id	sid	tid	token	lemma	pos
ejpam-5050	1	1	european	european	PROPN
ejpam-5050	1	2	journal	journal	PROPN
ejpam-5050	1	3	of	of	ADP
ejpam-5050	1	4	pure	pure	ADJ
ejpam-5050	1	5	and	and	CCONJ
ejpam-5050	1	6	applied	apply	VERB
ejpam-5050	1	7	mathematics	mathematic	NOUN
ejpam-5050	1	8	vol	vol	NOUN
ejpam-5050	1	9	.	.	PROPN
ejpam-5050	2	1	17	17	NUM
ejpam-5050	2	2	,	,	PUNCT
ejpam-5050	2	3	no	no	INTJ
ejpam-5050	2	4	.	.	NOUN
ejpam-5050	2	5	1	1	NUM
ejpam-5050	2	6	,	,	PUNCT
ejpam-5050	2	7	2024	2024	NUM
ejpam-5050	2	8	,	,	PUNCT
ejpam-5050	2	9	546	546	NUM
ejpam-5050	2	10	-	-	SYM
ejpam-5050	2	11	568	568	NUM
ejpam-5050	2	12	issn	issn	PROPN
ejpam-5050	2	13	1307	1307	NUM
ejpam-5050	2	14	-	-	SYM
ejpam-5050	2	15	5543	5543	NUM
ejpam-5050	2	16	–	–	PUNCT
ejpam-5050	3	1	ejpam.com	ejpam.com	X
ejpam-5050	3	2	published	publish	VERB
ejpam-5050	3	3	by	by	ADP
ejpam-5050	3	4	new	new	PROPN
ejpam-5050	3	5	york	york	PROPN
ejpam-5050	3	6	business	business	PROPN
ejpam-5050	3	7	global	global	ADJ
ejpam-5050	3	8	utilization	utilization	NOUN
ejpam-5050	3	9	of	of	ADP
ejpam-5050	3	10	the	the	DET
ejpam-5050	3	11	modified	modify	VERB
ejpam-5050	3	12	adomian	adomian	NOUN
ejpam-5050	3	13	decomposition	decomposition	NOUN
ejpam-5050	3	14	method	method	NOUN
ejpam-5050	3	15	on	on	ADP
ejpam-5050	3	16	the	the	DET
ejpam-5050	3	17	bagley	bagley	NOUN
ejpam-5050	3	18	-	-	PUNCT
ejpam-5050	3	19	torvik	torvik	NOUN
ejpam-5050	3	20	equation	equation	NOUN
ejpam-5050	3	21	amidst	amidst	ADP
ejpam-5050	3	22	dirichlet	dirichlet	PROPN
ejpam-5050	3	23	boundary	boundary	PROPN
ejpam-5050	3	24	conditions	condition	NOUN
ejpam-5050	3	25	mariam	mariam	PROPN
ejpam-5050	3	26	al	al	PROPN
ejpam-5050	3	27	-	-	PUNCT
ejpam-5050	3	28	mazmumy1	mazmumy1	PROPN
ejpam-5050	3	29	,	,	PUNCT
ejpam-5050	3	30	mona	mona	PROPN
ejpam-5050	3	31	alsulami1,∗	alsulami1,∗	PROPN
ejpam-5050	3	32	1	1	NUM
ejpam-5050	3	33	department	department	NOUN
ejpam-5050	3	34	of	of	ADP
ejpam-5050	3	35	mathematics	mathematic	NOUN
ejpam-5050	3	36	and	and	CCONJ
ejpam-5050	3	37	statistics	statistic	NOUN
ejpam-5050	3	38	,	,	PUNCT
ejpam-5050	3	39	faculty	faculty	NOUN
ejpam-5050	3	40	of	of	ADP
ejpam-5050	3	41	science	science	NOUN
ejpam-5050	3	42	,	,	PUNCT
ejpam-5050	3	43	university	university	NOUN
ejpam-5050	3	44	of	of	ADP
ejpam-5050	3	45	jeddah	jeddah	PROPN
ejpam-5050	3	46	,	,	PUNCT
ejpam-5050	3	47	jeddah	jeddah	PROPN
ejpam-5050	3	48	23218	23218	NUM
ejpam-5050	3	49	,	,	PUNCT
ejpam-5050	3	50	saudi	saudi	PROPN
ejpam-5050	3	51	arabia	arabia	PROPN
ejpam-5050	3	52	abstract	abstract	NOUN
ejpam-5050	3	53	.	.	PUNCT
ejpam-5050	4	1	the	the	DET
ejpam-5050	4	2	bagley	bagley	NOUN
ejpam-5050	4	3	-	-	PUNCT
ejpam-5050	4	4	torvik	torvik	NOUN
ejpam-5050	4	5	equation	equation	NOUN
ejpam-5050	4	6	is	be	AUX
ejpam-5050	4	7	an	an	DET
ejpam-5050	4	8	imperative	imperative	ADJ
ejpam-5050	4	9	differential	differential	NOUN
ejpam-5050	4	10	equation	equation	NOUN
ejpam-5050	4	11	that	that	PRON
ejpam-5050	4	12	considerably	considerably	ADV
ejpam-5050	4	13	arises	arise	VERB
ejpam-5050	4	14	in	in	ADP
ejpam-5050	4	15	various	various	ADJ
ejpam-5050	4	16	branches	branch	NOUN
ejpam-5050	4	17	of	of	ADP
ejpam-5050	4	18	mathematical	mathematical	ADJ
ejpam-5050	4	19	physics	physics	NOUN
ejpam-5050	4	20	and	and	CCONJ
ejpam-5050	4	21	mechanics	mechanic	NOUN
ejpam-5050	4	22	.	.	PUNCT
ejpam-5050	5	1	however	however	ADV
ejpam-5050	5	2	,	,	PUNCT
ejpam-5050	5	3	very	very	ADV
ejpam-5050	5	4	few	few	ADJ
ejpam-5050	5	5	methods	method	NOUN
ejpam-5050	5	6	exist	exist	VERB
ejpam-5050	5	7	for	for	ADP
ejpam-5050	5	8	the	the	DET
ejpam-5050	5	9	treatment	treatment	NOUN
ejpam-5050	5	10	of	of	ADP
ejpam-5050	5	11	the	the	DET
ejpam-5050	5	12	model	model	NOUN
ejpam-5050	5	13	analytically	analytically	ADV
ejpam-5050	5	14	;	;	PUNCT
ejpam-5050	5	15	in	in	ADP
ejpam-5050	5	16	fact	fact	NOUN
ejpam-5050	5	17	,	,	PUNCT
ejpam-5050	5	18	researchers	researcher	NOUN
ejpam-5050	5	19	frequently	frequently	ADV
ejpam-5050	5	20	shop	shop	VERB
ejpam-5050	5	21	for	for	ADP
ejpam-5050	5	22	semi	semi	ADJ
ejpam-5050	5	23	-	-	ADJ
ejpam-5050	5	24	analytical	analytical	ADJ
ejpam-5050	5	25	and	and	CCONJ
ejpam-5050	5	26	numerical	numerical	ADJ
ejpam-5050	5	27	methods	method	NOUN
ejpam-5050	5	28	in	in	ADP
ejpam-5050	5	29	their	their	PRON
ejpam-5050	5	30	studies	study	NOUN
ejpam-5050	5	31	.	.	PUNCT
ejpam-5050	6	1	therefore	therefore	ADV
ejpam-5050	6	2	,	,	PUNCT
ejpam-5050	6	3	the	the	DET
ejpam-5050	6	4	main	main	ADJ
ejpam-5050	6	5	goal	goal	NOUN
ejpam-5050	6	6	of	of	ADP
ejpam-5050	6	7	this	this	DET
ejpam-5050	6	8	research	research	NOUN
ejpam-5050	6	9	is	be	AUX
ejpam-5050	6	10	to	to	PART
ejpam-5050	6	11	find	find	VERB
ejpam-5050	6	12	the	the	DET
ejpam-5050	6	13	exact	exact	ADJ
ejpam-5050	6	14	analytical	analytical	ADJ
ejpam-5050	6	15	solution	solution	NOUN
ejpam-5050	6	16	for	for	ADP
ejpam-5050	6	17	the	the	DET
ejpam-5050	6	18	fractional	fractional	ADJ
ejpam-5050	6	19	bagley	bagley	NOUN
ejpam-5050	6	20	-	-	PUNCT
ejpam-5050	6	21	torvik	torvik	NOUN
ejpam-5050	6	22	equation	equation	NOUN
ejpam-5050	6	23	fitted	fit	VERB
ejpam-5050	6	24	with	with	ADP
ejpam-5050	6	25	dirichlet	dirichlet	PROPN
ejpam-5050	6	26	boundary	boundary	PROPN
ejpam-5050	6	27	data	data	PROPN
ejpam-5050	6	28	,	,	PUNCT
ejpam-5050	6	29	as	as	ADV
ejpam-5050	6	30	well	well	ADV
ejpam-5050	6	31	as	as	ADP
ejpam-5050	6	32	a	a	DET
ejpam-5050	6	33	system	system	NOUN
ejpam-5050	6	34	of	of	ADP
ejpam-5050	6	35	fractional	fractional	ADJ
ejpam-5050	6	36	bagley	bagley	NOUN
ejpam-5050	6	37	-	-	PUNCT
ejpam-5050	6	38	torvik	torvik	NOUN
ejpam-5050	6	39	equations	equation	NOUN
ejpam-5050	6	40	.	.	PUNCT
ejpam-5050	7	1	thus	thus	ADV
ejpam-5050	7	2	,	,	PUNCT
ejpam-5050	7	3	this	this	DET
ejpam-5050	7	4	research	research	NOUN
ejpam-5050	7	5	aims	aim	VERB
ejpam-5050	7	6	to	to	PART
ejpam-5050	7	7	show	show	VERB
ejpam-5050	7	8	that	that	SCONJ
ejpam-5050	7	9	the	the	DET
ejpam-5050	7	10	modified	modify	VERB
ejpam-5050	7	11	adomian	adomian	NOUN
ejpam-5050	7	12	decomposition	decomposition	NOUN
ejpam-5050	7	13	method	method	NOUN
ejpam-5050	7	14	(	(	PUNCT
ejpam-5050	7	15	madm	madm	NOUN
ejpam-5050	7	16	)	)	PUNCT
ejpam-5050	7	17	via	via	ADP
ejpam-5050	7	18	the	the	DET
ejpam-5050	7	19	proposed	propose	VERB
ejpam-5050	7	20	two	two	NUM
ejpam-5050	7	21	algorithms	algorithm	NOUN
ejpam-5050	7	22	is	be	AUX
ejpam-5050	7	23	a	a	DET
ejpam-5050	7	24	very	very	ADV
ejpam-5050	7	25	effective	effective	ADJ
ejpam-5050	7	26	method	method	NOUN
ejpam-5050	7	27	for	for	ADP
ejpam-5050	7	28	treating	treat	VERB
ejpam-5050	7	29	a	a	DET
ejpam-5050	7	30	class	class	NOUN
ejpam-5050	7	31	of	of	ADP
ejpam-5050	7	32	bagley	bagley	NOUN
ejpam-5050	7	33	-	-	PUNCT
ejpam-5050	7	34	torvik	torvik	NOUN
ejpam-5050	7	35	equations	equation	NOUN
ejpam-5050	7	36	endowed	endow	VERB
ejpam-5050	7	37	with	with	ADP
ejpam-5050	7	38	dirichlet	dirichlet	PROPN
ejpam-5050	7	39	boundary	boundary	PROPN
ejpam-5050	7	40	data	data	PROPN
ejpam-5050	7	41	.	.	PUNCT
ejpam-5050	8	1	certainly	certainly	ADV
ejpam-5050	8	2	,	,	PUNCT
ejpam-5050	8	3	madm	madm	PROPN
ejpam-5050	8	4	is	be	AUX
ejpam-5050	8	5	a	a	DET
ejpam-5050	8	6	very	very	ADV
ejpam-5050	8	7	powerful	powerful	ADJ
ejpam-5050	8	8	approach	approach	NOUN
ejpam-5050	8	9	for	for	ADP
ejpam-5050	8	10	solving	solve	VERB
ejpam-5050	8	11	dissimilar	dissimilar	ADJ
ejpam-5050	8	12	functional	functional	ADJ
ejpam-5050	8	13	equations	equation	NOUN
ejpam-5050	8	14	without	without	ADP
ejpam-5050	8	15	the	the	DET
ejpam-5050	8	16	need	need	NOUN
ejpam-5050	8	17	for	for	ADP
ejpam-5050	8	18	either	either	DET
ejpam-5050	8	19	linearization	linearization	NOUN
ejpam-5050	8	20	,	,	PUNCT
ejpam-5050	8	21	discretization	discretization	NOUN
ejpam-5050	8	22	,	,	PUNCT
ejpam-5050	8	23	perturbation	perturbation	NOUN
ejpam-5050	8	24	,	,	PUNCT
ejpam-5050	8	25	or	or	CCONJ
ejpam-5050	8	26	even	even	ADV
ejpam-5050	8	27	unnecessary	unnecessary	ADJ
ejpam-5050	8	28	restraining	restraining	NOUN
ejpam-5050	8	29	postulations	postulation	NOUN
ejpam-5050	8	30	.	.	PUNCT
ejpam-5050	9	1	additionally	additionally	ADV
ejpam-5050	9	2	,	,	PUNCT
ejpam-5050	9	3	the	the	DET
ejpam-5050	9	4	method	method	NOUN
ejpam-5050	9	5	reveals	reveal	VERB
ejpam-5050	9	6	exact	exact	ADJ
ejpam-5050	9	7	analytical	analytical	ADJ
ejpam-5050	9	8	solutions	solution	NOUN
ejpam-5050	9	9	whenever	whenever	SCONJ
ejpam-5050	9	10	obtainable	obtainable	ADJ
ejpam-5050	9	11	or	or	CCONJ
ejpam-5050	9	12	closed	closed	ADJ
ejpam-5050	9	13	-	-	PUNCT
ejpam-5050	9	14	form	form	NOUN
ejpam-5050	9	15	series	series	NOUN
ejpam-5050	9	16	solutions	solution	NOUN
ejpam-5050	9	17	whenever	whenever	SCONJ
ejpam-5050	9	18	exact	exact	ADJ
ejpam-5050	9	19	solutions	solution	NOUN
ejpam-5050	9	20	are	be	AUX
ejpam-5050	9	21	not	not	PART
ejpam-5050	9	22	feasible	feasible	ADJ
ejpam-5050	9	23	.	.	PUNCT
ejpam-5050	10	1	lastly	lastly	ADV
ejpam-5050	10	2	,	,	PUNCT
ejpam-5050	10	3	some	some	DET
ejpam-5050	10	4	illustrative	illustrative	ADJ
ejpam-5050	10	5	test	test	NOUN
ejpam-5050	10	6	problems	problem	NOUN
ejpam-5050	10	7	of	of	ADP
ejpam-5050	10	8	the	the	DET
ejpam-5050	10	9	governing	govern	VERB
ejpam-5050	10	10	model	model	NOUN
ejpam-5050	10	11	are	be	AUX
ejpam-5050	10	12	examined	examine	VERB
ejpam-5050	10	13	to	to	PART
ejpam-5050	10	14	demonstrate	demonstrate	VERB
ejpam-5050	10	15	the	the	DET
ejpam-5050	10	16	superiority	superiority	NOUN
ejpam-5050	10	17	of	of	ADP
ejpam-5050	10	18	the	the	DET
ejpam-5050	10	19	proposed	propose	VERB
ejpam-5050	10	20	algorithms	algorithm	NOUN
ejpam-5050	10	21	.	.	PUNCT
ejpam-5050	11	1	2020	2020	NUM
ejpam-5050	11	2	mathematics	mathematic	NOUN
ejpam-5050	11	3	subject	subject	NOUN
ejpam-5050	11	4	classifications	classification	NOUN
ejpam-5050	11	5	:	:	PUNCT
ejpam-5050	11	6	26a33	26a33	NUM
ejpam-5050	11	7	,	,	PUNCT
ejpam-5050	11	8	34a08	34a08	NUM
ejpam-5050	11	9	,	,	PUNCT
ejpam-5050	11	10	34b15	34b15	ADJ
ejpam-5050	11	11	.	.	PUNCT
ejpam-5050	12	1	key	key	ADJ
ejpam-5050	12	2	words	word	NOUN
ejpam-5050	12	3	and	and	CCONJ
ejpam-5050	12	4	phrases	phrase	NOUN
ejpam-5050	12	5	:	:	PUNCT
ejpam-5050	12	6	fractional	fractional	ADJ
ejpam-5050	12	7	calculus	calculus	NOUN
ejpam-5050	12	8	,	,	PUNCT
ejpam-5050	12	9	bagley	bagley	NOUN
ejpam-5050	12	10	-	-	PUNCT
ejpam-5050	12	11	torvik	torvik	NOUN
ejpam-5050	12	12	equation	equation	NOUN
ejpam-5050	12	13	,	,	PUNCT
ejpam-5050	12	14	dirichlet	dirichlet	PROPN
ejpam-5050	12	15	boundary	boundary	PROPN
ejpam-5050	12	16	condition	condition	NOUN
ejpam-5050	12	17	,	,	PUNCT
ejpam-5050	12	18	modified	modify	VERB
ejpam-5050	12	19	adomian	adomian	NOUN
ejpam-5050	12	20	decomposition	decomposition	NOUN
ejpam-5050	12	21	method	method	NOUN
ejpam-5050	12	22	,	,	PUNCT
ejpam-5050	12	23	boundary	boundary	ADJ
ejpam-5050	12	24	-	-	PUNCT
ejpam-5050	12	25	value	value	NOUN
ejpam-5050	12	26	problem	problem	NOUN
ejpam-5050	12	27	.	.	PUNCT
ejpam-5050	13	1	1	1	X
ejpam-5050	13	2	.	.	X
ejpam-5050	13	3	introduction	introduction	NOUN
ejpam-5050	13	4	fractional	fractional	ADJ
ejpam-5050	13	5	calculus	calculus	NOUN
ejpam-5050	13	6	is	be	AUX
ejpam-5050	13	7	an	an	DET
ejpam-5050	13	8	aged	aged	ADJ
ejpam-5050	13	9	area	area	NOUN
ejpam-5050	13	10	of	of	ADP
ejpam-5050	13	11	research	research	NOUN
ejpam-5050	13	12	that	that	PRON
ejpam-5050	13	13	recently	recently	ADV
ejpam-5050	13	14	reemerged	reemerge	VERB
ejpam-5050	13	15	more	more	ADV
ejpam-5050	13	16	strongly	strongly	ADV
ejpam-5050	13	17	with	with	ADP
ejpam-5050	13	18	burning	burn	VERB
ejpam-5050	13	19	applications	application	NOUN
ejpam-5050	13	20	that	that	PRON
ejpam-5050	13	21	cuts	cut	VERB
ejpam-5050	13	22	across	across	ADP
ejpam-5050	13	23	all	all	DET
ejpam-5050	13	24	aspects	aspect	NOUN
ejpam-5050	13	25	of	of	ADP
ejpam-5050	13	26	life	life	NOUN
ejpam-5050	13	27	.	.	PUNCT
ejpam-5050	14	1	indeed	indeed	ADV
ejpam-5050	14	2	,	,	PUNCT
ejpam-5050	14	3	the	the	DET
ejpam-5050	14	4	area	area	NOUN
ejpam-5050	14	5	started	start	VERB
ejpam-5050	14	6	off	off	ADP
ejpam-5050	14	7	by	by	ADP
ejpam-5050	14	8	the	the	DET
ejpam-5050	14	9	ignition	ignition	NOUN
ejpam-5050	14	10	put	put	VERB
ejpam-5050	14	11	forward	forward	ADV
ejpam-5050	14	12	by	by	ADP
ejpam-5050	14	13	leibniz	leibniz	PROPN
ejpam-5050	14	14	(	(	PUNCT
ejpam-5050	14	15	1695	1695	NUM
ejpam-5050	14	16	)	)	PUNCT
ejpam-5050	14	17	and	and	CCONJ
ejpam-5050	14	18	euler	euler	NOUN
ejpam-5050	14	19	(	(	PUNCT
ejpam-5050	14	20	1730	1730	NUM
ejpam-5050	14	21	)	)	PUNCT
ejpam-5050	15	1	[	[	X
ejpam-5050	15	2	28	28	NUM
ejpam-5050	15	3	,	,	PUNCT
ejpam-5050	15	4	30	30	NUM
ejpam-5050	15	5	]	]	PUNCT
ejpam-5050	15	6	,	,	PUNCT
ejpam-5050	15	7	and	and	CCONJ
ejpam-5050	15	8	since	since	SCONJ
ejpam-5050	15	9	then	then	ADV
ejpam-5050	15	10	keeps	keep	VERB
ejpam-5050	15	11	propelling	propel	VERB
ejpam-5050	15	12	to	to	ADP
ejpam-5050	15	13	date	date	NOUN
ejpam-5050	15	14	.	.	PUNCT
ejpam-5050	16	1	notably	notably	ADV
ejpam-5050	16	2	,	,	PUNCT
ejpam-5050	16	3	various	various	ADJ
ejpam-5050	16	4	real	real	ADJ
ejpam-5050	16	5	-	-	PUNCT
ejpam-5050	16	6	life	life	NOUN
ejpam-5050	16	7	models	model	NOUN
ejpam-5050	16	8	are	be	AUX
ejpam-5050	16	9	discovered	discover	VERB
ejpam-5050	16	10	to	to	PART
ejpam-5050	16	11	be	be	AUX
ejpam-5050	16	12	perfectly	perfectly	ADV
ejpam-5050	16	13	captured	capture	VERB
ejpam-5050	16	14	through	through	ADP
ejpam-5050	16	15	the	the	DET
ejpam-5050	16	16	application	application	NOUN
ejpam-5050	16	17	of	of	ADP
ejpam-5050	16	18	fractional	fractional	ADJ
ejpam-5050	16	19	differential	differential	ADJ
ejpam-5050	16	20	equations	equation	NOUN
ejpam-5050	16	21	(	(	PUNCT
ejpam-5050	16	22	fdes	fde	NOUN
ejpam-5050	16	23	)	)	PUNCT
ejpam-5050	16	24	.	.	PUNCT
ejpam-5050	17	1	these	these	DET
ejpam-5050	17	2	fdes	fde	NOUN
ejpam-5050	17	3	have	have	AUX
ejpam-5050	17	4	,	,	PUNCT
ejpam-5050	17	5	in	in	ADP
ejpam-5050	17	6	recent	recent	ADJ
ejpam-5050	17	7	times	time	NOUN
ejpam-5050	17	8	gained	gain	VERB
ejpam-5050	17	9	considerable	considerable	ADJ
ejpam-5050	17	10	relevance	relevance	NOUN
ejpam-5050	17	11	in	in	ADP
ejpam-5050	17	12	modeling	model	VERB
ejpam-5050	17	13	different	different	ADJ
ejpam-5050	17	14	∗corresponding	∗corresponding	NOUN
ejpam-5050	17	15	author	author	NOUN
ejpam-5050	17	16	.	.	PUNCT
ejpam-5050	18	1	doi	doi	NOUN
ejpam-5050	18	2	:	:	PUNCT
ejpam-5050	18	3	https://doi.org/10.29020/nybg.ejpam.v17i1.5050	https://doi.org/10.29020/nybg.ejpam.v17i1.5050	PROPN
ejpam-5050	18	4	email	email	NOUN
ejpam-5050	18	5	addresses	address	NOUN
ejpam-5050	18	6	:	:	PUNCT
ejpam-5050	18	7	mhalmazmumy@uj.edu.sa	mhalmazmumy@uj.edu.sa	PROPN
ejpam-5050	18	8	(	(	PUNCT
ejpam-5050	18	9	m.	m.	NOUN
ejpam-5050	18	10	al	al	PROPN
ejpam-5050	18	11	-	-	PUNCT
ejpam-5050	18	12	mazmumy	mazmumy	PROPN
ejpam-5050	18	13	)	)	PUNCT
ejpam-5050	18	14	,	,	PUNCT
ejpam-5050	18	15	mralsolami@uj.edu.sa	mralsolami@uj.edu.sa	PROPN
ejpam-5050	18	16	(	(	PUNCT
ejpam-5050	18	17	m.	m.	NOUN
ejpam-5050	18	18	alsulami	alsulami	NOUN
ejpam-5050	18	19	)	)	PUNCT
ejpam-5050	18	20	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5050	19	1	546	546	NUM
ejpam-5050	19	2	©	©	PROPN
ejpam-5050	19	3	2024	2024	NUM
ejpam-5050	19	4	ejpam	ejpam	NOUN
ejpam-5050	19	5	all	all	DET
ejpam-5050	19	6	rights	right	NOUN
ejpam-5050	19	7	reserved	reserve	VERB
ejpam-5050	19	8	.	.	PUNCT
ejpam-5050	20	1	m.	m.	NOUN
ejpam-5050	20	2	al	al	PROPN
ejpam-5050	20	3	-	-	PUNCT
ejpam-5050	20	4	mazmumy	mazmumy	PROPN
ejpam-5050	20	5	,	,	PUNCT
ejpam-5050	20	6	m.	m.	NOUN
ejpam-5050	20	7	alsulami	alsulami	PROPN
ejpam-5050	20	8	/	/	SYM
ejpam-5050	20	9	eur	eur	PROPN
ejpam-5050	20	10	.	.	PUNCT
ejpam-5050	21	1	j.	j.	PROPN
ejpam-5050	21	2	pure	pure	PROPN
ejpam-5050	21	3	appl	appl	PROPN
ejpam-5050	21	4	.	.	PROPN
ejpam-5050	21	5	math	math	PROPN
ejpam-5050	21	6	,	,	PUNCT
ejpam-5050	21	7	17	17	NUM
ejpam-5050	21	8	(	(	PUNCT
ejpam-5050	21	9	1	1	NUM
ejpam-5050	21	10	)	)	PUNCT
ejpam-5050	21	11	(	(	PUNCT
ejpam-5050	21	12	2024	2024	NUM
ejpam-5050	21	13	)	)	PUNCT
ejpam-5050	21	14	,	,	PUNCT
ejpam-5050	21	15	546	546	NUM
ejpam-5050	21	16	-	-	SYM
ejpam-5050	21	17	568	568	NUM
ejpam-5050	21	18	547	547	NUM
ejpam-5050	21	19	emerging	emerge	VERB
ejpam-5050	21	20	problems	problem	NOUN
ejpam-5050	21	21	arising	arise	VERB
ejpam-5050	21	22	in	in	ADP
ejpam-5050	21	23	,	,	PUNCT
ejpam-5050	21	24	for	for	ADP
ejpam-5050	21	25	instance	instance	NOUN
ejpam-5050	21	26	,	,	PUNCT
ejpam-5050	21	27	electrical	electrical	ADJ
ejpam-5050	21	28	networks	network	NOUN
ejpam-5050	21	29	,	,	PUNCT
ejpam-5050	21	30	electromagnetic	electromagnetic	ADJ
ejpam-5050	21	31	theory	theory	NOUN
ejpam-5050	21	32	,	,	PUNCT
ejpam-5050	21	33	fractals	fractal	VERB
ejpam-5050	21	34	theory	theory	NOUN
ejpam-5050	21	35	,	,	PUNCT
ejpam-5050	21	36	viscoelasticity	viscoelasticity	NOUN
ejpam-5050	21	37	,	,	PUNCT
ejpam-5050	21	38	control	control	NOUN
ejpam-5050	21	39	theory	theory	NOUN
ejpam-5050	21	40	,	,	PUNCT
ejpam-5050	21	41	material	material	NOUN
ejpam-5050	21	42	science	science	NOUN
ejpam-5050	21	43	,	,	PUNCT
ejpam-5050	21	44	chemistry	chemistry	NOUN
ejpam-5050	21	45	,	,	PUNCT
ejpam-5050	21	46	potential	potential	ADJ
ejpam-5050	21	47	theory	theory	NOUN
ejpam-5050	21	48	,	,	PUNCT
ejpam-5050	21	49	fluid	fluid	ADJ
ejpam-5050	21	50	flow	flow	NOUN
ejpam-5050	21	51	,	,	PUNCT
ejpam-5050	21	52	biology	biology	NOUN
ejpam-5050	21	53	,	,	PUNCT
ejpam-5050	21	54	and	and	CCONJ
ejpam-5050	21	55	statistics	statistic	NOUN
ejpam-5050	21	56	to	to	PART
ejpam-5050	21	57	mention	mention	VERB
ejpam-5050	21	58	but	but	CCONJ
ejpam-5050	21	59	a	a	DET
ejpam-5050	21	60	few	few	ADJ
ejpam-5050	21	61	[	[	X
ejpam-5050	21	62	5	5	NUM
ejpam-5050	21	63	,	,	PUNCT
ejpam-5050	21	64	6	6	NUM
ejpam-5050	21	65	,	,	PUNCT
ejpam-5050	21	66	10	10	NUM
ejpam-5050	21	67	,	,	PUNCT
ejpam-5050	21	68	11	11	NUM
ejpam-5050	21	69	,	,	PUNCT
ejpam-5050	21	70	24	24	NUM
ejpam-5050	21	71	,	,	PUNCT
ejpam-5050	21	72	26	26	NUM
ejpam-5050	21	73	,	,	PUNCT
ejpam-5050	21	74	27	27	NUM
ejpam-5050	21	75	,	,	PUNCT
ejpam-5050	21	76	33	33	NUM
ejpam-5050	21	77	,	,	PUNCT
ejpam-5050	21	78	34	34	NUM
ejpam-5050	21	79	,	,	PUNCT
ejpam-5050	21	80	39	39	NUM
ejpam-5050	21	81	,	,	PUNCT
ejpam-5050	21	82	41	41	NUM
ejpam-5050	21	83	]	]	PUNCT
ejpam-5050	21	84	.	.	PUNCT
ejpam-5050	22	1	in	in	ADP
ejpam-5050	22	2	light	light	NOUN
ejpam-5050	22	3	of	of	ADP
ejpam-5050	22	4	this	this	PRON
ejpam-5050	22	5	,	,	PUNCT
ejpam-5050	22	6	different	different	ADJ
ejpam-5050	22	7	researchers	researcher	NOUN
ejpam-5050	22	8	have	have	AUX
ejpam-5050	22	9	in	in	ADP
ejpam-5050	22	10	the	the	DET
ejpam-5050	22	11	past	past	NOUN
ejpam-5050	22	12	and	and	CCONJ
ejpam-5050	22	13	recent	recent	ADJ
ejpam-5050	22	14	times	time	NOUN
ejpam-5050	22	15	proposed	propose	VERB
ejpam-5050	22	16	a	a	DET
ejpam-5050	22	17	variety	variety	NOUN
ejpam-5050	22	18	of	of	ADP
ejpam-5050	22	19	methods	method	NOUN
ejpam-5050	22	20	,	,	PUNCT
ejpam-5050	22	21	including	include	VERB
ejpam-5050	22	22	analytical	analytical	ADJ
ejpam-5050	22	23	,	,	PUNCT
ejpam-5050	22	24	semi	semi	ADJ
ejpam-5050	22	25	-	-	ADJ
ejpam-5050	22	26	analytical	analytical	ADJ
ejpam-5050	22	27	,	,	PUNCT
ejpam-5050	22	28	and	and	CCONJ
ejpam-5050	22	29	computational	computational	ADJ
ejpam-5050	22	30	to	to	PART
ejpam-5050	22	31	deal	deal	VERB
ejpam-5050	22	32	with	with	ADP
ejpam-5050	22	33	fdes	fde	NOUN
ejpam-5050	22	34	.	.	PUNCT
ejpam-5050	23	1	in	in	ADP
ejpam-5050	23	2	this	this	DET
ejpam-5050	23	3	regard	regard	NOUN
ejpam-5050	23	4	,	,	PUNCT
ejpam-5050	23	5	the	the	DET
ejpam-5050	23	6	present	present	ADJ
ejpam-5050	23	7	paper	paper	NOUN
ejpam-5050	23	8	shops	shop	NOUN
ejpam-5050	23	9	for	for	ADP
ejpam-5050	23	10	an	an	DET
ejpam-5050	23	11	elegant	elegant	ADJ
ejpam-5050	23	12	semi	semi	ADJ
ejpam-5050	23	13	-	-	ADJ
ejpam-5050	23	14	analytical	analytical	ADJ
ejpam-5050	23	15	method	method	NOUN
ejpam-5050	23	16	that	that	PRON
ejpam-5050	23	17	is	be	AUX
ejpam-5050	23	18	founded	found	VERB
ejpam-5050	23	19	on	on	ADP
ejpam-5050	23	20	the	the	DET
ejpam-5050	23	21	utilization	utilization	NOUN
ejpam-5050	23	22	of	of	ADP
ejpam-5050	23	23	the	the	DET
ejpam-5050	23	24	famous	famous	ADJ
ejpam-5050	23	25	adomian	adomian	NOUN
ejpam-5050	23	26	decomposition	decomposition	NOUN
ejpam-5050	23	27	method	method	NOUN
ejpam-5050	23	28	(	(	PUNCT
ejpam-5050	23	29	adm	adm	PROPN
ejpam-5050	23	30	)	)	PUNCT
ejpam-5050	24	1	[	[	X
ejpam-5050	24	2	1	1	NUM
ejpam-5050	24	3	,	,	PUNCT
ejpam-5050	24	4	3	3	NUM
ejpam-5050	24	5	,	,	PUNCT
ejpam-5050	24	6	4	4	NUM
ejpam-5050	24	7	,	,	PUNCT
ejpam-5050	24	8	15	15	NUM
ejpam-5050	24	9	–	–	PUNCT
ejpam-5050	24	10	17	17	NUM
ejpam-5050	24	11	,	,	PUNCT
ejpam-5050	24	12	32	32	NUM
ejpam-5050	24	13	,	,	PUNCT
ejpam-5050	24	14	38	38	NUM
ejpam-5050	24	15	,	,	PUNCT
ejpam-5050	24	16	47	47	NUM
ejpam-5050	24	17	,	,	PUNCT
ejpam-5050	24	18	49	49	NUM
ejpam-5050	24	19	]	]	PUNCT
ejpam-5050	24	20	.	.	PUNCT
ejpam-5050	25	1	on	on	ADP
ejpam-5050	25	2	the	the	DET
ejpam-5050	25	3	other	other	ADJ
ejpam-5050	25	4	hand	hand	NOUN
ejpam-5050	25	5	,	,	PUNCT
ejpam-5050	25	6	the	the	DET
ejpam-5050	25	7	boundary	boundary	ADJ
ejpam-5050	25	8	-	-	PUNCT
ejpam-5050	25	9	value	value	NOUN
ejpam-5050	25	10	problems	problem	NOUN
ejpam-5050	25	11	(	(	PUNCT
ejpam-5050	25	12	bvps	bvps	NOUN
ejpam-5050	25	13	)	)	PUNCT
ejpam-5050	25	14	featuring	feature	VERB
ejpam-5050	25	15	fractional	fractional	ADJ
ejpam-5050	25	16	-	-	PUNCT
ejpam-5050	25	17	order	order	NOUN
ejpam-5050	25	18	derivatives	derivative	NOUN
ejpam-5050	25	19	have	have	AUX
ejpam-5050	25	20	in	in	ADP
ejpam-5050	25	21	recent	recent	ADJ
ejpam-5050	25	22	years	year	NOUN
ejpam-5050	25	23	fascinated	fascinated	ADJ
ejpam-5050	25	24	or	or	CCONJ
ejpam-5050	25	25	rather	rather	ADV
ejpam-5050	25	26	shaped	shape	VERB
ejpam-5050	25	27	the	the	DET
ejpam-5050	25	28	thoughts	thought	NOUN
ejpam-5050	25	29	of	of	ADP
ejpam-5050	25	30	various	various	ADJ
ejpam-5050	25	31	theoreticians	theoretician	NOUN
ejpam-5050	25	32	and	and	CCONJ
ejpam-5050	25	33	experimentalists	experimentalist	NOUN
ejpam-5050	25	34	in	in	ADP
ejpam-5050	25	35	diverse	diverse	ADJ
ejpam-5050	25	36	stems	stem	NOUN
ejpam-5050	25	37	of	of	ADP
ejpam-5050	25	38	applied	applied	ADJ
ejpam-5050	25	39	and	and	CCONJ
ejpam-5050	25	40	pure	pure	ADJ
ejpam-5050	25	41	sciences	science	NOUN
ejpam-5050	25	42	.	.	PUNCT
ejpam-5050	26	1	in	in	ADP
ejpam-5050	26	2	particular	particular	ADJ
ejpam-5050	26	3	,	,	PUNCT
ejpam-5050	26	4	we	we	PRON
ejpam-5050	26	5	make	make	VERB
ejpam-5050	26	6	mention	mention	NOUN
ejpam-5050	26	7	of	of	ADP
ejpam-5050	26	8	the	the	DET
ejpam-5050	26	9	bagley	bagley	NOUN
ejpam-5050	26	10	-	-	PUNCT
ejpam-5050	26	11	torvik	torvik	NOUN
ejpam-5050	26	12	equation	equation	NOUN
ejpam-5050	26	13	,	,	PUNCT
ejpam-5050	26	14	being	be	AUX
ejpam-5050	26	15	an	an	DET
ejpam-5050	26	16	imperative	imperative	ADJ
ejpam-5050	26	17	differential	differential	NOUN
ejpam-5050	26	18	equation	equation	NOUN
ejpam-5050	26	19	that	that	PRON
ejpam-5050	26	20	arises	arise	VERB
ejpam-5050	26	21	in	in	ADP
ejpam-5050	26	22	various	various	ADJ
ejpam-5050	26	23	branches	branch	NOUN
ejpam-5050	26	24	of	of	ADP
ejpam-5050	26	25	mathematical	mathematical	ADJ
ejpam-5050	26	26	physics	physics	NOUN
ejpam-5050	26	27	and	and	CCONJ
ejpam-5050	26	28	mechanics	mechanic	NOUN
ejpam-5050	26	29	[	[	X
ejpam-5050	26	30	46	46	NUM
ejpam-5050	26	31	]	]	PUNCT
ejpam-5050	26	32	.	.	PUNCT
ejpam-5050	27	1	this	this	DET
ejpam-5050	27	2	equation	equation	NOUN
ejpam-5050	27	3	is	be	AUX
ejpam-5050	27	4	,	,	PUNCT
ejpam-5050	27	5	however	however	ADV
ejpam-5050	27	6	,	,	PUNCT
ejpam-5050	27	7	used	use	VERB
ejpam-5050	27	8	in	in	ADP
ejpam-5050	27	9	modeling	model	VERB
ejpam-5050	27	10	various	various	ADJ
ejpam-5050	27	11	processes	process	NOUN
ejpam-5050	27	12	,	,	PUNCT
ejpam-5050	27	13	including	include	VERB
ejpam-5050	27	14	viscoelasticity	viscoelasticity	NOUN
ejpam-5050	27	15	,	,	PUNCT
ejpam-5050	27	16	the	the	DET
ejpam-5050	27	17	submergence	submergence	NOUN
ejpam-5050	27	18	of	of	ADP
ejpam-5050	27	19	solid	solid	ADJ
ejpam-5050	27	20	structures	structure	NOUN
ejpam-5050	27	21	in	in	ADP
ejpam-5050	27	22	fluids	fluid	NOUN
ejpam-5050	27	23	,	,	PUNCT
ejpam-5050	27	24	and	and	CCONJ
ejpam-5050	27	25	the	the	DET
ejpam-5050	27	26	interaction	interaction	NOUN
ejpam-5050	27	27	of	of	ADP
ejpam-5050	27	28	solid	solid	ADJ
ejpam-5050	27	29	media	medium	NOUN
ejpam-5050	27	30	with	with	ADP
ejpam-5050	27	31	fluids	fluid	NOUN
ejpam-5050	27	32	among	among	ADP
ejpam-5050	27	33	others	other	NOUN
ejpam-5050	27	34	;	;	PUNCT
ejpam-5050	27	35	for	for	ADP
ejpam-5050	27	36	more	more	ADJ
ejpam-5050	27	37	on	on	ADP
ejpam-5050	27	38	the	the	DET
ejpam-5050	27	39	uniqueness	uniqueness	NOUN
ejpam-5050	27	40	and	and	CCONJ
ejpam-5050	27	41	existence	existence	NOUN
ejpam-5050	27	42	results	result	NOUN
ejpam-5050	27	43	of	of	ADP
ejpam-5050	27	44	the	the	DET
ejpam-5050	27	45	model	model	NOUN
ejpam-5050	27	46	when	when	SCONJ
ejpam-5050	27	47	prescribed	prescribe	VERB
ejpam-5050	27	48	with	with	ADP
ejpam-5050	27	49	dirichlet	dirichlet	PROPN
ejpam-5050	27	50	boundary	boundary	PROPN
ejpam-5050	27	51	data	data	PROPN
ejpam-5050	27	52	,	,	PUNCT
ejpam-5050	27	53	an	an	DET
ejpam-5050	27	54	interested	interested	ADJ
ejpam-5050	27	55	reader	reader	NOUN
ejpam-5050	27	56	can	can	AUX
ejpam-5050	27	57	consult	consult	VERB
ejpam-5050	27	58	[	[	X
ejpam-5050	27	59	8	8	NUM
ejpam-5050	27	60	,	,	PUNCT
ejpam-5050	27	61	25	25	NUM
ejpam-5050	27	62	]	]	PUNCT
ejpam-5050	27	63	and	and	CCONJ
ejpam-5050	27	64	the	the	DET
ejpam-5050	27	65	references	reference	NOUN
ejpam-5050	27	66	therewith	therewith	VERB
ejpam-5050	27	67	.	.	PUNCT
ejpam-5050	28	1	moreover	moreover	ADV
ejpam-5050	28	2	,	,	PUNCT
ejpam-5050	28	3	as	as	SCONJ
ejpam-5050	28	4	it	it	PRON
ejpam-5050	28	5	is	be	AUX
ejpam-5050	28	6	always	always	ADV
ejpam-5050	28	7	thorny	thorny	ADJ
ejpam-5050	28	8	to	to	PART
ejpam-5050	28	9	tackle	tackle	VERB
ejpam-5050	28	10	fdes	fde	NOUN
ejpam-5050	28	11	analytically	analytically	ADV
ejpam-5050	28	12	,	,	PUNCT
ejpam-5050	28	13	many	many	ADJ
ejpam-5050	28	14	mathematicians	mathematician	NOUN
ejpam-5050	28	15	have	have	AUX
ejpam-5050	28	16	introduced	introduce	VERB
ejpam-5050	28	17	several	several	ADJ
ejpam-5050	28	18	efficient	efficient	ADJ
ejpam-5050	28	19	computational	computational	ADJ
ejpam-5050	28	20	schemes	scheme	NOUN
ejpam-5050	28	21	based	base	VERB
ejpam-5050	28	22	on	on	ADP
ejpam-5050	28	23	various	various	ADJ
ejpam-5050	28	24	concepts	concept	NOUN
ejpam-5050	28	25	to	to	PART
ejpam-5050	28	26	computationally	computationally	ADV
ejpam-5050	28	27	treat	treat	VERB
ejpam-5050	28	28	the	the	DET
ejpam-5050	28	29	class	class	NOUN
ejpam-5050	28	30	of	of	ADP
ejpam-5050	28	31	bagley	bagley	NOUN
ejpam-5050	28	32	-	-	PUNCT
ejpam-5050	28	33	torvik	torvik	NOUN
ejpam-5050	28	34	equations	equation	NOUN
ejpam-5050	28	35	.	.	PUNCT
ejpam-5050	29	1	here	here	ADV
ejpam-5050	29	2	,	,	PUNCT
ejpam-5050	29	3	we	we	PRON
ejpam-5050	29	4	make	make	VERB
ejpam-5050	29	5	mention	mention	NOUN
ejpam-5050	29	6	of	of	ADP
ejpam-5050	29	7	such	such	ADJ
ejpam-5050	29	8	approaches	approach	NOUN
ejpam-5050	29	9	that	that	PRON
ejpam-5050	29	10	are	be	AUX
ejpam-5050	29	11	applied	apply	VERB
ejpam-5050	29	12	on	on	ADP
ejpam-5050	29	13	the	the	DET
ejpam-5050	29	14	bagley	bagley	NOUN
ejpam-5050	29	15	-	-	PUNCT
ejpam-5050	29	16	torvik	torvik	NOUN
ejpam-5050	29	17	equation	equation	NOUN
ejpam-5050	29	18	in	in	ADP
ejpam-5050	29	19	recent	recent	ADJ
ejpam-5050	29	20	years	year	NOUN
ejpam-5050	29	21	to	to	PART
ejpam-5050	29	22	comprise	comprise	VERB
ejpam-5050	29	23	the	the	DET
ejpam-5050	29	24	quadratic	quadratic	ADJ
ejpam-5050	29	25	spline	spline	NOUN
ejpam-5050	29	26	solution	solution	NOUN
ejpam-5050	29	27	[	[	X
ejpam-5050	29	28	50	50	NUM
ejpam-5050	29	29	]	]	PUNCT
ejpam-5050	29	30	,	,	PUNCT
ejpam-5050	29	31	the	the	DET
ejpam-5050	29	32	cubic	cubic	ADJ
ejpam-5050	29	33	spline	spline	NOUN
ejpam-5050	29	34	polynomials	polynomial	NOUN
ejpam-5050	29	35	[	[	X
ejpam-5050	29	36	51	51	NUM
ejpam-5050	29	37	]	]	PUNCT
ejpam-5050	29	38	,	,	PUNCT
ejpam-5050	29	39	the	the	DET
ejpam-5050	29	40	chebyshev	chebyshev	PROPN
ejpam-5050	29	41	wavelet	wavelet	NOUN
ejpam-5050	29	42	method	method	NOUN
ejpam-5050	29	43	[	[	X
ejpam-5050	29	44	35	35	NUM
ejpam-5050	29	45	]	]	PUNCT
ejpam-5050	29	46	,	,	PUNCT
ejpam-5050	29	47	the	the	DET
ejpam-5050	29	48	shifted	shift	VERB
ejpam-5050	29	49	legendre	legendre	PROPN
ejpam-5050	29	50	polynomials	polynomial	NOUN
ejpam-5050	29	51	[	[	X
ejpam-5050	29	52	45	45	NUM
ejpam-5050	29	53	]	]	PUNCT
ejpam-5050	29	54	,	,	PUNCT
ejpam-5050	29	55	the	the	DET
ejpam-5050	29	56	taylor	taylor	PROPN
ejpam-5050	29	57	’s	’s	PART
ejpam-5050	29	58	method	method	NOUN
ejpam-5050	29	59	[	[	X
ejpam-5050	29	60	40	40	NUM
ejpam-5050	29	61	]	]	PUNCT
ejpam-5050	29	62	,	,	PUNCT
ejpam-5050	29	63	the	the	DET
ejpam-5050	29	64	exponential	exponential	ADJ
ejpam-5050	29	65	spline	spline	NOUN
ejpam-5050	29	66	technique	technique	NOUN
ejpam-5050	29	67	[	[	X
ejpam-5050	29	68	7	7	NUM
ejpam-5050	29	69	]	]	PUNCT
ejpam-5050	29	70	,	,	PUNCT
ejpam-5050	29	71	the	the	DET
ejpam-5050	29	72	chelyshkov	chelyshkov	NOUN
ejpam-5050	29	73	-	-	PUNCT
ejpam-5050	29	74	tau	tau	NOUN
ejpam-5050	29	75	approach	approach	NOUN
ejpam-5050	29	76	[	[	X
ejpam-5050	29	77	20	20	NUM
ejpam-5050	29	78	]	]	PUNCT
ejpam-5050	29	79	,	,	PUNCT
ejpam-5050	29	80	the	the	DET
ejpam-5050	29	81	chebyshev	chebyshev	NOUN
ejpam-5050	29	82	collocation	collocation	NOUN
ejpam-5050	29	83	method	method	NOUN
ejpam-5050	29	84	[	[	X
ejpam-5050	29	85	44	44	NUM
ejpam-5050	29	86	]	]	PUNCT
ejpam-5050	29	87	,	,	PUNCT
ejpam-5050	29	88	the	the	DET
ejpam-5050	29	89	quintic	quintic	ADJ
ejpam-5050	29	90	b	b	PROPN
ejpam-5050	29	91	-	-	PUNCT
ejpam-5050	29	92	spline	spline	NOUN
ejpam-5050	29	93	polynomial	polynomial	NOUN
ejpam-5050	29	94	[	[	X
ejpam-5050	29	95	23	23	NUM
ejpam-5050	29	96	]	]	PUNCT
ejpam-5050	29	97	,	,	PUNCT
ejpam-5050	29	98	the	the	DET
ejpam-5050	29	99	exponential	exponential	ADJ
ejpam-5050	29	100	spline	spline	NOUN
ejpam-5050	29	101	approximation	approximation	NOUN
ejpam-5050	30	1	[	[	X
ejpam-5050	30	2	21	21	NUM
ejpam-5050	30	3	]	]	PUNCT
ejpam-5050	30	4	,	,	PUNCT
ejpam-5050	30	5	the	the	DET
ejpam-5050	30	6	green	green	PROPN
ejpam-5050	30	7	’s	’s	PART
ejpam-5050	30	8	function	function	NOUN
ejpam-5050	30	9	iterative	iterative	NOUN
ejpam-5050	30	10	approach	approach	NOUN
ejpam-5050	30	11	[	[	X
ejpam-5050	30	12	22	22	NUM
ejpam-5050	30	13	]	]	PUNCT
ejpam-5050	30	14	and	and	CCONJ
ejpam-5050	30	15	the	the	DET
ejpam-5050	30	16	shifted	shift	VERB
ejpam-5050	30	17	chebyshev	chebyshev	NOUN
ejpam-5050	30	18	operational	operational	ADJ
ejpam-5050	30	19	matrix	matrix	NOUN
ejpam-5050	30	20	[	[	X
ejpam-5050	30	21	29	29	NUM
ejpam-5050	30	22	]	]	PUNCT
ejpam-5050	30	23	to	to	PART
ejpam-5050	30	24	review	review	VERB
ejpam-5050	30	25	but	but	CCONJ
ejpam-5050	30	26	just	just	ADV
ejpam-5050	30	27	a	a	DET
ejpam-5050	30	28	few	few	ADJ
ejpam-5050	30	29	;	;	PUNCT
ejpam-5050	30	30	yet	yet	ADV
ejpam-5050	30	31	,	,	PUNCT
ejpam-5050	30	32	read	read	VERB
ejpam-5050	30	33	[	[	X
ejpam-5050	30	34	14	14	NUM
ejpam-5050	30	35	]	]	PUNCT
ejpam-5050	30	36	for	for	ADP
ejpam-5050	30	37	a	a	DET
ejpam-5050	30	38	mesmerizing	mesmerizing	ADJ
ejpam-5050	30	39	study	study	NOUN
ejpam-5050	30	40	on	on	ADP
ejpam-5050	30	41	the	the	DET
ejpam-5050	30	42	bagley	bagley	NOUN
ejpam-5050	30	43	-	-	PUNCT
ejpam-5050	30	44	torvik	torvik	NOUN
ejpam-5050	30	45	equation	equation	NOUN
ejpam-5050	30	46	with	with	ADP
ejpam-5050	30	47	the	the	DET
ejpam-5050	30	48	aid	aid	NOUN
ejpam-5050	30	49	of	of	ADP
ejpam-5050	30	50	the	the	DET
ejpam-5050	30	51	differential	differential	ADJ
ejpam-5050	30	52	transform	transform	NOUN
ejpam-5050	30	53	approach	approach	NOUN
ejpam-5050	30	54	.	.	PUNCT
ejpam-5050	31	1	however	however	ADV
ejpam-5050	31	2	,	,	PUNCT
ejpam-5050	31	3	we	we	PRON
ejpam-5050	31	4	,	,	PUNCT
ejpam-5050	31	5	in	in	ADP
ejpam-5050	31	6	the	the	DET
ejpam-5050	31	7	current	current	ADJ
ejpam-5050	31	8	paper	paper	NOUN
ejpam-5050	31	9	aim	aim	VERB
ejpam-5050	31	10	to	to	PART
ejpam-5050	31	11	make	make	VERB
ejpam-5050	31	12	use	use	NOUN
ejpam-5050	31	13	of	of	ADP
ejpam-5050	31	14	the	the	DET
ejpam-5050	31	15	modified	modify	VERB
ejpam-5050	31	16	adomian	adomian	NOUN
ejpam-5050	31	17	decomposition	decomposition	NOUN
ejpam-5050	31	18	method	method	NOUN
ejpam-5050	31	19	(	(	PUNCT
ejpam-5050	31	20	madm	madm	NOUN
ejpam-5050	31	21	)	)	PUNCT
ejpam-5050	32	1	[	[	X
ejpam-5050	32	2	2	2	NUM
ejpam-5050	32	3	,	,	PUNCT
ejpam-5050	32	4	9	9	NUM
ejpam-5050	32	5	,	,	PUNCT
ejpam-5050	32	6	12	12	NUM
ejpam-5050	32	7	,	,	PUNCT
ejpam-5050	32	8	36	36	NUM
ejpam-5050	32	9	,	,	PUNCT
ejpam-5050	32	10	37	37	NUM
ejpam-5050	32	11	,	,	PUNCT
ejpam-5050	32	12	42	42	NUM
ejpam-5050	32	13	,	,	PUNCT
ejpam-5050	32	14	48	48	NUM
ejpam-5050	32	15	]	]	PUNCT
ejpam-5050	32	16	by	by	ADP
ejpam-5050	32	17	proposing	propose	VERB
ejpam-5050	32	18	two	two	NUM
ejpam-5050	32	19	different	different	ADJ
ejpam-5050	32	20	algorithms	algorithm	NOUN
ejpam-5050	32	21	to	to	PART
ejpam-5050	32	22	treat	treat	VERB
ejpam-5050	32	23	the	the	DET
ejpam-5050	32	24	bagley	bagley	NOUN
ejpam-5050	32	25	-	-	PUNCT
ejpam-5050	32	26	torvik	torvik	NOUN
ejpam-5050	32	27	equation	equation	NOUN
ejpam-5050	32	28	with	with	ADP
ejpam-5050	32	29	dirichlet	dirichlet	PROPN
ejpam-5050	32	30	boundary	boundary	PROPN
ejpam-5050	32	31	condition	condition	NOUN
ejpam-5050	32	32	.	.	PUNCT
ejpam-5050	33	1	madm	madm	PROPN
ejpam-5050	33	2	is	be	AUX
ejpam-5050	33	3	a	a	DET
ejpam-5050	33	4	semianalytical	semianalytical	ADJ
ejpam-5050	33	5	approach	approach	NOUN
ejpam-5050	33	6	that	that	PRON
ejpam-5050	33	7	was	be	AUX
ejpam-5050	33	8	improved	improve	VERB
ejpam-5050	33	9	upon	upon	SCONJ
ejpam-5050	33	10	the	the	DET
ejpam-5050	33	11	classical	classical	ADJ
ejpam-5050	33	12	adm	adm	PROPN
ejpam-5050	34	1	[	[	X
ejpam-5050	34	2	3]-[38	3]-[38	NOUN
ejpam-5050	34	3	]	]	PUNCT
ejpam-5050	34	4	to	to	PART
ejpam-5050	34	5	easily	easily	ADV
ejpam-5050	34	6	reveal	reveal	VERB
ejpam-5050	34	7	exact	exact	ADJ
ejpam-5050	34	8	analytical	analytical	ADJ
ejpam-5050	34	9	solutions	solution	NOUN
ejpam-5050	34	10	whenever	whenever	SCONJ
ejpam-5050	34	11	obtainable	obtainable	ADJ
ejpam-5050	34	12	or	or	CCONJ
ejpam-5050	34	13	closed	closed	ADJ
ejpam-5050	34	14	-	-	PUNCT
ejpam-5050	34	15	form	form	NOUN
ejpam-5050	34	16	series	series	NOUN
ejpam-5050	34	17	solutions	solution	NOUN
ejpam-5050	34	18	whenever	whenever	SCONJ
ejpam-5050	34	19	exact	exact	ADJ
ejpam-5050	34	20	solutions	solution	NOUN
ejpam-5050	34	21	are	be	AUX
ejpam-5050	34	22	not	not	PART
ejpam-5050	34	23	feasible	feasible	ADJ
ejpam-5050	34	24	.	.	PUNCT
ejpam-5050	35	1	in	in	ADP
ejpam-5050	35	2	fact	fact	NOUN
ejpam-5050	35	3	,	,	PUNCT
ejpam-5050	35	4	the	the	DET
ejpam-5050	35	5	approach	approach	NOUN
ejpam-5050	35	6	is	be	AUX
ejpam-5050	35	7	very	very	ADV
ejpam-5050	35	8	powerful	powerful	ADJ
ejpam-5050	35	9	in	in	ADP
ejpam-5050	35	10	solving	solve	VERB
ejpam-5050	35	11	dissimilar	dissimilar	ADJ
ejpam-5050	35	12	functional	functional	ADJ
ejpam-5050	35	13	equations	equation	NOUN
ejpam-5050	35	14	without	without	ADP
ejpam-5050	35	15	the	the	DET
ejpam-5050	35	16	need	need	NOUN
ejpam-5050	35	17	for	for	ADP
ejpam-5050	35	18	either	either	PRON
ejpam-5050	35	19	of	of	ADP
ejpam-5050	35	20	linearization	linearization	NOUN
ejpam-5050	35	21	,	,	PUNCT
ejpam-5050	35	22	discretization	discretization	NOUN
ejpam-5050	35	23	,	,	PUNCT
ejpam-5050	35	24	perturbation	perturbation	NOUN
ejpam-5050	35	25	,	,	PUNCT
ejpam-5050	35	26	or	or	CCONJ
ejpam-5050	35	27	even	even	ADV
ejpam-5050	35	28	unnecessary	unnecessary	ADJ
ejpam-5050	35	29	restraining	restraining	NOUN
ejpam-5050	35	30	postulations	postulation	NOUN
ejpam-5050	35	31	.	.	PUNCT
ejpam-5050	36	1	besides	besides	SCONJ
ejpam-5050	36	2	,	,	PUNCT
ejpam-5050	36	3	the	the	DET
ejpam-5050	36	4	method	method	NOUN
ejpam-5050	36	5	has	have	AUX
ejpam-5050	36	6	been	be	AUX
ejpam-5050	36	7	successfully	successfully	ADV
ejpam-5050	36	8	used	use	VERB
ejpam-5050	36	9	in	in	ADP
ejpam-5050	36	10	the	the	DET
ejpam-5050	36	11	literature	literature	NOUN
ejpam-5050	36	12	to	to	PART
ejpam-5050	36	13	solve	solve	VERB
ejpam-5050	36	14	various	various	ADJ
ejpam-5050	36	15	real	real	ADJ
ejpam-5050	36	16	-	-	PUNCT
ejpam-5050	36	17	life	life	NOUN
ejpam-5050	36	18	models	model	NOUN
ejpam-5050	36	19	.	.	PUNCT
ejpam-5050	37	1	in	in	ADP
ejpam-5050	37	2	addition	addition	NOUN
ejpam-5050	37	3	,	,	PUNCT
ejpam-5050	37	4	we	we	PRON
ejpam-5050	37	5	organize	organize	VERB
ejpam-5050	37	6	the	the	DET
ejpam-5050	37	7	paper	paper	NOUN
ejpam-5050	37	8	in	in	ADP
ejpam-5050	37	9	the	the	DET
ejpam-5050	37	10	following	follow	VERB
ejpam-5050	37	11	pattern	pattern	NOUN
ejpam-5050	37	12	:	:	PUNCT
ejpam-5050	37	13	section	section	NOUN
ejpam-5050	37	14	2	2	NUM
ejpam-5050	37	15	gives	give	VERB
ejpam-5050	37	16	certain	certain	ADJ
ejpam-5050	37	17	fundamental	fundamental	ADJ
ejpam-5050	37	18	definitions	definition	NOUN
ejpam-5050	37	19	of	of	ADP
ejpam-5050	37	20	features	feature	NOUN
ejpam-5050	37	21	with	with	ADP
ejpam-5050	37	22	regard	regard	NOUN
ejpam-5050	37	23	to	to	ADP
ejpam-5050	37	24	fractional	fractional	ADJ
ejpam-5050	37	25	calculus	calculus	NOUN
ejpam-5050	37	26	,	,	PUNCT
ejpam-5050	37	27	section	section	NOUN
ejpam-5050	37	28	3	3	NUM
ejpam-5050	37	29	gives	give	VERB
ejpam-5050	37	30	the	the	DET
ejpam-5050	37	31	procedures	procedure	NOUN
ejpam-5050	37	32	of	of	ADP
ejpam-5050	37	33	the	the	DET
ejpam-5050	37	34	devised	devise	VERB
ejpam-5050	37	35	madm	madm	NOUN
ejpam-5050	37	36	algorithms	algorithm	NOUN
ejpam-5050	37	37	on	on	ADP
ejpam-5050	37	38	bvp	bvp	NOUN
ejpam-5050	37	39	for	for	ADP
ejpam-5050	37	40	the	the	DET
ejpam-5050	37	41	bagley	bagley	NOUN
ejpam-5050	37	42	-	-	PUNCT
ejpam-5050	37	43	torvik	torvik	NOUN
ejpam-5050	37	44	equation	equation	NOUN
ejpam-5050	37	45	,	,	PUNCT
ejpam-5050	37	46	while	while	SCONJ
ejpam-5050	37	47	section	section	NOUN
ejpam-5050	37	48	4	4	NUM
ejpam-5050	37	49	demonstrates	demonstrate	VERB
ejpam-5050	37	50	the	the	DET
ejpam-5050	37	51	applicability	applicability	NOUN
ejpam-5050	37	52	of	of	ADP
ejpam-5050	37	53	the	the	DET
ejpam-5050	37	54	devised	devise	VERB
ejpam-5050	37	55	algorithms	algorithm	NOUN
ejpam-5050	37	56	,	,	PUNCT
ejpam-5050	37	57	and	and	CCONJ
ejpam-5050	37	58	section	section	NOUN
ejpam-5050	37	59	5	5	NUM
ejpam-5050	37	60	provides	provide	VERB
ejpam-5050	37	61	some	some	DET
ejpam-5050	37	62	concluding	concluding	NOUN
ejpam-5050	37	63	points	point	NOUN
ejpam-5050	37	64	.	.	PUNCT
ejpam-5050	38	1	m.	m.	NOUN
ejpam-5050	38	2	al	al	PROPN
ejpam-5050	38	3	-	-	PUNCT
ejpam-5050	38	4	mazmumy	mazmumy	PROPN
ejpam-5050	38	5	,	,	PUNCT
ejpam-5050	38	6	m.	m.	NOUN
ejpam-5050	38	7	alsulami	alsulami	PROPN
ejpam-5050	38	8	/	/	SYM
ejpam-5050	38	9	eur	eur	PROPN
ejpam-5050	38	10	.	.	PUNCT
ejpam-5050	39	1	j.	j.	PROPN
ejpam-5050	39	2	pure	pure	PROPN
ejpam-5050	39	3	appl	appl	PROPN
ejpam-5050	39	4	.	.	PROPN
ejpam-5050	39	5	math	math	PROPN
ejpam-5050	39	6	,	,	PUNCT
ejpam-5050	39	7	17	17	NUM
ejpam-5050	39	8	(	(	PUNCT
ejpam-5050	39	9	1	1	NUM
ejpam-5050	39	10	)	)	PUNCT
ejpam-5050	39	11	(	(	PUNCT
ejpam-5050	39	12	2024	2024	NUM
ejpam-5050	39	13	)	)	PUNCT
ejpam-5050	39	14	,	,	PUNCT
ejpam-5050	39	15	546	546	NUM
ejpam-5050	39	16	-	-	SYM
ejpam-5050	39	17	568	568	NUM
ejpam-5050	39	18	548	548	NUM
ejpam-5050	39	19	2	2	NUM
ejpam-5050	39	20	.	.	PUNCT
ejpam-5050	39	21	fractional	fractional	ADJ
ejpam-5050	39	22	calculus	calculus	NOUN
ejpam-5050	39	23	the	the	DET
ejpam-5050	39	24	current	current	ADJ
ejpam-5050	39	25	section	section	NOUN
ejpam-5050	39	26	introduces	introduce	VERB
ejpam-5050	39	27	certain	certain	ADJ
ejpam-5050	39	28	fundamental	fundamental	ADJ
ejpam-5050	39	29	definitions	definition	NOUN
ejpam-5050	39	30	and	and	CCONJ
ejpam-5050	39	31	features	feature	NOUN
ejpam-5050	39	32	for	for	ADP
ejpam-5050	39	33	fractional	fractional	ADJ
ejpam-5050	39	34	calculus	calculus	NOUN
ejpam-5050	39	35	,	,	PUNCT
ejpam-5050	39	36	consisting	consist	VERB
ejpam-5050	39	37	mainly	mainly	ADV
ejpam-5050	39	38	of	of	ADP
ejpam-5050	39	39	the	the	DET
ejpam-5050	39	40	fractional	fractional	ADJ
ejpam-5050	39	41	derivatives	derivative	NOUN
ejpam-5050	39	42	and	and	CCONJ
ejpam-5050	39	43	fractional	fractional	ADJ
ejpam-5050	39	44	integrals	integral	NOUN
ejpam-5050	39	45	that	that	PRON
ejpam-5050	39	46	were	be	AUX
ejpam-5050	39	47	put	put	VERB
ejpam-5050	39	48	forward	forward	ADV
ejpam-5050	39	49	based	base	VERB
ejpam-5050	39	50	on	on	ADP
ejpam-5050	39	51	the	the	DET
ejpam-5050	39	52	riemann	riemann	PROPN
ejpam-5050	39	53	-	-	PUNCT
ejpam-5050	39	54	liouville	liouville	VERB
ejpam-5050	39	55	fractional	fractional	ADJ
ejpam-5050	39	56	(	(	PUNCT
ejpam-5050	39	57	rlf	rlf	NOUN
ejpam-5050	39	58	)	)	PUNCT
ejpam-5050	39	59	and	and	CCONJ
ejpam-5050	39	60	the	the	DET
ejpam-5050	39	61	caputo	caputo	PROPN
ejpam-5050	39	62	fractional	fractional	PROPN
ejpam-5050	39	63	(	(	PUNCT
ejpam-5050	39	64	cf	cf	NOUN
ejpam-5050	39	65	)	)	PUNCT
ejpam-5050	39	66	integrals	integral	NOUN
ejpam-5050	39	67	/	/	SYM
ejpam-5050	39	68	derivatives	derivative	NOUN
ejpam-5050	39	69	.	.	PUNCT
ejpam-5050	40	1	for	for	ADP
ejpam-5050	40	2	more	more	ADJ
ejpam-5050	40	3	on	on	ADP
ejpam-5050	40	4	some	some	DET
ejpam-5050	40	5	basics	basic	NOUN
ejpam-5050	40	6	related	relate	VERB
ejpam-5050	40	7	to	to	ADP
ejpam-5050	40	8	this	this	DET
ejpam-5050	40	9	work	work	NOUN
ejpam-5050	40	10	;	;	PUNCT
ejpam-5050	40	11	an	an	DET
ejpam-5050	40	12	interested	interested	ADJ
ejpam-5050	40	13	reader	reader	NOUN
ejpam-5050	40	14	can	can	AUX
ejpam-5050	40	15	further	far	ADV
ejpam-5050	40	16	read	read	VERB
ejpam-5050	40	17	the	the	DET
ejpam-5050	40	18	famous	famous	ADJ
ejpam-5050	40	19	book	book	NOUN
ejpam-5050	40	20	by	by	ADP
ejpam-5050	40	21	kilbas	kilbas	PROPN
ejpam-5050	40	22	et	et	PROPN
ejpam-5050	40	23	al	al	PROPN
ejpam-5050	40	24	.	.	PUNCT
ejpam-5050	41	1	[	[	X
ejpam-5050	41	2	13	13	NUM
ejpam-5050	41	3	]	]	PUNCT
ejpam-5050	41	4	.	.	PUNCT
ejpam-5050	41	5	2.1	2.1	NUM
ejpam-5050	41	6	.	.	PUNCT
ejpam-5050	41	7	preliminaries	preliminary	NOUN
ejpam-5050	41	8	here	here	ADV
ejpam-5050	41	9	,	,	PUNCT
ejpam-5050	41	10	we	we	PRON
ejpam-5050	41	11	review	review	VERB
ejpam-5050	41	12	some	some	DET
ejpam-5050	41	13	definitions	definition	NOUN
ejpam-5050	41	14	of	of	ADP
ejpam-5050	41	15	the	the	DET
ejpam-5050	41	16	fractional	fractional	ADJ
ejpam-5050	41	17	-	-	PUNCT
ejpam-5050	41	18	order	order	NOUN
ejpam-5050	41	19	derivatives	derivative	NOUN
ejpam-5050	41	20	and	and	CCONJ
ejpam-5050	41	21	integrals	integral	NOUN
ejpam-5050	41	22	based	base	VERB
ejpam-5050	41	23	on	on	ADP
ejpam-5050	41	24	the	the	DET
ejpam-5050	41	25	definitions	definition	NOUN
ejpam-5050	41	26	put	put	VERB
ejpam-5050	41	27	forward	forward	ADV
ejpam-5050	41	28	by	by	ADP
ejpam-5050	41	29	riemann	riemann	PROPN
ejpam-5050	41	30	-	-	PUNCT
ejpam-5050	41	31	liouville	liouville	PROPN
ejpam-5050	41	32	and	and	CCONJ
ejpam-5050	41	33	caputo	caputo	PROPN
ejpam-5050	41	34	,	,	PUNCT
ejpam-5050	41	35	respectively	respectively	ADV
ejpam-5050	41	36	.	.	PUNCT
ejpam-5050	42	1	certainly	certainly	ADV
ejpam-5050	42	2	,	,	PUNCT
ejpam-5050	42	3	we	we	PRON
ejpam-5050	42	4	will	will	AUX
ejpam-5050	42	5	be	be	AUX
ejpam-5050	42	6	considering	consider	VERB
ejpam-5050	42	7	the	the	DET
ejpam-5050	42	8	set	set	NOUN
ejpam-5050	42	9	χ	χ	X
ejpam-5050	42	10	=	=	PUNCT
ejpam-5050	43	1	[	[	X
ejpam-5050	43	2	a	a	X
ejpam-5050	43	3	,	,	PUNCT
ejpam-5050	43	4	b	b	X
ejpam-5050	43	5	]	]	X
ejpam-5050	43	6	∈	∈	PROPN
ejpam-5050	43	7	r	r	NOUN
ejpam-5050	43	8	,	,	PUNCT
ejpam-5050	43	9	such	such	ADJ
ejpam-5050	43	10	that	that	SCONJ
ejpam-5050	43	11	a	a	DET
ejpam-5050	43	12	<	<	X
ejpam-5050	43	13	b	b	PROPN
ejpam-5050	43	14	,	,	PUNCT
ejpam-5050	43	15	a	a	DET
ejpam-5050	43	16	finite	finite	ADJ
ejpam-5050	43	17	closed	close	VERB
ejpam-5050	43	18	interval	interval	NOUN
ejpam-5050	43	19	on	on	ADP
ejpam-5050	43	20	r	r	NOUN
ejpam-5050	43	21	,	,	PUNCT
ejpam-5050	43	22	the	the	DET
ejpam-5050	43	23	set	set	NOUN
ejpam-5050	43	24	of	of	ADP
ejpam-5050	43	25	real	real	ADJ
ejpam-5050	43	26	numbers	number	NOUN
ejpam-5050	43	27	.	.	PUNCT
ejpam-5050	44	1	definition	definition	NOUN
ejpam-5050	44	2	1	1	NUM
ejpam-5050	44	3	.	.	PUNCT
ejpam-5050	45	1	(	(	PUNCT
ejpam-5050	45	2	rlf	rlf	NOUN
ejpam-5050	45	3	integrals	integral	NOUN
ejpam-5050	45	4	):	):	PUNCT
ejpam-5050	45	5	the	the	DET
ejpam-5050	45	6	rlf	rlf	PROPN
ejpam-5050	45	7	right	right	ADJ
ejpam-5050	45	8	-	-	PUNCT
ejpam-5050	45	9	sided	sided	ADJ
ejpam-5050	45	10	iαb−y	iαb−y	NOUN
ejpam-5050	45	11	and	and	CCONJ
ejpam-5050	45	12	left	left	ADJ
ejpam-5050	45	13	-	-	PUNCT
ejpam-5050	45	14	sided	side	VERB
ejpam-5050	45	15	iαa+y	iαa+y	PROPN
ejpam-5050	45	16	integrals	integral	NOUN
ejpam-5050	45	17	of	of	ADP
ejpam-5050	45	18	order	order	NOUN
ejpam-5050	45	19	α	α	X
ejpam-5050	45	20	∈	∈	NOUN
ejpam-5050	45	21	r	r	NOUN
ejpam-5050	45	22	are	be	AUX
ejpam-5050	45	23	respectively	respectively	ADV
ejpam-5050	45	24	defined	define	VERB
ejpam-5050	45	25	as	as	SCONJ
ejpam-5050	45	26	follows	follow	VERB
ejpam-5050	45	27	(	(	PUNCT
ejpam-5050	45	28	iαb−y)(x	iαb−y)(x	NOUN
ejpam-5050	45	29	)	)	PUNCT
ejpam-5050	45	30	:	:	PUNCT
ejpam-5050	45	31	=	=	SYM
ejpam-5050	45	32	1	1	NUM
ejpam-5050	45	33	γ(α	γ(α	NOUN
ejpam-5050	45	34	)	)	PUNCT
ejpam-5050	45	35	∫	∫	PROPN
ejpam-5050	46	1	b	b	PROPN
ejpam-5050	46	2	x	x	SYM
ejpam-5050	46	3	y(t	y(t	PROPN
ejpam-5050	46	4	)	)	PUNCT
ejpam-5050	46	5	(	(	PUNCT
ejpam-5050	47	1	t−	t−	PROPN
ejpam-5050	47	2	x)−α+1	x)−α+1	PROPN
ejpam-5050	47	3	dt	dt	X
ejpam-5050	47	4	,	,	PUNCT
ejpam-5050	47	5	(	(	PUNCT
ejpam-5050	47	6	x	x	SYM
ejpam-5050	47	7	<	<	X
ejpam-5050	47	8	b	b	PROPN
ejpam-5050	47	9	;	;	PUNCT
ejpam-5050	47	10	α	α	X
ejpam-5050	47	11	>	>	X
ejpam-5050	47	12	0	0	NUM
ejpam-5050	47	13	)	)	PUNCT
ejpam-5050	47	14	,	,	PUNCT
ejpam-5050	47	15	and	and	CCONJ
ejpam-5050	47	16	(	(	PUNCT
ejpam-5050	47	17	iαa+y)(x	iαa+y)(x	NOUN
ejpam-5050	47	18	)	)	PUNCT
ejpam-5050	47	19	:	:	PUNCT
ejpam-5050	47	20	=	=	SYM
ejpam-5050	47	21	1	1	NUM
ejpam-5050	47	22	γ(α	γ(α	NOUN
ejpam-5050	47	23	)	)	PUNCT
ejpam-5050	47	24	∫	∫	PROPN
ejpam-5050	47	25	x	x	X
ejpam-5050	47	26	a	a	DET
ejpam-5050	47	27	y(t	y(t	NOUN
ejpam-5050	47	28	)	)	PUNCT
ejpam-5050	47	29	(	(	PUNCT
ejpam-5050	47	30	x−	x−	PROPN
ejpam-5050	47	31	t)−α+1	t)−α+1	PRON
ejpam-5050	47	32	dt	dt	PROPN
ejpam-5050	47	33	,	,	PUNCT
ejpam-5050	47	34	(	(	PUNCT
ejpam-5050	47	35	x	x	X
ejpam-5050	47	36	>	>	X
ejpam-5050	47	37	a	a	PROPN
ejpam-5050	47	38	;	;	PUNCT
ejpam-5050	47	39	α	α	X
ejpam-5050	47	40	>	>	X
ejpam-5050	47	41	0	0	NUM
ejpam-5050	47	42	)	)	PUNCT
ejpam-5050	47	43	.	.	PUNCT
ejpam-5050	48	1	definition	definition	NOUN
ejpam-5050	48	2	2	2	NUM
ejpam-5050	48	3	.	.	PUNCT
ejpam-5050	49	1	(	(	PUNCT
ejpam-5050	49	2	rlf	rlf	NOUN
ejpam-5050	49	3	derivatives	derivative	NOUN
ejpam-5050	49	4	):	):	PUNCT
ejpam-5050	49	5	the	the	DET
ejpam-5050	49	6	rlf	rlf	PROPN
ejpam-5050	49	7	right	right	NOUN
ejpam-5050	49	8	-	-	PUNCT
ejpam-5050	49	9	sided	sided	ADJ
ejpam-5050	49	10	dα	dα	ADV
ejpam-5050	49	11	b−y	b−y	NOUN
ejpam-5050	49	12	and	and	CCONJ
ejpam-5050	49	13	left	leave	VERB
ejpam-5050	49	14	-	-	PUNCT
ejpam-5050	49	15	sided	side	VERB
ejpam-5050	49	16	dα	dα	X
ejpam-5050	49	17	a+y	a+y	NUM
ejpam-5050	49	18	derivatives	derivative	NOUN
ejpam-5050	49	19	of	of	ADP
ejpam-5050	49	20	order	order	NOUN
ejpam-5050	49	21	α	α	X
ejpam-5050	49	22	∈	∈	NOUN
ejpam-5050	49	23	r	r	NOUN
ejpam-5050	49	24	are	be	AUX
ejpam-5050	49	25	respectively	respectively	ADV
ejpam-5050	49	26	defined	define	VERB
ejpam-5050	49	27	as	as	SCONJ
ejpam-5050	49	28	follows	follow	VERB
ejpam-5050	49	29	dα	dα	ADJ
ejpam-5050	49	30	b−y(x	b−y(x	NOUN
ejpam-5050	49	31	)	)	PUNCT
ejpam-5050	49	32	:	:	PUNCT
ejpam-5050	50	1	=	=	PUNCT
ejpam-5050	50	2	−dn	−dn	PROPN
ejpam-5050	50	3	dxn	dxn	X
ejpam-5050	50	4	(	(	PUNCT
ejpam-5050	50	5	in−α	in−α	NOUN
ejpam-5050	50	6	b−	b−	PROPN
ejpam-5050	50	7	y)(x	y)(x	PROPN
ejpam-5050	50	8	)	)	PUNCT
ejpam-5050	50	9	,	,	PUNCT
ejpam-5050	50	10	:	:	PUNCT
ejpam-5050	50	11	=	=	SYM
ejpam-5050	50	12	1	1	NUM
ejpam-5050	50	13	γ(n−	γ(n−	PROPN
ejpam-5050	50	14	α	α	NOUN
ejpam-5050	50	15	)	)	PUNCT
ejpam-5050	50	16	−dn	−dn	PROPN
ejpam-5050	50	17	dxn	dxn	VERB
ejpam-5050	50	18	∫	∫	PROPN
ejpam-5050	50	19	b	b	PROPN
ejpam-5050	50	20	x	x	PROPN
ejpam-5050	50	21	y(t	y(t	PROPN
ejpam-5050	50	22	)	)	PUNCT
ejpam-5050	50	23	(	(	PUNCT
ejpam-5050	50	24	t−	t−	PROPN
ejpam-5050	50	25	x)α+1−n	x)α+1−n	PROPN
ejpam-5050	50	26	dt	dt	X
ejpam-5050	50	27	,	,	PUNCT
ejpam-5050	50	28	(	(	PUNCT
ejpam-5050	50	29	x	x	X
ejpam-5050	50	30	>	>	X
ejpam-5050	50	31	b	b	PROPN
ejpam-5050	50	32	;	;	PUNCT
ejpam-5050	50	33	α	α	PRON
ejpam-5050	50	34	≥	≥	NOUN
ejpam-5050	50	35	0	0	NUM
ejpam-5050	50	36	;	;	PUNCT
ejpam-5050	50	37	n	n	NOUN
ejpam-5050	50	38	=	=	PUNCT
ejpam-5050	51	1	[	[	X
ejpam-5050	51	2	α	α	X
ejpam-5050	51	3	]	]	X
ejpam-5050	51	4	+	+	NOUN
ejpam-5050	51	5	1	1	NUM
ejpam-5050	51	6	)	)	PUNCT
ejpam-5050	51	7	,	,	PUNCT
ejpam-5050	51	8	and	and	CCONJ
ejpam-5050	51	9	dα	dα	PRON
ejpam-5050	51	10	a+y(x	a+y(x	NOUN
ejpam-5050	51	11	)	)	PUNCT
ejpam-5050	51	12	:	:	PUNCT
ejpam-5050	51	13	=	=	PUNCT
ejpam-5050	51	14	dn	dn	PART
ejpam-5050	51	15	dxn	dxn	PROPN
ejpam-5050	51	16	(	(	PUNCT
ejpam-5050	51	17	in−α	in−α	NOUN
ejpam-5050	51	18	a+	a+	PUNCT
ejpam-5050	51	19	y)(x	y)(x	PROPN
ejpam-5050	51	20	)	)	PUNCT
ejpam-5050	51	21	,	,	PUNCT
ejpam-5050	51	22	:	:	PUNCT
ejpam-5050	51	23	=	=	SYM
ejpam-5050	51	24	1	1	NUM
ejpam-5050	51	25	γ(n−	γ(n−	PROPN
ejpam-5050	51	26	α	α	NOUN
ejpam-5050	51	27	)	)	PUNCT
ejpam-5050	51	28	dn	dn	NOUN
ejpam-5050	51	29	dxn	dxn	PROPN
ejpam-5050	51	30	∫	∫	PROPN
ejpam-5050	51	31	x	x	X
ejpam-5050	51	32	a	a	DET
ejpam-5050	51	33	y(t	y(t	NOUN
ejpam-5050	51	34	)	)	PUNCT
ejpam-5050	51	35	(	(	PUNCT
ejpam-5050	51	36	x−	x−	PROPN
ejpam-5050	51	37	t)α+1−n	t)α+1−n	PROPN
ejpam-5050	51	38	dt	dt	X
ejpam-5050	51	39	,	,	PUNCT
ejpam-5050	51	40	(	(	PUNCT
ejpam-5050	51	41	x	x	X
ejpam-5050	51	42	>	>	X
ejpam-5050	51	43	a	a	PROPN
ejpam-5050	51	44	;	;	PUNCT
ejpam-5050	51	45	α	α	PRON
ejpam-5050	51	46	≥	≥	NOUN
ejpam-5050	51	47	0	0	NUM
ejpam-5050	51	48	;	;	PUNCT
ejpam-5050	51	49	n	n	NOUN
ejpam-5050	51	50	=	=	PUNCT
ejpam-5050	52	1	[	[	X
ejpam-5050	52	2	α	α	X
ejpam-5050	52	3	]	]	X
ejpam-5050	52	4	+	+	NOUN
ejpam-5050	52	5	1	1	NUM
ejpam-5050	52	6	)	)	PUNCT
ejpam-5050	52	7	,	,	PUNCT
ejpam-5050	52	8	with	with	ADP
ejpam-5050	52	9	[	[	X
ejpam-5050	52	10	α	α	X
ejpam-5050	52	11	]	]	X
ejpam-5050	52	12	representing	represent	VERB
ejpam-5050	52	13	the	the	DET
ejpam-5050	52	14	integer	integer	ADJ
ejpam-5050	52	15	part	part	NOUN
ejpam-5050	52	16	of	of	ADP
ejpam-5050	52	17	the	the	DET
ejpam-5050	52	18	fractional	fractional	ADJ
ejpam-5050	52	19	-	-	PUNCT
ejpam-5050	52	20	order	order	NOUN
ejpam-5050	52	21	α	α	NOUN
ejpam-5050	52	22	.	.	PUNCT
ejpam-5050	52	23	definition	definition	NOUN
ejpam-5050	52	24	3	3	NUM
ejpam-5050	52	25	.	.	PUNCT
ejpam-5050	53	1	(	(	PUNCT
ejpam-5050	53	2	cf	cf	NOUN
ejpam-5050	53	3	derivatives	derivative	NOUN
ejpam-5050	53	4	):	):	PUNCT
ejpam-5050	53	5	the	the	DET
ejpam-5050	53	6	cf	cf	NOUN
ejpam-5050	53	7	right	right	ADV
ejpam-5050	53	8	-	-	PUNCT
ejpam-5050	53	9	sided	side	VERB
ejpam-5050	53	10	cdα	cdα	NOUN
ejpam-5050	53	11	b−y(x	b−y(x	NOUN
ejpam-5050	53	12	)	)	PUNCT
ejpam-5050	53	13	and	and	CCONJ
ejpam-5050	53	14	left	left	ADJ
ejpam-5050	53	15	-	-	PUNCT
ejpam-5050	53	16	sided	side	VERB
ejpam-5050	53	17	cdα	cdα	NOUN
ejpam-5050	53	18	a+y(x	a+y(x	NOUN
ejpam-5050	53	19	)	)	PUNCT
ejpam-5050	53	20	derivatives	derivative	NOUN
ejpam-5050	53	21	of	of	ADP
ejpam-5050	53	22	order	order	NOUN
ejpam-5050	53	23	α	α	X
ejpam-5050	53	24	∈	∈	PROPN
ejpam-5050	53	25	r+	r+	NOUN
ejpam-5050	53	26	on	on	ADP
ejpam-5050	53	27	[	[	X
ejpam-5050	53	28	a	a	X
ejpam-5050	53	29	,	,	PUNCT
ejpam-5050	53	30	b	b	NOUN
ejpam-5050	53	31	]	]	X
ejpam-5050	53	32	are	be	AUX
ejpam-5050	53	33	respectively	respectively	ADV
ejpam-5050	53	34	defined	define	VERB
ejpam-5050	53	35	via	via	ADP
ejpam-5050	53	36	the	the	DET
ejpam-5050	53	37	rlf	rlf	NOUN
ejpam-5050	53	38	derivatives	derivative	NOUN
ejpam-5050	53	39	as	as	SCONJ
ejpam-5050	53	40	follows	follow	VERB
ejpam-5050	53	41	cdα	cdα	NOUN
ejpam-5050	53	42	b−y(x	b−y(x	NOUN
ejpam-5050	53	43	)	)	PUNCT
ejpam-5050	53	44	:	:	PUNCT
ejpam-5050	54	1	=	=	SYM
ejpam-5050	54	2	(	(	PUNCT
ejpam-5050	54	3	dα	dα	INTJ
ejpam-5050	54	4	b−	b−	NOUN
ejpam-5050	54	5	[	[	PUNCT
ejpam-5050	54	6	y(t)−	y(t)−	PROPN
ejpam-5050	54	7	n−1∑	n−1∑	PROPN
ejpam-5050	54	8	k=0	k=0	PROPN
ejpam-5050	54	9	y(k)(b	y(k)(b	NUM
ejpam-5050	54	10	)	)	PUNCT
ejpam-5050	54	11	k	k	X
ejpam-5050	54	12	!	!	PUNCT
ejpam-5050	54	13	(	(	PUNCT
ejpam-5050	54	14	b−	b−	PROPN
ejpam-5050	54	15	t)k	t)k	ADJ
ejpam-5050	54	16	]	]	PUNCT
ejpam-5050	54	17	)	)	PUNCT
ejpam-5050	54	18	(	(	PUNCT
ejpam-5050	54	19	x	x	NOUN
ejpam-5050	54	20	)	)	PUNCT
ejpam-5050	54	21	,	,	PUNCT
ejpam-5050	54	22	(	(	PUNCT
ejpam-5050	54	23	1	1	X
ejpam-5050	54	24	)	)	PUNCT
ejpam-5050	54	25	m.	m.	NOUN
ejpam-5050	54	26	al	al	PROPN
ejpam-5050	54	27	-	-	PUNCT
ejpam-5050	54	28	mazmumy	mazmumy	PROPN
ejpam-5050	54	29	,	,	PUNCT
ejpam-5050	54	30	m.	m.	NOUN
ejpam-5050	54	31	alsulami	alsulami	PROPN
ejpam-5050	54	32	/	/	SYM
ejpam-5050	54	33	eur	eur	PROPN
ejpam-5050	54	34	.	.	PUNCT
ejpam-5050	55	1	j.	j.	PROPN
ejpam-5050	55	2	pure	pure	PROPN
ejpam-5050	55	3	appl	appl	PROPN
ejpam-5050	55	4	.	.	PROPN
ejpam-5050	55	5	math	math	PROPN
ejpam-5050	55	6	,	,	PUNCT
ejpam-5050	55	7	17	17	NUM
ejpam-5050	55	8	(	(	PUNCT
ejpam-5050	55	9	1	1	NUM
ejpam-5050	55	10	)	)	PUNCT
ejpam-5050	55	11	(	(	PUNCT
ejpam-5050	55	12	2024	2024	NUM
ejpam-5050	55	13	)	)	PUNCT
ejpam-5050	55	14	,	,	PUNCT
ejpam-5050	55	15	546	546	NUM
ejpam-5050	55	16	-	-	SYM
ejpam-5050	55	17	568	568	NUM
ejpam-5050	55	18	549	549	NUM
ejpam-5050	55	19	and	and	CCONJ
ejpam-5050	55	20	cdα	cdα	NOUN
ejpam-5050	55	21	a+y(x	a+y(x	NOUN
ejpam-5050	55	22	)	)	PUNCT
ejpam-5050	55	23	:	:	PUNCT
ejpam-5050	56	1	=	=	SYM
ejpam-5050	56	2	(	(	PUNCT
ejpam-5050	56	3	dα	dα	INTJ
ejpam-5050	56	4	a+	a+	PUNCT
ejpam-5050	56	5	[	[	PUNCT
ejpam-5050	56	6	y(t)−	y(t)−	PROPN
ejpam-5050	56	7	n−1∑	n−1∑	PROPN
ejpam-5050	56	8	k=0	k=0	PROPN
ejpam-5050	56	9	y(k)(a	y(k)(a	NUM
ejpam-5050	56	10	)	)	PUNCT
ejpam-5050	56	11	k	k	NOUN
ejpam-5050	56	12	!	!	PUNCT
ejpam-5050	57	1	(	(	PUNCT
ejpam-5050	57	2	t−	t−	X
ejpam-5050	57	3	a)k	a)k	NOUN
ejpam-5050	57	4	]	]	X
ejpam-5050	57	5	)	)	PUNCT
ejpam-5050	57	6	(	(	PUNCT
ejpam-5050	57	7	x	x	NOUN
ejpam-5050	57	8	)	)	PUNCT
ejpam-5050	57	9	,	,	PUNCT
ejpam-5050	57	10	(	(	PUNCT
ejpam-5050	57	11	2	2	X
ejpam-5050	57	12	)	)	PUNCT
ejpam-5050	57	13	with	with	ADP
ejpam-5050	57	14	n	n	NOUN
ejpam-5050	57	15	=	=	PUNCT
ejpam-5050	58	1	[	[	X
ejpam-5050	58	2	α	α	X
ejpam-5050	58	3	]	]	X
ejpam-5050	58	4	+	+	NOUN
ejpam-5050	58	5	1	1	NUM
ejpam-5050	58	6	,	,	PUNCT
ejpam-5050	58	7	when	when	SCONJ
ejpam-5050	58	8	α	α	NOUN
ejpam-5050	58	9	/∈	/∈	PUNCT
ejpam-5050	58	10	n	n	CCONJ
ejpam-5050	58	11	,	,	PUNCT
ejpam-5050	58	12	and	and	CCONJ
ejpam-5050	58	13	n	n	CCONJ
ejpam-5050	58	14	=	=	SYM
ejpam-5050	58	15	α	α	PROPN
ejpam-5050	58	16	,	,	PUNCT
ejpam-5050	58	17	for	for	ADP
ejpam-5050	58	18	α	α	PROPN
ejpam-5050	58	19	∈	∈	PROPN
ejpam-5050	58	20	n	n	AUX
ejpam-5050	58	21	;	;	PUNCT
ejpam-5050	58	22	with	with	ADP
ejpam-5050	58	23	n	n	CCONJ
ejpam-5050	58	24	denoting	denote	VERB
ejpam-5050	58	25	the	the	DET
ejpam-5050	58	26	set	set	NOUN
ejpam-5050	58	27	of	of	ADP
ejpam-5050	58	28	positive	positive	ADJ
ejpam-5050	58	29	whole	whole	ADJ
ejpam-5050	58	30	numbers	number	NOUN
ejpam-5050	58	31	.	.	PUNCT
ejpam-5050	59	1	note	note	VERB
ejpam-5050	59	2	that	that	SCONJ
ejpam-5050	59	3	,	,	PUNCT
ejpam-5050	59	4	as	as	ADP
ejpam-5050	59	5	a	a	DET
ejpam-5050	59	6	peculiar	peculiar	ADJ
ejpam-5050	59	7	case	case	NOUN
ejpam-5050	59	8	,	,	PUNCT
ejpam-5050	59	9	when	when	SCONJ
ejpam-5050	59	10	0	0	X
ejpam-5050	59	11	<	<	X
ejpam-5050	59	12	α	α	X
ejpam-5050	59	13	<	<	X
ejpam-5050	59	14	1	1	NUM
ejpam-5050	59	15	,	,	PUNCT
ejpam-5050	59	16	the	the	DET
ejpam-5050	59	17	formulae	formulae	NOUN
ejpam-5050	59	18	given	give	VERB
ejpam-5050	59	19	in	in	ADP
ejpam-5050	59	20	(	(	PUNCT
ejpam-5050	59	21	2	2	NUM
ejpam-5050	59	22	)	)	PUNCT
ejpam-5050	59	23	and	and	CCONJ
ejpam-5050	59	24	(	(	PUNCT
ejpam-5050	59	25	1	1	X
ejpam-5050	59	26	)	)	PUNCT
ejpam-5050	59	27	could	could	AUX
ejpam-5050	59	28	be	be	AUX
ejpam-5050	59	29	re	re	VERB
ejpam-5050	59	30	-	-	VERB
ejpam-5050	59	31	expressed	express	VERB
ejpam-5050	59	32	as	as	SCONJ
ejpam-5050	59	33	follows	follow	VERB
ejpam-5050	59	34	cdα	cdα	NOUN
ejpam-5050	59	35	b−y(x	b−y(x	NOUN
ejpam-5050	59	36	)	)	PUNCT
ejpam-5050	59	37	=	=	PUNCT
ejpam-5050	59	38	(	(	PUNCT
ejpam-5050	59	39	dα	dα	INTJ
ejpam-5050	59	40	b−	b−	PROPN
ejpam-5050	60	1	[	[	X
ejpam-5050	60	2	y(t)−	y(t)−	PROPN
ejpam-5050	60	3	y(b)])(x	y(b)])(x	PROPN
ejpam-5050	60	4	)	)	PUNCT
ejpam-5050	60	5	,	,	PUNCT
ejpam-5050	60	6	and	and	CCONJ
ejpam-5050	60	7	cdα	cdα	NOUN
ejpam-5050	60	8	a+y(x	a+y(x	NOUN
ejpam-5050	60	9	)	)	PUNCT
ejpam-5050	61	1	=	=	SYM
ejpam-5050	61	2	(	(	PUNCT
ejpam-5050	61	3	dα	dα	INTJ
ejpam-5050	61	4	a+	a+	PUNCT
ejpam-5050	62	1	[	[	X
ejpam-5050	62	2	y(t)−	y(t)−	PROPN
ejpam-5050	62	3	y(a)])(x	y(a)])(x	NUM
ejpam-5050	62	4	)	)	PUNCT
ejpam-5050	62	5	.	.	PUNCT
ejpam-5050	63	1	2.2	2.2	NUM
ejpam-5050	63	2	.	.	PUNCT
ejpam-5050	64	1	some	some	DET
ejpam-5050	64	2	useful	useful	ADJ
ejpam-5050	64	3	properties	property	NOUN
ejpam-5050	64	4	this	this	DET
ejpam-5050	64	5	subsection	subsection	NOUN
ejpam-5050	64	6	recalls	recall	VERB
ejpam-5050	64	7	some	some	DET
ejpam-5050	64	8	useful	useful	ADJ
ejpam-5050	64	9	properties	property	NOUN
ejpam-5050	64	10	of	of	ADP
ejpam-5050	64	11	the	the	DET
ejpam-5050	64	12	aforementioned	aforementioned	ADJ
ejpam-5050	64	13	rlf	rlf	NOUN
ejpam-5050	64	14	integrals	integral	NOUN
ejpam-5050	64	15	/	/	SYM
ejpam-5050	64	16	derivatives	derivative	NOUN
ejpam-5050	64	17	and	and	CCONJ
ejpam-5050	64	18	cf	cf	NOUN
ejpam-5050	64	19	derivatives	derivative	NOUN
ejpam-5050	64	20	that	that	PRON
ejpam-5050	64	21	will	will	AUX
ejpam-5050	64	22	be	be	AUX
ejpam-5050	64	23	greatly	greatly	ADV
ejpam-5050	64	24	utilized	utilize	VERB
ejpam-5050	64	25	in	in	ADP
ejpam-5050	64	26	the	the	DET
ejpam-5050	64	27	course	course	NOUN
ejpam-5050	64	28	of	of	ADP
ejpam-5050	64	29	the	the	DET
ejpam-5050	64	30	governing	govern	VERB
ejpam-5050	64	31	model	model	NOUN
ejpam-5050	64	32	.	.	PUNCT
ejpam-5050	65	1	lemma	lemma	PROPN
ejpam-5050	65	2	1	1	X
ejpam-5050	65	3	.	.	PUNCT
ejpam-5050	65	4	assume	assume	VERB
ejpam-5050	65	5	α	α	PROPN
ejpam-5050	65	6	>	>	X
ejpam-5050	65	7	0	0	NUM
ejpam-5050	65	8	,	,	PUNCT
ejpam-5050	65	9	and	and	CCONJ
ejpam-5050	65	10	further	far	ADV
ejpam-5050	65	11	assume	assume	VERB
ejpam-5050	65	12	n	n	NOUN
ejpam-5050	65	13	=	=	PUNCT
ejpam-5050	66	1	[	[	X
ejpam-5050	66	2	α	α	X
ejpam-5050	66	3	]	]	X
ejpam-5050	66	4	+	+	NOUN
ejpam-5050	66	5	1	1	NUM
ejpam-5050	66	6	,	,	PUNCT
ejpam-5050	66	7	when	when	SCONJ
ejpam-5050	66	8	α	α	NOUN
ejpam-5050	66	9	/∈	/∈	PUNCT
ejpam-5050	66	10	n	n	CCONJ
ejpam-5050	66	11	,	,	PUNCT
ejpam-5050	66	12	and	and	CCONJ
ejpam-5050	66	13	n	n	CCONJ
ejpam-5050	66	14	=	=	SYM
ejpam-5050	66	15	α	α	NOUN
ejpam-5050	66	16	,	,	PUNCT
ejpam-5050	66	17	when	when	SCONJ
ejpam-5050	66	18	α	α	PROPN
ejpam-5050	66	19	∈	∈	PROPN
ejpam-5050	66	20	n.	n.	NOUN
ejpam-5050	66	21	then	then	ADV
ejpam-5050	66	22	,	,	PUNCT
ejpam-5050	66	23	if	if	SCONJ
ejpam-5050	66	24	y(x	y(x	NOUN
ejpam-5050	66	25	)	)	PUNCT
ejpam-5050	66	26	∈	∈	PROPN
ejpam-5050	66	27	cn[a	cn[a	PROPN
ejpam-5050	66	28	,	,	PUNCT
ejpam-5050	66	29	b	b	NOUN
ejpam-5050	66	30	]	]	PUNCT
ejpam-5050	66	31	or	or	CCONJ
ejpam-5050	66	32	y(x	y(x	NOUN
ejpam-5050	66	33	)	)	PUNCT
ejpam-5050	66	34	∈	∈	PROPN
ejpam-5050	66	35	acn[a	acn[a	NOUN
ejpam-5050	66	36	,	,	PUNCT
ejpam-5050	66	37	b	b	NOUN
ejpam-5050	66	38	]	]	X
ejpam-5050	66	39	,	,	PUNCT
ejpam-5050	66	40	we	we	PRON
ejpam-5050	66	41	accordingly	accordingly	ADV
ejpam-5050	66	42	have	have	VERB
ejpam-5050	66	43	as	as	SCONJ
ejpam-5050	66	44	follows	follow	VERB
ejpam-5050	66	45	(	(	PUNCT
ejpam-5050	66	46	iαb−	iαb−	PROPN
ejpam-5050	66	47	cdα	cdα	NOUN
ejpam-5050	66	48	b−y)(x	b−y)(x	NOUN
ejpam-5050	66	49	)	)	PUNCT
ejpam-5050	67	1	=	=	SYM
ejpam-5050	68	1	y(x)−	y(x)−	PROPN
ejpam-5050	68	2	n−1∑	n−1∑	NUM
ejpam-5050	68	3	k=0	k=0	PROPN
ejpam-5050	68	4	(	(	PUNCT
ejpam-5050	68	5	−)ky(k)(b	−)ky(k)(b	ADJ
ejpam-5050	68	6	)	)	PUNCT
ejpam-5050	68	7	k	k	NOUN
ejpam-5050	68	8	!	!	PUNCT
ejpam-5050	69	1	(	(	PUNCT
ejpam-5050	69	2	b−	b−	PROPN
ejpam-5050	69	3	x)k	x)k	NOUN
ejpam-5050	69	4	,	,	PUNCT
ejpam-5050	69	5	(	(	PUNCT
ejpam-5050	69	6	3	3	X
ejpam-5050	69	7	)	)	PUNCT
ejpam-5050	69	8	and	and	CCONJ
ejpam-5050	69	9	(	(	PUNCT
ejpam-5050	69	10	iαa+	iαa+	PROPN
ejpam-5050	69	11	cdα	cdα	PROPN
ejpam-5050	69	12	a+y)(x	a+y)(x	PROPN
ejpam-5050	69	13	)	)	PUNCT
ejpam-5050	70	1	=	=	SYM
ejpam-5050	71	1	y(x)−	y(x)−	PROPN
ejpam-5050	71	2	n−1∑	n−1∑	NUM
ejpam-5050	71	3	k=0	k=0	PROPN
ejpam-5050	71	4	y(k)(a	y(k)(a	NUM
ejpam-5050	71	5	)	)	PUNCT
ejpam-5050	71	6	k	k	NOUN
ejpam-5050	71	7	!	!	PUNCT
ejpam-5050	71	8	(	(	PUNCT
ejpam-5050	71	9	x−	x−	PROPN
ejpam-5050	71	10	a)k	a)k	ADJ
ejpam-5050	71	11	.	.	PUNCT
ejpam-5050	72	1	(	(	PUNCT
ejpam-5050	72	2	4	4	X
ejpam-5050	72	3	)	)	PUNCT
ejpam-5050	72	4	consequently	consequently	ADV
ejpam-5050	72	5	,	,	PUNCT
ejpam-5050	72	6	when	when	SCONJ
ejpam-5050	72	7	0	0	ADP
ejpam-5050	72	8	<	<	X
ejpam-5050	72	9	α	α	PROPN
ejpam-5050	72	10	≦	≦	PROPN
ejpam-5050	72	11	1	1	NUM
ejpam-5050	72	12	and	and	CCONJ
ejpam-5050	72	13	y(x	y(x	NOUN
ejpam-5050	72	14	)	)	PUNCT
ejpam-5050	72	15	∈	∈	PROPN
ejpam-5050	72	16	c[a	c[a	PROPN
ejpam-5050	72	17	,	,	PUNCT
ejpam-5050	72	18	b	b	NOUN
ejpam-5050	72	19	]	]	PUNCT
ejpam-5050	72	20	or	or	CCONJ
ejpam-5050	72	21	y(x	y(x	NOUN
ejpam-5050	72	22	)	)	PUNCT
ejpam-5050	72	23	∈	∈	PROPN
ejpam-5050	72	24	ac[a	ac[a	PROPN
ejpam-5050	72	25	,	,	PUNCT
ejpam-5050	72	26	b	b	NOUN
ejpam-5050	72	27	]	]	X
ejpam-5050	72	28	,	,	PUNCT
ejpam-5050	72	29	the	the	DET
ejpam-5050	72	30	above	above	ADJ
ejpam-5050	72	31	results	result	NOUN
ejpam-5050	72	32	respectively	respectively	ADV
ejpam-5050	72	33	reduce	reduce	VERB
ejpam-5050	72	34	to	to	ADP
ejpam-5050	72	35	(	(	PUNCT
ejpam-5050	72	36	iαb−	iαb−	PROPN
ejpam-5050	72	37	cdα	cdα	NOUN
ejpam-5050	72	38	b−y)(x	b−y)(x	NOUN
ejpam-5050	72	39	)	)	PUNCT
ejpam-5050	73	1	=	=	X
ejpam-5050	73	2	y(x)−	y(x)−	PROPN
ejpam-5050	73	3	y(b	y(b	PROPN
ejpam-5050	73	4	)	)	PUNCT
ejpam-5050	73	5	,	,	PUNCT
ejpam-5050	73	6	and	and	CCONJ
ejpam-5050	73	7	(	(	PUNCT
ejpam-5050	73	8	iαa+	iαa+	PROPN
ejpam-5050	73	9	cdα	cdα	PROPN
ejpam-5050	73	10	a+y)(x	a+y)(x	PROPN
ejpam-5050	73	11	)	)	PUNCT
ejpam-5050	73	12	=	=	SYM
ejpam-5050	73	13	y(x)−	y(x)−	PROPN
ejpam-5050	73	14	y(a	y(a	PROPN
ejpam-5050	73	15	)	)	PUNCT
ejpam-5050	73	16	.	.	PUNCT
ejpam-5050	74	1	lemma	lemma	PROPN
ejpam-5050	74	2	2	2	NUM
ejpam-5050	74	3	.	.	PUNCT
ejpam-5050	75	1	the	the	DET
ejpam-5050	75	2	following	follow	VERB
ejpam-5050	75	3	results	result	NOUN
ejpam-5050	75	4	for	for	ADP
ejpam-5050	75	5	the	the	DET
ejpam-5050	75	6	fractional	fractional	ADJ
ejpam-5050	75	7	integral	integral	ADJ
ejpam-5050	75	8	/	/	SYM
ejpam-5050	75	9	derivative	derivative	ADJ
ejpam-5050	75	10	hold	hold	NOUN
ejpam-5050	75	11	[	[	X
ejpam-5050	75	12	45	45	NUM
ejpam-5050	75	13	]	]	PUNCT
ejpam-5050	75	14	(	(	PUNCT
ejpam-5050	75	15	i	i	NOUN
ejpam-5050	75	16	)	)	PUNCT
ejpam-5050	75	17	iα[c	iα[c	ADV
ejpam-5050	75	18	]	]	X
ejpam-5050	75	19	=	=	SYM
ejpam-5050	75	20	cxα	cxα	X
ejpam-5050	75	21	γ(α+	γ(α+	DET
ejpam-5050	75	22	1	1	NUM
ejpam-5050	75	23	)	)	PUNCT
ejpam-5050	75	24	,	,	PUNCT
ejpam-5050	75	25	if	if	SCONJ
ejpam-5050	75	26	c	c	PROPN
ejpam-5050	75	27	is	be	AUX
ejpam-5050	75	28	constant	constant	ADJ
ejpam-5050	75	29	,	,	PUNCT
ejpam-5050	75	30	(	(	PUNCT
ejpam-5050	75	31	5	5	NUM
ejpam-5050	75	32	)	)	PUNCT
ejpam-5050	75	33	(	(	PUNCT
ejpam-5050	75	34	ii	ii	NOUN
ejpam-5050	75	35	)	)	PUNCT
ejpam-5050	75	36	dαxn	dαxn	PROPN
ejpam-5050	75	37	=	=	PUNCT
ejpam-5050	75	38	γ(n+	γ(n+	NOUN
ejpam-5050	75	39	1)xn−α	1)xn−α	NUM
ejpam-5050	75	40	γ(n+	γ(n+	NOUN
ejpam-5050	75	41	1−	1−	NUM
ejpam-5050	75	42	α	α	NOUN
ejpam-5050	75	43	)	)	PUNCT
ejpam-5050	75	44	.	.	PUNCT
ejpam-5050	76	1	(	(	PUNCT
ejpam-5050	76	2	6	6	NUM
ejpam-5050	76	3	)	)	PUNCT
ejpam-5050	76	4	(	(	PUNCT
ejpam-5050	76	5	iii	iii	NOUN
ejpam-5050	76	6	)	)	PUNCT
ejpam-5050	76	7	iα[xn	iα[xn	NOUN
ejpam-5050	76	8	]	]	PUNCT
ejpam-5050	76	9	=	=	PUNCT
ejpam-5050	76	10	γ(n+	γ(n+	NOUN
ejpam-5050	77	1	1)xα+n	1)xα+n	NUM
ejpam-5050	77	2	γ(α+	γ(α+	X
ejpam-5050	77	3	n+	n+	NUM
ejpam-5050	77	4	1	1	NUM
ejpam-5050	77	5	)	)	PUNCT
ejpam-5050	77	6	,	,	PUNCT
ejpam-5050	77	7	(	(	PUNCT
ejpam-5050	77	8	7	7	X
ejpam-5050	77	9	)	)	PUNCT
ejpam-5050	77	10	m.	m.	NOUN
ejpam-5050	77	11	al	al	PROPN
ejpam-5050	77	12	-	-	PUNCT
ejpam-5050	77	13	mazmumy	mazmumy	PROPN
ejpam-5050	77	14	,	,	PUNCT
ejpam-5050	77	15	m.	m.	NOUN
ejpam-5050	77	16	alsulami	alsulami	PROPN
ejpam-5050	77	17	/	/	SYM
ejpam-5050	77	18	eur	eur	PROPN
ejpam-5050	77	19	.	.	PUNCT
ejpam-5050	78	1	j.	j.	PROPN
ejpam-5050	78	2	pure	pure	PROPN
ejpam-5050	78	3	appl	appl	PROPN
ejpam-5050	78	4	.	.	PROPN
ejpam-5050	78	5	math	math	PROPN
ejpam-5050	78	6	,	,	PUNCT
ejpam-5050	78	7	17	17	NUM
ejpam-5050	78	8	(	(	PUNCT
ejpam-5050	78	9	1	1	NUM
ejpam-5050	78	10	)	)	PUNCT
ejpam-5050	78	11	(	(	PUNCT
ejpam-5050	78	12	2024	2024	NUM
ejpam-5050	78	13	)	)	PUNCT
ejpam-5050	78	14	,	,	PUNCT
ejpam-5050	78	15	546	546	NUM
ejpam-5050	78	16	-	-	SYM
ejpam-5050	78	17	568	568	NUM
ejpam-5050	78	18	550	550	NUM
ejpam-5050	78	19	3	3	NUM
ejpam-5050	78	20	.	.	PUNCT
ejpam-5050	79	1	treatment	treatment	NOUN
ejpam-5050	79	2	of	of	ADP
ejpam-5050	79	3	bagley	bagley	NOUN
ejpam-5050	79	4	-	-	PUNCT
ejpam-5050	79	5	torvik	torvik	NOUN
ejpam-5050	79	6	bvps	bvps	NOUN
ejpam-5050	79	7	via	via	ADP
ejpam-5050	79	8	madm	madm	PROPN
ejpam-5050	79	9	the	the	DET
ejpam-5050	79	10	current	current	ADJ
ejpam-5050	79	11	section	section	NOUN
ejpam-5050	79	12	mainly	mainly	ADV
ejpam-5050	79	13	makes	make	VERB
ejpam-5050	79	14	use	use	NOUN
ejpam-5050	79	15	of	of	ADP
ejpam-5050	79	16	madm	madm	NOUN
ejpam-5050	79	17	[	[	X
ejpam-5050	79	18	2	2	NUM
ejpam-5050	79	19	,	,	PUNCT
ejpam-5050	79	20	9	9	NUM
ejpam-5050	79	21	,	,	PUNCT
ejpam-5050	79	22	12	12	NUM
ejpam-5050	79	23	,	,	PUNCT
ejpam-5050	79	24	36	36	NUM
ejpam-5050	79	25	,	,	PUNCT
ejpam-5050	79	26	37	37	NUM
ejpam-5050	79	27	,	,	PUNCT
ejpam-5050	79	28	42	42	NUM
ejpam-5050	79	29	,	,	PUNCT
ejpam-5050	79	30	48	48	NUM
ejpam-5050	79	31	]	]	PUNCT
ejpam-5050	79	32	to	to	PART
ejpam-5050	79	33	acquire	acquire	VERB
ejpam-5050	79	34	the	the	DET
ejpam-5050	79	35	exact	exact	ADJ
ejpam-5050	79	36	analytical	analytical	ADJ
ejpam-5050	79	37	solution	solution	NOUN
ejpam-5050	79	38	of	of	ADP
ejpam-5050	79	39	the	the	DET
ejpam-5050	79	40	bagley	bagley	NOUN
ejpam-5050	79	41	-	-	PUNCT
ejpam-5050	79	42	torvik	torvik	NOUN
ejpam-5050	79	43	bvp	bvp	NOUN
ejpam-5050	79	44	where	where	SCONJ
ejpam-5050	79	45	possible	possible	ADJ
ejpam-5050	79	46	;	;	PUNCT
ejpam-5050	79	47	moreover	moreover	ADV
ejpam-5050	79	48	,	,	PUNCT
ejpam-5050	79	49	when	when	SCONJ
ejpam-5050	79	50	the	the	DET
ejpam-5050	79	51	acquisition	acquisition	NOUN
ejpam-5050	79	52	of	of	ADP
ejpam-5050	79	53	such	such	DET
ejpam-5050	79	54	an	an	DET
ejpam-5050	79	55	exact	exact	ADJ
ejpam-5050	79	56	analytical	analytical	ADJ
ejpam-5050	79	57	solution	solution	NOUN
ejpam-5050	79	58	is	be	AUX
ejpam-5050	79	59	not	not	PART
ejpam-5050	79	60	feasible	feasible	ADJ
ejpam-5050	79	61	,	,	PUNCT
ejpam-5050	79	62	a	a	DET
ejpam-5050	79	63	closed	close	VERB
ejpam-5050	79	64	-	-	PUNCT
ejpam-5050	79	65	form	form	NOUN
ejpam-5050	79	66	series	series	NOUN
ejpam-5050	79	67	solution	solution	NOUN
ejpam-5050	79	68	of	of	ADP
ejpam-5050	79	69	the	the	DET
ejpam-5050	79	70	governing	govern	VERB
ejpam-5050	79	71	model	model	NOUN
ejpam-5050	79	72	will	will	AUX
ejpam-5050	79	73	be	be	AUX
ejpam-5050	79	74	acquired	acquire	VERB
ejpam-5050	79	75	.	.	PUNCT
ejpam-5050	80	1	in	in	ADP
ejpam-5050	80	2	fact	fact	NOUN
ejpam-5050	80	3	,	,	PUNCT
ejpam-5050	80	4	we	we	PRON
ejpam-5050	80	5	will	will	AUX
ejpam-5050	80	6	be	be	AUX
ejpam-5050	80	7	making	make	VERB
ejpam-5050	80	8	consideration	consideration	NOUN
ejpam-5050	80	9	to	to	ADP
ejpam-5050	80	10	the	the	DET
ejpam-5050	80	11	bvp	bvp	NOUN
ejpam-5050	80	12	of	of	ADP
ejpam-5050	80	13	the	the	DET
ejpam-5050	80	14	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5050	80	15	bagley	bagley	NOUN
ejpam-5050	80	16	-	-	PUNCT
ejpam-5050	80	17	torvik	torvik	NOUN
ejpam-5050	80	18	equation	equation	NOUN
ejpam-5050	80	19	endowed	endow	VERB
ejpam-5050	80	20	with	with	ADP
ejpam-5050	80	21	dirichlet	dirichlet	PROPN
ejpam-5050	80	22	boundary	boundary	ADJ
ejpam-5050	80	23	conditions	condition	NOUN
ejpam-5050	80	24	as	as	SCONJ
ejpam-5050	80	25	follows	follow	VERB
ejpam-5050	80	26	[	[	X
ejpam-5050	80	27	51]-[29	51]-[29	X
ejpam-5050	80	28	]	]	X
ejpam-5050	80	29	d2y(x	d2y(x	PROPN
ejpam-5050	80	30	)	)	PUNCT
ejpam-5050	81	1	+	+	NOUN
ejpam-5050	81	2	d3/2y(x	d3/2y(x	NOUN
ejpam-5050	81	3	)	)	PUNCT
ejpam-5050	82	1	+	+	NUM
ejpam-5050	82	2	y(x	y(x	NOUN
ejpam-5050	82	3	)	)	PUNCT
ejpam-5050	82	4	=	=	SYM
ejpam-5050	82	5	g(x	g(x	NOUN
ejpam-5050	82	6	)	)	PUNCT
ejpam-5050	82	7	,	,	PUNCT
ejpam-5050	82	8	a	a	DET
ejpam-5050	82	9	<	<	X
ejpam-5050	82	10	x	x	X
ejpam-5050	82	11	<	<	X
ejpam-5050	82	12	b	b	PROPN
ejpam-5050	82	13	,	,	PUNCT
ejpam-5050	82	14	a	a	PRON
ejpam-5050	82	15	,	,	PUNCT
ejpam-5050	82	16	b	b	PROPN
ejpam-5050	82	17	∈	∈	PROPN
ejpam-5050	82	18	r+	r+	NOUN
ejpam-5050	82	19	,	,	PUNCT
ejpam-5050	82	20	y(a	y(a	X
ejpam-5050	82	21	)	)	PUNCT
ejpam-5050	82	22	=	=	SYM
ejpam-5050	82	23	λ1	λ1	PROPN
ejpam-5050	82	24	,	,	PUNCT
ejpam-5050	82	25	y(b	y(b	PROPN
ejpam-5050	82	26	)	)	PUNCT
ejpam-5050	82	27	=	=	SYM
ejpam-5050	82	28	λ2	λ2	NOUN
ejpam-5050	82	29	,	,	PUNCT
ejpam-5050	82	30	(	(	PUNCT
ejpam-5050	82	31	8)	8)	NUM
ejpam-5050	82	32	with	with	ADP
ejpam-5050	82	33	g(x	g(x	NOUN
ejpam-5050	82	34	)	)	PUNCT
ejpam-5050	82	35	denoting	denote	VERB
ejpam-5050	82	36	the	the	DET
ejpam-5050	82	37	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5050	82	38	/	/	SYM
ejpam-5050	82	39	source	source	NOUN
ejpam-5050	82	40	term	term	NOUN
ejpam-5050	82	41	,	,	PUNCT
ejpam-5050	82	42	λ1	λ1	ADJ
ejpam-5050	82	43	and	and	CCONJ
ejpam-5050	82	44	λ2	λ2	NOUN
ejpam-5050	82	45	are	be	AUX
ejpam-5050	82	46	constants	constant	NOUN
ejpam-5050	82	47	;	;	PUNCT
ejpam-5050	82	48	while	while	SCONJ
ejpam-5050	82	49	the	the	DET
ejpam-5050	82	50	function	function	NOUN
ejpam-5050	82	51	y(x	y(x	PROPN
ejpam-5050	82	52	)	)	PUNCT
ejpam-5050	82	53	is	be	AUX
ejpam-5050	82	54	the	the	DET
ejpam-5050	82	55	solution	solution	NOUN
ejpam-5050	82	56	that	that	PRON
ejpam-5050	82	57	we	we	PRON
ejpam-5050	82	58	intend	intend	VERB
ejpam-5050	82	59	to	to	PART
ejpam-5050	82	60	determine	determine	VERB
ejpam-5050	82	61	.	.	PUNCT
ejpam-5050	83	1	certainly	certainly	ADV
ejpam-5050	83	2	,	,	PUNCT
ejpam-5050	83	3	the	the	DET
ejpam-5050	83	4	differential	differential	ADJ
ejpam-5050	83	5	equation	equation	NOUN
ejpam-5050	83	6	in	in	ADP
ejpam-5050	83	7	(	(	PUNCT
ejpam-5050	83	8	8)	8)	NUM
ejpam-5050	83	9	is	be	AUX
ejpam-5050	83	10	a	a	DET
ejpam-5050	83	11	fractional	fractional	ADJ
ejpam-5050	83	12	-	-	PUNCT
ejpam-5050	83	13	order	order	NOUN
ejpam-5050	83	14	differential	differential	ADJ
ejpam-5050	83	15	equation	equation	NOUN
ejpam-5050	83	16	defined	define	VERB
ejpam-5050	83	17	in	in	ADP
ejpam-5050	83	18	cf	cf	NOUN
ejpam-5050	83	19	derivative	derivative	ADJ
ejpam-5050	83	20	sense	sense	NOUN
ejpam-5050	83	21	with	with	ADP
ejpam-5050	83	22	the	the	DET
ejpam-5050	83	23	highest	high	ADJ
ejpam-5050	83	24	integer	integer	NOUN
ejpam-5050	83	25	-	-	PUNCT
ejpam-5050	83	26	order	order	NOUN
ejpam-5050	83	27	of	of	ADP
ejpam-5050	83	28	2	2	NUM
ejpam-5050	83	29	,	,	PUNCT
ejpam-5050	83	30	and	and	CCONJ
ejpam-5050	83	31	then	then	ADV
ejpam-5050	83	32	followed	follow	VERB
ejpam-5050	83	33	by	by	ADP
ejpam-5050	83	34	the	the	DET
ejpam-5050	83	35	cf	cf	NOUN
ejpam-5050	83	36	-	-	PUNCT
ejpam-5050	83	37	order	order	NOUN
ejpam-5050	83	38	of	of	ADP
ejpam-5050	83	39	3/2	3/2	NUM
ejpam-5050	83	40	.	.	PUNCT
ejpam-5050	84	1	in	in	ADP
ejpam-5050	84	2	addition	addition	NOUN
ejpam-5050	84	3	,	,	PUNCT
ejpam-5050	84	4	this	this	DET
ejpam-5050	84	5	fractional	fractional	ADJ
ejpam-5050	84	6	-	-	PUNCT
ejpam-5050	84	7	order	order	NOUN
ejpam-5050	84	8	model	model	NOUN
ejpam-5050	84	9	arises	arise	VERB
ejpam-5050	84	10	in	in	ADP
ejpam-5050	84	11	many	many	ADJ
ejpam-5050	84	12	physical	physical	ADJ
ejpam-5050	84	13	processes	process	NOUN
ejpam-5050	84	14	,	,	PUNCT
ejpam-5050	84	15	and	and	CCONJ
ejpam-5050	84	16	further	far	ADV
ejpam-5050	84	17	has	have	VERB
ejpam-5050	84	18	vast	vast	ADJ
ejpam-5050	84	19	relevance	relevance	NOUN
ejpam-5050	84	20	in	in	ADP
ejpam-5050	84	21	the	the	DET
ejpam-5050	84	22	study	study	NOUN
ejpam-5050	84	23	of	of	ADP
ejpam-5050	84	24	fluid	fluid	ADJ
ejpam-5050	84	25	flows	flow	NOUN
ejpam-5050	84	26	and	and	CCONJ
ejpam-5050	84	27	viscoelastic	viscoelastic	NOUN
ejpam-5050	84	28	materials	material	NOUN
ejpam-5050	84	29	[	[	X
ejpam-5050	84	30	14	14	NUM
ejpam-5050	84	31	]	]	PUNCT
ejpam-5050	84	32	,	,	PUNCT
ejpam-5050	84	33	among	among	ADP
ejpam-5050	84	34	others	other	NOUN
ejpam-5050	84	35	;	;	PUNCT
ejpam-5050	84	36	more	more	ADV
ejpam-5050	84	37	so	so	ADV
ejpam-5050	84	38	,	,	PUNCT
ejpam-5050	84	39	the	the	DET
ejpam-5050	84	40	highest	high	ADJ
ejpam-5050	84	41	-	-	PUNCT
ejpam-5050	84	42	order	order	NOUN
ejpam-5050	84	43	of	of	ADP
ejpam-5050	84	44	the	the	DET
ejpam-5050	84	45	equation	equation	NOUN
ejpam-5050	84	46	remains	remain	VERB
ejpam-5050	84	47	2	2	NUM
ejpam-5050	84	48	,	,	PUNCT
ejpam-5050	84	49	the	the	DET
ejpam-5050	84	50	integer	integer	NOUN
ejpam-5050	84	51	-	-	PUNCT
ejpam-5050	84	52	order	order	NOUN
ejpam-5050	84	53	,	,	PUNCT
ejpam-5050	84	54	then	then	ADV
ejpam-5050	84	55	follows	follow	VERB
ejpam-5050	84	56	by	by	ADP
ejpam-5050	84	57	the	the	DET
ejpam-5050	84	58	fractionalorder	fractionalorder	PROPN
ejpam-5050	84	59	derivative	derivative	NOUN
ejpam-5050	84	60	of	of	ADP
ejpam-5050	84	61	3/2	3/2	NUM
ejpam-5050	84	62	.	.	PUNCT
ejpam-5050	85	1	further	far	ADV
ejpam-5050	85	2	,	,	PUNCT
ejpam-5050	85	3	the	the	DET
ejpam-5050	85	4	bagley	bagley	NOUN
ejpam-5050	85	5	-	-	PUNCT
ejpam-5050	85	6	torvik	torvik	NOUN
ejpam-5050	85	7	equation	equation	NOUN
ejpam-5050	85	8	expressed	express	VERB
ejpam-5050	85	9	above	above	ADV
ejpam-5050	85	10	can	can	AUX
ejpam-5050	85	11	equally	equally	ADV
ejpam-5050	85	12	be	be	AUX
ejpam-5050	85	13	expressed	express	VERB
ejpam-5050	85	14	in	in	ADP
ejpam-5050	85	15	an	an	DET
ejpam-5050	85	16	operator	operator	NOUN
ejpam-5050	85	17	notation	notation	NOUN
ejpam-5050	85	18	upon	upon	SCONJ
ejpam-5050	85	19	making	make	VERB
ejpam-5050	85	20	use	use	NOUN
ejpam-5050	85	21	of	of	ADP
ejpam-5050	85	22	the	the	DET
ejpam-5050	85	23	differential	differential	ADJ
ejpam-5050	85	24	operator	operator	NOUN
ejpam-5050	85	25	notation	notation	NOUN
ejpam-5050	85	26	d	d	PROPN
ejpam-5050	85	27	as	as	SCONJ
ejpam-5050	85	28	follows	follow	VERB
ejpam-5050	85	29	ly	ly	ADP
ejpam-5050	85	30	=	=	PUNCT
ejpam-5050	85	31	d2y	d2y	PROPN
ejpam-5050	85	32	=	=	SYM
ejpam-5050	85	33	g(x)−d3/2y(x)−	g(x)−d3/2y(x)−	PROPN
ejpam-5050	85	34	y(x	y(x	PROPN
ejpam-5050	85	35	)	)	PUNCT
ejpam-5050	85	36	,	,	PUNCT
ejpam-5050	85	37	(	(	PUNCT
ejpam-5050	85	38	9	9	X
ejpam-5050	85	39	)	)	PUNCT
ejpam-5050	85	40	where	where	SCONJ
ejpam-5050	85	41	l	l	NOUN
ejpam-5050	85	42	=	=	SYM
ejpam-5050	85	43	d2	d2	PROPN
ejpam-5050	85	44	=	=	PUNCT
ejpam-5050	85	45	d2	d2	PROPN
ejpam-5050	85	46	dx2	dx2	PROPN
ejpam-5050	85	47	.	.	PUNCT
ejpam-5050	86	1	furthermore	furthermore	ADV
ejpam-5050	86	2	,	,	PUNCT
ejpam-5050	86	3	to	to	PART
ejpam-5050	86	4	determine	determine	VERB
ejpam-5050	86	5	the	the	DET
ejpam-5050	86	6	explicit	explicit	ADJ
ejpam-5050	86	7	exact	exact	ADJ
ejpam-5050	86	8	analytical	analytical	ADJ
ejpam-5050	86	9	solution	solution	NOUN
ejpam-5050	86	10	of	of	ADP
ejpam-5050	86	11	the	the	DET
ejpam-5050	86	12	bagley	bagley	NOUN
ejpam-5050	86	13	-	-	PUNCT
ejpam-5050	86	14	torvik	torvik	NOUN
ejpam-5050	86	15	bvp	bvp	PROPN
ejpam-5050	86	16	expressed	express	VERB
ejpam-5050	86	17	in	in	ADP
ejpam-5050	86	18	(	(	PUNCT
ejpam-5050	86	19	8)	8)	NUM
ejpam-5050	86	20	using	use	VERB
ejpam-5050	86	21	the	the	DET
ejpam-5050	86	22	version	version	NOUN
ejpam-5050	86	23	expressed	express	VERB
ejpam-5050	86	24	in	in	ADP
ejpam-5050	86	25	(	(	PUNCT
ejpam-5050	86	26	9	9	NUM
ejpam-5050	86	27	)	)	PUNCT
ejpam-5050	86	28	through	through	ADP
ejpam-5050	86	29	the	the	DET
ejpam-5050	86	30	differential	differential	ADJ
ejpam-5050	86	31	operator	operator	NOUN
ejpam-5050	86	32	the	the	DET
ejpam-5050	86	33	madm	madm	NOUN
ejpam-5050	87	1	[	[	X
ejpam-5050	87	2	36]-[42	36]-[42	X
ejpam-5050	87	3	]	]	PUNCT
ejpam-5050	87	4	will	will	AUX
ejpam-5050	87	5	be	be	AUX
ejpam-5050	87	6	utilized	utilize	VERB
ejpam-5050	87	7	.	.	PUNCT
ejpam-5050	88	1	in	in	ADP
ejpam-5050	88	2	fact	fact	NOUN
ejpam-5050	88	3	,	,	PUNCT
ejpam-5050	88	4	two	two	NUM
ejpam-5050	88	5	algorithms	algorithm	NOUN
ejpam-5050	88	6	based	base	VERB
ejpam-5050	88	7	on	on	ADP
ejpam-5050	88	8	madm	madm	NOUN
ejpam-5050	88	9	will	will	AUX
ejpam-5050	88	10	be	be	AUX
ejpam-5050	88	11	proposed	propose	VERB
ejpam-5050	88	12	in	in	ADP
ejpam-5050	88	13	this	this	DET
ejpam-5050	88	14	section	section	NOUN
ejpam-5050	88	15	for	for	ADP
ejpam-5050	88	16	the	the	DET
ejpam-5050	88	17	governing	govern	VERB
ejpam-5050	88	18	model	model	NOUN
ejpam-5050	88	19	in	in	ADP
ejpam-5050	88	20	what	what	PRON
ejpam-5050	88	21	follows	follow	VERB
ejpam-5050	88	22	.	.	PUNCT
ejpam-5050	89	1	3.1	3.1	NUM
ejpam-5050	89	2	.	.	PUNCT
ejpam-5050	89	3	algorithm	algorithm	PROPN
ejpam-5050	89	4	1	1	NUM
ejpam-5050	89	5	the	the	DET
ejpam-5050	89	6	first	first	ADJ
ejpam-5050	89	7	algorithm	algorithm	NOUN
ejpam-5050	89	8	can	can	AUX
ejpam-5050	89	9	be	be	AUX
ejpam-5050	89	10	summed	sum	VERB
ejpam-5050	89	11	up	up	ADP
ejpam-5050	89	12	in	in	ADP
ejpam-5050	89	13	the	the	DET
ejpam-5050	89	14	following	follow	VERB
ejpam-5050	89	15	bulleted	bulleted	ADJ
ejpam-5050	89	16	lists	list	NOUN
ejpam-5050	89	17	:	:	PUNCT
ejpam-5050	89	18	•	•	NUM
ejpam-5050	90	1	applying	apply	VERB
ejpam-5050	90	2	the	the	DET
ejpam-5050	90	3	inverse	inverse	NOUN
ejpam-5050	90	4	operator	operator	NOUN
ejpam-5050	90	5	l−1	l−1	PROPN
ejpam-5050	90	6	(	(	PUNCT
ejpam-5050	90	7	.	.	PUNCT
ejpam-5050	90	8	)	)	PUNCT
ejpam-5050	91	1	=	=	SYM
ejpam-5050	92	1	∫	∫	PROPN
ejpam-5050	92	2	x	x	X
ejpam-5050	92	3	a	a	DET
ejpam-5050	92	4	∫	∫	PROPN
ejpam-5050	92	5	x	x	X
ejpam-5050	92	6	a	a	DET
ejpam-5050	92	7	(	(	PUNCT
ejpam-5050	92	8	.)dxdx	.)dxdx	NOUN
ejpam-5050	92	9	,	,	PUNCT
ejpam-5050	92	10	on	on	ADP
ejpam-5050	92	11	(	(	PUNCT
ejpam-5050	92	12	9	9	NUM
ejpam-5050	92	13	)	)	PUNCT
ejpam-5050	92	14	,	,	PUNCT
ejpam-5050	92	15	one	one	PRON
ejpam-5050	92	16	gets	get	VERB
ejpam-5050	92	17	y(x	y(x	NOUN
ejpam-5050	92	18	)	)	PUNCT
ejpam-5050	92	19	=	=	SYM
ejpam-5050	92	20	y(a	y(a	X
ejpam-5050	92	21	)	)	PUNCT
ejpam-5050	93	1	+	+	CCONJ
ejpam-5050	93	2	xy′(a	xy′(a	PROPN
ejpam-5050	93	3	)	)	PUNCT
ejpam-5050	94	1	+	+	CCONJ
ejpam-5050	94	2	l−1[g(x)]−	l−1[g(x)]−	NUM
ejpam-5050	94	3	l−1[d3/2y(x)]−	l−1[d3/2y(x)]−	NOUN
ejpam-5050	94	4	l−1[y(x	l−1[y(x	NOUN
ejpam-5050	94	5	)	)	PUNCT
ejpam-5050	94	6	]	]	PUNCT
ejpam-5050	94	7	.	.	PUNCT
ejpam-5050	95	1	(	(	PUNCT
ejpam-5050	95	2	10	10	NUM
ejpam-5050	95	3	)	)	PUNCT
ejpam-5050	95	4	remarkably	remarkably	ADV
ejpam-5050	95	5	,	,	PUNCT
ejpam-5050	95	6	we	we	PRON
ejpam-5050	95	7	will	will	AUX
ejpam-5050	95	8	further	far	ADV
ejpam-5050	95	9	put	put	VERB
ejpam-5050	95	10	y′(a	y′(a	NUM
ejpam-5050	95	11	)	)	PUNCT
ejpam-5050	95	12	=	=	SYM
ejpam-5050	95	13	c1	c1	NOUN
ejpam-5050	95	14	;	;	PUNCT
ejpam-5050	95	15	because	because	SCONJ
ejpam-5050	95	16	we	we	PRON
ejpam-5050	95	17	do	do	AUX
ejpam-5050	95	18	not	not	PART
ejpam-5050	95	19	have	have	VERB
ejpam-5050	95	20	the	the	DET
ejpam-5050	95	21	value	value	NOUN
ejpam-5050	95	22	of	of	ADP
ejpam-5050	95	23	this	this	DET
ejpam-5050	95	24	condition	condition	NOUN
ejpam-5050	95	25	at	at	ADP
ejpam-5050	95	26	the	the	DET
ejpam-5050	95	27	present	present	ADJ
ejpam-5050	95	28	,	,	PUNCT
ejpam-5050	95	29	thereafter	thereafter	ADV
ejpam-5050	95	30	,	,	PUNCT
ejpam-5050	95	31	the	the	DET
ejpam-5050	95	32	prescribed	prescribed	ADJ
ejpam-5050	95	33	boundary	boundary	ADJ
ejpam-5050	95	34	data	datum	NOUN
ejpam-5050	95	35	will	will	AUX
ejpam-5050	95	36	help	help	VERB
ejpam-5050	95	37	in	in	ADP
ejpam-5050	95	38	getting	get	VERB
ejpam-5050	95	39	a	a	DET
ejpam-5050	95	40	hold	hold	NOUN
ejpam-5050	95	41	of	of	ADP
ejpam-5050	95	42	the	the	DET
ejpam-5050	95	43	real	real	ADJ
ejpam-5050	95	44	value	value	NOUN
ejpam-5050	95	45	of	of	ADP
ejpam-5050	95	46	c1	c1	PROPN
ejpam-5050	95	47	.	.	PUNCT
ejpam-5050	96	1	m.	m.	PROPN
ejpam-5050	96	2	al	al	PROPN
ejpam-5050	96	3	-	-	PUNCT
ejpam-5050	96	4	mazmumy	mazmumy	PROPN
ejpam-5050	96	5	,	,	PUNCT
ejpam-5050	96	6	m.	m.	NOUN
ejpam-5050	96	7	alsulami	alsulami	PROPN
ejpam-5050	96	8	/	/	SYM
ejpam-5050	96	9	eur	eur	PROPN
ejpam-5050	96	10	.	.	PUNCT
ejpam-5050	97	1	j.	j.	PROPN
ejpam-5050	97	2	pure	pure	PROPN
ejpam-5050	97	3	appl	appl	PROPN
ejpam-5050	97	4	.	.	PROPN
ejpam-5050	97	5	math	math	PROPN
ejpam-5050	97	6	,	,	PUNCT
ejpam-5050	97	7	17	17	NUM
ejpam-5050	97	8	(	(	PUNCT
ejpam-5050	97	9	1	1	NUM
ejpam-5050	97	10	)	)	PUNCT
ejpam-5050	97	11	(	(	PUNCT
ejpam-5050	97	12	2024	2024	NUM
ejpam-5050	97	13	)	)	PUNCT
ejpam-5050	97	14	,	,	PUNCT
ejpam-5050	97	15	546	546	NUM
ejpam-5050	97	16	-	-	SYM
ejpam-5050	97	17	568	568	NUM
ejpam-5050	97	18	551	551	NUM
ejpam-5050	97	19	•	•	NOUN
ejpam-5050	97	20	application	application	NOUN
ejpam-5050	97	21	of	of	ADP
ejpam-5050	97	22	madm	madm	NOUN
ejpam-5050	97	23	requires	require	VERB
ejpam-5050	97	24	that	that	SCONJ
ejpam-5050	97	25	the	the	DET
ejpam-5050	97	26	term	term	NOUN
ejpam-5050	97	27	−pl−1	−pl−1	X
ejpam-5050	97	28	[	[	PUNCT
ejpam-5050	97	29	∞∑	∞∑	NUM
ejpam-5050	97	30	n=0	n=0	NUM
ejpam-5050	97	31	anx	anx	NOUN
ejpam-5050	97	32	n	n	NOUN
ejpam-5050	97	33	]	]	PUNCT
ejpam-5050	98	1	+	+	CCONJ
ejpam-5050	98	2	l−1	l−1	NOUN
ejpam-5050	98	3	[	[	PUNCT
ejpam-5050	98	4	∞∑	∞∑	PROPN
ejpam-5050	98	5	n=0	n=0	NUM
ejpam-5050	98	6	anx	anx	NOUN
ejpam-5050	98	7	n	n	NOUN
ejpam-5050	98	8	]	]	PUNCT
ejpam-5050	98	9	(	(	PUNCT
ejpam-5050	98	10	11	11	NUM
ejpam-5050	98	11	)	)	PUNCT
ejpam-5050	98	12	should	should	AUX
ejpam-5050	98	13	be	be	AUX
ejpam-5050	98	14	added	add	VERB
ejpam-5050	98	15	to	to	ADP
ejpam-5050	98	16	(	(	PUNCT
ejpam-5050	98	17	10	10	NUM
ejpam-5050	98	18	)	)	PUNCT
ejpam-5050	98	19	,	,	PUNCT
ejpam-5050	98	20	with	with	ADP
ejpam-5050	98	21	p	p	PRON
ejpam-5050	98	22	as	as	ADP
ejpam-5050	98	23	a	a	DET
ejpam-5050	98	24	synthetic	synthetic	ADJ
ejpam-5050	98	25	parameter	parameter	NOUN
ejpam-5050	98	26	,	,	PUNCT
ejpam-5050	98	27	and	and	CCONJ
ejpam-5050	98	28	ai	ai	VERB
ejpam-5050	98	29	,	,	PUNCT
ejpam-5050	98	30	i	i	PRON
ejpam-5050	98	31	≥	≥	NOUN
ejpam-5050	98	32	0	0	NUM
ejpam-5050	98	33	are	be	AUX
ejpam-5050	98	34	obscure	obscure	ADJ
ejpam-5050	98	35	coefficients	coefficient	NOUN
ejpam-5050	98	36	.	.	PUNCT
ejpam-5050	99	1	moreover	moreover	ADV
ejpam-5050	99	2	,	,	PUNCT
ejpam-5050	99	3	recall	recall	VERB
ejpam-5050	99	4	that	that	SCONJ
ejpam-5050	99	5	the	the	DET
ejpam-5050	99	6	classical	classical	ADJ
ejpam-5050	99	7	adm	adm	PROPN
ejpam-5050	99	8	[	[	X
ejpam-5050	99	9	3]-[38	3]-[38	NOUN
ejpam-5050	99	10	]	]	PUNCT
ejpam-5050	99	11	expresses	express	VERB
ejpam-5050	99	12	the	the	DET
ejpam-5050	99	13	solution	solution	NOUN
ejpam-5050	99	14	function	function	NOUN
ejpam-5050	99	15	y(x	y(x	PROPN
ejpam-5050	99	16	)	)	PUNCT
ejpam-5050	99	17	as	as	ADP
ejpam-5050	99	18	y(x	y(x	NOUN
ejpam-5050	99	19	)	)	PUNCT
ejpam-5050	99	20	=	=	PUNCT
ejpam-5050	99	21	∑∞	∑∞	NOUN
ejpam-5050	99	22	n=0	n=0	NUM
ejpam-5050	99	23	yn(x	yn(x	NUM
ejpam-5050	99	24	)	)	PUNCT
ejpam-5050	99	25	.	.	PUNCT
ejpam-5050	100	1	consequently	consequently	ADV
ejpam-5050	100	2	,	,	PUNCT
ejpam-5050	100	3	one	one	PRON
ejpam-5050	100	4	gets	get	VERB
ejpam-5050	100	5	∑∞	∑∞	NOUN
ejpam-5050	100	6	n=0	n=0	NUM
ejpam-5050	100	7	yn(x	yn(x	PUNCT
ejpam-5050	100	8	)	)	PUNCT
ejpam-5050	100	9	=	=	SYM
ejpam-5050	101	1	λ1	λ1	ADJ
ejpam-5050	101	2	+	+	CCONJ
ejpam-5050	101	3	c1x−	c1x−	ADJ
ejpam-5050	101	4	pl−1	pl−1	NOUN
ejpam-5050	101	5	[	[	PUNCT
ejpam-5050	101	6	∞∑	∞∑	NUM
ejpam-5050	101	7	n=0	n=0	NUM
ejpam-5050	101	8	anx	anx	NOUN
ejpam-5050	101	9	n	n	NOUN
ejpam-5050	101	10	]	]	PUNCT
ejpam-5050	101	11	+	+	CCONJ
ejpam-5050	101	12	l−1	l−1	NOUN
ejpam-5050	101	13	[	[	PUNCT
ejpam-5050	101	14	∞∑	∞∑	PROPN
ejpam-5050	101	15	n=0	n=0	NUM
ejpam-5050	101	16	anx	anx	NOUN
ejpam-5050	101	17	n	n	NOUN
ejpam-5050	101	18	]	]	PUNCT
ejpam-5050	101	19	+	+	PUNCT
ejpam-5050	101	20	l−1[g(x	l−1[g(x	NOUN
ejpam-5050	101	21	)	)	PUNCT
ejpam-5050	101	22	]	]	PUNCT
ejpam-5050	102	1	−	−	PROPN
ejpam-5050	102	2	l−1	l−1	PROPN
ejpam-5050	102	3	[	[	PUNCT
ejpam-5050	102	4	d3/2	d3/2	ADJ
ejpam-5050	102	5	∞∑	∞∑	PROPN
ejpam-5050	102	6	n=0	n=0	NUM
ejpam-5050	102	7	yn(x	yn(x	X
ejpam-5050	102	8	)	)	PUNCT
ejpam-5050	102	9	]	]	PUNCT
ejpam-5050	103	1	−	−	PROPN
ejpam-5050	103	2	l−1	l−1	PROPN
ejpam-5050	103	3	[	[	PUNCT
ejpam-5050	103	4	∞∑	∞∑	PROPN
ejpam-5050	103	5	n=0	n=0	NUM
ejpam-5050	103	6	yn(x	yn(x	NOUN
ejpam-5050	103	7	)	)	PUNCT
ejpam-5050	103	8	]	]	PUNCT
ejpam-5050	103	9	.	.	PUNCT
ejpam-5050	104	1	(	(	PUNCT
ejpam-5050	104	2	12	12	NUM
ejpam-5050	104	3	)	)	PUNCT
ejpam-5050	104	4	•	•	NOUN
ejpam-5050	104	5	as	as	ADP
ejpam-5050	104	6	a	a	DET
ejpam-5050	104	7	result	result	NOUN
ejpam-5050	104	8	,	,	PUNCT
ejpam-5050	104	9	one	one	PRON
ejpam-5050	104	10	may	may	AUX
ejpam-5050	104	11	deduce	deduce	VERB
ejpam-5050	104	12	the	the	DET
ejpam-5050	104	13	resulting	result	VERB
ejpam-5050	104	14	recursive	recursive	ADJ
ejpam-5050	104	15	scheme	scheme	NOUN
ejpam-5050	104	16	from	from	ADP
ejpam-5050	104	17	(	(	PUNCT
ejpam-5050	104	18	12	12	NUM
ejpam-5050	104	19	)	)	PUNCT
ejpam-5050	104	20	as	as	SCONJ
ejpam-5050	104	21	follows	follow	VERB
ejpam-5050	104	22	y0(x	y0(x	NUM
ejpam-5050	104	23	)	)	PUNCT
ejpam-5050	105	1	=	=	SYM
ejpam-5050	105	2	λ1	λ1	PROPN
ejpam-5050	105	3	+	+	NUM
ejpam-5050	105	4	c1x+	c1x+	NOUN
ejpam-5050	105	5	l−1	l−1	PROPN
ejpam-5050	105	6	[	[	PUNCT
ejpam-5050	105	7	∞∑	∞∑	PROPN
ejpam-5050	105	8	n=0	n=0	NUM
ejpam-5050	105	9	anx	anx	NOUN
ejpam-5050	105	10	n	n	NOUN
ejpam-5050	105	11	]	]	PUNCT
ejpam-5050	105	12	,	,	PUNCT
ejpam-5050	105	13	y1(x	y1(x	PROPN
ejpam-5050	105	14	)	)	PUNCT
ejpam-5050	105	15	=	=	PUNCT
ejpam-5050	106	1	l−1[g(x)]−	l−1[g(x)]−	X
ejpam-5050	106	2	pl−1	pl−1	NOUN
ejpam-5050	106	3	[	[	PUNCT
ejpam-5050	106	4	∞∑	∞∑	NUM
ejpam-5050	106	5	n=0	n=0	NUM
ejpam-5050	106	6	anx	anx	NOUN
ejpam-5050	106	7	n	n	NOUN
ejpam-5050	106	8	]	]	PUNCT
ejpam-5050	106	9	−	−	PROPN
ejpam-5050	106	10	l−1[d3/2y0(x)]−	l−1[d3/2y0(x)]−	PROPN
ejpam-5050	106	11	l−1[y0(x	l−1[y0(x	PROPN
ejpam-5050	106	12	)	)	PUNCT
ejpam-5050	106	13	]	]	PUNCT
ejpam-5050	106	14	,	,	PUNCT
ejpam-5050	106	15	...	...	PUNCT
ejpam-5050	106	16	yn+1(x	yn+1(x	NOUN
ejpam-5050	106	17	)	)	PUNCT
ejpam-5050	106	18	=	=	SYM
ejpam-5050	106	19	−l−1[d3/2yn(x)]−	−l−1[d3/2yn(x)]−	PROPN
ejpam-5050	106	20	l−1[yn(x	l−1[yn(x	PROPN
ejpam-5050	106	21	)	)	PUNCT
ejpam-5050	106	22	]	]	PUNCT
ejpam-5050	106	23	,	,	PUNCT
ejpam-5050	106	24	n	n	CCONJ
ejpam-5050	106	25	⩾	⩾	NOUN
ejpam-5050	106	26	0	0	NUM
ejpam-5050	106	27	.	.	PUNCT
ejpam-5050	107	1	(	(	PUNCT
ejpam-5050	107	2	13	13	NUM
ejpam-5050	107	3	)	)	PUNCT
ejpam-5050	107	4	•	•	NUM
ejpam-5050	107	5	computation	computation	NOUN
ejpam-5050	107	6	of	of	ADP
ejpam-5050	107	7	the	the	DET
ejpam-5050	107	8	coefficients	coefficient	NOUN
ejpam-5050	107	9	ai	ai	VERB
ejpam-5050	107	10	,	,	PUNCT
ejpam-5050	107	11	for	for	SCONJ
ejpam-5050	107	12	i	i	PRON
ejpam-5050	107	13	≥	≥	VERB
ejpam-5050	107	14	0	0	NUM
ejpam-5050	107	15	by	by	ADP
ejpam-5050	107	16	taking	take	VERB
ejpam-5050	107	17	y1	y1	PROPN
ejpam-5050	107	18	=	=	SYM
ejpam-5050	107	19	0	0	NUM
ejpam-5050	107	20	and	and	CCONJ
ejpam-5050	107	21	subsequently	subsequently	ADV
ejpam-5050	107	22	fixing	fix	VERB
ejpam-5050	107	23	p	p	NOUN
ejpam-5050	107	24	=	=	SYM
ejpam-5050	107	25	1	1	NUM
ejpam-5050	107	26	reveals	reveal	VERB
ejpam-5050	107	27	the	the	DET
ejpam-5050	107	28	solution	solution	NOUN
ejpam-5050	107	29	of	of	ADP
ejpam-5050	107	30	(	(	PUNCT
ejpam-5050	107	31	8)	8)	NUM
ejpam-5050	107	32	in	in	ADP
ejpam-5050	107	33	form	form	NOUN
ejpam-5050	107	34	y(x	y(x	NOUN
ejpam-5050	107	35	)	)	PUNCT
ejpam-5050	107	36	=	=	SYM
ejpam-5050	108	1	y0(x	y0(x	PROPN
ejpam-5050	108	2	)	)	PUNCT
ejpam-5050	108	3	.	.	PUNCT
ejpam-5050	109	1	•	•	ADV
ejpam-5050	109	2	lastly	lastly	ADV
ejpam-5050	109	3	,	,	PUNCT
ejpam-5050	109	4	substituting	substitute	VERB
ejpam-5050	109	5	the	the	DET
ejpam-5050	109	6	values	value	NOUN
ejpam-5050	109	7	of	of	ADP
ejpam-5050	109	8	ai	ai	VERB
ejpam-5050	109	9	into	into	ADP
ejpam-5050	109	10	y0(x	y0(x	NUM
ejpam-5050	109	11	)	)	PUNCT
ejpam-5050	109	12	,	,	PUNCT
ejpam-5050	109	13	and	and	CCONJ
ejpam-5050	109	14	further	far	ADV
ejpam-5050	109	15	upon	upon	SCONJ
ejpam-5050	109	16	utilizing	utilize	VERB
ejpam-5050	109	17	the	the	DET
ejpam-5050	109	18	second	second	ADJ
ejpam-5050	109	19	boundary	boundary	ADJ
ejpam-5050	109	20	condition	condition	NOUN
ejpam-5050	109	21	y(1	y(1	PROPN
ejpam-5050	109	22	)	)	PUNCT
ejpam-5050	109	23	=	=	SYM
ejpam-5050	109	24	λ2	λ2	PROPN
ejpam-5050	109	25	,	,	PUNCT
ejpam-5050	109	26	the	the	DET
ejpam-5050	109	27	constant	constant	ADJ
ejpam-5050	109	28	c1	c1	NOUN
ejpam-5050	109	29	is	be	AUX
ejpam-5050	109	30	thus	thus	ADV
ejpam-5050	109	31	revealed	reveal	VERB
ejpam-5050	109	32	.	.	PUNCT
ejpam-5050	110	1	3.2	3.2	NUM
ejpam-5050	110	2	.	.	PUNCT
ejpam-5050	110	3	algorithm	algorithm	NOUN
ejpam-5050	110	4	2	2	NUM
ejpam-5050	110	5	algorithm	algorithm	NOUN
ejpam-5050	110	6	2	2	NUM
ejpam-5050	110	7	is	be	AUX
ejpam-5050	110	8	equally	equally	ADV
ejpam-5050	110	9	based	base	VERB
ejpam-5050	110	10	on	on	ADP
ejpam-5050	110	11	madm	madm	NOUN
ejpam-5050	110	12	,	,	PUNCT
ejpam-5050	110	13	which	which	PRON
ejpam-5050	110	14	possesses	possess	VERB
ejpam-5050	110	15	the	the	DET
ejpam-5050	110	16	following	follow	VERB
ejpam-5050	110	17	steps	step	NOUN
ejpam-5050	110	18	:	:	PUNCT
ejpam-5050	110	19	•	•	NUM
ejpam-5050	110	20	we	we	PRON
ejpam-5050	110	21	begin	begin	VERB
ejpam-5050	110	22	by	by	ADP
ejpam-5050	110	23	implementing	implement	VERB
ejpam-5050	110	24	the	the	DET
ejpam-5050	110	25	inverse	inverse	NOUN
ejpam-5050	110	26	operator	operator	NOUN
ejpam-5050	110	27	l−1	l−1	PROPN
ejpam-5050	110	28	(	(	PUNCT
ejpam-5050	110	29	.	.	PUNCT
ejpam-5050	110	30	)	)	PUNCT
ejpam-5050	110	31	that	that	PRON
ejpam-5050	110	32	takes	take	VERB
ejpam-5050	110	33	following	follow	VERB
ejpam-5050	110	34	representation	representation	NOUN
ejpam-5050	110	35	[	[	X
ejpam-5050	110	36	19	19	NUM
ejpam-5050	110	37	,	,	PUNCT
ejpam-5050	110	38	31	31	NUM
ejpam-5050	110	39	]	]	PUNCT
ejpam-5050	110	40	l−1	l−1	PROPN
ejpam-5050	110	41	(	(	PUNCT
ejpam-5050	110	42	.	.	PUNCT
ejpam-5050	110	43	)	)	PUNCT
ejpam-5050	111	1	=	=	SYM
ejpam-5050	112	1	∫	∫	PROPN
ejpam-5050	112	2	x	x	X
ejpam-5050	113	1	a	a	DET
ejpam-5050	113	2	dx′	dx′	PROPN
ejpam-5050	113	3	∫	∫	PROPN
ejpam-5050	113	4	x′′	x′′	PROPN
ejpam-5050	113	5	a	a	X
ejpam-5050	113	6	(	(	PUNCT
ejpam-5050	113	7	.)dx′′	.)dx′′	PROPN
ejpam-5050	113	8	−	−	PROPN
ejpam-5050	113	9	x−	x−	PROPN
ejpam-5050	114	1	a	a	DET
ejpam-5050	114	2	b−	b−	NOUN
ejpam-5050	114	3	a	a	DET
ejpam-5050	114	4	∫	∫	PROPN
ejpam-5050	114	5	b	b	PROPN
ejpam-5050	114	6	a	a	PRON
ejpam-5050	114	7	dx	dx	PROPN
ejpam-5050	114	8	∫	∫	PROPN
ejpam-5050	114	9	x′′	x′′	PROPN
ejpam-5050	115	1	a	a	DET
ejpam-5050	115	2	(	(	PUNCT
ejpam-5050	115	3	.)dx′′	.)dx′′	PROPN
ejpam-5050	115	4	,	,	PUNCT
ejpam-5050	115	5	(	(	PUNCT
ejpam-5050	115	6	14	14	NUM
ejpam-5050	115	7	)	)	PUNCT
ejpam-5050	115	8	on	on	ADP
ejpam-5050	115	9	(	(	PUNCT
ejpam-5050	115	10	9	9	NUM
ejpam-5050	115	11	)	)	PUNCT
ejpam-5050	115	12	,	,	PUNCT
ejpam-5050	115	13	which	which	PRON
ejpam-5050	115	14	reveals	reveal	VERB
ejpam-5050	115	15	y(x)−	y(x)−	PROPN
ejpam-5050	115	16	y(a)−	y(a)−	PRON
ejpam-5050	115	17	xy(b	xy(b	PUNCT
ejpam-5050	115	18	)	)	PUNCT
ejpam-5050	115	19	+	+	CCONJ
ejpam-5050	115	20	xy(a	xy(a	PUNCT
ejpam-5050	115	21	)	)	PUNCT
ejpam-5050	115	22	=	=	PUNCT
ejpam-5050	115	23	l−1[g(x)]−	l−1[g(x)]−	NUM
ejpam-5050	115	24	l−1[d3/2y(x)]−	l−1[d3/2y(x)]−	PROPN
ejpam-5050	115	25	l−1[y(x	l−1[y(x	NOUN
ejpam-5050	115	26	)	)	PUNCT
ejpam-5050	115	27	]	]	PUNCT
ejpam-5050	115	28	.	.	PUNCT
ejpam-5050	116	1	(	(	PUNCT
ejpam-5050	116	2	15	15	NUM
ejpam-5050	116	3	)	)	PUNCT
ejpam-5050	116	4	m.	m.	NOUN
ejpam-5050	116	5	al	al	PROPN
ejpam-5050	116	6	-	-	PUNCT
ejpam-5050	116	7	mazmumy	mazmumy	PROPN
ejpam-5050	116	8	,	,	PUNCT
ejpam-5050	116	9	m.	m.	NOUN
ejpam-5050	116	10	alsulami	alsulami	PROPN
ejpam-5050	116	11	/	/	SYM
ejpam-5050	116	12	eur	eur	PROPN
ejpam-5050	116	13	.	.	PUNCT
ejpam-5050	117	1	j.	j.	PROPN
ejpam-5050	117	2	pure	pure	PROPN
ejpam-5050	117	3	appl	appl	PROPN
ejpam-5050	117	4	.	.	PROPN
ejpam-5050	117	5	math	math	PROPN
ejpam-5050	117	6	,	,	PUNCT
ejpam-5050	117	7	17	17	NUM
ejpam-5050	117	8	(	(	PUNCT
ejpam-5050	117	9	1	1	NUM
ejpam-5050	117	10	)	)	PUNCT
ejpam-5050	117	11	(	(	PUNCT
ejpam-5050	117	12	2024	2024	NUM
ejpam-5050	117	13	)	)	PUNCT
ejpam-5050	117	14	,	,	PUNCT
ejpam-5050	117	15	546	546	NUM
ejpam-5050	117	16	-	-	SYM
ejpam-5050	117	17	568	568	NUM
ejpam-5050	117	18	552	552	NUM
ejpam-5050	117	19	•	•	NOUN
ejpam-5050	117	20	madm	madm	NOUN
ejpam-5050	117	21	requires	require	VERB
ejpam-5050	117	22	the	the	DET
ejpam-5050	117	23	addition	addition	NOUN
ejpam-5050	117	24	of	of	ADP
ejpam-5050	117	25	the	the	DET
ejpam-5050	117	26	expression	expression	NOUN
ejpam-5050	117	27	given	give	VERB
ejpam-5050	117	28	in	in	ADP
ejpam-5050	117	29	(	(	PUNCT
ejpam-5050	117	30	11	11	NUM
ejpam-5050	117	31	)	)	PUNCT
ejpam-5050	117	32	to	to	ADP
ejpam-5050	117	33	(	(	PUNCT
ejpam-5050	117	34	15	15	NUM
ejpam-5050	117	35	)	)	PUNCT
ejpam-5050	117	36	to	to	PART
ejpam-5050	117	37	yield	yield	VERB
ejpam-5050	117	38	the	the	DET
ejpam-5050	117	39	following	follow	VERB
ejpam-5050	117	40	equation	equation	NOUN
ejpam-5050	117	41	∑∞	∑∞	NOUN
ejpam-5050	117	42	n=0	n=0	NUM
ejpam-5050	117	43	yn(x	yn(x	PUNCT
ejpam-5050	117	44	)	)	PUNCT
ejpam-5050	117	45	=	=	SYM
ejpam-5050	118	1	λ1	λ1	PROPN
ejpam-5050	118	2	+	+	NUM
ejpam-5050	118	3	λ2x−	λ2x−	VERB
ejpam-5050	118	4	λ1x−	λ1x−	ADJ
ejpam-5050	118	5	pl−1	pl−1	NOUN
ejpam-5050	118	6	[	[	PUNCT
ejpam-5050	118	7	∞∑	∞∑	NUM
ejpam-5050	118	8	n=0	n=0	NUM
ejpam-5050	118	9	anx	anx	NOUN
ejpam-5050	118	10	n	n	NOUN
ejpam-5050	118	11	]	]	PUNCT
ejpam-5050	118	12	+	+	CCONJ
ejpam-5050	118	13	l−1	l−1	NOUN
ejpam-5050	118	14	[	[	PUNCT
ejpam-5050	118	15	∞∑	∞∑	PROPN
ejpam-5050	118	16	n=0	n=0	NUM
ejpam-5050	118	17	anx	anx	NOUN
ejpam-5050	118	18	n	n	NOUN
ejpam-5050	118	19	]	]	PUNCT
ejpam-5050	118	20	+	+	PUNCT
ejpam-5050	118	21	l−1[g(x	l−1[g(x	NOUN
ejpam-5050	118	22	)	)	PUNCT
ejpam-5050	118	23	]	]	PUNCT
ejpam-5050	119	1	−	−	PROPN
ejpam-5050	119	2	l−1	l−1	PROPN
ejpam-5050	119	3	[	[	PUNCT
ejpam-5050	119	4	d3/2	d3/2	ADJ
ejpam-5050	119	5	∞∑	∞∑	PROPN
ejpam-5050	119	6	n=0	n=0	NUM
ejpam-5050	119	7	yn(x	yn(x	X
ejpam-5050	119	8	)	)	PUNCT
ejpam-5050	119	9	]	]	PUNCT
ejpam-5050	120	1	−	−	PROPN
ejpam-5050	120	2	l−1	l−1	PROPN
ejpam-5050	120	3	[	[	PUNCT
ejpam-5050	120	4	∞∑	∞∑	PROPN
ejpam-5050	120	5	n=0	n=0	NUM
ejpam-5050	120	6	yn(x	yn(x	NOUN
ejpam-5050	120	7	)	)	PUNCT
ejpam-5050	120	8	]	]	PUNCT
ejpam-5050	120	9	.	.	PUNCT
ejpam-5050	121	1	(	(	PUNCT
ejpam-5050	121	2	16	16	NUM
ejpam-5050	121	3	)	)	PUNCT
ejpam-5050	121	4	•	•	NOUN
ejpam-5050	121	5	then	then	ADV
ejpam-5050	121	6	,	,	PUNCT
ejpam-5050	121	7	the	the	DET
ejpam-5050	121	8	formal	formal	ADJ
ejpam-5050	121	9	recursive	recursive	ADJ
ejpam-5050	121	10	relation	relation	NOUN
ejpam-5050	121	11	of	of	ADP
ejpam-5050	121	12	the	the	DET
ejpam-5050	121	13	governing	govern	VERB
ejpam-5050	121	14	model	model	NOUN
ejpam-5050	121	15	is	be	AUX
ejpam-5050	121	16	thus	thus	ADV
ejpam-5050	121	17	determined	determine	VERB
ejpam-5050	121	18	in	in	ADP
ejpam-5050	121	19	this	this	DET
ejpam-5050	121	20	regard	regard	NOUN
ejpam-5050	121	21	as	as	SCONJ
ejpam-5050	121	22	follows	follow	VERB
ejpam-5050	121	23	y0(x	y0(x	NUM
ejpam-5050	121	24	)	)	PUNCT
ejpam-5050	121	25	=	=	SYM
ejpam-5050	122	1	λ1	λ1	PROPN
ejpam-5050	122	2	+	+	CCONJ
ejpam-5050	122	3	(	(	PUNCT
ejpam-5050	122	4	λ2	λ2	NOUN
ejpam-5050	122	5	−	−	PROPN
ejpam-5050	122	6	λ1)x+	λ1)x+	PROPN
ejpam-5050	122	7	l−1	l−1	PROPN
ejpam-5050	122	8	[	[	PUNCT
ejpam-5050	122	9	∞∑	∞∑	PROPN
ejpam-5050	122	10	n=0	n=0	NUM
ejpam-5050	122	11	anx	anx	NOUN
ejpam-5050	122	12	n	n	NOUN
ejpam-5050	122	13	]	]	PUNCT
ejpam-5050	122	14	,	,	PUNCT
ejpam-5050	122	15	y1(x	y1(x	PROPN
ejpam-5050	122	16	)	)	PUNCT
ejpam-5050	122	17	=	=	PUNCT
ejpam-5050	122	18	l−1[g(x)]−	l−1[g(x)]−	X
ejpam-5050	122	19	pl−1	pl−1	NOUN
ejpam-5050	122	20	[	[	PUNCT
ejpam-5050	122	21	∞∑	∞∑	NUM
ejpam-5050	122	22	n=0	n=0	NUM
ejpam-5050	122	23	anx	anx	NOUN
ejpam-5050	122	24	n	n	NOUN
ejpam-5050	122	25	]	]	PUNCT
ejpam-5050	122	26	−	−	PROPN
ejpam-5050	122	27	l−1[d3/2y0(x)]−	l−1[d3/2y0(x)]−	PROPN
ejpam-5050	122	28	l−1[y0(x	l−1[y0(x	PROPN
ejpam-5050	122	29	)	)	PUNCT
ejpam-5050	122	30	]	]	PUNCT
ejpam-5050	122	31	,	,	PUNCT
ejpam-5050	122	32	...	...	PUNCT
ejpam-5050	122	33	yn+1(x	yn+1(x	NOUN
ejpam-5050	122	34	)	)	PUNCT
ejpam-5050	123	1	=	=	SYM
ejpam-5050	123	2	−l−1[d3/2yn(x)]−	−l−1[d3/2yn(x)]−	PROPN
ejpam-5050	123	3	l−1[yn(x	l−1[yn(x	PROPN
ejpam-5050	123	4	)	)	PUNCT
ejpam-5050	123	5	]	]	PUNCT
ejpam-5050	123	6	,	,	PUNCT
ejpam-5050	123	7	n	n	CCONJ
ejpam-5050	123	8	⩾	⩾	NOUN
ejpam-5050	123	9	0	0	NUM
ejpam-5050	123	10	.	.	PUNCT
ejpam-5050	124	1	(	(	PUNCT
ejpam-5050	124	2	17	17	NUM
ejpam-5050	124	3	)	)	PUNCT
ejpam-5050	124	4	therefore	therefore	ADV
ejpam-5050	124	5	,	,	PUNCT
ejpam-5050	124	6	the	the	DET
ejpam-5050	124	7	values	value	NOUN
ejpam-5050	124	8	of	of	ADP
ejpam-5050	124	9	the	the	DET
ejpam-5050	124	10	coefficients	coefficient	NOUN
ejpam-5050	124	11	ai	ai	VERB
ejpam-5050	124	12	,	,	PUNCT
ejpam-5050	124	13	for	for	SCONJ
ejpam-5050	124	14	i	i	PRON
ejpam-5050	124	15	≥	≥	NOUN
ejpam-5050	124	16	0	0	NUM
ejpam-5050	124	17	are	be	AUX
ejpam-5050	124	18	then	then	ADV
ejpam-5050	124	19	calculated	calculate	VERB
ejpam-5050	124	20	by	by	ADP
ejpam-5050	124	21	taking	take	VERB
ejpam-5050	124	22	y1	y1	NOUN
ejpam-5050	124	23	=	=	SYM
ejpam-5050	124	24	0	0	PUNCT
ejpam-5050	124	25	and	and	CCONJ
ejpam-5050	124	26	setting	set	VERB
ejpam-5050	124	27	p	p	X
ejpam-5050	124	28	=	=	NOUN
ejpam-5050	124	29	1	1	X
ejpam-5050	124	30	.	.	PUNCT
ejpam-5050	125	1	moreover	moreover	ADV
ejpam-5050	125	2	,	,	PUNCT
ejpam-5050	125	3	these	these	DET
ejpam-5050	125	4	values	value	NOUN
ejpam-5050	125	5	are	be	AUX
ejpam-5050	125	6	then	then	ADV
ejpam-5050	125	7	substituted	substitute	VERB
ejpam-5050	125	8	into	into	ADP
ejpam-5050	125	9	y0(x	y0(x	NUM
ejpam-5050	125	10	)	)	PUNCT
ejpam-5050	125	11	to	to	PART
ejpam-5050	125	12	obtain	obtain	VERB
ejpam-5050	125	13	y(x	y(x	NOUN
ejpam-5050	125	14	)	)	PUNCT
ejpam-5050	125	15	=	=	SYM
ejpam-5050	125	16	y0(x	y0(x	PROPN
ejpam-5050	125	17	)	)	PUNCT
ejpam-5050	125	18	.	.	PUNCT
ejpam-5050	126	1	4	4	X
ejpam-5050	126	2	.	.	X
ejpam-5050	126	3	applications	application	NOUN
ejpam-5050	126	4	this	this	DET
ejpam-5050	126	5	section	section	NOUN
ejpam-5050	126	6	applies	apply	VERB
ejpam-5050	126	7	the	the	DET
ejpam-5050	126	8	proposed	propose	VERB
ejpam-5050	126	9	madm	madm	NOUN
ejpam-5050	126	10	on	on	ADP
ejpam-5050	126	11	several	several	ADJ
ejpam-5050	126	12	test	test	NOUN
ejpam-5050	126	13	models	model	NOUN
ejpam-5050	126	14	,	,	PUNCT
ejpam-5050	126	15	featuring	feature	VERB
ejpam-5050	126	16	various	various	ADJ
ejpam-5050	126	17	forms	form	NOUN
ejpam-5050	126	18	of	of	ADP
ejpam-5050	126	19	bvp	bvp	NOUN
ejpam-5050	126	20	of	of	ADP
ejpam-5050	126	21	the	the	DET
ejpam-5050	126	22	bagley	bagley	NOUN
ejpam-5050	126	23	-	-	PUNCT
ejpam-5050	126	24	torvik	torvik	NOUN
ejpam-5050	126	25	equation	equation	NOUN
ejpam-5050	126	26	.	.	PUNCT
ejpam-5050	127	1	precisely	precisely	ADV
ejpam-5050	127	2	,	,	PUNCT
ejpam-5050	127	3	the	the	DET
ejpam-5050	127	4	proposed	propose	VERB
ejpam-5050	127	5	madm	madm	NOUN
ejpam-5050	127	6	through	through	ADP
ejpam-5050	127	7	the	the	DET
ejpam-5050	127	8	devised	devise	VERB
ejpam-5050	127	9	algorithms	algorithm	NOUN
ejpam-5050	127	10	1	1	NUM
ejpam-5050	127	11	and	and	CCONJ
ejpam-5050	127	12	2	2	NUM
ejpam-5050	127	13	will	will	AUX
ejpam-5050	127	14	be	be	AUX
ejpam-5050	127	15	applied	apply	VERB
ejpam-5050	127	16	to	to	ADP
ejpam-5050	127	17	the	the	DET
ejpam-5050	127	18	governing	governing	NOUN
ejpam-5050	127	19	model	model	NOUN
ejpam-5050	127	20	and	and	CCONJ
ejpam-5050	127	21	its	its	PRON
ejpam-5050	127	22	variant	variant	NOUN
ejpam-5050	127	23	,	,	PUNCT
ejpam-5050	127	24	including	include	VERB
ejpam-5050	127	25	the	the	DET
ejpam-5050	127	26	coupled	couple	VERB
ejpam-5050	127	27	system	system	NOUN
ejpam-5050	127	28	of	of	ADP
ejpam-5050	127	29	the	the	DET
ejpam-5050	127	30	fractional	fractional	ADJ
ejpam-5050	127	31	differential	differential	NOUN
ejpam-5050	127	32	equation	equation	NOUN
ejpam-5050	127	33	,	,	PUNCT
ejpam-5050	127	34	which	which	PRON
ejpam-5050	127	35	emanates	emanate	VERB
ejpam-5050	127	36	from	from	ADP
ejpam-5050	127	37	the	the	DET
ejpam-5050	127	38	bagley	bagley	NOUN
ejpam-5050	127	39	-	-	PUNCT
ejpam-5050	127	40	torvik	torvik	NOUN
ejpam-5050	127	41	equation	equation	NOUN
ejpam-5050	127	42	.	.	PUNCT
ejpam-5050	128	1	moreover	moreover	ADV
ejpam-5050	128	2	,	,	PUNCT
ejpam-5050	128	3	the	the	DET
ejpam-5050	128	4	test	test	NOUN
ejpam-5050	128	5	models	model	NOUN
ejpam-5050	128	6	of	of	ADP
ejpam-5050	128	7	interest	interest	NOUN
ejpam-5050	128	8	will	will	AUX
ejpam-5050	128	9	be	be	AUX
ejpam-5050	128	10	considered	consider	VERB
ejpam-5050	128	11	from	from	ADP
ejpam-5050	128	12	the	the	DET
ejpam-5050	128	13	open	open	ADJ
ejpam-5050	128	14	literature	literature	NOUN
ejpam-5050	128	15	in	in	ADP
ejpam-5050	128	16	order	order	NOUN
ejpam-5050	128	17	to	to	PART
ejpam-5050	128	18	draw	draw	VERB
ejpam-5050	128	19	a	a	DET
ejpam-5050	128	20	firm	firm	ADJ
ejpam-5050	128	21	conclusion	conclusion	NOUN
ejpam-5050	128	22	with	with	ADP
ejpam-5050	128	23	well	well	ADV
ejpam-5050	128	24	-	-	PUNCT
ejpam-5050	128	25	known	know	VERB
ejpam-5050	128	26	exact	exact	ADJ
ejpam-5050	128	27	solutions	solution	NOUN
ejpam-5050	128	28	.	.	PUNCT
ejpam-5050	129	1	example	example	NOUN
ejpam-5050	130	1	1	1	NUM
ejpam-5050	130	2	.	.	X
ejpam-5050	130	3	consider	consider	VERB
ejpam-5050	130	4	the	the	DET
ejpam-5050	130	5	bvp	bvp	NOUN
ejpam-5050	130	6	for	for	ADP
ejpam-5050	130	7	the	the	DET
ejpam-5050	130	8	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5050	130	9	bagley	bagley	NOUN
ejpam-5050	130	10	-	-	PUNCT
ejpam-5050	130	11	torvik	torvik	NOUN
ejpam-5050	130	12	equation	equation	NOUN
ejpam-5050	130	13	as	as	SCONJ
ejpam-5050	130	14	follows	follow	VERB
ejpam-5050	130	15	[	[	X
ejpam-5050	130	16	43	43	NUM
ejpam-5050	130	17	]	]	X
ejpam-5050	130	18	d2y(x	d2y(x	PROPN
ejpam-5050	130	19	)	)	PUNCT
ejpam-5050	130	20	+	+	NOUN
ejpam-5050	130	21	d3/2y(x	d3/2y(x	NOUN
ejpam-5050	130	22	)	)	PUNCT
ejpam-5050	131	1	+	+	NUM
ejpam-5050	131	2	y(x	y(x	NOUN
ejpam-5050	131	3	)	)	PUNCT
ejpam-5050	131	4	=	=	PUNCT
ejpam-5050	132	1	x3	x3	ADJ
ejpam-5050	132	2	+	+	CCONJ
ejpam-5050	132	3	5x+	5x+	NUM
ejpam-5050	132	4	8√	8√	NOUN
ejpam-5050	132	5	π	π	PROPN
ejpam-5050	132	6	x3/2	x3/2	NUM
ejpam-5050	132	7	,	,	PUNCT
ejpam-5050	132	8	y(0	y(0	PROPN
ejpam-5050	132	9	)	)	PUNCT
ejpam-5050	132	10	=	=	SYM
ejpam-5050	132	11	0	0	NUM
ejpam-5050	132	12	,	,	PUNCT
ejpam-5050	132	13	y(1	y(1	PROPN
ejpam-5050	132	14	)	)	PUNCT
ejpam-5050	132	15	=	=	SYM
ejpam-5050	133	1	0	0	X
ejpam-5050	133	2	.	.	PUNCT
ejpam-5050	134	1	(	(	PUNCT
ejpam-5050	134	2	18	18	NUM
ejpam-5050	134	3	)	)	PUNCT
ejpam-5050	134	4	the	the	DET
ejpam-5050	134	5	exact	exact	ADJ
ejpam-5050	134	6	analytical	analytical	ADJ
ejpam-5050	134	7	solution	solution	NOUN
ejpam-5050	134	8	of	of	ADP
ejpam-5050	134	9	the	the	DET
ejpam-5050	134	10	above	above	ADJ
ejpam-5050	134	11	bvp	bvp	NOUN
ejpam-5050	134	12	is	be	AUX
ejpam-5050	134	13	thus	thus	ADV
ejpam-5050	134	14	found	find	VERB
ejpam-5050	134	15	to	to	PART
ejpam-5050	134	16	be	be	AUX
ejpam-5050	134	17	y(x	y(x	NOUN
ejpam-5050	134	18	)	)	PUNCT
ejpam-5050	134	19	=	=	PUNCT
ejpam-5050	135	1	x3	x3	ADJ
ejpam-5050	135	2	−	−	NOUN
ejpam-5050	135	3	x.	x.	NOUN
ejpam-5050	135	4	algorithm	algorithm	PROPN
ejpam-5050	135	5	1	1	NUM
ejpam-5050	135	6	:	:	PUNCT
ejpam-5050	135	7	write	write	VERB
ejpam-5050	135	8	(	(	PUNCT
ejpam-5050	135	9	18	18	NUM
ejpam-5050	135	10	)	)	PUNCT
ejpam-5050	135	11	in	in	ADP
ejpam-5050	135	12	an	an	DET
ejpam-5050	135	13	operator	operator	NOUN
ejpam-5050	135	14	form	form	NOUN
ejpam-5050	135	15	as	as	SCONJ
ejpam-5050	135	16	follows	follow	VERB
ejpam-5050	135	17	ly	ly	ADP
ejpam-5050	135	18	=	=	PUNCT
ejpam-5050	135	19	d2y	d2y	PROPN
ejpam-5050	135	20	=	=	SYM
ejpam-5050	135	21	x3	x3	ADJ
ejpam-5050	135	22	+	+	CCONJ
ejpam-5050	135	23	5x+	5x+	NUM
ejpam-5050	135	24	8√	8√	NOUN
ejpam-5050	135	25	π	π	NOUN
ejpam-5050	135	26	x3/2	x3/2	NUM
ejpam-5050	135	27	−d3/2y(x)−	−d3/2y(x)−	PROPN
ejpam-5050	135	28	y(x	y(x	PROPN
ejpam-5050	135	29	)	)	PUNCT
ejpam-5050	135	30	.	.	PUNCT
ejpam-5050	136	1	(	(	PUNCT
ejpam-5050	136	2	19	19	NUM
ejpam-5050	136	3	)	)	PUNCT
ejpam-5050	136	4	m.	m.	NOUN
ejpam-5050	136	5	al	al	PROPN
ejpam-5050	136	6	-	-	PUNCT
ejpam-5050	136	7	mazmumy	mazmumy	PROPN
ejpam-5050	136	8	,	,	PUNCT
ejpam-5050	136	9	m.	m.	NOUN
ejpam-5050	136	10	alsulami	alsulami	PROPN
ejpam-5050	136	11	/	/	SYM
ejpam-5050	136	12	eur	eur	PROPN
ejpam-5050	136	13	.	.	PUNCT
ejpam-5050	137	1	j.	j.	PROPN
ejpam-5050	137	2	pure	pure	PROPN
ejpam-5050	137	3	appl	appl	PROPN
ejpam-5050	137	4	.	.	PROPN
ejpam-5050	137	5	math	math	PROPN
ejpam-5050	137	6	,	,	PUNCT
ejpam-5050	137	7	17	17	NUM
ejpam-5050	137	8	(	(	PUNCT
ejpam-5050	137	9	1	1	NUM
ejpam-5050	137	10	)	)	PUNCT
ejpam-5050	137	11	(	(	PUNCT
ejpam-5050	137	12	2024	2024	NUM
ejpam-5050	137	13	)	)	PUNCT
ejpam-5050	137	14	,	,	PUNCT
ejpam-5050	137	15	546	546	NUM
ejpam-5050	137	16	-	-	SYM
ejpam-5050	137	17	568	568	NUM
ejpam-5050	137	18	553	553	NUM
ejpam-5050	137	19	here	here	ADV
ejpam-5050	138	1	,	,	PUNCT
ejpam-5050	138	2	we	we	PRON
ejpam-5050	138	3	define	define	VERB
ejpam-5050	138	4	l−1	l−1	PROPN
ejpam-5050	138	5	(	(	PUNCT
ejpam-5050	138	6	.	.	PUNCT
ejpam-5050	138	7	)	)	PUNCT
ejpam-5050	139	1	=	=	PUNCT
ejpam-5050	140	1	∫	∫	PUNCT
ejpam-5050	140	2	x	x	SYM
ejpam-5050	140	3	0	0	NUM
ejpam-5050	140	4	∫	∫	PROPN
ejpam-5050	140	5	x	x	SYM
ejpam-5050	140	6	0	0	PUNCT
ejpam-5050	140	7	(	(	PUNCT
ejpam-5050	140	8	.)dxdx	.)dxdx	NOUN
ejpam-5050	140	9	to	to	PART
ejpam-5050	140	10	be	be	AUX
ejpam-5050	140	11	the	the	DET
ejpam-5050	140	12	inverse	inverse	NOUN
ejpam-5050	140	13	operator	operator	NOUN
ejpam-5050	140	14	.	.	PUNCT
ejpam-5050	141	1	therefore	therefore	ADV
ejpam-5050	141	2	,	,	PUNCT
ejpam-5050	141	3	applying	apply	VERB
ejpam-5050	141	4	l−1	l−1	PROPN
ejpam-5050	141	5	on	on	ADP
ejpam-5050	141	6	both	both	DET
ejpam-5050	141	7	sides	side	NOUN
ejpam-5050	141	8	of	of	ADP
ejpam-5050	141	9	(	(	PUNCT
ejpam-5050	141	10	19	19	NUM
ejpam-5050	141	11	)	)	PUNCT
ejpam-5050	141	12	such	such	ADJ
ejpam-5050	141	13	that	that	DET
ejpam-5050	141	14	y′(0	y′(0	NOUN
ejpam-5050	141	15	)	)	PUNCT
ejpam-5050	141	16	=	=	PROPN
ejpam-5050	141	17	c1	c1	PROPN
ejpam-5050	141	18	gives	give	VERB
ejpam-5050	141	19	y(x	y(x	NOUN
ejpam-5050	141	20	)	)	PUNCT
ejpam-5050	142	1	=	=	PUNCT
ejpam-5050	142	2	c1x−	c1x−	NOUN
ejpam-5050	142	3	l−1[d3/2y(x)]−	l−1[d3/2y(x)]−	NOUN
ejpam-5050	142	4	l−1[y(x	l−1[y(x	NOUN
ejpam-5050	142	5	)	)	PUNCT
ejpam-5050	142	6	]	]	PUNCT
ejpam-5050	143	1	+	+	CCONJ
ejpam-5050	143	2	l−1[x3	l−1[x3	ADJ
ejpam-5050	143	3	+	+	CCONJ
ejpam-5050	143	4	5x+	5x+	NUM
ejpam-5050	143	5	8√	8√	NOUN
ejpam-5050	143	6	π	π	NOUN
ejpam-5050	143	7	x3/2	x3/2	NUM
ejpam-5050	143	8	]	]	X
ejpam-5050	143	9	.	.	PUNCT
ejpam-5050	144	1	then	then	ADV
ejpam-5050	144	2	,	,	PUNCT
ejpam-5050	144	3	on	on	ADP
ejpam-5050	144	4	using	use	VERB
ejpam-5050	144	5	madm	madm	NOUN
ejpam-5050	144	6	as	as	SCONJ
ejpam-5050	144	7	explained	explain	VERB
ejpam-5050	144	8	in	in	ADP
ejpam-5050	144	9	the	the	DET
ejpam-5050	144	10	procedure	procedure	NOUN
ejpam-5050	144	11	,	,	PUNCT
ejpam-5050	144	12	we	we	PRON
ejpam-5050	144	13	write	write	VERB
ejpam-5050	144	14	∞∑	∞∑	PROPN
ejpam-5050	144	15	n=0	n=0	NUM
ejpam-5050	144	16	yn(x	yn(x	X
ejpam-5050	144	17	)	)	PUNCT
ejpam-5050	145	1	=	=	SYM
ejpam-5050	145	2	c1x−	c1x−	ADJ
ejpam-5050	145	3	pl−1	pl−1	NOUN
ejpam-5050	145	4	[	[	PUNCT
ejpam-5050	145	5	∞∑	∞∑	NUM
ejpam-5050	145	6	n=0	n=0	NUM
ejpam-5050	145	7	anx	anx	NOUN
ejpam-5050	145	8	n	n	NOUN
ejpam-5050	145	9	]	]	PUNCT
ejpam-5050	145	10	+	+	CCONJ
ejpam-5050	145	11	l−1	l−1	NOUN
ejpam-5050	145	12	[	[	PUNCT
ejpam-5050	145	13	∞∑	∞∑	PROPN
ejpam-5050	145	14	n=0	n=0	NUM
ejpam-5050	145	15	anx	anx	NOUN
ejpam-5050	145	16	n	n	NOUN
ejpam-5050	145	17	]	]	PUNCT
ejpam-5050	145	18	−	−	PROPN
ejpam-5050	146	1	l−1	l−1	PROPN
ejpam-5050	146	2	[	[	PUNCT
ejpam-5050	146	3	d3/2	d3/2	ADJ
ejpam-5050	146	4	∞∑	∞∑	PROPN
ejpam-5050	146	5	n=0	n=0	NUM
ejpam-5050	146	6	yn(x	yn(x	X
ejpam-5050	146	7	)	)	PUNCT
ejpam-5050	146	8	]	]	PUNCT
ejpam-5050	147	1	−	−	PROPN
ejpam-5050	147	2	l−1	l−1	PROPN
ejpam-5050	147	3	[	[	PUNCT
ejpam-5050	147	4	∞∑	∞∑	PROPN
ejpam-5050	147	5	n=0	n=0	NUM
ejpam-5050	147	6	yn(x	yn(x	NUM
ejpam-5050	147	7	)	)	PUNCT
ejpam-5050	147	8	]	]	PUNCT
ejpam-5050	148	1	+	+	CCONJ
ejpam-5050	148	2	l−1[x3	l−1[x3	ADJ
ejpam-5050	148	3	+	+	CCONJ
ejpam-5050	148	4	5x+	5x+	NUM
ejpam-5050	148	5	8√	8√	NOUN
ejpam-5050	148	6	π	π	NOUN
ejpam-5050	148	7	x3/2	x3/2	NUM
ejpam-5050	148	8	]	]	PUNCT
ejpam-5050	148	9	,	,	PUNCT
ejpam-5050	148	10	thereby	thereby	ADV
ejpam-5050	148	11	taking	take	VERB
ejpam-5050	148	12	y0(x	y0(x	NOUN
ejpam-5050	148	13	)	)	PUNCT
ejpam-5050	148	14	=	=	SYM
ejpam-5050	148	15	c1x+	c1x+	PRON
ejpam-5050	148	16	l−1[a0	l−1[a0	NOUN
ejpam-5050	149	1	+	+	NUM
ejpam-5050	149	2	a1x+	a1x+	NOUN
ejpam-5050	149	3	a2x	a2x	ADP
ejpam-5050	149	4	2	2	NUM
ejpam-5050	149	5	+	+	CCONJ
ejpam-5050	149	6	...	...	PUNCT
ejpam-5050	149	7	]	]	X
ejpam-5050	149	8	,	,	PUNCT
ejpam-5050	149	9	(	(	PUNCT
ejpam-5050	149	10	20	20	NUM
ejpam-5050	149	11	)	)	PUNCT
ejpam-5050	149	12	and	and	CCONJ
ejpam-5050	149	13	y1(x	y1(x	NOUN
ejpam-5050	149	14	)	)	PUNCT
ejpam-5050	149	15	=	=	SYM
ejpam-5050	150	1	−pl−1[a0+a1x+a2x	−pl−1[a0+a1x+a2x	NOUN
ejpam-5050	151	1	2+	2+	NUM
ejpam-5050	151	2	...	...	PUNCT
ejpam-5050	151	3	]+l−1[x3	]+l−1[x3	PUNCT
ejpam-5050	151	4	+	+	ADJ
ejpam-5050	151	5	5x+	5x+	NUM
ejpam-5050	151	6	8√	8√	ADJ
ejpam-5050	151	7	π	π	NOUN
ejpam-5050	151	8	x3/2]−l−1[d3/2y0(x)]−l−1[y0(x	x3/2]−l−1[d3/2y0(x)]−l−1[y0(x	NUM
ejpam-5050	151	9	)	)	PUNCT
ejpam-5050	151	10	]	]	PUNCT
ejpam-5050	151	11	.	.	PUNCT
ejpam-5050	152	1	(	(	PUNCT
ejpam-5050	152	2	21	21	NUM
ejpam-5050	152	3	)	)	PUNCT
ejpam-5050	152	4	computing	compute	VERB
ejpam-5050	152	5	the	the	DET
ejpam-5050	152	6	values	value	NOUN
ejpam-5050	152	7	of	of	ADP
ejpam-5050	152	8	y0(x	y0(x	NOUN
ejpam-5050	152	9	)	)	PUNCT
ejpam-5050	152	10	and	and	CCONJ
ejpam-5050	152	11	y1(x	y1(x	NOUN
ejpam-5050	152	12	)	)	PUNCT
ejpam-5050	152	13	from	from	ADP
ejpam-5050	152	14	(	(	PUNCT
ejpam-5050	152	15	20	20	NUM
ejpam-5050	152	16	)	)	PUNCT
ejpam-5050	152	17	and	and	CCONJ
ejpam-5050	152	18	(	(	PUNCT
ejpam-5050	152	19	21	21	NUM
ejpam-5050	152	20	)	)	PUNCT
ejpam-5050	152	21	,	,	PUNCT
ejpam-5050	152	22	respectively	respectively	ADV
ejpam-5050	152	23	by	by	ADP
ejpam-5050	152	24	using	use	VERB
ejpam-5050	152	25	l−1	l−1	PROPN
ejpam-5050	152	26	and	and	CCONJ
ejpam-5050	152	27	(	(	PUNCT
ejpam-5050	152	28	6	6	NUM
ejpam-5050	152	29	)	)	PUNCT
ejpam-5050	152	30	,	,	PUNCT
ejpam-5050	152	31	one	one	PRON
ejpam-5050	152	32	gets	get	VERB
ejpam-5050	152	33	y0(x	y0(x	NOUN
ejpam-5050	152	34	)	)	PUNCT
ejpam-5050	152	35	=	=	PUNCT
ejpam-5050	152	36	c1x+	c1x+	PRON
ejpam-5050	153	1	1	1	NUM
ejpam-5050	153	2	2	2	NUM
ejpam-5050	153	3	a0x	a0x	ADP
ejpam-5050	153	4	2	2	NUM
ejpam-5050	153	5	+	+	SYM
ejpam-5050	153	6	1	1	NUM
ejpam-5050	153	7	6	6	NUM
ejpam-5050	153	8	a1x	a1x	SYM
ejpam-5050	153	9	3	3	NUM
ejpam-5050	153	10	+	+	CCONJ
ejpam-5050	153	11	1	1	NUM
ejpam-5050	153	12	12	12	NUM
ejpam-5050	153	13	a2x	a2x	ADP
ejpam-5050	153	14	4	4	NUM
ejpam-5050	153	15	+	+	NUM
ejpam-5050	153	16	...	...	PUNCT
ejpam-5050	154	1	y1(x	y1(x	X
ejpam-5050	154	2	)	)	PUNCT
ejpam-5050	154	3	=	=	SYM
ejpam-5050	154	4	−p	−p	NOUN
ejpam-5050	154	5	[	[	PUNCT
ejpam-5050	154	6	1	1	NUM
ejpam-5050	154	7	2	2	NUM
ejpam-5050	154	8	a0x	a0x	ADP
ejpam-5050	154	9	2	2	NUM
ejpam-5050	154	10	+	+	SYM
ejpam-5050	154	11	1	1	NUM
ejpam-5050	154	12	6	6	NUM
ejpam-5050	154	13	a1x	a1x	SYM
ejpam-5050	154	14	3	3	NUM
ejpam-5050	154	15	+	+	CCONJ
ejpam-5050	154	16	1	1	NUM
ejpam-5050	154	17	12	12	NUM
ejpam-5050	154	18	a2x	a2x	ADP
ejpam-5050	154	19	4	4	NUM
ejpam-5050	154	20	+	+	NUM
ejpam-5050	154	21	...	...	PUNCT
ejpam-5050	154	22	]	]	PUNCT
ejpam-5050	155	1	+	+	CCONJ
ejpam-5050	155	2	1	1	NUM
ejpam-5050	155	3	20	20	NUM
ejpam-5050	155	4	x5	x5	NOUN
ejpam-5050	155	5	+	+	CCONJ
ejpam-5050	155	6	5	5	NUM
ejpam-5050	155	7	6	6	NUM
ejpam-5050	155	8	x3	x3	ADJ
ejpam-5050	155	9	+	+	CCONJ
ejpam-5050	155	10	32	32	NUM
ejpam-5050	155	11	35	35	NUM
ejpam-5050	155	12	√	√	PROPN
ejpam-5050	155	13	π	π	PROPN
ejpam-5050	155	14	x7/2	x7/2	PROPN
ejpam-5050	156	1	−	−	PROPN
ejpam-5050	156	2	4c	4c	NOUN
ejpam-5050	156	3	3	3	NUM
ejpam-5050	156	4	√	√	PROPN
ejpam-5050	156	5	π	π	PROPN
ejpam-5050	156	6	x3/2	x3/2	NUM
ejpam-5050	157	1	−	−	PROPN
ejpam-5050	157	2	8a0	8a0	NUM
ejpam-5050	157	3	15	15	NUM
ejpam-5050	158	1	√	√	PROPN
ejpam-5050	158	2	π	π	PROPN
ejpam-5050	158	3	x5/2	x5/2	PROPN
ejpam-5050	158	4	−	−	PROPN
ejpam-5050	159	1	16a1	16a1	NUM
ejpam-5050	159	2	105	105	NUM
ejpam-5050	159	3	√	√	PROPN
ejpam-5050	159	4	π	π	PROPN
ejpam-5050	159	5	x7/2	x7/2	PROPN
ejpam-5050	160	1	−	−	PROPN
ejpam-5050	161	1	64a2	64a2	NUM
ejpam-5050	161	2	945	945	NUM
ejpam-5050	161	3	√	√	PROPN
ejpam-5050	161	4	π	π	X
ejpam-5050	161	5	x9/2	x9/2	PUNCT
ejpam-5050	162	1	−	−	PROPN
ejpam-5050	162	2	c	c	PROPN
ejpam-5050	162	3	6	6	NUM
ejpam-5050	162	4	x3	x3	NOUN
ejpam-5050	162	5	−	−	PROPN
ejpam-5050	162	6	a0	a0	PROPN
ejpam-5050	162	7	24	24	NUM
ejpam-5050	162	8	x4	x4	PROPN
ejpam-5050	162	9	−	−	PROPN
ejpam-5050	162	10	a1	a1	NOUN
ejpam-5050	162	11	120	120	NUM
ejpam-5050	162	12	x5	x5	NOUN
ejpam-5050	162	13	−	−	PROPN
ejpam-5050	162	14	a2	a2	PROPN
ejpam-5050	162	15	360	360	NUM
ejpam-5050	162	16	x6	x6	PROPN
ejpam-5050	163	1	+	+	CCONJ
ejpam-5050	163	2	....	....	PUNCT
ejpam-5050	163	3	now	now	ADV
ejpam-5050	163	4	,	,	PUNCT
ejpam-5050	163	5	put	put	VERB
ejpam-5050	163	6	y1(x	y1(x	NOUN
ejpam-5050	163	7	)	)	PUNCT
ejpam-5050	163	8	=	=	SYM
ejpam-5050	163	9	0	0	PUNCT
ejpam-5050	163	10	and	and	CCONJ
ejpam-5050	163	11	collecting	collect	VERB
ejpam-5050	163	12	the	the	DET
ejpam-5050	163	13	like	like	ADJ
ejpam-5050	163	14	terms	term	NOUN
ejpam-5050	163	15	,	,	PUNCT
ejpam-5050	163	16	we	we	PRON
ejpam-5050	163	17	have	have	VERB
ejpam-5050	163	18	y1(x	y1(x	NOUN
ejpam-5050	163	19	)	)	PUNCT
ejpam-5050	163	20	=	=	SYM
ejpam-5050	164	1	−p	−p	ADJ
ejpam-5050	164	2	1	1	NUM
ejpam-5050	164	3	2	2	NUM
ejpam-5050	164	4	a0x	a0x	ADP
ejpam-5050	164	5	2	2	NUM
ejpam-5050	164	6	+	+	CCONJ
ejpam-5050	164	7	[	[	X
ejpam-5050	164	8	−p	−p	ADJ
ejpam-5050	164	9	1	1	NUM
ejpam-5050	164	10	6	6	NUM
ejpam-5050	164	11	a1	a1	NOUN
ejpam-5050	164	12	+	+	CCONJ
ejpam-5050	164	13	5	5	NUM
ejpam-5050	164	14	6	6	NUM
ejpam-5050	164	15	−	−	NOUN
ejpam-5050	164	16	c	c	NOUN
ejpam-5050	164	17	6	6	NUM
ejpam-5050	164	18	]	]	PUNCT
ejpam-5050	164	19	x3	x3	ADJ
ejpam-5050	165	1	+	+	X
ejpam-5050	166	1	[	[	X
ejpam-5050	166	2	−p	−p	ADJ
ejpam-5050	166	3	1	1	NUM
ejpam-5050	166	4	12	12	NUM
ejpam-5050	166	5	a2	a2	PROPN
ejpam-5050	166	6	−	−	PROPN
ejpam-5050	166	7	a0	a0	PROPN
ejpam-5050	166	8	24	24	NUM
ejpam-5050	166	9	]	]	PUNCT
ejpam-5050	166	10	x4	x4	PROPN
ejpam-5050	166	11	+	+	CCONJ
ejpam-5050	166	12	...	...	PUNCT
ejpam-5050	167	1	=	=	SYM
ejpam-5050	167	2	0	0	X
ejpam-5050	167	3	.	.	PUNCT
ejpam-5050	168	1	then	then	ADV
ejpam-5050	168	2	,	,	PUNCT
ejpam-5050	168	3	on	on	ADP
ejpam-5050	168	4	considering	consider	VERB
ejpam-5050	168	5	p	p	X
ejpam-5050	168	6	=	=	SYM
ejpam-5050	168	7	1	1	NUM
ejpam-5050	168	8	and	and	CCONJ
ejpam-5050	168	9	equating	equate	VERB
ejpam-5050	168	10	the	the	DET
ejpam-5050	168	11	coefficients	coefficient	NOUN
ejpam-5050	168	12	of	of	ADP
ejpam-5050	168	13	xn	xn	PROPN
ejpam-5050	168	14	from	from	ADP
ejpam-5050	168	15	the	the	DET
ejpam-5050	168	16	both	both	DET
ejpam-5050	168	17	sides	side	NOUN
ejpam-5050	168	18	of	of	ADP
ejpam-5050	168	19	the	the	DET
ejpam-5050	168	20	above	above	ADJ
ejpam-5050	168	21	equation	equation	NOUN
ejpam-5050	168	22	,	,	PUNCT
ejpam-5050	168	23	one	one	NUM
ejpam-5050	168	24	gains	gain	NOUN
ejpam-5050	168	25	a0	a0	NOUN
ejpam-5050	168	26	=	=	SYM
ejpam-5050	168	27	a2	a2	PROPN
ejpam-5050	168	28	=	=	SYM
ejpam-5050	168	29	0	0	NUM
ejpam-5050	168	30	,	,	PUNCT
ejpam-5050	168	31	and	and	CCONJ
ejpam-5050	168	32	a1	a1	NOUN
ejpam-5050	168	33	=	=	SYM
ejpam-5050	168	34	5	5	NUM
ejpam-5050	168	35	−	−	PROPN
ejpam-5050	168	36	c1	c1	NOUN
ejpam-5050	168	37	.	.	PUNCT
ejpam-5050	169	1	next	next	ADV
ejpam-5050	169	2	,	,	PUNCT
ejpam-5050	169	3	on	on	ADP
ejpam-5050	169	4	substituting	substitute	VERB
ejpam-5050	169	5	the	the	DET
ejpam-5050	169	6	values	value	NOUN
ejpam-5050	169	7	of	of	ADP
ejpam-5050	169	8	a0	a0	NOUN
ejpam-5050	169	9	,	,	PUNCT
ejpam-5050	169	10	a1	a1	NOUN
ejpam-5050	169	11	and	and	CCONJ
ejpam-5050	169	12	a2	a2	PROPN
ejpam-5050	169	13	in	in	ADP
ejpam-5050	169	14	y0(x	y0(x	PROPN
ejpam-5050	169	15	)	)	PUNCT
ejpam-5050	169	16	,	,	PUNCT
ejpam-5050	169	17	where	where	SCONJ
ejpam-5050	169	18	yn(x	yn(x	X
ejpam-5050	169	19	)	)	PUNCT
ejpam-5050	169	20	=	=	SYM
ejpam-5050	169	21	0	0	NUM
ejpam-5050	169	22	,	,	PUNCT
ejpam-5050	169	23	for	for	ADP
ejpam-5050	169	24	n	n	NOUN
ejpam-5050	169	25	⩾	⩾	NOUN
ejpam-5050	169	26	1	1	NUM
ejpam-5050	169	27	,	,	PUNCT
ejpam-5050	169	28	we	we	PRON
ejpam-5050	169	29	obtain	obtain	VERB
ejpam-5050	169	30	y(x	y(x	NOUN
ejpam-5050	169	31	)	)	PUNCT
ejpam-5050	169	32	=	=	SYM
ejpam-5050	169	33	y0(x	y0(x	X
ejpam-5050	169	34	)	)	PUNCT
ejpam-5050	169	35	=	=	PUNCT
ejpam-5050	169	36	c1x+	c1x+	VERB
ejpam-5050	169	37	1	1	NUM
ejpam-5050	169	38	6	6	NUM
ejpam-5050	169	39	(	(	PUNCT
ejpam-5050	169	40	5−	5−	NUM
ejpam-5050	169	41	c1)x	c1)x	NOUN
ejpam-5050	169	42	3	3	NUM
ejpam-5050	169	43	+	+	CCONJ
ejpam-5050	169	44	...	...	PUNCT
ejpam-5050	170	1	lastly	lastly	ADV
ejpam-5050	170	2	,	,	PUNCT
ejpam-5050	170	3	with	with	ADP
ejpam-5050	170	4	the	the	DET
ejpam-5050	170	5	aid	aid	NOUN
ejpam-5050	170	6	of	of	ADP
ejpam-5050	170	7	the	the	DET
ejpam-5050	170	8	second	second	ADJ
ejpam-5050	170	9	boundary	boundary	ADJ
ejpam-5050	170	10	prescription	prescription	NOUN
ejpam-5050	170	11	,	,	PUNCT
ejpam-5050	170	12	that	that	ADV
ejpam-5050	170	13	is	is	ADV
ejpam-5050	170	14	,	,	PUNCT
ejpam-5050	170	15	y(1	y(1	PROPN
ejpam-5050	170	16	)	)	PUNCT
ejpam-5050	171	1	=	=	SYM
ejpam-5050	171	2	0	0	NUM
ejpam-5050	171	3	,	,	PUNCT
ejpam-5050	171	4	we	we	PRON
ejpam-5050	171	5	have	have	VERB
ejpam-5050	171	6	c1	c1	PROPN
ejpam-5050	171	7	=	=	SYM
ejpam-5050	171	8	−1	−1	PROPN
ejpam-5050	171	9	,	,	PUNCT
ejpam-5050	171	10	which	which	PRON
ejpam-5050	171	11	finally	finally	ADV
ejpam-5050	171	12	yields	yield	VERB
ejpam-5050	171	13	y(x	y(x	NOUN
ejpam-5050	171	14	)	)	PUNCT
ejpam-5050	171	15	=	=	PUNCT
ejpam-5050	172	1	x3	x3	ADJ
ejpam-5050	172	2	−	−	PROPN
ejpam-5050	173	1	x	x	SYM
ejpam-5050	173	2	,	,	PUNCT
ejpam-5050	173	3	m.	m.	PROPN
ejpam-5050	173	4	al	al	PROPN
ejpam-5050	173	5	-	-	PUNCT
ejpam-5050	173	6	mazmumy	mazmumy	PROPN
ejpam-5050	173	7	,	,	PUNCT
ejpam-5050	173	8	m.	m.	NOUN
ejpam-5050	173	9	alsulami	alsulami	PROPN
ejpam-5050	173	10	/	/	SYM
ejpam-5050	173	11	eur	eur	PROPN
ejpam-5050	173	12	.	.	PUNCT
ejpam-5050	174	1	j.	j.	PROPN
ejpam-5050	174	2	pure	pure	PROPN
ejpam-5050	174	3	appl	appl	PROPN
ejpam-5050	174	4	.	.	PROPN
ejpam-5050	174	5	math	math	PROPN
ejpam-5050	174	6	,	,	PUNCT
ejpam-5050	174	7	17	17	NUM
ejpam-5050	174	8	(	(	PUNCT
ejpam-5050	174	9	1	1	NUM
ejpam-5050	174	10	)	)	PUNCT
ejpam-5050	174	11	(	(	PUNCT
ejpam-5050	174	12	2024	2024	NUM
ejpam-5050	174	13	)	)	PUNCT
ejpam-5050	174	14	,	,	PUNCT
ejpam-5050	174	15	546	546	NUM
ejpam-5050	174	16	-	-	SYM
ejpam-5050	174	17	568	568	NUM
ejpam-5050	174	18	554	554	NUM
ejpam-5050	174	19	that	that	PRON
ejpam-5050	174	20	exactly	exactly	ADV
ejpam-5050	174	21	matches	match	VERB
ejpam-5050	174	22	the	the	DET
ejpam-5050	174	23	exact	exact	ADJ
ejpam-5050	174	24	analytical	analytical	ADJ
ejpam-5050	174	25	solution	solution	NOUN
ejpam-5050	174	26	for	for	ADP
ejpam-5050	174	27	(	(	PUNCT
ejpam-5050	174	28	18	18	NUM
ejpam-5050	174	29	)	)	PUNCT
ejpam-5050	174	30	.	.	PUNCT
ejpam-5050	175	1	algorithm	algorithm	NOUN
ejpam-5050	175	2	2	2	NUM
ejpam-5050	175	3	:	:	PUNCT
ejpam-5050	175	4	applying	apply	VERB
ejpam-5050	175	5	the	the	DET
ejpam-5050	175	6	inverse	inverse	NOUN
ejpam-5050	175	7	operator	operator	NOUN
ejpam-5050	175	8	(	(	PUNCT
ejpam-5050	175	9	14	14	NUM
ejpam-5050	175	10	)	)	PUNCT
ejpam-5050	175	11	on	on	ADP
ejpam-5050	175	12	the	the	DET
ejpam-5050	175	13	left	left	ADJ
ejpam-5050	175	14	-	-	PUNCT
ejpam-5050	175	15	hand	hand	NOUN
ejpam-5050	175	16	side	side	NOUN
ejpam-5050	175	17	of	of	ADP
ejpam-5050	175	18	(	(	PUNCT
ejpam-5050	175	19	19	19	NUM
ejpam-5050	175	20	)	)	PUNCT
ejpam-5050	175	21	,	,	PUNCT
ejpam-5050	175	22	one	one	PRON
ejpam-5050	175	23	gets	get	VERB
ejpam-5050	175	24	l−1ly(x	l−1ly(x	NOUN
ejpam-5050	175	25	)	)	PUNCT
ejpam-5050	176	1	=	=	SYM
ejpam-5050	177	1	∫	∫	PUNCT
ejpam-5050	177	2	x	x	SYM
ejpam-5050	177	3	0	0	NUM
ejpam-5050	178	1	dx′	dx′	PROPN
ejpam-5050	178	2	∫	∫	PROPN
ejpam-5050	178	3	x′	x′	PROPN
ejpam-5050	178	4	0	0	NUM
ejpam-5050	178	5	d2y	d2y	PROPN
ejpam-5050	179	1	dx2	dx2	NOUN
ejpam-5050	179	2	dx′′	dx′′	PROPN
ejpam-5050	179	3	−	−	PROPN
ejpam-5050	180	1	x	x	SYM
ejpam-5050	180	2	∫	∫	PROPN
ejpam-5050	180	3	1	1	NUM
ejpam-5050	180	4	0	0	NUM
ejpam-5050	180	5	dx	dx	PROPN
ejpam-5050	180	6	∫	∫	PROPN
ejpam-5050	180	7	x′	x′	PROPN
ejpam-5050	180	8	0	0	NUM
ejpam-5050	180	9	d2y	d2y	PROPN
ejpam-5050	180	10	dx2	dx2	PROPN
ejpam-5050	180	11	dx′′	dx′′	PROPN
ejpam-5050	180	12	,	,	PUNCT
ejpam-5050	180	13	=	=	PUNCT
ejpam-5050	180	14	y(x)−	y(x)−	PROPN
ejpam-5050	180	15	y(0)−	y(0)−	PROPN
ejpam-5050	180	16	xy(1	xy(1	NUM
ejpam-5050	180	17	)	)	PUNCT
ejpam-5050	180	18	+	+	CCONJ
ejpam-5050	180	19	xy(0	xy(0	PROPN
ejpam-5050	180	20	)	)	PUNCT
ejpam-5050	180	21	,	,	PUNCT
ejpam-5050	180	22	=	=	PUNCT
ejpam-5050	180	23	y(x	y(x	PROPN
ejpam-5050	180	24	)	)	PUNCT
ejpam-5050	180	25	.	.	PUNCT
ejpam-5050	181	1	so	so	ADV
ejpam-5050	181	2	,	,	PUNCT
ejpam-5050	181	3	y(x	y(x	PROPN
ejpam-5050	181	4	)	)	PUNCT
ejpam-5050	181	5	=	=	SYM
ejpam-5050	181	6	l−1[x3	l−1[x3	PROPN
ejpam-5050	181	7	+	+	NOUN
ejpam-5050	181	8	5x+	5x+	NUM
ejpam-5050	181	9	8√	8√	NOUN
ejpam-5050	181	10	π	π	X
ejpam-5050	181	11	x3/2]−	x3/2]−	PUNCT
ejpam-5050	181	12	l−1[d3/2y(x)]−	l−1[d3/2y(x)]−	PROPN
ejpam-5050	181	13	l−1[y(x	l−1[y(x	NOUN
ejpam-5050	181	14	)	)	PUNCT
ejpam-5050	181	15	]	]	PUNCT
ejpam-5050	181	16	.	.	PUNCT
ejpam-5050	182	1	therefore	therefore	ADV
ejpam-5050	182	2	,	,	PUNCT
ejpam-5050	182	3	upon	upon	SCONJ
ejpam-5050	182	4	deploying	deploy	VERB
ejpam-5050	182	5	the	the	DET
ejpam-5050	182	6	madm	madm	NOUN
ejpam-5050	182	7	procedure	procedure	NOUN
ejpam-5050	182	8	,	,	PUNCT
ejpam-5050	182	9	we	we	PRON
ejpam-5050	182	10	have	have	VERB
ejpam-5050	182	11	∞∑	∞∑	NUM
ejpam-5050	182	12	n=0	n=0	NUM
ejpam-5050	182	13	yn(x	yn(x	PUNCT
ejpam-5050	182	14	)	)	PUNCT
ejpam-5050	182	15	=	=	SYM
ejpam-5050	183	1	l−1[x3	l−1[x3	PROPN
ejpam-5050	183	2	+	+	NOUN
ejpam-5050	183	3	5x+	5x+	NUM
ejpam-5050	183	4	8√	8√	NOUN
ejpam-5050	183	5	π	π	NOUN
ejpam-5050	183	6	x3/2]−	x3/2]−	PUNCT
ejpam-5050	183	7	pl−1	pl−1	NOUN
ejpam-5050	183	8	[	[	PUNCT
ejpam-5050	183	9	∞∑	∞∑	NUM
ejpam-5050	183	10	n=0	n=0	NUM
ejpam-5050	183	11	anx	anx	NOUN
ejpam-5050	183	12	n	n	NOUN
ejpam-5050	183	13	]	]	PUNCT
ejpam-5050	184	1	+	+	CCONJ
ejpam-5050	184	2	l−1	l−1	NOUN
ejpam-5050	184	3	[	[	PUNCT
ejpam-5050	184	4	∞∑	∞∑	PROPN
ejpam-5050	184	5	n=0	n=0	NUM
ejpam-5050	184	6	anx	anx	NOUN
ejpam-5050	184	7	n	n	NOUN
ejpam-5050	184	8	]	]	PUNCT
ejpam-5050	184	9	−	−	PROPN
ejpam-5050	185	1	l−1	l−1	PROPN
ejpam-5050	185	2	[	[	PUNCT
ejpam-5050	185	3	d3/2	d3/2	ADJ
ejpam-5050	185	4	∞∑	∞∑	PROPN
ejpam-5050	185	5	n=0	n=0	NUM
ejpam-5050	185	6	yn(x	yn(x	X
ejpam-5050	185	7	)	)	PUNCT
ejpam-5050	185	8	]	]	PUNCT
ejpam-5050	186	1	−	−	PROPN
ejpam-5050	186	2	l−1	l−1	PROPN
ejpam-5050	186	3	[	[	PUNCT
ejpam-5050	186	4	∞∑	∞∑	PROPN
ejpam-5050	186	5	n=0	n=0	NUM
ejpam-5050	186	6	yn(x	yn(x	NOUN
ejpam-5050	186	7	)	)	PUNCT
ejpam-5050	186	8	]	]	PUNCT
ejpam-5050	186	9	,	,	PUNCT
ejpam-5050	186	10	which	which	PRON
ejpam-5050	186	11	leads	lead	VERB
ejpam-5050	186	12	to	to	ADP
ejpam-5050	186	13	the	the	DET
ejpam-5050	186	14	recurrent	recurrent	ADJ
ejpam-5050	186	15	scheme	scheme	NOUN
ejpam-5050	186	16	as	as	SCONJ
ejpam-5050	186	17	follows	follow	VERB
ejpam-5050	186	18	y0(x	y0(x	NUM
ejpam-5050	186	19	)	)	PUNCT
ejpam-5050	186	20	=	=	SYM
ejpam-5050	187	1	l−1	l−1	NOUN
ejpam-5050	187	2	[	[	PUNCT
ejpam-5050	187	3	∞∑	∞∑	PROPN
ejpam-5050	187	4	n=0	n=0	NUM
ejpam-5050	187	5	anx	anx	NOUN
ejpam-5050	187	6	n	n	NOUN
ejpam-5050	187	7	]	]	PUNCT
ejpam-5050	187	8	,	,	PUNCT
ejpam-5050	187	9	and	and	CCONJ
ejpam-5050	187	10	y1(x	y1(x	NOUN
ejpam-5050	187	11	)	)	PUNCT
ejpam-5050	187	12	=	=	SYM
ejpam-5050	187	13	l−1	l−1	PROPN
ejpam-5050	187	14	[	[	PUNCT
ejpam-5050	187	15	x3	x3	ADJ
ejpam-5050	187	16	+	+	CCONJ
ejpam-5050	187	17	5x+	5x+	NUM
ejpam-5050	187	18	8√	8√	NOUN
ejpam-5050	187	19	π	π	NOUN
ejpam-5050	187	20	x3/2	x3/2	X
ejpam-5050	187	21	]	]	PUNCT
ejpam-5050	187	22	−	−	PROPN
ejpam-5050	187	23	pl−1	pl−1	NOUN
ejpam-5050	187	24	[	[	PUNCT
ejpam-5050	187	25	∞∑	∞∑	NUM
ejpam-5050	187	26	n=0	n=0	NUM
ejpam-5050	187	27	anx	anx	NOUN
ejpam-5050	187	28	n	n	NOUN
ejpam-5050	187	29	]	]	PUNCT
ejpam-5050	187	30	−	−	PROPN
ejpam-5050	187	31	l−1[d3/2y0(x)]−	l−1[d3/2y0(x)]−	PROPN
ejpam-5050	187	32	l−1[y0(x	l−1[y0(x	PROPN
ejpam-5050	187	33	)	)	PUNCT
ejpam-5050	187	34	]	]	PUNCT
ejpam-5050	187	35	.	.	PUNCT
ejpam-5050	188	1	in	in	ADP
ejpam-5050	188	2	fact	fact	NOUN
ejpam-5050	188	3	,	,	PUNCT
ejpam-5050	188	4	explicit	explicit	ADJ
ejpam-5050	188	5	expression	expression	NOUN
ejpam-5050	188	6	for	for	ADP
ejpam-5050	188	7	y0(x	y0(x	NUM
ejpam-5050	188	8	)	)	PUNCT
ejpam-5050	188	9	is	be	AUX
ejpam-5050	188	10	found	find	VERB
ejpam-5050	188	11	to	to	PART
ejpam-5050	188	12	be	be	AUX
ejpam-5050	188	13	y0(x	y0(x	NUM
ejpam-5050	188	14	)	)	PUNCT
ejpam-5050	188	15	=	=	SYM
ejpam-5050	188	16	a0	a0	PROPN
ejpam-5050	188	17	2	2	NUM
ejpam-5050	188	18	x2	x2	NOUN
ejpam-5050	189	1	+	+	CCONJ
ejpam-5050	189	2	a1	a1	NOUN
ejpam-5050	189	3	6	6	NUM
ejpam-5050	189	4	x3	x3	NOUN
ejpam-5050	189	5	+	+	CCONJ
ejpam-5050	189	6	a2	a2	PROPN
ejpam-5050	189	7	12	12	NUM
ejpam-5050	190	1	x4	x4	ADV
ejpam-5050	190	2	−	−	PROPN
ejpam-5050	190	3	x	x	SYM
ejpam-5050	190	4	(	(	PUNCT
ejpam-5050	190	5	a0	a0	NOUN
ejpam-5050	190	6	2	2	NUM
ejpam-5050	191	1	+	+	CCONJ
ejpam-5050	191	2	a1	a1	NOUN
ejpam-5050	191	3	6	6	NUM
ejpam-5050	191	4	+	+	NUM
ejpam-5050	191	5	a2	a2	PROPN
ejpam-5050	191	6	12	12	NUM
ejpam-5050	191	7	)	)	PUNCT
ejpam-5050	191	8	.	.	PUNCT
ejpam-5050	192	1	also	also	ADV
ejpam-5050	192	2	,	,	PUNCT
ejpam-5050	192	3	on	on	ADP
ejpam-5050	192	4	computing	compute	VERB
ejpam-5050	192	5	the	the	DET
ejpam-5050	192	6	component	component	NOUN
ejpam-5050	192	7	of	of	ADP
ejpam-5050	192	8	y1(x	y1(x	NOUN
ejpam-5050	192	9	)	)	PUNCT
ejpam-5050	192	10	using	use	VERB
ejpam-5050	192	11	the	the	DET
ejpam-5050	192	12	inverse	inverse	NOUN
ejpam-5050	192	13	operator	operator	NOUN
ejpam-5050	192	14	(	(	PUNCT
ejpam-5050	192	15	14	14	NUM
ejpam-5050	192	16	)	)	PUNCT
ejpam-5050	192	17	,	,	PUNCT
ejpam-5050	192	18	one	one	PRON
ejpam-5050	192	19	explicitly	explicitly	ADV
ejpam-5050	192	20	gets	get	VERB
ejpam-5050	192	21	y1(x	y1(x	NOUN
ejpam-5050	192	22	)	)	PUNCT
ejpam-5050	192	23	=	=	SYM
ejpam-5050	193	1	32	32	NUM
ejpam-5050	193	2	35	35	NUM
ejpam-5050	193	3	√	√	PROPN
ejpam-5050	193	4	π	π	X
ejpam-5050	193	5	x7/2	x7/2	PROPN
ejpam-5050	194	1	+	+	CCONJ
ejpam-5050	194	2	1	1	NUM
ejpam-5050	194	3	20	20	NUM
ejpam-5050	194	4	x5	x5	NOUN
ejpam-5050	194	5	+	+	CCONJ
ejpam-5050	194	6	5	5	NUM
ejpam-5050	194	7	6	6	NUM
ejpam-5050	194	8	x3	x3	ADJ
ejpam-5050	194	9	−	−	PROPN
ejpam-5050	194	10	(	(	PUNCT
ejpam-5050	194	11	53	53	NUM
ejpam-5050	194	12	60	60	NUM
ejpam-5050	194	13	+	+	NUM
ejpam-5050	194	14	32	32	NUM
ejpam-5050	194	15	35	35	NUM
ejpam-5050	194	16	√	√	PROPN
ejpam-5050	194	17	π	π	PROPN
ejpam-5050	194	18	)	)	PUNCT
ejpam-5050	195	1	x−	x−	PROPN
ejpam-5050	196	1	p	p	PROPN
ejpam-5050	197	1	[	[	X
ejpam-5050	197	2	a0	a0	PROPN
ejpam-5050	197	3	2	2	NUM
ejpam-5050	197	4	x2	x2	NOUN
ejpam-5050	197	5	+	+	CCONJ
ejpam-5050	197	6	a1	a1	NOUN
ejpam-5050	197	7	6	6	NUM
ejpam-5050	197	8	x3	x3	NOUN
ejpam-5050	197	9	+	+	CCONJ
ejpam-5050	197	10	a2	a2	PROPN
ejpam-5050	197	11	12	12	NUM
ejpam-5050	198	1	x4	x4	ADV
ejpam-5050	198	2	−	−	PROPN
ejpam-5050	198	3	x	x	SYM
ejpam-5050	198	4	(	(	PUNCT
ejpam-5050	198	5	a0	a0	NOUN
ejpam-5050	198	6	2	2	NUM
ejpam-5050	199	1	+	+	CCONJ
ejpam-5050	199	2	a1	a1	NOUN
ejpam-5050	199	3	6	6	NUM
ejpam-5050	199	4	+	+	NUM
ejpam-5050	199	5	a2	a2	PROPN
ejpam-5050	199	6	12	12	NUM
ejpam-5050	199	7	)	)	PUNCT
ejpam-5050	199	8	]	]	PUNCT
ejpam-5050	200	1	−	−	PROPN
ejpam-5050	200	2	1	1	NUM
ejpam-5050	200	3	945	945	NUM
ejpam-5050	200	4	√	√	NUM
ejpam-5050	200	5	π	π	PROPN
ejpam-5050	200	6	[	[	PUNCT
ejpam-5050	200	7	64a2x	64a2x	NOUN
ejpam-5050	200	8	9/2	9/2	NUM
ejpam-5050	200	9	+	+	CCONJ
ejpam-5050	200	10	144a1x	144a1x	NUM
ejpam-5050	200	11	7/2	7/2	NUM
ejpam-5050	200	12	+	+	CCONJ
ejpam-5050	200	13	504a0x	504a0x	NUM
ejpam-5050	200	14	5/2	5/2	NUM
ejpam-5050	200	15	−	−	NOUN
ejpam-5050	200	16	(	(	PUNCT
ejpam-5050	200	17	105a2	105a2	NUM
ejpam-5050	200	18	+	+	NUM
ejpam-5050	200	19	210a1	210a1	NUM
ejpam-5050	200	20	+	+	SYM
ejpam-5050	200	21	630a0	630a0	NUM
ejpam-5050	200	22	)	)	PUNCT
ejpam-5050	201	1	x3/2	x3/2	NOUN
ejpam-5050	201	2	]	]	PUNCT
ejpam-5050	202	1	−	−	PROPN
ejpam-5050	202	2	1	1	NUM
ejpam-5050	202	3	210	210	NUM
ejpam-5050	203	1	√	√	NOUN
ejpam-5050	203	2	π	π	PROPN
ejpam-5050	204	1	[	[	X
ejpam-5050	204	2	82	82	NUM
ejpam-5050	204	3	9	9	NUM
ejpam-5050	204	4	a2	a2	NOUN
ejpam-5050	204	5	+	+	CCONJ
ejpam-5050	204	6	44	44	NUM
ejpam-5050	204	7	3	3	NUM
ejpam-5050	204	8	a1	a1	NOUN
ejpam-5050	204	9	+	+	CCONJ
ejpam-5050	204	10	28a0	28a0	NUM
ejpam-5050	204	11	]	]	PUNCT
ejpam-5050	204	12	x−	x−	PROPN
ejpam-5050	204	13	a2	a2	PROPN
ejpam-5050	204	14	360	360	NUM
ejpam-5050	204	15	x6	x6	PROPN
ejpam-5050	204	16	−	−	NOUN
ejpam-5050	204	17	a1	a1	NOUN
ejpam-5050	204	18	120	120	NUM
ejpam-5050	204	19	x5	x5	PROPN
ejpam-5050	204	20	m.	m.	NOUN
ejpam-5050	204	21	al	al	PROPN
ejpam-5050	204	22	-	-	PUNCT
ejpam-5050	204	23	mazmumy	mazmumy	PROPN
ejpam-5050	204	24	,	,	PUNCT
ejpam-5050	204	25	m.	m.	NOUN
ejpam-5050	204	26	alsulami	alsulami	PROPN
ejpam-5050	204	27	/	/	SYM
ejpam-5050	204	28	eur	eur	PROPN
ejpam-5050	204	29	.	.	PUNCT
ejpam-5050	205	1	j.	j.	PROPN
ejpam-5050	205	2	pure	pure	PROPN
ejpam-5050	205	3	appl	appl	PROPN
ejpam-5050	205	4	.	.	PROPN
ejpam-5050	205	5	math	math	PROPN
ejpam-5050	205	6	,	,	PUNCT
ejpam-5050	205	7	17	17	NUM
ejpam-5050	205	8	(	(	PUNCT
ejpam-5050	205	9	1	1	NUM
ejpam-5050	205	10	)	)	PUNCT
ejpam-5050	205	11	(	(	PUNCT
ejpam-5050	205	12	2024	2024	NUM
ejpam-5050	205	13	)	)	PUNCT
ejpam-5050	205	14	,	,	PUNCT
ejpam-5050	205	15	546	546	NUM
ejpam-5050	205	16	-	-	SYM
ejpam-5050	205	17	568	568	NUM
ejpam-5050	205	18	555	555	NUM
ejpam-5050	205	19	−	−	PROPN
ejpam-5050	205	20	a0	a0	PROPN
ejpam-5050	205	21	24	24	NUM
ejpam-5050	205	22	x4	x4	PROPN
ejpam-5050	205	23	+	+	CCONJ
ejpam-5050	205	24	(	(	PUNCT
ejpam-5050	205	25	a2	a2	PROPN
ejpam-5050	205	26	72	72	NUM
ejpam-5050	205	27	+	+	CCONJ
ejpam-5050	205	28	a1	a1	VERB
ejpam-5050	205	29	36	36	NUM
ejpam-5050	205	30	+	+	NUM
ejpam-5050	205	31	a0	a0	PROPN
ejpam-5050	205	32	12	12	NUM
ejpam-5050	205	33	)	)	PUNCT
ejpam-5050	205	34	x3	x3	ADJ
ejpam-5050	205	35	−	−	PROPN
ejpam-5050	205	36	(	(	PUNCT
ejpam-5050	205	37	a2	a2	PROPN
ejpam-5050	205	38	90	90	NUM
ejpam-5050	205	39	+	+	NUM
ejpam-5050	205	40	7a1	7a1	NUM
ejpam-5050	205	41	360	360	NUM
ejpam-5050	206	1	+	+	CCONJ
ejpam-5050	206	2	a0	a0	PROPN
ejpam-5050	206	3	24	24	NUM
ejpam-5050	206	4	)	)	PUNCT
ejpam-5050	206	5	x.	x.	NOUN
ejpam-5050	207	1	more	more	ADV
ejpam-5050	207	2	so	so	ADV
ejpam-5050	207	3	,	,	PUNCT
ejpam-5050	207	4	upon	upon	SCONJ
ejpam-5050	207	5	collecting	collect	VERB
ejpam-5050	207	6	the	the	DET
ejpam-5050	207	7	related	related	ADJ
ejpam-5050	207	8	terms	term	NOUN
ejpam-5050	207	9	of	of	ADP
ejpam-5050	207	10	y1(x	y1(x	NOUN
ejpam-5050	207	11	)	)	PUNCT
ejpam-5050	207	12	from	from	ADP
ejpam-5050	207	13	the	the	DET
ejpam-5050	207	14	above	above	ADJ
ejpam-5050	207	15	equation	equation	NOUN
ejpam-5050	207	16	at	at	ADP
ejpam-5050	207	17	p	p	NOUN
ejpam-5050	207	18	=	=	NOUN
ejpam-5050	207	19	1	1	NUM
ejpam-5050	207	20	,	,	PUNCT
ejpam-5050	207	21	we	we	PRON
ejpam-5050	207	22	get	get	VERB
ejpam-5050	207	23	y1(x	y1(x	NOUN
ejpam-5050	207	24	)	)	PUNCT
ejpam-5050	207	25	=	=	PUNCT
ejpam-5050	208	1	−	−	PROPN
ejpam-5050	208	2	64a2	64a2	NUM
ejpam-5050	209	1	945	945	NUM
ejpam-5050	209	2	√	√	PROPN
ejpam-5050	209	3	π	π	X
ejpam-5050	209	4	x9/2	x9/2	PUNCT
ejpam-5050	210	1	+	+	CCONJ
ejpam-5050	210	2	(	(	PUNCT
ejpam-5050	210	3	32	32	NUM
ejpam-5050	210	4	35	35	NUM
ejpam-5050	210	5	√	√	NUM
ejpam-5050	211	1	π	π	PROPN
ejpam-5050	211	2	−	−	PROPN
ejpam-5050	211	3	16a1	16a1	NUM
ejpam-5050	211	4	105	105	NUM
ejpam-5050	211	5	√	√	PROPN
ejpam-5050	211	6	π	π	PROPN
ejpam-5050	211	7	)	)	PUNCT
ejpam-5050	211	8	x7/2	x7/2	PROPN
ejpam-5050	212	1	−	−	PROPN
ejpam-5050	212	2	8a0	8a0	NUM
ejpam-5050	212	3	15	15	NUM
ejpam-5050	212	4	√	√	PROPN
ejpam-5050	212	5	π	π	X
ejpam-5050	212	6	x5/2	x5/2	PROPN
ejpam-5050	213	1	+	+	CCONJ
ejpam-5050	213	2	1	1	NUM
ejpam-5050	213	3	945	945	NUM
ejpam-5050	213	4	√	√	NUM
ejpam-5050	213	5	π	π	PROPN
ejpam-5050	213	6	(	(	PUNCT
ejpam-5050	213	7	105a2	105a2	NUM
ejpam-5050	213	8	+	+	NUM
ejpam-5050	213	9	210a1	210a1	NUM
ejpam-5050	213	10	+	+	SYM
ejpam-5050	213	11	630a0	630a0	NUM
ejpam-5050	213	12	)	)	PUNCT
ejpam-5050	214	1	x3/2	x3/2	NUM
ejpam-5050	215	1	−	−	PROPN
ejpam-5050	215	2	a2	a2	PROPN
ejpam-5050	215	3	360	360	NUM
ejpam-5050	215	4	x6	x6	PROPN
ejpam-5050	215	5	+	+	CCONJ
ejpam-5050	215	6	(	(	PUNCT
ejpam-5050	215	7	1	1	NUM
ejpam-5050	215	8	20	20	NUM
ejpam-5050	215	9	−	−	NOUN
ejpam-5050	215	10	a1	a1	NOUN
ejpam-5050	215	11	120	120	NUM
ejpam-5050	215	12	)	)	PUNCT
ejpam-5050	215	13	x5	x5	NOUN
ejpam-5050	215	14	−	−	PROPN
ejpam-5050	215	15	(	(	PUNCT
ejpam-5050	215	16	a2	a2	PROPN
ejpam-5050	215	17	12	12	NUM
ejpam-5050	215	18	+	+	NUM
ejpam-5050	215	19	a0	a0	PROPN
ejpam-5050	215	20	24	24	NUM
ejpam-5050	215	21	)	)	PUNCT
ejpam-5050	215	22	x4	x4	PROPN
ejpam-5050	216	1	+	+	CCONJ
ejpam-5050	216	2	(	(	PUNCT
ejpam-5050	216	3	5	5	NUM
ejpam-5050	216	4	6	6	NUM
ejpam-5050	216	5	+	+	NUM
ejpam-5050	216	6	a2	a2	PROPN
ejpam-5050	216	7	72	72	NUM
ejpam-5050	216	8	−	−	NOUN
ejpam-5050	216	9	5a1	5a1	NUM
ejpam-5050	216	10	36	36	NUM
ejpam-5050	216	11	+	+	CCONJ
ejpam-5050	216	12	a0	a0	PROPN
ejpam-5050	216	13	12	12	NUM
ejpam-5050	216	14	)	)	PUNCT
ejpam-5050	216	15	x3	x3	ADJ
ejpam-5050	216	16	−	−	PROPN
ejpam-5050	216	17	a0	a0	PROPN
ejpam-5050	216	18	2	2	NUM
ejpam-5050	216	19	x2	x2	NOUN
ejpam-5050	217	1	+	+	X
ejpam-5050	218	1	[	[	X
ejpam-5050	218	2	13a2	13a2	NUM
ejpam-5050	218	3	180	180	NUM
ejpam-5050	218	4	+	+	NUM
ejpam-5050	218	5	53a1	53a1	NUM
ejpam-5050	218	6	360	360	NUM
ejpam-5050	218	7	+	+	NUM
ejpam-5050	218	8	11a0	11a0	NUM
ejpam-5050	218	9	24	24	NUM
ejpam-5050	218	10	−	−	NUM
ejpam-5050	218	11	1	1	NUM
ejpam-5050	218	12	210	210	NUM
ejpam-5050	218	13	√	√	NOUN
ejpam-5050	218	14	π	π	PROPN
ejpam-5050	218	15	(	(	PUNCT
ejpam-5050	218	16	82a2	82a2	NUM
ejpam-5050	218	17	9	9	NUM
ejpam-5050	218	18	+	+	CCONJ
ejpam-5050	218	19	44a1	44a1	NUM
ejpam-5050	218	20	3	3	NUM
ejpam-5050	218	21	+	+	SYM
ejpam-5050	218	22	28a0	28a0	NUM
ejpam-5050	218	23	)	)	PUNCT
ejpam-5050	218	24	−	−	PROPN
ejpam-5050	218	25	32	32	NUM
ejpam-5050	218	26	35	35	NUM
ejpam-5050	218	27	√	√	PROPN
ejpam-5050	218	28	π	π	PROPN
ejpam-5050	218	29	+	+	CCONJ
ejpam-5050	218	30	53	53	NUM
ejpam-5050	218	31	60	60	NUM
ejpam-5050	218	32	]	]	PUNCT
ejpam-5050	218	33	x.	x.	NOUN
ejpam-5050	218	34	indeed	indeed	ADV
ejpam-5050	218	35	,	,	PUNCT
ejpam-5050	218	36	on	on	ADP
ejpam-5050	218	37	taking	take	VERB
ejpam-5050	218	38	y1(x	y1(x	NOUN
ejpam-5050	218	39	)	)	PUNCT
ejpam-5050	218	40	=	=	SYM
ejpam-5050	218	41	0	0	NUM
ejpam-5050	218	42	,	,	PUNCT
ejpam-5050	218	43	and	and	CCONJ
ejpam-5050	218	44	thereafter	thereafter	ADV
ejpam-5050	218	45	equating	equate	VERB
ejpam-5050	218	46	the	the	DET
ejpam-5050	218	47	coefficients	coefficient	NOUN
ejpam-5050	218	48	of	of	ADP
ejpam-5050	218	49	xn	xn	PROPN
ejpam-5050	218	50	,	,	PUNCT
ejpam-5050	218	51	we	we	PRON
ejpam-5050	218	52	find	find	VERB
ejpam-5050	218	53	a0	a0	NOUN
ejpam-5050	218	54	=	=	SYM
ejpam-5050	218	55	0	0	PROPN
ejpam-5050	218	56	,	,	PUNCT
ejpam-5050	218	57	a1	a1	NOUN
ejpam-5050	218	58	=	=	SYM
ejpam-5050	218	59	6	6	NUM
ejpam-5050	218	60	,	,	PUNCT
ejpam-5050	218	61	and	and	CCONJ
ejpam-5050	218	62	a2	a2	PROPN
ejpam-5050	218	63	=	=	SYM
ejpam-5050	218	64	0	0	X
ejpam-5050	218	65	.	.	PUNCT
ejpam-5050	219	1	hence	hence	ADV
ejpam-5050	219	2	,	,	PUNCT
ejpam-5050	219	3	substituting	substitute	VERB
ejpam-5050	219	4	these	these	DET
ejpam-5050	219	5	values	value	NOUN
ejpam-5050	219	6	into	into	ADP
ejpam-5050	219	7	y0(x	y0(x	NUM
ejpam-5050	219	8	)	)	PUNCT
ejpam-5050	219	9	,	,	PUNCT
ejpam-5050	219	10	gives	give	VERB
ejpam-5050	219	11	y(x	y(x	NOUN
ejpam-5050	219	12	)	)	PUNCT
ejpam-5050	219	13	=	=	SYM
ejpam-5050	219	14	y0(x	y0(x	X
ejpam-5050	219	15	)	)	PUNCT
ejpam-5050	219	16	=	=	PUNCT
ejpam-5050	220	1	x3	x3	ADJ
ejpam-5050	220	2	−	−	PROPN
ejpam-5050	221	1	x	x	SYM
ejpam-5050	221	2	,	,	PUNCT
ejpam-5050	221	3	which	which	PRON
ejpam-5050	221	4	matches	match	VERB
ejpam-5050	221	5	the	the	DET
ejpam-5050	221	6	exact	exact	ADJ
ejpam-5050	221	7	analytical	analytical	ADJ
ejpam-5050	221	8	solution	solution	NOUN
ejpam-5050	221	9	of	of	ADP
ejpam-5050	221	10	(	(	PUNCT
ejpam-5050	221	11	18	18	NUM
ejpam-5050	221	12	)	)	PUNCT
ejpam-5050	221	13	.	.	PUNCT
ejpam-5050	222	1	example	example	NOUN
ejpam-5050	223	1	2	2	NUM
ejpam-5050	223	2	.	.	X
ejpam-5050	223	3	consider	consider	VERB
ejpam-5050	223	4	the	the	DET
ejpam-5050	223	5	bvp	bvp	NOUN
ejpam-5050	223	6	for	for	ADP
ejpam-5050	223	7	the	the	DET
ejpam-5050	223	8	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5050	223	9	bagley	bagley	NOUN
ejpam-5050	223	10	-	-	PUNCT
ejpam-5050	223	11	torvik	torvik	NOUN
ejpam-5050	223	12	equation	equation	NOUN
ejpam-5050	223	13	[	[	X
ejpam-5050	223	14	29	29	NUM
ejpam-5050	223	15	]	]	PUNCT
ejpam-5050	223	16	d3/2y(x	d3/2y(x	NOUN
ejpam-5050	223	17	)	)	PUNCT
ejpam-5050	224	1	+	+	NUM
ejpam-5050	224	2	y(x	y(x	NOUN
ejpam-5050	224	3	)	)	PUNCT
ejpam-5050	224	4	=	=	SYM
ejpam-5050	224	5	2x1/2	2x1/2	NUM
ejpam-5050	224	6	γ(3/2	γ(3/2	PROPN
ejpam-5050	224	7	)	)	PUNCT
ejpam-5050	225	1	+	+	CCONJ
ejpam-5050	226	1	x2	x2	NUM
ejpam-5050	226	2	−	−	PROPN
ejpam-5050	227	1	x	x	NOUN
ejpam-5050	227	2	,	,	PUNCT
ejpam-5050	227	3	y(0	y(0	PROPN
ejpam-5050	227	4	)	)	PUNCT
ejpam-5050	227	5	=	=	SYM
ejpam-5050	227	6	0	0	NUM
ejpam-5050	227	7	,	,	PUNCT
ejpam-5050	227	8	y(1	y(1	PROPN
ejpam-5050	227	9	)	)	PUNCT
ejpam-5050	227	10	=	=	SYM
ejpam-5050	227	11	0	0	NUM
ejpam-5050	227	12	,	,	PUNCT
ejpam-5050	227	13	(	(	PUNCT
ejpam-5050	227	14	22	22	NUM
ejpam-5050	227	15	)	)	PUNCT
ejpam-5050	227	16	which	which	PRON
ejpam-5050	227	17	admits	admit	VERB
ejpam-5050	227	18	the	the	DET
ejpam-5050	227	19	exact	exact	ADJ
ejpam-5050	227	20	analytical	analytical	ADJ
ejpam-5050	227	21	solution	solution	NOUN
ejpam-5050	227	22	as	as	SCONJ
ejpam-5050	227	23	follows	follow	VERB
ejpam-5050	227	24	y(x	y(x	NOUN
ejpam-5050	227	25	)	)	PUNCT
ejpam-5050	227	26	=	=	SYM
ejpam-5050	228	1	x2	x2	PROPN
ejpam-5050	228	2	−	−	PROPN
ejpam-5050	228	3	x.	x.	NOUN
ejpam-5050	228	4	to	to	PART
ejpam-5050	228	5	begin	begin	VERB
ejpam-5050	228	6	with	with	ADP
ejpam-5050	228	7	,	,	PUNCT
ejpam-5050	228	8	we	we	PRON
ejpam-5050	228	9	write	write	VERB
ejpam-5050	228	10	(	(	PUNCT
ejpam-5050	228	11	22	22	NUM
ejpam-5050	228	12	)	)	PUNCT
ejpam-5050	228	13	in	in	ADP
ejpam-5050	228	14	an	an	DET
ejpam-5050	228	15	operator	operator	NOUN
ejpam-5050	228	16	form	form	NOUN
ejpam-5050	228	17	as	as	SCONJ
ejpam-5050	228	18	follows	follow	VERB
ejpam-5050	228	19	d3/2y(x	d3/2y(x	NOUN
ejpam-5050	228	20	)	)	PUNCT
ejpam-5050	228	21	=	=	SYM
ejpam-5050	229	1	2x1/2	2x1/2	NUM
ejpam-5050	229	2	γ(3/2	γ(3/2	PROPN
ejpam-5050	229	3	)	)	PUNCT
ejpam-5050	230	1	+	+	CCONJ
ejpam-5050	231	1	x2	x2	PROPN
ejpam-5050	231	2	−	−	PROPN
ejpam-5050	231	3	x−	x−	PROPN
ejpam-5050	231	4	y(x	y(x	PROPN
ejpam-5050	231	5	)	)	PUNCT
ejpam-5050	231	6	.	.	PUNCT
ejpam-5050	232	1	(	(	PUNCT
ejpam-5050	232	2	23	23	NUM
ejpam-5050	232	3	)	)	PUNCT
ejpam-5050	232	4	next	next	ADV
ejpam-5050	232	5	,	,	PUNCT
ejpam-5050	232	6	upon	upon	SCONJ
ejpam-5050	232	7	deploying	deploy	VERB
ejpam-5050	232	8	the	the	DET
ejpam-5050	232	9	inverse	inverse	NOUN
ejpam-5050	232	10	operator	operator	NOUN
ejpam-5050	232	11	i3/2	i3/2	NOUN
ejpam-5050	232	12	on	on	ADP
ejpam-5050	232	13	both	both	DET
ejpam-5050	232	14	sides	side	NOUN
ejpam-5050	232	15	of	of	ADP
ejpam-5050	232	16	(	(	PUNCT
ejpam-5050	232	17	23	23	NUM
ejpam-5050	232	18	)	)	PUNCT
ejpam-5050	232	19	using	use	VERB
ejpam-5050	232	20	the	the	DET
ejpam-5050	232	21	property	property	NOUN
ejpam-5050	232	22	(	(	PUNCT
ejpam-5050	232	23	4	4	NUM
ejpam-5050	232	24	)	)	PUNCT
ejpam-5050	232	25	on	on	ADP
ejpam-5050	232	26	the	the	DET
ejpam-5050	232	27	left	left	ADJ
ejpam-5050	232	28	-	-	PUNCT
ejpam-5050	232	29	hand	hand	NOUN
ejpam-5050	232	30	side	side	NOUN
ejpam-5050	232	31	with	with	ADP
ejpam-5050	232	32	y′(0	y′(0	NOUN
ejpam-5050	232	33	)	)	PUNCT
ejpam-5050	232	34	=	=	SYM
ejpam-5050	232	35	c1	c1	NOUN
ejpam-5050	232	36	,	,	PUNCT
ejpam-5050	232	37	one	one	PRON
ejpam-5050	232	38	gets	get	VERB
ejpam-5050	232	39	i3/2[d3/2y(x	i3/2[d3/2y(x	NOUN
ejpam-5050	232	40	)	)	PUNCT
ejpam-5050	232	41	]	]	PUNCT
ejpam-5050	233	1	=	=	SYM
ejpam-5050	234	1	i3/2	i3/2	ADJ
ejpam-5050	234	2	[	[	PUNCT
ejpam-5050	234	3	2x1/2	2x1/2	NUM
ejpam-5050	234	4	γ(3/2	γ(3/2	PROPN
ejpam-5050	234	5	)	)	PUNCT
ejpam-5050	235	1	+	+	CCONJ
ejpam-5050	236	1	x2	x2	INTJ
ejpam-5050	236	2	−	−	PROPN
ejpam-5050	237	1	x	x	SYM
ejpam-5050	237	2	]	]	X
ejpam-5050	237	3	−	−	PROPN
ejpam-5050	237	4	i3/2[y(x	i3/2[y(x	NOUN
ejpam-5050	237	5	)	)	PUNCT
ejpam-5050	237	6	]	]	PUNCT
ejpam-5050	237	7	,	,	PUNCT
ejpam-5050	237	8	y(x)−	y(x)−	PROPN
ejpam-5050	237	9	1∑	1∑	PROPN
ejpam-5050	237	10	k=0	k=0	PROPN
ejpam-5050	237	11	yk(0	yk(0	PROPN
ejpam-5050	237	12	)	)	PUNCT
ejpam-5050	237	13	xk	xk	PROPN
ejpam-5050	238	1	γ(k	γ(k	PROPN
ejpam-5050	238	2	+	+	CCONJ
ejpam-5050	238	3	1	1	X
ejpam-5050	238	4	)	)	PUNCT
ejpam-5050	238	5	=	=	SYM
ejpam-5050	239	1	i3/2	i3/2	ADV
ejpam-5050	239	2	[	[	PUNCT
ejpam-5050	239	3	2x1/2	2x1/2	NUM
ejpam-5050	239	4	γ(3/2	γ(3/2	PROPN
ejpam-5050	239	5	)	)	PUNCT
ejpam-5050	240	1	+	+	CCONJ
ejpam-5050	241	1	x2	x2	INTJ
ejpam-5050	241	2	−	−	PROPN
ejpam-5050	242	1	x	x	SYM
ejpam-5050	242	2	]	]	X
ejpam-5050	242	3	−	−	PROPN
ejpam-5050	242	4	i3/2[y(x	i3/2[y(x	NOUN
ejpam-5050	242	5	)	)	PUNCT
ejpam-5050	242	6	]	]	PUNCT
ejpam-5050	242	7	,	,	PUNCT
ejpam-5050	242	8	y(x	y(x	PROPN
ejpam-5050	242	9	)	)	PUNCT
ejpam-5050	242	10	=	=	SYM
ejpam-5050	243	1	c1x+	c1x+	INTJ
ejpam-5050	244	1	i3/2	i3/2	NOUN
ejpam-5050	244	2	[	[	PUNCT
ejpam-5050	244	3	2x1/2	2x1/2	NUM
ejpam-5050	244	4	γ(3/2	γ(3/2	PROPN
ejpam-5050	244	5	)	)	PUNCT
ejpam-5050	245	1	+	+	CCONJ
ejpam-5050	246	1	x2	x2	INTJ
ejpam-5050	246	2	−	−	PROPN
ejpam-5050	247	1	x	x	SYM
ejpam-5050	247	2	]	]	X
ejpam-5050	247	3	−	−	NUM
ejpam-5050	247	4	i3/2[y(x	i3/2[y(x	NOUN
ejpam-5050	247	5	)	)	PUNCT
ejpam-5050	247	6	]	]	PUNCT
ejpam-5050	247	7	.	.	PUNCT
ejpam-5050	248	1	using	use	VERB
ejpam-5050	248	2	madm	madm	NOUN
ejpam-5050	248	3	and	and	CCONJ
ejpam-5050	248	4	the	the	DET
ejpam-5050	248	5	properties	property	NOUN
ejpam-5050	248	6	mentioned	mention	VERB
ejpam-5050	248	7	in	in	ADP
ejpam-5050	248	8	(	(	PUNCT
ejpam-5050	248	9	5	5	NUM
ejpam-5050	248	10	)	)	PUNCT
ejpam-5050	248	11	and	and	CCONJ
ejpam-5050	248	12	(	(	PUNCT
ejpam-5050	248	13	7	7	NUM
ejpam-5050	248	14	)	)	PUNCT
ejpam-5050	248	15	,	,	PUNCT
ejpam-5050	248	16	we	we	PRON
ejpam-5050	248	17	write	write	VERB
ejpam-5050	248	18	∞∑	∞∑	PROPN
ejpam-5050	248	19	n=0	n=0	NUM
ejpam-5050	248	20	yn(x	yn(x	X
ejpam-5050	248	21	)	)	PUNCT
ejpam-5050	249	1	=	=	SYM
ejpam-5050	249	2	c1x−pi3/2	c1x−pi3/2	PROPN
ejpam-5050	249	3	[	[	PUNCT
ejpam-5050	249	4	∞∑	∞∑	PROPN
ejpam-5050	249	5	n=0	n=0	NUM
ejpam-5050	249	6	anx	anx	NOUN
ejpam-5050	249	7	n	n	X
ejpam-5050	249	8	]	]	PUNCT
ejpam-5050	250	1	+	+	ADP
ejpam-5050	250	2	i3/2	i3/2	ADJ
ejpam-5050	250	3	[	[	PUNCT
ejpam-5050	250	4	∞∑	∞∑	ADJ
ejpam-5050	250	5	n=0	n=0	NUM
ejpam-5050	250	6	anx	anx	NOUN
ejpam-5050	250	7	n	n	X
ejpam-5050	250	8	]	]	PUNCT
ejpam-5050	251	1	+	+	ADP
ejpam-5050	251	2	i3/2	i3/2	ADV
ejpam-5050	251	3	[	[	PUNCT
ejpam-5050	251	4	2x1/2	2x1/2	NUM
ejpam-5050	251	5	γ(3/2	γ(3/2	PROPN
ejpam-5050	251	6	)	)	PUNCT
ejpam-5050	252	1	+	+	NOUN
ejpam-5050	252	2	x2−x	x2−x	PROPN
ejpam-5050	252	3	]	]	PUNCT
ejpam-5050	252	4	−i3/2[yn(x	−i3/2[yn(x	PROPN
ejpam-5050	252	5	)	)	PUNCT
ejpam-5050	252	6	]	]	PUNCT
ejpam-5050	252	7	,	,	PUNCT
ejpam-5050	252	8	m.	m.	PROPN
ejpam-5050	252	9	al	al	PROPN
ejpam-5050	252	10	-	-	PUNCT
ejpam-5050	252	11	mazmumy	mazmumy	PROPN
ejpam-5050	252	12	,	,	PUNCT
ejpam-5050	252	13	m.	m.	NOUN
ejpam-5050	252	14	alsulami	alsulami	PROPN
ejpam-5050	252	15	/	/	SYM
ejpam-5050	252	16	eur	eur	PROPN
ejpam-5050	252	17	.	.	PUNCT
ejpam-5050	253	1	j.	j.	PROPN
ejpam-5050	253	2	pure	pure	PROPN
ejpam-5050	253	3	appl	appl	PROPN
ejpam-5050	253	4	.	.	PROPN
ejpam-5050	253	5	math	math	PROPN
ejpam-5050	253	6	,	,	PUNCT
ejpam-5050	253	7	17	17	NUM
ejpam-5050	253	8	(	(	PUNCT
ejpam-5050	253	9	1	1	NUM
ejpam-5050	253	10	)	)	PUNCT
ejpam-5050	253	11	(	(	PUNCT
ejpam-5050	253	12	2024	2024	NUM
ejpam-5050	253	13	)	)	PUNCT
ejpam-5050	253	14	,	,	PUNCT
ejpam-5050	253	15	546	546	NUM
ejpam-5050	253	16	-	-	SYM
ejpam-5050	253	17	568	568	NUM
ejpam-5050	253	18	556	556	NUM
ejpam-5050	253	19	upon	upon	SCONJ
ejpam-5050	253	20	which	which	PRON
ejpam-5050	253	21	we	we	PRON
ejpam-5050	253	22	iteratively	iteratively	ADV
ejpam-5050	253	23	consider	consider	VERB
ejpam-5050	253	24	y0(x	y0(x	PRON
ejpam-5050	253	25	)	)	PUNCT
ejpam-5050	253	26	=	=	PUNCT
ejpam-5050	254	1	c1x+	c1x+	INTJ
ejpam-5050	255	1	i3/2	i3/2	NOUN
ejpam-5050	255	2	[	[	PUNCT
ejpam-5050	255	3	2x1/2	2x1/2	NUM
ejpam-5050	255	4	γ(3/2	γ(3/2	PROPN
ejpam-5050	255	5	)	)	PUNCT
ejpam-5050	256	1	+	+	CCONJ
ejpam-5050	257	1	x2	x2	INTJ
ejpam-5050	257	2	−	−	PROPN
ejpam-5050	257	3	x	x	X
ejpam-5050	257	4	]	]	X
ejpam-5050	258	1	+	+	CCONJ
ejpam-5050	258	2	i3/2	i3/2	ADV
ejpam-5050	258	3	[	[	PUNCT
ejpam-5050	258	4	∞∑	∞∑	ADJ
ejpam-5050	258	5	n=0	n=0	NUM
ejpam-5050	258	6	anx	anx	NOUN
ejpam-5050	258	7	n	n	NOUN
ejpam-5050	258	8	]	]	PUNCT
ejpam-5050	258	9	,	,	PUNCT
ejpam-5050	258	10	=	=	SYM
ejpam-5050	258	11	c1x+	c1x+	NOUN
ejpam-5050	258	12	x2	x2	NOUN
ejpam-5050	259	1	+	+	CCONJ
ejpam-5050	259	2	32	32	NUM
ejpam-5050	259	3	105	105	NUM
ejpam-5050	259	4	√	√	PROPN
ejpam-5050	259	5	π	π	PROPN
ejpam-5050	259	6	x7/2	x7/2	PROPN
ejpam-5050	260	1	−	−	NUM
ejpam-5050	260	2	8	8	NUM
ejpam-5050	260	3	15	15	NUM
ejpam-5050	260	4	√	√	PROPN
ejpam-5050	260	5	π	π	PROPN
ejpam-5050	260	6	x5/2	x5/2	PROPN
ejpam-5050	261	1	+	+	CCONJ
ejpam-5050	262	1	4a0	4a0	NUM
ejpam-5050	262	2	3	3	NUM
ejpam-5050	262	3	√	√	PROPN
ejpam-5050	262	4	π	π	PROPN
ejpam-5050	262	5	x3/2	x3/2	PROPN
ejpam-5050	263	1	+	+	NUM
ejpam-5050	263	2	8a1	8a1	NUM
ejpam-5050	263	3	15	15	NUM
ejpam-5050	263	4	√	√	PROPN
ejpam-5050	263	5	π	π	X
ejpam-5050	263	6	x5/2	x5/2	PROPN
ejpam-5050	264	1	+	+	CCONJ
ejpam-5050	265	1	32a2	32a2	NUM
ejpam-5050	265	2	105	105	NUM
ejpam-5050	265	3	√	√	PROPN
ejpam-5050	265	4	π	π	X
ejpam-5050	265	5	x7/2	x7/2	PROPN
ejpam-5050	266	1	+	+	CCONJ
ejpam-5050	267	1	64a3	64a3	NUM
ejpam-5050	267	2	315	315	NUM
ejpam-5050	267	3	√	√	PROPN
ejpam-5050	267	4	π	π	PROPN
ejpam-5050	267	5	x9/2	x9/2	PROPN
ejpam-5050	268	1	+	+	CCONJ
ejpam-5050	268	2	...	...	PUNCT
ejpam-5050	268	3	and	and	CCONJ
ejpam-5050	268	4	y1(x	y1(x	NOUN
ejpam-5050	268	5	)	)	PUNCT
ejpam-5050	268	6	=	=	VERB
ejpam-5050	269	1	−pi3/2	−pi3/2	NOUN
ejpam-5050	269	2	[	[	PUNCT
ejpam-5050	269	3	∞∑	∞∑	ADJ
ejpam-5050	269	4	n=0	n=0	NUM
ejpam-5050	269	5	anx	anx	NOUN
ejpam-5050	269	6	n	n	NOUN
ejpam-5050	269	7	]	]	PUNCT
ejpam-5050	269	8	−	−	ADP
ejpam-5050	269	9	i3/2[y0(x	i3/2[y0(x	NOUN
ejpam-5050	269	10	)	)	PUNCT
ejpam-5050	269	11	]	]	PUNCT
ejpam-5050	269	12	,	,	PUNCT
ejpam-5050	269	13	=	=	SYM
ejpam-5050	269	14	−p	−p	NOUN
ejpam-5050	269	15	[	[	PUNCT
ejpam-5050	269	16	4a0	4a0	NUM
ejpam-5050	269	17	3	3	NUM
ejpam-5050	269	18	√	√	PROPN
ejpam-5050	269	19	π	π	PROPN
ejpam-5050	269	20	x3/2	x3/2	PROPN
ejpam-5050	270	1	+	+	NUM
ejpam-5050	270	2	8a1	8a1	NUM
ejpam-5050	270	3	15	15	NUM
ejpam-5050	270	4	√	√	PROPN
ejpam-5050	270	5	π	π	X
ejpam-5050	270	6	x5/2	x5/2	PROPN
ejpam-5050	271	1	+	+	CCONJ
ejpam-5050	272	1	32a2	32a2	NUM
ejpam-5050	272	2	105	105	NUM
ejpam-5050	272	3	√	√	PROPN
ejpam-5050	272	4	π	π	X
ejpam-5050	272	5	x7/2	x7/2	PROPN
ejpam-5050	273	1	+	+	CCONJ
ejpam-5050	273	2	64a3	64a3	NUM
ejpam-5050	273	3	315	315	NUM
ejpam-5050	273	4	√	√	PROPN
ejpam-5050	273	5	π	π	PROPN
ejpam-5050	273	6	x9/2	x9/2	PUNCT
ejpam-5050	274	1	+	+	CCONJ
ejpam-5050	274	2	...	...	PUNCT
ejpam-5050	274	3	]	]	PUNCT
ejpam-5050	275	1	−	−	NOUN
ejpam-5050	276	1	8c1	8c1	NUM
ejpam-5050	276	2	15	15	NUM
ejpam-5050	276	3	√	√	PROPN
ejpam-5050	276	4	π	π	PROPN
ejpam-5050	276	5	x5/2	x5/2	PROPN
ejpam-5050	276	6	−	−	PROPN
ejpam-5050	276	7	32	32	NUM
ejpam-5050	276	8	105	105	NUM
ejpam-5050	277	1	√	√	PROPN
ejpam-5050	277	2	π	π	PROPN
ejpam-5050	277	3	x7/2	x7/2	PROPN
ejpam-5050	278	1	−	−	NUM
ejpam-5050	278	2	1	1	NUM
ejpam-5050	278	3	60	60	NUM
ejpam-5050	278	4	x5	x5	NOUN
ejpam-5050	278	5	+	+	CCONJ
ejpam-5050	278	6	1	1	NUM
ejpam-5050	278	7	24	24	NUM
ejpam-5050	278	8	x4	x4	PROPN
ejpam-5050	278	9	−	−	PROPN
ejpam-5050	278	10	a0	a0	PROPN
ejpam-5050	278	11	6	6	NUM
ejpam-5050	278	12	x3	x3	ADJ
ejpam-5050	278	13	−	−	NOUN
ejpam-5050	278	14	a1	a1	NOUN
ejpam-5050	278	15	24	24	NUM
ejpam-5050	278	16	x4	x4	PROPN
ejpam-5050	278	17	−	−	PROPN
ejpam-5050	278	18	a2	a2	PROPN
ejpam-5050	278	19	60	60	NUM
ejpam-5050	278	20	x5	x5	PROPN
ejpam-5050	278	21	−	−	PROPN
ejpam-5050	278	22	3a3	3a3	NUM
ejpam-5050	278	23	360	360	NUM
ejpam-5050	278	24	x6	x6	PROPN
ejpam-5050	278	25	+	+	CCONJ
ejpam-5050	278	26	...	...	PUNCT
ejpam-5050	278	27	now	now	ADV
ejpam-5050	278	28	,	,	PUNCT
ejpam-5050	278	29	setting	set	VERB
ejpam-5050	278	30	y1(x	y1(x	NOUN
ejpam-5050	278	31	)	)	PUNCT
ejpam-5050	278	32	=	=	SYM
ejpam-5050	278	33	0	0	NUM
ejpam-5050	278	34	with	with	ADP
ejpam-5050	278	35	p	p	NOUN
ejpam-5050	278	36	=	=	SYM
ejpam-5050	278	37	1	1	NUM
ejpam-5050	278	38	and	and	CCONJ
ejpam-5050	278	39	collecting	collect	VERB
ejpam-5050	278	40	the	the	DET
ejpam-5050	278	41	related	related	ADJ
ejpam-5050	278	42	terms	term	NOUN
ejpam-5050	278	43	while	while	SCONJ
ejpam-5050	278	44	equating	equate	VERB
ejpam-5050	278	45	the	the	DET
ejpam-5050	278	46	coefficients	coefficient	NOUN
ejpam-5050	278	47	of	of	ADP
ejpam-5050	278	48	xn	xn	PROPN
ejpam-5050	278	49	in	in	ADP
ejpam-5050	278	50	both	both	DET
ejpam-5050	278	51	sides	side	NOUN
ejpam-5050	278	52	of	of	ADP
ejpam-5050	278	53	the	the	DET
ejpam-5050	278	54	above	above	ADJ
ejpam-5050	278	55	expression	expression	NOUN
ejpam-5050	278	56	,	,	PUNCT
ejpam-5050	278	57	one	one	PRON
ejpam-5050	278	58	obtains	obtain	VERB
ejpam-5050	278	59	y1(x	y1(x	NOUN
ejpam-5050	278	60	)	)	PUNCT
ejpam-5050	278	61	=	=	PUNCT
ejpam-5050	279	1	−a0	−a0	ADJ
ejpam-5050	279	2	6	6	NUM
ejpam-5050	279	3	x3	x3	ADJ
ejpam-5050	279	4	+	+	CCONJ
ejpam-5050	279	5	(	(	PUNCT
ejpam-5050	279	6	1	1	NUM
ejpam-5050	279	7	24	24	NUM
ejpam-5050	279	8	−	−	PROPN
ejpam-5050	279	9	a1	a1	NOUN
ejpam-5050	279	10	24	24	NUM
ejpam-5050	279	11	)	)	PUNCT
ejpam-5050	279	12	x4	x4	PROPN
ejpam-5050	279	13	−	−	PROPN
ejpam-5050	280	1	(	(	PUNCT
ejpam-5050	280	2	1	1	NUM
ejpam-5050	280	3	60	60	NUM
ejpam-5050	280	4	+	+	NUM
ejpam-5050	280	5	a2	a2	PROPN
ejpam-5050	280	6	60	60	NUM
ejpam-5050	280	7	)	)	PUNCT
ejpam-5050	280	8	x5	x5	PROPN
ejpam-5050	280	9	−	−	PROPN
ejpam-5050	280	10	3a3	3a3	NUM
ejpam-5050	280	11	360	360	NUM
ejpam-5050	280	12	x6	x6	PROPN
ejpam-5050	280	13	+	+	CCONJ
ejpam-5050	280	14	...	...	PUNCT
ejpam-5050	281	1	=	=	SYM
ejpam-5050	281	2	0	0	X
ejpam-5050	281	3	.	.	PUNCT
ejpam-5050	282	1	hence	hence	ADV
ejpam-5050	282	2	,	,	PUNCT
ejpam-5050	282	3	we	we	PRON
ejpam-5050	282	4	acquire	acquire	VERB
ejpam-5050	282	5	a0	a0	NOUN
ejpam-5050	282	6	=	=	SYM
ejpam-5050	282	7	a3	a3	PROPN
ejpam-5050	282	8	=	=	SYM
ejpam-5050	282	9	0	0	NUM
ejpam-5050	282	10	,	,	PUNCT
ejpam-5050	282	11	a1	a1	NOUN
ejpam-5050	282	12	=	=	SYM
ejpam-5050	282	13	1	1	NUM
ejpam-5050	282	14	,	,	PUNCT
ejpam-5050	282	15	and	and	CCONJ
ejpam-5050	282	16	a2	a2	PROPN
ejpam-5050	282	17	=	=	SYM
ejpam-5050	282	18	−1	−1	NOUN
ejpam-5050	282	19	,	,	PUNCT
ejpam-5050	282	20	which	which	PRON
ejpam-5050	282	21	when	when	SCONJ
ejpam-5050	282	22	these	these	DET
ejpam-5050	282	23	values	value	NOUN
ejpam-5050	282	24	of	of	ADP
ejpam-5050	282	25	a0	a0	PROPN
ejpam-5050	282	26	,	,	PUNCT
ejpam-5050	282	27	a1	a1	PROPN
ejpam-5050	282	28	,	,	PUNCT
ejpam-5050	282	29	a2	a2	PROPN
ejpam-5050	282	30	and	and	CCONJ
ejpam-5050	282	31	a3	a3	NOUN
ejpam-5050	282	32	are	be	AUX
ejpam-5050	282	33	substituted	substitute	VERB
ejpam-5050	282	34	in	in	ADP
ejpam-5050	282	35	y0(x	y0(x	NOUN
ejpam-5050	282	36	)	)	PUNCT
ejpam-5050	282	37	,	,	PUNCT
ejpam-5050	282	38	where	where	SCONJ
ejpam-5050	282	39	yn(x	yn(x	X
ejpam-5050	282	40	)	)	PUNCT
ejpam-5050	282	41	=	=	SYM
ejpam-5050	282	42	0	0	NUM
ejpam-5050	282	43	,	,	PUNCT
ejpam-5050	282	44	for	for	ADP
ejpam-5050	282	45	n	n	PROPN
ejpam-5050	282	46	⩾	⩾	PROPN
ejpam-5050	282	47	1	1	NUM
ejpam-5050	282	48	reveals	reveal	VERB
ejpam-5050	282	49	y(x	y(x	NOUN
ejpam-5050	282	50	)	)	PUNCT
ejpam-5050	283	1	=	=	SYM
ejpam-5050	283	2	y0(x	y0(x	X
ejpam-5050	283	3	)	)	PUNCT
ejpam-5050	283	4	=	=	SYM
ejpam-5050	284	1	c1x+	c1x+	NOUN
ejpam-5050	285	1	x2	x2	NOUN
ejpam-5050	286	1	+	+	CCONJ
ejpam-5050	286	2	32	32	NUM
ejpam-5050	286	3	105	105	NUM
ejpam-5050	286	4	√	√	PROPN
ejpam-5050	286	5	π	π	PROPN
ejpam-5050	286	6	x7/2	x7/2	PROPN
ejpam-5050	287	1	−	−	NUM
ejpam-5050	287	2	8	8	NUM
ejpam-5050	287	3	15	15	NUM
ejpam-5050	287	4	√	√	PROPN
ejpam-5050	287	5	π	π	PROPN
ejpam-5050	287	6	x5/2	x5/2	PROPN
ejpam-5050	288	1	+	+	CCONJ
ejpam-5050	288	2	8	8	NUM
ejpam-5050	288	3	15	15	NUM
ejpam-5050	288	4	√	√	PROPN
ejpam-5050	288	5	π	π	PROPN
ejpam-5050	288	6	x5/2	x5/2	PROPN
ejpam-5050	289	1	−	−	PROPN
ejpam-5050	289	2	32	32	NUM
ejpam-5050	289	3	105	105	NUM
ejpam-5050	290	1	√	√	PROPN
ejpam-5050	290	2	π	π	X
ejpam-5050	290	3	x7/2	x7/2	PROPN
ejpam-5050	291	1	+	+	CCONJ
ejpam-5050	291	2	...	...	PUNCT
ejpam-5050	292	1	=	=	SYM
ejpam-5050	292	2	c1x+	c1x+	NOUN
ejpam-5050	292	3	x2	x2	NOUN
ejpam-5050	293	1	+	+	CCONJ
ejpam-5050	293	2	...	...	PUNCT
ejpam-5050	293	3	lastly	lastly	ADV
ejpam-5050	293	4	,	,	PUNCT
ejpam-5050	293	5	when	when	SCONJ
ejpam-5050	293	6	cancelling	cancel	VERB
ejpam-5050	293	7	the	the	DET
ejpam-5050	293	8	noise	noise	NOUN
ejpam-5050	293	9	terms	term	NOUN
ejpam-5050	293	10	,	,	PUNCT
ejpam-5050	293	11	alongside	alongside	ADP
ejpam-5050	293	12	using	use	VERB
ejpam-5050	293	13	the	the	DET
ejpam-5050	293	14	second	second	ADJ
ejpam-5050	293	15	boundary	boundary	ADJ
ejpam-5050	293	16	prescription	prescription	NOUN
ejpam-5050	293	17	of	of	ADP
ejpam-5050	293	18	y(1	y(1	PROPN
ejpam-5050	293	19	)	)	PUNCT
ejpam-5050	294	1	=	=	SYM
ejpam-5050	294	2	0	0	NUM
ejpam-5050	294	3	,	,	PUNCT
ejpam-5050	294	4	one	one	NOUN
ejpam-5050	294	5	obtains	obtain	VERB
ejpam-5050	294	6	c1	c1	NOUN
ejpam-5050	294	7	=	=	SYM
ejpam-5050	294	8	−1	−1	NOUN
ejpam-5050	294	9	,	,	PUNCT
ejpam-5050	294	10	so	so	SCONJ
ejpam-5050	294	11	that	that	SCONJ
ejpam-5050	294	12	y(x	y(x	VERB
ejpam-5050	294	13	)	)	PUNCT
ejpam-5050	295	1	=	=	SYM
ejpam-5050	295	2	x2	x2	NUM
ejpam-5050	295	3	−	−	PROPN
ejpam-5050	296	1	x	x	SYM
ejpam-5050	296	2	,	,	PUNCT
ejpam-5050	296	3	which	which	PRON
ejpam-5050	296	4	matches	match	VERB
ejpam-5050	296	5	the	the	DET
ejpam-5050	296	6	exact	exact	ADJ
ejpam-5050	296	7	analytical	analytical	ADJ
ejpam-5050	296	8	solution	solution	NOUN
ejpam-5050	296	9	for	for	ADP
ejpam-5050	296	10	(	(	PUNCT
ejpam-5050	296	11	22	22	NUM
ejpam-5050	296	12	)	)	PUNCT
ejpam-5050	296	13	.	.	PUNCT
ejpam-5050	297	1	example	example	NOUN
ejpam-5050	298	1	3	3	X
ejpam-5050	298	2	.	.	X
ejpam-5050	298	3	we	we	PRON
ejpam-5050	298	4	make	make	VERB
ejpam-5050	298	5	consideration	consideration	NOUN
ejpam-5050	298	6	to	to	ADP
ejpam-5050	298	7	the	the	DET
ejpam-5050	298	8	bvp	bvp	NOUN
ejpam-5050	298	9	for	for	ADP
ejpam-5050	298	10	the	the	DET
ejpam-5050	298	11	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5050	298	12	bagley	bagley	NOUN
ejpam-5050	298	13	-	-	PUNCT
ejpam-5050	298	14	torvik	torvik	NOUN
ejpam-5050	298	15	[	[	X
ejpam-5050	298	16	40	40	NUM
ejpam-5050	298	17	]	]	X
ejpam-5050	298	18	d2y(x	d2y(x	PROPN
ejpam-5050	298	19	)	)	PUNCT
ejpam-5050	298	20	+	+	NOUN
ejpam-5050	298	21	d3/2y(x	d3/2y(x	NOUN
ejpam-5050	298	22	)	)	PUNCT
ejpam-5050	299	1	+	+	NUM
ejpam-5050	299	2	y(x	y(x	NOUN
ejpam-5050	299	3	)	)	PUNCT
ejpam-5050	300	1	=	=	PUNCT
ejpam-5050	301	1	x+	x+	SYM
ejpam-5050	301	2	1	1	NUM
ejpam-5050	301	3	,	,	PUNCT
ejpam-5050	301	4	y(0	y(0	PROPN
ejpam-5050	301	5	)	)	PUNCT
ejpam-5050	301	6	=	=	SYM
ejpam-5050	301	7	1	1	NUM
ejpam-5050	301	8	,	,	PUNCT
ejpam-5050	301	9	y(1	y(1	PROPN
ejpam-5050	301	10	)	)	PUNCT
ejpam-5050	302	1	=	=	SYM
ejpam-5050	302	2	2	2	NUM
ejpam-5050	302	3	,	,	PUNCT
ejpam-5050	302	4	(	(	PUNCT
ejpam-5050	302	5	24	24	NUM
ejpam-5050	302	6	)	)	PUNCT
ejpam-5050	302	7	that	that	PRON
ejpam-5050	302	8	admits	admit	VERB
ejpam-5050	302	9	y(x	y(x	NOUN
ejpam-5050	302	10	)	)	PUNCT
ejpam-5050	302	11	=	=	PUNCT
ejpam-5050	303	1	x+	x+	PUNCT
ejpam-5050	303	2	1	1	NUM
ejpam-5050	303	3	as	as	ADP
ejpam-5050	303	4	its	its	PRON
ejpam-5050	303	5	exact	exact	ADJ
ejpam-5050	303	6	analytical	analytical	ADJ
ejpam-5050	303	7	solution	solution	NOUN
ejpam-5050	303	8	.	.	PUNCT
ejpam-5050	304	1	m.	m.	NOUN
ejpam-5050	304	2	al	al	PROPN
ejpam-5050	304	3	-	-	PUNCT
ejpam-5050	304	4	mazmumy	mazmumy	PROPN
ejpam-5050	304	5	,	,	PUNCT
ejpam-5050	304	6	m.	m.	NOUN
ejpam-5050	304	7	alsulami	alsulami	PROPN
ejpam-5050	304	8	/	/	SYM
ejpam-5050	304	9	eur	eur	PROPN
ejpam-5050	304	10	.	.	PUNCT
ejpam-5050	305	1	j.	j.	PROPN
ejpam-5050	305	2	pure	pure	PROPN
ejpam-5050	305	3	appl	appl	PROPN
ejpam-5050	305	4	.	.	PROPN
ejpam-5050	305	5	math	math	PROPN
ejpam-5050	305	6	,	,	PUNCT
ejpam-5050	305	7	17	17	NUM
ejpam-5050	305	8	(	(	PUNCT
ejpam-5050	305	9	1	1	NUM
ejpam-5050	305	10	)	)	PUNCT
ejpam-5050	305	11	(	(	PUNCT
ejpam-5050	305	12	2024	2024	NUM
ejpam-5050	305	13	)	)	PUNCT
ejpam-5050	305	14	,	,	PUNCT
ejpam-5050	305	15	546	546	NUM
ejpam-5050	305	16	-	-	SYM
ejpam-5050	305	17	568	568	NUM
ejpam-5050	305	18	557	557	NUM
ejpam-5050	305	19	algorithm	algorithm	NOUN
ejpam-5050	305	20	1	1	NUM
ejpam-5050	305	21	:	:	PUNCT
ejpam-5050	305	22	we	we	PRON
ejpam-5050	305	23	re	re	VERB
ejpam-5050	305	24	-	-	VERB
ejpam-5050	305	25	write	write	ADJ
ejpam-5050	305	26	(	(	PUNCT
ejpam-5050	305	27	24	24	NUM
ejpam-5050	305	28	)	)	PUNCT
ejpam-5050	305	29	using	use	VERB
ejpam-5050	305	30	operator	operator	NOUN
ejpam-5050	305	31	notation	notation	NOUN
ejpam-5050	305	32	as	as	SCONJ
ejpam-5050	305	33	follows	follow	VERB
ejpam-5050	305	34	ly(x	ly(x	PUNCT
ejpam-5050	305	35	)	)	PUNCT
ejpam-5050	305	36	=	=	SYM
ejpam-5050	305	37	x+	x+	PROPN
ejpam-5050	305	38	1−d3/2y(x)−	1−d3/2y(x)−	NUM
ejpam-5050	305	39	y(x	y(x	PROPN
ejpam-5050	305	40	)	)	PUNCT
ejpam-5050	305	41	.	.	PUNCT
ejpam-5050	306	1	(	(	PUNCT
ejpam-5050	306	2	25	25	NUM
ejpam-5050	306	3	)	)	PUNCT
ejpam-5050	306	4	applying	apply	VERB
ejpam-5050	306	5	inverse	inverse	NOUN
ejpam-5050	306	6	operator	operator	NOUN
ejpam-5050	306	7	l−1	l−1	PROPN
ejpam-5050	306	8	(	(	PUNCT
ejpam-5050	306	9	.	.	PUNCT
ejpam-5050	306	10	)	)	PUNCT
ejpam-5050	307	1	=	=	PUNCT
ejpam-5050	308	1	∫	∫	PUNCT
ejpam-5050	308	2	x	x	SYM
ejpam-5050	308	3	0	0	NUM
ejpam-5050	308	4	∫	∫	PROPN
ejpam-5050	308	5	x	x	SYM
ejpam-5050	308	6	0	0	PUNCT
ejpam-5050	308	7	(	(	PUNCT
ejpam-5050	308	8	.)dxdx	.)dxdx	X
ejpam-5050	308	9	on	on	ADP
ejpam-5050	308	10	both	both	DET
ejpam-5050	308	11	sides	side	NOUN
ejpam-5050	308	12	of	of	ADP
ejpam-5050	308	13	(	(	PUNCT
ejpam-5050	308	14	25	25	NUM
ejpam-5050	308	15	)	)	PUNCT
ejpam-5050	308	16	such	such	ADJ
ejpam-5050	308	17	that	that	DET
ejpam-5050	308	18	y′(0	y′(0	NOUN
ejpam-5050	308	19	)	)	PUNCT
ejpam-5050	308	20	=	=	PROPN
ejpam-5050	308	21	c1	c1	PROPN
ejpam-5050	308	22	gives	give	VERB
ejpam-5050	308	23	y(x	y(x	NOUN
ejpam-5050	308	24	)	)	PUNCT
ejpam-5050	308	25	=	=	SYM
ejpam-5050	308	26	1	1	NUM
ejpam-5050	308	27	+	+	NUM
ejpam-5050	308	28	c1x−	c1x−	NOUN
ejpam-5050	308	29	l−1[d3/2y(x)]−	l−1[d3/2y(x)]−	NOUN
ejpam-5050	308	30	l−1[y(x	l−1[y(x	NOUN
ejpam-5050	308	31	)	)	PUNCT
ejpam-5050	308	32	]	]	PUNCT
ejpam-5050	309	1	+	+	CCONJ
ejpam-5050	309	2	l−1[x+	l−1[x+	ADV
ejpam-5050	309	3	1	1	NUM
ejpam-5050	309	4	]	]	PUNCT
ejpam-5050	309	5	.	.	PUNCT
ejpam-5050	310	1	further	far	ADV
ejpam-5050	310	2	,	,	PUNCT
ejpam-5050	310	3	using	use	VERB
ejpam-5050	310	4	the	the	DET
ejpam-5050	310	5	madm	madm	ADJ
ejpam-5050	310	6	procedure	procedure	NOUN
ejpam-5050	310	7	along	along	ADP
ejpam-5050	310	8	with	with	ADP
ejpam-5050	310	9	(	(	PUNCT
ejpam-5050	310	10	6	6	NUM
ejpam-5050	310	11	)	)	PUNCT
ejpam-5050	310	12	,	,	PUNCT
ejpam-5050	310	13	we	we	PRON
ejpam-5050	310	14	gain	gain	VERB
ejpam-5050	310	15	∞∑	∞∑	PRON
ejpam-5050	310	16	n=0	n=0	NUM
ejpam-5050	310	17	yn(x	yn(x	X
ejpam-5050	310	18	)	)	PUNCT
ejpam-5050	310	19	=	=	SYM
ejpam-5050	311	1	1	1	NUM
ejpam-5050	311	2	+	+	CCONJ
ejpam-5050	311	3	c1x−	c1x−	ADJ
ejpam-5050	311	4	pl−1	pl−1	NOUN
ejpam-5050	311	5	[	[	PUNCT
ejpam-5050	311	6	∞∑	∞∑	NUM
ejpam-5050	311	7	n=0	n=0	NUM
ejpam-5050	311	8	anx	anx	NOUN
ejpam-5050	311	9	n	n	NOUN
ejpam-5050	311	10	]	]	PUNCT
ejpam-5050	311	11	+	+	CCONJ
ejpam-5050	311	12	l−1	l−1	NOUN
ejpam-5050	311	13	[	[	PUNCT
ejpam-5050	311	14	∞∑	∞∑	PROPN
ejpam-5050	311	15	n=0	n=0	NUM
ejpam-5050	311	16	anx	anx	NOUN
ejpam-5050	311	17	n	n	NOUN
ejpam-5050	311	18	]	]	PUNCT
ejpam-5050	311	19	−	−	PROPN
ejpam-5050	311	20	l−1	l−1	PROPN
ejpam-5050	311	21	[	[	PUNCT
ejpam-5050	311	22	d3/2	d3/2	ADJ
ejpam-5050	311	23	∞∑	∞∑	PROPN
ejpam-5050	311	24	n=0	n=0	NUM
ejpam-5050	311	25	yn(x	yn(x	X
ejpam-5050	311	26	)	)	PUNCT
ejpam-5050	311	27	]	]	PUNCT
ejpam-5050	312	1	−	−	PROPN
ejpam-5050	312	2	l−1	l−1	PROPN
ejpam-5050	312	3	[	[	PUNCT
ejpam-5050	312	4	∞∑	∞∑	PROPN
ejpam-5050	312	5	n=0	n=0	NUM
ejpam-5050	312	6	yn(x	yn(x	NUM
ejpam-5050	312	7	)	)	PUNCT
ejpam-5050	312	8	]	]	PUNCT
ejpam-5050	313	1	+	+	CCONJ
ejpam-5050	313	2	l−1[x+	l−1[x+	ADV
ejpam-5050	313	3	1	1	NUM
ejpam-5050	313	4	]	]	PUNCT
ejpam-5050	313	5	,	,	PUNCT
ejpam-5050	313	6	upon	upon	SCONJ
ejpam-5050	313	7	which	which	PRON
ejpam-5050	313	8	the	the	DET
ejpam-5050	313	9	related	relate	VERB
ejpam-5050	313	10	iterates	iterate	NOUN
ejpam-5050	313	11	y0(x	y0(x	NUM
ejpam-5050	313	12	)	)	PUNCT
ejpam-5050	313	13	and	and	CCONJ
ejpam-5050	313	14	y1(x	y1(x	NOUN
ejpam-5050	313	15	)	)	PUNCT
ejpam-5050	313	16	are	be	AUX
ejpam-5050	313	17	considered	consider	VERB
ejpam-5050	313	18	from	from	ADP
ejpam-5050	313	19	the	the	DET
ejpam-5050	313	20	latter	latter	ADJ
ejpam-5050	313	21	equation	equation	NOUN
ejpam-5050	313	22	as	as	SCONJ
ejpam-5050	313	23	follows	follow	VERB
ejpam-5050	313	24	y0(x	y0(x	NUM
ejpam-5050	313	25	)	)	PUNCT
ejpam-5050	313	26	=	=	SYM
ejpam-5050	314	1	1	1	NUM
ejpam-5050	314	2	+	+	NUM
ejpam-5050	314	3	c1x+	c1x+	PRON
ejpam-5050	314	4	l−1	l−1	PROPN
ejpam-5050	314	5	[	[	PUNCT
ejpam-5050	314	6	∞∑	∞∑	PROPN
ejpam-5050	314	7	n=0	n=0	NUM
ejpam-5050	314	8	anx	anx	NOUN
ejpam-5050	314	9	n	n	NOUN
ejpam-5050	314	10	]	]	PUNCT
ejpam-5050	314	11	,	,	PUNCT
ejpam-5050	314	12	=	=	SYM
ejpam-5050	314	13	1	1	NUM
ejpam-5050	314	14	+	+	NUM
ejpam-5050	314	15	c1x+	c1x+	VERB
ejpam-5050	314	16	1	1	NUM
ejpam-5050	314	17	2	2	NUM
ejpam-5050	314	18	a0x	a0x	ADP
ejpam-5050	314	19	2	2	NUM
ejpam-5050	314	20	+	+	SYM
ejpam-5050	314	21	1	1	NUM
ejpam-5050	314	22	6	6	NUM
ejpam-5050	314	23	a1x	a1x	SYM
ejpam-5050	314	24	3	3	NUM
ejpam-5050	314	25	+	+	CCONJ
ejpam-5050	314	26	1	1	NUM
ejpam-5050	314	27	12	12	NUM
ejpam-5050	314	28	a2x	a2x	ADP
ejpam-5050	314	29	4	4	NUM
ejpam-5050	314	30	+	+	NUM
ejpam-5050	314	31	...	...	PUNCT
ejpam-5050	314	32	and	and	CCONJ
ejpam-5050	314	33	y1(x	y1(x	NOUN
ejpam-5050	314	34	)	)	PUNCT
ejpam-5050	314	35	=	=	VERB
ejpam-5050	315	1	l−1[1	l−1[1	X
ejpam-5050	316	1	+	+	CCONJ
ejpam-5050	316	2	x]−	x]−	NUM
ejpam-5050	316	3	pl−1	pl−1	NOUN
ejpam-5050	316	4	[	[	PUNCT
ejpam-5050	316	5	∞∑	∞∑	NUM
ejpam-5050	316	6	n=0	n=0	NUM
ejpam-5050	316	7	anx	anx	NOUN
ejpam-5050	316	8	n	n	NOUN
ejpam-5050	316	9	]	]	PUNCT
ejpam-5050	316	10	−	−	PROPN
ejpam-5050	316	11	l−1	l−1	PROPN
ejpam-5050	316	12	[	[	PUNCT
ejpam-5050	316	13	d3/2y0(x	d3/2y0(x	NOUN
ejpam-5050	316	14	)	)	PUNCT
ejpam-5050	316	15	]	]	PUNCT
ejpam-5050	317	1	−	−	PROPN
ejpam-5050	317	2	l−1[y0(x	l−1[y0(x	NOUN
ejpam-5050	317	3	)	)	PUNCT
ejpam-5050	317	4	]	]	PUNCT
ejpam-5050	317	5	,	,	PUNCT
ejpam-5050	317	6	=	=	NOUN
ejpam-5050	317	7	1	1	NUM
ejpam-5050	317	8	2	2	NUM
ejpam-5050	317	9	x2	x2	NOUN
ejpam-5050	318	1	+	+	CCONJ
ejpam-5050	318	2	1	1	NUM
ejpam-5050	318	3	6	6	NUM
ejpam-5050	318	4	x3	x3	ADJ
ejpam-5050	318	5	−	−	PROPN
ejpam-5050	319	1	p	p	X
ejpam-5050	320	1	[	[	X
ejpam-5050	320	2	1	1	NUM
ejpam-5050	320	3	2	2	NUM
ejpam-5050	320	4	a0x	a0x	ADP
ejpam-5050	320	5	2	2	NUM
ejpam-5050	320	6	+	+	SYM
ejpam-5050	320	7	1	1	NUM
ejpam-5050	320	8	6	6	NUM
ejpam-5050	320	9	a1x	a1x	SYM
ejpam-5050	320	10	3	3	NUM
ejpam-5050	320	11	+	+	CCONJ
ejpam-5050	320	12	1	1	NUM
ejpam-5050	320	13	12	12	NUM
ejpam-5050	320	14	a2x	a2x	ADP
ejpam-5050	320	15	4	4	NUM
ejpam-5050	320	16	+	+	NUM
ejpam-5050	320	17	...	...	PUNCT
ejpam-5050	320	18	]	]	PUNCT
ejpam-5050	321	1	−	−	NOUN
ejpam-5050	321	2	4c1	4c1	NUM
ejpam-5050	321	3	3	3	NUM
ejpam-5050	321	4	√	√	PROPN
ejpam-5050	321	5	π	π	PROPN
ejpam-5050	321	6	x3/2	x3/2	NUM
ejpam-5050	322	1	−	−	PROPN
ejpam-5050	322	2	8a0	8a0	NUM
ejpam-5050	322	3	15	15	NUM
ejpam-5050	322	4	√	√	PROPN
ejpam-5050	322	5	π	π	PROPN
ejpam-5050	322	6	x5/2	x5/2	PROPN
ejpam-5050	322	7	,	,	PUNCT
ejpam-5050	322	8	−	−	PROPN
ejpam-5050	323	1	16a1	16a1	NUM
ejpam-5050	323	2	105	105	NUM
ejpam-5050	323	3	√	√	PROPN
ejpam-5050	323	4	π	π	PROPN
ejpam-5050	323	5	x7/2	x7/2	PROPN
ejpam-5050	324	1	−	−	PROPN
ejpam-5050	325	1	64a2	64a2	NUM
ejpam-5050	325	2	945	945	NUM
ejpam-5050	325	3	√	√	PROPN
ejpam-5050	325	4	π	π	X
ejpam-5050	325	5	x9/2	x9/2	PUNCT
ejpam-5050	326	1	−	−	PROPN
ejpam-5050	326	2	1	1	NUM
ejpam-5050	326	3	2	2	NUM
ejpam-5050	326	4	x2	x2	NOUN
ejpam-5050	326	5	−	−	PROPN
ejpam-5050	326	6	c1	c1	PROPN
ejpam-5050	326	7	6	6	NUM
ejpam-5050	326	8	x3	x3	PROPN
ejpam-5050	326	9	−	−	PROPN
ejpam-5050	326	10	a0	a0	PROPN
ejpam-5050	326	11	24	24	NUM
ejpam-5050	326	12	x4	x4	PROPN
ejpam-5050	326	13	−	−	PROPN
ejpam-5050	326	14	a1	a1	NOUN
ejpam-5050	326	15	120	120	NUM
ejpam-5050	326	16	x5	x5	NOUN
ejpam-5050	326	17	−	−	PROPN
ejpam-5050	326	18	a2	a2	PROPN
ejpam-5050	326	19	360	360	NUM
ejpam-5050	326	20	x6	x6	PROPN
ejpam-5050	326	21	+	+	CCONJ
ejpam-5050	326	22	...	...	PUNCT
ejpam-5050	326	23	next	next	ADV
ejpam-5050	326	24	,	,	PUNCT
ejpam-5050	326	25	collecting	collect	VERB
ejpam-5050	326	26	the	the	DET
ejpam-5050	326	27	like	like	ADJ
ejpam-5050	326	28	terms	term	NOUN
ejpam-5050	326	29	,	,	PUNCT
ejpam-5050	326	30	and	and	CCONJ
ejpam-5050	326	31	thereafter	thereafter	ADV
ejpam-5050	326	32	equating	equate	VERB
ejpam-5050	326	33	the	the	DET
ejpam-5050	326	34	coefficients	coefficient	NOUN
ejpam-5050	326	35	of	of	ADP
ejpam-5050	326	36	xn	xn	PROPN
ejpam-5050	326	37	in	in	ADP
ejpam-5050	326	38	both	both	DET
ejpam-5050	326	39	sides	side	NOUN
ejpam-5050	326	40	of	of	ADP
ejpam-5050	326	41	the	the	DET
ejpam-5050	326	42	above	above	ADJ
ejpam-5050	326	43	expression	expression	NOUN
ejpam-5050	326	44	,	,	PUNCT
ejpam-5050	326	45	where	where	SCONJ
ejpam-5050	326	46	y1(x	y1(x	NOUN
ejpam-5050	326	47	)	)	PUNCT
ejpam-5050	326	48	=	=	SYM
ejpam-5050	326	49	0	0	NUM
ejpam-5050	326	50	with	with	ADP
ejpam-5050	326	51	p	p	NOUN
ejpam-5050	326	52	=	=	SYM
ejpam-5050	326	53	1	1	NUM
ejpam-5050	326	54	gives	give	VERB
ejpam-5050	326	55	y1(x	y1(x	NOUN
ejpam-5050	326	56	)	)	PUNCT
ejpam-5050	326	57	=	=	SYM
ejpam-5050	326	58	1	1	NUM
ejpam-5050	326	59	6	6	NUM
ejpam-5050	326	60	x3	x3	ADJ
ejpam-5050	326	61	−	−	NOUN
ejpam-5050	326	62	1	1	NUM
ejpam-5050	326	63	2	2	NUM
ejpam-5050	326	64	a0x	a0x	ADP
ejpam-5050	326	65	2	2	NUM
ejpam-5050	326	66	−	−	NUM
ejpam-5050	326	67	1	1	NUM
ejpam-5050	326	68	6	6	NUM
ejpam-5050	326	69	a1x	a1x	SYM
ejpam-5050	326	70	3	3	NUM
ejpam-5050	326	71	−	−	NOUN
ejpam-5050	326	72	1	1	NUM
ejpam-5050	326	73	12	12	NUM
ejpam-5050	326	74	a2x	a2x	ADP
ejpam-5050	326	75	4	4	NUM
ejpam-5050	326	76	−	−	NOUN
ejpam-5050	326	77	4c1	4c1	NUM
ejpam-5050	326	78	3	3	NUM
ejpam-5050	326	79	√	√	PROPN
ejpam-5050	327	1	π	π	PROPN
ejpam-5050	328	1	x3/2	x3/2	NUM
ejpam-5050	329	1	−	−	PROPN
ejpam-5050	329	2	8a0	8a0	NUM
ejpam-5050	329	3	15	15	NUM
ejpam-5050	330	1	√	√	PROPN
ejpam-5050	330	2	π	π	PROPN
ejpam-5050	330	3	x5/2	x5/2	PROPN
ejpam-5050	330	4	−	−	PROPN
ejpam-5050	331	1	16a1	16a1	NUM
ejpam-5050	331	2	105	105	NUM
ejpam-5050	331	3	√	√	PROPN
ejpam-5050	331	4	π	π	PROPN
ejpam-5050	331	5	x7/2	x7/2	PROPN
ejpam-5050	332	1	−	−	PROPN
ejpam-5050	333	1	64a2	64a2	NUM
ejpam-5050	333	2	945	945	NUM
ejpam-5050	333	3	√	√	PROPN
ejpam-5050	333	4	π	π	X
ejpam-5050	333	5	x9/2	x9/2	PUNCT
ejpam-5050	334	1	−	−	PROPN
ejpam-5050	334	2	c1	c1	PROPN
ejpam-5050	334	3	6	6	NUM
ejpam-5050	334	4	x3	x3	PROPN
ejpam-5050	334	5	−	−	PROPN
ejpam-5050	334	6	a0	a0	PROPN
ejpam-5050	334	7	24	24	NUM
ejpam-5050	334	8	x4	x4	PROPN
ejpam-5050	334	9	−	−	PROPN
ejpam-5050	334	10	a1	a1	NOUN
ejpam-5050	334	11	120	120	NUM
ejpam-5050	334	12	x5	x5	NOUN
ejpam-5050	334	13	−	−	PROPN
ejpam-5050	334	14	a2	a2	PROPN
ejpam-5050	334	15	360	360	NUM
ejpam-5050	334	16	x6	x6	PROPN
ejpam-5050	334	17	+	+	CCONJ
ejpam-5050	334	18	...	...	PUNCT
ejpam-5050	335	1	=	=	SYM
ejpam-5050	335	2	0	0	X
ejpam-5050	335	3	.	.	PUNCT
ejpam-5050	335	4	m.	m.	PROPN
ejpam-5050	335	5	al	al	PROPN
ejpam-5050	335	6	-	-	PUNCT
ejpam-5050	335	7	mazmumy	mazmumy	PROPN
ejpam-5050	335	8	,	,	PUNCT
ejpam-5050	335	9	m.	m.	NOUN
ejpam-5050	335	10	alsulami	alsulami	PROPN
ejpam-5050	335	11	/	/	SYM
ejpam-5050	335	12	eur	eur	PROPN
ejpam-5050	335	13	.	.	PUNCT
ejpam-5050	336	1	j.	j.	PROPN
ejpam-5050	336	2	pure	pure	PROPN
ejpam-5050	336	3	appl	appl	PROPN
ejpam-5050	336	4	.	.	PROPN
ejpam-5050	336	5	math	math	PROPN
ejpam-5050	336	6	,	,	PUNCT
ejpam-5050	336	7	17	17	NUM
ejpam-5050	336	8	(	(	PUNCT
ejpam-5050	336	9	1	1	NUM
ejpam-5050	336	10	)	)	PUNCT
ejpam-5050	336	11	(	(	PUNCT
ejpam-5050	336	12	2024	2024	NUM
ejpam-5050	336	13	)	)	PUNCT
ejpam-5050	336	14	,	,	PUNCT
ejpam-5050	336	15	546	546	NUM
ejpam-5050	336	16	-	-	SYM
ejpam-5050	336	17	568	568	NUM
ejpam-5050	336	18	558	558	NUM
ejpam-5050	336	19	therefore	therefore	ADV
ejpam-5050	337	1	,	,	PUNCT
ejpam-5050	337	2	we	we	PRON
ejpam-5050	337	3	obtain	obtain	VERB
ejpam-5050	337	4	a0	a0	NOUN
ejpam-5050	337	5	=	=	SYM
ejpam-5050	337	6	0	0	PROPN
ejpam-5050	337	7	,	,	PUNCT
ejpam-5050	337	8	a1	a1	NOUN
ejpam-5050	337	9	=	=	SYM
ejpam-5050	337	10	1−c1	1−c1	NUM
ejpam-5050	337	11	,	,	PUNCT
ejpam-5050	337	12	and	and	CCONJ
ejpam-5050	337	13	a2	a2	PROPN
ejpam-5050	337	14	=	=	SYM
ejpam-5050	337	15	0	0	X
ejpam-5050	337	16	.	.	PUNCT
ejpam-5050	338	1	in	in	ADP
ejpam-5050	338	2	addition	addition	NOUN
ejpam-5050	338	3	,	,	PUNCT
ejpam-5050	338	4	substituting	substitute	VERB
ejpam-5050	338	5	these	these	DET
ejpam-5050	338	6	values	value	NOUN
ejpam-5050	338	7	in	in	ADP
ejpam-5050	338	8	y0(x	y0(x	NOUN
ejpam-5050	338	9	)	)	PUNCT
ejpam-5050	338	10	,	,	PUNCT
ejpam-5050	338	11	where	where	SCONJ
ejpam-5050	338	12	yn(x	yn(x	X
ejpam-5050	338	13	)	)	PUNCT
ejpam-5050	338	14	=	=	SYM
ejpam-5050	338	15	0	0	NUM
ejpam-5050	338	16	,	,	PUNCT
ejpam-5050	338	17	for	for	ADP
ejpam-5050	338	18	n	n	PROPN
ejpam-5050	338	19	⩾	⩾	PROPN
ejpam-5050	338	20	1	1	NUM
ejpam-5050	338	21	yields	yield	NOUN
ejpam-5050	338	22	y(x	y(x	NOUN
ejpam-5050	338	23	)	)	PUNCT
ejpam-5050	338	24	=	=	SYM
ejpam-5050	338	25	y0(x	y0(x	X
ejpam-5050	338	26	)	)	PUNCT
ejpam-5050	338	27	=	=	SYM
ejpam-5050	338	28	1	1	NUM
ejpam-5050	338	29	+	+	NUM
ejpam-5050	338	30	c1x+	c1x+	VERB
ejpam-5050	338	31	1	1	NUM
ejpam-5050	338	32	6	6	NUM
ejpam-5050	338	33	(	(	PUNCT
ejpam-5050	338	34	1−	1−	NUM
ejpam-5050	338	35	c)x3	c)x3	PROPN
ejpam-5050	338	36	.	.	PUNCT
ejpam-5050	339	1	moreover	moreover	ADV
ejpam-5050	339	2	,	,	PUNCT
ejpam-5050	339	3	on	on	ADP
ejpam-5050	339	4	using	use	VERB
ejpam-5050	339	5	the	the	DET
ejpam-5050	339	6	subsequent	subsequent	ADJ
ejpam-5050	339	7	boundary	boundary	ADJ
ejpam-5050	339	8	condition	condition	NOUN
ejpam-5050	339	9	y(1	y(1	PROPN
ejpam-5050	339	10	)	)	PUNCT
ejpam-5050	339	11	=	=	SYM
ejpam-5050	339	12	2	2	NUM
ejpam-5050	339	13	,	,	PUNCT
ejpam-5050	339	14	one	one	NOUN
ejpam-5050	339	15	acquires	acquire	VERB
ejpam-5050	339	16	c1	c1	NOUN
ejpam-5050	339	17	=	=	PROPN
ejpam-5050	339	18	1	1	NUM
ejpam-5050	339	19	,	,	PUNCT
ejpam-5050	339	20	so	so	SCONJ
ejpam-5050	339	21	that	that	SCONJ
ejpam-5050	339	22	y(x	y(x	VERB
ejpam-5050	339	23	)	)	PUNCT
ejpam-5050	339	24	=	=	PUNCT
ejpam-5050	340	1	x+	x+	PUNCT
ejpam-5050	340	2	1	1	NUM
ejpam-5050	340	3	,	,	PUNCT
ejpam-5050	340	4	which	which	PRON
ejpam-5050	340	5	is	be	AUX
ejpam-5050	340	6	indeed	indeed	ADV
ejpam-5050	340	7	the	the	DET
ejpam-5050	340	8	reported	report	VERB
ejpam-5050	340	9	exact	exact	ADJ
ejpam-5050	340	10	analytical	analytical	ADJ
ejpam-5050	340	11	solution	solution	NOUN
ejpam-5050	340	12	for	for	ADP
ejpam-5050	340	13	bvp	bvp	PROPN
ejpam-5050	340	14	(	(	PUNCT
ejpam-5050	340	15	24	24	NUM
ejpam-5050	340	16	)	)	PUNCT
ejpam-5050	340	17	.	.	PUNCT
ejpam-5050	341	1	algorithm	algorithm	NOUN
ejpam-5050	341	2	2	2	NUM
ejpam-5050	341	3	:	:	PUNCT
ejpam-5050	341	4	here	here	ADV
ejpam-5050	341	5	,	,	PUNCT
ejpam-5050	341	6	we	we	PRON
ejpam-5050	341	7	make	make	VERB
ejpam-5050	341	8	use	use	NOUN
ejpam-5050	341	9	of	of	ADP
ejpam-5050	341	10	the	the	DET
ejpam-5050	341	11	equation	equation	NOUN
ejpam-5050	341	12	represented	represent	VERB
ejpam-5050	341	13	in	in	ADP
ejpam-5050	341	14	an	an	DET
ejpam-5050	341	15	operator	operator	NOUN
ejpam-5050	341	16	notation	notation	NOUN
ejpam-5050	341	17	(	(	PUNCT
ejpam-5050	341	18	25	25	NUM
ejpam-5050	341	19	)	)	PUNCT
ejpam-5050	341	20	,	,	PUNCT
ejpam-5050	341	21	and	and	CCONJ
ejpam-5050	341	22	further	far	ADV
ejpam-5050	341	23	define	define	VERB
ejpam-5050	341	24	l−1	l−1	PROPN
ejpam-5050	341	25	as	as	SCONJ
ejpam-5050	341	26	given	give	VERB
ejpam-5050	341	27	in	in	ADP
ejpam-5050	341	28	(	(	PUNCT
ejpam-5050	341	29	14	14	NUM
ejpam-5050	341	30	)	)	PUNCT
ejpam-5050	341	31	.	.	PUNCT
ejpam-5050	342	1	thus	thus	ADV
ejpam-5050	342	2	,	,	PUNCT
ejpam-5050	342	3	implementing	implement	VERB
ejpam-5050	342	4	the	the	DET
ejpam-5050	342	5	inverse	inverse	NOUN
ejpam-5050	342	6	operator	operator	NOUN
ejpam-5050	342	7	on	on	ADP
ejpam-5050	342	8	equation	equation	NOUN
ejpam-5050	342	9	(	(	PUNCT
ejpam-5050	342	10	25	25	NUM
ejpam-5050	342	11	)	)	PUNCT
ejpam-5050	342	12	reveals	reveal	VERB
ejpam-5050	342	13	y(x	y(x	NOUN
ejpam-5050	342	14	)	)	PUNCT
ejpam-5050	342	15	=	=	PUNCT
ejpam-5050	343	1	x+	x+	PUNCT
ejpam-5050	343	2	1	1	NUM
ejpam-5050	344	1	+	+	CCONJ
ejpam-5050	344	2	l−1[x+	l−1[x+	ADV
ejpam-5050	344	3	1]−	1]−	NUM
ejpam-5050	344	4	l−1[d3/2y(x)]−	l−1[d3/2y(x)]−	NOUN
ejpam-5050	344	5	l−1[y(x	l−1[y(x	NOUN
ejpam-5050	344	6	)	)	PUNCT
ejpam-5050	344	7	]	]	PUNCT
ejpam-5050	344	8	.	.	PUNCT
ejpam-5050	345	1	using	use	VERB
ejpam-5050	345	2	madm	madm	NOUN
ejpam-5050	345	3	and	and	CCONJ
ejpam-5050	345	4	(	(	PUNCT
ejpam-5050	345	5	6	6	X
ejpam-5050	345	6	)	)	PUNCT
ejpam-5050	345	7	∞∑	∞∑	NUM
ejpam-5050	345	8	n=0	n=0	NUM
ejpam-5050	345	9	yn(x	yn(x	PUNCT
ejpam-5050	345	10	)	)	PUNCT
ejpam-5050	346	1	=	=	PUNCT
ejpam-5050	346	2	x+	x+	PUNCT
ejpam-5050	347	1	1	1	NUM
ejpam-5050	347	2	+	+	NUM
ejpam-5050	347	3	l−1[x+	l−1[x+	ADV
ejpam-5050	347	4	1]−	1]−	NUM
ejpam-5050	347	5	pl−1	pl−1	NOUN
ejpam-5050	347	6	[	[	PUNCT
ejpam-5050	347	7	∞∑	∞∑	NUM
ejpam-5050	347	8	n=0	n=0	NUM
ejpam-5050	347	9	anx	anx	NOUN
ejpam-5050	347	10	n	n	NOUN
ejpam-5050	347	11	]	]	PUNCT
ejpam-5050	348	1	+	+	CCONJ
ejpam-5050	348	2	l−1	l−1	NOUN
ejpam-5050	348	3	[	[	PUNCT
ejpam-5050	348	4	∞∑	∞∑	PROPN
ejpam-5050	348	5	n=0	n=0	NUM
ejpam-5050	348	6	anx	anx	NOUN
ejpam-5050	348	7	n	n	NOUN
ejpam-5050	348	8	]	]	PUNCT
ejpam-5050	348	9	−	−	PROPN
ejpam-5050	349	1	l−1	l−1	PROPN
ejpam-5050	349	2	[	[	PUNCT
ejpam-5050	349	3	d3/2	d3/2	ADJ
ejpam-5050	349	4	∞∑	∞∑	PROPN
ejpam-5050	349	5	n=0	n=0	NUM
ejpam-5050	349	6	yn(x	yn(x	X
ejpam-5050	349	7	)	)	PUNCT
ejpam-5050	349	8	]	]	PUNCT
ejpam-5050	350	1	−	−	PROPN
ejpam-5050	350	2	l−1	l−1	PROPN
ejpam-5050	350	3	[	[	PUNCT
ejpam-5050	350	4	∞∑	∞∑	PROPN
ejpam-5050	350	5	n=0	n=0	NUM
ejpam-5050	350	6	yn(x	yn(x	NOUN
ejpam-5050	350	7	)	)	PUNCT
ejpam-5050	350	8	]	]	PUNCT
ejpam-5050	350	9	.	.	PUNCT
ejpam-5050	351	1	now	now	ADV
ejpam-5050	351	2	,	,	PUNCT
ejpam-5050	351	3	let	let	VERB
ejpam-5050	351	4	y0(x	y0(x	PRON
ejpam-5050	351	5	)	)	PUNCT
ejpam-5050	351	6	=	=	PUNCT
ejpam-5050	352	1	x+	x+	PUNCT
ejpam-5050	352	2	1	1	NUM
ejpam-5050	353	1	+	+	X
ejpam-5050	353	2	l−1	l−1	PROPN
ejpam-5050	353	3	[	[	PUNCT
ejpam-5050	353	4	∞∑	∞∑	PROPN
ejpam-5050	353	5	n=0	n=0	NUM
ejpam-5050	353	6	anx	anx	NOUN
ejpam-5050	353	7	n	n	NOUN
ejpam-5050	353	8	]	]	PUNCT
ejpam-5050	353	9	,	,	PUNCT
ejpam-5050	353	10	and	and	CCONJ
ejpam-5050	353	11	y1(x	y1(x	NOUN
ejpam-5050	353	12	)	)	PUNCT
ejpam-5050	353	13	=	=	PUNCT
ejpam-5050	353	14	l−1[x+	l−1[x+	ADV
ejpam-5050	353	15	1]−	1]−	NUM
ejpam-5050	353	16	pl−1	pl−1	NOUN
ejpam-5050	353	17	[	[	PUNCT
ejpam-5050	353	18	∞∑	∞∑	NUM
ejpam-5050	353	19	n=0	n=0	NUM
ejpam-5050	353	20	anx	anx	NOUN
ejpam-5050	353	21	n	n	NOUN
ejpam-5050	353	22	]	]	PUNCT
ejpam-5050	353	23	−	−	PROPN
ejpam-5050	353	24	l−1[d3/2y0(x)]−	l−1[d3/2y0(x)]−	PROPN
ejpam-5050	353	25	l−1[y0(x	l−1[y0(x	PROPN
ejpam-5050	353	26	)	)	PUNCT
ejpam-5050	353	27	]	]	PUNCT
ejpam-5050	353	28	,	,	PUNCT
ejpam-5050	353	29	then	then	ADV
ejpam-5050	353	30	,	,	PUNCT
ejpam-5050	353	31	we	we	PRON
ejpam-5050	353	32	precisely	precisely	ADV
ejpam-5050	353	33	compute	compute	VERB
ejpam-5050	353	34	the	the	DET
ejpam-5050	353	35	expressions	expression	NOUN
ejpam-5050	353	36	for	for	ADP
ejpam-5050	353	37	y0(x	y0(x	NOUN
ejpam-5050	353	38	)	)	PUNCT
ejpam-5050	353	39	and	and	CCONJ
ejpam-5050	353	40	y1(x	y1(x	NOUN
ejpam-5050	353	41	)	)	PUNCT
ejpam-5050	353	42	via	via	ADP
ejpam-5050	353	43	the	the	DET
ejpam-5050	353	44	inverse	inverse	NOUN
ejpam-5050	353	45	operator	operator	NOUN
ejpam-5050	353	46	(	(	PUNCT
ejpam-5050	353	47	14	14	NUM
ejpam-5050	353	48	)	)	PUNCT
ejpam-5050	353	49	as	as	SCONJ
ejpam-5050	353	50	follows	follow	VERB
ejpam-5050	353	51	y0(x	y0(x	PRON
ejpam-5050	353	52	)	)	PUNCT
ejpam-5050	353	53	=	=	SYM
ejpam-5050	354	1	x+	x+	SYM
ejpam-5050	354	2	1	1	NUM
ejpam-5050	354	3	+	+	NUM
ejpam-5050	354	4	a0	a0	PROPN
ejpam-5050	354	5	2	2	NUM
ejpam-5050	354	6	x2	x2	NOUN
ejpam-5050	355	1	+	+	CCONJ
ejpam-5050	355	2	a1	a1	NOUN
ejpam-5050	355	3	6	6	NUM
ejpam-5050	355	4	x3	x3	NOUN
ejpam-5050	355	5	+	+	CCONJ
ejpam-5050	355	6	a2	a2	PROPN
ejpam-5050	355	7	12	12	NUM
ejpam-5050	356	1	x4	x4	ADV
ejpam-5050	356	2	−	−	PROPN
ejpam-5050	356	3	x	x	SYM
ejpam-5050	356	4	(	(	PUNCT
ejpam-5050	356	5	a0	a0	NOUN
ejpam-5050	356	6	2	2	NUM
ejpam-5050	357	1	+	+	CCONJ
ejpam-5050	357	2	a1	a1	NOUN
ejpam-5050	357	3	6	6	NUM
ejpam-5050	357	4	+	+	NUM
ejpam-5050	357	5	a2	a2	PROPN
ejpam-5050	357	6	12	12	NUM
ejpam-5050	357	7	)	)	PUNCT
ejpam-5050	357	8	,	,	PUNCT
ejpam-5050	357	9	and	and	CCONJ
ejpam-5050	357	10	y1(x	y1(x	NOUN
ejpam-5050	357	11	)	)	PUNCT
ejpam-5050	357	12	=	=	SYM
ejpam-5050	357	13	1	1	NUM
ejpam-5050	357	14	2	2	NUM
ejpam-5050	357	15	x2	x2	NOUN
ejpam-5050	358	1	+	+	CCONJ
ejpam-5050	358	2	1	1	NUM
ejpam-5050	358	3	6	6	NUM
ejpam-5050	358	4	x3	x3	ADJ
ejpam-5050	358	5	−	−	NOUN
ejpam-5050	358	6	2	2	NUM
ejpam-5050	358	7	3	3	NUM
ejpam-5050	358	8	x−	x−	PROPN
ejpam-5050	358	9	p	p	PROPN
ejpam-5050	359	1	[	[	X
ejpam-5050	359	2	a0	a0	PROPN
ejpam-5050	359	3	2	2	NUM
ejpam-5050	359	4	x2	x2	NOUN
ejpam-5050	359	5	+	+	CCONJ
ejpam-5050	359	6	a1	a1	NOUN
ejpam-5050	359	7	6	6	NUM
ejpam-5050	359	8	x3	x3	NOUN
ejpam-5050	359	9	+	+	CCONJ
ejpam-5050	359	10	a2	a2	PROPN
ejpam-5050	359	11	12	12	NUM
ejpam-5050	360	1	x4	x4	ADV
ejpam-5050	360	2	−	−	PROPN
ejpam-5050	360	3	x	x	SYM
ejpam-5050	360	4	(	(	PUNCT
ejpam-5050	360	5	a0	a0	NOUN
ejpam-5050	360	6	2	2	NUM
ejpam-5050	361	1	+	+	CCONJ
ejpam-5050	361	2	a1	a1	NOUN
ejpam-5050	361	3	6	6	NUM
ejpam-5050	361	4	+	+	NUM
ejpam-5050	361	5	a2	a2	PROPN
ejpam-5050	361	6	12	12	NUM
ejpam-5050	361	7	)	)	PUNCT
ejpam-5050	361	8	]	]	PUNCT
ejpam-5050	362	1	−	−	PROPN
ejpam-5050	362	2	1	1	NUM
ejpam-5050	362	3	945	945	NUM
ejpam-5050	362	4	√	√	NUM
ejpam-5050	362	5	π	π	PROPN
ejpam-5050	362	6	[	[	PUNCT
ejpam-5050	362	7	504a0x	504a0x	NUM
ejpam-5050	362	8	5/2	5/2	NUM
ejpam-5050	362	9	+	+	CCONJ
ejpam-5050	362	10	144a1x	144a1x	NUM
ejpam-5050	362	11	7/2	7/2	NUM
ejpam-5050	362	12	+	+	CCONJ
ejpam-5050	362	13	64a2x	64a2x	NOUN
ejpam-5050	362	14	9/2	9/2	NUM
ejpam-5050	362	15	−	−	PROPN
ejpam-5050	363	1	(	(	PUNCT
ejpam-5050	363	2	630a0	630a0	NUM
ejpam-5050	363	3	+	+	NUM
ejpam-5050	363	4	210a1	210a1	NUM
ejpam-5050	363	5	+	+	CCONJ
ejpam-5050	363	6	105a2	105a2	NUM
ejpam-5050	363	7	−	−	PROPN
ejpam-5050	363	8	1260	1260	NUM
ejpam-5050	363	9	)	)	PUNCT
ejpam-5050	364	1	x3/2	x3/2	NOUN
ejpam-5050	364	2	]	]	PUNCT
ejpam-5050	365	1	−	−	PROPN
ejpam-5050	365	2	1	1	NUM
ejpam-5050	365	3	210	210	NUM
ejpam-5050	366	1	√	√	NUM
ejpam-5050	366	2	π	π	PROPN
ejpam-5050	366	3	[	[	PUNCT
ejpam-5050	366	4	28a0	28a0	NUM
ejpam-5050	366	5	+	+	NUM
ejpam-5050	366	6	44	44	NUM
ejpam-5050	366	7	3	3	NUM
ejpam-5050	366	8	a1	a1	NOUN
ejpam-5050	366	9	+	+	CCONJ
ejpam-5050	366	10	82	82	NUM
ejpam-5050	366	11	9	9	NUM
ejpam-5050	366	12	a2	a2	NOUN
ejpam-5050	366	13	−	−	PROPN
ejpam-5050	366	14	280	280	NUM
ejpam-5050	366	15	]	]	PUNCT
ejpam-5050	366	16	x	x	PUNCT
ejpam-5050	366	17	m.	m.	PROPN
ejpam-5050	366	18	al	al	PROPN
ejpam-5050	366	19	-	-	PUNCT
ejpam-5050	366	20	mazmumy	mazmumy	PROPN
ejpam-5050	366	21	,	,	PUNCT
ejpam-5050	366	22	m.	m.	NOUN
ejpam-5050	366	23	alsulami	alsulami	PROPN
ejpam-5050	366	24	/	/	SYM
ejpam-5050	366	25	eur	eur	PROPN
ejpam-5050	366	26	.	.	PUNCT
ejpam-5050	367	1	j.	j.	PROPN
ejpam-5050	367	2	pure	pure	PROPN
ejpam-5050	367	3	appl	appl	PROPN
ejpam-5050	367	4	.	.	PROPN
ejpam-5050	367	5	math	math	PROPN
ejpam-5050	367	6	,	,	PUNCT
ejpam-5050	367	7	17	17	NUM
ejpam-5050	367	8	(	(	PUNCT
ejpam-5050	367	9	1	1	NUM
ejpam-5050	367	10	)	)	PUNCT
ejpam-5050	367	11	(	(	PUNCT
ejpam-5050	367	12	2024	2024	NUM
ejpam-5050	367	13	)	)	PUNCT
ejpam-5050	367	14	,	,	PUNCT
ejpam-5050	367	15	546	546	NUM
ejpam-5050	367	16	-	-	SYM
ejpam-5050	367	17	568	568	NUM
ejpam-5050	367	18	559	559	NUM
ejpam-5050	367	19	−	−	PROPN
ejpam-5050	367	20	a0	a0	PROPN
ejpam-5050	367	21	24	24	NUM
ejpam-5050	367	22	x4	x4	PROPN
ejpam-5050	367	23	−	−	PROPN
ejpam-5050	367	24	a1	a1	NOUN
ejpam-5050	367	25	120	120	NUM
ejpam-5050	367	26	x5	x5	NOUN
ejpam-5050	367	27	−	−	PROPN
ejpam-5050	367	28	a2	a2	PROPN
ejpam-5050	367	29	360	360	NUM
ejpam-5050	367	30	x6	x6	PROPN
ejpam-5050	367	31	+	+	CCONJ
ejpam-5050	367	32	(	(	PUNCT
ejpam-5050	367	33	a0	a0	PROPN
ejpam-5050	367	34	12	12	NUM
ejpam-5050	367	35	+	+	CCONJ
ejpam-5050	367	36	a1	a1	PROPN
ejpam-5050	367	37	36	36	NUM
ejpam-5050	367	38	+	+	NUM
ejpam-5050	367	39	a2	a2	PROPN
ejpam-5050	367	40	72	72	NUM
ejpam-5050	367	41	−	−	NOUN
ejpam-5050	367	42	1	1	NUM
ejpam-5050	367	43	6	6	NUM
ejpam-5050	367	44	)	)	PUNCT
ejpam-5050	368	1	x3	x3	ADV
ejpam-5050	368	2	−	−	NOUN
ejpam-5050	368	3	1	1	NUM
ejpam-5050	368	4	2	2	NUM
ejpam-5050	368	5	x2	x2	NOUN
ejpam-5050	368	6	−	−	PROPN
ejpam-5050	369	1	(	(	PUNCT
ejpam-5050	369	2	a0	a0	PROPN
ejpam-5050	369	3	24	24	NUM
ejpam-5050	369	4	+	+	NUM
ejpam-5050	369	5	7a1	7a1	NUM
ejpam-5050	369	6	360	360	NUM
ejpam-5050	369	7	+	+	NUM
ejpam-5050	369	8	a2	a2	PROPN
ejpam-5050	369	9	90	90	NUM
ejpam-5050	369	10	−	−	NOUN
ejpam-5050	369	11	2	2	NUM
ejpam-5050	369	12	3	3	NUM
ejpam-5050	369	13	)	)	PUNCT
ejpam-5050	369	14	x.	x.	NOUN
ejpam-5050	370	1	in	in	ADP
ejpam-5050	370	2	fact	fact	NOUN
ejpam-5050	370	3	,	,	PUNCT
ejpam-5050	370	4	the	the	DET
ejpam-5050	370	5	explicit	explicit	ADJ
ejpam-5050	370	6	expression	expression	NOUN
ejpam-5050	370	7	for	for	ADP
ejpam-5050	370	8	y1(x	y1(x	NOUN
ejpam-5050	370	9	)	)	PUNCT
ejpam-5050	370	10	will	will	AUX
ejpam-5050	370	11	be	be	AUX
ejpam-5050	370	12	found	find	VERB
ejpam-5050	370	13	after	after	ADP
ejpam-5050	370	14	collecting	collect	VERB
ejpam-5050	370	15	the	the	DET
ejpam-5050	370	16	like	like	ADJ
ejpam-5050	370	17	terms	term	NOUN
ejpam-5050	370	18	from	from	ADP
ejpam-5050	370	19	the	the	DET
ejpam-5050	370	20	equation	equation	NOUN
ejpam-5050	370	21	at	at	ADP
ejpam-5050	370	22	p	p	NOUN
ejpam-5050	370	23	=	=	NOUN
ejpam-5050	370	24	1	1	NUM
ejpam-5050	370	25	as	as	SCONJ
ejpam-5050	370	26	follows	follow	VERB
ejpam-5050	370	27	y1(x	y1(x	NOUN
ejpam-5050	370	28	)	)	PUNCT
ejpam-5050	370	29	=	=	PUNCT
ejpam-5050	371	1	−	−	PROPN
ejpam-5050	371	2	64a2	64a2	NUM
ejpam-5050	372	1	945	945	NUM
ejpam-5050	372	2	√	√	PROPN
ejpam-5050	372	3	π	π	X
ejpam-5050	372	4	x9/2	x9/2	PUNCT
ejpam-5050	373	1	−	−	PROPN
ejpam-5050	373	2	16a1	16a1	NUM
ejpam-5050	373	3	105	105	NUM
ejpam-5050	374	1	√	√	PROPN
ejpam-5050	374	2	π	π	PROPN
ejpam-5050	374	3	x7/2	x7/2	PROPN
ejpam-5050	375	1	−	−	NUM
ejpam-5050	375	2	8a0	8a0	NUM
ejpam-5050	375	3	15	15	NUM
ejpam-5050	375	4	√	√	PROPN
ejpam-5050	375	5	π	π	X
ejpam-5050	375	6	x5/2	x5/2	PROPN
ejpam-5050	376	1	+	+	CCONJ
ejpam-5050	376	2	1	1	NUM
ejpam-5050	376	3	945	945	NUM
ejpam-5050	376	4	√	√	NUM
ejpam-5050	376	5	π	π	PROPN
ejpam-5050	376	6	(	(	PUNCT
ejpam-5050	376	7	630a0	630a0	NUM
ejpam-5050	376	8	+	+	NUM
ejpam-5050	376	9	210a1	210a1	NUM
ejpam-5050	376	10	+	+	CCONJ
ejpam-5050	376	11	105a2	105a2	NUM
ejpam-5050	376	12	−	−	PROPN
ejpam-5050	376	13	1260	1260	NUM
ejpam-5050	376	14	)	)	PUNCT
ejpam-5050	377	1	x3/2	x3/2	NUM
ejpam-5050	377	2	−	−	PROPN
ejpam-5050	377	3	a2	a2	PROPN
ejpam-5050	377	4	360	360	NUM
ejpam-5050	377	5	x6	x6	PROPN
ejpam-5050	377	6	−	−	NOUN
ejpam-5050	377	7	a1	a1	NOUN
ejpam-5050	377	8	120	120	NUM
ejpam-5050	377	9	x5	x5	NOUN
ejpam-5050	377	10	−	−	PROPN
ejpam-5050	377	11	(	(	PUNCT
ejpam-5050	377	12	a2	a2	PROPN
ejpam-5050	377	13	12	12	NUM
ejpam-5050	377	14	+	+	NUM
ejpam-5050	377	15	a0	a0	PROPN
ejpam-5050	377	16	24	24	NUM
ejpam-5050	377	17	)	)	PUNCT
ejpam-5050	377	18	x4	x4	PROPN
ejpam-5050	378	1	+	+	CCONJ
ejpam-5050	378	2	(	(	PUNCT
ejpam-5050	378	3	a2	a2	PROPN
ejpam-5050	378	4	72	72	NUM
ejpam-5050	378	5	−	−	NOUN
ejpam-5050	378	6	5a1	5a1	NUM
ejpam-5050	378	7	36	36	NUM
ejpam-5050	378	8	+	+	CCONJ
ejpam-5050	378	9	a0	a0	PROPN
ejpam-5050	378	10	12	12	NUM
ejpam-5050	378	11	)	)	PUNCT
ejpam-5050	378	12	x3	x3	ADJ
ejpam-5050	378	13	−	−	PROPN
ejpam-5050	378	14	a0	a0	PROPN
ejpam-5050	378	15	2	2	NUM
ejpam-5050	378	16	x2	x2	NOUN
ejpam-5050	379	1	+	+	X
ejpam-5050	380	1	[	[	X
ejpam-5050	380	2	13a2	13a2	NUM
ejpam-5050	380	3	180	180	NUM
ejpam-5050	380	4	+	+	NUM
ejpam-5050	380	5	53a1	53a1	NUM
ejpam-5050	380	6	360	360	NUM
ejpam-5050	380	7	+	+	NUM
ejpam-5050	380	8	11a0	11a0	NUM
ejpam-5050	380	9	24	24	NUM
ejpam-5050	380	10	−	−	NUM
ejpam-5050	380	11	1	1	NUM
ejpam-5050	380	12	210	210	NUM
ejpam-5050	380	13	√	√	NOUN
ejpam-5050	380	14	π	π	PROPN
ejpam-5050	380	15	(	(	PUNCT
ejpam-5050	380	16	82a2	82a2	NUM
ejpam-5050	380	17	9	9	NUM
ejpam-5050	380	18	+	+	CCONJ
ejpam-5050	380	19	44a1	44a1	NUM
ejpam-5050	380	20	3	3	NUM
ejpam-5050	380	21	+	+	SYM
ejpam-5050	380	22	28a0	28a0	NUM
ejpam-5050	380	23	−	−	NUM
ejpam-5050	380	24	280	280	NUM
ejpam-5050	380	25	)	)	PUNCT
ejpam-5050	380	26	]	]	PUNCT
ejpam-5050	380	27	x.	x.	NOUN
ejpam-5050	380	28	finally	finally	ADV
ejpam-5050	380	29	,	,	PUNCT
ejpam-5050	380	30	setting	set	VERB
ejpam-5050	380	31	y1(x	y1(x	NOUN
ejpam-5050	380	32	)	)	PUNCT
ejpam-5050	380	33	=	=	SYM
ejpam-5050	380	34	0	0	NUM
ejpam-5050	380	35	,	,	PUNCT
ejpam-5050	380	36	and	and	CCONJ
ejpam-5050	380	37	thereafter	thereafter	ADV
ejpam-5050	380	38	equating	equate	VERB
ejpam-5050	380	39	the	the	DET
ejpam-5050	380	40	coefficients	coefficient	NOUN
ejpam-5050	380	41	of	of	ADP
ejpam-5050	380	42	xn	xn	PROPN
ejpam-5050	380	43	,	,	PUNCT
ejpam-5050	380	44	we	we	PRON
ejpam-5050	380	45	obtain	obtain	VERB
ejpam-5050	380	46	a0	a0	NOUN
ejpam-5050	380	47	=	=	SYM
ejpam-5050	380	48	a1	a1	PROPN
ejpam-5050	380	49	=	=	SYM
ejpam-5050	380	50	0	0	NUM
ejpam-5050	380	51	=	=	SYM
ejpam-5050	380	52	a2	a2	PROPN
ejpam-5050	380	53	=	=	SYM
ejpam-5050	380	54	0	0	X
ejpam-5050	380	55	.	.	PUNCT
ejpam-5050	381	1	we	we	PRON
ejpam-5050	381	2	,	,	PUNCT
ejpam-5050	381	3	therefore	therefore	ADV
ejpam-5050	381	4	,	,	PUNCT
ejpam-5050	381	5	obtain	obtain	VERB
ejpam-5050	381	6	y(x	y(x	NOUN
ejpam-5050	381	7	)	)	PUNCT
ejpam-5050	381	8	=	=	SYM
ejpam-5050	381	9	y0(x	y0(x	X
ejpam-5050	381	10	)	)	PUNCT
ejpam-5050	381	11	=	=	PUNCT
ejpam-5050	382	1	x+1	x+1	PROPN
ejpam-5050	382	2	as	as	ADP
ejpam-5050	382	3	the	the	DET
ejpam-5050	382	4	aiming	aim	VERB
ejpam-5050	382	5	solution	solution	NOUN
ejpam-5050	382	6	,	,	PUNCT
ejpam-5050	382	7	which	which	PRON
ejpam-5050	382	8	is	be	AUX
ejpam-5050	382	9	indeed	indeed	ADV
ejpam-5050	382	10	the	the	DET
ejpam-5050	382	11	reported	report	VERB
ejpam-5050	382	12	exact	exact	ADJ
ejpam-5050	382	13	analytical	analytical	ADJ
ejpam-5050	382	14	solution	solution	NOUN
ejpam-5050	382	15	for	for	ADP
ejpam-5050	382	16	(	(	PUNCT
ejpam-5050	382	17	24	24	NUM
ejpam-5050	382	18	)	)	PUNCT
ejpam-5050	382	19	.	.	PUNCT
ejpam-5050	383	1	example	example	NOUN
ejpam-5050	384	1	4	4	X
ejpam-5050	384	2	.	.	PUNCT
ejpam-5050	384	3	we	we	PRON
ejpam-5050	384	4	consider	consider	VERB
ejpam-5050	384	5	the	the	DET
ejpam-5050	384	6	bvp	bvp	NOUN
ejpam-5050	384	7	for	for	ADP
ejpam-5050	384	8	the	the	DET
ejpam-5050	384	9	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5050	384	10	bagley	bagley	NOUN
ejpam-5050	384	11	-	-	PUNCT
ejpam-5050	384	12	torvik	torvik	NOUN
ejpam-5050	384	13	equation	equation	NOUN
ejpam-5050	384	14	as	as	SCONJ
ejpam-5050	384	15	follows	follow	VERB
ejpam-5050	384	16	[	[	X
ejpam-5050	384	17	35	35	NUM
ejpam-5050	384	18	]	]	X
ejpam-5050	384	19	d2y(x	d2y(x	PROPN
ejpam-5050	384	20	)	)	PUNCT
ejpam-5050	385	1	+	+	NOUN
ejpam-5050	385	2	d3/2y(x	d3/2y(x	NOUN
ejpam-5050	385	3	)	)	PUNCT
ejpam-5050	386	1	+	+	NUM
ejpam-5050	386	2	y(x	y(x	NOUN
ejpam-5050	386	3	)	)	PUNCT
ejpam-5050	387	1	=	=	SYM
ejpam-5050	387	2	x2	x2	PROPN
ejpam-5050	388	1	+	+	CCONJ
ejpam-5050	388	2	2	2	NUM
ejpam-5050	388	3	+	+	CCONJ
ejpam-5050	388	4	4	4	NUM
ejpam-5050	388	5	√	√	NUM
ejpam-5050	388	6	x	x	SYM
ejpam-5050	388	7	π	π	PROPN
ejpam-5050	388	8	,	,	PUNCT
ejpam-5050	388	9	y(0	y(0	PROPN
ejpam-5050	388	10	)	)	PUNCT
ejpam-5050	388	11	=	=	SYM
ejpam-5050	388	12	0	0	NUM
ejpam-5050	388	13	,	,	PUNCT
ejpam-5050	388	14	y(5	y(5	PROPN
ejpam-5050	388	15	)	)	PUNCT
ejpam-5050	388	16	=	=	NOUN
ejpam-5050	388	17	25	25	NUM
ejpam-5050	388	18	,	,	PUNCT
ejpam-5050	388	19	(	(	PUNCT
ejpam-5050	388	20	26	26	NUM
ejpam-5050	388	21	)	)	PUNCT
ejpam-5050	388	22	that	that	PRON
ejpam-5050	388	23	admits	admit	VERB
ejpam-5050	388	24	y(x	y(x	NOUN
ejpam-5050	388	25	)	)	PUNCT
ejpam-5050	388	26	=	=	SYM
ejpam-5050	389	1	x2	x2	PROPN
ejpam-5050	389	2	as	as	ADP
ejpam-5050	389	3	its	its	PRON
ejpam-5050	389	4	exact	exact	ADJ
ejpam-5050	389	5	analytical	analytical	ADJ
ejpam-5050	389	6	solution	solution	NOUN
ejpam-5050	389	7	.	.	PUNCT
ejpam-5050	390	1	algorithm	algorithm	NOUN
ejpam-5050	390	2	1	1	NUM
ejpam-5050	390	3	:	:	PUNCT
ejpam-5050	390	4	illustrating	illustrate	VERB
ejpam-5050	390	5	(	(	PUNCT
ejpam-5050	390	6	26	26	NUM
ejpam-5050	390	7	)	)	PUNCT
ejpam-5050	390	8	via	via	ADP
ejpam-5050	390	9	operator	operator	NOUN
ejpam-5050	390	10	notation	notation	NOUN
ejpam-5050	390	11	,	,	PUNCT
ejpam-5050	390	12	one	one	NUM
ejpam-5050	390	13	writes	write	VERB
ejpam-5050	390	14	ly(x	ly(x	PUNCT
ejpam-5050	390	15	)	)	PUNCT
ejpam-5050	390	16	=	=	SYM
ejpam-5050	391	1	x2	x2	PROPN
ejpam-5050	392	1	+	+	CCONJ
ejpam-5050	392	2	2	2	NUM
ejpam-5050	392	3	+	+	CCONJ
ejpam-5050	392	4	4	4	NUM
ejpam-5050	392	5	√	√	NUM
ejpam-5050	392	6	x	x	PUNCT
ejpam-5050	392	7	π	π	X
ejpam-5050	392	8	−d3/2y(x)−	−d3/2y(x)−	PROPN
ejpam-5050	392	9	y(x	y(x	PROPN
ejpam-5050	392	10	)	)	PUNCT
ejpam-5050	392	11	.	.	PUNCT
ejpam-5050	393	1	(	(	PUNCT
ejpam-5050	393	2	27	27	NUM
ejpam-5050	393	3	)	)	PUNCT
ejpam-5050	393	4	next	next	ADV
ejpam-5050	393	5	,	,	PUNCT
ejpam-5050	393	6	on	on	ADP
ejpam-5050	393	7	enforcing	enforce	VERB
ejpam-5050	393	8	the	the	DET
ejpam-5050	393	9	inverse	inverse	NOUN
ejpam-5050	393	10	operator	operator	NOUN
ejpam-5050	393	11	l−1	l−1	PROPN
ejpam-5050	393	12	(	(	PUNCT
ejpam-5050	393	13	.	.	PUNCT
ejpam-5050	393	14	)	)	PUNCT
ejpam-5050	394	1	=	=	PUNCT
ejpam-5050	395	1	∫	∫	PUNCT
ejpam-5050	395	2	x	x	SYM
ejpam-5050	395	3	0	0	NUM
ejpam-5050	395	4	∫	∫	PROPN
ejpam-5050	395	5	x	x	SYM
ejpam-5050	395	6	0	0	PUNCT
ejpam-5050	395	7	(	(	PUNCT
ejpam-5050	395	8	.)dxdx	.)dxdx	X
ejpam-5050	395	9	on	on	ADP
ejpam-5050	395	10	both	both	DET
ejpam-5050	395	11	sides	side	NOUN
ejpam-5050	395	12	of	of	ADP
ejpam-5050	395	13	(	(	PUNCT
ejpam-5050	395	14	27	27	NUM
ejpam-5050	395	15	)	)	PUNCT
ejpam-5050	395	16	such	such	ADJ
ejpam-5050	395	17	that	that	DET
ejpam-5050	395	18	y′(0	y′(0	NOUN
ejpam-5050	395	19	)	)	PUNCT
ejpam-5050	395	20	=	=	SYM
ejpam-5050	395	21	c1	c1	PROPN
ejpam-5050	395	22	,	,	PUNCT
ejpam-5050	395	23	we	we	PRON
ejpam-5050	395	24	get	get	VERB
ejpam-5050	395	25	y(x	y(x	NOUN
ejpam-5050	395	26	)	)	PUNCT
ejpam-5050	396	1	=	=	PUNCT
ejpam-5050	396	2	c1x−	c1x−	NOUN
ejpam-5050	396	3	l−1[d3/2y(x)]−	l−1[d3/2y(x)]−	NOUN
ejpam-5050	396	4	l−1[y(x	l−1[y(x	NOUN
ejpam-5050	396	5	)	)	PUNCT
ejpam-5050	396	6	]	]	PUNCT
ejpam-5050	397	1	+	+	CCONJ
ejpam-5050	397	2	l−1	l−1	PROPN
ejpam-5050	397	3	[	[	PUNCT
ejpam-5050	397	4	x2	x2	NOUN
ejpam-5050	397	5	+	+	CCONJ
ejpam-5050	397	6	2	2	NUM
ejpam-5050	397	7	+	+	CCONJ
ejpam-5050	397	8	4	4	NUM
ejpam-5050	397	9	√	√	NUM
ejpam-5050	397	10	x	x	SYM
ejpam-5050	397	11	π	π	NOUN
ejpam-5050	397	12	]	]	PUNCT
ejpam-5050	397	13	.	.	PUNCT
ejpam-5050	398	1	using	use	VERB
ejpam-5050	398	2	madm	madm	NOUN
ejpam-5050	398	3	with	with	ADP
ejpam-5050	398	4	(	(	PUNCT
ejpam-5050	398	5	6	6	NUM
ejpam-5050	398	6	)	)	PUNCT
ejpam-5050	398	7	,	,	PUNCT
ejpam-5050	398	8	we	we	PRON
ejpam-5050	398	9	further	far	ADV
ejpam-5050	398	10	get	get	VERB
ejpam-5050	398	11	∞∑	∞∑	NUM
ejpam-5050	398	12	n=0	n=0	NUM
ejpam-5050	398	13	yn(x	yn(x	X
ejpam-5050	398	14	)	)	PUNCT
ejpam-5050	399	1	=	=	SYM
ejpam-5050	399	2	c1x−	c1x−	ADJ
ejpam-5050	399	3	pl−1	pl−1	NOUN
ejpam-5050	399	4	[	[	PUNCT
ejpam-5050	399	5	∞∑	∞∑	NUM
ejpam-5050	399	6	n=0	n=0	NUM
ejpam-5050	399	7	anx	anx	NOUN
ejpam-5050	399	8	n	n	NOUN
ejpam-5050	399	9	]	]	PUNCT
ejpam-5050	399	10	+	+	CCONJ
ejpam-5050	399	11	l−1	l−1	NOUN
ejpam-5050	399	12	[	[	PUNCT
ejpam-5050	399	13	∞∑	∞∑	PROPN
ejpam-5050	399	14	n=0	n=0	NUM
ejpam-5050	399	15	anx	anx	NOUN
ejpam-5050	399	16	n	n	NOUN
ejpam-5050	399	17	]	]	PUNCT
ejpam-5050	399	18	+	+	CCONJ
ejpam-5050	399	19	l−1	l−1	PROPN
ejpam-5050	399	20	[	[	PUNCT
ejpam-5050	399	21	x2	x2	NOUN
ejpam-5050	399	22	+	+	CCONJ
ejpam-5050	399	23	2	2	NUM
ejpam-5050	399	24	+	+	CCONJ
ejpam-5050	399	25	4	4	NUM
ejpam-5050	399	26	√	√	NUM
ejpam-5050	399	27	x	x	SYM
ejpam-5050	399	28	π	π	X
ejpam-5050	399	29	]	]	PUNCT
ejpam-5050	399	30	−	−	PROPN
ejpam-5050	399	31	l−1	l−1	PROPN
ejpam-5050	399	32	[	[	PUNCT
ejpam-5050	399	33	d3/2	d3/2	ADJ
ejpam-5050	399	34	∞∑	∞∑	PROPN
ejpam-5050	399	35	n=0	n=0	NUM
ejpam-5050	399	36	yn(x	yn(x	X
ejpam-5050	399	37	)	)	PUNCT
ejpam-5050	399	38	]	]	PUNCT
ejpam-5050	400	1	−	−	PROPN
ejpam-5050	400	2	l−1	l−1	PROPN
ejpam-5050	400	3	[	[	PUNCT
ejpam-5050	400	4	∞∑	∞∑	PROPN
ejpam-5050	400	5	n=0	n=0	NUM
ejpam-5050	400	6	yn(x	yn(x	NOUN
ejpam-5050	400	7	)	)	PUNCT
ejpam-5050	400	8	]	]	PUNCT
ejpam-5050	400	9	,	,	PUNCT
ejpam-5050	400	10	m.	m.	PROPN
ejpam-5050	400	11	al	al	PROPN
ejpam-5050	400	12	-	-	PUNCT
ejpam-5050	400	13	mazmumy	mazmumy	PROPN
ejpam-5050	400	14	,	,	PUNCT
ejpam-5050	400	15	m.	m.	NOUN
ejpam-5050	400	16	alsulami	alsulami	PROPN
ejpam-5050	400	17	/	/	SYM
ejpam-5050	400	18	eur	eur	PROPN
ejpam-5050	400	19	.	.	PUNCT
ejpam-5050	401	1	j.	j.	PROPN
ejpam-5050	401	2	pure	pure	PROPN
ejpam-5050	401	3	appl	appl	PROPN
ejpam-5050	401	4	.	.	PROPN
ejpam-5050	401	5	math	math	PROPN
ejpam-5050	401	6	,	,	PUNCT
ejpam-5050	401	7	17	17	NUM
ejpam-5050	401	8	(	(	PUNCT
ejpam-5050	401	9	1	1	NUM
ejpam-5050	401	10	)	)	PUNCT
ejpam-5050	401	11	(	(	PUNCT
ejpam-5050	401	12	2024	2024	NUM
ejpam-5050	401	13	)	)	PUNCT
ejpam-5050	401	14	,	,	PUNCT
ejpam-5050	401	15	546	546	NUM
ejpam-5050	401	16	-	-	SYM
ejpam-5050	401	17	568	568	NUM
ejpam-5050	401	18	560	560	NUM
ejpam-5050	401	19	and	and	CCONJ
ejpam-5050	401	20	thereafter	thereafter	ADV
ejpam-5050	401	21	take	take	VERB
ejpam-5050	401	22	into	into	ADP
ejpam-5050	401	23	account	account	NOUN
ejpam-5050	401	24	y0(x	y0(x	NUM
ejpam-5050	401	25	)	)	PUNCT
ejpam-5050	401	26	and	and	CCONJ
ejpam-5050	401	27	y1(x	y1(x	NOUN
ejpam-5050	401	28	)	)	PUNCT
ejpam-5050	401	29	as	as	SCONJ
ejpam-5050	401	30	follows	follow	VERB
ejpam-5050	401	31	y0(x	y0(x	NUM
ejpam-5050	401	32	)	)	PUNCT
ejpam-5050	401	33	=	=	SYM
ejpam-5050	402	1	c1x+	c1x+	PRON
ejpam-5050	402	2	l−1	l−1	PROPN
ejpam-5050	402	3	[	[	PUNCT
ejpam-5050	402	4	∞∑	∞∑	PROPN
ejpam-5050	402	5	n=0	n=0	NUM
ejpam-5050	402	6	anx	anx	NOUN
ejpam-5050	402	7	n	n	NOUN
ejpam-5050	402	8	]	]	PUNCT
ejpam-5050	402	9	,	,	PUNCT
ejpam-5050	402	10	=	=	SYM
ejpam-5050	402	11	c1x+	c1x+	NOUN
ejpam-5050	403	1	1	1	NUM
ejpam-5050	403	2	2	2	NUM
ejpam-5050	403	3	a0x	a0x	ADP
ejpam-5050	403	4	2	2	NUM
ejpam-5050	403	5	+	+	SYM
ejpam-5050	403	6	1	1	NUM
ejpam-5050	403	7	6	6	NUM
ejpam-5050	403	8	a1x	a1x	SYM
ejpam-5050	403	9	3	3	NUM
ejpam-5050	403	10	+	+	CCONJ
ejpam-5050	403	11	1	1	NUM
ejpam-5050	403	12	12	12	NUM
ejpam-5050	403	13	a2x	a2x	ADP
ejpam-5050	403	14	4	4	NUM
ejpam-5050	403	15	+	+	NUM
ejpam-5050	403	16	...	...	PUNCT
ejpam-5050	403	17	and	and	CCONJ
ejpam-5050	403	18	y1(x	y1(x	NOUN
ejpam-5050	403	19	)	)	PUNCT
ejpam-5050	403	20	=	=	SYM
ejpam-5050	403	21	−pl−1	−pl−1	NOUN
ejpam-5050	403	22	[	[	PUNCT
ejpam-5050	403	23	∞∑	∞∑	NUM
ejpam-5050	403	24	n=0	n=0	NUM
ejpam-5050	403	25	anx	anx	NOUN
ejpam-5050	403	26	n	n	NOUN
ejpam-5050	403	27	]	]	PUNCT
ejpam-5050	404	1	+	+	CCONJ
ejpam-5050	404	2	l−1	l−1	PROPN
ejpam-5050	404	3	[	[	PUNCT
ejpam-5050	404	4	x2	x2	NOUN
ejpam-5050	404	5	+	+	CCONJ
ejpam-5050	404	6	2	2	NUM
ejpam-5050	404	7	+	+	CCONJ
ejpam-5050	404	8	4	4	NUM
ejpam-5050	404	9	√	√	NUM
ejpam-5050	404	10	x	x	SYM
ejpam-5050	404	11	π	π	X
ejpam-5050	404	12	]	]	PUNCT
ejpam-5050	404	13	−	−	PROPN
ejpam-5050	404	14	l−1	l−1	PROPN
ejpam-5050	404	15	[	[	PUNCT
ejpam-5050	404	16	d3/2y0(x	d3/2y0(x	NOUN
ejpam-5050	404	17	)	)	PUNCT
ejpam-5050	404	18	]	]	PUNCT
ejpam-5050	404	19	−	−	PROPN
ejpam-5050	404	20	l−1[y0(x	l−1[y0(x	NOUN
ejpam-5050	404	21	)	)	PUNCT
ejpam-5050	404	22	]	]	PUNCT
ejpam-5050	404	23	,	,	PUNCT
ejpam-5050	404	24	=	=	PUNCT
ejpam-5050	405	1	−p	−p	NOUN
ejpam-5050	405	2	[	[	X
ejpam-5050	405	3	1	1	NUM
ejpam-5050	405	4	2	2	NUM
ejpam-5050	405	5	a0x	a0x	ADP
ejpam-5050	405	6	2	2	NUM
ejpam-5050	405	7	+	+	SYM
ejpam-5050	405	8	1	1	NUM
ejpam-5050	405	9	6	6	NUM
ejpam-5050	405	10	a1x	a1x	SYM
ejpam-5050	405	11	3	3	NUM
ejpam-5050	405	12	+	+	CCONJ
ejpam-5050	405	13	1	1	NUM
ejpam-5050	405	14	12	12	NUM
ejpam-5050	405	15	a2x	a2x	ADP
ejpam-5050	405	16	4	4	NUM
ejpam-5050	405	17	+	+	NUM
ejpam-5050	405	18	...	...	PUNCT
ejpam-5050	405	19	]	]	PUNCT
ejpam-5050	406	1	+	+	CCONJ
ejpam-5050	406	2	1	1	NUM
ejpam-5050	406	3	12	12	NUM
ejpam-5050	406	4	x4	x4	PROPN
ejpam-5050	406	5	+	+	CCONJ
ejpam-5050	406	6	x2	x2	PROPN
ejpam-5050	407	1	+	+	CCONJ
ejpam-5050	407	2	16	16	NUM
ejpam-5050	407	3	15	15	NUM
ejpam-5050	408	1	√	√	PROPN
ejpam-5050	408	2	π	π	PROPN
ejpam-5050	408	3	x5/2	x5/2	PROPN
ejpam-5050	408	4	−	−	PROPN
ejpam-5050	408	5	4c1	4c1	NUM
ejpam-5050	408	6	3	3	NUM
ejpam-5050	408	7	√	√	PROPN
ejpam-5050	408	8	π	π	PROPN
ejpam-5050	408	9	x3/2	x3/2	NUM
ejpam-5050	409	1	−	−	PROPN
ejpam-5050	409	2	8a0	8a0	NUM
ejpam-5050	409	3	15	15	NUM
ejpam-5050	410	1	√	√	PROPN
ejpam-5050	410	2	π	π	PROPN
ejpam-5050	410	3	x5/2	x5/2	PROPN
ejpam-5050	410	4	−	−	PROPN
ejpam-5050	411	1	16a1	16a1	NUM
ejpam-5050	411	2	105	105	NUM
ejpam-5050	411	3	√	√	PROPN
ejpam-5050	411	4	π	π	PROPN
ejpam-5050	411	5	x7/2	x7/2	PROPN
ejpam-5050	412	1	−	−	PROPN
ejpam-5050	413	1	64a2	64a2	NUM
ejpam-5050	413	2	945	945	NUM
ejpam-5050	413	3	√	√	PROPN
ejpam-5050	413	4	π	π	X
ejpam-5050	413	5	x9/2	x9/2	PUNCT
ejpam-5050	414	1	−	−	PROPN
ejpam-5050	414	2	c1	c1	PROPN
ejpam-5050	414	3	6	6	NUM
ejpam-5050	414	4	x3	x3	PROPN
ejpam-5050	414	5	−	−	PROPN
ejpam-5050	414	6	a0	a0	PROPN
ejpam-5050	414	7	24	24	NUM
ejpam-5050	414	8	x4	x4	PROPN
ejpam-5050	414	9	−	−	PROPN
ejpam-5050	414	10	a1	a1	NOUN
ejpam-5050	414	11	120	120	NUM
ejpam-5050	414	12	x5	x5	NOUN
ejpam-5050	414	13	−	−	PROPN
ejpam-5050	414	14	a2	a2	PROPN
ejpam-5050	414	15	360	360	NUM
ejpam-5050	414	16	x6	x6	PROPN
ejpam-5050	414	17	+	+	CCONJ
ejpam-5050	414	18	...	...	PUNCT
ejpam-5050	414	19	more	more	ADV
ejpam-5050	414	20	so	so	ADV
ejpam-5050	414	21	,	,	PUNCT
ejpam-5050	414	22	collecting	collect	VERB
ejpam-5050	414	23	the	the	DET
ejpam-5050	414	24	related	related	ADJ
ejpam-5050	414	25	terms	term	NOUN
ejpam-5050	414	26	,	,	PUNCT
ejpam-5050	414	27	and	and	CCONJ
ejpam-5050	414	28	subsequently	subsequently	ADV
ejpam-5050	414	29	the	the	DET
ejpam-5050	414	30	equating	equating	ADJ
ejpam-5050	414	31	coefficients	coefficient	NOUN
ejpam-5050	414	32	of	of	ADP
ejpam-5050	414	33	xn	xn	PROPN
ejpam-5050	414	34	in	in	ADP
ejpam-5050	414	35	both	both	DET
ejpam-5050	414	36	sides	side	NOUN
ejpam-5050	414	37	of	of	ADP
ejpam-5050	414	38	the	the	DET
ejpam-5050	414	39	above	above	ADJ
ejpam-5050	414	40	expression	expression	NOUN
ejpam-5050	414	41	,	,	PUNCT
ejpam-5050	414	42	where	where	SCONJ
ejpam-5050	414	43	y1(x	y1(x	NOUN
ejpam-5050	414	44	)	)	PUNCT
ejpam-5050	414	45	=	=	SYM
ejpam-5050	414	46	0	0	NUM
ejpam-5050	414	47	with	with	ADP
ejpam-5050	414	48	p	p	NOUN
ejpam-5050	414	49	=	=	SYM
ejpam-5050	414	50	1	1	NUM
ejpam-5050	414	51	,	,	PUNCT
ejpam-5050	414	52	one	one	PRON
ejpam-5050	414	53	gets	get	VERB
ejpam-5050	414	54	y1(x	y1(x	NOUN
ejpam-5050	414	55	)	)	PUNCT
ejpam-5050	414	56	=	=	SYM
ejpam-5050	415	1	(	(	PUNCT
ejpam-5050	415	2	−	−	PROPN
ejpam-5050	415	3	1	1	NUM
ejpam-5050	415	4	2	2	NUM
ejpam-5050	415	5	a0	a0	NOUN
ejpam-5050	415	6	+	+	CCONJ
ejpam-5050	415	7	1	1	NUM
ejpam-5050	415	8	)	)	PUNCT
ejpam-5050	415	9	x2	x2	NOUN
ejpam-5050	415	10	−	−	PROPN
ejpam-5050	416	1	(	(	PUNCT
ejpam-5050	416	2	1	1	NUM
ejpam-5050	416	3	6	6	NUM
ejpam-5050	416	4	a1	a1	NOUN
ejpam-5050	416	5	+	+	CCONJ
ejpam-5050	416	6	c1	c1	PROPN
ejpam-5050	416	7	6	6	NUM
ejpam-5050	416	8	)	)	PUNCT
ejpam-5050	416	9	x3	x3	VERB
ejpam-5050	416	10	+	+	CCONJ
ejpam-5050	416	11	(	(	PUNCT
ejpam-5050	416	12	1	1	NUM
ejpam-5050	416	13	12	12	NUM
ejpam-5050	416	14	−	−	NUM
ejpam-5050	416	15	1	1	NUM
ejpam-5050	416	16	12	12	NUM
ejpam-5050	416	17	a2	a2	PROPN
ejpam-5050	416	18	−	−	PROPN
ejpam-5050	416	19	a0	a0	PROPN
ejpam-5050	416	20	24	24	NUM
ejpam-5050	416	21	)	)	PUNCT
ejpam-5050	416	22	x4	x4	PROPN
ejpam-5050	417	1	+	+	CCONJ
ejpam-5050	417	2	16	16	NUM
ejpam-5050	417	3	15	15	NUM
ejpam-5050	417	4	√	√	PROPN
ejpam-5050	417	5	π	π	PROPN
ejpam-5050	417	6	x5/2	x5/2	PROPN
ejpam-5050	418	1	−	−	PROPN
ejpam-5050	418	2	4c1	4c1	NUM
ejpam-5050	418	3	3	3	NUM
ejpam-5050	418	4	√	√	PROPN
ejpam-5050	419	1	π	π	PROPN
ejpam-5050	419	2	x3/2	x3/2	NUM
ejpam-5050	420	1	−	−	PROPN
ejpam-5050	420	2	8a0	8a0	NUM
ejpam-5050	420	3	15	15	NUM
ejpam-5050	421	1	√	√	PROPN
ejpam-5050	421	2	π	π	PROPN
ejpam-5050	421	3	x5/2	x5/2	PROPN
ejpam-5050	421	4	−	−	PROPN
ejpam-5050	422	1	16a1	16a1	NUM
ejpam-5050	422	2	105	105	NUM
ejpam-5050	422	3	√	√	PROPN
ejpam-5050	422	4	π	π	PROPN
ejpam-5050	422	5	x7/2	x7/2	PROPN
ejpam-5050	423	1	−	−	PROPN
ejpam-5050	424	1	64a2	64a2	NUM
ejpam-5050	424	2	945	945	NUM
ejpam-5050	424	3	√	√	PROPN
ejpam-5050	424	4	π	π	X
ejpam-5050	424	5	x9/2	x9/2	PUNCT
ejpam-5050	425	1	+	+	CCONJ
ejpam-5050	425	2	...	...	PUNCT
ejpam-5050	426	1	=	=	SYM
ejpam-5050	426	2	0	0	X
ejpam-5050	426	3	.	.	PUNCT
ejpam-5050	427	1	therefore	therefore	ADV
ejpam-5050	427	2	,	,	PUNCT
ejpam-5050	427	3	we	we	PRON
ejpam-5050	427	4	get	get	VERB
ejpam-5050	427	5	a0	a0	NOUN
ejpam-5050	427	6	=	=	SYM
ejpam-5050	427	7	2	2	NUM
ejpam-5050	427	8	,	,	PUNCT
ejpam-5050	427	9	a1	a1	NOUN
ejpam-5050	427	10	=	=	SYM
ejpam-5050	427	11	−c1	−c1	PROPN
ejpam-5050	427	12	,	,	PUNCT
ejpam-5050	427	13	and	and	CCONJ
ejpam-5050	427	14	a2	a2	PROPN
ejpam-5050	427	15	=	=	SYM
ejpam-5050	427	16	0	0	X
ejpam-5050	427	17	.	.	PUNCT
ejpam-5050	428	1	more	more	ADV
ejpam-5050	428	2	so	so	ADV
ejpam-5050	428	3	,	,	PUNCT
ejpam-5050	428	4	putting	put	VERB
ejpam-5050	428	5	these	these	DET
ejpam-5050	428	6	values	value	NOUN
ejpam-5050	428	7	in	in	ADP
ejpam-5050	428	8	y0(x	y0(x	NOUN
ejpam-5050	428	9	)	)	PUNCT
ejpam-5050	428	10	,	,	PUNCT
ejpam-5050	428	11	where	where	SCONJ
ejpam-5050	428	12	yn(x	yn(x	X
ejpam-5050	428	13	)	)	PUNCT
ejpam-5050	428	14	=	=	SYM
ejpam-5050	428	15	0	0	NUM
ejpam-5050	428	16	,	,	PUNCT
ejpam-5050	428	17	for	for	ADP
ejpam-5050	428	18	n	n	NOUN
ejpam-5050	428	19	⩾	⩾	NOUN
ejpam-5050	428	20	1	1	NUM
ejpam-5050	428	21	,	,	PUNCT
ejpam-5050	428	22	we	we	PRON
ejpam-5050	428	23	get	get	VERB
ejpam-5050	428	24	y(x	y(x	NOUN
ejpam-5050	428	25	)	)	PUNCT
ejpam-5050	429	1	=	=	SYM
ejpam-5050	429	2	y0(x	y0(x	X
ejpam-5050	429	3	)	)	PUNCT
ejpam-5050	429	4	=	=	SYM
ejpam-5050	430	1	c1x+	c1x+	NOUN
ejpam-5050	431	1	x2	x2	INTJ
ejpam-5050	431	2	−	−	NOUN
ejpam-5050	431	3	1	1	NUM
ejpam-5050	431	4	6	6	NUM
ejpam-5050	431	5	c1x	c1x	NOUN
ejpam-5050	431	6	3	3	NUM
ejpam-5050	431	7	.	.	PUNCT
ejpam-5050	432	1	finally	finally	ADV
ejpam-5050	432	2	,	,	PUNCT
ejpam-5050	432	3	deploying	deploy	VERB
ejpam-5050	432	4	the	the	DET
ejpam-5050	432	5	second	second	ADJ
ejpam-5050	432	6	boundary	boundary	ADJ
ejpam-5050	432	7	condition	condition	NOUN
ejpam-5050	432	8	y(5	y(5	PROPN
ejpam-5050	432	9	)	)	PUNCT
ejpam-5050	433	1	=	=	SYM
ejpam-5050	433	2	25	25	NUM
ejpam-5050	433	3	,	,	PUNCT
ejpam-5050	433	4	we	we	PRON
ejpam-5050	433	5	get	get	VERB
ejpam-5050	433	6	c1	c1	PROPN
ejpam-5050	433	7	=	=	PUNCT
ejpam-5050	433	8	0	0	PROPN
ejpam-5050	433	9	,	,	PUNCT
ejpam-5050	433	10	which	which	PRON
ejpam-5050	433	11	leads	lead	VERB
ejpam-5050	433	12	to	to	ADP
ejpam-5050	433	13	the	the	DET
ejpam-5050	433	14	acquisition	acquisition	NOUN
ejpam-5050	433	15	of	of	ADP
ejpam-5050	433	16	y(x	y(x	PROPN
ejpam-5050	433	17	)	)	PUNCT
ejpam-5050	434	1	=	=	SYM
ejpam-5050	434	2	x2	x2	PROPN
ejpam-5050	434	3	,	,	PUNCT
ejpam-5050	434	4	as	as	ADP
ejpam-5050	434	5	the	the	DET
ejpam-5050	434	6	reported	report	VERB
ejpam-5050	434	7	exact	exact	ADJ
ejpam-5050	434	8	analytical	analytical	ADJ
ejpam-5050	434	9	solution	solution	NOUN
ejpam-5050	434	10	.	.	PUNCT
ejpam-5050	435	1	algorithm	algorithm	NOUN
ejpam-5050	435	2	2	2	NUM
ejpam-5050	435	3	:	:	PUNCT
ejpam-5050	435	4	as	as	SCONJ
ejpam-5050	435	5	represented	represent	VERB
ejpam-5050	435	6	in	in	ADP
ejpam-5050	435	7	(	(	PUNCT
ejpam-5050	435	8	27	27	NUM
ejpam-5050	435	9	)	)	PUNCT
ejpam-5050	435	10	,	,	PUNCT
ejpam-5050	435	11	we	we	PRON
ejpam-5050	435	12	define	define	VERB
ejpam-5050	435	13	the	the	DET
ejpam-5050	435	14	inverse	inverse	NOUN
ejpam-5050	435	15	operator	operator	NOUN
ejpam-5050	435	16	l−1	l−1	PROPN
ejpam-5050	435	17	in	in	ADP
ejpam-5050	435	18	(	(	PUNCT
ejpam-5050	435	19	14	14	NUM
ejpam-5050	435	20	)	)	PUNCT
ejpam-5050	435	21	.	.	PUNCT
ejpam-5050	436	1	further	far	ADV
ejpam-5050	436	2	,	,	PUNCT
ejpam-5050	436	3	we	we	PRON
ejpam-5050	436	4	deploy	deploy	VERB
ejpam-5050	436	5	l−1	l−1	PROPN
ejpam-5050	436	6	(	(	PUNCT
ejpam-5050	436	7	.	.	PUNCT
ejpam-5050	436	8	)	)	PUNCT
ejpam-5050	437	1	=	=	PUNCT
ejpam-5050	438	1	∫	∫	PUNCT
ejpam-5050	438	2	x	x	SYM
ejpam-5050	438	3	0	0	NUM
ejpam-5050	438	4	dx′	dx′	NOUN
ejpam-5050	438	5	∫	∫	PROPN
ejpam-5050	438	6	x′′	x′′	PROPN
ejpam-5050	438	7	0	0	PUNCT
ejpam-5050	439	1	(	(	PUNCT
ejpam-5050	439	2	.)dx′′	.)dx′′	PROPN
ejpam-5050	439	3	−	−	NOUN
ejpam-5050	440	1	x	x	SYM
ejpam-5050	440	2	5	5	NUM
ejpam-5050	440	3	∫	∫	NUM
ejpam-5050	440	4	5	5	NUM
ejpam-5050	440	5	0	0	NUM
ejpam-5050	440	6	dx	dx	PROPN
ejpam-5050	440	7	∫	∫	PROPN
ejpam-5050	440	8	x′′	x′′	PROPN
ejpam-5050	440	9	0	0	PUNCT
ejpam-5050	440	10	(	(	PUNCT
ejpam-5050	440	11	.)dx′′	.)dx′′	PROPN
ejpam-5050	440	12	,	,	PUNCT
ejpam-5050	440	13	on	on	ADP
ejpam-5050	440	14	both	both	DET
ejpam-5050	440	15	sides	side	NOUN
ejpam-5050	440	16	of	of	ADP
ejpam-5050	440	17	(	(	PUNCT
ejpam-5050	440	18	27	27	NUM
ejpam-5050	440	19	)	)	PUNCT
ejpam-5050	440	20	to	to	PART
ejpam-5050	440	21	get	get	VERB
ejpam-5050	440	22	y(x	y(x	NOUN
ejpam-5050	440	23	)	)	PUNCT
ejpam-5050	440	24	=	=	PUNCT
ejpam-5050	440	25	5x+	5x+	NUM
ejpam-5050	440	26	l−1	l−1	PROPN
ejpam-5050	440	27	[	[	PUNCT
ejpam-5050	440	28	x2	x2	NOUN
ejpam-5050	441	1	+	+	CCONJ
ejpam-5050	441	2	2	2	NUM
ejpam-5050	441	3	+	+	CCONJ
ejpam-5050	441	4	4	4	NUM
ejpam-5050	441	5	√	√	NUM
ejpam-5050	441	6	x	x	SYM
ejpam-5050	442	1	π	π	X
ejpam-5050	442	2	]	]	PUNCT
ejpam-5050	442	3	−	−	PROPN
ejpam-5050	442	4	l−1[d3/2y(x)]−	l−1[d3/2y(x)]−	NOUN
ejpam-5050	442	5	l−1[y(x	l−1[y(x	NOUN
ejpam-5050	442	6	)	)	PUNCT
ejpam-5050	442	7	]	]	PUNCT
ejpam-5050	442	8	using	use	VERB
ejpam-5050	442	9	madm	madm	NOUN
ejpam-5050	442	10	and	and	CCONJ
ejpam-5050	442	11	(	(	PUNCT
ejpam-5050	442	12	6	6	X
ejpam-5050	442	13	)	)	PUNCT
ejpam-5050	442	14	∞∑	∞∑	NUM
ejpam-5050	442	15	n=0	n=0	NUM
ejpam-5050	442	16	yn(x	yn(x	X
ejpam-5050	442	17	)	)	PUNCT
ejpam-5050	442	18	=	=	SYM
ejpam-5050	443	1	5x+	5x+	NUM
ejpam-5050	443	2	l−1	l−1	PROPN
ejpam-5050	443	3	[	[	PUNCT
ejpam-5050	443	4	x2	x2	NOUN
ejpam-5050	444	1	+	+	CCONJ
ejpam-5050	444	2	2	2	NUM
ejpam-5050	444	3	+	+	CCONJ
ejpam-5050	444	4	4	4	NUM
ejpam-5050	444	5	√	√	NUM
ejpam-5050	444	6	x	x	SYM
ejpam-5050	444	7	π	π	X
ejpam-5050	444	8	]	]	PUNCT
ejpam-5050	444	9	−	−	PROPN
ejpam-5050	444	10	pl−1	pl−1	NOUN
ejpam-5050	444	11	[	[	PUNCT
ejpam-5050	444	12	∞∑	∞∑	NUM
ejpam-5050	444	13	n=0	n=0	NUM
ejpam-5050	444	14	anx	anx	NOUN
ejpam-5050	444	15	n	n	NOUN
ejpam-5050	444	16	]	]	PUNCT
ejpam-5050	445	1	+	+	CCONJ
ejpam-5050	445	2	l−1	l−1	NOUN
ejpam-5050	445	3	[	[	PUNCT
ejpam-5050	445	4	∞∑	∞∑	PROPN
ejpam-5050	445	5	n=0	n=0	NUM
ejpam-5050	445	6	anx	anx	ADJ
ejpam-5050	445	7	n	n	NOUN
ejpam-5050	445	8	]	]	PUNCT
ejpam-5050	445	9	m.	m.	PROPN
ejpam-5050	445	10	al	al	PROPN
ejpam-5050	445	11	-	-	PUNCT
ejpam-5050	445	12	mazmumy	mazmumy	PROPN
ejpam-5050	445	13	,	,	PUNCT
ejpam-5050	445	14	m.	m.	NOUN
ejpam-5050	445	15	alsulami	alsulami	PROPN
ejpam-5050	445	16	/	/	SYM
ejpam-5050	445	17	eur	eur	PROPN
ejpam-5050	445	18	.	.	PUNCT
ejpam-5050	446	1	j.	j.	PROPN
ejpam-5050	446	2	pure	pure	PROPN
ejpam-5050	446	3	appl	appl	PROPN
ejpam-5050	446	4	.	.	PROPN
ejpam-5050	446	5	math	math	PROPN
ejpam-5050	446	6	,	,	PUNCT
ejpam-5050	446	7	17	17	NUM
ejpam-5050	446	8	(	(	PUNCT
ejpam-5050	446	9	1	1	NUM
ejpam-5050	446	10	)	)	PUNCT
ejpam-5050	446	11	(	(	PUNCT
ejpam-5050	446	12	2024	2024	NUM
ejpam-5050	446	13	)	)	PUNCT
ejpam-5050	446	14	,	,	PUNCT
ejpam-5050	446	15	546	546	NUM
ejpam-5050	446	16	-	-	SYM
ejpam-5050	446	17	568	568	NUM
ejpam-5050	446	18	561	561	NUM
ejpam-5050	446	19	−	−	PUNCT
ejpam-5050	446	20	l−1	l−1	PROPN
ejpam-5050	446	21	[	[	PUNCT
ejpam-5050	446	22	d3/2	d3/2	ADJ
ejpam-5050	446	23	∞∑	∞∑	PROPN
ejpam-5050	446	24	n=0	n=0	NUM
ejpam-5050	446	25	yn(x	yn(x	X
ejpam-5050	446	26	)	)	PUNCT
ejpam-5050	446	27	]	]	PUNCT
ejpam-5050	447	1	−	−	PROPN
ejpam-5050	447	2	l−1	l−1	PROPN
ejpam-5050	447	3	[	[	PUNCT
ejpam-5050	447	4	∞∑	∞∑	PROPN
ejpam-5050	447	5	n=0	n=0	NUM
ejpam-5050	447	6	yn(x	yn(x	NUM
ejpam-5050	447	7	)	)	PUNCT
ejpam-5050	447	8	]	]	PUNCT
ejpam-5050	447	9	.	.	PUNCT
ejpam-5050	448	1	in	in	ADP
ejpam-5050	448	2	addition	addition	NOUN
ejpam-5050	448	3	,	,	PUNCT
ejpam-5050	448	4	the	the	DET
ejpam-5050	448	5	latter	latter	ADJ
ejpam-5050	448	6	equation	equation	NOUN
ejpam-5050	448	7	further	further	ADJ
ejpam-5050	448	8	results	result	NOUN
ejpam-5050	448	9	in	in	ADP
ejpam-5050	448	10	y0(x	y0(x	NOUN
ejpam-5050	448	11	)	)	PUNCT
ejpam-5050	448	12	=	=	NOUN
ejpam-5050	448	13	5x+	5x+	NUM
ejpam-5050	448	14	l−1	l−1	NOUN
ejpam-5050	448	15	[	[	PUNCT
ejpam-5050	448	16	∞∑	∞∑	PROPN
ejpam-5050	448	17	n=0	n=0	NUM
ejpam-5050	448	18	anx	anx	NOUN
ejpam-5050	448	19	n	n	NOUN
ejpam-5050	448	20	]	]	PUNCT
ejpam-5050	448	21	,	,	PUNCT
ejpam-5050	448	22	and	and	CCONJ
ejpam-5050	448	23	y1(x	y1(x	NOUN
ejpam-5050	448	24	)	)	PUNCT
ejpam-5050	448	25	=	=	SYM
ejpam-5050	448	26	l−1	l−1	PROPN
ejpam-5050	448	27	[	[	PUNCT
ejpam-5050	448	28	x2	x2	NOUN
ejpam-5050	449	1	+	+	CCONJ
ejpam-5050	449	2	2	2	NUM
ejpam-5050	449	3	+	+	CCONJ
ejpam-5050	449	4	4	4	NUM
ejpam-5050	449	5	√	√	NUM
ejpam-5050	449	6	x	x	SYM
ejpam-5050	449	7	π	π	X
ejpam-5050	449	8	]	]	PUNCT
ejpam-5050	449	9	−	−	PROPN
ejpam-5050	449	10	pl−1	pl−1	NOUN
ejpam-5050	449	11	[	[	PUNCT
ejpam-5050	449	12	∞∑	∞∑	NUM
ejpam-5050	449	13	n=0	n=0	NUM
ejpam-5050	449	14	anx	anx	NOUN
ejpam-5050	449	15	n	n	NOUN
ejpam-5050	449	16	]	]	PUNCT
ejpam-5050	449	17	−	−	PROPN
ejpam-5050	449	18	l−1[d3/2y0(x)]−	l−1[d3/2y0(x)]−	PROPN
ejpam-5050	449	19	l−1[y0(x	l−1[y0(x	PROPN
ejpam-5050	449	20	)	)	PUNCT
ejpam-5050	449	21	]	]	PUNCT
ejpam-5050	449	22	,	,	PUNCT
ejpam-5050	449	23	then	then	ADV
ejpam-5050	449	24	,	,	PUNCT
ejpam-5050	449	25	evaluating	evaluate	VERB
ejpam-5050	449	26	y0(x	y0(x	NOUN
ejpam-5050	449	27	)	)	PUNCT
ejpam-5050	449	28	using	use	VERB
ejpam-5050	449	29	the	the	DET
ejpam-5050	449	30	inverse	inverse	NOUN
ejpam-5050	449	31	operator	operator	NOUN
ejpam-5050	449	32	(	(	PUNCT
ejpam-5050	449	33	14	14	NUM
ejpam-5050	449	34	)	)	PUNCT
ejpam-5050	449	35	yields	yield	NOUN
ejpam-5050	449	36	y0(x	y0(x	NUM
ejpam-5050	449	37	)	)	PUNCT
ejpam-5050	449	38	=	=	SYM
ejpam-5050	449	39	5x+	5x+	NUM
ejpam-5050	449	40	a0	a0	NOUN
ejpam-5050	449	41	2	2	NUM
ejpam-5050	449	42	x2	x2	NOUN
ejpam-5050	450	1	+	+	CCONJ
ejpam-5050	450	2	a1	a1	NOUN
ejpam-5050	450	3	6	6	NUM
ejpam-5050	450	4	x3	x3	NOUN
ejpam-5050	450	5	+	+	CCONJ
ejpam-5050	450	6	a2	a2	PROPN
ejpam-5050	450	7	12	12	NUM
ejpam-5050	450	8	x4	x4	PROPN
ejpam-5050	450	9	+	+	PROPN
ejpam-5050	450	10	a3	a3	VERB
ejpam-5050	450	11	20	20	NUM
ejpam-5050	450	12	x5	x5	NOUN
ejpam-5050	450	13	−	−	NOUN
ejpam-5050	451	1	x	x	SYM
ejpam-5050	452	1	(	(	PUNCT
ejpam-5050	452	2	5a0	5a0	NUM
ejpam-5050	452	3	2	2	NUM
ejpam-5050	452	4	+	+	CCONJ
ejpam-5050	452	5	25a1	25a1	NUM
ejpam-5050	452	6	6	6	NUM
ejpam-5050	452	7	+	+	SYM
ejpam-5050	452	8	125a2	125a2	NUM
ejpam-5050	452	9	12	12	NUM
ejpam-5050	452	10	+	+	CCONJ
ejpam-5050	452	11	125a3	125a3	NUM
ejpam-5050	452	12	4	4	NUM
ejpam-5050	452	13	)	)	PUNCT
ejpam-5050	452	14	,	,	PUNCT
ejpam-5050	452	15	while	while	SCONJ
ejpam-5050	452	16	y1(x	y1(x	NOUN
ejpam-5050	452	17	)	)	PUNCT
ejpam-5050	452	18	is	be	AUX
ejpam-5050	452	19	found	find	VERB
ejpam-5050	452	20	by	by	ADP
ejpam-5050	452	21	collecting	collect	VERB
ejpam-5050	452	22	out	out	ADP
ejpam-5050	452	23	the	the	DET
ejpam-5050	452	24	like	like	ADJ
ejpam-5050	452	25	terms	term	NOUN
ejpam-5050	452	26	by	by	ADP
ejpam-5050	452	27	using	use	VERB
ejpam-5050	452	28	the	the	DET
ejpam-5050	452	29	inverse	inverse	NOUN
ejpam-5050	452	30	operator	operator	NOUN
ejpam-5050	452	31	(	(	PUNCT
ejpam-5050	452	32	14	14	NUM
ejpam-5050	452	33	)	)	PUNCT
ejpam-5050	452	34	and	and	CCONJ
ejpam-5050	452	35	setting	set	VERB
ejpam-5050	452	36	p	p	NOUN
ejpam-5050	452	37	=	=	NOUN
ejpam-5050	452	38	1	1	NUM
ejpam-5050	452	39	as	as	SCONJ
ejpam-5050	452	40	follows	follow	VERB
ejpam-5050	452	41	y1(x	y1(x	NOUN
ejpam-5050	452	42	)	)	PUNCT
ejpam-5050	452	43	=	=	SYM
ejpam-5050	452	44	−	−	PROPN
ejpam-5050	452	45	a3	a3	NOUN
ejpam-5050	452	46	840	840	NUM
ejpam-5050	452	47	x7	x7	NOUN
ejpam-5050	452	48	−	−	PROPN
ejpam-5050	452	49	a2	a2	PROPN
ejpam-5050	452	50	360	360	NUM
ejpam-5050	452	51	x6	x6	PROPN
ejpam-5050	452	52	−	−	PROPN
ejpam-5050	452	53	(	(	PUNCT
ejpam-5050	452	54	a1	a1	NOUN
ejpam-5050	452	55	120	120	NUM
ejpam-5050	452	56	+	+	NOUN
ejpam-5050	452	57	a3	a3	NOUN
ejpam-5050	452	58	20	20	NUM
ejpam-5050	452	59	)	)	PUNCT
ejpam-5050	452	60	x5	x5	NOUN
ejpam-5050	453	1	+	+	CCONJ
ejpam-5050	453	2	(	(	PUNCT
ejpam-5050	453	3	1	1	NUM
ejpam-5050	453	4	12	12	NUM
ejpam-5050	453	5	−	−	PROPN
ejpam-5050	453	6	a2	a2	PROPN
ejpam-5050	453	7	12	12	NUM
ejpam-5050	453	8	−	−	PROPN
ejpam-5050	453	9	a0	a0	PROPN
ejpam-5050	453	10	24	24	NUM
ejpam-5050	453	11	)	)	PUNCT
ejpam-5050	453	12	x4	x4	PROPN
ejpam-5050	454	1	+	+	PUNCT
ejpam-5050	454	2	(	(	PUNCT
ejpam-5050	454	3	125a3	125a3	NUM
ejpam-5050	454	4	24	24	NUM
ejpam-5050	454	5	+	+	CCONJ
ejpam-5050	454	6	125a2	125a2	NUM
ejpam-5050	454	7	72	72	NUM
ejpam-5050	454	8	−	−	NUM
ejpam-5050	455	1	19a1	19a1	NUM
ejpam-5050	455	2	36	36	NUM
ejpam-5050	456	1	+	+	CCONJ
ejpam-5050	456	2	5a0	5a0	NUM
ejpam-5050	456	3	12	12	NUM
ejpam-5050	456	4	−	−	NOUN
ejpam-5050	456	5	25	25	NUM
ejpam-5050	456	6	6	6	NUM
ejpam-5050	456	7	)	)	PUNCT
ejpam-5050	456	8	x3	x3	PROPN
ejpam-5050	456	9	+	+	CCONJ
ejpam-5050	456	10	(	(	PUNCT
ejpam-5050	456	11	1−	1−	NUM
ejpam-5050	456	12	a0	a0	PROPN
ejpam-5050	456	13	2	2	NUM
ejpam-5050	456	14	)	)	PUNCT
ejpam-5050	457	1	x2	x2	NOUN
ejpam-5050	457	2	−	−	PUNCT
ejpam-5050	458	1	[	[	X
ejpam-5050	458	2	185	185	NUM
ejpam-5050	458	3	12	12	NUM
ejpam-5050	458	4	+	+	CCONJ
ejpam-5050	458	5	80	80	NUM
ejpam-5050	458	6	√	√	NUM
ejpam-5050	458	7	5	5	NUM
ejpam-5050	458	8	15	15	NUM
ejpam-5050	458	9	√	√	PROPN
ejpam-5050	458	10	π	π	PROPN
ejpam-5050	458	11	+	+	CCONJ
ejpam-5050	458	12	1125a3	1125a3	NUM
ejpam-5050	458	13	14	14	NUM
ejpam-5050	458	14	+	+	CCONJ
ejpam-5050	458	15	875a2	875a2	NUM
ejpam-5050	458	16	36	36	NUM
ejpam-5050	459	1	+	+	CCONJ
ejpam-5050	459	2	575a1	575a1	NUM
ejpam-5050	459	3	72	72	NUM
ejpam-5050	460	1	+	+	CCONJ
ejpam-5050	460	2	65a0	65a0	NUM
ejpam-5050	460	3	24	24	NUM
ejpam-5050	460	4	−	−	NUM
ejpam-5050	460	5	652	652	NUM
ejpam-5050	460	6	6	6	NUM
ejpam-5050	460	7	+	+	CCONJ
ejpam-5050	460	8	1	1	NUM
ejpam-5050	460	9	3150	3150	NUM
ejpam-5050	460	10	√	√	PROPN
ejpam-5050	460	11	π	π	PROPN
ejpam-5050	460	12	(	(	PUNCT
ejpam-5050	460	13	2100	2100	NUM
ejpam-5050	460	14	√	√	PROPN
ejpam-5050	460	15	5a0	5a0	NUM
ejpam-5050	460	16	+	+	CCONJ
ejpam-5050	460	17	5500	5500	NUM
ejpam-5050	460	18	√	√	NUM
ejpam-5050	460	19	5a1	5a1	NUM
ejpam-5050	460	20	+	+	CCONJ
ejpam-5050	460	21	51250	51250	NUM
ejpam-5050	460	22	√	√	NUM
ejpam-5050	460	23	5	5	NUM
ejpam-5050	460	24	3	3	NUM
ejpam-5050	460	25	a2	a2	PROPN
ejpam-5050	460	26	+	+	NOUN
ejpam-5050	460	27	643750	643750	NUM
ejpam-5050	460	28	√	√	NUM
ejpam-5050	460	29	5	5	NUM
ejpam-5050	460	30	11	11	NUM
ejpam-5050	460	31	a3	a3	NOUN
ejpam-5050	460	32	−	−	PROPN
ejpam-5050	460	33	105000	105000	NUM
ejpam-5050	460	34	√	√	NUM
ejpam-5050	460	35	5	5	NUM
ejpam-5050	460	36	)	)	PUNCT
ejpam-5050	460	37	]	]	PUNCT
ejpam-5050	461	1	x−	x−	PROPN
ejpam-5050	461	2	128a3	128a3	NUM
ejpam-5050	461	3	3465	3465	NUM
ejpam-5050	462	1	√	√	PROPN
ejpam-5050	462	2	π	π	PROPN
ejpam-5050	462	3	x11/2	x11/2	PUNCT
ejpam-5050	463	1	−	−	PROPN
ejpam-5050	463	2	64a2	64a2	NUM
ejpam-5050	464	1	945	945	NUM
ejpam-5050	464	2	√	√	PROPN
ejpam-5050	464	3	π	π	X
ejpam-5050	464	4	x9/2	x9/2	PUNCT
ejpam-5050	465	1	−	−	PROPN
ejpam-5050	465	2	16a1	16a1	NUM
ejpam-5050	465	3	105	105	NUM
ejpam-5050	466	1	√	√	PROPN
ejpam-5050	466	2	π	π	X
ejpam-5050	466	3	x7/2	x7/2	PROPN
ejpam-5050	467	1	+	+	CCONJ
ejpam-5050	467	2	(	(	PUNCT
ejpam-5050	467	3	16	16	NUM
ejpam-5050	467	4	15	15	NUM
ejpam-5050	467	5	√	√	PROPN
ejpam-5050	467	6	π	π	PROPN
ejpam-5050	467	7	−	−	PROPN
ejpam-5050	467	8	8a0	8a0	NUM
ejpam-5050	467	9	15	15	NUM
ejpam-5050	467	10	√	√	PROPN
ejpam-5050	467	11	π	π	PROPN
ejpam-5050	467	12	)	)	PUNCT
ejpam-5050	467	13	x5/2	x5/2	PROPN
ejpam-5050	468	1	+	+	CCONJ
ejpam-5050	468	2	1	1	NUM
ejpam-5050	468	3	10395	10395	NUM
ejpam-5050	468	4	√	√	PROPN
ejpam-5050	468	5	π	π	X
ejpam-5050	468	6	(	(	PUNCT
ejpam-5050	468	7	433125a3	433125a3	X
ejpam-5050	468	8	+	+	CCONJ
ejpam-5050	468	9	144375a2	144375a2	NUM
ejpam-5050	468	10	+	+	ADJ
ejpam-5050	468	11	57750a1	57750a1	NUM
ejpam-5050	468	12	+	+	SYM
ejpam-5050	468	13	34650a0	34650a0	PROPN
ejpam-5050	468	14	−	−	PROPN
ejpam-5050	468	15	346500	346500	NUM
ejpam-5050	468	16	)	)	PUNCT
ejpam-5050	468	17	x3/2	x3/2	NUM
ejpam-5050	468	18	.	.	PUNCT
ejpam-5050	469	1	moreover	moreover	ADV
ejpam-5050	469	2	,	,	PUNCT
ejpam-5050	469	3	setting	set	VERB
ejpam-5050	469	4	y1(x	y1(x	NOUN
ejpam-5050	469	5	)	)	PUNCT
ejpam-5050	469	6	=	=	SYM
ejpam-5050	469	7	0	0	PUNCT
ejpam-5050	469	8	while	while	SCONJ
ejpam-5050	469	9	equating	equate	VERB
ejpam-5050	469	10	the	the	DET
ejpam-5050	469	11	coefficients	coefficient	NOUN
ejpam-5050	469	12	of	of	ADP
ejpam-5050	469	13	xn	xn	PROPN
ejpam-5050	469	14	,	,	PUNCT
ejpam-5050	469	15	we	we	PRON
ejpam-5050	469	16	acquire	acquire	VERB
ejpam-5050	469	17	a0	a0	NOUN
ejpam-5050	469	18	=	=	SYM
ejpam-5050	469	19	2	2	NUM
ejpam-5050	469	20	,	,	PUNCT
ejpam-5050	469	21	and	and	CCONJ
ejpam-5050	469	22	a1	a1	NOUN
ejpam-5050	469	23	=	=	PROPN
ejpam-5050	469	24	a2	a2	PROPN
ejpam-5050	469	25	=	=	SYM
ejpam-5050	469	26	a3	a3	NOUN
ejpam-5050	469	27	=	=	SYM
ejpam-5050	469	28	0	0	X
ejpam-5050	469	29	.	.	PUNCT
ejpam-5050	470	1	hence	hence	ADV
ejpam-5050	470	2	,	,	PUNCT
ejpam-5050	470	3	y(x	y(x	PROPN
ejpam-5050	470	4	)	)	PUNCT
ejpam-5050	470	5	=	=	SYM
ejpam-5050	470	6	y0(x	y0(x	X
ejpam-5050	470	7	)	)	PUNCT
ejpam-5050	470	8	=	=	SYM
ejpam-5050	470	9	x2	x2	PROPN
ejpam-5050	470	10	,	,	PUNCT
ejpam-5050	470	11	which	which	PRON
ejpam-5050	470	12	happens	happen	VERB
ejpam-5050	470	13	to	to	PART
ejpam-5050	470	14	be	be	AUX
ejpam-5050	470	15	the	the	DET
ejpam-5050	470	16	reported	report	VERB
ejpam-5050	470	17	exact	exact	ADJ
ejpam-5050	470	18	analytical	analytical	ADJ
ejpam-5050	470	19	solution	solution	NOUN
ejpam-5050	470	20	of	of	ADP
ejpam-5050	470	21	(	(	PUNCT
ejpam-5050	470	22	26	26	NUM
ejpam-5050	470	23	)	)	PUNCT
ejpam-5050	470	24	.	.	PUNCT
ejpam-5050	471	1	example	example	NOUN
ejpam-5050	472	1	5	5	NUM
ejpam-5050	472	2	.	.	PUNCT
ejpam-5050	472	3	consider	consider	VERB
ejpam-5050	472	4	the	the	DET
ejpam-5050	472	5	bvp	bvp	NOUN
ejpam-5050	472	6	(	(	PUNCT
ejpam-5050	472	7	24	24	NUM
ejpam-5050	472	8	)	)	PUNCT
ejpam-5050	472	9	after	after	ADP
ejpam-5050	472	10	being	be	AUX
ejpam-5050	472	11	transformed	transform	VERB
ejpam-5050	472	12	into	into	ADP
ejpam-5050	472	13	a	a	DET
ejpam-5050	472	14	coupled	couple	VERB
ejpam-5050	472	15	system	system	NOUN
ejpam-5050	472	16	via	via	ADP
ejpam-5050	472	17	[	[	X
ejpam-5050	472	18	18	18	NUM
ejpam-5050	472	19	]	]	PUNCT
ejpam-5050	472	20	as	as	SCONJ
ejpam-5050	472	21	follows	follow	VERB
ejpam-5050	472	22	{	{	PUNCT
ejpam-5050	472	23	d1.5y1	d1.5y1	X
ejpam-5050	472	24	=	=	SYM
ejpam-5050	472	25	y2	y2	PROPN
ejpam-5050	472	26	,	,	PUNCT
ejpam-5050	472	27	y1(0	y1(0	PROPN
ejpam-5050	472	28	)	)	PUNCT
ejpam-5050	472	29	=	=	SYM
ejpam-5050	472	30	1	1	NUM
ejpam-5050	472	31	,	,	PUNCT
ejpam-5050	472	32	y1(1	y1(1	NOUN
ejpam-5050	472	33	)	)	PUNCT
ejpam-5050	472	34	=	=	SYM
ejpam-5050	472	35	2	2	NUM
ejpam-5050	472	36	,	,	PUNCT
ejpam-5050	472	37	d0.5y2	d0.5y2	VERB
ejpam-5050	472	38	=	=	SYM
ejpam-5050	472	39	−y2	−y2	PROPN
ejpam-5050	472	40	−	−	PROPN
ejpam-5050	472	41	y1	y1	NOUN
ejpam-5050	473	1	+	+	CCONJ
ejpam-5050	473	2	1	1	NUM
ejpam-5050	473	3	+	+	CCONJ
ejpam-5050	473	4	x	x	PROPN
ejpam-5050	473	5	,	,	PUNCT
ejpam-5050	473	6	y2(0	y2(0	PROPN
ejpam-5050	473	7	)	)	PUNCT
ejpam-5050	473	8	=	=	PUNCT
ejpam-5050	474	1	0	0	X
ejpam-5050	474	2	.	.	PUNCT
ejpam-5050	475	1	(	(	PUNCT
ejpam-5050	475	2	28	28	NUM
ejpam-5050	475	3	)	)	PUNCT
ejpam-5050	475	4	here	here	ADV
ejpam-5050	475	5	,	,	PUNCT
ejpam-5050	475	6	we	we	PRON
ejpam-5050	475	7	apply	apply	VERB
ejpam-5050	475	8	the	the	DET
ejpam-5050	475	9	inverse	inverse	NOUN
ejpam-5050	475	10	operator	operator	NOUN
ejpam-5050	475	11	on	on	ADP
ejpam-5050	475	12	both	both	DET
ejpam-5050	475	13	sides	side	NOUN
ejpam-5050	475	14	of	of	ADP
ejpam-5050	475	15	the	the	DET
ejpam-5050	475	16	equations	equation	NOUN
ejpam-5050	475	17	in	in	ADP
ejpam-5050	475	18	(	(	PUNCT
ejpam-5050	475	19	28	28	NUM
ejpam-5050	475	20	)	)	PUNCT
ejpam-5050	475	21	to	to	PART
ejpam-5050	475	22	get	get	VERB
ejpam-5050	475	23	{	{	PUNCT
ejpam-5050	475	24	i1.5[d1.5y1	i1.5[d1.5y1	NOUN
ejpam-5050	475	25	]	]	X
ejpam-5050	475	26	=	=	X
ejpam-5050	475	27	i1.5[y2	i1.5[y2	X
ejpam-5050	475	28	]	]	X
ejpam-5050	475	29	,	,	PUNCT
ejpam-5050	475	30	i0.5[d0.5y2	i0.5[d0.5y2	PROPN
ejpam-5050	475	31	]	]	X
ejpam-5050	475	32	=	=	PUNCT
ejpam-5050	475	33	i0.5[−y2	i0.5[−y2	X
ejpam-5050	475	34	−	−	NOUN
ejpam-5050	475	35	y1	y1	NOUN
ejpam-5050	475	36	+	+	CCONJ
ejpam-5050	475	37	1	1	NUM
ejpam-5050	475	38	+	+	CCONJ
ejpam-5050	475	39	x	x	X
ejpam-5050	475	40	]	]	X
ejpam-5050	475	41	.	.	PUNCT
ejpam-5050	476	1	(	(	PUNCT
ejpam-5050	476	2	29	29	NUM
ejpam-5050	476	3	)	)	PUNCT
ejpam-5050	476	4	m.	m.	NOUN
ejpam-5050	476	5	al	al	PROPN
ejpam-5050	476	6	-	-	PUNCT
ejpam-5050	476	7	mazmumy	mazmumy	PROPN
ejpam-5050	476	8	,	,	PUNCT
ejpam-5050	476	9	m.	m.	NOUN
ejpam-5050	476	10	alsulami	alsulami	PROPN
ejpam-5050	476	11	/	/	SYM
ejpam-5050	476	12	eur	eur	PROPN
ejpam-5050	476	13	.	.	PUNCT
ejpam-5050	477	1	j.	j.	PROPN
ejpam-5050	477	2	pure	pure	PROPN
ejpam-5050	477	3	appl	appl	PROPN
ejpam-5050	477	4	.	.	PROPN
ejpam-5050	477	5	math	math	PROPN
ejpam-5050	477	6	,	,	PUNCT
ejpam-5050	477	7	17	17	NUM
ejpam-5050	477	8	(	(	PUNCT
ejpam-5050	477	9	1	1	NUM
ejpam-5050	477	10	)	)	PUNCT
ejpam-5050	477	11	(	(	PUNCT
ejpam-5050	477	12	2024	2024	NUM
ejpam-5050	477	13	)	)	PUNCT
ejpam-5050	477	14	,	,	PUNCT
ejpam-5050	477	15	546	546	NUM
ejpam-5050	477	16	-	-	SYM
ejpam-5050	477	17	568	568	NUM
ejpam-5050	477	18	562	562	NUM
ejpam-5050	477	19	more	more	ADV
ejpam-5050	477	20	so	so	ADV
ejpam-5050	477	21	,	,	PUNCT
ejpam-5050	477	22	applying	apply	VERB
ejpam-5050	477	23	the	the	DET
ejpam-5050	477	24	property	property	NOUN
ejpam-5050	477	25	of	of	ADP
ejpam-5050	477	26	the	the	DET
ejpam-5050	477	27	fractional	fractional	ADJ
ejpam-5050	477	28	derivative	derivative	NOUN
ejpam-5050	477	29	mentioned	mention	VERB
ejpam-5050	477	30	in	in	ADP
ejpam-5050	477	31	(	(	PUNCT
ejpam-5050	477	32	4	4	NUM
ejpam-5050	477	33	)	)	PUNCT
ejpam-5050	477	34	on	on	ADP
ejpam-5050	477	35	the	the	DET
ejpam-5050	477	36	lefthand	lefthand	NOUN
ejpam-5050	477	37	sides	side	NOUN
ejpam-5050	477	38	of	of	ADP
ejpam-5050	477	39	the	the	DET
ejpam-5050	477	40	latter	latter	ADJ
ejpam-5050	477	41	equations	equation	NOUN
ejpam-5050	477	42	with	with	ADP
ejpam-5050	477	43	y′1(0	y′1(0	PROPN
ejpam-5050	477	44	)	)	PUNCT
ejpam-5050	477	45	=	=	SYM
ejpam-5050	477	46	c1	c1	PROPN
ejpam-5050	477	47	,	,	PUNCT
ejpam-5050	477	48	we	we	PRON
ejpam-5050	477	49	get	get	VERB
ejpam-5050	477	50	{	{	PUNCT
ejpam-5050	477	51	y1(x	y1(x	NOUN
ejpam-5050	477	52	)	)	PUNCT
ejpam-5050	477	53	=	=	SYM
ejpam-5050	477	54	1	1	NUM
ejpam-5050	477	55	+	+	NUM
ejpam-5050	477	56	c1x+	c1x+	PRON
ejpam-5050	477	57	i1.5[y2	i1.5[y2	VERB
ejpam-5050	477	58	]	]	X
ejpam-5050	477	59	,	,	PUNCT
ejpam-5050	477	60	y2(x	y2(x	PROPN
ejpam-5050	477	61	)	)	PUNCT
ejpam-5050	477	62	=	=	PRON
ejpam-5050	478	1	−i0.5[y2]−	−i0.5[y2]−	PROPN
ejpam-5050	479	1	i0.5[y1	i0.5[y1	X
ejpam-5050	479	2	]	]	PUNCT
ejpam-5050	479	3	+	+	CCONJ
ejpam-5050	479	4	i0.5[1	i0.5[1	ADJ
ejpam-5050	479	5	+	+	CCONJ
ejpam-5050	479	6	x	x	X
ejpam-5050	479	7	]	]	X
ejpam-5050	479	8	.	.	PUNCT
ejpam-5050	480	1	next	next	ADV
ejpam-5050	480	2	,	,	PUNCT
ejpam-5050	480	3	upon	upon	SCONJ
ejpam-5050	480	4	using	use	VERB
ejpam-5050	480	5	madm	madm	NOUN
ejpam-5050	480	6	,	,	PUNCT
ejpam-5050	480	7	one	one	PRON
ejpam-5050	480	8	gets	get	VERB
ejpam-5050	480	9	∞∑	∞∑	PRON
ejpam-5050	480	10	n=0	n=0	X
ejpam-5050	480	11	y1,n(x	y1,n(x	X
ejpam-5050	480	12	)	)	PUNCT
ejpam-5050	480	13	=	=	SYM
ejpam-5050	481	1	1	1	NUM
ejpam-5050	481	2	+	+	NUM
ejpam-5050	481	3	c1x+	c1x+	NOUN
ejpam-5050	481	4	i1.5	i1.5	NOUN
ejpam-5050	481	5	[	[	PUNCT
ejpam-5050	481	6	∞∑	∞∑	PROPN
ejpam-5050	481	7	n=0	n=0	NUM
ejpam-5050	481	8	y2,n]−	y2,n]−	ADP
ejpam-5050	481	9	pi1.5	pi1.5	NOUN
ejpam-5050	481	10	[	[	PUNCT
ejpam-5050	481	11	∞∑	∞∑	PROPN
ejpam-5050	481	12	n=0	n=0	NUM
ejpam-5050	481	13	anx	anx	NOUN
ejpam-5050	481	14	n	n	CCONJ
ejpam-5050	481	15	]	]	PUNCT
ejpam-5050	482	1	+	+	CCONJ
ejpam-5050	482	2	i1.5	i1.5	NOUN
ejpam-5050	482	3	[	[	PUNCT
ejpam-5050	482	4	∞∑	∞∑	PROPN
ejpam-5050	482	5	n=0	n=0	NUM
ejpam-5050	482	6	anx	anx	NOUN
ejpam-5050	482	7	n	n	CCONJ
ejpam-5050	482	8	]	]	X
ejpam-5050	482	9	,	,	PUNCT
ejpam-5050	482	10	∞∑	∞∑	ADJ
ejpam-5050	482	11	n=0	n=0	NUM
ejpam-5050	482	12	y2,n(x	y2,n(x	NOUN
ejpam-5050	482	13	)	)	PUNCT
ejpam-5050	482	14	=	=	PUNCT
ejpam-5050	482	15	−i0.5	−i0.5	PROPN
ejpam-5050	482	16	[	[	PUNCT
ejpam-5050	482	17	∞∑	∞∑	PROPN
ejpam-5050	482	18	n=0	n=0	NUM
ejpam-5050	482	19	y2,n]−	y2,n]−	ADP
ejpam-5050	482	20	i0.5	i0.5	NOUN
ejpam-5050	482	21	[	[	PUNCT
ejpam-5050	482	22	∞∑	∞∑	PROPN
ejpam-5050	482	23	n=0	n=0	NUM
ejpam-5050	482	24	y1,n	y1,n	NOUN
ejpam-5050	482	25	]	]	X
ejpam-5050	482	26	+	+	CCONJ
ejpam-5050	482	27	i0.5[1	i0.5[1	ADJ
ejpam-5050	482	28	+	+	CCONJ
ejpam-5050	482	29	x]−	x]−	X
ejpam-5050	483	1	pi0.5	pi0.5	PUNCT
ejpam-5050	483	2	[	[	PUNCT
ejpam-5050	483	3	∞∑	∞∑	ADJ
ejpam-5050	483	4	n=0	n=0	NUM
ejpam-5050	483	5	anx	anx	NOUN
ejpam-5050	483	6	n	n	X
ejpam-5050	483	7	]	]	PUNCT
ejpam-5050	483	8	+	+	CCONJ
ejpam-5050	483	9	i0.5	i0.5	NOUN
ejpam-5050	483	10	[	[	PUNCT
ejpam-5050	483	11	∞∑	∞∑	ADJ
ejpam-5050	483	12	n=0	n=0	NUM
ejpam-5050	483	13	anx	anx	NOUN
ejpam-5050	483	14	n	n	CCONJ
ejpam-5050	483	15	]	]	PUNCT
ejpam-5050	483	16	,	,	PUNCT
ejpam-5050	483	17	that	that	PRON
ejpam-5050	483	18	expands	expand	VERB
ejpam-5050	483	19	to	to	ADP
ejpam-5050	483	20			NUM
ejpam-5050	483	21	y1,0(x	y1,0(x	PROPN
ejpam-5050	483	22	)	)	PUNCT
ejpam-5050	483	23	=	=	SYM
ejpam-5050	484	1	1	1	NUM
ejpam-5050	484	2	+	+	NUM
ejpam-5050	484	3	c1x+	c1x+	PRON
ejpam-5050	484	4	i1.5	i1.5	NOUN
ejpam-5050	484	5	[	[	PUNCT
ejpam-5050	484	6	∑∞	∑∞	X
ejpam-5050	484	7	n=0	n=0	X
ejpam-5050	484	8	anx	anx	NOUN
ejpam-5050	484	9	n	n	CCONJ
ejpam-5050	484	10	]	]	PUNCT
ejpam-5050	484	11	,	,	PUNCT
ejpam-5050	484	12	y1,1(x	y1,1(x	PROPN
ejpam-5050	484	13	)	)	PUNCT
ejpam-5050	484	14	=	=	SYM
ejpam-5050	484	15	−pi1.5	−pi1.5	NOUN
ejpam-5050	484	16	[	[	PUNCT
ejpam-5050	484	17	∑∞	∑∞	NOUN
ejpam-5050	484	18	n=0	n=0	X
ejpam-5050	484	19	anx	anx	NOUN
ejpam-5050	484	20	n	n	X
ejpam-5050	484	21	]	]	PUNCT
ejpam-5050	484	22	+	+	CCONJ
ejpam-5050	484	23	i1.5[y2,0	i1.5[y2,0	NOUN
ejpam-5050	484	24	]	]	X
ejpam-5050	484	25	,	,	PUNCT
ejpam-5050	484	26	y2,0(x	y2,0(x	NOUN
ejpam-5050	484	27	)	)	PUNCT
ejpam-5050	484	28	=	=	VERB
ejpam-5050	485	1	i0.5[1	i0.5[1	ADJ
ejpam-5050	485	2	+	+	CCONJ
ejpam-5050	485	3	x	x	X
ejpam-5050	485	4	]	]	X
ejpam-5050	485	5	+	+	CCONJ
ejpam-5050	485	6	i0.5	i0.5	NOUN
ejpam-5050	485	7	[	[	PUNCT
ejpam-5050	485	8	∑∞	∑∞	NOUN
ejpam-5050	485	9	n=0	n=0	X
ejpam-5050	485	10	anx	anx	NOUN
ejpam-5050	485	11	n	n	CCONJ
ejpam-5050	485	12	]	]	PUNCT
ejpam-5050	485	13	,	,	PUNCT
ejpam-5050	485	14	y2,1(x	y2,1(x	PROPN
ejpam-5050	485	15	)	)	PUNCT
ejpam-5050	485	16	=	=	PUNCT
ejpam-5050	486	1	−pi0.5	−pi0.5	X
ejpam-5050	486	2	[	[	PUNCT
ejpam-5050	486	3	∑∞	∑∞	X
ejpam-5050	486	4	n=0	n=0	X
ejpam-5050	486	5	anx	anx	ADJ
ejpam-5050	486	6	n]−	n]−	ADV
ejpam-5050	486	7	i0.5[y2,0]−	i0.5[y2,0]−	NOUN
ejpam-5050	486	8	i0.5[y1	i0.5[y1	PROPN
ejpam-5050	486	9	]	]	PUNCT
ejpam-5050	486	10	.	.	PUNCT
ejpam-5050	487	1	(	(	PUNCT
ejpam-5050	487	2	30	30	NUM
ejpam-5050	487	3	)	)	PUNCT
ejpam-5050	487	4	additionally	additionally	ADV
ejpam-5050	487	5	,	,	PUNCT
ejpam-5050	487	6	upon	upon	SCONJ
ejpam-5050	487	7	deploying	deploy	VERB
ejpam-5050	487	8	(	(	PUNCT
ejpam-5050	487	9	7	7	NUM
ejpam-5050	487	10	)	)	PUNCT
ejpam-5050	487	11	,	,	PUNCT
ejpam-5050	487	12	one	one	PRON
ejpam-5050	487	13	can	can	AUX
ejpam-5050	487	14	iteratively	iteratively	ADV
ejpam-5050	487	15	solve	solve	VERB
ejpam-5050	487	16	the	the	DET
ejpam-5050	487	17	equations	equation	NOUN
ejpam-5050	487	18	in	in	ADP
ejpam-5050	487	19	(	(	PUNCT
ejpam-5050	487	20	30	30	NUM
ejpam-5050	487	21	)	)	PUNCT
ejpam-5050	487	22	concurrently	concurrently	ADV
ejpam-5050	487	23	as	as	SCONJ
ejpam-5050	487	24	follows	follow	VERB
ejpam-5050	487	25	y1,0(x	y1,0(x	NOUN
ejpam-5050	487	26	)	)	PUNCT
ejpam-5050	487	27	=	=	SYM
ejpam-5050	488	1	1	1	NUM
ejpam-5050	488	2	+	+	NUM
ejpam-5050	488	3	c1x+	c1x+	VERB
ejpam-5050	488	4	4a0	4a0	NUM
ejpam-5050	488	5	3	3	NUM
ejpam-5050	488	6	√	√	PROPN
ejpam-5050	488	7	π	π	PROPN
ejpam-5050	488	8	x3/2	x3/2	PROPN
ejpam-5050	489	1	+	+	NUM
ejpam-5050	489	2	8a1	8a1	NUM
ejpam-5050	489	3	15	15	NUM
ejpam-5050	489	4	√	√	PROPN
ejpam-5050	489	5	π	π	X
ejpam-5050	489	6	x5/2	x5/2	PROPN
ejpam-5050	490	1	+	+	CCONJ
ejpam-5050	491	1	32a2	32a2	NUM
ejpam-5050	491	2	105	105	NUM
ejpam-5050	491	3	√	√	PROPN
ejpam-5050	491	4	π	π	X
ejpam-5050	491	5	x7/2	x7/2	PROPN
ejpam-5050	492	1	+	+	CCONJ
ejpam-5050	493	1	64a3	64a3	NUM
ejpam-5050	493	2	315	315	NUM
ejpam-5050	493	3	√	√	PROPN
ejpam-5050	493	4	π	π	PROPN
ejpam-5050	493	5	x9/2	x9/2	PROPN
ejpam-5050	494	1	+	+	CCONJ
ejpam-5050	494	2	...	...	PUNCT
ejpam-5050	494	3	y1,1(x	y1,1(x	X
ejpam-5050	494	4	)	)	PUNCT
ejpam-5050	494	5	=	=	SYM
ejpam-5050	495	1	−p	−p	NOUN
ejpam-5050	495	2	[	[	PUNCT
ejpam-5050	495	3	4a0	4a0	NUM
ejpam-5050	495	4	3	3	NUM
ejpam-5050	495	5	√	√	PROPN
ejpam-5050	495	6	π	π	PROPN
ejpam-5050	495	7	x3/2	x3/2	PROPN
ejpam-5050	496	1	+	+	NUM
ejpam-5050	496	2	8a1	8a1	NUM
ejpam-5050	496	3	15	15	NUM
ejpam-5050	496	4	√	√	PROPN
ejpam-5050	496	5	π	π	X
ejpam-5050	496	6	x5/2	x5/2	PROPN
ejpam-5050	497	1	+	+	CCONJ
ejpam-5050	498	1	32a2	32a2	NUM
ejpam-5050	498	2	105	105	NUM
ejpam-5050	498	3	√	√	PROPN
ejpam-5050	498	4	π	π	X
ejpam-5050	498	5	x7/2	x7/2	PROPN
ejpam-5050	499	1	+	+	CCONJ
ejpam-5050	499	2	64a3	64a3	NUM
ejpam-5050	499	3	315	315	NUM
ejpam-5050	499	4	√	√	PROPN
ejpam-5050	499	5	π	π	PROPN
ejpam-5050	499	6	x9/2	x9/2	PUNCT
ejpam-5050	500	1	+	+	CCONJ
ejpam-5050	500	2	...	...	PUNCT
ejpam-5050	500	3	]	]	PUNCT
ejpam-5050	501	1	+	+	CCONJ
ejpam-5050	501	2	1	1	NUM
ejpam-5050	501	3	2	2	NUM
ejpam-5050	501	4	x2	x2	NOUN
ejpam-5050	501	5	+	+	CCONJ
ejpam-5050	501	6	1	1	NUM
ejpam-5050	501	7	6	6	NUM
ejpam-5050	501	8	x3	x3	NOUN
ejpam-5050	501	9	+	+	CCONJ
ejpam-5050	501	10	a0	a0	PROPN
ejpam-5050	501	11	2	2	NUM
ejpam-5050	501	12	x2	x2	NOUN
ejpam-5050	501	13	+	+	CCONJ
ejpam-5050	501	14	a1	a1	NOUN
ejpam-5050	501	15	6	6	NUM
ejpam-5050	501	16	x3	x3	NOUN
ejpam-5050	501	17	+	+	CCONJ
ejpam-5050	501	18	a2	a2	PROPN
ejpam-5050	501	19	12	12	NUM
ejpam-5050	501	20	x4	x4	PROPN
ejpam-5050	501	21	+	+	PROPN
ejpam-5050	501	22	a3	a3	VERB
ejpam-5050	501	23	20	20	NUM
ejpam-5050	501	24	x5	x5	NOUN
ejpam-5050	501	25	+	+	CCONJ
ejpam-5050	501	26	...	...	PUNCT
ejpam-5050	501	27	and	and	CCONJ
ejpam-5050	501	28	y2,0(x	y2,0(x	NOUN
ejpam-5050	501	29	)	)	PUNCT
ejpam-5050	501	30	=	=	SYM
ejpam-5050	502	1	2√	2√	NUM
ejpam-5050	502	2	π	π	X
ejpam-5050	502	3	x1/2	x1/2	PROPN
ejpam-5050	503	1	+	+	CCONJ
ejpam-5050	504	1	4	4	NUM
ejpam-5050	504	2	3	3	NUM
ejpam-5050	504	3	√	√	PROPN
ejpam-5050	504	4	π	π	PROPN
ejpam-5050	504	5	x3/2	x3/2	PROPN
ejpam-5050	505	1	+	+	CCONJ
ejpam-5050	505	2	2a0√	2a0√	NUM
ejpam-5050	505	3	π	π	NOUN
ejpam-5050	505	4	x1/2	x1/2	PROPN
ejpam-5050	506	1	+	+	CCONJ
ejpam-5050	506	2	4a1	4a1	NUM
ejpam-5050	506	3	3	3	NUM
ejpam-5050	506	4	√	√	PROPN
ejpam-5050	506	5	π	π	PROPN
ejpam-5050	506	6	x3/2	x3/2	PROPN
ejpam-5050	507	1	+	+	CCONJ
ejpam-5050	507	2	16a2	16a2	NUM
ejpam-5050	507	3	15	15	NUM
ejpam-5050	507	4	√	√	PROPN
ejpam-5050	507	5	π	π	PROPN
ejpam-5050	507	6	x5/2	x5/2	PROPN
ejpam-5050	508	1	+	+	CCONJ
ejpam-5050	509	1	32a3	32a3	NUM
ejpam-5050	509	2	35	35	NUM
ejpam-5050	509	3	√	√	PROPN
ejpam-5050	509	4	π	π	X
ejpam-5050	509	5	x7/2	x7/2	PROPN
ejpam-5050	510	1	+	+	CCONJ
ejpam-5050	510	2	...	...	PUNCT
ejpam-5050	510	3	y2,1(x	y2,1(x	NOUN
ejpam-5050	510	4	)	)	PUNCT
ejpam-5050	510	5	=	=	PUNCT
ejpam-5050	511	1	−p	−p	NOUN
ejpam-5050	511	2	[	[	X
ejpam-5050	511	3	2a0√	2a0√	NUM
ejpam-5050	511	4	π	π	PROPN
ejpam-5050	511	5	x1/2	x1/2	PROPN
ejpam-5050	512	1	+	+	CCONJ
ejpam-5050	512	2	4a1	4a1	NUM
ejpam-5050	512	3	3	3	NUM
ejpam-5050	512	4	√	√	PROPN
ejpam-5050	512	5	π	π	PROPN
ejpam-5050	512	6	x3/2	x3/2	PROPN
ejpam-5050	513	1	+	+	CCONJ
ejpam-5050	513	2	16a2	16a2	NUM
ejpam-5050	513	3	15	15	NUM
ejpam-5050	513	4	√	√	PROPN
ejpam-5050	513	5	π	π	PROPN
ejpam-5050	513	6	x5/2	x5/2	PROPN
ejpam-5050	514	1	+	+	CCONJ
ejpam-5050	514	2	32a3	32a3	NUM
ejpam-5050	514	3	35	35	NUM
ejpam-5050	514	4	√	√	PROPN
ejpam-5050	514	5	π	π	X
ejpam-5050	514	6	x7/2	x7/2	PROPN
ejpam-5050	515	1	+	+	CCONJ
ejpam-5050	515	2	...	...	PUNCT
ejpam-5050	515	3	]	]	PUNCT
ejpam-5050	515	4	−	−	PUNCT
ejpam-5050	515	5	x−	x−	NOUN
ejpam-5050	515	6	1	1	NUM
ejpam-5050	515	7	2	2	NUM
ejpam-5050	515	8	x2	x2	NOUN
ejpam-5050	515	9	−	−	PROPN
ejpam-5050	515	10	a0x−	a0x−	ADJ
ejpam-5050	515	11	a1	a1	NOUN
ejpam-5050	515	12	2	2	NUM
ejpam-5050	515	13	x2	x2	NOUN
ejpam-5050	515	14	−	−	PROPN
ejpam-5050	515	15	a2	a2	PROPN
ejpam-5050	515	16	3	3	NUM
ejpam-5050	515	17	x3	x3	NOUN
ejpam-5050	515	18	−	−	PROPN
ejpam-5050	515	19	a3	a3	NOUN
ejpam-5050	515	20	12	12	NUM
ejpam-5050	515	21	x4	x4	PROPN
ejpam-5050	515	22	−	−	PROPN
ejpam-5050	515	23	i0.5[y1	i0.5[y1	PROPN
ejpam-5050	515	24	]	]	PUNCT
ejpam-5050	515	25	.	.	PUNCT
ejpam-5050	516	1	m.	m.	PROPN
ejpam-5050	516	2	al	al	PROPN
ejpam-5050	516	3	-	-	PUNCT
ejpam-5050	516	4	mazmumy	mazmumy	PROPN
ejpam-5050	516	5	,	,	PUNCT
ejpam-5050	516	6	m.	m.	NOUN
ejpam-5050	516	7	alsulami	alsulami	PROPN
ejpam-5050	516	8	/	/	SYM
ejpam-5050	516	9	eur	eur	PROPN
ejpam-5050	516	10	.	.	PUNCT
ejpam-5050	517	1	j.	j.	PROPN
ejpam-5050	517	2	pure	pure	PROPN
ejpam-5050	517	3	appl	appl	PROPN
ejpam-5050	517	4	.	.	PROPN
ejpam-5050	517	5	math	math	PROPN
ejpam-5050	517	6	,	,	PUNCT
ejpam-5050	517	7	17	17	NUM
ejpam-5050	517	8	(	(	PUNCT
ejpam-5050	517	9	1	1	NUM
ejpam-5050	517	10	)	)	PUNCT
ejpam-5050	517	11	(	(	PUNCT
ejpam-5050	517	12	2024	2024	NUM
ejpam-5050	517	13	)	)	PUNCT
ejpam-5050	517	14	,	,	PUNCT
ejpam-5050	517	15	546	546	NUM
ejpam-5050	517	16	-	-	SYM
ejpam-5050	517	17	568	568	NUM
ejpam-5050	517	18	563	563	NUM
ejpam-5050	517	19	now	now	ADV
ejpam-5050	517	20	,	,	PUNCT
ejpam-5050	517	21	to	to	PART
ejpam-5050	517	22	compute	compute	VERB
ejpam-5050	517	23	the	the	DET
ejpam-5050	517	24	expression	expression	NOUN
ejpam-5050	517	25	for	for	ADP
ejpam-5050	517	26	the	the	DET
ejpam-5050	517	27	term	term	NOUN
ejpam-5050	517	28	i0.5[y1	i0.5[y1	X
ejpam-5050	517	29	]	]	PUNCT
ejpam-5050	517	30	in	in	ADP
ejpam-5050	517	31	the	the	DET
ejpam-5050	517	32	last	last	ADJ
ejpam-5050	517	33	equation	equation	NOUN
ejpam-5050	518	1	,	,	PUNCT
ejpam-5050	518	2	we	we	PRON
ejpam-5050	518	3	have	have	VERB
ejpam-5050	518	4	to	to	PART
ejpam-5050	518	5	find	find	VERB
ejpam-5050	518	6	y1(x	y1(x	NOUN
ejpam-5050	518	7	)	)	PUNCT
ejpam-5050	518	8	first	first	ADV
ejpam-5050	518	9	.	.	PUNCT
ejpam-5050	519	1	so	so	ADV
ejpam-5050	519	2	,	,	PUNCT
ejpam-5050	519	3	let	let	VERB
ejpam-5050	519	4	y1,1(x	y1,1(x	NOUN
ejpam-5050	519	5	)	)	PUNCT
ejpam-5050	520	1	=	=	SYM
ejpam-5050	520	2	0	0	NUM
ejpam-5050	521	1	with	with	ADP
ejpam-5050	521	2	p	p	NOUN
ejpam-5050	521	3	=	=	NOUN
ejpam-5050	521	4	1	1	NUM
ejpam-5050	521	5	,	,	PUNCT
ejpam-5050	521	6	and	and	CCONJ
ejpam-5050	521	7	equating	equate	VERB
ejpam-5050	521	8	coefficients	coefficient	NOUN
ejpam-5050	521	9	of	of	ADP
ejpam-5050	521	10	xn/2	xn/2	NOUN
ejpam-5050	521	11	,	,	PUNCT
ejpam-5050	521	12	we	we	PRON
ejpam-5050	521	13	get	get	VERB
ejpam-5050	521	14	a0	a0	NOUN
ejpam-5050	521	15	=	=	SYM
ejpam-5050	521	16	a1	a1	PROPN
ejpam-5050	521	17	=	=	PROPN
ejpam-5050	521	18	a2	a2	PROPN
ejpam-5050	521	19	=	=	SYM
ejpam-5050	521	20	a3	a3	NOUN
ejpam-5050	521	21	=	=	SYM
ejpam-5050	522	1	0	0	X
ejpam-5050	522	2	.	.	PUNCT
ejpam-5050	523	1	then	then	ADV
ejpam-5050	523	2	,	,	PUNCT
ejpam-5050	523	3	y1(x	y1(x	NOUN
ejpam-5050	523	4	)	)	PUNCT
ejpam-5050	523	5	=	=	SYM
ejpam-5050	523	6	y1,0(x	y1,0(x	NOUN
ejpam-5050	523	7	)	)	PUNCT
ejpam-5050	523	8	=	=	SYM
ejpam-5050	523	9	1	1	NUM
ejpam-5050	523	10	+	+	CCONJ
ejpam-5050	523	11	c1x	c1x	NOUN
ejpam-5050	523	12	=	=	SYM
ejpam-5050	523	13	1	1	NUM
ejpam-5050	523	14	+	+	CCONJ
ejpam-5050	523	15	x	x	NOUN
ejpam-5050	523	16	,	,	PUNCT
ejpam-5050	523	17	(	(	PUNCT
ejpam-5050	523	18	31	31	NUM
ejpam-5050	523	19	)	)	PUNCT
ejpam-5050	523	20	after	after	ADP
ejpam-5050	523	21	using	use	VERB
ejpam-5050	523	22	the	the	DET
ejpam-5050	523	23	second	second	ADJ
ejpam-5050	523	24	boundary	boundary	ADJ
ejpam-5050	523	25	condition	condition	NOUN
ejpam-5050	523	26	y1(1	y1(1	NOUN
ejpam-5050	523	27	)	)	PUNCT
ejpam-5050	523	28	=	=	SYM
ejpam-5050	523	29	2	2	X
ejpam-5050	523	30	.	.	PUNCT
ejpam-5050	523	31	further	far	ADV
ejpam-5050	523	32	,	,	PUNCT
ejpam-5050	523	33	we	we	PRON
ejpam-5050	523	34	get	get	VERB
ejpam-5050	523	35	i0.5[y1	i0.5[y1	NUM
ejpam-5050	523	36	]	]	X
ejpam-5050	523	37	=	=	SYM
ejpam-5050	524	1	i0.5[1	i0.5[1	ADJ
ejpam-5050	524	2	+	+	CCONJ
ejpam-5050	524	3	x	x	X
ejpam-5050	524	4	]	]	X
ejpam-5050	524	5	=	=	SYM
ejpam-5050	524	6	2√	2√	NUM
ejpam-5050	524	7	π	π	X
ejpam-5050	524	8	x1/2	x1/2	PROPN
ejpam-5050	525	1	+	+	CCONJ
ejpam-5050	526	1	4	4	NUM
ejpam-5050	526	2	3	3	NUM
ejpam-5050	526	3	√	√	PROPN
ejpam-5050	526	4	π	π	PROPN
ejpam-5050	526	5	x3/2	x3/2	NUM
ejpam-5050	526	6	.	.	PUNCT
ejpam-5050	527	1	next	next	ADV
ejpam-5050	527	2	,	,	PUNCT
ejpam-5050	527	3	substituting	substitute	VERB
ejpam-5050	527	4	i0.5[y1	i0.5[y1	NUM
ejpam-5050	527	5	]	]	PUNCT
ejpam-5050	527	6	in	in	ADP
ejpam-5050	527	7	y2,1(x	y2,1(x	PROPN
ejpam-5050	527	8	)	)	PUNCT
ejpam-5050	527	9	,	,	PUNCT
ejpam-5050	527	10	and	and	CCONJ
ejpam-5050	527	11	further	far	ADV
ejpam-5050	527	12	letting	let	VERB
ejpam-5050	527	13	y2,1(x	y2,1(x	NOUN
ejpam-5050	527	14	)	)	PUNCT
ejpam-5050	527	15	=	=	SYM
ejpam-5050	527	16	0	0	PUNCT
ejpam-5050	527	17	with	with	ADP
ejpam-5050	527	18	p	p	NOUN
ejpam-5050	527	19	=	=	NOUN
ejpam-5050	527	20	1	1	NUM
ejpam-5050	527	21	,	,	PUNCT
ejpam-5050	527	22	the	the	DET
ejpam-5050	527	23	resulting	result	VERB
ejpam-5050	527	24	coefficients	coefficient	NOUN
ejpam-5050	527	25	of	of	ADP
ejpam-5050	527	26	xn/2	xn/2	PROPN
ejpam-5050	527	27	are	be	AUX
ejpam-5050	527	28	equated	equate	VERB
ejpam-5050	527	29	to	to	PART
ejpam-5050	527	30	obtain	obtain	VERB
ejpam-5050	527	31	a0	a0	NOUN
ejpam-5050	527	32	=	=	SYM
ejpam-5050	527	33	a1	a1	PROPN
ejpam-5050	527	34	=	=	SYM
ejpam-5050	527	35	−1	−1	NOUN
ejpam-5050	527	36	,	,	PUNCT
ejpam-5050	527	37	and	and	CCONJ
ejpam-5050	527	38	a2	a2	PROPN
ejpam-5050	527	39	=	=	SYM
ejpam-5050	527	40	a3	a3	PROPN
ejpam-5050	527	41	=	=	SYM
ejpam-5050	528	1	0	0	X
ejpam-5050	528	2	.	.	PUNCT
ejpam-5050	529	1	hence	hence	ADV
ejpam-5050	529	2	,	,	PUNCT
ejpam-5050	529	3	substituting	substitute	VERB
ejpam-5050	529	4	these	these	DET
ejpam-5050	529	5	values	value	NOUN
ejpam-5050	529	6	in	in	ADP
ejpam-5050	529	7	y2,0(x	y2,0(x	PROPN
ejpam-5050	529	8	)	)	PUNCT
ejpam-5050	529	9	,	,	PUNCT
ejpam-5050	529	10	one	one	PRON
ejpam-5050	529	11	gets	get	VERB
ejpam-5050	529	12	y2(x	y2(x	NOUN
ejpam-5050	529	13	)	)	PUNCT
ejpam-5050	529	14	=	=	SYM
ejpam-5050	529	15	y2,0(x	y2,0(x	NOUN
ejpam-5050	529	16	)	)	PUNCT
ejpam-5050	529	17	=	=	SYM
ejpam-5050	530	1	2√	2√	NUM
ejpam-5050	530	2	π	π	X
ejpam-5050	530	3	x1/2	x1/2	PROPN
ejpam-5050	531	1	+	+	CCONJ
ejpam-5050	531	2	4	4	NUM
ejpam-5050	531	3	3	3	NUM
ejpam-5050	531	4	√	√	PROPN
ejpam-5050	531	5	π	π	PROPN
ejpam-5050	531	6	x3/2	x3/2	NUM
ejpam-5050	532	1	−	−	PUNCT
ejpam-5050	533	1	2√	2√	PROPN
ejpam-5050	533	2	π	π	NOUN
ejpam-5050	533	3	x1/2	x1/2	PROPN
ejpam-5050	533	4	−	−	NUM
ejpam-5050	533	5	4	4	NUM
ejpam-5050	533	6	3	3	NUM
ejpam-5050	533	7	√	√	PROPN
ejpam-5050	533	8	π	π	PROPN
ejpam-5050	533	9	x3/2	x3/2	PROPN
ejpam-5050	534	1	+	+	CCONJ
ejpam-5050	534	2	0	0	NUM
ejpam-5050	534	3	,	,	PUNCT
ejpam-5050	534	4	=	=	NOUN
ejpam-5050	534	5	0	0	X
ejpam-5050	534	6	.	.	PUNCT
ejpam-5050	535	1	(	(	PUNCT
ejpam-5050	535	2	32	32	NUM
ejpam-5050	535	3	)	)	PUNCT
ejpam-5050	535	4	we	we	PRON
ejpam-5050	535	5	,	,	PUNCT
ejpam-5050	535	6	therefore	therefore	ADV
ejpam-5050	535	7	,	,	PUNCT
ejpam-5050	535	8	conclude	conclude	VERB
ejpam-5050	535	9	from	from	ADP
ejpam-5050	535	10	(	(	PUNCT
ejpam-5050	535	11	31	31	NUM
ejpam-5050	535	12	)	)	PUNCT
ejpam-5050	535	13	and	and	CCONJ
ejpam-5050	535	14	(	(	PUNCT
ejpam-5050	535	15	32	32	NUM
ejpam-5050	535	16	)	)	PUNCT
ejpam-5050	535	17	that	that	SCONJ
ejpam-5050	535	18	the	the	DET
ejpam-5050	535	19	coupled	couple	VERB
ejpam-5050	535	20	system	system	NOUN
ejpam-5050	535	21	expressed	express	VERB
ejpam-5050	535	22	in	in	ADP
ejpam-5050	535	23	(	(	PUNCT
ejpam-5050	535	24	28	28	NUM
ejpam-5050	535	25	)	)	PUNCT
ejpam-5050	535	26	admits	admit	VERB
ejpam-5050	535	27	the	the	DET
ejpam-5050	535	28	following	following	ADJ
ejpam-5050	535	29	solution	solution	NOUN
ejpam-5050	535	30	y1(x	y1(x	NOUN
ejpam-5050	535	31	)	)	PUNCT
ejpam-5050	535	32	=	=	SYM
ejpam-5050	536	1	1	1	NUM
ejpam-5050	536	2	+	+	CCONJ
ejpam-5050	536	3	x	x	PROPN
ejpam-5050	536	4	,	,	PUNCT
ejpam-5050	536	5	y2(x	y2(x	PROPN
ejpam-5050	536	6	)	)	PUNCT
ejpam-5050	536	7	=	=	SYM
ejpam-5050	536	8	0	0	NUM
ejpam-5050	536	9	,	,	PUNCT
ejpam-5050	536	10	(	(	PUNCT
ejpam-5050	536	11	33	33	NUM
ejpam-5050	536	12	)	)	PUNCT
ejpam-5050	536	13	which	which	PRON
ejpam-5050	536	14	is	be	AUX
ejpam-5050	536	15	indeed	indeed	ADV
ejpam-5050	536	16	the	the	DET
ejpam-5050	536	17	exact	exact	ADJ
ejpam-5050	536	18	analytical	analytical	ADJ
ejpam-5050	536	19	solution	solution	NOUN
ejpam-5050	536	20	for	for	ADP
ejpam-5050	536	21	(	(	PUNCT
ejpam-5050	536	22	24	24	NUM
ejpam-5050	536	23	)	)	PUNCT
ejpam-5050	536	24	.	.	PUNCT
ejpam-5050	537	1	5	5	X
ejpam-5050	537	2	.	.	X
ejpam-5050	537	3	conclusion	conclusion	NOUN
ejpam-5050	537	4	in	in	ADP
ejpam-5050	537	5	conclusion	conclusion	NOUN
ejpam-5050	537	6	,	,	PUNCT
ejpam-5050	537	7	we	we	PRON
ejpam-5050	537	8	obtained	obtain	VERB
ejpam-5050	537	9	the	the	DET
ejpam-5050	537	10	exact	exact	ADJ
ejpam-5050	537	11	analytical	analytical	ADJ
ejpam-5050	537	12	solution	solution	NOUN
ejpam-5050	537	13	of	of	ADP
ejpam-5050	537	14	the	the	DET
ejpam-5050	537	15	fractional	fractional	ADJ
ejpam-5050	537	16	bagley	bagley	NOUN
ejpam-5050	537	17	-	-	PUNCT
ejpam-5050	537	18	torvik	torvik	NOUN
ejpam-5050	537	19	equation	equation	NOUN
ejpam-5050	537	20	,	,	PUNCT
ejpam-5050	537	21	as	as	ADV
ejpam-5050	537	22	well	well	ADV
ejpam-5050	537	23	as	as	ADP
ejpam-5050	537	24	a	a	DET
ejpam-5050	537	25	system	system	NOUN
ejpam-5050	537	26	of	of	ADP
ejpam-5050	537	27	fractional	fractional	ADJ
ejpam-5050	537	28	bagley	bagley	NOUN
ejpam-5050	537	29	-	-	PUNCT
ejpam-5050	537	30	torvik	torvik	NOUN
ejpam-5050	537	31	equations	equation	NOUN
ejpam-5050	537	32	fitted	fit	VERB
ejpam-5050	537	33	with	with	ADP
ejpam-5050	537	34	dirichlet	dirichlet	PROPN
ejpam-5050	537	35	boundary	boundary	PROPN
ejpam-5050	537	36	data	data	PROPN
ejpam-5050	537	37	.	.	PUNCT
ejpam-5050	538	1	we	we	PRON
ejpam-5050	538	2	introduced	introduce	VERB
ejpam-5050	538	3	two	two	NUM
ejpam-5050	538	4	algorithms	algorithm	NOUN
ejpam-5050	538	5	based	base	VERB
ejpam-5050	538	6	on	on	ADP
ejpam-5050	538	7	madm	madm	NOUN
ejpam-5050	538	8	to	to	AUX
ejpam-5050	538	9	semi	semi	ADV
ejpam-5050	538	10	-	-	ADJ
ejpam-5050	538	11	analytically	analytically	ADV
ejpam-5050	538	12	treat	treat	VERB
ejpam-5050	538	13	the	the	DET
ejpam-5050	538	14	class	class	NOUN
ejpam-5050	538	15	of	of	ADP
ejpam-5050	538	16	fractional	fractional	ADJ
ejpam-5050	538	17	bagley	bagley	NOUN
ejpam-5050	538	18	-	-	PUNCT
ejpam-5050	538	19	torvik	torvik	NOUN
ejpam-5050	538	20	equation	equation	NOUN
ejpam-5050	538	21	endowed	endow	VERB
ejpam-5050	538	22	with	with	ADP
ejpam-5050	538	23	dirichlet	dirichlet	PROPN
ejpam-5050	538	24	boundary	boundary	PROPN
ejpam-5050	538	25	data	data	PROPN
ejpam-5050	538	26	.	.	PUNCT
ejpam-5050	539	1	the	the	DET
ejpam-5050	539	2	algorithms	algorithm	NOUN
ejpam-5050	539	3	were	be	AUX
ejpam-5050	539	4	founded	found	VERB
ejpam-5050	539	5	by	by	ADP
ejpam-5050	539	6	the	the	DET
ejpam-5050	539	7	inverse	inverse	ADJ
ejpam-5050	539	8	linear	linear	NOUN
ejpam-5050	539	9	operator	operator	NOUN
ejpam-5050	539	10	theorems	theorem	NOUN
ejpam-5050	539	11	and	and	CCONJ
ejpam-5050	539	12	infused	infuse	VERB
ejpam-5050	539	13	in	in	ADP
ejpam-5050	539	14	madm	madm	NOUN
ejpam-5050	539	15	to	to	PART
ejpam-5050	539	16	calculate	calculate	VERB
ejpam-5050	539	17	only	only	ADV
ejpam-5050	539	18	the	the	DET
ejpam-5050	539	19	first	first	ADJ
ejpam-5050	539	20	and	and	CCONJ
ejpam-5050	539	21	second	second	ADJ
ejpam-5050	539	22	components	component	NOUN
ejpam-5050	539	23	y0	y0	PROPN
ejpam-5050	539	24	and	and	CCONJ
ejpam-5050	539	25	y1	y1	NOUN
ejpam-5050	539	26	;	;	PUNCT
ejpam-5050	539	27	indeed	indeed	ADV
ejpam-5050	539	28	,	,	PUNCT
ejpam-5050	539	29	this	this	PRON
ejpam-5050	539	30	is	be	AUX
ejpam-5050	539	31	one	one	NUM
ejpam-5050	539	32	of	of	ADP
ejpam-5050	539	33	the	the	DET
ejpam-5050	539	34	advantages	advantage	NOUN
ejpam-5050	539	35	of	of	ADP
ejpam-5050	539	36	madm	madm	NOUN
ejpam-5050	539	37	over	over	ADP
ejpam-5050	539	38	the	the	DET
ejpam-5050	539	39	classical	classical	ADJ
ejpam-5050	539	40	adm	adm	PROPN
ejpam-5050	539	41	,	,	PUNCT
ejpam-5050	539	42	which	which	PRON
ejpam-5050	539	43	computes	compute	VERB
ejpam-5050	539	44	several	several	ADJ
ejpam-5050	539	45	components	component	NOUN
ejpam-5050	539	46	most	most	ADV
ejpam-5050	539	47	at	at	ADP
ejpam-5050	539	48	times	time	NOUN
ejpam-5050	539	49	to	to	PART
ejpam-5050	539	50	arrive	arrive	VERB
ejpam-5050	539	51	as	as	ADP
ejpam-5050	539	52	the	the	DET
ejpam-5050	539	53	optimal	optimal	ADJ
ejpam-5050	539	54	solution	solution	NOUN
ejpam-5050	539	55	.	.	PUNCT
ejpam-5050	540	1	further	far	ADV
ejpam-5050	540	2	,	,	PUNCT
ejpam-5050	540	3	to	to	PART
ejpam-5050	540	4	demonstrate	demonstrate	VERB
ejpam-5050	540	5	the	the	DET
ejpam-5050	540	6	effectiveness	effectiveness	NOUN
ejpam-5050	540	7	and	and	CCONJ
ejpam-5050	540	8	application	application	NOUN
ejpam-5050	540	9	of	of	ADP
ejpam-5050	540	10	the	the	DET
ejpam-5050	540	11	new	new	ADJ
ejpam-5050	540	12	algorithms	algorithm	NOUN
ejpam-5050	540	13	,	,	PUNCT
ejpam-5050	540	14	maple	maple	NOUN
ejpam-5050	540	15	software	software	NOUN
ejpam-5050	540	16	2023	2023	NUM
ejpam-5050	540	17	has	have	AUX
ejpam-5050	540	18	been	be	AUX
ejpam-5050	540	19	used	use	VERB
ejpam-5050	540	20	for	for	ADP
ejpam-5050	540	21	the	the	DET
ejpam-5050	540	22	computational	computational	ADJ
ejpam-5050	540	23	simulation	simulation	NOUN
ejpam-5050	540	24	of	of	ADP
ejpam-5050	540	25	different	different	ADJ
ejpam-5050	540	26	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5050	540	27	bvp	bvp	NOUN
ejpam-5050	540	28	for	for	ADP
ejpam-5050	540	29	bagley	bagley	NOUN
ejpam-5050	540	30	-	-	PUNCT
ejpam-5050	540	31	torvik	torvik	NOUN
ejpam-5050	540	32	equations	equation	NOUN
ejpam-5050	540	33	,	,	PUNCT
ejpam-5050	540	34	which	which	PRON
ejpam-5050	540	35	are	be	AUX
ejpam-5050	540	36	indeed	indeed	ADV
ejpam-5050	540	37	more	more	ADV
ejpam-5050	540	38	complex	complex	ADJ
ejpam-5050	540	39	than	than	ADP
ejpam-5050	540	40	their	their	PRON
ejpam-5050	540	41	homogeneous	homogeneous	ADJ
ejpam-5050	540	42	counterparts	counterpart	NOUN
ejpam-5050	540	43	.	.	PUNCT
ejpam-5050	541	1	additionally	additionally	ADV
ejpam-5050	541	2	,	,	PUNCT
ejpam-5050	541	3	based	base	VERB
ejpam-5050	541	4	on	on	ADP
ejpam-5050	541	5	the	the	DET
ejpam-5050	541	6	results	result	NOUN
ejpam-5050	541	7	obtained	obtain	VERB
ejpam-5050	541	8	with	with	ADP
ejpam-5050	541	9	regard	regard	NOUN
ejpam-5050	541	10	to	to	ADP
ejpam-5050	541	11	the	the	DET
ejpam-5050	541	12	examined	examine	VERB
ejpam-5050	541	13	examples	example	NOUN
ejpam-5050	541	14	,	,	PUNCT
ejpam-5050	541	15	one	one	PRON
ejpam-5050	541	16	can	can	AUX
ejpam-5050	541	17	easily	easily	ADV
ejpam-5050	541	18	infer	infer	VERB
ejpam-5050	541	19	that	that	SCONJ
ejpam-5050	541	20	the	the	DET
ejpam-5050	541	21	devised	devised	ADJ
ejpam-5050	541	22	algorithms	algorithm	NOUN
ejpam-5050	541	23	are	be	AUX
ejpam-5050	541	24	efficient	efficient	ADJ
ejpam-5050	541	25	and	and	CCONJ
ejpam-5050	541	26	reliable	reliable	ADJ
ejpam-5050	541	27	methods	method	NOUN
ejpam-5050	541	28	for	for	ADP
ejpam-5050	541	29	solving	solve	VERB
ejpam-5050	541	30	bvps	bvps	NOUN
ejpam-5050	541	31	with	with	ADP
ejpam-5050	541	32	dirichlet	dirichlet	PROPN
ejpam-5050	541	33	boundary	boundary	ADJ
ejpam-5050	541	34	conditions	condition	NOUN
ejpam-5050	541	35	in	in	ADP
ejpam-5050	541	36	particular	particular	ADJ
ejpam-5050	541	37	,	,	PUNCT
ejpam-5050	541	38	and	and	CCONJ
ejpam-5050	541	39	in	in	ADP
ejpam-5050	541	40	general	general	ADJ
ejpam-5050	541	41	,	,	PUNCT
ejpam-5050	541	42	they	they	PRON
ejpam-5050	541	43	can	can	AUX
ejpam-5050	541	44	be	be	AUX
ejpam-5050	541	45	extended	extend	VERB
ejpam-5050	541	46	to	to	ADP
ejpam-5050	541	47	tackling	tackle	VERB
ejpam-5050	541	48	different	different	ADJ
ejpam-5050	541	49	types	type	NOUN
ejpam-5050	541	50	of	of	ADP
ejpam-5050	541	51	bvps	bvps	NOUN
ejpam-5050	541	52	,	,	PUNCT
ejpam-5050	541	53	such	such	ADJ
ejpam-5050	541	54	as	as	ADP
ejpam-5050	541	55	fractional	fractional	ADJ
ejpam-5050	541	56	pdes	pde	NOUN
ejpam-5050	541	57	and	and	CCONJ
ejpam-5050	541	58	fractional	fractional	ADJ
ejpam-5050	541	59	integral	integral	ADJ
ejpam-5050	541	60	ides	ide	NOUN
ejpam-5050	541	61	.	.	PUNCT
ejpam-5050	542	1	references	reference	NOUN
ejpam-5050	542	2	564	564	NUM
ejpam-5050	542	3	6	6	NUM
ejpam-5050	542	4	.	.	PUNCT
ejpam-5050	543	1	declaration	declaration	NOUN
ejpam-5050	543	2	•	•	NUM
ejpam-5050	543	3	authors	author	NOUN
ejpam-5050	543	4	’	'	PUNCT
ejpam-5050	543	5	contribution	contribution	NOUN
ejpam-5050	543	6	the	the	DET
ejpam-5050	543	7	authors	author	NOUN
ejpam-5050	543	8	collectively	collectively	ADV
ejpam-5050	543	9	worked	work	VERB
ejpam-5050	543	10	on	on	ADP
ejpam-5050	543	11	the	the	DET
ejpam-5050	543	12	manuscript	manuscript	NOUN
ejpam-5050	543	13	,	,	PUNCT
ejpam-5050	543	14	and	and	CCONJ
ejpam-5050	543	15	they	they	PRON
ejpam-5050	543	16	read	read	VERB
ejpam-5050	543	17	and	and	CCONJ
ejpam-5050	543	18	approved	approve	VERB
ejpam-5050	543	19	the	the	DET
ejpam-5050	543	20	final	final	ADJ
ejpam-5050	543	21	draft	draft	NOUN
ejpam-5050	543	22	.	.	PUNCT
ejpam-5050	544	1	•	•	NUM
ejpam-5050	544	2	availability	availability	NOUN
ejpam-5050	544	3	of	of	ADP
ejpam-5050	544	4	data	datum	NOUN
ejpam-5050	544	5	and	and	CCONJ
ejpam-5050	544	6	materials	material	NOUN
ejpam-5050	544	7	not	not	PART
ejpam-5050	544	8	applicable	applicable	ADJ
ejpam-5050	544	9	.	.	PUNCT
ejpam-5050	545	1	•	•	NUM
ejpam-5050	545	2	competing	compete	VERB
ejpam-5050	545	3	interests	interest	NOUN
ejpam-5050	545	4	the	the	DET
ejpam-5050	545	5	authors	author	NOUN
ejpam-5050	545	6	declare	declare	VERB
ejpam-5050	545	7	that	that	SCONJ
ejpam-5050	545	8	they	they	PRON
ejpam-5050	545	9	have	have	VERB
ejpam-5050	545	10	no	no	DET
ejpam-5050	545	11	competing	compete	VERB
ejpam-5050	545	12	interests	interest	NOUN
ejpam-5050	545	13	.	.	PUNCT
ejpam-5050	546	1	•	•	NUM
ejpam-5050	546	2	funding	funding	NOUN
ejpam-5050	546	3	there	there	PRON
ejpam-5050	546	4	is	be	VERB
ejpam-5050	546	5	no	no	DET
ejpam-5050	546	6	funding	funding	NOUN
ejpam-5050	546	7	for	for	ADP
ejpam-5050	546	8	this	this	DET
ejpam-5050	546	9	work	work	NOUN
ejpam-5050	546	10	.	.	PUNCT
ejpam-5050	547	1	references	reference	NOUN
ejpam-5050	547	2	[	[	X
ejpam-5050	547	3	1	1	NUM
ejpam-5050	547	4	]	]	X
ejpam-5050	547	5	k	k	PROPN
ejpam-5050	547	6	abbaoui	abbaoui	PROPN
ejpam-5050	547	7	and	and	CCONJ
ejpam-5050	547	8	y	y	PROPN
ejpam-5050	547	9	cherruault	cherruault	NOUN
ejpam-5050	547	10	.	.	PUNCT
ejpam-5050	548	1	convergence	convergence	NOUN
ejpam-5050	548	2	of	of	ADP
ejpam-5050	548	3	adomian	adomian	NOUN
ejpam-5050	548	4	’s	’s	PART
ejpam-5050	548	5	method	method	NOUN
ejpam-5050	548	6	applied	apply	VERB
ejpam-5050	548	7	to	to	ADP
ejpam-5050	548	8	differential	differential	ADJ
ejpam-5050	548	9	equations	equation	NOUN
ejpam-5050	548	10	.	.	PUNCT
ejpam-5050	549	1	computers	computer	NOUN
ejpam-5050	549	2	&	&	CCONJ
ejpam-5050	549	3	mathematics	mathematics	PROPN
ejpam-5050	549	4	with	with	ADP
ejpam-5050	549	5	applications	application	NOUN
ejpam-5050	549	6	,	,	PUNCT
ejpam-5050	549	7	28(5):103–109	28(5):103–109	NUM
ejpam-5050	549	8	,	,	PUNCT
ejpam-5050	549	9	1994	1994	NUM
ejpam-5050	549	10	.	.	PUNCT
ejpam-5050	550	1	[	[	X
ejpam-5050	550	2	2	2	X
ejpam-5050	550	3	]	]	X
ejpam-5050	550	4	aisha	aisha	PROPN
ejpam-5050	550	5	abdullah	abdullah	PROPN
ejpam-5050	550	6	alderremy	alderremy	PROPN
ejpam-5050	550	7	,	,	PUNCT
ejpam-5050	550	8	tarig	tarig	PROPN
ejpam-5050	550	9	m	m	VERB
ejpam-5050	550	10	elzaki	elzaki	ADJ
ejpam-5050	550	11	,	,	PUNCT
ejpam-5050	550	12	and	and	CCONJ
ejpam-5050	550	13	mourad	mourad	PROPN
ejpam-5050	550	14	chamekh	chamekh	PROPN
ejpam-5050	550	15	.	.	PUNCT
ejpam-5050	551	1	modified	modify	VERB
ejpam-5050	551	2	adomian	adomian	NOUN
ejpam-5050	551	3	decomposition	decomposition	NOUN
ejpam-5050	551	4	method	method	NOUN
ejpam-5050	551	5	to	to	PART
ejpam-5050	551	6	solve	solve	VERB
ejpam-5050	551	7	generalized	generalize	VERB
ejpam-5050	551	8	emden	emden	ADJ
ejpam-5050	551	9	–	–	PUNCT
ejpam-5050	551	10	fowler	fowler	PROPN
ejpam-5050	551	11	systems	system	NOUN
ejpam-5050	551	12	for	for	ADP
ejpam-5050	551	13	singular	singular	ADJ
ejpam-5050	551	14	ivp	ivp	PROPN
ejpam-5050	551	15	.	.	PUNCT
ejpam-5050	552	1	mathematical	mathematical	ADJ
ejpam-5050	552	2	problems	problem	NOUN
ejpam-5050	552	3	in	in	ADP
ejpam-5050	552	4	engineering	engineering	NOUN
ejpam-5050	552	5	,	,	PUNCT
ejpam-5050	552	6	2019:1–6	2019:1–6	NUM
ejpam-5050	552	7	,	,	PUNCT
ejpam-5050	552	8	2019	2019	NUM
ejpam-5050	552	9	.	.	PUNCT
ejpam-5050	553	1	[	[	X
ejpam-5050	553	2	3	3	X
ejpam-5050	553	3	]	]	SYM
ejpam-5050	553	4	g	g	NOUN
ejpam-5050	553	5	adomian	adomian	NOUN
ejpam-5050	553	6	and	and	CCONJ
ejpam-5050	553	7	r	r	NOUN
ejpam-5050	553	8	rach	rach	NOUN
ejpam-5050	553	9	.	.	PUNCT
ejpam-5050	554	1	modified	modify	VERB
ejpam-5050	554	2	adomian	adomian	NOUN
ejpam-5050	554	3	polynomials	polynomial	NOUN
ejpam-5050	554	4	.	.	PUNCT
ejpam-5050	555	1	mathematical	mathematical	ADJ
ejpam-5050	555	2	and	and	CCONJ
ejpam-5050	555	3	computer	computer	NOUN
ejpam-5050	555	4	modelling	modelling	NOUN
ejpam-5050	555	5	,	,	PUNCT
ejpam-5050	555	6	24(11):39–46	24(11):39–46	NUM
ejpam-5050	555	7	,	,	PUNCT
ejpam-5050	555	8	1996	1996	NUM
ejpam-5050	555	9	.	.	PUNCT
ejpam-5050	556	1	[	[	X
ejpam-5050	556	2	4	4	NUM
ejpam-5050	556	3	]	]	PUNCT
ejpam-5050	556	4	george	george	PROPN
ejpam-5050	556	5	adomian	adomian	NOUN
ejpam-5050	556	6	.	.	PUNCT
ejpam-5050	557	1	solving	solve	VERB
ejpam-5050	557	2	frontier	frontier	NOUN
ejpam-5050	557	3	problems	problem	NOUN
ejpam-5050	557	4	of	of	ADP
ejpam-5050	557	5	physics	physics	NOUN
ejpam-5050	557	6	:	:	PUNCT
ejpam-5050	557	7	the	the	DET
ejpam-5050	557	8	decomposition	decomposition	NOUN
ejpam-5050	557	9	method	method	NOUN
ejpam-5050	557	10	,	,	PUNCT
ejpam-5050	557	11	volume	volume	NOUN
ejpam-5050	557	12	60	60	NUM
ejpam-5050	557	13	.	.	PUNCT
ejpam-5050	558	1	springer	springer	NOUN
ejpam-5050	558	2	science	science	PROPN
ejpam-5050	558	3	&	&	CCONJ
ejpam-5050	558	4	business	business	NOUN
ejpam-5050	558	5	media	medium	NOUN
ejpam-5050	558	6	,	,	PUNCT
ejpam-5050	558	7	2013	2013	NUM
ejpam-5050	558	8	.	.	PUNCT
ejpam-5050	559	1	[	[	X
ejpam-5050	559	2	5	5	NUM
ejpam-5050	559	3	]	]	X
ejpam-5050	559	4	el	el	PROPN
ejpam-5050	559	5	-	-	PUNCT
ejpam-5050	559	6	mesiry	mesiry	PROPN
ejpam-5050	559	7	aem	aem	PROPN
ejpam-5050	559	8	,	,	PUNCT
ejpam-5050	559	9	el	el	PROPN
ejpam-5050	559	10	-	-	PUNCT
ejpam-5050	559	11	sayed	say	VERB
ejpam-5050	559	12	ama	ama	PROPN
ejpam-5050	559	13	,	,	PUNCT
ejpam-5050	559	14	and	and	CCONJ
ejpam-5050	559	15	el	el	PROPN
ejpam-5050	559	16	-	-	PUNCT
ejpam-5050	559	17	saka	saka	PROPN
ejpam-5050	559	18	haa	haa	PROPN
ejpam-5050	559	19	.	.	PUNCT
ejpam-5050	560	1	numerical	numerical	ADJ
ejpam-5050	560	2	methods	method	NOUN
ejpam-5050	560	3	for	for	ADP
ejpam-5050	560	4	multiterm	multiterm	NOUN
ejpam-5050	560	5	fractional	fractional	PROPN
ejpam-5050	560	6	(	(	PUNCT
ejpam-5050	560	7	arbitrary	arbitrary	ADJ
ejpam-5050	560	8	)	)	PUNCT
ejpam-5050	560	9	orders	order	NOUN
ejpam-5050	560	10	differential	differential	ADJ
ejpam-5050	560	11	equations	equation	NOUN
ejpam-5050	560	12	.	.	PUNCT
ejpam-5050	561	1	applied	apply	VERB
ejpam-5050	561	2	mathematics	mathematic	NOUN
ejpam-5050	561	3	and	and	CCONJ
ejpam-5050	561	4	computation	computation	NOUN
ejpam-5050	561	5	,	,	PUNCT
ejpam-5050	561	6	160(3):683–699	160(3):683–699	NUM
ejpam-5050	561	7	,	,	PUNCT
ejpam-5050	561	8	2005	2005	NUM
ejpam-5050	561	9	.	.	PUNCT
ejpam-5050	562	1	[	[	X
ejpam-5050	562	2	6	6	NUM
ejpam-5050	562	3	]	]	X
ejpam-5050	562	4	el	el	PROPN
ejpam-5050	562	5	-	-	PUNCT
ejpam-5050	562	6	sayed	say	VERB
ejpam-5050	562	7	ahmed	ahmed	PROPN
ejpam-5050	562	8	.	.	PUNCT
ejpam-5050	563	1	abstract	abstract	ADJ
ejpam-5050	563	2	differential	differential	ADJ
ejpam-5050	563	3	equations	equation	NOUN
ejpam-5050	563	4	of	of	ADP
ejpam-5050	563	5	arbitrary	arbitrary	ADJ
ejpam-5050	563	6	(	(	PUNCT
ejpam-5050	563	7	fractional	fractional	ADJ
ejpam-5050	563	8	)	)	PUNCT
ejpam-5050	563	9	orders	order	NOUN
ejpam-5050	563	10	.	.	PUNCT
ejpam-5050	564	1	proceedings	proceeding	NOUN
ejpam-5050	564	2	of	of	ADP
ejpam-5050	564	3	equadiff	equadiff	NOUN
ejpam-5050	564	4	9	9	NUM
ejpam-5050	564	5	,	,	PUNCT
ejpam-5050	564	6	pages	page	NOUN
ejpam-5050	564	7	93–99	93–99	NUM
ejpam-5050	564	8	,	,	PUNCT
ejpam-5050	564	9	1998	1998	NUM
ejpam-5050	564	10	.	.	PUNCT
ejpam-5050	565	1	[	[	X
ejpam-5050	565	2	7	7	X
ejpam-5050	565	3	]	]	X
ejpam-5050	565	4	ghazala	ghazala	PROPN
ejpam-5050	565	5	akram	akram	PROPN
ejpam-5050	565	6	and	and	CCONJ
ejpam-5050	565	7	hira	hira	PROPN
ejpam-5050	565	8	tariq	tariq	PROPN
ejpam-5050	565	9	.	.	PUNCT
ejpam-5050	566	1	an	an	DET
ejpam-5050	566	2	exponential	exponential	ADJ
ejpam-5050	566	3	spline	spline	NOUN
ejpam-5050	566	4	technique	technique	NOUN
ejpam-5050	566	5	for	for	ADP
ejpam-5050	566	6	solving	solve	VERB
ejpam-5050	566	7	fractional	fractional	ADJ
ejpam-5050	566	8	boundary	boundary	ADJ
ejpam-5050	566	9	value	value	NOUN
ejpam-5050	566	10	problem	problem	NOUN
ejpam-5050	566	11	.	.	PUNCT
ejpam-5050	567	1	calcolo	calcolo	PROPN
ejpam-5050	567	2	,	,	PUNCT
ejpam-5050	567	3	53:545–558	53:545–558	NUM
ejpam-5050	567	4	,	,	PUNCT
ejpam-5050	567	5	2016	2016	NUM
ejpam-5050	567	6	.	.	PUNCT
ejpam-5050	568	1	[	[	X
ejpam-5050	568	2	8	8	NUM
ejpam-5050	568	3	]	]	X
ejpam-5050	568	4	qasem	qasem	PROPN
ejpam-5050	568	5	m	m	PROPN
ejpam-5050	568	6	al	al	PROPN
ejpam-5050	568	7	-	-	PUNCT
ejpam-5050	568	8	mdallal	mdallal	PROPN
ejpam-5050	568	9	,	,	PUNCT
ejpam-5050	568	10	muhammed	muhamme	VERB
ejpam-5050	568	11	i	i	PRON
ejpam-5050	568	12	syam	syam	NOUN
ejpam-5050	568	13	,	,	PUNCT
ejpam-5050	568	14	and	and	CCONJ
ejpam-5050	568	15	mn	mn	PROPN
ejpam-5050	568	16	anwar	anwar	PROPN
ejpam-5050	568	17	.	.	PUNCT
ejpam-5050	569	1	a	a	DET
ejpam-5050	569	2	collocation	collocation	NOUN
ejpam-5050	569	3	-	-	PUNCT
ejpam-5050	569	4	shooting	shooting	NOUN
ejpam-5050	569	5	method	method	NOUN
ejpam-5050	569	6	for	for	ADP
ejpam-5050	569	7	solving	solve	VERB
ejpam-5050	569	8	fractional	fractional	ADJ
ejpam-5050	569	9	boundary	boundary	ADJ
ejpam-5050	569	10	value	value	NOUN
ejpam-5050	569	11	problems	problem	NOUN
ejpam-5050	569	12	.	.	PUNCT
ejpam-5050	570	1	communications	communication	NOUN
ejpam-5050	570	2	in	in	ADP
ejpam-5050	570	3	nonlinear	nonlinear	ADJ
ejpam-5050	570	4	science	science	NOUN
ejpam-5050	570	5	and	and	CCONJ
ejpam-5050	570	6	numerical	numerical	PROPN
ejpam-5050	570	7	simulation	simulation	PROPN
ejpam-5050	570	8	,	,	PUNCT
ejpam-5050	570	9	15(12):3814–3822	15(12):3814–3822	NUM
ejpam-5050	570	10	,	,	PUNCT
ejpam-5050	570	11	2010	2010	NUM
ejpam-5050	570	12	.	.	PUNCT
ejpam-5050	571	1	[	[	X
ejpam-5050	571	2	9	9	NUM
ejpam-5050	571	3	]	]	X
ejpam-5050	571	4	awad	awad	PROPN
ejpam-5050	571	5	t	t	PROPN
ejpam-5050	571	6	alabdala	alabdala	PROPN
ejpam-5050	571	7	,	,	PUNCT
ejpam-5050	571	8	saleh	saleh	PROPN
ejpam-5050	571	9	s	s	PART
ejpam-5050	571	10	redhwan	redhwan	NOUN
ejpam-5050	571	11	,	,	PUNCT
ejpam-5050	571	12	tariq	tariq	PROPN
ejpam-5050	571	13	a	a	DET
ejpam-5050	571	14	aljaaidi	aljaaidi	ADJ
ejpam-5050	571	15	,	,	PUNCT
ejpam-5050	571	16	et	et	PROPN
ejpam-5050	571	17	al	al	PROPN
ejpam-5050	571	18	.	.	PROPN
ejpam-5050	571	19	existence	existence	NOUN
ejpam-5050	571	20	and	and	CCONJ
ejpam-5050	571	21	approximate	approximate	ADJ
ejpam-5050	571	22	solution	solution	NOUN
ejpam-5050	571	23	for	for	ADP
ejpam-5050	571	24	the	the	DET
ejpam-5050	571	25	fractional	fractional	PROPN
ejpam-5050	571	26	volterra	volterra	PROPN
ejpam-5050	571	27	fredholm	fredholm	PROPN
ejpam-5050	571	28	integro	integro	ADJ
ejpam-5050	571	29	-	-	PUNCT
ejpam-5050	571	30	differential	differential	NOUN
ejpam-5050	571	31	equation	equation	NOUN
ejpam-5050	571	32	involving	involve	VERB
ejpam-5050	571	33	ζ	ζ	NOUN
ejpam-5050	571	34	-	-	PUNCT
ejpam-5050	571	35	hilfer	hilfer	NOUN
ejpam-5050	571	36	fractional	fractional	ADJ
ejpam-5050	571	37	derivative	derivative	NOUN
ejpam-5050	571	38	.	.	PUNCT
ejpam-5050	572	1	nonlinear	nonlinear	ADJ
ejpam-5050	572	2	functional	functional	ADJ
ejpam-5050	572	3	analysis	analysis	NOUN
ejpam-5050	572	4	and	and	CCONJ
ejpam-5050	572	5	applications	application	NOUN
ejpam-5050	572	6	,	,	PUNCT
ejpam-5050	572	7	pages	page	NOUN
ejpam-5050	572	8	989–1004	989–1004	NUM
ejpam-5050	572	9	,	,	PUNCT
ejpam-5050	572	10	2023	2023	NUM
ejpam-5050	572	11	.	.	PUNCT
ejpam-5050	573	1	references	reference	NOUN
ejpam-5050	573	2	565	565	NUM
ejpam-5050	573	3	[	[	SYM
ejpam-5050	573	4	10	10	NUM
ejpam-5050	573	5	]	]	X
ejpam-5050	573	6	carpinteri	carpinteri	NOUN
ejpam-5050	573	7	alberto	alberto	PROPN
ejpam-5050	573	8	and	and	CCONJ
ejpam-5050	573	9	mainardi	mainardi	PROPN
ejpam-5050	573	10	francesco	francesco	PROPN
ejpam-5050	573	11	.	.	PUNCT
ejpam-5050	574	1	fractals	fractal	NOUN
ejpam-5050	574	2	and	and	CCONJ
ejpam-5050	574	3	fractional	fractional	ADJ
ejpam-5050	574	4	calculus	calculus	NOUN
ejpam-5050	574	5	in	in	ADP
ejpam-5050	574	6	continuum	continuum	ADJ
ejpam-5050	574	7	mechanics	mechanic	NOUN
ejpam-5050	574	8	,	,	PUNCT
ejpam-5050	574	9	volume	volume	NOUN
ejpam-5050	574	10	378	378	NUM
ejpam-5050	574	11	.	.	PUNCT
ejpam-5050	574	12	springer	springer	NOUN
ejpam-5050	574	13	,	,	PUNCT
ejpam-5050	574	14	2014	2014	NUM
ejpam-5050	574	15	.	.	PUNCT
ejpam-5050	575	1	[	[	X
ejpam-5050	575	2	11	11	NUM
ejpam-5050	575	3	]	]	X
ejpam-5050	575	4	el	el	PROPN
ejpam-5050	575	5	-	-	PUNCT
ejpam-5050	575	6	sayed	say	VERB
ejpam-5050	575	7	ama	ama	PROPN
ejpam-5050	575	8	,	,	PUNCT
ejpam-5050	575	9	el	el	PROPN
ejpam-5050	575	10	-	-	PUNCT
ejpam-5050	575	11	mesiry	mesiry	PROPN
ejpam-5050	575	12	aem	aem	PROPN
ejpam-5050	575	13	,	,	PUNCT
ejpam-5050	575	14	and	and	CCONJ
ejpam-5050	575	15	el	el	PROPN
ejpam-5050	575	16	-	-	PUNCT
ejpam-5050	575	17	saka	saka	PROPN
ejpam-5050	575	18	haa	haa	PROPN
ejpam-5050	575	19	.	.	PROPN
ejpam-5050	575	20	numerical	numerical	ADJ
ejpam-5050	575	21	solution	solution	NOUN
ejpam-5050	575	22	for	for	ADP
ejpam-5050	575	23	multiterm	multiterm	NOUN
ejpam-5050	575	24	fractional	fractional	PROPN
ejpam-5050	575	25	(	(	PUNCT
ejpam-5050	575	26	arbitrary	arbitrary	ADJ
ejpam-5050	575	27	)	)	PUNCT
ejpam-5050	575	28	orders	order	NOUN
ejpam-5050	575	29	differential	differential	ADJ
ejpam-5050	575	30	equations	equation	NOUN
ejpam-5050	575	31	.	.	PUNCT
ejpam-5050	576	1	computational	computational	ADJ
ejpam-5050	576	2	&	&	CCONJ
ejpam-5050	576	3	applied	applied	ADJ
ejpam-5050	576	4	mathematics	mathematic	NOUN
ejpam-5050	576	5	,	,	PUNCT
ejpam-5050	576	6	23:33–54	23:33–54	NUM
ejpam-5050	576	7	,	,	PUNCT
ejpam-5050	576	8	2004	2004	NUM
ejpam-5050	576	9	.	.	PUNCT
ejpam-5050	577	1	[	[	X
ejpam-5050	577	2	12	12	NUM
ejpam-5050	577	3	]	]	X
ejpam-5050	577	4	hossein	hossein	PROPN
ejpam-5050	577	5	aminikhah	aminikhah	PROPN
ejpam-5050	577	6	and	and	CCONJ
ejpam-5050	577	7	jafar	jafar	PROPN
ejpam-5050	577	8	biazar	biazar	PROPN
ejpam-5050	577	9	.	.	PUNCT
ejpam-5050	578	1	a	a	DET
ejpam-5050	578	2	new	new	ADJ
ejpam-5050	578	3	hpm	hpm	NOUN
ejpam-5050	578	4	for	for	ADP
ejpam-5050	578	5	ordinary	ordinary	ADJ
ejpam-5050	578	6	differential	differential	ADJ
ejpam-5050	578	7	equations	equation	NOUN
ejpam-5050	578	8	.	.	PUNCT
ejpam-5050	579	1	numerical	numerical	ADJ
ejpam-5050	579	2	methods	method	NOUN
ejpam-5050	579	3	for	for	ADP
ejpam-5050	579	4	partial	partial	ADJ
ejpam-5050	579	5	differential	differential	ADJ
ejpam-5050	579	6	equations	equation	NOUN
ejpam-5050	579	7	:	:	PUNCT
ejpam-5050	579	8	an	an	DET
ejpam-5050	579	9	international	international	ADJ
ejpam-5050	579	10	journal	journal	NOUN
ejpam-5050	579	11	,	,	PUNCT
ejpam-5050	579	12	26(2):480–489	26(2):480–489	PROPN
ejpam-5050	579	13	,	,	PUNCT
ejpam-5050	579	14	2010	2010	NUM
ejpam-5050	579	15	.	.	PUNCT
ejpam-5050	580	1	[	[	X
ejpam-5050	580	2	13	13	NUM
ejpam-5050	580	3	]	]	PUNCT
ejpam-5050	580	4	kilbas	kilbas	PROPN
ejpam-5050	580	5	anatoli	anatoli	PROPN
ejpam-5050	580	6	,	,	PUNCT
ejpam-5050	580	7	srivastava	srivastava	PROPN
ejpam-5050	580	8	hari	hari	PROPN
ejpam-5050	580	9	m	m	PROPN
ejpam-5050	580	10	,	,	PUNCT
ejpam-5050	580	11	and	and	CCONJ
ejpam-5050	580	12	trujillo	trujillo	PROPN
ejpam-5050	580	13	juan	juan	PROPN
ejpam-5050	580	14	j.	j.	PROPN
ejpam-5050	580	15	theory	theory	PROPN
ejpam-5050	580	16	and	and	CCONJ
ejpam-5050	580	17	applications	application	NOUN
ejpam-5050	580	18	of	of	ADP
ejpam-5050	580	19	fractional	fractional	ADJ
ejpam-5050	580	20	differential	differential	ADJ
ejpam-5050	580	21	equations	equation	NOUN
ejpam-5050	580	22	,	,	PUNCT
ejpam-5050	580	23	volume	volume	NOUN
ejpam-5050	580	24	204	204	NUM
ejpam-5050	580	25	.	.	PUNCT
ejpam-5050	581	1	elsevier	elsevier	NOUN
ejpam-5050	581	2	,	,	PUNCT
ejpam-5050	581	3	2006	2006	NUM
ejpam-5050	581	4	.	.	PUNCT
ejpam-5050	582	1	[	[	X
ejpam-5050	582	2	14	14	NUM
ejpam-5050	582	3	]	]	X
ejpam-5050	582	4	geeta	geeta	PROPN
ejpam-5050	582	5	arora	arora	PROPN
ejpam-5050	582	6	and	and	CCONJ
ejpam-5050	582	7	pratiksha	pratiksha	PROPN
ejpam-5050	582	8	pratiksha	pratiksha	PROPN
ejpam-5050	582	9	.	.	PUNCT
ejpam-5050	583	1	solution	solution	NOUN
ejpam-5050	583	2	of	of	ADP
ejpam-5050	583	3	the	the	DET
ejpam-5050	583	4	bagley	bagley	NOUN
ejpam-5050	583	5	torvik	torvik	PROPN
ejpam-5050	583	6	equation	equation	NOUN
ejpam-5050	583	7	by	by	ADP
ejpam-5050	583	8	fractional	fractional	ADJ
ejpam-5050	583	9	dtm	dtm	PROPN
ejpam-5050	583	10	.	.	PROPN
ejpam-5050	583	11	in	in	ADP
ejpam-5050	583	12	aip	aip	PROPN
ejpam-5050	583	13	conference	conference	NOUN
ejpam-5050	583	14	proceedings	proceeding	NOUN
ejpam-5050	583	15	,	,	PUNCT
ejpam-5050	583	16	volume	volume	NOUN
ejpam-5050	583	17	1860	1860	NUM
ejpam-5050	583	18	.	.	PUNCT
ejpam-5050	584	1	aip	aip	PROPN
ejpam-5050	584	2	publishing	publishing	PROPN
ejpam-5050	584	3	,	,	PUNCT
ejpam-5050	584	4	2017	2017	NUM
ejpam-5050	584	5	.	.	PUNCT
ejpam-5050	585	1	[	[	X
ejpam-5050	585	2	15	15	NUM
ejpam-5050	585	3	]	]	X
ejpam-5050	585	4	ho	ho	ADJ
ejpam-5050	585	5	bakodah	bakodah	PROPN
ejpam-5050	585	6	,	,	PUNCT
ejpam-5050	585	7	ma	ma	PROPN
ejpam-5050	585	8	banaja	banaja	PROPN
ejpam-5050	585	9	,	,	PUNCT
ejpam-5050	585	10	ba	ba	PROPN
ejpam-5050	585	11	alrigi	alrigi	PROPN
ejpam-5050	585	12	,	,	PUNCT
ejpam-5050	585	13	a	a	DET
ejpam-5050	585	14	ebaid	ebaid	NOUN
ejpam-5050	585	15	,	,	PUNCT
ejpam-5050	585	16	and	and	CCONJ
ejpam-5050	585	17	r	r	NOUN
ejpam-5050	585	18	rach	rach	NOUN
ejpam-5050	585	19	.	.	PUNCT
ejpam-5050	586	1	an	an	DET
ejpam-5050	586	2	efficient	efficient	ADJ
ejpam-5050	586	3	modification	modification	NOUN
ejpam-5050	586	4	of	of	ADP
ejpam-5050	586	5	the	the	DET
ejpam-5050	586	6	decomposition	decomposition	NOUN
ejpam-5050	586	7	method	method	NOUN
ejpam-5050	586	8	with	with	ADP
ejpam-5050	586	9	a	a	DET
ejpam-5050	586	10	convergence	convergence	NOUN
ejpam-5050	586	11	parameter	parameter	NOUN
ejpam-5050	586	12	for	for	ADP
ejpam-5050	586	13	solving	solve	VERB
ejpam-5050	586	14	korteweg	korteweg	PROPN
ejpam-5050	586	15	de	de	PROPN
ejpam-5050	586	16	vries	vries	PROPN
ejpam-5050	586	17	equations	equation	NOUN
ejpam-5050	586	18	.	.	PUNCT
ejpam-5050	587	1	journal	journal	PROPN
ejpam-5050	587	2	of	of	ADP
ejpam-5050	587	3	king	king	PROPN
ejpam-5050	587	4	saud	saud	PROPN
ejpam-5050	587	5	university	university	PROPN
ejpam-5050	587	6	-	-	PUNCT
ejpam-5050	587	7	science	science	NOUN
ejpam-5050	587	8	,	,	PUNCT
ejpam-5050	587	9	31(4):1424–1430	31(4):1424–1430	PROPN
ejpam-5050	587	10	,	,	PUNCT
ejpam-5050	587	11	2019	2019	NUM
ejpam-5050	587	12	.	.	PUNCT
ejpam-5050	588	1	[	[	X
ejpam-5050	588	2	16	16	NUM
ejpam-5050	588	3	]	]	X
ejpam-5050	588	4	y	y	PROPN
ejpam-5050	588	5	cherruault	cherruault	NOUN
ejpam-5050	588	6	,	,	PUNCT
ejpam-5050	588	7	g	g	PROPN
ejpam-5050	588	8	adomian	adomian	NOUN
ejpam-5050	588	9	,	,	PUNCT
ejpam-5050	588	10	k	k	PROPN
ejpam-5050	588	11	abbaoui	abbaoui	PROPN
ejpam-5050	588	12	,	,	PUNCT
ejpam-5050	588	13	and	and	CCONJ
ejpam-5050	588	14	r	r	NOUN
ejpam-5050	588	15	rach	rach	NOUN
ejpam-5050	588	16	.	.	PUNCT
ejpam-5050	589	1	further	further	ADJ
ejpam-5050	589	2	remarks	remark	NOUN
ejpam-5050	589	3	on	on	ADP
ejpam-5050	589	4	convergence	convergence	NOUN
ejpam-5050	589	5	of	of	ADP
ejpam-5050	589	6	decomposition	decomposition	NOUN
ejpam-5050	589	7	method	method	NOUN
ejpam-5050	589	8	.	.	PUNCT
ejpam-5050	590	1	international	international	ADJ
ejpam-5050	590	2	journal	journal	PROPN
ejpam-5050	590	3	of	of	ADP
ejpam-5050	590	4	bio	bio	PROPN
ejpam-5050	590	5	-	-	ADJ
ejpam-5050	590	6	medical	medical	ADJ
ejpam-5050	590	7	computing	computing	NOUN
ejpam-5050	590	8	,	,	PUNCT
ejpam-5050	590	9	38(1):89	38(1):89	PROPN
ejpam-5050	590	10	–	–	PUNCT
ejpam-5050	590	11	93	93	NUM
ejpam-5050	590	12	,	,	PUNCT
ejpam-5050	590	13	1995	1995	NUM
ejpam-5050	590	14	.	.	PUNCT
ejpam-5050	591	1	[	[	X
ejpam-5050	591	2	17	17	NUM
ejpam-5050	591	3	]	]	X
ejpam-5050	591	4	varsha	varsha	PROPN
ejpam-5050	591	5	daftardar	daftardar	NOUN
ejpam-5050	591	6	-	-	PUNCT
ejpam-5050	591	7	gejji	gejji	NOUN
ejpam-5050	591	8	and	and	CCONJ
ejpam-5050	591	9	azizollah	azizollah	PROPN
ejpam-5050	591	10	babakhani	babakhani	PROPN
ejpam-5050	591	11	.	.	PUNCT
ejpam-5050	592	1	analysis	analysis	NOUN
ejpam-5050	592	2	of	of	ADP
ejpam-5050	592	3	a	a	DET
ejpam-5050	592	4	system	system	NOUN
ejpam-5050	592	5	of	of	ADP
ejpam-5050	592	6	fractional	fractional	ADJ
ejpam-5050	592	7	differential	differential	ADJ
ejpam-5050	592	8	equations	equation	NOUN
ejpam-5050	592	9	.	.	PUNCT
ejpam-5050	593	1	journal	journal	PROPN
ejpam-5050	593	2	of	of	ADP
ejpam-5050	593	3	mathematical	mathematical	ADJ
ejpam-5050	593	4	analysis	analysis	NOUN
ejpam-5050	593	5	and	and	CCONJ
ejpam-5050	593	6	applications	application	NOUN
ejpam-5050	593	7	,	,	PUNCT
ejpam-5050	593	8	293(2):511–522	293(2):511–522	NUM
ejpam-5050	593	9	,	,	PUNCT
ejpam-5050	593	10	2004	2004	NUM
ejpam-5050	593	11	.	.	PUNCT
ejpam-5050	594	1	[	[	X
ejpam-5050	594	2	18	18	NUM
ejpam-5050	594	3	]	]	X
ejpam-5050	594	4	varsha	varsha	PROPN
ejpam-5050	594	5	daftardar	daftardar	NOUN
ejpam-5050	594	6	-	-	PUNCT
ejpam-5050	594	7	gejji	gejji	NOUN
ejpam-5050	594	8	and	and	CCONJ
ejpam-5050	594	9	hossein	hossein	PROPN
ejpam-5050	594	10	jafari	jafari	PROPN
ejpam-5050	594	11	.	.	PUNCT
ejpam-5050	595	1	solving	solve	VERB
ejpam-5050	595	2	a	a	DET
ejpam-5050	595	3	multi	multi	ADJ
ejpam-5050	595	4	-	-	ADJ
ejpam-5050	595	5	order	order	ADJ
ejpam-5050	595	6	fractional	fractional	ADJ
ejpam-5050	595	7	differential	differential	NOUN
ejpam-5050	595	8	equation	equation	NOUN
ejpam-5050	595	9	using	use	VERB
ejpam-5050	595	10	adomian	adomian	NOUN
ejpam-5050	595	11	decomposition	decomposition	NOUN
ejpam-5050	595	12	.	.	PUNCT
ejpam-5050	596	1	applied	apply	VERB
ejpam-5050	596	2	mathematics	mathematic	NOUN
ejpam-5050	596	3	and	and	CCONJ
ejpam-5050	596	4	computation	computation	NOUN
ejpam-5050	596	5	,	,	PUNCT
ejpam-5050	596	6	189(1):541–548	189(1):541–548	NUM
ejpam-5050	596	7	,	,	PUNCT
ejpam-5050	596	8	2007	2007	NUM
ejpam-5050	596	9	.	.	PUNCT
ejpam-5050	597	1	[	[	X
ejpam-5050	597	2	19	19	NUM
ejpam-5050	597	3	]	]	PUNCT
ejpam-5050	597	4	abdelhalim	abdelhalim	PROPN
ejpam-5050	597	5	ebaid	ebaid	PROPN
ejpam-5050	597	6	.	.	PUNCT
ejpam-5050	598	1	a	a	DET
ejpam-5050	598	2	new	new	ADJ
ejpam-5050	598	3	analytical	analytical	ADJ
ejpam-5050	598	4	and	and	CCONJ
ejpam-5050	598	5	numerical	numerical	ADJ
ejpam-5050	598	6	treatment	treatment	NOUN
ejpam-5050	598	7	for	for	ADP
ejpam-5050	598	8	singular	singular	ADJ
ejpam-5050	598	9	two	two	NUM
ejpam-5050	598	10	-	-	PUNCT
ejpam-5050	598	11	point	point	NOUN
ejpam-5050	598	12	boundary	boundary	ADJ
ejpam-5050	598	13	value	value	NOUN
ejpam-5050	598	14	problems	problem	NOUN
ejpam-5050	598	15	via	via	ADP
ejpam-5050	598	16	the	the	DET
ejpam-5050	598	17	adomian	adomian	NOUN
ejpam-5050	598	18	decomposition	decomposition	NOUN
ejpam-5050	598	19	method	method	NOUN
ejpam-5050	598	20	.	.	PUNCT
ejpam-5050	599	1	journal	journal	NOUN
ejpam-5050	599	2	of	of	ADP
ejpam-5050	599	3	computational	computational	ADJ
ejpam-5050	599	4	and	and	CCONJ
ejpam-5050	599	5	applied	applied	ADJ
ejpam-5050	599	6	mathematics	mathematic	NOUN
ejpam-5050	599	7	,	,	PUNCT
ejpam-5050	599	8	235(8):1914–1924	235(8):1914–1924	PROPN
ejpam-5050	599	9	,	,	PUNCT
ejpam-5050	599	10	2011	2011	NUM
ejpam-5050	599	11	.	.	PUNCT
ejpam-5050	600	1	[	[	X
ejpam-5050	600	2	20	20	NUM
ejpam-5050	600	3	]	]	PUNCT
ejpam-5050	600	4	mohamed	mohamed	PROPN
ejpam-5050	600	5	el	el	PROPN
ejpam-5050	600	6	-	-	PROPN
ejpam-5050	600	7	gamel	gamel	PROPN
ejpam-5050	600	8	,	,	PUNCT
ejpam-5050	600	9	mahmoud	mahmoud	PROPN
ejpam-5050	600	10	abd	abd	PROPN
ejpam-5050	600	11	-	-	PROPN
ejpam-5050	600	12	el	el	PROPN
ejpam-5050	600	13	-	-	PUNCT
ejpam-5050	600	14	hady	hady	NOUN
ejpam-5050	600	15	,	,	PUNCT
ejpam-5050	600	16	magdy	magdy	PROPN
ejpam-5050	600	17	el	el	PROPN
ejpam-5050	600	18	-	-	PUNCT
ejpam-5050	600	19	azab	azab	PROPN
ejpam-5050	600	20	,	,	PUNCT
ejpam-5050	600	21	et	et	PROPN
ejpam-5050	600	22	al	al	PROPN
ejpam-5050	600	23	.	.	PUNCT
ejpam-5050	600	24	chelyshkov	chelyshkov	PROPN
ejpam-5050	600	25	-	-	PUNCT
ejpam-5050	600	26	tau	tau	PROPN
ejpam-5050	600	27	approach	approach	NOUN
ejpam-5050	600	28	for	for	ADP
ejpam-5050	600	29	solving	solve	VERB
ejpam-5050	600	30	bagley	bagley	NOUN
ejpam-5050	600	31	-	-	PUNCT
ejpam-5050	600	32	torvik	torvik	NOUN
ejpam-5050	600	33	equation	equation	NOUN
ejpam-5050	600	34	.	.	PUNCT
ejpam-5050	601	1	applied	apply	VERB
ejpam-5050	601	2	mathematics	mathematic	NOUN
ejpam-5050	601	3	,	,	PUNCT
ejpam-5050	601	4	8(12):1795	8(12):1795	NUM
ejpam-5050	601	5	,	,	PUNCT
ejpam-5050	601	6	2017	2017	NUM
ejpam-5050	601	7	.	.	PUNCT
ejpam-5050	602	1	[	[	X
ejpam-5050	602	2	21	21	NUM
ejpam-5050	602	3	]	]	X
ejpam-5050	602	4	homan	homan	PROPN
ejpam-5050	602	5	emadifar	emadifar	PROPN
ejpam-5050	602	6	and	and	CCONJ
ejpam-5050	602	7	reza	reza	PROPN
ejpam-5050	602	8	jalilian	jalilian	PROPN
ejpam-5050	602	9	.	.	PUNCT
ejpam-5050	603	1	an	an	DET
ejpam-5050	603	2	exponential	exponential	ADJ
ejpam-5050	603	3	spline	spline	NOUN
ejpam-5050	603	4	approximation	approximation	NOUN
ejpam-5050	603	5	for	for	ADP
ejpam-5050	603	6	fractional	fractional	ADJ
ejpam-5050	603	7	bagley	bagley	NOUN
ejpam-5050	603	8	–	–	PUNCT
ejpam-5050	603	9	torvik	torvik	NOUN
ejpam-5050	603	10	equation	equation	NOUN
ejpam-5050	603	11	.	.	PUNCT
ejpam-5050	604	1	boundary	boundary	ADJ
ejpam-5050	604	2	value	value	NOUN
ejpam-5050	604	3	problems	problem	NOUN
ejpam-5050	604	4	,	,	PUNCT
ejpam-5050	604	5	2020:1–20	2020:1–20	NUM
ejpam-5050	604	6	,	,	PUNCT
ejpam-5050	604	7	2020	2020	NUM
ejpam-5050	604	8	.	.	PUNCT
ejpam-5050	605	1	[	[	X
ejpam-5050	605	2	22	22	NUM
ejpam-5050	605	3	]	]	X
ejpam-5050	605	4	s	s	VERB
ejpam-5050	605	5	hadid	hadid	PROPN
ejpam-5050	605	6	,	,	PUNCT
ejpam-5050	605	7	sa	sa	PROPN
ejpam-5050	605	8	khuri	khuri	PROPN
ejpam-5050	605	9	,	,	PUNCT
ejpam-5050	605	10	and	and	CCONJ
ejpam-5050	605	11	a	a	DET
ejpam-5050	605	12	sayfy	sayfy	NOUN
ejpam-5050	605	13	.	.	PUNCT
ejpam-5050	606	1	a	a	DET
ejpam-5050	606	2	green	green	PROPN
ejpam-5050	606	3	’s	’s	PART
ejpam-5050	606	4	function	function	NOUN
ejpam-5050	606	5	iterative	iterative	NOUN
ejpam-5050	606	6	approach	approach	NOUN
ejpam-5050	606	7	for	for	ADP
ejpam-5050	606	8	the	the	DET
ejpam-5050	606	9	solution	solution	NOUN
ejpam-5050	606	10	of	of	ADP
ejpam-5050	606	11	a	a	DET
ejpam-5050	606	12	class	class	NOUN
ejpam-5050	606	13	of	of	ADP
ejpam-5050	606	14	fractional	fractional	ADJ
ejpam-5050	606	15	bvps	bvps	NOUN
ejpam-5050	606	16	arising	arise	VERB
ejpam-5050	606	17	in	in	ADP
ejpam-5050	606	18	physical	physical	ADJ
ejpam-5050	606	19	models	model	NOUN
ejpam-5050	606	20	.	.	PUNCT
ejpam-5050	607	1	international	international	ADJ
ejpam-5050	607	2	journal	journal	PROPN
ejpam-5050	607	3	of	of	ADP
ejpam-5050	607	4	applied	applied	ADJ
ejpam-5050	607	5	and	and	CCONJ
ejpam-5050	607	6	computational	computational	ADJ
ejpam-5050	607	7	mathematics	mathematic	NOUN
ejpam-5050	607	8	,	,	PUNCT
ejpam-5050	607	9	6:1–13	6:1–13	NUM
ejpam-5050	607	10	,	,	PUNCT
ejpam-5050	607	11	2020	2020	NUM
ejpam-5050	607	12	.	.	PUNCT
ejpam-5050	608	1	references	reference	NOUN
ejpam-5050	608	2	566	566	NUM
ejpam-5050	608	3	[	[	X
ejpam-5050	608	4	23	23	NUM
ejpam-5050	608	5	]	]	PUNCT
ejpam-5050	608	6	faraidun	faraidun	AUX
ejpam-5050	608	7	k	k	PROPN
ejpam-5050	608	8	hamasalh	hamasalh	PROPN
ejpam-5050	608	9	and	and	CCONJ
ejpam-5050	608	10	karzan	karzan	PROPN
ejpam-5050	608	11	abdulrahman	abdulrahman	PROPN
ejpam-5050	608	12	hamzah	hamzah	PROPN
ejpam-5050	608	13	.	.	PUNCT
ejpam-5050	609	1	quintic	quintic	ADJ
ejpam-5050	609	2	b	b	X
ejpam-5050	609	3	-	-	PUNCT
ejpam-5050	609	4	spline	spline	NOUN
ejpam-5050	609	5	polynomial	polynomial	NOUN
ejpam-5050	609	6	for	for	ADP
ejpam-5050	609	7	solving	solve	VERB
ejpam-5050	609	8	bagely	bagely	ADV
ejpam-5050	609	9	-	-	PUNCT
ejpam-5050	609	10	torvik	torvik	NOUN
ejpam-5050	609	11	fractional	fractional	ADJ
ejpam-5050	609	12	differential	differential	NOUN
ejpam-5050	609	13	problems	problem	NOUN
ejpam-5050	609	14	.	.	PUNCT
ejpam-5050	610	1	2020	2020	NUM
ejpam-5050	610	2	.	.	PUNCT
ejpam-5050	611	1	[	[	X
ejpam-5050	611	2	24	24	NUM
ejpam-5050	611	3	]	]	X
ejpam-5050	611	4	ahmad	ahmad	PROPN
ejpam-5050	611	5	hijaz	hijaz	PROPN
ejpam-5050	611	6	,	,	PUNCT
ejpam-5050	611	7	akgül	akgül	PROPN
ejpam-5050	611	8	ali	ali	PROPN
ejpam-5050	611	9	,	,	PUNCT
ejpam-5050	611	10	khan	khan	PROPN
ejpam-5050	611	11	tufail	tufail	PROPN
ejpam-5050	611	12	a	a	PRON
ejpam-5050	611	13	,	,	PUNCT
ejpam-5050	611	14	stanimirović	stanimirović	NOUN
ejpam-5050	611	15	predrag	predrag	PROPN
ejpam-5050	611	16	s	s	PROPN
ejpam-5050	611	17	,	,	PUNCT
ejpam-5050	611	18	and	and	CCONJ
ejpam-5050	611	19	chu	chu	PROPN
ejpam-5050	611	20	yu	yu	PROPN
ejpam-5050	611	21	-	-	PROPN
ejpam-5050	611	22	ming	ming	PROPN
ejpam-5050	611	23	.	.	PUNCT
ejpam-5050	612	1	new	new	ADJ
ejpam-5050	612	2	perspective	perspective	NOUN
ejpam-5050	612	3	on	on	ADP
ejpam-5050	612	4	the	the	DET
ejpam-5050	612	5	conventional	conventional	ADJ
ejpam-5050	612	6	solutions	solution	NOUN
ejpam-5050	612	7	of	of	ADP
ejpam-5050	612	8	the	the	DET
ejpam-5050	612	9	nonlinear	nonlinear	ADJ
ejpam-5050	612	10	time	time	NOUN
ejpam-5050	612	11	-	-	PUNCT
ejpam-5050	612	12	fractional	fractional	ADJ
ejpam-5050	612	13	partial	partial	ADJ
ejpam-5050	612	14	differential	differential	NOUN
ejpam-5050	612	15	equations	equation	NOUN
ejpam-5050	612	16	.	.	PUNCT
ejpam-5050	613	1	complexity	complexity	NOUN
ejpam-5050	613	2	,	,	PUNCT
ejpam-5050	613	3	2020:1–10	2020:1–10	NUM
ejpam-5050	613	4	,	,	PUNCT
ejpam-5050	613	5	2020	2020	NUM
ejpam-5050	613	6	.	.	PUNCT
ejpam-5050	614	1	[	[	X
ejpam-5050	614	2	25	25	NUM
ejpam-5050	614	3	]	]	PUNCT
ejpam-5050	614	4	badawi	badawi	PROPN
ejpam-5050	614	5	hamza	hamza	PROPN
ejpam-5050	614	6	elbadawi	elbadawi	PROPN
ejpam-5050	614	7	ibrahim	ibrahim	PROPN
ejpam-5050	614	8	,	,	PUNCT
ejpam-5050	614	9	qixiang	qixiang	PROPN
ejpam-5050	614	10	dong	dong	PROPN
ejpam-5050	614	11	,	,	PUNCT
ejpam-5050	614	12	and	and	CCONJ
ejpam-5050	614	13	zhenbin	zhenbin	PROPN
ejpam-5050	614	14	fan	fan	PROPN
ejpam-5050	614	15	.	.	PUNCT
ejpam-5050	615	1	existence	existence	NOUN
ejpam-5050	615	2	for	for	ADP
ejpam-5050	615	3	boundary	boundary	ADJ
ejpam-5050	615	4	value	value	NOUN
ejpam-5050	615	5	problems	problem	NOUN
ejpam-5050	615	6	of	of	ADP
ejpam-5050	615	7	two	two	NUM
ejpam-5050	615	8	-	-	PUNCT
ejpam-5050	615	9	term	term	NOUN
ejpam-5050	615	10	caputo	caputo	PROPN
ejpam-5050	615	11	fractional	fractional	PROPN
ejpam-5050	615	12	differential	differential	PROPN
ejpam-5050	615	13	equations	equation	NOUN
ejpam-5050	615	14	.	.	PUNCT
ejpam-5050	616	1	j.	j.	PROPN
ejpam-5050	616	2	nonlinear	nonlinear	PROPN
ejpam-5050	616	3	sci	sci	PROPN
ejpam-5050	616	4	.	.	PUNCT
ejpam-5050	616	5	appl	appl	PROPN
ejpam-5050	616	6	,	,	PUNCT
ejpam-5050	616	7	10(02):511–520	10(02):511–520	NUM
ejpam-5050	616	8	,	,	PUNCT
ejpam-5050	616	9	2017	2017	NUM
ejpam-5050	616	10	.	.	PUNCT
ejpam-5050	617	1	[	[	X
ejpam-5050	617	2	26	26	NUM
ejpam-5050	617	3	]	]	PUNCT
ejpam-5050	617	4	nuruddeen	nuruddeen	PROPN
ejpam-5050	617	5	rahmatullah	rahmatullah	PROPN
ejpam-5050	617	6	ibrahim	ibrahim	PROPN
ejpam-5050	617	7	,	,	PUNCT
ejpam-5050	617	8	zaman	zaman	NOUN
ejpam-5050	617	9	fd	fd	PROPN
ejpam-5050	617	10	,	,	PUNCT
ejpam-5050	617	11	and	and	CCONJ
ejpam-5050	617	12	zakariya	zakariya	PROPN
ejpam-5050	617	13	yusuf	yusuf	PROPN
ejpam-5050	617	14	f.	f.	PROPN
ejpam-5050	617	15	analysing	analyse	VERB
ejpam-5050	617	16	the	the	DET
ejpam-5050	617	17	fractional	fractional	ADJ
ejpam-5050	617	18	heat	heat	NOUN
ejpam-5050	617	19	diffusion	diffusion	NOUN
ejpam-5050	617	20	equation	equation	NOUN
ejpam-5050	617	21	solution	solution	NOUN
ejpam-5050	617	22	in	in	ADP
ejpam-5050	617	23	comparison	comparison	NOUN
ejpam-5050	617	24	with	with	ADP
ejpam-5050	617	25	the	the	DET
ejpam-5050	617	26	new	new	ADJ
ejpam-5050	617	27	fractional	fractional	ADJ
ejpam-5050	617	28	derivative	derivative	NOUN
ejpam-5050	617	29	by	by	ADP
ejpam-5050	617	30	decomposition	decomposition	NOUN
ejpam-5050	617	31	method	method	NOUN
ejpam-5050	617	32	.	.	PUNCT
ejpam-5050	618	1	malaya	malaya	PROPN
ejpam-5050	618	2	journal	journal	PROPN
ejpam-5050	618	3	of	of	ADP
ejpam-5050	618	4	matematik	matematik	PROPN
ejpam-5050	618	5	,	,	PUNCT
ejpam-5050	618	6	7(2):213–222	7(2):213–222	NUM
ejpam-5050	618	7	,	,	PUNCT
ejpam-5050	618	8	2019	2019	NUM
ejpam-5050	618	9	.	.	PUNCT
ejpam-5050	619	1	[	[	X
ejpam-5050	619	2	27	27	NUM
ejpam-5050	619	3	]	]	SYM
ejpam-5050	619	4	podlubny	podlubny	PROPN
ejpam-5050	619	5	igor	igor	PROPN
ejpam-5050	619	6	.	.	PUNCT
ejpam-5050	620	1	fractional	fractional	ADJ
ejpam-5050	620	2	differential	differential	ADJ
ejpam-5050	620	3	equations	equation	NOUN
ejpam-5050	620	4	:	:	PUNCT
ejpam-5050	620	5	an	an	DET
ejpam-5050	620	6	introduction	introduction	NOUN
ejpam-5050	620	7	to	to	ADP
ejpam-5050	620	8	fractional	fractional	ADJ
ejpam-5050	620	9	derivatives	derivative	NOUN
ejpam-5050	620	10	,	,	PUNCT
ejpam-5050	620	11	fractional	fractional	ADJ
ejpam-5050	620	12	differential	differential	ADJ
ejpam-5050	620	13	equations	equation	NOUN
ejpam-5050	620	14	,	,	PUNCT
ejpam-5050	620	15	to	to	ADP
ejpam-5050	620	16	methods	method	NOUN
ejpam-5050	620	17	of	of	ADP
ejpam-5050	620	18	their	their	PRON
ejpam-5050	620	19	solution	solution	NOUN
ejpam-5050	620	20	and	and	CCONJ
ejpam-5050	620	21	some	some	PRON
ejpam-5050	620	22	of	of	ADP
ejpam-5050	620	23	their	their	PRON
ejpam-5050	620	24	applications	application	NOUN
ejpam-5050	620	25	.	.	PUNCT
ejpam-5050	621	1	elsevier	elsevier	NOUN
ejpam-5050	621	2	,	,	PUNCT
ejpam-5050	621	3	1998	1998	NUM
ejpam-5050	621	4	.	.	PUNCT
ejpam-5050	622	1	[	[	X
ejpam-5050	622	2	28	28	NUM
ejpam-5050	622	3	]	]	PUNCT
ejpam-5050	622	4	podlubny	podlubny	PROPN
ejpam-5050	622	5	igor	igor	PROPN
ejpam-5050	622	6	.	.	PUNCT
ejpam-5050	623	1	matrix	matrix	NOUN
ejpam-5050	623	2	approach	approach	NOUN
ejpam-5050	623	3	to	to	PART
ejpam-5050	623	4	discrete	discrete	VERB
ejpam-5050	623	5	fractional	fractional	ADJ
ejpam-5050	623	6	calculus	calculus	NOUN
ejpam-5050	623	7	.	.	PUNCT
ejpam-5050	624	1	fractional	fractional	ADJ
ejpam-5050	624	2	calculus	calculus	NOUN
ejpam-5050	624	3	and	and	CCONJ
ejpam-5050	624	4	applied	apply	VERB
ejpam-5050	624	5	analysis	analysis	NOUN
ejpam-5050	624	6	,	,	PUNCT
ejpam-5050	624	7	3(4):359–386	3(4):359–386	NUM
ejpam-5050	624	8	,	,	PUNCT
ejpam-5050	624	9	2000	2000	NUM
ejpam-5050	624	10	.	.	PUNCT
ejpam-5050	625	1	[	[	X
ejpam-5050	625	2	29	29	NUM
ejpam-5050	625	3	]	]	X
ejpam-5050	625	4	tianfu	tianfu	PROPN
ejpam-5050	625	5	ji	ji	PROPN
ejpam-5050	625	6	,	,	PUNCT
ejpam-5050	625	7	jianhua	jianhua	PROPN
ejpam-5050	625	8	hou	hou	PROPN
ejpam-5050	625	9	,	,	PUNCT
ejpam-5050	625	10	and	and	CCONJ
ejpam-5050	625	11	changqing	changqe	VERB
ejpam-5050	625	12	yang	yang	PROPN
ejpam-5050	625	13	.	.	PUNCT
ejpam-5050	626	1	numerical	numerical	ADJ
ejpam-5050	626	2	solution	solution	NOUN
ejpam-5050	626	3	of	of	ADP
ejpam-5050	626	4	the	the	DET
ejpam-5050	626	5	bagley	bagley	NOUN
ejpam-5050	626	6	–	–	PUNCT
ejpam-5050	626	7	torvik	torvik	ADP
ejpam-5050	626	8	equation	equation	NOUN
ejpam-5050	626	9	using	use	VERB
ejpam-5050	626	10	shifted	shift	VERB
ejpam-5050	626	11	chebyshev	chebyshev	PROPN
ejpam-5050	626	12	operational	operational	ADJ
ejpam-5050	626	13	matrix	matrix	NOUN
ejpam-5050	626	14	.	.	PUNCT
ejpam-5050	627	1	advances	advance	NOUN
ejpam-5050	627	2	in	in	ADP
ejpam-5050	627	3	difference	difference	NOUN
ejpam-5050	627	4	equations	equation	NOUN
ejpam-5050	627	5	,	,	PUNCT
ejpam-5050	627	6	2020(1):648	2020(1):648	NUM
ejpam-5050	627	7	,	,	PUNCT
ejpam-5050	627	8	2020	2020	NUM
ejpam-5050	627	9	.	.	PUNCT
ejpam-5050	628	1	[	[	X
ejpam-5050	628	2	30	30	NUM
ejpam-5050	628	3	]	]	X
ejpam-5050	628	4	oldham	oldham	PROPN
ejpam-5050	628	5	keith	keith	PROPN
ejpam-5050	628	6	and	and	CCONJ
ejpam-5050	628	7	spanier	spanier	PROPN
ejpam-5050	628	8	jerome	jerome	PROPN
ejpam-5050	628	9	.	.	PUNCT
ejpam-5050	629	1	the	the	DET
ejpam-5050	629	2	fractional	fractional	ADJ
ejpam-5050	629	3	calculus	calculus	NOUN
ejpam-5050	629	4	theory	theory	NOUN
ejpam-5050	629	5	and	and	CCONJ
ejpam-5050	629	6	applications	application	NOUN
ejpam-5050	629	7	of	of	ADP
ejpam-5050	629	8	differentiation	differentiation	NOUN
ejpam-5050	629	9	and	and	CCONJ
ejpam-5050	629	10	integration	integration	NOUN
ejpam-5050	629	11	to	to	ADP
ejpam-5050	629	12	arbitrary	arbitrary	ADJ
ejpam-5050	629	13	order	order	NOUN
ejpam-5050	629	14	.	.	PUNCT
ejpam-5050	630	1	elsevier	elsevier	NOUN
ejpam-5050	630	2	,	,	PUNCT
ejpam-5050	630	3	1974	1974	NUM
ejpam-5050	630	4	.	.	PUNCT
ejpam-5050	631	1	[	[	X
ejpam-5050	631	2	31	31	NUM
ejpam-5050	631	3	]	]	X
ejpam-5050	631	4	daniel	daniel	PROPN
ejpam-5050	631	5	lesnic	lesnic	PROPN
ejpam-5050	631	6	.	.	PUNCT
ejpam-5050	632	1	a	a	DET
ejpam-5050	632	2	computational	computational	ADJ
ejpam-5050	632	3	algebraic	algebraic	ADJ
ejpam-5050	632	4	investigation	investigation	NOUN
ejpam-5050	632	5	of	of	ADP
ejpam-5050	632	6	the	the	DET
ejpam-5050	632	7	decomposition	decomposition	NOUN
ejpam-5050	632	8	method	method	NOUN
ejpam-5050	632	9	for	for	ADP
ejpam-5050	632	10	time	time	NOUN
ejpam-5050	632	11	-	-	PUNCT
ejpam-5050	632	12	dependent	dependent	ADJ
ejpam-5050	632	13	problems	problem	NOUN
ejpam-5050	632	14	.	.	PUNCT
ejpam-5050	633	1	applied	apply	VERB
ejpam-5050	633	2	mathematics	mathematic	NOUN
ejpam-5050	633	3	and	and	CCONJ
ejpam-5050	633	4	computation	computation	NOUN
ejpam-5050	633	5	,	,	PUNCT
ejpam-5050	633	6	119(2	119(2	NUM
ejpam-5050	633	7	-	-	SYM
ejpam-5050	633	8	3):197	3):197	NUM
ejpam-5050	633	9	–	–	PUNCT
ejpam-5050	633	10	206	206	NUM
ejpam-5050	633	11	,	,	PUNCT
ejpam-5050	633	12	2001	2001	NUM
ejpam-5050	633	13	.	.	PUNCT
ejpam-5050	634	1	[	[	X
ejpam-5050	634	2	32	32	NUM
ejpam-5050	634	3	]	]	PUNCT
ejpam-5050	634	4	changpin	changpin	NOUN
ejpam-5050	634	5	li	li	PROPN
ejpam-5050	634	6	and	and	CCONJ
ejpam-5050	634	7	yihong	yihong	PROPN
ejpam-5050	634	8	wang	wang	PROPN
ejpam-5050	634	9	.	.	PUNCT
ejpam-5050	635	1	numerical	numerical	PROPN
ejpam-5050	635	2	algorithm	algorithm	PROPN
ejpam-5050	635	3	based	base	VERB
ejpam-5050	635	4	on	on	ADP
ejpam-5050	635	5	adomian	adomian	NOUN
ejpam-5050	635	6	decomposition	decomposition	NOUN
ejpam-5050	635	7	for	for	ADP
ejpam-5050	635	8	fractional	fractional	ADJ
ejpam-5050	635	9	differential	differential	ADJ
ejpam-5050	635	10	equations	equation	NOUN
ejpam-5050	635	11	.	.	PUNCT
ejpam-5050	636	1	computers	computer	NOUN
ejpam-5050	636	2	&	&	CCONJ
ejpam-5050	636	3	mathematics	mathematics	PROPN
ejpam-5050	636	4	with	with	ADP
ejpam-5050	636	5	applications	application	NOUN
ejpam-5050	636	6	,	,	PUNCT
ejpam-5050	636	7	57(10):1672–1681	57(10):1672–1681	NUM
ejpam-5050	636	8	,	,	PUNCT
ejpam-5050	636	9	2009	2009	NUM
ejpam-5050	636	10	.	.	PUNCT
ejpam-5050	637	1	[	[	X
ejpam-5050	637	2	33	33	NUM
ejpam-5050	637	3	]	]	PUNCT
ejpam-5050	637	4	muhammad	muhammad	PROPN
ejpam-5050	637	5	imran	imran	PROPN
ejpam-5050	637	6	liaqat	liaqat	PROPN
ejpam-5050	637	7	,	,	PUNCT
ejpam-5050	637	8	ali	ali	PROPN
ejpam-5050	637	9	akgül	akgül	PROPN
ejpam-5050	637	10	,	,	PUNCT
ejpam-5050	637	11	and	and	CCONJ
ejpam-5050	637	12	evgenii	evgenii	VERB
ejpam-5050	637	13	yu	yu	PROPN
ejpam-5050	637	14	prosviryakov	prosviryakov	PROPN
ejpam-5050	637	15	.	.	PUNCT
ejpam-5050	638	1	an	an	DET
ejpam-5050	638	2	efficient	efficient	ADJ
ejpam-5050	638	3	method	method	NOUN
ejpam-5050	638	4	for	for	ADP
ejpam-5050	638	5	the	the	DET
ejpam-5050	638	6	analytical	analytical	ADJ
ejpam-5050	638	7	study	study	NOUN
ejpam-5050	638	8	of	of	ADP
ejpam-5050	638	9	linear	linear	PROPN
ejpam-5050	638	10	and	and	CCONJ
ejpam-5050	638	11	nonlinear	nonlinear	ADJ
ejpam-5050	638	12	time	time	NOUN
ejpam-5050	638	13	-	-	PUNCT
ejpam-5050	638	14	fractional	fractional	ADJ
ejpam-5050	638	15	partial	partial	ADJ
ejpam-5050	638	16	differential	differential	NOUN
ejpam-5050	638	17	equations	equation	NOUN
ejpam-5050	638	18	with	with	ADP
ejpam-5050	638	19	variable	variable	ADJ
ejpam-5050	638	20	coefficients	coefficient	NOUN
ejpam-5050	638	21	.	.	PUNCT
ejpam-5050	639	1	journal	journal	PROPN
ejpam-5050	639	2	of	of	ADP
ejpam-5050	639	3	samara	samara	PROPN
ejpam-5050	639	4	state	state	PROPN
ejpam-5050	639	5	technical	technical	PROPN
ejpam-5050	639	6	university	university	PROPN
ejpam-5050	639	7	,	,	PUNCT
ejpam-5050	639	8	ser	ser	PROPN
ejpam-5050	639	9	.	.	PROPN
ejpam-5050	640	1	physical	physical	ADJ
ejpam-5050	640	2	and	and	CCONJ
ejpam-5050	640	3	mathematical	mathematical	ADJ
ejpam-5050	640	4	sciences	science	NOUN
ejpam-5050	640	5	,	,	PUNCT
ejpam-5050	640	6	27(2):214–240	27(2):214–240	NUM
ejpam-5050	640	7	,	,	PUNCT
ejpam-5050	640	8	2023	2023	NUM
ejpam-5050	640	9	.	.	PUNCT
ejpam-5050	641	1	[	[	X
ejpam-5050	641	2	34	34	NUM
ejpam-5050	641	3	]	]	PUNCT
ejpam-5050	641	4	sultana	sultana	PROPN
ejpam-5050	641	5	mariam	mariam	PROPN
ejpam-5050	641	6	,	,	PUNCT
ejpam-5050	641	7	arshad	arshad	PROPN
ejpam-5050	641	8	uroosa	uroosa	PROPN
ejpam-5050	641	9	,	,	PUNCT
ejpam-5050	641	10	abdel	abdel	PROPN
ejpam-5050	641	11	-	-	PUNCT
ejpam-5050	641	12	aty	aty	PROPN
ejpam-5050	641	13	abdel	abdel	PROPN
ejpam-5050	641	14	-	-	PUNCT
ejpam-5050	641	15	haleem	haleem	PROPN
ejpam-5050	641	16	,	,	PUNCT
ejpam-5050	641	17	akgül	akgül	PROPN
ejpam-5050	641	18	ali	ali	PROPN
ejpam-5050	641	19	,	,	PUNCT
ejpam-5050	641	20	mahmoud	mahmoud	PROPN
ejpam-5050	641	21	mona	mona	PROPN
ejpam-5050	641	22	,	,	PUNCT
ejpam-5050	641	23	and	and	CCONJ
ejpam-5050	641	24	eleuch	eleuch	ADJ
ejpam-5050	641	25	hichem	hichem	NOUN
ejpam-5050	641	26	.	.	PUNCT
ejpam-5050	642	1	new	new	ADJ
ejpam-5050	642	2	numerical	numerical	ADJ
ejpam-5050	642	3	approach	approach	NOUN
ejpam-5050	642	4	of	of	ADP
ejpam-5050	642	5	solving	solve	VERB
ejpam-5050	642	6	highly	highly	ADV
ejpam-5050	642	7	nonlinear	nonlinear	ADJ
ejpam-5050	642	8	fractional	fractional	ADJ
ejpam-5050	642	9	partial	partial	ADJ
ejpam-5050	642	10	differential	differential	NOUN
ejpam-5050	642	11	equations	equation	NOUN
ejpam-5050	642	12	via	via	ADP
ejpam-5050	642	13	fractional	fractional	ADJ
ejpam-5050	642	14	novel	novel	ADJ
ejpam-5050	642	15	analytical	analytical	ADJ
ejpam-5050	642	16	method	method	NOUN
ejpam-5050	642	17	.	.	PUNCT
ejpam-5050	643	1	fractal	fractal	ADJ
ejpam-5050	643	2	and	and	CCONJ
ejpam-5050	643	3	fractional	fractional	ADJ
ejpam-5050	643	4	,	,	PUNCT
ejpam-5050	643	5	6(9):512	6(9):512	NUM
ejpam-5050	643	6	,	,	PUNCT
ejpam-5050	643	7	2022	2022	NUM
ejpam-5050	643	8	.	.	PUNCT
ejpam-5050	644	1	references	reference	NOUN
ejpam-5050	644	2	567	567	NUM
ejpam-5050	644	3	[	[	NOUN
ejpam-5050	644	4	35	35	NUM
ejpam-5050	644	5	]	]	PUNCT
ejpam-5050	644	6	fakhrodin	fakhrodin	NOUN
ejpam-5050	644	7	mohammadi	mohammadi	NOUN
ejpam-5050	644	8	.	.	PUNCT
ejpam-5050	645	1	numerical	numerical	ADJ
ejpam-5050	645	2	solution	solution	NOUN
ejpam-5050	645	3	of	of	ADP
ejpam-5050	645	4	bagley	bagley	NOUN
ejpam-5050	645	5	-	-	PUNCT
ejpam-5050	645	6	torvik	torvik	NOUN
ejpam-5050	645	7	equation	equation	NOUN
ejpam-5050	645	8	using	use	VERB
ejpam-5050	645	9	chebyshev	chebyshev	PROPN
ejpam-5050	645	10	wavelet	wavelet	NOUN
ejpam-5050	645	11	operational	operational	ADJ
ejpam-5050	645	12	matrix	matrix	NOUN
ejpam-5050	645	13	of	of	ADP
ejpam-5050	645	14	fractional	fractional	ADJ
ejpam-5050	645	15	derivative	derivative	NOUN
ejpam-5050	645	16	.	.	PUNCT
ejpam-5050	646	1	int	int	NOUN
ejpam-5050	646	2	.	.	PUNCT
ejpam-5050	647	1	j.	j.	PROPN
ejpam-5050	647	2	adv	adv	PROPN
ejpam-5050	647	3	.	.	PUNCT
ejpam-5050	647	4	appl	appl	PROPN
ejpam-5050	647	5	.	.	PROPN
ejpam-5050	648	1	math	math	PROPN
ejpam-5050	648	2	.	.	PUNCT
ejpam-5050	649	1	mech	mech	PROPN
ejpam-5050	649	2	,	,	PUNCT
ejpam-5050	649	3	2(1):83–91	2(1):83–91	NUM
ejpam-5050	649	4	,	,	PUNCT
ejpam-5050	649	5	2014	2014	NUM
ejpam-5050	649	6	.	.	PUNCT
ejpam-5050	650	1	[	[	X
ejpam-5050	650	2	36	36	NUM
ejpam-5050	650	3	]	]	X
ejpam-5050	650	4	justina	justina	PROPN
ejpam-5050	650	5	mulenga	mulenga	PROPN
ejpam-5050	650	6	and	and	CCONJ
ejpam-5050	650	7	patrick	patrick	PROPN
ejpam-5050	650	8	azere	azere	PROPN
ejpam-5050	650	9	phiri	phiri	PROPN
ejpam-5050	650	10	.	.	PUNCT
ejpam-5050	651	1	solution	solution	NOUN
ejpam-5050	651	2	of	of	ADP
ejpam-5050	651	3	two	two	NUM
ejpam-5050	651	4	-	-	PUNCT
ejpam-5050	651	5	point	point	NOUN
ejpam-5050	651	6	linear	linear	NOUN
ejpam-5050	651	7	and	and	CCONJ
ejpam-5050	651	8	nonlinear	nonlinear	ADJ
ejpam-5050	651	9	boundary	boundary	ADJ
ejpam-5050	651	10	value	value	NOUN
ejpam-5050	651	11	problems	problem	NOUN
ejpam-5050	651	12	with	with	ADP
ejpam-5050	651	13	neumann	neumann	PROPN
ejpam-5050	651	14	boundary	boundary	ADJ
ejpam-5050	651	15	conditions	condition	NOUN
ejpam-5050	651	16	using	use	VERB
ejpam-5050	651	17	a	a	DET
ejpam-5050	651	18	new	new	ADJ
ejpam-5050	651	19	modified	modify	VERB
ejpam-5050	651	20	adomian	adomian	NOUN
ejpam-5050	651	21	decomposition	decomposition	NOUN
ejpam-5050	651	22	method	method	NOUN
ejpam-5050	651	23	.	.	PUNCT
ejpam-5050	652	1	journal	journal	NOUN
ejpam-5050	652	2	of	of	ADP
ejpam-5050	652	3	advances	advance	NOUN
ejpam-5050	652	4	in	in	ADP
ejpam-5050	652	5	mathematics	mathematic	NOUN
ejpam-5050	652	6	and	and	CCONJ
ejpam-5050	652	7	computer	computer	NOUN
ejpam-5050	652	8	science	science	NOUN
ejpam-5050	652	9	,	,	PUNCT
ejpam-5050	652	10	35(7):49–60	35(7):49–60	NUM
ejpam-5050	652	11	,	,	PUNCT
ejpam-5050	652	12	2020	2020	NUM
ejpam-5050	652	13	.	.	PUNCT
ejpam-5050	653	1	[	[	X
ejpam-5050	653	2	37	37	NUM
ejpam-5050	653	3	]	]	PUNCT
ejpam-5050	653	4	justina	justina	PROPN
ejpam-5050	653	5	mulenga	mulenga	PROPN
ejpam-5050	653	6	and	and	CCONJ
ejpam-5050	653	7	patrick	patrick	PROPN
ejpam-5050	653	8	azere	azere	PROPN
ejpam-5050	653	9	phiri	phiri	PROPN
ejpam-5050	653	10	.	.	PUNCT
ejpam-5050	654	1	solution	solution	NOUN
ejpam-5050	654	2	of	of	ADP
ejpam-5050	654	3	two	two	NUM
ejpam-5050	654	4	-	-	PUNCT
ejpam-5050	654	5	point	point	NOUN
ejpam-5050	654	6	linear	linear	NOUN
ejpam-5050	654	7	and	and	CCONJ
ejpam-5050	654	8	nonlinear	nonlinear	ADJ
ejpam-5050	654	9	boundary	boundary	ADJ
ejpam-5050	654	10	value	value	NOUN
ejpam-5050	654	11	problems	problem	NOUN
ejpam-5050	654	12	with	with	ADP
ejpam-5050	654	13	neumann	neumann	PROPN
ejpam-5050	654	14	boundary	boundary	ADJ
ejpam-5050	654	15	conditions	condition	NOUN
ejpam-5050	654	16	using	use	VERB
ejpam-5050	654	17	a	a	DET
ejpam-5050	654	18	new	new	ADJ
ejpam-5050	654	19	modified	modify	VERB
ejpam-5050	654	20	adomian	adomian	NOUN
ejpam-5050	654	21	decomposition	decomposition	NOUN
ejpam-5050	654	22	method	method	NOUN
ejpam-5050	654	23	.	.	PUNCT
ejpam-5050	655	1	journal	journal	NOUN
ejpam-5050	655	2	of	of	ADP
ejpam-5050	655	3	advances	advance	NOUN
ejpam-5050	655	4	in	in	ADP
ejpam-5050	655	5	mathematics	mathematic	NOUN
ejpam-5050	655	6	and	and	CCONJ
ejpam-5050	655	7	computer	computer	NOUN
ejpam-5050	655	8	science	science	NOUN
ejpam-5050	655	9	,	,	PUNCT
ejpam-5050	655	10	35(7):49–60	35(7):49–60	NUM
ejpam-5050	655	11	,	,	PUNCT
ejpam-5050	655	12	2020	2020	NUM
ejpam-5050	655	13	.	.	PUNCT
ejpam-5050	656	1	[	[	X
ejpam-5050	656	2	38	38	NUM
ejpam-5050	656	3	]	]	PUNCT
ejpam-5050	656	4	ri	ri	X
ejpam-5050	656	5	nuruddeen	nuruddeen	PROPN
ejpam-5050	656	6	,	,	PUNCT
ejpam-5050	656	7	lawal	lawal	PROPN
ejpam-5050	656	8	muhammad	muhammad	PROPN
ejpam-5050	656	9	,	,	PUNCT
ejpam-5050	656	10	am	be	AUX
ejpam-5050	656	11	nass	nass	NOUN
ejpam-5050	656	12	,	,	PUNCT
ejpam-5050	656	13	and	and	CCONJ
ejpam-5050	656	14	ta	ta	ADP
ejpam-5050	656	15	sulaiman	sulaiman	PROPN
ejpam-5050	656	16	.	.	PUNCT
ejpam-5050	657	1	a	a	DET
ejpam-5050	657	2	review	review	NOUN
ejpam-5050	657	3	of	of	ADP
ejpam-5050	657	4	the	the	DET
ejpam-5050	657	5	integral	integral	ADJ
ejpam-5050	657	6	transforms	transform	NOUN
ejpam-5050	657	7	-	-	PUNCT
ejpam-5050	657	8	based	base	VERB
ejpam-5050	657	9	decomposition	decomposition	NOUN
ejpam-5050	657	10	methods	method	NOUN
ejpam-5050	657	11	and	and	CCONJ
ejpam-5050	657	12	their	their	PRON
ejpam-5050	657	13	applications	application	NOUN
ejpam-5050	657	14	in	in	ADP
ejpam-5050	657	15	solving	solve	VERB
ejpam-5050	657	16	nonlinear	nonlinear	ADJ
ejpam-5050	657	17	pdes	pde	NOUN
ejpam-5050	657	18	.	.	PUNCT
ejpam-5050	658	1	palestine	palestine	PROPN
ejpam-5050	658	2	journal	journal	PROPN
ejpam-5050	658	3	of	of	ADP
ejpam-5050	658	4	mathematics	mathematic	NOUN
ejpam-5050	658	5	,	,	PUNCT
ejpam-5050	658	6	7(1):262–280	7(1):262–280	NUM
ejpam-5050	658	7	,	,	PUNCT
ejpam-5050	658	8	2018	2018	NUM
ejpam-5050	658	9	.	.	PUNCT
ejpam-5050	659	1	[	[	X
ejpam-5050	659	2	39	39	NUM
ejpam-5050	659	3	]	]	X
ejpam-5050	659	4	kolade	kolade	ADJ
ejpam-5050	659	5	m	m	NOUN
ejpam-5050	659	6	owolabi	owolabi	NOUN
ejpam-5050	659	7	,	,	PUNCT
ejpam-5050	659	8	abdon	abdon	PROPN
ejpam-5050	659	9	atangana	atangana	PROPN
ejpam-5050	659	10	,	,	PUNCT
ejpam-5050	659	11	and	and	CCONJ
ejpam-5050	659	12	ali	ali	PROPN
ejpam-5050	659	13	akgul	akgul	PROPN
ejpam-5050	659	14	.	.	PUNCT
ejpam-5050	660	1	modelling	modelling	NOUN
ejpam-5050	660	2	and	and	CCONJ
ejpam-5050	660	3	analysis	analysis	NOUN
ejpam-5050	660	4	of	of	ADP
ejpam-5050	660	5	fractal	fractal	ADJ
ejpam-5050	660	6	-	-	PUNCT
ejpam-5050	660	7	fractional	fractional	ADJ
ejpam-5050	660	8	partial	partial	ADJ
ejpam-5050	660	9	differential	differential	NOUN
ejpam-5050	660	10	equations	equation	NOUN
ejpam-5050	660	11	:	:	PUNCT
ejpam-5050	660	12	application	application	NOUN
ejpam-5050	660	13	to	to	ADP
ejpam-5050	660	14	reaction	reaction	NOUN
ejpam-5050	660	15	-	-	PUNCT
ejpam-5050	660	16	diffusion	diffusion	NOUN
ejpam-5050	660	17	model	model	NOUN
ejpam-5050	660	18	.	.	PUNCT
ejpam-5050	661	1	alexandria	alexandria	PROPN
ejpam-5050	661	2	engineering	engineering	PROPN
ejpam-5050	661	3	journal	journal	PROPN
ejpam-5050	661	4	,	,	PUNCT
ejpam-5050	661	5	59(4):2477–2490	59(4):2477–2490	NUM
ejpam-5050	661	6	,	,	PUNCT
ejpam-5050	661	7	2020	2020	NUM
ejpam-5050	661	8	.	.	PUNCT
ejpam-5050	662	1	[	[	X
ejpam-5050	662	2	40	40	NUM
ejpam-5050	662	3	]	]	PUNCT
ejpam-5050	662	4	m	m	PROPN
ejpam-5050	662	5	razzaghi	razzaghi	PROPN
ejpam-5050	662	6	.	.	PUNCT
ejpam-5050	663	1	the	the	DET
ejpam-5050	663	2	numerical	numerical	ADJ
ejpam-5050	663	3	solution	solution	NOUN
ejpam-5050	663	4	of	of	ADP
ejpam-5050	663	5	the	the	DET
ejpam-5050	663	6	bagley	bagley	NOUN
ejpam-5050	663	7	–	–	PUNCT
ejpam-5050	663	8	torvik	torvik	PROPN
ejpam-5050	663	9	equation	equation	NOUN
ejpam-5050	663	10	with	with	ADP
ejpam-5050	663	11	fractional	fractional	ADJ
ejpam-5050	663	12	taylor	taylor	PROPN
ejpam-5050	663	13	method	method	NOUN
ejpam-5050	663	14	.	.	PUNCT
ejpam-5050	664	1	journal	journal	NOUN
ejpam-5050	664	2	of	of	ADP
ejpam-5050	664	3	computational	computational	ADJ
ejpam-5050	664	4	and	and	CCONJ
ejpam-5050	664	5	nonlinear	nonlinear	ADJ
ejpam-5050	664	6	dynamics	dynamic	NOUN
ejpam-5050	664	7	,	,	PUNCT
ejpam-5050	664	8	11:051010–1	11:051010–1	NUM
ejpam-5050	664	9	,	,	PUNCT
ejpam-5050	664	10	2016	2016	NUM
ejpam-5050	664	11	.	.	PUNCT
ejpam-5050	665	1	[	[	X
ejpam-5050	665	2	41	41	NUM
ejpam-5050	665	3	]	]	X
ejpam-5050	665	4	miller	miller	PROPN
ejpam-5050	665	5	kenneth	kenneth	PROPN
ejpam-5050	665	6	s	s	PROPN
ejpam-5050	665	7	and	and	CCONJ
ejpam-5050	665	8	ross	ross	PROPN
ejpam-5050	665	9	bertram	bertram	PROPN
ejpam-5050	665	10	.	.	PUNCT
ejpam-5050	666	1	an	an	DET
ejpam-5050	666	2	introduction	introduction	NOUN
ejpam-5050	666	3	to	to	ADP
ejpam-5050	666	4	the	the	DET
ejpam-5050	666	5	fractional	fractional	ADJ
ejpam-5050	666	6	calculus	calculus	NOUN
ejpam-5050	666	7	and	and	CCONJ
ejpam-5050	666	8	fractional	fractional	ADJ
ejpam-5050	666	9	differential	differential	ADJ
ejpam-5050	666	10	equations	equation	NOUN
ejpam-5050	666	11	.	.	PUNCT
ejpam-5050	667	1	(	(	PUNCT
ejpam-5050	667	2	no	no	DET
ejpam-5050	667	3	title	title	NOUN
ejpam-5050	667	4	)	)	PUNCT
ejpam-5050	667	5	,	,	PUNCT
ejpam-5050	667	6	1993	1993	NUM
ejpam-5050	667	7	.	.	PUNCT
ejpam-5050	668	1	[	[	X
ejpam-5050	668	2	42	42	NUM
ejpam-5050	668	3	]	]	X
ejpam-5050	668	4	jeerawan	jeerawan	PROPN
ejpam-5050	668	5	saelao	saelao	PROPN
ejpam-5050	668	6	and	and	CCONJ
ejpam-5050	668	7	natsuda	natsuda	PROPN
ejpam-5050	668	8	yokchoo	yokchoo	PROPN
ejpam-5050	668	9	.	.	PUNCT
ejpam-5050	669	1	the	the	DET
ejpam-5050	669	2	solution	solution	NOUN
ejpam-5050	669	3	of	of	ADP
ejpam-5050	669	4	klein	klein	PROPN
ejpam-5050	669	5	–	–	PUNCT
ejpam-5050	669	6	gordon	gordon	PROPN
ejpam-5050	669	7	equation	equation	NOUN
ejpam-5050	669	8	by	by	ADP
ejpam-5050	669	9	using	use	VERB
ejpam-5050	669	10	modified	modify	VERB
ejpam-5050	669	11	adomian	adomian	NOUN
ejpam-5050	669	12	decomposition	decomposition	NOUN
ejpam-5050	669	13	method	method	NOUN
ejpam-5050	669	14	.	.	PUNCT
ejpam-5050	670	1	mathematics	mathematic	NOUN
ejpam-5050	670	2	and	and	CCONJ
ejpam-5050	670	3	computers	computer	NOUN
ejpam-5050	670	4	in	in	ADP
ejpam-5050	670	5	simulation	simulation	NOUN
ejpam-5050	670	6	,	,	PUNCT
ejpam-5050	670	7	171:94–102	171:94–102	NUM
ejpam-5050	670	8	,	,	PUNCT
ejpam-5050	670	9	2020	2020	NUM
ejpam-5050	670	10	.	.	PUNCT
ejpam-5050	671	1	[	[	X
ejpam-5050	671	2	43	43	NUM
ejpam-5050	671	3	]	]	X
ejpam-5050	671	4	mehmet	mehmet	PROPN
ejpam-5050	671	5	giyas	giyas	PROPN
ejpam-5050	671	6	sakar	sakar	PROPN
ejpam-5050	671	7	,	,	PUNCT
ejpam-5050	671	8	onur	onur	PROPN
ejpam-5050	671	9	saldır	saldır	NOUN
ejpam-5050	671	10	,	,	PUNCT
ejpam-5050	671	11	and	and	CCONJ
ejpam-5050	671	12	ali	ali	PROPN
ejpam-5050	671	13	akgül	akgül	PROPN
ejpam-5050	671	14	.	.	PUNCT
ejpam-5050	672	1	a	a	DET
ejpam-5050	672	2	novel	novel	ADJ
ejpam-5050	672	3	technique	technique	NOUN
ejpam-5050	672	4	for	for	ADP
ejpam-5050	672	5	fractional	fractional	ADJ
ejpam-5050	672	6	bagley	bagley	NOUN
ejpam-5050	672	7	–	–	PUNCT
ejpam-5050	672	8	torvik	torvik	NOUN
ejpam-5050	672	9	equation	equation	NOUN
ejpam-5050	672	10	.	.	PUNCT
ejpam-5050	673	1	proceedings	proceeding	NOUN
ejpam-5050	673	2	of	of	ADP
ejpam-5050	673	3	the	the	DET
ejpam-5050	673	4	national	national	PROPN
ejpam-5050	673	5	academy	academy	PROPN
ejpam-5050	673	6	of	of	ADP
ejpam-5050	673	7	sciences	sciences	PROPN
ejpam-5050	673	8	,	,	PUNCT
ejpam-5050	673	9	india	india	PROPN
ejpam-5050	673	10	section	section	PROPN
ejpam-5050	673	11	a	a	DET
ejpam-5050	673	12	:	:	PUNCT
ejpam-5050	673	13	physical	physical	ADJ
ejpam-5050	673	14	sciences	science	NOUN
ejpam-5050	673	15	,	,	PUNCT
ejpam-5050	673	16	89:539–545	89:539–545	PROPN
ejpam-5050	673	17	,	,	PUNCT
ejpam-5050	673	18	2019	2019	NUM
ejpam-5050	673	19	.	.	PUNCT
ejpam-5050	674	1	[	[	X
ejpam-5050	674	2	44	44	NUM
ejpam-5050	674	3	]	]	PUNCT
ejpam-5050	674	4	vijay	vijay	NOUN
ejpam-5050	674	5	saw	see	VERB
ejpam-5050	674	6	and	and	CCONJ
ejpam-5050	674	7	sushil	sushil	PROPN
ejpam-5050	674	8	kumar	kumar	PROPN
ejpam-5050	674	9	.	.	PROPN
ejpam-5050	675	1	numerical	numerical	PROPN
ejpam-5050	675	2	scheme	scheme	NOUN
ejpam-5050	675	3	for	for	ADP
ejpam-5050	675	4	solving	solve	VERB
ejpam-5050	675	5	two	two	NUM
ejpam-5050	675	6	point	point	NOUN
ejpam-5050	675	7	fractional	fractional	ADJ
ejpam-5050	675	8	bagley	bagley	NOUN
ejpam-5050	675	9	-	-	PUNCT
ejpam-5050	675	10	torvik	torvik	NOUN
ejpam-5050	675	11	equation	equation	NOUN
ejpam-5050	675	12	using	use	VERB
ejpam-5050	675	13	chebyshev	chebyshev	NOUN
ejpam-5050	675	14	collocation	collocation	NOUN
ejpam-5050	675	15	method	method	NOUN
ejpam-5050	675	16	.	.	PUNCT
ejpam-5050	676	1	wseas	wseas	PROPN
ejpam-5050	676	2	trans	trans	PROPN
ejpam-5050	676	3	.	.	PUNCT
ejpam-5050	677	1	syst	syst	PROPN
ejpam-5050	677	2	,	,	PUNCT
ejpam-5050	677	3	17:166–177	17:166–177	NUM
ejpam-5050	677	4	,	,	PUNCT
ejpam-5050	677	5	2018	2018	NUM
ejpam-5050	677	6	.	.	PUNCT
ejpam-5050	678	1	[	[	X
ejpam-5050	678	2	45	45	NUM
ejpam-5050	678	3	]	]	X
ejpam-5050	678	4	kamal	kamal	PROPN
ejpam-5050	678	5	shah	shah	PROPN
ejpam-5050	678	6	,	,	PUNCT
ejpam-5050	678	7	amjad	amjad	PROPN
ejpam-5050	678	8	ali	ali	PROPN
ejpam-5050	678	9	,	,	PUNCT
ejpam-5050	678	10	and	and	CCONJ
ejpam-5050	678	11	rahmat	rahmat	PROPN
ejpam-5050	678	12	ali	ali	PROPN
ejpam-5050	678	13	khan	khan	PROPN
ejpam-5050	678	14	.	.	PUNCT
ejpam-5050	679	1	numerical	numerical	ADJ
ejpam-5050	679	2	solutions	solution	NOUN
ejpam-5050	679	3	of	of	ADP
ejpam-5050	679	4	fractional	fractional	ADJ
ejpam-5050	679	5	order	order	NOUN
ejpam-5050	679	6	system	system	NOUN
ejpam-5050	679	7	of	of	ADP
ejpam-5050	679	8	bagley	bagley	NOUN
ejpam-5050	679	9	-	-	PUNCT
ejpam-5050	679	10	torvik	torvik	NOUN
ejpam-5050	679	11	equation	equation	NOUN
ejpam-5050	679	12	using	use	VERB
ejpam-5050	679	13	operational	operational	ADJ
ejpam-5050	679	14	matrices	matrix	NOUN
ejpam-5050	679	15	.	.	PUNCT
ejpam-5050	680	1	sindh	sindh	PROPN
ejpam-5050	680	2	univ	univ	PROPN
ejpam-5050	680	3	.	.	PUNCT
ejpam-5050	681	1	res	re	NOUN
ejpam-5050	681	2	.	.	PUNCT
ejpam-5050	682	1	j.(sci	j.(sci	PROPN
ejpam-5050	682	2	.	.	PUNCT
ejpam-5050	683	1	ser	ser	PROPN
ejpam-5050	683	2	.	.	PUNCT
ejpam-5050	683	3	)	)	PUNCT
ejpam-5050	683	4	,	,	PUNCT
ejpam-5050	683	5	47(4):757–762	47(4):757–762	NOUN
ejpam-5050	683	6	,	,	PUNCT
ejpam-5050	683	7	2015	2015	NUM
ejpam-5050	683	8	.	.	PUNCT
ejpam-5050	684	1	[	[	X
ejpam-5050	684	2	46	46	NUM
ejpam-5050	684	3	]	]	X
ejpam-5050	684	4	peter	peter	PROPN
ejpam-5050	684	5	j	j	PROPN
ejpam-5050	684	6	torvik	torvik	PROPN
ejpam-5050	684	7	and	and	CCONJ
ejpam-5050	684	8	ronald	ronald	PROPN
ejpam-5050	684	9	l	l	PROPN
ejpam-5050	684	10	bagley	bagley	PROPN
ejpam-5050	684	11	.	.	PUNCT
ejpam-5050	685	1	on	on	ADP
ejpam-5050	685	2	the	the	DET
ejpam-5050	685	3	appearance	appearance	NOUN
ejpam-5050	685	4	of	of	ADP
ejpam-5050	685	5	the	the	DET
ejpam-5050	685	6	fractional	fractional	ADJ
ejpam-5050	685	7	derivative	derivative	NOUN
ejpam-5050	685	8	in	in	ADP
ejpam-5050	685	9	the	the	DET
ejpam-5050	685	10	behavior	behavior	NOUN
ejpam-5050	685	11	of	of	ADP
ejpam-5050	685	12	real	real	ADJ
ejpam-5050	685	13	materials	material	NOUN
ejpam-5050	685	14	.	.	PUNCT
ejpam-5050	685	15	1984	1984	NUM
ejpam-5050	685	16	.	.	PUNCT
ejpam-5050	685	17	references	reference	NOUN
ejpam-5050	685	18	568	568	NUM
ejpam-5050	685	19	[	[	X
ejpam-5050	685	20	47	47	NUM
ejpam-5050	685	21	]	]	PUNCT
ejpam-5050	685	22	abdul	abdul	PROPN
ejpam-5050	685	23	-	-	PUNCT
ejpam-5050	685	24	majid	majid	PROPN
ejpam-5050	685	25	wazwaz	wazwaz	NOUN
ejpam-5050	685	26	.	.	PUNCT
ejpam-5050	686	1	a	a	DET
ejpam-5050	686	2	reliable	reliable	ADJ
ejpam-5050	686	3	modification	modification	NOUN
ejpam-5050	686	4	of	of	ADP
ejpam-5050	686	5	adomian	adomian	ADJ
ejpam-5050	686	6	decomposition	decomposition	NOUN
ejpam-5050	686	7	method	method	NOUN
ejpam-5050	686	8	.	.	PUNCT
ejpam-5050	687	1	applied	apply	VERB
ejpam-5050	687	2	mathematics	mathematic	NOUN
ejpam-5050	687	3	and	and	CCONJ
ejpam-5050	687	4	computation	computation	NOUN
ejpam-5050	687	5	,	,	PUNCT
ejpam-5050	687	6	102(1):77–86	102(1):77–86	NUM
ejpam-5050	687	7	,	,	PUNCT
ejpam-5050	687	8	1999	1999	NUM
ejpam-5050	687	9	.	.	PUNCT
ejpam-5050	688	1	[	[	X
ejpam-5050	688	2	48	48	NUM
ejpam-5050	688	3	]	]	PUNCT
ejpam-5050	688	4	abdul	abdul	PROPN
ejpam-5050	688	5	-	-	PUNCT
ejpam-5050	688	6	majid	majid	PROPN
ejpam-5050	688	7	wazwaz	wazwaz	NOUN
ejpam-5050	688	8	.	.	PUNCT
ejpam-5050	689	1	a	a	DET
ejpam-5050	689	2	reliable	reliable	ADJ
ejpam-5050	689	3	modification	modification	NOUN
ejpam-5050	689	4	of	of	ADP
ejpam-5050	689	5	adomian	adomian	ADJ
ejpam-5050	689	6	decomposition	decomposition	NOUN
ejpam-5050	689	7	method	method	NOUN
ejpam-5050	689	8	.	.	PUNCT
ejpam-5050	690	1	applied	apply	VERB
ejpam-5050	690	2	mathematics	mathematic	NOUN
ejpam-5050	690	3	and	and	CCONJ
ejpam-5050	690	4	computation	computation	NOUN
ejpam-5050	690	5	,	,	PUNCT
ejpam-5050	690	6	102(1):77–86	102(1):77–86	NUM
ejpam-5050	690	7	,	,	PUNCT
ejpam-5050	690	8	1999	1999	NUM
ejpam-5050	690	9	.	.	PUNCT
ejpam-5050	691	1	[	[	X
ejpam-5050	691	2	49	49	NUM
ejpam-5050	691	3	]	]	X
ejpam-5050	691	4	abdul	abdul	PROPN
ejpam-5050	691	5	-	-	PUNCT
ejpam-5050	691	6	majid	majid	PROPN
ejpam-5050	691	7	wazwaz	wazwaz	NOUN
ejpam-5050	691	8	and	and	CCONJ
ejpam-5050	691	9	salah	salah	PROPN
ejpam-5050	691	10	m	m	PROPN
ejpam-5050	691	11	el	el	PROPN
ejpam-5050	691	12	-	-	PUNCT
ejpam-5050	691	13	sayed	say	VERB
ejpam-5050	691	14	.	.	PUNCT
ejpam-5050	692	1	a	a	DET
ejpam-5050	692	2	new	new	ADJ
ejpam-5050	692	3	modification	modification	NOUN
ejpam-5050	692	4	of	of	ADP
ejpam-5050	692	5	the	the	DET
ejpam-5050	692	6	adomian	adomian	NOUN
ejpam-5050	692	7	decomposition	decomposition	NOUN
ejpam-5050	692	8	method	method	NOUN
ejpam-5050	692	9	for	for	ADP
ejpam-5050	692	10	linear	linear	ADJ
ejpam-5050	692	11	and	and	CCONJ
ejpam-5050	692	12	nonlinear	nonlinear	ADJ
ejpam-5050	692	13	operators	operator	NOUN
ejpam-5050	692	14	.	.	PUNCT
ejpam-5050	693	1	applied	apply	VERB
ejpam-5050	693	2	mathematics	mathematic	NOUN
ejpam-5050	693	3	and	and	CCONJ
ejpam-5050	693	4	computation	computation	NOUN
ejpam-5050	693	5	,	,	PUNCT
ejpam-5050	693	6	122(3):393–405	122(3):393–405	NUM
ejpam-5050	693	7	,	,	PUNCT
ejpam-5050	693	8	2001	2001	NUM
ejpam-5050	693	9	.	.	PUNCT
ejpam-5050	694	1	[	[	X
ejpam-5050	694	2	50	50	NUM
ejpam-5050	694	3	]	]	PUNCT
ejpam-5050	694	4	waheed	waheed	PROPN
ejpam-5050	694	5	k	k	PROPN
ejpam-5050	694	6	zahra	zahra	PROPN
ejpam-5050	694	7	and	and	CCONJ
ejpam-5050	694	8	samah	samah	PROPN
ejpam-5050	694	9	m	m	PROPN
ejpam-5050	694	10	elkholy	elkholy	ADJ
ejpam-5050	694	11	.	.	PUNCT
ejpam-5050	695	1	quadratic	quadratic	ADJ
ejpam-5050	695	2	spline	spline	NOUN
ejpam-5050	695	3	solution	solution	NOUN
ejpam-5050	695	4	for	for	ADP
ejpam-5050	695	5	boundary	boundary	ADJ
ejpam-5050	695	6	value	value	NOUN
ejpam-5050	695	7	problem	problem	NOUN
ejpam-5050	695	8	of	of	ADP
ejpam-5050	695	9	fractional	fractional	ADJ
ejpam-5050	695	10	order	order	NOUN
ejpam-5050	695	11	.	.	PUNCT
ejpam-5050	696	1	numerical	numerical	ADJ
ejpam-5050	696	2	algorithms	algorithm	NOUN
ejpam-5050	696	3	,	,	PUNCT
ejpam-5050	696	4	59:373–391	59:373–391	NUM
ejpam-5050	696	5	,	,	PUNCT
ejpam-5050	696	6	2012	2012	NUM
ejpam-5050	696	7	.	.	PUNCT
ejpam-5050	697	1	[	[	X
ejpam-5050	697	2	51	51	NUM
ejpam-5050	697	3	]	]	SYM
ejpam-5050	697	4	wk	wk	X
ejpam-5050	697	5	zahra	zahra	PROPN
ejpam-5050	697	6	and	and	CCONJ
ejpam-5050	697	7	sm	sm	PROPN
ejpam-5050	697	8	elkholy	elkholy	ADJ
ejpam-5050	697	9	.	.	PUNCT
ejpam-5050	698	1	cubic	cubic	ADJ
ejpam-5050	698	2	spline	spline	NOUN
ejpam-5050	698	3	solution	solution	NOUN
ejpam-5050	698	4	of	of	ADP
ejpam-5050	698	5	fractional	fractional	ADJ
ejpam-5050	698	6	bagley	bagley	NOUN
ejpam-5050	698	7	-	-	PUNCT
ejpam-5050	698	8	torvik	torvik	NOUN
ejpam-5050	698	9	equation	equation	NOUN
ejpam-5050	698	10	.	.	PUNCT
ejpam-5050	699	1	electronic	electronic	ADJ
ejpam-5050	699	2	journal	journal	NOUN
ejpam-5050	699	3	of	of	ADP
ejpam-5050	699	4	mathematical	mathematical	ADJ
ejpam-5050	699	5	analysis	analysis	NOUN
ejpam-5050	699	6	and	and	CCONJ
ejpam-5050	699	7	applications	application	NOUN
ejpam-5050	699	8	,	,	PUNCT
ejpam-5050	699	9	1(2):230–241	1(2):230–241	NUM
ejpam-5050	699	10	,	,	PUNCT
ejpam-5050	699	11	2013	2013	NUM
ejpam-5050	699	12	.	.	PUNCT