id	sid	tid	token	lemma	pos
ejpam-4868	1	1	european	european	PROPN
ejpam-4868	1	2	journal	journal	PROPN
ejpam-4868	1	3	of	of	ADP
ejpam-4868	1	4	pure	pure	ADJ
ejpam-4868	1	5	and	and	CCONJ
ejpam-4868	1	6	applied	apply	VERB
ejpam-4868	1	7	mathematics	mathematic	NOUN
ejpam-4868	1	8	vol	vol	NOUN
ejpam-4868	1	9	.	.	PUNCT
ejpam-4868	2	1	16	16	NUM
ejpam-4868	2	2	,	,	PUNCT
ejpam-4868	2	3	no	no	INTJ
ejpam-4868	2	4	.	.	NOUN
ejpam-4868	2	5	4	4	NUM
ejpam-4868	2	6	,	,	PUNCT
ejpam-4868	2	7	2023	2023	NUM
ejpam-4868	2	8	,	,	PUNCT
ejpam-4868	2	9	2213	2213	NUM
ejpam-4868	2	10	-	-	SYM
ejpam-4868	2	11	2233	2233	NUM
ejpam-4868	2	12	issn	issn	VERB
ejpam-4868	2	13	1307	1307	NUM
ejpam-4868	2	14	-	-	SYM
ejpam-4868	2	15	5543	5543	NUM
ejpam-4868	2	16	–	–	PUNCT
ejpam-4868	3	1	ejpam.com	ejpam.com	X
ejpam-4868	3	2	published	publish	VERB
ejpam-4868	3	3	by	by	ADP
ejpam-4868	3	4	new	new	PROPN
ejpam-4868	3	5	york	york	PROPN
ejpam-4868	3	6	business	business	PROPN
ejpam-4868	3	7	global	global	ADJ
ejpam-4868	3	8	on	on	ADP
ejpam-4868	3	9	degenerate	degenerate	ADJ
ejpam-4868	3	10	laplace	laplace	NOUN
ejpam-4868	3	11	-	-	PUNCT
ejpam-4868	3	12	type	type	NOUN
ejpam-4868	3	13	integral	integral	ADJ
ejpam-4868	3	14	transform	transform	NOUN
ejpam-4868	3	15	harren	harren	PROPN
ejpam-4868	3	16	j.	j.	PROPN
ejpam-4868	3	17	campos1	campos1	PROPN
ejpam-4868	3	18	,	,	PUNCT
ejpam-4868	3	19	jezer	jezer	PROPN
ejpam-4868	3	20	c.	c.	PROPN
ejpam-4868	3	21	fernandez1,∗	fernandez1,∗	PROPN
ejpam-4868	3	22	,	,	PUNCT
ejpam-4868	3	23	jade	jade	PROPN
ejpam-4868	3	24	bong	bong	PROPN
ejpam-4868	3	25	m.	m.	PROPN
ejpam-4868	3	26	natuil1	natuil1	PROPN
ejpam-4868	3	27	1	1	NUM
ejpam-4868	3	28	department	department	NOUN
ejpam-4868	3	29	of	of	ADP
ejpam-4868	3	30	mathematics	mathematic	NOUN
ejpam-4868	3	31	,	,	PUNCT
ejpam-4868	3	32	mindanao	mindanao	PROPN
ejpam-4868	3	33	state	state	PROPN
ejpam-4868	3	34	university	university	PROPN
ejpam-4868	3	35	,	,	PUNCT
ejpam-4868	3	36	9700	9700	NUM
ejpam-4868	3	37	marawi	marawi	PROPN
ejpam-4868	3	38	city	city	PROPN
ejpam-4868	3	39	,	,	PUNCT
ejpam-4868	3	40	philippines	philippine	NOUN
ejpam-4868	3	41	abstract	abstract	ADJ
ejpam-4868	3	42	.	.	PUNCT
ejpam-4868	4	1	this	this	DET
ejpam-4868	4	2	paper	paper	NOUN
ejpam-4868	4	3	is	be	AUX
ejpam-4868	4	4	motivated	motivate	VERB
ejpam-4868	4	5	by	by	ADP
ejpam-4868	4	6	the	the	DET
ejpam-4868	4	7	work	work	NOUN
ejpam-4868	4	8	of	of	ADP
ejpam-4868	4	9	taekyun	taekyun	NOUN
ejpam-4868	4	10	kim	kim	PROPN
ejpam-4868	4	11	and	and	CCONJ
ejpam-4868	4	12	dae	dae	VERB
ejpam-4868	4	13	san	san	PROPN
ejpam-4868	4	14	kim	kim	PROPN
ejpam-4868	4	15	on	on	ADP
ejpam-4868	4	16	the	the	DET
ejpam-4868	4	17	degenerate	degenerate	ADJ
ejpam-4868	4	18	laplace	laplace	NOUN
ejpam-4868	4	19	transform	transform	NOUN
ejpam-4868	4	20	and	and	CCONJ
ejpam-4868	4	21	degenerate	degenerate	ADJ
ejpam-4868	4	22	gamma	gamma	NOUN
ejpam-4868	4	23	function	function	NOUN
ejpam-4868	4	24	,	,	PUNCT
ejpam-4868	4	25	as	as	SCONJ
ejpam-4868	4	26	published	publish	VERB
ejpam-4868	4	27	in	in	ADP
ejpam-4868	4	28	the	the	DET
ejpam-4868	4	29	russian	russian	ADJ
ejpam-4868	4	30	journal	journal	NOUN
ejpam-4868	4	31	of	of	ADP
ejpam-4868	4	32	mathematical	mathematical	ADJ
ejpam-4868	4	33	physics	physics	NOUN
ejpam-4868	4	34	.	.	PUNCT
ejpam-4868	5	1	we	we	PRON
ejpam-4868	5	2	introduce	introduce	VERB
ejpam-4868	5	3	the	the	DET
ejpam-4868	5	4	degenerate	degenerate	ADJ
ejpam-4868	5	5	laplace	laplace	NOUN
ejpam-4868	5	6	-	-	PUNCT
ejpam-4868	5	7	type	type	NOUN
ejpam-4868	5	8	integral	integral	ADJ
ejpam-4868	5	9	transform	transform	NOUN
ejpam-4868	5	10	and	and	CCONJ
ejpam-4868	5	11	delve	delve	VERB
ejpam-4868	5	12	into	into	ADP
ejpam-4868	5	13	its	its	PRON
ejpam-4868	5	14	properties	property	NOUN
ejpam-4868	5	15	and	and	CCONJ
ejpam-4868	5	16	interrelations	interrelation	NOUN
ejpam-4868	5	17	.	.	PUNCT
ejpam-4868	6	1	this	this	DET
ejpam-4868	6	2	paper	paper	NOUN
ejpam-4868	6	3	focuses	focus	VERB
ejpam-4868	6	4	on	on	ADP
ejpam-4868	6	5	the	the	DET
ejpam-4868	6	6	degenerate	degenerate	ADJ
ejpam-4868	6	7	laplace	laplace	NOUN
ejpam-4868	6	8	-	-	PUNCT
ejpam-4868	6	9	type	type	NOUN
ejpam-4868	6	10	integral	integral	ADJ
ejpam-4868	6	11	transforms	transform	NOUN
ejpam-4868	6	12	of	of	ADP
ejpam-4868	6	13	several	several	ADJ
ejpam-4868	6	14	fundamental	fundamental	ADJ
ejpam-4868	6	15	functions	function	NOUN
ejpam-4868	6	16	,	,	PUNCT
ejpam-4868	6	17	including	include	VERB
ejpam-4868	6	18	the	the	DET
ejpam-4868	6	19	degenerate	degenerate	ADJ
ejpam-4868	6	20	sine	sine	NOUN
ejpam-4868	6	21	,	,	PUNCT
ejpam-4868	6	22	degenerate	degenerate	ADJ
ejpam-4868	6	23	cosine	cosine	NOUN
ejpam-4868	6	24	,	,	PUNCT
ejpam-4868	6	25	degenerate	degenerate	ADJ
ejpam-4868	6	26	hyperbolic	hyperbolic	ADJ
ejpam-4868	6	27	sine	sine	NOUN
ejpam-4868	6	28	,	,	PUNCT
ejpam-4868	6	29	and	and	CCONJ
ejpam-4868	6	30	degenerate	degenerate	ADJ
ejpam-4868	6	31	hyperbolic	hyperbolic	ADJ
ejpam-4868	6	32	cosine	cosine	NOUN
ejpam-4868	6	33	functions	function	NOUN
ejpam-4868	6	34	.	.	PUNCT
ejpam-4868	7	1	furthermore	furthermore	ADV
ejpam-4868	7	2	,	,	PUNCT
ejpam-4868	7	3	we	we	PRON
ejpam-4868	7	4	establish	establish	VERB
ejpam-4868	7	5	crucial	crucial	ADJ
ejpam-4868	7	6	connections	connection	NOUN
ejpam-4868	7	7	between	between	ADP
ejpam-4868	7	8	the	the	DET
ejpam-4868	7	9	degenerate	degenerate	ADJ
ejpam-4868	7	10	laplace	laplace	NOUN
ejpam-4868	7	11	-	-	PUNCT
ejpam-4868	7	12	type	type	NOUN
ejpam-4868	7	13	integral	integral	ADJ
ejpam-4868	7	14	transform	transform	NOUN
ejpam-4868	7	15	and	and	CCONJ
ejpam-4868	7	16	existing	exist	VERB
ejpam-4868	7	17	degenerate	degenerate	ADJ
ejpam-4868	7	18	integral	integral	ADJ
ejpam-4868	7	19	transforms	transform	NOUN
ejpam-4868	7	20	.	.	PUNCT
ejpam-4868	8	1	specifically	specifically	ADV
ejpam-4868	8	2	,	,	PUNCT
ejpam-4868	8	3	we	we	PRON
ejpam-4868	8	4	explore	explore	VERB
ejpam-4868	8	5	its	its	PRON
ejpam-4868	8	6	relationships	relationship	NOUN
ejpam-4868	8	7	with	with	ADP
ejpam-4868	8	8	the	the	DET
ejpam-4868	8	9	degenerate	degenerate	ADJ
ejpam-4868	8	10	laplace	laplace	NOUN
ejpam-4868	8	11	transform	transform	NOUN
ejpam-4868	8	12	,	,	PUNCT
ejpam-4868	8	13	the	the	DET
ejpam-4868	8	14	degenerate	degenerate	ADJ
ejpam-4868	8	15	elzaki	elzaki	NOUN
ejpam-4868	8	16	transform	transform	NOUN
ejpam-4868	8	17	,	,	PUNCT
ejpam-4868	8	18	and	and	CCONJ
ejpam-4868	8	19	the	the	DET
ejpam-4868	8	20	degenerate	degenerate	ADJ
ejpam-4868	8	21	sumudu	sumudu	NOUN
ejpam-4868	8	22	transforms	transform	VERB
ejpam-4868	8	23	.	.	PUNCT
ejpam-4868	9	1	2020	2020	NUM
ejpam-4868	9	2	mathematics	mathematic	NOUN
ejpam-4868	9	3	subject	subject	NOUN
ejpam-4868	9	4	classifications	classification	NOUN
ejpam-4868	9	5	:	:	PUNCT
ejpam-4868	9	6	44a99	44a99	NUM
ejpam-4868	9	7	key	key	ADJ
ejpam-4868	9	8	words	word	NOUN
ejpam-4868	9	9	and	and	CCONJ
ejpam-4868	9	10	phrases	phrase	NOUN
ejpam-4868	9	11	:	:	PUNCT
ejpam-4868	9	12	degenerate	degenerate	ADJ
ejpam-4868	9	13	sumudu	sumudu	NOUN
ejpam-4868	9	14	transform	transform	NOUN
ejpam-4868	9	15	,	,	PUNCT
ejpam-4868	9	16	degenerate	degenerate	ADJ
ejpam-4868	9	17	elzaki	elzaki	NOUN
ejpam-4868	9	18	transform	transform	NOUN
ejpam-4868	9	19	,	,	PUNCT
ejpam-4868	9	20	degenerate	degenerate	ADJ
ejpam-4868	9	21	laplace	laplace	NOUN
ejpam-4868	9	22	transform	transform	NOUN
ejpam-4868	9	23	,	,	PUNCT
ejpam-4868	9	24	degenerate	degenerate	ADJ
ejpam-4868	9	25	laplace	laplace	NOUN
ejpam-4868	9	26	-	-	PUNCT
ejpam-4868	9	27	type	type	NOUN
ejpam-4868	9	28	integral	integral	ADJ
ejpam-4868	9	29	transform	transform	NOUN
ejpam-4868	9	30	1	1	NUM
ejpam-4868	9	31	.	.	PUNCT
ejpam-4868	10	1	introduction	introduction	NOUN
ejpam-4868	10	2	integral	integral	ADJ
ejpam-4868	10	3	transforms	transform	NOUN
ejpam-4868	10	4	have	have	AUX
ejpam-4868	10	5	long	long	ADV
ejpam-4868	10	6	captivated	captivate	VERB
ejpam-4868	10	7	the	the	DET
ejpam-4868	10	8	mathematical	mathematical	ADJ
ejpam-4868	10	9	world	world	NOUN
ejpam-4868	10	10	due	due	ADP
ejpam-4868	10	11	to	to	ADP
ejpam-4868	10	12	their	their	PRON
ejpam-4868	10	13	multifaceted	multifaceted	ADJ
ejpam-4868	10	14	properties	property	NOUN
ejpam-4868	10	15	and	and	CCONJ
ejpam-4868	10	16	widespread	widespread	ADJ
ejpam-4868	10	17	applications	application	NOUN
ejpam-4868	10	18	across	across	ADP
ejpam-4868	10	19	diverse	diverse	ADJ
ejpam-4868	10	20	scientific	scientific	ADJ
ejpam-4868	10	21	fields	field	NOUN
ejpam-4868	10	22	.	.	PUNCT
ejpam-4868	11	1	during	during	ADP
ejpam-4868	11	2	the	the	DET
ejpam-4868	11	3	20th	20th	ADJ
ejpam-4868	11	4	and	and	CCONJ
ejpam-4868	11	5	21st	21st	ADJ
ejpam-4868	11	6	centuries	century	NOUN
ejpam-4868	11	7	,	,	PUNCT
ejpam-4868	11	8	the	the	DET
ejpam-4868	11	9	laplace	laplace	NOUN
ejpam-4868	11	10	transform	transform	NOUN
ejpam-4868	11	11	has	have	AUX
ejpam-4868	11	12	been	be	AUX
ejpam-4868	11	13	extensively	extensively	ADV
ejpam-4868	11	14	studied	study	VERB
ejpam-4868	11	15	and	and	CCONJ
ejpam-4868	11	16	employed	employ	VERB
ejpam-4868	11	17	in	in	ADP
ejpam-4868	11	18	various	various	ADJ
ejpam-4868	11	19	scientific	scientific	ADJ
ejpam-4868	11	20	disciplines	discipline	NOUN
ejpam-4868	11	21	.	.	PUNCT
ejpam-4868	12	1	among	among	ADP
ejpam-4868	12	2	the	the	DET
ejpam-4868	12	3	noteworthy	noteworthy	ADJ
ejpam-4868	12	4	contributions	contribution	NOUN
ejpam-4868	12	5	in	in	ADP
ejpam-4868	12	6	this	this	DET
ejpam-4868	12	7	domain	domain	NOUN
ejpam-4868	12	8	is	be	AUX
ejpam-4868	12	9	the	the	DET
ejpam-4868	12	10	investigation	investigation	NOUN
ejpam-4868	12	11	of	of	ADP
ejpam-4868	12	12	work	work	NOUN
ejpam-4868	12	13	the	the	DET
ejpam-4868	12	14	intrinsic	intrinsic	ADJ
ejpam-4868	12	15	structure	structure	NOUN
ejpam-4868	12	16	and	and	CCONJ
ejpam-4868	12	17	properties	property	NOUN
ejpam-4868	12	18	of	of	ADP
ejpam-4868	12	19	laplace	laplace	NOUN
ejpam-4868	12	20	-	-	PUNCT
ejpam-4868	12	21	typed	type	VERB
ejpam-4868	12	22	integral	integral	ADJ
ejpam-4868	12	23	transforms	transform	NOUN
ejpam-4868	12	24	by	by	ADP
ejpam-4868	12	25	h.	h.	PROPN
ejpam-4868	12	26	kim	kim	PROPN
ejpam-4868	13	1	[	[	X
ejpam-4868	13	2	7	7	X
ejpam-4868	13	3	]	]	PUNCT
ejpam-4868	13	4	and	and	CCONJ
ejpam-4868	13	5	some	some	DET
ejpam-4868	13	6	additional	additional	ADJ
ejpam-4868	13	7	properties	property	NOUN
ejpam-4868	13	8	of	of	ADP
ejpam-4868	13	9	laplace	laplace	NOUN
ejpam-4868	13	10	-	-	PUNCT
ejpam-4868	13	11	type	type	NOUN
ejpam-4868	13	12	integral	integral	ADJ
ejpam-4868	13	13	transforms	transform	NOUN
ejpam-4868	13	14	by	by	ADP
ejpam-4868	13	15	h.	h.	PROPN
ejpam-4868	13	16	kim	kim	PROPN
ejpam-4868	13	17	et.al[5	et.al[5	PROPN
ejpam-4868	13	18	]	]	PUNCT
ejpam-4868	13	19	.	.	PUNCT
ejpam-4868	14	1	this	this	DET
ejpam-4868	14	2	integral	integral	ADJ
ejpam-4868	14	3	transform	transform	NOUN
ejpam-4868	14	4	is	be	AUX
ejpam-4868	14	5	defined	define	VERB
ejpam-4868	14	6	as	as	ADP
ejpam-4868	14	7	fα(u	fα(u	NOUN
ejpam-4868	14	8	)	)	PUNCT
ejpam-4868	14	9	=	=	PUNCT
ejpam-4868	15	1	gα{f(t	gα{f(t	NOUN
ejpam-4868	15	2	)	)	PUNCT
ejpam-4868	15	3	}	}	PUNCT
ejpam-4868	15	4	=	=	PUNCT
ejpam-4868	16	1	uα	uα	PROPN
ejpam-4868	16	2	∫	∫	PROPN
ejpam-4868	16	3	∞	∞	PROPN
ejpam-4868	16	4	0	0	PUNCT
ejpam-4868	17	1	e	e	PROPN
ejpam-4868	17	2	−t	−t	NOUN
ejpam-4868	17	3	u	u	NOUN
ejpam-4868	17	4	f(t)dt	f(t)dt	PROPN
ejpam-4868	17	5	,	,	PUNCT
ejpam-4868	17	6	where	where	SCONJ
ejpam-4868	17	7	α	α	PROPN
ejpam-4868	17	8	∈	∈	PROPN
ejpam-4868	17	9	z.	z.	PROPN
ejpam-4868	18	1	in	in	ADP
ejpam-4868	18	2	recent	recent	ADJ
ejpam-4868	18	3	years	year	NOUN
ejpam-4868	18	4	,	,	PUNCT
ejpam-4868	18	5	there	there	PRON
ejpam-4868	18	6	has	have	AUX
ejpam-4868	18	7	been	be	AUX
ejpam-4868	18	8	growing	grow	VERB
ejpam-4868	18	9	interest	interest	NOUN
ejpam-4868	18	10	in	in	ADP
ejpam-4868	18	11	degenerate	degenerate	ADJ
ejpam-4868	18	12	versions	version	NOUN
ejpam-4868	18	13	of	of	ADP
ejpam-4868	18	14	existing	exist	VERB
ejpam-4868	18	15	integral	integral	ADJ
ejpam-4868	18	16	transforms	transform	NOUN
ejpam-4868	18	17	.	.	PUNCT
ejpam-4868	19	1	pioneering	pioneer	VERB
ejpam-4868	19	2	work	work	NOUN
ejpam-4868	19	3	of	of	ADP
ejpam-4868	19	4	t.	t.	PROPN
ejpam-4868	19	5	kim	kim	PROPN
ejpam-4868	19	6	and	and	CCONJ
ejpam-4868	19	7	d.	d.	PROPN
ejpam-4868	19	8	s.	s.	PROPN
ejpam-4868	19	9	kim	kim	PROPN
ejpam-4868	20	1	[	[	X
ejpam-4868	20	2	8	8	NUM
ejpam-4868	20	3	]	]	PUNCT
ejpam-4868	20	4	introduced	introduce	VERB
ejpam-4868	20	5	the	the	DET
ejpam-4868	20	6	concept	concept	NOUN
ejpam-4868	20	7	of	of	ADP
ejpam-4868	20	8	∗corresponding	∗corresponde	VERB
ejpam-4868	20	9	author	author	NOUN
ejpam-4868	20	10	.	.	PUNCT
ejpam-4868	21	1	doi	doi	NOUN
ejpam-4868	21	2	:	:	PUNCT
ejpam-4868	21	3	https://doi.org/10.29020/nybg.ejpam.v16i4.4868	https://doi.org/10.29020/nybg.ejpam.v16i4.4868	ADJ
ejpam-4868	21	4	email	email	NOUN
ejpam-4868	21	5	addresses	address	VERB
ejpam-4868	21	6	:	:	PUNCT
ejpam-4868	21	7	harren.campos@msumain.edu.ph	harren.campos@msumain.edu.ph	PROPN
ejpam-4868	21	8	(	(	PUNCT
ejpam-4868	21	9	h.	h.	PROPN
ejpam-4868	21	10	campos	campos	PROPN
ejpam-4868	21	11	)	)	PUNCT
ejpam-4868	21	12	,	,	PUNCT
ejpam-4868	22	1	jezercastro.fernandez@msumain.edu.ph	jezercastro.fernandez@msumain.edu.ph	PROPN
ejpam-4868	22	2	(	(	PUNCT
ejpam-4868	22	3	j.	j.	PROPN
ejpam-4868	22	4	fernandez	fernandez	PROPN
ejpam-4868	22	5	)	)	PUNCT
ejpam-4868	22	6	,	,	PUNCT
ejpam-4868	22	7	natuil.jadebong@gmail.com	natuil.jadebong@gmail.com	X
ejpam-4868	22	8	(	(	PUNCT
ejpam-4868	22	9	j.	j.	PROPN
ejpam-4868	22	10	b.	b.	PROPN
ejpam-4868	22	11	natuil	natuil	PROPN
ejpam-4868	22	12	)	)	PUNCT
ejpam-4868	22	13	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4868	22	14	2213	2213	NUM
ejpam-4868	22	15	©	©	PROPN
ejpam-4868	22	16	2023	2023	NUM
ejpam-4868	22	17	ejpam	ejpam	NOUN
ejpam-4868	22	18	all	all	DET
ejpam-4868	22	19	rights	right	NOUN
ejpam-4868	22	20	reserved	reserve	VERB
ejpam-4868	22	21	.	.	PUNCT
ejpam-4868	23	1	h.	h.	PROPN
ejpam-4868	23	2	j.	j.	PROPN
ejpam-4868	23	3	campos	campos	PROPN
ejpam-4868	23	4	,	,	PUNCT
ejpam-4868	23	5	j.	j.	PROPN
ejpam-4868	23	6	c.	c.	PROPN
ejpam-4868	23	7	fernandez	fernandez	PROPN
ejpam-4868	23	8	,	,	PUNCT
ejpam-4868	23	9	j.	j.	PROPN
ejpam-4868	23	10	b.	b.	PROPN
ejpam-4868	23	11	m.	m.	PROPN
ejpam-4868	23	12	natuil	natuil	PROPN
ejpam-4868	23	13	/	/	SYM
ejpam-4868	23	14	eur	eur	PROPN
ejpam-4868	23	15	.	.	PUNCT
ejpam-4868	24	1	j.	j.	PROPN
ejpam-4868	24	2	pure	pure	PROPN
ejpam-4868	24	3	appl	appl	PROPN
ejpam-4868	24	4	.	.	PROPN
ejpam-4868	24	5	math	math	PROPN
ejpam-4868	24	6	,	,	PUNCT
ejpam-4868	24	7	16	16	NUM
ejpam-4868	24	8	(	(	PUNCT
ejpam-4868	24	9	4	4	NUM
ejpam-4868	24	10	)	)	PUNCT
ejpam-4868	24	11	(	(	PUNCT
ejpam-4868	24	12	2023	2023	NUM
ejpam-4868	24	13	)	)	PUNCT
ejpam-4868	24	14	,	,	PUNCT
ejpam-4868	24	15	2213	2213	NUM
ejpam-4868	24	16	-	-	SYM
ejpam-4868	24	17	2233	2233	NUM
ejpam-4868	24	18	2214	2214	NUM
ejpam-4868	24	19	degenerate	degenerate	ADJ
ejpam-4868	24	20	gamma	gamma	NOUN
ejpam-4868	24	21	functions	function	NOUN
ejpam-4868	24	22	and	and	CCONJ
ejpam-4868	24	23	degenerate	degenerate	ADJ
ejpam-4868	24	24	laplace	laplace	NOUN
ejpam-4868	24	25	transforms	transform	VERB
ejpam-4868	24	26	,	,	PUNCT
ejpam-4868	24	27	as	as	ADV
ejpam-4868	24	28	well	well	ADV
ejpam-4868	24	29	as	as	ADP
ejpam-4868	24	30	the	the	DET
ejpam-4868	24	31	derivation	derivation	NOUN
ejpam-4868	24	32	of	of	ADP
ejpam-4868	24	33	fundamental	fundamental	ADJ
ejpam-4868	24	34	properties	property	NOUN
ejpam-4868	24	35	.	.	PUNCT
ejpam-4868	25	1	subsequently	subsequently	ADV
ejpam-4868	25	2	,	,	PUNCT
ejpam-4868	25	3	l.	l.	PROPN
ejpam-4868	25	4	m.	m.	PROPN
ejpam-4868	25	5	upadhyaya	upadhyaya	PROPN
ejpam-4868	26	1	[	[	X
ejpam-4868	26	2	14–16	14–16	NUM
ejpam-4868	26	3	]	]	PUNCT
ejpam-4868	26	4	further	far	ADV
ejpam-4868	26	5	delved	delve	VERB
ejpam-4868	26	6	into	into	ADP
ejpam-4868	26	7	properties	property	NOUN
ejpam-4868	26	8	of	of	ADP
ejpam-4868	26	9	the	the	DET
ejpam-4868	26	10	degenerate	degenerate	ADJ
ejpam-4868	26	11	laplace	laplace	NOUN
ejpam-4868	26	12	transform	transform	NOUN
ejpam-4868	26	13	,	,	PUNCT
ejpam-4868	26	14	while	while	SCONJ
ejpam-4868	26	15	u.	u.	PROPN
ejpam-4868	26	16	duran	duran	NOUN
ejpam-4868	27	1	[	[	X
ejpam-4868	27	2	4	4	NUM
ejpam-4868	27	3	]	]	PUNCT
ejpam-4868	27	4	investigated	investigate	VERB
ejpam-4868	27	5	the	the	DET
ejpam-4868	27	6	degenerate	degenerate	ADJ
ejpam-4868	27	7	sumudu	sumudu	NOUN
ejpam-4868	27	8	transform	transform	NOUN
ejpam-4868	27	9	and	and	CCONJ
ejpam-4868	27	10	l.	l.	PROPN
ejpam-4868	27	11	m.	m.	PROPN
ejpam-4868	28	1	upadhyaya	upadhyaya	PROPN
ejpam-4868	28	2	et.al	et.al	PROPN
ejpam-4868	29	1	[	[	X
ejpam-4868	29	2	1	1	X
ejpam-4868	29	3	]	]	PUNCT
ejpam-4868	29	4	defined	define	VERB
ejpam-4868	29	5	the	the	DET
ejpam-4868	29	6	degenerate	degenerate	ADJ
ejpam-4868	29	7	elzaki	elzaki	NOUN
ejpam-4868	29	8	transform	transform	NOUN
ejpam-4868	29	9	and	and	CCONJ
ejpam-4868	29	10	its	its	PRON
ejpam-4868	29	11	properties	property	NOUN
ejpam-4868	29	12	.	.	PUNCT
ejpam-4868	30	1	in	in	ADP
ejpam-4868	30	2	light	light	NOUN
ejpam-4868	30	3	of	of	ADP
ejpam-4868	30	4	the	the	DET
ejpam-4868	30	5	growing	grow	VERB
ejpam-4868	30	6	significance	significance	NOUN
ejpam-4868	30	7	of	of	ADP
ejpam-4868	30	8	degenerate	degenerate	ADJ
ejpam-4868	30	9	integral	integral	ADJ
ejpam-4868	30	10	transforms	transform	NOUN
ejpam-4868	30	11	,	,	PUNCT
ejpam-4868	30	12	this	this	DET
ejpam-4868	30	13	article	article	NOUN
ejpam-4868	30	14	seeks	seek	VERB
ejpam-4868	30	15	to	to	PART
ejpam-4868	30	16	contribute	contribute	VERB
ejpam-4868	30	17	to	to	ADP
ejpam-4868	30	18	this	this	DET
ejpam-4868	30	19	research	research	NOUN
ejpam-4868	30	20	by	by	ADP
ejpam-4868	30	21	introducing	introduce	VERB
ejpam-4868	30	22	the	the	DET
ejpam-4868	30	23	degenerate	degenerate	ADJ
ejpam-4868	30	24	laplace	laplace	NOUN
ejpam-4868	30	25	-	-	PUNCT
ejpam-4868	30	26	type	type	NOUN
ejpam-4868	30	27	integral	integral	ADJ
ejpam-4868	30	28	transform	transform	NOUN
ejpam-4868	30	29	.	.	PUNCT
ejpam-4868	31	1	the	the	DET
ejpam-4868	31	2	goal	goal	NOUN
ejpam-4868	31	3	is	be	AUX
ejpam-4868	31	4	to	to	PART
ejpam-4868	31	5	derive	derive	VERB
ejpam-4868	31	6	some	some	DET
ejpam-4868	31	7	properties	property	NOUN
ejpam-4868	31	8	of	of	ADP
ejpam-4868	31	9	this	this	DET
ejpam-4868	31	10	transform	transform	NOUN
ejpam-4868	31	11	and	and	CCONJ
ejpam-4868	31	12	explore	explore	VERB
ejpam-4868	31	13	its	its	PRON
ejpam-4868	31	14	relationship	relationship	NOUN
ejpam-4868	31	15	with	with	ADP
ejpam-4868	31	16	other	other	ADJ
ejpam-4868	31	17	degenerate	degenerate	ADJ
ejpam-4868	31	18	integral	integral	ADJ
ejpam-4868	31	19	transforms	transform	NOUN
ejpam-4868	31	20	.	.	PUNCT
ejpam-4868	32	1	2	2	X
ejpam-4868	32	2	.	.	X
ejpam-4868	32	3	definition	definition	NOUN
ejpam-4868	32	4	and	and	CCONJ
ejpam-4868	32	5	some	some	DET
ejpam-4868	32	6	explicit	explicit	ADJ
ejpam-4868	32	7	formulas	formula	NOUN
ejpam-4868	32	8	taekyun	taekyun	VERB
ejpam-4868	32	9	kim	kim	PROPN
ejpam-4868	32	10	and	and	CCONJ
ejpam-4868	32	11	dae	dae	VERB
ejpam-4868	32	12	san	san	PROPN
ejpam-4868	32	13	kim	kim	PROPN
ejpam-4868	33	1	[	[	X
ejpam-4868	33	2	8	8	NUM
ejpam-4868	33	3	]	]	PUNCT
ejpam-4868	33	4	introduced	introduce	VERB
ejpam-4868	33	5	the	the	DET
ejpam-4868	33	6	concept	concept	NOUN
ejpam-4868	33	7	of	of	ADP
ejpam-4868	33	8	degenerate	degenerate	ADJ
ejpam-4868	33	9	laplace	laplace	NOUN
ejpam-4868	33	10	transform	transform	NOUN
ejpam-4868	33	11	,	,	PUNCT
ejpam-4868	33	12	where	where	SCONJ
ejpam-4868	33	13	f(t	f(t	NOUN
ejpam-4868	33	14	)	)	PUNCT
ejpam-4868	33	15	be	be	VERB
ejpam-4868	33	16	a	a	DET
ejpam-4868	33	17	function	function	NOUN
ejpam-4868	33	18	defined	define	VERB
ejpam-4868	33	19	for	for	ADP
ejpam-4868	33	20	t	t	PROPN
ejpam-4868	33	21	≥	≥	NOUN
ejpam-4868	33	22	0	0	NUM
ejpam-4868	33	23	and	and	CCONJ
ejpam-4868	33	24	λ	λ	PROPN
ejpam-4868	33	25	∈	∈	PROPN
ejpam-4868	33	26	(	(	PUNCT
ejpam-4868	33	27	0,∞	0,∞	NOUN
ejpam-4868	33	28	)	)	PUNCT
ejpam-4868	33	29	.	.	PUNCT
ejpam-4868	34	1	then	then	ADV
ejpam-4868	34	2	the	the	DET
ejpam-4868	34	3	integral	integral	ADJ
ejpam-4868	34	4	lλ{f(t	lλ{f(t	NOUN
ejpam-4868	34	5	)	)	PUNCT
ejpam-4868	34	6	}	}	PUNCT
ejpam-4868	35	1	=	=	SYM
ejpam-4868	35	2	∫	∫	PROPN
ejpam-4868	36	1	∞	∞	NUM
ejpam-4868	36	2	0	0	NUM
ejpam-4868	36	3	e−s	e−s	PROPN
ejpam-4868	36	4	λ	λ	PROPN
ejpam-4868	36	5	(	(	PUNCT
ejpam-4868	36	6	t)f(t)dt	t)f(t)dt	NOUN
ejpam-4868	36	7	=	=	SYM
ejpam-4868	36	8	∫	∫	PROPN
ejpam-4868	36	9	∞	∞	PROPN
ejpam-4868	36	10	0	0	NUM
ejpam-4868	36	11	(	(	PUNCT
ejpam-4868	36	12	1	1	NUM
ejpam-4868	36	13	+	+	CCONJ
ejpam-4868	36	14	λt)−	λt)−	PROPN
ejpam-4868	36	15	s	s	X
ejpam-4868	36	16	λ	λ	X
ejpam-4868	36	17	f(t)dt	f(t)dt	PROPN
ejpam-4868	36	18	,	,	PUNCT
ejpam-4868	36	19	(	(	PUNCT
ejpam-4868	36	20	1	1	X
ejpam-4868	36	21	)	)	PUNCT
ejpam-4868	36	22	is	be	AUX
ejpam-4868	36	23	said	say	VERB
ejpam-4868	36	24	to	to	PART
ejpam-4868	36	25	be	be	AUX
ejpam-4868	36	26	the	the	DET
ejpam-4868	36	27	degenerate	degenerate	ADJ
ejpam-4868	36	28	laplace	laplace	NOUN
ejpam-4868	36	29	transform	transform	NOUN
ejpam-4868	36	30	of	of	ADP
ejpam-4868	36	31	f	f	PROPN
ejpam-4868	36	32	if	if	SCONJ
ejpam-4868	36	33	the	the	DET
ejpam-4868	36	34	integral	integral	ADJ
ejpam-4868	36	35	converges	converge	NOUN
ejpam-4868	36	36	.	.	PUNCT
ejpam-4868	37	1	letting	let	VERB
ejpam-4868	37	2	s	s	X
ejpam-4868	37	3	=	=	SYM
ejpam-4868	37	4	1	1	NUM
ejpam-4868	37	5	u	u	NOUN
ejpam-4868	37	6	,	,	PUNCT
ejpam-4868	37	7	the	the	DET
ejpam-4868	37	8	degenerate	degenerate	ADJ
ejpam-4868	37	9	laplace	laplace	NOUN
ejpam-4868	37	10	transform	transform	NOUN
ejpam-4868	37	11	can	can	AUX
ejpam-4868	37	12	be	be	AUX
ejpam-4868	37	13	rewritten	rewrite	VERB
ejpam-4868	37	14	as	as	ADP
ejpam-4868	37	15	lλ{f(t	lλ{f(t	NOUN
ejpam-4868	37	16	)	)	PUNCT
ejpam-4868	37	17	}	}	PUNCT
ejpam-4868	38	1	=	=	SYM
ejpam-4868	38	2	∫	∫	PROPN
ejpam-4868	39	1	∞	∞	NUM
ejpam-4868	39	2	0	0	PUNCT
ejpam-4868	40	1	e	e	NOUN
ejpam-4868	40	2	−	−	PROPN
ejpam-4868	40	3	1	1	NUM
ejpam-4868	40	4	u	u	NOUN
ejpam-4868	40	5	λ	λ	X
ejpam-4868	40	6	(	(	PUNCT
ejpam-4868	40	7	t)f(t)dt	t)f(t)dt	NOUN
ejpam-4868	40	8	=	=	SYM
ejpam-4868	40	9	∫	∫	PROPN
ejpam-4868	40	10	∞	∞	PROPN
ejpam-4868	40	11	0	0	NUM
ejpam-4868	40	12	(	(	PUNCT
ejpam-4868	40	13	1	1	NUM
ejpam-4868	40	14	+	+	CCONJ
ejpam-4868	40	15	λt)−	λt)−	PROPN
ejpam-4868	40	16	1	1	X
ejpam-4868	40	17	uλ	uλ	ADP
ejpam-4868	40	18	f(t)dt	f(t)dt	PROPN
ejpam-4868	40	19	ugur	ugur	PROPN
ejpam-4868	40	20	duran	duran	NOUN
ejpam-4868	40	21	of	of	ADP
ejpam-4868	40	22	iskenderun	iskenderun	PROPN
ejpam-4868	40	23	technical	technical	ADJ
ejpam-4868	40	24	university	university	NOUN
ejpam-4868	40	25	[	[	X
ejpam-4868	40	26	4	4	NUM
ejpam-4868	40	27	]	]	PUNCT
ejpam-4868	40	28	introduced	introduce	VERB
ejpam-4868	40	29	the	the	DET
ejpam-4868	40	30	concept	concept	NOUN
ejpam-4868	40	31	of	of	ADP
ejpam-4868	40	32	degenerate	degenerate	ADJ
ejpam-4868	40	33	sumudu	sumudu	NOUN
ejpam-4868	40	34	transform	transform	NOUN
ejpam-4868	40	35	of	of	ADP
ejpam-4868	40	36	f(t	f(t	PROPN
ejpam-4868	40	37	)	)	PUNCT
ejpam-4868	40	38	which	which	PRON
ejpam-4868	40	39	is	be	AUX
ejpam-4868	40	40	defined	define	VERB
ejpam-4868	40	41	by	by	ADP
ejpam-4868	40	42	the	the	DET
ejpam-4868	40	43	improper	improper	ADJ
ejpam-4868	40	44	integral	integral	ADJ
ejpam-4868	40	45	sλ{f(t	sλ{f(t	NOUN
ejpam-4868	40	46	)	)	PUNCT
ejpam-4868	40	47	}	}	PUNCT
ejpam-4868	40	48	=	=	SYM
ejpam-4868	40	49	1	1	NUM
ejpam-4868	40	50	u	u	NOUN
ejpam-4868	40	51	∫	∫	PROPN
ejpam-4868	40	52	∞	∞	NOUN
ejpam-4868	40	53	0	0	PUNCT
ejpam-4868	41	1	e	e	NOUN
ejpam-4868	41	2	−1	−1	NOUN
ejpam-4868	41	3	u	u	X
ejpam-4868	41	4	λ	λ	PROPN
ejpam-4868	41	5	(	(	PUNCT
ejpam-4868	41	6	t)f(t)dt	t)f(t)dt	NOUN
ejpam-4868	41	7	=	=	SYM
ejpam-4868	41	8	1	1	NUM
ejpam-4868	41	9	u	u	NOUN
ejpam-4868	41	10	∫	∫	PROPN
ejpam-4868	41	11	∞	∞	NOUN
ejpam-4868	41	12	0	0	NUM
ejpam-4868	41	13	(	(	PUNCT
ejpam-4868	41	14	1	1	NUM
ejpam-4868	41	15	+	+	CCONJ
ejpam-4868	41	16	λt)−	λt)−	PROPN
ejpam-4868	41	17	1	1	X
ejpam-4868	41	18	uλ	uλ	ADP
ejpam-4868	41	19	f(t)dt	f(t)dt	PROPN
ejpam-4868	41	20	,	,	PUNCT
ejpam-4868	41	21	where	where	SCONJ
ejpam-4868	41	22	λ	λ	PROPN
ejpam-4868	41	23	∈	∈	PROPN
ejpam-4868	41	24	(	(	PUNCT
ejpam-4868	41	25	0,∞	0,∞	NOUN
ejpam-4868	41	26	)	)	PUNCT
ejpam-4868	41	27	,	,	PUNCT
ejpam-4868	41	28	and	and	CCONJ
ejpam-4868	41	29	f(t	f(t	NOUN
ejpam-4868	41	30	)	)	PUNCT
ejpam-4868	41	31	be	be	VERB
ejpam-4868	41	32	a	a	DET
ejpam-4868	41	33	function	function	NOUN
ejpam-4868	41	34	defined	define	VERB
ejpam-4868	41	35	for	for	ADP
ejpam-4868	41	36	t	t	PROPN
ejpam-4868	41	37	≥	≥	NOUN
ejpam-4868	41	38	0	0	NUM
ejpam-4868	41	39	.	.	PUNCT
ejpam-4868	42	1	on	on	ADP
ejpam-4868	42	2	the	the	DET
ejpam-4868	42	3	paper	paper	NOUN
ejpam-4868	42	4	of	of	ADP
ejpam-4868	42	5	lalit	lalit	PROPN
ejpam-4868	42	6	mohan	mohan	PROPN
ejpam-4868	42	7	upadhyaya	upadhyaya	PROPN
ejpam-4868	42	8	et.al	et.al	PROPN
ejpam-4868	43	1	[	[	X
ejpam-4868	43	2	1	1	NUM
ejpam-4868	43	3	]	]	PUNCT
ejpam-4868	43	4	,	,	PUNCT
ejpam-4868	43	5	they	they	PRON
ejpam-4868	43	6	defined	define	VERB
ejpam-4868	43	7	the	the	DET
ejpam-4868	43	8	degenerate	degenerate	NOUN
ejpam-4868	43	9	of	of	ADP
ejpam-4868	43	10	elzaki	elzaki	NOUN
ejpam-4868	43	11	transform	transform	NOUN
ejpam-4868	43	12	and	and	CCONJ
ejpam-4868	43	13	its	its	PRON
ejpam-4868	43	14	properties	property	NOUN
ejpam-4868	43	15	.	.	PUNCT
ejpam-4868	44	1	the	the	DET
ejpam-4868	44	2	degenerate	degenerate	ADJ
ejpam-4868	44	3	elzaki	elzaki	NOUN
ejpam-4868	44	4	transform	transform	NOUN
ejpam-4868	44	5	is	be	AUX
ejpam-4868	44	6	defined	define	VERB
ejpam-4868	44	7	by	by	ADP
ejpam-4868	44	8	the	the	DET
ejpam-4868	44	9	integral	integral	ADJ
ejpam-4868	44	10	eλ{f(t	eλ{f(t	NOUN
ejpam-4868	44	11	)	)	PUNCT
ejpam-4868	44	12	}	}	PUNCT
ejpam-4868	45	1	=	=	SYM
ejpam-4868	45	2	u	u	NOUN
ejpam-4868	45	3	∫	∫	PROPN
ejpam-4868	45	4	∞	∞	PROPN
ejpam-4868	45	5	0	0	PUNCT
ejpam-4868	46	1	e	e	NOUN
ejpam-4868	46	2	−	−	PROPN
ejpam-4868	46	3	1	1	NUM
ejpam-4868	46	4	u	u	NOUN
ejpam-4868	46	5	λ	λ	X
ejpam-4868	46	6	(	(	PUNCT
ejpam-4868	46	7	t)f(t)dt	t)f(t)dt	NOUN
ejpam-4868	46	8	=	=	SYM
ejpam-4868	46	9	u	u	NOUN
ejpam-4868	46	10	∫	∫	PROPN
ejpam-4868	46	11	∞	∞	PROPN
ejpam-4868	46	12	0	0	NUM
ejpam-4868	47	1	(	(	PUNCT
ejpam-4868	47	2	1	1	NUM
ejpam-4868	47	3	+	+	CCONJ
ejpam-4868	47	4	λt)−	λt)−	PROPN
ejpam-4868	47	5	1	1	X
ejpam-4868	47	6	uλ	uλ	ADP
ejpam-4868	47	7	f(t)dt	f(t)dt	PROPN
ejpam-4868	47	8	where	where	SCONJ
ejpam-4868	47	9	λ	λ	PROPN
ejpam-4868	47	10	∈	∈	PROPN
ejpam-4868	47	11	(	(	PUNCT
ejpam-4868	47	12	0,∞	0,∞	NOUN
ejpam-4868	47	13	)	)	PUNCT
ejpam-4868	47	14	,	,	PUNCT
ejpam-4868	47	15	and	and	CCONJ
ejpam-4868	47	16	f(t	f(t	NOUN
ejpam-4868	47	17	)	)	PUNCT
ejpam-4868	47	18	be	be	VERB
ejpam-4868	47	19	a	a	DET
ejpam-4868	47	20	function	function	NOUN
ejpam-4868	47	21	defined	define	VERB
ejpam-4868	47	22	for	for	ADP
ejpam-4868	47	23	t	t	PROPN
ejpam-4868	47	24	≥	≥	NOUN
ejpam-4868	47	25	0	0	NUM
ejpam-4868	47	26	.	.	PUNCT
ejpam-4868	48	1	we	we	PRON
ejpam-4868	48	2	now	now	ADV
ejpam-4868	48	3	have	have	VERB
ejpam-4868	48	4	the	the	DET
ejpam-4868	48	5	following	follow	VERB
ejpam-4868	48	6	definition	definition	NOUN
ejpam-4868	48	7	:	:	PUNCT
ejpam-4868	48	8	definition	definition	NOUN
ejpam-4868	48	9	1	1	NUM
ejpam-4868	48	10	.	.	PUNCT
ejpam-4868	49	1	[	[	X
ejpam-4868	49	2	3	3	NUM
ejpam-4868	49	3	,	,	PUNCT
ejpam-4868	49	4	8–14	8–14	PROPN
ejpam-4868	49	5	]	]	PUNCT
ejpam-4868	49	6	for	for	ADP
ejpam-4868	49	7	any	any	DET
ejpam-4868	49	8	nonzero	nonzero	ADJ
ejpam-4868	49	9	real	real	ADJ
ejpam-4868	49	10	number	number	NOUN
ejpam-4868	49	11	λ	λ	PROPN
ejpam-4868	49	12	,	,	PUNCT
ejpam-4868	49	13	the	the	DET
ejpam-4868	49	14	degenerate	degenerate	ADJ
ejpam-4868	49	15	exponential	exponential	ADJ
ejpam-4868	49	16	function	function	NOUN
ejpam-4868	49	17	is	be	AUX
ejpam-4868	49	18	defined	define	VERB
ejpam-4868	49	19	as	as	SCONJ
ejpam-4868	49	20	follows	follow	VERB
ejpam-4868	49	21	:	:	PUNCT
ejpam-4868	49	22	exλ(t	exλ(t	X
ejpam-4868	49	23	)	)	PUNCT
ejpam-4868	49	24	=	=	PUNCT
ejpam-4868	50	1	(	(	PUNCT
ejpam-4868	50	2	1	1	NUM
ejpam-4868	50	3	+	+	CCONJ
ejpam-4868	50	4	λt	λt	X
ejpam-4868	50	5	)	)	PUNCT
ejpam-4868	50	6	x	x	SYM
ejpam-4868	50	7	λ	λ	NOUN
ejpam-4868	50	8	,	,	PUNCT
ejpam-4868	50	9	eλ(t	eλ(t	ADV
ejpam-4868	50	10	)	)	PUNCT
ejpam-4868	50	11	=	=	SYM
ejpam-4868	50	12	e1λ(t	e1λ(t	NOUN
ejpam-4868	50	13	)	)	PUNCT
ejpam-4868	50	14	=	=	PUNCT
ejpam-4868	51	1	(	(	PUNCT
ejpam-4868	51	2	1	1	NUM
ejpam-4868	51	3	+	+	CCONJ
ejpam-4868	51	4	λt	λt	X
ejpam-4868	51	5	)	)	PUNCT
ejpam-4868	51	6	1	1	NUM
ejpam-4868	51	7	λ	λ	X
ejpam-4868	51	8	(	(	PUNCT
ejpam-4868	51	9	2	2	NUM
ejpam-4868	51	10	)	)	PUNCT
ejpam-4868	51	11	h.	h.	PROPN
ejpam-4868	51	12	j.	j.	PROPN
ejpam-4868	51	13	campos	campos	PROPN
ejpam-4868	51	14	,	,	PUNCT
ejpam-4868	51	15	j.	j.	PROPN
ejpam-4868	51	16	c.	c.	PROPN
ejpam-4868	51	17	fernandez	fernandez	PROPN
ejpam-4868	51	18	,	,	PUNCT
ejpam-4868	51	19	j.	j.	PROPN
ejpam-4868	51	20	b.	b.	PROPN
ejpam-4868	51	21	m.	m.	PROPN
ejpam-4868	51	22	natuil	natuil	PROPN
ejpam-4868	51	23	/	/	SYM
ejpam-4868	51	24	eur	eur	PROPN
ejpam-4868	51	25	.	.	PUNCT
ejpam-4868	52	1	j.	j.	PROPN
ejpam-4868	52	2	pure	pure	PROPN
ejpam-4868	52	3	appl	appl	PROPN
ejpam-4868	52	4	.	.	PROPN
ejpam-4868	52	5	math	math	PROPN
ejpam-4868	52	6	,	,	PUNCT
ejpam-4868	52	7	16	16	NUM
ejpam-4868	52	8	(	(	PUNCT
ejpam-4868	52	9	4	4	NUM
ejpam-4868	52	10	)	)	PUNCT
ejpam-4868	52	11	(	(	PUNCT
ejpam-4868	52	12	2023	2023	NUM
ejpam-4868	52	13	)	)	PUNCT
ejpam-4868	52	14	,	,	PUNCT
ejpam-4868	52	15	2213	2213	NUM
ejpam-4868	52	16	-	-	SYM
ejpam-4868	52	17	2233	2233	NUM
ejpam-4868	52	18	2215	2215	NUM
ejpam-4868	52	19	that	that	PRON
ejpam-4868	52	20	is	be	AUX
ejpam-4868	52	21	,	,	PUNCT
ejpam-4868	52	22	the	the	DET
ejpam-4868	52	23	degenerate	degenerate	NOUN
ejpam-4868	52	24	of	of	ADP
ejpam-4868	52	25	the	the	DET
ejpam-4868	52	26	exponential	exponential	ADJ
ejpam-4868	52	27	function	function	NOUN
ejpam-4868	52	28	ext	ext	NOUN
ejpam-4868	52	29	is	be	AUX
ejpam-4868	52	30	equal	equal	ADJ
ejpam-4868	52	31	to	to	ADP
ejpam-4868	52	32	exλ(t	exλ(t	PROPN
ejpam-4868	52	33	)	)	PUNCT
ejpam-4868	52	34	=	=	SYM
ejpam-4868	52	35	(	(	PUNCT
ejpam-4868	52	36	1+λt	1+λt	NUM
ejpam-4868	52	37	)	)	PUNCT
ejpam-4868	52	38	x	x	SYM
ejpam-4868	53	1	λ	λ	INTJ
ejpam-4868	53	2	,	,	PUNCT
ejpam-4868	53	3	where	where	SCONJ
ejpam-4868	53	4	λ	λ	PROPN
ejpam-4868	53	5	∈	∈	PROPN
ejpam-4868	53	6	r−	r−	PROPN
ejpam-4868	53	7	{	{	PUNCT
ejpam-4868	53	8	0	0	NUM
ejpam-4868	53	9	}	}	PUNCT
ejpam-4868	53	10	.	.	PUNCT
ejpam-4868	54	1	here	here	ADV
ejpam-4868	54	2	,	,	PUNCT
ejpam-4868	54	3	we	we	PRON
ejpam-4868	54	4	note	note	VERB
ejpam-4868	54	5	that	that	SCONJ
ejpam-4868	54	6	exλ(t	exλ(t	ADV
ejpam-4868	54	7	)	)	PUNCT
ejpam-4868	54	8	=	=	PUNCT
ejpam-4868	55	1	∞∑	∞∑	NUM
ejpam-4868	55	2	n=0	n=0	NUM
ejpam-4868	55	3	(	(	PUNCT
ejpam-4868	55	4	x)n	x)n	PROPN
ejpam-4868	55	5	,	,	PUNCT
ejpam-4868	55	6	λ	λ	PROPN
ejpam-4868	55	7	tn	tn	NOUN
ejpam-4868	55	8	n	n	X
ejpam-4868	55	9	!	!	PROPN
ejpam-4868	55	10	,	,	PUNCT
ejpam-4868	55	11	where	where	SCONJ
ejpam-4868	55	12	(	(	PUNCT
ejpam-4868	55	13	x)0,λ	x)0,λ	NOUN
ejpam-4868	55	14	=	=	SYM
ejpam-4868	55	15	1	1	NUM
ejpam-4868	55	16	,	,	PUNCT
ejpam-4868	55	17	(	(	PUNCT
ejpam-4868	55	18	x)n	x)n	PROPN
ejpam-4868	55	19	,	,	PUNCT
ejpam-4868	55	20	λ	λ	PROPN
ejpam-4868	55	21	=	=	SYM
ejpam-4868	55	22	x(x−	x(x−	PROPN
ejpam-4868	55	23	λ)(x−	λ)(x−	PROPN
ejpam-4868	55	24	2λ	2λ	NUM
ejpam-4868	55	25	)	)	PUNCT
ejpam-4868	55	26	·	·	PUNCT
ejpam-4868	55	27	·	·	PUNCT
ejpam-4868	55	28	·	·	PUNCT
ejpam-4868	56	1	(	(	PUNCT
ejpam-4868	56	2	x−	x−	X
ejpam-4868	56	3	(	(	PUNCT
ejpam-4868	56	4	n−	n−	NOUN
ejpam-4868	56	5	1)λ	1)λ	NOUN
ejpam-4868	56	6	)	)	PUNCT
ejpam-4868	56	7	for	for	ADP
ejpam-4868	56	8	n	n	PRON
ejpam-4868	56	9	≥	≥	NUM
ejpam-4868	56	10	1	1	NUM
ejpam-4868	56	11	.	.	PUNCT
ejpam-4868	57	1	it	it	PRON
ejpam-4868	57	2	is	be	AUX
ejpam-4868	57	3	noteworthy	noteworthy	ADJ
ejpam-4868	57	4	to	to	PART
ejpam-4868	57	5	mention	mention	VERB
ejpam-4868	58	1	that	that	SCONJ
ejpam-4868	58	2	lim	lim	PROPN
ejpam-4868	58	3	λ→0	λ→0	VERB
ejpam-4868	58	4	exλ(t	exλ(t	PROPN
ejpam-4868	58	5	)	)	PUNCT
ejpam-4868	58	6	=	=	SYM
ejpam-4868	58	7	lim	lim	PROPN
ejpam-4868	58	8	λ→0	λ→0	PUNCT
ejpam-4868	58	9	(	(	PUNCT
ejpam-4868	58	10	1	1	NUM
ejpam-4868	58	11	+	+	CCONJ
ejpam-4868	58	12	λt	λt	X
ejpam-4868	58	13	)	)	PUNCT
ejpam-4868	59	1	x	x	SYM
ejpam-4868	59	2	λ	λ	NOUN
ejpam-4868	59	3	=	=	SYM
ejpam-4868	59	4	ext	ext	NOUN
ejpam-4868	59	5	.	.	PUNCT
ejpam-4868	60	1	definition	definition	NOUN
ejpam-4868	60	2	2	2	NUM
ejpam-4868	60	3	.	.	PUNCT
ejpam-4868	61	1	[	[	X
ejpam-4868	61	2	8	8	NUM
ejpam-4868	61	3	]	]	PUNCT
ejpam-4868	61	4	a	a	DET
ejpam-4868	61	5	function	function	NOUN
ejpam-4868	61	6	f(t	f(t	NOUN
ejpam-4868	61	7	)	)	PUNCT
ejpam-4868	61	8	is	be	AUX
ejpam-4868	61	9	said	say	VERB
ejpam-4868	61	10	to	to	PART
ejpam-4868	61	11	be	be	AUX
ejpam-4868	61	12	of	of	ADP
ejpam-4868	61	13	degenerate	degenerate	ADJ
ejpam-4868	61	14	exponential	exponential	ADJ
ejpam-4868	61	15	order	order	NOUN
ejpam-4868	61	16	c	c	NOUN
ejpam-4868	62	1	if	if	SCONJ
ejpam-4868	62	2	there	there	PRON
ejpam-4868	62	3	exists	exist	VERB
ejpam-4868	62	4	c	c	NOUN
ejpam-4868	62	5	,	,	PUNCT
ejpam-4868	62	6	m	m	VERB
ejpam-4868	62	7	>	>	X
ejpam-4868	62	8	0	0	PUNCT
ejpam-4868	62	9	and	and	CCONJ
ejpam-4868	62	10	t	t	X
ejpam-4868	62	11	>	>	X
ejpam-4868	62	12	0	0	NUM
ejpam-4868	63	1	such	such	ADJ
ejpam-4868	63	2	that	that	SCONJ
ejpam-4868	63	3	|f(t)|	|f(t)|	ADJ
ejpam-4868	63	4	≤	≤	ADJ
ejpam-4868	63	5	m(1	m(1	NOUN
ejpam-4868	63	6	+	+	CCONJ
ejpam-4868	63	7	λt	λt	X
ejpam-4868	63	8	)	)	PUNCT
ejpam-4868	63	9	c	c	NOUN
ejpam-4868	63	10	λ	λ	NOUN
ejpam-4868	63	11	=	=	SYM
ejpam-4868	63	12	mecλ	mecλ	PROPN
ejpam-4868	63	13	(	(	PUNCT
ejpam-4868	63	14	t	t	PROPN
ejpam-4868	63	15	)	)	PUNCT
ejpam-4868	63	16	for	for	ADP
ejpam-4868	63	17	all	all	DET
ejpam-4868	63	18	t	t	NOUN
ejpam-4868	63	19	>	>	X
ejpam-4868	63	20	t.	t.	NOUN
ejpam-4868	63	21	definition	definition	NOUN
ejpam-4868	63	22	3	3	NUM
ejpam-4868	63	23	.	.	PUNCT
ejpam-4868	64	1	[	[	X
ejpam-4868	64	2	2	2	NUM
ejpam-4868	64	3	,	,	PUNCT
ejpam-4868	64	4	4	4	NUM
ejpam-4868	64	5	,	,	PUNCT
ejpam-4868	64	6	6	6	NUM
ejpam-4868	64	7	]	]	PUNCT
ejpam-4868	64	8	the	the	DET
ejpam-4868	64	9	degenerate	degenerate	ADJ
ejpam-4868	64	10	sine	sine	ADJ
ejpam-4868	64	11	function	function	NOUN
ejpam-4868	64	12	is	be	AUX
ejpam-4868	64	13	defined	define	VERB
ejpam-4868	64	14	by	by	ADP
ejpam-4868	64	15	the	the	DET
ejpam-4868	64	16	relation	relation	NOUN
ejpam-4868	64	17	sin	sin	NOUN
ejpam-4868	64	18	(	(	PUNCT
ejpam-4868	64	19	x	x	X
ejpam-4868	64	20	)	)	PUNCT
ejpam-4868	64	21	λ	λ	PROPN
ejpam-4868	64	22	(	(	PUNCT
ejpam-4868	64	23	t	t	PROPN
ejpam-4868	64	24	)	)	PUNCT
ejpam-4868	64	25	=	=	SYM
ejpam-4868	64	26	eixλ	eixλ	PROPN
ejpam-4868	64	27	(	(	PUNCT
ejpam-4868	64	28	t)−	t)−	PROPN
ejpam-4868	64	29	e−ix	e−ix	NOUN
ejpam-4868	64	30	λ	λ	PROPN
ejpam-4868	64	31	(	(	PUNCT
ejpam-4868	64	32	t	t	PROPN
ejpam-4868	64	33	)	)	PUNCT
ejpam-4868	64	34	2i	2i	NOUN
ejpam-4868	64	35	=	=	NOUN
ejpam-4868	64	36	sin	sin	NOUN
ejpam-4868	64	37	(	(	PUNCT
ejpam-4868	64	38	x	x	PUNCT
ejpam-4868	64	39	λ	λ	NOUN
ejpam-4868	64	40	log(1	log(1	NOUN
ejpam-4868	64	41	+	+	CCONJ
ejpam-4868	64	42	λt	λt	X
ejpam-4868	64	43	)	)	PUNCT
ejpam-4868	64	44	)	)	PUNCT
ejpam-4868	64	45	,	,	PUNCT
ejpam-4868	64	46	where	where	SCONJ
ejpam-4868	64	47	i	i	PRON
ejpam-4868	64	48	=	=	VERB
ejpam-4868	64	49	√	√	NUM
ejpam-4868	64	50	−1	−1	NOUN
ejpam-4868	64	51	.	.	PUNCT
ejpam-4868	65	1	(	(	PUNCT
ejpam-4868	65	2	3	3	X
ejpam-4868	65	3	)	)	PUNCT
ejpam-4868	65	4	it	it	PRON
ejpam-4868	65	5	can	can	AUX
ejpam-4868	65	6	be	be	AUX
ejpam-4868	65	7	noted	note	VERB
ejpam-4868	65	8	that	that	SCONJ
ejpam-4868	65	9	,	,	PUNCT
ejpam-4868	65	10	lim	lim	PROPN
ejpam-4868	65	11	λ→0	λ→0	PROPN
ejpam-4868	65	12	sin	sin	NOUN
ejpam-4868	65	13	(	(	PUNCT
ejpam-4868	65	14	x	x	X
ejpam-4868	65	15	)	)	PUNCT
ejpam-4868	65	16	λ	λ	PROPN
ejpam-4868	65	17	(	(	PUNCT
ejpam-4868	65	18	t	t	PROPN
ejpam-4868	65	19	)	)	PUNCT
ejpam-4868	65	20	=	=	VERB
ejpam-4868	65	21	sinxt	sinxt	NOUN
ejpam-4868	65	22	.	.	PUNCT
ejpam-4868	66	1	definition	definition	NOUN
ejpam-4868	66	2	4	4	NUM
ejpam-4868	66	3	.	.	PUNCT
ejpam-4868	67	1	[	[	X
ejpam-4868	67	2	2	2	NUM
ejpam-4868	67	3	,	,	PUNCT
ejpam-4868	67	4	4	4	NUM
ejpam-4868	67	5	,	,	PUNCT
ejpam-4868	67	6	6	6	NUM
ejpam-4868	67	7	]	]	PUNCT
ejpam-4868	67	8	the	the	DET
ejpam-4868	67	9	degenerate	degenerate	ADJ
ejpam-4868	67	10	cosine	cosine	NOUN
ejpam-4868	67	11	function	function	NOUN
ejpam-4868	67	12	is	be	AUX
ejpam-4868	67	13	defined	define	VERB
ejpam-4868	67	14	by	by	ADP
ejpam-4868	67	15	the	the	DET
ejpam-4868	67	16	relation	relation	NOUN
ejpam-4868	67	17	cos	cos	PROPN
ejpam-4868	67	18	(	(	PUNCT
ejpam-4868	67	19	x	x	X
ejpam-4868	67	20	)	)	PUNCT
ejpam-4868	67	21	λ	λ	PROPN
ejpam-4868	67	22	(	(	PUNCT
ejpam-4868	67	23	t	t	PROPN
ejpam-4868	67	24	)	)	PUNCT
ejpam-4868	67	25	=	=	SYM
ejpam-4868	67	26	eixλ	eixλ	PROPN
ejpam-4868	67	27	(	(	PUNCT
ejpam-4868	67	28	t	t	PROPN
ejpam-4868	67	29	)	)	PUNCT
ejpam-4868	67	30	+	+	CCONJ
ejpam-4868	67	31	e−ix	e−ix	PROPN
ejpam-4868	67	32	λ	λ	PROPN
ejpam-4868	67	33	(	(	PUNCT
ejpam-4868	67	34	t	t	PROPN
ejpam-4868	67	35	)	)	PUNCT
ejpam-4868	67	36	2	2	NUM
ejpam-4868	67	37	=	=	SYM
ejpam-4868	67	38	cos	cos	X
ejpam-4868	67	39	(	(	PUNCT
ejpam-4868	67	40	x	x	PUNCT
ejpam-4868	67	41	λ	λ	NOUN
ejpam-4868	67	42	log(1	log(1	NOUN
ejpam-4868	67	43	+	+	CCONJ
ejpam-4868	67	44	λt	λt	X
ejpam-4868	67	45	)	)	PUNCT
ejpam-4868	67	46	)	)	PUNCT
ejpam-4868	67	47	,	,	PUNCT
ejpam-4868	67	48	where	where	SCONJ
ejpam-4868	67	49	i	i	PRON
ejpam-4868	67	50	=	=	VERB
ejpam-4868	67	51	√	√	NUM
ejpam-4868	67	52	−1	−1	NOUN
ejpam-4868	67	53	.	.	PUNCT
ejpam-4868	68	1	(	(	PUNCT
ejpam-4868	68	2	4	4	X
ejpam-4868	68	3	)	)	PUNCT
ejpam-4868	68	4	it	it	PRON
ejpam-4868	68	5	can	can	AUX
ejpam-4868	68	6	be	be	AUX
ejpam-4868	68	7	noted	note	VERB
ejpam-4868	68	8	that	that	SCONJ
ejpam-4868	68	9	,	,	PUNCT
ejpam-4868	68	10	lim	lim	PROPN
ejpam-4868	68	11	λ→0	λ→0	PROPN
ejpam-4868	68	12	cos	cos	PROPN
ejpam-4868	68	13	(	(	PUNCT
ejpam-4868	68	14	x	x	X
ejpam-4868	68	15	)	)	PUNCT
ejpam-4868	68	16	λ	λ	PROPN
ejpam-4868	68	17	(	(	PUNCT
ejpam-4868	68	18	t	t	PROPN
ejpam-4868	68	19	)	)	PUNCT
ejpam-4868	68	20	=	=	SYM
ejpam-4868	68	21	cosxt	cosxt	NOUN
ejpam-4868	68	22	.	.	PUNCT
ejpam-4868	69	1	definition	definition	NOUN
ejpam-4868	69	2	5	5	NUM
ejpam-4868	69	3	.	.	PUNCT
ejpam-4868	70	1	[	[	X
ejpam-4868	70	2	4	4	NUM
ejpam-4868	70	3	,	,	PUNCT
ejpam-4868	70	4	6	6	NUM
ejpam-4868	70	5	,	,	PUNCT
ejpam-4868	70	6	14	14	NUM
ejpam-4868	70	7	]	]	PUNCT
ejpam-4868	70	8	the	the	DET
ejpam-4868	70	9	degenerate	degenerate	ADJ
ejpam-4868	70	10	euler	euler	NOUN
ejpam-4868	70	11	function	function	NOUN
ejpam-4868	70	12	is	be	AUX
ejpam-4868	70	13	defined	define	VERB
ejpam-4868	70	14	by	by	ADP
ejpam-4868	70	15	the	the	DET
ejpam-4868	70	16	relation	relation	NOUN
ejpam-4868	70	17	eixλ	eixλ	PROPN
ejpam-4868	70	18	(	(	PUNCT
ejpam-4868	70	19	t	t	PROPN
ejpam-4868	70	20	)	)	PUNCT
ejpam-4868	70	21	=	=	SYM
ejpam-4868	70	22	cos	cos	X
ejpam-4868	70	23	(	(	PUNCT
ejpam-4868	70	24	x	x	X
ejpam-4868	70	25	)	)	PUNCT
ejpam-4868	70	26	λ	λ	PROPN
ejpam-4868	70	27	(	(	PUNCT
ejpam-4868	70	28	t	t	PROPN
ejpam-4868	70	29	)	)	PUNCT
ejpam-4868	71	1	+	+	CCONJ
ejpam-4868	71	2	i	i	PRON
ejpam-4868	71	3	sin	sin	VERB
ejpam-4868	71	4	(	(	PUNCT
ejpam-4868	71	5	x	x	X
ejpam-4868	71	6	)	)	PUNCT
ejpam-4868	71	7	λ	λ	PROPN
ejpam-4868	71	8	(	(	PUNCT
ejpam-4868	71	9	t	t	PROPN
ejpam-4868	71	10	)	)	PUNCT
ejpam-4868	71	11	(	(	PUNCT
ejpam-4868	71	12	5	5	X
ejpam-4868	71	13	)	)	PUNCT
ejpam-4868	72	1	where	where	SCONJ
ejpam-4868	72	2	cos	cos	PROPN
ejpam-4868	72	3	(	(	PUNCT
ejpam-4868	72	4	x	x	X
ejpam-4868	72	5	)	)	PUNCT
ejpam-4868	72	6	λ	λ	PROPN
ejpam-4868	72	7	(	(	PUNCT
ejpam-4868	72	8	t	t	PROPN
ejpam-4868	72	9	)	)	PUNCT
ejpam-4868	72	10	=	=	SYM
ejpam-4868	72	11	cos	cos	PROPN
ejpam-4868	72	12	(	(	PUNCT
ejpam-4868	72	13	x	x	PUNCT
ejpam-4868	72	14	λ	λ	NOUN
ejpam-4868	72	15	log(1	log(1	NOUN
ejpam-4868	72	16	+	+	CCONJ
ejpam-4868	72	17	λt	λt	X
ejpam-4868	72	18	)	)	PUNCT
ejpam-4868	72	19	)	)	PUNCT
ejpam-4868	72	20	and	and	CCONJ
ejpam-4868	72	21	sin	sin	NOUN
ejpam-4868	72	22	(	(	PUNCT
ejpam-4868	72	23	x	x	NOUN
ejpam-4868	72	24	)	)	PUNCT
ejpam-4868	72	25	λ	λ	PROPN
ejpam-4868	72	26	(	(	PUNCT
ejpam-4868	72	27	t	t	PROPN
ejpam-4868	72	28	)	)	PUNCT
ejpam-4868	72	29	=	=	NOUN
ejpam-4868	72	30	sin	sin	NOUN
ejpam-4868	72	31	(	(	PUNCT
ejpam-4868	72	32	x	x	PUNCT
ejpam-4868	72	33	λ	λ	NOUN
ejpam-4868	72	34	log(1	log(1	NOUN
ejpam-4868	72	35	+	+	CCONJ
ejpam-4868	72	36	λt	λt	X
ejpam-4868	72	37	)	)	PUNCT
ejpam-4868	72	38	)	)	PUNCT
ejpam-4868	72	39	.	.	PUNCT
ejpam-4868	73	1	it	it	PRON
ejpam-4868	73	2	can	can	AUX
ejpam-4868	73	3	be	be	AUX
ejpam-4868	73	4	noted	note	VERB
ejpam-4868	73	5	that	that	SCONJ
ejpam-4868	73	6	,	,	PUNCT
ejpam-4868	73	7	lim	lim	PROPN
ejpam-4868	73	8	λ→0	λ→0	PROPN
ejpam-4868	73	9	eixλ	eixλ	PROPN
ejpam-4868	73	10	(	(	PUNCT
ejpam-4868	73	11	t	t	PROPN
ejpam-4868	73	12	)	)	PUNCT
ejpam-4868	73	13	=	=	VERB
ejpam-4868	74	1	cosxt+	cosxt+	NOUN
ejpam-4868	75	1	i	i	PRON
ejpam-4868	75	2	sinxt	sinxt	VERB
ejpam-4868	75	3	.	.	PUNCT
ejpam-4868	76	1	definition	definition	NOUN
ejpam-4868	76	2	6	6	NUM
ejpam-4868	76	3	.	.	PUNCT
ejpam-4868	77	1	[	[	X
ejpam-4868	77	2	4	4	NUM
ejpam-4868	77	3	,	,	PUNCT
ejpam-4868	77	4	8	8	NUM
ejpam-4868	77	5	,	,	PUNCT
ejpam-4868	77	6	14	14	NUM
ejpam-4868	77	7	]	]	PUNCT
ejpam-4868	77	8	the	the	DET
ejpam-4868	77	9	degenerate	degenerate	ADJ
ejpam-4868	77	10	hyperbolic	hyperbolic	ADJ
ejpam-4868	77	11	sine	sine	NOUN
ejpam-4868	77	12	function	function	NOUN
ejpam-4868	77	13	is	be	AUX
ejpam-4868	77	14	defined	define	VERB
ejpam-4868	77	15	by	by	ADP
ejpam-4868	77	16	the	the	DET
ejpam-4868	77	17	relation	relation	NOUN
ejpam-4868	77	18	sinh	sinh	NOUN
ejpam-4868	77	19	(	(	PUNCT
ejpam-4868	77	20	x	x	X
ejpam-4868	77	21	)	)	PUNCT
ejpam-4868	77	22	λ	λ	PROPN
ejpam-4868	77	23	(	(	PUNCT
ejpam-4868	77	24	t	t	PROPN
ejpam-4868	77	25	)	)	PUNCT
ejpam-4868	77	26	=	=	PUNCT
ejpam-4868	77	27	exλ(t)−	exλ(t)−	PROPN
ejpam-4868	77	28	e−x	e−x	PROPN
ejpam-4868	77	29	λ	λ	PROPN
ejpam-4868	77	30	(	(	PUNCT
ejpam-4868	77	31	t	t	PROPN
ejpam-4868	77	32	)	)	PUNCT
ejpam-4868	77	33	2	2	NUM
ejpam-4868	77	34	.	.	PUNCT
ejpam-4868	78	1	(	(	PUNCT
ejpam-4868	78	2	6	6	X
ejpam-4868	78	3	)	)	PUNCT
ejpam-4868	78	4	it	it	PRON
ejpam-4868	78	5	can	can	AUX
ejpam-4868	78	6	be	be	AUX
ejpam-4868	78	7	noted	note	VERB
ejpam-4868	78	8	that	that	SCONJ
ejpam-4868	78	9	,	,	PUNCT
ejpam-4868	78	10	lim	lim	PROPN
ejpam-4868	78	11	λ→0	λ→0	PROPN
ejpam-4868	78	12	sinh	sinh	PROPN
ejpam-4868	78	13	(	(	PUNCT
ejpam-4868	78	14	x	x	X
ejpam-4868	78	15	)	)	PUNCT
ejpam-4868	78	16	λ	λ	PROPN
ejpam-4868	78	17	(	(	PUNCT
ejpam-4868	78	18	t	t	PROPN
ejpam-4868	78	19	)	)	PUNCT
ejpam-4868	78	20	=	=	NOUN
ejpam-4868	78	21	sinhxt	sinhxt	NOUN
ejpam-4868	78	22	.	.	PUNCT
ejpam-4868	79	1	h.	h.	PROPN
ejpam-4868	79	2	j.	j.	PROPN
ejpam-4868	79	3	campos	campos	PROPN
ejpam-4868	79	4	,	,	PUNCT
ejpam-4868	79	5	j.	j.	PROPN
ejpam-4868	79	6	c.	c.	PROPN
ejpam-4868	79	7	fernandez	fernandez	PROPN
ejpam-4868	79	8	,	,	PUNCT
ejpam-4868	79	9	j.	j.	PROPN
ejpam-4868	79	10	b.	b.	PROPN
ejpam-4868	79	11	m.	m.	PROPN
ejpam-4868	79	12	natuil	natuil	PROPN
ejpam-4868	79	13	/	/	SYM
ejpam-4868	79	14	eur	eur	PROPN
ejpam-4868	79	15	.	.	PUNCT
ejpam-4868	80	1	j.	j.	PROPN
ejpam-4868	80	2	pure	pure	PROPN
ejpam-4868	80	3	appl	appl	PROPN
ejpam-4868	80	4	.	.	PROPN
ejpam-4868	80	5	math	math	PROPN
ejpam-4868	80	6	,	,	PUNCT
ejpam-4868	80	7	16	16	NUM
ejpam-4868	80	8	(	(	PUNCT
ejpam-4868	80	9	4	4	NUM
ejpam-4868	80	10	)	)	PUNCT
ejpam-4868	80	11	(	(	PUNCT
ejpam-4868	80	12	2023	2023	NUM
ejpam-4868	80	13	)	)	PUNCT
ejpam-4868	80	14	,	,	PUNCT
ejpam-4868	80	15	2213	2213	NUM
ejpam-4868	80	16	-	-	SYM
ejpam-4868	80	17	2233	2233	NUM
ejpam-4868	80	18	2216	2216	NUM
ejpam-4868	80	19	definition	definition	NOUN
ejpam-4868	80	20	7	7	NUM
ejpam-4868	80	21	.	.	PUNCT
ejpam-4868	81	1	[	[	X
ejpam-4868	81	2	4	4	NUM
ejpam-4868	81	3	,	,	PUNCT
ejpam-4868	81	4	8	8	NUM
ejpam-4868	81	5	,	,	PUNCT
ejpam-4868	81	6	14	14	NUM
ejpam-4868	81	7	]	]	PUNCT
ejpam-4868	81	8	the	the	DET
ejpam-4868	81	9	degenerate	degenerate	ADJ
ejpam-4868	81	10	hyperbolic	hyperbolic	ADJ
ejpam-4868	81	11	cosine	cosine	NOUN
ejpam-4868	81	12	function	function	NOUN
ejpam-4868	81	13	is	be	AUX
ejpam-4868	81	14	defined	define	VERB
ejpam-4868	81	15	by	by	ADP
ejpam-4868	81	16	the	the	DET
ejpam-4868	81	17	relation	relation	NOUN
ejpam-4868	81	18	cosh	cosh	NOUN
ejpam-4868	81	19	(	(	PUNCT
ejpam-4868	81	20	x	x	X
ejpam-4868	81	21	)	)	PUNCT
ejpam-4868	81	22	λ	λ	PROPN
ejpam-4868	81	23	(	(	PUNCT
ejpam-4868	81	24	t	t	PROPN
ejpam-4868	81	25	)	)	PUNCT
ejpam-4868	81	26	=	=	SYM
ejpam-4868	81	27	exλ(t	exλ(t	PROPN
ejpam-4868	81	28	)	)	PUNCT
ejpam-4868	82	1	+	+	NUM
ejpam-4868	82	2	e−x	e−x	PROPN
ejpam-4868	82	3	λ	λ	PROPN
ejpam-4868	82	4	(	(	PUNCT
ejpam-4868	82	5	t	t	PROPN
ejpam-4868	82	6	)	)	PUNCT
ejpam-4868	82	7	2	2	NUM
ejpam-4868	82	8	.	.	PUNCT
ejpam-4868	83	1	(	(	PUNCT
ejpam-4868	83	2	7	7	X
ejpam-4868	83	3	)	)	PUNCT
ejpam-4868	83	4	it	it	PRON
ejpam-4868	83	5	can	can	AUX
ejpam-4868	83	6	be	be	AUX
ejpam-4868	83	7	noted	note	VERB
ejpam-4868	83	8	that	that	SCONJ
ejpam-4868	83	9	,	,	PUNCT
ejpam-4868	83	10	lim	lim	PROPN
ejpam-4868	83	11	λ→0	λ→0	PROPN
ejpam-4868	83	12	cosh	cosh	PROPN
ejpam-4868	83	13	(	(	PUNCT
ejpam-4868	83	14	x	x	X
ejpam-4868	83	15	)	)	PUNCT
ejpam-4868	83	16	λ	λ	PROPN
ejpam-4868	83	17	(	(	PUNCT
ejpam-4868	83	18	t	t	NOUN
ejpam-4868	83	19	)	)	PUNCT
ejpam-4868	83	20	=	=	NOUN
ejpam-4868	83	21	coshxt	coshxt	NOUN
ejpam-4868	83	22	.	.	PUNCT
ejpam-4868	84	1	3	3	X
ejpam-4868	84	2	.	.	NOUN
ejpam-4868	84	3	degenerate	degenerate	ADJ
ejpam-4868	84	4	laplace	laplace	NOUN
ejpam-4868	84	5	-	-	PUNCT
ejpam-4868	84	6	type	type	NOUN
ejpam-4868	84	7	integral	integral	ADJ
ejpam-4868	84	8	transform	transform	NOUN
ejpam-4868	84	9	definition	definition	NOUN
ejpam-4868	84	10	8	8	NUM
ejpam-4868	84	11	.	.	PUNCT
ejpam-4868	85	1	let	let	VERB
ejpam-4868	85	2	λ	λ	X
ejpam-4868	85	3	∈	∈	PROPN
ejpam-4868	85	4	(	(	PUNCT
ejpam-4868	85	5	0,∞	0,∞	NOUN
ejpam-4868	85	6	)	)	PUNCT
ejpam-4868	85	7	,	,	PUNCT
ejpam-4868	85	8	α	α	PROPN
ejpam-4868	85	9	∈	∈	PROPN
ejpam-4868	85	10	z	z	NOUN
ejpam-4868	85	11	and	and	CCONJ
ejpam-4868	85	12	let	let	VERB
ejpam-4868	85	13	f(t	f(t	NOUN
ejpam-4868	85	14	)	)	PUNCT
ejpam-4868	85	15	be	be	VERB
ejpam-4868	85	16	a	a	DET
ejpam-4868	85	17	function	function	NOUN
ejpam-4868	85	18	defined	define	VERB
ejpam-4868	85	19	for	for	ADP
ejpam-4868	85	20	t	t	PROPN
ejpam-4868	85	21	≥	≥	NOUN
ejpam-4868	85	22	0	0	NUM
ejpam-4868	85	23	.	.	PUNCT
ejpam-4868	86	1	then	then	ADV
ejpam-4868	86	2	the	the	DET
ejpam-4868	86	3	integral	integral	ADJ
ejpam-4868	86	4	fα	fα	NOUN
ejpam-4868	86	5	,	,	PUNCT
ejpam-4868	86	6	λ(u	λ(u	PROPN
ejpam-4868	86	7	)	)	PUNCT
ejpam-4868	86	8	=	=	SYM
ejpam-4868	86	9	gα	gα	NOUN
ejpam-4868	86	10	,	,	PUNCT
ejpam-4868	86	11	λ{f(t	λ{f(t	NUM
ejpam-4868	86	12	)	)	PUNCT
ejpam-4868	86	13	}	}	PUNCT
ejpam-4868	86	14	=	=	PUNCT
ejpam-4868	86	15	uα	uα	PROPN
ejpam-4868	86	16	∫	∫	PROPN
ejpam-4868	86	17	∞	∞	PROPN
ejpam-4868	86	18	0	0	PUNCT
ejpam-4868	87	1	e	e	NOUN
ejpam-4868	87	2	−	−	PROPN
ejpam-4868	87	3	1	1	NUM
ejpam-4868	87	4	u	u	NOUN
ejpam-4868	87	5	λ	λ	X
ejpam-4868	87	6	(	(	PUNCT
ejpam-4868	87	7	t)f(t)dt	t)f(t)dt	NOUN
ejpam-4868	87	8	=	=	PUNCT
ejpam-4868	87	9	uα	uα	PROPN
ejpam-4868	87	10	∫	∫	PROPN
ejpam-4868	87	11	∞	∞	PROPN
ejpam-4868	87	12	0	0	NUM
ejpam-4868	88	1	(	(	PUNCT
ejpam-4868	88	2	1	1	NUM
ejpam-4868	88	3	+	+	CCONJ
ejpam-4868	88	4	λt)−	λt)−	PROPN
ejpam-4868	88	5	1	1	X
ejpam-4868	88	6	uλ	uλ	ADP
ejpam-4868	88	7	f(t)dt	f(t)dt	PROPN
ejpam-4868	88	8	,	,	PUNCT
ejpam-4868	88	9	(	(	PUNCT
ejpam-4868	88	10	8)	8)	NUM
ejpam-4868	88	11	is	be	AUX
ejpam-4868	88	12	said	say	VERB
ejpam-4868	88	13	to	to	PART
ejpam-4868	88	14	be	be	AUX
ejpam-4868	88	15	the	the	DET
ejpam-4868	88	16	degenerate	degenerate	ADJ
ejpam-4868	88	17	laplace	laplace	NOUN
ejpam-4868	88	18	-	-	PUNCT
ejpam-4868	88	19	type	type	NOUN
ejpam-4868	88	20	integral	integral	ADJ
ejpam-4868	88	21	transform	transform	NOUN
ejpam-4868	88	22	of	of	ADP
ejpam-4868	88	23	f(t	f(t	NOUN
ejpam-4868	88	24	)	)	PUNCT
ejpam-4868	88	25	.	.	PUNCT
ejpam-4868	89	1	if	if	SCONJ
ejpam-4868	89	2	the	the	DET
ejpam-4868	89	3	improper	improper	ADJ
ejpam-4868	89	4	integral	integral	NOUN
ejpam-4868	89	5	is	be	AUX
ejpam-4868	89	6	convergent	convergent	NOUN
ejpam-4868	89	7	,	,	PUNCT
ejpam-4868	89	8	then	then	ADV
ejpam-4868	89	9	we	we	PRON
ejpam-4868	89	10	say	say	VERB
ejpam-4868	89	11	that	that	SCONJ
ejpam-4868	89	12	the	the	DET
ejpam-4868	89	13	function	function	NOUN
ejpam-4868	89	14	f(t	f(t	PROPN
ejpam-4868	89	15	)	)	PUNCT
ejpam-4868	89	16	possesses	possess	VERB
ejpam-4868	89	17	a	a	DET
ejpam-4868	89	18	degenerate	degenerate	ADJ
ejpam-4868	89	19	laplacetype	laplacetype	NOUN
ejpam-4868	89	20	integral	integral	ADJ
ejpam-4868	89	21	transform	transform	NOUN
ejpam-4868	89	22	.	.	PUNCT
ejpam-4868	90	1	we	we	PRON
ejpam-4868	90	2	note	note	VERB
ejpam-4868	90	3	that	that	SCONJ
ejpam-4868	90	4	lim	lim	PROPN
ejpam-4868	90	5	λ→0	λ→0	PUNCT
ejpam-4868	90	6	gα	gα	PROPN
ejpam-4868	90	7	,	,	PUNCT
ejpam-4868	90	8	λ{f(t	λ{f(t	NUM
ejpam-4868	90	9	)	)	PUNCT
ejpam-4868	90	10	}	}	PUNCT
ejpam-4868	90	11	=	=	SYM
ejpam-4868	90	12	gα{f(t	gα{f(t	NOUN
ejpam-4868	90	13	)	)	PUNCT
ejpam-4868	90	14	}	}	PUNCT
ejpam-4868	90	15	.	.	PUNCT
ejpam-4868	91	1	(	(	PUNCT
ejpam-4868	91	2	9	9	X
ejpam-4868	91	3	)	)	PUNCT
ejpam-4868	91	4	theorem	theorem	NOUN
ejpam-4868	91	5	1	1	NUM
ejpam-4868	91	6	.	.	PUNCT
ejpam-4868	91	7	suppose	suppose	VERB
ejpam-4868	91	8	that	that	SCONJ
ejpam-4868	91	9	f(t	f(t	PROPN
ejpam-4868	91	10	)	)	PUNCT
ejpam-4868	91	11	is	be	AUX
ejpam-4868	91	12	a	a	DET
ejpam-4868	91	13	piecewise	piecewise	NOUN
ejpam-4868	91	14	-	-	PUNCT
ejpam-4868	91	15	continuous	continuous	ADJ
ejpam-4868	91	16	function	function	NOUN
ejpam-4868	91	17	on	on	ADP
ejpam-4868	91	18	the	the	DET
ejpam-4868	91	19	interval	interval	NOUN
ejpam-4868	91	20	[	[	X
ejpam-4868	91	21	0,∞	0,∞	NOUN
ejpam-4868	91	22	)	)	PUNCT
ejpam-4868	91	23	and	and	CCONJ
ejpam-4868	91	24	has	have	VERB
ejpam-4868	91	25	a	a	DET
ejpam-4868	91	26	degenerate	degenerate	ADJ
ejpam-4868	91	27	exponential	exponential	ADJ
ejpam-4868	91	28	order	order	NOUN
ejpam-4868	91	29	at	at	ADP
ejpam-4868	91	30	infinity	infinity	NOUN
ejpam-4868	91	31	with	with	ADP
ejpam-4868	91	32	|f(t)|	|f(t)|	ADJ
ejpam-4868	91	33	≤	≤	ADJ
ejpam-4868	91	34	mecλ	mecλ	NOUN
ejpam-4868	91	35	(	(	PUNCT
ejpam-4868	91	36	t	t	PROPN
ejpam-4868	91	37	)	)	PUNCT
ejpam-4868	91	38	for	for	ADP
ejpam-4868	91	39	t	t	PROPN
ejpam-4868	91	40	>	>	X
ejpam-4868	91	41	p	p	X
ejpam-4868	91	42	,	,	PUNCT
ejpam-4868	91	43	where	where	SCONJ
ejpam-4868	91	44	m	m	PROPN
ejpam-4868	91	45	≥	≥	VERB
ejpam-4868	91	46	0	0	NUM
ejpam-4868	91	47	and	and	CCONJ
ejpam-4868	91	48	p	p	X
ejpam-4868	91	49	,	,	PUNCT
ejpam-4868	91	50	c	c	PROPN
ejpam-4868	91	51	are	be	AUX
ejpam-4868	91	52	constants	constant	NOUN
ejpam-4868	91	53	.	.	PUNCT
ejpam-4868	92	1	then	then	ADV
ejpam-4868	92	2	,	,	PUNCT
ejpam-4868	92	3	gα	gα	ADP
ejpam-4868	92	4	,	,	PUNCT
ejpam-4868	92	5	λ{f(t	λ{f(t	NUM
ejpam-4868	92	6	)	)	PUNCT
ejpam-4868	92	7	}	}	PUNCT
ejpam-4868	92	8	exists	exist	VERB
ejpam-4868	92	9	for	for	ADP
ejpam-4868	92	10	1−	1−	NUM
ejpam-4868	92	11	uc	uc	INTJ
ejpam-4868	92	12	λu	λu	X
ejpam-4868	92	13	>	>	X
ejpam-4868	92	14	1	1	X
ejpam-4868	92	15	.	.	PUNCT
ejpam-4868	92	16	proof	proof	NOUN
ejpam-4868	92	17	.	.	PUNCT
ejpam-4868	93	1	suppose	suppose	VERB
ejpam-4868	93	2	that	that	SCONJ
ejpam-4868	93	3	f(t	f(t	PROPN
ejpam-4868	93	4	)	)	PUNCT
ejpam-4868	93	5	is	be	AUX
ejpam-4868	93	6	a	a	DET
ejpam-4868	93	7	piecewise	piecewise	NOUN
ejpam-4868	93	8	-	-	PUNCT
ejpam-4868	93	9	continuous	continuous	ADJ
ejpam-4868	93	10	function	function	NOUN
ejpam-4868	93	11	on	on	ADP
ejpam-4868	93	12	the	the	DET
ejpam-4868	93	13	interval	interval	NOUN
ejpam-4868	93	14	[	[	X
ejpam-4868	93	15	0,∞	0,∞	NOUN
ejpam-4868	93	16	)	)	PUNCT
ejpam-4868	93	17	and	and	CCONJ
ejpam-4868	93	18	has	have	VERB
ejpam-4868	93	19	a	a	DET
ejpam-4868	93	20	degenerate	degenerate	ADJ
ejpam-4868	93	21	exponential	exponential	ADJ
ejpam-4868	93	22	order	order	NOUN
ejpam-4868	93	23	at	at	ADP
ejpam-4868	93	24	infinity	infinity	NOUN
ejpam-4868	93	25	with	with	ADP
ejpam-4868	93	26	|f(t)|	|f(t)|	ADJ
ejpam-4868	93	27	≤	≤	ADJ
ejpam-4868	93	28	mecλ	mecλ	NOUN
ejpam-4868	93	29	(	(	PUNCT
ejpam-4868	93	30	t	t	PROPN
ejpam-4868	93	31	)	)	PUNCT
ejpam-4868	93	32	.	.	PUNCT
ejpam-4868	94	1	then	then	ADV
ejpam-4868	94	2	uα	uα	PROPN
ejpam-4868	94	3	∫	∫	PROPN
ejpam-4868	94	4	∞	∞	PROPN
ejpam-4868	94	5	0	0	PUNCT
ejpam-4868	95	1	e	e	NOUN
ejpam-4868	95	2	−	−	PROPN
ejpam-4868	95	3	1	1	NUM
ejpam-4868	95	4	u	u	NOUN
ejpam-4868	95	5	λ	λ	X
ejpam-4868	95	6	(	(	PUNCT
ejpam-4868	95	7	t)f(t)dt	t)f(t)dt	NOUN
ejpam-4868	95	8	=	=	PUNCT
ejpam-4868	95	9	uα	uα	PROPN
ejpam-4868	95	10	∫	∫	PROPN
ejpam-4868	95	11	p	p	NOUN
ejpam-4868	95	12	0	0	NUM
ejpam-4868	95	13	e	e	NOUN
ejpam-4868	95	14	−	−	PROPN
ejpam-4868	95	15	1	1	NUM
ejpam-4868	95	16	u	u	NOUN
ejpam-4868	95	17	λ	λ	X
ejpam-4868	95	18	(	(	PUNCT
ejpam-4868	95	19	t)f(t)dt+	t)f(t)dt+	NOUN
ejpam-4868	95	20	uα	uα	PROPN
ejpam-4868	95	21	∫	∫	PROPN
ejpam-4868	95	22	∞	∞	PROPN
ejpam-4868	95	23	p	p	PROPN
ejpam-4868	95	24	e	e	X
ejpam-4868	95	25	−	−	PROPN
ejpam-4868	95	26	1	1	NUM
ejpam-4868	95	27	u	u	NOUN
ejpam-4868	95	28	λ	λ	PROPN
ejpam-4868	95	29	(	(	PUNCT
ejpam-4868	95	30	t)f(t)dt	t)f(t)dt	NOUN
ejpam-4868	95	31	.	.	PUNCT
ejpam-4868	96	1	(	(	PUNCT
ejpam-4868	96	2	10	10	NUM
ejpam-4868	96	3	)	)	PUNCT
ejpam-4868	96	4	since	since	SCONJ
ejpam-4868	96	5	the	the	DET
ejpam-4868	96	6	function	function	NOUN
ejpam-4868	96	7	f(t	f(t	NOUN
ejpam-4868	96	8	)	)	PUNCT
ejpam-4868	96	9	is	be	AUX
ejpam-4868	96	10	piecewise	piecewise	NOUN
ejpam-4868	96	11	-	-	PUNCT
ejpam-4868	96	12	continuous	continuous	ADJ
ejpam-4868	96	13	in	in	ADP
ejpam-4868	96	14	every	every	DET
ejpam-4868	96	15	finite	finite	ADJ
ejpam-4868	96	16	interval	interval	NOUN
ejpam-4868	96	17	0	0	NUM
ejpam-4868	96	18	≤	≤	NUM
ejpam-4868	96	19	t	t	NOUN
ejpam-4868	96	20	≤	≤	ADJ
ejpam-4868	96	21	p	p	NOUN
ejpam-4868	96	22	,	,	PUNCT
ejpam-4868	96	23	the	the	DET
ejpam-4868	96	24	first	first	ADJ
ejpam-4868	96	25	integral	integral	NOUN
ejpam-4868	96	26	on	on	ADP
ejpam-4868	96	27	the	the	DET
ejpam-4868	96	28	right	right	ADJ
ejpam-4868	96	29	-	-	PUNCT
ejpam-4868	96	30	hand	hand	NOUN
ejpam-4868	96	31	side	side	NOUN
ejpam-4868	96	32	of	of	ADP
ejpam-4868	96	33	equation	equation	NOUN
ejpam-4868	96	34	(	(	PUNCT
ejpam-4868	96	35	10	10	NUM
ejpam-4868	96	36	)	)	PUNCT
ejpam-4868	96	37	exists	exist	VERB
ejpam-4868	96	38	.	.	PUNCT
ejpam-4868	97	1	since∣∣∣∣e−	since∣∣∣∣e−	NOUN
ejpam-4868	97	2	1	1	NUM
ejpam-4868	97	3	u	u	NOUN
ejpam-4868	97	4	λ	λ	PROPN
ejpam-4868	97	5	(	(	PUNCT
ejpam-4868	97	6	t)f(t	t)f(t	VERB
ejpam-4868	97	7	)	)	PUNCT
ejpam-4868	97	8	∣∣∣∣≤	∣∣∣∣≤	PRON
ejpam-4868	98	1	me	i	PRON
ejpam-4868	98	2	−	−	NUM
ejpam-4868	98	3	1	1	NUM
ejpam-4868	98	4	u	u	NOUN
ejpam-4868	98	5	λ	λ	X
ejpam-4868	98	6	(	(	PUNCT
ejpam-4868	98	7	t)ecλ	t)ecλ	PROPN
ejpam-4868	98	8	(	(	PUNCT
ejpam-4868	98	9	t	t	PROPN
ejpam-4868	98	10	)	)	PUNCT
ejpam-4868	98	11	for	for	ADP
ejpam-4868	98	12	t	t	PROPN
ejpam-4868	98	13	>	>	X
ejpam-4868	98	14	p	p	X
ejpam-4868	98	15	,	,	PUNCT
ejpam-4868	98	16	we	we	PRON
ejpam-4868	98	17	have∣∣∣∣uα	have∣∣∣∣uα	VERB
ejpam-4868	98	18	∫	∫	NOUN
ejpam-4868	98	19	∞	∞	PROPN
ejpam-4868	98	20	p	p	PROPN
ejpam-4868	98	21	e	e	NOUN
ejpam-4868	98	22	−	−	PROPN
ejpam-4868	98	23	1	1	NUM
ejpam-4868	98	24	u	u	NOUN
ejpam-4868	98	25	λ	λ	PROPN
ejpam-4868	98	26	(	(	PUNCT
ejpam-4868	98	27	t)f(t)dt	t)f(t)dt	PROPN
ejpam-4868	98	28	∣∣∣∣≤uα	∣∣∣∣≤uα	PROPN
ejpam-4868	98	29	∫	∫	PROPN
ejpam-4868	99	1	∞	∞	PROPN
ejpam-4868	99	2	p	p	PROPN
ejpam-4868	99	3	∣∣∣∣e−	∣∣∣∣e−	PROPN
ejpam-4868	99	4	1	1	NUM
ejpam-4868	99	5	u	u	NOUN
ejpam-4868	99	6	λ	λ	PROPN
ejpam-4868	99	7	(	(	PUNCT
ejpam-4868	99	8	t)f(t	t)f(t	ADJ
ejpam-4868	99	9	)	)	PUNCT
ejpam-4868	99	10	∣∣∣∣dt	∣∣∣∣dt	NOUN
ejpam-4868	99	11	≤uα	≤uα	PROPN
ejpam-4868	99	12	∫	∫	PROPN
ejpam-4868	99	13	∞	∞	PROPN
ejpam-4868	99	14	p	p	PROPN
ejpam-4868	99	15	e	e	X
ejpam-4868	99	16	−	−	PROPN
ejpam-4868	99	17	1	1	NUM
ejpam-4868	99	18	u	u	NOUN
ejpam-4868	99	19	λ	λ	X
ejpam-4868	99	20	(	(	PUNCT
ejpam-4868	99	21	t)mecλ	t)mecλ	PROPN
ejpam-4868	99	22	(	(	PUNCT
ejpam-4868	99	23	t)dt	t)dt	PROPN
ejpam-4868	99	24	=	=	PRON
ejpam-4868	99	25	muα	muα	NOUN
ejpam-4868	99	26	∫	∫	PROPN
ejpam-4868	99	27	∞	∞	PROPN
ejpam-4868	99	28	p	p	NOUN
ejpam-4868	99	29	(	(	PUNCT
ejpam-4868	99	30	1	1	NUM
ejpam-4868	99	31	+	+	CCONJ
ejpam-4868	99	32	λt	λt	ADP
ejpam-4868	99	33	)	)	PUNCT
ejpam-4868	99	34	−1+uc	−1+uc	PROPN
ejpam-4868	99	35	uλ	uλ	ADP
ejpam-4868	99	36	dt	dt	PROPN
ejpam-4868	99	37	h.	h.	PROPN
ejpam-4868	99	38	j.	j.	PROPN
ejpam-4868	99	39	campos	campos	PROPN
ejpam-4868	99	40	,	,	PUNCT
ejpam-4868	99	41	j.	j.	PROPN
ejpam-4868	99	42	c.	c.	PROPN
ejpam-4868	99	43	fernandez	fernandez	PROPN
ejpam-4868	99	44	,	,	PUNCT
ejpam-4868	99	45	j.	j.	PROPN
ejpam-4868	99	46	b.	b.	PROPN
ejpam-4868	99	47	m.	m.	PROPN
ejpam-4868	99	48	natuil	natuil	PROPN
ejpam-4868	99	49	/	/	SYM
ejpam-4868	99	50	eur	eur	PROPN
ejpam-4868	99	51	.	.	PUNCT
ejpam-4868	100	1	j.	j.	PROPN
ejpam-4868	100	2	pure	pure	PROPN
ejpam-4868	100	3	appl	appl	PROPN
ejpam-4868	100	4	.	.	PROPN
ejpam-4868	100	5	math	math	PROPN
ejpam-4868	100	6	,	,	PUNCT
ejpam-4868	100	7	16	16	NUM
ejpam-4868	100	8	(	(	PUNCT
ejpam-4868	100	9	4	4	NUM
ejpam-4868	100	10	)	)	PUNCT
ejpam-4868	100	11	(	(	PUNCT
ejpam-4868	100	12	2023	2023	NUM
ejpam-4868	100	13	)	)	PUNCT
ejpam-4868	100	14	,	,	PUNCT
ejpam-4868	100	15	2213	2213	NUM
ejpam-4868	100	16	-	-	SYM
ejpam-4868	100	17	2233	2233	NUM
ejpam-4868	100	18	2217	2217	NUM
ejpam-4868	100	19	=	=	NOUN
ejpam-4868	100	20	muα	muα	NOUN
ejpam-4868	100	21	lim	lim	PROPN
ejpam-4868	100	22	r→∞	r→∞	PUNCT
ejpam-4868	100	23	∫	∫	PROPN
ejpam-4868	100	24	r	r	PROPN
ejpam-4868	100	25	p	p	PROPN
ejpam-4868	100	26	(	(	PUNCT
ejpam-4868	100	27	1	1	NUM
ejpam-4868	100	28	+	+	CCONJ
ejpam-4868	100	29	λt)−	λt)−	PROPN
ejpam-4868	100	30	(	(	PUNCT
ejpam-4868	100	31	1−uc	1−uc	NUM
ejpam-4868	100	32	uλ	uλ	NOUN
ejpam-4868	100	33	)	)	PUNCT
ejpam-4868	100	34	dt	dt	X
ejpam-4868	101	1	=	=	SYM
ejpam-4868	101	2	muα	muα	PROPN
ejpam-4868	101	3	λ	λ	PROPN
ejpam-4868	101	4	lim	lim	PROPN
ejpam-4868	101	5	r→∞	r→∞	NUM
ejpam-4868	101	6	[	[	PUNCT
ejpam-4868	101	7	(	(	PUNCT
ejpam-4868	101	8	1	1	NUM
ejpam-4868	101	9	+	+	NUM
ejpam-4868	101	10	λt)1−	λt)1−	PROPN
ejpam-4868	101	11	(	(	PUNCT
ejpam-4868	101	12	1−uc	1−uc	NUM
ejpam-4868	101	13	uλ	uλ	NOUN
ejpam-4868	101	14	)	)	PUNCT
ejpam-4868	101	15	1	1	NUM
ejpam-4868	101	16	uλ	uλ	NOUN
ejpam-4868	101	17	(	(	PUNCT
ejpam-4868	101	18	uλ−	uλ−	X
ejpam-4868	101	19	(	(	PUNCT
ejpam-4868	101	20	1−	1−	NUM
ejpam-4868	101	21	uc	uc	NOUN
ejpam-4868	101	22	)	)	PUNCT
ejpam-4868	101	23	)	)	PUNCT
ejpam-4868	101	24	]	]	PUNCT
ejpam-4868	101	25	∣∣∣∣r	∣∣∣∣r	NOUN
ejpam-4868	101	26	p	p	NOUN
ejpam-4868	101	27	=	=	NOUN
ejpam-4868	101	28	muα+1	muα+1	NOUN
ejpam-4868	101	29	lim	lim	NOUN
ejpam-4868	101	30	r→∞	r→∞	X
ejpam-4868	101	31	[	[	PUNCT
ejpam-4868	101	32	(	(	PUNCT
ejpam-4868	101	33	1	1	NUM
ejpam-4868	101	34	+	+	CCONJ
ejpam-4868	101	35	λ(r))1−	λ(r))1−	ADJ
ejpam-4868	101	36	(	(	PUNCT
ejpam-4868	101	37	1−uc	1−uc	NUM
ejpam-4868	101	38	uλ	uλ	NOUN
ejpam-4868	101	39	)	)	PUNCT
ejpam-4868	101	40	uλ−	uλ−	NUM
ejpam-4868	101	41	1	1	NUM
ejpam-4868	102	1	+	+	CCONJ
ejpam-4868	102	2	uc	uc	ADJ
ejpam-4868	102	3	−	−	PROPN
ejpam-4868	102	4	(	(	PUNCT
ejpam-4868	102	5	1	1	NUM
ejpam-4868	102	6	+	+	CCONJ
ejpam-4868	102	7	λ(p	λ(p	PROPN
ejpam-4868	102	8	)	)	PUNCT
ejpam-4868	102	9	)	)	PUNCT
ejpam-4868	103	1	1−	1−	NUM
ejpam-4868	103	2	(	(	PUNCT
ejpam-4868	103	3	1−uc	1−uc	NUM
ejpam-4868	103	4	uλ	uλ	NOUN
ejpam-4868	103	5	)	)	PUNCT
ejpam-4868	103	6	uλ−	uλ−	NUM
ejpam-4868	103	7	1	1	NUM
ejpam-4868	104	1	+	+	CCONJ
ejpam-4868	104	2	uc	uc	X
ejpam-4868	104	3	]	]	X
ejpam-4868	104	4	=	=	SYM
ejpam-4868	104	5	muα+1	muα+1	NOUN
ejpam-4868	104	6	1−	1−	NUM
ejpam-4868	104	7	uλ−	uλ−	NUM
ejpam-4868	104	8	uc	uc	NOUN
ejpam-4868	104	9	(	(	PUNCT
ejpam-4868	104	10	1	1	NUM
ejpam-4868	104	11	+	+	NUM
ejpam-4868	104	12	pλ)1−	pλ)1−	NOUN
ejpam-4868	104	13	(	(	PUNCT
ejpam-4868	104	14	1−uc	1−uc	NUM
ejpam-4868	104	15	uλ	uλ	ADP
ejpam-4868	104	16	)	)	PUNCT
ejpam-4868	104	17	<	<	X
ejpam-4868	104	18	∞	∞	PROPN
ejpam-4868	104	19	,	,	PUNCT
ejpam-4868	104	20	for	for	ADP
ejpam-4868	104	21	1−	1−	NUM
ejpam-4868	104	22	uc	uc	PROPN
ejpam-4868	104	23	uλ	uλ	X
ejpam-4868	104	24	>	>	X
ejpam-4868	104	25	1	1	X
ejpam-4868	104	26	.	.	PUNCT
ejpam-4868	105	1	hence	hence	ADV
ejpam-4868	105	2	,	,	PUNCT
ejpam-4868	105	3	the	the	DET
ejpam-4868	105	4	second	second	ADJ
ejpam-4868	105	5	integral	integral	ADJ
ejpam-4868	105	6	converges	converge	NOUN
ejpam-4868	105	7	for	for	ADP
ejpam-4868	105	8	1−	1−	NUM
ejpam-4868	105	9	uc	uc	PROPN
ejpam-4868	105	10	uλ	uλ	X
ejpam-4868	105	11	>	>	X
ejpam-4868	105	12	1	1	X
ejpam-4868	105	13	.	.	PUNCT
ejpam-4868	106	1	since	since	SCONJ
ejpam-4868	106	2	the	the	DET
ejpam-4868	106	3	first	first	ADJ
ejpam-4868	106	4	integral	integral	NOUN
ejpam-4868	106	5	on	on	ADP
ejpam-4868	106	6	the	the	DET
ejpam-4868	106	7	right	right	ADJ
ejpam-4868	106	8	hand	hand	NOUN
ejpam-4868	106	9	side	side	NOUN
ejpam-4868	106	10	of	of	ADP
ejpam-4868	106	11	equation	equation	NOUN
ejpam-4868	106	12	(	(	PUNCT
ejpam-4868	106	13	10	10	NUM
ejpam-4868	106	14	)	)	PUNCT
ejpam-4868	106	15	converges	converge	NOUN
ejpam-4868	106	16	and	and	CCONJ
ejpam-4868	106	17	the	the	DET
ejpam-4868	106	18	second	second	ADJ
ejpam-4868	106	19	integral	integral	ADJ
ejpam-4868	106	20	on	on	ADP
ejpam-4868	106	21	the	the	DET
ejpam-4868	106	22	right	right	ADJ
ejpam-4868	106	23	hand	hand	NOUN
ejpam-4868	106	24	side	side	NOUN
ejpam-4868	106	25	of	of	ADP
ejpam-4868	106	26	equation	equation	NOUN
ejpam-4868	106	27	(	(	PUNCT
ejpam-4868	106	28	10	10	NUM
ejpam-4868	106	29	)	)	PUNCT
ejpam-4868	106	30	also	also	ADV
ejpam-4868	106	31	converges	converge	VERB
ejpam-4868	106	32	for	for	ADP
ejpam-4868	106	33	1−	1−	NUM
ejpam-4868	106	34	uc	uc	PROPN
ejpam-4868	106	35	uλ	uλ	X
ejpam-4868	106	36	>	>	X
ejpam-4868	106	37	1	1	X
ejpam-4868	106	38	.	.	PUNCT
ejpam-4868	107	1	thus	thus	ADV
ejpam-4868	107	2	f(t	f(t	NOUN
ejpam-4868	107	3	)	)	PUNCT
ejpam-4868	107	4	has	have	VERB
ejpam-4868	107	5	a	a	DET
ejpam-4868	107	6	degenerate	degenerate	ADJ
ejpam-4868	107	7	laplace	laplace	NOUN
ejpam-4868	107	8	-	-	PUNCT
ejpam-4868	107	9	type	type	NOUN
ejpam-4868	107	10	integral	integral	ADJ
ejpam-4868	107	11	transform	transform	NOUN
ejpam-4868	107	12	,	,	PUNCT
ejpam-4868	107	13	for	for	ADP
ejpam-4868	107	14	1−	1−	NUM
ejpam-4868	107	15	uc	uc	PROPN
ejpam-4868	107	16	uλ	uλ	X
ejpam-4868	107	17	>	>	X
ejpam-4868	107	18	1	1	X
ejpam-4868	107	19	.	.	PUNCT
ejpam-4868	107	20	theorem	theorem	NOUN
ejpam-4868	107	21	2	2	NUM
ejpam-4868	107	22	.	.	PUNCT
ejpam-4868	108	1	let	let	VERB
ejpam-4868	108	2	a	a	DET
ejpam-4868	108	3	,	,	PUNCT
ejpam-4868	108	4	b	b	X
ejpam-4868	108	5	∈	∈	NOUN
ejpam-4868	108	6	r	r	NOUN
ejpam-4868	108	7	and	and	CCONJ
ejpam-4868	108	8	let	let	VERB
ejpam-4868	108	9	f(t	f(t	NOUN
ejpam-4868	108	10	)	)	PUNCT
ejpam-4868	108	11	and	and	CCONJ
ejpam-4868	108	12	h(t	h(t	PROPN
ejpam-4868	108	13	)	)	PUNCT
ejpam-4868	108	14	be	be	AUX
ejpam-4868	108	15	function	function	NOUN
ejpam-4868	109	1	whose	whose	DET
ejpam-4868	109	2	degenerate	degenerate	ADJ
ejpam-4868	109	3	laplace	laplace	NOUN
ejpam-4868	109	4	-	-	PUNCT
ejpam-4868	109	5	type	type	NOUN
ejpam-4868	109	6	integral	integral	ADJ
ejpam-4868	109	7	exists	exist	NOUN
ejpam-4868	109	8	.	.	PUNCT
ejpam-4868	110	1	then	then	ADV
ejpam-4868	110	2	gα	gα	ADP
ejpam-4868	110	3	,	,	PUNCT
ejpam-4868	110	4	λ{af(t	λ{af(t	ADJ
ejpam-4868	110	5	)	)	PUNCT
ejpam-4868	110	6	+	+	NUM
ejpam-4868	110	7	bh(t	bh(t	NOUN
ejpam-4868	110	8	)	)	PUNCT
ejpam-4868	110	9	}	}	PUNCT
ejpam-4868	110	10	=	=	SYM
ejpam-4868	110	11	agα	agα	NOUN
ejpam-4868	110	12	,	,	PUNCT
ejpam-4868	110	13	λ{f(t)}+	λ{f(t)}+	VERB
ejpam-4868	110	14	bgα	bgα	ADJ
ejpam-4868	110	15	,	,	PUNCT
ejpam-4868	110	16	λ{h(t	λ{h(t	NUM
ejpam-4868	110	17	)	)	PUNCT
ejpam-4868	110	18	}	}	PUNCT
ejpam-4868	110	19	.	.	PUNCT
ejpam-4868	111	1	proof	proof	NOUN
ejpam-4868	111	2	.	.	PUNCT
ejpam-4868	112	1	let	let	VERB
ejpam-4868	112	2	a	a	DET
ejpam-4868	112	3	,	,	PUNCT
ejpam-4868	112	4	b	b	X
ejpam-4868	112	5	∈	∈	PROPN
ejpam-4868	112	6	r	r	NOUN
ejpam-4868	112	7	and	and	CCONJ
ejpam-4868	112	8	f(t	f(t	NOUN
ejpam-4868	112	9	)	)	PUNCT
ejpam-4868	112	10	and	and	CCONJ
ejpam-4868	112	11	h(t	h(t	PROPN
ejpam-4868	112	12	)	)	PUNCT
ejpam-4868	112	13	be	be	VERB
ejpam-4868	112	14	any	any	DET
ejpam-4868	112	15	function	function	NOUN
ejpam-4868	112	16	whose	whose	DET
ejpam-4868	112	17	degenerate	degenerate	ADJ
ejpam-4868	112	18	laplace	laplace	NOUN
ejpam-4868	112	19	-	-	PUNCT
ejpam-4868	112	20	type	type	NOUN
ejpam-4868	112	21	integral	integral	ADJ
ejpam-4868	112	22	exists	exist	NOUN
ejpam-4868	112	23	.	.	PUNCT
ejpam-4868	113	1	then	then	ADV
ejpam-4868	113	2	gα	gα	ADP
ejpam-4868	113	3	,	,	PUNCT
ejpam-4868	113	4	λ{af(t	λ{af(t	ADJ
ejpam-4868	113	5	)	)	PUNCT
ejpam-4868	113	6	+	+	NUM
ejpam-4868	113	7	bh(t	bh(t	NOUN
ejpam-4868	113	8	)	)	PUNCT
ejpam-4868	113	9	}	}	PUNCT
ejpam-4868	114	1	=	=	X
ejpam-4868	114	2	uα	uα	PROPN
ejpam-4868	114	3	∫	∫	PROPN
ejpam-4868	114	4	∞	∞	PROPN
ejpam-4868	114	5	0	0	PUNCT
ejpam-4868	115	1	e	e	NOUN
ejpam-4868	115	2	−	−	PROPN
ejpam-4868	115	3	1	1	NUM
ejpam-4868	115	4	u	u	NOUN
ejpam-4868	115	5	λ	λ	PROPN
ejpam-4868	115	6	(	(	PUNCT
ejpam-4868	115	7	t	t	NOUN
ejpam-4868	115	8	)	)	PUNCT
ejpam-4868	115	9	[	[	PUNCT
ejpam-4868	115	10	af(t	af(t	X
ejpam-4868	115	11	)	)	PUNCT
ejpam-4868	115	12	+	+	CCONJ
ejpam-4868	115	13	bh(t	bh(t	NOUN
ejpam-4868	115	14	)	)	PUNCT
ejpam-4868	115	15	]	]	PUNCT
ejpam-4868	115	16	dt	dt	X
ejpam-4868	116	1	=	=	NOUN
ejpam-4868	116	2	auα	auα	PROPN
ejpam-4868	116	3	∫	∫	PROPN
ejpam-4868	116	4	∞	∞	NUM
ejpam-4868	116	5	0	0	PUNCT
ejpam-4868	116	6	e	e	NOUN
ejpam-4868	116	7	−	−	PROPN
ejpam-4868	116	8	1	1	NUM
ejpam-4868	116	9	u	u	NOUN
ejpam-4868	116	10	λ	λ	X
ejpam-4868	116	11	(	(	PUNCT
ejpam-4868	116	12	t)f(t)dt+	t)f(t)dt+	PRON
ejpam-4868	116	13	buα	buα	VERB
ejpam-4868	116	14	∫	∫	PROPN
ejpam-4868	116	15	∞	∞	PROPN
ejpam-4868	116	16	0	0	PUNCT
ejpam-4868	117	1	e	e	NOUN
ejpam-4868	117	2	−	−	PROPN
ejpam-4868	117	3	1	1	NUM
ejpam-4868	117	4	u	u	NOUN
ejpam-4868	117	5	λ	λ	PROPN
ejpam-4868	117	6	(	(	PUNCT
ejpam-4868	117	7	t)h(t)dt	t)h(t)dt	PROPN
ejpam-4868	117	8	=	=	SYM
ejpam-4868	117	9	agα	agα	PROPN
ejpam-4868	117	10	,	,	PUNCT
ejpam-4868	117	11	λ{f(t)}+	λ{f(t)}+	VERB
ejpam-4868	117	12	bgα	bgα	ADJ
ejpam-4868	117	13	,	,	PUNCT
ejpam-4868	117	14	λ{h(t	λ{h(t	NUM
ejpam-4868	117	15	)	)	PUNCT
ejpam-4868	117	16	}	}	PUNCT
ejpam-4868	117	17	.	.	PUNCT
ejpam-4868	118	1	thus	thus	ADV
ejpam-4868	118	2	,	,	PUNCT
ejpam-4868	118	3	linearity	linearity	NOUN
ejpam-4868	118	4	property	property	NOUN
ejpam-4868	118	5	of	of	ADP
ejpam-4868	118	6	the	the	DET
ejpam-4868	118	7	degenerate	degenerate	ADJ
ejpam-4868	118	8	laplace	laplace	NOUN
ejpam-4868	118	9	-	-	PUNCT
ejpam-4868	118	10	type	type	NOUN
ejpam-4868	118	11	integral	integral	ADJ
ejpam-4868	118	12	transform	transform	NOUN
ejpam-4868	118	13	holds	hold	VERB
ejpam-4868	118	14	true	true	ADJ
ejpam-4868	118	15	.	.	PUNCT
ejpam-4868	119	1	4	4	X
ejpam-4868	119	2	.	.	NOUN
ejpam-4868	119	3	degenerate	degenerate	ADJ
ejpam-4868	119	4	laplace	laplace	NOUN
ejpam-4868	119	5	-	-	PUNCT
ejpam-4868	119	6	type	type	NOUN
ejpam-4868	119	7	integral	integral	ADJ
ejpam-4868	119	8	transform	transform	NOUN
ejpam-4868	119	9	of	of	ADP
ejpam-4868	119	10	some	some	DET
ejpam-4868	119	11	elementary	elementary	ADJ
ejpam-4868	119	12	functions	function	NOUN
ejpam-4868	119	13	in	in	ADP
ejpam-4868	119	14	this	this	DET
ejpam-4868	119	15	section	section	NOUN
ejpam-4868	119	16	the	the	DET
ejpam-4868	119	17	researcher	researcher	NOUN
ejpam-4868	119	18	establish	establish	VERB
ejpam-4868	119	19	the	the	DET
ejpam-4868	119	20	degenerate	degenerate	ADJ
ejpam-4868	119	21	laplace	laplace	NOUN
ejpam-4868	119	22	-	-	PUNCT
ejpam-4868	119	23	type	type	NOUN
ejpam-4868	119	24	integral	integral	ADJ
ejpam-4868	119	25	transform	transform	NOUN
ejpam-4868	119	26	of	of	ADP
ejpam-4868	119	27	some	some	DET
ejpam-4868	119	28	elementary	elementary	ADJ
ejpam-4868	119	29	functions	function	NOUN
ejpam-4868	119	30	.	.	PUNCT
ejpam-4868	120	1	theorem	theorem	NOUN
ejpam-4868	120	2	3	3	NUM
ejpam-4868	120	3	.	.	PUNCT
ejpam-4868	121	1	the	the	DET
ejpam-4868	121	2	degenerate	degenerate	ADJ
ejpam-4868	121	3	laplace	laplace	NOUN
ejpam-4868	121	4	-	-	PUNCT
ejpam-4868	121	5	type	type	NOUN
ejpam-4868	121	6	integral	integral	ADJ
ejpam-4868	121	7	transform	transform	NOUN
ejpam-4868	121	8	of	of	ADP
ejpam-4868	121	9	the	the	DET
ejpam-4868	121	10	function	function	NOUN
ejpam-4868	121	11	f(t	f(t	NOUN
ejpam-4868	121	12	)	)	PUNCT
ejpam-4868	122	1	=	=	SYM
ejpam-4868	122	2	1	1	NUM
ejpam-4868	122	3	is	be	AUX
ejpam-4868	122	4	given	give	VERB
ejpam-4868	122	5	by	by	ADP
ejpam-4868	122	6	gα	gα	NOUN
ejpam-4868	122	7	,	,	PUNCT
ejpam-4868	122	8	λ{1	λ{1	PROPN
ejpam-4868	122	9	}	}	PUNCT
ejpam-4868	122	10	=	=	NOUN
ejpam-4868	122	11	uα+1	uα+1	NOUN
ejpam-4868	122	12	1−	1−	NUM
ejpam-4868	122	13	λu	λu	X
ejpam-4868	122	14	,	,	PUNCT
ejpam-4868	122	15	for	for	ADP
ejpam-4868	122	16	λu	λu	X
ejpam-4868	122	17	<	<	X
ejpam-4868	122	18	1	1	NUM
ejpam-4868	122	19	.	.	PUNCT
ejpam-4868	123	1	(	(	PUNCT
ejpam-4868	123	2	11	11	NUM
ejpam-4868	123	3	)	)	PUNCT
ejpam-4868	123	4	h.	h.	PROPN
ejpam-4868	123	5	j.	j.	PROPN
ejpam-4868	123	6	campos	campos	PROPN
ejpam-4868	123	7	,	,	PUNCT
ejpam-4868	123	8	j.	j.	PROPN
ejpam-4868	123	9	c.	c.	PROPN
ejpam-4868	123	10	fernandez	fernandez	PROPN
ejpam-4868	123	11	,	,	PUNCT
ejpam-4868	123	12	j.	j.	PROPN
ejpam-4868	123	13	b.	b.	PROPN
ejpam-4868	123	14	m.	m.	PROPN
ejpam-4868	123	15	natuil	natuil	PROPN
ejpam-4868	123	16	/	/	SYM
ejpam-4868	123	17	eur	eur	PROPN
ejpam-4868	123	18	.	.	PUNCT
ejpam-4868	124	1	j.	j.	PROPN
ejpam-4868	124	2	pure	pure	PROPN
ejpam-4868	124	3	appl	appl	PROPN
ejpam-4868	124	4	.	.	PROPN
ejpam-4868	124	5	math	math	PROPN
ejpam-4868	124	6	,	,	PUNCT
ejpam-4868	124	7	16	16	NUM
ejpam-4868	124	8	(	(	PUNCT
ejpam-4868	124	9	4	4	NUM
ejpam-4868	124	10	)	)	PUNCT
ejpam-4868	124	11	(	(	PUNCT
ejpam-4868	124	12	2023	2023	NUM
ejpam-4868	124	13	)	)	PUNCT
ejpam-4868	124	14	,	,	PUNCT
ejpam-4868	124	15	2213	2213	NUM
ejpam-4868	124	16	-	-	SYM
ejpam-4868	124	17	2233	2233	NUM
ejpam-4868	124	18	2218	2218	NUM
ejpam-4868	124	19	proof	proof	NOUN
ejpam-4868	124	20	.	.	PUNCT
ejpam-4868	125	1	by	by	ADP
ejpam-4868	125	2	definition	definition	NOUN
ejpam-4868	125	3	8	8	NUM
ejpam-4868	125	4	,	,	PUNCT
ejpam-4868	125	5	for	for	ADP
ejpam-4868	125	6	f(t	f(t	NOUN
ejpam-4868	125	7	)	)	PUNCT
ejpam-4868	125	8	=	=	SYM
ejpam-4868	125	9	1	1	NUM
ejpam-4868	125	10	,	,	PUNCT
ejpam-4868	125	11	we	we	PRON
ejpam-4868	125	12	have	have	VERB
ejpam-4868	125	13	gα	gα	ADP
ejpam-4868	125	14	,	,	PUNCT
ejpam-4868	125	15	λ{1	λ{1	PROPN
ejpam-4868	125	16	}	}	PUNCT
ejpam-4868	125	17	=	=	NOUN
ejpam-4868	125	18	uα	uα	PROPN
ejpam-4868	125	19	∫	∫	PROPN
ejpam-4868	125	20	∞	∞	PROPN
ejpam-4868	125	21	0	0	PUNCT
ejpam-4868	126	1	e	e	NOUN
ejpam-4868	126	2	−	−	PROPN
ejpam-4868	126	3	1	1	NUM
ejpam-4868	126	4	u	u	NOUN
ejpam-4868	126	5	λ	λ	X
ejpam-4868	126	6	(	(	PUNCT
ejpam-4868	126	7	t)dt	t)dt	PROPN
ejpam-4868	126	8	=	=	SYM
ejpam-4868	126	9	uα	uα	PROPN
ejpam-4868	126	10	lim	lim	PROPN
ejpam-4868	126	11	r→∞	r→∞	PUNCT
ejpam-4868	126	12	∫	∫	PROPN
ejpam-4868	126	13	r	r	NOUN
ejpam-4868	126	14	0	0	NUM
ejpam-4868	126	15	(	(	PUNCT
ejpam-4868	126	16	1	1	NUM
ejpam-4868	126	17	+	+	CCONJ
ejpam-4868	126	18	λt)−	λt)−	PROPN
ejpam-4868	126	19	1	1	NUM
ejpam-4868	126	20	uλdt	uλdt	NOUN
ejpam-4868	126	21	=	=	NOUN
ejpam-4868	126	22	uα+1	uα+1	NUM
ejpam-4868	126	23	lim	lim	NOUN
ejpam-4868	126	24	r→∞	r→∞	NUM
ejpam-4868	126	25	[	[	PUNCT
ejpam-4868	126	26	(	(	PUNCT
ejpam-4868	126	27	1	1	NUM
ejpam-4868	126	28	+	+	CCONJ
ejpam-4868	126	29	λt)1−	λt)1−	PROPN
ejpam-4868	126	30	1	1	NUM
ejpam-4868	126	31	uλ	uλ	NOUN
ejpam-4868	126	32	(	(	PUNCT
ejpam-4868	126	33	λu−	λu−	NOUN
ejpam-4868	126	34	1	1	NUM
ejpam-4868	126	35	)	)	PUNCT
ejpam-4868	126	36	]	]	PUNCT
ejpam-4868	127	1	∣∣∣∣∣	∣∣∣∣∣	SYM
ejpam-4868	127	2	r	r	NOUN
ejpam-4868	127	3	0	0	PUNCT
ejpam-4868	127	4	=	=	NOUN
ejpam-4868	127	5	uα+1	uα+1	NOUN
ejpam-4868	127	6	lim	lim	NOUN
ejpam-4868	127	7	r→∞	r→∞	NUM
ejpam-4868	127	8	[	[	PUNCT
ejpam-4868	127	9	(	(	PUNCT
ejpam-4868	127	10	1	1	NUM
ejpam-4868	127	11	+	+	CCONJ
ejpam-4868	127	12	λr)1−	λr)1−	NOUN
ejpam-4868	127	13	1	1	NUM
ejpam-4868	127	14	uλ	uλ	NOUN
ejpam-4868	127	15	(	(	PUNCT
ejpam-4868	127	16	λu−	λu−	NUM
ejpam-4868	127	17	1	1	NUM
ejpam-4868	127	18	)	)	PUNCT
ejpam-4868	127	19	−	−	NOUN
ejpam-4868	127	20	1	1	NUM
ejpam-4868	127	21	(	(	PUNCT
ejpam-4868	127	22	λu−	λu−	NOUN
ejpam-4868	127	23	1	1	NUM
ejpam-4868	127	24	)	)	PUNCT
ejpam-4868	127	25	]	]	PUNCT
ejpam-4868	128	1	=	=	PUNCT
ejpam-4868	128	2	uα+1	uα+1	NOUN
ejpam-4868	128	3	1−	1−	NUM
ejpam-4868	128	4	λu	λu	X
ejpam-4868	128	5	,	,	PUNCT
ejpam-4868	128	6	for	for	ADP
ejpam-4868	128	7	λu	λu	X
ejpam-4868	128	8	<	<	X
ejpam-4868	128	9	1	1	NUM
ejpam-4868	128	10	.	.	PUNCT
ejpam-4868	128	11	remark	remark	NOUN
ejpam-4868	128	12	1	1	NUM
ejpam-4868	128	13	.	.	PUNCT
ejpam-4868	129	1	it	it	PRON
ejpam-4868	129	2	is	be	AUX
ejpam-4868	129	3	clear	clear	ADJ
ejpam-4868	129	4	from	from	ADP
ejpam-4868	129	5	theorem	theorem	ADJ
ejpam-4868	129	6	3	3	NUM
ejpam-4868	129	7	and	and	CCONJ
ejpam-4868	129	8	equation	equation	NOUN
ejpam-4868	129	9	(	(	PUNCT
ejpam-4868	129	10	9	9	NUM
ejpam-4868	129	11	)	)	PUNCT
ejpam-4868	129	12	that	that	PRON
ejpam-4868	129	13	lim	lim	PROPN
ejpam-4868	130	1	λ→0	λ→0	PUNCT
ejpam-4868	130	2	gα	gα	PROPN
ejpam-4868	130	3	,	,	PUNCT
ejpam-4868	130	4	λ{1	λ{1	PROPN
ejpam-4868	130	5	}	}	PUNCT
ejpam-4868	130	6	=	=	SYM
ejpam-4868	130	7	lim	lim	PROPN
ejpam-4868	130	8	λ→0	λ→0	PUNCT
ejpam-4868	130	9	uα+1	uα+1	NUM
ejpam-4868	130	10	1−	1−	NUM
ejpam-4868	130	11	λu	λu	X
ejpam-4868	130	12	=	=	PUNCT
ejpam-4868	130	13	uα+1	uα+1	PROPN
ejpam-4868	130	14	=	=	SYM
ejpam-4868	130	15	gα{1	gα{1	NOUN
ejpam-4868	130	16	}	}	PUNCT
ejpam-4868	130	17	.	.	PUNCT
ejpam-4868	131	1	theorem	theorem	VERB
ejpam-4868	131	2	4	4	NUM
ejpam-4868	131	3	.	.	PUNCT
ejpam-4868	132	1	the	the	DET
ejpam-4868	132	2	degenerate	degenerate	ADJ
ejpam-4868	132	3	laplace	laplace	NOUN
ejpam-4868	132	4	-	-	PUNCT
ejpam-4868	132	5	type	type	NOUN
ejpam-4868	132	6	integral	integral	ADJ
ejpam-4868	132	7	transform	transform	NOUN
ejpam-4868	132	8	of	of	ADP
ejpam-4868	132	9	the	the	DET
ejpam-4868	132	10	function	function	NOUN
ejpam-4868	132	11	f(t	f(t	PROPN
ejpam-4868	132	12	)	)	PUNCT
ejpam-4868	133	1	=	=	SYM
ejpam-4868	133	2	t	t	PROPN
ejpam-4868	133	3	is	be	AUX
ejpam-4868	133	4	given	give	VERB
ejpam-4868	133	5	by	by	ADP
ejpam-4868	133	6	gα	gα	NOUN
ejpam-4868	133	7	,	,	PUNCT
ejpam-4868	133	8	λ{t	λ{t	X
ejpam-4868	133	9	}	}	PUNCT
ejpam-4868	133	10	=	=	SYM
ejpam-4868	133	11	uα+2	uα+2	PROPN
ejpam-4868	133	12	(	(	PUNCT
ejpam-4868	133	13	1−	1−	NUM
ejpam-4868	133	14	uλ)(1−	uλ)(1−	ADJ
ejpam-4868	133	15	2uλ	2uλ	NOUN
ejpam-4868	133	16	)	)	PUNCT
ejpam-4868	133	17	,	,	PUNCT
ejpam-4868	133	18	for	for	ADP
ejpam-4868	133	19	2uλ	2uλ	NOUN
ejpam-4868	133	20	<	<	X
ejpam-4868	133	21	1	1	NUM
ejpam-4868	133	22	.	.	PUNCT
ejpam-4868	133	23	(	(	PUNCT
ejpam-4868	133	24	12	12	NUM
ejpam-4868	133	25	)	)	PUNCT
ejpam-4868	133	26	proof	proof	NOUN
ejpam-4868	133	27	.	.	PUNCT
ejpam-4868	134	1	by	by	ADP
ejpam-4868	134	2	definition	definition	NOUN
ejpam-4868	134	3	8	8	NUM
ejpam-4868	134	4	,	,	PUNCT
ejpam-4868	134	5	for	for	ADP
ejpam-4868	134	6	f(t	f(t	NOUN
ejpam-4868	134	7	)	)	PUNCT
ejpam-4868	134	8	=	=	SYM
ejpam-4868	134	9	t	t	PROPN
ejpam-4868	134	10	,	,	PUNCT
ejpam-4868	134	11	we	we	PRON
ejpam-4868	134	12	have	have	VERB
ejpam-4868	134	13	gα	gα	ADP
ejpam-4868	134	14	,	,	PUNCT
ejpam-4868	134	15	λ{t	λ{t	X
ejpam-4868	134	16	}	}	PUNCT
ejpam-4868	134	17	=	=	SYM
ejpam-4868	134	18	uα	uα	PROPN
ejpam-4868	134	19	∫	∫	PROPN
ejpam-4868	134	20	∞	∞	PROPN
ejpam-4868	134	21	0	0	PUNCT
ejpam-4868	135	1	e	e	NOUN
ejpam-4868	135	2	−	−	PROPN
ejpam-4868	135	3	1	1	NUM
ejpam-4868	135	4	u	u	NOUN
ejpam-4868	135	5	λ	λ	X
ejpam-4868	135	6	(	(	PUNCT
ejpam-4868	135	7	t)tdt	t)tdt	X
ejpam-4868	135	8	=	=	PUNCT
ejpam-4868	135	9	uα	uα	PROPN
ejpam-4868	135	10	λ2	λ2	PROPN
ejpam-4868	135	11	lim	lim	PROPN
ejpam-4868	135	12	r→∞	r→∞	NUM
ejpam-4868	135	13	[	[	PUNCT
ejpam-4868	135	14	(	(	PUNCT
ejpam-4868	135	15	1	1	NUM
ejpam-4868	135	16	+	+	NUM
ejpam-4868	135	17	λt)2−	λt)2−	NOUN
ejpam-4868	135	18	1	1	NUM
ejpam-4868	135	19	uλ	uλ	ADP
ejpam-4868	135	20	1	1	NUM
ejpam-4868	135	21	uλ(2uλ−	uλ(2uλ−	PROPN
ejpam-4868	135	22	1	1	NUM
ejpam-4868	135	23	)	)	PUNCT
ejpam-4868	135	24	−	−	PROPN
ejpam-4868	135	25	(	(	PUNCT
ejpam-4868	135	26	1	1	NUM
ejpam-4868	135	27	+	+	CCONJ
ejpam-4868	135	28	λt)1−	λt)1−	PROPN
ejpam-4868	135	29	1	1	NUM
ejpam-4868	135	30	uλ	uλ	ADP
ejpam-4868	135	31	1	1	NUM
ejpam-4868	135	32	uλ(uλ−	uλ(uλ−	NOUN
ejpam-4868	135	33	1	1	NUM
ejpam-4868	135	34	)	)	PUNCT
ejpam-4868	135	35	]	]	PUNCT
ejpam-4868	136	1	∣∣∣∣∣	∣∣∣∣∣	SYM
ejpam-4868	136	2	r	r	NOUN
ejpam-4868	136	3	0	0	NUM
ejpam-4868	136	4	=	=	NOUN
ejpam-4868	136	5	uα+1	uα+1	NOUN
ejpam-4868	136	6	λ	λ	PROPN
ejpam-4868	136	7	lim	lim	PROPN
ejpam-4868	136	8	r→∞	r→∞	NUM
ejpam-4868	137	1	[	[	X
ejpam-4868	137	2	(	(	PUNCT
ejpam-4868	137	3	(	(	PUNCT
ejpam-4868	137	4	1	1	NUM
ejpam-4868	137	5	+	+	NUM
ejpam-4868	137	6	λr	λr	NOUN
ejpam-4868	137	7	)	)	PUNCT
ejpam-4868	137	8	2uλ−1	2uλ−1	NUM
ejpam-4868	137	9	uλ	uλ	ADP
ejpam-4868	137	10	2uλ−	2uλ−	NUM
ejpam-4868	137	11	1	1	NUM
ejpam-4868	137	12	−	−	PROPN
ejpam-4868	137	13	(	(	PUNCT
ejpam-4868	137	14	1	1	NUM
ejpam-4868	137	15	+	+	NUM
ejpam-4868	137	16	λr	λr	NOUN
ejpam-4868	137	17	)	)	PUNCT
ejpam-4868	137	18	uλ−1	uλ−1	NOUN
ejpam-4868	137	19	uλ	uλ	ADP
ejpam-4868	137	20	uλ−	uλ−	NUM
ejpam-4868	137	21	1	1	NUM
ejpam-4868	137	22	)	)	PUNCT
ejpam-4868	137	23	−	−	PROPN
ejpam-4868	138	1	(	(	PUNCT
ejpam-4868	138	2	1	1	NUM
ejpam-4868	138	3	2uλ−	2uλ−	NUM
ejpam-4868	138	4	1	1	NUM
ejpam-4868	138	5	−	−	NUM
ejpam-4868	138	6	1	1	NUM
ejpam-4868	138	7	uλ−	uλ−	NUM
ejpam-4868	138	8	1	1	NUM
ejpam-4868	138	9	)	)	PUNCT
ejpam-4868	138	10	]	]	PUNCT
ejpam-4868	139	1	=	=	SYM
ejpam-4868	139	2	uα+2	uα+2	PROPN
ejpam-4868	139	3	(	(	PUNCT
ejpam-4868	139	4	1−	1−	NUM
ejpam-4868	139	5	uλ)(1−	uλ)(1−	ADJ
ejpam-4868	139	6	2uλ	2uλ	NOUN
ejpam-4868	139	7	)	)	PUNCT
ejpam-4868	139	8	,	,	PUNCT
ejpam-4868	139	9	for	for	ADP
ejpam-4868	139	10	2uλ	2uλ	ADJ
ejpam-4868	139	11	<	<	X
ejpam-4868	139	12	1	1	X
ejpam-4868	139	13	.	.	NOUN
ejpam-4868	139	14	remark	remark	NOUN
ejpam-4868	139	15	2	2	NUM
ejpam-4868	139	16	.	.	PUNCT
ejpam-4868	140	1	it	it	PRON
ejpam-4868	140	2	is	be	AUX
ejpam-4868	140	3	clear	clear	ADJ
ejpam-4868	140	4	from	from	ADP
ejpam-4868	140	5	theorem	theorem	ADJ
ejpam-4868	140	6	4	4	NUM
ejpam-4868	140	7	and	and	CCONJ
ejpam-4868	140	8	equation	equation	NOUN
ejpam-4868	140	9	(	(	PUNCT
ejpam-4868	140	10	9	9	NUM
ejpam-4868	140	11	)	)	PUNCT
ejpam-4868	141	1	that	that	PRON
ejpam-4868	141	2	lim	lim	PROPN
ejpam-4868	141	3	λ→0	λ→0	PUNCT
ejpam-4868	141	4	gα	gα	PROPN
ejpam-4868	141	5	,	,	PUNCT
ejpam-4868	141	6	λ{t	λ{t	X
ejpam-4868	141	7	}	}	PUNCT
ejpam-4868	141	8	=	=	SYM
ejpam-4868	141	9	lim	lim	PROPN
ejpam-4868	141	10	λ→0	λ→0	PUNCT
ejpam-4868	141	11	[	[	PUNCT
ejpam-4868	141	12	uα+2	uα+2	PROPN
ejpam-4868	141	13	(	(	PUNCT
ejpam-4868	141	14	1−	1−	NUM
ejpam-4868	141	15	uλ)(1−	uλ)(1−	ADJ
ejpam-4868	141	16	2uλ	2uλ	NOUN
ejpam-4868	141	17	)	)	PUNCT
ejpam-4868	141	18	]	]	PUNCT
ejpam-4868	142	1	=	=	PUNCT
ejpam-4868	142	2	uα+2	uα+2	PROPN
ejpam-4868	142	3	=	=	PUNCT
ejpam-4868	142	4	gα{t	gα{t	PROPN
ejpam-4868	142	5	}	}	PUNCT
ejpam-4868	142	6	.	.	PUNCT
ejpam-4868	143	1	theorem	theorem	NOUN
ejpam-4868	143	2	5	5	NUM
ejpam-4868	143	3	.	.	PUNCT
ejpam-4868	144	1	the	the	DET
ejpam-4868	144	2	degenerate	degenerate	ADJ
ejpam-4868	144	3	laplace	laplace	NOUN
ejpam-4868	144	4	-	-	PUNCT
ejpam-4868	144	5	type	type	NOUN
ejpam-4868	144	6	integral	integral	ADJ
ejpam-4868	144	7	transform	transform	NOUN
ejpam-4868	144	8	of	of	ADP
ejpam-4868	144	9	the	the	DET
ejpam-4868	144	10	function	function	NOUN
ejpam-4868	144	11	f(t	f(t	PROPN
ejpam-4868	144	12	)	)	PUNCT
ejpam-4868	144	13	=	=	SYM
ejpam-4868	144	14	tn	tn	NOUN
ejpam-4868	144	15	is	be	AUX
ejpam-4868	144	16	given	give	VERB
ejpam-4868	144	17	by	by	ADP
ejpam-4868	144	18	gα	gα	NOUN
ejpam-4868	144	19	,	,	PUNCT
ejpam-4868	144	20	λ{tn	λ{tn	PROPN
ejpam-4868	144	21	}	}	PUNCT
ejpam-4868	144	22	=	=	SYM
ejpam-4868	144	23	n!uα+1+n	n!uα+1+n	PROPN
ejpam-4868	144	24	(	(	PUNCT
ejpam-4868	144	25	1−	1−	NUM
ejpam-4868	144	26	uλ	uλ	NOUN
ejpam-4868	144	27	)	)	PUNCT
ejpam-4868	144	28	·	·	PUNCT
ejpam-4868	144	29	·	·	PUNCT
ejpam-4868	144	30	·	·	PUNCT
ejpam-4868	145	1	(	(	PUNCT
ejpam-4868	145	2	1−	1−	NUM
ejpam-4868	145	3	(	(	PUNCT
ejpam-4868	145	4	n+	n+	NUM
ejpam-4868	145	5	1)uλ	1)uλ	NUM
ejpam-4868	145	6	)	)	PUNCT
ejpam-4868	145	7	,	,	PUNCT
ejpam-4868	145	8	for	for	ADP
ejpam-4868	145	9	(	(	PUNCT
ejpam-4868	145	10	n−	n−	NOUN
ejpam-4868	145	11	k	k	PROPN
ejpam-4868	145	12	+	+	CCONJ
ejpam-4868	145	13	1)uλ	1)uλ	PROPN
ejpam-4868	145	14	<	<	X
ejpam-4868	145	15	1	1	NUM
ejpam-4868	145	16	.	.	PUNCT
ejpam-4868	145	17	(	(	PUNCT
ejpam-4868	145	18	13	13	NUM
ejpam-4868	145	19	)	)	PUNCT
ejpam-4868	145	20	h.	h.	PROPN
ejpam-4868	145	21	j.	j.	PROPN
ejpam-4868	145	22	campos	campos	PROPN
ejpam-4868	145	23	,	,	PUNCT
ejpam-4868	145	24	j.	j.	PROPN
ejpam-4868	145	25	c.	c.	PROPN
ejpam-4868	145	26	fernandez	fernandez	PROPN
ejpam-4868	145	27	,	,	PUNCT
ejpam-4868	145	28	j.	j.	PROPN
ejpam-4868	145	29	b.	b.	PROPN
ejpam-4868	145	30	m.	m.	PROPN
ejpam-4868	145	31	natuil	natuil	PROPN
ejpam-4868	145	32	/	/	SYM
ejpam-4868	145	33	eur	eur	PROPN
ejpam-4868	145	34	.	.	PUNCT
ejpam-4868	146	1	j.	j.	PROPN
ejpam-4868	146	2	pure	pure	PROPN
ejpam-4868	146	3	appl	appl	PROPN
ejpam-4868	146	4	.	.	PROPN
ejpam-4868	146	5	math	math	PROPN
ejpam-4868	146	6	,	,	PUNCT
ejpam-4868	146	7	16	16	NUM
ejpam-4868	146	8	(	(	PUNCT
ejpam-4868	146	9	4	4	NUM
ejpam-4868	146	10	)	)	PUNCT
ejpam-4868	146	11	(	(	PUNCT
ejpam-4868	146	12	2023	2023	NUM
ejpam-4868	146	13	)	)	PUNCT
ejpam-4868	146	14	,	,	PUNCT
ejpam-4868	146	15	2213	2213	NUM
ejpam-4868	146	16	-	-	SYM
ejpam-4868	146	17	2233	2233	NUM
ejpam-4868	146	18	2219	2219	NUM
ejpam-4868	146	19	proof	proof	NOUN
ejpam-4868	146	20	.	.	PUNCT
ejpam-4868	147	1	by	by	ADP
ejpam-4868	147	2	definition	definition	NOUN
ejpam-4868	147	3	8	8	NUM
ejpam-4868	147	4	,	,	PUNCT
ejpam-4868	147	5	for	for	ADP
ejpam-4868	147	6	f(t	f(t	NOUN
ejpam-4868	147	7	)	)	PUNCT
ejpam-4868	147	8	=	=	SYM
ejpam-4868	147	9	tn	tn	PROPN
ejpam-4868	147	10	,	,	PUNCT
ejpam-4868	147	11	we	we	PRON
ejpam-4868	147	12	obtain	obtain	VERB
ejpam-4868	147	13	gα	gα	ADP
ejpam-4868	147	14	,	,	PUNCT
ejpam-4868	147	15	λ{tn	λ{tn	PROPN
ejpam-4868	147	16	}	}	PUNCT
ejpam-4868	148	1	=	=	NOUN
ejpam-4868	148	2	uα	uα	PROPN
ejpam-4868	148	3	∫	∫	PROPN
ejpam-4868	148	4	∞	∞	PROPN
ejpam-4868	148	5	0	0	NUM
ejpam-4868	148	6	tne	tne	NOUN
ejpam-4868	148	7	−	−	PROPN
ejpam-4868	148	8	1	1	NUM
ejpam-4868	148	9	u	u	NOUN
ejpam-4868	148	10	λ	λ	X
ejpam-4868	148	11	(	(	PUNCT
ejpam-4868	148	12	t)dt	t)dt	PROPN
ejpam-4868	148	13	=	=	SYM
ejpam-4868	148	14	uα	uα	PROPN
ejpam-4868	148	15	λn+1	λn+1	PROPN
ejpam-4868	148	16	n∑	n∑	PROPN
ejpam-4868	148	17	k=0	k=0	PROPN
ejpam-4868	148	18	(	(	PUNCT
ejpam-4868	148	19	n	n	X
ejpam-4868	148	20	k	k	NOUN
ejpam-4868	148	21	)	)	PUNCT
ejpam-4868	148	22	(	(	PUNCT
ejpam-4868	148	23	−1)k	−1)k	PROPN
ejpam-4868	148	24	lim	lim	PROPN
ejpam-4868	148	25	r→∞	r→∞	PRON
ejpam-4868	148	26	[	[	PUNCT
ejpam-4868	148	27	(	(	PUNCT
ejpam-4868	148	28	1	1	NUM
ejpam-4868	148	29	+	+	NUM
ejpam-4868	148	30	λt)n−k−	λt)n−k−	PROPN
ejpam-4868	148	31	1	1	NUM
ejpam-4868	148	32	uλ	uλ	ADP
ejpam-4868	148	33	+1	+1	PROPN
ejpam-4868	148	34	1	1	NUM
ejpam-4868	148	35	uλ(nuλ−	uλ(nuλ−	NOUN
ejpam-4868	148	36	kuλ−	kuλ−	PROPN
ejpam-4868	148	37	1	1	NUM
ejpam-4868	148	38	+	+	SYM
ejpam-4868	148	39	uλ	uλ	NOUN
ejpam-4868	148	40	)	)	PUNCT
ejpam-4868	148	41	]	]	PUNCT
ejpam-4868	148	42	∣∣∣∣∣	∣∣∣∣∣	SYM
ejpam-4868	148	43	r	r	NOUN
ejpam-4868	148	44	0	0	NUM
ejpam-4868	148	45	=	=	NOUN
ejpam-4868	148	46	uα+1	uα+1	NOUN
ejpam-4868	148	47	λn	λn	PROPN
ejpam-4868	148	48	n∑	n∑	PROPN
ejpam-4868	148	49	k=0	k=0	PROPN
ejpam-4868	148	50	(	(	PUNCT
ejpam-4868	148	51	n	n	X
ejpam-4868	148	52	k	k	NOUN
ejpam-4868	148	53	)	)	PUNCT
ejpam-4868	148	54	(	(	PUNCT
ejpam-4868	148	55	−1)k	−1)k	PROPN
ejpam-4868	148	56	[	[	PUNCT
ejpam-4868	148	57	−	−	PROPN
ejpam-4868	148	58	1	1	NUM
ejpam-4868	148	59	nuλ−	nuλ−	PROPN
ejpam-4868	148	60	kuλ−	kuλ−	PROPN
ejpam-4868	148	61	1	1	NUM
ejpam-4868	148	62	+	+	CCONJ
ejpam-4868	148	63	uλ	uλ	ADV
ejpam-4868	148	64	]	]	X
ejpam-4868	148	65	,	,	PUNCT
ejpam-4868	148	66	for	for	ADP
ejpam-4868	148	67	(	(	PUNCT
ejpam-4868	148	68	n−	n−	NOUN
ejpam-4868	148	69	k	k	PROPN
ejpam-4868	149	1	+	+	CCONJ
ejpam-4868	149	2	1)uλ	1)uλ	PROPN
ejpam-4868	149	3	<	<	X
ejpam-4868	149	4	1	1	NUM
ejpam-4868	149	5	=	=	NOUN
ejpam-4868	149	6	uα+1	uα+1	NOUN
ejpam-4868	149	7	λn	λn	NOUN
ejpam-4868	149	8	[	[	PUNCT
ejpam-4868	149	9	n!unλn	n!unλn	NOUN
ejpam-4868	149	10	(	(	PUNCT
ejpam-4868	149	11	1−	1−	NUM
ejpam-4868	149	12	(	(	PUNCT
ejpam-4868	149	13	1)uλ)(1−	1)uλ)(1−	NUM
ejpam-4868	149	14	(	(	PUNCT
ejpam-4868	149	15	2)uλ	2)uλ	NOUN
ejpam-4868	149	16	)	)	PUNCT
ejpam-4868	149	17	·	·	PUNCT
ejpam-4868	149	18	·	·	PUNCT
ejpam-4868	149	19	·	·	PUNCT
ejpam-4868	149	20	(	(	PUNCT
ejpam-4868	149	21	1−	1−	NUM
ejpam-4868	149	22	(	(	PUNCT
ejpam-4868	149	23	n)uλ)(1−	n)uλ)(1−	X
ejpam-4868	149	24	(	(	PUNCT
ejpam-4868	149	25	n+	n+	NUM
ejpam-4868	149	26	1)uλ	1)uλ	NUM
ejpam-4868	149	27	)	)	PUNCT
ejpam-4868	149	28	]	]	PUNCT
ejpam-4868	149	29	,	,	PUNCT
ejpam-4868	149	30	for	for	ADP
ejpam-4868	149	31	(	(	PUNCT
ejpam-4868	149	32	n−	n−	NOUN
ejpam-4868	149	33	k	k	PROPN
ejpam-4868	150	1	+	+	CCONJ
ejpam-4868	150	2	1)uλ	1)uλ	PROPN
ejpam-4868	150	3	<	<	X
ejpam-4868	150	4	1	1	NUM
ejpam-4868	150	5	=	=	SYM
ejpam-4868	150	6	n!uα+1+n	n!uα+1+n	PROPN
ejpam-4868	150	7	(	(	PUNCT
ejpam-4868	150	8	1−	1−	NUM
ejpam-4868	150	9	uλ)(1−	uλ)(1−	ADJ
ejpam-4868	150	10	2uλ	2uλ	NOUN
ejpam-4868	150	11	)	)	PUNCT
ejpam-4868	150	12	·	·	PUNCT
ejpam-4868	150	13	·	·	PUNCT
ejpam-4868	150	14	·	·	PUNCT
ejpam-4868	151	1	(	(	PUNCT
ejpam-4868	151	2	1−	1−	NUM
ejpam-4868	151	3	nuλ)(1−	nuλ)(1−	PROPN
ejpam-4868	151	4	(	(	PUNCT
ejpam-4868	151	5	n+	n+	NUM
ejpam-4868	151	6	1)uλ	1)uλ	NUM
ejpam-4868	151	7	)	)	PUNCT
ejpam-4868	151	8	,	,	PUNCT
ejpam-4868	151	9	for	for	ADP
ejpam-4868	151	10	(	(	PUNCT
ejpam-4868	151	11	n−	n−	NOUN
ejpam-4868	151	12	k	k	PROPN
ejpam-4868	151	13	+	+	CCONJ
ejpam-4868	152	1	1)uλ	1)uλ	PROPN
ejpam-4868	152	2	<	<	X
ejpam-4868	152	3	1	1	NUM
ejpam-4868	152	4	.	.	PUNCT
ejpam-4868	152	5	remark	remark	NOUN
ejpam-4868	152	6	3	3	NUM
ejpam-4868	152	7	.	.	PUNCT
ejpam-4868	153	1	it	it	PRON
ejpam-4868	153	2	is	be	AUX
ejpam-4868	153	3	clear	clear	ADJ
ejpam-4868	153	4	from	from	ADP
ejpam-4868	153	5	theorem	theorem	ADJ
ejpam-4868	153	6	5	5	NUM
ejpam-4868	153	7	and	and	CCONJ
ejpam-4868	153	8	equation	equation	NOUN
ejpam-4868	153	9	(	(	PUNCT
ejpam-4868	153	10	9	9	NUM
ejpam-4868	153	11	)	)	PUNCT
ejpam-4868	154	1	that	that	PRON
ejpam-4868	154	2	lim	lim	PROPN
ejpam-4868	154	3	λ→0	λ→0	PUNCT
ejpam-4868	154	4	gα	gα	NOUN
ejpam-4868	154	5	,	,	PUNCT
ejpam-4868	154	6	λ{tn	λ{tn	PROPN
ejpam-4868	154	7	}	}	PUNCT
ejpam-4868	154	8	=	=	SYM
ejpam-4868	154	9	lim	lim	PROPN
ejpam-4868	154	10	λ→0	λ→0	PUNCT
ejpam-4868	154	11	[	[	PUNCT
ejpam-4868	154	12	n!uα+1+n	n!uα+1+n	PROPN
ejpam-4868	154	13	(	(	PUNCT
ejpam-4868	154	14	1−	1−	NUM
ejpam-4868	154	15	uλ)(1−	uλ)(1−	ADJ
ejpam-4868	154	16	2uλ	2uλ	NOUN
ejpam-4868	154	17	)	)	PUNCT
ejpam-4868	154	18	·	·	PUNCT
ejpam-4868	154	19	·	·	PUNCT
ejpam-4868	154	20	·	·	PUNCT
ejpam-4868	154	21	(	(	PUNCT
ejpam-4868	154	22	1−	1−	NUM
ejpam-4868	154	23	(	(	PUNCT
ejpam-4868	154	24	n+	n+	NUM
ejpam-4868	154	25	1)uλ	1)uλ	NUM
ejpam-4868	154	26	)	)	PUNCT
ejpam-4868	154	27	]	]	PUNCT
ejpam-4868	155	1	=	=	PUNCT
ejpam-4868	155	2	n!uα+1+n	n!uα+1+n	ADJ
ejpam-4868	155	3	=	=	SYM
ejpam-4868	155	4	gα{tn	gα{tn	ADJ
ejpam-4868	155	5	}	}	PUNCT
ejpam-4868	155	6	.	.	PUNCT
ejpam-4868	156	1	theorem	theorem	NOUN
ejpam-4868	156	2	6	6	NUM
ejpam-4868	156	3	.	.	PUNCT
ejpam-4868	157	1	the	the	DET
ejpam-4868	157	2	degenerate	degenerate	ADJ
ejpam-4868	157	3	laplace	laplace	NOUN
ejpam-4868	157	4	-	-	PUNCT
ejpam-4868	157	5	type	type	NOUN
ejpam-4868	157	6	integral	integral	ADJ
ejpam-4868	157	7	transform	transform	NOUN
ejpam-4868	157	8	of	of	ADP
ejpam-4868	157	9	a	a	DET
ejpam-4868	157	10	function	function	NOUN
ejpam-4868	157	11	f(t	f(t	NOUN
ejpam-4868	157	12	)	)	PUNCT
ejpam-4868	157	13	=	=	SYM
ejpam-4868	157	14	eaλ(t	eaλ(t	PROPN
ejpam-4868	157	15	)	)	PUNCT
ejpam-4868	157	16	is	be	AUX
ejpam-4868	157	17	given	give	VERB
ejpam-4868	157	18	by	by	ADP
ejpam-4868	157	19	gα	gα	NOUN
ejpam-4868	157	20	,	,	PUNCT
ejpam-4868	157	21	λ{eaλ(t	λ{eaλ(t	NOUN
ejpam-4868	157	22	)	)	PUNCT
ejpam-4868	157	23	}	}	PUNCT
ejpam-4868	157	24	=	=	PUNCT
ejpam-4868	157	25	uα+1	uα+1	NOUN
ejpam-4868	157	26	1−	1−	NUM
ejpam-4868	157	27	u(a+	u(a+	ADJ
ejpam-4868	157	28	λ	λ	NOUN
ejpam-4868	157	29	)	)	PUNCT
ejpam-4868	157	30	,	,	PUNCT
ejpam-4868	157	31	for	for	ADP
ejpam-4868	157	32	(	(	PUNCT
ejpam-4868	157	33	a+	a+	X
ejpam-4868	157	34	λ)u	λ)u	X
ejpam-4868	157	35	<	<	X
ejpam-4868	157	36	1	1	NUM
ejpam-4868	157	37	.	.	PUNCT
ejpam-4868	157	38	(	(	PUNCT
ejpam-4868	157	39	14	14	NUM
ejpam-4868	157	40	)	)	PUNCT
ejpam-4868	157	41	proof	proof	NOUN
ejpam-4868	157	42	.	.	PUNCT
ejpam-4868	158	1	by	by	ADP
ejpam-4868	158	2	definition	definition	NOUN
ejpam-4868	158	3	8	8	NUM
ejpam-4868	158	4	,	,	PUNCT
ejpam-4868	158	5	for	for	ADP
ejpam-4868	158	6	f(t	f(t	NOUN
ejpam-4868	158	7	)	)	PUNCT
ejpam-4868	158	8	=	=	SYM
ejpam-4868	158	9	eaλ(t	eaλ(t	PROPN
ejpam-4868	158	10	)	)	PUNCT
ejpam-4868	158	11	,	,	PUNCT
ejpam-4868	158	12	we	we	PRON
ejpam-4868	158	13	set	set	VERB
ejpam-4868	158	14	gα	gα	ADP
ejpam-4868	158	15	,	,	PUNCT
ejpam-4868	158	16	λ{eaλ(t	λ{eaλ(t	NOUN
ejpam-4868	158	17	)	)	PUNCT
ejpam-4868	158	18	}	}	PUNCT
ejpam-4868	159	1	=	=	SYM
ejpam-4868	159	2	uα	uα	PROPN
ejpam-4868	159	3	∫	∫	PROPN
ejpam-4868	159	4	∞	∞	PROPN
ejpam-4868	159	5	0	0	PUNCT
ejpam-4868	160	1	e	e	NOUN
ejpam-4868	160	2	−	−	PROPN
ejpam-4868	160	3	1	1	NUM
ejpam-4868	160	4	u	u	NOUN
ejpam-4868	160	5	λ	λ	PROPN
ejpam-4868	160	6	(	(	PUNCT
ejpam-4868	160	7	t	t	PROPN
ejpam-4868	160	8	)	)	PUNCT
ejpam-4868	160	9	[	[	PUNCT
ejpam-4868	160	10	eaλ(t	eaλ(t	PROPN
ejpam-4868	160	11	)	)	PUNCT
ejpam-4868	160	12	]	]	PUNCT
ejpam-4868	160	13	dt	dt	X
ejpam-4868	161	1	=	=	PUNCT
ejpam-4868	161	2	uα	uα	PROPN
ejpam-4868	161	3	lim	lim	PROPN
ejpam-4868	161	4	r→∞	r→∞	PUNCT
ejpam-4868	161	5	∫	∫	PROPN
ejpam-4868	162	1	r	r	NOUN
ejpam-4868	162	2	0	0	NUM
ejpam-4868	162	3	(	(	PUNCT
ejpam-4868	162	4	1	1	NUM
ejpam-4868	162	5	+	+	CCONJ
ejpam-4868	162	6	λt	λt	X
ejpam-4868	162	7	)	)	PUNCT
ejpam-4868	162	8	ua−1	ua−1	NOUN
ejpam-4868	162	9	uλ	uλ	NOUN
ejpam-4868	162	10	dt	dt	PROPN
ejpam-4868	162	11	.	.	PUNCT
ejpam-4868	163	1	=	=	NOUN
ejpam-4868	163	2	uα+1	uα+1	NUM
ejpam-4868	163	3	lim	lim	NOUN
ejpam-4868	163	4	r→∞	r→∞	NUM
ejpam-4868	163	5	[	[	PUNCT
ejpam-4868	163	6	(	(	PUNCT
ejpam-4868	163	7	1	1	NUM
ejpam-4868	163	8	+	+	CCONJ
ejpam-4868	163	9	λt	λt	X
ejpam-4868	163	10	)	)	PUNCT
ejpam-4868	163	11	ua−1+uλ	ua−1+uλ	ADJ
ejpam-4868	163	12	uλ	uλ	ADP
ejpam-4868	163	13	ua−	ua−	NUM
ejpam-4868	163	14	1	1	NUM
ejpam-4868	163	15	+	+	NUM
ejpam-4868	163	16	uλ	uλ	X
ejpam-4868	163	17	]	]	X
ejpam-4868	163	18	∣∣∣∣∣	∣∣∣∣∣	NOUN
ejpam-4868	163	19	r	r	NOUN
ejpam-4868	163	20	0	0	PUNCT
ejpam-4868	163	21	=	=	NOUN
ejpam-4868	163	22	uα+1	uα+1	NOUN
ejpam-4868	163	23	[	[	PUNCT
ejpam-4868	163	24	−	−	PROPN
ejpam-4868	163	25	1	1	NUM
ejpam-4868	163	26	u(a+	u(a+	NOUN
ejpam-4868	163	27	λ)−	λ)−	ADV
ejpam-4868	163	28	1	1	NUM
ejpam-4868	163	29	]	]	PUNCT
ejpam-4868	163	30	,	,	PUNCT
ejpam-4868	163	31	for	for	ADP
ejpam-4868	163	32	(	(	PUNCT
ejpam-4868	163	33	a+	a+	X
ejpam-4868	163	34	λ)u	λ)u	X
ejpam-4868	163	35	<	<	X
ejpam-4868	163	36	1	1	NUM
ejpam-4868	163	37	=	=	NOUN
ejpam-4868	163	38	uα+1	uα+1	NOUN
ejpam-4868	163	39	1−	1−	NUM
ejpam-4868	163	40	u(a+	u(a+	PROPN
ejpam-4868	163	41	λ	λ	NOUN
ejpam-4868	163	42	)	)	PUNCT
ejpam-4868	163	43	,	,	PUNCT
ejpam-4868	163	44	for	for	ADP
ejpam-4868	163	45	(	(	PUNCT
ejpam-4868	163	46	a+	a+	X
ejpam-4868	163	47	λ)u	λ)u	X
ejpam-4868	163	48	<	<	X
ejpam-4868	163	49	1	1	X
ejpam-4868	163	50	.	.	PUNCT
ejpam-4868	163	51	remark	remark	NOUN
ejpam-4868	163	52	4	4	NUM
ejpam-4868	163	53	.	.	PUNCT
ejpam-4868	164	1	it	it	PRON
ejpam-4868	164	2	is	be	AUX
ejpam-4868	164	3	clear	clear	ADJ
ejpam-4868	164	4	from	from	ADP
ejpam-4868	164	5	theorem	theorem	ADJ
ejpam-4868	164	6	6	6	NUM
ejpam-4868	164	7	and	and	CCONJ
ejpam-4868	164	8	equation	equation	NOUN
ejpam-4868	164	9	(	(	PUNCT
ejpam-4868	164	10	9	9	NUM
ejpam-4868	164	11	)	)	PUNCT
ejpam-4868	164	12	that	that	PRON
ejpam-4868	164	13	lim	lim	PROPN
ejpam-4868	164	14	λ→0	λ→0	PUNCT
ejpam-4868	164	15	gα	gα	PROPN
ejpam-4868	164	16	,	,	PUNCT
ejpam-4868	164	17	λ{eaλ(t	λ{eaλ(t	NOUN
ejpam-4868	164	18	)	)	PUNCT
ejpam-4868	164	19	}	}	PUNCT
ejpam-4868	164	20	=	=	SYM
ejpam-4868	164	21	lim	lim	PROPN
ejpam-4868	164	22	λ→0	λ→0	PUNCT
ejpam-4868	164	23	[	[	PUNCT
ejpam-4868	164	24	uα+1	uα+1	NUM
ejpam-4868	164	25	1−	1−	NUM
ejpam-4868	164	26	u(a+	u(a+	ADJ
ejpam-4868	164	27	λ	λ	NOUN
ejpam-4868	164	28	)	)	PUNCT
ejpam-4868	164	29	]	]	PUNCT
ejpam-4868	165	1	=	=	PUNCT
ejpam-4868	165	2	uα+1	uα+1	NOUN
ejpam-4868	165	3	1−	1−	NUM
ejpam-4868	165	4	ua	ua	NOUN
ejpam-4868	165	5	=	=	PUNCT
ejpam-4868	165	6	gα{eat	gα{eat	PROPN
ejpam-4868	165	7	}	}	PUNCT
ejpam-4868	165	8	.	.	PUNCT
ejpam-4868	166	1	h.	h.	PROPN
ejpam-4868	166	2	j.	j.	PROPN
ejpam-4868	166	3	campos	campos	PROPN
ejpam-4868	166	4	,	,	PUNCT
ejpam-4868	166	5	j.	j.	PROPN
ejpam-4868	166	6	c.	c.	PROPN
ejpam-4868	166	7	fernandez	fernandez	PROPN
ejpam-4868	166	8	,	,	PUNCT
ejpam-4868	166	9	j.	j.	PROPN
ejpam-4868	166	10	b.	b.	PROPN
ejpam-4868	166	11	m.	m.	PROPN
ejpam-4868	166	12	natuil	natuil	PROPN
ejpam-4868	166	13	/	/	SYM
ejpam-4868	166	14	eur	eur	PROPN
ejpam-4868	166	15	.	.	PUNCT
ejpam-4868	167	1	j.	j.	PROPN
ejpam-4868	167	2	pure	pure	PROPN
ejpam-4868	167	3	appl	appl	PROPN
ejpam-4868	167	4	.	.	PROPN
ejpam-4868	167	5	math	math	PROPN
ejpam-4868	167	6	,	,	PUNCT
ejpam-4868	167	7	16	16	NUM
ejpam-4868	167	8	(	(	PUNCT
ejpam-4868	167	9	4	4	NUM
ejpam-4868	167	10	)	)	PUNCT
ejpam-4868	167	11	(	(	PUNCT
ejpam-4868	167	12	2023	2023	NUM
ejpam-4868	167	13	)	)	PUNCT
ejpam-4868	167	14	,	,	PUNCT
ejpam-4868	167	15	2213	2213	NUM
ejpam-4868	167	16	-	-	SYM
ejpam-4868	167	17	2233	2233	NUM
ejpam-4868	167	18	2220	2220	NUM
ejpam-4868	167	19	theorem	theorem	VERB
ejpam-4868	167	20	7	7	NUM
ejpam-4868	167	21	.	.	PUNCT
ejpam-4868	168	1	the	the	DET
ejpam-4868	168	2	degenerate	degenerate	ADJ
ejpam-4868	168	3	laplace	laplace	NOUN
ejpam-4868	168	4	-	-	PUNCT
ejpam-4868	168	5	type	type	NOUN
ejpam-4868	168	6	integral	integral	ADJ
ejpam-4868	168	7	transform	transform	NOUN
ejpam-4868	168	8	of	of	ADP
ejpam-4868	168	9	a	a	DET
ejpam-4868	168	10	function	function	NOUN
ejpam-4868	168	11	f(t	f(t	NOUN
ejpam-4868	168	12	)	)	PUNCT
ejpam-4868	168	13	=	=	SYM
ejpam-4868	168	14	eiaλ	eiaλ	NOUN
ejpam-4868	168	15	(	(	PUNCT
ejpam-4868	168	16	t	t	NOUN
ejpam-4868	168	17	)	)	PUNCT
ejpam-4868	168	18	is	be	AUX
ejpam-4868	168	19	given	give	VERB
ejpam-4868	168	20	by	by	ADP
ejpam-4868	168	21	gα	gα	NOUN
ejpam-4868	168	22	,	,	PUNCT
ejpam-4868	168	23	λ{eiaλ	λ{eiaλ	PROPN
ejpam-4868	168	24	(	(	PUNCT
ejpam-4868	168	25	t	t	NOUN
ejpam-4868	168	26	)	)	PUNCT
ejpam-4868	168	27	}	}	PUNCT
ejpam-4868	169	1	=	=	PUNCT
ejpam-4868	169	2	uα+1	uα+1	NOUN
ejpam-4868	169	3	1−	1−	NUM
ejpam-4868	169	4	u(ia+	u(ia+	NUM
ejpam-4868	169	5	λ	λ	NOUN
ejpam-4868	169	6	)	)	PUNCT
ejpam-4868	169	7	,	,	PUNCT
ejpam-4868	169	8	for	for	ADP
ejpam-4868	169	9	uλ	uλ	PRON
ejpam-4868	169	10	<	<	X
ejpam-4868	169	11	1	1	NUM
ejpam-4868	169	12	,	,	PUNCT
ejpam-4868	169	13	(	(	PUNCT
ejpam-4868	169	14	15	15	NUM
ejpam-4868	169	15	)	)	PUNCT
ejpam-4868	169	16	where	where	SCONJ
ejpam-4868	169	17	a	a	PRON
ejpam-4868	169	18	is	be	AUX
ejpam-4868	169	19	any	any	DET
ejpam-4868	169	20	positive	positive	ADJ
ejpam-4868	169	21	constant	constant	NOUN
ejpam-4868	169	22	.	.	PUNCT
ejpam-4868	170	1	proof	proof	NOUN
ejpam-4868	170	2	.	.	PUNCT
ejpam-4868	171	1	by	by	ADP
ejpam-4868	171	2	definition	definition	NOUN
ejpam-4868	171	3	8	8	NUM
ejpam-4868	171	4	,	,	PUNCT
ejpam-4868	171	5	for	for	ADP
ejpam-4868	171	6	f(t	f(t	NOUN
ejpam-4868	171	7	)	)	PUNCT
ejpam-4868	171	8	=	=	SYM
ejpam-4868	171	9	eiaλ	eiaλ	NOUN
ejpam-4868	171	10	(	(	PUNCT
ejpam-4868	171	11	t	t	PROPN
ejpam-4868	171	12	)	)	PUNCT
ejpam-4868	171	13	,	,	PUNCT
ejpam-4868	171	14	we	we	PRON
ejpam-4868	171	15	set	set	VERB
ejpam-4868	171	16	gα	gα	ADP
ejpam-4868	171	17	,	,	PUNCT
ejpam-4868	171	18	λ{eiaλ	λ{eiaλ	PROPN
ejpam-4868	171	19	(	(	PUNCT
ejpam-4868	171	20	t	t	NOUN
ejpam-4868	171	21	)	)	PUNCT
ejpam-4868	171	22	}	}	PUNCT
ejpam-4868	172	1	=	=	X
ejpam-4868	172	2	uα	uα	PROPN
ejpam-4868	172	3	∫	∫	PROPN
ejpam-4868	172	4	∞	∞	PROPN
ejpam-4868	172	5	0	0	PUNCT
ejpam-4868	173	1	e	e	NOUN
ejpam-4868	173	2	−	−	PROPN
ejpam-4868	173	3	1	1	NUM
ejpam-4868	173	4	u	u	NOUN
ejpam-4868	173	5	λ	λ	PROPN
ejpam-4868	173	6	(	(	PUNCT
ejpam-4868	173	7	t	t	PROPN
ejpam-4868	173	8	)	)	PUNCT
ejpam-4868	173	9	[	[	PUNCT
ejpam-4868	173	10	eiaλ	eiaλ	NOUN
ejpam-4868	173	11	(	(	PUNCT
ejpam-4868	173	12	t	t	PROPN
ejpam-4868	173	13	)	)	PUNCT
ejpam-4868	173	14	]	]	PUNCT
ejpam-4868	174	1	dt	dt	X
ejpam-4868	175	1	=	=	PUNCT
ejpam-4868	175	2	uα	uα	PROPN
ejpam-4868	175	3	lim	lim	PROPN
ejpam-4868	175	4	r→∞	r→∞	PUNCT
ejpam-4868	175	5	∫	∫	PROPN
ejpam-4868	176	1	r	r	NOUN
ejpam-4868	176	2	0	0	NUM
ejpam-4868	176	3	(	(	PUNCT
ejpam-4868	176	4	1	1	NUM
ejpam-4868	176	5	+	+	CCONJ
ejpam-4868	176	6	λt	λt	X
ejpam-4868	176	7	)	)	PUNCT
ejpam-4868	176	8	uia−1	uia−1	PROPN
ejpam-4868	176	9	uλ	uλ	ADP
ejpam-4868	176	10	dt	dt	X
ejpam-4868	177	1	=	=	NOUN
ejpam-4868	177	2	uα+1	uα+1	NOUN
ejpam-4868	177	3	lim	lim	NOUN
ejpam-4868	177	4	r→∞	r→∞	NUM
ejpam-4868	177	5	[	[	PUNCT
ejpam-4868	177	6	(	(	PUNCT
ejpam-4868	177	7	1	1	NUM
ejpam-4868	177	8	+	+	CCONJ
ejpam-4868	177	9	λt	λt	ADP
ejpam-4868	177	10	)	)	PUNCT
ejpam-4868	177	11	−1+uλ	−1+uλ	PROPN
ejpam-4868	177	12	uλ	uλ	PRON
ejpam-4868	177	13	eiaλ	eiaλ	PROPN
ejpam-4868	177	14	(	(	PUNCT
ejpam-4868	177	15	t	t	NOUN
ejpam-4868	177	16	)	)	PUNCT
ejpam-4868	177	17	uia−	uia−	PROPN
ejpam-4868	177	18	1	1	NUM
ejpam-4868	177	19	+	+	NUM
ejpam-4868	177	20	uλ	uλ	ADP
ejpam-4868	177	21	]	]	X
ejpam-4868	177	22	∣∣∣∣∣	∣∣∣∣∣	NOUN
ejpam-4868	177	23	r	r	NOUN
ejpam-4868	177	24	0	0	NUM
ejpam-4868	177	25	.	.	PUNCT
ejpam-4868	178	1	by	by	ADP
ejpam-4868	178	2	the	the	DET
ejpam-4868	178	3	definition	definition	NOUN
ejpam-4868	178	4	of	of	ADP
ejpam-4868	178	5	degenerate	degenerate	ADJ
ejpam-4868	178	6	euler	euler	NOUN
ejpam-4868	178	7	formula	formula	NOUN
ejpam-4868	178	8	in	in	ADP
ejpam-4868	178	9	definition	definition	NOUN
ejpam-4868	178	10	5	5	NUM
ejpam-4868	178	11	,	,	PUNCT
ejpam-4868	178	12	eiaλ	eiaλ	NOUN
ejpam-4868	178	13	(	(	PUNCT
ejpam-4868	178	14	t	t	NOUN
ejpam-4868	178	15	)	)	PUNCT
ejpam-4868	178	16	=	=	SYM
ejpam-4868	178	17	cos	cos	X
ejpam-4868	178	18	(	(	PUNCT
ejpam-4868	178	19	a	a	X
ejpam-4868	178	20	)	)	PUNCT
ejpam-4868	178	21	λ	λ	PROPN
ejpam-4868	178	22	(	(	PUNCT
ejpam-4868	178	23	t	t	PROPN
ejpam-4868	178	24	)	)	PUNCT
ejpam-4868	179	1	+	+	CCONJ
ejpam-4868	179	2	i	i	PRON
ejpam-4868	179	3	sin	sin	VERB
ejpam-4868	179	4	(	(	PUNCT
ejpam-4868	179	5	a	a	X
ejpam-4868	179	6	)	)	PUNCT
ejpam-4868	179	7	λ	λ	PROPN
ejpam-4868	179	8	(	(	PUNCT
ejpam-4868	179	9	t	t	PROPN
ejpam-4868	179	10	)	)	PUNCT
ejpam-4868	179	11	=	=	SYM
ejpam-4868	180	1	cos	cos	PROPN
ejpam-4868	180	2	(	(	PUNCT
ejpam-4868	180	3	a	a	DET
ejpam-4868	180	4	λ	λ	PROPN
ejpam-4868	180	5	log	log	NOUN
ejpam-4868	180	6	(	(	PUNCT
ejpam-4868	180	7	1	1	NUM
ejpam-4868	180	8	+	+	CCONJ
ejpam-4868	180	9	λt	λt	ADP
ejpam-4868	180	10	)	)	PUNCT
ejpam-4868	180	11	)	)	PUNCT
ejpam-4868	181	1	+	+	CCONJ
ejpam-4868	181	2	i	i	PRON
ejpam-4868	181	3	sin	sin	VERB
ejpam-4868	181	4	(	(	PUNCT
ejpam-4868	181	5	a	a	DET
ejpam-4868	181	6	λ	λ	NOUN
ejpam-4868	181	7	log	log	NOUN
ejpam-4868	181	8	(	(	PUNCT
ejpam-4868	181	9	1	1	NUM
ejpam-4868	181	10	+	+	CCONJ
ejpam-4868	181	11	λt	λt	ADP
ejpam-4868	181	12	)	)	PUNCT
ejpam-4868	181	13	)	)	PUNCT
ejpam-4868	181	14	.	.	PUNCT
ejpam-4868	182	1	thus	thus	ADV
ejpam-4868	182	2	,	,	PUNCT
ejpam-4868	182	3	we	we	PRON
ejpam-4868	182	4	have	have	VERB
ejpam-4868	182	5	gα	gα	ADP
ejpam-4868	182	6	,	,	PUNCT
ejpam-4868	182	7	λ{eiaλ	λ{eiaλ	X
ejpam-4868	182	8	(	(	PUNCT
ejpam-4868	182	9	t	t	NOUN
ejpam-4868	182	10	)	)	PUNCT
ejpam-4868	182	11	}	}	PUNCT
ejpam-4868	183	1	=	=	NOUN
ejpam-4868	183	2	uα+1	uα+1	NUM
ejpam-4868	183	3	lim	lim	NOUN
ejpam-4868	183	4	r→∞	r→∞	NUM
ejpam-4868	183	5	[	[	PUNCT
ejpam-4868	183	6	(	(	PUNCT
ejpam-4868	183	7	1	1	NUM
ejpam-4868	183	8	+	+	CCONJ
ejpam-4868	183	9	λt	λt	ADP
ejpam-4868	183	10	)	)	PUNCT
ejpam-4868	183	11	−1+uλ	−1+uλ	PROPN
ejpam-4868	183	12	uλ	uλ	PRON
ejpam-4868	183	13	eiaλ	eiaλ	PROPN
ejpam-4868	183	14	(	(	PUNCT
ejpam-4868	183	15	t	t	NOUN
ejpam-4868	183	16	)	)	PUNCT
ejpam-4868	183	17	uia−	uia−	PROPN
ejpam-4868	183	18	1	1	NUM
ejpam-4868	183	19	+	+	NUM
ejpam-4868	183	20	uλ	uλ	ADP
ejpam-4868	183	21	]	]	X
ejpam-4868	183	22	∣∣∣∣∣	∣∣∣∣∣	NOUN
ejpam-4868	183	23	r	r	NOUN
ejpam-4868	183	24	0	0	PUNCT
ejpam-4868	183	25	=	=	NOUN
ejpam-4868	183	26	uα+1	uα+1	NOUN
ejpam-4868	183	27	lim	lim	NOUN
ejpam-4868	183	28	r→∞	r→∞	NUM
ejpam-4868	183	29	[	[	PUNCT
ejpam-4868	183	30	(	(	PUNCT
ejpam-4868	183	31	1	1	NUM
ejpam-4868	183	32	+	+	CCONJ
ejpam-4868	183	33	λt	λt	ADP
ejpam-4868	183	34	)	)	PUNCT
ejpam-4868	183	35	−1+uλ	−1+uλ	PROPN
ejpam-4868	183	36	uλ	uλ	X
ejpam-4868	183	37	[	[	PUNCT
ejpam-4868	183	38	cos	cos	X
ejpam-4868	183	39	(	(	PUNCT
ejpam-4868	183	40	a	a	DET
ejpam-4868	183	41	λ	λ	X
ejpam-4868	183	42	log(1	log(1	NOUN
ejpam-4868	183	43	+	+	CCONJ
ejpam-4868	183	44	λt	λt	X
ejpam-4868	183	45	)	)	PUNCT
ejpam-4868	183	46	)	)	PUNCT
ejpam-4868	184	1	+	+	ADV
ejpam-4868	184	2	i	i	PRON
ejpam-4868	184	3	sin	sin	VERB
ejpam-4868	184	4	(	(	PUNCT
ejpam-4868	184	5	a	a	DET
ejpam-4868	184	6	λ	λ	X
ejpam-4868	184	7	log(1	log(1	NOUN
ejpam-4868	184	8	+	+	CCONJ
ejpam-4868	184	9	λt	λt	X
ejpam-4868	184	10	)	)	PUNCT
ejpam-4868	184	11	)	)	PUNCT
ejpam-4868	184	12	]	]	PUNCT
ejpam-4868	185	1	uia−	uia−	NOUN
ejpam-4868	185	2	1	1	NUM
ejpam-4868	185	3	+	+	CCONJ
ejpam-4868	185	4	uλ	uλ	ADP
ejpam-4868	185	5	]	]	X
ejpam-4868	185	6	∣∣∣∣∣	∣∣∣∣∣	NOUN
ejpam-4868	185	7	r	r	NOUN
ejpam-4868	185	8	0	0	PUNCT
ejpam-4868	185	9	=	=	NOUN
ejpam-4868	185	10	uα+1	uα+1	NOUN
ejpam-4868	185	11	[	[	PUNCT
ejpam-4868	185	12	−	−	PROPN
ejpam-4868	185	13	1	1	NUM
ejpam-4868	185	14	uia−	uia−	PROPN
ejpam-4868	185	15	1	1	NUM
ejpam-4868	185	16	+	+	NOUN
ejpam-4868	185	17	uλ	uλ	ADP
ejpam-4868	185	18	]	]	X
ejpam-4868	185	19	=	=	SYM
ejpam-4868	185	20	uα+1	uα+1	NOUN
ejpam-4868	185	21	1−	1−	NUM
ejpam-4868	185	22	u(ia−	u(ia−	SYM
ejpam-4868	185	23	λ	λ	NOUN
ejpam-4868	185	24	)	)	PUNCT
ejpam-4868	185	25	,	,	PUNCT
ejpam-4868	185	26	for	for	ADP
ejpam-4868	185	27	uλ	uλ	PRON
ejpam-4868	185	28	<	<	X
ejpam-4868	185	29	1	1	NUM
ejpam-4868	185	30	.	.	PUNCT
ejpam-4868	185	31	theorem	theorem	NOUN
ejpam-4868	185	32	8	8	NUM
ejpam-4868	185	33	.	.	PUNCT
ejpam-4868	186	1	the	the	DET
ejpam-4868	186	2	degenerate	degenerate	ADJ
ejpam-4868	186	3	laplace	laplace	NOUN
ejpam-4868	186	4	-	-	PUNCT
ejpam-4868	186	5	type	type	NOUN
ejpam-4868	186	6	integral	integral	ADJ
ejpam-4868	186	7	transform	transform	NOUN
ejpam-4868	186	8	of	of	ADP
ejpam-4868	186	9	the	the	DET
ejpam-4868	186	10	degenerate	degenerate	ADJ
ejpam-4868	186	11	sine	sine	ADJ
ejpam-4868	186	12	function	function	NOUN
ejpam-4868	186	13	f(t	f(t	NOUN
ejpam-4868	186	14	)	)	PUNCT
ejpam-4868	187	1	=	=	SYM
ejpam-4868	187	2	sin	sin	NOUN
ejpam-4868	187	3	(	(	PUNCT
ejpam-4868	187	4	a	a	X
ejpam-4868	187	5	)	)	PUNCT
ejpam-4868	187	6	λ	λ	PROPN
ejpam-4868	187	7	(	(	PUNCT
ejpam-4868	187	8	t	t	PROPN
ejpam-4868	187	9	)	)	PUNCT
ejpam-4868	187	10	is	be	AUX
ejpam-4868	187	11	given	give	VERB
ejpam-4868	187	12	by	by	ADP
ejpam-4868	187	13	gα	gα	NOUN
ejpam-4868	187	14	,	,	PUNCT
ejpam-4868	187	15	λ{sin	λ{sin	PROPN
ejpam-4868	187	16	(	(	PUNCT
ejpam-4868	187	17	a	a	X
ejpam-4868	187	18	)	)	PUNCT
ejpam-4868	187	19	λ	λ	PROPN
ejpam-4868	187	20	(	(	PUNCT
ejpam-4868	187	21	t	t	NOUN
ejpam-4868	187	22	)	)	PUNCT
ejpam-4868	187	23	}	}	PUNCT
ejpam-4868	187	24	=	=	SYM
ejpam-4868	187	25	auα+2	auα+2	X
ejpam-4868	187	26	(	(	PUNCT
ejpam-4868	187	27	1−	1−	NUM
ejpam-4868	187	28	λu)2	λu)2	PROPN
ejpam-4868	187	29	+	+	CCONJ
ejpam-4868	187	30	u2a2	u2a2	X
ejpam-4868	187	31	.	.	PUNCT
ejpam-4868	188	1	(	(	PUNCT
ejpam-4868	188	2	16	16	X
ejpam-4868	188	3	)	)	PUNCT
ejpam-4868	188	4	proof	proof	NOUN
ejpam-4868	188	5	.	.	PUNCT
ejpam-4868	189	1	by	by	ADP
ejpam-4868	189	2	the	the	DET
ejpam-4868	189	3	definition	definition	NOUN
ejpam-4868	189	4	of	of	ADP
ejpam-4868	189	5	the	the	DET
ejpam-4868	189	6	degenerate	degenerate	ADJ
ejpam-4868	189	7	sine	sine	NOUN
ejpam-4868	189	8	in	in	ADP
ejpam-4868	189	9	definition	definition	NOUN
ejpam-4868	189	10	3	3	NUM
ejpam-4868	189	11	,	,	PUNCT
ejpam-4868	189	12	we	we	PRON
ejpam-4868	189	13	have	have	VERB
ejpam-4868	189	14	gα	gα	ADP
ejpam-4868	189	15	,	,	PUNCT
ejpam-4868	189	16	λ{sin	λ{sin	PROPN
ejpam-4868	189	17	(	(	PUNCT
ejpam-4868	189	18	a	a	X
ejpam-4868	189	19	)	)	PUNCT
ejpam-4868	189	20	λ	λ	PROPN
ejpam-4868	189	21	(	(	PUNCT
ejpam-4868	189	22	t	t	NOUN
ejpam-4868	189	23	)	)	PUNCT
ejpam-4868	189	24	}	}	PUNCT
ejpam-4868	190	1	=	=	X
ejpam-4868	190	2	gα	gα	NOUN
ejpam-4868	190	3	,	,	PUNCT
ejpam-4868	190	4	λ	λ	PROPN
ejpam-4868	190	5	{	{	PUNCT
ejpam-4868	190	6	eiaλ	eiaλ	NOUN
ejpam-4868	190	7	(	(	PUNCT
ejpam-4868	190	8	t)−	t)−	PROPN
ejpam-4868	190	9	e−ia	e−ia	PRON
ejpam-4868	190	10	λ	λ	PROPN
ejpam-4868	190	11	(	(	PUNCT
ejpam-4868	190	12	t	t	PROPN
ejpam-4868	190	13	)	)	PUNCT
ejpam-4868	190	14	2i	2i	NOUN
ejpam-4868	190	15	}	}	PUNCT
ejpam-4868	190	16	.	.	PUNCT
ejpam-4868	191	1	now	now	ADV
ejpam-4868	191	2	using	use	VERB
ejpam-4868	191	3	theorem	theorem	ADJ
ejpam-4868	191	4	2	2	NUM
ejpam-4868	191	5	and	and	CCONJ
ejpam-4868	191	6	theorem	theorem	VERB
ejpam-4868	191	7	7	7	NUM
ejpam-4868	191	8	,	,	PUNCT
ejpam-4868	191	9	we	we	PRON
ejpam-4868	191	10	obtain	obtain	VERB
ejpam-4868	191	11	gα	gα	ADP
ejpam-4868	191	12	,	,	PUNCT
ejpam-4868	191	13	λ{sin	λ{sin	PROPN
ejpam-4868	191	14	(	(	PUNCT
ejpam-4868	191	15	a	a	X
ejpam-4868	191	16	)	)	PUNCT
ejpam-4868	191	17	λ	λ	PROPN
ejpam-4868	191	18	(	(	PUNCT
ejpam-4868	191	19	t	t	NOUN
ejpam-4868	191	20	)	)	PUNCT
ejpam-4868	191	21	}	}	PUNCT
ejpam-4868	191	22	=	=	SYM
ejpam-4868	191	23	1	1	NUM
ejpam-4868	191	24	2i	2i	NOUN
ejpam-4868	191	25	[	[	PUNCT
ejpam-4868	191	26	gα	gα	NOUN
ejpam-4868	191	27	,	,	PUNCT
ejpam-4868	191	28	λ{eiaλ	λ{eiaλ	PROPN
ejpam-4868	191	29	(	(	PUNCT
ejpam-4868	191	30	t	t	NOUN
ejpam-4868	191	31	)	)	PUNCT
ejpam-4868	191	32	}	}	PUNCT
ejpam-4868	191	33	−	−	ADP
ejpam-4868	191	34	gα	gα	NOUN
ejpam-4868	191	35	,	,	PUNCT
ejpam-4868	191	36	λ{e−ia	λ{e−ia	PROPN
ejpam-4868	191	37	λ	λ	PROPN
ejpam-4868	191	38	(	(	PUNCT
ejpam-4868	191	39	t	t	PROPN
ejpam-4868	191	40	)	)	PUNCT
ejpam-4868	191	41	}	}	PUNCT
ejpam-4868	191	42	]	]	PUNCT
ejpam-4868	192	1	h.	h.	PROPN
ejpam-4868	192	2	j.	j.	PROPN
ejpam-4868	192	3	campos	campos	PROPN
ejpam-4868	192	4	,	,	PUNCT
ejpam-4868	192	5	j.	j.	PROPN
ejpam-4868	192	6	c.	c.	PROPN
ejpam-4868	192	7	fernandez	fernandez	PROPN
ejpam-4868	192	8	,	,	PUNCT
ejpam-4868	192	9	j.	j.	PROPN
ejpam-4868	192	10	b.	b.	PROPN
ejpam-4868	192	11	m.	m.	PROPN
ejpam-4868	192	12	natuil	natuil	PROPN
ejpam-4868	192	13	/	/	SYM
ejpam-4868	192	14	eur	eur	PROPN
ejpam-4868	192	15	.	.	PUNCT
ejpam-4868	193	1	j.	j.	PROPN
ejpam-4868	193	2	pure	pure	PROPN
ejpam-4868	193	3	appl	appl	PROPN
ejpam-4868	193	4	.	.	PROPN
ejpam-4868	193	5	math	math	PROPN
ejpam-4868	193	6	,	,	PUNCT
ejpam-4868	193	7	16	16	NUM
ejpam-4868	193	8	(	(	PUNCT
ejpam-4868	193	9	4	4	NUM
ejpam-4868	193	10	)	)	PUNCT
ejpam-4868	193	11	(	(	PUNCT
ejpam-4868	193	12	2023	2023	NUM
ejpam-4868	193	13	)	)	PUNCT
ejpam-4868	193	14	,	,	PUNCT
ejpam-4868	193	15	2213	2213	NUM
ejpam-4868	193	16	-	-	SYM
ejpam-4868	193	17	2233	2233	NUM
ejpam-4868	193	18	2221	2221	NUM
ejpam-4868	193	19	=	=	SYM
ejpam-4868	193	20	1	1	NUM
ejpam-4868	193	21	2i	2i	NUM
ejpam-4868	193	22	[	[	PUNCT
ejpam-4868	193	23	uα+1	uα+1	NUM
ejpam-4868	193	24	1−	1−	NUM
ejpam-4868	193	25	u(ia+	u(ia+	NUM
ejpam-4868	193	26	λ	λ	NOUN
ejpam-4868	193	27	)	)	PUNCT
ejpam-4868	193	28	−	−	NOUN
ejpam-4868	193	29	uα+1	uα+1	NOUN
ejpam-4868	193	30	1−	1−	NUM
ejpam-4868	193	31	u(−ia+	u(−ia+	PROPN
ejpam-4868	193	32	λ	λ	PROPN
ejpam-4868	193	33	)	)	PUNCT
ejpam-4868	193	34	]	]	PUNCT
ejpam-4868	194	1	=	=	SYM
ejpam-4868	194	2	auα+2	auα+2	X
ejpam-4868	194	3	(	(	PUNCT
ejpam-4868	194	4	1−	1−	NUM
ejpam-4868	194	5	λu)2	λu)2	PROPN
ejpam-4868	194	6	+	+	CCONJ
ejpam-4868	194	7	u2a2	u2a2	PROPN
ejpam-4868	194	8	.	.	PUNCT
ejpam-4868	195	1	remark	remark	PROPN
ejpam-4868	195	2	5	5	NUM
ejpam-4868	195	3	.	.	PUNCT
ejpam-4868	196	1	it	it	PRON
ejpam-4868	196	2	is	be	AUX
ejpam-4868	196	3	clear	clear	ADJ
ejpam-4868	196	4	from	from	ADP
ejpam-4868	196	5	theorem	theorem	ADJ
ejpam-4868	196	6	8	8	NUM
ejpam-4868	196	7	and	and	CCONJ
ejpam-4868	196	8	equation	equation	NOUN
ejpam-4868	196	9	(	(	PUNCT
ejpam-4868	196	10	9	9	NUM
ejpam-4868	196	11	)	)	PUNCT
ejpam-4868	197	1	that	that	PRON
ejpam-4868	197	2	lim	lim	PROPN
ejpam-4868	197	3	λ→0	λ→0	PUNCT
ejpam-4868	197	4	gα	gα	PROPN
ejpam-4868	197	5	,	,	PUNCT
ejpam-4868	197	6	λ{sin	λ{sin	PROPN
ejpam-4868	197	7	(	(	PUNCT
ejpam-4868	197	8	a	a	X
ejpam-4868	197	9	)	)	PUNCT
ejpam-4868	197	10	λ	λ	PROPN
ejpam-4868	197	11	(	(	PUNCT
ejpam-4868	197	12	t	t	NOUN
ejpam-4868	197	13	)	)	PUNCT
ejpam-4868	197	14	}	}	PUNCT
ejpam-4868	197	15	=	=	SYM
ejpam-4868	197	16	lim	lim	PROPN
ejpam-4868	197	17	λ→0	λ→0	PUNCT
ejpam-4868	197	18	[	[	PUNCT
ejpam-4868	197	19	auα+2	auα+2	X
ejpam-4868	197	20	(	(	PUNCT
ejpam-4868	197	21	1−	1−	NUM
ejpam-4868	197	22	λu)2	λu)2	PROPN
ejpam-4868	197	23	+	+	CCONJ
ejpam-4868	197	24	u2a2	u2a2	NOUN
ejpam-4868	197	25	]	]	X
ejpam-4868	197	26	=	=	SYM
ejpam-4868	197	27	auα+2	auα+2	ADJ
ejpam-4868	197	28	1	1	NUM
ejpam-4868	198	1	+	+	CCONJ
ejpam-4868	198	2	u2a2	u2a2	NOUN
ejpam-4868	198	3	=	=	PUNCT
ejpam-4868	198	4	gα{sin	gα{sin	NOUN
ejpam-4868	198	5	at	at	ADP
ejpam-4868	198	6	}	}	PUNCT
ejpam-4868	198	7	.	.	PUNCT
ejpam-4868	199	1	theorem	theorem	NOUN
ejpam-4868	199	2	9	9	NUM
ejpam-4868	199	3	.	.	PUNCT
ejpam-4868	200	1	the	the	DET
ejpam-4868	200	2	degenerate	degenerate	ADJ
ejpam-4868	200	3	laplace	laplace	NOUN
ejpam-4868	200	4	-	-	PUNCT
ejpam-4868	200	5	type	type	NOUN
ejpam-4868	200	6	integral	integral	ADJ
ejpam-4868	200	7	transform	transform	NOUN
ejpam-4868	200	8	of	of	ADP
ejpam-4868	200	9	the	the	DET
ejpam-4868	200	10	degenerate	degenerate	ADJ
ejpam-4868	200	11	cosine	cosine	NOUN
ejpam-4868	200	12	function	function	NOUN
ejpam-4868	200	13	f(t	f(t	PROPN
ejpam-4868	200	14	)	)	PUNCT
ejpam-4868	200	15	=	=	SYM
ejpam-4868	200	16	cos	cos	X
ejpam-4868	200	17	(	(	PUNCT
ejpam-4868	200	18	a	a	X
ejpam-4868	200	19	)	)	PUNCT
ejpam-4868	200	20	λ	λ	PROPN
ejpam-4868	200	21	(	(	PUNCT
ejpam-4868	200	22	t	t	PROPN
ejpam-4868	200	23	)	)	PUNCT
ejpam-4868	200	24	is	be	AUX
ejpam-4868	200	25	given	give	VERB
ejpam-4868	200	26	by	by	ADP
ejpam-4868	200	27	gα	gα	NOUN
ejpam-4868	200	28	,	,	PUNCT
ejpam-4868	200	29	λ{cos	λ{cos	PROPN
ejpam-4868	200	30	(	(	PUNCT
ejpam-4868	200	31	a	a	X
ejpam-4868	200	32	)	)	PUNCT
ejpam-4868	200	33	λ	λ	PROPN
ejpam-4868	200	34	(	(	PUNCT
ejpam-4868	200	35	t	t	NOUN
ejpam-4868	200	36	)	)	PUNCT
ejpam-4868	200	37	}	}	PUNCT
ejpam-4868	200	38	=	=	SYM
ejpam-4868	200	39	(	(	PUNCT
ejpam-4868	200	40	1−	1−	NUM
ejpam-4868	200	41	λu)uα+1	λu)uα+1	NOUN
ejpam-4868	200	42	(	(	PUNCT
ejpam-4868	200	43	1−	1−	NUM
ejpam-4868	200	44	λu)2	λu)2	PROPN
ejpam-4868	200	45	+	+	CCONJ
ejpam-4868	200	46	u2a2	u2a2	X
ejpam-4868	200	47	.	.	PUNCT
ejpam-4868	201	1	(	(	PUNCT
ejpam-4868	201	2	17	17	NUM
ejpam-4868	201	3	)	)	PUNCT
ejpam-4868	201	4	proof	proof	NOUN
ejpam-4868	201	5	.	.	PUNCT
ejpam-4868	202	1	by	by	ADP
ejpam-4868	202	2	the	the	DET
ejpam-4868	202	3	definition	definition	NOUN
ejpam-4868	202	4	of	of	ADP
ejpam-4868	202	5	the	the	DET
ejpam-4868	202	6	degenerate	degenerate	ADJ
ejpam-4868	202	7	cosine	cosine	NOUN
ejpam-4868	202	8	in	in	ADP
ejpam-4868	202	9	definition	definition	NOUN
ejpam-4868	202	10	4	4	NUM
ejpam-4868	202	11	and	and	CCONJ
ejpam-4868	202	12	using	use	VERB
ejpam-4868	202	13	theorem	theorem	ADJ
ejpam-4868	202	14	2	2	NUM
ejpam-4868	202	15	and	and	CCONJ
ejpam-4868	202	16	theorem	theorem	VERB
ejpam-4868	202	17	7	7	NUM
ejpam-4868	202	18	,	,	PUNCT
ejpam-4868	202	19	we	we	PRON
ejpam-4868	202	20	obtain	obtain	VERB
ejpam-4868	202	21	gα	gα	ADP
ejpam-4868	202	22	,	,	PUNCT
ejpam-4868	202	23	λ{cos	λ{cos	PROPN
ejpam-4868	202	24	(	(	PUNCT
ejpam-4868	202	25	a	a	X
ejpam-4868	202	26	)	)	PUNCT
ejpam-4868	202	27	λ	λ	PROPN
ejpam-4868	202	28	(	(	PUNCT
ejpam-4868	202	29	t	t	NOUN
ejpam-4868	202	30	)	)	PUNCT
ejpam-4868	202	31	}	}	PUNCT
ejpam-4868	202	32	=	=	SYM
ejpam-4868	202	33	1	1	NUM
ejpam-4868	202	34	2	2	NUM
ejpam-4868	202	35	[	[	PUNCT
ejpam-4868	202	36	gα	gα	NOUN
ejpam-4868	202	37	,	,	PUNCT
ejpam-4868	202	38	λ{eiaλ	λ{eiaλ	X
ejpam-4868	202	39	(	(	PUNCT
ejpam-4868	202	40	t)}+	t)}+	NOUN
ejpam-4868	202	41	gα	gα	ADP
ejpam-4868	202	42	,	,	PUNCT
ejpam-4868	202	43	λ{e−ia	λ{e−ia	PROPN
ejpam-4868	202	44	λ	λ	PROPN
ejpam-4868	202	45	(	(	PUNCT
ejpam-4868	202	46	t	t	PROPN
ejpam-4868	202	47	)	)	PUNCT
ejpam-4868	202	48	}	}	PUNCT
ejpam-4868	202	49	]	]	PUNCT
ejpam-4868	203	1	=	=	PUNCT
ejpam-4868	203	2	(	(	PUNCT
ejpam-4868	203	3	1−	1−	NUM
ejpam-4868	203	4	λu)uα+1	λu)uα+1	NOUN
ejpam-4868	203	5	(	(	PUNCT
ejpam-4868	203	6	1−	1−	NUM
ejpam-4868	203	7	λu)2	λu)2	PROPN
ejpam-4868	203	8	+	+	CCONJ
ejpam-4868	203	9	u2a2	u2a2	PROPN
ejpam-4868	203	10	.	.	PUNCT
ejpam-4868	204	1	remark	remark	PROPN
ejpam-4868	204	2	6	6	NUM
ejpam-4868	204	3	.	.	PUNCT
ejpam-4868	205	1	it	it	PRON
ejpam-4868	205	2	is	be	AUX
ejpam-4868	205	3	clear	clear	ADJ
ejpam-4868	205	4	from	from	ADP
ejpam-4868	205	5	theorem	theorem	ADJ
ejpam-4868	205	6	9	9	NUM
ejpam-4868	205	7	and	and	CCONJ
ejpam-4868	205	8	equation	equation	NOUN
ejpam-4868	205	9	(	(	PUNCT
ejpam-4868	205	10	9	9	NUM
ejpam-4868	205	11	)	)	PUNCT
ejpam-4868	206	1	that	that	PRON
ejpam-4868	206	2	lim	lim	PROPN
ejpam-4868	206	3	λ→0	λ→0	PUNCT
ejpam-4868	206	4	gα	gα	PROPN
ejpam-4868	206	5	,	,	PUNCT
ejpam-4868	206	6	λ{cos	λ{cos	PROPN
ejpam-4868	206	7	(	(	PUNCT
ejpam-4868	206	8	a	a	X
ejpam-4868	206	9	)	)	PUNCT
ejpam-4868	206	10	λ	λ	PROPN
ejpam-4868	206	11	(	(	PUNCT
ejpam-4868	206	12	t	t	NOUN
ejpam-4868	206	13	)	)	PUNCT
ejpam-4868	206	14	}	}	PUNCT
ejpam-4868	206	15	=	=	SYM
ejpam-4868	206	16	lim	lim	PROPN
ejpam-4868	206	17	λ→0	λ→0	PUNCT
ejpam-4868	206	18	[	[	PUNCT
ejpam-4868	206	19	(	(	PUNCT
ejpam-4868	206	20	1−	1−	NUM
ejpam-4868	206	21	λu)uα+1	λu)uα+1	NOUN
ejpam-4868	206	22	(	(	PUNCT
ejpam-4868	206	23	1−	1−	NUM
ejpam-4868	206	24	λu)2	λu)2	PROPN
ejpam-4868	206	25	+	+	CCONJ
ejpam-4868	206	26	u2a2	u2a2	NOUN
ejpam-4868	206	27	]	]	X
ejpam-4868	206	28	=	=	PUNCT
ejpam-4868	206	29	uα+1	uα+1	NOUN
ejpam-4868	206	30	1	1	NUM
ejpam-4868	206	31	+	+	CCONJ
ejpam-4868	206	32	u2a2	u2a2	NOUN
ejpam-4868	206	33	=	=	NOUN
ejpam-4868	206	34	gα{cos	gα{cos	ADJ
ejpam-4868	206	35	at	at	ADP
ejpam-4868	206	36	}	}	PUNCT
ejpam-4868	206	37	.	.	PUNCT
ejpam-4868	207	1	theorem	theorem	ADJ
ejpam-4868	207	2	10	10	NUM
ejpam-4868	207	3	.	.	PUNCT
ejpam-4868	208	1	the	the	DET
ejpam-4868	208	2	degenerate	degenerate	ADJ
ejpam-4868	208	3	laplace	laplace	NOUN
ejpam-4868	208	4	-	-	PUNCT
ejpam-4868	208	5	type	type	NOUN
ejpam-4868	208	6	integral	integral	ADJ
ejpam-4868	208	7	transform	transform	NOUN
ejpam-4868	208	8	of	of	ADP
ejpam-4868	208	9	the	the	DET
ejpam-4868	208	10	degenerate	degenerate	ADJ
ejpam-4868	208	11	hyperbolic	hyperbolic	ADJ
ejpam-4868	208	12	sine	sine	NOUN
ejpam-4868	208	13	function	function	NOUN
ejpam-4868	208	14	f(t	f(t	NOUN
ejpam-4868	208	15	)	)	PUNCT
ejpam-4868	208	16	=	=	X
ejpam-4868	208	17	sinh	sinh	NOUN
ejpam-4868	208	18	(	(	PUNCT
ejpam-4868	208	19	a	a	NOUN
ejpam-4868	208	20	)	)	PUNCT
ejpam-4868	208	21	λ	λ	PROPN
ejpam-4868	208	22	(	(	PUNCT
ejpam-4868	208	23	t	t	PROPN
ejpam-4868	208	24	)	)	PUNCT
ejpam-4868	208	25	is	be	AUX
ejpam-4868	208	26	given	give	VERB
ejpam-4868	208	27	by	by	ADP
ejpam-4868	208	28	gα	gα	NOUN
ejpam-4868	208	29	,	,	PUNCT
ejpam-4868	208	30	λ{sinh	λ{sinh	X
ejpam-4868	208	31	(	(	PUNCT
ejpam-4868	208	32	a	a	X
ejpam-4868	208	33	)	)	PUNCT
ejpam-4868	208	34	λ	λ	PROPN
ejpam-4868	208	35	(	(	PUNCT
ejpam-4868	208	36	t	t	NOUN
ejpam-4868	208	37	)	)	PUNCT
ejpam-4868	208	38	}	}	PUNCT
ejpam-4868	208	39	=	=	SYM
ejpam-4868	208	40	auα+2	auα+2	X
ejpam-4868	208	41	(	(	PUNCT
ejpam-4868	208	42	1−	1−	NUM
ejpam-4868	208	43	λu)2	λu)2	NOUN
ejpam-4868	208	44	−	−	PROPN
ejpam-4868	208	45	u2a2	u2a2	INTJ
ejpam-4868	208	46	.	.	PUNCT
ejpam-4868	209	1	(	(	PUNCT
ejpam-4868	209	2	18	18	NUM
ejpam-4868	209	3	)	)	PUNCT
ejpam-4868	209	4	proof	proof	NOUN
ejpam-4868	209	5	.	.	PUNCT
ejpam-4868	210	1	by	by	ADP
ejpam-4868	210	2	the	the	DET
ejpam-4868	210	3	definition	definition	NOUN
ejpam-4868	210	4	of	of	ADP
ejpam-4868	210	5	the	the	DET
ejpam-4868	210	6	degenerate	degenerate	ADJ
ejpam-4868	210	7	hyperbolic	hyperbolic	ADJ
ejpam-4868	210	8	sine	sine	NOUN
ejpam-4868	210	9	in	in	ADP
ejpam-4868	210	10	definition	definition	NOUN
ejpam-4868	210	11	6	6	NUM
ejpam-4868	210	12	,	,	PUNCT
ejpam-4868	210	13	we	we	PRON
ejpam-4868	210	14	have	have	VERB
ejpam-4868	210	15	gα	gα	ADP
ejpam-4868	210	16	,	,	PUNCT
ejpam-4868	210	17	λ{sinh	λ{sinh	X
ejpam-4868	210	18	(	(	PUNCT
ejpam-4868	210	19	a	a	X
ejpam-4868	210	20	)	)	PUNCT
ejpam-4868	210	21	λ	λ	PROPN
ejpam-4868	210	22	(	(	PUNCT
ejpam-4868	210	23	t	t	NOUN
ejpam-4868	210	24	)	)	PUNCT
ejpam-4868	210	25	}	}	PUNCT
ejpam-4868	211	1	=	=	X
ejpam-4868	211	2	gα	gα	NOUN
ejpam-4868	211	3	,	,	PUNCT
ejpam-4868	211	4	λ	λ	X
ejpam-4868	211	5	{	{	PUNCT
ejpam-4868	211	6	eaλ(t)−	eaλ(t)−	PROPN
ejpam-4868	211	7	e−a	e−a	PROPN
ejpam-4868	211	8	λ	λ	PROPN
ejpam-4868	211	9	(	(	PUNCT
ejpam-4868	211	10	t	t	PROPN
ejpam-4868	211	11	)	)	PUNCT
ejpam-4868	211	12	2	2	NUM
ejpam-4868	211	13	}	}	PUNCT
ejpam-4868	211	14	.	.	PUNCT
ejpam-4868	212	1	now	now	ADV
ejpam-4868	212	2	,	,	PUNCT
ejpam-4868	212	3	using	use	VERB
ejpam-4868	212	4	theorem	theorem	ADJ
ejpam-4868	212	5	2	2	NUM
ejpam-4868	212	6	and	and	CCONJ
ejpam-4868	212	7	theorem	theorem	VERB
ejpam-4868	212	8	6	6	NUM
ejpam-4868	212	9	,	,	PUNCT
ejpam-4868	212	10	we	we	PRON
ejpam-4868	212	11	obtain	obtain	VERB
ejpam-4868	212	12	gα	gα	ADP
ejpam-4868	212	13	,	,	PUNCT
ejpam-4868	212	14	λ{sinh	λ{sinh	X
ejpam-4868	212	15	(	(	PUNCT
ejpam-4868	212	16	a	a	X
ejpam-4868	212	17	)	)	PUNCT
ejpam-4868	212	18	λ	λ	PROPN
ejpam-4868	212	19	(	(	PUNCT
ejpam-4868	212	20	t	t	NOUN
ejpam-4868	212	21	)	)	PUNCT
ejpam-4868	212	22	}	}	PUNCT
ejpam-4868	212	23	=	=	SYM
ejpam-4868	212	24	1	1	NUM
ejpam-4868	212	25	2	2	NUM
ejpam-4868	212	26	[	[	PUNCT
ejpam-4868	212	27	gα	gα	NOUN
ejpam-4868	212	28	,	,	PUNCT
ejpam-4868	212	29	λ{eaλ(t	λ{eaλ(t	NOUN
ejpam-4868	212	30	)	)	PUNCT
ejpam-4868	212	31	}	}	PUNCT
ejpam-4868	212	32	−	−	ADP
ejpam-4868	212	33	gα	gα	NOUN
ejpam-4868	212	34	,	,	PUNCT
ejpam-4868	212	35	λ{e−a	λ{e−a	ADJ
ejpam-4868	212	36	λ	λ	X
ejpam-4868	212	37	(	(	PUNCT
ejpam-4868	212	38	t	t	PROPN
ejpam-4868	212	39	)	)	PUNCT
ejpam-4868	212	40	}	}	PUNCT
ejpam-4868	212	41	]	]	PUNCT
ejpam-4868	213	1	=	=	SYM
ejpam-4868	213	2	1	1	NUM
ejpam-4868	213	3	2	2	NUM
ejpam-4868	213	4	[	[	PUNCT
ejpam-4868	213	5	uα+1	uα+1	NUM
ejpam-4868	213	6	1−	1−	NUM
ejpam-4868	213	7	u(a+	u(a+	ADJ
ejpam-4868	213	8	λ	λ	NOUN
ejpam-4868	213	9	)	)	PUNCT
ejpam-4868	213	10	−	−	NOUN
ejpam-4868	213	11	uα+1	uα+1	NUM
ejpam-4868	213	12	1−	1−	NUM
ejpam-4868	213	13	u(−a+	u(−a+	PROPN
ejpam-4868	213	14	λ	λ	NOUN
ejpam-4868	213	15	)	)	PUNCT
ejpam-4868	213	16	]	]	PUNCT
ejpam-4868	214	1	=	=	PUNCT
ejpam-4868	214	2	uα+1	uα+1	NOUN
ejpam-4868	214	3	2	2	NUM
ejpam-4868	214	4	[	[	PUNCT
ejpam-4868	214	5	2au	2au	ADJ
ejpam-4868	214	6	(	(	PUNCT
ejpam-4868	214	7	1−	1−	NUM
ejpam-4868	214	8	λu)2	λu)2	NOUN
ejpam-4868	214	9	−	−	PROPN
ejpam-4868	215	1	u2a2	u2a2	NOUN
ejpam-4868	215	2	]	]	X
ejpam-4868	215	3	=	=	SYM
ejpam-4868	215	4	auα+2	auα+2	X
ejpam-4868	215	5	(	(	PUNCT
ejpam-4868	215	6	1−	1−	NUM
ejpam-4868	215	7	λu)2	λu)2	NOUN
ejpam-4868	215	8	−	−	PROPN
ejpam-4868	215	9	u2a2	u2a2	PROPN
ejpam-4868	215	10	.	.	PUNCT
ejpam-4868	216	1	h.	h.	PROPN
ejpam-4868	216	2	j.	j.	PROPN
ejpam-4868	216	3	campos	campos	PROPN
ejpam-4868	216	4	,	,	PUNCT
ejpam-4868	216	5	j.	j.	PROPN
ejpam-4868	216	6	c.	c.	PROPN
ejpam-4868	216	7	fernandez	fernandez	PROPN
ejpam-4868	216	8	,	,	PUNCT
ejpam-4868	216	9	j.	j.	PROPN
ejpam-4868	216	10	b.	b.	PROPN
ejpam-4868	216	11	m.	m.	PROPN
ejpam-4868	216	12	natuil	natuil	PROPN
ejpam-4868	216	13	/	/	SYM
ejpam-4868	216	14	eur	eur	PROPN
ejpam-4868	216	15	.	.	PUNCT
ejpam-4868	217	1	j.	j.	PROPN
ejpam-4868	217	2	pure	pure	PROPN
ejpam-4868	217	3	appl	appl	PROPN
ejpam-4868	217	4	.	.	PROPN
ejpam-4868	217	5	math	math	PROPN
ejpam-4868	217	6	,	,	PUNCT
ejpam-4868	217	7	16	16	NUM
ejpam-4868	217	8	(	(	PUNCT
ejpam-4868	217	9	4	4	NUM
ejpam-4868	217	10	)	)	PUNCT
ejpam-4868	217	11	(	(	PUNCT
ejpam-4868	217	12	2023	2023	NUM
ejpam-4868	217	13	)	)	PUNCT
ejpam-4868	217	14	,	,	PUNCT
ejpam-4868	217	15	2213	2213	NUM
ejpam-4868	217	16	-	-	SYM
ejpam-4868	217	17	2233	2233	NUM
ejpam-4868	217	18	2222	2222	NUM
ejpam-4868	217	19	remark	remark	NOUN
ejpam-4868	217	20	7	7	NUM
ejpam-4868	217	21	.	.	PUNCT
ejpam-4868	218	1	it	it	PRON
ejpam-4868	218	2	is	be	AUX
ejpam-4868	218	3	clear	clear	ADJ
ejpam-4868	218	4	from	from	ADP
ejpam-4868	218	5	theorem	theorem	ADJ
ejpam-4868	218	6	10	10	NUM
ejpam-4868	218	7	and	and	CCONJ
ejpam-4868	218	8	equation	equation	NOUN
ejpam-4868	218	9	(	(	PUNCT
ejpam-4868	218	10	9	9	NUM
ejpam-4868	218	11	)	)	PUNCT
ejpam-4868	219	1	that	that	PRON
ejpam-4868	219	2	lim	lim	PROPN
ejpam-4868	219	3	λ→0	λ→0	PUNCT
ejpam-4868	219	4	gα	gα	PROPN
ejpam-4868	219	5	,	,	PUNCT
ejpam-4868	219	6	λ{sinh	λ{sinh	X
ejpam-4868	219	7	(	(	PUNCT
ejpam-4868	219	8	a	a	X
ejpam-4868	219	9	)	)	PUNCT
ejpam-4868	219	10	λ	λ	PROPN
ejpam-4868	219	11	(	(	PUNCT
ejpam-4868	219	12	t	t	NOUN
ejpam-4868	219	13	)	)	PUNCT
ejpam-4868	219	14	}	}	PUNCT
ejpam-4868	219	15	=	=	SYM
ejpam-4868	219	16	lim	lim	PROPN
ejpam-4868	219	17	λ→0	λ→0	PUNCT
ejpam-4868	219	18	[	[	PUNCT
ejpam-4868	219	19	auα+2	auα+2	X
ejpam-4868	219	20	(	(	PUNCT
ejpam-4868	219	21	1−	1−	NUM
ejpam-4868	219	22	λu)2	λu)2	NOUN
ejpam-4868	219	23	−	−	PROPN
ejpam-4868	219	24	u2a2	u2a2	NOUN
ejpam-4868	219	25	]	]	X
ejpam-4868	219	26	=	=	SYM
ejpam-4868	219	27	auα+2	auα+2	ADJ
ejpam-4868	219	28	1−	1−	NUM
ejpam-4868	220	1	u2a2	u2a2	PUNCT
ejpam-4868	220	2	=	=	SYM
ejpam-4868	221	1	gα{sinh	gα{sinh	PROPN
ejpam-4868	221	2	at	at	ADP
ejpam-4868	221	3	}	}	PUNCT
ejpam-4868	221	4	.	.	PUNCT
ejpam-4868	222	1	theorem	theorem	VERB
ejpam-4868	222	2	11	11	NUM
ejpam-4868	222	3	.	.	PUNCT
ejpam-4868	223	1	the	the	DET
ejpam-4868	223	2	degenerate	degenerate	ADJ
ejpam-4868	223	3	laplace	laplace	NOUN
ejpam-4868	223	4	-	-	PUNCT
ejpam-4868	223	5	type	type	NOUN
ejpam-4868	223	6	integral	integral	ADJ
ejpam-4868	223	7	transform	transform	NOUN
ejpam-4868	223	8	of	of	ADP
ejpam-4868	223	9	the	the	DET
ejpam-4868	223	10	degenerate	degenerate	ADJ
ejpam-4868	223	11	hyperbolic	hyperbolic	ADJ
ejpam-4868	223	12	cosine	cosine	NOUN
ejpam-4868	223	13	function	function	NOUN
ejpam-4868	223	14	f(t	f(t	NOUN
ejpam-4868	223	15	)	)	PUNCT
ejpam-4868	224	1	=	=	SYM
ejpam-4868	224	2	cosh	cosh	NOUN
ejpam-4868	224	3	(	(	PUNCT
ejpam-4868	224	4	a	a	X
ejpam-4868	224	5	)	)	PUNCT
ejpam-4868	224	6	λ	λ	PROPN
ejpam-4868	224	7	(	(	PUNCT
ejpam-4868	224	8	t	t	PROPN
ejpam-4868	224	9	)	)	PUNCT
ejpam-4868	224	10	is	be	AUX
ejpam-4868	224	11	given	give	VERB
ejpam-4868	224	12	by	by	ADP
ejpam-4868	224	13	gα	gα	NOUN
ejpam-4868	224	14	,	,	PUNCT
ejpam-4868	224	15	λ{cosh	λ{cosh	PRON
ejpam-4868	224	16	(	(	PUNCT
ejpam-4868	224	17	a	a	X
ejpam-4868	224	18	)	)	PUNCT
ejpam-4868	224	19	λ	λ	PROPN
ejpam-4868	224	20	(	(	PUNCT
ejpam-4868	224	21	t	t	NOUN
ejpam-4868	224	22	)	)	PUNCT
ejpam-4868	224	23	}	}	PUNCT
ejpam-4868	224	24	=	=	SYM
ejpam-4868	224	25	(	(	PUNCT
ejpam-4868	224	26	1−	1−	NUM
ejpam-4868	224	27	λu)uα+1	λu)uα+1	NOUN
ejpam-4868	224	28	(	(	PUNCT
ejpam-4868	224	29	1−	1−	NUM
ejpam-4868	224	30	λu)2	λu)2	NOUN
ejpam-4868	224	31	−	−	PROPN
ejpam-4868	224	32	u2a2	u2a2	INTJ
ejpam-4868	224	33	.	.	PUNCT
ejpam-4868	225	1	(	(	PUNCT
ejpam-4868	225	2	19	19	NUM
ejpam-4868	225	3	)	)	PUNCT
ejpam-4868	225	4	proof	proof	NOUN
ejpam-4868	225	5	.	.	PUNCT
ejpam-4868	226	1	by	by	ADP
ejpam-4868	226	2	the	the	DET
ejpam-4868	226	3	definition	definition	NOUN
ejpam-4868	226	4	of	of	ADP
ejpam-4868	226	5	the	the	DET
ejpam-4868	226	6	degenerate	degenerate	ADJ
ejpam-4868	226	7	hyperbolic	hyperbolic	ADJ
ejpam-4868	226	8	cosine	cosine	NOUN
ejpam-4868	226	9	in	in	ADP
ejpam-4868	226	10	[	[	X
ejpam-4868	226	11	?	?	PUNCT
ejpam-4868	226	12	]	]	PUNCT
ejpam-4868	226	13	and	and	CCONJ
ejpam-4868	226	14	using	use	VERB
ejpam-4868	226	15	theorem	theorem	ADJ
ejpam-4868	226	16	2	2	NUM
ejpam-4868	226	17	and	and	CCONJ
ejpam-4868	226	18	theorem	theorem	VERB
ejpam-4868	226	19	7	7	NUM
ejpam-4868	226	20	,	,	PUNCT
ejpam-4868	226	21	we	we	PRON
ejpam-4868	226	22	obtain	obtain	VERB
ejpam-4868	226	23	gα	gα	ADP
ejpam-4868	226	24	,	,	PUNCT
ejpam-4868	226	25	λ{cosh	λ{cosh	PRON
ejpam-4868	226	26	(	(	PUNCT
ejpam-4868	226	27	a	a	X
ejpam-4868	226	28	)	)	PUNCT
ejpam-4868	226	29	λ	λ	PROPN
ejpam-4868	226	30	(	(	PUNCT
ejpam-4868	226	31	t	t	NOUN
ejpam-4868	226	32	)	)	PUNCT
ejpam-4868	226	33	}	}	PUNCT
ejpam-4868	226	34	=	=	SYM
ejpam-4868	226	35	1	1	NUM
ejpam-4868	226	36	2	2	NUM
ejpam-4868	226	37	[	[	PUNCT
ejpam-4868	226	38	gα	gα	NOUN
ejpam-4868	226	39	,	,	PUNCT
ejpam-4868	226	40	λ{eaλ(t)}+	λ{eaλ(t)}+	PRON
ejpam-4868	226	41	gα	gα	NOUN
ejpam-4868	226	42	,	,	PUNCT
ejpam-4868	226	43	λ{e−a	λ{e−a	ADJ
ejpam-4868	226	44	λ	λ	X
ejpam-4868	226	45	(	(	PUNCT
ejpam-4868	226	46	t	t	PROPN
ejpam-4868	226	47	)	)	PUNCT
ejpam-4868	226	48	}	}	PUNCT
ejpam-4868	226	49	]	]	PUNCT
ejpam-4868	227	1	=	=	SYM
ejpam-4868	227	2	1	1	NUM
ejpam-4868	227	3	2	2	NUM
ejpam-4868	227	4	[	[	PUNCT
ejpam-4868	227	5	uα+1	uα+1	NUM
ejpam-4868	227	6	1−	1−	NUM
ejpam-4868	227	7	u(a+	u(a+	ADJ
ejpam-4868	227	8	λ	λ	NOUN
ejpam-4868	227	9	)	)	PUNCT
ejpam-4868	228	1	+	+	NUM
ejpam-4868	228	2	uα+1	uα+1	NUM
ejpam-4868	228	3	1−	1−	NUM
ejpam-4868	228	4	u(−a+	u(−a+	PROPN
ejpam-4868	228	5	λ	λ	NOUN
ejpam-4868	228	6	)	)	PUNCT
ejpam-4868	228	7	]	]	PUNCT
ejpam-4868	229	1	=	=	PUNCT
ejpam-4868	229	2	(	(	PUNCT
ejpam-4868	229	3	1−	1−	NUM
ejpam-4868	229	4	λu)uα+1	λu)uα+1	NOUN
ejpam-4868	229	5	(	(	PUNCT
ejpam-4868	229	6	1−	1−	NUM
ejpam-4868	229	7	λu)2	λu)2	NOUN
ejpam-4868	229	8	−	−	PROPN
ejpam-4868	230	1	u2a2	u2a2	INTJ
ejpam-4868	230	2	.	.	PUNCT
ejpam-4868	231	1	remark	remark	PROPN
ejpam-4868	231	2	8	8	NUM
ejpam-4868	231	3	.	.	PUNCT
ejpam-4868	232	1	it	it	PRON
ejpam-4868	232	2	is	be	AUX
ejpam-4868	232	3	clear	clear	ADJ
ejpam-4868	232	4	from	from	ADP
ejpam-4868	232	5	theorem	theorem	ADJ
ejpam-4868	232	6	11	11	NUM
ejpam-4868	232	7	and	and	CCONJ
ejpam-4868	232	8	equation	equation	NOUN
ejpam-4868	232	9	(	(	PUNCT
ejpam-4868	232	10	9	9	NUM
ejpam-4868	232	11	)	)	PUNCT
ejpam-4868	233	1	that	that	PRON
ejpam-4868	233	2	lim	lim	PROPN
ejpam-4868	233	3	λ→0	λ→0	PUNCT
ejpam-4868	233	4	gα	gα	PROPN
ejpam-4868	233	5	,	,	PUNCT
ejpam-4868	233	6	λ{cosh	λ{cosh	PRON
ejpam-4868	233	7	(	(	PUNCT
ejpam-4868	233	8	a	a	X
ejpam-4868	233	9	)	)	PUNCT
ejpam-4868	233	10	λ	λ	PROPN
ejpam-4868	233	11	(	(	PUNCT
ejpam-4868	233	12	t	t	NOUN
ejpam-4868	233	13	)	)	PUNCT
ejpam-4868	233	14	}	}	PUNCT
ejpam-4868	233	15	=	=	SYM
ejpam-4868	233	16	lim	lim	PROPN
ejpam-4868	233	17	λ→0	λ→0	PUNCT
ejpam-4868	233	18	[	[	PUNCT
ejpam-4868	233	19	(	(	PUNCT
ejpam-4868	233	20	1−	1−	NUM
ejpam-4868	233	21	λu)uα+1	λu)uα+1	NOUN
ejpam-4868	233	22	(	(	PUNCT
ejpam-4868	233	23	1−	1−	NUM
ejpam-4868	233	24	λu)2	λu)2	NOUN
ejpam-4868	233	25	−	−	PROPN
ejpam-4868	234	1	u2a2	u2a2	NOUN
ejpam-4868	234	2	]	]	X
ejpam-4868	234	3	=	=	PUNCT
ejpam-4868	234	4	uα+1	uα+1	NOUN
ejpam-4868	234	5	1−	1−	NUM
ejpam-4868	234	6	u2a2	u2a2	X
ejpam-4868	234	7	=	=	NOUN
ejpam-4868	234	8	gα{cosh	gα{cosh	PROPN
ejpam-4868	234	9	at	at	ADP
ejpam-4868	234	10	}	}	PUNCT
ejpam-4868	234	11	.	.	PUNCT
ejpam-4868	235	1	theorem	theorem	NOUN
ejpam-4868	235	2	12	12	NUM
ejpam-4868	235	3	.	.	PUNCT
ejpam-4868	236	1	the	the	DET
ejpam-4868	236	2	degenerate	degenerate	ADJ
ejpam-4868	236	3	laplace	laplace	NOUN
ejpam-4868	236	4	-	-	PUNCT
ejpam-4868	236	5	type	type	NOUN
ejpam-4868	236	6	integral	integral	ADJ
ejpam-4868	236	7	transform	transform	NOUN
ejpam-4868	236	8	of	of	ADP
ejpam-4868	236	9	the	the	DET
ejpam-4868	236	10	function	function	NOUN
ejpam-4868	236	11	f(t	f(t	PROPN
ejpam-4868	236	12	)	)	PUNCT
ejpam-4868	236	13	=	=	SYM
ejpam-4868	236	14	eaλ(t	eaλ(t	PROPN
ejpam-4868	236	15	)	)	PUNCT
ejpam-4868	236	16	sin	sin	NOUN
ejpam-4868	236	17	(	(	PUNCT
ejpam-4868	236	18	b	b	NOUN
ejpam-4868	236	19	)	)	PUNCT
ejpam-4868	236	20	λ	λ	PROPN
ejpam-4868	236	21	(	(	PUNCT
ejpam-4868	236	22	t	t	PROPN
ejpam-4868	236	23	)	)	PUNCT
ejpam-4868	236	24	is	be	AUX
ejpam-4868	236	25	given	give	VERB
ejpam-4868	236	26	by	by	ADP
ejpam-4868	236	27	gα	gα	NOUN
ejpam-4868	236	28	,	,	PUNCT
ejpam-4868	236	29	λ{eaλ(t	λ{eaλ(t	NOUN
ejpam-4868	236	30	)	)	PUNCT
ejpam-4868	236	31	sin	sin	NOUN
ejpam-4868	236	32	(	(	PUNCT
ejpam-4868	236	33	b	b	NOUN
ejpam-4868	236	34	)	)	PUNCT
ejpam-4868	236	35	λ	λ	PROPN
ejpam-4868	236	36	(	(	PUNCT
ejpam-4868	236	37	t	t	NOUN
ejpam-4868	236	38	)	)	PUNCT
ejpam-4868	236	39	}	}	PUNCT
ejpam-4868	237	1	=	=	PUNCT
ejpam-4868	237	2	buα+2	buα+2	X
ejpam-4868	237	3	(	(	PUNCT
ejpam-4868	237	4	1−	1−	NUM
ejpam-4868	237	5	au−	au−	PUNCT
ejpam-4868	237	6	uλ)2	uλ)2	PROPN
ejpam-4868	237	7	+	+	CCONJ
ejpam-4868	237	8	b2u2	b2u2	PROPN
ejpam-4868	237	9	.	.	PUNCT
ejpam-4868	238	1	(	(	PUNCT
ejpam-4868	238	2	20	20	NUM
ejpam-4868	238	3	)	)	PUNCT
ejpam-4868	238	4	proof	proof	NOUN
ejpam-4868	238	5	.	.	PUNCT
ejpam-4868	239	1	by	by	ADP
ejpam-4868	239	2	the	the	DET
ejpam-4868	239	3	definition	definition	NOUN
ejpam-4868	239	4	of	of	ADP
ejpam-4868	239	5	the	the	DET
ejpam-4868	239	6	degenerate	degenerate	ADJ
ejpam-4868	239	7	sine	sine	NOUN
ejpam-4868	239	8	in	in	ADP
ejpam-4868	239	9	in	in	ADP
ejpam-4868	239	10	definition	definition	NOUN
ejpam-4868	239	11	3	3	NUM
ejpam-4868	239	12	,	,	PUNCT
ejpam-4868	239	13	we	we	PRON
ejpam-4868	239	14	have	have	VERB
ejpam-4868	239	15	eaλ(t	eaλ(t	PROPN
ejpam-4868	239	16	)	)	PUNCT
ejpam-4868	239	17	sin	sin	NOUN
ejpam-4868	239	18	(	(	PUNCT
ejpam-4868	239	19	b	b	NOUN
ejpam-4868	239	20	)	)	PUNCT
ejpam-4868	239	21	λ	λ	PROPN
ejpam-4868	239	22	(	(	PUNCT
ejpam-4868	239	23	t	t	NOUN
ejpam-4868	239	24	)	)	PUNCT
ejpam-4868	240	1	=	=	SYM
ejpam-4868	240	2	eaλ(t	eaλ(t	ADV
ejpam-4868	240	3	)	)	PUNCT
ejpam-4868	240	4	[	[	PUNCT
ejpam-4868	240	5	eibλ	eibλ	NOUN
ejpam-4868	240	6	(	(	PUNCT
ejpam-4868	240	7	t)−	t)−	PROPN
ejpam-4868	240	8	e−ib	e−ib	NOUN
ejpam-4868	240	9	λ	λ	PROPN
ejpam-4868	240	10	(	(	PUNCT
ejpam-4868	240	11	t	t	PROPN
ejpam-4868	240	12	)	)	PUNCT
ejpam-4868	240	13	2i	2i	NOUN
ejpam-4868	240	14	]	]	PUNCT
ejpam-4868	240	15	=	=	PUNCT
ejpam-4868	240	16	ea+ib	ea+ib	SYM
ejpam-4868	240	17	λ	λ	PROPN
ejpam-4868	240	18	(	(	PUNCT
ejpam-4868	240	19	t)−	t)−	PROPN
ejpam-4868	240	20	ea−ib	ea−ib	PROPN
ejpam-4868	240	21	λ	λ	X
ejpam-4868	240	22	(	(	PUNCT
ejpam-4868	240	23	t	t	PROPN
ejpam-4868	240	24	)	)	PUNCT
ejpam-4868	240	25	2i	2i	NOUN
ejpam-4868	240	26	.	.	PUNCT
ejpam-4868	241	1	hence	hence	ADV
ejpam-4868	241	2	,	,	PUNCT
ejpam-4868	241	3	by	by	ADP
ejpam-4868	241	4	theorem	theorem	NOUN
ejpam-4868	241	5	2	2	NUM
ejpam-4868	241	6	and	and	CCONJ
ejpam-4868	241	7	theorem	theorem	VERB
ejpam-4868	241	8	7	7	NUM
ejpam-4868	241	9	,	,	PUNCT
ejpam-4868	241	10	we	we	PRON
ejpam-4868	241	11	obtain	obtain	VERB
ejpam-4868	241	12	gα	gα	ADP
ejpam-4868	241	13	,	,	PUNCT
ejpam-4868	241	14	λ{eaλ(t	λ{eaλ(t	NOUN
ejpam-4868	241	15	)	)	PUNCT
ejpam-4868	241	16	sin	sin	NOUN
ejpam-4868	241	17	(	(	PUNCT
ejpam-4868	241	18	b	b	NOUN
ejpam-4868	241	19	)	)	PUNCT
ejpam-4868	241	20	λ	λ	PROPN
ejpam-4868	241	21	(	(	PUNCT
ejpam-4868	241	22	t	t	NOUN
ejpam-4868	241	23	)	)	PUNCT
ejpam-4868	241	24	}	}	PUNCT
ejpam-4868	242	1	=	=	X
ejpam-4868	242	2	gα	gα	NOUN
ejpam-4868	242	3	,	,	PUNCT
ejpam-4868	242	4	λ	λ	PROPN
ejpam-4868	242	5	{	{	PUNCT
ejpam-4868	242	6	ea+ib	ea+ib	NOUN
ejpam-4868	242	7	λ	λ	PROPN
ejpam-4868	242	8	(	(	PUNCT
ejpam-4868	242	9	t)−	t)−	PROPN
ejpam-4868	242	10	ea−ib	ea−ib	PROPN
ejpam-4868	242	11	λ	λ	X
ejpam-4868	242	12	(	(	PUNCT
ejpam-4868	242	13	t	t	PROPN
ejpam-4868	242	14	)	)	PUNCT
ejpam-4868	242	15	2i	2i	NOUN
ejpam-4868	242	16	}	}	PUNCT
ejpam-4868	242	17	=	=	SYM
ejpam-4868	242	18	1	1	NUM
ejpam-4868	242	19	2i	2i	NUM
ejpam-4868	242	20	[	[	PUNCT
ejpam-4868	242	21	gα	gα	NOUN
ejpam-4868	242	22	,	,	PUNCT
ejpam-4868	242	23	λ	λ	PROPN
ejpam-4868	242	24	{	{	PUNCT
ejpam-4868	242	25	ea+ib	ea+ib	NOUN
ejpam-4868	242	26	λ	λ	PROPN
ejpam-4868	242	27	(	(	PUNCT
ejpam-4868	242	28	t	t	PROPN
ejpam-4868	242	29	)	)	PUNCT
ejpam-4868	242	30	}	}	PUNCT
ejpam-4868	242	31	−	−	ADP
ejpam-4868	242	32	gα	gα	NOUN
ejpam-4868	242	33	,	,	PUNCT
ejpam-4868	242	34	λ	λ	PROPN
ejpam-4868	242	35	{	{	PUNCT
ejpam-4868	242	36	ea−ib	ea−ib	PROPN
ejpam-4868	242	37	λ	λ	PROPN
ejpam-4868	242	38	(	(	PUNCT
ejpam-4868	242	39	t	t	PROPN
ejpam-4868	242	40	)	)	PUNCT
ejpam-4868	242	41	}	}	PUNCT
ejpam-4868	242	42	]	]	PUNCT
ejpam-4868	242	43	=	=	SYM
ejpam-4868	242	44	1	1	NUM
ejpam-4868	242	45	2i	2i	NUM
ejpam-4868	242	46	[	[	PUNCT
ejpam-4868	242	47	uα+1	uα+1	NUM
ejpam-4868	242	48	1−	1−	NUM
ejpam-4868	242	49	u((a+	u((a+	PROPN
ejpam-4868	242	50	ib	ib	X
ejpam-4868	242	51	)	)	PUNCT
ejpam-4868	242	52	+	+	NUM
ejpam-4868	242	53	λ	λ	X
ejpam-4868	242	54	)	)	PUNCT
ejpam-4868	242	55	−	−	NOUN
ejpam-4868	242	56	uα+1	uα+1	NOUN
ejpam-4868	242	57	1−	1−	NUM
ejpam-4868	242	58	u((a−	u((a−	PROPN
ejpam-4868	242	59	ib	ib	X
ejpam-4868	242	60	)	)	PUNCT
ejpam-4868	242	61	+	+	NUM
ejpam-4868	243	1	λ	λ	NOUN
ejpam-4868	243	2	)	)	PUNCT
ejpam-4868	243	3	]	]	PUNCT
ejpam-4868	244	1	=	=	SYM
ejpam-4868	244	2	buα+2	buα+2	X
ejpam-4868	244	3	(	(	PUNCT
ejpam-4868	244	4	1−	1−	NUM
ejpam-4868	244	5	au−	au−	PUNCT
ejpam-4868	244	6	uλ)2	uλ)2	PROPN
ejpam-4868	244	7	+	+	CCONJ
ejpam-4868	244	8	b2u2	b2u2	PROPN
ejpam-4868	244	9	.	.	PUNCT
ejpam-4868	245	1	h.	h.	PROPN
ejpam-4868	245	2	j.	j.	PROPN
ejpam-4868	245	3	campos	campos	PROPN
ejpam-4868	245	4	,	,	PUNCT
ejpam-4868	245	5	j.	j.	PROPN
ejpam-4868	245	6	c.	c.	PROPN
ejpam-4868	245	7	fernandez	fernandez	PROPN
ejpam-4868	245	8	,	,	PUNCT
ejpam-4868	245	9	j.	j.	PROPN
ejpam-4868	245	10	b.	b.	PROPN
ejpam-4868	245	11	m.	m.	PROPN
ejpam-4868	245	12	natuil	natuil	PROPN
ejpam-4868	245	13	/	/	SYM
ejpam-4868	245	14	eur	eur	PROPN
ejpam-4868	245	15	.	.	PUNCT
ejpam-4868	246	1	j.	j.	PROPN
ejpam-4868	246	2	pure	pure	PROPN
ejpam-4868	246	3	appl	appl	PROPN
ejpam-4868	246	4	.	.	PROPN
ejpam-4868	246	5	math	math	PROPN
ejpam-4868	246	6	,	,	PUNCT
ejpam-4868	246	7	16	16	NUM
ejpam-4868	246	8	(	(	PUNCT
ejpam-4868	246	9	4	4	NUM
ejpam-4868	246	10	)	)	PUNCT
ejpam-4868	246	11	(	(	PUNCT
ejpam-4868	246	12	2023	2023	NUM
ejpam-4868	246	13	)	)	PUNCT
ejpam-4868	246	14	,	,	PUNCT
ejpam-4868	246	15	2213	2213	NUM
ejpam-4868	246	16	-	-	SYM
ejpam-4868	246	17	2233	2233	NUM
ejpam-4868	246	18	2223	2223	NUM
ejpam-4868	246	19	remark	remark	NOUN
ejpam-4868	246	20	9	9	NUM
ejpam-4868	246	21	.	.	PUNCT
ejpam-4868	247	1	it	it	PRON
ejpam-4868	247	2	is	be	AUX
ejpam-4868	247	3	clear	clear	ADJ
ejpam-4868	247	4	from	from	ADP
ejpam-4868	247	5	theorem	theorem	ADJ
ejpam-4868	247	6	12	12	NUM
ejpam-4868	247	7	and	and	CCONJ
ejpam-4868	247	8	equation	equation	NOUN
ejpam-4868	247	9	(	(	PUNCT
ejpam-4868	247	10	9	9	NUM
ejpam-4868	247	11	)	)	PUNCT
ejpam-4868	247	12	that	that	PRON
ejpam-4868	247	13	lim	lim	PROPN
ejpam-4868	247	14	λ→0	λ→0	PUNCT
ejpam-4868	247	15	gα	gα	PROPN
ejpam-4868	247	16	,	,	PUNCT
ejpam-4868	247	17	λ{eaλ(t	λ{eaλ(t	NOUN
ejpam-4868	247	18	)	)	PUNCT
ejpam-4868	247	19	sin	sin	NOUN
ejpam-4868	247	20	(	(	PUNCT
ejpam-4868	247	21	b	b	NOUN
ejpam-4868	247	22	)	)	PUNCT
ejpam-4868	247	23	λ	λ	PROPN
ejpam-4868	247	24	(	(	PUNCT
ejpam-4868	247	25	t	t	NOUN
ejpam-4868	247	26	)	)	PUNCT
ejpam-4868	247	27	}	}	PUNCT
ejpam-4868	248	1	=	=	SYM
ejpam-4868	248	2	lim	lim	PROPN
ejpam-4868	248	3	λ→0	λ→0	PROPN
ejpam-4868	248	4	[	[	PUNCT
ejpam-4868	248	5	buα+2	buα+2	X
ejpam-4868	248	6	(	(	PUNCT
ejpam-4868	248	7	1−	1−	NUM
ejpam-4868	248	8	au−	au−	PUNCT
ejpam-4868	248	9	uλ)2	uλ)2	PROPN
ejpam-4868	248	10	+	+	CCONJ
ejpam-4868	248	11	b2u2	b2u2	PROPN
ejpam-4868	248	12	]	]	PUNCT
ejpam-4868	248	13	=	=	SYM
ejpam-4868	248	14	buα+2	buα+2	X
ejpam-4868	248	15	(	(	PUNCT
ejpam-4868	248	16	1−	1−	NUM
ejpam-4868	248	17	au)2	au)2	ADP
ejpam-4868	248	18	+	+	PUNCT
ejpam-4868	248	19	b2u2	b2u2	PROPN
ejpam-4868	248	20	=	=	SYM
ejpam-4868	248	21	gα{eat	gα{eat	ADJ
ejpam-4868	248	22	sin	sin	NOUN
ejpam-4868	248	23	bt	bt	NOUN
ejpam-4868	248	24	}	}	PUNCT
ejpam-4868	248	25	.	.	PUNCT
ejpam-4868	249	1	theorem	theorem	VERB
ejpam-4868	249	2	13	13	NUM
ejpam-4868	249	3	.	.	PUNCT
ejpam-4868	250	1	the	the	DET
ejpam-4868	250	2	degenerate	degenerate	ADJ
ejpam-4868	250	3	laplace	laplace	NOUN
ejpam-4868	250	4	-	-	PUNCT
ejpam-4868	250	5	type	type	NOUN
ejpam-4868	250	6	integral	integral	ADJ
ejpam-4868	250	7	transform	transform	NOUN
ejpam-4868	250	8	of	of	ADP
ejpam-4868	250	9	the	the	DET
ejpam-4868	250	10	function	function	NOUN
ejpam-4868	250	11	f(t	f(t	PROPN
ejpam-4868	250	12	)	)	PUNCT
ejpam-4868	250	13	=	=	SYM
ejpam-4868	251	1	eaλ(t	eaλ(t	PROPN
ejpam-4868	251	2	)	)	PUNCT
ejpam-4868	251	3	cos	cos	PROPN
ejpam-4868	251	4	(	(	PUNCT
ejpam-4868	251	5	b	b	X
ejpam-4868	251	6	)	)	PUNCT
ejpam-4868	251	7	λ	λ	PROPN
ejpam-4868	251	8	(	(	PUNCT
ejpam-4868	251	9	t	t	PROPN
ejpam-4868	251	10	)	)	PUNCT
ejpam-4868	251	11	is	be	AUX
ejpam-4868	251	12	given	give	VERB
ejpam-4868	251	13	by	by	ADP
ejpam-4868	251	14	gα	gα	NOUN
ejpam-4868	251	15	,	,	PUNCT
ejpam-4868	251	16	λ{eaλ(t	λ{eaλ(t	X
ejpam-4868	251	17	)	)	PUNCT
ejpam-4868	251	18	cos	cos	PROPN
ejpam-4868	251	19	(	(	PUNCT
ejpam-4868	251	20	b	b	X
ejpam-4868	251	21	)	)	PUNCT
ejpam-4868	251	22	λ	λ	PROPN
ejpam-4868	251	23	(	(	PUNCT
ejpam-4868	251	24	t	t	NOUN
ejpam-4868	251	25	)	)	PUNCT
ejpam-4868	251	26	}	}	PUNCT
ejpam-4868	251	27	=	=	SYM
ejpam-4868	251	28	(	(	PUNCT
ejpam-4868	251	29	1−	1−	NUM
ejpam-4868	251	30	au−	au−	NUM
ejpam-4868	251	31	uλ)uα+1	uλ)uα+1	NOUN
ejpam-4868	251	32	(	(	PUNCT
ejpam-4868	251	33	1−	1−	NUM
ejpam-4868	251	34	au−	au−	PUNCT
ejpam-4868	251	35	uλ)2	uλ)2	PROPN
ejpam-4868	251	36	+	+	CCONJ
ejpam-4868	251	37	b2u2	b2u2	PROPN
ejpam-4868	251	38	.	.	PUNCT
ejpam-4868	252	1	(	(	PUNCT
ejpam-4868	252	2	21	21	NUM
ejpam-4868	252	3	)	)	PUNCT
ejpam-4868	252	4	proof	proof	NOUN
ejpam-4868	252	5	.	.	PUNCT
ejpam-4868	253	1	by	by	ADP
ejpam-4868	253	2	the	the	DET
ejpam-4868	253	3	definition	definition	NOUN
ejpam-4868	253	4	of	of	ADP
ejpam-4868	253	5	the	the	DET
ejpam-4868	253	6	degenerate	degenerate	ADJ
ejpam-4868	253	7	hyperbolic	hyperbolic	ADJ
ejpam-4868	253	8	cosine	cosine	NOUN
ejpam-4868	253	9	in	in	ADP
ejpam-4868	253	10	definition	definition	NOUN
ejpam-4868	253	11	7	7	NUM
ejpam-4868	253	12	,	,	PUNCT
ejpam-4868	253	13	theorem	theorem	ADJ
ejpam-4868	253	14	2	2	NUM
ejpam-4868	253	15	and	and	CCONJ
ejpam-4868	253	16	theorem	theorem	VERB
ejpam-4868	253	17	7	7	NUM
ejpam-4868	253	18	,	,	PUNCT
ejpam-4868	253	19	we	we	PRON
ejpam-4868	253	20	obtain	obtain	VERB
ejpam-4868	253	21	gα	gα	ADP
ejpam-4868	253	22	,	,	PUNCT
ejpam-4868	253	23	λ{eaλ(t	λ{eaλ(t	X
ejpam-4868	253	24	)	)	PUNCT
ejpam-4868	253	25	cos	cos	PROPN
ejpam-4868	253	26	(	(	PUNCT
ejpam-4868	253	27	b	b	X
ejpam-4868	253	28	)	)	PUNCT
ejpam-4868	253	29	λ	λ	PROPN
ejpam-4868	253	30	(	(	PUNCT
ejpam-4868	253	31	t	t	NOUN
ejpam-4868	253	32	)	)	PUNCT
ejpam-4868	253	33	}	}	PUNCT
ejpam-4868	254	1	=	=	X
ejpam-4868	254	2	gα	gα	NOUN
ejpam-4868	254	3	,	,	PUNCT
ejpam-4868	254	4	λ	λ	PROPN
ejpam-4868	254	5	{	{	PUNCT
ejpam-4868	254	6	ea+ib	ea+ib	NOUN
ejpam-4868	254	7	λ	λ	PROPN
ejpam-4868	254	8	(	(	PUNCT
ejpam-4868	254	9	t	t	PROPN
ejpam-4868	254	10	)	)	PUNCT
ejpam-4868	254	11	+	+	CCONJ
ejpam-4868	254	12	ea−ib	ea−ib	X
ejpam-4868	254	13	λ	λ	X
ejpam-4868	254	14	(	(	PUNCT
ejpam-4868	254	15	t	t	PROPN
ejpam-4868	254	16	)	)	PUNCT
ejpam-4868	254	17	2	2	NUM
ejpam-4868	254	18	}	}	PUNCT
ejpam-4868	254	19	=	=	SYM
ejpam-4868	254	20	(	(	PUNCT
ejpam-4868	254	21	1−	1−	NUM
ejpam-4868	254	22	au−	au−	NUM
ejpam-4868	254	23	uλ)uα+1	uλ)uα+1	NOUN
ejpam-4868	254	24	(	(	PUNCT
ejpam-4868	254	25	1−	1−	NUM
ejpam-4868	254	26	au−	au−	PUNCT
ejpam-4868	254	27	uλ)2	uλ)2	PROPN
ejpam-4868	254	28	+	+	CCONJ
ejpam-4868	254	29	b2u2	b2u2	PROPN
ejpam-4868	254	30	.	.	PUNCT
ejpam-4868	254	31	remark	remark	PROPN
ejpam-4868	254	32	10	10	NUM
ejpam-4868	254	33	.	.	PUNCT
ejpam-4868	255	1	it	it	PRON
ejpam-4868	255	2	is	be	AUX
ejpam-4868	255	3	clear	clear	ADJ
ejpam-4868	255	4	from	from	ADP
ejpam-4868	255	5	theorem	theorem	ADJ
ejpam-4868	255	6	13	13	NUM
ejpam-4868	255	7	and	and	CCONJ
ejpam-4868	255	8	equation	equation	NOUN
ejpam-4868	255	9	(	(	PUNCT
ejpam-4868	255	10	9	9	NUM
ejpam-4868	255	11	)	)	PUNCT
ejpam-4868	255	12	that	that	PRON
ejpam-4868	255	13	lim	lim	PROPN
ejpam-4868	255	14	λ→0	λ→0	PUNCT
ejpam-4868	255	15	gα	gα	PROPN
ejpam-4868	255	16	,	,	PUNCT
ejpam-4868	255	17	λ{eaλ(t	λ{eaλ(t	X
ejpam-4868	255	18	)	)	PUNCT
ejpam-4868	255	19	cos	cos	PROPN
ejpam-4868	255	20	(	(	PUNCT
ejpam-4868	255	21	b	b	X
ejpam-4868	255	22	)	)	PUNCT
ejpam-4868	255	23	λ	λ	PROPN
ejpam-4868	255	24	(	(	PUNCT
ejpam-4868	255	25	t	t	NOUN
ejpam-4868	255	26	)	)	PUNCT
ejpam-4868	255	27	}	}	PUNCT
ejpam-4868	256	1	=	=	SYM
ejpam-4868	256	2	lim	lim	PROPN
ejpam-4868	256	3	λ→0	λ→0	PUNCT
ejpam-4868	256	4	[	[	PUNCT
ejpam-4868	256	5	(	(	PUNCT
ejpam-4868	256	6	1−	1−	NUM
ejpam-4868	256	7	au−	au−	NUM
ejpam-4868	256	8	uλ)uα+1	uλ)uα+1	NOUN
ejpam-4868	256	9	(	(	PUNCT
ejpam-4868	256	10	1−	1−	NUM
ejpam-4868	256	11	au−	au−	PUNCT
ejpam-4868	256	12	uλ)2	uλ)2	PROPN
ejpam-4868	256	13	+	+	CCONJ
ejpam-4868	256	14	b2u2	b2u2	PROPN
ejpam-4868	256	15	]	]	X
ejpam-4868	256	16	=	=	PUNCT
ejpam-4868	256	17	(	(	PUNCT
ejpam-4868	256	18	1−	1−	NUM
ejpam-4868	256	19	au)uα+1	au)uα+1	NOUN
ejpam-4868	256	20	(	(	PUNCT
ejpam-4868	256	21	1−	1−	NUM
ejpam-4868	256	22	au)2	au)2	ADV
ejpam-4868	256	23	+	+	PUNCT
ejpam-4868	256	24	b2u2	b2u2	PROPN
ejpam-4868	256	25	=	=	SYM
ejpam-4868	256	26	gα{eat	gα{eat	PROPN
ejpam-4868	256	27	cos	cos	PROPN
ejpam-4868	256	28	bt	bt	PROPN
ejpam-4868	256	29	}	}	PUNCT
ejpam-4868	256	30	.	.	PUNCT
ejpam-4868	257	1	4.1	4.1	NUM
ejpam-4868	257	2	.	.	PUNCT
ejpam-4868	257	3	degenerate	degenerate	ADJ
ejpam-4868	257	4	laplace	laplace	NOUN
ejpam-4868	257	5	-	-	PUNCT
ejpam-4868	257	6	type	type	NOUN
ejpam-4868	257	7	integral	integral	ADJ
ejpam-4868	257	8	transform	transform	NOUN
ejpam-4868	257	9	of	of	ADP
ejpam-4868	257	10	derivative	derivative	ADJ
ejpam-4868	257	11	theorem	theorem	NOUN
ejpam-4868	257	12	14	14	NUM
ejpam-4868	257	13	.	.	PUNCT
ejpam-4868	258	1	if	if	SCONJ
ejpam-4868	258	2	f(t	f(t	NOUN
ejpam-4868	258	3	)	)	PUNCT
ejpam-4868	258	4	,	,	PUNCT
ejpam-4868	258	5	f	f	PROPN
ejpam-4868	258	6	′(t	′(t	PROPN
ejpam-4868	258	7	)	)	PUNCT
ejpam-4868	258	8	,	,	PUNCT
ejpam-4868	258	9	...	...	PUNCT
ejpam-4868	258	10	,	,	PUNCT
ejpam-4868	258	11	f	f	PROPN
ejpam-4868	258	12	(	(	PUNCT
ejpam-4868	258	13	n−1)(t	n−1)(t	PROPN
ejpam-4868	258	14	)	)	PUNCT
ejpam-4868	258	15	are	be	AUX
ejpam-4868	258	16	continuous	continuous	ADJ
ejpam-4868	258	17	and	and	CCONJ
ejpam-4868	258	18	f	f	PROPN
ejpam-4868	258	19	(	(	PUNCT
ejpam-4868	258	20	n)(t	n)(t	PROPN
ejpam-4868	258	21	)	)	PUNCT
ejpam-4868	258	22	is	be	AUX
ejpam-4868	258	23	a	a	DET
ejpam-4868	258	24	piecewise	piecewise	NOUN
ejpam-4868	258	25	-	-	PUNCT
ejpam-4868	258	26	continuous	continuous	ADJ
ejpam-4868	258	27	function	function	NOUN
ejpam-4868	258	28	on	on	ADP
ejpam-4868	258	29	[	[	X
ejpam-4868	258	30	0,∞	0,∞	NOUN
ejpam-4868	258	31	)	)	PUNCT
ejpam-4868	258	32	and	and	CCONJ
ejpam-4868	258	33	has	have	VERB
ejpam-4868	258	34	a	a	DET
ejpam-4868	258	35	degenerate	degenerate	ADJ
ejpam-4868	258	36	exponential	exponential	ADJ
ejpam-4868	258	37	order	order	NOUN
ejpam-4868	258	38	at	at	ADP
ejpam-4868	258	39	infinity	infinity	NOUN
ejpam-4868	258	40	with	with	ADP
ejpam-4868	258	41	∣∣f	∣∣f	NOUN
ejpam-4868	258	42	(	(	PUNCT
ejpam-4868	258	43	n)(t	n)(t	PROPN
ejpam-4868	258	44	)	)	PUNCT
ejpam-4868	259	1	∣∣	∣∣	NUM
ejpam-4868	259	2	≤	≤	PROPN
ejpam-4868	259	3	mecλ	mecλ	PROPN
ejpam-4868	259	4	(	(	PUNCT
ejpam-4868	259	5	t	t	PROPN
ejpam-4868	259	6	)	)	PUNCT
ejpam-4868	259	7	for	for	ADP
ejpam-4868	259	8	t	t	PROPN
ejpam-4868	259	9	≥	≥	X
ejpam-4868	259	10	c	c	NOUN
ejpam-4868	259	11	,	,	PUNCT
ejpam-4868	259	12	where	where	SCONJ
ejpam-4868	259	13	c	c	PROPN
ejpam-4868	259	14	is	be	AUX
ejpam-4868	259	15	a	a	DET
ejpam-4868	259	16	constant	constant	ADJ
ejpam-4868	259	17	,	,	PUNCT
ejpam-4868	259	18	then	then	ADV
ejpam-4868	259	19	the	the	DET
ejpam-4868	259	20	following	follow	VERB
ejpam-4868	259	21	hold	hold	NOUN
ejpam-4868	259	22	:	:	PUNCT
ejpam-4868	259	23	(	(	PUNCT
ejpam-4868	259	24	i.	i.	NOUN
ejpam-4868	259	25	)	)	PUNCT
ejpam-4868	259	26	gα	gα	ADP
ejpam-4868	259	27	,	,	PUNCT
ejpam-4868	259	28	λ{f	λ{f	NOUN
ejpam-4868	259	29	′(t	′(t	NOUN
ejpam-4868	259	30	)	)	PUNCT
ejpam-4868	259	31	}	}	PUNCT
ejpam-4868	259	32	=	=	SYM
ejpam-4868	259	33	1	1	NUM
ejpam-4868	259	34	u	u	NOUN
ejpam-4868	259	35	gα	gα	NOUN
ejpam-4868	259	36	,	,	PUNCT
ejpam-4868	259	37	λ	λ	X
ejpam-4868	259	38	{	{	PUNCT
ejpam-4868	259	39	(	(	PUNCT
ejpam-4868	259	40	1	1	NUM
ejpam-4868	259	41	+	+	NUM
ejpam-4868	259	42	λt)−1f(t	λt)−1f(t	NOUN
ejpam-4868	259	43	)	)	PUNCT
ejpam-4868	259	44	}	}	PUNCT
ejpam-4868	259	45	−	−	PROPN
ejpam-4868	259	46	uαf(0	uαf(0	NOUN
ejpam-4868	259	47	)	)	PUNCT
ejpam-4868	259	48	(	(	PUNCT
ejpam-4868	259	49	ii	ii	NOUN
ejpam-4868	259	50	.	.	PUNCT
ejpam-4868	259	51	)	)	PUNCT
ejpam-4868	260	1	gα	gα	ADP
ejpam-4868	260	2	,	,	PUNCT
ejpam-4868	260	3	λ{f	λ{f	NOUN
ejpam-4868	260	4	′′(t	′′(t	NOUN
ejpam-4868	260	5	)	)	PUNCT
ejpam-4868	260	6	}	}	PUNCT
ejpam-4868	260	7	=	=	SYM
ejpam-4868	260	8	1	1	NUM
ejpam-4868	260	9	u2	u2	NOUN
ejpam-4868	260	10	(	(	PUNCT
ejpam-4868	260	11	1	1	NUM
ejpam-4868	260	12	+	+	CCONJ
ejpam-4868	260	13	λu)gα	λu)gα	PROPN
ejpam-4868	260	14	,	,	PUNCT
ejpam-4868	260	15	λ	λ	INTJ
ejpam-4868	260	16	{	{	PUNCT
ejpam-4868	260	17	(	(	PUNCT
ejpam-4868	260	18	1	1	NUM
ejpam-4868	260	19	+	+	NUM
ejpam-4868	260	20	λt)−2f(t	λt)−2f(t	NOUN
ejpam-4868	260	21	)	)	PUNCT
ejpam-4868	260	22	}	}	PUNCT
ejpam-4868	260	23	−	−	ADP
ejpam-4868	260	24	uα−1f(0)−	uα−1f(0)−	NOUN
ejpam-4868	260	25	uαf	uαf	X
ejpam-4868	260	26	′(0	′(0	PROPN
ejpam-4868	260	27	)	)	PUNCT
ejpam-4868	260	28	(	(	PUNCT
ejpam-4868	260	29	iii	iii	NOUN
ejpam-4868	260	30	.	.	PUNCT
ejpam-4868	260	31	)	)	PUNCT
ejpam-4868	261	1	gα	gα	ADP
ejpam-4868	261	2	,	,	PUNCT
ejpam-4868	261	3	λ{f	λ{f	NOUN
ejpam-4868	261	4	(	(	PUNCT
ejpam-4868	261	5	n)(t	n)(t	PROPN
ejpam-4868	261	6	)	)	PUNCT
ejpam-4868	261	7	}	}	PUNCT
ejpam-4868	261	8	=	=	SYM
ejpam-4868	261	9	1	1	NUM
ejpam-4868	261	10	un	un	PROPN
ejpam-4868	261	11	gα	gα	PROPN
ejpam-4868	261	12	,	,	PUNCT
ejpam-4868	261	13	λ	λ	PROPN
ejpam-4868	261	14	{	{	PUNCT
ejpam-4868	261	15	(	(	PUNCT
ejpam-4868	261	16	1	1	NUM
ejpam-4868	261	17	+	+	NUM
ejpam-4868	261	18	λt)−nf(t	λt)−nf(t	NOUN
ejpam-4868	261	19	)	)	PUNCT
ejpam-4868	261	20	}	}	PUNCT
ejpam-4868	261	21	n−1∏	n−1∏	NUM
ejpam-4868	261	22	l=1	l=1	PROPN
ejpam-4868	261	23	(	(	PUNCT
ejpam-4868	261	24	1	1	NUM
ejpam-4868	261	25	+	+	CCONJ
ejpam-4868	261	26	luλ	luλ	NOUN
ejpam-4868	261	27	)	)	PUNCT
ejpam-4868	261	28	−	−	PUNCT
ejpam-4868	262	1	uα+1−n	uα+1−n	PROPN
ejpam-4868	262	2	n−1∑	n−1∑	PROPN
ejpam-4868	262	3	i=0	i=0	PROPN
ejpam-4868	262	4	uif	uif	PROPN
ejpam-4868	262	5	(	(	PUNCT
ejpam-4868	262	6	i)(0	i)(0	PROPN
ejpam-4868	262	7	)	)	PUNCT
ejpam-4868	262	8	[	[	PUNCT
ejpam-4868	262	9	n−i−2∏	n−i−2∏	NOUN
ejpam-4868	262	10	l=1	l=1	PROPN
ejpam-4868	262	11	(	(	PUNCT
ejpam-4868	262	12	1	1	NUM
ejpam-4868	262	13	+	+	CCONJ
ejpam-4868	262	14	luλ	luλ	NOUN
ejpam-4868	262	15	)	)	PUNCT
ejpam-4868	262	16	]	]	PUNCT
ejpam-4868	262	17	,	,	PUNCT
ejpam-4868	262	18	where	where	SCONJ
ejpam-4868	262	19	f	f	PROPN
ejpam-4868	262	20	(	(	PUNCT
ejpam-4868	262	21	n)(t	n)(t	PROPN
ejpam-4868	262	22	)	)	PUNCT
ejpam-4868	262	23	=	=	PUNCT
ejpam-4868	262	24	(	(	PUNCT
ejpam-4868	262	25	d	d	X
ejpam-4868	262	26	dt	dt	NOUN
ejpam-4868	262	27	)	)	PUNCT
ejpam-4868	262	28	n	n	PRON
ejpam-4868	262	29	f(t	f(t	NOUN
ejpam-4868	262	30	)	)	PUNCT
ejpam-4868	262	31	and	and	CCONJ
ejpam-4868	262	32	n	n	CCONJ
ejpam-4868	262	33	=	=	SYM
ejpam-4868	262	34	1	1	NUM
ejpam-4868	262	35	,	,	PUNCT
ejpam-4868	262	36	2	2	NUM
ejpam-4868	262	37	,	,	PUNCT
ejpam-4868	262	38	3	3	NUM
ejpam-4868	262	39	,	,	PUNCT
ejpam-4868	262	40	4	4	NUM
ejpam-4868	262	41	,	,	PUNCT
ejpam-4868	262	42	·	·	PUNCT
ejpam-4868	262	43	·	·	PUNCT
ejpam-4868	262	44	·	·	PUNCT
ejpam-4868	262	45	.	.	PUNCT
ejpam-4868	263	1	h.	h.	PROPN
ejpam-4868	263	2	j.	j.	PROPN
ejpam-4868	263	3	campos	campos	PROPN
ejpam-4868	263	4	,	,	PUNCT
ejpam-4868	263	5	j.	j.	PROPN
ejpam-4868	263	6	c.	c.	PROPN
ejpam-4868	263	7	fernandez	fernandez	PROPN
ejpam-4868	263	8	,	,	PUNCT
ejpam-4868	263	9	j.	j.	PROPN
ejpam-4868	263	10	b.	b.	PROPN
ejpam-4868	263	11	m.	m.	PROPN
ejpam-4868	263	12	natuil	natuil	PROPN
ejpam-4868	263	13	/	/	SYM
ejpam-4868	263	14	eur	eur	PROPN
ejpam-4868	263	15	.	.	PUNCT
ejpam-4868	264	1	j.	j.	PROPN
ejpam-4868	264	2	pure	pure	PROPN
ejpam-4868	264	3	appl	appl	PROPN
ejpam-4868	264	4	.	.	PROPN
ejpam-4868	264	5	math	math	PROPN
ejpam-4868	264	6	,	,	PUNCT
ejpam-4868	264	7	16	16	NUM
ejpam-4868	264	8	(	(	PUNCT
ejpam-4868	264	9	4	4	NUM
ejpam-4868	264	10	)	)	PUNCT
ejpam-4868	264	11	(	(	PUNCT
ejpam-4868	264	12	2023	2023	NUM
ejpam-4868	264	13	)	)	PUNCT
ejpam-4868	264	14	,	,	PUNCT
ejpam-4868	264	15	2213	2213	NUM
ejpam-4868	264	16	-	-	SYM
ejpam-4868	264	17	2233	2233	NUM
ejpam-4868	264	18	2224	2224	NUM
ejpam-4868	264	19	proof	proof	NOUN
ejpam-4868	264	20	.	.	PUNCT
ejpam-4868	265	1	first	first	ADV
ejpam-4868	265	2	we	we	PRON
ejpam-4868	265	3	prove	prove	VERB
ejpam-4868	265	4	(	(	PUNCT
ejpam-4868	265	5	i.	i.	NOUN
ejpam-4868	265	6	)	)	PUNCT
ejpam-4868	265	7	.	.	PUNCT
ejpam-4868	266	1	by	by	ADP
ejpam-4868	266	2	definition	definition	NOUN
ejpam-4868	266	3	8	8	NUM
ejpam-4868	266	4	,	,	PUNCT
ejpam-4868	266	5	we	we	PRON
ejpam-4868	266	6	have	have	VERB
ejpam-4868	266	7	gα	gα	ADP
ejpam-4868	266	8	,	,	PUNCT
ejpam-4868	266	9	λ{f	λ{f	NOUN
ejpam-4868	266	10	′(t	′(t	NOUN
ejpam-4868	266	11	)	)	PUNCT
ejpam-4868	266	12	}	}	PUNCT
ejpam-4868	267	1	=	=	PUNCT
ejpam-4868	267	2	uα	uα	PROPN
ejpam-4868	267	3	∫	∫	PROPN
ejpam-4868	267	4	∞	∞	PROPN
ejpam-4868	267	5	0	0	NUM
ejpam-4868	268	1	(	(	PUNCT
ejpam-4868	268	2	1	1	NUM
ejpam-4868	268	3	+	+	CCONJ
ejpam-4868	268	4	λt)−	λt)−	PROPN
ejpam-4868	268	5	1	1	X
ejpam-4868	268	6	uλ	uλ	ADP
ejpam-4868	268	7	f	f	PROPN
ejpam-4868	268	8	′(t)dt	′(t)dt	PROPN
ejpam-4868	268	9	=	=	PUNCT
ejpam-4868	268	10	uα	uα	PROPN
ejpam-4868	268	11	lim	lim	PROPN
ejpam-4868	268	12	r→∞	r→∞	PUNCT
ejpam-4868	268	13	∫	∫	PROPN
ejpam-4868	269	1	r	r	NOUN
ejpam-4868	269	2	0	0	NUM
ejpam-4868	269	3	(	(	PUNCT
ejpam-4868	269	4	1	1	NUM
ejpam-4868	269	5	+	+	CCONJ
ejpam-4868	269	6	λt)−	λt)−	PROPN
ejpam-4868	269	7	1	1	NUM
ejpam-4868	269	8	uλ	uλ	ADP
ejpam-4868	269	9	f	f	PROPN
ejpam-4868	269	10	′(t)dt	′(t)dt	PROPN
ejpam-4868	269	11	.	.	PUNCT
ejpam-4868	270	1	using	use	VERB
ejpam-4868	270	2	integration	integration	NOUN
ejpam-4868	270	3	by	by	ADP
ejpam-4868	270	4	parts	part	NOUN
ejpam-4868	270	5	,	,	PUNCT
ejpam-4868	270	6	we	we	PRON
ejpam-4868	270	7	get	get	VERB
ejpam-4868	270	8	gα	gα	ADP
ejpam-4868	270	9	,	,	PUNCT
ejpam-4868	270	10	λ{f	λ{f	NOUN
ejpam-4868	270	11	′(t	′(t	NOUN
ejpam-4868	270	12	)	)	PUNCT
ejpam-4868	270	13	}	}	PUNCT
ejpam-4868	271	1	=	=	NUM
ejpam-4868	271	2	uα	uα	PROPN
ejpam-4868	271	3	lim	lim	PROPN
ejpam-4868	271	4	r→∞	r→∞	NUM
ejpam-4868	271	5	[	[	PUNCT
ejpam-4868	271	6	(	(	PUNCT
ejpam-4868	271	7	1	1	NUM
ejpam-4868	271	8	+	+	CCONJ
ejpam-4868	271	9	λt)−	λt)−	PROPN
ejpam-4868	271	10	1	1	NUM
ejpam-4868	271	11	uλ	uλ	ADP
ejpam-4868	271	12	f(t	f(t	PROPN
ejpam-4868	271	13	)	)	PUNCT
ejpam-4868	271	14	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-4868	272	1	r	r	NOUN
ejpam-4868	272	2	0	0	NUM
ejpam-4868	272	3	]	]	PUNCT
ejpam-4868	273	1	+	+	CCONJ
ejpam-4868	273	2	uα	uα	PROPN
ejpam-4868	273	3	u	u	PROPN
ejpam-4868	273	4	lim	lim	PROPN
ejpam-4868	273	5	r→∞	r→∞	NUM
ejpam-4868	274	1	[	[	X
ejpam-4868	274	2	∫	∫	X
ejpam-4868	274	3	r	r	NOUN
ejpam-4868	274	4	0	0	NUM
ejpam-4868	274	5	(	(	PUNCT
ejpam-4868	274	6	1	1	NUM
ejpam-4868	274	7	+	+	CCONJ
ejpam-4868	274	8	λt)−1−	λt)−1−	NOUN
ejpam-4868	274	9	1	1	NUM
ejpam-4868	274	10	uλ	uλ	ADP
ejpam-4868	274	11	f(t)dt	f(t)dt	PROPN
ejpam-4868	274	12	]	]	PUNCT
ejpam-4868	274	13	=	=	NOUN
ejpam-4868	274	14	uα	uα	PROPN
ejpam-4868	274	15	lim	lim	PROPN
ejpam-4868	274	16	r→∞	r→∞	NUM
ejpam-4868	274	17	[	[	PUNCT
ejpam-4868	274	18	(	(	PUNCT
ejpam-4868	274	19	1	1	NUM
ejpam-4868	274	20	+	+	CCONJ
ejpam-4868	274	21	λr)−	λr)−	NOUN
ejpam-4868	274	22	1	1	NUM
ejpam-4868	274	23	uλ	uλ	ADP
ejpam-4868	274	24	f(r)−	f(r)−	PROPN
ejpam-4868	274	25	(	(	PUNCT
ejpam-4868	274	26	1	1	NUM
ejpam-4868	274	27	+	+	CCONJ
ejpam-4868	274	28	λ0)−	λ0)−	PROPN
ejpam-4868	274	29	1	1	NUM
ejpam-4868	274	30	uλ	uλ	ADP
ejpam-4868	274	31	f(0	f(0	NOUN
ejpam-4868	274	32	)	)	PUNCT
ejpam-4868	274	33	]	]	PUNCT
ejpam-4868	275	1	+	+	CCONJ
ejpam-4868	275	2	1	1	NUM
ejpam-4868	275	3	u	u	NOUN
ejpam-4868	275	4	gα	gα	NOUN
ejpam-4868	275	5	,	,	PUNCT
ejpam-4868	275	6	λ	λ	X
ejpam-4868	275	7	{	{	PUNCT
ejpam-4868	275	8	(	(	PUNCT
ejpam-4868	275	9	1	1	NUM
ejpam-4868	275	10	+	+	NUM
ejpam-4868	275	11	λt)−1f(t	λt)−1f(t	NOUN
ejpam-4868	275	12	)	)	PUNCT
ejpam-4868	275	13	}	}	PUNCT
ejpam-4868	275	14	=	=	SYM
ejpam-4868	275	15	1	1	NUM
ejpam-4868	275	16	u	u	NOUN
ejpam-4868	275	17	gα	gα	NOUN
ejpam-4868	275	18	,	,	PUNCT
ejpam-4868	275	19	λ	λ	X
ejpam-4868	275	20	{	{	PUNCT
ejpam-4868	275	21	(	(	PUNCT
ejpam-4868	275	22	1	1	NUM
ejpam-4868	275	23	+	+	NUM
ejpam-4868	275	24	λt)−1f(t	λt)−1f(t	NOUN
ejpam-4868	275	25	)	)	PUNCT
ejpam-4868	275	26	}	}	PUNCT
ejpam-4868	275	27	−	−	PROPN
ejpam-4868	275	28	uαf(0	uαf(0	NOUN
ejpam-4868	275	29	)	)	PUNCT
ejpam-4868	275	30	.	.	PUNCT
ejpam-4868	276	1	for	for	ADP
ejpam-4868	276	2	(	(	PUNCT
ejpam-4868	276	3	ii	ii	NOUN
ejpam-4868	276	4	.	.	PUNCT
ejpam-4868	276	5	)	)	PUNCT
ejpam-4868	276	6	,	,	PUNCT
ejpam-4868	276	7	using	use	VERB
ejpam-4868	276	8	definition	definition	NOUN
ejpam-4868	276	9	8	8	NUM
ejpam-4868	276	10	,	,	PUNCT
ejpam-4868	276	11	we	we	PRON
ejpam-4868	276	12	have	have	VERB
ejpam-4868	276	13	gα	gα	ADP
ejpam-4868	276	14	,	,	PUNCT
ejpam-4868	276	15	λ{f	λ{f	NOUN
ejpam-4868	276	16	′′(t	′′(t	NOUN
ejpam-4868	276	17	)	)	PUNCT
ejpam-4868	276	18	}	}	PUNCT
ejpam-4868	277	1	=	=	PUNCT
ejpam-4868	277	2	uα	uα	PROPN
ejpam-4868	277	3	∫	∫	PROPN
ejpam-4868	277	4	∞	∞	PROPN
ejpam-4868	277	5	0	0	NUM
ejpam-4868	278	1	(	(	PUNCT
ejpam-4868	278	2	1	1	NUM
ejpam-4868	278	3	+	+	CCONJ
ejpam-4868	278	4	λt)−	λt)−	PROPN
ejpam-4868	278	5	1	1	X
ejpam-4868	278	6	uλ	uλ	ADP
ejpam-4868	278	7	f	f	PROPN
ejpam-4868	278	8	′′(t)dt	′′(t)dt	PROPN
ejpam-4868	278	9	=	=	PRON
ejpam-4868	278	10	uα	uα	PROPN
ejpam-4868	278	11	lim	lim	PROPN
ejpam-4868	278	12	r→∞	r→∞	PUNCT
ejpam-4868	278	13	∫	∫	PROPN
ejpam-4868	279	1	r	r	NOUN
ejpam-4868	279	2	0	0	NUM
ejpam-4868	279	3	(	(	PUNCT
ejpam-4868	279	4	1	1	NUM
ejpam-4868	279	5	+	+	CCONJ
ejpam-4868	279	6	λt)−	λt)−	PROPN
ejpam-4868	279	7	1	1	NUM
ejpam-4868	279	8	uλ	uλ	ADP
ejpam-4868	279	9	f	f	PROPN
ejpam-4868	279	10	′′(t)dt	′′(t)dt	PROPN
ejpam-4868	279	11	.	.	PUNCT
ejpam-4868	280	1	using	use	VERB
ejpam-4868	280	2	integration	integration	NOUN
ejpam-4868	280	3	by	by	ADP
ejpam-4868	280	4	parts	part	NOUN
ejpam-4868	280	5	,	,	PUNCT
ejpam-4868	280	6	we	we	PRON
ejpam-4868	280	7	have	have	VERB
ejpam-4868	280	8	gα	gα	ADP
ejpam-4868	280	9	,	,	PUNCT
ejpam-4868	280	10	λ{f	λ{f	NOUN
ejpam-4868	280	11	′′(t	′′(t	NOUN
ejpam-4868	280	12	)	)	PUNCT
ejpam-4868	280	13	}	}	PUNCT
ejpam-4868	281	1	=	=	NUM
ejpam-4868	281	2	uα	uα	PROPN
ejpam-4868	281	3	lim	lim	PROPN
ejpam-4868	281	4	r→∞	r→∞	NUM
ejpam-4868	281	5	[	[	PUNCT
ejpam-4868	281	6	(	(	PUNCT
ejpam-4868	281	7	1	1	NUM
ejpam-4868	281	8	+	+	CCONJ
ejpam-4868	281	9	λt)−	λt)−	PROPN
ejpam-4868	281	10	1	1	X
ejpam-4868	281	11	uλ	uλ	ADP
ejpam-4868	281	12	f	f	PROPN
ejpam-4868	281	13	′(t	′(t	PROPN
ejpam-4868	281	14	)	)	PUNCT
ejpam-4868	281	15	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-4868	282	1	r	r	NOUN
ejpam-4868	282	2	0	0	NUM
ejpam-4868	282	3	−	−	NOUN
ejpam-4868	282	4	∫	∫	PROPN
ejpam-4868	282	5	r	r	NOUN
ejpam-4868	282	6	0	0	NUM
ejpam-4868	283	1	(	(	PUNCT
ejpam-4868	283	2	−	−	PROPN
ejpam-4868	283	3	1	1	NUM
ejpam-4868	283	4	u	u	NOUN
ejpam-4868	283	5	)	)	PUNCT
ejpam-4868	283	6	(	(	PUNCT
ejpam-4868	283	7	1	1	NUM
ejpam-4868	283	8	+	+	CCONJ
ejpam-4868	283	9	λt)−1−	λt)−1−	NOUN
ejpam-4868	283	10	1	1	NUM
ejpam-4868	283	11	uλ	uλ	ADP
ejpam-4868	283	12	f	f	PROPN
ejpam-4868	283	13	′(t)dt	′(t)dt	PROPN
ejpam-4868	283	14	]	]	PUNCT
ejpam-4868	284	1	=	=	NOUN
ejpam-4868	284	2	−	−	NOUN
ejpam-4868	284	3	uαf	uαf	NOUN
ejpam-4868	284	4	′(0	′(0	PROPN
ejpam-4868	284	5	)	)	PUNCT
ejpam-4868	285	1	+	+	CCONJ
ejpam-4868	285	2	uα	uα	PROPN
ejpam-4868	285	3	u	u	PROPN
ejpam-4868	285	4	lim	lim	PROPN
ejpam-4868	285	5	r→∞	r→∞	NUM
ejpam-4868	286	1	[	[	X
ejpam-4868	286	2	∫	∫	X
ejpam-4868	286	3	r	r	NOUN
ejpam-4868	286	4	0	0	NUM
ejpam-4868	286	5	(	(	PUNCT
ejpam-4868	286	6	1	1	NUM
ejpam-4868	286	7	+	+	CCONJ
ejpam-4868	286	8	λt)−1−	λt)−1−	NOUN
ejpam-4868	286	9	1	1	NUM
ejpam-4868	286	10	uλ	uλ	ADP
ejpam-4868	286	11	f	f	PROPN
ejpam-4868	286	12	′(t)dt	′(t)dt	PROPN
ejpam-4868	286	13	]	]	PUNCT
ejpam-4868	287	1	=	=	NOUN
ejpam-4868	287	2	−	−	NOUN
ejpam-4868	287	3	uαf	uαf	NOUN
ejpam-4868	287	4	′(0	′(0	PROPN
ejpam-4868	287	5	)	)	PUNCT
ejpam-4868	288	1	+	+	CCONJ
ejpam-4868	288	2	uα	uα	PROPN
ejpam-4868	288	3	u	u	PROPN
ejpam-4868	288	4	lim	lim	PROPN
ejpam-4868	288	5	r→∞	r→∞	NUM
ejpam-4868	288	6	[	[	PUNCT
ejpam-4868	288	7	(	(	PUNCT
ejpam-4868	288	8	1	1	NUM
ejpam-4868	288	9	+	+	CCONJ
ejpam-4868	288	10	λt)−1−	λt)−1−	VERB
ejpam-4868	288	11	1	1	NUM
ejpam-4868	288	12	uλ	uλ	ADP
ejpam-4868	288	13	f(t	f(t	PROPN
ejpam-4868	288	14	)	)	PUNCT
ejpam-4868	288	15	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-4868	288	16	r	r	NOUN
ejpam-4868	288	17	0	0	NUM
ejpam-4868	288	18	−	−	NOUN
ejpam-4868	288	19	∫	∫	PROPN
ejpam-4868	288	20	r	r	NOUN
ejpam-4868	288	21	0	0	NUM
ejpam-4868	289	1	(	(	PUNCT
ejpam-4868	289	2	−	−	PROPN
ejpam-4868	289	3	λ−	λ−	PROPN
ejpam-4868	289	4	1	1	NUM
ejpam-4868	289	5	u	u	NOUN
ejpam-4868	289	6	)	)	PUNCT
ejpam-4868	289	7	(	(	PUNCT
ejpam-4868	289	8	1	1	X
ejpam-4868	289	9	+	+	CCONJ
ejpam-4868	289	10	λt)−2−	λt)−2−	PROPN
ejpam-4868	289	11	1	1	NUM
ejpam-4868	289	12	uλ	uλ	ADP
ejpam-4868	289	13	f(t)dt	f(t)dt	PROPN
ejpam-4868	289	14	]	]	PUNCT
ejpam-4868	289	15	=	=	X
ejpam-4868	289	16	−	−	NOUN
ejpam-4868	289	17	uαf	uαf	NOUN
ejpam-4868	289	18	′(0)−	′(0)−	NOUN
ejpam-4868	289	19	uα−1f(0	uα−1f(0	NOUN
ejpam-4868	289	20	)	)	PUNCT
ejpam-4868	289	21	+	+	CCONJ
ejpam-4868	289	22	1	1	NUM
ejpam-4868	289	23	u2	u2	NOUN
ejpam-4868	289	24	(	(	PUNCT
ejpam-4868	289	25	1	1	NUM
ejpam-4868	289	26	+	+	NUM
ejpam-4868	289	27	λu)uα	λu)uα	X
ejpam-4868	289	28	lim	lim	NOUN
ejpam-4868	289	29	r→∞	r→∞	NUM
ejpam-4868	290	1	[	[	X
ejpam-4868	290	2	∫	∫	X
ejpam-4868	290	3	r	r	NOUN
ejpam-4868	290	4	0	0	NUM
ejpam-4868	290	5	(	(	PUNCT
ejpam-4868	290	6	1	1	NUM
ejpam-4868	290	7	+	+	CCONJ
ejpam-4868	290	8	λt)−2−	λt)−2−	PROPN
ejpam-4868	290	9	1	1	NUM
ejpam-4868	290	10	uλ	uλ	ADP
ejpam-4868	290	11	f(t)dt	f(t)dt	PROPN
ejpam-4868	290	12	]	]	PUNCT
ejpam-4868	290	13	=	=	SYM
ejpam-4868	290	14	1	1	NUM
ejpam-4868	290	15	u2	u2	NOUN
ejpam-4868	290	16	(	(	PUNCT
ejpam-4868	290	17	1	1	NUM
ejpam-4868	290	18	+	+	CCONJ
ejpam-4868	290	19	λu)gα	λu)gα	PROPN
ejpam-4868	290	20	,	,	PUNCT
ejpam-4868	290	21	λ	λ	INTJ
ejpam-4868	290	22	{	{	PUNCT
ejpam-4868	290	23	(	(	PUNCT
ejpam-4868	290	24	1	1	NUM
ejpam-4868	290	25	+	+	NUM
ejpam-4868	290	26	λt)−2f(t	λt)−2f(t	NOUN
ejpam-4868	290	27	)	)	PUNCT
ejpam-4868	290	28	}	}	PUNCT
ejpam-4868	290	29	−	−	ADP
ejpam-4868	290	30	uα−1f(0)−	uα−1f(0)−	NOUN
ejpam-4868	290	31	uαf	uαf	NOUN
ejpam-4868	290	32	′(0	′(0	NOUN
ejpam-4868	290	33	)	)	PUNCT
ejpam-4868	290	34	.	.	PUNCT
ejpam-4868	291	1	for	for	ADP
ejpam-4868	291	2	(	(	PUNCT
ejpam-4868	291	3	iii	iii	NOUN
ejpam-4868	291	4	.	.	PUNCT
ejpam-4868	291	5	)	)	PUNCT
ejpam-4868	291	6	,	,	PUNCT
ejpam-4868	291	7	we	we	PRON
ejpam-4868	291	8	prove	prove	VERB
ejpam-4868	291	9	gα	gα	ADP
ejpam-4868	291	10	,	,	PUNCT
ejpam-4868	291	11	λ{f	λ{f	NOUN
ejpam-4868	291	12	(	(	PUNCT
ejpam-4868	291	13	n)(t	n)(t	PROPN
ejpam-4868	291	14	)	)	PUNCT
ejpam-4868	291	15	}	}	PUNCT
ejpam-4868	291	16	=	=	SYM
ejpam-4868	291	17	1	1	NUM
ejpam-4868	291	18	un	un	PROPN
ejpam-4868	291	19	gα	gα	PROPN
ejpam-4868	291	20	,	,	PUNCT
ejpam-4868	291	21	λ	λ	PROPN
ejpam-4868	291	22	{	{	PUNCT
ejpam-4868	291	23	(	(	PUNCT
ejpam-4868	291	24	1	1	NUM
ejpam-4868	291	25	+	+	NUM
ejpam-4868	291	26	λt)−nf(t	λt)−nf(t	NOUN
ejpam-4868	291	27	)	)	PUNCT
ejpam-4868	291	28	}	}	PUNCT
ejpam-4868	291	29	n−1∏	n−1∏	NUM
ejpam-4868	291	30	l=1	l=1	PROPN
ejpam-4868	291	31	(	(	PUNCT
ejpam-4868	291	32	1	1	NUM
ejpam-4868	291	33	+	+	CCONJ
ejpam-4868	291	34	luλ	luλ	NOUN
ejpam-4868	291	35	)	)	PUNCT
ejpam-4868	291	36	−	−	PUNCT
ejpam-4868	292	1	uα+1−n	uα+1−n	PROPN
ejpam-4868	292	2	n−1∑	n−1∑	PROPN
ejpam-4868	292	3	i=0	i=0	PROPN
ejpam-4868	292	4	uif	uif	PROPN
ejpam-4868	292	5	(	(	PUNCT
ejpam-4868	292	6	i)(0	i)(0	PROPN
ejpam-4868	292	7	)	)	PUNCT
ejpam-4868	292	8	[	[	PUNCT
ejpam-4868	292	9	n−i−2∏	n−i−2∏	NOUN
ejpam-4868	292	10	l=1	l=1	PROPN
ejpam-4868	292	11	(	(	PUNCT
ejpam-4868	292	12	1	1	NUM
ejpam-4868	292	13	+	+	CCONJ
ejpam-4868	292	14	luλ	luλ	NOUN
ejpam-4868	292	15	)	)	PUNCT
ejpam-4868	292	16	]	]	PUNCT
ejpam-4868	293	1	(	(	PUNCT
ejpam-4868	293	2	22	22	X
ejpam-4868	293	3	)	)	PUNCT
ejpam-4868	293	4	h.	h.	PROPN
ejpam-4868	293	5	j.	j.	PROPN
ejpam-4868	293	6	campos	campos	PROPN
ejpam-4868	293	7	,	,	PUNCT
ejpam-4868	293	8	j.	j.	PROPN
ejpam-4868	293	9	c.	c.	PROPN
ejpam-4868	293	10	fernandez	fernandez	PROPN
ejpam-4868	293	11	,	,	PUNCT
ejpam-4868	293	12	j.	j.	PROPN
ejpam-4868	293	13	b.	b.	PROPN
ejpam-4868	293	14	m.	m.	PROPN
ejpam-4868	293	15	natuil	natuil	PROPN
ejpam-4868	293	16	/	/	SYM
ejpam-4868	293	17	eur	eur	PROPN
ejpam-4868	293	18	.	.	PUNCT
ejpam-4868	294	1	j.	j.	PROPN
ejpam-4868	294	2	pure	pure	PROPN
ejpam-4868	294	3	appl	appl	PROPN
ejpam-4868	294	4	.	.	PROPN
ejpam-4868	294	5	math	math	PROPN
ejpam-4868	294	6	,	,	PUNCT
ejpam-4868	294	7	16	16	NUM
ejpam-4868	294	8	(	(	PUNCT
ejpam-4868	294	9	4	4	NUM
ejpam-4868	294	10	)	)	PUNCT
ejpam-4868	294	11	(	(	PUNCT
ejpam-4868	294	12	2023	2023	NUM
ejpam-4868	294	13	)	)	PUNCT
ejpam-4868	294	14	,	,	PUNCT
ejpam-4868	294	15	2213	2213	NUM
ejpam-4868	294	16	-	-	SYM
ejpam-4868	294	17	2233	2233	NUM
ejpam-4868	294	18	2225	2225	NUM
ejpam-4868	294	19	by	by	ADP
ejpam-4868	294	20	induction	induction	NOUN
ejpam-4868	294	21	.	.	PUNCT
ejpam-4868	295	1	from	from	ADP
ejpam-4868	295	2	results	result	NOUN
ejpam-4868	295	3	(	(	PUNCT
ejpam-4868	295	4	i.	i.	NOUN
ejpam-4868	295	5	)	)	PUNCT
ejpam-4868	295	6	and	and	CCONJ
ejpam-4868	295	7	(	(	PUNCT
ejpam-4868	295	8	ii	ii	NOUN
ejpam-4868	295	9	.	.	PUNCT
ejpam-4868	295	10	)	)	PUNCT
ejpam-4868	295	11	,	,	PUNCT
ejpam-4868	295	12	equation	equation	NOUN
ejpam-4868	295	13	(	(	PUNCT
ejpam-4868	295	14	22	22	NUM
ejpam-4868	295	15	)	)	PUNCT
ejpam-4868	295	16	holds	hold	VERB
ejpam-4868	295	17	for	for	ADP
ejpam-4868	295	18	n	n	NOUN
ejpam-4868	295	19	=	=	SYM
ejpam-4868	295	20	1	1	NUM
ejpam-4868	295	21	and	and	CCONJ
ejpam-4868	295	22	n	n	CCONJ
ejpam-4868	295	23	=	=	SYM
ejpam-4868	295	24	2	2	X
ejpam-4868	295	25	.	.	X
ejpam-4868	295	26	assume	assume	VERB
ejpam-4868	295	27	that	that	SCONJ
ejpam-4868	295	28	equation	equation	NOUN
ejpam-4868	295	29	(	(	PUNCT
ejpam-4868	295	30	22	22	NUM
ejpam-4868	295	31	)	)	PUNCT
ejpam-4868	295	32	is	be	AUX
ejpam-4868	295	33	true	true	ADJ
ejpam-4868	295	34	for	for	ADP
ejpam-4868	295	35	n	n	PROPN
ejpam-4868	295	36	=	=	SYM
ejpam-4868	295	37	k.	k.	PROPN
ejpam-4868	295	38	let	let	VERB
ejpam-4868	295	39	g(t	g(t	PROPN
ejpam-4868	295	40	)	)	PUNCT
ejpam-4868	296	1	=	=	SYM
ejpam-4868	296	2	f	f	PROPN
ejpam-4868	296	3	(	(	PUNCT
ejpam-4868	296	4	k)(t	k)(t	PROPN
ejpam-4868	296	5	)	)	PUNCT
ejpam-4868	296	6	,	,	PUNCT
ejpam-4868	296	7	then	then	ADV
ejpam-4868	296	8	by	by	ADP
ejpam-4868	296	9	the	the	DET
ejpam-4868	296	10	result	result	NOUN
ejpam-4868	296	11	of	of	ADP
ejpam-4868	296	12	(	(	PUNCT
ejpam-4868	296	13	i.	i.	NOUN
ejpam-4868	296	14	)	)	PUNCT
ejpam-4868	296	15	,	,	PUNCT
ejpam-4868	296	16	gα	gα	ADP
ejpam-4868	296	17	,	,	PUNCT
ejpam-4868	296	18	λ{f	λ{f	NOUN
ejpam-4868	296	19	(	(	PUNCT
ejpam-4868	296	20	k+1)(t	k+1)(t	PROPN
ejpam-4868	296	21	)	)	PUNCT
ejpam-4868	296	22	}	}	PUNCT
ejpam-4868	297	1	=	=	NOUN
ejpam-4868	297	2	gα	gα	NOUN
ejpam-4868	297	3	,	,	PUNCT
ejpam-4868	297	4	λ{g′(t	λ{g′(t	NOUN
ejpam-4868	297	5	)	)	PUNCT
ejpam-4868	297	6	}	}	PUNCT
ejpam-4868	297	7	=	=	SYM
ejpam-4868	297	8	1	1	NUM
ejpam-4868	297	9	u	u	NOUN
ejpam-4868	297	10	gα	gα	NOUN
ejpam-4868	297	11	,	,	PUNCT
ejpam-4868	297	12	λ	λ	X
ejpam-4868	297	13	{	{	PUNCT
ejpam-4868	297	14	(	(	PUNCT
ejpam-4868	297	15	1	1	NUM
ejpam-4868	297	16	+	+	CCONJ
ejpam-4868	297	17	λt)−1g(t	λt)−1g(t	ADJ
ejpam-4868	297	18	)	)	PUNCT
ejpam-4868	297	19	}	}	PUNCT
ejpam-4868	297	20	−	−	NOUN
ejpam-4868	297	21	uαg(0	uαg(0	NOUN
ejpam-4868	297	22	)	)	PUNCT
ejpam-4868	297	23	=	=	SYM
ejpam-4868	297	24	1	1	NUM
ejpam-4868	297	25	u	u	NOUN
ejpam-4868	297	26	gα	gα	NOUN
ejpam-4868	297	27	,	,	PUNCT
ejpam-4868	297	28	λ	λ	X
ejpam-4868	297	29	{	{	PUNCT
ejpam-4868	297	30	(	(	PUNCT
ejpam-4868	297	31	1	1	NUM
ejpam-4868	297	32	+	+	CCONJ
ejpam-4868	297	33	λt)−1f	λt)−1f	ADJ
ejpam-4868	297	34	(	(	PUNCT
ejpam-4868	297	35	k)(t	k)(t	PROPN
ejpam-4868	297	36	)	)	PUNCT
ejpam-4868	297	37	}	}	PUNCT
ejpam-4868	297	38	−	−	PROPN
ejpam-4868	297	39	uαf	uαf	NOUN
ejpam-4868	297	40	(	(	PUNCT
ejpam-4868	297	41	k)(0	k)(0	ADJ
ejpam-4868	297	42	)	)	PUNCT
ejpam-4868	297	43	.	.	PUNCT
ejpam-4868	298	1	(	(	PUNCT
ejpam-4868	298	2	23	23	NUM
ejpam-4868	298	3	)	)	PUNCT
ejpam-4868	298	4	now	now	ADV
ejpam-4868	298	5	,	,	PUNCT
ejpam-4868	298	6	gα	gα	ADP
ejpam-4868	298	7	,	,	PUNCT
ejpam-4868	298	8	λ	λ	X
ejpam-4868	298	9	{	{	PUNCT
ejpam-4868	298	10	(	(	PUNCT
ejpam-4868	298	11	1	1	NUM
ejpam-4868	298	12	+	+	CCONJ
ejpam-4868	298	13	λt)−1f	λt)−1f	ADJ
ejpam-4868	298	14	(	(	PUNCT
ejpam-4868	298	15	k)(t	k)(t	PROPN
ejpam-4868	298	16	)	)	PUNCT
ejpam-4868	298	17	}	}	PUNCT
ejpam-4868	299	1	=	=	X
ejpam-4868	299	2	uα	uα	PROPN
ejpam-4868	299	3	∫	∫	PROPN
ejpam-4868	299	4	∞	∞	PROPN
ejpam-4868	299	5	0	0	PUNCT
ejpam-4868	300	1	e	e	NOUN
ejpam-4868	300	2	−	−	PROPN
ejpam-4868	300	3	1	1	NUM
ejpam-4868	300	4	u	u	NOUN
ejpam-4868	300	5	λ	λ	X
ejpam-4868	300	6	(	(	PUNCT
ejpam-4868	300	7	t)(1	t)(1	X
ejpam-4868	300	8	+	+	X
ejpam-4868	300	9	λt)−1f	λt)−1f	PROPN
ejpam-4868	300	10	(	(	PUNCT
ejpam-4868	300	11	k)(t)dt	k)(t)dt	NOUN
ejpam-4868	300	12	=	=	NOUN
ejpam-4868	300	13	uα	uα	PROPN
ejpam-4868	300	14	∫	∫	PROPN
ejpam-4868	300	15	∞	∞	PROPN
ejpam-4868	300	16	0	0	NUM
ejpam-4868	300	17	(	(	PUNCT
ejpam-4868	300	18	1	1	NUM
ejpam-4868	300	19	+	+	CCONJ
ejpam-4868	300	20	λt)−	λt)−	PROPN
ejpam-4868	300	21	(	(	PUNCT
ejpam-4868	300	22	1+uλ	1+uλ	NUM
ejpam-4868	300	23	uλ	uλ	NOUN
ejpam-4868	300	24	)	)	PUNCT
ejpam-4868	300	25	f	f	PROPN
ejpam-4868	300	26	(	(	PUNCT
ejpam-4868	300	27	k)(t)dt	k)(t)dt	NOUN
ejpam-4868	300	28	=(	=(	NOUN
ejpam-4868	300	29	1	1	NUM
ejpam-4868	301	1	+	+	CCONJ
ejpam-4868	301	2	uλ)α	uλ)α	PROPN
ejpam-4868	301	3	(	(	PUNCT
ejpam-4868	301	4	u	u	NOUN
ejpam-4868	301	5	1	1	NUM
ejpam-4868	301	6	+	+	NUM
ejpam-4868	301	7	uλ	uλ	X
ejpam-4868	301	8	)	)	PUNCT
ejpam-4868	301	9	α∫	α∫	NUM
ejpam-4868	301	10	∞	∞	PROPN
ejpam-4868	301	11	0	0	PUNCT
ejpam-4868	302	1	e	e	NOUN
ejpam-4868	302	2	−	−	PROPN
ejpam-4868	302	3	1	1	NUM
ejpam-4868	302	4	u	u	NOUN
ejpam-4868	302	5	1+uλ	1+uλ	NUM
ejpam-4868	302	6	λ	λ	X
ejpam-4868	302	7	(	(	PUNCT
ejpam-4868	302	8	t)f	t)f	X
ejpam-4868	302	9	(	(	PUNCT
ejpam-4868	302	10	k)(t)dt	k)(t)dt	NOUN
ejpam-4868	302	11	.	.	PUNCT
ejpam-4868	303	1	(	(	PUNCT
ejpam-4868	303	2	24	24	NUM
ejpam-4868	303	3	)	)	PUNCT
ejpam-4868	303	4	by	by	ADP
ejpam-4868	303	5	inductive	inductive	ADJ
ejpam-4868	303	6	hypothesis	hypothesis	NOUN
ejpam-4868	303	7	,	,	PUNCT
ejpam-4868	303	8	we	we	PRON
ejpam-4868	303	9	have	have	VERB
ejpam-4868	303	10	(	(	PUNCT
ejpam-4868	303	11	u	u	NOUN
ejpam-4868	303	12	1	1	NUM
ejpam-4868	303	13	+	+	NUM
ejpam-4868	303	14	uλ	uλ	X
ejpam-4868	303	15	)	)	PUNCT
ejpam-4868	304	1	α∫	α∫	NUM
ejpam-4868	305	1	∞	∞	PROPN
ejpam-4868	305	2	0	0	PUNCT
ejpam-4868	305	3	e	e	NOUN
ejpam-4868	305	4	−	−	PROPN
ejpam-4868	305	5	1	1	NUM
ejpam-4868	305	6	u	u	NOUN
ejpam-4868	305	7	1+uλ	1+uλ	NUM
ejpam-4868	305	8	λ	λ	X
ejpam-4868	305	9	(	(	PUNCT
ejpam-4868	305	10	t)f	t)f	X
ejpam-4868	305	11	(	(	PUNCT
ejpam-4868	305	12	k)(t)dt	k)(t)dt	NOUN
ejpam-4868	305	13	=	=	SYM
ejpam-4868	305	14	1	1	NUM
ejpam-4868	305	15	(	(	PUNCT
ejpam-4868	305	16	u	u	NOUN
ejpam-4868	305	17	1+uλ	1+uλ	PROPN
ejpam-4868	305	18	)	)	PUNCT
ejpam-4868	306	1	k	k	PROPN
ejpam-4868	306	2	gα	gα	PROPN
ejpam-4868	306	3	,	,	PUNCT
ejpam-4868	306	4	λ	λ	X
ejpam-4868	306	5	{	{	PUNCT
ejpam-4868	306	6	(	(	PUNCT
ejpam-4868	306	7	1	1	NUM
ejpam-4868	306	8	+	+	NUM
ejpam-4868	306	9	λt)−kf(t	λt)−kf(t	NOUN
ejpam-4868	306	10	)	)	PUNCT
ejpam-4868	306	11	}	}	PUNCT
ejpam-4868	307	1	k−1∏	k−1∏	PROPN
ejpam-4868	307	2	l=1	l=1	PROPN
ejpam-4868	307	3	(	(	PUNCT
ejpam-4868	307	4	1	1	NUM
ejpam-4868	307	5	+	+	NUM
ejpam-4868	307	6	luλ	luλ	NOUN
ejpam-4868	307	7	1	1	NUM
ejpam-4868	307	8	+	+	CCONJ
ejpam-4868	307	9	uλ	uλ	NOUN
ejpam-4868	307	10	)	)	PUNCT
ejpam-4868	307	11	−	−	PROPN
ejpam-4868	307	12	(	(	PUNCT
ejpam-4868	307	13	u	u	NOUN
ejpam-4868	307	14	1	1	NUM
ejpam-4868	307	15	+	+	NUM
ejpam-4868	307	16	uλ	uλ	NOUN
ejpam-4868	307	17	)	)	PUNCT
ejpam-4868	307	18	α+1−kk−1∑	α+1−kk−1∑	PROPN
ejpam-4868	307	19	i=0	i=0	PROPN
ejpam-4868	307	20	(	(	PUNCT
ejpam-4868	307	21	u	u	NOUN
ejpam-4868	307	22	1	1	NUM
ejpam-4868	307	23	+	+	NUM
ejpam-4868	307	24	uλ	uλ	NOUN
ejpam-4868	307	25	)	)	PUNCT
ejpam-4868	308	1	i	i	PRON
ejpam-4868	308	2	f	f	X
ejpam-4868	308	3	(	(	PUNCT
ejpam-4868	308	4	i)(0	i)(0	NUM
ejpam-4868	308	5	)	)	PUNCT
ejpam-4868	308	6	[	[	PUNCT
ejpam-4868	308	7	k−i−2∏	k−i−2∏	PROPN
ejpam-4868	308	8	l=1	l=1	PROPN
ejpam-4868	308	9	(	(	PUNCT
ejpam-4868	308	10	1	1	NUM
ejpam-4868	308	11	+	+	NUM
ejpam-4868	308	12	luλ	luλ	NOUN
ejpam-4868	308	13	1	1	NUM
ejpam-4868	308	14	+	+	CCONJ
ejpam-4868	308	15	uλ	uλ	NOUN
ejpam-4868	308	16	)	)	PUNCT
ejpam-4868	308	17	]	]	PUNCT
ejpam-4868	308	18	.	.	PUNCT
ejpam-4868	309	1	observe	observe	VERB
ejpam-4868	309	2	that	that	SCONJ
ejpam-4868	309	3	gα	gα	NOUN
ejpam-4868	309	4	,	,	PUNCT
ejpam-4868	309	5	λ	λ	X
ejpam-4868	309	6	{	{	PUNCT
ejpam-4868	309	7	(	(	PUNCT
ejpam-4868	309	8	1	1	NUM
ejpam-4868	309	9	+	+	NUM
ejpam-4868	309	10	λt)−kf(t	λt)−kf(t	NOUN
ejpam-4868	309	11	)	)	PUNCT
ejpam-4868	309	12	}	}	PUNCT
ejpam-4868	309	13	=	=	SYM
ejpam-4868	309	14	(	(	PUNCT
ejpam-4868	309	15	u	u	NOUN
ejpam-4868	309	16	1	1	NUM
ejpam-4868	309	17	+	+	NUM
ejpam-4868	309	18	uλ	uλ	X
ejpam-4868	309	19	)	)	PUNCT
ejpam-4868	309	20	α∫	α∫	NUM
ejpam-4868	309	21	∞	∞	PROPN
ejpam-4868	309	22	0	0	PUNCT
ejpam-4868	310	1	e	e	NOUN
ejpam-4868	310	2	−	−	PROPN
ejpam-4868	310	3	1	1	NUM
ejpam-4868	310	4	u	u	NOUN
ejpam-4868	310	5	1+uλ	1+uλ	NUM
ejpam-4868	310	6	λ	λ	X
ejpam-4868	310	7	(	(	PUNCT
ejpam-4868	310	8	t)(1	t)(1	X
ejpam-4868	310	9	+	+	CCONJ
ejpam-4868	310	10	λt)−kf(t)dt	λt)−kf(t)dt	X
ejpam-4868	310	11	=	=	SYM
ejpam-4868	310	12	1	1	NUM
ejpam-4868	310	13	(	(	PUNCT
ejpam-4868	310	14	1	1	NUM
ejpam-4868	310	15	+	+	CCONJ
ejpam-4868	310	16	uλ)α	uλ)α	PROPN
ejpam-4868	310	17	[	[	PUNCT
ejpam-4868	310	18	gα	gα	NOUN
ejpam-4868	310	19	,	,	PUNCT
ejpam-4868	310	20	λ	λ	X
ejpam-4868	310	21	{	{	PUNCT
ejpam-4868	310	22	(	(	PUNCT
ejpam-4868	310	23	1	1	NUM
ejpam-4868	310	24	+	+	NUM
ejpam-4868	310	25	λt)−(k+1)f(t	λt)−(k+1)f(t	NOUN
ejpam-4868	310	26	)	)	PUNCT
ejpam-4868	310	27	}	}	PUNCT
ejpam-4868	310	28	]	]	PUNCT
ejpam-4868	310	29	.	.	PUNCT
ejpam-4868	311	1	thus	thus	ADV
ejpam-4868	311	2	,	,	PUNCT
ejpam-4868	311	3	the	the	DET
ejpam-4868	311	4	rhs	rhs	PROPN
ejpam-4868	311	5	of	of	ADP
ejpam-4868	311	6	equation	equation	NOUN
ejpam-4868	311	7	(	(	PUNCT
ejpam-4868	311	8	23	23	NUM
ejpam-4868	311	9	)	)	PUNCT
ejpam-4868	311	10	becomes	become	VERB
ejpam-4868	311	11	rhs	rhs	PROPN
ejpam-4868	311	12	=	=	PUNCT
ejpam-4868	311	13	(	(	PUNCT
ejpam-4868	311	14	1	1	NUM
ejpam-4868	311	15	+	+	NUM
ejpam-4868	311	16	uλ)k	uλ)k	PROPN
ejpam-4868	311	17	uk	uk	PROPN
ejpam-4868	311	18	[	[	PUNCT
ejpam-4868	311	19	1	1	NUM
ejpam-4868	311	20	(	(	PUNCT
ejpam-4868	311	21	1	1	NUM
ejpam-4868	311	22	+	+	CCONJ
ejpam-4868	311	23	uλ)α	uλ)α	PROPN
ejpam-4868	311	24	gα	gα	NOUN
ejpam-4868	311	25	,	,	PUNCT
ejpam-4868	311	26	λ	λ	X
ejpam-4868	311	27	{	{	PUNCT
ejpam-4868	311	28	(	(	PUNCT
ejpam-4868	311	29	1	1	NUM
ejpam-4868	311	30	+	+	NUM
ejpam-4868	311	31	λt)−(k+1)f(t	λt)−(k+1)f(t	NOUN
ejpam-4868	311	32	)	)	PUNCT
ejpam-4868	311	33	}	}	PUNCT
ejpam-4868	311	34	]	]	PUNCT
ejpam-4868	312	1	k−1∏	k−1∏	PRON
ejpam-4868	312	2	l=1	l=1	PROPN
ejpam-4868	312	3	(	(	PUNCT
ejpam-4868	312	4	1	1	NUM
ejpam-4868	312	5	+	+	CCONJ
ejpam-4868	312	6	(	(	PUNCT
ejpam-4868	312	7	l	l	PROPN
ejpam-4868	312	8	+	+	X
ejpam-4868	312	9	1)uλ	1)uλ	NUM
ejpam-4868	312	10	)	)	PUNCT
ejpam-4868	312	11	1	1	NUM
ejpam-4868	313	1	+	+	CCONJ
ejpam-4868	313	2	uλ	uλ	ADP
ejpam-4868	313	3	−	−	PROPN
ejpam-4868	313	4	uα+1−k	uα+1−k	NOUN
ejpam-4868	313	5	(	(	PUNCT
ejpam-4868	313	6	1	1	NUM
ejpam-4868	313	7	+	+	NUM
ejpam-4868	313	8	uλ)α+1−k	uλ)α+1−k	PROPN
ejpam-4868	313	9	k−1∑	k−1∑	PROPN
ejpam-4868	313	10	i=0	i=0	PROPN
ejpam-4868	313	11	ui	ui	PROPN
ejpam-4868	313	12	(	(	PUNCT
ejpam-4868	313	13	1	1	NUM
ejpam-4868	313	14	+	+	CCONJ
ejpam-4868	313	15	uλ)i	uλ)i	PROPN
ejpam-4868	313	16	f	f	PROPN
ejpam-4868	313	17	(	(	PUNCT
ejpam-4868	313	18	i)(0	i)(0	PROPN
ejpam-4868	313	19	)	)	PUNCT
ejpam-4868	313	20	k−i−2∏	k−i−2∏	PROPN
ejpam-4868	313	21	l=1	l=1	PROPN
ejpam-4868	313	22	(	(	PUNCT
ejpam-4868	313	23	1	1	NUM
ejpam-4868	313	24	+	+	CCONJ
ejpam-4868	313	25	(	(	PUNCT
ejpam-4868	313	26	l	l	PROPN
ejpam-4868	313	27	+	+	X
ejpam-4868	313	28	1)uλ	1)uλ	NUM
ejpam-4868	313	29	)	)	PUNCT
ejpam-4868	313	30	1	1	NUM
ejpam-4868	314	1	+	+	CCONJ
ejpam-4868	314	2	uλ	uλ	NOUN
ejpam-4868	314	3	=	=	SYM
ejpam-4868	314	4	1	1	NUM
ejpam-4868	314	5	uk(1	uk(1	PROPN
ejpam-4868	314	6	+	+	CCONJ
ejpam-4868	314	7	uλ)α	uλ)α	PROPN
ejpam-4868	314	8	[	[	PUNCT
ejpam-4868	314	9	gα	gα	NOUN
ejpam-4868	314	10	,	,	PUNCT
ejpam-4868	314	11	λ	λ	X
ejpam-4868	314	12	{	{	PUNCT
ejpam-4868	314	13	(	(	PUNCT
ejpam-4868	314	14	1	1	NUM
ejpam-4868	314	15	+	+	NUM
ejpam-4868	314	16	λt)−(k+1)f(t	λt)−(k+1)f(t	NOUN
ejpam-4868	314	17	)	)	PUNCT
ejpam-4868	314	18	}	}	PUNCT
ejpam-4868	314	19	]	]	PUNCT
ejpam-4868	314	20	[	[	PUNCT
ejpam-4868	314	21	(	(	PUNCT
ejpam-4868	314	22	1	1	NUM
ejpam-4868	314	23	+	+	NUM
ejpam-4868	314	24	uλ	uλ	NOUN
ejpam-4868	314	25	)	)	PUNCT
ejpam-4868	315	1	k−1∏	k−1∏	PROPN
ejpam-4868	315	2	l=1	l=1	PROPN
ejpam-4868	315	3	(	(	PUNCT
ejpam-4868	315	4	1	1	NUM
ejpam-4868	315	5	+	+	CCONJ
ejpam-4868	315	6	(	(	PUNCT
ejpam-4868	315	7	l	l	PROPN
ejpam-4868	315	8	+	+	X
ejpam-4868	315	9	1)uλ	1)uλ	NOUN
ejpam-4868	315	10	)	)	PUNCT
ejpam-4868	315	11	]	]	PUNCT
ejpam-4868	316	1	−	−	PROPN
ejpam-4868	316	2	(	(	PUNCT
ejpam-4868	316	3	uα−k	uα−k	NOUN
ejpam-4868	316	4	(	(	PUNCT
ejpam-4868	316	5	1	1	NUM
ejpam-4868	316	6	+	+	CCONJ
ejpam-4868	316	7	uλ)α−k	uλ)α−k	X
ejpam-4868	316	8	)	)	PUNCT
ejpam-4868	317	1	k−1∑	k−1∑	PROPN
ejpam-4868	317	2	i=0	i=0	PROPN
ejpam-4868	317	3	(	(	PUNCT
ejpam-4868	317	4	u	u	NOUN
ejpam-4868	317	5	1	1	NUM
ejpam-4868	317	6	+	+	NUM
ejpam-4868	317	7	uλ	uλ	NOUN
ejpam-4868	317	8	)	)	PUNCT
ejpam-4868	317	9	i+1	i+1	NOUN
ejpam-4868	317	10	f	f	PROPN
ejpam-4868	317	11	(	(	PUNCT
ejpam-4868	317	12	i)(0	i)(0	PROPN
ejpam-4868	317	13	)	)	PUNCT
ejpam-4868	317	14	[	[	PUNCT
ejpam-4868	317	15	1	1	NUM
ejpam-4868	317	16	(	(	PUNCT
ejpam-4868	317	17	1	1	NUM
ejpam-4868	317	18	+	+	NUM
ejpam-4868	317	19	uλ)k−i−2	uλ)k−i−2	NOUN
ejpam-4868	317	20	k−i−2∏	k−i−2∏	PROPN
ejpam-4868	317	21	l=1	l=1	PROPN
ejpam-4868	317	22	(	(	PUNCT
ejpam-4868	317	23	1	1	NUM
ejpam-4868	317	24	+	+	CCONJ
ejpam-4868	317	25	(	(	PUNCT
ejpam-4868	317	26	l	l	PROPN
ejpam-4868	317	27	+	+	X
ejpam-4868	317	28	1)uλ	1)uλ	PROPN
ejpam-4868	317	29	)	)	PUNCT
ejpam-4868	317	30	]	]	PUNCT
ejpam-4868	318	1	h.	h.	PROPN
ejpam-4868	318	2	j.	j.	PROPN
ejpam-4868	318	3	campos	campos	PROPN
ejpam-4868	318	4	,	,	PUNCT
ejpam-4868	318	5	j.	j.	PROPN
ejpam-4868	318	6	c.	c.	PROPN
ejpam-4868	318	7	fernandez	fernandez	PROPN
ejpam-4868	318	8	,	,	PUNCT
ejpam-4868	318	9	j.	j.	PROPN
ejpam-4868	318	10	b.	b.	PROPN
ejpam-4868	318	11	m.	m.	PROPN
ejpam-4868	318	12	natuil	natuil	PROPN
ejpam-4868	318	13	/	/	SYM
ejpam-4868	318	14	eur	eur	PROPN
ejpam-4868	318	15	.	.	PUNCT
ejpam-4868	319	1	j.	j.	PROPN
ejpam-4868	319	2	pure	pure	PROPN
ejpam-4868	319	3	appl	appl	PROPN
ejpam-4868	319	4	.	.	PROPN
ejpam-4868	319	5	math	math	PROPN
ejpam-4868	319	6	,	,	PUNCT
ejpam-4868	319	7	16	16	NUM
ejpam-4868	319	8	(	(	PUNCT
ejpam-4868	319	9	4	4	NUM
ejpam-4868	319	10	)	)	PUNCT
ejpam-4868	319	11	(	(	PUNCT
ejpam-4868	319	12	2023	2023	NUM
ejpam-4868	319	13	)	)	PUNCT
ejpam-4868	319	14	,	,	PUNCT
ejpam-4868	319	15	2213	2213	NUM
ejpam-4868	319	16	-	-	SYM
ejpam-4868	319	17	2233	2233	NUM
ejpam-4868	319	18	2226	2226	NUM
ejpam-4868	319	19	=	=	SYM
ejpam-4868	319	20	1	1	NUM
ejpam-4868	319	21	uk(1	uk(1	PROPN
ejpam-4868	319	22	+	+	CCONJ
ejpam-4868	319	23	uλ)α	uλ)α	PROPN
ejpam-4868	320	1	[	[	PUNCT
ejpam-4868	320	2	gα	gα	NOUN
ejpam-4868	320	3	,	,	PUNCT
ejpam-4868	320	4	λ	λ	X
ejpam-4868	320	5	{	{	PUNCT
ejpam-4868	320	6	(	(	PUNCT
ejpam-4868	320	7	1	1	NUM
ejpam-4868	320	8	+	+	NUM
ejpam-4868	320	9	λt)−(k+1)f(t	λt)−(k+1)f(t	NOUN
ejpam-4868	320	10	)	)	PUNCT
ejpam-4868	320	11	}	}	PUNCT
ejpam-4868	320	12	]	]	PUNCT
ejpam-4868	320	13	[	[	PUNCT
ejpam-4868	320	14	k∏	k∏	PROPN
ejpam-4868	320	15	l=1	l=1	PROPN
ejpam-4868	320	16	(	(	PUNCT
ejpam-4868	320	17	1	1	NUM
ejpam-4868	320	18	+	+	CCONJ
ejpam-4868	320	19	luλ	luλ	NOUN
ejpam-4868	320	20	)	)	PUNCT
ejpam-4868	320	21	]	]	PUNCT
ejpam-4868	321	1	−	−	PROPN
ejpam-4868	321	2	(	(	PUNCT
ejpam-4868	321	3	uα−k	uα−k	NOUN
ejpam-4868	321	4	(	(	PUNCT
ejpam-4868	321	5	1	1	NUM
ejpam-4868	321	6	+	+	CCONJ
ejpam-4868	321	7	uλ)α	uλ)α	PROPN
ejpam-4868	321	8	)	)	PUNCT
ejpam-4868	321	9	k−1∑	k−1∑	PROPN
ejpam-4868	321	10	i=0	i=0	PROPN
ejpam-4868	321	11	ui+1f	ui+1f	X
ejpam-4868	321	12	(	(	PUNCT
ejpam-4868	321	13	i)(0	i)(0	NUM
ejpam-4868	321	14	)	)	PUNCT
ejpam-4868	321	15	[	[	PUNCT
ejpam-4868	321	16	k−i−1∏	k−i−1∏	NUM
ejpam-4868	321	17	l=1	l=1	SYM
ejpam-4868	321	18	(	(	PUNCT
ejpam-4868	321	19	1	1	NUM
ejpam-4868	321	20	+	+	CCONJ
ejpam-4868	321	21	luλ	luλ	NOUN
ejpam-4868	321	22	)	)	PUNCT
ejpam-4868	321	23	]	]	PUNCT
ejpam-4868	321	24	.	.	PUNCT
ejpam-4868	322	1	hence	hence	ADV
ejpam-4868	322	2	,	,	PUNCT
ejpam-4868	322	3	the	the	DET
ejpam-4868	322	4	rhs	rhs	PROPN
ejpam-4868	322	5	of	of	ADP
ejpam-4868	322	6	equation	equation	NOUN
ejpam-4868	322	7	(	(	PUNCT
ejpam-4868	322	8	22	22	NUM
ejpam-4868	322	9	)	)	PUNCT
ejpam-4868	322	10	becomes	become	VERB
ejpam-4868	322	11	rhs	rhs	PROPN
ejpam-4868	322	12	=(	=(	NOUN
ejpam-4868	322	13	1	1	NUM
ejpam-4868	323	1	+	+	CCONJ
ejpam-4868	323	2	uλ)α	uλ)α	PROPN
ejpam-4868	323	3	[	[	PUNCT
ejpam-4868	323	4	1	1	NUM
ejpam-4868	323	5	uk(1	uk(1	NOUN
ejpam-4868	323	6	+	+	CCONJ
ejpam-4868	323	7	uλ)α	uλ)α	PROPN
ejpam-4868	323	8	gα	gα	NOUN
ejpam-4868	323	9	,	,	PUNCT
ejpam-4868	323	10	λ	λ	X
ejpam-4868	323	11	{	{	PUNCT
ejpam-4868	323	12	(	(	PUNCT
ejpam-4868	323	13	1	1	NUM
ejpam-4868	323	14	+	+	NUM
ejpam-4868	323	15	λt)−(k+1)f(t	λt)−(k+1)f(t	NOUN
ejpam-4868	323	16	)	)	PUNCT
ejpam-4868	323	17	}	}	PUNCT
ejpam-4868	324	1	k∏	k∏	PROPN
ejpam-4868	324	2	l=1	l=1	PROPN
ejpam-4868	324	3	(	(	PUNCT
ejpam-4868	324	4	1	1	NUM
ejpam-4868	324	5	+	+	CCONJ
ejpam-4868	324	6	luλ	luλ	NOUN
ejpam-4868	324	7	)	)	PUNCT
ejpam-4868	324	8	−	−	PROPN
ejpam-4868	324	9	uα−k	uα−k	NOUN
ejpam-4868	324	10	(	(	PUNCT
ejpam-4868	324	11	1	1	NUM
ejpam-4868	324	12	+	+	CCONJ
ejpam-4868	324	13	uλ)α	uλ)α	PROPN
ejpam-4868	324	14	k−1∑	k−1∑	PROPN
ejpam-4868	324	15	i=0	i=0	PROPN
ejpam-4868	324	16	ui+1f	ui+1f	X
ejpam-4868	324	17	(	(	PUNCT
ejpam-4868	324	18	i)(0	i)(0	NUM
ejpam-4868	324	19	)	)	PUNCT
ejpam-4868	324	20	k−i−1∏	k−i−1∏	PROPN
ejpam-4868	325	1	l=1	l=1	PROPN
ejpam-4868	325	2	(	(	PUNCT
ejpam-4868	325	3	1	1	NUM
ejpam-4868	325	4	+	+	CCONJ
ejpam-4868	325	5	luλ	luλ	NOUN
ejpam-4868	325	6	)	)	PUNCT
ejpam-4868	325	7	]	]	PUNCT
ejpam-4868	326	1	=	=	SYM
ejpam-4868	326	2	1	1	NUM
ejpam-4868	326	3	uk	uk	PROPN
ejpam-4868	326	4	gα	gα	NOUN
ejpam-4868	326	5	,	,	PUNCT
ejpam-4868	326	6	λ	λ	PROPN
ejpam-4868	326	7	{	{	PUNCT
ejpam-4868	326	8	(	(	PUNCT
ejpam-4868	326	9	1	1	NUM
ejpam-4868	326	10	+	+	NUM
ejpam-4868	326	11	λt)−(k+1)f(t	λt)−(k+1)f(t	NOUN
ejpam-4868	326	12	)	)	PUNCT
ejpam-4868	326	13	}	}	PUNCT
ejpam-4868	327	1	k∏	k∏	PROPN
ejpam-4868	327	2	l=1	l=1	PROPN
ejpam-4868	327	3	(	(	PUNCT
ejpam-4868	327	4	1	1	NUM
ejpam-4868	327	5	+	+	CCONJ
ejpam-4868	327	6	luλ	luλ	NOUN
ejpam-4868	327	7	)	)	PUNCT
ejpam-4868	327	8	−	−	PROPN
ejpam-4868	328	1	uα−k	uα−k	PROPN
ejpam-4868	328	2	k−1∑	k−1∑	PROPN
ejpam-4868	328	3	i=0	i=0	PROPN
ejpam-4868	328	4	ui+1f	ui+1f	X
ejpam-4868	328	5	(	(	PUNCT
ejpam-4868	328	6	i)(0	i)(0	NUM
ejpam-4868	328	7	)	)	PUNCT
ejpam-4868	328	8	k−i−1∏	k−i−1∏	PROPN
ejpam-4868	329	1	l=1	l=1	PROPN
ejpam-4868	329	2	(	(	PUNCT
ejpam-4868	329	3	1	1	NUM
ejpam-4868	329	4	+	+	CCONJ
ejpam-4868	329	5	luλ	luλ	NOUN
ejpam-4868	329	6	)	)	PUNCT
ejpam-4868	329	7	.	.	PUNCT
ejpam-4868	330	1	so	so	ADV
ejpam-4868	330	2	,	,	PUNCT
ejpam-4868	330	3	the	the	DET
ejpam-4868	330	4	rhs	rhs	PROPN
ejpam-4868	330	5	of	of	ADP
ejpam-4868	330	6	equation	equation	NOUN
ejpam-4868	330	7	(	(	PUNCT
ejpam-4868	330	8	24	24	NUM
ejpam-4868	330	9	)	)	PUNCT
ejpam-4868	330	10	becomes	become	VERB
ejpam-4868	330	11	rhs	rhs	PROPN
ejpam-4868	330	12	=	=	SYM
ejpam-4868	330	13	1	1	NUM
ejpam-4868	330	14	u	u	NOUN
ejpam-4868	330	15	[	[	PUNCT
ejpam-4868	330	16	1	1	NUM
ejpam-4868	330	17	uk	uk	PROPN
ejpam-4868	330	18	gα	gα	NOUN
ejpam-4868	330	19	,	,	PUNCT
ejpam-4868	330	20	λ	λ	PROPN
ejpam-4868	330	21	{	{	PUNCT
ejpam-4868	330	22	(	(	PUNCT
ejpam-4868	330	23	1	1	NUM
ejpam-4868	330	24	+	+	NUM
ejpam-4868	330	25	λt)−(k+1)f(t	λt)−(k+1)f(t	NOUN
ejpam-4868	330	26	)	)	PUNCT
ejpam-4868	330	27	}	}	PUNCT
ejpam-4868	330	28	k∏	k∏	PROPN
ejpam-4868	330	29	l=1	l=1	PROPN
ejpam-4868	330	30	(	(	PUNCT
ejpam-4868	330	31	1	1	NUM
ejpam-4868	330	32	+	+	CCONJ
ejpam-4868	330	33	luλ	luλ	NOUN
ejpam-4868	330	34	)	)	PUNCT
ejpam-4868	330	35	−	−	PROPN
ejpam-4868	331	1	uα−k	uα−k	PROPN
ejpam-4868	331	2	k−1∑	k−1∑	PROPN
ejpam-4868	331	3	i=0	i=0	PROPN
ejpam-4868	331	4	ui+1f	ui+1f	X
ejpam-4868	331	5	(	(	PUNCT
ejpam-4868	331	6	i)(0	i)(0	NUM
ejpam-4868	331	7	)	)	PUNCT
ejpam-4868	331	8	k−i−1∏	k−i−1∏	PROPN
ejpam-4868	331	9	l=1	l=1	SYM
ejpam-4868	331	10	(	(	PUNCT
ejpam-4868	331	11	1	1	NUM
ejpam-4868	331	12	+	+	NUM
ejpam-4868	331	13	luλ	luλ	NOUN
ejpam-4868	331	14	)	)	PUNCT
ejpam-4868	331	15	]	]	PUNCT
ejpam-4868	332	1	−uαfk(0	−uαfk(0	NOUN
ejpam-4868	332	2	)	)	PUNCT
ejpam-4868	332	3	=	=	SYM
ejpam-4868	332	4	1	1	NUM
ejpam-4868	332	5	uk+1	uk+1	X
ejpam-4868	332	6	gα	gα	NOUN
ejpam-4868	332	7	,	,	PUNCT
ejpam-4868	332	8	λ	λ	X
ejpam-4868	332	9	{	{	PUNCT
ejpam-4868	332	10	(	(	PUNCT
ejpam-4868	332	11	1	1	NUM
ejpam-4868	332	12	+	+	NUM
ejpam-4868	332	13	λt)−(k+1)f(t	λt)−(k+1)f(t	NOUN
ejpam-4868	332	14	)	)	PUNCT
ejpam-4868	332	15	}	}	PUNCT
ejpam-4868	332	16	k∏	k∏	PROPN
ejpam-4868	332	17	l=1	l=1	PROPN
ejpam-4868	332	18	(	(	PUNCT
ejpam-4868	332	19	1	1	NUM
ejpam-4868	332	20	+	+	NUM
ejpam-4868	332	21	luλ	luλ	NOUN
ejpam-4868	332	22	)	)	PUNCT
ejpam-4868	332	23	−	−	PROPN
ejpam-4868	332	24	uα−k	uα−k	PROPN
ejpam-4868	332	25	k∑	k∑	PROPN
ejpam-4868	333	1	i=0	i=0	PROPN
ejpam-4868	333	2	uif	uif	PROPN
ejpam-4868	333	3	(	(	PUNCT
ejpam-4868	333	4	i)(0	i)(0	PROPN
ejpam-4868	333	5	)	)	PUNCT
ejpam-4868	333	6	k−i−1∏	k−i−1∏	PROPN
ejpam-4868	334	1	l=1	l=1	PROPN
ejpam-4868	334	2	(	(	PUNCT
ejpam-4868	334	3	1	1	NUM
ejpam-4868	334	4	+	+	CCONJ
ejpam-4868	334	5	luλ	luλ	NOUN
ejpam-4868	334	6	)	)	PUNCT
ejpam-4868	334	7	.	.	PUNCT
ejpam-4868	335	1	hence	hence	ADV
ejpam-4868	335	2	,	,	PUNCT
ejpam-4868	335	3	gα	gα	ADP
ejpam-4868	335	4	,	,	PUNCT
ejpam-4868	335	5	λ{f	λ{f	NOUN
ejpam-4868	335	6	(	(	PUNCT
ejpam-4868	335	7	k+1)(t	k+1)(t	PROPN
ejpam-4868	335	8	)	)	PUNCT
ejpam-4868	335	9	}	}	PUNCT
ejpam-4868	335	10	holds	hold	VERB
ejpam-4868	335	11	.	.	PUNCT
ejpam-4868	336	1	therefore	therefore	ADV
ejpam-4868	336	2	,	,	PUNCT
ejpam-4868	336	3	by	by	ADP
ejpam-4868	336	4	induction	induction	NOUN
ejpam-4868	336	5	equation	equation	NOUN
ejpam-4868	336	6	(	(	PUNCT
ejpam-4868	336	7	22	22	NUM
ejpam-4868	336	8	)	)	PUNCT
ejpam-4868	336	9	holds	hold	VERB
ejpam-4868	336	10	for	for	ADP
ejpam-4868	336	11	all	all	DET
ejpam-4868	336	12	n	n	PRON
ejpam-4868	336	13	≥	≥	NOUN
ejpam-4868	336	14	1	1	NUM
ejpam-4868	336	15	.	.	X
ejpam-4868	336	16	4.2	4.2	NUM
ejpam-4868	336	17	.	.	PUNCT
ejpam-4868	336	18	degenerate	degenerate	ADJ
ejpam-4868	336	19	laplace	laplace	NOUN
ejpam-4868	336	20	-	-	PUNCT
ejpam-4868	336	21	type	type	NOUN
ejpam-4868	336	22	integral	integral	ADJ
ejpam-4868	336	23	transform	transform	NOUN
ejpam-4868	336	24	of	of	ADP
ejpam-4868	336	25	an	an	DET
ejpam-4868	336	26	integral	integral	ADJ
ejpam-4868	336	27	theorem	theorem	NOUN
ejpam-4868	336	28	15	15	NUM
ejpam-4868	336	29	.	.	PUNCT
ejpam-4868	337	1	let	let	VERB
ejpam-4868	337	2	gα	gα	ADP
ejpam-4868	337	3	,	,	PUNCT
ejpam-4868	337	4	λ{f(t	λ{f(t	NUM
ejpam-4868	337	5	)	)	PUNCT
ejpam-4868	337	6	}	}	PUNCT
ejpam-4868	337	7	=	=	SYM
ejpam-4868	337	8	fαλ(u	fαλ(u	PROPN
ejpam-4868	337	9	)	)	PUNCT
ejpam-4868	337	10	.	.	PUNCT
ejpam-4868	338	1	then	then	ADV
ejpam-4868	338	2	gα	gα	ADP
ejpam-4868	338	3	,	,	PUNCT
ejpam-4868	338	4	λ{f(t	λ{f(t	NUM
ejpam-4868	338	5	)	)	PUNCT
ejpam-4868	338	6	}	}	PUNCT
ejpam-4868	338	7	=	=	SYM
ejpam-4868	338	8	1	1	NUM
ejpam-4868	338	9	u	u	NOUN
ejpam-4868	338	10	gα	gα	NOUN
ejpam-4868	338	11	,	,	PUNCT
ejpam-4868	338	12	λ	λ	X
ejpam-4868	338	13	{	{	PUNCT
ejpam-4868	338	14	(	(	PUNCT
ejpam-4868	338	15	1	1	NUM
ejpam-4868	338	16	+	+	NUM
ejpam-4868	338	17	λt)−1	λt)−1	NOUN
ejpam-4868	338	18	∫	∫	PROPN
ejpam-4868	338	19	t	t	PROPN
ejpam-4868	338	20	0	0	PUNCT
ejpam-4868	338	21	f(s)ds	f(s)ds	PROPN
ejpam-4868	338	22	}	}	PUNCT
ejpam-4868	338	23	.	.	PUNCT
ejpam-4868	339	1	h.	h.	PROPN
ejpam-4868	339	2	j.	j.	PROPN
ejpam-4868	339	3	campos	campos	PROPN
ejpam-4868	339	4	,	,	PUNCT
ejpam-4868	339	5	j.	j.	PROPN
ejpam-4868	339	6	c.	c.	PROPN
ejpam-4868	339	7	fernandez	fernandez	PROPN
ejpam-4868	339	8	,	,	PUNCT
ejpam-4868	339	9	j.	j.	PROPN
ejpam-4868	339	10	b.	b.	PROPN
ejpam-4868	339	11	m.	m.	PROPN
ejpam-4868	339	12	natuil	natuil	PROPN
ejpam-4868	339	13	/	/	SYM
ejpam-4868	339	14	eur	eur	PROPN
ejpam-4868	339	15	.	.	PUNCT
ejpam-4868	340	1	j.	j.	PROPN
ejpam-4868	340	2	pure	pure	PROPN
ejpam-4868	340	3	appl	appl	PROPN
ejpam-4868	340	4	.	.	PROPN
ejpam-4868	340	5	math	math	PROPN
ejpam-4868	340	6	,	,	PUNCT
ejpam-4868	340	7	16	16	NUM
ejpam-4868	340	8	(	(	PUNCT
ejpam-4868	340	9	4	4	NUM
ejpam-4868	340	10	)	)	PUNCT
ejpam-4868	340	11	(	(	PUNCT
ejpam-4868	340	12	2023	2023	NUM
ejpam-4868	340	13	)	)	PUNCT
ejpam-4868	340	14	,	,	PUNCT
ejpam-4868	340	15	2213	2213	NUM
ejpam-4868	340	16	-	-	SYM
ejpam-4868	340	17	2233	2233	NUM
ejpam-4868	340	18	2227	2227	NUM
ejpam-4868	340	19	proof	proof	NOUN
ejpam-4868	340	20	.	.	PUNCT
ejpam-4868	341	1	let	let	VERB
ejpam-4868	341	2	g(t	g(t	PROPN
ejpam-4868	341	3	)	)	PUNCT
ejpam-4868	342	1	=	=	SYM
ejpam-4868	343	1	∫	∫	PROPN
ejpam-4868	343	2	t	t	PROPN
ejpam-4868	343	3	0	0	NUM
ejpam-4868	343	4	f(s)ds	f(s)ds	PROPN
ejpam-4868	343	5	.	.	PUNCT
ejpam-4868	344	1	then	then	ADV
ejpam-4868	344	2	g′(t	g′(t	VERB
ejpam-4868	344	3	)	)	PUNCT
ejpam-4868	344	4	=	=	PUNCT
ejpam-4868	345	1	d	d	NOUN
ejpam-4868	345	2	dt	dt	X
ejpam-4868	345	3	{	{	PUNCT
ejpam-4868	345	4	∫	∫	PROPN
ejpam-4868	345	5	t	t	PROPN
ejpam-4868	345	6	0	0	NUM
ejpam-4868	345	7	f(s)ds	f(s)ds	PROPN
ejpam-4868	345	8	}	}	PUNCT
ejpam-4868	345	9	=	=	SYM
ejpam-4868	345	10	f(t	f(t	NOUN
ejpam-4868	345	11	)	)	PUNCT
ejpam-4868	345	12	and	and	CCONJ
ejpam-4868	345	13	g(0	g(0	PROPN
ejpam-4868	345	14	)	)	PUNCT
ejpam-4868	345	15	=	=	SYM
ejpam-4868	345	16	0	0	X
ejpam-4868	345	17	.	.	X
ejpam-4868	345	18	note	note	VERB
ejpam-4868	345	19	that	that	SCONJ
ejpam-4868	345	20	by	by	ADP
ejpam-4868	345	21	theorem	theorem	NOUN
ejpam-4868	345	22	14	14	NUM
ejpam-4868	345	23	(	(	PUNCT
ejpam-4868	345	24	i.	i.	NOUN
ejpam-4868	345	25	)	)	PUNCT
ejpam-4868	345	26	we	we	PRON
ejpam-4868	345	27	have	have	VERB
ejpam-4868	345	28	gα	gα	NOUN
ejpam-4868	345	29	,	,	PUNCT
ejpam-4868	345	30	λ{g′(t	λ{g′(t	NOUN
ejpam-4868	345	31	)	)	PUNCT
ejpam-4868	345	32	}	}	PUNCT
ejpam-4868	345	33	=	=	SYM
ejpam-4868	345	34	1	1	NUM
ejpam-4868	345	35	u	u	NOUN
ejpam-4868	345	36	gα	gα	NOUN
ejpam-4868	345	37	,	,	PUNCT
ejpam-4868	345	38	λ	λ	X
ejpam-4868	345	39	{	{	PUNCT
ejpam-4868	345	40	(	(	PUNCT
ejpam-4868	345	41	1	1	NUM
ejpam-4868	345	42	+	+	CCONJ
ejpam-4868	345	43	λt)−1g(t	λt)−1g(t	ADJ
ejpam-4868	345	44	)	)	PUNCT
ejpam-4868	345	45	}	}	PUNCT
ejpam-4868	345	46	−	−	NOUN
ejpam-4868	345	47	uαg(0	uαg(0	NOUN
ejpam-4868	345	48	)	)	PUNCT
ejpam-4868	345	49	=	=	SYM
ejpam-4868	345	50	1	1	NUM
ejpam-4868	345	51	u	u	NOUN
ejpam-4868	345	52	gα	gα	NOUN
ejpam-4868	345	53	,	,	PUNCT
ejpam-4868	345	54	λ	λ	X
ejpam-4868	345	55	{	{	PUNCT
ejpam-4868	345	56	(	(	PUNCT
ejpam-4868	345	57	1	1	NUM
ejpam-4868	345	58	+	+	NUM
ejpam-4868	345	59	λt)−1	λt)−1	NOUN
ejpam-4868	345	60	∫	∫	PROPN
ejpam-4868	345	61	t	t	PROPN
ejpam-4868	345	62	0	0	PUNCT
ejpam-4868	345	63	f(s)ds	f(s)ds	PROPN
ejpam-4868	345	64	}	}	PUNCT
ejpam-4868	345	65	.	.	PUNCT
ejpam-4868	346	1	4.3	4.3	NUM
ejpam-4868	346	2	.	.	PUNCT
ejpam-4868	347	1	the	the	DET
ejpam-4868	347	2	first	first	ADJ
ejpam-4868	347	3	translation	translation	NOUN
ejpam-4868	347	4	theorem	theorem	VERB
ejpam-4868	347	5	for	for	ADP
ejpam-4868	347	6	the	the	DET
ejpam-4868	347	7	degenerate	degenerate	ADJ
ejpam-4868	347	8	laplace	laplace	NOUN
ejpam-4868	347	9	-	-	PUNCT
ejpam-4868	347	10	type	type	NOUN
ejpam-4868	347	11	integral	integral	ADJ
ejpam-4868	347	12	transform	transform	NOUN
ejpam-4868	347	13	theorem	theorem	ADJ
ejpam-4868	347	14	16	16	NUM
ejpam-4868	347	15	.	.	PUNCT
ejpam-4868	348	1	if	if	SCONJ
ejpam-4868	348	2	gα	gα	ADP
ejpam-4868	348	3	,	,	PUNCT
ejpam-4868	348	4	λ{f(t	λ{f(t	NUM
ejpam-4868	348	5	)	)	PUNCT
ejpam-4868	348	6	}	}	PUNCT
ejpam-4868	348	7	=	=	SYM
ejpam-4868	348	8	fαλ(u	fαλ(u	PROPN
ejpam-4868	348	9	)	)	PUNCT
ejpam-4868	348	10	then	then	ADV
ejpam-4868	348	11	gα	gα	ADP
ejpam-4868	348	12	,	,	PUNCT
ejpam-4868	348	13	λ{eaλ(t)f(t	λ{eaλ(t)f(t	NOUN
ejpam-4868	348	14	)	)	PUNCT
ejpam-4868	348	15	}	}	PUNCT
ejpam-4868	348	16	=	=	SYM
ejpam-4868	348	17	(	(	PUNCT
ejpam-4868	348	18	1−	1−	NUM
ejpam-4868	348	19	au)αfα	au)αfα	NOUN
ejpam-4868	348	20	,	,	PUNCT
ejpam-4868	348	21	λ	λ	PROPN
ejpam-4868	348	22	(	(	PUNCT
ejpam-4868	348	23	u	u	PROPN
ejpam-4868	348	24	1−	1−	PROPN
ejpam-4868	348	25	ua	ua	PROPN
ejpam-4868	348	26	)	)	PUNCT
ejpam-4868	348	27	,	,	PUNCT
ejpam-4868	348	28	for	for	ADP
ejpam-4868	348	29	a	a	DET
ejpam-4868	348	30	̸=	̸=	PROPN
ejpam-4868	348	31	1	1	NUM
ejpam-4868	348	32	u	u	NOUN
ejpam-4868	348	33	.	.	PUNCT
ejpam-4868	349	1	proof	proof	NOUN
ejpam-4868	349	2	.	.	PUNCT
ejpam-4868	350	1	from	from	ADP
ejpam-4868	350	2	definition	definition	NOUN
ejpam-4868	350	3	8	8	NUM
ejpam-4868	350	4	,	,	PUNCT
ejpam-4868	350	5	it	it	PRON
ejpam-4868	350	6	follows	follow	VERB
ejpam-4868	350	7	that	that	SCONJ
ejpam-4868	350	8	gα	gα	ADP
ejpam-4868	350	9	,	,	PUNCT
ejpam-4868	350	10	λ{eaλ(t)f(t	λ{eaλ(t)f(t	NOUN
ejpam-4868	350	11	)	)	PUNCT
ejpam-4868	350	12	}	}	PUNCT
ejpam-4868	351	1	=	=	X
ejpam-4868	351	2	uα	uα	PROPN
ejpam-4868	351	3	∫	∫	PROPN
ejpam-4868	351	4	∞	∞	NUM
ejpam-4868	351	5	0	0	NUM
ejpam-4868	351	6	eaλ(t)e	eaλ(t)e	NOUN
ejpam-4868	351	7	−	−	PROPN
ejpam-4868	351	8	1	1	NUM
ejpam-4868	351	9	u	u	NOUN
ejpam-4868	351	10	λ	λ	PROPN
ejpam-4868	351	11	(	(	PUNCT
ejpam-4868	351	12	t)f(t)dt	t)f(t)dt	NOUN
ejpam-4868	351	13	=	=	SYM
ejpam-4868	351	14	(	(	PUNCT
ejpam-4868	351	15	1−	1−	NUM
ejpam-4868	351	16	au)α	au)α	PROPN
ejpam-4868	351	17	(	(	PUNCT
ejpam-4868	351	18	1−	1−	NUM
ejpam-4868	351	19	au)α	au)α	NOUN
ejpam-4868	351	20	uα	uα	PROPN
ejpam-4868	351	21	∫	∫	PROPN
ejpam-4868	351	22	∞	∞	PROPN
ejpam-4868	351	23	0	0	NUM
ejpam-4868	352	1	(	(	PUNCT
ejpam-4868	352	2	1	1	NUM
ejpam-4868	352	3	+	+	CCONJ
ejpam-4868	352	4	λt	λt	X
ejpam-4868	352	5	)	)	PUNCT
ejpam-4868	352	6	−	−	PROPN
ejpam-4868	352	7	1	1	NUM
ejpam-4868	352	8	(	(	PUNCT
ejpam-4868	352	9	u	u	NOUN
ejpam-4868	352	10	1−au	1−au	PROPN
ejpam-4868	352	11	)	)	PUNCT
ejpam-4868	353	1	λ	λ	NOUN
ejpam-4868	353	2	f(t)dt	f(t)dt	NOUN
ejpam-4868	353	3	=(	=(	NOUN
ejpam-4868	353	4	1−	1−	NUM
ejpam-4868	354	1	au)α	au)α	PROPN
ejpam-4868	354	2	(	(	PUNCT
ejpam-4868	354	3	u	u	NOUN
ejpam-4868	354	4	1−	1−	NUM
ejpam-4868	354	5	au	au	X
ejpam-4868	354	6	)	)	PUNCT
ejpam-4868	354	7	α∫	α∫	NUM
ejpam-4868	354	8	∞	∞	PROPN
ejpam-4868	354	9	0	0	PUNCT
ejpam-4868	354	10	(	(	PUNCT
ejpam-4868	354	11	1	1	NUM
ejpam-4868	354	12	+	+	CCONJ
ejpam-4868	354	13	λt	λt	X
ejpam-4868	354	14	)	)	PUNCT
ejpam-4868	354	15	−	−	PROPN
ejpam-4868	354	16	1	1	NUM
ejpam-4868	354	17	(	(	PUNCT
ejpam-4868	354	18	u	u	NOUN
ejpam-4868	354	19	1−au	1−au	PROPN
ejpam-4868	354	20	)	)	PUNCT
ejpam-4868	355	1	λ	λ	NOUN
ejpam-4868	355	2	f(t)dt	f(t)dt	NOUN
ejpam-4868	355	3	=(	=(	NOUN
ejpam-4868	355	4	1−	1−	NUM
ejpam-4868	355	5	au)αfα	au)αfα	NOUN
ejpam-4868	355	6	,	,	PUNCT
ejpam-4868	355	7	λ	λ	PROPN
ejpam-4868	355	8	(	(	PUNCT
ejpam-4868	355	9	u	u	PROPN
ejpam-4868	355	10	1−	1−	PROPN
ejpam-4868	355	11	ua	ua	PROPN
ejpam-4868	355	12	)	)	PUNCT
ejpam-4868	355	13	,	,	PUNCT
ejpam-4868	355	14	for	for	ADP
ejpam-4868	355	15	a	a	DET
ejpam-4868	355	16	̸=	̸=	PROPN
ejpam-4868	355	17	1	1	NUM
ejpam-4868	355	18	u	u	NOUN
ejpam-4868	355	19	.	.	PUNCT
ejpam-4868	356	1	4.4	4.4	NUM
ejpam-4868	356	2	.	.	PUNCT
ejpam-4868	357	1	the	the	DET
ejpam-4868	357	2	change	change	NOUN
ejpam-4868	357	3	of	of	ADP
ejpam-4868	357	4	scale	scale	NOUN
ejpam-4868	357	5	property	property	NOUN
ejpam-4868	357	6	for	for	ADP
ejpam-4868	357	7	the	the	DET
ejpam-4868	357	8	degenerate	degenerate	ADJ
ejpam-4868	357	9	laplace	laplace	NOUN
ejpam-4868	357	10	-	-	PUNCT
ejpam-4868	357	11	type	type	NOUN
ejpam-4868	357	12	integral	integral	ADJ
ejpam-4868	357	13	transform	transform	NOUN
ejpam-4868	357	14	theorem	theorem	ADJ
ejpam-4868	357	15	17	17	NUM
ejpam-4868	357	16	.	.	PUNCT
ejpam-4868	358	1	if	if	SCONJ
ejpam-4868	358	2	gα	gα	ADP
ejpam-4868	358	3	,	,	PUNCT
ejpam-4868	358	4	λ{f(t	λ{f(t	NUM
ejpam-4868	358	5	)	)	PUNCT
ejpam-4868	358	6	}	}	PUNCT
ejpam-4868	358	7	=	=	SYM
ejpam-4868	358	8	fα	fα	NOUN
ejpam-4868	358	9	,	,	PUNCT
ejpam-4868	358	10	λ(u	λ(u	PROPN
ejpam-4868	358	11	)	)	PUNCT
ejpam-4868	358	12	then	then	ADV
ejpam-4868	358	13	gα	gα	ADP
ejpam-4868	358	14	,	,	PUNCT
ejpam-4868	358	15	λ{f(at	λ{f(at	PROPN
ejpam-4868	358	16	)	)	PUNCT
ejpam-4868	358	17	}	}	PUNCT
ejpam-4868	358	18	=	=	SYM
ejpam-4868	358	19	1	1	NUM
ejpam-4868	358	20	aα+1	aα+1	NOUN
ejpam-4868	358	21	fα	fα	ADP
ejpam-4868	358	22	,	,	PUNCT
ejpam-4868	358	23	λ	λ	PROPN
ejpam-4868	358	24	a	a	DET
ejpam-4868	358	25	(	(	PUNCT
ejpam-4868	358	26	au	au	PROPN
ejpam-4868	358	27	)	)	PUNCT
ejpam-4868	358	28	,	,	PUNCT
ejpam-4868	358	29	for	for	ADP
ejpam-4868	358	30	a	a	DET
ejpam-4868	358	31	>	>	X
ejpam-4868	358	32	0	0	NUM
ejpam-4868	358	33	.	.	PUNCT
ejpam-4868	359	1	proof	proof	NOUN
ejpam-4868	359	2	.	.	PUNCT
ejpam-4868	360	1	from	from	ADP
ejpam-4868	360	2	definition	definition	NOUN
ejpam-4868	360	3	8	8	NUM
ejpam-4868	360	4	,	,	PUNCT
ejpam-4868	360	5	it	it	PRON
ejpam-4868	360	6	follows	follow	VERB
ejpam-4868	360	7	that	that	SCONJ
ejpam-4868	360	8	gα	gα	ADP
ejpam-4868	360	9	,	,	PUNCT
ejpam-4868	360	10	λ{f(at	λ{f(at	PROPN
ejpam-4868	360	11	)	)	PUNCT
ejpam-4868	360	12	}	}	PUNCT
ejpam-4868	361	1	=	=	X
ejpam-4868	361	2	uα	uα	PROPN
ejpam-4868	361	3	∫	∫	PROPN
ejpam-4868	361	4	∞	∞	PROPN
ejpam-4868	361	5	0	0	PUNCT
ejpam-4868	362	1	e	e	NOUN
ejpam-4868	362	2	−	−	PROPN
ejpam-4868	362	3	1	1	NUM
ejpam-4868	362	4	u	u	NOUN
ejpam-4868	362	5	λ	λ	PROPN
ejpam-4868	362	6	(	(	PUNCT
ejpam-4868	362	7	t)f(at)dt	t)f(at)dt	X
ejpam-4868	362	8	=	=	PUNCT
ejpam-4868	362	9	uα	uα	PROPN
ejpam-4868	362	10	∫	∫	PROPN
ejpam-4868	362	11	∞	∞	PROPN
ejpam-4868	362	12	0	0	NUM
ejpam-4868	363	1	(	(	PUNCT
ejpam-4868	363	2	1	1	NUM
ejpam-4868	363	3	+	+	CCONJ
ejpam-4868	363	4	λt)−	λt)−	PROPN
ejpam-4868	363	5	1	1	NUM
ejpam-4868	363	6	uλ	uλ	ADP
ejpam-4868	363	7	f(at)dt	f(at)dt	NOUN
ejpam-4868	363	8	.	.	PUNCT
ejpam-4868	364	1	h.	h.	PROPN
ejpam-4868	364	2	j.	j.	PROPN
ejpam-4868	364	3	campos	campos	PROPN
ejpam-4868	364	4	,	,	PUNCT
ejpam-4868	364	5	j.	j.	PROPN
ejpam-4868	364	6	c.	c.	PROPN
ejpam-4868	364	7	fernandez	fernandez	PROPN
ejpam-4868	364	8	,	,	PUNCT
ejpam-4868	364	9	j.	j.	PROPN
ejpam-4868	364	10	b.	b.	PROPN
ejpam-4868	364	11	m.	m.	PROPN
ejpam-4868	364	12	natuil	natuil	PROPN
ejpam-4868	364	13	/	/	SYM
ejpam-4868	364	14	eur	eur	PROPN
ejpam-4868	364	15	.	.	PUNCT
ejpam-4868	365	1	j.	j.	PROPN
ejpam-4868	365	2	pure	pure	PROPN
ejpam-4868	365	3	appl	appl	PROPN
ejpam-4868	365	4	.	.	PROPN
ejpam-4868	365	5	math	math	PROPN
ejpam-4868	365	6	,	,	PUNCT
ejpam-4868	365	7	16	16	NUM
ejpam-4868	365	8	(	(	PUNCT
ejpam-4868	365	9	4	4	NUM
ejpam-4868	365	10	)	)	PUNCT
ejpam-4868	365	11	(	(	PUNCT
ejpam-4868	365	12	2023	2023	NUM
ejpam-4868	365	13	)	)	PUNCT
ejpam-4868	365	14	,	,	PUNCT
ejpam-4868	365	15	2213	2213	NUM
ejpam-4868	365	16	-	-	SYM
ejpam-4868	365	17	2233	2233	NUM
ejpam-4868	365	18	2228	2228	NUM
ejpam-4868	365	19	let	let	VERB
ejpam-4868	365	20	w	w	NOUN
ejpam-4868	365	21	=	=	PUNCT
ejpam-4868	365	22	at	at	ADP
ejpam-4868	365	23	,	,	PUNCT
ejpam-4868	365	24	then	then	ADV
ejpam-4868	365	25	dw	dw	PROPN
ejpam-4868	365	26	=	=	PUNCT
ejpam-4868	365	27	adt	adt	PROPN
ejpam-4868	365	28	and	and	CCONJ
ejpam-4868	365	29	t	t	NOUN
ejpam-4868	365	30	=	=	PUNCT
ejpam-4868	366	1	w	w	PROPN
ejpam-4868	366	2	a	a	NOUN
ejpam-4868	366	3	.	.	PUNCT
ejpam-4868	367	1	hence	hence	ADV
ejpam-4868	367	2	gα	gα	ADP
ejpam-4868	367	3	,	,	PUNCT
ejpam-4868	367	4	λ{f(at	λ{f(at	PROPN
ejpam-4868	367	5	)	)	PUNCT
ejpam-4868	367	6	}	}	PUNCT
ejpam-4868	368	1	=	=	X
ejpam-4868	368	2	uα	uα	PROPN
ejpam-4868	368	3	∫	∫	PROPN
ejpam-4868	368	4	∞	∞	PROPN
ejpam-4868	368	5	0	0	NUM
ejpam-4868	369	1	(	(	PUNCT
ejpam-4868	369	2	1	1	NUM
ejpam-4868	369	3	+	+	CCONJ
ejpam-4868	369	4	λt)−	λt)−	PROPN
ejpam-4868	369	5	1	1	NUM
ejpam-4868	369	6	uλ	uλ	ADP
ejpam-4868	369	7	f(at)dt	f(at)dt	NOUN
ejpam-4868	369	8	=	=	SYM
ejpam-4868	369	9	1	1	NUM
ejpam-4868	369	10	aα+1	aα+1	NOUN
ejpam-4868	369	11	[	[	PUNCT
ejpam-4868	369	12	(	(	PUNCT
ejpam-4868	369	13	ua)α	ua)α	PROPN
ejpam-4868	369	14	∫	∫	PROPN
ejpam-4868	369	15	∞	∞	PROPN
ejpam-4868	369	16	0	0	NUM
ejpam-4868	370	1	(	(	PUNCT
ejpam-4868	370	2	1	1	NUM
ejpam-4868	370	3	+	+	CCONJ
ejpam-4868	370	4	(	(	PUNCT
ejpam-4868	370	5	λ	λ	INTJ
ejpam-4868	370	6	a	a	NOUN
ejpam-4868	370	7	)	)	PUNCT
ejpam-4868	370	8	w	w	NOUN
ejpam-4868	370	9	)	)	PUNCT
ejpam-4868	370	10	−	−	PROPN
ejpam-4868	371	1	1	1	NUM
ejpam-4868	371	2	(	(	PUNCT
ejpam-4868	371	3	λa	λa	NOUN
ejpam-4868	371	4	)	)	PUNCT
ejpam-4868	371	5	au	au	PROPN
ejpam-4868	371	6	f(w)dw	f(w)dw	NOUN
ejpam-4868	371	7	]	]	PUNCT
ejpam-4868	372	1	=	=	SYM
ejpam-4868	372	2	1	1	NUM
ejpam-4868	372	3	aα+1	aα+1	NOUN
ejpam-4868	372	4	fα	fα	ADP
ejpam-4868	372	5	,	,	PUNCT
ejpam-4868	372	6	λ	λ	PROPN
ejpam-4868	372	7	a	a	DET
ejpam-4868	372	8	(	(	PUNCT
ejpam-4868	372	9	au	au	PROPN
ejpam-4868	372	10	)	)	PUNCT
ejpam-4868	372	11	,	,	PUNCT
ejpam-4868	372	12	for	for	ADP
ejpam-4868	372	13	a	a	DET
ejpam-4868	372	14	>	>	X
ejpam-4868	372	15	0	0	NUM
ejpam-4868	372	16	.	.	NOUN
ejpam-4868	372	17	5	5	NUM
ejpam-4868	372	18	.	.	X
ejpam-4868	372	19	generalization	generalization	NOUN
ejpam-4868	372	20	of	of	ADP
ejpam-4868	372	21	the	the	DET
ejpam-4868	372	22	degenerate	degenerate	ADJ
ejpam-4868	372	23	laplace	laplace	NOUN
ejpam-4868	372	24	,	,	PUNCT
ejpam-4868	372	25	degenerate	degenerate	ADJ
ejpam-4868	372	26	sumudu	sumudu	NOUN
ejpam-4868	372	27	and	and	CCONJ
ejpam-4868	372	28	degenerate	degenerate	ADJ
ejpam-4868	372	29	elzaki	elzaki	NOUN
ejpam-4868	372	30	transform	transform	VERB
ejpam-4868	372	31	definition	definition	NOUN
ejpam-4868	372	32	9	9	NUM
ejpam-4868	372	33	.	.	PUNCT
ejpam-4868	373	1	the	the	DET
ejpam-4868	373	2	degenerate	degenerate	ADJ
ejpam-4868	373	3	laplace	laplace	NOUN
ejpam-4868	373	4	-	-	PUNCT
ejpam-4868	373	5	type	type	NOUN
ejpam-4868	373	6	integral	integral	ADJ
ejpam-4868	373	7	transform	transform	NOUN
ejpam-4868	373	8	gα	gα	NOUN
ejpam-4868	373	9	,	,	PUNCT
ejpam-4868	373	10	λ{f(t	λ{f(t	NUM
ejpam-4868	373	11	)	)	PUNCT
ejpam-4868	373	12	}	}	PUNCT
ejpam-4868	373	13	=	=	SYM
ejpam-4868	373	14	fα	fα	NOUN
ejpam-4868	373	15	,	,	PUNCT
ejpam-4868	373	16	λ(u	λ(u	PROPN
ejpam-4868	373	17	)	)	PUNCT
ejpam-4868	373	18	=	=	PUNCT
ejpam-4868	374	1	uα	uα	PROPN
ejpam-4868	374	2	∫	∫	PROPN
ejpam-4868	374	3	∞	∞	PROPN
ejpam-4868	374	4	0	0	PUNCT
ejpam-4868	375	1	e	e	NOUN
ejpam-4868	375	2	−	−	PROPN
ejpam-4868	375	3	1	1	NUM
ejpam-4868	375	4	u	u	NOUN
ejpam-4868	375	5	λ	λ	X
ejpam-4868	375	6	(	(	PUNCT
ejpam-4868	375	7	t)f(t)dt	t)f(t)dt	NOUN
ejpam-4868	375	8	=	=	PUNCT
ejpam-4868	375	9	uα	uα	PROPN
ejpam-4868	375	10	∫	∫	PROPN
ejpam-4868	375	11	∞	∞	PROPN
ejpam-4868	375	12	0	0	NUM
ejpam-4868	376	1	(	(	PUNCT
ejpam-4868	376	2	1	1	NUM
ejpam-4868	376	3	+	+	CCONJ
ejpam-4868	376	4	λt)−	λt)−	PROPN
ejpam-4868	376	5	1	1	X
ejpam-4868	376	6	uλ	uλ	ADP
ejpam-4868	376	7	f(t)dt	f(t)dt	PROPN
ejpam-4868	376	8	,	,	PUNCT
ejpam-4868	376	9	is	be	AUX
ejpam-4868	376	10	the	the	DET
ejpam-4868	376	11	generalization	generalization	NOUN
ejpam-4868	376	12	of	of	ADP
ejpam-4868	376	13	the	the	DET
ejpam-4868	376	14	degenerate	degenerate	ADJ
ejpam-4868	376	15	laplace	laplace	NOUN
ejpam-4868	376	16	,	,	PUNCT
ejpam-4868	376	17	degenerate	degenerate	ADJ
ejpam-4868	376	18	sumudu	sumudu	NOUN
ejpam-4868	376	19	and	and	CCONJ
ejpam-4868	376	20	degenerate	degenerate	ADJ
ejpam-4868	376	21	elzaki	elzaki	NOUN
ejpam-4868	376	22	transform	transform	NOUN
ejpam-4868	376	23	,	,	PUNCT
ejpam-4868	376	24	where	where	SCONJ
ejpam-4868	376	25	α	α	NOUN
ejpam-4868	376	26	=	=	SYM
ejpam-4868	376	27	0	0	PROPN
ejpam-4868	376	28	,	,	PUNCT
ejpam-4868	376	29	α	α	NOUN
ejpam-4868	376	30	=	=	PUNCT
ejpam-4868	376	31	−1	−1	NOUN
ejpam-4868	376	32	and	and	CCONJ
ejpam-4868	376	33	α	α	NOUN
ejpam-4868	376	34	=	=	SYM
ejpam-4868	376	35	1	1	NUM
ejpam-4868	376	36	,	,	PUNCT
ejpam-4868	376	37	respectively	respectively	ADV
ejpam-4868	376	38	.	.	PUNCT
ejpam-4868	377	1	that	that	PRON
ejpam-4868	377	2	is	be	AUX
ejpam-4868	377	3	,	,	PUNCT
ejpam-4868	377	4	when	when	SCONJ
ejpam-4868	377	5	α	α	PROPN
ejpam-4868	377	6	=	=	SYM
ejpam-4868	377	7	0	0	NUM
ejpam-4868	377	8	,	,	PUNCT
ejpam-4868	377	9	we	we	PRON
ejpam-4868	377	10	can	can	AUX
ejpam-4868	377	11	have	have	VERB
ejpam-4868	377	12	the	the	DET
ejpam-4868	377	13	degenerate	degenerate	ADJ
ejpam-4868	377	14	laplace	laplace	NOUN
ejpam-4868	377	15	transform	transform	NOUN
ejpam-4868	377	16	,	,	PUNCT
ejpam-4868	377	17	that	that	PRON
ejpam-4868	377	18	is	be	AUX
ejpam-4868	377	19	g0,λ{f(t	g0,λ{f(t	NOUN
ejpam-4868	377	20	)	)	PUNCT
ejpam-4868	377	21	}	}	PUNCT
ejpam-4868	377	22	=	=	SYM
ejpam-4868	377	23	f0,λ(u	f0,λ(u	X
ejpam-4868	377	24	)	)	PUNCT
ejpam-4868	377	25	=	=	PRON
ejpam-4868	377	26	u0	u0	ADJ
ejpam-4868	377	27	∫	∫	PROPN
ejpam-4868	377	28	∞	∞	PROPN
ejpam-4868	377	29	0	0	PUNCT
ejpam-4868	378	1	e	e	NOUN
ejpam-4868	378	2	−	−	PROPN
ejpam-4868	378	3	1	1	NUM
ejpam-4868	378	4	u	u	NOUN
ejpam-4868	378	5	λ	λ	X
ejpam-4868	378	6	(	(	PUNCT
ejpam-4868	378	7	t)f(t)dt	t)f(t)dt	NOUN
ejpam-4868	378	8	=	=	SYM
ejpam-4868	378	9	∫	∫	PROPN
ejpam-4868	378	10	∞	∞	PROPN
ejpam-4868	378	11	0	0	NUM
ejpam-4868	378	12	(	(	PUNCT
ejpam-4868	378	13	1	1	NUM
ejpam-4868	378	14	+	+	CCONJ
ejpam-4868	378	15	λt)−	λt)−	PROPN
ejpam-4868	378	16	1	1	X
ejpam-4868	378	17	uλ	uλ	ADP
ejpam-4868	378	18	f(t)dt	f(t)dt	PROPN
ejpam-4868	378	19	=	=	SYM
ejpam-4868	378	20	∫	∫	PROPN
ejpam-4868	378	21	∞	∞	PROPN
ejpam-4868	378	22	0	0	PUNCT
ejpam-4868	379	1	e	e	NOUN
ejpam-4868	379	2	−	−	PROPN
ejpam-4868	379	3	1	1	NUM
ejpam-4868	379	4	u	u	NOUN
ejpam-4868	379	5	λ	λ	X
ejpam-4868	379	6	(	(	PUNCT
ejpam-4868	379	7	t)f(t)dt	t)f(t)dt	NOUN
ejpam-4868	379	8	=	=	SYM
ejpam-4868	379	9	lλ{f(t	lλ{f(t	NOUN
ejpam-4868	379	10	)	)	PUNCT
ejpam-4868	379	11	}	}	PUNCT
ejpam-4868	379	12	.	.	PUNCT
ejpam-4868	380	1	when	when	SCONJ
ejpam-4868	380	2	α	α	PROPN
ejpam-4868	380	3	=	=	SYM
ejpam-4868	380	4	−1	−1	NOUN
ejpam-4868	380	5	,	,	PUNCT
ejpam-4868	380	6	we	we	PRON
ejpam-4868	380	7	can	can	AUX
ejpam-4868	380	8	have	have	VERB
ejpam-4868	380	9	the	the	DET
ejpam-4868	380	10	degenerate	degenerate	ADJ
ejpam-4868	380	11	sumudu	sumudu	NOUN
ejpam-4868	380	12	transform	transform	NOUN
ejpam-4868	380	13	,	,	PUNCT
ejpam-4868	380	14	that	that	PRON
ejpam-4868	380	15	is	is	AUX
ejpam-4868	380	16	g−1,λ{f(t	g−1,λ{f(t	ADJ
ejpam-4868	380	17	)	)	PUNCT
ejpam-4868	380	18	}	}	PUNCT
ejpam-4868	380	19	=	=	SYM
ejpam-4868	380	20	f−1,λ(u	f−1,λ(u	NOUN
ejpam-4868	380	21	)	)	PUNCT
ejpam-4868	381	1	=	=	SYM
ejpam-4868	381	2	u−1	u−1	PROPN
ejpam-4868	381	3	∫	∫	PROPN
ejpam-4868	381	4	∞	∞	NOUN
ejpam-4868	381	5	0	0	PUNCT
ejpam-4868	382	1	e	e	NOUN
ejpam-4868	382	2	−	−	PROPN
ejpam-4868	382	3	1	1	NUM
ejpam-4868	382	4	u	u	NOUN
ejpam-4868	382	5	λ	λ	X
ejpam-4868	382	6	(	(	PUNCT
ejpam-4868	382	7	t)f(t)dt	t)f(t)dt	NOUN
ejpam-4868	382	8	=	=	SYM
ejpam-4868	382	9	1	1	NUM
ejpam-4868	382	10	u	u	NOUN
ejpam-4868	382	11	∫	∫	PROPN
ejpam-4868	382	12	∞	∞	NOUN
ejpam-4868	382	13	0	0	NUM
ejpam-4868	383	1	(	(	PUNCT
ejpam-4868	383	2	1	1	NUM
ejpam-4868	383	3	+	+	CCONJ
ejpam-4868	383	4	λt)−	λt)−	PROPN
ejpam-4868	383	5	1	1	X
ejpam-4868	383	6	uλ	uλ	ADP
ejpam-4868	383	7	f(t)dt	f(t)dt	PROPN
ejpam-4868	383	8	=	=	SYM
ejpam-4868	383	9	1	1	NUM
ejpam-4868	383	10	u	u	NOUN
ejpam-4868	383	11	∫	∫	PROPN
ejpam-4868	383	12	∞	∞	NOUN
ejpam-4868	383	13	0	0	PUNCT
ejpam-4868	384	1	e	e	NOUN
ejpam-4868	384	2	−	−	PROPN
ejpam-4868	384	3	1	1	NUM
ejpam-4868	384	4	u	u	NOUN
ejpam-4868	384	5	λ	λ	X
ejpam-4868	384	6	(	(	PUNCT
ejpam-4868	384	7	t)f(t)dt	t)f(t)dt	NOUN
ejpam-4868	384	8	=	=	SYM
ejpam-4868	384	9	sλ{f(t	sλ{f(t	NOUN
ejpam-4868	384	10	)	)	PUNCT
ejpam-4868	384	11	}	}	PUNCT
ejpam-4868	384	12	.	.	PUNCT
ejpam-4868	385	1	lastly	lastly	ADV
ejpam-4868	385	2	,	,	PUNCT
ejpam-4868	385	3	when	when	SCONJ
ejpam-4868	385	4	α	α	PROPN
ejpam-4868	385	5	=	=	SYM
ejpam-4868	385	6	1	1	NUM
ejpam-4868	385	7	,	,	PUNCT
ejpam-4868	385	8	we	we	PRON
ejpam-4868	385	9	can	can	AUX
ejpam-4868	385	10	have	have	VERB
ejpam-4868	385	11	the	the	DET
ejpam-4868	385	12	degenerate	degenerate	ADJ
ejpam-4868	385	13	elzaki	elzaki	NOUN
ejpam-4868	385	14	transform	transform	NOUN
ejpam-4868	385	15	,	,	PUNCT
ejpam-4868	385	16	given	give	VERB
ejpam-4868	385	17	by	by	ADP
ejpam-4868	385	18	g1,λ{f(t	g1,λ{f(t	NOUN
ejpam-4868	385	19	)	)	PUNCT
ejpam-4868	385	20	}	}	PUNCT
ejpam-4868	385	21	=	=	SYM
ejpam-4868	385	22	f1,λ(u	f1,λ(u	X
ejpam-4868	385	23	)	)	PUNCT
ejpam-4868	386	1	=	=	NOUN
ejpam-4868	386	2	u1	u1	NOUN
ejpam-4868	386	3	∫	∫	PROPN
ejpam-4868	386	4	∞	∞	PROPN
ejpam-4868	386	5	0	0	PUNCT
ejpam-4868	387	1	e	e	NOUN
ejpam-4868	387	2	−	−	PROPN
ejpam-4868	387	3	1	1	NUM
ejpam-4868	387	4	u	u	NOUN
ejpam-4868	387	5	λ	λ	X
ejpam-4868	387	6	(	(	PUNCT
ejpam-4868	387	7	t)f(t)dt	t)f(t)dt	NOUN
ejpam-4868	387	8	=	=	SYM
ejpam-4868	387	9	u	u	NOUN
ejpam-4868	387	10	∫	∫	PROPN
ejpam-4868	387	11	∞	∞	PROPN
ejpam-4868	387	12	0	0	NUM
ejpam-4868	388	1	(	(	PUNCT
ejpam-4868	388	2	1	1	NUM
ejpam-4868	388	3	+	+	CCONJ
ejpam-4868	388	4	λt)−	λt)−	PROPN
ejpam-4868	388	5	1	1	X
ejpam-4868	388	6	uλ	uλ	ADP
ejpam-4868	388	7	f(t)dt	f(t)dt	PROPN
ejpam-4868	388	8	=	=	NOUN
ejpam-4868	388	9	u	u	NOUN
ejpam-4868	388	10	∫	∫	PROPN
ejpam-4868	388	11	∞	∞	NOUN
ejpam-4868	388	12	0	0	PUNCT
ejpam-4868	389	1	e	e	NOUN
ejpam-4868	389	2	−	−	PROPN
ejpam-4868	389	3	1	1	NUM
ejpam-4868	389	4	u	u	NOUN
ejpam-4868	389	5	λ	λ	X
ejpam-4868	389	6	(	(	PUNCT
ejpam-4868	389	7	t)f(t)dt	t)f(t)dt	NOUN
ejpam-4868	389	8	=	=	SYM
ejpam-4868	389	9	eλ{f(t	eλ{f(t	NOUN
ejpam-4868	389	10	)	)	PUNCT
ejpam-4868	389	11	}	}	PUNCT
ejpam-4868	389	12	.	.	PUNCT
ejpam-4868	389	13	.	.	PUNCT
ejpam-4868	390	1	h.	h.	PROPN
ejpam-4868	390	2	j.	j.	PROPN
ejpam-4868	390	3	campos	campos	PROPN
ejpam-4868	390	4	,	,	PUNCT
ejpam-4868	390	5	j.	j.	PROPN
ejpam-4868	390	6	c.	c.	PROPN
ejpam-4868	390	7	fernandez	fernandez	PROPN
ejpam-4868	390	8	,	,	PUNCT
ejpam-4868	390	9	j.	j.	PROPN
ejpam-4868	390	10	b.	b.	PROPN
ejpam-4868	390	11	m.	m.	PROPN
ejpam-4868	390	12	natuil	natuil	PROPN
ejpam-4868	390	13	/	/	SYM
ejpam-4868	390	14	eur	eur	PROPN
ejpam-4868	390	15	.	.	PUNCT
ejpam-4868	391	1	j.	j.	PROPN
ejpam-4868	391	2	pure	pure	PROPN
ejpam-4868	391	3	appl	appl	PROPN
ejpam-4868	391	4	.	.	PROPN
ejpam-4868	391	5	math	math	PROPN
ejpam-4868	391	6	,	,	PUNCT
ejpam-4868	391	7	16	16	NUM
ejpam-4868	391	8	(	(	PUNCT
ejpam-4868	391	9	4	4	NUM
ejpam-4868	391	10	)	)	PUNCT
ejpam-4868	391	11	(	(	PUNCT
ejpam-4868	391	12	2023	2023	NUM
ejpam-4868	391	13	)	)	PUNCT
ejpam-4868	391	14	,	,	PUNCT
ejpam-4868	391	15	2213	2213	NUM
ejpam-4868	391	16	-	-	SYM
ejpam-4868	391	17	2233	2233	NUM
ejpam-4868	391	18	2229	2229	NUM
ejpam-4868	391	19	table	table	NOUN
ejpam-4868	391	20	1	1	NUM
ejpam-4868	391	21	gives	give	VERB
ejpam-4868	391	22	the	the	DET
ejpam-4868	391	23	summary	summary	NOUN
ejpam-4868	391	24	of	of	ADP
ejpam-4868	391	25	some	some	DET
ejpam-4868	391	26	elementary	elementary	ADJ
ejpam-4868	391	27	functions	function	NOUN
ejpam-4868	391	28	of	of	ADP
ejpam-4868	391	29	the	the	DET
ejpam-4868	391	30	degenerate	degenerate	ADJ
ejpam-4868	391	31	laplacetype	laplacetype	NOUN
ejpam-4868	391	32	and	and	CCONJ
ejpam-4868	391	33	degenerate	degenerate	ADJ
ejpam-4868	391	34	laplace	laplace	NOUN
ejpam-4868	391	35	[	[	X
ejpam-4868	391	36	8	8	NUM
ejpam-4868	391	37	,	,	PUNCT
ejpam-4868	391	38	14–16	14–16	NUM
ejpam-4868	391	39	]	]	PUNCT
ejpam-4868	391	40	.	.	PUNCT
ejpam-4868	392	1	f(t	f(t	NOUN
ejpam-4868	392	2	)	)	PUNCT
ejpam-4868	392	3	gα	gα	ADP
ejpam-4868	392	4	,	,	PUNCT
ejpam-4868	392	5	λ{f(t	λ{f(t	NUM
ejpam-4868	392	6	)	)	PUNCT
ejpam-4868	392	7	}	}	PUNCT
ejpam-4868	392	8	g0,λ{f(t	g0,λ{f(t	NOUN
ejpam-4868	392	9	)	)	PUNCT
ejpam-4868	392	10	}	}	PUNCT
ejpam-4868	392	11	=	=	SYM
ejpam-4868	392	12	lλ{f(t	lλ{f(t	NOUN
ejpam-4868	392	13	)	)	PUNCT
ejpam-4868	392	14	}	}	PUNCT
ejpam-4868	392	15	,	,	PUNCT
ejpam-4868	392	16	α	α	NOUN
ejpam-4868	392	17	=	=	SYM
ejpam-4868	392	18	0	0	NUM
ejpam-4868	392	19	1	1	NUM
ejpam-4868	392	20	uα+1	uα+1	NUM
ejpam-4868	392	21	1−	1−	NUM
ejpam-4868	392	22	λu	λu	PART
ejpam-4868	392	23	u	u	PROPN
ejpam-4868	392	24	1−	1−	NUM
ejpam-4868	392	25	λu	λu	INTJ
ejpam-4868	392	26	t	t	PROPN
ejpam-4868	392	27	uα+2	uα+2	PROPN
ejpam-4868	393	1	(	(	PUNCT
ejpam-4868	393	2	1−	1−	NUM
ejpam-4868	393	3	uλ)(1−	uλ)(1−	ADJ
ejpam-4868	393	4	2uλ	2uλ	NOUN
ejpam-4868	393	5	)	)	PUNCT
ejpam-4868	394	1	u2	u2	NOUN
ejpam-4868	394	2	(	(	PUNCT
ejpam-4868	394	3	1−	1−	NUM
ejpam-4868	394	4	uλ)(1−	uλ)(1−	ADJ
ejpam-4868	394	5	2uλ	2uλ	NOUN
ejpam-4868	394	6	)	)	PUNCT
ejpam-4868	394	7	tn(n	tn(n	NUM
ejpam-4868	395	1	=	=	SYM
ejpam-4868	395	2	0	0	NUM
ejpam-4868	395	3	,	,	PUNCT
ejpam-4868	395	4	1	1	NUM
ejpam-4868	395	5	,	,	PUNCT
ejpam-4868	395	6	2	2	NUM
ejpam-4868	395	7	,	,	PUNCT
ejpam-4868	395	8	·	·	PUNCT
ejpam-4868	395	9	·	·	PUNCT
ejpam-4868	395	10	·	·	PUNCT
ejpam-4868	395	11	)	)	PUNCT
ejpam-4868	396	1	n!uα+1+n	n!uα+1+n	INTJ
ejpam-4868	396	2	(	(	PUNCT
ejpam-4868	396	3	1−	1−	NUM
ejpam-4868	396	4	uλ	uλ	NOUN
ejpam-4868	396	5	)	)	PUNCT
ejpam-4868	396	6	·	·	PUNCT
ejpam-4868	396	7	·	·	PUNCT
ejpam-4868	396	8	·	·	PUNCT
ejpam-4868	396	9	(	(	PUNCT
ejpam-4868	396	10	1−	1−	NUM
ejpam-4868	396	11	(	(	PUNCT
ejpam-4868	396	12	n+	n+	NUM
ejpam-4868	396	13	1)uλ	1)uλ	NUM
ejpam-4868	396	14	)	)	PUNCT
ejpam-4868	396	15	n!u1+n	n!u1+n	PUNCT
ejpam-4868	396	16	(	(	PUNCT
ejpam-4868	396	17	1−	1−	NUM
ejpam-4868	396	18	uλ	uλ	NOUN
ejpam-4868	396	19	)	)	PUNCT
ejpam-4868	396	20	·	·	PUNCT
ejpam-4868	396	21	·	·	PUNCT
ejpam-4868	396	22	·	·	PUNCT
ejpam-4868	396	23	(	(	PUNCT
ejpam-4868	396	24	1−	1−	NUM
ejpam-4868	396	25	(	(	PUNCT
ejpam-4868	396	26	n+	n+	NUM
ejpam-4868	396	27	1)uλ	1)uλ	NUM
ejpam-4868	396	28	)	)	PUNCT
ejpam-4868	396	29	eaλ(t	eaλ(t	PROPN
ejpam-4868	396	30	)	)	PUNCT
ejpam-4868	396	31	uα+1	uα+1	NUM
ejpam-4868	396	32	1−	1−	NUM
ejpam-4868	396	33	u(a+	u(a+	ADJ
ejpam-4868	396	34	λ	λ	NOUN
ejpam-4868	396	35	)	)	PUNCT
ejpam-4868	396	36	u	u	NOUN
ejpam-4868	396	37	1−	1−	NUM
ejpam-4868	396	38	u(a+	u(a+	PROPN
ejpam-4868	396	39	λ	λ	NOUN
ejpam-4868	396	40	)	)	PUNCT
ejpam-4868	396	41	sin	sin	NOUN
ejpam-4868	396	42	(	(	PUNCT
ejpam-4868	396	43	a	a	X
ejpam-4868	396	44	)	)	PUNCT
ejpam-4868	396	45	λ	λ	PROPN
ejpam-4868	396	46	(	(	PUNCT
ejpam-4868	396	47	t	t	PROPN
ejpam-4868	396	48	)	)	PUNCT
ejpam-4868	396	49	auα+2	auα+2	PROPN
ejpam-4868	396	50	(	(	PUNCT
ejpam-4868	396	51	1−	1−	NUM
ejpam-4868	396	52	λu)2	λu)2	PROPN
ejpam-4868	396	53	+	+	CCONJ
ejpam-4868	397	1	u2a2	u2a2	PROPN
ejpam-4868	397	2	au2	au2	NOUN
ejpam-4868	397	3	(	(	PUNCT
ejpam-4868	397	4	1−	1−	NUM
ejpam-4868	397	5	λu)2	λu)2	PROPN
ejpam-4868	397	6	+	+	CCONJ
ejpam-4868	397	7	u2a2	u2a2	PROPN
ejpam-4868	397	8	cos	cos	X
ejpam-4868	397	9	(	(	PUNCT
ejpam-4868	397	10	a	a	X
ejpam-4868	397	11	)	)	PUNCT
ejpam-4868	397	12	λ	λ	PROPN
ejpam-4868	397	13	(	(	PUNCT
ejpam-4868	397	14	t	t	PROPN
ejpam-4868	397	15	)	)	PUNCT
ejpam-4868	397	16	(	(	PUNCT
ejpam-4868	397	17	1−	1−	NUM
ejpam-4868	397	18	λu)uα+1	λu)uα+1	NOUN
ejpam-4868	397	19	(	(	PUNCT
ejpam-4868	397	20	1−	1−	NUM
ejpam-4868	397	21	λu)2	λu)2	PROPN
ejpam-4868	397	22	+	+	CCONJ
ejpam-4868	397	23	u2a2	u2a2	PROPN
ejpam-4868	397	24	(	(	PUNCT
ejpam-4868	397	25	1−	1−	NUM
ejpam-4868	397	26	λu)u	λu)u	PROPN
ejpam-4868	397	27	(	(	PUNCT
ejpam-4868	397	28	1−	1−	NUM
ejpam-4868	397	29	λu)2	λu)2	PROPN
ejpam-4868	397	30	+	+	CCONJ
ejpam-4868	397	31	u2a2	u2a2	PROPN
ejpam-4868	397	32	sinh	sinh	NOUN
ejpam-4868	397	33	(	(	PUNCT
ejpam-4868	397	34	a	a	NOUN
ejpam-4868	397	35	)	)	PUNCT
ejpam-4868	397	36	λ	λ	PROPN
ejpam-4868	397	37	(	(	PUNCT
ejpam-4868	397	38	t	t	PROPN
ejpam-4868	397	39	)	)	PUNCT
ejpam-4868	397	40	auα+2	auα+2	PROPN
ejpam-4868	397	41	(	(	PUNCT
ejpam-4868	397	42	1−	1−	NUM
ejpam-4868	397	43	λu)2	λu)2	NOUN
ejpam-4868	397	44	−	−	PROPN
ejpam-4868	398	1	u2a2	u2a2	PROPN
ejpam-4868	398	2	au2	au2	NOUN
ejpam-4868	398	3	(	(	PUNCT
ejpam-4868	398	4	1−	1−	NUM
ejpam-4868	398	5	λu)2	λu)2	NOUN
ejpam-4868	398	6	−	−	PROPN
ejpam-4868	398	7	u2a2	u2a2	INTJ
ejpam-4868	398	8	cosh	cosh	PROPN
ejpam-4868	398	9	(	(	PUNCT
ejpam-4868	398	10	a	a	X
ejpam-4868	398	11	)	)	PUNCT
ejpam-4868	398	12	λ	λ	PROPN
ejpam-4868	398	13	(	(	PUNCT
ejpam-4868	398	14	t	t	PROPN
ejpam-4868	398	15	)	)	PUNCT
ejpam-4868	398	16	(	(	PUNCT
ejpam-4868	398	17	1−	1−	NUM
ejpam-4868	398	18	λu)uα+1	λu)uα+1	NOUN
ejpam-4868	398	19	(	(	PUNCT
ejpam-4868	398	20	1−	1−	NUM
ejpam-4868	398	21	λu)2	λu)2	NOUN
ejpam-4868	398	22	−	−	PROPN
ejpam-4868	398	23	u2a2	u2a2	PROPN
ejpam-4868	398	24	(	(	PUNCT
ejpam-4868	398	25	1−	1−	NUM
ejpam-4868	398	26	λu)u	λu)u	PROPN
ejpam-4868	398	27	(	(	PUNCT
ejpam-4868	398	28	1−	1−	NUM
ejpam-4868	398	29	λu)2	λu)2	PROPN
ejpam-4868	398	30	−	−	PROPN
ejpam-4868	398	31	u2a2	u2a2	ADV
ejpam-4868	398	32	eaλ(t	eaλ(t	ADV
ejpam-4868	398	33	)	)	PUNCT
ejpam-4868	398	34	sin	sin	NOUN
ejpam-4868	398	35	(	(	PUNCT
ejpam-4868	398	36	b	b	NOUN
ejpam-4868	398	37	)	)	PUNCT
ejpam-4868	398	38	λ	λ	PROPN
ejpam-4868	398	39	(	(	PUNCT
ejpam-4868	398	40	t	t	PROPN
ejpam-4868	398	41	)	)	PUNCT
ejpam-4868	398	42	buα+2	buα+2	PROPN
ejpam-4868	398	43	(	(	PUNCT
ejpam-4868	398	44	1−	1−	NUM
ejpam-4868	398	45	au−	au−	NUM
ejpam-4868	398	46	uλ)2	uλ)2	PROPN
ejpam-4868	398	47	+	+	CCONJ
ejpam-4868	398	48	b2u2	b2u2	PROPN
ejpam-4868	398	49	bu2	bu2	X
ejpam-4868	398	50	(	(	PUNCT
ejpam-4868	398	51	1−	1−	NUM
ejpam-4868	398	52	au−	au−	PUNCT
ejpam-4868	398	53	uλ)2	uλ)2	PROPN
ejpam-4868	398	54	+	+	CCONJ
ejpam-4868	398	55	b2u2	b2u2	PROPN
ejpam-4868	398	56	eaλ(t	eaλ(t	PROPN
ejpam-4868	398	57	)	)	PUNCT
ejpam-4868	398	58	cos	cos	PROPN
ejpam-4868	398	59	(	(	PUNCT
ejpam-4868	398	60	b	b	X
ejpam-4868	398	61	)	)	PUNCT
ejpam-4868	398	62	λ	λ	PROPN
ejpam-4868	398	63	(	(	PUNCT
ejpam-4868	398	64	t	t	PROPN
ejpam-4868	398	65	)	)	PUNCT
ejpam-4868	398	66	(	(	PUNCT
ejpam-4868	398	67	1−	1−	NUM
ejpam-4868	398	68	au−	au−	NUM
ejpam-4868	398	69	uλ)uα+1	uλ)uα+1	NOUN
ejpam-4868	398	70	(	(	PUNCT
ejpam-4868	398	71	1−	1−	NUM
ejpam-4868	398	72	au−	au−	PUNCT
ejpam-4868	398	73	uλ)2	uλ)2	PROPN
ejpam-4868	398	74	+	+	CCONJ
ejpam-4868	398	75	b2u2	b2u2	PROPN
ejpam-4868	398	76	(	(	PUNCT
ejpam-4868	398	77	1−	1−	NUM
ejpam-4868	398	78	au−	au−	SYM
ejpam-4868	398	79	uλ)u	uλ)u	PROPN
ejpam-4868	398	80	(	(	PUNCT
ejpam-4868	398	81	1−	1−	NUM
ejpam-4868	398	82	au−	au−	PUNCT
ejpam-4868	398	83	uλ)2	uλ)2	PROPN
ejpam-4868	398	84	+	+	CCONJ
ejpam-4868	398	85	b2u2	b2u2	ADP
ejpam-4868	398	86	table	table	NOUN
ejpam-4868	398	87	1	1	NUM
ejpam-4868	398	88	:	:	PUNCT
ejpam-4868	398	89	the	the	DET
ejpam-4868	398	90	degenerate	degenerate	ADJ
ejpam-4868	398	91	laplace	laplace	NOUN
ejpam-4868	398	92	-	-	PUNCT
ejpam-4868	398	93	type	type	NOUN
ejpam-4868	398	94	and	and	CCONJ
ejpam-4868	398	95	degenerate	degenerate	ADJ
ejpam-4868	398	96	laplace	laplace	NOUN
ejpam-4868	398	97	transform	transform	NOUN
ejpam-4868	398	98	.	.	PUNCT
ejpam-4868	399	1	h.	h.	PROPN
ejpam-4868	399	2	j.	j.	PROPN
ejpam-4868	399	3	campos	campos	PROPN
ejpam-4868	399	4	,	,	PUNCT
ejpam-4868	399	5	j.	j.	PROPN
ejpam-4868	399	6	c.	c.	PROPN
ejpam-4868	399	7	fernandez	fernandez	PROPN
ejpam-4868	399	8	,	,	PUNCT
ejpam-4868	399	9	j.	j.	PROPN
ejpam-4868	399	10	b.	b.	PROPN
ejpam-4868	399	11	m.	m.	PROPN
ejpam-4868	399	12	natuil	natuil	PROPN
ejpam-4868	399	13	/	/	SYM
ejpam-4868	399	14	eur	eur	PROPN
ejpam-4868	399	15	.	.	PUNCT
ejpam-4868	400	1	j.	j.	PROPN
ejpam-4868	400	2	pure	pure	PROPN
ejpam-4868	400	3	appl	appl	PROPN
ejpam-4868	400	4	.	.	PROPN
ejpam-4868	400	5	math	math	PROPN
ejpam-4868	400	6	,	,	PUNCT
ejpam-4868	400	7	16	16	NUM
ejpam-4868	400	8	(	(	PUNCT
ejpam-4868	400	9	4	4	NUM
ejpam-4868	400	10	)	)	PUNCT
ejpam-4868	400	11	(	(	PUNCT
ejpam-4868	400	12	2023	2023	NUM
ejpam-4868	400	13	)	)	PUNCT
ejpam-4868	400	14	,	,	PUNCT
ejpam-4868	400	15	2213	2213	NUM
ejpam-4868	400	16	-	-	SYM
ejpam-4868	400	17	2233	2233	NUM
ejpam-4868	400	18	2230	2230	NUM
ejpam-4868	400	19	table	table	NOUN
ejpam-4868	400	20	2	2	NUM
ejpam-4868	400	21	gives	give	VERB
ejpam-4868	400	22	the	the	DET
ejpam-4868	400	23	summary	summary	NOUN
ejpam-4868	400	24	of	of	ADP
ejpam-4868	400	25	some	some	DET
ejpam-4868	400	26	elementary	elementary	ADJ
ejpam-4868	400	27	functions	function	NOUN
ejpam-4868	400	28	degenerate	degenerate	ADJ
ejpam-4868	400	29	laplace	laplace	NOUN
ejpam-4868	400	30	-	-	PUNCT
ejpam-4868	400	31	type	type	NOUN
ejpam-4868	400	32	and	and	CCONJ
ejpam-4868	400	33	degenerate	degenerate	ADJ
ejpam-4868	400	34	sumudu	sumudu	NOUN
ejpam-4868	400	35	transforms[4	transforms[4	PROPN
ejpam-4868	400	36	]	]	PUNCT
ejpam-4868	400	37	.	.	PUNCT
ejpam-4868	401	1	f(t	f(t	NOUN
ejpam-4868	401	2	)	)	PUNCT
ejpam-4868	401	3	gα	gα	ADP
ejpam-4868	401	4	,	,	PUNCT
ejpam-4868	401	5	λ{f(t	λ{f(t	NUM
ejpam-4868	401	6	)	)	PUNCT
ejpam-4868	401	7	}	}	PUNCT
ejpam-4868	401	8	g−1,λ{f(t	g−1,λ{f(t	NOUN
ejpam-4868	401	9	)	)	PUNCT
ejpam-4868	401	10	}	}	PUNCT
ejpam-4868	401	11	=	=	SYM
ejpam-4868	401	12	sλ{f(t	sλ{f(t	NOUN
ejpam-4868	401	13	)	)	PUNCT
ejpam-4868	401	14	}	}	PUNCT
ejpam-4868	401	15	,	,	PUNCT
ejpam-4868	401	16	α	α	PROPN
ejpam-4868	401	17	=	=	SYM
ejpam-4868	401	18	−1	−1	NOUN
ejpam-4868	401	19	1	1	NUM
ejpam-4868	401	20	uα+1	uα+1	NUM
ejpam-4868	401	21	1−	1−	NUM
ejpam-4868	401	22	λu	λu	INTJ
ejpam-4868	401	23	1	1	NUM
ejpam-4868	401	24	1−	1−	NUM
ejpam-4868	401	25	λu	λu	X
ejpam-4868	401	26	t	t	PROPN
ejpam-4868	401	27	uα+2	uα+2	PROPN
ejpam-4868	402	1	(	(	PUNCT
ejpam-4868	402	2	1−	1−	NUM
ejpam-4868	402	3	uλ)(1−	uλ)(1−	ADJ
ejpam-4868	402	4	2uλ	2uλ	NOUN
ejpam-4868	402	5	)	)	PUNCT
ejpam-4868	402	6	u	u	NOUN
ejpam-4868	402	7	(	(	PUNCT
ejpam-4868	402	8	1−	1−	NUM
ejpam-4868	402	9	uλ)(1−	uλ)(1−	ADJ
ejpam-4868	402	10	2uλ	2uλ	NOUN
ejpam-4868	402	11	)	)	PUNCT
ejpam-4868	402	12	tn(n	tn(n	NUM
ejpam-4868	403	1	=	=	SYM
ejpam-4868	403	2	0	0	NUM
ejpam-4868	403	3	,	,	PUNCT
ejpam-4868	403	4	1	1	NUM
ejpam-4868	403	5	,	,	PUNCT
ejpam-4868	403	6	2	2	NUM
ejpam-4868	403	7	,	,	PUNCT
ejpam-4868	403	8	·	·	PUNCT
ejpam-4868	403	9	·	·	PUNCT
ejpam-4868	403	10	·	·	PUNCT
ejpam-4868	403	11	)	)	PUNCT
ejpam-4868	404	1	n!uα+1+n	n!uα+1+n	INTJ
ejpam-4868	404	2	(	(	PUNCT
ejpam-4868	404	3	1−	1−	NUM
ejpam-4868	404	4	uλ	uλ	NOUN
ejpam-4868	404	5	)	)	PUNCT
ejpam-4868	404	6	·	·	PUNCT
ejpam-4868	404	7	·	·	PUNCT
ejpam-4868	404	8	·	·	PUNCT
ejpam-4868	404	9	(	(	PUNCT
ejpam-4868	404	10	1−	1−	NUM
ejpam-4868	404	11	(	(	PUNCT
ejpam-4868	404	12	n+	n+	NUM
ejpam-4868	404	13	1)uλ	1)uλ	NUM
ejpam-4868	404	14	)	)	PUNCT
ejpam-4868	404	15	n!un	n!un	X
ejpam-4868	404	16	(	(	PUNCT
ejpam-4868	404	17	1−	1−	NUM
ejpam-4868	404	18	uλ	uλ	NOUN
ejpam-4868	404	19	)	)	PUNCT
ejpam-4868	404	20	·	·	PUNCT
ejpam-4868	404	21	·	·	PUNCT
ejpam-4868	404	22	·	·	PUNCT
ejpam-4868	404	23	(	(	PUNCT
ejpam-4868	404	24	1−	1−	NUM
ejpam-4868	404	25	(	(	PUNCT
ejpam-4868	404	26	n+	n+	NUM
ejpam-4868	404	27	1)uλ	1)uλ	NUM
ejpam-4868	404	28	)	)	PUNCT
ejpam-4868	404	29	eaλ(t	eaλ(t	PROPN
ejpam-4868	404	30	)	)	PUNCT
ejpam-4868	404	31	uα+1	uα+1	NUM
ejpam-4868	404	32	1−	1−	NUM
ejpam-4868	404	33	u(a+	u(a+	PROPN
ejpam-4868	404	34	λ	λ	NOUN
ejpam-4868	404	35	)	)	PUNCT
ejpam-4868	404	36	1	1	NUM
ejpam-4868	404	37	1−	1−	NUM
ejpam-4868	404	38	u(a+	u(a+	PROPN
ejpam-4868	404	39	λ	λ	NOUN
ejpam-4868	404	40	)	)	PUNCT
ejpam-4868	404	41	sin	sin	NOUN
ejpam-4868	404	42	(	(	PUNCT
ejpam-4868	404	43	a	a	X
ejpam-4868	404	44	)	)	PUNCT
ejpam-4868	404	45	λ	λ	PROPN
ejpam-4868	404	46	(	(	PUNCT
ejpam-4868	404	47	t	t	PROPN
ejpam-4868	404	48	)	)	PUNCT
ejpam-4868	404	49	auα+2	auα+2	PROPN
ejpam-4868	404	50	(	(	PUNCT
ejpam-4868	405	1	1−	1−	NUM
ejpam-4868	405	2	λu)2	λu)2	PROPN
ejpam-4868	405	3	+	+	CCONJ
ejpam-4868	405	4	u2a2	u2a2	ADV
ejpam-4868	405	5	au	au	X
ejpam-4868	405	6	(	(	PUNCT
ejpam-4868	405	7	1−	1−	NUM
ejpam-4868	405	8	λu)2	λu)2	PROPN
ejpam-4868	405	9	+	+	CCONJ
ejpam-4868	405	10	u2a2	u2a2	PROPN
ejpam-4868	405	11	cos	cos	X
ejpam-4868	405	12	(	(	PUNCT
ejpam-4868	405	13	a	a	X
ejpam-4868	405	14	)	)	PUNCT
ejpam-4868	405	15	λ	λ	PROPN
ejpam-4868	405	16	(	(	PUNCT
ejpam-4868	405	17	t	t	PROPN
ejpam-4868	405	18	)	)	PUNCT
ejpam-4868	405	19	(	(	PUNCT
ejpam-4868	405	20	1−	1−	NUM
ejpam-4868	405	21	λu)uα+1	λu)uα+1	NOUN
ejpam-4868	405	22	(	(	PUNCT
ejpam-4868	405	23	1−	1−	NUM
ejpam-4868	405	24	λu)2	λu)2	PROPN
ejpam-4868	405	25	+	+	CCONJ
ejpam-4868	405	26	u2a2	u2a2	PROPN
ejpam-4868	405	27	1−	1−	NUM
ejpam-4868	405	28	λu	λu	X
ejpam-4868	405	29	(	(	PUNCT
ejpam-4868	405	30	1−	1−	NUM
ejpam-4868	405	31	λu)2	λu)2	PROPN
ejpam-4868	405	32	+	+	CCONJ
ejpam-4868	405	33	u2a2	u2a2	PROPN
ejpam-4868	405	34	sinh	sinh	NOUN
ejpam-4868	405	35	(	(	PUNCT
ejpam-4868	405	36	a	a	NOUN
ejpam-4868	405	37	)	)	PUNCT
ejpam-4868	405	38	λ	λ	PROPN
ejpam-4868	405	39	(	(	PUNCT
ejpam-4868	405	40	t	t	PROPN
ejpam-4868	405	41	)	)	PUNCT
ejpam-4868	405	42	auα+2	auα+2	PROPN
ejpam-4868	405	43	(	(	PUNCT
ejpam-4868	405	44	1−	1−	NUM
ejpam-4868	405	45	λu)2	λu)2	NOUN
ejpam-4868	405	46	−	−	PROPN
ejpam-4868	405	47	u2a2	u2a2	ADV
ejpam-4868	405	48	au	au	X
ejpam-4868	405	49	(	(	PUNCT
ejpam-4868	405	50	1−	1−	NUM
ejpam-4868	405	51	λu)2	λu)2	NOUN
ejpam-4868	405	52	−	−	PROPN
ejpam-4868	405	53	u2a2	u2a2	INTJ
ejpam-4868	405	54	cosh	cosh	PROPN
ejpam-4868	405	55	(	(	PUNCT
ejpam-4868	405	56	a	a	X
ejpam-4868	405	57	)	)	PUNCT
ejpam-4868	405	58	λ	λ	PROPN
ejpam-4868	405	59	(	(	PUNCT
ejpam-4868	405	60	t	t	PROPN
ejpam-4868	405	61	)	)	PUNCT
ejpam-4868	405	62	(	(	PUNCT
ejpam-4868	405	63	1−	1−	NUM
ejpam-4868	405	64	λu)uα+1	λu)uα+1	NOUN
ejpam-4868	405	65	(	(	PUNCT
ejpam-4868	405	66	1−	1−	NUM
ejpam-4868	405	67	λu)2	λu)2	NOUN
ejpam-4868	405	68	−	−	PROPN
ejpam-4868	406	1	u2a2	u2a2	PROPN
ejpam-4868	406	2	1−	1−	NUM
ejpam-4868	406	3	λu	λu	X
ejpam-4868	406	4	(	(	PUNCT
ejpam-4868	406	5	1−	1−	NUM
ejpam-4868	406	6	λu)2	λu)2	NOUN
ejpam-4868	406	7	−	−	PROPN
ejpam-4868	406	8	u2a2	u2a2	ADV
ejpam-4868	406	9	eaλ(t	eaλ(t	ADV
ejpam-4868	406	10	)	)	PUNCT
ejpam-4868	406	11	sin	sin	NOUN
ejpam-4868	406	12	(	(	PUNCT
ejpam-4868	406	13	b	b	NOUN
ejpam-4868	406	14	)	)	PUNCT
ejpam-4868	406	15	λ	λ	PROPN
ejpam-4868	406	16	(	(	PUNCT
ejpam-4868	406	17	t	t	PROPN
ejpam-4868	406	18	)	)	PUNCT
ejpam-4868	406	19	buα+2	buα+2	PROPN
ejpam-4868	406	20	(	(	PUNCT
ejpam-4868	406	21	1−	1−	NUM
ejpam-4868	406	22	au−	au−	PUNCT
ejpam-4868	406	23	uλ)2	uλ)2	PROPN
ejpam-4868	406	24	+	+	CCONJ
ejpam-4868	406	25	b2u2	b2u2	ADP
ejpam-4868	406	26	bu	bu	PROPN
ejpam-4868	406	27	(	(	PUNCT
ejpam-4868	406	28	1−	1−	NUM
ejpam-4868	406	29	au−	au−	NUM
ejpam-4868	406	30	uλ)2	uλ)2	PROPN
ejpam-4868	406	31	+	+	CCONJ
ejpam-4868	406	32	b2u2	b2u2	PROPN
ejpam-4868	406	33	eaλ(t	eaλ(t	PROPN
ejpam-4868	406	34	)	)	PUNCT
ejpam-4868	406	35	cos	cos	PROPN
ejpam-4868	406	36	(	(	PUNCT
ejpam-4868	406	37	b	b	X
ejpam-4868	406	38	)	)	PUNCT
ejpam-4868	406	39	λ	λ	PROPN
ejpam-4868	406	40	(	(	PUNCT
ejpam-4868	406	41	t	t	PROPN
ejpam-4868	406	42	)	)	PUNCT
ejpam-4868	406	43	(	(	PUNCT
ejpam-4868	406	44	1−	1−	NUM
ejpam-4868	406	45	au−	au−	NUM
ejpam-4868	406	46	uλ)uα+1	uλ)uα+1	NOUN
ejpam-4868	406	47	(	(	PUNCT
ejpam-4868	406	48	1−	1−	NUM
ejpam-4868	406	49	au−	au−	NUM
ejpam-4868	406	50	uλ)2	uλ)2	PROPN
ejpam-4868	406	51	+	+	CCONJ
ejpam-4868	406	52	b2u2	b2u2	PROPN
ejpam-4868	406	53	1−	1−	NUM
ejpam-4868	406	54	au−	au−	PUNCT
ejpam-4868	406	55	uλ	uλ	X
ejpam-4868	406	56	(	(	PUNCT
ejpam-4868	406	57	1−	1−	NUM
ejpam-4868	406	58	au−	au−	NUM
ejpam-4868	406	59	uλ)2	uλ)2	PROPN
ejpam-4868	406	60	+	+	CCONJ
ejpam-4868	406	61	b2u2	b2u2	ADP
ejpam-4868	406	62	table	table	NOUN
ejpam-4868	406	63	2	2	NUM
ejpam-4868	406	64	:	:	PUNCT
ejpam-4868	406	65	the	the	DET
ejpam-4868	406	66	degenerate	degenerate	ADJ
ejpam-4868	406	67	laplace	laplace	NOUN
ejpam-4868	406	68	-	-	PUNCT
ejpam-4868	406	69	type	type	NOUN
ejpam-4868	406	70	and	and	CCONJ
ejpam-4868	406	71	degenerate	degenerate	ADJ
ejpam-4868	406	72	sumudu	sumudu	NOUN
ejpam-4868	406	73	transform	transform	NOUN
ejpam-4868	406	74	.	.	PUNCT
ejpam-4868	407	1	h.	h.	PROPN
ejpam-4868	407	2	j.	j.	PROPN
ejpam-4868	407	3	campos	campos	PROPN
ejpam-4868	407	4	,	,	PUNCT
ejpam-4868	407	5	j.	j.	PROPN
ejpam-4868	407	6	c.	c.	PROPN
ejpam-4868	407	7	fernandez	fernandez	PROPN
ejpam-4868	407	8	,	,	PUNCT
ejpam-4868	407	9	j.	j.	PROPN
ejpam-4868	407	10	b.	b.	PROPN
ejpam-4868	407	11	m.	m.	PROPN
ejpam-4868	407	12	natuil	natuil	PROPN
ejpam-4868	407	13	/	/	SYM
ejpam-4868	407	14	eur	eur	PROPN
ejpam-4868	407	15	.	.	PUNCT
ejpam-4868	408	1	j.	j.	PROPN
ejpam-4868	408	2	pure	pure	PROPN
ejpam-4868	408	3	appl	appl	PROPN
ejpam-4868	408	4	.	.	PROPN
ejpam-4868	408	5	math	math	PROPN
ejpam-4868	408	6	,	,	PUNCT
ejpam-4868	408	7	16	16	NUM
ejpam-4868	408	8	(	(	PUNCT
ejpam-4868	408	9	4	4	NUM
ejpam-4868	408	10	)	)	PUNCT
ejpam-4868	408	11	(	(	PUNCT
ejpam-4868	408	12	2023	2023	NUM
ejpam-4868	408	13	)	)	PUNCT
ejpam-4868	408	14	,	,	PUNCT
ejpam-4868	408	15	2213	2213	NUM
ejpam-4868	408	16	-	-	SYM
ejpam-4868	408	17	2233	2233	NUM
ejpam-4868	408	18	2231	2231	NUM
ejpam-4868	408	19	table	table	NOUN
ejpam-4868	408	20	3	3	NUM
ejpam-4868	408	21	gives	give	VERB
ejpam-4868	408	22	the	the	DET
ejpam-4868	408	23	summary	summary	NOUN
ejpam-4868	408	24	of	of	ADP
ejpam-4868	408	25	some	some	DET
ejpam-4868	408	26	elementary	elementary	ADJ
ejpam-4868	408	27	functions	function	NOUN
ejpam-4868	408	28	degenerate	degenerate	ADJ
ejpam-4868	408	29	laplace	laplace	NOUN
ejpam-4868	408	30	-	-	PUNCT
ejpam-4868	408	31	type	type	NOUN
ejpam-4868	408	32	and	and	CCONJ
ejpam-4868	408	33	degenerate	degenerate	ADJ
ejpam-4868	408	34	elzaki	elzaki	NOUN
ejpam-4868	408	35	transforms	transform	VERB
ejpam-4868	408	36	[	[	X
ejpam-4868	408	37	1	1	NUM
ejpam-4868	408	38	]	]	PUNCT
ejpam-4868	408	39	.	.	PUNCT
ejpam-4868	409	1	f(t	f(t	NOUN
ejpam-4868	409	2	)	)	PUNCT
ejpam-4868	409	3	gα	gα	ADP
ejpam-4868	409	4	,	,	PUNCT
ejpam-4868	409	5	λ{f(t	λ{f(t	NUM
ejpam-4868	409	6	)	)	PUNCT
ejpam-4868	409	7	}	}	PUNCT
ejpam-4868	409	8	g1,λ{f(t	g1,λ{f(t	NOUN
ejpam-4868	409	9	)	)	PUNCT
ejpam-4868	409	10	}	}	PUNCT
ejpam-4868	409	11	=	=	SYM
ejpam-4868	409	12	eλ{f(t	eλ{f(t	NOUN
ejpam-4868	409	13	)	)	PUNCT
ejpam-4868	409	14	}	}	PUNCT
ejpam-4868	409	15	,	,	PUNCT
ejpam-4868	409	16	α	α	NOUN
ejpam-4868	409	17	=	=	SYM
ejpam-4868	409	18	1	1	NUM
ejpam-4868	409	19	1	1	NUM
ejpam-4868	409	20	uα+1	uα+1	NUM
ejpam-4868	409	21	1−	1−	NUM
ejpam-4868	409	22	λu	λu	PROPN
ejpam-4868	409	23	u2	u2	PROPN
ejpam-4868	410	1	1−	1−	NUM
ejpam-4868	410	2	λu	λu	INTJ
ejpam-4868	410	3	t	t	PROPN
ejpam-4868	410	4	uα+2	uα+2	PROPN
ejpam-4868	411	1	(	(	PUNCT
ejpam-4868	411	2	1−	1−	NUM
ejpam-4868	411	3	uλ)(1−	uλ)(1−	ADJ
ejpam-4868	411	4	2uλ	2uλ	NOUN
ejpam-4868	411	5	)	)	PUNCT
ejpam-4868	411	6	u3	u3	NOUN
ejpam-4868	411	7	(	(	PUNCT
ejpam-4868	411	8	1−	1−	NUM
ejpam-4868	411	9	uλ)(1−	uλ)(1−	ADJ
ejpam-4868	411	10	2uλ	2uλ	NOUN
ejpam-4868	411	11	)	)	PUNCT
ejpam-4868	411	12	tn(n	tn(n	NUM
ejpam-4868	412	1	=	=	SYM
ejpam-4868	412	2	0	0	NUM
ejpam-4868	412	3	,	,	PUNCT
ejpam-4868	412	4	1	1	NUM
ejpam-4868	412	5	,	,	PUNCT
ejpam-4868	412	6	2	2	NUM
ejpam-4868	412	7	,	,	PUNCT
ejpam-4868	412	8	·	·	PUNCT
ejpam-4868	412	9	·	·	PUNCT
ejpam-4868	412	10	·	·	PUNCT
ejpam-4868	412	11	)	)	PUNCT
ejpam-4868	413	1	n!uα+1+n	n!uα+1+n	INTJ
ejpam-4868	413	2	(	(	PUNCT
ejpam-4868	413	3	1−	1−	NUM
ejpam-4868	413	4	uλ	uλ	NOUN
ejpam-4868	413	5	)	)	PUNCT
ejpam-4868	413	6	·	·	PUNCT
ejpam-4868	413	7	·	·	PUNCT
ejpam-4868	413	8	·	·	PUNCT
ejpam-4868	413	9	(	(	PUNCT
ejpam-4868	413	10	1−	1−	NUM
ejpam-4868	413	11	(	(	PUNCT
ejpam-4868	413	12	n+	n+	NUM
ejpam-4868	413	13	1)uλ	1)uλ	NUM
ejpam-4868	413	14	)	)	PUNCT
ejpam-4868	413	15	n!u2+n	n!u2+n	PROPN
ejpam-4868	413	16	(	(	PUNCT
ejpam-4868	413	17	1−	1−	NUM
ejpam-4868	413	18	uλ	uλ	NOUN
ejpam-4868	413	19	)	)	PUNCT
ejpam-4868	413	20	·	·	PUNCT
ejpam-4868	413	21	·	·	PUNCT
ejpam-4868	413	22	·	·	PUNCT
ejpam-4868	413	23	(	(	PUNCT
ejpam-4868	413	24	1−	1−	NUM
ejpam-4868	413	25	(	(	PUNCT
ejpam-4868	413	26	n+	n+	NUM
ejpam-4868	413	27	1)uλ	1)uλ	NUM
ejpam-4868	413	28	)	)	PUNCT
ejpam-4868	413	29	eaλ(t	eaλ(t	PROPN
ejpam-4868	413	30	)	)	PUNCT
ejpam-4868	413	31	uα+1	uα+1	NUM
ejpam-4868	414	1	1−	1−	NUM
ejpam-4868	414	2	u(a+	u(a+	PROPN
ejpam-4868	414	3	λ	λ	NOUN
ejpam-4868	414	4	)	)	PUNCT
ejpam-4868	414	5	u2	u2	PROPN
ejpam-4868	414	6	1−	1−	NUM
ejpam-4868	414	7	u(a+	u(a+	PROPN
ejpam-4868	414	8	λ	λ	NOUN
ejpam-4868	414	9	)	)	PUNCT
ejpam-4868	414	10	sin	sin	NOUN
ejpam-4868	414	11	(	(	PUNCT
ejpam-4868	414	12	a	a	X
ejpam-4868	414	13	)	)	PUNCT
ejpam-4868	414	14	λ	λ	PROPN
ejpam-4868	414	15	(	(	PUNCT
ejpam-4868	414	16	t	t	PROPN
ejpam-4868	414	17	)	)	PUNCT
ejpam-4868	414	18	auα+2	auα+2	PROPN
ejpam-4868	414	19	(	(	PUNCT
ejpam-4868	414	20	1−	1−	NUM
ejpam-4868	414	21	λu)2	λu)2	PROPN
ejpam-4868	414	22	+	+	CCONJ
ejpam-4868	414	23	u2a2	u2a2	ADV
ejpam-4868	414	24	au3	au3	INTJ
ejpam-4868	414	25	(	(	PUNCT
ejpam-4868	414	26	1−	1−	NUM
ejpam-4868	414	27	λu)2	λu)2	PROPN
ejpam-4868	414	28	+	+	CCONJ
ejpam-4868	414	29	u2a2	u2a2	PROPN
ejpam-4868	414	30	cos	cos	X
ejpam-4868	414	31	(	(	PUNCT
ejpam-4868	414	32	a	a	X
ejpam-4868	414	33	)	)	PUNCT
ejpam-4868	414	34	λ	λ	PROPN
ejpam-4868	414	35	(	(	PUNCT
ejpam-4868	414	36	t	t	PROPN
ejpam-4868	414	37	)	)	PUNCT
ejpam-4868	414	38	(	(	PUNCT
ejpam-4868	414	39	1−	1−	NUM
ejpam-4868	414	40	λu)uα+1	λu)uα+1	NOUN
ejpam-4868	414	41	(	(	PUNCT
ejpam-4868	414	42	1−	1−	NUM
ejpam-4868	414	43	λu)2	λu)2	PROPN
ejpam-4868	414	44	+	+	CCONJ
ejpam-4868	414	45	u2a2	u2a2	PROPN
ejpam-4868	414	46	(	(	PUNCT
ejpam-4868	414	47	1−	1−	NUM
ejpam-4868	414	48	λu)u2	λu)u2	NOUN
ejpam-4868	414	49	(	(	PUNCT
ejpam-4868	414	50	1−	1−	NUM
ejpam-4868	414	51	λu)2	λu)2	PROPN
ejpam-4868	414	52	+	+	CCONJ
ejpam-4868	414	53	u2a2	u2a2	PROPN
ejpam-4868	414	54	sinh	sinh	NOUN
ejpam-4868	414	55	(	(	PUNCT
ejpam-4868	414	56	a	a	NOUN
ejpam-4868	414	57	)	)	PUNCT
ejpam-4868	414	58	λ	λ	PROPN
ejpam-4868	414	59	(	(	PUNCT
ejpam-4868	414	60	t	t	PROPN
ejpam-4868	414	61	)	)	PUNCT
ejpam-4868	414	62	auα+2	auα+2	PROPN
ejpam-4868	414	63	(	(	PUNCT
ejpam-4868	414	64	1−	1−	NUM
ejpam-4868	414	65	λu)2	λu)2	NOUN
ejpam-4868	414	66	−	−	PROPN
ejpam-4868	415	1	u2a2	u2a2	INTJ
ejpam-4868	416	1	au3	au3	INTJ
ejpam-4868	417	1	(	(	PUNCT
ejpam-4868	417	2	1−	1−	NUM
ejpam-4868	417	3	λu)2	λu)2	NOUN
ejpam-4868	417	4	−	−	PROPN
ejpam-4868	417	5	u2a2	u2a2	INTJ
ejpam-4868	417	6	cosh	cosh	PROPN
ejpam-4868	417	7	(	(	PUNCT
ejpam-4868	417	8	a	a	X
ejpam-4868	417	9	)	)	PUNCT
ejpam-4868	417	10	λ	λ	PROPN
ejpam-4868	417	11	(	(	PUNCT
ejpam-4868	417	12	t	t	PROPN
ejpam-4868	417	13	)	)	PUNCT
ejpam-4868	417	14	(	(	PUNCT
ejpam-4868	417	15	1−	1−	NUM
ejpam-4868	417	16	λu)uα+1	λu)uα+1	NOUN
ejpam-4868	417	17	(	(	PUNCT
ejpam-4868	417	18	1−	1−	NUM
ejpam-4868	417	19	λu)2	λu)2	NOUN
ejpam-4868	417	20	−	−	PROPN
ejpam-4868	417	21	u2a2	u2a2	PROPN
ejpam-4868	417	22	(	(	PUNCT
ejpam-4868	417	23	1−	1−	NUM
ejpam-4868	417	24	λu)u2	λu)u2	NOUN
ejpam-4868	417	25	(	(	PUNCT
ejpam-4868	417	26	1−	1−	NUM
ejpam-4868	417	27	λu)2	λu)2	NOUN
ejpam-4868	417	28	−	−	PROPN
ejpam-4868	417	29	u2a2	u2a2	ADV
ejpam-4868	417	30	eaλ(t	eaλ(t	ADV
ejpam-4868	417	31	)	)	PUNCT
ejpam-4868	417	32	sin	sin	NOUN
ejpam-4868	417	33	(	(	PUNCT
ejpam-4868	417	34	b	b	NOUN
ejpam-4868	417	35	)	)	PUNCT
ejpam-4868	417	36	λ	λ	PROPN
ejpam-4868	417	37	(	(	PUNCT
ejpam-4868	417	38	t	t	PROPN
ejpam-4868	417	39	)	)	PUNCT
ejpam-4868	417	40	buα+2	buα+2	PROPN
ejpam-4868	417	41	(	(	PUNCT
ejpam-4868	417	42	1−	1−	NUM
ejpam-4868	417	43	au−	au−	NUM
ejpam-4868	417	44	uλ)2	uλ)2	PROPN
ejpam-4868	417	45	+	+	CCONJ
ejpam-4868	417	46	b2u2	b2u2	ADV
ejpam-4868	417	47	bu3	bu3	NOUN
ejpam-4868	417	48	(	(	PUNCT
ejpam-4868	417	49	1−	1−	NUM
ejpam-4868	417	50	au−	au−	NUM
ejpam-4868	417	51	uλ)2	uλ)2	PROPN
ejpam-4868	417	52	+	+	CCONJ
ejpam-4868	417	53	b2u2	b2u2	PROPN
ejpam-4868	417	54	eaλ(t	eaλ(t	PROPN
ejpam-4868	417	55	)	)	PUNCT
ejpam-4868	417	56	cos	cos	PROPN
ejpam-4868	417	57	(	(	PUNCT
ejpam-4868	417	58	b	b	X
ejpam-4868	417	59	)	)	PUNCT
ejpam-4868	417	60	λ	λ	PROPN
ejpam-4868	417	61	(	(	PUNCT
ejpam-4868	417	62	t	t	PROPN
ejpam-4868	417	63	)	)	PUNCT
ejpam-4868	417	64	(	(	PUNCT
ejpam-4868	417	65	1−	1−	NUM
ejpam-4868	417	66	au−	au−	NUM
ejpam-4868	417	67	uλ)uα+1	uλ)uα+1	NOUN
ejpam-4868	417	68	(	(	PUNCT
ejpam-4868	417	69	1−	1−	NUM
ejpam-4868	417	70	au−	au−	PUNCT
ejpam-4868	417	71	uλ)2	uλ)2	PROPN
ejpam-4868	417	72	+	+	CCONJ
ejpam-4868	417	73	b2u2	b2u2	PROPN
ejpam-4868	417	74	(	(	PUNCT
ejpam-4868	417	75	1−	1−	NUM
ejpam-4868	417	76	au−	au−	SYM
ejpam-4868	417	77	uλ)u2	uλ)u2	PROPN
ejpam-4868	417	78	(	(	PUNCT
ejpam-4868	417	79	1−	1−	NUM
ejpam-4868	417	80	au−	au−	NUM
ejpam-4868	417	81	uλ)2	uλ)2	PROPN
ejpam-4868	417	82	+	+	CCONJ
ejpam-4868	417	83	b2u2	b2u2	AUX
ejpam-4868	417	84	table	table	NOUN
ejpam-4868	417	85	3	3	NUM
ejpam-4868	417	86	:	:	PUNCT
ejpam-4868	417	87	the	the	DET
ejpam-4868	417	88	degenerate	degenerate	ADJ
ejpam-4868	417	89	laplace	laplace	NOUN
ejpam-4868	417	90	-	-	PUNCT
ejpam-4868	417	91	type	type	NOUN
ejpam-4868	417	92	and	and	CCONJ
ejpam-4868	417	93	degenerate	degenerate	ADJ
ejpam-4868	417	94	elzaki	elzaki	NOUN
ejpam-4868	417	95	transform	transform	NOUN
ejpam-4868	417	96	.	.	PUNCT
ejpam-4868	418	1	6	6	NUM
ejpam-4868	418	2	.	.	X
ejpam-4868	418	3	conclusion	conclusion	NOUN
ejpam-4868	418	4	and	and	CCONJ
ejpam-4868	418	5	recommendations	recommendation	NOUN
ejpam-4868	418	6	the	the	DET
ejpam-4868	418	7	concept	concept	NOUN
ejpam-4868	418	8	of	of	ADP
ejpam-4868	418	9	degenerate	degenerate	ADJ
ejpam-4868	418	10	laplace	laplace	NOUN
ejpam-4868	418	11	-	-	PUNCT
ejpam-4868	418	12	type	type	NOUN
ejpam-4868	418	13	integral	integral	ADJ
ejpam-4868	418	14	transform	transform	NOUN
ejpam-4868	418	15	is	be	AUX
ejpam-4868	418	16	introduced	introduce	VERB
ejpam-4868	418	17	in	in	ADP
ejpam-4868	418	18	this	this	DET
ejpam-4868	418	19	work	work	NOUN
ejpam-4868	418	20	,	,	PUNCT
ejpam-4868	418	21	and	and	CCONJ
ejpam-4868	418	22	it	it	PRON
ejpam-4868	418	23	includes	include	VERB
ejpam-4868	418	24	three	three	NUM
ejpam-4868	418	25	essential	essential	ADJ
ejpam-4868	418	26	degenerate	degenerate	ADJ
ejpam-4868	418	27	integral	integral	ADJ
ejpam-4868	418	28	transforms	transform	NOUN
ejpam-4868	418	29	:	:	PUNCT
ejpam-4868	418	30	the	the	DET
ejpam-4868	418	31	degenerate	degenerate	ADJ
ejpam-4868	418	32	laplace	laplace	NOUN
ejpam-4868	418	33	integral	integral	ADJ
ejpam-4868	418	34	transform	transform	NOUN
ejpam-4868	418	35	,	,	PUNCT
ejpam-4868	418	36	the	the	DET
ejpam-4868	418	37	degenerate	degenerate	ADJ
ejpam-4868	418	38	sumudu	sumudu	NOUN
ejpam-4868	418	39	integral	integral	ADJ
ejpam-4868	418	40	transform	transform	NOUN
ejpam-4868	418	41	,	,	PUNCT
ejpam-4868	418	42	and	and	CCONJ
ejpam-4868	418	43	the	the	DET
ejpam-4868	418	44	degenerate	degenerate	ADJ
ejpam-4868	418	45	elzaki	elzaki	NOUN
ejpam-4868	418	46	integral	integral	ADJ
ejpam-4868	418	47	transform	transform	NOUN
ejpam-4868	418	48	.	.	PUNCT
ejpam-4868	419	1	these	these	DET
ejpam-4868	419	2	transformations	transformation	NOUN
ejpam-4868	419	3	offer	offer	VERB
ejpam-4868	419	4	potentially	potentially	ADV
ejpam-4868	419	5	powerful	powerful	ADJ
ejpam-4868	419	6	mathematical	mathematical	ADJ
ejpam-4868	419	7	tools	tool	NOUN
ejpam-4868	419	8	for	for	ADP
ejpam-4868	419	9	addressing	address	VERB
ejpam-4868	419	10	a	a	DET
ejpam-4868	419	11	wide	wide	ADJ
ejpam-4868	419	12	range	range	NOUN
ejpam-4868	419	13	of	of	ADP
ejpam-4868	419	14	problems	problem	NOUN
ejpam-4868	419	15	in	in	ADP
ejpam-4868	419	16	engineering	engineering	NOUN
ejpam-4868	419	17	,	,	PUNCT
ejpam-4868	419	18	physics	physics	NOUN
ejpam-4868	419	19	,	,	PUNCT
ejpam-4868	419	20	and	and	CCONJ
ejpam-4868	419	21	other	other	ADJ
ejpam-4868	419	22	scientific	scientific	ADJ
ejpam-4868	419	23	fields	field	NOUN
ejpam-4868	419	24	.	.	PUNCT
ejpam-4868	420	1	the	the	DET
ejpam-4868	420	2	degenerate	degenerate	ADJ
ejpam-4868	420	3	laplace	laplace	NOUN
ejpam-4868	420	4	-	-	PUNCT
ejpam-4868	420	5	type	type	NOUN
ejpam-4868	420	6	integral	integral	ADJ
ejpam-4868	420	7	transform	transform	NOUN
ejpam-4868	420	8	is	be	AUX
ejpam-4868	420	9	a	a	DET
ejpam-4868	420	10	unifying	unifying	ADJ
ejpam-4868	420	11	framework	framework	NOUN
ejpam-4868	420	12	from	from	ADP
ejpam-4868	420	13	which	which	PRON
ejpam-4868	420	14	the	the	DET
ejpam-4868	420	15	degenerates	degenerate	NOUN
ejpam-4868	420	16	of	of	ADP
ejpam-4868	420	17	several	several	ADJ
ejpam-4868	420	18	current	current	ADJ
ejpam-4868	420	19	integral	integral	ADJ
ejpam-4868	420	20	transforms	transform	NOUN
ejpam-4868	420	21	may	may	AUX
ejpam-4868	420	22	be	be	AUX
ejpam-4868	420	23	derived	derive	VERB
ejpam-4868	420	24	.	.	PUNCT
ejpam-4868	421	1	this	this	DET
ejpam-4868	421	2	degenerate	degenerate	ADJ
ejpam-4868	421	3	laplace	laplace	NOUN
ejpam-4868	421	4	-	-	PUNCT
ejpam-4868	421	5	type	type	NOUN
ejpam-4868	421	6	integral	integral	ADJ
ejpam-4868	421	7	transform	transform	NOUN
ejpam-4868	421	8	has	have	VERB
ejpam-4868	421	9	a	a	DET
ejpam-4868	421	10	lot	lot	NOUN
ejpam-4868	421	11	of	of	ADP
ejpam-4868	421	12	promise	promise	NOUN
ejpam-4868	421	13	and	and	CCONJ
ejpam-4868	421	14	is	be	AUX
ejpam-4868	421	15	still	still	ADV
ejpam-4868	421	16	being	be	AUX
ejpam-4868	421	17	researched	research	VERB
ejpam-4868	421	18	and	and	CCONJ
ejpam-4868	421	19	developed	develop	VERB
ejpam-4868	421	20	.	.	PUNCT
ejpam-4868	422	1	as	as	ADP
ejpam-4868	422	2	a	a	DET
ejpam-4868	422	3	result	result	NOUN
ejpam-4868	422	4	,	,	PUNCT
ejpam-4868	422	5	more	more	ADJ
ejpam-4868	422	6	study	study	NOUN
ejpam-4868	422	7	may	may	AUX
ejpam-4868	422	8	uncover	uncover	VERB
ejpam-4868	422	9	new	new	ADJ
ejpam-4868	422	10	applications	application	NOUN
ejpam-4868	422	11	,	,	PUNCT
ejpam-4868	422	12	features	feature	NOUN
ejpam-4868	422	13	,	,	PUNCT
ejpam-4868	422	14	and	and	CCONJ
ejpam-4868	422	15	generalizations	generalization	NOUN
ejpam-4868	422	16	of	of	ADP
ejpam-4868	422	17	this	this	DET
ejpam-4868	422	18	groundbreaking	groundbreake	VERB
ejpam-4868	422	19	concept	concept	NOUN
ejpam-4868	422	20	.	.	PUNCT
ejpam-4868	423	1	references	reference	NOUN
ejpam-4868	423	2	2232	2232	NUM
ejpam-4868	423	3	acknowledgements	acknowledgement	NOUN
ejpam-4868	423	4	the	the	DET
ejpam-4868	423	5	authors	author	NOUN
ejpam-4868	423	6	would	would	AUX
ejpam-4868	423	7	like	like	VERB
ejpam-4868	423	8	to	to	PART
ejpam-4868	423	9	express	express	VERB
ejpam-4868	423	10	their	their	PRON
ejpam-4868	423	11	heartfelt	heartfelt	ADJ
ejpam-4868	423	12	appreciation	appreciation	NOUN
ejpam-4868	423	13	to	to	ADP
ejpam-4868	423	14	the	the	DET
ejpam-4868	423	15	science	science	NOUN
ejpam-4868	423	16	and	and	CCONJ
ejpam-4868	423	17	technology	technology	NOUN
ejpam-4868	423	18	regional	regional	ADJ
ejpam-4868	423	19	alliance	alliance	NOUN
ejpam-4868	423	20	of	of	ADP
ejpam-4868	423	21	universities	university	NOUN
ejpam-4868	423	22	for	for	ADP
ejpam-4868	423	23	national	national	ADJ
ejpam-4868	423	24	development	development	NOUN
ejpam-4868	423	25	(	(	PUNCT
ejpam-4868	423	26	strand	strand	NOUN
ejpam-4868	423	27	)	)	PUNCT
ejpam-4868	423	28	scholarship	scholarship	NOUN
ejpam-4868	423	29	for	for	ADP
ejpam-4868	423	30	your	your	PRON
ejpam-4868	423	31	unwavering	unwavering	ADJ
ejpam-4868	423	32	commitment	commitment	NOUN
ejpam-4868	423	33	to	to	ADP
ejpam-4868	423	34	research	research	NOUN
ejpam-4868	423	35	and	and	CCONJ
ejpam-4868	423	36	development	development	NOUN
ejpam-4868	423	37	,	,	PUNCT
ejpam-4868	423	38	for	for	ADP
ejpam-4868	423	39	the	the	DET
ejpam-4868	423	40	financial	financial	ADJ
ejpam-4868	423	41	support	support	NOUN
ejpam-4868	423	42	and	and	CCONJ
ejpam-4868	423	43	for	for	ADP
ejpam-4868	423	44	making	make	VERB
ejpam-4868	423	45	a	a	DET
ejpam-4868	423	46	difference	difference	NOUN
ejpam-4868	423	47	in	in	ADP
ejpam-4868	423	48	the	the	DET
ejpam-4868	423	49	lives	life	NOUN
ejpam-4868	423	50	of	of	ADP
ejpam-4868	423	51	aspiring	aspire	VERB
ejpam-4868	423	52	scientists	scientist	NOUN
ejpam-4868	423	53	and	and	CCONJ
ejpam-4868	423	54	researchers	researcher	NOUN
ejpam-4868	423	55	.	.	PUNCT
ejpam-4868	424	1	references	reference	NOUN
ejpam-4868	424	2	[	[	X
ejpam-4868	424	3	1	1	NUM
ejpam-4868	424	4	]	]	PUNCT
ejpam-4868	424	5	t	t	PROPN
ejpam-4868	424	6	kohila	kohila	PROPN
ejpam-4868	424	7	a	a	DET
ejpam-4868	424	8	kalavathi	kalavathi	ADJ
ejpam-4868	424	9	and	and	CCONJ
ejpam-4868	424	10	l	l	NOUN
ejpam-4868	424	11	m	m	VERB
ejpam-4868	424	12	upadhyaya	upadhyaya	NOUN
ejpam-4868	424	13	.	.	PUNCT
ejpam-4868	425	1	on	on	ADP
ejpam-4868	425	2	the	the	DET
ejpam-4868	425	3	degenerate	degenerate	ADJ
ejpam-4868	425	4	elzaki	elzaki	NOUN
ejpam-4868	425	5	transform	transform	NOUN
ejpam-4868	425	6	.	.	PUNCT
ejpam-4868	425	7	bulletin	bulletin	NOUN
ejpam-4868	425	8	of	of	ADP
ejpam-4868	425	9	pure	pure	ADJ
ejpam-4868	425	10	and	and	CCONJ
ejpam-4868	425	11	applied	applied	ADJ
ejpam-4868	425	12	sciences	science	NOUN
ejpam-4868	425	13	section	section	NOUN
ejpam-4868	425	14	-e	-e	NOUN
ejpam-4868	425	15	-	-	PUNCT
ejpam-4868	425	16	mathematics	mathematic	NOUN
ejpam-4868	425	17	&	&	CCONJ
ejpam-4868	425	18	statistics	statistic	NOUN
ejpam-4868	425	19	,	,	PUNCT
ejpam-4868	425	20	40e(1):99	40e(1):99	NOUN
ejpam-4868	425	21	–	–	PUNCT
ejpam-4868	425	22	107	107	NUM
ejpam-4868	425	23	,	,	PUNCT
ejpam-4868	425	24	2021	2021	NUM
ejpam-4868	425	25	.	.	PUNCT
ejpam-4868	426	1	[	[	X
ejpam-4868	426	2	2	2	NUM
ejpam-4868	426	3	]	]	PUNCT
ejpam-4868	426	4	t	t	PROPN
ejpam-4868	426	5	kim	kim	PROPN
ejpam-4868	426	6	d	d	PROPN
ejpam-4868	426	7	s	s	PROPN
ejpam-4868	426	8	kim	kim	PROPN
ejpam-4868	426	9	and	and	CCONJ
ejpam-4868	426	10	h	h	PROPN
ejpam-4868	426	11	lee	lee	PROPN
ejpam-4868	426	12	.	.	PUNCT
ejpam-4868	427	1	a	a	DET
ejpam-4868	427	2	note	note	NOUN
ejpam-4868	427	3	on	on	ADP
ejpam-4868	427	4	degenerate	degenerate	ADJ
ejpam-4868	427	5	euler	euler	NOUN
ejpam-4868	427	6	and	and	CCONJ
ejpam-4868	427	7	bernoulli	bernoulli	NOUN
ejpam-4868	427	8	polynomials	polynomial	NOUN
ejpam-4868	427	9	of	of	ADP
ejpam-4868	427	10	complex	complex	ADJ
ejpam-4868	427	11	variable	variable	NOUN
ejpam-4868	427	12	.	.	PUNCT
ejpam-4868	428	1	symmetry	symmetry	NOUN
ejpam-4868	428	2	,	,	PUNCT
ejpam-4868	428	3	11(1339):1–14	11(1339):1–14	PROPN
ejpam-4868	428	4	,	,	PUNCT
ejpam-4868	428	5	2019	2019	NUM
ejpam-4868	428	6	.	.	PUNCT
ejpam-4868	429	1	[	[	X
ejpam-4868	429	2	3	3	X
ejpam-4868	429	3	]	]	PUNCT
ejpam-4868	429	4	t	t	PROPN
ejpam-4868	429	5	kim	kim	PROPN
ejpam-4868	429	6	ds	ds	PROPN
ejpam-4868	429	7	kim	kim	PROPN
ejpam-4868	429	8	and	and	CCONJ
ejpam-4868	429	9	gw	gw	PROPN
ejpam-4868	429	10	jang	jang	PROPN
ejpam-4868	429	11	.	.	PUNCT
ejpam-4868	430	1	a	a	DET
ejpam-4868	430	2	note	note	NOUN
ejpam-4868	430	3	on	on	ADP
ejpam-4868	430	4	degenerate	degenerate	ADJ
ejpam-4868	430	5	fubini	fubini	ADJ
ejpam-4868	430	6	polynomials	polynomial	NOUN
ejpam-4868	430	7	.	.	PUNCT
ejpam-4868	431	1	in	in	ADP
ejpam-4868	431	2	proceeding	proceeding	NOUN
ejpam-4868	431	3	of	of	ADP
ejpam-4868	431	4	the	the	DET
ejpam-4868	431	5	jangjeon	jangjeon	PROPN
ejpam-4868	431	6	mathematical	mathematical	PROPN
ejpam-4868	431	7	society	society	NOUN
ejpam-4868	431	8	,	,	PUNCT
ejpam-4868	431	9	pages	page	NOUN
ejpam-4868	431	10	521–531	521–531	NUM
ejpam-4868	431	11	,	,	PUNCT
ejpam-4868	431	12	korea	korea	PROPN
ejpam-4868	431	13	,	,	PUNCT
ejpam-4868	431	14	2017	2017	NUM
ejpam-4868	431	15	.	.	PUNCT
ejpam-4868	432	1	[	[	X
ejpam-4868	432	2	4	4	NUM
ejpam-4868	432	3	]	]	X
ejpam-4868	432	4	u	u	PROPN
ejpam-4868	432	5	duran	duran	PROPN
ejpam-4868	432	6	.	.	PUNCT
ejpam-4868	432	7	degenerate	degenerate	ADJ
ejpam-4868	432	8	sumudu	sumudu	NOUN
ejpam-4868	432	9	transform	transform	NOUN
ejpam-4868	432	10	and	and	CCONJ
ejpam-4868	432	11	its	its	PRON
ejpam-4868	432	12	properties	property	NOUN
ejpam-4868	432	13	.	.	PUNCT
ejpam-4868	433	1	filomat	filomat	NOUN
ejpam-4868	433	2	,	,	PUNCT
ejpam-4868	433	3	35(14):4731	35(14):4731	NUM
ejpam-4868	433	4	–	–	PUNCT
ejpam-4868	433	5	4741	4741	NUM
ejpam-4868	433	6	,	,	PUNCT
ejpam-4868	433	7	2021	2021	NUM
ejpam-4868	433	8	.	.	PUNCT
ejpam-4868	434	1	[	[	X
ejpam-4868	434	2	5	5	NUM
ejpam-4868	434	3	]	]	PUNCT
ejpam-4868	434	4	s	s	PART
ejpam-4868	434	5	supaknarre	supaknarre	PROPN
ejpam-4868	434	6	h	h	PROPN
ejpam-4868	434	7	kim	kim	PROPN
ejpam-4868	434	8	and	and	CCONJ
ejpam-4868	434	9	k	k	PROPN
ejpam-4868	434	10	nonlaopon	nonlaopon	ADV
ejpam-4868	434	11	.	.	PUNCT
ejpam-4868	435	1	further	further	ADJ
ejpam-4868	435	2	properties	property	NOUN
ejpam-4868	435	3	of	of	ADP
ejpam-4868	435	4	laplace	laplace	NOUN
ejpam-4868	435	5	-	-	PUNCT
ejpam-4868	435	6	type	type	NOUN
ejpam-4868	435	7	integral	integral	ADJ
ejpam-4868	435	8	transforms	transform	NOUN
ejpam-4868	435	9	.	.	PUNCT
ejpam-4868	436	1	dynamic	dynamic	ADJ
ejpam-4868	436	2	systems	system	NOUN
ejpam-4868	436	3	and	and	CCONJ
ejpam-4868	436	4	applications	application	NOUN
ejpam-4868	436	5	,	,	PUNCT
ejpam-4868	436	6	28(1):195–215	28(1):195–215	PROPN
ejpam-4868	436	7	,	,	PUNCT
ejpam-4868	436	8	2019	2019	NUM
ejpam-4868	436	9	.	.	PUNCT
ejpam-4868	437	1	[	[	X
ejpam-4868	437	2	6	6	NUM
ejpam-4868	437	3	]	]	PUNCT
ejpam-4868	437	4	d	d	X
ejpam-4868	437	5	kim	kim	PROPN
ejpam-4868	437	6	.	.	PUNCT
ejpam-4868	438	1	a	a	DET
ejpam-4868	438	2	note	note	NOUN
ejpam-4868	438	3	on	on	ADP
ejpam-4868	438	4	the	the	DET
ejpam-4868	438	5	degenerate	degenerate	ADJ
ejpam-4868	438	6	type	type	NOUN
ejpam-4868	438	7	of	of	ADP
ejpam-4868	438	8	complex	complex	ADJ
ejpam-4868	438	9	appell	appell	ADJ
ejpam-4868	438	10	polynomials	polynomial	NOUN
ejpam-4868	438	11	.	.	PUNCT
ejpam-4868	439	1	symmetry	symmetry	NOUN
ejpam-4868	439	2	,	,	PUNCT
ejpam-4868	439	3	11:1339	11:1339	NUM
ejpam-4868	439	4	,	,	PUNCT
ejpam-4868	439	5	2019	2019	NUM
ejpam-4868	439	6	.	.	PUNCT
ejpam-4868	440	1	[	[	X
ejpam-4868	440	2	7	7	X
ejpam-4868	440	3	]	]	X
ejpam-4868	440	4	h	h	NOUN
ejpam-4868	440	5	kim	kim	PROPN
ejpam-4868	440	6	.	.	PUNCT
ejpam-4868	441	1	the	the	DET
ejpam-4868	441	2	intrinsic	intrinsic	ADJ
ejpam-4868	441	3	structure	structure	NOUN
ejpam-4868	441	4	and	and	CCONJ
ejpam-4868	441	5	properties	property	NOUN
ejpam-4868	441	6	of	of	ADP
ejpam-4868	441	7	laplace	laplace	NOUN
ejpam-4868	441	8	-	-	PUNCT
ejpam-4868	441	9	typed	type	VERB
ejpam-4868	441	10	integral	integral	ADJ
ejpam-4868	441	11	transforms	transform	NOUN
ejpam-4868	441	12	.	.	PUNCT
ejpam-4868	442	1	math	math	NOUN
ejpam-4868	442	2	.	.	PUNCT
ejpam-4868	443	1	prob	prob	PROPN
ejpam-4868	443	2	.	.	PUNCT
ejpam-4868	444	1	engi	engi	PROPN
ejpam-4868	444	2	.	.	PROPN
ejpam-4868	444	3	,	,	PUNCT
ejpam-4868	444	4	2017:1–8	2017:1–8	PROPN
ejpam-4868	444	5	,	,	PUNCT
ejpam-4868	444	6	2017	2017	NUM
ejpam-4868	444	7	.	.	PUNCT
ejpam-4868	445	1	[	[	X
ejpam-4868	445	2	8	8	NUM
ejpam-4868	445	3	]	]	PUNCT
ejpam-4868	445	4	t	t	PROPN
ejpam-4868	445	5	kim	kim	PROPN
ejpam-4868	445	6	and	and	CCONJ
ejpam-4868	445	7	ds	ds	PROPN
ejpam-4868	445	8	kim	kim	PROPN
ejpam-4868	445	9	.	.	PUNCT
ejpam-4868	446	1	degenerate	degenerate	ADJ
ejpam-4868	446	2	laplace	laplace	NOUN
ejpam-4868	446	3	transform	transform	NOUN
ejpam-4868	446	4	and	and	CCONJ
ejpam-4868	446	5	degenerate	degenerate	ADJ
ejpam-4868	446	6	gamma	gamma	NOUN
ejpam-4868	446	7	function	function	NOUN
ejpam-4868	446	8	.	.	PUNCT
ejpam-4868	447	1	russian	russian	ADJ
ejpam-4868	447	2	journal	journal	PROPN
ejpam-4868	447	3	of	of	ADP
ejpam-4868	447	4	mathematical	mathematical	ADJ
ejpam-4868	447	5	physics	physics	NOUN
ejpam-4868	447	6	,	,	PUNCT
ejpam-4868	447	7	24(2):241–248	24(2):241–248	PROPN
ejpam-4868	447	8	,	,	PUNCT
ejpam-4868	447	9	2017	2017	NUM
ejpam-4868	447	10	.	.	PUNCT
ejpam-4868	448	1	[	[	X
ejpam-4868	448	2	9	9	NUM
ejpam-4868	448	3	]	]	PUNCT
ejpam-4868	448	4	t	t	PROPN
ejpam-4868	448	5	kim	kim	PROPN
ejpam-4868	448	6	and	and	CCONJ
ejpam-4868	448	7	ds	ds	PROPN
ejpam-4868	448	8	kim	kim	PROPN
ejpam-4868	448	9	.	.	PUNCT
ejpam-4868	449	1	note	note	VERB
ejpam-4868	449	2	on	on	ADP
ejpam-4868	449	3	the	the	DET
ejpam-4868	449	4	degenerate	degenerate	ADJ
ejpam-4868	449	5	gamma	gamma	NOUN
ejpam-4868	449	6	function	function	NOUN
ejpam-4868	449	7	.	.	PUNCT
ejpam-4868	450	1	russ	russ	PROPN
ejpam-4868	450	2	.	.	PUNCT
ejpam-4868	451	1	j.	j.	PROPN
ejpam-4868	451	2	math	math	PROPN
ejpam-4868	451	3	.	.	PUNCT
ejpam-4868	452	1	phys	phy	NOUN
ejpam-4868	452	2	.	.	PUNCT
ejpam-4868	452	3	,	,	PUNCT
ejpam-4868	453	1	27(3):352–358	27(3):352–358	NOUN
ejpam-4868	453	2	,	,	PUNCT
ejpam-4868	453	3	2020	2020	NUM
ejpam-4868	453	4	.	.	PUNCT
ejpam-4868	454	1	[	[	X
ejpam-4868	454	2	10	10	NUM
ejpam-4868	454	3	]	]	X
ejpam-4868	454	4	t	t	PROPN
ejpam-4868	454	5	kim	kim	PROPN
ejpam-4868	454	6	and	and	CCONJ
ejpam-4868	454	7	ds	ds	PROPN
ejpam-4868	454	8	kim	kim	PROPN
ejpam-4868	454	9	.	.	PUNCT
ejpam-4868	455	1	some	some	DET
ejpam-4868	455	2	identities	identity	NOUN
ejpam-4868	455	3	on	on	ADP
ejpam-4868	455	4	truncated	truncated	ADJ
ejpam-4868	455	5	polynomials	polynomial	NOUN
ejpam-4868	455	6	associated	associate	VERB
ejpam-4868	455	7	with	with	ADP
ejpam-4868	455	8	degenerate	degenerate	ADJ
ejpam-4868	455	9	bell	bell	NOUN
ejpam-4868	455	10	polynomials	polynomial	NOUN
ejpam-4868	455	11	.	.	PUNCT
ejpam-4868	456	1	russ	russ	PROPN
ejpam-4868	456	2	.	.	PUNCT
ejpam-4868	457	1	j.	j.	PROPN
ejpam-4868	457	2	math	math	PROPN
ejpam-4868	457	3	.	.	PUNCT
ejpam-4868	458	1	phys	phy	NOUN
ejpam-4868	458	2	.	.	PUNCT
ejpam-4868	458	3	,	,	PUNCT
ejpam-4868	458	4	28(3):342–355	28(3):342–355	NUM
ejpam-4868	458	5	,	,	PUNCT
ejpam-4868	458	6	2021	2021	NUM
ejpam-4868	458	7	.	.	PUNCT
ejpam-4868	459	1	[	[	X
ejpam-4868	459	2	11	11	NUM
ejpam-4868	459	3	]	]	PUNCT
ejpam-4868	459	4	t	t	PROPN
ejpam-4868	459	5	kim	kim	PROPN
ejpam-4868	459	6	and	and	CCONJ
ejpam-4868	459	7	ds	ds	PROPN
ejpam-4868	459	8	kim	kim	PROPN
ejpam-4868	459	9	.	.	PUNCT
ejpam-4868	460	1	combinatorial	combinatorial	ADJ
ejpam-4868	460	2	identities	identity	NOUN
ejpam-4868	460	3	involving	involve	VERB
ejpam-4868	460	4	degenerate	degenerate	ADJ
ejpam-4868	460	5	harmonic	harmonic	ADJ
ejpam-4868	460	6	and	and	CCONJ
ejpam-4868	460	7	hyperharmonic	hyperharmonic	ADJ
ejpam-4868	460	8	numbers	number	NOUN
ejpam-4868	460	9	.	.	PUNCT
ejpam-4868	461	1	advances	advance	NOUN
ejpam-4868	461	2	in	in	ADP
ejpam-4868	461	3	applied	apply	VERB
ejpam-4868	461	4	mathematics	mathematic	NOUN
ejpam-4868	461	5	,	,	PUNCT
ejpam-4868	461	6	148:102535	148:102535	NUM
ejpam-4868	461	7	,	,	PUNCT
ejpam-4868	461	8	2023	2023	NUM
ejpam-4868	461	9	.	.	PUNCT
ejpam-4868	462	1	[	[	X
ejpam-4868	462	2	12	12	NUM
ejpam-4868	462	3	]	]	PUNCT
ejpam-4868	462	4	t	t	PROPN
ejpam-4868	462	5	kim	kim	PROPN
ejpam-4868	462	6	and	and	CCONJ
ejpam-4868	462	7	ds	ds	PROPN
ejpam-4868	462	8	kim	kim	PROPN
ejpam-4868	462	9	.	.	PUNCT
ejpam-4868	463	1	some	some	DET
ejpam-4868	463	2	identities	identity	NOUN
ejpam-4868	463	3	involving	involve	VERB
ejpam-4868	463	4	degenerate	degenerate	ADJ
ejpam-4868	463	5	stirling	stirling	NOUN
ejpam-4868	463	6	numbers	number	NOUN
ejpam-4868	463	7	associated	associate	VERB
ejpam-4868	463	8	with	with	ADP
ejpam-4868	463	9	several	several	ADJ
ejpam-4868	463	10	degenerate	degenerate	ADJ
ejpam-4868	463	11	polynomials	polynomial	NOUN
ejpam-4868	463	12	and	and	CCONJ
ejpam-4868	463	13	numbers	number	NOUN
ejpam-4868	463	14	.	.	PUNCT
ejpam-4868	464	1	russ	russ	PROPN
ejpam-4868	464	2	.	.	PUNCT
ejpam-4868	465	1	j.	j.	PROPN
ejpam-4868	465	2	math	math	PROPN
ejpam-4868	465	3	.	.	PUNCT
ejpam-4868	466	1	phys	phy	NOUN
ejpam-4868	466	2	.	.	PUNCT
ejpam-4868	466	3	,	,	PUNCT
ejpam-4868	466	4	30(1):62–75	30(1):62–75	NUM
ejpam-4868	466	5	,	,	PUNCT
ejpam-4868	466	6	2023	2023	NUM
ejpam-4868	466	7	.	.	PUNCT
ejpam-4868	467	1	references	reference	NOUN
ejpam-4868	467	2	2233	2233	NUM
ejpam-4868	467	3	[	[	X
ejpam-4868	467	4	13	13	NUM
ejpam-4868	467	5	]	]	X
ejpam-4868	467	6	j	j	PROPN
ejpam-4868	467	7	kwon	kwon	PROPN
ejpam-4868	467	8	t	t	PROPN
ejpam-4868	467	9	kim	kim	PROPN
ejpam-4868	467	10	,	,	PUNCT
ejpam-4868	467	11	ds	ds	PROPN
ejpam-4868	467	12	kim	kim	PROPN
ejpam-4868	467	13	and	and	CCONJ
ejpam-4868	467	14	h	h	PROPN
ejpam-4868	467	15	lee	lee	PROPN
ejpam-4868	467	16	.	.	PUNCT
ejpam-4868	468	1	a	a	DET
ejpam-4868	468	2	note	note	NOUN
ejpam-4868	468	3	on	on	ADP
ejpam-4868	468	4	degenerate	degenerate	ADJ
ejpam-4868	468	5	gamma	gamma	NOUN
ejpam-4868	468	6	random	random	ADJ
ejpam-4868	468	7	variables	variable	NOUN
ejpam-4868	468	8	.	.	PUNCT
ejpam-4868	469	1	revista	revista	PROPN
ejpam-4868	469	2	de	de	PROPN
ejpam-4868	469	3	educacion	educacion	PROPN
ejpam-4868	469	4	,	,	PUNCT
ejpam-4868	469	5	388:39	388:39	PROPN
ejpam-4868	469	6	,	,	PUNCT
ejpam-4868	469	7	04	04	NUM
ejpam-4868	469	8	2020	2020	NUM
ejpam-4868	469	9	.	.	PUNCT
ejpam-4868	470	1	[	[	X
ejpam-4868	470	2	14	14	NUM
ejpam-4868	470	3	]	]	X
ejpam-4868	470	4	l	l	NOUN
ejpam-4868	470	5	m	m	VERB
ejpam-4868	470	6	upadhyaya	upadhyaya	NOUN
ejpam-4868	470	7	.	.	PUNCT
ejpam-4868	471	1	on	on	ADP
ejpam-4868	471	2	the	the	DET
ejpam-4868	471	3	degenerate	degenerate	ADJ
ejpam-4868	471	4	laplace	laplace	NOUN
ejpam-4868	471	5	transform	transform	NOUN
ejpam-4868	471	6	–	–	PUNCT
ejpam-4868	471	7	ii	ii	NOUN
ejpam-4868	471	8	.	.	PUNCT
ejpam-4868	471	9	international	international	PROPN
ejpam-4868	471	10	journal	journal	PROPN
ejpam-4868	471	11	of	of	ADP
ejpam-4868	471	12	engineering	engineering	NOUN
ejpam-4868	471	13	and	and	CCONJ
ejpam-4868	471	14	scientific	scientific	ADJ
ejpam-4868	471	15	research	research	NOUN
ejpam-4868	471	16	,	,	PUNCT
ejpam-4868	471	17	5(12):63–71	5(12):63–71	NUM
ejpam-4868	471	18	,	,	PUNCT
ejpam-4868	471	19	2017	2017	NUM
ejpam-4868	471	20	.	.	PUNCT
ejpam-4868	472	1	[	[	X
ejpam-4868	472	2	15	15	NUM
ejpam-4868	472	3	]	]	X
ejpam-4868	472	4	l	l	NOUN
ejpam-4868	472	5	m	m	VERB
ejpam-4868	472	6	upadhyaya	upadhyaya	NOUN
ejpam-4868	472	7	.	.	PUNCT
ejpam-4868	473	1	on	on	ADP
ejpam-4868	473	2	the	the	DET
ejpam-4868	473	3	degenerate	degenerate	ADJ
ejpam-4868	473	4	laplace	laplace	NOUN
ejpam-4868	473	5	transform	transform	NOUN
ejpam-4868	473	6	–	–	PUNCT
ejpam-4868	473	7	i.	i.	NOUN
ejpam-4868	473	8	bulletin	bulletin	NOUN
ejpam-4868	473	9	of	of	ADP
ejpam-4868	473	10	pure	pure	ADJ
ejpam-4868	473	11	and	and	CCONJ
ejpam-4868	473	12	applied	applied	ADJ
ejpam-4868	473	13	sciences	science	NOUN
ejpam-4868	473	14	section	section	NOUN
ejpam-4868	473	15	-e	-e	NOUN
ejpam-4868	473	16	-	-	PUNCT
ejpam-4868	473	17	mathematics	mathematic	NOUN
ejpam-4868	473	18	&	&	CCONJ
ejpam-4868	473	19	statistics	statistic	NOUN
ejpam-4868	473	20	,	,	PUNCT
ejpam-4868	473	21	37e(1):1–8	37e(1):1–8	NUM
ejpam-4868	473	22	,	,	PUNCT
ejpam-4868	473	23	2018	2018	NUM
ejpam-4868	473	24	.	.	PUNCT
ejpam-4868	474	1	[	[	X
ejpam-4868	474	2	16	16	NUM
ejpam-4868	474	3	]	]	X
ejpam-4868	474	4	l	l	NOUN
ejpam-4868	474	5	m	m	VERB
ejpam-4868	474	6	upadhyaya	upadhyaya	NOUN
ejpam-4868	474	7	.	.	PUNCT
ejpam-4868	475	1	on	on	ADP
ejpam-4868	475	2	the	the	DET
ejpam-4868	475	3	degenerate	degenerate	ADJ
ejpam-4868	475	4	laplace	laplace	NOUN
ejpam-4868	475	5	transform	transform	NOUN
ejpam-4868	475	6	–	–	PUNCT
ejpam-4868	475	7	iii	iii	NOUN
ejpam-4868	475	8	.	.	PUNCT
ejpam-4868	475	9	international	international	ADJ
ejpam-4868	475	10	journal	journal	PROPN
ejpam-4868	475	11	of	of	ADP
ejpam-4868	475	12	engineering	engineering	NOUN
ejpam-4868	475	13	and	and	CCONJ
ejpam-4868	475	14	scientific	scientific	ADJ
ejpam-4868	475	15	research	research	NOUN
ejpam-4868	475	16	,	,	PUNCT
ejpam-4868	475	17	7(1):400–410	7(1):400–410	NUM
ejpam-4868	475	18	,	,	PUNCT
ejpam-4868	475	19	2018	2018	NUM
ejpam-4868	475	20	.	.	PUNCT