id	sid	tid	token	lemma	pos
ejpam-7023	1	1	european	european	PROPN
ejpam-7023	1	2	journal	journal	PROPN
ejpam-7023	1	3	of	of	ADP
ejpam-7023	1	4	pure	pure	ADJ
ejpam-7023	1	5	and	and	CCONJ
ejpam-7023	1	6	applied	applied	ADJ
ejpam-7023	1	7	mathematics	mathematic	NOUN
ejpam-7023	1	8	2025	2025	NUM
ejpam-7023	1	9	,	,	PUNCT
ejpam-7023	1	10	vol	vol	NOUN
ejpam-7023	1	11	.	.	PROPN
ejpam-7023	1	12	18	18	NUM
ejpam-7023	1	13	,	,	PUNCT
ejpam-7023	1	14	issue	issue	NOUN
ejpam-7023	1	15	4	4	NUM
ejpam-7023	1	16	,	,	PUNCT
ejpam-7023	1	17	article	article	NOUN
ejpam-7023	1	18	number	number	NOUN
ejpam-7023	1	19	7023	7023	NUM
ejpam-7023	1	20	issn	issn	VERB
ejpam-7023	1	21	1307	1307	NUM
ejpam-7023	1	22	-	-	SYM
ejpam-7023	1	23	5543	5543	NUM
ejpam-7023	1	24	–	–	PUNCT
ejpam-7023	1	25	ejpam.com	ejpam.com	X
ejpam-7023	1	26	published	publish	VERB
ejpam-7023	1	27	by	by	ADP
ejpam-7023	1	28	new	new	PROPN
ejpam-7023	1	29	york	york	PROPN
ejpam-7023	1	30	business	business	PROPN
ejpam-7023	1	31	global	global	ADJ
ejpam-7023	1	32	generalization	generalization	NOUN
ejpam-7023	1	33	of	of	ADP
ejpam-7023	1	34	an	an	DET
ejpam-7023	1	35	integral	integral	ADJ
ejpam-7023	1	36	related	relate	VERB
ejpam-7023	1	37	to	to	ADP
ejpam-7023	1	38	stieltjes	stieltjes	PROPN
ejpam-7023	1	39	moment	moment	PROPN
ejpam-7023	1	40	problem	problem	PROPN
ejpam-7023	1	41	irshad	irshad	PROPN
ejpam-7023	1	42	ayoob	ayoob	PROPN
ejpam-7023	1	43	department	department	PROPN
ejpam-7023	1	44	of	of	ADP
ejpam-7023	1	45	mathematics	mathematics	PROPN
ejpam-7023	1	46	and	and	CCONJ
ejpam-7023	1	47	sciences	science	NOUN
ejpam-7023	1	48	,	,	PUNCT
ejpam-7023	1	49	prince	prince	PROPN
ejpam-7023	1	50	sultan	sultan	PROPN
ejpam-7023	1	51	university	university	PROPN
ejpam-7023	1	52	,	,	PUNCT
ejpam-7023	1	53	p.o	p.o	PROPN
ejpam-7023	1	54	.	.	PROPN
ejpam-7023	1	55	box	box	PROPN
ejpam-7023	1	56	66833	66833	NUM
ejpam-7023	1	57	,	,	PUNCT
ejpam-7023	1	58	riyadh	riyadh	PROPN
ejpam-7023	1	59	11586	11586	NUM
ejpam-7023	1	60	,	,	PUNCT
ejpam-7023	1	61	saudi	saudi	PROPN
ejpam-7023	1	62	arabia	arabia	PROPN
ejpam-7023	1	63	abstract	abstract	NOUN
ejpam-7023	1	64	.	.	PUNCT
ejpam-7023	2	1	in	in	ADP
ejpam-7023	2	2	connection	connection	NOUN
ejpam-7023	2	3	with	with	ADP
ejpam-7023	2	4	the	the	DET
ejpam-7023	2	5	non	non	NOUN
ejpam-7023	2	6	-	-	NOUN
ejpam-7023	2	7	uniqueness	uniqueness	NOUN
ejpam-7023	2	8	of	of	ADP
ejpam-7023	2	9	the	the	DET
ejpam-7023	2	10	stieltjes	stieltjes	NOUN
ejpam-7023	2	11	moment	moment	NOUN
ejpam-7023	2	12	problem	problem	NOUN
ejpam-7023	2	13	on	on	ADP
ejpam-7023	2	14	(	(	PUNCT
ejpam-7023	2	15	0,∞	0,∞	NUM
ejpam-7023	2	16	)	)	PUNCT
ejpam-7023	2	17	,	,	PUNCT
ejpam-7023	2	18	stieltjes	stieltjes	PROPN
ejpam-7023	2	19	constructed	construct	VERB
ejpam-7023	2	20	the	the	DET
ejpam-7023	2	21	nontrivial	nontrivial	NOUN
ejpam-7023	2	22	function	function	NOUN
ejpam-7023	2	23	f(x	f(x	PROPN
ejpam-7023	2	24	)	)	PUNCT
ejpam-7023	3	1	=	=	PUNCT
ejpam-7023	3	2	e−x1/4	e−x1/4	PROPN
ejpam-7023	3	3	sin	sin	NOUN
ejpam-7023	3	4	(	(	PUNCT
ejpam-7023	3	5	x1/4	x1/4	PROPN
ejpam-7023	3	6	)	)	PUNCT
ejpam-7023	4	1	satisfying	satisfy	VERB
ejpam-7023	4	2	∫∞	∫∞	NOUN
ejpam-7023	4	3	0	0	PUNCT
ejpam-7023	4	4	xnf(x	xnf(x	NOUN
ejpam-7023	4	5	)	)	PUNCT
ejpam-7023	4	6	dx	dx	PROPN
ejpam-7023	5	1	=	=	SYM
ejpam-7023	5	2	0	0	PROPN
ejpam-7023	5	3	for	for	ADP
ejpam-7023	5	4	all	all	DET
ejpam-7023	5	5	integers	integer	NOUN
ejpam-7023	5	6	n	n	PRON
ejpam-7023	5	7	≥	≥	NOUN
ejpam-7023	5	8	0	0	NUM
ejpam-7023	5	9	.	.	PUNCT
ejpam-7023	6	1	we	we	PRON
ejpam-7023	6	2	extend	extend	VERB
ejpam-7023	6	3	this	this	PRON
ejpam-7023	6	4	by	by	ADP
ejpam-7023	6	5	considering	consider	VERB
ejpam-7023	6	6	i(k	i(k	PROPN
ejpam-7023	6	7	)	)	PUNCT
ejpam-7023	6	8	=	=	SYM
ejpam-7023	7	1	∫	∫	PROPN
ejpam-7023	7	2	∞	∞	NUM
ejpam-7023	7	3	0	0	NUM
ejpam-7023	8	1	e−x1/4	e−x1/4	PROPN
ejpam-7023	8	2	sin	sin	NOUN
ejpam-7023	8	3	(	(	PUNCT
ejpam-7023	8	4	x1/4	x1/4	PROPN
ejpam-7023	8	5	)	)	PUNCT
ejpam-7023	9	1	xk	xk	PROPN
ejpam-7023	9	2	dx	dx	PROPN
ejpam-7023	9	3	for	for	ADP
ejpam-7023	9	4	real	real	ADJ
ejpam-7023	9	5	k	k	PROPN
ejpam-7023	9	6	≥	≥	PROPN
ejpam-7023	9	7	0	0	NUM
ejpam-7023	9	8	,	,	PUNCT
ejpam-7023	9	9	evaluating	evaluate	VERB
ejpam-7023	9	10	i(k	i(k	PROPN
ejpam-7023	9	11	)	)	PUNCT
ejpam-7023	9	12	explicitly	explicitly	ADV
ejpam-7023	9	13	and	and	CCONJ
ejpam-7023	9	14	proving	prove	VERB
ejpam-7023	9	15	i(k	i(k	PROPN
ejpam-7023	9	16	)	)	PUNCT
ejpam-7023	10	1	=	=	SYM
ejpam-7023	10	2	0	0	PUNCT
ejpam-7023	11	1	if	if	SCONJ
ejpam-7023	11	2	and	and	CCONJ
ejpam-7023	11	3	only	only	ADV
ejpam-7023	11	4	if	if	SCONJ
ejpam-7023	11	5	k	k	PROPN
ejpam-7023	11	6	∈	∈	PROPN
ejpam-7023	11	7	z≥0	z≥0	PROPN
ejpam-7023	11	8	.	.	PUNCT
ejpam-7023	12	1	more	more	ADV
ejpam-7023	12	2	generally	generally	ADV
ejpam-7023	12	3	,	,	PUNCT
ejpam-7023	12	4	for	for	ADP
ejpam-7023	12	5	parameters	parameter	NOUN
ejpam-7023	12	6	m	m	VERB
ejpam-7023	12	7	>	>	X
ejpam-7023	12	8	0	0	PROPN
ejpam-7023	12	9	,	,	PUNCT
ejpam-7023	12	10	α	α	NOUN
ejpam-7023	12	11	>	>	X
ejpam-7023	12	12	0	0	PROPN
ejpam-7023	12	13	,	,	PUNCT
ejpam-7023	12	14	β	β	X
ejpam-7023	12	15	∈	∈	NOUN
ejpam-7023	12	16	r	r	NOUN
ejpam-7023	12	17	,	,	PUNCT
ejpam-7023	12	18	q	q	NOUN
ejpam-7023	12	19	,	,	PUNCT
ejpam-7023	12	20	k	k	PROPN
ejpam-7023	12	21	∈	∈	PROPN
ejpam-7023	13	1	r	r	NOUN
ejpam-7023	13	2	we	we	PRON
ejpam-7023	13	3	analyze	analyze	VERB
ejpam-7023	13	4	im	im	PRON
ejpam-7023	13	5	,	,	PUNCT
ejpam-7023	13	6	q(k	q(k	PROPN
ejpam-7023	13	7	,	,	PUNCT
ejpam-7023	13	8	α	α	X
ejpam-7023	13	9	,	,	PUNCT
ejpam-7023	13	10	β	β	NOUN
ejpam-7023	13	11	)	)	PUNCT
ejpam-7023	13	12	=	=	SYM
ejpam-7023	14	1	∫	∫	PROPN
ejpam-7023	14	2	∞	∞	NUM
ejpam-7023	14	3	0	0	NUM
ejpam-7023	14	4	e−αx1	e−αx1	PROPN
ejpam-7023	14	5	/	/	SYM
ejpam-7023	14	6	m	m	NOUN
ejpam-7023	14	7	sin	sin	NOUN
ejpam-7023	14	8	(	(	PUNCT
ejpam-7023	14	9	βx1	βx1	PROPN
ejpam-7023	14	10	/	/	SYM
ejpam-7023	14	11	m	m	NOUN
ejpam-7023	14	12	)	)	PUNCT
ejpam-7023	14	13	xk(x1	xk(x1	PROPN
ejpam-7023	14	14	/	/	SYM
ejpam-7023	14	15	m)q	m)q	PROPN
ejpam-7023	14	16	dx	dx	PROPN
ejpam-7023	14	17	,	,	PUNCT
ejpam-7023	14	18	derive	derive	VERB
ejpam-7023	14	19	a	a	DET
ejpam-7023	14	20	closed	closed	ADJ
ejpam-7023	14	21	form	form	NOUN
ejpam-7023	14	22	,	,	PUNCT
ejpam-7023	14	23	and	and	CCONJ
ejpam-7023	14	24	give	give	VERB
ejpam-7023	14	25	necessary	necessary	ADJ
ejpam-7023	14	26	and	and	CCONJ
ejpam-7023	14	27	sufficient	sufficient	ADJ
ejpam-7023	14	28	conditions	condition	NOUN
ejpam-7023	14	29	for	for	ADP
ejpam-7023	14	30	its	its	PRON
ejpam-7023	14	31	vanishing	vanishing	NOUN
ejpam-7023	14	32	.	.	PUNCT
ejpam-7023	15	1	we	we	PRON
ejpam-7023	15	2	also	also	ADV
ejpam-7023	15	3	establish	establish	VERB
ejpam-7023	15	4	cosine	cosine	NOUN
ejpam-7023	15	5	analogues	analogue	NOUN
ejpam-7023	15	6	,	,	PUNCT
ejpam-7023	15	7	both	both	PRON
ejpam-7023	15	8	for	for	ADP
ejpam-7023	15	9	the	the	DET
ejpam-7023	15	10	stieltjes	stieltjes	PROPN
ejpam-7023	15	11	example	example	NOUN
ejpam-7023	15	12	and	and	CCONJ
ejpam-7023	15	13	for	for	SCONJ
ejpam-7023	15	14	the	the	DET
ejpam-7023	15	15	generalized	generalized	ADJ
ejpam-7023	15	16	integral	integral	ADJ
ejpam-7023	15	17	mentioned	mention	VERB
ejpam-7023	15	18	above	above	ADV
ejpam-7023	15	19	.	.	PUNCT
ejpam-7023	16	1	as	as	ADP
ejpam-7023	16	2	a	a	DET
ejpam-7023	16	3	consequence	consequence	NOUN
ejpam-7023	16	4	,	,	PUNCT
ejpam-7023	16	5	we	we	PRON
ejpam-7023	16	6	obtain	obtain	VERB
ejpam-7023	16	7	integral	integral	ADJ
ejpam-7023	16	8	representations	representation	NOUN
ejpam-7023	16	9	of	of	ADP
ejpam-7023	16	10	γ(a	γ(a	NOUN
ejpam-7023	16	11	)	)	PUNCT
ejpam-7023	16	12	for	for	ADP
ejpam-7023	16	13	suitable	suitable	ADJ
ejpam-7023	16	14	a	a	DET
ejpam-7023	16	15	>	>	X
ejpam-7023	16	16	0	0	NUM
ejpam-7023	16	17	,	,	PUNCT
ejpam-7023	16	18	as	as	ADV
ejpam-7023	16	19	well	well	ADV
ejpam-7023	16	20	as	as	ADP
ejpam-7023	16	21	integral	integral	ADJ
ejpam-7023	16	22	formulas	formula	NOUN
ejpam-7023	16	23	for	for	ADP
ejpam-7023	16	24	several	several	ADJ
ejpam-7023	16	25	classical	classical	ADJ
ejpam-7023	16	26	constants	constant	NOUN
ejpam-7023	16	27	arising	arise	VERB
ejpam-7023	16	28	from	from	ADP
ejpam-7023	16	29	gamma	gamma	NOUN
ejpam-7023	16	30	function	function	NOUN
ejpam-7023	16	31	.	.	PUNCT
ejpam-7023	17	1	to	to	PART
ejpam-7023	17	2	understand	understand	VERB
ejpam-7023	17	3	the	the	DET
ejpam-7023	17	4	importance	importance	NOUN
ejpam-7023	17	5	of	of	ADP
ejpam-7023	17	6	integrals	integral	NOUN
ejpam-7023	17	7	that	that	PRON
ejpam-7023	17	8	vanish	vanish	VERB
ejpam-7023	17	9	for	for	ADP
ejpam-7023	17	10	every	every	DET
ejpam-7023	17	11	value	value	NOUN
ejpam-7023	17	12	of	of	ADP
ejpam-7023	17	13	a	a	DET
ejpam-7023	17	14	continuous	continuous	ADJ
ejpam-7023	17	15	parameter	parameter	NOUN
ejpam-7023	17	16	,	,	PUNCT
ejpam-7023	17	17	we	we	PRON
ejpam-7023	17	18	will	will	AUX
ejpam-7023	17	19	also	also	ADV
ejpam-7023	17	20	discuss	discuss	VERB
ejpam-7023	17	21	salem	salem	NOUN
ejpam-7023	17	22	’s	’s	PART
ejpam-7023	17	23	equivalence	equivalence	NOUN
ejpam-7023	17	24	of	of	ADP
ejpam-7023	17	25	the	the	DET
ejpam-7023	17	26	riemann	riemann	PROPN
ejpam-7023	17	27	hypothesis	hypothesis	NOUN
ejpam-7023	17	28	,	,	PUNCT
ejpam-7023	17	29	which	which	PRON
ejpam-7023	17	30	is	be	AUX
ejpam-7023	17	31	formulated	formulate	VERB
ejpam-7023	17	32	in	in	ADP
ejpam-7023	17	33	terms	term	NOUN
ejpam-7023	17	34	of	of	ADP
ejpam-7023	17	35	such	such	DET
ejpam-7023	17	36	a	a	DET
ejpam-7023	17	37	parameter	parameter	NOUN
ejpam-7023	17	38	-	-	PUNCT
ejpam-7023	17	39	dependent	dependent	ADJ
ejpam-7023	17	40	integral	integral	ADJ
ejpam-7023	17	41	.	.	PUNCT
ejpam-7023	18	1	2020	2020	NUM
ejpam-7023	18	2	mathematics	mathematic	NOUN
ejpam-7023	18	3	subject	subject	NOUN
ejpam-7023	18	4	classifications	classification	NOUN
ejpam-7023	18	5	:	:	PUNCT
ejpam-7023	18	6	44a60	44a60	NUM
ejpam-7023	18	7	,	,	PUNCT
ejpam-7023	18	8	33b15	33b15	NUM
ejpam-7023	18	9	,	,	PUNCT
ejpam-7023	18	10	26b15	26b15	NUM
ejpam-7023	18	11	key	key	ADJ
ejpam-7023	18	12	words	word	NOUN
ejpam-7023	18	13	and	and	CCONJ
ejpam-7023	18	14	phrases	phrase	NOUN
ejpam-7023	18	15	:	:	PUNCT
ejpam-7023	18	16	moment	moment	NOUN
ejpam-7023	18	17	problem	problem	NOUN
ejpam-7023	18	18	,	,	PUNCT
ejpam-7023	18	19	gamma	gamma	NOUN
ejpam-7023	18	20	function	function	PROPN
ejpam-7023	18	21	,	,	PUNCT
ejpam-7023	18	22	definite	definite	ADJ
ejpam-7023	18	23	integral	integral	ADJ
ejpam-7023	18	24	1	1	NUM
ejpam-7023	18	25	.	.	PUNCT
ejpam-7023	19	1	introduction	introduction	NOUN
ejpam-7023	19	2	definite	definite	ADJ
ejpam-7023	19	3	integrals	integral	NOUN
ejpam-7023	19	4	are	be	AUX
ejpam-7023	19	5	widely	widely	ADV
ejpam-7023	19	6	used	use	VERB
ejpam-7023	19	7	in	in	ADP
ejpam-7023	19	8	both	both	CCONJ
ejpam-7023	19	9	pure	pure	ADJ
ejpam-7023	19	10	and	and	CCONJ
ejpam-7023	19	11	applied	applied	ADJ
ejpam-7023	19	12	mathematics	mathematic	NOUN
ejpam-7023	19	13	.	.	PUNCT
ejpam-7023	20	1	while	while	SCONJ
ejpam-7023	20	2	many	many	ADJ
ejpam-7023	20	3	can	can	AUX
ejpam-7023	20	4	be	be	AUX
ejpam-7023	20	5	solved	solve	VERB
ejpam-7023	20	6	with	with	ADP
ejpam-7023	20	7	basic	basic	ADJ
ejpam-7023	20	8	methods	method	NOUN
ejpam-7023	20	9	like	like	ADP
ejpam-7023	20	10	substitution	substitution	NOUN
ejpam-7023	20	11	or	or	CCONJ
ejpam-7023	20	12	integration	integration	NOUN
ejpam-7023	20	13	by	by	ADP
ejpam-7023	20	14	parts	part	NOUN
ejpam-7023	20	15	,	,	PUNCT
ejpam-7023	20	16	numerous	numerous	ADJ
ejpam-7023	20	17	integrals	integral	NOUN
ejpam-7023	20	18	are	be	AUX
ejpam-7023	20	19	non	non	ADJ
ejpam-7023	20	20	-	-	ADJ
ejpam-7023	20	21	elementary	elementary	ADJ
ejpam-7023	20	22	and	and	CCONJ
ejpam-7023	20	23	can	can	AUX
ejpam-7023	20	24	not	not	PART
ejpam-7023	20	25	be	be	AUX
ejpam-7023	20	26	expressed	express	VERB
ejpam-7023	20	27	using	use	VERB
ejpam-7023	20	28	standard	standard	ADJ
ejpam-7023	20	29	functions	function	NOUN
ejpam-7023	20	30	.	.	PUNCT
ejpam-7023	21	1	evaluating	evaluate	VERB
ejpam-7023	21	2	these	these	PRON
ejpam-7023	21	3	requires	require	VERB
ejpam-7023	21	4	advanced	advanced	ADJ
ejpam-7023	21	5	techniques	technique	NOUN
ejpam-7023	21	6	,	,	PUNCT
ejpam-7023	21	7	such	such	ADJ
ejpam-7023	21	8	as	as	ADP
ejpam-7023	21	9	transformations	transformation	NOUN
ejpam-7023	21	10	(	(	PUNCT
ejpam-7023	21	11	laplace	laplace	NOUN
ejpam-7023	21	12	,	,	PUNCT
ejpam-7023	21	13	mellin	mellin	PROPN
ejpam-7023	21	14	)	)	PUNCT
ejpam-7023	21	15	,	,	PUNCT
ejpam-7023	21	16	complex	complex	ADJ
ejpam-7023	21	17	doi	doi	NOUN
ejpam-7023	21	18	:	:	PUNCT
ejpam-7023	21	19	https://doi.org/10.29020/nybg.ejpam.v18i4.7023	https://doi.org/10.29020/nybg.ejpam.v18i4.7023	NUM
ejpam-7023	21	20	email	email	NOUN
ejpam-7023	21	21	address	address	NOUN
ejpam-7023	21	22	:	:	PUNCT
ejpam-7023	21	23	iayoub@psu.edu.sa	iayoub@psu.edu.sa	PROPN
ejpam-7023	21	24	(	(	PUNCT
ejpam-7023	21	25	i.	i.	PROPN
ejpam-7023	21	26	ayoob	ayoob	PROPN
ejpam-7023	21	27	)	)	PUNCT
ejpam-7023	21	28	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-7023	22	1	1	1	NUM
ejpam-7023	22	2	copyright	copyright	NOUN
ejpam-7023	22	3	:	:	PUNCT
ejpam-7023	22	4	©	©	PROPN
ejpam-7023	22	5	2025	2025	NUM
ejpam-7023	22	6	the	the	DET
ejpam-7023	22	7	author(s	author(s	NOUN
ejpam-7023	22	8	)	)	PUNCT
ejpam-7023	22	9	.	.	PUNCT
ejpam-7023	23	1	(	(	PUNCT
ejpam-7023	23	2	cc	cc	NOUN
ejpam-7023	23	3	by	by	ADP
ejpam-7023	23	4	-	-	PUNCT
ejpam-7023	23	5	nc	nc	PROPN
ejpam-7023	23	6	4.0	4.0	NUM
ejpam-7023	23	7	)	)	PUNCT
ejpam-7023	23	8	i.	i.	NOUN
ejpam-7023	23	9	ayoob	ayoob	PROPN
ejpam-7023	23	10	/	/	SYM
ejpam-7023	23	11	eur	eur	PROPN
ejpam-7023	23	12	.	.	PUNCT
ejpam-7023	24	1	j.	j.	PROPN
ejpam-7023	24	2	pure	pure	PROPN
ejpam-7023	24	3	appl	appl	PROPN
ejpam-7023	24	4	.	.	PROPN
ejpam-7023	24	5	math	math	PROPN
ejpam-7023	24	6	,	,	PUNCT
ejpam-7023	24	7	18	18	NUM
ejpam-7023	24	8	(	(	PUNCT
ejpam-7023	24	9	4	4	NUM
ejpam-7023	24	10	)	)	PUNCT
ejpam-7023	24	11	(	(	PUNCT
ejpam-7023	24	12	2025	2025	NUM
ejpam-7023	24	13	)	)	PUNCT
ejpam-7023	24	14	,	,	PUNCT
ejpam-7023	24	15	7023	7023	NUM
ejpam-7023	24	16	2	2	NUM
ejpam-7023	24	17	of	of	ADP
ejpam-7023	24	18	16	16	NUM
ejpam-7023	24	19	analysis	analysis	NOUN
ejpam-7023	24	20	(	(	PUNCT
ejpam-7023	24	21	contour	contour	NOUN
ejpam-7023	24	22	integration	integration	NOUN
ejpam-7023	24	23	,	,	PUNCT
ejpam-7023	24	24	residues	residue	NOUN
ejpam-7023	24	25	)	)	PUNCT
ejpam-7023	24	26	,	,	PUNCT
ejpam-7023	24	27	and	and	CCONJ
ejpam-7023	24	28	special	special	ADJ
ejpam-7023	24	29	functions	function	NOUN
ejpam-7023	24	30	(	(	PUNCT
ejpam-7023	24	31	gamma	gamma	NOUN
ejpam-7023	24	32	,	,	PUNCT
ejpam-7023	24	33	beta	beta	NOUN
ejpam-7023	24	34	,	,	PUNCT
ejpam-7023	24	35	hypergeometric	hypergeometric	ADJ
ejpam-7023	24	36	)	)	PUNCT
ejpam-7023	24	37	.	.	PUNCT
ejpam-7023	25	1	exact	exact	ADJ
ejpam-7023	25	2	solutions	solution	NOUN
ejpam-7023	25	3	are	be	AUX
ejpam-7023	25	4	valuable	valuable	ADJ
ejpam-7023	25	5	for	for	ADP
ejpam-7023	25	6	precise	precise	ADJ
ejpam-7023	25	7	predictions	prediction	NOUN
ejpam-7023	25	8	,	,	PUNCT
ejpam-7023	25	9	deeper	deep	ADJ
ejpam-7023	25	10	theoretical	theoretical	ADJ
ejpam-7023	25	11	insight	insight	NOUN
ejpam-7023	25	12	,	,	PUNCT
ejpam-7023	25	13	and	and	CCONJ
ejpam-7023	25	14	verifying	verify	VERB
ejpam-7023	25	15	numerical	numerical	ADJ
ejpam-7023	25	16	methods	method	NOUN
ejpam-7023	25	17	.	.	PUNCT
ejpam-7023	26	1	consequently	consequently	ADV
ejpam-7023	26	2	,	,	PUNCT
ejpam-7023	26	3	research	research	NOUN
ejpam-7023	26	4	on	on	ADP
ejpam-7023	26	5	advanced	advanced	ADJ
ejpam-7023	26	6	methods	method	NOUN
ejpam-7023	26	7	for	for	ADP
ejpam-7023	26	8	definite	definite	ADJ
ejpam-7023	26	9	integrals	integral	NOUN
ejpam-7023	26	10	remains	remain	VERB
ejpam-7023	26	11	active	active	ADJ
ejpam-7023	26	12	,	,	PUNCT
ejpam-7023	26	13	with	with	ADP
ejpam-7023	26	14	comprehensive	comprehensive	ADJ
ejpam-7023	26	15	compilations	compilation	NOUN
ejpam-7023	26	16	and	and	CCONJ
ejpam-7023	26	17	recent	recent	ADJ
ejpam-7023	26	18	studies	study	NOUN
ejpam-7023	26	19	highlighting	highlight	VERB
ejpam-7023	26	20	ongoing	ongoing	ADJ
ejpam-7023	26	21	developments	development	NOUN
ejpam-7023	26	22	and	and	CCONJ
ejpam-7023	26	23	continued	continued	ADJ
ejpam-7023	26	24	interest	interest	NOUN
ejpam-7023	26	25	in	in	ADP
ejpam-7023	26	26	the	the	DET
ejpam-7023	26	27	field	field	NOUN
ejpam-7023	26	28	.	.	PUNCT
ejpam-7023	27	1	for	for	ADP
ejpam-7023	27	2	the	the	DET
ejpam-7023	27	3	extensive	extensive	ADJ
ejpam-7023	27	4	list	list	NOUN
ejpam-7023	27	5	of	of	ADP
ejpam-7023	27	6	definite	definite	ADJ
ejpam-7023	27	7	integrals	integral	NOUN
ejpam-7023	27	8	and	and	CCONJ
ejpam-7023	27	9	some	some	DET
ejpam-7023	27	10	recent	recent	ADJ
ejpam-7023	27	11	recsults	recsult	NOUN
ejpam-7023	27	12	,	,	PUNCT
ejpam-7023	27	13	one	one	PRON
ejpam-7023	27	14	may	may	AUX
ejpam-7023	27	15	look	look	VERB
ejpam-7023	27	16	for	for	ADP
ejpam-7023	27	17	the	the	DET
ejpam-7023	27	18	references	reference	NOUN
ejpam-7023	27	19	[	[	X
ejpam-7023	27	20	1–10	1–10	NOUN
ejpam-7023	27	21	]	]	PUNCT
ejpam-7023	27	22	.	.	PUNCT
ejpam-7023	28	1	this	this	DET
ejpam-7023	28	2	paper	paper	NOUN
ejpam-7023	28	3	deals	deal	NOUN
ejpam-7023	28	4	with	with	ADP
ejpam-7023	28	5	the	the	DET
ejpam-7023	28	6	evaluation	evaluation	NOUN
ejpam-7023	28	7	of	of	ADP
ejpam-7023	28	8	an	an	DET
ejpam-7023	28	9	integral	integral	ADJ
ejpam-7023	28	10	related	relate	VERB
ejpam-7023	28	11	to	to	ADP
ejpam-7023	28	12	the	the	DET
ejpam-7023	28	13	steiltjes	steiltjes	ADJ
ejpam-7023	28	14	moment	moment	NOUN
ejpam-7023	28	15	problem	problem	NOUN
ejpam-7023	28	16	.	.	PUNCT
ejpam-7023	29	1	we	we	PRON
ejpam-7023	29	2	recall	recall	VERB
ejpam-7023	29	3	few	few	ADJ
ejpam-7023	29	4	definitions	definition	NOUN
ejpam-7023	29	5	from	from	ADP
ejpam-7023	29	6	the	the	DET
ejpam-7023	29	7	moment	moment	NOUN
ejpam-7023	29	8	problem	problem	NOUN
ejpam-7023	29	9	.	.	PUNCT
ejpam-7023	30	1	the	the	DET
ejpam-7023	30	2	classical	classical	ADJ
ejpam-7023	30	3	moment	moment	NOUN
ejpam-7023	30	4	problem	problem	NOUN
ejpam-7023	30	5	asks	ask	VERB
ejpam-7023	30	6	[	[	X
ejpam-7023	30	7	11	11	NUM
ejpam-7023	30	8	]	]	PUNCT
ejpam-7023	30	9	:	:	PUNCT
ejpam-7023	30	10	given	give	VERB
ejpam-7023	30	11	a	a	DET
ejpam-7023	30	12	sequence	sequence	NOUN
ejpam-7023	30	13	of	of	ADP
ejpam-7023	30	14	real	real	ADJ
ejpam-7023	30	15	numbers	number	NOUN
ejpam-7023	30	16	{	{	PUNCT
ejpam-7023	30	17	mn}∞n=0	mn}∞n=0	NUM
ejpam-7023	30	18	,	,	PUNCT
ejpam-7023	30	19	does	do	AUX
ejpam-7023	30	20	there	there	PRON
ejpam-7023	30	21	exist	exist	VERB
ejpam-7023	30	22	a	a	DET
ejpam-7023	30	23	positive	positive	ADJ
ejpam-7023	30	24	borel	borel	NOUN
ejpam-7023	30	25	measure	measure	NOUN
ejpam-7023	30	26	µ	µ	X
ejpam-7023	30	27	on	on	ADP
ejpam-7023	30	28	some	some	DET
ejpam-7023	30	29	subset	subset	NOUN
ejpam-7023	30	30	of	of	ADP
ejpam-7023	30	31	r	r	NOUN
ejpam-7023	30	32	such	such	ADJ
ejpam-7023	30	33	that	that	PRON
ejpam-7023	30	34	mn	mn	PROPN
ejpam-7023	31	1	=	=	SYM
ejpam-7023	31	2	∫	∫	PROPN
ejpam-7023	31	3	xn	xn	PROPN
ejpam-7023	31	4	dµ(x	dµ(x	PROPN
ejpam-7023	31	5	)	)	PUNCT
ejpam-7023	31	6	,	,	PUNCT
ejpam-7023	31	7	n	n	NOUN
ejpam-7023	31	8	=	=	SYM
ejpam-7023	31	9	0	0	NUM
ejpam-7023	31	10	,	,	PUNCT
ejpam-7023	31	11	1	1	NUM
ejpam-7023	31	12	,	,	PUNCT
ejpam-7023	31	13	2	2	NUM
ejpam-7023	31	14	,	,	PUNCT
ejpam-7023	31	15	.	.	PUNCT
ejpam-7023	31	16	.	.	PUNCT
ejpam-7023	31	17	.	.	PUNCT
ejpam-7023	31	18	?	?	PUNCT
ejpam-7023	32	1	depending	depend	VERB
ejpam-7023	32	2	on	on	ADP
ejpam-7023	32	3	the	the	DET
ejpam-7023	32	4	support	support	NOUN
ejpam-7023	32	5	allowed	allow	VERB
ejpam-7023	32	6	for	for	ADP
ejpam-7023	32	7	µ	µ	NUM
ejpam-7023	32	8	,	,	PUNCT
ejpam-7023	32	9	one	one	NUM
ejpam-7023	32	10	obtains	obtain	VERB
ejpam-7023	32	11	three	three	NUM
ejpam-7023	32	12	classical	classical	ADJ
ejpam-7023	32	13	versions	version	NOUN
ejpam-7023	32	14	as	as	SCONJ
ejpam-7023	32	15	stated	state	VERB
ejpam-7023	32	16	below	below	ADV
ejpam-7023	32	17	.	.	PUNCT
ejpam-7023	33	1	definition	definition	NOUN
ejpam-7023	33	2	1	1	NUM
ejpam-7023	33	3	(	(	PUNCT
ejpam-7023	33	4	hamburger	hamburger	NOUN
ejpam-7023	33	5	moment	moment	NOUN
ejpam-7023	33	6	problem	problem	NOUN
ejpam-7023	33	7	)	)	PUNCT
ejpam-7023	33	8	.	.	PUNCT
ejpam-7023	34	1	this	this	DET
ejpam-7023	34	2	problem	problem	NOUN
ejpam-7023	34	3	seeks	seek	VERB
ejpam-7023	34	4	the	the	DET
ejpam-7023	34	5	measure	measure	NOUN
ejpam-7023	34	6	µ	µ	X
ejpam-7023	34	7	on	on	ADP
ejpam-7023	34	8	the	the	DET
ejpam-7023	34	9	entire	entire	ADJ
ejpam-7023	34	10	real	real	ADJ
ejpam-7023	34	11	line	line	NOUN
ejpam-7023	34	12	(	(	PUNCT
ejpam-7023	34	13	−∞,∞	−∞,∞	NOUN
ejpam-7023	34	14	)	)	PUNCT
ejpam-7023	34	15	.	.	PUNCT
ejpam-7023	35	1	that	that	PRON
ejpam-7023	35	2	is	is	AUX
ejpam-7023	35	3	,	,	PUNCT
ejpam-7023	35	4	given	give	VERB
ejpam-7023	35	5	{	{	PUNCT
ejpam-7023	35	6	mn	mn	NOUN
ejpam-7023	35	7	}	}	PUNCT
ejpam-7023	35	8	,	,	PUNCT
ejpam-7023	35	9	does	do	AUX
ejpam-7023	35	10	there	there	PRON
ejpam-7023	35	11	exist	exist	VERB
ejpam-7023	35	12	a	a	DET
ejpam-7023	35	13	positive	positive	ADJ
ejpam-7023	35	14	measure	measure	NOUN
ejpam-7023	35	15	µ	µ	X
ejpam-7023	35	16	with	with	ADP
ejpam-7023	35	17	mn	mn	PROPN
ejpam-7023	36	1	=	=	SYM
ejpam-7023	36	2	∫	∫	PROPN
ejpam-7023	36	3	∞	∞	PROPN
ejpam-7023	37	1	−∞	−∞	ADP
ejpam-7023	37	2	xn	xn	PROPN
ejpam-7023	37	3	dµ(x	dµ(x	PUNCT
ejpam-7023	37	4	)	)	PUNCT
ejpam-7023	37	5	,	,	PUNCT
ejpam-7023	37	6	n	n	NOUN
ejpam-7023	37	7	=	=	SYM
ejpam-7023	37	8	0	0	NUM
ejpam-7023	37	9	,	,	PUNCT
ejpam-7023	37	10	1	1	NUM
ejpam-7023	37	11	,	,	PUNCT
ejpam-7023	37	12	2	2	NUM
ejpam-7023	37	13	,	,	PUNCT
ejpam-7023	37	14	.	.	PUNCT
ejpam-7023	37	15	.	.	PUNCT
ejpam-7023	37	16	.	.	PUNCT
ejpam-7023	37	17	?	?	PUNCT
ejpam-7023	38	1	this	this	PRON
ejpam-7023	38	2	is	be	AUX
ejpam-7023	38	3	the	the	DET
ejpam-7023	38	4	most	most	ADV
ejpam-7023	38	5	general	general	ADJ
ejpam-7023	38	6	form	form	NOUN
ejpam-7023	38	7	of	of	ADP
ejpam-7023	38	8	the	the	DET
ejpam-7023	38	9	problem	problem	NOUN
ejpam-7023	38	10	.	.	PUNCT
ejpam-7023	39	1	definition	definition	NOUN
ejpam-7023	39	2	2	2	NUM
ejpam-7023	39	3	(	(	PUNCT
ejpam-7023	39	4	stieltjes	stieltjes	PROPN
ejpam-7023	39	5	moment	moment	PROPN
ejpam-7023	39	6	problem	problem	NOUN
ejpam-7023	39	7	)	)	PUNCT
ejpam-7023	39	8	.	.	PUNCT
ejpam-7023	40	1	this	this	DET
ejpam-7023	40	2	problem	problem	NOUN
ejpam-7023	40	3	seeks	seek	VERB
ejpam-7023	40	4	the	the	DET
ejpam-7023	40	5	measure	measure	NOUN
ejpam-7023	40	6	µ	µ	X
ejpam-7023	40	7	on	on	ADP
ejpam-7023	40	8	the	the	DET
ejpam-7023	40	9	half	half	ADJ
ejpam-7023	40	10	–	–	PUNCT
ejpam-7023	40	11	line	line	NOUN
ejpam-7023	40	12	[	[	X
ejpam-7023	40	13	0,∞	0,∞	NOUN
ejpam-7023	40	14	)	)	PUNCT
ejpam-7023	40	15	.	.	PUNCT
ejpam-7023	41	1	that	that	PRON
ejpam-7023	41	2	is	be	AUX
ejpam-7023	41	3	,	,	PUNCT
ejpam-7023	41	4	one	one	NUM
ejpam-7023	41	5	asks	ask	VERB
ejpam-7023	41	6	whether	whether	SCONJ
ejpam-7023	41	7	there	there	PRON
ejpam-7023	41	8	exists	exist	VERB
ejpam-7023	41	9	µ	µ	X
ejpam-7023	41	10	with	with	ADP
ejpam-7023	41	11	mn	mn	PROPN
ejpam-7023	41	12	=	=	SYM
ejpam-7023	41	13	∫	∫	PROPN
ejpam-7023	42	1	∞	∞	PROPN
ejpam-7023	42	2	0	0	PROPN
ejpam-7023	42	3	xn	xn	PROPN
ejpam-7023	42	4	dµ(x	dµ(x	PUNCT
ejpam-7023	42	5	)	)	PUNCT
ejpam-7023	42	6	,	,	PUNCT
ejpam-7023	42	7	n	n	NOUN
ejpam-7023	42	8	=	=	SYM
ejpam-7023	42	9	0	0	NUM
ejpam-7023	42	10	,	,	PUNCT
ejpam-7023	42	11	1	1	NUM
ejpam-7023	42	12	,	,	PUNCT
ejpam-7023	42	13	2	2	NUM
ejpam-7023	42	14	,	,	PUNCT
ejpam-7023	42	15	.	.	PUNCT
ejpam-7023	42	16	.	.	PUNCT
ejpam-7023	42	17	.	.	PUNCT
ejpam-7023	42	18	?	?	PUNCT
ejpam-7023	43	1	such	such	ADJ
ejpam-7023	43	2	sequences	sequence	NOUN
ejpam-7023	43	3	{	{	PUNCT
ejpam-7023	43	4	mn	mn	NOUN
ejpam-7023	43	5	}	}	PUNCT
ejpam-7023	43	6	are	be	AUX
ejpam-7023	43	7	called	call	VERB
ejpam-7023	43	8	stieltjes	stieltjes	PROPN
ejpam-7023	43	9	moment	moment	PROPN
ejpam-7023	43	10	sequences	sequence	NOUN
ejpam-7023	43	11	.	.	PUNCT
ejpam-7023	44	1	this	this	DET
ejpam-7023	44	2	version	version	NOUN
ejpam-7023	44	3	is	be	AUX
ejpam-7023	44	4	closely	closely	ADV
ejpam-7023	44	5	connected	connect	VERB
ejpam-7023	44	6	to	to	ADP
ejpam-7023	44	7	continued	continue	VERB
ejpam-7023	44	8	fractions	fraction	NOUN
ejpam-7023	44	9	and	and	CCONJ
ejpam-7023	44	10	orthogonal	orthogonal	ADJ
ejpam-7023	44	11	polynomials	polynomial	NOUN
ejpam-7023	44	12	on	on	ADP
ejpam-7023	44	13	[	[	X
ejpam-7023	44	14	0,∞	0,∞	NOUN
ejpam-7023	44	15	)	)	PUNCT
ejpam-7023	44	16	.	.	PUNCT
ejpam-7023	45	1	definition	definition	NOUN
ejpam-7023	45	2	3	3	NUM
ejpam-7023	45	3	(	(	PUNCT
ejpam-7023	45	4	hausdorff	hausdorff	NOUN
ejpam-7023	45	5	moment	moment	PROPN
ejpam-7023	45	6	problem	problem	NOUN
ejpam-7023	45	7	)	)	PUNCT
ejpam-7023	45	8	.	.	PUNCT
ejpam-7023	46	1	here	here	ADV
ejpam-7023	46	2	the	the	DET
ejpam-7023	46	3	measure	measure	NOUN
ejpam-7023	46	4	µ	µ	NOUN
ejpam-7023	46	5	is	be	AUX
ejpam-7023	46	6	confined	confine	VERB
ejpam-7023	46	7	to	to	ADP
ejpam-7023	46	8	the	the	DET
ejpam-7023	46	9	compact	compact	ADJ
ejpam-7023	46	10	interval	interval	NOUN
ejpam-7023	46	11	[	[	X
ejpam-7023	46	12	0	0	NUM
ejpam-7023	46	13	,	,	PUNCT
ejpam-7023	46	14	1	1	NUM
ejpam-7023	46	15	]	]	PUNCT
ejpam-7023	46	16	.	.	PUNCT
ejpam-7023	47	1	that	that	PRON
ejpam-7023	47	2	is	be	AUX
ejpam-7023	47	3	,	,	PUNCT
ejpam-7023	47	4	does	do	AUX
ejpam-7023	47	5	there	there	PRON
ejpam-7023	47	6	exist	exist	VERB
ejpam-7023	47	7	µ	µ	X
ejpam-7023	47	8	with	with	ADP
ejpam-7023	47	9	mn	mn	PROPN
ejpam-7023	47	10	=	=	SYM
ejpam-7023	47	11	∫	∫	PROPN
ejpam-7023	47	12	1	1	NUM
ejpam-7023	47	13	0	0	NUM
ejpam-7023	47	14	xn	xn	NUM
ejpam-7023	47	15	dµ(x	dµ(x	PUNCT
ejpam-7023	47	16	)	)	PUNCT
ejpam-7023	47	17	,	,	PUNCT
ejpam-7023	47	18	n	n	NOUN
ejpam-7023	47	19	=	=	SYM
ejpam-7023	47	20	0	0	NUM
ejpam-7023	47	21	,	,	PUNCT
ejpam-7023	47	22	1	1	NUM
ejpam-7023	47	23	,	,	PUNCT
ejpam-7023	47	24	2	2	NUM
ejpam-7023	47	25	,	,	PUNCT
ejpam-7023	47	26	.	.	PUNCT
ejpam-7023	47	27	.	.	PUNCT
ejpam-7023	47	28	.	.	PUNCT
ejpam-7023	47	29	?	?	PUNCT
ejpam-7023	48	1	in	in	ADP
ejpam-7023	48	2	every	every	DET
ejpam-7023	48	3	version	version	NOUN
ejpam-7023	48	4	of	of	ADP
ejpam-7023	48	5	the	the	DET
ejpam-7023	48	6	moment	moment	NOUN
ejpam-7023	48	7	problem	problem	NOUN
ejpam-7023	48	8	,	,	PUNCT
ejpam-7023	48	9	the	the	DET
ejpam-7023	48	10	issue	issue	NOUN
ejpam-7023	48	11	of	of	ADP
ejpam-7023	48	12	uniqueness	uniqueness	NOUN
ejpam-7023	48	13	is	be	AUX
ejpam-7023	48	14	crucial	crucial	ADJ
ejpam-7023	48	15	.	.	PUNCT
ejpam-7023	49	1	for	for	ADP
ejpam-7023	49	2	the	the	DET
ejpam-7023	49	3	stieltjes	stieltjes	NOUN
ejpam-7023	49	4	and	and	CCONJ
ejpam-7023	49	5	hamburger	hamburger	NOUN
ejpam-7023	49	6	cases	case	NOUN
ejpam-7023	49	7	,	,	PUNCT
ejpam-7023	49	8	whenever	whenever	SCONJ
ejpam-7023	49	9	a	a	DET
ejpam-7023	49	10	solution	solution	NOUN
ejpam-7023	49	11	exists	exist	VERB
ejpam-7023	49	12	it	it	PRON
ejpam-7023	49	13	need	need	AUX
ejpam-7023	49	14	not	not	PART
ejpam-7023	49	15	be	be	AUX
ejpam-7023	49	16	unique	unique	ADJ
ejpam-7023	49	17	,	,	PUNCT
ejpam-7023	49	18	there	there	PRON
ejpam-7023	49	19	may	may	AUX
ejpam-7023	49	20	be	be	AUX
ejpam-7023	49	21	infinitely	infinitely	ADV
ejpam-7023	49	22	many	many	ADJ
ejpam-7023	49	23	measures	measure	NOUN
ejpam-7023	49	24	producing	produce	VERB
ejpam-7023	49	25	the	the	DET
ejpam-7023	49	26	same	same	ADJ
ejpam-7023	49	27	moment	moment	NOUN
ejpam-7023	49	28	sequence	sequence	NOUN
ejpam-7023	49	29	(	(	PUNCT
ejpam-7023	49	30	the	the	DET
ejpam-7023	49	31	indeterminate	indeterminate	ADJ
ejpam-7023	49	32	case	case	NOUN
ejpam-7023	49	33	)	)	PUNCT
ejpam-7023	49	34	.	.	PUNCT
ejpam-7023	50	1	by	by	ADP
ejpam-7023	50	2	contrast	contrast	NOUN
ejpam-7023	50	3	,	,	PUNCT
ejpam-7023	50	4	the	the	DET
ejpam-7023	50	5	hausdorff	hausdorff	NOUN
ejpam-7023	50	6	moment	moment	NOUN
ejpam-7023	50	7	problem	problem	NOUN
ejpam-7023	50	8	,	,	PUNCT
ejpam-7023	50	9	when	when	SCONJ
ejpam-7023	50	10	solvable	solvable	ADJ
ejpam-7023	50	11	,	,	PUNCT
ejpam-7023	50	12	always	always	ADV
ejpam-7023	50	13	yields	yield	VERB
ejpam-7023	50	14	a	a	DET
ejpam-7023	50	15	single	single	ADJ
ejpam-7023	50	16	i.	i.	NOUN
ejpam-7023	50	17	ayoob	ayoob	PROPN
ejpam-7023	50	18	/	/	SYM
ejpam-7023	50	19	eur	eur	PROPN
ejpam-7023	50	20	.	.	PUNCT
ejpam-7023	51	1	j.	j.	PROPN
ejpam-7023	51	2	pure	pure	PROPN
ejpam-7023	51	3	appl	appl	PROPN
ejpam-7023	51	4	.	.	PROPN
ejpam-7023	51	5	math	math	PROPN
ejpam-7023	51	6	,	,	PUNCT
ejpam-7023	51	7	18	18	NUM
ejpam-7023	51	8	(	(	PUNCT
ejpam-7023	51	9	4	4	NUM
ejpam-7023	51	10	)	)	PUNCT
ejpam-7023	51	11	(	(	PUNCT
ejpam-7023	51	12	2025	2025	NUM
ejpam-7023	51	13	)	)	PUNCT
ejpam-7023	51	14	,	,	PUNCT
ejpam-7023	51	15	7023	7023	NUM
ejpam-7023	51	16	3	3	NUM
ejpam-7023	51	17	of	of	ADP
ejpam-7023	51	18	16	16	NUM
ejpam-7023	51	19	measure	measure	NOUN
ejpam-7023	51	20	,	,	PUNCT
ejpam-7023	51	21	making	make	VERB
ejpam-7023	51	22	it	it	PRON
ejpam-7023	51	23	determinate	determinate	VERB
ejpam-7023	51	24	.	.	PUNCT
ejpam-7023	52	1	thus	thus	ADV
ejpam-7023	52	2	,	,	PUNCT
ejpam-7023	52	3	in	in	ADP
ejpam-7023	52	4	the	the	DET
ejpam-7023	52	5	indeterminate	indeterminate	ADJ
ejpam-7023	52	6	situations	situation	NOUN
ejpam-7023	52	7	,	,	PUNCT
ejpam-7023	52	8	one	one	NUM
ejpam-7023	52	9	encounters	encounter	VERB
ejpam-7023	52	10	infinitely	infinitely	ADV
ejpam-7023	52	11	many	many	ADJ
ejpam-7023	52	12	distinct	distinct	ADJ
ejpam-7023	52	13	measures	measure	NOUN
ejpam-7023	52	14	that	that	PRON
ejpam-7023	52	15	share	share	VERB
ejpam-7023	52	16	the	the	DET
ejpam-7023	52	17	same	same	ADJ
ejpam-7023	52	18	prescribed	prescribed	ADJ
ejpam-7023	52	19	moments	moment	NOUN
ejpam-7023	52	20	.	.	PUNCT
ejpam-7023	53	1	the	the	DET
ejpam-7023	53	2	nonuniqueness	nonuniqueness	NOUN
ejpam-7023	53	3	of	of	ADP
ejpam-7023	53	4	moments	moment	NOUN
ejpam-7023	53	5	is	be	AUX
ejpam-7023	53	6	classically	classically	ADV
ejpam-7023	53	7	studied	study	VERB
ejpam-7023	53	8	through	through	ADP
ejpam-7023	53	9	carleman	carleman	NOUN
ejpam-7023	53	10	’s	’s	PART
ejpam-7023	53	11	condition	condition	NOUN
ejpam-7023	53	12	and	and	CCONJ
ejpam-7023	53	13	krein	krein	PROPN
ejpam-7023	53	14	’s	’s	PART
ejpam-7023	53	15	condition	condition	NOUN
ejpam-7023	53	16	.	.	PUNCT
ejpam-7023	54	1	related	relate	VERB
ejpam-7023	54	2	to	to	ADP
ejpam-7023	54	3	hausdorff	hausdorff	PROPN
ejpam-7023	54	4	moment	moment	NOUN
ejpam-7023	54	5	problem	problem	NOUN
ejpam-7023	54	6	,	,	PUNCT
ejpam-7023	54	7	we	we	PRON
ejpam-7023	54	8	have	have	VERB
ejpam-7023	54	9	the	the	DET
ejpam-7023	54	10	classical	classical	ADJ
ejpam-7023	54	11	result	result	NOUN
ejpam-7023	54	12	proved	prove	VERB
ejpam-7023	54	13	through	through	ADP
ejpam-7023	54	14	weierstrass	weierstrass	NOUN
ejpam-7023	54	15	approximation	approximation	NOUN
ejpam-7023	54	16	theorem	theorem	NOUN
ejpam-7023	54	17	,	,	PUNCT
ejpam-7023	54	18	proposition	proposition	NOUN
ejpam-7023	54	19	1	1	NUM
ejpam-7023	54	20	.	.	PUNCT
ejpam-7023	55	1	[	[	X
ejpam-7023	55	2	12	12	NUM
ejpam-7023	55	3	]	]	PUNCT
ejpam-7023	55	4	let	let	VERB
ejpam-7023	55	5	f	f	PROPN
ejpam-7023	55	6	∈	∈	PROPN
ejpam-7023	55	7	c([0	c([0	PROPN
ejpam-7023	55	8	,	,	PUNCT
ejpam-7023	55	9	1	1	NUM
ejpam-7023	55	10	]	]	NUM
ejpam-7023	55	11	)	)	PUNCT
ejpam-7023	55	12	.	.	PUNCT
ejpam-7023	56	1	if∫	if∫	PROPN
ejpam-7023	56	2	1	1	NUM
ejpam-7023	56	3	0	0	NUM
ejpam-7023	56	4	xnf(x	xnf(x	PROPN
ejpam-7023	56	5	)	)	PUNCT
ejpam-7023	56	6	dx	dx	PROPN
ejpam-7023	57	1	=	=	SYM
ejpam-7023	57	2	0	0	PROPN
ejpam-7023	57	3	for	for	ADP
ejpam-7023	57	4	all	all	DET
ejpam-7023	57	5	n	n	NOUN
ejpam-7023	57	6	=	=	SYM
ejpam-7023	57	7	0	0	NUM
ejpam-7023	57	8	,	,	PUNCT
ejpam-7023	57	9	1	1	NUM
ejpam-7023	57	10	,	,	PUNCT
ejpam-7023	57	11	2	2	NUM
ejpam-7023	57	12	,	,	PUNCT
ejpam-7023	57	13	.	.	PUNCT
ejpam-7023	57	14	.	.	PUNCT
ejpam-7023	58	1	.	.	PUNCT
ejpam-7023	59	1	,	,	PUNCT
ejpam-7023	59	2	then	then	ADV
ejpam-7023	59	3	f	f	PROPN
ejpam-7023	59	4	≡	≡	PROPN
ejpam-7023	59	5	0	0	PUNCT
ejpam-7023	59	6	on	on	ADP
ejpam-7023	59	7	[	[	X
ejpam-7023	59	8	0	0	NUM
ejpam-7023	59	9	,	,	PUNCT
ejpam-7023	59	10	1	1	NUM
ejpam-7023	59	11	]	]	PUNCT
ejpam-7023	59	12	.	.	PUNCT
ejpam-7023	60	1	about	about	ADP
ejpam-7023	60	2	the	the	DET
ejpam-7023	60	3	infinite	infinite	ADJ
ejpam-7023	60	4	case	case	NOUN
ejpam-7023	60	5	,	,	PUNCT
ejpam-7023	60	6	we	we	PRON
ejpam-7023	60	7	may	may	AUX
ejpam-7023	60	8	pose	pose	VERB
ejpam-7023	60	9	a	a	DET
ejpam-7023	60	10	similar	similar	ADJ
ejpam-7023	60	11	question	question	NOUN
ejpam-7023	60	12	:	:	PUNCT
ejpam-7023	60	13	question	question	NOUN
ejpam-7023	60	14	1	1	NUM
ejpam-7023	60	15	.	.	PUNCT
ejpam-7023	60	16	suppose	suppose	VERB
ejpam-7023	60	17	f	f	PROPN
ejpam-7023	60	18	∈	∈	PROPN
ejpam-7023	60	19	c([0,∞	c([0,∞	PROPN
ejpam-7023	60	20	)	)	PUNCT
ejpam-7023	60	21	)	)	PUNCT
ejpam-7023	61	1	and∫	and∫	PROPN
ejpam-7023	61	2	∞	∞	PROPN
ejpam-7023	61	3	0	0	NUM
ejpam-7023	62	1	xnf(x	xnf(x	PROPN
ejpam-7023	62	2	)	)	PUNCT
ejpam-7023	62	3	dx	dx	PROPN
ejpam-7023	63	1	=	=	SYM
ejpam-7023	63	2	0	0	PROPN
ejpam-7023	63	3	for	for	ADP
ejpam-7023	63	4	all	all	DET
ejpam-7023	63	5	n	n	NOUN
ejpam-7023	63	6	=	=	SYM
ejpam-7023	63	7	0	0	NUM
ejpam-7023	63	8	,	,	PUNCT
ejpam-7023	63	9	1	1	NUM
ejpam-7023	63	10	,	,	PUNCT
ejpam-7023	63	11	2	2	NUM
ejpam-7023	63	12	,	,	PUNCT
ejpam-7023	63	13	.	.	PUNCT
ejpam-7023	63	14	.	.	PUNCT
ejpam-7023	63	15	.	.	PUNCT
ejpam-7023	64	1	.	.	PUNCT
ejpam-7023	65	1	does	do	AUX
ejpam-7023	65	2	it	it	PRON
ejpam-7023	65	3	follow	follow	VERB
ejpam-7023	65	4	that	that	SCONJ
ejpam-7023	65	5	f	f	PROPN
ejpam-7023	65	6	≡	≡	PROPN
ejpam-7023	65	7	0	0	PUNCT
ejpam-7023	66	1	on	on	ADP
ejpam-7023	66	2	[	[	X
ejpam-7023	66	3	0,∞	0,∞	NOUN
ejpam-7023	66	4	)	)	PUNCT
ejpam-7023	66	5	?	?	PUNCT
ejpam-7023	67	1	in	in	ADP
ejpam-7023	67	2	relation	relation	NOUN
ejpam-7023	67	3	to	to	ADP
ejpam-7023	67	4	the	the	DET
ejpam-7023	67	5	non	non	NOUN
ejpam-7023	67	6	-	-	NOUN
ejpam-7023	67	7	uniqueness	uniqueness	NOUN
ejpam-7023	67	8	of	of	ADP
ejpam-7023	67	9	the	the	DET
ejpam-7023	67	10	moment	moment	NOUN
ejpam-7023	67	11	problem	problem	NOUN
ejpam-7023	67	12	,	,	PUNCT
ejpam-7023	67	13	stieltjes	stieltjes	PROPN
ejpam-7023	67	14	showed	show	VERB
ejpam-7023	67	15	[	[	X
ejpam-7023	67	16	13](see	13](see	NUM
ejpam-7023	67	17	p.506	p.506	NOUN
ejpam-7023	67	18	)	)	PUNCT
ejpam-7023	67	19	that	that	PRON
ejpam-7023	67	20	function	function	VERB
ejpam-7023	67	21	f	f	X
ejpam-7023	67	22	in	in	ADP
ejpam-7023	67	23	question	question	NOUN
ejpam-7023	67	24	1	1	NUM
ejpam-7023	67	25	may	may	AUX
ejpam-7023	67	26	be	be	AUX
ejpam-7023	67	27	non	non	ADJ
ejpam-7023	67	28	-	-	ADJ
ejpam-7023	67	29	zero	zero	NUM
ejpam-7023	67	30	by	by	ADP
ejpam-7023	67	31	giving	give	VERB
ejpam-7023	67	32	the	the	DET
ejpam-7023	67	33	following	follow	VERB
ejpam-7023	67	34	example	example	NOUN
ejpam-7023	67	35	:	:	PUNCT
ejpam-7023	67	36	example	example	NOUN
ejpam-7023	67	37	1	1	NUM
ejpam-7023	67	38	.	.	PUNCT
ejpam-7023	68	1	the	the	DET
ejpam-7023	68	2	integral	integral	ADJ
ejpam-7023	68	3	i(n	i(n	NOUN
ejpam-7023	68	4	)	)	PUNCT
ejpam-7023	68	5	=	=	SYM
ejpam-7023	69	1	∫	∫	PROPN
ejpam-7023	69	2	∞	∞	NUM
ejpam-7023	69	3	0	0	NUM
ejpam-7023	70	1	xnf(x	xnf(x	PROPN
ejpam-7023	70	2	)	)	PUNCT
ejpam-7023	70	3	dx	dx	PROPN
ejpam-7023	71	1	=	=	SYM
ejpam-7023	71	2	0	0	PUNCT
ejpam-7023	71	3	(	(	PUNCT
ejpam-7023	71	4	n	n	NOUN
ejpam-7023	71	5	=	=	SYM
ejpam-7023	71	6	0	0	NUM
ejpam-7023	71	7	,	,	PUNCT
ejpam-7023	71	8	1	1	NUM
ejpam-7023	71	9	,	,	PUNCT
ejpam-7023	71	10	2	2	NUM
ejpam-7023	71	11	,	,	PUNCT
ejpam-7023	71	12	.	.	PUNCT
ejpam-7023	71	13	.	.	PUNCT
ejpam-7023	71	14	.	.	PUNCT
ejpam-7023	71	15	)	)	PUNCT
ejpam-7023	71	16	,	,	PUNCT
ejpam-7023	71	17	(	(	PUNCT
ejpam-7023	71	18	1	1	X
ejpam-7023	71	19	)	)	PUNCT
ejpam-7023	71	20	for	for	ADP
ejpam-7023	71	21	the	the	DET
ejpam-7023	71	22	non	non	ADJ
ejpam-7023	71	23	-	-	ADJ
ejpam-7023	71	24	trivial	trivial	ADJ
ejpam-7023	71	25	function	function	NOUN
ejpam-7023	71	26	,	,	PUNCT
ejpam-7023	71	27	f(x	f(x	PROPN
ejpam-7023	71	28	)	)	PUNCT
ejpam-7023	71	29	=	=	PUNCT
ejpam-7023	72	1	e−x1/4	e−x1/4	PROPN
ejpam-7023	72	2	sin	sin	NOUN
ejpam-7023	72	3	(	(	PUNCT
ejpam-7023	72	4	x1/4	x1/4	PROPN
ejpam-7023	72	5	)	)	PUNCT
ejpam-7023	72	6	,	,	PUNCT
ejpam-7023	72	7	x	x	X
ejpam-7023	72	8	≥	≥	NOUN
ejpam-7023	72	9	0	0	NUM
ejpam-7023	72	10	.	.	PUNCT
ejpam-7023	73	1	(	(	PUNCT
ejpam-7023	73	2	2	2	X
ejpam-7023	73	3	)	)	PUNCT
ejpam-7023	73	4	this	this	DET
ejpam-7023	73	5	paper	paper	NOUN
ejpam-7023	73	6	studies	study	NOUN
ejpam-7023	73	7	the	the	DET
ejpam-7023	73	8	following	follow	VERB
ejpam-7023	73	9	questions	question	NOUN
ejpam-7023	73	10	related	relate	VERB
ejpam-7023	73	11	to	to	ADP
ejpam-7023	73	12	stieltjes	stieltjes	PROPN
ejpam-7023	73	13	example	example	NOUN
ejpam-7023	73	14	1	1	NUM
ejpam-7023	73	15	:	:	PUNCT
ejpam-7023	73	16	question	question	NOUN
ejpam-7023	73	17	2	2	NUM
ejpam-7023	73	18	.	.	PUNCT
ejpam-7023	74	1	the	the	DET
ejpam-7023	74	2	integral	integral	ADJ
ejpam-7023	74	3	i(n	i(n	PROPN
ejpam-7023	74	4	)	)	PUNCT
ejpam-7023	74	5	=	=	SYM
ejpam-7023	74	6	∫∞	∫∞	NOUN
ejpam-7023	74	7	0	0	PUNCT
ejpam-7023	75	1	xnf(x	xnf(x	X
ejpam-7023	75	2	)	)	PUNCT
ejpam-7023	75	3	dx	dx	PROPN
ejpam-7023	76	1	=	=	SYM
ejpam-7023	76	2	0	0	NUM
ejpam-7023	76	3	for	for	ADP
ejpam-7023	76	4	f(x	f(x	PROPN
ejpam-7023	76	5	)	)	PUNCT
ejpam-7023	77	1	=	=	PUNCT
ejpam-7023	77	2	e−x1/4	e−x1/4	PROPN
ejpam-7023	77	3	sin	sin	NOUN
ejpam-7023	77	4	(	(	PUNCT
ejpam-7023	77	5	x1/4	x1/4	PROPN
ejpam-7023	77	6	)	)	PUNCT
ejpam-7023	77	7	,	,	PUNCT
ejpam-7023	77	8	x	x	X
ejpam-7023	77	9	≥	≥	X
ejpam-7023	77	10	0	0	NUM
ejpam-7023	77	11	for	for	ADP
ejpam-7023	77	12	all	all	DET
ejpam-7023	77	13	n	n	NOUN
ejpam-7023	77	14	=	=	SYM
ejpam-7023	77	15	0	0	NUM
ejpam-7023	77	16	,	,	PUNCT
ejpam-7023	77	17	1	1	NUM
ejpam-7023	77	18	,	,	PUNCT
ejpam-7023	77	19	2	2	NUM
ejpam-7023	77	20	,	,	PUNCT
ejpam-7023	77	21	.	.	PUNCT
ejpam-7023	77	22	.	.	PUNCT
ejpam-7023	77	23	.	.	PUNCT
ejpam-7023	77	24	.	.	PUNCT
ejpam-7023	78	1	what	what	PRON
ejpam-7023	78	2	if	if	SCONJ
ejpam-7023	78	3	non	non	ADJ
ejpam-7023	78	4	-	-	ADJ
ejpam-7023	78	5	negative	negative	ADJ
ejpam-7023	78	6	integer	integer	NOUN
ejpam-7023	78	7	n	n	PRON
ejpam-7023	78	8	is	be	AUX
ejpam-7023	78	9	replaced	replace	VERB
ejpam-7023	78	10	by	by	ADP
ejpam-7023	78	11	non	non	ADJ
ejpam-7023	78	12	-	-	ADJ
ejpam-7023	78	13	negative	negative	ADJ
ejpam-7023	78	14	real	real	ADJ
ejpam-7023	78	15	number	number	NOUN
ejpam-7023	78	16	k	k	NOUN
ejpam-7023	78	17	,	,	PUNCT
ejpam-7023	78	18	that	that	ADV
ejpam-7023	78	19	is	is	ADV
ejpam-7023	78	20	,	,	PUNCT
ejpam-7023	78	21	for	for	ADP
ejpam-7023	78	22	what	what	PRON
ejpam-7023	78	23	real	real	ADJ
ejpam-7023	78	24	numbers	number	NOUN
ejpam-7023	78	25	k	k	PROPN
ejpam-7023	78	26	≥	≥	PROPN
ejpam-7023	78	27	0	0	NUM
ejpam-7023	78	28	,	,	PUNCT
ejpam-7023	78	29	we	we	PRON
ejpam-7023	78	30	have	have	VERB
ejpam-7023	78	31	that	that	DET
ejpam-7023	78	32	i(k	i(k	PROPN
ejpam-7023	78	33	)	)	PUNCT
ejpam-7023	78	34	=	=	SYM
ejpam-7023	78	35	∫∞	∫∞	NOUN
ejpam-7023	78	36	0	0	NUM
ejpam-7023	78	37	xke−x1/4	xke−x1/4	PROPN
ejpam-7023	78	38	sin	sin	PROPN
ejpam-7023	78	39	(	(	PUNCT
ejpam-7023	78	40	x1/4	x1/4	PROPN
ejpam-7023	78	41	)	)	PUNCT
ejpam-7023	78	42	dx	dx	PROPN
ejpam-7023	79	1	=	=	PUNCT
ejpam-7023	79	2	0	0	PROPN
ejpam-7023	79	3	.	.	PUNCT
ejpam-7023	80	1	the	the	DET
ejpam-7023	80	2	second	second	ADJ
ejpam-7023	80	3	question	question	NOUN
ejpam-7023	80	4	deals	deal	NOUN
ejpam-7023	80	5	with	with	ADP
ejpam-7023	80	6	the	the	DET
ejpam-7023	80	7	following	follow	VERB
ejpam-7023	80	8	generalization	generalization	NOUN
ejpam-7023	80	9	of	of	ADP
ejpam-7023	80	10	the	the	DET
ejpam-7023	80	11	steiltjes	steiltjes	PROPN
ejpam-7023	80	12	integral	integral	ADJ
ejpam-7023	80	13	.	.	PUNCT
ejpam-7023	81	1	question	question	NOUN
ejpam-7023	81	2	3	3	NUM
ejpam-7023	81	3	.	.	PUNCT
ejpam-7023	81	4	evaluate	evaluate	VERB
ejpam-7023	81	5	the	the	DET
ejpam-7023	81	6	following	follow	VERB
ejpam-7023	81	7	generalized	generalized	ADJ
ejpam-7023	81	8	integral	integral	ADJ
ejpam-7023	81	9	explicitly	explicitly	ADV
ejpam-7023	81	10	(	(	PUNCT
ejpam-7023	81	11	for	for	ADP
ejpam-7023	81	12	appropriate	appropriate	ADJ
ejpam-7023	81	13	parameters	parameter	NOUN
ejpam-7023	81	14	)	)	PUNCT
ejpam-7023	81	15	and	and	CCONJ
ejpam-7023	81	16	determine	determine	VERB
ejpam-7023	81	17	the	the	DET
ejpam-7023	81	18	necessary	necessary	ADJ
ejpam-7023	81	19	and	and	CCONJ
ejpam-7023	81	20	sufficient	sufficient	ADJ
ejpam-7023	81	21	conditions	condition	NOUN
ejpam-7023	81	22	on	on	ADP
ejpam-7023	81	23	the	the	DET
ejpam-7023	81	24	parameters	parameter	NOUN
ejpam-7023	81	25	so	so	SCONJ
ejpam-7023	81	26	that	that	SCONJ
ejpam-7023	81	27	the	the	DET
ejpam-7023	81	28	integral	integral	ADJ
ejpam-7023	81	29	vanishes	vanishe	NOUN
ejpam-7023	81	30	,	,	PUNCT
ejpam-7023	81	31	im	im	ADV
ejpam-7023	81	32	,	,	PUNCT
ejpam-7023	81	33	q(k	q(k	NOUN
ejpam-7023	81	34	)	)	PUNCT
ejpam-7023	82	1	=	=	SYM
ejpam-7023	82	2	∫	∫	PROPN
ejpam-7023	83	1	∞	∞	NUM
ejpam-7023	83	2	0	0	NUM
ejpam-7023	83	3	e−αx1	e−αx1	PROPN
ejpam-7023	83	4	/	/	SYM
ejpam-7023	83	5	m	m	NOUN
ejpam-7023	83	6	sin	sin	NOUN
ejpam-7023	83	7	(	(	PUNCT
ejpam-7023	83	8	βx1	βx1	PROPN
ejpam-7023	83	9	/	/	SYM
ejpam-7023	83	10	m	m	NOUN
ejpam-7023	83	11	)	)	PUNCT
ejpam-7023	83	12	xk	xk	PROPN
ejpam-7023	83	13	(	(	PUNCT
ejpam-7023	83	14	x1	x1	PROPN
ejpam-7023	83	15	/	/	SYM
ejpam-7023	83	16	m)q	m)q	PROPN
ejpam-7023	83	17	dx	dx	PROPN
ejpam-7023	83	18	,	,	PUNCT
ejpam-7023	83	19	(	(	PUNCT
ejpam-7023	83	20	3	3	X
ejpam-7023	83	21	)	)	PUNCT
ejpam-7023	83	22	where	where	SCONJ
ejpam-7023	83	23	k	k	PROPN
ejpam-7023	83	24	≥	≥	X
ejpam-7023	83	25	0	0	NUM
ejpam-7023	83	26	is	be	AUX
ejpam-7023	83	27	a	a	DET
ejpam-7023	83	28	real	real	ADJ
ejpam-7023	83	29	number	number	NOUN
ejpam-7023	83	30	.	.	PUNCT
ejpam-7023	84	1	i.	i.	PROPN
ejpam-7023	84	2	ayoob	ayoob	PROPN
ejpam-7023	84	3	/	/	SYM
ejpam-7023	84	4	eur	eur	PROPN
ejpam-7023	84	5	.	.	PUNCT
ejpam-7023	85	1	j.	j.	PROPN
ejpam-7023	85	2	pure	pure	PROPN
ejpam-7023	85	3	appl	appl	PROPN
ejpam-7023	85	4	.	.	PROPN
ejpam-7023	85	5	math	math	PROPN
ejpam-7023	85	6	,	,	PUNCT
ejpam-7023	85	7	18	18	NUM
ejpam-7023	85	8	(	(	PUNCT
ejpam-7023	85	9	4	4	NUM
ejpam-7023	85	10	)	)	PUNCT
ejpam-7023	85	11	(	(	PUNCT
ejpam-7023	85	12	2025	2025	NUM
ejpam-7023	85	13	)	)	PUNCT
ejpam-7023	85	14	,	,	PUNCT
ejpam-7023	85	15	7023	7023	NUM
ejpam-7023	85	16	4	4	NUM
ejpam-7023	85	17	of	of	ADP
ejpam-7023	85	18	16	16	NUM
ejpam-7023	85	19	we	we	PRON
ejpam-7023	85	20	will	will	AUX
ejpam-7023	85	21	solve	solve	VERB
ejpam-7023	85	22	the	the	DET
ejpam-7023	85	23	integrals	integral	NOUN
ejpam-7023	85	24	i(k	i(k	PROPN
ejpam-7023	85	25	)	)	PUNCT
ejpam-7023	85	26	and	and	CCONJ
ejpam-7023	85	27	im	im	NOUN
ejpam-7023	85	28	,	,	PUNCT
ejpam-7023	85	29	q(k	q(k	NOUN
ejpam-7023	85	30	)	)	PUNCT
ejpam-7023	85	31	given	give	VERB
ejpam-7023	85	32	in	in	ADP
ejpam-7023	85	33	questions	question	NOUN
ejpam-7023	85	34	2	2	NUM
ejpam-7023	85	35	and	and	CCONJ
ejpam-7023	85	36	3	3	NUM
ejpam-7023	85	37	explicitly	explicitly	ADV
ejpam-7023	85	38	,	,	PUNCT
ejpam-7023	85	39	and	and	CCONJ
ejpam-7023	85	40	establish	establish	VERB
ejpam-7023	85	41	the	the	DET
ejpam-7023	85	42	necessary	necessary	ADJ
ejpam-7023	85	43	and	and	CCONJ
ejpam-7023	85	44	sufficient	sufficient	ADJ
ejpam-7023	85	45	conditions	condition	NOUN
ejpam-7023	85	46	for	for	ADP
ejpam-7023	85	47	the	the	DET
ejpam-7023	85	48	vanishing	vanishing	NOUN
ejpam-7023	85	49	of	of	ADP
ejpam-7023	85	50	these	these	PRON
ejpam-7023	85	51	of	of	ADP
ejpam-7023	85	52	integrals	integral	NOUN
ejpam-7023	85	53	.	.	PUNCT
ejpam-7023	86	1	this	this	DET
ejpam-7023	86	2	question	question	NOUN
ejpam-7023	86	3	is	be	AUX
ejpam-7023	86	4	interesting	interesting	ADJ
ejpam-7023	86	5	as	as	SCONJ
ejpam-7023	86	6	there	there	PRON
ejpam-7023	86	7	exist	exist	VERB
ejpam-7023	86	8	integrals	integral	NOUN
ejpam-7023	86	9	which	which	PRON
ejpam-7023	86	10	vanish	vanish	VERB
ejpam-7023	86	11	for	for	ADP
ejpam-7023	86	12	all	all	DET
ejpam-7023	86	13	values	value	NOUN
ejpam-7023	86	14	of	of	ADP
ejpam-7023	86	15	the	the	DET
ejpam-7023	86	16	continuous	continuous	ADJ
ejpam-7023	86	17	parameter	parameter	NOUN
ejpam-7023	86	18	(	(	PUNCT
ejpam-7023	86	19	not	not	PART
ejpam-7023	86	20	only	only	ADV
ejpam-7023	86	21	on	on	ADP
ejpam-7023	86	22	discrete	discrete	ADJ
ejpam-7023	86	23	subsets	subset	NOUN
ejpam-7023	86	24	of	of	ADP
ejpam-7023	86	25	reals	real	NOUN
ejpam-7023	86	26	as	as	ADP
ejpam-7023	86	27	in	in	ADP
ejpam-7023	86	28	the	the	DET
ejpam-7023	86	29	case	case	NOUN
ejpam-7023	86	30	of	of	ADP
ejpam-7023	86	31	example	example	NOUN
ejpam-7023	86	32	1	1	NUM
ejpam-7023	86	33	with	with	ADP
ejpam-7023	86	34	parameter	parameter	PROPN
ejpam-7023	86	35	n.	n.	PROPN
ejpam-7023	86	36	)	)	PUNCT
ejpam-7023	86	37	for	for	ADP
ejpam-7023	86	38	instance	instance	NOUN
ejpam-7023	86	39	,	,	PUNCT
ejpam-7023	86	40	example	example	NOUN
ejpam-7023	86	41	2	2	NUM
ejpam-7023	86	42	.	.	PUNCT
ejpam-7023	86	43	i(a	i(a	PROPN
ejpam-7023	86	44	)	)	PUNCT
ejpam-7023	87	1	=	=	SYM
ejpam-7023	88	1	∫	∫	PROPN
ejpam-7023	89	1	∞	∞	NOUN
ejpam-7023	89	2	0	0	NUM
ejpam-7023	90	1	sin(ax)−	sin(ax)−	PROPN
ejpam-7023	90	2	sin((a+	sin((a+	NUM
ejpam-7023	90	3	1)x	1)x	NUM
ejpam-7023	90	4	)	)	PUNCT
ejpam-7023	90	5	x	x	SYM
ejpam-7023	90	6	dx	dx	PROPN
ejpam-7023	90	7	=	=	SYM
ejpam-7023	90	8	0	0	PROPN
ejpam-7023	90	9	,	,	PUNCT
ejpam-7023	90	10	a	a	DET
ejpam-7023	90	11	>	>	X
ejpam-7023	90	12	0	0	NUM
ejpam-7023	90	13	.	.	PUNCT
ejpam-7023	91	1	this	this	PRON
ejpam-7023	91	2	follows	follow	VERB
ejpam-7023	91	3	from	from	ADP
ejpam-7023	91	4	the	the	DET
ejpam-7023	91	5	dirichlet	dirichlet	PROPN
ejpam-7023	91	6	integral	integral	ADJ
ejpam-7023	91	7	∫	∫	PROPN
ejpam-7023	91	8	∞	∞	PROPN
ejpam-7023	91	9	0	0	NUM
ejpam-7023	91	10	sin(αx	sin(αx	NOUN
ejpam-7023	91	11	)	)	PUNCT
ejpam-7023	91	12	x	x	SYM
ejpam-7023	91	13	dx	dx	PROPN
ejpam-7023	91	14	=	=	PUNCT
ejpam-7023	91	15	π	π	PROPN
ejpam-7023	91	16	2	2	NUM
ejpam-7023	91	17	sgn(α	sgn(α	PROPN
ejpam-7023	91	18	)	)	PUNCT
ejpam-7023	91	19	,	,	PUNCT
ejpam-7023	91	20	and	and	CCONJ
ejpam-7023	91	21	since	since	SCONJ
ejpam-7023	91	22	a	a	DET
ejpam-7023	91	23	>	>	X
ejpam-7023	91	24	0	0	NUM
ejpam-7023	91	25	and	and	CCONJ
ejpam-7023	91	26	a+	a+	PUNCT
ejpam-7023	91	27	1	1	NUM
ejpam-7023	91	28	>	>	SYM
ejpam-7023	91	29	0	0	NUM
ejpam-7023	91	30	,	,	PUNCT
ejpam-7023	91	31	i(a	i(a	PROPN
ejpam-7023	91	32	)	)	PUNCT
ejpam-7023	91	33	=	=	PUNCT
ejpam-7023	92	1	π	π	NOUN
ejpam-7023	92	2	2	2	X
ejpam-7023	92	3	−	−	NOUN
ejpam-7023	92	4	π	π	NOUN
ejpam-7023	92	5	2	2	NUM
ejpam-7023	92	6	=	=	SYM
ejpam-7023	92	7	0	0	NUM
ejpam-7023	92	8	.	.	PUNCT
ejpam-7023	92	9	thus	thus	ADV
ejpam-7023	92	10	i(a	i(a	X
ejpam-7023	92	11	)	)	PUNCT
ejpam-7023	92	12	=	=	SYM
ejpam-7023	92	13	0	0	NUM
ejpam-7023	92	14	for	for	ADP
ejpam-7023	92	15	a	a	DET
ejpam-7023	92	16	>	>	X
ejpam-7023	92	17	0	0	NUM
ejpam-7023	92	18	.	.	PUNCT
ejpam-7023	93	1	another	another	DET
ejpam-7023	93	2	motivating	motivating	NOUN
ejpam-7023	93	3	example	example	NOUN
ejpam-7023	93	4	for	for	ADP
ejpam-7023	93	5	studying	study	VERB
ejpam-7023	93	6	question	question	NOUN
ejpam-7023	93	7	1	1	NUM
ejpam-7023	93	8	and	and	CCONJ
ejpam-7023	93	9	question	question	NOUN
ejpam-7023	93	10	2	2	NUM
ejpam-7023	93	11	,	,	PUNCT
ejpam-7023	93	12	and	and	CCONJ
ejpam-7023	93	13	more	more	ADV
ejpam-7023	93	14	broadly	broadly	ADV
ejpam-7023	93	15	,	,	PUNCT
ejpam-7023	93	16	integrals	integral	NOUN
ejpam-7023	93	17	that	that	PRON
ejpam-7023	93	18	vanish	vanish	VERB
ejpam-7023	93	19	for	for	ADP
ejpam-7023	93	20	every	every	DET
ejpam-7023	93	21	value	value	NOUN
ejpam-7023	93	22	of	of	ADP
ejpam-7023	93	23	a	a	DET
ejpam-7023	93	24	continuous	continuous	ADJ
ejpam-7023	93	25	parameter	parameter	NOUN
ejpam-7023	93	26	,	,	PUNCT
ejpam-7023	93	27	is	be	AUX
ejpam-7023	93	28	salem	salem	NOUN
ejpam-7023	93	29	’s	’s	PART
ejpam-7023	93	30	equivalence	equivalence	NOUN
ejpam-7023	93	31	of	of	ADP
ejpam-7023	93	32	the	the	DET
ejpam-7023	93	33	riemann	riemann	PROPN
ejpam-7023	93	34	hypothesis	hypothesis	NOUN
ejpam-7023	93	35	.	.	PUNCT
ejpam-7023	94	1	this	this	DET
ejpam-7023	94	2	equivalence	equivalence	NOUN
ejpam-7023	94	3	is	be	AUX
ejpam-7023	94	4	expressed	express	VERB
ejpam-7023	94	5	through	through	ADP
ejpam-7023	94	6	an	an	DET
ejpam-7023	94	7	integral	integral	ADJ
ejpam-7023	94	8	involving	involve	VERB
ejpam-7023	94	9	a	a	DET
ejpam-7023	94	10	continuous	continuous	ADJ
ejpam-7023	94	11	parameter	parameter	NOUN
ejpam-7023	94	12	,	,	PUNCT
ejpam-7023	94	13	as	as	SCONJ
ejpam-7023	94	14	stated	state	VERB
ejpam-7023	94	15	below	below	ADV
ejpam-7023	94	16	:	:	PUNCT
ejpam-7023	94	17	theorem	theorem	NOUN
ejpam-7023	94	18	1	1	NUM
ejpam-7023	94	19	.	.	PUNCT
ejpam-7023	95	1	[	[	X
ejpam-7023	95	2	14	14	NUM
ejpam-7023	95	3	]	]	PUNCT
ejpam-7023	95	4	the	the	DET
ejpam-7023	95	5	riemann	riemann	PROPN
ejpam-7023	95	6	hypothesis	hypothesis	NOUN
ejpam-7023	95	7	is	be	AUX
ejpam-7023	95	8	true	true	ADJ
ejpam-7023	95	9	if	if	SCONJ
ejpam-7023	95	10	and	and	CCONJ
ejpam-7023	95	11	only	only	ADV
ejpam-7023	95	12	if	if	SCONJ
ejpam-7023	95	13	the	the	DET
ejpam-7023	95	14	integral	integral	ADJ
ejpam-7023	95	15	equation∫	equation∫	NOUN
ejpam-7023	95	16	∞	∞	PROPN
ejpam-7023	95	17	0	0	NUM
ejpam-7023	95	18	xr−1f(x	xr−1f(x	PROPN
ejpam-7023	95	19	)	)	PUNCT
ejpam-7023	95	20	ext	ext	NOUN
ejpam-7023	96	1	+	+	CCONJ
ejpam-7023	96	2	1	1	NUM
ejpam-7023	96	3	dx	dx	NOUN
ejpam-7023	96	4	=	=	SYM
ejpam-7023	96	5	0	0	PROPN
ejpam-7023	96	6	,	,	PUNCT
ejpam-7023	96	7	for	for	ADP
ejpam-7023	96	8	all	all	DET
ejpam-7023	96	9	t	t	PROPN
ejpam-7023	96	10	>	>	X
ejpam-7023	96	11	0	0	PROPN
ejpam-7023	96	12	,	,	PUNCT
ejpam-7023	96	13	admits	admit	VERB
ejpam-7023	96	14	only	only	ADV
ejpam-7023	96	15	the	the	DET
ejpam-7023	96	16	trivial	trivial	ADJ
ejpam-7023	96	17	bounded	bounded	ADJ
ejpam-7023	96	18	measurable	measurable	ADJ
ejpam-7023	96	19	solution	solution	NOUN
ejpam-7023	96	20	f(x	f(x	PROPN
ejpam-7023	96	21	)	)	PUNCT
ejpam-7023	96	22	≡	≡	PROPN
ejpam-7023	96	23	0	0	NUM
ejpam-7023	96	24	,	,	PUNCT
ejpam-7023	96	25	for	for	ADP
ejpam-7023	96	26	a	a	DET
ejpam-7023	96	27	fixed	fix	VERB
ejpam-7023	96	28	parameter	parameter	NOUN
ejpam-7023	96	29	r	r	NOUN
ejpam-7023	96	30	satisfying	satisfy	VERB
ejpam-7023	96	31	1	1	NUM
ejpam-7023	96	32	2	2	NUM
ejpam-7023	96	33	<	<	X
ejpam-7023	96	34	r	r	NOUN
ejpam-7023	96	35	<	<	X
ejpam-7023	96	36	1	1	NUM
ejpam-7023	96	37	.	.	PUNCT
ejpam-7023	97	1	equivalently	equivalently	ADV
ejpam-7023	97	2	,	,	PUNCT
ejpam-7023	97	3	we	we	PRON
ejpam-7023	97	4	we	we	PRON
ejpam-7023	97	5	may	may	AUX
ejpam-7023	97	6	write	write	VERB
ejpam-7023	97	7	theorem	theorem	NOUN
ejpam-7023	97	8	1	1	NUM
ejpam-7023	97	9	as	as	ADP
ejpam-7023	97	10	following	follow	VERB
ejpam-7023	97	11	:	:	PUNCT
ejpam-7023	97	12	theorem	theorem	NOUN
ejpam-7023	97	13	2	2	NUM
ejpam-7023	97	14	.	.	PUNCT
ejpam-7023	98	1	the	the	DET
ejpam-7023	98	2	riemann	riemann	PROPN
ejpam-7023	98	3	hypothesis	hypothesis	NOUN
ejpam-7023	98	4	is	be	AUX
ejpam-7023	98	5	false	false	ADJ
ejpam-7023	98	6	if	if	SCONJ
ejpam-7023	99	1	and	and	CCONJ
ejpam-7023	99	2	only	only	ADV
ejpam-7023	99	3	if	if	SCONJ
ejpam-7023	99	4	there	there	PRON
ejpam-7023	99	5	exists	exist	VERB
ejpam-7023	99	6	a	a	DET
ejpam-7023	99	7	nontrivial	nontrivial	NOUN
ejpam-7023	99	8	bounded	bound	VERB
ejpam-7023	99	9	measurable	measurable	ADJ
ejpam-7023	99	10	function	function	NOUN
ejpam-7023	99	11	f(x	f(x	PROPN
ejpam-7023	99	12	)	)	PUNCT
ejpam-7023	99	13	̸≡	̸≡	NOUN
ejpam-7023	99	14	0	0	PUNCT
ejpam-7023	100	1	satisfying	satisfy	VERB
ejpam-7023	100	2	the	the	DET
ejpam-7023	100	3	integral	integral	ADJ
ejpam-7023	100	4	equation∫	equation∫	NOUN
ejpam-7023	100	5	∞	∞	PROPN
ejpam-7023	100	6	0	0	NUM
ejpam-7023	100	7	xr−1f(x	xr−1f(x	PROPN
ejpam-7023	100	8	)	)	PUNCT
ejpam-7023	100	9	ext	ext	NOUN
ejpam-7023	101	1	+	+	CCONJ
ejpam-7023	101	2	1	1	NUM
ejpam-7023	101	3	dx	dx	NOUN
ejpam-7023	101	4	=	=	SYM
ejpam-7023	101	5	0	0	PROPN
ejpam-7023	101	6	,	,	PUNCT
ejpam-7023	101	7	for	for	ADP
ejpam-7023	101	8	all	all	DET
ejpam-7023	101	9	t	t	PROPN
ejpam-7023	101	10	>	>	X
ejpam-7023	101	11	0	0	NUM
ejpam-7023	101	12	,	,	PUNCT
ejpam-7023	101	13	for	for	ADP
ejpam-7023	101	14	fixed	fix	VERB
ejpam-7023	101	15	parameter	parameter	NOUN
ejpam-7023	101	16	r	r	NOUN
ejpam-7023	101	17	such	such	ADJ
ejpam-7023	101	18	that	that	SCONJ
ejpam-7023	101	19	1	1	NUM
ejpam-7023	101	20	2	2	NUM
ejpam-7023	101	21	<	<	X
ejpam-7023	101	22	r	r	NOUN
ejpam-7023	101	23	<	<	X
ejpam-7023	101	24	1	1	NUM
ejpam-7023	101	25	.	.	PUNCT
ejpam-7023	101	26	salem	salem	NOUN
ejpam-7023	101	27	’s	’s	PART
ejpam-7023	101	28	criterion	criterion	NOUN
ejpam-7023	101	29	has	have	AUX
ejpam-7023	101	30	been	be	AUX
ejpam-7023	101	31	the	the	DET
ejpam-7023	101	32	subject	subject	NOUN
ejpam-7023	101	33	of	of	ADP
ejpam-7023	101	34	recent	recent	ADJ
ejpam-7023	101	35	investigations	investigation	NOUN
ejpam-7023	101	36	by	by	ADP
ejpam-7023	101	37	several	several	ADJ
ejpam-7023	101	38	authors	author	NOUN
ejpam-7023	101	39	(	(	PUNCT
ejpam-7023	101	40	[	[	X
ejpam-7023	101	41	15	15	NUM
ejpam-7023	101	42	–	–	SYM
ejpam-7023	101	43	18	18	NUM
ejpam-7023	101	44	]	]	PUNCT
ejpam-7023	101	45	)	)	PUNCT
ejpam-7023	101	46	using	use	VERB
ejpam-7023	101	47	a	a	DET
ejpam-7023	101	48	variety	variety	NOUN
ejpam-7023	101	49	of	of	ADP
ejpam-7023	101	50	integral	integral	ADJ
ejpam-7023	101	51	transform	transform	NOUN
ejpam-7023	101	52	techniques	technique	NOUN
ejpam-7023	101	53	.	.	PUNCT
ejpam-7023	102	1	in	in	ADP
ejpam-7023	102	2	particular	particular	ADJ
ejpam-7023	102	3	,	,	PUNCT
ejpam-7023	102	4	the	the	DET
ejpam-7023	102	5	following	following	ADJ
ejpam-7023	102	6	result	result	NOUN
ejpam-7023	102	7	was	be	AUX
ejpam-7023	102	8	obtained	obtain	VERB
ejpam-7023	102	9	in	in	ADP
ejpam-7023	102	10	[	[	X
ejpam-7023	102	11	17	17	NUM
ejpam-7023	102	12	]	]	PUNCT
ejpam-7023	102	13	(	(	PUNCT
ejpam-7023	102	14	see	see	VERB
ejpam-7023	102	15	corollary	corollary	ADJ
ejpam-7023	102	16	3.3	3.3	NUM
ejpam-7023	102	17	):	):	PUNCT
ejpam-7023	102	18	theorem	theorem	ADJ
ejpam-7023	102	19	3	3	X
ejpam-7023	102	20	.	.	PUNCT
ejpam-7023	103	1	let	let	VERB
ejpam-7023	103	2	f(x	f(x	PROPN
ejpam-7023	103	3	)	)	PUNCT
ejpam-7023	103	4	be	be	AUX
ejpam-7023	103	5	a	a	DET
ejpam-7023	103	6	bounded	bounded	ADJ
ejpam-7023	103	7	measurable	measurable	ADJ
ejpam-7023	103	8	function	function	NOUN
ejpam-7023	103	9	on	on	ADP
ejpam-7023	103	10	r+	r+	NOUN
ejpam-7023	104	1	such	such	ADJ
ejpam-7023	104	2	that	that	SCONJ
ejpam-7023	104	3	f(x	f(x	NOUN
ejpam-7023	104	4	)	)	PUNCT
ejpam-7023	104	5	=	=	SYM
ejpam-7023	104	6	o(x1/2	o(x1/2	PROPN
ejpam-7023	104	7	)	)	PUNCT
ejpam-7023	104	8	as	as	ADP
ejpam-7023	104	9	x	x	X
ejpam-7023	104	10	→	→	SYM
ejpam-7023	104	11	0	0	NUM
ejpam-7023	104	12	+	+	NOUN
ejpam-7023	104	13	.	.	PUNCT
ejpam-7023	105	1	if	if	SCONJ
ejpam-7023	105	2	f(x	f(x	PROPN
ejpam-7023	105	3	)	)	PUNCT
ejpam-7023	105	4	satisfies	satisfy	VERB
ejpam-7023	105	5	the	the	DET
ejpam-7023	105	6	integral	integral	ADJ
ejpam-7023	105	7	equation	equation	NOUN
ejpam-7023	105	8	given	give	VERB
ejpam-7023	105	9	in	in	ADP
ejpam-7023	105	10	theorem	theorem	NOUN
ejpam-7023	105	11	1	1	NUM
ejpam-7023	105	12	for	for	ADP
ejpam-7023	105	13	given	give	VERB
ejpam-7023	105	14	k	k	PROPN
ejpam-7023	105	15	with	with	ADP
ejpam-7023	105	16	1	1	NUM
ejpam-7023	105	17	2	2	NUM
ejpam-7023	105	18	<	<	X
ejpam-7023	105	19	k	k	X
ejpam-7023	105	20	<	<	X
ejpam-7023	105	21	1	1	NUM
ejpam-7023	105	22	and	and	CCONJ
ejpam-7023	105	23	for	for	ADP
ejpam-7023	105	24	all	all	DET
ejpam-7023	105	25	t	t	PROPN
ejpam-7023	105	26	>	>	X
ejpam-7023	105	27	0	0	NUM
ejpam-7023	105	28	,	,	PUNCT
ejpam-7023	105	29	then	then	ADV
ejpam-7023	105	30	f(x	f(x	PROPN
ejpam-7023	105	31	)	)	PUNCT
ejpam-7023	105	32	vanishes	vanish	VERB
ejpam-7023	105	33	almost	almost	ADV
ejpam-7023	105	34	everywhere	everywhere	ADV
ejpam-7023	105	35	on	on	ADP
ejpam-7023	105	36	r+	r+	X
ejpam-7023	105	37	.	.	PUNCT
ejpam-7023	106	1	i.	i.	PROPN
ejpam-7023	106	2	ayoob	ayoob	PROPN
ejpam-7023	106	3	/	/	SYM
ejpam-7023	106	4	eur	eur	PROPN
ejpam-7023	106	5	.	.	PUNCT
ejpam-7023	107	1	j.	j.	PROPN
ejpam-7023	107	2	pure	pure	PROPN
ejpam-7023	107	3	appl	appl	PROPN
ejpam-7023	107	4	.	.	PROPN
ejpam-7023	107	5	math	math	PROPN
ejpam-7023	107	6	,	,	PUNCT
ejpam-7023	107	7	18	18	NUM
ejpam-7023	107	8	(	(	PUNCT
ejpam-7023	107	9	4	4	NUM
ejpam-7023	107	10	)	)	PUNCT
ejpam-7023	107	11	(	(	PUNCT
ejpam-7023	107	12	2025	2025	NUM
ejpam-7023	107	13	)	)	PUNCT
ejpam-7023	107	14	,	,	PUNCT
ejpam-7023	107	15	7023	7023	NUM
ejpam-7023	107	16	5	5	NUM
ejpam-7023	107	17	of	of	ADP
ejpam-7023	107	18	16	16	NUM
ejpam-7023	107	19	it	it	PRON
ejpam-7023	107	20	is	be	AUX
ejpam-7023	107	21	important	important	ADJ
ejpam-7023	107	22	to	to	PART
ejpam-7023	107	23	note	note	VERB
ejpam-7023	107	24	that	that	SCONJ
ejpam-7023	107	25	if	if	SCONJ
ejpam-7023	107	26	there	there	PRON
ejpam-7023	107	27	exists	exist	VERB
ejpam-7023	107	28	a	a	DET
ejpam-7023	107	29	nontrivial	nontrivial	NOUN
ejpam-7023	107	30	bounded	bound	VERB
ejpam-7023	107	31	measurable	measurable	ADJ
ejpam-7023	107	32	function	function	NOUN
ejpam-7023	107	33	f(x	f(x	PROPN
ejpam-7023	107	34	)	)	PUNCT
ejpam-7023	107	35	satisfying	satisfy	VERB
ejpam-7023	107	36	the	the	DET
ejpam-7023	107	37	integral	integral	ADJ
ejpam-7023	107	38	equation	equation	NOUN
ejpam-7023	107	39	presented	present	VERB
ejpam-7023	107	40	in	in	ADP
ejpam-7023	107	41	theorem	theorem	NOUN
ejpam-7023	107	42	2	2	NUM
ejpam-7023	107	43	for	for	ADP
ejpam-7023	107	44	all	all	DET
ejpam-7023	107	45	continuous	continuous	ADJ
ejpam-7023	107	46	parameters	parameter	NOUN
ejpam-7023	107	47	t	t	PROPN
ejpam-7023	107	48	>	>	X
ejpam-7023	107	49	0	0	PROPN
ejpam-7023	107	50	,	,	PUNCT
ejpam-7023	107	51	then	then	ADV
ejpam-7023	107	52	such	such	DET
ejpam-7023	107	53	an	an	DET
ejpam-7023	107	54	f(x	f(x	PROPN
ejpam-7023	107	55	)	)	PUNCT
ejpam-7023	107	56	would	would	AUX
ejpam-7023	107	57	constitute	constitute	VERB
ejpam-7023	107	58	a	a	DET
ejpam-7023	107	59	counterexample	counterexample	NOUN
ejpam-7023	107	60	to	to	ADP
ejpam-7023	107	61	salem	salem	PROPN
ejpam-7023	107	62	’s	’s	PART
ejpam-7023	107	63	equivalence	equivalence	NOUN
ejpam-7023	107	64	of	of	ADP
ejpam-7023	107	65	the	the	DET
ejpam-7023	107	66	riemann	riemann	PROPN
ejpam-7023	107	67	hypothesis	hypothesis	NOUN
ejpam-7023	107	68	.	.	PUNCT
ejpam-7023	108	1	emphasis	emphasis	NOUN
ejpam-7023	108	2	should	should	AUX
ejpam-7023	108	3	be	be	AUX
ejpam-7023	108	4	placed	place	VERB
ejpam-7023	108	5	on	on	ADP
ejpam-7023	108	6	the	the	DET
ejpam-7023	108	7	fact	fact	NOUN
ejpam-7023	108	8	that	that	SCONJ
ejpam-7023	108	9	this	this	DET
ejpam-7023	108	10	nontrivial	nontrivial	NOUN
ejpam-7023	108	11	bounded	bound	VERB
ejpam-7023	108	12	function	function	NOUN
ejpam-7023	108	13	must	must	AUX
ejpam-7023	108	14	cause	cause	VERB
ejpam-7023	108	15	the	the	DET
ejpam-7023	108	16	integral	integral	NOUN
ejpam-7023	108	17	on	on	ADP
ejpam-7023	108	18	the	the	DET
ejpam-7023	108	19	left	left	ADJ
ejpam-7023	108	20	-	-	PUNCT
ejpam-7023	108	21	hand	hand	NOUN
ejpam-7023	108	22	side	side	NOUN
ejpam-7023	108	23	of	of	ADP
ejpam-7023	108	24	theorem	theorem	NOUN
ejpam-7023	108	25	2	2	NUM
ejpam-7023	108	26	to	to	PART
ejpam-7023	108	27	vanish	vanish	VERB
ejpam-7023	108	28	for	for	ADP
ejpam-7023	108	29	all	all	DET
ejpam-7023	108	30	t	t	PROPN
ejpam-7023	108	31	>	>	X
ejpam-7023	108	32	0	0	X
ejpam-7023	108	33	.	.	PUNCT
ejpam-7023	109	1	consequently	consequently	ADV
ejpam-7023	109	2	,	,	PUNCT
ejpam-7023	109	3	the	the	DET
ejpam-7023	109	4	study	study	NOUN
ejpam-7023	109	5	of	of	ADP
ejpam-7023	109	6	such	such	ADJ
ejpam-7023	109	7	parameter	parameter	NOUN
ejpam-7023	109	8	-	-	PUNCT
ejpam-7023	109	9	dependent	dependent	ADJ
ejpam-7023	109	10	improper	improper	ADJ
ejpam-7023	109	11	integrals	integral	NOUN
ejpam-7023	109	12	that	that	PRON
ejpam-7023	109	13	vanish	vanish	VERB
ejpam-7023	109	14	for	for	ADP
ejpam-7023	109	15	every	every	DET
ejpam-7023	109	16	value	value	NOUN
ejpam-7023	109	17	of	of	ADP
ejpam-7023	109	18	a	a	DET
ejpam-7023	109	19	continuous	continuous	ADJ
ejpam-7023	109	20	parameter	parameter	NOUN
ejpam-7023	109	21	becomes	become	VERB
ejpam-7023	109	22	particularly	particularly	ADV
ejpam-7023	109	23	interesting	interesting	ADJ
ejpam-7023	109	24	depending	depend	VERB
ejpam-7023	109	25	upon	upon	SCONJ
ejpam-7023	109	26	the	the	DET
ejpam-7023	109	27	context	context	NOUN
ejpam-7023	109	28	.	.	PUNCT
ejpam-7023	110	1	this	this	DET
ejpam-7023	110	2	paper	paper	NOUN
ejpam-7023	110	3	examines	examine	VERB
ejpam-7023	110	4	a	a	DET
ejpam-7023	110	5	parameter	parameter	NOUN
ejpam-7023	110	6	-	-	PUNCT
ejpam-7023	110	7	dependent	dependent	ADJ
ejpam-7023	110	8	improper	improper	ADJ
ejpam-7023	110	9	integral	integral	ADJ
ejpam-7023	110	10	,	,	PUNCT
ejpam-7023	110	11	inspired	inspire	VERB
ejpam-7023	110	12	by	by	ADP
ejpam-7023	110	13	the	the	DET
ejpam-7023	110	14	stieltjes	stieltjes	PROPN
ejpam-7023	110	15	moment	moment	NOUN
ejpam-7023	110	16	problem	problem	NOUN
ejpam-7023	110	17	,	,	PUNCT
ejpam-7023	110	18	which	which	PRON
ejpam-7023	110	19	vanishes	vanish	VERB
ejpam-7023	110	20	for	for	ADP
ejpam-7023	110	21	all	all	DET
ejpam-7023	110	22	continuous	continuous	ADJ
ejpam-7023	110	23	parameter	parameter	NOUN
ejpam-7023	110	24	values	value	NOUN
ejpam-7023	110	25	.	.	PUNCT
ejpam-7023	111	1	2	2	X
ejpam-7023	111	2	.	.	X
ejpam-7023	111	3	main	main	ADJ
ejpam-7023	111	4	results	result	NOUN
ejpam-7023	111	5	we	we	PRON
ejpam-7023	111	6	begin	begin	VERB
ejpam-7023	111	7	with	with	ADP
ejpam-7023	111	8	the	the	DET
ejpam-7023	111	9	explicit	explicit	ADJ
ejpam-7023	111	10	evaluation	evaluation	NOUN
ejpam-7023	111	11	of	of	ADP
ejpam-7023	111	12	steiltjes	steiltjes	PROPN
ejpam-7023	111	13	integral	integral	ADJ
ejpam-7023	111	14	.	.	PUNCT
ejpam-7023	112	1	theorem	theorem	ADJ
ejpam-7023	112	2	4	4	NUM
ejpam-7023	112	3	.	.	X
ejpam-7023	113	1	for	for	ADP
ejpam-7023	113	2	a	a	DET
ejpam-7023	113	3	real	real	ADJ
ejpam-7023	113	4	number	number	NOUN
ejpam-7023	113	5	k	k	PROPN
ejpam-7023	113	6	>	>	X
ejpam-7023	113	7	−1	−1	NOUN
ejpam-7023	113	8	define	define	VERB
ejpam-7023	113	9	i(k	i(k	PROPN
ejpam-7023	113	10	)	)	PUNCT
ejpam-7023	113	11	=	=	SYM
ejpam-7023	114	1	∫	∫	PROPN
ejpam-7023	114	2	∞	∞	NUM
ejpam-7023	114	3	0	0	NUM
ejpam-7023	115	1	e−x1/4	e−x1/4	PROPN
ejpam-7023	115	2	sin	sin	NOUN
ejpam-7023	115	3	(	(	PUNCT
ejpam-7023	115	4	x1/4	x1/4	PROPN
ejpam-7023	115	5	)	)	PUNCT
ejpam-7023	115	6	xk	xk	PROPN
ejpam-7023	115	7	dx	dx	PROPN
ejpam-7023	115	8	.	.	PUNCT
ejpam-7023	116	1	(	(	PUNCT
ejpam-7023	116	2	4	4	NUM
ejpam-7023	116	3	)	)	PUNCT
ejpam-7023	116	4	then	then	ADV
ejpam-7023	116	5	i(k	i(k	PROPN
ejpam-7023	116	6	)	)	PUNCT
ejpam-7023	116	7	is	be	AUX
ejpam-7023	116	8	absolutely	absolutely	ADV
ejpam-7023	116	9	convergent	convergent	ADJ
ejpam-7023	116	10	for	for	ADP
ejpam-7023	116	11	k	k	PROPN
ejpam-7023	116	12	>	>	X
ejpam-7023	116	13	−1	−1	NOUN
ejpam-7023	116	14	and	and	CCONJ
ejpam-7023	116	15	,	,	PUNCT
ejpam-7023	116	16	i(k	i(k	PROPN
ejpam-7023	116	17	)	)	PUNCT
ejpam-7023	117	1	=	=	SYM
ejpam-7023	117	2	2−2k	2−2k	NUM
ejpam-7023	117	3	γ(4k	γ(4k	NOUN
ejpam-7023	117	4	+	+	CCONJ
ejpam-7023	117	5	4	4	X
ejpam-7023	117	6	)	)	PUNCT
ejpam-7023	117	7	sin	sin	NOUN
ejpam-7023	117	8	(	(	PUNCT
ejpam-7023	117	9	(	(	PUNCT
ejpam-7023	117	10	k	k	X
ejpam-7023	117	11	+	+	PROPN
ejpam-7023	117	12	1)π	1)π	NUM
ejpam-7023	117	13	)	)	PUNCT
ejpam-7023	117	14	,	,	PUNCT
ejpam-7023	117	15	(	(	PUNCT
ejpam-7023	117	16	5	5	NUM
ejpam-7023	117	17	)	)	PUNCT
ejpam-7023	117	18	and	and	CCONJ
ejpam-7023	117	19	,	,	PUNCT
ejpam-7023	117	20	in	in	ADP
ejpam-7023	117	21	particular	particular	ADJ
ejpam-7023	117	22	,	,	PUNCT
ejpam-7023	117	23	i(k	i(k	PROPN
ejpam-7023	117	24	)	)	PUNCT
ejpam-7023	117	25	=	=	SYM
ejpam-7023	117	26	0	0	PUNCT
ejpam-7023	118	1	if	if	SCONJ
ejpam-7023	118	2	and	and	CCONJ
ejpam-7023	118	3	only	only	ADV
ejpam-7023	118	4	if	if	SCONJ
ejpam-7023	118	5	k	k	PROPN
ejpam-7023	118	6	∈	∈	PROPN
ejpam-7023	118	7	{	{	PUNCT
ejpam-7023	118	8	0	0	NUM
ejpam-7023	118	9	,	,	PUNCT
ejpam-7023	118	10	1	1	NUM
ejpam-7023	118	11	,	,	PUNCT
ejpam-7023	118	12	2	2	NUM
ejpam-7023	118	13	,	,	PUNCT
ejpam-7023	118	14	.	.	PUNCT
ejpam-7023	118	15	.	.	PUNCT
ejpam-7023	118	16	.	.	PUNCT
ejpam-7023	118	17	}	}	PUNCT
ejpam-7023	118	18	.	.	PUNCT
ejpam-7023	118	19	proof	proof	NOUN
ejpam-7023	118	20	.	.	PUNCT
ejpam-7023	119	1	absolute	absolute	ADJ
ejpam-7023	119	2	convergence	convergence	NOUN
ejpam-7023	119	3	of	of	ADP
ejpam-7023	119	4	(	(	PUNCT
ejpam-7023	119	5	4	4	NUM
ejpam-7023	119	6	)	)	PUNCT
ejpam-7023	119	7	holds	hold	VERB
ejpam-7023	119	8	for	for	ADP
ejpam-7023	119	9	k	k	PROPN
ejpam-7023	119	10	>	>	X
ejpam-7023	119	11	−1	−1	NOUN
ejpam-7023	119	12	because	because	SCONJ
ejpam-7023	119	13	on	on	ADP
ejpam-7023	119	14	[	[	X
ejpam-7023	119	15	0	0	NUM
ejpam-7023	119	16	,	,	PUNCT
ejpam-7023	119	17	1],∣∣e−x1/4	1],∣∣e−x1/4	NUM
ejpam-7023	119	18	sin(x1/4)xk	sin(x1/4)xk	NOUN
ejpam-7023	119	19	∣∣	∣∣	X
ejpam-7023	119	20	≤	≤	NOUN
ejpam-7023	119	21	x1/4xk	x1/4xk	PUNCT
ejpam-7023	119	22	=	=	SYM
ejpam-7023	119	23	xk+1/4	xk+1/4	PROPN
ejpam-7023	119	24	≤	≤	PROPN
ejpam-7023	120	1	xk	xk	PROPN
ejpam-7023	120	2	,	,	PUNCT
ejpam-7023	120	3	∫	∫	PROPN
ejpam-7023	120	4	1	1	NUM
ejpam-7023	120	5	0	0	NUM
ejpam-7023	120	6	xk	xk	PROPN
ejpam-7023	120	7	dx	dx	PROPN
ejpam-7023	120	8	=	=	SYM
ejpam-7023	120	9	1	1	NUM
ejpam-7023	120	10	k	k	X
ejpam-7023	120	11	+	+	CCONJ
ejpam-7023	120	12	1	1	NUM
ejpam-7023	120	13	<	<	X
ejpam-7023	120	14	∞	∞	PROPN
ejpam-7023	120	15	,	,	PUNCT
ejpam-7023	120	16	and	and	CCONJ
ejpam-7023	120	17	on	on	ADP
ejpam-7023	120	18	[	[	X
ejpam-7023	120	19	1,∞	1,∞	NUM
ejpam-7023	120	20	)	)	PUNCT
ejpam-7023	120	21	we	we	PRON
ejpam-7023	120	22	have	have	AUX
ejpam-7023	120	23	|	|	ADV
ejpam-7023	120	24	sin(x1/4)|	sin(x1/4)|	VERB
ejpam-7023	120	25	≤	≤	NUM
ejpam-7023	120	26	1	1	NUM
ejpam-7023	120	27	and	and	CCONJ
ejpam-7023	120	28	the	the	DET
ejpam-7023	120	29	factor	factor	NOUN
ejpam-7023	120	30	e−x1/4	e−x1/4	PROPN
ejpam-7023	120	31	decays	decay	VERB
ejpam-7023	120	32	super	super	ADJ
ejpam-7023	120	33	–	–	PUNCT
ejpam-7023	120	34	polynomially	polynomially	ADJ
ejpam-7023	120	35	,	,	PUNCT
ejpam-7023	120	36	so∫∞	so∫∞	ADJ
ejpam-7023	120	37	1	1	NUM
ejpam-7023	120	38	e−x1/4	e−x1/4	PROPN
ejpam-7023	120	39	xk	xk	PROPN
ejpam-7023	120	40	dx	dx	PROPN
ejpam-7023	120	41	<	<	X
ejpam-7023	120	42	∞.	∞.	PROPN
ejpam-7023	120	43	we	we	PRON
ejpam-7023	120	44	make	make	VERB
ejpam-7023	120	45	the	the	DET
ejpam-7023	120	46	substitution	substitution	NOUN
ejpam-7023	120	47	,	,	PUNCT
ejpam-7023	120	48	u	u	NOUN
ejpam-7023	120	49	=	=	PROPN
ejpam-7023	120	50	x1/4	x1/4	PROPN
ejpam-7023	120	51	,	,	PUNCT
ejpam-7023	120	52	x	x	X
ejpam-7023	120	53	=	=	SYM
ejpam-7023	120	54	u4	u4	PROPN
ejpam-7023	120	55	,	,	PUNCT
ejpam-7023	120	56	dx	dx	PROPN
ejpam-7023	120	57	=	=	SYM
ejpam-7023	120	58	4u3	4u3	NUM
ejpam-7023	120	59	du	du	X
ejpam-7023	120	60	,	,	PUNCT
ejpam-7023	120	61	(	(	PUNCT
ejpam-7023	120	62	6	6	NUM
ejpam-7023	120	63	)	)	PUNCT
ejpam-7023	120	64	to	to	PART
ejpam-7023	120	65	obtain	obtain	VERB
ejpam-7023	120	66	i(k	i(k	PROPN
ejpam-7023	120	67	)	)	PUNCT
ejpam-7023	121	1	=	=	SYM
ejpam-7023	121	2	∫	∫	PROPN
ejpam-7023	122	1	∞	∞	NUM
ejpam-7023	122	2	0	0	NUM
ejpam-7023	122	3	e−u	e−u	PROPN
ejpam-7023	122	4	sin(u	sin(u	PROPN
ejpam-7023	122	5	)	)	PUNCT
ejpam-7023	122	6	(	(	PUNCT
ejpam-7023	122	7	u4)k	u4)k	PROPN
ejpam-7023	122	8	(	(	PUNCT
ejpam-7023	122	9	4u3	4u3	NUM
ejpam-7023	122	10	)	)	PUNCT
ejpam-7023	122	11	du	du	PROPN
ejpam-7023	123	1	=	=	SYM
ejpam-7023	123	2	4	4	NUM
ejpam-7023	123	3	∫	∫	NOUN
ejpam-7023	123	4	∞	∞	NUM
ejpam-7023	123	5	0	0	NUM
ejpam-7023	123	6	e−u	e−u	PROPN
ejpam-7023	123	7	sin(u)u4k+3	sin(u)u4k+3	ADV
ejpam-7023	123	8	du	du	PROPN
ejpam-7023	123	9	.	.	PUNCT
ejpam-7023	123	10	(	(	PUNCT
ejpam-7023	123	11	7	7	X
ejpam-7023	123	12	)	)	PUNCT
ejpam-7023	123	13	we	we	PRON
ejpam-7023	123	14	denote	denote	VERB
ejpam-7023	123	15	real	real	ADJ
ejpam-7023	123	16	and	and	CCONJ
ejpam-7023	123	17	imaginary	imaginary	ADJ
ejpam-7023	123	18	parts	part	NOUN
ejpam-7023	123	19	by	by	ADP
ejpam-7023	123	20	ℜ	ℜ	PROPN
ejpam-7023	123	21	and	and	CCONJ
ejpam-7023	123	22	ℑ	ℑ	PROPN
ejpam-7023	123	23	,	,	PUNCT
ejpam-7023	123	24	and	and	CCONJ
ejpam-7023	123	25	write	write	VERB
ejpam-7023	123	26	sinu	sinu	NOUN
ejpam-7023	123	27	=	=	SYM
ejpam-7023	123	28	ℑ(eiu	ℑ(eiu	PROPN
ejpam-7023	123	29	)	)	PUNCT
ejpam-7023	123	30	,	,	PUNCT
ejpam-7023	123	31	we	we	PRON
ejpam-7023	123	32	have	have	VERB
ejpam-7023	123	33	e−u	e−u	PROPN
ejpam-7023	123	34	sinu	sinu	NOUN
ejpam-7023	123	35	=	=	SYM
ejpam-7023	123	36	ℑ	ℑ	PROPN
ejpam-7023	123	37	(	(	PUNCT
ejpam-7023	123	38	e−ueiu	e−ueiu	NOUN
ejpam-7023	123	39	)	)	PUNCT
ejpam-7023	124	1	=	=	SYM
ejpam-7023	124	2	ℑ	ℑ	PROPN
ejpam-7023	124	3	(	(	PUNCT
ejpam-7023	124	4	e−(1−i)u	e−(1−i)u	NOUN
ejpam-7023	124	5	)	)	PUNCT
ejpam-7023	124	6	,	,	PUNCT
ejpam-7023	124	7	⇒	⇒	VERB
ejpam-7023	124	8	∫	∫	PROPN
ejpam-7023	124	9	∞	∞	PROPN
ejpam-7023	124	10	0	0	NUM
ejpam-7023	124	11	u4k+3e−u	u4k+3e−u	ADJ
ejpam-7023	124	12	sinu	sinu	NOUN
ejpam-7023	124	13	du	du	PROPN
ejpam-7023	124	14	=	=	SYM
ejpam-7023	124	15	ℑ	ℑ	PROPN
ejpam-7023	124	16	∫	∫	PROPN
ejpam-7023	124	17	∞	∞	PROPN
ejpam-7023	124	18	0	0	PUNCT
ejpam-7023	125	1	u4k+3e−(1−i)u	u4k+3e−(1−i)u	VERB
ejpam-7023	125	2	du	du	X
ejpam-7023	125	3	.	.	PUNCT
ejpam-7023	126	1	(	(	PUNCT
ejpam-7023	126	2	8)	8)	NUM
ejpam-7023	126	3	combining	combine	VERB
ejpam-7023	126	4	(	(	PUNCT
ejpam-7023	126	5	7	7	NUM
ejpam-7023	126	6	)	)	PUNCT
ejpam-7023	126	7	and	and	CCONJ
ejpam-7023	126	8	(	(	PUNCT
ejpam-7023	126	9	8)	8)	NUM
ejpam-7023	126	10	yields	yield	VERB
ejpam-7023	126	11	the	the	DET
ejpam-7023	126	12	identity	identity	NOUN
ejpam-7023	126	13	,	,	PUNCT
ejpam-7023	126	14	i(k	i(k	PROPN
ejpam-7023	126	15	)	)	PUNCT
ejpam-7023	126	16	=	=	SYM
ejpam-7023	127	1	4ℑ	4ℑ	NOUN
ejpam-7023	127	2	∫	∫	PROPN
ejpam-7023	127	3	∞	∞	PROPN
ejpam-7023	127	4	0	0	PUNCT
ejpam-7023	128	1	u4k+3	u4k+3	PROPN
ejpam-7023	128	2	e−(1−i)u	e−(1−i)u	PROPN
ejpam-7023	128	3	du	du	PROPN
ejpam-7023	128	4	.	.	PUNCT
ejpam-7023	129	1	(	(	PUNCT
ejpam-7023	129	2	9	9	X
ejpam-7023	129	3	)	)	PUNCT
ejpam-7023	129	4	i.	i.	NOUN
ejpam-7023	129	5	ayoob	ayoob	PROPN
ejpam-7023	129	6	/	/	SYM
ejpam-7023	129	7	eur	eur	PROPN
ejpam-7023	129	8	.	.	PUNCT
ejpam-7023	130	1	j.	j.	PROPN
ejpam-7023	130	2	pure	pure	PROPN
ejpam-7023	130	3	appl	appl	PROPN
ejpam-7023	130	4	.	.	PROPN
ejpam-7023	130	5	math	math	PROPN
ejpam-7023	130	6	,	,	PUNCT
ejpam-7023	130	7	18	18	NUM
ejpam-7023	130	8	(	(	PUNCT
ejpam-7023	130	9	4	4	NUM
ejpam-7023	130	10	)	)	PUNCT
ejpam-7023	130	11	(	(	PUNCT
ejpam-7023	130	12	2025	2025	NUM
ejpam-7023	130	13	)	)	PUNCT
ejpam-7023	130	14	,	,	PUNCT
ejpam-7023	130	15	7023	7023	NUM
ejpam-7023	130	16	6	6	NUM
ejpam-7023	130	17	of	of	ADP
ejpam-7023	130	18	16	16	NUM
ejpam-7023	130	19	now	now	ADV
ejpam-7023	130	20	we	we	PRON
ejpam-7023	130	21	set	set	VERB
ejpam-7023	130	22	,	,	PUNCT
ejpam-7023	130	23	a	a	DET
ejpam-7023	130	24	=	=	X
ejpam-7023	130	25	4k	4k	NOUN
ejpam-7023	130	26	+	+	CCONJ
ejpam-7023	130	27	4	4	NUM
ejpam-7023	130	28	>	>	SYM
ejpam-7023	130	29	0	0	NUM
ejpam-7023	130	30	,	,	PUNCT
ejpam-7023	130	31	λ	λ	X
ejpam-7023	130	32	=	=	SYM
ejpam-7023	130	33	1−	1−	NUM
ejpam-7023	131	1	i	i	PRON
ejpam-7023	131	2	(	(	PUNCT
ejpam-7023	131	3	ℜλ	ℜλ	NOUN
ejpam-7023	131	4	=	=	SYM
ejpam-7023	131	5	1	1	NUM
ejpam-7023	131	6	>	>	PUNCT
ejpam-7023	131	7	0	0	NUM
ejpam-7023	131	8	)	)	PUNCT
ejpam-7023	131	9	.	.	PUNCT
ejpam-7023	132	1	(	(	PUNCT
ejpam-7023	132	2	10	10	NUM
ejpam-7023	132	3	)	)	PUNCT
ejpam-7023	132	4	by	by	ADP
ejpam-7023	132	5	the	the	DET
ejpam-7023	132	6	gamma	gamma	NOUN
ejpam-7023	132	7	function	function	NOUN
ejpam-7023	132	8	(	(	PUNCT
ejpam-7023	132	9	with	with	ADP
ejpam-7023	132	10	the	the	DET
ejpam-7023	132	11	substitution	substitution	NOUN
ejpam-7023	132	12	t	t	NOUN
ejpam-7023	132	13	=	=	SYM
ejpam-7023	132	14	λu	λu	PROPN
ejpam-7023	132	15	)	)	PUNCT
ejpam-7023	132	16	,	,	PUNCT
ejpam-7023	132	17	we	we	PRON
ejpam-7023	132	18	obtain∫	obtain∫	VERB
ejpam-7023	132	19	∞	∞	PROPN
ejpam-7023	132	20	0	0	PUNCT
ejpam-7023	132	21	ua−1e−λu	ua−1e−λu	NOUN
ejpam-7023	132	22	du	du	PROPN
ejpam-7023	132	23	=	=	SYM
ejpam-7023	132	24	∫	∫	PROPN
ejpam-7023	132	25	∞	∞	PROPN
ejpam-7023	132	26	0	0	NUM
ejpam-7023	133	1	(	(	PUNCT
ejpam-7023	133	2	t	t	NOUN
ejpam-7023	133	3	λ	λ	PROPN
ejpam-7023	133	4	)	)	PUNCT
ejpam-7023	133	5	a−1	a−1	PROPN
ejpam-7023	133	6	e−t	e−t	NOUN
ejpam-7023	133	7	dt	dt	X
ejpam-7023	133	8	λ	λ	X
ejpam-7023	133	9	=	=	SYM
ejpam-7023	133	10	λ−a	λ−a	X
ejpam-7023	133	11	∫	∫	PROPN
ejpam-7023	134	1	∞	∞	PROPN
ejpam-7023	134	2	0	0	NUM
ejpam-7023	134	3	ta−1e−t	ta−1e−t	NOUN
ejpam-7023	134	4	dt	dt	X
ejpam-7023	134	5	=	=	SYM
ejpam-7023	134	6	γ(a	γ(a	PROPN
ejpam-7023	134	7	)	)	PUNCT
ejpam-7023	134	8	λa	λa	X
ejpam-7023	134	9	,	,	PUNCT
ejpam-7023	134	10	(	(	PUNCT
ejpam-7023	134	11	11	11	NUM
ejpam-7023	134	12	)	)	PUNCT
ejpam-7023	134	13	we	we	PRON
ejpam-7023	134	14	have	have	VERB
ejpam-7023	134	15	,	,	PUNCT
ejpam-7023	134	16	with	with	ADP
ejpam-7023	134	17	a	a	DET
ejpam-7023	134	18	=	=	SYM
ejpam-7023	134	19	4k	4k	NOUN
ejpam-7023	134	20	+	+	NOUN
ejpam-7023	134	21	4	4	NUM
ejpam-7023	134	22	,	,	PUNCT
ejpam-7023	134	23	∫	∫	PROPN
ejpam-7023	134	24	∞	∞	PROPN
ejpam-7023	134	25	0	0	PUNCT
ejpam-7023	135	1	u4k+3e−(1−i)u	u4k+3e−(1−i)u	VERB
ejpam-7023	135	2	du	du	NOUN
ejpam-7023	135	3	=	=	NOUN
ejpam-7023	135	4	γ(4k	γ(4k	NOUN
ejpam-7023	135	5	+	+	NOUN
ejpam-7023	135	6	4	4	NUM
ejpam-7023	135	7	)	)	PUNCT
ejpam-7023	135	8	(	(	PUNCT
ejpam-7023	135	9	1−	1−	NUM
ejpam-7023	135	10	i	i	NOUN
ejpam-7023	135	11	)	)	PUNCT
ejpam-7023	136	1	4k+4	4k+4	PROPN
ejpam-7023	136	2	.	.	PUNCT
ejpam-7023	137	1	(	(	PUNCT
ejpam-7023	137	2	12	12	NUM
ejpam-7023	137	3	)	)	PUNCT
ejpam-7023	137	4	next	next	ADV
ejpam-7023	137	5	we	we	PRON
ejpam-7023	137	6	compute	compute	VERB
ejpam-7023	137	7	the	the	DET
ejpam-7023	137	8	complex	complex	ADJ
ejpam-7023	137	9	power	power	NOUN
ejpam-7023	137	10	explicitly	explicitly	ADV
ejpam-7023	137	11	using	use	VERB
ejpam-7023	137	12	the	the	DET
ejpam-7023	137	13	polar	polar	ADJ
ejpam-7023	137	14	form	form	NOUN
ejpam-7023	137	15	1−	1−	NUM
ejpam-7023	138	1	i	i	NOUN
ejpam-7023	138	2	=	=	PUNCT
ejpam-7023	138	3	√	√	PROPN
ejpam-7023	138	4	2	2	NUM
ejpam-7023	138	5	e−iπ/4	e−iπ/4	ADV
ejpam-7023	138	6	:	:	PUNCT
ejpam-7023	138	7	(	(	PUNCT
ejpam-7023	138	8	1−	1−	NUM
ejpam-7023	138	9	i)−(4k+4	i)−(4k+4	NOUN
ejpam-7023	138	10	)	)	PUNCT
ejpam-7023	138	11	=	=	PUNCT
ejpam-7023	138	12	(	(	PUNCT
ejpam-7023	138	13	√	√	ADP
ejpam-7023	138	14	2	2	NUM
ejpam-7023	138	15	e−iπ/4	e−iπ/4	CCONJ
ejpam-7023	138	16	)	)	PUNCT
ejpam-7023	138	17	−(4k+4	−(4k+4	PROPN
ejpam-7023	138	18	)	)	PUNCT
ejpam-7023	138	19	=	=	SYM
ejpam-7023	138	20	2−(2k+2	2−(2k+2	NUM
ejpam-7023	138	21	)	)	PUNCT
ejpam-7023	138	22	e	e	NOUN
ejpam-7023	138	23	i(4k+4)π/4	i(4k+4)π/4	X
ejpam-7023	138	24	=	=	SYM
ejpam-7023	138	25	2−(2k+2	2−(2k+2	PROPN
ejpam-7023	138	26	)	)	PUNCT
ejpam-7023	138	27	e	e	PROPN
ejpam-7023	138	28	i(k+1)π	i(k+1)π	PROPN
ejpam-7023	138	29	.	.	PUNCT
ejpam-7023	139	1	(	(	PUNCT
ejpam-7023	139	2	13	13	NUM
ejpam-7023	139	3	)	)	PUNCT
ejpam-7023	139	4	substituting	substituting	NOUN
ejpam-7023	139	5	(	(	PUNCT
ejpam-7023	139	6	12	12	NUM
ejpam-7023	139	7	)	)	PUNCT
ejpam-7023	139	8	and	and	CCONJ
ejpam-7023	139	9	(	(	PUNCT
ejpam-7023	139	10	13	13	NUM
ejpam-7023	139	11	)	)	PUNCT
ejpam-7023	139	12	into	into	ADP
ejpam-7023	139	13	(	(	PUNCT
ejpam-7023	139	14	9	9	NUM
ejpam-7023	139	15	)	)	PUNCT
ejpam-7023	139	16	and	and	CCONJ
ejpam-7023	139	17	taking	take	VERB
ejpam-7023	139	18	imaginary	imaginary	ADJ
ejpam-7023	139	19	parts	part	NOUN
ejpam-7023	139	20	gives	give	VERB
ejpam-7023	139	21	,	,	PUNCT
ejpam-7023	139	22	i(k	i(k	PROPN
ejpam-7023	139	23	)	)	PUNCT
ejpam-7023	139	24	=	=	SYM
ejpam-7023	139	25	4ℑ	4ℑ	NOUN
ejpam-7023	139	26	(	(	PUNCT
ejpam-7023	139	27	γ(4k	γ(4k	NOUN
ejpam-7023	139	28	+	+	CCONJ
ejpam-7023	139	29	4	4	NUM
ejpam-7023	139	30	)	)	PUNCT
ejpam-7023	139	31	(	(	PUNCT
ejpam-7023	139	32	1−	1−	NUM
ejpam-7023	139	33	i)−(4k+4	i)−(4k+4	NOUN
ejpam-7023	139	34	)	)	PUNCT
ejpam-7023	139	35	)	)	PUNCT
ejpam-7023	140	1	=	=	PUNCT
ejpam-7023	140	2	4γ(4k	4γ(4k	NUM
ejpam-7023	140	3	+	+	CCONJ
ejpam-7023	140	4	4	4	X
ejpam-7023	140	5	)	)	PUNCT
ejpam-7023	140	6	2−(2k+2)ℑ	2−(2k+2)ℑ	NOUN
ejpam-7023	140	7	(	(	PUNCT
ejpam-7023	140	8	e	e	X
ejpam-7023	140	9	i(k+1)π	i(k+1)π	PROPN
ejpam-7023	140	10	)	)	PUNCT
ejpam-7023	140	11	=	=	SYM
ejpam-7023	140	12	2−2k	2−2k	NUM
ejpam-7023	140	13	γ(4k	γ(4k	NOUN
ejpam-7023	140	14	+	+	CCONJ
ejpam-7023	140	15	4	4	X
ejpam-7023	140	16	)	)	PUNCT
ejpam-7023	140	17	sin	sin	NOUN
ejpam-7023	140	18	(	(	PUNCT
ejpam-7023	140	19	(	(	PUNCT
ejpam-7023	140	20	k	k	X
ejpam-7023	140	21	+	+	PROPN
ejpam-7023	140	22	1)π	1)π	NUM
ejpam-7023	140	23	)	)	PUNCT
ejpam-7023	140	24	,	,	PUNCT
ejpam-7023	140	25	(	(	PUNCT
ejpam-7023	140	26	14	14	NUM
ejpam-7023	140	27	)	)	PUNCT
ejpam-7023	140	28	which	which	PRON
ejpam-7023	140	29	proves	prove	VERB
ejpam-7023	140	30	(	(	PUNCT
ejpam-7023	140	31	5	5	NUM
ejpam-7023	140	32	)	)	PUNCT
ejpam-7023	140	33	.	.	PUNCT
ejpam-7023	141	1	since	since	SCONJ
ejpam-7023	141	2	2−2k	2−2k	NUM
ejpam-7023	141	3	>	>	SYM
ejpam-7023	141	4	0	0	NUM
ejpam-7023	141	5	and	and	CCONJ
ejpam-7023	141	6	γ(4k	γ(4k	PRON
ejpam-7023	141	7	+	+	X
ejpam-7023	141	8	4	4	NUM
ejpam-7023	141	9	)	)	PUNCT
ejpam-7023	141	10	>	>	X
ejpam-7023	141	11	0	0	PUNCT
ejpam-7023	142	1	for	for	ADP
ejpam-7023	142	2	k	k	PROPN
ejpam-7023	142	3	>	>	X
ejpam-7023	142	4	−1	−1	NOUN
ejpam-7023	142	5	,	,	PUNCT
ejpam-7023	142	6	the	the	DET
ejpam-7023	142	7	equality	equality	NOUN
ejpam-7023	142	8	i(k	i(k	PROPN
ejpam-7023	142	9	)	)	PUNCT
ejpam-7023	142	10	=	=	SYM
ejpam-7023	142	11	0	0	NUM
ejpam-7023	142	12	holds	hold	VERB
ejpam-7023	142	13	if	if	SCONJ
ejpam-7023	142	14	and	and	CCONJ
ejpam-7023	142	15	only	only	ADV
ejpam-7023	142	16	if	if	SCONJ
ejpam-7023	142	17	sin((k	sin((k	PROPN
ejpam-7023	142	18	+	+	NOUN
ejpam-7023	142	19	1)π	1)π	NUM
ejpam-7023	142	20	)	)	PUNCT
ejpam-7023	142	21	=	=	SYM
ejpam-7023	142	22	0	0	NUM
ejpam-7023	142	23	,	,	PUNCT
ejpam-7023	142	24	i.e.	i.e.	X
ejpam-7023	142	25	,	,	PUNCT
ejpam-7023	142	26	(	(	PUNCT
ejpam-7023	142	27	k	k	X
ejpam-7023	142	28	+	+	PROPN
ejpam-7023	142	29	1)π	1)π	NUM
ejpam-7023	142	30	=	=	NOUN
ejpam-7023	142	31	mπ	mπ	NOUN
ejpam-7023	142	32	for	for	ADP
ejpam-7023	142	33	some	some	DET
ejpam-7023	142	34	m	m	NOUN
ejpam-7023	142	35	∈	∈	PROPN
ejpam-7023	142	36	z	z	NOUN
ejpam-7023	142	37	⇐	⇐	PROPN
ejpam-7023	142	38	⇒	⇒	NOUN
ejpam-7023	142	39	k	k	PROPN
ejpam-7023	143	1	=	=	PUNCT
ejpam-7023	143	2	m−	m−	PROPN
ejpam-7023	143	3	1	1	NUM
ejpam-7023	143	4	.	.	PUNCT
ejpam-7023	144	1	under	under	ADP
ejpam-7023	144	2	the	the	DET
ejpam-7023	144	3	constraint	constraint	NOUN
ejpam-7023	144	4	k	k	PROPN
ejpam-7023	144	5	>	>	X
ejpam-7023	144	6	−1	−1	NOUN
ejpam-7023	144	7	,	,	PUNCT
ejpam-7023	144	8	this	this	DET
ejpam-7023	144	9	forces	force	NOUN
ejpam-7023	144	10	m	m	VERB
ejpam-7023	144	11	≥	≥	NUM
ejpam-7023	144	12	1	1	NUM
ejpam-7023	144	13	,	,	PUNCT
ejpam-7023	144	14	so	so	ADV
ejpam-7023	144	15	precisely	precisely	ADV
ejpam-7023	144	16	k	k	PROPN
ejpam-7023	144	17	∈	∈	PROPN
ejpam-7023	144	18	{	{	PUNCT
ejpam-7023	144	19	0	0	NUM
ejpam-7023	144	20	,	,	PUNCT
ejpam-7023	144	21	1	1	NUM
ejpam-7023	144	22	,	,	PUNCT
ejpam-7023	144	23	2	2	NUM
ejpam-7023	144	24	,	,	PUNCT
ejpam-7023	144	25	.	.	PUNCT
ejpam-7023	144	26	.	.	PUNCT
ejpam-7023	144	27	.	.	PUNCT
ejpam-7023	145	1	}	}	PUNCT
ejpam-7023	145	2	yield	yield	VERB
ejpam-7023	145	3	i(k	i(k	PROPN
ejpam-7023	145	4	)	)	PUNCT
ejpam-7023	145	5	=	=	SYM
ejpam-7023	145	6	0	0	NUM
ejpam-7023	145	7	,	,	PUNCT
ejpam-7023	145	8	and	and	CCONJ
ejpam-7023	145	9	conversely	conversely	ADV
ejpam-7023	145	10	any	any	DET
ejpam-7023	145	11	such	such	ADJ
ejpam-7023	145	12	k	k	PROPN
ejpam-7023	145	13	makes	make	VERB
ejpam-7023	145	14	sin((k	sin((k	PROPN
ejpam-7023	145	15	+	+	PROPN
ejpam-7023	145	16	1)π	1)π	NUM
ejpam-7023	145	17	)	)	PUNCT
ejpam-7023	145	18	=	=	SYM
ejpam-7023	145	19	0	0	NUM
ejpam-7023	145	20	,	,	PUNCT
ejpam-7023	145	21	establishing	establish	VERB
ejpam-7023	145	22	the	the	DET
ejpam-7023	145	23	stated	state	VERB
ejpam-7023	145	24	equivalence	equivalence	NOUN
ejpam-7023	145	25	.	.	PUNCT
ejpam-7023	146	1	now	now	ADV
ejpam-7023	146	2	we	we	PRON
ejpam-7023	146	3	have	have	VERB
ejpam-7023	146	4	the	the	DET
ejpam-7023	146	5	following	following	ADJ
ejpam-7023	146	6	generalization	generalization	NOUN
ejpam-7023	146	7	of	of	ADP
ejpam-7023	146	8	theorem	theorem	ADJ
ejpam-7023	146	9	4	4	NUM
ejpam-7023	146	10	.	.	NOUN
ejpam-7023	146	11	remark	remark	NOUN
ejpam-7023	146	12	1	1	NUM
ejpam-7023	146	13	.	.	PUNCT
ejpam-7023	147	1	the	the	DET
ejpam-7023	147	2	above	above	ADJ
ejpam-7023	147	3	theorem	theorem	NOUN
ejpam-7023	147	4	provides	provide	VERB
ejpam-7023	147	5	an	an	DET
ejpam-7023	147	6	explicit	explicit	ADJ
ejpam-7023	147	7	closed	closed	ADJ
ejpam-7023	147	8	-	-	PUNCT
ejpam-7023	147	9	form	form	NOUN
ejpam-7023	147	10	evaluation	evaluation	NOUN
ejpam-7023	147	11	of	of	ADP
ejpam-7023	147	12	the	the	DET
ejpam-7023	147	13	integral	integral	ADJ
ejpam-7023	147	14	i(k	i(k	NOUN
ejpam-7023	147	15	)	)	PUNCT
ejpam-7023	147	16	in	in	ADP
ejpam-7023	147	17	terms	term	NOUN
ejpam-7023	147	18	of	of	ADP
ejpam-7023	147	19	the	the	DET
ejpam-7023	147	20	gamma	gamma	NOUN
ejpam-7023	147	21	function	function	NOUN
ejpam-7023	147	22	and	and	CCONJ
ejpam-7023	147	23	the	the	DET
ejpam-7023	147	24	sine	sine	ADJ
ejpam-7023	147	25	function	function	NOUN
ejpam-7023	147	26	.	.	PUNCT
ejpam-7023	148	1	it	it	PRON
ejpam-7023	148	2	demonstrates	demonstrate	VERB
ejpam-7023	148	3	that	that	SCONJ
ejpam-7023	148	4	the	the	DET
ejpam-7023	148	5	vanishing	vanishing	NOUN
ejpam-7023	148	6	of	of	ADP
ejpam-7023	148	7	i(k	i(k	PROPN
ejpam-7023	148	8	)	)	PUNCT
ejpam-7023	148	9	occurs	occur	VERB
ejpam-7023	148	10	only	only	ADV
ejpam-7023	148	11	for	for	ADP
ejpam-7023	148	12	nonnegative	nonnegative	ADJ
ejpam-7023	148	13	integer	integer	NOUN
ejpam-7023	148	14	values	value	NOUN
ejpam-7023	148	15	of	of	ADP
ejpam-7023	148	16	k.	k.	PROPN
ejpam-7023	148	17	theorem	theorem	PROPN
ejpam-7023	148	18	5	5	NUM
ejpam-7023	148	19	.	.	PUNCT
ejpam-7023	149	1	let	let	VERB
ejpam-7023	149	2	m	m	PRON
ejpam-7023	149	3	>	>	X
ejpam-7023	149	4	0	0	PROPN
ejpam-7023	149	5	,	,	PUNCT
ejpam-7023	149	6	α	α	NOUN
ejpam-7023	149	7	>	>	X
ejpam-7023	149	8	0	0	PROPN
ejpam-7023	149	9	,	,	PUNCT
ejpam-7023	149	10	β	β	X
ejpam-7023	149	11	∈	∈	NOUN
ejpam-7023	149	12	r	r	NOUN
ejpam-7023	149	13	,	,	PUNCT
ejpam-7023	149	14	q	q	NOUN
ejpam-7023	149	15	∈	∈	PROPN
ejpam-7023	149	16	r	r	NOUN
ejpam-7023	149	17	,	,	PUNCT
ejpam-7023	149	18	and	and	CCONJ
ejpam-7023	149	19	k	k	PROPN
ejpam-7023	149	20	∈	∈	PROPN
ejpam-7023	149	21	r.	r.	PROPN
ejpam-7023	149	22	define	define	VERB
ejpam-7023	149	23	im	im	PRON
ejpam-7023	149	24	,	,	PUNCT
ejpam-7023	149	25	q(k	q(k	PROPN
ejpam-7023	149	26	,	,	PUNCT
ejpam-7023	149	27	α	α	X
ejpam-7023	149	28	,	,	PUNCT
ejpam-7023	149	29	β	β	NOUN
ejpam-7023	149	30	)	)	PUNCT
ejpam-7023	149	31	=	=	SYM
ejpam-7023	150	1	∫	∫	PROPN
ejpam-7023	150	2	∞	∞	NUM
ejpam-7023	150	3	0	0	NUM
ejpam-7023	150	4	e−αx1	e−αx1	PROPN
ejpam-7023	150	5	/	/	SYM
ejpam-7023	150	6	m	m	NOUN
ejpam-7023	150	7	sin	sin	NOUN
ejpam-7023	150	8	(	(	PUNCT
ejpam-7023	150	9	βx1	βx1	PROPN
ejpam-7023	150	10	/	/	SYM
ejpam-7023	150	11	m	m	NOUN
ejpam-7023	150	12	)	)	PUNCT
ejpam-7023	150	13	xk	xk	PROPN
ejpam-7023	150	14	(	(	PUNCT
ejpam-7023	150	15	x1	x1	PROPN
ejpam-7023	150	16	/	/	SYM
ejpam-7023	150	17	m)q	m)q	PROPN
ejpam-7023	150	18	dx	dx	PROPN
ejpam-7023	150	19	,	,	PUNCT
ejpam-7023	150	20	(	(	PUNCT
ejpam-7023	150	21	15	15	NUM
ejpam-7023	150	22	)	)	PUNCT
ejpam-7023	150	23	and	and	CCONJ
ejpam-7023	150	24	set	set	VERB
ejpam-7023	150	25	a	a	DET
ejpam-7023	150	26	=	=	SYM
ejpam-7023	150	27	mk	mk	NOUN
ejpam-7023	150	28	+	+	CCONJ
ejpam-7023	150	29	q	q	X
ejpam-7023	151	1	+	+	NOUN
ejpam-7023	151	2	m.	m.	NOUN
ejpam-7023	151	3	(	(	PUNCT
ejpam-7023	151	4	16	16	NUM
ejpam-7023	151	5	)	)	PUNCT
ejpam-7023	151	6	i.	i.	NOUN
ejpam-7023	151	7	ayoob	ayoob	PROPN
ejpam-7023	151	8	/	/	SYM
ejpam-7023	151	9	eur	eur	PROPN
ejpam-7023	151	10	.	.	PUNCT
ejpam-7023	152	1	j.	j.	PROPN
ejpam-7023	152	2	pure	pure	PROPN
ejpam-7023	152	3	appl	appl	PROPN
ejpam-7023	152	4	.	.	PROPN
ejpam-7023	152	5	math	math	PROPN
ejpam-7023	152	6	,	,	PUNCT
ejpam-7023	152	7	18	18	NUM
ejpam-7023	152	8	(	(	PUNCT
ejpam-7023	152	9	4	4	NUM
ejpam-7023	152	10	)	)	PUNCT
ejpam-7023	152	11	(	(	PUNCT
ejpam-7023	152	12	2025	2025	NUM
ejpam-7023	152	13	)	)	PUNCT
ejpam-7023	152	14	,	,	PUNCT
ejpam-7023	152	15	7023	7023	NUM
ejpam-7023	152	16	7	7	NUM
ejpam-7023	152	17	of	of	ADP
ejpam-7023	152	18	16	16	NUM
ejpam-7023	152	19	then	then	ADV
ejpam-7023	152	20	the	the	DET
ejpam-7023	152	21	integral	integral	ADJ
ejpam-7023	152	22	in	in	ADP
ejpam-7023	152	23	(	(	PUNCT
ejpam-7023	152	24	15	15	NUM
ejpam-7023	152	25	)	)	PUNCT
ejpam-7023	152	26	converges	converge	NOUN
ejpam-7023	152	27	for	for	ADP
ejpam-7023	152	28	every	every	DET
ejpam-7023	152	29	a	a	DET
ejpam-7023	152	30	>	>	X
ejpam-7023	152	31	−1	−1	NOUN
ejpam-7023	152	32	.	.	PUNCT
ejpam-7023	153	1	moreover	moreover	ADV
ejpam-7023	153	2	,	,	PUNCT
ejpam-7023	153	3	if	if	SCONJ
ejpam-7023	153	4	a	a	PRON
ejpam-7023	153	5	>	>	X
ejpam-7023	153	6	0	0	PUNCT
ejpam-7023	153	7	(	(	PUNCT
ejpam-7023	153	8	which	which	PRON
ejpam-7023	153	9	we	we	PRON
ejpam-7023	153	10	assume	assume	VERB
ejpam-7023	153	11	for	for	ADP
ejpam-7023	153	12	the	the	DET
ejpam-7023	153	13	evaluation	evaluation	NOUN
ejpam-7023	153	14	below	below	ADP
ejpam-7023	153	15	)	)	PUNCT
ejpam-7023	153	16	,	,	PUNCT
ejpam-7023	153	17	one	one	PRON
ejpam-7023	153	18	has	have	VERB
ejpam-7023	153	19	the	the	DET
ejpam-7023	153	20	closed	closed	ADJ
ejpam-7023	153	21	form	form	NOUN
ejpam-7023	153	22	im	im	ADV
ejpam-7023	153	23	,	,	PUNCT
ejpam-7023	153	24	q(k	q(k	PROPN
ejpam-7023	153	25	,	,	PUNCT
ejpam-7023	153	26	α	α	X
ejpam-7023	153	27	,	,	PUNCT
ejpam-7023	153	28	β	β	NOUN
ejpam-7023	153	29	)	)	PUNCT
ejpam-7023	153	30	=	=	SYM
ejpam-7023	153	31	mγ(a	mγ(a	X
ejpam-7023	153	32	)	)	PUNCT
ejpam-7023	153	33	(	(	PUNCT
ejpam-7023	153	34	α2	α2	ADJ
ejpam-7023	153	35	+	+	CCONJ
ejpam-7023	153	36	β2)−a/2	β2)−a/2	X
ejpam-7023	153	37	sin	sin	NOUN
ejpam-7023	153	38	(	(	PUNCT
ejpam-7023	153	39	a	a	DET
ejpam-7023	153	40	arctan	arctan	PROPN
ejpam-7023	153	41	β	β	X
ejpam-7023	153	42	α	α	NOUN
ejpam-7023	153	43	)	)	PUNCT
ejpam-7023	153	44	.	.	PUNCT
ejpam-7023	154	1	(	(	PUNCT
ejpam-7023	154	2	17	17	NUM
ejpam-7023	154	3	)	)	PUNCT
ejpam-7023	154	4	consequently	consequently	ADV
ejpam-7023	154	5	,	,	PUNCT
ejpam-7023	154	6	if	if	SCONJ
ejpam-7023	154	7	β	β	PROPN
ejpam-7023	154	8	̸=	̸=	PROPN
ejpam-7023	154	9	0	0	NUM
ejpam-7023	154	10	then	then	ADV
ejpam-7023	154	11	im	im	X
ejpam-7023	154	12	,	,	PUNCT
ejpam-7023	154	13	q(k	q(k	PROPN
ejpam-7023	154	14	,	,	PUNCT
ejpam-7023	154	15	α	α	X
ejpam-7023	154	16	,	,	PUNCT
ejpam-7023	154	17	β	β	NOUN
ejpam-7023	154	18	)	)	PUNCT
ejpam-7023	155	1	=	=	SYM
ejpam-7023	155	2	0	0	PUNCT
ejpam-7023	156	1	if	if	SCONJ
ejpam-7023	156	2	and	and	CCONJ
ejpam-7023	156	3	only	only	ADV
ejpam-7023	156	4	if	if	SCONJ
ejpam-7023	156	5	a	a	DET
ejpam-7023	156	6	arctan	arctan	PROPN
ejpam-7023	156	7	β	β	X
ejpam-7023	156	8	α	α	PROPN
ejpam-7023	156	9	∈	∈	PROPN
ejpam-7023	156	10	πz	πz	NOUN
ejpam-7023	156	11	;	;	PUNCT
ejpam-7023	156	12	(	(	PUNCT
ejpam-7023	156	13	18	18	NUM
ejpam-7023	156	14	)	)	PUNCT
ejpam-7023	156	15	if	if	SCONJ
ejpam-7023	156	16	β	β	X
ejpam-7023	156	17	=	=	NOUN
ejpam-7023	156	18	0	0	PUNCT
ejpam-7023	156	19	then	then	ADV
ejpam-7023	156	20	im	im	X
ejpam-7023	156	21	,	,	PUNCT
ejpam-7023	156	22	q(k	q(k	PROPN
ejpam-7023	156	23	,	,	PUNCT
ejpam-7023	156	24	α	α	NOUN
ejpam-7023	156	25	,	,	PUNCT
ejpam-7023	156	26	0	0	NUM
ejpam-7023	156	27	)	)	PUNCT
ejpam-7023	156	28	=	=	SYM
ejpam-7023	156	29	0	0	NUM
ejpam-7023	156	30	for	for	ADP
ejpam-7023	156	31	all	all	DET
ejpam-7023	156	32	admissible	admissible	ADJ
ejpam-7023	156	33	parameters	parameter	NOUN
ejpam-7023	156	34	.	.	PUNCT
ejpam-7023	157	1	proof	proof	NOUN
ejpam-7023	157	2	.	.	PUNCT
ejpam-7023	158	1	write	write	VERB
ejpam-7023	158	2	the	the	DET
ejpam-7023	158	3	integrand	integrand	NOUN
ejpam-7023	158	4	as	as	ADP
ejpam-7023	158	5	e−αx1	e−αx1	PROPN
ejpam-7023	158	6	/	/	SYM
ejpam-7023	158	7	m	m	VERB
ejpam-7023	158	8	sin(βx1	sin(βx1	NOUN
ejpam-7023	158	9	/	/	SYM
ejpam-7023	158	10	m)xk+q	m)xk+q	ADP
ejpam-7023	158	11	/	/	SYM
ejpam-7023	158	12	m.	m.	NOUN
ejpam-7023	158	13	for	for	ADP
ejpam-7023	158	14	convergence	convergence	NOUN
ejpam-7023	158	15	near	near	ADP
ejpam-7023	158	16	x	x	PUNCT
ejpam-7023	158	17	=	=	SYM
ejpam-7023	158	18	0	0	NUM
ejpam-7023	158	19	,	,	PUNCT
ejpam-7023	158	20	use	use	NOUN
ejpam-7023	158	21	|	|	ADV
ejpam-7023	158	22	sin	sin	VERB
ejpam-7023	158	23	t|	t|	PROPN
ejpam-7023	158	24	≤	≤	PROPN
ejpam-7023	158	25	min{1	min{1	PROPN
ejpam-7023	158	26	,	,	PUNCT
ejpam-7023	158	27	|t|	|t|	PROPN
ejpam-7023	158	28	}	}	PUNCT
ejpam-7023	158	29	.	.	PUNCT
ejpam-7023	159	1	as	as	SCONJ
ejpam-7023	159	2	x	x	PROPN
ejpam-7023	159	3	↓	↓	PROPN
ejpam-7023	159	4	0	0	NUM
ejpam-7023	159	5	,	,	PUNCT
ejpam-7023	159	6	we	we	PRON
ejpam-7023	159	7	have	have	VERB
ejpam-7023	159	8	t	t	NOUN
ejpam-7023	160	1	=	=	SYM
ejpam-7023	160	2	x1	x1	PROPN
ejpam-7023	160	3	/	/	SYM
ejpam-7023	160	4	m	m	PROPN
ejpam-7023	160	5	↓	↓	NOUN
ejpam-7023	160	6	0	0	NUM
ejpam-7023	160	7	,	,	PUNCT
ejpam-7023	160	8	thus	thus	ADV
ejpam-7023	160	9	|	|	ADV
ejpam-7023	160	10	sin(βx1	sin(βx1	ADJ
ejpam-7023	160	11	/	/	SYM
ejpam-7023	160	12	m)|	m)|	ADJ
ejpam-7023	160	13	≤	≤	NOUN
ejpam-7023	160	14	|β|x1	|β|x1	PROPN
ejpam-7023	160	15	/	/	SYM
ejpam-7023	160	16	m	m	PROPN
ejpam-7023	160	17	,	,	PUNCT
ejpam-7023	160	18	which	which	PRON
ejpam-7023	160	19	gives	give	VERB
ejpam-7023	160	20	∣∣e−αx1	∣∣e−αx1	NUM
ejpam-7023	160	21	/	/	SYM
ejpam-7023	160	22	m	m	PRON
ejpam-7023	160	23	sin(βx1	sin(βx1	NOUN
ejpam-7023	160	24	/	/	SYM
ejpam-7023	160	25	m)xk+q	m)xk+q	PROPN
ejpam-7023	160	26	/	/	SYM
ejpam-7023	160	27	m	m	NOUN
ejpam-7023	160	28	∣∣	∣∣	NUM
ejpam-7023	160	29	≪	≪	PUNCT
ejpam-7023	160	30	xk+q	xk+q	PROPN
ejpam-7023	160	31	/	/	SYM
ejpam-7023	160	32	m+1	m+1	PROPN
ejpam-7023	160	33	/	/	SYM
ejpam-7023	160	34	m	m	VERB
ejpam-7023	160	35	(	(	PUNCT
ejpam-7023	160	36	x	x	X
ejpam-7023	160	37	↓	↓	NOUN
ejpam-7023	160	38	0	0	NUM
ejpam-7023	160	39	)	)	PUNCT
ejpam-7023	160	40	.	.	PUNCT
ejpam-7023	161	1	(	(	PUNCT
ejpam-7023	161	2	19	19	NUM
ejpam-7023	161	3	)	)	PUNCT
ejpam-7023	161	4	hence	hence	ADV
ejpam-7023	161	5	∫	∫	PROPN
ejpam-7023	161	6	1	1	NUM
ejpam-7023	161	7	0	0	NUM
ejpam-7023	161	8	|e−αx1	|e−αx1	PROPN
ejpam-7023	161	9	/	/	SYM
ejpam-7023	161	10	m	m	PRON
ejpam-7023	161	11	sin(βx1	sin(βx1	NOUN
ejpam-7023	161	12	/	/	SYM
ejpam-7023	161	13	m)xk+q	m)xk+q	ADP
ejpam-7023	161	14	/	/	SYM
ejpam-7023	161	15	m|	m|	NOUN
ejpam-7023	161	16	dx	dx	PROPN
ejpam-7023	161	17	<	<	X
ejpam-7023	161	18	∞	∞	PROPN
ejpam-7023	161	19	provided	provide	VERB
ejpam-7023	161	20	k	k	PROPN
ejpam-7023	162	1	+	+	CCONJ
ejpam-7023	162	2	q	q	ADJ
ejpam-7023	162	3	/	/	SYM
ejpam-7023	162	4	m+	m+	NUM
ejpam-7023	162	5	1	1	NUM
ejpam-7023	162	6	/	/	SYM
ejpam-7023	162	7	m	m	VERB
ejpam-7023	162	8	>	>	X
ejpam-7023	162	9	−1	−1	NOUN
ejpam-7023	162	10	,	,	PUNCT
ejpam-7023	162	11	i.e.	i.e.	X
ejpam-7023	162	12	mk	mk	X
ejpam-7023	162	13	+	+	CCONJ
ejpam-7023	162	14	q	q	PROPN
ejpam-7023	163	1	+	+	NOUN
ejpam-7023	163	2	m	m	NOUN
ejpam-7023	163	3	>	>	X
ejpam-7023	163	4	−1	−1	NOUN
ejpam-7023	163	5	⇐	⇐	PROPN
ejpam-7023	163	6	⇒	⇒	PROPN
ejpam-7023	163	7	a	a	DET
ejpam-7023	163	8	>	>	X
ejpam-7023	163	9	−1	−1	NOUN
ejpam-7023	163	10	.	.	PUNCT
ejpam-7023	164	1	(	(	PUNCT
ejpam-7023	164	2	20	20	NUM
ejpam-7023	164	3	)	)	PUNCT
ejpam-7023	164	4	as	as	SCONJ
ejpam-7023	164	5	x	x	X
ejpam-7023	164	6	→	→	SYM
ejpam-7023	164	7	∞	∞	NUM
ejpam-7023	164	8	we	we	PRON
ejpam-7023	164	9	have	have	VERB
ejpam-7023	164	10	|	|	ADV
ejpam-7023	164	11	sin(βx1	sin(βx1	ADJ
ejpam-7023	164	12	/	/	SYM
ejpam-7023	164	13	m)|	m)|	ADJ
ejpam-7023	164	14	≤	≤	ADJ
ejpam-7023	164	15	1	1	NUM
ejpam-7023	164	16	and	and	CCONJ
ejpam-7023	164	17	the	the	DET
ejpam-7023	164	18	factor	factor	NOUN
ejpam-7023	164	19	e−αx1	e−αx1	PROPN
ejpam-7023	164	20	/	/	SYM
ejpam-7023	164	21	m	m	NOUN
ejpam-7023	164	22	decays	decay	NOUN
ejpam-7023	164	23	faster	fast	ADV
ejpam-7023	164	24	than	than	ADP
ejpam-7023	164	25	any	any	DET
ejpam-7023	164	26	power	power	NOUN
ejpam-7023	164	27	,	,	PUNCT
ejpam-7023	164	28	so	so	CCONJ
ejpam-7023	165	1	∫	∫	PROPN
ejpam-7023	165	2	∞	∞	NUM
ejpam-7023	165	3	1	1	NUM
ejpam-7023	165	4	∣∣e−αx1	∣∣e−αx1	NUM
ejpam-7023	165	5	/	/	SYM
ejpam-7023	165	6	m	m	VERB
ejpam-7023	165	7	sin(βx1	sin(βx1	NOUN
ejpam-7023	165	8	/	/	SYM
ejpam-7023	165	9	m)xk+q	m)xk+q	PROPN
ejpam-7023	165	10	/	/	SYM
ejpam-7023	165	11	m	m	PROPN
ejpam-7023	165	12	∣∣	∣∣	NUM
ejpam-7023	165	13	dx	dx	X
ejpam-7023	165	14	<	<	X
ejpam-7023	165	15	∞	∞	PROPN
ejpam-7023	165	16	for	for	ADP
ejpam-7023	165	17	every	every	DET
ejpam-7023	165	18	k	k	NOUN
ejpam-7023	165	19	,	,	PUNCT
ejpam-7023	165	20	q	q	X
ejpam-7023	165	21	when	when	SCONJ
ejpam-7023	165	22	α	α	X
ejpam-7023	165	23	>	>	X
ejpam-7023	165	24	0	0	PROPN
ejpam-7023	165	25	.	.	PUNCT
ejpam-7023	166	1	(	(	PUNCT
ejpam-7023	166	2	21	21	NUM
ejpam-7023	166	3	)	)	PUNCT
ejpam-7023	166	4	therefore	therefore	ADV
ejpam-7023	166	5	(	(	PUNCT
ejpam-7023	166	6	15	15	X
ejpam-7023	166	7	)	)	PUNCT
ejpam-7023	166	8	converges	converge	VERB
ejpam-7023	166	9	for	for	ADP
ejpam-7023	166	10	all	all	DET
ejpam-7023	166	11	a	a	DET
ejpam-7023	166	12	>	>	X
ejpam-7023	166	13	−1	−1	NOUN
ejpam-7023	166	14	.	.	PUNCT
ejpam-7023	167	1	for	for	ADP
ejpam-7023	167	2	evaluation	evaluation	NOUN
ejpam-7023	167	3	assume	assume	VERB
ejpam-7023	167	4	a	a	DET
ejpam-7023	167	5	>	>	X
ejpam-7023	167	6	0	0	X
ejpam-7023	167	7	.	.	PUNCT
ejpam-7023	168	1	we	we	PRON
ejpam-7023	168	2	make	make	VERB
ejpam-7023	168	3	the	the	DET
ejpam-7023	168	4	substitution	substitution	NOUN
ejpam-7023	168	5	u	u	NOUN
ejpam-7023	168	6	=	=	PROPN
ejpam-7023	168	7	x1	x1	PROPN
ejpam-7023	168	8	/	/	SYM
ejpam-7023	168	9	m	m	PROPN
ejpam-7023	168	10	,	,	PUNCT
ejpam-7023	168	11	x	x	SYM
ejpam-7023	168	12	=	=	SYM
ejpam-7023	168	13	um	um	INTJ
ejpam-7023	168	14	,	,	PUNCT
ejpam-7023	168	15	dx	dx	PROPN
ejpam-7023	168	16	=	=	PUNCT
ejpam-7023	168	17	mum−1	mum−1	PROPN
ejpam-7023	168	18	du	du	PROPN
ejpam-7023	168	19	,	,	PUNCT
ejpam-7023	168	20	(	(	PUNCT
ejpam-7023	168	21	22	22	NUM
ejpam-7023	168	22	)	)	PUNCT
ejpam-7023	168	23	and	and	CCONJ
ejpam-7023	168	24	note	note	VERB
ejpam-7023	168	25	xk(x1	xk(x1	NOUN
ejpam-7023	168	26	/	/	SYM
ejpam-7023	168	27	m)q	m)q	NOUN
ejpam-7023	168	28	=	=	SYM
ejpam-7023	169	1	umk+q	umk+q	PROPN
ejpam-7023	169	2	.	.	PUNCT
ejpam-7023	170	1	then	then	ADV
ejpam-7023	170	2	im	im	X
ejpam-7023	170	3	,	,	PUNCT
ejpam-7023	170	4	q(k	q(k	PROPN
ejpam-7023	170	5	,	,	PUNCT
ejpam-7023	170	6	α	α	X
ejpam-7023	170	7	,	,	PUNCT
ejpam-7023	170	8	β	β	NOUN
ejpam-7023	170	9	)	)	PUNCT
ejpam-7023	170	10	=	=	SYM
ejpam-7023	171	1	∫	∫	PROPN
ejpam-7023	171	2	∞	∞	PROPN
ejpam-7023	171	3	0	0	NUM
ejpam-7023	171	4	e−αu	e−αu	PROPN
ejpam-7023	171	5	sin(βu)umk+q	sin(βu)umk+q	X
ejpam-7023	171	6	(	(	PUNCT
ejpam-7023	171	7	mum−1	mum−1	PROPN
ejpam-7023	171	8	)	)	PUNCT
ejpam-7023	171	9	du	du	PROPN
ejpam-7023	172	1	=	=	SYM
ejpam-7023	172	2	m	m	PROPN
ejpam-7023	172	3	∫	∫	PROPN
ejpam-7023	172	4	∞	∞	PROPN
ejpam-7023	172	5	0	0	NUM
ejpam-7023	172	6	e−αu	e−αu	PROPN
ejpam-7023	172	7	sin(βu)ua−1	sin(βu)ua−1	PROPN
ejpam-7023	172	8	du	du	PROPN
ejpam-7023	172	9	.	.	PUNCT
ejpam-7023	173	1	(	(	PUNCT
ejpam-7023	173	2	23	23	NUM
ejpam-7023	173	3	)	)	PUNCT
ejpam-7023	173	4	using	use	VERB
ejpam-7023	173	5	sin(βu	sin(βu	NOUN
ejpam-7023	173	6	)	)	PUNCT
ejpam-7023	173	7	=	=	SYM
ejpam-7023	173	8	ℑ(eiβu	ℑ(eiβu	ADJ
ejpam-7023	173	9	)	)	PUNCT
ejpam-7023	173	10	and	and	CCONJ
ejpam-7023	173	11	the	the	DET
ejpam-7023	173	12	absolute	absolute	ADJ
ejpam-7023	173	13	integrability	integrability	NOUN
ejpam-7023	173	14	guaranteed	guarantee	VERB
ejpam-7023	173	15	by	by	ADP
ejpam-7023	173	16	a	a	DET
ejpam-7023	173	17	>	>	X
ejpam-7023	173	18	−1	−1	NOUN
ejpam-7023	173	19	and	and	CCONJ
ejpam-7023	173	20	α	α	NOUN
ejpam-7023	173	21	>	>	X
ejpam-7023	173	22	0	0	NUM
ejpam-7023	173	23	,	,	PUNCT
ejpam-7023	173	24	we	we	PRON
ejpam-7023	173	25	may	may	AUX
ejpam-7023	173	26	pass	pass	VERB
ejpam-7023	173	27	the	the	DET
ejpam-7023	173	28	imaginary	imaginary	ADJ
ejpam-7023	173	29	part	part	NOUN
ejpam-7023	173	30	inside	inside	ADP
ejpam-7023	173	31	the	the	DET
ejpam-7023	173	32	integral	integral	ADJ
ejpam-7023	173	33	:	:	PUNCT
ejpam-7023	173	34	e−αu	e−αu	NOUN
ejpam-7023	173	35	sin(βu	sin(βu	NOUN
ejpam-7023	173	36	)	)	PUNCT
ejpam-7023	173	37	=	=	SYM
ejpam-7023	173	38	ℑ	ℑ	PROPN
ejpam-7023	173	39	(	(	PUNCT
ejpam-7023	173	40	e−(α−iβ)u	e−(α−iβ)u	PROPN
ejpam-7023	173	41	)	)	PUNCT
ejpam-7023	174	1	=	=	VERB
ejpam-7023	174	2	⇒	⇒	NOUN
ejpam-7023	174	3	im	im	PRON
ejpam-7023	174	4	,	,	PUNCT
ejpam-7023	174	5	q(k	q(k	PROPN
ejpam-7023	174	6	,	,	PUNCT
ejpam-7023	174	7	α	α	X
ejpam-7023	174	8	,	,	PUNCT
ejpam-7023	174	9	β	β	NOUN
ejpam-7023	174	10	)	)	PUNCT
ejpam-7023	174	11	=	=	NOUN
ejpam-7023	175	1	mℑ	mℑ	ADJ
ejpam-7023	175	2	∫	∫	PROPN
ejpam-7023	175	3	∞	∞	PROPN
ejpam-7023	175	4	0	0	NUM
ejpam-7023	176	1	ua−1	ua−1	PROPN
ejpam-7023	176	2	e−(α−iβ)u	e−(α−iβ)u	PROPN
ejpam-7023	176	3	du	du	X
ejpam-7023	176	4	.	.	PUNCT
ejpam-7023	177	1	(	(	PUNCT
ejpam-7023	177	2	24	24	NUM
ejpam-7023	177	3	)	)	PUNCT
ejpam-7023	177	4	put	put	VERB
ejpam-7023	177	5	λ	λ	NOUN
ejpam-7023	177	6	=	=	PUNCT
ejpam-7023	178	1	α−	α−	ADP
ejpam-7023	178	2	iβ	iβ	X
ejpam-7023	178	3	(	(	PUNCT
ejpam-7023	178	4	ℜλ	ℜλ	PROPN
ejpam-7023	178	5	=	=	SYM
ejpam-7023	178	6	α	α	X
ejpam-7023	178	7	>	>	X
ejpam-7023	178	8	0	0	NUM
ejpam-7023	178	9	)	)	PUNCT
ejpam-7023	178	10	.	.	PUNCT
ejpam-7023	179	1	(	(	PUNCT
ejpam-7023	179	2	25	25	NUM
ejpam-7023	179	3	)	)	PUNCT
ejpam-7023	179	4	i.	i.	NOUN
ejpam-7023	179	5	ayoob	ayoob	PROPN
ejpam-7023	179	6	/	/	SYM
ejpam-7023	179	7	eur	eur	PROPN
ejpam-7023	179	8	.	.	PUNCT
ejpam-7023	180	1	j.	j.	PROPN
ejpam-7023	180	2	pure	pure	PROPN
ejpam-7023	180	3	appl	appl	PROPN
ejpam-7023	180	4	.	.	PROPN
ejpam-7023	180	5	math	math	PROPN
ejpam-7023	180	6	,	,	PUNCT
ejpam-7023	180	7	18	18	NUM
ejpam-7023	180	8	(	(	PUNCT
ejpam-7023	180	9	4	4	NUM
ejpam-7023	180	10	)	)	PUNCT
ejpam-7023	180	11	(	(	PUNCT
ejpam-7023	180	12	2025	2025	NUM
ejpam-7023	180	13	)	)	PUNCT
ejpam-7023	180	14	,	,	PUNCT
ejpam-7023	180	15	7023	7023	NUM
ejpam-7023	180	16	8	8	NUM
ejpam-7023	180	17	of	of	ADP
ejpam-7023	180	18	16	16	NUM
ejpam-7023	180	19	for	for	ADP
ejpam-7023	180	20	a	a	DET
ejpam-7023	180	21	>	>	SYM
ejpam-7023	180	22	0	0	NUM
ejpam-7023	180	23	the	the	DET
ejpam-7023	180	24	gamma	gamma	NOUN
ejpam-7023	180	25	gamma	gamma	PROPN
ejpam-7023	180	26	function	function	PROPN
ejpam-7023	180	27	(	(	PUNCT
ejpam-7023	180	28	by	by	ADP
ejpam-7023	180	29	the	the	DET
ejpam-7023	180	30	substitution	substitution	NOUN
ejpam-7023	180	31	t	t	NOUN
ejpam-7023	180	32	=	=	SYM
ejpam-7023	180	33	λu	λu	NOUN
ejpam-7023	180	34	)	)	PUNCT
ejpam-7023	180	35	gives,∫	gives,∫	NOUN
ejpam-7023	180	36	∞	∞	PROPN
ejpam-7023	180	37	0	0	PUNCT
ejpam-7023	180	38	ua−1e−λu	ua−1e−λu	NOUN
ejpam-7023	180	39	du	du	PROPN
ejpam-7023	180	40	=	=	SYM
ejpam-7023	180	41	∫	∫	PROPN
ejpam-7023	180	42	∞	∞	PROPN
ejpam-7023	180	43	0	0	NUM
ejpam-7023	181	1	(	(	PUNCT
ejpam-7023	181	2	t	t	NOUN
ejpam-7023	181	3	λ	λ	PROPN
ejpam-7023	181	4	)	)	PUNCT
ejpam-7023	181	5	a−1	a−1	PROPN
ejpam-7023	181	6	e−t	e−t	NOUN
ejpam-7023	181	7	dt	dt	X
ejpam-7023	181	8	λ	λ	X
ejpam-7023	181	9	=	=	SYM
ejpam-7023	181	10	λ−a	λ−a	X
ejpam-7023	181	11	∫	∫	PROPN
ejpam-7023	182	1	∞	∞	PROPN
ejpam-7023	182	2	0	0	NUM
ejpam-7023	182	3	ta−1e−t	ta−1e−t	NOUN
ejpam-7023	182	4	dt	dt	X
ejpam-7023	182	5	=	=	SYM
ejpam-7023	182	6	γ(a	γ(a	PROPN
ejpam-7023	182	7	)	)	PUNCT
ejpam-7023	182	8	λa	λa	X
ejpam-7023	182	9	.	.	PUNCT
ejpam-7023	183	1	(	(	PUNCT
ejpam-7023	183	2	26	26	NUM
ejpam-7023	183	3	)	)	PUNCT
ejpam-7023	183	4	applying	apply	VERB
ejpam-7023	183	5	(	(	PUNCT
ejpam-7023	183	6	26	26	NUM
ejpam-7023	183	7	)	)	PUNCT
ejpam-7023	183	8	with	with	ADP
ejpam-7023	183	9	(	(	PUNCT
ejpam-7023	183	10	25	25	NUM
ejpam-7023	183	11	)	)	PUNCT
ejpam-7023	183	12	in	in	ADP
ejpam-7023	183	13	(	(	PUNCT
ejpam-7023	183	14	24	24	NUM
ejpam-7023	183	15	)	)	PUNCT
ejpam-7023	183	16	yields	yield	NOUN
ejpam-7023	183	17	im	im	ADV
ejpam-7023	183	18	,	,	PUNCT
ejpam-7023	183	19	q(k	q(k	PROPN
ejpam-7023	183	20	,	,	PUNCT
ejpam-7023	183	21	α	α	X
ejpam-7023	183	22	,	,	PUNCT
ejpam-7023	183	23	β	β	NOUN
ejpam-7023	183	24	)	)	PUNCT
ejpam-7023	183	25	=	=	SYM
ejpam-7023	184	1	mℑ	mℑ	ADJ
ejpam-7023	184	2	(	(	PUNCT
ejpam-7023	184	3	γ(a	γ(a	PROPN
ejpam-7023	184	4	)	)	PUNCT
ejpam-7023	184	5	(	(	PUNCT
ejpam-7023	184	6	α−	α−	ADP
ejpam-7023	184	7	iβ)a	iβ)a	PROPN
ejpam-7023	184	8	)	)	PUNCT
ejpam-7023	184	9	.	.	PUNCT
ejpam-7023	185	1	(	(	PUNCT
ejpam-7023	185	2	27	27	NUM
ejpam-7023	185	3	)	)	PUNCT
ejpam-7023	185	4	we	we	PRON
ejpam-7023	185	5	write	write	VERB
ejpam-7023	185	6	α−	α−	ADP
ejpam-7023	185	7	iβ	iβ	ADP
ejpam-7023	185	8	in	in	ADP
ejpam-7023	185	9	polar	polar	ADJ
ejpam-7023	185	10	form	form	NOUN
ejpam-7023	185	11	,	,	PUNCT
ejpam-7023	185	12	with	with	ADP
ejpam-7023	185	13	r	r	NOUN
ejpam-7023	185	14	=	=	PUNCT
ejpam-7023	185	15	√	√	NOUN
ejpam-7023	185	16	α2	α2	NOUN
ejpam-7023	185	17	+	+	CCONJ
ejpam-7023	185	18	β2	β2	VERB
ejpam-7023	185	19	,	,	PUNCT
ejpam-7023	185	20	θ	θ	PROPN
ejpam-7023	185	21	=	=	SYM
ejpam-7023	185	22	arctan	arctan	PROPN
ejpam-7023	185	23	β	β	PROPN
ejpam-7023	185	24	α	α	PROPN
ejpam-7023	185	25	∈	∈	PROPN
ejpam-7023	185	26	(	(	PUNCT
ejpam-7023	185	27	−π	−π	ADV
ejpam-7023	185	28	2	2	NUM
ejpam-7023	185	29	,	,	PUNCT
ejpam-7023	185	30	π	π	PROPN
ejpam-7023	185	31	2	2	NUM
ejpam-7023	185	32	)	)	PUNCT
ejpam-7023	185	33	,	,	PUNCT
ejpam-7023	185	34	(	(	PUNCT
ejpam-7023	185	35	28	28	X
ejpam-7023	185	36	)	)	PUNCT
ejpam-7023	185	37	we	we	PRON
ejpam-7023	185	38	have	have	VERB
ejpam-7023	185	39	α−	α−	ADP
ejpam-7023	185	40	iβ	iβ	ADP
ejpam-7023	185	41	=	=	NOUN
ejpam-7023	185	42	r	r	NOUN
ejpam-7023	185	43	e−iθ	e−iθ	NOUN
ejpam-7023	185	44	and	and	CCONJ
ejpam-7023	185	45	hence	hence	ADV
ejpam-7023	185	46	(	(	PUNCT
ejpam-7023	185	47	α−	α−	ADP
ejpam-7023	185	48	iβ)−a	iβ)−a	PROPN
ejpam-7023	185	49	=	=	SYM
ejpam-7023	185	50	r−a	r−a	PROPN
ejpam-7023	185	51	e	e	PROPN
ejpam-7023	185	52	iaθ	iaθ	PROPN
ejpam-7023	185	53	.	.	PUNCT
ejpam-7023	186	1	(	(	PUNCT
ejpam-7023	186	2	29	29	NUM
ejpam-7023	186	3	)	)	PUNCT
ejpam-7023	186	4	substituting	substituting	NOUN
ejpam-7023	186	5	(	(	PUNCT
ejpam-7023	186	6	29	29	NUM
ejpam-7023	186	7	)	)	PUNCT
ejpam-7023	186	8	into	into	ADP
ejpam-7023	186	9	(	(	PUNCT
ejpam-7023	186	10	27	27	NUM
ejpam-7023	186	11	)	)	PUNCT
ejpam-7023	186	12	and	and	CCONJ
ejpam-7023	186	13	using	use	VERB
ejpam-7023	186	14	ℑ(eiaθ	ℑ(eiaθ	NOUN
ejpam-7023	186	15	)	)	PUNCT
ejpam-7023	186	16	=	=	SYM
ejpam-7023	186	17	sin(aθ	sin(aθ	NOUN
ejpam-7023	186	18	)	)	PUNCT
ejpam-7023	186	19	gives	give	VERB
ejpam-7023	186	20	im	im	PRON
ejpam-7023	186	21	,	,	PUNCT
ejpam-7023	186	22	q(k	q(k	PROPN
ejpam-7023	186	23	,	,	PUNCT
ejpam-7023	186	24	α	α	X
ejpam-7023	186	25	,	,	PUNCT
ejpam-7023	186	26	β	β	NOUN
ejpam-7023	186	27	)	)	PUNCT
ejpam-7023	187	1	=	=	SYM
ejpam-7023	187	2	mγ(a)ℑ	mγ(a)ℑ	NOUN
ejpam-7023	187	3	(	(	PUNCT
ejpam-7023	187	4	r−ae	r−ae	PROPN
ejpam-7023	187	5	iaθ	iaθ	NOUN
ejpam-7023	187	6	)	)	PUNCT
ejpam-7023	187	7	=	=	SYM
ejpam-7023	187	8	mγ(a	mγ(a	X
ejpam-7023	187	9	)	)	PUNCT
ejpam-7023	187	10	r−a	r−a	NOUN
ejpam-7023	187	11	sin(aθ	sin(aθ	NOUN
ejpam-7023	187	12	)	)	PUNCT
ejpam-7023	187	13	=	=	SYM
ejpam-7023	187	14	mγ(a	mγ(a	X
ejpam-7023	187	15	)	)	PUNCT
ejpam-7023	187	16	(	(	PUNCT
ejpam-7023	187	17	α2	α2	ADJ
ejpam-7023	187	18	+	+	CCONJ
ejpam-7023	187	19	β2)−a/2	β2)−a/2	X
ejpam-7023	187	20	sin	sin	NOUN
ejpam-7023	187	21	(	(	PUNCT
ejpam-7023	187	22	a	a	DET
ejpam-7023	187	23	arctan	arctan	PROPN
ejpam-7023	187	24	β	β	X
ejpam-7023	187	25	α	α	PROPN
ejpam-7023	187	26	)	)	PUNCT
ejpam-7023	187	27	,	,	PUNCT
ejpam-7023	187	28	(	(	PUNCT
ejpam-7023	187	29	30	30	NUM
ejpam-7023	187	30	)	)	PUNCT
ejpam-7023	187	31	which	which	PRON
ejpam-7023	187	32	is	be	AUX
ejpam-7023	187	33	(	(	PUNCT
ejpam-7023	187	34	17	17	NUM
ejpam-7023	187	35	)	)	PUNCT
ejpam-7023	187	36	.	.	PUNCT
ejpam-7023	188	1	since	since	SCONJ
ejpam-7023	188	2	m	m	PROPN
ejpam-7023	188	3	>	>	X
ejpam-7023	188	4	0	0	NUM
ejpam-7023	188	5	,	,	PUNCT
ejpam-7023	188	6	γ(a	γ(a	PROPN
ejpam-7023	188	7	)	)	PUNCT
ejpam-7023	188	8	>	>	X
ejpam-7023	188	9	0	0	PUNCT
ejpam-7023	189	1	for	for	ADP
ejpam-7023	189	2	a	a	DET
ejpam-7023	189	3	>	>	X
ejpam-7023	189	4	0	0	NUM
ejpam-7023	189	5	,	,	PUNCT
ejpam-7023	189	6	and	and	CCONJ
ejpam-7023	189	7	(	(	PUNCT
ejpam-7023	189	8	α2	α2	ADJ
ejpam-7023	189	9	+	+	CCONJ
ejpam-7023	189	10	β2)−a/2	β2)−a/2	NOUN
ejpam-7023	189	11	>	>	X
ejpam-7023	189	12	0	0	NUM
ejpam-7023	189	13	,	,	PUNCT
ejpam-7023	189	14	the	the	DET
ejpam-7023	189	15	vanishing	vanishing	NOUN
ejpam-7023	189	16	im	im	PRON
ejpam-7023	189	17	,	,	PUNCT
ejpam-7023	189	18	q(k	q(k	PROPN
ejpam-7023	189	19	,	,	PUNCT
ejpam-7023	189	20	α	α	X
ejpam-7023	189	21	,	,	PUNCT
ejpam-7023	189	22	β	β	NOUN
ejpam-7023	189	23	)	)	PUNCT
ejpam-7023	189	24	=	=	SYM
ejpam-7023	189	25	0	0	PUNCT
ejpam-7023	189	26	(	(	PUNCT
ejpam-7023	189	27	when	when	SCONJ
ejpam-7023	189	28	β	β	X
ejpam-7023	189	29	̸=	̸=	PROPN
ejpam-7023	189	30	0	0	NUM
ejpam-7023	189	31	)	)	PUNCT
ejpam-7023	189	32	is	be	AUX
ejpam-7023	189	33	equivalent	equivalent	ADJ
ejpam-7023	189	34	to	to	PART
ejpam-7023	189	35	sin(aθ	sin(aθ	VERB
ejpam-7023	189	36	)	)	PUNCT
ejpam-7023	189	37	=	=	SYM
ejpam-7023	189	38	0	0	NUM
ejpam-7023	189	39	,	,	PUNCT
ejpam-7023	189	40	i.e.	i.e.	X
ejpam-7023	189	41	(	(	PUNCT
ejpam-7023	189	42	18	18	NUM
ejpam-7023	189	43	)	)	PUNCT
ejpam-7023	189	44	.	.	PUNCT
ejpam-7023	190	1	if	if	SCONJ
ejpam-7023	190	2	β	β	X
ejpam-7023	190	3	=	=	SYM
ejpam-7023	190	4	0	0	PUNCT
ejpam-7023	190	5	then	then	ADV
ejpam-7023	190	6	sin(βx1	sin(βx1	NOUN
ejpam-7023	190	7	/	/	SYM
ejpam-7023	190	8	m	m	NOUN
ejpam-7023	190	9	)	)	PUNCT
ejpam-7023	190	10	≡	≡	PROPN
ejpam-7023	190	11	0	0	PUNCT
ejpam-7023	191	1	and	and	CCONJ
ejpam-7023	191	2	(	(	PUNCT
ejpam-7023	191	3	15	15	NUM
ejpam-7023	191	4	)	)	PUNCT
ejpam-7023	191	5	gives	give	VERB
ejpam-7023	191	6	im	im	PRON
ejpam-7023	191	7	,	,	PUNCT
ejpam-7023	191	8	q(k	q(k	PROPN
ejpam-7023	191	9	,	,	PUNCT
ejpam-7023	191	10	α	α	NOUN
ejpam-7023	191	11	,	,	PUNCT
ejpam-7023	191	12	0	0	NUM
ejpam-7023	191	13	)	)	PUNCT
ejpam-7023	191	14	=	=	SYM
ejpam-7023	192	1	0	0	X
ejpam-7023	192	2	.	.	PUNCT
ejpam-7023	193	1	the	the	DET
ejpam-7023	193	2	following	follow	VERB
ejpam-7023	193	3	corollary	corollary	ADJ
ejpam-7023	193	4	recovers	recover	NOUN
ejpam-7023	193	5	theorem	theorem	VERB
ejpam-7023	193	6	4	4	NUM
ejpam-7023	193	7	from	from	ADP
ejpam-7023	193	8	theorem	theorem	ADJ
ejpam-7023	193	9	5	5	NUM
ejpam-7023	193	10	.	.	PUNCT
ejpam-7023	193	11	corollary	corollary	ADJ
ejpam-7023	193	12	1	1	NUM
ejpam-7023	193	13	.	.	PUNCT
ejpam-7023	194	1	let	let	VERB
ejpam-7023	194	2	m	m	VERB
ejpam-7023	194	3	=	=	NOUN
ejpam-7023	194	4	4	4	NUM
ejpam-7023	194	5	,	,	PUNCT
ejpam-7023	194	6	α	α	NOUN
ejpam-7023	194	7	=	=	SYM
ejpam-7023	194	8	1	1	NUM
ejpam-7023	194	9	,	,	PUNCT
ejpam-7023	194	10	β	β	X
ejpam-7023	194	11	=	=	SYM
ejpam-7023	194	12	1	1	NUM
ejpam-7023	194	13	,	,	PUNCT
ejpam-7023	194	14	q	q	NOUN
ejpam-7023	194	15	=	=	NOUN
ejpam-7023	194	16	0	0	NUM
ejpam-7023	194	17	.	.	PUNCT
ejpam-7023	195	1	for	for	ADP
ejpam-7023	195	2	k	k	PROPN
ejpam-7023	195	3	>	>	X
ejpam-7023	195	4	−1	−1	NOUN
ejpam-7023	195	5	,	,	PUNCT
ejpam-7023	195	6	i4,0(k	i4,0(k	PROPN
ejpam-7023	195	7	,	,	PUNCT
ejpam-7023	195	8	1	1	NUM
ejpam-7023	195	9	,	,	PUNCT
ejpam-7023	195	10	1	1	NUM
ejpam-7023	195	11	)	)	PUNCT
ejpam-7023	195	12	=	=	SYM
ejpam-7023	195	13	∫	∫	PROPN
ejpam-7023	195	14	∞	∞	NUM
ejpam-7023	195	15	0	0	NUM
ejpam-7023	196	1	e−x1/4	e−x1/4	PROPN
ejpam-7023	196	2	sin	sin	NOUN
ejpam-7023	196	3	(	(	PUNCT
ejpam-7023	196	4	x1/4	x1/4	PROPN
ejpam-7023	196	5	)	)	PUNCT
ejpam-7023	197	1	xk	xk	PROPN
ejpam-7023	197	2	dx	dx	PROPN
ejpam-7023	197	3	=	=	SYM
ejpam-7023	197	4	2−2k	2−2k	NUM
ejpam-7023	197	5	γ(4k	γ(4k	NOUN
ejpam-7023	197	6	+	+	CCONJ
ejpam-7023	197	7	4	4	X
ejpam-7023	197	8	)	)	PUNCT
ejpam-7023	197	9	sin	sin	NOUN
ejpam-7023	197	10	(	(	PUNCT
ejpam-7023	197	11	(	(	PUNCT
ejpam-7023	197	12	k	k	X
ejpam-7023	197	13	+	+	PROPN
ejpam-7023	197	14	1)π	1)π	NUM
ejpam-7023	197	15	)	)	PUNCT
ejpam-7023	197	16	.	.	PUNCT
ejpam-7023	198	1	proof	proof	NOUN
ejpam-7023	198	2	.	.	PUNCT
ejpam-7023	199	1	here	here	ADV
ejpam-7023	199	2	a	a	DET
ejpam-7023	199	3	=	=	SYM
ejpam-7023	199	4	mk+	mk+	NOUN
ejpam-7023	199	5	q+m	q+m	NUM
ejpam-7023	199	6	=	=	SYM
ejpam-7023	199	7	4k+4	4k+4	NUM
ejpam-7023	199	8	,	,	PUNCT
ejpam-7023	199	9	r	r	NOUN
ejpam-7023	199	10	=	=	NOUN
ejpam-7023	199	11	√	√	NOUN
ejpam-7023	199	12	α2	α2	NOUN
ejpam-7023	199	13	+	+	CCONJ
ejpam-7023	199	14	β2	β2	NOUN
ejpam-7023	199	15	=	=	NOUN
ejpam-7023	199	16	√	√	ADP
ejpam-7023	199	17	2	2	NUM
ejpam-7023	199	18	,	,	PUNCT
ejpam-7023	199	19	and	and	CCONJ
ejpam-7023	199	20	θ	θ	NOUN
ejpam-7023	199	21	=	=	SYM
ejpam-7023	199	22	arctan(1	arctan(1	X
ejpam-7023	199	23	)	)	PUNCT
ejpam-7023	199	24	=	=	PUNCT
ejpam-7023	199	25	π/4	π/4	NOUN
ejpam-7023	199	26	.	.	PUNCT
ejpam-7023	200	1	substituting	substitute	VERB
ejpam-7023	200	2	these	these	PRON
ejpam-7023	200	3	into	into	ADP
ejpam-7023	200	4	(	(	PUNCT
ejpam-7023	200	5	17	17	NUM
ejpam-7023	200	6	)	)	PUNCT
ejpam-7023	200	7	gives	give	VERB
ejpam-7023	200	8	i4,0(k	i4,0(k	NOUN
ejpam-7023	200	9	,	,	PUNCT
ejpam-7023	200	10	1	1	NUM
ejpam-7023	200	11	,	,	PUNCT
ejpam-7023	200	12	1	1	NUM
ejpam-7023	200	13	)	)	PUNCT
ejpam-7023	200	14	=	=	SYM
ejpam-7023	200	15	4γ(4k	4γ(4k	NUM
ejpam-7023	200	16	+	+	CCONJ
ejpam-7023	200	17	4	4	NUM
ejpam-7023	200	18	)	)	PUNCT
ejpam-7023	200	19	(	(	PUNCT
ejpam-7023	200	20	√	√	NUM
ejpam-7023	200	21	2)−(4k+4	2)−(4k+4	NUM
ejpam-7023	200	22	)	)	PUNCT
ejpam-7023	200	23	sin	sin	NOUN
ejpam-7023	200	24	(	(	PUNCT
ejpam-7023	200	25	(	(	PUNCT
ejpam-7023	200	26	4k	4k	NOUN
ejpam-7023	200	27	+	+	NOUN
ejpam-7023	200	28	4)π4	4)π4	NUM
ejpam-7023	200	29	)	)	PUNCT
ejpam-7023	201	1	=	=	SYM
ejpam-7023	201	2	2−2k	2−2k	NUM
ejpam-7023	201	3	γ(4k	γ(4k	NOUN
ejpam-7023	201	4	+	+	CCONJ
ejpam-7023	201	5	4	4	X
ejpam-7023	201	6	)	)	PUNCT
ejpam-7023	201	7	sin	sin	NOUN
ejpam-7023	201	8	(	(	PUNCT
ejpam-7023	201	9	(	(	PUNCT
ejpam-7023	201	10	k	k	X
ejpam-7023	201	11	+	+	PROPN
ejpam-7023	201	12	1)π	1)π	NUM
ejpam-7023	201	13	)	)	PUNCT
ejpam-7023	201	14	.	.	PUNCT
ejpam-7023	202	1	we	we	PRON
ejpam-7023	202	2	also	also	ADV
ejpam-7023	202	3	have	have	VERB
ejpam-7023	202	4	the	the	DET
ejpam-7023	202	5	following	follow	VERB
ejpam-7023	202	6	special	special	ADJ
ejpam-7023	202	7	cases	case	NOUN
ejpam-7023	202	8	.	.	PUNCT
ejpam-7023	203	1	corollary	corollary	ADJ
ejpam-7023	203	2	2	2	NUM
ejpam-7023	203	3	(	(	PUNCT
ejpam-7023	203	4	equal	equal	ADJ
ejpam-7023	203	5	parameters	parameter	NOUN
ejpam-7023	203	6	α	α	NOUN
ejpam-7023	203	7	=	=	PUNCT
ejpam-7023	203	8	β	β	X
ejpam-7023	203	9	>	>	X
ejpam-7023	203	10	0	0	NUM
ejpam-7023	203	11	)	)	PUNCT
ejpam-7023	203	12	.	.	PUNCT
ejpam-7023	204	1	for	for	ADP
ejpam-7023	204	2	any	any	DET
ejpam-7023	204	3	m	m	NOUN
ejpam-7023	204	4	>	>	X
ejpam-7023	204	5	0	0	PUNCT
ejpam-7023	204	6	and	and	CCONJ
ejpam-7023	204	7	any	any	DET
ejpam-7023	204	8	k	k	NOUN
ejpam-7023	204	9	,	,	PUNCT
ejpam-7023	204	10	q	q	NOUN
ejpam-7023	204	11	with	with	ADP
ejpam-7023	204	12	a	a	DET
ejpam-7023	204	13	>	>	X
ejpam-7023	204	14	0	0	NUM
ejpam-7023	204	15	,	,	PUNCT
ejpam-7023	204	16	im	im	X
ejpam-7023	204	17	,	,	PUNCT
ejpam-7023	204	18	q(k	q(k	PROPN
ejpam-7023	204	19	,	,	PUNCT
ejpam-7023	204	20	α	α	X
ejpam-7023	204	21	,	,	PUNCT
ejpam-7023	204	22	α	α	NOUN
ejpam-7023	204	23	)	)	PUNCT
ejpam-7023	204	24	=	=	SYM
ejpam-7023	204	25	mγ(a	mγ(a	X
ejpam-7023	204	26	)	)	PUNCT
ejpam-7023	204	27	2−a/2	2−a/2	NUM
ejpam-7023	204	28	α−a	α−a	ADJ
ejpam-7023	204	29	sin	sin	NOUN
ejpam-7023	204	30	(	(	PUNCT
ejpam-7023	204	31	a	a	DET
ejpam-7023	204	32	π	π	PROPN
ejpam-7023	204	33	4	4	NUM
ejpam-7023	204	34	)	)	PUNCT
ejpam-7023	204	35	.	.	PUNCT
ejpam-7023	205	1	in	in	ADP
ejpam-7023	205	2	particular	particular	ADJ
ejpam-7023	205	3	,	,	PUNCT
ejpam-7023	205	4	im	im	ADV
ejpam-7023	205	5	,	,	PUNCT
ejpam-7023	205	6	q(k	q(k	PROPN
ejpam-7023	205	7	,	,	PUNCT
ejpam-7023	205	8	α	α	X
ejpam-7023	205	9	,	,	PUNCT
ejpam-7023	205	10	α	α	NOUN
ejpam-7023	205	11	)	)	PUNCT
ejpam-7023	205	12	=	=	SYM
ejpam-7023	205	13	0	0	PUNCT
ejpam-7023	206	1	if	if	SCONJ
ejpam-7023	206	2	and	and	CCONJ
ejpam-7023	206	3	only	only	ADV
ejpam-7023	206	4	if	if	SCONJ
ejpam-7023	206	5	a	a	DET
ejpam-7023	206	6	∈	∈	PROPN
ejpam-7023	206	7	4z	4z	NOUN
ejpam-7023	206	8	.	.	PUNCT
ejpam-7023	207	1	i.	i.	PROPN
ejpam-7023	207	2	ayoob	ayoob	PROPN
ejpam-7023	207	3	/	/	SYM
ejpam-7023	207	4	eur	eur	PROPN
ejpam-7023	207	5	.	.	PUNCT
ejpam-7023	208	1	j.	j.	PROPN
ejpam-7023	208	2	pure	pure	PROPN
ejpam-7023	208	3	appl	appl	PROPN
ejpam-7023	208	4	.	.	PROPN
ejpam-7023	208	5	math	math	PROPN
ejpam-7023	208	6	,	,	PUNCT
ejpam-7023	208	7	18	18	NUM
ejpam-7023	208	8	(	(	PUNCT
ejpam-7023	208	9	4	4	NUM
ejpam-7023	208	10	)	)	PUNCT
ejpam-7023	208	11	(	(	PUNCT
ejpam-7023	208	12	2025	2025	NUM
ejpam-7023	208	13	)	)	PUNCT
ejpam-7023	208	14	,	,	PUNCT
ejpam-7023	208	15	7023	7023	NUM
ejpam-7023	208	16	9	9	NUM
ejpam-7023	208	17	of	of	ADP
ejpam-7023	208	18	16	16	NUM
ejpam-7023	208	19	proof	proof	NOUN
ejpam-7023	208	20	.	.	PUNCT
ejpam-7023	209	1	when	when	SCONJ
ejpam-7023	209	2	α	α	PRON
ejpam-7023	209	3	=	=	SYM
ejpam-7023	209	4	β	β	NOUN
ejpam-7023	209	5	,	,	PUNCT
ejpam-7023	209	6	we	we	PRON
ejpam-7023	209	7	have	have	VERB
ejpam-7023	209	8	r	r	NOUN
ejpam-7023	209	9	=	=	PUNCT
ejpam-7023	209	10	√	√	PROPN
ejpam-7023	209	11	2α	2α	NOUN
ejpam-7023	209	12	and	and	CCONJ
ejpam-7023	209	13	θ	θ	NOUN
ejpam-7023	209	14	=	=	PUNCT
ejpam-7023	209	15	π/4	π/4	PROPN
ejpam-7023	209	16	,	,	PUNCT
ejpam-7023	209	17	so	so	CCONJ
ejpam-7023	209	18	(	(	PUNCT
ejpam-7023	209	19	17	17	NUM
ejpam-7023	209	20	)	)	PUNCT
ejpam-7023	209	21	reduces	reduce	VERB
ejpam-7023	209	22	to	to	ADP
ejpam-7023	209	23	the	the	DET
ejpam-7023	209	24	displayed	display	VERB
ejpam-7023	209	25	formula	formula	NOUN
ejpam-7023	209	26	.	.	PUNCT
ejpam-7023	210	1	the	the	DET
ejpam-7023	210	2	zero	zero	NUM
ejpam-7023	210	3	condition	condition	NOUN
ejpam-7023	210	4	follows	follow	VERB
ejpam-7023	210	5	from	from	ADP
ejpam-7023	210	6	sin(aπ/4	sin(aπ/4	NOUN
ejpam-7023	210	7	)	)	PUNCT
ejpam-7023	211	1	=	=	SYM
ejpam-7023	211	2	0	0	X
ejpam-7023	211	3	.	.	PUNCT
ejpam-7023	211	4	corollary	corollary	ADJ
ejpam-7023	211	5	3	3	NUM
ejpam-7023	211	6	(	(	PUNCT
ejpam-7023	211	7	q	q	NOUN
ejpam-7023	211	8	=	=	NOUN
ejpam-7023	211	9	0	0	NUM
ejpam-7023	211	10	)	)	PUNCT
ejpam-7023	211	11	.	.	PUNCT
ejpam-7023	212	1	if	if	SCONJ
ejpam-7023	212	2	q	q	NOUN
ejpam-7023	212	3	=	=	SYM
ejpam-7023	212	4	0	0	NUM
ejpam-7023	212	5	and	and	CCONJ
ejpam-7023	212	6	k	k	ADJ
ejpam-7023	212	7	>	>	X
ejpam-7023	212	8	−1	−1	NOUN
ejpam-7023	212	9	,	,	PUNCT
ejpam-7023	212	10	then	then	ADV
ejpam-7023	212	11	a	a	DET
ejpam-7023	212	12	=	=	X
ejpam-7023	212	13	m(k	m(k	PROPN
ejpam-7023	212	14	+	+	CCONJ
ejpam-7023	212	15	1	1	NUM
ejpam-7023	212	16	)	)	PUNCT
ejpam-7023	212	17	and	and	CCONJ
ejpam-7023	212	18	im,0(k	im,0(k	PROPN
ejpam-7023	212	19	,	,	PUNCT
ejpam-7023	212	20	α	α	NOUN
ejpam-7023	212	21	,	,	PUNCT
ejpam-7023	212	22	β	β	NOUN
ejpam-7023	212	23	)	)	PUNCT
ejpam-7023	212	24	=	=	SYM
ejpam-7023	212	25	mγ	mγ	NOUN
ejpam-7023	212	26	(	(	PUNCT
ejpam-7023	212	27	m(k	m(k	PROPN
ejpam-7023	212	28	+	+	CCONJ
ejpam-7023	212	29	1	1	NUM
ejpam-7023	212	30	)	)	PUNCT
ejpam-7023	212	31	)	)	PUNCT
ejpam-7023	213	1	(	(	PUNCT
ejpam-7023	213	2	α2	α2	ADJ
ejpam-7023	213	3	+	+	CCONJ
ejpam-7023	213	4	β2)−m(k+1)/2	β2)−m(k+1)/2	ADJ
ejpam-7023	213	5	sin	sin	NOUN
ejpam-7023	213	6	(	(	PUNCT
ejpam-7023	213	7	m(k	m(k	NOUN
ejpam-7023	213	8	+	+	CCONJ
ejpam-7023	213	9	1	1	NUM
ejpam-7023	213	10	)	)	PUNCT
ejpam-7023	213	11	arctan	arctan	PROPN
ejpam-7023	213	12	β	β	PROPN
ejpam-7023	213	13	α	α	PROPN
ejpam-7023	213	14	)	)	PUNCT
ejpam-7023	213	15	.	.	PUNCT
ejpam-7023	214	1	proof	proof	NOUN
ejpam-7023	214	2	.	.	PUNCT
ejpam-7023	215	1	put	put	VERB
ejpam-7023	215	2	q	q	NOUN
ejpam-7023	215	3	=	=	NOUN
ejpam-7023	215	4	0	0	NUM
ejpam-7023	215	5	in	in	ADP
ejpam-7023	215	6	(	(	PUNCT
ejpam-7023	215	7	17	17	NUM
ejpam-7023	215	8	)	)	PUNCT
ejpam-7023	215	9	.	.	PUNCT
ejpam-7023	216	1	next	next	ADV
ejpam-7023	216	2	,	,	PUNCT
ejpam-7023	216	3	we	we	PRON
ejpam-7023	216	4	give	give	VERB
ejpam-7023	216	5	the	the	DET
ejpam-7023	216	6	cosine	cosine	NOUN
ejpam-7023	216	7	variant	variant	NOUN
ejpam-7023	216	8	of	of	ADP
ejpam-7023	216	9	theorem	theorem	ADJ
ejpam-7023	216	10	4	4	NUM
ejpam-7023	216	11	.	.	PUNCT
ejpam-7023	217	1	the	the	DET
ejpam-7023	217	2	proof	proof	NOUN
ejpam-7023	217	3	is	be	AUX
ejpam-7023	217	4	similar	similar	ADJ
ejpam-7023	217	5	as	as	ADP
ejpam-7023	217	6	in	in	ADP
ejpam-7023	217	7	theorem	theorem	NOUN
ejpam-7023	217	8	5	5	NUM
ejpam-7023	217	9	but	but	CCONJ
ejpam-7023	217	10	for	for	ADP
ejpam-7023	217	11	the	the	DET
ejpam-7023	217	12	completeness	completeness	NOUN
ejpam-7023	217	13	,	,	PUNCT
ejpam-7023	217	14	we	we	PRON
ejpam-7023	217	15	write	write	VERB
ejpam-7023	217	16	it	it	PRON
ejpam-7023	217	17	here	here	ADV
ejpam-7023	217	18	.	.	PUNCT
ejpam-7023	218	1	theorem	theorem	VERB
ejpam-7023	218	2	6	6	NUM
ejpam-7023	218	3	.	.	PUNCT
ejpam-7023	219	1	let	let	VERB
ejpam-7023	219	2	m	m	PRON
ejpam-7023	219	3	>	>	X
ejpam-7023	219	4	0	0	PROPN
ejpam-7023	219	5	,	,	PUNCT
ejpam-7023	219	6	α	α	NOUN
ejpam-7023	219	7	>	>	X
ejpam-7023	219	8	0	0	PROPN
ejpam-7023	219	9	,	,	PUNCT
ejpam-7023	219	10	β	β	X
ejpam-7023	219	11	∈	∈	NOUN
ejpam-7023	219	12	r	r	NOUN
ejpam-7023	219	13	,	,	PUNCT
ejpam-7023	219	14	q	q	NOUN
ejpam-7023	219	15	∈	∈	PROPN
ejpam-7023	219	16	r	r	NOUN
ejpam-7023	219	17	,	,	PUNCT
ejpam-7023	219	18	and	and	CCONJ
ejpam-7023	219	19	k	k	PROPN
ejpam-7023	219	20	∈	∈	PROPN
ejpam-7023	219	21	r.	r.	PROPN
ejpam-7023	219	22	define	define	VERB
ejpam-7023	219	23	jm	jm	PROPN
ejpam-7023	219	24	,	,	PUNCT
ejpam-7023	219	25	q(k	q(k	PROPN
ejpam-7023	219	26	,	,	PUNCT
ejpam-7023	219	27	α	α	X
ejpam-7023	219	28	,	,	PUNCT
ejpam-7023	219	29	β	β	NOUN
ejpam-7023	219	30	)	)	PUNCT
ejpam-7023	219	31	=	=	SYM
ejpam-7023	220	1	∫	∫	PROPN
ejpam-7023	220	2	∞	∞	NUM
ejpam-7023	220	3	0	0	NUM
ejpam-7023	220	4	e−αx1	e−αx1	PROPN
ejpam-7023	220	5	/	/	SYM
ejpam-7023	220	6	m	m	NOUN
ejpam-7023	220	7	cos	cos	NOUN
ejpam-7023	220	8	(	(	PUNCT
ejpam-7023	220	9	βx1	βx1	PROPN
ejpam-7023	220	10	/	/	SYM
ejpam-7023	220	11	m	m	NOUN
ejpam-7023	220	12	)	)	PUNCT
ejpam-7023	220	13	xk	xk	PROPN
ejpam-7023	220	14	(	(	PUNCT
ejpam-7023	220	15	x1	x1	PROPN
ejpam-7023	220	16	/	/	SYM
ejpam-7023	220	17	m)q	m)q	PROPN
ejpam-7023	220	18	dx	dx	PROPN
ejpam-7023	220	19	,	,	PUNCT
ejpam-7023	220	20	(	(	PUNCT
ejpam-7023	220	21	31	31	NUM
ejpam-7023	220	22	)	)	PUNCT
ejpam-7023	220	23	and	and	CCONJ
ejpam-7023	220	24	set	set	VERB
ejpam-7023	220	25	a	a	DET
ejpam-7023	220	26	=	=	SYM
ejpam-7023	220	27	mk	mk	NOUN
ejpam-7023	220	28	+	+	CCONJ
ejpam-7023	220	29	q	q	X
ejpam-7023	221	1	+	+	ADJ
ejpam-7023	221	2	m.	m.	NOUN
ejpam-7023	221	3	(	(	PUNCT
ejpam-7023	221	4	32	32	NUM
ejpam-7023	221	5	)	)	PUNCT
ejpam-7023	221	6	then	then	ADV
ejpam-7023	221	7	the	the	DET
ejpam-7023	221	8	integral	integral	ADJ
ejpam-7023	221	9	in	in	ADP
ejpam-7023	221	10	(	(	PUNCT
ejpam-7023	221	11	31	31	NUM
ejpam-7023	221	12	)	)	PUNCT
ejpam-7023	221	13	converges	converge	VERB
ejpam-7023	221	14	for	for	ADP
ejpam-7023	221	15	every	every	DET
ejpam-7023	221	16	a	a	DET
ejpam-7023	221	17	>	>	X
ejpam-7023	221	18	−1	−1	NOUN
ejpam-7023	221	19	.	.	PUNCT
ejpam-7023	222	1	moreover	moreover	ADV
ejpam-7023	222	2	,	,	PUNCT
ejpam-7023	222	3	if	if	SCONJ
ejpam-7023	222	4	a	a	PRON
ejpam-7023	222	5	>	>	X
ejpam-7023	222	6	0	0	PUNCT
ejpam-7023	222	7	(	(	PUNCT
ejpam-7023	222	8	which	which	PRON
ejpam-7023	222	9	we	we	PRON
ejpam-7023	222	10	assume	assume	VERB
ejpam-7023	222	11	for	for	ADP
ejpam-7023	222	12	the	the	DET
ejpam-7023	222	13	evaluation	evaluation	NOUN
ejpam-7023	222	14	below	below	ADP
ejpam-7023	222	15	)	)	PUNCT
ejpam-7023	222	16	,	,	PUNCT
ejpam-7023	222	17	one	one	PRON
ejpam-7023	222	18	has	have	VERB
ejpam-7023	222	19	the	the	DET
ejpam-7023	222	20	closed	closed	ADJ
ejpam-7023	222	21	form	form	NOUN
ejpam-7023	222	22	jm	jm	PROPN
ejpam-7023	222	23	,	,	PUNCT
ejpam-7023	222	24	q(k	q(k	PROPN
ejpam-7023	222	25	,	,	PUNCT
ejpam-7023	222	26	α	α	X
ejpam-7023	222	27	,	,	PUNCT
ejpam-7023	222	28	β	β	NOUN
ejpam-7023	222	29	)	)	PUNCT
ejpam-7023	222	30	=	=	SYM
ejpam-7023	222	31	mγ(a	mγ(a	X
ejpam-7023	222	32	)	)	PUNCT
ejpam-7023	222	33	(	(	PUNCT
ejpam-7023	222	34	α2	α2	ADJ
ejpam-7023	222	35	+	+	CCONJ
ejpam-7023	222	36	β2)−a/2	β2)−a/2	PUNCT
ejpam-7023	222	37	cos	cos	ADP
ejpam-7023	222	38	(	(	PUNCT
ejpam-7023	222	39	a	a	DET
ejpam-7023	222	40	arctan	arctan	PROPN
ejpam-7023	222	41	β	β	X
ejpam-7023	222	42	α	α	NOUN
ejpam-7023	222	43	)	)	PUNCT
ejpam-7023	222	44	.	.	PUNCT
ejpam-7023	223	1	(	(	PUNCT
ejpam-7023	223	2	33	33	NUM
ejpam-7023	223	3	)	)	PUNCT
ejpam-7023	223	4	consequently	consequently	ADV
ejpam-7023	223	5	,	,	PUNCT
ejpam-7023	223	6	if	if	SCONJ
ejpam-7023	223	7	β	β	PROPN
ejpam-7023	223	8	̸=	̸=	PROPN
ejpam-7023	223	9	0	0	NUM
ejpam-7023	223	10	then	then	ADV
ejpam-7023	223	11	jm	jm	PROPN
ejpam-7023	223	12	,	,	PUNCT
ejpam-7023	223	13	q(k	q(k	PROPN
ejpam-7023	223	14	,	,	PUNCT
ejpam-7023	223	15	α	α	X
ejpam-7023	223	16	,	,	PUNCT
ejpam-7023	223	17	β	β	NOUN
ejpam-7023	223	18	)	)	PUNCT
ejpam-7023	224	1	=	=	SYM
ejpam-7023	224	2	0	0	PUNCT
ejpam-7023	225	1	if	if	SCONJ
ejpam-7023	225	2	and	and	CCONJ
ejpam-7023	225	3	only	only	ADV
ejpam-7023	225	4	if	if	SCONJ
ejpam-7023	225	5	a	a	DET
ejpam-7023	225	6	arctan	arctan	PROPN
ejpam-7023	225	7	β	β	X
ejpam-7023	225	8	α	α	PROPN
ejpam-7023	225	9	∈	∈	PROPN
ejpam-7023	225	10	π	π	X
ejpam-7023	225	11	2	2	NUM
ejpam-7023	225	12	+	+	CCONJ
ejpam-7023	225	13	πz	πz	PRON
ejpam-7023	225	14	;	;	PUNCT
ejpam-7023	225	15	(	(	PUNCT
ejpam-7023	225	16	34	34	NUM
ejpam-7023	225	17	)	)	PUNCT
ejpam-7023	225	18	if	if	SCONJ
ejpam-7023	225	19	β	β	X
ejpam-7023	225	20	=	=	SYM
ejpam-7023	225	21	0	0	PUNCT
ejpam-7023	225	22	then	then	ADV
ejpam-7023	225	23	jm	jm	PROPN
ejpam-7023	225	24	,	,	PUNCT
ejpam-7023	225	25	q(k	q(k	PROPN
ejpam-7023	225	26	,	,	PUNCT
ejpam-7023	225	27	α	α	NOUN
ejpam-7023	225	28	,	,	PUNCT
ejpam-7023	225	29	0	0	NUM
ejpam-7023	225	30	)	)	PUNCT
ejpam-7023	225	31	=	=	SYM
ejpam-7023	225	32	mγ(a)α−a	mγ(a)α−a	NOUN
ejpam-7023	225	33	.	.	PUNCT
ejpam-7023	225	34	(	(	PUNCT
ejpam-7023	225	35	35	35	NUM
ejpam-7023	225	36	)	)	PUNCT
ejpam-7023	225	37	proof	proof	NOUN
ejpam-7023	225	38	.	.	PUNCT
ejpam-7023	226	1	we	we	PRON
ejpam-7023	226	2	write	write	VERB
ejpam-7023	226	3	the	the	DET
ejpam-7023	226	4	integrand	integrand	NOUN
ejpam-7023	226	5	as	as	ADP
ejpam-7023	226	6	e−αx1	e−αx1	PROPN
ejpam-7023	226	7	/	/	SYM
ejpam-7023	226	8	m	m	VERB
ejpam-7023	226	9	cos(βx1	cos(βx1	NOUN
ejpam-7023	226	10	/	/	SYM
ejpam-7023	226	11	m)xk+q	m)xk+q	ADP
ejpam-7023	226	12	/	/	SYM
ejpam-7023	226	13	m.	m.	NOUN
ejpam-7023	226	14	for	for	ADP
ejpam-7023	226	15	x	x	PUNCT
ejpam-7023	226	16	↓	↓	PROPN
ejpam-7023	226	17	0	0	NUM
ejpam-7023	226	18	we	we	PRON
ejpam-7023	226	19	use	use	VERB
ejpam-7023	226	20	|	|	ADV
ejpam-7023	226	21	cos	cos	ADP
ejpam-7023	226	22	t|	t|	PROPN
ejpam-7023	226	23	≤	≤	ADV
ejpam-7023	226	24	1	1	NUM
ejpam-7023	226	25	to	to	PART
ejpam-7023	226	26	obtain	obtain	VERB
ejpam-7023	226	27	∣∣e−αx1	∣∣e−αx1	NUM
ejpam-7023	226	28	/	/	SYM
ejpam-7023	226	29	m	m	VERB
ejpam-7023	226	30	cos(βx1	cos(βx1	NOUN
ejpam-7023	226	31	/	/	SYM
ejpam-7023	227	1	m)xk+q	m)xk+q	PROPN
ejpam-7023	227	2	/	/	SYM
ejpam-7023	227	3	m	m	NOUN
ejpam-7023	227	4	∣∣	∣∣	NUM
ejpam-7023	227	5	≪	≪	PUNCT
ejpam-7023	227	6	xk+q	xk+q	PROPN
ejpam-7023	227	7	/	/	SYM
ejpam-7023	227	8	m	m	PROPN
ejpam-7023	227	9	(	(	PUNCT
ejpam-7023	227	10	x	x	PROPN
ejpam-7023	227	11	↓	↓	PROPN
ejpam-7023	227	12	0	0	NUM
ejpam-7023	227	13	)	)	PUNCT
ejpam-7023	227	14	,	,	PUNCT
ejpam-7023	227	15	(	(	PUNCT
ejpam-7023	227	16	36	36	NUM
ejpam-7023	227	17	)	)	PUNCT
ejpam-7023	227	18	so	so	ADV
ejpam-7023	227	19	∫	∫	PROPN
ejpam-7023	227	20	1	1	NUM
ejpam-7023	227	21	0	0	NUM
ejpam-7023	227	22	|e−αx1	|e−αx1	PROPN
ejpam-7023	227	23	/	/	SYM
ejpam-7023	227	24	m	m	VERB
ejpam-7023	227	25	cos(βx1	cos(βx1	NOUN
ejpam-7023	227	26	/	/	SYM
ejpam-7023	227	27	m)xk+q	m)xk+q	PROPN
ejpam-7023	227	28	/	/	SYM
ejpam-7023	227	29	m|	m|	NOUN
ejpam-7023	227	30	dx	dx	PROPN
ejpam-7023	227	31	<	<	X
ejpam-7023	227	32	∞	∞	PROPN
ejpam-7023	227	33	provided	provide	VERB
ejpam-7023	227	34	k	k	PROPN
ejpam-7023	228	1	+	+	CCONJ
ejpam-7023	228	2	q	q	PROPN
ejpam-7023	228	3	/	/	SYM
ejpam-7023	228	4	m	m	VERB
ejpam-7023	228	5	>	>	X
ejpam-7023	228	6	−1	−1	NOUN
ejpam-7023	228	7	,	,	PUNCT
ejpam-7023	228	8	i.e.	i.e.	X
ejpam-7023	228	9	mk	mk	X
ejpam-7023	228	10	+	+	CCONJ
ejpam-7023	228	11	q	q	ADJ
ejpam-7023	228	12	>	>	X
ejpam-7023	228	13	−1	−1	NOUN
ejpam-7023	228	14	⇐	⇐	ADJ
ejpam-7023	228	15	⇒	⇒	PROPN
ejpam-7023	228	16	a−m	a−m	PROPN
ejpam-7023	228	17	>	>	X
ejpam-7023	228	18	−1	−1	NOUN
ejpam-7023	228	19	⇐	⇐	PROPN
ejpam-7023	228	20	⇒	⇒	PROPN
ejpam-7023	228	21	a	a	DET
ejpam-7023	228	22	>	>	X
ejpam-7023	228	23	−1	−1	NOUN
ejpam-7023	228	24	.	.	PUNCT
ejpam-7023	229	1	(	(	PUNCT
ejpam-7023	229	2	37	37	NUM
ejpam-7023	229	3	)	)	PUNCT
ejpam-7023	229	4	as	as	SCONJ
ejpam-7023	229	5	x	x	X
ejpam-7023	229	6	→	→	SYM
ejpam-7023	229	7	∞	∞	NUM
ejpam-7023	229	8	we	we	PRON
ejpam-7023	229	9	have	have	VERB
ejpam-7023	229	10	|	|	ADV
ejpam-7023	229	11	cos(βx1	cos(βx1	NOUN
ejpam-7023	229	12	/	/	SYM
ejpam-7023	229	13	m)|	m)|	ADJ
ejpam-7023	229	14	≤	≤	ADJ
ejpam-7023	229	15	1	1	NUM
ejpam-7023	229	16	and	and	CCONJ
ejpam-7023	229	17	the	the	DET
ejpam-7023	229	18	factor	factor	NOUN
ejpam-7023	229	19	e−αx1	e−αx1	PROPN
ejpam-7023	229	20	/	/	SYM
ejpam-7023	229	21	m	m	PROPN
ejpam-7023	229	22	yields	yield	NOUN
ejpam-7023	229	23	super	super	ADJ
ejpam-7023	229	24	–	–	PUNCT
ejpam-7023	229	25	polynomial	polynomial	ADJ
ejpam-7023	229	26	decay	decay	NOUN
ejpam-7023	229	27	,	,	PUNCT
ejpam-7023	229	28	hence∫	hence∫	X
ejpam-7023	229	29	∞	∞	PROPN
ejpam-7023	229	30	1	1	NUM
ejpam-7023	229	31	∣∣e−αx1	∣∣e−αx1	NUM
ejpam-7023	229	32	/	/	SYM
ejpam-7023	229	33	m	m	VERB
ejpam-7023	229	34	cos(βx1	cos(βx1	NOUN
ejpam-7023	229	35	/	/	SYM
ejpam-7023	229	36	m)xk+q	m)xk+q	PROPN
ejpam-7023	229	37	/	/	SYM
ejpam-7023	229	38	m	m	PROPN
ejpam-7023	229	39	∣∣	∣∣	NUM
ejpam-7023	229	40	dx	dx	X
ejpam-7023	229	41	<	<	X
ejpam-7023	229	42	∞	∞	PROPN
ejpam-7023	229	43	for	for	ADP
ejpam-7023	229	44	every	every	DET
ejpam-7023	229	45	k	k	NOUN
ejpam-7023	229	46	,	,	PUNCT
ejpam-7023	229	47	q	q	X
ejpam-7023	229	48	when	when	SCONJ
ejpam-7023	229	49	α	α	X
ejpam-7023	229	50	>	>	X
ejpam-7023	229	51	0	0	PROPN
ejpam-7023	229	52	.	.	PUNCT
ejpam-7023	230	1	(	(	PUNCT
ejpam-7023	230	2	38	38	NUM
ejpam-7023	230	3	)	)	PUNCT
ejpam-7023	230	4	therefore	therefore	ADV
ejpam-7023	230	5	(	(	PUNCT
ejpam-7023	230	6	31	31	NUM
ejpam-7023	230	7	)	)	PUNCT
ejpam-7023	230	8	converges	converge	VERB
ejpam-7023	230	9	for	for	ADP
ejpam-7023	230	10	all	all	DET
ejpam-7023	230	11	a	a	DET
ejpam-7023	230	12	>	>	X
ejpam-7023	230	13	−1	−1	NOUN
ejpam-7023	230	14	.	.	PUNCT
ejpam-7023	231	1	i.	i.	PROPN
ejpam-7023	231	2	ayoob	ayoob	PROPN
ejpam-7023	231	3	/	/	SYM
ejpam-7023	231	4	eur	eur	PROPN
ejpam-7023	231	5	.	.	PUNCT
ejpam-7023	232	1	j.	j.	PROPN
ejpam-7023	232	2	pure	pure	PROPN
ejpam-7023	232	3	appl	appl	PROPN
ejpam-7023	232	4	.	.	PROPN
ejpam-7023	232	5	math	math	PROPN
ejpam-7023	232	6	,	,	PUNCT
ejpam-7023	232	7	18	18	NUM
ejpam-7023	232	8	(	(	PUNCT
ejpam-7023	232	9	4	4	NUM
ejpam-7023	232	10	)	)	PUNCT
ejpam-7023	232	11	(	(	PUNCT
ejpam-7023	232	12	2025	2025	NUM
ejpam-7023	232	13	)	)	PUNCT
ejpam-7023	232	14	,	,	PUNCT
ejpam-7023	232	15	7023	7023	NUM
ejpam-7023	232	16	10	10	NUM
ejpam-7023	232	17	of	of	ADP
ejpam-7023	232	18	16	16	NUM
ejpam-7023	232	19	assume	assume	VERB
ejpam-7023	232	20	a	a	DET
ejpam-7023	232	21	>	>	X
ejpam-7023	232	22	0	0	PUNCT
ejpam-7023	232	23	for	for	ADP
ejpam-7023	232	24	evaluation	evaluation	NOUN
ejpam-7023	232	25	.	.	PUNCT
ejpam-7023	233	1	we	we	PRON
ejpam-7023	233	2	make	make	VERB
ejpam-7023	233	3	the	the	DET
ejpam-7023	233	4	substitution	substitution	NOUN
ejpam-7023	233	5	u	u	NOUN
ejpam-7023	233	6	=	=	PROPN
ejpam-7023	233	7	x1	x1	PROPN
ejpam-7023	233	8	/	/	SYM
ejpam-7023	233	9	m	m	PROPN
ejpam-7023	233	10	,	,	PUNCT
ejpam-7023	233	11	x	x	SYM
ejpam-7023	233	12	=	=	SYM
ejpam-7023	233	13	um	um	INTJ
ejpam-7023	233	14	,	,	PUNCT
ejpam-7023	233	15	dx	dx	PROPN
ejpam-7023	233	16	=	=	PUNCT
ejpam-7023	233	17	mum−1	mum−1	PROPN
ejpam-7023	233	18	du	du	PROPN
ejpam-7023	233	19	,	,	PUNCT
ejpam-7023	233	20	(	(	PUNCT
ejpam-7023	233	21	39	39	NUM
ejpam-7023	233	22	)	)	PUNCT
ejpam-7023	233	23	and	and	CCONJ
ejpam-7023	233	24	note	note	VERB
ejpam-7023	233	25	xk(x1	xk(x1	NOUN
ejpam-7023	233	26	/	/	SYM
ejpam-7023	233	27	m)q	m)q	NOUN
ejpam-7023	233	28	=	=	SYM
ejpam-7023	234	1	umk+q	umk+q	NOUN
ejpam-7023	234	2	,	,	PUNCT
ejpam-7023	234	3	to	to	PART
ejpam-7023	234	4	obtain	obtain	VERB
ejpam-7023	234	5	jm	jm	PROPN
ejpam-7023	234	6	,	,	PUNCT
ejpam-7023	234	7	q(k	q(k	PROPN
ejpam-7023	234	8	,	,	PUNCT
ejpam-7023	234	9	α	α	X
ejpam-7023	234	10	,	,	PUNCT
ejpam-7023	234	11	β	β	NOUN
ejpam-7023	234	12	)	)	PUNCT
ejpam-7023	234	13	=	=	SYM
ejpam-7023	235	1	∫	∫	PROPN
ejpam-7023	235	2	∞	∞	PROPN
ejpam-7023	235	3	0	0	NUM
ejpam-7023	236	1	e−αu	e−αu	PROPN
ejpam-7023	236	2	cos(βu)umk+q	cos(βu)umk+q	ADP
ejpam-7023	236	3	(	(	PUNCT
ejpam-7023	236	4	mum−1	mum−1	PROPN
ejpam-7023	236	5	)	)	PUNCT
ejpam-7023	236	6	du	du	PROPN
ejpam-7023	237	1	=	=	SYM
ejpam-7023	237	2	m	m	PROPN
ejpam-7023	237	3	∫	∫	PROPN
ejpam-7023	237	4	∞	∞	PROPN
ejpam-7023	237	5	0	0	NUM
ejpam-7023	237	6	e−αu	e−αu	PROPN
ejpam-7023	237	7	cos(βu)ua−1	cos(βu)ua−1	VERB
ejpam-7023	237	8	du	du	PROPN
ejpam-7023	237	9	.	.	PUNCT
ejpam-7023	238	1	(	(	PUNCT
ejpam-7023	238	2	40	40	NUM
ejpam-7023	238	3	)	)	PUNCT
ejpam-7023	238	4	using	use	VERB
ejpam-7023	238	5	cos(βu	cos(βu	NOUN
ejpam-7023	238	6	)	)	PUNCT
ejpam-7023	238	7	=	=	SYM
ejpam-7023	238	8	ℜ	ℜ	PROPN
ejpam-7023	238	9	(	(	PUNCT
ejpam-7023	238	10	eiβu	eiβu	NOUN
ejpam-7023	238	11	)	)	PUNCT
ejpam-7023	238	12	and	and	CCONJ
ejpam-7023	238	13	absolute	absolute	ADJ
ejpam-7023	238	14	integrability	integrability	NOUN
ejpam-7023	238	15	for	for	ADP
ejpam-7023	238	16	a	a	DET
ejpam-7023	238	17	>	>	X
ejpam-7023	238	18	−1	−1	NOUN
ejpam-7023	238	19	,	,	PUNCT
ejpam-7023	238	20	we	we	PRON
ejpam-7023	238	21	may	may	AUX
ejpam-7023	238	22	pass	pass	VERB
ejpam-7023	238	23	the	the	DET
ejpam-7023	238	24	real	real	ADJ
ejpam-7023	238	25	part	part	NOUN
ejpam-7023	238	26	inside	inside	ADP
ejpam-7023	238	27	the	the	DET
ejpam-7023	238	28	integral	integral	ADJ
ejpam-7023	238	29	:	:	PUNCT
ejpam-7023	238	30	e−αu	e−αu	NOUN
ejpam-7023	238	31	cos(βu	cos(βu	NOUN
ejpam-7023	238	32	)	)	PUNCT
ejpam-7023	238	33	=	=	SYM
ejpam-7023	238	34	ℜ	ℜ	PROPN
ejpam-7023	238	35	(	(	PUNCT
ejpam-7023	238	36	e−(α−iβ)u	e−(α−iβ)u	PROPN
ejpam-7023	238	37	)	)	PUNCT
ejpam-7023	239	1	=	=	VERB
ejpam-7023	239	2	⇒	⇒	NOUN
ejpam-7023	239	3	jm	jm	PROPN
ejpam-7023	239	4	,	,	PUNCT
ejpam-7023	239	5	q(k	q(k	PROPN
ejpam-7023	239	6	,	,	PUNCT
ejpam-7023	239	7	α	α	X
ejpam-7023	239	8	,	,	PUNCT
ejpam-7023	239	9	β	β	NOUN
ejpam-7023	239	10	)	)	PUNCT
ejpam-7023	240	1	=	=	PUNCT
ejpam-7023	240	2	mℜ	mℜ	NOUN
ejpam-7023	240	3	∫	∫	PROPN
ejpam-7023	240	4	∞	∞	NOUN
ejpam-7023	240	5	0	0	NUM
ejpam-7023	241	1	ua−1	ua−1	PROPN
ejpam-7023	241	2	e−(α−iβ)u	e−(α−iβ)u	PROPN
ejpam-7023	241	3	du	du	X
ejpam-7023	241	4	.	.	PUNCT
ejpam-7023	242	1	(	(	PUNCT
ejpam-7023	242	2	41	41	NUM
ejpam-7023	242	3	)	)	PUNCT
ejpam-7023	242	4	let	let	VERB
ejpam-7023	242	5	λ	λ	INTJ
ejpam-7023	242	6	=	=	PUNCT
ejpam-7023	242	7	α−	α−	ADP
ejpam-7023	242	8	iβ	iβ	X
ejpam-7023	242	9	(	(	PUNCT
ejpam-7023	242	10	ℜλ	ℜλ	PROPN
ejpam-7023	242	11	=	=	SYM
ejpam-7023	242	12	α	α	X
ejpam-7023	242	13	>	>	X
ejpam-7023	242	14	0	0	NUM
ejpam-7023	242	15	)	)	PUNCT
ejpam-7023	242	16	.	.	PUNCT
ejpam-7023	243	1	(	(	PUNCT
ejpam-7023	243	2	42	42	NUM
ejpam-7023	243	3	)	)	PUNCT
ejpam-7023	243	4	for	for	ADP
ejpam-7023	243	5	a	a	DET
ejpam-7023	243	6	>	>	X
ejpam-7023	243	7	0	0	NUM
ejpam-7023	243	8	,	,	PUNCT
ejpam-7023	243	9	the	the	DET
ejpam-7023	243	10	gamma	gamma	PROPN
ejpam-7023	243	11	function	function	NOUN
ejpam-7023	243	12	,	,	PUNCT
ejpam-7023	243	13	obtained	obtain	VERB
ejpam-7023	243	14	by	by	ADP
ejpam-7023	243	15	the	the	DET
ejpam-7023	243	16	substitution	substitution	NOUN
ejpam-7023	243	17	t	t	NOUN
ejpam-7023	243	18	=	=	SYM
ejpam-7023	243	19	λu	λu	PROPN
ejpam-7023	243	20	,	,	PUNCT
ejpam-7023	243	21	gives∫	gives∫	VERB
ejpam-7023	243	22	∞	∞	NOUN
ejpam-7023	243	23	0	0	PUNCT
ejpam-7023	244	1	ua−1e−λu	ua−1e−λu	NOUN
ejpam-7023	244	2	du	du	PROPN
ejpam-7023	244	3	=	=	SYM
ejpam-7023	244	4	∫	∫	PROPN
ejpam-7023	244	5	∞	∞	PROPN
ejpam-7023	244	6	0	0	NUM
ejpam-7023	245	1	(	(	PUNCT
ejpam-7023	245	2	t	t	NOUN
ejpam-7023	245	3	λ	λ	PROPN
ejpam-7023	245	4	)	)	PUNCT
ejpam-7023	245	5	a−1	a−1	PROPN
ejpam-7023	245	6	e−t	e−t	NOUN
ejpam-7023	245	7	dt	dt	X
ejpam-7023	246	1	λ	λ	X
ejpam-7023	246	2	=	=	SYM
ejpam-7023	246	3	1	1	NUM
ejpam-7023	246	4	λa	λa	X
ejpam-7023	246	5	∫	∫	PROPN
ejpam-7023	246	6	∞	∞	PROPN
ejpam-7023	246	7	0	0	NUM
ejpam-7023	247	1	ta−1e−t	ta−1e−t	NOUN
ejpam-7023	247	2	dt	dt	X
ejpam-7023	247	3	=	=	SYM
ejpam-7023	247	4	γ(a	γ(a	PROPN
ejpam-7023	247	5	)	)	PUNCT
ejpam-7023	247	6	λa	λa	X
ejpam-7023	247	7	.	.	PUNCT
ejpam-7023	248	1	(	(	PUNCT
ejpam-7023	248	2	43	43	X
ejpam-7023	248	3	)	)	PUNCT
ejpam-7023	248	4	applying	apply	VERB
ejpam-7023	248	5	(	(	PUNCT
ejpam-7023	248	6	43	43	NUM
ejpam-7023	248	7	)	)	PUNCT
ejpam-7023	248	8	in	in	ADP
ejpam-7023	248	9	(	(	PUNCT
ejpam-7023	248	10	41	41	NUM
ejpam-7023	248	11	)	)	PUNCT
ejpam-7023	248	12	yields	yield	NOUN
ejpam-7023	248	13	jm	jm	PROPN
ejpam-7023	248	14	,	,	PUNCT
ejpam-7023	248	15	q(k	q(k	PROPN
ejpam-7023	248	16	,	,	PUNCT
ejpam-7023	248	17	α	α	X
ejpam-7023	248	18	,	,	PUNCT
ejpam-7023	248	19	β	β	NOUN
ejpam-7023	248	20	)	)	PUNCT
ejpam-7023	249	1	=	=	PUNCT
ejpam-7023	249	2	mℜ	mℜ	NOUN
ejpam-7023	249	3	(	(	PUNCT
ejpam-7023	249	4	γ(a	γ(a	PROPN
ejpam-7023	249	5	)	)	PUNCT
ejpam-7023	249	6	(	(	PUNCT
ejpam-7023	249	7	α−	α−	ADP
ejpam-7023	249	8	iβ)a	iβ)a	PROPN
ejpam-7023	249	9	)	)	PUNCT
ejpam-7023	249	10	.	.	PUNCT
ejpam-7023	250	1	(	(	PUNCT
ejpam-7023	250	2	44	44	NUM
ejpam-7023	250	3	)	)	PUNCT
ejpam-7023	250	4	we	we	PRON
ejpam-7023	250	5	write	write	VERB
ejpam-7023	250	6	α−	α−	ADP
ejpam-7023	250	7	iβ	iβ	ADP
ejpam-7023	250	8	in	in	ADP
ejpam-7023	250	9	polar	polar	ADJ
ejpam-7023	250	10	form	form	NOUN
ejpam-7023	250	11	.	.	PUNCT
ejpam-7023	251	1	with	with	ADP
ejpam-7023	251	2	r	r	NOUN
ejpam-7023	251	3	=	=	PUNCT
ejpam-7023	251	4	√	√	NOUN
ejpam-7023	251	5	α2	α2	NOUN
ejpam-7023	251	6	+	+	CCONJ
ejpam-7023	251	7	β2	β2	VERB
ejpam-7023	251	8	,	,	PUNCT
ejpam-7023	251	9	θ	θ	PROPN
ejpam-7023	251	10	=	=	SYM
ejpam-7023	251	11	arctan	arctan	PROPN
ejpam-7023	251	12	β	β	PROPN
ejpam-7023	251	13	α	α	PROPN
ejpam-7023	251	14	∈	∈	PROPN
ejpam-7023	251	15	(	(	PUNCT
ejpam-7023	251	16	−π	−π	ADV
ejpam-7023	251	17	2	2	NUM
ejpam-7023	251	18	,	,	PUNCT
ejpam-7023	251	19	π	π	PROPN
ejpam-7023	251	20	2	2	NUM
ejpam-7023	251	21	)	)	PUNCT
ejpam-7023	251	22	,	,	PUNCT
ejpam-7023	251	23	(	(	PUNCT
ejpam-7023	251	24	45	45	NUM
ejpam-7023	251	25	)	)	PUNCT
ejpam-7023	251	26	we	we	PRON
ejpam-7023	251	27	have	have	VERB
ejpam-7023	251	28	α−	α−	ADP
ejpam-7023	251	29	iβ	iβ	ADP
ejpam-7023	251	30	=	=	NOUN
ejpam-7023	251	31	r	r	NOUN
ejpam-7023	251	32	e−iθ	e−iθ	PROPN
ejpam-7023	251	33	,	,	PUNCT
ejpam-7023	251	34	hence	hence	ADV
ejpam-7023	251	35	(	(	PUNCT
ejpam-7023	251	36	α−	α−	ADP
ejpam-7023	251	37	iβ)−a	iβ)−a	PROPN
ejpam-7023	251	38	=	=	SYM
ejpam-7023	251	39	r−a	r−a	PROPN
ejpam-7023	251	40	e	e	PROPN
ejpam-7023	251	41	iaθ	iaθ	PROPN
ejpam-7023	251	42	.	.	PUNCT
ejpam-7023	252	1	(	(	PUNCT
ejpam-7023	252	2	46	46	X
ejpam-7023	252	3	)	)	PUNCT
ejpam-7023	252	4	substituting	substitute	VERB
ejpam-7023	252	5	(	(	PUNCT
ejpam-7023	252	6	46	46	NUM
ejpam-7023	252	7	)	)	PUNCT
ejpam-7023	252	8	into	into	ADP
ejpam-7023	252	9	(	(	PUNCT
ejpam-7023	252	10	44	44	NUM
ejpam-7023	252	11	)	)	PUNCT
ejpam-7023	252	12	and	and	CCONJ
ejpam-7023	252	13	using	use	VERB
ejpam-7023	252	14	ℜ(eiaθ	ℜ(eiaθ	NOUN
ejpam-7023	252	15	)	)	PUNCT
ejpam-7023	252	16	=	=	SYM
ejpam-7023	252	17	cos(aθ	cos(aθ	NOUN
ejpam-7023	252	18	)	)	PUNCT
ejpam-7023	252	19	gives	give	VERB
ejpam-7023	252	20	jm	jm	PROPN
ejpam-7023	252	21	,	,	PUNCT
ejpam-7023	252	22	q(k	q(k	PROPN
ejpam-7023	252	23	,	,	PUNCT
ejpam-7023	252	24	α	α	X
ejpam-7023	252	25	,	,	PUNCT
ejpam-7023	252	26	β	β	NOUN
ejpam-7023	252	27	)	)	PUNCT
ejpam-7023	253	1	=	=	SYM
ejpam-7023	253	2	mγ(a)ℜ	mγ(a)ℜ	NOUN
ejpam-7023	253	3	(	(	PUNCT
ejpam-7023	253	4	r−ae	r−ae	PROPN
ejpam-7023	253	5	iaθ	iaθ	NOUN
ejpam-7023	253	6	)	)	PUNCT
ejpam-7023	253	7	=	=	SYM
ejpam-7023	253	8	mγ(a	mγ(a	X
ejpam-7023	253	9	)	)	PUNCT
ejpam-7023	253	10	r−a	r−a	NOUN
ejpam-7023	253	11	cos(aθ	cos(aθ	NOUN
ejpam-7023	253	12	)	)	PUNCT
ejpam-7023	253	13	=	=	SYM
ejpam-7023	253	14	mγ(a	mγ(a	X
ejpam-7023	253	15	)	)	PUNCT
ejpam-7023	253	16	(	(	PUNCT
ejpam-7023	253	17	α2	α2	ADJ
ejpam-7023	253	18	+	+	CCONJ
ejpam-7023	253	19	β2)−a/2	β2)−a/2	PUNCT
ejpam-7023	253	20	cos	cos	ADP
ejpam-7023	253	21	(	(	PUNCT
ejpam-7023	253	22	a	a	DET
ejpam-7023	253	23	arctan	arctan	PROPN
ejpam-7023	253	24	β	β	X
ejpam-7023	253	25	α	α	PROPN
ejpam-7023	253	26	)	)	PUNCT
ejpam-7023	253	27	,	,	PUNCT
ejpam-7023	253	28	(	(	PUNCT
ejpam-7023	253	29	47	47	NUM
ejpam-7023	253	30	)	)	PUNCT
ejpam-7023	253	31	which	which	PRON
ejpam-7023	253	32	proves	prove	VERB
ejpam-7023	253	33	(	(	PUNCT
ejpam-7023	253	34	33	33	NUM
ejpam-7023	253	35	)	)	PUNCT
ejpam-7023	253	36	.	.	PUNCT
ejpam-7023	254	1	the	the	DET
ejpam-7023	254	2	zero	zero	NUM
ejpam-7023	254	3	condition	condition	NOUN
ejpam-7023	254	4	(	(	PUNCT
ejpam-7023	254	5	34	34	NUM
ejpam-7023	254	6	)	)	PUNCT
ejpam-7023	254	7	follows	follow	VERB
ejpam-7023	254	8	since	since	SCONJ
ejpam-7023	254	9	m	m	PROPN
ejpam-7023	254	10	>	>	X
ejpam-7023	254	11	0	0	NUM
ejpam-7023	254	12	,	,	PUNCT
ejpam-7023	254	13	γ(a	γ(a	PROPN
ejpam-7023	254	14	)	)	PUNCT
ejpam-7023	254	15	>	>	X
ejpam-7023	254	16	0	0	PUNCT
ejpam-7023	254	17	for	for	ADP
ejpam-7023	254	18	a	a	DET
ejpam-7023	254	19	>	>	X
ejpam-7023	254	20	0	0	NUM
ejpam-7023	254	21	,	,	PUNCT
ejpam-7023	254	22	and	and	CCONJ
ejpam-7023	254	23	(	(	PUNCT
ejpam-7023	254	24	α2	α2	ADJ
ejpam-7023	254	25	+	+	CCONJ
ejpam-7023	254	26	β2)−a/2	β2)−a/2	NOUN
ejpam-7023	254	27	>	>	X
ejpam-7023	254	28	0	0	NUM
ejpam-7023	254	29	,	,	PUNCT
ejpam-7023	254	30	so	so	ADV
ejpam-7023	254	31	jm	jm	PROPN
ejpam-7023	254	32	,	,	PUNCT
ejpam-7023	254	33	q(k	q(k	PROPN
ejpam-7023	254	34	,	,	PUNCT
ejpam-7023	254	35	α	α	X
ejpam-7023	254	36	,	,	PUNCT
ejpam-7023	254	37	β	β	NOUN
ejpam-7023	254	38	)	)	PUNCT
ejpam-7023	254	39	=	=	SYM
ejpam-7023	254	40	0	0	PUNCT
ejpam-7023	255	1	if	if	SCONJ
ejpam-7023	255	2	and	and	CCONJ
ejpam-7023	255	3	only	only	ADV
ejpam-7023	255	4	if	if	SCONJ
ejpam-7023	255	5	cos(aθ	cos(aθ	NOUN
ejpam-7023	255	6	)	)	PUNCT
ejpam-7023	255	7	=	=	SYM
ejpam-7023	255	8	0	0	NUM
ejpam-7023	255	9	,	,	PUNCT
ejpam-7023	255	10	i.e.	i.e.	X
ejpam-7023	255	11	aθ	aθ	ADP
ejpam-7023	255	12	∈	∈	PROPN
ejpam-7023	255	13	π	π	X
ejpam-7023	255	14	2	2	NUM
ejpam-7023	255	15	+	+	CCONJ
ejpam-7023	255	16	πz	πz	PROPN
ejpam-7023	255	17	.	.	NOUN
ejpam-7023	255	18	when	when	SCONJ
ejpam-7023	255	19	β	β	X
ejpam-7023	255	20	=	=	SYM
ejpam-7023	255	21	0	0	NUM
ejpam-7023	255	22	,	,	PUNCT
ejpam-7023	255	23	we	we	PRON
ejpam-7023	255	24	have	have	VERB
ejpam-7023	255	25	θ	θ	NOUN
ejpam-7023	255	26	=	=	SYM
ejpam-7023	255	27	0	0	NUM
ejpam-7023	255	28	and	and	CCONJ
ejpam-7023	255	29	cos(aθ	cos(aθ	NOUN
ejpam-7023	255	30	)	)	PUNCT
ejpam-7023	256	1	=	=	PUNCT
ejpam-7023	256	2	cos	cos	ADP
ejpam-7023	256	3	0	0	NUM
ejpam-7023	256	4	=	=	SYM
ejpam-7023	256	5	1	1	NUM
ejpam-7023	256	6	,	,	PUNCT
ejpam-7023	256	7	and	and	CCONJ
ejpam-7023	256	8	(	(	PUNCT
ejpam-7023	256	9	47	47	NUM
ejpam-7023	256	10	)	)	PUNCT
ejpam-7023	256	11	reduces	reduce	VERB
ejpam-7023	256	12	to	to	ADP
ejpam-7023	256	13	(	(	PUNCT
ejpam-7023	256	14	35	35	NUM
ejpam-7023	256	15	)	)	PUNCT
ejpam-7023	256	16	.	.	PUNCT
ejpam-7023	257	1	we	we	PRON
ejpam-7023	257	2	have	have	VERB
ejpam-7023	257	3	the	the	DET
ejpam-7023	257	4	following	follow	VERB
ejpam-7023	257	5	cosine	cosine	NOUN
ejpam-7023	257	6	analog	analog	NOUN
ejpam-7023	257	7	of	of	ADP
ejpam-7023	257	8	the	the	DET
ejpam-7023	257	9	steiltjes	steiltjes	ADJ
ejpam-7023	257	10	example	example	NOUN
ejpam-7023	257	11	.	.	PUNCT
ejpam-7023	258	1	i.	i.	PROPN
ejpam-7023	258	2	ayoob	ayoob	PROPN
ejpam-7023	258	3	/	/	SYM
ejpam-7023	258	4	eur	eur	PROPN
ejpam-7023	258	5	.	.	PUNCT
ejpam-7023	259	1	j.	j.	PROPN
ejpam-7023	259	2	pure	pure	PROPN
ejpam-7023	259	3	appl	appl	PROPN
ejpam-7023	259	4	.	.	PROPN
ejpam-7023	259	5	math	math	PROPN
ejpam-7023	259	6	,	,	PUNCT
ejpam-7023	259	7	18	18	NUM
ejpam-7023	259	8	(	(	PUNCT
ejpam-7023	259	9	4	4	NUM
ejpam-7023	259	10	)	)	PUNCT
ejpam-7023	259	11	(	(	PUNCT
ejpam-7023	259	12	2025	2025	NUM
ejpam-7023	259	13	)	)	PUNCT
ejpam-7023	259	14	,	,	PUNCT
ejpam-7023	259	15	7023	7023	NUM
ejpam-7023	259	16	11	11	NUM
ejpam-7023	259	17	of	of	ADP
ejpam-7023	259	18	16	16	NUM
ejpam-7023	259	19	corollary	corollary	ADJ
ejpam-7023	259	20	4	4	NUM
ejpam-7023	259	21	.	.	PUNCT
ejpam-7023	260	1	let	let	VERB
ejpam-7023	260	2	m	m	VERB
ejpam-7023	260	3	=	=	NOUN
ejpam-7023	260	4	4	4	NUM
ejpam-7023	260	5	,	,	PUNCT
ejpam-7023	260	6	α	α	NOUN
ejpam-7023	260	7	=	=	SYM
ejpam-7023	260	8	1	1	NUM
ejpam-7023	260	9	,	,	PUNCT
ejpam-7023	260	10	β	β	X
ejpam-7023	260	11	=	=	SYM
ejpam-7023	260	12	1	1	NUM
ejpam-7023	260	13	,	,	PUNCT
ejpam-7023	260	14	q	q	NOUN
ejpam-7023	260	15	=	=	NOUN
ejpam-7023	260	16	0	0	NUM
ejpam-7023	260	17	.	.	PUNCT
ejpam-7023	261	1	for	for	ADP
ejpam-7023	261	2	k	k	PROPN
ejpam-7023	261	3	>	>	X
ejpam-7023	261	4	−1	−1	NOUN
ejpam-7023	261	5	,	,	PUNCT
ejpam-7023	261	6	g(k	g(k	NOUN
ejpam-7023	261	7	)	)	PUNCT
ejpam-7023	261	8	=	=	SYM
ejpam-7023	261	9	∫	∫	PROPN
ejpam-7023	261	10	∞	∞	NUM
ejpam-7023	261	11	0	0	NUM
ejpam-7023	262	1	e−x1/4	e−x1/4	PROPN
ejpam-7023	262	2	cos	cos	PROPN
ejpam-7023	262	3	(	(	PUNCT
ejpam-7023	262	4	x1/4	x1/4	PROPN
ejpam-7023	262	5	)	)	PUNCT
ejpam-7023	262	6	xk	xk	PROPN
ejpam-7023	263	1	dx	dx	PROPN
ejpam-7023	263	2	=	=	SYM
ejpam-7023	263	3	2−2k	2−2k	NUM
ejpam-7023	263	4	γ(4k	γ(4k	NOUN
ejpam-7023	263	5	+	+	CCONJ
ejpam-7023	263	6	4	4	X
ejpam-7023	263	7	)	)	PUNCT
ejpam-7023	263	8	cos	co	NOUN
ejpam-7023	263	9	(	(	PUNCT
ejpam-7023	263	10	(	(	PUNCT
ejpam-7023	263	11	k	k	X
ejpam-7023	263	12	+	+	PROPN
ejpam-7023	263	13	1)π	1)π	NUM
ejpam-7023	263	14	)	)	PUNCT
ejpam-7023	263	15	.	.	PUNCT
ejpam-7023	264	1	furthermore	furthermore	ADV
ejpam-7023	264	2	,	,	PUNCT
ejpam-7023	264	3	g(k	g(k	VERB
ejpam-7023	264	4	)	)	PUNCT
ejpam-7023	264	5	=	=	SYM
ejpam-7023	264	6	0	0	PUNCT
ejpam-7023	265	1	if	if	SCONJ
ejpam-7023	265	2	and	and	CCONJ
ejpam-7023	265	3	only	only	ADV
ejpam-7023	265	4	if	if	SCONJ
ejpam-7023	265	5	k	k	PROPN
ejpam-7023	265	6	=	=	PUNCT
ejpam-7023	265	7	n−	n−	NOUN
ejpam-7023	265	8	1	1	NUM
ejpam-7023	265	9	2	2	NUM
ejpam-7023	265	10	,	,	PUNCT
ejpam-7023	265	11	n	n	PRON
ejpam-7023	265	12	∈	∈	PROPN
ejpam-7023	265	13	{	{	PUNCT
ejpam-7023	265	14	0	0	NUM
ejpam-7023	265	15	,	,	PUNCT
ejpam-7023	265	16	1	1	NUM
ejpam-7023	265	17	,	,	PUNCT
ejpam-7023	265	18	2	2	NUM
ejpam-7023	265	19	,	,	PUNCT
ejpam-7023	265	20	3	3	NUM
ejpam-7023	265	21	....	....	PUNCT
ejpam-7023	265	22	}	}	PUNCT
ejpam-7023	265	23	.	.	PUNCT
ejpam-7023	266	1	proof	proof	NOUN
ejpam-7023	266	2	.	.	PUNCT
ejpam-7023	267	1	here	here	ADV
ejpam-7023	267	2	a	a	DET
ejpam-7023	267	3	=	=	SYM
ejpam-7023	267	4	4k	4k	NOUN
ejpam-7023	267	5	+	+	NOUN
ejpam-7023	267	6	4	4	NUM
ejpam-7023	267	7	,	,	PUNCT
ejpam-7023	267	8	r	r	NOUN
ejpam-7023	267	9	=	=	PUNCT
ejpam-7023	267	10	√	√	NUM
ejpam-7023	267	11	2	2	NUM
ejpam-7023	267	12	,	,	PUNCT
ejpam-7023	267	13	and	and	CCONJ
ejpam-7023	267	14	θ	θ	NOUN
ejpam-7023	267	15	=	=	SYM
ejpam-7023	267	16	arctan(1	arctan(1	X
ejpam-7023	267	17	)	)	PUNCT
ejpam-7023	267	18	=	=	PUNCT
ejpam-7023	267	19	π/4	π/4	NOUN
ejpam-7023	267	20	.	.	PUNCT
ejpam-7023	268	1	substituting	substitute	VERB
ejpam-7023	268	2	into	into	ADP
ejpam-7023	268	3	(	(	PUNCT
ejpam-7023	268	4	33	33	NUM
ejpam-7023	268	5	)	)	PUNCT
ejpam-7023	268	6	,	,	PUNCT
ejpam-7023	268	7	j4,0(k	j4,0(k	PROPN
ejpam-7023	268	8	,	,	PUNCT
ejpam-7023	268	9	1	1	NUM
ejpam-7023	268	10	,	,	PUNCT
ejpam-7023	268	11	1	1	NUM
ejpam-7023	268	12	)	)	PUNCT
ejpam-7023	268	13	=	=	SYM
ejpam-7023	268	14	4γ(4k	4γ(4k	NUM
ejpam-7023	268	15	+	+	CCONJ
ejpam-7023	268	16	4	4	NUM
ejpam-7023	268	17	)	)	PUNCT
ejpam-7023	268	18	(	(	PUNCT
ejpam-7023	268	19	√	√	NUM
ejpam-7023	268	20	2)−(4k+4	2)−(4k+4	NUM
ejpam-7023	268	21	)	)	PUNCT
ejpam-7023	268	22	cos	cos	PROPN
ejpam-7023	268	23	(	(	PUNCT
ejpam-7023	268	24	(	(	PUNCT
ejpam-7023	268	25	4k	4k	NOUN
ejpam-7023	268	26	+	+	NOUN
ejpam-7023	268	27	4)π4	4)π4	NUM
ejpam-7023	268	28	)	)	PUNCT
ejpam-7023	269	1	=	=	SYM
ejpam-7023	269	2	2−2k	2−2k	NUM
ejpam-7023	269	3	γ(4k	γ(4k	NOUN
ejpam-7023	269	4	+	+	CCONJ
ejpam-7023	269	5	4	4	X
ejpam-7023	269	6	)	)	PUNCT
ejpam-7023	269	7	cos	co	NOUN
ejpam-7023	269	8	(	(	PUNCT
ejpam-7023	269	9	(	(	PUNCT
ejpam-7023	269	10	k	k	X
ejpam-7023	269	11	+	+	PROPN
ejpam-7023	269	12	1)π	1)π	NUM
ejpam-7023	269	13	)	)	PUNCT
ejpam-7023	269	14	.	.	PUNCT
ejpam-7023	270	1	note	note	VERB
ejpam-7023	270	2	that	that	SCONJ
ejpam-7023	270	3	in	in	ADP
ejpam-7023	270	4	corollary	corollary	ADJ
ejpam-7023	270	5	4	4	NUM
ejpam-7023	270	6	,	,	PUNCT
ejpam-7023	270	7	for	for	ADP
ejpam-7023	270	8	the	the	DET
ejpam-7023	270	9	vanishing	vanishing	NOUN
ejpam-7023	270	10	of	of	ADP
ejpam-7023	270	11	g(k	g(k	NOUN
ejpam-7023	270	12	)	)	PUNCT
ejpam-7023	270	13	,	,	PUNCT
ejpam-7023	270	14	the	the	DET
ejpam-7023	270	15	values	value	NOUN
ejpam-7023	270	16	of	of	ADP
ejpam-7023	270	17	k	k	PROPN
ejpam-7023	270	18	are	be	AUX
ejpam-7023	270	19	not	not	PART
ejpam-7023	270	20	non	non	ADJ
ejpam-7023	270	21	-	-	ADJ
ejpam-7023	270	22	negative	negative	ADJ
ejpam-7023	270	23	fractions	fraction	NOUN
ejpam-7023	270	24	,	,	PUNCT
ejpam-7023	270	25	whereas	whereas	SCONJ
ejpam-7023	270	26	the	the	DET
ejpam-7023	270	27	steiltjes	steiltjes	ADJ
ejpam-7023	270	28	type	type	PROPN
ejpam-7023	270	29	moment	moment	NOUN
ejpam-7023	270	30	problem	problem	NOUN
ejpam-7023	270	31	requires	require	VERB
ejpam-7023	270	32	k	k	PROPN
ejpam-7023	270	33	to	to	PART
ejpam-7023	270	34	be	be	AUX
ejpam-7023	270	35	non	non	ADJ
ejpam-7023	270	36	-	-	ADJ
ejpam-7023	270	37	negative	negative	ADJ
ejpam-7023	270	38	integers	integer	NOUN
ejpam-7023	270	39	.	.	PUNCT
ejpam-7023	271	1	to	to	PART
ejpam-7023	271	2	have	have	VERB
ejpam-7023	271	3	k	k	PROPN
ejpam-7023	271	4	non	non	ADJ
ejpam-7023	271	5	-	-	ADJ
ejpam-7023	271	6	negative	negative	ADJ
ejpam-7023	271	7	integers	integer	NOUN
ejpam-7023	271	8	and	and	CCONJ
ejpam-7023	271	9	a	a	DET
ejpam-7023	271	10	cosine	cosine	ADJ
ejpam-7023	271	11	variant	variant	NOUN
ejpam-7023	271	12	of	of	ADP
ejpam-7023	271	13	steiltjes	steiltjes	PROPN
ejpam-7023	271	14	,	,	PUNCT
ejpam-7023	271	15	we	we	PRON
ejpam-7023	271	16	have	have	VERB
ejpam-7023	271	17	the	the	DET
ejpam-7023	271	18	following	follow	VERB
ejpam-7023	271	19	result	result	NOUN
ejpam-7023	271	20	.	.	PUNCT
ejpam-7023	272	1	corollary	corollary	ADJ
ejpam-7023	272	2	5	5	NUM
ejpam-7023	272	3	.	.	PUNCT
ejpam-7023	273	1	let	let	VERB
ejpam-7023	273	2	m	m	PRON
ejpam-7023	273	3	>	>	X
ejpam-7023	273	4	2	2	NUM
ejpam-7023	273	5	and	and	CCONJ
ejpam-7023	273	6	α	α	NOUN
ejpam-7023	273	7	>	>	X
ejpam-7023	273	8	0	0	NUM
ejpam-7023	273	9	,	,	PUNCT
ejpam-7023	273	10	and	and	CCONJ
ejpam-7023	273	11	set	set	VERB
ejpam-7023	273	12	θ	θ	X
ejpam-7023	273	13	=	=	PUNCT
ejpam-7023	274	1	π	π	X
ejpam-7023	274	2	m	m	VERB
ejpam-7023	274	3	,	,	PUNCT
ejpam-7023	274	4	β	β	PROPN
ejpam-7023	274	5	=	=	SYM
ejpam-7023	274	6	α	α	NUM
ejpam-7023	274	7	tan	tan	NOUN
ejpam-7023	274	8	θ	θ	NOUN
ejpam-7023	275	1	=	=	PUNCT
ejpam-7023	275	2	α	α	NUM
ejpam-7023	275	3	tan	tan	PROPN
ejpam-7023	275	4	(	(	PUNCT
ejpam-7023	275	5	π	π	PROPN
ejpam-7023	275	6	m	m	PROPN
ejpam-7023	275	7	)	)	PUNCT
ejpam-7023	275	8	,	,	PUNCT
ejpam-7023	275	9	q	q	NOUN
ejpam-7023	275	10	=	=	PUNCT
ejpam-7023	275	11	−m	−m	NOUN
ejpam-7023	275	12	2	2	NUM
ejpam-7023	275	13	.	.	PUNCT
ejpam-7023	276	1	(	(	PUNCT
ejpam-7023	276	2	48	48	NUM
ejpam-7023	276	3	)	)	PUNCT
ejpam-7023	276	4	for	for	ADP
ejpam-7023	276	5	k	k	PROPN
ejpam-7023	276	6	∈	∈	PROPN
ejpam-7023	276	7	r	r	NOUN
ejpam-7023	276	8	define	define	NOUN
ejpam-7023	276	9	jm	jm	PROPN
ejpam-7023	276	10	,	,	PUNCT
ejpam-7023	276	11	q(k	q(k	PROPN
ejpam-7023	276	12	,	,	PUNCT
ejpam-7023	276	13	α	α	X
ejpam-7023	276	14	,	,	PUNCT
ejpam-7023	276	15	β	β	NOUN
ejpam-7023	276	16	)	)	PUNCT
ejpam-7023	276	17	=	=	SYM
ejpam-7023	277	1	∫	∫	PROPN
ejpam-7023	277	2	∞	∞	NUM
ejpam-7023	277	3	0	0	NUM
ejpam-7023	277	4	e−αx1	e−αx1	PROPN
ejpam-7023	277	5	/	/	SYM
ejpam-7023	277	6	m	m	NOUN
ejpam-7023	277	7	cos	cos	NOUN
ejpam-7023	277	8	(	(	PUNCT
ejpam-7023	277	9	βx1	βx1	PROPN
ejpam-7023	277	10	/	/	SYM
ejpam-7023	277	11	m	m	NOUN
ejpam-7023	277	12	)	)	PUNCT
ejpam-7023	277	13	xk	xk	PROPN
ejpam-7023	277	14	(	(	PUNCT
ejpam-7023	277	15	x1	x1	PROPN
ejpam-7023	277	16	/	/	SYM
ejpam-7023	277	17	m)q	m)q	X
ejpam-7023	277	18	dx	dx	PROPN
ejpam-7023	277	19	.	.	PUNCT
ejpam-7023	278	1	(	(	PUNCT
ejpam-7023	278	2	49	49	NUM
ejpam-7023	278	3	)	)	PUNCT
ejpam-7023	278	4	then	then	ADV
ejpam-7023	278	5	jm	jm	PROPN
ejpam-7023	278	6	,	,	PUNCT
ejpam-7023	278	7	q(k	q(k	PROPN
ejpam-7023	278	8	,	,	PUNCT
ejpam-7023	278	9	α	α	X
ejpam-7023	278	10	,	,	PUNCT
ejpam-7023	278	11	β	β	NOUN
ejpam-7023	278	12	)	)	PUNCT
ejpam-7023	278	13	converges	converge	VERB
ejpam-7023	278	14	for	for	ADP
ejpam-7023	278	15	k	k	PROPN
ejpam-7023	278	16	>	>	X
ejpam-7023	278	17	−1	−1	NOUN
ejpam-7023	278	18	2	2	NUM
ejpam-7023	278	19	and	and	CCONJ
ejpam-7023	278	20	jm	jm	PROPN
ejpam-7023	278	21	,	,	PUNCT
ejpam-7023	278	22	q(k	q(k	PROPN
ejpam-7023	278	23	,	,	PUNCT
ejpam-7023	278	24	α	α	X
ejpam-7023	278	25	,	,	PUNCT
ejpam-7023	278	26	β	β	NOUN
ejpam-7023	278	27	)	)	PUNCT
ejpam-7023	279	1	=	=	SYM
ejpam-7023	279	2	mγ	mγ	NOUN
ejpam-7023	279	3	(	(	PUNCT
ejpam-7023	279	4	m(k	m(k	PROPN
ejpam-7023	279	5	+	+	CCONJ
ejpam-7023	279	6	1	1	NUM
ejpam-7023	279	7	2	2	NUM
ejpam-7023	279	8	)	)	PUNCT
ejpam-7023	279	9	)	)	PUNCT
ejpam-7023	279	10	(	(	PUNCT
ejpam-7023	279	11	α2	α2	ADJ
ejpam-7023	279	12	+	+	CCONJ
ejpam-7023	279	13	β2)−	β2)−	ADJ
ejpam-7023	279	14	m(k+1/2	m(k+1/2	ADJ
ejpam-7023	279	15	)	)	PUNCT
ejpam-7023	279	16	2	2	NUM
ejpam-7023	279	17	cos	cos	X
ejpam-7023	279	18	(	(	PUNCT
ejpam-7023	279	19	π	π	X
ejpam-7023	279	20	(	(	PUNCT
ejpam-7023	279	21	k	k	PROPN
ejpam-7023	279	22	+	+	PROPN
ejpam-7023	279	23	1	1	NUM
ejpam-7023	279	24	2	2	NUM
ejpam-7023	279	25	)	)	PUNCT
ejpam-7023	279	26	)	)	PUNCT
ejpam-7023	279	27	.	.	PUNCT
ejpam-7023	280	1	(	(	PUNCT
ejpam-7023	280	2	50	50	NUM
ejpam-7023	280	3	)	)	PUNCT
ejpam-7023	280	4	in	in	ADP
ejpam-7023	280	5	particular	particular	ADJ
ejpam-7023	280	6	,	,	PUNCT
ejpam-7023	280	7	jm	jm	PROPN
ejpam-7023	280	8	,	,	PUNCT
ejpam-7023	280	9	q(k	q(k	PROPN
ejpam-7023	280	10	,	,	PUNCT
ejpam-7023	280	11	α	α	X
ejpam-7023	280	12	,	,	PUNCT
ejpam-7023	280	13	β	β	NOUN
ejpam-7023	280	14	)	)	PUNCT
ejpam-7023	280	15	=	=	SYM
ejpam-7023	280	16	0	0	NUM
ejpam-7023	280	17	⇐	⇐	ADJ
ejpam-7023	280	18	⇒	⇒	PROPN
ejpam-7023	280	19	k	k	PROPN
ejpam-7023	280	20	∈	∈	PROPN
ejpam-7023	280	21	z≥0	z≥0	PROPN
ejpam-7023	280	22	.	.	PUNCT
ejpam-7023	281	1	(	(	PUNCT
ejpam-7023	281	2	51	51	NUM
ejpam-7023	281	3	)	)	PUNCT
ejpam-7023	281	4	proof	proof	NOUN
ejpam-7023	281	5	.	.	PUNCT
ejpam-7023	282	1	by	by	ADP
ejpam-7023	282	2	theorem	theorem	NOUN
ejpam-7023	282	3	6	6	NUM
ejpam-7023	282	4	,	,	PUNCT
ejpam-7023	282	5	for	for	ADP
ejpam-7023	282	6	a	a	DET
ejpam-7023	282	7	=	=	SYM
ejpam-7023	282	8	mk	mk	NOUN
ejpam-7023	282	9	+	+	CCONJ
ejpam-7023	282	10	q	q	PROPN
ejpam-7023	282	11	+	+	NOUN
ejpam-7023	282	12	m	m	NOUN
ejpam-7023	282	13	and	and	CCONJ
ejpam-7023	282	14	θ	θ	NOUN
ejpam-7023	282	15	=	=	SYM
ejpam-7023	282	16	arctan(β	arctan(β	NOUN
ejpam-7023	282	17	/	/	SYM
ejpam-7023	282	18	α	α	NOUN
ejpam-7023	282	19	)	)	PUNCT
ejpam-7023	282	20	∈	∈	PROPN
ejpam-7023	282	21	(	(	PUNCT
ejpam-7023	282	22	−π	−π	ADV
ejpam-7023	282	23	2	2	NUM
ejpam-7023	282	24	,	,	PUNCT
ejpam-7023	282	25	π	π	PROPN
ejpam-7023	282	26	2	2	X
ejpam-7023	282	27	)	)	PUNCT
ejpam-7023	282	28	one	one	NOUN
ejpam-7023	282	29	has	have	VERB
ejpam-7023	282	30	jm	jm	PROPN
ejpam-7023	282	31	,	,	PUNCT
ejpam-7023	282	32	q(k	q(k	PROPN
ejpam-7023	282	33	,	,	PUNCT
ejpam-7023	282	34	α	α	X
ejpam-7023	282	35	,	,	PUNCT
ejpam-7023	282	36	β	β	NOUN
ejpam-7023	282	37	)	)	PUNCT
ejpam-7023	282	38	=	=	SYM
ejpam-7023	282	39	mγ(a	mγ(a	X
ejpam-7023	282	40	)	)	PUNCT
ejpam-7023	282	41	(	(	PUNCT
ejpam-7023	282	42	α2	α2	ADJ
ejpam-7023	282	43	+	+	CCONJ
ejpam-7023	282	44	β2)−a/2	β2)−a/2	PUNCT
ejpam-7023	282	45	cos	cos	X
ejpam-7023	282	46	(	(	PUNCT
ejpam-7023	282	47	aθ	aθ	INTJ
ejpam-7023	282	48	)	)	PUNCT
ejpam-7023	282	49	,	,	PUNCT
ejpam-7023	282	50	(	(	PUNCT
ejpam-7023	282	51	52	52	NUM
ejpam-7023	282	52	)	)	PUNCT
ejpam-7023	282	53	whenever	whenever	SCONJ
ejpam-7023	282	54	a	a	DET
ejpam-7023	282	55	>	>	X
ejpam-7023	282	56	0	0	NUM
ejpam-7023	282	57	(	(	PUNCT
ejpam-7023	282	58	and	and	CCONJ
ejpam-7023	282	59	convergence	convergence	NOUN
ejpam-7023	282	60	holds	hold	VERB
ejpam-7023	282	61	for	for	ADP
ejpam-7023	282	62	a	a	DET
ejpam-7023	282	63	>	>	X
ejpam-7023	282	64	−1	−1	NOUN
ejpam-7023	282	65	)	)	PUNCT
ejpam-7023	282	66	.	.	PUNCT
ejpam-7023	283	1	with	with	ADP
ejpam-7023	283	2	the	the	DET
ejpam-7023	283	3	parameter	parameter	NOUN
ejpam-7023	283	4	choice	choice	NOUN
ejpam-7023	283	5	(	(	PUNCT
ejpam-7023	283	6	48	48	NUM
ejpam-7023	283	7	)	)	PUNCT
ejpam-7023	283	8	we	we	PRON
ejpam-7023	283	9	have	have	VERB
ejpam-7023	283	10	θ	θ	NOUN
ejpam-7023	283	11	=	=	SYM
ejpam-7023	283	12	π	π	X
ejpam-7023	283	13	/	/	SYM
ejpam-7023	283	14	m	m	VERB
ejpam-7023	283	15	∈	∈	NOUN
ejpam-7023	283	16	(	(	PUNCT
ejpam-7023	283	17	0	0	NUM
ejpam-7023	283	18	,	,	PUNCT
ejpam-7023	283	19	π2	π2	NOUN
ejpam-7023	283	20	)	)	PUNCT
ejpam-7023	283	21	,	,	PUNCT
ejpam-7023	283	22	a	a	DET
ejpam-7023	283	23	=	=	NOUN
ejpam-7023	283	24	mk	mk	NOUN
ejpam-7023	283	25	+	+	CCONJ
ejpam-7023	283	26	q	q	PROPN
ejpam-7023	284	1	+	+	NOUN
ejpam-7023	284	2	m	m	NOUN
ejpam-7023	284	3	=	=	VERB
ejpam-7023	284	4	m	m	VERB
ejpam-7023	284	5	(	(	PUNCT
ejpam-7023	284	6	k	k	X
ejpam-7023	284	7	+	+	PROPN
ejpam-7023	284	8	1	1	NUM
ejpam-7023	284	9	2	2	NUM
ejpam-7023	284	10	)	)	PUNCT
ejpam-7023	284	11	,	,	PUNCT
ejpam-7023	284	12	and	and	CCONJ
ejpam-7023	284	13	hence	hence	ADV
ejpam-7023	284	14	aθ	aθ	VERB
ejpam-7023	284	15	=	=	VERB
ejpam-7023	284	16	m	m	ADJ
ejpam-7023	284	17	(	(	PUNCT
ejpam-7023	284	18	k	k	X
ejpam-7023	284	19	+	+	PROPN
ejpam-7023	284	20	1	1	NUM
ejpam-7023	284	21	2	2	NUM
ejpam-7023	284	22	)	)	PUNCT
ejpam-7023	284	23	·	·	PUNCT
ejpam-7023	285	1	π	π	X
ejpam-7023	285	2	m	m	VERB
ejpam-7023	285	3	=	=	SYM
ejpam-7023	285	4	π	π	X
ejpam-7023	285	5	(	(	PUNCT
ejpam-7023	285	6	k	k	PROPN
ejpam-7023	285	7	+	+	PROPN
ejpam-7023	285	8	1	1	NUM
ejpam-7023	285	9	2	2	NUM
ejpam-7023	285	10	)	)	PUNCT
ejpam-7023	285	11	.	.	PUNCT
ejpam-7023	286	1	(	(	PUNCT
ejpam-7023	286	2	53	53	NUM
ejpam-7023	286	3	)	)	PUNCT
ejpam-7023	286	4	substituting	substitute	VERB
ejpam-7023	286	5	(	(	PUNCT
ejpam-7023	286	6	53	53	NUM
ejpam-7023	286	7	)	)	PUNCT
ejpam-7023	286	8	and	and	CCONJ
ejpam-7023	286	9	a	a	DET
ejpam-7023	286	10	=	=	X
ejpam-7023	286	11	m(k	m(k	PROPN
ejpam-7023	287	1	+	+	CCONJ
ejpam-7023	287	2	1	1	NUM
ejpam-7023	287	3	2	2	NUM
ejpam-7023	287	4	)	)	PUNCT
ejpam-7023	287	5	into	into	ADP
ejpam-7023	287	6	(	(	PUNCT
ejpam-7023	287	7	52	52	NUM
ejpam-7023	287	8	)	)	PUNCT
ejpam-7023	287	9	yields	yield	NOUN
ejpam-7023	287	10	(	(	PUNCT
ejpam-7023	287	11	50	50	NUM
ejpam-7023	287	12	)	)	PUNCT
ejpam-7023	287	13	.	.	PUNCT
ejpam-7023	288	1	since	since	SCONJ
ejpam-7023	288	2	a	a	DET
ejpam-7023	288	3	>	>	SYM
ejpam-7023	288	4	0	0	NUM
ejpam-7023	288	5	is	be	AUX
ejpam-7023	288	6	equivalent	equivalent	ADJ
ejpam-7023	288	7	to	to	ADP
ejpam-7023	288	8	k	k	PROPN
ejpam-7023	288	9	>	>	X
ejpam-7023	288	10	−1	−1	NOUN
ejpam-7023	288	11	2	2	NUM
ejpam-7023	288	12	,	,	PUNCT
ejpam-7023	288	13	convergence	convergence	NOUN
ejpam-7023	288	14	and	and	CCONJ
ejpam-7023	288	15	evaluation	evaluation	NOUN
ejpam-7023	288	16	hold	hold	VERB
ejpam-7023	288	17	precisely	precisely	ADV
ejpam-7023	288	18	on	on	ADP
ejpam-7023	288	19	k	k	PROPN
ejpam-7023	288	20	>	>	X
ejpam-7023	288	21	−1	−1	NOUN
ejpam-7023	288	22	2	2	NUM
ejpam-7023	288	23	.	.	PUNCT
ejpam-7023	289	1	in	in	ADP
ejpam-7023	289	2	(	(	PUNCT
ejpam-7023	289	3	50	50	NUM
ejpam-7023	289	4	)	)	PUNCT
ejpam-7023	289	5	the	the	DET
ejpam-7023	289	6	prefactor	prefactor	NOUN
ejpam-7023	289	7	mγ(m(k	mγ(m(k	PROPN
ejpam-7023	289	8	+	+	CCONJ
ejpam-7023	289	9	1	1	NUM
ejpam-7023	289	10	2	2	NUM
ejpam-7023	289	11	)	)	PUNCT
ejpam-7023	289	12	)	)	PUNCT
ejpam-7023	289	13	(	(	PUNCT
ejpam-7023	289	14	α	α	NOUN
ejpam-7023	289	15	2	2	NUM
ejpam-7023	289	16	+	+	CCONJ
ejpam-7023	289	17	β2)−m(k+1/2)/2	β2)−m(k+1/2)/2	NOUN
ejpam-7023	289	18	is	be	AUX
ejpam-7023	289	19	strictly	strictly	ADV
ejpam-7023	289	20	positive	positive	ADJ
ejpam-7023	289	21	for	for	ADP
ejpam-7023	289	22	k	k	PROPN
ejpam-7023	289	23	>	>	X
ejpam-7023	289	24	−1	−1	NOUN
ejpam-7023	289	25	2	2	NUM
ejpam-7023	289	26	,	,	PUNCT
ejpam-7023	289	27	so	so	ADV
ejpam-7023	289	28	jm	jm	PROPN
ejpam-7023	289	29	,	,	PUNCT
ejpam-7023	289	30	q(k	q(k	PROPN
ejpam-7023	289	31	,	,	PUNCT
ejpam-7023	289	32	α	α	X
ejpam-7023	289	33	,	,	PUNCT
ejpam-7023	289	34	β	β	NOUN
ejpam-7023	289	35	)	)	PUNCT
ejpam-7023	290	1	=	=	SYM
ejpam-7023	290	2	0	0	NUM
ejpam-7023	291	1	⇐	⇐	ADJ
ejpam-7023	291	2	⇒	⇒	NOUN
ejpam-7023	291	3	cos	cos	PROPN
ejpam-7023	291	4	(	(	PUNCT
ejpam-7023	292	1	π(k	π(k	PROPN
ejpam-7023	292	2	+	+	CCONJ
ejpam-7023	292	3	1	1	NUM
ejpam-7023	292	4	2	2	NUM
ejpam-7023	292	5	)	)	PUNCT
ejpam-7023	292	6	)	)	PUNCT
ejpam-7023	293	1	=	=	SYM
ejpam-7023	293	2	0	0	NUM
ejpam-7023	293	3	⇐	⇐	ADJ
ejpam-7023	293	4	⇒	⇒	NOUN
ejpam-7023	293	5	k	k	PROPN
ejpam-7023	294	1	+	+	CCONJ
ejpam-7023	294	2	1	1	NUM
ejpam-7023	294	3	2	2	NUM
ejpam-7023	294	4	∈	∈	NOUN
ejpam-7023	294	5	z	z	NOUN
ejpam-7023	294	6	⇐	⇐	PROPN
ejpam-7023	294	7	⇒	⇒	PROPN
ejpam-7023	294	8	k	k	PROPN
ejpam-7023	294	9	∈	∈	PROPN
ejpam-7023	294	10	z.	z.	PROPN
ejpam-7023	294	11	intersecting	intersect	VERB
ejpam-7023	294	12	with	with	ADP
ejpam-7023	294	13	k	k	PROPN
ejpam-7023	294	14	>	>	X
ejpam-7023	294	15	−1	−1	NOUN
ejpam-7023	294	16	2	2	NUM
ejpam-7023	294	17	gives	give	VERB
ejpam-7023	294	18	k	k	PROPN
ejpam-7023	294	19	∈	∈	PROPN
ejpam-7023	294	20	{	{	PUNCT
ejpam-7023	294	21	0	0	NUM
ejpam-7023	294	22	,	,	PUNCT
ejpam-7023	294	23	1	1	NUM
ejpam-7023	294	24	,	,	PUNCT
ejpam-7023	294	25	2	2	NUM
ejpam-7023	294	26	,	,	PUNCT
ejpam-7023	294	27	.	.	PUNCT
ejpam-7023	294	28	.	.	PUNCT
ejpam-7023	294	29	.	.	PUNCT
ejpam-7023	295	1	}	}	PUNCT
ejpam-7023	295	2	,	,	PUNCT
ejpam-7023	295	3	which	which	PRON
ejpam-7023	295	4	is	be	AUX
ejpam-7023	295	5	(	(	PUNCT
ejpam-7023	295	6	51	51	NUM
ejpam-7023	295	7	)	)	PUNCT
ejpam-7023	295	8	.	.	PUNCT
ejpam-7023	296	1	corollary	corollary	ADJ
ejpam-7023	296	2	5	5	NUM
ejpam-7023	296	3	gives	give	VERB
ejpam-7023	296	4	the	the	DET
ejpam-7023	296	5	following	follow	VERB
ejpam-7023	296	6	explicit	explicit	ADJ
ejpam-7023	296	7	examples	example	NOUN
ejpam-7023	296	8	,	,	PUNCT
ejpam-7023	296	9	i.	i.	PROPN
ejpam-7023	296	10	ayoob	ayoob	PROPN
ejpam-7023	296	11	/	/	SYM
ejpam-7023	296	12	eur	eur	PROPN
ejpam-7023	296	13	.	.	PUNCT
ejpam-7023	297	1	j.	j.	PROPN
ejpam-7023	297	2	pure	pure	PROPN
ejpam-7023	297	3	appl	appl	PROPN
ejpam-7023	297	4	.	.	PROPN
ejpam-7023	297	5	math	math	PROPN
ejpam-7023	297	6	,	,	PUNCT
ejpam-7023	297	7	18	18	NUM
ejpam-7023	297	8	(	(	PUNCT
ejpam-7023	297	9	4	4	NUM
ejpam-7023	297	10	)	)	PUNCT
ejpam-7023	297	11	(	(	PUNCT
ejpam-7023	297	12	2025	2025	NUM
ejpam-7023	297	13	)	)	PUNCT
ejpam-7023	297	14	,	,	PUNCT
ejpam-7023	297	15	7023	7023	NUM
ejpam-7023	297	16	12	12	NUM
ejpam-7023	297	17	of	of	ADP
ejpam-7023	297	18	16	16	NUM
ejpam-7023	297	19	example	example	NOUN
ejpam-7023	297	20	3	3	NUM
ejpam-7023	297	21	.	.	PUNCT
ejpam-7023	298	1	set	set	VERB
ejpam-7023	298	2	m	m	PROPN
ejpam-7023	298	3	=	=	NOUN
ejpam-7023	298	4	4	4	NUM
ejpam-7023	298	5	,	,	PUNCT
ejpam-7023	298	6	α	α	NOUN
ejpam-7023	298	7	=	=	SYM
ejpam-7023	298	8	1	1	NUM
ejpam-7023	298	9	,	,	PUNCT
ejpam-7023	298	10	β	β	X
ejpam-7023	298	11	=	=	SYM
ejpam-7023	298	12	α	α	PROPN
ejpam-7023	298	13	tan	tan	PROPN
ejpam-7023	298	14	(	(	PUNCT
ejpam-7023	298	15	π	π	PROPN
ejpam-7023	298	16	4	4	NUM
ejpam-7023	298	17	)	)	PUNCT
ejpam-7023	298	18	=	=	SYM
ejpam-7023	298	19	1	1	NUM
ejpam-7023	298	20	,	,	PUNCT
ejpam-7023	298	21	q	q	NOUN
ejpam-7023	298	22	=	=	PUNCT
ejpam-7023	298	23	−m	−m	ADJ
ejpam-7023	298	24	2	2	NUM
ejpam-7023	298	25	=	=	SYM
ejpam-7023	298	26	−2	−2	NOUN
ejpam-7023	298	27	,	,	PUNCT
ejpam-7023	298	28	and	and	CCONJ
ejpam-7023	298	29	define	define	VERB
ejpam-7023	298	30	,	,	PUNCT
ejpam-7023	298	31	f1(x	f1(x	NOUN
ejpam-7023	298	32	)	)	PUNCT
ejpam-7023	299	1	=	=	PUNCT
ejpam-7023	299	2	e−x1/4	e−x1/4	PROPN
ejpam-7023	299	3	cos	cos	PROPN
ejpam-7023	299	4	(	(	PUNCT
ejpam-7023	299	5	x1/4	x1/4	PROPN
ejpam-7023	299	6	)	)	PUNCT
ejpam-7023	300	1	(	(	PUNCT
ejpam-7023	300	2	x1/4)−2	x1/4)−2	PUNCT
ejpam-7023	300	3	=	=	SYM
ejpam-7023	301	1	e−x1/4	e−x1/4	PROPN
ejpam-7023	301	2	cos	cos	PROPN
ejpam-7023	301	3	(	(	PUNCT
ejpam-7023	301	4	x1/4	x1/4	PROPN
ejpam-7023	301	5	)	)	PUNCT
ejpam-7023	301	6	x−1/2	x−1/2	PROPN
ejpam-7023	301	7	.	.	PUNCT
ejpam-7023	302	1	then	then	ADV
ejpam-7023	302	2	for	for	ADP
ejpam-7023	302	3	k	k	PROPN
ejpam-7023	302	4	>	>	X
ejpam-7023	302	5	−1	−1	NOUN
ejpam-7023	302	6	2	2	NUM
ejpam-7023	302	7	,	,	PUNCT
ejpam-7023	302	8	j4,−2(k	j4,−2(k	PROPN
ejpam-7023	302	9	,	,	PUNCT
ejpam-7023	302	10	1	1	NUM
ejpam-7023	302	11	,	,	PUNCT
ejpam-7023	302	12	1	1	NUM
ejpam-7023	302	13	)	)	PUNCT
ejpam-7023	302	14	=	=	SYM
ejpam-7023	302	15	∫	∫	PROPN
ejpam-7023	302	16	∞	∞	PROPN
ejpam-7023	302	17	0	0	NUM
ejpam-7023	302	18	f1(x)x	f1(x)x	PROPN
ejpam-7023	302	19	k	k	PROPN
ejpam-7023	302	20	dx	dx	PROPN
ejpam-7023	302	21	=	=	SYM
ejpam-7023	302	22	4γ(4k	4γ(4k	NUM
ejpam-7023	302	23	+	+	CCONJ
ejpam-7023	302	24	2	2	X
ejpam-7023	302	25	)	)	PUNCT
ejpam-7023	302	26	2−(2k+1	2−(2k+1	PROPN
ejpam-7023	302	27	)	)	PUNCT
ejpam-7023	302	28	cos	cos	PROPN
ejpam-7023	302	29	(	(	PUNCT
ejpam-7023	303	1	π(k	π(k	PROPN
ejpam-7023	303	2	+	+	CCONJ
ejpam-7023	303	3	1	1	NUM
ejpam-7023	303	4	2	2	NUM
ejpam-7023	303	5	)	)	PUNCT
ejpam-7023	303	6	)	)	PUNCT
ejpam-7023	303	7	,	,	PUNCT
ejpam-7023	303	8	and	and	CCONJ
ejpam-7023	303	9	therefore	therefore	ADV
ejpam-7023	303	10	j4,−2(k	j4,−2(k	PROPN
ejpam-7023	303	11	,	,	PUNCT
ejpam-7023	303	12	1	1	NUM
ejpam-7023	303	13	,	,	PUNCT
ejpam-7023	303	14	1	1	NUM
ejpam-7023	303	15	)	)	PUNCT
ejpam-7023	303	16	=	=	SYM
ejpam-7023	304	1	0	0	NUM
ejpam-7023	305	1	⇐	⇐	ADJ
ejpam-7023	305	2	⇒	⇒	PROPN
ejpam-7023	305	3	k	k	PROPN
ejpam-7023	305	4	∈	∈	PROPN
ejpam-7023	305	5	z≥0	z≥0	PROPN
ejpam-7023	305	6	.	.	PUNCT
ejpam-7023	306	1	example	example	NOUN
ejpam-7023	307	1	4	4	NUM
ejpam-7023	307	2	.	.	X
ejpam-7023	307	3	choose	choose	VERB
ejpam-7023	307	4	m	m	PROPN
ejpam-7023	307	5	=	=	SYM
ejpam-7023	307	6	6	6	NUM
ejpam-7023	307	7	,	,	PUNCT
ejpam-7023	307	8	α	α	NOUN
ejpam-7023	307	9	=	=	PUNCT
ejpam-7023	307	10	√	√	NUM
ejpam-7023	307	11	3	3	NUM
ejpam-7023	307	12	,	,	PUNCT
ejpam-7023	307	13	β	β	X
ejpam-7023	307	14	=	=	SYM
ejpam-7023	307	15	α	α	PROPN
ejpam-7023	307	16	tan	tan	PROPN
ejpam-7023	307	17	(	(	PUNCT
ejpam-7023	307	18	π	π	PROPN
ejpam-7023	307	19	6	6	NUM
ejpam-7023	307	20	)	)	PUNCT
ejpam-7023	307	21	=	=	SYM
ejpam-7023	307	22	1	1	NUM
ejpam-7023	307	23	,	,	PUNCT
ejpam-7023	307	24	q	q	NOUN
ejpam-7023	307	25	=	=	PUNCT
ejpam-7023	307	26	−m	−m	ADJ
ejpam-7023	307	27	2	2	NUM
ejpam-7023	307	28	=	=	SYM
ejpam-7023	307	29	−3	−3	ADV
ejpam-7023	307	30	,	,	PUNCT
ejpam-7023	307	31	and	and	CCONJ
ejpam-7023	307	32	define	define	VERB
ejpam-7023	307	33	f2(x	f2(x	NUM
ejpam-7023	307	34	)	)	PUNCT
ejpam-7023	307	35	=	=	NOUN
ejpam-7023	308	1	e−	e−	PROPN
ejpam-7023	308	2	√	√	NUM
ejpam-7023	308	3	3x1/6	3x1/6	PROPN
ejpam-7023	308	4	cos	cos	PROPN
ejpam-7023	308	5	(	(	PUNCT
ejpam-7023	308	6	x1/6	x1/6	PROPN
ejpam-7023	308	7	)	)	PUNCT
ejpam-7023	308	8	(	(	PUNCT
ejpam-7023	308	9	x1/6)−3	x1/6)−3	PROPN
ejpam-7023	308	10	=	=	PUNCT
ejpam-7023	308	11	e−	e−	PROPN
ejpam-7023	308	12	√	√	NUM
ejpam-7023	308	13	3x1/6	3x1/6	PROPN
ejpam-7023	308	14	cos	cos	PROPN
ejpam-7023	308	15	(	(	PUNCT
ejpam-7023	308	16	x1/6	x1/6	PROPN
ejpam-7023	308	17	)	)	PUNCT
ejpam-7023	308	18	x−1/2	x−1/2	PROPN
ejpam-7023	308	19	.	.	PUNCT
ejpam-7023	309	1	then	then	ADV
ejpam-7023	309	2	for	for	ADP
ejpam-7023	309	3	k	k	PROPN
ejpam-7023	309	4	>	>	X
ejpam-7023	309	5	−1	−1	NOUN
ejpam-7023	309	6	2	2	NUM
ejpam-7023	309	7	,	,	PUNCT
ejpam-7023	309	8	j6,−3	j6,−3	VERB
ejpam-7023	309	9	(	(	PUNCT
ejpam-7023	309	10	k	k	NOUN
ejpam-7023	309	11	,	,	PUNCT
ejpam-7023	309	12	√	√	NOUN
ejpam-7023	309	13	3	3	NUM
ejpam-7023	309	14	,	,	PUNCT
ejpam-7023	309	15	1	1	NUM
ejpam-7023	309	16	)	)	PUNCT
ejpam-7023	309	17	=	=	SYM
ejpam-7023	309	18	∫	∫	PROPN
ejpam-7023	309	19	∞	∞	NOUN
ejpam-7023	309	20	0	0	NUM
ejpam-7023	309	21	f2(x)x	f2(x)x	ADV
ejpam-7023	309	22	k	k	PROPN
ejpam-7023	309	23	dx	dx	PROPN
ejpam-7023	310	1	=	=	PUNCT
ejpam-7023	310	2	6γ(6k	6γ(6k	PROPN
ejpam-7023	310	3	+	+	CCONJ
ejpam-7023	310	4	3	3	X
ejpam-7023	310	5	)	)	PUNCT
ejpam-7023	310	6	2−(6k+3	2−(6k+3	PROPN
ejpam-7023	310	7	)	)	PUNCT
ejpam-7023	310	8	cos	cos	PROPN
ejpam-7023	311	1	(	(	PUNCT
ejpam-7023	311	2	π(k	π(k	PROPN
ejpam-7023	311	3	+	+	CCONJ
ejpam-7023	311	4	1	1	NUM
ejpam-7023	311	5	2	2	NUM
ejpam-7023	311	6	)	)	PUNCT
ejpam-7023	311	7	)	)	PUNCT
ejpam-7023	311	8	,	,	PUNCT
ejpam-7023	311	9	which	which	PRON
ejpam-7023	311	10	gives	give	VERB
ejpam-7023	311	11	j6,−3	j6,−3	VERB
ejpam-7023	311	12	(	(	PUNCT
ejpam-7023	311	13	k	k	NOUN
ejpam-7023	311	14	,	,	PUNCT
ejpam-7023	311	15	√	√	NOUN
ejpam-7023	311	16	3	3	NUM
ejpam-7023	311	17	,	,	PUNCT
ejpam-7023	311	18	1	1	NUM
ejpam-7023	311	19	)	)	PUNCT
ejpam-7023	311	20	=	=	SYM
ejpam-7023	311	21	0	0	NUM
ejpam-7023	311	22	⇐	⇐	ADJ
ejpam-7023	311	23	⇒	⇒	PROPN
ejpam-7023	311	24	k	k	PROPN
ejpam-7023	311	25	∈	∈	PROPN
ejpam-7023	311	26	z≥0	z≥0	PROPN
ejpam-7023	311	27	.	.	PUNCT
ejpam-7023	312	1	we	we	PRON
ejpam-7023	312	2	also	also	ADV
ejpam-7023	312	3	have	have	VERB
ejpam-7023	312	4	the	the	DET
ejpam-7023	312	5	following	follow	VERB
ejpam-7023	312	6	integral	integral	ADJ
ejpam-7023	312	7	representations	representation	NOUN
ejpam-7023	312	8	of	of	ADP
ejpam-7023	312	9	the	the	DET
ejpam-7023	312	10	important	important	ADJ
ejpam-7023	312	11	constants	constant	NOUN
ejpam-7023	312	12	,	,	PUNCT
ejpam-7023	312	13	corollary	corollary	ADJ
ejpam-7023	312	14	6	6	NUM
ejpam-7023	312	15	.	.	PUNCT
ejpam-7023	313	1	in	in	ADP
ejpam-7023	313	2	theorem	theorem	NOUN
ejpam-7023	313	3	5	5	NUM
ejpam-7023	313	4	,	,	PUNCT
ejpam-7023	313	5	choose	choose	VERB
ejpam-7023	313	6	m	m	NOUN
ejpam-7023	313	7	=	=	SYM
ejpam-7023	313	8	2	2	NUM
ejpam-7023	313	9	,	,	PUNCT
ejpam-7023	313	10	α	α	NOUN
ejpam-7023	313	11	=	=	SYM
ejpam-7023	313	12	1	1	NUM
ejpam-7023	313	13	,	,	PUNCT
ejpam-7023	313	14	β	β	X
ejpam-7023	313	15	=	=	SYM
ejpam-7023	313	16	1	1	NUM
ejpam-7023	313	17	,	,	PUNCT
ejpam-7023	313	18	k	k	NOUN
ejpam-7023	313	19	=	=	SYM
ejpam-7023	313	20	0	0	NUM
ejpam-7023	313	21	,	,	PUNCT
ejpam-7023	313	22	q	q	NOUN
ejpam-7023	314	1	=	=	NOUN
ejpam-7023	314	2	0	0	PROPN
ejpam-7023	314	3	.	.	PUNCT
ejpam-7023	315	1	then	then	ADV
ejpam-7023	315	2	a	a	DET
ejpam-7023	315	3	=	=	X
ejpam-7023	315	4	mk+	mk+	X
ejpam-7023	315	5	q+m	q+m	NUM
ejpam-7023	315	6	=	=	SYM
ejpam-7023	315	7	2	2	NUM
ejpam-7023	315	8	and	and	CCONJ
ejpam-7023	315	9	θ	θ	NOUN
ejpam-7023	315	10	=	=	SYM
ejpam-7023	315	11	arctan(β	arctan(β	NOUN
ejpam-7023	315	12	/	/	SYM
ejpam-7023	315	13	α	α	NOUN
ejpam-7023	315	14	)	)	PUNCT
ejpam-7023	315	15	=	=	SYM
ejpam-7023	315	16	arctan(1	arctan(1	X
ejpam-7023	315	17	)	)	PUNCT
ejpam-7023	315	18	(	(	PUNCT
ejpam-7023	315	19	so	so	ADV
ejpam-7023	315	20	sin(2θ	sin(2θ	NOUN
ejpam-7023	315	21	)	)	PUNCT
ejpam-7023	316	1	=	=	SYM
ejpam-7023	316	2	1	1	NUM
ejpam-7023	316	3	)	)	PUNCT
ejpam-7023	316	4	,	,	PUNCT
ejpam-7023	316	5	which	which	PRON
ejpam-7023	316	6	gives∫	gives∫	VERB
ejpam-7023	316	7	∞	∞	PROPN
ejpam-7023	316	8	0	0	PUNCT
ejpam-7023	316	9	e−x1/2	e−x1/2	PROPN
ejpam-7023	316	10	sin	sin	NOUN
ejpam-7023	316	11	(	(	PUNCT
ejpam-7023	316	12	x1/2	x1/2	PROPN
ejpam-7023	316	13	)	)	PUNCT
ejpam-7023	316	14	dx	dx	PROPN
ejpam-7023	317	1	=	=	SYM
ejpam-7023	317	2	1	1	NUM
ejpam-7023	317	3	(	(	PUNCT
ejpam-7023	317	4	converges	converge	NOUN
ejpam-7023	317	5	since	since	SCONJ
ejpam-7023	317	6	a	a	DET
ejpam-7023	317	7	=	=	SYM
ejpam-7023	317	8	2	2	NUM
ejpam-7023	317	9	>	>	PUNCT
ejpam-7023	317	10	0	0	NUM
ejpam-7023	317	11	)	)	PUNCT
ejpam-7023	317	12	.	.	PUNCT
ejpam-7023	318	1	(	(	PUNCT
ejpam-7023	318	2	54	54	NUM
ejpam-7023	318	3	)	)	PUNCT
ejpam-7023	318	4	proof	proof	NOUN
ejpam-7023	318	5	.	.	PUNCT
ejpam-7023	319	1	by	by	ADP
ejpam-7023	319	2	(	(	PUNCT
ejpam-7023	319	3	17	17	NUM
ejpam-7023	319	4	)	)	PUNCT
ejpam-7023	319	5	,	,	PUNCT
ejpam-7023	319	6	i	i	PRON
ejpam-7023	319	7	=	=	PUNCT
ejpam-7023	319	8	mγ(2)r−1	mγ(2)r−1	ADJ
ejpam-7023	319	9	sin(2θ	sin(2θ	PROPN
ejpam-7023	319	10	)	)	PUNCT
ejpam-7023	319	11	with	with	ADP
ejpam-7023	319	12	m	m	PROPN
ejpam-7023	319	13	=	=	SYM
ejpam-7023	319	14	2	2	NUM
ejpam-7023	319	15	,	,	PUNCT
ejpam-7023	319	16	r	r	NOUN
ejpam-7023	319	17	=	=	SYM
ejpam-7023	319	18	α2	α2	ADJ
ejpam-7023	319	19	+	+	CCONJ
ejpam-7023	319	20	β2	β2	NOUN
ejpam-7023	319	21	=	=	NOUN
ejpam-7023	319	22	2	2	NUM
ejpam-7023	319	23	.	.	PUNCT
ejpam-7023	320	1	thus	thus	ADV
ejpam-7023	320	2	i	i	PRON
ejpam-7023	320	3	=	=	SYM
ejpam-7023	320	4	2	2	X
ejpam-7023	320	5	·	·	SYM
ejpam-7023	320	6	1	1	NUM
ejpam-7023	320	7	·	·	PUNCT
ejpam-7023	320	8	(	(	PUNCT
ejpam-7023	320	9	1/2	1/2	NUM
ejpam-7023	320	10	)	)	PUNCT
ejpam-7023	320	11	·	·	PUNCT
ejpam-7023	320	12	1	1	NUM
ejpam-7023	320	13	=	=	SYM
ejpam-7023	320	14	1	1	X
ejpam-7023	320	15	.	.	PUNCT
ejpam-7023	321	1	the	the	DET
ejpam-7023	321	2	following	follow	VERB
ejpam-7023	321	3	theorem	theorem	NOUN
ejpam-7023	321	4	gives	give	VERB
ejpam-7023	321	5	integral	integral	ADJ
ejpam-7023	321	6	representation	representation	NOUN
ejpam-7023	321	7	of	of	ADP
ejpam-7023	321	8	specific	specific	ADJ
ejpam-7023	321	9	values	value	NOUN
ejpam-7023	321	10	of	of	ADP
ejpam-7023	321	11	the	the	DET
ejpam-7023	321	12	gamma	gamma	NOUN
ejpam-7023	321	13	function	function	NOUN
ejpam-7023	321	14	.	.	PUNCT
ejpam-7023	322	1	i.	i.	PROPN
ejpam-7023	322	2	ayoob	ayoob	PROPN
ejpam-7023	322	3	/	/	SYM
ejpam-7023	322	4	eur	eur	PROPN
ejpam-7023	322	5	.	.	PUNCT
ejpam-7023	323	1	j.	j.	PROPN
ejpam-7023	323	2	pure	pure	PROPN
ejpam-7023	323	3	appl	appl	PROPN
ejpam-7023	323	4	.	.	PROPN
ejpam-7023	323	5	math	math	PROPN
ejpam-7023	323	6	,	,	PUNCT
ejpam-7023	323	7	18	18	NUM
ejpam-7023	323	8	(	(	PUNCT
ejpam-7023	323	9	4	4	NUM
ejpam-7023	323	10	)	)	PUNCT
ejpam-7023	323	11	(	(	PUNCT
ejpam-7023	323	12	2025	2025	NUM
ejpam-7023	323	13	)	)	PUNCT
ejpam-7023	323	14	,	,	PUNCT
ejpam-7023	323	15	7023	7023	NUM
ejpam-7023	323	16	13	13	NUM
ejpam-7023	323	17	of	of	ADP
ejpam-7023	323	18	16	16	NUM
ejpam-7023	323	19	theorem	theorem	NOUN
ejpam-7023	323	20	7	7	NUM
ejpam-7023	323	21	.	.	PUNCT
ejpam-7023	324	1	let	let	VERB
ejpam-7023	324	2	a	a	DET
ejpam-7023	324	3	>	>	X
ejpam-7023	324	4	0	0	NUM
ejpam-7023	324	5	,	,	PUNCT
ejpam-7023	324	6	m	m	VERB
ejpam-7023	324	7	>	>	X
ejpam-7023	324	8	0	0	NUM
ejpam-7023	324	9	,	,	PUNCT
ejpam-7023	324	10	and	and	CCONJ
ejpam-7023	324	11	choose	choose	VERB
ejpam-7023	324	12	any	any	DET
ejpam-7023	324	13	angle	angle	NOUN
ejpam-7023	324	14	θ	θ	PROPN
ejpam-7023	324	15	∈	∈	PROPN
ejpam-7023	324	16	(	(	PUNCT
ejpam-7023	324	17	0	0	NUM
ejpam-7023	324	18	,	,	PUNCT
ejpam-7023	324	19	π2	π2	NOUN
ejpam-7023	324	20	)	)	PUNCT
ejpam-7023	324	21	.	.	PUNCT
ejpam-7023	325	1	define	define	VERB
ejpam-7023	325	2	r	r	NOUN
ejpam-7023	325	3	=	=	SYM
ejpam-7023	325	4	(	(	PUNCT
ejpam-7023	325	5	m	m	NOUN
ejpam-7023	325	6	sin(aθ	sin(aθ	NOUN
ejpam-7023	325	7	)	)	PUNCT
ejpam-7023	325	8	)	)	PUNCT
ejpam-7023	325	9	2	2	NUM
ejpam-7023	325	10	a	a	PRON
ejpam-7023	325	11	,	,	PUNCT
ejpam-7023	325	12	α	α	NOUN
ejpam-7023	325	13	=	=	NOUN
ejpam-7023	325	14	√	√	PROPN
ejpam-7023	325	15	r	r	NOUN
ejpam-7023	325	16	cos	cos	PROPN
ejpam-7023	325	17	θ	θ	PROPN
ejpam-7023	325	18	>	>	X
ejpam-7023	325	19	0	0	PROPN
ejpam-7023	325	20	,	,	PUNCT
ejpam-7023	325	21	β	β	X
ejpam-7023	325	22	=	=	PUNCT
ejpam-7023	325	23	√	√	NUM
ejpam-7023	325	24	r	r	NOUN
ejpam-7023	325	25	sin	sin	NOUN
ejpam-7023	325	26	θ	θ	PROPN
ejpam-7023	325	27	,	,	PUNCT
ejpam-7023	325	28	(	(	PUNCT
ejpam-7023	325	29	55	55	NUM
ejpam-7023	325	30	)	)	PUNCT
ejpam-7023	325	31	and	and	CCONJ
ejpam-7023	325	32	set	set	VERB
ejpam-7023	325	33	k	k	PROPN
ejpam-7023	325	34	=	=	SYM
ejpam-7023	325	35	0	0	NUM
ejpam-7023	325	36	,	,	PUNCT
ejpam-7023	325	37	q	q	NOUN
ejpam-7023	325	38	=	=	NOUN
ejpam-7023	325	39	a−m	a−m	NOUN
ejpam-7023	325	40	.	.	PUNCT
ejpam-7023	326	1	(	(	PUNCT
ejpam-7023	326	2	56	56	NUM
ejpam-7023	326	3	)	)	PUNCT
ejpam-7023	326	4	then	then	ADV
ejpam-7023	326	5	a	a	DET
ejpam-7023	326	6	=	=	PUNCT
ejpam-7023	326	7	mk	mk	NOUN
ejpam-7023	326	8	+	+	CCONJ
ejpam-7023	326	9	q	q	PROPN
ejpam-7023	327	1	+	+	NOUN
ejpam-7023	327	2	m	m	VERB
ejpam-7023	327	3	and	and	CCONJ
ejpam-7023	327	4	,	,	PUNCT
ejpam-7023	327	5	with	with	ADP
ejpam-7023	327	6	im	im	PRON
ejpam-7023	327	7	,	,	PUNCT
ejpam-7023	327	8	q(k	q(k	PROPN
ejpam-7023	327	9	,	,	PUNCT
ejpam-7023	327	10	α	α	X
ejpam-7023	327	11	,	,	PUNCT
ejpam-7023	327	12	β	β	NOUN
ejpam-7023	327	13	)	)	PUNCT
ejpam-7023	327	14	=	=	SYM
ejpam-7023	328	1	∫	∫	PROPN
ejpam-7023	328	2	∞	∞	NUM
ejpam-7023	328	3	0	0	NUM
ejpam-7023	328	4	e−αx1	e−αx1	PROPN
ejpam-7023	328	5	/	/	SYM
ejpam-7023	328	6	m	m	NOUN
ejpam-7023	328	7	sin	sin	NOUN
ejpam-7023	328	8	(	(	PUNCT
ejpam-7023	328	9	βx1	βx1	PROPN
ejpam-7023	328	10	/	/	SYM
ejpam-7023	328	11	m	m	NOUN
ejpam-7023	328	12	)	)	PUNCT
ejpam-7023	328	13	xk	xk	PROPN
ejpam-7023	328	14	(	(	PUNCT
ejpam-7023	328	15	x1	x1	PROPN
ejpam-7023	328	16	/	/	SYM
ejpam-7023	328	17	m)q	m)q	PROPN
ejpam-7023	328	18	dx	dx	PROPN
ejpam-7023	328	19	,	,	PUNCT
ejpam-7023	328	20	(	(	PUNCT
ejpam-7023	328	21	57	57	NUM
ejpam-7023	328	22	)	)	PUNCT
ejpam-7023	328	23	we	we	PRON
ejpam-7023	328	24	have	have	AUX
ejpam-7023	328	25	a	a	DET
ejpam-7023	328	26	>	>	X
ejpam-7023	328	27	−1	−1	NOUN
ejpam-7023	328	28	(	(	PUNCT
ejpam-7023	328	29	indeed	indeed	ADV
ejpam-7023	328	30	a	a	DET
ejpam-7023	328	31	>	>	X
ejpam-7023	328	32	0	0	NUM
ejpam-7023	328	33	)	)	PUNCT
ejpam-7023	328	34	so	so	SCONJ
ejpam-7023	328	35	the	the	DET
ejpam-7023	328	36	integral	integral	ADJ
ejpam-7023	328	37	converges	converge	NOUN
ejpam-7023	328	38	,	,	PUNCT
ejpam-7023	328	39	and	and	CCONJ
ejpam-7023	328	40	moreover	moreover	ADV
ejpam-7023	328	41	im	im	ADV
ejpam-7023	328	42	,	,	PUNCT
ejpam-7023	328	43	q(k	q(k	PROPN
ejpam-7023	328	44	,	,	PUNCT
ejpam-7023	328	45	α	α	X
ejpam-7023	328	46	,	,	PUNCT
ejpam-7023	328	47	β	β	NOUN
ejpam-7023	328	48	)	)	PUNCT
ejpam-7023	328	49	=	=	SYM
ejpam-7023	328	50	γ(a	γ(a	PROPN
ejpam-7023	328	51	)	)	PUNCT
ejpam-7023	328	52	.	.	PUNCT
ejpam-7023	329	1	(	(	PUNCT
ejpam-7023	329	2	58	58	X
ejpam-7023	329	3	)	)	PUNCT
ejpam-7023	329	4	proof	proof	NOUN
ejpam-7023	329	5	.	.	PUNCT
ejpam-7023	330	1	by	by	ADP
ejpam-7023	330	2	(	(	PUNCT
ejpam-7023	330	3	56	56	NUM
ejpam-7023	330	4	)	)	PUNCT
ejpam-7023	330	5	,	,	PUNCT
ejpam-7023	330	6	a	a	DET
ejpam-7023	330	7	=	=	NOUN
ejpam-7023	330	8	mk	mk	NOUN
ejpam-7023	330	9	+	+	CCONJ
ejpam-7023	330	10	q	q	PROPN
ejpam-7023	331	1	+	+	NUM
ejpam-7023	331	2	m	m	VERB
ejpam-7023	331	3	=	=	SYM
ejpam-7023	331	4	0	0	PUNCT
ejpam-7023	332	1	+	+	CCONJ
ejpam-7023	332	2	(	(	PUNCT
ejpam-7023	332	3	a	a	DET
ejpam-7023	332	4	−	−	PROPN
ejpam-7023	332	5	m	m	NOUN
ejpam-7023	332	6	)	)	PUNCT
ejpam-7023	333	1	+	+	CCONJ
ejpam-7023	333	2	m	m	VERB
ejpam-7023	333	3	=	=	SYM
ejpam-7023	333	4	a	a	NOUN
ejpam-7023	333	5	,	,	PUNCT
ejpam-7023	333	6	so	so	SCONJ
ejpam-7023	333	7	the	the	DET
ejpam-7023	333	8	parameter	parameter	NOUN
ejpam-7023	333	9	a	a	PRON
ejpam-7023	333	10	in	in	ADP
ejpam-7023	333	11	theorem	theorem	ADJ
ejpam-7023	333	12	5	5	NUM
ejpam-7023	333	13	agrees	agree	VERB
ejpam-7023	333	14	with	with	ADP
ejpam-7023	333	15	the	the	DET
ejpam-7023	333	16	present	present	ADJ
ejpam-7023	333	17	a.	a.	NOUN
ejpam-7023	333	18	using	use	VERB
ejpam-7023	333	19	θ	θ	PROPN
ejpam-7023	333	20	=	=	SYM
ejpam-7023	333	21	arctan(β	arctan(β	PROPN
ejpam-7023	333	22	/	/	SYM
ejpam-7023	333	23	α	α	NOUN
ejpam-7023	333	24	)	)	PUNCT
ejpam-7023	333	25	∈	∈	PROPN
ejpam-7023	333	26	(	(	PUNCT
ejpam-7023	333	27	0	0	NUM
ejpam-7023	333	28	,	,	PUNCT
ejpam-7023	333	29	π2	π2	ADJ
ejpam-7023	333	30	)	)	PUNCT
ejpam-7023	333	31	and	and	CCONJ
ejpam-7023	333	32	r	r	NOUN
ejpam-7023	333	33	=	=	SYM
ejpam-7023	333	34	α2	α2	PROPN
ejpam-7023	333	35	+	+	CCONJ
ejpam-7023	333	36	β2	β2	VERB
ejpam-7023	333	37	from	from	ADP
ejpam-7023	333	38	(	(	PUNCT
ejpam-7023	333	39	55	55	NUM
ejpam-7023	333	40	)	)	PUNCT
ejpam-7023	333	41	,	,	PUNCT
ejpam-7023	333	42	theorem	theorem	VERB
ejpam-7023	333	43	5	5	NUM
ejpam-7023	333	44	gives	give	NOUN
ejpam-7023	333	45	(	(	PUNCT
ejpam-7023	333	46	for	for	ADP
ejpam-7023	333	47	a	a	DET
ejpam-7023	333	48	>	>	X
ejpam-7023	333	49	0	0	NUM
ejpam-7023	333	50	)	)	PUNCT
ejpam-7023	333	51	im	im	ADP
ejpam-7023	333	52	,	,	PUNCT
ejpam-7023	333	53	q(k	q(k	PROPN
ejpam-7023	333	54	,	,	PUNCT
ejpam-7023	333	55	α	α	X
ejpam-7023	333	56	,	,	PUNCT
ejpam-7023	333	57	β	β	NOUN
ejpam-7023	333	58	)	)	PUNCT
ejpam-7023	333	59	=	=	SYM
ejpam-7023	333	60	mγ(a	mγ(a	X
ejpam-7023	333	61	)	)	PUNCT
ejpam-7023	333	62	r−a/2	r−a/2	NOUN
ejpam-7023	333	63	sin(aθ	sin(aθ	NOUN
ejpam-7023	333	64	)	)	PUNCT
ejpam-7023	333	65	.	.	PUNCT
ejpam-7023	334	1	(	(	PUNCT
ejpam-7023	334	2	59	59	NUM
ejpam-7023	334	3	)	)	PUNCT
ejpam-7023	334	4	by	by	ADP
ejpam-7023	334	5	construction	construction	NOUN
ejpam-7023	334	6	,	,	PUNCT
ejpam-7023	334	7	ra/2	ra/2	NOUN
ejpam-7023	334	8	=	=	PUNCT
ejpam-7023	334	9	(	(	PUNCT
ejpam-7023	334	10	m	m	NOUN
ejpam-7023	334	11	sin(aθ	sin(aθ	NOUN
ejpam-7023	334	12	)	)	PUNCT
ejpam-7023	334	13	)	)	PUNCT
ejpam-7023	334	14	,	,	PUNCT
ejpam-7023	334	15	hence	hence	ADV
ejpam-7023	334	16	r−a/2	r−a/2	NOUN
ejpam-7023	334	17	sin(aθ	sin(aθ	VERB
ejpam-7023	334	18	)	)	PUNCT
ejpam-7023	334	19	=	=	SYM
ejpam-7023	334	20	sin(aθ	sin(aθ	NOUN
ejpam-7023	334	21	)	)	PUNCT
ejpam-7023	334	22	m	m	VERB
ejpam-7023	334	23	sin(aθ	sin(aθ	NOUN
ejpam-7023	334	24	)	)	PUNCT
ejpam-7023	334	25	=	=	SYM
ejpam-7023	334	26	1	1	NUM
ejpam-7023	334	27	m	m	NOUN
ejpam-7023	334	28	.	.	PUNCT
ejpam-7023	335	1	(	(	PUNCT
ejpam-7023	335	2	60	60	NUM
ejpam-7023	335	3	)	)	PUNCT
ejpam-7023	335	4	substituting	substituting	NOUN
ejpam-7023	335	5	(	(	PUNCT
ejpam-7023	335	6	60	60	NUM
ejpam-7023	335	7	)	)	PUNCT
ejpam-7023	335	8	into	into	ADP
ejpam-7023	335	9	(	(	PUNCT
ejpam-7023	335	10	59	59	NUM
ejpam-7023	335	11	)	)	PUNCT
ejpam-7023	335	12	yields	yield	NOUN
ejpam-7023	335	13	im	im	ADV
ejpam-7023	335	14	,	,	PUNCT
ejpam-7023	335	15	q	q	PROPN
ejpam-7023	335	16	=	=	PUNCT
ejpam-7023	335	17	γ(a	γ(a	PROPN
ejpam-7023	335	18	)	)	PUNCT
ejpam-7023	335	19	,	,	PUNCT
ejpam-7023	335	20	i.e.	i.e.	X
ejpam-7023	335	21	(	(	PUNCT
ejpam-7023	335	22	58	58	NUM
ejpam-7023	335	23	)	)	PUNCT
ejpam-7023	335	24	.	.	PUNCT
ejpam-7023	336	1	convergence	convergence	NOUN
ejpam-7023	336	2	is	be	AUX
ejpam-7023	336	3	ensured	ensure	VERB
ejpam-7023	336	4	because	because	SCONJ
ejpam-7023	336	5	a	a	DET
ejpam-7023	336	6	>	>	SYM
ejpam-7023	336	7	0	0	NUM
ejpam-7023	336	8	implies	imply	VERB
ejpam-7023	336	9	the	the	DET
ejpam-7023	336	10	hypothesis	hypothesis	NOUN
ejpam-7023	336	11	a	a	DET
ejpam-7023	336	12	>	>	X
ejpam-7023	336	13	−1	−1	NOUN
ejpam-7023	336	14	in	in	ADP
ejpam-7023	336	15	theorem	theorem	ADJ
ejpam-7023	336	16	5	5	NUM
ejpam-7023	336	17	.	.	PUNCT
ejpam-7023	336	18	remark	remark	NOUN
ejpam-7023	336	19	2	2	NUM
ejpam-7023	336	20	.	.	PUNCT
ejpam-7023	337	1	the	the	DET
ejpam-7023	337	2	choice	choice	NOUN
ejpam-7023	337	3	of	of	ADP
ejpam-7023	337	4	θ	θ	PROPN
ejpam-7023	337	5	∈	∈	PROPN
ejpam-7023	337	6	(	(	PUNCT
ejpam-7023	337	7	0	0	NUM
ejpam-7023	337	8	,	,	PUNCT
ejpam-7023	337	9	π2	π2	X
ejpam-7023	337	10	)	)	PUNCT
ejpam-7023	337	11	guarantees	guarantee	VERB
ejpam-7023	337	12	α	α	X
ejpam-7023	337	13	>	>	X
ejpam-7023	337	14	0	0	PUNCT
ejpam-7023	337	15	and	and	CCONJ
ejpam-7023	337	16	is	be	AUX
ejpam-7023	337	17	compatible	compatible	ADJ
ejpam-7023	337	18	with	with	ADP
ejpam-7023	337	19	θ	θ	X
ejpam-7023	337	20	=	=	SYM
ejpam-7023	337	21	arctan(β	arctan(β	PROPN
ejpam-7023	337	22	/	/	SYM
ejpam-7023	337	23	α	α	NOUN
ejpam-7023	337	24	)	)	PUNCT
ejpam-7023	337	25	.	.	PUNCT
ejpam-7023	338	1	the	the	DET
ejpam-7023	338	2	representation	representation	NOUN
ejpam-7023	338	3	(	(	PUNCT
ejpam-7023	338	4	58	58	NUM
ejpam-7023	338	5	)	)	PUNCT
ejpam-7023	338	6	uses	use	VERB
ejpam-7023	338	7	only	only	ADV
ejpam-7023	338	8	the	the	DET
ejpam-7023	338	9	freely	freely	ADV
ejpam-7023	338	10	chosen	choose	VERB
ejpam-7023	338	11	numerical	numerical	ADJ
ejpam-7023	338	12	parameters	parameter	NOUN
ejpam-7023	338	13	(	(	PUNCT
ejpam-7023	338	14	m	m	PROPN
ejpam-7023	338	15	,	,	PUNCT
ejpam-7023	338	16	θ	θ	PROPN
ejpam-7023	338	17	)	)	PUNCT
ejpam-7023	338	18	and	and	CCONJ
ejpam-7023	338	19	the	the	DET
ejpam-7023	338	20	target	target	NOUN
ejpam-7023	338	21	parameter	parameter	NOUN
ejpam-7023	338	22	a	a	NOUN
ejpam-7023	338	23	,	,	PUNCT
ejpam-7023	338	24	the	the	DET
ejpam-7023	338	25	constants	constant	NOUN
ejpam-7023	338	26	α	α	NOUN
ejpam-7023	338	27	,	,	PUNCT
ejpam-7023	338	28	β	β	X
ejpam-7023	338	29	are	be	AUX
ejpam-7023	338	30	then	then	ADV
ejpam-7023	338	31	determined	determine	VERB
ejpam-7023	338	32	by	by	ADP
ejpam-7023	338	33	(	(	PUNCT
ejpam-7023	338	34	55	55	NUM
ejpam-7023	338	35	)	)	PUNCT
ejpam-7023	338	36	and	and	CCONJ
ejpam-7023	338	37	do	do	AUX
ejpam-7023	338	38	not	not	PART
ejpam-7023	338	39	involve	involve	VERB
ejpam-7023	338	40	γ(a	γ(a	NOUN
ejpam-7023	338	41	)	)	PUNCT
ejpam-7023	338	42	.	.	PUNCT
ejpam-7023	339	1	corollary	corollary	ADJ
ejpam-7023	339	2	7	7	NUM
ejpam-7023	339	3	(	(	PUNCT
ejpam-7023	339	4	integer	integer	NOUN
ejpam-7023	339	5	case	case	NOUN
ejpam-7023	339	6	a	a	PRON
ejpam-7023	339	7	=	=	NOUN
ejpam-7023	339	8	n	n	SYM
ejpam-7023	339	9	∈	∈	PROPN
ejpam-7023	339	10	n	n	NOUN
ejpam-7023	339	11	with	with	ADP
ejpam-7023	339	12	m	m	PROPN
ejpam-7023	339	13	=	=	NOUN
ejpam-7023	339	14	1	1	NUM
ejpam-7023	339	15	)	)	PUNCT
ejpam-7023	339	16	.	.	PUNCT
ejpam-7023	340	1	let	let	VERB
ejpam-7023	340	2	n	n	PRON
ejpam-7023	340	3	∈	∈	PROPN
ejpam-7023	340	4	n	n	NOUN
ejpam-7023	340	5	and	and	CCONJ
ejpam-7023	340	6	m	m	PROPN
ejpam-7023	340	7	=	=	ADJ
ejpam-7023	340	8	1	1	X
ejpam-7023	340	9	.	.	PUNCT
ejpam-7023	340	10	choose	choose	VERB
ejpam-7023	340	11	any	any	DET
ejpam-7023	340	12	θ	θ	PROPN
ejpam-7023	340	13	∈	∈	PROPN
ejpam-7023	340	14	(	(	PUNCT
ejpam-7023	340	15	0	0	NUM
ejpam-7023	340	16	,	,	PUNCT
ejpam-7023	340	17	π2	π2	NOUN
ejpam-7023	340	18	)	)	PUNCT
ejpam-7023	340	19	and	and	CCONJ
ejpam-7023	340	20	define	define	VERB
ejpam-7023	340	21	α	α	NOUN
ejpam-7023	340	22	=	=	SYM
ejpam-7023	340	23	(	(	PUNCT
ejpam-7023	340	24	sin(nθ	sin(nθ	NUM
ejpam-7023	340	25	)	)	PUNCT
ejpam-7023	340	26	)	)	PUNCT
ejpam-7023	340	27	2	2	NUM
ejpam-7023	340	28	/	/	SYM
ejpam-7023	340	29	n	n	PROPN
ejpam-7023	340	30	cos	cos	PROPN
ejpam-7023	340	31	θ	θ	PROPN
ejpam-7023	340	32	,	,	PUNCT
ejpam-7023	340	33	β	β	X
ejpam-7023	340	34	=	=	SYM
ejpam-7023	340	35	(	(	PUNCT
ejpam-7023	340	36	sin(nθ	sin(nθ	NUM
ejpam-7023	340	37	)	)	PUNCT
ejpam-7023	340	38	)	)	PUNCT
ejpam-7023	340	39	2	2	NUM
ejpam-7023	340	40	/	/	SYM
ejpam-7023	340	41	n	n	PRON
ejpam-7023	340	42	sin	sin	NOUN
ejpam-7023	340	43	θ	θ	PROPN
ejpam-7023	340	44	,	,	PUNCT
ejpam-7023	340	45	k	k	X
ejpam-7023	340	46	=	=	SYM
ejpam-7023	340	47	0	0	NUM
ejpam-7023	340	48	,	,	PUNCT
ejpam-7023	340	49	q	q	NOUN
ejpam-7023	341	1	=	=	PUNCT
ejpam-7023	341	2	n−	n−	NOUN
ejpam-7023	341	3	1	1	NUM
ejpam-7023	341	4	.	.	PUNCT
ejpam-7023	342	1	(	(	PUNCT
ejpam-7023	342	2	61	61	NUM
ejpam-7023	342	3	)	)	PUNCT
ejpam-7023	342	4	then	then	ADV
ejpam-7023	342	5	∫	∫	PROPN
ejpam-7023	343	1	∞	∞	PROPN
ejpam-7023	343	2	0	0	NUM
ejpam-7023	343	3	e−αx	e−αx	NOUN
ejpam-7023	343	4	sin(βx)xn−1	sin(βx)xn−1	ADJ
ejpam-7023	343	5	dx	dx	PROPN
ejpam-7023	343	6	=	=	SYM
ejpam-7023	343	7	γ(n	γ(n	X
ejpam-7023	343	8	)	)	PUNCT
ejpam-7023	344	1	=	=	PUNCT
ejpam-7023	344	2	(	(	PUNCT
ejpam-7023	344	3	n−	n−	NOUN
ejpam-7023	344	4	1	1	NUM
ejpam-7023	344	5	)	)	PUNCT
ejpam-7023	344	6	!	!	PUNCT
ejpam-7023	344	7	.	.	PUNCT
ejpam-7023	345	1	(	(	PUNCT
ejpam-7023	345	2	62	62	NUM
ejpam-7023	345	3	)	)	PUNCT
ejpam-7023	345	4	proof	proof	NOUN
ejpam-7023	345	5	.	.	PUNCT
ejpam-7023	346	1	this	this	PRON
ejpam-7023	346	2	is	be	AUX
ejpam-7023	346	3	theorem	theorem	VERB
ejpam-7023	346	4	7	7	NUM
ejpam-7023	346	5	with	with	ADP
ejpam-7023	346	6	a	a	DET
ejpam-7023	346	7	=	=	SYM
ejpam-7023	346	8	n	n	NOUN
ejpam-7023	346	9	and	and	CCONJ
ejpam-7023	346	10	m	m	PROPN
ejpam-7023	346	11	=	=	ADJ
ejpam-7023	346	12	1	1	NUM
ejpam-7023	346	13	,	,	PUNCT
ejpam-7023	346	14	note	note	VERB
ejpam-7023	346	15	r	r	NOUN
ejpam-7023	346	16	=	=	SYM
ejpam-7023	346	17	(	(	PUNCT
ejpam-7023	346	18	sin(nθ))2	sin(nθ))2	PROPN
ejpam-7023	346	19	/	/	SYM
ejpam-7023	346	20	n	n	PROPN
ejpam-7023	346	21	so	so	SCONJ
ejpam-7023	346	22	that	that	SCONJ
ejpam-7023	346	23	rn/2	rn/2	NOUN
ejpam-7023	346	24	=	=	SYM
ejpam-7023	346	25	sin(nθ	sin(nθ	X
ejpam-7023	346	26	)	)	PUNCT
ejpam-7023	346	27	and	and	CCONJ
ejpam-7023	346	28	(	(	PUNCT
ejpam-7023	346	29	60	60	NUM
ejpam-7023	346	30	)	)	PUNCT
ejpam-7023	346	31	holds	hold	VERB
ejpam-7023	346	32	.	.	PUNCT
ejpam-7023	347	1	i.	i.	PROPN
ejpam-7023	347	2	ayoob	ayoob	PROPN
ejpam-7023	347	3	/	/	SYM
ejpam-7023	347	4	eur	eur	PROPN
ejpam-7023	347	5	.	.	PUNCT
ejpam-7023	348	1	j.	j.	PROPN
ejpam-7023	348	2	pure	pure	PROPN
ejpam-7023	348	3	appl	appl	PROPN
ejpam-7023	348	4	.	.	PROPN
ejpam-7023	348	5	math	math	PROPN
ejpam-7023	348	6	,	,	PUNCT
ejpam-7023	348	7	18	18	NUM
ejpam-7023	348	8	(	(	PUNCT
ejpam-7023	348	9	4	4	NUM
ejpam-7023	348	10	)	)	PUNCT
ejpam-7023	348	11	(	(	PUNCT
ejpam-7023	348	12	2025	2025	NUM
ejpam-7023	348	13	)	)	PUNCT
ejpam-7023	348	14	,	,	PUNCT
ejpam-7023	348	15	7023	7023	NUM
ejpam-7023	348	16	14	14	NUM
ejpam-7023	348	17	of	of	ADP
ejpam-7023	348	18	16	16	NUM
ejpam-7023	348	19	corollary	corollary	ADJ
ejpam-7023	348	20	8	8	NUM
ejpam-7023	348	21	(	(	PUNCT
ejpam-7023	348	22	half	half	ADJ
ejpam-7023	348	23	–	–	PUNCT
ejpam-7023	348	24	integer	integer	NOUN
ejpam-7023	348	25	case	case	NOUN
ejpam-7023	348	26	a	a	DET
ejpam-7023	348	27	=	=	SYM
ejpam-7023	348	28	ℓ	ℓ	NOUN
ejpam-7023	348	29	+	+	NOUN
ejpam-7023	348	30	1	1	NUM
ejpam-7023	348	31	2	2	NUM
ejpam-7023	348	32	)	)	PUNCT
ejpam-7023	348	33	.	.	PUNCT
ejpam-7023	349	1	let	let	VERB
ejpam-7023	349	2	ℓ	ℓ	INTJ
ejpam-7023	349	3	>	>	X
ejpam-7023	349	4	0	0	PROPN
ejpam-7023	350	1	and	and	CCONJ
ejpam-7023	350	2	a	a	DET
ejpam-7023	350	3	=	=	SYM
ejpam-7023	350	4	ℓ	ℓ	NOUN
ejpam-7023	350	5	+	+	NOUN
ejpam-7023	350	6	1	1	NUM
ejpam-7023	350	7	2	2	NUM
ejpam-7023	350	8	,	,	PUNCT
ejpam-7023	350	9	m	m	VERB
ejpam-7023	350	10	=	=	NOUN
ejpam-7023	350	11	1	1	X
ejpam-7023	350	12	.	.	PUNCT
ejpam-7023	351	1	choosing	choose	VERB
ejpam-7023	351	2	any	any	DET
ejpam-7023	351	3	θ	θ	PROPN
ejpam-7023	351	4	∈	∈	PROPN
ejpam-7023	351	5	(	(	PUNCT
ejpam-7023	351	6	0	0	NUM
ejpam-7023	351	7	,	,	PUNCT
ejpam-7023	351	8	π2	π2	NOUN
ejpam-7023	351	9	)	)	PUNCT
ejpam-7023	351	10	and	and	CCONJ
ejpam-7023	351	11	α	α	NOUN
ejpam-7023	351	12	=	=	SYM
ejpam-7023	351	13	(	(	PUNCT
ejpam-7023	351	14	sin(aθ	sin(aθ	NOUN
ejpam-7023	351	15	)	)	PUNCT
ejpam-7023	351	16	)	)	PUNCT
ejpam-7023	351	17	2	2	X
ejpam-7023	351	18	/	/	SYM
ejpam-7023	351	19	a	a	DET
ejpam-7023	351	20	cos	cos	PROPN
ejpam-7023	351	21	θ	θ	PROPN
ejpam-7023	351	22	,	,	PUNCT
ejpam-7023	351	23	β	β	X
ejpam-7023	351	24	=	=	SYM
ejpam-7023	351	25	(	(	PUNCT
ejpam-7023	351	26	sin(aθ	sin(aθ	NOUN
ejpam-7023	351	27	)	)	PUNCT
ejpam-7023	351	28	)	)	PUNCT
ejpam-7023	352	1	2	2	X
ejpam-7023	352	2	/	/	SYM
ejpam-7023	352	3	a	a	DET
ejpam-7023	352	4	sin	sin	NOUN
ejpam-7023	352	5	θ	θ	NOUN
ejpam-7023	352	6	,	,	PUNCT
ejpam-7023	352	7	k	k	NOUN
ejpam-7023	352	8	=	=	SYM
ejpam-7023	352	9	0	0	NUM
ejpam-7023	352	10	,	,	PUNCT
ejpam-7023	352	11	q	q	NOUN
ejpam-7023	352	12	=	=	SYM
ejpam-7023	352	13	a−	a−	PROPN
ejpam-7023	352	14	1	1	NUM
ejpam-7023	352	15	,	,	PUNCT
ejpam-7023	352	16	(	(	PUNCT
ejpam-7023	352	17	63	63	NUM
ejpam-7023	352	18	)	)	PUNCT
ejpam-7023	352	19	one	one	NOUN
ejpam-7023	352	20	obtains	obtain	VERB
ejpam-7023	352	21	∫	∫	PROPN
ejpam-7023	352	22	∞	∞	NUM
ejpam-7023	352	23	0	0	NUM
ejpam-7023	352	24	e−αx	e−αx	NOUN
ejpam-7023	352	25	sin(βx)xa−1	sin(βx)xa−1	NOUN
ejpam-7023	352	26	dx	dx	PROPN
ejpam-7023	352	27	=	=	SYM
ejpam-7023	352	28	γ	γ	X
ejpam-7023	352	29	(	(	PUNCT
ejpam-7023	352	30	ℓ+	ℓ+	X
ejpam-7023	352	31	1	1	NUM
ejpam-7023	352	32	2	2	NUM
ejpam-7023	352	33	)	)	PUNCT
ejpam-7023	352	34	=	=	SYM
ejpam-7023	352	35	(	(	PUNCT
ejpam-7023	352	36	2ℓ	2ℓ	PROPN
ejpam-7023	352	37	)	)	PUNCT
ejpam-7023	352	38	!	!	PUNCT
ejpam-7023	353	1	4ℓ	4ℓ	PROPN
ejpam-7023	353	2	ℓ	ℓ	INTJ
ejpam-7023	353	3	!	!	PUNCT
ejpam-7023	353	4	√	√	PROPN
ejpam-7023	354	1	π	π	PROPN
ejpam-7023	354	2	(	(	PUNCT
ejpam-7023	354	3	ℓ	ℓ	PROPN
ejpam-7023	354	4	∈	∈	PROPN
ejpam-7023	354	5	1	1	NUM
ejpam-7023	354	6	2n	2n	NUM
ejpam-7023	354	7	)	)	PUNCT
ejpam-7023	354	8	.	.	PUNCT
ejpam-7023	355	1	(	(	PUNCT
ejpam-7023	355	2	64	64	NUM
ejpam-7023	355	3	)	)	PUNCT
ejpam-7023	355	4	proof	proof	NOUN
ejpam-7023	355	5	.	.	PUNCT
ejpam-7023	356	1	immediate	immediate	ADJ
ejpam-7023	356	2	from	from	ADP
ejpam-7023	356	3	theorem	theorem	NOUN
ejpam-7023	356	4	7	7	NUM
ejpam-7023	356	5	with	with	ADP
ejpam-7023	356	6	m	m	PROPN
ejpam-7023	356	7	=	=	SYM
ejpam-7023	356	8	1	1	NUM
ejpam-7023	356	9	,	,	PUNCT
ejpam-7023	356	10	a	a	PRON
ejpam-7023	356	11	=	=	X
ejpam-7023	356	12	ℓ+	ℓ+	PUNCT
ejpam-7023	356	13	1	1	NUM
ejpam-7023	356	14	2	2	NUM
ejpam-7023	356	15	.	.	PUNCT
ejpam-7023	357	1	corollary	corollary	ADJ
ejpam-7023	357	2	9	9	NUM
ejpam-7023	357	3	.	.	PUNCT
ejpam-7023	358	1	let	let	VERB
ejpam-7023	358	2	a	a	DET
ejpam-7023	358	3	>	>	SYM
ejpam-7023	358	4	1	1	NUM
ejpam-7023	358	5	and	and	CCONJ
ejpam-7023	358	6	θ	θ	NOUN
ejpam-7023	358	7	=	=	PUNCT
ejpam-7023	359	1	π	π	X
ejpam-7023	359	2	2a	2a	NUM
ejpam-7023	359	3	∈	∈	PROPN
ejpam-7023	359	4	(	(	PUNCT
ejpam-7023	359	5	0	0	NUM
ejpam-7023	359	6	,	,	PUNCT
ejpam-7023	359	7	π2	π2	NOUN
ejpam-7023	359	8	)	)	PUNCT
ejpam-7023	359	9	.	.	PUNCT
ejpam-7023	360	1	for	for	ADP
ejpam-7023	360	2	any	any	DET
ejpam-7023	360	3	m	m	NOUN
ejpam-7023	360	4	>	>	X
ejpam-7023	360	5	0	0	NUM
ejpam-7023	360	6	,	,	PUNCT
ejpam-7023	360	7	set	set	VERB
ejpam-7023	360	8	α	α	NOUN
ejpam-7023	360	9	=	=	SYM
ejpam-7023	360	10	m1	m1	PROPN
ejpam-7023	360	11	/	/	SYM
ejpam-7023	360	12	a	a	DET
ejpam-7023	360	13	cos	cos	PROPN
ejpam-7023	360	14	(	(	PUNCT
ejpam-7023	360	15	π	π	PROPN
ejpam-7023	360	16	2a	2a	NUM
ejpam-7023	360	17	)	)	PUNCT
ejpam-7023	360	18	,	,	PUNCT
ejpam-7023	360	19	β	β	X
ejpam-7023	360	20	=	=	SYM
ejpam-7023	360	21	m1	m1	PROPN
ejpam-7023	360	22	/	/	SYM
ejpam-7023	360	23	a	a	DET
ejpam-7023	360	24	sin	sin	NOUN
ejpam-7023	360	25	(	(	PUNCT
ejpam-7023	360	26	π	π	PROPN
ejpam-7023	360	27	2a	2a	NUM
ejpam-7023	360	28	)	)	PUNCT
ejpam-7023	360	29	,	,	PUNCT
ejpam-7023	360	30	k	k	X
ejpam-7023	361	1	=	=	SYM
ejpam-7023	361	2	0	0	NUM
ejpam-7023	361	3	,	,	PUNCT
ejpam-7023	361	4	q	q	NOUN
ejpam-7023	361	5	=	=	NOUN
ejpam-7023	361	6	a−m	a−m	NOUN
ejpam-7023	361	7	.	.	PUNCT
ejpam-7023	362	1	(	(	PUNCT
ejpam-7023	362	2	65	65	NUM
ejpam-7023	362	3	)	)	PUNCT
ejpam-7023	362	4	then	then	ADV
ejpam-7023	362	5	sin(aθ	sin(aθ	VERB
ejpam-7023	362	6	)	)	PUNCT
ejpam-7023	362	7	=	=	SYM
ejpam-7023	363	1	1	1	NUM
ejpam-7023	363	2	and	and	CCONJ
ejpam-7023	363	3	r	r	NOUN
ejpam-7023	363	4	=	=	SYM
ejpam-7023	363	5	α2	α2	ADJ
ejpam-7023	363	6	+	+	CCONJ
ejpam-7023	363	7	β2	β2	NOUN
ejpam-7023	363	8	=	=	SYM
ejpam-7023	363	9	m2	m2	PROPN
ejpam-7023	363	10	/	/	SYM
ejpam-7023	363	11	a	a	PROPN
ejpam-7023	363	12	,	,	PUNCT
ejpam-7023	363	13	so∫	so∫	PROPN
ejpam-7023	363	14	∞	∞	PROPN
ejpam-7023	363	15	0	0	NUM
ejpam-7023	363	16	e−αx1	e−αx1	PROPN
ejpam-7023	363	17	/	/	SYM
ejpam-7023	363	18	m	m	NOUN
ejpam-7023	363	19	sin	sin	NOUN
ejpam-7023	363	20	(	(	PUNCT
ejpam-7023	363	21	βx1	βx1	PROPN
ejpam-7023	363	22	/	/	SYM
ejpam-7023	363	23	m	m	NOUN
ejpam-7023	363	24	)	)	PUNCT
ejpam-7023	363	25	x	x	X
ejpam-7023	364	1	a	a	DET
ejpam-7023	364	2	m	m	NOUN
ejpam-7023	364	3	−1	−1	NOUN
ejpam-7023	364	4	dx	dx	PROPN
ejpam-7023	364	5	=	=	SYM
ejpam-7023	364	6	γ(a	γ(a	PROPN
ejpam-7023	364	7	)	)	PUNCT
ejpam-7023	364	8	.	.	PUNCT
ejpam-7023	365	1	(	(	PUNCT
ejpam-7023	365	2	66	66	NUM
ejpam-7023	365	3	)	)	PUNCT
ejpam-7023	365	4	proof	proof	NOUN
ejpam-7023	365	5	.	.	PUNCT
ejpam-7023	366	1	here	here	ADV
ejpam-7023	366	2	ra/2	ra/2	PROPN
ejpam-7023	366	3	=	=	PROPN
ejpam-7023	366	4	m	m	NOUN
ejpam-7023	366	5	and	and	CCONJ
ejpam-7023	366	6	sin(aθ	sin(aθ	ADJ
ejpam-7023	366	7	)	)	PUNCT
ejpam-7023	366	8	=	=	SYM
ejpam-7023	366	9	1	1	NUM
ejpam-7023	366	10	,	,	PUNCT
ejpam-7023	366	11	(	(	PUNCT
ejpam-7023	366	12	59	59	NUM
ejpam-7023	366	13	)	)	PUNCT
ejpam-7023	366	14	yields	yield	NOUN
ejpam-7023	366	15	im	im	ADV
ejpam-7023	366	16	,	,	PUNCT
ejpam-7023	366	17	q	q	X
ejpam-7023	366	18	=	=	SYM
ejpam-7023	366	19	mγ(a)m−1	mγ(a)m−1	PROPN
ejpam-7023	366	20	·	·	PUNCT
ejpam-7023	366	21	1	1	NUM
ejpam-7023	366	22	=	=	SYM
ejpam-7023	366	23	γ(a	γ(a	PROPN
ejpam-7023	366	24	)	)	PUNCT
ejpam-7023	366	25	.	.	PUNCT
ejpam-7023	367	1	3	3	X
ejpam-7023	367	2	.	.	X
ejpam-7023	367	3	conclusion	conclusion	NOUN
ejpam-7023	367	4	motivated	motivate	VERB
ejpam-7023	367	5	by	by	ADP
ejpam-7023	367	6	stieltjes	stieltjes	NOUN
ejpam-7023	367	7	’	'	PUNCT
ejpam-7023	367	8	classical	classical	ADJ
ejpam-7023	367	9	counterexample	counterexample	NOUN
ejpam-7023	367	10	in	in	ADP
ejpam-7023	367	11	the	the	DET
ejpam-7023	367	12	(	(	PUNCT
ejpam-7023	367	13	indeterminate	indeterminate	ADJ
ejpam-7023	367	14	)	)	PUNCT
ejpam-7023	367	15	stieltjes	stieltjes	NOUN
ejpam-7023	367	16	moment	moment	NOUN
ejpam-7023	367	17	problem	problem	NOUN
ejpam-7023	367	18	,	,	PUNCT
ejpam-7023	367	19	we	we	PRON
ejpam-7023	367	20	revisited	revisit	VERB
ejpam-7023	367	21	the	the	DET
ejpam-7023	367	22	kernel	kernel	PROPN
ejpam-7023	367	23	f(x	f(x	PROPN
ejpam-7023	367	24	)	)	PUNCT
ejpam-7023	368	1	=	=	PUNCT
ejpam-7023	368	2	e−x1/4	e−x1/4	PROPN
ejpam-7023	368	3	sin	sin	NOUN
ejpam-7023	368	4	(	(	PUNCT
ejpam-7023	368	5	x1/4	x1/4	PROPN
ejpam-7023	368	6	)	)	PUNCT
ejpam-7023	368	7	and	and	CCONJ
ejpam-7023	368	8	evaluated	evaluate	VERB
ejpam-7023	368	9	its	its	PRON
ejpam-7023	368	10	moments	moment	NOUN
ejpam-7023	368	11	against	against	ADP
ejpam-7023	368	12	continuous	continuous	ADJ
ejpam-7023	368	13	powers	power	NOUN
ejpam-7023	368	14	.	.	PUNCT
ejpam-7023	369	1	theorem	theorem	NOUN
ejpam-7023	369	2	4	4	NUM
ejpam-7023	369	3	gives	give	VERB
ejpam-7023	369	4	the	the	DET
ejpam-7023	369	5	exact	exact	ADJ
ejpam-7023	369	6	formula	formula	NOUN
ejpam-7023	369	7	i(k	i(k	PROPN
ejpam-7023	369	8	)	)	PUNCT
ejpam-7023	370	1	=	=	SYM
ejpam-7023	370	2	∫	∫	PROPN
ejpam-7023	371	1	∞	∞	NUM
ejpam-7023	371	2	0	0	NUM
ejpam-7023	372	1	e−x1/4	e−x1/4	PROPN
ejpam-7023	372	2	sin	sin	NOUN
ejpam-7023	372	3	(	(	PUNCT
ejpam-7023	372	4	x1/4	x1/4	PROPN
ejpam-7023	372	5	)	)	PUNCT
ejpam-7023	373	1	xk	xk	PROPN
ejpam-7023	373	2	dx	dx	PROPN
ejpam-7023	373	3	=	=	PUNCT
ejpam-7023	373	4	2−2kγ(4k	2−2kγ(4k	NUM
ejpam-7023	373	5	+	+	CCONJ
ejpam-7023	373	6	4	4	X
ejpam-7023	373	7	)	)	PUNCT
ejpam-7023	373	8	sin	sin	NOUN
ejpam-7023	373	9	(	(	PUNCT
ejpam-7023	373	10	(	(	PUNCT
ejpam-7023	373	11	k	k	X
ejpam-7023	373	12	+	+	PROPN
ejpam-7023	373	13	1)π	1)π	NUM
ejpam-7023	373	14	)	)	PUNCT
ejpam-7023	373	15	,	,	PUNCT
ejpam-7023	373	16	from	from	ADP
ejpam-7023	373	17	which	which	PRON
ejpam-7023	373	18	it	it	PRON
ejpam-7023	373	19	follows	follow	VERB
ejpam-7023	373	20	that	that	SCONJ
ejpam-7023	373	21	i(k	i(k	PROPN
ejpam-7023	373	22	)	)	PUNCT
ejpam-7023	373	23	=	=	SYM
ejpam-7023	373	24	0	0	PUNCT
ejpam-7023	374	1	if	if	SCONJ
ejpam-7023	374	2	and	and	CCONJ
ejpam-7023	374	3	only	only	ADV
ejpam-7023	374	4	if	if	SCONJ
ejpam-7023	374	5	k	k	PROPN
ejpam-7023	374	6	∈	∈	PROPN
ejpam-7023	374	7	z≥0	z≥0	PROPN
ejpam-7023	374	8	.	.	PUNCT
ejpam-7023	375	1	this	this	DET
ejpam-7023	375	2	settles	settle	NOUN
ejpam-7023	375	3	,	,	PUNCT
ejpam-7023	375	4	in	in	ADP
ejpam-7023	375	5	the	the	DET
ejpam-7023	375	6	affirmative	affirmative	NOUN
ejpam-7023	375	7	and	and	CCONJ
ejpam-7023	375	8	with	with	ADP
ejpam-7023	375	9	a	a	DET
ejpam-7023	375	10	complete	complete	ADJ
ejpam-7023	375	11	characterization	characterization	NOUN
ejpam-7023	375	12	,	,	PUNCT
ejpam-7023	375	13	the	the	DET
ejpam-7023	375	14	question	question	NOUN
ejpam-7023	375	15	of	of	ADP
ejpam-7023	375	16	which	which	DET
ejpam-7023	375	17	non	non	ADJ
ejpam-7023	375	18	-	-	ADJ
ejpam-7023	375	19	negative	negative	ADJ
ejpam-7023	375	20	real	real	ADJ
ejpam-7023	375	21	exponents	exponent	NOUN
ejpam-7023	375	22	yield	yield	VERB
ejpam-7023	375	23	vanishing	vanish	VERB
ejpam-7023	375	24	moments	moment	NOUN
ejpam-7023	375	25	for	for	ADP
ejpam-7023	375	26	the	the	DET
ejpam-7023	375	27	stieltjes	stieltjes	PROPN
ejpam-7023	375	28	kernel	kernel	PROPN
ejpam-7023	375	29	.	.	PUNCT
ejpam-7023	376	1	we	we	PRON
ejpam-7023	376	2	then	then	ADV
ejpam-7023	376	3	proved	prove	VERB
ejpam-7023	376	4	a	a	DET
ejpam-7023	376	5	generalization	generalization	NOUN
ejpam-7023	376	6	(	(	PUNCT
ejpam-7023	376	7	theorem	theorem	NOUN
ejpam-7023	376	8	5	5	NUM
ejpam-7023	376	9	)	)	PUNCT
ejpam-7023	376	10	to	to	ADP
ejpam-7023	376	11	the	the	DET
ejpam-7023	376	12	family	family	NOUN
ejpam-7023	376	13	im	im	ADV
ejpam-7023	376	14	,	,	PUNCT
ejpam-7023	376	15	q(k	q(k	PROPN
ejpam-7023	376	16	,	,	PUNCT
ejpam-7023	376	17	α	α	X
ejpam-7023	376	18	,	,	PUNCT
ejpam-7023	376	19	β	β	NOUN
ejpam-7023	376	20	)	)	PUNCT
ejpam-7023	376	21	=	=	SYM
ejpam-7023	377	1	∫	∫	PROPN
ejpam-7023	377	2	∞	∞	NUM
ejpam-7023	377	3	0	0	NUM
ejpam-7023	377	4	e−αx1	e−αx1	PROPN
ejpam-7023	377	5	/	/	SYM
ejpam-7023	377	6	m	m	NOUN
ejpam-7023	377	7	sin	sin	NOUN
ejpam-7023	377	8	(	(	PUNCT
ejpam-7023	377	9	βx1	βx1	PROPN
ejpam-7023	377	10	/	/	SYM
ejpam-7023	377	11	m	m	NOUN
ejpam-7023	377	12	)	)	PUNCT
ejpam-7023	377	13	xk(x1	xk(x1	PROPN
ejpam-7023	377	14	/	/	SYM
ejpam-7023	377	15	m)q	m)q	PROPN
ejpam-7023	377	16	dx	dx	PROPN
ejpam-7023	377	17	,	,	PUNCT
ejpam-7023	377	18	a	a	DET
ejpam-7023	377	19	=	=	X
ejpam-7023	377	20	mk	mk	NOUN
ejpam-7023	377	21	+	+	CCONJ
ejpam-7023	377	22	q	q	PROPN
ejpam-7023	377	23	+	+	NOUN
ejpam-7023	377	24	m	m	X
ejpam-7023	377	25	,	,	PUNCT
ejpam-7023	377	26	establishing	establish	VERB
ejpam-7023	377	27	:	:	PUNCT
ejpam-7023	377	28	(	(	PUNCT
ejpam-7023	377	29	i	i	NOUN
ejpam-7023	377	30	)	)	PUNCT
ejpam-7023	377	31	sharp	sharp	ADJ
ejpam-7023	377	32	convergence	convergence	NOUN
ejpam-7023	377	33	for	for	ADP
ejpam-7023	377	34	a	a	DET
ejpam-7023	377	35	>	>	X
ejpam-7023	377	36	−1	−1	NOUN
ejpam-7023	377	37	,	,	PUNCT
ejpam-7023	377	38	(	(	PUNCT
ejpam-7023	377	39	ii	ii	NOUN
ejpam-7023	377	40	)	)	PUNCT
ejpam-7023	377	41	the	the	DET
ejpam-7023	377	42	closed	closed	ADJ
ejpam-7023	377	43	form	form	NOUN
ejpam-7023	377	44	im	im	PRON
ejpam-7023	377	45	,	,	PUNCT
ejpam-7023	377	46	q	q	X
ejpam-7023	377	47	=	=	SYM
ejpam-7023	377	48	mγ(a	mγ(a	X
ejpam-7023	377	49	)	)	PUNCT
ejpam-7023	377	50	(	(	PUNCT
ejpam-7023	377	51	α2	α2	ADJ
ejpam-7023	377	52	+	+	CCONJ
ejpam-7023	377	53	β2)−a/2	β2)−a/2	X
ejpam-7023	377	54	sin	sin	NOUN
ejpam-7023	377	55	(	(	PUNCT
ejpam-7023	377	56	a	a	DET
ejpam-7023	377	57	arctan(β	arctan(β	NOUN
ejpam-7023	377	58	/	/	SYM
ejpam-7023	377	59	α	α	NOUN
ejpam-7023	377	60	)	)	PUNCT
ejpam-7023	377	61	)	)	PUNCT
ejpam-7023	377	62	;	;	PUNCT
ejpam-7023	377	63	and	and	CCONJ
ejpam-7023	377	64	(	(	PUNCT
ejpam-7023	377	65	iii	iii	X
ejpam-7023	377	66	)	)	PUNCT
ejpam-7023	377	67	a	a	DET
ejpam-7023	377	68	necessary	necessary	ADJ
ejpam-7023	377	69	and	and	CCONJ
ejpam-7023	377	70	sufficient	sufficient	ADJ
ejpam-7023	377	71	vanishing	vanishing	NOUN
ejpam-7023	377	72	criterion	criterion	NOUN
ejpam-7023	377	73	a	a	DET
ejpam-7023	377	74	arctan(β	arctan(β	NOUN
ejpam-7023	377	75	/	/	SYM
ejpam-7023	377	76	α	α	NOUN
ejpam-7023	377	77	)	)	PUNCT
ejpam-7023	377	78	∈	∈	PROPN
ejpam-7023	377	79	i.	i.	NOUN
ejpam-7023	377	80	ayoob	ayoob	PROPN
ejpam-7023	377	81	/	/	SYM
ejpam-7023	377	82	eur	eur	PROPN
ejpam-7023	377	83	.	.	PUNCT
ejpam-7023	378	1	j.	j.	PROPN
ejpam-7023	378	2	pure	pure	PROPN
ejpam-7023	378	3	appl	appl	PROPN
ejpam-7023	378	4	.	.	PROPN
ejpam-7023	378	5	math	math	PROPN
ejpam-7023	378	6	,	,	PUNCT
ejpam-7023	378	7	18	18	NUM
ejpam-7023	378	8	(	(	PUNCT
ejpam-7023	378	9	4	4	NUM
ejpam-7023	378	10	)	)	PUNCT
ejpam-7023	378	11	(	(	PUNCT
ejpam-7023	378	12	2025	2025	NUM
ejpam-7023	378	13	)	)	PUNCT
ejpam-7023	378	14	,	,	PUNCT
ejpam-7023	378	15	7023	7023	NUM
ejpam-7023	378	16	15	15	NUM
ejpam-7023	378	17	of	of	ADP
ejpam-7023	378	18	16	16	NUM
ejpam-7023	378	19	πz	πz	NOUN
ejpam-7023	378	20	.	.	PUNCT
ejpam-7023	379	1	a	a	DET
ejpam-7023	379	2	parallel	parallel	ADJ
ejpam-7023	379	3	cosine	cosine	NOUN
ejpam-7023	379	4	variant	variant	NOUN
ejpam-7023	379	5	(	(	PUNCT
ejpam-7023	379	6	theorem	theorem	VERB
ejpam-7023	379	7	6	6	NUM
ejpam-7023	379	8	)	)	PUNCT
ejpam-7023	379	9	yields	yield	NOUN
ejpam-7023	379	10	jm	jm	PROPN
ejpam-7023	379	11	,	,	PUNCT
ejpam-7023	379	12	q	q	NOUN
ejpam-7023	379	13	=	=	SYM
ejpam-7023	379	14	mγ(a	mγ(a	X
ejpam-7023	379	15	)	)	PUNCT
ejpam-7023	379	16	(	(	PUNCT
ejpam-7023	379	17	α2+β2)−a/2	α2+β2)−a/2	PROPN
ejpam-7023	379	18	cos	cos	PROPN
ejpam-7023	379	19	(	(	PUNCT
ejpam-7023	379	20	a	a	DET
ejpam-7023	379	21	arctan(β	arctan(β	NOUN
ejpam-7023	379	22	/	/	SYM
ejpam-7023	379	23	α	α	NOUN
ejpam-7023	379	24	)	)	PUNCT
ejpam-7023	379	25	)	)	PUNCT
ejpam-7023	379	26	with	with	ADP
ejpam-7023	379	27	the	the	DET
ejpam-7023	379	28	expected	expect	VERB
ejpam-7023	379	29	zero	zero	NUM
ejpam-7023	379	30	set	set	NOUN
ejpam-7023	379	31	cos	cos	PROPN
ejpam-7023	379	32	(	(	PUNCT
ejpam-7023	379	33	a	a	DET
ejpam-7023	379	34	arctan(β	arctan(β	NOUN
ejpam-7023	379	35	/	/	SYM
ejpam-7023	379	36	α	α	NOUN
ejpam-7023	379	37	)	)	PUNCT
ejpam-7023	379	38	)	)	PUNCT
ejpam-7023	380	1	=	=	PUNCT
ejpam-7023	380	2	0	0	X
ejpam-7023	380	3	.	.	PUNCT
ejpam-7023	381	1	a	a	DET
ejpam-7023	381	2	particularly	particularly	ADV
ejpam-7023	381	3	effective	effective	ADJ
ejpam-7023	381	4	parameterization	parameterization	NOUN
ejpam-7023	381	5	(	(	PUNCT
ejpam-7023	381	6	corollary	corollary	ADJ
ejpam-7023	381	7	5	5	NUM
ejpam-7023	381	8	)	)	PUNCT
ejpam-7023	381	9	,	,	PUNCT
ejpam-7023	381	10	taking	take	VERB
ejpam-7023	381	11	θ	θ	X
ejpam-7023	381	12	=	=	PUNCT
ejpam-7023	381	13	π	π	X
ejpam-7023	381	14	/	/	SYM
ejpam-7023	381	15	m	m	PROPN
ejpam-7023	381	16	,	,	PUNCT
ejpam-7023	381	17	β	β	X
ejpam-7023	381	18	=	=	SYM
ejpam-7023	381	19	α	α	PROPN
ejpam-7023	381	20	tan	tan	PROPN
ejpam-7023	381	21	θ	θ	PROPN
ejpam-7023	381	22	,	,	PUNCT
ejpam-7023	381	23	and	and	CCONJ
ejpam-7023	381	24	q	q	NOUN
ejpam-7023	381	25	=	=	SYM
ejpam-7023	381	26	−m/2	−m/2	NOUN
ejpam-7023	381	27	,	,	PUNCT
ejpam-7023	381	28	forces	force	NOUN
ejpam-7023	381	29	jm	jm	PROPN
ejpam-7023	381	30	,	,	PUNCT
ejpam-7023	381	31	q(k	q(k	PROPN
ejpam-7023	381	32	,	,	PUNCT
ejpam-7023	381	33	α	α	X
ejpam-7023	381	34	,	,	PUNCT
ejpam-7023	381	35	β	β	NOUN
ejpam-7023	381	36	)	)	PUNCT
ejpam-7023	381	37	=	=	SYM
ejpam-7023	381	38	0	0	NUM
ejpam-7023	381	39	⇐	⇐	ADJ
ejpam-7023	381	40	⇒	⇒	PROPN
ejpam-7023	381	41	k	k	PROPN
ejpam-7023	381	42	∈	∈	PROPN
ejpam-7023	381	43	z≥0	z≥0	PROPN
ejpam-7023	381	44	,	,	PUNCT
ejpam-7023	381	45	thus	thus	ADV
ejpam-7023	381	46	providing	provide	VERB
ejpam-7023	381	47	a	a	DET
ejpam-7023	381	48	cosine	cosine	NOUN
ejpam-7023	381	49	analogue	analogue	NOUN
ejpam-7023	381	50	that	that	PRON
ejpam-7023	381	51	vanishes	vanish	VERB
ejpam-7023	381	52	exactly	exactly	ADV
ejpam-7023	381	53	at	at	ADP
ejpam-7023	381	54	the	the	DET
ejpam-7023	381	55	nonnegative	nonnegative	ADJ
ejpam-7023	381	56	integers	integer	NOUN
ejpam-7023	381	57	.	.	PUNCT
ejpam-7023	382	1	beyond	beyond	ADP
ejpam-7023	382	2	vanishing	vanish	VERB
ejpam-7023	382	3	criteria	criterion	NOUN
ejpam-7023	382	4	,	,	PUNCT
ejpam-7023	382	5	we	we	PRON
ejpam-7023	382	6	showed	show	VERB
ejpam-7023	382	7	that	that	SCONJ
ejpam-7023	382	8	this	this	DET
ejpam-7023	382	9	framework	framework	NOUN
ejpam-7023	382	10	generates	generate	VERB
ejpam-7023	382	11	gamma	gamma	NOUN
ejpam-7023	382	12	values	value	NOUN
ejpam-7023	382	13	.	.	PUNCT
ejpam-7023	383	1	theorem	theorem	VERB
ejpam-7023	383	2	7	7	NUM
ejpam-7023	383	3	prescribes	prescribe	NOUN
ejpam-7023	383	4	(	(	PUNCT
ejpam-7023	383	5	α	α	X
ejpam-7023	383	6	,	,	PUNCT
ejpam-7023	383	7	β	β	NOUN
ejpam-7023	383	8	)	)	PUNCT
ejpam-7023	383	9	via	via	ADP
ejpam-7023	383	10	r	r	NOUN
ejpam-7023	383	11	=	=	SYM
ejpam-7023	383	12	(	(	PUNCT
ejpam-7023	383	13	m	m	PROPN
ejpam-7023	383	14	sin(aθ))2	sin(aθ))2	PROPN
ejpam-7023	383	15	/	/	SYM
ejpam-7023	383	16	a	a	PRON
ejpam-7023	383	17	to	to	PART
ejpam-7023	383	18	give	give	VERB
ejpam-7023	383	19	the	the	DET
ejpam-7023	383	20	exact	exact	ADJ
ejpam-7023	383	21	representation.∫	representation.∫	NOUN
ejpam-7023	383	22	∞	∞	PROPN
ejpam-7023	383	23	0	0	NUM
ejpam-7023	383	24	e−αx1	e−αx1	PROPN
ejpam-7023	383	25	/	/	SYM
ejpam-7023	383	26	m	m	NOUN
ejpam-7023	383	27	sin	sin	NOUN
ejpam-7023	383	28	(	(	PUNCT
ejpam-7023	383	29	βx1	βx1	PROPN
ejpam-7023	383	30	/	/	SYM
ejpam-7023	383	31	m	m	NOUN
ejpam-7023	383	32	)	)	PUNCT
ejpam-7023	384	1	xa	xa	PROPN
ejpam-7023	384	2	/	/	SYM
ejpam-7023	384	3	m−1	m−1	PROPN
ejpam-7023	384	4	dx	dx	PROPN
ejpam-7023	384	5	=	=	SYM
ejpam-7023	384	6	γ(a	γ(a	PROPN
ejpam-7023	384	7	)	)	PUNCT
ejpam-7023	384	8	,	,	PUNCT
ejpam-7023	384	9	from	from	ADP
ejpam-7023	384	10	which	which	PRON
ejpam-7023	384	11	the	the	DET
ejpam-7023	384	12	integer	integer	NOUN
ejpam-7023	384	13	and	and	CCONJ
ejpam-7023	384	14	half	half	ADJ
ejpam-7023	384	15	-	-	PUNCT
ejpam-7023	384	16	integer	integer	NOUN
ejpam-7023	384	17	cases	case	NOUN
ejpam-7023	384	18	follow	follow	VERB
ejpam-7023	384	19	transparently	transparently	ADV
ejpam-7023	384	20	,	,	PUNCT
ejpam-7023	384	21	recovering	recover	VERB
ejpam-7023	384	22	factorials	factorial	NOUN
ejpam-7023	384	23	and	and	CCONJ
ejpam-7023	384	24	√	√	NUM
ejpam-7023	384	25	π	π	PROPN
ejpam-7023	384	26	factors	factor	NOUN
ejpam-7023	384	27	in	in	ADP
ejpam-7023	384	28	a	a	DET
ejpam-7023	384	29	unified	unified	ADJ
ejpam-7023	384	30	way	way	NOUN
ejpam-7023	384	31	.	.	PUNCT
ejpam-7023	385	1	this	this	DET
ejpam-7023	385	2	paper	paper	NOUN
ejpam-7023	385	3	also	also	ADV
ejpam-7023	385	4	includes	include	VERB
ejpam-7023	385	5	a	a	DET
ejpam-7023	385	6	brief	brief	ADJ
ejpam-7023	385	7	discussion	discussion	NOUN
ejpam-7023	385	8	of	of	ADP
ejpam-7023	385	9	salem	salem	NOUN
ejpam-7023	385	10	’s	’s	PART
ejpam-7023	385	11	equivalence	equivalence	NOUN
ejpam-7023	385	12	of	of	ADP
ejpam-7023	385	13	the	the	DET
ejpam-7023	385	14	riemann	riemann	PROPN
ejpam-7023	385	15	hypothesis	hypothesis	NOUN
ejpam-7023	385	16	,	,	PUNCT
ejpam-7023	385	17	which	which	PRON
ejpam-7023	385	18	is	be	AUX
ejpam-7023	385	19	based	base	VERB
ejpam-7023	385	20	on	on	ADP
ejpam-7023	385	21	the	the	DET
ejpam-7023	385	22	vanishing	vanishing	NOUN
ejpam-7023	385	23	of	of	ADP
ejpam-7023	385	24	an	an	DET
ejpam-7023	385	25	integral	integral	ADJ
ejpam-7023	385	26	dependent	dependent	NOUN
ejpam-7023	385	27	on	on	ADP
ejpam-7023	385	28	a	a	DET
ejpam-7023	385	29	continuous	continuous	ADJ
ejpam-7023	385	30	parameter	parameter	NOUN
ejpam-7023	385	31	.	.	PUNCT
ejpam-7023	386	1	acknowledgements	acknowledgement	VERB
ejpam-7023	386	2	the	the	DET
ejpam-7023	386	3	author	author	NOUN
ejpam-7023	386	4	would	would	AUX
ejpam-7023	386	5	like	like	VERB
ejpam-7023	386	6	to	to	PART
ejpam-7023	386	7	thank	thank	VERB
ejpam-7023	386	8	the	the	DET
ejpam-7023	386	9	prince	prince	PROPN
ejpam-7023	386	10	sultan	sultan	PROPN
ejpam-7023	386	11	university	university	PROPN
ejpam-7023	386	12	for	for	ADP
ejpam-7023	386	13	paying	pay	VERB
ejpam-7023	386	14	the	the	DET
ejpam-7023	386	15	publication	publication	NOUN
ejpam-7023	386	16	fees	fee	NOUN
ejpam-7023	386	17	for	for	ADP
ejpam-7023	386	18	this	this	DET
ejpam-7023	386	19	work	work	NOUN
ejpam-7023	386	20	through	through	ADP
ejpam-7023	386	21	tas	ta	NOUN
ejpam-7023	386	22	lab	lab	NOUN
ejpam-7023	386	23	.	.	PUNCT
ejpam-7023	387	1	references	reference	NOUN
ejpam-7023	387	2	[	[	X
ejpam-7023	387	3	1	1	NUM
ejpam-7023	387	4	]	]	X
ejpam-7023	387	5	i.	i.	PROPN
ejpam-7023	387	6	s.	s.	PROPN
ejpam-7023	387	7	gradshteyn	gradshteyn	PROPN
ejpam-7023	387	8	and	and	CCONJ
ejpam-7023	387	9	i.	i.	PROPN
ejpam-7023	387	10	m.	m.	PROPN
ejpam-7023	387	11	ryzhik	ryzhik	PROPN
ejpam-7023	387	12	.	.	PUNCT
ejpam-7023	388	1	table	table	NOUN
ejpam-7023	388	2	of	of	ADP
ejpam-7023	388	3	integrals	integral	NOUN
ejpam-7023	388	4	,	,	PUNCT
ejpam-7023	388	5	series	series	NOUN
ejpam-7023	388	6	,	,	PUNCT
ejpam-7023	388	7	and	and	CCONJ
ejpam-7023	388	8	products	product	NOUN
ejpam-7023	388	9	.	.	PUNCT
ejpam-7023	389	1	academic	academic	ADJ
ejpam-7023	389	2	press	press	NOUN
ejpam-7023	389	3	,	,	PUNCT
ejpam-7023	389	4	new	new	PROPN
ejpam-7023	389	5	york	york	PROPN
ejpam-7023	389	6	,	,	PUNCT
ejpam-7023	389	7	7th	7th	ADJ
ejpam-7023	389	8	edition	edition	NOUN
ejpam-7023	389	9	,	,	PUNCT
ejpam-7023	389	10	2007	2007	NUM
ejpam-7023	389	11	.	.	PUNCT
ejpam-7023	390	1	[	[	X
ejpam-7023	390	2	2	2	X
ejpam-7023	390	3	]	]	PUNCT
ejpam-7023	390	4	christophe	christophe	PROPN
ejpam-7023	390	5	chesneau	chesneau	PROPN
ejpam-7023	390	6	.	.	PUNCT
ejpam-7023	391	1	new	new	ADJ
ejpam-7023	391	2	integral	integral	ADJ
ejpam-7023	391	3	formulas	formula	NOUN
ejpam-7023	391	4	inspired	inspire	VERB
ejpam-7023	391	5	by	by	ADP
ejpam-7023	391	6	an	an	DET
ejpam-7023	391	7	old	old	ADJ
ejpam-7023	391	8	integral	integral	ADJ
ejpam-7023	391	9	result	result	NOUN
ejpam-7023	391	10	.	.	PUNCT
ejpam-7023	392	1	international	international	ADJ
ejpam-7023	392	2	journal	journal	NOUN
ejpam-7023	392	3	of	of	ADP
ejpam-7023	392	4	open	open	ADJ
ejpam-7023	392	5	problems	problem	NOUN
ejpam-7023	392	6	in	in	ADP
ejpam-7023	392	7	computer	computer	NOUN
ejpam-7023	392	8	science	science	NOUN
ejpam-7023	392	9	and	and	CCONJ
ejpam-7023	392	10	mathematics	mathematic	NOUN
ejpam-7023	392	11	,	,	PUNCT
ejpam-7023	392	12	18(2):53	18(2):53	NUM
ejpam-7023	392	13	–	–	PUNCT
ejpam-7023	392	14	71	71	NUM
ejpam-7023	392	15	,	,	PUNCT
ejpam-7023	392	16	2025	2025	NUM
ejpam-7023	392	17	.	.	PUNCT
ejpam-7023	393	1	[	[	X
ejpam-7023	393	2	3	3	X
ejpam-7023	393	3	]	]	X
ejpam-7023	393	4	robert	robert	PROPN
ejpam-7023	393	5	reynolds	reynolds	PROPN
ejpam-7023	393	6	and	and	CCONJ
ejpam-7023	393	7	andrew	andrew	PROPN
ejpam-7023	393	8	stauffer	stauffer	PROPN
ejpam-7023	393	9	.	.	PUNCT
ejpam-7023	394	1	a	a	DET
ejpam-7023	394	2	definite	definite	ADJ
ejpam-7023	394	3	integral	integral	ADJ
ejpam-7023	394	4	involving	involve	VERB
ejpam-7023	394	5	the	the	DET
ejpam-7023	394	6	logarithmic	logarithmic	ADJ
ejpam-7023	394	7	function	function	NOUN
ejpam-7023	394	8	in	in	ADP
ejpam-7023	394	9	terms	term	NOUN
ejpam-7023	394	10	of	of	ADP
ejpam-7023	394	11	the	the	DET
ejpam-7023	394	12	lerch	lerch	PROPN
ejpam-7023	394	13	function	function	PROPN
ejpam-7023	394	14	.	.	PUNCT
ejpam-7023	395	1	mathematics	mathematic	NOUN
ejpam-7023	395	2	,	,	PUNCT
ejpam-7023	395	3	7(1):1–5	7(1):1–5	NUM
ejpam-7023	395	4	,	,	PUNCT
ejpam-7023	395	5	2019	2019	NUM
ejpam-7023	395	6	.	.	PUNCT
ejpam-7023	396	1	[	[	X
ejpam-7023	396	2	4	4	X
ejpam-7023	396	3	]	]	X
ejpam-7023	396	4	robert	robert	PROPN
ejpam-7023	396	5	reynolds	reynolds	PROPN
ejpam-7023	396	6	and	and	CCONJ
ejpam-7023	396	7	andrew	andrew	PROPN
ejpam-7023	396	8	stauffer	stauffer	PROPN
ejpam-7023	396	9	.	.	PUNCT
ejpam-7023	397	1	definite	definite	ADJ
ejpam-7023	397	2	integral	integral	ADJ
ejpam-7023	397	3	of	of	ADP
ejpam-7023	397	4	arctangent	arctangent	NOUN
ejpam-7023	397	5	and	and	CCONJ
ejpam-7023	397	6	polylogarithmic	polylogarithmic	ADJ
ejpam-7023	397	7	functions	function	NOUN
ejpam-7023	397	8	expressed	express	VERB
ejpam-7023	397	9	as	as	ADP
ejpam-7023	397	10	a	a	DET
ejpam-7023	397	11	series	series	NOUN
ejpam-7023	397	12	.	.	PUNCT
ejpam-7023	398	1	mathematics	mathematic	NOUN
ejpam-7023	398	2	,	,	PUNCT
ejpam-7023	398	3	7(7):1–7	7(7):1–7	PROPN
ejpam-7023	398	4	,	,	PUNCT
ejpam-7023	398	5	2019	2019	NUM
ejpam-7023	398	6	.	.	PUNCT
ejpam-7023	399	1	[	[	X
ejpam-7023	399	2	5	5	X
ejpam-7023	399	3	]	]	X
ejpam-7023	399	4	robert	robert	PROPN
ejpam-7023	399	5	reynolds	reynolds	PROPN
ejpam-7023	399	6	and	and	CCONJ
ejpam-7023	399	7	andrew	andrew	PROPN
ejpam-7023	399	8	stauffer	stauffer	PROPN
ejpam-7023	399	9	.	.	PUNCT
ejpam-7023	400	1	derivation	derivation	NOUN
ejpam-7023	400	2	of	of	ADP
ejpam-7023	400	3	logarithmic	logarithmic	ADJ
ejpam-7023	400	4	and	and	CCONJ
ejpam-7023	400	5	logarithmic	logarithmic	ADJ
ejpam-7023	400	6	hyperbolic	hyperbolic	ADJ
ejpam-7023	400	7	tangent	tangent	NOUN
ejpam-7023	400	8	integrals	integral	NOUN
ejpam-7023	400	9	expressed	express	VERB
ejpam-7023	400	10	in	in	ADP
ejpam-7023	400	11	terms	term	NOUN
ejpam-7023	400	12	of	of	ADP
ejpam-7023	400	13	special	special	ADJ
ejpam-7023	400	14	functions	function	NOUN
ejpam-7023	400	15	.	.	PUNCT
ejpam-7023	401	1	mathematics	mathematic	NOUN
ejpam-7023	401	2	,	,	PUNCT
ejpam-7023	401	3	8:1–6	8:1–6	NUM
ejpam-7023	401	4	,	,	PUNCT
ejpam-7023	401	5	2020	2020	NUM
ejpam-7023	401	6	.	.	PUNCT
ejpam-7023	402	1	[	[	X
ejpam-7023	402	2	6	6	NUM
ejpam-7023	402	3	]	]	X
ejpam-7023	402	4	robert	robert	PROPN
ejpam-7023	402	5	reynolds	reynolds	PROPN
ejpam-7023	402	6	and	and	CCONJ
ejpam-7023	402	7	andrew	andrew	PROPN
ejpam-7023	402	8	stauffer	stauffer	PROPN
ejpam-7023	402	9	.	.	PUNCT
ejpam-7023	403	1	a	a	DET
ejpam-7023	403	2	quadruple	quadruple	ADJ
ejpam-7023	403	3	definite	definite	ADJ
ejpam-7023	403	4	integral	integral	NOUN
ejpam-7023	403	5	expressed	express	VERB
ejpam-7023	403	6	in	in	ADP
ejpam-7023	403	7	terms	term	NOUN
ejpam-7023	403	8	of	of	ADP
ejpam-7023	403	9	the	the	DET
ejpam-7023	403	10	lerch	lerch	PROPN
ejpam-7023	403	11	function	function	PROPN
ejpam-7023	403	12	.	.	PUNCT
ejpam-7023	404	1	symmetry	symmetry	PROPN
ejpam-7023	404	2	,	,	PUNCT
ejpam-7023	404	3	13(1):1–8	13(1):1–8	NUM
ejpam-7023	404	4	,	,	PUNCT
ejpam-7023	404	5	2021	2021	NUM
ejpam-7023	404	6	.	.	PUNCT
ejpam-7023	405	1	[	[	X
ejpam-7023	405	2	7	7	NUM
ejpam-7023	405	3	]	]	PUNCT
ejpam-7023	405	4	irshad	irshad	ADJ
ejpam-7023	405	5	ayoob	ayoob	NOUN
ejpam-7023	405	6	.	.	PUNCT
ejpam-7023	406	1	on	on	ADP
ejpam-7023	406	2	the	the	DET
ejpam-7023	406	3	evaluation	evaluation	NOUN
ejpam-7023	406	4	of	of	ADP
ejpam-7023	406	5	certain	certain	ADJ
ejpam-7023	406	6	unsolved	unsolved	ADJ
ejpam-7023	406	7	definite	definite	ADJ
ejpam-7023	406	8	integrals	integral	NOUN
ejpam-7023	406	9	.	.	PUNCT
ejpam-7023	407	1	european	european	ADJ
ejpam-7023	407	2	journal	journal	PROPN
ejpam-7023	407	3	of	of	ADP
ejpam-7023	407	4	pure	pure	ADJ
ejpam-7023	407	5	and	and	CCONJ
ejpam-7023	407	6	applied	applied	ADJ
ejpam-7023	407	7	mathematics	mathematic	NOUN
ejpam-7023	407	8	,	,	PUNCT
ejpam-7023	407	9	18(3):65–75	18(3):65–75	NUM
ejpam-7023	407	10	,	,	PUNCT
ejpam-7023	407	11	2025	2025	NUM
ejpam-7023	407	12	.	.	PUNCT
ejpam-7023	408	1	[	[	X
ejpam-7023	408	2	8	8	NUM
ejpam-7023	408	3	]	]	X
ejpam-7023	408	4	christophe	christophe	PROPN
ejpam-7023	408	5	chesneau	chesneau	PROPN
ejpam-7023	408	6	.	.	PUNCT
ejpam-7023	409	1	new	new	ADJ
ejpam-7023	409	2	two	two	NUM
ejpam-7023	409	3	-	-	PUNCT
ejpam-7023	409	4	parameter	parameter	NOUN
ejpam-7023	409	5	integral	integral	ADJ
ejpam-7023	409	6	formulas	formula	NOUN
ejpam-7023	409	7	proved	prove	VERB
ejpam-7023	409	8	via	via	ADP
ejpam-7023	409	9	the	the	DET
ejpam-7023	409	10	digamma	digamma	PROPN
ejpam-7023	409	11	function	function	NOUN
ejpam-7023	409	12	.	.	PUNCT
ejpam-7023	410	1	international	international	ADJ
ejpam-7023	410	2	journal	journal	NOUN
ejpam-7023	410	3	of	of	ADP
ejpam-7023	410	4	open	open	ADJ
ejpam-7023	410	5	problems	problem	NOUN
ejpam-7023	410	6	in	in	ADP
ejpam-7023	410	7	computer	computer	NOUN
ejpam-7023	410	8	science	science	NOUN
ejpam-7023	410	9	and	and	CCONJ
ejpam-7023	410	10	mathematics	mathematic	NOUN
ejpam-7023	410	11	,	,	PUNCT
ejpam-7023	410	12	18(4):32–38	18(4):32–38	NUM
ejpam-7023	410	13	,	,	PUNCT
ejpam-7023	410	14	december	december	PROPN
ejpam-7023	410	15	2025	2025	NUM
ejpam-7023	410	16	.	.	PUNCT
ejpam-7023	411	1	[	[	X
ejpam-7023	411	2	9	9	NUM
ejpam-7023	411	3	]	]	PUNCT
ejpam-7023	411	4	christophe	christophe	PROPN
ejpam-7023	411	5	chesneau	chesneau	PROPN
ejpam-7023	411	6	.	.	PUNCT
ejpam-7023	412	1	on	on	ADP
ejpam-7023	412	2	some	some	DET
ejpam-7023	412	3	trigonometric	trigonometric	NOUN
ejpam-7023	412	4	and	and	CCONJ
ejpam-7023	412	5	inverse	inverse	NOUN
ejpam-7023	412	6	trigonometric	trigonometric	ADJ
ejpam-7023	412	7	integral	integral	ADJ
ejpam-7023	412	8	formulas	formula	NOUN
ejpam-7023	412	9	.	.	PUNCT
ejpam-7023	413	1	annals	annal	NOUN
ejpam-7023	413	2	of	of	ADP
ejpam-7023	413	3	communications	communication	NOUN
ejpam-7023	413	4	in	in	ADP
ejpam-7023	413	5	mathematics	mathematic	NOUN
ejpam-7023	413	6	,	,	PUNCT
ejpam-7023	413	7	8(3):386–392	8(3):386–392	NUM
ejpam-7023	413	8	,	,	PUNCT
ejpam-7023	413	9	september	september	PROPN
ejpam-7023	413	10	2025	2025	NUM
ejpam-7023	413	11	.	.	PUNCT
ejpam-7023	414	1	i.	i.	PROPN
ejpam-7023	414	2	ayoob	ayoob	PROPN
ejpam-7023	414	3	/	/	SYM
ejpam-7023	414	4	eur	eur	PROPN
ejpam-7023	414	5	.	.	PUNCT
ejpam-7023	415	1	j.	j.	PROPN
ejpam-7023	415	2	pure	pure	PROPN
ejpam-7023	415	3	appl	appl	PROPN
ejpam-7023	415	4	.	.	PROPN
ejpam-7023	415	5	math	math	PROPN
ejpam-7023	415	6	,	,	PUNCT
ejpam-7023	415	7	18	18	NUM
ejpam-7023	415	8	(	(	PUNCT
ejpam-7023	415	9	4	4	NUM
ejpam-7023	415	10	)	)	PUNCT
ejpam-7023	415	11	(	(	PUNCT
ejpam-7023	415	12	2025	2025	NUM
ejpam-7023	415	13	)	)	PUNCT
ejpam-7023	415	14	,	,	PUNCT
ejpam-7023	415	15	7023	7023	NUM
ejpam-7023	415	16	16	16	NUM
ejpam-7023	415	17	of	of	ADP
ejpam-7023	415	18	16	16	NUM
ejpam-7023	415	19	[	[	X
ejpam-7023	415	20	10	10	NUM
ejpam-7023	415	21	]	]	X
ejpam-7023	415	22	daniel	daniel	PROPN
ejpam-7023	415	23	felipe	felipe	PROPN
ejpam-7023	415	24	martinez	martinez	PROPN
ejpam-7023	415	25	barreto	barreto	PROPN
ejpam-7023	415	26	and	and	CCONJ
ejpam-7023	415	27	christophe	christophe	PROPN
ejpam-7023	415	28	chesneau	chesneau	PROPN
ejpam-7023	415	29	.	.	PUNCT
ejpam-7023	416	1	study	study	NOUN
ejpam-7023	416	2	of	of	ADP
ejpam-7023	416	3	a	a	DET
ejpam-7023	416	4	particular	particular	ADJ
ejpam-7023	416	5	class	class	NOUN
ejpam-7023	416	6	of	of	ADP
ejpam-7023	416	7	integrals	integral	NOUN
ejpam-7023	416	8	.	.	PUNCT
ejpam-7023	417	1	international	international	ADJ
ejpam-7023	417	2	journal	journal	NOUN
ejpam-7023	417	3	of	of	ADP
ejpam-7023	417	4	open	open	ADJ
ejpam-7023	417	5	problems	problem	NOUN
ejpam-7023	417	6	in	in	ADP
ejpam-7023	417	7	computer	computer	NOUN
ejpam-7023	417	8	science	science	NOUN
ejpam-7023	417	9	and	and	CCONJ
ejpam-7023	417	10	mathematics	mathematic	NOUN
ejpam-7023	417	11	,	,	PUNCT
ejpam-7023	417	12	18(4):119–127	18(4):119–127	NUM
ejpam-7023	417	13	,	,	PUNCT
ejpam-7023	417	14	december	december	PROPN
ejpam-7023	417	15	2025	2025	NUM
ejpam-7023	417	16	.	.	PUNCT
ejpam-7023	418	1	[	[	X
ejpam-7023	418	2	11	11	NUM
ejpam-7023	418	3	]	]	X
ejpam-7023	418	4	konrad	konrad	PROPN
ejpam-7023	418	5	schmüdgen	schmüdgen	PROPN
ejpam-7023	418	6	.	.	PUNCT
ejpam-7023	419	1	the	the	DET
ejpam-7023	419	2	moment	moment	NOUN
ejpam-7023	419	3	problem	problem	NOUN
ejpam-7023	419	4	,	,	PUNCT
ejpam-7023	419	5	volume	volume	NOUN
ejpam-7023	419	6	277	277	NUM
ejpam-7023	419	7	of	of	ADP
ejpam-7023	419	8	graduate	graduate	ADJ
ejpam-7023	419	9	texts	text	NOUN
ejpam-7023	419	10	in	in	ADP
ejpam-7023	419	11	mathematics	mathematic	NOUN
ejpam-7023	419	12	.	.	PUNCT
ejpam-7023	420	1	springer	springer	NOUN
ejpam-7023	420	2	international	international	ADJ
ejpam-7023	420	3	publishing	publishing	NOUN
ejpam-7023	420	4	,	,	PUNCT
ejpam-7023	420	5	cham	cham	NOUN
ejpam-7023	420	6	,	,	PUNCT
ejpam-7023	420	7	2017	2017	NUM
ejpam-7023	420	8	.	.	PUNCT
ejpam-7023	421	1	[	[	X
ejpam-7023	421	2	12	12	NUM
ejpam-7023	421	3	]	]	PUNCT
ejpam-7023	421	4	b.	b.	PROPN
ejpam-7023	421	5	sury	sury	PROPN
ejpam-7023	421	6	.	.	PUNCT
ejpam-7023	422	1	weierstrass	weierstrass	PROPN
ejpam-7023	422	2	’s	’s	PART
ejpam-7023	422	3	theorem	theorem	NOUN
ejpam-7023	422	4	–	–	PUNCT
ejpam-7023	422	5	leaving	leave	VERB
ejpam-7023	422	6	no	no	DET
ejpam-7023	422	7	stone	stone	NOUN
ejpam-7023	422	8	unturned	unturned	ADJ
ejpam-7023	422	9	.	.	PUNCT
ejpam-7023	423	1	2003	2003	NUM
ejpam-7023	423	2	.	.	PUNCT
ejpam-7023	424	1	available	available	ADJ
ejpam-7023	424	2	at	at	ADP
ejpam-7023	424	3	:	:	PUNCT
ejpam-7023	424	4	https://www.isibang.ac.in/	https://www.isibang.ac.in/	NOUN
ejpam-7023	424	5	sury	sury	NOUN
ejpam-7023	424	6	/	/	SYM
ejpam-7023	424	7	hyderstone.pdf	hyderstone.pdf	NOUN
ejpam-7023	424	8	.	.	PUNCT
ejpam-7023	425	1	[	[	X
ejpam-7023	425	2	13	13	NUM
ejpam-7023	425	3	]	]	PUNCT
ejpam-7023	425	4	thomas	thomas	PROPN
ejpam-7023	425	5	joannes	joannes	PROPN
ejpam-7023	425	6	stieltjes	stieltjes	PROPN
ejpam-7023	425	7	.	.	PUNCT
ejpam-7023	426	1	œuvres	œuvres	PROPN
ejpam-7023	426	2	complètes	complètes	PROPN
ejpam-7023	426	3	,	,	PUNCT
ejpam-7023	426	4	vol	vol	NOUN
ejpam-7023	426	5	.	.	PROPN
ejpam-7023	427	1	2	2	NUM
ejpam-7023	427	2	.	.	X
ejpam-7023	427	3	wiskundig	wiskundig	PROPN
ejpam-7023	427	4	genootschap	genootschap	PROPN
ejpam-7023	427	5	/	/	PUNCT
ejpam-7023	427	6	p.	p.	NOUN
ejpam-7023	427	7	noordhoff	noordhoff	PROPN
ejpam-7023	427	8	,	,	PUNCT
ejpam-7023	427	9	groningen	groningen	PROPN
ejpam-7023	427	10	,	,	PUNCT
ejpam-7023	427	11	1914–1918	1914–1918	NUM
ejpam-7023	427	12	.	.	PUNCT
ejpam-7023	427	13	available	available	ADJ
ejpam-7023	427	14	online	online	ADV
ejpam-7023	427	15	:	:	PUNCT
ejpam-7023	427	16	https://archive.org/details/oeuvresthomasja02stierich	https://archive.org/details/oeuvresthomasja02stierich	X
ejpam-7023	427	17	.	.	PUNCT
ejpam-7023	428	1	[	[	X
ejpam-7023	428	2	14	14	NUM
ejpam-7023	428	3	]	]	PUNCT
ejpam-7023	428	4	raphaël	raphaël	NOUN
ejpam-7023	428	5	salem	salem	NOUN
ejpam-7023	428	6	.	.	PUNCT
ejpam-7023	429	1	sur	sur	PROPN
ejpam-7023	429	2	une	une	PROPN
ejpam-7023	429	3	proposition	proposition	PROPN
ejpam-7023	429	4	équivalente	équivalente	VERB
ejpam-7023	429	5	à	à	X
ejpam-7023	429	6	l’hypothèse	l’hypothèse	PROPN
ejpam-7023	429	7	de	de	X
ejpam-7023	429	8	riemann	riemann	PROPN
ejpam-7023	429	9	.	.	PUNCT
ejpam-7023	430	1	comptes	compte	VERB
ejpam-7023	430	2	rendus	rendus	PROPN
ejpam-7023	430	3	de	de	PROPN
ejpam-7023	430	4	l’académie	l’académie	PROPN
ejpam-7023	430	5	des	des	PROPN
ejpam-7023	430	6	sciences	sciences	PROPN
ejpam-7023	430	7	de	de	PROPN
ejpam-7023	430	8	paris	paris	PROPN
ejpam-7023	430	9	,	,	PUNCT
ejpam-7023	430	10	236:127–128	236:127–128	NUM
ejpam-7023	430	11	,	,	PUNCT
ejpam-7023	430	12	1953	1953	NUM
ejpam-7023	430	13	.	.	PUNCT
ejpam-7023	431	1	[	[	X
ejpam-7023	431	2	15	15	NUM
ejpam-7023	432	1	]	]	X
ejpam-7023	432	2	s.	s.	PROPN
ejpam-7023	432	3	yakubovich	yakubovich	PROPN
ejpam-7023	432	4	.	.	PUNCT
ejpam-7023	433	1	integral	integral	ADJ
ejpam-7023	433	2	and	and	CCONJ
ejpam-7023	433	3	series	series	NOUN
ejpam-7023	433	4	transformations	transformation	NOUN
ejpam-7023	433	5	via	via	ADP
ejpam-7023	433	6	ramanujan	ramanujan	PROPN
ejpam-7023	433	7	’s	’s	PART
ejpam-7023	433	8	identities	identity	NOUN
ejpam-7023	433	9	and	and	CCONJ
ejpam-7023	433	10	salem	salem	NOUN
ejpam-7023	433	11	’s	’s	PART
ejpam-7023	433	12	type	type	NOUN
ejpam-7023	433	13	equivalences	equivalence	VERB
ejpam-7023	433	14	to	to	ADP
ejpam-7023	433	15	the	the	DET
ejpam-7023	433	16	riemann	riemann	PROPN
ejpam-7023	433	17	hypothesis	hypothesis	NOUN
ejpam-7023	433	18	.	.	PUNCT
ejpam-7023	434	1	integral	integral	ADJ
ejpam-7023	434	2	transforms	transform	NOUN
ejpam-7023	434	3	and	and	CCONJ
ejpam-7023	434	4	special	special	ADJ
ejpam-7023	434	5	functions	function	NOUN
ejpam-7023	434	6	,	,	PUNCT
ejpam-7023	434	7	25(4):255–271	25(4):255–271	NOUN
ejpam-7023	434	8	,	,	PUNCT
ejpam-7023	434	9	2014	2014	NUM
ejpam-7023	434	10	.	.	PUNCT
ejpam-7023	435	1	[	[	X
ejpam-7023	435	2	16	16	NUM
ejpam-7023	435	3	]	]	X
ejpam-7023	435	4	b.	b.	PROPN
ejpam-7023	435	5	j.	j.	PROPN
ejpam-7023	435	6	gonzález	gonzález	PROPN
ejpam-7023	435	7	and	and	CCONJ
ejpam-7023	435	8	e.	e.	PROPN
ejpam-7023	435	9	r.	r.	PROPN
ejpam-7023	435	10	negrín	negrín	PROPN
ejpam-7023	435	11	.	.	PUNCT
ejpam-7023	436	1	inversion	inversion	NOUN
ejpam-7023	436	2	formulae	formulae	NOUN
ejpam-7023	436	3	for	for	ADP
ejpam-7023	436	4	a	a	DET
ejpam-7023	436	5	lambert	lambert	NOUN
ejpam-7023	436	6	-	-	PUNCT
ejpam-7023	436	7	type	type	NOUN
ejpam-7023	436	8	transform	transform	NOUN
ejpam-7023	436	9	and	and	CCONJ
ejpam-7023	436	10	the	the	DET
ejpam-7023	436	11	salem	salem	NOUN
ejpam-7023	436	12	’s	’s	PART
ejpam-7023	436	13	equivalence	equivalence	NOUN
ejpam-7023	436	14	to	to	ADP
ejpam-7023	436	15	the	the	DET
ejpam-7023	436	16	riemann	riemann	PROPN
ejpam-7023	436	17	hypothesis	hypothesis	NOUN
ejpam-7023	436	18	.	.	PUNCT
ejpam-7023	437	1	integral	integral	ADJ
ejpam-7023	437	2	transforms	transform	NOUN
ejpam-7023	437	3	and	and	CCONJ
ejpam-7023	437	4	special	special	ADJ
ejpam-7023	437	5	functions	function	NOUN
ejpam-7023	437	6	,	,	PUNCT
ejpam-7023	437	7	34(8):614–618	34(8):614–618	NUM
ejpam-7023	437	8	,	,	PUNCT
ejpam-7023	437	9	2023	2023	NUM
ejpam-7023	437	10	.	.	PUNCT
ejpam-7023	438	1	[	[	X
ejpam-7023	438	2	17	17	NUM
ejpam-7023	438	3	]	]	X
ejpam-7023	438	4	b.	b.	PROPN
ejpam-7023	438	5	j.	j.	PROPN
ejpam-7023	438	6	gonzález	gonzález	PROPN
ejpam-7023	438	7	and	and	CCONJ
ejpam-7023	438	8	e.	e.	PROPN
ejpam-7023	438	9	r.	r.	PROPN
ejpam-7023	438	10	negrín	negrín	PROPN
ejpam-7023	438	11	.	.	PUNCT
ejpam-7023	439	1	approaching	approach	VERB
ejpam-7023	439	2	the	the	DET
ejpam-7023	439	3	riemann	riemann	PROPN
ejpam-7023	439	4	hypothesis	hypothesis	NOUN
ejpam-7023	439	5	using	use	VERB
ejpam-7023	439	6	salem	salem	NOUN
ejpam-7023	439	7	’s	’s	PART
ejpam-7023	439	8	equivalence	equivalence	NOUN
ejpam-7023	439	9	and	and	CCONJ
ejpam-7023	439	10	inversion	inversion	NOUN
ejpam-7023	439	11	formulae	formulae	NOUN
ejpam-7023	439	12	of	of	ADP
ejpam-7023	439	13	a	a	DET
ejpam-7023	439	14	widder	widder	ADJ
ejpam-7023	439	15	–	–	PUNCT
ejpam-7023	439	16	lambert	lambert	NOUN
ejpam-7023	439	17	-	-	PUNCT
ejpam-7023	439	18	type	type	NOUN
ejpam-7023	439	19	transform	transform	NOUN
ejpam-7023	439	20	.	.	PUNCT
ejpam-7023	440	1	integral	integral	ADJ
ejpam-7023	440	2	transforms	transform	NOUN
ejpam-7023	440	3	and	and	CCONJ
ejpam-7023	440	4	special	special	ADJ
ejpam-7023	440	5	functions	function	NOUN
ejpam-7023	440	6	,	,	PUNCT
ejpam-7023	440	7	35(4):291–297	35(4):291–297	PROPN
ejpam-7023	440	8	,	,	PUNCT
ejpam-7023	440	9	2024	2024	NUM
ejpam-7023	440	10	.	.	PUNCT
ejpam-7023	441	1	[	[	X
ejpam-7023	441	2	18	18	NUM
ejpam-7023	441	3	]	]	X
ejpam-7023	441	4	e.	e.	PROPN
ejpam-7023	441	5	r.	r.	PROPN
ejpam-7023	441	6	negrín	negrín	PROPN
ejpam-7023	441	7	and	and	CCONJ
ejpam-7023	441	8	j.	j.	PROPN
ejpam-7023	441	9	maan	maan	PROPN
ejpam-7023	441	10	.	.	PUNCT
ejpam-7023	442	1	new	new	ADJ
ejpam-7023	442	2	inversion	inversion	NOUN
ejpam-7023	442	3	formulae	formulae	NOUN
ejpam-7023	442	4	for	for	ADP
ejpam-7023	442	5	the	the	DET
ejpam-7023	442	6	widder	widder	NOUN
ejpam-7023	442	7	–	–	PUNCT
ejpam-7023	442	8	lambert	lambert	NOUN
ejpam-7023	442	9	and	and	CCONJ
ejpam-7023	442	10	stieltjes	stieltjes	PROPN
ejpam-7023	442	11	–	–	PUNCT
ejpam-7023	442	12	poisson	poisson	NOUN
ejpam-7023	442	13	transforms	transform	VERB
ejpam-7023	442	14	.	.	PUNCT
ejpam-7023	443	1	axioms	axiom	NOUN
ejpam-7023	443	2	,	,	PUNCT
ejpam-7023	443	3	14(4):291	14(4):291	NUM
ejpam-7023	443	4	,	,	PUNCT
ejpam-7023	443	5	2025	2025	NUM
ejpam-7023	443	6	.	.	PUNCT