id	sid	tid	token	lemma	pos
ejpam-6575	1	1	european	european	PROPN
ejpam-6575	1	2	journal	journal	PROPN
ejpam-6575	1	3	of	of	ADP
ejpam-6575	1	4	pure	pure	ADJ
ejpam-6575	1	5	and	and	CCONJ
ejpam-6575	1	6	applied	applied	ADJ
ejpam-6575	1	7	mathematics	mathematic	NOUN
ejpam-6575	1	8	2025	2025	NUM
ejpam-6575	1	9	,	,	PUNCT
ejpam-6575	1	10	vol	vol	NOUN
ejpam-6575	1	11	.	.	PROPN
ejpam-6575	1	12	18	18	NUM
ejpam-6575	1	13	,	,	PUNCT
ejpam-6575	1	14	issue	issue	NOUN
ejpam-6575	1	15	3	3	NUM
ejpam-6575	1	16	,	,	PUNCT
ejpam-6575	1	17	article	article	NOUN
ejpam-6575	1	18	number	number	NOUN
ejpam-6575	1	19	6575	6575	NUM
ejpam-6575	1	20	issn	issn	PROPN
ejpam-6575	1	21	1307	1307	NUM
ejpam-6575	1	22	-	-	SYM
ejpam-6575	1	23	5543	5543	NUM
ejpam-6575	1	24	–	–	PUNCT
ejpam-6575	1	25	ejpam.com	ejpam.com	X
ejpam-6575	1	26	published	publish	VERB
ejpam-6575	1	27	by	by	ADP
ejpam-6575	1	28	new	new	PROPN
ejpam-6575	1	29	york	york	PROPN
ejpam-6575	1	30	business	business	PROPN
ejpam-6575	1	31	global	global	PROPN
ejpam-6575	1	32	on	on	ADP
ejpam-6575	1	33	the	the	DET
ejpam-6575	1	34	evaluation	evaluation	NOUN
ejpam-6575	1	35	of	of	ADP
ejpam-6575	1	36	certain	certain	ADJ
ejpam-6575	1	37	unsolved	unsolved	ADJ
ejpam-6575	1	38	definite	definite	ADJ
ejpam-6575	1	39	integrals	integral	NOUN
ejpam-6575	1	40	irshad	irshad	VERB
ejpam-6575	1	41	ayoob	ayoob	PROPN
ejpam-6575	1	42	1	1	NUM
ejpam-6575	1	43	department	department	NOUN
ejpam-6575	1	44	of	of	ADP
ejpam-6575	1	45	mathematics	mathematic	NOUN
ejpam-6575	1	46	and	and	CCONJ
ejpam-6575	1	47	sciences	science	NOUN
ejpam-6575	1	48	,	,	PUNCT
ejpam-6575	1	49	prince	prince	PROPN
ejpam-6575	1	50	sultan	sultan	PROPN
ejpam-6575	1	51	university	university	PROPN
ejpam-6575	1	52	,	,	PUNCT
ejpam-6575	1	53	p.o	p.o	PROPN
ejpam-6575	1	54	.	.	PROPN
ejpam-6575	1	55	box	box	PROPN
ejpam-6575	1	56	66833	66833	NUM
ejpam-6575	1	57	,	,	PUNCT
ejpam-6575	1	58	riyadh	riyadh	PROPN
ejpam-6575	1	59	11586	11586	NUM
ejpam-6575	1	60	,	,	PUNCT
ejpam-6575	1	61	saudi	saudi	PROPN
ejpam-6575	1	62	arabia	arabia	PROPN
ejpam-6575	1	63	abstract	abstract	NOUN
ejpam-6575	1	64	.	.	PUNCT
ejpam-6575	2	1	we	we	PRON
ejpam-6575	2	2	study	study	VERB
ejpam-6575	2	3	the	the	DET
ejpam-6575	2	4	following	follow	VERB
ejpam-6575	2	5	three	three	NUM
ejpam-6575	2	6	definite	definite	ADJ
ejpam-6575	2	7	integrals	integral	NOUN
ejpam-6575	2	8	,	,	PUNCT
ejpam-6575	2	9	previously	previously	ADV
ejpam-6575	2	10	posed	pose	VERB
ejpam-6575	2	11	as	as	ADP
ejpam-6575	2	12	open	open	ADJ
ejpam-6575	2	13	problems	problem	NOUN
ejpam-6575	2	14	by	by	ADP
ejpam-6575	2	15	another	another	DET
ejpam-6575	2	16	researcher	researcher	NOUN
ejpam-6575	2	17	:	:	PUNCT
ejpam-6575	2	18	i(α	i(α	PROPN
ejpam-6575	2	19	)	)	PUNCT
ejpam-6575	3	1	=	=	PRON
ejpam-6575	3	2	∫∞	∫∞	NOUN
ejpam-6575	3	3	0	0	PUNCT
ejpam-6575	3	4	x−1/2	x−1/2	PROPN
ejpam-6575	4	1	ln(1	ln(1	PROPN
ejpam-6575	4	2	+	+	NUM
ejpam-6575	4	3	x−α	x−α	NOUN
ejpam-6575	4	4	)	)	PUNCT
ejpam-6575	4	5	dx	dx	PROPN
ejpam-6575	4	6	,	,	PUNCT
ejpam-6575	4	7	in(α	in(α	PUNCT
ejpam-6575	4	8	)	)	PUNCT
ejpam-6575	5	1	=	=	SYM
ejpam-6575	5	2	∫∞	∫∞	NOUN
ejpam-6575	5	3	0	0	NUM
ejpam-6575	5	4	1√	1√	NUM
ejpam-6575	5	5	x(x2	x(x2	PROPN
ejpam-6575	6	1	+	+	PROPN
ejpam-6575	6	2	4α2)n	4α2)n	PROPN
ejpam-6575	6	3	dx	dx	PROPN
ejpam-6575	6	4	,	,	PUNCT
ejpam-6575	6	5	and	and	CCONJ
ejpam-6575	6	6	i(β	i(β	NOUN
ejpam-6575	6	7	)	)	PUNCT
ejpam-6575	7	1	=	=	NOUN
ejpam-6575	7	2	∫∞	∫∞	NOUN
ejpam-6575	7	3	0	0	NUM
ejpam-6575	8	1	x−3/2	x−3/2	PROPN
ejpam-6575	8	2	[	[	PUNCT
ejpam-6575	8	3	f(2β	f(2β	NOUN
ejpam-6575	8	4	/	/	SYM
ejpam-6575	8	5	x	x	NOUN
ejpam-6575	8	6	)	)	PUNCT
ejpam-6575	8	7	−	−	PROPN
ejpam-6575	8	8	f(2	f(2	PROPN
ejpam-6575	8	9	/	/	SYM
ejpam-6575	8	10	x	x	NOUN
ejpam-6575	8	11	)	)	PUNCT
ejpam-6575	8	12	]	]	PUNCT
ejpam-6575	9	1	dx	dx	PROPN
ejpam-6575	9	2	.	.	PUNCT
ejpam-6575	10	1	we	we	PRON
ejpam-6575	10	2	establish	establish	VERB
ejpam-6575	10	3	sufficient	sufficient	ADJ
ejpam-6575	10	4	conditions	condition	NOUN
ejpam-6575	10	5	for	for	ADP
ejpam-6575	10	6	the	the	DET
ejpam-6575	10	7	convergence	convergence	NOUN
ejpam-6575	10	8	of	of	ADP
ejpam-6575	10	9	these	these	DET
ejpam-6575	10	10	integrals	integral	NOUN
ejpam-6575	10	11	and	and	CCONJ
ejpam-6575	10	12	evaluate	evaluate	VERB
ejpam-6575	10	13	them	they	PRON
ejpam-6575	10	14	in	in	ADP
ejpam-6575	10	15	closed	closed	ADJ
ejpam-6575	10	16	form	form	NOUN
ejpam-6575	10	17	using	use	VERB
ejpam-6575	10	18	special	special	ADJ
ejpam-6575	10	19	functions	function	NOUN
ejpam-6575	10	20	.	.	PUNCT
ejpam-6575	11	1	in	in	ADP
ejpam-6575	11	2	particular	particular	ADJ
ejpam-6575	11	3	,	,	PUNCT
ejpam-6575	11	4	the	the	DET
ejpam-6575	11	5	third	third	ADJ
ejpam-6575	11	6	integral	integral	ADJ
ejpam-6575	11	7	i(β	i(β	NOUN
ejpam-6575	11	8	)	)	PUNCT
ejpam-6575	11	9	turns	turn	VERB
ejpam-6575	11	10	out	out	ADP
ejpam-6575	11	11	to	to	PART
ejpam-6575	11	12	be	be	AUX
ejpam-6575	11	13	similar	similar	ADJ
ejpam-6575	11	14	to	to	ADP
ejpam-6575	11	15	frullani	frullani	ADJ
ejpam-6575	11	16	integral	integral	ADJ
ejpam-6575	11	17	,	,	PUNCT
ejpam-6575	11	18	and	and	CCONJ
ejpam-6575	11	19	we	we	PRON
ejpam-6575	11	20	obtain	obtain	VERB
ejpam-6575	11	21	two	two	NUM
ejpam-6575	11	22	interesting	interesting	ADJ
ejpam-6575	11	23	formulas	formula	NOUN
ejpam-6575	11	24	for	for	ADP
ejpam-6575	11	25	this	this	DET
ejpam-6575	11	26	integral	integral	ADJ
ejpam-6575	11	27	.	.	PUNCT
ejpam-6575	12	1	these	these	DET
ejpam-6575	12	2	types	type	NOUN
ejpam-6575	12	3	of	of	ADP
ejpam-6575	12	4	integrals	integral	NOUN
ejpam-6575	12	5	have	have	AUX
ejpam-6575	12	6	been	be	AUX
ejpam-6575	12	7	used	use	VERB
ejpam-6575	12	8	to	to	PART
ejpam-6575	12	9	establish	establish	VERB
ejpam-6575	12	10	logarithmic	logarithmic	ADJ
ejpam-6575	12	11	hardy	hardy	ADJ
ejpam-6575	12	12	-	-	PUNCT
ejpam-6575	12	13	hilbert	hilbert	NOUN
ejpam-6575	12	14	-	-	PUNCT
ejpam-6575	12	15	type	type	NOUN
ejpam-6575	12	16	inequalities	inequality	NOUN
ejpam-6575	12	17	.	.	PUNCT
ejpam-6575	13	1	2020	2020	NUM
ejpam-6575	13	2	mathematics	mathematic	NOUN
ejpam-6575	13	3	subject	subject	NOUN
ejpam-6575	13	4	classifications	classification	NOUN
ejpam-6575	13	5	:	:	PUNCT
ejpam-6575	13	6	26a42	26a42	NUM
ejpam-6575	13	7	,	,	PUNCT
ejpam-6575	13	8	33b15	33b15	NUM
ejpam-6575	13	9	,	,	PUNCT
ejpam-6575	13	10	26a06	26a06	NUM
ejpam-6575	13	11	,	,	PUNCT
ejpam-6575	13	12	44a20	44a20	NUM
ejpam-6575	13	13	key	key	ADJ
ejpam-6575	13	14	words	word	NOUN
ejpam-6575	13	15	and	and	CCONJ
ejpam-6575	13	16	phrases	phrase	NOUN
ejpam-6575	13	17	:	:	PUNCT
ejpam-6575	13	18	definite	definite	ADJ
ejpam-6575	13	19	integral	integral	ADJ
ejpam-6575	13	20	,	,	PUNCT
ejpam-6575	13	21	beta	beta	ADJ
ejpam-6575	13	22	function	function	NOUN
ejpam-6575	13	23	,	,	PUNCT
ejpam-6575	13	24	leibniz	leibniz	PROPN
ejpam-6575	13	25	integral	integral	ADJ
ejpam-6575	13	26	rule	rule	NOUN
ejpam-6575	13	27	,	,	PUNCT
ejpam-6575	13	28	mellin	mellin	PROPN
ejpam-6575	13	29	transform	transform	VERB
ejpam-6575	13	30	definite	definite	ADJ
ejpam-6575	13	31	integrals	integral	NOUN
ejpam-6575	13	32	appear	appear	VERB
ejpam-6575	13	33	in	in	ADP
ejpam-6575	13	34	various	various	ADJ
ejpam-6575	13	35	contexts	context	NOUN
ejpam-6575	13	36	across	across	ADP
ejpam-6575	13	37	both	both	CCONJ
ejpam-6575	13	38	pure	pure	ADJ
ejpam-6575	13	39	and	and	CCONJ
ejpam-6575	13	40	applied	applied	ADJ
ejpam-6575	13	41	branches	branch	NOUN
ejpam-6575	13	42	of	of	ADP
ejpam-6575	13	43	mathematics	mathematic	NOUN
ejpam-6575	13	44	.	.	PUNCT
ejpam-6575	14	1	while	while	SCONJ
ejpam-6575	14	2	many	many	ADJ
ejpam-6575	14	3	definite	definite	ADJ
ejpam-6575	14	4	integrals	integral	NOUN
ejpam-6575	14	5	can	can	AUX
ejpam-6575	14	6	be	be	AUX
ejpam-6575	14	7	solved	solve	VERB
ejpam-6575	14	8	with	with	ADP
ejpam-6575	14	9	elementary	elementary	ADJ
ejpam-6575	14	10	techniques	technique	NOUN
ejpam-6575	14	11	such	such	ADJ
ejpam-6575	14	12	as	as	ADP
ejpam-6575	14	13	substitution	substitution	NOUN
ejpam-6575	14	14	or	or	CCONJ
ejpam-6575	14	15	integration	integration	NOUN
ejpam-6575	14	16	by	by	ADP
ejpam-6575	14	17	parts	part	NOUN
ejpam-6575	14	18	,	,	PUNCT
ejpam-6575	14	19	a	a	DET
ejpam-6575	14	20	significant	significant	ADJ
ejpam-6575	14	21	number	number	NOUN
ejpam-6575	14	22	of	of	ADP
ejpam-6575	14	23	them	they	PRON
ejpam-6575	14	24	are	be	AUX
ejpam-6575	14	25	non	non	ADJ
ejpam-6575	14	26	-	-	ADJ
ejpam-6575	14	27	elementary	elementary	ADJ
ejpam-6575	14	28	that	that	PRON
ejpam-6575	14	29	can	can	AUX
ejpam-6575	14	30	not	not	PART
ejpam-6575	14	31	be	be	AUX
ejpam-6575	14	32	expressed	express	VERB
ejpam-6575	14	33	in	in	ADP
ejpam-6575	14	34	terms	term	NOUN
ejpam-6575	14	35	of	of	ADP
ejpam-6575	14	36	basic	basic	ADJ
ejpam-6575	14	37	functions	function	NOUN
ejpam-6575	14	38	.	.	PUNCT
ejpam-6575	15	1	these	these	DET
ejpam-6575	15	2	integrals	integral	NOUN
ejpam-6575	15	3	demand	demand	VERB
ejpam-6575	15	4	more	more	ADJ
ejpam-6575	15	5	advanced	advanced	ADJ
ejpam-6575	15	6	methods	method	NOUN
ejpam-6575	15	7	for	for	ADP
ejpam-6575	15	8	exact	exact	ADJ
ejpam-6575	15	9	evaluation	evaluation	NOUN
ejpam-6575	15	10	,	,	PUNCT
ejpam-6575	15	11	including	include	VERB
ejpam-6575	15	12	transformations	transformation	NOUN
ejpam-6575	15	13	(	(	PUNCT
ejpam-6575	15	14	e.g.	e.g.	ADV
ejpam-6575	15	15	,	,	PUNCT
ejpam-6575	15	16	laplace	laplace	NOUN
ejpam-6575	15	17	or	or	CCONJ
ejpam-6575	15	18	mellin	mellin	PROPN
ejpam-6575	15	19	)	)	PUNCT
ejpam-6575	15	20	,	,	PUNCT
ejpam-6575	15	21	complex	complex	ADJ
ejpam-6575	15	22	analysis	analysis	NOUN
ejpam-6575	15	23	(	(	PUNCT
ejpam-6575	15	24	e.g.	e.g.	ADV
ejpam-6575	15	25	,	,	PUNCT
ejpam-6575	15	26	contour	contour	NOUN
ejpam-6575	15	27	integration	integration	NOUN
ejpam-6575	15	28	and	and	CCONJ
ejpam-6575	15	29	residue	residue	NOUN
ejpam-6575	15	30	theory	theory	NOUN
ejpam-6575	15	31	)	)	PUNCT
ejpam-6575	15	32	,	,	PUNCT
ejpam-6575	15	33	and	and	CCONJ
ejpam-6575	15	34	special	special	ADJ
ejpam-6575	15	35	functions	function	NOUN
ejpam-6575	15	36	(	(	PUNCT
ejpam-6575	15	37	such	such	ADJ
ejpam-6575	15	38	as	as	ADP
ejpam-6575	15	39	the	the	DET
ejpam-6575	15	40	gamma	gamma	NOUN
ejpam-6575	15	41	,	,	PUNCT
ejpam-6575	15	42	beta	beta	NOUN
ejpam-6575	15	43	,	,	PUNCT
ejpam-6575	15	44	and	and	CCONJ
ejpam-6575	15	45	hypergeometric	hypergeometric	ADJ
ejpam-6575	15	46	functions	function	NOUN
ejpam-6575	15	47	)	)	PUNCT
ejpam-6575	15	48	.	.	PUNCT
ejpam-6575	16	1	finding	find	VERB
ejpam-6575	16	2	exact	exact	ADJ
ejpam-6575	16	3	solutions	solution	NOUN
ejpam-6575	16	4	,	,	PUNCT
ejpam-6575	16	5	when	when	SCONJ
ejpam-6575	16	6	possible	possible	ADJ
ejpam-6575	16	7	,	,	PUNCT
ejpam-6575	16	8	is	be	AUX
ejpam-6575	16	9	of	of	ADP
ejpam-6575	16	10	high	high	ADJ
ejpam-6575	16	11	practical	practical	ADJ
ejpam-6575	16	12	and	and	CCONJ
ejpam-6575	16	13	theoretical	theoretical	ADJ
ejpam-6575	16	14	importance	importance	NOUN
ejpam-6575	16	15	as	as	SCONJ
ejpam-6575	16	16	it	it	PRON
ejpam-6575	16	17	allows	allow	VERB
ejpam-6575	16	18	for	for	ADP
ejpam-6575	16	19	precise	precise	ADJ
ejpam-6575	16	20	predictions	prediction	NOUN
ejpam-6575	16	21	,	,	PUNCT
ejpam-6575	16	22	deeper	deep	ADJ
ejpam-6575	16	23	analytic	analytic	ADJ
ejpam-6575	16	24	understanding	understanding	NOUN
ejpam-6575	16	25	,	,	PUNCT
ejpam-6575	16	26	and	and	CCONJ
ejpam-6575	16	27	verification	verification	NOUN
ejpam-6575	16	28	of	of	ADP
ejpam-6575	16	29	numerical	numerical	ADJ
ejpam-6575	16	30	methods	method	NOUN
ejpam-6575	16	31	.	.	PUNCT
ejpam-6575	17	1	as	as	ADP
ejpam-6575	17	2	such	such	ADJ
ejpam-6575	17	3	,	,	PUNCT
ejpam-6575	17	4	the	the	DET
ejpam-6575	17	5	study	study	NOUN
ejpam-6575	17	6	of	of	ADP
ejpam-6575	17	7	advanced	advanced	ADJ
ejpam-6575	17	8	techniques	technique	NOUN
ejpam-6575	17	9	for	for	ADP
ejpam-6575	17	10	evaluating	evaluate	VERB
ejpam-6575	17	11	definite	definite	ADJ
ejpam-6575	17	12	integrals	integral	NOUN
ejpam-6575	17	13	remains	remain	VERB
ejpam-6575	17	14	an	an	DET
ejpam-6575	17	15	active	active	ADJ
ejpam-6575	17	16	area	area	NOUN
ejpam-6575	17	17	of	of	ADP
ejpam-6575	17	18	research	research	NOUN
ejpam-6575	17	19	.	.	PUNCT
ejpam-6575	18	1	an	an	DET
ejpam-6575	18	2	extensive	extensive	ADJ
ejpam-6575	18	3	compilation	compilation	NOUN
ejpam-6575	18	4	of	of	ADP
ejpam-6575	18	5	definite	definite	ADJ
ejpam-6575	18	6	integrals	integral	NOUN
ejpam-6575	18	7	,	,	PUNCT
ejpam-6575	18	8	ranging	range	VERB
ejpam-6575	18	9	from	from	ADP
ejpam-6575	18	10	elementary	elementary	NOUN
ejpam-6575	18	11	to	to	ADP
ejpam-6575	18	12	non	non	ADJ
ejpam-6575	18	13	-	-	ADJ
ejpam-6575	18	14	elementary	elementary	ADJ
ejpam-6575	18	15	forms	form	NOUN
ejpam-6575	18	16	,	,	PUNCT
ejpam-6575	18	17	is	be	AUX
ejpam-6575	18	18	available	available	ADJ
ejpam-6575	18	19	in	in	ADP
ejpam-6575	18	20	[	[	X
ejpam-6575	18	21	1	1	NUM
ejpam-6575	18	22	]	]	PUNCT
ejpam-6575	18	23	and	and	CCONJ
ejpam-6575	18	24	the	the	DET
ejpam-6575	18	25	references	reference	NOUN
ejpam-6575	18	26	cited	cite	VERB
ejpam-6575	18	27	therein	therein	ADV
ejpam-6575	18	28	.	.	PUNCT
ejpam-6575	19	1	recent	recent	ADJ
ejpam-6575	19	2	studies	study	NOUN
ejpam-6575	19	3	,	,	PUNCT
ejpam-6575	19	4	such	such	ADJ
ejpam-6575	19	5	as	as	ADP
ejpam-6575	19	6	those	those	PRON
ejpam-6575	19	7	presented	present	VERB
ejpam-6575	19	8	in	in	ADP
ejpam-6575	19	9	[	[	X
ejpam-6575	19	10	2–7	2–7	NOUN
ejpam-6575	19	11	]	]	X
ejpam-6575	19	12	,	,	PUNCT
ejpam-6575	19	13	highlight	highlight	VERB
ejpam-6575	19	14	ongoing	ongoing	ADJ
ejpam-6575	19	15	developments	development	NOUN
ejpam-6575	19	16	and	and	CCONJ
ejpam-6575	19	17	underscore	underscore	VERB
ejpam-6575	19	18	the	the	DET
ejpam-6575	19	19	sustained	sustained	ADJ
ejpam-6575	19	20	interest	interest	NOUN
ejpam-6575	19	21	in	in	ADP
ejpam-6575	19	22	this	this	DET
ejpam-6575	19	23	field	field	NOUN
ejpam-6575	19	24	.	.	PUNCT
ejpam-6575	20	1	the	the	DET
ejpam-6575	20	2	evaluation	evaluation	NOUN
ejpam-6575	20	3	of	of	ADP
ejpam-6575	20	4	the	the	DET
ejpam-6575	20	5	following	following	ADJ
ejpam-6575	20	6	definite	definite	ADJ
ejpam-6575	20	7	integrals	integral	NOUN
ejpam-6575	20	8	are	be	AUX
ejpam-6575	20	9	posed	pose	VERB
ejpam-6575	20	10	as	as	ADP
ejpam-6575	20	11	open	open	ADJ
ejpam-6575	20	12	problems	problem	NOUN
ejpam-6575	20	13	in	in	ADP
ejpam-6575	20	14	[	[	X
ejpam-6575	20	15	8	8	NUM
ejpam-6575	20	16	]	]	PUNCT
ejpam-6575	20	17	.	.	PUNCT
ejpam-6575	21	1	doi	doi	NOUN
ejpam-6575	21	2	:	:	PUNCT
ejpam-6575	21	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6575	https://doi.org/10.29020/nybg.ejpam.v18i3.6575	ADJ
ejpam-6575	21	4	email	email	NOUN
ejpam-6575	21	5	address	address	NOUN
ejpam-6575	21	6	:	:	PUNCT
ejpam-6575	21	7	iayoub@psu.edu.sa	iayoub@psu.edu.sa	PROPN
ejpam-6575	21	8	(	(	PUNCT
ejpam-6575	21	9	i.	i.	PROPN
ejpam-6575	21	10	ayoob	ayoob	PROPN
ejpam-6575	21	11	)	)	PUNCT
ejpam-6575	21	12	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6575	22	1	1	1	NUM
ejpam-6575	22	2	copyright	copyright	NOUN
ejpam-6575	22	3	:	:	PUNCT
ejpam-6575	22	4	©	©	PROPN
ejpam-6575	22	5	2025	2025	NUM
ejpam-6575	22	6	the	the	DET
ejpam-6575	22	7	author(s	author(s	NOUN
ejpam-6575	22	8	)	)	PUNCT
ejpam-6575	22	9	.	.	PUNCT
ejpam-6575	23	1	(	(	PUNCT
ejpam-6575	23	2	cc	cc	NOUN
ejpam-6575	23	3	by	by	ADP
ejpam-6575	23	4	-	-	PUNCT
ejpam-6575	23	5	nc	nc	PROPN
ejpam-6575	23	6	4.0	4.0	NUM
ejpam-6575	23	7	)	)	PUNCT
ejpam-6575	23	8	i.	i.	NOUN
ejpam-6575	23	9	ayoob	ayoob	PROPN
ejpam-6575	23	10	/	/	SYM
ejpam-6575	23	11	eur	eur	PROPN
ejpam-6575	23	12	.	.	PUNCT
ejpam-6575	24	1	j.	j.	PROPN
ejpam-6575	24	2	pure	pure	PROPN
ejpam-6575	24	3	appl	appl	PROPN
ejpam-6575	24	4	.	.	PROPN
ejpam-6575	24	5	math	math	PROPN
ejpam-6575	24	6	,	,	PUNCT
ejpam-6575	24	7	18	18	NUM
ejpam-6575	24	8	(	(	PUNCT
ejpam-6575	24	9	3	3	NUM
ejpam-6575	24	10	)	)	PUNCT
ejpam-6575	24	11	(	(	PUNCT
ejpam-6575	24	12	2025	2025	NUM
ejpam-6575	24	13	)	)	PUNCT
ejpam-6575	24	14	,	,	PUNCT
ejpam-6575	24	15	6575	6575	NUM
ejpam-6575	24	16	2	2	NUM
ejpam-6575	24	17	of	of	ADP
ejpam-6575	24	18	12	12	NUM
ejpam-6575	24	19	problem	problem	NOUN
ejpam-6575	24	20	1	1	NUM
ejpam-6575	24	21	.	.	X
ejpam-6575	24	22	evaluate	evaluate	VERB
ejpam-6575	24	23	the	the	DET
ejpam-6575	24	24	integral	integral	ADJ
ejpam-6575	24	25	i(α	i(α	PROPN
ejpam-6575	24	26	)	)	PUNCT
ejpam-6575	25	1	=	=	SYM
ejpam-6575	26	1	∫	∫	PROPN
ejpam-6575	27	1	∞	∞	PROPN
ejpam-6575	27	2	0	0	NUM
ejpam-6575	28	1	x−1/2	x−1/2	PROPN
ejpam-6575	28	2	ln	ln	NOUN
ejpam-6575	28	3	(	(	PUNCT
ejpam-6575	28	4	1	1	NUM
ejpam-6575	28	5	+	+	NUM
ejpam-6575	28	6	x−α	x−α	NOUN
ejpam-6575	28	7	)	)	PUNCT
ejpam-6575	29	1	dx	dx	PROPN
ejpam-6575	29	2	,	,	PUNCT
ejpam-6575	29	3	for	for	ADP
ejpam-6575	29	4	α	α	PROPN
ejpam-6575	29	5	>	>	X
ejpam-6575	29	6	1	1	NUM
ejpam-6575	29	7	2	2	NUM
ejpam-6575	29	8	.	.	PUNCT
ejpam-6575	30	1	problem	problem	NOUN
ejpam-6575	30	2	2	2	NUM
ejpam-6575	30	3	.	.	PUNCT
ejpam-6575	30	4	determine	determine	VERB
ejpam-6575	30	5	a	a	DET
ejpam-6575	30	6	closed	closed	ADJ
ejpam-6575	30	7	-	-	PUNCT
ejpam-6575	30	8	form	form	NOUN
ejpam-6575	30	9	expression	expression	NOUN
ejpam-6575	30	10	for	for	ADP
ejpam-6575	30	11	in(α	in(α	PUNCT
ejpam-6575	30	12	)	)	PUNCT
ejpam-6575	31	1	=	=	SYM
ejpam-6575	31	2	∫	∫	PROPN
ejpam-6575	32	1	∞	∞	NUM
ejpam-6575	32	2	0	0	NUM
ejpam-6575	32	3	1√	1√	NUM
ejpam-6575	32	4	x	x	SYM
ejpam-6575	32	5	(	(	PUNCT
ejpam-6575	32	6	x2	x2	PROPN
ejpam-6575	32	7	+	+	CCONJ
ejpam-6575	32	8	4α2)n	4α2)n	NUM
ejpam-6575	32	9	dx	dx	PROPN
ejpam-6575	32	10	,	,	PUNCT
ejpam-6575	32	11	for	for	ADP
ejpam-6575	32	12	α	α	PROPN
ejpam-6575	32	13	>	>	X
ejpam-6575	32	14	0	0	NUM
ejpam-6575	32	15	,	,	PUNCT
ejpam-6575	32	16	n	n	DET
ejpam-6575	32	17	∈	∈	PROPN
ejpam-6575	32	18	n.	n.	NOUN
ejpam-6575	32	19	problem	problem	NOUN
ejpam-6575	32	20	3	3	X
ejpam-6575	32	21	.	.	PUNCT
ejpam-6575	32	22	evaluate	evaluate	VERB
ejpam-6575	32	23	i(β	i(β	NOUN
ejpam-6575	32	24	)	)	PUNCT
ejpam-6575	33	1	=	=	SYM
ejpam-6575	34	1	∫	∫	PROPN
ejpam-6575	35	1	∞	∞	NUM
ejpam-6575	35	2	0	0	NUM
ejpam-6575	36	1	x−3/2	x−3/2	PROPN
ejpam-6575	36	2	[	[	PUNCT
ejpam-6575	36	3	f	f	X
ejpam-6575	36	4	(	(	PUNCT
ejpam-6575	36	5	2β	2β	NOUN
ejpam-6575	36	6	x	x	SYM
ejpam-6575	36	7	)	)	PUNCT
ejpam-6575	37	1	−	−	PROPN
ejpam-6575	38	1	f	f	PROPN
ejpam-6575	38	2	(	(	PUNCT
ejpam-6575	38	3	2	2	NUM
ejpam-6575	38	4	x	x	NOUN
ejpam-6575	38	5	)	)	PUNCT
ejpam-6575	38	6	]	]	PUNCT
ejpam-6575	39	1	dx	dx	PROPN
ejpam-6575	39	2	,	,	PUNCT
ejpam-6575	39	3	for	for	ADP
ejpam-6575	39	4	a	a	DET
ejpam-6575	39	5	suitable	suitable	ADJ
ejpam-6575	39	6	function	function	NOUN
ejpam-6575	39	7	f	f	PROPN
ejpam-6575	39	8	and	and	CCONJ
ejpam-6575	39	9	β	β	X
ejpam-6575	39	10	>	>	X
ejpam-6575	39	11	0	0	X
ejpam-6575	39	12	.	.	PUNCT
ejpam-6575	40	1	the	the	DET
ejpam-6575	40	2	author	author	NOUN
ejpam-6575	40	3	in	in	ADP
ejpam-6575	40	4	[	[	X
ejpam-6575	40	5	8	8	NUM
ejpam-6575	40	6	]	]	PUNCT
ejpam-6575	40	7	has	have	AUX
ejpam-6575	40	8	evaluated	evaluate	VERB
ejpam-6575	40	9	the	the	DET
ejpam-6575	40	10	special	special	ADJ
ejpam-6575	40	11	cases	case	NOUN
ejpam-6575	40	12	of	of	ADP
ejpam-6575	40	13	the	the	DET
ejpam-6575	40	14	mentioned	mention	VERB
ejpam-6575	40	15	integrals	integral	NOUN
ejpam-6575	40	16	.	.	PUNCT
ejpam-6575	41	1	we	we	PRON
ejpam-6575	41	2	list	list	VERB
ejpam-6575	41	3	the	the	DET
ejpam-6575	41	4	special	special	ADJ
ejpam-6575	41	5	cases	case	NOUN
ejpam-6575	41	6	as	as	ADP
ejpam-6575	41	7	following	follow	VERB
ejpam-6575	41	8	.	.	PUNCT
ejpam-6575	42	1	corollary	corollary	ADJ
ejpam-6575	42	2	1	1	NUM
ejpam-6575	42	3	.	.	PUNCT
ejpam-6575	42	4	proposition	proposition	NOUN
ejpam-6575	42	5	2.8	2.8	NUM
ejpam-6575	42	6	in	in	ADP
ejpam-6575	42	7	[	[	X
ejpam-6575	42	8	8	8	NUM
ejpam-6575	42	9	]	]	PUNCT
ejpam-6575	42	10	is	be	AUX
ejpam-6575	42	11	a	a	DET
ejpam-6575	42	12	special	special	ADJ
ejpam-6575	42	13	case	case	NOUN
ejpam-6575	42	14	of	of	ADP
ejpam-6575	42	15	problem	problem	NOUN
ejpam-6575	42	16	1	1	NUM
ejpam-6575	42	17	with	with	ADP
ejpam-6575	42	18	α	α	NOUN
ejpam-6575	42	19	=	=	SYM
ejpam-6575	42	20	2	2	NUM
ejpam-6575	42	21	.	.	PUNCT
ejpam-6575	42	22	corollary	corollary	ADJ
ejpam-6575	42	23	2	2	NUM
ejpam-6575	42	24	.	.	PUNCT
ejpam-6575	42	25	proposition	proposition	NOUN
ejpam-6575	42	26	2.2	2.2	NUM
ejpam-6575	42	27	,	,	PUNCT
ejpam-6575	42	28	2.3	2.3	NUM
ejpam-6575	42	29	,	,	PUNCT
ejpam-6575	42	30	and	and	CCONJ
ejpam-6575	42	31	2.4	2.4	NUM
ejpam-6575	42	32	in	in	ADP
ejpam-6575	42	33	[	[	X
ejpam-6575	42	34	8	8	NUM
ejpam-6575	42	35	]	]	PUNCT
ejpam-6575	42	36	are	be	AUX
ejpam-6575	42	37	special	special	ADJ
ejpam-6575	42	38	cases	case	NOUN
ejpam-6575	42	39	of	of	ADP
ejpam-6575	42	40	problem	problem	NOUN
ejpam-6575	42	41	2	2	NUM
ejpam-6575	42	42	with	with	ADP
ejpam-6575	42	43	n	n	NOUN
ejpam-6575	42	44	=	=	SYM
ejpam-6575	42	45	1	1	NUM
ejpam-6575	42	46	,	,	PUNCT
ejpam-6575	42	47	2	2	NUM
ejpam-6575	42	48	and	and	CCONJ
ejpam-6575	42	49	n	n	NOUN
ejpam-6575	42	50	=	=	NOUN
ejpam-6575	42	51	3	3	NUM
ejpam-6575	42	52	respectively	respectively	ADV
ejpam-6575	42	53	.	.	PUNCT
ejpam-6575	43	1	corollary	corollary	ADJ
ejpam-6575	43	2	3	3	NUM
ejpam-6575	43	3	.	.	PUNCT
ejpam-6575	43	4	proposition	proposition	NOUN
ejpam-6575	43	5	2.5	2.5	NUM
ejpam-6575	43	6	in	in	ADP
ejpam-6575	43	7	[	[	X
ejpam-6575	43	8	8	8	NUM
ejpam-6575	43	9	]	]	PUNCT
ejpam-6575	43	10	is	be	AUX
ejpam-6575	43	11	a	a	DET
ejpam-6575	43	12	special	special	ADJ
ejpam-6575	43	13	case	case	NOUN
ejpam-6575	43	14	of	of	ADP
ejpam-6575	43	15	problem	problem	NOUN
ejpam-6575	43	16	3	3	NUM
ejpam-6575	43	17	with	with	ADP
ejpam-6575	43	18	f(x	f(x	PROPN
ejpam-6575	43	19	)	)	PUNCT
ejpam-6575	44	1	=	=	SYM
ejpam-6575	44	2	arctan(x	arctan(x	PROPN
ejpam-6575	44	3	)	)	PUNCT
ejpam-6575	44	4	.	.	PUNCT
ejpam-6575	45	1	the	the	DET
ejpam-6575	45	2	further	further	ADJ
ejpam-6575	45	3	implications	implication	NOUN
ejpam-6575	45	4	of	of	ADP
ejpam-6575	45	5	these	these	DET
ejpam-6575	45	6	corollaries	corollary	NOUN
ejpam-6575	45	7	yield	yield	VERB
ejpam-6575	45	8	some	some	DET
ejpam-6575	45	9	integral	integral	ADJ
ejpam-6575	45	10	formulas	formula	NOUN
ejpam-6575	45	11	for	for	ADP
ejpam-6575	45	12	π	π	PROPN
ejpam-6575	45	13	(	(	PUNCT
ejpam-6575	45	14	see	see	VERB
ejpam-6575	45	15	[	[	X
ejpam-6575	45	16	8	8	NUM
ejpam-6575	45	17	]	]	NUM
ejpam-6575	45	18	)	)	PUNCT
ejpam-6575	45	19	.	.	PUNCT
ejpam-6575	46	1	as	as	ADP
ejpam-6575	46	2	a	a	DET
ejpam-6575	46	3	further	further	ADJ
ejpam-6575	46	4	applications	application	NOUN
ejpam-6575	46	5	,	,	PUNCT
ejpam-6575	46	6	the	the	DET
ejpam-6575	46	7	author	author	NOUN
ejpam-6575	46	8	in	in	ADP
ejpam-6575	46	9	[	[	X
ejpam-6575	46	10	8	8	NUM
ejpam-6575	46	11	]	]	PUNCT
ejpam-6575	46	12	has	have	AUX
ejpam-6575	46	13	applied	apply	VERB
ejpam-6575	46	14	the	the	DET
ejpam-6575	46	15	special	special	ADJ
ejpam-6575	46	16	cases	case	NOUN
ejpam-6575	46	17	of	of	ADP
ejpam-6575	46	18	the	the	DET
ejpam-6575	46	19	integrals	integral	NOUN
ejpam-6575	46	20	given	give	VERB
ejpam-6575	46	21	in	in	ADP
ejpam-6575	46	22	problem	problem	NOUN
ejpam-6575	46	23	1,2	1,2	NUM
ejpam-6575	46	24	and	and	CCONJ
ejpam-6575	46	25	3	3	NUM
ejpam-6575	46	26	to	to	PART
ejpam-6575	46	27	obtain	obtain	VERB
ejpam-6575	46	28	the	the	DET
ejpam-6575	46	29	logarithmic	logarithmic	ADJ
ejpam-6575	46	30	hardy	hardy	ADJ
ejpam-6575	46	31	-	-	PUNCT
ejpam-6575	46	32	hilbert	hilbert	NOUN
ejpam-6575	46	33	-	-	PUNCT
ejpam-6575	46	34	type	type	NOUN
ejpam-6575	46	35	inequalities	inequality	NOUN
ejpam-6575	46	36	[	[	X
ejpam-6575	46	37	9	9	NUM
ejpam-6575	46	38	]	]	PUNCT
ejpam-6575	46	39	(	(	PUNCT
ejpam-6575	46	40	for	for	ADP
ejpam-6575	46	41	example	example	NOUN
ejpam-6575	46	42	see	see	VERB
ejpam-6575	46	43	proposition	proposition	NOUN
ejpam-6575	46	44	2.11	2.11	NUM
ejpam-6575	46	45	etc	etc	X
ejpam-6575	46	46	)	)	PUNCT
ejpam-6575	46	47	.	.	PUNCT
ejpam-6575	47	1	our	our	PRON
ejpam-6575	47	2	goal	goal	NOUN
ejpam-6575	47	3	is	be	AUX
ejpam-6575	47	4	to	to	PART
ejpam-6575	47	5	establish	establish	VERB
ejpam-6575	47	6	the	the	DET
ejpam-6575	47	7	convergence	convergence	NOUN
ejpam-6575	47	8	results	result	NOUN
ejpam-6575	47	9	for	for	ADP
ejpam-6575	47	10	the	the	DET
ejpam-6575	47	11	integrals	integral	NOUN
ejpam-6575	47	12	given	give	VERB
ejpam-6575	47	13	in	in	ADP
ejpam-6575	47	14	problem	problem	NOUN
ejpam-6575	47	15	1	1	NUM
ejpam-6575	47	16	,	,	PUNCT
ejpam-6575	47	17	2	2	NUM
ejpam-6575	47	18	and	and	CCONJ
ejpam-6575	47	19	3	3	NUM
ejpam-6575	47	20	,	,	PUNCT
ejpam-6575	47	21	and	and	CCONJ
ejpam-6575	47	22	evaluate	evaluate	VERB
ejpam-6575	47	23	them	they	PRON
ejpam-6575	47	24	in	in	ADP
ejpam-6575	47	25	closed	closed	ADJ
ejpam-6575	47	26	form	form	NOUN
ejpam-6575	47	27	for	for	ADP
ejpam-6575	47	28	general	general	ADJ
ejpam-6575	47	29	parameters	parameter	NOUN
ejpam-6575	47	30	n	n	CCONJ
ejpam-6575	47	31	,	,	PUNCT
ejpam-6575	47	32	α	α	PROPN
ejpam-6575	47	33	and	and	CCONJ
ejpam-6575	47	34	β	β	NOUN
ejpam-6575	47	35	.	.	NOUN
ejpam-6575	48	1	1	1	X
ejpam-6575	48	2	.	.	X
ejpam-6575	48	3	main	main	ADJ
ejpam-6575	48	4	results	result	NOUN
ejpam-6575	48	5	1.1	1.1	NUM
ejpam-6575	48	6	.	.	PUNCT
ejpam-6575	49	1	convergence	convergence	NOUN
ejpam-6575	49	2	and	and	CCONJ
ejpam-6575	49	3	evaluation	evaluation	NOUN
ejpam-6575	49	4	of	of	ADP
ejpam-6575	49	5	the	the	DET
ejpam-6575	49	6	first	first	ADJ
ejpam-6575	49	7	integral	integral	NOUN
ejpam-6575	49	8	.	.	PUNCT
ejpam-6575	50	1	here	here	ADV
ejpam-6575	50	2	is	be	AUX
ejpam-6575	50	3	the	the	DET
ejpam-6575	50	4	convergence	convergence	NOUN
ejpam-6575	50	5	result	result	NOUN
ejpam-6575	50	6	for	for	ADP
ejpam-6575	50	7	the	the	DET
ejpam-6575	50	8	first	first	ADJ
ejpam-6575	50	9	integral	integral	ADJ
ejpam-6575	50	10	.	.	PUNCT
ejpam-6575	51	1	proposition	proposition	NOUN
ejpam-6575	51	2	1	1	NUM
ejpam-6575	51	3	.	.	PUNCT
ejpam-6575	52	1	let	let	VERB
ejpam-6575	52	2	i(α	i(α	PROPN
ejpam-6575	52	3	)	)	PUNCT
ejpam-6575	53	1	=	=	SYM
ejpam-6575	54	1	∫	∫	PROPN
ejpam-6575	55	1	∞	∞	PROPN
ejpam-6575	55	2	0	0	NUM
ejpam-6575	56	1	x−	x−	PROPN
ejpam-6575	56	2	1	1	NUM
ejpam-6575	56	3	2	2	NUM
ejpam-6575	56	4	ln	ln	NOUN
ejpam-6575	56	5	(	(	PUNCT
ejpam-6575	56	6	1	1	NUM
ejpam-6575	56	7	+	+	NUM
ejpam-6575	56	8	x−α	x−α	NOUN
ejpam-6575	56	9	)	)	PUNCT
ejpam-6575	56	10	dx	dx	PROPN
ejpam-6575	56	11	.	.	PUNCT
ejpam-6575	57	1	if	if	SCONJ
ejpam-6575	57	2	α	α	PROPN
ejpam-6575	57	3	>	>	X
ejpam-6575	57	4	1	1	NUM
ejpam-6575	57	5	2	2	NUM
ejpam-6575	57	6	,	,	PUNCT
ejpam-6575	57	7	then	then	ADV
ejpam-6575	57	8	the	the	DET
ejpam-6575	57	9	improper	improper	ADJ
ejpam-6575	57	10	integral	integral	ADJ
ejpam-6575	57	11	i(α	i(α	PROPN
ejpam-6575	57	12	)	)	PUNCT
ejpam-6575	57	13	converges	converge	NOUN
ejpam-6575	57	14	.	.	PUNCT
ejpam-6575	58	1	proof	proof	NOUN
ejpam-6575	58	2	.	.	PUNCT
ejpam-6575	59	1	we	we	PRON
ejpam-6575	59	2	split	split	VERB
ejpam-6575	59	3	the	the	DET
ejpam-6575	59	4	integral	integral	ADJ
ejpam-6575	59	5	at	at	ADP
ejpam-6575	59	6	x	x	X
ejpam-6575	59	7	=	=	SYM
ejpam-6575	59	8	1	1	NUM
ejpam-6575	59	9	,	,	PUNCT
ejpam-6575	59	10	i(α	i(α	PROPN
ejpam-6575	59	11	)	)	PUNCT
ejpam-6575	60	1	=	=	PUNCT
ejpam-6575	60	2	∫	∫	PROPN
ejpam-6575	61	1	1	1	NUM
ejpam-6575	61	2	0	0	NUM
ejpam-6575	61	3	x−	x−	PROPN
ejpam-6575	61	4	1	1	NUM
ejpam-6575	61	5	2	2	NUM
ejpam-6575	61	6	ln	ln	NOUN
ejpam-6575	61	7	(	(	PUNCT
ejpam-6575	61	8	1	1	NUM
ejpam-6575	61	9	+	+	NUM
ejpam-6575	61	10	x−α	x−α	NOUN
ejpam-6575	61	11	)	)	PUNCT
ejpam-6575	61	12	dx	dx	PROPN
ejpam-6575	62	1	+	+	CCONJ
ejpam-6575	62	2	∫	∫	PROPN
ejpam-6575	62	3	∞	∞	NUM
ejpam-6575	62	4	1	1	NUM
ejpam-6575	62	5	x−	x−	PROPN
ejpam-6575	62	6	1	1	NUM
ejpam-6575	62	7	2	2	NUM
ejpam-6575	62	8	ln	ln	NOUN
ejpam-6575	62	9	(	(	PUNCT
ejpam-6575	62	10	1	1	NUM
ejpam-6575	62	11	+	+	NUM
ejpam-6575	62	12	x−α	x−α	NOUN
ejpam-6575	62	13	)	)	PUNCT
ejpam-6575	62	14	dx	dx	PROPN
ejpam-6575	62	15	=	=	PROPN
ejpam-6575	62	16	i1	i1	PROPN
ejpam-6575	62	17	+	+	CCONJ
ejpam-6575	62	18	i2	i2	PROPN
ejpam-6575	62	19	.	.	PUNCT
ejpam-6575	63	1	i.	i.	PROPN
ejpam-6575	63	2	ayoob	ayoob	PROPN
ejpam-6575	63	3	/	/	SYM
ejpam-6575	63	4	eur	eur	PROPN
ejpam-6575	63	5	.	.	PUNCT
ejpam-6575	64	1	j.	j.	PROPN
ejpam-6575	64	2	pure	pure	PROPN
ejpam-6575	64	3	appl	appl	PROPN
ejpam-6575	64	4	.	.	PROPN
ejpam-6575	64	5	math	math	PROPN
ejpam-6575	64	6	,	,	PUNCT
ejpam-6575	64	7	18	18	NUM
ejpam-6575	64	8	(	(	PUNCT
ejpam-6575	64	9	3	3	NUM
ejpam-6575	64	10	)	)	PUNCT
ejpam-6575	64	11	(	(	PUNCT
ejpam-6575	64	12	2025	2025	NUM
ejpam-6575	64	13	)	)	PUNCT
ejpam-6575	64	14	,	,	PUNCT
ejpam-6575	64	15	6575	6575	NUM
ejpam-6575	64	16	3	3	NUM
ejpam-6575	64	17	of	of	ADP
ejpam-6575	64	18	12	12	NUM
ejpam-6575	64	19	(	(	PUNCT
ejpam-6575	64	20	i	i	NOUN
ejpam-6575	64	21	)	)	PUNCT
ejpam-6575	64	22	convergence	convergence	NOUN
ejpam-6575	64	23	of	of	ADP
ejpam-6575	64	24	i2	i2	PROPN
ejpam-6575	64	25	:	:	PUNCT
ejpam-6575	64	26	for	for	ADP
ejpam-6575	64	27	x	x	X
ejpam-6575	64	28	≥	≥	NOUN
ejpam-6575	64	29	1	1	NUM
ejpam-6575	64	30	,	,	PUNCT
ejpam-6575	64	31	0	0	NUM
ejpam-6575	64	32	≤	≤	NUM
ejpam-6575	64	33	x−α	x−α	PROPN
ejpam-6575	64	34	≤	≤	ADV
ejpam-6575	64	35	1	1	NUM
ejpam-6575	64	36	,	,	PUNCT
ejpam-6575	64	37	and	and	CCONJ
ejpam-6575	64	38	since	since	SCONJ
ejpam-6575	64	39	ln(1	ln(1	PROPN
ejpam-6575	64	40	+	+	NUM
ejpam-6575	64	41	u	u	NOUN
ejpam-6575	64	42	)	)	PUNCT
ejpam-6575	64	43	≤	≤	NUM
ejpam-6575	64	44	u	u	NOUN
ejpam-6575	64	45	for	for	ADP
ejpam-6575	64	46	u	u	PRON
ejpam-6575	64	47	≥	≥	NUM
ejpam-6575	64	48	0	0	NUM
ejpam-6575	64	49	,	,	PUNCT
ejpam-6575	64	50	we	we	PRON
ejpam-6575	64	51	have	have	VERB
ejpam-6575	65	1	0	0	NUM
ejpam-6575	65	2	≤	≤	NOUN
ejpam-6575	65	3	ln	ln	ADJ
ejpam-6575	65	4	(	(	PUNCT
ejpam-6575	65	5	1	1	NUM
ejpam-6575	65	6	+	+	NUM
ejpam-6575	65	7	x−α	x−α	NOUN
ejpam-6575	65	8	)	)	PUNCT
ejpam-6575	66	1	≤	≤	NUM
ejpam-6575	66	2	x−α	x−α	NOUN
ejpam-6575	66	3	.	.	PUNCT
ejpam-6575	67	1	hence	hence	ADV
ejpam-6575	67	2	0	0	NUM
ejpam-6575	67	3	≤	≤	NUM
ejpam-6575	67	4	i2	i2	PROPN
ejpam-6575	67	5	≤	≤	NUM
ejpam-6575	67	6	∫	∫	PROPN
ejpam-6575	68	1	∞	∞	PROPN
ejpam-6575	68	2	1	1	NUM
ejpam-6575	68	3	x−	x−	PROPN
ejpam-6575	68	4	1	1	NUM
ejpam-6575	68	5	2x−α	2x−α	NOUN
ejpam-6575	68	6	dx	dx	PROPN
ejpam-6575	68	7	=	=	SYM
ejpam-6575	69	1	∫	∫	PROPN
ejpam-6575	69	2	∞	∞	PROPN
ejpam-6575	69	3	1	1	NUM
ejpam-6575	69	4	x−(α+	x−(α+	PROPN
ejpam-6575	69	5	1	1	NUM
ejpam-6575	69	6	2	2	NUM
ejpam-6575	69	7	)	)	PUNCT
ejpam-6575	69	8	dx	dx	PROPN
ejpam-6575	69	9	.	.	PUNCT
ejpam-6575	70	1	because	because	SCONJ
ejpam-6575	70	2	α+	α+	PRON
ejpam-6575	70	3	1	1	NUM
ejpam-6575	70	4	2	2	NUM
ejpam-6575	70	5	>	>	SYM
ejpam-6575	70	6	1	1	NUM
ejpam-6575	70	7	,	,	PUNCT
ejpam-6575	70	8	this	this	DET
ejpam-6575	70	9	last	last	ADJ
ejpam-6575	70	10	integral	integral	ADJ
ejpam-6575	70	11	converges	converge	NOUN
ejpam-6575	70	12	,	,	PUNCT
ejpam-6575	70	13	so	so	ADV
ejpam-6575	70	14	i2	i2	PROPN
ejpam-6575	70	15	<	<	X
ejpam-6575	70	16	∞.	∞.	PROPN
ejpam-6575	70	17	(	(	PUNCT
ejpam-6575	70	18	ii	ii	NOUN
ejpam-6575	70	19	)	)	PUNCT
ejpam-6575	70	20	convergence	convergence	NOUN
ejpam-6575	70	21	of	of	ADP
ejpam-6575	70	22	i1	i1	NOUN
ejpam-6575	70	23	:	:	PUNCT
ejpam-6575	70	24	on	on	ADP
ejpam-6575	70	25	(	(	PUNCT
ejpam-6575	70	26	0	0	NUM
ejpam-6575	70	27	,	,	PUNCT
ejpam-6575	70	28	1	1	NUM
ejpam-6575	70	29	]	]	PUNCT
ejpam-6575	70	30	,	,	PUNCT
ejpam-6575	70	31	x−α	x−α	PROPN
ejpam-6575	70	32	≥	≥	NUM
ejpam-6575	70	33	1	1	NUM
ejpam-6575	70	34	.	.	PUNCT
ejpam-6575	71	1	for	for	ADP
ejpam-6575	71	2	u	u	PRON
ejpam-6575	71	3	≥	≥	NUM
ejpam-6575	71	4	1	1	NUM
ejpam-6575	71	5	,	,	PUNCT
ejpam-6575	71	6	ln(1	ln(1	PROPN
ejpam-6575	71	7	+	+	NUM
ejpam-6575	71	8	u	u	NOUN
ejpam-6575	71	9	)	)	PUNCT
ejpam-6575	71	10	=	=	SYM
ejpam-6575	72	1	lnu+	lnu+	PROPN
ejpam-6575	72	2	ln(1	ln(1	PROPN
ejpam-6575	72	3	+	+	CCONJ
ejpam-6575	72	4	u−1	u−1	PROPN
ejpam-6575	72	5	)	)	PUNCT
ejpam-6575	72	6	≤	≤	PUNCT
ejpam-6575	73	1	lnu+	lnu+	PROPN
ejpam-6575	73	2	ln	ln	ADJ
ejpam-6575	73	3	2	2	X
ejpam-6575	73	4	.	.	PUNCT
ejpam-6575	73	5	setting	set	VERB
ejpam-6575	73	6	u	u	NOUN
ejpam-6575	73	7	=	=	NOUN
ejpam-6575	73	8	x−α	x−α	PROPN
ejpam-6575	73	9	gives	give	VERB
ejpam-6575	73	10	ln	ln	NOUN
ejpam-6575	73	11	(	(	PUNCT
ejpam-6575	73	12	1	1	NUM
ejpam-6575	73	13	+	+	NUM
ejpam-6575	73	14	x−α	x−α	NOUN
ejpam-6575	73	15	)	)	PUNCT
ejpam-6575	74	1	≤	≤	PUNCT
ejpam-6575	75	1	ln	ln	ADJ
ejpam-6575	75	2	2	2	NUM
ejpam-6575	75	3	+	+	SYM
ejpam-6575	75	4	α(−	α(−	NUM
ejpam-6575	75	5	lnx	lnx	NOUN
ejpam-6575	75	6	)	)	PUNCT
ejpam-6575	75	7	.	.	PUNCT
ejpam-6575	76	1	therefore	therefore	ADV
ejpam-6575	76	2	for	for	ADP
ejpam-6575	76	3	0	0	NUM
ejpam-6575	76	4	<	<	X
ejpam-6575	76	5	x	x	SYM
ejpam-6575	76	6	≤	≤	NUM
ejpam-6575	76	7	1	1	NUM
ejpam-6575	76	8	,	,	PUNCT
ejpam-6575	76	9	0	0	NUM
ejpam-6575	76	10	≤	≤	NUM
ejpam-6575	76	11	x−	x−	PROPN
ejpam-6575	76	12	1	1	NUM
ejpam-6575	76	13	2	2	NUM
ejpam-6575	76	14	ln	ln	NOUN
ejpam-6575	76	15	(	(	PUNCT
ejpam-6575	76	16	1	1	NUM
ejpam-6575	76	17	+	+	NUM
ejpam-6575	76	18	x−α	x−α	NOUN
ejpam-6575	76	19	)	)	PUNCT
ejpam-6575	76	20	≤	≤	NOUN
ejpam-6575	76	21	(	(	PUNCT
ejpam-6575	76	22	ln	ln	NOUN
ejpam-6575	76	23	2)x−	2)x−	NUM
ejpam-6575	76	24	1	1	NUM
ejpam-6575	76	25	2	2	NUM
ejpam-6575	76	26	+	+	CCONJ
ejpam-6575	76	27	αx−	αx−	NUM
ejpam-6575	76	28	1	1	NUM
ejpam-6575	76	29	2	2	NUM
ejpam-6575	76	30	(	(	PUNCT
ejpam-6575	76	31	−	−	PROPN
ejpam-6575	76	32	lnx	lnx	PROPN
ejpam-6575	76	33	)	)	PUNCT
ejpam-6575	76	34	.	.	PUNCT
ejpam-6575	77	1	we	we	PRON
ejpam-6575	77	2	check	check	VERB
ejpam-6575	77	3	each	each	DET
ejpam-6575	77	4	term	term	NOUN
ejpam-6575	77	5	:	:	PUNCT
ejpam-6575	77	6	∫	∫	PROPN
ejpam-6575	77	7	1	1	NUM
ejpam-6575	77	8	0	0	NUM
ejpam-6575	77	9	x−	x−	PROPN
ejpam-6575	77	10	1	1	NUM
ejpam-6575	77	11	2	2	NUM
ejpam-6575	77	12	dx	dx	NOUN
ejpam-6575	77	13	=	=	SYM
ejpam-6575	77	14	2	2	NUM
ejpam-6575	77	15	,	,	PUNCT
ejpam-6575	77	16	∫	∫	PROPN
ejpam-6575	77	17	1	1	NUM
ejpam-6575	77	18	0	0	NUM
ejpam-6575	77	19	x−	x−	PROPN
ejpam-6575	77	20	1	1	NUM
ejpam-6575	77	21	2	2	NUM
ejpam-6575	77	22	(	(	PUNCT
ejpam-6575	77	23	−	−	PROPN
ejpam-6575	77	24	lnx	lnx	PROPN
ejpam-6575	77	25	)	)	PUNCT
ejpam-6575	77	26	dx	dx	PROPN
ejpam-6575	78	1	=	=	SYM
ejpam-6575	78	2	4	4	X
ejpam-6575	78	3	.	.	X
ejpam-6575	78	4	hence	hence	ADV
ejpam-6575	78	5	i1	i1	PROPN
ejpam-6575	78	6	≤	≤	PROPN
ejpam-6575	78	7	(	(	PUNCT
ejpam-6575	78	8	ln	ln	NOUN
ejpam-6575	78	9	2	2	NUM
ejpam-6575	78	10	)	)	PUNCT
ejpam-6575	78	11	·	·	PUNCT
ejpam-6575	79	1	2	2	NUM
ejpam-6575	79	2	+	+	CCONJ
ejpam-6575	79	3	α	α	NOUN
ejpam-6575	79	4	·	·	PUNCT
ejpam-6575	79	5	4	4	NUM
ejpam-6575	79	6	<	<	X
ejpam-6575	79	7	∞.	∞.	PROPN
ejpam-6575	79	8	combining	combine	VERB
ejpam-6575	79	9	(	(	PUNCT
ejpam-6575	79	10	i	i	NOUN
ejpam-6575	79	11	)	)	PUNCT
ejpam-6575	79	12	and	and	CCONJ
ejpam-6575	79	13	(	(	PUNCT
ejpam-6575	79	14	ii	ii	NOUN
ejpam-6575	79	15	)	)	PUNCT
ejpam-6575	79	16	shows	show	VERB
ejpam-6575	79	17	i1	i1	PROPN
ejpam-6575	79	18	<	<	X
ejpam-6575	79	19	∞	∞	PROPN
ejpam-6575	79	20	and	and	CCONJ
ejpam-6575	79	21	i2	i2	PROPN
ejpam-6575	79	22	<	<	X
ejpam-6575	79	23	∞.	∞.	PROPN
ejpam-6575	79	24	thus	thus	ADV
ejpam-6575	79	25	i(α	i(α	PROPN
ejpam-6575	79	26	)	)	PUNCT
ejpam-6575	79	27	converges	converge	VERB
ejpam-6575	79	28	for	for	ADP
ejpam-6575	79	29	all	all	DET
ejpam-6575	79	30	α	α	NOUN
ejpam-6575	79	31	>	>	X
ejpam-6575	79	32	1	1	NUM
ejpam-6575	79	33	2	2	NUM
ejpam-6575	79	34	.	.	PUNCT
ejpam-6575	80	1	now	now	ADV
ejpam-6575	80	2	we	we	PRON
ejpam-6575	80	3	solve	solve	VERB
ejpam-6575	80	4	the	the	DET
ejpam-6575	80	5	first	first	ADJ
ejpam-6575	80	6	integral	integral	ADJ
ejpam-6575	80	7	.	.	PUNCT
ejpam-6575	81	1	theorem	theorem	NOUN
ejpam-6575	81	2	1	1	NUM
ejpam-6575	81	3	.	.	PUNCT
ejpam-6575	82	1	for	for	ADP
ejpam-6575	82	2	every	every	DET
ejpam-6575	82	3	α	α	NOUN
ejpam-6575	82	4	>	>	X
ejpam-6575	82	5	1	1	NUM
ejpam-6575	82	6	2	2	NUM
ejpam-6575	82	7	,	,	PUNCT
ejpam-6575	82	8	we	we	PRON
ejpam-6575	82	9	have	have	VERB
ejpam-6575	82	10	i(α	i(α	PROPN
ejpam-6575	82	11	)	)	PUNCT
ejpam-6575	83	1	=	=	SYM
ejpam-6575	84	1	∫	∫	PROPN
ejpam-6575	85	1	∞	∞	PROPN
ejpam-6575	85	2	0	0	NUM
ejpam-6575	86	1	x−	x−	PROPN
ejpam-6575	86	2	1	1	NUM
ejpam-6575	86	3	2	2	NUM
ejpam-6575	86	4	ln	ln	NOUN
ejpam-6575	86	5	(	(	PUNCT
ejpam-6575	86	6	1	1	NUM
ejpam-6575	86	7	+	+	NUM
ejpam-6575	86	8	x−α	x−α	NOUN
ejpam-6575	86	9	)	)	PUNCT
ejpam-6575	86	10	dx	dx	PROPN
ejpam-6575	87	1	=	=	SYM
ejpam-6575	87	2	2π	2π	PROPN
ejpam-6575	87	3	csc	csc	PROPN
ejpam-6575	87	4	(	(	PUNCT
ejpam-6575	87	5	π	π	PROPN
ejpam-6575	87	6	2α	2α	NOUN
ejpam-6575	87	7	)	)	PUNCT
ejpam-6575	87	8	.	.	PUNCT
ejpam-6575	88	1	proof	proof	NOUN
ejpam-6575	88	2	.	.	PUNCT
ejpam-6575	89	1	we	we	PRON
ejpam-6575	89	2	write	write	VERB
ejpam-6575	89	3	i(α	i(α	PROPN
ejpam-6575	89	4	)	)	PUNCT
ejpam-6575	90	1	=	=	PUNCT
ejpam-6575	91	1	∫	∫	PROPN
ejpam-6575	92	1	∞	∞	PROPN
ejpam-6575	92	2	0	0	NUM
ejpam-6575	93	1	x−	x−	PROPN
ejpam-6575	93	2	1	1	NUM
ejpam-6575	93	3	2	2	NUM
ejpam-6575	93	4	ln	ln	NOUN
ejpam-6575	93	5	(	(	PUNCT
ejpam-6575	93	6	1	1	NUM
ejpam-6575	93	7	+	+	NUM
ejpam-6575	93	8	x−α	x−α	NOUN
ejpam-6575	93	9	)	)	PUNCT
ejpam-6575	93	10	dx	dx	PROPN
ejpam-6575	93	11	.	.	PUNCT
ejpam-6575	94	1	since	since	SCONJ
ejpam-6575	94	2	∂	∂	NUM
ejpam-6575	94	3	∂α	∂α	NOUN
ejpam-6575	94	4	ln	ln	NOUN
ejpam-6575	94	5	(	(	PUNCT
ejpam-6575	94	6	1	1	NUM
ejpam-6575	94	7	+	+	NUM
ejpam-6575	94	8	x−α	x−α	NOUN
ejpam-6575	94	9	)	)	PUNCT
ejpam-6575	95	1	=	=	PUNCT
ejpam-6575	96	1	−x−α	−x−α	PROPN
ejpam-6575	96	2	lnx	lnx	NOUN
ejpam-6575	96	3	1	1	NUM
ejpam-6575	96	4	+	+	NUM
ejpam-6575	96	5	x−α	x−α	PROPN
ejpam-6575	96	6	,	,	PUNCT
ejpam-6575	96	7	we	we	PRON
ejpam-6575	96	8	may	may	AUX
ejpam-6575	96	9	differentiate	differentiate	VERB
ejpam-6575	96	10	under	under	ADP
ejpam-6575	96	11	the	the	DET
ejpam-6575	96	12	integral	integral	ADJ
ejpam-6575	96	13	sign	sign	NOUN
ejpam-6575	96	14	to	to	PART
ejpam-6575	96	15	obtain	obtain	VERB
ejpam-6575	96	16	di	di	X
ejpam-6575	96	17	dα	dα	NOUN
ejpam-6575	96	18	=	=	PUNCT
ejpam-6575	96	19	−	−	PROPN
ejpam-6575	96	20	∫	∫	PROPN
ejpam-6575	96	21	∞	∞	PROPN
ejpam-6575	96	22	0	0	NUM
ejpam-6575	97	1	x−	x−	PROPN
ejpam-6575	97	2	1	1	NUM
ejpam-6575	97	3	2	2	NUM
ejpam-6575	97	4	x−α	x−α	NOUN
ejpam-6575	97	5	lnx	lnx	NOUN
ejpam-6575	97	6	1	1	NUM
ejpam-6575	98	1	+	+	NUM
ejpam-6575	98	2	x−α	x−α	PROPN
ejpam-6575	98	3	dx	dx	PROPN
ejpam-6575	99	1	=	=	PUNCT
ejpam-6575	100	1	−	−	PROPN
ejpam-6575	100	2	∫	∫	PROPN
ejpam-6575	100	3	∞	∞	PROPN
ejpam-6575	100	4	0	0	NUM
ejpam-6575	100	5	x−	x−	PROPN
ejpam-6575	100	6	1	1	NUM
ejpam-6575	100	7	2	2	NUM
ejpam-6575	100	8	lnx	lnx	NOUN
ejpam-6575	100	9	xα	xα	PUNCT
ejpam-6575	101	1	+	+	CCONJ
ejpam-6575	101	2	1	1	NUM
ejpam-6575	101	3	dx	dx	PROPN
ejpam-6575	101	4	.	.	PUNCT
ejpam-6575	101	5	i.	i.	PROPN
ejpam-6575	101	6	ayoob	ayoob	PROPN
ejpam-6575	101	7	/	/	SYM
ejpam-6575	101	8	eur	eur	PROPN
ejpam-6575	101	9	.	.	PUNCT
ejpam-6575	102	1	j.	j.	PROPN
ejpam-6575	102	2	pure	pure	PROPN
ejpam-6575	102	3	appl	appl	PROPN
ejpam-6575	102	4	.	.	PROPN
ejpam-6575	102	5	math	math	PROPN
ejpam-6575	102	6	,	,	PUNCT
ejpam-6575	102	7	18	18	NUM
ejpam-6575	102	8	(	(	PUNCT
ejpam-6575	102	9	3	3	NUM
ejpam-6575	102	10	)	)	PUNCT
ejpam-6575	102	11	(	(	PUNCT
ejpam-6575	102	12	2025	2025	NUM
ejpam-6575	102	13	)	)	PUNCT
ejpam-6575	102	14	,	,	PUNCT
ejpam-6575	102	15	6575	6575	NUM
ejpam-6575	102	16	4	4	NUM
ejpam-6575	102	17	of	of	ADP
ejpam-6575	102	18	12	12	NUM
ejpam-6575	102	19	set	set	NOUN
ejpam-6575	102	20	u	u	NOUN
ejpam-6575	102	21	=	=	PUNCT
ejpam-6575	102	22	xα	xα	PROPN
ejpam-6575	102	23	,	,	PUNCT
ejpam-6575	102	24	so	so	SCONJ
ejpam-6575	102	25	that	that	SCONJ
ejpam-6575	102	26	x	x	X
ejpam-6575	102	27	=	=	SYM
ejpam-6575	102	28	u1	u1	PROPN
ejpam-6575	102	29	/	/	SYM
ejpam-6575	102	30	α	α	PROPN
ejpam-6575	102	31	,	,	PUNCT
ejpam-6575	102	32	dx	dx	PROPN
ejpam-6575	102	33	=	=	NOUN
ejpam-6575	102	34	1	1	NUM
ejpam-6575	102	35	α	α	NUM
ejpam-6575	102	36	u	u	NOUN
ejpam-6575	102	37	1	1	NUM
ejpam-6575	102	38	α−1du	α−1du	ADV
ejpam-6575	102	39	,	,	PUNCT
ejpam-6575	102	40	lnx	lnx	PROPN
ejpam-6575	102	41	=	=	SYM
ejpam-6575	102	42	1	1	NUM
ejpam-6575	102	43	α	α	PRON
ejpam-6575	102	44	lnu	lnu	PROPN
ejpam-6575	102	45	,	,	PUNCT
ejpam-6575	102	46	x−	x−	PROPN
ejpam-6575	102	47	1	1	NUM
ejpam-6575	102	48	2	2	NUM
ejpam-6575	102	49	=	=	SYM
ejpam-6575	102	50	u−	u−	PROPN
ejpam-6575	102	51	1	1	NUM
ejpam-6575	102	52	2α	2α	NOUN
ejpam-6575	102	53	.	.	PUNCT
ejpam-6575	103	1	then	then	ADV
ejpam-6575	103	2	di	di	VERB
ejpam-6575	103	3	dα	dα	NOUN
ejpam-6575	104	1	=	=	PUNCT
ejpam-6575	104	2	−	−	PROPN
ejpam-6575	104	3	1	1	NUM
ejpam-6575	104	4	α2	α2	ADJ
ejpam-6575	104	5	∫	∫	PROPN
ejpam-6575	104	6	∞	∞	PROPN
ejpam-6575	104	7	0	0	NUM
ejpam-6575	104	8	u−	u−	PROPN
ejpam-6575	104	9	1	1	NUM
ejpam-6575	104	10	2α+	2α+	NUM
ejpam-6575	104	11	1	1	NUM
ejpam-6575	104	12	α−1	α−1	PROPN
ejpam-6575	104	13	lnu	lnu	NOUN
ejpam-6575	104	14	u+	u+	NOUN
ejpam-6575	104	15	1	1	NUM
ejpam-6575	104	16	du	du	NOUN
ejpam-6575	104	17	=	=	SYM
ejpam-6575	104	18	−	−	PROPN
ejpam-6575	104	19	1	1	NUM
ejpam-6575	104	20	α2	α2	ADJ
ejpam-6575	104	21	∫	∫	PROPN
ejpam-6575	104	22	∞	∞	NOUN
ejpam-6575	104	23	0	0	X
ejpam-6575	105	1	us−1	us−1	NOUN
ejpam-6575	105	2	lnu	lnu	VERB
ejpam-6575	105	3	1	1	NUM
ejpam-6575	105	4	+	+	NUM
ejpam-6575	105	5	u	u	NOUN
ejpam-6575	105	6	du	du	NOUN
ejpam-6575	105	7	,	,	PUNCT
ejpam-6575	105	8	where	where	SCONJ
ejpam-6575	105	9	s	s	AUX
ejpam-6575	105	10	=	=	SYM
ejpam-6575	105	11	1	1	NUM
ejpam-6575	105	12	2α	2α	NOUN
ejpam-6575	105	13	∈	∈	PROPN
ejpam-6575	105	14	(	(	PUNCT
ejpam-6575	105	15	0	0	NUM
ejpam-6575	105	16	,	,	PUNCT
ejpam-6575	105	17	1	1	NUM
ejpam-6575	105	18	)	)	PUNCT
ejpam-6575	105	19	.	.	PUNCT
ejpam-6575	106	1	the	the	DET
ejpam-6575	106	2	following	follow	VERB
ejpam-6575	106	3	integral	integral	ADJ
ejpam-6575	106	4	is	be	AUX
ejpam-6575	106	5	well	well	ADV
ejpam-6575	106	6	-	-	PUNCT
ejpam-6575	106	7	known	know	VERB
ejpam-6575	106	8	(	(	PUNCT
ejpam-6575	106	9	see	see	VERB
ejpam-6575	106	10	[	[	PUNCT
ejpam-6575	106	11	1]),∫	1]),∫	NUM
ejpam-6575	106	12	∞	∞	NOUN
ejpam-6575	106	13	0	0	PUNCT
ejpam-6575	107	1	us−1	us−1	NOUN
ejpam-6575	107	2	1	1	NUM
ejpam-6575	107	3	+	+	NUM
ejpam-6575	107	4	u	u	NOUN
ejpam-6575	107	5	du	du	NOUN
ejpam-6575	107	6	=	=	SYM
ejpam-6575	107	7	π	π	PROPN
ejpam-6575	107	8	sin(πs	sin(πs	ADV
ejpam-6575	107	9	)	)	PUNCT
ejpam-6575	107	10	,	,	PUNCT
ejpam-6575	107	11	and	and	CCONJ
ejpam-6575	107	12	differentiating	differentiate	VERB
ejpam-6575	107	13	in	in	ADP
ejpam-6575	107	14	s	s	PRON
ejpam-6575	107	15	yields∫	yields∫	NOUN
ejpam-6575	107	16	∞	∞	NOUN
ejpam-6575	107	17	0	0	PUNCT
ejpam-6575	108	1	us−1	us−1	NOUN
ejpam-6575	108	2	lnu	lnu	VERB
ejpam-6575	108	3	1	1	NUM
ejpam-6575	108	4	+	+	NUM
ejpam-6575	108	5	u	u	NOUN
ejpam-6575	108	6	du	du	X
ejpam-6575	108	7	=	=	NOUN
ejpam-6575	108	8	−π2	−π2	PROPN
ejpam-6575	108	9	cos(πs	cos(π	NOUN
ejpam-6575	108	10	)	)	PUNCT
ejpam-6575	108	11	sin2(πs	sin2(πs	NOUN
ejpam-6575	108	12	)	)	PUNCT
ejpam-6575	108	13	.	.	PUNCT
ejpam-6575	109	1	hence	hence	ADV
ejpam-6575	109	2	di	di	VERB
ejpam-6575	109	3	dα	dα	NOUN
ejpam-6575	109	4	=	=	PROPN
ejpam-6575	109	5	π2	π2	PROPN
ejpam-6575	109	6	α2	α2	PROPN
ejpam-6575	109	7	cos	cos	PROPN
ejpam-6575	109	8	(	(	PUNCT
ejpam-6575	109	9	π	π	PROPN
ejpam-6575	109	10	2α	2α	NOUN
ejpam-6575	109	11	)	)	PUNCT
ejpam-6575	109	12	sin2	sin2	NOUN
ejpam-6575	109	13	(	(	PUNCT
ejpam-6575	109	14	π	π	NOUN
ejpam-6575	109	15	2α	2α	NOUN
ejpam-6575	109	16	)	)	PUNCT
ejpam-6575	109	17	.	.	PUNCT
ejpam-6575	110	1	next	next	ADV
ejpam-6575	110	2	,	,	PUNCT
ejpam-6575	110	3	we	we	PRON
ejpam-6575	110	4	set	set	VERB
ejpam-6575	110	5	t	t	NOUN
ejpam-6575	110	6	=	=	PUNCT
ejpam-6575	111	1	π	π	X
ejpam-6575	111	2	2α	2α	NOUN
ejpam-6575	111	3	,	,	PUNCT
ejpam-6575	111	4	so	so	SCONJ
ejpam-6575	111	5	that	that	SCONJ
ejpam-6575	111	6	α	α	PRON
ejpam-6575	111	7	=	=	PUNCT
ejpam-6575	111	8	π	π	PROPN
ejpam-6575	111	9	2	2	NUM
ejpam-6575	111	10	t	t	NOUN
ejpam-6575	111	11	and	and	CCONJ
ejpam-6575	111	12	dα	dα	ADJ
ejpam-6575	111	13	=	=	PUNCT
ejpam-6575	111	14	−	−	PROPN
ejpam-6575	111	15	π	π	PROPN
ejpam-6575	111	16	2t2	2t2	NUM
ejpam-6575	111	17	dt	dt	X
ejpam-6575	111	18	,	,	PUNCT
ejpam-6575	111	19	π2	π2	ADJ
ejpam-6575	111	20	α2	α2	PROPN
ejpam-6575	111	21	=	=	SYM
ejpam-6575	111	22	4t2	4t2	PROPN
ejpam-6575	111	23	.	.	PUNCT
ejpam-6575	112	1	thus	thus	ADV
ejpam-6575	112	2	di	di	VERB
ejpam-6575	112	3	dα	dα	PROPN
ejpam-6575	112	4	dα	dα	PROPN
ejpam-6575	112	5	=	=	PROPN
ejpam-6575	112	6	4t2	4t2	PROPN
ejpam-6575	112	7	cos	cos	PROPN
ejpam-6575	112	8	t	t	PROPN
ejpam-6575	112	9	sin2	sin2	PROPN
ejpam-6575	112	10	t	t	PROPN
ejpam-6575	112	11	(	(	PUNCT
ejpam-6575	112	12	−	−	PROPN
ejpam-6575	112	13	π	π	PROPN
ejpam-6575	112	14	2t2	2t2	NUM
ejpam-6575	112	15	dt	dt	NOUN
ejpam-6575	112	16	)	)	PUNCT
ejpam-6575	113	1	=	=	SYM
ejpam-6575	113	2	−2π	−2π	PROPN
ejpam-6575	113	3	cos	cos	PROPN
ejpam-6575	113	4	t	t	PROPN
ejpam-6575	113	5	sin2	sin2	PROPN
ejpam-6575	113	6	t	t	PROPN
ejpam-6575	113	7	dt	dt	NOUN
ejpam-6575	114	1	=	=	PUNCT
ejpam-6575	114	2	2π	2π	PROPN
ejpam-6575	114	3	d	d	X
ejpam-6575	114	4	(	(	PUNCT
ejpam-6575	114	5	csc	csc	PROPN
ejpam-6575	114	6	t	t	PROPN
ejpam-6575	114	7	)	)	PUNCT
ejpam-6575	114	8	.	.	PUNCT
ejpam-6575	115	1	integrating	integrate	VERB
ejpam-6575	115	2	shows	show	VERB
ejpam-6575	115	3	i(α	i(α	PROPN
ejpam-6575	115	4	)	)	PUNCT
ejpam-6575	116	1	=	=	SYM
ejpam-6575	117	1	2π	2π	PROPN
ejpam-6575	117	2	csc	csc	PROPN
ejpam-6575	117	3	(	(	PUNCT
ejpam-6575	117	4	π	π	PROPN
ejpam-6575	117	5	2α	2α	NOUN
ejpam-6575	117	6	)	)	PUNCT
ejpam-6575	118	1	+	+	CCONJ
ejpam-6575	118	2	c.	c.	NOUN
ejpam-6575	118	3	finally	finally	ADV
ejpam-6575	118	4	,	,	PUNCT
ejpam-6575	118	5	i(2	i(2	PROPN
ejpam-6575	118	6	)	)	PUNCT
ejpam-6575	118	7	=	=	SYM
ejpam-6575	118	8	2π	2π	PROPN
ejpam-6575	118	9	csc	csc	PROPN
ejpam-6575	118	10	(	(	PUNCT
ejpam-6575	118	11	π	π	PROPN
ejpam-6575	118	12	2·2	2·2	NUM
ejpam-6575	118	13	)	)	PUNCT
ejpam-6575	119	1	+	+	CCONJ
ejpam-6575	119	2	c	c	X
ejpam-6575	119	3	=	=	SYM
ejpam-6575	119	4	2π	2π	PROPN
ejpam-6575	119	5	csc	csc	PROPN
ejpam-6575	119	6	(	(	PUNCT
ejpam-6575	119	7	π	π	PROPN
ejpam-6575	119	8	4	4	NUM
ejpam-6575	119	9	)	)	PUNCT
ejpam-6575	119	10	+	+	NUM
ejpam-6575	119	11	c	c	X
ejpam-6575	119	12	=	=	SYM
ejpam-6575	119	13	2π	2π	NOUN
ejpam-6575	119	14	√	√	VERB
ejpam-6575	119	15	2	2	NUM
ejpam-6575	119	16	+	+	CCONJ
ejpam-6575	119	17	c.	c.	NOUN
ejpam-6575	119	18	since	since	SCONJ
ejpam-6575	119	19	we	we	PRON
ejpam-6575	119	20	know	know	VERB
ejpam-6575	119	21	[	[	X
ejpam-6575	119	22	8	8	NUM
ejpam-6575	119	23	]	]	PUNCT
ejpam-6575	119	24	that	that	SCONJ
ejpam-6575	119	25	i(2	i(2	PROPN
ejpam-6575	119	26	)	)	PUNCT
ejpam-6575	119	27	=	=	NUM
ejpam-6575	119	28	2π	2π	NOUN
ejpam-6575	119	29	√	√	VERB
ejpam-6575	119	30	2	2	NUM
ejpam-6575	119	31	,	,	PUNCT
ejpam-6575	119	32	it	it	PRON
ejpam-6575	119	33	follows	follow	VERB
ejpam-6575	119	34	that	that	SCONJ
ejpam-6575	119	35	2π	2π	NOUN
ejpam-6575	119	36	√	√	ADV
ejpam-6575	119	37	2	2	NUM
ejpam-6575	119	38	=	=	SYM
ejpam-6575	119	39	2π	2π	NOUN
ejpam-6575	119	40	√	√	VERB
ejpam-6575	119	41	2	2	NUM
ejpam-6575	119	42	+	+	CCONJ
ejpam-6575	119	43	c	c	NOUN
ejpam-6575	119	44	=	=	NOUN
ejpam-6575	119	45	⇒	⇒	NOUN
ejpam-6575	119	46	c	c	NOUN
ejpam-6575	119	47	=	=	SYM
ejpam-6575	119	48	0	0	PROPN
ejpam-6575	119	49	.	.	PUNCT
ejpam-6575	119	50	i.	i.	PROPN
ejpam-6575	119	51	ayoob	ayoob	PROPN
ejpam-6575	119	52	/	/	SYM
ejpam-6575	119	53	eur	eur	PROPN
ejpam-6575	119	54	.	.	PUNCT
ejpam-6575	120	1	j.	j.	PROPN
ejpam-6575	120	2	pure	pure	PROPN
ejpam-6575	120	3	appl	appl	PROPN
ejpam-6575	120	4	.	.	PROPN
ejpam-6575	120	5	math	math	PROPN
ejpam-6575	120	6	,	,	PUNCT
ejpam-6575	120	7	18	18	NUM
ejpam-6575	120	8	(	(	PUNCT
ejpam-6575	120	9	3	3	NUM
ejpam-6575	120	10	)	)	PUNCT
ejpam-6575	120	11	(	(	PUNCT
ejpam-6575	120	12	2025	2025	NUM
ejpam-6575	120	13	)	)	PUNCT
ejpam-6575	120	14	,	,	PUNCT
ejpam-6575	120	15	6575	6575	NUM
ejpam-6575	120	16	5	5	NUM
ejpam-6575	120	17	of	of	ADP
ejpam-6575	120	18	12	12	NUM
ejpam-6575	120	19	1.2	1.2	NUM
ejpam-6575	120	20	.	.	PUNCT
ejpam-6575	121	1	convergence	convergence	NOUN
ejpam-6575	121	2	and	and	CCONJ
ejpam-6575	121	3	evaluation	evaluation	NOUN
ejpam-6575	121	4	of	of	ADP
ejpam-6575	121	5	the	the	DET
ejpam-6575	121	6	second	second	ADJ
ejpam-6575	121	7	integral	integral	NOUN
ejpam-6575	121	8	.	.	PUNCT
ejpam-6575	122	1	here	here	ADV
ejpam-6575	122	2	is	be	AUX
ejpam-6575	122	3	the	the	DET
ejpam-6575	122	4	convergence	convergence	NOUN
ejpam-6575	122	5	result	result	NOUN
ejpam-6575	122	6	for	for	ADP
ejpam-6575	122	7	the	the	DET
ejpam-6575	122	8	second	second	ADJ
ejpam-6575	122	9	integral	integral	ADJ
ejpam-6575	122	10	.	.	PUNCT
ejpam-6575	123	1	proposition	proposition	NOUN
ejpam-6575	123	2	2	2	NUM
ejpam-6575	123	3	.	.	PUNCT
ejpam-6575	124	1	let	let	VERB
ejpam-6575	124	2	α	α	PRON
ejpam-6575	124	3	>	>	X
ejpam-6575	124	4	0	0	PUNCT
ejpam-6575	125	1	and	and	CCONJ
ejpam-6575	125	2	n	n	PRON
ejpam-6575	125	3	∈	∈	PROPN
ejpam-6575	125	4	n	n	CCONJ
ejpam-6575	125	5	,	,	PUNCT
ejpam-6575	125	6	n	n	PRON
ejpam-6575	125	7	≥	≥	NOUN
ejpam-6575	125	8	1	1	NUM
ejpam-6575	125	9	.	.	PUNCT
ejpam-6575	126	1	then	then	ADV
ejpam-6575	126	2	in(α	in(α	PUNCT
ejpam-6575	126	3	)	)	PUNCT
ejpam-6575	127	1	=	=	SYM
ejpam-6575	127	2	∫	∫	PROPN
ejpam-6575	128	1	∞	∞	NUM
ejpam-6575	128	2	0	0	NUM
ejpam-6575	128	3	1	1	NUM
ejpam-6575	128	4	√	√	NUM
ejpam-6575	128	5	x	x	SYM
ejpam-6575	128	6	(	(	PUNCT
ejpam-6575	128	7	x2	x2	NOUN
ejpam-6575	128	8	+	+	NUM
ejpam-6575	128	9	4α2	4α2	NUM
ejpam-6575	128	10	)	)	PUNCT
ejpam-6575	128	11	n	n	CCONJ
ejpam-6575	128	12	dx	dx	PROPN
ejpam-6575	128	13	converges	converge	NOUN
ejpam-6575	128	14	.	.	PUNCT
ejpam-6575	129	1	proof	proof	NOUN
ejpam-6575	129	2	.	.	PUNCT
ejpam-6575	130	1	we	we	PRON
ejpam-6575	130	2	split	split	VERB
ejpam-6575	130	3	the	the	DET
ejpam-6575	130	4	integral	integral	ADJ
ejpam-6575	130	5	at	at	ADP
ejpam-6575	130	6	x	x	X
ejpam-6575	130	7	=	=	SYM
ejpam-6575	130	8	1	1	NUM
ejpam-6575	130	9	,	,	PUNCT
ejpam-6575	130	10	in(α	in(α	PUNCT
ejpam-6575	130	11	)	)	PUNCT
ejpam-6575	131	1	=	=	SYM
ejpam-6575	131	2	∫	∫	PROPN
ejpam-6575	131	3	1	1	NUM
ejpam-6575	131	4	0	0	NUM
ejpam-6575	131	5	dx√	dx√	NOUN
ejpam-6575	131	6	x	x	SYM
ejpam-6575	132	1	(	(	PUNCT
ejpam-6575	132	2	x2	x2	NOUN
ejpam-6575	132	3	+	+	NUM
ejpam-6575	132	4	4α2)n	4α2)n	NUM
ejpam-6575	132	5	+	+	CCONJ
ejpam-6575	132	6	∫	∫	PROPN
ejpam-6575	132	7	∞	∞	NUM
ejpam-6575	132	8	1	1	NUM
ejpam-6575	132	9	dx√	dx√	NOUN
ejpam-6575	132	10	x	x	SYM
ejpam-6575	132	11	(	(	PUNCT
ejpam-6575	132	12	x2	x2	NOUN
ejpam-6575	132	13	+	+	NUM
ejpam-6575	132	14	4α2)n	4α2)n	PROPN
ejpam-6575	132	15	=	=	PROPN
ejpam-6575	132	16	i1	i1	PROPN
ejpam-6575	132	17	+	+	CCONJ
ejpam-6575	132	18	i2	i2	PROPN
ejpam-6575	132	19	.	.	PROPN
ejpam-6575	133	1	1	1	X
ejpam-6575	133	2	.	.	X
ejpam-6575	133	3	convergence	convergence	NOUN
ejpam-6575	133	4	on	on	ADP
ejpam-6575	133	5	[	[	X
ejpam-6575	133	6	0	0	NUM
ejpam-6575	133	7	,	,	PUNCT
ejpam-6575	133	8	1	1	NUM
ejpam-6575	133	9	]	]	PUNCT
ejpam-6575	133	10	:	:	PUNCT
ejpam-6575	133	11	for	for	SCONJ
ejpam-6575	133	12	0	0	NUM
ejpam-6575	133	13	<	<	X
ejpam-6575	133	14	x	x	SYM
ejpam-6575	133	15	≤	≤	NUM
ejpam-6575	133	16	1	1	NUM
ejpam-6575	133	17	,	,	PUNCT
ejpam-6575	133	18	we	we	PRON
ejpam-6575	133	19	have	have	VERB
ejpam-6575	133	20	x2	x2	PROPN
ejpam-6575	134	1	+	+	NUM
ejpam-6575	134	2	4α2	4α2	NUM
ejpam-6575	134	3	≥	≥	NOUN
ejpam-6575	134	4	4α2	4α2	NUM
ejpam-6575	134	5	,	,	PUNCT
ejpam-6575	134	6	so	so	ADV
ejpam-6575	134	7	1√	1√	PROPN
ejpam-6575	134	8	x	x	SYM
ejpam-6575	134	9	(	(	PUNCT
ejpam-6575	135	1	x2	x2	NOUN
ejpam-6575	135	2	+	+	CCONJ
ejpam-6575	135	3	4α2)n	4α2)n	NUM
ejpam-6575	135	4	≤	≤	X
ejpam-6575	135	5	1√	1√	PROPN
ejpam-6575	135	6	x	x	SYM
ejpam-6575	135	7	(	(	PUNCT
ejpam-6575	135	8	4α2)n	4α2)n	NUM
ejpam-6575	135	9	=	=	SYM
ejpam-6575	135	10	(	(	PUNCT
ejpam-6575	135	11	4α2)−n	4α2)−n	NOUN
ejpam-6575	135	12	x−	x−	PROPN
ejpam-6575	135	13	1	1	NUM
ejpam-6575	135	14	2	2	NUM
ejpam-6575	135	15	.	.	PUNCT
ejpam-6575	136	1	since	since	SCONJ
ejpam-6575	136	2	∫	∫	PROPN
ejpam-6575	136	3	1	1	NUM
ejpam-6575	136	4	0	0	NUM
ejpam-6575	136	5	x−	x−	PROPN
ejpam-6575	136	6	1	1	NUM
ejpam-6575	136	7	2	2	NUM
ejpam-6575	136	8	dx	dx	NOUN
ejpam-6575	136	9	=	=	SYM
ejpam-6575	136	10	2	2	NUM
ejpam-6575	136	11	<	<	X
ejpam-6575	136	12	∞	∞	PROPN
ejpam-6575	136	13	,	,	PUNCT
ejpam-6575	136	14	it	it	PRON
ejpam-6575	136	15	follows	follow	VERB
ejpam-6575	136	16	by	by	ADP
ejpam-6575	136	17	the	the	DET
ejpam-6575	136	18	comparison	comparison	NOUN
ejpam-6575	136	19	test	test	NOUN
ejpam-6575	136	20	that	that	PRON
ejpam-6575	136	21	i1	i1	PROPN
ejpam-6575	136	22	<	<	X
ejpam-6575	136	23	∞.	∞.	PROPN
ejpam-6575	136	24	2	2	NUM
ejpam-6575	136	25	.	.	PUNCT
ejpam-6575	137	1	convergence	convergence	NOUN
ejpam-6575	137	2	on	on	ADP
ejpam-6575	137	3	[	[	X
ejpam-6575	137	4	1,∞	1,∞	NUM
ejpam-6575	137	5	)	)	PUNCT
ejpam-6575	137	6	:	:	PUNCT
ejpam-6575	137	7	for	for	ADP
ejpam-6575	137	8	x	x	X
ejpam-6575	137	9	≥	≥	NOUN
ejpam-6575	137	10	1	1	NUM
ejpam-6575	137	11	,	,	PUNCT
ejpam-6575	137	12	we	we	PRON
ejpam-6575	137	13	have	have	VERB
ejpam-6575	137	14	x2	x2	PROPN
ejpam-6575	138	1	+	+	NUM
ejpam-6575	138	2	4α2	4α2	NUM
ejpam-6575	138	3	≥	≥	NOUN
ejpam-6575	138	4	x2	x2	NUM
ejpam-6575	138	5	,	,	PUNCT
ejpam-6575	138	6	so	so	ADV
ejpam-6575	138	7	1√	1√	PROPN
ejpam-6575	138	8	x	x	SYM
ejpam-6575	138	9	(	(	PUNCT
ejpam-6575	138	10	x2	x2	NOUN
ejpam-6575	138	11	+	+	CCONJ
ejpam-6575	138	12	4α2)n	4α2)n	PROPN
ejpam-6575	138	13	≤	≤	NUM
ejpam-6575	138	14	1√	1√	PROPN
ejpam-6575	138	15	xx2n	xx2n	PROPN
ejpam-6575	138	16	=	=	SYM
ejpam-6575	138	17	x−	x−	PROPN
ejpam-6575	138	18	(	(	PUNCT
ejpam-6575	138	19	2n+	2n+	NUM
ejpam-6575	138	20	1	1	NUM
ejpam-6575	138	21	2	2	NUM
ejpam-6575	138	22	)	)	PUNCT
ejpam-6575	138	23	.	.	PUNCT
ejpam-6575	139	1	since	since	SCONJ
ejpam-6575	139	2	2n+	2n+	NUM
ejpam-6575	139	3	1	1	NUM
ejpam-6575	139	4	2	2	NUM
ejpam-6575	139	5	>	>	SYM
ejpam-6575	139	6	1	1	NUM
ejpam-6575	139	7	,	,	PUNCT
ejpam-6575	139	8	the	the	DET
ejpam-6575	139	9	p	p	NOUN
ejpam-6575	139	10	-	-	PUNCT
ejpam-6575	139	11	integral	integral	ADJ
ejpam-6575	139	12	∫	∫	PROPN
ejpam-6575	139	13	∞	∞	PROPN
ejpam-6575	139	14	1	1	NUM
ejpam-6575	139	15	x−	x−	PROPN
ejpam-6575	139	16	(	(	PUNCT
ejpam-6575	139	17	2n+	2n+	NUM
ejpam-6575	139	18	1	1	NUM
ejpam-6575	139	19	2)dx	2)dx	PROPN
ejpam-6575	139	20	converges	converge	NOUN
ejpam-6575	139	21	.	.	PUNCT
ejpam-6575	140	1	hence	hence	ADV
ejpam-6575	140	2	i2	i2	PROPN
ejpam-6575	140	3	<	<	X
ejpam-6575	140	4	∞	∞	PROPN
ejpam-6575	140	5	by	by	ADP
ejpam-6575	140	6	comparison	comparison	NOUN
ejpam-6575	140	7	.	.	PUNCT
ejpam-6575	141	1	combining	combine	VERB
ejpam-6575	141	2	these	these	DET
ejpam-6575	141	3	two	two	NUM
ejpam-6575	141	4	estimates	estimate	NOUN
ejpam-6575	141	5	shows	show	VERB
ejpam-6575	141	6	in(α	in(α	PRON
ejpam-6575	141	7	)	)	PUNCT
ejpam-6575	141	8	=	=	SYM
ejpam-6575	141	9	i1	i1	PROPN
ejpam-6575	141	10	+	+	CCONJ
ejpam-6575	141	11	i2	i2	PROPN
ejpam-6575	141	12	<	<	X
ejpam-6575	141	13	∞	∞	PROPN
ejpam-6575	141	14	,	,	PUNCT
ejpam-6575	141	15	as	as	SCONJ
ejpam-6575	141	16	claimed	claim	VERB
ejpam-6575	141	17	.	.	PUNCT
ejpam-6575	142	1	next	next	ADV
ejpam-6575	142	2	,	,	PUNCT
ejpam-6575	142	3	we	we	PRON
ejpam-6575	142	4	solve	solve	VERB
ejpam-6575	142	5	the	the	DET
ejpam-6575	142	6	second	second	ADJ
ejpam-6575	142	7	integral	integral	ADJ
ejpam-6575	142	8	.	.	PUNCT
ejpam-6575	143	1	theorem	theorem	NOUN
ejpam-6575	143	2	2	2	NUM
ejpam-6575	143	3	.	.	X
ejpam-6575	143	4	for	for	ADP
ejpam-6575	143	5	every	every	DET
ejpam-6575	143	6	α	α	NOUN
ejpam-6575	143	7	>	>	X
ejpam-6575	143	8	0	0	PUNCT
ejpam-6575	143	9	and	and	CCONJ
ejpam-6575	143	10	integer	integer	PROPN
ejpam-6575	143	11	n	n	PRON
ejpam-6575	143	12	≥	≥	NUM
ejpam-6575	143	13	1	1	NUM
ejpam-6575	143	14	,	,	PUNCT
ejpam-6575	143	15	we	we	PRON
ejpam-6575	143	16	have	have	VERB
ejpam-6575	143	17	the	the	DET
ejpam-6575	143	18	following	follow	VERB
ejpam-6575	143	19	integral	integral	ADJ
ejpam-6575	143	20	in(α	in(α	PUNCT
ejpam-6575	143	21	)	)	PUNCT
ejpam-6575	143	22	=	=	SYM
ejpam-6575	144	1	∫	∫	PROPN
ejpam-6575	144	2	∞	∞	NUM
ejpam-6575	144	3	0	0	NUM
ejpam-6575	144	4	dx√	dx√	NOUN
ejpam-6575	144	5	x	x	X
ejpam-6575	145	1	(	(	PUNCT
ejpam-6575	145	2	x2	x2	NOUN
ejpam-6575	145	3	+	+	NUM
ejpam-6575	145	4	4α2)n	4α2)n	NUM
ejpam-6575	145	5	=	=	SYM
ejpam-6575	145	6	1	1	NUM
ejpam-6575	145	7	2	2	NUM
ejpam-6575	145	8	(	(	PUNCT
ejpam-6575	145	9	4α2)−	4α2)−	NUM
ejpam-6575	145	10	(	(	PUNCT
ejpam-6575	145	11	n−1	n−1	PROPN
ejpam-6575	145	12	4	4	NUM
ejpam-6575	145	13	)	)	PUNCT
ejpam-6575	145	14	γ	γ	X
ejpam-6575	145	15	(	(	PUNCT
ejpam-6575	145	16	1	1	NUM
ejpam-6575	145	17	4	4	NUM
ejpam-6575	145	18	)	)	PUNCT
ejpam-6575	145	19	γ	γ	PROPN
ejpam-6575	145	20	(	(	PUNCT
ejpam-6575	145	21	n−	n−	NOUN
ejpam-6575	145	22	1	1	NUM
ejpam-6575	145	23	4	4	NUM
ejpam-6575	145	24	)	)	PUNCT
ejpam-6575	145	25	γ(n	γ(n	PROPN
ejpam-6575	145	26	)	)	PUNCT
ejpam-6575	145	27	.	.	PUNCT
ejpam-6575	146	1	i.	i.	PROPN
ejpam-6575	146	2	ayoob	ayoob	PROPN
ejpam-6575	146	3	/	/	SYM
ejpam-6575	146	4	eur	eur	PROPN
ejpam-6575	146	5	.	.	PUNCT
ejpam-6575	147	1	j.	j.	PROPN
ejpam-6575	147	2	pure	pure	PROPN
ejpam-6575	147	3	appl	appl	PROPN
ejpam-6575	147	4	.	.	PROPN
ejpam-6575	147	5	math	math	PROPN
ejpam-6575	147	6	,	,	PUNCT
ejpam-6575	147	7	18	18	NUM
ejpam-6575	147	8	(	(	PUNCT
ejpam-6575	147	9	3	3	NUM
ejpam-6575	147	10	)	)	PUNCT
ejpam-6575	147	11	(	(	PUNCT
ejpam-6575	147	12	2025	2025	NUM
ejpam-6575	147	13	)	)	PUNCT
ejpam-6575	147	14	,	,	PUNCT
ejpam-6575	147	15	6575	6575	NUM
ejpam-6575	147	16	6	6	NUM
ejpam-6575	147	17	of	of	ADP
ejpam-6575	147	18	12	12	NUM
ejpam-6575	147	19	proof	proof	NOUN
ejpam-6575	147	20	.	.	PUNCT
ejpam-6575	148	1	we	we	PRON
ejpam-6575	148	2	set	set	VERB
ejpam-6575	148	3	x	x	PUNCT
ejpam-6575	149	1	=	=	VERB
ejpam-6575	149	2	2α	2α	PROPN
ejpam-6575	149	3	t	t	PROPN
ejpam-6575	149	4	,	,	PUNCT
ejpam-6575	149	5	dx	dx	PROPN
ejpam-6575	149	6	=	=	SYM
ejpam-6575	149	7	2αdt	2αdt	NUM
ejpam-6575	149	8	,	,	PUNCT
ejpam-6575	149	9	√	√	ADP
ejpam-6575	149	10	x	x	PUNCT
ejpam-6575	149	11	=	=	PRON
ejpam-6575	149	12	(	(	PUNCT
ejpam-6575	149	13	2α	2α	NOUN
ejpam-6575	149	14	)	)	PUNCT
ejpam-6575	149	15	1	1	NUM
ejpam-6575	149	16	2	2	NUM
ejpam-6575	149	17	t	t	NOUN
ejpam-6575	149	18	1	1	NUM
ejpam-6575	149	19	2	2	NUM
ejpam-6575	149	20	,	,	PUNCT
ejpam-6575	149	21	x2	x2	PROPN
ejpam-6575	150	1	+	+	NUM
ejpam-6575	150	2	4α2	4α2	NUM
ejpam-6575	150	3	=	=	SYM
ejpam-6575	150	4	4α2(1	4α2(1	NUM
ejpam-6575	150	5	+	+	CCONJ
ejpam-6575	150	6	t2	t2	NOUN
ejpam-6575	150	7	)	)	PUNCT
ejpam-6575	150	8	.	.	PUNCT
ejpam-6575	151	1	therefore	therefore	ADV
ejpam-6575	151	2	in(α	in(α	PUNCT
ejpam-6575	151	3	)	)	PUNCT
ejpam-6575	152	1	=	=	SYM
ejpam-6575	152	2	∫	∫	PROPN
ejpam-6575	153	1	∞	∞	NUM
ejpam-6575	153	2	0	0	NUM
ejpam-6575	153	3	1	1	NUM
ejpam-6575	153	4	(	(	PUNCT
ejpam-6575	153	5	2α	2α	NOUN
ejpam-6575	153	6	)	)	PUNCT
ejpam-6575	153	7	1	1	NUM
ejpam-6575	153	8	2	2	NUM
ejpam-6575	153	9	t	t	NOUN
ejpam-6575	153	10	1	1	NUM
ejpam-6575	153	11	2	2	NUM
ejpam-6575	153	12	[	[	X
ejpam-6575	153	13	4α2(1	4α2(1	NUM
ejpam-6575	153	14	+	+	CCONJ
ejpam-6575	153	15	t2)]n	t2)]n	PROPN
ejpam-6575	153	16	(	(	PUNCT
ejpam-6575	153	17	2αdt	2αdt	NOUN
ejpam-6575	153	18	)	)	PUNCT
ejpam-6575	153	19	=	=	SYM
ejpam-6575	153	20	(	(	PUNCT
ejpam-6575	153	21	2α	2α	NOUN
ejpam-6575	153	22	)	)	PUNCT
ejpam-6575	153	23	1	1	NUM
ejpam-6575	153	24	2	2	NUM
ejpam-6575	153	25	(	(	PUNCT
ejpam-6575	153	26	4α2)−n	4α2)−n	NOUN
ejpam-6575	153	27	∫	∫	PROPN
ejpam-6575	153	28	∞	∞	PROPN
ejpam-6575	153	29	0	0	NUM
ejpam-6575	154	1	dt	dt	X
ejpam-6575	154	2	t	t	PROPN
ejpam-6575	154	3	1	1	NUM
ejpam-6575	154	4	2	2	NUM
ejpam-6575	154	5	(	(	PUNCT
ejpam-6575	154	6	1	1	NUM
ejpam-6575	154	7	+	+	CCONJ
ejpam-6575	154	8	t2)n	t2)n	NOUN
ejpam-6575	154	9	.	.	PUNCT
ejpam-6575	155	1	since	since	SCONJ
ejpam-6575	155	2	(	(	PUNCT
ejpam-6575	155	3	2α	2α	NOUN
ejpam-6575	155	4	)	)	PUNCT
ejpam-6575	155	5	1	1	NUM
ejpam-6575	155	6	2	2	NUM
ejpam-6575	155	7	(	(	PUNCT
ejpam-6575	155	8	4α2)−n	4α2)−n	NOUN
ejpam-6575	155	9	=	=	SYM
ejpam-6575	155	10	2	2	NUM
ejpam-6575	155	11	1	1	NUM
ejpam-6575	155	12	2−2n	2−2n	NUM
ejpam-6575	155	13	α	α	NOUN
ejpam-6575	155	14	1	1	NUM
ejpam-6575	155	15	2−2n	2−2n	NUM
ejpam-6575	155	16	,	,	PUNCT
ejpam-6575	155	17	we	we	PRON
ejpam-6575	155	18	have	have	VERB
ejpam-6575	155	19	in(α	in(α	VERB
ejpam-6575	155	20	)	)	PUNCT
ejpam-6575	155	21	=	=	SYM
ejpam-6575	155	22	2	2	NUM
ejpam-6575	155	23	1	1	NUM
ejpam-6575	155	24	2−2n	2−2n	NUM
ejpam-6575	155	25	α	α	NOUN
ejpam-6575	155	26	1	1	NUM
ejpam-6575	155	27	2−2n	2−2n	NUM
ejpam-6575	155	28	∫	∫	NOUN
ejpam-6575	155	29	∞	∞	NOUN
ejpam-6575	155	30	0	0	NUM
ejpam-6575	156	1	t−	t−	PROPN
ejpam-6575	156	2	1	1	NUM
ejpam-6575	156	3	2	2	NUM
ejpam-6575	156	4	(	(	PUNCT
ejpam-6575	156	5	1	1	NUM
ejpam-6575	156	6	+	+	PROPN
ejpam-6575	156	7	t2)−n	t2)−n	PROPN
ejpam-6575	156	8	dt	dt	PROPN
ejpam-6575	156	9	.	.	PUNCT
ejpam-6575	156	10	set	set	VERB
ejpam-6575	156	11	jn	jn	PROPN
ejpam-6575	157	1	=	=	SYM
ejpam-6575	158	1	∫	∫	PROPN
ejpam-6575	159	1	∞	∞	PROPN
ejpam-6575	159	2	0	0	NUM
ejpam-6575	160	1	t−	t−	PROPN
ejpam-6575	160	2	1	1	NUM
ejpam-6575	160	3	2	2	NUM
ejpam-6575	160	4	(	(	PUNCT
ejpam-6575	160	5	1	1	NUM
ejpam-6575	160	6	+	+	PROPN
ejpam-6575	160	7	t2)−n	t2)−n	PROPN
ejpam-6575	160	8	dt	dt	PROPN
ejpam-6575	160	9	.	.	PUNCT
ejpam-6575	161	1	with	with	ADP
ejpam-6575	161	2	the	the	DET
ejpam-6575	161	3	substitution	substitution	NOUN
ejpam-6575	161	4	u	u	NOUN
ejpam-6575	161	5	=	=	PROPN
ejpam-6575	161	6	t2	t2	PROPN
ejpam-6575	161	7	,	,	PUNCT
ejpam-6575	161	8	du	du	PROPN
ejpam-6575	161	9	=	=	SYM
ejpam-6575	161	10	2	2	NUM
ejpam-6575	161	11	t	t	NOUN
ejpam-6575	161	12	dt	dt	NOUN
ejpam-6575	161	13	,	,	PUNCT
ejpam-6575	161	14	t−	t−	PROPN
ejpam-6575	161	15	1	1	NUM
ejpam-6575	161	16	2	2	NUM
ejpam-6575	161	17	=	=	SYM
ejpam-6575	161	18	u−	u−	PROPN
ejpam-6575	161	19	1	1	NUM
ejpam-6575	161	20	4	4	NUM
ejpam-6575	161	21	,	,	PUNCT
ejpam-6575	161	22	we	we	PRON
ejpam-6575	161	23	get	get	VERB
ejpam-6575	162	1	jn	jn	PROPN
ejpam-6575	163	1	=	=	SYM
ejpam-6575	164	1	∫	∫	PROPN
ejpam-6575	165	1	∞	∞	PROPN
ejpam-6575	165	2	0	0	NUM
ejpam-6575	166	1	u−	u−	PROPN
ejpam-6575	166	2	1	1	NUM
ejpam-6575	166	3	4	4	NUM
ejpam-6575	166	4	(	(	PUNCT
ejpam-6575	166	5	1	1	NUM
ejpam-6575	166	6	+	+	NUM
ejpam-6575	166	7	u)−n	u)−n	PROPN
ejpam-6575	166	8	du	du	PROPN
ejpam-6575	166	9	2u	2u	PROPN
ejpam-6575	166	10	1	1	NUM
ejpam-6575	166	11	2	2	NUM
ejpam-6575	166	12	=	=	SYM
ejpam-6575	166	13	1	1	NUM
ejpam-6575	166	14	2	2	NUM
ejpam-6575	166	15	∫	∫	NOUN
ejpam-6575	166	16	∞	∞	NUM
ejpam-6575	166	17	0	0	NUM
ejpam-6575	166	18	u	u	NOUN
ejpam-6575	166	19	1	1	NUM
ejpam-6575	166	20	4−1(1	4−1(1	NUM
ejpam-6575	166	21	+	+	NUM
ejpam-6575	166	22	u)−n	u)−n	X
ejpam-6575	166	23	du	du	X
ejpam-6575	166	24	=	=	NOUN
ejpam-6575	166	25	1	1	NUM
ejpam-6575	166	26	2	2	NUM
ejpam-6575	166	27	b	b	PROPN
ejpam-6575	166	28	(	(	PUNCT
ejpam-6575	166	29	1	1	NUM
ejpam-6575	166	30	4	4	NUM
ejpam-6575	166	31	,	,	PUNCT
ejpam-6575	166	32	n−	n−	NOUN
ejpam-6575	166	33	1	1	NUM
ejpam-6575	166	34	4	4	NUM
ejpam-6575	166	35	)	)	PUNCT
ejpam-6575	166	36	.	.	PUNCT
ejpam-6575	167	1	for	for	ADP
ejpam-6575	167	2	s	s	PROPN
ejpam-6575	167	3	>	>	X
ejpam-6575	167	4	0	0	PROPN
ejpam-6575	167	5	,	,	PUNCT
ejpam-6575	167	6	recall	recall	VERB
ejpam-6575	167	7	the	the	DET
ejpam-6575	167	8	definition	definition	NOUN
ejpam-6575	167	9	of	of	ADP
ejpam-6575	167	10	gamma	gamma	PROPN
ejpam-6575	167	11	function	function	PROPN
ejpam-6575	167	12	γ(s	γ(s	PROPN
ejpam-6575	167	13	)	)	PUNCT
ejpam-6575	168	1	=	=	PUNCT
ejpam-6575	168	2	∫∞	∫∞	NOUN
ejpam-6575	168	3	0	0	NUM
ejpam-6575	168	4	ts−1e−t	ts−1e−t	NUM
ejpam-6575	168	5	dt	dt	NOUN
ejpam-6575	168	6	,	,	PUNCT
ejpam-6575	168	7	and	and	CCONJ
ejpam-6575	168	8	the	the	DET
ejpam-6575	168	9	relationship	relationship	NOUN
ejpam-6575	168	10	with	with	ADP
ejpam-6575	168	11	the	the	DET
ejpam-6575	168	12	beta	beta	NOUN
ejpam-6575	168	13	function	function	NOUN
ejpam-6575	168	14	,	,	PUNCT
ejpam-6575	168	15	b(x	b(x	NOUN
ejpam-6575	168	16	,	,	PUNCT
ejpam-6575	168	17	y	y	NOUN
ejpam-6575	168	18	)	)	PUNCT
ejpam-6575	168	19	=	=	PUNCT
ejpam-6575	169	1	γ(x)γ(y)/γ(x+	γ(x)γ(y)/γ(x+	PROPN
ejpam-6575	169	2	y	y	PROPN
ejpam-6575	169	3	)	)	PUNCT
ejpam-6575	169	4	,	,	PUNCT
ejpam-6575	169	5	it	it	PRON
ejpam-6575	169	6	follows	follow	VERB
ejpam-6575	169	7	that	that	SCONJ
ejpam-6575	169	8	jn	jn	PROPN
ejpam-6575	169	9	=	=	NOUN
ejpam-6575	169	10	1	1	NUM
ejpam-6575	169	11	2	2	NUM
ejpam-6575	169	12	γ(14	γ(14	NOUN
ejpam-6575	169	13	)	)	PUNCT
ejpam-6575	169	14	γ(n−	γ(n−	PROPN
ejpam-6575	169	15	1	1	NUM
ejpam-6575	169	16	4	4	NUM
ejpam-6575	169	17	)	)	PUNCT
ejpam-6575	169	18	γ(n	γ(n	X
ejpam-6575	169	19	)	)	PUNCT
ejpam-6575	169	20	.	.	PUNCT
ejpam-6575	170	1	hence	hence	ADV
ejpam-6575	170	2	in(α	in(α	PUNCT
ejpam-6575	170	3	)	)	PUNCT
ejpam-6575	170	4	=	=	SYM
ejpam-6575	171	1	2	2	NUM
ejpam-6575	171	2	1	1	NUM
ejpam-6575	171	3	2−2n	2−2n	NUM
ejpam-6575	171	4	α	α	NOUN
ejpam-6575	171	5	1	1	NUM
ejpam-6575	171	6	2−2n	2−2n	NUM
ejpam-6575	171	7	1	1	NUM
ejpam-6575	171	8	2	2	NUM
ejpam-6575	171	9	γ(14	γ(14	NOUN
ejpam-6575	171	10	)	)	PUNCT
ejpam-6575	171	11	γ(n−	γ(n−	PROPN
ejpam-6575	171	12	1	1	NUM
ejpam-6575	171	13	4	4	NUM
ejpam-6575	171	14	)	)	PUNCT
ejpam-6575	171	15	γ(n	γ(n	X
ejpam-6575	171	16	)	)	PUNCT
ejpam-6575	171	17	=	=	SYM
ejpam-6575	171	18	1	1	NUM
ejpam-6575	171	19	2	2	NUM
ejpam-6575	171	20	(	(	PUNCT
ejpam-6575	171	21	4α2)−(n−	4α2)−(n−	NOUN
ejpam-6575	171	22	1	1	NUM
ejpam-6575	171	23	4	4	NUM
ejpam-6575	171	24	)	)	PUNCT
ejpam-6575	171	25	γ(14	γ(14	NOUN
ejpam-6575	171	26	)	)	PUNCT
ejpam-6575	171	27	γ(n−	γ(n−	PROPN
ejpam-6575	171	28	1	1	NUM
ejpam-6575	171	29	4	4	NUM
ejpam-6575	171	30	)	)	PUNCT
ejpam-6575	171	31	γ(n	γ(n	X
ejpam-6575	171	32	)	)	PUNCT
ejpam-6575	171	33	,	,	PUNCT
ejpam-6575	171	34	as	as	SCONJ
ejpam-6575	171	35	claimed	claim	VERB
ejpam-6575	171	36	.	.	PUNCT
ejpam-6575	172	1	1.3	1.3	NUM
ejpam-6575	172	2	.	.	PUNCT
ejpam-6575	172	3	convergence	convergence	NOUN
ejpam-6575	172	4	and	and	CCONJ
ejpam-6575	172	5	evaluation	evaluation	NOUN
ejpam-6575	172	6	of	of	ADP
ejpam-6575	172	7	the	the	DET
ejpam-6575	172	8	third	third	ADJ
ejpam-6575	172	9	integral	integral	NOUN
ejpam-6575	172	10	.	.	PUNCT
ejpam-6575	173	1	here	here	ADV
ejpam-6575	173	2	is	be	AUX
ejpam-6575	173	3	the	the	DET
ejpam-6575	173	4	convergence	convergence	NOUN
ejpam-6575	173	5	result	result	NOUN
ejpam-6575	173	6	for	for	ADP
ejpam-6575	173	7	the	the	DET
ejpam-6575	173	8	third	third	ADJ
ejpam-6575	173	9	integral	integral	ADJ
ejpam-6575	173	10	.	.	PUNCT
ejpam-6575	174	1	proposition	proposition	NOUN
ejpam-6575	174	2	3	3	X
ejpam-6575	174	3	.	.	PUNCT
ejpam-6575	175	1	let	let	VERB
ejpam-6575	175	2	f	f	PROPN
ejpam-6575	175	3	:	:	PUNCT
ejpam-6575	175	4	(	(	PUNCT
ejpam-6575	175	5	0,∞	0,∞	NOUN
ejpam-6575	175	6	)	)	PUNCT
ejpam-6575	176	1	→	→	PUNCT
ejpam-6575	176	2	r	r	NOUN
ejpam-6575	176	3	be	be	AUX
ejpam-6575	176	4	a	a	DET
ejpam-6575	176	5	continuously	continuously	ADV
ejpam-6575	176	6	differentiable	differentiable	ADJ
ejpam-6575	176	7	function	function	NOUN
ejpam-6575	176	8	such	such	ADJ
ejpam-6575	176	9	that	that	SCONJ
ejpam-6575	176	10	lim	lim	PROPN
ejpam-6575	176	11	t→0	t→0	AUX
ejpam-6575	176	12	+	+	CCONJ
ejpam-6575	176	13	f(t	f(t	NOUN
ejpam-6575	176	14	)	)	PUNCT
ejpam-6575	176	15	=	=	SYM
ejpam-6575	176	16	f(0	f(0	NOUN
ejpam-6575	176	17	)	)	PUNCT
ejpam-6575	176	18	∈	∈	PROPN
ejpam-6575	176	19	r	r	NOUN
ejpam-6575	176	20	,	,	PUNCT
ejpam-6575	176	21	lim	lim	PROPN
ejpam-6575	176	22	t→∞	t→∞	PRON
ejpam-6575	176	23	f(t	f(t	PROPN
ejpam-6575	176	24	)	)	PUNCT
ejpam-6575	176	25	=	=	SYM
ejpam-6575	176	26	f(∞	f(∞	NOUN
ejpam-6575	176	27	)	)	PUNCT
ejpam-6575	176	28	∈	∈	PROPN
ejpam-6575	176	29	r	r	NOUN
ejpam-6575	176	30	,	,	PUNCT
ejpam-6575	176	31	i.	i.	PROPN
ejpam-6575	176	32	ayoob	ayoob	PROPN
ejpam-6575	176	33	/	/	SYM
ejpam-6575	176	34	eur	eur	PROPN
ejpam-6575	176	35	.	.	PUNCT
ejpam-6575	177	1	j.	j.	PROPN
ejpam-6575	177	2	pure	pure	PROPN
ejpam-6575	177	3	appl	appl	PROPN
ejpam-6575	177	4	.	.	PROPN
ejpam-6575	177	5	math	math	PROPN
ejpam-6575	177	6	,	,	PUNCT
ejpam-6575	177	7	18	18	NUM
ejpam-6575	177	8	(	(	PUNCT
ejpam-6575	177	9	3	3	NUM
ejpam-6575	177	10	)	)	PUNCT
ejpam-6575	177	11	(	(	PUNCT
ejpam-6575	177	12	2025	2025	NUM
ejpam-6575	177	13	)	)	PUNCT
ejpam-6575	177	14	,	,	PUNCT
ejpam-6575	177	15	6575	6575	NUM
ejpam-6575	177	16	7	7	NUM
ejpam-6575	177	17	of	of	ADP
ejpam-6575	177	18	12	12	NUM
ejpam-6575	177	19	and	and	CCONJ
ejpam-6575	177	20	∫	∫	PROPN
ejpam-6575	178	1	∞	∞	PROPN
ejpam-6575	178	2	0	0	NUM
ejpam-6575	178	3	t	t	NOUN
ejpam-6575	178	4	1	1	NUM
ejpam-6575	178	5	2	2	NUM
ejpam-6575	178	6	∣∣f	∣∣f	NOUN
ejpam-6575	178	7	′(t	′(t	NOUN
ejpam-6575	178	8	)	)	PUNCT
ejpam-6575	178	9	∣∣	∣∣	X
ejpam-6575	178	10	dt	dt	PUNCT
ejpam-6575	178	11	<	<	X
ejpam-6575	178	12	∞.	∞.	PROPN
ejpam-6575	178	13	then	then	ADV
ejpam-6575	178	14	for	for	ADP
ejpam-6575	178	15	each	each	DET
ejpam-6575	178	16	fixed	fix	VERB
ejpam-6575	178	17	β	β	X
ejpam-6575	178	18	>	>	X
ejpam-6575	178	19	0	0	PUNCT
ejpam-6575	179	1	the	the	DET
ejpam-6575	179	2	integral	integral	ADJ
ejpam-6575	179	3	i(β	i(β	NOUN
ejpam-6575	179	4	)	)	PUNCT
ejpam-6575	180	1	=	=	SYM
ejpam-6575	180	2	∫	∫	PROPN
ejpam-6575	181	1	∞	∞	PROPN
ejpam-6575	181	2	0	0	NUM
ejpam-6575	181	3	x−	x−	PROPN
ejpam-6575	181	4	3	3	NUM
ejpam-6575	181	5	2	2	NUM
ejpam-6575	181	6	[	[	PUNCT
ejpam-6575	181	7	f	f	X
ejpam-6575	181	8	(	(	PUNCT
ejpam-6575	181	9	2β	2β	NOUN
ejpam-6575	181	10	x	x	SYM
ejpam-6575	181	11	)	)	PUNCT
ejpam-6575	182	1	−	−	PROPN
ejpam-6575	182	2	f	f	PROPN
ejpam-6575	182	3	(	(	PUNCT
ejpam-6575	182	4	2	2	NUM
ejpam-6575	182	5	x	x	NOUN
ejpam-6575	182	6	)	)	PUNCT
ejpam-6575	182	7	]	]	PUNCT
ejpam-6575	182	8	dx	dx	PROPN
ejpam-6575	182	9	converges	converge	VERB
ejpam-6575	182	10	absolutely	absolutely	ADV
ejpam-6575	182	11	.	.	PUNCT
ejpam-6575	183	1	proof	proof	NOUN
ejpam-6575	183	2	.	.	PUNCT
ejpam-6575	184	1	fix	fix	VERB
ejpam-6575	184	2	β	β	PRON
ejpam-6575	184	3	>	>	X
ejpam-6575	184	4	0	0	X
ejpam-6575	184	5	.	.	PUNCT
ejpam-6575	185	1	we	we	PRON
ejpam-6575	185	2	may	may	AUX
ejpam-6575	185	3	write	write	VERB
ejpam-6575	185	4	i(β	i(β	PROPN
ejpam-6575	185	5	)	)	PUNCT
ejpam-6575	186	1	=	=	SYM
ejpam-6575	187	1	∫	∫	PROPN
ejpam-6575	188	1	∞	∞	NUM
ejpam-6575	188	2	0	0	NUM
ejpam-6575	189	1	x−3/2	x−3/2	PROPN
ejpam-6575	189	2	[	[	PUNCT
ejpam-6575	189	3	f(2β	f(2β	NOUN
ejpam-6575	189	4	/	/	SYM
ejpam-6575	189	5	x)−f(2	x)−f(2	ADJ
ejpam-6575	189	6	/	/	SYM
ejpam-6575	189	7	x	x	NOUN
ejpam-6575	189	8	)	)	PUNCT
ejpam-6575	189	9	]	]	PUNCT
ejpam-6575	190	1	dx	dx	PROPN
ejpam-6575	191	1	=	=	SYM
ejpam-6575	191	2	∫	∫	PROPN
ejpam-6575	191	3	x0	x0	PROPN
ejpam-6575	191	4	0	0	PUNCT
ejpam-6575	192	1	+	+	CCONJ
ejpam-6575	192	2	∫	∫	PROPN
ejpam-6575	193	1	x1	x1	NOUN
ejpam-6575	193	2	x0	x0	PROPN
ejpam-6575	194	1	+	+	CCONJ
ejpam-6575	195	1	∫	∫	PROPN
ejpam-6575	196	1	∞	∞	NUM
ejpam-6575	196	2	x1	x1	PROPN
ejpam-6575	196	3	x−3/2	x−3/2	PROPN
ejpam-6575	196	4	[	[	PUNCT
ejpam-6575	196	5	f(2β	f(2β	NOUN
ejpam-6575	196	6	/	/	SYM
ejpam-6575	196	7	x)−f(2	x)−f(2	ADJ
ejpam-6575	196	8	/	/	SYM
ejpam-6575	196	9	x	x	NOUN
ejpam-6575	196	10	)	)	PUNCT
ejpam-6575	196	11	]	]	PUNCT
ejpam-6575	197	1	dx	dx	PROPN
ejpam-6575	197	2	,	,	PUNCT
ejpam-6575	197	3	where	where	SCONJ
ejpam-6575	197	4	we	we	PRON
ejpam-6575	197	5	choose	choose	VERB
ejpam-6575	197	6	0	0	PUNCT
ejpam-6575	197	7	<	<	X
ejpam-6575	197	8	x0	x0	PROPN
ejpam-6575	197	9	<	<	X
ejpam-6575	198	1	x1	x1	X
ejpam-6575	198	2	<	<	X
ejpam-6575	198	3	∞	∞	PUNCT
ejpam-6575	199	1	so	so	SCONJ
ejpam-6575	199	2	that	that	DET
ejpam-6575	199	3	2β	2β	NOUN
ejpam-6575	199	4	x0	x0	PROPN
ejpam-6575	199	5	≥	≥	NUM
ejpam-6575	199	6	t	t	PROPN
ejpam-6575	199	7	,	,	PUNCT
ejpam-6575	199	8	2	2	NUM
ejpam-6575	199	9	x1	x1	PROPN
ejpam-6575	199	10	≤	≤	NUM
ejpam-6575	199	11	s	s	PART
ejpam-6575	199	12	,	,	PUNCT
ejpam-6575	199	13	with	with	ADP
ejpam-6575	199	14	t	t	PROPN
ejpam-6575	199	15	large	large	ADJ
ejpam-6575	199	16	and	and	CCONJ
ejpam-6575	199	17	s	s	VERB
ejpam-6575	199	18	small	small	ADJ
ejpam-6575	199	19	enough	enough	ADV
ejpam-6575	199	20	that	that	SCONJ
ejpam-6575	199	21	∫∞	∫∞	PROPN
ejpam-6575	199	22	t	t	PROPN
ejpam-6575	199	23	t	t	PROPN
ejpam-6575	199	24	1	1	NUM
ejpam-6575	199	25	2	2	NUM
ejpam-6575	199	26	|f	|f	ADP
ejpam-6575	200	1	′(t)|	′(t)|	ADJ
ejpam-6575	200	2	dt	dt	X
ejpam-6575	200	3	<	<	X
ejpam-6575	200	4	ε	ε	PROPN
ejpam-6575	200	5	and	and	CCONJ
ejpam-6575	200	6	∫	∫	PROPN
ejpam-6575	200	7	s	s	PART
ejpam-6575	200	8	0	0	NUM
ejpam-6575	200	9	t	t	PROPN
ejpam-6575	200	10	1	1	NUM
ejpam-6575	200	11	2	2	NUM
ejpam-6575	200	12	|f	|f	ADP
ejpam-6575	200	13	′(t)|	′(t)|	ADJ
ejpam-6575	200	14	dt	dt	X
ejpam-6575	200	15	<	<	X
ejpam-6575	200	16	ε	ε	PROPN
ejpam-6575	200	17	.	.	PUNCT
ejpam-6575	201	1	(	(	PUNCT
ejpam-6575	201	2	i	i	NOUN
ejpam-6575	201	3	)	)	PUNCT
ejpam-6575	201	4	tail	tail	NOUN
ejpam-6575	201	5	as	as	ADP
ejpam-6575	201	6	x	x	X
ejpam-6575	201	7	→	→	SYM
ejpam-6575	201	8	0	0	NUM
ejpam-6575	201	9	+	+	NOUN
ejpam-6575	201	10	:	:	PUNCT
ejpam-6575	201	11	for	for	ADP
ejpam-6575	201	12	0	0	NUM
ejpam-6575	201	13	<	<	X
ejpam-6575	201	14	x	x	SYM
ejpam-6575	201	15	≤	≤	NOUN
ejpam-6575	201	16	x0	x0	PROPN
ejpam-6575	201	17	,	,	PUNCT
ejpam-6575	201	18	both	both	DET
ejpam-6575	201	19	2β	2β	NOUN
ejpam-6575	201	20	x	x	X
ejpam-6575	201	21	and	and	CCONJ
ejpam-6575	201	22	2	2	NUM
ejpam-6575	201	23	x	x	NOUN
ejpam-6575	201	24	lie	lie	VERB
ejpam-6575	201	25	in	in	ADP
ejpam-6575	201	26	[	[	X
ejpam-6575	201	27	t,∞	t,∞	NUM
ejpam-6575	201	28	)	)	PUNCT
ejpam-6575	201	29	.	.	PUNCT
ejpam-6575	202	1	by	by	ADP
ejpam-6575	202	2	the	the	DET
ejpam-6575	202	3	mean	mean	ADJ
ejpam-6575	202	4	-	-	PUNCT
ejpam-6575	202	5	value	value	NOUN
ejpam-6575	202	6	theorem	theorem	NOUN
ejpam-6575	202	7	there	there	PRON
ejpam-6575	202	8	exists	exist	VERB
ejpam-6575	202	9	ξ	ξ	PROPN
ejpam-6575	202	10	∈	∈	PROPN
ejpam-6575	202	11	[	[	PUNCT
ejpam-6575	202	12	2x	2x	NUM
ejpam-6575	202	13	,	,	PUNCT
ejpam-6575	202	14	2β	2β	NOUN
ejpam-6575	202	15	x	x	X
ejpam-6575	202	16	]	]	PUNCT
ejpam-6575	202	17	such	such	ADJ
ejpam-6575	202	18	that	that	SCONJ
ejpam-6575	202	19	f	f	PROPN
ejpam-6575	202	20	(	(	PUNCT
ejpam-6575	202	21	2β	2β	NOUN
ejpam-6575	202	22	x	x	SYM
ejpam-6575	202	23	)	)	PUNCT
ejpam-6575	203	1	−	−	PROPN
ejpam-6575	203	2	f	f	PROPN
ejpam-6575	203	3	(	(	PUNCT
ejpam-6575	203	4	2	2	NUM
ejpam-6575	203	5	x	x	NOUN
ejpam-6575	203	6	)	)	PUNCT
ejpam-6575	204	1	=	=	SYM
ejpam-6575	204	2	f	f	PROPN
ejpam-6575	204	3	′(ξ	′(ξ	NOUN
ejpam-6575	204	4	)	)	PUNCT
ejpam-6575	204	5	(	(	PUNCT
ejpam-6575	204	6	2β	2β	NOUN
ejpam-6575	204	7	x	x	PUNCT
ejpam-6575	204	8	−	−	PROPN
ejpam-6575	204	9	2	2	NUM
ejpam-6575	204	10	x	x	NOUN
ejpam-6575	204	11	)	)	PUNCT
ejpam-6575	204	12	=	=	SYM
ejpam-6575	204	13	(	(	PUNCT
ejpam-6575	204	14	β	β	NOUN
ejpam-6575	204	15	−	−	NOUN
ejpam-6575	204	16	1	1	NUM
ejpam-6575	204	17	)	)	SYM
ejpam-6575	204	18	2	2	NUM
ejpam-6575	204	19	x	x	SYM
ejpam-6575	204	20	f	f	NOUN
ejpam-6575	204	21	′(ξ	′(ξ	PROPN
ejpam-6575	204	22	)	)	PUNCT
ejpam-6575	204	23	.	.	PUNCT
ejpam-6575	205	1	hence	hence	ADV
ejpam-6575	205	2	∣∣x−3/2	∣∣x−3/2	NOUN
ejpam-6575	205	3	[	[	PUNCT
ejpam-6575	205	4	f(2β	f(2β	PROPN
ejpam-6575	205	5	/	/	SYM
ejpam-6575	205	6	x)−	x)−	PROPN
ejpam-6575	205	7	f(2	f(2	PROPN
ejpam-6575	205	8	/	/	SYM
ejpam-6575	205	9	x	x	NOUN
ejpam-6575	205	10	)	)	PUNCT
ejpam-6575	205	11	]	]	PUNCT
ejpam-6575	206	1	∣∣	∣∣	PUNCT
ejpam-6575	206	2	=	=	SYM
ejpam-6575	206	3	2|β	2|β	PROPN
ejpam-6575	206	4	−	−	NUM
ejpam-6575	206	5	1|	1|	NUM
ejpam-6575	206	6	x−5/2	x−5/2	PROPN
ejpam-6575	206	7	∣∣f	∣∣f	NOUN
ejpam-6575	206	8	′(ξ	′(ξ	NOUN
ejpam-6575	206	9	)	)	PUNCT
ejpam-6575	206	10	∣∣.	∣∣.	NOUN
ejpam-6575	206	11	since	since	SCONJ
ejpam-6575	206	12	ξ	ξ	PROPN
ejpam-6575	206	13	≥	≥	NOUN
ejpam-6575	206	14	t	t	NOUN
ejpam-6575	206	15	and	and	CCONJ
ejpam-6575	206	16	t	t	PROPN
ejpam-6575	206	17	7→	7→	NUM
ejpam-6575	206	18	t1/2|f	t1/2|f	NOUN
ejpam-6575	207	1	′(t)|	′(t)|	NOUN
ejpam-6575	207	2	is	be	AUX
ejpam-6575	207	3	integrable	integrable	ADJ
ejpam-6575	207	4	on	on	ADP
ejpam-6575	207	5	[	[	X
ejpam-6575	207	6	t,∞	t,∞	NUM
ejpam-6575	207	7	)	)	PUNCT
ejpam-6575	207	8	,	,	PUNCT
ejpam-6575	207	9	the	the	DET
ejpam-6575	207	10	change	change	NOUN
ejpam-6575	207	11	of	of	ADP
ejpam-6575	207	12	variable	variable	NOUN
ejpam-6575	207	13	ξ	ξ	NOUN
ejpam-6575	207	14	=	=	SYM
ejpam-6575	207	15	2θ	2θ	NUM
ejpam-6575	207	16	/	/	SYM
ejpam-6575	207	17	x	x	SYM
ejpam-6575	207	18	shows	show	VERB
ejpam-6575	207	19	∫	∫	PROPN
ejpam-6575	207	20	x0	x0	PROPN
ejpam-6575	207	21	0	0	PROPN
ejpam-6575	208	1	x−3/2	x−3/2	ADJ
ejpam-6575	208	2	∣∣f(2β	∣∣f(2β	PROPN
ejpam-6575	208	3	/	/	SYM
ejpam-6575	208	4	x)−	x)−	PROPN
ejpam-6575	208	5	f(2	f(2	PROPN
ejpam-6575	208	6	/	/	SYM
ejpam-6575	208	7	x	x	NOUN
ejpam-6575	208	8	)	)	PUNCT
ejpam-6575	208	9	∣∣	∣∣	X
ejpam-6575	208	10	dx	dx	PROPN
ejpam-6575	209	1	=	=	SYM
ejpam-6575	210	1	2|β	2|β	PROPN
ejpam-6575	211	1	−	−	NOUN
ejpam-6575	212	1	1|	1|	NUM
ejpam-6575	212	2	∫	∫	PROPN
ejpam-6575	213	1	∞	∞	PROPN
ejpam-6575	213	2	t	t	PROPN
ejpam-6575	213	3	t	t	NOUN
ejpam-6575	213	4	1	1	NUM
ejpam-6575	213	5	2	2	NUM
ejpam-6575	213	6	∣∣f	∣∣f	NOUN
ejpam-6575	213	7	′(t	′(t	NOUN
ejpam-6575	213	8	)	)	PUNCT
ejpam-6575	213	9	∣∣	∣∣	X
ejpam-6575	213	10	dt	dt	X
ejpam-6575	214	1	<	<	X
ejpam-6575	214	2	2|β	2|β	PROPN
ejpam-6575	214	3	−	−	NUM
ejpam-6575	214	4	1|	1|	NUM
ejpam-6575	214	5	ε	ε	PROPN
ejpam-6575	214	6	.	.	PUNCT
ejpam-6575	214	7	(	(	PUNCT
ejpam-6575	214	8	ii	ii	NOUN
ejpam-6575	214	9	)	)	PUNCT
ejpam-6575	214	10	tail	tail	NOUN
ejpam-6575	214	11	as	as	ADP
ejpam-6575	214	12	x	x	X
ejpam-6575	214	13	→	→	SYM
ejpam-6575	214	14	∞	∞	NUM
ejpam-6575	214	15	:	:	PUNCT
ejpam-6575	214	16	for	for	ADP
ejpam-6575	214	17	x	x	X
ejpam-6575	214	18	≥	≥	NOUN
ejpam-6575	214	19	x1	x1	NUM
ejpam-6575	214	20	,	,	PUNCT
ejpam-6575	215	1	both	both	DET
ejpam-6575	215	2	2β	2β	NOUN
ejpam-6575	215	3	x	x	X
ejpam-6575	215	4	and	and	CCONJ
ejpam-6575	215	5	2	2	NUM
ejpam-6575	215	6	x	x	NOUN
ejpam-6575	215	7	lie	lie	VERB
ejpam-6575	215	8	in	in	ADP
ejpam-6575	215	9	(	(	PUNCT
ejpam-6575	215	10	0	0	NUM
ejpam-6575	215	11	,	,	PUNCT
ejpam-6575	215	12	s	s	PART
ejpam-6575	215	13	]	]	X
ejpam-6575	215	14	.	.	PUNCT
ejpam-6575	216	1	again	again	ADV
ejpam-6575	216	2	by	by	ADP
ejpam-6575	216	3	the	the	DET
ejpam-6575	216	4	mean	mean	ADJ
ejpam-6575	216	5	-	-	PUNCT
ejpam-6575	216	6	value	value	NOUN
ejpam-6575	216	7	theorem	theorem	NOUN
ejpam-6575	216	8	there	there	PRON
ejpam-6575	216	9	is	be	VERB
ejpam-6575	216	10	η	η	PROPN
ejpam-6575	216	11	∈	∈	PROPN
ejpam-6575	216	12	[	[	PUNCT
ejpam-6575	216	13	2x	2x	NUM
ejpam-6575	216	14	,	,	PUNCT
ejpam-6575	216	15	2β	2β	NOUN
ejpam-6575	216	16	x	x	X
ejpam-6575	216	17	]	]	X
ejpam-6575	217	1	⊂	⊂	X
ejpam-6575	217	2	(	(	PUNCT
ejpam-6575	217	3	0	0	NUM
ejpam-6575	217	4	,	,	PUNCT
ejpam-6575	217	5	s	s	X
ejpam-6575	217	6	]	]	X
ejpam-6575	217	7	such	such	ADJ
ejpam-6575	217	8	that	that	SCONJ
ejpam-6575	217	9	f	f	PROPN
ejpam-6575	217	10	(	(	PUNCT
ejpam-6575	217	11	2β	2β	NOUN
ejpam-6575	217	12	x	x	SYM
ejpam-6575	217	13	)	)	PUNCT
ejpam-6575	218	1	−	−	PROPN
ejpam-6575	218	2	f	f	PROPN
ejpam-6575	218	3	(	(	PUNCT
ejpam-6575	218	4	2	2	NUM
ejpam-6575	218	5	x	x	NOUN
ejpam-6575	218	6	)	)	PUNCT
ejpam-6575	219	1	=	=	SYM
ejpam-6575	219	2	f	f	PROPN
ejpam-6575	219	3	′(η	′(η	NOUN
ejpam-6575	219	4	)	)	PUNCT
ejpam-6575	220	1	(	(	PUNCT
ejpam-6575	220	2	2β	2β	NOUN
ejpam-6575	220	3	x	x	PUNCT
ejpam-6575	220	4	−	−	PROPN
ejpam-6575	220	5	2	2	NUM
ejpam-6575	220	6	x	x	NOUN
ejpam-6575	220	7	)	)	PUNCT
ejpam-6575	220	8	=	=	SYM
ejpam-6575	220	9	(	(	PUNCT
ejpam-6575	220	10	β	β	NOUN
ejpam-6575	220	11	−	−	NOUN
ejpam-6575	220	12	1	1	NUM
ejpam-6575	220	13	)	)	SYM
ejpam-6575	220	14	2	2	NUM
ejpam-6575	220	15	x	x	SYM
ejpam-6575	220	16	f	f	PROPN
ejpam-6575	220	17	′(η	′(η	NOUN
ejpam-6575	220	18	)	)	PUNCT
ejpam-6575	220	19	,	,	PUNCT
ejpam-6575	220	20	and	and	CCONJ
ejpam-6575	220	21	hence∫	hence∫	VERB
ejpam-6575	220	22	∞	∞	NUM
ejpam-6575	220	23	x1	x1	PROPN
ejpam-6575	220	24	x−3/2	x−3/2	PROPN
ejpam-6575	220	25	∣∣f(2β	∣∣f(2β	X
ejpam-6575	220	26	/	/	SYM
ejpam-6575	220	27	x)−	x)−	PROPN
ejpam-6575	220	28	f(2	f(2	PROPN
ejpam-6575	220	29	/	/	SYM
ejpam-6575	220	30	x	x	NOUN
ejpam-6575	220	31	)	)	PUNCT
ejpam-6575	220	32	∣∣	∣∣	X
ejpam-6575	220	33	dx	dx	PROPN
ejpam-6575	220	34	=	=	SYM
ejpam-6575	220	35	2|β	2|β	PROPN
ejpam-6575	220	36	−	−	NOUN
ejpam-6575	221	1	1|	1|	NUM
ejpam-6575	221	2	∫	∫	PROPN
ejpam-6575	221	3	s	s	PART
ejpam-6575	221	4	0	0	NUM
ejpam-6575	221	5	t	t	NOUN
ejpam-6575	221	6	1	1	NUM
ejpam-6575	221	7	2	2	NUM
ejpam-6575	221	8	∣∣f	∣∣f	NOUN
ejpam-6575	221	9	′(t	′(t	NOUN
ejpam-6575	221	10	)	)	PUNCT
ejpam-6575	221	11	∣∣	∣∣	X
ejpam-6575	221	12	dt	dt	X
ejpam-6575	221	13	<	<	X
ejpam-6575	221	14	2|β	2|β	PROPN
ejpam-6575	221	15	−	−	NUM
ejpam-6575	221	16	1|	1|	NUM
ejpam-6575	221	17	ε	ε	PROPN
ejpam-6575	221	18	.	.	PUNCT
ejpam-6575	221	19	i.	i.	PROPN
ejpam-6575	221	20	ayoob	ayoob	PROPN
ejpam-6575	221	21	/	/	SYM
ejpam-6575	221	22	eur	eur	PROPN
ejpam-6575	221	23	.	.	PUNCT
ejpam-6575	222	1	j.	j.	PROPN
ejpam-6575	222	2	pure	pure	PROPN
ejpam-6575	222	3	appl	appl	PROPN
ejpam-6575	222	4	.	.	PROPN
ejpam-6575	222	5	math	math	PROPN
ejpam-6575	222	6	,	,	PUNCT
ejpam-6575	222	7	18	18	NUM
ejpam-6575	222	8	(	(	PUNCT
ejpam-6575	222	9	3	3	NUM
ejpam-6575	222	10	)	)	PUNCT
ejpam-6575	222	11	(	(	PUNCT
ejpam-6575	222	12	2025	2025	NUM
ejpam-6575	222	13	)	)	PUNCT
ejpam-6575	222	14	,	,	PUNCT
ejpam-6575	222	15	6575	6575	NUM
ejpam-6575	222	16	8	8	NUM
ejpam-6575	222	17	of	of	ADP
ejpam-6575	222	18	12	12	NUM
ejpam-6575	222	19	(	(	PUNCT
ejpam-6575	222	20	iii	iii	NOUN
ejpam-6575	222	21	)	)	PUNCT
ejpam-6575	222	22	middle	middle	ADJ
ejpam-6575	222	23	region	region	NOUN
ejpam-6575	222	24	:	:	PUNCT
ejpam-6575	222	25	on	on	ADP
ejpam-6575	222	26	the	the	DET
ejpam-6575	222	27	compact	compact	ADJ
ejpam-6575	222	28	interval	interval	NOUN
ejpam-6575	223	1	[	[	X
ejpam-6575	223	2	x0	x0	PROPN
ejpam-6575	223	3	,	,	PUNCT
ejpam-6575	223	4	x1	x1	PROPN
ejpam-6575	223	5	]	]	X
ejpam-6575	223	6	,	,	PUNCT
ejpam-6575	223	7	the	the	DET
ejpam-6575	223	8	function	function	NOUN
ejpam-6575	223	9	x	x	X
ejpam-6575	223	10	7→	7→	NUM
ejpam-6575	223	11	x−3/2	x−3/2	PROPN
ejpam-6575	223	12	[	[	PUNCT
ejpam-6575	223	13	f(2β	f(2β	PROPN
ejpam-6575	223	14	/	/	SYM
ejpam-6575	223	15	x)−	x)−	PROPN
ejpam-6575	223	16	f(2	f(2	PROPN
ejpam-6575	223	17	/	/	SYM
ejpam-6575	223	18	x	x	NOUN
ejpam-6575	223	19	)	)	PUNCT
ejpam-6575	223	20	]	]	PUNCT
ejpam-6575	223	21	is	be	AUX
ejpam-6575	223	22	continuous	continuous	ADJ
ejpam-6575	223	23	and	and	CCONJ
ejpam-6575	223	24	hence	hence	ADV
ejpam-6575	223	25	bounded	bound	VERB
ejpam-6575	223	26	,	,	PUNCT
ejpam-6575	223	27	so	so	ADV
ejpam-6575	223	28	its	its	PRON
ejpam-6575	223	29	integral	integral	NOUN
ejpam-6575	223	30	is	be	AUX
ejpam-6575	223	31	finite	finite	ADJ
ejpam-6575	223	32	.	.	PUNCT
ejpam-6575	224	1	combining	combine	VERB
ejpam-6575	224	2	(	(	PUNCT
ejpam-6575	224	3	i	i	NOUN
ejpam-6575	224	4	)	)	PUNCT
ejpam-6575	224	5	,	,	PUNCT
ejpam-6575	224	6	(	(	PUNCT
ejpam-6575	224	7	ii	ii	NOUN
ejpam-6575	224	8	)	)	PUNCT
ejpam-6575	224	9	,	,	PUNCT
ejpam-6575	224	10	and	and	CCONJ
ejpam-6575	224	11	(	(	PUNCT
ejpam-6575	224	12	iii	iii	X
ejpam-6575	224	13	)	)	PUNCT
ejpam-6575	224	14	shows	show	VERB
ejpam-6575	224	15	i(β	i(β	NOUN
ejpam-6575	224	16	)	)	PUNCT
ejpam-6575	225	1	=	=	SYM
ejpam-6575	225	2	∫	∫	PROPN
ejpam-6575	226	1	∞	∞	PROPN
ejpam-6575	226	2	0	0	NUM
ejpam-6575	226	3	x−	x−	PROPN
ejpam-6575	226	4	3	3	NUM
ejpam-6575	226	5	2	2	NUM
ejpam-6575	226	6	[	[	PUNCT
ejpam-6575	226	7	f	f	X
ejpam-6575	226	8	(	(	PUNCT
ejpam-6575	226	9	2β	2β	NOUN
ejpam-6575	226	10	x	x	SYM
ejpam-6575	226	11	)	)	PUNCT
ejpam-6575	227	1	−	−	PROPN
ejpam-6575	227	2	f	f	PROPN
ejpam-6575	227	3	(	(	PUNCT
ejpam-6575	227	4	2	2	NUM
ejpam-6575	227	5	x	x	NOUN
ejpam-6575	227	6	)	)	PUNCT
ejpam-6575	227	7	]	]	PUNCT
ejpam-6575	227	8	dx	dx	PROPN
ejpam-6575	227	9	<	<	X
ejpam-6575	227	10	∞.	∞.	PROPN
ejpam-6575	227	11	therefore	therefore	ADV
ejpam-6575	227	12	i(β	i(β	PROPN
ejpam-6575	227	13	)	)	PUNCT
ejpam-6575	227	14	converges	converge	VERB
ejpam-6575	227	15	absolutely	absolutely	ADV
ejpam-6575	227	16	.	.	PUNCT
ejpam-6575	228	1	we	we	PRON
ejpam-6575	228	2	have	have	VERB
ejpam-6575	228	3	the	the	DET
ejpam-6575	228	4	following	following	ADJ
ejpam-6575	228	5	result	result	NOUN
ejpam-6575	228	6	which	which	PRON
ejpam-6575	228	7	is	be	AUX
ejpam-6575	228	8	similar	similar	ADJ
ejpam-6575	228	9	to	to	ADP
ejpam-6575	228	10	frullani	frullani	ADJ
ejpam-6575	228	11	type	type	NOUN
ejpam-6575	228	12	integral	integral	ADJ
ejpam-6575	228	13	.	.	PUNCT
ejpam-6575	229	1	theorem	theorem	NOUN
ejpam-6575	229	2	3	3	X
ejpam-6575	229	3	.	.	PUNCT
ejpam-6575	230	1	let	let	VERB
ejpam-6575	230	2	f	f	PROPN
ejpam-6575	230	3	:	:	PUNCT
ejpam-6575	230	4	(	(	PUNCT
ejpam-6575	230	5	0,∞	0,∞	NOUN
ejpam-6575	230	6	)	)	PUNCT
ejpam-6575	231	1	→	→	PUNCT
ejpam-6575	231	2	r	r	NOUN
ejpam-6575	231	3	be	be	AUX
ejpam-6575	231	4	a	a	DET
ejpam-6575	231	5	continuously	continuously	ADV
ejpam-6575	231	6	differentiable	differentiable	ADJ
ejpam-6575	231	7	function	function	NOUN
ejpam-6575	231	8	such	such	ADJ
ejpam-6575	231	9	that	that	SCONJ
ejpam-6575	231	10	lim	lim	PROPN
ejpam-6575	231	11	t→0	t→0	AUX
ejpam-6575	231	12	+	+	CCONJ
ejpam-6575	231	13	f(t	f(t	NOUN
ejpam-6575	231	14	)	)	PUNCT
ejpam-6575	231	15	=	=	SYM
ejpam-6575	231	16	f(0	f(0	NOUN
ejpam-6575	231	17	)	)	PUNCT
ejpam-6575	231	18	∈	∈	PROPN
ejpam-6575	231	19	r	r	NOUN
ejpam-6575	231	20	,	,	PUNCT
ejpam-6575	231	21	lim	lim	PROPN
ejpam-6575	231	22	t→∞	t→∞	PRON
ejpam-6575	231	23	f(t	f(t	PROPN
ejpam-6575	231	24	)	)	PUNCT
ejpam-6575	231	25	=	=	SYM
ejpam-6575	231	26	f(∞	f(∞	NOUN
ejpam-6575	231	27	)	)	PUNCT
ejpam-6575	231	28	∈	∈	PROPN
ejpam-6575	231	29	r	r	NOUN
ejpam-6575	231	30	,	,	PUNCT
ejpam-6575	231	31	and	and	CCONJ
ejpam-6575	231	32	a	a	DET
ejpam-6575	231	33	=	=	X
ejpam-6575	231	34	∫	∫	PROPN
ejpam-6575	231	35	∞	∞	NUM
ejpam-6575	231	36	0	0	NUM
ejpam-6575	231	37	t	t	NOUN
ejpam-6575	231	38	1	1	NUM
ejpam-6575	231	39	2	2	NUM
ejpam-6575	231	40	∣∣f	∣∣f	NOUN
ejpam-6575	231	41	′(t	′(t	NOUN
ejpam-6575	231	42	)	)	PUNCT
ejpam-6575	231	43	∣∣	∣∣	X
ejpam-6575	231	44	dt	dt	PUNCT
ejpam-6575	231	45	<	<	X
ejpam-6575	231	46	∞.	∞.	PROPN
ejpam-6575	231	47	then	then	ADV
ejpam-6575	231	48	for	for	ADP
ejpam-6575	231	49	every	every	DET
ejpam-6575	231	50	β	β	X
ejpam-6575	231	51	>	>	X
ejpam-6575	231	52	0,∫	0,∫	PROPN
ejpam-6575	231	53	∞	∞	PROPN
ejpam-6575	231	54	0	0	NUM
ejpam-6575	232	1	x−	x−	PROPN
ejpam-6575	232	2	3	3	NUM
ejpam-6575	232	3	2	2	NUM
ejpam-6575	232	4	[	[	PUNCT
ejpam-6575	232	5	f	f	X
ejpam-6575	232	6	(	(	PUNCT
ejpam-6575	232	7	2β	2β	NOUN
ejpam-6575	232	8	x	x	SYM
ejpam-6575	232	9	)	)	PUNCT
ejpam-6575	233	1	−	−	PROPN
ejpam-6575	233	2	f	f	PROPN
ejpam-6575	233	3	(	(	PUNCT
ejpam-6575	233	4	2	2	NUM
ejpam-6575	233	5	x	x	NOUN
ejpam-6575	233	6	)	)	PUNCT
ejpam-6575	233	7	]	]	PUNCT
ejpam-6575	233	8	dx	dx	PROPN
ejpam-6575	233	9	=	=	SYM
ejpam-6575	233	10	√	√	PROPN
ejpam-6575	233	11	2a	2a	NUM
ejpam-6575	233	12	(	(	PUNCT
ejpam-6575	233	13	1−	1−	NUM
ejpam-6575	233	14	β−1	β−1	SYM
ejpam-6575	233	15	2	2	NUM
ejpam-6575	233	16	)	)	PUNCT
ejpam-6575	233	17	.	.	PUNCT
ejpam-6575	234	1	proof	proof	NOUN
ejpam-6575	234	2	.	.	PUNCT
ejpam-6575	235	1	define	define	VERB
ejpam-6575	235	2	i(β	i(β	NOUN
ejpam-6575	235	3	)	)	PUNCT
ejpam-6575	236	1	=	=	SYM
ejpam-6575	236	2	∫	∫	PROPN
ejpam-6575	237	1	∞	∞	PROPN
ejpam-6575	237	2	0	0	NUM
ejpam-6575	237	3	x−	x−	PROPN
ejpam-6575	237	4	3	3	NUM
ejpam-6575	237	5	2	2	NUM
ejpam-6575	237	6	[	[	PUNCT
ejpam-6575	237	7	f	f	X
ejpam-6575	237	8	(	(	PUNCT
ejpam-6575	237	9	2β	2β	NOUN
ejpam-6575	237	10	x	x	SYM
ejpam-6575	237	11	)	)	PUNCT
ejpam-6575	238	1	−	−	PROPN
ejpam-6575	238	2	f	f	PROPN
ejpam-6575	238	3	(	(	PUNCT
ejpam-6575	238	4	2	2	NUM
ejpam-6575	238	5	x	x	NOUN
ejpam-6575	238	6	)	)	PUNCT
ejpam-6575	238	7	]	]	PUNCT
ejpam-6575	239	1	dx	dx	PROPN
ejpam-6575	239	2	.	.	PROPN
ejpam-6575	240	1	since	since	SCONJ
ejpam-6575	240	2	f	f	PROPN
ejpam-6575	240	3	is	be	AUX
ejpam-6575	240	4	c1	c1	PROPN
ejpam-6575	240	5	and	and	CCONJ
ejpam-6575	240	6	the	the	DET
ejpam-6575	240	7	subtraction	subtraction	NOUN
ejpam-6575	240	8	makes	make	VERB
ejpam-6575	240	9	the	the	DET
ejpam-6575	240	10	integrand	integrand	NOUN
ejpam-6575	240	11	absolutely	absolutely	ADV
ejpam-6575	240	12	convergent	convergent	ADJ
ejpam-6575	240	13	at	at	ADP
ejpam-6575	240	14	both	both	DET
ejpam-6575	240	15	ends	end	NOUN
ejpam-6575	240	16	,	,	PUNCT
ejpam-6575	240	17	we	we	PRON
ejpam-6575	240	18	may	may	AUX
ejpam-6575	240	19	differentiate	differentiate	VERB
ejpam-6575	240	20	under	under	ADP
ejpam-6575	240	21	the	the	DET
ejpam-6575	240	22	integral	integral	ADJ
ejpam-6575	240	23	sign	sign	NOUN
ejpam-6575	240	24	:	:	PUNCT
ejpam-6575	240	25	di	di	NOUN
ejpam-6575	241	1	dβ	dβ	PROPN
ejpam-6575	241	2	=	=	SYM
ejpam-6575	241	3	∫	∫	PROPN
ejpam-6575	241	4	∞	∞	PROPN
ejpam-6575	241	5	0	0	NUM
ejpam-6575	241	6	x−	x−	PROPN
ejpam-6575	241	7	3	3	NUM
ejpam-6575	241	8	2	2	NUM
ejpam-6575	241	9	∂	∂	NUM
ejpam-6575	241	10	∂β	∂β	PROPN
ejpam-6575	242	1	[	[	PUNCT
ejpam-6575	242	2	f	f	X
ejpam-6575	242	3	(	(	PUNCT
ejpam-6575	242	4	2β	2β	NOUN
ejpam-6575	242	5	x	x	X
ejpam-6575	242	6	)	)	PUNCT
ejpam-6575	242	7	]	]	PUNCT
ejpam-6575	242	8	dx	dx	PROPN
ejpam-6575	243	1	=	=	SYM
ejpam-6575	243	2	2	2	NUM
ejpam-6575	243	3	∫	∫	NOUN
ejpam-6575	243	4	∞	∞	PROPN
ejpam-6575	243	5	0	0	NUM
ejpam-6575	244	1	x−	x−	PROPN
ejpam-6575	244	2	5	5	NUM
ejpam-6575	244	3	2	2	NUM
ejpam-6575	244	4	f	f	NOUN
ejpam-6575	244	5	′(2β	′(2β	NOUN
ejpam-6575	244	6	x	x	SYM
ejpam-6575	244	7	)	)	PUNCT
ejpam-6575	244	8	dx	dx	PROPN
ejpam-6575	244	9	.	.	PROPN
ejpam-6575	244	10	perform	perform	VERB
ejpam-6575	244	11	the	the	DET
ejpam-6575	244	12	substitution	substitution	NOUN
ejpam-6575	244	13	t	t	NOUN
ejpam-6575	245	1	=	=	SYM
ejpam-6575	245	2	2β	2β	NUM
ejpam-6575	245	3	x	x	X
ejpam-6575	245	4	,	,	PUNCT
ejpam-6575	245	5	so	so	CCONJ
ejpam-6575	245	6	x	x	SYM
ejpam-6575	246	1	=	=	SYM
ejpam-6575	246	2	2β	2β	NOUN
ejpam-6575	246	3	t	t	NOUN
ejpam-6575	246	4	and	and	CCONJ
ejpam-6575	246	5	dx	dx	PROPN
ejpam-6575	246	6	=	=	SYM
ejpam-6575	247	1	−	−	PROPN
ejpam-6575	247	2	2β	2β	NOUN
ejpam-6575	247	3	t2	t2	NOUN
ejpam-6575	247	4	dt	dt	NOUN
ejpam-6575	247	5	.	.	PUNCT
ejpam-6575	248	1	then	then	ADV
ejpam-6575	248	2	x−	x−	PROPN
ejpam-6575	248	3	5	5	NUM
ejpam-6575	248	4	2	2	NUM
ejpam-6575	248	5	=	=	SYM
ejpam-6575	248	6	(	(	PUNCT
ejpam-6575	248	7	2β	2β	NOUN
ejpam-6575	248	8	t	t	NOUN
ejpam-6575	248	9	)	)	PUNCT
ejpam-6575	248	10	−	−	PROPN
ejpam-6575	248	11	5	5	NUM
ejpam-6575	248	12	2	2	NUM
ejpam-6575	248	13	=	=	SYM
ejpam-6575	248	14	(	(	PUNCT
ejpam-6575	248	15	2β)−	2β)−	NUM
ejpam-6575	248	16	5	5	NUM
ejpam-6575	248	17	2	2	NUM
ejpam-6575	248	18	t	t	NOUN
ejpam-6575	248	19	5	5	NUM
ejpam-6575	248	20	2	2	NUM
ejpam-6575	248	21	,	,	PUNCT
ejpam-6575	248	22	and	and	CCONJ
ejpam-6575	248	23	x−	x−	PROPN
ejpam-6575	248	24	5	5	NUM
ejpam-6575	248	25	2	2	NUM
ejpam-6575	248	26	dx	dx	NOUN
ejpam-6575	248	27	=	=	SYM
ejpam-6575	248	28	(	(	PUNCT
ejpam-6575	248	29	2β)−	2β)−	NUM
ejpam-6575	248	30	5	5	NUM
ejpam-6575	248	31	2	2	NUM
ejpam-6575	248	32	t	t	NOUN
ejpam-6575	248	33	5	5	NUM
ejpam-6575	248	34	2	2	NUM
ejpam-6575	248	35	(	(	PUNCT
ejpam-6575	248	36	−2β	−2β	PROPN
ejpam-6575	248	37	t2	t2	NOUN
ejpam-6575	248	38	)	)	PUNCT
ejpam-6575	248	39	dt	dt	X
ejpam-6575	249	1	=	=	PUNCT
ejpam-6575	249	2	−(2β)−	−(2β)−	NOUN
ejpam-6575	249	3	3	3	NUM
ejpam-6575	249	4	2	2	NUM
ejpam-6575	249	5	t	t	NOUN
ejpam-6575	249	6	1	1	NUM
ejpam-6575	249	7	2	2	NUM
ejpam-6575	249	8	dt	dt	NOUN
ejpam-6575	249	9	.	.	PUNCT
ejpam-6575	250	1	hence∫	hence∫	PROPN
ejpam-6575	251	1	∞	∞	PROPN
ejpam-6575	251	2	0	0	NUM
ejpam-6575	251	3	x−	x−	PROPN
ejpam-6575	251	4	5	5	NUM
ejpam-6575	251	5	2	2	NUM
ejpam-6575	251	6	f	f	NOUN
ejpam-6575	251	7	′(2β	′(2β	NOUN
ejpam-6575	251	8	x	x	SYM
ejpam-6575	251	9	)	)	PUNCT
ejpam-6575	251	10	dx	dx	PROPN
ejpam-6575	252	1	=	=	PUNCT
ejpam-6575	252	2	(	(	PUNCT
ejpam-6575	252	3	2β)−	2β)−	NUM
ejpam-6575	252	4	3	3	NUM
ejpam-6575	252	5	2	2	NUM
ejpam-6575	252	6	∫	∫	NOUN
ejpam-6575	252	7	0	0	NUM
ejpam-6575	253	1	∞	∞	NUM
ejpam-6575	253	2	t	t	NOUN
ejpam-6575	253	3	1	1	NUM
ejpam-6575	253	4	2	2	NUM
ejpam-6575	253	5	f	f	PROPN
ejpam-6575	253	6	′(t	′(t	PROPN
ejpam-6575	253	7	)	)	PUNCT
ejpam-6575	253	8	(	(	PUNCT
ejpam-6575	253	9	−dt	−dt	X
ejpam-6575	253	10	)	)	PUNCT
ejpam-6575	253	11	=	=	SYM
ejpam-6575	254	1	(	(	PUNCT
ejpam-6575	254	2	2β)−	2β)−	NUM
ejpam-6575	254	3	3	3	NUM
ejpam-6575	254	4	2	2	NUM
ejpam-6575	254	5	∫	∫	NOUN
ejpam-6575	254	6	∞	∞	NUM
ejpam-6575	254	7	0	0	NUM
ejpam-6575	254	8	t	t	NOUN
ejpam-6575	254	9	1	1	NUM
ejpam-6575	254	10	2	2	NUM
ejpam-6575	254	11	f	f	PROPN
ejpam-6575	254	12	′(t	′(t	NOUN
ejpam-6575	254	13	)	)	PUNCT
ejpam-6575	255	1	dt	dt	NOUN
ejpam-6575	256	1	=	=	PUNCT
ejpam-6575	257	1	(	(	PUNCT
ejpam-6575	257	2	2β)−	2β)−	NUM
ejpam-6575	257	3	3	3	NUM
ejpam-6575	257	4	2	2	NUM
ejpam-6575	257	5	a	a	NOUN
ejpam-6575	257	6	,	,	PUNCT
ejpam-6575	257	7	where	where	SCONJ
ejpam-6575	257	8	a	a	DET
ejpam-6575	257	9	=	=	NOUN
ejpam-6575	257	10	∫∞	∫∞	NOUN
ejpam-6575	257	11	0	0	PUNCT
ejpam-6575	257	12	t	t	PROPN
ejpam-6575	257	13	1	1	NUM
ejpam-6575	257	14	2	2	NUM
ejpam-6575	257	15	∣∣f	∣∣f	NOUN
ejpam-6575	257	16	′(t	′(t	NOUN
ejpam-6575	257	17	)	)	PUNCT
ejpam-6575	257	18	∣∣	∣∣	X
ejpam-6575	257	19	dt	dt	X
ejpam-6575	257	20	<	<	X
ejpam-6575	257	21	∞.	∞.	PROPN
ejpam-6575	257	22	thus	thus	ADV
ejpam-6575	257	23	di	di	X
ejpam-6575	257	24	dβ	dβ	NOUN
ejpam-6575	257	25	=	=	SYM
ejpam-6575	257	26	2	2	NUM
ejpam-6575	257	27	(	(	PUNCT
ejpam-6575	257	28	2β)−	2β)−	NUM
ejpam-6575	257	29	3	3	NUM
ejpam-6575	257	30	2	2	NUM
ejpam-6575	257	31	a	a	PRON
ejpam-6575	257	32	=	=	SYM
ejpam-6575	257	33	2−	2−	NUM
ejpam-6575	257	34	1	1	NUM
ejpam-6575	257	35	2	2	NUM
ejpam-6575	257	36	aβ−	aβ−	NUM
ejpam-6575	257	37	3	3	NUM
ejpam-6575	257	38	2	2	NUM
ejpam-6575	257	39	.	.	PUNCT
ejpam-6575	258	1	i.	i.	PROPN
ejpam-6575	258	2	ayoob	ayoob	PROPN
ejpam-6575	258	3	/	/	SYM
ejpam-6575	258	4	eur	eur	PROPN
ejpam-6575	258	5	.	.	PUNCT
ejpam-6575	259	1	j.	j.	PROPN
ejpam-6575	259	2	pure	pure	PROPN
ejpam-6575	259	3	appl	appl	PROPN
ejpam-6575	259	4	.	.	PROPN
ejpam-6575	259	5	math	math	PROPN
ejpam-6575	259	6	,	,	PUNCT
ejpam-6575	259	7	18	18	NUM
ejpam-6575	259	8	(	(	PUNCT
ejpam-6575	259	9	3	3	NUM
ejpam-6575	259	10	)	)	PUNCT
ejpam-6575	259	11	(	(	PUNCT
ejpam-6575	259	12	2025	2025	NUM
ejpam-6575	259	13	)	)	PUNCT
ejpam-6575	259	14	,	,	PUNCT
ejpam-6575	259	15	6575	6575	NUM
ejpam-6575	259	16	9	9	NUM
ejpam-6575	259	17	of	of	ADP
ejpam-6575	259	18	12	12	NUM
ejpam-6575	259	19	integrating	integrating	NOUN
ejpam-6575	259	20	from	from	ADP
ejpam-6575	259	21	β	β	X
ejpam-6575	259	22	=	=	SYM
ejpam-6575	259	23	1	1	NUM
ejpam-6575	259	24	(	(	PUNCT
ejpam-6575	259	25	where	where	SCONJ
ejpam-6575	259	26	clearly	clearly	ADV
ejpam-6575	259	27	i(1	i(1	NOUN
ejpam-6575	259	28	)	)	PUNCT
ejpam-6575	259	29	=	=	SYM
ejpam-6575	259	30	0	0	X
ejpam-6575	259	31	)	)	PUNCT
ejpam-6575	259	32	to	to	ADP
ejpam-6575	259	33	a	a	DET
ejpam-6575	259	34	general	general	ADJ
ejpam-6575	259	35	β	β	X
ejpam-6575	259	36	>	>	X
ejpam-6575	259	37	0	0	PUNCT
ejpam-6575	259	38	gives	give	VERB
ejpam-6575	259	39	i(β	i(β	PROPN
ejpam-6575	259	40	)	)	PUNCT
ejpam-6575	260	1	=	=	PUNCT
ejpam-6575	261	1	∫	∫	PROPN
ejpam-6575	261	2	β	β	PROPN
ejpam-6575	261	3	1	1	NUM
ejpam-6575	261	4	di	di	INTJ
ejpam-6575	261	5	db	db	PROPN
ejpam-6575	261	6	db	db	PROPN
ejpam-6575	261	7	=	=	SYM
ejpam-6575	261	8	2−	2−	NUM
ejpam-6575	261	9	1	1	NUM
ejpam-6575	261	10	2	2	NUM
ejpam-6575	261	11	a	a	DET
ejpam-6575	261	12	∫	∫	PROPN
ejpam-6575	261	13	β	β	NOUN
ejpam-6575	261	14	1	1	NUM
ejpam-6575	261	15	b−	b−	NOUN
ejpam-6575	261	16	3	3	NUM
ejpam-6575	261	17	2	2	NUM
ejpam-6575	261	18	db	db	NOUN
ejpam-6575	261	19	=	=	NOUN
ejpam-6575	261	20	2−	2−	NUM
ejpam-6575	261	21	1	1	NUM
ejpam-6575	261	22	2	2	NUM
ejpam-6575	261	23	a	a	DET
ejpam-6575	261	24	[	[	PUNCT
ejpam-6575	261	25	−2	−2	NOUN
ejpam-6575	261	26	b−	b−	NOUN
ejpam-6575	261	27	1	1	NUM
ejpam-6575	261	28	2	2	NUM
ejpam-6575	261	29	]	]	PUNCT
ejpam-6575	261	30	β	β	X
ejpam-6575	261	31	1	1	NUM
ejpam-6575	261	32	=	=	SYM
ejpam-6575	261	33	√	√	NUM
ejpam-6575	261	34	2a	2a	NUM
ejpam-6575	261	35	(	(	PUNCT
ejpam-6575	261	36	1−	1−	NUM
ejpam-6575	261	37	β−1	β−1	SYM
ejpam-6575	261	38	2	2	NUM
ejpam-6575	261	39	)	)	PUNCT
ejpam-6575	261	40	.	.	PUNCT
ejpam-6575	262	1	this	this	PRON
ejpam-6575	262	2	proves	prove	VERB
ejpam-6575	262	3	the	the	DET
ejpam-6575	262	4	general	general	ADJ
ejpam-6575	262	5	formula	formula	NOUN
ejpam-6575	262	6	.	.	PUNCT
ejpam-6575	263	1	the	the	DET
ejpam-6575	263	2	following	follow	VERB
ejpam-6575	263	3	special	special	ADJ
ejpam-6575	263	4	case	case	NOUN
ejpam-6575	263	5	in	in	ADP
ejpam-6575	263	6	[	[	NOUN
ejpam-6575	263	7	8	8	NUM
ejpam-6575	263	8	]	]	PUNCT
ejpam-6575	263	9	is	be	AUX
ejpam-6575	263	10	deduced	deduce	VERB
ejpam-6575	263	11	from	from	ADP
ejpam-6575	263	12	theorem	theorem	ADJ
ejpam-6575	263	13	3	3	NUM
ejpam-6575	263	14	.	.	NOUN
ejpam-6575	263	15	remark	remark	NOUN
ejpam-6575	263	16	1	1	NUM
ejpam-6575	263	17	.	.	PUNCT
ejpam-6575	264	1	in	in	ADP
ejpam-6575	264	2	the	the	DET
ejpam-6575	264	3	special	special	ADJ
ejpam-6575	264	4	case	case	NOUN
ejpam-6575	264	5	,	,	PUNCT
ejpam-6575	264	6	f(x	f(x	PROPN
ejpam-6575	264	7	)	)	PUNCT
ejpam-6575	265	1	=	=	SYM
ejpam-6575	265	2	arctanx	arctanx	NOUN
ejpam-6575	265	3	,	,	PUNCT
ejpam-6575	265	4	we	we	PRON
ejpam-6575	265	5	have	have	VERB
ejpam-6575	265	6	f	f	PROPN
ejpam-6575	265	7	′(t	′(t	PROPN
ejpam-6575	265	8	)	)	PUNCT
ejpam-6575	265	9	=	=	SYM
ejpam-6575	266	1	1/(1	1/(1	NUM
ejpam-6575	266	2	+	+	NUM
ejpam-6575	266	3	t2	t2	NOUN
ejpam-6575	266	4	)	)	PUNCT
ejpam-6575	266	5	,	,	PUNCT
ejpam-6575	266	6	and	and	CCONJ
ejpam-6575	266	7	the	the	DET
ejpam-6575	266	8	constant	constant	ADJ
ejpam-6575	266	9	a	a	PRON
ejpam-6575	266	10	=	=	SYM
ejpam-6575	266	11	∫	∫	PROPN
ejpam-6575	266	12	∞	∞	NUM
ejpam-6575	266	13	0	0	NUM
ejpam-6575	267	1	t	t	NOUN
ejpam-6575	267	2	1	1	NUM
ejpam-6575	267	3	2	2	NUM
ejpam-6575	267	4	1	1	NUM
ejpam-6575	267	5	+	+	NUM
ejpam-6575	267	6	t2	t2	NOUN
ejpam-6575	267	7	dt	dt	NOUN
ejpam-6575	267	8	=	=	NOUN
ejpam-6575	267	9	1	1	NUM
ejpam-6575	267	10	2	2	NUM
ejpam-6575	267	11	b	b	PROPN
ejpam-6575	267	12	(	(	PUNCT
ejpam-6575	267	13	3	3	NUM
ejpam-6575	267	14	4	4	NUM
ejpam-6575	267	15	,	,	PUNCT
ejpam-6575	267	16	1	1	NUM
ejpam-6575	267	17	4	4	NUM
ejpam-6575	267	18	)	)	PUNCT
ejpam-6575	267	19	=	=	PUNCT
ejpam-6575	268	1	π	π	NOUN
ejpam-6575	268	2	√	√	NUM
ejpam-6575	268	3	2	2	NUM
ejpam-6575	268	4	2	2	NUM
ejpam-6575	268	5	,	,	PUNCT
ejpam-6575	268	6	yielding	yield	VERB
ejpam-6575	268	7	∫	∫	PROPN
ejpam-6575	268	8	∞	∞	PROPN
ejpam-6575	268	9	0	0	PROPN
ejpam-6575	268	10	arctan	arctan	PROPN
ejpam-6575	268	11	(	(	PUNCT
ejpam-6575	268	12	2β	2β	NOUN
ejpam-6575	268	13	x	x	SYM
ejpam-6575	268	14	)	)	PUNCT
ejpam-6575	268	15	−	−	PROPN
ejpam-6575	268	16	arctan	arctan	PROPN
ejpam-6575	268	17	(	(	PUNCT
ejpam-6575	268	18	2	2	NUM
ejpam-6575	268	19	x	x	NOUN
ejpam-6575	268	20	)	)	PUNCT
ejpam-6575	268	21	x	x	SYM
ejpam-6575	268	22	√	√	PUNCT
ejpam-6575	268	23	x	x	X
ejpam-6575	268	24	dx	dx	PROPN
ejpam-6575	268	25	=	=	SYM
ejpam-6575	268	26	π	π	PROPN
ejpam-6575	268	27	(	(	PUNCT
ejpam-6575	268	28	1−	1−	NUM
ejpam-6575	268	29	β−1	β−1	SYM
ejpam-6575	268	30	2	2	NUM
ejpam-6575	268	31	)	)	PUNCT
ejpam-6575	268	32	.	.	PUNCT
ejpam-6575	269	1	note	note	VERB
ejpam-6575	269	2	that	that	SCONJ
ejpam-6575	269	3	theorem	theorem	VERB
ejpam-6575	269	4	3	3	NUM
ejpam-6575	269	5	requires	require	VERB
ejpam-6575	269	6	f	f	PROPN
ejpam-6575	269	7	to	to	PART
ejpam-6575	269	8	be	be	AUX
ejpam-6575	269	9	continuously	continuously	ADV
ejpam-6575	269	10	differentiable	differentiable	ADJ
ejpam-6575	269	11	.	.	PUNCT
ejpam-6575	270	1	the	the	DET
ejpam-6575	270	2	following	following	ADJ
ejpam-6575	270	3	result	result	NOUN
ejpam-6575	270	4	gives	give	VERB
ejpam-6575	270	5	one	one	NUM
ejpam-6575	270	6	more	more	ADV
ejpam-6575	270	7	closed	closed	ADJ
ejpam-6575	270	8	form	form	NOUN
ejpam-6575	270	9	solution	solution	NOUN
ejpam-6575	270	10	of	of	ADP
ejpam-6575	270	11	the	the	DET
ejpam-6575	270	12	integral	integral	ADJ
ejpam-6575	270	13	i(β	i(β	NOUN
ejpam-6575	270	14	)	)	PUNCT
ejpam-6575	270	15	for	for	ADP
ejpam-6575	270	16	more	more	ADJ
ejpam-6575	270	17	general	general	ADJ
ejpam-6575	270	18	class	class	NOUN
ejpam-6575	270	19	of	of	ADP
ejpam-6575	270	20	functions	function	NOUN
ejpam-6575	270	21	in	in	ADP
ejpam-6575	270	22	terms	term	NOUN
ejpam-6575	270	23	of	of	ADP
ejpam-6575	270	24	mellin	mellin	PROPN
ejpam-6575	270	25	transform	transform	NOUN
ejpam-6575	270	26	.	.	PUNCT
ejpam-6575	271	1	proposition	proposition	NOUN
ejpam-6575	271	2	4	4	NUM
ejpam-6575	271	3	.	.	PUNCT
ejpam-6575	272	1	let	let	VERB
ejpam-6575	272	2	f	f	PROPN
ejpam-6575	272	3	:	:	PUNCT
ejpam-6575	272	4	(	(	PUNCT
ejpam-6575	272	5	0,∞	0,∞	NOUN
ejpam-6575	272	6	)	)	PUNCT
ejpam-6575	273	1	→	→	PUNCT
ejpam-6575	273	2	r	r	NOUN
ejpam-6575	273	3	be	be	AUX
ejpam-6575	273	4	measurable	measurable	ADJ
ejpam-6575	273	5	and	and	CCONJ
ejpam-6575	273	6	suppose	suppose	VERB
ejpam-6575	273	7	its	its	PRON
ejpam-6575	273	8	mellin	mellin	NOUN
ejpam-6575	273	9	transform	transform	NOUN
ejpam-6575	273	10	mf	mf	X
ejpam-6575	273	11	(	(	PUNCT
ejpam-6575	273	12	s	s	X
ejpam-6575	273	13	)	)	PUNCT
ejpam-6575	273	14	=	=	SYM
ejpam-6575	274	1	∫	∫	PROPN
ejpam-6575	274	2	∞	∞	NUM
ejpam-6575	274	3	0	0	NUM
ejpam-6575	274	4	ts−1f(t	ts−1f(t	NOUN
ejpam-6575	274	5	)	)	PUNCT
ejpam-6575	274	6	dt	dt	PUNCT
ejpam-6575	274	7	converges	converge	VERB
ejpam-6575	274	8	at	at	ADP
ejpam-6575	274	9	s	s	NOUN
ejpam-6575	274	10	=	=	SYM
ejpam-6575	274	11	1	1	NUM
ejpam-6575	274	12	2	2	NUM
ejpam-6575	274	13	,	,	PUNCT
ejpam-6575	274	14	i.e.	i.e.	X
ejpam-6575	274	15	∫	∫	PROPN
ejpam-6575	274	16	∞	∞	PROPN
ejpam-6575	274	17	0	0	NUM
ejpam-6575	275	1	t−1/2	t−1/2	PROPN
ejpam-6575	275	2	∣∣f(t)∣∣	∣∣f(t)∣∣	PUNCT
ejpam-6575	275	3	dt	dt	X
ejpam-6575	275	4	<	<	X
ejpam-6575	275	5	∞.	∞.	PROPN
ejpam-6575	275	6	then	then	ADV
ejpam-6575	275	7	for	for	ADP
ejpam-6575	275	8	each	each	DET
ejpam-6575	275	9	fixed	fix	VERB
ejpam-6575	275	10	β	β	X
ejpam-6575	275	11	>	>	X
ejpam-6575	275	12	0	0	PUNCT
ejpam-6575	276	1	the	the	DET
ejpam-6575	276	2	integral	integral	ADJ
ejpam-6575	276	3	i(β	i(β	NOUN
ejpam-6575	276	4	)	)	PUNCT
ejpam-6575	277	1	=	=	SYM
ejpam-6575	278	1	∫	∫	PROPN
ejpam-6575	279	1	∞	∞	NUM
ejpam-6575	279	2	0	0	NUM
ejpam-6575	279	3	1	1	NUM
ejpam-6575	279	4	x	x	SYM
ejpam-6575	279	5	√	√	NUM
ejpam-6575	279	6	x	x	X
ejpam-6575	279	7	[	[	PUNCT
ejpam-6575	279	8	f	f	X
ejpam-6575	279	9	(	(	PUNCT
ejpam-6575	279	10	2β	2β	NOUN
ejpam-6575	279	11	x	x	SYM
ejpam-6575	279	12	)	)	PUNCT
ejpam-6575	280	1	−	−	PROPN
ejpam-6575	280	2	f	f	PROPN
ejpam-6575	280	3	(	(	PUNCT
ejpam-6575	280	4	2	2	NUM
ejpam-6575	280	5	x	x	NOUN
ejpam-6575	280	6	)	)	PUNCT
ejpam-6575	280	7	]	]	PUNCT
ejpam-6575	280	8	dx	dx	PROPN
ejpam-6575	280	9	converges	converge	VERB
ejpam-6575	280	10	absolutely	absolutely	ADV
ejpam-6575	280	11	.	.	PUNCT
ejpam-6575	281	1	proof	proof	NOUN
ejpam-6575	281	2	.	.	PUNCT
ejpam-6575	282	1	we	we	PRON
ejpam-6575	282	2	set	set	VERB
ejpam-6575	282	3	g(x	g(x	NOUN
ejpam-6575	282	4	)	)	PUNCT
ejpam-6575	282	5	=	=	SYM
ejpam-6575	283	1	1	1	NUM
ejpam-6575	283	2	x	x	SYM
ejpam-6575	283	3	√	√	NUM
ejpam-6575	283	4	x	x	X
ejpam-6575	283	5	[	[	PUNCT
ejpam-6575	283	6	f	f	X
ejpam-6575	283	7	(	(	PUNCT
ejpam-6575	283	8	2β	2β	NOUN
ejpam-6575	283	9	x	x	SYM
ejpam-6575	283	10	)	)	PUNCT
ejpam-6575	283	11	−	−	PROPN
ejpam-6575	283	12	f	f	PROPN
ejpam-6575	283	13	(	(	PUNCT
ejpam-6575	283	14	2	2	NUM
ejpam-6575	283	15	x	x	NOUN
ejpam-6575	283	16	)	)	PUNCT
ejpam-6575	283	17	]	]	PUNCT
ejpam-6575	283	18	.	.	PUNCT
ejpam-6575	284	1	make	make	VERB
ejpam-6575	284	2	the	the	DET
ejpam-6575	284	3	substitution	substitution	NOUN
ejpam-6575	284	4	t	t	NOUN
ejpam-6575	284	5	=	=	SYM
ejpam-6575	284	6	2	2	NUM
ejpam-6575	284	7	x	x	NOUN
ejpam-6575	284	8	,	,	PUNCT
ejpam-6575	284	9	x	x	PUNCT
ejpam-6575	284	10	=	=	SYM
ejpam-6575	284	11	2	2	NUM
ejpam-6575	284	12	t	t	NOUN
ejpam-6575	284	13	,	,	PUNCT
ejpam-6575	284	14	dx	dx	PROPN
ejpam-6575	285	1	=	=	SYM
ejpam-6575	285	2	−	−	PROPN
ejpam-6575	285	3	2	2	NUM
ejpam-6575	285	4	t2	t2	NOUN
ejpam-6575	285	5	dt	dt	NOUN
ejpam-6575	285	6	.	.	PUNCT
ejpam-6575	286	1	then	then	ADV
ejpam-6575	286	2	dx	dx	PROPN
ejpam-6575	286	3	x	x	INTJ
ejpam-6575	287	1	√	√	PROPN
ejpam-6575	287	2	x	x	X
ejpam-6575	287	3	=	=	NOUN
ejpam-6575	287	4	−2	−2	NOUN
ejpam-6575	287	5	t2	t2	NOUN
ejpam-6575	287	6	1	1	NUM
ejpam-6575	287	7	(	(	PUNCT
ejpam-6575	287	8	2	2	NUM
ejpam-6575	287	9	/	/	SYM
ejpam-6575	287	10	t	t	PROPN
ejpam-6575	287	11	)	)	PUNCT
ejpam-6575	287	12	√	√	NOUN
ejpam-6575	287	13	2	2	NUM
ejpam-6575	287	14	/	/	SYM
ejpam-6575	287	15	t	t	NOUN
ejpam-6575	287	16	=	=	SYM
ejpam-6575	288	1	−2−	−2−	NUM
ejpam-6575	288	2	1	1	NUM
ejpam-6575	288	3	2	2	NUM
ejpam-6575	288	4	t−	t−	PROPN
ejpam-6575	288	5	1	1	NUM
ejpam-6575	288	6	2	2	NUM
ejpam-6575	288	7	dt	dt	NOUN
ejpam-6575	288	8	,	,	PUNCT
ejpam-6575	288	9	and	and	CCONJ
ejpam-6575	288	10	2β	2β	NOUN
ejpam-6575	289	1	x	x	X
ejpam-6575	289	2	=	=	SYM
ejpam-6575	289	3	βt	βt	PROPN
ejpam-6575	289	4	,	,	PUNCT
ejpam-6575	289	5	2	2	NUM
ejpam-6575	289	6	x	x	X
ejpam-6575	289	7	=	=	PUNCT
ejpam-6575	289	8	t.	t.	PROPN
ejpam-6575	289	9	i.	i.	PROPN
ejpam-6575	289	10	ayoob	ayoob	PROPN
ejpam-6575	289	11	/	/	SYM
ejpam-6575	289	12	eur	eur	PROPN
ejpam-6575	289	13	.	.	PUNCT
ejpam-6575	290	1	j.	j.	PROPN
ejpam-6575	290	2	pure	pure	PROPN
ejpam-6575	290	3	appl	appl	PROPN
ejpam-6575	290	4	.	.	PROPN
ejpam-6575	290	5	math	math	PROPN
ejpam-6575	290	6	,	,	PUNCT
ejpam-6575	290	7	18	18	NUM
ejpam-6575	290	8	(	(	PUNCT
ejpam-6575	290	9	3	3	NUM
ejpam-6575	290	10	)	)	PUNCT
ejpam-6575	290	11	(	(	PUNCT
ejpam-6575	290	12	2025	2025	NUM
ejpam-6575	290	13	)	)	PUNCT
ejpam-6575	290	14	,	,	PUNCT
ejpam-6575	290	15	6575	6575	NUM
ejpam-6575	290	16	10	10	NUM
ejpam-6575	290	17	of	of	ADP
ejpam-6575	290	18	12	12	NUM
ejpam-6575	290	19	hence	hence	ADV
ejpam-6575	290	20	i(β	i(β	NOUN
ejpam-6575	290	21	)	)	PUNCT
ejpam-6575	290	22	=	=	SYM
ejpam-6575	291	1	∫	∫	PROPN
ejpam-6575	292	1	∞	∞	NUM
ejpam-6575	292	2	0	0	PUNCT
ejpam-6575	293	1	g(x	g(x	NOUN
ejpam-6575	293	2	)	)	PUNCT
ejpam-6575	293	3	dx	dx	PROPN
ejpam-6575	294	1	=	=	SYM
ejpam-6575	294	2	∫	∫	PROPN
ejpam-6575	294	3	0	0	NUM
ejpam-6575	294	4	∞	∞	PROPN
ejpam-6575	294	5	f(βt)−	f(βt)−	PROPN
ejpam-6575	294	6	f(t	f(t	NOUN
ejpam-6575	294	7	)	)	PUNCT
ejpam-6575	294	8	(	(	PUNCT
ejpam-6575	294	9	−2−	−2−	NOUN
ejpam-6575	294	10	1	1	NUM
ejpam-6575	294	11	2	2	NUM
ejpam-6575	294	12	t−	t−	PROPN
ejpam-6575	294	13	1	1	NUM
ejpam-6575	294	14	2	2	NUM
ejpam-6575	294	15	)	)	PUNCT
ejpam-6575	294	16	dt	dt	NOUN
ejpam-6575	295	1	=	=	SYM
ejpam-6575	295	2	2−	2−	NUM
ejpam-6575	295	3	1	1	NUM
ejpam-6575	295	4	2	2	NUM
ejpam-6575	295	5	∫	∫	NOUN
ejpam-6575	295	6	∞	∞	NOUN
ejpam-6575	295	7	0	0	NUM
ejpam-6575	296	1	t−	t−	PROPN
ejpam-6575	296	2	1	1	NUM
ejpam-6575	296	3	2	2	NUM
ejpam-6575	296	4	[	[	PUNCT
ejpam-6575	296	5	f(βt)−	f(βt)−	NOUN
ejpam-6575	296	6	f(t	f(t	PROPN
ejpam-6575	296	7	)	)	PUNCT
ejpam-6575	296	8	]	]	PUNCT
ejpam-6575	297	1	dt	dt	X
ejpam-6575	297	2	.	.	PUNCT
ejpam-6575	298	1	it	it	PRON
ejpam-6575	298	2	suffices	suffice	VERB
ejpam-6575	298	3	to	to	PART
ejpam-6575	298	4	show	show	VERB
ejpam-6575	298	5	∫	∫	PROPN
ejpam-6575	298	6	∞	∞	PROPN
ejpam-6575	298	7	0	0	NUM
ejpam-6575	299	1	t−	t−	PROPN
ejpam-6575	299	2	1	1	NUM
ejpam-6575	299	3	2	2	NUM
ejpam-6575	299	4	∣∣f(βt)−	∣∣f(βt)−	PRON
ejpam-6575	299	5	f(t	f(t	NOUN
ejpam-6575	299	6	)	)	PUNCT
ejpam-6575	299	7	∣∣	∣∣	X
ejpam-6575	299	8	dt	dt	X
ejpam-6575	299	9	<	<	X
ejpam-6575	299	10	∞.	∞.	PROPN
ejpam-6575	299	11	by	by	ADP
ejpam-6575	299	12	the	the	DET
ejpam-6575	299	13	triangle	triangle	NOUN
ejpam-6575	299	14	inequality	inequality	NOUN
ejpam-6575	299	15	,	,	PUNCT
ejpam-6575	299	16	∣∣f(βt)−	∣∣f(βt)−	PUNCT
ejpam-6575	299	17	f(t	f(t	NOUN
ejpam-6575	299	18	)	)	PUNCT
ejpam-6575	300	1	∣∣	∣∣	NUM
ejpam-6575	300	2	≤	≤	NOUN
ejpam-6575	301	1	|f(βt)|+	|f(βt)|+	PROPN
ejpam-6575	301	2	|f(t)|	|f(t)|	ADJ
ejpam-6575	301	3	,	,	PUNCT
ejpam-6575	301	4	so	so	ADV
ejpam-6575	301	5	∫	∫	PROPN
ejpam-6575	301	6	∞	∞	NUM
ejpam-6575	301	7	0	0	NUM
ejpam-6575	302	1	t−	t−	PROPN
ejpam-6575	302	2	1	1	NUM
ejpam-6575	302	3	2	2	NUM
ejpam-6575	302	4	∣∣f(βt)−	∣∣f(βt)−	PRON
ejpam-6575	302	5	f(t	f(t	NOUN
ejpam-6575	302	6	)	)	PUNCT
ejpam-6575	303	1	∣∣	∣∣	NUM
ejpam-6575	303	2	dt	dt	X
ejpam-6575	303	3	≤	≤	NUM
ejpam-6575	303	4	∫	∫	PROPN
ejpam-6575	303	5	∞	∞	NOUN
ejpam-6575	303	6	0	0	NUM
ejpam-6575	304	1	t−	t−	PROPN
ejpam-6575	304	2	1	1	NUM
ejpam-6575	304	3	2	2	NUM
ejpam-6575	304	4	|f(βt)|	|f(βt)|	NOUN
ejpam-6575	304	5	dt+	dt+	NOUN
ejpam-6575	304	6	∫	∫	PROPN
ejpam-6575	304	7	∞	∞	NOUN
ejpam-6575	304	8	0	0	NUM
ejpam-6575	305	1	t−	t−	DET
ejpam-6575	305	2	1	1	NUM
ejpam-6575	305	3	2	2	NUM
ejpam-6575	305	4	|f(t)|	|f(t)|	ADJ
ejpam-6575	305	5	dt	dt	PROPN
ejpam-6575	305	6	.	.	PUNCT
ejpam-6575	306	1	for	for	ADP
ejpam-6575	306	2	the	the	DET
ejpam-6575	306	3	first	first	ADJ
ejpam-6575	306	4	term	term	NOUN
ejpam-6575	306	5	,	,	PUNCT
ejpam-6575	306	6	substitute	substitute	NOUN
ejpam-6575	306	7	u	u	NOUN
ejpam-6575	306	8	=	=	SYM
ejpam-6575	306	9	βt	βt	PROPN
ejpam-6575	306	10	,	,	PUNCT
ejpam-6575	306	11	du	du	PROPN
ejpam-6575	306	12	=	=	SYM
ejpam-6575	306	13	β	β	X
ejpam-6575	306	14	dt:∫	dt:∫	X
ejpam-6575	306	15	∞	∞	PROPN
ejpam-6575	306	16	0	0	NUM
ejpam-6575	307	1	t−	t−	PROPN
ejpam-6575	307	2	1	1	NUM
ejpam-6575	307	3	2	2	NUM
ejpam-6575	307	4	|f(βt)|	|f(βt)|	NOUN
ejpam-6575	307	5	dt	dt	NOUN
ejpam-6575	307	6	=	=	SYM
ejpam-6575	307	7	β−1	β−1	SYM
ejpam-6575	307	8	2	2	NUM
ejpam-6575	307	9	∫	∫	NOUN
ejpam-6575	307	10	∞	∞	PROPN
ejpam-6575	307	11	0	0	NUM
ejpam-6575	308	1	u−	u−	PROPN
ejpam-6575	308	2	1	1	NUM
ejpam-6575	308	3	2	2	NUM
ejpam-6575	308	4	|f(u)|	|f(u)|	PROPN
ejpam-6575	308	5	du	du	PROPN
ejpam-6575	308	6	.	.	PROPN
ejpam-6575	309	1	hence	hence	ADV
ejpam-6575	309	2	∫	∫	PROPN
ejpam-6575	310	1	∞	∞	PROPN
ejpam-6575	310	2	0	0	NUM
ejpam-6575	311	1	t−	t−	PROPN
ejpam-6575	311	2	1	1	NUM
ejpam-6575	311	3	2	2	NUM
ejpam-6575	311	4	(	(	PUNCT
ejpam-6575	311	5	|f(βt)|+	|f(βt)|+	PROPN
ejpam-6575	311	6	|f(t)|	|f(t)|	ADJ
ejpam-6575	311	7	)	)	PUNCT
ejpam-6575	311	8	dt	dt	NOUN
ejpam-6575	311	9	=	=	PUNCT
ejpam-6575	312	1	(	(	PUNCT
ejpam-6575	312	2	1	1	NUM
ejpam-6575	312	3	+	+	CCONJ
ejpam-6575	312	4	β−1	β−1	SYM
ejpam-6575	312	5	2	2	X
ejpam-6575	312	6	)	)	PUNCT
ejpam-6575	312	7	∫	∫	PROPN
ejpam-6575	313	1	∞	∞	PROPN
ejpam-6575	313	2	0	0	NUM
ejpam-6575	314	1	t−	t−	DET
ejpam-6575	314	2	1	1	NUM
ejpam-6575	314	3	2	2	NUM
ejpam-6575	314	4	|f(t)|	|f(t)|	ADJ
ejpam-6575	314	5	dt	dt	PROPN
ejpam-6575	314	6	,	,	PUNCT
ejpam-6575	314	7	which	which	PRON
ejpam-6575	314	8	is	be	AUX
ejpam-6575	314	9	finite	finite	VERB
ejpam-6575	314	10	by	by	ADP
ejpam-6575	314	11	hypothesis	hypothesis	NOUN
ejpam-6575	314	12	.	.	PUNCT
ejpam-6575	315	1	therefore	therefore	ADV
ejpam-6575	315	2	i(β	i(β	PROPN
ejpam-6575	315	3	)	)	PUNCT
ejpam-6575	315	4	converges	converge	VERB
ejpam-6575	315	5	absolutely	absolutely	ADV
ejpam-6575	315	6	.	.	PUNCT
ejpam-6575	316	1	theorem	theorem	ADJ
ejpam-6575	316	2	4	4	NUM
ejpam-6575	316	3	.	.	PUNCT
ejpam-6575	317	1	let	let	VERB
ejpam-6575	317	2	f	f	PROPN
ejpam-6575	317	3	:	:	PUNCT
ejpam-6575	317	4	(	(	PUNCT
ejpam-6575	317	5	0,∞	0,∞	NOUN
ejpam-6575	317	6	)	)	PUNCT
ejpam-6575	318	1	→	→	PUNCT
ejpam-6575	318	2	r	r	NOUN
ejpam-6575	318	3	be	be	AUX
ejpam-6575	318	4	measurable	measurable	ADJ
ejpam-6575	318	5	and	and	CCONJ
ejpam-6575	318	6	suppose	suppose	VERB
ejpam-6575	318	7	its	its	PRON
ejpam-6575	318	8	mellin	mellin	NOUN
ejpam-6575	318	9	transform	transform	NOUN
ejpam-6575	318	10	mf	mf	X
ejpam-6575	318	11	(	(	PUNCT
ejpam-6575	318	12	s	s	X
ejpam-6575	318	13	)	)	PUNCT
ejpam-6575	318	14	=	=	SYM
ejpam-6575	319	1	∫	∫	PROPN
ejpam-6575	319	2	∞	∞	NUM
ejpam-6575	319	3	0	0	NUM
ejpam-6575	319	4	ts−1f(t	ts−1f(t	NOUN
ejpam-6575	319	5	)	)	PUNCT
ejpam-6575	319	6	dt	dt	PUNCT
ejpam-6575	319	7	converges	converge	VERB
ejpam-6575	319	8	at	at	ADP
ejpam-6575	319	9	s	s	NOUN
ejpam-6575	319	10	=	=	SYM
ejpam-6575	319	11	1	1	NUM
ejpam-6575	319	12	2	2	NUM
ejpam-6575	319	13	,	,	PUNCT
ejpam-6575	319	14	i.e.	i.e.	X
ejpam-6575	319	15	∫	∫	PROPN
ejpam-6575	319	16	∞	∞	PROPN
ejpam-6575	319	17	0	0	NUM
ejpam-6575	320	1	t−1/2	t−1/2	PROPN
ejpam-6575	320	2	∣∣f(t)∣∣	∣∣f(t)∣∣	PUNCT
ejpam-6575	320	3	dt	dt	X
ejpam-6575	320	4	<	<	X
ejpam-6575	320	5	∞.	∞.	PROPN
ejpam-6575	320	6	then	then	ADV
ejpam-6575	320	7	we	we	PRON
ejpam-6575	320	8	have	have	VERB
ejpam-6575	320	9	,	,	PUNCT
ejpam-6575	320	10	i(β	i(β	PROPN
ejpam-6575	320	11	)	)	PUNCT
ejpam-6575	321	1	=	=	SYM
ejpam-6575	322	1	∫	∫	PROPN
ejpam-6575	323	1	∞	∞	NUM
ejpam-6575	323	2	0	0	NUM
ejpam-6575	323	3	1	1	NUM
ejpam-6575	323	4	x	x	SYM
ejpam-6575	323	5	√	√	NUM
ejpam-6575	323	6	x	x	X
ejpam-6575	323	7	[	[	PUNCT
ejpam-6575	323	8	f	f	X
ejpam-6575	323	9	(	(	PUNCT
ejpam-6575	323	10	2β	2β	NOUN
ejpam-6575	323	11	x	x	SYM
ejpam-6575	323	12	)	)	PUNCT
ejpam-6575	324	1	−	−	PROPN
ejpam-6575	324	2	f	f	PROPN
ejpam-6575	324	3	(	(	PUNCT
ejpam-6575	324	4	2	2	NUM
ejpam-6575	324	5	x	x	NOUN
ejpam-6575	324	6	)	)	PUNCT
ejpam-6575	324	7	]	]	PUNCT
ejpam-6575	324	8	dx	dx	PROPN
ejpam-6575	325	1	=	=	SYM
ejpam-6575	325	2	1√	1√	PROPN
ejpam-6575	325	3	2	2	NUM
ejpam-6575	325	4	(	(	PUNCT
ejpam-6575	325	5	β−1/2	β−1/2	NOUN
ejpam-6575	325	6	−	−	NOUN
ejpam-6575	325	7	1	1	X
ejpam-6575	325	8	)	)	PUNCT
ejpam-6575	325	9	mf	mf	X
ejpam-6575	325	10	(	(	PUNCT
ejpam-6575	325	11	1	1	NUM
ejpam-6575	325	12	2	2	NUM
ejpam-6575	325	13	)	)	PUNCT
ejpam-6575	325	14	.	.	PUNCT
ejpam-6575	326	1	proof	proof	NOUN
ejpam-6575	326	2	.	.	PUNCT
ejpam-6575	327	1	starting	start	VERB
ejpam-6575	327	2	from	from	ADP
ejpam-6575	327	3	the	the	DET
ejpam-6575	327	4	following	follow	VERB
ejpam-6575	327	5	convergent	convergent	ADJ
ejpam-6575	327	6	integral	integral	ADJ
ejpam-6575	327	7	(	(	PUNCT
ejpam-6575	327	8	proposition	proposition	NOUN
ejpam-6575	327	9	4	4	NUM
ejpam-6575	327	10	ensures	ensure	VERB
ejpam-6575	327	11	convergence	convergence	NOUN
ejpam-6575	327	12	)	)	PUNCT
ejpam-6575	327	13	,	,	PUNCT
ejpam-6575	327	14	i(β	i(β	NOUN
ejpam-6575	327	15	)	)	PUNCT
ejpam-6575	327	16	=	=	SYM
ejpam-6575	328	1	∫	∫	PROPN
ejpam-6575	329	1	∞	∞	NUM
ejpam-6575	329	2	0	0	NUM
ejpam-6575	329	3	1	1	NUM
ejpam-6575	329	4	x	x	SYM
ejpam-6575	329	5	√	√	NUM
ejpam-6575	329	6	x	x	SYM
ejpam-6575	329	7	[	[	PUNCT
ejpam-6575	329	8	f(2β	f(2β	PROPN
ejpam-6575	329	9	/	/	SYM
ejpam-6575	329	10	x)−	x)−	PROPN
ejpam-6575	329	11	f(2	f(2	PROPN
ejpam-6575	329	12	/	/	SYM
ejpam-6575	329	13	x	x	NOUN
ejpam-6575	329	14	)	)	PUNCT
ejpam-6575	329	15	]	]	PUNCT
ejpam-6575	329	16	dx	dx	PROPN
ejpam-6575	329	17	,	,	PUNCT
ejpam-6575	329	18	i.	i.	PROPN
ejpam-6575	329	19	ayoob	ayoob	PROPN
ejpam-6575	329	20	/	/	SYM
ejpam-6575	329	21	eur	eur	PROPN
ejpam-6575	329	22	.	.	PUNCT
ejpam-6575	330	1	j.	j.	PROPN
ejpam-6575	330	2	pure	pure	PROPN
ejpam-6575	330	3	appl	appl	PROPN
ejpam-6575	330	4	.	.	PROPN
ejpam-6575	330	5	math	math	PROPN
ejpam-6575	330	6	,	,	PUNCT
ejpam-6575	330	7	18	18	NUM
ejpam-6575	330	8	(	(	PUNCT
ejpam-6575	330	9	3	3	NUM
ejpam-6575	330	10	)	)	PUNCT
ejpam-6575	330	11	(	(	PUNCT
ejpam-6575	330	12	2025	2025	NUM
ejpam-6575	330	13	)	)	PUNCT
ejpam-6575	330	14	,	,	PUNCT
ejpam-6575	330	15	6575	6575	NUM
ejpam-6575	330	16	11	11	NUM
ejpam-6575	330	17	of	of	ADP
ejpam-6575	330	18	12	12	NUM
ejpam-6575	330	19	we	we	PRON
ejpam-6575	330	20	perform	perform	VERB
ejpam-6575	330	21	the	the	DET
ejpam-6575	330	22	change	change	NOUN
ejpam-6575	330	23	of	of	ADP
ejpam-6575	330	24	variable	variable	ADJ
ejpam-6575	330	25	t	t	NOUN
ejpam-6575	330	26	=	=	SYM
ejpam-6575	330	27	2	2	NUM
ejpam-6575	330	28	/	/	SYM
ejpam-6575	330	29	x	x	NOUN
ejpam-6575	330	30	,	,	PUNCT
ejpam-6575	331	1	so	so	SCONJ
ejpam-6575	331	2	that	that	SCONJ
ejpam-6575	331	3	x	x	X
ejpam-6575	331	4	=	=	SYM
ejpam-6575	331	5	2	2	NUM
ejpam-6575	331	6	/	/	SYM
ejpam-6575	331	7	t	t	PROPN
ejpam-6575	331	8	and	and	CCONJ
ejpam-6575	331	9	dx	dx	PROPN
ejpam-6575	331	10	=	=	SYM
ejpam-6575	331	11	−2	−2	NOUN
ejpam-6575	331	12	t−2dt	t−2dt	ADJ
ejpam-6575	331	13	.	.	PUNCT
ejpam-6575	332	1	as	as	ADP
ejpam-6575	332	2	in	in	ADP
ejpam-6575	332	3	the	the	DET
ejpam-6575	332	4	proof	proof	NOUN
ejpam-6575	332	5	of	of	ADP
ejpam-6575	332	6	proposition	proposition	NOUN
ejpam-6575	332	7	4	4	NUM
ejpam-6575	332	8	,	,	PUNCT
ejpam-6575	332	9	dx	dx	PROPN
ejpam-6575	332	10	x	x	SYM
ejpam-6575	332	11	√	√	PUNCT
ejpam-6575	332	12	x	x	X
ejpam-6575	332	13	=	=	SYM
ejpam-6575	332	14	−2−	−2−	NUM
ejpam-6575	332	15	1	1	NUM
ejpam-6575	332	16	2	2	NUM
ejpam-6575	332	17	t−	t−	PROPN
ejpam-6575	332	18	1	1	NUM
ejpam-6575	332	19	2	2	NUM
ejpam-6575	332	20	dt	dt	NOUN
ejpam-6575	332	21	,	,	PUNCT
ejpam-6575	332	22	2β	2β	NOUN
ejpam-6575	332	23	x	x	NOUN
ejpam-6575	332	24	=	=	SYM
ejpam-6575	332	25	βt	βt	PROPN
ejpam-6575	332	26	,	,	PUNCT
ejpam-6575	332	27	2	2	NUM
ejpam-6575	332	28	x	x	X
ejpam-6575	332	29	=	=	PUNCT
ejpam-6575	332	30	t.	t.	NOUN
ejpam-6575	332	31	hence	hence	ADV
ejpam-6575	332	32	i(β	i(β	PROPN
ejpam-6575	332	33	)	)	PUNCT
ejpam-6575	333	1	=	=	SYM
ejpam-6575	333	2	∫	∫	PROPN
ejpam-6575	333	3	0	0	NUM
ejpam-6575	334	1	∞	∞	PROPN
ejpam-6575	334	2	[	[	PUNCT
ejpam-6575	334	3	f(βt)−	f(βt)−	NOUN
ejpam-6575	334	4	f(t	f(t	PROPN
ejpam-6575	334	5	)	)	PUNCT
ejpam-6575	334	6	]	]	PUNCT
ejpam-6575	335	1	(	(	PUNCT
ejpam-6575	335	2	−2−	−2−	NOUN
ejpam-6575	335	3	1	1	NUM
ejpam-6575	335	4	2	2	NUM
ejpam-6575	335	5	t−	t−	PROPN
ejpam-6575	335	6	1	1	NUM
ejpam-6575	335	7	2	2	NUM
ejpam-6575	335	8	)	)	PUNCT
ejpam-6575	335	9	dt	dt	NOUN
ejpam-6575	336	1	=	=	SYM
ejpam-6575	336	2	2−	2−	NUM
ejpam-6575	336	3	1	1	NUM
ejpam-6575	336	4	2	2	NUM
ejpam-6575	336	5	∫	∫	NOUN
ejpam-6575	336	6	∞	∞	NOUN
ejpam-6575	336	7	0	0	NUM
ejpam-6575	337	1	t−	t−	PROPN
ejpam-6575	337	2	1	1	NUM
ejpam-6575	337	3	2	2	NUM
ejpam-6575	337	4	[	[	PUNCT
ejpam-6575	337	5	f(βt)−	f(βt)−	NOUN
ejpam-6575	337	6	f(t	f(t	PROPN
ejpam-6575	337	7	)	)	PUNCT
ejpam-6575	337	8	]	]	PUNCT
ejpam-6575	337	9	dt	dt	X
ejpam-6575	337	10	=	=	SYM
ejpam-6575	337	11	2−	2−	NUM
ejpam-6575	337	12	1	1	NUM
ejpam-6575	337	13	2	2	NUM
ejpam-6575	338	1	[	[	X
ejpam-6575	338	2	∫	∫	X
ejpam-6575	338	3	∞	∞	NUM
ejpam-6575	338	4	0	0	NUM
ejpam-6575	339	1	t−	t−	PROPN
ejpam-6575	339	2	1	1	NUM
ejpam-6575	339	3	2	2	NUM
ejpam-6575	339	4	f(βt	f(βt	NOUN
ejpam-6575	339	5	)	)	PUNCT
ejpam-6575	340	1	dt−	dt−	CCONJ
ejpam-6575	340	2	∫	∫	PROPN
ejpam-6575	340	3	∞	∞	PROPN
ejpam-6575	340	4	0	0	NUM
ejpam-6575	341	1	t−	t−	PROPN
ejpam-6575	341	2	1	1	NUM
ejpam-6575	341	3	2	2	NUM
ejpam-6575	341	4	f(t	f(t	NOUN
ejpam-6575	341	5	)	)	PUNCT
ejpam-6575	341	6	dt	dt	PUNCT
ejpam-6575	341	7	]	]	PUNCT
ejpam-6575	341	8	.	.	PUNCT
ejpam-6575	342	1	in	in	ADP
ejpam-6575	342	2	the	the	DET
ejpam-6575	342	3	first	first	ADJ
ejpam-6575	342	4	integral	integral	ADJ
ejpam-6575	342	5	substitute	substitute	NOUN
ejpam-6575	342	6	u	u	NOUN
ejpam-6575	342	7	=	=	SYM
ejpam-6575	342	8	βt	βt	PROPN
ejpam-6575	342	9	,	,	PUNCT
ejpam-6575	342	10	du	du	X
ejpam-6575	342	11	=	=	SYM
ejpam-6575	342	12	β	β	X
ejpam-6575	342	13	dt	dt	PROPN
ejpam-6575	342	14	,	,	PUNCT
ejpam-6575	342	15	giving∫	giving∫	NOUN
ejpam-6575	342	16	∞	∞	PROPN
ejpam-6575	342	17	0	0	NUM
ejpam-6575	343	1	t−	t−	PROPN
ejpam-6575	343	2	1	1	NUM
ejpam-6575	343	3	2	2	NUM
ejpam-6575	343	4	f(βt	f(βt	NOUN
ejpam-6575	343	5	)	)	PUNCT
ejpam-6575	343	6	dt	dt	NOUN
ejpam-6575	343	7	=	=	SYM
ejpam-6575	344	1	β−1	β−1	SYM
ejpam-6575	344	2	2	2	NUM
ejpam-6575	344	3	∫	∫	NOUN
ejpam-6575	344	4	∞	∞	PROPN
ejpam-6575	344	5	0	0	NUM
ejpam-6575	344	6	u−	u−	PROPN
ejpam-6575	344	7	1	1	NUM
ejpam-6575	344	8	2	2	NUM
ejpam-6575	344	9	f(u	f(u	PROPN
ejpam-6575	344	10	)	)	PUNCT
ejpam-6575	344	11	du	du	NOUN
ejpam-6575	344	12	=	=	SYM
ejpam-6575	344	13	β−1	β−1	SYM
ejpam-6575	344	14	2	2	NUM
ejpam-6575	344	15	mf	mf	X
ejpam-6575	344	16	(	(	PUNCT
ejpam-6575	344	17	1	1	NUM
ejpam-6575	344	18	2	2	NUM
ejpam-6575	344	19	)	)	PUNCT
ejpam-6575	344	20	.	.	PUNCT
ejpam-6575	345	1	the	the	DET
ejpam-6575	345	2	second	second	ADJ
ejpam-6575	345	3	integral	integral	NOUN
ejpam-6575	345	4	is	be	AUX
ejpam-6575	345	5	exactly	exactly	ADV
ejpam-6575	345	6	mf	mf	X
ejpam-6575	345	7	(	(	PUNCT
ejpam-6575	345	8	1	1	NUM
ejpam-6575	345	9	2	2	NUM
ejpam-6575	345	10	)	)	PUNCT
ejpam-6575	345	11	.	.	PUNCT
ejpam-6575	346	1	therefore	therefore	ADV
ejpam-6575	346	2	i(β	i(β	ADV
ejpam-6575	346	3	)	)	PUNCT
ejpam-6575	346	4	=	=	PUNCT
ejpam-6575	347	1	2−	2−	NUM
ejpam-6575	347	2	1	1	NUM
ejpam-6575	347	3	2	2	NUM
ejpam-6575	347	4	[	[	PUNCT
ejpam-6575	347	5	β−1	β−1	NUM
ejpam-6575	347	6	2mf	2mf	NOUN
ejpam-6575	347	7	(	(	PUNCT
ejpam-6575	347	8	1	1	NUM
ejpam-6575	347	9	2	2	NUM
ejpam-6575	347	10	)	)	PUNCT
ejpam-6575	347	11	−	−	NOUN
ejpam-6575	348	1	mf	mf	NOUN
ejpam-6575	348	2	(	(	PUNCT
ejpam-6575	348	3	1	1	NUM
ejpam-6575	348	4	2	2	NUM
ejpam-6575	348	5	)	)	PUNCT
ejpam-6575	348	6	]	]	PUNCT
ejpam-6575	349	1	=	=	SYM
ejpam-6575	349	2	mf	mf	X
ejpam-6575	349	3	(	(	PUNCT
ejpam-6575	349	4	1	1	NUM
ejpam-6575	349	5	2)√	2)√	NUM
ejpam-6575	349	6	2	2	NUM
ejpam-6575	349	7	(	(	PUNCT
ejpam-6575	349	8	β−1	β−1	ADP
ejpam-6575	349	9	2	2	NUM
ejpam-6575	349	10	−	−	NOUN
ejpam-6575	349	11	1	1	NUM
ejpam-6575	349	12	)	)	PUNCT
ejpam-6575	349	13	,	,	PUNCT
ejpam-6575	349	14	as	as	SCONJ
ejpam-6575	349	15	claimed	claim	VERB
ejpam-6575	349	16	.	.	PUNCT
ejpam-6575	350	1	2	2	X
ejpam-6575	350	2	.	.	X
ejpam-6575	350	3	conclusion	conclusion	NOUN
ejpam-6575	350	4	in	in	ADP
ejpam-6575	350	5	this	this	DET
ejpam-6575	350	6	work	work	NOUN
ejpam-6575	350	7	,	,	PUNCT
ejpam-6575	350	8	we	we	PRON
ejpam-6575	350	9	have	have	AUX
ejpam-6575	350	10	evaluated	evaluate	VERB
ejpam-6575	350	11	three	three	NUM
ejpam-6575	350	12	classes	class	NOUN
ejpam-6575	350	13	of	of	ADP
ejpam-6575	350	14	definite	definite	ADJ
ejpam-6575	350	15	integrals	integral	NOUN
ejpam-6575	350	16	that	that	PRON
ejpam-6575	350	17	were	be	AUX
ejpam-6575	350	18	originally	originally	ADV
ejpam-6575	350	19	posed	pose	VERB
ejpam-6575	350	20	as	as	ADP
ejpam-6575	350	21	open	open	ADJ
ejpam-6575	350	22	problems	problem	NOUN
ejpam-6575	350	23	in	in	ADP
ejpam-6575	350	24	the	the	DET
ejpam-6575	350	25	literature	literature	NOUN
ejpam-6575	350	26	.	.	PUNCT
ejpam-6575	351	1	our	our	PRON
ejpam-6575	351	2	approach	approach	NOUN
ejpam-6575	351	3	involved	involve	VERB
ejpam-6575	351	4	rigorously	rigorously	ADV
ejpam-6575	351	5	establishing	establish	VERB
ejpam-6575	351	6	sufficient	sufficient	ADJ
ejpam-6575	351	7	conditions	condition	NOUN
ejpam-6575	351	8	under	under	ADP
ejpam-6575	351	9	which	which	PRON
ejpam-6575	351	10	these	these	DET
ejpam-6575	351	11	integrals	integral	NOUN
ejpam-6575	351	12	converge	converge	VERB
ejpam-6575	351	13	,	,	PUNCT
ejpam-6575	351	14	followed	follow	VERB
ejpam-6575	351	15	by	by	ADP
ejpam-6575	351	16	the	the	DET
ejpam-6575	351	17	derivation	derivation	NOUN
ejpam-6575	351	18	of	of	ADP
ejpam-6575	351	19	explicit	explicit	ADJ
ejpam-6575	351	20	closed	closed	ADJ
ejpam-6575	351	21	-	-	PUNCT
ejpam-6575	351	22	form	form	NOUN
ejpam-6575	351	23	expressions	expression	NOUN
ejpam-6575	351	24	.	.	PUNCT
ejpam-6575	352	1	these	these	DET
ejpam-6575	352	2	results	result	NOUN
ejpam-6575	352	3	are	be	AUX
ejpam-6575	352	4	presented	present	VERB
ejpam-6575	352	5	in	in	ADP
ejpam-6575	352	6	theorems	theorem	NOUN
ejpam-6575	352	7	1	1	NUM
ejpam-6575	352	8	,	,	PUNCT
ejpam-6575	352	9	2	2	NUM
ejpam-6575	352	10	,	,	PUNCT
ejpam-6575	352	11	3	3	NUM
ejpam-6575	352	12	and	and	CCONJ
ejpam-6575	352	13	4	4	NUM
ejpam-6575	352	14	of	of	ADP
ejpam-6575	352	15	the	the	DET
ejpam-6575	352	16	paper	paper	NOUN
ejpam-6575	352	17	.	.	PUNCT
ejpam-6575	353	1	beyond	beyond	ADP
ejpam-6575	353	2	their	their	PRON
ejpam-6575	353	3	intrinsic	intrinsic	ADJ
ejpam-6575	353	4	analytical	analytical	ADJ
ejpam-6575	353	5	interest	interest	NOUN
ejpam-6575	353	6	,	,	PUNCT
ejpam-6575	353	7	these	these	DET
ejpam-6575	353	8	integrals	integral	NOUN
ejpam-6575	353	9	serve	serve	VERB
ejpam-6575	353	10	as	as	ADP
ejpam-6575	353	11	foundational	foundational	ADJ
ejpam-6575	353	12	kernels	kernel	NOUN
ejpam-6575	353	13	in	in	ADP
ejpam-6575	353	14	constructing	construct	VERB
ejpam-6575	353	15	a	a	DET
ejpam-6575	353	16	new	new	ADJ
ejpam-6575	353	17	class	class	NOUN
ejpam-6575	353	18	of	of	ADP
ejpam-6575	353	19	generalized	generalized	ADJ
ejpam-6575	353	20	logarithmic	logarithmic	ADJ
ejpam-6575	353	21	hardy	hardy	ADJ
ejpam-6575	353	22	–	–	PUNCT
ejpam-6575	353	23	hilbert	hilbert	NOUN
ejpam-6575	353	24	-	-	PUNCT
ejpam-6575	353	25	type	type	NOUN
ejpam-6575	353	26	inequalities	inequality	NOUN
ejpam-6575	353	27	,	,	PUNCT
ejpam-6575	353	28	extending	extend	VERB
ejpam-6575	353	29	those	those	PRON
ejpam-6575	353	30	previously	previously	ADV
ejpam-6575	353	31	established	establish	VERB
ejpam-6575	353	32	in	in	ADP
ejpam-6575	353	33	[	[	X
ejpam-6575	353	34	8	8	NUM
ejpam-6575	353	35	]	]	PUNCT
ejpam-6575	353	36	.	.	PUNCT
ejpam-6575	354	1	the	the	DET
ejpam-6575	354	2	identification	identification	NOUN
ejpam-6575	354	3	of	of	ADP
ejpam-6575	354	4	optimal	optimal	ADJ
ejpam-6575	354	5	constants	constant	NOUN
ejpam-6575	354	6	,	,	PUNCT
ejpam-6575	354	7	further	further	ADJ
ejpam-6575	354	8	generalization	generalization	NOUN
ejpam-6575	354	9	to	to	ADP
ejpam-6575	354	10	multidimensional	multidimensional	ADJ
ejpam-6575	354	11	or	or	CCONJ
ejpam-6575	354	12	operator	operator	NOUN
ejpam-6575	354	13	-	-	PUNCT
ejpam-6575	354	14	theoretic	theoretic	NOUN
ejpam-6575	354	15	settings	setting	NOUN
ejpam-6575	354	16	,	,	PUNCT
ejpam-6575	354	17	and	and	CCONJ
ejpam-6575	354	18	exploration	exploration	NOUN
ejpam-6575	354	19	of	of	ADP
ejpam-6575	354	20	applications	application	NOUN
ejpam-6575	354	21	in	in	ADP
ejpam-6575	354	22	functional	functional	ADJ
ejpam-6575	354	23	inequalities	inequality	NOUN
ejpam-6575	354	24	represent	represent	VERB
ejpam-6575	354	25	promising	promising	ADJ
ejpam-6575	354	26	directions	direction	NOUN
ejpam-6575	354	27	for	for	ADP
ejpam-6575	354	28	future	future	ADJ
ejpam-6575	354	29	research	research	NOUN
ejpam-6575	354	30	.	.	PUNCT
ejpam-6575	355	1	acknowledgements	acknowledgement	NOUN
ejpam-6575	355	2	the	the	DET
ejpam-6575	355	3	author	author	NOUN
ejpam-6575	355	4	would	would	AUX
ejpam-6575	355	5	like	like	VERB
ejpam-6575	355	6	to	to	PART
ejpam-6575	355	7	thank	thank	VERB
ejpam-6575	355	8	the	the	DET
ejpam-6575	355	9	prince	prince	PROPN
ejpam-6575	355	10	sultan	sultan	PROPN
ejpam-6575	355	11	university	university	PROPN
ejpam-6575	355	12	for	for	ADP
ejpam-6575	355	13	paying	pay	VERB
ejpam-6575	355	14	the	the	DET
ejpam-6575	355	15	publication	publication	NOUN
ejpam-6575	355	16	fees	fee	NOUN
ejpam-6575	355	17	for	for	ADP
ejpam-6575	355	18	this	this	DET
ejpam-6575	355	19	work	work	NOUN
ejpam-6575	355	20	through	through	ADP
ejpam-6575	355	21	tas	ta	NOUN
ejpam-6575	355	22	lab	lab	PROPN
ejpam-6575	355	23	.	.	PUNCT
ejpam-6575	356	1	i.	i.	PROPN
ejpam-6575	356	2	ayoob	ayoob	PROPN
ejpam-6575	356	3	/	/	SYM
ejpam-6575	356	4	eur	eur	PROPN
ejpam-6575	356	5	.	.	PUNCT
ejpam-6575	357	1	j.	j.	PROPN
ejpam-6575	357	2	pure	pure	PROPN
ejpam-6575	357	3	appl	appl	PROPN
ejpam-6575	357	4	.	.	PROPN
ejpam-6575	357	5	math	math	PROPN
ejpam-6575	357	6	,	,	PUNCT
ejpam-6575	357	7	18	18	NUM
ejpam-6575	357	8	(	(	PUNCT
ejpam-6575	357	9	3	3	NUM
ejpam-6575	357	10	)	)	PUNCT
ejpam-6575	357	11	(	(	PUNCT
ejpam-6575	357	12	2025	2025	NUM
ejpam-6575	357	13	)	)	PUNCT
ejpam-6575	357	14	,	,	PUNCT
ejpam-6575	357	15	6575	6575	NUM
ejpam-6575	357	16	12	12	NUM
ejpam-6575	357	17	of	of	ADP
ejpam-6575	357	18	12	12	NUM
ejpam-6575	357	19	references	reference	NOUN
ejpam-6575	357	20	[	[	X
ejpam-6575	357	21	1	1	NUM
ejpam-6575	357	22	]	]	PUNCT
ejpam-6575	357	23	s.	s.	PROPN
ejpam-6575	357	24	gradshteyn	gradshteyn	PROPN
ejpam-6575	357	25	,	,	PUNCT
ejpam-6575	357	26	i.	i.	NOUN
ejpam-6575	357	27	and	and	CCONJ
ejpam-6575	357	28	m.	m.	NOUN
ejpam-6575	357	29	ryzhik	ryzhik	PROPN
ejpam-6575	357	30	,	,	PUNCT
ejpam-6575	357	31	i.˙table	i.˙table	PROPN
ejpam-6575	357	32	of	of	ADP
ejpam-6575	357	33	integrals	integral	NOUN
ejpam-6575	357	34	,	,	PUNCT
ejpam-6575	357	35	series	series	NOUN
ejpam-6575	357	36	,	,	PUNCT
ejpam-6575	357	37	and	and	CCONJ
ejpam-6575	357	38	products	product	NOUN
ejpam-6575	357	39	.	.	PUNCT
ejpam-6575	358	1	academic	academic	ADJ
ejpam-6575	358	2	press	press	NOUN
ejpam-6575	358	3	,	,	PUNCT
ejpam-6575	358	4	new	new	PROPN
ejpam-6575	358	5	york	york	PROPN
ejpam-6575	358	6	,	,	PUNCT
ejpam-6575	358	7	7th	7th	ADJ
ejpam-6575	358	8	edition	edition	NOUN
ejpam-6575	358	9	,	,	PUNCT
ejpam-6575	358	10	2007	2007	NUM
ejpam-6575	358	11	.	.	PUNCT
ejpam-6575	359	1	[	[	X
ejpam-6575	359	2	2	2	X
ejpam-6575	359	3	]	]	PUNCT
ejpam-6575	359	4	christophe	christophe	PROPN
ejpam-6575	359	5	chesneau	chesneau	PROPN
ejpam-6575	359	6	.	.	PUNCT
ejpam-6575	360	1	on	on	ADP
ejpam-6575	360	2	a	a	DET
ejpam-6575	360	3	new	new	ADJ
ejpam-6575	360	4	one	one	NUM
ejpam-6575	360	5	-	-	PUNCT
ejpam-6575	360	6	parameter	parameter	NOUN
ejpam-6575	360	7	arctangent	arctangent	NOUN
ejpam-6575	360	8	-	-	PUNCT
ejpam-6575	360	9	power	power	NOUN
ejpam-6575	360	10	integral	integral	ADJ
ejpam-6575	360	11	.	.	PUNCT
ejpam-6575	361	1	international	international	ADJ
ejpam-6575	361	2	journal	journal	NOUN
ejpam-6575	361	3	of	of	ADP
ejpam-6575	361	4	open	open	ADJ
ejpam-6575	361	5	problems	problem	NOUN
ejpam-6575	361	6	in	in	ADP
ejpam-6575	361	7	computer	computer	NOUN
ejpam-6575	361	8	science	science	NOUN
ejpam-6575	361	9	and	and	CCONJ
ejpam-6575	361	10	mathematics	mathematic	NOUN
ejpam-6575	361	11	,	,	PUNCT
ejpam-6575	361	12	17(4):1–8	17(4):1–8	NOUN
ejpam-6575	361	13	,	,	PUNCT
ejpam-6575	361	14	2024	2024	NUM
ejpam-6575	361	15	.	.	PUNCT
ejpam-6575	362	1	[	[	X
ejpam-6575	362	2	3	3	X
ejpam-6575	362	3	]	]	X
ejpam-6575	362	4	christophe	christophe	PROPN
ejpam-6575	362	5	chesneau	chesneau	PROPN
ejpam-6575	362	6	.	.	PUNCT
ejpam-6575	363	1	new	new	ADJ
ejpam-6575	363	2	integral	integral	ADJ
ejpam-6575	363	3	formulas	formula	NOUN
ejpam-6575	363	4	inspired	inspire	VERB
ejpam-6575	363	5	by	by	ADP
ejpam-6575	363	6	an	an	DET
ejpam-6575	363	7	old	old	ADJ
ejpam-6575	363	8	integral	integral	ADJ
ejpam-6575	363	9	result	result	NOUN
ejpam-6575	363	10	.	.	PUNCT
ejpam-6575	364	1	international	international	ADJ
ejpam-6575	364	2	journal	journal	NOUN
ejpam-6575	364	3	of	of	ADP
ejpam-6575	364	4	open	open	ADJ
ejpam-6575	364	5	problems	problem	NOUN
ejpam-6575	364	6	in	in	ADP
ejpam-6575	364	7	computer	computer	NOUN
ejpam-6575	364	8	science	science	NOUN
ejpam-6575	364	9	and	and	CCONJ
ejpam-6575	364	10	mathematics	mathematic	NOUN
ejpam-6575	364	11	,	,	PUNCT
ejpam-6575	364	12	18(2):53–71	18(2):53–71	NUM
ejpam-6575	364	13	,	,	PUNCT
ejpam-6575	364	14	2025	2025	NUM
ejpam-6575	364	15	.	.	PUNCT
ejpam-6575	365	1	[	[	X
ejpam-6575	365	2	4	4	NUM
ejpam-6575	365	3	]	]	PUNCT
ejpam-6575	365	4	r.	r.	PROPN
ejpam-6575	365	5	reynolds	reynolds	PROPN
ejpam-6575	365	6	and	and	CCONJ
ejpam-6575	365	7	a.	a.	PROPN
ejpam-6575	365	8	stauffer	stauffer	PROPN
ejpam-6575	365	9	.	.	PUNCT
ejpam-6575	366	1	a	a	DET
ejpam-6575	366	2	definite	definite	ADJ
ejpam-6575	366	3	integral	integral	ADJ
ejpam-6575	366	4	involving	involve	VERB
ejpam-6575	366	5	the	the	DET
ejpam-6575	366	6	logarithmic	logarithmic	ADJ
ejpam-6575	366	7	function	function	NOUN
ejpam-6575	366	8	in	in	ADP
ejpam-6575	366	9	terms	term	NOUN
ejpam-6575	366	10	of	of	ADP
ejpam-6575	366	11	the	the	DET
ejpam-6575	366	12	lerch	lerch	PROPN
ejpam-6575	366	13	function	function	PROPN
ejpam-6575	366	14	.	.	PUNCT
ejpam-6575	367	1	mathematics	mathematic	NOUN
ejpam-6575	367	2	,	,	PUNCT
ejpam-6575	367	3	7(1):1–5	7(1):1–5	NUM
ejpam-6575	367	4	,	,	PUNCT
ejpam-6575	367	5	2019	2019	NUM
ejpam-6575	367	6	.	.	PUNCT
ejpam-6575	368	1	[	[	X
ejpam-6575	368	2	5	5	NUM
ejpam-6575	368	3	]	]	PUNCT
ejpam-6575	368	4	r.	r.	PROPN
ejpam-6575	368	5	reynolds	reynolds	PROPN
ejpam-6575	368	6	and	and	CCONJ
ejpam-6575	368	7	a.	a.	PROPN
ejpam-6575	368	8	stauffer	stauffer	PROPN
ejpam-6575	368	9	.	.	PUNCT
ejpam-6575	369	1	definite	definite	ADJ
ejpam-6575	369	2	integral	integral	ADJ
ejpam-6575	369	3	of	of	ADP
ejpam-6575	369	4	arctangent	arctangent	NOUN
ejpam-6575	369	5	and	and	CCONJ
ejpam-6575	369	6	polylogarithmic	polylogarithmic	ADJ
ejpam-6575	369	7	functions	function	NOUN
ejpam-6575	369	8	expressed	express	VERB
ejpam-6575	369	9	as	as	ADP
ejpam-6575	369	10	a	a	DET
ejpam-6575	369	11	series	series	NOUN
ejpam-6575	369	12	.	.	PUNCT
ejpam-6575	370	1	mathematics	mathematic	NOUN
ejpam-6575	370	2	,	,	PUNCT
ejpam-6575	370	3	7(7):1–7	7(7):1–7	PROPN
ejpam-6575	370	4	,	,	PUNCT
ejpam-6575	370	5	2019	2019	NUM
ejpam-6575	370	6	.	.	PUNCT
ejpam-6575	371	1	[	[	X
ejpam-6575	371	2	6	6	NUM
ejpam-6575	371	3	]	]	PUNCT
ejpam-6575	371	4	r.	r.	PROPN
ejpam-6575	371	5	reynolds	reynolds	PROPN
ejpam-6575	371	6	and	and	CCONJ
ejpam-6575	371	7	a.	a.	PROPN
ejpam-6575	371	8	stauffer	stauffer	PROPN
ejpam-6575	371	9	.	.	PUNCT
ejpam-6575	372	1	derivation	derivation	NOUN
ejpam-6575	372	2	of	of	ADP
ejpam-6575	372	3	logarithmic	logarithmic	ADJ
ejpam-6575	372	4	and	and	CCONJ
ejpam-6575	372	5	logarithmic	logarithmic	ADJ
ejpam-6575	372	6	hyperbolic	hyperbolic	ADJ
ejpam-6575	372	7	tangent	tangent	NOUN
ejpam-6575	372	8	integrals	integral	NOUN
ejpam-6575	372	9	expressed	express	VERB
ejpam-6575	372	10	in	in	ADP
ejpam-6575	372	11	terms	term	NOUN
ejpam-6575	372	12	of	of	ADP
ejpam-6575	372	13	special	special	ADJ
ejpam-6575	372	14	functions	function	NOUN
ejpam-6575	372	15	.	.	PUNCT
ejpam-6575	373	1	mathematics	mathematic	NOUN
ejpam-6575	373	2	,	,	PUNCT
ejpam-6575	373	3	8:1–6	8:1–6	NUM
ejpam-6575	373	4	,	,	PUNCT
ejpam-6575	373	5	2020	2020	NUM
ejpam-6575	373	6	.	.	PUNCT
ejpam-6575	374	1	[	[	X
ejpam-6575	374	2	7	7	X
ejpam-6575	374	3	]	]	X
ejpam-6575	374	4	r.	r.	PROPN
ejpam-6575	374	5	reynolds	reynolds	PROPN
ejpam-6575	374	6	and	and	CCONJ
ejpam-6575	374	7	a.	a.	PROPN
ejpam-6575	374	8	stauffer	stauffer	PROPN
ejpam-6575	374	9	.	.	PUNCT
ejpam-6575	375	1	a	a	DET
ejpam-6575	375	2	quadruple	quadruple	ADJ
ejpam-6575	375	3	definite	definite	ADJ
ejpam-6575	375	4	integral	integral	NOUN
ejpam-6575	375	5	expressed	express	VERB
ejpam-6575	375	6	in	in	ADP
ejpam-6575	375	7	terms	term	NOUN
ejpam-6575	375	8	of	of	ADP
ejpam-6575	375	9	the	the	DET
ejpam-6575	375	10	lerch	lerch	PROPN
ejpam-6575	375	11	function	function	PROPN
ejpam-6575	375	12	.	.	PUNCT
ejpam-6575	376	1	symmetry	symmetry	PROPN
ejpam-6575	376	2	,	,	PUNCT
ejpam-6575	376	3	13(1):1–8	13(1):1–8	NUM
ejpam-6575	376	4	,	,	PUNCT
ejpam-6575	376	5	2021	2021	NUM
ejpam-6575	376	6	.	.	PUNCT
ejpam-6575	377	1	[	[	X
ejpam-6575	377	2	8	8	NUM
ejpam-6575	377	3	]	]	X
ejpam-6575	377	4	christophe	christophe	PROPN
ejpam-6575	377	5	chesneau	chesneau	PROPN
ejpam-6575	377	6	.	.	PUNCT
ejpam-6575	378	1	on	on	ADP
ejpam-6575	378	2	some	some	DET
ejpam-6575	378	3	new	new	ADJ
ejpam-6575	378	4	integral	integral	ADJ
ejpam-6575	378	5	formulas	formula	NOUN
ejpam-6575	378	6	with	with	ADP
ejpam-6575	378	7	applications	application	NOUN
ejpam-6575	378	8	.	.	PUNCT
ejpam-6575	379	1	international	international	ADJ
ejpam-6575	379	2	journal	journal	NOUN
ejpam-6575	379	3	of	of	ADP
ejpam-6575	379	4	open	open	ADJ
ejpam-6575	379	5	problems	problem	NOUN
ejpam-6575	379	6	in	in	ADP
ejpam-6575	379	7	computer	computer	NOUN
ejpam-6575	379	8	science	science	NOUN
ejpam-6575	379	9	and	and	CCONJ
ejpam-6575	379	10	mathematics	mathematic	NOUN
ejpam-6575	379	11	,	,	PUNCT
ejpam-6575	379	12	18(3):1–21	18(3):1–21	NUM
ejpam-6575	379	13	,	,	PUNCT
ejpam-6575	379	14	september	september	PROPN
ejpam-6575	379	15	2025	2025	NUM
ejpam-6575	379	16	.	.	PUNCT
ejpam-6575	380	1	[	[	X
ejpam-6575	380	2	9	9	NUM
ejpam-6575	380	3	]	]	X
ejpam-6575	380	4	h.	h.	NOUN
ejpam-6575	380	5	hardy	hardy	PROPN
ejpam-6575	380	6	,	,	PUNCT
ejpam-6575	380	7	g.	g.	PROPN
ejpam-6575	380	8	e.	e.	PROPN
ejpam-6575	380	9	littlewood	littlewood	PROPN
ejpam-6575	380	10	,	,	PUNCT
ejpam-6575	380	11	j.	j.	PROPN
ejpam-6575	380	12	and	and	CCONJ
ejpam-6575	380	13	g.	g.	PROPN
ejpam-6575	380	14	pólya	pólya	PROPN
ejpam-6575	380	15	.	.	PUNCT
ejpam-6575	381	1	inequalities	inequality	NOUN
ejpam-6575	381	2	.	.	PUNCT
ejpam-6575	382	1	cambridge	cambridge	PROPN
ejpam-6575	382	2	university	university	PROPN
ejpam-6575	382	3	press	press	PROPN
ejpam-6575	382	4	,	,	PUNCT
ejpam-6575	382	5	cambridge	cambridge	PROPN
ejpam-6575	382	6	,	,	PUNCT
ejpam-6575	382	7	1934	1934	NUM
ejpam-6575	382	8	.	.	PUNCT