id	sid	tid	token	lemma	pos
ejpam-2531	1	1	compile	compile	VERB
ejpam-2531	1	2	/	/	SYM
ejpam-2531	1	3	output.dvi	output.dvi	NOUN
ejpam-2531	1	4	polynomial	polynomial	ADJ
ejpam-2531	1	5	integral	integral	ADJ
ejpam-2531	1	6	transform	transform	NOUN
ejpam-2531	1	7	for	for	ADP
ejpam-2531	1	8	solving	solve	VERB
ejpam-2531	1	9	differential	differential	ADJ
ejpam-2531	1	10	equations	equation	NOUN
ejpam-2531	1	11	benedict	benedict	PROPN
ejpam-2531	1	12	barnes	barnes	PROPN
ejpam-2531	1	13	school	school	PROPN
ejpam-2531	1	14	of	of	ADP
ejpam-2531	1	15	agriculture	agriculture	NOUN
ejpam-2531	1	16	and	and	CCONJ
ejpam-2531	1	17	social	social	ADJ
ejpam-2531	1	18	sciences	science	NOUN
ejpam-2531	1	19	,	,	PUNCT
ejpam-2531	1	20	anglican	anglican	ADJ
ejpam-2531	1	21	university	university	NOUN
ejpam-2531	1	22	of	of	ADP
ejpam-2531	1	23	college	college	PROPN
ejpam-2531	1	24	of	of	ADP
ejpam-2531	1	25	technology	technology	NOUN
ejpam-2531	1	26	,	,	PUNCT
ejpam-2531	1	27	nkoranza	nkoranza	PROPN
ejpam-2531	1	28	campus	campus	PROPN
ejpam-2531	1	29	,	,	PUNCT
ejpam-2531	1	30	brong	brong	PROPN
ejpam-2531	1	31	ahafo	ahafo	PROPN
ejpam-2531	1	32	,	,	PUNCT
ejpam-2531	1	33	ghana	ghana	PROPN
ejpam-2531	1	34	department	department	PROPN
ejpam-2531	1	35	of	of	ADP
ejpam-2531	1	36	mathematics	mathematics	PROPN
ejpam-2531	1	37	,	,	PUNCT
ejpam-2531	1	38	knust	knust	PROPN
ejpam-2531	1	39	,	,	PUNCT
ejpam-2531	1	40	kumasi	kumasi	PROPN
ejpam-2531	1	41	,	,	PUNCT
ejpam-2531	1	42	ghana	ghana	PROPN
ejpam-2531	1	43	abstract	abstract	NOUN
ejpam-2531	1	44	.	.	PUNCT
ejpam-2531	2	1	in	in	ADP
ejpam-2531	2	2	this	this	DET
ejpam-2531	2	3	paper	paper	NOUN
ejpam-2531	2	4	,	,	PUNCT
ejpam-2531	2	5	we	we	PRON
ejpam-2531	2	6	propose	propose	VERB
ejpam-2531	2	7	polynomial	polynomial	ADJ
ejpam-2531	2	8	integral	integral	ADJ
ejpam-2531	2	9	transform	transform	NOUN
ejpam-2531	2	10	for	for	ADP
ejpam-2531	2	11	solving	solve	VERB
ejpam-2531	2	12	differential	differential	ADJ
ejpam-2531	2	13	equations	equation	NOUN
ejpam-2531	2	14	.	.	PUNCT
ejpam-2531	3	1	unlike	unlike	ADP
ejpam-2531	3	2	the	the	DET
ejpam-2531	3	3	laplace	laplace	NOUN
ejpam-2531	3	4	transform	transform	NOUN
ejpam-2531	3	5	and	and	CCONJ
ejpam-2531	3	6	others	other	NOUN
ejpam-2531	3	7	,	,	PUNCT
ejpam-2531	3	8	the	the	DET
ejpam-2531	3	9	polynomial	polynomial	ADJ
ejpam-2531	3	10	integral	integral	ADJ
ejpam-2531	3	11	transform	transform	NOUN
ejpam-2531	3	12	solves	solve	NOUN
ejpam-2531	3	13	differential	differential	NOUN
ejpam-2531	3	14	equations	equation	NOUN
ejpam-2531	3	15	with	with	ADP
ejpam-2531	3	16	a	a	DET
ejpam-2531	3	17	little	little	ADJ
ejpam-2531	3	18	computational	computational	ADJ
ejpam-2531	3	19	effort	effort	NOUN
ejpam-2531	3	20	as	as	ADV
ejpam-2531	3	21	well	well	ADV
ejpam-2531	3	22	as	as	ADP
ejpam-2531	3	23	time	time	NOUN
ejpam-2531	3	24	.	.	PUNCT
ejpam-2531	4	1	in	in	ADP
ejpam-2531	4	2	addition	addition	NOUN
ejpam-2531	4	3	,	,	PUNCT
ejpam-2531	4	4	the	the	DET
ejpam-2531	4	5	polynomial	polynomial	ADJ
ejpam-2531	4	6	integral	integral	ADJ
ejpam-2531	4	7	transform	transform	NOUN
ejpam-2531	4	8	entails	entail	VERB
ejpam-2531	4	9	a	a	DET
ejpam-2531	4	10	polynomial	polynomial	ADJ
ejpam-2531	4	11	function	function	NOUN
ejpam-2531	4	12	as	as	ADP
ejpam-2531	4	13	its	its	PRON
ejpam-2531	4	14	kernel	kernel	NOUN
ejpam-2531	4	15	,	,	PUNCT
ejpam-2531	4	16	which	which	PRON
ejpam-2531	4	17	ensures	ensure	VERB
ejpam-2531	4	18	the	the	DET
ejpam-2531	4	19	rapid	rapid	ADJ
ejpam-2531	4	20	convergence	convergence	NOUN
ejpam-2531	4	21	of	of	ADP
ejpam-2531	4	22	the	the	DET
ejpam-2531	4	23	solution	solution	NOUN
ejpam-2531	4	24	to	to	ADP
ejpam-2531	4	25	a	a	DET
ejpam-2531	4	26	differential	differential	ADJ
ejpam-2531	4	27	equation	equation	NOUN
ejpam-2531	4	28	.	.	PUNCT
ejpam-2531	5	1	thus	thus	ADV
ejpam-2531	5	2	,	,	PUNCT
ejpam-2531	5	3	this	this	DET
ejpam-2531	5	4	method	method	NOUN
ejpam-2531	5	5	transforms	transform	VERB
ejpam-2531	5	6	a	a	DET
ejpam-2531	5	7	linear	linear	ADJ
ejpam-2531	5	8	differential	differential	ADJ
ejpam-2531	5	9	equation	equation	NOUN
ejpam-2531	5	10	into	into	ADP
ejpam-2531	5	11	an	an	DET
ejpam-2531	5	12	algebraic	algebraic	ADJ
ejpam-2531	5	13	equation	equation	NOUN
ejpam-2531	5	14	,	,	PUNCT
ejpam-2531	5	15	from	from	ADP
ejpam-2531	5	16	which	which	PRON
ejpam-2531	5	17	the	the	DET
ejpam-2531	5	18	solution	solution	NOUN
ejpam-2531	5	19	is	be	AUX
ejpam-2531	5	20	obtained	obtain	VERB
ejpam-2531	5	21	.	.	PUNCT
ejpam-2531	6	1	moreover	moreover	ADV
ejpam-2531	6	2	,	,	PUNCT
ejpam-2531	6	3	we	we	PRON
ejpam-2531	6	4	show	show	VERB
ejpam-2531	6	5	the	the	DET
ejpam-2531	6	6	applicabilities	applicability	NOUN
ejpam-2531	6	7	of	of	ADP
ejpam-2531	6	8	the	the	DET
ejpam-2531	6	9	polynomial	polynomial	ADJ
ejpam-2531	6	10	integral	integral	ADJ
ejpam-2531	6	11	transform	transform	NOUN
ejpam-2531	6	12	and	and	CCONJ
ejpam-2531	6	13	its	its	PRON
ejpam-2531	6	14	properties	property	NOUN
ejpam-2531	6	15	.	.	PUNCT
ejpam-2531	7	1	2010	2010	NUM
ejpam-2531	7	2	mathematics	mathematic	NOUN
ejpam-2531	7	3	subject	subject	NOUN
ejpam-2531	7	4	classifications	classification	NOUN
ejpam-2531	7	5	:	:	PUNCT
ejpam-2531	7	6	44b24	44b24	NUM
ejpam-2531	7	7	;	;	PUNCT
ejpam-2531	7	8	44b21	44b21	NUM
ejpam-2531	7	9	key	key	ADJ
ejpam-2531	7	10	words	word	NOUN
ejpam-2531	7	11	and	and	CCONJ
ejpam-2531	7	12	phrases	phrase	NOUN
ejpam-2531	7	13	:	:	PUNCT
ejpam-2531	7	14	polynomial	polynomial	ADJ
ejpam-2531	7	15	integral	integral	ADJ
ejpam-2531	7	16	transform	transform	NOUN
ejpam-2531	7	17	,	,	PUNCT
ejpam-2531	7	18	polynomial	polynomial	ADJ
ejpam-2531	7	19	function	function	NOUN
ejpam-2531	7	20	,	,	PUNCT
ejpam-2531	7	21	kernel	kernel	PROPN
ejpam-2531	7	22	,	,	PUNCT
ejpam-2531	7	23	differential	differential	ADJ
ejpam-2531	7	24	equations	equation	NOUN
ejpam-2531	7	25	1	1	NUM
ejpam-2531	7	26	.	.	X
ejpam-2531	8	1	introduction	introduction	NOUN
ejpam-2531	8	2	most	most	ADJ
ejpam-2531	8	3	of	of	ADP
ejpam-2531	8	4	the	the	DET
ejpam-2531	8	5	problems	problem	NOUN
ejpam-2531	8	6	encountered	encounter	VERB
ejpam-2531	8	7	in	in	ADP
ejpam-2531	8	8	science	science	NOUN
ejpam-2531	8	9	,	,	PUNCT
ejpam-2531	8	10	engineering	engineering	NOUN
ejpam-2531	8	11	and	and	CCONJ
ejpam-2531	8	12	physics	physics	NOUN
ejpam-2531	8	13	involve	involve	VERB
ejpam-2531	8	14	rates	rate	NOUN
ejpam-2531	8	15	of	of	ADP
ejpam-2531	8	16	change	change	NOUN
ejpam-2531	8	17	.	.	PUNCT
ejpam-2531	9	1	initial	initial	ADJ
ejpam-2531	9	2	condition	condition	NOUN
ejpam-2531	9	3	of	of	ADP
ejpam-2531	9	4	the	the	DET
ejpam-2531	9	5	dependent	dependent	ADJ
ejpam-2531	9	6	variable	variable	NOUN
ejpam-2531	9	7	is	be	AUX
ejpam-2531	9	8	usually	usually	ADV
ejpam-2531	9	9	measured	measure	VERB
ejpam-2531	9	10	at	at	ADP
ejpam-2531	9	11	a	a	DET
ejpam-2531	9	12	point	point	NOUN
ejpam-2531	9	13	.	.	PUNCT
ejpam-2531	10	1	finding	find	VERB
ejpam-2531	10	2	solutions	solution	NOUN
ejpam-2531	10	3	to	to	ADP
ejpam-2531	10	4	these	these	DET
ejpam-2531	10	5	problems	problem	NOUN
ejpam-2531	10	6	are	be	AUX
ejpam-2531	10	7	often	often	ADV
ejpam-2531	10	8	either	either	CCONJ
ejpam-2531	10	9	difficult	difficult	ADJ
ejpam-2531	10	10	or	or	CCONJ
ejpam-2531	10	11	not	not	PART
ejpam-2531	10	12	feasible	feasible	ADJ
ejpam-2531	10	13	at	at	ADV
ejpam-2531	10	14	all	all	ADV
ejpam-2531	10	15	.	.	PUNCT
ejpam-2531	11	1	there	there	PRON
ejpam-2531	11	2	are	be	VERB
ejpam-2531	11	3	many	many	ADJ
ejpam-2531	11	4	approaches	approach	NOUN
ejpam-2531	11	5	to	to	PART
ejpam-2531	11	6	search	search	VERB
ejpam-2531	11	7	for	for	ADP
ejpam-2531	11	8	solution	solution	NOUN
ejpam-2531	11	9	to	to	ADP
ejpam-2531	11	10	the	the	DET
ejpam-2531	11	11	differential	differential	ADJ
ejpam-2531	11	12	equation	equation	NOUN
ejpam-2531	11	13	.	.	PUNCT
ejpam-2531	12	1	special	special	ADJ
ejpam-2531	12	2	substitution	substitution	NOUN
ejpam-2531	12	3	techniques	technique	NOUN
ejpam-2531	12	4	have	have	AUX
ejpam-2531	12	5	been	be	AUX
ejpam-2531	12	6	adopted	adopt	VERB
ejpam-2531	12	7	in	in	ADP
ejpam-2531	12	8	finding	find	VERB
ejpam-2531	12	9	solution	solution	NOUN
ejpam-2531	12	10	to	to	PART
ejpam-2531	12	11	differential	differential	VERB
ejpam-2531	12	12	equation	equation	NOUN
ejpam-2531	12	13	with	with	ADP
ejpam-2531	12	14	variable	variable	ADJ
ejpam-2531	12	15	coefficients	coefficient	NOUN
ejpam-2531	12	16	.	.	PUNCT
ejpam-2531	13	1	the	the	DET
ejpam-2531	13	2	cauchy	cauchy	PROPN
ejpam-2531	13	3	-	-	PUNCT
ejpam-2531	13	4	euler	euler	NOUN
ejpam-2531	13	5	method	method	NOUN
ejpam-2531	13	6	transforms	transform	VERB
ejpam-2531	13	7	a	a	DET
ejpam-2531	13	8	linear	linear	ADJ
ejpam-2531	13	9	differential	differential	ADJ
ejpam-2531	13	10	equation	equation	NOUN
ejpam-2531	13	11	into	into	ADP
ejpam-2531	13	12	an	an	DET
ejpam-2531	13	13	algebraic	algebraic	ADJ
ejpam-2531	13	14	equation	equation	NOUN
ejpam-2531	13	15	with	with	ADP
ejpam-2531	13	16	the	the	DET
ejpam-2531	13	17	use	use	NOUN
ejpam-2531	13	18	of	of	ADP
ejpam-2531	13	19	appropriate	appropriate	ADJ
ejpam-2531	13	20	substitution	substitution	NOUN
ejpam-2531	13	21	technique	technique	NOUN
ejpam-2531	13	22	.	.	PUNCT
ejpam-2531	14	1	other	other	ADJ
ejpam-2531	14	2	methods	method	NOUN
ejpam-2531	14	3	such	such	ADJ
ejpam-2531	14	4	as	as	ADP
ejpam-2531	14	5	methods	method	NOUN
ejpam-2531	14	6	of	of	ADP
ejpam-2531	14	7	undetermined	undetermined	ADJ
ejpam-2531	14	8	coefficients	coefficient	NOUN
ejpam-2531	14	9	,	,	PUNCT
ejpam-2531	14	10	variation	variation	NOUN
ejpam-2531	14	11	of	of	ADP
ejpam-2531	14	12	parameters	parameter	NOUN
ejpam-2531	14	13	are	be	AUX
ejpam-2531	14	14	limited	limit	VERB
ejpam-2531	14	15	in	in	ADP
ejpam-2531	14	16	usage	usage	NOUN
ejpam-2531	14	17	,	,	PUNCT
ejpam-2531	14	18	see	see	VERB
ejpam-2531	14	19	[	[	X
ejpam-2531	14	20	8	8	NUM
ejpam-2531	14	21	]	]	PUNCT
ejpam-2531	14	22	.	.	PUNCT
ejpam-2531	15	1	in	in	ADP
ejpam-2531	15	2	addition	addition	NOUN
ejpam-2531	15	3	,	,	PUNCT
ejpam-2531	15	4	these	these	DET
ejpam-2531	15	5	classical	classical	ADJ
ejpam-2531	15	6	methods	method	NOUN
ejpam-2531	15	7	for	for	ADP
ejpam-2531	15	8	search	search	NOUN
ejpam-2531	15	9	of	of	ADP
ejpam-2531	15	10	solutions	solution	NOUN
ejpam-2531	15	11	to	to	ADP
ejpam-2531	15	12	the	the	DET
ejpam-2531	15	13	differential	differential	ADJ
ejpam-2531	15	14	equations	equation	NOUN
ejpam-2531	15	15	are	be	AUX
ejpam-2531	15	16	tedious	tedious	ADJ
ejpam-2531	15	17	and	and	CCONJ
ejpam-2531	15	18	cumbersome	cumbersome	ADJ
ejpam-2531	15	19	as	as	ADP
ejpam-2531	15	20	one	one	NUM
ejpam-2531	15	21	has	have	VERB
ejpam-2531	15	22	to	to	PART
ejpam-2531	15	23	look	look	VERB
ejpam-2531	15	24	for	for	ADP
ejpam-2531	15	25	the	the	DET
ejpam-2531	15	26	appropriate	appropriate	ADJ
ejpam-2531	15	27	substitution	substitution	NOUN
ejpam-2531	15	28	expression	expression	NOUN
ejpam-2531	15	29	.	.	PUNCT
ejpam-2531	16	1	thus	thus	ADV
ejpam-2531	16	2	,	,	PUNCT
ejpam-2531	16	3	there	there	PRON
ejpam-2531	16	4	is	be	VERB
ejpam-2531	16	5	no	no	DET
ejpam-2531	16	6	single	single	ADJ
ejpam-2531	16	7	substitution	substitution	NOUN
ejpam-2531	16	8	expression	expression	NOUN
ejpam-2531	16	9	for	for	ADP
ejpam-2531	16	10	a	a	DET
ejpam-2531	16	11	single	single	ADJ
ejpam-2531	16	12	type	type	NOUN
ejpam-2531	16	13	of	of	ADP
ejpam-2531	16	14	differential	differential	ADJ
ejpam-2531	16	15	equation	equation	NOUN
ejpam-2531	16	16	.	.	PUNCT
ejpam-2531	17	1	email	email	NOUN
ejpam-2531	17	2	addresses	address	NOUN
ejpam-2531	17	3	:	:	PUNCT
ejpam-2531	17	4	ewiekwamina@gmail.com	ewiekwamina@gmail.com	X
ejpam-2531	17	5	,	,	PUNCT
ejpam-2531	17	6	fkofi33@yahoomail.com	fkofi33@yahoomail.com	X
ejpam-2531	17	7	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2531	17	8	140	140	NUM
ejpam-2531	18	1	c	c	NOUN
ejpam-2531	18	2	©	©	PROPN
ejpam-2531	18	3	2016	2016	NUM
ejpam-2531	18	4	ejpam	ejpam	VERB
ejpam-2531	18	5	all	all	DET
ejpam-2531	18	6	rights	right	NOUN
ejpam-2531	18	7	reserved	reserve	VERB
ejpam-2531	18	8	.	.	PUNCT
ejpam-2531	19	1	european	european	ADJ
ejpam-2531	19	2	journal	journal	PROPN
ejpam-2531	19	3	of	of	ADP
ejpam-2531	19	4	pure	pure	ADJ
ejpam-2531	19	5	and	and	CCONJ
ejpam-2531	19	6	applied	apply	VERB
ejpam-2531	19	7	mathematics	mathematic	NOUN
ejpam-2531	19	8	vol	vol	NOUN
ejpam-2531	19	9	.	.	PROPN
ejpam-2531	20	1	9	9	NUM
ejpam-2531	20	2	,	,	PUNCT
ejpam-2531	20	3	no	no	INTJ
ejpam-2531	20	4	.	.	NOUN
ejpam-2531	20	5	2	2	NUM
ejpam-2531	20	6	,	,	PUNCT
ejpam-2531	20	7	2016	2016	NUM
ejpam-2531	20	8	,	,	PUNCT
ejpam-2531	20	9	140	140	NUM
ejpam-2531	20	10	-	-	SYM
ejpam-2531	20	11	151	151	NUM
ejpam-2531	20	12	issn	issn	PROPN
ejpam-2531	20	13	1307	1307	NUM
ejpam-2531	20	14	-	-	SYM
ejpam-2531	20	15	5543	5543	NUM
ejpam-2531	20	16	–	–	PUNCT
ejpam-2531	20	17	www.ejpam.com	www.ejpam.com	X
ejpam-2531	20	18	b.	b.	PROPN
ejpam-2531	20	19	barnes	barnes	PROPN
ejpam-2531	20	20	/	/	SYM
ejpam-2531	20	21	eur	eur	PROPN
ejpam-2531	20	22	.	.	PUNCT
ejpam-2531	21	1	j.	j.	PROPN
ejpam-2531	21	2	pure	pure	PROPN
ejpam-2531	21	3	appl	appl	PROPN
ejpam-2531	21	4	.	.	PROPN
ejpam-2531	21	5	math	math	PROPN
ejpam-2531	21	6	,	,	PUNCT
ejpam-2531	21	7	9	9	NUM
ejpam-2531	21	8	(	(	PUNCT
ejpam-2531	21	9	2016	2016	NUM
ejpam-2531	21	10	)	)	PUNCT
ejpam-2531	21	11	,	,	PUNCT
ejpam-2531	21	12	140	140	NUM
ejpam-2531	21	13	-	-	SYM
ejpam-2531	21	14	151	151	NUM
ejpam-2531	21	15	141	141	NUM
ejpam-2531	21	16	currently	currently	ADV
ejpam-2531	21	17	,	,	PUNCT
ejpam-2531	21	18	integral	integral	ADJ
ejpam-2531	21	19	transform	transform	NOUN
ejpam-2531	21	20	method	method	NOUN
ejpam-2531	21	21	is	be	AUX
ejpam-2531	21	22	the	the	DET
ejpam-2531	21	23	concern	concern	NOUN
ejpam-2531	21	24	of	of	ADP
ejpam-2531	21	25	mathematicians	mathematician	NOUN
ejpam-2531	21	26	and	and	CCONJ
ejpam-2531	21	27	scientists	scientist	NOUN
ejpam-2531	21	28	in	in	ADP
ejpam-2531	21	29	general	general	ADJ
ejpam-2531	21	30	.	.	PUNCT
ejpam-2531	22	1	since	since	SCONJ
ejpam-2531	22	2	the	the	DET
ejpam-2531	22	3	introduction	introduction	NOUN
ejpam-2531	22	4	of	of	ADP
ejpam-2531	22	5	the	the	DET
ejpam-2531	22	6	laplace	laplace	NOUN
ejpam-2531	22	7	integral	integral	ADJ
ejpam-2531	22	8	transform	transform	NOUN
ejpam-2531	22	9	,	,	PUNCT
ejpam-2531	22	10	a	a	DET
ejpam-2531	22	11	number	number	NOUN
ejpam-2531	22	12	of	of	ADP
ejpam-2531	22	13	integral	integral	ADJ
ejpam-2531	22	14	transforms	transform	NOUN
ejpam-2531	22	15	have	have	AUX
ejpam-2531	22	16	been	be	AUX
ejpam-2531	22	17	proposed	propose	VERB
ejpam-2531	22	18	for	for	ADP
ejpam-2531	22	19	solving	solve	VERB
ejpam-2531	22	20	differential	differential	ADJ
ejpam-2531	22	21	equations	equation	NOUN
ejpam-2531	22	22	.	.	PUNCT
ejpam-2531	23	1	an	an	DET
ejpam-2531	23	2	alternative	alternative	ADJ
ejpam-2531	23	3	integral	integral	ADJ
ejpam-2531	23	4	transform	transform	NOUN
ejpam-2531	23	5	,	,	PUNCT
ejpam-2531	23	6	laplace	laplace	NOUN
ejpam-2531	23	7	substitution	substitution	NOUN
ejpam-2531	23	8	method	method	NOUN
ejpam-2531	23	9	,	,	PUNCT
ejpam-2531	23	10	for	for	ADP
ejpam-2531	23	11	the	the	DET
ejpam-2531	23	12	construction	construction	NOUN
ejpam-2531	23	13	of	of	ADP
ejpam-2531	23	14	solutions	solution	NOUN
ejpam-2531	23	15	of	of	ADP
ejpam-2531	23	16	the	the	DET
ejpam-2531	23	17	partial	partial	ADJ
ejpam-2531	23	18	differential	differential	NOUN
ejpam-2531	23	19	equations	equation	NOUN
ejpam-2531	23	20	was	be	AUX
ejpam-2531	23	21	observed	observe	VERB
ejpam-2531	23	22	by	by	ADP
ejpam-2531	23	23	[	[	X
ejpam-2531	23	24	11	11	NUM
ejpam-2531	23	25	]	]	PUNCT
ejpam-2531	23	26	.	.	PUNCT
ejpam-2531	24	1	the	the	DET
ejpam-2531	24	2	sumudu	sumudu	NOUN
ejpam-2531	24	3	integral	integral	ADJ
ejpam-2531	24	4	transform	transform	NOUN
ejpam-2531	24	5	f(u	f(u	PROPN
ejpam-2531	24	6	)	)	PUNCT
ejpam-2531	24	7	=	=	SYM
ejpam-2531	25	1	s	s	X
ejpam-2531	25	2	[	[	PUNCT
ejpam-2531	25	3	f	f	X
ejpam-2531	25	4	(	(	PUNCT
ejpam-2531	25	5	t	t	PROPN
ejpam-2531	25	6	)	)	PUNCT
ejpam-2531	25	7	;	;	PUNCT
ejpam-2531	26	1	u	u	SYM
ejpam-2531	26	2	]	]	X
ejpam-2531	26	3	=	=	SYM
ejpam-2531	26	4	1	1	NUM
ejpam-2531	26	5	u	u	NOUN
ejpam-2531	26	6	∫	∫	PROPN
ejpam-2531	26	7	∞	∞	NOUN
ejpam-2531	26	8	0	0	NUM
ejpam-2531	27	1	e−	e−	PROPN
ejpam-2531	27	2	t	t	PROPN
ejpam-2531	27	3	u	u	X
ejpam-2531	27	4	f	f	PROPN
ejpam-2531	27	5	(	(	PUNCT
ejpam-2531	27	6	t)d	t)d	PROPN
ejpam-2531	27	7	t	t	PROPN
ejpam-2531	27	8	,	,	PUNCT
ejpam-2531	27	9	u	u	PROPN
ejpam-2531	27	10	∈	∈	PROPN
ejpam-2531	27	11	(	(	PUNCT
ejpam-2531	27	12	−τ	−τ	PROPN
ejpam-2531	27	13	,	,	PUNCT
ejpam-2531	27	14	τ	τ	PROPN
ejpam-2531	27	15	)	)	PUNCT
ejpam-2531	27	16	.	.	PUNCT
ejpam-2531	28	1	was	be	AUX
ejpam-2531	28	2	proposed	propose	VERB
ejpam-2531	28	3	by	by	ADP
ejpam-2531	28	4	[	[	X
ejpam-2531	28	5	15	15	NUM
ejpam-2531	28	6	]	]	PUNCT
ejpam-2531	28	7	and	and	CCONJ
ejpam-2531	28	8	applied	apply	VERB
ejpam-2531	28	9	to	to	ADP
ejpam-2531	28	10	some	some	DET
ejpam-2531	28	11	controlled	control	VERB
ejpam-2531	28	12	problems	problem	NOUN
ejpam-2531	28	13	in	in	ADP
ejpam-2531	28	14	engineering	engineering	NOUN
ejpam-2531	28	15	.	.	PUNCT
ejpam-2531	29	1	this	this	DET
ejpam-2531	29	2	method	method	NOUN
ejpam-2531	29	3	faces	face	VERB
ejpam-2531	29	4	the	the	DET
ejpam-2531	29	5	similar	similar	ADJ
ejpam-2531	29	6	challenges	challenge	NOUN
ejpam-2531	29	7	as	as	ADP
ejpam-2531	29	8	the	the	DET
ejpam-2531	29	9	laplace	laplace	NOUN
ejpam-2531	29	10	integral	integral	ADJ
ejpam-2531	29	11	transform	transform	NOUN
ejpam-2531	29	12	.	.	PUNCT
ejpam-2531	30	1	thus	thus	ADV
ejpam-2531	30	2	,	,	PUNCT
ejpam-2531	30	3	sumudu	sumudu	VERB
ejpam-2531	30	4	integral	integral	ADJ
ejpam-2531	30	5	transform	transform	NOUN
ejpam-2531	30	6	solves	solve	VERB
ejpam-2531	30	7	a	a	DET
ejpam-2531	30	8	linear	linear	ADJ
ejpam-2531	30	9	differential	differential	ADJ
ejpam-2531	30	10	equation	equation	NOUN
ejpam-2531	30	11	with	with	ADP
ejpam-2531	30	12	constant	constant	ADJ
ejpam-2531	30	13	coefficients	coefficient	NOUN
ejpam-2531	30	14	.	.	PUNCT
ejpam-2531	31	1	the	the	DET
ejpam-2531	31	2	author	author	NOUN
ejpam-2531	31	3	in	in	ADP
ejpam-2531	31	4	[	[	X
ejpam-2531	31	5	4	4	NUM
ejpam-2531	31	6	]	]	PUNCT
ejpam-2531	31	7	,	,	PUNCT
ejpam-2531	31	8	observed	observe	VERB
ejpam-2531	31	9	some	some	DET
ejpam-2531	31	10	properties	property	NOUN
ejpam-2531	31	11	of	of	ADP
ejpam-2531	31	12	the	the	DET
ejpam-2531	31	13	sumudu	sumudu	NOUN
ejpam-2531	31	14	integral	integral	ADJ
ejpam-2531	31	15	transform	transform	NOUN
ejpam-2531	31	16	.	.	PUNCT
ejpam-2531	32	1	several	several	ADJ
ejpam-2531	32	2	studies	study	NOUN
ejpam-2531	32	3	have	have	AUX
ejpam-2531	32	4	made	make	VERB
ejpam-2531	32	5	use	use	NOUN
ejpam-2531	32	6	of	of	ADP
ejpam-2531	32	7	the	the	DET
ejpam-2531	32	8	sumudu	sumudu	NOUN
ejpam-2531	32	9	integral	integral	ADJ
ejpam-2531	32	10	transform	transform	NOUN
ejpam-2531	32	11	to	to	PART
ejpam-2531	32	12	obtain	obtain	VERB
ejpam-2531	32	13	the	the	DET
ejpam-2531	32	14	solutions	solution	NOUN
ejpam-2531	32	15	of	of	ADP
ejpam-2531	32	16	the	the	DET
ejpam-2531	32	17	differential	differential	ADJ
ejpam-2531	32	18	equations	equation	NOUN
ejpam-2531	32	19	.	.	PUNCT
ejpam-2531	33	1	for	for	ADP
ejpam-2531	33	2	example	example	NOUN
ejpam-2531	33	3	,	,	PUNCT
ejpam-2531	33	4	see	see	VERB
ejpam-2531	33	5	research	research	NOUN
ejpam-2531	33	6	papers	paper	NOUN
ejpam-2531	33	7	by	by	ADP
ejpam-2531	33	8	[	[	X
ejpam-2531	33	9	5	5	NUM
ejpam-2531	33	10	,	,	PUNCT
ejpam-2531	33	11	6	6	NUM
ejpam-2531	33	12	,	,	PUNCT
ejpam-2531	33	13	9	9	NUM
ejpam-2531	33	14	]	]	PUNCT
ejpam-2531	33	15	.	.	PUNCT
ejpam-2531	34	1	recently	recently	ADV
ejpam-2531	34	2	,	,	PUNCT
ejpam-2531	34	3	in	in	ADP
ejpam-2531	34	4	[	[	X
ejpam-2531	34	5	10	10	NUM
ejpam-2531	34	6	]	]	PUNCT
ejpam-2531	34	7	,	,	PUNCT
ejpam-2531	34	8	they	they	PRON
ejpam-2531	34	9	compared	compare	VERB
ejpam-2531	34	10	both	both	CCONJ
ejpam-2531	34	11	the	the	DET
ejpam-2531	34	12	laplace	laplace	NOUN
ejpam-2531	34	13	integral	integral	ADJ
ejpam-2531	34	14	transform	transform	NOUN
ejpam-2531	34	15	and	and	CCONJ
ejpam-2531	34	16	sumudu	sumudu	VERB
ejpam-2531	34	17	integral	integral	ADJ
ejpam-2531	34	18	transforms	transform	NOUN
ejpam-2531	34	19	.	.	PUNCT
ejpam-2531	35	1	in	in	ADP
ejpam-2531	35	2	[	[	X
ejpam-2531	35	3	12	12	NUM
ejpam-2531	35	4	]	]	PUNCT
ejpam-2531	35	5	,	,	PUNCT
ejpam-2531	35	6	the	the	DET
ejpam-2531	35	7	authors	author	NOUN
ejpam-2531	35	8	introduced	introduce	VERB
ejpam-2531	35	9	the	the	DET
ejpam-2531	35	10	natural	natural	ADJ
ejpam-2531	35	11	integral	integral	ADJ
ejpam-2531	35	12	transform	transform	NOUN
ejpam-2531	35	13	and	and	CCONJ
ejpam-2531	35	14	applied	apply	VERB
ejpam-2531	35	15	it	it	PRON
ejpam-2531	35	16	to	to	PART
ejpam-2531	35	17	obtain	obtain	VERB
ejpam-2531	35	18	solutions	solution	NOUN
ejpam-2531	35	19	of	of	ADP
ejpam-2531	35	20	the	the	DET
ejpam-2531	35	21	differential	differential	ADJ
ejpam-2531	35	22	equations	equation	NOUN
ejpam-2531	35	23	.	.	PUNCT
ejpam-2531	36	1	unlike	unlike	ADP
ejpam-2531	36	2	the	the	DET
ejpam-2531	36	3	laplace	laplace	NOUN
ejpam-2531	36	4	and	and	CCONJ
ejpam-2531	36	5	sumudu	sumudu	VERB
ejpam-2531	36	6	integral	integral	ADJ
ejpam-2531	36	7	transforms	transform	NOUN
ejpam-2531	36	8	,	,	PUNCT
ejpam-2531	36	9	the	the	DET
ejpam-2531	36	10	natural	natural	ADJ
ejpam-2531	36	11	integral	integral	ADJ
ejpam-2531	36	12	transform	transform	NOUN
ejpam-2531	36	13	entails	entail	VERB
ejpam-2531	36	14	k(u	k(u	NOUN
ejpam-2531	36	15	,	,	PUNCT
ejpam-2531	36	16	v	v	NOUN
ejpam-2531	36	17	,	,	PUNCT
ejpam-2531	36	18	x	x	NOUN
ejpam-2531	36	19	)	)	PUNCT
ejpam-2531	36	20	=	=	SYM
ejpam-2531	36	21	e−	e−	PROPN
ejpam-2531	36	22	vx	vx	PROPN
ejpam-2531	36	23	u	u	PROPN
ejpam-2531	36	24	,	,	PUNCT
ejpam-2531	36	25	where	where	SCONJ
ejpam-2531	36	26	u	u	NOUN
ejpam-2531	36	27	and	and	CCONJ
ejpam-2531	36	28	v	v	NOUN
ejpam-2531	36	29	are	be	AUX
ejpam-2531	36	30	parameters	parameter	NOUN
ejpam-2531	36	31	,	,	PUNCT
ejpam-2531	36	32	as	as	ADP
ejpam-2531	36	33	its	its	PRON
ejpam-2531	36	34	kernel	kernel	NOUN
ejpam-2531	36	35	,	,	PUNCT
ejpam-2531	36	36	which	which	PRON
ejpam-2531	36	37	transforms	transform	VERB
ejpam-2531	36	38	a	a	DET
ejpam-2531	36	39	linear	linear	ADJ
ejpam-2531	36	40	differential	differential	ADJ
ejpam-2531	36	41	equation	equation	NOUN
ejpam-2531	36	42	into	into	ADP
ejpam-2531	36	43	an	an	DET
ejpam-2531	36	44	algebraic	algebraic	ADJ
ejpam-2531	36	45	equation	equation	NOUN
ejpam-2531	36	46	.	.	PUNCT
ejpam-2531	37	1	the	the	DET
ejpam-2531	37	2	duality	duality	NOUN
ejpam-2531	37	3	of	of	ADP
ejpam-2531	37	4	both	both	CCONJ
ejpam-2531	37	5	the	the	DET
ejpam-2531	37	6	natural	natural	ADJ
ejpam-2531	37	7	and	and	CCONJ
ejpam-2531	37	8	laplace	laplace	NOUN
ejpam-2531	37	9	integral	integral	ADJ
ejpam-2531	37	10	transforms	transform	NOUN
ejpam-2531	37	11	was	be	AUX
ejpam-2531	37	12	studied	study	VERB
ejpam-2531	37	13	by	by	ADP
ejpam-2531	37	14	[	[	X
ejpam-2531	37	15	7	7	NUM
ejpam-2531	37	16	]	]	PUNCT
ejpam-2531	37	17	.	.	PUNCT
ejpam-2531	38	1	using	use	VERB
ejpam-2531	38	2	the	the	DET
ejpam-2531	38	3	natural	natural	ADJ
ejpam-2531	38	4	integral	integral	ADJ
ejpam-2531	38	5	transform	transform	NOUN
ejpam-2531	38	6	,	,	PUNCT
ejpam-2531	38	7	[	[	X
ejpam-2531	38	8	2	2	NUM
ejpam-2531	38	9	]	]	PUNCT
ejpam-2531	38	10	sought	seek	VERB
ejpam-2531	38	11	the	the	DET
ejpam-2531	38	12	solution	solution	NOUN
ejpam-2531	38	13	of	of	ADP
ejpam-2531	38	14	differential	differential	ADJ
ejpam-2531	38	15	equation	equation	NOUN
ejpam-2531	38	16	on	on	ADP
ejpam-2531	38	17	the	the	DET
ejpam-2531	38	18	spaces	space	NOUN
ejpam-2531	38	19	of	of	ADP
ejpam-2531	38	20	generalized	generalized	ADJ
ejpam-2531	38	21	functions	function	NOUN
ejpam-2531	38	22	.	.	PUNCT
ejpam-2531	39	1	also	also	ADV
ejpam-2531	39	2	,	,	PUNCT
ejpam-2531	39	3	in	in	ADP
ejpam-2531	39	4	[	[	PUNCT
ejpam-2531	39	5	1	1	NUM
ejpam-2531	39	6	]	]	PUNCT
ejpam-2531	39	7	,	,	PUNCT
ejpam-2531	39	8	the	the	DET
ejpam-2531	39	9	author	author	NOUN
ejpam-2531	39	10	extended	extend	VERB
ejpam-2531	39	11	the	the	DET
ejpam-2531	39	12	applications	application	NOUN
ejpam-2531	39	13	of	of	ADP
ejpam-2531	39	14	the	the	DET
ejpam-2531	39	15	hartley	hartley	PROPN
ejpam-2531	39	16	transform	transform	NOUN
ejpam-2531	39	17	of	of	ADP
ejpam-2531	39	18	differential	differential	ADJ
ejpam-2531	39	19	equation	equation	NOUN
ejpam-2531	39	20	on	on	ADP
ejpam-2531	39	21	the	the	DET
ejpam-2531	39	22	space	space	NOUN
ejpam-2531	39	23	of	of	ADP
ejpam-2531	39	24	the	the	DET
ejpam-2531	39	25	generalized	generalize	VERB
ejpam-2531	39	26	functions	function	NOUN
ejpam-2531	39	27	.	.	PUNCT
ejpam-2531	40	1	in	in	ADP
ejpam-2531	40	2	order	order	NOUN
ejpam-2531	40	3	to	to	PART
ejpam-2531	40	4	ensure	ensure	VERB
ejpam-2531	40	5	the	the	DET
ejpam-2531	40	6	rapid	rapid	ADJ
ejpam-2531	40	7	convergence	convergence	NOUN
ejpam-2531	40	8	of	of	ADP
ejpam-2531	40	9	solution	solution	NOUN
ejpam-2531	40	10	of	of	ADP
ejpam-2531	40	11	the	the	DET
ejpam-2531	40	12	differential	differential	ADJ
ejpam-2531	40	13	equation	equation	NOUN
ejpam-2531	40	14	,	,	PUNCT
ejpam-2531	40	15	the	the	DET
ejpam-2531	40	16	fresnel	fresnel	ADJ
ejpam-2531	40	17	integral	integral	ADJ
ejpam-2531	40	18	transform	transform	NOUN
ejpam-2531	40	19	with	with	ADP
ejpam-2531	40	20	variables	variable	NOUN
ejpam-2531	40	21	in	in	ADP
ejpam-2531	40	22	the	the	DET
ejpam-2531	40	23	boehmains	boehmain	NOUN
ejpam-2531	40	24	space	space	NOUN
ejpam-2531	40	25	has	have	AUX
ejpam-2531	40	26	been	be	AUX
ejpam-2531	40	27	obtained	obtain	VERB
ejpam-2531	40	28	.	.	PUNCT
ejpam-2531	41	1	for	for	ADP
ejpam-2531	41	2	example	example	NOUN
ejpam-2531	41	3	,	,	PUNCT
ejpam-2531	41	4	see	see	VERB
ejpam-2531	41	5	a	a	DET
ejpam-2531	41	6	research	research	NOUN
ejpam-2531	41	7	paper	paper	NOUN
ejpam-2531	41	8	by	by	ADP
ejpam-2531	41	9	[	[	X
ejpam-2531	41	10	3	3	NUM
ejpam-2531	41	11	]	]	PUNCT
ejpam-2531	41	12	.	.	PUNCT
ejpam-2531	42	1	on	on	ADP
ejpam-2531	42	2	the	the	DET
ejpam-2531	42	3	contrary	contrary	NOUN
ejpam-2531	42	4	,	,	PUNCT
ejpam-2531	42	5	the	the	DET
ejpam-2531	42	6	integral	integral	ADJ
ejpam-2531	42	7	transform	transform	NOUN
ejpam-2531	42	8	method	method	NOUN
ejpam-2531	42	9	for	for	ADP
ejpam-2531	42	10	the	the	DET
ejpam-2531	42	11	fractional	fractional	ADJ
ejpam-2531	42	12	difference	difference	NOUN
ejpam-2531	42	13	equation	equation	NOUN
ejpam-2531	42	14	has	have	AUX
ejpam-2531	42	15	been	be	AUX
ejpam-2531	42	16	obtained	obtain	VERB
ejpam-2531	42	17	.	.	PUNCT
ejpam-2531	43	1	the	the	DET
ejpam-2531	43	2	authors	author	NOUN
ejpam-2531	43	3	in	in	ADP
ejpam-2531	43	4	[	[	X
ejpam-2531	43	5	14	14	NUM
ejpam-2531	43	6	]	]	PUNCT
ejpam-2531	43	7	,	,	PUNCT
ejpam-2531	43	8	implemented	implement	VERB
ejpam-2531	43	9	the	the	DET
ejpam-2531	43	10	s	s	NOUN
ejpam-2531	43	11	-	-	PUNCT
ejpam-2531	43	12	transforms	transform	VERB
ejpam-2531	43	13	for	for	ADP
ejpam-2531	43	14	solving	solve	VERB
ejpam-2531	43	15	such	such	ADJ
ejpam-2531	43	16	problems	problem	NOUN
ejpam-2531	43	17	in	in	ADP
ejpam-2531	43	18	engineering	engineering	NOUN
ejpam-2531	43	19	.	.	PUNCT
ejpam-2531	44	1	we	we	PRON
ejpam-2531	44	2	outline	outline	VERB
ejpam-2531	44	3	of	of	ADP
ejpam-2531	44	4	this	this	DET
ejpam-2531	44	5	paper	paper	NOUN
ejpam-2531	44	6	is	be	AUX
ejpam-2531	44	7	as	as	SCONJ
ejpam-2531	44	8	follows	follow	VERB
ejpam-2531	44	9	.	.	PUNCT
ejpam-2531	45	1	in	in	ADP
ejpam-2531	45	2	section	section	NOUN
ejpam-2531	45	3	1	1	NUM
ejpam-2531	45	4	,	,	PUNCT
ejpam-2531	45	5	we	we	PRON
ejpam-2531	45	6	give	give	VERB
ejpam-2531	45	7	the	the	DET
ejpam-2531	45	8	introduction	introduction	NOUN
ejpam-2531	45	9	to	to	ADP
ejpam-2531	45	10	integral	integral	ADJ
ejpam-2531	45	11	transform	transform	NOUN
ejpam-2531	45	12	methods	method	NOUN
ejpam-2531	45	13	.	.	PUNCT
ejpam-2531	46	1	in	in	ADP
ejpam-2531	46	2	this	this	DET
ejpam-2531	46	3	section	section	NOUN
ejpam-2531	46	4	,	,	PUNCT
ejpam-2531	46	5	we	we	PRON
ejpam-2531	46	6	discuss	discuss	VERB
ejpam-2531	46	7	the	the	DET
ejpam-2531	46	8	integral	integral	ADJ
ejpam-2531	46	9	transform	transform	NOUN
ejpam-2531	46	10	methods	method	NOUN
ejpam-2531	46	11	for	for	ADP
ejpam-2531	46	12	solving	solve	VERB
ejpam-2531	46	13	differential	differential	ADJ
ejpam-2531	46	14	equations	equation	NOUN
ejpam-2531	46	15	.	.	PUNCT
ejpam-2531	47	1	in	in	ADP
ejpam-2531	47	2	section	section	NOUN
ejpam-2531	47	3	2	2	NUM
ejpam-2531	47	4	,	,	PUNCT
ejpam-2531	47	5	we	we	PRON
ejpam-2531	47	6	present	present	VERB
ejpam-2531	47	7	the	the	DET
ejpam-2531	47	8	definition	definition	NOUN
ejpam-2531	47	9	and	and	CCONJ
ejpam-2531	47	10	also	also	ADV
ejpam-2531	47	11	,	,	PUNCT
ejpam-2531	47	12	give	give	VERB
ejpam-2531	47	13	the	the	DET
ejpam-2531	47	14	proof	proof	NOUN
ejpam-2531	47	15	for	for	ADP
ejpam-2531	47	16	the	the	DET
ejpam-2531	47	17	polynomial	polynomial	ADJ
ejpam-2531	47	18	integral	integral	ADJ
ejpam-2531	47	19	transform	transform	NOUN
ejpam-2531	47	20	.	.	PUNCT
ejpam-2531	48	1	using	use	VERB
ejpam-2531	48	2	the	the	DET
ejpam-2531	48	3	polynomial	polynomial	ADJ
ejpam-2531	48	4	integral	integral	ADJ
ejpam-2531	48	5	transform	transform	NOUN
ejpam-2531	48	6	,	,	PUNCT
ejpam-2531	48	7	we	we	PRON
ejpam-2531	48	8	show	show	VERB
ejpam-2531	48	9	that	that	SCONJ
ejpam-2531	48	10	the	the	DET
ejpam-2531	48	11	solution	solution	NOUN
ejpam-2531	48	12	of	of	ADP
ejpam-2531	48	13	the	the	DET
ejpam-2531	48	14	differential	differential	ADJ
ejpam-2531	48	15	equation	equation	NOUN
ejpam-2531	48	16	converges	converge	VERB
ejpam-2531	48	17	for	for	ADP
ejpam-2531	48	18	x	x	PROPN
ejpam-2531	48	19	∈	∈	PROPN
ejpam-2531	48	20	[	[	X
ejpam-2531	48	21	1,∞	1,∞	NUM
ejpam-2531	48	22	)	)	PUNCT
ejpam-2531	48	23	.	.	PUNCT
ejpam-2531	49	1	the	the	DET
ejpam-2531	49	2	properties	property	NOUN
ejpam-2531	49	3	of	of	ADP
ejpam-2531	49	4	the	the	DET
ejpam-2531	49	5	polynomial	polynomial	ADJ
ejpam-2531	49	6	integral	integral	ADJ
ejpam-2531	49	7	transform	transform	NOUN
ejpam-2531	49	8	is	be	AUX
ejpam-2531	49	9	contained	contain	VERB
ejpam-2531	49	10	in	in	ADP
ejpam-2531	49	11	section	section	NOUN
ejpam-2531	49	12	3	3	NUM
ejpam-2531	49	13	.	.	PUNCT
ejpam-2531	50	1	in	in	ADP
ejpam-2531	50	2	section	section	NOUN
ejpam-2531	50	3	4	4	NUM
ejpam-2531	50	4	,	,	PUNCT
ejpam-2531	50	5	we	we	PRON
ejpam-2531	50	6	apply	apply	VERB
ejpam-2531	50	7	the	the	DET
ejpam-2531	50	8	polynomial	polynomial	ADJ
ejpam-2531	50	9	integral	integral	ADJ
ejpam-2531	50	10	transform	transform	NOUN
ejpam-2531	50	11	to	to	ADP
ejpam-2531	50	12	derivatives	derivative	NOUN
ejpam-2531	50	13	,	,	PUNCT
ejpam-2531	50	14	some	some	DET
ejpam-2531	50	15	ordinary	ordinary	ADJ
ejpam-2531	50	16	differential	differential	ADJ
ejpam-2531	50	17	equations	equation	NOUN
ejpam-2531	50	18	and	and	CCONJ
ejpam-2531	50	19	partial	partial	ADJ
ejpam-2531	50	20	differential	differential	NOUN
ejpam-2531	50	21	equation	equation	NOUN
ejpam-2531	50	22	.	.	PUNCT
ejpam-2531	51	1	section	section	NOUN
ejpam-2531	51	2	5	5	NUM
ejpam-2531	51	3	contains	contain	VERB
ejpam-2531	51	4	the	the	DET
ejpam-2531	51	5	conclusion	conclusion	NOUN
ejpam-2531	51	6	of	of	ADP
ejpam-2531	51	7	this	this	DET
ejpam-2531	51	8	paper	paper	NOUN
ejpam-2531	51	9	.	.	PUNCT
ejpam-2531	52	1	b.	b.	PROPN
ejpam-2531	52	2	barnes	barnes	PROPN
ejpam-2531	52	3	/	/	SYM
ejpam-2531	52	4	eur	eur	PROPN
ejpam-2531	52	5	.	.	PUNCT
ejpam-2531	53	1	j.	j.	PROPN
ejpam-2531	53	2	pure	pure	PROPN
ejpam-2531	53	3	appl	appl	PROPN
ejpam-2531	53	4	.	.	PROPN
ejpam-2531	53	5	math	math	PROPN
ejpam-2531	53	6	,	,	PUNCT
ejpam-2531	53	7	9	9	NUM
ejpam-2531	53	8	(	(	PUNCT
ejpam-2531	53	9	2016	2016	NUM
ejpam-2531	53	10	)	)	PUNCT
ejpam-2531	53	11	,	,	PUNCT
ejpam-2531	53	12	140	140	NUM
ejpam-2531	53	13	-	-	SYM
ejpam-2531	53	14	151	151	NUM
ejpam-2531	53	15	142	142	NUM
ejpam-2531	53	16	2	2	NUM
ejpam-2531	53	17	.	.	PUNCT
ejpam-2531	54	1	the	the	DET
ejpam-2531	54	2	polynomial	polynomial	ADJ
ejpam-2531	54	3	integral	integral	ADJ
ejpam-2531	54	4	transform	transform	NOUN
ejpam-2531	54	5	in	in	ADP
ejpam-2531	54	6	the	the	DET
ejpam-2531	54	7	previous	previous	ADJ
ejpam-2531	54	8	section	section	NOUN
ejpam-2531	54	9	,	,	PUNCT
ejpam-2531	54	10	we	we	PRON
ejpam-2531	54	11	observed	observe	VERB
ejpam-2531	54	12	that	that	SCONJ
ejpam-2531	54	13	the	the	DET
ejpam-2531	54	14	discussed	discuss	VERB
ejpam-2531	54	15	integral	integral	ADJ
ejpam-2531	54	16	transforms	transform	NOUN
ejpam-2531	54	17	are	be	AUX
ejpam-2531	54	18	either	either	CCONJ
ejpam-2531	54	19	prototypes	prototype	NOUN
ejpam-2531	54	20	or	or	CCONJ
ejpam-2531	54	21	have	have	VERB
ejpam-2531	54	22	almost	almost	ADV
ejpam-2531	54	23	the	the	DET
ejpam-2531	54	24	same	same	ADJ
ejpam-2531	54	25	applicabilities	applicability	NOUN
ejpam-2531	54	26	as	as	ADP
ejpam-2531	54	27	the	the	DET
ejpam-2531	54	28	laplace	laplace	NOUN
ejpam-2531	54	29	integral	integral	ADJ
ejpam-2531	54	30	transform	transform	NOUN
ejpam-2531	54	31	.	.	PUNCT
ejpam-2531	55	1	in	in	ADP
ejpam-2531	55	2	addition	addition	NOUN
ejpam-2531	55	3	,	,	PUNCT
ejpam-2531	55	4	almost	almost	ADV
ejpam-2531	55	5	all	all	PRON
ejpam-2531	55	6	of	of	ADP
ejpam-2531	55	7	these	these	DET
ejpam-2531	55	8	integral	integral	ADJ
ejpam-2531	55	9	transforms	transform	NOUN
ejpam-2531	55	10	use	use	VERB
ejpam-2531	55	11	exponential	exponential	ADJ
ejpam-2531	55	12	function	function	NOUN
ejpam-2531	55	13	of	of	ADP
ejpam-2531	55	14	parameter(s	parameter(s	NOUN
ejpam-2531	55	15	)	)	PUNCT
ejpam-2531	55	16	as	as	ADP
ejpam-2531	55	17	their	their	PRON
ejpam-2531	55	18	kernels	kernel	NOUN
ejpam-2531	55	19	.	.	PUNCT
ejpam-2531	56	1	using	use	VERB
ejpam-2531	56	2	the	the	DET
ejpam-2531	56	3	exponential	exponential	ADJ
ejpam-2531	56	4	function	function	NOUN
ejpam-2531	56	5	kernel	kernel	NOUN
ejpam-2531	56	6	does	do	AUX
ejpam-2531	56	7	not	not	PART
ejpam-2531	56	8	only	only	ADV
ejpam-2531	56	9	requires	require	VERB
ejpam-2531	56	10	complex	complex	ADJ
ejpam-2531	56	11	mathematical	mathematical	ADJ
ejpam-2531	56	12	structures	structure	NOUN
ejpam-2531	56	13	but	but	CCONJ
ejpam-2531	56	14	also	also	ADV
ejpam-2531	56	15	takes	take	VERB
ejpam-2531	56	16	a	a	DET
ejpam-2531	56	17	long	long	ADJ
ejpam-2531	56	18	time	time	NOUN
ejpam-2531	56	19	before	before	SCONJ
ejpam-2531	56	20	the	the	DET
ejpam-2531	56	21	solution	solution	NOUN
ejpam-2531	56	22	is	be	AUX
ejpam-2531	56	23	obtained	obtain	VERB
ejpam-2531	56	24	.	.	PUNCT
ejpam-2531	57	1	one	one	NUM
ejpam-2531	57	2	of	of	ADP
ejpam-2531	57	3	the	the	DET
ejpam-2531	57	4	interesting	interesting	ADJ
ejpam-2531	57	5	papers	paper	NOUN
ejpam-2531	57	6	which	which	PRON
ejpam-2531	57	7	has	have	AUX
ejpam-2531	57	8	drawn	draw	VERB
ejpam-2531	57	9	much	much	ADJ
ejpam-2531	57	10	attention	attention	NOUN
ejpam-2531	57	11	in	in	ADP
ejpam-2531	57	12	the	the	DET
ejpam-2531	57	13	21st	21st	ADJ
ejpam-2531	57	14	century	century	NOUN
ejpam-2531	57	15	is	be	AUX
ejpam-2531	57	16	the	the	DET
ejpam-2531	57	17	one	one	NOUN
ejpam-2531	57	18	given	give	VERB
ejpam-2531	57	19	by	by	ADP
ejpam-2531	57	20	[	[	PUNCT
ejpam-2531	57	21	13	13	NUM
ejpam-2531	57	22	]	]	PUNCT
ejpam-2531	57	23	.	.	PUNCT
ejpam-2531	58	1	using	use	VERB
ejpam-2531	58	2	the	the	DET
ejpam-2531	58	3	mellin	mellin	ADJ
ejpam-2531	58	4	-	-	PUNCT
ejpam-2531	58	5	barnes	barne	NOUN
ejpam-2531	58	6	integrals	integral	NOUN
ejpam-2531	58	7	poses	pose	VERB
ejpam-2531	58	8	the	the	DET
ejpam-2531	58	9	similar	similar	ADJ
ejpam-2531	58	10	challenges	challenge	NOUN
ejpam-2531	58	11	as	as	ADP
ejpam-2531	58	12	the	the	DET
ejpam-2531	58	13	laplace	laplace	NOUN
ejpam-2531	58	14	integral	integral	ADJ
ejpam-2531	58	15	transform	transform	NOUN
ejpam-2531	58	16	and	and	CCONJ
ejpam-2531	58	17	its	its	PRON
ejpam-2531	58	18	prototypes	prototype	NOUN
ejpam-2531	58	19	.	.	PUNCT
ejpam-2531	59	1	an	an	DET
ejpam-2531	59	2	integral	integral	ADJ
ejpam-2531	59	3	transform	transform	NOUN
ejpam-2531	59	4	which	which	PRON
ejpam-2531	59	5	uses	use	VERB
ejpam-2531	59	6	polynomial	polynomial	ADJ
ejpam-2531	59	7	function	function	NOUN
ejpam-2531	59	8	as	as	SCONJ
ejpam-2531	59	9	its	its	PRON
ejpam-2531	59	10	kernel	kernel	NOUN
ejpam-2531	59	11	requires	require	VERB
ejpam-2531	59	12	a	a	DET
ejpam-2531	59	13	few	few	ADJ
ejpam-2531	59	14	time	time	NOUN
ejpam-2531	59	15	for	for	ADP
ejpam-2531	59	16	computation	computation	NOUN
ejpam-2531	59	17	as	as	ADV
ejpam-2531	59	18	well	well	ADV
ejpam-2531	59	19	as	as	ADP
ejpam-2531	59	20	the	the	DET
ejpam-2531	59	21	convergence	convergence	NOUN
ejpam-2531	59	22	of	of	ADP
ejpam-2531	59	23	the	the	DET
ejpam-2531	59	24	solution	solution	NOUN
ejpam-2531	59	25	of	of	ADP
ejpam-2531	59	26	the	the	DET
ejpam-2531	59	27	differential	differential	ADJ
ejpam-2531	59	28	equation	equation	NOUN
ejpam-2531	59	29	.	.	PUNCT
ejpam-2531	60	1	in	in	ADP
ejpam-2531	60	2	this	this	DET
ejpam-2531	60	3	paper	paper	NOUN
ejpam-2531	60	4	,	,	PUNCT
ejpam-2531	60	5	we	we	PRON
ejpam-2531	60	6	introduce	introduce	VERB
ejpam-2531	60	7	a	a	DET
ejpam-2531	60	8	polynomial	polynomial	ADJ
ejpam-2531	60	9	integral	integral	ADJ
ejpam-2531	60	10	transform	transform	NOUN
ejpam-2531	60	11	to	to	PART
ejpam-2531	60	12	solve	solve	VERB
ejpam-2531	60	13	differential	differential	ADJ
ejpam-2531	60	14	equations	equation	NOUN
ejpam-2531	60	15	in	in	ADP
ejpam-2531	60	16	hilbert	hilbert	PROPN
ejpam-2531	60	17	space	space	NOUN
ejpam-2531	60	18	.	.	PUNCT
ejpam-2531	61	1	this	this	DET
ejpam-2531	61	2	method	method	NOUN
ejpam-2531	61	3	entails	entail	VERB
ejpam-2531	61	4	a	a	DET
ejpam-2531	61	5	polynomial	polynomial	ADJ
ejpam-2531	61	6	function	function	NOUN
ejpam-2531	61	7	as	as	SCONJ
ejpam-2531	61	8	its	its	PRON
ejpam-2531	61	9	kernel	kernel	NOUN
ejpam-2531	61	10	to	to	PART
ejpam-2531	61	11	transform	transform	VERB
ejpam-2531	61	12	the	the	DET
ejpam-2531	61	13	differential	differential	ADJ
ejpam-2531	61	14	equation	equation	NOUN
ejpam-2531	61	15	into	into	ADP
ejpam-2531	61	16	the	the	DET
ejpam-2531	61	17	algebraic	algebraic	ADJ
ejpam-2531	61	18	equation	equation	NOUN
ejpam-2531	61	19	.	.	PUNCT
ejpam-2531	62	1	the	the	DET
ejpam-2531	62	2	algebraic	algebraic	ADJ
ejpam-2531	62	3	equation	equation	NOUN
ejpam-2531	62	4	is	be	AUX
ejpam-2531	62	5	then	then	ADV
ejpam-2531	62	6	solved	solve	VERB
ejpam-2531	62	7	to	to	PART
ejpam-2531	62	8	obtain	obtain	VERB
ejpam-2531	62	9	the	the	DET
ejpam-2531	62	10	solution	solution	NOUN
ejpam-2531	62	11	of	of	ADP
ejpam-2531	62	12	the	the	DET
ejpam-2531	62	13	differential	differential	ADJ
ejpam-2531	62	14	equation	equation	NOUN
ejpam-2531	62	15	.	.	PUNCT
ejpam-2531	63	1	we	we	PRON
ejpam-2531	63	2	state	state	VERB
ejpam-2531	63	3	the	the	DET
ejpam-2531	63	4	polynomial	polynomial	ADJ
ejpam-2531	63	5	integral	integral	ADJ
ejpam-2531	63	6	transform	transform	NOUN
ejpam-2531	63	7	theorem	theorem	NOUN
ejpam-2531	63	8	for	for	ADP
ejpam-2531	63	9	the	the	DET
ejpam-2531	63	10	ordinary	ordinary	ADJ
ejpam-2531	63	11	differential	differential	ADJ
ejpam-2531	63	12	equation	equation	NOUN
ejpam-2531	63	13	.	.	PUNCT
ejpam-2531	64	1	theorem	theorem	NOUN
ejpam-2531	64	2	1	1	NUM
ejpam-2531	64	3	(	(	PUNCT
ejpam-2531	64	4	a	a	DET
ejpam-2531	64	5	polynomial	polynomial	ADJ
ejpam-2531	64	6	integral	integral	ADJ
ejpam-2531	64	7	transform	transform	NOUN
ejpam-2531	64	8	)	)	PUNCT
ejpam-2531	64	9	.	.	PUNCT
ejpam-2531	65	1	let	let	VERB
ejpam-2531	65	2	f	f	PROPN
ejpam-2531	65	3	(	(	PUNCT
ejpam-2531	65	4	x	x	X
ejpam-2531	65	5	)	)	PUNCT
ejpam-2531	65	6	be	be	VERB
ejpam-2531	65	7	a	a	DET
ejpam-2531	65	8	function	function	NOUN
ejpam-2531	65	9	defined	define	VERB
ejpam-2531	65	10	for	for	ADP
ejpam-2531	65	11	x	x	X
ejpam-2531	65	12	≥	≥	NUM
ejpam-2531	65	13	1	1	NUM
ejpam-2531	65	14	.	.	PUNCT
ejpam-2531	66	1	then	then	ADV
ejpam-2531	66	2	the	the	DET
ejpam-2531	66	3	integral	integral	ADJ
ejpam-2531	66	4	b	b	PROPN
ejpam-2531	66	5	(	(	PUNCT
ejpam-2531	66	6	f	f	PROPN
ejpam-2531	66	7	(	(	PUNCT
ejpam-2531	66	8	x	x	NOUN
ejpam-2531	66	9	)	)	PUNCT
ejpam-2531	66	10	)	)	PUNCT
ejpam-2531	67	1	=	=	PUNCT
ejpam-2531	67	2	f(s	f(s	X
ejpam-2531	67	3	)	)	PUNCT
ejpam-2531	67	4	=	=	SYM
ejpam-2531	68	1	∫	∫	PROPN
ejpam-2531	68	2	∞	∞	NUM
ejpam-2531	68	3	1	1	NUM
ejpam-2531	68	4	f	f	X
ejpam-2531	68	5	(	(	PUNCT
ejpam-2531	68	6	ln	ln	X
ejpam-2531	68	7	x).x−s−1d	x).x−s−1d	PROPN
ejpam-2531	68	8	x	x	X
ejpam-2531	68	9	,	,	PUNCT
ejpam-2531	68	10	is	be	AUX
ejpam-2531	68	11	the	the	DET
ejpam-2531	68	12	polynomial	polynomial	ADJ
ejpam-2531	68	13	integral	integral	ADJ
ejpam-2531	68	14	transform	transform	NOUN
ejpam-2531	68	15	of	of	ADP
ejpam-2531	68	16	f	f	PROPN
ejpam-2531	68	17	(	(	PUNCT
ejpam-2531	68	18	x	x	NOUN
ejpam-2531	68	19	)	)	PUNCT
ejpam-2531	68	20	for	for	ADP
ejpam-2531	68	21	x	x	PROPN
ejpam-2531	68	22	∈	∈	PROPN
ejpam-2531	68	23	[	[	X
ejpam-2531	68	24	1,∞	1,∞	NUM
ejpam-2531	68	25	)	)	PUNCT
ejpam-2531	68	26	,	,	PUNCT
ejpam-2531	68	27	provided	provide	VERB
ejpam-2531	68	28	the	the	DET
ejpam-2531	68	29	integral	integral	ADJ
ejpam-2531	68	30	converges	converge	NOUN
ejpam-2531	68	31	.	.	PUNCT
ejpam-2531	69	1	proof	proof	NOUN
ejpam-2531	69	2	.	.	PUNCT
ejpam-2531	70	1	we	we	PRON
ejpam-2531	70	2	consider	consider	VERB
ejpam-2531	70	3	the	the	DET
ejpam-2531	70	4	homogeneous	homogeneous	ADJ
ejpam-2531	70	5	cauchy	cauchy	PROPN
ejpam-2531	70	6	-	-	PUNCT
ejpam-2531	70	7	euler	euler	NOUN
ejpam-2531	70	8	equation	equation	NOUN
ejpam-2531	70	9	of	of	ADP
ejpam-2531	70	10	the	the	DET
ejpam-2531	70	11	form	form	NOUN
ejpam-2531	70	12	:	:	PUNCT
ejpam-2531	70	13	an	an	DET
ejpam-2531	70	14	xn	xn	NOUN
ejpam-2531	70	15	dn	dn	NOUN
ejpam-2531	70	16	y	y	PROPN
ejpam-2531	70	17	d	d	PROPN
ejpam-2531	70	18	xn	xn	PROPN
ejpam-2531	71	1	+	+	CCONJ
ejpam-2531	71	2	an−1	an−1	PROPN
ejpam-2531	72	1	xn−1	xn−1	PROPN
ejpam-2531	72	2	dn−1	dn−1	PROPN
ejpam-2531	72	3	y	y	PROPN
ejpam-2531	73	1	d	d	PROPN
ejpam-2531	73	2	xn−1	xn−1	PROPN
ejpam-2531	74	1	+	+	CCONJ
ejpam-2531	74	2	.	.	PUNCT
ejpam-2531	74	3	.	.	PUNCT
ejpam-2531	75	1	.+	.+	NOUN
ejpam-2531	75	2	a1	a1	NOUN
ejpam-2531	75	3	x	x	PUNCT
ejpam-2531	75	4	d	d	X
ejpam-2531	75	5	y	y	PROPN
ejpam-2531	75	6	d	d	X
ejpam-2531	75	7	x	x	PROPN
ejpam-2531	76	1	+	+	CCONJ
ejpam-2531	76	2	a0	a0	PROPN
ejpam-2531	76	3	y	y	PROPN
ejpam-2531	76	4	=	=	PROPN
ejpam-2531	76	5	0	0	PROPN
ejpam-2531	76	6	.	.	PUNCT
ejpam-2531	77	1	with	with	ADP
ejpam-2531	77	2	the	the	DET
ejpam-2531	77	3	corresponding	correspond	VERB
ejpam-2531	77	4	distinct	distinct	ADJ
ejpam-2531	77	5	roots	root	NOUN
ejpam-2531	77	6	y(x	y(x	NOUN
ejpam-2531	77	7	)	)	PUNCT
ejpam-2531	77	8	=	=	SYM
ejpam-2531	77	9	c1es1	c1es1	NOUN
ejpam-2531	77	10	ln	ln	NOUN
ejpam-2531	77	11	x	x	X
ejpam-2531	77	12	+	+	CCONJ
ejpam-2531	77	13	c2es2	c2es2	ADJ
ejpam-2531	77	14	ln	ln	NOUN
ejpam-2531	77	15	x	x	X
ejpam-2531	77	16	+	+	CCONJ
ejpam-2531	77	17	.	.	PUNCT
ejpam-2531	77	18	.	.	PUNCT
ejpam-2531	78	1	.+	.+	NOUN
ejpam-2531	78	2	cnesn	cnesn	PROPN
ejpam-2531	78	3	ln	ln	NOUN
ejpam-2531	78	4	x	x	X
ejpam-2531	78	5	,	,	PUNCT
ejpam-2531	78	6	where	where	SCONJ
ejpam-2531	78	7	c1	c1	PROPN
ejpam-2531	78	8	,	,	PUNCT
ejpam-2531	78	9	c2	c2	PROPN
ejpam-2531	78	10	,	,	PUNCT
ejpam-2531	78	11	.	.	PUNCT
ejpam-2531	78	12	.	.	PUNCT
ejpam-2531	78	13	.	.	PUNCT
ejpam-2531	79	1	,	,	PUNCT
ejpam-2531	79	2	cn	cn	PROPN
ejpam-2531	79	3	are	be	AUX
ejpam-2531	79	4	constants	constant	NOUN
ejpam-2531	79	5	.	.	PUNCT
ejpam-2531	80	1	also	also	ADV
ejpam-2531	80	2	,	,	PUNCT
ejpam-2531	80	3	consider	consider	VERB
ejpam-2531	80	4	a	a	DET
ejpam-2531	80	5	constant	constant	ADJ
ejpam-2531	80	6	linear	linear	NOUN
ejpam-2531	80	7	differential	differential	NOUN
ejpam-2531	80	8	equation	equation	NOUN
ejpam-2531	80	9	an	an	DET
ejpam-2531	80	10	dn	dn	NOUN
ejpam-2531	80	11	y	y	PROPN
ejpam-2531	80	12	d	d	PROPN
ejpam-2531	80	13	tn	tn	PROPN
ejpam-2531	81	1	+	+	CCONJ
ejpam-2531	81	2	an−1	an−1	PROPN
ejpam-2531	81	3	dn−1	dn−1	PROPN
ejpam-2531	81	4	y	y	PROPN
ejpam-2531	82	1	d	d	X
ejpam-2531	82	2	tn−1	tn−1	PROPN
ejpam-2531	82	3	+	+	CCONJ
ejpam-2531	82	4	.	.	PUNCT
ejpam-2531	82	5	.	.	PUNCT
ejpam-2531	83	1	.+	.+	NOUN
ejpam-2531	83	2	a1	a1	NOUN
ejpam-2531	83	3	d	d	X
ejpam-2531	83	4	y	y	PROPN
ejpam-2531	83	5	d	d	PROPN
ejpam-2531	83	6	t	t	PROPN
ejpam-2531	83	7	+	+	CCONJ
ejpam-2531	83	8	a0	a0	PROPN
ejpam-2531	83	9	y	y	PROPN
ejpam-2531	83	10	=	=	PROPN
ejpam-2531	83	11	0	0	PROPN
ejpam-2531	83	12	,	,	PUNCT
ejpam-2531	83	13	with	with	ADP
ejpam-2531	83	14	a	a	DET
ejpam-2531	83	15	solution	solution	NOUN
ejpam-2531	83	16	y(x	y(x	NOUN
ejpam-2531	83	17	)	)	PUNCT
ejpam-2531	84	1	=	=	SYM
ejpam-2531	84	2	c1es1	c1es1	NOUN
ejpam-2531	84	3	t	t	PROPN
ejpam-2531	84	4	+	+	CCONJ
ejpam-2531	84	5	c2es1	c2es1	PROPN
ejpam-2531	84	6	t	t	PROPN
ejpam-2531	84	7	+	+	X
ejpam-2531	84	8	.	.	PUNCT
ejpam-2531	84	9	.	.	PUNCT
ejpam-2531	85	1	.+	.+	NOUN
ejpam-2531	85	2	cnesn	cnesn	PROPN
ejpam-2531	85	3	t	t	PROPN
ejpam-2531	85	4	.	.	PUNCT
ejpam-2531	86	1	we	we	PRON
ejpam-2531	86	2	can	can	AUX
ejpam-2531	86	3	see	see	VERB
ejpam-2531	86	4	that	that	DET
ejpam-2531	86	5	equation	equation	NOUN
ejpam-2531	86	6	(	(	PUNCT
ejpam-2531	86	7	3	3	X
ejpam-2531	86	8	)	)	PUNCT
ejpam-2531	86	9	has	have	VERB
ejpam-2531	86	10	an	an	DET
ejpam-2531	86	11	integral	integral	ADJ
ejpam-2531	86	12	transform	transform	NOUN
ejpam-2531	86	13	b	b	X
ejpam-2531	86	14	(	(	PUNCT
ejpam-2531	86	15	f	f	PROPN
ejpam-2531	86	16	(	(	PUNCT
ejpam-2531	86	17	t	t	PROPN
ejpam-2531	86	18	)	)	PUNCT
ejpam-2531	86	19	)	)	PUNCT
ejpam-2531	87	1	=	=	PUNCT
ejpam-2531	87	2	f(s	f(s	X
ejpam-2531	87	3	)	)	PUNCT
ejpam-2531	87	4	=	=	SYM
ejpam-2531	88	1	∫	∫	PROPN
ejpam-2531	89	1	∞	∞	NUM
ejpam-2531	89	2	0	0	NUM
ejpam-2531	89	3	f	f	PROPN
ejpam-2531	89	4	(	(	PUNCT
ejpam-2531	89	5	t)e−st	t)e−st	NOUN
ejpam-2531	89	6	d	d	PROPN
ejpam-2531	89	7	t.	t.	PROPN
ejpam-2531	89	8	b.	b.	PROPN
ejpam-2531	89	9	barnes	barnes	PROPN
ejpam-2531	89	10	/	/	SYM
ejpam-2531	89	11	eur	eur	PROPN
ejpam-2531	89	12	.	.	PUNCT
ejpam-2531	90	1	j.	j.	PROPN
ejpam-2531	90	2	pure	pure	PROPN
ejpam-2531	90	3	appl	appl	PROPN
ejpam-2531	90	4	.	.	PROPN
ejpam-2531	90	5	math	math	PROPN
ejpam-2531	90	6	,	,	PUNCT
ejpam-2531	90	7	9	9	NUM
ejpam-2531	90	8	(	(	PUNCT
ejpam-2531	90	9	2016	2016	NUM
ejpam-2531	90	10	)	)	PUNCT
ejpam-2531	90	11	,	,	PUNCT
ejpam-2531	90	12	140	140	NUM
ejpam-2531	90	13	-	-	SYM
ejpam-2531	90	14	151	151	NUM
ejpam-2531	90	15	143	143	NUM
ejpam-2531	90	16	again	again	ADV
ejpam-2531	90	17	,	,	PUNCT
ejpam-2531	90	18	we	we	PRON
ejpam-2531	90	19	see	see	VERB
ejpam-2531	90	20	from	from	ADP
ejpam-2531	90	21	equations	equation	NOUN
ejpam-2531	90	22	(	(	PUNCT
ejpam-2531	90	23	2	2	NUM
ejpam-2531	90	24	)	)	PUNCT
ejpam-2531	90	25	and	and	CCONJ
ejpam-2531	90	26	(	(	PUNCT
ejpam-2531	90	27	4	4	X
ejpam-2531	90	28	)	)	PUNCT
ejpam-2531	90	29	that	that	PRON
ejpam-2531	90	30	t	t	NOUN
ejpam-2531	91	1	=	=	PUNCT
ejpam-2531	91	2	ln	ln	ADJ
ejpam-2531	91	3	x	x	PUNCT
ejpam-2531	91	4	substituting	substitute	VERB
ejpam-2531	91	5	equation	equation	NOUN
ejpam-2531	91	6	(	(	PUNCT
ejpam-2531	91	7	6	6	NUM
ejpam-2531	91	8	)	)	PUNCT
ejpam-2531	91	9	into	into	ADP
ejpam-2531	91	10	equation	equation	NOUN
ejpam-2531	91	11	(	(	PUNCT
ejpam-2531	91	12	5	5	NUM
ejpam-2531	91	13	)	)	PUNCT
ejpam-2531	91	14	,	,	PUNCT
ejpam-2531	91	15	we	we	PRON
ejpam-2531	91	16	obtain	obtain	VERB
ejpam-2531	91	17	b	b	X
ejpam-2531	91	18	(	(	PUNCT
ejpam-2531	91	19	f	f	PROPN
ejpam-2531	91	20	(	(	PUNCT
ejpam-2531	91	21	x	x	NOUN
ejpam-2531	91	22	)	)	PUNCT
ejpam-2531	91	23	)	)	PUNCT
ejpam-2531	92	1	=	=	NOUN
ejpam-2531	92	2	f(s	f(s	X
ejpam-2531	92	3	)	)	PUNCT
ejpam-2531	92	4	=	=	SYM
ejpam-2531	93	1	∫	∫	PROPN
ejpam-2531	93	2	∞	∞	NUM
ejpam-2531	93	3	1	1	NUM
ejpam-2531	93	4	f	f	X
ejpam-2531	93	5	(	(	PUNCT
ejpam-2531	93	6	ln	ln	NOUN
ejpam-2531	93	7	x	x	NOUN
ejpam-2531	93	8	)	)	PUNCT
ejpam-2531	93	9	.	.	PUNCT
ejpam-2531	94	1	1	1	NUM
ejpam-2531	94	2	x	x	SYM
ejpam-2531	94	3	e−s	e−s	X
ejpam-2531	94	4	ln	ln	NOUN
ejpam-2531	94	5	x	x	PUNCT
ejpam-2531	94	6	d	d	NOUN
ejpam-2531	94	7	x	x	SYM
ejpam-2531	94	8	b	b	PROPN
ejpam-2531	94	9	(	(	PUNCT
ejpam-2531	94	10	f	f	PROPN
ejpam-2531	94	11	(	(	PUNCT
ejpam-2531	94	12	x	x	NOUN
ejpam-2531	94	13	)	)	PUNCT
ejpam-2531	94	14	)	)	PUNCT
ejpam-2531	95	1	=	=	SYM
ejpam-2531	95	2	∫	∫	PROPN
ejpam-2531	96	1	∞	∞	NUM
ejpam-2531	96	2	1	1	NUM
ejpam-2531	96	3	f	f	NOUN
ejpam-2531	96	4	(	(	PUNCT
ejpam-2531	96	5	ln	ln	PROPN
ejpam-2531	96	6	x).x−(s+1)d	x).x−(s+1)d	PROPN
ejpam-2531	96	7	x	x	PUNCT
ejpam-2531	96	8	is	be	AUX
ejpam-2531	96	9	the	the	DET
ejpam-2531	96	10	polynomial	polynomial	ADJ
ejpam-2531	96	11	integral	integral	ADJ
ejpam-2531	96	12	transform	transform	NOUN
ejpam-2531	96	13	of	of	ADP
ejpam-2531	96	14	f	f	PROPN
ejpam-2531	96	15	(	(	PUNCT
ejpam-2531	96	16	x	x	NOUN
ejpam-2531	96	17	)	)	PUNCT
ejpam-2531	96	18	for	for	ADP
ejpam-2531	96	19	x	x	PROPN
ejpam-2531	96	20	∈	∈	PROPN
ejpam-2531	96	21	[	[	X
ejpam-2531	96	22	1,∞	1,∞	NUM
ejpam-2531	96	23	)	)	PUNCT
ejpam-2531	96	24	,	,	PUNCT
ejpam-2531	96	25	provided	provide	VERB
ejpam-2531	96	26	the	the	DET
ejpam-2531	96	27	integral	integral	ADJ
ejpam-2531	96	28	converges	converge	NOUN
ejpam-2531	96	29	.	.	PUNCT
ejpam-2531	97	1	2.1	2.1	NUM
ejpam-2531	97	2	.	.	PUNCT
ejpam-2531	98	1	the	the	DET
ejpam-2531	98	2	convergence	convergence	NOUN
ejpam-2531	98	3	of	of	ADP
ejpam-2531	98	4	the	the	DET
ejpam-2531	98	5	polynomial	polynomial	ADJ
ejpam-2531	98	6	integral	integral	ADJ
ejpam-2531	98	7	transform	transform	NOUN
ejpam-2531	98	8	in	in	ADP
ejpam-2531	98	9	this	this	DET
ejpam-2531	98	10	subsection	subsection	NOUN
ejpam-2531	98	11	,	,	PUNCT
ejpam-2531	98	12	we	we	PRON
ejpam-2531	98	13	show	show	VERB
ejpam-2531	98	14	that	that	SCONJ
ejpam-2531	98	15	the	the	DET
ejpam-2531	98	16	polynomial	polynomial	ADJ
ejpam-2531	98	17	integral	integral	ADJ
ejpam-2531	98	18	transform	transform	NOUN
ejpam-2531	98	19	converges	converge	NOUN
ejpam-2531	98	20	for	for	ADP
ejpam-2531	98	21	variable	variable	NOUN
ejpam-2531	98	22	defined	define	VERB
ejpam-2531	98	23	in	in	ADP
ejpam-2531	98	24	[	[	NOUN
ejpam-2531	98	25	1,∞	1,∞	NUM
ejpam-2531	98	26	)	)	PUNCT
ejpam-2531	98	27	.	.	PUNCT
ejpam-2531	99	1	by	by	ADP
ejpam-2531	99	2	taylor	taylor	PROPN
ejpam-2531	99	3	series	series	PROPN
ejpam-2531	99	4	expansion	expansion	PROPN
ejpam-2531	99	5	,	,	PUNCT
ejpam-2531	99	6	we	we	PRON
ejpam-2531	99	7	obtain	obtain	VERB
ejpam-2531	99	8	eln	eln	X
ejpam-2531	99	9	x−s−1	x−s−1	PUNCT
ejpam-2531	100	1	=	=	PUNCT
ejpam-2531	100	2	1	1	NUM
ejpam-2531	100	3	+	+	NUM
ejpam-2531	100	4	ln	ln	ADJ
ejpam-2531	100	5	x−s−1	x−s−1	PROPN
ejpam-2531	100	6	+	+	CCONJ
ejpam-2531	100	7	(	(	PUNCT
ejpam-2531	100	8	ln	ln	ADJ
ejpam-2531	100	9	x−(s+1))2	x−(s+1))2	PROPN
ejpam-2531	100	10	2	2	NUM
ejpam-2531	100	11	!	!	PUNCT
ejpam-2531	101	1	+	+	CCONJ
ejpam-2531	101	2	(	(	PUNCT
ejpam-2531	101	3	ln	ln	X
ejpam-2531	101	4	x−(s+1))3	x−(s+1))3	X
ejpam-2531	101	5	3	3	NUM
ejpam-2531	101	6	!	!	PUNCT
ejpam-2531	102	1	+	+	CCONJ
ejpam-2531	102	2	(	(	PUNCT
ejpam-2531	102	3	ln	ln	ADJ
ejpam-2531	102	4	x−(s+1))4	x−(s+1))4	PROPN
ejpam-2531	102	5	4	4	NUM
ejpam-2531	102	6	!	!	PUNCT
ejpam-2531	103	1	+	+	CCONJ
ejpam-2531	103	2	.	.	PUNCT
ejpam-2531	103	3	.	.	PUNCT
ejpam-2531	104	1	.+	.+	NOUN
ejpam-2531	105	1	∞	∞	NUM
ejpam-2531	105	2	∑	∑	PROPN
ejpam-2531	105	3	n=0	n=0	NUM
ejpam-2531	105	4	(	(	PUNCT
ejpam-2531	105	5	ln	ln	NOUN
ejpam-2531	105	6	x−(s+1))n	x−(s+1))n	PROPN
ejpam-2531	105	7	n	n	X
ejpam-2531	105	8	!	!	PUNCT
ejpam-2531	106	1	+	+	CCONJ
ejpam-2531	106	2	.	.	PUNCT
ejpam-2531	106	3	.	.	PUNCT
ejpam-2531	106	4	.	.	PUNCT
ejpam-2531	107	1	eln	eln	PROPN
ejpam-2531	107	2	x−s−1	x−s−1	PROPN
ejpam-2531	108	1	=	=	PUNCT
ejpam-2531	108	2	∞	∞	PROPN
ejpam-2531	108	3	∑	∑	SYM
ejpam-2531	108	4	n=0	n=0	NUM
ejpam-2531	108	5	(	(	PUNCT
ejpam-2531	108	6	ln	ln	NOUN
ejpam-2531	108	7	x−(s+1))n	x−(s+1))n	PROPN
ejpam-2531	108	8	n	n	X
ejpam-2531	108	9	!	!	PUNCT
ejpam-2531	109	1	by	by	ADP
ejpam-2531	109	2	the	the	DET
ejpam-2531	109	3	d’lambert	d’lambert	PROPN
ejpam-2531	109	4	ratio	ratio	PROPN
ejpam-2531	109	5	test	test	NOUN
ejpam-2531	109	6	,	,	PUNCT
ejpam-2531	109	7	we	we	PRON
ejpam-2531	109	8	obtain	obtain	VERB
ejpam-2531	109	9	lim	lim	PROPN
ejpam-2531	109	10	n→∞	n→∞	PRON
ejpam-2531	110	1	|	|	ADV
ejpam-2531	110	2	(	(	PUNCT
ejpam-2531	110	3	∞	∞	PROPN
ejpam-2531	110	4	∑	∑	PROPN
ejpam-2531	110	5	n=0	n=0	NUM
ejpam-2531	110	6	(	(	PUNCT
ejpam-2531	110	7	ln	ln	PROPN
ejpam-2531	110	8	x−(s+1))n+1	x−(s+1))n+1	PROPN
ejpam-2531	110	9	(	(	PUNCT
ejpam-2531	110	10	n+	n+	NOUN
ejpam-2531	110	11	1	1	NUM
ejpam-2531	110	12	)	)	PUNCT
ejpam-2531	110	13	!	!	PUNCT
ejpam-2531	111	1	÷	÷	NUM
ejpam-2531	112	1	∞	∞	NUM
ejpam-2531	112	2	∑	∑	PUNCT
ejpam-2531	112	3	n=0	n=0	NUM
ejpam-2531	112	4	(	(	PUNCT
ejpam-2531	112	5	ln	ln	NOUN
ejpam-2531	112	6	x−(s+1))n	x−(s+1))n	PROPN
ejpam-2531	112	7	n	n	X
ejpam-2531	112	8	!	!	PUNCT
ejpam-2531	112	9	)	)	PUNCT
ejpam-2531	113	1	|	|	ADV
ejpam-2531	113	2	⇒0	⇒0	NOUN
ejpam-2531	113	3	.	.	PUNCT
ejpam-2531	114	1	ln	ln	ADJ
ejpam-2531	114	2	x−(s+1	x−(s+1	PROPN
ejpam-2531	114	3	)	)	PUNCT
ejpam-2531	114	4	⇒0	⇒0	PROPN
ejpam-2531	114	5	.	.	PUNCT
ejpam-2531	115	1	then	then	ADV
ejpam-2531	115	2	b	b	X
ejpam-2531	115	3	(	(	PUNCT
ejpam-2531	115	4	f	f	PROPN
ejpam-2531	115	5	(	(	PUNCT
ejpam-2531	115	6	x	x	NOUN
ejpam-2531	115	7	)	)	PUNCT
ejpam-2531	115	8	)	)	PUNCT
ejpam-2531	116	1	=	=	PUNCT
ejpam-2531	116	2	sup	sup	NOUN
ejpam-2531	116	3	1≤x<∞	1≤x<∞	NUM
ejpam-2531	116	4	∫	∫	PROPN
ejpam-2531	116	5	∞	∞	NUM
ejpam-2531	116	6	1	1	NUM
ejpam-2531	117	1	|	|	ADV
ejpam-2531	117	2	f	f	X
ejpam-2531	117	3	(	(	PUNCT
ejpam-2531	117	4	ln	ln	ADJ
ejpam-2531	117	5	x).x−s−1|d	x).x−s−1|d	PUNCT
ejpam-2531	118	1	x	x	SYM
ejpam-2531	118	2	b	b	X
ejpam-2531	118	3	(	(	PUNCT
ejpam-2531	118	4	f	f	X
ejpam-2531	118	5	(	(	PUNCT
ejpam-2531	118	6	x))≤	x))≤	PROPN
ejpam-2531	118	7	sup	sup	NOUN
ejpam-2531	118	8	1≤x<∞	1≤x<∞	NUM
ejpam-2531	118	9	∫	∫	PROPN
ejpam-2531	118	10	∞	∞	NUM
ejpam-2531	118	11	1	1	NUM
ejpam-2531	119	1	|	|	ADV
ejpam-2531	119	2	f	f	X
ejpam-2531	119	3	(	(	PUNCT
ejpam-2531	119	4	ln	ln	NOUN
ejpam-2531	119	5	x)||x−s−1|d	x)||x−s−1|d	X
ejpam-2531	119	6	x	x	SYM
ejpam-2531	119	7	b	b	X
ejpam-2531	119	8	(	(	PUNCT
ejpam-2531	119	9	f	f	PROPN
ejpam-2531	119	10	(	(	PUNCT
ejpam-2531	119	11	x))≤m	x))≤m	PROPN
ejpam-2531	119	12	∫	∫	PROPN
ejpam-2531	119	13	∞	∞	NUM
ejpam-2531	119	14	1	1	NUM
ejpam-2531	120	1	|	|	ADV
ejpam-2531	120	2	f	f	X
ejpam-2531	120	3	(	(	PUNCT
ejpam-2531	120	4	ln	ln	PROPN
ejpam-2531	120	5	x)|d	x)|d	PROPN
ejpam-2531	120	6	x	x	X
ejpam-2531	120	7	,	,	PUNCT
ejpam-2531	120	8	where	where	SCONJ
ejpam-2531	120	9	m	m	VERB
ejpam-2531	120	10	>	>	X
ejpam-2531	120	11	0	0	X
ejpam-2531	120	12	.	.	PUNCT
ejpam-2531	121	1	it	it	PRON
ejpam-2531	121	2	implies	imply	VERB
ejpam-2531	121	3	that	that	SCONJ
ejpam-2531	121	4	the	the	DET
ejpam-2531	121	5	polynomial	polynomial	ADJ
ejpam-2531	121	6	integral	integral	ADJ
ejpam-2531	121	7	transform	transform	NOUN
ejpam-2531	121	8	converges	converge	VERB
ejpam-2531	121	9	uniformly	uniformly	ADV
ejpam-2531	121	10	for	for	ADP
ejpam-2531	121	11	a	a	DET
ejpam-2531	121	12	given	give	VERB
ejpam-2531	121	13	s.	s.	PROPN
ejpam-2531	121	14	the	the	DET
ejpam-2531	121	15	function	function	NOUN
ejpam-2531	121	16	f	f	PROPN
ejpam-2531	121	17	(	(	PUNCT
ejpam-2531	121	18	x	x	X
ejpam-2531	121	19	)	)	PUNCT
ejpam-2531	121	20	must	must	AUX
ejpam-2531	121	21	be	be	AUX
ejpam-2531	121	22	piecewise	piecewise	NOUN
ejpam-2531	121	23	continuous	continuous	ADJ
ejpam-2531	121	24	.	.	PUNCT
ejpam-2531	122	1	thus	thus	ADV
ejpam-2531	122	2	,	,	PUNCT
ejpam-2531	122	3	f	f	PROPN
ejpam-2531	122	4	(	(	PUNCT
ejpam-2531	122	5	x	x	X
ejpam-2531	122	6	)	)	PUNCT
ejpam-2531	122	7	has	have	VERB
ejpam-2531	122	8	at	at	ADP
ejpam-2531	122	9	most	most	ADJ
ejpam-2531	122	10	a	a	DET
ejpam-2531	122	11	finite	finite	ADJ
ejpam-2531	122	12	number	number	NOUN
ejpam-2531	122	13	of	of	ADP
ejpam-2531	122	14	discontinuities	discontinuity	NOUN
ejpam-2531	122	15	on	on	ADP
ejpam-2531	122	16	any	any	DET
ejpam-2531	122	17	interval	interval	NOUN
ejpam-2531	122	18	1≤	1≤	NOUN
ejpam-2531	123	1	x	x	SYM
ejpam-2531	123	2	≤	≤	ADV
ejpam-2531	123	3	a	a	PRON
ejpam-2531	123	4	,	,	PUNCT
ejpam-2531	123	5	and	and	CCONJ
ejpam-2531	123	6	the	the	DET
ejpam-2531	123	7	limit	limit	NOUN
ejpam-2531	123	8	of	of	ADP
ejpam-2531	123	9	f	f	PROPN
ejpam-2531	123	10	(	(	PUNCT
ejpam-2531	123	11	x	x	X
ejpam-2531	123	12	)	)	PUNCT
ejpam-2531	123	13	exist	exist	VERB
ejpam-2531	123	14	at	at	ADP
ejpam-2531	123	15	every	every	DET
ejpam-2531	123	16	point	point	NOUN
ejpam-2531	123	17	of	of	ADP
ejpam-2531	123	18	discontinuity	discontinuity	NOUN
ejpam-2531	123	19	.	.	PUNCT
ejpam-2531	124	1	b.	b.	PROPN
ejpam-2531	124	2	barnes	barnes	PROPN
ejpam-2531	124	3	/	/	SYM
ejpam-2531	124	4	eur	eur	PROPN
ejpam-2531	124	5	.	.	PUNCT
ejpam-2531	125	1	j.	j.	PROPN
ejpam-2531	125	2	pure	pure	PROPN
ejpam-2531	125	3	appl	appl	PROPN
ejpam-2531	125	4	.	.	PROPN
ejpam-2531	125	5	math	math	PROPN
ejpam-2531	125	6	,	,	PUNCT
ejpam-2531	125	7	9	9	NUM
ejpam-2531	125	8	(	(	PUNCT
ejpam-2531	125	9	2016	2016	NUM
ejpam-2531	125	10	)	)	PUNCT
ejpam-2531	125	11	,	,	PUNCT
ejpam-2531	125	12	140	140	NUM
ejpam-2531	125	13	-	-	SYM
ejpam-2531	125	14	151	151	NUM
ejpam-2531	125	15	144	144	NUM
ejpam-2531	125	16	2.2	2.2	NUM
ejpam-2531	125	17	.	.	PUNCT
ejpam-2531	126	1	existence	existence	NOUN
ejpam-2531	126	2	of	of	ADP
ejpam-2531	126	3	the	the	DET
ejpam-2531	126	4	polynomial	polynomial	ADJ
ejpam-2531	126	5	integral	integral	ADJ
ejpam-2531	126	6	transform	transform	NOUN
ejpam-2531	126	7	in	in	ADP
ejpam-2531	126	8	this	this	DET
ejpam-2531	126	9	subsection	subsection	NOUN
ejpam-2531	126	10	,	,	PUNCT
ejpam-2531	126	11	we	we	PRON
ejpam-2531	126	12	show	show	VERB
ejpam-2531	126	13	that	that	SCONJ
ejpam-2531	126	14	the	the	DET
ejpam-2531	126	15	polynomial	polynomial	ADJ
ejpam-2531	126	16	integral	integral	ADJ
ejpam-2531	126	17	transform	transform	NOUN
ejpam-2531	126	18	exists	exist	VERB
ejpam-2531	126	19	for	for	ADP
ejpam-2531	126	20	x	x	PROPN
ejpam-2531	126	21	∈	∈	PROPN
ejpam-2531	126	22	[	[	X
ejpam-2531	126	23	1,∞	1,∞	NUM
ejpam-2531	126	24	)	)	PUNCT
ejpam-2531	126	25	.	.	PUNCT
ejpam-2531	127	1	to	to	PART
ejpam-2531	127	2	see	see	VERB
ejpam-2531	127	3	this	this	PRON
ejpam-2531	127	4	,	,	PUNCT
ejpam-2531	127	5	we	we	PRON
ejpam-2531	127	6	state	state	VERB
ejpam-2531	127	7	the	the	DET
ejpam-2531	127	8	existence	existence	NOUN
ejpam-2531	127	9	theorem	theorem	VERB
ejpam-2531	127	10	for	for	ADP
ejpam-2531	127	11	the	the	DET
ejpam-2531	127	12	polynomial	polynomial	ADJ
ejpam-2531	127	13	integral	integral	ADJ
ejpam-2531	127	14	transform	transform	NOUN
ejpam-2531	127	15	.	.	PUNCT
ejpam-2531	128	1	theorem	theorem	NOUN
ejpam-2531	128	2	2	2	NUM
ejpam-2531	128	3	.	.	PUNCT
ejpam-2531	129	1	let	let	VERB
ejpam-2531	129	2	f	f	PROPN
ejpam-2531	129	3	(	(	PUNCT
ejpam-2531	129	4	x	x	X
ejpam-2531	129	5	)	)	PUNCT
ejpam-2531	129	6	be	be	AUX
ejpam-2531	129	7	a	a	DET
ejpam-2531	129	8	piecewise	piecewise	NOUN
ejpam-2531	129	9	continuous	continuous	ADJ
ejpam-2531	129	10	function	function	NOUN
ejpam-2531	129	11	on	on	ADP
ejpam-2531	129	12	[	[	X
ejpam-2531	129	13	1,∞	1,∞	NUM
ejpam-2531	129	14	)	)	PUNCT
ejpam-2531	129	15	and	and	CCONJ
ejpam-2531	129	16	of	of	ADP
ejpam-2531	129	17	exponential	exponential	ADJ
ejpam-2531	129	18	order	order	NOUN
ejpam-2531	129	19	,	,	PUNCT
ejpam-2531	129	20	then	then	ADV
ejpam-2531	129	21	the	the	DET
ejpam-2531	129	22	polynomial	polynomial	ADJ
ejpam-2531	129	23	integral	integral	ADJ
ejpam-2531	129	24	transform	transform	NOUN
ejpam-2531	129	25	exists	exist	VERB
ejpam-2531	129	26	.	.	PUNCT
ejpam-2531	130	1	proof	proof	NOUN
ejpam-2531	130	2	.	.	PUNCT
ejpam-2531	131	1	by	by	ADP
ejpam-2531	131	2	the	the	DET
ejpam-2531	131	3	definition	definition	NOUN
ejpam-2531	131	4	of	of	ADP
ejpam-2531	131	5	polynomial	polynomial	ADJ
ejpam-2531	131	6	integral	integral	ADJ
ejpam-2531	131	7	transform	transform	NOUN
ejpam-2531	131	8	,	,	PUNCT
ejpam-2531	131	9	we	we	PRON
ejpam-2531	131	10	obtain	obtain	VERB
ejpam-2531	131	11	i	i	PRON
ejpam-2531	131	12	=	=	PUNCT
ejpam-2531	131	13	∫	∫	PROPN
ejpam-2531	132	1	∞	∞	NUM
ejpam-2531	132	2	1	1	NUM
ejpam-2531	132	3	f	f	PROPN
ejpam-2531	132	4	(	(	PUNCT
ejpam-2531	132	5	x).x−(s+1)d	x).x−(s+1)d	PUNCT
ejpam-2531	132	6	x	x	SYM
ejpam-2531	133	1	i	i	NOUN
ejpam-2531	133	2	=	=	PUNCT
ejpam-2531	133	3	∫	∫	PROPN
ejpam-2531	134	1	a	a	DET
ejpam-2531	134	2	1	1	NUM
ejpam-2531	134	3	f	f	NOUN
ejpam-2531	134	4	(	(	PUNCT
ejpam-2531	134	5	x).x−(s+1)d	x).x−(s+1)d	PUNCT
ejpam-2531	134	6	x	x	PROPN
ejpam-2531	135	1	+	+	NUM
ejpam-2531	135	2	∫	∫	PROPN
ejpam-2531	135	3	∞	∞	PROPN
ejpam-2531	135	4	a	a	DET
ejpam-2531	135	5	f	f	PROPN
ejpam-2531	135	6	(	(	PUNCT
ejpam-2531	135	7	x).x−(s+1)d	x).x−(s+1)d	PUNCT
ejpam-2531	135	8	x	x	SYM
ejpam-2531	136	1	i	i	PROPN
ejpam-2531	136	2	=	=	PROPN
ejpam-2531	136	3	i1	i1	PROPN
ejpam-2531	136	4	+	+	CCONJ
ejpam-2531	136	5	i2	i2	PROPN
ejpam-2531	136	6	,	,	PUNCT
ejpam-2531	136	7	where	where	SCONJ
ejpam-2531	136	8	i1	i1	PROPN
ejpam-2531	136	9	=	=	PUNCT
ejpam-2531	136	10	∫	∫	PROPN
ejpam-2531	137	1	a	a	PRON
ejpam-2531	137	2	1	1	NUM
ejpam-2531	137	3	f	f	NOUN
ejpam-2531	137	4	(	(	PUNCT
ejpam-2531	137	5	x).x−(s+1)d	x).x−(s+1)d	PROPN
ejpam-2531	137	6	x	x	NOUN
ejpam-2531	137	7	and	and	CCONJ
ejpam-2531	137	8	i2	i2	PROPN
ejpam-2531	137	9	=	=	SYM
ejpam-2531	137	10	∫	∫	PROPN
ejpam-2531	137	11	∞	∞	PROPN
ejpam-2531	137	12	a	a	DET
ejpam-2531	137	13	f	f	PROPN
ejpam-2531	137	14	(	(	PUNCT
ejpam-2531	137	15	x).x−(s+1)d	x).x−(s+1)d	PROPN
ejpam-2531	137	16	x	x	X
ejpam-2531	137	17	.	.	PUNCT
ejpam-2531	138	1	the	the	DET
ejpam-2531	138	2	integral	integral	ADJ
ejpam-2531	138	3	i1	i1	PROPN
ejpam-2531	138	4	exists	exist	VERB
ejpam-2531	138	5	since	since	SCONJ
ejpam-2531	138	6	f	f	PROPN
ejpam-2531	138	7	(	(	PUNCT
ejpam-2531	138	8	x	x	X
ejpam-2531	138	9	)	)	PUNCT
ejpam-2531	138	10	is	be	AUX
ejpam-2531	138	11	piecewise	piecewise	NOUN
ejpam-2531	138	12	continuous	continuous	ADJ
ejpam-2531	138	13	.	.	PUNCT
ejpam-2531	139	1	taking	take	VERB
ejpam-2531	139	2	i2	i2	PROPN
ejpam-2531	139	3	=	=	SYM
ejpam-2531	140	1	∫	∫	PROPN
ejpam-2531	140	2	∞	∞	PROPN
ejpam-2531	140	3	a	a	DET
ejpam-2531	140	4	f	f	PROPN
ejpam-2531	140	5	(	(	PUNCT
ejpam-2531	140	6	x).x−(s+1)d	x).x−(s+1)d	PROPN
ejpam-2531	140	7	x	x	PROPN
ejpam-2531	140	8	i2	i2	PROPN
ejpam-2531	140	9	=	=	SYM
ejpam-2531	141	1	∫	∫	PROPN
ejpam-2531	141	2	∞	∞	PROPN
ejpam-2531	141	3	a	a	DET
ejpam-2531	141	4	f	f	PROPN
ejpam-2531	141	5	(	(	PUNCT
ejpam-2531	141	6	x).x−(s+1)d	x).x−(s+1)d	PROPN
ejpam-2531	141	7	x	x	SYM
ejpam-2531	141	8	≤	≤	NUM
ejpam-2531	141	9	m	m	VERB
ejpam-2531	141	10	∫	∫	PROPN
ejpam-2531	141	11	∞	∞	PROPN
ejpam-2531	141	12	a	a	DET
ejpam-2531	141	13	eαx	eαx	NOUN
ejpam-2531	141	14	.x−(s+1)d	.x−(s+1)d	NOUN
ejpam-2531	142	1	x	x	INTJ
ejpam-2531	142	2	.	.	PUNCT
ejpam-2531	143	1	by	by	ADP
ejpam-2531	143	2	the	the	DET
ejpam-2531	143	3	taylor	taylor	PROPN
ejpam-2531	143	4	series	series	PROPN
ejpam-2531	143	5	expansion	expansion	NOUN
ejpam-2531	143	6	,	,	PUNCT
ejpam-2531	143	7	we	we	PRON
ejpam-2531	143	8	obtain	obtain	VERB
ejpam-2531	143	9	eαx	eαx	PROPN
ejpam-2531	144	1	≈	≈	PROPN
ejpam-2531	144	2	∞	∞	PROPN
ejpam-2531	144	3	∑	∑	PROPN
ejpam-2531	144	4	n=0	n=0	PUNCT
ejpam-2531	144	5	α	α	NOUN
ejpam-2531	144	6	n	n	NOUN
ejpam-2531	144	7	xn	xn	PROPN
ejpam-2531	144	8	n	n	CCONJ
ejpam-2531	144	9	!	!	PUNCT
ejpam-2531	144	10	.	.	PUNCT
ejpam-2531	145	1	substituting	substitute	VERB
ejpam-2531	145	2	the	the	DET
ejpam-2531	145	3	expression	expression	NOUN
ejpam-2531	145	4	for	for	ADP
ejpam-2531	145	5	eαx	eαx	PROPN
ejpam-2531	145	6	in	in	ADP
ejpam-2531	145	7	equation	equation	NOUN
ejpam-2531	145	8	(	(	PUNCT
ejpam-2531	145	9	7	7	NUM
ejpam-2531	145	10	)	)	PUNCT
ejpam-2531	145	11	,	,	PUNCT
ejpam-2531	145	12	we	we	PRON
ejpam-2531	145	13	obtain	obtain	VERB
ejpam-2531	145	14	i2	i2	PROPN
ejpam-2531	145	15	≈m	≈m	PROPN
ejpam-2531	145	16	∞	∞	PROPN
ejpam-2531	145	17	∑	∑	PROPN
ejpam-2531	145	18	n=0	n=0	PROPN
ejpam-2531	145	19	α	α	NOUN
ejpam-2531	145	20	n	n	NOUN
ejpam-2531	145	21	n	n	CCONJ
ejpam-2531	145	22	!	!	PUNCT
ejpam-2531	146	1	∫	∫	PROPN
ejpam-2531	147	1	∞	∞	PROPN
ejpam-2531	147	2	a	a	DET
ejpam-2531	147	3	x−(s+1−n)d	x−(s+1−n)d	PROPN
ejpam-2531	147	4	x	x	PROPN
ejpam-2531	147	5	i2	i2	PROPN
ejpam-2531	147	6	≈m	≈m	PROPN
ejpam-2531	147	7	∞	∞	PROPN
ejpam-2531	147	8	∑	∑	PROPN
ejpam-2531	147	9	n=0	n=0	PROPN
ejpam-2531	147	10	α	α	NOUN
ejpam-2531	147	11	n	n	NOUN
ejpam-2531	147	12	n	n	CCONJ
ejpam-2531	147	13	!	!	PUNCT
ejpam-2531	148	1	∫	∫	PROPN
ejpam-2531	149	1	∞	∞	NUM
ejpam-2531	149	2	1	1	NUM
ejpam-2531	149	3	x−(s+1−n)d	x−(s+1−n)d	PROPN
ejpam-2531	149	4	x	x	PROPN
ejpam-2531	149	5	i2	i2	PROPN
ejpam-2531	149	6	=	=	PROPN
ejpam-2531	149	7	m	m	NOUN
ejpam-2531	149	8	∞	∞	NUM
ejpam-2531	149	9	∑	∑	PROPN
ejpam-2531	149	10	n=0	n=0	PROPN
ejpam-2531	149	11	mαn	mαn	ADJ
ejpam-2531	149	12	n!(s−	n!(s−	NOUN
ejpam-2531	149	13	n	n	CCONJ
ejpam-2531	149	14	)	)	PUNCT
ejpam-2531	149	15	,	,	PUNCT
ejpam-2531	149	16	s	s	VERB
ejpam-2531	149	17	>	>	X
ejpam-2531	149	18	n	n	PROPN
ejpam-2531	149	19	b.	b.	PROPN
ejpam-2531	149	20	barnes	barnes	PROPN
ejpam-2531	149	21	/	/	SYM
ejpam-2531	149	22	eur	eur	PROPN
ejpam-2531	149	23	.	.	PUNCT
ejpam-2531	150	1	j.	j.	PROPN
ejpam-2531	150	2	pure	pure	PROPN
ejpam-2531	150	3	appl	appl	PROPN
ejpam-2531	150	4	.	.	PROPN
ejpam-2531	150	5	math	math	PROPN
ejpam-2531	150	6	,	,	PUNCT
ejpam-2531	150	7	9	9	NUM
ejpam-2531	150	8	(	(	PUNCT
ejpam-2531	150	9	2016	2016	NUM
ejpam-2531	150	10	)	)	PUNCT
ejpam-2531	150	11	,	,	PUNCT
ejpam-2531	150	12	140	140	NUM
ejpam-2531	150	13	-	-	SYM
ejpam-2531	150	14	151	151	NUM
ejpam-2531	150	15	145	145	NUM
ejpam-2531	150	16	∫	∫	NOUN
ejpam-2531	150	17	∞	∞	NUM
ejpam-2531	150	18	1	1	NUM
ejpam-2531	150	19	f	f	PROPN
ejpam-2531	150	20	(	(	PUNCT
ejpam-2531	150	21	x).x−(s+1)d	x).x−(s+1)d	PUNCT
ejpam-2531	150	22	x	x	SYM
ejpam-2531	151	1	=	=	NOUN
ejpam-2531	151	2	m	m	NOUN
ejpam-2531	151	3	∞	∞	NUM
ejpam-2531	151	4	∑	∑	PROPN
ejpam-2531	151	5	n=0	n=0	PROPN
ejpam-2531	151	6	mαn	mαn	ADJ
ejpam-2531	151	7	n!(s−	n!(s−	NOUN
ejpam-2531	151	8	n	n	CCONJ
ejpam-2531	151	9	)	)	PUNCT
ejpam-2531	151	10	,	,	PUNCT
ejpam-2531	151	11	s	s	VERB
ejpam-2531	151	12	>	>	X
ejpam-2531	151	13	n	n	CCONJ
ejpam-2531	151	14	this	this	PRON
ejpam-2531	151	15	completes	complete	VERB
ejpam-2531	151	16	the	the	DET
ejpam-2531	151	17	proof	proof	NOUN
ejpam-2531	151	18	.	.	PUNCT
ejpam-2531	152	1	3	3	X
ejpam-2531	152	2	.	.	X
ejpam-2531	152	3	properties	property	NOUN
ejpam-2531	152	4	of	of	ADP
ejpam-2531	152	5	the	the	DET
ejpam-2531	152	6	polynomial	polynomial	ADJ
ejpam-2531	152	7	integral	integral	ADJ
ejpam-2531	152	8	transform	transform	NOUN
ejpam-2531	152	9	in	in	ADP
ejpam-2531	152	10	this	this	DET
ejpam-2531	152	11	section	section	NOUN
ejpam-2531	152	12	,	,	PUNCT
ejpam-2531	152	13	we	we	PRON
ejpam-2531	152	14	give	give	VERB
ejpam-2531	152	15	the	the	DET
ejpam-2531	152	16	properties	property	NOUN
ejpam-2531	152	17	of	of	ADP
ejpam-2531	152	18	the	the	DET
ejpam-2531	152	19	polynomial	polynomial	ADJ
ejpam-2531	152	20	integral	integral	ADJ
ejpam-2531	152	21	transform	transform	NOUN
ejpam-2531	152	22	.	.	PUNCT
ejpam-2531	153	1	theorem	theorem	NOUN
ejpam-2531	153	2	3	3	NUM
ejpam-2531	153	3	.	.	PUNCT
ejpam-2531	154	1	the	the	DET
ejpam-2531	154	2	polynomial	polynomial	ADJ
ejpam-2531	154	3	integral	integral	ADJ
ejpam-2531	154	4	transform	transform	NOUN
ejpam-2531	154	5	is	be	AUX
ejpam-2531	154	6	a	a	DET
ejpam-2531	154	7	linear	linear	ADJ
ejpam-2531	154	8	operator	operator	NOUN
ejpam-2531	154	9	.	.	PUNCT
ejpam-2531	155	1	proof	proof	NOUN
ejpam-2531	155	2	.	.	PUNCT
ejpam-2531	156	1	suppose	suppose	VERB
ejpam-2531	156	2	that	that	SCONJ
ejpam-2531	156	3	f	f	PROPN
ejpam-2531	156	4	(	(	PUNCT
ejpam-2531	156	5	x	x	NOUN
ejpam-2531	156	6	)	)	PUNCT
ejpam-2531	156	7	and	and	CCONJ
ejpam-2531	156	8	g(x	g(x	NOUN
ejpam-2531	156	9	)	)	PUNCT
ejpam-2531	156	10	are	be	AUX
ejpam-2531	156	11	functions	function	NOUN
ejpam-2531	156	12	and	and	CCONJ
ejpam-2531	156	13	α1	α1	PROPN
ejpam-2531	156	14	and	and	CCONJ
ejpam-2531	156	15	α2	α2	NOUN
ejpam-2531	156	16	are	be	AUX
ejpam-2531	156	17	real	real	ADJ
ejpam-2531	156	18	constants	constant	NOUN
ejpam-2531	156	19	.	.	PUNCT
ejpam-2531	157	1	b(α1	b(α1	NOUN
ejpam-2531	158	1	f	f	X
ejpam-2531	158	2	(	(	PUNCT
ejpam-2531	158	3	x	x	X
ejpam-2531	158	4	)	)	PUNCT
ejpam-2531	158	5	+	+	ADJ
ejpam-2531	158	6	α2	α2	ADJ
ejpam-2531	158	7	g(x	g(x	NOUN
ejpam-2531	158	8	)	)	PUNCT
ejpam-2531	158	9	)	)	PUNCT
ejpam-2531	159	1	=	=	SYM
ejpam-2531	159	2	∫	∫	PROPN
ejpam-2531	160	1	∞	∞	NUM
ejpam-2531	160	2	1	1	NUM
ejpam-2531	160	3	(	(	PUNCT
ejpam-2531	160	4	α1	α1	PROPN
ejpam-2531	160	5	f	f	PROPN
ejpam-2531	160	6	(	(	PUNCT
ejpam-2531	160	7	ln	ln	NOUN
ejpam-2531	160	8	x	x	NOUN
ejpam-2531	160	9	)	)	PUNCT
ejpam-2531	160	10	+	+	ADJ
ejpam-2531	160	11	α2	α2	ADJ
ejpam-2531	160	12	g(ln	g(ln	NOUN
ejpam-2531	160	13	x)).x−s−1d	x)).x−s−1d	SYM
ejpam-2531	160	14	x	x	X
ejpam-2531	160	15	b(α1	b(α1	NOUN
ejpam-2531	160	16	f	f	X
ejpam-2531	160	17	(	(	PUNCT
ejpam-2531	160	18	x	x	X
ejpam-2531	160	19	)	)	PUNCT
ejpam-2531	160	20	+	+	ADJ
ejpam-2531	160	21	α2	α2	ADJ
ejpam-2531	160	22	g(x	g(x	NOUN
ejpam-2531	160	23	)	)	PUNCT
ejpam-2531	160	24	)	)	PUNCT
ejpam-2531	161	1	=	=	SYM
ejpam-2531	161	2	α1	α1	PROPN
ejpam-2531	161	3	∫	∫	X
ejpam-2531	161	4	∞	∞	NUM
ejpam-2531	161	5	1	1	NUM
ejpam-2531	161	6	f	f	NOUN
ejpam-2531	161	7	(	(	PUNCT
ejpam-2531	161	8	ln	ln	X
ejpam-2531	161	9	x).x−s−1d	x).x−s−1d	PROPN
ejpam-2531	161	10	x	x	PUNCT
ejpam-2531	162	1	+	+	ADJ
ejpam-2531	162	2	α2	α2	ADJ
ejpam-2531	162	3	∫	∫	PROPN
ejpam-2531	162	4	∞	∞	NUM
ejpam-2531	162	5	1	1	NUM
ejpam-2531	162	6	g(ln	g(ln	PROPN
ejpam-2531	162	7	x).x−s−1d	x).x−s−1d	NOUN
ejpam-2531	162	8	x	x	SYM
ejpam-2531	162	9	b(α1	b(α1	NOUN
ejpam-2531	162	10	f	f	X
ejpam-2531	162	11	(	(	PUNCT
ejpam-2531	162	12	x	x	X
ejpam-2531	162	13	)	)	PUNCT
ejpam-2531	162	14	+	+	ADJ
ejpam-2531	162	15	α2	α2	ADJ
ejpam-2531	162	16	g(x	g(x	NOUN
ejpam-2531	162	17	)	)	PUNCT
ejpam-2531	162	18	)	)	PUNCT
ejpam-2531	163	1	=	=	SYM
ejpam-2531	163	2	α1b	α1b	PROPN
ejpam-2531	163	3	(	(	PUNCT
ejpam-2531	163	4	f	f	PROPN
ejpam-2531	163	5	(	(	PUNCT
ejpam-2531	163	6	x	x	NOUN
ejpam-2531	163	7	)	)	PUNCT
ejpam-2531	163	8	)	)	PUNCT
ejpam-2531	164	1	+	+	NOUN
ejpam-2531	164	2	α2b(g(x	α2b(g(x	NOUN
ejpam-2531	164	3	)	)	PUNCT
ejpam-2531	164	4	)	)	PUNCT
ejpam-2531	165	1	theorem	theorem	VERB
ejpam-2531	165	2	4	4	NUM
ejpam-2531	165	3	.	.	PUNCT
ejpam-2531	166	1	the	the	DET
ejpam-2531	166	2	inverse	inverse	ADJ
ejpam-2531	166	3	polynomial	polynomial	ADJ
ejpam-2531	166	4	integral	integral	ADJ
ejpam-2531	166	5	transform	transform	NOUN
ejpam-2531	166	6	is	be	AUX
ejpam-2531	166	7	a	a	DET
ejpam-2531	166	8	also	also	ADV
ejpam-2531	166	9	linear	linear	ADJ
ejpam-2531	166	10	operator	operator	NOUN
ejpam-2531	166	11	.	.	PUNCT
ejpam-2531	167	1	proof	proof	NOUN
ejpam-2531	167	2	.	.	PUNCT
ejpam-2531	168	1	taking	take	VERB
ejpam-2531	168	2	the	the	DET
ejpam-2531	168	3	inverse	inverse	ADJ
ejpam-2531	168	4	integral	integral	ADJ
ejpam-2531	168	5	transform	transform	NOUN
ejpam-2531	168	6	of	of	ADP
ejpam-2531	168	7	the	the	DET
ejpam-2531	168	8	both	both	DET
ejpam-2531	168	9	sides	side	NOUN
ejpam-2531	168	10	of	of	ADP
ejpam-2531	168	11	the	the	DET
ejpam-2531	168	12	above	above	ADJ
ejpam-2531	168	13	equation	equation	NOUN
ejpam-2531	168	14	,	,	PUNCT
ejpam-2531	168	15	we	we	PRON
ejpam-2531	168	16	obtain	obtain	VERB
ejpam-2531	168	17	α1	α1	PROPN
ejpam-2531	168	18	f	f	PROPN
ejpam-2531	168	19	(	(	PUNCT
ejpam-2531	168	20	x	x	X
ejpam-2531	168	21	)	)	PUNCT
ejpam-2531	168	22	+	+	ADJ
ejpam-2531	168	23	α2	α2	ADJ
ejpam-2531	168	24	g(x	g(x	NOUN
ejpam-2531	168	25	)	)	PUNCT
ejpam-2531	169	1	=	=	NOUN
ejpam-2531	169	2	b−1(α1	b−1(α1	NOUN
ejpam-2531	169	3	(	(	PUNCT
ejpam-2531	169	4	f	f	PROPN
ejpam-2531	169	5	(	(	PUNCT
ejpam-2531	169	6	x	x	NOUN
ejpam-2531	169	7	)	)	PUNCT
ejpam-2531	169	8	)	)	PUNCT
ejpam-2531	170	1	+	+	NOUN
ejpam-2531	170	2	α2b(g(x	α2b(g(x	NOUN
ejpam-2531	170	3	)	)	PUNCT
ejpam-2531	170	4	)	)	PUNCT
ejpam-2531	170	5	)	)	PUNCT
ejpam-2531	171	1	α1	α1	PROPN
ejpam-2531	171	2	f	f	PROPN
ejpam-2531	171	3	(	(	PUNCT
ejpam-2531	171	4	x	x	X
ejpam-2531	171	5	)	)	PUNCT
ejpam-2531	171	6	+	+	ADJ
ejpam-2531	171	7	α2	α2	ADJ
ejpam-2531	171	8	g(x	g(x	NOUN
ejpam-2531	171	9	)	)	PUNCT
ejpam-2531	172	1	=	=	X
ejpam-2531	172	2	α1b−1	α1b−1	NOUN
ejpam-2531	172	3	(	(	PUNCT
ejpam-2531	172	4	(	(	PUNCT
ejpam-2531	172	5	f	f	X
ejpam-2531	172	6	(	(	PUNCT
ejpam-2531	172	7	x	x	NOUN
ejpam-2531	172	8	)	)	PUNCT
ejpam-2531	172	9	)	)	PUNCT
ejpam-2531	172	10	)	)	PUNCT
ejpam-2531	173	1	+	+	VERB
ejpam-2531	173	2	α2b−1(l(g(x	α2b−1(l(g(x	ADJ
ejpam-2531	173	3	)	)	PUNCT
ejpam-2531	173	4	)	)	PUNCT
ejpam-2531	173	5	)	)	PUNCT
ejpam-2531	174	1	α1	α1	PROPN
ejpam-2531	174	2	f	f	PROPN
ejpam-2531	174	3	(	(	PUNCT
ejpam-2531	174	4	x	x	X
ejpam-2531	174	5	)	)	PUNCT
ejpam-2531	174	6	+	+	ADJ
ejpam-2531	174	7	α2	α2	ADJ
ejpam-2531	174	8	g(x	g(x	NOUN
ejpam-2531	174	9	)	)	PUNCT
ejpam-2531	175	1	=	=	SYM
ejpam-2531	175	2	α1b−1(f(s	α1b−1(f(	NOUN
ejpam-2531	175	3	)	)	PUNCT
ejpam-2531	175	4	)	)	PUNCT
ejpam-2531	176	1	+	+	NOUN
ejpam-2531	176	2	α2b−1(g(s	α2b−1(g(s	NUM
ejpam-2531	176	3	)	)	PUNCT
ejpam-2531	176	4	)	)	PUNCT
ejpam-2531	176	5	α1	α1	PROPN
ejpam-2531	176	6	f	f	PROPN
ejpam-2531	176	7	(	(	PUNCT
ejpam-2531	176	8	x	x	X
ejpam-2531	176	9	)	)	PUNCT
ejpam-2531	176	10	+	+	ADJ
ejpam-2531	176	11	α2	α2	ADJ
ejpam-2531	176	12	g(x	g(x	NOUN
ejpam-2531	176	13	)	)	PUNCT
ejpam-2531	177	1	=	=	X
ejpam-2531	177	2	b−1(α1f(s	b−1(α1f(s	NOUN
ejpam-2531	177	3	)	)	PUNCT
ejpam-2531	177	4	+	+	ADJ
ejpam-2531	177	5	α2g(s	α2g(s	NOUN
ejpam-2531	177	6	)	)	PUNCT
ejpam-2531	177	7	)	)	PUNCT
ejpam-2531	177	8	,	,	PUNCT
ejpam-2531	177	9	where	where	SCONJ
ejpam-2531	177	10	b	b	X
ejpam-2531	177	11	(	(	PUNCT
ejpam-2531	177	12	f	f	PROPN
ejpam-2531	177	13	(	(	PUNCT
ejpam-2531	177	14	x	x	NOUN
ejpam-2531	177	15	)	)	PUNCT
ejpam-2531	177	16	)	)	PUNCT
ejpam-2531	177	17	=	=	PUNCT
ejpam-2531	177	18	f(s	f(s	X
ejpam-2531	177	19	)	)	PUNCT
ejpam-2531	177	20	and	and	CCONJ
ejpam-2531	177	21	b(g(x	b(g(x	NOUN
ejpam-2531	177	22	)	)	PUNCT
ejpam-2531	177	23	)	)	PUNCT
ejpam-2531	177	24	=	=	SYM
ejpam-2531	177	25	g(s	g(s	PROPN
ejpam-2531	177	26	)	)	PUNCT
ejpam-2531	177	27	,	,	PUNCT
ejpam-2531	177	28	respectively	respectively	ADV
ejpam-2531	177	29	.	.	PUNCT
ejpam-2531	178	1	theorem	theorem	VERB
ejpam-2531	178	2	5	5	NUM
ejpam-2531	178	3	(	(	PUNCT
ejpam-2531	178	4	first	first	ADJ
ejpam-2531	178	5	shifting	shift	VERB
ejpam-2531	178	6	theorem	theorem	VERB
ejpam-2531	178	7	)	)	PUNCT
ejpam-2531	178	8	.	.	PUNCT
ejpam-2531	179	1	if	if	SCONJ
ejpam-2531	179	2	b	b	X
ejpam-2531	179	3	(	(	PUNCT
ejpam-2531	179	4	f	f	PROPN
ejpam-2531	179	5	(	(	PUNCT
ejpam-2531	179	6	x	x	NOUN
ejpam-2531	179	7	)	)	PUNCT
ejpam-2531	179	8	)	)	PUNCT
ejpam-2531	179	9	=	=	SYM
ejpam-2531	179	10	b(s	b(	NOUN
ejpam-2531	179	11	)	)	PUNCT
ejpam-2531	179	12	,	,	PUNCT
ejpam-2531	179	13	then	then	ADV
ejpam-2531	179	14	b(eax	b(eax	PROPN
ejpam-2531	179	15	f	f	PROPN
ejpam-2531	179	16	(	(	PUNCT
ejpam-2531	179	17	x	x	NOUN
ejpam-2531	179	18	)	)	PUNCT
ejpam-2531	179	19	)	)	PUNCT
ejpam-2531	180	1	=	=	PUNCT
ejpam-2531	180	2	b(s−	b(s−	PROPN
ejpam-2531	180	3	a	a	PRON
ejpam-2531	180	4	)	)	PUNCT
ejpam-2531	180	5	,	,	PUNCT
ejpam-2531	180	6	for	for	ADP
ejpam-2531	180	7	s	s	PROPN
ejpam-2531	180	8	>	>	X
ejpam-2531	180	9	1	1	NUM
ejpam-2531	180	10	.	.	PUNCT
ejpam-2531	180	11	proof	proof	NOUN
ejpam-2531	180	12	.	.	PUNCT
ejpam-2531	181	1	let	let	VERB
ejpam-2531	181	2	b(eax	b(eax	PROPN
ejpam-2531	181	3	f	f	X
ejpam-2531	181	4	(	(	PUNCT
ejpam-2531	181	5	x	x	NOUN
ejpam-2531	181	6	)	)	PUNCT
ejpam-2531	181	7	)	)	PUNCT
ejpam-2531	182	1	=	=	SYM
ejpam-2531	182	2	∫	∫	PROPN
ejpam-2531	183	1	∞	∞	NUM
ejpam-2531	183	2	1	1	NUM
ejpam-2531	183	3	ea	ea	NOUN
ejpam-2531	183	4	ln	ln	NOUN
ejpam-2531	183	5	x	x	X
ejpam-2531	183	6	f	f	PROPN
ejpam-2531	183	7	(	(	PUNCT
ejpam-2531	183	8	ln	ln	X
ejpam-2531	183	9	x).x−s−1d	x).x−s−1d	PROPN
ejpam-2531	183	10	x	x	PUNCT
ejpam-2531	183	11	b(eax	b(eax	NOUN
ejpam-2531	183	12	f	f	PROPN
ejpam-2531	183	13	(	(	PUNCT
ejpam-2531	183	14	x	x	NOUN
ejpam-2531	183	15	)	)	PUNCT
ejpam-2531	183	16	)	)	PUNCT
ejpam-2531	184	1	=	=	SYM
ejpam-2531	184	2	∫	∫	PROPN
ejpam-2531	185	1	∞	∞	NUM
ejpam-2531	185	2	1	1	NUM
ejpam-2531	185	3	xa	xa	PROPN
ejpam-2531	185	4	f	f	PROPN
ejpam-2531	185	5	(	(	PUNCT
ejpam-2531	185	6	ln	ln	X
ejpam-2531	185	7	x).x−s−1d	x).x−s−1d	PROPN
ejpam-2531	185	8	x	x	PUNCT
ejpam-2531	185	9	b(eax	b(eax	NOUN
ejpam-2531	185	10	f	f	PROPN
ejpam-2531	185	11	(	(	PUNCT
ejpam-2531	185	12	x	x	NOUN
ejpam-2531	185	13	)	)	PUNCT
ejpam-2531	185	14	)	)	PUNCT
ejpam-2531	186	1	=	=	SYM
ejpam-2531	186	2	∫	∫	PROPN
ejpam-2531	187	1	∞	∞	NUM
ejpam-2531	187	2	1	1	NUM
ejpam-2531	187	3	f	f	NOUN
ejpam-2531	187	4	(	(	PUNCT
ejpam-2531	187	5	ln	ln	PROPN
ejpam-2531	187	6	x).x−(s−a+1)d	x).x−(s−a+1)d	PROPN
ejpam-2531	187	7	x	x	PROPN
ejpam-2531	187	8	b.	b.	PROPN
ejpam-2531	187	9	barnes	barnes	PROPN
ejpam-2531	187	10	/	/	SYM
ejpam-2531	187	11	eur	eur	PROPN
ejpam-2531	187	12	.	.	PUNCT
ejpam-2531	188	1	j.	j.	PROPN
ejpam-2531	188	2	pure	pure	PROPN
ejpam-2531	188	3	appl	appl	PROPN
ejpam-2531	188	4	.	.	PROPN
ejpam-2531	188	5	math	math	PROPN
ejpam-2531	188	6	,	,	PUNCT
ejpam-2531	188	7	9	9	NUM
ejpam-2531	188	8	(	(	PUNCT
ejpam-2531	188	9	2016	2016	NUM
ejpam-2531	188	10	)	)	PUNCT
ejpam-2531	188	11	,	,	PUNCT
ejpam-2531	188	12	140	140	NUM
ejpam-2531	188	13	-	-	SYM
ejpam-2531	188	14	151	151	NUM
ejpam-2531	188	15	146	146	NUM
ejpam-2531	188	16	b(eax	b(eax	NOUN
ejpam-2531	188	17	f	f	NOUN
ejpam-2531	188	18	(	(	PUNCT
ejpam-2531	188	19	x	x	NOUN
ejpam-2531	188	20	)	)	PUNCT
ejpam-2531	188	21	)	)	PUNCT
ejpam-2531	189	1	=	=	NOUN
ejpam-2531	189	2	b(s−	b(s−	PROPN
ejpam-2531	189	3	a	a	NOUN
ejpam-2531	189	4	)	)	PUNCT
ejpam-2531	189	5	.	.	PUNCT
ejpam-2531	190	1	theorem	theorem	ADJ
ejpam-2531	190	2	6	6	NUM
ejpam-2531	190	3	(	(	PUNCT
ejpam-2531	190	4	second	second	ADV
ejpam-2531	190	5	shifting	shifting	NOUN
ejpam-2531	190	6	theorem	theorem	NOUN
ejpam-2531	190	7	)	)	PUNCT
ejpam-2531	190	8	.	.	PUNCT
ejpam-2531	191	1	let	let	VERB
ejpam-2531	191	2	hc(x	hc(x	NOUN
ejpam-2531	191	3	)	)	PUNCT
ejpam-2531	191	4	=	=	SYM
ejpam-2531	192	1	¨	¨	NOUN
ejpam-2531	192	2	0	0	NUM
ejpam-2531	192	3	0≤	0≤	NUM
ejpam-2531	192	4	x	x	X
ejpam-2531	192	5	<	<	X
ejpam-2531	192	6	c	c	X
ejpam-2531	192	7	1	1	NUM
ejpam-2531	192	8	x	x	SYM
ejpam-2531	192	9	≥	≥	NOUN
ejpam-2531	192	10	c	c	AUX
ejpam-2531	192	11	be	be	AUX
ejpam-2531	192	12	a	a	DET
ejpam-2531	192	13	unit	unit	NOUN
ejpam-2531	192	14	step	step	NOUN
ejpam-2531	192	15	function	function	NOUN
ejpam-2531	192	16	.	.	PUNCT
ejpam-2531	193	1	then	then	ADV
ejpam-2531	193	2	b(hc	b(hc	PROPN
ejpam-2531	193	3	f	f	PROPN
ejpam-2531	193	4	(	(	PUNCT
ejpam-2531	193	5	x	x	X
ejpam-2531	193	6	−	−	PROPN
ejpam-2531	193	7	c	c	NOUN
ejpam-2531	193	8	)	)	PUNCT
ejpam-2531	193	9	)	)	PUNCT
ejpam-2531	194	1	=	=	SYM
ejpam-2531	194	2	f(s−	f(s−	PROPN
ejpam-2531	194	3	c	c	NOUN
ejpam-2531	194	4	)	)	PUNCT
ejpam-2531	194	5	proof	proof	NOUN
ejpam-2531	194	6	.	.	PUNCT
ejpam-2531	195	1	by	by	ADP
ejpam-2531	195	2	applying	apply	VERB
ejpam-2531	195	3	the	the	DET
ejpam-2531	195	4	polynomial	polynomial	ADJ
ejpam-2531	195	5	integral	integral	ADJ
ejpam-2531	195	6	transform	transform	NOUN
ejpam-2531	195	7	,	,	PUNCT
ejpam-2531	195	8	we	we	PRON
ejpam-2531	195	9	obtain	obtain	VERB
ejpam-2531	195	10	b(hc(x	b(hc(x	NOUN
ejpam-2531	195	11	)	)	PUNCT
ejpam-2531	195	12	f	f	NOUN
ejpam-2531	195	13	(	(	PUNCT
ejpam-2531	195	14	x	x	X
ejpam-2531	195	15	−	−	PROPN
ejpam-2531	195	16	c	c	NOUN
ejpam-2531	195	17	)	)	PUNCT
ejpam-2531	195	18	)	)	PUNCT
ejpam-2531	196	1	=	=	SYM
ejpam-2531	196	2	∫	∫	PROPN
ejpam-2531	197	1	∞	∞	NUM
ejpam-2531	197	2	1	1	NUM
ejpam-2531	197	3	hc(ln	hc(ln	PROPN
ejpam-2531	197	4	x	x	NOUN
ejpam-2531	197	5	)	)	PUNCT
ejpam-2531	197	6	f	f	PROPN
ejpam-2531	197	7	(	(	PUNCT
ejpam-2531	197	8	ln(x	ln(x	X
ejpam-2531	197	9	−	−	PROPN
ejpam-2531	197	10	c)).x−s−1d	c)).x−s−1d	SYM
ejpam-2531	197	11	x	x	SYM
ejpam-2531	197	12	b(hc(x	b(hc(x	NOUN
ejpam-2531	197	13	)	)	PUNCT
ejpam-2531	197	14	f	f	NOUN
ejpam-2531	197	15	(	(	PUNCT
ejpam-2531	197	16	x	x	X
ejpam-2531	197	17	−	−	PROPN
ejpam-2531	197	18	c	c	NOUN
ejpam-2531	197	19	)	)	PUNCT
ejpam-2531	197	20	)	)	PUNCT
ejpam-2531	198	1	=	=	SYM
ejpam-2531	198	2	lim	lim	PROPN
ejpam-2531	198	3	t→∞	t→∞	X
ejpam-2531	198	4	∫	∫	PROPN
ejpam-2531	198	5	t	t	PROPN
ejpam-2531	198	6	1	1	NUM
ejpam-2531	198	7	1	1	NUM
ejpam-2531	198	8	.	.	PUNCT
ejpam-2531	199	1	f	f	PROPN
ejpam-2531	199	2	(	(	PUNCT
ejpam-2531	199	3	ln(x	ln(x	X
ejpam-2531	199	4	−	−	PROPN
ejpam-2531	199	5	c)).x−s−1d	c)).x−s−1d	SYM
ejpam-2531	199	6	x	x	SYM
ejpam-2531	199	7	b(hc(x	b(hc(x	NOUN
ejpam-2531	199	8	)	)	PUNCT
ejpam-2531	199	9	f	f	NOUN
ejpam-2531	199	10	(	(	PUNCT
ejpam-2531	199	11	x	x	X
ejpam-2531	199	12	−	−	PROPN
ejpam-2531	199	13	c	c	NOUN
ejpam-2531	199	14	)	)	PUNCT
ejpam-2531	199	15	)	)	PUNCT
ejpam-2531	200	1	=	=	SYM
ejpam-2531	200	2	lim	lim	PROPN
ejpam-2531	200	3	t→∞	t→∞	PRON
ejpam-2531	200	4	∫	∫	PROPN
ejpam-2531	200	5	t	t	PROPN
ejpam-2531	200	6	1	1	NUM
ejpam-2531	200	7	f	f	PROPN
ejpam-2531	200	8	(	(	PUNCT
ejpam-2531	200	9	ln(x	ln(x	X
ejpam-2531	200	10	−	−	PROPN
ejpam-2531	200	11	c)).x−s−1d	c)).x−s−1d	ADP
ejpam-2531	200	12	x	x	SYM
ejpam-2531	200	13	we	we	PRON
ejpam-2531	200	14	set	set	VERB
ejpam-2531	200	15	u=	u=	NOUN
ejpam-2531	200	16	x	x	NOUN
ejpam-2531	200	17	−	−	PROPN
ejpam-2531	200	18	c	c	NOUN
ejpam-2531	200	19	and	and	CCONJ
ejpam-2531	200	20	substituting	substitute	VERB
ejpam-2531	200	21	u	u	NOUN
ejpam-2531	200	22	into	into	ADP
ejpam-2531	200	23	right	right	ADJ
ejpam-2531	200	24	hand	hand	NOUN
ejpam-2531	200	25	side	side	NOUN
ejpam-2531	200	26	of	of	ADP
ejpam-2531	200	27	the	the	DET
ejpam-2531	200	28	above	above	ADJ
ejpam-2531	200	29	equation	equation	NOUN
ejpam-2531	200	30	,	,	PUNCT
ejpam-2531	200	31	we	we	PRON
ejpam-2531	200	32	obtain	obtain	VERB
ejpam-2531	200	33	b(hc(x	b(hc(x	NOUN
ejpam-2531	200	34	)	)	PUNCT
ejpam-2531	200	35	f	f	NOUN
ejpam-2531	200	36	(	(	PUNCT
ejpam-2531	200	37	x	x	X
ejpam-2531	200	38	−	−	PROPN
ejpam-2531	200	39	c	c	NOUN
ejpam-2531	200	40	)	)	PUNCT
ejpam-2531	200	41	)	)	PUNCT
ejpam-2531	201	1	=	=	SYM
ejpam-2531	201	2	lim	lim	PROPN
ejpam-2531	201	3	t→∞	t→∞	PRON
ejpam-2531	201	4	∫	∫	PROPN
ejpam-2531	201	5	t−c	t−c	PROPN
ejpam-2531	201	6	1−c	1−c	NUM
ejpam-2531	201	7	f	f	NOUN
ejpam-2531	201	8	(	(	PUNCT
ejpam-2531	201	9	ln	ln	PROPN
ejpam-2531	201	10	u).(u+	u).(u+	PROPN
ejpam-2531	201	11	c)−s−1du	c)−s−1du	ADV
ejpam-2531	201	12	b(hc(x	b(hc(x	PROPN
ejpam-2531	201	13	)	)	PUNCT
ejpam-2531	201	14	f	f	NOUN
ejpam-2531	201	15	(	(	PUNCT
ejpam-2531	201	16	x	x	X
ejpam-2531	201	17	−	−	PROPN
ejpam-2531	201	18	c	c	NOUN
ejpam-2531	201	19	)	)	PUNCT
ejpam-2531	201	20	)	)	PUNCT
ejpam-2531	202	1	=	=	SYM
ejpam-2531	202	2	lim	lim	PROPN
ejpam-2531	202	3	t→∞	t→∞	PRON
ejpam-2531	202	4	∫	∫	PROPN
ejpam-2531	202	5	t	t	PROPN
ejpam-2531	202	6	1	1	NUM
ejpam-2531	202	7	f	f	PROPN
ejpam-2531	202	8	(	(	PUNCT
ejpam-2531	202	9	ln(v	ln(v	PROPN
ejpam-2531	202	10	−	−	PROPN
ejpam-2531	202	11	c)).v−s−1dv	c)).v−s−1dv	NOUN
ejpam-2531	202	12	b(hc(x	b(hc(x	PROPN
ejpam-2531	202	13	)	)	PUNCT
ejpam-2531	202	14	f	f	NOUN
ejpam-2531	202	15	(	(	PUNCT
ejpam-2531	202	16	x	x	X
ejpam-2531	202	17	−	−	PROPN
ejpam-2531	202	18	c	c	NOUN
ejpam-2531	202	19	)	)	PUNCT
ejpam-2531	202	20	)	)	PUNCT
ejpam-2531	203	1	=	=	NOUN
ejpam-2531	203	2	f(s−	f(s−	PROPN
ejpam-2531	203	3	c	c	NOUN
ejpam-2531	203	4	)	)	PUNCT
ejpam-2531	203	5	,	,	PUNCT
ejpam-2531	203	6	where	where	SCONJ
ejpam-2531	203	7	v	v	NOUN
ejpam-2531	203	8	=	=	SYM
ejpam-2531	203	9	u+	u+	NOUN
ejpam-2531	203	10	c.	c.	NOUN
ejpam-2531	203	11	theorem	theorem	VERB
ejpam-2531	203	12	7	7	NUM
ejpam-2531	203	13	.	.	PUNCT
ejpam-2531	204	1	if	if	SCONJ
ejpam-2531	204	2	f	f	PROPN
ejpam-2531	204	3	(	(	PUNCT
ejpam-2531	204	4	x	x	X
ejpam-2531	204	5	)	)	PUNCT
ejpam-2531	204	6	is	be	AUX
ejpam-2531	204	7	a	a	DET
ejpam-2531	204	8	piecewise	piecewise	NOUN
ejpam-2531	204	9	continuous	continuous	ADJ
ejpam-2531	204	10	function	function	NOUN
ejpam-2531	204	11	on	on	ADP
ejpam-2531	204	12	[	[	X
ejpam-2531	204	13	0,∞	0,∞	NOUN
ejpam-2531	204	14	)	)	PUNCT
ejpam-2531	204	15	,	,	PUNCT
ejpam-2531	204	16	but	but	CCONJ
ejpam-2531	204	17	not	not	PART
ejpam-2531	204	18	of	of	ADP
ejpam-2531	204	19	exponential	exponential	ADJ
ejpam-2531	204	20	order	order	NOUN
ejpam-2531	204	21	,	,	PUNCT
ejpam-2531	204	22	then	then	ADV
ejpam-2531	204	23	a	a	DET
ejpam-2531	204	24	polynomial	polynomial	ADJ
ejpam-2531	204	25	integral	integral	ADJ
ejpam-2531	204	26	transform	transform	NOUN
ejpam-2531	204	27	b	b	X
ejpam-2531	204	28	(	(	PUNCT
ejpam-2531	204	29	f	f	X
ejpam-2531	204	30	(	(	PUNCT
ejpam-2531	204	31	x))→	x))→	NOUN
ejpam-2531	204	32	0	0	PUNCT
ejpam-2531	204	33	as	as	ADP
ejpam-2531	204	34	s→∞.	s→∞.	VERB
ejpam-2531	204	35	proof	proof	ADJ
ejpam-2531	204	36	.	.	PUNCT
ejpam-2531	205	1	let	let	VERB
ejpam-2531	205	2	|b	|b	NOUN
ejpam-2531	205	3	(	(	PUNCT
ejpam-2531	205	4	f	f	PROPN
ejpam-2531	205	5	(	(	PUNCT
ejpam-2531	205	6	x))|=|	x))|=|	PROPN
ejpam-2531	205	7	∫	∫	PROPN
ejpam-2531	205	8	∞	∞	NUM
ejpam-2531	205	9	1	1	NUM
ejpam-2531	205	10	f	f	X
ejpam-2531	205	11	(	(	PUNCT
ejpam-2531	205	12	ln	ln	ADJ
ejpam-2531	205	13	x)x−s−1d	x)x−s−1d	PROPN
ejpam-2531	205	14	x	x	SYM
ejpam-2531	205	15	|	|	PROPN
ejpam-2531	205	16	b.	b.	PROPN
ejpam-2531	205	17	barnes	barnes	PROPN
ejpam-2531	205	18	/	/	SYM
ejpam-2531	205	19	eur	eur	PROPN
ejpam-2531	205	20	.	.	PUNCT
ejpam-2531	206	1	j.	j.	PROPN
ejpam-2531	206	2	pure	pure	PROPN
ejpam-2531	206	3	appl	appl	PROPN
ejpam-2531	206	4	.	.	PROPN
ejpam-2531	206	5	math	math	PROPN
ejpam-2531	206	6	,	,	PUNCT
ejpam-2531	206	7	9	9	NUM
ejpam-2531	206	8	(	(	PUNCT
ejpam-2531	206	9	2016	2016	NUM
ejpam-2531	206	10	)	)	PUNCT
ejpam-2531	206	11	,	,	PUNCT
ejpam-2531	206	12	140	140	NUM
ejpam-2531	206	13	-	-	SYM
ejpam-2531	206	14	151	151	NUM
ejpam-2531	206	15	147	147	NUM
ejpam-2531	206	16	|b	|b	ADJ
ejpam-2531	206	17	(	(	PUNCT
ejpam-2531	206	18	f	f	PROPN
ejpam-2531	206	19	(	(	PUNCT
ejpam-2531	206	20	x))|	x))|	PROPN
ejpam-2531	206	21	≤	≤	PROPN
ejpam-2531	206	22	∫	∫	PROPN
ejpam-2531	207	1	∞	∞	NUM
ejpam-2531	207	2	1	1	NUM
ejpam-2531	208	1	|	|	ADV
ejpam-2531	208	2	f	f	X
ejpam-2531	208	3	(	(	PUNCT
ejpam-2531	208	4	ln	ln	NOUN
ejpam-2531	208	5	x)x−s−1|d	x)x−s−1|d	NOUN
ejpam-2531	208	6	x	x	X
ejpam-2531	208	7	|b	|b	X
ejpam-2531	208	8	(	(	PUNCT
ejpam-2531	208	9	f	f	PROPN
ejpam-2531	208	10	(	(	PUNCT
ejpam-2531	208	11	x))|=	x))|=	X
ejpam-2531	208	12	∫	∫	PROPN
ejpam-2531	208	13	∞	∞	NUM
ejpam-2531	208	14	1	1	NUM
ejpam-2531	208	15	f	f	NOUN
ejpam-2531	208	16	(	(	PUNCT
ejpam-2531	208	17	ln	ln	NOUN
ejpam-2531	208	18	x)|x−(s+1)|d	x)|x−(s+1)|d	PROPN
ejpam-2531	208	19	x	x	INTJ
ejpam-2531	208	20	.	.	PUNCT
ejpam-2531	209	1	but	but	CCONJ
ejpam-2531	209	2	,	,	PUNCT
ejpam-2531	209	3	we	we	PRON
ejpam-2531	209	4	observe	observe	VERB
ejpam-2531	209	5	that	that	SCONJ
ejpam-2531	209	6	:	:	PUNCT
ejpam-2531	209	7	|x−(s+1)|	|x−(s+1)|	X
ejpam-2531	209	8	→	→	SYM
ejpam-2531	209	9	0	0	PUNCT
ejpam-2531	209	10	as	as	ADP
ejpam-2531	209	11	s→∞.	s→∞.	VERB
ejpam-2531	209	12	it	it	PRON
ejpam-2531	209	13	follows	follow	VERB
ejpam-2531	209	14	that	that	SCONJ
ejpam-2531	209	15	b	b	X
ejpam-2531	209	16	(	(	PUNCT
ejpam-2531	209	17	f	f	X
ejpam-2531	209	18	(	(	PUNCT
ejpam-2531	209	19	x))→	x))→	NOUN
ejpam-2531	209	20	0	0	PUNCT
ejpam-2531	209	21	as	as	ADP
ejpam-2531	209	22	s→∞.	s→∞.	NOUN
ejpam-2531	209	23	4	4	NUM
ejpam-2531	209	24	.	.	PUNCT
ejpam-2531	210	1	the	the	DET
ejpam-2531	210	2	polynomial	polynomial	ADJ
ejpam-2531	210	3	integral	integral	ADJ
ejpam-2531	210	4	transform	transform	NOUN
ejpam-2531	210	5	of	of	ADP
ejpam-2531	210	6	derivatives	derivative	NOUN
ejpam-2531	210	7	in	in	ADP
ejpam-2531	210	8	this	this	DET
ejpam-2531	210	9	section	section	NOUN
ejpam-2531	210	10	,	,	PUNCT
ejpam-2531	210	11	we	we	PRON
ejpam-2531	210	12	give	give	VERB
ejpam-2531	210	13	the	the	DET
ejpam-2531	210	14	polynomial	polynomial	ADJ
ejpam-2531	210	15	integral	integral	ADJ
ejpam-2531	210	16	transform	transform	NOUN
ejpam-2531	210	17	of	of	ADP
ejpam-2531	210	18	derivatives	derivative	NOUN
ejpam-2531	210	19	of	of	ADP
ejpam-2531	210	20	the	the	DET
ejpam-2531	210	21	function	function	NOUN
ejpam-2531	210	22	f	f	PROPN
ejpam-2531	210	23	(	(	PUNCT
ejpam-2531	210	24	x	x	X
ejpam-2531	210	25	)	)	PUNCT
ejpam-2531	210	26	with	with	ADP
ejpam-2531	210	27	respect	respect	NOUN
ejpam-2531	210	28	to	to	ADP
ejpam-2531	210	29	x	x	X
ejpam-2531	210	30	.	.	PUNCT
ejpam-2531	211	1	theorem	theorem	ADJ
ejpam-2531	211	2	8	8	NUM
ejpam-2531	211	3	.	.	PUNCT
ejpam-2531	212	1	if	if	SCONJ
ejpam-2531	212	2	f	f	PROPN
ejpam-2531	212	3	,	,	PUNCT
ejpam-2531	212	4	f	f	PROPN
ejpam-2531	212	5	′	′	NOUN
ejpam-2531	212	6	,	,	PUNCT
ejpam-2531	212	7	.	.	PUNCT
ejpam-2531	212	8	.	.	PUNCT
ejpam-2531	212	9	.	.	PUNCT
ejpam-2531	213	1	f	f	PROPN
ejpam-2531	213	2	n−1	n−1	PROPN
ejpam-2531	213	3	are	be	AUX
ejpam-2531	213	4	continuous	continuous	ADJ
ejpam-2531	213	5	on	on	ADP
ejpam-2531	213	6	[	[	X
ejpam-2531	213	7	1,∞	1,∞	NUM
ejpam-2531	213	8	)	)	PUNCT
ejpam-2531	213	9	and	and	CCONJ
ejpam-2531	213	10	if	if	SCONJ
ejpam-2531	213	11	f	f	PROPN
ejpam-2531	213	12	n(x	n(x	PROPN
ejpam-2531	213	13	)	)	PUNCT
ejpam-2531	213	14	is	be	AUX
ejpam-2531	213	15	piecewise	piecewise	NOUN
ejpam-2531	213	16	continuous	continuous	ADJ
ejpam-2531	213	17	on	on	ADP
ejpam-2531	213	18	[	[	X
ejpam-2531	213	19	1,∞	1,∞	NUM
ejpam-2531	213	20	)	)	PUNCT
ejpam-2531	213	21	,	,	PUNCT
ejpam-2531	213	22	then	then	ADV
ejpam-2531	213	23	b	b	X
ejpam-2531	213	24	(	(	PUNCT
ejpam-2531	213	25	f	f	PROPN
ejpam-2531	213	26	(	(	PUNCT
ejpam-2531	213	27	n)(x	n)(x	PROPN
ejpam-2531	213	28	)	)	PUNCT
ejpam-2531	213	29	)	)	PUNCT
ejpam-2531	214	1	=	=	SYM
ejpam-2531	214	2	snf(s)−	snf(s)−	PROPN
ejpam-2531	214	3	sn−1	sn−1	PROPN
ejpam-2531	214	4	f	f	PROPN
ejpam-2531	214	5	(	(	PUNCT
ejpam-2531	214	6	0)−	0)−	PROPN
ejpam-2531	215	1	sn−2	sn−2	PROPN
ejpam-2531	215	2	f	f	PROPN
ejpam-2531	215	3	′(0)−	′(0)−	PROPN
ejpam-2531	215	4	.	.	PUNCT
ejpam-2531	215	5	.	.	PUNCT
ejpam-2531	216	1	.−	.−	PUNCT
ejpam-2531	217	1	f	f	X
ejpam-2531	217	2	(	(	PUNCT
ejpam-2531	217	3	n−1)(0	n−1)(0	PROPN
ejpam-2531	217	4	)	)	PUNCT
ejpam-2531	217	5	,	,	PUNCT
ejpam-2531	217	6	where	where	SCONJ
ejpam-2531	217	7	f(s	f(	VERB
ejpam-2531	217	8	)	)	PUNCT
ejpam-2531	217	9	=	=	SYM
ejpam-2531	217	10	b	b	X
ejpam-2531	217	11	(	(	PUNCT
ejpam-2531	217	12	f	f	PROPN
ejpam-2531	217	13	(	(	PUNCT
ejpam-2531	217	14	x	x	NOUN
ejpam-2531	217	15	)	)	PUNCT
ejpam-2531	217	16	)	)	PUNCT
ejpam-2531	217	17	.	.	PUNCT
ejpam-2531	218	1	proof	proof	NOUN
ejpam-2531	218	2	.	.	PUNCT
ejpam-2531	219	1	let	let	VERB
ejpam-2531	219	2	b	b	X
ejpam-2531	219	3	(	(	PUNCT
ejpam-2531	219	4	f	f	NOUN
ejpam-2531	219	5	′(x	′(x	NOUN
ejpam-2531	219	6	)	)	PUNCT
ejpam-2531	219	7	)	)	PUNCT
ejpam-2531	220	1	=	=	SYM
ejpam-2531	220	2	∫	∫	PROPN
ejpam-2531	221	1	∞	∞	NUM
ejpam-2531	221	2	1	1	NUM
ejpam-2531	221	3	f	f	PROPN
ejpam-2531	221	4	′(ln	′(ln	PROPN
ejpam-2531	221	5	x).x−s−1d	x).x−s−1d	PROPN
ejpam-2531	221	6	x	x	VERB
ejpam-2531	221	7	using	use	VERB
ejpam-2531	221	8	integration	integration	NOUN
ejpam-2531	221	9	by	by	ADP
ejpam-2531	221	10	parts	part	NOUN
ejpam-2531	221	11	,	,	PUNCT
ejpam-2531	221	12	we	we	PRON
ejpam-2531	221	13	obtain	obtain	VERB
ejpam-2531	221	14	l	l	NOUN
ejpam-2531	221	15	(	(	PUNCT
ejpam-2531	221	16	f	f	NOUN
ejpam-2531	221	17	′(x	′(x	NOUN
ejpam-2531	221	18	)	)	PUNCT
ejpam-2531	221	19	)	)	PUNCT
ejpam-2531	222	1	=	=	SYM
ejpam-2531	222	2	lim	lim	PROPN
ejpam-2531	222	3	t→∞	t→∞	X
ejpam-2531	223	1	[	[	PUNCT
ejpam-2531	223	2	f	f	X
ejpam-2531	223	3	(	(	PUNCT
ejpam-2531	223	4	ln	ln	NOUN
ejpam-2531	223	5	x)x−s]t1	x)x−s]t1	NOUN
ejpam-2531	224	1	+	+	CCONJ
ejpam-2531	225	1	lim	lim	PROPN
ejpam-2531	225	2	t→∞	t→∞	PRON
ejpam-2531	225	3	∫	∫	PROPN
ejpam-2531	225	4	t	t	PROPN
ejpam-2531	225	5	1	1	NUM
ejpam-2531	225	6	f	f	NOUN
ejpam-2531	225	7	(	(	PUNCT
ejpam-2531	225	8	ln	ln	NOUN
ejpam-2531	225	9	x	x	NOUN
ejpam-2531	225	10	)	)	PUNCT
ejpam-2531	225	11	1	1	NUM
ejpam-2531	225	12	x	x	SYM
ejpam-2531	225	13	x−sd	x−sd	PROPN
ejpam-2531	225	14	x	x	PUNCT
ejpam-2531	225	15	l	l	NOUN
ejpam-2531	225	16	(	(	PUNCT
ejpam-2531	225	17	f	f	NOUN
ejpam-2531	225	18	′(x	′(x	PROPN
ejpam-2531	225	19	)	)	PUNCT
ejpam-2531	225	20	)	)	PUNCT
ejpam-2531	226	1	=	=	SYM
ejpam-2531	226	2	sf(s)−	sf(s)−	PROPN
ejpam-2531	226	3	f	f	PROPN
ejpam-2531	226	4	(	(	PUNCT
ejpam-2531	226	5	0	0	NUM
ejpam-2531	226	6	)	)	PUNCT
ejpam-2531	226	7	.	.	PUNCT
ejpam-2531	227	1	proceeding	proceed	VERB
ejpam-2531	227	2	a	a	DET
ejpam-2531	227	3	similar	similar	ADJ
ejpam-2531	227	4	as	as	ADP
ejpam-2531	227	5	above	above	ADV
ejpam-2531	227	6	,	,	PUNCT
ejpam-2531	227	7	we	we	PRON
ejpam-2531	227	8	obtain	obtain	VERB
ejpam-2531	227	9	b	b	X
ejpam-2531	227	10	(	(	PUNCT
ejpam-2531	227	11	f	f	PROPN
ejpam-2531	227	12	′′(x	′′(x	PROPN
ejpam-2531	227	13	)	)	PUNCT
ejpam-2531	227	14	)	)	PUNCT
ejpam-2531	228	1	=	=	SYM
ejpam-2531	228	2	∫	∫	PROPN
ejpam-2531	229	1	∞	∞	NUM
ejpam-2531	229	2	1	1	NUM
ejpam-2531	229	3	f	f	PROPN
ejpam-2531	229	4	′′(ln	′′(ln	NOUN
ejpam-2531	229	5	x).x−s−1d	x).x−s−1d	PROPN
ejpam-2531	229	6	x	x	SYM
ejpam-2531	229	7	b	b	X
ejpam-2531	229	8	(	(	PUNCT
ejpam-2531	229	9	f	f	PROPN
ejpam-2531	229	10	′′(x	′′(x	PROPN
ejpam-2531	229	11	)	)	PUNCT
ejpam-2531	229	12	)	)	PUNCT
ejpam-2531	230	1	=	=	SYM
ejpam-2531	230	2	−	−	PROPN
ejpam-2531	230	3	f	f	PROPN
ejpam-2531	230	4	′(0	′(0	PROPN
ejpam-2531	230	5	)	)	PUNCT
ejpam-2531	231	1	+	+	CCONJ
ejpam-2531	231	2	sl	sl	PROPN
ejpam-2531	231	3	(	(	PUNCT
ejpam-2531	231	4	f	f	PROPN
ejpam-2531	231	5	′(x	′(x	PROPN
ejpam-2531	231	6	)	)	PUNCT
ejpam-2531	231	7	)	)	PUNCT
ejpam-2531	231	8	substituting	substitute	VERB
ejpam-2531	231	9	the	the	DET
ejpam-2531	231	10	expression	expression	NOUN
ejpam-2531	231	11	of	of	ADP
ejpam-2531	231	12	f	f	PROPN
ejpam-2531	231	13	′(x	′(x	PROPN
ejpam-2531	231	14	)	)	PUNCT
ejpam-2531	231	15	into	into	ADP
ejpam-2531	231	16	the	the	DET
ejpam-2531	231	17	above	above	ADJ
ejpam-2531	231	18	equation	equation	NOUN
ejpam-2531	231	19	,	,	PUNCT
ejpam-2531	231	20	we	we	PRON
ejpam-2531	231	21	obtain	obtain	VERB
ejpam-2531	231	22	b	b	X
ejpam-2531	231	23	(	(	PUNCT
ejpam-2531	231	24	f	f	PROPN
ejpam-2531	231	25	′′(x	′′(x	PROPN
ejpam-2531	231	26	)	)	PUNCT
ejpam-2531	231	27	)	)	PUNCT
ejpam-2531	232	1	=	=	PUNCT
ejpam-2531	233	1	s2f(s)−	s2f(s)−	PUNCT
ejpam-2531	233	2	s	s	PART
ejpam-2531	233	3	f	f	X
ejpam-2531	233	4	(	(	PUNCT
ejpam-2531	233	5	0)−	0)−	NUM
ejpam-2531	233	6	f	f	PROPN
ejpam-2531	233	7	′(0	′(0	PROPN
ejpam-2531	233	8	)	)	PUNCT
ejpam-2531	233	9	.	.	PUNCT
ejpam-2531	234	1	by	by	ADP
ejpam-2531	234	2	induction	induction	NOUN
ejpam-2531	234	3	,	,	PUNCT
ejpam-2531	234	4	we	we	PRON
ejpam-2531	234	5	obtain	obtain	VERB
ejpam-2531	234	6	b	b	X
ejpam-2531	234	7	(	(	PUNCT
ejpam-2531	234	8	f	f	PROPN
ejpam-2531	234	9	(	(	PUNCT
ejpam-2531	234	10	n)(x	n)(x	PROPN
ejpam-2531	234	11	)	)	PUNCT
ejpam-2531	234	12	)	)	PUNCT
ejpam-2531	235	1	=	=	SYM
ejpam-2531	235	2	snf(s)−	snf(s)−	PROPN
ejpam-2531	235	3	sn−1	sn−1	PROPN
ejpam-2531	235	4	f	f	PROPN
ejpam-2531	235	5	(	(	PUNCT
ejpam-2531	235	6	0)−	0)−	PROPN
ejpam-2531	236	1	sn−2	sn−2	PROPN
ejpam-2531	236	2	f	f	PROPN
ejpam-2531	236	3	′(0)−	′(0)−	PROPN
ejpam-2531	236	4	.	.	PUNCT
ejpam-2531	236	5	.	.	PUNCT
ejpam-2531	237	1	.−	.−	PUNCT
ejpam-2531	238	1	f	f	X
ejpam-2531	238	2	(	(	PUNCT
ejpam-2531	238	3	n−1)(0	n−1)(0	PROPN
ejpam-2531	238	4	)	)	PUNCT
ejpam-2531	238	5	,	,	PUNCT
ejpam-2531	238	6	where	where	SCONJ
ejpam-2531	238	7	f(s	f(	VERB
ejpam-2531	238	8	)	)	PUNCT
ejpam-2531	238	9	=	=	SYM
ejpam-2531	238	10	b	b	X
ejpam-2531	238	11	(	(	PUNCT
ejpam-2531	238	12	f	f	PROPN
ejpam-2531	238	13	(	(	PUNCT
ejpam-2531	238	14	x	x	NOUN
ejpam-2531	238	15	)	)	PUNCT
ejpam-2531	238	16	)	)	PUNCT
ejpam-2531	238	17	.	.	PUNCT
ejpam-2531	239	1	b.	b.	PROPN
ejpam-2531	239	2	barnes	barnes	PROPN
ejpam-2531	239	3	/	/	SYM
ejpam-2531	239	4	eur	eur	PROPN
ejpam-2531	239	5	.	.	PUNCT
ejpam-2531	240	1	j.	j.	PROPN
ejpam-2531	240	2	pure	pure	PROPN
ejpam-2531	240	3	appl	appl	PROPN
ejpam-2531	240	4	.	.	PROPN
ejpam-2531	240	5	math	math	PROPN
ejpam-2531	240	6	,	,	PUNCT
ejpam-2531	240	7	9	9	NUM
ejpam-2531	240	8	(	(	PUNCT
ejpam-2531	240	9	2016	2016	NUM
ejpam-2531	240	10	)	)	PUNCT
ejpam-2531	240	11	,	,	PUNCT
ejpam-2531	240	12	140	140	NUM
ejpam-2531	240	13	-	-	SYM
ejpam-2531	240	14	151	151	NUM
ejpam-2531	240	15	148	148	NUM
ejpam-2531	240	16	corollary	corollary	NOUN
ejpam-2531	240	17	1	1	NUM
ejpam-2531	240	18	.	.	PUNCT
ejpam-2531	240	19	suppose	suppose	VERB
ejpam-2531	240	20	f	f	PROPN
ejpam-2531	240	21	is	be	AUX
ejpam-2531	240	22	a	a	DET
ejpam-2531	240	23	piecewise	piecewise	NOUN
ejpam-2531	240	24	function	function	NOUN
ejpam-2531	240	25	and	and	CCONJ
ejpam-2531	240	26	let	let	VERB
ejpam-2531	240	27	f(s	f(	NOUN
ejpam-2531	240	28	)	)	PUNCT
ejpam-2531	240	29	by	by	ADP
ejpam-2531	240	30	the	the	DET
ejpam-2531	240	31	polynomial	polynomial	ADJ
ejpam-2531	240	32	integral	integral	ADJ
ejpam-2531	240	33	transform	transform	NOUN
ejpam-2531	240	34	by	by	ADP
ejpam-2531	240	35	equation	equation	NOUN
ejpam-2531	240	36	(	(	PUNCT
ejpam-2531	240	37	4	4	NUM
ejpam-2531	240	38	)	)	PUNCT
ejpam-2531	240	39	.	.	PUNCT
ejpam-2531	241	1	then	then	ADV
ejpam-2531	241	2	,	,	PUNCT
ejpam-2531	241	3	we	we	PRON
ejpam-2531	241	4	obtain	obtain	VERB
ejpam-2531	241	5	l(xn	l(xn	PROPN
ejpam-2531	241	6	f	f	PROPN
ejpam-2531	241	7	(	(	PUNCT
ejpam-2531	241	8	x))(s	x))(s	PROPN
ejpam-2531	241	9	)	)	PUNCT
ejpam-2531	241	10	=	=	PUNCT
ejpam-2531	241	11	(	(	PUNCT
ejpam-2531	241	12	−1)nf	−1)nf	PROPN
ejpam-2531	241	13	(	(	PUNCT
ejpam-2531	241	14	n)(s	n)(s	NOUN
ejpam-2531	241	15	)	)	PUNCT
ejpam-2531	241	16	proof	proof	NOUN
ejpam-2531	241	17	.	.	PUNCT
ejpam-2531	242	1	by	by	ADP
ejpam-2531	242	2	applying	apply	VERB
ejpam-2531	242	3	the	the	DET
ejpam-2531	242	4	polynomial	polynomial	ADJ
ejpam-2531	242	5	integral	integral	ADJ
ejpam-2531	242	6	transform	transform	NOUN
ejpam-2531	242	7	,	,	PUNCT
ejpam-2531	242	8	we	we	PRON
ejpam-2531	242	9	obtain	obtain	VERB
ejpam-2531	242	10	f	f	PROPN
ejpam-2531	242	11	′(s	′(s	NOUN
ejpam-2531	242	12	)	)	PUNCT
ejpam-2531	242	13	=	=	PUNCT
ejpam-2531	243	1	d	d	NOUN
ejpam-2531	243	2	ds	ds	ADJ
ejpam-2531	243	3	∫	∫	NOUN
ejpam-2531	243	4	∞	∞	NUM
ejpam-2531	243	5	1	1	NUM
ejpam-2531	243	6	f	f	NOUN
ejpam-2531	243	7	(	(	PUNCT
ejpam-2531	243	8	ln	ln	X
ejpam-2531	243	9	x).x−s−1d	x).x−s−1d	PROPN
ejpam-2531	243	10	x	x	X
ejpam-2531	243	11	f	f	PROPN
ejpam-2531	243	12	′(s	′(s	NOUN
ejpam-2531	243	13	)	)	PUNCT
ejpam-2531	243	14	=	=	SYM
ejpam-2531	244	1	∫	∫	PROPN
ejpam-2531	244	2	∞	∞	NUM
ejpam-2531	244	3	1	1	NUM
ejpam-2531	244	4	f	f	X
ejpam-2531	244	5	(	(	PUNCT
ejpam-2531	244	6	ln	ln	PROPN
ejpam-2531	244	7	x).x−1	x).x−1	PROPN
ejpam-2531	244	8	∂	∂	PROPN
ejpam-2531	244	9	∂	∂	NOUN
ejpam-2531	244	10	s	s	PART
ejpam-2531	244	11	eln	eln	NOUN
ejpam-2531	244	12	x−s	x−s	PUNCT
ejpam-2531	245	1	d	d	X
ejpam-2531	245	2	x	x	X
ejpam-2531	245	3	f	f	PROPN
ejpam-2531	245	4	′(s	′(s	NOUN
ejpam-2531	245	5	)	)	PUNCT
ejpam-2531	245	6	=	=	SYM
ejpam-2531	246	1	∫	∫	PROPN
ejpam-2531	246	2	∞	∞	NUM
ejpam-2531	246	3	1	1	NUM
ejpam-2531	246	4	f	f	X
ejpam-2531	246	5	(	(	PUNCT
ejpam-2531	246	6	ln	ln	PROPN
ejpam-2531	246	7	x).x−1	x).x−1	PROPN
ejpam-2531	246	8	∂	∂	NUM
ejpam-2531	246	9	∂	∂	NUM
ejpam-2531	246	10	s	s	PART
ejpam-2531	246	11	e−s	e−s	NOUN
ejpam-2531	246	12	ln	ln	NOUN
ejpam-2531	246	13	x	x	PUNCT
ejpam-2531	246	14	d	d	X
ejpam-2531	246	15	x	x	X
ejpam-2531	246	16	f	f	PROPN
ejpam-2531	246	17	′(s	′(s	NOUN
ejpam-2531	246	18	)	)	PUNCT
ejpam-2531	247	1	=	=	NOUN
ejpam-2531	247	2	−	−	PROPN
ejpam-2531	247	3	∫	∫	PROPN
ejpam-2531	247	4	∞	∞	NUM
ejpam-2531	247	5	1	1	NUM
ejpam-2531	247	6	ln	ln	NOUN
ejpam-2531	247	7	x	x	X
ejpam-2531	247	8	f	f	X
ejpam-2531	247	9	(	(	PUNCT
ejpam-2531	247	10	ln	ln	X
ejpam-2531	247	11	x).x−s−1d	x).x−s−1d	PROPN
ejpam-2531	247	12	x	x	PROPN
ejpam-2531	247	13	−f	−f	PROPN
ejpam-2531	247	14	′(s	′(s	NOUN
ejpam-2531	247	15	)	)	PUNCT
ejpam-2531	248	1	=	=	NOUN
ejpam-2531	248	2	l(x	l(x	X
ejpam-2531	248	3	f	f	X
ejpam-2531	248	4	(	(	PUNCT
ejpam-2531	248	5	x	x	NOUN
ejpam-2531	248	6	)	)	PUNCT
ejpam-2531	248	7	)	)	PUNCT
ejpam-2531	248	8	proceeding	proceed	VERB
ejpam-2531	248	9	in	in	ADP
ejpam-2531	248	10	a	a	DET
ejpam-2531	248	11	similar	similar	ADJ
ejpam-2531	248	12	manner	manner	NOUN
ejpam-2531	248	13	,	,	PUNCT
ejpam-2531	248	14	we	we	PRON
ejpam-2531	248	15	obtain	obtain	VERB
ejpam-2531	248	16	f	f	PROPN
ejpam-2531	248	17	′′(s	′′(s	NOUN
ejpam-2531	248	18	)	)	PUNCT
ejpam-2531	248	19	=	=	PUNCT
ejpam-2531	249	1	d	d	NOUN
ejpam-2531	249	2	ds	ds	ADJ
ejpam-2531	249	3	∫	∫	NOUN
ejpam-2531	249	4	∞	∞	NUM
ejpam-2531	249	5	1	1	NUM
ejpam-2531	249	6	ln	ln	NOUN
ejpam-2531	249	7	x	x	X
ejpam-2531	249	8	f	f	X
ejpam-2531	249	9	(	(	PUNCT
ejpam-2531	249	10	ln	ln	X
ejpam-2531	249	11	x).x−s−1d	x).x−s−1d	PROPN
ejpam-2531	249	12	x	x	X
ejpam-2531	249	13	f	f	PROPN
ejpam-2531	249	14	′′(s	′′(s	NOUN
ejpam-2531	249	15	)	)	PUNCT
ejpam-2531	249	16	=	=	NOUN
ejpam-2531	249	17	l(x2	l(x2	NOUN
ejpam-2531	249	18	f	f	X
ejpam-2531	249	19	(	(	PUNCT
ejpam-2531	249	20	x	x	NOUN
ejpam-2531	249	21	)	)	PUNCT
ejpam-2531	249	22	)	)	PUNCT
ejpam-2531	249	23	...	...	PUNCT
ejpam-2531	250	1	(	(	PUNCT
ejpam-2531	250	2	−1)nf	−1)nf	PROPN
ejpam-2531	250	3	(	(	PUNCT
ejpam-2531	250	4	n)(s	n)(s	NOUN
ejpam-2531	250	5	)	)	PUNCT
ejpam-2531	250	6	=	=	NOUN
ejpam-2531	250	7	l(xn	l(xn	X
ejpam-2531	250	8	f	f	PROPN
ejpam-2531	250	9	(	(	PUNCT
ejpam-2531	250	10	x))(s	x))(s	PROPN
ejpam-2531	250	11	)	)	PUNCT
ejpam-2531	250	12	,	,	PUNCT
ejpam-2531	250	13	where	where	SCONJ
ejpam-2531	250	14	n=	n=	ADJ
ejpam-2531	250	15	1,2	1,2	NUM
ejpam-2531	250	16	,	,	PUNCT
ejpam-2531	250	17	.	.	PUNCT
ejpam-2531	250	18	.	.	PUNCT
ejpam-2531	251	1	..	..	PUNCT
ejpam-2531	252	1	4.1	4.1	NUM
ejpam-2531	252	2	.	.	PUNCT
ejpam-2531	252	3	applications	application	NOUN
ejpam-2531	252	4	of	of	ADP
ejpam-2531	252	5	polynomial	polynomial	ADJ
ejpam-2531	252	6	integral	integral	ADJ
ejpam-2531	252	7	transform	transform	NOUN
ejpam-2531	252	8	to	to	PART
ejpam-2531	252	9	linear	linear	VERB
ejpam-2531	252	10	ordinary	ordinary	ADJ
ejpam-2531	252	11	differential	differential	ADJ
ejpam-2531	252	12	equation	equation	NOUN
ejpam-2531	252	13	with	with	ADP
ejpam-2531	252	14	constant	constant	ADJ
ejpam-2531	252	15	coefficients	coefficient	NOUN
ejpam-2531	252	16	we	we	PRON
ejpam-2531	252	17	apply	apply	VERB
ejpam-2531	252	18	the	the	DET
ejpam-2531	252	19	polynomial	polynomial	ADJ
ejpam-2531	252	20	integral	integral	ADJ
ejpam-2531	252	21	transform	transform	NOUN
ejpam-2531	252	22	to	to	PART
ejpam-2531	252	23	obtain	obtain	VERB
ejpam-2531	252	24	the	the	DET
ejpam-2531	252	25	solutions	solution	NOUN
ejpam-2531	252	26	of	of	ADP
ejpam-2531	252	27	the	the	DET
ejpam-2531	252	28	ordinary	ordinary	ADJ
ejpam-2531	252	29	differential	differential	ADJ
ejpam-2531	252	30	equations	equation	NOUN
ejpam-2531	252	31	as	as	SCONJ
ejpam-2531	252	32	follows	follow	VERB
ejpam-2531	252	33	:	:	PUNCT
ejpam-2531	252	34	example	example	NOUN
ejpam-2531	252	35	1	1	X
ejpam-2531	252	36	.	.	PUNCT
ejpam-2531	253	1	d2	d2	PROPN
ejpam-2531	253	2	y	y	PROPN
ejpam-2531	253	3	d	d	PROPN
ejpam-2531	253	4	x2	x2	PROPN
ejpam-2531	254	1	−	−	PROPN
ejpam-2531	254	2	d	d	X
ejpam-2531	254	3	y	y	PROPN
ejpam-2531	254	4	d	d	NOUN
ejpam-2531	254	5	x	x	PROPN
ejpam-2531	254	6	−	−	PROPN
ejpam-2531	254	7	6y(x	6y(x	NOUN
ejpam-2531	254	8	)	)	PUNCT
ejpam-2531	254	9	=	=	SYM
ejpam-2531	255	1	0	0	NUM
ejpam-2531	255	2	,	,	PUNCT
ejpam-2531	255	3	y(0	y(0	PROPN
ejpam-2531	255	4	)	)	PUNCT
ejpam-2531	255	5	=	=	SYM
ejpam-2531	255	6	0	0	NUM
ejpam-2531	255	7	,	,	PUNCT
ejpam-2531	255	8	y	y	PROPN
ejpam-2531	255	9	′(0	′(0	PROPN
ejpam-2531	255	10	)	)	PUNCT
ejpam-2531	256	1	=	=	PRON
ejpam-2531	256	2	−7	−7	ADP
ejpam-2531	256	3	using	use	VERB
ejpam-2531	256	4	the	the	DET
ejpam-2531	256	5	polynomial	polynomial	ADJ
ejpam-2531	256	6	integral	integral	ADJ
ejpam-2531	256	7	transform	transform	NOUN
ejpam-2531	256	8	,	,	PUNCT
ejpam-2531	256	9	we	we	PRON
ejpam-2531	256	10	obtain	obtain	VERB
ejpam-2531	256	11	b(y	b(y	PRON
ejpam-2531	256	12	′′(x)−	′′(x)−	PROPN
ejpam-2531	256	13	y	y	PROPN
ejpam-2531	256	14	′(x)−	′(x)−	PROPN
ejpam-2531	256	15	6y(x	6y(x	NOUN
ejpam-2531	256	16	)	)	PUNCT
ejpam-2531	256	17	)	)	PUNCT
ejpam-2531	257	1	=	=	SYM
ejpam-2531	257	2	b(0	b(0	NOUN
ejpam-2531	257	3	)	)	PUNCT
ejpam-2531	257	4	y(x	y(x	NOUN
ejpam-2531	257	5	)	)	PUNCT
ejpam-2531	258	1	=	=	SYM
ejpam-2531	258	2	b−1	b−1	NOUN
ejpam-2531	258	3	(	(	PUNCT
ejpam-2531	258	4	−1	−1	NOUN
ejpam-2531	258	5	(	(	PUNCT
ejpam-2531	258	6	s−	s−	PROPN
ejpam-2531	258	7	3	3	NUM
ejpam-2531	258	8	)	)	PUNCT
ejpam-2531	258	9	+	+	CCONJ
ejpam-2531	258	10	2	2	NUM
ejpam-2531	258	11	(	(	PUNCT
ejpam-2531	258	12	s+	s+	X
ejpam-2531	258	13	2	2	NUM
ejpam-2531	258	14	)	)	PUNCT
ejpam-2531	258	15	)	)	PUNCT
ejpam-2531	258	16	y(x	y(x	PROPN
ejpam-2531	258	17	)	)	PUNCT
ejpam-2531	259	1	=	=	NOUN
ejpam-2531	259	2	−	−	ADP
ejpam-2531	259	3	e3x	e3x	PROPN
ejpam-2531	259	4	+	+	PROPN
ejpam-2531	259	5	2e−2x	2e−2x	NOUN
ejpam-2531	259	6	.	.	PUNCT
ejpam-2531	260	1	b.	b.	PROPN
ejpam-2531	260	2	barnes	barnes	PROPN
ejpam-2531	260	3	/	/	SYM
ejpam-2531	260	4	eur	eur	PROPN
ejpam-2531	260	5	.	.	PUNCT
ejpam-2531	261	1	j.	j.	PROPN
ejpam-2531	261	2	pure	pure	PROPN
ejpam-2531	261	3	appl	appl	PROPN
ejpam-2531	261	4	.	.	PROPN
ejpam-2531	261	5	math	math	PROPN
ejpam-2531	261	6	,	,	PUNCT
ejpam-2531	261	7	9	9	NUM
ejpam-2531	261	8	(	(	PUNCT
ejpam-2531	261	9	2016	2016	NUM
ejpam-2531	261	10	)	)	PUNCT
ejpam-2531	261	11	,	,	PUNCT
ejpam-2531	261	12	140	140	NUM
ejpam-2531	261	13	-	-	SYM
ejpam-2531	261	14	151	151	NUM
ejpam-2531	261	15	149	149	NUM
ejpam-2531	261	16	example	example	NOUN
ejpam-2531	261	17	2	2	NUM
ejpam-2531	261	18	.	.	PUNCT
ejpam-2531	262	1	d2	d2	PROPN
ejpam-2531	262	2	y	y	PROPN
ejpam-2531	262	3	d	d	PROPN
ejpam-2531	262	4	x2	x2	PROPN
ejpam-2531	263	1	−	−	PROPN
ejpam-2531	263	2	3	3	NUM
ejpam-2531	264	1	d	d	X
ejpam-2531	264	2	y	y	PROPN
ejpam-2531	264	3	d	d	NOUN
ejpam-2531	264	4	x	x	X
ejpam-2531	264	5	+	+	NUM
ejpam-2531	264	6	2y(x	2y(x	NUM
ejpam-2531	264	7	)	)	PUNCT
ejpam-2531	265	1	=	=	SYM
ejpam-2531	265	2	x	x	X
ejpam-2531	265	3	,	,	PUNCT
ejpam-2531	265	4	y(0	y(0	PROPN
ejpam-2531	265	5	)	)	PUNCT
ejpam-2531	265	6	=	=	SYM
ejpam-2531	265	7	0	0	NUM
ejpam-2531	265	8	,	,	PUNCT
ejpam-2531	265	9	y	y	PROPN
ejpam-2531	265	10	′(0	′(0	PROPN
ejpam-2531	265	11	)	)	PUNCT
ejpam-2531	265	12	=	=	SYM
ejpam-2531	265	13	1	1	NUM
ejpam-2531	265	14	applying	apply	VERB
ejpam-2531	265	15	polynomial	polynomial	ADJ
ejpam-2531	265	16	integral	integral	ADJ
ejpam-2531	265	17	transform	transform	NOUN
ejpam-2531	265	18	to	to	ADP
ejpam-2531	265	19	the	the	DET
ejpam-2531	265	20	above	above	ADJ
ejpam-2531	265	21	equation	equation	NOUN
ejpam-2531	265	22	,	,	PUNCT
ejpam-2531	265	23	we	we	PRON
ejpam-2531	265	24	obtain	obtain	VERB
ejpam-2531	265	25	b(y	b(y	NOUN
ejpam-2531	265	26	′′(x)−3y	′′(x)−3y	X
ejpam-2531	265	27	′(x	′(x	NOUN
ejpam-2531	265	28	)	)	PUNCT
ejpam-2531	265	29	+	+	NUM
ejpam-2531	265	30	2y(x	2y(x	NUM
ejpam-2531	265	31	)	)	PUNCT
ejpam-2531	265	32	)	)	PUNCT
ejpam-2531	266	1	=	=	SYM
ejpam-2531	266	2	b(x	b(x	NOUN
ejpam-2531	266	3	)	)	PUNCT
ejpam-2531	266	4	y(x	y(x	NOUN
ejpam-2531	266	5	)	)	PUNCT
ejpam-2531	267	1	=	=	SYM
ejpam-2531	267	2	b−1	b−1	NOUN
ejpam-2531	267	3	(	(	PUNCT
ejpam-2531	267	4	3	3	NUM
ejpam-2531	267	5	4	4	NUM
ejpam-2531	267	6	.	.	PUNCT
ejpam-2531	268	1	1	1	NUM
ejpam-2531	268	2	s	s	NOUN
ejpam-2531	268	3	+	+	NOUN
ejpam-2531	268	4	1	1	NUM
ejpam-2531	268	5	4	4	NUM
ejpam-2531	268	6	.	.	SYM
ejpam-2531	268	7	1	1	NUM
ejpam-2531	268	8	s2	s2	NOUN
ejpam-2531	268	9	−	−	NOUN
ejpam-2531	268	10	2	2	NUM
ejpam-2531	268	11	.	.	SYM
ejpam-2531	268	12	1	1	NUM
ejpam-2531	268	13	(	(	PUNCT
ejpam-2531	268	14	s−	s−	PROPN
ejpam-2531	268	15	1	1	NUM
ejpam-2531	268	16	)	)	PUNCT
ejpam-2531	268	17	+	+	CCONJ
ejpam-2531	268	18	5	5	NUM
ejpam-2531	268	19	4	4	NUM
ejpam-2531	268	20	.	.	NOUN
ejpam-2531	268	21	1	1	NUM
ejpam-2531	268	22	(	(	PUNCT
ejpam-2531	268	23	s−	s−	PROPN
ejpam-2531	268	24	2	2	NUM
ejpam-2531	268	25	)	)	PUNCT
ejpam-2531	268	26	)	)	PUNCT
ejpam-2531	268	27	y(x	y(x	PROPN
ejpam-2531	268	28	)	)	PUNCT
ejpam-2531	268	29	=	=	PUNCT
ejpam-2531	268	30	3	3	NUM
ejpam-2531	268	31	4	4	NUM
ejpam-2531	268	32	+	+	CCONJ
ejpam-2531	268	33	1	1	NUM
ejpam-2531	268	34	2	2	NUM
ejpam-2531	268	35	x	x	NOUN
ejpam-2531	268	36	−	−	NOUN
ejpam-2531	268	37	2ex	2ex	NOUN
ejpam-2531	269	1	+	+	CCONJ
ejpam-2531	269	2	5	5	NUM
ejpam-2531	269	3	4	4	NUM
ejpam-2531	269	4	e2x	e2x	NOUN
ejpam-2531	269	5	4.2	4.2	NUM
ejpam-2531	269	6	.	.	PUNCT
ejpam-2531	270	1	a	a	DET
ejpam-2531	270	2	polynomial	polynomial	ADJ
ejpam-2531	270	3	integral	integral	ADJ
ejpam-2531	270	4	transform	transform	NOUN
ejpam-2531	270	5	in	in	ADP
ejpam-2531	270	6	two	two	NUM
ejpam-2531	270	7	variables	variable	NOUN
ejpam-2531	270	8	in	in	ADP
ejpam-2531	270	9	order	order	NOUN
ejpam-2531	270	10	to	to	PART
ejpam-2531	270	11	obtain	obtain	VERB
ejpam-2531	270	12	analytic	analytic	ADJ
ejpam-2531	270	13	solution	solution	NOUN
ejpam-2531	270	14	of	of	ADP
ejpam-2531	270	15	the	the	DET
ejpam-2531	270	16	partial	partial	ADJ
ejpam-2531	270	17	differential	differential	ADJ
ejpam-2531	270	18	equations	equation	NOUN
ejpam-2531	270	19	pdes	pde	NOUN
ejpam-2531	270	20	,	,	PUNCT
ejpam-2531	270	21	we	we	PRON
ejpam-2531	270	22	extend	extend	VERB
ejpam-2531	270	23	the	the	DET
ejpam-2531	270	24	polynomial	polynomial	ADJ
ejpam-2531	270	25	integral	integral	ADJ
ejpam-2531	270	26	transform	transform	NOUN
ejpam-2531	270	27	to	to	PART
ejpam-2531	270	28	solve	solve	VERB
ejpam-2531	270	29	the	the	DET
ejpam-2531	270	30	functions	function	NOUN
ejpam-2531	270	31	in	in	ADP
ejpam-2531	270	32	two	two	NUM
ejpam-2531	270	33	dimensions	dimension	NOUN
ejpam-2531	270	34	as	as	ADP
ejpam-2531	270	35	below	below	ADV
ejpam-2531	270	36	:	:	PUNCT
ejpam-2531	270	37	theorem	theorem	NOUN
ejpam-2531	270	38	9	9	NUM
ejpam-2531	270	39	.	.	PUNCT
ejpam-2531	271	1	let	let	VERB
ejpam-2531	271	2	f	f	PRON
ejpam-2531	271	3	be	be	AUX
ejpam-2531	271	4	a	a	DET
ejpam-2531	271	5	function	function	NOUN
ejpam-2531	271	6	defined	define	VERB
ejpam-2531	271	7	for	for	ADP
ejpam-2531	271	8	x	x	SYM
ejpam-2531	271	9	,	,	PUNCT
ejpam-2531	271	10	t	t	PROPN
ejpam-2531	271	11	≥	≥	NUM
ejpam-2531	271	12	1	1	NUM
ejpam-2531	271	13	.	.	PUNCT
ejpam-2531	272	1	then	then	ADV
ejpam-2531	272	2	the	the	DET
ejpam-2531	272	3	integral	integral	ADJ
ejpam-2531	272	4	bx	bx	NOUN
ejpam-2531	272	5	bt	bt	PROPN
ejpam-2531	272	6	(	(	PUNCT
ejpam-2531	272	7	f	f	PROPN
ejpam-2531	272	8	(	(	PUNCT
ejpam-2531	272	9	x	x	PROPN
ejpam-2531	272	10	,	,	PUNCT
ejpam-2531	272	11	t	t	PROPN
ejpam-2531	272	12	)	)	PUNCT
ejpam-2531	272	13	;	;	PUNCT
ejpam-2531	272	14	(	(	PUNCT
ejpam-2531	272	15	p	p	X
ejpam-2531	272	16	,	,	PUNCT
ejpam-2531	272	17	s	s	NOUN
ejpam-2531	272	18	)	)	PUNCT
ejpam-2531	272	19	)	)	PUNCT
ejpam-2531	273	1	=	=	SYM
ejpam-2531	273	2	f(p	f(p	PROPN
ejpam-2531	273	3	,	,	PUNCT
ejpam-2531	273	4	s	s	PART
ejpam-2531	273	5	)	)	PUNCT
ejpam-2531	273	6	=	=	SYM
ejpam-2531	273	7	∫	∫	PROPN
ejpam-2531	274	1	∞	∞	NUM
ejpam-2531	274	2	1	1	NUM
ejpam-2531	274	3	∫	∫	NOUN
ejpam-2531	274	4	∞	∞	NUM
ejpam-2531	274	5	1	1	NUM
ejpam-2531	274	6	f	f	NOUN
ejpam-2531	274	7	(	(	PUNCT
ejpam-2531	274	8	ln	ln	NOUN
ejpam-2531	274	9	x	x	X
ejpam-2531	274	10	,	,	PUNCT
ejpam-2531	274	11	ln	ln	ADV
ejpam-2531	274	12	t).x−p−1	t).x−p−1	PRON
ejpam-2531	274	13	t−s−1d	t−s−1d	NOUN
ejpam-2531	274	14	xd	xd	INTJ
ejpam-2531	274	15	t	t	PROPN
ejpam-2531	274	16	,	,	PUNCT
ejpam-2531	274	17	is	be	AUX
ejpam-2531	274	18	the	the	DET
ejpam-2531	274	19	integral	integral	ADJ
ejpam-2531	274	20	transform	transform	NOUN
ejpam-2531	274	21	of	of	ADP
ejpam-2531	274	22	f	f	PROPN
ejpam-2531	274	23	(	(	PUNCT
ejpam-2531	274	24	x	x	PROPN
ejpam-2531	274	25	,	,	PUNCT
ejpam-2531	274	26	t	t	PROPN
ejpam-2531	274	27	)	)	PUNCT
ejpam-2531	274	28	for	for	ADP
ejpam-2531	274	29	x	x	SYM
ejpam-2531	274	30	,	,	PUNCT
ejpam-2531	274	31	t	t	PROPN
ejpam-2531	274	32	∈	∈	PROPN
ejpam-2531	275	1	[	[	X
ejpam-2531	275	2	1,∞	1,∞	NUM
ejpam-2531	275	3	)	)	PUNCT
ejpam-2531	275	4	,	,	PUNCT
ejpam-2531	275	5	provided	provide	VERB
ejpam-2531	275	6	the	the	DET
ejpam-2531	275	7	integral	integral	ADJ
ejpam-2531	275	8	converges	converge	NOUN
ejpam-2531	275	9	.	.	PUNCT
ejpam-2531	276	1	proof	proof	NOUN
ejpam-2531	276	2	.	.	PUNCT
ejpam-2531	277	1	it	it	PRON
ejpam-2531	277	2	follows	follow	VERB
ejpam-2531	277	3	from	from	ADP
ejpam-2531	277	4	theorem	theorem	ADJ
ejpam-2531	277	5	1	1	NUM
ejpam-2531	277	6	.	.	PUNCT
ejpam-2531	278	1	we	we	PRON
ejpam-2531	278	2	then	then	ADV
ejpam-2531	278	3	apply	apply	VERB
ejpam-2531	278	4	polynomial	polynomial	ADJ
ejpam-2531	278	5	integral	integral	ADJ
ejpam-2531	278	6	transform	transform	NOUN
ejpam-2531	278	7	to	to	PART
ejpam-2531	278	8	transform	transform	VERB
ejpam-2531	278	9	partial	partial	ADJ
ejpam-2531	278	10	derivatives	derivative	NOUN
ejpam-2531	278	11	.	.	PUNCT
ejpam-2531	279	1	by	by	ADP
ejpam-2531	279	2	the	the	DET
ejpam-2531	279	3	definition	definition	NOUN
ejpam-2531	279	4	of	of	ADP
ejpam-2531	279	5	the	the	DET
ejpam-2531	279	6	polynomial	polynomial	ADJ
ejpam-2531	279	7	integral	integral	ADJ
ejpam-2531	279	8	transform	transform	NOUN
ejpam-2531	279	9	in	in	ADP
ejpam-2531	279	10	two	two	NUM
ejpam-2531	279	11	variables	variable	NOUN
ejpam-2531	279	12	,	,	PUNCT
ejpam-2531	279	13	we	we	PRON
ejpam-2531	279	14	obtain	obtain	VERB
ejpam-2531	279	15	following	follow	VERB
ejpam-2531	279	16	results	result	NOUN
ejpam-2531	279	17	:	:	PUNCT
ejpam-2531	279	18	bx	bx	PROPN
ejpam-2531	279	19	bt	bt	PROPN
ejpam-2531	279	20	(	(	PUNCT
ejpam-2531	279	21	∂	∂	NUM
ejpam-2531	279	22	f	f	NOUN
ejpam-2531	279	23	(	(	PUNCT
ejpam-2531	279	24	x	x	PROPN
ejpam-2531	279	25	,	,	PUNCT
ejpam-2531	279	26	t	t	PROPN
ejpam-2531	279	27	)	)	PUNCT
ejpam-2531	279	28	∂	∂	NUM
ejpam-2531	279	29	x	x	NOUN
ejpam-2531	279	30	;	;	PUNCT
ejpam-2531	279	31	(	(	PUNCT
ejpam-2531	279	32	p	p	X
ejpam-2531	279	33	,	,	PUNCT
ejpam-2531	279	34	s	s	NOUN
ejpam-2531	279	35	)	)	PUNCT
ejpam-2531	279	36	)	)	PUNCT
ejpam-2531	280	1	=	=	NOUN
ejpam-2531	280	2	pf(p	pf(p	NOUN
ejpam-2531	280	3	,	,	PUNCT
ejpam-2531	280	4	s)−	s)−	PROPN
ejpam-2531	280	5	f(0	f(0	PROPN
ejpam-2531	280	6	,	,	PUNCT
ejpam-2531	280	7	s	s	PART
ejpam-2531	280	8	)	)	PUNCT
ejpam-2531	280	9	bx	bx	PROPN
ejpam-2531	280	10	bt	bt	PROPN
ejpam-2531	280	11	(	(	PUNCT
ejpam-2531	280	12	∂	∂	NUM
ejpam-2531	280	13	2	2	NUM
ejpam-2531	280	14	f	f	NOUN
ejpam-2531	280	15	(	(	PUNCT
ejpam-2531	280	16	x	x	PROPN
ejpam-2531	280	17	,	,	PUNCT
ejpam-2531	280	18	t	t	PROPN
ejpam-2531	280	19	)	)	PUNCT
ejpam-2531	280	20	∂	∂	NUM
ejpam-2531	280	21	x∂	x∂	PROPN
ejpam-2531	280	22	t	t	PROPN
ejpam-2531	280	23	;	;	PUNCT
ejpam-2531	280	24	(	(	PUNCT
ejpam-2531	280	25	p	p	X
ejpam-2531	280	26	,	,	PUNCT
ejpam-2531	280	27	s	s	NOUN
ejpam-2531	280	28	)	)	PUNCT
ejpam-2531	280	29	)	)	PUNCT
ejpam-2531	281	1	=	=	SYM
ejpam-2531	281	2	psf(p	psf(p	PROPN
ejpam-2531	281	3	,	,	PUNCT
ejpam-2531	281	4	s)−	s)−	PROPN
ejpam-2531	281	5	pf(p	pf(p	NOUN
ejpam-2531	281	6	,	,	PUNCT
ejpam-2531	281	7	0)−	0)−	PUNCT
ejpam-2531	282	1	sf(0	sf(0	PROPN
ejpam-2531	282	2	,	,	PUNCT
ejpam-2531	282	3	s	s	PART
ejpam-2531	282	4	)	)	PUNCT
ejpam-2531	283	1	+	+	NUM
ejpam-2531	283	2	f	f	X
ejpam-2531	283	3	(	(	PUNCT
ejpam-2531	283	4	0,0	0,0	NOUN
ejpam-2531	283	5	)	)	PUNCT
ejpam-2531	283	6	bx	bx	PROPN
ejpam-2531	283	7	bt	bt	PROPN
ejpam-2531	283	8	(	(	PUNCT
ejpam-2531	283	9	∂	∂	NUM
ejpam-2531	283	10	2	2	NUM
ejpam-2531	283	11	f	f	NOUN
ejpam-2531	283	12	(	(	PUNCT
ejpam-2531	283	13	x	x	PROPN
ejpam-2531	283	14	,	,	PUNCT
ejpam-2531	283	15	t	t	PROPN
ejpam-2531	283	16	)	)	PUNCT
ejpam-2531	283	17	∂	∂	NOUN
ejpam-2531	283	18	x2	x2	NOUN
ejpam-2531	283	19	;	;	PUNCT
ejpam-2531	283	20	(	(	PUNCT
ejpam-2531	283	21	p	p	X
ejpam-2531	283	22	,	,	PUNCT
ejpam-2531	283	23	s	s	NOUN
ejpam-2531	283	24	)	)	PUNCT
ejpam-2531	283	25	)	)	PUNCT
ejpam-2531	284	1	=	=	SYM
ejpam-2531	284	2	p2f(p	p2f(p	PROPN
ejpam-2531	284	3	,	,	PUNCT
ejpam-2531	284	4	s)−	s)−	PROPN
ejpam-2531	284	5	pf(0	pf(0	PROPN
ejpam-2531	284	6	,	,	PUNCT
ejpam-2531	284	7	s)−	s)−	PROPN
ejpam-2531	284	8	∂	∂	NUM
ejpam-2531	284	9	f(0	f(0	NOUN
ejpam-2531	284	10	,	,	PUNCT
ejpam-2531	284	11	s	s	NOUN
ejpam-2531	284	12	)	)	PUNCT
ejpam-2531	284	13	∂	∂	NOUN
ejpam-2531	284	14	x	x	SYM
ejpam-2531	284	15	bx	bx	PROPN
ejpam-2531	284	16	bt	bt	PROPN
ejpam-2531	284	17	(	(	PUNCT
ejpam-2531	284	18	∂	∂	NUM
ejpam-2531	284	19	2	2	NUM
ejpam-2531	284	20	f	f	NOUN
ejpam-2531	284	21	(	(	PUNCT
ejpam-2531	284	22	x	x	PROPN
ejpam-2531	284	23	,	,	PUNCT
ejpam-2531	284	24	t	t	PROPN
ejpam-2531	284	25	)	)	PUNCT
ejpam-2531	284	26	∂	∂	NOUN
ejpam-2531	285	1	t2	t2	NOUN
ejpam-2531	286	1	;	;	PUNCT
ejpam-2531	286	2	(	(	PUNCT
ejpam-2531	286	3	p	p	X
ejpam-2531	286	4	,	,	PUNCT
ejpam-2531	286	5	s	s	NOUN
ejpam-2531	286	6	)	)	PUNCT
ejpam-2531	286	7	)	)	PUNCT
ejpam-2531	287	1	=	=	SYM
ejpam-2531	287	2	s2f(p	s2f(p	PROPN
ejpam-2531	287	3	,	,	PUNCT
ejpam-2531	287	4	s)−	s)−	PROPN
ejpam-2531	287	5	sf(p	sf(p	PROPN
ejpam-2531	287	6	,	,	PUNCT
ejpam-2531	287	7	0)−	0)−	NUM
ejpam-2531	287	8	∂	∂	NUM
ejpam-2531	287	9	f	f	X
ejpam-2531	287	10	(	(	PUNCT
ejpam-2531	287	11	p	p	X
ejpam-2531	287	12	,	,	PUNCT
ejpam-2531	287	13	0	0	NUM
ejpam-2531	287	14	)	)	PUNCT
ejpam-2531	287	15	∂	∂	NOUN
ejpam-2531	288	1	t	t	NOUN
ejpam-2531	289	1	we	we	PRON
ejpam-2531	289	2	consider	consider	VERB
ejpam-2531	289	3	a	a	DET
ejpam-2531	289	4	wave	wave	NOUN
ejpam-2531	289	5	equation	equation	NOUN
ejpam-2531	289	6	below	below	ADP
ejpam-2531	289	7	:	:	PUNCT
ejpam-2531	289	8	∂	∂	NUM
ejpam-2531	289	9	2w	2w	NUM
ejpam-2531	289	10	∂	∂	NOUN
ejpam-2531	289	11	t2	t2	NOUN
ejpam-2531	289	12	=	=	SYM
ejpam-2531	289	13	∂	∂	NUM
ejpam-2531	289	14	2w	2w	NUM
ejpam-2531	289	15	∂	∂	NOUN
ejpam-2531	290	1	x2	x2	NOUN
ejpam-2531	290	2	x	x	X
ejpam-2531	290	3	,	,	PUNCT
ejpam-2531	290	4	t	t	PROPN
ejpam-2531	290	5	≥	≥	NOUN
ejpam-2531	290	6	0	0	NUM
ejpam-2531	291	1	w(0	w(0	PROPN
ejpam-2531	291	2	,	,	PUNCT
ejpam-2531	291	3	t	t	PROPN
ejpam-2531	291	4	)	)	PUNCT
ejpam-2531	291	5	=	=	SYM
ejpam-2531	291	6	g(t	g(t	PROPN
ejpam-2531	291	7	)	)	PUNCT
ejpam-2531	291	8	,	,	PUNCT
ejpam-2531	291	9	lim	lim	PROPN
ejpam-2531	291	10	x→∞	x→∞	NUM
ejpam-2531	292	1	w(x	w(x	PROPN
ejpam-2531	292	2	,	,	PUNCT
ejpam-2531	292	3	t	t	PROPN
ejpam-2531	292	4	)	)	PUNCT
ejpam-2531	292	5	=	=	SYM
ejpam-2531	293	1	0	0	NUM
ejpam-2531	293	2	,	,	PUNCT
ejpam-2531	293	3	x	x	PRON
ejpam-2531	293	4	,	,	PUNCT
ejpam-2531	293	5	t	t	PROPN
ejpam-2531	293	6	≥	≥	PROPN
ejpam-2531	293	7	0	0	NUM
ejpam-2531	294	1	w(x	w(x	NUM
ejpam-2531	294	2	,	,	PUNCT
ejpam-2531	294	3	0	0	NUM
ejpam-2531	294	4	)	)	PUNCT
ejpam-2531	294	5	=	=	SYM
ejpam-2531	295	1	∂	∂	NUM
ejpam-2531	295	2	w	w	NOUN
ejpam-2531	295	3	∂	∂	PROPN
ejpam-2531	295	4	t	t	NOUN
ejpam-2531	295	5	(	(	PUNCT
ejpam-2531	295	6	x	x	INTJ
ejpam-2531	295	7	,	,	PUNCT
ejpam-2531	295	8	0	0	NUM
ejpam-2531	295	9	)	)	PUNCT
ejpam-2531	295	10	=	=	SYM
ejpam-2531	295	11	0	0	NUM
ejpam-2531	295	12	,	,	PUNCT
ejpam-2531	295	13	references	reference	NOUN
ejpam-2531	295	14	150	150	NUM
ejpam-2531	295	15	where	where	SCONJ
ejpam-2531	295	16	w	w	NOUN
ejpam-2531	295	17	is	be	AUX
ejpam-2531	295	18	the	the	DET
ejpam-2531	295	19	deflection	deflection	NOUN
ejpam-2531	295	20	of	of	ADP
ejpam-2531	295	21	a	a	DET
ejpam-2531	295	22	string	string	NOUN
ejpam-2531	295	23	released	release	VERB
ejpam-2531	295	24	from	from	ADP
ejpam-2531	295	25	rest	rest	NOUN
ejpam-2531	295	26	on	on	ADP
ejpam-2531	295	27	the	the	DET
ejpam-2531	295	28	x	x	NOUN
ejpam-2531	295	29	-	-	NOUN
ejpam-2531	295	30	axis	axis	NOUN
ejpam-2531	295	31	.	.	PUNCT
ejpam-2531	296	1	applying	apply	VERB
ejpam-2531	296	2	the	the	DET
ejpam-2531	296	3	polynomial	polynomial	ADJ
ejpam-2531	296	4	integral	integral	ADJ
ejpam-2531	296	5	transform	transform	NOUN
ejpam-2531	296	6	in	in	ADP
ejpam-2531	296	7	two	two	NUM
ejpam-2531	296	8	variables	variable	NOUN
ejpam-2531	296	9	,	,	PUNCT
ejpam-2531	296	10	we	we	PRON
ejpam-2531	296	11	obtain	obtain	VERB
ejpam-2531	296	12	b(wt	b(wt	PROPN
ejpam-2531	296	13	t	t	PROPN
ejpam-2531	296	14	)	)	PUNCT
ejpam-2531	296	15	=	=	NOUN
ejpam-2531	296	16	b(wx	b(wx	NOUN
ejpam-2531	296	17	x	x	NOUN
ejpam-2531	296	18	)	)	PUNCT
ejpam-2531	296	19	⇒wx	⇒wx	PUNCT
ejpam-2531	296	20	x	x	X
ejpam-2531	296	21	−	−	PROPN
ejpam-2531	297	1	s2w	s2w	PROPN
ejpam-2531	298	1	=	=	NOUN
ejpam-2531	298	2	0	0	SYM
ejpam-2531	298	3	w	w	NOUN
ejpam-2531	298	4	(	(	PUNCT
ejpam-2531	298	5	x	x	INTJ
ejpam-2531	298	6	,	,	PUNCT
ejpam-2531	298	7	s	s	X
ejpam-2531	298	8	)	)	PUNCT
ejpam-2531	298	9	=	=	NOUN
ejpam-2531	298	10	a(s)esx	a(s)esx	PROPN
ejpam-2531	298	11	+	+	CCONJ
ejpam-2531	298	12	b(s)e−sx	b(s)e−sx	NOUN
ejpam-2531	298	13	w	w	PROPN
ejpam-2531	298	14	(	(	PUNCT
ejpam-2531	298	15	x	x	INTJ
ejpam-2531	298	16	,	,	PUNCT
ejpam-2531	298	17	s	s	PART
ejpam-2531	298	18	)	)	PUNCT
ejpam-2531	299	1	=	=	NOUN
ejpam-2531	299	2	g(s)e−sx	g(s)e−sx	NOUN
ejpam-2531	299	3	w(x	w(x	PROPN
ejpam-2531	299	4	,	,	PUNCT
ejpam-2531	299	5	t	t	PROPN
ejpam-2531	299	6	)	)	PUNCT
ejpam-2531	300	1	=	=	NOUN
ejpam-2531	300	2	b−1(w	b−1(w	NOUN
ejpam-2531	300	3	(	(	PUNCT
ejpam-2531	300	4	x	x	INTJ
ejpam-2531	300	5	,	,	PUNCT
ejpam-2531	300	6	s	s	NOUN
ejpam-2531	300	7	)	)	PUNCT
ejpam-2531	300	8	)	)	PUNCT
ejpam-2531	301	1	w(x	w(x	NOUN
ejpam-2531	301	2	,	,	PUNCT
ejpam-2531	301	3	t	t	PROPN
ejpam-2531	301	4	)	)	PUNCT
ejpam-2531	301	5	=	=	NOUN
ejpam-2531	301	6	xu(t	xu(t	NUM
ejpam-2531	301	7	−	−	PROPN
ejpam-2531	301	8	1)g(t	1)g(t	NUM
ejpam-2531	301	9	−	−	NOUN
ejpam-2531	301	10	1	1	NUM
ejpam-2531	301	11	)	)	PUNCT
ejpam-2531	301	12	,	,	PUNCT
ejpam-2531	301	13	where	where	SCONJ
ejpam-2531	301	14	g(t	g(t	NOUN
ejpam-2531	301	15	)	)	PUNCT
ejpam-2531	301	16	=	=	SYM
ejpam-2531	301	17	b−1(g(s	b−1(g(s	NOUN
ejpam-2531	301	18	)	)	PUNCT
ejpam-2531	301	19	)	)	PUNCT
ejpam-2531	301	20	.	.	PUNCT
ejpam-2531	302	1	5	5	X
ejpam-2531	302	2	.	.	X
ejpam-2531	302	3	conclusion	conclusion	NOUN
ejpam-2531	302	4	we	we	PRON
ejpam-2531	302	5	observed	observe	VERB
ejpam-2531	302	6	that	that	SCONJ
ejpam-2531	302	7	the	the	DET
ejpam-2531	302	8	polynomial	polynomial	ADJ
ejpam-2531	302	9	integral	integral	ADJ
ejpam-2531	302	10	transform	transform	NOUN
ejpam-2531	302	11	solves	solve	NOUN
ejpam-2531	302	12	differential	differential	ADJ
ejpam-2531	302	13	equation	equation	NOUN
ejpam-2531	302	14	with	with	ADP
ejpam-2531	302	15	a	a	DET
ejpam-2531	302	16	few	few	ADJ
ejpam-2531	302	17	computations	computation	NOUN
ejpam-2531	302	18	as	as	ADV
ejpam-2531	302	19	well	well	ADV
ejpam-2531	302	20	as	as	ADP
ejpam-2531	302	21	time	time	NOUN
ejpam-2531	302	22	.	.	PUNCT
ejpam-2531	303	1	unlike	unlike	ADP
ejpam-2531	303	2	the	the	DET
ejpam-2531	303	3	laplace	laplace	NOUN
ejpam-2531	303	4	integral	integral	ADJ
ejpam-2531	303	5	transform	transform	NOUN
ejpam-2531	303	6	and	and	CCONJ
ejpam-2531	303	7	others	other	NOUN
ejpam-2531	303	8	,	,	PUNCT
ejpam-2531	303	9	the	the	DET
ejpam-2531	303	10	polynomial	polynomial	ADJ
ejpam-2531	303	11	integral	integral	ADJ
ejpam-2531	303	12	transform	transform	NOUN
ejpam-2531	303	13	involves	involve	VERB
ejpam-2531	303	14	a	a	DET
ejpam-2531	303	15	polynomial	polynomial	ADJ
ejpam-2531	303	16	function	function	NOUN
ejpam-2531	303	17	as	as	ADP
ejpam-2531	303	18	its	its	PRON
ejpam-2531	303	19	kernel	kernel	NOUN
ejpam-2531	303	20	,	,	PUNCT
ejpam-2531	303	21	which	which	PRON
ejpam-2531	303	22	is	be	AUX
ejpam-2531	303	23	easier	easy	ADJ
ejpam-2531	303	24	and	and	CCONJ
ejpam-2531	303	25	transforms	transform	VERB
ejpam-2531	303	26	complicated	complicated	ADJ
ejpam-2531	303	27	functions	function	NOUN
ejpam-2531	303	28	into	into	ADP
ejpam-2531	303	29	algebraic	algebraic	ADJ
ejpam-2531	303	30	equations	equation	NOUN
ejpam-2531	303	31	.	.	PUNCT
ejpam-2531	304	1	the	the	DET
ejpam-2531	304	2	solution	solution	NOUN
ejpam-2531	304	3	of	of	ADP
ejpam-2531	304	4	the	the	DET
ejpam-2531	304	5	differential	differential	ADJ
ejpam-2531	304	6	equation	equation	NOUN
ejpam-2531	304	7	is	be	AUX
ejpam-2531	304	8	then	then	ADV
ejpam-2531	304	9	obtained	obtain	VERB
ejpam-2531	304	10	from	from	ADP
ejpam-2531	304	11	the	the	DET
ejpam-2531	304	12	algebraic	algebraic	ADJ
ejpam-2531	304	13	equation	equation	NOUN
ejpam-2531	304	14	.	.	PUNCT
ejpam-2531	305	1	also	also	ADV
ejpam-2531	305	2	,	,	PUNCT
ejpam-2531	305	3	using	use	VERB
ejpam-2531	305	4	the	the	DET
ejpam-2531	305	5	polynomial	polynomial	ADJ
ejpam-2531	305	6	integral	integral	ADJ
ejpam-2531	305	7	transform	transform	NOUN
ejpam-2531	305	8	,	,	PUNCT
ejpam-2531	305	9	the	the	DET
ejpam-2531	305	10	convergence	convergence	NOUN
ejpam-2531	305	11	of	of	ADP
ejpam-2531	305	12	the	the	DET
ejpam-2531	305	13	solution	solution	NOUN
ejpam-2531	305	14	of	of	ADP
ejpam-2531	305	15	the	the	DET
ejpam-2531	305	16	differential	differential	ADJ
ejpam-2531	305	17	equation	equation	NOUN
ejpam-2531	305	18	is	be	AUX
ejpam-2531	305	19	faster	fast	ADJ
ejpam-2531	305	20	as	as	SCONJ
ejpam-2531	305	21	compared	compare	VERB
ejpam-2531	305	22	with	with	ADP
ejpam-2531	305	23	the	the	DET
ejpam-2531	305	24	laplace	laplace	NOUN
ejpam-2531	305	25	integral	integral	ADJ
ejpam-2531	305	26	transform	transform	NOUN
ejpam-2531	305	27	and	and	CCONJ
ejpam-2531	305	28	others	other	NOUN
ejpam-2531	305	29	.	.	PUNCT
ejpam-2531	306	1	we	we	PRON
ejpam-2531	306	2	observed	observe	VERB
ejpam-2531	306	3	that	that	SCONJ
ejpam-2531	306	4	the	the	DET
ejpam-2531	306	5	polynomial	polynomial	ADJ
ejpam-2531	306	6	integral	integral	ADJ
ejpam-2531	306	7	transform	transform	NOUN
ejpam-2531	306	8	is	be	AUX
ejpam-2531	306	9	defined	define	VERB
ejpam-2531	306	10	on	on	ADP
ejpam-2531	306	11	the	the	DET
ejpam-2531	306	12	interval	interval	NOUN
ejpam-2531	306	13	[	[	X
ejpam-2531	306	14	1,∞	1,∞	NUM
ejpam-2531	306	15	)	)	PUNCT
ejpam-2531	306	16	.	.	PUNCT
ejpam-2531	307	1	acknowledgements	acknowledgement	VERB
ejpam-2531	307	2	the	the	DET
ejpam-2531	307	3	authors	author	NOUN
ejpam-2531	307	4	thank	thank	VERB
ejpam-2531	307	5	the	the	DET
ejpam-2531	307	6	readers	reader	NOUN
ejpam-2531	307	7	of	of	ADP
ejpam-2531	307	8	european	european	PROPN
ejpam-2531	307	9	journal	journal	PROPN
ejpam-2531	307	10	of	of	ADP
ejpam-2531	307	11	pure	pure	ADJ
ejpam-2531	307	12	and	and	CCONJ
ejpam-2531	307	13	applied	applied	ADJ
ejpam-2531	307	14	mathematics	mathematic	NOUN
ejpam-2531	307	15	,	,	PUNCT
ejpam-2531	307	16	for	for	ADP
ejpam-2531	307	17	making	make	VERB
ejpam-2531	307	18	our	our	PRON
ejpam-2531	307	19	journal	journal	NOUN
ejpam-2531	307	20	successful	successful	ADJ
ejpam-2531	307	21	.	.	PUNCT
ejpam-2531	308	1	references	reference	NOUN
ejpam-2531	308	2	[	[	X
ejpam-2531	308	3	1	1	X
ejpam-2531	308	4	]	]	PUNCT
ejpam-2531	309	1	s.	s.	PROPN
ejpam-2531	309	2	k.	k.	PROPN
ejpam-2531	309	3	q.	q.	PROPN
ejpam-2531	309	4	al	al	PROPN
ejpam-2531	309	5	-	-	PUNCT
ejpam-2531	309	6	omari	omari	PROPN
ejpam-2531	309	7	.	.	PUNCT
ejpam-2531	310	1	notes	note	NOUN
ejpam-2531	310	2	for	for	ADP
ejpam-2531	310	3	hartley	hartley	NOUN
ejpam-2531	310	4	transforms	transform	VERB
ejpam-2531	310	5	of	of	ADP
ejpam-2531	310	6	generalized	generalized	ADJ
ejpam-2531	310	7	functions	function	NOUN
ejpam-2531	310	8	.	.	PUNCT
ejpam-2531	311	1	italian	italian	ADJ
ejpam-2531	311	2	journal	journal	NOUN
ejpam-2531	311	3	of	of	ADP
ejpam-2531	311	4	pure	pure	ADJ
ejpam-2531	311	5	and	and	CCONJ
ejpam-2531	311	6	applied	applied	ADJ
ejpam-2531	311	7	mathematics	mathematic	NOUN
ejpam-2531	311	8	,	,	PUNCT
ejpam-2531	311	9	28:21–30	28:21–30	NUM
ejpam-2531	311	10	,	,	PUNCT
ejpam-2531	311	11	2011	2011	NUM
ejpam-2531	311	12	.	.	PUNCT
ejpam-2531	312	1	[	[	X
ejpam-2531	312	2	2	2	X
ejpam-2531	312	3	]	]	PUNCT
ejpam-2531	312	4	s.	s.	PROPN
ejpam-2531	312	5	k.	k.	PROPN
ejpam-2531	312	6	q.	q.	PROPN
ejpam-2531	312	7	al	al	PROPN
ejpam-2531	312	8	-	-	PUNCT
ejpam-2531	312	9	omari	omari	PROPN
ejpam-2531	312	10	.	.	PUNCT
ejpam-2531	313	1	on	on	ADP
ejpam-2531	313	2	the	the	DET
ejpam-2531	313	3	applications	application	NOUN
ejpam-2531	313	4	of	of	ADP
ejpam-2531	313	5	natural	natural	ADJ
ejpam-2531	313	6	transforms	transform	NOUN
ejpam-2531	313	7	.	.	PUNCT
ejpam-2531	314	1	international	international	ADJ
ejpam-2531	314	2	journal	journal	NOUN
ejpam-2531	314	3	of	of	ADP
ejpam-2531	314	4	pure	pure	ADJ
ejpam-2531	314	5	and	and	CCONJ
ejpam-2531	314	6	applied	applied	ADJ
ejpam-2531	314	7	mathematics	mathematic	NOUN
ejpam-2531	314	8	,	,	PUNCT
ejpam-2531	314	9	85(4):729–744	85(4):729–744	NOUN
ejpam-2531	314	10	,	,	PUNCT
ejpam-2531	314	11	2013	2013	NUM
ejpam-2531	314	12	.	.	PUNCT
ejpam-2531	315	1	[	[	X
ejpam-2531	315	2	3	3	X
ejpam-2531	315	3	]	]	PUNCT
ejpam-2531	315	4	s.	s.	PROPN
ejpam-2531	315	5	k.	k.	PROPN
ejpam-2531	315	6	q.	q.	PROPN
ejpam-2531	315	7	al	al	PROPN
ejpam-2531	315	8	-	-	PUNCT
ejpam-2531	315	9	omari	omari	PROPN
ejpam-2531	315	10	and	and	CCONJ
ejpam-2531	315	11	a.	a.	NOUN
ejpam-2531	315	12	kilicman	kilicman	NOUN
ejpam-2531	315	13	.	.	PUNCT
ejpam-2531	316	1	on	on	ADP
ejpam-2531	316	2	diffraction	diffraction	NOUN
ejpam-2531	316	3	fresnel	fresnel	NOUN
ejpam-2531	316	4	transform	transform	NOUN
ejpam-2531	316	5	for	for	ADP
ejpam-2531	316	6	boehmians	boehmian	NOUN
ejpam-2531	316	7	.	.	PUNCT
ejpam-2531	317	1	abstract	abstract	ADJ
ejpam-2531	317	2	and	and	CCONJ
ejpam-2531	317	3	applied	apply	VERB
ejpam-2531	317	4	analysis	analysis	NOUN
ejpam-2531	317	5	,	,	PUNCT
ejpam-2531	317	6	2011	2011	NUM
ejpam-2531	317	7	,	,	PUNCT
ejpam-2531	317	8	2011	2011	NUM
ejpam-2531	317	9	.	.	PUNCT
ejpam-2531	318	1	[	[	X
ejpam-2531	318	2	4	4	X
ejpam-2531	318	3	]	]	PUNCT
ejpam-2531	318	4	m.	m.	NOUN
ejpam-2531	318	5	a.	a.	NOUN
ejpam-2531	318	6	asiru	asiru	PROPN
ejpam-2531	318	7	.	.	PUNCT
ejpam-2531	319	1	further	further	ADJ
ejpam-2531	319	2	properties	property	NOUN
ejpam-2531	319	3	of	of	ADP
ejpam-2531	319	4	the	the	DET
ejpam-2531	319	5	sumudu	sumudu	NOUN
ejpam-2531	319	6	transform	transform	NOUN
ejpam-2531	319	7	and	and	CCONJ
ejpam-2531	319	8	its	its	PRON
ejpam-2531	319	9	applications	application	NOUN
ejpam-2531	319	10	.	.	PUNCT
ejpam-2531	320	1	international	international	ADJ
ejpam-2531	320	2	journal	journal	PROPN
ejpam-2531	320	3	of	of	ADP
ejpam-2531	320	4	mathematical	mathematical	ADJ
ejpam-2531	320	5	education	education	NOUN
ejpam-2531	320	6	in	in	ADP
ejpam-2531	320	7	science	science	NOUN
ejpam-2531	320	8	and	and	CCONJ
ejpam-2531	320	9	technology	technology	NOUN
ejpam-2531	320	10	,	,	PUNCT
ejpam-2531	320	11	301(2):441–449	301(2):441–449	PROPN
ejpam-2531	320	12	,	,	PUNCT
ejpam-2531	320	13	2011	2011	NUM
ejpam-2531	320	14	.	.	PUNCT
ejpam-2531	321	1	[	[	X
ejpam-2531	321	2	5	5	NUM
ejpam-2531	321	3	]	]	PUNCT
ejpam-2531	321	4	a.	a.	NOUN
ejpam-2531	321	5	atangana	atangana	PROPN
ejpam-2531	321	6	and	and	CCONJ
ejpam-2531	321	7	a.	a.	NOUN
ejpam-2531	321	8	kilicman	kilicman	PROPN
ejpam-2531	321	9	.	.	PUNCT
ejpam-2531	322	1	the	the	DET
ejpam-2531	322	2	use	use	NOUN
ejpam-2531	322	3	of	of	ADP
ejpam-2531	322	4	sumudu	sumudu	NOUN
ejpam-2531	322	5	transform	transform	NOUN
ejpam-2531	322	6	for	for	ADP
ejpam-2531	322	7	solving	solve	VERB
ejpam-2531	322	8	certain	certain	ADJ
ejpam-2531	322	9	nonlinear	nonlinear	ADJ
ejpam-2531	322	10	fractional	fractional	ADJ
ejpam-2531	322	11	heat	heat	NOUN
ejpam-2531	322	12	-	-	PUNCT
ejpam-2531	322	13	like	like	ADJ
ejpam-2531	322	14	equations	equation	NOUN
ejpam-2531	322	15	.	.	PUNCT
ejpam-2531	323	1	abstract	abstract	ADJ
ejpam-2531	323	2	and	and	CCONJ
ejpam-2531	323	3	applied	apply	VERB
ejpam-2531	323	4	analysis	analysis	NOUN
ejpam-2531	323	5	,	,	PUNCT
ejpam-2531	323	6	2013	2013	NUM
ejpam-2531	323	7	,	,	PUNCT
ejpam-2531	323	8	2013	2013	NUM
ejpam-2531	323	9	.	.	PUNCT
ejpam-2531	324	1	references	reference	NOUN
ejpam-2531	324	2	151	151	NUM
ejpam-2531	324	3	[	[	SYM
ejpam-2531	324	4	6	6	NUM
ejpam-2531	324	5	]	]	PUNCT
ejpam-2531	324	6	f.	f.	PROPN
ejpam-2531	324	7	b.	b.	PROPN
ejpam-2531	324	8	m.	m.	PROPN
ejpam-2531	324	9	belgacem	belgacem	NOUN
ejpam-2531	324	10	and	and	CCONJ
ejpam-2531	324	11	a.	a.	NOUN
ejpam-2531	324	12	a.	a.	PROPN
ejpam-2531	324	13	karaballi	karaballi	PROPN
ejpam-2531	324	14	.	.	PUNCT
ejpam-2531	325	1	sumudu	sumudu	NOUN
ejpam-2531	325	2	transform	transform	VERB
ejpam-2531	325	3	fundamental	fundamental	ADJ
ejpam-2531	325	4	properties	property	NOUN
ejpam-2531	325	5	investigations	investigation	NOUN
ejpam-2531	325	6	and	and	CCONJ
ejpam-2531	325	7	applications	application	NOUN
ejpam-2531	325	8	.	.	PUNCT
ejpam-2531	326	1	journal	journal	NOUN
ejpam-2531	326	2	of	of	ADP
ejpam-2531	326	3	applied	apply	VERB
ejpam-2531	326	4	mathematics	mathematic	NOUN
ejpam-2531	326	5	and	and	CCONJ
ejpam-2531	326	6	stochastic	stochastic	ADJ
ejpam-2531	326	7	analysis	analysis	NOUN
ejpam-2531	326	8	,	,	PUNCT
ejpam-2531	326	9	2006	2006	NUM
ejpam-2531	326	10	,	,	PUNCT
ejpam-2531	326	11	2006	2006	NUM
ejpam-2531	326	12	.	.	PUNCT
ejpam-2531	327	1	[	[	X
ejpam-2531	327	2	7	7	X
ejpam-2531	327	3	]	]	X
ejpam-2531	327	4	f.	f.	PROPN
ejpam-2531	327	5	b.	b.	PROPN
ejpam-2531	327	6	m.	m.	PROPN
ejpam-2531	327	7	belgacem	belgacem	PROPN
ejpam-2531	327	8	and	and	CCONJ
ejpam-2531	327	9	r.	r.	PROPN
ejpam-2531	327	10	silambarasan	silambarasan	PROPN
ejpam-2531	327	11	.	.	PUNCT
ejpam-2531	328	1	advances	advance	NOUN
ejpam-2531	328	2	in	in	ADP
ejpam-2531	328	3	the	the	DET
ejpam-2531	328	4	natural	natural	ADJ
ejpam-2531	328	5	transform	transform	NOUN
ejpam-2531	328	6	.	.	PUNCT
ejpam-2531	329	1	volume	volume	NOUN
ejpam-2531	329	2	1493	1493	NUM
ejpam-2531	329	3	.	.	PUNCT
ejpam-2531	330	1	aip	aip	PROPN
ejpam-2531	330	2	conference	conference	NOUN
ejpam-2531	330	3	proceedings	proceeding	NOUN
ejpam-2531	330	4	,	,	PUNCT
ejpam-2531	330	5	2012	2012	NUM
ejpam-2531	330	6	.	.	PUNCT
ejpam-2531	331	1	[	[	X
ejpam-2531	331	2	8	8	NUM
ejpam-2531	331	3	]	]	X
ejpam-2531	331	4	w.	w.	PROPN
ejpam-2531	331	5	e.	e.	PROPN
ejpam-2531	331	6	boyce	boyce	PROPN
ejpam-2531	331	7	and	and	CCONJ
ejpam-2531	331	8	r.	r.	PROPN
ejpam-2531	331	9	c.	c.	PROPN
ejpam-2531	331	10	diprima	diprima	PROPN
ejpam-2531	331	11	.	.	PUNCT
ejpam-2531	332	1	elementary	elementary	PROPN
ejpam-2531	332	2	differential	differential	PROPN
ejpam-2531	332	3	equations	equation	NOUN
ejpam-2531	332	4	and	and	CCONJ
ejpam-2531	332	5	boundary	boundary	ADJ
ejpam-2531	332	6	value	value	NOUN
ejpam-2531	332	7	problems	problem	NOUN
ejpam-2531	332	8	.	.	PUNCT
ejpam-2531	333	1	john	john	PROPN
ejpam-2531	333	2	wiley	wiley	PROPN
ejpam-2531	333	3	and	and	CCONJ
ejpam-2531	333	4	sons	son	NOUN
ejpam-2531	333	5	,	,	PUNCT
ejpam-2531	333	6	inc	inc	PROPN
ejpam-2531	333	7	„	„	PROPN
ejpam-2531	333	8	uk	uk	PROPN
ejpam-2531	333	9	,	,	PUNCT
ejpam-2531	333	10	2001	2001	NUM
ejpam-2531	333	11	.	.	PUNCT
ejpam-2531	334	1	[	[	X
ejpam-2531	334	2	9	9	NUM
ejpam-2531	334	3	]	]	PUNCT
ejpam-2531	334	4	v.	v.	PROPN
ejpam-2531	334	5	b.	b.	PROPN
ejpam-2531	334	6	l.	l.	PROPN
ejpam-2531	334	7	chaurasia	chaurasia	PROPN
ejpam-2531	334	8	.	.	PUNCT
ejpam-2531	335	1	application	application	NOUN
ejpam-2531	335	2	of	of	ADP
ejpam-2531	335	3	sumudu	sumudu	NOUN
ejpam-2531	335	4	transform	transform	NOUN
ejpam-2531	335	5	in	in	ADP
ejpam-2531	335	6	schödinger	schödinger	NOUN
ejpam-2531	335	7	equation	equation	NOUN
ejpam-2531	335	8	occurring	occur	VERB
ejpam-2531	335	9	in	in	ADP
ejpam-2531	335	10	quantum	quantum	ADJ
ejpam-2531	335	11	mechanics	mechanic	NOUN
ejpam-2531	335	12	.	.	PUNCT
ejpam-2531	336	1	applied	apply	VERB
ejpam-2531	336	2	mathematical	mathematical	ADJ
ejpam-2531	336	3	sciences	science	NOUN
ejpam-2531	336	4	,	,	PUNCT
ejpam-2531	336	5	,	,	PUNCT
ejpam-2531	336	6	4(57):2843–2850	4(57):2843–2850	NUM
ejpam-2531	336	7	,	,	PUNCT
ejpam-2531	336	8	2010	2010	NUM
ejpam-2531	336	9	.	.	PUNCT
ejpam-2531	337	1	[	[	X
ejpam-2531	337	2	10	10	NUM
ejpam-2531	337	3	]	]	X
ejpam-2531	337	4	h.	h.	PROPN
ejpam-2531	337	5	eltayeb	eltayeb	PROPN
ejpam-2531	337	6	and	and	CCONJ
ejpam-2531	337	7	a.	a.	NOUN
ejpam-2531	337	8	kilicman	kilicman	NOUN
ejpam-2531	337	9	.	.	PUNCT
ejpam-2531	338	1	on	on	ADP
ejpam-2531	338	2	double	double	ADJ
ejpam-2531	338	3	sumudu	sumudu	NOUN
ejpam-2531	338	4	transform	transform	NOUN
ejpam-2531	338	5	and	and	CCONJ
ejpam-2531	338	6	double	double	ADJ
ejpam-2531	338	7	laplace	laplace	NOUN
ejpam-2531	338	8	transform	transform	NOUN
ejpam-2531	338	9	.	.	PUNCT
ejpam-2531	338	10	malaysian	malaysian	ADJ
ejpam-2531	338	11	journal	journal	PROPN
ejpam-2531	338	12	of	of	ADP
ejpam-2531	338	13	mathematical	mathematical	ADJ
ejpam-2531	338	14	sciences	science	NOUN
ejpam-2531	338	15	,	,	PUNCT
ejpam-2531	338	16	4(1):17–30	4(1):17–30	NUM
ejpam-2531	338	17	,	,	PUNCT
ejpam-2531	338	18	2010	2010	NUM
ejpam-2531	338	19	.	.	PUNCT
ejpam-2531	339	1	[	[	X
ejpam-2531	339	2	11	11	NUM
ejpam-2531	339	3	]	]	PUNCT
ejpam-2531	339	4	s.	s.	PROPN
ejpam-2531	339	5	handibag	handibag	PROPN
ejpam-2531	339	6	and	and	CCONJ
ejpam-2531	339	7	b.	b.	PROPN
ejpam-2531	339	8	d.	d.	PROPN
ejpam-2531	339	9	karande	karande	PROPN
ejpam-2531	339	10	.	.	PUNCT
ejpam-2531	340	1	laplace	laplace	NOUN
ejpam-2531	340	2	substitution	substitution	NOUN
ejpam-2531	340	3	method	method	NOUN
ejpam-2531	340	4	for	for	ADP
ejpam-2531	340	5	solving	solve	VERB
ejpam-2531	340	6	partial	partial	ADJ
ejpam-2531	340	7	differential	differential	ADJ
ejpam-2531	340	8	equations	equation	NOUN
ejpam-2531	340	9	involving	involve	VERB
ejpam-2531	340	10	mixed	mixed	ADJ
ejpam-2531	340	11	partial	partial	ADJ
ejpam-2531	340	12	derivatives	derivative	NOUN
ejpam-2531	340	13	.	.	PUNCT
ejpam-2531	341	1	international	international	ADJ
ejpam-2531	341	2	journal	journal	NOUN
ejpam-2531	341	3	of	of	ADP
ejpam-2531	341	4	pure	pure	ADJ
ejpam-2531	341	5	and	and	CCONJ
ejpam-2531	341	6	applied	applied	ADJ
ejpam-2531	341	7	mathematics	mathematic	NOUN
ejpam-2531	341	8	,	,	PUNCT
ejpam-2531	341	9	78(7):973–979	78(7):973–979	PROPN
ejpam-2531	341	10	,	,	PUNCT
ejpam-2531	341	11	2012	2012	NUM
ejpam-2531	341	12	.	.	PUNCT
ejpam-2531	342	1	[	[	X
ejpam-2531	342	2	12	12	NUM
ejpam-2531	342	3	]	]	PUNCT
ejpam-2531	342	4	z.	z.	PROPN
ejpam-2531	342	5	h.	h.	PROPN
ejpam-2531	342	6	khan	khan	PROPN
ejpam-2531	342	7	and	and	CCONJ
ejpam-2531	342	8	w.	w.	PROPN
ejpam-2531	342	9	a.	a.	PROPN
ejpam-2531	342	10	khan	khan	PROPN
ejpam-2531	342	11	.	.	PUNCT
ejpam-2531	343	1	natural	natural	ADJ
ejpam-2531	343	2	transform	transform	NOUN
ejpam-2531	343	3	-	-	PUNCT
ejpam-2531	343	4	properties	property	NOUN
ejpam-2531	343	5	and	and	CCONJ
ejpam-2531	343	6	applications	application	NOUN
ejpam-2531	343	7	.	.	PUNCT
ejpam-2531	344	1	nust	nust	PROPN
ejpam-2531	344	2	journal	journal	PROPN
ejpam-2531	344	3	of	of	ADP
ejpam-2531	344	4	engineering	engineering	NOUN
ejpam-2531	344	5	sciences	science	NOUN
ejpam-2531	344	6	,	,	PUNCT
ejpam-2531	344	7	1(1):127–133	1(1):127–133	NUM
ejpam-2531	344	8	,	,	PUNCT
ejpam-2531	344	9	2008	2008	NUM
ejpam-2531	344	10	.	.	PUNCT
ejpam-2531	345	1	[	[	X
ejpam-2531	345	2	13	13	NUM
ejpam-2531	345	3	]	]	X
ejpam-2531	345	4	f.	f.	PROPN
ejpam-2531	345	5	mainardi	mainardi	PROPN
ejpam-2531	345	6	and	and	CCONJ
ejpam-2531	345	7	g.	g.	PROPN
ejpam-2531	345	8	pagnini	pagnini	PROPN
ejpam-2531	345	9	.	.	PUNCT
ejpam-2531	346	1	mellin	mellin	ADJ
ejpam-2531	346	2	-	-	PUNCT
ejpam-2531	346	3	barnes	barnes	PROPN
ejpam-2531	346	4	integrals	integral	NOUN
ejpam-2531	346	5	for	for	ADP
ejpam-2531	346	6	stable	stable	ADJ
ejpam-2531	346	7	distributions	distribution	NOUN
ejpam-2531	346	8	and	and	CCONJ
ejpam-2531	346	9	their	their	PRON
ejpam-2531	346	10	convolutions	convolution	NOUN
ejpam-2531	346	11	.	.	PUNCT
ejpam-2531	347	1	fractional	fractional	ADJ
ejpam-2531	347	2	calculus	calculus	NOUN
ejpam-2531	347	3	and	and	CCONJ
ejpam-2531	347	4	applied	apply	VERB
ejpam-2531	347	5	mathematics	mathematic	NOUN
ejpam-2531	347	6	:	:	PUNCT
ejpam-2531	347	7	an	an	DET
ejpam-2531	347	8	international	international	ADJ
ejpam-2531	347	9	journal	journal	NOUN
ejpam-2531	347	10	of	of	ADP
ejpam-2531	347	11	theory	theory	NOUN
ejpam-2531	347	12	and	and	CCONJ
ejpam-2531	347	13	applications	application	NOUN
ejpam-2531	347	14	,	,	PUNCT
ejpam-2531	347	15	11(4	11(4	NUM
ejpam-2531	347	16	)	)	PUNCT
ejpam-2531	347	17	,	,	PUNCT
ejpam-2531	347	18	2008	2008	NUM
ejpam-2531	347	19	.	.	PUNCT
ejpam-2531	348	1	[	[	X
ejpam-2531	348	2	14	14	NUM
ejpam-2531	348	3	]	]	PUNCT
ejpam-2531	348	4	j.	j.	PROPN
ejpam-2531	348	5	j.	j.	PROPN
ejpam-2531	348	6	mohan	mohan	PROPN
ejpam-2531	348	7	and	and	CCONJ
ejpam-2531	348	8	g.	g.	PROPN
ejpam-2531	348	9	v.	v.	PROPN
ejpam-2531	348	10	s.	s.	PROPN
ejpam-2531	348	11	r.	r.	PROPN
ejpam-2531	348	12	deekshitulu	deekshitulu	PROPN
ejpam-2531	348	13	.	.	PUNCT
ejpam-2531	349	1	solutions	solution	NOUN
ejpam-2531	349	2	of	of	ADP
ejpam-2531	349	3	fractional	fractional	ADJ
ejpam-2531	349	4	difference	difference	NOUN
ejpam-2531	349	5	equations	equation	NOUN
ejpam-2531	349	6	using	use	VERB
ejpam-2531	349	7	s	s	NOUN
ejpam-2531	349	8	-	-	PUNCT
ejpam-2531	349	9	transforms	transform	NOUN
ejpam-2531	349	10	.	.	PUNCT
ejpam-2531	350	1	malaya	malaya	PROPN
ejpam-2531	350	2	journal	journal	PROPN
ejpam-2531	350	3	of	of	ADP
ejpam-2531	350	4	matematik	matematik	PROPN
ejpam-2531	350	5	,	,	PUNCT
ejpam-2531	350	6	3(1):1–13	3(1):1–13	NUM
ejpam-2531	350	7	,	,	PUNCT
ejpam-2531	350	8	2013	2013	NUM
ejpam-2531	350	9	.	.	PUNCT
ejpam-2531	351	1	[	[	X
ejpam-2531	351	2	15	15	NUM
ejpam-2531	351	3	]	]	X
ejpam-2531	351	4	g.	g.	PROPN
ejpam-2531	351	5	k.	k.	PROPN
ejpam-2531	351	6	watugala	watugala	PROPN
ejpam-2531	351	7	.	.	PUNCT
ejpam-2531	352	1	sumudu	sumudu	NOUN
ejpam-2531	352	2	transform	transform	VERB
ejpam-2531	352	3	-	-	PUNCT
ejpam-2531	352	4	a	a	DET
ejpam-2531	352	5	new	new	ADJ
ejpam-2531	352	6	integral	integral	ADJ
ejpam-2531	352	7	transform	transform	NOUN
ejpam-2531	352	8	to	to	PART
ejpam-2531	352	9	solve	solve	VERB
ejpam-2531	352	10	differential	differential	ADJ
ejpam-2531	352	11	equations	equation	NOUN
ejpam-2531	352	12	and	and	CCONJ
ejpam-2531	352	13	control	control	NOUN
ejpam-2531	352	14	engineering	engineering	NOUN
ejpam-2531	352	15	problems	problem	NOUN
ejpam-2531	352	16	.	.	PUNCT
ejpam-2531	353	1	mathematical	mathematical	ADJ
ejpam-2531	353	2	engineering	engineering	NOUN
ejpam-2531	353	3	in	in	ADP
ejpam-2531	353	4	industry	industry	NOUN
ejpam-2531	353	5	,	,	PUNCT
ejpam-2531	353	6	6(4):319	6(4):319	NUM
ejpam-2531	353	7	–	–	PUNCT
ejpam-2531	353	8	329	329	NUM
ejpam-2531	353	9	,	,	PUNCT
ejpam-2531	353	10	1993	1993	NUM
ejpam-2531	353	11	.	.	PUNCT