id	sid	tid	token	lemma	pos
ejpam-5080	1	1	european	european	PROPN
ejpam-5080	1	2	journal	journal	PROPN
ejpam-5080	1	3	of	of	ADP
ejpam-5080	1	4	pure	pure	ADJ
ejpam-5080	1	5	and	and	CCONJ
ejpam-5080	1	6	applied	apply	VERB
ejpam-5080	1	7	mathematics	mathematic	NOUN
ejpam-5080	1	8	vol	vol	NOUN
ejpam-5080	1	9	.	.	PROPN
ejpam-5080	2	1	17	17	NUM
ejpam-5080	2	2	,	,	PUNCT
ejpam-5080	2	3	no	no	INTJ
ejpam-5080	2	4	.	.	NOUN
ejpam-5080	2	5	3	3	NUM
ejpam-5080	2	6	,	,	PUNCT
ejpam-5080	2	7	2024	2024	NUM
ejpam-5080	2	8	,	,	PUNCT
ejpam-5080	2	9	1982	1982	NUM
ejpam-5080	2	10	-	-	SYM
ejpam-5080	2	11	2000	2000	NUM
ejpam-5080	2	12	issn	issn	PROPN
ejpam-5080	2	13	1307	1307	NUM
ejpam-5080	2	14	-	-	SYM
ejpam-5080	2	15	5543	5543	NUM
ejpam-5080	2	16	–	–	PUNCT
ejpam-5080	3	1	ejpam.com	ejpam.com	X
ejpam-5080	3	2	published	publish	VERB
ejpam-5080	3	3	by	by	ADP
ejpam-5080	3	4	new	new	PROPN
ejpam-5080	3	5	york	york	PROPN
ejpam-5080	3	6	business	business	PROPN
ejpam-5080	3	7	global	global	PROPN
ejpam-5080	3	8	adomian	adomian	PROPN
ejpam-5080	3	9	modification	modification	NOUN
ejpam-5080	3	10	methods	method	NOUN
ejpam-5080	3	11	via	via	ADP
ejpam-5080	3	12	orthogonal	orthogonal	ADJ
ejpam-5080	3	13	polynomials	polynomial	NOUN
ejpam-5080	3	14	:	:	PUNCT
ejpam-5080	3	15	a	a	DET
ejpam-5080	3	16	comparative	comparative	ADJ
ejpam-5080	3	17	study	study	NOUN
ejpam-5080	3	18	mariam	mariam	PROPN
ejpam-5080	3	19	al	al	PROPN
ejpam-5080	3	20	-	-	PUNCT
ejpam-5080	3	21	mazmumy1	mazmumy1	PROPN
ejpam-5080	3	22	,	,	PUNCT
ejpam-5080	3	23	huda	huda	PROPN
ejpam-5080	3	24	bakodah1	bakodah1	PROPN
ejpam-5080	3	25	,	,	PUNCT
ejpam-5080	3	26	aishah	aishah	PROPN
ejpam-5080	3	27	alsulami1	alsulami1	PROPN
ejpam-5080	3	28	,	,	PUNCT
ejpam-5080	3	29	nawal	nawal	PROPN
ejpam-5080	3	30	alzaid1,∗	alzaid1,∗	NOUN
ejpam-5080	3	31	1	1	NUM
ejpam-5080	3	32	department	department	NOUN
ejpam-5080	3	33	of	of	ADP
ejpam-5080	3	34	mathematics	mathematic	NOUN
ejpam-5080	3	35	and	and	CCONJ
ejpam-5080	3	36	statistics	statistic	NOUN
ejpam-5080	3	37	,	,	PUNCT
ejpam-5080	3	38	college	college	NOUN
ejpam-5080	3	39	of	of	ADP
ejpam-5080	3	40	science	science	NOUN
ejpam-5080	3	41	,	,	PUNCT
ejpam-5080	3	42	university	university	NOUN
ejpam-5080	3	43	of	of	ADP
ejpam-5080	3	44	jeddah	jeddah	PROPN
ejpam-5080	3	45	,	,	PUNCT
ejpam-5080	3	46	p.o	p.o	PROPN
ejpam-5080	3	47	.	.	PROPN
ejpam-5080	3	48	box	box	PROPN
ejpam-5080	3	49	80327	80327	NUM
ejpam-5080	3	50	,	,	PUNCT
ejpam-5080	3	51	jeddah	jeddah	PROPN
ejpam-5080	3	52	,	,	PUNCT
ejpam-5080	3	53	saudi	saudi	PROPN
ejpam-5080	3	54	arabia	arabia	PROPN
ejpam-5080	3	55	.	.	PUNCT
ejpam-5080	4	1	abstract	abstract	PROPN
ejpam-5080	4	2	.	.	PUNCT
ejpam-5080	5	1	the	the	DET
ejpam-5080	5	2	present	present	ADJ
ejpam-5080	5	3	manuscript	manuscript	NOUN
ejpam-5080	5	4	proposes	propose	VERB
ejpam-5080	5	5	different	different	ADJ
ejpam-5080	5	6	modification	modification	NOUN
ejpam-5080	5	7	procedures	procedure	NOUN
ejpam-5080	5	8	for	for	ADP
ejpam-5080	5	9	the	the	DET
ejpam-5080	5	10	standard	standard	ADJ
ejpam-5080	5	11	adomian	adomian	NOUN
ejpam-5080	5	12	decomposition	decomposition	NOUN
ejpam-5080	5	13	method	method	NOUN
ejpam-5080	5	14	(	(	PUNCT
ejpam-5080	5	15	adm	adm	PROPN
ejpam-5080	5	16	)	)	PUNCT
ejpam-5080	5	17	.	.	PUNCT
ejpam-5080	6	1	these	these	DET
ejpam-5080	6	2	procedures	procedure	NOUN
ejpam-5080	6	3	are	be	AUX
ejpam-5080	6	4	based	base	VERB
ejpam-5080	6	5	on	on	ADP
ejpam-5080	6	6	the	the	DET
ejpam-5080	6	7	application	application	NOUN
ejpam-5080	6	8	of	of	ADP
ejpam-5080	6	9	orthogonal	orthogonal	ADJ
ejpam-5080	6	10	polynomials	polynomial	NOUN
ejpam-5080	6	11	that	that	PRON
ejpam-5080	6	12	play	play	VERB
ejpam-5080	6	13	vital	vital	ADJ
ejpam-5080	6	14	parts	part	NOUN
ejpam-5080	6	15	in	in	ADP
ejpam-5080	6	16	approximation	approximation	NOUN
ejpam-5080	6	17	theories	theory	NOUN
ejpam-5080	6	18	.	.	PUNCT
ejpam-5080	7	1	moreover	moreover	ADV
ejpam-5080	7	2	,	,	PUNCT
ejpam-5080	7	3	the	the	DET
ejpam-5080	7	4	study	study	NOUN
ejpam-5080	7	5	also	also	ADV
ejpam-5080	7	6	scrutinizes	scrutinize	VERB
ejpam-5080	7	7	four	four	NUM
ejpam-5080	7	8	nonlinear	nonlinear	ADJ
ejpam-5080	7	9	inhomogeneous	inhomogeneous	ADJ
ejpam-5080	7	10	initial	initial	ADJ
ejpam-5080	7	11	-	-	PUNCT
ejpam-5080	7	12	value	value	NOUN
ejpam-5080	7	13	problems	problem	NOUN
ejpam-5080	7	14	,	,	PUNCT
ejpam-5080	7	15	and	and	CCONJ
ejpam-5080	7	16	distinctively	distinctively	ADV
ejpam-5080	7	17	examines	examine	VERB
ejpam-5080	7	18	their	their	PRON
ejpam-5080	7	19	respective	respective	ADJ
ejpam-5080	7	20	absolute	absolute	ADJ
ejpam-5080	7	21	error	error	NOUN
ejpam-5080	7	22	differences	difference	NOUN
ejpam-5080	7	23	.	.	PUNCT
ejpam-5080	8	1	remarkably	remarkably	ADV
ejpam-5080	8	2	,	,	PUNCT
ejpam-5080	8	3	different	different	ADJ
ejpam-5080	8	4	computational	computational	ADJ
ejpam-5080	8	5	benefits	benefit	NOUN
ejpam-5080	8	6	of	of	ADP
ejpam-5080	8	7	the	the	DET
ejpam-5080	8	8	proposed	propose	VERB
ejpam-5080	8	9	modification	modification	NOUN
ejpam-5080	8	10	are	be	AUX
ejpam-5080	8	11	noted	note	VERB
ejpam-5080	8	12	with	with	ADP
ejpam-5080	8	13	regard	regard	NOUN
ejpam-5080	8	14	high	high	ADJ
ejpam-5080	8	15	-	-	PUNCT
ejpam-5080	8	16	level	level	NOUN
ejpam-5080	8	17	of	of	ADP
ejpam-5080	8	18	accuracy	accuracy	NOUN
ejpam-5080	8	19	and	and	CCONJ
ejpam-5080	8	20	fewer	few	ADJ
ejpam-5080	8	21	computational	computational	ADJ
ejpam-5080	8	22	steps	step	NOUN
ejpam-5080	8	23	.	.	PUNCT
ejpam-5080	9	1	2020	2020	NUM
ejpam-5080	9	2	mathematics	mathematic	NOUN
ejpam-5080	9	3	subject	subject	NOUN
ejpam-5080	9	4	classifications	classification	NOUN
ejpam-5080	9	5	:	:	PUNCT
ejpam-5080	9	6	33c45,34a34,34a12	33c45,34a34,34a12	NUM
ejpam-5080	9	7	key	key	ADJ
ejpam-5080	9	8	words	word	NOUN
ejpam-5080	9	9	and	and	CCONJ
ejpam-5080	9	10	phrases	phrase	NOUN
ejpam-5080	9	11	:	:	PUNCT
ejpam-5080	9	12	adm	adm	PROPN
ejpam-5080	9	13	,	,	PUNCT
ejpam-5080	9	14	adomian	adomian	NOUN
ejpam-5080	9	15	modification	modification	NOUN
ejpam-5080	9	16	methods	method	NOUN
ejpam-5080	9	17	,	,	PUNCT
ejpam-5080	9	18	adomian	adomian	NOUN
ejpam-5080	9	19	polynomials	polynomial	NOUN
ejpam-5080	9	20	,	,	PUNCT
ejpam-5080	9	21	orthogonal	orthogonal	ADJ
ejpam-5080	9	22	polynomials	polynomial	NOUN
ejpam-5080	9	23	,	,	PUNCT
ejpam-5080	9	24	ordinary	ordinary	ADJ
ejpam-5080	9	25	differential	differential	ADJ
ejpam-5080	9	26	equations	equation	NOUN
ejpam-5080	9	27	(	(	PUNCT
ejpam-5080	9	28	odes	ode	NOUN
ejpam-5080	9	29	)	)	PUNCT
ejpam-5080	9	30	,	,	PUNCT
ejpam-5080	9	31	initial	initial	ADJ
ejpam-5080	9	32	-	-	PUNCT
ejpam-5080	9	33	value	value	NOUN
ejpam-5080	9	34	problems	problem	NOUN
ejpam-5080	9	35	(	(	PUNCT
ejpam-5080	9	36	ivps	ivps	PROPN
ejpam-5080	9	37	)	)	PUNCT
ejpam-5080	9	38	1	1	NUM
ejpam-5080	9	39	.	.	PUNCT
ejpam-5080	9	40	introduction	introduction	NOUN
ejpam-5080	9	41	the	the	DET
ejpam-5080	9	42	celebrated	celebrated	ADJ
ejpam-5080	9	43	adomian	adomian	NOUN
ejpam-5080	9	44	decomposition	decomposition	NOUN
ejpam-5080	9	45	method	method	NOUN
ejpam-5080	9	46	(	(	PUNCT
ejpam-5080	9	47	adm	adm	PROPN
ejpam-5080	9	48	)	)	PUNCT
ejpam-5080	10	1	[	[	X
ejpam-5080	10	2	2	2	X
ejpam-5080	10	3	]	]	PUNCT
ejpam-5080	10	4	has	have	AUX
ejpam-5080	10	5	in	in	ADP
ejpam-5080	10	6	the	the	DET
ejpam-5080	10	7	past	past	NOUN
ejpam-5080	10	8	and	and	CCONJ
ejpam-5080	10	9	present	present	ADJ
ejpam-5080	10	10	decades	decade	NOUN
ejpam-5080	10	11	been	be	AUX
ejpam-5080	10	12	greatly	greatly	ADV
ejpam-5080	10	13	utilized	utilize	VERB
ejpam-5080	10	14	to	to	PART
ejpam-5080	10	15	solve	solve	VERB
ejpam-5080	10	16	a	a	DET
ejpam-5080	10	17	variety	variety	NOUN
ejpam-5080	10	18	of	of	ADP
ejpam-5080	10	19	functional	functional	ADJ
ejpam-5080	10	20	equations	equation	NOUN
ejpam-5080	10	21	.	.	PUNCT
ejpam-5080	11	1	the	the	DET
ejpam-5080	11	2	method	method	NOUN
ejpam-5080	11	3	that	that	PRON
ejpam-5080	11	4	was	be	AUX
ejpam-5080	11	5	proposed	propose	VERB
ejpam-5080	11	6	by	by	ADP
ejpam-5080	11	7	george	george	PROPN
ejpam-5080	11	8	adomian	adomian	PROPN
ejpam-5080	11	9	(	(	PUNCT
ejpam-5080	11	10	in	in	ADP
ejpam-5080	11	11	the	the	DET
ejpam-5080	11	12	1980s	1980s	NUM
ejpam-5080	11	13	)	)	PUNCT
ejpam-5080	11	14	has	have	AUX
ejpam-5080	11	15	further	far	ADV
ejpam-5080	11	16	undergone	undergo	VERB
ejpam-5080	11	17	different	different	ADJ
ejpam-5080	11	18	stages	stage	NOUN
ejpam-5080	11	19	of	of	ADP
ejpam-5080	11	20	reformations	reformation	NOUN
ejpam-5080	11	21	,	,	PUNCT
ejpam-5080	11	22	modifications	modification	NOUN
ejpam-5080	11	23	,	,	PUNCT
ejpam-5080	11	24	and	and	CCONJ
ejpam-5080	11	25	improvements	improvement	NOUN
ejpam-5080	11	26	.	.	PUNCT
ejpam-5080	12	1	indeed	indeed	ADV
ejpam-5080	12	2	,	,	PUNCT
ejpam-5080	12	3	there	there	PRON
ejpam-5080	12	4	exist	exist	VERB
ejpam-5080	12	5	a	a	DET
ejpam-5080	12	6	huge	huge	ADJ
ejpam-5080	12	7	number	number	NOUN
ejpam-5080	12	8	of	of	ADP
ejpam-5080	12	9	related	related	ADJ
ejpam-5080	12	10	literature	literature	NOUN
ejpam-5080	12	11	with	with	ADP
ejpam-5080	12	12	regards	regard	NOUN
ejpam-5080	12	13	to	to	ADP
ejpam-5080	12	14	the	the	DET
ejpam-5080	12	15	development	development	NOUN
ejpam-5080	12	16	of	of	ADP
ejpam-5080	12	17	adm	adm	PROPN
ejpam-5080	12	18	associated	associate	VERB
ejpam-5080	12	19	with	with	ADP
ejpam-5080	12	20	its	its	PRON
ejpam-5080	12	21	applicability	applicability	NOUN
ejpam-5080	12	22	in	in	ADP
ejpam-5080	12	23	solving	solve	VERB
ejpam-5080	12	24	various	various	ADJ
ejpam-5080	12	25	forms	form	NOUN
ejpam-5080	12	26	of	of	ADP
ejpam-5080	12	27	ivps	ivps	PROPN
ejpam-5080	12	28	of	of	ADP
ejpam-5080	12	29	both	both	CCONJ
ejpam-5080	12	30	the	the	DET
ejpam-5080	12	31	ordinary	ordinary	ADJ
ejpam-5080	12	32	and	and	CCONJ
ejpam-5080	12	33	partial	partial	ADJ
ejpam-5080	12	34	differential	differential	NOUN
ejpam-5080	12	35	equation	equation	NOUN
ejpam-5080	12	36	types	type	NOUN
ejpam-5080	12	37	[	[	X
ejpam-5080	12	38	1	1	NUM
ejpam-5080	12	39	,	,	PUNCT
ejpam-5080	12	40	3	3	NUM
ejpam-5080	12	41	,	,	PUNCT
ejpam-5080	12	42	4	4	NUM
ejpam-5080	12	43	,	,	PUNCT
ejpam-5080	12	44	13	13	NUM
ejpam-5080	12	45	]	]	PUNCT
ejpam-5080	12	46	.	.	PUNCT
ejpam-5080	13	1	on	on	ADP
ejpam-5080	13	2	the	the	DET
ejpam-5080	13	3	other	other	ADJ
ejpam-5080	13	4	hand	hand	NOUN
ejpam-5080	13	5	,	,	PUNCT
ejpam-5080	13	6	orthogonal	orthogonal	ADJ
ejpam-5080	13	7	functions	function	NOUN
ejpam-5080	13	8	are	be	AUX
ejpam-5080	13	9	regarded	regard	VERB
ejpam-5080	13	10	with	with	ADP
ejpam-5080	13	11	high	high	ADJ
ejpam-5080	13	12	admiration	admiration	NOUN
ejpam-5080	13	13	in	in	ADP
ejpam-5080	13	14	the	the	DET
ejpam-5080	13	15	fields	field	NOUN
ejpam-5080	13	16	of	of	ADP
ejpam-5080	13	17	numerical	numerical	ADJ
ejpam-5080	13	18	methods	method	NOUN
ejpam-5080	13	19	,	,	PUNCT
ejpam-5080	13	20	and	and	CCONJ
ejpam-5080	13	21	approximation	approximation	NOUN
ejpam-5080	13	22	theories	theory	NOUN
ejpam-5080	13	23	among	among	ADP
ejpam-5080	13	24	others	other	NOUN
ejpam-5080	13	25	.	.	PUNCT
ejpam-5080	14	1	however	however	ADV
ejpam-5080	14	2	,	,	PUNCT
ejpam-5080	14	3	in	in	ADP
ejpam-5080	14	4	line	line	NOUN
ejpam-5080	14	5	with	with	ADP
ejpam-5080	14	6	their	their	PRON
ejpam-5080	14	7	applications	application	NOUN
ejpam-5080	14	8	,	,	PUNCT
ejpam-5080	14	9	hosseini	hosseini	PROPN
ejpam-5080	15	1	[	[	X
ejpam-5080	15	2	7	7	NUM
ejpam-5080	15	3	]	]	PUNCT
ejpam-5080	15	4	demonstrated	demonstrate	VERB
ejpam-5080	15	5	the	the	DET
ejpam-5080	15	6	relevance	relevance	NOUN
ejpam-5080	15	7	of	of	ADP
ejpam-5080	15	8	chebyshev	chebyshev	PROPN
ejpam-5080	15	9	’s	’s	PART
ejpam-5080	15	10	polynomials	polynomial	NOUN
ejpam-5080	15	11	in	in	ADP
ejpam-5080	15	12	improving	improve	VERB
ejpam-5080	15	13	the	the	DET
ejpam-5080	15	14	known	know	VERB
ejpam-5080	15	15	accuracy	accuracy	NOUN
ejpam-5080	15	16	of	of	ADP
ejpam-5080	15	17	the	the	DET
ejpam-5080	15	18	standard	standard	ADJ
ejpam-5080	15	19	adm	adm	PROPN
ejpam-5080	15	20	.	.	PUNCT
ejpam-5080	16	1	in	in	ADP
ejpam-5080	16	2	fact	fact	NOUN
ejpam-5080	16	3	,	,	PUNCT
ejpam-5080	16	4	different	different	ADJ
ejpam-5080	16	5	nonlinear	nonlinear	ADJ
ejpam-5080	16	6	and	and	CCONJ
ejpam-5080	16	7	linear	linear	ADJ
ejpam-5080	16	8	models	model	NOUN
ejpam-5080	16	9	were	be	AUX
ejpam-5080	16	10	examined	examine	VERB
ejpam-5080	16	11	via	via	ADP
ejpam-5080	16	12	the	the	DET
ejpam-5080	16	13	method	method	NOUN
ejpam-5080	16	14	to	to	PART
ejpam-5080	16	15	have	have	AUX
ejpam-5080	16	16	good	good	ADJ
ejpam-5080	16	17	approximate	approximate	ADJ
ejpam-5080	16	18	solutions	solution	NOUN
ejpam-5080	16	19	.	.	PUNCT
ejpam-5080	17	1	we	we	PRON
ejpam-5080	17	2	mention	mention	VERB
ejpam-5080	17	3	also	also	ADV
ejpam-5080	17	4	the	the	DET
ejpam-5080	17	5	excellent	excellent	ADJ
ejpam-5080	17	6	work	work	NOUN
ejpam-5080	17	7	of	of	ADP
ejpam-5080	17	8	liu	liu	PROPN
ejpam-5080	18	1	[	[	X
ejpam-5080	18	2	8	8	NUM
ejpam-5080	18	3	]	]	PUNCT
ejpam-5080	18	4	where	where	SCONJ
ejpam-5080	18	5	legendre	legendre	PROPN
ejpam-5080	18	6	’s	’s	PART
ejpam-5080	18	7	polynomials	polynomial	NOUN
ejpam-5080	18	8	were	be	AUX
ejpam-5080	18	9	coupled	couple	VERB
ejpam-5080	18	10	in	in	ADP
ejpam-5080	18	11	the	the	DET
ejpam-5080	18	12	adm	adm	PROPN
ejpam-5080	18	13	instead	instead	ADV
ejpam-5080	18	14	of	of	ADP
ejpam-5080	18	15	the	the	DET
ejpam-5080	18	16	ordinary	ordinary	ADJ
ejpam-5080	18	17	adomian	adomian	NOUN
ejpam-5080	18	18	procedure	procedure	NOUN
ejpam-5080	18	19	.	.	PUNCT
ejpam-5080	19	1	additionally	additionally	ADV
ejpam-5080	19	2	,	,	PUNCT
ejpam-5080	19	3	adm	adm	PROPN
ejpam-5080	19	4	∗corresponding	∗corresponde	VERB
ejpam-5080	19	5	author	author	NOUN
ejpam-5080	19	6	.	.	PUNCT
ejpam-5080	20	1	doi	doi	NOUN
ejpam-5080	20	2	:	:	PUNCT
ejpam-5080	20	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5080	https://doi.org/10.29020/nybg.ejpam.v17i3.5080	NOUN
ejpam-5080	20	4	email	email	NOUN
ejpam-5080	20	5	addresses	address	NOUN
ejpam-5080	20	6	:	:	PUNCT
ejpam-5080	21	1	mhalmazmumy@uj.edu.sa	mhalmazmumy@uj.edu.sa	PROPN
ejpam-5080	21	2	(	(	PUNCT
ejpam-5080	21	3	m.	m.	NOUN
ejpam-5080	21	4	al-mazmumy),hobakodah@uj.edu.sa	al-mazmumy),hobakodah@uj.edu.sa	PROPN
ejpam-5080	21	5	(	(	PUNCT
ejpam-5080	21	6	h.	h.	NOUN
ejpam-5080	21	7	bakodah	bakodah	PROPN
ejpam-5080	21	8	)	)	PUNCT
ejpam-5080	21	9	,	,	PUNCT
ejpam-5080	21	10	aalsulami1183.stu@uj.edu.sa	aalsulami1183.stu@uj.edu.sa	NOUN
ejpam-5080	21	11	(	(	PUNCT
ejpam-5080	21	12	a.	a.	NOUN
ejpam-5080	21	13	alsulami	alsulami	NOUN
ejpam-5080	21	14	)	)	PUNCT
ejpam-5080	21	15	,	,	PUNCT
ejpam-5080	21	16	naalzaid@uj.edu.sa	naalzaid@uj.edu.sa	PROPN
ejpam-5080	21	17	(	(	PUNCT
ejpam-5080	21	18	n.	n.	NOUN
ejpam-5080	21	19	alzaid	alzaid	PROPN
ejpam-5080	21	20	)	)	PUNCT
ejpam-5080	21	21	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5080	21	22	1982	1982	NUM
ejpam-5080	21	23	©	©	PROPN
ejpam-5080	21	24	2024	2024	NUM
ejpam-5080	21	25	ejpam	ejpam	NOUN
ejpam-5080	21	26	all	all	DET
ejpam-5080	21	27	rights	right	NOUN
ejpam-5080	21	28	reserved	reserve	VERB
ejpam-5080	21	29	.	.	PUNCT
ejpam-5080	22	1	n.	n.	PROPN
ejpam-5080	22	2	alzaid	alzaid	PROPN
ejpam-5080	22	3	et	et	PROPN
ejpam-5080	22	4	al	al	PROPN
ejpam-5080	22	5	.	.	PUNCT
ejpam-5080	22	6	/	/	SYM
ejpam-5080	22	7	eur	eur	PROPN
ejpam-5080	22	8	.	.	PUNCT
ejpam-5080	23	1	j.	j.	PROPN
ejpam-5080	23	2	pure	pure	PROPN
ejpam-5080	23	3	appl	appl	PROPN
ejpam-5080	23	4	.	.	PROPN
ejpam-5080	23	5	math	math	PROPN
ejpam-5080	23	6	,	,	PUNCT
ejpam-5080	23	7	17	17	NUM
ejpam-5080	23	8	(	(	PUNCT
ejpam-5080	23	9	3	3	NUM
ejpam-5080	23	10	)	)	PUNCT
ejpam-5080	23	11	(	(	PUNCT
ejpam-5080	23	12	2024	2024	NUM
ejpam-5080	23	13	)	)	PUNCT
ejpam-5080	23	14	,	,	PUNCT
ejpam-5080	23	15	1982	1982	NUM
ejpam-5080	23	16	-	-	SYM
ejpam-5080	23	17	2000	2000	NUM
ejpam-5080	23	18	1983	1983	NUM
ejpam-5080	23	19	was	be	AUX
ejpam-5080	23	20	equally	equally	ADV
ejpam-5080	23	21	enhanced	enhance	VERB
ejpam-5080	23	22	using	use	VERB
ejpam-5080	23	23	the	the	DET
ejpam-5080	23	24	gegenbauer	gegenbauer	NOUN
ejpam-5080	23	25	’s	’s	PART
ejpam-5080	23	26	and	and	CCONJ
ejpam-5080	23	27	jacobi	jacobi	PROPN
ejpam-5080	23	28	’s	’s	PART
ejpam-5080	23	29	orthogonal	orthogonal	ADJ
ejpam-5080	23	30	polynomials	polynomial	NOUN
ejpam-5080	23	31	[	[	X
ejpam-5080	23	32	6	6	NUM
ejpam-5080	23	33	]	]	PUNCT
ejpam-5080	23	34	to	to	PART
ejpam-5080	23	35	solve	solve	VERB
ejpam-5080	23	36	some	some	DET
ejpam-5080	23	37	important	important	ADJ
ejpam-5080	23	38	models	model	NOUN
ejpam-5080	23	39	of	of	ADP
ejpam-5080	23	40	mathematical	mathematical	ADJ
ejpam-5080	23	41	physics	physics	NOUN
ejpam-5080	23	42	;	;	PUNCT
ejpam-5080	23	43	one	one	NUM
ejpam-5080	23	44	may	may	AUX
ejpam-5080	23	45	in	in	ADP
ejpam-5080	23	46	the	the	DET
ejpam-5080	23	47	same	same	ADJ
ejpam-5080	23	48	fashion	fashion	NOUN
ejpam-5080	23	49	read	read	VERB
ejpam-5080	23	50	about	about	ADP
ejpam-5080	23	51	the	the	DET
ejpam-5080	23	52	relevance	relevance	NOUN
ejpam-5080	23	53	of	of	ADP
ejpam-5080	23	54	laguerre	laguerre	NOUN
ejpam-5080	23	55	’s	’s	PART
ejpam-5080	23	56	and	and	CCONJ
ejpam-5080	23	57	hermite	hermite	PROPN
ejpam-5080	23	58	’s	’s	PART
ejpam-5080	23	59	orthogonal	orthogonal	ADJ
ejpam-5080	23	60	polynomials	polynomial	NOUN
ejpam-5080	23	61	in	in	ADP
ejpam-5080	23	62	optimizing	optimize	VERB
ejpam-5080	23	63	the	the	DET
ejpam-5080	23	64	standard	standard	ADJ
ejpam-5080	23	65	adm	adm	NOUN
ejpam-5080	23	66	procedure	procedure	NOUN
ejpam-5080	23	67	in	in	ADP
ejpam-5080	23	68	[	[	X
ejpam-5080	23	69	11	11	NUM
ejpam-5080	23	70	,	,	PUNCT
ejpam-5080	23	71	12	12	NUM
ejpam-5080	23	72	]	]	PUNCT
ejpam-5080	23	73	.	.	PUNCT
ejpam-5080	24	1	however	however	ADV
ejpam-5080	24	2	,	,	PUNCT
ejpam-5080	24	3	the	the	DET
ejpam-5080	24	4	present	present	ADJ
ejpam-5080	24	5	manuscript	manuscript	NOUN
ejpam-5080	24	6	proposes	propose	VERB
ejpam-5080	24	7	different	different	ADJ
ejpam-5080	24	8	modification	modification	NOUN
ejpam-5080	24	9	procedures	procedure	NOUN
ejpam-5080	24	10	for	for	ADP
ejpam-5080	24	11	the	the	DET
ejpam-5080	24	12	standard	standard	ADJ
ejpam-5080	24	13	adm	adm	PROPN
ejpam-5080	24	14	.	.	PUNCT
ejpam-5080	25	1	these	these	DET
ejpam-5080	25	2	procedures	procedure	NOUN
ejpam-5080	25	3	are	be	AUX
ejpam-5080	25	4	based	base	VERB
ejpam-5080	25	5	on	on	ADP
ejpam-5080	25	6	the	the	DET
ejpam-5080	25	7	application	application	NOUN
ejpam-5080	25	8	of	of	ADP
ejpam-5080	25	9	orthogonal	orthogonal	ADJ
ejpam-5080	25	10	polynomials	polynomial	NOUN
ejpam-5080	25	11	that	that	PRON
ejpam-5080	25	12	play	play	VERB
ejpam-5080	25	13	vital	vital	ADJ
ejpam-5080	25	14	parts	part	NOUN
ejpam-5080	25	15	in	in	ADP
ejpam-5080	25	16	approximation	approximation	NOUN
ejpam-5080	25	17	theories	theory	NOUN
ejpam-5080	25	18	as	as	SCONJ
ejpam-5080	25	19	rightly	rightly	ADV
ejpam-5080	25	20	mentioned	mention	VERB
ejpam-5080	25	21	.	.	PUNCT
ejpam-5080	26	1	more	more	ADV
ejpam-5080	26	2	specifically	specifically	ADV
ejpam-5080	26	3	,	,	PUNCT
ejpam-5080	26	4	the	the	DET
ejpam-5080	26	5	following	follow	VERB
ejpam-5080	26	6	orthogonal	orthogonal	ADJ
ejpam-5080	26	7	polynomials	polynomial	NOUN
ejpam-5080	26	8	:	:	PUNCT
ejpam-5080	26	9	legendre	legendre	PROPN
ejpam-5080	26	10	’s	’s	PROPN
ejpam-5080	26	11	,	,	PUNCT
ejpam-5080	26	12	chebyshev	chebyshev	VERB
ejpam-5080	26	13	’s	’s	NOUN
ejpam-5080	26	14	,	,	PUNCT
ejpam-5080	26	15	laguerre	laguerre	PROPN
ejpam-5080	26	16	’s	’s	PART
ejpam-5080	26	17	,	,	PUNCT
ejpam-5080	26	18	hermite	hermite	PROPN
ejpam-5080	26	19	’s	’s	PROPN
ejpam-5080	26	20	,	,	PUNCT
ejpam-5080	26	21	gegenbauer	gegenbauer	PROPN
ejpam-5080	26	22	’s	’s	PART
ejpam-5080	26	23	,	,	PUNCT
ejpam-5080	26	24	and	and	CCONJ
ejpam-5080	26	25	lastly	lastly	ADV
ejpam-5080	26	26	the	the	DET
ejpam-5080	26	27	jacobi	jacobi	PROPN
ejpam-5080	26	28	’s	’s	PART
ejpam-5080	26	29	polynomials	polynomial	NOUN
ejpam-5080	26	30	will	will	AUX
ejpam-5080	26	31	be	be	AUX
ejpam-5080	26	32	considered	consider	VERB
ejpam-5080	26	33	to	to	PART
ejpam-5080	26	34	devise	devise	VERB
ejpam-5080	26	35	modification	modification	NOUN
ejpam-5080	26	36	methods	method	NOUN
ejpam-5080	26	37	for	for	ADP
ejpam-5080	26	38	the	the	DET
ejpam-5080	26	39	standard	standard	ADJ
ejpam-5080	26	40	adm	adm	PROPN
ejpam-5080	26	41	.	.	PUNCT
ejpam-5080	27	1	moreover	moreover	ADV
ejpam-5080	27	2	,	,	PUNCT
ejpam-5080	27	3	the	the	DET
ejpam-5080	27	4	present	present	ADJ
ejpam-5080	27	5	study	study	NOUN
ejpam-5080	27	6	will	will	AUX
ejpam-5080	27	7	scrutinize	scrutinize	VERB
ejpam-5080	27	8	four	four	NUM
ejpam-5080	27	9	test	test	NOUN
ejpam-5080	27	10	problems	problem	NOUN
ejpam-5080	27	11	and	and	CCONJ
ejpam-5080	27	12	distinctively	distinctively	ADV
ejpam-5080	27	13	examines	examine	VERB
ejpam-5080	27	14	their	their	PRON
ejpam-5080	27	15	respective	respective	ADJ
ejpam-5080	27	16	absolute	absolute	ADJ
ejpam-5080	27	17	error	error	NOUN
ejpam-5080	27	18	differences	difference	NOUN
ejpam-5080	27	19	.	.	PUNCT
ejpam-5080	28	1	additionally	additionally	ADV
ejpam-5080	28	2	,	,	PUNCT
ejpam-5080	28	3	we	we	PRON
ejpam-5080	28	4	organize	organize	VERB
ejpam-5080	28	5	the	the	DET
ejpam-5080	28	6	paper	paper	NOUN
ejpam-5080	28	7	in	in	ADP
ejpam-5080	28	8	the	the	DET
ejpam-5080	28	9	following	following	ADJ
ejpam-5080	28	10	manner	manner	NOUN
ejpam-5080	28	11	:	:	PUNCT
ejpam-5080	28	12	section	section	NOUN
ejpam-5080	28	13	2	2	NUM
ejpam-5080	28	14	gives	give	VERB
ejpam-5080	28	15	the	the	DET
ejpam-5080	28	16	standard	standard	ADJ
ejpam-5080	28	17	adm	adm	NOUN
ejpam-5080	28	18	procedure	procedure	NOUN
ejpam-5080	28	19	;	;	PUNCT
ejpam-5080	28	20	while	while	SCONJ
ejpam-5080	28	21	its	its	PRON
ejpam-5080	28	22	modifications	modification	NOUN
ejpam-5080	28	23	based	base	VERB
ejpam-5080	28	24	on	on	ADP
ejpam-5080	28	25	orthogonal	orthogonal	ADJ
ejpam-5080	28	26	polynomials	polynomial	NOUN
ejpam-5080	28	27	are	be	AUX
ejpam-5080	28	28	presented	present	VERB
ejpam-5080	28	29	in	in	ADP
ejpam-5080	28	30	section	section	NOUN
ejpam-5080	28	31	3	3	NUM
ejpam-5080	28	32	.	.	PUNCT
ejpam-5080	28	33	section	section	NOUN
ejpam-5080	28	34	4	4	NUM
ejpam-5080	28	35	makes	make	VERB
ejpam-5080	28	36	consideration	consideration	NOUN
ejpam-5080	28	37	to	to	ADP
ejpam-5080	28	38	certain	certain	ADJ
ejpam-5080	28	39	illustrative	illustrative	ADJ
ejpam-5080	28	40	test	test	NOUN
ejpam-5080	28	41	examples	example	NOUN
ejpam-5080	28	42	;	;	PUNCT
ejpam-5080	28	43	while	while	SCONJ
ejpam-5080	28	44	section	section	NOUN
ejpam-5080	28	45	5	5	NUM
ejpam-5080	28	46	gives	give	VERB
ejpam-5080	28	47	certain	certain	ADJ
ejpam-5080	28	48	concluding	concluding	NOUN
ejpam-5080	28	49	comments	comment	NOUN
ejpam-5080	28	50	.	.	PUNCT
ejpam-5080	29	1	2	2	X
ejpam-5080	29	2	.	.	X
ejpam-5080	29	3	standard	standard	ADJ
ejpam-5080	29	4	adm	adm	PROPN
ejpam-5080	29	5	procedure	procedure	NOUN
ejpam-5080	29	6	the	the	DET
ejpam-5080	29	7	present	present	ADJ
ejpam-5080	29	8	section	section	NOUN
ejpam-5080	29	9	gives	give	VERB
ejpam-5080	29	10	a	a	DET
ejpam-5080	29	11	generalized	generalized	ADJ
ejpam-5080	29	12	derivation	derivation	NOUN
ejpam-5080	29	13	procedure	procedure	NOUN
ejpam-5080	29	14	for	for	ADP
ejpam-5080	29	15	tackling	tackle	VERB
ejpam-5080	29	16	nonlinear	nonlinear	ADJ
ejpam-5080	29	17	initial	initial	ADJ
ejpam-5080	29	18	-	-	PUNCT
ejpam-5080	29	19	value	value	NOUN
ejpam-5080	29	20	problems	problem	NOUN
ejpam-5080	29	21	(	(	PUNCT
ejpam-5080	29	22	ivps	ivps	PROPN
ejpam-5080	29	23	)	)	PUNCT
ejpam-5080	29	24	based	base	VERB
ejpam-5080	29	25	on	on	ADP
ejpam-5080	29	26	the	the	DET
ejpam-5080	29	27	adm	adm	PROPN
ejpam-5080	29	28	.	.	PUNCT
ejpam-5080	30	1	to	to	PART
ejpam-5080	30	2	do	do	VERB
ejpam-5080	30	3	so	so	ADV
ejpam-5080	30	4	,	,	PUNCT
ejpam-5080	30	5	let	let	VERB
ejpam-5080	30	6	us	we	PRON
ejpam-5080	30	7	consider	consider	VERB
ejpam-5080	30	8	the	the	DET
ejpam-5080	30	9	following	follow	VERB
ejpam-5080	30	10	differential	differential	ADJ
ejpam-5080	30	11	equation	equation	NOUN
ejpam-5080	30	12	g(u(x	g(u(x	NOUN
ejpam-5080	30	13	)	)	PUNCT
ejpam-5080	30	14	)	)	PUNCT
ejpam-5080	31	1	=	=	PUNCT
ejpam-5080	31	2	g(x	g(x	NOUN
ejpam-5080	31	3	)	)	PUNCT
ejpam-5080	31	4	,	,	PUNCT
ejpam-5080	31	5	(	(	PUNCT
ejpam-5080	31	6	1	1	X
ejpam-5080	31	7	)	)	PUNCT
ejpam-5080	31	8	with	with	ADP
ejpam-5080	31	9	g	g	NOUN
ejpam-5080	31	10	representing	represent	VERB
ejpam-5080	31	11	a	a	DET
ejpam-5080	31	12	generalized	generalized	ADJ
ejpam-5080	31	13	ordinary	ordinary	ADJ
ejpam-5080	31	14	(	(	PUNCT
ejpam-5080	31	15	or	or	CCONJ
ejpam-5080	31	16	partial	partial	ADJ
ejpam-5080	31	17	)	)	PUNCT
ejpam-5080	31	18	differential	differential	NOUN
ejpam-5080	31	19	operator	operator	NOUN
ejpam-5080	31	20	,	,	PUNCT
ejpam-5080	31	21	and	and	CCONJ
ejpam-5080	31	22	g(x	g(x	NOUN
ejpam-5080	31	23	)	)	PUNCT
ejpam-5080	31	24	as	as	ADP
ejpam-5080	31	25	a	a	DET
ejpam-5080	31	26	source	source	NOUN
ejpam-5080	31	27	term	term	NOUN
ejpam-5080	31	28	.	.	PUNCT
ejpam-5080	32	1	this	this	DET
ejpam-5080	32	2	operator	operator	NOUN
ejpam-5080	32	3	being	be	AUX
ejpam-5080	32	4	general	general	ADJ
ejpam-5080	32	5	,	,	PUNCT
ejpam-5080	32	6	it	it	PRON
ejpam-5080	32	7	can	can	AUX
ejpam-5080	32	8	equally	equally	ADV
ejpam-5080	32	9	be	be	AUX
ejpam-5080	32	10	expressed	express	VERB
ejpam-5080	32	11	to	to	PART
ejpam-5080	32	12	involve	involve	VERB
ejpam-5080	32	13	both	both	PRON
ejpam-5080	32	14	linear	linear	ADJ
ejpam-5080	32	15	and	and	CCONJ
ejpam-5080	32	16	nonlinear	nonlinear	ADJ
ejpam-5080	32	17	operators	operator	NOUN
ejpam-5080	32	18	.	.	PUNCT
ejpam-5080	33	1	thus	thus	ADV
ejpam-5080	33	2	,	,	PUNCT
ejpam-5080	33	3	we	we	PRON
ejpam-5080	33	4	decompose	decompose	VERB
ejpam-5080	33	5	the	the	DET
ejpam-5080	33	6	operator	operator	NOUN
ejpam-5080	33	7	further	far	ADV
ejpam-5080	33	8	,	,	PUNCT
ejpam-5080	33	9	and	and	CCONJ
ejpam-5080	33	10	rewrite	rewrite	VERB
ejpam-5080	33	11	the	the	DET
ejpam-5080	33	12	above	above	ADJ
ejpam-5080	33	13	equation	equation	NOUN
ejpam-5080	33	14	as	as	SCONJ
ejpam-5080	33	15	follows	follow	VERB
ejpam-5080	33	16	lu+ru+nu	lu+ru+nu	PROPN
ejpam-5080	33	17	=	=	SYM
ejpam-5080	33	18	g	g	NOUN
ejpam-5080	33	19	,	,	PUNCT
ejpam-5080	33	20	(	(	PUNCT
ejpam-5080	33	21	2	2	X
ejpam-5080	33	22	)	)	PUNCT
ejpam-5080	33	23	where	where	SCONJ
ejpam-5080	33	24	l	l	NOUN
ejpam-5080	33	25	is	be	AUX
ejpam-5080	33	26	the	the	DET
ejpam-5080	33	27	highest	high	ADJ
ejpam-5080	33	28	linear	linear	ADJ
ejpam-5080	33	29	operator	operator	NOUN
ejpam-5080	33	30	that	that	PRON
ejpam-5080	33	31	is	be	AUX
ejpam-5080	33	32	invertible	invertible	ADJ
ejpam-5080	33	33	,	,	PUNCT
ejpam-5080	33	34	with	with	ADP
ejpam-5080	33	35	r	r	NOUN
ejpam-5080	33	36	<	<	X
ejpam-5080	33	37	l	l	NOUN
ejpam-5080	33	38	;	;	PUNCT
ejpam-5080	33	39	while	while	SCONJ
ejpam-5080	33	40	n	n	PRON
ejpam-5080	33	41	is	be	AUX
ejpam-5080	33	42	specifically	specifically	ADV
ejpam-5080	33	43	the	the	DET
ejpam-5080	33	44	nonlinear	nonlinear	ADJ
ejpam-5080	33	45	operator	operator	NOUN
ejpam-5080	33	46	.	.	PUNCT
ejpam-5080	34	1	more	more	ADV
ejpam-5080	34	2	so	so	ADV
ejpam-5080	34	3	,	,	PUNCT
ejpam-5080	34	4	we	we	PRON
ejpam-5080	34	5	rewrite	rewrite	VERB
ejpam-5080	34	6	the	the	DET
ejpam-5080	34	7	latter	latter	ADJ
ejpam-5080	34	8	equation	equation	NOUN
ejpam-5080	34	9	as	as	SCONJ
ejpam-5080	34	10	follows	follow	VERB
ejpam-5080	34	11	lu	lu	PROPN
ejpam-5080	34	12	=	=	NOUN
ejpam-5080	34	13	g	g	PROPN
ejpam-5080	34	14	−ru−nu	−ru−nu	PROPN
ejpam-5080	34	15	,	,	PUNCT
ejpam-5080	34	16	(	(	PUNCT
ejpam-5080	34	17	3	3	X
ejpam-5080	34	18	)	)	PUNCT
ejpam-5080	34	19	such	such	ADJ
ejpam-5080	34	20	that	that	SCONJ
ejpam-5080	34	21	applying	apply	VERB
ejpam-5080	34	22	the	the	DET
ejpam-5080	34	23	inverse	inverse	ADJ
ejpam-5080	34	24	linear	linear	NOUN
ejpam-5080	34	25	operator	operator	NOUN
ejpam-5080	34	26	l−1	l−1	NOUN
ejpam-5080	34	27	to	to	ADP
ejpam-5080	34	28	both	both	DET
ejpam-5080	34	29	sides	side	NOUN
ejpam-5080	34	30	of	of	ADP
ejpam-5080	34	31	the	the	DET
ejpam-5080	34	32	above	above	ADJ
ejpam-5080	34	33	equation	equation	NOUN
ejpam-5080	34	34	yields	yield	VERB
ejpam-5080	34	35	u	u	NOUN
ejpam-5080	34	36	=	=	PUNCT
ejpam-5080	34	37	ϕ(x	ϕ(x	X
ejpam-5080	34	38	)	)	PUNCT
ejpam-5080	35	1	+	+	PUNCT
ejpam-5080	36	1	l−1	l−1	PROPN
ejpam-5080	36	2	g	g	NOUN
ejpam-5080	36	3	−	−	PROPN
ejpam-5080	36	4	l−1ru−	l−1ru−	PROPN
ejpam-5080	36	5	l−1nu	l−1nu	NOUN
ejpam-5080	36	6	.	.	PUNCT
ejpam-5080	37	1	(	(	PUNCT
ejpam-5080	37	2	4	4	NUM
ejpam-5080	37	3	)	)	PUNCT
ejpam-5080	37	4	where	where	SCONJ
ejpam-5080	37	5	ϕ(x	ϕ(x	X
ejpam-5080	37	6	)	)	PUNCT
ejpam-5080	37	7	is	be	AUX
ejpam-5080	37	8	the	the	DET
ejpam-5080	37	9	function	function	NOUN
ejpam-5080	37	10	emanating	emanate	VERB
ejpam-5080	37	11	from	from	ADP
ejpam-5080	37	12	the	the	DET
ejpam-5080	37	13	prescribed	prescribed	ADJ
ejpam-5080	37	14	initial	initial	ADJ
ejpam-5080	37	15	data	datum	NOUN
ejpam-5080	37	16	.	.	PUNCT
ejpam-5080	38	1	further	far	ADV
ejpam-5080	38	2	,	,	PUNCT
ejpam-5080	38	3	the	the	DET
ejpam-5080	38	4	iterative	iterative	NOUN
ejpam-5080	38	5	procedure	procedure	NOUN
ejpam-5080	38	6	by	by	ADP
ejpam-5080	38	7	the	the	DET
ejpam-5080	38	8	name	name	NOUN
ejpam-5080	38	9	adm	adm	NOUN
ejpam-5080	38	10	decomposes	decompose	VERB
ejpam-5080	38	11	the	the	DET
ejpam-5080	38	12	solution	solution	NOUN
ejpam-5080	38	13	u(x	u(x	NOUN
ejpam-5080	38	14	)	)	PUNCT
ejpam-5080	38	15	using	use	VERB
ejpam-5080	38	16	an	an	DET
ejpam-5080	38	17	infinite	infinite	ADJ
ejpam-5080	38	18	series	series	NOUN
ejpam-5080	38	19	of	of	ADP
ejpam-5080	38	20	the	the	DET
ejpam-5080	38	21	following	follow	VERB
ejpam-5080	38	22	form	form	NOUN
ejpam-5080	38	23	u(x	u(x	NOUN
ejpam-5080	38	24	)	)	PUNCT
ejpam-5080	38	25	=	=	SYM
ejpam-5080	39	1	∞∑	∞∑	PRON
ejpam-5080	39	2	n=0	n=0	NUM
ejpam-5080	39	3	un(x	un(x	NOUN
ejpam-5080	39	4	)	)	PUNCT
ejpam-5080	39	5	,	,	PUNCT
ejpam-5080	39	6	(	(	PUNCT
ejpam-5080	39	7	5	5	X
ejpam-5080	39	8	)	)	PUNCT
ejpam-5080	39	9	n.	n.	NOUN
ejpam-5080	39	10	alzaid	alzaid	PROPN
ejpam-5080	39	11	et	et	PROPN
ejpam-5080	39	12	al	al	PROPN
ejpam-5080	39	13	.	.	PUNCT
ejpam-5080	39	14	/	/	SYM
ejpam-5080	39	15	eur	eur	PROPN
ejpam-5080	39	16	.	.	PUNCT
ejpam-5080	40	1	j.	j.	PROPN
ejpam-5080	40	2	pure	pure	PROPN
ejpam-5080	40	3	appl	appl	PROPN
ejpam-5080	40	4	.	.	PROPN
ejpam-5080	40	5	math	math	PROPN
ejpam-5080	40	6	,	,	PUNCT
ejpam-5080	40	7	17	17	NUM
ejpam-5080	40	8	(	(	PUNCT
ejpam-5080	40	9	3	3	NUM
ejpam-5080	40	10	)	)	PUNCT
ejpam-5080	40	11	(	(	PUNCT
ejpam-5080	40	12	2024	2024	NUM
ejpam-5080	40	13	)	)	PUNCT
ejpam-5080	40	14	,	,	PUNCT
ejpam-5080	40	15	1982	1982	NUM
ejpam-5080	40	16	-	-	SYM
ejpam-5080	40	17	2000	2000	NUM
ejpam-5080	40	18	1984	1984	NUM
ejpam-5080	40	19	while	while	SCONJ
ejpam-5080	40	20	the	the	DET
ejpam-5080	40	21	nonlinear	nonlinear	ADJ
ejpam-5080	40	22	component	component	NOUN
ejpam-5080	40	23	nu	nu	PROPN
ejpam-5080	40	24	is	be	AUX
ejpam-5080	40	25	equally	equally	ADV
ejpam-5080	40	26	decomposed	decompose	VERB
ejpam-5080	40	27	using	use	VERB
ejpam-5080	40	28	the	the	DET
ejpam-5080	40	29	following	follow	VERB
ejpam-5080	40	30	infinite	infinite	ADJ
ejpam-5080	40	31	series	series	NOUN
ejpam-5080	40	32	n(u	n(u	PROPN
ejpam-5080	40	33	)	)	PUNCT
ejpam-5080	40	34	=	=	PUNCT
ejpam-5080	41	1	∞∑	∞∑	PRON
ejpam-5080	41	2	n=0	n=0	NUM
ejpam-5080	41	3	an(u0	an(u0	NOUN
ejpam-5080	41	4	,	,	PUNCT
ejpam-5080	41	5	u1	u1	NOUN
ejpam-5080	41	6	,	,	PUNCT
ejpam-5080	41	7	...	...	PUNCT
ejpam-5080	41	8	)	)	PUNCT
ejpam-5080	41	9	,	,	PUNCT
ejpam-5080	41	10	(	(	PUNCT
ejpam-5080	41	11	6	6	NUM
ejpam-5080	41	12	)	)	PUNCT
ejpam-5080	41	13	where	where	SCONJ
ejpam-5080	41	14	an	an	DET
ejpam-5080	41	15	’s	’s	NOUN
ejpam-5080	41	16	are	be	AUX
ejpam-5080	41	17	polynomials	polynomial	NOUN
ejpam-5080	41	18	devised	devise	VERB
ejpam-5080	41	19	by	by	ADP
ejpam-5080	41	20	adomian	adomian	NOUN
ejpam-5080	41	21	,	,	PUNCT
ejpam-5080	41	22	and	and	CCONJ
ejpam-5080	41	23	recursively	recursively	ADV
ejpam-5080	41	24	determined	determine	VERB
ejpam-5080	41	25	using	use	VERB
ejpam-5080	41	26	the	the	DET
ejpam-5080	41	27	following	follow	VERB
ejpam-5080	41	28	scheme	scheme	NOUN
ejpam-5080	41	29	an(u0	an(u0	NOUN
ejpam-5080	41	30	,	,	PUNCT
ejpam-5080	41	31	u1	u1	NOUN
ejpam-5080	41	32	,	,	PUNCT
ejpam-5080	41	33	...	...	PUNCT
ejpam-5080	41	34	)	)	PUNCT
ejpam-5080	42	1	=	=	SYM
ejpam-5080	42	2	1	1	NUM
ejpam-5080	42	3	n	n	CCONJ
ejpam-5080	42	4	!	!	PUNCT
ejpam-5080	43	1	dn	dn	PROPN
ejpam-5080	43	2	dλn	dλn	PROPN
ejpam-5080	43	3	n	n	PROPN
ejpam-5080	43	4			PROPN
ejpam-5080	43	5	n∑	n∑	PROPN
ejpam-5080	43	6	j=0	j=0	PROPN
ejpam-5080	44	1	λjuj	λjuj	INTJ
ejpam-5080	44	2			PROPN
ejpam-5080	44	3	λ=0	λ=0	PROPN
ejpam-5080	44	4	,	,	PUNCT
ejpam-5080	44	5	n	n	PROPN
ejpam-5080	44	6	=	=	SYM
ejpam-5080	44	7	0	0	NUM
ejpam-5080	44	8	,	,	PUNCT
ejpam-5080	44	9	1	1	NUM
ejpam-5080	44	10	,	,	PUNCT
ejpam-5080	44	11	2	2	NUM
ejpam-5080	44	12	,	,	PUNCT
ejpam-5080	44	13	...	...	PUNCT
ejpam-5080	44	14	(	(	PUNCT
ejpam-5080	44	15	7	7	X
ejpam-5080	44	16	)	)	PUNCT
ejpam-5080	44	17	therefore	therefore	ADV
ejpam-5080	44	18	,	,	PUNCT
ejpam-5080	44	19	upon	upon	SCONJ
ejpam-5080	44	20	substituting	substitute	VERB
ejpam-5080	44	21	eqs	eqs	PROPN
ejpam-5080	44	22	.	.	PUNCT
ejpam-5080	45	1	(	(	PUNCT
ejpam-5080	45	2	5	5	NUM
ejpam-5080	45	3	)	)	PUNCT
ejpam-5080	45	4	and	and	CCONJ
ejpam-5080	45	5	(	(	PUNCT
ejpam-5080	45	6	6	6	NUM
ejpam-5080	45	7	)	)	PUNCT
ejpam-5080	45	8	into	into	ADP
ejpam-5080	45	9	eq	eq	NOUN
ejpam-5080	45	10	.	.	PUNCT
ejpam-5080	46	1	(	(	PUNCT
ejpam-5080	46	2	4	4	NUM
ejpam-5080	46	3	)	)	PUNCT
ejpam-5080	46	4	,	,	PUNCT
ejpam-5080	46	5	one	one	PRON
ejpam-5080	46	6	gets	get	VERB
ejpam-5080	46	7	∞∑	∞∑	PRON
ejpam-5080	46	8	n=0	n=0	NOUN
ejpam-5080	46	9	un(x	un(x	NOUN
ejpam-5080	46	10	)	)	PUNCT
ejpam-5080	46	11	=	=	SYM
ejpam-5080	46	12	ϕ(x	ϕ(x	PROPN
ejpam-5080	46	13	)	)	PUNCT
ejpam-5080	47	1	+	+	CCONJ
ejpam-5080	47	2	l−1g(x)−	l−1g(x)−	PROPN
ejpam-5080	47	3	l−1r	l−1r	PROPN
ejpam-5080	47	4	∞∑	∞∑	PROPN
ejpam-5080	47	5	n=0	n=0	PUNCT
ejpam-5080	47	6	un(x)−	un(x)−	NOUN
ejpam-5080	47	7	l−1	l−1	PROPN
ejpam-5080	47	8	∞∑	∞∑	ADJ
ejpam-5080	47	9	n=0	n=0	NUM
ejpam-5080	47	10	an(u0	an(u0	NOUN
ejpam-5080	47	11	,	,	PUNCT
ejpam-5080	47	12	u1	u1	NOUN
ejpam-5080	47	13	,	,	PUNCT
ejpam-5080	47	14	...	...	PUNCT
ejpam-5080	47	15	)	)	PUNCT
ejpam-5080	47	16	,	,	PUNCT
ejpam-5080	47	17	(	(	PUNCT
ejpam-5080	47	18	8)	8)	NUM
ejpam-5080	47	19	furthermore	furthermore	ADV
ejpam-5080	47	20	,	,	PUNCT
ejpam-5080	47	21	the	the	DET
ejpam-5080	47	22	adm	adm	NOUN
ejpam-5080	47	23	procedure	procedure	NOUN
ejpam-5080	47	24	swiftly	swiftly	ADV
ejpam-5080	47	25	reveals	reveal	VERB
ejpam-5080	47	26	the	the	DET
ejpam-5080	47	27	generalized	generalized	ADJ
ejpam-5080	47	28	recursive	recursive	ADJ
ejpam-5080	47	29	solution	solution	NOUN
ejpam-5080	47	30	for	for	ADP
ejpam-5080	47	31	the	the	DET
ejpam-5080	47	32	problem	problem	NOUN
ejpam-5080	47	33	from	from	ADP
ejpam-5080	47	34	the	the	DET
ejpam-5080	47	35	above	above	ADJ
ejpam-5080	47	36	equation	equation	NOUN
ejpam-5080	47	37	as	as	ADP
ejpam-5080	47	38	follows	follows	NUM
ejpam-5080	47	39	u0	u0	ADJ
ejpam-5080	47	40	=	=	PUNCT
ejpam-5080	47	41	ϕ(x	ϕ(x	NOUN
ejpam-5080	47	42	)	)	PUNCT
ejpam-5080	47	43	+	+	CCONJ
ejpam-5080	47	44	l−1g(x	l−1g(x	X
ejpam-5080	47	45	)	)	PUNCT
ejpam-5080	47	46	,	,	PUNCT
ejpam-5080	47	47	un+1	un+1	NOUN
ejpam-5080	47	48	=	=	SYM
ejpam-5080	47	49	−l−1run	−l−1run	NOUN
ejpam-5080	48	1	−	−	NOUN
ejpam-5080	48	2	l−1an(u0	l−1an(u0	PROPN
ejpam-5080	48	3	,	,	PUNCT
ejpam-5080	48	4	u1	u1	NOUN
ejpam-5080	48	5	,	,	PUNCT
ejpam-5080	48	6	...	...	PUNCT
ejpam-5080	48	7	)	)	PUNCT
ejpam-5080	48	8	,	,	PUNCT
ejpam-5080	48	9	n	n	X
ejpam-5080	48	10	≥	≥	NOUN
ejpam-5080	48	11	0	0	NUM
ejpam-5080	48	12	,	,	PUNCT
ejpam-5080	48	13	(	(	PUNCT
ejpam-5080	48	14	9	9	NUM
ejpam-5080	48	15	)	)	PUNCT
ejpam-5080	48	16	where	where	SCONJ
ejpam-5080	48	17	an	an	DET
ejpam-5080	48	18	’s	’s	NOUN
ejpam-5080	48	19	are	be	AUX
ejpam-5080	48	20	the	the	DET
ejpam-5080	48	21	adomian	adomian	NOUN
ejpam-5080	48	22	polynomials	polynomial	NOUN
ejpam-5080	48	23	computed	compute	VERB
ejpam-5080	48	24	from	from	ADP
ejpam-5080	48	25	eq	eq	PROPN
ejpam-5080	48	26	.	.	PUNCT
ejpam-5080	48	27	(	(	PUNCT
ejpam-5080	48	28	7	7	NUM
ejpam-5080	48	29	)	)	PUNCT
ejpam-5080	48	30	.	.	PUNCT
ejpam-5080	49	1	expressing	express	VERB
ejpam-5080	49	2	few	few	ADJ
ejpam-5080	49	3	of	of	ADP
ejpam-5080	49	4	these	these	DET
ejpam-5080	49	5	terms	term	NOUN
ejpam-5080	49	6	,	,	PUNCT
ejpam-5080	49	7	we	we	PRON
ejpam-5080	49	8	get	get	VERB
ejpam-5080	49	9	a0(u0	a0(u0	NOUN
ejpam-5080	49	10	)	)	PUNCT
ejpam-5080	49	11	=	=	SYM
ejpam-5080	50	1	n	n	CCONJ
ejpam-5080	50	2	(	(	PUNCT
ejpam-5080	50	3	u0	u0	PROPN
ejpam-5080	50	4	)	)	PUNCT
ejpam-5080	50	5	,	,	PUNCT
ejpam-5080	50	6	a1(u0	a1(u0	NOUN
ejpam-5080	50	7	,	,	PUNCT
ejpam-5080	50	8	u1	u1	NOUN
ejpam-5080	50	9	)	)	PUNCT
ejpam-5080	50	10	=	=	SYM
ejpam-5080	51	1	dn	dn	PROPN
ejpam-5080	51	2	(	(	PUNCT
ejpam-5080	51	3	u0	u0	ADJ
ejpam-5080	51	4	)	)	PUNCT
ejpam-5080	51	5	du0	du0	NOUN
ejpam-5080	51	6	u1	u1	NOUN
ejpam-5080	51	7	,	,	PUNCT
ejpam-5080	51	8	a2(u0	a2(u0	NOUN
ejpam-5080	51	9	,	,	PUNCT
ejpam-5080	51	10	u1	u1	NOUN
ejpam-5080	51	11	,	,	PUNCT
ejpam-5080	51	12	u2	u2	NOUN
ejpam-5080	51	13	)	)	PUNCT
ejpam-5080	51	14	=	=	SYM
ejpam-5080	52	1	dn	dn	PROPN
ejpam-5080	52	2	(	(	PUNCT
ejpam-5080	52	3	u0	u0	ADJ
ejpam-5080	52	4	)	)	PUNCT
ejpam-5080	52	5	du0	du0	ADP
ejpam-5080	52	6	u2	u2	NOUN
ejpam-5080	52	7	+	+	CCONJ
ejpam-5080	52	8	1	1	NUM
ejpam-5080	52	9	2	2	NUM
ejpam-5080	52	10	d2n	d2n	NOUN
ejpam-5080	52	11	(	(	PUNCT
ejpam-5080	52	12	u0	u0	ADJ
ejpam-5080	52	13	)	)	PUNCT
ejpam-5080	52	14	du20	du20	PROPN
ejpam-5080	52	15	u21	u21	PROPN
ejpam-5080	52	16	,	,	PUNCT
ejpam-5080	52	17	a3(u0	a3(u0	NUM
ejpam-5080	52	18	,	,	PUNCT
ejpam-5080	52	19	u1	u1	NOUN
ejpam-5080	52	20	,	,	PUNCT
ejpam-5080	52	21	u2	u2	NOUN
ejpam-5080	52	22	,	,	PUNCT
ejpam-5080	52	23	u3	u3	NOUN
ejpam-5080	52	24	)	)	PUNCT
ejpam-5080	52	25	=	=	SYM
ejpam-5080	52	26	dn	dn	PROPN
ejpam-5080	52	27	(	(	PUNCT
ejpam-5080	52	28	u0	u0	ADJ
ejpam-5080	52	29	)	)	PUNCT
ejpam-5080	52	30	du0	du0	NOUN
ejpam-5080	52	31	u3	u3	NOUN
ejpam-5080	52	32	+	+	CCONJ
ejpam-5080	52	33	d2n	d2n	PROPN
ejpam-5080	52	34	(	(	PUNCT
ejpam-5080	52	35	u0	u0	ADJ
ejpam-5080	52	36	)	)	PUNCT
ejpam-5080	53	1	du20	du20	PROPN
ejpam-5080	53	2	u1u2	u1u2	X
ejpam-5080	53	3	+	+	NOUN
ejpam-5080	53	4	1	1	NUM
ejpam-5080	53	5	3	3	NUM
ejpam-5080	53	6	!	!	PUNCT
ejpam-5080	54	1	d3n	d3n	PROPN
ejpam-5080	54	2	(	(	PUNCT
ejpam-5080	54	3	u0	u0	ADJ
ejpam-5080	54	4	)	)	PUNCT
ejpam-5080	54	5	du30	du30	PROPN
ejpam-5080	54	6	u31	u31	NOUN
ejpam-5080	54	7	,	,	PUNCT
ejpam-5080	54	8	...	...	PUNCT
ejpam-5080	54	9	remarkable	remarkable	ADJ
ejpam-5080	54	10	,	,	PUNCT
ejpam-5080	54	11	it	it	PRON
ejpam-5080	54	12	is	be	AUX
ejpam-5080	54	13	obvious	obvious	ADJ
ejpam-5080	54	14	that	that	SCONJ
ejpam-5080	54	15	the	the	DET
ejpam-5080	54	16	adomian	adomian	NOUN
ejpam-5080	54	17	polynomials	polynomial	VERB
ejpam-5080	54	18	an	an	DET
ejpam-5080	54	19	’s	’s	NOUN
ejpam-5080	54	20	depend	depend	NOUN
ejpam-5080	54	21	on	on	ADP
ejpam-5080	54	22	the	the	DET
ejpam-5080	54	23	solution	solution	NOUN
ejpam-5080	54	24	components	component	NOUN
ejpam-5080	54	25	un	un	PROPN
ejpam-5080	54	26	.	.	PROPN
ejpam-5080	54	27	for	for	ADP
ejpam-5080	54	28	instance	instance	NOUN
ejpam-5080	54	29	,	,	PUNCT
ejpam-5080	54	30	a0	a0	PROPN
ejpam-5080	54	31	relies	rely	VERB
ejpam-5080	54	32	merely	merely	ADV
ejpam-5080	54	33	on	on	ADP
ejpam-5080	54	34	u0	u0	ADJ
ejpam-5080	54	35	;	;	PUNCT
ejpam-5080	54	36	a1	a1	NOUN
ejpam-5080	54	37	relies	rely	VERB
ejpam-5080	54	38	merely	merely	ADV
ejpam-5080	54	39	on	on	ADP
ejpam-5080	54	40	u0	u0	ADJ
ejpam-5080	54	41	and	and	CCONJ
ejpam-5080	54	42	u1	u1	NOUN
ejpam-5080	54	43	;	;	PUNCT
ejpam-5080	54	44	a2	a2	PROPN
ejpam-5080	54	45	relies	rely	VERB
ejpam-5080	54	46	merely	merely	ADV
ejpam-5080	54	47	on	on	ADP
ejpam-5080	54	48	u0	u0	ADJ
ejpam-5080	54	49	,	,	PUNCT
ejpam-5080	54	50	u1	u1	NOUN
ejpam-5080	54	51	and	and	CCONJ
ejpam-5080	54	52	u2	u2	NOUN
ejpam-5080	54	53	,	,	PUNCT
ejpam-5080	54	54	and	and	CCONJ
ejpam-5080	54	55	so	so	ADV
ejpam-5080	54	56	on	on	ADV
ejpam-5080	54	57	.	.	PUNCT
ejpam-5080	55	1	finally	finally	ADV
ejpam-5080	55	2	,	,	PUNCT
ejpam-5080	55	3	a	a	DET
ejpam-5080	55	4	realistic	realistic	ADJ
ejpam-5080	55	5	solution	solution	NOUN
ejpam-5080	55	6	is	be	AUX
ejpam-5080	55	7	obtained	obtain	VERB
ejpam-5080	55	8	by	by	ADP
ejpam-5080	55	9	considering	consider	VERB
ejpam-5080	55	10	the	the	DET
ejpam-5080	55	11	following	follow	VERB
ejpam-5080	55	12	m	m	ADJ
ejpam-5080	55	13	-	-	PUNCT
ejpam-5080	55	14	term	term	NOUN
ejpam-5080	55	15	approximations	approximation	NOUN
ejpam-5080	55	16	as	as	ADP
ejpam-5080	55	17	ψn	ψn	VERB
ejpam-5080	55	18	=	=	PROPN
ejpam-5080	55	19	n−1∑	n−1∑	PROPN
ejpam-5080	55	20	j=0	j=0	PROPN
ejpam-5080	55	21	uj	uj	PROPN
ejpam-5080	55	22	,	,	PUNCT
ejpam-5080	55	23	(	(	PUNCT
ejpam-5080	55	24	10	10	NUM
ejpam-5080	55	25	)	)	PUNCT
ejpam-5080	55	26	where	where	SCONJ
ejpam-5080	55	27	u(x	u(x	VERB
ejpam-5080	55	28	)	)	PUNCT
ejpam-5080	55	29	=	=	SYM
ejpam-5080	55	30	lim	lim	PROPN
ejpam-5080	55	31	n→∞	n→∞	X
ejpam-5080	55	32	ψn(x	ψn(x	PUNCT
ejpam-5080	55	33	)	)	PUNCT
ejpam-5080	55	34	=	=	SYM
ejpam-5080	56	1	∞∑	∞∑	NUM
ejpam-5080	56	2	j=0	j=0	PROPN
ejpam-5080	56	3	uj(x	uj(x	NUM
ejpam-5080	56	4	)	)	PUNCT
ejpam-5080	56	5	.	.	PUNCT
ejpam-5080	57	1	(	(	PUNCT
ejpam-5080	57	2	11	11	NUM
ejpam-5080	57	3	)	)	PUNCT
ejpam-5080	57	4	n.	n.	NOUN
ejpam-5080	57	5	alzaid	alzaid	PROPN
ejpam-5080	57	6	et	et	PROPN
ejpam-5080	57	7	al	al	PROPN
ejpam-5080	57	8	.	.	PUNCT
ejpam-5080	57	9	/	/	SYM
ejpam-5080	57	10	eur	eur	PROPN
ejpam-5080	57	11	.	.	PUNCT
ejpam-5080	58	1	j.	j.	PROPN
ejpam-5080	58	2	pure	pure	PROPN
ejpam-5080	58	3	appl	appl	PROPN
ejpam-5080	58	4	.	.	PROPN
ejpam-5080	58	5	math	math	PROPN
ejpam-5080	58	6	,	,	PUNCT
ejpam-5080	58	7	17	17	NUM
ejpam-5080	58	8	(	(	PUNCT
ejpam-5080	58	9	3	3	NUM
ejpam-5080	58	10	)	)	PUNCT
ejpam-5080	58	11	(	(	PUNCT
ejpam-5080	58	12	2024	2024	NUM
ejpam-5080	58	13	)	)	PUNCT
ejpam-5080	58	14	,	,	PUNCT
ejpam-5080	58	15	1982	1982	NUM
ejpam-5080	58	16	-	-	SYM
ejpam-5080	58	17	2000	2000	NUM
ejpam-5080	58	18	1985	1985	NUM
ejpam-5080	58	19	3	3	NUM
ejpam-5080	58	20	.	.	PUNCT
ejpam-5080	58	21	adomian	adomian	NOUN
ejpam-5080	58	22	modification	modification	NOUN
ejpam-5080	58	23	methods	method	NOUN
ejpam-5080	58	24	via	via	ADP
ejpam-5080	58	25	orthogonal	orthogonal	ADJ
ejpam-5080	58	26	polynomials	polynomial	NOUN
ejpam-5080	58	27	the	the	DET
ejpam-5080	58	28	present	present	ADJ
ejpam-5080	58	29	section	section	NOUN
ejpam-5080	58	30	gives	give	VERB
ejpam-5080	58	31	some	some	DET
ejpam-5080	58	32	important	important	ADJ
ejpam-5080	58	33	modifications	modification	NOUN
ejpam-5080	58	34	of	of	ADP
ejpam-5080	58	35	the	the	DET
ejpam-5080	58	36	standard	standard	ADJ
ejpam-5080	58	37	adm	adm	PROPN
ejpam-5080	58	38	that	that	PRON
ejpam-5080	58	39	are	be	AUX
ejpam-5080	58	40	based	base	VERB
ejpam-5080	58	41	on	on	ADP
ejpam-5080	58	42	the	the	DET
ejpam-5080	58	43	application	application	NOUN
ejpam-5080	58	44	of	of	ADP
ejpam-5080	58	45	orthogonal	orthogonal	ADJ
ejpam-5080	58	46	polynomials	polynomial	NOUN
ejpam-5080	58	47	.	.	PUNCT
ejpam-5080	59	1	one	one	PRON
ejpam-5080	59	2	could	could	AUX
ejpam-5080	59	3	easily	easily	ADV
ejpam-5080	59	4	recall	recall	VERB
ejpam-5080	59	5	the	the	DET
ejpam-5080	59	6	importance	importance	NOUN
ejpam-5080	59	7	of	of	ADP
ejpam-5080	59	8	orthogonal	orthogonal	ADJ
ejpam-5080	59	9	functions	function	NOUN
ejpam-5080	59	10	in	in	ADP
ejpam-5080	59	11	approximation	approximation	NOUN
ejpam-5080	59	12	theory	theory	NOUN
ejpam-5080	59	13	and	and	CCONJ
ejpam-5080	59	14	numerical	numerical	ADJ
ejpam-5080	59	15	methods	method	NOUN
ejpam-5080	59	16	.	.	PUNCT
ejpam-5080	60	1	thus	thus	ADV
ejpam-5080	60	2	,	,	PUNCT
ejpam-5080	60	3	these	these	DET
ejpam-5080	60	4	functions	function	NOUN
ejpam-5080	60	5	/	/	SYM
ejpam-5080	60	6	polynomials	polynomial	NOUN
ejpam-5080	60	7	are	be	AUX
ejpam-5080	60	8	equally	equally	ADV
ejpam-5080	60	9	used	use	VERB
ejpam-5080	60	10	in	in	ADP
ejpam-5080	60	11	the	the	DET
ejpam-5080	60	12	present	present	ADJ
ejpam-5080	60	13	study	study	NOUN
ejpam-5080	60	14	to	to	PART
ejpam-5080	60	15	further	far	ADV
ejpam-5080	60	16	optimize	optimize	VERB
ejpam-5080	60	17	the	the	DET
ejpam-5080	60	18	exactness	exactness	NOUN
ejpam-5080	60	19	of	of	ADP
ejpam-5080	60	20	the	the	DET
ejpam-5080	60	21	standard	standard	ADJ
ejpam-5080	60	22	adm	adm	PROPN
ejpam-5080	60	23	.	.	PUNCT
ejpam-5080	61	1	to	to	PART
ejpam-5080	61	2	begin	begin	VERB
ejpam-5080	61	3	with	with	ADP
ejpam-5080	61	4	,	,	PUNCT
ejpam-5080	61	5	let	let	VERB
ejpam-5080	61	6	us	we	PRON
ejpam-5080	61	7	make	make	VERB
ejpam-5080	61	8	use	use	NOUN
ejpam-5080	61	9	of	of	ADP
ejpam-5080	61	10	the	the	DET
ejpam-5080	61	11	taylor	taylor	PROPN
ejpam-5080	61	12	’s	’s	PART
ejpam-5080	61	13	series	series	PROPN
ejpam-5080	61	14	expansion	expansion	NOUN
ejpam-5080	61	15	to	to	PART
ejpam-5080	61	16	expand	expand	VERB
ejpam-5080	61	17	the	the	DET
ejpam-5080	61	18	given	give	VERB
ejpam-5080	61	19	source	source	NOUN
ejpam-5080	61	20	term	term	NOUN
ejpam-5080	61	21	g(x	g(x	NOUN
ejpam-5080	61	22	)	)	PUNCT
ejpam-5080	61	23	in	in	ADP
ejpam-5080	61	24	eq	eq	ADP
ejpam-5080	61	25	.	.	PUNCT
ejpam-5080	62	1	(	(	PUNCT
ejpam-5080	62	2	2	2	NUM
ejpam-5080	62	3	)	)	PUNCT
ejpam-5080	62	4	for	for	ADP
ejpam-5080	62	5	an	an	DET
ejpam-5080	62	6	arbitrary	arbitrary	ADJ
ejpam-5080	62	7	positive	positive	ADJ
ejpam-5080	62	8	integer	integer	NOUN
ejpam-5080	62	9	,	,	PUNCT
ejpam-5080	62	10	say	say	VERB
ejpam-5080	62	11	m	m	ADV
ejpam-5080	62	12	as	as	SCONJ
ejpam-5080	62	13	follows	follow	VERB
ejpam-5080	62	14	g(x	g(x	NOUN
ejpam-5080	62	15	)	)	PUNCT
ejpam-5080	63	1	=	=	PUNCT
ejpam-5080	63	2	m∑	m∑	CCONJ
ejpam-5080	63	3	n=0	n=0	NUM
ejpam-5080	63	4	gn(0	gn(0	PROPN
ejpam-5080	63	5	)	)	PUNCT
ejpam-5080	63	6	n	n	CCONJ
ejpam-5080	63	7	!	!	PUNCT
ejpam-5080	64	1	xn	xn	PROPN
ejpam-5080	64	2	.	.	PUNCT
ejpam-5080	65	1	(	(	PUNCT
ejpam-5080	65	2	12	12	NUM
ejpam-5080	65	3	)	)	PUNCT
ejpam-5080	65	4	therefore	therefore	ADV
ejpam-5080	65	5	,	,	PUNCT
ejpam-5080	65	6	in	in	ADP
ejpam-5080	65	7	what	what	PRON
ejpam-5080	65	8	follows	follow	VERB
ejpam-5080	65	9	,	,	PUNCT
ejpam-5080	65	10	we	we	PRON
ejpam-5080	65	11	have	have	AUX
ejpam-5080	65	12	obtained	obtain	VERB
ejpam-5080	65	13	series	series	NOUN
ejpam-5080	65	14	of	of	ADP
ejpam-5080	65	15	adomian	adomian	ADJ
ejpam-5080	65	16	modification	modification	NOUN
ejpam-5080	65	17	methods	method	NOUN
ejpam-5080	65	18	via	via	ADP
ejpam-5080	65	19	orthogonal	orthogonal	ADJ
ejpam-5080	65	20	polynomials	polynomial	NOUN
ejpam-5080	65	21	.	.	PUNCT
ejpam-5080	66	1	more	more	ADV
ejpam-5080	66	2	specifically	specifically	ADV
ejpam-5080	66	3	,	,	PUNCT
ejpam-5080	66	4	we	we	PRON
ejpam-5080	66	5	have	have	AUX
ejpam-5080	66	6	utilized	utilize	VERB
ejpam-5080	66	7	the	the	DET
ejpam-5080	66	8	following	follow	VERB
ejpam-5080	66	9	orthogonal	orthogonal	ADJ
ejpam-5080	66	10	polynomials	polynomial	NOUN
ejpam-5080	66	11	including	include	VERB
ejpam-5080	66	12	the	the	DET
ejpam-5080	66	13	legendre	legendre	PROPN
ejpam-5080	66	14	’s	’s	PART
ejpam-5080	66	15	,	,	PUNCT
ejpam-5080	66	16	chebyshev	chebyshev	VERB
ejpam-5080	66	17	’s	’s	NOUN
ejpam-5080	66	18	,	,	PUNCT
ejpam-5080	66	19	laguerre	laguerre	PROPN
ejpam-5080	66	20	’s	’s	PART
ejpam-5080	66	21	,	,	PUNCT
ejpam-5080	66	22	hermit	hermit	INTJ
ejpam-5080	66	23	,	,	PUNCT
ejpam-5080	66	24	gegenbauer	gegenbauer	PROPN
ejpam-5080	66	25	’s	’s	PART
ejpam-5080	66	26	and	and	CCONJ
ejpam-5080	66	27	jacobi	jacobi	PROPN
ejpam-5080	66	28	’s	’s	PART
ejpam-5080	66	29	polynomials	polynomial	NOUN
ejpam-5080	66	30	[	[	X
ejpam-5080	66	31	5	5	NUM
ejpam-5080	66	32	]	]	PUNCT
ejpam-5080	66	33	.	.	PUNCT
ejpam-5080	67	1	3.1	3.1	NUM
ejpam-5080	67	2	.	.	PUNCT
ejpam-5080	67	3	adomian	adomian	PROPN
ejpam-5080	67	4	modification	modification	NOUN
ejpam-5080	67	5	via	via	ADP
ejpam-5080	67	6	legendre	legendre	PROPN
ejpam-5080	67	7	’s	’s	PART
ejpam-5080	67	8	polynomials	polynomial	NOUN
ejpam-5080	67	9	to	to	PART
ejpam-5080	67	10	present	present	VERB
ejpam-5080	67	11	a	a	DET
ejpam-5080	67	12	modification	modification	NOUN
ejpam-5080	67	13	method	method	NOUN
ejpam-5080	67	14	based	base	VERB
ejpam-5080	67	15	on	on	ADP
ejpam-5080	67	16	the	the	DET
ejpam-5080	67	17	application	application	NOUN
ejpam-5080	67	18	of	of	ADP
ejpam-5080	67	19	the	the	DET
ejpam-5080	67	20	legendre	legendre	PROPN
ejpam-5080	67	21	’s	’s	PART
ejpam-5080	67	22	polynomials	polynomial	NOUN
ejpam-5080	67	23	,	,	PUNCT
ejpam-5080	67	24	we	we	PRON
ejpam-5080	67	25	express	express	VERB
ejpam-5080	67	26	the	the	DET
ejpam-5080	67	27	source	source	NOUN
ejpam-5080	67	28	term	term	NOUN
ejpam-5080	67	29	g(x	g(x	NOUN
ejpam-5080	67	30	)	)	PUNCT
ejpam-5080	67	31	given	give	VERB
ejpam-5080	67	32	in	in	ADP
ejpam-5080	67	33	eq	eq	ADP
ejpam-5080	67	34	.	.	PUNCT
ejpam-5080	68	1	(	(	PUNCT
ejpam-5080	68	2	2	2	NUM
ejpam-5080	68	3	)	)	PUNCT
ejpam-5080	68	4	as	as	ADP
ejpam-5080	68	5	a	a	DET
ejpam-5080	68	6	series	series	NOUN
ejpam-5080	68	7	of	of	ADP
ejpam-5080	68	8	legendre	legendre	PROPN
ejpam-5080	68	9	’s	’s	PART
ejpam-5080	68	10	polynomial	polynomial	PROPN
ejpam-5080	68	11	as	as	SCONJ
ejpam-5080	68	12	follows	follow	VERB
ejpam-5080	68	13	[	[	X
ejpam-5080	68	14	8	8	NUM
ejpam-5080	68	15	,	,	PUNCT
ejpam-5080	68	16	10	10	NUM
ejpam-5080	68	17	]	]	X
ejpam-5080	68	18	g(x	g(x	NOUN
ejpam-5080	68	19	)	)	PUNCT
ejpam-5080	68	20	=	=	PUNCT
ejpam-5080	69	1	m∑	m∑	CCONJ
ejpam-5080	69	2	n=0	n=0	NUM
ejpam-5080	69	3	cnpn(x	cnpn(x	NOUN
ejpam-5080	69	4	)	)	PUNCT
ejpam-5080	69	5	,	,	PUNCT
ejpam-5080	69	6	(	(	PUNCT
ejpam-5080	69	7	13	13	NUM
ejpam-5080	69	8	)	)	PUNCT
ejpam-5080	70	1	where	where	SCONJ
ejpam-5080	70	2	pn(x	pn(x	X
ejpam-5080	70	3	)	)	PUNCT
ejpam-5080	70	4	are	be	AUX
ejpam-5080	70	5	the	the	DET
ejpam-5080	70	6	orthogonal	orthogonal	PROPN
ejpam-5080	70	7	legendre	legendre	PROPN
ejpam-5080	70	8	’s	’s	PART
ejpam-5080	70	9	polynomials	polynomial	NOUN
ejpam-5080	70	10	,	,	PUNCT
ejpam-5080	70	11	and	and	CCONJ
ejpam-5080	70	12	the	the	DET
ejpam-5080	70	13	coefficients	coefficient	NOUN
ejpam-5080	70	14	of	of	ADP
ejpam-5080	70	15	legendre	legendre	PROPN
ejpam-5080	70	16	’s	’s	PART
ejpam-5080	70	17	expansion	expansion	NOUN
ejpam-5080	70	18	ci	ci	NOUN
ejpam-5080	70	19	are	be	AUX
ejpam-5080	70	20	determined	determine	VERB
ejpam-5080	70	21	through	through	ADP
ejpam-5080	70	22	ci	ci	NOUN
ejpam-5080	70	23	=	=	SYM
ejpam-5080	70	24	2i+	2i+	NUM
ejpam-5080	70	25	1	1	NUM
ejpam-5080	70	26	2	2	NUM
ejpam-5080	70	27	∫	∫	NOUN
ejpam-5080	70	28	1	1	NUM
ejpam-5080	70	29	−1	−1	NOUN
ejpam-5080	70	30	g(x)pi(x)dx	g(x)pi(x)dx	PROPN
ejpam-5080	70	31	,	,	PUNCT
ejpam-5080	70	32	i	i	PRON
ejpam-5080	70	33	=	=	NOUN
ejpam-5080	70	34	0	0	NUM
ejpam-5080	70	35	,	,	PUNCT
ejpam-5080	70	36	1	1	NUM
ejpam-5080	70	37	,	,	PUNCT
ejpam-5080	70	38	·	·	PUNCT
ejpam-5080	70	39	·	·	PUNCT
ejpam-5080	70	40	·	·	PUNCT
ejpam-5080	71	1	thus	thus	ADV
ejpam-5080	71	2	,	,	PUNCT
ejpam-5080	71	3	substituting	substitute	VERB
ejpam-5080	71	4	eq	eq	ADP
ejpam-5080	71	5	.	.	PUNCT
ejpam-5080	72	1	(	(	PUNCT
ejpam-5080	72	2	13	13	NUM
ejpam-5080	72	3	)	)	PUNCT
ejpam-5080	72	4	into	into	ADP
ejpam-5080	72	5	eq	eq	NOUN
ejpam-5080	72	6	.	.	PUNCT
ejpam-5080	73	1	(	(	PUNCT
ejpam-5080	73	2	9	9	NUM
ejpam-5080	73	3	)	)	PUNCT
ejpam-5080	73	4	,	,	PUNCT
ejpam-5080	73	5	we	we	PRON
ejpam-5080	73	6	get	get	VERB
ejpam-5080	73	7	the	the	DET
ejpam-5080	73	8	following	follow	VERB
ejpam-5080	73	9	recursive	recursive	ADJ
ejpam-5080	73	10	solution	solution	NUM
ejpam-5080	73	11	u0	u0	ADJ
ejpam-5080	73	12	=	=	PUNCT
ejpam-5080	73	13	ϕ(x	ϕ(x	PROPN
ejpam-5080	73	14	)	)	PUNCT
ejpam-5080	73	15	+	+	NUM
ejpam-5080	73	16	l−1[c0p0(x	l−1[c0p0(x	NOUN
ejpam-5080	73	17	)	)	PUNCT
ejpam-5080	74	1	+	+	CCONJ
ejpam-5080	74	2	c1p1(x	c1p1(x	NOUN
ejpam-5080	74	3	)	)	PUNCT
ejpam-5080	74	4	+	+	CCONJ
ejpam-5080	74	5	c2p2(x	c2p2(x	X
ejpam-5080	74	6	)	)	PUNCT
ejpam-5080	74	7	+	+	CCONJ
ejpam-5080	75	1	·	·	PUNCT
ejpam-5080	75	2	·	·	PUNCT
ejpam-5080	75	3	·	·	PUNCT
ejpam-5080	75	4	+	+	NUM
ejpam-5080	75	5	cmpm(x	cmpm(x	NOUN
ejpam-5080	75	6	)	)	PUNCT
ejpam-5080	75	7	]	]	PUNCT
ejpam-5080	75	8	,	,	PUNCT
ejpam-5080	75	9	un+1	un+1	NOUN
ejpam-5080	75	10	=	=	SYM
ejpam-5080	75	11	−l−1run	−l−1run	NOUN
ejpam-5080	75	12	−	−	PROPN
ejpam-5080	75	13	l−1an	l−1an	NOUN
ejpam-5080	75	14	,	,	PUNCT
ejpam-5080	75	15	n	n	X
ejpam-5080	75	16	≥	≥	NOUN
ejpam-5080	75	17	0	0	NUM
ejpam-5080	75	18	.	.	PUNCT
ejpam-5080	76	1	(	(	PUNCT
ejpam-5080	76	2	14	14	NUM
ejpam-5080	76	3	)	)	PUNCT
ejpam-5080	76	4	finally	finally	ADV
ejpam-5080	76	5	,	,	PUNCT
ejpam-5080	76	6	a	a	DET
ejpam-5080	76	7	realistic	realistic	ADJ
ejpam-5080	76	8	solution	solution	NOUN
ejpam-5080	76	9	via	via	ADP
ejpam-5080	76	10	the	the	DET
ejpam-5080	76	11	application	application	NOUN
ejpam-5080	76	12	of	of	ADP
ejpam-5080	76	13	legendre	legendre	PROPN
ejpam-5080	76	14	’s	’s	PART
ejpam-5080	76	15	polynomial	polynomial	NOUN
ejpam-5080	76	16	is	be	AUX
ejpam-5080	76	17	thus	thus	ADV
ejpam-5080	76	18	obtained	obtain	VERB
ejpam-5080	76	19	in	in	ADP
ejpam-5080	76	20	this	this	DET
ejpam-5080	76	21	regard	regard	NOUN
ejpam-5080	76	22	by	by	ADP
ejpam-5080	76	23	considering	consider	VERB
ejpam-5080	76	24	the	the	DET
ejpam-5080	76	25	following	follow	VERB
ejpam-5080	76	26	m	m	ADJ
ejpam-5080	76	27	-	-	PUNCT
ejpam-5080	76	28	term	term	NOUN
ejpam-5080	76	29	approximations	approximation	NOUN
ejpam-5080	76	30	using	use	VERB
ejpam-5080	76	31	u(x	u(x	NOUN
ejpam-5080	76	32	)	)	PUNCT
ejpam-5080	77	1	=	=	PUNCT
ejpam-5080	77	2	∑m	∑m	PROPN
ejpam-5080	77	3	n=0	n=0	NUM
ejpam-5080	77	4	un	un	NOUN
ejpam-5080	77	5	,	,	PUNCT
ejpam-5080	77	6	where	where	SCONJ
ejpam-5080	77	7	m	m	PROPN
ejpam-5080	77	8	is	be	AUX
ejpam-5080	77	9	the	the	DET
ejpam-5080	77	10	order	order	NOUN
ejpam-5080	77	11	of	of	ADP
ejpam-5080	77	12	the	the	DET
ejpam-5080	77	13	solution	solution	NOUN
ejpam-5080	77	14	.	.	PUNCT
ejpam-5080	78	1	3.2	3.2	NUM
ejpam-5080	78	2	.	.	PUNCT
ejpam-5080	78	3	adomian	adomian	NOUN
ejpam-5080	78	4	modification	modification	NOUN
ejpam-5080	78	5	method	method	NOUN
ejpam-5080	78	6	via	via	ADP
ejpam-5080	78	7	chebyshev	chebyshev	PROPN
ejpam-5080	78	8	’s	’s	PART
ejpam-5080	78	9	polynomials	polynomial	NOUN
ejpam-5080	78	10	(	(	PUNCT
ejpam-5080	78	11	i	i	NOUN
ejpam-5080	78	12	)	)	PUNCT
ejpam-5080	78	13	first	first	ADV
ejpam-5080	78	14	kind	kind	NOUN
ejpam-5080	78	15	chebyshev	chebyshev	PROPN
ejpam-5080	78	16	’s	’s	PART
ejpam-5080	78	17	polynomials	polynomial	NOUN
ejpam-5080	78	18	in	in	ADP
ejpam-5080	78	19	hosseini	hosseini	PROPN
ejpam-5080	78	20	[	[	X
ejpam-5080	78	21	7	7	NUM
ejpam-5080	78	22	]	]	PUNCT
ejpam-5080	78	23	,	,	PUNCT
ejpam-5080	78	24	the	the	DET
ejpam-5080	78	25	source	source	NOUN
ejpam-5080	78	26	term	term	NOUN
ejpam-5080	78	27	g(x	g(x	NOUN
ejpam-5080	78	28	)	)	PUNCT
ejpam-5080	78	29	is	be	AUX
ejpam-5080	78	30	suggested	suggest	VERB
ejpam-5080	78	31	to	to	PART
ejpam-5080	78	32	be	be	AUX
ejpam-5080	78	33	decomposed	decompose	VERB
ejpam-5080	78	34	using	use	VERB
ejpam-5080	78	35	chebyshev	chebyshev	PROPN
ejpam-5080	78	36	’s	’s	PART
ejpam-5080	78	37	series	series	NOUN
ejpam-5080	78	38	as	as	SCONJ
ejpam-5080	78	39	follows	follow	VERB
ejpam-5080	78	40	g(x	g(x	NOUN
ejpam-5080	78	41	)	)	PUNCT
ejpam-5080	79	1	=	=	PUNCT
ejpam-5080	79	2	m∑	m∑	CCONJ
ejpam-5080	79	3	n=0	n=0	NUM
ejpam-5080	79	4	cntn(x	cntn(x	NOUN
ejpam-5080	79	5	)	)	PUNCT
ejpam-5080	79	6	,	,	PUNCT
ejpam-5080	79	7	(	(	PUNCT
ejpam-5080	79	8	15	15	X
ejpam-5080	79	9	)	)	PUNCT
ejpam-5080	79	10	n.	n.	NOUN
ejpam-5080	79	11	alzaid	alzaid	PROPN
ejpam-5080	79	12	et	et	PROPN
ejpam-5080	79	13	al	al	PROPN
ejpam-5080	79	14	.	.	PUNCT
ejpam-5080	79	15	/	/	SYM
ejpam-5080	79	16	eur	eur	PROPN
ejpam-5080	79	17	.	.	PUNCT
ejpam-5080	80	1	j.	j.	PROPN
ejpam-5080	80	2	pure	pure	PROPN
ejpam-5080	80	3	appl	appl	PROPN
ejpam-5080	80	4	.	.	PROPN
ejpam-5080	80	5	math	math	PROPN
ejpam-5080	80	6	,	,	PUNCT
ejpam-5080	80	7	17	17	NUM
ejpam-5080	80	8	(	(	PUNCT
ejpam-5080	80	9	3	3	NUM
ejpam-5080	80	10	)	)	PUNCT
ejpam-5080	80	11	(	(	PUNCT
ejpam-5080	80	12	2024	2024	NUM
ejpam-5080	80	13	)	)	PUNCT
ejpam-5080	80	14	,	,	PUNCT
ejpam-5080	80	15	1982	1982	NUM
ejpam-5080	80	16	-	-	SYM
ejpam-5080	80	17	2000	2000	NUM
ejpam-5080	80	18	1986	1986	NUM
ejpam-5080	80	19	where	where	SCONJ
ejpam-5080	80	20	tn(x	tn(x	PUNCT
ejpam-5080	80	21	)	)	PUNCT
ejpam-5080	80	22	are	be	AUX
ejpam-5080	80	23	the	the	DET
ejpam-5080	80	24	orthogonal	orthogonal	ADJ
ejpam-5080	80	25	chebyshev	chebyshev	PROPN
ejpam-5080	80	26	’s	’s	PART
ejpam-5080	80	27	polynomial	polynomial	NOUN
ejpam-5080	80	28	of	of	ADP
ejpam-5080	80	29	the	the	DET
ejpam-5080	80	30	first	first	ADJ
ejpam-5080	80	31	kind	kind	NOUN
ejpam-5080	80	32	;	;	PUNCT
ejpam-5080	80	33	while	while	SCONJ
ejpam-5080	80	34	the	the	DET
ejpam-5080	80	35	coefficient	coefficient	NOUN
ejpam-5080	80	36	of	of	ADP
ejpam-5080	80	37	chebyshev	chebyshev	PROPN
ejpam-5080	80	38	’s	’s	PART
ejpam-5080	80	39	expansion	expansion	NOUN
ejpam-5080	80	40	ci	ci	NOUN
ejpam-5080	80	41	are	be	AUX
ejpam-5080	80	42	expressed	express	VERB
ejpam-5080	80	43	as	as	SCONJ
ejpam-5080	80	44	follows	follow	VERB
ejpam-5080	80	45	c0	c0	NOUN
ejpam-5080	80	46	=	=	SYM
ejpam-5080	80	47	1	1	NUM
ejpam-5080	80	48	π	π	NOUN
ejpam-5080	80	49	∫	∫	PROPN
ejpam-5080	80	50	1	1	NUM
ejpam-5080	80	51	−1	−1	NOUN
ejpam-5080	80	52	g(x)t0(x)√	g(x)t0(x)√	ADJ
ejpam-5080	80	53	1−	1−	NUM
ejpam-5080	80	54	x2	x2	NUM
ejpam-5080	80	55	dx	dx	PROPN
ejpam-5080	80	56	,	,	PUNCT
ejpam-5080	80	57	ci	ci	PROPN
ejpam-5080	80	58	=	=	SYM
ejpam-5080	80	59	2	2	NUM
ejpam-5080	80	60	π	π	NOUN
ejpam-5080	80	61	∫	∫	PROPN
ejpam-5080	80	62	1	1	NUM
ejpam-5080	80	63	−1	−1	NOUN
ejpam-5080	80	64	g(x)ti(x)√	g(x)ti(x)√	PROPN
ejpam-5080	80	65	1−	1−	NUM
ejpam-5080	80	66	x2	x2	NUM
ejpam-5080	80	67	dx	dx	PROPN
ejpam-5080	80	68	,	,	PUNCT
ejpam-5080	80	69	i	i	PRON
ejpam-5080	80	70	=	=	NOUN
ejpam-5080	80	71	1	1	NUM
ejpam-5080	80	72	,	,	PUNCT
ejpam-5080	80	73	2	2	NUM
ejpam-5080	80	74	,	,	PUNCT
ejpam-5080	80	75	·	·	PUNCT
ejpam-5080	80	76	·	·	PUNCT
ejpam-5080	80	77	·	·	PUNCT
ejpam-5080	80	78	(	(	PUNCT
ejpam-5080	80	79	16	16	NUM
ejpam-5080	80	80	)	)	PUNCT
ejpam-5080	80	81	thus	thus	ADV
ejpam-5080	80	82	,	,	PUNCT
ejpam-5080	80	83	upon	upon	SCONJ
ejpam-5080	80	84	using	use	VERB
ejpam-5080	80	85	eqs	eqs	PROPN
ejpam-5080	80	86	.	.	PUNCT
ejpam-5080	81	1	(	(	PUNCT
ejpam-5080	81	2	9	9	NUM
ejpam-5080	81	3	)	)	PUNCT
ejpam-5080	81	4	and	and	CCONJ
ejpam-5080	81	5	(	(	PUNCT
ejpam-5080	81	6	15	15	NUM
ejpam-5080	81	7	)	)	PUNCT
ejpam-5080	81	8	,	,	PUNCT
ejpam-5080	81	9	we	we	PRON
ejpam-5080	81	10	get	get	VERB
ejpam-5080	81	11	the	the	DET
ejpam-5080	81	12	following	follow	VERB
ejpam-5080	81	13	recursive	recursive	ADJ
ejpam-5080	81	14	solution	solution	NOUN
ejpam-5080	81	15	{	{	PUNCT
ejpam-5080	81	16	u0	u0	NOUN
ejpam-5080	81	17	=	=	PUNCT
ejpam-5080	81	18	ϕ(x	ϕ(x	PROPN
ejpam-5080	81	19	)	)	PUNCT
ejpam-5080	81	20	+	+	NUM
ejpam-5080	81	21	l−1[c0t0(x	l−1[c0t0(x	NOUN
ejpam-5080	81	22	)	)	PUNCT
ejpam-5080	82	1	+	+	PUNCT
ejpam-5080	83	1	c1t1(x	c1t1(x	NOUN
ejpam-5080	83	2	)	)	PUNCT
ejpam-5080	84	1	+	+	NUM
ejpam-5080	84	2	c2t2(x	c2t2(x	X
ejpam-5080	84	3	)	)	PUNCT
ejpam-5080	85	1	+	+	CCONJ
ejpam-5080	85	2	·	·	PUNCT
ejpam-5080	85	3	·	·	PUNCT
ejpam-5080	85	4	·	·	PUNCT
ejpam-5080	85	5	+	+	NUM
ejpam-5080	85	6	cmtm(x	cmtm(x	NOUN
ejpam-5080	85	7	)	)	PUNCT
ejpam-5080	85	8	]	]	PUNCT
ejpam-5080	85	9	,	,	PUNCT
ejpam-5080	85	10	un+1	un+1	NOUN
ejpam-5080	85	11	=	=	SYM
ejpam-5080	85	12	−l−1run	−l−1run	NOUN
ejpam-5080	85	13	−	−	PROPN
ejpam-5080	85	14	l−1an	l−1an	NOUN
ejpam-5080	85	15	,	,	PUNCT
ejpam-5080	85	16	n	n	X
ejpam-5080	85	17	≥	≥	NOUN
ejpam-5080	85	18	0	0	NUM
ejpam-5080	85	19	.	.	PUNCT
ejpam-5080	86	1	(	(	PUNCT
ejpam-5080	86	2	17	17	NUM
ejpam-5080	86	3	)	)	PUNCT
ejpam-5080	86	4	(	(	PUNCT
ejpam-5080	86	5	ii	ii	NOUN
ejpam-5080	86	6	)	)	PUNCT
ejpam-5080	86	7	second	second	ADJ
ejpam-5080	86	8	kind	kind	NOUN
ejpam-5080	86	9	chebyshev	chebyshev	PROPN
ejpam-5080	86	10	’s	’s	PART
ejpam-5080	86	11	polynomials	polynomial	NOUN
ejpam-5080	86	12	in	in	ADP
ejpam-5080	86	13	the	the	DET
ejpam-5080	86	14	same	same	ADJ
ejpam-5080	86	15	fashion	fashion	NOUN
ejpam-5080	86	16	,	,	PUNCT
ejpam-5080	86	17	we	we	PRON
ejpam-5080	86	18	make	make	VERB
ejpam-5080	86	19	use	use	NOUN
ejpam-5080	86	20	of	of	ADP
ejpam-5080	86	21	the	the	DET
ejpam-5080	86	22	second	second	ADJ
ejpam-5080	86	23	kind	kind	NOUN
ejpam-5080	86	24	chebyshev	chebyshev	NOUN
ejpam-5080	86	25	’s	’s	PART
ejpam-5080	86	26	polynomials	polynomial	NOUN
ejpam-5080	86	27	in	in	ADP
ejpam-5080	86	28	approximating	approximate	VERB
ejpam-5080	86	29	the	the	DET
ejpam-5080	86	30	source	source	NOUN
ejpam-5080	86	31	term	term	NOUN
ejpam-5080	86	32	g(x	g(x	NOUN
ejpam-5080	86	33	)	)	PUNCT
ejpam-5080	86	34	instead	instead	ADV
ejpam-5080	86	35	of	of	ADP
ejpam-5080	86	36	the	the	DET
ejpam-5080	86	37	first	first	ADJ
ejpam-5080	86	38	kind	kind	NOUN
ejpam-5080	86	39	chebyshev	chebyshev	PROPN
ejpam-5080	86	40	’s	’s	PART
ejpam-5080	86	41	polynomials	polynomial	NOUN
ejpam-5080	86	42	[	[	X
ejpam-5080	86	43	9	9	NUM
ejpam-5080	86	44	,	,	PUNCT
ejpam-5080	86	45	14	14	NUM
ejpam-5080	86	46	]	]	PUNCT
ejpam-5080	86	47	as	as	SCONJ
ejpam-5080	86	48	follows	follow	VERB
ejpam-5080	86	49	g(x	g(x	NOUN
ejpam-5080	86	50	)	)	PUNCT
ejpam-5080	87	1	=	=	PUNCT
ejpam-5080	87	2	m∑	m∑	CCONJ
ejpam-5080	87	3	n=0	n=0	NUM
ejpam-5080	87	4	cnun(x	cnun(x	NOUN
ejpam-5080	87	5	)	)	PUNCT
ejpam-5080	87	6	,	,	PUNCT
ejpam-5080	87	7	(	(	PUNCT
ejpam-5080	87	8	18	18	NUM
ejpam-5080	87	9	)	)	PUNCT
ejpam-5080	88	1	where	where	SCONJ
ejpam-5080	88	2	un(x	un(x	NOUN
ejpam-5080	88	3	)	)	PUNCT
ejpam-5080	88	4	are	be	AUX
ejpam-5080	88	5	the	the	DET
ejpam-5080	88	6	orthogonal	orthogonal	ADJ
ejpam-5080	88	7	chebyshev	chebyshev	PROPN
ejpam-5080	88	8	’s	’s	PART
ejpam-5080	88	9	polynomial	polynomial	NOUN
ejpam-5080	88	10	of	of	ADP
ejpam-5080	88	11	the	the	DET
ejpam-5080	88	12	second	second	ADJ
ejpam-5080	88	13	kind	kind	NOUN
ejpam-5080	88	14	;	;	PUNCT
ejpam-5080	88	15	while	while	SCONJ
ejpam-5080	88	16	the	the	DET
ejpam-5080	88	17	coefficients	coefficient	NOUN
ejpam-5080	88	18	of	of	ADP
ejpam-5080	88	19	the	the	DET
ejpam-5080	88	20	chebyshev	chebyshev	NOUN
ejpam-5080	88	21	’s	’s	PART
ejpam-5080	88	22	expansion	expansion	NOUN
ejpam-5080	88	23	ci	ci	NOUN
ejpam-5080	88	24	are	be	AUX
ejpam-5080	88	25	given	give	VERB
ejpam-5080	88	26	by	by	ADP
ejpam-5080	88	27	ci	ci	NOUN
ejpam-5080	88	28	=	=	SYM
ejpam-5080	88	29	2	2	NUM
ejpam-5080	88	30	π	π	NOUN
ejpam-5080	88	31	∫	∫	PROPN
ejpam-5080	88	32	1	1	NUM
ejpam-5080	88	33	−1	−1	NOUN
ejpam-5080	88	34	√	√	NOUN
ejpam-5080	88	35	1−	1−	NUM
ejpam-5080	88	36	x2g(x)ui(x)dx	x2g(x)ui(x)dx	NOUN
ejpam-5080	88	37	,	,	PUNCT
ejpam-5080	88	38	i	i	PRON
ejpam-5080	88	39	=	=	NOUN
ejpam-5080	88	40	0	0	NUM
ejpam-5080	88	41	,	,	PUNCT
ejpam-5080	88	42	1	1	NUM
ejpam-5080	88	43	,	,	PUNCT
ejpam-5080	88	44	2	2	NUM
ejpam-5080	88	45	,	,	PUNCT
ejpam-5080	88	46	·	·	PUNCT
ejpam-5080	88	47	·	·	PUNCT
ejpam-5080	89	1	·	·	PUNCT
ejpam-5080	89	2	(	(	PUNCT
ejpam-5080	89	3	19	19	NUM
ejpam-5080	89	4	)	)	PUNCT
ejpam-5080	89	5	now	now	ADV
ejpam-5080	89	6	,	,	PUNCT
ejpam-5080	89	7	on	on	ADP
ejpam-5080	89	8	using	use	VERB
ejpam-5080	89	9	eqs	eqs	PROPN
ejpam-5080	89	10	.	.	PUNCT
ejpam-5080	89	11	(	(	PUNCT
ejpam-5080	89	12	9	9	NUM
ejpam-5080	89	13	)	)	PUNCT
ejpam-5080	89	14	and	and	CCONJ
ejpam-5080	89	15	(	(	PUNCT
ejpam-5080	89	16	18	18	NUM
ejpam-5080	89	17	)	)	PUNCT
ejpam-5080	89	18	,	,	PUNCT
ejpam-5080	89	19	we	we	PRON
ejpam-5080	89	20	get	get	VERB
ejpam-5080	89	21	the	the	DET
ejpam-5080	89	22	following	follow	VERB
ejpam-5080	89	23	recursive	recursive	ADJ
ejpam-5080	89	24	solution	solution	NOUN
ejpam-5080	89	25	{	{	PUNCT
ejpam-5080	89	26	u0	u0	NOUN
ejpam-5080	89	27	=	=	PUNCT
ejpam-5080	89	28	ϕ(x	ϕ(x	PROPN
ejpam-5080	89	29	)	)	PUNCT
ejpam-5080	89	30	+	+	NUM
ejpam-5080	89	31	l−1[c0u0(x	l−1[c0u0(x	NOUN
ejpam-5080	89	32	)	)	PUNCT
ejpam-5080	89	33	+	+	NUM
ejpam-5080	89	34	c1u1(x	c1u1(x	NOUN
ejpam-5080	89	35	)	)	PUNCT
ejpam-5080	89	36	+	+	NUM
ejpam-5080	89	37	c2u2(x	c2u2(x	NOUN
ejpam-5080	89	38	)	)	PUNCT
ejpam-5080	90	1	+	+	CCONJ
ejpam-5080	90	2	·	·	PUNCT
ejpam-5080	90	3	·	·	PUNCT
ejpam-5080	90	4	·	·	PUNCT
ejpam-5080	90	5	+	+	NUM
ejpam-5080	90	6	cmum(x	cmum(x	NOUN
ejpam-5080	90	7	)	)	PUNCT
ejpam-5080	90	8	]	]	PUNCT
ejpam-5080	90	9	,	,	PUNCT
ejpam-5080	90	10	un+1	un+1	NOUN
ejpam-5080	90	11	=	=	SYM
ejpam-5080	90	12	−l−1run	−l−1run	NOUN
ejpam-5080	90	13	−	−	PROPN
ejpam-5080	90	14	l−1an	l−1an	NOUN
ejpam-5080	90	15	,	,	PUNCT
ejpam-5080	90	16	n	n	X
ejpam-5080	90	17	≥	≥	NOUN
ejpam-5080	90	18	0	0	NUM
ejpam-5080	90	19	.	.	PUNCT
ejpam-5080	91	1	(	(	PUNCT
ejpam-5080	91	2	20	20	NUM
ejpam-5080	91	3	)	)	PUNCT
ejpam-5080	91	4	thus	thus	ADV
ejpam-5080	91	5	,	,	PUNCT
ejpam-5080	91	6	realistic	realistic	ADJ
ejpam-5080	91	7	solutions	solution	NOUN
ejpam-5080	91	8	via	via	ADP
ejpam-5080	91	9	the	the	DET
ejpam-5080	91	10	application	application	NOUN
ejpam-5080	91	11	of	of	ADP
ejpam-5080	91	12	the	the	DET
ejpam-5080	91	13	chebyshev	chebyshev	NOUN
ejpam-5080	91	14	’s	’s	PART
ejpam-5080	91	15	polynomials	polynomial	NOUN
ejpam-5080	91	16	of	of	ADP
ejpam-5080	91	17	the	the	DET
ejpam-5080	91	18	first	first	ADJ
ejpam-5080	91	19	and	and	CCONJ
ejpam-5080	91	20	second	second	ADJ
ejpam-5080	91	21	kinds	kind	NOUN
ejpam-5080	91	22	are	be	AUX
ejpam-5080	91	23	thus	thus	ADV
ejpam-5080	91	24	obtained	obtain	VERB
ejpam-5080	91	25	in	in	ADP
ejpam-5080	91	26	this	this	DET
ejpam-5080	91	27	regard	regard	NOUN
ejpam-5080	91	28	by	by	ADP
ejpam-5080	91	29	considering	consider	VERB
ejpam-5080	91	30	the	the	DET
ejpam-5080	91	31	following	follow	VERB
ejpam-5080	91	32	m	m	ADJ
ejpam-5080	91	33	-	-	PUNCT
ejpam-5080	91	34	term	term	NOUN
ejpam-5080	91	35	approximations	approximation	NOUN
ejpam-5080	91	36	using	use	VERB
ejpam-5080	91	37	u(x	u(x	NOUN
ejpam-5080	91	38	)	)	PUNCT
ejpam-5080	92	1	=	=	PUNCT
ejpam-5080	92	2	∑m	∑m	PROPN
ejpam-5080	92	3	n=0	n=0	NUM
ejpam-5080	92	4	un	un	NOUN
ejpam-5080	92	5	,	,	PUNCT
ejpam-5080	92	6	where	where	SCONJ
ejpam-5080	92	7	m	m	PROPN
ejpam-5080	92	8	is	be	AUX
ejpam-5080	92	9	the	the	DET
ejpam-5080	92	10	order	order	NOUN
ejpam-5080	92	11	of	of	ADP
ejpam-5080	92	12	the	the	DET
ejpam-5080	92	13	solution	solution	NOUN
ejpam-5080	92	14	.	.	PUNCT
ejpam-5080	93	1	3.3	3.3	NUM
ejpam-5080	93	2	.	.	PUNCT
ejpam-5080	94	1	adomian	adomian	NOUN
ejpam-5080	94	2	modification	modification	NOUN
ejpam-5080	94	3	method	method	NOUN
ejpam-5080	94	4	via	via	ADP
ejpam-5080	94	5	laguerre	laguerre	NOUN
ejpam-5080	94	6	’s	’s	PART
ejpam-5080	94	7	polynomials	polynomial	NOUN
ejpam-5080	94	8	in	in	ADP
ejpam-5080	94	9	the	the	DET
ejpam-5080	94	10	same	same	ADJ
ejpam-5080	94	11	way	way	NOUN
ejpam-5080	95	1	,	,	PUNCT
ejpam-5080	95	2	it	it	PRON
ejpam-5080	95	3	is	be	AUX
ejpam-5080	95	4	suggested	suggest	VERB
ejpam-5080	95	5	that	that	SCONJ
ejpam-5080	95	6	the	the	DET
ejpam-5080	95	7	source	source	NOUN
ejpam-5080	95	8	term	term	NOUN
ejpam-5080	95	9	g(x	g(x	NOUN
ejpam-5080	95	10	)	)	PUNCT
ejpam-5080	95	11	to	to	PART
ejpam-5080	95	12	be	be	AUX
ejpam-5080	95	13	decomposed	decompose	VERB
ejpam-5080	95	14	using	use	VERB
ejpam-5080	95	15	laguerre	laguerre	NOUN
ejpam-5080	95	16	’s	’s	PART
ejpam-5080	95	17	series	series	NOUN
ejpam-5080	95	18	[	[	X
ejpam-5080	95	19	11	11	NUM
ejpam-5080	95	20	]	]	PUNCT
ejpam-5080	95	21	as	as	SCONJ
ejpam-5080	95	22	follows	follow	VERB
ejpam-5080	95	23	g(x	g(x	NOUN
ejpam-5080	95	24	)	)	PUNCT
ejpam-5080	95	25	=	=	PUNCT
ejpam-5080	96	1	m∑	m∑	CCONJ
ejpam-5080	96	2	n=0	n=0	SYM
ejpam-5080	96	3	cnln(x	cnln(x	PROPN
ejpam-5080	96	4	)	)	PUNCT
ejpam-5080	96	5	(	(	PUNCT
ejpam-5080	96	6	21	21	NUM
ejpam-5080	96	7	)	)	PUNCT
ejpam-5080	96	8	where	where	SCONJ
ejpam-5080	96	9	ln(x	ln(x	X
ejpam-5080	96	10	)	)	PUNCT
ejpam-5080	96	11	are	be	AUX
ejpam-5080	96	12	orthogonal	orthogonal	ADJ
ejpam-5080	96	13	laguerre	laguerre	NOUN
ejpam-5080	96	14	’s	’s	PART
ejpam-5080	96	15	polynomials	polynomial	NOUN
ejpam-5080	96	16	,	,	PUNCT
ejpam-5080	96	17	and	and	CCONJ
ejpam-5080	96	18	ci	ci	NOUN
ejpam-5080	96	19	are	be	AUX
ejpam-5080	96	20	given	give	VERB
ejpam-5080	96	21	by	by	ADP
ejpam-5080	96	22	ci	ci	NOUN
ejpam-5080	96	23	=	=	SYM
ejpam-5080	96	24	∫	∫	PROPN
ejpam-5080	96	25	∞	∞	PROPN
ejpam-5080	96	26	0	0	PUNCT
ejpam-5080	97	1	e−xli(x)g(x)dx	e−xli(x)g(x)dx	NOUN
ejpam-5080	97	2	,	,	PUNCT
ejpam-5080	97	3	i	i	NOUN
ejpam-5080	97	4	=	=	NOUN
ejpam-5080	97	5	0	0	NUM
ejpam-5080	97	6	,	,	PUNCT
ejpam-5080	97	7	1	1	NUM
ejpam-5080	97	8	,	,	PUNCT
ejpam-5080	97	9	·	·	PUNCT
ejpam-5080	97	10	·	·	PUNCT
ejpam-5080	97	11	·	·	PUNCT
ejpam-5080	97	12	(	(	PUNCT
ejpam-5080	97	13	22	22	X
ejpam-5080	97	14	)	)	PUNCT
ejpam-5080	97	15	n.	n.	NOUN
ejpam-5080	97	16	alzaid	alzaid	PROPN
ejpam-5080	97	17	et	et	PROPN
ejpam-5080	97	18	al	al	PROPN
ejpam-5080	97	19	.	.	PUNCT
ejpam-5080	97	20	/	/	SYM
ejpam-5080	97	21	eur	eur	PROPN
ejpam-5080	97	22	.	.	PUNCT
ejpam-5080	98	1	j.	j.	PROPN
ejpam-5080	98	2	pure	pure	PROPN
ejpam-5080	98	3	appl	appl	PROPN
ejpam-5080	98	4	.	.	PROPN
ejpam-5080	98	5	math	math	PROPN
ejpam-5080	98	6	,	,	PUNCT
ejpam-5080	98	7	17	17	NUM
ejpam-5080	98	8	(	(	PUNCT
ejpam-5080	98	9	3	3	NUM
ejpam-5080	98	10	)	)	PUNCT
ejpam-5080	98	11	(	(	PUNCT
ejpam-5080	98	12	2024	2024	NUM
ejpam-5080	98	13	)	)	PUNCT
ejpam-5080	98	14	,	,	PUNCT
ejpam-5080	98	15	1982	1982	NUM
ejpam-5080	98	16	-	-	SYM
ejpam-5080	98	17	2000	2000	NUM
ejpam-5080	98	18	1987	1987	NUM
ejpam-5080	98	19	accordingly	accordingly	ADV
ejpam-5080	98	20	eqs.(9	eqs.(9	PROPN
ejpam-5080	98	21	)	)	PUNCT
ejpam-5080	98	22	and	and	CCONJ
ejpam-5080	98	23	(	(	PUNCT
ejpam-5080	98	24	21	21	NUM
ejpam-5080	98	25	)	)	PUNCT
ejpam-5080	99	1	,	,	PUNCT
ejpam-5080	99	2	we	we	PRON
ejpam-5080	99	3	get	get	VERB
ejpam-5080	99	4	the	the	DET
ejpam-5080	99	5	recursive	recursive	ADJ
ejpam-5080	99	6	solution	solution	NOUN
ejpam-5080	99	7	as	as	ADP
ejpam-5080	99	8	in	in	ADP
ejpam-5080	99	9	the	the	DET
ejpam-5080	99	10	preceding	precede	VERB
ejpam-5080	99	11	method	method	NOUN
ejpam-5080	99	12	as	as	SCONJ
ejpam-5080	99	13	follows	follow	VERB
ejpam-5080	99	14	{	{	PUNCT
ejpam-5080	99	15	u0	u0	NOUN
ejpam-5080	99	16	=	=	PUNCT
ejpam-5080	99	17	ϕ(x	ϕ(x	NOUN
ejpam-5080	99	18	)	)	PUNCT
ejpam-5080	99	19	+	+	NUM
ejpam-5080	99	20	l−1[c0l0(x	l−1[c0l0(x	NOUN
ejpam-5080	99	21	)	)	PUNCT
ejpam-5080	100	1	+	+	CCONJ
ejpam-5080	100	2	c1l1(x	c1l1(x	NOUN
ejpam-5080	100	3	)	)	PUNCT
ejpam-5080	100	4	+	+	CCONJ
ejpam-5080	100	5	c2l2(x	c2l2(x	X
ejpam-5080	100	6	)	)	PUNCT
ejpam-5080	100	7	+	+	NUM
ejpam-5080	101	1	·	·	PUNCT
ejpam-5080	101	2	·	·	PUNCT
ejpam-5080	101	3	·	·	PUNCT
ejpam-5080	101	4	+	+	NUM
ejpam-5080	101	5	cmlm(x	cmlm(x	NOUN
ejpam-5080	101	6	)	)	PUNCT
ejpam-5080	101	7	]	]	PUNCT
ejpam-5080	101	8	,	,	PUNCT
ejpam-5080	101	9	un+1	un+1	NOUN
ejpam-5080	101	10	=	=	SYM
ejpam-5080	101	11	−l−1run	−l−1run	NOUN
ejpam-5080	101	12	−	−	PROPN
ejpam-5080	101	13	l−1an	l−1an	NOUN
ejpam-5080	101	14	,	,	PUNCT
ejpam-5080	101	15	n	n	X
ejpam-5080	101	16	≥	≥	NOUN
ejpam-5080	101	17	0	0	NUM
ejpam-5080	101	18	,	,	PUNCT
ejpam-5080	101	19	(	(	PUNCT
ejpam-5080	101	20	23	23	NUM
ejpam-5080	101	21	)	)	PUNCT
ejpam-5080	101	22	where	where	SCONJ
ejpam-5080	101	23	the	the	DET
ejpam-5080	101	24	closed	closed	ADJ
ejpam-5080	101	25	-	-	PUNCT
ejpam-5080	101	26	form	form	NOUN
ejpam-5080	101	27	solution	solution	NOUN
ejpam-5080	101	28	u(x	u(x	NOUN
ejpam-5080	101	29	)	)	PUNCT
ejpam-5080	101	30	is	be	AUX
ejpam-5080	101	31	obtained	obtain	VERB
ejpam-5080	101	32	upon	upon	SCONJ
ejpam-5080	101	33	summing	sum	VERB
ejpam-5080	101	34	the	the	DET
ejpam-5080	101	35	individual	individual	ADJ
ejpam-5080	101	36	components	component	NOUN
ejpam-5080	101	37	as	as	SCONJ
ejpam-5080	101	38	suggested	suggest	VERB
ejpam-5080	101	39	by	by	ADP
ejpam-5080	101	40	adm	adm	PROPN
ejpam-5080	101	41	.	.	PUNCT
ejpam-5080	102	1	3.4	3.4	NUM
ejpam-5080	102	2	.	.	PUNCT
ejpam-5080	102	3	adomian	adomian	NOUN
ejpam-5080	102	4	modification	modification	NOUN
ejpam-5080	102	5	method	method	NOUN
ejpam-5080	102	6	via	via	ADP
ejpam-5080	102	7	hermite	hermite	PROPN
ejpam-5080	102	8	’s	’s	PART
ejpam-5080	102	9	polynomials	polynomial	NOUN
ejpam-5080	102	10	in	in	ADP
ejpam-5080	102	11	the	the	DET
ejpam-5080	102	12	same	same	ADJ
ejpam-5080	102	13	way	way	NOUN
ejpam-5080	102	14	,	,	PUNCT
ejpam-5080	102	15	it	it	PRON
ejpam-5080	102	16	is	be	AUX
ejpam-5080	102	17	suggested	suggest	VERB
ejpam-5080	102	18	that	that	SCONJ
ejpam-5080	102	19	the	the	DET
ejpam-5080	102	20	source	source	NOUN
ejpam-5080	102	21	term	term	NOUN
ejpam-5080	102	22	g(x	g(x	NOUN
ejpam-5080	102	23	)	)	PUNCT
ejpam-5080	102	24	to	to	PART
ejpam-5080	102	25	be	be	AUX
ejpam-5080	102	26	decomposed	decompose	VERB
ejpam-5080	102	27	using	use	VERB
ejpam-5080	102	28	hermite	hermite	PROPN
ejpam-5080	102	29	’s	’s	PART
ejpam-5080	102	30	series	series	NOUN
ejpam-5080	102	31	[	[	X
ejpam-5080	102	32	12	12	NUM
ejpam-5080	102	33	]	]	PUNCT
ejpam-5080	102	34	as	as	SCONJ
ejpam-5080	102	35	follows	follow	VERB
ejpam-5080	102	36	g(x	g(x	NOUN
ejpam-5080	102	37	)	)	PUNCT
ejpam-5080	102	38	=	=	PUNCT
ejpam-5080	102	39	m∑	m∑	CCONJ
ejpam-5080	103	1	n=0	n=0	SYM
ejpam-5080	103	2	cnhn(x	cnhn(x	PROPN
ejpam-5080	103	3	)	)	PUNCT
ejpam-5080	103	4	,	,	PUNCT
ejpam-5080	103	5	(	(	PUNCT
ejpam-5080	103	6	24	24	NUM
ejpam-5080	103	7	)	)	PUNCT
ejpam-5080	104	1	where	where	SCONJ
ejpam-5080	104	2	hn(x	hn(x	X
ejpam-5080	104	3	)	)	PUNCT
ejpam-5080	104	4	are	be	AUX
ejpam-5080	104	5	orthogonal	orthogonal	ADJ
ejpam-5080	104	6	hermite	hermite	PROPN
ejpam-5080	104	7	’s	’s	PART
ejpam-5080	104	8	polynomials	polynomial	NOUN
ejpam-5080	104	9	,	,	PUNCT
ejpam-5080	104	10	and	and	CCONJ
ejpam-5080	104	11	the	the	DET
ejpam-5080	104	12	coefficient	coefficient	NOUN
ejpam-5080	104	13	ci	ci	PROPN
ejpam-5080	104	14	are	be	AUX
ejpam-5080	104	15	determined	determine	VERB
ejpam-5080	104	16	using	use	VERB
ejpam-5080	104	17	ci	ci	NOUN
ejpam-5080	104	18	=	=	SYM
ejpam-5080	104	19	1	1	NUM
ejpam-5080	104	20	2ii	2ii	NOUN
ejpam-5080	104	21	!	!	PUNCT
ejpam-5080	105	1	√	√	PUNCT
ejpam-5080	106	1	π	π	X
ejpam-5080	106	2	∫	∫	PROPN
ejpam-5080	106	3	∞	∞	PROPN
ejpam-5080	106	4	−∞	−∞	ADP
ejpam-5080	106	5	e−x2	e−x2	NOUN
ejpam-5080	106	6	hi(x)g(x)dx	hi(x)g(x)dx	NOUN
ejpam-5080	106	7	,	,	PUNCT
ejpam-5080	106	8	i	i	PRON
ejpam-5080	106	9	=	=	NOUN
ejpam-5080	106	10	0	0	NUM
ejpam-5080	106	11	,	,	PUNCT
ejpam-5080	106	12	1	1	NUM
ejpam-5080	106	13	,	,	PUNCT
ejpam-5080	106	14	·	·	PUNCT
ejpam-5080	106	15	·	·	PUNCT
ejpam-5080	106	16	·	·	PUNCT
ejpam-5080	106	17	(	(	PUNCT
ejpam-5080	106	18	25	25	NUM
ejpam-5080	106	19	)	)	PUNCT
ejpam-5080	106	20	what	what	PRON
ejpam-5080	106	21	’s	’	VERB
ejpam-5080	106	22	more	more	ADJ
ejpam-5080	106	23	from	from	ADP
ejpam-5080	106	24	eqs.(9	eqs.(9	PROPN
ejpam-5080	106	25	)	)	PUNCT
ejpam-5080	106	26	and	and	CCONJ
ejpam-5080	106	27	(	(	PUNCT
ejpam-5080	106	28	21	21	NUM
ejpam-5080	106	29	)	)	PUNCT
ejpam-5080	106	30	,	,	PUNCT
ejpam-5080	106	31	we	we	PRON
ejpam-5080	106	32	get	get	VERB
ejpam-5080	106	33	the	the	DET
ejpam-5080	106	34	following	follow	VERB
ejpam-5080	106	35	recursive	recursive	ADJ
ejpam-5080	106	36	solution	solution	NOUN
ejpam-5080	106	37	as	as	SCONJ
ejpam-5080	106	38	explained	explain	VERB
ejpam-5080	106	39	earlier	early	ADV
ejpam-5080	106	40	as	as	SCONJ
ejpam-5080	106	41	follows	follow	VERB
ejpam-5080	106	42	{	{	PUNCT
ejpam-5080	106	43	u0	u0	NOUN
ejpam-5080	106	44	=	=	PUNCT
ejpam-5080	106	45	ϕ(x	ϕ(x	NOUN
ejpam-5080	106	46	)	)	PUNCT
ejpam-5080	106	47	+	+	SYM
ejpam-5080	106	48	l−1[c0h0(x	l−1[c0h0(x	NOUN
ejpam-5080	106	49	)	)	PUNCT
ejpam-5080	107	1	+	+	CCONJ
ejpam-5080	107	2	c1h1(x	c1h1(x	NOUN
ejpam-5080	107	3	)	)	PUNCT
ejpam-5080	107	4	+	+	CCONJ
ejpam-5080	107	5	c2h2(x	c2h2(x	NOUN
ejpam-5080	107	6	)	)	PUNCT
ejpam-5080	108	1	+	+	NUM
ejpam-5080	108	2	·	·	PUNCT
ejpam-5080	108	3	·	·	PUNCT
ejpam-5080	108	4	·	·	PUNCT
ejpam-5080	108	5	+	+	NUM
ejpam-5080	108	6	cmhm(x	cmhm(x	NOUN
ejpam-5080	108	7	)	)	PUNCT
ejpam-5080	108	8	]	]	PUNCT
ejpam-5080	108	9	,	,	PUNCT
ejpam-5080	108	10	un+1	un+1	NOUN
ejpam-5080	108	11	=	=	SYM
ejpam-5080	108	12	−l−1run	−l−1run	NOUN
ejpam-5080	108	13	−	−	PROPN
ejpam-5080	108	14	l−1an	l−1an	NOUN
ejpam-5080	108	15	,	,	PUNCT
ejpam-5080	108	16	n	n	X
ejpam-5080	108	17	≥	≥	NOUN
ejpam-5080	108	18	0	0	NUM
ejpam-5080	108	19	,	,	PUNCT
ejpam-5080	108	20	(	(	PUNCT
ejpam-5080	108	21	26	26	NUM
ejpam-5080	108	22	)	)	PUNCT
ejpam-5080	108	23	where	where	SCONJ
ejpam-5080	108	24	the	the	DET
ejpam-5080	108	25	closed	closed	ADJ
ejpam-5080	108	26	-	-	PUNCT
ejpam-5080	108	27	form	form	NOUN
ejpam-5080	108	28	solution	solution	NOUN
ejpam-5080	108	29	u(x	u(x	NOUN
ejpam-5080	108	30	)	)	PUNCT
ejpam-5080	108	31	is	be	AUX
ejpam-5080	108	32	obtained	obtain	VERB
ejpam-5080	108	33	upon	upon	SCONJ
ejpam-5080	108	34	summing	sum	VERB
ejpam-5080	108	35	the	the	DET
ejpam-5080	108	36	individual	individual	ADJ
ejpam-5080	108	37	components	component	NOUN
ejpam-5080	108	38	as	as	SCONJ
ejpam-5080	108	39	suggested	suggest	VERB
ejpam-5080	108	40	by	by	ADP
ejpam-5080	108	41	adm	adm	PROPN
ejpam-5080	108	42	.	.	PUNCT
ejpam-5080	109	1	3.5	3.5	NUM
ejpam-5080	109	2	.	.	PUNCT
ejpam-5080	110	1	adomian	adomian	NOUN
ejpam-5080	110	2	modification	modification	NOUN
ejpam-5080	110	3	methods	method	NOUN
ejpam-5080	110	4	via	via	ADP
ejpam-5080	110	5	gegenbauer	gegenbauer	PROPN
ejpam-5080	110	6	’s	’s	PART
ejpam-5080	110	7	and	and	CCONJ
ejpam-5080	110	8	jacobi	jacobi	PROPN
ejpam-5080	110	9	’s	’s	PART
ejpam-5080	110	10	polynomials	polynomial	NOUN
ejpam-5080	110	11	(	(	PUNCT
ejpam-5080	110	12	i	i	NOUN
ejpam-5080	110	13	)	)	PUNCT
ejpam-5080	110	14	gegenbauer	gegenbauer	PROPN
ejpam-5080	110	15	’s	’s	PART
ejpam-5080	110	16	polynomials	polynomial	NOUN
ejpam-5080	110	17	firstly	firstly	ADV
ejpam-5080	110	18	,	,	PUNCT
ejpam-5080	110	19	we	we	PRON
ejpam-5080	110	20	express	express	VERB
ejpam-5080	110	21	the	the	DET
ejpam-5080	110	22	source	source	NOUN
ejpam-5080	110	23	term	term	NOUN
ejpam-5080	110	24	g(x	g(x	NOUN
ejpam-5080	110	25	)	)	PUNCT
ejpam-5080	110	26	via	via	ADP
ejpam-5080	110	27	the	the	DET
ejpam-5080	110	28	gegenbauer	gegenbauer	NOUN
ejpam-5080	110	29	’s	’s	PART
ejpam-5080	110	30	series	series	NOUN
ejpam-5080	111	1	[	[	X
ejpam-5080	111	2	6	6	NUM
ejpam-5080	111	3	]	]	PUNCT
ejpam-5080	111	4	as	as	SCONJ
ejpam-5080	111	5	follows	follow	VERB
ejpam-5080	111	6	g(x	g(x	NOUN
ejpam-5080	111	7	)	)	PUNCT
ejpam-5080	111	8	=	=	PUNCT
ejpam-5080	112	1	m∑	m∑	CCONJ
ejpam-5080	112	2	n=0	n=0	PROPN
ejpam-5080	112	3	cnc	cnc	PROPN
ejpam-5080	112	4	α	α	PROPN
ejpam-5080	112	5	n	n	PROPN
ejpam-5080	112	6	(	(	PUNCT
ejpam-5080	112	7	x	x	NOUN
ejpam-5080	112	8	)	)	PUNCT
ejpam-5080	112	9	,	,	PUNCT
ejpam-5080	112	10	(	(	PUNCT
ejpam-5080	112	11	27	27	NUM
ejpam-5080	112	12	)	)	PUNCT
ejpam-5080	112	13	where	where	SCONJ
ejpam-5080	112	14	cα	cα	ADP
ejpam-5080	112	15	n	n	X
ejpam-5080	112	16	(	(	PUNCT
ejpam-5080	112	17	x	x	X
ejpam-5080	112	18	)	)	PUNCT
ejpam-5080	112	19	are	be	AUX
ejpam-5080	112	20	the	the	DET
ejpam-5080	112	21	orthogonal	orthogonal	ADJ
ejpam-5080	112	22	gegenbauer	gegenbauer	NOUN
ejpam-5080	112	23	’s	’s	PART
ejpam-5080	112	24	polynomials	polynomial	NOUN
ejpam-5080	112	25	,	,	PUNCT
ejpam-5080	112	26	and	and	CCONJ
ejpam-5080	112	27	the	the	DET
ejpam-5080	112	28	coefficients	coefficient	NOUN
ejpam-5080	112	29	of	of	ADP
ejpam-5080	112	30	gegenbauer	gegenbauer	NOUN
ejpam-5080	112	31	’s	’s	PART
ejpam-5080	112	32	expansion	expansion	NOUN
ejpam-5080	112	33	ci	ci	NOUN
ejpam-5080	112	34	are	be	AUX
ejpam-5080	112	35	defined	define	VERB
ejpam-5080	112	36	as	as	SCONJ
ejpam-5080	112	37	follows	follow	VERB
ejpam-5080	112	38	ci	ci	PROPN
ejpam-5080	112	39	=	=	SYM
ejpam-5080	112	40	∫	∫	PROPN
ejpam-5080	113	1	1	1	NUM
ejpam-5080	113	2	−1	−1	NOUN
ejpam-5080	113	3	g(x)c	g(x)c	PROPN
ejpam-5080	113	4	α	α	INTJ
ejpam-5080	114	1	i	i	INTJ
ejpam-5080	114	2	(	(	PUNCT
ejpam-5080	114	3	x)(1−	x)(1−	PROPN
ejpam-5080	114	4	x2)α−1/2dx∫	x2)α−1/2dx∫	PROPN
ejpam-5080	114	5	1	1	NUM
ejpam-5080	114	6	−1[c	−1[c	NOUN
ejpam-5080	114	7	α	α	NOUN
ejpam-5080	114	8	i	i	PRON
ejpam-5080	114	9	(	(	PUNCT
ejpam-5080	114	10	x	x	NOUN
ejpam-5080	114	11	)	)	PUNCT
ejpam-5080	114	12	]	]	PUNCT
ejpam-5080	115	1	2(1−	2(1−	X
ejpam-5080	116	1	x2)α−1/2dx	x2)α−1/2dx	X
ejpam-5080	116	2	,	,	PUNCT
ejpam-5080	116	3	i	i	PRON
ejpam-5080	116	4	=	=	NOUN
ejpam-5080	116	5	0	0	NUM
ejpam-5080	116	6	,	,	PUNCT
ejpam-5080	116	7	1	1	NUM
ejpam-5080	116	8	,	,	PUNCT
ejpam-5080	116	9	2	2	NUM
ejpam-5080	116	10	,	,	PUNCT
ejpam-5080	116	11	·	·	PUNCT
ejpam-5080	116	12	·	·	PUNCT
ejpam-5080	116	13	·	·	PUNCT
ejpam-5080	116	14	(	(	PUNCT
ejpam-5080	116	15	28	28	X
ejpam-5080	116	16	)	)	PUNCT
ejpam-5080	116	17	n.	n.	NOUN
ejpam-5080	116	18	alzaid	alzaid	PROPN
ejpam-5080	116	19	et	et	PROPN
ejpam-5080	116	20	al	al	PROPN
ejpam-5080	116	21	.	.	PUNCT
ejpam-5080	116	22	/	/	SYM
ejpam-5080	116	23	eur	eur	PROPN
ejpam-5080	116	24	.	.	PUNCT
ejpam-5080	117	1	j.	j.	PROPN
ejpam-5080	117	2	pure	pure	PROPN
ejpam-5080	117	3	appl	appl	PROPN
ejpam-5080	117	4	.	.	PROPN
ejpam-5080	117	5	math	math	PROPN
ejpam-5080	117	6	,	,	PUNCT
ejpam-5080	117	7	17	17	NUM
ejpam-5080	117	8	(	(	PUNCT
ejpam-5080	117	9	3	3	NUM
ejpam-5080	117	10	)	)	PUNCT
ejpam-5080	117	11	(	(	PUNCT
ejpam-5080	117	12	2024	2024	NUM
ejpam-5080	117	13	)	)	PUNCT
ejpam-5080	117	14	,	,	PUNCT
ejpam-5080	117	15	1982	1982	NUM
ejpam-5080	117	16	-	-	SYM
ejpam-5080	117	17	2000	2000	NUM
ejpam-5080	117	18	1988	1988	NUM
ejpam-5080	117	19	where	where	SCONJ
ejpam-5080	117	20	the	the	DET
ejpam-5080	117	21	normalization	normalization	NOUN
ejpam-5080	117	22	of	of	ADP
ejpam-5080	117	23	the	the	DET
ejpam-5080	117	24	functions	function	NOUN
ejpam-5080	117	25	are	be	AUX
ejpam-5080	117	26	done	do	VERB
ejpam-5080	117	27	using	use	VERB
ejpam-5080	117	28	as	as	ADP
ejpam-5080	117	29	(	(	PUNCT
ejpam-5080	117	30	1	1	NUM
ejpam-5080	117	31	−	−	NOUN
ejpam-5080	117	32	x2)α−1/2	x2)α−1/2	PROPN
ejpam-5080	117	33	as	as	ADP
ejpam-5080	117	34	the	the	DET
ejpam-5080	117	35	weight	weight	NOUN
ejpam-5080	117	36	function	function	NOUN
ejpam-5080	117	37	.	.	PUNCT
ejpam-5080	118	1	lastly	lastly	ADV
ejpam-5080	118	2	,	,	PUNCT
ejpam-5080	118	3	substituting	substitute	VERB
ejpam-5080	118	4	eq	eq	ADP
ejpam-5080	118	5	.	.	PUNCT
ejpam-5080	119	1	(	(	PUNCT
ejpam-5080	119	2	27	27	NUM
ejpam-5080	119	3	)	)	PUNCT
ejpam-5080	119	4	into	into	ADP
ejpam-5080	119	5	eq	eq	NOUN
ejpam-5080	119	6	.	.	PUNCT
ejpam-5080	120	1	(	(	PUNCT
ejpam-5080	120	2	9	9	NUM
ejpam-5080	120	3	)	)	PUNCT
ejpam-5080	120	4	,	,	PUNCT
ejpam-5080	120	5	we	we	PRON
ejpam-5080	120	6	get	get	VERB
ejpam-5080	120	7	the	the	DET
ejpam-5080	120	8	recursive	recursive	ADJ
ejpam-5080	120	9	solution	solution	NOUN
ejpam-5080	120	10	without	without	ADP
ejpam-5080	120	11	further	further	ADJ
ejpam-5080	120	12	delay	delay	NOUN
ejpam-5080	120	13	as	as	SCONJ
ejpam-5080	120	14	follows	follow	VERB
ejpam-5080	120	15	{	{	PUNCT
ejpam-5080	120	16	u0	u0	NOUN
ejpam-5080	120	17	=	=	PUNCT
ejpam-5080	120	18	ϕ(x	ϕ(x	PROPN
ejpam-5080	120	19	)	)	PUNCT
ejpam-5080	121	1	+	+	CCONJ
ejpam-5080	121	2	l−1[c0c	l−1[c0c	NOUN
ejpam-5080	121	3	α	α	NOUN
ejpam-5080	121	4	0	0	PUNCT
ejpam-5080	121	5	(	(	PUNCT
ejpam-5080	121	6	x	x	X
ejpam-5080	121	7	)	)	PUNCT
ejpam-5080	121	8	+	+	CCONJ
ejpam-5080	121	9	c1c	c1c	VERB
ejpam-5080	121	10	α	α	PRON
ejpam-5080	121	11	1	1	NUM
ejpam-5080	121	12	(	(	PUNCT
ejpam-5080	121	13	x	x	NOUN
ejpam-5080	121	14	)	)	PUNCT
ejpam-5080	122	1	+	+	NUM
ejpam-5080	122	2	c2c	c2c	PROPN
ejpam-5080	122	3	α	α	NOUN
ejpam-5080	122	4	2	2	NUM
ejpam-5080	122	5	(	(	PUNCT
ejpam-5080	122	6	x	x	X
ejpam-5080	122	7	)	)	PUNCT
ejpam-5080	122	8	+	+	CCONJ
ejpam-5080	122	9	·	·	PUNCT
ejpam-5080	122	10	·	·	PUNCT
ejpam-5080	122	11	·	·	PUNCT
ejpam-5080	122	12	+	+	NUM
ejpam-5080	122	13	cmcα	cmcα	ADJ
ejpam-5080	122	14	m(x	m(x	NOUN
ejpam-5080	122	15	)	)	PUNCT
ejpam-5080	122	16	]	]	PUNCT
ejpam-5080	122	17	,	,	PUNCT
ejpam-5080	122	18	un+1	un+1	NOUN
ejpam-5080	122	19	=	=	SYM
ejpam-5080	122	20	−l−1run	−l−1run	NOUN
ejpam-5080	122	21	−	−	PROPN
ejpam-5080	122	22	l−1an	l−1an	NOUN
ejpam-5080	122	23	,	,	PUNCT
ejpam-5080	122	24	n	n	X
ejpam-5080	122	25	≥	≥	NOUN
ejpam-5080	122	26	0	0	NUM
ejpam-5080	122	27	.	.	PUNCT
ejpam-5080	123	1	(	(	PUNCT
ejpam-5080	123	2	29	29	NUM
ejpam-5080	123	3	)	)	PUNCT
ejpam-5080	123	4	(	(	PUNCT
ejpam-5080	123	5	ii	ii	X
ejpam-5080	123	6	)	)	PUNCT
ejpam-5080	123	7	jacobi	jacobi	PROPN
ejpam-5080	123	8	’s	’s	PART
ejpam-5080	123	9	polynomials	polynomial	NOUN
ejpam-5080	123	10	considering	consider	VERB
ejpam-5080	123	11	jacobi	jacobi	PROPN
ejpam-5080	123	12	’s	’s	PART
ejpam-5080	123	13	orthogonal	orthogonal	ADJ
ejpam-5080	123	14	polynomials	polynomial	NOUN
ejpam-5080	123	15	over	over	ADP
ejpam-5080	123	16	[	[	X
ejpam-5080	123	17	–	–	PUNCT
ejpam-5080	123	18	1	1	NUM
ejpam-5080	123	19	,	,	PUNCT
ejpam-5080	123	20	1	1	NUM
ejpam-5080	123	21	]	]	PUNCT
ejpam-5080	123	22	,	,	PUNCT
ejpam-5080	123	23	we	we	PRON
ejpam-5080	123	24	in	in	ADP
ejpam-5080	123	25	the	the	DET
ejpam-5080	123	26	same	same	ADJ
ejpam-5080	123	27	way	way	NOUN
ejpam-5080	123	28	decompose	decompose	VERB
ejpam-5080	123	29	the	the	DET
ejpam-5080	123	30	source	source	NOUN
ejpam-5080	123	31	term	term	NOUN
ejpam-5080	123	32	g(x	g(x	NOUN
ejpam-5080	123	33	)	)	PUNCT
ejpam-5080	123	34	as	as	SCONJ
ejpam-5080	123	35	follows	follow	VERB
ejpam-5080	123	36	g(x	g(x	NOUN
ejpam-5080	123	37	)	)	PUNCT
ejpam-5080	124	1	=	=	PUNCT
ejpam-5080	124	2	m∑	m∑	CCONJ
ejpam-5080	124	3	n=0	n=0	SYM
ejpam-5080	124	4	cnp	cnp	PROPN
ejpam-5080	124	5	(	(	PUNCT
ejpam-5080	124	6	α	α	NOUN
ejpam-5080	124	7	,	,	PUNCT
ejpam-5080	124	8	β	β	NOUN
ejpam-5080	124	9	)	)	PUNCT
ejpam-5080	124	10	n	n	PROPN
ejpam-5080	124	11	(	(	PUNCT
ejpam-5080	124	12	x	x	NOUN
ejpam-5080	124	13	)	)	PUNCT
ejpam-5080	124	14	,	,	PUNCT
ejpam-5080	124	15	(	(	PUNCT
ejpam-5080	124	16	30	30	NUM
ejpam-5080	124	17	)	)	PUNCT
ejpam-5080	124	18	where	where	SCONJ
ejpam-5080	124	19	α	α	X
ejpam-5080	124	20	,	,	PUNCT
ejpam-5080	124	21	β	β	X
ejpam-5080	124	22	>	>	X
ejpam-5080	124	23	−1	−1	NOUN
ejpam-5080	124	24	and	and	CCONJ
ejpam-5080	124	25	p	p	X
ejpam-5080	124	26	(	(	PUNCT
ejpam-5080	124	27	α	α	X
ejpam-5080	124	28	,	,	PUNCT
ejpam-5080	124	29	β	β	NOUN
ejpam-5080	124	30	)	)	PUNCT
ejpam-5080	124	31	n	n	PROPN
ejpam-5080	124	32	(	(	PUNCT
ejpam-5080	124	33	x	x	X
ejpam-5080	124	34	)	)	PUNCT
ejpam-5080	124	35	are	be	AUX
ejpam-5080	124	36	the	the	DET
ejpam-5080	124	37	jacobi	jacobi	PROPN
ejpam-5080	124	38	’s	’s	PART
ejpam-5080	124	39	polynomials	polynomial	NOUN
ejpam-5080	124	40	that	that	PRON
ejpam-5080	124	41	are	be	AUX
ejpam-5080	124	42	orthogonal	orthogonal	ADJ
ejpam-5080	124	43	,	,	PUNCT
ejpam-5080	124	44	and	and	CCONJ
ejpam-5080	124	45	the	the	DET
ejpam-5080	124	46	coefficients	coefficient	NOUN
ejpam-5080	124	47	ci	ci	PROPN
ejpam-5080	124	48	of	of	ADP
ejpam-5080	124	49	jacobi	jacobi	PROPN
ejpam-5080	124	50	expansion	expansion	NOUN
ejpam-5080	124	51	are	be	AUX
ejpam-5080	124	52	defined	define	VERB
ejpam-5080	124	53	as	as	SCONJ
ejpam-5080	124	54	follows	follow	VERB
ejpam-5080	124	55	ci	ci	PROPN
ejpam-5080	124	56	=	=	SYM
ejpam-5080	124	57	∫	∫	PROPN
ejpam-5080	124	58	1	1	NUM
ejpam-5080	124	59	−1	−1	NOUN
ejpam-5080	124	60	g(x)p	g(x)p	PROPN
ejpam-5080	124	61	(	(	PUNCT
ejpam-5080	124	62	α	α	X
ejpam-5080	124	63	,	,	PUNCT
ejpam-5080	124	64	β	β	NOUN
ejpam-5080	124	65	)	)	PUNCT
ejpam-5080	125	1	i	i	PRON
ejpam-5080	125	2	(	(	PUNCT
ejpam-5080	125	3	x)(1−	x)(1−	PROPN
ejpam-5080	125	4	x)α(1	x)α(1	PROPN
ejpam-5080	126	1	+	+	NUM
ejpam-5080	126	2	x)βdx∫	x)βdx∫	PROPN
ejpam-5080	126	3	1	1	NUM
ejpam-5080	126	4	−1[p	−1[p	PROPN
ejpam-5080	126	5	(	(	PUNCT
ejpam-5080	126	6	α	α	X
ejpam-5080	126	7	,	,	PUNCT
ejpam-5080	126	8	β	β	NOUN
ejpam-5080	126	9	)	)	PUNCT
ejpam-5080	126	10	i	i	PRON
ejpam-5080	126	11	(	(	PUNCT
ejpam-5080	126	12	x)]2(1−	x)]2(1−	PUNCT
ejpam-5080	126	13	x)α(1	x)α(1	PROPN
ejpam-5080	127	1	+	+	CCONJ
ejpam-5080	127	2	x)βdx	x)βdx	PROPN
ejpam-5080	127	3	,	,	PUNCT
ejpam-5080	127	4	i	i	PRON
ejpam-5080	127	5	=	=	NOUN
ejpam-5080	127	6	0	0	NUM
ejpam-5080	127	7	,	,	PUNCT
ejpam-5080	127	8	1	1	NUM
ejpam-5080	127	9	,	,	PUNCT
ejpam-5080	127	10	2	2	NUM
ejpam-5080	127	11	,	,	PUNCT
ejpam-5080	127	12	·	·	PUNCT
ejpam-5080	127	13	·	·	PUNCT
ejpam-5080	127	14	·	·	PUNCT
ejpam-5080	127	15	(	(	PUNCT
ejpam-5080	127	16	31	31	NUM
ejpam-5080	127	17	)	)	PUNCT
ejpam-5080	127	18	where	where	SCONJ
ejpam-5080	127	19	the	the	DET
ejpam-5080	127	20	weight	weight	NOUN
ejpam-5080	127	21	function	function	NOUN
ejpam-5080	127	22	(	(	PUNCT
ejpam-5080	127	23	1	1	NUM
ejpam-5080	127	24	−	−	NOUN
ejpam-5080	127	25	x)α(1	x)α(1	PROPN
ejpam-5080	128	1	+	+	SYM
ejpam-5080	128	2	x)β	x)β	NOUN
ejpam-5080	128	3	is	be	AUX
ejpam-5080	128	4	used	use	VERB
ejpam-5080	128	5	for	for	ADP
ejpam-5080	128	6	the	the	DET
ejpam-5080	128	7	normalization	normalization	NOUN
ejpam-5080	128	8	in	in	ADP
ejpam-5080	128	9	this	this	DET
ejpam-5080	128	10	equation	equation	NOUN
ejpam-5080	128	11	.	.	PUNCT
ejpam-5080	129	1	thus	thus	ADV
ejpam-5080	129	2	,	,	PUNCT
ejpam-5080	129	3	the	the	DET
ejpam-5080	129	4	following	follow	VERB
ejpam-5080	129	5	recursive	recursive	ADJ
ejpam-5080	129	6	solution	solution	NOUN
ejpam-5080	129	7	is	be	AUX
ejpam-5080	129	8	obtained	obtain	VERB
ejpam-5080	129	9	from	from	ADP
ejpam-5080	129	10	eqs	eqs	PROPN
ejpam-5080	129	11	.	.	PUNCT
ejpam-5080	130	1	(	(	PUNCT
ejpam-5080	130	2	30	30	NUM
ejpam-5080	130	3	)	)	PUNCT
ejpam-5080	130	4	and	and	CCONJ
ejpam-5080	130	5	(	(	PUNCT
ejpam-5080	130	6	9	9	X
ejpam-5080	130	7	)	)	PUNCT
ejpam-5080	130	8	as	as	SCONJ
ejpam-5080	130	9	follows	follow	VERB
ejpam-5080	130	10	{	{	PUNCT
ejpam-5080	130	11	u0	u0	NOUN
ejpam-5080	130	12	=	=	PUNCT
ejpam-5080	130	13	ϕ(x	ϕ(x	PROPN
ejpam-5080	130	14	)	)	PUNCT
ejpam-5080	131	1	+	+	CCONJ
ejpam-5080	131	2	l−1[c0p	l−1[c0p	VERB
ejpam-5080	131	3	(	(	PUNCT
ejpam-5080	131	4	α	α	X
ejpam-5080	131	5	,	,	PUNCT
ejpam-5080	131	6	β	β	NOUN
ejpam-5080	131	7	)	)	PUNCT
ejpam-5080	131	8	0	0	NUM
ejpam-5080	132	1	(	(	PUNCT
ejpam-5080	132	2	x	x	X
ejpam-5080	132	3	)	)	PUNCT
ejpam-5080	133	1	+	+	NUM
ejpam-5080	133	2	c1p	c1p	NOUN
ejpam-5080	133	3	(	(	PUNCT
ejpam-5080	133	4	α	α	NOUN
ejpam-5080	133	5	,	,	PUNCT
ejpam-5080	133	6	β	β	NOUN
ejpam-5080	133	7	)	)	PUNCT
ejpam-5080	133	8	1	1	NUM
ejpam-5080	133	9	(	(	PUNCT
ejpam-5080	133	10	x	x	NOUN
ejpam-5080	133	11	)	)	PUNCT
ejpam-5080	133	12	+	+	CCONJ
ejpam-5080	133	13	c2p	c2p	NOUN
ejpam-5080	133	14	(	(	PUNCT
ejpam-5080	133	15	α	α	X
ejpam-5080	133	16	,	,	PUNCT
ejpam-5080	133	17	β	β	NOUN
ejpam-5080	133	18	)	)	PUNCT
ejpam-5080	133	19	2	2	NUM
ejpam-5080	133	20	(	(	PUNCT
ejpam-5080	133	21	x	x	NOUN
ejpam-5080	133	22	)	)	PUNCT
ejpam-5080	133	23	+	+	CCONJ
ejpam-5080	133	24	·	·	PUNCT
ejpam-5080	133	25	·	·	PUNCT
ejpam-5080	133	26	·	·	PUNCT
ejpam-5080	133	27	+	+	NUM
ejpam-5080	133	28	cmp	cmp	PROPN
ejpam-5080	133	29	(	(	PUNCT
ejpam-5080	133	30	α	α	NOUN
ejpam-5080	133	31	,	,	PUNCT
ejpam-5080	133	32	β	β	NOUN
ejpam-5080	133	33	)	)	PUNCT
ejpam-5080	133	34	m	m	VERB
ejpam-5080	133	35	(	(	PUNCT
ejpam-5080	133	36	x	x	X
ejpam-5080	133	37	)	)	PUNCT
ejpam-5080	133	38	]	]	PUNCT
ejpam-5080	133	39	,	,	PUNCT
ejpam-5080	133	40	un+1	un+1	NOUN
ejpam-5080	133	41	=	=	SYM
ejpam-5080	133	42	−l−1run	−l−1run	NOUN
ejpam-5080	133	43	−	−	PROPN
ejpam-5080	133	44	l−1an	l−1an	NOUN
ejpam-5080	133	45	,	,	PUNCT
ejpam-5080	133	46	n	n	X
ejpam-5080	133	47	≥	≥	NOUN
ejpam-5080	133	48	0	0	NUM
ejpam-5080	133	49	.	.	PUNCT
ejpam-5080	134	1	(	(	PUNCT
ejpam-5080	134	2	32	32	NUM
ejpam-5080	134	3	)	)	PUNCT
ejpam-5080	134	4	moreover	moreover	ADV
ejpam-5080	134	5	,	,	PUNCT
ejpam-5080	134	6	realistic	realistic	ADJ
ejpam-5080	134	7	solutions	solution	NOUN
ejpam-5080	134	8	via	via	ADP
ejpam-5080	134	9	the	the	DET
ejpam-5080	134	10	application	application	NOUN
ejpam-5080	134	11	of	of	ADP
ejpam-5080	134	12	the	the	DET
ejpam-5080	134	13	above	above	ADJ
ejpam-5080	134	14	polynomials	polynomial	NOUN
ejpam-5080	134	15	could	could	AUX
ejpam-5080	134	16	be	be	AUX
ejpam-5080	134	17	obtained	obtain	VERB
ejpam-5080	134	18	in	in	ADP
ejpam-5080	134	19	the	the	DET
ejpam-5080	134	20	same	same	ADJ
ejpam-5080	134	21	manner	manner	NOUN
ejpam-5080	134	22	by	by	ADP
ejpam-5080	134	23	considering	consider	VERB
ejpam-5080	134	24	the	the	DET
ejpam-5080	134	25	following	follow	VERB
ejpam-5080	134	26	m	m	ADJ
ejpam-5080	134	27	-	-	PUNCT
ejpam-5080	134	28	term	term	NOUN
ejpam-5080	134	29	approximations	approximation	NOUN
ejpam-5080	134	30	using	use	VERB
ejpam-5080	134	31	u(x	u(x	NOUN
ejpam-5080	134	32	)	)	PUNCT
ejpam-5080	135	1	=	=	NOUN
ejpam-5080	135	2	∑m	∑m	PROPN
ejpam-5080	135	3	n=0	n=0	NUM
ejpam-5080	135	4	un	un	NOUN
ejpam-5080	135	5	.	.	PROPN
ejpam-5080	135	6	4	4	NUM
ejpam-5080	135	7	.	.	X
ejpam-5080	135	8	illustrative	illustrative	ADJ
ejpam-5080	135	9	examples	example	NOUN
ejpam-5080	135	10	the	the	DET
ejpam-5080	135	11	current	current	ADJ
ejpam-5080	135	12	section	section	NOUN
ejpam-5080	135	13	demonstrates	demonstrate	VERB
ejpam-5080	135	14	the	the	DET
ejpam-5080	135	15	application	application	NOUN
ejpam-5080	135	16	of	of	ADP
ejpam-5080	135	17	the	the	DET
ejpam-5080	135	18	adomian	adomian	NOUN
ejpam-5080	135	19	modification	modification	NOUN
ejpam-5080	135	20	methods	method	NOUN
ejpam-5080	135	21	via	via	ADP
ejpam-5080	135	22	orthogonal	orthogonal	ADJ
ejpam-5080	135	23	polynomials	polynomial	NOUN
ejpam-5080	135	24	to	to	PART
ejpam-5080	135	25	comparatively	comparatively	ADV
ejpam-5080	135	26	examine	examine	VERB
ejpam-5080	135	27	different	different	ADJ
ejpam-5080	135	28	forms	form	NOUN
ejpam-5080	135	29	of	of	ADP
ejpam-5080	135	30	ivps	ivps	PROPN
ejpam-5080	135	31	of	of	ADP
ejpam-5080	135	32	odes	ode	NOUN
ejpam-5080	135	33	as	as	ADP
ejpam-5080	135	34	test	test	NOUN
ejpam-5080	135	35	examples	example	NOUN
ejpam-5080	135	36	.	.	PUNCT
ejpam-5080	136	1	moreover	moreover	ADV
ejpam-5080	136	2	,	,	PUNCT
ejpam-5080	136	3	we	we	PRON
ejpam-5080	136	4	shall	shall	AUX
ejpam-5080	136	5	utilize	utilize	VERB
ejpam-5080	136	6	seven	seven	NUM
ejpam-5080	136	7	-	-	PUNCT
ejpam-5080	136	8	term	term	NOUN
ejpam-5080	136	9	approximations	approximation	NOUN
ejpam-5080	136	10	via	via	ADP
ejpam-5080	136	11	the	the	DET
ejpam-5080	136	12	maple	maple	NOUN
ejpam-5080	136	13	18	18	NUM
ejpam-5080	136	14	package	package	NOUN
ejpam-5080	136	15	programmer	programmer	NOUN
ejpam-5080	136	16	for	for	ADP
ejpam-5080	136	17	the	the	DET
ejpam-5080	136	18	computational	computational	ADJ
ejpam-5080	136	19	simulation	simulation	NOUN
ejpam-5080	136	20	.	.	PUNCT
ejpam-5080	136	21	example	example	NOUN
ejpam-5080	137	1	1	1	NUM
ejpam-5080	137	2	.	.	X
ejpam-5080	137	3	consider	consider	VERB
ejpam-5080	137	4	the	the	DET
ejpam-5080	137	5	ivp	ivp	NOUN
ejpam-5080	137	6	of	of	ADP
ejpam-5080	137	7	duffing	duffing	NOUN
ejpam-5080	137	8	’s	’s	PART
ejpam-5080	137	9	equation	equation	NOUN
ejpam-5080	137	10	[	[	X
ejpam-5080	137	11	6	6	NUM
ejpam-5080	137	12	]	]	X
ejpam-5080	137	13	u′′	u′′	PROPN
ejpam-5080	137	14	+	+	PROPN
ejpam-5080	137	15	3u−	3u−	PROPN
ejpam-5080	137	16	2u3	2u3	NUM
ejpam-5080	137	17	=	=	SYM
ejpam-5080	137	18	sin(2x	sin(2x	VERB
ejpam-5080	137	19	)	)	PUNCT
ejpam-5080	137	20	cos(x	cos(x	PROPN
ejpam-5080	137	21	)	)	PUNCT
ejpam-5080	137	22	,	,	PUNCT
ejpam-5080	137	23	0	0	NUM
ejpam-5080	137	24	≤	≤	NUM
ejpam-5080	137	25	x	x	SYM
ejpam-5080	137	26	≤	≤	NUM
ejpam-5080	137	27	1	1	NUM
ejpam-5080	137	28	,	,	PUNCT
ejpam-5080	137	29	u(0	u(0	NOUN
ejpam-5080	137	30	)	)	PUNCT
ejpam-5080	137	31	=	=	SYM
ejpam-5080	138	1	0	0	NUM
ejpam-5080	138	2	,	,	PUNCT
ejpam-5080	138	3	u′(0	u′(0	PROPN
ejpam-5080	138	4	)	)	PUNCT
ejpam-5080	138	5	=	=	SYM
ejpam-5080	138	6	1	1	NUM
ejpam-5080	138	7	,	,	PUNCT
ejpam-5080	138	8	(	(	PUNCT
ejpam-5080	138	9	33	33	NUM
ejpam-5080	138	10	)	)	PUNCT
ejpam-5080	138	11	that	that	PRON
ejpam-5080	138	12	admits	admit	VERB
ejpam-5080	138	13	the	the	DET
ejpam-5080	138	14	following	follow	VERB
ejpam-5080	138	15	exact	exact	ADJ
ejpam-5080	138	16	solution	solution	NOUN
ejpam-5080	138	17	u(x	u(x	NOUN
ejpam-5080	138	18	)	)	PUNCT
ejpam-5080	138	19	=	=	SYM
ejpam-5080	138	20	sin(x	sin(x	PROPN
ejpam-5080	138	21	)	)	PUNCT
ejpam-5080	138	22	.	.	PUNCT
ejpam-5080	139	1	n.	n.	PROPN
ejpam-5080	139	2	alzaid	alzaid	PROPN
ejpam-5080	139	3	et	et	PROPN
ejpam-5080	139	4	al	al	PROPN
ejpam-5080	139	5	.	.	PUNCT
ejpam-5080	139	6	/	/	SYM
ejpam-5080	139	7	eur	eur	PROPN
ejpam-5080	139	8	.	.	PUNCT
ejpam-5080	140	1	j.	j.	PROPN
ejpam-5080	140	2	pure	pure	PROPN
ejpam-5080	140	3	appl	appl	PROPN
ejpam-5080	140	4	.	.	PROPN
ejpam-5080	140	5	math	math	PROPN
ejpam-5080	140	6	,	,	PUNCT
ejpam-5080	140	7	17	17	NUM
ejpam-5080	140	8	(	(	PUNCT
ejpam-5080	140	9	3	3	NUM
ejpam-5080	140	10	)	)	PUNCT
ejpam-5080	140	11	(	(	PUNCT
ejpam-5080	140	12	2024	2024	NUM
ejpam-5080	140	13	)	)	PUNCT
ejpam-5080	140	14	,	,	PUNCT
ejpam-5080	140	15	1982	1982	NUM
ejpam-5080	140	16	-	-	SYM
ejpam-5080	140	17	2000	2000	NUM
ejpam-5080	140	18	1989	1989	NUM
ejpam-5080	140	19	firstly	firstly	ADV
ejpam-5080	140	20	,	,	PUNCT
ejpam-5080	140	21	we	we	PRON
ejpam-5080	140	22	express	express	VERB
ejpam-5080	140	23	the	the	DET
ejpam-5080	140	24	given	give	VERB
ejpam-5080	140	25	equation	equation	NOUN
ejpam-5080	140	26	in	in	ADP
ejpam-5080	140	27	operator	operator	NOUN
ejpam-5080	140	28	form	form	NOUN
ejpam-5080	140	29	as	as	SCONJ
ejpam-5080	140	30	follows	follow	VERB
ejpam-5080	140	31	u	u	NOUN
ejpam-5080	140	32	=	=	SYM
ejpam-5080	140	33	x+	x+	X
ejpam-5080	140	34	l−1(sin(2x	l−1(sin(2x	ADJ
ejpam-5080	140	35	)	)	PUNCT
ejpam-5080	140	36	cos(x))−	cos(x))−	NOUN
ejpam-5080	140	37	3l−1(u	3l−1(u	NUM
ejpam-5080	140	38	)	)	PUNCT
ejpam-5080	141	1	+	+	NUM
ejpam-5080	142	1	2l−1(u3	2l−1(u3	NUM
ejpam-5080	142	2	)	)	PUNCT
ejpam-5080	142	3	,	,	PUNCT
ejpam-5080	142	4	(	(	PUNCT
ejpam-5080	142	5	34	34	NUM
ejpam-5080	142	6	)	)	PUNCT
ejpam-5080	142	7	where	where	SCONJ
ejpam-5080	142	8	l−1	l−1	PROPN
ejpam-5080	142	9	(	(	PUNCT
ejpam-5080	142	10	.	.	PUNCT
ejpam-5080	142	11	)	)	PUNCT
ejpam-5080	142	12	is	be	AUX
ejpam-5080	142	13	the	the	DET
ejpam-5080	142	14	inverse	inverse	NOUN
ejpam-5080	142	15	operator	operator	NOUN
ejpam-5080	142	16	defined	define	VERB
ejpam-5080	142	17	by	by	ADP
ejpam-5080	142	18	l−1	l−1	PROPN
ejpam-5080	142	19	(	(	PUNCT
ejpam-5080	142	20	.	.	PUNCT
ejpam-5080	142	21	)	)	PUNCT
ejpam-5080	143	1	=	=	PUNCT
ejpam-5080	144	1	∫	∫	PUNCT
ejpam-5080	144	2	x	x	SYM
ejpam-5080	144	3	0	0	NUM
ejpam-5080	144	4	∫	∫	PROPN
ejpam-5080	144	5	x	x	SYM
ejpam-5080	144	6	0	0	PUNCT
ejpam-5080	144	7	(	(	PUNCT
ejpam-5080	144	8	.)dxdx	.)dxdx	PROPN
ejpam-5080	144	9	and	and	CCONJ
ejpam-5080	144	10	n(u	n(u	PROPN
ejpam-5080	144	11	)	)	PUNCT
ejpam-5080	145	1	=	=	NOUN
ejpam-5080	145	2	u3	u3	NOUN
ejpam-5080	145	3	substituting	substitute	VERB
ejpam-5080	145	4	eqs.(5	eqs.(5	PROPN
ejpam-5080	145	5	)	)	PUNCT
ejpam-5080	145	6	and	and	CCONJ
ejpam-5080	145	7	(	(	PUNCT
ejpam-5080	145	8	6	6	NUM
ejpam-5080	145	9	)	)	PUNCT
ejpam-5080	145	10	into	into	ADP
ejpam-5080	145	11	eqs	eqs	PROPN
ejpam-5080	145	12	.	.	PUNCT
ejpam-5080	146	1	(	(	PUNCT
ejpam-5080	146	2	34	34	NUM
ejpam-5080	146	3	)	)	PUNCT
ejpam-5080	146	4	,	,	PUNCT
ejpam-5080	146	5	we	we	PRON
ejpam-5080	146	6	get	get	VERB
ejpam-5080	146	7	the	the	DET
ejpam-5080	146	8	following	follow	VERB
ejpam-5080	146	9	recursive	recursive	ADJ
ejpam-5080	146	10	solution	solution	NOUN
ejpam-5080	146	11	u0	u0	ADJ
ejpam-5080	146	12	=	=	SYM
ejpam-5080	146	13	x+	x+	ADJ
ejpam-5080	146	14	l−1(sin(2x)cos(x	l−1(sin(2x)cos(x	NOUN
ejpam-5080	146	15	)	)	PUNCT
ejpam-5080	146	16	)	)	PUNCT
ejpam-5080	146	17	,	,	PUNCT
ejpam-5080	146	18	un+1	un+1	X
ejpam-5080	146	19	=	=	SYM
ejpam-5080	146	20	−3l−1(un	−3l−1(un	NOUN
ejpam-5080	146	21	)	)	PUNCT
ejpam-5080	147	1	+	+	CCONJ
ejpam-5080	147	2	2l−1an(u0	2l−1an(u0	NUM
ejpam-5080	147	3	,	,	PUNCT
ejpam-5080	147	4	u1	u1	NOUN
ejpam-5080	147	5	,	,	PUNCT
ejpam-5080	147	6	·	·	PUNCT
ejpam-5080	147	7	·	·	PUNCT
ejpam-5080	147	8	·	·	PUNCT
ejpam-5080	147	9	)	)	PUNCT
ejpam-5080	147	10	,	,	PUNCT
ejpam-5080	147	11	n	n	X
ejpam-5080	147	12	≥	≥	NOUN
ejpam-5080	147	13	0	0	NUM
ejpam-5080	147	14	,	,	PUNCT
ejpam-5080	147	15	from	from	ADP
ejpam-5080	147	16	eq.(7	eq.(7	NOUN
ejpam-5080	147	17	)	)	PUNCT
ejpam-5080	147	18	,	,	PUNCT
ejpam-5080	147	19	the	the	DET
ejpam-5080	147	20	nonlinear	nonlinear	ADJ
ejpam-5080	147	21	tearm	tearm	PROPN
ejpam-5080	147	22	n(u	n(u	PROPN
ejpam-5080	147	23	)	)	PUNCT
ejpam-5080	148	1	=	=	NOUN
ejpam-5080	148	2	u3	u3	NOUN
ejpam-5080	148	3	requires	require	VERB
ejpam-5080	148	4	the	the	DET
ejpam-5080	148	5	following	follow	VERB
ejpam-5080	148	6	adomian	adomian	NOUN
ejpam-5080	148	7	polynomials	polynomial	VERB
ejpam-5080	148	8	a0	a0	PROPN
ejpam-5080	148	9	=	=	SYM
ejpam-5080	148	10	u30	u30	PROPN
ejpam-5080	148	11	,	,	PUNCT
ejpam-5080	148	12	a1	a1	NOUN
ejpam-5080	148	13	=	=	SYM
ejpam-5080	148	14	(	(	PUNCT
ejpam-5080	148	15	3u20u1	3u20u1	NOUN
ejpam-5080	148	16	)	)	PUNCT
ejpam-5080	148	17	,	,	PUNCT
ejpam-5080	148	18	a2	a2	PROPN
ejpam-5080	148	19	=	=	SYM
ejpam-5080	148	20	(	(	PUNCT
ejpam-5080	148	21	3u20u2	3u20u2	PROPN
ejpam-5080	148	22	+	+	NUM
ejpam-5080	148	23	3u0u	3u0u	ADJ
ejpam-5080	148	24	2	2	NUM
ejpam-5080	148	25	1	1	NUM
ejpam-5080	148	26	)	)	PUNCT
ejpam-5080	148	27	,	,	PUNCT
ejpam-5080	148	28	a3	a3	NOUN
ejpam-5080	148	29	=	=	SYM
ejpam-5080	148	30	(	(	PUNCT
ejpam-5080	148	31	3u20u3	3u20u3	PROPN
ejpam-5080	148	32	+	+	CCONJ
ejpam-5080	148	33	6u0u1u2	6u0u1u2	NUM
ejpam-5080	148	34	+	+	CCONJ
ejpam-5080	148	35	u31	u31	NOUN
ejpam-5080	148	36	)	)	PUNCT
ejpam-5080	148	37	,	,	PUNCT
ejpam-5080	148	38	...	...	PUNCT
ejpam-5080	148	39	(	(	PUNCT
ejpam-5080	148	40	35	35	NUM
ejpam-5080	148	41	)	)	PUNCT
ejpam-5080	148	42	in	in	ADP
ejpam-5080	148	43	what	what	PRON
ejpam-5080	148	44	follows	follow	VERB
ejpam-5080	148	45	,	,	PUNCT
ejpam-5080	148	46	we	we	PRON
ejpam-5080	148	47	shall	shall	AUX
ejpam-5080	148	48	be	be	AUX
ejpam-5080	148	49	utilizing	utilize	VERB
ejpam-5080	148	50	the	the	DET
ejpam-5080	148	51	proposed	propose	VERB
ejpam-5080	148	52	modification	modification	NOUN
ejpam-5080	148	53	methods	method	NOUN
ejpam-5080	148	54	to	to	PART
ejpam-5080	148	55	treat	treat	VERB
ejpam-5080	148	56	the	the	DET
ejpam-5080	148	57	governing	govern	VERB
ejpam-5080	148	58	duffing	duffing	NOUN
ejpam-5080	148	59	’s	’s	PART
ejpam-5080	148	60	equation	equation	NOUN
ejpam-5080	148	61	.	.	PUNCT
ejpam-5080	149	1	more	more	ADV
ejpam-5080	149	2	so	so	ADV
ejpam-5080	149	3	,	,	PUNCT
ejpam-5080	149	4	we	we	PRON
ejpam-5080	149	5	shall	shall	AUX
ejpam-5080	149	6	be	be	AUX
ejpam-5080	149	7	starting	start	VERB
ejpam-5080	149	8	with	with	ADP
ejpam-5080	149	9	the	the	DET
ejpam-5080	149	10	classical	classical	ADJ
ejpam-5080	149	11	taylor	taylor	PROPN
ejpam-5080	149	12	’s	’s	PART
ejpam-5080	149	13	series	series	NOUN
ejpam-5080	149	14	before	before	ADP
ejpam-5080	149	15	the	the	DET
ejpam-5080	149	16	proposed	propose	VERB
ejpam-5080	149	17	schemes	scheme	NOUN
ejpam-5080	149	18	.	.	PUNCT
ejpam-5080	150	1	additionally	additionally	ADV
ejpam-5080	150	2	,	,	PUNCT
ejpam-5080	150	3	we	we	PRON
ejpam-5080	150	4	denote	denote	VERB
ejpam-5080	150	5	the	the	DET
ejpam-5080	150	6	solution	solution	NOUN
ejpam-5080	150	7	u(x	u(x	NOUN
ejpam-5080	150	8	)	)	PUNCT
ejpam-5080	150	9	based	base	VERB
ejpam-5080	150	10	on	on	ADP
ejpam-5080	150	11	the	the	DET
ejpam-5080	150	12	respective	respective	ADJ
ejpam-5080	150	13	modifications	modification	NOUN
ejpam-5080	150	14	as	as	SCONJ
ejpam-5080	150	15	follows	follow	VERB
ejpam-5080	150	16	:	:	PUNCT
ejpam-5080	150	17	ut(x	ut(x	NOUN
ejpam-5080	150	18	)	)	PUNCT
ejpam-5080	150	19	via	via	ADP
ejpam-5080	150	20	the	the	DET
ejpam-5080	150	21	taylor	taylor	PROPN
ejpam-5080	150	22	’s	’s	PART
ejpam-5080	150	23	series	series	NOUN
ejpam-5080	150	24	expansion	expansion	NOUN
ejpam-5080	150	25	;	;	PUNCT
ejpam-5080	150	26	up	up	ADV
ejpam-5080	150	27	(	(	PUNCT
ejpam-5080	150	28	x	x	NOUN
ejpam-5080	150	29	)	)	PUNCT
ejpam-5080	150	30	via	via	ADP
ejpam-5080	150	31	the	the	DET
ejpam-5080	150	32	legendre	legendre	PROPN
ejpam-5080	150	33	’s	’s	PART
ejpam-5080	150	34	series	series	PROPN
ejpam-5080	150	35	expansion	expansion	NOUN
ejpam-5080	150	36	;	;	PUNCT
ejpam-5080	150	37	ut	ut	PROPN
ejpam-5080	150	38	(	(	PUNCT
ejpam-5080	150	39	x	x	X
ejpam-5080	150	40	)	)	PUNCT
ejpam-5080	150	41	via	via	ADP
ejpam-5080	150	42	the	the	DET
ejpam-5080	150	43	chebyshev	chebyshev	PROPN
ejpam-5080	150	44	’s	’s	PART
ejpam-5080	150	45	series	series	NOUN
ejpam-5080	150	46	expansion	expansion	NOUN
ejpam-5080	150	47	;	;	PUNCT
ejpam-5080	150	48	ul(x	ul(x	NOUN
ejpam-5080	150	49	)	)	PUNCT
ejpam-5080	150	50	via	via	ADP
ejpam-5080	150	51	the	the	DET
ejpam-5080	150	52	laguerre	laguerre	NOUN
ejpam-5080	150	53	’s	’s	PART
ejpam-5080	150	54	series	series	NOUN
ejpam-5080	150	55	expansion	expansion	NOUN
ejpam-5080	150	56	;	;	PUNCT
ejpam-5080	150	57	uh(x	uh(x	NUM
ejpam-5080	150	58	)	)	PUNCT
ejpam-5080	150	59	via	via	ADP
ejpam-5080	150	60	the	the	DET
ejpam-5080	150	61	hermite	hermite	PROPN
ejpam-5080	150	62	’s	’s	PART
ejpam-5080	150	63	series	series	NOUN
ejpam-5080	150	64	expansion	expansion	NOUN
ejpam-5080	150	65	;	;	PUNCT
ejpam-5080	150	66	u1g(x	u1g(x	X
ejpam-5080	150	67	)	)	PUNCT
ejpam-5080	150	68	via	via	ADP
ejpam-5080	150	69	the	the	DET
ejpam-5080	150	70	gegenbauer	gegenbauer	NOUN
ejpam-5080	150	71	’s	’s	PART
ejpam-5080	150	72	series	series	PROPN
ejpam-5080	150	73	expansion	expansion	NOUN
ejpam-5080	150	74	(	(	PUNCT
ejpam-5080	150	75	α	α	NOUN
ejpam-5080	150	76	=	=	NOUN
ejpam-5080	150	77	1	1	NUM
ejpam-5080	150	78	)	)	PUNCT
ejpam-5080	150	79	;	;	PUNCT
ejpam-5080	150	80	and	and	CCONJ
ejpam-5080	150	81	lastly	lastly	ADV
ejpam-5080	150	82	u	u	NOUN
ejpam-5080	150	83	(	(	PUNCT
ejpam-5080	150	84	1,1	1,1	NUM
ejpam-5080	150	85	)	)	PUNCT
ejpam-5080	150	86	j	j	NOUN
ejpam-5080	150	87	(	(	PUNCT
ejpam-5080	150	88	x	x	NOUN
ejpam-5080	150	89	)	)	PUNCT
ejpam-5080	150	90	via	via	ADP
ejpam-5080	150	91	the	the	DET
ejpam-5080	150	92	jacobi	jacobi	PROPN
ejpam-5080	150	93	’s	’s	PART
ejpam-5080	150	94	series	series	PROPN
ejpam-5080	150	95	expansion	expansion	NOUN
ejpam-5080	150	96	(	(	PUNCT
ejpam-5080	150	97	α	α	NOUN
ejpam-5080	150	98	=	=	SYM
ejpam-5080	150	99	1	1	NUM
ejpam-5080	150	100	,	,	PUNCT
ejpam-5080	150	101	β	β	X
ejpam-5080	150	102	=	=	SYM
ejpam-5080	150	103	1	1	NUM
ejpam-5080	150	104	)	)	PUNCT
ejpam-5080	150	105	.	.	PUNCT
ejpam-5080	151	1	modification	modification	NOUN
ejpam-5080	151	2	method	method	NOUN
ejpam-5080	151	3	via	via	ADP
ejpam-5080	151	4	taylor	taylor	PROPN
ejpam-5080	151	5	’s	’s	PART
ejpam-5080	151	6	series	series	NOUN
ejpam-5080	151	7	will	will	AUX
ejpam-5080	151	8	be	be	AUX
ejpam-5080	151	9	used	use	VERB
ejpam-5080	151	10	for	for	ADP
ejpam-5080	151	11	the	the	DET
ejpam-5080	151	12	expansion	expansion	NOUN
ejpam-5080	151	13	of	of	ADP
ejpam-5080	151	14	the	the	DET
ejpam-5080	151	15	source	source	NOUN
ejpam-5080	151	16	term	term	NOUN
ejpam-5080	151	17	g(x	g(x	NOUN
ejpam-5080	151	18	)	)	PUNCT
ejpam-5080	151	19	for	for	ADP
ejpam-5080	151	20	m	m	PROPN
ejpam-5080	151	21	=	=	NOUN
ejpam-5080	151	22	6	6	NUM
ejpam-5080	151	23	as	as	SCONJ
ejpam-5080	151	24	follows	follow	VERB
ejpam-5080	151	25	g(x	g(x	NOUN
ejpam-5080	151	26	)	)	PUNCT
ejpam-5080	152	1	=	=	PUNCT
ejpam-5080	153	1	2x−	2x−	NUM
ejpam-5080	153	2	7	7	NUM
ejpam-5080	153	3	3	3	NUM
ejpam-5080	153	4	x3	x3	NOUN
ejpam-5080	153	5	+	+	CCONJ
ejpam-5080	153	6	61	61	NUM
ejpam-5080	153	7	60	60	NUM
ejpam-5080	153	8	x5	x5	NOUN
ejpam-5080	153	9	+	+	NOUN
ejpam-5080	153	10	o(x7	o(x7	NOUN
ejpam-5080	153	11	)	)	PUNCT
ejpam-5080	153	12	,	,	PUNCT
ejpam-5080	153	13	(	(	PUNCT
ejpam-5080	153	14	36	36	NUM
ejpam-5080	153	15	)	)	PUNCT
ejpam-5080	153	16	then	then	ADV
ejpam-5080	153	17	,	,	PUNCT
ejpam-5080	153	18	we	we	PRON
ejpam-5080	153	19	get	get	VERB
ejpam-5080	153	20	the	the	DET
ejpam-5080	153	21	following	following	ADJ
ejpam-5080	153	22	iterative	iterative	NOUN
ejpam-5080	153	23	components	component	NOUN
ejpam-5080	153	24	u0	u0	NOUN
ejpam-5080	153	25	=	=	PROPN
ejpam-5080	153	26	u(0	u(0	PROPN
ejpam-5080	153	27	)	)	PUNCT
ejpam-5080	154	1	+	+	CCONJ
ejpam-5080	154	2	xu′(0	xu′(0	NOUN
ejpam-5080	154	3	)	)	PUNCT
ejpam-5080	155	1	+	+	NUM
ejpam-5080	155	2	l−1(2x−	l−1(2x−	NUM
ejpam-5080	155	3	7	7	NUM
ejpam-5080	155	4	3x	3x	NUM
ejpam-5080	155	5	3	3	NUM
ejpam-5080	155	6	+	+	SYM
ejpam-5080	155	7	61	61	NUM
ejpam-5080	155	8	60x	60x	NOUN
ejpam-5080	155	9	5	5	NUM
ejpam-5080	155	10	)	)	PUNCT
ejpam-5080	155	11	=	=	SYM
ejpam-5080	156	1	x+	x+	PUNCT
ejpam-5080	156	2	1	1	NUM
ejpam-5080	156	3	3x	3x	NUM
ejpam-5080	156	4	3	3	NUM
ejpam-5080	156	5	−	−	NOUN
ejpam-5080	156	6	7	7	NUM
ejpam-5080	156	7	60x	60x	NOUN
ejpam-5080	156	8	5	5	NUM
ejpam-5080	156	9	+	+	SYM
ejpam-5080	156	10	61	61	NUM
ejpam-5080	156	11	2520x	2520x	NUM
ejpam-5080	156	12	7	7	NUM
ejpam-5080	156	13	,	,	PUNCT
ejpam-5080	156	14	u1	u1	NOUN
ejpam-5080	156	15	=	=	SYM
ejpam-5080	156	16	−3l−1(u0	−3l−1(u0	NOUN
ejpam-5080	156	17	)	)	PUNCT
ejpam-5080	157	1	+	+	CCONJ
ejpam-5080	157	2	2l−1a0	2l−1a0	NUM
ejpam-5080	157	3	=	=	SYM
ejpam-5080	157	4	−1	−1	NOUN
ejpam-5080	157	5	2x	2x	NUM
ejpam-5080	157	6	3	3	NUM
ejpam-5080	157	7	+	+	SYM
ejpam-5080	157	8	1	1	NUM
ejpam-5080	157	9	20x	20x	NOUN
ejpam-5080	157	10	5	5	NUM
ejpam-5080	157	11	+	+	CCONJ
ejpam-5080	157	12	47	47	NUM
ejpam-5080	157	13	840x	840x	NOUN
ejpam-5080	157	14	7	7	NUM
ejpam-5080	157	15	−	−	NUM
ejpam-5080	157	16	89	89	NUM
ejpam-5080	157	17	60480x	60480x	NOUN
ejpam-5080	157	18	9	9	NUM
ejpam-5080	157	19	+	+	CCONJ
ejpam-5080	157	20	·	·	PUNCT
ejpam-5080	157	21	·	·	PUNCT
ejpam-5080	157	22	·	·	PUNCT
ejpam-5080	157	23	,	,	PUNCT
ejpam-5080	157	24	u2	u2	NOUN
ejpam-5080	157	25	=	=	SYM
ejpam-5080	157	26	−3l−1(u1	−3l−1(u1	PROPN
ejpam-5080	157	27	)	)	PUNCT
ejpam-5080	158	1	+	+	CCONJ
ejpam-5080	158	2	2l−1a1	2l−1a1	NUM
ejpam-5080	158	3	=	=	SYM
ejpam-5080	158	4	3	3	NUM
ejpam-5080	158	5	40x	40x	NUM
ejpam-5080	158	6	5	5	NUM
ejpam-5080	158	7	−	−	NOUN
ejpam-5080	158	8	3	3	NUM
ejpam-5080	158	9	40x	40x	NUM
ejpam-5080	158	10	7	7	NUM
ejpam-5080	158	11	−	−	PROPN
ejpam-5080	158	12	523	523	NUM
ejpam-5080	158	13	20160x	20160x	NUM
ejpam-5080	158	14	9	9	NUM
ejpam-5080	158	15	+	+	CCONJ
ejpam-5080	158	16	·	·	PUNCT
ejpam-5080	158	17	·	·	PUNCT
ejpam-5080	158	18	·	·	PUNCT
ejpam-5080	158	19	,	,	PUNCT
ejpam-5080	158	20	u3	u3	NOUN
ejpam-5080	158	21	=	=	SYM
ejpam-5080	158	22	−3l−1(u2	−3l−1(u2	PROPN
ejpam-5080	158	23	)	)	PUNCT
ejpam-5080	159	1	+	+	CCONJ
ejpam-5080	159	2	2l−1a2	2l−1a2	NUM
ejpam-5080	159	3	=	=	SYM
ejpam-5080	159	4	−	−	PROPN
ejpam-5080	159	5	3	3	NUM
ejpam-5080	159	6	560x	560x	PROPN
ejpam-5080	159	7	7	7	NUM
ejpam-5080	159	8	+	+	CCONJ
ejpam-5080	159	9	29	29	NUM
ejpam-5080	159	10	960x	960x	NOUN
ejpam-5080	159	11	9	9	NUM
ejpam-5080	159	12	+	+	CCONJ
ejpam-5080	159	13	·	·	PUNCT
ejpam-5080	159	14	·	·	PUNCT
ejpam-5080	159	15	·	·	PUNCT
ejpam-5080	159	16	,	,	PUNCT
ejpam-5080	159	17	u4	u4	PROPN
ejpam-5080	159	18	=	=	PUNCT
ejpam-5080	159	19	−3l−1(u3	−3l−1(u3	PROPN
ejpam-5080	159	20	)	)	PUNCT
ejpam-5080	160	1	+	+	CCONJ
ejpam-5080	160	2	2l−1a3	2l−1a3	NUM
ejpam-5080	160	3	=	=	SYM
ejpam-5080	160	4	1	1	NUM
ejpam-5080	160	5	4480x	4480x	NUM
ejpam-5080	160	6	9	9	NUM
ejpam-5080	160	7	+	+	CCONJ
ejpam-5080	160	8	·	·	PUNCT
ejpam-5080	160	9	·	·	PUNCT
ejpam-5080	160	10	·	·	PUNCT
ejpam-5080	160	11	,	,	PUNCT
ejpam-5080	160	12	...	...	PUNCT
ejpam-5080	160	13	such	such	ADJ
ejpam-5080	160	14	that	that	SCONJ
ejpam-5080	160	15	upon	upon	SCONJ
ejpam-5080	160	16	summing	sum	VERB
ejpam-5080	160	17	the	the	DET
ejpam-5080	160	18	above	above	ADJ
ejpam-5080	160	19	components	component	NOUN
ejpam-5080	160	20	yields	yield	VERB
ejpam-5080	160	21	the	the	DET
ejpam-5080	160	22	following	follow	VERB
ejpam-5080	160	23	series	series	NOUN
ejpam-5080	160	24	solution	solution	NOUN
ejpam-5080	160	25	ut(x	ut(x	NOUN
ejpam-5080	160	26	)	)	PUNCT
ejpam-5080	161	1	=	=	SYM
ejpam-5080	161	2	6∑	6∑	PROPN
ejpam-5080	161	3	n=0	n=0	NUM
ejpam-5080	161	4	un(x	un(x	SYM
ejpam-5080	161	5	)	)	PUNCT
ejpam-5080	162	1	=	=	SYM
ejpam-5080	162	2	x−	x−	PROPN
ejpam-5080	162	3	1	1	NUM
ejpam-5080	162	4	6	6	NUM
ejpam-5080	162	5	x3	x3	ADJ
ejpam-5080	162	6	+	+	CCONJ
ejpam-5080	162	7	1	1	NUM
ejpam-5080	162	8	120	120	NUM
ejpam-5080	162	9	x5	x5	NOUN
ejpam-5080	162	10	−	−	NUM
ejpam-5080	162	11	1	1	NUM
ejpam-5080	162	12	5040	5040	NUM
ejpam-5080	162	13	x7	x7	NOUN
ejpam-5080	162	14	+	+	CCONJ
ejpam-5080	162	15	73	73	NUM
ejpam-5080	162	16	24192	24192	NUM
ejpam-5080	162	17	x9	x9	NOUN
ejpam-5080	162	18	+	+	CCONJ
ejpam-5080	162	19	·	·	PUNCT
ejpam-5080	162	20	·	·	PUNCT
ejpam-5080	162	21	·	·	PUNCT
ejpam-5080	162	22	(	(	PUNCT
ejpam-5080	162	23	37	37	NUM
ejpam-5080	162	24	)	)	PUNCT
ejpam-5080	162	25	n.	n.	NOUN
ejpam-5080	162	26	alzaid	alzaid	PROPN
ejpam-5080	162	27	et	et	PROPN
ejpam-5080	162	28	al	al	PROPN
ejpam-5080	162	29	.	.	PUNCT
ejpam-5080	162	30	/	/	SYM
ejpam-5080	162	31	eur	eur	PROPN
ejpam-5080	162	32	.	.	PUNCT
ejpam-5080	163	1	j.	j.	PROPN
ejpam-5080	163	2	pure	pure	PROPN
ejpam-5080	163	3	appl	appl	PROPN
ejpam-5080	163	4	.	.	PROPN
ejpam-5080	163	5	math	math	PROPN
ejpam-5080	163	6	,	,	PUNCT
ejpam-5080	163	7	17	17	NUM
ejpam-5080	163	8	(	(	PUNCT
ejpam-5080	163	9	3	3	NUM
ejpam-5080	163	10	)	)	PUNCT
ejpam-5080	163	11	(	(	PUNCT
ejpam-5080	163	12	2024	2024	NUM
ejpam-5080	163	13	)	)	PUNCT
ejpam-5080	163	14	,	,	PUNCT
ejpam-5080	163	15	1982	1982	NUM
ejpam-5080	163	16	-	-	SYM
ejpam-5080	163	17	2000	2000	NUM
ejpam-5080	163	18	1990	1990	NUM
ejpam-5080	163	19	modification	modification	NOUN
ejpam-5080	163	20	method	method	NOUN
ejpam-5080	163	21	via	via	ADP
ejpam-5080	163	22	legendre	legendre	PROPN
ejpam-5080	163	23	’s	’s	PART
ejpam-5080	163	24	polynomials	polynomial	NOUN
ejpam-5080	163	25	is	be	AUX
ejpam-5080	163	26	up	up	ADV
ejpam-5080	163	27	now	now	ADV
ejpam-5080	163	28	.	.	PUNCT
ejpam-5080	164	1	expanding	expand	VERB
ejpam-5080	164	2	of	of	ADP
ejpam-5080	164	3	the	the	DET
ejpam-5080	164	4	source	source	NOUN
ejpam-5080	164	5	term	term	NOUN
ejpam-5080	164	6	g(x	g(x	NOUN
ejpam-5080	164	7	)	)	PUNCT
ejpam-5080	164	8	via	via	ADP
ejpam-5080	164	9	legendre	legendre	PROPN
ejpam-5080	164	10	’s	’s	PART
ejpam-5080	164	11	polynomials	polynomial	NOUN
ejpam-5080	164	12	for	for	ADP
ejpam-5080	164	13	m	m	PROPN
ejpam-5080	164	14	=	=	NOUN
ejpam-5080	164	15	6	6	NUM
ejpam-5080	164	16	gives	give	VERB
ejpam-5080	164	17	g(x	g(x	NOUN
ejpam-5080	164	18	)	)	PUNCT
ejpam-5080	165	1	=	=	SYM
ejpam-5080	165	2	6∑	6∑	NUM
ejpam-5080	165	3	n=0	n=0	NUM
ejpam-5080	165	4	cnpn(2x−	cnpn(2x−	NOUN
ejpam-5080	165	5	1	1	NUM
ejpam-5080	165	6	)	)	PUNCT
ejpam-5080	165	7	,	,	PUNCT
ejpam-5080	165	8	0	0	NUM
ejpam-5080	165	9	≤	≤	NUM
ejpam-5080	165	10	x	x	SYM
ejpam-5080	165	11	≤	≤	NUM
ejpam-5080	165	12	1	1	NUM
ejpam-5080	165	13	,	,	PUNCT
ejpam-5080	165	14	(	(	PUNCT
ejpam-5080	165	15	38	38	NUM
ejpam-5080	165	16	)	)	PUNCT
ejpam-5080	165	17	where	where	SCONJ
ejpam-5080	165	18	pn	pn	PROPN
ejpam-5080	165	19	(	(	PUNCT
ejpam-5080	165	20	.	.	PUNCT
ejpam-5080	165	21	)	)	PUNCT
ejpam-5080	165	22	are	be	AUX
ejpam-5080	165	23	orthogonal	orthogonal	PROPN
ejpam-5080	165	24	legendre	legendre	PROPN
ejpam-5080	165	25	’s	’s	PART
ejpam-5080	165	26	polynomials	polynomial	NOUN
ejpam-5080	165	27	,	,	PUNCT
ejpam-5080	165	28	and	and	CCONJ
ejpam-5080	165	29	ci	ci	NOUN
ejpam-5080	165	30	are	be	AUX
ejpam-5080	165	31	given	give	VERB
ejpam-5080	165	32	by	by	ADP
ejpam-5080	165	33	ci	ci	NOUN
ejpam-5080	165	34	=	=	SYM
ejpam-5080	165	35	2i+	2i+	NUM
ejpam-5080	165	36	1	1	NUM
ejpam-5080	165	37	2	2	NUM
ejpam-5080	165	38	∫	∫	NOUN
ejpam-5080	165	39	1	1	NUM
ejpam-5080	165	40	−1	−1	NOUN
ejpam-5080	165	41	g(0.5x+	g(0.5x+	NOUN
ejpam-5080	165	42	0.5)pi(x)dx	0.5)pi(x)dx	NUM
ejpam-5080	165	43	,	,	PUNCT
ejpam-5080	165	44	i	i	PRON
ejpam-5080	165	45	=	=	NOUN
ejpam-5080	165	46	0	0	NUM
ejpam-5080	165	47	,	,	PUNCT
ejpam-5080	165	48	1	1	NUM
ejpam-5080	165	49	,	,	PUNCT
ejpam-5080	165	50	·	·	PUNCT
ejpam-5080	165	51	·	·	PUNCT
ejpam-5080	165	52	·	·	PUNCT
ejpam-5080	165	53	(	(	PUNCT
ejpam-5080	165	54	39	39	NUM
ejpam-5080	165	55	)	)	PUNCT
ejpam-5080	165	56	this	this	PRON
ejpam-5080	165	57	means	mean	VERB
ejpam-5080	165	58	that	that	SCONJ
ejpam-5080	165	59	g(x	g(x	NOUN
ejpam-5080	165	60	)	)	PUNCT
ejpam-5080	166	1	≈	≈	NUM
ejpam-5080	166	2	−0.00001047	−0.00001047	NUM
ejpam-5080	166	3	+	+	CCONJ
ejpam-5080	166	4	2.000674384x−	2.000674384x−	NUM
ejpam-5080	166	5	0.106599082x2	0.106599082x2	NUM
ejpam-5080	166	6	+	+	NUM
ejpam-5080	166	7	·	·	PUNCT
ejpam-5080	166	8	·	·	PUNCT
ejpam-5080	166	9	·	·	PUNCT
ejpam-5080	167	1	−	−	PUNCT
ejpam-5080	167	2	0.4690686000x6	0.4690686000x6	NUM
ejpam-5080	167	3	.	.	PUNCT
ejpam-5080	168	1	(	(	PUNCT
ejpam-5080	168	2	40	40	NUM
ejpam-5080	168	3	)	)	PUNCT
ejpam-5080	168	4	thus	thus	ADV
ejpam-5080	168	5	,	,	PUNCT
ejpam-5080	168	6	we	we	PRON
ejpam-5080	168	7	get	get	VERB
ejpam-5080	168	8	the	the	DET
ejpam-5080	168	9	following	follow	VERB
ejpam-5080	168	10	solution	solution	NOUN
ejpam-5080	168	11	components	component	NOUN
ejpam-5080	168	12	u0	u0	PROPN
ejpam-5080	168	13	=	=	PROPN
ejpam-5080	168	14	u(0	u(0	PROPN
ejpam-5080	168	15	)	)	PUNCT
ejpam-5080	169	1	+	+	CCONJ
ejpam-5080	169	2	xu′(0	xu′(0	NOUN
ejpam-5080	169	3	)	)	PUNCT
ejpam-5080	170	1	+	+	CCONJ
ejpam-5080	170	2	l−1(−0.00001047	l−1(−0.00001047	NOUN
ejpam-5080	170	3	+	+	CCONJ
ejpam-5080	170	4	2.000674384x+	2.000674384x+	NUM
ejpam-5080	170	5	·	·	PUNCT
ejpam-5080	170	6	·	·	PUNCT
ejpam-5080	170	7	·	·	PUNCT
ejpam-5080	171	1	−	−	PROPN
ejpam-5080	171	2	0.4690686000x6	0.4690686000x6	NUM
ejpam-5080	171	3	)	)	PUNCT
ejpam-5080	171	4	,	,	PUNCT
ejpam-5080	172	1	=	=	SYM
ejpam-5080	172	2	x−	x−	PROPN
ejpam-5080	172	3	0.000005237x2	0.000005237x2	NUM
ejpam-5080	172	4	+	+	PUNCT
ejpam-5080	172	5	0.3334454093x3	0.3334454093x3	NUM
ejpam-5080	172	6	+	+	X
ejpam-5080	172	7	·	·	PUNCT
ejpam-5080	172	8	·	·	PUNCT
ejpam-5080	172	9	·	·	PUNCT
ejpam-5080	173	1	−	−	PROPN
ejpam-5080	173	2	0.008375467814x8	0.008375467814x8	NUM
ejpam-5080	173	3	,	,	PUNCT
ejpam-5080	173	4	u1	u1	NOUN
ejpam-5080	173	5	=	=	PUNCT
ejpam-5080	173	6	−0.5x3	−0.5x3	NOUN
ejpam-5080	173	7	+	+	NUM
ejpam-5080	173	8	0.00000130940075x4	0.00000130940075x4	NUM
ejpam-5080	173	9	+	+	X
ejpam-5080	173	10	·	·	PUNCT
ejpam-5080	173	11	·	·	PUNCT
ejpam-5080	173	12	·	·	PUNCT
ejpam-5080	173	13	,	,	PUNCT
ejpam-5080	173	14	u2	u2	NOUN
ejpam-5080	173	15	=	=	NOUN
ejpam-5080	173	16	0.075x5	0.075x5	NUM
ejpam-5080	173	17	−	−	NUM
ejpam-5080	173	18	1.307582000×	1.307582000×	NUM
ejpam-5080	173	19	10−7x6	10−7x6	NUM
ejpam-5080	173	20	+	+	X
ejpam-5080	173	21	·	·	PUNCT
ejpam-5080	173	22	·	·	PUNCT
ejpam-5080	173	23	·	·	PUNCT
ejpam-5080	173	24	,	,	PUNCT
ejpam-5080	173	25	u3	u3	NOUN
ejpam-5080	173	26	=	=	SYM
ejpam-5080	173	27	−0.005357142858x7	−0.005357142858x7	X
ejpam-5080	173	28	+	+	X
ejpam-5080	173	29	·	·	PUNCT
ejpam-5080	173	30	·	·	PUNCT
ejpam-5080	173	31	·	·	PUNCT
ejpam-5080	173	32	,	,	PUNCT
ejpam-5080	173	33	...	...	PUNCT
ejpam-5080	173	34	such	such	ADJ
ejpam-5080	173	35	that	that	SCONJ
ejpam-5080	173	36	their	their	PRON
ejpam-5080	173	37	summation	summation	NOUN
ejpam-5080	173	38	yields	yield	VERB
ejpam-5080	173	39	up	up	ADP
ejpam-5080	173	40	(	(	PUNCT
ejpam-5080	173	41	x	x	NOUN
ejpam-5080	173	42	)	)	PUNCT
ejpam-5080	173	43	=	=	SYM
ejpam-5080	173	44	6∑	6∑	PROPN
ejpam-5080	173	45	n=0	n=0	NUM
ejpam-5080	173	46	un(x	un(x	SYM
ejpam-5080	173	47	)	)	PUNCT
ejpam-5080	173	48	=	=	PUNCT
ejpam-5080	174	1	x−0.000005237603000x2−0.1665545908x3−0.00088541019923x4	x−0.000005237603000x2−0.1665545908x3−0.00088541019923x4	PROPN
ejpam-5080	174	2	+	+	PROPN
ejpam-5080	174	3	·	·	PUNCT
ejpam-5080	174	4	·	·	PUNCT
ejpam-5080	174	5	·	·	PUNCT
ejpam-5080	174	6	(	(	PUNCT
ejpam-5080	174	7	41	41	NUM
ejpam-5080	174	8	)	)	PUNCT
ejpam-5080	174	9	modification	modification	NOUN
ejpam-5080	174	10	method	method	NOUN
ejpam-5080	174	11	via	via	ADP
ejpam-5080	174	12	chebyshev	chebyshev	PROPN
ejpam-5080	174	13	’s	’s	PART
ejpam-5080	174	14	polynomials	polynomial	NOUN
ejpam-5080	174	15	goes	go	VERB
ejpam-5080	174	16	off	off	ADP
ejpam-5080	174	17	by	by	ADP
ejpam-5080	174	18	expanding	expand	VERB
ejpam-5080	174	19	the	the	DET
ejpam-5080	174	20	source	source	NOUN
ejpam-5080	174	21	term	term	NOUN
ejpam-5080	174	22	g(x	g(x	NOUN
ejpam-5080	174	23	)	)	PUNCT
ejpam-5080	174	24	as	as	SCONJ
ejpam-5080	174	25	follows	follow	VERB
ejpam-5080	174	26	g(x	g(x	NOUN
ejpam-5080	174	27	)	)	PUNCT
ejpam-5080	175	1	=	=	SYM
ejpam-5080	176	1	6∑	6∑	NUM
ejpam-5080	177	1	n=0	n=0	NUM
ejpam-5080	177	2	cntn(2x−	cntn(2x−	NOUN
ejpam-5080	177	3	1	1	NUM
ejpam-5080	177	4	)	)	PUNCT
ejpam-5080	177	5	,	,	PUNCT
ejpam-5080	177	6	0	0	NUM
ejpam-5080	177	7	≤	≤	NUM
ejpam-5080	177	8	x	x	SYM
ejpam-5080	177	9	≤	≤	NUM
ejpam-5080	177	10	1	1	NUM
ejpam-5080	177	11	,	,	PUNCT
ejpam-5080	177	12	(	(	PUNCT
ejpam-5080	177	13	42	42	NUM
ejpam-5080	177	14	)	)	PUNCT
ejpam-5080	177	15	where	where	SCONJ
ejpam-5080	177	16	tn	tn	PROPN
ejpam-5080	177	17	(	(	PUNCT
ejpam-5080	177	18	.	.	PUNCT
ejpam-5080	177	19	)	)	PUNCT
ejpam-5080	177	20	are	be	AUX
ejpam-5080	177	21	orthogonal	orthogonal	ADJ
ejpam-5080	177	22	chebyshev	chebyshev	PROPN
ejpam-5080	177	23	’s	’s	PART
ejpam-5080	177	24	polynomials	polynomial	NOUN
ejpam-5080	177	25	,	,	PUNCT
ejpam-5080	177	26	and	and	CCONJ
ejpam-5080	177	27	ci	ci	NOUN
ejpam-5080	177	28	are	be	AUX
ejpam-5080	177	29	given	give	VERB
ejpam-5080	177	30	by	by	ADP
ejpam-5080	177	31	where	where	SCONJ
ejpam-5080	177	32	c0	c0	NOUN
ejpam-5080	177	33	=	=	PROPN
ejpam-5080	177	34	1	1	NUM
ejpam-5080	177	35	π	π	NOUN
ejpam-5080	177	36	∫	∫	PROPN
ejpam-5080	177	37	1	1	NUM
ejpam-5080	177	38	−1	−1	NOUN
ejpam-5080	177	39	g(0.5x+	g(0.5x+	NOUN
ejpam-5080	177	40	0.5)t0(x)√	0.5)t0(x)√	NUM
ejpam-5080	177	41	1−	1−	NUM
ejpam-5080	177	42	x2	x2	NUM
ejpam-5080	177	43	dx	dx	PROPN
ejpam-5080	177	44	,	,	PUNCT
ejpam-5080	177	45	ci	ci	PROPN
ejpam-5080	177	46	=	=	SYM
ejpam-5080	177	47	2	2	NUM
ejpam-5080	177	48	π	π	NOUN
ejpam-5080	177	49	∫	∫	PROPN
ejpam-5080	177	50	1	1	NUM
ejpam-5080	177	51	−1	−1	NOUN
ejpam-5080	177	52	g(0.5x+	g(0.5x+	NOUN
ejpam-5080	177	53	0.5)ti(x)√	0.5)ti(x)√	NUM
ejpam-5080	177	54	1−	1−	NUM
ejpam-5080	177	55	x2	x2	NUM
ejpam-5080	177	56	dx	dx	PROPN
ejpam-5080	177	57	,	,	PUNCT
ejpam-5080	177	58	i	i	PRON
ejpam-5080	177	59	=	=	NOUN
ejpam-5080	177	60	1	1	NUM
ejpam-5080	177	61	,	,	PUNCT
ejpam-5080	177	62	2	2	NUM
ejpam-5080	177	63	,	,	PUNCT
ejpam-5080	177	64	·	·	PUNCT
ejpam-5080	177	65	·	·	PUNCT
ejpam-5080	177	66	·	·	PUNCT
ejpam-5080	177	67	(	(	PUNCT
ejpam-5080	177	68	43	43	NUM
ejpam-5080	177	69	)	)	PUNCT
ejpam-5080	177	70	such	such	ADJ
ejpam-5080	177	71	that	that	DET
ejpam-5080	177	72	g(x	g(x	NOUN
ejpam-5080	177	73	)	)	PUNCT
ejpam-5080	178	1	≈	≈	PROPN
ejpam-5080	178	2	−0.000004054169	−0.000004054169	PROPN
ejpam-5080	178	3	+	+	X
ejpam-5080	178	4	2.000464751x−	2.000464751x−	NUM
ejpam-5080	178	5	0.0088519738x2	0.0088519738x2	NUM
ejpam-5080	178	6	+	+	CCONJ
ejpam-5080	178	7	·	·	PUNCT
ejpam-5080	178	8	·	·	PUNCT
ejpam-5080	178	9	·	·	PUNCT
ejpam-5080	179	1	−	−	NOUN
ejpam-5080	179	2	0.4661302071x6	0.4661302071x6	NUM
ejpam-5080	179	3	.	.	PUNCT
ejpam-5080	180	1	(	(	PUNCT
ejpam-5080	180	2	44	44	NUM
ejpam-5080	180	3	)	)	PUNCT
ejpam-5080	180	4	n.	n.	NOUN
ejpam-5080	180	5	alzaid	alzaid	PROPN
ejpam-5080	180	6	et	et	PROPN
ejpam-5080	180	7	al	al	PROPN
ejpam-5080	180	8	.	.	PUNCT
ejpam-5080	180	9	/	/	SYM
ejpam-5080	180	10	eur	eur	PROPN
ejpam-5080	180	11	.	.	PUNCT
ejpam-5080	181	1	j.	j.	PROPN
ejpam-5080	181	2	pure	pure	PROPN
ejpam-5080	181	3	appl	appl	PROPN
ejpam-5080	181	4	.	.	PROPN
ejpam-5080	181	5	math	math	PROPN
ejpam-5080	181	6	,	,	PUNCT
ejpam-5080	181	7	17	17	NUM
ejpam-5080	181	8	(	(	PUNCT
ejpam-5080	181	9	3	3	NUM
ejpam-5080	181	10	)	)	PUNCT
ejpam-5080	181	11	(	(	PUNCT
ejpam-5080	181	12	2024	2024	NUM
ejpam-5080	181	13	)	)	PUNCT
ejpam-5080	181	14	,	,	PUNCT
ejpam-5080	181	15	1982	1982	NUM
ejpam-5080	181	16	-	-	SYM
ejpam-5080	181	17	2000	2000	NUM
ejpam-5080	181	18	1991	1991	NUM
ejpam-5080	181	19	therefore	therefore	ADV
ejpam-5080	181	20	,	,	PUNCT
ejpam-5080	181	21	the	the	DET
ejpam-5080	181	22	solution	solution	NOUN
ejpam-5080	181	23	components	component	NOUN
ejpam-5080	181	24	are	be	AUX
ejpam-5080	181	25	as	as	SCONJ
ejpam-5080	181	26	follows	follow	VERB
ejpam-5080	181	27	u0	u0	ADJ
ejpam-5080	181	28	=	=	PROPN
ejpam-5080	181	29	u(0	u(0	PROPN
ejpam-5080	181	30	)	)	PUNCT
ejpam-5080	182	1	+	+	CCONJ
ejpam-5080	182	2	xu′(0	xu′(0	NOUN
ejpam-5080	182	3	)	)	PUNCT
ejpam-5080	183	1	+	+	CCONJ
ejpam-5080	183	2	l−1(−0.000004054169	l−1(−0.000004054169	PROPN
ejpam-5080	183	3	+	+	CCONJ
ejpam-5080	183	4	2.000464751x−	2.000464751x−	NUM
ejpam-5080	183	5	0.0088519738x2	0.0088519738x2	NUM
ejpam-5080	183	6	+	+	CCONJ
ejpam-5080	183	7	·	·	PUNCT
ejpam-5080	183	8	·	·	PUNCT
ejpam-5080	183	9	·	·	PUNCT
ejpam-5080	184	1	−	−	NOUN
ejpam-5080	184	2	0.4661302071x6	0.4661302071x6	NUM
ejpam-5080	184	3	)	)	PUNCT
ejpam-5080	184	4	,	,	PUNCT
ejpam-5080	185	1	=	=	SYM
ejpam-5080	185	2	x−	x−	PROPN
ejpam-5080	185	3	0.0000020270845x2	0.0000020270845x2	PUNCT
ejpam-5080	185	4	+	+	CCONJ
ejpam-5080	185	5	0.3334107920x3	0.3334107920x3	NUM
ejpam-5080	186	1	+	+	CCONJ
ejpam-5080	186	2	·	·	PUNCT
ejpam-5080	186	3	·	·	PUNCT
ejpam-5080	186	4	·	·	PUNCT
ejpam-5080	187	1	−	−	PROPN
ejpam-5080	187	2	0.008323753699x8	0.008323753699x8	NOUN
ejpam-5080	187	3	,	,	PUNCT
ejpam-5080	187	4	u1	u1	NOUN
ejpam-5080	187	5	=	=	PUNCT
ejpam-5080	187	6	−0.5x3	−0.5x3	NOUN
ejpam-5080	187	7	+	+	CCONJ
ejpam-5080	187	8	5.06771124910−7x4	5.06771124910−7x4	NUM
ejpam-5080	187	9	+	+	NUM
ejpam-5080	187	10	·	·	PUNCT
ejpam-5080	187	11	·	·	PUNCT
ejpam-5080	187	12	·	·	PUNCT
ejpam-5080	187	13	,	,	PUNCT
ejpam-5080	187	14	u2	u2	NOUN
ejpam-5080	187	15	=	=	NOUN
ejpam-5080	187	16	0.075x5	0.075x5	NUM
ejpam-5080	187	17	−	−	PROPN
ejpam-5080	187	18	5.06771124910−8x6	5.06771124910−8x6	NUM
ejpam-5080	187	19	+	+	CCONJ
ejpam-5080	187	20	·	·	PUNCT
ejpam-5080	187	21	·	·	PUNCT
ejpam-5080	187	22	·	·	PUNCT
ejpam-5080	187	23	,	,	PUNCT
ejpam-5080	187	24	u3	u3	NOUN
ejpam-5080	187	25	=	=	SYM
ejpam-5080	187	26	−0.005357142858x7	−0.005357142858x7	X
ejpam-5080	187	27	+	+	X
ejpam-5080	187	28	·	·	PUNCT
ejpam-5080	187	29	·	·	PUNCT
ejpam-5080	187	30	·	·	PUNCT
ejpam-5080	187	31	,	,	PUNCT
ejpam-5080	187	32	...	...	PUNCT
ejpam-5080	187	33	that	that	PRON
ejpam-5080	187	34	leads	lead	VERB
ejpam-5080	187	35	to	to	ADP
ejpam-5080	187	36	the	the	DET
ejpam-5080	187	37	following	follow	VERB
ejpam-5080	187	38	series	series	PROPN
ejpam-5080	187	39	solution	solution	NOUN
ejpam-5080	187	40	ut	ut	PROPN
ejpam-5080	187	41	(	(	PUNCT
ejpam-5080	187	42	x	x	X
ejpam-5080	187	43	)	)	PUNCT
ejpam-5080	187	44	=	=	SYM
ejpam-5080	187	45	6∑	6∑	PROPN
ejpam-5080	187	46	n=0	n=0	NUM
ejpam-5080	187	47	un(x	un(x	SYM
ejpam-5080	187	48	)	)	PUNCT
ejpam-5080	188	1	=	=	SYM
ejpam-5080	188	2	x−	x−	PROPN
ejpam-5080	188	3	0.0000020270845x2	0.0000020270845x2	NUM
ejpam-5080	188	4	−	−	NOUN
ejpam-5080	188	5	0.1665892081x3	0.1665892081x3	PRON
ejpam-5080	189	1	−	−	VERB
ejpam-5080	189	2	0.0007371577121x4	0.0007371577121x4	X
ejpam-5080	190	1	+	+	CCONJ
ejpam-5080	190	2	·	·	PUNCT
ejpam-5080	190	3	·	·	PUNCT
ejpam-5080	190	4	·	·	PUNCT
ejpam-5080	190	5	(	(	PUNCT
ejpam-5080	190	6	45	45	NUM
ejpam-5080	190	7	)	)	PUNCT
ejpam-5080	190	8	modification	modification	NOUN
ejpam-5080	190	9	method	method	NOUN
ejpam-5080	190	10	via	via	ADP
ejpam-5080	190	11	laguerre	laguerre	NOUN
ejpam-5080	190	12	’s	’s	PART
ejpam-5080	190	13	polynomials	polynomial	NOUN
ejpam-5080	190	14	starts	start	VERB
ejpam-5080	190	15	off	off	ADP
ejpam-5080	190	16	by	by	ADP
ejpam-5080	190	17	expanding	expand	VERB
ejpam-5080	190	18	the	the	DET
ejpam-5080	190	19	source	source	NOUN
ejpam-5080	190	20	term	term	NOUN
ejpam-5080	190	21	g(x	g(x	NOUN
ejpam-5080	190	22	)	)	PUNCT
ejpam-5080	190	23	in	in	ADP
ejpam-5080	190	24	the	the	DET
ejpam-5080	190	25	following	follow	VERB
ejpam-5080	190	26	form	form	NOUN
ejpam-5080	190	27	g(x	g(x	NOUN
ejpam-5080	190	28	)	)	PUNCT
ejpam-5080	191	1	=	=	SYM
ejpam-5080	192	1	6∑	6∑	NUM
ejpam-5080	192	2	n=0	n=0	SYM
ejpam-5080	193	1	cnln(x	cnln(x	PROPN
ejpam-5080	193	2	)	)	PUNCT
ejpam-5080	193	3	,	,	PUNCT
ejpam-5080	193	4	0	0	NUM
ejpam-5080	193	5	≤	≤	NUM
ejpam-5080	193	6	x	x	SYM
ejpam-5080	193	7	≤	≤	NUM
ejpam-5080	193	8	1	1	NUM
ejpam-5080	193	9	,	,	PUNCT
ejpam-5080	193	10	(	(	PUNCT
ejpam-5080	193	11	46	46	NUM
ejpam-5080	193	12	)	)	PUNCT
ejpam-5080	193	13	where	where	SCONJ
ejpam-5080	193	14	ln	ln	ADJ
ejpam-5080	193	15	(	(	PUNCT
ejpam-5080	193	16	.	.	PUNCT
ejpam-5080	193	17	)	)	PUNCT
ejpam-5080	193	18	are	be	AUX
ejpam-5080	193	19	orthogonal	orthogonal	ADJ
ejpam-5080	193	20	laguerre	laguerre	NOUN
ejpam-5080	193	21	’s	’s	PART
ejpam-5080	193	22	polynomials	polynomial	NOUN
ejpam-5080	193	23	,	,	PUNCT
ejpam-5080	193	24	and	and	CCONJ
ejpam-5080	193	25	ci	ci	NOUN
ejpam-5080	193	26	are	be	AUX
ejpam-5080	193	27	given	give	VERB
ejpam-5080	193	28	by	by	ADP
ejpam-5080	193	29	ci	ci	NOUN
ejpam-5080	193	30	=	=	SYM
ejpam-5080	193	31	∫	∫	PROPN
ejpam-5080	193	32	∞	∞	PROPN
ejpam-5080	193	33	0	0	PUNCT
ejpam-5080	194	1	e−xli(x)g(x)dx	e−xli(x)g(x)dx	NOUN
ejpam-5080	194	2	,	,	PUNCT
ejpam-5080	194	3	i	i	NOUN
ejpam-5080	194	4	=	=	NOUN
ejpam-5080	194	5	0	0	NUM
ejpam-5080	194	6	,	,	PUNCT
ejpam-5080	194	7	1	1	NUM
ejpam-5080	194	8	,	,	PUNCT
ejpam-5080	194	9	·	·	PUNCT
ejpam-5080	194	10	·	·	PUNCT
ejpam-5080	194	11	·	·	PUNCT
ejpam-5080	195	1	(	(	PUNCT
ejpam-5080	195	2	47	47	NUM
ejpam-5080	195	3	)	)	PUNCT
ejpam-5080	195	4	such	such	ADJ
ejpam-5080	195	5	that	that	PRON
ejpam-5080	195	6	g(x	g(x	NOUN
ejpam-5080	195	7	)	)	PUNCT
ejpam-5080	196	1	≈	≈	PROPN
ejpam-5080	196	2	148321	148321	NUM
ejpam-5080	196	3	625000	625000	NUM
ejpam-5080	196	4	+	+	CCONJ
ejpam-5080	196	5	150161	150161	NUM
ejpam-5080	196	6	156250	156250	NUM
ejpam-5080	196	7	x−	x−	PROPN
ejpam-5080	196	8	219727	219727	NUM
ejpam-5080	196	9	250000	250000	NUM
ejpam-5080	197	1	x2	x2	PROPN
ejpam-5080	198	1	+	+	CCONJ
ejpam-5080	198	2	·	·	PUNCT
ejpam-5080	198	3	·	·	PUNCT
ejpam-5080	198	4	·	·	PUNCT
ejpam-5080	199	1	−	−	PROPN
ejpam-5080	199	2	25849	25849	NUM
ejpam-5080	199	3	450000000	450000000	NUM
ejpam-5080	199	4	x6	x6	PROPN
ejpam-5080	199	5	.	.	PUNCT
ejpam-5080	200	1	(	(	PUNCT
ejpam-5080	200	2	48	48	NUM
ejpam-5080	200	3	)	)	PUNCT
ejpam-5080	200	4	this	this	PRON
ejpam-5080	200	5	gives	give	VERB
ejpam-5080	200	6	the	the	DET
ejpam-5080	200	7	following	follow	VERB
ejpam-5080	200	8	iterative	iterative	NOUN
ejpam-5080	200	9	solutions	solution	NOUN
ejpam-5080	200	10	u0	u0	NOUN
ejpam-5080	200	11	=	=	PROPN
ejpam-5080	200	12	u(0	u(0	PROPN
ejpam-5080	200	13	)	)	PUNCT
ejpam-5080	201	1	+	+	CCONJ
ejpam-5080	201	2	xu′(0	xu′(0	NOUN
ejpam-5080	201	3	)	)	PUNCT
ejpam-5080	202	1	+	+	PUNCT
ejpam-5080	202	2	l−1	l−1	PROPN
ejpam-5080	202	3	(	(	PUNCT
ejpam-5080	202	4	148321	148321	NUM
ejpam-5080	202	5	625000	625000	NUM
ejpam-5080	202	6	+	+	CCONJ
ejpam-5080	202	7	150161	150161	NUM
ejpam-5080	202	8	156250	156250	NUM
ejpam-5080	202	9	x−	x−	PROPN
ejpam-5080	202	10	219727	219727	NUM
ejpam-5080	202	11	250000	250000	NUM
ejpam-5080	202	12	x2	x2	PROPN
ejpam-5080	203	1	+	+	CCONJ
ejpam-5080	203	2	·	·	PUNCT
ejpam-5080	203	3	·	·	PUNCT
ejpam-5080	203	4	·	·	PUNCT
ejpam-5080	204	1	−	−	PROPN
ejpam-5080	204	2	25849	25849	NUM
ejpam-5080	204	3	450000000	450000000	NUM
ejpam-5080	204	4	x6	x6	PROPN
ejpam-5080	204	5	)	)	PUNCT
ejpam-5080	204	6	,	,	PUNCT
ejpam-5080	205	1	=	=	PUNCT
ejpam-5080	205	2	x+	x+	X
ejpam-5080	205	3	0.118656800x2	0.118656800x2	NUM
ejpam-5080	205	4	+	+	CCONJ
ejpam-5080	205	5	0.160171733x3	0.160171733x3	NUM
ejpam-5080	205	6	−	−	NOUN
ejpam-5080	205	7	0.07324233332x4	0.07324233332x4	NUM
ejpam-5080	206	1	+	+	X
ejpam-5080	206	2	·	·	PUNCT
ejpam-5080	206	3	·	·	PUNCT
ejpam-5080	206	4	·	·	PUNCT
ejpam-5080	207	1	−	−	PROPN
ejpam-5080	207	2	0.000001025753968x8	0.000001025753968x8	NUM
ejpam-5080	207	3	,	,	PUNCT
ejpam-5080	207	4	u1	u1	NOUN
ejpam-5080	207	5	=	=	PUNCT
ejpam-5080	207	6	−0.5x3	−0.5x3	NOUN
ejpam-5080	207	7	−	−	NOUN
ejpam-5080	207	8	0.02966420000x4	0.02966420000x4	NUM
ejpam-5080	207	9	−	−	NOUN
ejpam-5080	207	10	0.07597424000x5	0.07597424000x5	NUM
ejpam-5080	207	11	+	+	CCONJ
ejpam-5080	207	12	·	·	PUNCT
ejpam-5080	207	13	·	·	PUNCT
ejpam-5080	207	14	·	·	PUNCT
ejpam-5080	207	15	,	,	PUNCT
ejpam-5080	207	16	u2	u2	NOUN
ejpam-5080	207	17	=	=	NOUN
ejpam-5080	207	18	0.075x5	0.075x5	NOUN
ejpam-5080	208	1	+	+	CCONJ
ejpam-5080	208	2	0.002966420000x6	0.002966420000x6	NUM
ejpam-5080	208	3	−	−	X
ejpam-5080	208	4	0.07685530286x7	0.07685530286x7	X
ejpam-5080	209	1	+	+	NUM
ejpam-5080	209	2	·	·	PUNCT
ejpam-5080	209	3	·	·	PUNCT
ejpam-5080	209	4	·	·	PUNCT
ejpam-5080	209	5	,	,	PUNCT
ejpam-5080	209	6	u3	u3	NOUN
ejpam-5080	209	7	=	=	SYM
ejpam-5080	209	8	−0.005357142857x7	−0.005357142857x7	PROPN
ejpam-5080	209	9	+	+	X
ejpam-5080	209	10	·	·	PUNCT
ejpam-5080	209	11	·	·	PUNCT
ejpam-5080	209	12	·	·	PUNCT
ejpam-5080	209	13	,	,	PUNCT
ejpam-5080	209	14	...	...	PUNCT
ejpam-5080	209	15	that	that	PRON
ejpam-5080	209	16	sums	sum	VERB
ejpam-5080	209	17	to	to	ADP
ejpam-5080	209	18	the	the	DET
ejpam-5080	209	19	following	follow	VERB
ejpam-5080	209	20	ul(x	ul(x	NOUN
ejpam-5080	209	21	)	)	PUNCT
ejpam-5080	210	1	=	=	SYM
ejpam-5080	210	2	6∑	6∑	PROPN
ejpam-5080	210	3	n=0	n=0	NUM
ejpam-5080	210	4	un(x	un(x	SYM
ejpam-5080	210	5	)	)	PUNCT
ejpam-5080	211	1	=	=	SYM
ejpam-5080	211	2	x+	x+	PUNCT
ejpam-5080	211	3	0.1186568000x2	0.1186568000x2	NUM
ejpam-5080	211	4	−	−	NUM
ejpam-5080	211	5	0.3398282667x3	0.3398282667x3	NUM
ejpam-5080	211	6	−	−	NOUN
ejpam-5080	211	7	0.1029065333x4	0.1029065333x4	NUM
ejpam-5080	212	1	+	+	NUM
ejpam-5080	213	1	·	·	PUNCT
ejpam-5080	213	2	·	·	PUNCT
ejpam-5080	213	3	·	·	PUNCT
ejpam-5080	213	4	(	(	PUNCT
ejpam-5080	213	5	49	49	X
ejpam-5080	213	6	)	)	PUNCT
ejpam-5080	213	7	n.	n.	NOUN
ejpam-5080	213	8	alzaid	alzaid	PROPN
ejpam-5080	213	9	et	et	PROPN
ejpam-5080	213	10	al	al	PROPN
ejpam-5080	213	11	.	.	PUNCT
ejpam-5080	213	12	/	/	SYM
ejpam-5080	213	13	eur	eur	PROPN
ejpam-5080	213	14	.	.	PUNCT
ejpam-5080	214	1	j.	j.	PROPN
ejpam-5080	214	2	pure	pure	PROPN
ejpam-5080	214	3	appl	appl	PROPN
ejpam-5080	214	4	.	.	PROPN
ejpam-5080	214	5	math	math	PROPN
ejpam-5080	214	6	,	,	PUNCT
ejpam-5080	214	7	17	17	NUM
ejpam-5080	214	8	(	(	PUNCT
ejpam-5080	214	9	3	3	NUM
ejpam-5080	214	10	)	)	PUNCT
ejpam-5080	214	11	(	(	PUNCT
ejpam-5080	214	12	2024	2024	NUM
ejpam-5080	214	13	)	)	PUNCT
ejpam-5080	214	14	,	,	PUNCT
ejpam-5080	214	15	1982	1982	NUM
ejpam-5080	214	16	-	-	SYM
ejpam-5080	214	17	2000	2000	NUM
ejpam-5080	214	18	1992	1992	NUM
ejpam-5080	214	19	modification	modification	NOUN
ejpam-5080	214	20	method	method	NOUN
ejpam-5080	214	21	via	via	ADP
ejpam-5080	214	22	hermite	hermite	PROPN
ejpam-5080	214	23	’s	’s	PART
ejpam-5080	214	24	polynomials	polynomial	NOUN
ejpam-5080	214	25	expands	expand	VERB
ejpam-5080	214	26	the	the	DET
ejpam-5080	214	27	source	source	NOUN
ejpam-5080	214	28	term	term	NOUN
ejpam-5080	214	29	g(x	g(x	NOUN
ejpam-5080	214	30	)	)	PUNCT
ejpam-5080	214	31	as	as	SCONJ
ejpam-5080	214	32	follows	follow	VERB
ejpam-5080	214	33	g(x	g(x	NOUN
ejpam-5080	214	34	)	)	PUNCT
ejpam-5080	215	1	=	=	SYM
ejpam-5080	216	1	6∑	6∑	NUM
ejpam-5080	216	2	n=0	n=0	SYM
ejpam-5080	216	3	cnhn(x	cnhn(x	PROPN
ejpam-5080	216	4	)	)	PUNCT
ejpam-5080	216	5	,	,	PUNCT
ejpam-5080	216	6	0	0	NUM
ejpam-5080	216	7	≤	≤	NUM
ejpam-5080	216	8	x	x	SYM
ejpam-5080	216	9	≤	≤	NUM
ejpam-5080	216	10	1	1	NUM
ejpam-5080	216	11	,	,	PUNCT
ejpam-5080	216	12	(	(	PUNCT
ejpam-5080	216	13	50	50	NUM
ejpam-5080	216	14	)	)	PUNCT
ejpam-5080	216	15	where	where	SCONJ
ejpam-5080	216	16	hn	hn	PROPN
ejpam-5080	216	17	(	(	PUNCT
ejpam-5080	216	18	.	.	PUNCT
ejpam-5080	216	19	)	)	PUNCT
ejpam-5080	216	20	are	be	AUX
ejpam-5080	216	21	orthogonal	orthogonal	ADJ
ejpam-5080	216	22	hermite	hermite	PROPN
ejpam-5080	216	23	’s	’s	PART
ejpam-5080	216	24	polynomials	polynomial	NOUN
ejpam-5080	216	25	,	,	PUNCT
ejpam-5080	216	26	and	and	CCONJ
ejpam-5080	216	27	ci	ci	NOUN
ejpam-5080	216	28	are	be	AUX
ejpam-5080	216	29	given	give	VERB
ejpam-5080	216	30	by	by	ADP
ejpam-5080	216	31	ci	ci	NOUN
ejpam-5080	216	32	=	=	SYM
ejpam-5080	216	33	1	1	NUM
ejpam-5080	216	34	2ii	2ii	NOUN
ejpam-5080	216	35	!	!	PUNCT
ejpam-5080	217	1	√	√	PUNCT
ejpam-5080	218	1	π	π	X
ejpam-5080	218	2	∫	∫	PROPN
ejpam-5080	218	3	∞	∞	PROPN
ejpam-5080	218	4	−∞	−∞	ADP
ejpam-5080	218	5	e−x2	e−x2	NOUN
ejpam-5080	218	6	hi(x)g(x)dx	hi(x)g(x)dx	NOUN
ejpam-5080	218	7	,	,	PUNCT
ejpam-5080	218	8	i	i	PRON
ejpam-5080	218	9	=	=	NOUN
ejpam-5080	218	10	0	0	NUM
ejpam-5080	218	11	,	,	PUNCT
ejpam-5080	218	12	1	1	NUM
ejpam-5080	218	13	,	,	PUNCT
ejpam-5080	218	14	·	·	PUNCT
ejpam-5080	218	15	·	·	PUNCT
ejpam-5080	218	16	·	·	PUNCT
ejpam-5080	218	17	(	(	PUNCT
ejpam-5080	218	18	51	51	NUM
ejpam-5080	218	19	)	)	PUNCT
ejpam-5080	218	20	such	such	ADJ
ejpam-5080	218	21	that	that	DET
ejpam-5080	218	22	g(x	g(x	NOUN
ejpam-5080	218	23	)	)	PUNCT
ejpam-5080	219	1	≈	≈	NOUN
ejpam-5080	219	2	1.412928152x−	1.412928152x−	NUM
ejpam-5080	219	3	0.8518569111x3	0.8518569111x3	PRON
ejpam-5080	219	4	+	+	NOUN
ejpam-5080	219	5	0.1099617181x5	0.1099617181x5	NUM
ejpam-5080	219	6	.	.	PUNCT
ejpam-5080	220	1	(	(	PUNCT
ejpam-5080	220	2	52	52	NUM
ejpam-5080	220	3	)	)	PUNCT
ejpam-5080	220	4	we	we	PRON
ejpam-5080	220	5	,	,	PUNCT
ejpam-5080	220	6	therefore	therefore	ADV
ejpam-5080	220	7	,	,	PUNCT
ejpam-5080	220	8	obtain	obtain	VERB
ejpam-5080	220	9	u0	u0	ADJ
ejpam-5080	220	10	=	=	PROPN
ejpam-5080	220	11	u(0	u(0	NOUN
ejpam-5080	220	12	)	)	PUNCT
ejpam-5080	221	1	+	+	CCONJ
ejpam-5080	221	2	xu′(0	xu′(0	NOUN
ejpam-5080	221	3	)	)	PUNCT
ejpam-5080	222	1	+	+	CCONJ
ejpam-5080	222	2	l−1(1.412928152x−	l−1(1.412928152x−	X
ejpam-5080	222	3	0.8518569111x3	0.8518569111x3	X
ejpam-5080	222	4	+	+	PUNCT
ejpam-5080	222	5	0.1099617181x5	0.1099617181x5	NUM
ejpam-5080	222	6	)	)	PUNCT
ejpam-5080	222	7	,	,	PUNCT
ejpam-5080	222	8	=	=	PUNCT
ejpam-5080	222	9	x+	x+	X
ejpam-5080	222	10	0.2354880253x3	0.2354880253x3	NUM
ejpam-5080	222	11	−	−	PROPN
ejpam-5080	222	12	0.04259284556x5	0.04259284556x5	NUM
ejpam-5080	223	1	+	+	CCONJ
ejpam-5080	223	2	0.002618136146x7	0.002618136146x7	NUM
ejpam-5080	223	3	,	,	PUNCT
ejpam-5080	223	4	u1	u1	NOUN
ejpam-5080	223	5	=	=	PUNCT
ejpam-5080	223	6	−0.5x3	−0.5x3	NOUN
ejpam-5080	223	7	+	+	NUM
ejpam-5080	223	8	0.06467679622x5	0.06467679622x5	NUM
ejpam-5080	223	9	+	+	CCONJ
ejpam-5080	223	10	·	·	PUNCT
ejpam-5080	223	11	·	·	PUNCT
ejpam-5080	223	12	·	·	PUNCT
ejpam-5080	223	13	,	,	PUNCT
ejpam-5080	223	14	u2	u2	NOUN
ejpam-5080	223	15	=	=	NOUN
ejpam-5080	223	16	0.075x5	0.075x5	NUM
ejpam-5080	223	17	−	−	PROPN
ejpam-5080	223	18	0.07604834258x7	0.07604834258x7	X
ejpam-5080	223	19	+	+	X
ejpam-5080	223	20	·	·	PUNCT
ejpam-5080	223	21	·	·	PUNCT
ejpam-5080	223	22	·	·	PUNCT
ejpam-5080	223	23	,	,	PUNCT
ejpam-5080	223	24	u3	u3	NOUN
ejpam-5080	223	25	=	=	SYM
ejpam-5080	223	26	−0.005357142858x7	−0.005357142858x7	X
ejpam-5080	223	27	+	+	X
ejpam-5080	223	28	·	·	PUNCT
ejpam-5080	223	29	·	·	PUNCT
ejpam-5080	223	30	·	·	PUNCT
ejpam-5080	223	31	,	,	PUNCT
ejpam-5080	223	32	...	...	PUNCT
ejpam-5080	223	33	and	and	CCONJ
ejpam-5080	223	34	leading	lead	VERB
ejpam-5080	223	35	to	to	ADP
ejpam-5080	223	36	the	the	DET
ejpam-5080	223	37	following	follow	VERB
ejpam-5080	223	38	series	series	NOUN
ejpam-5080	223	39	solution	solution	NOUN
ejpam-5080	223	40	uh(x	uh(x	PUNCT
ejpam-5080	223	41	)	)	PUNCT
ejpam-5080	224	1	=	=	SYM
ejpam-5080	224	2	6∑	6∑	PROPN
ejpam-5080	224	3	n=0	n=0	NUM
ejpam-5080	224	4	un(x	un(x	SYM
ejpam-5080	224	5	)	)	PUNCT
ejpam-5080	224	6	=	=	SYM
ejpam-5080	224	7	x−	x−	X
ejpam-5080	224	8	0.2645119748x3	0.2645119748x3	X
ejpam-5080	225	1	+	+	CCONJ
ejpam-5080	225	2	0.09708395066x5	0.09708395066x5	NUM
ejpam-5080	225	3	+	+	X
ejpam-5080	225	4	·	·	PUNCT
ejpam-5080	225	5	·	·	PUNCT
ejpam-5080	225	6	·	·	PUNCT
ejpam-5080	225	7	(	(	PUNCT
ejpam-5080	225	8	53	53	NUM
ejpam-5080	225	9	)	)	PUNCT
ejpam-5080	225	10	modification	modification	NOUN
ejpam-5080	225	11	method	method	NOUN
ejpam-5080	225	12	via	via	ADP
ejpam-5080	225	13	gegenbauer	gegenbauer	PROPN
ejpam-5080	225	14	’s	’s	PART
ejpam-5080	225	15	polynomials	polynomial	NOUN
ejpam-5080	225	16	equally	equally	ADV
ejpam-5080	225	17	starts	start	VERB
ejpam-5080	225	18	off	off	ADP
ejpam-5080	225	19	by	by	ADP
ejpam-5080	225	20	expanding	expand	VERB
ejpam-5080	225	21	the	the	DET
ejpam-5080	225	22	function	function	NOUN
ejpam-5080	225	23	g(x	g(x	NOUN
ejpam-5080	225	24	)	)	PUNCT
ejpam-5080	225	25	as	as	SCONJ
ejpam-5080	225	26	follows	follow	VERB
ejpam-5080	225	27	g(x	g(x	NOUN
ejpam-5080	225	28	)	)	PUNCT
ejpam-5080	226	1	=	=	SYM
ejpam-5080	226	2	6∑	6∑	PROPN
ejpam-5080	226	3	n=0	n=0	SYM
ejpam-5080	226	4	cnc	cnc	PROPN
ejpam-5080	226	5	α	α	PROPN
ejpam-5080	226	6	n	n	PROPN
ejpam-5080	226	7	(	(	PUNCT
ejpam-5080	226	8	2x−	2x−	PROPN
ejpam-5080	226	9	1	1	NUM
ejpam-5080	226	10	)	)	PUNCT
ejpam-5080	226	11	,	,	PUNCT
ejpam-5080	226	12	0	0	NUM
ejpam-5080	226	13	≤	≤	NUM
ejpam-5080	226	14	x	x	SYM
ejpam-5080	226	15	≤	≤	NUM
ejpam-5080	226	16	1	1	NUM
ejpam-5080	226	17	,	,	PUNCT
ejpam-5080	226	18	(	(	PUNCT
ejpam-5080	226	19	54	54	NUM
ejpam-5080	226	20	)	)	PUNCT
ejpam-5080	226	21	where	where	SCONJ
ejpam-5080	226	22	cα	cα	ADP
ejpam-5080	226	23	n	n	PROPN
ejpam-5080	226	24	(	(	PUNCT
ejpam-5080	226	25	.	.	PUNCT
ejpam-5080	226	26	)	)	PUNCT
ejpam-5080	226	27	are	be	AUX
ejpam-5080	226	28	orthogonal	orthogonal	ADJ
ejpam-5080	226	29	gegenbauer	gegenbauer	NOUN
ejpam-5080	226	30	’s	’s	PART
ejpam-5080	226	31	polynomials	polynomial	NOUN
ejpam-5080	226	32	,	,	PUNCT
ejpam-5080	226	33	and	and	CCONJ
ejpam-5080	226	34	ci	ci	NOUN
ejpam-5080	226	35	are	be	AUX
ejpam-5080	226	36	given	give	VERB
ejpam-5080	226	37	by	by	ADP
ejpam-5080	226	38	ci	ci	NOUN
ejpam-5080	226	39	=	=	SYM
ejpam-5080	226	40	∫	∫	PROPN
ejpam-5080	226	41	1	1	NUM
ejpam-5080	226	42	−1	−1	NOUN
ejpam-5080	226	43	g(0.5x+	g(0.5x+	NOUN
ejpam-5080	226	44	0.5)cα	0.5)cα	VERB
ejpam-5080	227	1	i	i	PRON
ejpam-5080	227	2	(	(	PUNCT
ejpam-5080	227	3	x)(1−	x)(1−	PROPN
ejpam-5080	227	4	x2)α−1/2dx∫	x2)α−1/2dx∫	PROPN
ejpam-5080	227	5	1	1	NUM
ejpam-5080	227	6	−1[c	−1[c	NOUN
ejpam-5080	227	7	α	α	NOUN
ejpam-5080	227	8	i	i	PRON
ejpam-5080	227	9	(	(	PUNCT
ejpam-5080	227	10	x	x	NOUN
ejpam-5080	227	11	)	)	PUNCT
ejpam-5080	227	12	]	]	PUNCT
ejpam-5080	228	1	2(1−	2(1−	X
ejpam-5080	229	1	x2)α−1/2dx	x2)α−1/2dx	X
ejpam-5080	229	2	,	,	PUNCT
ejpam-5080	229	3	i	i	PRON
ejpam-5080	229	4	=	=	NOUN
ejpam-5080	229	5	0	0	NUM
ejpam-5080	229	6	,	,	PUNCT
ejpam-5080	229	7	1	1	NUM
ejpam-5080	229	8	,	,	PUNCT
ejpam-5080	229	9	2	2	NUM
ejpam-5080	229	10	,	,	PUNCT
ejpam-5080	229	11	·	·	PUNCT
ejpam-5080	229	12	·	·	PUNCT
ejpam-5080	229	13	·	·	PUNCT
ejpam-5080	230	1	(	(	PUNCT
ejpam-5080	230	2	55	55	NUM
ejpam-5080	230	3	)	)	PUNCT
ejpam-5080	230	4	such	such	ADJ
ejpam-5080	230	5	that	that	PRON
ejpam-5080	230	6	for	for	ADP
ejpam-5080	230	7	α	α	NOUN
ejpam-5080	230	8	=	=	SYM
ejpam-5080	230	9	1	1	NUM
ejpam-5080	230	10	,	,	PUNCT
ejpam-5080	230	11	we	we	PRON
ejpam-5080	230	12	get	get	VERB
ejpam-5080	230	13	g(x	g(x	NOUN
ejpam-5080	230	14	)	)	PUNCT
ejpam-5080	231	1	≈	≈	NOUN
ejpam-5080	231	2	−0.000017465407	−0.000017465407	PROPN
ejpam-5080	231	3	+	+	CCONJ
ejpam-5080	231	4	2.000848250x−	2.000848250x−	NUM
ejpam-5080	231	5	0.0119838208x2	0.0119838208x2	NUM
ejpam-5080	231	6	+	+	CCONJ
ejpam-5080	231	7	·	·	PUNCT
ejpam-5080	231	8	·	·	PUNCT
ejpam-5080	231	9	·	·	PUNCT
ejpam-5080	232	1	−	−	ADP
ejpam-5080	232	2	0.4708946817x6	0.4708946817x6	NUM
ejpam-5080	232	3	.	.	PUNCT
ejpam-5080	233	1	(	(	PUNCT
ejpam-5080	233	2	56	56	NUM
ejpam-5080	233	3	)	)	PUNCT
ejpam-5080	233	4	n.	n.	NOUN
ejpam-5080	233	5	alzaid	alzaid	PROPN
ejpam-5080	233	6	et	et	PROPN
ejpam-5080	233	7	al	al	PROPN
ejpam-5080	233	8	.	.	PUNCT
ejpam-5080	233	9	/	/	SYM
ejpam-5080	233	10	eur	eur	PROPN
ejpam-5080	233	11	.	.	PUNCT
ejpam-5080	234	1	j.	j.	PROPN
ejpam-5080	234	2	pure	pure	PROPN
ejpam-5080	234	3	appl	appl	PROPN
ejpam-5080	234	4	.	.	PROPN
ejpam-5080	234	5	math	math	PROPN
ejpam-5080	234	6	,	,	PUNCT
ejpam-5080	234	7	17	17	NUM
ejpam-5080	234	8	(	(	PUNCT
ejpam-5080	234	9	3	3	NUM
ejpam-5080	234	10	)	)	PUNCT
ejpam-5080	234	11	(	(	PUNCT
ejpam-5080	234	12	2024	2024	NUM
ejpam-5080	234	13	)	)	PUNCT
ejpam-5080	234	14	,	,	PUNCT
ejpam-5080	234	15	1982	1982	NUM
ejpam-5080	234	16	-	-	SYM
ejpam-5080	234	17	2000	2000	NUM
ejpam-5080	234	18	1993	1993	NUM
ejpam-5080	234	19	accodingly	accodingly	ADV
ejpam-5080	234	20	,	,	PUNCT
ejpam-5080	234	21	we	we	PRON
ejpam-5080	234	22	get	get	VERB
ejpam-5080	234	23	u0	u0	ADJ
ejpam-5080	234	24	=	=	SYM
ejpam-5080	234	25	u(0	u(0	NOUN
ejpam-5080	234	26	)	)	PUNCT
ejpam-5080	235	1	+	+	CCONJ
ejpam-5080	235	2	xu′(0	xu′(0	NOUN
ejpam-5080	235	3	)	)	PUNCT
ejpam-5080	236	1	+	+	CCONJ
ejpam-5080	236	2	l−1(−0.000017465407	l−1(−0.000017465407	PROPN
ejpam-5080	236	3	+	+	CCONJ
ejpam-5080	236	4	2.000848250x−	2.000848250x−	NUM
ejpam-5080	236	5	0.0119838208x2	0.0119838208x2	NUM
ejpam-5080	236	6	+	+	CCONJ
ejpam-5080	236	7	·	·	PUNCT
ejpam-5080	236	8	·	·	PUNCT
ejpam-5080	236	9	·	·	PUNCT
ejpam-5080	237	1	−	−	ADP
ejpam-5080	237	2	0.4708946817x6	0.4708946817x6	NUM
ejpam-5080	237	3	)	)	PUNCT
ejpam-5080	237	4	,	,	PUNCT
ejpam-5080	237	5	=	=	SYM
ejpam-5080	237	6	x−	x−	NOUN
ejpam-5080	237	7	0.0000087327035x2	0.0000087327035x2	NUM
ejpam-5080	237	8	+	+	CCONJ
ejpam-5080	237	9	0.3334747083x3	0.3334747083x3	NUM
ejpam-5080	237	10	+	+	X
ejpam-5080	237	11	·	·	PUNCT
ejpam-5080	237	12	·	·	PUNCT
ejpam-5080	237	13	·	·	PUNCT
ejpam-5080	238	1	−	−	PROPN
ejpam-5080	238	2	0.008408833601x8	0.008408833601x8	NUM
ejpam-5080	238	3	,	,	PUNCT
ejpam-5080	238	4	u1	u1	NOUN
ejpam-5080	238	5	=	=	PUNCT
ejpam-5080	238	6	−0.5x3	−0.5x3	NOUN
ejpam-5080	238	7	+	+	NUM
ejpam-5080	238	8	0.000002183175875x4	0.000002183175875x4	NOUN
ejpam-5080	238	9	+	+	CCONJ
ejpam-5080	238	10	·	·	PUNCT
ejpam-5080	238	11	·	·	PUNCT
ejpam-5080	238	12	·	·	PUNCT
ejpam-5080	238	13	,	,	PUNCT
ejpam-5080	238	14	u2	u2	NOUN
ejpam-5080	238	15	=	=	NOUN
ejpam-5080	238	16	0.075x5	0.075x5	NUM
ejpam-5080	239	1	−	−	NUM
ejpam-5080	239	2	2.183175875×	2.183175875×	NOUN
ejpam-5080	239	3	10−7x6	10−7x6	NUM
ejpam-5080	239	4	+	+	X
ejpam-5080	239	5	·	·	PUNCT
ejpam-5080	239	6	·	·	PUNCT
ejpam-5080	239	7	·	·	PUNCT
ejpam-5080	239	8	,	,	PUNCT
ejpam-5080	239	9	u3	u3	NOUN
ejpam-5080	239	10	=	=	SYM
ejpam-5080	239	11	−0.005357142858x7	−0.005357142858x7	X
ejpam-5080	239	12	+	+	X
ejpam-5080	239	13	·	·	PUNCT
ejpam-5080	239	14	·	·	PUNCT
ejpam-5080	239	15	·	·	PUNCT
ejpam-5080	239	16	,	,	PUNCT
ejpam-5080	239	17	...	...	PUNCT
ejpam-5080	239	18	that	that	PRON
ejpam-5080	239	19	leads	lead	VERB
ejpam-5080	239	20	to	to	ADP
ejpam-5080	239	21	the	the	DET
ejpam-5080	239	22	following	follow	VERB
ejpam-5080	239	23	series	series	NOUN
ejpam-5080	239	24	solution	solution	NOUN
ejpam-5080	239	25	ug(x	ug(x	PUNCT
ejpam-5080	239	26	)	)	PUNCT
ejpam-5080	240	1	=	=	SYM
ejpam-5080	240	2	6∑	6∑	PROPN
ejpam-5080	240	3	n=0	n=0	NUM
ejpam-5080	240	4	un(x	un(x	SYM
ejpam-5080	240	5	)	)	PUNCT
ejpam-5080	240	6	=	=	SYM
ejpam-5080	240	7	x−	x−	PROPN
ejpam-5080	240	8	0.0000087327035x2	0.0000087327035x2	NUM
ejpam-5080	240	9	−	−	NOUN
ejpam-5080	240	10	0.1665252918x3	0.1665252918x3	NUM
ejpam-5080	240	11	−	−	NOUN
ejpam-5080	240	12	0.0009964685573x4	0.0009964685573x4	NUM
ejpam-5080	240	13	+	+	NUM
ejpam-5080	240	14	·	·	PUNCT
ejpam-5080	240	15	·	·	PUNCT
ejpam-5080	240	16	·	·	PUNCT
ejpam-5080	240	17	(	(	PUNCT
ejpam-5080	240	18	57	57	NUM
ejpam-5080	240	19	)	)	PUNCT
ejpam-5080	240	20	modification	modification	NOUN
ejpam-5080	240	21	method	method	NOUN
ejpam-5080	240	22	via	via	ADP
ejpam-5080	240	23	jacobi	jacobi	PROPN
ejpam-5080	240	24	’s	’s	PART
ejpam-5080	240	25	polynomials	polynomial	NOUN
ejpam-5080	240	26	also	also	ADV
ejpam-5080	240	27	goes	go	VERB
ejpam-5080	240	28	as	as	SCONJ
ejpam-5080	240	29	explained	explain	VERB
ejpam-5080	240	30	by	by	ADP
ejpam-5080	240	31	expanding	expand	VERB
ejpam-5080	240	32	g(x	g(x	PROPN
ejpam-5080	240	33	)	)	PUNCT
ejpam-5080	240	34	as	as	ADP
ejpam-5080	240	35	g(x	g(x	NOUN
ejpam-5080	240	36	)	)	PUNCT
ejpam-5080	241	1	=	=	SYM
ejpam-5080	241	2	6∑	6∑	NUM
ejpam-5080	241	3	n=0	n=0	ADJ
ejpam-5080	242	1	cnp	cnp	NOUN
ejpam-5080	242	2	(	(	PUNCT
ejpam-5080	242	3	α	α	NOUN
ejpam-5080	242	4	,	,	PUNCT
ejpam-5080	242	5	β	β	NOUN
ejpam-5080	242	6	)	)	PUNCT
ejpam-5080	242	7	n	n	PROPN
ejpam-5080	242	8	(	(	PUNCT
ejpam-5080	242	9	2x−	2x−	PROPN
ejpam-5080	242	10	1	1	NUM
ejpam-5080	242	11	)	)	PUNCT
ejpam-5080	242	12	,	,	PUNCT
ejpam-5080	242	13	0	0	NUM
ejpam-5080	242	14	≤	≤	NUM
ejpam-5080	242	15	x	x	SYM
ejpam-5080	242	16	≤	≤	NUM
ejpam-5080	242	17	1	1	NUM
ejpam-5080	242	18	(	(	PUNCT
ejpam-5080	242	19	58	58	NUM
ejpam-5080	242	20	)	)	PUNCT
ejpam-5080	242	21	where	where	SCONJ
ejpam-5080	242	22	pn	pn	PROPN
ejpam-5080	242	23	(	(	PUNCT
ejpam-5080	242	24	.	.	PUNCT
ejpam-5080	242	25	)	)	PUNCT
ejpam-5080	242	26	are	be	AUX
ejpam-5080	242	27	orthogonal	orthogonal	ADJ
ejpam-5080	242	28	jacobi	jacobi	PROPN
ejpam-5080	242	29	’s	’s	PART
ejpam-5080	242	30	polynomials	polynomial	NOUN
ejpam-5080	242	31	,	,	PUNCT
ejpam-5080	242	32	and	and	CCONJ
ejpam-5080	242	33	ci	ci	NOUN
ejpam-5080	242	34	are	be	AUX
ejpam-5080	242	35	given	give	VERB
ejpam-5080	242	36	by	by	ADP
ejpam-5080	242	37	ci	ci	NOUN
ejpam-5080	242	38	=	=	SYM
ejpam-5080	242	39	∫	∫	PROPN
ejpam-5080	242	40	1	1	NUM
ejpam-5080	242	41	−1	−1	NOUN
ejpam-5080	242	42	g(0.5x+	g(0.5x+	NOUN
ejpam-5080	242	43	0.5)p	0.5)p	PUNCT
ejpam-5080	242	44	(	(	PUNCT
ejpam-5080	242	45	α	α	X
ejpam-5080	242	46	,	,	PUNCT
ejpam-5080	242	47	β	β	NOUN
ejpam-5080	242	48	)	)	PUNCT
ejpam-5080	242	49	i	i	PRON
ejpam-5080	242	50	(	(	PUNCT
ejpam-5080	242	51	x)(1−	x)(1−	PROPN
ejpam-5080	242	52	x)α(1	x)α(1	PROPN
ejpam-5080	242	53	+	+	NUM
ejpam-5080	243	1	x)βdx∫	x)βdx∫	PROPN
ejpam-5080	243	2	1	1	NUM
ejpam-5080	243	3	−1[p	−1[p	PROPN
ejpam-5080	243	4	(	(	PUNCT
ejpam-5080	243	5	α	α	X
ejpam-5080	243	6	,	,	PUNCT
ejpam-5080	243	7	β	β	NOUN
ejpam-5080	243	8	)	)	PUNCT
ejpam-5080	243	9	i	i	PRON
ejpam-5080	243	10	(	(	PUNCT
ejpam-5080	243	11	x)]2(1−	x)]2(1−	PUNCT
ejpam-5080	243	12	x)α(1	x)α(1	PROPN
ejpam-5080	243	13	+	+	CCONJ
ejpam-5080	243	14	x)βdx	x)βdx	PROPN
ejpam-5080	243	15	,	,	PUNCT
ejpam-5080	243	16	i	i	PRON
ejpam-5080	243	17	=	=	NOUN
ejpam-5080	243	18	0	0	NUM
ejpam-5080	243	19	,	,	PUNCT
ejpam-5080	243	20	1	1	NUM
ejpam-5080	243	21	,	,	PUNCT
ejpam-5080	243	22	2	2	NUM
ejpam-5080	243	23	,	,	PUNCT
ejpam-5080	243	24	·	·	PUNCT
ejpam-5080	243	25	·	·	PUNCT
ejpam-5080	243	26	·	·	PUNCT
ejpam-5080	243	27	(	(	PUNCT
ejpam-5080	243	28	59	59	NUM
ejpam-5080	243	29	)	)	PUNCT
ejpam-5080	243	30	such	such	ADJ
ejpam-5080	243	31	that	that	PRON
ejpam-5080	243	32	for	for	ADP
ejpam-5080	243	33	α	α	NOUN
ejpam-5080	243	34	=	=	SYM
ejpam-5080	243	35	β	β	X
ejpam-5080	243	36	=	=	SYM
ejpam-5080	243	37	1	1	NUM
ejpam-5080	243	38	,	,	PUNCT
ejpam-5080	243	39	one	one	PRON
ejpam-5080	243	40	gets	get	VERB
ejpam-5080	243	41	g(x	g(x	NOUN
ejpam-5080	243	42	)	)	PUNCT
ejpam-5080	244	1	≈	≈	PROPN
ejpam-5080	244	2	0.0001041764	0.0001041764	NUM
ejpam-5080	245	1	+	+	CCONJ
ejpam-5080	245	2	1.997243414x+	1.997243414x+	NUM
ejpam-5080	245	3	0.020167913x2	0.020167913x2	NUM
ejpam-5080	245	4	+	+	CCONJ
ejpam-5080	245	5	·	·	PUNCT
ejpam-5080	245	6	·	·	PUNCT
ejpam-5080	245	7	·	·	PUNCT
ejpam-5080	246	1	−	−	PUNCT
ejpam-5080	246	2	0.3992660100x6	0.3992660100x6	NUM
ejpam-5080	246	3	.	.	PUNCT
ejpam-5080	247	1	(	(	PUNCT
ejpam-5080	247	2	60	60	NUM
ejpam-5080	247	3	)	)	PUNCT
ejpam-5080	247	4	in	in	ADP
ejpam-5080	247	5	the	the	DET
ejpam-5080	247	6	same	same	ADJ
ejpam-5080	247	7	manner	manner	NOUN
ejpam-5080	247	8	,	,	PUNCT
ejpam-5080	247	9	we	we	PRON
ejpam-5080	247	10	get	get	VERB
ejpam-5080	247	11	the	the	DET
ejpam-5080	247	12	following	follow	VERB
ejpam-5080	247	13	solution	solution	NOUN
ejpam-5080	247	14	components	component	NOUN
ejpam-5080	247	15	u0	u0	PROPN
ejpam-5080	247	16	=	=	PROPN
ejpam-5080	247	17	u(0	u(0	PROPN
ejpam-5080	247	18	)	)	PUNCT
ejpam-5080	248	1	+	+	CCONJ
ejpam-5080	248	2	xu′(0	xu′(0	NOUN
ejpam-5080	248	3	)	)	PUNCT
ejpam-5080	249	1	+	+	CCONJ
ejpam-5080	249	2	l−1(0.0001041764	l−1(0.0001041764	PROPN
ejpam-5080	249	3	+	+	CCONJ
ejpam-5080	249	4	1.997243414x+	1.997243414x+	NUM
ejpam-5080	249	5	0.020167913x2	0.020167913x2	NUM
ejpam-5080	249	6	+	+	CCONJ
ejpam-5080	249	7	·	·	PUNCT
ejpam-5080	249	8	·	·	PUNCT
ejpam-5080	249	9	·	·	PUNCT
ejpam-5080	250	1	−	−	PROPN
ejpam-5080	250	2	0.3992660100x6	0.3992660100x6	NUM
ejpam-5080	250	3	)	)	PUNCT
ejpam-5080	250	4	,	,	PUNCT
ejpam-5080	250	5	=	=	PUNCT
ejpam-5080	250	6	x+	x+	PUNCT
ejpam-5080	250	7	0.0000520882000x2	0.0000520882000x2	NUM
ejpam-5080	251	1	+	+	CCONJ
ejpam-5080	251	2	0.332873902x3	0.332873902x3	NUM
ejpam-5080	251	3	+	+	X
ejpam-5080	251	4	·	·	PUNCT
ejpam-5080	251	5	·	·	PUNCT
ejpam-5080	251	6	·	·	PUNCT
ejpam-5080	252	1	−	−	NOUN
ejpam-5080	252	2	0.007129750179x8	0.007129750179x8	NUM
ejpam-5080	252	3	,	,	PUNCT
ejpam-5080	252	4	u1	u1	NOUN
ejpam-5080	252	5	=	=	PUNCT
ejpam-5080	252	6	−0.5x3	−0.5x3	NOUN
ejpam-5080	252	7	−	−	NOUN
ejpam-5080	252	8	0.00001302205000x4	0.00001302205000x4	X
ejpam-5080	252	9	+	+	CCONJ
ejpam-5080	252	10	·	·	PUNCT
ejpam-5080	252	11	·	·	PUNCT
ejpam-5080	252	12	·	·	PUNCT
ejpam-5080	252	13	,	,	PUNCT
ejpam-5080	252	14	u2	u2	NOUN
ejpam-5080	252	15	=	=	NOUN
ejpam-5080	252	16	0.075x5	0.075x5	NOUN
ejpam-5080	253	1	+	+	CCONJ
ejpam-5080	253	2	1.30220500×	1.30220500×	NUM
ejpam-5080	253	3	10−6x6	10−6x6	NUM
ejpam-5080	253	4	+	+	NUM
ejpam-5080	253	5	·	·	PUNCT
ejpam-5080	253	6	·	·	PUNCT
ejpam-5080	253	7	·	·	PUNCT
ejpam-5080	253	8	,	,	PUNCT
ejpam-5080	253	9	u3	u3	NOUN
ejpam-5080	253	10	=	=	PUNCT
ejpam-5080	253	11	−0.00535714285x7	−0.00535714285x7	NOUN
ejpam-5080	253	12	+	+	X
ejpam-5080	253	13	·	·	PUNCT
ejpam-5080	253	14	·	·	PUNCT
ejpam-5080	253	15	·	·	PUNCT
ejpam-5080	253	16	,	,	PUNCT
ejpam-5080	253	17	...	...	PUNCT
ejpam-5080	253	18	that	that	PRON
ejpam-5080	253	19	sums	sum	VERB
ejpam-5080	253	20	to	to	ADP
ejpam-5080	253	21	the	the	DET
ejpam-5080	253	22	following	follow	VERB
ejpam-5080	253	23	uj(x	uj(x	NOUN
ejpam-5080	253	24	)	)	PUNCT
ejpam-5080	254	1	=	=	SYM
ejpam-5080	254	2	6∑	6∑	PROPN
ejpam-5080	254	3	n=0	n=0	NUM
ejpam-5080	254	4	un(x	un(x	PUNCT
ejpam-5080	254	5	)	)	PUNCT
ejpam-5080	254	6	=	=	SYM
ejpam-5080	255	1	x+	x+	X
ejpam-5080	255	2	0.00005208820000x2	0.00005208820000x2	X
ejpam-5080	256	1	−	−	NOUN
ejpam-5080	256	2	0.1671260977x3	0.1671260977x3	NUM
ejpam-5080	257	1	+	+	CCONJ
ejpam-5080	257	2	0.00166763736x4	0.00166763736x4	NUM
ejpam-5080	258	1	+	+	CCONJ
ejpam-5080	258	2	·	·	PUNCT
ejpam-5080	258	3	·	·	PUNCT
ejpam-5080	258	4	·	·	PUNCT
ejpam-5080	258	5	(	(	PUNCT
ejpam-5080	258	6	61	61	NUM
ejpam-5080	258	7	)	)	PUNCT
ejpam-5080	258	8	n.	n.	NOUN
ejpam-5080	258	9	alzaid	alzaid	PROPN
ejpam-5080	258	10	et	et	PROPN
ejpam-5080	258	11	al	al	PROPN
ejpam-5080	258	12	.	.	PUNCT
ejpam-5080	258	13	/	/	SYM
ejpam-5080	258	14	eur	eur	PROPN
ejpam-5080	258	15	.	.	PUNCT
ejpam-5080	259	1	j.	j.	PROPN
ejpam-5080	259	2	pure	pure	PROPN
ejpam-5080	259	3	appl	appl	PROPN
ejpam-5080	259	4	.	.	PROPN
ejpam-5080	259	5	math	math	PROPN
ejpam-5080	259	6	,	,	PUNCT
ejpam-5080	259	7	17	17	NUM
ejpam-5080	259	8	(	(	PUNCT
ejpam-5080	259	9	3	3	NUM
ejpam-5080	259	10	)	)	PUNCT
ejpam-5080	259	11	(	(	PUNCT
ejpam-5080	259	12	2024	2024	NUM
ejpam-5080	259	13	)	)	PUNCT
ejpam-5080	259	14	,	,	PUNCT
ejpam-5080	259	15	1982	1982	NUM
ejpam-5080	259	16	-	-	SYM
ejpam-5080	259	17	2000	2000	NUM
ejpam-5080	259	18	1994	1994	NUM
ejpam-5080	259	19	finally	finally	ADV
ejpam-5080	259	20	,	,	PUNCT
ejpam-5080	259	21	we	we	PRON
ejpam-5080	259	22	report	report	VERB
ejpam-5080	259	23	the	the	DET
ejpam-5080	259	24	absolute	absolute	ADJ
ejpam-5080	259	25	error	error	NOUN
ejpam-5080	259	26	differences	difference	NOUN
ejpam-5080	259	27	between	between	ADP
ejpam-5080	259	28	the	the	DET
ejpam-5080	259	29	exact	exact	ADJ
ejpam-5080	259	30	solution	solution	NOUN
ejpam-5080	259	31	u(x	u(x	NOUN
ejpam-5080	259	32	)	)	PUNCT
ejpam-5080	259	33	and	and	CCONJ
ejpam-5080	259	34	the	the	DET
ejpam-5080	259	35	respective	respective	ADJ
ejpam-5080	259	36	modification	modification	NOUN
ejpam-5080	259	37	solutions	solution	NOUN
ejpam-5080	259	38	in	in	ADP
ejpam-5080	259	39	table	table	NOUN
ejpam-5080	259	40	1	1	NUM
ejpam-5080	259	41	.	.	PUNCT
ejpam-5080	260	1	in	in	ADP
ejpam-5080	260	2	this	this	DET
ejpam-5080	260	3	table	table	NOUN
ejpam-5080	260	4	,	,	PUNCT
ejpam-5080	260	5	ut(x	ut(x	NOUN
ejpam-5080	260	6	)	)	PUNCT
ejpam-5080	260	7	stands	stand	VERB
ejpam-5080	260	8	for	for	ADP
ejpam-5080	260	9	the	the	DET
ejpam-5080	260	10	modification	modification	NOUN
ejpam-5080	260	11	via	via	ADP
ejpam-5080	260	12	the	the	DET
ejpam-5080	260	13	taylor	taylor	PROPN
ejpam-5080	260	14	series	series	PROPN
ejpam-5080	260	15	;	;	PUNCT
ejpam-5080	260	16	up	up	ADV
ejpam-5080	260	17	(	(	PUNCT
ejpam-5080	260	18	x	x	NOUN
ejpam-5080	260	19	)	)	PUNCT
ejpam-5080	260	20	via	via	ADP
ejpam-5080	260	21	the	the	DET
ejpam-5080	260	22	legendre	legendre	PROPN
ejpam-5080	260	23	’s	’s	PART
ejpam-5080	260	24	series	series	NOUN
ejpam-5080	260	25	;	;	PUNCT
ejpam-5080	260	26	ut	ut	PROPN
ejpam-5080	260	27	(	(	PUNCT
ejpam-5080	260	28	x	x	X
ejpam-5080	260	29	)	)	PUNCT
ejpam-5080	260	30	via	via	ADP
ejpam-5080	260	31	the	the	DET
ejpam-5080	260	32	chebyshev	chebyshev	PROPN
ejpam-5080	260	33	’s	’s	PART
ejpam-5080	260	34	series	series	NOUN
ejpam-5080	260	35	;	;	PUNCT
ejpam-5080	260	36	ul(x	ul(x	NOUN
ejpam-5080	260	37	)	)	PUNCT
ejpam-5080	260	38	via	via	ADP
ejpam-5080	260	39	the	the	DET
ejpam-5080	260	40	laguerre	laguerre	NOUN
ejpam-5080	260	41	’s	’s	PART
ejpam-5080	260	42	series	series	NOUN
ejpam-5080	260	43	;	;	PUNCT
ejpam-5080	260	44	uh(x	uh(x	NUM
ejpam-5080	260	45	)	)	PUNCT
ejpam-5080	260	46	via	via	ADP
ejpam-5080	260	47	the	the	DET
ejpam-5080	260	48	hermite	hermite	PROPN
ejpam-5080	260	49	’s	’s	PART
ejpam-5080	260	50	series	series	NOUN
ejpam-5080	260	51	;	;	PUNCT
ejpam-5080	260	52	ug(x	ug(x	X
ejpam-5080	260	53	)	)	PUNCT
ejpam-5080	260	54	via	via	ADP
ejpam-5080	260	55	the	the	DET
ejpam-5080	260	56	gegenbauer	gegenbauer	NOUN
ejpam-5080	260	57	’s	’s	PART
ejpam-5080	260	58	series	series	NOUN
ejpam-5080	260	59	(	(	PUNCT
ejpam-5080	260	60	α	α	NOUN
ejpam-5080	260	61	=	=	NOUN
ejpam-5080	260	62	1	1	NUM
ejpam-5080	260	63	)	)	PUNCT
ejpam-5080	260	64	;	;	PUNCT
ejpam-5080	260	65	and	and	CCONJ
ejpam-5080	260	66	finally	finally	ADV
ejpam-5080	260	67	uj(x	uj(x	PUNCT
ejpam-5080	260	68	)	)	PUNCT
ejpam-5080	260	69	via	via	ADP
ejpam-5080	260	70	the	the	DET
ejpam-5080	260	71	jacobi	jacobi	PROPN
ejpam-5080	260	72	series	series	PROPN
ejpam-5080	260	73	(	(	PUNCT
ejpam-5080	260	74	α	α	NOUN
ejpam-5080	260	75	=	=	SYM
ejpam-5080	260	76	1	1	NUM
ejpam-5080	260	77	,	,	PUNCT
ejpam-5080	260	78	β	β	X
ejpam-5080	260	79	=	=	SYM
ejpam-5080	260	80	1	1	NUM
ejpam-5080	260	81	)	)	PUNCT
ejpam-5080	260	82	.	.	PUNCT
ejpam-5080	261	1	table	table	NOUN
ejpam-5080	261	2	1	1	NUM
ejpam-5080	261	3	:	:	PUNCT
ejpam-5080	261	4	absolute	absolute	ADJ
ejpam-5080	261	5	error	error	NOUN
ejpam-5080	261	6	comparisons	comparison	NOUN
ejpam-5080	261	7	via	via	ADP
ejpam-5080	261	8	the	the	DET
ejpam-5080	261	9	proposed	propose	VERB
ejpam-5080	261	10	modifications	modification	NOUN
ejpam-5080	261	11	for	for	ADP
ejpam-5080	261	12	example	example	NOUN
ejpam-5080	261	13	1	1	NUM
ejpam-5080	261	14	x	x	NOUN
ejpam-5080	261	15	|u(x)−	|u(x)−	NOUN
ejpam-5080	261	16	ut(x)|	ut(x)|	VERB
ejpam-5080	261	17	|u(x)−	|u(x)−	PROPN
ejpam-5080	261	18	up	up	ADP
ejpam-5080	261	19	(	(	PUNCT
ejpam-5080	261	20	x)|	x)|	PROPN
ejpam-5080	261	21	|u(x)−	|u(x)−	PROPN
ejpam-5080	261	22	ut	ut	PROPN
ejpam-5080	262	1	(	(	PUNCT
ejpam-5080	262	2	x)|	x)|	PROPN
ejpam-5080	262	3	|u(x)−	|u(x)−	PROPN
ejpam-5080	262	4	ug(x)|	ug(x)|	VERB
ejpam-5080	262	5	|u(x)−	|u(x)−	PROPN
ejpam-5080	262	6	uj(x)|	uj(x)|	PROPN
ejpam-5080	262	7	0	0	NUM
ejpam-5080	262	8	0	0	NUM
ejpam-5080	262	9	0	0	NUM
ejpam-5080	262	10	0	0	NUM
ejpam-5080	262	11	0	0	NUM
ejpam-5080	262	12	0	0	NUM
ejpam-5080	262	13	0.25	0.25	NUM
ejpam-5080	262	14	1.130×	1.130×	NUM
ejpam-5080	262	15	10−8	10−8	NUM
ejpam-5080	262	16	1.50×	1.50×	NUM
ejpam-5080	262	17	10−9	10−9	NUM
ejpam-5080	262	18	6.80×	6.80×	SYM
ejpam-5080	262	19	10−9	10−9	NUM
ejpam-5080	262	20	2.750×	2.750×	NUM
ejpam-5080	262	21	10−8	10−8	NUM
ejpam-5080	262	22	3.852×	3.852×	NUM
ejpam-5080	262	23	10−7	10−7	NUM
ejpam-5080	262	24	0.50	0.50	NUM
ejpam-5080	263	1	5.743×	5.743×	NUM
ejpam-5080	263	2	10−6	10−6	NUM
ejpam-5080	263	3	5.10×	5.10×	NUM
ejpam-5080	263	4	10−9	10−9	NUM
ejpam-5080	263	5	2.680×	2.680×	NUM
ejpam-5080	263	6	10−8	10−8	NUM
ejpam-5080	263	7	5.050×	5.050×	NUM
ejpam-5080	263	8	10−8	10−8	NUM
ejpam-5080	263	9	8.532×	8.532×	NUM
ejpam-5080	263	10	10−7	10−7	NUM
ejpam-5080	263	11	0.75	0.75	NUM
ejpam-5080	263	12	2.154×	2.154×	NUM
ejpam-5080	263	13	10−4	10−4	NUM
ejpam-5080	263	14	1.508×	1.508×	NUM
ejpam-5080	263	15	10−7	10−7	NUM
ejpam-5080	263	16	1.710×	1.710×	NUM
ejpam-5080	263	17	10−7	10−7	NUM
ejpam-5080	263	18	7.830×	7.830×	NUM
ejpam-5080	263	19	10−8	10−8	NUM
ejpam-5080	263	20	1.199×	1.199×	NUM
ejpam-5080	264	1	10−6	10−6	NUM
ejpam-5080	264	2	1	1	NUM
ejpam-5080	264	3	2.790×	2.790×	NUM
ejpam-5080	264	4	10−3	10−3	NUM
ejpam-5080	264	5	1.365×	1.365×	NUM
ejpam-5080	264	6	10−6	10−6	NUM
ejpam-5080	264	7	1.394×	1.394×	NUM
ejpam-5080	264	8	10−6	10−6	NUM
ejpam-5080	264	9	1.272×	1.272×	NUM
ejpam-5080	264	10	10−6	10−6	NUM
ejpam-5080	265	1	2.724×	2.724×	NUM
ejpam-5080	265	2	10−6	10−6	NUM
ejpam-5080	266	1	x	x	X
ejpam-5080	266	2	|u(x)−	|u(x)−	PROPN
ejpam-5080	266	3	ul(x)|	ul(x)|	VERB
ejpam-5080	266	4	|u(x)−	|u(x)−	X
ejpam-5080	266	5	uh(x)|	uh(x)|	ADP
ejpam-5080	266	6	0	0	NUM
ejpam-5080	266	7	0	0	NUM
ejpam-5080	266	8	0	0	NUM
ejpam-5080	266	9	0.25	0.25	NUM
ejpam-5080	266	10	4.465×	4.465×	NUM
ejpam-5080	266	11	10−3	10−3	NUM
ejpam-5080	266	12	1.444×	1.444×	NUM
ejpam-5080	266	13	10−3	10−3	NUM
ejpam-5080	266	14	0.50	0.50	NUM
ejpam-5080	267	1	6.491×	6.491×	NUM
ejpam-5080	267	2	10−3	10−3	NUM
ejpam-5080	267	3	9.756×	9.756×	NUM
ejpam-5080	267	4	10−3	10−3	NUM
ejpam-5080	267	5	0.75	0.75	NUM
ejpam-5080	267	6	3.965×	3.965×	NUM
ejpam-5080	267	7	10−3	10−3	NUM
ejpam-5080	267	8	2.484×	2.484×	NUM
ejpam-5080	267	9	10−2	10−2	NUM
ejpam-5080	267	10	1	1	NUM
ejpam-5080	267	11	2.387×	2.387×	NUM
ejpam-5080	267	12	10−2	10−2	NUM
ejpam-5080	267	13	3.959×	3.959×	NUM
ejpam-5080	267	14	10−2	10−2	NUM
ejpam-5080	267	15	example	example	NOUN
ejpam-5080	267	16	2	2	NUM
ejpam-5080	267	17	.	.	X
ejpam-5080	267	18	consider	consider	VERB
ejpam-5080	267	19	the	the	DET
ejpam-5080	267	20	following	follow	VERB
ejpam-5080	267	21	nonlinear	nonlinear	ADJ
ejpam-5080	267	22	ivp	ivp	NOUN
ejpam-5080	267	23	of	of	ADP
ejpam-5080	267	24	ode	ode	PROPN
ejpam-5080	268	1	[	[	X
ejpam-5080	268	2	7	7	NUM
ejpam-5080	268	3	]	]	X
ejpam-5080	268	4	u′′	u′′	PROPN
ejpam-5080	268	5	+	+	CCONJ
ejpam-5080	268	6	uu′	uu′	PROPN
ejpam-5080	268	7	=	=	SYM
ejpam-5080	268	8	2	2	NUM
ejpam-5080	268	9	cos(x2	cos(x2	NOUN
ejpam-5080	268	10	)	)	PUNCT
ejpam-5080	269	1	+	+	CCONJ
ejpam-5080	269	2	x	x	SYM
ejpam-5080	269	3	sin(2x2)−	sin(2x2)−	VERB
ejpam-5080	269	4	4x2	4x2	NUM
ejpam-5080	269	5	sin(x2	sin(x2	NOUN
ejpam-5080	269	6	)	)	PUNCT
ejpam-5080	269	7	,	,	PUNCT
ejpam-5080	269	8	0	0	NUM
ejpam-5080	269	9	≤	≤	NUM
ejpam-5080	269	10	x	x	SYM
ejpam-5080	269	11	≤	≤	NUM
ejpam-5080	269	12	1	1	NUM
ejpam-5080	269	13	,	,	PUNCT
ejpam-5080	269	14	u(0	u(0	NOUN
ejpam-5080	269	15	)	)	PUNCT
ejpam-5080	269	16	=	=	SYM
ejpam-5080	269	17	0	0	NUM
ejpam-5080	269	18	,	,	PUNCT
ejpam-5080	269	19	u′(0	u′(0	PROPN
ejpam-5080	269	20	)	)	PUNCT
ejpam-5080	269	21	=	=	SYM
ejpam-5080	269	22	0	0	NUM
ejpam-5080	269	23	,	,	PUNCT
ejpam-5080	269	24	(	(	PUNCT
ejpam-5080	269	25	62	62	NUM
ejpam-5080	269	26	)	)	PUNCT
ejpam-5080	269	27	admiting	admit	VERB
ejpam-5080	269	28	the	the	DET
ejpam-5080	269	29	exact	exact	ADJ
ejpam-5080	269	30	solution	solution	NOUN
ejpam-5080	269	31	u(x	u(x	NOUN
ejpam-5080	269	32	)	)	PUNCT
ejpam-5080	269	33	=	=	SYM
ejpam-5080	269	34	sin(x2	sin(x2	NOUN
ejpam-5080	269	35	)	)	PUNCT
ejpam-5080	269	36	.	.	PUNCT
ejpam-5080	270	1	as	as	ADP
ejpam-5080	270	2	in	in	ADP
ejpam-5080	270	3	the	the	DET
ejpam-5080	270	4	preceding	precede	VERB
ejpam-5080	270	5	example	example	NOUN
ejpam-5080	270	6	1	1	NUM
ejpam-5080	270	7	,	,	PUNCT
ejpam-5080	270	8	we	we	PRON
ejpam-5080	270	9	start	start	VERB
ejpam-5080	270	10	off	off	ADP
ejpam-5080	270	11	by	by	ADP
ejpam-5080	270	12	expressing	express	VERB
ejpam-5080	270	13	the	the	DET
ejpam-5080	270	14	governing	govern	VERB
ejpam-5080	270	15	model	model	NOUN
ejpam-5080	270	16	in	in	ADP
ejpam-5080	270	17	the	the	DET
ejpam-5080	270	18	adm	adm	NOUN
ejpam-5080	270	19	operator	operator	NOUN
ejpam-5080	270	20	form	form	NOUN
ejpam-5080	270	21	u	u	NOUN
ejpam-5080	270	22	=	=	PROPN
ejpam-5080	270	23	l−1(2	l−1(2	PROPN
ejpam-5080	270	24	cos(x2	cos(x2	NOUN
ejpam-5080	270	25	)	)	PUNCT
ejpam-5080	271	1	+	+	CCONJ
ejpam-5080	271	2	x	x	PUNCT
ejpam-5080	271	3	sin(2x2)−	sin(2x2)−	VERB
ejpam-5080	271	4	4x2	4x2	NUM
ejpam-5080	272	1	sin(x2))−	sin(x2))−	PROPN
ejpam-5080	272	2	l−1(uu′	l−1(uu′	PROPN
ejpam-5080	272	3	)	)	PUNCT
ejpam-5080	272	4	,	,	PUNCT
ejpam-5080	272	5	(	(	PUNCT
ejpam-5080	272	6	63	63	NUM
ejpam-5080	272	7	)	)	PUNCT
ejpam-5080	272	8	where	where	SCONJ
ejpam-5080	272	9	the	the	DET
ejpam-5080	272	10	inverse	inverse	NOUN
ejpam-5080	272	11	operator	operator	NOUN
ejpam-5080	272	12	takes	take	VERB
ejpam-5080	272	13	the	the	DET
ejpam-5080	272	14	expression	expression	NOUN
ejpam-5080	272	15	l−1	l−1	PROPN
ejpam-5080	272	16	(	(	PUNCT
ejpam-5080	272	17	.	.	PUNCT
ejpam-5080	272	18	)	)	PUNCT
ejpam-5080	273	1	=	=	PUNCT
ejpam-5080	274	1	∫	∫	PUNCT
ejpam-5080	274	2	x	x	SYM
ejpam-5080	274	3	0	0	NUM
ejpam-5080	274	4	∫	∫	PROPN
ejpam-5080	274	5	x	x	SYM
ejpam-5080	274	6	0	0	PUNCT
ejpam-5080	274	7	(	(	PUNCT
ejpam-5080	274	8	.)dxdx	.)dxdx	PROPN
ejpam-5080	274	9	and	and	CCONJ
ejpam-5080	274	10	n(u	n(u	PROPN
ejpam-5080	274	11	)	)	PUNCT
ejpam-5080	274	12	=	=	SYM
ejpam-5080	274	13	uu′.	uu′.	PROPN
ejpam-5080	274	14	substituting	substitute	VERB
ejpam-5080	274	15	eqs	eqs	PROPN
ejpam-5080	274	16	.	.	PUNCT
ejpam-5080	275	1	(	(	PUNCT
ejpam-5080	275	2	5	5	NUM
ejpam-5080	275	3	)	)	PUNCT
ejpam-5080	275	4	and	and	CCONJ
ejpam-5080	275	5	(	(	PUNCT
ejpam-5080	275	6	6	6	NUM
ejpam-5080	275	7	)	)	PUNCT
ejpam-5080	275	8	into	into	ADP
ejpam-5080	275	9	eq	eq	NOUN
ejpam-5080	275	10	.	.	PUNCT
ejpam-5080	276	1	(	(	PUNCT
ejpam-5080	276	2	63	63	NUM
ejpam-5080	276	3	)	)	PUNCT
ejpam-5080	276	4	,	,	PUNCT
ejpam-5080	276	5	we	we	PRON
ejpam-5080	276	6	get	get	VERB
ejpam-5080	276	7	the	the	DET
ejpam-5080	276	8	following	follow	VERB
ejpam-5080	276	9	recursive	recursive	ADJ
ejpam-5080	276	10	solution	solution	NOUN
ejpam-5080	276	11	u0	u0	NOUN
ejpam-5080	276	12	=	=	NOUN
ejpam-5080	276	13	l−1(2cos(x2	l−1(2cos(x2	NOUN
ejpam-5080	276	14	)	)	PUNCT
ejpam-5080	277	1	+	+	CCONJ
ejpam-5080	277	2	xsin(2x2)−	xsin(2x2)−	ADJ
ejpam-5080	277	3	4x2	4x2	NUM
ejpam-5080	277	4	sin(x2	sin(x2	NOUN
ejpam-5080	277	5	)	)	PUNCT
ejpam-5080	277	6	)	)	PUNCT
ejpam-5080	277	7	,	,	PUNCT
ejpam-5080	278	1	un+1	un+1	NOUN
ejpam-5080	278	2	=	=	SYM
ejpam-5080	278	3	−l−1an(u0	−l−1an(u0	NOUN
ejpam-5080	278	4	,	,	PUNCT
ejpam-5080	278	5	u1	u1	NOUN
ejpam-5080	278	6	,	,	PUNCT
ejpam-5080	278	7	·	·	PUNCT
ejpam-5080	278	8	·	·	PUNCT
ejpam-5080	278	9	·	·	PUNCT
ejpam-5080	278	10	)	)	PUNCT
ejpam-5080	278	11	,	,	PUNCT
ejpam-5080	278	12	n	n	X
ejpam-5080	278	13	≥	≥	NOUN
ejpam-5080	278	14	0	0	NUM
ejpam-5080	278	15	,	,	PUNCT
ejpam-5080	278	16	from	from	ADP
ejpam-5080	278	17	eq	eq	ADP
ejpam-5080	278	18	.	.	PUNCT
ejpam-5080	279	1	(	(	PUNCT
ejpam-5080	279	2	7	7	NUM
ejpam-5080	279	3	)	)	PUNCT
ejpam-5080	279	4	,	,	PUNCT
ejpam-5080	279	5	the	the	DET
ejpam-5080	279	6	nonlinear	nonlinear	ADJ
ejpam-5080	279	7	term	term	NOUN
ejpam-5080	279	8	n(u	n(u	PROPN
ejpam-5080	279	9	)	)	PUNCT
ejpam-5080	280	1	=	=	SYM
ejpam-5080	280	2	uu′	uu′	PROPN
ejpam-5080	280	3	is	be	AUX
ejpam-5080	280	4	also	also	ADV
ejpam-5080	280	5	expressed	express	VERB
ejpam-5080	280	6	through	through	ADP
ejpam-5080	280	7	the	the	DET
ejpam-5080	280	8	following	follow	VERB
ejpam-5080	280	9	adomian	adomian	NOUN
ejpam-5080	280	10	polynomials	polynomial	NOUN
ejpam-5080	280	11	n.	n.	PROPN
ejpam-5080	280	12	alzaid	alzaid	PROPN
ejpam-5080	281	1	et	et	PROPN
ejpam-5080	281	2	al	al	PROPN
ejpam-5080	281	3	.	.	PUNCT
ejpam-5080	281	4	/	/	SYM
ejpam-5080	281	5	eur	eur	PROPN
ejpam-5080	281	6	.	.	PUNCT
ejpam-5080	282	1	j.	j.	PROPN
ejpam-5080	282	2	pure	pure	PROPN
ejpam-5080	282	3	appl	appl	PROPN
ejpam-5080	282	4	.	.	PROPN
ejpam-5080	282	5	math	math	PROPN
ejpam-5080	282	6	,	,	PUNCT
ejpam-5080	282	7	17	17	NUM
ejpam-5080	282	8	(	(	PUNCT
ejpam-5080	282	9	3	3	NUM
ejpam-5080	282	10	)	)	PUNCT
ejpam-5080	282	11	(	(	PUNCT
ejpam-5080	282	12	2024	2024	NUM
ejpam-5080	282	13	)	)	PUNCT
ejpam-5080	282	14	,	,	PUNCT
ejpam-5080	282	15	1982	1982	NUM
ejpam-5080	282	16	-	-	SYM
ejpam-5080	282	17	2000	2000	NUM
ejpam-5080	282	18	1995	1995	NUM
ejpam-5080	282	19	a0	a0	NOUN
ejpam-5080	282	20	=	=	PUNCT
ejpam-5080	282	21	u0u	u0u	PROPN
ejpam-5080	283	1	′	′	NUM
ejpam-5080	283	2	0	0	NUM
ejpam-5080	283	3	,	,	PUNCT
ejpam-5080	283	4	a1	a1	NOUN
ejpam-5080	283	5	=	=	PUNCT
ejpam-5080	283	6	u1u	u1u	PROPN
ejpam-5080	283	7	′	′	NOUN
ejpam-5080	283	8	0	0	PUNCT
ejpam-5080	284	1	+	+	CCONJ
ejpam-5080	284	2	u0u	u0u	PRON
ejpam-5080	284	3	′	′	NUM
ejpam-5080	284	4	1	1	NUM
ejpam-5080	284	5	,	,	PUNCT
ejpam-5080	284	6	a2	a2	NOUN
ejpam-5080	284	7	=	=	PUNCT
ejpam-5080	284	8	u2u	u2u	ADJ
ejpam-5080	284	9	′	′	NOUN
ejpam-5080	284	10	0	0	PUNCT
ejpam-5080	285	1	+	+	CCONJ
ejpam-5080	285	2	u1u	u1u	ADJ
ejpam-5080	285	3	′	′	NOUN
ejpam-5080	285	4	1	1	NUM
ejpam-5080	286	1	+	+	CCONJ
ejpam-5080	286	2	u0u	u0u	PRON
ejpam-5080	286	3	′	′	NUM
ejpam-5080	286	4	2	2	NUM
ejpam-5080	286	5	,	,	PUNCT
ejpam-5080	286	6	a3	a3	NOUN
ejpam-5080	286	7	=	=	PUNCT
ejpam-5080	286	8	u3u	u3u	INTJ
ejpam-5080	287	1	′	′	NOUN
ejpam-5080	287	2	0	0	PUNCT
ejpam-5080	288	1	+	+	CCONJ
ejpam-5080	288	2	u2u	u2u	ADJ
ejpam-5080	288	3	′	′	NOUN
ejpam-5080	288	4	1	1	NUM
ejpam-5080	289	1	+	+	CCONJ
ejpam-5080	289	2	u1u	u1u	ADJ
ejpam-5080	289	3	′	′	NOUN
ejpam-5080	289	4	2	2	NUM
ejpam-5080	290	1	+	+	CCONJ
ejpam-5080	290	2	u0u	u0u	PRON
ejpam-5080	290	3	′	′	NUM
ejpam-5080	290	4	3	3	NUM
ejpam-5080	290	5	,	,	PUNCT
ejpam-5080	290	6	...	...	PUNCT
ejpam-5080	290	7	thus	thus	ADV
ejpam-5080	290	8	,	,	PUNCT
ejpam-5080	290	9	without	without	ADP
ejpam-5080	290	10	further	further	ADJ
ejpam-5080	290	11	delay	delay	NOUN
ejpam-5080	290	12	,	,	PUNCT
ejpam-5080	290	13	by	by	ADP
ejpam-5080	290	14	the	the	DET
ejpam-5080	290	15	same	same	ADJ
ejpam-5080	290	16	procedure	procedure	NOUN
ejpam-5080	290	17	as	as	ADP
ejpam-5080	290	18	in	in	ADP
ejpam-5080	290	19	example	example	NOUN
ejpam-5080	290	20	1	1	NUM
ejpam-5080	290	21	,	,	PUNCT
ejpam-5080	290	22	we	we	PRON
ejpam-5080	290	23	present	present	VERB
ejpam-5080	290	24	the	the	DET
ejpam-5080	290	25	respective	respective	ADJ
ejpam-5080	290	26	solution	solution	NOUN
ejpam-5080	290	27	via	via	ADP
ejpam-5080	290	28	the	the	DET
ejpam-5080	290	29	application	application	NOUN
ejpam-5080	290	30	of	of	ADP
ejpam-5080	290	31	the	the	DET
ejpam-5080	290	32	proposed	propose	VERB
ejpam-5080	290	33	modification	modification	NOUN
ejpam-5080	290	34	methods	method	NOUN
ejpam-5080	290	35	for	for	ADP
ejpam-5080	290	36	m	m	PROPN
ejpam-5080	290	37	=	=	NOUN
ejpam-5080	290	38	6	6	NUM
ejpam-5080	290	39	as	as	SCONJ
ejpam-5080	290	40	follows	follow	VERB
ejpam-5080	290	41	ut(x	ut(x	PUNCT
ejpam-5080	290	42	)	)	PUNCT
ejpam-5080	291	1	=	=	SYM
ejpam-5080	291	2	6∑	6∑	PROPN
ejpam-5080	291	3	n=0	n=0	NUM
ejpam-5080	291	4	un(x	un(x	PUNCT
ejpam-5080	291	5	)	)	PUNCT
ejpam-5080	291	6	=	=	SYM
ejpam-5080	292	1	x2	x2	NUM
ejpam-5080	292	2	−	−	NOUN
ejpam-5080	293	1	1	1	NUM
ejpam-5080	293	2	6	6	NUM
ejpam-5080	293	3	x6	x6	NOUN
ejpam-5080	293	4	+	+	CCONJ
ejpam-5080	293	5	1	1	NUM
ejpam-5080	293	6	54	54	NUM
ejpam-5080	293	7	x9	x9	NOUN
ejpam-5080	293	8	−	−	ADP
ejpam-5080	293	9	1	1	NUM
ejpam-5080	293	10	648	648	NUM
ejpam-5080	293	11	x12	x12	NUM
ejpam-5080	293	12	+	+	CCONJ
ejpam-5080	293	13	·	·	PUNCT
ejpam-5080	293	14	·	·	PUNCT
ejpam-5080	293	15	·	·	PUNCT
ejpam-5080	293	16	,	,	PUNCT
ejpam-5080	293	17	up	up	ADV
ejpam-5080	293	18	(	(	PUNCT
ejpam-5080	293	19	x	x	NOUN
ejpam-5080	293	20	)	)	PUNCT
ejpam-5080	293	21	=	=	SYM
ejpam-5080	293	22	6∑	6∑	PROPN
ejpam-5080	293	23	n=0	n=0	NUM
ejpam-5080	293	24	un(x	un(x	PUNCT
ejpam-5080	293	25	)	)	PUNCT
ejpam-5080	293	26	=	=	PUNCT
ejpam-5080	294	1	1.000731859x2	1.000731859x2	NUM
ejpam-5080	294	2	−	−	NOUN
ejpam-5080	294	3	0.01306146233x3	0.01306146233x3	NUM
ejpam-5080	294	4	+	+	CCONJ
ejpam-5080	294	5	0.08294338582x4	0.08294338582x4	NUM
ejpam-5080	294	6	+	+	X
ejpam-5080	294	7	·	·	PUNCT
ejpam-5080	294	8	·	·	PUNCT
ejpam-5080	294	9	·	·	PUNCT
ejpam-5080	294	10	,	,	PUNCT
ejpam-5080	294	11	ut	ut	PROPN
ejpam-5080	294	12	(	(	PUNCT
ejpam-5080	294	13	x	x	X
ejpam-5080	294	14	)	)	PUNCT
ejpam-5080	294	15	=	=	SYM
ejpam-5080	294	16	6∑	6∑	PROPN
ejpam-5080	294	17	n=0	n=0	NUM
ejpam-5080	294	18	un(x	un(x	SYM
ejpam-5080	294	19	)	)	PUNCT
ejpam-5080	294	20	=	=	SYM
ejpam-5080	295	1	1.000309776x2	1.000309776x2	NUM
ejpam-5080	295	2	−	−	NOUN
ejpam-5080	295	3	0.009680124167x3	0.009680124167x3	NUM
ejpam-5080	295	4	+	+	CCONJ
ejpam-5080	295	5	0.07289912332x4	0.07289912332x4	NUM
ejpam-5080	295	6	+	+	X
ejpam-5080	295	7	·	·	PUNCT
ejpam-5080	295	8	·	·	PUNCT
ejpam-5080	295	9	·	·	PUNCT
ejpam-5080	295	10	,	,	PUNCT
ejpam-5080	295	11	ul(x	ul(x	PROPN
ejpam-5080	295	12	)	)	PUNCT
ejpam-5080	296	1	=	=	SYM
ejpam-5080	296	2	6∑	6∑	PROPN
ejpam-5080	296	3	n=0	n=0	NUM
ejpam-5080	296	4	un(x	un(x	SYM
ejpam-5080	296	5	)	)	PUNCT
ejpam-5080	296	6	=	=	SYM
ejpam-5080	297	1	1.964424074x2	1.964424074x2	NUM
ejpam-5080	297	2	−	−	NOUN
ejpam-5080	297	3	1.747651757x3	1.747651757x3	NUM
ejpam-5080	298	1	+	+	CCONJ
ejpam-5080	298	2	0.5839657700x4	0.5839657700x4	NUM
ejpam-5080	298	3	+	+	CCONJ
ejpam-5080	298	4	·	·	PUNCT
ejpam-5080	298	5	·	·	PUNCT
ejpam-5080	298	6	·	·	PUNCT
ejpam-5080	298	7	uh(x	uh(x	X
ejpam-5080	298	8	)	)	PUNCT
ejpam-5080	298	9	=	=	SYM
ejpam-5080	299	1	6∑	6∑	PROPN
ejpam-5080	299	2	n=0	n=0	NUM
ejpam-5080	299	3	un(x	un(x	SYM
ejpam-5080	299	4	)	)	PUNCT
ejpam-5080	299	5	=	=	PUNCT
ejpam-5080	300	1	1.501201152x2	1.501201152x2	NUM
ejpam-5080	300	2	+	+	NUM
ejpam-5080	300	3	0.1619524511x3	0.1619524511x3	NUM
ejpam-5080	301	1	−	−	NOUN
ejpam-5080	301	2	0.7135433355x4	0.7135433355x4	NOUN
ejpam-5080	301	3	+	+	PUNCT
ejpam-5080	301	4	·	·	PUNCT
ejpam-5080	301	5	·	·	PUNCT
ejpam-5080	301	6	·	·	PUNCT
ejpam-5080	301	7	,	,	PUNCT
ejpam-5080	301	8	ug(x	ug(x	X
ejpam-5080	301	9	)	)	PUNCT
ejpam-5080	302	1	=	=	SYM
ejpam-5080	302	2	6∑	6∑	PROPN
ejpam-5080	302	3	n=0	n=0	NUM
ejpam-5080	302	4	un(x	un(x	SYM
ejpam-5080	302	5	)	)	PUNCT
ejpam-5080	302	6	=	=	SYM
ejpam-5080	303	1	1.001214606x2	1.001214606x2	NUM
ejpam-5080	303	2	−	−	NOUN
ejpam-5080	303	3	0.01625100983x3	0.01625100983x3	NUM
ejpam-5080	304	1	+	+	CCONJ
ejpam-5080	304	2	0.0916858975x4	0.0916858975x4	NUM
ejpam-5080	304	3	+	+	X
ejpam-5080	304	4	·	·	PUNCT
ejpam-5080	304	5	·	·	PUNCT
ejpam-5080	304	6	·	·	PUNCT
ejpam-5080	304	7	uj(x	uj(x	X
ejpam-5080	304	8	)	)	PUNCT
ejpam-5080	304	9	=	=	SYM
ejpam-5080	304	10	6∑	6∑	PROPN
ejpam-5080	304	11	n=0	n=0	NUM
ejpam-5080	304	12	un(x	un(x	PUNCT
ejpam-5080	304	13	)	)	PUNCT
ejpam-5080	304	14	=	=	PUNCT
ejpam-5080	305	1	1.001718846x2	1.001718846x2	NUM
ejpam-5080	305	2	−	−	NOUN
ejpam-5080	305	3	0.01916817000x3	0.01916817000x3	X
ejpam-5080	306	1	+	+	CCONJ
ejpam-5080	306	2	0.09913448668x4	0.09913448668x4	NUM
ejpam-5080	306	3	+	+	NUM
ejpam-5080	306	4	·	·	PUNCT
ejpam-5080	306	5	·	·	PUNCT
ejpam-5080	306	6	·	·	PUNCT
ejpam-5080	306	7	,	,	PUNCT
ejpam-5080	306	8	(	(	PUNCT
ejpam-5080	306	9	64	64	NUM
ejpam-5080	306	10	)	)	PUNCT
ejpam-5080	306	11	similarly	similarly	ADV
ejpam-5080	306	12	,	,	PUNCT
ejpam-5080	306	13	we	we	PRON
ejpam-5080	306	14	report	report	VERB
ejpam-5080	306	15	in	in	ADP
ejpam-5080	306	16	table	table	NOUN
ejpam-5080	306	17	2	2	NUM
ejpam-5080	306	18	the	the	DET
ejpam-5080	306	19	absolute	absolute	ADJ
ejpam-5080	306	20	error	error	NOUN
ejpam-5080	306	21	differences	difference	NOUN
ejpam-5080	306	22	between	between	ADP
ejpam-5080	306	23	the	the	DET
ejpam-5080	306	24	exact	exact	ADJ
ejpam-5080	306	25	solution	solution	NOUN
ejpam-5080	306	26	u(x	u(x	NOUN
ejpam-5080	306	27	)	)	PUNCT
ejpam-5080	306	28	and	and	CCONJ
ejpam-5080	306	29	the	the	DET
ejpam-5080	306	30	respective	respective	ADJ
ejpam-5080	306	31	solutions	solution	NOUN
ejpam-5080	306	32	by	by	ADP
ejpam-5080	306	33	the	the	DET
ejpam-5080	306	34	proposed	propose	VERB
ejpam-5080	306	35	modification	modification	NOUN
ejpam-5080	306	36	methods	method	NOUN
ejpam-5080	306	37	.	.	PUNCT
ejpam-5080	307	1	table	table	NOUN
ejpam-5080	307	2	2	2	NUM
ejpam-5080	307	3	:	:	PUNCT
ejpam-5080	307	4	absolute	absolute	ADJ
ejpam-5080	307	5	error	error	NOUN
ejpam-5080	307	6	comparisons	comparison	NOUN
ejpam-5080	307	7	via	via	ADP
ejpam-5080	307	8	the	the	DET
ejpam-5080	307	9	proposed	propose	VERB
ejpam-5080	307	10	modifications	modification	NOUN
ejpam-5080	307	11	for	for	ADP
ejpam-5080	307	12	example	example	NOUN
ejpam-5080	307	13	2	2	NUM
ejpam-5080	307	14	x	x	PART
ejpam-5080	307	15	|u(x)−	|u(x)−	NOUN
ejpam-5080	307	16	ut(x)|	ut(x)|	VERB
ejpam-5080	307	17	|u(x)−	|u(x)−	PROPN
ejpam-5080	307	18	up	up	ADP
ejpam-5080	307	19	(	(	PUNCT
ejpam-5080	307	20	x)|	x)|	PROPN
ejpam-5080	307	21	|u(x)−	|u(x)−	PROPN
ejpam-5080	307	22	ut	ut	PROPN
ejpam-5080	308	1	(	(	PUNCT
ejpam-5080	308	2	x)|	x)|	PROPN
ejpam-5080	308	3	|u(x)−	|u(x)−	PROPN
ejpam-5080	308	4	ug(x)|	ug(x)|	VERB
ejpam-5080	308	5	|u(x)−	|u(x)−	PROPN
ejpam-5080	308	6	uj(x)|	uj(x)|	PROPN
ejpam-5080	308	7	0	0	NUM
ejpam-5080	308	8	0	0	NUM
ejpam-5080	308	9	0	0	NUM
ejpam-5080	308	10	0	0	NUM
ejpam-5080	308	11	0	0	NUM
ejpam-5080	308	12	0	0	NUM
ejpam-5080	308	13	0.25	0.25	NUM
ejpam-5080	308	14	6.259×	6.259×	NUM
ejpam-5080	308	15	10−8	10−8	NUM
ejpam-5080	308	16	1.174×	1.174×	NUM
ejpam-5080	309	1	10−6	10−6	NUM
ejpam-5080	309	2	2.881×	2.881×	NUM
ejpam-5080	309	3	10−6	10−6	NUM
ejpam-5080	310	1	4.032×	4.032×	NUM
ejpam-5080	310	2	10−6	10−6	NUM
ejpam-5080	310	3	1.150×	1.150×	NUM
ejpam-5080	310	4	10−5	10−5	NUM
ejpam-5080	310	5	0.50	0.50	NUM
ejpam-5080	310	6	2.754×	2.754×	NUM
ejpam-5080	310	7	10−5	10−5	NUM
ejpam-5080	310	8	2×	2×	NUM
ejpam-5080	310	9	10−7	10−7	PROPN
ejpam-5080	311	1	3.136×	3.136×	NUM
ejpam-5080	311	2	10−6	10−6	NUM
ejpam-5080	312	1	9.808×	9.808×	NUM
ejpam-5080	312	2	10−6	10−6	NUM
ejpam-5080	313	1	2.402×	2.402×	NUM
ejpam-5080	313	2	10−5	10−5	NUM
ejpam-5080	313	3	0.75	0.75	NUM
ejpam-5080	313	4	8.542×	8.542×	NUM
ejpam-5080	313	5	10−4	10−4	NUM
ejpam-5080	313	6	1.10×	1.10×	NUM
ejpam-5080	313	7	10−6	10−6	NUM
ejpam-5080	313	8	3.980×	3.980×	PROPN
ejpam-5080	313	9	10−6	10−6	NUM
ejpam-5080	313	10	1.448×	1.448×	NUM
ejpam-5080	313	11	10−5	10−5	NUM
ejpam-5080	313	12	3.430×	3.430×	NUM
ejpam-5080	313	13	10−5	10−5	NUM
ejpam-5080	313	14	1	1	NUM
ejpam-5080	313	15	8.087×	8.087×	NUM
ejpam-5080	313	16	10−3	10−3	NUM
ejpam-5080	313	17	3.201×	3.201×	NUM
ejpam-5080	313	18	10−7	10−7	NUM
ejpam-5080	314	1	5.459×	5.459×	NUM
ejpam-5080	314	2	10−6	10−6	NUM
ejpam-5080	314	3	1.631×	1.631×	NUM
ejpam-5080	314	4	10−5	10−5	NUM
ejpam-5080	314	5	3.972×	3.972×	NUM
ejpam-5080	314	6	10−5	10−5	NUM
ejpam-5080	314	7	n.	n.	NOUN
ejpam-5080	314	8	alzaid	alzaid	PROPN
ejpam-5080	314	9	et	et	PROPN
ejpam-5080	314	10	al	al	PROPN
ejpam-5080	314	11	.	.	PUNCT
ejpam-5080	314	12	/	/	SYM
ejpam-5080	314	13	eur	eur	PROPN
ejpam-5080	314	14	.	.	PUNCT
ejpam-5080	315	1	j.	j.	PROPN
ejpam-5080	315	2	pure	pure	PROPN
ejpam-5080	315	3	appl	appl	PROPN
ejpam-5080	315	4	.	.	PROPN
ejpam-5080	315	5	math	math	PROPN
ejpam-5080	315	6	,	,	PUNCT
ejpam-5080	315	7	17	17	NUM
ejpam-5080	315	8	(	(	PUNCT
ejpam-5080	315	9	3	3	NUM
ejpam-5080	315	10	)	)	PUNCT
ejpam-5080	315	11	(	(	PUNCT
ejpam-5080	315	12	2024	2024	NUM
ejpam-5080	315	13	)	)	PUNCT
ejpam-5080	315	14	,	,	PUNCT
ejpam-5080	315	15	1982	1982	NUM
ejpam-5080	315	16	-	-	SYM
ejpam-5080	315	17	2000	2000	NUM
ejpam-5080	315	18	1996	1996	NUM
ejpam-5080	315	19	x	x	X
ejpam-5080	316	1	|u(x)−	|u(x)−	PROPN
ejpam-5080	316	2	ul(x)|	ul(x)|	VERB
ejpam-5080	316	3	|u(x)−	|u(x)−	X
ejpam-5080	316	4	uh(x)|	uh(x)|	ADP
ejpam-5080	316	5	0	0	NUM
ejpam-5080	316	6	0	0	NUM
ejpam-5080	316	7	0	0	NUM
ejpam-5080	316	8	0.25	0.25	NUM
ejpam-5080	316	9	3.494×	3.494×	NUM
ejpam-5080	316	10	10−2	10−2	NUM
ejpam-5080	316	11	3.088×	3.088×	NUM
ejpam-5080	316	12	10−2	10−2	NUM
ejpam-5080	316	13	0.50	0.50	NUM
ejpam-5080	317	1	5.352×	5.352×	NUM
ejpam-5080	317	2	10−2	10−2	NUM
ejpam-5080	317	3	9.762×	9.762×	NUM
ejpam-5080	317	4	10−2	10−2	NUM
ejpam-5080	317	5	0.75	0.75	NUM
ejpam-5080	317	6	2.793×	2.793×	NUM
ejpam-5080	317	7	10−2	10−2	NUM
ejpam-5080	317	8	1.235×	1.235×	NUM
ejpam-5080	317	9	10−1	10−1	NUM
ejpam-5080	317	10	1	1	NUM
ejpam-5080	317	11	1.948×	1.948×	PROPN
ejpam-5080	317	12	10−1	10−1	NUM
ejpam-5080	317	13	5.025×	5.025×	NUM
ejpam-5080	317	14	10−2	10−2	NUM
ejpam-5080	317	15	example	example	NOUN
ejpam-5080	317	16	3	3	NUM
ejpam-5080	317	17	.	.	PUNCT
ejpam-5080	318	1	let	let	VERB
ejpam-5080	318	2	us	we	PRON
ejpam-5080	318	3	consider	consider	VERB
ejpam-5080	318	4	the	the	DET
ejpam-5080	318	5	following	following	ADJ
ejpam-5080	318	6	nonlinear	nonlinear	ADJ
ejpam-5080	318	7	ivp	ivp	NOUN
ejpam-5080	318	8	of	of	ADP
ejpam-5080	318	9	ode	ode	PROPN
ejpam-5080	319	1	[	[	X
ejpam-5080	319	2	11	11	NUM
ejpam-5080	319	3	]	]	X
ejpam-5080	319	4	u′′	u′′	PROPN
ejpam-5080	319	5	+	+	CCONJ
ejpam-5080	319	6	u′	u′	PROPN
ejpam-5080	319	7	+	+	CCONJ
ejpam-5080	319	8	2xu3	2xu3	NUM
ejpam-5080	319	9	=	=	NOUN
ejpam-5080	319	10	2xe−3x	2xe−3x	ADJ
ejpam-5080	319	11	,	,	PUNCT
ejpam-5080	319	12	0	0	NUM
ejpam-5080	319	13	≤	≤	NUM
ejpam-5080	319	14	x	x	SYM
ejpam-5080	319	15	≤	≤	NUM
ejpam-5080	319	16	1	1	NUM
ejpam-5080	319	17	,	,	PUNCT
ejpam-5080	319	18	u(0	u(0	NOUN
ejpam-5080	319	19	)	)	PUNCT
ejpam-5080	319	20	=	=	SYM
ejpam-5080	319	21	1	1	NUM
ejpam-5080	319	22	,	,	PUNCT
ejpam-5080	319	23	u′(0	u′(0	PROPN
ejpam-5080	319	24	)	)	PUNCT
ejpam-5080	319	25	=	=	SYM
ejpam-5080	319	26	−1	−1	NOUN
ejpam-5080	319	27	,	,	PUNCT
ejpam-5080	319	28	(	(	PUNCT
ejpam-5080	319	29	65	65	X
ejpam-5080	319	30	)	)	PUNCT
ejpam-5080	319	31	having	have	VERB
ejpam-5080	319	32	the	the	DET
ejpam-5080	319	33	exact	exact	ADJ
ejpam-5080	319	34	solution	solution	NOUN
ejpam-5080	319	35	u(x	u(x	NOUN
ejpam-5080	319	36	)	)	PUNCT
ejpam-5080	319	37	=	=	SYM
ejpam-5080	319	38	e−x	e−x	NOUN
ejpam-5080	319	39	.	.	PUNCT
ejpam-5080	320	1	firstly	firstly	ADV
ejpam-5080	320	2	,	,	PUNCT
ejpam-5080	320	3	we	we	PRON
ejpam-5080	320	4	express	express	VERB
ejpam-5080	320	5	the	the	DET
ejpam-5080	320	6	equation	equation	NOUN
ejpam-5080	320	7	in	in	ADP
ejpam-5080	320	8	the	the	DET
ejpam-5080	320	9	following	follow	VERB
ejpam-5080	320	10	operator	operator	NOUN
ejpam-5080	320	11	form	form	NOUN
ejpam-5080	320	12	u	u	NOUN
ejpam-5080	320	13	=	=	PROPN
ejpam-5080	320	14	1−	1−	NUM
ejpam-5080	320	15	x+	x+	X
ejpam-5080	320	16	l−1(2xe−3x)−	l−1(2xe−3x)−	NOUN
ejpam-5080	321	1	l−1(u′)−	l−1(u′)−	ADV
ejpam-5080	321	2	2l−1(xu3	2l−1(xu3	NUM
ejpam-5080	321	3	)	)	PUNCT
ejpam-5080	321	4	(	(	PUNCT
ejpam-5080	321	5	66	66	NUM
ejpam-5080	321	6	)	)	PUNCT
ejpam-5080	321	7	where	where	SCONJ
ejpam-5080	321	8	l−1	l−1	PROPN
ejpam-5080	321	9	(	(	PUNCT
ejpam-5080	321	10	.	.	PUNCT
ejpam-5080	321	11	)	)	PUNCT
ejpam-5080	322	1	=	=	PUNCT
ejpam-5080	323	1	∫	∫	PUNCT
ejpam-5080	323	2	x	x	SYM
ejpam-5080	323	3	0	0	NUM
ejpam-5080	323	4	∫	∫	PROPN
ejpam-5080	323	5	x	x	SYM
ejpam-5080	323	6	0	0	PUNCT
ejpam-5080	323	7	(	(	PUNCT
ejpam-5080	323	8	.)dxdx	.)dxdx	PROPN
ejpam-5080	323	9	and	and	CCONJ
ejpam-5080	323	10	n(u	n(u	PROPN
ejpam-5080	323	11	)	)	PUNCT
ejpam-5080	323	12	=	=	SYM
ejpam-5080	323	13	u3	u3	PROPN
ejpam-5080	323	14	.	.	PUNCT
ejpam-5080	323	15	substituting	substitute	VERB
ejpam-5080	323	16	eqs	eqs	PROPN
ejpam-5080	323	17	.	.	PUNCT
ejpam-5080	324	1	(	(	PUNCT
ejpam-5080	324	2	5	5	NUM
ejpam-5080	324	3	)	)	PUNCT
ejpam-5080	324	4	and	and	CCONJ
ejpam-5080	324	5	(	(	PUNCT
ejpam-5080	324	6	6	6	NUM
ejpam-5080	324	7	)	)	PUNCT
ejpam-5080	324	8	into	into	ADP
ejpam-5080	324	9	eq	eq	NOUN
ejpam-5080	324	10	.	.	PUNCT
ejpam-5080	325	1	(	(	PUNCT
ejpam-5080	325	2	66	66	NUM
ejpam-5080	325	3	)	)	PUNCT
ejpam-5080	325	4	,	,	PUNCT
ejpam-5080	325	5	we	we	PRON
ejpam-5080	325	6	get	get	VERB
ejpam-5080	325	7	the	the	DET
ejpam-5080	325	8	following	follow	VERB
ejpam-5080	325	9	recursive	recursive	ADJ
ejpam-5080	325	10	solution	solution	NOUN
ejpam-5080	325	11	u0	u0	NOUN
ejpam-5080	325	12	=	=	SYM
ejpam-5080	325	13	1−	1−	NUM
ejpam-5080	325	14	x+	x+	X
ejpam-5080	325	15	l−1(2xe−3x	l−1(2xe−3x	NOUN
ejpam-5080	325	16	)	)	PUNCT
ejpam-5080	325	17	,	,	PUNCT
ejpam-5080	325	18	un+1	un+1	NOUN
ejpam-5080	325	19	=	=	SYM
ejpam-5080	325	20	−l−1(u	−l−1(u	NOUN
ejpam-5080	325	21	′	′	NUM
ejpam-5080	326	1	n)−	n)−	NOUN
ejpam-5080	326	2	2l−1xan(u0	2l−1xan(u0	NUM
ejpam-5080	326	3	,	,	PUNCT
ejpam-5080	326	4	u1	u1	NOUN
ejpam-5080	326	5	,	,	PUNCT
ejpam-5080	326	6	·	·	PUNCT
ejpam-5080	326	7	·	·	PUNCT
ejpam-5080	326	8	·	·	PUNCT
ejpam-5080	326	9	)	)	PUNCT
ejpam-5080	326	10	,	,	PUNCT
ejpam-5080	326	11	n	n	X
ejpam-5080	326	12	≥	≥	NOUN
ejpam-5080	326	13	0	0	NUM
ejpam-5080	326	14	,	,	PUNCT
ejpam-5080	326	15	the	the	DET
ejpam-5080	326	16	nonlinear	nonlinear	ADJ
ejpam-5080	326	17	term	term	NOUN
ejpam-5080	326	18	n(u	n(u	PROPN
ejpam-5080	326	19	)	)	PUNCT
ejpam-5080	326	20	=	=	NOUN
ejpam-5080	326	21	u3	u3	NOUN
ejpam-5080	326	22	is	be	AUX
ejpam-5080	326	23	given	give	VERB
ejpam-5080	326	24	as	as	ADP
ejpam-5080	326	25	in	in	ADP
ejpam-5080	326	26	example	example	NOUN
ejpam-5080	326	27	1	1	NUM
ejpam-5080	326	28	.	.	PUNCT
ejpam-5080	327	1	thus	thus	ADV
ejpam-5080	327	2	,	,	PUNCT
ejpam-5080	327	3	by	by	ADP
ejpam-5080	327	4	the	the	DET
ejpam-5080	327	5	same	same	ADJ
ejpam-5080	327	6	procedure	procedure	NOUN
ejpam-5080	327	7	as	as	ADP
ejpam-5080	327	8	in	in	ADP
ejpam-5080	327	9	example	example	NOUN
ejpam-5080	327	10	1	1	NUM
ejpam-5080	327	11	,	,	PUNCT
ejpam-5080	327	12	we	we	PRON
ejpam-5080	327	13	present	present	VERB
ejpam-5080	327	14	the	the	DET
ejpam-5080	327	15	respective	respective	ADJ
ejpam-5080	327	16	solution	solution	NOUN
ejpam-5080	327	17	via	via	ADP
ejpam-5080	327	18	the	the	DET
ejpam-5080	327	19	application	application	NOUN
ejpam-5080	327	20	of	of	ADP
ejpam-5080	327	21	the	the	DET
ejpam-5080	327	22	proposed	propose	VERB
ejpam-5080	327	23	modification	modification	NOUN
ejpam-5080	327	24	methods	method	NOUN
ejpam-5080	327	25	for	for	ADP
ejpam-5080	327	26	m	m	PROPN
ejpam-5080	327	27	=	=	NOUN
ejpam-5080	327	28	6	6	NUM
ejpam-5080	327	29	as	as	SCONJ
ejpam-5080	327	30	follows	follow	VERB
ejpam-5080	327	31	ut(x	ut(x	PUNCT
ejpam-5080	327	32	)	)	PUNCT
ejpam-5080	328	1	=	=	SYM
ejpam-5080	328	2	6∑	6∑	PROPN
ejpam-5080	328	3	n=0	n=0	NUM
ejpam-5080	328	4	un(x	un(x	SYM
ejpam-5080	328	5	)	)	PUNCT
ejpam-5080	328	6	=	=	SYM
ejpam-5080	328	7	1−	1−	NUM
ejpam-5080	328	8	x+	x+	SYM
ejpam-5080	328	9	1	1	NUM
ejpam-5080	328	10	2	2	NUM
ejpam-5080	328	11	x2	x2	NOUN
ejpam-5080	328	12	−	−	NOUN
ejpam-5080	328	13	1	1	NUM
ejpam-5080	328	14	6	6	NUM
ejpam-5080	328	15	x3	x3	ADJ
ejpam-5080	328	16	+	+	CCONJ
ejpam-5080	328	17	1	1	NUM
ejpam-5080	328	18	24	24	NUM
ejpam-5080	328	19	x4	x4	NOUN
ejpam-5080	328	20	−	−	PROPN
ejpam-5080	328	21	1	1	NUM
ejpam-5080	328	22	120	120	NUM
ejpam-5080	328	23	x5	x5	NOUN
ejpam-5080	328	24	+	+	CCONJ
ejpam-5080	328	25	1	1	NUM
ejpam-5080	328	26	720	720	NUM
ejpam-5080	328	27	x6	x6	NOUN
ejpam-5080	328	28	−	−	NOUN
ejpam-5080	328	29	1	1	NUM
ejpam-5080	328	30	5040	5040	NUM
ejpam-5080	328	31	x7	x7	NOUN
ejpam-5080	328	32	+	+	CCONJ
ejpam-5080	328	33	81	81	NUM
ejpam-5080	328	34	1120	1120	NUM
ejpam-5080	328	35	x8	x8	NOUN
ejpam-5080	328	36	+	+	CCONJ
ejpam-5080	328	37	·	·	PUNCT
ejpam-5080	328	38	·	·	PUNCT
ejpam-5080	328	39	·	·	PUNCT
ejpam-5080	328	40	,	,	PUNCT
ejpam-5080	328	41	up	up	ADV
ejpam-5080	328	42	(	(	PUNCT
ejpam-5080	328	43	x	x	NOUN
ejpam-5080	328	44	)	)	PUNCT
ejpam-5080	328	45	=	=	SYM
ejpam-5080	328	46	6∑	6∑	PROPN
ejpam-5080	328	47	n=0	n=0	NUM
ejpam-5080	328	48	un(x	un(x	SYM
ejpam-5080	328	49	)	)	PUNCT
ejpam-5080	328	50	=	=	SYM
ejpam-5080	328	51	1−	1−	NUM
ejpam-5080	328	52	x+	x+	NUM
ejpam-5080	328	53	0.5000639003x2	0.5000639003x2	NUM
ejpam-5080	328	54	−	−	NOUN
ejpam-5080	328	55	0.1679247192x3	0.1679247192x3	NUM
ejpam-5080	329	1	+	+	NOUN
ejpam-5080	329	2	0.05074785700x4	0.05074785700x4	NUM
ejpam-5080	329	3	+	+	CCONJ
ejpam-5080	329	4	·	·	PUNCT
ejpam-5080	329	5	·	·	PUNCT
ejpam-5080	329	6	·	·	PUNCT
ejpam-5080	329	7	,	,	PUNCT
ejpam-5080	329	8	ut	ut	PROPN
ejpam-5080	329	9	(	(	PUNCT
ejpam-5080	329	10	x	x	X
ejpam-5080	329	11	)	)	PUNCT
ejpam-5080	329	12	=	=	SYM
ejpam-5080	329	13	6∑	6∑	PROPN
ejpam-5080	329	14	n=0	n=0	NUM
ejpam-5080	329	15	un(x	un(x	SYM
ejpam-5080	329	16	)	)	PUNCT
ejpam-5080	329	17	=	=	SYM
ejpam-5080	330	1	1−	1−	NUM
ejpam-5080	330	2	x+	x+	X
ejpam-5080	330	3	0.5000267045x2	0.5000267045x2	NUM
ejpam-5080	330	4	−	−	NOUN
ejpam-5080	330	5	0.1675800359x3	0.1675800359x3	PUNCT
ejpam-5080	331	1	+	+	CCONJ
ejpam-5080	331	2	0.04949342753x4	0.04949342753x4	NUM
ejpam-5080	331	3	+	+	CCONJ
ejpam-5080	331	4	·	·	PUNCT
ejpam-5080	331	5	·	·	PUNCT
ejpam-5080	331	6	·	·	PUNCT
ejpam-5080	331	7	,	,	PUNCT
ejpam-5080	331	8	ul(x	ul(x	PROPN
ejpam-5080	331	9	)	)	PUNCT
ejpam-5080	332	1	=	=	SYM
ejpam-5080	332	2	6∑	6∑	PROPN
ejpam-5080	332	3	n=0	n=0	NUM
ejpam-5080	332	4	un(x	un(x	SYM
ejpam-5080	332	5	)	)	PUNCT
ejpam-5080	332	6	=	=	SYM
ejpam-5080	332	7	1−	1−	NUM
ejpam-5080	332	8	x+	x+	NUM
ejpam-5080	332	9	0.5778656006x2	0.5778656006x2	NUM
ejpam-5080	332	10	−	−	PROPN
ejpam-5080	332	11	0.4966684977x3	0.4966684977x3	NUM
ejpam-5080	333	1	+	+	CCONJ
ejpam-5080	333	2	0.5997034709x4	0.5997034709x4	NUM
ejpam-5080	333	3	+	+	X
ejpam-5080	333	4	·	·	PUNCT
ejpam-5080	333	5	·	·	PUNCT
ejpam-5080	333	6	·	·	PUNCT
ejpam-5080	333	7	,	,	PUNCT
ejpam-5080	333	8	ug(x	ug(x	X
ejpam-5080	333	9	)	)	PUNCT
ejpam-5080	333	10	=	=	SYM
ejpam-5080	333	11	6∑	6∑	PROPN
ejpam-5080	333	12	n=0	n=0	NUM
ejpam-5080	333	13	un(x	un(x	SYM
ejpam-5080	333	14	)	)	PUNCT
ejpam-5080	333	15	=	=	SYM
ejpam-5080	333	16	1−	1−	NUM
ejpam-5080	333	17	x+	x+	X
ejpam-5080	333	18	0.5001073089x2	0.5001073089x2	PUNCT
ejpam-5080	333	19	−	−	NOUN
ejpam-5080	333	20	0.1682601554x3	0.1682601554x3	NUM
ejpam-5080	334	1	+	+	PUNCT
ejpam-5080	334	2	0.05188023933x4	0.05188023933x4	NUM
ejpam-5080	334	3	+	+	X
ejpam-5080	334	4	·	·	PUNCT
ejpam-5080	334	5	·	·	PUNCT
ejpam-5080	334	6	·	·	PUNCT
ejpam-5080	334	7	,	,	PUNCT
ejpam-5080	334	8	uj(x	uj(x	NOUN
ejpam-5080	334	9	)	)	PUNCT
ejpam-5080	335	1	=	=	SYM
ejpam-5080	335	2	6∑	6∑	PROPN
ejpam-5080	335	3	n=0	n=0	NUM
ejpam-5080	335	4	un(x	un(x	SYM
ejpam-5080	335	5	)	)	PUNCT
ejpam-5080	335	6	=	=	SYM
ejpam-5080	335	7	1−	1−	NUM
ejpam-5080	335	8	x+	x+	NUM
ejpam-5080	335	9	0.500154036x2	0.500154036x2	NUM
ejpam-5080	335	10	−	−	NOUN
ejpam-5080	335	11	0.1685812115x3	0.1685812115x3	NUM
ejpam-5080	335	12	+	+	SYM
ejpam-5080	335	13	0.0529062453x4	0.0529062453x4	NUM
ejpam-5080	335	14	+	+	NUM
ejpam-5080	335	15	·	·	PUNCT
ejpam-5080	335	16	·	·	PUNCT
ejpam-5080	335	17	·	·	PUNCT
ejpam-5080	335	18	,	,	PUNCT
ejpam-5080	335	19	(	(	PUNCT
ejpam-5080	335	20	67	67	NUM
ejpam-5080	335	21	)	)	PUNCT
ejpam-5080	335	22	n.	n.	NOUN
ejpam-5080	335	23	alzaid	alzaid	PROPN
ejpam-5080	335	24	et	et	PROPN
ejpam-5080	335	25	al	al	PROPN
ejpam-5080	335	26	.	.	PUNCT
ejpam-5080	335	27	/	/	SYM
ejpam-5080	335	28	eur	eur	PROPN
ejpam-5080	335	29	.	.	PUNCT
ejpam-5080	336	1	j.	j.	PROPN
ejpam-5080	336	2	pure	pure	PROPN
ejpam-5080	336	3	appl	appl	PROPN
ejpam-5080	336	4	.	.	PROPN
ejpam-5080	336	5	math	math	PROPN
ejpam-5080	336	6	,	,	PUNCT
ejpam-5080	336	7	17	17	NUM
ejpam-5080	336	8	(	(	PUNCT
ejpam-5080	336	9	3	3	NUM
ejpam-5080	336	10	)	)	PUNCT
ejpam-5080	336	11	(	(	PUNCT
ejpam-5080	336	12	2024	2024	NUM
ejpam-5080	336	13	)	)	PUNCT
ejpam-5080	336	14	,	,	PUNCT
ejpam-5080	336	15	1982	1982	NUM
ejpam-5080	336	16	-	-	SYM
ejpam-5080	336	17	2000	2000	NUM
ejpam-5080	336	18	1997	1997	NUM
ejpam-5080	336	19	accordingly	accordingly	ADV
ejpam-5080	336	20	,	,	PUNCT
ejpam-5080	336	21	we	we	PRON
ejpam-5080	336	22	report	report	VERB
ejpam-5080	336	23	in	in	ADP
ejpam-5080	336	24	table	table	NOUN
ejpam-5080	336	25	3	3	NUM
ejpam-5080	336	26	the	the	DET
ejpam-5080	336	27	absolute	absolute	ADJ
ejpam-5080	336	28	error	error	NOUN
ejpam-5080	336	29	differences	difference	NOUN
ejpam-5080	336	30	between	between	ADP
ejpam-5080	336	31	the	the	DET
ejpam-5080	336	32	exact	exact	ADJ
ejpam-5080	336	33	solution	solution	NOUN
ejpam-5080	336	34	u(x	u(x	NOUN
ejpam-5080	336	35	)	)	PUNCT
ejpam-5080	336	36	and	and	CCONJ
ejpam-5080	336	37	the	the	DET
ejpam-5080	336	38	respective	respective	ADJ
ejpam-5080	336	39	solutions	solution	NOUN
ejpam-5080	336	40	by	by	ADP
ejpam-5080	336	41	the	the	DET
ejpam-5080	336	42	proposed	propose	VERB
ejpam-5080	336	43	modification	modification	NOUN
ejpam-5080	336	44	methods	method	NOUN
ejpam-5080	336	45	.	.	PUNCT
ejpam-5080	337	1	table	table	NOUN
ejpam-5080	337	2	3	3	NUM
ejpam-5080	337	3	:	:	PUNCT
ejpam-5080	337	4	absolute	absolute	ADJ
ejpam-5080	337	5	error	error	NOUN
ejpam-5080	337	6	comparisons	comparison	NOUN
ejpam-5080	337	7	via	via	ADP
ejpam-5080	337	8	the	the	DET
ejpam-5080	337	9	proposed	propose	VERB
ejpam-5080	337	10	modifications	modification	NOUN
ejpam-5080	337	11	for	for	ADP
ejpam-5080	337	12	example	example	NOUN
ejpam-5080	337	13	3	3	NUM
ejpam-5080	337	14	x	x	PART
ejpam-5080	337	15	|u(x)−	|u(x)−	NOUN
ejpam-5080	337	16	ut(x)|	ut(x)|	VERB
ejpam-5080	337	17	|u(x)−	|u(x)−	PROPN
ejpam-5080	337	18	up	up	ADP
ejpam-5080	337	19	(	(	PUNCT
ejpam-5080	337	20	x)|	x)|	PROPN
ejpam-5080	337	21	|u(x)−	|u(x)−	PROPN
ejpam-5080	337	22	ut	ut	PROPN
ejpam-5080	338	1	(	(	PUNCT
ejpam-5080	338	2	x)|	x)|	PROPN
ejpam-5080	338	3	|u(x)−	|u(x)−	PROPN
ejpam-5080	338	4	ug(x)|	ug(x)|	VERB
ejpam-5080	338	5	|u(x)−	|u(x)−	PROPN
ejpam-5080	338	6	uj(x)|	uj(x)|	PROPN
ejpam-5080	338	7	0	0	NUM
ejpam-5080	338	8	0	0	NUM
ejpam-5080	338	9	0	0	NUM
ejpam-5080	338	10	0	0	NUM
ejpam-5080	338	11	0	0	NUM
ejpam-5080	338	12	0	0	NUM
ejpam-5080	338	13	0.25	0.25	NUM
ejpam-5080	338	14	9.764×	9.764×	NUM
ejpam-5080	338	15	10−7	10−7	NUM
ejpam-5080	339	1	6.150×	6.150×	NUM
ejpam-5080	339	2	10−8	10−8	NUM
ejpam-5080	339	3	1.585×	1.585×	NUM
ejpam-5080	339	4	10−7	10−7	NUM
ejpam-5080	339	5	3.051×	3.051×	NUM
ejpam-5080	339	6	10−7	10−7	NUM
ejpam-5080	339	7	8.615×	8.615×	PROPN
ejpam-5080	339	8	10−7	10−7	NUM
ejpam-5080	339	9	0.50	0.50	NUM
ejpam-5080	339	10	2.223×	2.223×	NUM
ejpam-5080	339	11	10−4	10−4	NUM
ejpam-5080	339	12	9.90×	9.90×	NUM
ejpam-5080	339	13	10−8	10−8	NUM
ejpam-5080	339	14	3.338×	3.338×	NUM
ejpam-5080	339	15	10−7	10−7	NUM
ejpam-5080	339	16	5.373×	5.373×	NUM
ejpam-5080	339	17	10−7	10−7	NUM
ejpam-5080	340	1	1.497×	1.497×	NUM
ejpam-5080	340	2	10−6	10−6	NUM
ejpam-5080	340	3	0.75	0.75	NUM
ejpam-5080	340	4	5.086×	5.086×	NUM
ejpam-5080	340	5	10−3	10−3	NUM
ejpam-5080	340	6	6.693×	6.693×	NUM
ejpam-5080	340	7	10−6	10−6	NUM
ejpam-5080	340	8	6.967×	6.967×	NUM
ejpam-5080	340	9	10−6	10−6	NUM
ejpam-5080	341	1	5.916×	5.916×	NUM
ejpam-5080	341	2	10−6	10−6	NUM
ejpam-5080	341	3	4.718×	4.718×	NUM
ejpam-5080	342	1	10−6	10−6	NUM
ejpam-5080	342	2	1	1	NUM
ejpam-5080	342	3	4.545×	4.545×	NUM
ejpam-5080	342	4	10−2	10−2	NUM
ejpam-5080	342	5	2.439×	2.439×	NUM
ejpam-5080	342	6	10−4	10−4	NUM
ejpam-5080	342	7	2.443×	2.443×	NUM
ejpam-5080	342	8	10−4	10−4	NUM
ejpam-5080	342	9	2.431×	2.431×	NUM
ejpam-5080	342	10	10−4	10−4	NUM
ejpam-5080	342	11	2.417×	2.417×	NUM
ejpam-5080	342	12	10−4	10−4	NUM
ejpam-5080	342	13	x	x	SYM
ejpam-5080	342	14	|u(x)−	|u(x)−	PROPN
ejpam-5080	342	15	ul(x)|	ul(x)|	VERB
ejpam-5080	342	16	0	0	NUM
ejpam-5080	342	17	0	0	NUM
ejpam-5080	343	1	0.25	0.25	NUM
ejpam-5080	343	2	1.424×	1.424×	NUM
ejpam-5080	343	3	10−3	10−3	NUM
ejpam-5080	343	4	0.50	0.50	NUM
ejpam-5080	343	5	4.071×	4.071×	NUM
ejpam-5080	343	6	10−4	10−4	NUM
ejpam-5080	343	7	0.75	0.75	NUM
ejpam-5080	343	8	2.418×	2.418×	PROPN
ejpam-5080	343	9	10−3	10−3	NUM
ejpam-5080	343	10	1	1	NUM
ejpam-5080	343	11	4.348×	4.348×	NUM
ejpam-5080	343	12	10−3	10−3	NUM
ejpam-5080	343	13	example	example	NOUN
ejpam-5080	343	14	4	4	NUM
ejpam-5080	343	15	.	.	PUNCT
ejpam-5080	343	16	consider	consider	VERB
ejpam-5080	343	17	the	the	DET
ejpam-5080	343	18	following	following	ADJ
ejpam-5080	343	19	nonlinear	nonlinear	NOUN
ejpam-5080	343	20	ivp	ivp	NOUN
ejpam-5080	343	21	[	[	X
ejpam-5080	343	22	11	11	NUM
ejpam-5080	343	23	]	]	X
ejpam-5080	343	24	u′′	u′′	PROPN
ejpam-5080	343	25	+	+	PROPN
ejpam-5080	343	26	u′	u′	PROPN
ejpam-5080	343	27	−	−	NOUN
ejpam-5080	343	28	uu′	uu′	PROPN
ejpam-5080	344	1	=	=	PUNCT
ejpam-5080	344	2	(	(	PUNCT
ejpam-5080	344	3	−2	−2	NOUN
ejpam-5080	345	1	+	+	CCONJ
ejpam-5080	345	2	4x2	4x2	NUM
ejpam-5080	345	3	−	−	NOUN
ejpam-5080	345	4	2x)e−x2	2x)e−x2	NOUN
ejpam-5080	345	5	+	+	X
ejpam-5080	345	6	2xe−2x2	2xe−2x2	NUM
ejpam-5080	345	7	,	,	PUNCT
ejpam-5080	345	8	0	0	NUM
ejpam-5080	345	9	≤	≤	NUM
ejpam-5080	345	10	x	x	SYM
ejpam-5080	345	11	≤	≤	NUM
ejpam-5080	345	12	1	1	NUM
ejpam-5080	345	13	,	,	PUNCT
ejpam-5080	345	14	u(0	u(0	NOUN
ejpam-5080	345	15	)	)	PUNCT
ejpam-5080	345	16	=	=	SYM
ejpam-5080	345	17	1	1	NUM
ejpam-5080	345	18	,	,	PUNCT
ejpam-5080	345	19	u′(0	u′(0	PROPN
ejpam-5080	345	20	)	)	PUNCT
ejpam-5080	345	21	=	=	SYM
ejpam-5080	345	22	0	0	NUM
ejpam-5080	345	23	,	,	PUNCT
ejpam-5080	345	24	that	that	PRON
ejpam-5080	345	25	admits	admit	VERB
ejpam-5080	345	26	the	the	DET
ejpam-5080	345	27	exact	exact	ADJ
ejpam-5080	345	28	solution	solution	NOUN
ejpam-5080	345	29	u(x	u(x	NOUN
ejpam-5080	345	30	)	)	PUNCT
ejpam-5080	345	31	=	=	SYM
ejpam-5080	345	32	e−x2	e−x2	NOUN
ejpam-5080	345	33	.	.	PUNCT
ejpam-5080	346	1	we	we	PRON
ejpam-5080	346	2	start	start	VERB
ejpam-5080	346	3	by	by	ADP
ejpam-5080	346	4	expressing	express	VERB
ejpam-5080	346	5	the	the	DET
ejpam-5080	346	6	model	model	NOUN
ejpam-5080	346	7	in	in	ADP
ejpam-5080	346	8	an	an	DET
ejpam-5080	346	9	operator	operator	NOUN
ejpam-5080	346	10	notation	notation	NOUN
ejpam-5080	346	11	as	as	SCONJ
ejpam-5080	346	12	follows	follow	VERB
ejpam-5080	346	13	u	u	NOUN
ejpam-5080	346	14	=	=	NOUN
ejpam-5080	346	15	1	1	NUM
ejpam-5080	346	16	+	+	NUM
ejpam-5080	346	17	l−1((−2	l−1((−2	X
ejpam-5080	346	18	+	+	CCONJ
ejpam-5080	346	19	4x2	4x2	NUM
ejpam-5080	347	1	−	−	NOUN
ejpam-5080	347	2	2x)e−x2	2x)e−x2	NOUN
ejpam-5080	347	3	+	+	CCONJ
ejpam-5080	347	4	2xe−2x2	2xe−2x2	NUM
ejpam-5080	347	5	)	)	PUNCT
ejpam-5080	347	6	−	−	PROPN
ejpam-5080	347	7	l−1(u′	l−1(u′	NOUN
ejpam-5080	347	8	)	)	PUNCT
ejpam-5080	348	1	+	+	CCONJ
ejpam-5080	349	1	l−1(uu	l−1(uu	PROPN
ejpam-5080	349	2	′	′	NOUN
ejpam-5080	349	3	)	)	PUNCT
ejpam-5080	349	4	,	,	PUNCT
ejpam-5080	349	5	(	(	PUNCT
ejpam-5080	349	6	68	68	NUM
ejpam-5080	349	7	)	)	PUNCT
ejpam-5080	349	8	where	where	SCONJ
ejpam-5080	349	9	l−1	l−1	PROPN
ejpam-5080	349	10	(	(	PUNCT
ejpam-5080	349	11	.	.	PUNCT
ejpam-5080	349	12	)	)	PUNCT
ejpam-5080	350	1	=	=	PUNCT
ejpam-5080	351	1	∫	∫	PUNCT
ejpam-5080	351	2	x	x	SYM
ejpam-5080	351	3	0	0	NUM
ejpam-5080	351	4	∫	∫	PROPN
ejpam-5080	351	5	x	x	SYM
ejpam-5080	351	6	0	0	PUNCT
ejpam-5080	351	7	(	(	PUNCT
ejpam-5080	351	8	.)dxdx	.)dxdx	PROPN
ejpam-5080	351	9	and	and	CCONJ
ejpam-5080	351	10	n(u	n(u	PROPN
ejpam-5080	351	11	)	)	PUNCT
ejpam-5080	351	12	=	=	SYM
ejpam-5080	351	13	uu′.	uu′.	PROPN
ejpam-5080	351	14	substituting	substitute	VERB
ejpam-5080	351	15	eqs	eqs	PROPN
ejpam-5080	351	16	.	.	PUNCT
ejpam-5080	352	1	(	(	PUNCT
ejpam-5080	352	2	5	5	NUM
ejpam-5080	352	3	)	)	PUNCT
ejpam-5080	352	4	and	and	CCONJ
ejpam-5080	352	5	(	(	PUNCT
ejpam-5080	352	6	6	6	NUM
ejpam-5080	352	7	)	)	PUNCT
ejpam-5080	352	8	into	into	ADP
ejpam-5080	352	9	eq	eq	NOUN
ejpam-5080	352	10	.	.	PUNCT
ejpam-5080	353	1	(	(	PUNCT
ejpam-5080	353	2	68	68	NUM
ejpam-5080	353	3	)	)	PUNCT
ejpam-5080	353	4	,	,	PUNCT
ejpam-5080	353	5	we	we	PRON
ejpam-5080	353	6	get	get	VERB
ejpam-5080	353	7	the	the	DET
ejpam-5080	353	8	following	follow	VERB
ejpam-5080	353	9	recursive	recursive	ADJ
ejpam-5080	353	10	solution	solution	NOUN
ejpam-5080	353	11	u0	u0	NOUN
ejpam-5080	353	12	=	=	NOUN
ejpam-5080	353	13	1	1	NUM
ejpam-5080	353	14	+	+	NUM
ejpam-5080	353	15	l−1(−2	l−1(−2	NOUN
ejpam-5080	353	16	+	+	CCONJ
ejpam-5080	354	1	4x2	4x2	NUM
ejpam-5080	354	2	−	−	NOUN
ejpam-5080	354	3	2x)e−x2	2x)e−x2	NOUN
ejpam-5080	354	4	+	+	X
ejpam-5080	354	5	2xe−2x2	2xe−2x2	NUM
ejpam-5080	354	6	)	)	PUNCT
ejpam-5080	354	7	,	,	PUNCT
ejpam-5080	354	8	un+1	un+1	NOUN
ejpam-5080	354	9	=	=	SYM
ejpam-5080	354	10	−l−1(u	−l−1(u	NOUN
ejpam-5080	354	11	′	′	NUM
ejpam-5080	354	12	n	n	CCONJ
ejpam-5080	354	13	)	)	PUNCT
ejpam-5080	354	14	+	+	CCONJ
ejpam-5080	354	15	l−1an(u0	l−1an(u0	PROPN
ejpam-5080	354	16	,	,	PUNCT
ejpam-5080	354	17	u1	u1	NOUN
ejpam-5080	354	18	,	,	PUNCT
ejpam-5080	354	19	·	·	PUNCT
ejpam-5080	354	20	·	·	PUNCT
ejpam-5080	354	21	·	·	PUNCT
ejpam-5080	354	22	)	)	PUNCT
ejpam-5080	354	23	,	,	PUNCT
ejpam-5080	354	24	n	n	X
ejpam-5080	354	25	≥	≥	NOUN
ejpam-5080	354	26	0	0	NUM
ejpam-5080	354	27	,	,	PUNCT
ejpam-5080	354	28	the	the	DET
ejpam-5080	354	29	nonlinear	nonlinear	ADJ
ejpam-5080	354	30	term	term	NOUN
ejpam-5080	354	31	n(u	n(u	PROPN
ejpam-5080	354	32	)	)	PUNCT
ejpam-5080	355	1	=	=	SYM
ejpam-5080	355	2	uu′	uu′	PROPN
ejpam-5080	355	3	is	be	AUX
ejpam-5080	355	4	given	give	VERB
ejpam-5080	355	5	as	as	ADP
ejpam-5080	355	6	in	in	ADP
ejpam-5080	355	7	example	example	NOUN
ejpam-5080	355	8	2	2	NUM
ejpam-5080	355	9	.	.	PUNCT
ejpam-5080	356	1	also	also	ADV
ejpam-5080	356	2	,	,	PUNCT
ejpam-5080	356	3	without	without	ADP
ejpam-5080	356	4	lost	lose	VERB
ejpam-5080	356	5	of	of	ADP
ejpam-5080	356	6	generality	generality	NOUN
ejpam-5080	356	7	,	,	PUNCT
ejpam-5080	356	8	by	by	ADP
ejpam-5080	356	9	the	the	DET
ejpam-5080	356	10	same	same	ADJ
ejpam-5080	356	11	procedure	procedure	NOUN
ejpam-5080	356	12	as	as	ADP
ejpam-5080	356	13	in	in	ADP
ejpam-5080	356	14	example	example	NOUN
ejpam-5080	356	15	1	1	NUM
ejpam-5080	356	16	,	,	PUNCT
ejpam-5080	356	17	we	we	PRON
ejpam-5080	356	18	present	present	VERB
ejpam-5080	356	19	the	the	DET
ejpam-5080	356	20	respective	respective	ADJ
ejpam-5080	356	21	solutions	solution	NOUN
ejpam-5080	356	22	via	via	ADP
ejpam-5080	356	23	the	the	DET
ejpam-5080	356	24	application	application	NOUN
ejpam-5080	356	25	of	of	ADP
ejpam-5080	356	26	the	the	DET
ejpam-5080	356	27	proposed	propose	VERB
ejpam-5080	356	28	modification	modification	NOUN
ejpam-5080	356	29	methods	method	NOUN
ejpam-5080	356	30	for	for	ADP
ejpam-5080	356	31	m	m	PROPN
ejpam-5080	356	32	=	=	SYM
ejpam-5080	356	33	6	6	NUM
ejpam-5080	356	34	n.	n.	NOUN
ejpam-5080	356	35	alzaid	alzaid	PROPN
ejpam-5080	356	36	et	et	PROPN
ejpam-5080	356	37	al	al	PROPN
ejpam-5080	356	38	.	.	PUNCT
ejpam-5080	356	39	/	/	SYM
ejpam-5080	356	40	eur	eur	PROPN
ejpam-5080	356	41	.	.	PUNCT
ejpam-5080	357	1	j.	j.	PROPN
ejpam-5080	357	2	pure	pure	PROPN
ejpam-5080	357	3	appl	appl	PROPN
ejpam-5080	357	4	.	.	PROPN
ejpam-5080	357	5	math	math	PROPN
ejpam-5080	357	6	,	,	PUNCT
ejpam-5080	357	7	17	17	NUM
ejpam-5080	357	8	(	(	PUNCT
ejpam-5080	357	9	3	3	NUM
ejpam-5080	357	10	)	)	PUNCT
ejpam-5080	357	11	(	(	PUNCT
ejpam-5080	357	12	2024	2024	NUM
ejpam-5080	357	13	)	)	PUNCT
ejpam-5080	357	14	,	,	PUNCT
ejpam-5080	357	15	1982	1982	NUM
ejpam-5080	357	16	-	-	SYM
ejpam-5080	357	17	2000	2000	NUM
ejpam-5080	357	18	1998	1998	NUM
ejpam-5080	357	19	as	as	SCONJ
ejpam-5080	357	20	follows	follow	VERB
ejpam-5080	357	21	ut(x	ut(x	PUNCT
ejpam-5080	357	22	)	)	PUNCT
ejpam-5080	358	1	=	=	SYM
ejpam-5080	358	2	6∑	6∑	PROPN
ejpam-5080	358	3	n=0	n=0	NUM
ejpam-5080	358	4	un(x	un(x	SYM
ejpam-5080	358	5	)	)	PUNCT
ejpam-5080	358	6	=	=	SYM
ejpam-5080	359	1	1−	1−	NUM
ejpam-5080	359	2	x2	x2	NOUN
ejpam-5080	360	1	+	+	CCONJ
ejpam-5080	360	2	1	1	NUM
ejpam-5080	360	3	2	2	NUM
ejpam-5080	360	4	x4	x4	NOUN
ejpam-5080	360	5	−	−	PROPN
ejpam-5080	360	6	1	1	NUM
ejpam-5080	360	7	6	6	NUM
ejpam-5080	360	8	x6	x6	NOUN
ejpam-5080	360	9	+	+	CCONJ
ejpam-5080	360	10	7	7	NUM
ejpam-5080	360	11	216	216	NUM
ejpam-5080	360	12	x9	x9	NOUN
ejpam-5080	360	13	+	+	CCONJ
ejpam-5080	360	14	·	·	PUNCT
ejpam-5080	360	15	·	·	PUNCT
ejpam-5080	360	16	·	·	PUNCT
ejpam-5080	360	17	,	,	PUNCT
ejpam-5080	360	18	up	up	ADV
ejpam-5080	360	19	(	(	PUNCT
ejpam-5080	360	20	x	x	NOUN
ejpam-5080	360	21	)	)	PUNCT
ejpam-5080	360	22	=	=	SYM
ejpam-5080	360	23	6∑	6∑	PROPN
ejpam-5080	360	24	n=0	n=0	NUM
ejpam-5080	360	25	un(x	un(x	SYM
ejpam-5080	360	26	)	)	PUNCT
ejpam-5080	360	27	=	=	SYM
ejpam-5080	361	1	1−	1−	NUM
ejpam-5080	361	2	0.9999424490x2	0.9999424490x2	NUM
ejpam-5080	362	1	−	−	PUNCT
ejpam-5080	362	2	0.0009236505467x3	0.0009236505467x3	NUM
ejpam-5080	363	1	+	+	NUM
ejpam-5080	363	2	0.5047677208x4	0.5047677208x4	NUM
ejpam-5080	363	3	,	,	PUNCT
ejpam-5080	363	4	ut	ut	PROPN
ejpam-5080	363	5	(	(	PUNCT
ejpam-5080	363	6	x	x	X
ejpam-5080	363	7	)	)	PUNCT
ejpam-5080	363	8	=	=	SYM
ejpam-5080	363	9	6∑	6∑	PROPN
ejpam-5080	363	10	n=0	n=0	NUM
ejpam-5080	363	11	un(x	un(x	SYM
ejpam-5080	363	12	)	)	PUNCT
ejpam-5080	363	13	=	=	SYM
ejpam-5080	364	1	1−	1−	NUM
ejpam-5080	364	2	0.9999762780x2	0.9999762780x2	NUM
ejpam-5080	365	1	−	−	NOUN
ejpam-5080	365	2	0.0006668175867x3	0.0006668175867x3	NUM
ejpam-5080	365	3	+	+	PUNCT
ejpam-5080	365	4	0.504082822x4	0.504082822x4	NUM
ejpam-5080	365	5	+	+	X
ejpam-5080	365	6	·	·	PUNCT
ejpam-5080	365	7	·	·	PUNCT
ejpam-5080	365	8	·	·	PUNCT
ejpam-5080	365	9	,	,	PUNCT
ejpam-5080	365	10	ul(x	ul(x	PROPN
ejpam-5080	365	11	)	)	PUNCT
ejpam-5080	366	1	=	=	SYM
ejpam-5080	366	2	6∑	6∑	PROPN
ejpam-5080	366	3	n=0	n=0	NUM
ejpam-5080	366	4	un(x	un(x	SYM
ejpam-5080	366	5	)	)	PUNCT
ejpam-5080	366	6	=	=	SYM
ejpam-5080	367	1	1−	1−	NUM
ejpam-5080	367	2	1.224806499x2	1.224806499x2	NUM
ejpam-5080	368	1	+	+	CCONJ
ejpam-5080	369	1	0.7301686677x3	0.7301686677x3	NUM
ejpam-5080	369	2	−	−	NOUN
ejpam-5080	369	3	0.1966821240x4	0.1966821240x4	NUM
ejpam-5080	370	1	+	+	CCONJ
ejpam-5080	370	2	·	·	PUNCT
ejpam-5080	370	3	·	·	PUNCT
ejpam-5080	370	4	·	·	PUNCT
ejpam-5080	370	5	,	,	PUNCT
ejpam-5080	370	6	uh(x	uh(x	NOUN
ejpam-5080	370	7	)	)	PUNCT
ejpam-5080	371	1	=	=	SYM
ejpam-5080	371	2	6∑	6∑	PROPN
ejpam-5080	371	3	n=0	n=0	NUM
ejpam-5080	371	4	un(x	un(x	SYM
ejpam-5080	371	5	)	)	PUNCT
ejpam-5080	371	6	=	=	SYM
ejpam-5080	371	7	1−	1−	NUM
ejpam-5080	371	8	0.8811213405x2	0.8811213405x2	NUM
ejpam-5080	371	9	−	−	X
ejpam-5080	371	10	0.07972377693x3	0.07972377693x3	NUM
ejpam-5080	372	1	+	+	PUNCT
ejpam-5080	372	2	0.2955485375x4	0.2955485375x4	NUM
ejpam-5080	372	3	+	+	X
ejpam-5080	372	4	·	·	PUNCT
ejpam-5080	372	5	·	·	PUNCT
ejpam-5080	372	6	·	·	PUNCT
ejpam-5080	372	7	,	,	PUNCT
ejpam-5080	372	8	ug(x	ug(x	X
ejpam-5080	372	9	)	)	PUNCT
ejpam-5080	373	1	=	=	SYM
ejpam-5080	373	2	6∑	6∑	PROPN
ejpam-5080	373	3	n=0	n=0	NUM
ejpam-5080	373	4	un(x	un(x	SYM
ejpam-5080	373	5	)	)	PUNCT
ejpam-5080	373	6	=	=	SYM
ejpam-5080	374	1	1−	1−	NUM
ejpam-5080	374	2	0.9999022015x2	0.9999022015x2	NUM
ejpam-5080	374	3	−	−	NOUN
ejpam-5080	374	4	0.001176415607x3	0.001176415607x3	NUM
ejpam-5080	375	1	+	+	CCONJ
ejpam-5080	375	2	0.505394132x4	0.505394132x4	X
ejpam-5080	375	3	+	+	X
ejpam-5080	375	4	·	·	PUNCT
ejpam-5080	375	5	·	·	PUNCT
ejpam-5080	375	6	·	·	PUNCT
ejpam-5080	375	7	,	,	PUNCT
ejpam-5080	375	8	uj(x	uj(x	NOUN
ejpam-5080	375	9	)	)	PUNCT
ejpam-5080	375	10	=	=	SYM
ejpam-5080	375	11	6∑	6∑	PROPN
ejpam-5080	375	12	n=0	n=0	NUM
ejpam-5080	375	13	un(x	un(x	SYM
ejpam-5080	375	14	)	)	PUNCT
ejpam-5080	375	15	=	=	SYM
ejpam-5080	375	16	1−	1−	NUM
ejpam-5080	375	17	0.9998581770x2	0.9998581770x2	NUM
ejpam-5080	376	1	−	−	NOUN
ejpam-5080	376	2	0.001420987833x3	0.001420987833x3	NUM
ejpam-5080	377	1	+	+	CCONJ
ejpam-5080	377	2	0.5059695492x4	0.5059695492x4	NUM
ejpam-5080	377	3	+	+	X
ejpam-5080	377	4	·	·	PUNCT
ejpam-5080	377	5	·	·	PUNCT
ejpam-5080	377	6	·	·	PUNCT
ejpam-5080	377	7	,	,	PUNCT
ejpam-5080	377	8	(	(	PUNCT
ejpam-5080	377	9	69	69	NUM
ejpam-5080	377	10	)	)	PUNCT
ejpam-5080	377	11	therefore	therefore	ADV
ejpam-5080	377	12	,	,	PUNCT
ejpam-5080	377	13	we	we	PRON
ejpam-5080	377	14	report	report	VERB
ejpam-5080	377	15	in	in	ADP
ejpam-5080	377	16	table	table	NOUN
ejpam-5080	377	17	4	4	NUM
ejpam-5080	377	18	the	the	DET
ejpam-5080	377	19	absolute	absolute	ADJ
ejpam-5080	377	20	error	error	NOUN
ejpam-5080	377	21	differences	difference	NOUN
ejpam-5080	377	22	between	between	ADP
ejpam-5080	377	23	the	the	DET
ejpam-5080	377	24	exact	exact	ADJ
ejpam-5080	377	25	solution	solution	NOUN
ejpam-5080	377	26	u(x	u(x	NOUN
ejpam-5080	377	27	)	)	PUNCT
ejpam-5080	377	28	and	and	CCONJ
ejpam-5080	377	29	the	the	DET
ejpam-5080	377	30	respective	respective	ADJ
ejpam-5080	377	31	solutions	solution	NOUN
ejpam-5080	377	32	by	by	ADP
ejpam-5080	377	33	the	the	DET
ejpam-5080	377	34	proposed	propose	VERB
ejpam-5080	377	35	modification	modification	NOUN
ejpam-5080	377	36	methods	method	NOUN
ejpam-5080	377	37	.	.	PUNCT
ejpam-5080	378	1	table	table	NOUN
ejpam-5080	378	2	4	4	NUM
ejpam-5080	378	3	:	:	PUNCT
ejpam-5080	378	4	absolute	absolute	ADJ
ejpam-5080	378	5	error	error	NOUN
ejpam-5080	378	6	comparisons	comparison	NOUN
ejpam-5080	378	7	via	via	ADP
ejpam-5080	378	8	the	the	DET
ejpam-5080	378	9	proposed	propose	VERB
ejpam-5080	378	10	modifications	modification	NOUN
ejpam-5080	378	11	for	for	ADP
ejpam-5080	378	12	example	example	NOUN
ejpam-5080	378	13	4	4	NUM
ejpam-5080	378	14	x	x	NOUN
ejpam-5080	378	15	|u(x)−	|u(x)−	NOUN
ejpam-5080	378	16	ut(x)|	ut(x)|	VERB
ejpam-5080	378	17	|u(x)−	|u(x)−	PROPN
ejpam-5080	378	18	up	up	ADP
ejpam-5080	378	19	(	(	PUNCT
ejpam-5080	378	20	x)|	x)|	PROPN
ejpam-5080	378	21	|u(x)−	|u(x)−	PROPN
ejpam-5080	378	22	ut	ut	PROPN
ejpam-5080	379	1	(	(	PUNCT
ejpam-5080	379	2	x)|	x)|	PROPN
ejpam-5080	379	3	|u(x)−	|u(x)−	PROPN
ejpam-5080	379	4	ug(x)|	ug(x)|	VERB
ejpam-5080	379	5	|u(x)−	|u(x)−	PROPN
ejpam-5080	379	6	uj(x)|	uj(x)|	PROPN
ejpam-5080	379	7	0	0	NUM
ejpam-5080	379	8	0	0	NUM
ejpam-5080	379	9	0	0	NUM
ejpam-5080	379	10	0	0	NUM
ejpam-5080	379	11	0	0	NUM
ejpam-5080	379	12	0	0	NUM
ejpam-5080	379	13	0.25	0.25	NUM
ejpam-5080	379	14	5.058×	5.058×	NUM
ejpam-5080	379	15	10−7	10−7	NUM
ejpam-5080	379	16	1.208×	1.208×	NUM
ejpam-5080	379	17	10−7	10−7	NUM
ejpam-5080	379	18	2.654×	2.654×	NUM
ejpam-5080	379	19	10−7	10−7	NUM
ejpam-5080	380	1	3.305×	3.305×	NUM
ejpam-5080	380	2	10−7	10−7	NUM
ejpam-5080	381	1	1.001×	1.001×	NUM
ejpam-5080	381	2	10−6	10−6	NUM
ejpam-5080	382	1	0.50	0.50	NUM
ejpam-5080	382	2	9.578×	9.578×	NUM
ejpam-5080	382	3	10−5	10−5	NUM
ejpam-5080	382	4	2.950×	2.950×	NUM
ejpam-5080	382	5	10−8	10−8	PROPN
ejpam-5080	382	6	2.344×	2.344×	NUM
ejpam-5080	382	7	10−7	10−7	NUM
ejpam-5080	382	8	8.493×	8.493×	NUM
ejpam-5080	382	9	10−7	10−7	NUM
ejpam-5080	382	10	2.121×	2.121×	NUM
ejpam-5080	382	11	10−6	10−6	NUM
ejpam-5080	382	12	0.75	0.75	NUM
ejpam-5080	382	13	1.663×	1.663×	NUM
ejpam-5080	382	14	10−3	10−3	NUM
ejpam-5080	382	15	1.045×	1.045×	NUM
ejpam-5080	382	16	10−7	10−7	NUM
ejpam-5080	382	17	3.259×	3.259×	NUM
ejpam-5080	382	18	10−7	10−7	NUM
ejpam-5080	382	19	1.272×	1.272×	NUM
ejpam-5080	382	20	10−6	10−6	NUM
ejpam-5080	383	1	3.070×	3.070×	NUM
ejpam-5080	383	2	10−6	10−6	NUM
ejpam-5080	383	3	1	1	NUM
ejpam-5080	383	4	1.011×	1.011×	NUM
ejpam-5080	383	5	10−2	10−2	NUM
ejpam-5080	383	6	6.420×	6.420×	NUM
ejpam-5080	383	7	10−8	10−8	NUM
ejpam-5080	383	8	5.574×	5.574×	NUM
ejpam-5080	383	9	10−7	10−7	NUM
ejpam-5080	383	10	1.371×	1.371×	NUM
ejpam-5080	383	11	10−6	10−6	NUM
ejpam-5080	384	1	3.558×	3.558×	NUM
ejpam-5080	384	2	10−6	10−6	NUM
ejpam-5080	384	3	x	x	X
ejpam-5080	384	4	|u(x)−	|u(x)−	PROPN
ejpam-5080	384	5	ul(x)|	ul(x)|	VERB
ejpam-5080	384	6	|u(x)−	|u(x)−	X
ejpam-5080	384	7	uh(x)|	uh(x)|	ADP
ejpam-5080	384	8	0	0	NUM
ejpam-5080	384	9	0	0	NUM
ejpam-5080	384	10	0	0	NUM
ejpam-5080	384	11	0.25	0.25	NUM
ejpam-5080	384	12	5.183×	5.183×	PROPN
ejpam-5080	384	13	10−3	10−3	NUM
ejpam-5080	384	14	5.497×	5.497×	NUM
ejpam-5080	384	15	10−3	10−3	NUM
ejpam-5080	384	16	0.50	0.50	NUM
ejpam-5080	384	17	2.399×	2.399×	NUM
ejpam-5080	384	18	10−3	10−3	NUM
ejpam-5080	384	19	1.126×	1.126×	NUM
ejpam-5080	384	20	10−2	10−2	NUM
ejpam-5080	384	21	0.75	0.75	NUM
ejpam-5080	384	22	9.282×	9.282×	NUM
ejpam-5080	384	23	10−3	10−3	NUM
ejpam-5080	384	24	3.958×	3.958×	NUM
ejpam-5080	384	25	10−3	10−3	NUM
ejpam-5080	384	26	1	1	NUM
ejpam-5080	384	27	1.642×	1.642×	NUM
ejpam-5080	384	28	10−2	10−2	NUM
ejpam-5080	384	29	1.438×	1.438×	NUM
ejpam-5080	384	30	10−2	10−2	NUM
ejpam-5080	384	31	references	reference	NOUN
ejpam-5080	384	32	1999	1999	NUM
ejpam-5080	384	33	5	5	NUM
ejpam-5080	384	34	.	.	PUNCT
ejpam-5080	384	35	conclusion	conclusion	NOUN
ejpam-5080	384	36	the	the	DET
ejpam-5080	384	37	present	present	ADJ
ejpam-5080	384	38	study	study	NOUN
ejpam-5080	384	39	proposed	propose	VERB
ejpam-5080	384	40	different	different	ADJ
ejpam-5080	384	41	modification	modification	NOUN
ejpam-5080	384	42	methods	method	NOUN
ejpam-5080	384	43	for	for	ADP
ejpam-5080	384	44	the	the	DET
ejpam-5080	384	45	standard	standard	ADJ
ejpam-5080	384	46	adomian	adomian	NOUN
ejpam-5080	384	47	decomposition	decomposition	NOUN
ejpam-5080	384	48	method	method	NOUN
ejpam-5080	384	49	(	(	PUNCT
ejpam-5080	384	50	adm	adm	PROPN
ejpam-5080	384	51	)	)	PUNCT
ejpam-5080	384	52	to	to	PART
ejpam-5080	384	53	tackle	tackle	VERB
ejpam-5080	384	54	a	a	DET
ejpam-5080	384	55	variety	variety	NOUN
ejpam-5080	384	56	of	of	ADP
ejpam-5080	384	57	problems	problem	NOUN
ejpam-5080	384	58	of	of	ADP
ejpam-5080	384	59	mathematical	mathematical	ADJ
ejpam-5080	384	60	physics	physics	NOUN
ejpam-5080	384	61	.	.	PUNCT
ejpam-5080	385	1	these	these	DET
ejpam-5080	385	2	modification	modification	NOUN
ejpam-5080	385	3	methods	method	NOUN
ejpam-5080	385	4	were	be	AUX
ejpam-5080	385	5	based	base	VERB
ejpam-5080	385	6	on	on	ADP
ejpam-5080	385	7	the	the	DET
ejpam-5080	385	8	application	application	NOUN
ejpam-5080	385	9	of	of	ADP
ejpam-5080	385	10	orthogonal	orthogonal	ADJ
ejpam-5080	385	11	polynomials	polynomial	NOUN
ejpam-5080	385	12	that	that	PRON
ejpam-5080	385	13	play	play	VERB
ejpam-5080	385	14	vital	vital	ADJ
ejpam-5080	385	15	parts	part	NOUN
ejpam-5080	385	16	in	in	ADP
ejpam-5080	385	17	numerical	numerical	ADJ
ejpam-5080	385	18	methods	method	NOUN
ejpam-5080	385	19	,	,	PUNCT
ejpam-5080	385	20	as	as	ADV
ejpam-5080	385	21	well	well	ADV
ejpam-5080	385	22	as	as	ADP
ejpam-5080	385	23	in	in	ADP
ejpam-5080	385	24	approximation	approximation	NOUN
ejpam-5080	385	25	theories	theory	NOUN
ejpam-5080	385	26	.	.	PUNCT
ejpam-5080	386	1	furthermore	furthermore	ADV
ejpam-5080	386	2	,	,	PUNCT
ejpam-5080	386	3	the	the	DET
ejpam-5080	386	4	study	study	NOUN
ejpam-5080	386	5	also	also	ADV
ejpam-5080	386	6	scrutinized	scrutinize	VERB
ejpam-5080	386	7	four	four	NUM
ejpam-5080	386	8	different	different	ADJ
ejpam-5080	386	9	test	test	NOUN
ejpam-5080	386	10	nonlinear	nonlinear	PROPN
ejpam-5080	386	11	inhomogeneous	inhomogeneous	ADJ
ejpam-5080	386	12	ivps	ivps	PROPN
ejpam-5080	386	13	,	,	PUNCT
ejpam-5080	386	14	and	and	CCONJ
ejpam-5080	386	15	distinctively	distinctively	ADV
ejpam-5080	386	16	examined	examine	VERB
ejpam-5080	386	17	their	their	PRON
ejpam-5080	386	18	respective	respective	ADJ
ejpam-5080	386	19	absolute	absolute	ADJ
ejpam-5080	386	20	error	error	NOUN
ejpam-5080	386	21	differences	difference	NOUN
ejpam-5080	386	22	.	.	PUNCT
ejpam-5080	387	1	notably	notably	ADV
ejpam-5080	387	2	,	,	PUNCT
ejpam-5080	387	3	the	the	DET
ejpam-5080	387	4	proposed	propose	VERB
ejpam-5080	387	5	modification	modification	NOUN
ejpam-5080	387	6	methods	method	NOUN
ejpam-5080	387	7	based	base	VERB
ejpam-5080	387	8	on	on	ADP
ejpam-5080	387	9	the	the	DET
ejpam-5080	387	10	application	application	NOUN
ejpam-5080	387	11	of	of	ADP
ejpam-5080	387	12	legendre	legendre	PROPN
ejpam-5080	387	13	’s	’s	PART
ejpam-5080	387	14	orthogonal	orthogonal	ADJ
ejpam-5080	387	15	polynomials	polynomial	NOUN
ejpam-5080	387	16	up	up	ADP
ejpam-5080	387	17	(	(	PUNCT
ejpam-5080	387	18	x	x	X
ejpam-5080	387	19	)	)	PUNCT
ejpam-5080	387	20	was	be	AUX
ejpam-5080	387	21	noted	note	VERB
ejpam-5080	387	22	to	to	PART
ejpam-5080	387	23	have	have	VERB
ejpam-5080	387	24	the	the	DET
ejpam-5080	387	25	least	least	ADJ
ejpam-5080	387	26	error	error	NOUN
ejpam-5080	387	27	among	among	ADP
ejpam-5080	387	28	its	its	PRON
ejpam-5080	387	29	contending	contend	VERB
ejpam-5080	387	30	companions	companion	NOUN
ejpam-5080	387	31	in	in	ADP
ejpam-5080	387	32	three	three	NUM
ejpam-5080	387	33	of	of	ADP
ejpam-5080	387	34	the	the	DET
ejpam-5080	387	35	test	test	NOUN
ejpam-5080	387	36	problems	problem	NOUN
ejpam-5080	387	37	;	;	PUNCT
ejpam-5080	387	38	it	it	PRON
ejpam-5080	387	39	also	also	ADV
ejpam-5080	387	40	performed	perform	VERB
ejpam-5080	387	41	outstandingly	outstandingly	ADV
ejpam-5080	387	42	in	in	ADP
ejpam-5080	387	43	the	the	DET
ejpam-5080	387	44	remaining	remain	VERB
ejpam-5080	387	45	problem	problem	NOUN
ejpam-5080	387	46	.	.	PUNCT
ejpam-5080	388	1	finally	finally	ADV
ejpam-5080	388	2	,	,	PUNCT
ejpam-5080	388	3	as	as	SCONJ
ejpam-5080	388	4	certain	certain	ADJ
ejpam-5080	388	5	computational	computational	ADJ
ejpam-5080	388	6	benefits	benefit	NOUN
ejpam-5080	388	7	of	of	ADP
ejpam-5080	388	8	the	the	DET
ejpam-5080	388	9	proposed	propose	VERB
ejpam-5080	388	10	modification	modification	NOUN
ejpam-5080	388	11	are	be	AUX
ejpam-5080	388	12	realized	realize	VERB
ejpam-5080	388	13	with	with	ADP
ejpam-5080	388	14	regards	regard	VERB
ejpam-5080	388	15	high	high	ADJ
ejpam-5080	388	16	-	-	PUNCT
ejpam-5080	388	17	level	level	NOUN
ejpam-5080	388	18	of	of	ADP
ejpam-5080	388	19	accuracy	accuracy	NOUN
ejpam-5080	388	20	and	and	CCONJ
ejpam-5080	388	21	fewer	few	ADJ
ejpam-5080	388	22	computational	computational	ADJ
ejpam-5080	388	23	steps	step	NOUN
ejpam-5080	388	24	in	in	ADP
ejpam-5080	388	25	the	the	DET
ejpam-5080	388	26	study	study	NOUN
ejpam-5080	388	27	,	,	PUNCT
ejpam-5080	388	28	it	it	PRON
ejpam-5080	388	29	is	be	AUX
ejpam-5080	388	30	therefore	therefore	ADV
ejpam-5080	388	31	recommended	recommend	VERB
ejpam-5080	388	32	to	to	PART
ejpam-5080	388	33	implement	implement	VERB
ejpam-5080	388	34	these	these	DET
ejpam-5080	388	35	methods	method	NOUN
ejpam-5080	388	36	on	on	ADP
ejpam-5080	388	37	high	high	ADJ
ejpam-5080	388	38	-	-	PUNCT
ejpam-5080	388	39	order	order	NOUN
ejpam-5080	388	40	ivps	ivps	NOUN
ejpam-5080	388	41	arising	arise	VERB
ejpam-5080	388	42	in	in	ADP
ejpam-5080	388	43	the	the	DET
ejpam-5080	388	44	general	general	ADJ
ejpam-5080	388	45	science	science	NOUN
ejpam-5080	388	46	and	and	CCONJ
ejpam-5080	388	47	engineering	engineering	NOUN
ejpam-5080	388	48	applications	application	NOUN
ejpam-5080	388	49	.	.	PUNCT
ejpam-5080	389	1	references	reference	NOUN
ejpam-5080	389	2	[	[	X
ejpam-5080	389	3	1	1	NUM
ejpam-5080	389	4	]	]	PUNCT
ejpam-5080	389	5	g	g	PROPN
ejpam-5080	389	6	adomian	adomian	NOUN
ejpam-5080	389	7	.	.	PUNCT
ejpam-5080	390	1	a	a	DET
ejpam-5080	390	2	review	review	NOUN
ejpam-5080	390	3	of	of	ADP
ejpam-5080	390	4	the	the	DET
ejpam-5080	390	5	decomposition	decomposition	NOUN
ejpam-5080	390	6	method	method	NOUN
ejpam-5080	390	7	and	and	CCONJ
ejpam-5080	390	8	some	some	DET
ejpam-5080	390	9	recent	recent	ADJ
ejpam-5080	390	10	results	result	NOUN
ejpam-5080	390	11	for	for	ADP
ejpam-5080	390	12	nonlinear	nonlinear	ADJ
ejpam-5080	390	13	equations	equation	NOUN
ejpam-5080	390	14	.	.	PUNCT
ejpam-5080	391	1	mathematical	mathematical	ADJ
ejpam-5080	391	2	and	and	CCONJ
ejpam-5080	391	3	computer	computer	NOUN
ejpam-5080	391	4	modelling	modelling	NOUN
ejpam-5080	391	5	,	,	PUNCT
ejpam-5080	391	6	13(7):17–43	13(7):17–43	NUM
ejpam-5080	391	7	,	,	PUNCT
ejpam-5080	391	8	1990	1990	NUM
ejpam-5080	391	9	.	.	PUNCT
ejpam-5080	392	1	[	[	X
ejpam-5080	392	2	2	2	NUM
ejpam-5080	392	3	]	]	PUNCT
ejpam-5080	392	4	george	george	PROPN
ejpam-5080	392	5	adomian	adomian	NOUN
ejpam-5080	392	6	.	.	PUNCT
ejpam-5080	393	1	solving	solve	VERB
ejpam-5080	393	2	frontier	frontier	NOUN
ejpam-5080	393	3	problems	problem	NOUN
ejpam-5080	393	4	of	of	ADP
ejpam-5080	393	5	physics	physics	NOUN
ejpam-5080	393	6	:	:	PUNCT
ejpam-5080	393	7	the	the	DET
ejpam-5080	393	8	decomposition	decomposition	NOUN
ejpam-5080	393	9	method	method	NOUN
ejpam-5080	393	10	,	,	PUNCT
ejpam-5080	393	11	with	with	ADP
ejpam-5080	393	12	a	a	DET
ejpam-5080	393	13	preface	preface	NOUN
ejpam-5080	393	14	by	by	ADP
ejpam-5080	393	15	yves	yve	NOUN
ejpam-5080	393	16	cherruault	cherruault	NOUN
ejpam-5080	393	17	.	.	PUNCT
ejpam-5080	394	1	fundamental	fundamental	ADJ
ejpam-5080	394	2	theories	theory	NOUN
ejpam-5080	394	3	of	of	ADP
ejpam-5080	394	4	physics	physics	PROPN
ejpam-5080	394	5	,	,	PUNCT
ejpam-5080	394	6	kluwer	kluwer	PROPN
ejpam-5080	394	7	academic	academic	ADJ
ejpam-5080	394	8	publishers	publisher	NOUN
ejpam-5080	394	9	group	group	NOUN
ejpam-5080	394	10	,	,	PUNCT
ejpam-5080	394	11	dordrecht	dordrecht	PROPN
ejpam-5080	394	12	,	,	PUNCT
ejpam-5080	394	13	1	1	NUM
ejpam-5080	394	14	,	,	PUNCT
ejpam-5080	394	15	1994	1994	NUM
ejpam-5080	394	16	.	.	PUNCT
ejpam-5080	395	1	[	[	X
ejpam-5080	395	2	3	3	X
ejpam-5080	395	3	]	]	X
ejpam-5080	395	4	m	m	VERB
ejpam-5080	395	5	almazmumy	almazmumy	PROPN
ejpam-5080	395	6	,	,	PUNCT
ejpam-5080	395	7	fa	fa	PROPN
ejpam-5080	395	8	hendi	hendi	NOUN
ejpam-5080	395	9	,	,	PUNCT
ejpam-5080	395	10	ho	ho	PROPN
ejpam-5080	395	11	bakodah	bakodah	NOUN
ejpam-5080	395	12	,	,	PUNCT
ejpam-5080	395	13	and	and	CCONJ
ejpam-5080	395	14	h	h	PROPN
ejpam-5080	395	15	alzumi	alzumi	PROPN
ejpam-5080	395	16	.	.	PUNCT
ejpam-5080	396	1	recent	recent	ADJ
ejpam-5080	396	2	modifications	modification	NOUN
ejpam-5080	396	3	of	of	ADP
ejpam-5080	396	4	adomian	adomian	ADJ
ejpam-5080	396	5	decomposition	decomposition	NOUN
ejpam-5080	396	6	method	method	NOUN
ejpam-5080	396	7	for	for	ADP
ejpam-5080	396	8	initial	initial	ADJ
ejpam-5080	396	9	value	value	NOUN
ejpam-5080	396	10	problem	problem	NOUN
ejpam-5080	396	11	in	in	ADP
ejpam-5080	396	12	ordinary	ordinary	ADJ
ejpam-5080	396	13	differential	differential	ADJ
ejpam-5080	396	14	equations	equation	NOUN
ejpam-5080	396	15	.	.	PUNCT
ejpam-5080	397	1	2012	2012	NUM
ejpam-5080	397	2	.	.	PUNCT
ejpam-5080	398	1	[	[	X
ejpam-5080	398	2	4	4	NUM
ejpam-5080	398	3	]	]	SYM
ejpam-5080	398	4	ho	ho	ADJ
ejpam-5080	398	5	bakodah	bakodah	PROPN
ejpam-5080	398	6	,	,	PUNCT
ejpam-5080	398	7	ma	ma	PROPN
ejpam-5080	398	8	banaja	banaja	PROPN
ejpam-5080	398	9	,	,	PUNCT
ejpam-5080	398	10	ba	ba	PROPN
ejpam-5080	398	11	alrigi	alrigi	PROPN
ejpam-5080	398	12	,	,	PUNCT
ejpam-5080	398	13	a	a	DET
ejpam-5080	398	14	ebaid	ebaid	NOUN
ejpam-5080	398	15	,	,	PUNCT
ejpam-5080	398	16	and	and	CCONJ
ejpam-5080	398	17	r	r	NOUN
ejpam-5080	398	18	rach	rach	NOUN
ejpam-5080	398	19	.	.	PUNCT
ejpam-5080	399	1	an	an	DET
ejpam-5080	399	2	efficient	efficient	ADJ
ejpam-5080	399	3	modification	modification	NOUN
ejpam-5080	399	4	of	of	ADP
ejpam-5080	399	5	the	the	DET
ejpam-5080	399	6	decomposition	decomposition	NOUN
ejpam-5080	399	7	method	method	NOUN
ejpam-5080	399	8	with	with	ADP
ejpam-5080	399	9	a	a	DET
ejpam-5080	399	10	convergence	convergence	NOUN
ejpam-5080	399	11	parameter	parameter	NOUN
ejpam-5080	399	12	for	for	ADP
ejpam-5080	399	13	solving	solve	VERB
ejpam-5080	399	14	korteweg	korteweg	PROPN
ejpam-5080	399	15	de	de	PROPN
ejpam-5080	399	16	vries	vries	PROPN
ejpam-5080	399	17	equations	equation	NOUN
ejpam-5080	399	18	.	.	PUNCT
ejpam-5080	400	1	journal	journal	PROPN
ejpam-5080	400	2	of	of	ADP
ejpam-5080	400	3	king	king	PROPN
ejpam-5080	400	4	saud	saud	PROPN
ejpam-5080	400	5	university	university	PROPN
ejpam-5080	400	6	-	-	PUNCT
ejpam-5080	400	7	science	science	NOUN
ejpam-5080	400	8	,	,	PUNCT
ejpam-5080	400	9	31(4):1424–1430	31(4):1424–1430	PROPN
ejpam-5080	400	10	,	,	PUNCT
ejpam-5080	400	11	2019	2019	NUM
ejpam-5080	400	12	.	.	PUNCT
ejpam-5080	401	1	[	[	X
ejpam-5080	401	2	5	5	X
ejpam-5080	401	3	]	]	PUNCT
ejpam-5080	401	4	william	william	PROPN
ejpam-5080	401	5	wallace	wallace	PROPN
ejpam-5080	401	6	bell	bell	PROPN
ejpam-5080	401	7	.	.	PUNCT
ejpam-5080	402	1	special	special	ADJ
ejpam-5080	402	2	functions	function	NOUN
ejpam-5080	402	3	for	for	ADP
ejpam-5080	402	4	scientists	scientist	NOUN
ejpam-5080	402	5	and	and	CCONJ
ejpam-5080	402	6	engineers	engineer	NOUN
ejpam-5080	402	7	.	.	PUNCT
ejpam-5080	403	1	courier	courier	NOUN
ejpam-5080	403	2	corporation	corporation	NOUN
ejpam-5080	403	3	,	,	PUNCT
ejpam-5080	403	4	2004	2004	NUM
ejpam-5080	403	5	.	.	PUNCT
ejpam-5080	404	1	[	[	X
ejpam-5080	404	2	6	6	NUM
ejpam-5080	404	3	]	]	PUNCT
ejpam-5080	404	4	yücel	yücel	X
ejpam-5080	404	5	çenesiz	çenesiz	ADV
ejpam-5080	404	6	and	and	CCONJ
ejpam-5080	404	7	aydın	aydın	PROPN
ejpam-5080	404	8	kurnaz	kurnaz	PROPN
ejpam-5080	404	9	.	.	PUNCT
ejpam-5080	405	1	adomian	adomian	NOUN
ejpam-5080	405	2	decomposition	decomposition	NOUN
ejpam-5080	405	3	method	method	NOUN
ejpam-5080	405	4	by	by	ADP
ejpam-5080	405	5	gegenbauer	gegenbauer	NOUN
ejpam-5080	405	6	and	and	CCONJ
ejpam-5080	405	7	jacobi	jacobi	PROPN
ejpam-5080	405	8	polynomials	polynomial	NOUN
ejpam-5080	405	9	.	.	PUNCT
ejpam-5080	406	1	international	international	ADJ
ejpam-5080	406	2	journal	journal	PROPN
ejpam-5080	406	3	of	of	ADP
ejpam-5080	406	4	computer	computer	NOUN
ejpam-5080	406	5	mathematics	mathematic	NOUN
ejpam-5080	406	6	,	,	PUNCT
ejpam-5080	406	7	88(17):3666	88(17):3666	NUM
ejpam-5080	406	8	–	–	PUNCT
ejpam-5080	406	9	3676	3676	NUM
ejpam-5080	406	10	,	,	PUNCT
ejpam-5080	406	11	2011	2011	NUM
ejpam-5080	406	12	.	.	PUNCT
ejpam-5080	407	1	[	[	X
ejpam-5080	407	2	7	7	X
ejpam-5080	407	3	]	]	X
ejpam-5080	407	4	mohammad	mohammad	PROPN
ejpam-5080	407	5	mahdi	mahdi	PROPN
ejpam-5080	407	6	hosseini	hosseini	PROPN
ejpam-5080	407	7	.	.	PUNCT
ejpam-5080	408	1	adomian	adomian	PROPN
ejpam-5080	408	2	decomposition	decomposition	NOUN
ejpam-5080	408	3	method	method	NOUN
ejpam-5080	408	4	with	with	ADP
ejpam-5080	408	5	chebyshev	chebyshev	NOUN
ejpam-5080	408	6	polynomials	polynomial	NOUN
ejpam-5080	408	7	.	.	PUNCT
ejpam-5080	409	1	applied	apply	VERB
ejpam-5080	409	2	mathematics	mathematic	NOUN
ejpam-5080	409	3	and	and	CCONJ
ejpam-5080	409	4	computation	computation	NOUN
ejpam-5080	409	5	,	,	PUNCT
ejpam-5080	409	6	175(2):1685–1693	175(2):1685–1693	NUM
ejpam-5080	409	7	,	,	PUNCT
ejpam-5080	409	8	2006	2006	NUM
ejpam-5080	409	9	.	.	PUNCT
ejpam-5080	410	1	[	[	X
ejpam-5080	410	2	8	8	NUM
ejpam-5080	410	3	]	]	X
ejpam-5080	410	4	yucheng	yucheng	PROPN
ejpam-5080	410	5	liu	liu	PROPN
ejpam-5080	410	6	.	.	PROPN
ejpam-5080	411	1	adomian	adomian	PROPN
ejpam-5080	411	2	decomposition	decomposition	NOUN
ejpam-5080	411	3	method	method	NOUN
ejpam-5080	411	4	with	with	ADP
ejpam-5080	411	5	orthogonal	orthogonal	ADJ
ejpam-5080	411	6	polynomials	polynomial	NOUN
ejpam-5080	411	7	:	:	PUNCT
ejpam-5080	411	8	legendre	legendre	NOUN
ejpam-5080	411	9	polynomials	polynomial	NOUN
ejpam-5080	411	10	.	.	PUNCT
ejpam-5080	412	1	mathematical	mathematical	ADJ
ejpam-5080	412	2	and	and	CCONJ
ejpam-5080	412	3	computer	computer	NOUN
ejpam-5080	412	4	modelling	modelling	NOUN
ejpam-5080	412	5	,	,	PUNCT
ejpam-5080	412	6	49(5	49(5	NUM
ejpam-5080	412	7	-	-	SYM
ejpam-5080	412	8	6):1268–1273	6):1268–1273	NUM
ejpam-5080	412	9	,	,	PUNCT
ejpam-5080	412	10	2009	2009	NUM
ejpam-5080	412	11	.	.	PUNCT
ejpam-5080	413	1	references	reference	NOUN
ejpam-5080	413	2	2000	2000	NUM
ejpam-5080	414	1	[	[	X
ejpam-5080	414	2	9	9	NUM
ejpam-5080	414	3	]	]	X
ejpam-5080	414	4	yucheng	yucheng	PROPN
ejpam-5080	414	5	liu	liu	PROPN
ejpam-5080	414	6	.	.	PROPN
ejpam-5080	415	1	adomian	adomian	PROPN
ejpam-5080	415	2	decomposition	decomposition	NOUN
ejpam-5080	415	3	method	method	NOUN
ejpam-5080	415	4	with	with	ADP
ejpam-5080	415	5	second	second	ADJ
ejpam-5080	415	6	kind	kind	ADJ
ejpam-5080	415	7	chebyshev	chebyshev	NOUN
ejpam-5080	415	8	polynomials	polynomial	NOUN
ejpam-5080	415	9	.	.	PUNCT
ejpam-5080	416	1	in	in	ADP
ejpam-5080	416	2	proceedings	proceeding	NOUN
ejpam-5080	416	3	of	of	ADP
ejpam-5080	416	4	the	the	DET
ejpam-5080	416	5	jangjeon	jangjeon	PROPN
ejpam-5080	416	6	mathematical	mathematical	PROPN
ejpam-5080	416	7	society	society	NOUN
ejpam-5080	416	8	,	,	PUNCT
ejpam-5080	416	9	volume	volume	NOUN
ejpam-5080	416	10	12	12	NUM
ejpam-5080	416	11	,	,	PUNCT
ejpam-5080	416	12	pages	page	NOUN
ejpam-5080	416	13	57–67	57–67	NUM
ejpam-5080	416	14	.	.	PUNCT
ejpam-5080	417	1	the	the	DET
ejpam-5080	417	2	society	society	NOUN
ejpam-5080	417	3	,	,	PUNCT
ejpam-5080	417	4	2009	2009	NUM
ejpam-5080	417	5	.	.	PUNCT
ejpam-5080	418	1	[	[	X
ejpam-5080	418	2	10	10	NUM
ejpam-5080	418	3	]	]	X
ejpam-5080	418	4	yucheng	yucheng	PROPN
ejpam-5080	418	5	liu	liu	PROPN
ejpam-5080	418	6	.	.	PUNCT
ejpam-5080	419	1	application	application	NOUN
ejpam-5080	419	2	of	of	ADP
ejpam-5080	419	3	legendre	legendre	PROPN
ejpam-5080	419	4	polynomials	polynomial	NOUN
ejpam-5080	419	5	in	in	ADP
ejpam-5080	419	6	adomian	adomian	ADJ
ejpam-5080	419	7	decomposition	decomposition	NOUN
ejpam-5080	419	8	method	method	NOUN
ejpam-5080	419	9	.	.	PUNCT
ejpam-5080	420	1	in	in	ADP
ejpam-5080	420	2	proceedings	proceeding	NOUN
ejpam-5080	420	3	of	of	ADP
ejpam-5080	420	4	2012	2012	NUM
ejpam-5080	420	5	international	international	ADJ
ejpam-5080	420	6	conference	conference	NOUN
ejpam-5080	420	7	on	on	ADP
ejpam-5080	420	8	computer	computer	NOUN
ejpam-5080	420	9	,	,	PUNCT
ejpam-5080	420	10	electrical	electrical	ADJ
ejpam-5080	420	11	,	,	PUNCT
ejpam-5080	420	12	and	and	CCONJ
ejpam-5080	420	13	systems	system	NOUN
ejpam-5080	420	14	sciences	science	NOUN
ejpam-5080	420	15	,	,	PUNCT
ejpam-5080	420	16	amsterdam	amsterdam	PROPN
ejpam-5080	420	17	,	,	PUNCT
ejpam-5080	420	18	pages	page	NOUN
ejpam-5080	420	19	13–14	13–14	NUM
ejpam-5080	420	20	,	,	PUNCT
ejpam-5080	420	21	2012	2012	NUM
ejpam-5080	420	22	.	.	PUNCT
ejpam-5080	421	1	[	[	X
ejpam-5080	421	2	11	11	NUM
ejpam-5080	421	3	]	]	X
ejpam-5080	421	4	y	y	PROPN
ejpam-5080	421	5	mahmoudi	mahmoudi	NOUN
ejpam-5080	421	6	,	,	PUNCT
ejpam-5080	421	7	m	m	VERB
ejpam-5080	421	8	abdollahi	abdollahi	ADJ
ejpam-5080	421	9	,	,	PUNCT
ejpam-5080	421	10	n	n	DET
ejpam-5080	421	11	karimian	karimian	NOUN
ejpam-5080	421	12	,	,	PUNCT
ejpam-5080	421	13	and	and	CCONJ
ejpam-5080	421	14	h	h	PROPN
ejpam-5080	421	15	khalili	khalili	PROPN
ejpam-5080	421	16	.	.	PUNCT
ejpam-5080	422	1	adomian	adomian	PROPN
ejpam-5080	422	2	decomposition	decomposition	NOUN
ejpam-5080	422	3	method	method	NOUN
ejpam-5080	422	4	with	with	ADP
ejpam-5080	422	5	laguerre	laguerre	NOUN
ejpam-5080	422	6	polynomials	polynomial	NOUN
ejpam-5080	422	7	for	for	ADP
ejpam-5080	422	8	solving	solve	VERB
ejpam-5080	422	9	ordinary	ordinary	ADJ
ejpam-5080	422	10	differential	differential	ADJ
ejpam-5080	422	11	equation	equation	NOUN
ejpam-5080	422	12	.	.	PUNCT
ejpam-5080	423	1	journal	journal	PROPN
ejpam-5080	423	2	of	of	ADP
ejpam-5080	423	3	basic	basic	ADJ
ejpam-5080	423	4	and	and	CCONJ
ejpam-5080	423	5	applied	apply	VERB
ejpam-5080	423	6	scientific	scientific	ADJ
ejpam-5080	423	7	research	research	NOUN
ejpam-5080	423	8	,	,	PUNCT
ejpam-5080	423	9	2(12):12236–12241	2(12):12236–12241	NUM
ejpam-5080	423	10	,	,	PUNCT
ejpam-5080	423	11	2012	2012	NUM
ejpam-5080	423	12	.	.	PUNCT
ejpam-5080	424	1	[	[	X
ejpam-5080	424	2	12	12	NUM
ejpam-5080	424	3	]	]	X
ejpam-5080	424	4	y	y	PROPN
ejpam-5080	424	5	mahmoudi	mahmoudi	NOUN
ejpam-5080	424	6	,	,	PUNCT
ejpam-5080	424	7	n	n	PRON
ejpam-5080	424	8	karimian	karimian	NOUN
ejpam-5080	424	9	,	,	PUNCT
ejpam-5080	424	10	and	and	CCONJ
ejpam-5080	424	11	m	m	PROPN
ejpam-5080	424	12	abdollahi	abdollahi	ADJ
ejpam-5080	424	13	.	.	PUNCT
ejpam-5080	425	1	adomian	adomian	NOUN
ejpam-5080	425	2	decomposition	decomposition	NOUN
ejpam-5080	425	3	method	method	NOUN
ejpam-5080	425	4	with	with	ADP
ejpam-5080	425	5	hermite	hermite	ADJ
ejpam-5080	425	6	polynomials	polynomial	NOUN
ejpam-5080	425	7	for	for	ADP
ejpam-5080	425	8	solving	solve	VERB
ejpam-5080	425	9	ordinary	ordinary	ADJ
ejpam-5080	425	10	differential	differential	ADJ
ejpam-5080	425	11	equations	equation	NOUN
ejpam-5080	425	12	.	.	PUNCT
ejpam-5080	426	1	journal	journal	NOUN
ejpam-5080	426	2	of	of	ADP
ejpam-5080	426	3	basic	basic	ADJ
ejpam-5080	426	4	and	and	CCONJ
ejpam-5080	426	5	applied	apply	VERB
ejpam-5080	426	6	scientific	scientific	ADJ
ejpam-5080	426	7	research	research	NOUN
ejpam-5080	426	8	,	,	PUNCT
ejpam-5080	426	9	3(3):255–258	3(3):255–258	NUM
ejpam-5080	426	10	,	,	PUNCT
ejpam-5080	426	11	2013	2013	NUM
ejpam-5080	426	12	.	.	PUNCT
ejpam-5080	427	1	[	[	X
ejpam-5080	427	2	13	13	NUM
ejpam-5080	427	3	]	]	X
ejpam-5080	427	4	abdul	abdul	PROPN
ejpam-5080	427	5	-	-	PUNCT
ejpam-5080	427	6	majid	majid	PROPN
ejpam-5080	427	7	wazwaz	wazwaz	NOUN
ejpam-5080	427	8	.	.	PUNCT
ejpam-5080	428	1	a	a	DET
ejpam-5080	428	2	reliable	reliable	ADJ
ejpam-5080	428	3	modification	modification	NOUN
ejpam-5080	428	4	of	of	ADP
ejpam-5080	428	5	adomian	adomian	ADJ
ejpam-5080	428	6	decomposition	decomposition	NOUN
ejpam-5080	428	7	method	method	NOUN
ejpam-5080	428	8	.	.	PUNCT
ejpam-5080	429	1	applied	apply	VERB
ejpam-5080	429	2	mathematics	mathematic	NOUN
ejpam-5080	429	3	and	and	CCONJ
ejpam-5080	429	4	computation	computation	NOUN
ejpam-5080	429	5	,	,	PUNCT
ejpam-5080	429	6	102(1):77–86	102(1):77–86	NUM
ejpam-5080	429	7	,	,	PUNCT
ejpam-5080	429	8	1999	1999	NUM
ejpam-5080	429	9	.	.	PUNCT
ejpam-5080	430	1	[	[	X
ejpam-5080	430	2	14	14	NUM
ejpam-5080	430	3	]	]	X
ejpam-5080	430	4	yingying	yingying	PROPN
ejpam-5080	430	5	xie	xie	PROPN
ejpam-5080	430	6	,	,	PUNCT
ejpam-5080	430	7	lingfei	lingfei	PROPN
ejpam-5080	430	8	li	li	PROPN
ejpam-5080	430	9	,	,	PUNCT
ejpam-5080	430	10	and	and	CCONJ
ejpam-5080	430	11	mancang	mancang	PROPN
ejpam-5080	430	12	wang	wang	PROPN
ejpam-5080	430	13	.	.	PUNCT
ejpam-5080	431	1	adomian	adomian	PROPN
ejpam-5080	431	2	decomposition	decomposition	NOUN
ejpam-5080	431	3	method	method	NOUN
ejpam-5080	431	4	with	with	ADP
ejpam-5080	431	5	orthogonal	orthogonal	ADJ
ejpam-5080	431	6	polynomials	polynomial	NOUN
ejpam-5080	431	7	:	:	PUNCT
ejpam-5080	431	8	laguerre	laguerre	NOUN
ejpam-5080	431	9	polynomials	polynomial	NOUN
ejpam-5080	431	10	and	and	CCONJ
ejpam-5080	431	11	the	the	DET
ejpam-5080	431	12	second	second	ADJ
ejpam-5080	431	13	kind	kind	NOUN
ejpam-5080	431	14	of	of	ADP
ejpam-5080	431	15	chebyshev	chebyshev	NOUN
ejpam-5080	431	16	polynomials	polynomial	NOUN
ejpam-5080	431	17	.	.	PUNCT
ejpam-5080	432	1	mathematics	mathematic	NOUN
ejpam-5080	432	2	,	,	PUNCT
ejpam-5080	432	3	9(15):1796	9(15):1796	NOUN
ejpam-5080	432	4	,	,	PUNCT
ejpam-5080	432	5	2021	2021	NUM
ejpam-5080	432	6	.	.	PUNCT