id	sid	tid	token	lemma	pos
ejpam-4203	1	1	european	european	PROPN
ejpam-4203	1	2	journal	journal	PROPN
ejpam-4203	1	3	of	of	ADP
ejpam-4203	1	4	pure	pure	ADJ
ejpam-4203	1	5	and	and	CCONJ
ejpam-4203	1	6	applied	apply	VERB
ejpam-4203	1	7	mathematics	mathematic	NOUN
ejpam-4203	1	8	vol	vol	NOUN
ejpam-4203	1	9	.	.	PROPN
ejpam-4203	2	1	15	15	NUM
ejpam-4203	2	2	,	,	PUNCT
ejpam-4203	2	3	no	no	INTJ
ejpam-4203	2	4	.	.	NOUN
ejpam-4203	2	5	2	2	NUM
ejpam-4203	2	6	,	,	PUNCT
ejpam-4203	2	7	2022	2022	NUM
ejpam-4203	2	8	,	,	PUNCT
ejpam-4203	2	9	390	390	NUM
ejpam-4203	2	10	-	-	SYM
ejpam-4203	2	11	396	396	NUM
ejpam-4203	2	12	issn	issn	PROPN
ejpam-4203	2	13	1307	1307	NUM
ejpam-4203	2	14	-	-	SYM
ejpam-4203	2	15	5543	5543	NUM
ejpam-4203	2	16	–	–	PUNCT
ejpam-4203	3	1	ejpam.com	ejpam.com	X
ejpam-4203	3	2	published	publish	VERB
ejpam-4203	3	3	by	by	ADP
ejpam-4203	3	4	new	new	PROPN
ejpam-4203	3	5	york	york	PROPN
ejpam-4203	3	6	business	business	PROPN
ejpam-4203	3	7	global	global	ADJ
ejpam-4203	3	8	triple	triple	ADJ
ejpam-4203	3	9	integral	integral	ADJ
ejpam-4203	3	10	involving	involve	VERB
ejpam-4203	3	11	the	the	DET
ejpam-4203	3	12	product	product	NOUN
ejpam-4203	3	13	of	of	ADP
ejpam-4203	3	14	the	the	DET
ejpam-4203	3	15	logarithmic	logarithmic	ADJ
ejpam-4203	3	16	and	and	CCONJ
ejpam-4203	3	17	bessel	bessel	ADJ
ejpam-4203	3	18	functions	function	NOUN
ejpam-4203	3	19	expressed	express	VERB
ejpam-4203	3	20	in	in	ADP
ejpam-4203	3	21	terms	term	NOUN
ejpam-4203	3	22	of	of	ADP
ejpam-4203	3	23	the	the	DET
ejpam-4203	3	24	lerch	lerch	PROPN
ejpam-4203	3	25	function	function	PROPN
ejpam-4203	3	26	robert	robert	PROPN
ejpam-4203	3	27	reynolds1,∗	reynolds1,∗	PROPN
ejpam-4203	3	28	,	,	PUNCT
ejpam-4203	3	29	allan	allan	PROPN
ejpam-4203	3	30	stauffer1	stauffer1	PROPN
ejpam-4203	3	31	1	1	NUM
ejpam-4203	3	32	department	department	NOUN
ejpam-4203	3	33	of	of	ADP
ejpam-4203	3	34	mathematics	mathematic	NOUN
ejpam-4203	3	35	and	and	CCONJ
ejpam-4203	3	36	statistics	statistic	NOUN
ejpam-4203	3	37	,	,	PUNCT
ejpam-4203	3	38	faculty	faculty	NOUN
ejpam-4203	3	39	of	of	ADP
ejpam-4203	3	40	science	science	PROPN
ejpam-4203	3	41	,	,	PUNCT
ejpam-4203	3	42	york	york	PROPN
ejpam-4203	3	43	university	university	PROPN
ejpam-4203	3	44	,	,	PUNCT
ejpam-4203	3	45	toronto	toronto	PROPN
ejpam-4203	3	46	,	,	PUNCT
ejpam-4203	3	47	ontario	ontario	PROPN
ejpam-4203	3	48	,	,	PUNCT
ejpam-4203	3	49	canada	canada	PROPN
ejpam-4203	3	50	,	,	PUNCT
ejpam-4203	3	51	m3j1p3	m3j1p3	PROPN
ejpam-4203	3	52	abstract	abstract	NOUN
ejpam-4203	3	53	.	.	PUNCT
ejpam-4203	4	1	the	the	DET
ejpam-4203	4	2	aim	aim	NOUN
ejpam-4203	4	3	of	of	ADP
ejpam-4203	4	4	the	the	DET
ejpam-4203	4	5	present	present	ADJ
ejpam-4203	4	6	document	document	NOUN
ejpam-4203	4	7	is	be	AUX
ejpam-4203	4	8	to	to	PART
ejpam-4203	4	9	evaluate	evaluate	VERB
ejpam-4203	4	10	a	a	DET
ejpam-4203	4	11	triple	triple	ADJ
ejpam-4203	4	12	integral	integral	ADJ
ejpam-4203	4	13	involving	involve	VERB
ejpam-4203	4	14	the	the	DET
ejpam-4203	4	15	product	product	NOUN
ejpam-4203	4	16	a	a	DET
ejpam-4203	4	17	general	general	ADJ
ejpam-4203	4	18	class	class	NOUN
ejpam-4203	4	19	of	of	ADP
ejpam-4203	4	20	logarithmic	logarithmic	ADJ
ejpam-4203	4	21	,	,	PUNCT
ejpam-4203	4	22	special	special	ADJ
ejpam-4203	4	23	and	and	CCONJ
ejpam-4203	4	24	exponential	exponential	ADJ
ejpam-4203	4	25	functions	function	NOUN
ejpam-4203	4	26	.	.	PUNCT
ejpam-4203	5	1	importance	importance	NOUN
ejpam-4203	5	2	of	of	ADP
ejpam-4203	5	3	our	our	PRON
ejpam-4203	5	4	results	result	NOUN
ejpam-4203	5	5	lies	lie	VERB
ejpam-4203	5	6	in	in	ADP
ejpam-4203	5	7	the	the	DET
ejpam-4203	5	8	fact	fact	NOUN
ejpam-4203	5	9	that	that	SCONJ
ejpam-4203	5	10	they	they	PRON
ejpam-4203	5	11	involve	involve	VERB
ejpam-4203	5	12	the	the	DET
ejpam-4203	5	13	bessel	bessel	ADJ
ejpam-4203	5	14	function	function	NOUN
ejpam-4203	5	15	of	of	ADP
ejpam-4203	5	16	the	the	DET
ejpam-4203	5	17	first	first	ADJ
ejpam-4203	5	18	kind	kind	NOUN
ejpam-4203	5	19	,	,	PUNCT
ejpam-4203	5	20	which	which	PRON
ejpam-4203	5	21	is	be	AUX
ejpam-4203	5	22	used	use	VERB
ejpam-4203	5	23	in	in	ADP
ejpam-4203	5	24	a	a	DET
ejpam-4203	5	25	wide	wide	ADJ
ejpam-4203	5	26	range	range	NOUN
ejpam-4203	5	27	of	of	ADP
ejpam-4203	5	28	areas	area	NOUN
ejpam-4203	5	29	spanning	span	VERB
ejpam-4203	5	30	science	science	NOUN
ejpam-4203	5	31	and	and	CCONJ
ejpam-4203	5	32	engineering	engineering	NOUN
ejpam-4203	5	33	.	.	PUNCT
ejpam-4203	6	1	further	far	ADV
ejpam-4203	6	2	we	we	PRON
ejpam-4203	6	3	establish	establish	VERB
ejpam-4203	6	4	some	some	DET
ejpam-4203	6	5	special	special	ADJ
ejpam-4203	6	6	cases	case	NOUN
ejpam-4203	6	7	.	.	PUNCT
ejpam-4203	7	1	2020	2020	NUM
ejpam-4203	7	2	mathematics	mathematic	NOUN
ejpam-4203	7	3	subject	subject	NOUN
ejpam-4203	7	4	classifications	classification	NOUN
ejpam-4203	7	5	:	:	PUNCT
ejpam-4203	7	6	30e20	30e20	NUM
ejpam-4203	7	7	,	,	PUNCT
ejpam-4203	7	8	33	33	NUM
ejpam-4203	7	9	-	-	SYM
ejpam-4203	7	10	01	01	NUM
ejpam-4203	7	11	,	,	PUNCT
ejpam-4203	7	12	33	33	NUM
ejpam-4203	7	13	-	-	SYM
ejpam-4203	7	14	03	03	NUM
ejpam-4203	7	15	,	,	PUNCT
ejpam-4203	7	16	33	33	NUM
ejpam-4203	7	17	-	-	PUNCT
ejpam-4203	7	18	04	04	NUM
ejpam-4203	7	19	,	,	PUNCT
ejpam-4203	7	20	33	33	NUM
ejpam-4203	7	21	-	-	PUNCT
ejpam-4203	7	22	33b	33b	NUM
ejpam-4203	7	23	key	key	ADJ
ejpam-4203	7	24	words	word	NOUN
ejpam-4203	7	25	and	and	CCONJ
ejpam-4203	7	26	phrases	phrase	NOUN
ejpam-4203	7	27	:	:	PUNCT
ejpam-4203	7	28	triple	triple	ADJ
ejpam-4203	7	29	integral	integral	ADJ
ejpam-4203	7	30	,	,	PUNCT
ejpam-4203	7	31	bessel	bessel	ADJ
ejpam-4203	7	32	function	function	NOUN
ejpam-4203	7	33	,	,	PUNCT
ejpam-4203	7	34	catalan	catalan	NOUN
ejpam-4203	7	35	’s	’s	PART
ejpam-4203	7	36	constant	constant	ADJ
ejpam-4203	7	37	,	,	PUNCT
ejpam-4203	7	38	apéry	apéry	PROPN
ejpam-4203	7	39	’s	’s	PART
ejpam-4203	7	40	constant	constant	ADJ
ejpam-4203	7	41	,	,	PUNCT
ejpam-4203	7	42	cauchy	cauchy	ADJ
ejpam-4203	7	43	integral	integral	ADJ
ejpam-4203	7	44	1	1	NUM
ejpam-4203	7	45	.	.	PUNCT
ejpam-4203	7	46	significance	significance	NOUN
ejpam-4203	7	47	statement	statement	NOUN
ejpam-4203	7	48	triple	triple	ADJ
ejpam-4203	7	49	integrals	integral	NOUN
ejpam-4203	7	50	whose	whose	DET
ejpam-4203	7	51	kernels	kernel	NOUN
ejpam-4203	7	52	feature	feature	VERB
ejpam-4203	7	53	special	special	ADJ
ejpam-4203	7	54	functions	function	NOUN
ejpam-4203	7	55	are	be	AUX
ejpam-4203	7	56	tabled	table	VERB
ejpam-4203	7	57	in	in	ADP
ejpam-4203	7	58	the	the	DET
ejpam-4203	7	59	book	book	NOUN
ejpam-4203	7	60	of	of	ADP
ejpam-4203	7	61	prudnikov	prudnikov	PROPN
ejpam-4203	7	62	et	et	PROPN
ejpam-4203	7	63	al	al	PROPN
ejpam-4203	7	64	.	.	PUNCT
ejpam-4203	8	1	[	[	X
ejpam-4203	8	2	9	9	NUM
ejpam-4203	8	3	]	]	PUNCT
ejpam-4203	8	4	,	,	PUNCT
ejpam-4203	8	5	in	in	ADP
ejpam-4203	8	6	evaluating	evaluate	VERB
ejpam-4203	8	7	euler	euler	NOUN
ejpam-4203	8	8	type	type	NOUN
ejpam-4203	8	9	integrals	integral	NOUN
ejpam-4203	8	10	involving	involve	VERB
ejpam-4203	8	11	a	a	DET
ejpam-4203	8	12	general	general	ADJ
ejpam-4203	8	13	class	class	NOUN
ejpam-4203	8	14	of	of	ADP
ejpam-4203	8	15	polynomials	polynomial	NOUN
ejpam-4203	8	16	,	,	PUNCT
ejpam-4203	8	17	special	special	ADJ
ejpam-4203	8	18	functions	function	NOUN
ejpam-4203	8	19	and	and	CCONJ
ejpam-4203	8	20	multivariable	multivariable	ADJ
ejpam-4203	8	21	a	a	DET
ejpam-4203	8	22	-	-	PUNCT
ejpam-4203	8	23	function	function	NOUN
ejpam-4203	8	24	[	[	X
ejpam-4203	8	25	4	4	NUM
ejpam-4203	8	26	]	]	PUNCT
ejpam-4203	8	27	,	,	PUNCT
ejpam-4203	8	28	in	in	ADP
ejpam-4203	8	29	the	the	DET
ejpam-4203	8	30	study	study	NOUN
ejpam-4203	8	31	of	of	ADP
ejpam-4203	8	32	celestial	celestial	ADJ
ejpam-4203	8	33	mechanics	mechanic	NOUN
ejpam-4203	8	34	or	or	CCONJ
ejpam-4203	8	35	hamiltonian	hamiltonian	ADJ
ejpam-4203	8	36	dynamics	dynamic	NOUN
ejpam-4203	8	37	,	,	PUNCT
ejpam-4203	8	38	as	as	SCONJ
ejpam-4203	8	39	applied	apply	VERB
ejpam-4203	8	40	to	to	ADP
ejpam-4203	8	41	the	the	DET
ejpam-4203	8	42	ellipsoidal	ellipsoidal	ADJ
ejpam-4203	8	43	components	component	NOUN
ejpam-4203	8	44	of	of	ADP
ejpam-4203	8	45	galaxies	galaxy	NOUN
ejpam-4203	8	46	[	[	X
ejpam-4203	8	47	1	1	NUM
ejpam-4203	8	48	]	]	PUNCT
ejpam-4203	8	49	,	,	PUNCT
ejpam-4203	8	50	in	in	ADP
ejpam-4203	8	51	the	the	DET
ejpam-4203	8	52	theory	theory	NOUN
ejpam-4203	8	53	of	of	ADP
ejpam-4203	8	54	eisentein	eisentein	ADJ
ejpam-4203	8	55	series	series	NOUN
ejpam-4203	8	56	for	for	ADP
ejpam-4203	8	57	the	the	DET
ejpam-4203	8	58	group	group	NOUN
ejpam-4203	8	59	sl(3,r	sl(3,r	ADJ
ejpam-4203	8	60	)	)	PUNCT
ejpam-4203	8	61	and	and	CCONJ
ejpam-4203	8	62	its	its	PRON
ejpam-4203	8	63	applications	application	NOUN
ejpam-4203	8	64	to	to	ADP
ejpam-4203	8	65	a	a	DET
ejpam-4203	8	66	binary	binary	ADJ
ejpam-4203	8	67	problem	problem	NOUN
ejpam-4203	8	68	,	,	PUNCT
ejpam-4203	8	69	and	and	CCONJ
ejpam-4203	8	70	in	in	ADP
ejpam-4203	8	71	the	the	DET
ejpam-4203	8	72	theory	theory	NOUN
ejpam-4203	8	73	of	of	ADP
ejpam-4203	8	74	automorphic	automorphic	ADJ
ejpam-4203	8	75	forms	form	NOUN
ejpam-4203	8	76	,	,	PUNCT
ejpam-4203	8	77	which	which	PRON
ejpam-4203	8	78	are	be	AUX
ejpam-4203	8	79	defined	define	VERB
ejpam-4203	8	80	arithmetically	arithmetically	ADV
ejpam-4203	8	81	on	on	ADP
ejpam-4203	8	82	any	any	DET
ejpam-4203	8	83	reductive	reductive	ADJ
ejpam-4203	8	84	lie	lie	NOUN
ejpam-4203	8	85	group	group	NOUN
ejpam-4203	8	86	,	,	PUNCT
ejpam-4203	8	87	which	which	PRON
ejpam-4203	8	88	have	have	AUX
ejpam-4203	8	89	been	be	AUX
ejpam-4203	8	90	studied	study	VERB
ejpam-4203	8	91	intensively	intensively	ADV
ejpam-4203	8	92	for	for	ADP
ejpam-4203	8	93	many	many	ADJ
ejpam-4203	8	94	years	year	NOUN
ejpam-4203	9	1	[	[	X
ejpam-4203	9	2	2	2	NUM
ejpam-4203	9	3	]	]	PUNCT
ejpam-4203	9	4	.	.	PUNCT
ejpam-4203	10	1	based	base	VERB
ejpam-4203	10	2	on	on	ADP
ejpam-4203	10	3	current	current	ADJ
ejpam-4203	10	4	literature	literature	NOUN
ejpam-4203	10	5	triple	triple	ADJ
ejpam-4203	10	6	integrals	integral	NOUN
ejpam-4203	10	7	of	of	ADP
ejpam-4203	10	8	special	special	ADJ
ejpam-4203	10	9	functions	function	NOUN
ejpam-4203	10	10	is	be	AUX
ejpam-4203	10	11	of	of	ADP
ejpam-4203	10	12	high	high	ADJ
ejpam-4203	10	13	importance	importance	NOUN
ejpam-4203	10	14	,	,	PUNCT
ejpam-4203	10	15	researched	research	VERB
ejpam-4203	10	16	and	and	CCONJ
ejpam-4203	10	17	used	use	VERB
ejpam-4203	10	18	widely	widely	ADV
ejpam-4203	10	19	.	.	PUNCT
ejpam-4203	11	1	one	one	NUM
ejpam-4203	11	2	feature	feature	NOUN
ejpam-4203	11	3	of	of	ADP
ejpam-4203	11	4	current	current	ADJ
ejpam-4203	11	5	work	work	NOUN
ejpam-4203	11	6	on	on	ADP
ejpam-4203	11	7	these	these	DET
ejpam-4203	11	8	integrals	integral	NOUN
ejpam-4203	11	9	which	which	PRON
ejpam-4203	11	10	is	be	AUX
ejpam-4203	11	11	not	not	PART
ejpam-4203	11	12	present	present	ADJ
ejpam-4203	11	13	is	be	AUX
ejpam-4203	11	14	a	a	DET
ejpam-4203	11	15	closed	closed	ADJ
ejpam-4203	11	16	form	form	NOUN
ejpam-4203	11	17	solution	solution	NOUN
ejpam-4203	11	18	where	where	SCONJ
ejpam-4203	11	19	possible	possible	ADJ
ejpam-4203	11	20	.	.	PUNCT
ejpam-4203	12	1	in	in	ADP
ejpam-4203	12	2	our	our	PRON
ejpam-4203	12	3	present	present	ADJ
ejpam-4203	12	4	work	work	NOUN
ejpam-4203	12	5	we	we	PRON
ejpam-4203	12	6	derive	derive	VERB
ejpam-4203	12	7	a	a	DET
ejpam-4203	12	8	triple	triple	ADJ
ejpam-4203	12	9	integral	integral	ADJ
ejpam-4203	12	10	whose	whose	DET
ejpam-4203	12	11	kernel	kernel	NOUN
ejpam-4203	12	12	involves	involve	VERB
ejpam-4203	12	13	the	the	DET
ejpam-4203	12	14	bessel	bessel	ADJ
ejpam-4203	12	15	function	function	NOUN
ejpam-4203	12	16	of	of	ADP
ejpam-4203	12	17	the	the	DET
ejpam-4203	12	18	first	first	ADJ
ejpam-4203	12	19	kind	kind	NOUN
ejpam-4203	12	20	jv(t	jv(t	NOUN
ejpam-4203	12	21	)	)	PUNCT
ejpam-4203	12	22	and	and	CCONJ
ejpam-4203	12	23	expressed	express	VERB
ejpam-4203	12	24	it	it	PRON
ejpam-4203	12	25	in	in	ADP
ejpam-4203	12	26	terms	term	NOUN
ejpam-4203	12	27	of	of	ADP
ejpam-4203	12	28	the	the	DET
ejpam-4203	12	29	hurwitz	hurwitz	PROPN
ejpam-4203	12	30	-	-	PUNCT
ejpam-4203	12	31	lerch	lerch	PROPN
ejpam-4203	12	32	zeta	zeta	PROPN
ejpam-4203	12	33	function	function	PROPN
ejpam-4203	12	34	.	.	PUNCT
ejpam-4203	13	1	the	the	DET
ejpam-4203	13	2	bessel	bessel	NOUN
ejpam-4203	13	3	function	function	VERB
ejpam-4203	13	4	itself	itself	PRON
ejpam-4203	13	5	is	be	AUX
ejpam-4203	13	6	a	a	DET
ejpam-4203	13	7	very	very	ADV
ejpam-4203	13	8	important	important	ADJ
ejpam-4203	13	9	function	function	NOUN
ejpam-4203	13	10	and	and	CCONJ
ejpam-4203	13	11	are	be	AUX
ejpam-4203	13	12	a	a	DET
ejpam-4203	13	13	set	set	NOUN
ejpam-4203	13	14	of	of	ADP
ejpam-4203	13	15	solutions	solution	NOUN
ejpam-4203	13	16	to	to	ADP
ejpam-4203	13	17	a	a	DET
ejpam-4203	13	18	second	second	ADJ
ejpam-4203	13	19	-	-	PUNCT
ejpam-4203	13	20	order	order	NOUN
ejpam-4203	13	21	differential	differential	ADJ
ejpam-4203	13	22	equation	equation	NOUN
ejpam-4203	13	23	that	that	PRON
ejpam-4203	13	24	can	can	AUX
ejpam-4203	13	25	appear	appear	VERB
ejpam-4203	13	26	in	in	ADP
ejpam-4203	13	27	a	a	DET
ejpam-4203	13	28	variety	variety	NOUN
ejpam-4203	13	29	of	of	ADP
ejpam-4203	13	30	contexts	context	NOUN
ejpam-4203	14	1	[	[	X
ejpam-4203	14	2	6	6	NUM
ejpam-4203	14	3	]	]	PUNCT
ejpam-4203	14	4	.	.	PUNCT
ejpam-4203	15	1	∗corresponding	∗corresponde	VERB
ejpam-4203	15	2	author	author	NOUN
ejpam-4203	15	3	.	.	PUNCT
ejpam-4203	16	1	doi	doi	NOUN
ejpam-4203	16	2	:	:	PUNCT
ejpam-4203	16	3	https://doi.org/10.29020/nybg.ejpam.v15i2.4203	https://doi.org/10.29020/nybg.ejpam.v15i2.4203	X
ejpam-4203	16	4	email	email	NOUN
ejpam-4203	16	5	addresses	address	NOUN
ejpam-4203	16	6	:	:	PUNCT
ejpam-4203	17	1	milver@my.yorku.ca	milver@my.yorku.ca	NOUN
ejpam-4203	17	2	(	(	PUNCT
ejpam-4203	17	3	r.	r.	PROPN
ejpam-4203	17	4	reynolds	reynolds	PROPN
ejpam-4203	17	5	)	)	PUNCT
ejpam-4203	17	6	,	,	PUNCT
ejpam-4203	17	7	stauffer@yorku.ca	stauffer@yorku.ca	NOUN
ejpam-4203	17	8	(	(	PUNCT
ejpam-4203	17	9	a.	a.	NOUN
ejpam-4203	17	10	stauffer	stauffer	PROPN
ejpam-4203	17	11	)	)	PUNCT
ejpam-4203	17	12	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4203	18	1	390	390	NUM
ejpam-4203	19	1	©	©	PROPN
ejpam-4203	19	2	2022	2022	NUM
ejpam-4203	19	3	ejpam	ejpam	VERB
ejpam-4203	19	4	all	all	DET
ejpam-4203	19	5	rights	right	NOUN
ejpam-4203	19	6	reserved	reserve	VERB
ejpam-4203	19	7	.	.	PUNCT
ejpam-4203	20	1	r.	r.	PROPN
ejpam-4203	20	2	reynolds	reynolds	PROPN
ejpam-4203	20	3	,	,	PUNCT
ejpam-4203	20	4	a.	a.	PROPN
ejpam-4203	20	5	stauffer	stauffer	PROPN
ejpam-4203	20	6	/	/	SYM
ejpam-4203	20	7	eur	eur	PROPN
ejpam-4203	20	8	.	.	PUNCT
ejpam-4203	21	1	j.	j.	PROPN
ejpam-4203	21	2	pure	pure	PROPN
ejpam-4203	21	3	appl	appl	PROPN
ejpam-4203	21	4	.	.	PROPN
ejpam-4203	21	5	math	math	PROPN
ejpam-4203	21	6	,	,	PUNCT
ejpam-4203	21	7	15	15	NUM
ejpam-4203	21	8	(	(	PUNCT
ejpam-4203	21	9	2	2	NUM
ejpam-4203	21	10	)	)	PUNCT
ejpam-4203	21	11	(	(	PUNCT
ejpam-4203	21	12	2022	2022	NUM
ejpam-4203	21	13	)	)	PUNCT
ejpam-4203	21	14	,	,	PUNCT
ejpam-4203	21	15	390	390	NUM
ejpam-4203	21	16	-	-	SYM
ejpam-4203	21	17	396	396	NUM
ejpam-4203	21	18	391	391	NUM
ejpam-4203	21	19	2	2	NUM
ejpam-4203	21	20	.	.	PUNCT
ejpam-4203	21	21	introduction	introduction	NOUN
ejpam-4203	21	22	in	in	ADP
ejpam-4203	21	23	this	this	DET
ejpam-4203	21	24	paper	paper	NOUN
ejpam-4203	21	25	we	we	PRON
ejpam-4203	21	26	derive	derive	VERB
ejpam-4203	21	27	the	the	DET
ejpam-4203	21	28	triple	triple	ADJ
ejpam-4203	21	29	definite	definite	ADJ
ejpam-4203	21	30	integral	integral	ADJ
ejpam-4203	21	31	given	give	VERB
ejpam-4203	21	32	by	by	ADP
ejpam-4203	21	33	(	(	PUNCT
ejpam-4203	21	34	1	1	NUM
ejpam-4203	21	35	)	)	PUNCT
ejpam-4203	21	36	∫	∫	PROPN
ejpam-4203	22	1	∞	∞	PROPN
ejpam-4203	22	2	0	0	NUM
ejpam-4203	23	1	∫	∫	PROPN
ejpam-4203	23	2	∞	∞	PROPN
ejpam-4203	23	3	0	0	NUM
ejpam-4203	23	4	∫	∫	PROPN
ejpam-4203	23	5	∞	∞	PROPN
ejpam-4203	23	6	0	0	NUM
ejpam-4203	24	1	tmxv−my	tmxv−my	NOUN
ejpam-4203	24	2	1	1	NUM
ejpam-4203	24	3	2	2	NUM
ejpam-4203	24	4	(	(	PUNCT
ejpam-4203	24	5	−m−v−1)jv(t)e	−m−v−1)jv(t)e	PROPN
ejpam-4203	24	6	−bx2−cy	−bx2−cy	X
ejpam-4203	24	7	logk	logk	NOUN
ejpam-4203	24	8	(	(	PUNCT
ejpam-4203	24	9	at	at	ADP
ejpam-4203	24	10	x	x	SYM
ejpam-4203	24	11	√	√	PROPN
ejpam-4203	24	12	y	y	PROPN
ejpam-4203	24	13	)	)	PUNCT
ejpam-4203	24	14	dxdydt	dxdydt	NOUN
ejpam-4203	24	15	where	where	SCONJ
ejpam-4203	24	16	the	the	DET
ejpam-4203	24	17	parameters	parameter	NOUN
ejpam-4203	24	18	k	k	PROPN
ejpam-4203	24	19	,	,	PUNCT
ejpam-4203	24	20	a	a	PRON
ejpam-4203	24	21	,	,	PUNCT
ejpam-4203	24	22	b	b	NOUN
ejpam-4203	24	23	,	,	PUNCT
ejpam-4203	24	24	c	c	NOUN
ejpam-4203	24	25	,	,	PUNCT
ejpam-4203	24	26	v	v	NOUN
ejpam-4203	24	27	,	,	PUNCT
ejpam-4203	24	28	m	m	VERB
ejpam-4203	24	29	are	be	AUX
ejpam-4203	24	30	general	general	ADJ
ejpam-4203	24	31	complex	complex	ADJ
ejpam-4203	24	32	numbers	number	NOUN
ejpam-4203	24	33	and	and	CCONJ
ejpam-4203	24	34	re(b	re(b	X
ejpam-4203	24	35	)	)	PUNCT
ejpam-4203	24	36	>	>	X
ejpam-4203	24	37	0	0	NUM
ejpam-4203	24	38	,	,	PUNCT
ejpam-4203	24	39	re(c	re(c	NUM
ejpam-4203	24	40	)	)	PUNCT
ejpam-4203	24	41	>	>	X
ejpam-4203	24	42	0	0	NUM
ejpam-4203	24	43	,	,	PUNCT
ejpam-4203	24	44	re(v	re(v	NOUN
ejpam-4203	24	45	)	)	PUNCT
ejpam-4203	24	46	>	>	X
ejpam-4203	24	47	0	0	NUM
ejpam-4203	24	48	,	,	PUNCT
ejpam-4203	24	49	re(m	re(m	NUM
ejpam-4203	24	50	)	)	PUNCT
ejpam-4203	24	51	<	<	X
ejpam-4203	24	52	−1	−1	NOUN
ejpam-4203	24	53	.	.	PUNCT
ejpam-4203	25	1	this	this	DET
ejpam-4203	25	2	definite	definite	ADJ
ejpam-4203	25	3	integral	integral	ADJ
ejpam-4203	25	4	will	will	AUX
ejpam-4203	25	5	be	be	AUX
ejpam-4203	25	6	used	use	VERB
ejpam-4203	25	7	to	to	PART
ejpam-4203	25	8	derive	derive	VERB
ejpam-4203	25	9	special	special	ADJ
ejpam-4203	25	10	cases	case	NOUN
ejpam-4203	25	11	in	in	ADP
ejpam-4203	25	12	terms	term	NOUN
ejpam-4203	25	13	of	of	ADP
ejpam-4203	25	14	special	special	ADJ
ejpam-4203	25	15	functions	function	NOUN
ejpam-4203	25	16	and	and	CCONJ
ejpam-4203	25	17	fundamental	fundamental	ADJ
ejpam-4203	25	18	constants	constant	NOUN
ejpam-4203	25	19	.	.	PUNCT
ejpam-4203	26	1	the	the	DET
ejpam-4203	26	2	derivations	derivation	NOUN
ejpam-4203	26	3	follow	follow	VERB
ejpam-4203	26	4	the	the	DET
ejpam-4203	26	5	method	method	NOUN
ejpam-4203	26	6	used	use	VERB
ejpam-4203	26	7	by	by	ADP
ejpam-4203	26	8	us	we	PRON
ejpam-4203	26	9	in	in	ADP
ejpam-4203	26	10	[	[	X
ejpam-4203	26	11	10	10	NUM
ejpam-4203	26	12	]	]	PUNCT
ejpam-4203	26	13	.	.	PUNCT
ejpam-4203	27	1	this	this	DET
ejpam-4203	27	2	method	method	NOUN
ejpam-4203	27	3	involves	involve	VERB
ejpam-4203	27	4	using	use	VERB
ejpam-4203	27	5	a	a	DET
ejpam-4203	27	6	form	form	NOUN
ejpam-4203	27	7	of	of	ADP
ejpam-4203	27	8	the	the	DET
ejpam-4203	27	9	generalized	generalize	VERB
ejpam-4203	27	10	cauchy	cauchy	PROPN
ejpam-4203	27	11	’s	’s	PART
ejpam-4203	27	12	integral	integral	ADJ
ejpam-4203	27	13	formula	formula	NOUN
ejpam-4203	27	14	given	give	VERB
ejpam-4203	27	15	by	by	ADP
ejpam-4203	27	16	yk	yk	PROPN
ejpam-4203	27	17	γ(k	γ(k	PROPN
ejpam-4203	27	18	+	+	CCONJ
ejpam-4203	27	19	1	1	X
ejpam-4203	27	20	)	)	PUNCT
ejpam-4203	27	21	=	=	SYM
ejpam-4203	27	22	1	1	NUM
ejpam-4203	27	23	2πi	2πi	ADJ
ejpam-4203	27	24	∫	∫	PROPN
ejpam-4203	27	25	c	c	PROPN
ejpam-4203	27	26	ewy	ewy	PROPN
ejpam-4203	27	27	wk+1	wk+1	PROPN
ejpam-4203	27	28	dw	dw	PROPN
ejpam-4203	27	29	.	.	PUNCT
ejpam-4203	28	1	(	(	PUNCT
ejpam-4203	28	2	2	2	X
ejpam-4203	28	3	)	)	PUNCT
ejpam-4203	28	4	where	where	SCONJ
ejpam-4203	28	5	c	c	NOUN
ejpam-4203	28	6	is	be	AUX
ejpam-4203	28	7	in	in	ADP
ejpam-4203	28	8	general	general	ADJ
ejpam-4203	28	9	an	an	DET
ejpam-4203	28	10	open	open	ADJ
ejpam-4203	28	11	contour	contour	NOUN
ejpam-4203	28	12	in	in	ADP
ejpam-4203	28	13	the	the	DET
ejpam-4203	28	14	complex	complex	ADJ
ejpam-4203	28	15	plane	plane	NOUN
ejpam-4203	28	16	where	where	SCONJ
ejpam-4203	28	17	the	the	DET
ejpam-4203	28	18	bilinear	bilinear	NOUN
ejpam-4203	28	19	concomitant	concomitant	NOUN
ejpam-4203	28	20	has	have	VERB
ejpam-4203	28	21	the	the	DET
ejpam-4203	28	22	same	same	ADJ
ejpam-4203	28	23	value	value	NOUN
ejpam-4203	28	24	at	at	ADP
ejpam-4203	28	25	the	the	DET
ejpam-4203	28	26	end	end	NOUN
ejpam-4203	28	27	points	point	NOUN
ejpam-4203	28	28	of	of	ADP
ejpam-4203	28	29	the	the	DET
ejpam-4203	28	30	contour	contour	NOUN
ejpam-4203	28	31	.	.	PUNCT
ejpam-4203	29	1	we	we	PRON
ejpam-4203	29	2	then	then	ADV
ejpam-4203	29	3	multiply	multiply	VERB
ejpam-4203	29	4	both	both	DET
ejpam-4203	29	5	sides	side	NOUN
ejpam-4203	29	6	by	by	ADP
ejpam-4203	29	7	a	a	DET
ejpam-4203	29	8	function	function	NOUN
ejpam-4203	29	9	of	of	ADP
ejpam-4203	29	10	x	x	PROPN
ejpam-4203	29	11	,	,	PUNCT
ejpam-4203	29	12	y	y	PROPN
ejpam-4203	29	13	and	and	CCONJ
ejpam-4203	29	14	t	t	PROPN
ejpam-4203	29	15	,	,	PUNCT
ejpam-4203	29	16	then	then	ADV
ejpam-4203	29	17	take	take	VERB
ejpam-4203	29	18	a	a	DET
ejpam-4203	29	19	definite	definite	ADJ
ejpam-4203	29	20	triple	triple	ADJ
ejpam-4203	29	21	integral	integral	ADJ
ejpam-4203	29	22	of	of	ADP
ejpam-4203	29	23	both	both	DET
ejpam-4203	29	24	sides	side	NOUN
ejpam-4203	29	25	.	.	PUNCT
ejpam-4203	30	1	this	this	PRON
ejpam-4203	30	2	yields	yield	VERB
ejpam-4203	30	3	a	a	DET
ejpam-4203	30	4	definite	definite	ADJ
ejpam-4203	30	5	integral	integral	ADJ
ejpam-4203	30	6	in	in	ADP
ejpam-4203	30	7	terms	term	NOUN
ejpam-4203	30	8	of	of	ADP
ejpam-4203	30	9	a	a	DET
ejpam-4203	30	10	contour	contour	NOUN
ejpam-4203	30	11	integral	integral	NOUN
ejpam-4203	30	12	.	.	PUNCT
ejpam-4203	31	1	then	then	ADV
ejpam-4203	31	2	we	we	PRON
ejpam-4203	31	3	multiply	multiply	VERB
ejpam-4203	31	4	both	both	DET
ejpam-4203	31	5	sides	side	NOUN
ejpam-4203	31	6	of	of	ADP
ejpam-4203	31	7	equation	equation	NOUN
ejpam-4203	31	8	(	(	PUNCT
ejpam-4203	31	9	2	2	NUM
ejpam-4203	31	10	)	)	PUNCT
ejpam-4203	31	11	by	by	ADP
ejpam-4203	31	12	another	another	DET
ejpam-4203	31	13	function	function	NOUN
ejpam-4203	31	14	of	of	ADP
ejpam-4203	31	15	y	y	PRON
ejpam-4203	31	16	take	take	VERB
ejpam-4203	31	17	the	the	DET
ejpam-4203	31	18	infinite	infinite	ADJ
ejpam-4203	31	19	sum	sum	NOUN
ejpam-4203	31	20	of	of	ADP
ejpam-4203	31	21	both	both	DET
ejpam-4203	31	22	sides	side	NOUN
ejpam-4203	31	23	such	such	ADJ
ejpam-4203	31	24	that	that	SCONJ
ejpam-4203	31	25	the	the	DET
ejpam-4203	31	26	contour	contour	NOUN
ejpam-4203	31	27	integral	integral	NOUN
ejpam-4203	31	28	of	of	ADP
ejpam-4203	31	29	both	both	DET
ejpam-4203	31	30	equations	equation	NOUN
ejpam-4203	31	31	are	be	AUX
ejpam-4203	31	32	the	the	DET
ejpam-4203	31	33	same	same	ADJ
ejpam-4203	31	34	.	.	PUNCT
ejpam-4203	32	1	3	3	X
ejpam-4203	32	2	.	.	X
ejpam-4203	32	3	definite	definite	ADJ
ejpam-4203	32	4	integral	integral	ADJ
ejpam-4203	32	5	of	of	ADP
ejpam-4203	32	6	the	the	DET
ejpam-4203	32	7	contour	contour	NOUN
ejpam-4203	32	8	integral	integral	NOUN
ejpam-4203	32	9	we	we	PRON
ejpam-4203	32	10	use	use	VERB
ejpam-4203	32	11	the	the	DET
ejpam-4203	32	12	method	method	NOUN
ejpam-4203	32	13	in	in	ADP
ejpam-4203	32	14	[	[	X
ejpam-4203	32	15	10	10	NUM
ejpam-4203	32	16	]	]	PUNCT
ejpam-4203	32	17	.	.	PUNCT
ejpam-4203	33	1	the	the	DET
ejpam-4203	33	2	variable	variable	NOUN
ejpam-4203	33	3	of	of	ADP
ejpam-4203	33	4	integration	integration	NOUN
ejpam-4203	33	5	in	in	ADP
ejpam-4203	33	6	the	the	DET
ejpam-4203	33	7	contour	contour	NOUN
ejpam-4203	33	8	integral	integral	NOUN
ejpam-4203	33	9	is	be	AUX
ejpam-4203	33	10	s	s	NOUN
ejpam-4203	33	11	=	=	NOUN
ejpam-4203	33	12	w+m+v	w+m+v	NOUN
ejpam-4203	33	13	.	.	PUNCT
ejpam-4203	34	1	the	the	DET
ejpam-4203	34	2	cut	cut	NOUN
ejpam-4203	34	3	and	and	CCONJ
ejpam-4203	34	4	contour	contour	NOUN
ejpam-4203	34	5	are	be	AUX
ejpam-4203	34	6	in	in	ADP
ejpam-4203	34	7	the	the	DET
ejpam-4203	34	8	first	first	ADJ
ejpam-4203	34	9	or	or	CCONJ
ejpam-4203	34	10	second	second	ADJ
ejpam-4203	34	11	quadrant	quadrant	NOUN
ejpam-4203	34	12	of	of	ADP
ejpam-4203	34	13	the	the	DET
ejpam-4203	34	14	complex	complex	ADJ
ejpam-4203	34	15	s	s	NOUN
ejpam-4203	34	16	-	-	NOUN
ejpam-4203	34	17	plane	plane	NOUN
ejpam-4203	34	18	depending	depend	VERB
ejpam-4203	34	19	on	on	ADP
ejpam-4203	34	20	the	the	DET
ejpam-4203	34	21	sign	sign	NOUN
ejpam-4203	34	22	of	of	ADP
ejpam-4203	34	23	s.	s.	PROPN
ejpam-4203	34	24	the	the	DET
ejpam-4203	34	25	cut	cut	NOUN
ejpam-4203	34	26	approaches	approach	VERB
ejpam-4203	34	27	the	the	DET
ejpam-4203	34	28	origin	origin	NOUN
ejpam-4203	34	29	from	from	ADP
ejpam-4203	34	30	the	the	DET
ejpam-4203	34	31	interior	interior	NOUN
ejpam-4203	34	32	of	of	ADP
ejpam-4203	34	33	the	the	DET
ejpam-4203	34	34	first	first	ADJ
ejpam-4203	34	35	or	or	CCONJ
ejpam-4203	34	36	second	second	ADJ
ejpam-4203	34	37	quadrant	quadrant	NOUN
ejpam-4203	34	38	and	and	CCONJ
ejpam-4203	34	39	the	the	DET
ejpam-4203	34	40	contour	contour	NOUN
ejpam-4203	34	41	goes	go	VERB
ejpam-4203	34	42	round	round	ADP
ejpam-4203	34	43	the	the	DET
ejpam-4203	34	44	origin	origin	NOUN
ejpam-4203	34	45	with	with	ADP
ejpam-4203	34	46	zero	zero	NUM
ejpam-4203	34	47	radius	radius	NOUN
ejpam-4203	34	48	and	and	CCONJ
ejpam-4203	34	49	is	be	AUX
ejpam-4203	34	50	on	on	ADP
ejpam-4203	34	51	opposite	opposite	ADJ
ejpam-4203	34	52	sides	side	NOUN
ejpam-4203	34	53	of	of	ADP
ejpam-4203	34	54	the	the	DET
ejpam-4203	34	55	cut	cut	NOUN
ejpam-4203	34	56	.	.	PUNCT
ejpam-4203	35	1	using	use	VERB
ejpam-4203	35	2	a	a	DET
ejpam-4203	35	3	generalization	generalization	NOUN
ejpam-4203	35	4	of	of	ADP
ejpam-4203	35	5	cauchy	cauchy	PROPN
ejpam-4203	35	6	’s	’s	PART
ejpam-4203	35	7	integral	integral	ADJ
ejpam-4203	35	8	formula	formula	NOUN
ejpam-4203	35	9	we	we	PRON
ejpam-4203	35	10	form	form	VERB
ejpam-4203	35	11	the	the	DET
ejpam-4203	35	12	triple	triple	ADJ
ejpam-4203	35	13	integral	integral	ADJ
ejpam-4203	35	14	by	by	ADP
ejpam-4203	35	15	replacing	replace	VERB
ejpam-4203	35	16	y	y	PRON
ejpam-4203	35	17	by	by	ADP
ejpam-4203	35	18	log	log	NOUN
ejpam-4203	35	19	(	(	PUNCT
ejpam-4203	35	20	at	at	ADP
ejpam-4203	35	21	x	x	SYM
ejpam-4203	35	22	√	√	PROPN
ejpam-4203	35	23	y	y	PROPN
ejpam-4203	35	24	)	)	PUNCT
ejpam-4203	35	25	and	and	CCONJ
ejpam-4203	35	26	multiplying	multiply	VERB
ejpam-4203	35	27	by	by	ADP
ejpam-4203	35	28	tmxv−my	tmxv−my	NOUN
ejpam-4203	35	29	1	1	NUM
ejpam-4203	35	30	2	2	NUM
ejpam-4203	35	31	(	(	PUNCT
ejpam-4203	35	32	−m−v−1)jv(t)e	−m−v−1)jv(t)e	X
ejpam-4203	35	33	−bx2−cy	−bx2−cy	X
ejpam-4203	35	34	then	then	ADV
ejpam-4203	35	35	taking	take	VERB
ejpam-4203	35	36	the	the	DET
ejpam-4203	35	37	definite	definite	ADJ
ejpam-4203	35	38	triple	triple	ADJ
ejpam-4203	35	39	integral	integral	ADJ
ejpam-4203	35	40	with	with	ADP
ejpam-4203	35	41	respect	respect	NOUN
ejpam-4203	35	42	to	to	ADP
ejpam-4203	35	43	x	x	PUNCT
ejpam-4203	35	44	∈	∈	PROPN
ejpam-4203	35	45	[	[	X
ejpam-4203	35	46	0,∞	0,∞	NOUN
ejpam-4203	35	47	)	)	PUNCT
ejpam-4203	35	48	and	and	CCONJ
ejpam-4203	35	49	y	y	PROPN
ejpam-4203	35	50	∈	∈	PROPN
ejpam-4203	36	1	[	[	X
ejpam-4203	36	2	0,∞	0,∞	NOUN
ejpam-4203	36	3	)	)	PUNCT
ejpam-4203	36	4	and	and	CCONJ
ejpam-4203	36	5	r.	r.	PROPN
ejpam-4203	36	6	reynolds	reynolds	PROPN
ejpam-4203	36	7	,	,	PUNCT
ejpam-4203	36	8	a.	a.	PROPN
ejpam-4203	36	9	stauffer	stauffer	PROPN
ejpam-4203	36	10	/	/	SYM
ejpam-4203	36	11	eur	eur	PROPN
ejpam-4203	36	12	.	.	PUNCT
ejpam-4203	37	1	j.	j.	PROPN
ejpam-4203	37	2	pure	pure	PROPN
ejpam-4203	37	3	appl	appl	PROPN
ejpam-4203	37	4	.	.	PROPN
ejpam-4203	37	5	math	math	PROPN
ejpam-4203	37	6	,	,	PUNCT
ejpam-4203	37	7	15	15	NUM
ejpam-4203	37	8	(	(	PUNCT
ejpam-4203	37	9	2	2	NUM
ejpam-4203	37	10	)	)	PUNCT
ejpam-4203	37	11	(	(	PUNCT
ejpam-4203	37	12	2022	2022	NUM
ejpam-4203	37	13	)	)	PUNCT
ejpam-4203	37	14	,	,	PUNCT
ejpam-4203	37	15	390	390	NUM
ejpam-4203	37	16	-	-	SYM
ejpam-4203	37	17	396	396	NUM
ejpam-4203	37	18	392	392	NUM
ejpam-4203	37	19	t	t	NOUN
ejpam-4203	37	20	∈	∈	PROPN
ejpam-4203	38	1	[	[	X
ejpam-4203	38	2	0,∞	0,∞	NOUN
ejpam-4203	38	3	)	)	PUNCT
ejpam-4203	38	4	to	to	PART
ejpam-4203	38	5	obtain	obtain	VERB
ejpam-4203	38	6	(	(	PUNCT
ejpam-4203	38	7	3	3	NUM
ejpam-4203	38	8	)	)	SYM
ejpam-4203	38	9	1	1	NUM
ejpam-4203	39	1	γ(k	γ(k	NOUN
ejpam-4203	39	2	+	+	CCONJ
ejpam-4203	39	3	1	1	X
ejpam-4203	39	4	)	)	PUNCT
ejpam-4203	39	5	∫	∫	PROPN
ejpam-4203	40	1	∞	∞	PROPN
ejpam-4203	40	2	0	0	NUM
ejpam-4203	41	1	∫	∫	PROPN
ejpam-4203	41	2	∞	∞	PROPN
ejpam-4203	41	3	0	0	NUM
ejpam-4203	41	4	∫	∫	PROPN
ejpam-4203	41	5	∞	∞	PROPN
ejpam-4203	41	6	0	0	NUM
ejpam-4203	42	1	tmxv−my	tmxv−my	NOUN
ejpam-4203	42	2	1	1	NUM
ejpam-4203	42	3	2	2	NUM
ejpam-4203	42	4	(	(	PUNCT
ejpam-4203	42	5	−m−v−1)jv(t)e	−m−v−1)jv(t)e	PROPN
ejpam-4203	42	6	−bx2−cy	−bx2−cy	X
ejpam-4203	42	7	logk	logk	NOUN
ejpam-4203	42	8	(	(	PUNCT
ejpam-4203	42	9	at	at	ADP
ejpam-4203	42	10	x	x	SYM
ejpam-4203	42	11	√	√	PROPN
ejpam-4203	42	12	y	y	PROPN
ejpam-4203	42	13	)	)	PUNCT
ejpam-4203	42	14	dxdydt	dxdydt	NOUN
ejpam-4203	42	15	=	=	SYM
ejpam-4203	42	16	1	1	NUM
ejpam-4203	42	17	2πi	2πi	NOUN
ejpam-4203	42	18	∫	∫	PROPN
ejpam-4203	42	19	∞	∞	PROPN
ejpam-4203	42	20	0	0	NUM
ejpam-4203	42	21	∫	∫	PROPN
ejpam-4203	42	22	∞	∞	PROPN
ejpam-4203	42	23	0	0	NUM
ejpam-4203	42	24	∫	∫	PROPN
ejpam-4203	42	25	∞	∞	PROPN
ejpam-4203	42	26	0	0	NUM
ejpam-4203	43	1	∫	∫	PROPN
ejpam-4203	43	2	c	c	PROPN
ejpam-4203	43	3	aww−k−1tm+wjv(t)e	aww−k−1tm+wjv(t)e	PROPN
ejpam-4203	43	4	−bx2−cyx−m+v−w	−bx2−cyx−m+v−w	NOUN
ejpam-4203	43	5	y	y	PROPN
ejpam-4203	43	6	1	1	NUM
ejpam-4203	43	7	2	2	NUM
ejpam-4203	43	8	(	(	PUNCT
ejpam-4203	43	9	−m−v−w−1)dwdxdydt	−m−v−w−1)dwdxdydt	NOUN
ejpam-4203	43	10	=	=	SYM
ejpam-4203	43	11	1	1	NUM
ejpam-4203	43	12	2πi	2πi	NOUN
ejpam-4203	43	13	∫	∫	PROPN
ejpam-4203	44	1	c	c	PROPN
ejpam-4203	44	2	∫	∫	PROPN
ejpam-4203	45	1	∞	∞	NUM
ejpam-4203	45	2	0	0	NUM
ejpam-4203	46	1	∫	∫	PROPN
ejpam-4203	46	2	∞	∞	PROPN
ejpam-4203	46	3	0	0	NUM
ejpam-4203	47	1	∫	∫	PROPN
ejpam-4203	47	2	∞	∞	PROPN
ejpam-4203	47	3	0	0	PUNCT
ejpam-4203	48	1	aww−k−1tm+wjv(t)e	aww−k−1tm+wjv(t)e	ADP
ejpam-4203	48	2	−bx2−cyx−m+v−w	−bx2−cyx−m+v−w	NOUN
ejpam-4203	48	3	y	y	PROPN
ejpam-4203	48	4	1	1	NUM
ejpam-4203	48	5	2	2	NUM
ejpam-4203	48	6	(	(	PUNCT
ejpam-4203	48	7	−m−v−w−1)dxdydtdw	−m−v−w−1)dxdydtdw	NOUN
ejpam-4203	48	8	=	=	SYM
ejpam-4203	49	1	1	1	NUM
ejpam-4203	49	2	2πi	2πi	NOUN
ejpam-4203	49	3	∫	∫	PROPN
ejpam-4203	50	1	c	c	PROPN
ejpam-4203	51	1	πaww−k−12m+w−1b	πaww−k−12m+w−1b	PROPN
ejpam-4203	51	2	1	1	NUM
ejpam-4203	51	3	2	2	NUM
ejpam-4203	51	4	(	(	PUNCT
ejpam-4203	51	5	m−v+w−1)c	m−v+w−1)c	NOUN
ejpam-4203	51	6	1	1	NUM
ejpam-4203	51	7	2	2	NUM
ejpam-4203	51	8	(	(	PUNCT
ejpam-4203	51	9	m+v+w−1	m+v+w−1	NOUN
ejpam-4203	51	10	)	)	PUNCT
ejpam-4203	51	11	sec	sec	PROPN
ejpam-4203	51	12	(	(	PUNCT
ejpam-4203	51	13	1	1	NUM
ejpam-4203	51	14	2	2	NUM
ejpam-4203	51	15	π(m+	π(m+	X
ejpam-4203	51	16	v	v	ADP
ejpam-4203	51	17	+	+	CCONJ
ejpam-4203	51	18	w	w	NOUN
ejpam-4203	51	19	)	)	PUNCT
ejpam-4203	51	20	)	)	PUNCT
ejpam-4203	51	21	dw	dw	NOUN
ejpam-4203	51	22	from	from	ADP
ejpam-4203	51	23	equation	equation	NOUN
ejpam-4203	51	24	(	(	PUNCT
ejpam-4203	51	25	10.22.43	10.22.43	NUM
ejpam-4203	51	26	)	)	PUNCT
ejpam-4203	51	27	in	in	ADP
ejpam-4203	51	28	[	[	X
ejpam-4203	51	29	3	3	NUM
ejpam-4203	51	30	]	]	PUNCT
ejpam-4203	51	31	and	and	CCONJ
ejpam-4203	51	32	(	(	PUNCT
ejpam-4203	51	33	3.326.2	3.326.2	NOUN
ejpam-4203	51	34	)	)	PUNCT
ejpam-4203	51	35	in	in	ADP
ejpam-4203	51	36	[	[	X
ejpam-4203	51	37	5	5	NUM
ejpam-4203	51	38	]	]	PUNCT
ejpam-4203	51	39	where	where	SCONJ
ejpam-4203	51	40	re(w+m+v	re(w+m+v	PROPN
ejpam-4203	51	41	)	)	PUNCT
ejpam-4203	51	42	>	>	PUNCT
ejpam-4203	52	1	−1	−1	NOUN
ejpam-4203	52	2	,	,	PUNCT
ejpam-4203	52	3	re(w+m	re(w+m	PROPN
ejpam-4203	52	4	)	)	PUNCT
ejpam-4203	52	5	<	<	X
ejpam-4203	52	6	−1/2	−1/2	VERB
ejpam-4203	52	7	and	and	CCONJ
ejpam-4203	52	8	using	use	VERB
ejpam-4203	52	9	the	the	DET
ejpam-4203	52	10	reflection	reflection	NOUN
ejpam-4203	52	11	formula	formula	NOUN
ejpam-4203	52	12	(	(	PUNCT
ejpam-4203	52	13	8.334.3	8.334.3	NUM
ejpam-4203	52	14	)	)	PUNCT
ejpam-4203	52	15	in	in	ADP
ejpam-4203	52	16	[	[	X
ejpam-4203	52	17	5	5	NUM
ejpam-4203	52	18	]	]	PUNCT
ejpam-4203	52	19	for	for	ADP
ejpam-4203	52	20	the	the	DET
ejpam-4203	52	21	gamma	gamma	PROPN
ejpam-4203	52	22	function	function	NOUN
ejpam-4203	52	23	.	.	PUNCT
ejpam-4203	53	1	we	we	PRON
ejpam-4203	53	2	are	be	AUX
ejpam-4203	53	3	able	able	ADJ
ejpam-4203	53	4	to	to	PART
ejpam-4203	53	5	switch	switch	VERB
ejpam-4203	53	6	the	the	DET
ejpam-4203	53	7	order	order	NOUN
ejpam-4203	53	8	of	of	ADP
ejpam-4203	53	9	integration	integration	NOUN
ejpam-4203	53	10	over	over	ADP
ejpam-4203	53	11	w	w	PROPN
ejpam-4203	53	12	,	,	PUNCT
ejpam-4203	53	13	x	x	NOUN
ejpam-4203	53	14	,	,	PUNCT
ejpam-4203	53	15	y	y	PROPN
ejpam-4203	53	16	and	and	CCONJ
ejpam-4203	53	17	t	t	PROPN
ejpam-4203	53	18	using	use	VERB
ejpam-4203	53	19	fubini	fubini	NOUN
ejpam-4203	53	20	’s	’s	PART
ejpam-4203	53	21	theorem	theorem	NOUN
ejpam-4203	53	22	since	since	SCONJ
ejpam-4203	53	23	the	the	DET
ejpam-4203	53	24	integrand	integrand	NOUN
ejpam-4203	53	25	is	be	AUX
ejpam-4203	53	26	of	of	ADP
ejpam-4203	53	27	bounded	bounded	ADJ
ejpam-4203	53	28	measure	measure	NOUN
ejpam-4203	53	29	over	over	ADP
ejpam-4203	53	30	the	the	DET
ejpam-4203	53	31	space	space	NOUN
ejpam-4203	53	32	c×	c×	NOUN
ejpam-4203	54	1	[	[	X
ejpam-4203	54	2	0,∞)×	0,∞)×	NUM
ejpam-4203	54	3	[	[	X
ejpam-4203	54	4	0,∞)×	0,∞)×	NUM
ejpam-4203	54	5	[	[	X
ejpam-4203	54	6	0,∞	0,∞	NUM
ejpam-4203	54	7	)	)	PUNCT
ejpam-4203	54	8	4	4	NUM
ejpam-4203	54	9	.	.	PUNCT
ejpam-4203	55	1	the	the	DET
ejpam-4203	55	2	hurwitz	hurwitz	PROPN
ejpam-4203	55	3	-	-	PUNCT
ejpam-4203	55	4	lerch	lerch	PROPN
ejpam-4203	55	5	zeta	zeta	PROPN
ejpam-4203	55	6	function	function	PROPN
ejpam-4203	55	7	and	and	CCONJ
ejpam-4203	55	8	infinite	infinite	ADJ
ejpam-4203	55	9	sum	sum	NOUN
ejpam-4203	55	10	of	of	ADP
ejpam-4203	55	11	the	the	DET
ejpam-4203	55	12	contour	contour	NOUN
ejpam-4203	55	13	integral	integral	NOUN
ejpam-4203	55	14	in	in	ADP
ejpam-4203	55	15	this	this	DET
ejpam-4203	55	16	section	section	NOUN
ejpam-4203	55	17	we	we	PRON
ejpam-4203	55	18	use	use	VERB
ejpam-4203	55	19	equation	equation	NOUN
ejpam-4203	55	20	(	(	PUNCT
ejpam-4203	55	21	2	2	NUM
ejpam-4203	55	22	)	)	PUNCT
ejpam-4203	55	23	to	to	PART
ejpam-4203	55	24	derive	derive	VERB
ejpam-4203	55	25	the	the	DET
ejpam-4203	55	26	contour	contour	NOUN
ejpam-4203	55	27	integral	integral	ADJ
ejpam-4203	55	28	representations	representation	NOUN
ejpam-4203	55	29	for	for	ADP
ejpam-4203	55	30	the	the	DET
ejpam-4203	55	31	hurwitz	hurwitz	PROPN
ejpam-4203	55	32	-	-	PUNCT
ejpam-4203	55	33	lerch	lerch	PROPN
ejpam-4203	55	34	zeta	zeta	PROPN
ejpam-4203	55	35	function	function	PROPN
ejpam-4203	55	36	.	.	PUNCT
ejpam-4203	56	1	4.1	4.1	NUM
ejpam-4203	56	2	.	.	PUNCT
ejpam-4203	57	1	the	the	DET
ejpam-4203	57	2	hurwitz	hurwitz	PROPN
ejpam-4203	57	3	-	-	PUNCT
ejpam-4203	57	4	lerch	lerch	PROPN
ejpam-4203	57	5	zeta	zeta	PROPN
ejpam-4203	57	6	function	function	VERB
ejpam-4203	57	7	the	the	DET
ejpam-4203	57	8	hurwitz	hurwitz	PROPN
ejpam-4203	57	9	-	-	PUNCT
ejpam-4203	57	10	lerch	lerch	PROPN
ejpam-4203	57	11	zeta	zeta	PROPN
ejpam-4203	57	12	function	function	PROPN
ejpam-4203	57	13	(	(	PUNCT
ejpam-4203	57	14	25.14	25.14	NUM
ejpam-4203	57	15	)	)	PUNCT
ejpam-4203	57	16	in	in	ADP
ejpam-4203	57	17	[	[	X
ejpam-4203	57	18	3	3	X
ejpam-4203	57	19	]	]	PUNCT
ejpam-4203	57	20	has	have	VERB
ejpam-4203	57	21	a	a	DET
ejpam-4203	57	22	series	series	NOUN
ejpam-4203	57	23	representation	representation	NOUN
ejpam-4203	57	24	given	give	VERB
ejpam-4203	57	25	by	by	ADP
ejpam-4203	57	26	φ(z	φ(z	PROPN
ejpam-4203	57	27	,	,	PUNCT
ejpam-4203	57	28	s	s	NOUN
ejpam-4203	57	29	,	,	PUNCT
ejpam-4203	57	30	v	v	NOUN
ejpam-4203	57	31	)	)	PUNCT
ejpam-4203	57	32	=	=	PUNCT
ejpam-4203	58	1	∞∑	∞∑	NUM
ejpam-4203	58	2	n=0	n=0	NUM
ejpam-4203	58	3	(	(	PUNCT
ejpam-4203	58	4	v	v	NOUN
ejpam-4203	58	5	+	+	PRON
ejpam-4203	58	6	n)−szn	n)−szn	NUM
ejpam-4203	58	7	(	(	PUNCT
ejpam-4203	58	8	4	4	NUM
ejpam-4203	58	9	)	)	PUNCT
ejpam-4203	58	10	where	where	SCONJ
ejpam-4203	58	11	|z|	|z|	VERB
ejpam-4203	58	12	<	<	X
ejpam-4203	58	13	1	1	NUM
ejpam-4203	58	14	,	,	PUNCT
ejpam-4203	58	15	v	v	NOUN
ejpam-4203	58	16	6=	6=	ADP
ejpam-4203	58	17	0,−1	0,−1	PROPN
ejpam-4203	58	18	,	,	PUNCT
ejpam-4203	58	19	..	..	PUNCT
ejpam-4203	58	20	and	and	CCONJ
ejpam-4203	58	21	is	be	AUX
ejpam-4203	58	22	continued	continue	VERB
ejpam-4203	58	23	analytically	analytically	ADV
ejpam-4203	58	24	by	by	ADP
ejpam-4203	58	25	its	its	PRON
ejpam-4203	58	26	integral	integral	ADJ
ejpam-4203	58	27	representation	representation	NOUN
ejpam-4203	58	28	given	give	VERB
ejpam-4203	58	29	by	by	ADP
ejpam-4203	58	30	φ(z	φ(z	PROPN
ejpam-4203	58	31	,	,	PUNCT
ejpam-4203	58	32	s	s	NOUN
ejpam-4203	58	33	,	,	PUNCT
ejpam-4203	58	34	v	v	NOUN
ejpam-4203	58	35	)	)	PUNCT
ejpam-4203	58	36	=	=	SYM
ejpam-4203	58	37	1	1	NUM
ejpam-4203	58	38	γ(s	γ(	NOUN
ejpam-4203	58	39	)	)	PUNCT
ejpam-4203	58	40	∫	∫	PROPN
ejpam-4203	59	1	∞	∞	PROPN
ejpam-4203	59	2	0	0	NUM
ejpam-4203	60	1	ts−1e−vt	ts−1e−vt	PRON
ejpam-4203	61	1	1−	1−	NUM
ejpam-4203	61	2	ze−t	ze−t	NOUN
ejpam-4203	61	3	dt	dt	NOUN
ejpam-4203	62	1	=	=	SYM
ejpam-4203	62	2	1	1	NUM
ejpam-4203	62	3	γ(s	γ(s	PROPN
ejpam-4203	62	4	)	)	PUNCT
ejpam-4203	62	5	∫	∫	PROPN
ejpam-4203	63	1	∞	∞	NUM
ejpam-4203	63	2	0	0	NUM
ejpam-4203	64	1	ts−1e−(v−1)t	ts−1e−(v−1)t	PROPN
ejpam-4203	64	2	et	et	NOUN
ejpam-4203	64	3	−	−	NOUN
ejpam-4203	64	4	z	z	NOUN
ejpam-4203	64	5	dt	dt	X
ejpam-4203	64	6	(	(	PUNCT
ejpam-4203	64	7	5	5	NUM
ejpam-4203	64	8	)	)	PUNCT
ejpam-4203	64	9	where	where	SCONJ
ejpam-4203	64	10	re(v	re(v	NOUN
ejpam-4203	64	11	)	)	PUNCT
ejpam-4203	64	12	>	>	X
ejpam-4203	64	13	0	0	NUM
ejpam-4203	64	14	,	,	PUNCT
ejpam-4203	64	15	and	and	CCONJ
ejpam-4203	64	16	either	either	ADV
ejpam-4203	64	17	|z|≤	|z|≤	SYM
ejpam-4203	64	18	1	1	NUM
ejpam-4203	64	19	,	,	PUNCT
ejpam-4203	64	20	z	z	NOUN
ejpam-4203	64	21	6=	6=	NUM
ejpam-4203	64	22	1	1	NUM
ejpam-4203	64	23	,	,	PUNCT
ejpam-4203	64	24	re(s	re(s	ADJ
ejpam-4203	64	25	)	)	PUNCT
ejpam-4203	64	26	>	>	X
ejpam-4203	64	27	0	0	NUM
ejpam-4203	64	28	,	,	PUNCT
ejpam-4203	64	29	or	or	CCONJ
ejpam-4203	64	30	z	z	NOUN
ejpam-4203	64	31	=	=	SYM
ejpam-4203	64	32	1	1	NUM
ejpam-4203	64	33	,	,	PUNCT
ejpam-4203	64	34	re(s	re(s	ADJ
ejpam-4203	64	35	)	)	PUNCT
ejpam-4203	64	36	>	>	X
ejpam-4203	65	1	1	1	X
ejpam-4203	65	2	.	.	PUNCT
ejpam-4203	65	3	r.	r.	PROPN
ejpam-4203	65	4	reynolds	reynolds	PROPN
ejpam-4203	65	5	,	,	PUNCT
ejpam-4203	65	6	a.	a.	PROPN
ejpam-4203	65	7	stauffer	stauffer	PROPN
ejpam-4203	65	8	/	/	SYM
ejpam-4203	65	9	eur	eur	PROPN
ejpam-4203	65	10	.	.	PUNCT
ejpam-4203	66	1	j.	j.	PROPN
ejpam-4203	66	2	pure	pure	PROPN
ejpam-4203	66	3	appl	appl	PROPN
ejpam-4203	66	4	.	.	PROPN
ejpam-4203	66	5	math	math	PROPN
ejpam-4203	66	6	,	,	PUNCT
ejpam-4203	66	7	15	15	NUM
ejpam-4203	66	8	(	(	PUNCT
ejpam-4203	66	9	2	2	NUM
ejpam-4203	66	10	)	)	PUNCT
ejpam-4203	66	11	(	(	PUNCT
ejpam-4203	66	12	2022	2022	NUM
ejpam-4203	66	13	)	)	PUNCT
ejpam-4203	66	14	,	,	PUNCT
ejpam-4203	66	15	390	390	NUM
ejpam-4203	66	16	-	-	SYM
ejpam-4203	66	17	396	396	NUM
ejpam-4203	66	18	393	393	NUM
ejpam-4203	66	19	4.2	4.2	NUM
ejpam-4203	66	20	.	.	PUNCT
ejpam-4203	67	1	infinite	infinite	ADJ
ejpam-4203	67	2	sum	sum	NOUN
ejpam-4203	67	3	of	of	ADP
ejpam-4203	67	4	the	the	DET
ejpam-4203	67	5	contour	contour	NOUN
ejpam-4203	67	6	integral	integral	ADJ
ejpam-4203	67	7	using	use	VERB
ejpam-4203	67	8	equation	equation	NOUN
ejpam-4203	67	9	(	(	PUNCT
ejpam-4203	67	10	2	2	NUM
ejpam-4203	67	11	)	)	PUNCT
ejpam-4203	67	12	and	and	CCONJ
ejpam-4203	67	13	replacing	replace	VERB
ejpam-4203	67	14	y	y	PRON
ejpam-4203	67	15	by	by	ADP
ejpam-4203	67	16	log(a)+	log(a)+	PROPN
ejpam-4203	67	17	log(b	log(b	PROPN
ejpam-4203	67	18	)	)	PUNCT
ejpam-4203	67	19	2	2	NUM
ejpam-4203	67	20	+	+	SYM
ejpam-4203	67	21	log(c	log(c	VERB
ejpam-4203	67	22	)	)	PUNCT
ejpam-4203	67	23	2	2	NUM
ejpam-4203	68	1	+	+	CCONJ
ejpam-4203	68	2	1	1	NUM
ejpam-4203	68	3	2	2	NUM
ejpam-4203	68	4	iπ(2y+1)+log(2	iπ(2y+1)+log(2	NOUN
ejpam-4203	68	5	)	)	PUNCT
ejpam-4203	68	6	then	then	ADV
ejpam-4203	68	7	multiplying	multiply	VERB
ejpam-4203	68	8	both	both	DET
ejpam-4203	68	9	sides	side	NOUN
ejpam-4203	68	10	by	by	ADP
ejpam-4203	68	11	π2m(−1)yb	π2m(−1)yb	PROPN
ejpam-4203	68	12	1	1	NUM
ejpam-4203	68	13	2	2	NUM
ejpam-4203	68	14	(	(	PUNCT
ejpam-4203	68	15	m−v−1)c	m−v−1)c	NOUN
ejpam-4203	68	16	1	1	NUM
ejpam-4203	68	17	2	2	NUM
ejpam-4203	68	18	(	(	PUNCT
ejpam-4203	68	19	m+v−1)e	m+v−1)e	NOUN
ejpam-4203	68	20	1	1	NUM
ejpam-4203	68	21	2	2	NUM
ejpam-4203	68	22	iπ(2y+1)(m+v	iπ(2y+1)(m+v	NUM
ejpam-4203	68	23	)	)	PUNCT
ejpam-4203	68	24	taking	take	VERB
ejpam-4203	68	25	the	the	DET
ejpam-4203	68	26	infinite	infinite	ADJ
ejpam-4203	68	27	sum	sum	NOUN
ejpam-4203	68	28	over	over	ADP
ejpam-4203	68	29	y	y	PROPN
ejpam-4203	68	30	∈	∈	PROPN
ejpam-4203	69	1	[	[	X
ejpam-4203	69	2	0,∞	0,∞	NOUN
ejpam-4203	69	3	)	)	PUNCT
ejpam-4203	69	4	and	and	CCONJ
ejpam-4203	69	5	simplifying	simplify	VERB
ejpam-4203	69	6	in	in	ADP
ejpam-4203	69	7	terms	term	NOUN
ejpam-4203	69	8	of	of	ADP
ejpam-4203	69	9	the	the	DET
ejpam-4203	69	10	hurwitz	hurwitz	PROPN
ejpam-4203	69	11	-	-	PUNCT
ejpam-4203	69	12	lerch	lerch	PROPN
ejpam-4203	69	13	zeta	zeta	PROPN
ejpam-4203	69	14	function	function	VERB
ejpam-4203	69	15	we	we	PRON
ejpam-4203	69	16	obtain	obtain	VERB
ejpam-4203	69	17	(	(	PUNCT
ejpam-4203	69	18	6	6	NUM
ejpam-4203	69	19	)	)	SYM
ejpam-4203	69	20	1	1	NUM
ejpam-4203	70	1	γ(k	γ(k	NOUN
ejpam-4203	70	2	+	+	CCONJ
ejpam-4203	70	3	1	1	X
ejpam-4203	70	4	)	)	PUNCT
ejpam-4203	70	5	πk+12	πk+12	NOUN
ejpam-4203	70	6	mb	mb	ADP
ejpam-4203	70	7	1	1	NUM
ejpam-4203	70	8	2	2	NUM
ejpam-4203	70	9	(	(	PUNCT
ejpam-4203	70	10	m−v−1)c	m−v−1)c	NOUN
ejpam-4203	70	11	1	1	NUM
ejpam-4203	70	12	2	2	NUM
ejpam-4203	70	13	(	(	PUNCT
ejpam-4203	70	14	m+v−1)e	m+v−1)e	NOUN
ejpam-4203	70	15	1	1	NUM
ejpam-4203	70	16	2	2	NUM
ejpam-4203	70	17	iπ(k+m+v	iπ(k+m+v	NOUN
ejpam-4203	70	18	)	)	PUNCT
ejpam-4203	70	19	φ	φ	PROPN
ejpam-4203	70	20	(	(	PUNCT
ejpam-4203	70	21	−eiπ(m+v),−k	−eiπ(m+v),−k	NOUN
ejpam-4203	70	22	,	,	PUNCT
ejpam-4203	70	23	−2i	−2i	NUM
ejpam-4203	70	24	log(2a)−	log(2a)−	VERB
ejpam-4203	71	1	i	i	PRON
ejpam-4203	71	2	log(b)−	log(b)−	VERB
ejpam-4203	71	3	i	i	PRON
ejpam-4203	71	4	log(c	log(c	VERB
ejpam-4203	71	5	)	)	PUNCT
ejpam-4203	72	1	+	+	NUM
ejpam-4203	72	2	π	π	PROPN
ejpam-4203	72	3	2π	2π	NOUN
ejpam-4203	72	4	)	)	PUNCT
ejpam-4203	72	5	=	=	SYM
ejpam-4203	73	1	1	1	NUM
ejpam-4203	73	2	2πi	2πi	NOUN
ejpam-4203	73	3	∞∑	∞∑	NUM
ejpam-4203	73	4	y=0	y=0	NUM
ejpam-4203	73	5	∫	∫	PROPN
ejpam-4203	73	6	c	c	PROPN
ejpam-4203	73	7	π(−1)yaww−k−12m+wb	π(−1)yaww−k−12m+wb	X
ejpam-4203	73	8	1	1	NUM
ejpam-4203	73	9	2	2	NUM
ejpam-4203	73	10	(	(	PUNCT
ejpam-4203	73	11	m−v+w−1)c	m−v+w−1)c	NOUN
ejpam-4203	73	12	1	1	NUM
ejpam-4203	73	13	2	2	NUM
ejpam-4203	73	14	(	(	PUNCT
ejpam-4203	73	15	m+v+w−1)e	m+v+w−1)e	NOUN
ejpam-4203	73	16	1	1	NUM
ejpam-4203	73	17	2	2	NUM
ejpam-4203	73	18	iπ(2y+1)(m+v+w)dw	iπ(2y+1)(m+v+w)dw	NOUN
ejpam-4203	73	19	=	=	NOUN
ejpam-4203	73	20	1	1	NUM
ejpam-4203	73	21	2πi	2πi	NOUN
ejpam-4203	73	22	∫	∫	PROPN
ejpam-4203	74	1	c	c	NOUN
ejpam-4203	74	2	∞∑	∞∑	NUM
ejpam-4203	74	3	y=0	y=0	NOUN
ejpam-4203	74	4	π(−1)yaww−k−12m+wb	π(−1)yaww−k−12m+wb	X
ejpam-4203	74	5	1	1	NUM
ejpam-4203	74	6	2	2	NUM
ejpam-4203	74	7	(	(	PUNCT
ejpam-4203	74	8	m−v+w−1)c	m−v+w−1)c	NOUN
ejpam-4203	74	9	1	1	NUM
ejpam-4203	74	10	2	2	NUM
ejpam-4203	74	11	(	(	PUNCT
ejpam-4203	74	12	m+v+w−1)e	m+v+w−1)e	NOUN
ejpam-4203	74	13	1	1	NUM
ejpam-4203	74	14	2	2	NUM
ejpam-4203	74	15	iπ(2y+1)(m+v+w)dw	iπ(2y+1)(m+v+w)dw	NOUN
ejpam-4203	74	16	=	=	NOUN
ejpam-4203	75	1	1	1	NUM
ejpam-4203	75	2	2πi	2πi	NOUN
ejpam-4203	75	3	∫	∫	PROPN
ejpam-4203	75	4	c	c	PROPN
ejpam-4203	76	1	πaww−k−12m+w−1b	πaww−k−12m+w−1b	PROPN
ejpam-4203	76	2	1	1	NUM
ejpam-4203	76	3	2	2	NUM
ejpam-4203	76	4	(	(	PUNCT
ejpam-4203	76	5	m−v+w−1)c	m−v+w−1)c	NOUN
ejpam-4203	76	6	1	1	NUM
ejpam-4203	76	7	2	2	NUM
ejpam-4203	76	8	(	(	PUNCT
ejpam-4203	76	9	m+v+w−1	m+v+w−1	NOUN
ejpam-4203	76	10	)	)	PUNCT
ejpam-4203	76	11	sec	sec	PROPN
ejpam-4203	76	12	(	(	PUNCT
ejpam-4203	76	13	1	1	NUM
ejpam-4203	76	14	2	2	NUM
ejpam-4203	76	15	π(m+	π(m+	X
ejpam-4203	76	16	v	v	ADP
ejpam-4203	76	17	+	+	CCONJ
ejpam-4203	76	18	w	w	NOUN
ejpam-4203	76	19	)	)	PUNCT
ejpam-4203	76	20	)	)	PUNCT
ejpam-4203	76	21	dw	dw	NOUN
ejpam-4203	76	22	from	from	ADP
ejpam-4203	76	23	equation	equation	NOUN
ejpam-4203	76	24	(	(	PUNCT
ejpam-4203	76	25	1.232.2	1.232.2	NUM
ejpam-4203	76	26	)	)	PUNCT
ejpam-4203	76	27	in	in	ADP
ejpam-4203	76	28	[	[	X
ejpam-4203	76	29	5	5	NUM
ejpam-4203	76	30	]	]	PUNCT
ejpam-4203	76	31	where	where	SCONJ
ejpam-4203	76	32	i	i	PRON
ejpam-4203	76	33	m	m	VERB
ejpam-4203	76	34	(	(	PUNCT
ejpam-4203	76	35	1	1	NUM
ejpam-4203	76	36	2π(m+	2π(m+	NUM
ejpam-4203	76	37	v	v	NOUN
ejpam-4203	76	38	+	+	NOUN
ejpam-4203	76	39	w	w	NOUN
ejpam-4203	76	40	)	)	PUNCT
ejpam-4203	76	41	)	)	PUNCT
ejpam-4203	77	1	>	>	X
ejpam-4203	77	2	0	0	PUNCT
ejpam-4203	78	1	in	in	ADP
ejpam-4203	78	2	order	order	NOUN
ejpam-4203	78	3	for	for	SCONJ
ejpam-4203	78	4	the	the	DET
ejpam-4203	78	5	sum	sum	NOUN
ejpam-4203	78	6	to	to	PART
ejpam-4203	78	7	converge	converge	VERB
ejpam-4203	78	8	.	.	PUNCT
ejpam-4203	79	1	5	5	X
ejpam-4203	79	2	.	.	X
ejpam-4203	79	3	definite	definite	ADJ
ejpam-4203	79	4	integral	integral	ADJ
ejpam-4203	79	5	in	in	ADP
ejpam-4203	79	6	terms	term	NOUN
ejpam-4203	79	7	of	of	ADP
ejpam-4203	79	8	the	the	DET
ejpam-4203	79	9	hurwitz	hurwitz	PROPN
ejpam-4203	79	10	-	-	PUNCT
ejpam-4203	79	11	lerch	lerch	PROPN
ejpam-4203	79	12	zeta	zeta	PROPN
ejpam-4203	79	13	function	function	PROPN
ejpam-4203	79	14	theorem	theorem	VERB
ejpam-4203	79	15	1	1	NUM
ejpam-4203	79	16	.	.	PUNCT
ejpam-4203	80	1	for	for	ADP
ejpam-4203	80	2	all	all	DET
ejpam-4203	80	3	k	k	NOUN
ejpam-4203	80	4	,	,	PUNCT
ejpam-4203	80	5	a	a	DET
ejpam-4203	80	6	∈	∈	PROPN
ejpam-4203	80	7	c	c	NOUN
ejpam-4203	80	8	,	,	PUNCT
ejpam-4203	80	9	re(b	re(b	X
ejpam-4203	80	10	)	)	PUNCT
ejpam-4203	80	11	>	>	X
ejpam-4203	80	12	0	0	NUM
ejpam-4203	80	13	,	,	PUNCT
ejpam-4203	80	14	re(c	re(c	NUM
ejpam-4203	80	15	)	)	PUNCT
ejpam-4203	80	16	>	>	X
ejpam-4203	80	17	0	0	NUM
ejpam-4203	80	18	,	,	PUNCT
ejpam-4203	80	19	re(v	re(v	NOUN
ejpam-4203	80	20	)	)	PUNCT
ejpam-4203	80	21	>	>	X
ejpam-4203	80	22	0	0	NUM
ejpam-4203	80	23	,	,	PUNCT
ejpam-4203	80	24	re(m	re(m	NUM
ejpam-4203	80	25	)	)	PUNCT
ejpam-4203	80	26	<	<	X
ejpam-4203	80	27	−1	−1	NOUN
ejpam-4203	80	28	,	,	PUNCT
ejpam-4203	80	29	(	(	PUNCT
ejpam-4203	80	30	7	7	X
ejpam-4203	80	31	)	)	PUNCT
ejpam-4203	80	32	∫	∫	PROPN
ejpam-4203	80	33	∞	∞	PROPN
ejpam-4203	80	34	0	0	NUM
ejpam-4203	80	35	∫	∫	PROPN
ejpam-4203	80	36	∞	∞	PROPN
ejpam-4203	80	37	0	0	NUM
ejpam-4203	80	38	∫	∫	PROPN
ejpam-4203	80	39	∞	∞	PROPN
ejpam-4203	80	40	0	0	NUM
ejpam-4203	81	1	tmxv−my	tmxv−my	NOUN
ejpam-4203	81	2	1	1	NUM
ejpam-4203	81	3	2	2	NUM
ejpam-4203	81	4	(	(	PUNCT
ejpam-4203	81	5	−m−v−1)jv(t)e	−m−v−1)jv(t)e	PROPN
ejpam-4203	81	6	−bx2−cy	−bx2−cy	X
ejpam-4203	81	7	logk	logk	NOUN
ejpam-4203	81	8	(	(	PUNCT
ejpam-4203	81	9	at	at	ADP
ejpam-4203	81	10	x	x	SYM
ejpam-4203	81	11	√	√	PROPN
ejpam-4203	81	12	y	y	PROPN
ejpam-4203	81	13	)	)	PUNCT
ejpam-4203	81	14	dxdydt	dxdydt	NOUN
ejpam-4203	81	15	=	=	PUNCT
ejpam-4203	82	1	πk+12	πk+12	PROPN
ejpam-4203	82	2	mb	mb	ADP
ejpam-4203	82	3	1	1	NUM
ejpam-4203	82	4	2	2	NUM
ejpam-4203	82	5	(	(	PUNCT
ejpam-4203	82	6	m−v−1)c	m−v−1)c	NOUN
ejpam-4203	82	7	1	1	NUM
ejpam-4203	82	8	2	2	NUM
ejpam-4203	82	9	(	(	PUNCT
ejpam-4203	82	10	m+v−1)e	m+v−1)e	NOUN
ejpam-4203	82	11	1	1	NUM
ejpam-4203	82	12	2	2	NUM
ejpam-4203	82	13	iπ(k+m+v	iπ(k+m+v	NOUN
ejpam-4203	82	14	)	)	PUNCT
ejpam-4203	82	15	φ	φ	PROPN
ejpam-4203	82	16	(	(	PUNCT
ejpam-4203	82	17	−eiπ(m+v),−k	−eiπ(m+v),−k	NOUN
ejpam-4203	82	18	,	,	PUNCT
ejpam-4203	82	19	−2i	−2i	NUM
ejpam-4203	82	20	log(2a)−	log(2a)−	VERB
ejpam-4203	83	1	i	i	PRON
ejpam-4203	83	2	log(b)−	log(b)−	VERB
ejpam-4203	83	3	i	i	PRON
ejpam-4203	83	4	log(c	log(c	VERB
ejpam-4203	83	5	)	)	PUNCT
ejpam-4203	84	1	+	+	NUM
ejpam-4203	84	2	π	π	PROPN
ejpam-4203	84	3	2π	2π	NOUN
ejpam-4203	84	4	)	)	PUNCT
ejpam-4203	84	5	proof	proof	NOUN
ejpam-4203	84	6	.	.	PUNCT
ejpam-4203	85	1	the	the	DET
ejpam-4203	85	2	right	right	ADJ
ejpam-4203	85	3	-	-	PUNCT
ejpam-4203	85	4	hand	hand	NOUN
ejpam-4203	85	5	sides	side	NOUN
ejpam-4203	85	6	of	of	ADP
ejpam-4203	85	7	relations	relation	NOUN
ejpam-4203	85	8	(	(	PUNCT
ejpam-4203	85	9	3	3	NUM
ejpam-4203	85	10	)	)	PUNCT
ejpam-4203	85	11	and	and	CCONJ
ejpam-4203	85	12	(	(	PUNCT
ejpam-4203	85	13	6	6	NUM
ejpam-4203	85	14	)	)	PUNCT
ejpam-4203	85	15	are	be	AUX
ejpam-4203	85	16	identical	identical	ADJ
ejpam-4203	85	17	;	;	PUNCT
ejpam-4203	85	18	hence	hence	ADV
ejpam-4203	85	19	,	,	PUNCT
ejpam-4203	85	20	the	the	DET
ejpam-4203	85	21	left	leave	VERB
ejpam-4203	85	22	-	-	PUNCT
ejpam-4203	85	23	hand	hand	NOUN
ejpam-4203	85	24	sides	side	NOUN
ejpam-4203	85	25	of	of	ADP
ejpam-4203	85	26	the	the	DET
ejpam-4203	85	27	same	same	ADJ
ejpam-4203	85	28	are	be	AUX
ejpam-4203	85	29	identical	identical	ADJ
ejpam-4203	85	30	too	too	ADV
ejpam-4203	85	31	.	.	PUNCT
ejpam-4203	86	1	simplifying	simplify	VERB
ejpam-4203	86	2	with	with	ADP
ejpam-4203	86	3	the	the	DET
ejpam-4203	86	4	gamma	gamma	NOUN
ejpam-4203	86	5	function	function	NOUN
ejpam-4203	86	6	yields	yield	VERB
ejpam-4203	86	7	the	the	DET
ejpam-4203	86	8	desired	desire	VERB
ejpam-4203	86	9	conclusion	conclusion	NOUN
ejpam-4203	86	10	.	.	PUNCT
ejpam-4203	87	1	example	example	NOUN
ejpam-4203	88	1	1	1	NUM
ejpam-4203	88	2	.	.	PUNCT
ejpam-4203	89	1	the	the	DET
ejpam-4203	89	2	degenerate	degenerate	ADJ
ejpam-4203	89	3	case	case	NOUN
ejpam-4203	89	4	.	.	PUNCT
ejpam-4203	90	1	(	(	PUNCT
ejpam-4203	90	2	8)	8)	NUM
ejpam-4203	90	3	∫	∫	NOUN
ejpam-4203	90	4	∞	∞	PROPN
ejpam-4203	90	5	0	0	NUM
ejpam-4203	91	1	∫	∫	PROPN
ejpam-4203	91	2	∞	∞	PROPN
ejpam-4203	91	3	0	0	NUM
ejpam-4203	92	1	∫	∫	PROPN
ejpam-4203	92	2	∞	∞	PROPN
ejpam-4203	92	3	0	0	NUM
ejpam-4203	93	1	tmxv−my	tmxv−my	NOUN
ejpam-4203	93	2	1	1	NUM
ejpam-4203	93	3	2	2	NUM
ejpam-4203	93	4	(	(	PUNCT
ejpam-4203	93	5	−m−v−1)jv(t)e	−m−v−1)jv(t)e	NOUN
ejpam-4203	93	6	−bx2−cydxdydt	−bx2−cydxdydt	NOUN
ejpam-4203	93	7	=	=	SYM
ejpam-4203	93	8	π2m−1b	π2m−1b	PROPN
ejpam-4203	93	9	1	1	NUM
ejpam-4203	93	10	2	2	NUM
ejpam-4203	93	11	(	(	PUNCT
ejpam-4203	93	12	m−v−1)c	m−v−1)c	NOUN
ejpam-4203	93	13	1	1	NUM
ejpam-4203	93	14	2	2	NUM
ejpam-4203	93	15	(	(	PUNCT
ejpam-4203	93	16	m+v−1	m+v−1	PROPN
ejpam-4203	93	17	)	)	PUNCT
ejpam-4203	93	18	sec	sec	PROPN
ejpam-4203	93	19	(	(	PUNCT
ejpam-4203	93	20	1	1	NUM
ejpam-4203	93	21	2	2	NUM
ejpam-4203	93	22	π(m+	π(m+	NOUN
ejpam-4203	93	23	v	v	NOUN
ejpam-4203	93	24	)	)	PUNCT
ejpam-4203	93	25	)	)	PUNCT
ejpam-4203	94	1	r.	r.	PROPN
ejpam-4203	94	2	reynolds	reynolds	PROPN
ejpam-4203	94	3	,	,	PUNCT
ejpam-4203	94	4	a.	a.	PROPN
ejpam-4203	94	5	stauffer	stauffer	PROPN
ejpam-4203	94	6	/	/	SYM
ejpam-4203	94	7	eur	eur	PROPN
ejpam-4203	94	8	.	.	PUNCT
ejpam-4203	95	1	j.	j.	PROPN
ejpam-4203	95	2	pure	pure	PROPN
ejpam-4203	95	3	appl	appl	PROPN
ejpam-4203	95	4	.	.	PROPN
ejpam-4203	95	5	math	math	PROPN
ejpam-4203	95	6	,	,	PUNCT
ejpam-4203	95	7	15	15	NUM
ejpam-4203	95	8	(	(	PUNCT
ejpam-4203	95	9	2	2	NUM
ejpam-4203	95	10	)	)	PUNCT
ejpam-4203	95	11	(	(	PUNCT
ejpam-4203	95	12	2022	2022	NUM
ejpam-4203	95	13	)	)	PUNCT
ejpam-4203	95	14	,	,	PUNCT
ejpam-4203	95	15	390	390	NUM
ejpam-4203	95	16	-	-	SYM
ejpam-4203	95	17	396	396	NUM
ejpam-4203	95	18	394	394	NUM
ejpam-4203	95	19	proof	proof	NOUN
ejpam-4203	95	20	.	.	PUNCT
ejpam-4203	96	1	use	use	VERB
ejpam-4203	96	2	equation	equation	NOUN
ejpam-4203	96	3	(	(	PUNCT
ejpam-4203	96	4	7	7	NUM
ejpam-4203	96	5	)	)	PUNCT
ejpam-4203	96	6	and	and	CCONJ
ejpam-4203	96	7	set	set	VERB
ejpam-4203	96	8	k	k	PROPN
ejpam-4203	96	9	=	=	PUNCT
ejpam-4203	96	10	0	0	PUNCT
ejpam-4203	96	11	and	and	CCONJ
ejpam-4203	96	12	simplify	simplify	VERB
ejpam-4203	96	13	using	use	VERB
ejpam-4203	96	14	entry	entry	NOUN
ejpam-4203	96	15	(	(	PUNCT
ejpam-4203	96	16	2	2	NUM
ejpam-4203	96	17	)	)	PUNCT
ejpam-4203	96	18	in	in	ADP
ejpam-4203	96	19	table	table	NOUN
ejpam-4203	96	20	below	below	ADV
ejpam-4203	96	21	(	(	PUNCT
ejpam-4203	96	22	64:12:7	64:12:7	NUM
ejpam-4203	96	23	)	)	PUNCT
ejpam-4203	96	24	in	in	ADP
ejpam-4203	96	25	[	[	X
ejpam-4203	96	26	8	8	NUM
ejpam-4203	96	27	]	]	PUNCT
ejpam-4203	96	28	.	.	PUNCT
ejpam-4203	96	29	example	example	NOUN
ejpam-4203	97	1	2	2	NUM
ejpam-4203	97	2	.	.	PUNCT
ejpam-4203	97	3	(	(	PUNCT
ejpam-4203	97	4	9	9	NUM
ejpam-4203	97	5	)	)	PUNCT
ejpam-4203	97	6	∫	∫	PROPN
ejpam-4203	97	7	∞	∞	PROPN
ejpam-4203	97	8	0	0	NUM
ejpam-4203	98	1	∫	∫	PROPN
ejpam-4203	98	2	∞	∞	PROPN
ejpam-4203	98	3	0	0	NUM
ejpam-4203	98	4	∫	∫	PROPN
ejpam-4203	98	5	∞	∞	NUM
ejpam-4203	98	6	0	0	NUM
ejpam-4203	98	7	tme−x2−yxv−my	tme−x2−yxv−my	NUM
ejpam-4203	98	8	1	1	NUM
ejpam-4203	98	9	2	2	NUM
ejpam-4203	98	10	(	(	PUNCT
ejpam-4203	98	11	−m−v−1)jv(t	−m−v−1)jv(t	NOUN
ejpam-4203	98	12	)	)	PUNCT
ejpam-4203	98	13	log	log	NOUN
ejpam-4203	98	14	(	(	PUNCT
ejpam-4203	98	15	−	−	PROPN
ejpam-4203	98	16	t	t	PROPN
ejpam-4203	98	17	2x	2x	NUM
ejpam-4203	98	18	√	√	PROPN
ejpam-4203	98	19	y	y	NOUN
ejpam-4203	98	20	)	)	PUNCT
ejpam-4203	98	21	dxdydt	dxdydt	NOUN
ejpam-4203	98	22	=	=	PUNCT
ejpam-4203	99	1	2m+1e−	2m+1e−	NUM
ejpam-4203	99	2	1	1	NUM
ejpam-4203	99	3	2	2	NUM
ejpam-4203	99	4	iπ(2m+2v+1	iπ(2m+2v+1	NOUN
ejpam-4203	99	5	)	)	PUNCT
ejpam-4203	99	6	(	(	PUNCT
ejpam-4203	99	7	e	e	NOUN
ejpam-4203	99	8	1	1	NUM
ejpam-4203	99	9	2	2	NUM
ejpam-4203	99	10	iπ(m+v	iπ(m+v	NOUN
ejpam-4203	99	11	)	)	PUNCT
ejpam-4203	99	12	−	−	PROPN
ejpam-4203	100	1	tan−1	tan−1	PROPN
ejpam-4203	100	2	(	(	PUNCT
ejpam-4203	100	3	e	e	NOUN
ejpam-4203	100	4	1	1	NUM
ejpam-4203	100	5	2	2	NUM
ejpam-4203	100	6	iπ(m+v	iπ(m+v	NOUN
ejpam-4203	100	7	)	)	PUNCT
ejpam-4203	100	8	)	)	PUNCT
ejpam-4203	100	9	)	)	PUNCT
ejpam-4203	100	10	proof	proof	NOUN
ejpam-4203	100	11	.	.	PUNCT
ejpam-4203	101	1	use	use	VERB
ejpam-4203	101	2	equation	equation	NOUN
ejpam-4203	101	3	(	(	PUNCT
ejpam-4203	101	4	7	7	NUM
ejpam-4203	101	5	)	)	PUNCT
ejpam-4203	101	6	and	and	CCONJ
ejpam-4203	101	7	set	set	VERB
ejpam-4203	101	8	k	k	PROPN
ejpam-4203	101	9	=	=	PUNCT
ejpam-4203	101	10	−1	−1	NOUN
ejpam-4203	101	11	,	,	PUNCT
ejpam-4203	101	12	a	a	DET
ejpam-4203	101	13	=	=	PUNCT
ejpam-4203	101	14	−1/2	−1/2	ADJ
ejpam-4203	101	15	,	,	PUNCT
ejpam-4203	101	16	b	b	X
ejpam-4203	101	17	=	=	SYM
ejpam-4203	101	18	c	c	NOUN
ejpam-4203	101	19	=	=	SYM
ejpam-4203	101	20	1	1	NUM
ejpam-4203	101	21	and	and	CCONJ
ejpam-4203	101	22	simplify	simplify	VERB
ejpam-4203	101	23	using	use	VERB
ejpam-4203	101	24	entry	entry	NOUN
ejpam-4203	101	25	(	(	PUNCT
ejpam-4203	101	26	3	3	NUM
ejpam-4203	101	27	)	)	PUNCT
ejpam-4203	101	28	in	in	ADP
ejpam-4203	101	29	table	table	NOUN
ejpam-4203	101	30	below	below	ADV
ejpam-4203	101	31	(	(	PUNCT
ejpam-4203	101	32	64:12:7	64:12:7	NUM
ejpam-4203	101	33	)	)	PUNCT
ejpam-4203	101	34	in	in	ADP
ejpam-4203	101	35	[	[	X
ejpam-4203	101	36	8	8	NUM
ejpam-4203	101	37	]	]	PUNCT
ejpam-4203	101	38	.	.	PUNCT
ejpam-4203	101	39	example	example	NOUN
ejpam-4203	102	1	3	3	NUM
ejpam-4203	102	2	.	.	PUNCT
ejpam-4203	102	3	(	(	PUNCT
ejpam-4203	102	4	10	10	NUM
ejpam-4203	102	5	)	)	PUNCT
ejpam-4203	102	6	∫	∫	PROPN
ejpam-4203	102	7	∞	∞	PROPN
ejpam-4203	102	8	0	0	NUM
ejpam-4203	103	1	∫	∫	PROPN
ejpam-4203	103	2	∞	∞	PROPN
ejpam-4203	103	3	0	0	NUM
ejpam-4203	103	4	∫	∫	PROPN
ejpam-4203	103	5	∞	∞	PROPN
ejpam-4203	103	6	0	0	NUM
ejpam-4203	104	1	x3j	x3j	NOUN
ejpam-4203	104	2	5	5	NUM
ejpam-4203	104	3	3	3	NUM
ejpam-4203	104	4	(	(	PUNCT
ejpam-4203	104	5	t)e−x2−y	t)e−x2−y	PROPN
ejpam-4203	104	6	t4/3y2/3	t4/3y2/3	PROPN
ejpam-4203	104	7	(	(	PUNCT
ejpam-4203	104	8	log2	log2	PROPN
ejpam-4203	104	9	(	(	PUNCT
ejpam-4203	104	10	t	t	PROPN
ejpam-4203	104	11	2x	2x	NUM
ejpam-4203	104	12	√	√	PROPN
ejpam-4203	104	13	y	y	PROPN
ejpam-4203	104	14	)	)	PUNCT
ejpam-4203	105	1	+	+	CCONJ
ejpam-4203	105	2	π2	π2	ADJ
ejpam-4203	105	3	)	)	PUNCT
ejpam-4203	105	4	dxdydt	dxdydt	NOUN
ejpam-4203	105	5	=	=	PUNCT
ejpam-4203	106	1	−π	−π	PROPN
ejpam-4203	106	2	+	+	CCONJ
ejpam-4203	106	3	√	√	ADV
ejpam-4203	106	4	3(log(3)−	3(log(3)−	NUM
ejpam-4203	106	5	4	4	NUM
ejpam-4203	106	6	)	)	PUNCT
ejpam-4203	106	7	8	8	NUM
ejpam-4203	106	8	3	3	NUM
ejpam-4203	106	9	√	√	PROPN
ejpam-4203	106	10	2π	2π	PROPN
ejpam-4203	106	11	and	and	CCONJ
ejpam-4203	106	12	(	(	PUNCT
ejpam-4203	106	13	11	11	NUM
ejpam-4203	106	14	)	)	PUNCT
ejpam-4203	106	15	∫	∫	PROPN
ejpam-4203	107	1	∞	∞	PROPN
ejpam-4203	107	2	0	0	NUM
ejpam-4203	108	1	∫	∫	PROPN
ejpam-4203	108	2	∞	∞	PROPN
ejpam-4203	108	3	0	0	NUM
ejpam-4203	108	4	∫	∫	PROPN
ejpam-4203	108	5	∞	∞	PROPN
ejpam-4203	108	6	0	0	NUM
ejpam-4203	109	1	x3j	x3j	NOUN
ejpam-4203	109	2	5	5	NUM
ejpam-4203	109	3	3	3	NUM
ejpam-4203	109	4	(	(	PUNCT
ejpam-4203	109	5	t)e−x2−y	t)e−x2−y	PROPN
ejpam-4203	109	6	log	log	NOUN
ejpam-4203	109	7	(	(	PUNCT
ejpam-4203	109	8	t	t	PROPN
ejpam-4203	109	9	2x	2x	NUM
ejpam-4203	109	10	√	√	PROPN
ejpam-4203	109	11	y	y	PROPN
ejpam-4203	109	12	)	)	PUNCT
ejpam-4203	109	13	t4/3y2/3	t4/3y2/3	PROPN
ejpam-4203	109	14	(	(	PUNCT
ejpam-4203	109	15	log2	log2	PROPN
ejpam-4203	109	16	(	(	PUNCT
ejpam-4203	109	17	t	t	PROPN
ejpam-4203	109	18	2x	2x	NUM
ejpam-4203	110	1	√	√	PROPN
ejpam-4203	110	2	y	y	PROPN
ejpam-4203	110	3	)	)	PUNCT
ejpam-4203	111	1	+	+	CCONJ
ejpam-4203	111	2	π2	π2	ADJ
ejpam-4203	111	3	)	)	PUNCT
ejpam-4203	111	4	dxdtdt	dxdtdt	NOUN
ejpam-4203	112	1	=	=	NOUN
ejpam-4203	112	2	−4	−4	PROPN
ejpam-4203	113	1	+	+	CCONJ
ejpam-4203	113	2	√	√	ADJ
ejpam-4203	113	3	3π	3π	NOUN
ejpam-4203	113	4	−	−	NOUN
ejpam-4203	113	5	log(3	log(3	NOUN
ejpam-4203	113	6	)	)	PUNCT
ejpam-4203	113	7	8	8	NUM
ejpam-4203	113	8	3	3	NUM
ejpam-4203	113	9	√	√	NUM
ejpam-4203	113	10	2	2	NUM
ejpam-4203	113	11	proof	proof	NOUN
ejpam-4203	113	12	.	.	PUNCT
ejpam-4203	114	1	use	use	VERB
ejpam-4203	114	2	equation	equation	NOUN
ejpam-4203	114	3	(	(	PUNCT
ejpam-4203	114	4	9	9	NUM
ejpam-4203	114	5	)	)	PUNCT
ejpam-4203	114	6	and	and	CCONJ
ejpam-4203	114	7	set	set	VERB
ejpam-4203	114	8	m	m	PROPN
ejpam-4203	114	9	=	=	SYM
ejpam-4203	114	10	−4/3	−4/3	NOUN
ejpam-4203	114	11	,	,	PUNCT
ejpam-4203	114	12	v	v	NOUN
ejpam-4203	114	13	=	=	SYM
ejpam-4203	114	14	5/3	5/3	NUM
ejpam-4203	114	15	rationalize	rationalize	VERB
ejpam-4203	114	16	the	the	DET
ejpam-4203	114	17	denominator	denominator	NOUN
ejpam-4203	114	18	and	and	CCONJ
ejpam-4203	114	19	simplify	simplify	NOUN
ejpam-4203	114	20	.	.	PUNCT
ejpam-4203	115	1	example	example	NOUN
ejpam-4203	115	2	4	4	NUM
ejpam-4203	115	3	.	.	PUNCT
ejpam-4203	116	1	the	the	DET
ejpam-4203	116	2	polylogarithm	polylogarithm	PROPN
ejpam-4203	116	3	function	function	VERB
ejpam-4203	116	4	lik(z	lik(z	PROPN
ejpam-4203	116	5	)	)	PUNCT
ejpam-4203	116	6	,	,	PUNCT
ejpam-4203	116	7	(	(	PUNCT
ejpam-4203	116	8	12	12	NUM
ejpam-4203	116	9	)	)	PUNCT
ejpam-4203	116	10	∫	∫	PROPN
ejpam-4203	117	1	∞	∞	PROPN
ejpam-4203	117	2	0	0	NUM
ejpam-4203	118	1	∫	∫	PROPN
ejpam-4203	118	2	∞	∞	PROPN
ejpam-4203	118	3	0	0	NUM
ejpam-4203	118	4	∫	∫	PROPN
ejpam-4203	118	5	∞	∞	NUM
ejpam-4203	118	6	0	0	NUM
ejpam-4203	118	7	tme−x2−yxv−my	tme−x2−yxv−my	NUM
ejpam-4203	118	8	1	1	NUM
ejpam-4203	118	9	2	2	NUM
ejpam-4203	118	10	(	(	PUNCT
ejpam-4203	118	11	−m−v−1)jv(t	−m−v−1)jv(t	NOUN
ejpam-4203	118	12	)	)	PUNCT
ejpam-4203	118	13	log	log	NOUN
ejpam-4203	118	14	k	k	PROPN
ejpam-4203	118	15	(	(	PUNCT
ejpam-4203	118	16	it	it	PRON
ejpam-4203	118	17	2x	2x	VERB
ejpam-4203	118	18	√	√	PROPN
ejpam-4203	118	19	y	y	NOUN
ejpam-4203	118	20	)	)	PUNCT
ejpam-4203	118	21	dxdydt	dxdydt	NOUN
ejpam-4203	118	22	=	=	PUNCT
ejpam-4203	118	23	πk+1	πk+1	NOUN
ejpam-4203	118	24	(	(	PUNCT
ejpam-4203	118	25	−2	−2	NOUN
ejpam-4203	118	26	m	m	NOUN
ejpam-4203	118	27	)	)	PUNCT
ejpam-4203	118	28	e	e	NOUN
ejpam-4203	118	29	1	1	NUM
ejpam-4203	118	30	2	2	NUM
ejpam-4203	118	31	iπ(k+m+v)−iπ(m+v)li−k	iπ(k+m+v)−iπ(m+v)li−k	NOUN
ejpam-4203	118	32	(	(	PUNCT
ejpam-4203	118	33	−eiπ(m+v	−eiπ(m+v	NOUN
ejpam-4203	118	34	)	)	PUNCT
ejpam-4203	118	35	)	)	PUNCT
ejpam-4203	118	36	proof	proof	NOUN
ejpam-4203	118	37	.	.	PUNCT
ejpam-4203	119	1	use	use	VERB
ejpam-4203	119	2	equation	equation	NOUN
ejpam-4203	119	3	(	(	PUNCT
ejpam-4203	119	4	7	7	NUM
ejpam-4203	119	5	)	)	PUNCT
ejpam-4203	119	6	and	and	CCONJ
ejpam-4203	119	7	set	set	VERB
ejpam-4203	119	8	a	a	DET
ejpam-4203	119	9	=	=	SYM
ejpam-4203	119	10	i/2	i/2	X
ejpam-4203	119	11	,	,	PUNCT
ejpam-4203	119	12	b	b	X
ejpam-4203	119	13	=	=	SYM
ejpam-4203	119	14	c	c	NOUN
ejpam-4203	119	15	=	=	SYM
ejpam-4203	119	16	1	1	NUM
ejpam-4203	119	17	and	and	CCONJ
ejpam-4203	119	18	simplify	simplify	VERB
ejpam-4203	119	19	using	use	VERB
ejpam-4203	119	20	equation	equation	NOUN
ejpam-4203	119	21	(	(	PUNCT
ejpam-4203	119	22	64:12:2	64:12:2	NUM
ejpam-4203	119	23	)	)	PUNCT
ejpam-4203	119	24	in	in	ADP
ejpam-4203	119	25	[	[	X
ejpam-4203	119	26	8	8	NUM
ejpam-4203	119	27	]	]	PUNCT
ejpam-4203	119	28	.	.	PUNCT
ejpam-4203	120	1	example	example	NOUN
ejpam-4203	120	2	5	5	NUM
ejpam-4203	120	3	.	.	X
ejpam-4203	120	4	catalan	catalan	PROPN
ejpam-4203	120	5	’s	’s	PART
ejpam-4203	120	6	constant	constant	ADJ
ejpam-4203	120	7	g	g	NOUN
ejpam-4203	120	8	(	(	PUNCT
ejpam-4203	120	9	13	13	NUM
ejpam-4203	120	10	)	)	PUNCT
ejpam-4203	120	11	∫	∫	PROPN
ejpam-4203	121	1	∞	∞	PROPN
ejpam-4203	121	2	0	0	NUM
ejpam-4203	122	1	∫	∫	PROPN
ejpam-4203	122	2	∞	∞	PROPN
ejpam-4203	122	3	0	0	NUM
ejpam-4203	123	1	∫	∫	PROPN
ejpam-4203	123	2	∞	∞	PROPN
ejpam-4203	123	3	0	0	NUM
ejpam-4203	124	1	x2j	x2j	PUNCT
ejpam-4203	124	2	5	5	NUM
ejpam-4203	124	3	4	4	NUM
ejpam-4203	124	4	(	(	PUNCT
ejpam-4203	124	5	t)e−x2−y	t)e−x2−y	PROPN
ejpam-4203	124	6	t3/4y3/4	t3/4y3/4	PROPN
ejpam-4203	124	7	log2	log2	PROPN
ejpam-4203	124	8	(	(	PUNCT
ejpam-4203	124	9	it	it	PRON
ejpam-4203	124	10	2x	2x	VERB
ejpam-4203	124	11	√	√	PROPN
ejpam-4203	124	12	y	y	X
ejpam-4203	124	13	)	)	PUNCT
ejpam-4203	124	14	dxdydt	dxdydt	NOUN
ejpam-4203	124	15	=	=	PUNCT
ejpam-4203	124	16	(	(	PUNCT
ejpam-4203	124	17	−1	−1	NOUN
ejpam-4203	124	18	2	2	NUM
ejpam-4203	124	19	)	)	PUNCT
ejpam-4203	124	20	3/4	3/4	NUM
ejpam-4203	124	21	(	(	PUNCT
ejpam-4203	124	22	π2	π2	X
ejpam-4203	124	23	+	+	CCONJ
ejpam-4203	124	24	48ig	48ig	ADJ
ejpam-4203	124	25	)	)	PUNCT
ejpam-4203	124	26	48π	48π	PROPN
ejpam-4203	125	1	r.	r.	PROPN
ejpam-4203	125	2	reynolds	reynolds	PROPN
ejpam-4203	125	3	,	,	PUNCT
ejpam-4203	125	4	a.	a.	PROPN
ejpam-4203	125	5	stauffer	stauffer	PROPN
ejpam-4203	125	6	/	/	SYM
ejpam-4203	125	7	eur	eur	PROPN
ejpam-4203	125	8	.	.	PUNCT
ejpam-4203	126	1	j.	j.	PROPN
ejpam-4203	126	2	pure	pure	PROPN
ejpam-4203	126	3	appl	appl	PROPN
ejpam-4203	126	4	.	.	PROPN
ejpam-4203	126	5	math	math	PROPN
ejpam-4203	126	6	,	,	PUNCT
ejpam-4203	126	7	15	15	NUM
ejpam-4203	126	8	(	(	PUNCT
ejpam-4203	126	9	2	2	NUM
ejpam-4203	126	10	)	)	PUNCT
ejpam-4203	126	11	(	(	PUNCT
ejpam-4203	126	12	2022	2022	NUM
ejpam-4203	126	13	)	)	PUNCT
ejpam-4203	126	14	,	,	PUNCT
ejpam-4203	126	15	390	390	NUM
ejpam-4203	126	16	-	-	SYM
ejpam-4203	126	17	396	396	NUM
ejpam-4203	126	18	395	395	NUM
ejpam-4203	126	19	proof	proof	NOUN
ejpam-4203	126	20	.	.	PUNCT
ejpam-4203	127	1	use	use	VERB
ejpam-4203	127	2	equation	equation	NOUN
ejpam-4203	127	3	(	(	PUNCT
ejpam-4203	127	4	12	12	NUM
ejpam-4203	127	5	)	)	PUNCT
ejpam-4203	127	6	and	and	CCONJ
ejpam-4203	127	7	set	set	VERB
ejpam-4203	127	8	k	k	PROPN
ejpam-4203	127	9	=	=	PUNCT
ejpam-4203	127	10	−2,m	−2,m	PROPN
ejpam-4203	127	11	=	=	SYM
ejpam-4203	127	12	−3/4	−3/4	NOUN
ejpam-4203	127	13	,	,	PUNCT
ejpam-4203	127	14	v	v	NOUN
ejpam-4203	127	15	=	=	SYM
ejpam-4203	127	16	5/4	5/4	NUM
ejpam-4203	127	17	and	and	CCONJ
ejpam-4203	127	18	simplify	simplify	VERB
ejpam-4203	127	19	using	use	VERB
ejpam-4203	127	20	equation	equation	NOUN
ejpam-4203	127	21	(	(	PUNCT
ejpam-4203	127	22	2.2.1.2.7	2.2.1.2.7	X
ejpam-4203	127	23	)	)	PUNCT
ejpam-4203	127	24	in	in	ADP
ejpam-4203	127	25	[	[	X
ejpam-4203	127	26	7	7	NUM
ejpam-4203	127	27	]	]	PUNCT
ejpam-4203	127	28	.	.	PUNCT
ejpam-4203	127	29	example	example	NOUN
ejpam-4203	128	1	6	6	NUM
ejpam-4203	128	2	.	.	PUNCT
ejpam-4203	129	1	(	(	PUNCT
ejpam-4203	129	2	14	14	NUM
ejpam-4203	129	3	)	)	PUNCT
ejpam-4203	129	4	∫	∫	PROPN
ejpam-4203	130	1	∞	∞	PROPN
ejpam-4203	130	2	0	0	NUM
ejpam-4203	131	1	∫	∫	PROPN
ejpam-4203	131	2	∞	∞	PROPN
ejpam-4203	131	3	0	0	NUM
ejpam-4203	132	1	∫	∫	PROPN
ejpam-4203	132	2	∞	∞	NOUN
ejpam-4203	132	3	0	0	NUM
ejpam-4203	133	1	x3/2j	x3/2j	PROPN
ejpam-4203	133	2	3	3	NUM
ejpam-4203	133	3	4	4	NUM
ejpam-4203	133	4	(	(	PUNCT
ejpam-4203	133	5	t)e−x2−y	t)e−x2−y	PROPN
ejpam-4203	133	6	logk	logk	NOUN
ejpam-4203	133	7	(	(	PUNCT
ejpam-4203	133	8	it	it	PRON
ejpam-4203	133	9	2x	2x	VERB
ejpam-4203	133	10	√	√	PROPN
ejpam-4203	133	11	y	y	X
ejpam-4203	133	12	)	)	PUNCT
ejpam-4203	133	13	t3/4	t3/4	NOUN
ejpam-4203	134	1	√	√	NUM
ejpam-4203	134	2	y	y	PROPN
ejpam-4203	134	3	dxdydt	dxdydt	NOUN
ejpam-4203	134	4	=	=	PUNCT
ejpam-4203	135	1	−	−	PROPN
ejpam-4203	135	2	(	(	PUNCT
ejpam-4203	135	3	2k+1	2k+1	NOUN
ejpam-4203	135	4	−	−	NOUN
ejpam-4203	135	5	1	1	NUM
ejpam-4203	135	6	)	)	PUNCT
ejpam-4203	135	7	e	e	NOUN
ejpam-4203	135	8	iπk	iπk	VERB
ejpam-4203	135	9	2	2	NUM
ejpam-4203	135	10	πk+1ζ(−k	πk+1ζ(−k	NOUN
ejpam-4203	135	11	)	)	PUNCT
ejpam-4203	135	12	23/4	23/4	NUM
ejpam-4203	135	13	proof	proof	NOUN
ejpam-4203	135	14	.	.	PUNCT
ejpam-4203	136	1	use	use	VERB
ejpam-4203	136	2	equation	equation	NOUN
ejpam-4203	136	3	(	(	PUNCT
ejpam-4203	136	4	12	12	NUM
ejpam-4203	136	5	)	)	PUNCT
ejpam-4203	136	6	and	and	CCONJ
ejpam-4203	136	7	set	set	VERB
ejpam-4203	136	8	m	m	PROPN
ejpam-4203	136	9	=	=	NOUN
ejpam-4203	136	10	−3/4	−3/4	NOUN
ejpam-4203	136	11	,	,	PUNCT
ejpam-4203	136	12	v	v	NOUN
ejpam-4203	136	13	=	=	SYM
ejpam-4203	136	14	3/4	3/4	NUM
ejpam-4203	136	15	and	and	CCONJ
ejpam-4203	136	16	simplify	simplify	VERB
ejpam-4203	136	17	using	use	VERB
ejpam-4203	136	18	entry	entry	NOUN
ejpam-4203	136	19	(	(	PUNCT
ejpam-4203	136	20	2	2	NUM
ejpam-4203	136	21	)	)	PUNCT
ejpam-4203	136	22	in	in	ADP
ejpam-4203	136	23	table	table	NOUN
ejpam-4203	136	24	below	below	ADV
ejpam-4203	136	25	(	(	PUNCT
ejpam-4203	136	26	64:7	64:7	NUM
ejpam-4203	136	27	)	)	PUNCT
ejpam-4203	136	28	in	in	ADP
ejpam-4203	136	29	[	[	X
ejpam-4203	136	30	8	8	NUM
ejpam-4203	136	31	]	]	PUNCT
ejpam-4203	136	32	.	.	PUNCT
ejpam-4203	136	33	example	example	NOUN
ejpam-4203	137	1	7	7	NUM
ejpam-4203	137	2	.	.	PUNCT
ejpam-4203	138	1	the	the	DET
ejpam-4203	138	2	fundamental	fundamental	ADJ
ejpam-4203	138	3	constant	constant	ADJ
ejpam-4203	138	4	log(2	log(2	NOUN
ejpam-4203	138	5	)	)	PUNCT
ejpam-4203	138	6	,	,	PUNCT
ejpam-4203	138	7	(	(	PUNCT
ejpam-4203	138	8	15	15	NUM
ejpam-4203	138	9	)	)	PUNCT
ejpam-4203	138	10	∫	∫	PROPN
ejpam-4203	139	1	∞	∞	PROPN
ejpam-4203	139	2	0	0	NUM
ejpam-4203	140	1	∫	∫	PROPN
ejpam-4203	140	2	∞	∞	PROPN
ejpam-4203	140	3	0	0	NUM
ejpam-4203	141	1	∫	∫	PROPN
ejpam-4203	141	2	∞	∞	NOUN
ejpam-4203	141	3	0	0	NUM
ejpam-4203	142	1	x3/2j	x3/2j	PROPN
ejpam-4203	142	2	3	3	NUM
ejpam-4203	142	3	4	4	NUM
ejpam-4203	142	4	(	(	PUNCT
ejpam-4203	142	5	t)e−x2−y	t)e−x2−y	PROPN
ejpam-4203	142	6	t3/4	t3/4	NOUN
ejpam-4203	142	7	√	√	NUM
ejpam-4203	142	8	y	y	PROPN
ejpam-4203	142	9	log	log	NOUN
ejpam-4203	142	10	(	(	PUNCT
ejpam-4203	142	11	it	it	PRON
ejpam-4203	142	12	2x	2x	VERB
ejpam-4203	142	13	√	√	PROPN
ejpam-4203	142	14	y	y	X
ejpam-4203	142	15	)	)	PUNCT
ejpam-4203	142	16	dxdydt	dxdydt	NOUN
ejpam-4203	142	17	=	=	PUNCT
ejpam-4203	143	1	−	−	PROPN
ejpam-4203	143	2	i	i	PRON
ejpam-4203	143	3	log(2	log(2	VERB
ejpam-4203	143	4	)	)	PUNCT
ejpam-4203	144	1	23/4	23/4	NUM
ejpam-4203	144	2	proof	proof	NOUN
ejpam-4203	144	3	.	.	PUNCT
ejpam-4203	145	1	use	use	VERB
ejpam-4203	145	2	equation	equation	NOUN
ejpam-4203	145	3	(	(	PUNCT
ejpam-4203	145	4	14	14	NUM
ejpam-4203	145	5	)	)	PUNCT
ejpam-4203	145	6	apply	apply	VERB
ejpam-4203	145	7	l’hopital	l’hopital	PROPN
ejpam-4203	145	8	’s	’s	PART
ejpam-4203	145	9	rule	rule	NOUN
ejpam-4203	145	10	as	as	ADP
ejpam-4203	145	11	k	k	PROPN
ejpam-4203	145	12	→	→	SYM
ejpam-4203	145	13	−1	−1	NOUN
ejpam-4203	145	14	and	and	CCONJ
ejpam-4203	145	15	simplify	simplify	NOUN
ejpam-4203	145	16	.	.	PUNCT
ejpam-4203	145	17	example	example	NOUN
ejpam-4203	146	1	8	8	NUM
ejpam-4203	146	2	.	.	PUNCT
ejpam-4203	147	1	apéry	apéry	PROPN
ejpam-4203	147	2	’s	’s	PART
ejpam-4203	147	3	constant	constant	ADJ
ejpam-4203	147	4	ζ(3	ζ(3	NOUN
ejpam-4203	147	5	)	)	PUNCT
ejpam-4203	147	6	(	(	PUNCT
ejpam-4203	147	7	16	16	NUM
ejpam-4203	147	8	)	)	PUNCT
ejpam-4203	147	9	∫	∫	PROPN
ejpam-4203	148	1	∞	∞	PROPN
ejpam-4203	148	2	0	0	NUM
ejpam-4203	149	1	∫	∫	PROPN
ejpam-4203	149	2	∞	∞	PROPN
ejpam-4203	149	3	0	0	NUM
ejpam-4203	150	1	∫	∫	PROPN
ejpam-4203	150	2	∞	∞	NOUN
ejpam-4203	150	3	0	0	NUM
ejpam-4203	151	1	x3/2j	x3/2j	PROPN
ejpam-4203	151	2	3	3	NUM
ejpam-4203	151	3	4	4	NUM
ejpam-4203	151	4	(	(	PUNCT
ejpam-4203	151	5	t)e−x2−y	t)e−x2−y	PROPN
ejpam-4203	151	6	t3/4	t3/4	NOUN
ejpam-4203	151	7	√	√	NUM
ejpam-4203	151	8	y	y	PROPN
ejpam-4203	151	9	log3	log3	PROPN
ejpam-4203	151	10	(	(	PUNCT
ejpam-4203	151	11	it	it	PRON
ejpam-4203	151	12	2x	2x	VERB
ejpam-4203	151	13	√	√	PROPN
ejpam-4203	151	14	y	y	X
ejpam-4203	151	15	)	)	PUNCT
ejpam-4203	151	16	dxdydt	dxdydt	NOUN
ejpam-4203	151	17	=	=	SYM
ejpam-4203	151	18	3iζ(3	3iζ(3	ADJ
ejpam-4203	151	19	)	)	PUNCT
ejpam-4203	151	20	4	4	NUM
ejpam-4203	151	21	23/4π2	23/4π2	NUM
ejpam-4203	151	22	proof	proof	NOUN
ejpam-4203	151	23	.	.	PUNCT
ejpam-4203	152	1	use	use	VERB
ejpam-4203	152	2	equation	equation	NOUN
ejpam-4203	152	3	(	(	PUNCT
ejpam-4203	152	4	14	14	NUM
ejpam-4203	152	5	)	)	PUNCT
ejpam-4203	152	6	set	set	VERB
ejpam-4203	152	7	k	k	NOUN
ejpam-4203	152	8	=	=	X
ejpam-4203	152	9	−3	−3	PROPN
ejpam-4203	152	10	and	and	CCONJ
ejpam-4203	152	11	simplify	simplify	VERB
ejpam-4203	152	12	.	.	PUNCT
ejpam-4203	152	13	example	example	NOUN
ejpam-4203	153	1	9	9	NUM
ejpam-4203	153	2	.	.	PUNCT
ejpam-4203	154	1	the	the	DET
ejpam-4203	154	2	fundamental	fundamental	ADJ
ejpam-4203	154	3	constant	constant	ADJ
ejpam-4203	154	4	ζ(5	ζ(5	PROPN
ejpam-4203	154	5	)	)	PUNCT
ejpam-4203	154	6	,	,	PUNCT
ejpam-4203	154	7	(	(	PUNCT
ejpam-4203	154	8	17	17	NUM
ejpam-4203	154	9	)	)	PUNCT
ejpam-4203	154	10	∫	∫	PROPN
ejpam-4203	155	1	∞	∞	PROPN
ejpam-4203	155	2	0	0	NUM
ejpam-4203	156	1	∫	∫	PROPN
ejpam-4203	156	2	∞	∞	PROPN
ejpam-4203	156	3	0	0	NUM
ejpam-4203	157	1	∫	∫	PROPN
ejpam-4203	157	2	∞	∞	NOUN
ejpam-4203	157	3	0	0	NUM
ejpam-4203	158	1	x3/2j	x3/2j	PROPN
ejpam-4203	158	2	3	3	NUM
ejpam-4203	158	3	4	4	NUM
ejpam-4203	158	4	(	(	PUNCT
ejpam-4203	158	5	t)e−x2−y	t)e−x2−y	PROPN
ejpam-4203	158	6	t3/4	t3/4	NOUN
ejpam-4203	158	7	√	√	NUM
ejpam-4203	159	1	y	y	PROPN
ejpam-4203	159	2	log5	log5	PROPN
ejpam-4203	159	3	(	(	PUNCT
ejpam-4203	159	4	it	it	PRON
ejpam-4203	159	5	2x	2x	VERB
ejpam-4203	159	6	√	√	PROPN
ejpam-4203	159	7	y	y	X
ejpam-4203	159	8	)	)	PUNCT
ejpam-4203	159	9	dxdydt	dxdydt	NOUN
ejpam-4203	159	10	=	=	PUNCT
ejpam-4203	159	11	−	−	PROPN
ejpam-4203	159	12	15iζ(5	15iζ(5	NOUN
ejpam-4203	159	13	)	)	PUNCT
ejpam-4203	159	14	16	16	NUM
ejpam-4203	159	15	23/4π4	23/4π4	NUM
ejpam-4203	159	16	proof	proof	NOUN
ejpam-4203	159	17	.	.	PUNCT
ejpam-4203	160	1	use	use	VERB
ejpam-4203	160	2	equation	equation	NOUN
ejpam-4203	160	3	(	(	PUNCT
ejpam-4203	160	4	14	14	NUM
ejpam-4203	160	5	)	)	PUNCT
ejpam-4203	160	6	set	set	VERB
ejpam-4203	160	7	k	k	NOUN
ejpam-4203	160	8	=	=	PUNCT
ejpam-4203	160	9	−5	−5	NOUN
ejpam-4203	160	10	and	and	CCONJ
ejpam-4203	160	11	simplify	simplify	VERB
ejpam-4203	160	12	.	.	PUNCT
ejpam-4203	161	1	6	6	X
ejpam-4203	161	2	.	.	X
ejpam-4203	161	3	discussion	discussion	NOUN
ejpam-4203	161	4	in	in	ADP
ejpam-4203	161	5	this	this	DET
ejpam-4203	161	6	paper	paper	NOUN
ejpam-4203	161	7	,	,	PUNCT
ejpam-4203	161	8	we	we	PRON
ejpam-4203	161	9	have	have	AUX
ejpam-4203	161	10	presented	present	VERB
ejpam-4203	161	11	a	a	DET
ejpam-4203	161	12	novel	novel	ADJ
ejpam-4203	161	13	method	method	NOUN
ejpam-4203	161	14	for	for	ADP
ejpam-4203	161	15	deriving	derive	VERB
ejpam-4203	161	16	a	a	DET
ejpam-4203	161	17	new	new	ADJ
ejpam-4203	161	18	bessel	bessel	NOUN
ejpam-4203	161	19	function	function	VERB
ejpam-4203	161	20	integral	integral	ADJ
ejpam-4203	161	21	transform	transform	NOUN
ejpam-4203	161	22	along	along	ADP
ejpam-4203	161	23	with	with	ADP
ejpam-4203	161	24	some	some	DET
ejpam-4203	161	25	interesting	interesting	ADJ
ejpam-4203	161	26	definite	definite	ADJ
ejpam-4203	161	27	integrals	integral	NOUN
ejpam-4203	161	28	similar	similar	ADJ
ejpam-4203	161	29	to	to	ADP
ejpam-4203	161	30	those	those	PRON
ejpam-4203	161	31	published	publish	VERB
ejpam-4203	161	32	by	by	ADP
ejpam-4203	161	33	prudnikov	prudnikov	PROPN
ejpam-4203	161	34	et	et	PROPN
ejpam-4203	161	35	al	al	PROPN
ejpam-4203	161	36	.	.	PUNCT
ejpam-4203	162	1	[	[	X
ejpam-4203	162	2	9	9	NUM
ejpam-4203	162	3	]	]	PUNCT
ejpam-4203	162	4	,	,	PUNCT
ejpam-4203	162	5	using	use	VERB
ejpam-4203	162	6	contour	contour	NOUN
ejpam-4203	162	7	integration	integration	NOUN
ejpam-4203	162	8	.	.	PUNCT
ejpam-4203	163	1	the	the	DET
ejpam-4203	163	2	results	result	NOUN
ejpam-4203	163	3	presented	present	VERB
ejpam-4203	163	4	were	be	AUX
ejpam-4203	163	5	numerically	numerically	ADV
ejpam-4203	163	6	verified	verify	VERB
ejpam-4203	163	7	for	for	ADP
ejpam-4203	163	8	both	both	CCONJ
ejpam-4203	163	9	real	real	ADJ
ejpam-4203	163	10	and	and	CCONJ
ejpam-4203	163	11	imaginary	imaginary	ADJ
ejpam-4203	163	12	and	and	CCONJ
ejpam-4203	163	13	complex	complex	ADJ
ejpam-4203	163	14	values	value	NOUN
ejpam-4203	163	15	of	of	ADP
ejpam-4203	163	16	the	the	DET
ejpam-4203	163	17	parameters	parameter	NOUN
ejpam-4203	163	18	in	in	ADP
ejpam-4203	163	19	the	the	DET
ejpam-4203	163	20	integrals	integral	NOUN
ejpam-4203	163	21	using	use	VERB
ejpam-4203	163	22	mathematica	mathematica	PROPN
ejpam-4203	163	23	by	by	ADP
ejpam-4203	163	24	wolfram	wolfram	PROPN
ejpam-4203	163	25	.	.	PUNCT
ejpam-4203	164	1	acknowledgements	acknowledgement	NOUN
ejpam-4203	164	2	this	this	DET
ejpam-4203	164	3	research	research	NOUN
ejpam-4203	164	4	is	be	AUX
ejpam-4203	164	5	supported	support	VERB
ejpam-4203	164	6	by	by	ADP
ejpam-4203	164	7	nserc	nserc	PROPN
ejpam-4203	164	8	canada	canada	PROPN
ejpam-4203	164	9	under	under	ADP
ejpam-4203	164	10	grant	grant	PROPN
ejpam-4203	164	11	504070	504070	NUM
ejpam-4203	164	12	.	.	PUNCT
ejpam-4203	165	1	references	reference	NOUN
ejpam-4203	165	2	396	396	NUM
ejpam-4203	165	3	references	reference	NOUN
ejpam-4203	165	4	[	[	X
ejpam-4203	165	5	1	1	NUM
ejpam-4203	165	6	]	]	X
ejpam-4203	165	7	daniel	daniel	PROPN
ejpam-4203	165	8	benest	benest	PROPN
ejpam-4203	165	9	,	,	PUNCT
ejpam-4203	165	10	claude	claude	PROPN
ejpam-4203	165	11	froeschle	froeschle	PROPN
ejpam-4203	165	12	,	,	PUNCT
ejpam-4203	165	13	and	and	CCONJ
ejpam-4203	165	14	elena	elena	PROPN
ejpam-4203	165	15	lega	lega	PROPN
ejpam-4203	165	16	.	.	PUNCT
ejpam-4203	166	1	topics	topic	NOUN
ejpam-4203	166	2	in	in	ADP
ejpam-4203	166	3	gravitational	gravitational	ADJ
ejpam-4203	166	4	dynamics	dynamic	NOUN
ejpam-4203	166	5	.	.	PUNCT
ejpam-4203	167	1	springer	springer	PROPN
ejpam-4203	167	2	berlin	berlin	PROPN
ejpam-4203	167	3	heidelberg	heidelberg	PROPN
ejpam-4203	167	4	,	,	PUNCT
ejpam-4203	167	5	2007	2007	NUM
ejpam-4203	167	6	.	.	PUNCT
ejpam-4203	168	1	[	[	X
ejpam-4203	168	2	2	2	X
ejpam-4203	168	3	]	]	X
ejpam-4203	168	4	daniel	daniel	PROPN
ejpam-4203	168	5	bump	bump	PROPN
ejpam-4203	168	6	.	.	PUNCT
ejpam-4203	169	1	automorphic	automorphic	ADJ
ejpam-4203	169	2	forms	form	NOUN
ejpam-4203	169	3	on	on	ADP
ejpam-4203	169	4	gl	gl	PROPN
ejpam-4203	169	5	(	(	PUNCT
ejpam-4203	169	6	3,pir	3,pir	PROPN
ejpam-4203	169	7	)	)	PUNCT
ejpam-4203	169	8	.	.	PUNCT
ejpam-4203	170	1	springer	springer	NOUN
ejpam-4203	170	2	,	,	PUNCT
ejpam-4203	170	3	cop	cop	NOUN
ejpam-4203	170	4	,	,	PUNCT
ejpam-4203	170	5	1984	1984	NUM
ejpam-4203	170	6	.	.	PUNCT
ejpam-4203	171	1	[	[	X
ejpam-4203	171	2	3	3	X
ejpam-4203	171	3	]	]	PUNCT
ejpam-4203	171	4	nist	nist	NOUN
ejpam-4203	171	5	digital	digital	PROPN
ejpam-4203	171	6	library	library	NOUN
ejpam-4203	171	7	of	of	ADP
ejpam-4203	171	8	mathematical	mathematical	ADJ
ejpam-4203	171	9	functions	function	NOUN
ejpam-4203	171	10	.	.	PUNCT
ejpam-4203	172	1	f.	f.	PROPN
ejpam-4203	172	2	w.	w.	PROPN
ejpam-4203	172	3	j.	j.	PROPN
ejpam-4203	172	4	olver	olver	PROPN
ejpam-4203	172	5	,	,	PUNCT
ejpam-4203	172	6	a.	a.	PROPN
ejpam-4203	172	7	b.	b.	PROPN
ejpam-4203	172	8	olde	olde	PROPN
ejpam-4203	172	9	daalhuis	daalhuis	PROPN
ejpam-4203	172	10	,	,	PUNCT
ejpam-4203	172	11	d.	d.	PROPN
ejpam-4203	172	12	w.	w.	PROPN
ejpam-4203	172	13	lozier	lozier	PROPN
ejpam-4203	172	14	,	,	PUNCT
ejpam-4203	172	15	b.	b.	PROPN
ejpam-4203	172	16	i.	i.	PROPN
ejpam-4203	172	17	schneider	schneider	PROPN
ejpam-4203	172	18	,	,	PUNCT
ejpam-4203	172	19	r.	r.	PROPN
ejpam-4203	172	20	f.	f.	PROPN
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ejpam-4203	172	22	,	,	PUNCT
ejpam-4203	172	23	c.	c.	PROPN
ejpam-4203	172	24	w.	w.	PROPN
ejpam-4203	172	25	clark	clark	PROPN
ejpam-4203	172	26	,	,	PUNCT
ejpam-4203	172	27	b.	b.	PROPN
ejpam-4203	172	28	r.	r.	PROPN
ejpam-4203	172	29	miller	miller	PROPN
ejpam-4203	172	30	,	,	PUNCT
ejpam-4203	172	31	b.	b.	PROPN
ejpam-4203	173	1	v.	v.	PROPN
ejpam-4203	173	2	saunders	saunders	PROPN
ejpam-4203	173	3	,	,	PUNCT
ejpam-4203	173	4	h.	h.	PROPN
ejpam-4203	173	5	s.	s.	PROPN
ejpam-4203	173	6	cohl	cohl	PROPN
ejpam-4203	173	7	,	,	PUNCT
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ejpam-4203	173	9	m.	m.	PROPN
ejpam-4203	173	10	a.	a.	PROPN
ejpam-4203	173	11	mcclain	mcclain	PROPN
ejpam-4203	173	12	,	,	PUNCT
ejpam-4203	173	13	eds	eds	PROPN
ejpam-4203	173	14	.	.	PUNCT
ejpam-4203	174	1	[	[	X
ejpam-4203	174	2	4	4	NUM
ejpam-4203	174	3	]	]	X
ejpam-4203	174	4	f.y.ayant	f.y.ayant	ADJ
ejpam-4203	174	5	.	.	PUNCT
ejpam-4203	174	6	euler	euler	PROPN
ejpam-4203	174	7	type	type	NOUN
ejpam-4203	174	8	triple	triple	ADJ
ejpam-4203	174	9	integrals	integral	NOUN
ejpam-4203	174	10	involving	involve	VERB
ejpam-4203	174	11	,	,	PUNCT
ejpam-4203	174	12	general	general	ADJ
ejpam-4203	174	13	class	class	NOUN
ejpam-4203	174	14	of	of	ADP
ejpam-4203	174	15	polynomialsand	polynomialsand	PROPN
ejpam-4203	174	16	multivariable	multivariable	PROPN
ejpam-4203	174	17	a	a	DET
ejpam-4203	174	18	-	-	PUNCT
ejpam-4203	174	19	function	function	NOUN
ejpam-4203	174	20	.	.	PUNCT
ejpam-4203	175	1	international	international	ADJ
ejpam-4203	175	2	journal	journal	PROPN
ejpam-4203	175	3	of	of	ADP
ejpam-4203	175	4	mathematics	mathematics	NOUN
ejpam-4203	175	5	trends	trend	NOUN
ejpam-4203	175	6	and	and	CCONJ
ejpam-4203	175	7	technology	technology	NOUN
ejpam-4203	175	8	ijmtt	ijmtt	ADJ
ejpam-4203	175	9	.	.	PUNCT
ejpam-4203	176	1	[	[	X
ejpam-4203	176	2	5	5	NUM
ejpam-4203	176	3	]	]	PUNCT
ejpam-4203	176	4	i.	i.	PROPN
ejpam-4203	176	5	s.	s.	PROPN
ejpam-4203	176	6	gradshteyn	gradshteyn	PROPN
ejpam-4203	176	7	and	and	CCONJ
ejpam-4203	176	8	i.	i.	PROPN
ejpam-4203	176	9	m.	m.	PROPN
ejpam-4203	176	10	ryzhik	ryzhik	PROPN
ejpam-4203	176	11	.	.	PUNCT
ejpam-4203	177	1	table	table	NOUN
ejpam-4203	177	2	of	of	ADP
ejpam-4203	177	3	integrals	integral	NOUN
ejpam-4203	177	4	,	,	PUNCT
ejpam-4203	177	5	series	series	NOUN
ejpam-4203	177	6	,	,	PUNCT
ejpam-4203	177	7	and	and	CCONJ
ejpam-4203	177	8	products	product	NOUN
ejpam-4203	177	9	.	.	PUNCT
ejpam-4203	178	1	elsevier	elsevier	NOUN
ejpam-4203	178	2	/	/	SYM
ejpam-4203	178	3	academic	academic	ADJ
ejpam-4203	178	4	press	press	NOUN
ejpam-4203	178	5	,	,	PUNCT
ejpam-4203	178	6	amsterdam	amsterdam	PROPN
ejpam-4203	178	7	,	,	PUNCT
ejpam-4203	178	8	seventh	seventh	ADJ
ejpam-4203	178	9	edition	edition	NOUN
ejpam-4203	178	10	,	,	PUNCT
ejpam-4203	178	11	2007	2007	NUM
ejpam-4203	178	12	.	.	PUNCT
ejpam-4203	179	1	[	[	X
ejpam-4203	179	2	6	6	NUM
ejpam-4203	179	3	]	]	PUNCT
ejpam-4203	179	4	b.	b.	PROPN
ejpam-4203	179	5	g.	g.	PROPN
ejpam-4203	179	6	korenev	korenev	PROPN
ejpam-4203	179	7	.	.	PROPN
ejpam-4203	179	8	bessel	bessel	ADJ
ejpam-4203	179	9	functions	function	NOUN
ejpam-4203	179	10	and	and	CCONJ
ejpam-4203	179	11	their	their	PRON
ejpam-4203	179	12	applications	application	NOUN
ejpam-4203	179	13	.	.	PUNCT
ejpam-4203	180	1	crc	crc	PROPN
ejpam-4203	180	2	press	press	PROPN
ejpam-4203	180	3	,	,	PUNCT
ejpam-4203	180	4	07	07	NUM
ejpam-4203	180	5	2002	2002	NUM
ejpam-4203	180	6	.	.	PUNCT
ejpam-4203	181	1	[	[	X
ejpam-4203	181	2	7	7	X
ejpam-4203	181	3	]	]	X
ejpam-4203	181	4	leonard	leonard	PROPN
ejpam-4203	181	5	lewin	lewin	PROPN
ejpam-4203	181	6	.	.	PUNCT
ejpam-4203	182	1	polylogarithms	polylogarithm	NOUN
ejpam-4203	182	2	and	and	CCONJ
ejpam-4203	182	3	associated	associated	ADJ
ejpam-4203	182	4	functions	function	NOUN
ejpam-4203	182	5	.	.	PUNCT
ejpam-4203	183	1	north	north	NOUN
ejpam-4203	183	2	holland	holland	PROPN
ejpam-4203	183	3	,	,	PUNCT
ejpam-4203	183	4	1981	1981	NUM
ejpam-4203	183	5	.	.	PUNCT
ejpam-4203	184	1	[	[	X
ejpam-4203	184	2	8	8	X
ejpam-4203	184	3	]	]	X
ejpam-4203	184	4	keith	keith	PROPN
ejpam-4203	184	5	b.	b.	PROPN
ejpam-4203	184	6	oldham	oldham	PROPN
ejpam-4203	184	7	,	,	PUNCT
ejpam-4203	184	8	jan	jan	PROPN
ejpam-4203	184	9	myland	myland	PROPN
ejpam-4203	184	10	,	,	PUNCT
ejpam-4203	184	11	and	and	CCONJ
ejpam-4203	184	12	jerome	jerome	PROPN
ejpam-4203	184	13	spanier	spanier	NOUN
ejpam-4203	184	14	.	.	PUNCT
ejpam-4203	185	1	an	an	DET
ejpam-4203	185	2	atlas	atlas	PROPN
ejpam-4203	185	3	of	of	ADP
ejpam-4203	185	4	functions	function	NOUN
ejpam-4203	185	5	:	:	PUNCT
ejpam-4203	185	6	with	with	ADP
ejpam-4203	185	7	equator	equator	NOUN
ejpam-4203	185	8	,	,	PUNCT
ejpam-4203	185	9	the	the	DET
ejpam-4203	185	10	atlas	atlas	PROPN
ejpam-4203	185	11	function	function	PROPN
ejpam-4203	185	12	calculator	calculator	NOUN
ejpam-4203	185	13	.	.	PUNCT
ejpam-4203	186	1	springer	springer	NOUN
ejpam-4203	186	2	science	science	PROPN
ejpam-4203	186	3	&	&	CCONJ
ejpam-4203	186	4	business	business	NOUN
ejpam-4203	186	5	media	medium	NOUN
ejpam-4203	186	6	,	,	PUNCT
ejpam-4203	186	7	07	07	NUM
ejpam-4203	186	8	2010	2010	NUM
ejpam-4203	186	9	.	.	PUNCT
ejpam-4203	187	1	[	[	X
ejpam-4203	187	2	9	9	NUM
ejpam-4203	187	3	]	]	PUNCT
ejpam-4203	187	4	anatoliĭ	anatoliĭ	NOUN
ejpam-4203	187	5	platonovich	platonovich	PROPN
ejpam-4203	187	6	prudnikov	prudnikov	PROPN
ejpam-4203	187	7	,	,	PUNCT
ejpam-4203	187	8	yuriĭ	yuriĭ	NOUN
ejpam-4203	187	9	aleksandrovich	aleksandrovich	NOUN
ejpam-4203	187	10	brychkov	brychkov	NOUN
ejpam-4203	187	11	,	,	PUNCT
ejpam-4203	187	12	and	and	CCONJ
ejpam-4203	187	13	oleg	oleg	PROPN
ejpam-4203	187	14	igorevich	igorevich	PROPN
ejpam-4203	187	15	marichev	marichev	PROPN
ejpam-4203	187	16	.	.	PUNCT
ejpam-4203	188	1	integrals	integral	NOUN
ejpam-4203	188	2	and	and	CCONJ
ejpam-4203	188	3	series	series	NOUN
ejpam-4203	188	4	:	:	PUNCT
ejpam-4203	188	5	special	special	ADJ
ejpam-4203	188	6	functions	function	NOUN
ejpam-4203	188	7	volume	volume	NOUN
ejpam-4203	188	8	2	2	NUM
ejpam-4203	188	9	.	.	PUNCT
ejpam-4203	188	10	crc	crc	PROPN
ejpam-4203	188	11	press	press	PROPN
ejpam-4203	188	12	,	,	PUNCT
ejpam-4203	188	13	1986	1986	NUM
ejpam-4203	188	14	.	.	PUNCT
ejpam-4203	189	1	[	[	X
ejpam-4203	189	2	10	10	NUM
ejpam-4203	189	3	]	]	X
ejpam-4203	189	4	robert	robert	PROPN
ejpam-4203	189	5	reynolds	reynolds	PROPN
ejpam-4203	189	6	and	and	CCONJ
ejpam-4203	189	7	allan	allan	PROPN
ejpam-4203	189	8	stauffer	stauffer	PROPN
ejpam-4203	189	9	.	.	PUNCT
ejpam-4203	190	1	a	a	DET
ejpam-4203	190	2	method	method	NOUN
ejpam-4203	190	3	for	for	ADP
ejpam-4203	190	4	evaluating	evaluate	VERB
ejpam-4203	190	5	definite	definite	ADJ
ejpam-4203	190	6	integrals	integral	NOUN
ejpam-4203	190	7	in	in	ADP
ejpam-4203	190	8	terms	term	NOUN
ejpam-4203	190	9	of	of	ADP
ejpam-4203	190	10	special	special	ADJ
ejpam-4203	190	11	functions	function	NOUN
ejpam-4203	190	12	with	with	ADP
ejpam-4203	190	13	examples	example	NOUN
ejpam-4203	190	14	.	.	PUNCT
ejpam-4203	191	1	international	international	ADJ
ejpam-4203	191	2	mathematical	mathematical	PROPN
ejpam-4203	191	3	forum	forum	PROPN
ejpam-4203	191	4	,	,	PUNCT
ejpam-4203	191	5	15:235–244	15:235–244	PROPN
ejpam-4203	191	6	,	,	PUNCT
ejpam-4203	191	7	2020	2020	NUM
ejpam-4203	191	8	.	.	PUNCT