id	sid	tid	token	lemma	pos
ejpam-4239	1	1	european	european	PROPN
ejpam-4239	1	2	journal	journal	PROPN
ejpam-4239	1	3	of	of	ADP
ejpam-4239	1	4	pure	pure	ADJ
ejpam-4239	1	5	and	and	CCONJ
ejpam-4239	1	6	applied	apply	VERB
ejpam-4239	1	7	mathematics	mathematic	NOUN
ejpam-4239	1	8	vol	vol	NOUN
ejpam-4239	1	9	.	.	PROPN
ejpam-4239	2	1	15	15	NUM
ejpam-4239	2	2	,	,	PUNCT
ejpam-4239	2	3	no	no	INTJ
ejpam-4239	2	4	.	.	NOUN
ejpam-4239	2	5	3	3	NUM
ejpam-4239	2	6	,	,	PUNCT
ejpam-4239	2	7	2022	2022	NUM
ejpam-4239	2	8	,	,	PUNCT
ejpam-4239	2	9	856	856	NUM
ejpam-4239	2	10	-	-	SYM
ejpam-4239	2	11	863	863	NUM
ejpam-4239	2	12	issn	issn	PROPN
ejpam-4239	2	13	1307	1307	NUM
ejpam-4239	2	14	-	-	SYM
ejpam-4239	2	15	5543	5543	NUM
ejpam-4239	2	16	–	–	PUNCT
ejpam-4239	2	17	ejpam.com	ejpam.com	X
ejpam-4239	2	18	published	publish	VERB
ejpam-4239	2	19	by	by	ADP
ejpam-4239	2	20	new	new	PROPN
ejpam-4239	2	21	york	york	PROPN
ejpam-4239	2	22	business	business	PROPN
ejpam-4239	2	23	global	global	ADJ
ejpam-4239	2	24	double	double	ADJ
ejpam-4239	2	25	integral	integral	ADJ
ejpam-4239	2	26	involving	involve	VERB
ejpam-4239	2	27	the	the	DET
ejpam-4239	2	28	product	product	NOUN
ejpam-4239	2	29	of	of	ADP
ejpam-4239	2	30	the	the	DET
ejpam-4239	2	31	bessel	bessel	ADJ
ejpam-4239	2	32	function	function	NOUN
ejpam-4239	2	33	of	of	ADP
ejpam-4239	2	34	the	the	DET
ejpam-4239	2	35	first	first	ADJ
ejpam-4239	2	36	kind	kind	NOUN
ejpam-4239	2	37	and	and	CCONJ
ejpam-4239	2	38	modified	modified	ADJ
ejpam-4239	2	39	bessel	bessel	NOUN
ejpam-4239	2	40	function	function	NOUN
ejpam-4239	2	41	of	of	ADP
ejpam-4239	2	42	the	the	DET
ejpam-4239	2	43	second	second	ADJ
ejpam-4239	2	44	kind	kind	NOUN
ejpam-4239	2	45	:	:	PUNCT
ejpam-4239	2	46	derivation	derivation	NOUN
ejpam-4239	2	47	and	and	CCONJ
ejpam-4239	2	48	evaluation	evaluation	NOUN
ejpam-4239	2	49	robert	robert	PROPN
ejpam-4239	2	50	reynolds1,∗	reynolds1,∗	PROPN
ejpam-4239	2	51	,	,	PUNCT
ejpam-4239	2	52	allan	allan	PROPN
ejpam-4239	2	53	stauffer1	stauffer1	PROPN
ejpam-4239	2	54	1	1	NUM
ejpam-4239	2	55	department	department	NOUN
ejpam-4239	2	56	of	of	ADP
ejpam-4239	2	57	mathematics	mathematic	NOUN
ejpam-4239	2	58	and	and	CCONJ
ejpam-4239	2	59	statistics	statistic	NOUN
ejpam-4239	2	60	,	,	PUNCT
ejpam-4239	2	61	faculty	faculty	NOUN
ejpam-4239	2	62	of	of	ADP
ejpam-4239	2	63	science	science	PROPN
ejpam-4239	2	64	,	,	PUNCT
ejpam-4239	2	65	york	york	PROPN
ejpam-4239	2	66	university	university	PROPN
ejpam-4239	2	67	,	,	PUNCT
ejpam-4239	2	68	toronto	toronto	PROPN
ejpam-4239	2	69	,	,	PUNCT
ejpam-4239	2	70	ontario	ontario	PROPN
ejpam-4239	2	71	,	,	PUNCT
ejpam-4239	2	72	canada	canada	PROPN
ejpam-4239	2	73	,	,	PUNCT
ejpam-4239	2	74	m3j1p3	m3j1p3	PROPN
ejpam-4239	2	75	abstract	abstract	NOUN
ejpam-4239	2	76	.	.	PUNCT
ejpam-4239	3	1	a	a	DET
ejpam-4239	3	2	double	double	ADJ
ejpam-4239	3	3	integral	integral	NOUN
ejpam-4239	3	4	whose	whose	DET
ejpam-4239	3	5	kernel	kernel	NOUN
ejpam-4239	3	6	involves	involve	VERB
ejpam-4239	3	7	the	the	DET
ejpam-4239	3	8	bessel	bessel	NOUN
ejpam-4239	3	9	functions	function	NOUN
ejpam-4239	3	10	kv(xβ	kv(xβ	PROPN
ejpam-4239	3	11	)	)	PUNCT
ejpam-4239	3	12	and	and	CCONJ
ejpam-4239	3	13	jv(yα	jv(yα	NOUN
ejpam-4239	3	14	)	)	PUNCT
ejpam-4239	3	15	is	be	AUX
ejpam-4239	3	16	derived	derive	VERB
ejpam-4239	3	17	.	.	PUNCT
ejpam-4239	4	1	this	this	DET
ejpam-4239	4	2	integral	integral	NOUN
ejpam-4239	4	3	is	be	AUX
ejpam-4239	4	4	expressed	express	VERB
ejpam-4239	4	5	in	in	ADP
ejpam-4239	4	6	terms	term	NOUN
ejpam-4239	4	7	of	of	ADP
ejpam-4239	4	8	the	the	DET
ejpam-4239	4	9	hurwitz	hurwitz	PROPN
ejpam-4239	4	10	-	-	PUNCT
ejpam-4239	4	11	lerch	lerch	PROPN
ejpam-4239	4	12	zeta	zeta	PROPN
ejpam-4239	4	13	function	function	PROPN
ejpam-4239	4	14	and	and	CCONJ
ejpam-4239	4	15	evaluated	evaluate	VERB
ejpam-4239	4	16	for	for	ADP
ejpam-4239	4	17	various	various	ADJ
ejpam-4239	4	18	values	value	NOUN
ejpam-4239	4	19	of	of	ADP
ejpam-4239	4	20	the	the	DET
ejpam-4239	4	21	parameters	parameter	NOUN
ejpam-4239	4	22	involved	involve	VERB
ejpam-4239	4	23	.	.	PUNCT
ejpam-4239	5	1	some	some	DET
ejpam-4239	5	2	examples	example	NOUN
ejpam-4239	5	3	are	be	AUX
ejpam-4239	5	4	evaluated	evaluate	VERB
ejpam-4239	5	5	and	and	CCONJ
ejpam-4239	5	6	expressed	express	VERB
ejpam-4239	5	7	in	in	ADP
ejpam-4239	5	8	terms	term	NOUN
ejpam-4239	5	9	of	of	ADP
ejpam-4239	5	10	fundamental	fundamental	ADJ
ejpam-4239	5	11	constants	constant	NOUN
ejpam-4239	5	12	.	.	PUNCT
ejpam-4239	6	1	all	all	DET
ejpam-4239	6	2	the	the	DET
ejpam-4239	6	3	results	result	NOUN
ejpam-4239	6	4	in	in	ADP
ejpam-4239	6	5	this	this	DET
ejpam-4239	6	6	work	work	NOUN
ejpam-4239	6	7	are	be	AUX
ejpam-4239	6	8	new	new	ADJ
ejpam-4239	6	9	.	.	PUNCT
ejpam-4239	7	1	2020	2020	NUM
ejpam-4239	7	2	mathematics	mathematic	NOUN
ejpam-4239	7	3	subject	subject	NOUN
ejpam-4239	7	4	classifications	classification	NOUN
ejpam-4239	7	5	:	:	PUNCT
ejpam-4239	7	6	30e20	30e20	NUM
ejpam-4239	7	7	,	,	PUNCT
ejpam-4239	7	8	33	33	NUM
ejpam-4239	7	9	-	-	SYM
ejpam-4239	7	10	01	01	NUM
ejpam-4239	7	11	,	,	PUNCT
ejpam-4239	7	12	33	33	NUM
ejpam-4239	7	13	-	-	SYM
ejpam-4239	7	14	03	03	NUM
ejpam-4239	7	15	,	,	PUNCT
ejpam-4239	7	16	33	33	NUM
ejpam-4239	7	17	-	-	PUNCT
ejpam-4239	7	18	04	04	NUM
ejpam-4239	7	19	,	,	PUNCT
ejpam-4239	7	20	33	33	NUM
ejpam-4239	7	21	-	-	PUNCT
ejpam-4239	7	22	33b	33b	NUM
ejpam-4239	7	23	key	key	ADJ
ejpam-4239	7	24	words	word	NOUN
ejpam-4239	7	25	and	and	CCONJ
ejpam-4239	7	26	phrases	phrase	NOUN
ejpam-4239	7	27	:	:	PUNCT
ejpam-4239	7	28	bessel	bessel	ADJ
ejpam-4239	7	29	functions	function	NOUN
ejpam-4239	7	30	,	,	PUNCT
ejpam-4239	7	31	double	double	ADJ
ejpam-4239	7	32	integral	integral	ADJ
ejpam-4239	7	33	,	,	PUNCT
ejpam-4239	7	34	cauchy	cauchy	ADJ
ejpam-4239	7	35	integral	integral	ADJ
ejpam-4239	7	36	1	1	NUM
ejpam-4239	7	37	.	.	PUNCT
ejpam-4239	7	38	introduction	introduction	NOUN
ejpam-4239	7	39	integrals	integral	NOUN
ejpam-4239	7	40	involving	involve	VERB
ejpam-4239	7	41	bessel	bessel	NOUN
ejpam-4239	7	42	functions	function	NOUN
ejpam-4239	7	43	have	have	AUX
ejpam-4239	7	44	been	be	AUX
ejpam-4239	7	45	studied	study	VERB
ejpam-4239	7	46	in	in	ADP
ejpam-4239	7	47	the	the	DET
ejpam-4239	7	48	works	work	NOUN
ejpam-4239	7	49	by	by	ADP
ejpam-4239	7	50	glasser	glasser	NOUN
ejpam-4239	7	51	[	[	X
ejpam-4239	7	52	3	3	NUM
ejpam-4239	7	53	]	]	PUNCT
ejpam-4239	7	54	,	,	PUNCT
ejpam-4239	7	55	where	where	SCONJ
ejpam-4239	7	56	the	the	DET
ejpam-4239	7	57	study	study	NOUN
ejpam-4239	7	58	of	of	ADP
ejpam-4239	7	59	wave	wave	NOUN
ejpam-4239	7	60	propagation	propagation	NOUN
ejpam-4239	7	61	along	along	ADP
ejpam-4239	7	62	a	a	DET
ejpam-4239	7	63	coaxial	coaxial	ADJ
ejpam-4239	7	64	cable	cable	NOUN
ejpam-4239	7	65	was	be	AUX
ejpam-4239	7	66	investigated	investigate	VERB
ejpam-4239	7	67	,	,	PUNCT
ejpam-4239	7	68	temme	temme	VERB
ejpam-4239	8	1	[	[	X
ejpam-4239	8	2	7	7	NUM
ejpam-4239	8	3	]	]	PUNCT
ejpam-4239	8	4	,	,	PUNCT
ejpam-4239	8	5	where	where	SCONJ
ejpam-4239	8	6	the	the	DET
ejpam-4239	8	7	mathematical	mathematical	ADJ
ejpam-4239	8	8	discussion	discussion	NOUN
ejpam-4239	8	9	of	of	ADP
ejpam-4239	8	10	the	the	DET
ejpam-4239	8	11	exchange	exchange	NOUN
ejpam-4239	8	12	processes	process	NOUN
ejpam-4239	8	13	,	,	PUNCT
ejpam-4239	8	14	of	of	ADP
ejpam-4239	8	15	heat	heat	NOUN
ejpam-4239	8	16	or	or	CCONJ
ejpam-4239	8	17	of	of	ADP
ejpam-4239	8	18	matter	matter	NOUN
ejpam-4239	8	19	(	(	PUNCT
ejpam-4239	8	20	as	as	ADP
ejpam-4239	8	21	in	in	ADP
ejpam-4239	8	22	ion	ion	NOUN
ejpam-4239	8	23	exchange	exchange	NOUN
ejpam-4239	8	24	or	or	CCONJ
ejpam-4239	8	25	adsorption	adsorption	NOUN
ejpam-4239	8	26	)	)	PUNCT
ejpam-4239	8	27	,	,	PUNCT
ejpam-4239	8	28	that	that	PRON
ejpam-4239	8	29	arise	arise	VERB
ejpam-4239	8	30	when	when	SCONJ
ejpam-4239	8	31	a	a	DET
ejpam-4239	8	32	fluid	fluid	NOUN
ejpam-4239	8	33	flows	flow	VERB
ejpam-4239	8	34	through	through	ADP
ejpam-4239	8	35	the	the	DET
ejpam-4239	8	36	pores	pore	NOUN
ejpam-4239	8	37	or	or	CCONJ
ejpam-4239	8	38	voids	voids	NOUN
ejpam-4239	8	39	along	along	ADP
ejpam-4239	8	40	a	a	DET
ejpam-4239	8	41	column	column	NOUN
ejpam-4239	8	42	containing	contain	VERB
ejpam-4239	8	43	matter	matter	NOUN
ejpam-4239	8	44	in	in	ADP
ejpam-4239	8	45	the	the	DET
ejpam-4239	8	46	solid	solid	ADJ
ejpam-4239	8	47	state	state	NOUN
ejpam-4239	8	48	,	,	PUNCT
ejpam-4239	8	49	was	be	AUX
ejpam-4239	8	50	studied	study	VERB
ejpam-4239	8	51	.	.	PUNCT
ejpam-4239	9	1	throughout	throughout	ADP
ejpam-4239	9	2	these	these	DET
ejpam-4239	9	3	works	work	NOUN
ejpam-4239	9	4	the	the	DET
ejpam-4239	9	5	authors	author	NOUN
ejpam-4239	9	6	derive	derive	VERB
ejpam-4239	9	7	definite	definite	ADJ
ejpam-4239	9	8	integrals	integral	NOUN
ejpam-4239	9	9	involving	involve	VERB
ejpam-4239	9	10	the	the	DET
ejpam-4239	9	11	bessel	bessel	ADJ
ejpam-4239	9	12	function	function	NOUN
ejpam-4239	9	13	or	or	CCONJ
ejpam-4239	9	14	the	the	DET
ejpam-4239	9	15	product	product	NOUN
ejpam-4239	9	16	of	of	ADP
ejpam-4239	9	17	bessel	bessel	NOUN
ejpam-4239	9	18	functions	function	NOUN
ejpam-4239	9	19	for	for	ADP
ejpam-4239	9	20	specific	specific	ADJ
ejpam-4239	9	21	orders	order	NOUN
ejpam-4239	9	22	.	.	PUNCT
ejpam-4239	10	1	in	in	ADP
ejpam-4239	10	2	our	our	PRON
ejpam-4239	10	3	present	present	ADJ
ejpam-4239	10	4	paper	paper	NOUN
ejpam-4239	10	5	we	we	PRON
ejpam-4239	10	6	will	will	AUX
ejpam-4239	10	7	be	be	AUX
ejpam-4239	10	8	expanding	expand	VERB
ejpam-4239	10	9	on	on	ADP
ejpam-4239	10	10	the	the	DET
ejpam-4239	10	11	previous	previous	ADJ
ejpam-4239	10	12	formulae	formulae	NOUN
ejpam-4239	10	13	by	by	ADP
ejpam-4239	10	14	deriving	derive	VERB
ejpam-4239	10	15	a	a	DET
ejpam-4239	10	16	double	double	ADJ
ejpam-4239	10	17	integral	integral	NOUN
ejpam-4239	10	18	of	of	ADP
ejpam-4239	10	19	the	the	DET
ejpam-4239	10	20	product	product	NOUN
ejpam-4239	10	21	of	of	ADP
ejpam-4239	10	22	bessel	bessel	NOUN
ejpam-4239	10	23	functions	function	NOUN
ejpam-4239	10	24	over	over	ADP
ejpam-4239	10	25	a	a	DET
ejpam-4239	10	26	general	general	ADJ
ejpam-4239	10	27	order	order	NOUN
ejpam-4239	10	28	.	.	PUNCT
ejpam-4239	11	1	in	in	ADP
ejpam-4239	11	2	this	this	DET
ejpam-4239	11	3	paper	paper	NOUN
ejpam-4239	11	4	we	we	PRON
ejpam-4239	11	5	derive	derive	VERB
ejpam-4239	11	6	the	the	DET
ejpam-4239	11	7	double	double	ADJ
ejpam-4239	11	8	definite	definite	ADJ
ejpam-4239	11	9	integral	integral	ADJ
ejpam-4239	11	10	given	give	VERB
ejpam-4239	11	11	by	by	ADP
ejpam-4239	11	12	(	(	PUNCT
ejpam-4239	11	13	1	1	NUM
ejpam-4239	11	14	)	)	PUNCT
ejpam-4239	11	15	∫	∫	PROPN
ejpam-4239	11	16	∞	∞	PROPN
ejpam-4239	11	17	0	0	NUM
ejpam-4239	12	1	∫	∫	PROPN
ejpam-4239	12	2	∞	∞	PROPN
ejpam-4239	12	3	0	0	NUM
ejpam-4239	12	4	xm−1y1−mkv(xβ)jv(yα	xm−1y1−mkv(xβ)jv(yα	PROPN
ejpam-4239	12	5	)	)	PUNCT
ejpam-4239	12	6	log	log	NOUN
ejpam-4239	12	7	k	k	NOUN
ejpam-4239	13	1	(	(	PUNCT
ejpam-4239	13	2	ax	ax	NOUN
ejpam-4239	13	3	y	y	PROPN
ejpam-4239	13	4	)	)	PUNCT
ejpam-4239	13	5	dxdy	dxdy	PROPN
ejpam-4239	13	6	where	where	SCONJ
ejpam-4239	13	7	the	the	DET
ejpam-4239	13	8	parameters	parameter	NOUN
ejpam-4239	13	9	k	k	PROPN
ejpam-4239	13	10	,	,	PUNCT
ejpam-4239	13	11	a	a	PRON
ejpam-4239	13	12	,	,	PUNCT
ejpam-4239	13	13	α	α	NOUN
ejpam-4239	13	14	,	,	PUNCT
ejpam-4239	13	15	β	β	NOUN
ejpam-4239	13	16	,	,	PUNCT
ejpam-4239	13	17	v	v	PROPN
ejpam-4239	13	18	,	,	PUNCT
ejpam-4239	13	19	m	m	VERB
ejpam-4239	13	20	are	be	AUX
ejpam-4239	13	21	general	general	ADJ
ejpam-4239	13	22	complex	complex	ADJ
ejpam-4239	13	23	numbers	number	NOUN
ejpam-4239	13	24	and	and	CCONJ
ejpam-4239	13	25	re(α	re(α	NOUN
ejpam-4239	13	26	,	,	PUNCT
ejpam-4239	13	27	β	β	X
ejpam-4239	13	28	,	,	PUNCT
ejpam-4239	13	29	v	v	NOUN
ejpam-4239	13	30	,	,	PUNCT
ejpam-4239	13	31	m	m	NOUN
ejpam-4239	13	32	)	)	PUNCT
ejpam-4239	13	33	>	>	X
ejpam-4239	13	34	0	0	NUM
ejpam-4239	13	35	,	,	PUNCT
ejpam-4239	13	36	re(v	re(v	NOUN
ejpam-4239	13	37	)	)	PUNCT
ejpam-4239	13	38	<	<	X
ejpam-4239	13	39	re(m	re(m	PROPN
ejpam-4239	13	40	)	)	PUNCT
ejpam-4239	13	41	<	<	X
ejpam-4239	14	1	3/2	3/2	NUM
ejpam-4239	14	2	.	.	PUNCT
ejpam-4239	15	1	this	this	DET
ejpam-4239	15	2	definite	definite	ADJ
ejpam-4239	15	3	integral	integral	ADJ
ejpam-4239	15	4	will	will	AUX
ejpam-4239	15	5	be	be	AUX
ejpam-4239	15	6	used	use	VERB
ejpam-4239	15	7	to	to	PART
ejpam-4239	15	8	derive	derive	VERB
ejpam-4239	15	9	special	special	ADJ
ejpam-4239	15	10	cases	case	NOUN
ejpam-4239	15	11	in	in	ADP
ejpam-4239	15	12	∗corresponding	∗corresponde	VERB
ejpam-4239	15	13	author	author	NOUN
ejpam-4239	15	14	.	.	PUNCT
ejpam-4239	16	1	doi	doi	NOUN
ejpam-4239	16	2	:	:	PUNCT
ejpam-4239	16	3	https://doi.org/10.29020/nybg.ejpam.v15i3.4239	https://doi.org/10.29020/nybg.ejpam.v15i3.4239	NUM
ejpam-4239	16	4	email	email	NOUN
ejpam-4239	16	5	addresses	address	NOUN
ejpam-4239	16	6	:	:	PUNCT
ejpam-4239	16	7	milver@my.yorku.ca	milver@my.yorku.ca	NOUN
ejpam-4239	16	8	(	(	PUNCT
ejpam-4239	16	9	r.	r.	PROPN
ejpam-4239	16	10	reynolds	reynolds	PROPN
ejpam-4239	16	11	)	)	PUNCT
ejpam-4239	16	12	,	,	PUNCT
ejpam-4239	16	13	stauffer@yorku.ca	stauffer@yorku.ca	NOUN
ejpam-4239	16	14	(	(	PUNCT
ejpam-4239	16	15	a.	a.	NOUN
ejpam-4239	16	16	stauffer	stauffer	PROPN
ejpam-4239	16	17	)	)	PUNCT
ejpam-4239	16	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4239	17	1	856	856	NUM
ejpam-4239	17	2	©	©	ADP
ejpam-4239	17	3	2022	2022	NUM
ejpam-4239	17	4	ejpam	ejpam	VERB
ejpam-4239	17	5	all	all	DET
ejpam-4239	17	6	rights	right	NOUN
ejpam-4239	17	7	reserved	reserve	VERB
ejpam-4239	17	8	.	.	PUNCT
ejpam-4239	18	1	r.	r.	PROPN
ejpam-4239	18	2	reynolds	reynolds	PROPN
ejpam-4239	18	3	,	,	PUNCT
ejpam-4239	18	4	a.	a.	PROPN
ejpam-4239	18	5	stauffer	stauffer	PROPN
ejpam-4239	18	6	/	/	SYM
ejpam-4239	18	7	eur	eur	PROPN
ejpam-4239	18	8	.	.	PUNCT
ejpam-4239	19	1	j.	j.	PROPN
ejpam-4239	19	2	pure	pure	PROPN
ejpam-4239	19	3	appl	appl	PROPN
ejpam-4239	19	4	.	.	PROPN
ejpam-4239	19	5	math	math	PROPN
ejpam-4239	19	6	,	,	PUNCT
ejpam-4239	19	7	15	15	NUM
ejpam-4239	19	8	(	(	PUNCT
ejpam-4239	19	9	3	3	NUM
ejpam-4239	19	10	)	)	PUNCT
ejpam-4239	19	11	(	(	PUNCT
ejpam-4239	19	12	2022	2022	NUM
ejpam-4239	19	13	)	)	PUNCT
ejpam-4239	19	14	,	,	PUNCT
ejpam-4239	19	15	856	856	NUM
ejpam-4239	19	16	-	-	SYM
ejpam-4239	19	17	863	863	NUM
ejpam-4239	19	18	857	857	NUM
ejpam-4239	19	19	terms	term	NOUN
ejpam-4239	19	20	of	of	ADP
ejpam-4239	19	21	special	special	ADJ
ejpam-4239	19	22	functions	function	NOUN
ejpam-4239	19	23	and	and	CCONJ
ejpam-4239	19	24	fundamental	fundamental	ADJ
ejpam-4239	19	25	constants	constant	NOUN
ejpam-4239	19	26	.	.	PUNCT
ejpam-4239	20	1	the	the	DET
ejpam-4239	20	2	derivations	derivation	NOUN
ejpam-4239	20	3	follow	follow	VERB
ejpam-4239	20	4	the	the	DET
ejpam-4239	20	5	method	method	NOUN
ejpam-4239	20	6	used	use	VERB
ejpam-4239	20	7	by	by	ADP
ejpam-4239	20	8	us	we	PRON
ejpam-4239	20	9	in	in	ADP
ejpam-4239	20	10	[	[	X
ejpam-4239	20	11	6	6	NUM
ejpam-4239	20	12	]	]	PUNCT
ejpam-4239	20	13	.	.	PUNCT
ejpam-4239	21	1	this	this	DET
ejpam-4239	21	2	method	method	NOUN
ejpam-4239	21	3	involves	involve	VERB
ejpam-4239	21	4	using	use	VERB
ejpam-4239	21	5	a	a	DET
ejpam-4239	21	6	form	form	NOUN
ejpam-4239	21	7	of	of	ADP
ejpam-4239	21	8	the	the	DET
ejpam-4239	21	9	generalized	generalize	VERB
ejpam-4239	21	10	cauchy	cauchy	PROPN
ejpam-4239	21	11	’s	’s	PART
ejpam-4239	21	12	integral	integral	ADJ
ejpam-4239	21	13	formula	formula	NOUN
ejpam-4239	21	14	given	give	VERB
ejpam-4239	21	15	by	by	ADP
ejpam-4239	21	16	yk	yk	PROPN
ejpam-4239	21	17	γ(k	γ(k	PROPN
ejpam-4239	21	18	+	+	CCONJ
ejpam-4239	21	19	1	1	X
ejpam-4239	21	20	)	)	PUNCT
ejpam-4239	21	21	=	=	SYM
ejpam-4239	21	22	1	1	NUM
ejpam-4239	21	23	2πi	2πi	ADJ
ejpam-4239	21	24	∫	∫	PROPN
ejpam-4239	21	25	c	c	PROPN
ejpam-4239	21	26	ewy	ewy	PROPN
ejpam-4239	21	27	wk+1	wk+1	PROPN
ejpam-4239	21	28	dw	dw	PROPN
ejpam-4239	21	29	.	.	PUNCT
ejpam-4239	22	1	(	(	PUNCT
ejpam-4239	22	2	2	2	X
ejpam-4239	22	3	)	)	PUNCT
ejpam-4239	22	4	where	where	SCONJ
ejpam-4239	22	5	c	c	NOUN
ejpam-4239	22	6	is	be	AUX
ejpam-4239	22	7	in	in	ADP
ejpam-4239	22	8	general	general	ADJ
ejpam-4239	22	9	an	an	DET
ejpam-4239	22	10	open	open	ADJ
ejpam-4239	22	11	contour	contour	NOUN
ejpam-4239	22	12	in	in	ADP
ejpam-4239	22	13	the	the	DET
ejpam-4239	22	14	complex	complex	ADJ
ejpam-4239	22	15	plane	plane	NOUN
ejpam-4239	22	16	where	where	SCONJ
ejpam-4239	22	17	the	the	DET
ejpam-4239	22	18	bilinear	bilinear	NOUN
ejpam-4239	22	19	concomitant	concomitant	NOUN
ejpam-4239	22	20	has	have	VERB
ejpam-4239	22	21	the	the	DET
ejpam-4239	22	22	same	same	ADJ
ejpam-4239	22	23	value	value	NOUN
ejpam-4239	22	24	at	at	ADP
ejpam-4239	22	25	the	the	DET
ejpam-4239	22	26	end	end	NOUN
ejpam-4239	22	27	points	point	NOUN
ejpam-4239	22	28	of	of	ADP
ejpam-4239	22	29	the	the	DET
ejpam-4239	22	30	contour	contour	NOUN
ejpam-4239	22	31	.	.	PUNCT
ejpam-4239	23	1	we	we	PRON
ejpam-4239	23	2	then	then	ADV
ejpam-4239	23	3	multiply	multiply	VERB
ejpam-4239	23	4	both	both	DET
ejpam-4239	23	5	sides	side	NOUN
ejpam-4239	23	6	by	by	ADP
ejpam-4239	23	7	a	a	DET
ejpam-4239	23	8	function	function	NOUN
ejpam-4239	23	9	of	of	ADP
ejpam-4239	23	10	x	x	PUNCT
ejpam-4239	23	11	and	and	CCONJ
ejpam-4239	23	12	y	y	PROPN
ejpam-4239	23	13	,	,	PUNCT
ejpam-4239	23	14	then	then	ADV
ejpam-4239	23	15	take	take	VERB
ejpam-4239	23	16	a	a	DET
ejpam-4239	23	17	definite	definite	ADJ
ejpam-4239	23	18	double	double	ADJ
ejpam-4239	23	19	integral	integral	NOUN
ejpam-4239	23	20	of	of	ADP
ejpam-4239	23	21	both	both	DET
ejpam-4239	23	22	sides	side	NOUN
ejpam-4239	23	23	.	.	PUNCT
ejpam-4239	24	1	this	this	PRON
ejpam-4239	24	2	yields	yield	VERB
ejpam-4239	24	3	a	a	DET
ejpam-4239	24	4	definite	definite	ADJ
ejpam-4239	24	5	integral	integral	ADJ
ejpam-4239	24	6	in	in	ADP
ejpam-4239	24	7	terms	term	NOUN
ejpam-4239	24	8	of	of	ADP
ejpam-4239	24	9	a	a	DET
ejpam-4239	24	10	contour	contour	NOUN
ejpam-4239	24	11	integral	integral	NOUN
ejpam-4239	24	12	.	.	PUNCT
ejpam-4239	25	1	then	then	ADV
ejpam-4239	25	2	we	we	PRON
ejpam-4239	25	3	multiply	multiply	VERB
ejpam-4239	25	4	both	both	DET
ejpam-4239	25	5	sides	side	NOUN
ejpam-4239	25	6	of	of	ADP
ejpam-4239	25	7	equation	equation	NOUN
ejpam-4239	25	8	(	(	PUNCT
ejpam-4239	25	9	2	2	NUM
ejpam-4239	25	10	)	)	PUNCT
ejpam-4239	25	11	by	by	ADP
ejpam-4239	25	12	another	another	DET
ejpam-4239	25	13	function	function	NOUN
ejpam-4239	25	14	of	of	ADP
ejpam-4239	25	15	x	x	PUNCT
ejpam-4239	25	16	and	and	CCONJ
ejpam-4239	25	17	y	y	PROPN
ejpam-4239	25	18	and	and	CCONJ
ejpam-4239	25	19	take	take	VERB
ejpam-4239	25	20	the	the	DET
ejpam-4239	25	21	infinite	infinite	ADJ
ejpam-4239	25	22	sums	sum	NOUN
ejpam-4239	25	23	of	of	ADP
ejpam-4239	25	24	both	both	DET
ejpam-4239	25	25	sides	side	NOUN
ejpam-4239	25	26	such	such	ADJ
ejpam-4239	25	27	that	that	SCONJ
ejpam-4239	25	28	the	the	DET
ejpam-4239	25	29	contour	contour	NOUN
ejpam-4239	25	30	integral	integral	NOUN
ejpam-4239	25	31	of	of	ADP
ejpam-4239	25	32	both	both	DET
ejpam-4239	25	33	equations	equation	NOUN
ejpam-4239	25	34	are	be	AUX
ejpam-4239	25	35	the	the	DET
ejpam-4239	25	36	same	same	ADJ
ejpam-4239	25	37	.	.	PUNCT
ejpam-4239	26	1	2	2	X
ejpam-4239	26	2	.	.	X
ejpam-4239	26	3	definite	definite	ADJ
ejpam-4239	26	4	integral	integral	ADJ
ejpam-4239	26	5	of	of	ADP
ejpam-4239	26	6	the	the	DET
ejpam-4239	26	7	contour	contour	NOUN
ejpam-4239	26	8	integral	integral	NOUN
ejpam-4239	26	9	we	we	PRON
ejpam-4239	26	10	use	use	VERB
ejpam-4239	26	11	the	the	DET
ejpam-4239	26	12	method	method	NOUN
ejpam-4239	26	13	in	in	ADP
ejpam-4239	26	14	[	[	X
ejpam-4239	26	15	6	6	NUM
ejpam-4239	26	16	]	]	PUNCT
ejpam-4239	26	17	.	.	PUNCT
ejpam-4239	27	1	the	the	DET
ejpam-4239	27	2	variable	variable	NOUN
ejpam-4239	27	3	of	of	ADP
ejpam-4239	27	4	integration	integration	NOUN
ejpam-4239	27	5	in	in	ADP
ejpam-4239	27	6	the	the	DET
ejpam-4239	27	7	contour	contour	NOUN
ejpam-4239	27	8	integral	integral	NOUN
ejpam-4239	27	9	is	be	AUX
ejpam-4239	27	10	t	t	X
ejpam-4239	27	11	=	=	SYM
ejpam-4239	27	12	w	w	PROPN
ejpam-4239	27	13	+	+	NUM
ejpam-4239	27	14	m.	m.	NOUN
ejpam-4239	27	15	the	the	DET
ejpam-4239	27	16	cut	cut	NOUN
ejpam-4239	27	17	and	and	CCONJ
ejpam-4239	27	18	contour	contour	NOUN
ejpam-4239	27	19	are	be	AUX
ejpam-4239	27	20	in	in	ADP
ejpam-4239	27	21	the	the	DET
ejpam-4239	27	22	first	first	ADJ
ejpam-4239	27	23	quadrant	quadrant	NOUN
ejpam-4239	27	24	of	of	ADP
ejpam-4239	27	25	the	the	DET
ejpam-4239	27	26	complex	complex	ADJ
ejpam-4239	27	27	t	t	NOUN
ejpam-4239	27	28	-	-	PUNCT
ejpam-4239	27	29	plane	plane	NOUN
ejpam-4239	27	30	.	.	PUNCT
ejpam-4239	28	1	the	the	DET
ejpam-4239	28	2	cut	cut	NOUN
ejpam-4239	28	3	approaches	approach	VERB
ejpam-4239	28	4	the	the	DET
ejpam-4239	28	5	origin	origin	NOUN
ejpam-4239	28	6	from	from	ADP
ejpam-4239	28	7	the	the	DET
ejpam-4239	28	8	interior	interior	NOUN
ejpam-4239	28	9	of	of	ADP
ejpam-4239	28	10	the	the	DET
ejpam-4239	28	11	first	first	ADJ
ejpam-4239	28	12	quadrant	quadrant	NOUN
ejpam-4239	28	13	and	and	CCONJ
ejpam-4239	28	14	the	the	DET
ejpam-4239	28	15	contour	contour	NOUN
ejpam-4239	28	16	goes	go	VERB
ejpam-4239	28	17	round	round	ADP
ejpam-4239	28	18	the	the	DET
ejpam-4239	28	19	origin	origin	NOUN
ejpam-4239	28	20	with	with	ADP
ejpam-4239	28	21	zero	zero	NUM
ejpam-4239	28	22	radius	radius	NOUN
ejpam-4239	28	23	and	and	CCONJ
ejpam-4239	28	24	is	be	AUX
ejpam-4239	28	25	on	on	ADP
ejpam-4239	28	26	opposite	opposite	ADJ
ejpam-4239	28	27	sides	side	NOUN
ejpam-4239	28	28	of	of	ADP
ejpam-4239	28	29	the	the	DET
ejpam-4239	28	30	cut	cut	NOUN
ejpam-4239	28	31	.	.	PUNCT
ejpam-4239	29	1	using	use	VERB
ejpam-4239	29	2	a	a	DET
ejpam-4239	29	3	generalization	generalization	NOUN
ejpam-4239	29	4	of	of	ADP
ejpam-4239	29	5	cauchy	cauchy	PROPN
ejpam-4239	29	6	’s	’s	PART
ejpam-4239	29	7	integral	integral	ADJ
ejpam-4239	29	8	formula	formula	NOUN
ejpam-4239	29	9	we	we	PRON
ejpam-4239	29	10	form	form	VERB
ejpam-4239	29	11	the	the	DET
ejpam-4239	29	12	double	double	ADJ
ejpam-4239	29	13	integral	integral	NOUN
ejpam-4239	29	14	by	by	ADP
ejpam-4239	29	15	replacing	replace	VERB
ejpam-4239	29	16	y	y	PRON
ejpam-4239	29	17	by	by	ADP
ejpam-4239	29	18	log	log	NOUN
ejpam-4239	29	19	(	(	PUNCT
ejpam-4239	29	20	ax	ax	NOUN
ejpam-4239	29	21	y	y	PROPN
ejpam-4239	29	22	)	)	PUNCT
ejpam-4239	29	23	and	and	CCONJ
ejpam-4239	29	24	multiplying	multiply	VERB
ejpam-4239	29	25	by	by	ADP
ejpam-4239	29	26	xm−1y1−mkv(xβ)jv(yα	xm−1y1−mkv(xβ)jv(yα	NOUN
ejpam-4239	29	27	)	)	PUNCT
ejpam-4239	29	28	then	then	ADV
ejpam-4239	29	29	taking	take	VERB
ejpam-4239	29	30	the	the	DET
ejpam-4239	29	31	definite	definite	ADJ
ejpam-4239	29	32	integral	integral	ADJ
ejpam-4239	29	33	with	with	ADP
ejpam-4239	29	34	respect	respect	NOUN
ejpam-4239	29	35	to	to	ADP
ejpam-4239	29	36	x	x	PUNCT
ejpam-4239	29	37	∈	∈	PROPN
ejpam-4239	30	1	[	[	X
ejpam-4239	30	2	0,∞	0,∞	NOUN
ejpam-4239	30	3	)	)	PUNCT
ejpam-4239	30	4	and	and	CCONJ
ejpam-4239	30	5	y	y	PROPN
ejpam-4239	30	6	∈	∈	PROPN
ejpam-4239	31	1	[	[	X
ejpam-4239	31	2	0,∞	0,∞	NOUN
ejpam-4239	31	3	)	)	PUNCT
ejpam-4239	31	4	to	to	PART
ejpam-4239	31	5	obtain	obtain	VERB
ejpam-4239	31	6	(	(	PUNCT
ejpam-4239	31	7	3	3	NUM
ejpam-4239	31	8	)	)	SYM
ejpam-4239	31	9	1	1	NUM
ejpam-4239	32	1	γ(k	γ(k	NOUN
ejpam-4239	32	2	+	+	CCONJ
ejpam-4239	32	3	1	1	X
ejpam-4239	32	4	)	)	PUNCT
ejpam-4239	32	5	∫	∫	PROPN
ejpam-4239	33	1	∞	∞	PROPN
ejpam-4239	33	2	0	0	NUM
ejpam-4239	34	1	∫	∫	PROPN
ejpam-4239	34	2	∞	∞	PROPN
ejpam-4239	34	3	0	0	NUM
ejpam-4239	34	4	xm−1y1−mkv(xβ)jv(yα	xm−1y1−mkv(xβ)jv(yα	PROPN
ejpam-4239	34	5	)	)	PUNCT
ejpam-4239	34	6	log	log	NOUN
ejpam-4239	34	7	k	k	NOUN
ejpam-4239	35	1	(	(	PUNCT
ejpam-4239	35	2	ax	ax	NOUN
ejpam-4239	35	3	y	y	PROPN
ejpam-4239	35	4	)	)	PUNCT
ejpam-4239	35	5	dxdy	dxdy	PROPN
ejpam-4239	35	6	=	=	SYM
ejpam-4239	35	7	1	1	NUM
ejpam-4239	35	8	2πi	2πi	NOUN
ejpam-4239	35	9	∫	∫	PROPN
ejpam-4239	35	10	∞	∞	PROPN
ejpam-4239	35	11	0	0	NUM
ejpam-4239	36	1	∫	∫	PROPN
ejpam-4239	36	2	∞	∞	PROPN
ejpam-4239	36	3	0	0	NUM
ejpam-4239	37	1	∫	∫	PROPN
ejpam-4239	37	2	c	c	PROPN
ejpam-4239	37	3	aww−k−1xm+w−1y−m−w+1kv(xβ)jv(yα)dwdxdy	aww−k−1xm+w−1y−m−w+1kv(xβ)jv(yα)dwdxdy	PROPN
ejpam-4239	37	4	=	=	PUNCT
ejpam-4239	37	5	1	1	NUM
ejpam-4239	37	6	2πi	2πi	NOUN
ejpam-4239	37	7	∫	∫	PROPN
ejpam-4239	38	1	c	c	PROPN
ejpam-4239	38	2	∫	∫	PROPN
ejpam-4239	39	1	∞	∞	NUM
ejpam-4239	39	2	0	0	NUM
ejpam-4239	40	1	∫	∫	PROPN
ejpam-4239	40	2	∞	∞	NOUN
ejpam-4239	40	3	0	0	NUM
ejpam-4239	41	1	aww−k−1xm+w−1y−m−w+1kv(xβ)jv(yα)dxdydw	aww−k−1xm+w−1y−m−w+1kv(xβ)jv(yα)dxdydw	PROPN
ejpam-4239	41	2	=	=	SYM
ejpam-4239	41	3	1	1	NUM
ejpam-4239	41	4	2πi	2πi	ADJ
ejpam-4239	41	5	∫	∫	PROPN
ejpam-4239	41	6	c	c	NOUN
ejpam-4239	41	7	1	1	NUM
ejpam-4239	41	8	2	2	NUM
ejpam-4239	41	9	πaww−k−1αm+w−2β−m−w	πaww−k−1αm+w−2β−m−w	PROPN
ejpam-4239	41	10	csc	csc	PROPN
ejpam-4239	41	11	(	(	PUNCT
ejpam-4239	41	12	1	1	NUM
ejpam-4239	41	13	2	2	NUM
ejpam-4239	41	14	π(m−	π(m−	NOUN
ejpam-4239	41	15	v	v	ADP
ejpam-4239	41	16	+	+	CCONJ
ejpam-4239	41	17	w	w	NOUN
ejpam-4239	41	18	)	)	PUNCT
ejpam-4239	41	19	)	)	PUNCT
ejpam-4239	41	20	dw	dw	PROPN
ejpam-4239	41	21	from	from	ADP
ejpam-4239	41	22	equations	equation	NOUN
ejpam-4239	41	23	(	(	PUNCT
ejpam-4239	41	24	3.10.1.2	3.10.1.2	NUM
ejpam-4239	41	25	)	)	PUNCT
ejpam-4239	41	26	and	and	CCONJ
ejpam-4239	41	27	(	(	PUNCT
ejpam-4239	41	28	3.14.3	3.14.3	NUM
ejpam-4239	41	29	)	)	PUNCT
ejpam-4239	41	30	in	in	ADP
ejpam-4239	41	31	[	[	X
ejpam-4239	41	32	1	1	X
ejpam-4239	41	33	]	]	PUNCT
ejpam-4239	41	34	where	where	SCONJ
ejpam-4239	41	35	re(α	re(α	NOUN
ejpam-4239	41	36	)	)	PUNCT
ejpam-4239	41	37	>	>	X
ejpam-4239	41	38	0	0	NUM
ejpam-4239	41	39	,	,	PUNCT
ejpam-4239	41	40	|re(v)|	|re(v)|	NOUN
ejpam-4239	41	41	<	<	X
ejpam-4239	41	42	re(w	re(w	X
ejpam-4239	41	43	+	+	NOUN
ejpam-4239	41	44	m−	m−	PROPN
ejpam-4239	41	45	v	v	NOUN
ejpam-4239	41	46	)	)	PUNCT
ejpam-4239	41	47	<	<	X
ejpam-4239	41	48	3/2	3/2	NUM
ejpam-4239	41	49	and	and	CCONJ
ejpam-4239	41	50	using	use	VERB
ejpam-4239	41	51	the	the	DET
ejpam-4239	41	52	reflection	reflection	NOUN
ejpam-4239	41	53	formula	formula	NOUN
ejpam-4239	41	54	(	(	PUNCT
ejpam-4239	41	55	8.334.3	8.334.3	NUM
ejpam-4239	41	56	)	)	PUNCT
ejpam-4239	41	57	in	in	ADP
ejpam-4239	41	58	[	[	X
ejpam-4239	41	59	4	4	X
ejpam-4239	41	60	]	]	PUNCT
ejpam-4239	41	61	for	for	ADP
ejpam-4239	41	62	the	the	DET
ejpam-4239	41	63	gamma	gamma	PROPN
ejpam-4239	41	64	function	function	NOUN
ejpam-4239	41	65	.	.	PUNCT
ejpam-4239	42	1	we	we	PRON
ejpam-4239	42	2	are	be	AUX
ejpam-4239	42	3	able	able	ADJ
ejpam-4239	42	4	to	to	PART
ejpam-4239	42	5	switch	switch	VERB
ejpam-4239	42	6	the	the	DET
ejpam-4239	42	7	order	order	NOUN
ejpam-4239	42	8	of	of	ADP
ejpam-4239	42	9	integration	integration	NOUN
ejpam-4239	42	10	over	over	ADP
ejpam-4239	42	11	x	x	PUNCT
ejpam-4239	42	12	and	and	CCONJ
ejpam-4239	42	13	y	y	PROPN
ejpam-4239	42	14	using	use	VERB
ejpam-4239	42	15	fubini	fubini	NOUN
ejpam-4239	42	16	’s	’s	PART
ejpam-4239	42	17	theorem	theorem	NOUN
ejpam-4239	42	18	since	since	SCONJ
ejpam-4239	42	19	the	the	DET
ejpam-4239	42	20	integrand	integrand	NOUN
ejpam-4239	42	21	is	be	AUX
ejpam-4239	42	22	of	of	ADP
ejpam-4239	42	23	bounded	bounded	ADJ
ejpam-4239	42	24	measure	measure	NOUN
ejpam-4239	42	25	over	over	ADP
ejpam-4239	42	26	the	the	DET
ejpam-4239	42	27	space	space	NOUN
ejpam-4239	42	28	c×	c×	NOUN
ejpam-4239	43	1	[	[	X
ejpam-4239	43	2	0,∞)×	0,∞)×	NUM
ejpam-4239	43	3	[	[	X
ejpam-4239	43	4	0,∞	0,∞	NUM
ejpam-4239	43	5	)	)	PUNCT
ejpam-4239	43	6	3	3	NUM
ejpam-4239	43	7	.	.	PUNCT
ejpam-4239	44	1	the	the	DET
ejpam-4239	44	2	hurwitz	hurwitz	PROPN
ejpam-4239	44	3	-	-	PUNCT
ejpam-4239	44	4	lerch	lerch	PROPN
ejpam-4239	44	5	zeta	zeta	PROPN
ejpam-4239	44	6	function	function	PROPN
ejpam-4239	44	7	and	and	CCONJ
ejpam-4239	44	8	infinite	infinite	ADJ
ejpam-4239	44	9	sum	sum	NOUN
ejpam-4239	44	10	of	of	ADP
ejpam-4239	44	11	the	the	DET
ejpam-4239	44	12	contour	contour	NOUN
ejpam-4239	44	13	integral	integral	NOUN
ejpam-4239	44	14	in	in	ADP
ejpam-4239	44	15	this	this	DET
ejpam-4239	44	16	section	section	NOUN
ejpam-4239	44	17	we	we	PRON
ejpam-4239	44	18	use	use	VERB
ejpam-4239	44	19	equation	equation	NOUN
ejpam-4239	44	20	(	(	PUNCT
ejpam-4239	44	21	2	2	NUM
ejpam-4239	44	22	)	)	PUNCT
ejpam-4239	44	23	to	to	PART
ejpam-4239	44	24	derive	derive	VERB
ejpam-4239	44	25	the	the	DET
ejpam-4239	44	26	contour	contour	NOUN
ejpam-4239	44	27	integral	integral	ADJ
ejpam-4239	44	28	representations	representation	NOUN
ejpam-4239	44	29	for	for	ADP
ejpam-4239	44	30	the	the	DET
ejpam-4239	44	31	hurwitz	hurwitz	PROPN
ejpam-4239	44	32	-	-	PUNCT
ejpam-4239	44	33	lerch	lerch	PROPN
ejpam-4239	44	34	zeta	zeta	PROPN
ejpam-4239	44	35	function	function	PROPN
ejpam-4239	44	36	.	.	PUNCT
ejpam-4239	45	1	r.	r.	PROPN
ejpam-4239	45	2	reynolds	reynolds	PROPN
ejpam-4239	45	3	,	,	PUNCT
ejpam-4239	45	4	a.	a.	PROPN
ejpam-4239	45	5	stauffer	stauffer	PROPN
ejpam-4239	45	6	/	/	SYM
ejpam-4239	45	7	eur	eur	PROPN
ejpam-4239	45	8	.	.	PUNCT
ejpam-4239	46	1	j.	j.	PROPN
ejpam-4239	46	2	pure	pure	PROPN
ejpam-4239	46	3	appl	appl	PROPN
ejpam-4239	46	4	.	.	PROPN
ejpam-4239	46	5	math	math	PROPN
ejpam-4239	46	6	,	,	PUNCT
ejpam-4239	46	7	15	15	NUM
ejpam-4239	46	8	(	(	PUNCT
ejpam-4239	46	9	3	3	NUM
ejpam-4239	46	10	)	)	PUNCT
ejpam-4239	46	11	(	(	PUNCT
ejpam-4239	46	12	2022	2022	NUM
ejpam-4239	46	13	)	)	PUNCT
ejpam-4239	46	14	,	,	PUNCT
ejpam-4239	46	15	856	856	NUM
ejpam-4239	46	16	-	-	SYM
ejpam-4239	46	17	863	863	NUM
ejpam-4239	46	18	858	858	NUM
ejpam-4239	46	19	3.1	3.1	NUM
ejpam-4239	46	20	.	.	PUNCT
ejpam-4239	47	1	the	the	DET
ejpam-4239	47	2	hurwitz	hurwitz	PROPN
ejpam-4239	47	3	-	-	PUNCT
ejpam-4239	47	4	lerch	lerch	PROPN
ejpam-4239	47	5	zeta	zeta	PROPN
ejpam-4239	47	6	function	function	VERB
ejpam-4239	47	7	the	the	DET
ejpam-4239	47	8	hurwitz	hurwitz	PROPN
ejpam-4239	47	9	-	-	PUNCT
ejpam-4239	47	10	lerch	lerch	PROPN
ejpam-4239	47	11	zeta	zeta	PROPN
ejpam-4239	47	12	function	function	PROPN
ejpam-4239	47	13	(	(	PUNCT
ejpam-4239	47	14	25.14	25.14	NUM
ejpam-4239	47	15	)	)	PUNCT
ejpam-4239	47	16	in	in	ADP
ejpam-4239	47	17	[	[	X
ejpam-4239	47	18	2	2	X
ejpam-4239	47	19	]	]	PUNCT
ejpam-4239	47	20	has	have	VERB
ejpam-4239	47	21	a	a	DET
ejpam-4239	47	22	series	series	NOUN
ejpam-4239	47	23	representation	representation	NOUN
ejpam-4239	47	24	given	give	VERB
ejpam-4239	47	25	by	by	ADP
ejpam-4239	47	26	φ(z	φ(z	PROPN
ejpam-4239	47	27	,	,	PUNCT
ejpam-4239	47	28	s	s	NOUN
ejpam-4239	47	29	,	,	PUNCT
ejpam-4239	47	30	v	v	NOUN
ejpam-4239	47	31	)	)	PUNCT
ejpam-4239	47	32	=	=	PUNCT
ejpam-4239	48	1	∞∑	∞∑	NUM
ejpam-4239	48	2	n=0	n=0	NUM
ejpam-4239	48	3	(	(	PUNCT
ejpam-4239	48	4	v	v	NOUN
ejpam-4239	48	5	+	+	PRON
ejpam-4239	48	6	n)−szn	n)−szn	NUM
ejpam-4239	48	7	(	(	PUNCT
ejpam-4239	48	8	4	4	NUM
ejpam-4239	48	9	)	)	PUNCT
ejpam-4239	48	10	where	where	SCONJ
ejpam-4239	48	11	|z|	|z|	VERB
ejpam-4239	48	12	<	<	X
ejpam-4239	48	13	1	1	NUM
ejpam-4239	48	14	,	,	PUNCT
ejpam-4239	48	15	v	v	ADP
ejpam-4239	48	16	̸=	̸=	PROPN
ejpam-4239	48	17	0,−1	0,−1	PROPN
ejpam-4239	48	18	,	,	PUNCT
ejpam-4239	48	19	..	..	PUNCT
ejpam-4239	48	20	and	and	CCONJ
ejpam-4239	48	21	is	be	AUX
ejpam-4239	48	22	continued	continue	VERB
ejpam-4239	48	23	analytically	analytically	ADV
ejpam-4239	48	24	by	by	ADP
ejpam-4239	48	25	its	its	PRON
ejpam-4239	48	26	integral	integral	ADJ
ejpam-4239	48	27	representation	representation	NOUN
ejpam-4239	48	28	given	give	VERB
ejpam-4239	48	29	by	by	ADP
ejpam-4239	48	30	φ(z	φ(z	PROPN
ejpam-4239	48	31	,	,	PUNCT
ejpam-4239	48	32	s	s	NOUN
ejpam-4239	48	33	,	,	PUNCT
ejpam-4239	48	34	v	v	NOUN
ejpam-4239	48	35	)	)	PUNCT
ejpam-4239	48	36	=	=	SYM
ejpam-4239	48	37	1	1	NUM
ejpam-4239	48	38	γ(s	γ(	NOUN
ejpam-4239	48	39	)	)	PUNCT
ejpam-4239	48	40	∫	∫	PROPN
ejpam-4239	49	1	∞	∞	PROPN
ejpam-4239	49	2	0	0	NUM
ejpam-4239	50	1	ts−1e−vt	ts−1e−vt	PRON
ejpam-4239	51	1	1−	1−	NUM
ejpam-4239	51	2	ze−t	ze−t	NOUN
ejpam-4239	51	3	dt	dt	NOUN
ejpam-4239	52	1	=	=	SYM
ejpam-4239	52	2	1	1	NUM
ejpam-4239	52	3	γ(s	γ(s	PROPN
ejpam-4239	52	4	)	)	PUNCT
ejpam-4239	52	5	∫	∫	PROPN
ejpam-4239	53	1	∞	∞	NUM
ejpam-4239	53	2	0	0	NUM
ejpam-4239	54	1	ts−1e−(v−1)t	ts−1e−(v−1)t	PROPN
ejpam-4239	54	2	et	et	NOUN
ejpam-4239	54	3	−	−	NOUN
ejpam-4239	54	4	z	z	NOUN
ejpam-4239	54	5	dt	dt	X
ejpam-4239	54	6	(	(	PUNCT
ejpam-4239	54	7	5	5	NUM
ejpam-4239	54	8	)	)	PUNCT
ejpam-4239	54	9	where	where	SCONJ
ejpam-4239	54	10	re(v	re(v	NOUN
ejpam-4239	54	11	)	)	PUNCT
ejpam-4239	54	12	>	>	X
ejpam-4239	54	13	0	0	NUM
ejpam-4239	54	14	,	,	PUNCT
ejpam-4239	54	15	and	and	CCONJ
ejpam-4239	54	16	either	either	ADV
ejpam-4239	54	17	|z|≤	|z|≤	SYM
ejpam-4239	54	18	1	1	NUM
ejpam-4239	54	19	,	,	PUNCT
ejpam-4239	54	20	z	z	NOUN
ejpam-4239	54	21	̸=	̸=	PROPN
ejpam-4239	54	22	1	1	NUM
ejpam-4239	54	23	,	,	PUNCT
ejpam-4239	54	24	re(s	re(s	ADJ
ejpam-4239	54	25	)	)	PUNCT
ejpam-4239	54	26	>	>	X
ejpam-4239	54	27	0	0	NUM
ejpam-4239	54	28	,	,	PUNCT
ejpam-4239	54	29	or	or	CCONJ
ejpam-4239	54	30	z	z	NOUN
ejpam-4239	54	31	=	=	SYM
ejpam-4239	54	32	1	1	NUM
ejpam-4239	54	33	,	,	PUNCT
ejpam-4239	54	34	re(s	re(s	ADJ
ejpam-4239	54	35	)	)	PUNCT
ejpam-4239	54	36	>	>	X
ejpam-4239	55	1	1	1	NUM
ejpam-4239	55	2	.	.	X
ejpam-4239	55	3	3.2	3.2	NUM
ejpam-4239	55	4	.	.	PUNCT
ejpam-4239	55	5	infinite	infinite	ADJ
ejpam-4239	55	6	sum	sum	NOUN
ejpam-4239	55	7	of	of	ADP
ejpam-4239	55	8	the	the	DET
ejpam-4239	55	9	contour	contour	NOUN
ejpam-4239	55	10	integral	integral	ADJ
ejpam-4239	55	11	using	use	VERB
ejpam-4239	55	12	equation	equation	NOUN
ejpam-4239	55	13	(	(	PUNCT
ejpam-4239	55	14	2	2	NUM
ejpam-4239	55	15	)	)	PUNCT
ejpam-4239	55	16	and	and	CCONJ
ejpam-4239	55	17	replacing	replace	VERB
ejpam-4239	55	18	y	y	PRON
ejpam-4239	55	19	by	by	ADP
ejpam-4239	55	20	log(a	log(a	PROPN
ejpam-4239	55	21	)	)	PUNCT
ejpam-4239	56	1	+	+	PUNCT
ejpam-4239	56	2	log(α	log(α	X
ejpam-4239	56	3	)	)	PUNCT
ejpam-4239	56	4	−	−	PROPN
ejpam-4239	56	5	log(β	log(β	PROPN
ejpam-4239	56	6	)	)	PUNCT
ejpam-4239	56	7	+	+	CCONJ
ejpam-4239	56	8	1	1	NUM
ejpam-4239	56	9	2	2	NUM
ejpam-4239	56	10	iπ(2y	iπ(2y	NOUN
ejpam-4239	56	11	+	+	NOUN
ejpam-4239	56	12	1	1	X
ejpam-4239	56	13	)	)	PUNCT
ejpam-4239	56	14	then	then	ADV
ejpam-4239	56	15	multiplying	multiply	VERB
ejpam-4239	56	16	both	both	DET
ejpam-4239	56	17	sides	side	NOUN
ejpam-4239	56	18	by	by	ADP
ejpam-4239	56	19	−iπαm−2β−me	−iπαm−2β−me	PROPN
ejpam-4239	56	20	1	1	NUM
ejpam-4239	56	21	2	2	NUM
ejpam-4239	56	22	iπ(2y+1)(m−v	iπ(2y+1)(m−v	NOUN
ejpam-4239	56	23	)	)	PUNCT
ejpam-4239	56	24	taking	take	VERB
ejpam-4239	56	25	the	the	DET
ejpam-4239	56	26	infinite	infinite	ADJ
ejpam-4239	56	27	sum	sum	NOUN
ejpam-4239	56	28	over	over	ADP
ejpam-4239	56	29	y	y	PROPN
ejpam-4239	56	30	∈	∈	PROPN
ejpam-4239	57	1	[	[	X
ejpam-4239	57	2	0,∞	0,∞	NOUN
ejpam-4239	57	3	)	)	PUNCT
ejpam-4239	57	4	and	and	CCONJ
ejpam-4239	57	5	simplifying	simplify	VERB
ejpam-4239	57	6	in	in	ADP
ejpam-4239	57	7	terms	term	NOUN
ejpam-4239	57	8	of	of	ADP
ejpam-4239	57	9	the	the	DET
ejpam-4239	57	10	hurwitz	hurwitz	PROPN
ejpam-4239	57	11	-	-	PUNCT
ejpam-4239	57	12	lerch	lerch	PROPN
ejpam-4239	57	13	zeta	zeta	PROPN
ejpam-4239	57	14	function	function	VERB
ejpam-4239	57	15	we	we	PRON
ejpam-4239	57	16	obtain	obtain	VERB
ejpam-4239	57	17	(	(	PUNCT
ejpam-4239	57	18	6	6	NUM
ejpam-4239	57	19	)	)	PUNCT
ejpam-4239	57	20	−	−	PROPN
ejpam-4239	57	21	1	1	NUM
ejpam-4239	58	1	γ(k	γ(k	NOUN
ejpam-4239	58	2	+	+	CCONJ
ejpam-4239	58	3	1	1	X
ejpam-4239	58	4	)	)	PUNCT
ejpam-4239	58	5	iπk+1αm−2β−me	iπk+1αm−2β−me	NOUN
ejpam-4239	58	6	1	1	NUM
ejpam-4239	58	7	2	2	NUM
ejpam-4239	58	8	iπ(k+m−v	iπ(k+m−v	NOUN
ejpam-4239	58	9	)	)	PUNCT
ejpam-4239	58	10	φ	φ	PROPN
ejpam-4239	58	11	(	(	PUNCT
ejpam-4239	58	12	eiπ(m−v),−k	eiπ(m−v),−k	PROPN
ejpam-4239	58	13	,	,	PUNCT
ejpam-4239	58	14	−2i	−2i	PROPN
ejpam-4239	58	15	log(a)−	log(a)−	NOUN
ejpam-4239	58	16	2i	2i	NOUN
ejpam-4239	58	17	log(α	log(α	PROPN
ejpam-4239	58	18	)	)	PUNCT
ejpam-4239	59	1	+	+	NUM
ejpam-4239	59	2	2i	2i	NUM
ejpam-4239	59	3	log(β	log(β	PROPN
ejpam-4239	59	4	)	)	PUNCT
ejpam-4239	59	5	+	+	NUM
ejpam-4239	59	6	π	π	PROPN
ejpam-4239	59	7	2π	2π	NOUN
ejpam-4239	59	8	)	)	PUNCT
ejpam-4239	60	1	=	=	PUNCT
ejpam-4239	61	1	−	−	PROPN
ejpam-4239	61	2	1	1	NUM
ejpam-4239	61	3	2πi	2πi	NOUN
ejpam-4239	61	4	∞∑	∞∑	NUM
ejpam-4239	61	5	y=0	y=0	NUM
ejpam-4239	61	6	∫	∫	X
ejpam-4239	61	7	c	c	PROPN
ejpam-4239	61	8	iπw−k−1αm−2β−m	iπw−k−1αm−2β−m	VERB
ejpam-4239	61	9	exp	exp	X
ejpam-4239	61	10	(	(	PUNCT
ejpam-4239	61	11	w(log(a	w(log(a	PROPN
ejpam-4239	61	12	)	)	PUNCT
ejpam-4239	62	1	+	+	CCONJ
ejpam-4239	62	2	log(α)−	log(α)−	PROPN
ejpam-4239	62	3	log(β	log(β	PROPN
ejpam-4239	62	4	)	)	PUNCT
ejpam-4239	62	5	)	)	PUNCT
ejpam-4239	63	1	+	+	CCONJ
ejpam-4239	63	2	1	1	NUM
ejpam-4239	63	3	2	2	NUM
ejpam-4239	63	4	iπ(2y	iπ(2y	NOUN
ejpam-4239	63	5	+	+	NOUN
ejpam-4239	63	6	1)(m−	1)(m−	NUM
ejpam-4239	63	7	v	v	NUM
ejpam-4239	63	8	+	+	CCONJ
ejpam-4239	63	9	w	w	NOUN
ejpam-4239	63	10	)	)	PUNCT
ejpam-4239	63	11	)	)	PUNCT
ejpam-4239	63	12	dw	dw	NOUN
ejpam-4239	63	13	=	=	SYM
ejpam-4239	64	1	−	−	PROPN
ejpam-4239	64	2	1	1	NUM
ejpam-4239	64	3	2πi	2πi	NOUN
ejpam-4239	64	4	∫	∫	PROPN
ejpam-4239	65	1	c	c	NOUN
ejpam-4239	65	2	∞∑	∞∑	NUM
ejpam-4239	65	3	y=0	y=0	NOUN
ejpam-4239	65	4	iπw−k−1αm−2β−m	iπw−k−1αm−2β−m	VERB
ejpam-4239	65	5	exp	exp	NOUN
ejpam-4239	65	6	(	(	PUNCT
ejpam-4239	65	7	w(log(a	w(log(a	PROPN
ejpam-4239	65	8	)	)	PUNCT
ejpam-4239	65	9	+	+	CCONJ
ejpam-4239	65	10	log(α)−	log(α)−	PROPN
ejpam-4239	65	11	log(β	log(β	PROPN
ejpam-4239	65	12	)	)	PUNCT
ejpam-4239	65	13	)	)	PUNCT
ejpam-4239	66	1	+	+	CCONJ
ejpam-4239	66	2	1	1	NUM
ejpam-4239	66	3	2	2	NUM
ejpam-4239	66	4	iπ(2y	iπ(2y	NOUN
ejpam-4239	66	5	+	+	NOUN
ejpam-4239	66	6	1)(m−	1)(m−	NUM
ejpam-4239	66	7	v	v	NUM
ejpam-4239	66	8	+	+	CCONJ
ejpam-4239	66	9	w	w	NOUN
ejpam-4239	66	10	)	)	PUNCT
ejpam-4239	66	11	)	)	PUNCT
ejpam-4239	66	12	dw	dw	NOUN
ejpam-4239	66	13	=	=	SYM
ejpam-4239	66	14	1	1	NUM
ejpam-4239	66	15	2πi	2πi	ADJ
ejpam-4239	66	16	∫	∫	PROPN
ejpam-4239	66	17	c	c	NOUN
ejpam-4239	66	18	1	1	NUM
ejpam-4239	66	19	2	2	NUM
ejpam-4239	66	20	πaww−k−1αm+w−2β−m−w	πaww−k−1αm+w−2β−m−w	PROPN
ejpam-4239	66	21	csc	csc	PROPN
ejpam-4239	66	22	(	(	PUNCT
ejpam-4239	66	23	1	1	NUM
ejpam-4239	66	24	2	2	NUM
ejpam-4239	66	25	π(m−	π(m−	NOUN
ejpam-4239	66	26	v	v	ADP
ejpam-4239	66	27	+	+	CCONJ
ejpam-4239	66	28	w	w	NOUN
ejpam-4239	66	29	)	)	PUNCT
ejpam-4239	66	30	)	)	PUNCT
ejpam-4239	66	31	dw	dw	NOUN
ejpam-4239	66	32	from	from	ADP
ejpam-4239	66	33	equation	equation	NOUN
ejpam-4239	66	34	(	(	PUNCT
ejpam-4239	66	35	1.232.2	1.232.2	NUM
ejpam-4239	66	36	)	)	PUNCT
ejpam-4239	66	37	in	in	ADP
ejpam-4239	66	38	[	[	X
ejpam-4239	66	39	4	4	X
ejpam-4239	66	40	]	]	PUNCT
ejpam-4239	66	41	where	where	SCONJ
ejpam-4239	66	42	i	i	PRON
ejpam-4239	66	43	m	m	VERB
ejpam-4239	66	44	(	(	PUNCT
ejpam-4239	66	45	1	1	NUM
ejpam-4239	66	46	2π(m−	2π(m−	NUM
ejpam-4239	66	47	v	v	ADP
ejpam-4239	66	48	+	+	CCONJ
ejpam-4239	66	49	w	w	NOUN
ejpam-4239	66	50	)	)	PUNCT
ejpam-4239	66	51	)	)	PUNCT
ejpam-4239	66	52	>	>	X
ejpam-4239	66	53	0	0	PUNCT
ejpam-4239	67	1	in	in	ADP
ejpam-4239	67	2	order	order	NOUN
ejpam-4239	67	3	for	for	SCONJ
ejpam-4239	67	4	the	the	DET
ejpam-4239	67	5	sum	sum	NOUN
ejpam-4239	67	6	to	to	PART
ejpam-4239	67	7	converge	converge	VERB
ejpam-4239	67	8	.	.	PUNCT
ejpam-4239	67	9	r.	r.	PROPN
ejpam-4239	67	10	reynolds	reynolds	PROPN
ejpam-4239	67	11	,	,	PUNCT
ejpam-4239	67	12	a.	a.	PROPN
ejpam-4239	67	13	stauffer	stauffer	PROPN
ejpam-4239	67	14	/	/	SYM
ejpam-4239	67	15	eur	eur	PROPN
ejpam-4239	67	16	.	.	PUNCT
ejpam-4239	68	1	j.	j.	PROPN
ejpam-4239	68	2	pure	pure	PROPN
ejpam-4239	68	3	appl	appl	PROPN
ejpam-4239	68	4	.	.	PROPN
ejpam-4239	68	5	math	math	PROPN
ejpam-4239	68	6	,	,	PUNCT
ejpam-4239	68	7	15	15	NUM
ejpam-4239	68	8	(	(	PUNCT
ejpam-4239	68	9	3	3	NUM
ejpam-4239	68	10	)	)	PUNCT
ejpam-4239	68	11	(	(	PUNCT
ejpam-4239	68	12	2022	2022	NUM
ejpam-4239	68	13	)	)	PUNCT
ejpam-4239	68	14	,	,	PUNCT
ejpam-4239	68	15	856	856	NUM
ejpam-4239	68	16	-	-	SYM
ejpam-4239	68	17	863	863	NUM
ejpam-4239	68	18	859	859	NUM
ejpam-4239	68	19	4	4	NUM
ejpam-4239	68	20	.	.	PUNCT
ejpam-4239	69	1	definite	definite	ADJ
ejpam-4239	69	2	integral	integral	ADJ
ejpam-4239	69	3	in	in	ADP
ejpam-4239	69	4	terms	term	NOUN
ejpam-4239	69	5	of	of	ADP
ejpam-4239	69	6	the	the	DET
ejpam-4239	69	7	hurwitz	hurwitz	PROPN
ejpam-4239	69	8	-	-	PUNCT
ejpam-4239	69	9	lerch	lerch	PROPN
ejpam-4239	69	10	zeta	zeta	PROPN
ejpam-4239	69	11	function	function	PROPN
ejpam-4239	69	12	theorem	theorem	VERB
ejpam-4239	69	13	1	1	NUM
ejpam-4239	69	14	.	.	PUNCT
ejpam-4239	70	1	for	for	ADP
ejpam-4239	70	2	all	all	DET
ejpam-4239	70	3	k	k	NOUN
ejpam-4239	70	4	,	,	PUNCT
ejpam-4239	70	5	a	a	DET
ejpam-4239	70	6	∈	∈	PROPN
ejpam-4239	70	7	c	c	NOUN
ejpam-4239	70	8	,	,	PUNCT
ejpam-4239	70	9	re(α	re(α	PROPN
ejpam-4239	70	10	,	,	PUNCT
ejpam-4239	70	11	β	β	X
ejpam-4239	70	12	,	,	PUNCT
ejpam-4239	70	13	v	v	NOUN
ejpam-4239	70	14	,	,	PUNCT
ejpam-4239	70	15	m	m	NOUN
ejpam-4239	70	16	)	)	PUNCT
ejpam-4239	70	17	>	>	X
ejpam-4239	70	18	0	0	NUM
ejpam-4239	70	19	,	,	PUNCT
ejpam-4239	70	20	re(v	re(v	NOUN
ejpam-4239	70	21	)	)	PUNCT
ejpam-4239	70	22	<	<	X
ejpam-4239	70	23	re(m	re(m	PROPN
ejpam-4239	70	24	)	)	PUNCT
ejpam-4239	70	25	<	<	X
ejpam-4239	70	26	3/2	3/2	NUM
ejpam-4239	70	27	,	,	PUNCT
ejpam-4239	70	28	(	(	PUNCT
ejpam-4239	70	29	7	7	NUM
ejpam-4239	70	30	)	)	PUNCT
ejpam-4239	70	31	∫	∫	PROPN
ejpam-4239	70	32	∞	∞	PROPN
ejpam-4239	70	33	0	0	NUM
ejpam-4239	70	34	∫	∫	PROPN
ejpam-4239	70	35	∞	∞	PROPN
ejpam-4239	70	36	0	0	NUM
ejpam-4239	70	37	xm−1y1−mkv(xβ)jv(yα	xm−1y1−mkv(xβ)jv(yα	PROPN
ejpam-4239	70	38	)	)	PUNCT
ejpam-4239	70	39	log	log	NOUN
ejpam-4239	71	1	k	k	NOUN
ejpam-4239	72	1	(	(	PUNCT
ejpam-4239	72	2	ax	ax	NOUN
ejpam-4239	72	3	y	y	PROPN
ejpam-4239	72	4	)	)	PUNCT
ejpam-4239	72	5	dxdy	dxdy	PROPN
ejpam-4239	72	6	=	=	PUNCT
ejpam-4239	73	1	−iπk+1αm−2β−me	−iπk+1αm−2β−me	NOUN
ejpam-4239	73	2	1	1	NUM
ejpam-4239	73	3	2	2	NUM
ejpam-4239	73	4	iπ(k+m−v	iπ(k+m−v	NOUN
ejpam-4239	73	5	)	)	PUNCT
ejpam-4239	73	6	φ	φ	PROPN
ejpam-4239	73	7	(	(	PUNCT
ejpam-4239	73	8	eiπ(m−v),−k	eiπ(m−v),−k	PROPN
ejpam-4239	73	9	,	,	PUNCT
ejpam-4239	73	10	−2i	−2i	PROPN
ejpam-4239	73	11	log(a)−	log(a)−	NOUN
ejpam-4239	73	12	2i	2i	NOUN
ejpam-4239	73	13	log(α	log(α	PROPN
ejpam-4239	73	14	)	)	PUNCT
ejpam-4239	74	1	+	+	NUM
ejpam-4239	74	2	2i	2i	NUM
ejpam-4239	74	3	log(β	log(β	PROPN
ejpam-4239	74	4	)	)	PUNCT
ejpam-4239	74	5	+	+	NUM
ejpam-4239	74	6	π	π	PROPN
ejpam-4239	74	7	2π	2π	NOUN
ejpam-4239	74	8	)	)	PUNCT
ejpam-4239	74	9	proof	proof	NOUN
ejpam-4239	74	10	.	.	PUNCT
ejpam-4239	75	1	the	the	DET
ejpam-4239	75	2	right	right	ADJ
ejpam-4239	75	3	-	-	PUNCT
ejpam-4239	75	4	hand	hand	NOUN
ejpam-4239	75	5	sides	side	NOUN
ejpam-4239	75	6	of	of	ADP
ejpam-4239	75	7	relations	relation	NOUN
ejpam-4239	75	8	(	(	PUNCT
ejpam-4239	75	9	3	3	NUM
ejpam-4239	75	10	)	)	PUNCT
ejpam-4239	75	11	and	and	CCONJ
ejpam-4239	75	12	(	(	PUNCT
ejpam-4239	75	13	6	6	NUM
ejpam-4239	75	14	)	)	PUNCT
ejpam-4239	75	15	are	be	AUX
ejpam-4239	75	16	identical	identical	ADJ
ejpam-4239	75	17	;	;	PUNCT
ejpam-4239	75	18	hence	hence	ADV
ejpam-4239	75	19	,	,	PUNCT
ejpam-4239	75	20	the	the	DET
ejpam-4239	75	21	left	leave	VERB
ejpam-4239	75	22	-	-	PUNCT
ejpam-4239	75	23	hand	hand	NOUN
ejpam-4239	75	24	sides	side	NOUN
ejpam-4239	75	25	of	of	ADP
ejpam-4239	75	26	the	the	DET
ejpam-4239	75	27	same	same	ADJ
ejpam-4239	75	28	are	be	AUX
ejpam-4239	75	29	identical	identical	ADJ
ejpam-4239	75	30	too	too	ADV
ejpam-4239	75	31	.	.	PUNCT
ejpam-4239	76	1	simplifying	simplify	VERB
ejpam-4239	76	2	with	with	ADP
ejpam-4239	76	3	the	the	DET
ejpam-4239	76	4	gamma	gamma	NOUN
ejpam-4239	76	5	function	function	NOUN
ejpam-4239	76	6	yields	yield	VERB
ejpam-4239	76	7	the	the	DET
ejpam-4239	76	8	desired	desire	VERB
ejpam-4239	76	9	conclusion	conclusion	NOUN
ejpam-4239	76	10	.	.	PUNCT
ejpam-4239	77	1	example	example	NOUN
ejpam-4239	78	1	1	1	NUM
ejpam-4239	78	2	.	.	PUNCT
ejpam-4239	79	1	the	the	DET
ejpam-4239	79	2	degenerate	degenerate	ADJ
ejpam-4239	79	3	case.∫	case.∫	NOUN
ejpam-4239	79	4	∞	∞	PROPN
ejpam-4239	79	5	0	0	NUM
ejpam-4239	79	6	∫	∫	PROPN
ejpam-4239	79	7	∞	∞	NOUN
ejpam-4239	79	8	0	0	NUM
ejpam-4239	79	9	xm−1y1−mkv(xβ)jv(yα)dxdy	xm−1y1−mkv(xβ)jv(yα)dxdy	PUNCT
ejpam-4239	80	1	=	=	NOUN
ejpam-4239	80	2	1	1	NUM
ejpam-4239	80	3	2	2	NUM
ejpam-4239	80	4	παm−2β−m	παm−2β−m	X
ejpam-4239	80	5	csc	csc	X
ejpam-4239	80	6	(	(	PUNCT
ejpam-4239	80	7	1	1	NUM
ejpam-4239	80	8	2	2	NUM
ejpam-4239	80	9	π(m−	π(m−	PROPN
ejpam-4239	80	10	v	v	NOUN
ejpam-4239	80	11	)	)	PUNCT
ejpam-4239	80	12	)	)	PUNCT
ejpam-4239	81	1	(	(	PUNCT
ejpam-4239	81	2	8)	8)	NUM
ejpam-4239	81	3	proof	proof	NOUN
ejpam-4239	81	4	.	.	PUNCT
ejpam-4239	82	1	use	use	VERB
ejpam-4239	82	2	equation	equation	NOUN
ejpam-4239	82	3	(	(	PUNCT
ejpam-4239	82	4	7	7	NUM
ejpam-4239	82	5	)	)	PUNCT
ejpam-4239	82	6	and	and	CCONJ
ejpam-4239	82	7	set	set	VERB
ejpam-4239	82	8	k	k	PROPN
ejpam-4239	82	9	=	=	PUNCT
ejpam-4239	82	10	0	0	PUNCT
ejpam-4239	82	11	and	and	CCONJ
ejpam-4239	82	12	simplify	simplify	VERB
ejpam-4239	82	13	using	use	VERB
ejpam-4239	82	14	entry	entry	NOUN
ejpam-4239	82	15	(	(	PUNCT
ejpam-4239	82	16	2	2	NUM
ejpam-4239	82	17	)	)	PUNCT
ejpam-4239	82	18	in	in	ADP
ejpam-4239	82	19	table	table	NOUN
ejpam-4239	82	20	below	below	ADV
ejpam-4239	82	21	(	(	PUNCT
ejpam-4239	82	22	64:12:7	64:12:7	NUM
ejpam-4239	82	23	)	)	PUNCT
ejpam-4239	82	24	in	in	ADP
ejpam-4239	82	25	[	[	X
ejpam-4239	82	26	5	5	NUM
ejpam-4239	82	27	]	]	PUNCT
ejpam-4239	82	28	.	.	PUNCT
ejpam-4239	82	29	example	example	NOUN
ejpam-4239	83	1	2	2	NUM
ejpam-4239	83	2	.	.	PUNCT
ejpam-4239	83	3	the	the	DET
ejpam-4239	83	4	hurwitz	hurwitz	PROPN
ejpam-4239	83	5	zeta	zeta	PROPN
ejpam-4239	83	6	function	function	VERB
ejpam-4239	83	7	ζ(s	ζ(s	PROPN
ejpam-4239	83	8	,	,	PUNCT
ejpam-4239	83	9	v	v	NOUN
ejpam-4239	83	10	)	)	PUNCT
ejpam-4239	83	11	(	(	PUNCT
ejpam-4239	83	12	9	9	NUM
ejpam-4239	83	13	)	)	PUNCT
ejpam-4239	83	14	∫	∫	PROPN
ejpam-4239	84	1	∞	∞	PROPN
ejpam-4239	84	2	0	0	NUM
ejpam-4239	84	3	∫	∫	PROPN
ejpam-4239	84	4	∞	∞	NUM
ejpam-4239	84	5	0	0	NUM
ejpam-4239	84	6	√	√	PROPN
ejpam-4239	84	7	xeβ(−x	xeβ(−x	PROPN
ejpam-4239	84	8	)	)	PUNCT
ejpam-4239	84	9	sin(αy	sin(αy	PROPN
ejpam-4239	84	10	)	)	PUNCT
ejpam-4239	84	11	logk	logk	NOUN
ejpam-4239	84	12	(	(	PUNCT
ejpam-4239	84	13	ax	ax	NOUN
ejpam-4239	84	14	y	y	PROPN
ejpam-4239	84	15	)	)	PUNCT
ejpam-4239	84	16	√	√	PROPN
ejpam-4239	85	1	y	y	PROPN
ejpam-4239	85	2	√	√	NOUN
ejpam-4239	85	3	βx	βx	ADP
ejpam-4239	85	4	√	√	PROPN
ejpam-4239	85	5	αy	αy	ADP
ejpam-4239	85	6	dxdy	dxdy	PROPN
ejpam-4239	85	7	=	=	PUNCT
ejpam-4239	86	1	−	−	PROPN
ejpam-4239	86	2	1	1	NUM
ejpam-4239	87	1	√	√	NOUN
ejpam-4239	87	2	αβ3/2	αβ3/2	PROPN
ejpam-4239	87	3	ie	ie	PRON
ejpam-4239	87	4	1	1	NUM
ejpam-4239	87	5	2	2	NUM
ejpam-4239	87	6	iπ(k+1)πk+1	iπ(k+1)πk+1	NOUN
ejpam-4239	87	7	(	(	PUNCT
ejpam-4239	87	8	2kζ	2kζ	ADJ
ejpam-4239	87	9	(	(	PUNCT
ejpam-4239	87	10	−k	−k	PROPN
ejpam-4239	87	11	,	,	PUNCT
ejpam-4239	87	12	−2i	−2i	PROPN
ejpam-4239	87	13	log(a)−	log(a)−	NOUN
ejpam-4239	87	14	2i	2i	NOUN
ejpam-4239	87	15	log(α	log(α	PROPN
ejpam-4239	87	16	)	)	PUNCT
ejpam-4239	87	17	+	+	NUM
ejpam-4239	87	18	2i	2i	NUM
ejpam-4239	87	19	log(β	log(β	PROPN
ejpam-4239	87	20	)	)	PUNCT
ejpam-4239	88	1	+	+	CCONJ
ejpam-4239	89	1	π	π	NOUN
ejpam-4239	89	2	4π	4π	NUM
ejpam-4239	89	3	)	)	PUNCT
ejpam-4239	89	4	−	−	PROPN
ejpam-4239	89	5	2kζ	2kζ	ADJ
ejpam-4239	89	6	(	(	PUNCT
ejpam-4239	89	7	−k	−k	PROPN
ejpam-4239	89	8	,	,	PUNCT
ejpam-4239	89	9	1	1	NUM
ejpam-4239	89	10	2	2	NUM
ejpam-4239	89	11	(	(	PUNCT
ejpam-4239	89	12	−2i	−2i	PROPN
ejpam-4239	89	13	log(a)−	log(a)−	NOUN
ejpam-4239	89	14	2i	2i	NOUN
ejpam-4239	89	15	log(α	log(α	PROPN
ejpam-4239	89	16	)	)	PUNCT
ejpam-4239	89	17	+	+	NUM
ejpam-4239	89	18	2i	2i	NUM
ejpam-4239	89	19	log(β	log(β	PROPN
ejpam-4239	89	20	)	)	PUNCT
ejpam-4239	89	21	+	+	NUM
ejpam-4239	89	22	π	π	PROPN
ejpam-4239	89	23	2π	2π	NOUN
ejpam-4239	89	24	+	+	CCONJ
ejpam-4239	89	25	1	1	NUM
ejpam-4239	89	26	)	)	PUNCT
ejpam-4239	89	27	)	)	PUNCT
ejpam-4239	89	28	)	)	PUNCT
ejpam-4239	89	29	proof	proof	NOUN
ejpam-4239	89	30	.	.	PUNCT
ejpam-4239	90	1	use	use	VERB
ejpam-4239	90	2	equation	equation	NOUN
ejpam-4239	90	3	(	(	PUNCT
ejpam-4239	90	4	7	7	NUM
ejpam-4239	90	5	)	)	PUNCT
ejpam-4239	90	6	and	and	CCONJ
ejpam-4239	90	7	set	set	VERB
ejpam-4239	90	8	m	m	PROPN
ejpam-4239	90	9	=	=	SYM
ejpam-4239	90	10	3/2	3/2	NUM
ejpam-4239	90	11	,	,	PUNCT
ejpam-4239	90	12	v	v	NOUN
ejpam-4239	90	13	=	=	SYM
ejpam-4239	90	14	1/2	1/2	NUM
ejpam-4239	90	15	and	and	CCONJ
ejpam-4239	90	16	simplify	simplify	VERB
ejpam-4239	90	17	using	use	VERB
ejpam-4239	90	18	entry	entry	NOUN
ejpam-4239	90	19	(	(	PUNCT
ejpam-4239	90	20	4	4	NUM
ejpam-4239	90	21	)	)	PUNCT
ejpam-4239	90	22	in	in	ADP
ejpam-4239	90	23	table	table	NOUN
ejpam-4239	90	24	below	below	ADV
ejpam-4239	90	25	(	(	PUNCT
ejpam-4239	90	26	64:12:7	64:12:7	NUM
ejpam-4239	90	27	)	)	PUNCT
ejpam-4239	90	28	in	in	ADP
ejpam-4239	90	29	[	[	X
ejpam-4239	90	30	5	5	NUM
ejpam-4239	90	31	]	]	PUNCT
ejpam-4239	90	32	.	.	PUNCT
ejpam-4239	90	33	example	example	NOUN
ejpam-4239	91	1	3	3	NUM
ejpam-4239	91	2	.	.	PUNCT
ejpam-4239	91	3	(	(	PUNCT
ejpam-4239	91	4	10	10	NUM
ejpam-4239	91	5	)	)	PUNCT
ejpam-4239	91	6	∫	∫	PROPN
ejpam-4239	92	1	∞	∞	PROPN
ejpam-4239	92	2	0	0	NUM
ejpam-4239	92	3	∫	∫	PROPN
ejpam-4239	92	4	∞	∞	PROPN
ejpam-4239	92	5	0	0	NUM
ejpam-4239	93	1	e−x	e−x	PROPN
ejpam-4239	93	2	sin(y	sin(y	PROPN
ejpam-4239	93	3	)	)	PUNCT
ejpam-4239	93	4	log	log	NOUN
ejpam-4239	93	5	(	(	PUNCT
ejpam-4239	93	6	x	x	NOUN
ejpam-4239	93	7	y	y	PROPN
ejpam-4239	93	8	)	)	PUNCT
ejpam-4239	93	9	y	y	PROPN
ejpam-4239	93	10	(	(	PUNCT
ejpam-4239	93	11	log2	log2	PROPN
ejpam-4239	93	12	(	(	PUNCT
ejpam-4239	93	13	x	x	NOUN
ejpam-4239	93	14	y	y	PROPN
ejpam-4239	93	15	)	)	PUNCT
ejpam-4239	94	1	+	+	CCONJ
ejpam-4239	94	2	π2	π2	ADJ
ejpam-4239	94	3	)	)	PUNCT
ejpam-4239	94	4	dxdy	dxdy	NOUN
ejpam-4239	94	5	=	=	SYM
ejpam-4239	94	6	0	0	PROPN
ejpam-4239	95	1	and	and	CCONJ
ejpam-4239	95	2	(	(	PUNCT
ejpam-4239	95	3	11	11	NUM
ejpam-4239	95	4	)	)	PUNCT
ejpam-4239	95	5	∫	∫	PROPN
ejpam-4239	96	1	∞	∞	PROPN
ejpam-4239	96	2	0	0	NUM
ejpam-4239	97	1	∫	∫	PROPN
ejpam-4239	97	2	∞	∞	PROPN
ejpam-4239	97	3	0	0	NUM
ejpam-4239	98	1	e−x	e−x	PROPN
ejpam-4239	98	2	sin(y	sin(y	PROPN
ejpam-4239	98	3	)	)	PUNCT
ejpam-4239	98	4	y	y	PROPN
ejpam-4239	98	5	(	(	PUNCT
ejpam-4239	98	6	log2	log2	PROPN
ejpam-4239	98	7	(	(	PUNCT
ejpam-4239	98	8	x	x	NOUN
ejpam-4239	98	9	y	y	PROPN
ejpam-4239	98	10	)	)	PUNCT
ejpam-4239	99	1	+	+	CCONJ
ejpam-4239	99	2	π2	π2	ADJ
ejpam-4239	99	3	)	)	PUNCT
ejpam-4239	99	4	dxdy	dxdy	NOUN
ejpam-4239	99	5	=	=	SYM
ejpam-4239	99	6	2	2	NUM
ejpam-4239	99	7	π	π	NOUN
ejpam-4239	99	8	−	−	PROPN
ejpam-4239	99	9	1	1	NUM
ejpam-4239	99	10	2	2	NUM
ejpam-4239	99	11	r.	r.	PROPN
ejpam-4239	99	12	reynolds	reynolds	PROPN
ejpam-4239	99	13	,	,	PUNCT
ejpam-4239	99	14	a.	a.	PROPN
ejpam-4239	99	15	stauffer	stauffer	PROPN
ejpam-4239	99	16	/	/	SYM
ejpam-4239	99	17	eur	eur	PROPN
ejpam-4239	99	18	.	.	PUNCT
ejpam-4239	100	1	j.	j.	PROPN
ejpam-4239	100	2	pure	pure	PROPN
ejpam-4239	100	3	appl	appl	PROPN
ejpam-4239	100	4	.	.	PROPN
ejpam-4239	100	5	math	math	PROPN
ejpam-4239	100	6	,	,	PUNCT
ejpam-4239	100	7	15	15	NUM
ejpam-4239	100	8	(	(	PUNCT
ejpam-4239	100	9	3	3	NUM
ejpam-4239	100	10	)	)	PUNCT
ejpam-4239	100	11	(	(	PUNCT
ejpam-4239	100	12	2022	2022	NUM
ejpam-4239	100	13	)	)	PUNCT
ejpam-4239	100	14	,	,	PUNCT
ejpam-4239	100	15	856	856	NUM
ejpam-4239	100	16	-	-	SYM
ejpam-4239	100	17	863	863	NUM
ejpam-4239	100	18	860	860	NUM
ejpam-4239	100	19	proof	proof	NOUN
ejpam-4239	100	20	.	.	PUNCT
ejpam-4239	101	1	use	use	VERB
ejpam-4239	101	2	equation	equation	NOUN
ejpam-4239	101	3	(	(	PUNCT
ejpam-4239	101	4	9	9	X
ejpam-4239	101	5	)	)	PUNCT
ejpam-4239	101	6	apply	apply	VERB
ejpam-4239	101	7	l’hopital	l’hopital	PROPN
ejpam-4239	101	8	’s	’s	PART
ejpam-4239	101	9	rule	rule	NOUN
ejpam-4239	101	10	as	as	ADP
ejpam-4239	101	11	k	k	PROPN
ejpam-4239	101	12	→	→	SYM
ejpam-4239	101	13	−1	−1	NOUN
ejpam-4239	101	14	and	and	CCONJ
ejpam-4239	101	15	set	set	VERB
ejpam-4239	101	16	a	a	DET
ejpam-4239	101	17	=	=	SYM
ejpam-4239	101	18	−1	−1	NOUN
ejpam-4239	101	19	,	,	PUNCT
ejpam-4239	101	20	α	α	X
ejpam-4239	101	21	=	=	X
ejpam-4239	101	22	β	β	X
ejpam-4239	101	23	=	=	SYM
ejpam-4239	101	24	1	1	NUM
ejpam-4239	101	25	rationalize	rationalize	VERB
ejpam-4239	101	26	the	the	DET
ejpam-4239	101	27	denominator	denominator	NOUN
ejpam-4239	101	28	and	and	CCONJ
ejpam-4239	101	29	simplify	simplify	VERB
ejpam-4239	101	30	using	use	VERB
ejpam-4239	101	31	entry	entry	NOUN
ejpam-4239	101	32	(	(	PUNCT
ejpam-4239	101	33	2	2	NUM
ejpam-4239	101	34	)	)	PUNCT
ejpam-4239	101	35	in	in	ADP
ejpam-4239	101	36	table	table	NOUN
ejpam-4239	101	37	below	below	ADV
ejpam-4239	101	38	(	(	PUNCT
ejpam-4239	101	39	64:7	64:7	NUM
ejpam-4239	101	40	)	)	PUNCT
ejpam-4239	101	41	in	in	ADP
ejpam-4239	101	42	[	[	X
ejpam-4239	101	43	5	5	NUM
ejpam-4239	101	44	]	]	PUNCT
ejpam-4239	101	45	.	.	PUNCT
ejpam-4239	102	1	example	example	NOUN
ejpam-4239	103	1	4	4	NUM
ejpam-4239	103	2	.	.	PUNCT
ejpam-4239	103	3	∫	∫	PROPN
ejpam-4239	104	1	∞	∞	PROPN
ejpam-4239	104	2	0	0	NUM
ejpam-4239	105	1	∫	∫	PROPN
ejpam-4239	105	2	∞	∞	NUM
ejpam-4239	105	3	0	0	NUM
ejpam-4239	106	1	√	√	NUM
ejpam-4239	106	2	xk	xk	PROPN
ejpam-4239	106	3	1	1	NUM
ejpam-4239	106	4	4	4	NUM
ejpam-4239	106	5	(	(	PUNCT
ejpam-4239	106	6	x)j	x)j	PROPN
ejpam-4239	106	7	1	1	NUM
ejpam-4239	106	8	4	4	NUM
ejpam-4239	106	9	(	(	PUNCT
ejpam-4239	106	10	y	y	NOUN
ejpam-4239	106	11	)	)	PUNCT
ejpam-4239	106	12	log	log	NOUN
ejpam-4239	106	13	(	(	PUNCT
ejpam-4239	106	14	x	x	NOUN
ejpam-4239	106	15	y	y	PROPN
ejpam-4239	106	16	)	)	PUNCT
ejpam-4239	106	17	√	√	PROPN
ejpam-4239	107	1	y	y	PROPN
ejpam-4239	107	2	(	(	PUNCT
ejpam-4239	107	3	log2	log2	PROPN
ejpam-4239	107	4	(	(	PUNCT
ejpam-4239	107	5	x	x	NOUN
ejpam-4239	107	6	y	y	PROPN
ejpam-4239	107	7	)	)	PUNCT
ejpam-4239	108	1	+	+	CCONJ
ejpam-4239	108	2	π2	π2	X
ejpam-4239	108	3	)	)	PUNCT
ejpam-4239	108	4	dxdy	dxdy	NOUN
ejpam-4239	108	5	=	=	NOUN
ejpam-4239	108	6	1	1	NUM
ejpam-4239	108	7	4	4	NUM
ejpam-4239	108	8	(	(	PUNCT
ejpam-4239	108	9	√	√	PROPN
ejpam-4239	108	10	2π	2π	NOUN
ejpam-4239	108	11	−	−	NUM
ejpam-4239	108	12	8	8	NUM
ejpam-4239	108	13	sin	sin	NOUN
ejpam-4239	108	14	(	(	PUNCT
ejpam-4239	108	15	π	π	NOUN
ejpam-4239	108	16	8	8	NUM
ejpam-4239	108	17	)	)	PUNCT
ejpam-4239	108	18	−	−	PROPN
ejpam-4239	108	19	2	2	NUM
ejpam-4239	108	20	√	√	NUM
ejpam-4239	108	21	2	2	NUM
ejpam-4239	108	22	tanh−1	tanh−1	PROPN
ejpam-4239	108	23	(	(	PUNCT
ejpam-4239	108	24	sin	sin	NOUN
ejpam-4239	108	25	(	(	PUNCT
ejpam-4239	108	26	π	π	NOUN
ejpam-4239	108	27	8	8	NUM
ejpam-4239	108	28	)	)	PUNCT
ejpam-4239	108	29	)	)	PUNCT
ejpam-4239	108	30	)	)	PUNCT
ejpam-4239	109	1	(	(	PUNCT
ejpam-4239	109	2	12	12	NUM
ejpam-4239	109	3	)	)	PUNCT
ejpam-4239	109	4	and	and	CCONJ
ejpam-4239	109	5	(	(	PUNCT
ejpam-4239	109	6	13	13	NUM
ejpam-4239	109	7	)	)	PUNCT
ejpam-4239	109	8	∫	∫	PROPN
ejpam-4239	110	1	∞	∞	PROPN
ejpam-4239	110	2	0	0	NUM
ejpam-4239	110	3	∫	∫	PROPN
ejpam-4239	110	4	∞	∞	NUM
ejpam-4239	110	5	0	0	NUM
ejpam-4239	111	1	√	√	NUM
ejpam-4239	111	2	xk	xk	PROPN
ejpam-4239	111	3	1	1	NUM
ejpam-4239	111	4	4	4	NUM
ejpam-4239	111	5	(	(	PUNCT
ejpam-4239	111	6	x)j	x)j	PROPN
ejpam-4239	111	7	1	1	NUM
ejpam-4239	111	8	4	4	NUM
ejpam-4239	111	9	(	(	PUNCT
ejpam-4239	111	10	y	y	NOUN
ejpam-4239	111	11	)	)	PUNCT
ejpam-4239	111	12	√	√	PROPN
ejpam-4239	111	13	y	y	PROPN
ejpam-4239	111	14	(	(	PUNCT
ejpam-4239	111	15	log2	log2	PROPN
ejpam-4239	111	16	(	(	PUNCT
ejpam-4239	111	17	x	x	NOUN
ejpam-4239	111	18	y	y	PROPN
ejpam-4239	111	19	)	)	PUNCT
ejpam-4239	112	1	+	+	CCONJ
ejpam-4239	112	2	π2	π2	ADJ
ejpam-4239	112	3	)	)	PUNCT
ejpam-4239	112	4	dxdy	dxdy	NOUN
ejpam-4239	112	5	=	=	SYM
ejpam-4239	112	6	8	8	NUM
ejpam-4239	112	7	cos	cos	X
ejpam-4239	112	8	(	(	PUNCT
ejpam-4239	112	9	π	π	PROPN
ejpam-4239	112	10	8	8	NUM
ejpam-4239	112	11	)	)	PUNCT
ejpam-4239	112	12	−	−	NOUN
ejpam-4239	113	1	√	√	NOUN
ejpam-4239	113	2	2	2	NUM
ejpam-4239	113	3	(	(	PUNCT
ejpam-4239	113	4	π	π	NOUN
ejpam-4239	113	5	+	+	CCONJ
ejpam-4239	113	6	2	2	NUM
ejpam-4239	113	7	tanh−1	tanh−1	PROPN
ejpam-4239	113	8	(	(	PUNCT
ejpam-4239	113	9	sin	sin	NOUN
ejpam-4239	113	10	(	(	PUNCT
ejpam-4239	113	11	π	π	NOUN
ejpam-4239	113	12	8	8	NUM
ejpam-4239	113	13	)	)	PUNCT
ejpam-4239	113	14	)	)	PUNCT
ejpam-4239	113	15	)	)	PUNCT
ejpam-4239	114	1	4π	4π	NUM
ejpam-4239	114	2	proof	proof	NOUN
ejpam-4239	114	3	.	.	PUNCT
ejpam-4239	115	1	use	use	VERB
ejpam-4239	115	2	equation	equation	NOUN
ejpam-4239	115	3	(	(	PUNCT
ejpam-4239	115	4	7	7	NUM
ejpam-4239	115	5	)	)	PUNCT
ejpam-4239	115	6	and	and	CCONJ
ejpam-4239	115	7	set	set	VERB
ejpam-4239	115	8	k	k	PROPN
ejpam-4239	115	9	=	=	PUNCT
ejpam-4239	115	10	−1,m	−1,m	PROPN
ejpam-4239	115	11	=	=	SYM
ejpam-4239	115	12	3/2	3/2	NUM
ejpam-4239	115	13	,	,	PUNCT
ejpam-4239	115	14	v	v	NOUN
ejpam-4239	115	15	=	=	SYM
ejpam-4239	115	16	1/4	1/4	NUM
ejpam-4239	115	17	,	,	PUNCT
ejpam-4239	115	18	α	α	X
ejpam-4239	115	19	=	=	PUNCT
ejpam-4239	115	20	β	β	X
ejpam-4239	115	21	=	=	SYM
ejpam-4239	115	22	1	1	NUM
ejpam-4239	115	23	,	,	PUNCT
ejpam-4239	115	24	a	a	DET
ejpam-4239	115	25	=	=	X
ejpam-4239	115	26	−1	−1	NOUN
ejpam-4239	115	27	and	and	CCONJ
ejpam-4239	115	28	simplify	simplify	VERB
ejpam-4239	115	29	using	use	VERB
ejpam-4239	115	30	entry	entry	NOUN
ejpam-4239	115	31	(	(	PUNCT
ejpam-4239	115	32	3	3	NUM
ejpam-4239	115	33	)	)	PUNCT
ejpam-4239	115	34	in	in	ADP
ejpam-4239	115	35	table	table	NOUN
ejpam-4239	115	36	below	below	ADV
ejpam-4239	115	37	(	(	PUNCT
ejpam-4239	115	38	64:12:7	64:12:7	NUM
ejpam-4239	115	39	)	)	PUNCT
ejpam-4239	115	40	in	in	ADP
ejpam-4239	115	41	[	[	X
ejpam-4239	115	42	5	5	NUM
ejpam-4239	115	43	]	]	PUNCT
ejpam-4239	115	44	.	.	PUNCT
ejpam-4239	115	45	example	example	NOUN
ejpam-4239	116	1	5	5	NUM
ejpam-4239	116	2	.	.	PUNCT
ejpam-4239	116	3	(	(	PUNCT
ejpam-4239	116	4	14	14	NUM
ejpam-4239	116	5	)	)	PUNCT
ejpam-4239	116	6	∫	∫	PROPN
ejpam-4239	117	1	∞	∞	PROPN
ejpam-4239	117	2	0	0	NUM
ejpam-4239	118	1	∫	∫	PROPN
ejpam-4239	118	2	∞	∞	PROPN
ejpam-4239	118	3	0	0	NUM
ejpam-4239	118	4	xm−1y1−mkv(xβ)jv(yα	xm−1y1−mkv(xβ)jv(yα	PROPN
ejpam-4239	118	5	)	)	PUNCT
ejpam-4239	118	6	log	log	NOUN
ejpam-4239	118	7	(	(	PUNCT
ejpam-4239	118	8	−βx	−βx	NOUN
ejpam-4239	118	9	αy	αy	PROPN
ejpam-4239	118	10	)	)	PUNCT
ejpam-4239	118	11	dxdy	dxdy	PROPN
ejpam-4239	118	12	=	=	PROPN
ejpam-4239	119	1	2iαm−2β−me−	2iαm−2β−me−	NUM
ejpam-4239	119	2	1	1	NUM
ejpam-4239	119	3	2	2	NUM
ejpam-4239	119	4	iπ(2m−2v+1	iπ(2m−2v+1	NUM
ejpam-4239	119	5	)	)	PUNCT
ejpam-4239	120	1	(	(	PUNCT
ejpam-4239	120	2	e	e	NOUN
ejpam-4239	120	3	1	1	NUM
ejpam-4239	120	4	2	2	NUM
ejpam-4239	120	5	iπ(m−v	iπ(m−v	NOUN
ejpam-4239	120	6	)	)	PUNCT
ejpam-4239	120	7	−	−	NOUN
ejpam-4239	121	1	tanh−1	tanh−1	ADJ
ejpam-4239	121	2	(	(	PUNCT
ejpam-4239	121	3	e	e	NOUN
ejpam-4239	121	4	1	1	NUM
ejpam-4239	121	5	2	2	NUM
ejpam-4239	121	6	iπ(m−v	iπ(m−v	NOUN
ejpam-4239	121	7	)	)	PUNCT
ejpam-4239	121	8	)	)	PUNCT
ejpam-4239	121	9	)	)	PUNCT
ejpam-4239	122	1	proof	proof	NOUN
ejpam-4239	122	2	.	.	PUNCT
ejpam-4239	123	1	use	use	VERB
ejpam-4239	123	2	equation	equation	NOUN
ejpam-4239	123	3	(	(	PUNCT
ejpam-4239	123	4	7	7	NUM
ejpam-4239	123	5	)	)	PUNCT
ejpam-4239	123	6	and	and	CCONJ
ejpam-4239	123	7	set	set	VERB
ejpam-4239	123	8	k	k	PROPN
ejpam-4239	123	9	=	=	PUNCT
ejpam-4239	123	10	−1,m	−1,m	PROPN
ejpam-4239	123	11	=	=	SYM
ejpam-4239	123	12	3/2	3/2	NUM
ejpam-4239	123	13	,	,	PUNCT
ejpam-4239	123	14	v	v	NOUN
ejpam-4239	123	15	=	=	SYM
ejpam-4239	123	16	1/4	1/4	NUM
ejpam-4239	123	17	,	,	PUNCT
ejpam-4239	123	18	a	a	DET
ejpam-4239	123	19	=	=	X
ejpam-4239	123	20	β	β	NOUN
ejpam-4239	123	21	/	/	SYM
ejpam-4239	123	22	α	α	NOUN
ejpam-4239	123	23	and	and	CCONJ
ejpam-4239	123	24	simplify	simplify	VERB
ejpam-4239	123	25	using	use	VERB
ejpam-4239	123	26	entry	entry	NOUN
ejpam-4239	123	27	(	(	PUNCT
ejpam-4239	123	28	3	3	NUM
ejpam-4239	123	29	)	)	PUNCT
ejpam-4239	123	30	in	in	ADP
ejpam-4239	123	31	table	table	NOUN
ejpam-4239	123	32	below	below	ADV
ejpam-4239	123	33	(	(	PUNCT
ejpam-4239	123	34	64:12:7	64:12:7	NUM
ejpam-4239	123	35	)	)	PUNCT
ejpam-4239	123	36	in	in	ADP
ejpam-4239	123	37	[	[	X
ejpam-4239	123	38	5	5	NUM
ejpam-4239	123	39	]	]	PUNCT
ejpam-4239	123	40	.	.	PUNCT
ejpam-4239	123	41	example	example	NOUN
ejpam-4239	124	1	6	6	NUM
ejpam-4239	124	2	.	.	PUNCT
ejpam-4239	125	1	the	the	DET
ejpam-4239	125	2	polylogarithm	polylogarithm	PROPN
ejpam-4239	125	3	function	function	PROPN
ejpam-4239	125	4	lik(z),∫	lik(z),∫	PROPN
ejpam-4239	125	5	∞	∞	PROPN
ejpam-4239	125	6	0	0	NUM
ejpam-4239	126	1	∫	∫	PROPN
ejpam-4239	126	2	∞	∞	PROPN
ejpam-4239	126	3	0	0	NUM
ejpam-4239	126	4	xm−1y1−mkv(x)jv(y	xm−1y1−mkv(x)jv(y	PROPN
ejpam-4239	126	5	)	)	PUNCT
ejpam-4239	126	6	log	log	NOUN
ejpam-4239	126	7	k	k	PROPN
ejpam-4239	127	1	(	(	PUNCT
ejpam-4239	127	2	ix	ix	PROPN
ejpam-4239	127	3	y	y	PROPN
ejpam-4239	127	4	)	)	PUNCT
ejpam-4239	127	5	dxdy	dxdy	PROPN
ejpam-4239	127	6	=	=	SYM
ejpam-4239	127	7	−iπk+1e	−iπk+1e	NOUN
ejpam-4239	127	8	1	1	NUM
ejpam-4239	127	9	2	2	NUM
ejpam-4239	127	10	iπ(k−m+v)li−k	iπ(k−m+v)li−k	NOUN
ejpam-4239	127	11	(	(	PUNCT
ejpam-4239	127	12	eiπ(m−v	eiπ(m−v	NOUN
ejpam-4239	127	13	)	)	PUNCT
ejpam-4239	127	14	)	)	PUNCT
ejpam-4239	127	15	(	(	PUNCT
ejpam-4239	127	16	15	15	X
ejpam-4239	127	17	)	)	PUNCT
ejpam-4239	127	18	proof	proof	NOUN
ejpam-4239	127	19	.	.	PUNCT
ejpam-4239	128	1	use	use	VERB
ejpam-4239	128	2	equation	equation	NOUN
ejpam-4239	128	3	(	(	PUNCT
ejpam-4239	128	4	7	7	NUM
ejpam-4239	128	5	)	)	PUNCT
ejpam-4239	128	6	and	and	CCONJ
ejpam-4239	128	7	set	set	VERB
ejpam-4239	128	8	a	a	DET
ejpam-4239	128	9	=	=	X
ejpam-4239	128	10	i	i	PROPN
ejpam-4239	128	11	,	,	PUNCT
ejpam-4239	128	12	β	β	X
ejpam-4239	128	13	=	=	PUNCT
ejpam-4239	128	14	α	α	NOUN
ejpam-4239	128	15	=	=	SYM
ejpam-4239	128	16	1	1	NUM
ejpam-4239	128	17	and	and	CCONJ
ejpam-4239	128	18	simplify	simplify	VERB
ejpam-4239	128	19	using	use	VERB
ejpam-4239	128	20	equation	equation	NOUN
ejpam-4239	128	21	(	(	PUNCT
ejpam-4239	128	22	64:12:2	64:12:2	NUM
ejpam-4239	128	23	)	)	PUNCT
ejpam-4239	128	24	in	in	ADP
ejpam-4239	128	25	[	[	X
ejpam-4239	128	26	5	5	NUM
ejpam-4239	128	27	]	]	PUNCT
ejpam-4239	128	28	.	.	PUNCT
ejpam-4239	128	29	example	example	NOUN
ejpam-4239	129	1	7	7	NUM
ejpam-4239	129	2	.	.	PUNCT
ejpam-4239	130	1	the	the	DET
ejpam-4239	130	2	polylogarithm	polylogarithm	PROPN
ejpam-4239	130	3	function	function	VERB
ejpam-4239	130	4	li2(z	li2(z	NOUN
ejpam-4239	130	5	)	)	PUNCT
ejpam-4239	130	6	,	,	PUNCT
ejpam-4239	130	7	(	(	PUNCT
ejpam-4239	130	8	16	16	NUM
ejpam-4239	130	9	)	)	PUNCT
ejpam-4239	130	10	∫	∫	PROPN
ejpam-4239	131	1	∞	∞	PROPN
ejpam-4239	131	2	0	0	NUM
ejpam-4239	132	1	∫	∫	PROPN
ejpam-4239	132	2	∞	∞	PROPN
ejpam-4239	132	3	0	0	NUM
ejpam-4239	132	4	xm−1y1−mkv(x)jv(y	xm−1y1−mkv(x)jv(y	PROPN
ejpam-4239	132	5	)	)	PUNCT
ejpam-4239	132	6	log2	log2	PROPN
ejpam-4239	132	7	(	(	PUNCT
ejpam-4239	132	8	ix	ix	PROPN
ejpam-4239	132	9	y	y	PROPN
ejpam-4239	132	10	)	)	PUNCT
ejpam-4239	132	11	dxdy	dxdy	PROPN
ejpam-4239	132	12	=	=	PUNCT
ejpam-4239	133	1	−	−	PROPN
ejpam-4239	133	2	ie−	ie−	NOUN
ejpam-4239	133	3	1	1	NUM
ejpam-4239	133	4	2	2	NUM
ejpam-4239	133	5	iπ(m−v+2)li2	iπ(m−v+2)li2	NOUN
ejpam-4239	133	6	(	(	PUNCT
ejpam-4239	133	7	eiπ(m−v	eiπ(m−v	NOUN
ejpam-4239	133	8	)	)	PUNCT
ejpam-4239	133	9	)	)	PUNCT
ejpam-4239	134	1	π	π	NOUN
ejpam-4239	134	2	proof	proof	NOUN
ejpam-4239	134	3	.	.	PUNCT
ejpam-4239	135	1	use	use	VERB
ejpam-4239	135	2	equation	equation	NOUN
ejpam-4239	135	3	(	(	PUNCT
ejpam-4239	135	4	7	7	NUM
ejpam-4239	135	5	)	)	PUNCT
ejpam-4239	135	6	and	and	CCONJ
ejpam-4239	135	7	set	set	VERB
ejpam-4239	135	8	k	k	PROPN
ejpam-4239	135	9	=	=	SYM
ejpam-4239	135	10	−2	−2	PROPN
ejpam-4239	135	11	,	,	PUNCT
ejpam-4239	135	12	a	a	DET
ejpam-4239	135	13	=	=	X
ejpam-4239	135	14	i	i	PROPN
ejpam-4239	135	15	,	,	PUNCT
ejpam-4239	135	16	β	β	X
ejpam-4239	135	17	=	=	PUNCT
ejpam-4239	135	18	α	α	NOUN
ejpam-4239	135	19	=	=	SYM
ejpam-4239	135	20	1	1	NUM
ejpam-4239	135	21	and	and	CCONJ
ejpam-4239	135	22	simplify	simplify	VERB
ejpam-4239	135	23	using	use	VERB
ejpam-4239	135	24	equation	equation	NOUN
ejpam-4239	135	25	(	(	PUNCT
ejpam-4239	135	26	64:12:2	64:12:2	NUM
ejpam-4239	135	27	)	)	PUNCT
ejpam-4239	135	28	in	in	ADP
ejpam-4239	135	29	[	[	X
ejpam-4239	135	30	5	5	NUM
ejpam-4239	135	31	]	]	PUNCT
ejpam-4239	135	32	.	.	PUNCT
ejpam-4239	136	1	r.	r.	PROPN
ejpam-4239	136	2	reynolds	reynolds	PROPN
ejpam-4239	136	3	,	,	PUNCT
ejpam-4239	136	4	a.	a.	PROPN
ejpam-4239	136	5	stauffer	stauffer	PROPN
ejpam-4239	136	6	/	/	SYM
ejpam-4239	136	7	eur	eur	PROPN
ejpam-4239	136	8	.	.	PUNCT
ejpam-4239	137	1	j.	j.	PROPN
ejpam-4239	137	2	pure	pure	PROPN
ejpam-4239	137	3	appl	appl	PROPN
ejpam-4239	137	4	.	.	PROPN
ejpam-4239	137	5	math	math	PROPN
ejpam-4239	137	6	,	,	PUNCT
ejpam-4239	137	7	15	15	NUM
ejpam-4239	137	8	(	(	PUNCT
ejpam-4239	137	9	3	3	NUM
ejpam-4239	137	10	)	)	PUNCT
ejpam-4239	137	11	(	(	PUNCT
ejpam-4239	137	12	2022	2022	NUM
ejpam-4239	137	13	)	)	PUNCT
ejpam-4239	137	14	,	,	PUNCT
ejpam-4239	137	15	856	856	NUM
ejpam-4239	137	16	-	-	SYM
ejpam-4239	137	17	863	863	NUM
ejpam-4239	137	18	861	861	NUM
ejpam-4239	137	19	example	example	NOUN
ejpam-4239	137	20	8	8	NUM
ejpam-4239	137	21	.	.	X
ejpam-4239	138	1	catalan	catalan	NOUN
ejpam-4239	138	2	’s	’s	PART
ejpam-4239	138	3	constant	constant	ADJ
ejpam-4239	138	4	g	g	NOUN
ejpam-4239	138	5	,	,	PUNCT
ejpam-4239	138	6	(	(	PUNCT
ejpam-4239	138	7	17	17	NUM
ejpam-4239	138	8	)	)	PUNCT
ejpam-4239	138	9	∫	∫	PROPN
ejpam-4239	139	1	∞	∞	PROPN
ejpam-4239	139	2	0	0	NUM
ejpam-4239	140	1	∫	∫	PROPN
ejpam-4239	140	2	∞	∞	PROPN
ejpam-4239	140	3	0	0	NUM
ejpam-4239	141	1	e−x√x	e−x√x	PROPN
ejpam-4239	141	2	sin(y	sin(y	PROPN
ejpam-4239	141	3	)	)	PUNCT
ejpam-4239	141	4	(	(	PUNCT
ejpam-4239	141	5	π2	π2	ADV
ejpam-4239	141	6	−	−	PROPN
ejpam-4239	141	7	4	4	NUM
ejpam-4239	141	8	log2	log2	NOUN
ejpam-4239	141	9	(	(	PUNCT
ejpam-4239	141	10	x	x	NOUN
ejpam-4239	141	11	y	y	PROPN
ejpam-4239	141	12	)	)	PUNCT
ejpam-4239	141	13	)	)	PUNCT
ejpam-4239	142	1	y3/2	y3/2	NOUN
ejpam-4239	142	2	(	(	PUNCT
ejpam-4239	142	3	4	4	NUM
ejpam-4239	142	4	log2	log2	NOUN
ejpam-4239	142	5	(	(	PUNCT
ejpam-4239	142	6	x	x	NOUN
ejpam-4239	142	7	y	y	PROPN
ejpam-4239	142	8	)	)	PUNCT
ejpam-4239	143	1	+	+	CCONJ
ejpam-4239	143	2	π2	π2	ADJ
ejpam-4239	143	3	)	)	PUNCT
ejpam-4239	143	4	2	2	NUM
ejpam-4239	143	5	dxdy	dxdy	NOUN
ejpam-4239	143	6	=	=	SYM
ejpam-4239	143	7	48g+	48g+	PROPN
ejpam-4239	143	8	π2	π2	ADV
ejpam-4239	143	9	192	192	NUM
ejpam-4239	143	10	√	√	PROPN
ejpam-4239	143	11	2π	2π	NOUN
ejpam-4239	143	12	and	and	CCONJ
ejpam-4239	143	13	(	(	PUNCT
ejpam-4239	143	14	18	18	NUM
ejpam-4239	143	15	)	)	PUNCT
ejpam-4239	143	16	∫	∫	PROPN
ejpam-4239	144	1	∞	∞	PROPN
ejpam-4239	144	2	0	0	NUM
ejpam-4239	145	1	∫	∫	PROPN
ejpam-4239	145	2	∞	∞	PROPN
ejpam-4239	145	3	0	0	NUM
ejpam-4239	146	1	e−x√x	e−x√x	PROPN
ejpam-4239	146	2	sin(y	sin(y	PROPN
ejpam-4239	146	3	)	)	PUNCT
ejpam-4239	146	4	log	log	NOUN
ejpam-4239	146	5	(	(	PUNCT
ejpam-4239	146	6	x	x	NOUN
ejpam-4239	146	7	y	y	PROPN
ejpam-4239	146	8	)	)	PUNCT
ejpam-4239	146	9	y3/2	y3/2	NOUN
ejpam-4239	146	10	(	(	PUNCT
ejpam-4239	146	11	4	4	NUM
ejpam-4239	146	12	log2	log2	NOUN
ejpam-4239	146	13	(	(	PUNCT
ejpam-4239	146	14	x	x	NOUN
ejpam-4239	146	15	y	y	PROPN
ejpam-4239	146	16	)	)	PUNCT
ejpam-4239	147	1	+	+	CCONJ
ejpam-4239	147	2	π2	π2	ADJ
ejpam-4239	147	3	)	)	PUNCT
ejpam-4239	147	4	2dxdy	2dxdy	NUM
ejpam-4239	147	5	=	=	SYM
ejpam-4239	147	6	−π2	−π2	NOUN
ejpam-4239	147	7	−	−	PROPN
ejpam-4239	147	8	48	48	NUM
ejpam-4239	147	9	g	g	PROPN
ejpam-4239	147	10	768	768	NUM
ejpam-4239	147	11	√	√	NUM
ejpam-4239	147	12	2π2	2π2	NUM
ejpam-4239	147	13	proof	proof	NOUN
ejpam-4239	147	14	.	.	PUNCT
ejpam-4239	148	1	use	use	VERB
ejpam-4239	148	2	equation	equation	NOUN
ejpam-4239	148	3	(	(	PUNCT
ejpam-4239	148	4	16	16	NUM
ejpam-4239	148	5	)	)	PUNCT
ejpam-4239	148	6	and	and	CCONJ
ejpam-4239	148	7	set	set	VERB
ejpam-4239	148	8	m	m	PROPN
ejpam-4239	148	9	=	=	SYM
ejpam-4239	148	10	2	2	NUM
ejpam-4239	148	11	,	,	PUNCT
ejpam-4239	148	12	v	v	NOUN
ejpam-4239	148	13	=	=	SYM
ejpam-4239	148	14	1/2	1/2	NUM
ejpam-4239	148	15	and	and	CCONJ
ejpam-4239	148	16	simplify	simplify	NOUN
ejpam-4239	148	17	.	.	PUNCT
ejpam-4239	148	18	example	example	NOUN
ejpam-4239	149	1	9.∫	9.∫	NUM
ejpam-4239	149	2	∞	∞	NOUN
ejpam-4239	149	3	0	0	NUM
ejpam-4239	149	4	∫	∫	PROPN
ejpam-4239	149	5	∞	∞	PROPN
ejpam-4239	149	6	0	0	PROPN
ejpam-4239	149	7	y−m−p+1kv(x)jv(y	y−m−p+1kv(x)jv(y	NUM
ejpam-4239	149	8	)	)	PUNCT
ejpam-4239	149	9	(	(	PUNCT
ejpam-4239	149	10	y	y	PROPN
ejpam-4239	149	11	mxp	mxp	PROPN
ejpam-4239	149	12	−	−	PROPN
ejpam-4239	149	13	xmyp	xmyp	PROPN
ejpam-4239	149	14	)	)	PUNCT
ejpam-4239	150	1	x	x	X
ejpam-4239	150	2	log	log	VERB
ejpam-4239	150	3	(	(	PUNCT
ejpam-4239	150	4	x	x	SYM
ejpam-4239	150	5	y	y	PROPN
ejpam-4239	150	6	)	)	PUNCT
ejpam-4239	150	7	dxdy	dxdy	NOUN
ejpam-4239	150	8	=	=	SYM
ejpam-4239	150	9	2	2	NUM
ejpam-4239	150	10	(	(	PUNCT
ejpam-4239	150	11	tanh−1	tanh−1	NOUN
ejpam-4239	150	12	(	(	PUNCT
ejpam-4239	150	13	e	e	NOUN
ejpam-4239	150	14	1	1	NUM
ejpam-4239	150	15	2	2	NUM
ejpam-4239	150	16	iπ(m−v	iπ(m−v	NOUN
ejpam-4239	150	17	)	)	PUNCT
ejpam-4239	150	18	)	)	PUNCT
ejpam-4239	150	19	−	−	PROPN
ejpam-4239	151	1	tanh−1	tanh−1	ADJ
ejpam-4239	151	2	(	(	PUNCT
ejpam-4239	151	3	e	e	NOUN
ejpam-4239	151	4	1	1	NUM
ejpam-4239	151	5	2	2	NUM
ejpam-4239	151	6	iπ(p−v	iπ(p−v	PROPN
ejpam-4239	151	7	)	)	PUNCT
ejpam-4239	151	8	)	)	PUNCT
ejpam-4239	151	9	)	)	PUNCT
ejpam-4239	151	10	(	(	PUNCT
ejpam-4239	151	11	19	19	NUM
ejpam-4239	151	12	)	)	PUNCT
ejpam-4239	151	13	proof	proof	NOUN
ejpam-4239	151	14	.	.	PUNCT
ejpam-4239	152	1	use	use	VERB
ejpam-4239	152	2	equation	equation	NOUN
ejpam-4239	152	3	(	(	PUNCT
ejpam-4239	152	4	7	7	NUM
ejpam-4239	152	5	)	)	PUNCT
ejpam-4239	152	6	and	and	CCONJ
ejpam-4239	152	7	form	form	VERB
ejpam-4239	152	8	a	a	DET
ejpam-4239	152	9	second	second	ADJ
ejpam-4239	152	10	equation	equation	NOUN
ejpam-4239	152	11	by	by	ADP
ejpam-4239	152	12	replacing	replace	VERB
ejpam-4239	152	13	m	m	PRON
ejpam-4239	152	14	→	→	SYM
ejpam-4239	152	15	p	p	X
ejpam-4239	152	16	and	and	CCONJ
ejpam-4239	152	17	taking	take	VERB
ejpam-4239	152	18	their	their	PRON
ejpam-4239	152	19	difference	difference	NOUN
ejpam-4239	152	20	.	.	PUNCT
ejpam-4239	153	1	next	next	ADJ
ejpam-4239	153	2	set	set	VERB
ejpam-4239	153	3	k	k	PROPN
ejpam-4239	153	4	=	=	PUNCT
ejpam-4239	153	5	−1	−1	NOUN
ejpam-4239	153	6	,	,	PUNCT
ejpam-4239	153	7	a	a	DET
ejpam-4239	153	8	=	=	SYM
ejpam-4239	153	9	1	1	NUM
ejpam-4239	153	10	,	,	PUNCT
ejpam-4239	153	11	α	α	NOUN
ejpam-4239	153	12	=	=	PUNCT
ejpam-4239	153	13	β	β	X
ejpam-4239	153	14	=	=	SYM
ejpam-4239	153	15	1	1	NUM
ejpam-4239	153	16	and	and	CCONJ
ejpam-4239	153	17	simplify	simplify	VERB
ejpam-4239	153	18	using	use	VERB
ejpam-4239	153	19	entry	entry	NOUN
ejpam-4239	153	20	(	(	PUNCT
ejpam-4239	153	21	3	3	NUM
ejpam-4239	153	22	)	)	PUNCT
ejpam-4239	153	23	in	in	ADP
ejpam-4239	153	24	table	table	NOUN
ejpam-4239	153	25	below	below	ADV
ejpam-4239	153	26	(	(	PUNCT
ejpam-4239	153	27	64:12:7	64:12:7	NUM
ejpam-4239	153	28	)	)	PUNCT
ejpam-4239	153	29	in	in	ADP
ejpam-4239	153	30	[	[	X
ejpam-4239	153	31	5	5	NUM
ejpam-4239	153	32	]	]	PUNCT
ejpam-4239	153	33	.	.	PUNCT
ejpam-4239	154	1	example	example	NOUN
ejpam-4239	155	1	10.∫	10.∫	NUM
ejpam-4239	155	2	∞	∞	NUM
ejpam-4239	155	3	0	0	NUM
ejpam-4239	155	4	∫	∫	PROPN
ejpam-4239	155	5	∞	∞	PROPN
ejpam-4239	155	6	0	0	NUM
ejpam-4239	156	1	(	(	PUNCT
ejpam-4239	156	2	x−	x−	PROPN
ejpam-4239	156	3	√	√	PROPN
ejpam-4239	156	4	x	x	SYM
ejpam-4239	156	5	√	√	PROPN
ejpam-4239	156	6	y	y	PROPN
ejpam-4239	156	7	)	)	PUNCT
ejpam-4239	157	1	k	k	NOUN
ejpam-4239	157	2	1	1	NUM
ejpam-4239	157	3	3	3	NUM
ejpam-4239	157	4	(	(	PUNCT
ejpam-4239	157	5	x)j	x)j	PROPN
ejpam-4239	157	6	1	1	NUM
ejpam-4239	157	7	3	3	NUM
ejpam-4239	157	8	(	(	PUNCT
ejpam-4239	157	9	y	y	NOUN
ejpam-4239	157	10	)	)	PUNCT
ejpam-4239	157	11	y	y	PROPN
ejpam-4239	157	12	log	log	VERB
ejpam-4239	157	13	(	(	PUNCT
ejpam-4239	157	14	x	x	SYM
ejpam-4239	157	15	y	y	PROPN
ejpam-4239	157	16	)	)	PUNCT
ejpam-4239	157	17	dxdy	dxdy	NOUN
ejpam-4239	157	18	=	=	SYM
ejpam-4239	157	19	2	2	NUM
ejpam-4239	157	20	tanh−1	tanh−1	PROPN
ejpam-4239	157	21	(	(	PUNCT
ejpam-4239	157	22	1−	1−	NUM
ejpam-4239	157	23	√	√	NUM
ejpam-4239	157	24	3	3	NUM
ejpam-4239	157	25	2	2	NUM
ejpam-4239	157	26	+	+	CCONJ
ejpam-4239	157	27	1√	1√	PROPN
ejpam-4239	157	28	2	2	NUM
ejpam-4239	157	29	)	)	PUNCT
ejpam-4239	157	30	(	(	PUNCT
ejpam-4239	157	31	20	20	X
ejpam-4239	157	32	)	)	PUNCT
ejpam-4239	157	33	proof	proof	NOUN
ejpam-4239	157	34	.	.	PUNCT
ejpam-4239	158	1	use	use	VERB
ejpam-4239	158	2	equation	equation	NOUN
ejpam-4239	158	3	(	(	PUNCT
ejpam-4239	158	4	19	19	NUM
ejpam-4239	158	5	)	)	PUNCT
ejpam-4239	158	6	set	set	VERB
ejpam-4239	158	7	v	v	NOUN
ejpam-4239	158	8	=	=	SYM
ejpam-4239	158	9	1/3,m	1/3,m	NUM
ejpam-4239	158	10	=	=	SYM
ejpam-4239	158	11	3/2	3/2	NUM
ejpam-4239	158	12	,	,	PUNCT
ejpam-4239	158	13	p	p	NOUN
ejpam-4239	158	14	=	=	SYM
ejpam-4239	158	15	2	2	NUM
ejpam-4239	158	16	and	and	CCONJ
ejpam-4239	158	17	simplify	simplify	NOUN
ejpam-4239	158	18	.	.	PUNCT
ejpam-4239	158	19	example	example	NOUN
ejpam-4239	159	1	11	11	NUM
ejpam-4239	159	2	.	.	PUNCT
ejpam-4239	160	1	(	(	PUNCT
ejpam-4239	160	2	21	21	NUM
ejpam-4239	160	3	)	)	PUNCT
ejpam-4239	160	4	∫	∫	PROPN
ejpam-4239	161	1	∞	∞	PROPN
ejpam-4239	161	2	0	0	NUM
ejpam-4239	161	3	∫	∫	PROPN
ejpam-4239	161	4	∞	∞	PROPN
ejpam-4239	161	5	0	0	NUM
ejpam-4239	162	1	x2/5	x2/5	PROPN
ejpam-4239	162	2	(	(	PUNCT
ejpam-4239	162	3	10	10	NUM
ejpam-4239	162	4	√	√	NUM
ejpam-4239	162	5	y	y	NUM
ejpam-4239	162	6	−	−	PROPN
ejpam-4239	162	7	10	10	NUM
ejpam-4239	162	8	√	√	PROPN
ejpam-4239	162	9	x	x	SYM
ejpam-4239	162	10	)	)	PUNCT
ejpam-4239	162	11	k0(x)j0(y	k0(x)j0(y	X
ejpam-4239	162	12	)	)	PUNCT
ejpam-4239	162	13	√	√	VERB
ejpam-4239	162	14	y	y	PROPN
ejpam-4239	162	15	log	log	NOUN
ejpam-4239	162	16	(	(	PUNCT
ejpam-4239	162	17	x	x	NOUN
ejpam-4239	162	18	y	y	PROPN
ejpam-4239	162	19	)	)	PUNCT
ejpam-4239	162	20	dxdy	dxdy	PROPN
ejpam-4239	162	21	=	=	PUNCT
ejpam-4239	163	1	−	−	PROPN
ejpam-4239	164	1	tanh−1	tanh−1	NOUN
ejpam-4239	164	2	(	(	PUNCT
ejpam-4239	164	3	1	1	NUM
ejpam-4239	164	4	29	29	NUM
ejpam-4239	164	5	√	√	NUM
ejpam-4239	164	6	2	2	NUM
ejpam-4239	164	7	(	(	PUNCT
ejpam-4239	164	8	254−	254−	NUM
ejpam-4239	164	9	31	31	NUM
ejpam-4239	164	10	√	√	NUM
ejpam-4239	164	11	5−	5−	NUM
ejpam-4239	164	12	2	2	NUM
ejpam-4239	164	13	√	√	PROPN
ejpam-4239	164	14	4505	4505	NUM
ejpam-4239	164	15	+	+	CCONJ
ejpam-4239	164	16	1109	1109	NUM
ejpam-4239	164	17	√	√	NUM
ejpam-4239	164	18	5	5	NUM
ejpam-4239	164	19	)	)	PUNCT
ejpam-4239	164	20	)	)	PUNCT
ejpam-4239	164	21	proof	proof	NOUN
ejpam-4239	164	22	.	.	PUNCT
ejpam-4239	165	1	use	use	VERB
ejpam-4239	165	2	equation	equation	NOUN
ejpam-4239	165	3	(	(	PUNCT
ejpam-4239	165	4	19	19	NUM
ejpam-4239	165	5	)	)	PUNCT
ejpam-4239	165	6	set	set	VERB
ejpam-4239	165	7	v	v	NOUN
ejpam-4239	165	8	=	=	SYM
ejpam-4239	165	9	0,m	0,m	NOUN
ejpam-4239	166	1	=	=	SYM
ejpam-4239	166	2	3/2	3/2	NUM
ejpam-4239	166	3	,	,	PUNCT
ejpam-4239	166	4	p	p	X
ejpam-4239	166	5	=	=	SYM
ejpam-4239	166	6	7/5	7/5	NUM
ejpam-4239	166	7	and	and	CCONJ
ejpam-4239	166	8	simplify	simplify	NOUN
ejpam-4239	166	9	.	.	PUNCT
ejpam-4239	167	1	r.	r.	PROPN
ejpam-4239	167	2	reynolds	reynolds	PROPN
ejpam-4239	167	3	,	,	PUNCT
ejpam-4239	167	4	a.	a.	PROPN
ejpam-4239	167	5	stauffer	stauffer	PROPN
ejpam-4239	167	6	/	/	SYM
ejpam-4239	167	7	eur	eur	PROPN
ejpam-4239	167	8	.	.	PUNCT
ejpam-4239	168	1	j.	j.	PROPN
ejpam-4239	168	2	pure	pure	PROPN
ejpam-4239	168	3	appl	appl	PROPN
ejpam-4239	168	4	.	.	PROPN
ejpam-4239	168	5	math	math	PROPN
ejpam-4239	168	6	,	,	PUNCT
ejpam-4239	168	7	15	15	NUM
ejpam-4239	168	8	(	(	PUNCT
ejpam-4239	168	9	3	3	NUM
ejpam-4239	168	10	)	)	PUNCT
ejpam-4239	168	11	(	(	PUNCT
ejpam-4239	168	12	2022	2022	NUM
ejpam-4239	168	13	)	)	PUNCT
ejpam-4239	168	14	,	,	PUNCT
ejpam-4239	168	15	856	856	NUM
ejpam-4239	168	16	-	-	SYM
ejpam-4239	168	17	863	863	NUM
ejpam-4239	168	18	862	862	NUM
ejpam-4239	168	19	example	example	NOUN
ejpam-4239	168	20	12.∫	12.∫	NUM
ejpam-4239	168	21	∞	∞	NOUN
ejpam-4239	168	22	0	0	NUM
ejpam-4239	169	1	∫	∫	PROPN
ejpam-4239	169	2	∞	∞	PROPN
ejpam-4239	169	3	0	0	NUM
ejpam-4239	170	1	(	(	PUNCT
ejpam-4239	170	2	√	√	INTJ
ejpam-4239	170	3	x−	x−	PROPN
ejpam-4239	170	4	x2/5	x2/5	PROPN
ejpam-4239	170	5	10	10	NUM
ejpam-4239	170	6	√	√	PROPN
ejpam-4239	170	7	y	y	PROPN
ejpam-4239	170	8	)	)	PUNCT
ejpam-4239	171	1	k	k	NOUN
ejpam-4239	171	2	1	1	NUM
ejpam-4239	171	3	5	5	NUM
ejpam-4239	171	4	(	(	PUNCT
ejpam-4239	171	5	x)j	x)j	PROPN
ejpam-4239	171	6	1	1	NUM
ejpam-4239	171	7	5	5	NUM
ejpam-4239	171	8	(	(	PUNCT
ejpam-4239	171	9	y	y	NOUN
ejpam-4239	171	10	)	)	PUNCT
ejpam-4239	171	11	√	√	VERB
ejpam-4239	172	1	y	y	PROPN
ejpam-4239	172	2	log	log	NOUN
ejpam-4239	172	3	(	(	PUNCT
ejpam-4239	172	4	x	x	NOUN
ejpam-4239	172	5	y	y	PROPN
ejpam-4239	172	6	)	)	PUNCT
ejpam-4239	172	7	dxdy	dxdy	PROPN
ejpam-4239	172	8	=	=	NOUN
ejpam-4239	172	9	1	1	NUM
ejpam-4239	172	10	2	2	NUM
ejpam-4239	172	11	(	(	PUNCT
ejpam-4239	172	12	log	log	NOUN
ejpam-4239	172	13	(	(	PUNCT
ejpam-4239	172	14	5−	5−	NUM
ejpam-4239	172	15	2	2	NUM
ejpam-4239	172	16	√	√	NUM
ejpam-4239	172	17	5	5	NUM
ejpam-4239	172	18	)	)	PUNCT
ejpam-4239	172	19	+	+	CCONJ
ejpam-4239	172	20	4	4	NUM
ejpam-4239	172	21	tanh−1	tanh−1	NOUN
ejpam-4239	172	22	(	(	PUNCT
ejpam-4239	172	23	tan	tan	PROPN
ejpam-4239	172	24	(	(	PUNCT
ejpam-4239	172	25	3π	3π	NUM
ejpam-4239	172	26	40	40	NUM
ejpam-4239	172	27	)	)	PUNCT
ejpam-4239	172	28	)	)	PUNCT
ejpam-4239	172	29	)	)	PUNCT
ejpam-4239	173	1	(	(	PUNCT
ejpam-4239	173	2	22	22	X
ejpam-4239	173	3	)	)	PUNCT
ejpam-4239	173	4	proof	proof	NOUN
ejpam-4239	173	5	.	.	PUNCT
ejpam-4239	174	1	use	use	VERB
ejpam-4239	174	2	equation	equation	NOUN
ejpam-4239	174	3	(	(	PUNCT
ejpam-4239	174	4	19	19	NUM
ejpam-4239	174	5	)	)	PUNCT
ejpam-4239	174	6	set	set	VERB
ejpam-4239	174	7	v	v	NOUN
ejpam-4239	174	8	=	=	SYM
ejpam-4239	174	9	1/5,m	1/5,m	NUM
ejpam-4239	174	10	=	=	SYM
ejpam-4239	174	11	3/2	3/2	NUM
ejpam-4239	174	12	,	,	PUNCT
ejpam-4239	174	13	p	p	X
ejpam-4239	174	14	=	=	SYM
ejpam-4239	174	15	7/5	7/5	NUM
ejpam-4239	174	16	and	and	CCONJ
ejpam-4239	174	17	simplify	simplify	ADJ
ejpam-4239	174	18	.	.	PUNCT
ejpam-4239	174	19	example	example	NOUN
ejpam-4239	175	1	13	13	NUM
ejpam-4239	175	2	.	.	PUNCT
ejpam-4239	176	1	(	(	PUNCT
ejpam-4239	176	2	23	23	NUM
ejpam-4239	176	3	)	)	PUNCT
ejpam-4239	176	4	∫	∫	PROPN
ejpam-4239	177	1	∞	∞	PROPN
ejpam-4239	177	2	0	0	NUM
ejpam-4239	178	1	∫	∫	PROPN
ejpam-4239	178	2	∞	∞	NOUN
ejpam-4239	178	3	0	0	NUM
ejpam-4239	178	4	5	5	NUM
ejpam-4239	178	5	√	√	NUM
ejpam-4239	178	6	x	x	SYM
ejpam-4239	178	7	(	(	PUNCT
ejpam-4239	178	8	y3/10	y3/10	ADV
ejpam-4239	178	9	−	−	PROPN
ejpam-4239	178	10	x3/10	x3/10	PUNCT
ejpam-4239	178	11	)	)	PUNCT
ejpam-4239	179	1	k	k	NOUN
ejpam-4239	179	2	2	2	NUM
ejpam-4239	179	3	9	9	NUM
ejpam-4239	179	4	(	(	PUNCT
ejpam-4239	179	5	x)j	x)j	X
ejpam-4239	179	6	2	2	NUM
ejpam-4239	179	7	9	9	NUM
ejpam-4239	179	8	(	(	PUNCT
ejpam-4239	179	9	y	y	NOUN
ejpam-4239	179	10	)	)	PUNCT
ejpam-4239	179	11	√	√	VERB
ejpam-4239	180	1	y	y	PROPN
ejpam-4239	180	2	log	log	NOUN
ejpam-4239	180	3	(	(	PUNCT
ejpam-4239	180	4	x	x	NOUN
ejpam-4239	180	5	y	y	PROPN
ejpam-4239	180	6	)	)	PUNCT
ejpam-4239	180	7	dxdy	dxdy	PROPN
ejpam-4239	180	8	=	=	PUNCT
ejpam-4239	180	9	−	−	PROPN
ejpam-4239	181	1	tanh−1	tanh−1	NOUN
ejpam-4239	181	2	(	(	PUNCT
ejpam-4239	181	3	sin	sin	NOUN
ejpam-4239	181	4	(	(	PUNCT
ejpam-4239	181	5	π	π	PROPN
ejpam-4239	181	6	90	90	NUM
ejpam-4239	181	7	)	)	PUNCT
ejpam-4239	181	8	)	)	PUNCT
ejpam-4239	182	1	−	−	ADP
ejpam-4239	182	2	2	2	NUM
ejpam-4239	182	3	tanh−1	tanh−1	NOUN
ejpam-4239	182	4	(	(	PUNCT
ejpam-4239	182	5	tan	tan	PROPN
ejpam-4239	182	6	(	(	PUNCT
ejpam-4239	182	7	5π	5π	PROPN
ejpam-4239	182	8	72	72	NUM
ejpam-4239	182	9	)	)	PUNCT
ejpam-4239	182	10	)	)	PUNCT
ejpam-4239	182	11	proof	proof	NOUN
ejpam-4239	182	12	.	.	PUNCT
ejpam-4239	183	1	use	use	VERB
ejpam-4239	183	2	equation	equation	NOUN
ejpam-4239	183	3	(	(	PUNCT
ejpam-4239	183	4	19	19	NUM
ejpam-4239	183	5	)	)	PUNCT
ejpam-4239	183	6	set	set	VERB
ejpam-4239	183	7	v	v	NOUN
ejpam-4239	183	8	=	=	SYM
ejpam-4239	183	9	2/9,m	2/9,m	NUM
ejpam-4239	183	10	=	=	SYM
ejpam-4239	183	11	3/2	3/2	NUM
ejpam-4239	183	12	,	,	PUNCT
ejpam-4239	183	13	p	p	X
ejpam-4239	183	14	=	=	PROPN
ejpam-4239	183	15	6/5	6/5	NUM
ejpam-4239	183	16	and	and	CCONJ
ejpam-4239	183	17	simplify	simplify	ADJ
ejpam-4239	183	18	.	.	PUNCT
ejpam-4239	183	19	example	example	NOUN
ejpam-4239	184	1	14	14	NUM
ejpam-4239	184	2	.	.	PUNCT
ejpam-4239	185	1	(	(	PUNCT
ejpam-4239	185	2	24	24	NUM
ejpam-4239	185	3	)	)	PUNCT
ejpam-4239	185	4	∫	∫	PROPN
ejpam-4239	186	1	∞	∞	PROPN
ejpam-4239	186	2	0	0	NUM
ejpam-4239	187	1	∫	∫	PROPN
ejpam-4239	187	2	∞	∞	PROPN
ejpam-4239	187	3	0	0	NUM
ejpam-4239	188	1	(	(	PUNCT
ejpam-4239	188	2	x−	x−	PROPN
ejpam-4239	188	3	√	√	PROPN
ejpam-4239	188	4	x	x	SYM
ejpam-4239	188	5	√	√	PROPN
ejpam-4239	188	6	y	y	PROPN
ejpam-4239	188	7	)	)	PUNCT
ejpam-4239	189	1	k	k	NOUN
ejpam-4239	189	2	1	1	NUM
ejpam-4239	189	3	3	3	NUM
ejpam-4239	189	4	(	(	PUNCT
ejpam-4239	189	5	4	4	NUM
ejpam-4239	189	6	√	√	NUM
ejpam-4239	189	7	3x	3x	NUM
ejpam-4239	189	8	)	)	PUNCT
ejpam-4239	190	1	j	j	PROPN
ejpam-4239	190	2	1	1	NUM
ejpam-4239	190	3	3	3	NUM
ejpam-4239	190	4	(	(	PUNCT
ejpam-4239	190	5	2	2	NUM
ejpam-4239	190	6	√	√	PROPN
ejpam-4239	190	7	2y	2y	NUM
ejpam-4239	190	8	)	)	PUNCT
ejpam-4239	191	1	y	y	PROPN
ejpam-4239	191	2	log	log	VERB
ejpam-4239	191	3	(	(	PUNCT
ejpam-4239	191	4	x	x	SYM
ejpam-4239	191	5	y	y	PROPN
ejpam-4239	191	6	)	)	PUNCT
ejpam-4239	191	7	dxdy	dxdy	PROPN
ejpam-4239	191	8	=	=	PUNCT
ejpam-4239	191	9	1	1	NUM
ejpam-4239	191	10	48	48	NUM
ejpam-4239	191	11	(	(	PUNCT
ejpam-4239	191	12	(	(	PUNCT
ejpam-4239	191	13	−1)7/12	−1)7/12	NOUN
ejpam-4239	191	14	4	4	NUM
ejpam-4239	191	15	√	√	NOUN
ejpam-4239	191	16	6φ	6φ	NOUN
ejpam-4239	191	17	(	(	PUNCT
ejpam-4239	191	18	−	−	PROPN
ejpam-4239	191	19	6	6	NUM
ejpam-4239	191	20	√	√	NUM
ejpam-4239	191	21	−1	−1	NOUN
ejpam-4239	191	22	,	,	PUNCT
ejpam-4239	191	23	1	1	NUM
ejpam-4239	191	24	,	,	PUNCT
ejpam-4239	191	25	π	π	PROPN
ejpam-4239	191	26	+	+	CCONJ
ejpam-4239	191	27	i	i	PRON
ejpam-4239	191	28	log(6	log(6	ADJ
ejpam-4239	191	29	)	)	PUNCT
ejpam-4239	191	30	2π	2π	PROPN
ejpam-4239	191	31	)	)	PUNCT
ejpam-4239	191	32	−	−	PROPN
ejpam-4239	192	1	(	(	PUNCT
ejpam-4239	192	2	−1)5/6φ	−1)5/6φ	PROPN
ejpam-4239	192	3	(	(	PUNCT
ejpam-4239	192	4	−(−1)2/3	−(−1)2/3	PROPN
ejpam-4239	192	5	,	,	PUNCT
ejpam-4239	192	6	1	1	NUM
ejpam-4239	192	7	,	,	PUNCT
ejpam-4239	192	8	π	π	PROPN
ejpam-4239	192	9	+	+	CCONJ
ejpam-4239	192	10	i	i	PRON
ejpam-4239	192	11	log(6	log(6	ADJ
ejpam-4239	192	12	)	)	PUNCT
ejpam-4239	192	13	2π	2π	NOUN
ejpam-4239	192	14	)	)	PUNCT
ejpam-4239	192	15	)	)	PUNCT
ejpam-4239	192	16	proof	proof	NOUN
ejpam-4239	192	17	.	.	PUNCT
ejpam-4239	193	1	use	use	VERB
ejpam-4239	193	2	equation	equation	NOUN
ejpam-4239	193	3	(	(	PUNCT
ejpam-4239	193	4	7	7	NUM
ejpam-4239	193	5	)	)	PUNCT
ejpam-4239	193	6	and	and	CCONJ
ejpam-4239	193	7	form	form	VERB
ejpam-4239	193	8	a	a	DET
ejpam-4239	193	9	second	second	ADJ
ejpam-4239	193	10	equation	equation	NOUN
ejpam-4239	193	11	by	by	ADP
ejpam-4239	193	12	replacing	replace	VERB
ejpam-4239	193	13	m	m	PRON
ejpam-4239	193	14	→	→	SYM
ejpam-4239	193	15	p	p	X
ejpam-4239	193	16	and	and	CCONJ
ejpam-4239	193	17	taking	take	VERB
ejpam-4239	193	18	their	their	PRON
ejpam-4239	193	19	difference	difference	NOUN
ejpam-4239	193	20	.	.	PUNCT
ejpam-4239	194	1	next	next	ADJ
ejpam-4239	194	2	set	set	VERB
ejpam-4239	194	3	k	k	PROPN
ejpam-4239	194	4	=	=	PUNCT
ejpam-4239	194	5	−1	−1	NOUN
ejpam-4239	194	6	,	,	PUNCT
ejpam-4239	194	7	a	a	DET
ejpam-4239	194	8	=	=	SYM
ejpam-4239	194	9	1	1	NUM
ejpam-4239	194	10	,	,	PUNCT
ejpam-4239	194	11	α	α	NOUN
ejpam-4239	194	12	=	=	PUNCT
ejpam-4239	194	13	√	√	NUM
ejpam-4239	194	14	2	2	NUM
ejpam-4239	194	15	,	,	PUNCT
ejpam-4239	194	16	β	β	X
ejpam-4239	194	17	=	=	PUNCT
ejpam-4239	194	18	√	√	PROPN
ejpam-4239	194	19	3,m	3,m	NUM
ejpam-4239	194	20	=	=	SYM
ejpam-4239	194	21	3/2	3/2	NUM
ejpam-4239	194	22	,	,	PUNCT
ejpam-4239	194	23	p	p	NOUN
ejpam-4239	194	24	=	=	SYM
ejpam-4239	194	25	2	2	NUM
ejpam-4239	194	26	,	,	PUNCT
ejpam-4239	194	27	v	v	NOUN
ejpam-4239	194	28	=	=	SYM
ejpam-4239	194	29	1/7	1/7	NUM
ejpam-4239	194	30	and	and	CCONJ
ejpam-4239	194	31	simplify	simplify	ADJ
ejpam-4239	194	32	.	.	PUNCT
ejpam-4239	195	1	example	example	NOUN
ejpam-4239	195	2	15	15	NUM
ejpam-4239	195	3	.	.	PUNCT
ejpam-4239	196	1	(	(	PUNCT
ejpam-4239	196	2	25	25	NUM
ejpam-4239	196	3	)	)	PUNCT
ejpam-4239	196	4	∫	∫	PROPN
ejpam-4239	197	1	∞	∞	PROPN
ejpam-4239	197	2	0	0	NUM
ejpam-4239	197	3	∫	∫	PROPN
ejpam-4239	197	4	∞	∞	NUM
ejpam-4239	197	5	0	0	NUM
ejpam-4239	198	1	√	√	NUM
ejpam-4239	198	2	xk	xk	PROPN
ejpam-4239	198	3	1	1	NUM
ejpam-4239	198	4	3	3	NUM
ejpam-4239	198	5	(	(	PUNCT
ejpam-4239	198	6	3x)j	3x)j	NUM
ejpam-4239	198	7	1	1	NUM
ejpam-4239	198	8	3	3	NUM
ejpam-4239	198	9	(	(	PUNCT
ejpam-4239	198	10	2y	2y	NUM
ejpam-4239	198	11	)	)	PUNCT
ejpam-4239	198	12	√	√	PROPN
ejpam-4239	199	1	y	y	PROPN
ejpam-4239	199	2	log	log	NOUN
ejpam-4239	199	3	(	(	PUNCT
ejpam-4239	199	4	−2x	−2x	PROPN
ejpam-4239	199	5	y	y	PROPN
ejpam-4239	199	6	)	)	PUNCT
ejpam-4239	199	7	dxdy	dxdy	PROPN
ejpam-4239	199	8	=	=	SYM
ejpam-4239	199	9	−	−	PROPN
ejpam-4239	200	1	(	(	PUNCT
ejpam-4239	200	2	−1)7/12φ	−1)7/12φ	INTJ
ejpam-4239	200	3	(	(	PUNCT
ejpam-4239	200	4	−	−	PROPN
ejpam-4239	200	5	6	6	NUM
ejpam-4239	200	6	√	√	NUM
ejpam-4239	200	7	−1	−1	NOUN
ejpam-4239	200	8	,	,	PUNCT
ejpam-4239	200	9	1	1	NUM
ejpam-4239	200	10	,	,	PUNCT
ejpam-4239	200	11	3π−4i	3π−4i	NUM
ejpam-4239	200	12	log(2)+2i	log(2)+2i	NOUN
ejpam-4239	200	13	log(3	log(3	NOUN
ejpam-4239	200	14	)	)	PUNCT
ejpam-4239	200	15	2π	2π	NOUN
ejpam-4239	200	16	)	)	PUNCT
ejpam-4239	200	17	3	3	NUM
ejpam-4239	200	18	√	√	NUM
ejpam-4239	200	19	6	6	NUM
ejpam-4239	200	20	proof	proof	NOUN
ejpam-4239	200	21	.	.	PUNCT
ejpam-4239	201	1	use	use	VERB
ejpam-4239	201	2	equation	equation	NOUN
ejpam-4239	201	3	(	(	PUNCT
ejpam-4239	201	4	7	7	X
ejpam-4239	201	5	)	)	PUNCT
ejpam-4239	201	6	set	set	NOUN
ejpam-4239	201	7	k	k	NOUN
ejpam-4239	201	8	=	=	SYM
ejpam-4239	201	9	−1	−1	NOUN
ejpam-4239	201	10	,	,	PUNCT
ejpam-4239	201	11	a	a	DET
ejpam-4239	201	12	=	=	X
ejpam-4239	201	13	−2,m	−2,m	PROPN
ejpam-4239	201	14	=	=	SYM
ejpam-4239	201	15	3/2	3/2	NUM
ejpam-4239	201	16	,	,	PUNCT
ejpam-4239	201	17	v	v	NOUN
ejpam-4239	201	18	=	=	SYM
ejpam-4239	201	19	1/3	1/3	NUM
ejpam-4239	201	20	,	,	PUNCT
ejpam-4239	201	21	,	,	PUNCT
ejpam-4239	201	22	α	α	NOUN
ejpam-4239	201	23	=	=	SYM
ejpam-4239	201	24	2	2	NUM
ejpam-4239	201	25	,	,	PUNCT
ejpam-4239	201	26	β	β	X
ejpam-4239	201	27	=	=	SYM
ejpam-4239	201	28	3	3	NUM
ejpam-4239	201	29	and	and	CCONJ
ejpam-4239	201	30	simplify	simplify	NOUN
ejpam-4239	201	31	.	.	PUNCT
ejpam-4239	202	1	references	reference	NOUN
ejpam-4239	202	2	863	863	NUM
ejpam-4239	202	3	example	example	NOUN
ejpam-4239	202	4	16	16	NUM
ejpam-4239	202	5	.	.	PUNCT
ejpam-4239	203	1	(	(	PUNCT
ejpam-4239	203	2	26	26	NUM
ejpam-4239	203	3	)	)	PUNCT
ejpam-4239	203	4	∫	∫	PROPN
ejpam-4239	204	1	∞	∞	PROPN
ejpam-4239	204	2	0	0	NUM
ejpam-4239	204	3	∫	∫	PROPN
ejpam-4239	204	4	∞	∞	NUM
ejpam-4239	204	5	0	0	NUM
ejpam-4239	205	1	√	√	NUM
ejpam-4239	205	2	xk	xk	PROPN
ejpam-4239	205	3	1√	1√	PROPN
ejpam-4239	205	4	5	5	NUM
ejpam-4239	205	5	(	(	PUNCT
ejpam-4239	205	6	5x√	5x√	NUM
ejpam-4239	205	7	11	11	NUM
ejpam-4239	205	8	)	)	PUNCT
ejpam-4239	206	1	j	j	PROPN
ejpam-4239	206	2	1√	1√	PROPN
ejpam-4239	206	3	5	5	NUM
ejpam-4239	206	4	(	(	PUNCT
ejpam-4239	206	5	y√	y√	NOUN
ejpam-4239	206	6	7	7	NUM
ejpam-4239	206	7	)	)	PUNCT
ejpam-4239	206	8	√	√	PROPN
ejpam-4239	207	1	y	y	PROPN
ejpam-4239	207	2	√	√	PROPN
ejpam-4239	207	3	log	log	NOUN
ejpam-4239	207	4	(	(	PUNCT
ejpam-4239	207	5	−3x	−3x	PROPN
ejpam-4239	207	6	y	y	PROPN
ejpam-4239	207	7	)	)	PUNCT
ejpam-4239	207	8	dxdy	dxdy	PROPN
ejpam-4239	207	9	=	=	NOUN
ejpam-4239	207	10	1	1	NUM
ejpam-4239	207	11	5	5	NUM
ejpam-4239	207	12	4	4	NUM
ejpam-4239	207	13	√	√	NUM
ejpam-4239	207	14	7113/4e	7113/4e	NUM
ejpam-4239	208	1	−	−	NOUN
ejpam-4239	209	1	iπ	iπ	ADV
ejpam-4239	209	2	2	2	NUM
ejpam-4239	209	3	√	√	NUM
ejpam-4239	209	4	5	5	NUM
ejpam-4239	209	5	√	√	PROPN
ejpam-4239	209	6	π	π	PROPN
ejpam-4239	209	7	5	5	NUM
ejpam-4239	209	8	φ	φ	PROPN
ejpam-4239	209	9	(	(	PUNCT
ejpam-4239	209	10	−ie	−ie	PROPN
ejpam-4239	209	11	−	−	PROPN
ejpam-4239	209	12	iπ√	iπ√	NOUN
ejpam-4239	209	13	5	5	NUM
ejpam-4239	209	14	,	,	PUNCT
ejpam-4239	209	15	1	1	NUM
ejpam-4239	209	16	2	2	NUM
ejpam-4239	209	17	,	,	PUNCT
ejpam-4239	209	18	3	3	NUM
ejpam-4239	209	19	2	2	NUM
ejpam-4239	209	20	+	+	CCONJ
ejpam-4239	209	21	i	i	PRON
ejpam-4239	209	22	log	log	VERB
ejpam-4239	209	23	(	(	PUNCT
ejpam-4239	209	24	175	175	NUM
ejpam-4239	209	25	99	99	NUM
ejpam-4239	209	26	)	)	PUNCT
ejpam-4239	209	27	2π	2π	NOUN
ejpam-4239	209	28	)	)	PUNCT
ejpam-4239	209	29	proof	proof	NOUN
ejpam-4239	209	30	.	.	PUNCT
ejpam-4239	210	1	use	use	VERB
ejpam-4239	210	2	equation	equation	NOUN
ejpam-4239	210	3	(	(	PUNCT
ejpam-4239	210	4	7	7	X
ejpam-4239	210	5	)	)	PUNCT
ejpam-4239	210	6	set	set	NOUN
ejpam-4239	210	7	k	k	NOUN
ejpam-4239	211	1	=	=	PUNCT
ejpam-4239	211	2	−1/2	−1/2	ADJ
ejpam-4239	211	3	,	,	PUNCT
ejpam-4239	211	4	a	a	DET
ejpam-4239	211	5	=	=	X
ejpam-4239	211	6	−3,m	−3,m	PROPN
ejpam-4239	211	7	=	=	SYM
ejpam-4239	211	8	3/2	3/2	NUM
ejpam-4239	211	9	,	,	PUNCT
ejpam-4239	211	10	v	v	NOUN
ejpam-4239	211	11	=	=	SYM
ejpam-4239	211	12	1/	1/	NUM
ejpam-4239	211	13	√	√	NUM
ejpam-4239	211	14	5	5	NUM
ejpam-4239	211	15	,	,	PUNCT
ejpam-4239	211	16	,	,	PUNCT
ejpam-4239	211	17	α	α	X
ejpam-4239	211	18	=	=	SYM
ejpam-4239	211	19	1/	1/	NUM
ejpam-4239	211	20	√	√	NUM
ejpam-4239	211	21	7	7	NUM
ejpam-4239	211	22	,	,	PUNCT
ejpam-4239	211	23	β	β	X
ejpam-4239	211	24	=	=	SYM
ejpam-4239	211	25	5/	5/	NUM
ejpam-4239	211	26	√	√	NUM
ejpam-4239	211	27	11	11	NUM
ejpam-4239	211	28	and	and	CCONJ
ejpam-4239	211	29	simplify	simplify	VERB
ejpam-4239	211	30	.	.	PUNCT
ejpam-4239	212	1	5	5	X
ejpam-4239	212	2	.	.	X
ejpam-4239	212	3	discussion	discussion	NOUN
ejpam-4239	212	4	in	in	ADP
ejpam-4239	212	5	this	this	DET
ejpam-4239	212	6	paper	paper	NOUN
ejpam-4239	212	7	,	,	PUNCT
ejpam-4239	212	8	we	we	PRON
ejpam-4239	212	9	have	have	AUX
ejpam-4239	212	10	presented	present	VERB
ejpam-4239	212	11	a	a	DET
ejpam-4239	212	12	novel	novel	ADJ
ejpam-4239	212	13	method	method	NOUN
ejpam-4239	212	14	for	for	ADP
ejpam-4239	212	15	deriving	derive	VERB
ejpam-4239	212	16	a	a	DET
ejpam-4239	212	17	new	new	ADJ
ejpam-4239	212	18	double	double	ADJ
ejpam-4239	212	19	integral	integral	NOUN
ejpam-4239	212	20	involving	involve	VERB
ejpam-4239	212	21	the	the	DET
ejpam-4239	212	22	product	product	NOUN
ejpam-4239	212	23	of	of	ADP
ejpam-4239	212	24	bessel	bessel	NOUN
ejpam-4239	212	25	functions	function	NOUN
ejpam-4239	212	26	along	along	ADP
ejpam-4239	212	27	with	with	ADP
ejpam-4239	212	28	some	some	DET
ejpam-4239	212	29	interesting	interesting	ADJ
ejpam-4239	212	30	definite	definite	ADJ
ejpam-4239	212	31	integrals	integral	NOUN
ejpam-4239	212	32	using	use	VERB
ejpam-4239	212	33	contour	contour	NOUN
ejpam-4239	212	34	integration	integration	NOUN
ejpam-4239	212	35	.	.	PUNCT
ejpam-4239	213	1	the	the	DET
ejpam-4239	213	2	results	result	NOUN
ejpam-4239	213	3	presented	present	VERB
ejpam-4239	213	4	were	be	AUX
ejpam-4239	213	5	numerically	numerically	ADV
ejpam-4239	213	6	verified	verify	VERB
ejpam-4239	213	7	for	for	ADP
ejpam-4239	213	8	both	both	CCONJ
ejpam-4239	213	9	real	real	ADJ
ejpam-4239	213	10	and	and	CCONJ
ejpam-4239	213	11	imaginary	imaginary	ADJ
ejpam-4239	213	12	and	and	CCONJ
ejpam-4239	213	13	complex	complex	ADJ
ejpam-4239	213	14	values	value	NOUN
ejpam-4239	213	15	of	of	ADP
ejpam-4239	213	16	the	the	DET
ejpam-4239	213	17	parameters	parameter	NOUN
ejpam-4239	213	18	in	in	ADP
ejpam-4239	213	19	the	the	DET
ejpam-4239	213	20	integrals	integral	NOUN
ejpam-4239	213	21	using	use	VERB
ejpam-4239	213	22	mathematica	mathematica	PROPN
ejpam-4239	213	23	by	by	ADP
ejpam-4239	213	24	wolfram	wolfram	PROPN
ejpam-4239	213	25	.	.	PUNCT
ejpam-4239	214	1	references	reference	NOUN
ejpam-4239	214	2	[	[	X
ejpam-4239	214	3	1	1	NUM
ejpam-4239	214	4	]	]	X
ejpam-4239	214	5	yu	yu	PROPN
ejpam-4239	214	6	.	.	PUNCT
ejpam-4239	214	7	a.	a.	PROPN
ejpam-4239	214	8	brychkov	brychkov	PROPN
ejpam-4239	214	9	,	,	PUNCT
ejpam-4239	214	10	o.	o.	PROPN
ejpam-4239	214	11	i.	i.	PROPN
ejpam-4239	214	12	marichev	marichev	PROPN
ejpam-4239	214	13	,	,	PUNCT
ejpam-4239	214	14	and	and	CCONJ
ejpam-4239	214	15	n.	n.	PROPN
ejpam-4239	214	16	v.	v.	PROPN
ejpam-4239	214	17	savischenko	savischenko	PROPN
ejpam-4239	214	18	.	.	PUNCT
ejpam-4239	215	1	handbook	handbook	NOUN
ejpam-4239	215	2	of	of	ADP
ejpam-4239	215	3	mellin	mellin	PROPN
ejpam-4239	215	4	tranforms	tranform	NOUN
ejpam-4239	215	5	.	.	PUNCT
ejpam-4239	216	1	crc	crc	NOUN
ejpam-4239	216	2	press	press	PROPN
ejpam-4239	216	3	.	.	PUNCT
ejpam-4239	216	4	,	,	PUNCT
ejpam-4239	216	5	2019	2019	NUM
ejpam-4239	216	6	.	.	PUNCT
ejpam-4239	217	1	[	[	X
ejpam-4239	217	2	2	2	NUM
ejpam-4239	217	3	]	]	PUNCT
ejpam-4239	217	4	nist	nist	NOUN
ejpam-4239	217	5	digital	digital	PROPN
ejpam-4239	217	6	library	library	NOUN
ejpam-4239	217	7	of	of	ADP
ejpam-4239	217	8	mathematical	mathematical	ADJ
ejpam-4239	217	9	functions	function	NOUN
ejpam-4239	217	10	.	.	PUNCT
ejpam-4239	218	1	f.	f.	PROPN
ejpam-4239	218	2	w.	w.	PROPN
ejpam-4239	218	3	j.	j.	PROPN
ejpam-4239	218	4	olver	olver	PROPN
ejpam-4239	218	5	,	,	PUNCT
ejpam-4239	218	6	a.	a.	PROPN
ejpam-4239	218	7	b.	b.	PROPN
ejpam-4239	218	8	olde	olde	PROPN
ejpam-4239	218	9	daalhuis	daalhuis	PROPN
ejpam-4239	218	10	,	,	PUNCT
ejpam-4239	218	11	d.	d.	PROPN
ejpam-4239	218	12	w.	w.	PROPN
ejpam-4239	218	13	lozier	lozier	PROPN
ejpam-4239	218	14	,	,	PUNCT
ejpam-4239	218	15	b.	b.	PROPN
ejpam-4239	218	16	i.	i.	PROPN
ejpam-4239	218	17	schneider	schneider	PROPN
ejpam-4239	218	18	,	,	PUNCT
ejpam-4239	218	19	r.	r.	PROPN
ejpam-4239	218	20	f.	f.	PROPN
ejpam-4239	218	21	boisvert	boisvert	PROPN
ejpam-4239	218	22	,	,	PUNCT
ejpam-4239	218	23	c.	c.	PROPN
ejpam-4239	218	24	w.	w.	PROPN
ejpam-4239	218	25	clark	clark	PROPN
ejpam-4239	218	26	,	,	PUNCT
ejpam-4239	218	27	b.	b.	PROPN
ejpam-4239	218	28	r.	r.	PROPN
ejpam-4239	218	29	miller	miller	PROPN
ejpam-4239	218	30	,	,	PUNCT
ejpam-4239	218	31	b.	b.	PROPN
ejpam-4239	219	1	v.	v.	PROPN
ejpam-4239	219	2	saunders	saunders	PROPN
ejpam-4239	219	3	,	,	PUNCT
ejpam-4239	219	4	h.	h.	PROPN
ejpam-4239	219	5	s.	s.	PROPN
ejpam-4239	219	6	cohl	cohl	PROPN
ejpam-4239	219	7	,	,	PUNCT
ejpam-4239	219	8	and	and	CCONJ
ejpam-4239	219	9	m.	m.	PROPN
ejpam-4239	219	10	a.	a.	PROPN
ejpam-4239	219	11	mcclain	mcclain	PROPN
ejpam-4239	219	12	,	,	PUNCT
ejpam-4239	219	13	eds	eds	PROPN
ejpam-4239	219	14	.	.	PUNCT
ejpam-4239	220	1	[	[	X
ejpam-4239	220	2	3	3	X
ejpam-4239	220	3	]	]	PUNCT
ejpam-4239	220	4	m.	m.	NOUN
ejpam-4239	220	5	l.	l.	PROPN
ejpam-4239	220	6	glasser	glasser	PROPN
ejpam-4239	220	7	.	.	PUNCT
ejpam-4239	221	1	integral	integral	ADJ
ejpam-4239	221	2	representations	representation	NOUN
ejpam-4239	221	3	for	for	ADP
ejpam-4239	221	4	the	the	DET
ejpam-4239	221	5	exceptional	exceptional	ADJ
ejpam-4239	221	6	univariate	univariate	ADJ
ejpam-4239	221	7	lommel	lommel	ADJ
ejpam-4239	221	8	functions	function	NOUN
ejpam-4239	221	9	.	.	PUNCT
ejpam-4239	222	1	j.	j.	PROPN
ejpam-4239	222	2	phys	phys	PROPN
ejpam-4239	222	3	.	.	PUNCT
ejpam-4239	223	1	a	a	DET
ejpam-4239	223	2	,	,	PUNCT
ejpam-4239	223	3	43	43	NUM
ejpam-4239	223	4	,	,	PUNCT
ejpam-4239	223	5	2010	2010	NUM
ejpam-4239	223	6	.	.	PUNCT
ejpam-4239	224	1	[	[	X
ejpam-4239	224	2	4	4	X
ejpam-4239	224	3	]	]	X
ejpam-4239	224	4	i.	i.	PROPN
ejpam-4239	224	5	s.	s.	PROPN
ejpam-4239	224	6	gradshteyn	gradshteyn	PROPN
ejpam-4239	224	7	and	and	CCONJ
ejpam-4239	224	8	i.	i.	PROPN
ejpam-4239	224	9	m.	m.	PROPN
ejpam-4239	224	10	ryzhik	ryzhik	PROPN
ejpam-4239	224	11	.	.	PUNCT
ejpam-4239	225	1	table	table	NOUN
ejpam-4239	225	2	of	of	ADP
ejpam-4239	225	3	integrals	integral	NOUN
ejpam-4239	225	4	,	,	PUNCT
ejpam-4239	225	5	series	series	NOUN
ejpam-4239	225	6	,	,	PUNCT
ejpam-4239	225	7	and	and	CCONJ
ejpam-4239	225	8	products	product	NOUN
ejpam-4239	225	9	.	.	PUNCT
ejpam-4239	226	1	elsevier	elsevier	NOUN
ejpam-4239	226	2	/	/	SYM
ejpam-4239	226	3	academic	academic	ADJ
ejpam-4239	226	4	press	press	NOUN
ejpam-4239	226	5	,	,	PUNCT
ejpam-4239	226	6	amsterdam	amsterdam	PROPN
ejpam-4239	226	7	,	,	PUNCT
ejpam-4239	226	8	seventh	seventh	ADJ
ejpam-4239	226	9	edition	edition	NOUN
ejpam-4239	226	10	,	,	PUNCT
ejpam-4239	226	11	2007	2007	NUM
ejpam-4239	226	12	.	.	PUNCT
ejpam-4239	227	1	[	[	X
ejpam-4239	227	2	5	5	X
ejpam-4239	227	3	]	]	PUNCT
ejpam-4239	227	4	keith	keith	PROPN
ejpam-4239	227	5	b.	b.	PROPN
ejpam-4239	227	6	oldham	oldham	PROPN
ejpam-4239	227	7	,	,	PUNCT
ejpam-4239	227	8	jan	jan	PROPN
ejpam-4239	227	9	myland	myland	PROPN
ejpam-4239	227	10	,	,	PUNCT
ejpam-4239	227	11	and	and	CCONJ
ejpam-4239	227	12	jerome	jerome	PROPN
ejpam-4239	227	13	spanier	spanier	NOUN
ejpam-4239	227	14	.	.	PUNCT
ejpam-4239	228	1	an	an	DET
ejpam-4239	228	2	atlas	atlas	PROPN
ejpam-4239	228	3	of	of	ADP
ejpam-4239	228	4	functions	function	NOUN
ejpam-4239	228	5	:	:	PUNCT
ejpam-4239	228	6	with	with	ADP
ejpam-4239	228	7	equator	equator	NOUN
ejpam-4239	228	8	,	,	PUNCT
ejpam-4239	228	9	the	the	DET
ejpam-4239	228	10	atlas	atlas	PROPN
ejpam-4239	228	11	function	function	PROPN
ejpam-4239	228	12	calculator	calculator	NOUN
ejpam-4239	228	13	.	.	PUNCT
ejpam-4239	229	1	springer	springer	NOUN
ejpam-4239	229	2	science	science	PROPN
ejpam-4239	229	3	&	&	CCONJ
ejpam-4239	229	4	business	business	NOUN
ejpam-4239	229	5	media	medium	NOUN
ejpam-4239	229	6	,	,	PUNCT
ejpam-4239	229	7	07	07	NUM
ejpam-4239	229	8	2010	2010	NUM
ejpam-4239	229	9	.	.	PUNCT
ejpam-4239	230	1	[	[	X
ejpam-4239	230	2	6	6	NUM
ejpam-4239	230	3	]	]	X
ejpam-4239	230	4	robert	robert	PROPN
ejpam-4239	230	5	reynolds	reynolds	PROPN
ejpam-4239	230	6	and	and	CCONJ
ejpam-4239	230	7	allan	allan	PROPN
ejpam-4239	230	8	stauffer	stauffer	PROPN
ejpam-4239	230	9	.	.	PUNCT
ejpam-4239	231	1	a	a	DET
ejpam-4239	231	2	method	method	NOUN
ejpam-4239	231	3	for	for	ADP
ejpam-4239	231	4	evaluating	evaluate	VERB
ejpam-4239	231	5	definite	definite	ADJ
ejpam-4239	231	6	integrals	integral	NOUN
ejpam-4239	231	7	in	in	ADP
ejpam-4239	231	8	terms	term	NOUN
ejpam-4239	231	9	of	of	ADP
ejpam-4239	231	10	special	special	ADJ
ejpam-4239	231	11	functions	function	NOUN
ejpam-4239	231	12	with	with	ADP
ejpam-4239	231	13	examples	example	NOUN
ejpam-4239	231	14	.	.	PUNCT
ejpam-4239	232	1	international	international	ADJ
ejpam-4239	232	2	mathematical	mathematical	PROPN
ejpam-4239	232	3	forum	forum	PROPN
ejpam-4239	232	4	,	,	PUNCT
ejpam-4239	232	5	15:235	15:235	NUM
ejpam-4239	232	6	–	–	PUNCT
ejpam-4239	232	7	244	244	NUM
ejpam-4239	232	8	,	,	PUNCT
ejpam-4239	232	9	2020	2020	NUM
ejpam-4239	232	10	.	.	PUNCT
ejpam-4239	233	1	[	[	X
ejpam-4239	233	2	7	7	X
ejpam-4239	233	3	]	]	X
ejpam-4239	233	4	n.m	n.m	PROPN
ejpam-4239	233	5	.	.	PROPN
ejpam-4239	233	6	temme	temme	PROPN
ejpam-4239	233	7	.	.	PUNCT
ejpam-4239	234	1	a	a	DET
ejpam-4239	234	2	double	double	ADJ
ejpam-4239	234	3	integral	integral	ADJ
ejpam-4239	234	4	containing	contain	VERB
ejpam-4239	234	5	the	the	DET
ejpam-4239	234	6	modified	modify	VERB
ejpam-4239	234	7	bessel	bessel	NOUN
ejpam-4239	234	8	function	function	NOUN
ejpam-4239	234	9	:	:	PUNCT
ejpam-4239	234	10	asymptotics	asymptotic	NOUN
ejpam-4239	234	11	and	and	CCONJ
ejpam-4239	234	12	computation	computation	NOUN
ejpam-4239	234	13	.	.	PUNCT
ejpam-4239	235	1	mathematics	mathematic	NOUN
ejpam-4239	235	2	of	of	ADP
ejpam-4239	235	3	compijtation	compijtation	NOUN
ejpam-4239	235	4	,	,	PUNCT
ejpam-4239	235	5	47:683–691	47:683–691	PROPN
ejpam-4239	235	6	,	,	PUNCT
ejpam-4239	235	7	1986	1986	NUM
ejpam-4239	235	8	.	.	PUNCT