)	)	PUNCT
ejpam-4063	182	7	sinh(2x	sinh(2x	PROPN
ejpam-4063	182	8	)	)	PUNCT
ejpam-4063	182	9	(	(	PUNCT
ejpam-4063	182	10	2	2	NUM
ejpam-4063	182	11	cosh(2x	cosh(2x	VERB
ejpam-4063	182	12	)	)	PUNCT
ejpam-4063	182	13	+	+	PROPN
ejpam-4063	183	1	1)2	1)2	NUM
ejpam-4063	183	2	dx	dx	X
ejpam-4063	183	3	=	=	SYM
ejpam-4063	183	4	1	1	NUM
ejpam-4063	183	5	288	288	NUM
ejpam-4063	183	6	(	(	PUNCT
ejpam-4063	183	7	10	10	NUM
ejpam-4063	183	8	√	√	PROPN
ejpam-4063	183	9	3π	3π	NOUN
ejpam-4063	183	10	log(2	log(2	NOUN
ejpam-4063	183	11	)	)	PUNCT
ejpam-4063	184	1	+	+	CCONJ
ejpam-4063	184	2	6	6	NUM
ejpam-4063	184	3	log(64	log(64	NOUN
ejpam-4063	184	4	)	)	PUNCT
ejpam-4063	185	1	+	+	CCONJ
ejpam-4063	185	2	9	9	NUM
ejpam-4063	185	3	√	√	NUM
ejpam-4063	185	4	3π	3π	NOUN
ejpam-4063	185	5	log(π	log(π	NOUN
ejpam-4063	185	6	)	)	PUNCT
ejpam-4063	185	7	+	+	CCONJ
ejpam-4063	185	8	6	6	NUM
ejpam-4063	185	9	√	√	NUM
ejpam-4063	185	10	3π	3π	NUM
ejpam-4063	185	11	log	log	NOUN
ejpam-4063	185	12	(	(	PUNCT
ejpam-4063	185	13	γ	γ	X
ejpam-4063	185	14	(	(	PUNCT
ejpam-4063	185	15	5	5	NUM
ejpam-4063	185	16	6	6	NUM
ejpam-4063	185	17	)	)	PUNCT
ejpam-4063	185	18	γ	γ	X
ejpam-4063	185	19	(	(	PUNCT
ejpam-4063	185	20	1	1	NUM
ejpam-4063	185	21	6	6	NUM
ejpam-4063	185	22	)	)	SYM
ejpam-4063	185	23	2	2	NUM
ejpam-4063	185	24	)	)	PUNCT
ejpam-4063	185	25	)	)	PUNCT
ejpam-4063	186	1	r.	r.	PROPN
ejpam-4063	186	2	reynolds	reynolds	PROPN
ejpam-4063	186	3	,	,	PUNCT
ejpam-4063	186	4	a.	a.	PROPN
ejpam-4063	186	5	stauffer	stauffer	PROPN
ejpam-4063	186	6	/	/	SYM
ejpam-4063	186	7	eur	eur	PROPN
ejpam-4063	186	8	.	.	PUNCT
ejpam-4063	187	1	j.	j.	PROPN
ejpam-4063	187	2	pure	pure	PROPN
ejpam-4063	187	3	appl	appl	PROPN
ejpam-4063	187	4	.	.	PROPN
ejpam-4063	187	5	math	math	PROPN
ejpam-4063	187	6	,	,	PUNCT
ejpam-4063	187	7	14	14	NUM
ejpam-4063	187	8	(	(	PUNCT
ejpam-4063	187	9	4	4	NUM
ejpam-4063	187	10	)	)	PUNCT
ejpam-4063	187	11	(	(	PUNCT
ejpam-4063	187	12	2021	2021	NUM
ejpam-4063	187	13	)	)	PUNCT
ejpam-4063	187	14	,	,	PUNCT
ejpam-4063	187	15	1249	1249	NUM
ejpam-4063	187	16	-	-	SYM
ejpam-4063	187	17	1265	1265	NUM
ejpam-4063	187	18	1261	1261	NUM
ejpam-4063	187	19	11.3	11.3	NUM
ejpam-4063	187	20	.	.	PUNCT
ejpam-4063	188	1	example	example	NOUN
ejpam-4063	188	2	3	3	NUM
ejpam-4063	188	3	using	use	VERB
ejpam-4063	188	4	equation	equation	NOUN
ejpam-4063	188	5	(	(	PUNCT
ejpam-4063	188	6	21	21	NUM
ejpam-4063	188	7	)	)	PUNCT
ejpam-4063	188	8	and	and	CCONJ
ejpam-4063	188	9	setting	set	VERB
ejpam-4063	188	10	t	t	NOUN
ejpam-4063	188	11	=	=	PUNCT
ejpam-4063	188	12	π/4	π/4	VERB
ejpam-4063	188	13	simplifying	simplify	VERB
ejpam-4063	188	14	to	to	PART
ejpam-4063	188	15	get	get	VERB
ejpam-4063	188	16	(	(	PUNCT
ejpam-4063	188	17	24	24	NUM
ejpam-4063	188	18	)	)	PUNCT
ejpam-4063	188	19	∫	∫	PROPN
ejpam-4063	189	1	∞	∞	PROPN
ejpam-4063	189	2	0	0	NUM
ejpam-4063	189	3	log(x	log(x	NUM
ejpam-4063	189	4	)	)	PUNCT
ejpam-4063	189	5	sinh(x	sinh(x	PROPN
ejpam-4063	189	6	)	)	PUNCT
ejpam-4063	189	7	sinh(2x	sinh(2x	PROPN
ejpam-4063	189	8	)	)	PUNCT
ejpam-4063	189	9	(	(	PUNCT
ejpam-4063	189	10	2	2	NUM
ejpam-4063	189	11	cosh(2x	cosh(2x	VERB
ejpam-4063	189	12	)	)	PUNCT
ejpam-4063	189	13	+	+	PROPN
ejpam-4063	190	1	1)2	1)2	NUM
ejpam-4063	190	2	dx	dx	X
ejpam-4063	190	3	=	=	SYM
ejpam-4063	190	4	1	1	NUM
ejpam-4063	190	5	288	288	NUM
ejpam-4063	190	6	(	(	PUNCT
ejpam-4063	190	7	10	10	NUM
ejpam-4063	190	8	√	√	PROPN
ejpam-4063	190	9	3π	3π	NOUN
ejpam-4063	190	10	log(2	log(2	NOUN
ejpam-4063	190	11	)	)	PUNCT
ejpam-4063	191	1	+	+	CCONJ
ejpam-4063	191	2	6	6	NUM
ejpam-4063	191	3	log(64	log(64	NOUN
ejpam-4063	191	4	)	)	PUNCT
ejpam-4063	192	1	+	+	CCONJ
ejpam-4063	192	2	9	9	NUM
ejpam-4063	192	3	√	√	NUM
ejpam-4063	192	4	3π	3π	NOUN
ejpam-4063	192	5	log(π	log(π	NOUN
ejpam-4063	192	6	)	)	PUNCT
ejpam-4063	192	7	+	+	CCONJ
ejpam-4063	192	8	6	6	NUM
ejpam-4063	192	9	√	√	NUM
ejpam-4063	192	10	3π	3π	NUM
ejpam-4063	192	11	log	log	NOUN
ejpam-4063	192	12	(	(	PUNCT
ejpam-4063	192	13	γ	γ	X
ejpam-4063	192	14	(	(	PUNCT
ejpam-4063	192	15	5	5	NUM
ejpam-4063	192	16	6	6	NUM
ejpam-4063	192	17	)	)	PUNCT
ejpam-4063	192	18	γ	γ	X
ejpam-4063	192	19	(	(	PUNCT
ejpam-4063	192	20	1	1	NUM
ejpam-4063	192	21	6	6	NUM
ejpam-4063	192	22	)	)	SYM
ejpam-4063	192	23	2	2	NUM
ejpam-4063	192	24	)	)	PUNCT
ejpam-4063	192	25	)	)	PUNCT
ejpam-4063	193	1	11.4	11.4	NUM
ejpam-4063	193	2	.	.	PUNCT
ejpam-4063	193	3	example	example	NOUN
ejpam-4063	193	4	4	4	NUM
ejpam-4063	193	5	using	use	VERB
ejpam-4063	193	6	equation	equation	NOUN
ejpam-4063	193	7	(	(	PUNCT
ejpam-4063	193	8	21	21	NUM
ejpam-4063	193	9	)	)	PUNCT
ejpam-4063	193	10	and	and	CCONJ
ejpam-4063	193	11	setting	set	VERB
ejpam-4063	193	12	t	t	NOUN
ejpam-4063	193	13	=	=	SYM
ejpam-4063	193	14	2π/3	2π/3	NUM
ejpam-4063	193	15	simplifying	simplify	VERB
ejpam-4063	193	16	to	to	PART
ejpam-4063	193	17	get	get	VERB
ejpam-4063	193	18	(	(	PUNCT
ejpam-4063	193	19	25	25	NUM
ejpam-4063	193	20	)	)	PUNCT
ejpam-4063	193	21	∫	∫	PROPN
ejpam-4063	194	1	∞	∞	PROPN
ejpam-4063	194	2	0	0	NUM
ejpam-4063	194	3	log(x	log(x	NUM
ejpam-4063	194	4	)	)	PUNCT
ejpam-4063	194	5	sinh(x	sinh(x	PROPN
ejpam-4063	194	6	)	)	PUNCT
ejpam-4063	194	7	sinh(2x	sinh(2x	PROPN
ejpam-4063	194	8	)	)	PUNCT
ejpam-4063	194	9	(	(	PUNCT
ejpam-4063	194	10	2	2	NUM
ejpam-4063	194	11	cosh(2x)−	cosh(2x)−	NOUN
ejpam-4063	194	12	1)2	1)2	NUM
ejpam-4063	194	13	dx	dx	X
ejpam-4063	195	1	=	=	SYM
ejpam-4063	195	2	1	1	NUM
ejpam-4063	195	3	16	16	NUM
ejpam-4063	195	4	(	(	PUNCT
ejpam-4063	195	5	4	4	NUM
ejpam-4063	195	6	coth−1	coth−1	NOUN
ejpam-4063	195	7	(	(	PUNCT
ejpam-4063	195	8	√	√	NUM
ejpam-4063	195	9	3	3	NUM
ejpam-4063	195	10	)	)	PUNCT
ejpam-4063	195	11	+	+	CCONJ
ejpam-4063	195	12	π	π	X
ejpam-4063	195	13	log	log	NOUN
ejpam-4063	195	14	(	(	PUNCT
ejpam-4063	195	15	2πγ	2πγ	NOUN
ejpam-4063	195	16	(	(	PUNCT
ejpam-4063	195	17	7	7	NUM
ejpam-4063	195	18	12	12	NUM
ejpam-4063	195	19	)	)	PUNCT
ejpam-4063	195	20	γ	γ	X
ejpam-4063	195	21	(	(	PUNCT
ejpam-4063	195	22	11	11	NUM
ejpam-4063	195	23	12	12	NUM
ejpam-4063	195	24	)	)	PUNCT
ejpam-4063	195	25	γ	γ	X
ejpam-4063	195	26	(	(	PUNCT
ejpam-4063	195	27	1	1	NUM
ejpam-4063	195	28	12	12	NUM
ejpam-4063	195	29	)	)	PUNCT
ejpam-4063	195	30	γ	γ	X
ejpam-4063	195	31	(	(	PUNCT
ejpam-4063	195	32	5	5	NUM
ejpam-4063	195	33	12	12	NUM
ejpam-4063	195	34	)	)	PUNCT
ejpam-4063	195	35	)	)	PUNCT
ejpam-4063	195	36	)	)	PUNCT
ejpam-4063	195	37	11.5	11.5	NUM
ejpam-4063	195	38	.	.	PUNCT
ejpam-4063	195	39	example	example	NOUN
ejpam-4063	195	40	5	5	NUM
ejpam-4063	195	41	using	use	VERB
ejpam-4063	195	42	equation	equation	NOUN
ejpam-4063	195	43	(	(	PUNCT
ejpam-4063	195	44	21	21	NUM
ejpam-4063	195	45	)	)	PUNCT
ejpam-4063	195	46	and	and	CCONJ
ejpam-4063	195	47	setting	set	VERB
ejpam-4063	195	48	t	t	NOUN
ejpam-4063	195	49	=	=	SYM
ejpam-4063	195	50	0	0	PUNCT
ejpam-4063	195	51	and	and	CCONJ
ejpam-4063	195	52	applying	apply	VERB
ejpam-4063	195	53	l’hopital	l’hopital	PROPN
ejpam-4063	195	54	’s	’s	PART
ejpam-4063	195	55	rule	rule	NOUN
ejpam-4063	195	56	as	as	ADP
ejpam-4063	195	57	t→	t→	X
ejpam-4063	195	58	0	0	NUM
ejpam-4063	195	59	simplifying	simplify	VERB
ejpam-4063	195	60	to	to	PART
ejpam-4063	195	61	get	get	VERB
ejpam-4063	195	62	(	(	PUNCT
ejpam-4063	195	63	26	26	NUM
ejpam-4063	195	64	)	)	PUNCT
ejpam-4063	195	65	∫	∫	PROPN
ejpam-4063	196	1	∞	∞	PROPN
ejpam-4063	196	2	0	0	NUM
ejpam-4063	196	3	log(x	log(x	NUM
ejpam-4063	196	4	)	)	PUNCT
ejpam-4063	196	5	tanh2(x)sech(x)dx	tanh2(x)sech(x)dx	NOUN
ejpam-4063	196	6	=	=	SYM
ejpam-4063	196	7	2c	2c	NUM
ejpam-4063	196	8	π	π	NOUN
ejpam-4063	196	9	+	+	CCONJ
ejpam-4063	196	10	1	1	NUM
ejpam-4063	196	11	4	4	NUM
ejpam-4063	196	12	π	π	NOUN
ejpam-4063	196	13	log	log	NOUN
ejpam-4063	196	14	(	(	PUNCT
ejpam-4063	196	15	2πγ	2πγ	NOUN
ejpam-4063	196	16	(	(	PUNCT
ejpam-4063	196	17	3	3	NUM
ejpam-4063	196	18	4	4	NUM
ejpam-4063	196	19	)	)	SYM
ejpam-4063	196	20	2	2	NUM
ejpam-4063	196	21	γ	γ	X
ejpam-4063	196	22	(	(	PUNCT
ejpam-4063	196	23	1	1	NUM
ejpam-4063	196	24	4	4	NUM
ejpam-4063	196	25	)	)	SYM
ejpam-4063	196	26	2	2	NUM
ejpam-4063	196	27	)	)	PUNCT
ejpam-4063	196	28	12	12	NUM
ejpam-4063	196	29	.	.	PUNCT
ejpam-4063	197	1	derivation	derivation	NOUN
ejpam-4063	197	2	of	of	ADP
ejpam-4063	197	3	hyperbolic	hyperbolic	ADJ
ejpam-4063	197	4	and	and	CCONJ
ejpam-4063	197	5	algebraic	algebraic	ADJ
ejpam-4063	197	6	forms	form	NOUN
ejpam-4063	197	7	12.1	12.1	NUM
ejpam-4063	197	8	.	.	PUNCT
ejpam-4063	197	9	example	example	NOUN
ejpam-4063	197	10	1	1	NUM
ejpam-4063	197	11	using	use	VERB
ejpam-4063	197	12	equation	equation	NOUN
ejpam-4063	197	13	(	(	PUNCT
ejpam-4063	197	14	12	12	NUM
ejpam-4063	197	15	)	)	PUNCT
ejpam-4063	197	16	setting	set	VERB
ejpam-4063	197	17	k	k	PROPN
ejpam-4063	197	18	=	=	PUNCT
ejpam-4063	197	19	−1	−1	NOUN
ejpam-4063	197	20	,	,	PUNCT
ejpam-4063	197	21	t	t	PROPN
ejpam-4063	197	22	=	=	PUNCT
ejpam-4063	197	23	π/2	π/2	PUNCT
ejpam-4063	197	24	and	and	CCONJ
ejpam-4063	197	25	replacing	replace	VERB
ejpam-4063	197	26	α	α	NOUN
ejpam-4063	197	27	by	by	ADP
ejpam-4063	197	28	eiβ	eiβ	NOUN
ejpam-4063	197	29	simplifying	simplify	VERB
ejpam-4063	197	30	we	we	PRON
ejpam-4063	197	31	get	get	VERB
ejpam-4063	197	32	r.	r.	PROPN
ejpam-4063	197	33	reynolds	reynolds	PROPN
ejpam-4063	197	34	,	,	PUNCT
ejpam-4063	197	35	a.	a.	PROPN
ejpam-4063	197	36	stauffer	stauffer	PROPN
ejpam-4063	197	37	/	/	SYM
ejpam-4063	197	38	eur	eur	PROPN
ejpam-4063	197	39	.	.	PUNCT
ejpam-4063	198	1	j.	j.	PROPN
ejpam-4063	198	2	pure	pure	PROPN
ejpam-4063	198	3	appl	appl	PROPN
ejpam-4063	198	4	.	.	PROPN
ejpam-4063	198	5	math	math	PROPN
ejpam-4063	198	6	,	,	PUNCT
ejpam-4063	198	7	14	14	NUM
ejpam-4063	198	8	(	(	PUNCT
ejpam-4063	198	9	4	4	NUM
ejpam-4063	198	10	)	)	PUNCT
ejpam-4063	198	11	(	(	PUNCT
ejpam-4063	198	12	2021	2021	NUM
ejpam-4063	198	13	)	)	PUNCT
ejpam-4063	198	14	,	,	PUNCT
ejpam-4063	198	15	1249	1249	NUM
ejpam-4063	198	16	-	-	SYM
ejpam-4063	198	17	1265	1265	NUM
ejpam-4063	198	18	1262	1262	NUM
ejpam-4063	198	19	(	(	PUNCT
ejpam-4063	198	20	27	27	NUM
ejpam-4063	198	21	)	)	PUNCT
ejpam-4063	198	22	∫	∫	PROPN
ejpam-4063	199	1	∞	∞	NUM
ejpam-4063	199	2	0	0	NUM
ejpam-4063	199	3	x	x	SYM
ejpam-4063	199	4	tanh(ax)sech(ax	tanh(ax)sech(ax	PROPN
ejpam-4063	199	5	)	)	PUNCT
ejpam-4063	199	6	cosh(mx	cosh(mx	PROPN
ejpam-4063	199	7	)	)	PUNCT
ejpam-4063	199	8	β2	β2	NOUN
ejpam-4063	200	1	+	+	CCONJ
ejpam-4063	201	1	x2	x2	PROPN
ejpam-4063	201	2	dx	dx	PROPN
ejpam-4063	201	3	=	=	PUNCT
ejpam-4063	202	1	e−	e−	PROPN
ejpam-4063	202	2	3iπm	3iπm	NUM
ejpam-4063	202	3	2a	2a	NUM
ejpam-4063	202	4	8πa	8πa	NOUN
ejpam-4063	202	5	(	(	PUNCT
ejpam-4063	202	6	−2iπmφ	−2iπmφ	X
ejpam-4063	202	7	(	(	PUNCT
ejpam-4063	202	8	e−	e−	PROPN
ejpam-4063	202	9	2imπ	2imπ	NUM
ejpam-4063	202	10	a	a	DET
ejpam-4063	202	11	,	,	PUNCT
ejpam-4063	202	12	1	1	NUM
ejpam-4063	202	13	,	,	PUNCT
ejpam-4063	202	14	aβ	aβ	PRON
ejpam-4063	202	15	2π	2π	NOUN
ejpam-4063	202	16	+	+	CCONJ
ejpam-4063	202	17	3	3	NUM
ejpam-4063	202	18	4	4	NUM
ejpam-4063	202	19	)	)	PUNCT
ejpam-4063	203	1	+	+	CCONJ
ejpam-4063	203	2	e	e	NOUN
ejpam-4063	203	3	iπm	iπm	VERB
ejpam-4063	203	4	a	a	DET
ejpam-4063	203	5	(	(	PUNCT
ejpam-4063	203	6	2iπmφ	2iπmφ	NUM
ejpam-4063	203	7	(	(	PUNCT
ejpam-4063	203	8	e−	e−	PROPN
ejpam-4063	203	9	2imπ	2imπ	NUM
ejpam-4063	203	10	a	a	DET
ejpam-4063	203	11	,	,	PUNCT
ejpam-4063	203	12	1	1	NUM
ejpam-4063	203	13	,	,	PUNCT
ejpam-4063	203	14	2aβ	2aβ	NOUN
ejpam-4063	203	15	+	+	CCONJ
ejpam-4063	203	16	π	π	X
ejpam-4063	203	17	4π	4π	NUM
ejpam-4063	203	18	)	)	PUNCT
ejpam-4063	204	1	+	+	CCONJ
ejpam-4063	204	2	aφ	aφ	ADP
ejpam-4063	204	3	(	(	PUNCT
ejpam-4063	204	4	e−	e−	PROPN
ejpam-4063	204	5	2imπ	2imπ	NUM
ejpam-4063	204	6	a	a	DET
ejpam-4063	204	7	,	,	PUNCT
ejpam-4063	204	8	2	2	NUM
ejpam-4063	204	9	,	,	PUNCT
ejpam-4063	204	10	2aβ	2aβ	NOUN
ejpam-4063	204	11	+	+	CCONJ
ejpam-4063	204	12	π	π	X
ejpam-4063	204	13	4π	4π	NUM
ejpam-4063	204	14	)	)	PUNCT
ejpam-4063	204	15	)	)	PUNCT
ejpam-4063	205	1	−	−	PROPN
ejpam-4063	205	2	aφ	aφ	NOUN
ejpam-4063	205	3	(	(	PUNCT
ejpam-4063	205	4	e−	e−	PROPN
ejpam-4063	205	5	2imπ	2imπ	NUM
ejpam-4063	205	6	a	a	DET
ejpam-4063	205	7	,	,	PUNCT
ejpam-4063	205	8	2	2	NUM
ejpam-4063	205	9	,	,	PUNCT
ejpam-4063	205	10	aβ	aβ	PRON
ejpam-4063	205	11	2π	2π	NOUN
ejpam-4063	205	12	+	+	CCONJ
ejpam-4063	205	13	3	3	NUM
ejpam-4063	205	14	4	4	NUM
ejpam-4063	205	15	)	)	PUNCT
ejpam-4063	206	1	+	+	CCONJ
ejpam-4063	206	2	e	e	X
ejpam-4063	206	3	2iπm	2iπm	NUM
ejpam-4063	206	4	a	a	DET
ejpam-4063	206	5	(	(	PUNCT
ejpam-4063	206	6	aφ	aφ	NOUN
ejpam-4063	206	7	(	(	PUNCT
ejpam-4063	206	8	e	e	X
ejpam-4063	206	9	2imπ	2imπ	NUM
ejpam-4063	206	10	a	a	DET
ejpam-4063	206	11	,	,	PUNCT
ejpam-4063	206	12	2	2	NUM
ejpam-4063	206	13	,	,	PUNCT
ejpam-4063	206	14	2aβ	2aβ	NOUN
ejpam-4063	206	15	+	+	CCONJ
ejpam-4063	206	16	π	π	X
ejpam-4063	206	17	4π	4π	NUM
ejpam-4063	206	18	)	)	PUNCT
ejpam-4063	207	1	−	−	PROPN
ejpam-4063	208	1	2iπmφ	2iπmφ	NUM
ejpam-4063	208	2	(	(	PUNCT
ejpam-4063	208	3	e	e	X
ejpam-4063	208	4	2imπ	2imπ	NUM
ejpam-4063	208	5	a	a	DET
ejpam-4063	208	6	,	,	PUNCT
ejpam-4063	208	7	1	1	NUM
ejpam-4063	208	8	,	,	PUNCT
ejpam-4063	208	9	2aβ	2aβ	NOUN
ejpam-4063	208	10	+	+	CCONJ
ejpam-4063	208	11	π	π	X
ejpam-4063	208	12	4π	4π	NUM
ejpam-4063	208	13	)	)	PUNCT
ejpam-4063	208	14	)	)	PUNCT
ejpam-4063	209	1	+	+	CCONJ
ejpam-4063	209	2	ie	ie	PRON
ejpam-4063	209	3	3iπm	3iπm	NUM
ejpam-4063	209	4	a	a	DET
ejpam-4063	209	5	(	(	PUNCT
ejpam-4063	209	6	2πmφ	2πmφ	NUM
ejpam-4063	209	7	(	(	PUNCT
ejpam-4063	209	8	e	e	X
ejpam-4063	209	9	2imπ	2imπ	NUM
ejpam-4063	209	10	a	a	DET
ejpam-4063	209	11	,	,	PUNCT
ejpam-4063	209	12	1	1	NUM
ejpam-4063	209	13	,	,	PUNCT
ejpam-4063	209	14	aβ	aβ	DET
ejpam-4063	209	15	2π	2π	NOUN
ejpam-4063	209	16	+	+	CCONJ
ejpam-4063	209	17	3	3	NUM
ejpam-4063	209	18	4	4	NUM
ejpam-4063	209	19	)	)	PUNCT
ejpam-4063	209	20	+	+	CCONJ
ejpam-4063	209	21	iaφ	iaφ	NOUN
ejpam-4063	209	22	(	(	PUNCT
ejpam-4063	209	23	e	e	X
ejpam-4063	209	24	2imπ	2imπ	NUM
ejpam-4063	209	25	a	a	DET
ejpam-4063	209	26	,	,	PUNCT
ejpam-4063	209	27	2	2	NUM
ejpam-4063	209	28	,	,	PUNCT
ejpam-4063	209	29	aβ	aβ	DET
ejpam-4063	209	30	2π	2π	NOUN
ejpam-4063	209	31	+	+	CCONJ
ejpam-4063	209	32	3	3	NUM
ejpam-4063	209	33	4	4	NUM
ejpam-4063	209	34	)	)	PUNCT
ejpam-4063	209	35	)	)	PUNCT
ejpam-4063	209	36	)	)	PUNCT
ejpam-4063	210	1	next	next	ADV
ejpam-4063	210	2	we	we	PRON
ejpam-4063	210	3	take	take	VERB
ejpam-4063	210	4	the	the	DET
ejpam-4063	210	5	first	first	ADJ
ejpam-4063	210	6	partial	partial	ADJ
ejpam-4063	210	7	derivative	derivative	NOUN
ejpam-4063	210	8	with	with	ADP
ejpam-4063	210	9	respect	respect	NOUN
ejpam-4063	210	10	to	to	ADP
ejpam-4063	210	11	m	m	PRON
ejpam-4063	210	12	and	and	CCONJ
ejpam-4063	210	13	simplifying	simplify	VERB
ejpam-4063	210	14	to	to	PART
ejpam-4063	210	15	get	get	VERB
ejpam-4063	210	16	r.	r.	PROPN
ejpam-4063	210	17	reynolds	reynolds	PROPN
ejpam-4063	210	18	,	,	PUNCT
ejpam-4063	210	19	a.	a.	PROPN
ejpam-4063	210	20	stauffer	stauffer	PROPN
ejpam-4063	210	21	/	/	SYM
ejpam-4063	210	22	eur	eur	PROPN
ejpam-4063	210	23	.	.	PUNCT
ejpam-4063	211	1	j.	j.	PROPN
ejpam-4063	211	2	pure	pure	PROPN
ejpam-4063	211	3	appl	appl	PROPN
ejpam-4063	211	4	.	.	PROPN
ejpam-4063	211	5	math	math	PROPN
ejpam-4063	211	6	,	,	PUNCT
ejpam-4063	211	7	14	14	NUM
ejpam-4063	211	8	(	(	PUNCT
ejpam-4063	211	9	4	4	NUM
ejpam-4063	211	10	)	)	PUNCT
ejpam-4063	211	11	(	(	PUNCT
ejpam-4063	211	12	2021	2021	NUM
ejpam-4063	211	13	)	)	PUNCT
ejpam-4063	211	14	,	,	PUNCT
ejpam-4063	211	15	1249	1249	NUM
ejpam-4063	211	16	-	-	SYM
ejpam-4063	211	17	1265	1265	NUM
ejpam-4063	211	18	1263	1263	NUM
ejpam-4063	211	19	(	(	PUNCT
ejpam-4063	211	20	28	28	NUM
ejpam-4063	211	21	)	)	PUNCT
ejpam-4063	211	22	∫	∫	PROPN
ejpam-4063	212	1	∞	∞	NUM
ejpam-4063	212	2	0	0	NUM
ejpam-4063	212	3	x	x	SYM
ejpam-4063	212	4	tanh(ax)sech(ax	tanh(ax)sech(ax	PROPN
ejpam-4063	212	5	)	)	PUNCT
ejpam-4063	212	6	cosh(mx	cosh(mx	PROPN
ejpam-4063	212	7	)	)	PUNCT
ejpam-4063	212	8	β2	β2	NOUN
ejpam-4063	213	1	+	+	CCONJ
ejpam-4063	214	1	x2	x2	PROPN
ejpam-4063	214	2	dx	dx	PROPN
ejpam-4063	214	3	=	=	PUNCT
ejpam-4063	215	1	e−	e−	PROPN
ejpam-4063	215	2	3iπm	3iπm	NUM
ejpam-4063	215	3	2a	2a	NUM
ejpam-4063	215	4	8πa	8πa	NOUN
ejpam-4063	215	5	(	(	PUNCT
ejpam-4063	215	6	−2iπmφ	−2iπmφ	X
ejpam-4063	215	7	(	(	PUNCT
ejpam-4063	215	8	e−	e−	PROPN
ejpam-4063	215	9	2imπ	2imπ	NUM
ejpam-4063	215	10	a	a	DET
ejpam-4063	215	11	,	,	PUNCT
ejpam-4063	215	12	1	1	NUM
ejpam-4063	215	13	,	,	PUNCT
ejpam-4063	215	14	aβ	aβ	PRON
ejpam-4063	215	15	2π	2π	NOUN
ejpam-4063	215	16	+	+	CCONJ
ejpam-4063	215	17	3	3	NUM
ejpam-4063	215	18	4	4	NUM
ejpam-4063	215	19	)	)	PUNCT
ejpam-4063	216	1	+	+	CCONJ
ejpam-4063	216	2	e	e	NOUN
ejpam-4063	216	3	iπm	iπm	VERB
ejpam-4063	216	4	a	a	DET
ejpam-4063	216	5	(	(	PUNCT
ejpam-4063	216	6	2iπmφ	2iπmφ	NUM
ejpam-4063	216	7	(	(	PUNCT
ejpam-4063	216	8	e−	e−	PROPN
ejpam-4063	216	9	2imπ	2imπ	NUM
ejpam-4063	216	10	a	a	DET
ejpam-4063	216	11	,	,	PUNCT
ejpam-4063	216	12	1	1	NUM
ejpam-4063	216	13	,	,	PUNCT
ejpam-4063	216	14	2aβ	2aβ	NOUN
ejpam-4063	216	15	+	+	CCONJ
ejpam-4063	216	16	π	π	X
ejpam-4063	216	17	4π	4π	NUM
ejpam-4063	216	18	)	)	PUNCT
ejpam-4063	217	1	+	+	CCONJ
ejpam-4063	217	2	aφ	aφ	ADP
ejpam-4063	217	3	(	(	PUNCT
ejpam-4063	217	4	e−	e−	PROPN
ejpam-4063	217	5	2imπ	2imπ	NUM
ejpam-4063	217	6	a	a	DET
ejpam-4063	217	7	,	,	PUNCT
ejpam-4063	217	8	2	2	NUM
ejpam-4063	217	9	,	,	PUNCT
ejpam-4063	217	10	2aβ	2aβ	NOUN
ejpam-4063	217	11	+	+	CCONJ
ejpam-4063	217	12	π	π	X
ejpam-4063	217	13	4π	4π	NUM
ejpam-4063	217	14	)	)	PUNCT
ejpam-4063	217	15	)	)	PUNCT
ejpam-4063	218	1	−	−	PROPN
ejpam-4063	218	2	aφ	aφ	NOUN
ejpam-4063	218	3	(	(	PUNCT
ejpam-4063	218	4	e−	e−	PROPN
ejpam-4063	218	5	2imπ	2imπ	NUM
ejpam-4063	218	6	a	a	DET
ejpam-4063	218	7	,	,	PUNCT
ejpam-4063	218	8	2	2	NUM
ejpam-4063	218	9	,	,	PUNCT
ejpam-4063	218	10	aβ	aβ	PRON
ejpam-4063	218	11	2π	2π	NOUN
ejpam-4063	218	12	+	+	CCONJ
ejpam-4063	218	13	3	3	NUM
ejpam-4063	218	14	4	4	NUM
ejpam-4063	218	15	)	)	PUNCT
ejpam-4063	219	1	+	+	CCONJ
ejpam-4063	219	2	e	e	X
ejpam-4063	219	3	2iπm	2iπm	NUM
ejpam-4063	219	4	a	a	DET
ejpam-4063	219	5	(	(	PUNCT
ejpam-4063	219	6	aφ	aφ	NOUN
ejpam-4063	219	7	(	(	PUNCT
ejpam-4063	219	8	e	e	X
ejpam-4063	219	9	2imπ	2imπ	NUM
ejpam-4063	219	10	a	a	DET
ejpam-4063	219	11	,	,	PUNCT
ejpam-4063	219	12	2	2	NUM
ejpam-4063	219	13	,	,	PUNCT
ejpam-4063	219	14	2aβ	2aβ	NOUN
ejpam-4063	219	15	+	+	CCONJ
ejpam-4063	219	16	π	π	X
ejpam-4063	219	17	4π	4π	NUM
ejpam-4063	219	18	)	)	PUNCT
ejpam-4063	220	1	−	−	PROPN
ejpam-4063	221	1	2iπmφ	2iπmφ	NUM
ejpam-4063	221	2	(	(	PUNCT
ejpam-4063	221	3	e	e	X
ejpam-4063	221	4	2imπ	2imπ	NUM
ejpam-4063	221	5	a	a	DET
ejpam-4063	221	6	,	,	PUNCT
ejpam-4063	221	7	1	1	NUM
ejpam-4063	221	8	,	,	PUNCT
ejpam-4063	221	9	2aβ	2aβ	NOUN
ejpam-4063	221	10	+	+	CCONJ
ejpam-4063	221	11	π	π	X
ejpam-4063	221	12	4π	4π	NUM
ejpam-4063	221	13	)	)	PUNCT
ejpam-4063	221	14	)	)	PUNCT
ejpam-4063	222	1	+	+	CCONJ
ejpam-4063	222	2	ie	ie	PRON
ejpam-4063	222	3	3iπm	3iπm	NUM
ejpam-4063	222	4	a	a	DET
ejpam-4063	222	5	(	(	PUNCT
ejpam-4063	222	6	2πmφ	2πmφ	NUM
ejpam-4063	222	7	(	(	PUNCT
ejpam-4063	222	8	e	e	X
ejpam-4063	222	9	2imπ	2imπ	NUM
ejpam-4063	222	10	a	a	DET
ejpam-4063	222	11	,	,	PUNCT
ejpam-4063	222	12	1	1	NUM
ejpam-4063	222	13	,	,	PUNCT
ejpam-4063	222	14	aβ	aβ	DET
ejpam-4063	222	15	2π	2π	NOUN
ejpam-4063	222	16	+	+	CCONJ
ejpam-4063	222	17	3	3	NUM
ejpam-4063	222	18	4	4	NUM
ejpam-4063	222	19	)	)	PUNCT
ejpam-4063	222	20	+	+	CCONJ
ejpam-4063	222	21	iaφ	iaφ	NOUN
ejpam-4063	222	22	(	(	PUNCT
ejpam-4063	222	23	e	e	X
ejpam-4063	222	24	2imπ	2imπ	NUM
ejpam-4063	222	25	a	a	DET
ejpam-4063	222	26	,	,	PUNCT
ejpam-4063	222	27	2	2	NUM
ejpam-4063	222	28	,	,	PUNCT
ejpam-4063	222	29	aβ	aβ	DET
ejpam-4063	222	30	2π	2π	NOUN
ejpam-4063	222	31	+	+	CCONJ
ejpam-4063	222	32	3	3	NUM
ejpam-4063	222	33	4	4	NUM
ejpam-4063	222	34	)	)	PUNCT
ejpam-4063	222	35	)	)	PUNCT
ejpam-4063	222	36	)	)	PUNCT
ejpam-4063	222	37	from	from	ADP
ejpam-4063	222	38	equation	equation	NOUN
ejpam-4063	222	39	(	(	PUNCT
ejpam-4063	222	40	9.550	9.550	NUM
ejpam-4063	222	41	)	)	PUNCT
ejpam-4063	222	42	in	in	ADP
ejpam-4063	222	43	[	[	X
ejpam-4063	222	44	3	3	NUM
ejpam-4063	222	45	]	]	PUNCT
ejpam-4063	222	46	.	.	PUNCT
ejpam-4063	223	1	next	next	ADV
ejpam-4063	223	2	we	we	PRON
ejpam-4063	223	3	set	set	VERB
ejpam-4063	223	4	m	m	VERB
ejpam-4063	223	5	=	=	SYM
ejpam-4063	223	6	0	0	NUM
ejpam-4063	223	7	simplifying	simplify	VERB
ejpam-4063	223	8	in	in	ADP
ejpam-4063	223	9	terms	term	NOUN
ejpam-4063	223	10	of	of	ADP
ejpam-4063	223	11	the	the	DET
ejpam-4063	223	12	trigamma	trigamma	PROPN
ejpam-4063	223	13	function	function	PROPN
ejpam-4063	223	14	ψ(1)(z	ψ(1)(z	PROPN
ejpam-4063	223	15	)	)	PUNCT
ejpam-4063	223	16	to	to	PART
ejpam-4063	223	17	get	get	VERB
ejpam-4063	223	18	(	(	PUNCT
ejpam-4063	223	19	29	29	NUM
ejpam-4063	223	20	)	)	PUNCT
ejpam-4063	223	21	∫	∫	PROPN
ejpam-4063	224	1	∞	∞	NUM
ejpam-4063	224	2	0	0	NUM
ejpam-4063	224	3	x	x	SYM
ejpam-4063	224	4	tanh(ax)sech(ax	tanh(ax)sech(ax	PROPN
ejpam-4063	224	5	)	)	PUNCT
ejpam-4063	224	6	β2	β2	NOUN
ejpam-4063	225	1	+	+	CCONJ
ejpam-4063	225	2	x2	x2	PROPN
ejpam-4063	225	3	dx	dx	PROPN
ejpam-4063	225	4	=	=	SYM
ejpam-4063	225	5	ψ(1	ψ(1	PROPN
ejpam-4063	225	6	)	)	PUNCT
ejpam-4063	225	7	(	(	PUNCT
ejpam-4063	225	8	2aβ+π	2aβ+π	NUM
ejpam-4063	225	9	4π	4π	NUM
ejpam-4063	225	10	)	)	PUNCT
ejpam-4063	225	11	−	−	PROPN
ejpam-4063	226	1	ψ(1	ψ(1	PROPN
ejpam-4063	226	2	)	)	PUNCT
ejpam-4063	226	3	(	(	PUNCT
ejpam-4063	227	1	aβ	aβ	PRON
ejpam-4063	227	2	2π	2π	NOUN
ejpam-4063	227	3	+	+	CCONJ
ejpam-4063	227	4	3	3	NUM
ejpam-4063	227	5	4	4	NUM
ejpam-4063	227	6	)	)	PUNCT
ejpam-4063	227	7	4π	4π	NUM
ejpam-4063	227	8	from	from	ADP
ejpam-4063	227	9	equation	equation	NOUN
ejpam-4063	227	10	(	(	PUNCT
ejpam-4063	227	11	64:4:1	64:4:1	NUM
ejpam-4063	227	12	)	)	PUNCT
ejpam-4063	227	13	in	in	ADP
ejpam-4063	227	14	[	[	X
ejpam-4063	227	15	5	5	NUM
ejpam-4063	227	16	]	]	PUNCT
ejpam-4063	227	17	.	.	PUNCT
ejpam-4063	228	1	12.2	12.2	NUM
ejpam-4063	228	2	.	.	PUNCT
ejpam-4063	228	3	example	example	NOUN
ejpam-4063	228	4	2	2	NUM
ejpam-4063	228	5	using	use	VERB
ejpam-4063	228	6	equation	equation	NOUN
ejpam-4063	228	7	(	(	PUNCT
ejpam-4063	228	8	12	12	NUM
ejpam-4063	228	9	)	)	PUNCT
ejpam-4063	228	10	and	and	CCONJ
ejpam-4063	228	11	setting	set	VERB
ejpam-4063	228	12	k	k	PROPN
ejpam-4063	228	13	=	=	SYM
ejpam-4063	228	14	−2	−2	PROPN
ejpam-4063	228	15	,	,	PUNCT
ejpam-4063	228	16	t	t	PROPN
ejpam-4063	228	17	=	=	SYM
ejpam-4063	228	18	π/2	π/2	PUNCT
ejpam-4063	228	19	and	and	CCONJ
ejpam-4063	228	20	replacing	replace	VERB
ejpam-4063	228	21	α	α	NOUN
ejpam-4063	228	22	by	by	ADP
ejpam-4063	228	23	eiβ	eiβ	NOUN
ejpam-4063	228	24	simplifying	simplify	VERB
ejpam-4063	228	25	we	we	PRON
ejpam-4063	228	26	get	get	VERB
ejpam-4063	228	27	r.	r.	PROPN
ejpam-4063	228	28	reynolds	reynolds	PROPN
ejpam-4063	228	29	,	,	PUNCT
ejpam-4063	228	30	a.	a.	PROPN
ejpam-4063	228	31	stauffer	stauffer	PROPN
ejpam-4063	228	32	/	/	SYM
ejpam-4063	228	33	eur	eur	PROPN
ejpam-4063	228	34	.	.	PUNCT
ejpam-4063	229	1	j.	j.	PROPN
ejpam-4063	229	2	pure	pure	PROPN
ejpam-4063	229	3	appl	appl	PROPN
ejpam-4063	229	4	.	.	PROPN
ejpam-4063	229	5	math	math	PROPN
ejpam-4063	229	6	,	,	PUNCT
ejpam-4063	229	7	14	14	NUM
ejpam-4063	229	8	(	(	PUNCT
ejpam-4063	229	9	4	4	NUM
ejpam-4063	229	10	)	)	PUNCT
ejpam-4063	229	11	(	(	PUNCT
ejpam-4063	229	12	2021	2021	NUM
ejpam-4063	229	13	)	)	PUNCT
ejpam-4063	229	14	,	,	PUNCT
ejpam-4063	229	15	1249	1249	NUM
ejpam-4063	229	16	-	-	SYM
ejpam-4063	229	17	1265	1265	NUM
ejpam-4063	229	18	1264	1264	NUM
ejpam-4063	229	19	(	(	PUNCT
ejpam-4063	229	20	30	30	NUM
ejpam-4063	229	21	)	)	PUNCT
ejpam-4063	229	22	∫	∫	PROPN
ejpam-4063	230	1	∞	∞	PROPN
ejpam-4063	230	2	0	0	NUM
ejpam-4063	230	3	(	(	PUNCT
ejpam-4063	230	4	1	1	NUM
ejpam-4063	230	5	(	(	PUNCT
ejpam-4063	230	6	x+	x+	X
ejpam-4063	230	7	iβ)2	iβ)2	NOUN
ejpam-4063	230	8	+	+	NOUN
ejpam-4063	230	9	1	1	NUM
ejpam-4063	230	10	(	(	PUNCT
ejpam-4063	230	11	x−	x−	PROPN
ejpam-4063	230	12	iβ)2	iβ)2	PROPN
ejpam-4063	230	13	)	)	PUNCT
ejpam-4063	230	14	tanh(ax)sech(ax	tanh(ax)sech(ax	PROPN
ejpam-4063	230	15	)	)	PUNCT
ejpam-4063	230	16	sinh(mx)dx	sinh(mx)dx	VERB
ejpam-4063	230	17	=	=	PUNCT
ejpam-4063	230	18	e−	e−	X
ejpam-4063	230	19	3iπm	3iπm	NUM
ejpam-4063	230	20	2a	2a	NUM
ejpam-4063	230	21	4π2	4π2	NUM
ejpam-4063	231	1	(	(	PUNCT
ejpam-4063	231	2	πmφ	πmφ	INTJ
ejpam-4063	231	3	(	(	PUNCT
ejpam-4063	231	4	e−	e−	PROPN
ejpam-4063	231	5	2imπ	2imπ	NUM
ejpam-4063	231	6	a	a	DET
ejpam-4063	231	7	,	,	PUNCT
ejpam-4063	231	8	2	2	NUM
ejpam-4063	231	9	,	,	PUNCT
ejpam-4063	231	10	aβ	aβ	DET
ejpam-4063	231	11	2π	2π	NOUN
ejpam-4063	231	12	+	+	CCONJ
ejpam-4063	231	13	3	3	NUM
ejpam-4063	231	14	4	4	NUM
ejpam-4063	231	15	)	)	PUNCT
ejpam-4063	232	1	+	+	CCONJ
ejpam-4063	232	2	e	e	NOUN
ejpam-4063	232	3	iπm	iπm	VERB
ejpam-4063	232	4	a	a	DET
ejpam-4063	232	5	(	(	PUNCT
ejpam-4063	232	6	iaφ	iaφ	NOUN
ejpam-4063	232	7	(	(	PUNCT
ejpam-4063	232	8	e−	e−	PROPN
ejpam-4063	232	9	2imπ	2imπ	NUM
ejpam-4063	232	10	a	a	DET
ejpam-4063	232	11	,	,	PUNCT
ejpam-4063	232	12	3	3	NUM
ejpam-4063	232	13	,	,	PUNCT
ejpam-4063	232	14	2aβ	2aβ	NOUN
ejpam-4063	233	1	+	+	CCONJ
ejpam-4063	233	2	π	π	X
ejpam-4063	233	3	4π	4π	NUM
ejpam-4063	233	4	)	)	PUNCT
ejpam-4063	234	1	−	−	PROPN
ejpam-4063	234	2	πmφ	πmφ	INTJ
ejpam-4063	234	3	(	(	PUNCT
ejpam-4063	234	4	e−	e−	PROPN
ejpam-4063	234	5	2imπ	2imπ	NUM
ejpam-4063	234	6	a	a	DET
ejpam-4063	234	7	,	,	PUNCT
ejpam-4063	234	8	2	2	NUM
ejpam-4063	234	9	,	,	PUNCT
ejpam-4063	234	10	2aβ	2aβ	NOUN
ejpam-4063	234	11	+	+	CCONJ
ejpam-4063	234	12	π	π	X
ejpam-4063	234	13	4π	4π	NUM
ejpam-4063	234	14	)	)	PUNCT
ejpam-4063	234	15	)	)	PUNCT
ejpam-4063	235	1	−	−	PROPN
ejpam-4063	235	2	iaφ	iaφ	NOUN
ejpam-4063	235	3	(	(	PUNCT
ejpam-4063	235	4	e−	e−	PROPN
ejpam-4063	235	5	2imπ	2imπ	NUM
ejpam-4063	235	6	a	a	DET
ejpam-4063	235	7	,	,	PUNCT
ejpam-4063	235	8	3	3	NUM
ejpam-4063	235	9	,	,	PUNCT
ejpam-4063	235	10	aβ	aβ	PRON
ejpam-4063	235	11	2π	2π	NOUN
ejpam-4063	235	12	+	+	CCONJ
ejpam-4063	235	13	3	3	NUM
ejpam-4063	235	14	4	4	NUM
ejpam-4063	235	15	)	)	PUNCT
ejpam-4063	235	16	−	−	NOUN
ejpam-4063	235	17	e	e	X
ejpam-4063	235	18	2iπm	2iπm	NUM
ejpam-4063	235	19	a	a	DET
ejpam-4063	235	20	(	(	PUNCT
ejpam-4063	235	21	πmφ	πmφ	INTJ
ejpam-4063	235	22	(	(	PUNCT
ejpam-4063	235	23	e	e	X
ejpam-4063	235	24	2imπ	2imπ	NUM
ejpam-4063	235	25	a	a	DET
ejpam-4063	235	26	,	,	PUNCT
ejpam-4063	235	27	2	2	NUM
ejpam-4063	235	28	,	,	PUNCT
ejpam-4063	235	29	2aβ	2aβ	NOUN
ejpam-4063	235	30	+	+	CCONJ
ejpam-4063	235	31	π	π	X
ejpam-4063	235	32	4π	4π	NUM
ejpam-4063	235	33	)	)	PUNCT
ejpam-4063	236	1	+	+	PUNCT
ejpam-4063	236	2	iaφ	iaφ	NOUN
ejpam-4063	236	3	(	(	PUNCT
ejpam-4063	236	4	e	e	X
ejpam-4063	236	5	2imπ	2imπ	NUM
ejpam-4063	236	6	a	a	DET
ejpam-4063	236	7	,	,	PUNCT
ejpam-4063	236	8	3	3	NUM
ejpam-4063	236	9	,	,	PUNCT
ejpam-4063	236	10	2aβ	2aβ	NOUN
ejpam-4063	236	11	+	+	CCONJ
ejpam-4063	236	12	π	π	X
ejpam-4063	236	13	4π	4π	NUM
ejpam-4063	236	14	)	)	PUNCT
ejpam-4063	236	15	)	)	PUNCT
ejpam-4063	237	1	+	+	CCONJ
ejpam-4063	237	2	e	e	X
ejpam-4063	237	3	3iπm	3iπm	NUM
ejpam-4063	237	4	a	a	DET
ejpam-4063	237	5	(	(	PUNCT
ejpam-4063	237	6	πmφ	πmφ	INTJ
ejpam-4063	237	7	(	(	PUNCT
ejpam-4063	237	8	e	e	X
ejpam-4063	237	9	2imπ	2imπ	NUM
ejpam-4063	237	10	a	a	DET
ejpam-4063	237	11	,	,	PUNCT
ejpam-4063	237	12	2	2	NUM
ejpam-4063	237	13	,	,	PUNCT
ejpam-4063	237	14	aβ	aβ	DET
ejpam-4063	237	15	2π	2π	NOUN
ejpam-4063	237	16	+	+	CCONJ
ejpam-4063	237	17	3	3	NUM
ejpam-4063	237	18	4	4	NUM
ejpam-4063	237	19	)	)	PUNCT
ejpam-4063	237	20	+	+	CCONJ
ejpam-4063	237	21	iaφ	iaφ	NOUN
ejpam-4063	237	22	(	(	PUNCT
ejpam-4063	237	23	e	e	X
ejpam-4063	237	24	2imπ	2imπ	NUM
ejpam-4063	237	25	a	a	DET
ejpam-4063	237	26	,	,	PUNCT
ejpam-4063	237	27	3	3	NUM
ejpam-4063	237	28	,	,	PUNCT
ejpam-4063	237	29	aβ	aβ	PRON
ejpam-4063	237	30	2π	2π	NOUN
ejpam-4063	237	31	+	+	CCONJ
ejpam-4063	237	32	3	3	NUM
ejpam-4063	237	33	4	4	NUM
ejpam-4063	237	34	)	)	PUNCT
ejpam-4063	237	35	)	)	PUNCT
ejpam-4063	237	36	)	)	PUNCT
ejpam-4063	238	1	next	next	ADV
ejpam-4063	238	2	we	we	PRON
ejpam-4063	238	3	take	take	VERB
ejpam-4063	238	4	the	the	DET
ejpam-4063	238	5	first	first	ADJ
ejpam-4063	238	6	partial	partial	ADJ
ejpam-4063	238	7	derivative	derivative	NOUN
ejpam-4063	238	8	with	with	ADP
ejpam-4063	238	9	respect	respect	NOUN
ejpam-4063	238	10	tom	tom	PROPN
ejpam-4063	238	11	and	and	CCONJ
ejpam-4063	238	12	settingm	settingm	NOUN
ejpam-4063	238	13	=	=	SYM
ejpam-4063	238	14	0	0	NUM
ejpam-4063	238	15	simplifying	simplify	VERB
ejpam-4063	238	16	to	to	PART
ejpam-4063	238	17	get	get	VERB
ejpam-4063	238	18	(	(	PUNCT
ejpam-4063	238	19	31	31	NUM
ejpam-4063	238	20	)	)	PUNCT
ejpam-4063	238	21	∫	∫	PROPN
ejpam-4063	238	22	∞	∞	PROPN
ejpam-4063	238	23	0	0	NUM
ejpam-4063	238	24	x(x−	x(x−	PROPN
ejpam-4063	238	25	β)(β	β)(β	PUNCT
ejpam-4063	238	26	+	+	SYM
ejpam-4063	238	27	x	x	X
ejpam-4063	238	28	)	)	PUNCT
ejpam-4063	238	29	tanh(ax)sech(ax	tanh(ax)sech(ax	PROPN
ejpam-4063	238	30	)	)	PUNCT
ejpam-4063	238	31	(	(	PUNCT
ejpam-4063	238	32	β2	β2	VERB
ejpam-4063	238	33	+	+	CCONJ
ejpam-4063	238	34	x2)2	x2)2	NUM
ejpam-4063	238	35	dx	dx	PROPN
ejpam-4063	238	36	=	=	SYM
ejpam-4063	238	37	πψ(1	πψ(1	PROPN
ejpam-4063	238	38	)	)	PUNCT
ejpam-4063	238	39	(	(	PUNCT
ejpam-4063	238	40	2aβ+π	2aβ+π	NUM
ejpam-4063	238	41	4π	4π	NUM
ejpam-4063	238	42	)	)	PUNCT
ejpam-4063	238	43	−	−	PROPN
ejpam-4063	239	1	πψ(1	πψ(1	NOUN
ejpam-4063	239	2	)	)	PUNCT
ejpam-4063	239	3	(	(	PUNCT
ejpam-4063	239	4	aβ	aβ	PRON
ejpam-4063	239	5	2π	2π	NOUN
ejpam-4063	239	6	+	+	CCONJ
ejpam-4063	239	7	3	3	NUM
ejpam-4063	239	8	4	4	NUM
ejpam-4063	239	9	)	)	PUNCT
ejpam-4063	240	1	+	+	CCONJ
ejpam-4063	240	2	aβ	aβ	PRON
ejpam-4063	240	3	(	(	PUNCT
ejpam-4063	240	4	ζ	ζ	X
ejpam-4063	240	5	(	(	PUNCT
ejpam-4063	240	6	3	3	NUM
ejpam-4063	240	7	,	,	PUNCT
ejpam-4063	240	8	aβ2π	aβ2π	ADJ
ejpam-4063	240	9	+	+	CCONJ
ejpam-4063	240	10	3	3	NUM
ejpam-4063	240	11	4	4	NUM
ejpam-4063	240	12	)	)	PUNCT
ejpam-4063	241	1	−	−	PROPN
ejpam-4063	241	2	ζ	ζ	NOUN
ejpam-4063	241	3	(	(	PUNCT
ejpam-4063	241	4	3	3	NUM
ejpam-4063	241	5	,	,	PUNCT
ejpam-4063	241	6	2aβ+π	2aβ+π	NUM
ejpam-4063	241	7	4π	4π	NUM
ejpam-4063	241	8	)	)	PUNCT
ejpam-4063	241	9	)	)	PUNCT
ejpam-4063	241	10	4π2	4π2	PRON
ejpam-4063	241	11	from	from	ADP
ejpam-4063	241	12	equations	equation	NOUN
ejpam-4063	241	13	(	(	PUNCT
ejpam-4063	241	14	64:12:1	64:12:1	NUM
ejpam-4063	241	15	)	)	PUNCT
ejpam-4063	241	16	(	(	PUNCT
ejpam-4063	241	17	64:13:3	64:13:3	NUM
ejpam-4063	241	18	)	)	PUNCT
ejpam-4063	241	19	and	and	CCONJ
ejpam-4063	241	20	(	(	PUNCT
ejpam-4063	241	21	64:4:1	64:4:1	NUM
ejpam-4063	241	22	)	)	PUNCT
ejpam-4063	241	23	in	in	ADP
ejpam-4063	241	24	[	[	X
ejpam-4063	241	25	5	5	NUM
ejpam-4063	241	26	]	]	PUNCT
ejpam-4063	241	27	.	.	PUNCT
ejpam-4063	242	1	13	13	NUM
ejpam-4063	242	2	.	.	PUNCT
ejpam-4063	242	3	discussion	discussion	NOUN
ejpam-4063	242	4	in	in	ADP
ejpam-4063	242	5	this	this	DET
ejpam-4063	242	6	article	article	NOUN
ejpam-4063	242	7	we	we	PRON
ejpam-4063	242	8	derived	derive	VERB
ejpam-4063	242	9	the	the	DET
ejpam-4063	242	10	integrals	integral	NOUN
ejpam-4063	242	11	of	of	ADP
ejpam-4063	242	12	hyperbolic	hyperbolic	ADJ
ejpam-4063	242	13	and	and	CCONJ
ejpam-4063	242	14	logarithmic	logarithmic	ADJ
ejpam-4063	242	15	functions	function	NOUN
ejpam-4063	242	16	in	in	ADP
ejpam-4063	242	17	terms	term	NOUN
ejpam-4063	242	18	of	of	ADP
ejpam-4063	242	19	the	the	DET
ejpam-4063	242	20	lerch	lerch	PROPN
ejpam-4063	242	21	function	function	PROPN
ejpam-4063	242	22	.	.	PUNCT
ejpam-4063	243	1	then	then	ADV
ejpam-4063	243	2	we	we	PRON
ejpam-4063	243	3	used	use	VERB
ejpam-4063	243	4	these	these	DET
ejpam-4063	243	5	integral	integral	ADJ
ejpam-4063	243	6	formula	formula	NOUN
ejpam-4063	243	7	to	to	PART
ejpam-4063	243	8	derive	derive	VERB
ejpam-4063	243	9	known	known	ADJ
ejpam-4063	243	10	and	and	CCONJ
ejpam-4063	243	11	new	new	ADJ
ejpam-4063	243	12	results	result	NOUN
ejpam-4063	243	13	.	.	PUNCT
ejpam-4063	244	1	we	we	PRON
ejpam-4063	244	2	were	be	AUX
ejpam-4063	244	3	able	able	ADJ
ejpam-4063	244	4	to	to	PART
ejpam-4063	244	5	produce	produce	VERB
ejpam-4063	244	6	a	a	DET
ejpam-4063	244	7	formal	formal	ADJ
ejpam-4063	244	8	derivation	derivation	NOUN
ejpam-4063	244	9	for	for	ADP
ejpam-4063	244	10	equation	equation	NOUN
ejpam-4063	244	11	(	(	PUNCT
ejpam-4063	244	12	27	27	NUM
ejpam-4063	244	13	)	)	PUNCT
ejpam-4063	244	14	table	table	NOUN
ejpam-4063	244	15	27	27	NUM
ejpam-4063	244	16	in	in	ADP
ejpam-4063	244	17	bierens	bieren	NOUN
ejpam-4063	244	18	de	de	X
ejpam-4063	244	19	haan	haan	X
ejpam-4063	245	1	[	[	X
ejpam-4063	245	2	4	4	NUM
ejpam-4063	245	3	]	]	PUNCT
ejpam-4063	245	4	and	and	CCONJ
ejpam-4063	245	5	equation	equation	NOUN
ejpam-4063	245	6	(	(	PUNCT
ejpam-4063	245	7	3.514.4	3.514.4	NUM
ejpam-4063	245	8	)	)	PUNCT
ejpam-4063	245	9	in	in	ADP
ejpam-4063	245	10	[	[	X
ejpam-4063	245	11	3	3	X
ejpam-4063	245	12	]	]	PUNCT
ejpam-4063	245	13	not	not	PART
ejpam-4063	245	14	previously	previously	ADV
ejpam-4063	245	15	published	publish	VERB
ejpam-4063	245	16	.	.	PUNCT
ejpam-4063	246	1	the	the	DET
ejpam-4063	246	2	results	result	NOUN
ejpam-4063	246	3	presented	present	VERB
ejpam-4063	246	4	were	be	AUX
ejpam-4063	246	5	numerically	numerically	ADV
ejpam-4063	246	6	verified	verify	VERB
ejpam-4063	246	7	for	for	ADP
ejpam-4063	246	8	both	both	CCONJ
ejpam-4063	246	9	real	real	ADJ
ejpam-4063	246	10	and	and	CCONJ
ejpam-4063	246	11	imaginary	imaginary	ADJ
ejpam-4063	246	12	values	value	NOUN
ejpam-4063	246	13	of	of	ADP
ejpam-4063	246	14	the	the	DET
ejpam-4063	246	15	parameters	parameter	NOUN
ejpam-4063	246	16	in	in	ADP
ejpam-4063	246	17	the	the	DET
ejpam-4063	246	18	integrals	integral	NOUN
ejpam-4063	246	19	using	use	VERB
ejpam-4063	246	20	mathematica	mathematica	PROPN
ejpam-4063	246	21	by	by	ADP
ejpam-4063	246	22	wolfram	wolfram	PROPN
ejpam-4063	246	23	.	.	PUNCT
ejpam-4063	247	1	in	in	ADP
ejpam-4063	247	2	this	this	DET
ejpam-4063	247	3	work	work	NOUN
ejpam-4063	247	4	we	we	PRON
ejpam-4063	247	5	used	use	VERB
ejpam-4063	247	6	mathematica	mathematica	PROPN
ejpam-4063	247	7	software	software	PROPN
ejpam-4063	247	8	to	to	PART
ejpam-4063	247	9	numerically	numerically	ADV
ejpam-4063	247	10	evaluate	evaluate	VERB
ejpam-4063	247	11	both	both	CCONJ
ejpam-4063	247	12	the	the	DET
ejpam-4063	247	13	definite	definite	ADJ
ejpam-4063	247	14	integral	integral	ADJ
ejpam-4063	247	15	and	and	CCONJ
ejpam-4063	247	16	associated	associate	VERB
ejpam-4063	247	17	special	special	ADJ
ejpam-4063	247	18	function	function	NOUN
ejpam-4063	247	19	for	for	ADP
ejpam-4063	247	20	complex	complex	ADJ
ejpam-4063	247	21	values	value	NOUN
ejpam-4063	247	22	of	of	ADP
ejpam-4063	247	23	the	the	DET
ejpam-4063	247	24	parameters	parameter	NOUN
ejpam-4063	247	25	k	k	PROPN
ejpam-4063	247	26	,	,	PUNCT
ejpam-4063	247	27	α	α	PROPN
ejpam-4063	247	28	,	,	PUNCT
ejpam-4063	247	29	a	a	PRON
ejpam-4063	247	30	,	,	PUNCT
ejpam-4063	247	31	m	m	PRON
ejpam-4063	247	32	and	and	CCONJ
ejpam-4063	247	33	t.	t.	NOUN
ejpam-4063	247	34	we	we	PRON
ejpam-4063	247	35	considered	consider	VERB
ejpam-4063	247	36	various	various	ADJ
ejpam-4063	247	37	ranges	range	NOUN
ejpam-4063	247	38	of	of	ADP
ejpam-4063	247	39	these	these	DET
ejpam-4063	247	40	references	reference	NOUN
ejpam-4063	247	41	1265	1265	NUM
ejpam-4063	247	42	parameters	parameter	NOUN
ejpam-4063	247	43	for	for	ADP
ejpam-4063	247	44	real	real	ADJ
ejpam-4063	247	45	,	,	PUNCT
ejpam-4063	247	46	integer	integer	NOUN
ejpam-4063	247	47	,	,	PUNCT
ejpam-4063	247	48	negative	negative	ADJ
ejpam-4063	247	49	and	and	CCONJ
ejpam-4063	247	50	positive	positive	ADJ
ejpam-4063	247	51	values	value	NOUN
ejpam-4063	247	52	.	.	PUNCT
ejpam-4063	248	1	we	we	PRON
ejpam-4063	248	2	compared	compare	VERB
ejpam-4063	248	3	the	the	DET
ejpam-4063	248	4	evaluation	evaluation	NOUN
ejpam-4063	248	5	of	of	ADP
ejpam-4063	248	6	the	the	DET
ejpam-4063	248	7	definite	definite	ADJ
ejpam-4063	248	8	integral	integral	ADJ
ejpam-4063	248	9	to	to	ADP
ejpam-4063	248	10	the	the	DET
ejpam-4063	248	11	evaluated	evaluated	ADJ
ejpam-4063	248	12	special	special	ADJ
ejpam-4063	248	13	function	function	NOUN
ejpam-4063	248	14	and	and	CCONJ
ejpam-4063	248	15	ensured	ensure	VERB
ejpam-4063	248	16	agreement	agreement	NOUN
ejpam-4063	248	17	.	.	PUNCT
ejpam-4063	249	1	14	14	NUM
ejpam-4063	249	2	.	.	PUNCT
ejpam-4063	249	3	conclusion	conclusion	NOUN
ejpam-4063	249	4	in	in	ADP
ejpam-4063	249	5	this	this	DET
ejpam-4063	249	6	paper	paper	NOUN
ejpam-4063	249	7	,	,	PUNCT
ejpam-4063	249	8	we	we	PRON
ejpam-4063	249	9	have	have	AUX
ejpam-4063	249	10	derived	derive	VERB
ejpam-4063	249	11	a	a	DET
ejpam-4063	249	12	method	method	NOUN
ejpam-4063	249	13	for	for	ADP
ejpam-4063	249	14	expressing	express	VERB
ejpam-4063	249	15	definite	definite	ADJ
ejpam-4063	249	16	integrals	integral	NOUN
ejpam-4063	249	17	in	in	ADP
ejpam-4063	249	18	terms	term	NOUN
ejpam-4063	249	19	of	of	ADP
ejpam-4063	249	20	special	special	ADJ
ejpam-4063	249	21	functions	function	NOUN
ejpam-4063	249	22	using	use	VERB
ejpam-4063	249	23	contour	contour	NOUN
ejpam-4063	249	24	integration	integration	NOUN
ejpam-4063	249	25	.	.	PUNCT
ejpam-4063	250	1	the	the	DET
ejpam-4063	250	2	contour	contour	NOUN
ejpam-4063	250	3	we	we	PRON
ejpam-4063	250	4	used	use	VERB
ejpam-4063	250	5	was	be	AUX
ejpam-4063	250	6	specific	specific	ADJ
ejpam-4063	250	7	to	to	ADP
ejpam-4063	250	8	solving	solve	VERB
ejpam-4063	250	9	integral	integral	ADJ
ejpam-4063	250	10	representations	representation	NOUN
ejpam-4063	250	11	in	in	ADP
ejpam-4063	250	12	terms	term	NOUN
ejpam-4063	250	13	of	of	ADP
ejpam-4063	250	14	the	the	DET
ejpam-4063	250	15	hurwitz	hurwitz	PROPN
ejpam-4063	250	16	zeta	zeta	PROPN
ejpam-4063	250	17	function	function	PROPN
ejpam-4063	250	18	.	.	PUNCT
ejpam-4063	251	1	we	we	PRON
ejpam-4063	251	2	expect	expect	VERB
ejpam-4063	251	3	that	that	SCONJ
ejpam-4063	251	4	other	other	ADJ
ejpam-4063	251	5	contours	contours	NOUN
ejpam-4063	251	6	and	and	CCONJ
ejpam-4063	251	7	integrals	integral	NOUN
ejpam-4063	251	8	can	can	AUX
ejpam-4063	251	9	be	be	AUX
ejpam-4063	251	10	derived	derive	VERB
ejpam-4063	251	11	using	use	VERB
ejpam-4063	251	12	this	this	DET
ejpam-4063	251	13	method	method	NOUN
ejpam-4063	251	14	.	.	PUNCT
ejpam-4063	252	1	acknowledgements	acknowledgement	NOUN
ejpam-4063	252	2	this	this	DET
ejpam-4063	252	3	paper	paper	NOUN
ejpam-4063	252	4	is	be	AUX
ejpam-4063	252	5	fully	fully	ADV
ejpam-4063	252	6	supported	support	VERB
ejpam-4063	252	7	by	by	ADP
ejpam-4063	252	8	the	the	DET
ejpam-4063	252	9	natural	natural	ADJ
ejpam-4063	252	10	sciences	sciences	PROPN
ejpam-4063	252	11	and	and	CCONJ
ejpam-4063	252	12	engineering	engineering	NOUN
ejpam-4063	252	13	research	research	NOUN
ejpam-4063	252	14	council	council	PROPN
ejpam-4063	252	15	(	(	PUNCT
ejpam-4063	252	16	nserc	nserc	PROPN
ejpam-4063	252	17	)	)	PUNCT
ejpam-4063	252	18	grant	grant	VERB
ejpam-4063	252	19	no	no	NOUN
ejpam-4063	252	20	.	.	NOUN
ejpam-4063	252	21	504070	504070	NUM
ejpam-4063	252	22	.	.	PUNCT
ejpam-4063	253	1	references	reference	NOUN
ejpam-4063	253	2	[	[	X
ejpam-4063	253	3	1	1	X
ejpam-4063	253	4	]	]	X
ejpam-4063	253	5	milton	milton	PROPN
ejpam-4063	253	6	abramowitz	abramowitz	PROPN
ejpam-4063	253	7	and	and	CCONJ
ejpam-4063	253	8	irene	irene	PROPN
ejpam-4063	253	9	a.	a.	PROPN
ejpam-4063	253	10	stegun	stegun	PROPN
ejpam-4063	253	11	.	.	PUNCT
ejpam-4063	254	1	handbook	handbook	NOUN
ejpam-4063	254	2	of	of	ADP
ejpam-4063	254	3	mathematical	mathematical	ADJ
ejpam-4063	254	4	functions	function	NOUN
ejpam-4063	254	5	:	:	PUNCT
ejpam-4063	254	6	with	with	ADP
ejpam-4063	254	7	formulas	formula	NOUN
ejpam-4063	254	8	,	,	PUNCT
ejpam-4063	254	9	graphs	graph	NOUN
ejpam-4063	254	10	,	,	PUNCT
ejpam-4063	254	11	and	and	CCONJ
ejpam-4063	254	12	mathematical	mathematical	ADJ
ejpam-4063	254	13	tables	table	NOUN
ejpam-4063	254	14	.	.	PUNCT
ejpam-4063	255	1	courier	courier	NOUN
ejpam-4063	255	2	corporation	corporation	NOUN
ejpam-4063	255	3	,	,	PUNCT
ejpam-4063	255	4	01	01	NUM
ejpam-4063	255	5	1965	1965	NUM
ejpam-4063	255	6	.	.	PUNCT
ejpam-4063	256	1	[	[	X
ejpam-4063	256	2	2	2	NUM
ejpam-4063	256	3	]	]	PUNCT
ejpam-4063	256	4	yu	yu	PROPN
ejpam-4063	256	5	a.	a.	NOUN
ejpam-4063	256	6	brychkov	brychkov	PROPN
ejpam-4063	256	7	,	,	PUNCT
ejpam-4063	256	8	o.	o.	PROPN
ejpam-4063	256	9	i.	i.	PROPN
ejpam-4063	256	10	marichev	marichev	PROPN
ejpam-4063	256	11	,	,	PUNCT
ejpam-4063	256	12	and	and	CCONJ
ejpam-4063	256	13	n.	n.	PROPN
ejpam-4063	256	14	v.	v.	PROPN
ejpam-4063	256	15	savischenko	savischenko	PROPN
ejpam-4063	256	16	.	.	PUNCT
ejpam-4063	257	1	handbook	handbook	NOUN
ejpam-4063	257	2	of	of	ADP
ejpam-4063	257	3	mellin	mellin	PROPN
ejpam-4063	257	4	transforms	transform	VERB
ejpam-4063	257	5	.	.	PUNCT
ejpam-4063	258	1	crc	crc	PROPN
ejpam-4063	258	2	press	press	PROPN
ejpam-4063	258	3	,	,	PUNCT
ejpam-4063	258	4	10	10	NUM
ejpam-4063	258	5	2018	2018	NUM
ejpam-4063	258	6	.	.	PUNCT
ejpam-4063	259	1	[	[	X
ejpam-4063	259	2	3	3	NUM
ejpam-4063	259	3	]	]	X
ejpam-4063	259	4	i.	i.	PROPN
ejpam-4063	259	5	s.	s.	PROPN
ejpam-4063	259	6	gradshteyn	gradshteyn	PROPN
ejpam-4063	259	7	and	and	CCONJ
ejpam-4063	259	8	i.	i.	PROPN
ejpam-4063	259	9	m.	m.	PROPN
ejpam-4063	259	10	ryzhik	ryzhik	PROPN
ejpam-4063	259	11	.	.	PUNCT
ejpam-4063	260	1	table	table	NOUN
ejpam-4063	260	2	of	of	ADP
ejpam-4063	260	3	integrals	integral	NOUN
ejpam-4063	260	4	,	,	PUNCT
ejpam-4063	260	5	series	series	NOUN
ejpam-4063	260	6	,	,	PUNCT
ejpam-4063	260	7	and	and	CCONJ
ejpam-4063	260	8	products	product	NOUN
ejpam-4063	260	9	.	.	PUNCT
ejpam-4063	261	1	academic	academic	ADJ
ejpam-4063	261	2	press	press	NOUN
ejpam-4063	261	3	,	,	PUNCT
ejpam-4063	261	4	05	05	NUM
ejpam-4063	261	5	2014	2014	NUM
ejpam-4063	261	6	.	.	PUNCT
ejpam-4063	262	1	[	[	X
ejpam-4063	262	2	4	4	X
ejpam-4063	262	3	]	]	X
ejpam-4063	262	4	david	david	PROPN
ejpam-4063	262	5	bierens	bierens	PROPN
ejpam-4063	262	6	de	de	PROPN
ejpam-4063	262	7	haan	haan	PROPN
ejpam-4063	262	8	.	.	PUNCT
ejpam-4063	263	1	nouvelles	nouvelles	PROPN
ejpam-4063	263	2	tables	table	NOUN
ejpam-4063	263	3	d’intégrales	d’intégrales	PROPN
ejpam-4063	263	4	définies	définies	PROPN
ejpam-4063	263	5	.	.	PUNCT
ejpam-4063	264	1	p.	p.	NOUN
ejpam-4063	264	2	engels	engels	PROPN
ejpam-4063	264	3	,	,	PUNCT
ejpam-4063	264	4	1867	1867	NUM
ejpam-4063	264	5	.	.	PUNCT
ejpam-4063	265	1	[	[	X
ejpam-4063	265	2	5	5	X
ejpam-4063	265	3	]	]	PUNCT
ejpam-4063	265	4	keith	keith	PROPN
ejpam-4063	265	5	b.	b.	PROPN
ejpam-4063	265	6	oldham	oldham	PROPN
ejpam-4063	265	7	,	,	PUNCT
ejpam-4063	265	8	jan	jan	PROPN
ejpam-4063	265	9	myland	myland	PROPN
ejpam-4063	265	10	,	,	PUNCT
ejpam-4063	265	11	and	and	CCONJ
ejpam-4063	265	12	jerome	jerome	PROPN
ejpam-4063	265	13	spanier	spanier	NOUN
ejpam-4063	265	14	.	.	PUNCT
ejpam-4063	266	1	an	an	DET
ejpam-4063	266	2	atlas	atlas	PROPN
ejpam-4063	266	3	of	of	ADP
ejpam-4063	266	4	functions	function	NOUN
ejpam-4063	266	5	:	:	PUNCT
ejpam-4063	266	6	with	with	ADP
ejpam-4063	266	7	equator	equator	NOUN
ejpam-4063	266	8	,	,	PUNCT
ejpam-4063	266	9	the	the	DET
ejpam-4063	266	10	atlas	atlas	PROPN
ejpam-4063	266	11	function	function	PROPN
ejpam-4063	266	12	calculator	calculator	NOUN
ejpam-4063	266	13	.	.	PUNCT
ejpam-4063	267	1	springer	springer	NOUN
ejpam-4063	267	2	science	science	PROPN
ejpam-4063	267	3	&	&	CCONJ
ejpam-4063	267	4	business	business	NOUN
ejpam-4063	267	5	media	medium	NOUN
ejpam-4063	267	6	,	,	PUNCT
ejpam-4063	267	7	07	07	NUM
ejpam-4063	267	8	2010	2010	NUM
ejpam-4063	267	9	.	.	PUNCT
ejpam-4063	268	1	[	[	X
ejpam-4063	268	2	6	6	NUM
ejpam-4063	268	3	]	]	X
ejpam-4063	268	4	f.w.j	f.w.j	NOUN
ejpam-4063	268	5	.	.	PUNCT
ejpam-4063	268	6	olver	olver	PROPN
ejpam-4063	268	7	,	,	PUNCT
ejpam-4063	268	8	a.	a.	PROPN
ejpam-4063	268	9	b.	b.	PROPN
ejpam-4063	268	10	olde	olde	PROPN
ejpam-4063	268	11	daalhuis	daalhuis	PROPN
ejpam-4063	268	12	,	,	PUNCT
ejpam-4063	268	13	d.	d.	PROPN
ejpam-4063	268	14	w.	w.	PROPN
ejpam-4063	268	15	lozier	lozier	PROPN
ejpam-4063	268	16	,	,	PUNCT
ejpam-4063	268	17	b.	b.	PROPN
ejpam-4063	268	18	i.	i.	PROPN
ejpam-4063	268	19	schneider	schneider	PROPN
ejpam-4063	268	20	,	,	PUNCT
ejpam-4063	268	21	r.	r.	PROPN
ejpam-4063	268	22	f.	f.	PROPN
ejpam-4063	268	23	boisvert	boisvert	PROPN
ejpam-4063	268	24	,	,	PUNCT
ejpam-4063	268	25	c.	c.	PROPN
ejpam-4063	268	26	w.	w.	PROPN
ejpam-4063	268	27	clark	clark	PROPN
ejpam-4063	268	28	,	,	PUNCT
ejpam-4063	268	29	b.	b.	PROPN
ejpam-4063	268	30	r.	r.	PROPN
ejpam-4063	268	31	miller	miller	PROPN
ejpam-4063	268	32	,	,	PUNCT
ejpam-4063	268	33	b.	b.	PROPN
ejpam-4063	269	1	v.	v.	PROPN
ejpam-4063	269	2	saunders	saunders	PROPN
ejpam-4063	269	3	,	,	PUNCT
ejpam-4063	269	4	h.	h.	PROPN
ejpam-4063	269	5	s.	s.	PROPN
ejpam-4063	269	6	cohl	cohl	PROPN
ejpam-4063	269	7	,	,	PUNCT
ejpam-4063	269	8	and	and	CCONJ
ejpam-4063	269	9	m.	m.	NOUN
ejpam-4063	269	10	a.	a.	PROPN
ejpam-4063	269	11	mcclain	mcclain	PROPN
ejpam-4063	269	12	.	.	PUNCT
ejpam-4063	270	1	nist	nist	PROPN
ejpam-4063	270	2	digital	digital	PROPN
ejpam-4063	270	3	library	library	NOUN
ejpam-4063	270	4	of	of	ADP
ejpam-4063	270	5	mathematical	mathematical	ADJ
ejpam-4063	270	6	functions	function	NOUN
ejpam-4063	270	7	,	,	PUNCT
ejpam-4063	270	8	09	09	NUM
ejpam-4063	270	9	2021	2021	NUM
ejpam-4063	270	10	.	.	PUNCT
ejpam-4063	271	1	[	[	X
ejpam-4063	271	2	7	7	NUM
ejpam-4063	271	3	]	]	PUNCT
ejpam-4063	271	4	a.	a.	NOUN
ejpam-4063	271	5	p.	p.	PROPN
ejpam-4063	271	6	prudnikov	prudnikov	PROPN
ejpam-4063	271	7	.	.	PUNCT
ejpam-4063	272	1	integrals	integral	NOUN
ejpam-4063	272	2	and	and	CCONJ
ejpam-4063	272	3	series	series	NOUN
ejpam-4063	272	4	:	:	PUNCT
ejpam-4063	272	5	volume	volume	NOUN
ejpam-4063	272	6	1	1	NUM
ejpam-4063	272	7	:	:	PUNCT
ejpam-4063	272	8	elementary	elementary	ADJ
ejpam-4063	272	9	functions	function	NOUN
ejpam-4063	272	10	;	;	PUNCT
ejpam-4063	272	11	volume	volume	NOUN
ejpam-4063	272	12	2	2	NUM
ejpam-4063	272	13	:	:	PUNCT
ejpam-4063	272	14	special	special	ADJ
ejpam-4063	272	15	functions	function	NOUN
ejpam-4063	272	16	.	.	PUNCT
ejpam-4063	273	1	taylor	taylor	PROPN
ejpam-4063	273	2	&	&	CCONJ
ejpam-4063	273	3	francis	francis	PROPN
ejpam-4063	273	4	,	,	PUNCT
ejpam-4063	273	5	11	11	NUM
ejpam-4063	273	6	1986	1986	NUM
ejpam-4063	273	7	.	.	PUNCT
ejpam-4063	274	1	[	[	X
ejpam-4063	274	2	8	8	NUM
ejpam-4063	274	3	]	]	X
ejpam-4063	274	4	robert	robert	PROPN
ejpam-4063	274	5	reynolds	reynolds	PROPN
ejpam-4063	274	6	and	and	CCONJ
ejpam-4063	274	7	allan	allan	PROPN
ejpam-4063	274	8	stauffer	stauffer	PROPN
ejpam-4063	274	9	.	.	PUNCT
ejpam-4063	275	1	a	a	DET
ejpam-4063	275	2	method	method	NOUN
ejpam-4063	275	3	for	for	ADP
ejpam-4063	275	4	evaluating	evaluate	VERB
ejpam-4063	275	5	definite	definite	ADJ
ejpam-4063	275	6	integrals	integral	NOUN
ejpam-4063	275	7	in	in	ADP
ejpam-4063	275	8	terms	term	NOUN
ejpam-4063	275	9	of	of	ADP
ejpam-4063	275	10	special	special	ADJ
ejpam-4063	275	11	functions	function	NOUN
ejpam-4063	275	12	with	with	ADP
ejpam-4063	275	13	examples	example	NOUN
ejpam-4063	275	14	.	.	PUNCT
ejpam-4063	276	1	international	international	ADJ
ejpam-4063	276	2	mathematical	mathematical	PROPN
ejpam-4063	276	3	forum	forum	PROPN
ejpam-4063	276	4	,	,	PUNCT
ejpam-4063	276	5	15:235	15:235	NUM
ejpam-4063	276	6	–	–	PUNCT
ejpam-4063	276	7	244	244	NUM
ejpam-4063	276	8	,	,	PUNCT
ejpam-4063	276	9	2020	2020	NUM
ejpam-4063	276	10	.	.	PUNCT