id	sid	tid	token	lemma	pos
cuesj-478	1	1	tx_1	tx_1	PROPN
cuesj-478	1	2	~	~	X
cuesj-478	1	3	abs	ab	NOUN
cuesj-478	1	4	:	:	PUNCT
cuesj-478	1	5	at	at	ADP
cuesj-478	1	6	/	/	SYM
cuesj-478	1	7	add	add	VERB
cuesj-478	1	8	:	:	PUNCT
cuesj-478	1	9	tx_2	tx_2	PROPN
cuesj-478	1	10	~	~	NOUN
cuesj-478	1	11	abs	ab	NOUN
cuesj-478	1	12	:	:	PUNCT
cuesj-478	1	13	at	at	ADP
cuesj-478	1	14	64	64	NUM
cuesj-478	1	15	http://journals.cihanuniversity.edu.iq/index.php/cuesj	http://journals.cihanuniversity.edu.iq/index.php/cuesj	ADJ
cuesj-478	1	16	cuesj	cuesj	ADJ
cuesj-478	1	17	2021	2021	NUM
cuesj-478	1	18	,	,	PUNCT
cuesj-478	1	19	5	5	NUM
cuesj-478	1	20	(	(	PUNCT
cuesj-478	1	21	2	2	NUM
cuesj-478	1	22	):	):	PUNCT
cuesj-478	1	23	64	64	NUM
cuesj-478	1	24	-	-	SYM
cuesj-478	1	25	68	68	NUM
cuesj-478	1	26	research	research	NOUN
cuesj-478	1	27	article	article	NOUN
cuesj-478	1	28	solution	solution	NOUN
cuesj-478	1	29	of	of	ADP
cuesj-478	1	30	multi	multi	ADJ
cuesj-478	1	31	-	-	ADJ
cuesj-478	1	32	order	order	ADJ
cuesj-478	1	33	fractional	fractional	ADJ
cuesj-478	1	34	differential	differential	NOUN
cuesj-478	1	35	equation	equation	NOUN
cuesj-478	1	36	based	base	VERB
cuesj-478	1	37	on	on	ADP
cuesj-478	1	38	conformable	conformable	ADJ
cuesj-478	1	39	derivative	derivative	NOUN
cuesj-478	1	40	by	by	ADP
cuesj-478	1	41	shifted	shift	VERB
cuesj-478	1	42	legendre	legendre	PROPN
cuesj-478	1	43	polynomial	polynomial	PROPN
cuesj-478	1	44	salim	salim	PROPN
cuesj-478	1	45	s.	s.	PROPN
cuesj-478	1	46	mahmood1	mahmood1	PROPN
cuesj-478	1	47	,	,	PUNCT
cuesj-478	1	48	kamaran	kamaran	PROPN
cuesj-478	1	49	j.	j.	PROPN
cuesj-478	1	50	hamad1	hamad1	PROPN
cuesj-478	1	51	,	,	PUNCT
cuesj-478	1	52	milad	milad	NOUN
cuesj-478	1	53	a.	a.	PROPN
cuesj-478	1	54	kareem1	kareem1	PROPN
cuesj-478	1	55	,	,	PUNCT
cuesj-478	1	56	asrin	asrin	PROPN
cuesj-478	1	57	f.	f.	PROPN
cuesj-478	1	58	shekh2	shekh2	PROPN
cuesj-478	2	1	1department	1department	NUM
cuesj-478	2	2	of	of	ADP
cuesj-478	2	3	mathematic	mathematic	ADJ
cuesj-478	2	4	,	,	PUNCT
cuesj-478	2	5	faculty	faculty	NOUN
cuesj-478	2	6	of	of	ADP
cuesj-478	2	7	science	science	NOUN
cuesj-478	2	8	,	,	PUNCT
cuesj-478	2	9	soran	soran	PROPN
cuesj-478	2	10	university	university	PROPN
cuesj-478	2	11	,	,	PUNCT
cuesj-478	2	12	kurdistan	kurdistan	PROPN
cuesj-478	2	13	region	region	NOUN
cuesj-478	2	14	,	,	PUNCT
cuesj-478	2	15	iraq	iraq	PROPN
cuesj-478	2	16	,	,	PUNCT
cuesj-478	2	17	2department	2department	NUM
cuesj-478	2	18	information	information	NOUN
cuesj-478	2	19	technology	technology	NOUN
cuesj-478	2	20	,	,	PUNCT
cuesj-478	2	21	erbil	erbil	PROPN
cuesj-478	2	22	polytechnic	polytechnic	PROPN
cuesj-478	2	23	university	university	PROPN
cuesj-478	2	24	,	,	PUNCT
cuesj-478	2	25	kurdistan	kurdistan	PROPN
cuesj-478	2	26	region	region	NOUN
cuesj-478	2	27	,	,	PUNCT
cuesj-478	2	28	iraq	iraq	PROPN
cuesj-478	2	29	abstract	abstract	NOUN
cuesj-478	2	30	the	the	DET
cuesj-478	2	31	aim	aim	NOUN
cuesj-478	2	32	of	of	ADP
cuesj-478	2	33	this	this	DET
cuesj-478	2	34	article	article	NOUN
cuesj-478	2	35	is	be	AUX
cuesj-478	2	36	the	the	DET
cuesj-478	2	37	way	way	NOUN
cuesj-478	2	38	for	for	ADP
cuesj-478	2	39	finding	find	VERB
cuesj-478	2	40	approximation	approximation	NOUN
cuesj-478	2	41	solution	solution	NOUN
cuesj-478	2	42	of	of	ADP
cuesj-478	2	43	multi	multi	ADJ
cuesj-478	2	44	-	-	ADJ
cuesj-478	2	45	order	order	ADJ
cuesj-478	2	46	fractional	fractional	ADJ
cuesj-478	2	47	differential	differential	ADJ
cuesj-478	2	48	equation	equation	NOUN
cuesj-478	2	49	with	with	ADP
cuesj-478	2	50	conformable	conformable	ADJ
cuesj-478	2	51	sense	sense	NOUN
cuesj-478	2	52	with	with	ADP
cuesj-478	2	53	use	use	NOUN
cuesj-478	2	54	approximated	approximate	VERB
cuesj-478	2	55	function	function	NOUN
cuesj-478	2	56	by	by	ADP
cuesj-478	2	57	shifted	shift	VERB
cuesj-478	2	58	legendre	legendre	PROPN
cuesj-478	2	59	polynomial	polynomial	PROPN
cuesj-478	2	60	,	,	PUNCT
cuesj-478	2	61	the	the	DET
cuesj-478	2	62	method	method	NOUN
cuesj-478	2	63	is	be	AUX
cuesj-478	2	64	easy	easy	ADJ
cuesj-478	2	65	and	and	CCONJ
cuesj-478	2	66	powerful	powerful	ADJ
cuesj-478	2	67	for	for	SCONJ
cuesj-478	2	68	get	get	VERB
cuesj-478	2	69	our	our	PRON
cuesj-478	2	70	results	result	NOUN
cuesj-478	2	71	of	of	ADP
cuesj-478	2	72	linear	linear	ADJ
cuesj-478	2	73	and	and	CCONJ
cuesj-478	2	74	non	non	ADJ
cuesj-478	2	75	-	-	ADJ
cuesj-478	2	76	linear	linear	ADJ
cuesj-478	2	77	equation	equation	NOUN
cuesj-478	2	78	,	,	PUNCT
cuesj-478	2	79	the	the	DET
cuesj-478	2	80	background	background	NOUN
cuesj-478	2	81	idea	idea	NOUN
cuesj-478	2	82	behind	behind	ADP
cuesj-478	2	83	this	this	DET
cuesj-478	2	84	method	method	NOUN
cuesj-478	2	85	is	be	AUX
cuesj-478	2	86	finding	find	VERB
cuesj-478	2	87	system	system	NOUN
cuesj-478	2	88	of	of	ADP
cuesj-478	2	89	algebra	algebra	NOUN
cuesj-478	2	90	after	after	SCONJ
cuesj-478	2	91	achieve	achieve	VERB
cuesj-478	2	92	messing	mess	VERB
cuesj-478	2	93	variable	variable	NOUN
cuesj-478	2	94	is	be	AUX
cuesj-478	2	95	that	that	PRON
cuesj-478	2	96	mean	mean	NOUN
cuesj-478	2	97	obtains	obtain	VERB
cuesj-478	2	98	approximate	approximate	ADJ
cuesj-478	2	99	solution	solution	NOUN
cuesj-478	2	100	,	,	PUNCT
cuesj-478	2	101	a	a	DET
cuesj-478	2	102	few	few	ADJ
cuesj-478	2	103	example	example	NOUN
cuesj-478	2	104	are	be	AUX
cuesj-478	2	105	illustrate	illustrate	ADJ
cuesj-478	2	106	for	for	SCONJ
cuesj-478	2	107	presented	present	VERB
cuesj-478	2	108	how	how	SCONJ
cuesj-478	2	109	much	much	ADJ
cuesj-478	2	110	our	our	PRON
cuesj-478	2	111	method	method	NOUN
cuesj-478	2	112	is	be	AUX
cuesj-478	2	113	capable	capable	ADJ
cuesj-478	2	114	.	.	PUNCT
cuesj-478	3	1	keywords	keyword	NOUN
cuesj-478	3	2	:	:	PUNCT
cuesj-478	3	3	conformable	conformable	ADJ
cuesj-478	3	4	derivative	derivative	ADJ
cuesj-478	3	5	,	,	PUNCT
cuesj-478	3	6	fractional	fractional	ADJ
cuesj-478	3	7	derivative	derivative	NOUN
cuesj-478	3	8	,	,	PUNCT
cuesj-478	3	9	shifted	shift	VERB
cuesj-478	3	10	legendre	legendre	PROPN
cuesj-478	3	11	polynomial	polynomial	ADJ
cuesj-478	3	12	,	,	PUNCT
cuesj-478	3	13	fractional	fractional	ADJ
cuesj-478	3	14	deferential	deferential	ADJ
cuesj-478	3	15	equation	equation	NOUN
cuesj-478	3	16	,	,	PUNCT
cuesj-478	3	17	python	python	NOUN
cuesj-478	3	18	program	program	NOUN
cuesj-478	3	19	introduction	introduction	NOUN
cuesj-478	3	20	there	there	PRON
cuesj-478	3	21	are	be	VERB
cuesj-478	3	22	numerous	numerous	ADJ
cuesj-478	3	23	phenomena	phenomenon	NOUN
cuesj-478	3	24	in	in	ADP
cuesj-478	3	25	various	various	ADJ
cuesj-478	3	26	disciplines	discipline	NOUN
cuesj-478	3	27	of	of	ADP
cuesj-478	3	28	research	research	NOUN
cuesj-478	3	29	can	can	AUX
cuesj-478	3	30	work	work	VERB
cuesj-478	3	31	quite	quite	ADV
cuesj-478	3	32	well	well	ADV
cuesj-478	3	33	represented	represent	VERB
cuesj-478	3	34	by	by	ADP
cuesj-478	3	35	models	model	NOUN
cuesj-478	3	36	using	use	VERB
cuesj-478	3	37	fractional	fractional	ADJ
cuesj-478	3	38	calculus	calculus	NOUN
cuesj-478	3	39	mathematic	mathematic	ADJ
cuesj-478	3	40	techniques	technique	NOUN
cuesj-478	3	41	.	.	PUNCT
cuesj-478	4	1	in	in	ADP
cuesj-478	4	2	many	many	ADJ
cuesj-478	4	3	circumstances	circumstance	NOUN
cuesj-478	4	4	,	,	PUNCT
cuesj-478	4	5	there	there	PRON
cuesj-478	4	6	are	be	VERB
cuesj-478	4	7	no	no	DET
cuesj-478	4	8	analytic	analytic	ADJ
cuesj-478	4	9	or	or	CCONJ
cuesj-478	4	10	precise	precise	ADJ
cuesj-478	4	11	solutions	solution	NOUN
cuesj-478	4	12	to	to	ADP
cuesj-478	4	13	fractional	fractional	ADJ
cuesj-478	4	14	differential	differential	ADJ
cuesj-478	4	15	equations	equation	NOUN
cuesj-478	4	16	.	.	PUNCT
cuesj-478	5	1	as	as	ADP
cuesj-478	5	2	a	a	DET
cuesj-478	5	3	result	result	NOUN
cuesj-478	5	4	,	,	PUNCT
cuesj-478	5	5	novel	novel	ADJ
cuesj-478	5	6	approaches	approach	NOUN
cuesj-478	5	7	for	for	ADP
cuesj-478	5	8	deriving	derive	VERB
cuesj-478	5	9	analytical	analytical	ADJ
cuesj-478	5	10	and	and	CCONJ
cuesj-478	5	11	approximation	approximation	NOUN
cuesj-478	5	12	fractional	fractional	ADJ
cuesj-478	5	13	differential	differential	NOUN
cuesj-478	5	14	equation	equation	NOUN
cuesj-478	5	15	solutions	solution	NOUN
cuesj-478	5	16	have	have	AUX
cuesj-478	5	17	been	be	AUX
cuesj-478	5	18	devised.[1,2	devised.[1,2	ADJ
cuesj-478	5	19	]	]	X
cuesj-478	5	20	little	little	ADJ
cuesj-478	5	21	number	number	NOUN
cuesj-478	5	22	techniques	technique	NOUN
cuesj-478	5	23	and	and	CCONJ
cuesj-478	5	24	methods	method	NOUN
cuesj-478	5	25	have	have	AUX
cuesj-478	5	26	gotten	get	VERB
cuesj-478	5	27	a	a	DET
cuesj-478	5	28	lot	lot	NOUN
cuesj-478	5	29	of	of	ADP
cuesj-478	5	30	attention	attention	NOUN
cuesj-478	5	31	in	in	ADP
cuesj-478	5	32	recent	recent	ADJ
cuesj-478	5	33	years	year	NOUN
cuesj-478	5	34	and	and	CCONJ
cuesj-478	5	35	have	have	AUX
cuesj-478	5	36	proven	prove	VERB
cuesj-478	5	37	to	to	PART
cuesj-478	5	38	be	be	AUX
cuesj-478	5	39	a	a	DET
cuesj-478	5	40	useful	useful	ADJ
cuesj-478	5	41	tool	tool	NOUN
cuesj-478	5	42	for	for	ADP
cuesj-478	5	43	fractional	fractional	ADJ
cuesj-478	5	44	calculus	calculus	NOUN
cuesj-478	5	45	.	.	PUNCT
cuesj-478	6	1	according	accord	VERB
cuesj-478	6	2	to	to	ADP
cuesj-478	6	3	the	the	DET
cuesj-478	6	4	studies	study	NOUN
cuesj-478	6	5	,	,	PUNCT
cuesj-478	6	6	the	the	DET
cuesj-478	6	7	caputo	caputo	PROPN
cuesj-478	6	8	fractional	fractional	PROPN
cuesj-478	6	9	derivative	derivative	NOUN
cuesj-478	6	10	is	be	AUX
cuesj-478	6	11	commonly	commonly	ADV
cuesj-478	6	12	incorporated	incorporate	VERB
cuesj-478	6	13	in	in	ADP
cuesj-478	6	14	fractional	fractional	ADJ
cuesj-478	6	15	calculus	calculus	NOUN
cuesj-478	6	16	computed	compute	VERB
cuesj-478	6	17	using	use	VERB
cuesj-478	6	18	spectral	spectral	ADJ
cuesj-478	6	19	methods	method	NOUN
cuesj-478	6	20	.	.	PUNCT
cuesj-478	7	1	to	to	PART
cuesj-478	7	2	compute	compute	VERB
cuesj-478	7	3	fractional	fractional	ADJ
cuesj-478	7	4	differential	differential	NOUN
cuesj-478	7	5	equations	equation	NOUN
cuesj-478	7	6	with	with	ADP
cuesj-478	7	7	caputo	caputo	PROPN
cuesj-478	7	8	derivatives	derivative	NOUN
cuesj-478	7	9	,	,	PUNCT
cuesj-478	7	10	legendre	legendre	PROPN
cuesj-478	7	11	polynomial	polynomial	PROPN
cuesj-478	7	12	has	have	AUX
cuesj-478	7	13	been	be	AUX
cuesj-478	7	14	employed.[3	employed.[3	NUM
cuesj-478	7	15	]	]	PUNCT
cuesj-478	7	16	in	in	ADP
cuesj-478	7	17	addition	addition	NOUN
cuesj-478	7	18	,	,	PUNCT
cuesj-478	7	19	chebyshev	chebyshev	PROPN
cuesj-478	7	20	wavelet	wavelet	NOUN
cuesj-478	7	21	is	be	AUX
cuesj-478	7	22	used	use	VERB
cuesj-478	7	23	for	for	ADP
cuesj-478	7	24	solving	solve	VERB
cuesj-478	7	25	nonlinear	nonlinear	ADJ
cuesj-478	7	26	fractional	fractional	ADJ
cuesj-478	7	27	differential	differential	NOUN
cuesj-478	7	28	equation,[4,5	equation,[4,5	PROPN
cuesj-478	7	29	]	]	PUNCT
cuesj-478	7	30	operation	operation	NOUN
cuesj-478	7	31	matrix	matrix	NOUN
cuesj-478	7	32	is	be	AUX
cuesj-478	7	33	used	use	VERB
cuesj-478	7	34	for	for	ADP
cuesj-478	7	35	solving	solve	VERB
cuesj-478	7	36	fractional	fractional	ADJ
cuesj-478	7	37	multi	multi	ADJ
cuesj-478	7	38	-	-	ADJ
cuesj-478	7	39	order	order	ADJ
cuesj-478	7	40	differential	differential	NOUN
cuesj-478	7	41	equation,[3	equation,[3	NUM
cuesj-478	7	42	]	]	PUNCT
cuesj-478	7	43	and	and	CCONJ
cuesj-478	7	44	spectral	spectral	ADJ
cuesj-478	7	45	collocation	collocation	NOUN
cuesj-478	7	46	method	method	NOUN
cuesj-478	7	47	is	be	AUX
cuesj-478	7	48	used	use	VERB
cuesj-478	7	49	for	for	ADP
cuesj-478	7	50	compute	compute	NOUN
cuesj-478	7	51	this	this	DET
cuesj-478	7	52	kind	kind	NOUN
cuesj-478	7	53	of	of	ADP
cuesj-478	7	54	differential	differential	ADJ
cuesj-478	7	55	equation	equation	NOUN
cuesj-478	7	56	by	by	ADP
cuesj-478	7	57	laguerre	laguerre	NOUN
cuesj-478	7	58	polynomial	polynomial	ADJ
cuesj-478	7	59	(	(	PUNCT
cuesj-478	7	60	lp).[6	lp).[6	PROPN
cuesj-478	7	61	]	]	PUNCT
cuesj-478	7	62	the	the	DET
cuesj-478	7	63	aim	aim	NOUN
cuesj-478	7	64	of	of	ADP
cuesj-478	7	65	this	this	DET
cuesj-478	7	66	article	article	NOUN
cuesj-478	7	67	is	be	AUX
cuesj-478	7	68	finding	find	VERB
cuesj-478	7	69	a	a	DET
cuesj-478	7	70	solution	solution	NOUN
cuesj-478	7	71	to	to	ADP
cuesj-478	7	72	our	our	PRON
cuesj-478	7	73	fractional	fractional	ADJ
cuesj-478	7	74	equations	equation	NOUN
cuesj-478	7	75	both	both	DET
cuesj-478	7	76	kinds	kind	NOUN
cuesj-478	7	77	linear	linear	ADJ
cuesj-478	7	78	and	and	CCONJ
cuesj-478	7	79	non	non	ADJ
cuesj-478	7	80	-	-	ADJ
cuesj-478	7	81	linear	linear	ADJ
cuesj-478	7	82	using	using	NOUN
cuesj-478	7	83	shifted	shift	VERB
cuesj-478	7	84	lp	lp	NOUN
cuesj-478	7	85	.	.	PUNCT
cuesj-478	8	1	in	in	ADP
cuesj-478	8	2	this	this	DET
cuesj-478	8	3	case	case	NOUN
cuesj-478	8	4	,	,	PUNCT
cuesj-478	8	5	if	if	SCONJ
cuesj-478	8	6	number	number	NOUN
cuesj-478	8	7	of	of	ADP
cuesj-478	8	8	n	n	NOUN
cuesj-478	8	9	is	be	AUX
cuesj-478	8	10	large	large	ADJ
cuesj-478	8	11	means	mean	VERB
cuesj-478	8	12	our	our	PRON
cuesj-478	8	13	approximate	approximate	NOUN
cuesj-478	8	14	,	,	PUNCT
cuesj-478	8	15	you	you	PRON
cuesj-478	8	16	ca	can	AUX
cuesj-478	8	17	n’t	not	PART
cuesj-478	8	18	use	use	VERB
cuesj-478	8	19	hand	hand	NOUN
cuesj-478	8	20	writing	writing	NOUN
cuesj-478	8	21	for	for	ADP
cuesj-478	8	22	find	find	NOUN
cuesj-478	8	23	solution	solution	NOUN
cuesj-478	8	24	,	,	PUNCT
cuesj-478	8	25	so	so	CCONJ
cuesj-478	8	26	we	we	PRON
cuesj-478	8	27	prefer	prefer	VERB
cuesj-478	8	28	write	write	VERB
cuesj-478	8	29	a	a	DET
cuesj-478	8	30	program	program	NOUN
cuesj-478	8	31	for	for	ADP
cuesj-478	8	32	such	such	ADJ
cuesj-478	8	33	case	case	NOUN
cuesj-478	8	34	by	by	ADP
cuesj-478	8	35	python	python	PROPN
cuesj-478	8	36	.	.	PUNCT
cuesj-478	9	1	hence	hence	ADV
cuesj-478	9	2	,	,	PUNCT
cuesj-478	9	3	in	in	ADP
cuesj-478	9	4	our	our	PRON
cuesj-478	9	5	method	method	NOUN
cuesj-478	9	6	,	,	PUNCT
cuesj-478	9	7	try	try	VERB
cuesj-478	9	8	to	to	PART
cuesj-478	9	9	find	find	VERB
cuesj-478	9	10	approximating	approximate	VERB
cuesj-478	9	11	solution	solution	NOUN
cuesj-478	9	12	of	of	ADP
cuesj-478	9	13	multi	multi	ADJ
cuesj-478	9	14	-	-	ADJ
cuesj-478	9	15	order	order	ADJ
cuesj-478	9	16	fractional	fractional	ADJ
cuesj-478	9	17	differential	differential	NOUN
cuesj-478	9	18	equation	equation	NOUN
cuesj-478	9	19	based	base	VERB
cuesj-478	9	20	on	on	ADP
cuesj-478	9	21	conformable	conformable	ADJ
cuesj-478	9	22	derivative	derivative	ADJ
cuesj-478	9	23	using	using	NOUN
cuesj-478	9	24	shifted	shift	VERB
cuesj-478	9	25	legendre	legendre	PROPN
cuesj-478	9	26	polynomial	polynomial	PROPN
cuesj-478	9	27	with	with	ADP
cuesj-478	9	28	program	program	NOUN
cuesj-478	9	29	of	of	ADP
cuesj-478	9	30	python	python	PROPN
cuesj-478	9	31	.	.	PUNCT
cuesj-478	10	1	preliminaries	preliminary	NOUN
cuesj-478	10	2	definition	definition	NOUN
cuesj-478	10	3	1	1	NUM
cuesj-478	10	4	:	:	PUNCT
cuesj-478	10	5	given	give	VERB
cuesj-478	10	6	function	function	NOUN
cuesj-478	10	7	h	h	NOUN
cuesj-478	10	8	:	:	PUNCT
cuesj-478	11	1	[	[	X
cuesj-478	11	2	0	0	NUM
cuesj-478	11	3	,	,	PUNCT
cuesj-478	11	4	∞)→r	∞)→r	PROPN
cuesj-478	11	5	then	then	ADV
cuesj-478	11	6	the	the	DET
cuesj-478	11	7	conformable	conformable	ADJ
cuesj-478	11	8	fractional	fractional	ADJ
cuesj-478	11	9	derivative	derivative	NOUN
cuesj-478	11	10	of	of	ADP
cuesj-478	11	11	h	h	NOUN
cuesj-478	11	12	of	of	ADP
cuesj-478	11	13	order	order	NOUN
cuesj-478	11	14	α	α	NOUN
cuesj-478	11	15	is	be	AUX
cuesj-478	11	16	determined	determine	VERB
cuesj-478	11	17	by	by	ADP
cuesj-478	11	18	d	d	PROPN
cuesj-478	11	19	h	h	NOUN
cuesj-478	11	20	x	x	NOUN
cuesj-478	11	21	h	h	NOUN
cuesj-478	11	22	x	x	X
cuesj-478	11	23	x	x	SYM
cuesj-478	11	24	h	h	NOUN
cuesj-478	11	25	x	x	SYM
cuesj-478	11	26	x	x	X
cuesj-478	11	27	�	�	PROPN
cuesj-478	11	28	�	�	PROPN
cuesj-478	11	29	�	�	PROPN
cuesj-478	11	30	(	(	PUNCT
cuesj-478	11	31	)	)	PUNCT
cuesj-478	11	32	lim	lim	PROPN
cuesj-478	11	33	(	(	PUNCT
cuesj-478	11	34	)	)	PUNCT
cuesj-478	11	35	(	(	PUNCT
cuesj-478	11	36	)	)	PUNCT
cuesj-478	11	37	,	,	PUNCT
cuesj-478	11	38	,	,	PUNCT
cuesj-478	11	39	(	(	PUNCT
cuesj-478	11	40	,	,	PUNCT
cuesj-478	11	41	)	)	PUNCT
cuesj-478	11	42	�	�	PROPN
cuesj-478	11	43	�	�	PROPN
cuesj-478	11	44	�	�	PROPN
cuesj-478	11	45	�	�	PROPN
cuesj-478	11	46	�	�	PROPN
cuesj-478	11	47	�	�	PROPN
cuesj-478	11	48	�	�	PROPN
cuesj-478	11	49	�	�	PROPN
cuesj-478	11	50			NOUN
cuesj-478	11	51			PROPN
cuesj-478	11	52	0	0	SYM
cuesj-478	11	53	1	1	NUM
cuesj-478	11	54	0	0	NUM
cuesj-478	11	55	0	0	NUM
cuesj-478	11	56	1	1	NUM
cuesj-478	11	57	some	some	DET
cuesj-478	11	58	time	time	NOUN
cuesj-478	11	59	,	,	PUNCT
cuesj-478	11	60	write	write	VERB
cuesj-478	11	61	ha	ha	INTJ
cuesj-478	11	62	(	(	PUNCT
cuesj-478	11	63	x	x	NOUN
cuesj-478	11	64	)	)	PUNCT
cuesj-478	11	65	for	for	ADP
cuesj-478	11	66	da	da	PROPN
cuesj-478	11	67	h	h	PROPN
cuesj-478	11	68	(	(	PUNCT
cuesj-478	11	69	x	x	X
cuesj-478	11	70	)	)	PUNCT
cuesj-478	11	71	to	to	PART
cuesj-478	11	72	indicate	indicate	VERB
cuesj-478	11	73	the	the	DET
cuesj-478	11	74	conformable	conformable	ADJ
cuesj-478	11	75	derivative	derivative	NOUN
cuesj-478	11	76	of	of	ADP
cuesj-478	11	77	h	h	NOUN
cuesj-478	11	78	of	of	ADP
cuesj-478	11	79	order	order	NOUN
cuesj-478	11	80	α	α	NOUN
cuesj-478	11	81	definition	definition	NOUN
cuesj-478	11	82	2	2	NUM
cuesj-478	11	83	:	:	PUNCT
cuesj-478	11	84	in	in	ADP
cuesj-478	11	85	this	this	DET
cuesj-478	11	86	paper	paper	NOUN
cuesj-478	11	87	,	,	PUNCT
cuesj-478	11	88	we	we	PRON
cuesj-478	11	89	need	need	VERB
cuesj-478	11	90	to	to	PART
cuesj-478	11	91	use	use	VERB
cuesj-478	11	92	legendre	legendre	NOUN
cuesj-478	11	93	polynomials	polynomial	NOUN
cuesj-478	11	94	in	in	ADP
cuesj-478	11	95	distance	distance	NOUN
cuesj-478	11	96	x=[0,1	x=[0,1	PROPN
cuesj-478	11	97	]	]	X
cuesj-478	11	98	so	so	ADV
cuesj-478	11	99	using	use	VERB
cuesj-478	11	100	change	change	NOUN
cuesj-478	11	101	variable	variable	NOUN
cuesj-478	11	102	x=2x−1	x=2x−1	ADV
cuesj-478	11	103	,	,	PUNCT
cuesj-478	11	104	these	these	DET
cuesj-478	11	105	polynomials	polynomial	NOUN
cuesj-478	11	106	can	can	AUX
cuesj-478	11	107	be	be	AUX
cuesj-478	11	108	obtained	obtain	VERB
cuesj-478	11	109	as	as	SCONJ
cuesj-478	11	110	follows	follow	VERB
cuesj-478	11	111	e	e	NOUN
cuesj-478	11	112	x	x	SYM
cuesj-478	11	113	n	n	PROPN
cuesj-478	11	114	k	k	PROPN
cuesj-478	12	1	n	n	CCONJ
cuesj-478	12	2	k	k	PROPN
cuesj-478	12	3	k	k	PROPN
cuesj-478	12	4	xn	xn	PROPN
cuesj-478	12	5	n	n	CCONJ
cuesj-478	12	6	k	k	PROPN
cuesj-478	12	7	n	n	ADV
cuesj-478	12	8	k	k	NOUN
cuesj-478	12	9	(	(	PUNCT
cuesj-478	12	10	)	)	PUNCT
cuesj-478	12	11	(	(	PUNCT
cuesj-478	12	12	)	)	PUNCT
cuesj-478	12	13	(	(	PUNCT
cuesj-478	12	14	)	)	PUNCT
cuesj-478	12	15	�	�	PROPN
cuesj-478	12	16	�	�	PROPN
cuesj-478	12	17	�	�	PROPN
cuesj-478	12	18	�	�	PROPN
cuesj-478	12	19	�	�	PROPN
cuesj-478	12	20	�	�	PROPN
cuesj-478	12	21	�	�	PROPN
cuesj-478	12	22	�	�	PROPN
cuesj-478	12	23	�	�	PROPN
cuesj-478	12	24	�	�	PROPN
cuesj-478	12	25	�	�	PROPN
cuesj-478	12	26	�	�	PROPN
cuesj-478	12	27	�	�	PROPN
cuesj-478	12	28	�	�	PROPN
cuesj-478	12	29	�	�	PROPN
cuesj-478	12	30	�	�	PROPN
cuesj-478	12	31	�	�	PROPN
cuesj-478	12	32	�	�	PROPN
cuesj-478	12	33	1	1	NUM
cuesj-478	12	34	0	0	NUM
cuesj-478	12	35	(	(	PUNCT
cuesj-478	12	36	2	2	NUM
cuesj-478	12	37	)	)	PUNCT
cuesj-478	12	38	where	where	SCONJ
cuesj-478	12	39	e0(x)=1	e0(x)=1	NOUN
cuesj-478	12	40	,	,	PUNCT
cuesj-478	12	41	e0(x)=	e0(x)=	ADJ
cuesj-478	12	42	2x−1	2x−1	NUM
cuesj-478	12	43	on	on	ADP
cuesj-478	12	44	the	the	DET
cuesj-478	12	45	interval	interval	NOUN
cuesj-478	12	46	[	[	X
cuesj-478	12	47	0,1	0,1	NUM
cuesj-478	12	48	]	]	PUNCT
cuesj-478	12	49	,	,	PUNCT
cuesj-478	12	50	the	the	DET
cuesj-478	12	51	shifted	shift	VERB
cuesj-478	12	52	lp	lp	NOUN
cuesj-478	12	53	is	be	AUX
cuesj-478	12	54	defined	define	VERB
cuesj-478	12	55	as	as	ADP
cuesj-478	12	56	e	e	NOUN
cuesj-478	12	57	x	x	PROPN
cuesj-478	12	58	n	n	PROPN
cuesj-478	13	1	k	k	NOUN
cuesj-478	13	2	x	x	PUNCT
cuesj-478	13	3	n	n	PROPN
cuesj-478	13	4	k	k	PROPN
cuesj-478	13	5	k	k	PROPN
cuesj-478	13	6	nn	nn	PROPN
cuesj-478	13	7	n	n	PROPN
cuesj-478	13	8	k	k	PROPN
cuesj-478	13	9	k	k	PROPN
cuesj-478	14	1	n	n	PROPN
cuesj-478	15	1	k	k	X
cuesj-478	16	1	(	(	PUNCT
cuesj-478	16	2	)	)	PUNCT
cuesj-478	16	3	(	(	PUNCT
cuesj-478	16	4	)	)	PUNCT
cuesj-478	16	5	(	(	PUNCT
cuesj-478	16	6	)	)	PUNCT
cuesj-478	16	7	!	!	PUNCT
cuesj-478	17	1	(	(	PUNCT
cuesj-478	17	2	)	)	PUNCT
cuesj-478	17	3	!	!	PUNCT
cuesj-478	18	1	(	(	PUNCT
cuesj-478	18	2	!	!	PUNCT
cuesj-478	18	3	)	)	PUNCT
cuesj-478	18	4	,	,	PUNCT
cuesj-478	18	5	,	,	PUNCT
cuesj-478	18	6	,	,	PUNCT
cuesj-478	18	7	,	,	PUNCT
cuesj-478	18	8	...	...	PUNCT
cuesj-478	18	9	�	�	PROPN
cuesj-478	18	10	�	�	PROPN
cuesj-478	18	11	�	�	PROPN
cuesj-478	18	12	�	�	PROPN
cuesj-478	18	13	�	�	PROPN
cuesj-478	18	14	�	�	PROPN
cuesj-478	18	15	�	�	PROPN
cuesj-478	18	16	�	�	PROPN
cuesj-478	18	17	1	1	NUM
cuesj-478	18	18	0	0	NUM
cuesj-478	18	19	1	1	NUM
cuesj-478	18	20	2	2	NUM
cuesj-478	18	21	0	0	NUM
cuesj-478	18	22	2	2	NUM
cuesj-478	18	23	(	(	PUNCT
cuesj-478	18	24	3	3	NUM
cuesj-478	18	25	)	)	PUNCT
cuesj-478	18	26	corresponding	correspond	VERB
cuesj-478	18	27	author	author	NOUN
cuesj-478	18	28	:	:	PUNCT
cuesj-478	18	29	salim	salim	PROPN
cuesj-478	18	30	s.	s.	PROPN
cuesj-478	18	31	mahmood	mahmood	PROPN
cuesj-478	18	32	,	,	PUNCT
cuesj-478	18	33	department	department	PROPN
cuesj-478	18	34	of	of	ADP
cuesj-478	18	35	mathematic	mathematic	PROPN
cuesj-478	18	36	,	,	PUNCT
cuesj-478	18	37	faculty	faculty	NOUN
cuesj-478	18	38	of	of	ADP
cuesj-478	18	39	science	science	NOUN
cuesj-478	18	40	,	,	PUNCT
cuesj-478	18	41	soran	soran	PROPN
cuesj-478	18	42	university	university	PROPN
cuesj-478	18	43	,	,	PUNCT
cuesj-478	18	44	kurdistan	kurdistan	PROPN
cuesj-478	18	45	region	region	NOUN
cuesj-478	18	46	,	,	PUNCT
cuesj-478	18	47	iraq	iraq	PROPN
cuesj-478	18	48	.	.	PUNCT
cuesj-478	19	1	e	e	X
cuesj-478	19	2	-	-	NOUN
cuesj-478	19	3	mail	mail	NOUN
cuesj-478	19	4	:	:	PUNCT
cuesj-478	19	5	salimsaeedmahmood@gmail.com	salimsaeedmahmood@gmail.com	X
cuesj-478	19	6	received	receive	VERB
cuesj-478	19	7	:	:	PUNCT
cuesj-478	19	8	august	august	PROPN
cuesj-478	19	9	25	25	NUM
cuesj-478	19	10	,	,	PUNCT
cuesj-478	19	11	2021	2021	NUM
cuesj-478	19	12	accepted	accept	VERB
cuesj-478	19	13	:	:	PUNCT
cuesj-478	19	14	november	november	PROPN
cuesj-478	19	15	11	11	NUM
cuesj-478	19	16	,	,	PUNCT
cuesj-478	19	17	2021	2021	NUM
cuesj-478	19	18	published	publish	VERB
cuesj-478	19	19	:	:	PUNCT
cuesj-478	19	20	december	december	PROPN
cuesj-478	19	21	20	20	NUM
cuesj-478	19	22	,	,	PUNCT
cuesj-478	19	23	2021	2021	NUM
cuesj-478	19	24	doi	doi	NOUN
cuesj-478	19	25	:	:	PUNCT
cuesj-478	19	26	10.24086	10.24086	NUM
cuesj-478	19	27	/	/	SYM
cuesj-478	19	28	cuesj.v5n2y2021.pp64	cuesj.v5n2y2021.pp64	NUM
cuesj-478	19	29	-	-	SYM
cuesj-478	19	30	68	68	NUM
cuesj-478	19	31	copyright	copyright	NOUN
cuesj-478	19	32	©	©	PROPN
cuesj-478	19	33	2021	2021	NUM
cuesj-478	19	34	salim	salim	PROPN
cuesj-478	19	35	s.	s.	PROPN
cuesj-478	19	36	mahmood	mahmood	PROPN
cuesj-478	19	37	,	,	PUNCT
cuesj-478	19	38	kamaran	kamaran	PROPN
cuesj-478	19	39	j.	j.	PROPN
cuesj-478	19	40	hamad	hamad	PROPN
cuesj-478	19	41	,	,	PUNCT
cuesj-478	19	42	milad	milad	NOUN
cuesj-478	19	43	a.	a.	PROPN
cuesj-478	19	44	kareem	kareem	PROPN
cuesj-478	19	45	.	.	PUNCT
cuesj-478	20	1	this	this	PRON
cuesj-478	20	2	is	be	AUX
cuesj-478	20	3	an	an	DET
cuesj-478	20	4	open	open	ADJ
cuesj-478	20	5	-	-	PUNCT
cuesj-478	20	6	access	access	NOUN
cuesj-478	20	7	article	article	NOUN
cuesj-478	20	8	distributed	distribute	VERB
cuesj-478	20	9	under	under	ADP
cuesj-478	20	10	the	the	DET
cuesj-478	20	11	creative	creative	ADJ
cuesj-478	20	12	commons	common	NOUN
cuesj-478	20	13	attribution	attribution	NOUN
cuesj-478	20	14	license	license	NOUN
cuesj-478	20	15	(	(	PUNCT
cuesj-478	20	16	cc	cc	NOUN
cuesj-478	20	17	by	by	ADP
cuesj-478	20	18	-	-	PUNCT
cuesj-478	20	19	nc	nc	VERB
cuesj-478	20	20	-	-	PROPN
cuesj-478	20	21	nd	nd	PRON
cuesj-478	20	22	4.0	4.0	NUM
cuesj-478	20	23	)	)	PUNCT
cuesj-478	20	24	.	.	PUNCT
cuesj-478	21	1	cihan	cihan	VERB
cuesj-478	21	2	university	university	NOUN
cuesj-478	21	3	-	-	PUNCT
cuesj-478	21	4	erbil	erbil	PROPN
cuesj-478	21	5	scientific	scientific	ADJ
cuesj-478	21	6	journal	journal	NOUN
cuesj-478	21	7	(	(	PUNCT
cuesj-478	21	8	cuesj	cuesj	PROPN
cuesj-478	21	9	)	)	PUNCT
cuesj-478	21	10	mahmood	mahmood	PROPN
cuesj-478	21	11	,	,	PUNCT
cuesj-478	21	12	et	et	PROPN
cuesj-478	21	13	al	al	PROPN
cuesj-478	21	14	.	.	PUNCT
cuesj-478	21	15	:	:	PUNCT
cuesj-478	22	1	multi	multi	ADJ
cuesj-478	22	2	-	-	ADJ
cuesj-478	22	3	order	order	NOUN
cuesj-478	22	4	fde	fde	NOUN
cuesj-478	22	5	based	base	VERB
cuesj-478	22	6	on	on	ADP
cuesj-478	22	7	cd	cd	PROPN
cuesj-478	22	8	by	by	ADP
cuesj-478	22	9	shifted	shift	VERB
cuesj-478	22	10	lp	lp	PROPN
cuesj-478	22	11	65	65	NUM
cuesj-478	22	12	http://journals.cihanuniversity.edu.iq/index.php/cuesj	http://journals.cihanuniversity.edu.iq/index.php/cuesj	ADJ
cuesj-478	22	13	cuesj	cuesj	ADJ
cuesj-478	22	14	2021	2021	NUM
cuesj-478	22	15	,	,	PUNCT
cuesj-478	22	16	5	5	NUM
cuesj-478	22	17	(	(	PUNCT
cuesj-478	22	18	2	2	NUM
cuesj-478	22	19	):	):	PUNCT
cuesj-478	22	20	64	64	NUM
cuesj-478	22	21	-	-	SYM
cuesj-478	22	22	68	68	NUM
cuesj-478	22	23	and	and	CCONJ
cuesj-478	22	24	explicit	explicit	ADJ
cuesj-478	22	25	way	way	NOUN
cuesj-478	22	26	for	for	ADP
cuesj-478	22	27	finding	find	VERB
cuesj-478	22	28	shifted	shift	VERB
cuesj-478	22	29	legendre	legendre	PROPN
cuesj-478	22	30	polynomial	polynomial	PROPN
cuesj-478	22	31	is	be	AUX
cuesj-478	22	32	“	"	PUNCT
cuesj-478	22	33	rodrigues	rodrigues	PROPN
cuesj-478	22	34	formula	formula	NOUN
cuesj-478	22	35	”	"	PUNCT
cuesj-478	22	36	e	e	NOUN
cuesj-478	22	37	x	x	SYM
cuesj-478	22	38	n	n	PROPN
cuesj-478	22	39	d	d	NOUN
cuesj-478	22	40	dx	dx	PROPN
cuesj-478	22	41	x	x	SYM
cuesj-478	22	42	xn	xn	PROPN
cuesj-478	22	43	n	n	CCONJ
cuesj-478	22	44	n	n	CCONJ
cuesj-478	22	45	n	n	CCONJ
cuesj-478	22	46	(	(	PUNCT
cuesj-478	22	47	)	)	PUNCT
cuesj-478	22	48	!	!	PUNCT
cuesj-478	23	1	(	(	PUNCT
cuesj-478	23	2	)	)	PUNCT
cuesj-478	23	3	�	�	PROPN
cuesj-478	23	4	�	�	PROPN
cuesj-478	23	5	1	1	NUM
cuesj-478	23	6	2	2	NUM
cuesj-478	23	7	(	(	PUNCT
cuesj-478	23	8	4	4	NUM
cuesj-478	23	9	)	)	PUNCT
cuesj-478	23	10	each	each	DET
cuesj-478	23	11	continuous	continuous	ADJ
cuesj-478	23	12	function	function	NOUN
cuesj-478	23	13	h	h	NOUN
cuesj-478	23	14	(	(	PUNCT
cuesj-478	23	15	x	x	X
cuesj-478	23	16	)	)	PUNCT
cuesj-478	23	17	in	in	ADP
cuesj-478	23	18	the	the	DET
cuesj-478	23	19	interval	interval	NOUN
cuesj-478	23	20	[	[	X
cuesj-478	23	21	0,1	0,1	NUM
cuesj-478	23	22	]	]	PUNCT
cuesj-478	23	23	can	can	AUX
cuesj-478	23	24	be	be	AUX
cuesj-478	23	25	written	write	VERB
cuesj-478	23	26	using	use	VERB
cuesj-478	23	27	the	the	DET
cuesj-478	23	28	transferred	transfer	VERB
cuesj-478	23	29	legendre	legendre	NOUN
cuesj-478	23	30	polynomials	polynomial	NOUN
cuesj-478	23	31	as	as	SCONJ
cuesj-478	23	32	follows	follow	VERB
cuesj-478	23	33	:	:	PUNCT
cuesj-478	23	34	h	h	NOUN
cuesj-478	23	35	x	x	PUNCT
cuesj-478	23	36	e	e	NOUN
cuesj-478	23	37	xai	xai	PROPN
cuesj-478	23	38	i	i	PROPN
cuesj-478	23	39	n	n	VERB
cuesj-478	23	40	i	i	PRON
cuesj-478	23	41	(	(	PUNCT
cuesj-478	23	42	)	)	PUNCT
cuesj-478	23	43	(	(	PUNCT
cuesj-478	23	44	)	)	PUNCT
cuesj-478	23	45	�	�	PROPN
cuesj-478	23	46	�	�	PROPN
cuesj-478	23	47	�	�	PROPN
cuesj-478	23	48	0	0	NUM
cuesj-478	23	49	(	(	PUNCT
cuesj-478	23	50	5	5	NUM
cuesj-478	23	51	)	)	PUNCT
cuesj-478	23	52	where	where	SCONJ
cuesj-478	23	53	,	,	PUNCT
cuesj-478	23	54	ai	ai	INTJ
cuesj-478	23	55	is	be	AUX
cuesj-478	23	56	obtained	obtain	VERB
cuesj-478	23	57	using	use	VERB
cuesj-478	23	58	the	the	DET
cuesj-478	23	59	following	follow	VERB
cuesj-478	23	60	relation	relation	NOUN
cuesj-478	23	61	:	:	PUNCT
cuesj-478	23	62	a	a	DET
cuesj-478	23	63	hi	hi	INTJ
cuesj-478	23	64	x	x	X
cuesj-478	23	65	e	e	NOUN
cuesj-478	23	66	x	x	PROPN
cuesj-478	23	67	dxi	dxi	PROPN
cuesj-478	23	68	i	i	PROPN
cuesj-478	23	69	�	�	PROPN
cuesj-478	23	70	�	�	PROPN
cuesj-478	23	71	�	�	PROPN
cuesj-478	23	72	(	(	PUNCT
cuesj-478	23	73	)	)	PUNCT
cuesj-478	23	74	(	(	PUNCT
cuesj-478	23	75	)	)	PUNCT
cuesj-478	23	76	(	(	PUNCT
cuesj-478	23	77	)	)	SYM
cuesj-478	23	78	2	2	NUM
cuesj-478	23	79	1	1	NUM
cuesj-478	23	80	0	0	NUM
cuesj-478	23	81	1	1	NUM
cuesj-478	23	82	(	(	PUNCT
cuesj-478	23	83	6	6	NUM
cuesj-478	23	84	)	)	PUNCT
cuesj-478	23	85	definition	definition	NOUN
cuesj-478	23	86	3	3	NUM
cuesj-478	23	87	:	:	PUNCT
cuesj-478	23	88	the	the	DET
cuesj-478	23	89	orthogonal	orthogonal	ADJ
cuesj-478	23	90	property	property	NOUN
cuesj-478	23	91	of	of	ADP
cuesj-478	23	92	these	these	DET
cuesj-478	23	93	polynomials	polynomial	NOUN
cuesj-478	23	94	is	be	AUX
cuesj-478	23	95	as	as	SCONJ
cuesj-478	23	96	follows	follow	VERB
cuesj-478	23	97	e	e	NOUN
cuesj-478	23	98	x	x	PUNCT
cuesj-478	23	99	e	e	NOUN
cuesj-478	23	100	x	x	X
cuesj-478	23	101	dx	dx	PROPN
cuesj-478	24	1	i	i	INTJ
cuesj-478	24	2	i	i	INTJ
cuesj-478	25	1	j	j	VERB
cuesj-478	26	1	i	i	PRON
cuesj-478	26	2	j	j	VERB
cuesj-478	27	1	i	i	PRON
cuesj-478	27	2	j	j	NOUN
cuesj-478	27	3	0	0	NUM
cuesj-478	27	4	1	1	NUM
cuesj-478	27	5	2	2	NUM
cuesj-478	27	6	2	2	NUM
cuesj-478	27	7	1	1	NUM
cuesj-478	27	8	0	0	NUM
cuesj-478	27	9	�	�	PROPN
cuesj-478	27	10	�	�	PROPN
cuesj-478	27	11	�	�	PROPN
cuesj-478	27	12	�	�	PROPN
cuesj-478	27	13	�	�	PROPN
cuesj-478	27	14	�	�	PROPN
cuesj-478	27	15	�	�	PROPN
cuesj-478	27	16	�	�	PROPN
cuesj-478	27	17	�	�	PROPN
cuesj-478	27	18	�	�	PROPN
cuesj-478	27	19	(	(	PUNCT
cuesj-478	27	20	)	)	PUNCT
cuesj-478	27	21	(	(	PUNCT
cuesj-478	27	22	)	)	PUNCT
cuesj-478	27	23	(	(	PUNCT
cuesj-478	27	24	7	7	X
cuesj-478	27	25	)	)	PUNCT
cuesj-478	27	26	the	the	DET
cuesj-478	27	27	orthogonal	orthogonal	ADJ
cuesj-478	27	28	property	property	NOUN
cuesj-478	27	29	of	of	ADP
cuesj-478	27	30	the	the	DET
cuesj-478	27	31	expansion	expansion	NOUN
cuesj-478	27	32	of	of	ADP
cuesj-478	27	33	any	any	DET
cuesj-478	27	34	function	function	NOUN
cuesj-478	27	35	makes	make	VERB
cuesj-478	27	36	it	it	PRON
cuesj-478	27	37	possible	possible	ADJ
cuesj-478	27	38	in	in	ADP
cuesj-478	27	39	terms	term	NOUN
cuesj-478	27	40	of	of	ADP
cuesj-478	27	41	legendre	legendre	PROPN
cuesj-478	27	42	polynomials	polynomial	NOUN
cuesj-478	27	43	.	.	PUNCT
cuesj-478	28	1	theorem	theorem	NOUN
cuesj-478	28	2	1	1	NUM
cuesj-478	28	3	:	:	PUNCT
cuesj-478	28	4	let	let	VERB
cuesj-478	28	5	hn	hn	PROPN
cuesj-478	28	6	(	(	PUNCT
cuesj-478	28	7	x	x	NOUN
cuesj-478	28	8	)	)	PUNCT
cuesj-478	28	9	function	function	NOUN
cuesj-478	28	10	can	can	AUX
cuesj-478	28	11	be	be	AUX
cuesj-478	28	12	approximate	approximate	VERB
cuesj-478	28	13	by	by	ADP
cuesj-478	28	14	shifted	shift	VERB
cuesj-478	28	15	lp	lp	ADV
cuesj-478	28	16	like	like	ADP
cuesj-478	28	17	that	that	DET
cuesj-478	28	18	h	h	NOUN
cuesj-478	28	19	ax	ax	NOUN
cuesj-478	29	1	e	e	X
cuesj-478	29	2	xn	xn	PROPN
cuesj-478	30	1	i	i	PRON
cuesj-478	30	2	i	i	PRON
cuesj-478	30	3	n	n	VERB
cuesj-478	30	4	i	i	PRON
cuesj-478	30	5	(	(	PUNCT
cuesj-478	30	6	)	)	PUNCT
cuesj-478	30	7	(	(	PUNCT
cuesj-478	30	8	)	)	PUNCT
cuesj-478	30	9	�	�	PROPN
cuesj-478	30	10	�	�	PROPN
cuesj-478	30	11	�	�	PROPN
cuesj-478	30	12	0	0	NUM
cuesj-478	31	1	(	(	PUNCT
cuesj-478	31	2	8)	8)	NUM
cuesj-478	31	3	after	after	ADP
cuesj-478	31	4	that	that	PRON
cuesj-478	31	5	,	,	PUNCT
cuesj-478	31	6	for	for	ADP
cuesj-478	31	7	any	any	DET
cuesj-478	31	8	derivative	derivative	NOUN
cuesj-478	31	9	we	we	PRON
cuesj-478	31	10	use[7	use[7	NOUN
cuesj-478	31	11	]	]	X
cuesj-478	32	1	d	d	X
cuesj-478	32	2	ah	ah	INTJ
cuesj-478	32	3	x	x	X
cuesj-478	32	4	w	w	NOUN
cuesj-478	32	5	xn	xn	PROPN
cuesj-478	33	1	i	i	PRON
cuesj-478	33	2	k	k	INTJ
cuesj-478	34	1	i	i	PRON
cuesj-478	34	2	i	i	PRON
cuesj-478	35	1	n	n	VERB
cuesj-478	35	2	i	i	PRON
cuesj-478	35	3	k	k	PROPN
cuesj-478	35	4	k	k	PROPN
cuesj-478	35	5	�	�	PROPN
cuesj-478	35	6	�	�	PROPN
cuesj-478	35	7	�	�	PROPN
cuesj-478	35	8	�	�	PROPN
cuesj-478	35	9	�	�	PROPN
cuesj-478	35	10	(	(	PUNCT
cuesj-478	35	11	(	(	PUNCT
cuesj-478	35	12	)	)	PUNCT
cuesj-478	35	13	)	)	PUNCT
cuesj-478	35	14	,	,	PUNCT
cuesj-478	35	15	�	�	PROPN
cuesj-478	35	16	�	�	PROPN
cuesj-478	35	17	�	�	PROPN
cuesj-478	35	18	�	�	PROPN
cuesj-478	35	19	�	�	PROPN
cuesj-478	35	20	�	�	PROPN
cuesj-478	35	21	(	(	PUNCT
cuesj-478	35	22	9	9	NUM
cuesj-478	35	23	)	)	PUNCT
cuesj-478	35	24	where	where	SCONJ
cuesj-478	35	25	,	,	PUNCT
cuesj-478	35	26	α	α	PROPN
cuesj-478	35	27	is	be	AUX
cuesj-478	35	28	define	define	VERB
cuesj-478	35	29	as	as	ADV
cuesj-478	35	30	least	least	ADJ
cuesj-478	35	31	integer	integer	NOUN
cuesj-478	35	32	greater	great	ADJ
cuesj-478	35	33	than	than	ADP
cuesj-478	35	34	or	or	CCONJ
cuesj-478	35	35	equal	equal	ADJ
cuesj-478	35	36	to	to	ADP
cuesj-478	35	37	α	α	NOUN
cuesj-478	35	38	and	and	CCONJ
cuesj-478	35	39	w	w	NOUN
cuesj-478	35	40	x	x	PROPN
cuesj-478	36	1	i	i	PRON
cuesj-478	36	2	k	k	NOUN
cuesj-478	37	1	i	i	PRON
cuesj-478	37	2	k	k	PROPN
cuesj-478	38	1	k	k	PROPN
cuesj-478	38	2	k	k	PROPN
cuesj-478	38	3	ni	ni	PROPN
cuesj-478	39	1	k	k	PROPN
cuesj-478	39	2	k	k	PROPN
cuesj-478	40	1	i	i	PRON
cuesj-478	40	2	k	k	PROPN
cuesj-478	40	3	,	,	PUNCT
cuesj-478	40	4	(	(	PUNCT
cuesj-478	40	5	)	)	PUNCT
cuesj-478	40	6	(	(	PUNCT
cuesj-478	40	7	)	)	PUNCT
cuesj-478	40	8	(	(	PUNCT
cuesj-478	40	9	)	)	PUNCT
cuesj-478	40	10	(	(	PUNCT
cuesj-478	40	11	)	)	PUNCT
cuesj-478	40	12	(	(	PUNCT
cuesj-478	40	13	)	)	PUNCT
cuesj-478	40	14	(	(	PUNCT
cuesj-478	40	15	)	)	PUNCT
cuesj-478	40	16	�	�	PROPN
cuesj-478	40	17	�	�	PROPN
cuesj-478	40	18	�	�	PROPN
cuesj-478	40	19	�	�	PROPN
cuesj-478	40	20	�	�	PROPN
cuesj-478	40	21	�	�	PROPN
cuesj-478	40	22	�	�	PROPN
cuesj-478	40	23	�	�	PROPN
cuesj-478	40	24	�	�	PROPN
cuesj-478	40	25	�	�	PROPN
cuesj-478	40	26	�	�	PROPN
cuesj-478	40	27	�	�	PROPN
cuesj-478	40	28	�	�	PROPN
cuesj-478	40	29	1	1	NUM
cuesj-478	40	30	1	1	NUM
cuesj-478	40	31	1	1	NUM
cuesj-478	40	32	1	1	NUM
cuesj-478	40	33	1	1	NUM
cuesj-478	40	34	�	�	PROPN
cuesj-478	40	35	�	�	PROPN
cuesj-478	40	36	�	�	PROPN
cuesj-478	40	37	�	�	PROPN
cuesj-478	40	38	(	(	PUNCT
cuesj-478	40	39	10	10	NUM
cuesj-478	40	40	)	)	PUNCT
cuesj-478	40	41	proof	proof	NOUN
cuesj-478	40	42	:	:	PUNCT
cuesj-478	40	43	according	accord	VERB
cuesj-478	40	44	to	to	ADP
cuesj-478	40	45	the	the	DET
cuesj-478	40	46	property	property	NOUN
cuesj-478	40	47	of	of	ADP
cuesj-478	40	48	the	the	DET
cuesj-478	40	49	conformable	conformable	ADJ
cuesj-478	40	50	derivative	derivative	NOUN
cuesj-478	40	51	and	and	CCONJ
cuesj-478	40	52	using	use	VERB
cuesj-478	40	53	the	the	DET
cuesj-478	40	54	estimated	estimate	VERB
cuesj-478	40	55	function	function	NOUN
cuesj-478	40	56	definition	definition	NOUN
cuesj-478	40	57	hn	hn	PROPN
cuesj-478	40	58	(	(	PUNCT
cuesj-478	40	59	x	x	X
cuesj-478	40	60	)	)	PUNCT
cuesj-478	40	61	,	,	PUNCT
cuesj-478	40	62	we	we	PRON
cuesj-478	40	63	get	get	VERB
cuesj-478	40	64	the	the	DET
cuesj-478	40	65	following	follow	VERB
cuesj-478	40	66	results	result	NOUN
cuesj-478	40	67	:	:	PUNCT
cuesj-478	41	1	d	d	X
cuesj-478	41	2	ah	ah	INTJ
cuesj-478	41	3	x	x	X
cuesj-478	41	4	d	d	NOUN
cuesj-478	41	5	e	e	NOUN
cuesj-478	41	6	xn	xn	PROPN
cuesj-478	42	1	i	i	PRON
cuesj-478	42	2	i	i	PRON
cuesj-478	43	1	n	n	VERB
cuesj-478	43	2	i	i	PROPN
cuesj-478	43	3	�	�	PROPN
cuesj-478	43	4	�	�	PROPN
cuesj-478	43	5	(	(	PUNCT
cuesj-478	43	6	(	(	PUNCT
cuesj-478	43	7	)	)	PUNCT
cuesj-478	43	8	)	)	PUNCT
cuesj-478	43	9	(	(	PUNCT
cuesj-478	43	10	(	(	PUNCT
cuesj-478	43	11	)	)	PUNCT
cuesj-478	43	12	)	)	PUNCT
cuesj-478	43	13	�	�	PROPN
cuesj-478	43	14	�	�	PROPN
cuesj-478	43	15	�	�	PROPN
cuesj-478	43	16	0	0	NUM
cuesj-478	43	17	(	(	PUNCT
cuesj-478	43	18	11	11	NUM
cuesj-478	43	19	)	)	PUNCT
cuesj-478	43	20	d	d	NOUN
cuesj-478	44	1	e	e	NOUN
cuesj-478	45	1	x	x	X
cuesj-478	46	1	i	i	PRON
cuesj-478	47	1	k	k	NOUN
cuesj-478	48	1	i	i	PRON
cuesj-478	48	2	k	k	PROPN
cuesj-478	48	3	k	k	PROPN
cuesj-478	48	4	k	k	PROPN
cuesj-478	49	1	n	n	CCONJ
cuesj-478	49	2	xi	xi	INTJ
cuesj-478	50	1	i	i	INTJ
cuesj-478	50	2	k	k	PROPN
cuesj-478	51	1	k	k	PROPN
cuesj-478	51	2	i	i	PRON
cuesj-478	51	3	k	k	PROPN
cuesj-478	51	4	�	�	PROPN
cuesj-478	51	5	�	�	PROPN
cuesj-478	51	6	�	�	PROPN
cuesj-478	51	7	(	(	PUNCT
cuesj-478	51	8	(	(	PUNCT
cuesj-478	51	9	)	)	PUNCT
cuesj-478	51	10	)	)	PUNCT
cuesj-478	51	11	(	(	PUNCT
cuesj-478	51	12	)	)	PUNCT
cuesj-478	51	13	(	(	PUNCT
cuesj-478	51	14	)	)	PUNCT
cuesj-478	51	15	(	(	PUNCT
cuesj-478	51	16	)	)	PUNCT
cuesj-478	51	17	(	(	PUNCT
cuesj-478	51	18	)	)	PUNCT
cuesj-478	51	19	(	(	PUNCT
cuesj-478	51	20	)	)	PUNCT
cuesj-478	51	21	�	�	PROPN
cuesj-478	51	22	�	�	PROPN
cuesj-478	51	23	�	�	PROPN
cuesj-478	51	24	�	�	PROPN
cuesj-478	51	25	�	�	PROPN
cuesj-478	51	26	�	�	PROPN
cuesj-478	51	27	�	�	PROPN
cuesj-478	51	28	�	�	PROPN
cuesj-478	51	29	�	�	PROPN
cuesj-478	51	30	�	�	PROPN
cuesj-478	51	31	�	�	PROPN
cuesj-478	51	32	�	�	PROPN
cuesj-478	51	33	�	�	PROPN
cuesj-478	51	34	1	1	NUM
cuesj-478	51	35	1	1	NUM
cuesj-478	51	36	1	1	NUM
cuesj-478	51	37	1	1	NUM
cuesj-478	51	38	1	1	NUM
cuesj-478	51	39	�	�	PROPN
cuesj-478	51	40	�	�	PROPN
cuesj-478	51	41	�	�	PROPN
cuesj-478	51	42	�	�	PROPN
cuesj-478	51	43	(	(	PUNCT
cuesj-478	51	44	12	12	NUM
cuesj-478	51	45	)	)	PUNCT
cuesj-478	51	46	by	by	ADP
cuesj-478	51	47	substitution	substitution	NOUN
cuesj-478	51	48	,	,	PUNCT
cuesj-478	51	49	we	we	PRON
cuesj-478	51	50	get	get	VERB
cuesj-478	51	51	d	d	NOUN
cuesj-478	51	52	h	h	NOUN
cuesj-478	52	1	x	x	NOUN
cuesj-478	53	1	i	i	PRON
cuesj-478	53	2	k	k	NOUN
cuesj-478	54	1	i	i	PRON
cuesj-478	54	2	k	k	PROPN
cuesj-478	55	1	k	k	PROPN
cuesj-478	55	2	k	k	PROPN
cuesj-478	55	3	n	n	CCONJ
cuesj-478	56	1	an	an	PRON
cuesj-478	57	1	i	i	PRON
cuesj-478	58	1	k	k	PROPN
cuesj-478	59	1	i	i	PRON
cuesj-478	60	1	i	i	PRON
cuesj-478	61	1	n	n	VERB
cuesj-478	62	1	i	i	PRON
cuesj-478	62	2	k	k	PROPN
cuesj-478	62	3	�	�	PROPN
cuesj-478	62	4	�	�	PROPN
cuesj-478	62	5	�	�	PROPN
cuesj-478	62	6	(	(	PUNCT
cuesj-478	62	7	(	(	PUNCT
cuesj-478	62	8	)	)	PUNCT
cuesj-478	62	9	)	)	PUNCT
cuesj-478	63	1	(	(	PUNCT
cuesj-478	63	2	)	)	PUNCT
cuesj-478	63	3	(	(	PUNCT
cuesj-478	63	4	)	)	PUNCT
cuesj-478	63	5	(	(	PUNCT
cuesj-478	63	6	)	)	PUNCT
cuesj-478	63	7	(	(	PUNCT
cuesj-478	63	8	)	)	PUNCT
cuesj-478	63	9	(	(	PUNCT
cuesj-478	63	10	�	�	PROPN
cuesj-478	63	11	�	�	PROPN
cuesj-478	63	12	�	�	PROPN
cuesj-478	63	13	�	�	PROPN
cuesj-478	63	14	�	�	PROPN
cuesj-478	63	15	�	�	PROPN
cuesj-478	63	16	�	�	PROPN
cuesj-478	63	17	�	�	PROPN
cuesj-478	63	18	�	�	PROPN
cuesj-478	63	19	�	�	PROPN
cuesj-478	63	20	�	�	PROPN
cuesj-478	63	21	�	�	PROPN
cuesj-478	63	22	�	�	PROPN
cuesj-478	63	23	�	�	PROPN
cuesj-478	63	24	1	1	NUM
cuesj-478	63	25	1	1	NUM
cuesj-478	63	26	1	1	NUM
cuesj-478	63	27	1	1	NUM
cuesj-478	63	28	1	1	NUM
cuesj-478	63	29	�	�	PROPN
cuesj-478	63	30	�	�	PROPN
cuesj-478	63	31	�	�	PROPN
cuesj-478	63	32	�	�	PROPN
cuesj-478	63	33	)	)	PUNCT
cuesj-478	63	34	)	)	PUNCT
cuesj-478	64	1	xk	xk	PROPN
cuesj-478	64	2	�	�	PROPN
cuesj-478	64	3	�	�	PROPN
cuesj-478	64	4	(	(	PUNCT
cuesj-478	64	5	13	13	NUM
cuesj-478	64	6	)	)	PUNCT
cuesj-478	64	7	numerical	numerical	ADJ
cuesj-478	64	8	scheme	scheme	NOUN
cuesj-478	64	9	in	in	ADP
cuesj-478	64	10	here	here	ADV
cuesj-478	64	11	presented	present	VERB
cuesj-478	64	12	how	how	SCONJ
cuesj-478	64	13	solve	solve	VERB
cuesj-478	64	14	the	the	DET
cuesj-478	64	15	multi	multi	ADJ
cuesj-478	64	16	-	-	ADJ
cuesj-478	64	17	order	order	ADJ
cuesj-478	64	18	fraction	fraction	NOUN
cuesj-478	64	19	differential	differential	NOUN
cuesj-478	64	20	equation	equation	NOUN
cuesj-478	64	21	by	by	ADP
cuesj-478	64	22	python	python	NOUN
cuesj-478	64	23	program	program	NOUN
cuesj-478	64	24	for	for	AUX
cuesj-478	64	25	get	get	VERB
cuesj-478	64	26	analytic	analytic	ADJ
cuesj-478	64	27	and	and	CCONJ
cuesj-478	64	28	numerical	numerical	ADJ
cuesj-478	64	29	results	result	NOUN
cuesj-478	64	30	.	.	PUNCT
cuesj-478	65	1	assume	assume	VERB
cuesj-478	65	2	the	the	DET
cuesj-478	65	3	initial	initial	ADJ
cuesj-478	65	4	condition	condition	NOUN
cuesj-478	65	5	for	for	ADP
cuesj-478	65	6	this	this	DET
cuesj-478	65	7	equation	equation	NOUN
cuesj-478	65	8	which	which	PRON
cuesj-478	65	9	is	be	AUX
cuesj-478	65	10	a	a	DET
cuesj-478	65	11	multiorder	multiorder	NOUN
cuesj-478	65	12	fractional	fractional	ADJ
cuesj-478	65	13	differential	differential	NOUN
cuesj-478	65	14	equation[8	equation[8	NOUN
cuesj-478	65	15	]	]	PUNCT
cuesj-478	65	16	d	d	X
cuesj-478	65	17	h	h	NOUN
cuesj-478	65	18	x	x	PUNCT
cuesj-478	66	1	x	x	SYM
cuesj-478	66	2	h	h	NOUN
cuesj-478	66	3	x	x	SYM
cuesj-478	66	4	b	b	X
cuesj-478	66	5	x	x	SYM
cuesj-478	66	6	h	h	NOUN
cuesj-478	66	7	x	x	X
cuesj-478	66	8	f	f	NOUN
cuesj-478	66	9	x	x	SYM
cuesj-478	66	10	xbk	xbk	PROPN
cuesj-478	66	11	k	k	PROPN
cuesj-478	66	12	r	r	NOUN
cuesj-478	66	13	r	r	NOUN
cuesj-478	66	14	�	�	PROPN
cuesj-478	66	15	(	(	PUNCT
cuesj-478	66	16	(	(	PUNCT
cuesj-478	66	17	)	)	PUNCT
cuesj-478	66	18	)	)	PUNCT
cuesj-478	66	19	(	(	PUNCT
cuesj-478	66	20	)	)	PUNCT
cuesj-478	66	21	(	(	PUNCT
cuesj-478	66	22	)	)	PUNCT
cuesj-478	66	23	(	(	PUNCT
cuesj-478	66	24	)	)	PUNCT
cuesj-478	66	25	(	(	PUNCT
cuesj-478	66	26	)	)	PUNCT
cuesj-478	66	27	(	(	PUNCT
cuesj-478	66	28	)	)	PUNCT
cuesj-478	66	29	,	,	PUNCT
cuesj-478	66	30	[	[	PUNCT
cuesj-478	66	31	,	,	PUNCT
cuesj-478	66	32	]	]	PUNCT
cuesj-478	66	33	�	�	PROPN
cuesj-478	66	34	�	�	PROPN
cuesj-478	66	35	�	�	PROPN
cuesj-478	66	36	�	�	PROPN
cuesj-478	66	37	�	�	PROPN
cuesj-478	66	38	�	�	PROPN
cuesj-478	66	39	�	�	PROPN
cuesj-478	66	40	1	1	NUM
cuesj-478	66	41	1	1	NUM
cuesj-478	66	42	0	0	NUM
cuesj-478	66	43	1	1	NUM
cuesj-478	66	44	(	(	PUNCT
cuesj-478	66	45	14	14	NUM
cuesj-478	66	46	)	)	PUNCT
cuesj-478	66	47	h	h	NOUN
cuesj-478	66	48	q	q	PROPN
cuesj-478	66	49	ii	ii	PROPN
cuesj-478	67	1	i	i	NOUN
cuesj-478	67	2	(	(	PUNCT
cuesj-478	67	3	)	)	PUNCT
cuesj-478	67	4	,	,	PUNCT
cuesj-478	67	5	,	,	PUNCT
cuesj-478	67	6	,	,	PUNCT
cuesj-478	67	7	...	...	PUNCT
cuesj-478	67	8	,	,	PUNCT
cuesj-478	67	9	0	0	NUM
cuesj-478	67	10	0	0	NUM
cuesj-478	67	11	1	1	NUM
cuesj-478	67	12	1	1	NUM
cuesj-478	67	13	�	�	PROPN
cuesj-478	67	14	�	�	PROPN
cuesj-478	67	15	�	�	PROPN
cuesj-478	67	16	�	�	PROPN
cuesj-478	67	17	(	(	PUNCT
cuesj-478	67	18	15	15	NUM
cuesj-478	67	19	)	)	PUNCT
cuesj-478	67	20	where	where	SCONJ
cuesj-478	67	21	,	,	PUNCT
cuesj-478	67	22	n−1	n−1	PROPN
cuesj-478	67	23	<	<	X
cuesj-478	67	24	α≤n	α≤n	PROPN
cuesj-478	67	25	,	,	PUNCT
cuesj-478	67	26	bk	bk	X
cuesj-478	67	27	(	(	PUNCT
cuesj-478	67	28	x	x	NOUN
cuesj-478	67	29	)	)	PUNCT
cuesj-478	67	30	,	,	PUNCT
cuesj-478	67	31	k=1,2,	k=1,2,	PROPN
cuesj-478	67	32	…	…	SYM
cuesj-478	67	33	.r	.r	NOUN
cuesj-478	67	34	and	and	CCONJ
cuesj-478	67	35	f	f	PROPN
cuesj-478	67	36	(	(	PUNCT
cuesj-478	67	37	x	x	X
cuesj-478	67	38	)	)	PUNCT
cuesj-478	67	39	are	be	AUX
cuesj-478	67	40	functions	function	NOUN
cuesj-478	67	41	that	that	PRON
cuesj-478	67	42	are	be	AUX
cuesj-478	67	43	well	well	ADV
cuesj-478	67	44	-	-	PUNCT
cuesj-478	67	45	known	know	VERB
cuesj-478	67	46	to	to	PART
cuesj-478	67	47	be	be	AUX
cuesj-478	67	48	continuous	continuous	ADJ
cuesj-478	67	49	on	on	ADP
cuesj-478	67	50	[	[	X
cuesj-478	67	51	0,1	0,1	NUM
cuesj-478	67	52	]	]	PUNCT
cuesj-478	67	53	and	and	CCONJ
cuesj-478	67	54	q	q	PROPN
cuesj-478	67	55	ii	ii	PROPN
cuesj-478	67	56	,	,	PUNCT
cuesj-478	67	57	,	,	PUNCT
cuesj-478	67	58	,	,	PUNCT
cuesj-478	67	59	...	...	PUNCT
cuesj-478	67	60	,	,	PUNCT
cuesj-478	67	61	�	�	PROPN
cuesj-478	67	62	�	�	PROPN
cuesj-478	67	63	0	0	NUM
cuesj-478	67	64	1	1	NUM
cuesj-478	67	65	1	1	NUM
cuesj-478	67	66	�	�	PROPN
cuesj-478	67	67	,	,	PUNCT
cuesj-478	67	68	constants	constant	NOUN
cuesj-478	67	69	are	be	AUX
cuesj-478	67	70	provided	provide	VERB
cuesj-478	67	71	.	.	PUNCT
cuesj-478	68	1	assume	assume	VERB
cuesj-478	68	2	the	the	DET
cuesj-478	68	3	fractional	fractional	ADJ
cuesj-478	68	4	differential	differential	ADJ
cuesj-478	68	5	equation	equation	NOUN
cuesj-478	68	6	(	(	PUNCT
cuesj-478	68	7	14	14	NUM
cuesj-478	68	8	)	)	PUNCT
cuesj-478	68	9	has	have	VERB
cuesj-478	68	10	an	an	DET
cuesj-478	68	11	answer	answer	NOUN
cuesj-478	68	12	that	that	PRON
cuesj-478	68	13	may	may	AUX
cuesj-478	68	14	be	be	AUX
cuesj-478	68	15	represented	represent	VERB
cuesj-478	68	16	as	as	ADP
cuesj-478	68	17	0	0	NUM
cuesj-478	68	18	(	(	PUNCT
cuesj-478	68	19	)	)	PUNCT
cuesj-478	68	20	(	(	PUNCT
cuesj-478	68	21	)	)	PUNCT
cuesj-478	69	1	n	n	CCONJ
cuesj-478	70	1	n	n	ADV
cuesj-478	71	1	i	i	PRON
cuesj-478	72	1	i	i	PRON
cuesj-478	73	1	i	i	PRON
cuesj-478	73	2	h	h	VERB
cuesj-478	73	3	ax	ax	NOUN
cuesj-478	73	4	e	e	NOUN
cuesj-478	73	5	x	x	PUNCT
cuesj-478	73	6	=	=	SYM
cuesj-478	73	7	=	=	SYM
cuesj-478	73	8	∑	∑	PUNCT
cuesj-478	73	9	(	(	PUNCT
cuesj-478	73	10	16	16	NUM
cuesj-478	73	11	)	)	PUNCT
cuesj-478	73	12	by	by	ADP
cuesj-478	73	13	the	the	DET
cuesj-478	73	14	initial	initial	ADJ
cuesj-478	73	15	equation	equation	NOUN
cuesj-478	73	16	,	,	PUNCT
cuesj-478	73	17	we	we	PRON
cuesj-478	73	18	have	have	VERB
cuesj-478	73	19	α	α	PRON
cuesj-478	73	20	equation	equation	NOUN
cuesj-478	73	21	and	and	CCONJ
cuesj-478	73	22	is	be	AUX
cuesj-478	73	23	depend	depend	VERB
cuesj-478	73	24	on	on	ADP
cuesj-478	73	25	our	our	PRON
cuesj-478	73	26	approximate	approximate	NOUN
cuesj-478	73	27	about	about	ADP
cuesj-478	73	28	n	n	ADV
cuesj-478	73	29	so	so	ADV
cuesj-478	73	30	all	all	DET
cuesj-478	73	31	equation	equation	NOUN
cuesj-478	73	32	number	number	NOUN
cuesj-478	73	33	is	be	AUX
cuesj-478	73	34	n+1	n+1	PROPN
cuesj-478	73	35	,	,	PUNCT
cuesj-478	73	36	except	except	SCONJ
cuesj-478	73	37	α	α	PRON
cuesj-478	73	38	equation	equation	NOUN
cuesj-478	73	39	other	other	ADJ
cuesj-478	73	40	equation	equation	NOUN
cuesj-478	73	41	get	get	VERB
cuesj-478	73	42	by	by	ADP
cuesj-478	73	43	the	the	DET
cuesj-478	73	44	finding	finding	NOUN
cuesj-478	73	45	root	root	NOUN
cuesj-478	73	46	of	of	ADP
cuesj-478	73	47	shifted	shift	VERB
cuesj-478	73	48	legendre	legendre	PROPN
cuesj-478	73	49	polynomial	polynomial	PROPN
cuesj-478	73	50	e	e	PROPN
cuesj-478	73	51	x	x	SYM
cuesj-478	73	52	n	n	PRON
cuesj-478	73	53	�	�	PROPN
cuesj-478	73	54	�	�	PROPN
cuesj-478	73	55	1	1	NUM
cuesj-478	73	56	�	�	PROPN
cuesj-478	73	57	(	(	PUNCT
cuesj-478	73	58	)	)	PUNCT
cuesj-478	73	59	and	and	CCONJ
cuesj-478	73	60	put	put	VERB
cuesj-478	73	61	on	on	ADP
cuesj-478	73	62	equation	equation	NOUN
cuesj-478	73	63	(	(	PUNCT
cuesj-478	73	64	14	14	NUM
cuesj-478	73	65	)	)	PUNCT
cuesj-478	73	66	.	.	PUNCT
cuesj-478	74	1	so	so	ADV
cuesj-478	74	2	solving	solve	VERB
cuesj-478	74	3	this	this	DET
cuesj-478	74	4	system	system	NOUN
cuesj-478	74	5	of	of	ADP
cuesj-478	74	6	equation	equation	NOUN
cuesj-478	74	7	is	be	AUX
cuesj-478	74	8	our	our	PRON
cuesj-478	74	9	approximation	approximation	NOUN
cuesj-478	74	10	solution	solution	NOUN
cuesj-478	74	11	for	for	ADP
cuesj-478	74	12	multi	multi	ADJ
cuesj-478	74	13	-	-	ADJ
cuesj-478	74	14	order	order	ADJ
cuesj-478	74	15	fractional	fractional	ADJ
cuesj-478	74	16	differential	differential	NOUN
cuesj-478	74	17	equation	equation	NOUN
cuesj-478	74	18	(	(	PUNCT
cuesj-478	74	19	14	14	NUM
cuesj-478	74	20	)	)	PUNCT
cuesj-478	74	21	.	.	PUNCT
cuesj-478	75	1	example	example	NOUN
cuesj-478	76	1	1	1	NUM
cuesj-478	76	2	:	:	PUNCT
cuesj-478	76	3	(	(	PUNCT
cuesj-478	76	4	bagley	bagley	NOUN
cuesj-478	76	5	-	-	PUNCT
cuesj-478	76	6	torvik	torvik	NOUN
cuesj-478	76	7	equation	equation	NOUN
cuesj-478	76	8	)	)	PUNCT
cuesj-478	76	9	.	.	PUNCT
cuesj-478	77	1	the	the	DET
cuesj-478	77	2	inhomogeneous	inhomogeneous	ADJ
cuesj-478	77	3	bagley	bagley	NOUN
cuesj-478	77	4	-	-	PUNCT
cuesj-478	77	5	torvik	torvik	NOUN
cuesj-478	77	6	initial	initial	ADJ
cuesj-478	77	7	value	value	NOUN
cuesj-478	77	8	problem	problem	NOUN
cuesj-478	77	9	is	be	AUX
cuesj-478	77	10	d	d	NOUN
cuesj-478	77	11	h	h	NOUN
cuesj-478	77	12	x	x	PUNCT
cuesj-478	78	1	d	d	NOUN
cuesj-478	78	2	h	h	NOUN
cuesj-478	78	3	x	x	NOUN
cuesj-478	78	4	h	h	NOUN
cuesj-478	79	1	x	x	PUNCT
cuesj-478	79	2	x	x	SYM
cuesj-478	79	3	x2	x2	NOUN
cuesj-478	79	4	3	3	NUM
cuesj-478	79	5	2	2	NUM
cuesj-478	79	6	1	1	NUM
cuesj-478	79	7	0	0	NUM
cuesj-478	79	8	1	1	NUM
cuesj-478	79	9	(	(	PUNCT
cuesj-478	79	10	(	(	PUNCT
cuesj-478	79	11	)	)	PUNCT
cuesj-478	79	12	)	)	PUNCT
cuesj-478	79	13	(	(	PUNCT
cuesj-478	79	14	(	(	PUNCT
cuesj-478	79	15	)	)	PUNCT
cuesj-478	79	16	)	)	PUNCT
cuesj-478	79	17	(	(	PUNCT
cuesj-478	79	18	)	)	PUNCT
cuesj-478	79	19	,	,	PUNCT
cuesj-478	79	20	[	[	PUNCT
cuesj-478	79	21	,	,	PUNCT
cuesj-478	79	22	]	]	PUNCT
cuesj-478	79	23	�	�	PROPN
cuesj-478	79	24	�	�	PROPN
cuesj-478	79	25	�	�	PROPN
cuesj-478	79	26	�	�	PROPN
cuesj-478	79	27	�	�	PROPN
cuesj-478	79	28	(	(	PUNCT
cuesj-478	79	29	17	17	NUM
cuesj-478	79	30	)	)	PUNCT
cuesj-478	79	31	with	with	ADP
cuesj-478	79	32	initial	initial	ADJ
cuesj-478	79	33	assumption	assumption	NOUN
cuesj-478	79	34	h(0)=1	h(0)=1	PROPN
cuesj-478	79	35	,	,	PUNCT
cuesj-478	79	36	h’(0)=1	h’(0)=1	NOUN
cuesj-478	79	37	and	and	CCONJ
cuesj-478	79	38	n=2	n=2	ADV
cuesj-478	79	39	solution	solution	NOUN
cuesj-478	79	40	:	:	PUNCT
cuesj-478	79	41	h	h	NOUN
cuesj-478	79	42	a	a	DET
cuesj-478	79	43	h	h	NOUN
cuesj-478	79	44	a	a	DET
cuesj-478	79	45	a	a	DET
cuesj-478	79	46	e	e	NOUN
cuesj-478	79	47	e	e	NOUN
cuesj-478	79	48	e	e	NOUN
cuesj-478	79	49	h	h	NOUN
cuesj-478	79	50	x	x	PUNCT
cuesj-478	79	51	e	e	NOUN
cuesj-478	79	52	x	x	X
cuesj-478	79	53	e	e	NOUN
cuesj-478	79	54	x	x	X
cuesj-478	79	55	a	a	PRON
cuesj-478	79	56	x	x	SYM
cuesj-478	79	57	a	a	DET
cuesj-478	79	58	x	x	SYM
cuesj-478	79	59	x	x	NOUN
cuesj-478	79	60	n	n	INTJ
cuesj-478	79	61	i	i	PRON
cuesj-478	79	62	i	i	PRON
cuesj-478	80	1	n	n	VERB
cuesj-478	81	1	i	i	PRON
cuesj-478	82	1	i	i	PRON
cuesj-478	83	1	i	i	PRON
cuesj-478	83	2	i	i	INTJ
cuesj-478	83	3	(	(	PUNCT
cuesj-478	83	4	)	)	PUNCT
cuesj-478	83	5	(	(	PUNCT
cuesj-478	83	6	)	)	PUNCT
cuesj-478	83	7	(	(	PUNCT
cuesj-478	83	8	)	)	PUNCT
cuesj-478	83	9	(	(	PUNCT
cuesj-478	83	10	)	)	PUNCT
cuesj-478	83	11	(	(	PUNCT
cuesj-478	83	12	)	)	PUNCT
cuesj-478	83	13	(	(	PUNCT
cuesj-478	83	14	�	�	PROPN
cuesj-478	83	15	�	�	PROPN
cuesj-478	83	16	�	�	PROPN
cuesj-478	83	17	�	�	PROPN
cuesj-478	83	18	�	�	PROPN
cuesj-478	83	19	�	�	PROPN
cuesj-478	83	20	�	�	PROPN
cuesj-478	83	21	�	�	PROPN
cuesj-478	83	22	�	�	PROPN
cuesj-478	83	23	0	0	NUM
cuesj-478	83	24	2	2	NUM
cuesj-478	83	25	0	0	NUM
cuesj-478	83	26	2	2	NUM
cuesj-478	83	27	0	0	NUM
cuesj-478	83	28	0	0	NUM
cuesj-478	83	29	1	1	NUM
cuesj-478	83	30	1	1	NUM
cuesj-478	83	31	2	2	NUM
cuesj-478	83	32	2	2	NUM
cuesj-478	83	33	2	2	NUM
cuesj-478	83	34	)	)	PUNCT
cuesj-478	83	35	)	)	PUNCT
cuesj-478	83	36	�	�	PROPN
cuesj-478	83	37	�	�	PROPN
cuesj-478	83	38	�	�	PROPN
cuesj-478	83	39	�	�	PROPN
cuesj-478	83	40	�	�	PROPN
cuesj-478	83	41	�	�	PROPN
cuesj-478	83	42	a	a	PRON
cuesj-478	83	43	a	a	NOUN
cuesj-478	83	44	x	x	NOUN
cuesj-478	83	45	a	a	DET
cuesj-478	83	46	a	a	NOUN
cuesj-478	83	47	x	x	SYM
cuesj-478	83	48	a	a	DET
cuesj-478	83	49	x	x	X
cuesj-478	83	50	a0	a0	NOUN
cuesj-478	83	51	1	1	NUM
cuesj-478	83	52	1	1	NUM
cuesj-478	83	53	2	2	NUM
cuesj-478	83	54	2	2	NUM
cuesj-478	83	55	2	2	NUM
cuesj-478	83	56	22	22	NUM
cuesj-478	83	57	6	6	NUM
cuesj-478	83	58	6	6	NUM
cuesj-478	83	59	so	so	ADV
cuesj-478	83	60	use	use	VERB
cuesj-478	83	61	initial	initial	ADJ
cuesj-478	83	62	condition	condition	NOUN
cuesj-478	83	63	for	for	ADP
cuesj-478	83	64	finding	find	VERB
cuesj-478	83	65	the	the	DET
cuesj-478	83	66	α	α	NOUN
cuesj-478	83	67	equation	equation	NOUN
cuesj-478	83	68	and	and	CCONJ
cuesj-478	83	69	for	for	ADP
cuesj-478	83	70	any	any	DET
cuesj-478	83	71	derivative	derivative	NOUN
cuesj-478	83	72	,	,	PUNCT
cuesj-478	83	73	we	we	PRON
cuesj-478	83	74	use	use	VERB
cuesj-478	83	75	d	d	X
cuesj-478	83	76	ah	ah	INTJ
cuesj-478	83	77	x	x	X
cuesj-478	83	78	w	w	NOUN
cuesj-478	83	79	xn	xn	PROPN
cuesj-478	84	1	i	i	PRON
cuesj-478	84	2	k	k	INTJ
cuesj-478	85	1	i	i	PRON
cuesj-478	85	2	i	i	PRON
cuesj-478	86	1	n	n	VERB
cuesj-478	86	2	i	i	PRON
cuesj-478	86	3	k	k	PROPN
cuesj-478	86	4	k	k	PROPN
cuesj-478	86	5	�	�	PROPN
cuesj-478	86	6	�	�	PROPN
cuesj-478	86	7	�	�	PROPN
cuesj-478	86	8	�	�	PROPN
cuesj-478	86	9	�	�	PROPN
cuesj-478	86	10	(	(	PUNCT
cuesj-478	86	11	(	(	PUNCT
cuesj-478	86	12	)	)	PUNCT
cuesj-478	86	13	)	)	PUNCT
cuesj-478	86	14	,	,	PUNCT
cuesj-478	86	15	�	�	PROPN
cuesj-478	86	16	�	�	PROPN
cuesj-478	86	17	�	�	PROPN
cuesj-478	86	18	�	�	PROPN
cuesj-478	86	19	�	�	PROPN
cuesj-478	86	20	�	�	PROPN
cuesj-478	86	21	h	h	NOUN
cuesj-478	87	1	d	d	PROPN
cuesj-478	87	2	a	a	DET
cuesj-478	87	3	a	a	DET
cuesj-478	87	4	a	a	DET
cuesj-478	87	5	h	h	NOUN
cuesj-478	87	6	a	a	DET
cuesj-478	87	7	a	a	DET
cuesj-478	87	8	2	2	NUM
cuesj-478	87	9	0	0	NUM
cuesj-478	87	10	1	1	NUM
cuesj-478	87	11	2	2	NUM
cuesj-478	87	12	1	1	NUM
cuesj-478	87	13	2	2	NUM
cuesj-478	87	14	1	1	NUM
cuesj-478	87	15	2	2	NUM
cuesj-478	87	16	0	0	NUM
cuesj-478	87	17	1	1	NUM
cuesj-478	87	18	1	1	NUM
cuesj-478	87	19	0	0	NUM
cuesj-478	87	20	2	2	NUM
cuesj-478	87	21	6	6	NUM
cuesj-478	87	22	1	1	NUM
cuesj-478	87	23	2	2	NUM
cuesj-478	87	24	(	(	PUNCT
cuesj-478	87	25	)	)	PUNCT
cuesj-478	87	26	(	(	PUNCT
cuesj-478	87	27	)	)	PUNCT
cuesj-478	87	28	(	(	PUNCT
cuesj-478	87	29	(	(	PUNCT
cuesj-478	87	30	(	(	PUNCT
cuesj-478	87	31	)	)	PUNCT
cuesj-478	87	32	)	)	PUNCT
cuesj-478	87	33	(	(	PUNCT
cuesj-478	87	34	)	)	PUNCT
cuesj-478	87	35	�	�	PROPN
cuesj-478	87	36	�	�	PROPN
cuesj-478	87	37	�	�	PROPN
cuesj-478	87	38	�	�	PROPN
cuesj-478	87	39	�	�	PROPN
cuesj-478	87	40	�	�	PROPN
cuesj-478	87	41	�	�	PROPN
cuesj-478	87	42	�	�	PROPN
cuesj-478	87	43	�	�	PROPN
cuesj-478	87	44	for	for	ADP
cuesj-478	87	45	finding	find	VERB
cuesj-478	87	46	n+1	n+1	NUM
cuesj-478	87	47	equation	equation	NOUN
cuesj-478	87	48	,	,	PUNCT
cuesj-478	87	49	we	we	PRON
cuesj-478	87	50	need	need	AUX
cuesj-478	87	51	use	use	VERB
cuesj-478	87	52	the	the	DET
cuesj-478	87	53	root	root	NOUN
cuesj-478	87	54	of	of	ADP
cuesj-478	87	55	the	the	DET
cuesj-478	87	56	polynomial	polynomial	ADJ
cuesj-478	87	57	e	e	NOUN
cuesj-478	87	58	x	x	PUNCT
cuesj-478	87	59	e	e	NOUN
cuesj-478	87	60	x	x	SYM
cuesj-478	87	61	x	x	SYM
cuesj-478	87	62	x	x	SYM
cuesj-478	87	63	n	n	PRON
cuesj-478	87	64	�	�	PROPN
cuesj-478	87	65	�	�	PROPN
cuesj-478	87	66	�	�	PROPN
cuesj-478	87	67	�	�	PROPN
cuesj-478	87	68	�	�	PROPN
cuesj-478	87	69	�	�	PROPN
cuesj-478	87	70	�	�	PROPN
cuesj-478	87	71	�	�	PROPN
cuesj-478	87	72	1	1	NUM
cuesj-478	87	73	1	1	NUM
cuesj-478	87	74	2	2	NUM
cuesj-478	87	75	1	1	NUM
cuesj-478	87	76	0	0	NUM
cuesj-478	87	77	0	0	NUM
cuesj-478	87	78	5	5	NUM
cuesj-478	87	79	�	�	PROPN
cuesj-478	87	80	(	(	PUNCT
cuesj-478	87	81	)	)	PUNCT
cuesj-478	87	82	(	(	PUNCT
cuesj-478	87	83	)	)	PUNCT
cuesj-478	87	84	.	.	PUNCT
cuesj-478	88	1	so	so	ADV
cuesj-478	88	2	put	put	VERB
cuesj-478	88	3	the	the	DET
cuesj-478	88	4	root	root	NOUN
cuesj-478	88	5	in	in	ADP
cuesj-478	88	6	the	the	DET
cuesj-478	88	7	equation	equation	NOUN
cuesj-478	88	8	(	(	PUNCT
cuesj-478	88	9	17	17	NUM
cuesj-478	88	10	)	)	PUNCT
cuesj-478	88	11	after	after	ADP
cuesj-478	88	12	,	,	PUNCT
cuesj-478	88	13	we	we	PRON
cuesj-478	88	14	calculate	calculate	VERB
cuesj-478	88	15	all	all	DET
cuesj-478	88	16	structure	structure	NOUN
cuesj-478	88	17	instead	instead	ADV
cuesj-478	88	18	each	each	DET
cuesj-478	88	19	x	x	SYM
cuesj-478	88	20	variable	variable	ADJ
cuesj-478	88	21	.	.	PUNCT
cuesj-478	89	1	mahmood	mahmood	PROPN
cuesj-478	89	2	,	,	PUNCT
cuesj-478	89	3	et	et	PROPN
cuesj-478	89	4	al	al	PROPN
cuesj-478	89	5	.	.	PUNCT
cuesj-478	89	6	:	:	PUNCT
cuesj-478	90	1	multi	multi	ADJ
cuesj-478	90	2	-	-	ADJ
cuesj-478	90	3	order	order	NOUN
cuesj-478	90	4	fde	fde	NOUN
cuesj-478	90	5	based	base	VERB
cuesj-478	90	6	on	on	ADP
cuesj-478	90	7	cd	cd	PROPN
cuesj-478	90	8	by	by	ADP
cuesj-478	90	9	shifted	shift	VERB
cuesj-478	90	10	lp	lp	PROPN
cuesj-478	90	11	66	66	NUM
cuesj-478	90	12	http://journals.cihanuniversity.edu.iq/index.php/cuesj	http://journals.cihanuniversity.edu.iq/index.php/cuesj	ADJ
cuesj-478	90	13	cuesj	cuesj	ADJ
cuesj-478	90	14	2021	2021	NUM
cuesj-478	90	15	,	,	PUNCT
cuesj-478	90	16	5	5	NUM
cuesj-478	90	17	(	(	PUNCT
cuesj-478	90	18	2	2	NUM
cuesj-478	90	19	):	):	PUNCT
cuesj-478	90	20	64	64	NUM
cuesj-478	90	21	-	-	SYM
cuesj-478	90	22	68	68	NUM
cuesj-478	91	1	d	d	NOUN
cuesj-478	92	1	d	d	NOUN
cuesj-478	93	1	h	h	NOUN
cuesj-478	94	1	h	h	NOUN
cuesj-478	95	1	a	a	DET
cuesj-478	95	2	h	h	NOUN
cuesj-478	95	3	a	a	PRON
cuesj-478	95	4	a	a	PRON
cuesj-478	95	5	a	a	DET
cuesj-478	95	6	2	2	NUM
cuesj-478	95	7	2	2	NUM
cuesj-478	95	8	2	2	NUM
cuesj-478	95	9	3	3	NUM
cuesj-478	95	10	2	2	NUM
cuesj-478	95	11	2	2	NUM
cuesj-478	95	12	2	2	NUM
cuesj-478	95	13	2	2	NUM
cuesj-478	95	14	0	0	NUM
cuesj-478	95	15	2	2	NUM
cuesj-478	95	16	0	0	NUM
cuesj-478	95	17	5	5	NUM
cuesj-478	95	18	12	12	NUM
cuesj-478	95	19	0	0	NUM
cuesj-478	95	20	5	5	NUM
cuesj-478	95	21	12	12	NUM
cuesj-478	95	22	0	0	NUM
cuesj-478	95	23	5	5	NUM
cuesj-478	95	24	0	0	NUM
cuesj-478	95	25	5	5	NUM
cuesj-478	95	26	1	1	NUM
cuesj-478	95	27	2	2	NUM
cuesj-478	95	28	(	(	PUNCT
cuesj-478	95	29	(	(	PUNCT
cuesj-478	95	30	.	.	PUNCT
cuesj-478	95	31	)	)	PUNCT
cuesj-478	95	32	)	)	PUNCT
cuesj-478	96	1	(	(	PUNCT
cuesj-478	96	2	(	(	PUNCT
cuesj-478	96	3	.	.	PUNCT
cuesj-478	96	4	)	)	PUNCT
cuesj-478	96	5	)	)	PUNCT
cuesj-478	96	6	.	.	PUNCT
cuesj-478	97	1	(	(	PUNCT
cuesj-478	97	2	.	.	PUNCT
cuesj-478	97	3	)	)	PUNCT
cuesj-478	97	4	�	�	PROPN
cuesj-478	97	5	�	�	PROPN
cuesj-478	97	6	�	�	PROPN
cuesj-478	97	7	�	�	PROPN
cuesj-478	97	8	substitute	substitute	VERB
cuesj-478	97	9	each	each	DET
cuesj-478	97	10	one	one	NUM
cuesj-478	97	11	of	of	ADP
cuesj-478	97	12	d	d	PROPN
cuesj-478	97	13	h	h	NOUN
cuesj-478	97	14	d	d	PROPN
cuesj-478	97	15	h2	h2	NOUN
cuesj-478	97	16	2	2	NUM
cuesj-478	97	17	3	3	NUM
cuesj-478	97	18	2	2	NUM
cuesj-478	97	19	20	20	NUM
cuesj-478	97	20	5	5	NUM
cuesj-478	97	21	0	0	NUM
cuesj-478	97	22	5	5	NUM
cuesj-478	97	23	(	(	PUNCT
cuesj-478	97	24	(	(	PUNCT
cuesj-478	97	25	.	.	PUNCT
cuesj-478	97	26	)	)	PUNCT
cuesj-478	97	27	)	)	PUNCT
cuesj-478	97	28	,	,	PUNCT
cuesj-478	97	29	(	(	PUNCT
cuesj-478	97	30	(	(	PUNCT
cuesj-478	97	31	.	.	PUNCT
cuesj-478	97	32	)	)	PUNCT
cuesj-478	97	33	)	)	PUNCT
cuesj-478	98	1	and	and	CCONJ
cuesj-478	98	2	h2	h2	NOUN
cuesj-478	98	3	(	(	PUNCT
cuesj-478	98	4	0.5	0.5	NUM
cuesj-478	98	5	)	)	PUNCT
cuesj-478	98	6	in	in	ADP
cuesj-478	98	7	the	the	DET
cuesj-478	98	8	equation	equation	NOUN
cuesj-478	98	9	(	(	PUNCT
cuesj-478	98	10	17	17	NUM
cuesj-478	98	11	)	)	PUNCT
cuesj-478	98	12	and	and	CCONJ
cuesj-478	98	13	instead	instead	ADV
cuesj-478	98	14	of	of	ADP
cuesj-478	98	15	each	each	PRON
cuesj-478	98	16	x	x	PUNCT
cuesj-478	98	17	put	put	VERB
cuesj-478	98	18	root	root	NOUN
cuesj-478	98	19	of	of	ADP
cuesj-478	98	20	shifted	shift	VERB
cuesj-478	98	21	legendre	legendre	PROPN
cuesj-478	98	22	polynomial	polynomial	PROPN
cuesj-478	98	23	12	12	NUM
cuesj-478	98	24	12	12	NUM
cuesj-478	98	25	0	0	NUM
cuesj-478	98	26	5	5	NUM
cuesj-478	98	27	1	1	NUM
cuesj-478	98	28	2	2	NUM
cuesj-478	98	29	1	1	NUM
cuesj-478	98	30	1	1	NUM
cuesj-478	98	31	2	2	NUM
cuesj-478	98	32	23	23	NUM
cuesj-478	98	33	2	2	NUM
cuesj-478	98	34	6	6	NUM
cuesj-478	98	35	2	2	NUM
cuesj-478	98	36	3	3	NUM
cuesj-478	98	37	2	2	NUM
cuesj-478	98	38	3	3	NUM
cuesj-478	98	39	2	2	NUM
cuesj-478	98	40	2	2	NUM
cuesj-478	98	41	0	0	NUM
cuesj-478	98	42	2	2	NUM
cuesj-478	98	43	0	0	NUM
cuesj-478	98	44	2	2	NUM
cuesj-478	98	45	a	a	DET
cuesj-478	98	46	a	a	DET
cuesj-478	98	47	a	a	DET
cuesj-478	98	48	a	a	DET
cuesj-478	98	49	a	a	DET
cuesj-478	98	50	a	a	DET
cuesj-478	98	51	�	�	PROPN
cuesj-478	98	52	�	�	PROPN
cuesj-478	98	53	�	�	PROPN
cuesj-478	98	54	�	�	PROPN
cuesj-478	98	55	�	�	PROPN
cuesj-478	98	56	�	�	PROPN
cuesj-478	98	57	�	�	PROPN
cuesj-478	98	58	�	�	PROPN
cuesj-478	98	59	�	�	PROPN
cuesj-478	98	60	�	�	PROPN
cuesj-478	98	61	.	.	PUNCT
cuesj-478	99	1	(	(	PUNCT
cuesj-478	99	2	)	)	PUNCT
cuesj-478	99	3	(	(	PUNCT
cuesj-478	99	4	)	)	PUNCT
cuesj-478	99	5	so	so	ADV
cuesj-478	99	6	we	we	PRON
cuesj-478	99	7	have	have	VERB
cuesj-478	99	8	a	a	DET
cuesj-478	99	9	linear	linear	ADJ
cuesj-478	99	10	system	system	NOUN
cuesj-478	99	11	after	after	ADP
cuesj-478	99	12	solve	solve	NOUN
cuesj-478	99	13	by	by	ADP
cuesj-478	99	14	matrix	matrix	NOUN
cuesj-478	99	15	operation	operation	NOUN
cuesj-478	99	16	,	,	PUNCT
cuesj-478	99	17	we	we	PRON
cuesj-478	99	18	get	get	VERB
cuesj-478	99	19	1	1	NUM
cuesj-478	99	20	1	1	NUM
cuesj-478	99	21	1	1	NUM
cuesj-478	99	22	0	0	NUM
cuesj-478	99	23	2	2	NUM
cuesj-478	99	24	6	6	NUM
cuesj-478	99	25	1	1	NUM
cuesj-478	99	26	0	0	NUM
cuesj-478	99	27	23	23	NUM
cuesj-478	99	28	2	2	NUM
cuesj-478	99	29	6	6	NUM
cuesj-478	99	30	2	2	NUM
cuesj-478	99	31	1	1	NUM
cuesj-478	99	32	1	1	NUM
cuesj-478	99	33	3	3	NUM
cuesj-478	99	34	2	2	NUM
cuesj-478	99	35	0	0	NUM
cuesj-478	99	36	1	1	NUM
cuesj-478	99	37	2	2	NUM
cuesj-478	99	38	�	�	PROPN
cuesj-478	99	39	�	�	PROPN
cuesj-478	99	40	�	�	PROPN
cuesj-478	99	41	�	�	PROPN
cuesj-478	99	42	�	�	PROPN
cuesj-478	99	43	�	�	PROPN
cuesj-478	99	44	�	�	PROPN
cuesj-478	99	45	�	�	PROPN
cuesj-478	99	46	�	�	PROPN
cuesj-478	99	47	�	�	PROPN
cuesj-478	99	48	�	�	PROPN
cuesj-478	99	49	�	�	PROPN
cuesj-478	99	50	�	�	PROPN
cuesj-478	99	51	�	�	PROPN
cuesj-478	99	52	�	�	PROPN
cuesj-478	99	53	�	�	PROPN
cuesj-478	99	54	�	�	PROPN
cuesj-478	99	55	�	�	PROPN
cuesj-478	99	56	�	�	PROPN
cuesj-478	99	57	�	�	PROPN
cuesj-478	99	58	�	�	PROPN
cuesj-478	99	59	�	�	PROPN
cuesj-478	99	60	�	�	PROPN
cuesj-478	99	61	�	�	PROPN
cuesj-478	99	62	�	�	PROPN
cuesj-478	99	63	�	�	PROPN
cuesj-478	99	64	�	�	PROPN
cuesj-478	99	65	�	�	PROPN
cuesj-478	99	66	�	�	PROPN
cuesj-478	99	67	�	�	PROPN
cuesj-478	99	68	�	�	PROPN
cuesj-478	99	69	�	�	PROPN
cuesj-478	99	70	�	�	PROPN
cuesj-478	99	71	�	�	PROPN
cuesj-478	99	72	�	�	PROPN
cuesj-478	99	73	a	a	DET
cuesj-478	99	74	a	a	DET
cuesj-478	99	75	a	a	DET
cuesj-478	99	76	�	�	PROPN
cuesj-478	99	77	�	�	PROPN
cuesj-478	99	78	�	�	PROPN
cuesj-478	99	79	�	�	PROPN
cuesj-478	99	80	�	�	PROPN
cuesj-478	99	81	�	�	PROPN
cuesj-478	99	82	�	�	PROPN
cuesj-478	99	83	�	�	PROPN
cuesj-478	99	84	�	�	PROPN
cuesj-478	99	85	�	�	PROPN
cuesj-478	99	86	�	�	PROPN
cuesj-478	99	87	�	�	PROPN
cuesj-478	99	88	�	�	PROPN
cuesj-478	99	89	a	a	DET
cuesj-478	99	90	h	h	NOUN
cuesj-478	99	91	a	a	DET
cuesj-478	99	92	a	a	NOUN
cuesj-478	99	93	x	x	SYM
cuesj-478	99	94	x	x	SYM
cuesj-478	99	95	0	0	NUM
cuesj-478	99	96	1	1	NUM
cuesj-478	99	97	2	2	NUM
cuesj-478	99	98	2	2	NUM
cuesj-478	99	99	3	3	NUM
cuesj-478	99	100	2	2	NUM
cuesj-478	99	101	1	1	NUM
cuesj-478	99	102	2	2	NUM
cuesj-478	99	103	0	0	NUM
cuesj-478	99	104	1	1	NUM
cuesj-478	99	105	,	,	PUNCT
cuesj-478	99	106	,	,	PUNCT
cuesj-478	99	107	(	(	PUNCT
cuesj-478	99	108	)	)	PUNCT
cuesj-478	99	109	therefore	therefore	ADV
cuesj-478	99	110	,	,	PUNCT
cuesj-478	99	111	the	the	DET
cuesj-478	99	112	obtained	obtain	VERB
cuesj-478	99	113	solution	solution	NOUN
cuesj-478	99	114	is	be	AUX
cuesj-478	99	115	the	the	DET
cuesj-478	99	116	exact	exact	ADJ
cuesj-478	99	117	solution	solution	NOUN
cuesj-478	99	118	of	of	ADP
cuesj-478	99	119	this	this	DET
cuesj-478	99	120	problem	problem	NOUN
cuesj-478	99	121	,	,	PUNCT
cuesj-478	99	122	code	code	NOUN
cuesj-478	99	123	of	of	ADP
cuesj-478	99	124	python	python	NOUN
cuesj-478	99	125	for	for	ADP
cuesj-478	99	126	this	this	DET
cuesj-478	99	127	example	example	NOUN
cuesj-478	99	128	is	be	AUX
cuesj-478	99	129	given.[9	given.[9	NOUN
cuesj-478	99	130	]	]	X
cuesj-478	99	131	example	example	NOUN
cuesj-478	100	1	2	2	NUM
cuesj-478	100	2	:	:	PUNCT
cuesj-478	100	3	suppose	suppose	VERB
cuesj-478	100	4	the	the	DET
cuesj-478	100	5	following	follow	VERB
cuesj-478	100	6	fractional	fractional	ADJ
cuesj-478	100	7	linear	linear	PROPN
cuesj-478	100	8	differential	differential	NOUN
cuesj-478	100	9	equation	equation	NOUN
cuesj-478	100	10	with	with	ADP
cuesj-478	100	11	variable	variable	ADJ
cuesj-478	100	12	coefficients	coefficient	NOUN
cuesj-478	100	13	d	d	X
cuesj-478	100	14	h	h	NOUN
cuesj-478	100	15	x	x	PUNCT
cuesj-478	100	16	d	d	NOUN
cuesj-478	100	17	h	h	NOUN
cuesj-478	100	18	x	x	NOUN
cuesj-478	100	19	xd	xd	INTJ
cuesj-478	100	20	h	h	NOUN
cuesj-478	100	21	x	x	PUNCT
cuesj-478	101	1	x	x	PUNCT
cuesj-478	101	2	h	h	NOUN
cuesj-478	101	3	x	x	X
cuesj-478	101	4	x	x	PUNCT
cuesj-478	101	5	x	x	PUNCT
cuesj-478	101	6	x	x	PUNCT
cuesj-478	101	7	x	x	SYM
cuesj-478	101	8	x	x	SYM
cuesj-478	101	9	3	3	NUM
cuesj-478	101	10	2	2	NUM
cuesj-478	101	11	1	1	NUM
cuesj-478	101	12	2	2	NUM
cuesj-478	101	13	2	2	NUM
cuesj-478	101	14	3	3	NUM
cuesj-478	101	15	2	2	NUM
cuesj-478	101	16	3	3	NUM
cuesj-478	101	17	1	1	NUM
cuesj-478	101	18	2	2	NUM
cuesj-478	101	19	4	4	NUM
cuesj-478	101	20	7	7	NUM
cuesj-478	101	21	0	0	NUM
cuesj-478	101	22	(	(	PUNCT
cuesj-478	101	23	(	(	PUNCT
cuesj-478	101	24	)	)	PUNCT
cuesj-478	101	25	)	)	PUNCT
cuesj-478	101	26	(	(	PUNCT
cuesj-478	101	27	(	(	PUNCT
cuesj-478	101	28	)	)	PUNCT
cuesj-478	101	29	)	)	PUNCT
cuesj-478	101	30	(	(	PUNCT
cuesj-478	101	31	(	(	PUNCT
cuesj-478	101	32	)	)	PUNCT
cuesj-478	101	33	)	)	PUNCT
cuesj-478	101	34	(	(	PUNCT
cuesj-478	101	35	)	)	PUNCT
cuesj-478	101	36	(	(	PUNCT
cuesj-478	101	37	)	)	PUNCT
cuesj-478	101	38	,	,	PUNCT
cuesj-478	101	39	(	(	PUNCT
cuesj-478	101	40	�	�	PROPN
cuesj-478	101	41	�	�	PROPN
cuesj-478	101	42	�	�	PROPN
cuesj-478	101	43	�	�	PROPN
cuesj-478	101	44	�	�	PROPN
cuesj-478	101	45	�	�	PROPN
cuesj-478	101	46	�	�	PROPN
cuesj-478	101	47	�	�	PROPN
cuesj-478	101	48	�	�	PROPN
cuesj-478	101	49	,	,	PUNCT
cuesj-478	101	50	,	,	PUNCT
cuesj-478	101	51	]	]	X
cuesj-478	101	52	1	1	NUM
cuesj-478	101	53	with	with	ADP
cuesj-478	101	54	the	the	DET
cuesj-478	101	55	primary	primary	ADJ
cuesj-478	101	56	conditions	condition	NOUN
cuesj-478	101	57	h(0)=0	h(0)=0	NOUN
cuesj-478	101	58	,	,	PUNCT
cuesj-478	101	59	h’(0)=0	h’(0)=0	ADJ
cuesj-478	101	60	and	and	CCONJ
cuesj-478	101	61	n=2	n=2	ADV
cuesj-478	101	62	solution	solution	NOUN
cuesj-478	101	63	:	:	PUNCT
cuesj-478	102	1	h	h	NOUN
cuesj-478	102	2	a	a	DET
cuesj-478	102	3	h	h	NOUN
cuesj-478	102	4	e	e	NOUN
cuesj-478	102	5	e	e	NOUN
cuesj-478	102	6	e	e	X
cuesj-478	102	7	h	h	NOUN
cuesj-478	102	8	x	x	PUNCT
cuesj-478	102	9	e	e	NOUN
cuesj-478	102	10	x	x	X
cuesj-478	102	11	a	a	PRON
cuesj-478	102	12	x	x	SYM
cuesj-478	102	13	a	a	DET
cuesj-478	102	14	x	x	SYM
cuesj-478	102	15	a	a	X
cuesj-478	102	16	x	x	X
cuesj-478	102	17	x	x	X
cuesj-478	102	18	a	a	DET
cuesj-478	102	19	a	a	NOUN
cuesj-478	102	20	x	x	SYM
cuesj-478	102	21	n	n	NOUN
cuesj-478	102	22	i	i	PRON
cuesj-478	102	23	i	i	PRON
cuesj-478	102	24	n	n	VERB
cuesj-478	102	25	i	i	PRON
cuesj-478	102	26	(	(	PUNCT
cuesj-478	102	27	)	)	PUNCT
cuesj-478	102	28	(	(	PUNCT
cuesj-478	102	29	)	)	PUNCT
cuesj-478	102	30	(	(	PUNCT
cuesj-478	102	31	)	)	PUNCT
cuesj-478	102	32	(	(	PUNCT
cuesj-478	102	33	)	)	PUNCT
cuesj-478	102	34	(	(	PUNCT
cuesj-478	102	35	)	)	PUNCT
cuesj-478	102	36	(	(	PUNCT
cuesj-478	102	37	)	)	PUNCT
cuesj-478	102	38	�	�	PROPN
cuesj-478	102	39	�	�	PROPN
cuesj-478	102	40	�	�	PROPN
cuesj-478	102	41	�	�	PROPN
cuesj-478	102	42	�	�	PROPN
cuesj-478	102	43	�	�	PROPN
cuesj-478	102	44	�	�	PROPN
cuesj-478	102	45	�	�	PROPN
cuesj-478	102	46	�	�	PROPN
cuesj-478	102	47	0	0	NUM
cuesj-478	102	48	2	2	NUM
cuesj-478	102	49	0	0	NUM
cuesj-478	102	50	0	0	NUM
cuesj-478	102	51	1	1	NUM
cuesj-478	102	52	1	1	NUM
cuesj-478	102	53	2	2	NUM
cuesj-478	102	54	2	2	NUM
cuesj-478	102	55	2	2	NUM
cuesj-478	102	56	0	0	NUM
cuesj-478	102	57	12	12	NUM
cuesj-478	102	58	aa	aa	NOUN
cuesj-478	102	59	a	a	PRON
cuesj-478	102	60	x	x	SYM
cuesj-478	102	61	a	a	DET
cuesj-478	102	62	x	x	X
cuesj-478	102	63	a1	a1	NOUN
cuesj-478	102	64	2	2	NUM
cuesj-478	102	65	2	2	NUM
cuesj-478	102	66	2	2	NUM
cuesj-478	102	67	26	26	NUM
cuesj-478	102	68	6	6	NUM
cuesj-478	102	69	�	�	PROPN
cuesj-478	102	70	�	�	PROPN
cuesj-478	102	71	�	�	PROPN
cuesj-478	102	72	for	for	ADP
cuesj-478	102	73	finding	find	VERB
cuesj-478	102	74	n+1	n+1	NUM
cuesj-478	102	75	equation	equation	NOUN
cuesj-478	102	76	,	,	PUNCT
cuesj-478	102	77	we	we	PRON
cuesj-478	102	78	need	need	AUX
cuesj-478	102	79	use	use	VERB
cuesj-478	102	80	the	the	DET
cuesj-478	102	81	root	root	NOUN
cuesj-478	102	82	of	of	ADP
cuesj-478	102	83	the	the	DET
cuesj-478	102	84	polynomial	polynomial	ADJ
cuesj-478	102	85	e	e	NOUN
cuesj-478	102	86	x	x	PUNCT
cuesj-478	102	87	e	e	NOUN
cuesj-478	102	88	x	x	SYM
cuesj-478	102	89	x	x	SYM
cuesj-478	102	90	x	x	SYM
cuesj-478	102	91	n	n	PRON
cuesj-478	102	92	�	�	PROPN
cuesj-478	102	93	�	�	PROPN
cuesj-478	102	94	�	�	PROPN
cuesj-478	102	95	�	�	PROPN
cuesj-478	102	96	�	�	PROPN
cuesj-478	102	97	�	�	PROPN
cuesj-478	102	98	�	�	PROPN
cuesj-478	102	99	�	�	PROPN
cuesj-478	102	100	1	1	NUM
cuesj-478	102	101	1	1	NUM
cuesj-478	102	102	2	2	NUM
cuesj-478	102	103	1	1	NUM
cuesj-478	102	104	0	0	NUM
cuesj-478	102	105	0	0	NUM
cuesj-478	102	106	5	5	NUM
cuesj-478	102	107	�	�	PROPN
cuesj-478	102	108	(	(	PUNCT
cuesj-478	102	109	)	)	PUNCT
cuesj-478	102	110	(	(	PUNCT
cuesj-478	102	111	)	)	PUNCT
cuesj-478	102	112	.	.	PUNCT
cuesj-478	103	1	so	so	ADV
cuesj-478	103	2	we	we	PRON
cuesj-478	103	3	put	put	VERB
cuesj-478	103	4	the	the	DET
cuesj-478	103	5	root	root	NOUN
cuesj-478	103	6	in	in	ADP
cuesj-478	103	7	the	the	DET
cuesj-478	103	8	equation	equation	NOUN
cuesj-478	103	9	(	(	PUNCT
cuesj-478	103	10	18	18	NUM
cuesj-478	103	11	)	)	PUNCT
cuesj-478	103	12	after	after	ADP
cuesj-478	103	13	,	,	PUNCT
cuesj-478	103	14	we	we	PRON
cuesj-478	103	15	calculate	calculate	VERB
cuesj-478	103	16	all	all	DET
cuesj-478	103	17	structure	structure	NOUN
cuesj-478	103	18	instead	instead	ADV
cuesj-478	103	19	each	each	DET
cuesj-478	103	20	x	x	SYM
cuesj-478	103	21	variable	variable	NOUN
cuesj-478	103	22	d	d	NOUN
cuesj-478	103	23	h	h	NOUN
cuesj-478	104	1	a	a	DET
cuesj-478	104	2	h	h	NOUN
cuesj-478	104	3	a	a	DET
cuesj-478	104	4	h	h	NOUN
cuesj-478	105	1	a	a	DET
cuesj-478	105	2	d	d	X
cuesj-478	105	3	d	d	SYM
cuesj-478	105	4	3	3	NUM
cuesj-478	105	5	2	2	NUM
cuesj-478	105	6	2	2	NUM
cuesj-478	105	7	2	2	NUM
cuesj-478	105	8	1	1	NUM
cuesj-478	105	9	2	2	NUM
cuesj-478	105	10	1	1	NUM
cuesj-478	105	11	2	2	NUM
cuesj-478	105	12	1	1	NUM
cuesj-478	105	13	1	1	NUM
cuesj-478	105	14	2	2	NUM
cuesj-478	105	15	2	2	NUM
cuesj-478	105	16	1	1	NUM
cuesj-478	105	17	0	0	NUM
cuesj-478	105	18	5	5	NUM
cuesj-478	105	19	12	12	NUM
cuesj-478	105	20	1	1	NUM
cuesj-478	105	21	2	2	NUM
cuesj-478	105	22	0	0	NUM
cuesj-478	105	23	5	5	NUM
cuesj-478	105	24	2	2	NUM
cuesj-478	105	25	0	0	NUM
cuesj-478	105	26	5	5	NUM
cuesj-478	105	27	2	2	NUM
cuesj-478	105	28	0	0	NUM
cuesj-478	105	29	5	5	NUM
cuesj-478	105	30	(	(	PUNCT
cuesj-478	105	31	(	(	PUNCT
cuesj-478	105	32	.	.	PUNCT
cuesj-478	105	33	)	)	PUNCT
cuesj-478	105	34	)	)	PUNCT
cuesj-478	106	1	(	(	PUNCT
cuesj-478	106	2	)	)	PUNCT
cuesj-478	106	3	(	(	PUNCT
cuesj-478	106	4	(	(	PUNCT
cuesj-478	106	5	.	.	PUNCT
cuesj-478	106	6	)	)	PUNCT
cuesj-478	106	7	)	)	PUNCT
cuesj-478	107	1	(	(	PUNCT
cuesj-478	107	2	(	(	PUNCT
cuesj-478	107	3	.	.	PUNCT
cuesj-478	107	4	)	)	PUNCT
cuesj-478	107	5	)	)	PUNCT
cuesj-478	107	6	.	.	PUNCT
cuesj-478	108	1	�	�	PROPN
cuesj-478	108	2	�	�	PROPN
cuesj-478	108	3	�	�	PROPN
cuesj-478	108	4	�	�	PROPN
cuesj-478	108	5	66	66	NUM
cuesj-478	108	6	5	5	NUM
cuesj-478	108	7	12	12	NUM
cuesj-478	108	8	0	0	NUM
cuesj-478	108	9	5	5	NUM
cuesj-478	108	10	0	0	NUM
cuesj-478	108	11	5	5	NUM
cuesj-478	108	12	1	1	NUM
cuesj-478	108	13	2	2	NUM
cuesj-478	108	14	2	2	NUM
cuesj-478	108	15	2	2	NUM
cuesj-478	108	16	2	2	NUM
cuesj-478	108	17	0	0	NUM
cuesj-478	108	18	2	2	NUM
cuesj-478	108	19	a	a	DET
cuesj-478	108	20	o	o	NOUN
cuesj-478	108	21	a	a	DET
cuesj-478	108	22	a	a	DET
cuesj-478	108	23	ah	ah	INTJ
cuesj-478	108	24	.	.	PUNCT
cuesj-478	108	25	.	.	PUNCT
cuesj-478	109	1	(	(	PUNCT
cuesj-478	109	2	.	.	PUNCT
cuesj-478	109	3	)	)	PUNCT
cuesj-478	109	4	�	�	PROPN
cuesj-478	109	5	�	�	PROPN
cuesj-478	109	6	�	�	PROPN
cuesj-478	109	7	we	we	PRON
cuesj-478	109	8	substitute	substitute	VERB
cuesj-478	109	9	each	each	DET
cuesj-478	109	10	one	one	NUM
cuesj-478	109	11	of	of	ADP
cuesj-478	109	12	d	d	NOUN
cuesj-478	109	13	h	h	NOUN
cuesj-478	110	1	d	d	NOUN
cuesj-478	110	2	h	h	NOUN
cuesj-478	111	1	d	d	NOUN
cuesj-478	111	2	h	h	NOUN
cuesj-478	112	1	3	3	NUM
cuesj-478	112	2	2	2	NUM
cuesj-478	112	3	2	2	NUM
cuesj-478	112	4	1	1	NUM
cuesj-478	112	5	2	2	NUM
cuesj-478	112	6	1	1	NUM
cuesj-478	112	7	2	2	NUM
cuesj-478	112	8	20	20	NUM
cuesj-478	112	9	5	5	NUM
cuesj-478	112	10	0	0	NUM
cuesj-478	112	11	5	5	NUM
cuesj-478	112	12	0	0	NUM
cuesj-478	112	13	5	5	NUM
cuesj-478	112	14	(	(	PUNCT
cuesj-478	112	15	(	(	PUNCT
cuesj-478	112	16	.	.	PUNCT
cuesj-478	112	17	)	)	PUNCT
cuesj-478	112	18	)	)	PUNCT
cuesj-478	112	19	,	,	PUNCT
cuesj-478	112	20	(	(	PUNCT
cuesj-478	112	21	(	(	PUNCT
cuesj-478	112	22	.	.	PUNCT
cuesj-478	112	23	)	)	PUNCT
cuesj-478	112	24	)	)	PUNCT
cuesj-478	112	25	,	,	PUNCT
cuesj-478	112	26	(	(	PUNCT
cuesj-478	112	27	(	(	PUNCT
cuesj-478	112	28	.	.	PUNCT
cuesj-478	112	29	)	)	PUNCT
cuesj-478	112	30	)	)	PUNCT
cuesj-478	113	1	and	and	CCONJ
cuesj-478	113	2	h2	h2	PROPN
cuesj-478	113	3	 	 	SPACE
cuesj-478	113	4	(	(	PUNCT
cuesj-478	113	5	0.5	0.5	NUM
cuesj-478	113	6	)	)	PUNCT
cuesj-478	113	7	in	in	ADP
cuesj-478	113	8	the	the	DET
cuesj-478	113	9	equation	equation	NOUN
cuesj-478	113	10	(	(	PUNCT
cuesj-478	113	11	18	18	NUM
cuesj-478	113	12	)	)	PUNCT
cuesj-478	113	13	and	and	CCONJ
cuesj-478	113	14	instead	instead	ADV
cuesj-478	113	15	of	of	ADP
cuesj-478	113	16	each	each	PRON
cuesj-478	113	17	x	x	NOUN
cuesj-478	113	18	we	we	PRON
cuesj-478	113	19	put	put	VERB
cuesj-478	113	20	root	root	NOUN
cuesj-478	113	21	(	(	PUNCT
cuesj-478	113	22	0.5	0.5	NUM
cuesj-478	113	23	)	)	PUNCT
cuesj-478	113	24	1	1	NUM
cuesj-478	113	25	2	2	NUM
cuesj-478	113	26	7	7	NUM
cuesj-478	113	27	8	8	NUM
cuesj-478	113	28	2352813742238570	2352813742238570	NUM
cuesj-478	113	29	5	5	NUM
cuesj-478	113	30	03921356237095	03921356237095	NUM
cuesj-478	113	31	10	10	NUM
cuesj-478	113	32	1	1	NUM
cuesj-478	113	33	2a	2a	NUM
cuesj-478	113	34	a	a	DET
cuesj-478	113	35	a	a	DET
cuesj-478	113	36	�	�	PROPN
cuesj-478	113	37	�	�	PROPN
cuesj-478	113	38	�	�	PROPN
cuesj-478	113	39	�	�	PROPN
cuesj-478	113	40	.	.	PUNCT
cuesj-478	113	41	.	.	PUNCT
cuesj-478	114	1	(	(	PUNCT
cuesj-478	114	2	)	)	PUNCT
cuesj-478	114	3	h	h	NOUN
cuesj-478	114	4	a	a	DET
cuesj-478	114	5	a	a	DET
cuesj-478	114	6	a	a	PROPN
cuesj-478	114	7	d	d	NOUN
cuesj-478	114	8	h	h	NOUN
cuesj-478	114	9	a	a	PRON
cuesj-478	114	10	a	a	DET
cuesj-478	114	11	2	2	NUM
cuesj-478	114	12	0	0	NUM
cuesj-478	114	13	1	1	NUM
cuesj-478	114	14	2	2	NUM
cuesj-478	114	15	1	1	NUM
cuesj-478	114	16	2	2	NUM
cuesj-478	114	17	1	1	NUM
cuesj-478	114	18	2	2	NUM
cuesj-478	114	19	0	0	NUM
cuesj-478	114	20	0	0	NUM
cuesj-478	114	21	2	2	NUM
cuesj-478	114	22	0	0	NUM
cuesj-478	114	23	2	2	NUM
cuesj-478	114	24	6	6	NUM
cuesj-478	114	25	0	0	NUM
cuesj-478	114	26	3	3	NUM
cuesj-478	114	27	(	(	PUNCT
cuesj-478	114	28	)	)	PUNCT
cuesj-478	114	29	(	(	PUNCT
cuesj-478	114	30	)	)	PUNCT
cuesj-478	114	31	(	(	PUNCT
cuesj-478	114	32	(	(	PUNCT
cuesj-478	114	33	(	(	PUNCT
cuesj-478	114	34	)	)	PUNCT
cuesj-478	114	35	)	)	PUNCT
cuesj-478	114	36	(	(	PUNCT
cuesj-478	114	37	)	)	PUNCT
cuesj-478	114	38	�	�	PROPN
cuesj-478	114	39	�	�	PROPN
cuesj-478	114	40	�	�	PROPN
cuesj-478	114	41	�	�	PROPN
cuesj-478	114	42	�	�	PROPN
cuesj-478	114	43	�	�	PROPN
cuesj-478	114	44	�	�	PROPN
cuesj-478	114	45	�	�	PROPN
cuesj-478	114	46	�	�	PROPN
cuesj-478	115	1	so	so	SCONJ
cuesj-478	115	2	we	we	PRON
cuesj-478	115	3	have	have	VERB
cuesj-478	115	4	a	a	DET
cuesj-478	115	5	linear	linear	ADJ
cuesj-478	115	6	system	system	NOUN
cuesj-478	115	7	,	,	PUNCT
cuesj-478	115	8	we	we	PRON
cuesj-478	115	9	solved	solve	VERB
cuesj-478	115	10	by	by	ADP
cuesj-478	115	11	matrix	matrix	NOUN
cuesj-478	115	12	operation	operation	NOUN
cuesj-478	115	13	1	1	NUM
cuesj-478	115	14	2	2	NUM
cuesj-478	115	15	7	7	NUM
cuesj-478	115	16	8	8	NUM
cuesj-478	115	17	2352813742238570	2352813742238570	NUM
cuesj-478	115	18	1	1	NUM
cuesj-478	115	19	1	1	NUM
cuesj-478	115	20	1	1	NUM
cuesj-478	115	21	0	0	NUM
cuesj-478	115	22	2	2	NUM
cuesj-478	115	23	6	6	NUM
cuesj-478	115	24	0	0	NUM
cuesj-478	115	25	1	1	NUM
cuesj-478	115	26	2	2	NUM
cuesj-478	115	27	.	.	PUNCT
cuesj-478	115	28	�	�	PROPN
cuesj-478	115	29	�	�	PROPN
cuesj-478	115	30	�	�	PROPN
cuesj-478	115	31	�	�	PROPN
cuesj-478	115	32	�	�	PROPN
cuesj-478	115	33	�	�	PROPN
cuesj-478	115	34	�	�	PROPN
cuesj-478	115	35	�	�	PROPN
cuesj-478	115	36	�	�	PROPN
cuesj-478	115	37	�	�	PROPN
cuesj-478	115	38	�	�	PROPN
cuesj-478	115	39	�	�	PROPN
cuesj-478	115	40	�	�	PROPN
cuesj-478	115	41	�	�	PROPN
cuesj-478	115	42	�	�	PROPN
cuesj-478	115	43	�	�	PROPN
cuesj-478	115	44	�	�	PROPN
cuesj-478	115	45	�	�	PROPN
cuesj-478	115	46	�	�	PROPN
cuesj-478	115	47	�	�	PROPN
cuesj-478	115	48	�	�	PROPN
cuesj-478	115	49	�	�	PROPN
cuesj-478	115	50	�	�	PROPN
cuesj-478	115	51	�	�	PROPN
cuesj-478	115	52	�	�	PROPN
cuesj-478	115	53	a	a	DET
cuesj-478	115	54	a	a	DET
cuesj-478	115	55	a	a	DET
cuesj-478	115	56	�	�	PROPN
cuesj-478	115	57	�	�	PROPN
cuesj-478	115	58	�	�	PROPN
cuesj-478	115	59	�	�	PROPN
cuesj-478	115	60	�	�	PROPN
cuesj-478	115	61	�	�	PROPN
cuesj-478	115	62	�	�	PROPN
cuesj-478	115	63	�	�	PROPN
cuesj-478	115	64	�	�	PROPN
cuesj-478	115	65	�	�	PROPN
cuesj-478	115	66	�	�	PROPN
cuesj-478	115	67	�	�	PROPN
cuesj-478	115	68	�	�	PROPN
cuesj-478	115	69	�	�	PROPN
cuesj-478	115	70	�	�	PROPN
cuesj-478	115	71	5	5	NUM
cuesj-478	115	72	03921356237095	03921356237095	NUM
cuesj-478	115	73	0	0	NUM
cuesj-478	115	74	0	0	NUM
cuesj-478	115	75	.	.	PUNCT
cuesj-478	116	1	a	a	DET
cuesj-478	116	2	a	a	DET
cuesj-478	116	3	a	a	DET
cuesj-478	116	4	h	h	NOUN
cuesj-478	116	5	x	x	NOUN
cuesj-478	116	6	x	x	SYM
cuesj-478	116	7	0	0	NUM
cuesj-478	116	8	1	1	NUM
cuesj-478	116	9	2	2	NUM
cuesj-478	116	10	2	2	NUM
cuesj-478	116	11	2	2	NUM
cuesj-478	116	12	1	1	NUM
cuesj-478	116	13	3	3	NUM
cuesj-478	116	14	1	1	NUM
cuesj-478	116	15	2	2	NUM
cuesj-478	116	16	1	1	NUM
cuesj-478	116	17	6	6	NUM
cuesj-478	116	18	=	=	SYM
cuesj-478	116	19	=	=	SYM
cuesj-478	116	20	=	=	SYM
cuesj-478	117	1	=	=	PUNCT
cuesj-478	117	2	,	,	PUNCT
cuesj-478	117	3	,	,	PUNCT
cuesj-478	117	4	(	(	PUNCT
cuesj-478	117	5	)	)	PUNCT
cuesj-478	117	6	therefore	therefore	ADV
cuesj-478	117	7	,	,	PUNCT
cuesj-478	117	8	the	the	DET
cuesj-478	117	9	obtained	obtain	VERB
cuesj-478	117	10	solution	solution	NOUN
cuesj-478	117	11	is	be	AUX
cuesj-478	117	12	the	the	DET
cuesj-478	117	13	precise	precise	ADJ
cuesj-478	117	14	solution	solution	NOUN
cuesj-478	117	15	to	to	ADP
cuesj-478	117	16	this	this	DET
cuesj-478	117	17	problem	problem	NOUN
cuesj-478	117	18	.	.	PUNCT
cuesj-478	118	1	example	example	NOUN
cuesj-478	118	2	3	3	NUM
cuesj-478	118	3	:	:	PUNCT
cuesj-478	118	4	consider	consider	VERB
cuesj-478	118	5	the	the	DET
cuesj-478	118	6	following	follow	VERB
cuesj-478	118	7	problem	problem	NOUN
cuesj-478	118	8	with	with	ADP
cuesj-478	118	9	an	an	DET
cuesj-478	118	10	initial	initial	ADJ
cuesj-478	118	11	value	value	NOUN
cuesj-478	118	12	.	.	PUNCT
cuesj-478	119	1	d	d	NOUN
cuesj-478	119	2	h	h	NOUN
cuesj-478	120	1	x	x	PUNCT
cuesj-478	120	2	d	d	NOUN
cuesj-478	120	3	h	h	NOUN
cuesj-478	120	4	x	x	NOUN
cuesj-478	120	5	h	h	NOUN
cuesj-478	120	6	x	x	PUNCT
cuesj-478	120	7	x	x	SYM
cuesj-478	120	8	x4	x4	PROPN
cuesj-478	120	9	7	7	NUM
cuesj-478	120	10	2	2	NUM
cuesj-478	120	11	3	3	NUM
cuesj-478	120	12	9	9	NUM
cuesj-478	120	13	0	0	NUM
cuesj-478	120	14	1	1	NUM
cuesj-478	120	15	(	(	PUNCT
cuesj-478	120	16	(	(	PUNCT
cuesj-478	120	17	)	)	PUNCT
cuesj-478	120	18	)	)	PUNCT
cuesj-478	120	19	(	(	PUNCT
cuesj-478	120	20	(	(	PUNCT
cuesj-478	120	21	)	)	PUNCT
cuesj-478	120	22	)	)	PUNCT
cuesj-478	120	23	(	(	PUNCT
cuesj-478	120	24	)	)	PUNCT
cuesj-478	120	25	,	,	PUNCT
cuesj-478	120	26	(	(	PUNCT
cuesj-478	120	27	,	,	PUNCT
cuesj-478	120	28	]	]	PUNCT
cuesj-478	120	29	�	�	PROPN
cuesj-478	120	30	�	�	PROPN
cuesj-478	120	31	�	�	PROPN
cuesj-478	120	32	�	�	PROPN
cuesj-478	120	33	(	(	PUNCT
cuesj-478	120	34	18	18	NUM
cuesj-478	120	35	)	)	PUNCT
cuesj-478	120	36	with	with	ADP
cuesj-478	120	37	initial	initial	ADJ
cuesj-478	120	38	condition	condition	NOUN
cuesj-478	120	39	h(0)=0	h(0)=0	NOUN
cuesj-478	120	40	,	,	PUNCT
cuesj-478	120	41	h’(0)=	h’(0)=	NOUN
cuesj-478	120	42	h”(0)=0	h”(0)=0	ADJ
cuesj-478	120	43	and	and	CCONJ
cuesj-478	120	44	h”’(0)=6	h”’(0)=6	NOUN
cuesj-478	120	45	,	,	PUNCT
cuesj-478	120	46	n=4	n=4	X
cuesj-478	120	47	h	h	NOUN
cuesj-478	120	48	x	x	VERB
cuesj-478	120	49	a	a	DET
cuesj-478	120	50	e	e	NOUN
cuesj-478	120	51	a	a	X
cuesj-478	120	52	e	e	NOUN
cuesj-478	120	53	x	x	X
cuesj-478	120	54	a	a	DET
cuesj-478	120	55	e	e	NOUN
cuesj-478	120	56	x	x	X
cuesj-478	120	57	a	a	DET
cuesj-478	120	58	e	e	NOUN
cuesj-478	120	59	x	x	X
cuesj-478	120	60	a	a	DET
cuesj-478	120	61	e	e	NOUN
cuesj-478	120	62	x	x	X
cuesj-478	120	63	a	a	DET
cuesj-478	120	64	e	e	NOUN
cuesj-478	120	65	x	x	SYM
cuesj-478	120	66	h	h	NOUN
cuesj-478	121	1	n	n	CCONJ
cuesj-478	121	2	i	i	PRON
cuesj-478	122	1	i	i	PRON
cuesj-478	122	2	n	n	VERB
cuesj-478	122	3	i	i	PRON
cuesj-478	122	4	(	(	PUNCT
cuesj-478	122	5	)	)	PUNCT
cuesj-478	122	6	(	(	PUNCT
cuesj-478	122	7	)	)	PUNCT
cuesj-478	122	8	(	(	PUNCT
cuesj-478	122	9	)	)	PUNCT
cuesj-478	122	10	(	(	PUNCT
cuesj-478	122	11	)	)	PUNCT
cuesj-478	122	12	(	(	PUNCT
cuesj-478	122	13	)	)	PUNCT
cuesj-478	122	14	(	(	PUNCT
cuesj-478	122	15	)	)	PUNCT
cuesj-478	122	16	(	(	PUNCT
cuesj-478	122	17	�	�	PROPN
cuesj-478	122	18	�	�	PROPN
cuesj-478	122	19	�	�	PROPN
cuesj-478	122	20	�	�	PROPN
cuesj-478	122	21	�	�	PROPN
cuesj-478	122	22	�	�	PROPN
cuesj-478	122	23	�	�	PROPN
cuesj-478	122	24	�	�	PROPN
cuesj-478	122	25	0	0	NUM
cuesj-478	122	26	0	0	NUM
cuesj-478	122	27	0	0	NUM
cuesj-478	122	28	1	1	NUM
cuesj-478	122	29	1	1	NUM
cuesj-478	122	30	2	2	NUM
cuesj-478	122	31	2	2	NUM
cuesj-478	122	32	3	3	NUM
cuesj-478	122	33	3	3	NUM
cuesj-478	122	34	4	4	NUM
cuesj-478	122	35	4	4	NUM
cuesj-478	122	36	4	4	NUM
cuesj-478	122	37	xx	xx	NUM
cuesj-478	122	38	a	a	DET
cuesj-478	122	39	x	x	NOUN
cuesj-478	122	40	a	a	DET
cuesj-478	122	41	a	a	NOUN
cuesj-478	122	42	x	x	NOUN
cuesj-478	122	43	a	a	DET
cuesj-478	122	44	a	a	PRON
cuesj-478	122	45	a	a	NOUN
cuesj-478	122	46	x	x	NOUN
cuesj-478	122	47	a	a	DET
cuesj-478	122	48	a	a	DET
cuesj-478	122	49	a	a	DET
cuesj-478	122	50	)	)	PUNCT
cuesj-478	122	51	�	�	PROPN
cuesj-478	122	52	�	�	PROPN
cuesj-478	122	53	�	�	PROPN
cuesj-478	122	54	�	�	PROPN
cuesj-478	122	55	�	�	PROPN
cuesj-478	122	56	�	�	PROPN
cuesj-478	122	57	�	�	PROPN
cuesj-478	122	58	�	�	PROPN
cuesj-478	122	59	�	�	PROPN
cuesj-478	122	60	�	�	PROPN
cuesj-478	122	61	�	�	PROPN
cuesj-478	122	62	�	�	PROPN
cuesj-478	122	63	�	�	PROPN
cuesj-478	122	64	�	�	PROPN
cuesj-478	122	65	70	70	NUM
cuesj-478	122	66	20	20	NUM
cuesj-478	122	67	140	140	NUM
cuesj-478	122	68	6	6	NUM
cuesj-478	122	69	30	30	NUM
cuesj-478	122	70	90	90	NUM
cuesj-478	122	71	2	2	NUM
cuesj-478	122	72	6	6	NUM
cuesj-478	122	73	12	12	NUM
cuesj-478	122	74	2	2	NUM
cuesj-478	122	75	4	4	NUM
cuesj-478	122	76	4	4	NUM
cuesj-478	122	77	3	3	NUM
cuesj-478	122	78	4	4	NUM
cuesj-478	122	79	3	3	NUM
cuesj-478	122	80	2	2	NUM
cuesj-478	122	81	3	3	NUM
cuesj-478	122	82	4	4	NUM
cuesj-478	122	83	2	2	NUM
cuesj-478	122	84	1	1	NUM
cuesj-478	122	85	2	2	NUM
cuesj-478	122	86	3	3	NUM
cuesj-478	122	87	00	00	NUM
cuesj-478	122	88	4	4	NUM
cuesj-478	122	89	0	0	NUM
cuesj-478	122	90	1	1	NUM
cuesj-478	122	91	2	2	NUM
cuesj-478	122	92	3	3	NUM
cuesj-478	122	93	4a	4a	NOUN
cuesj-478	122	94	x	x	PUNCT
cuesj-478	122	95	a	a	DET
cuesj-478	122	96	a	a	DET
cuesj-478	122	97	a	a	DET
cuesj-478	122	98	a	a	DET
cuesj-478	122	99	a	a	DET
cuesj-478	122	100	�	�	PROPN
cuesj-478	122	101	�	�	PROPN
cuesj-478	122	102	�	�	PROPN
cuesj-478	122	103	�	�	PROPN
cuesj-478	122	104	�	�	PROPN
cuesj-478	122	105	�	�	PROPN
cuesj-478	122	106	�	�	PROPN
cuesj-478	122	107	for	for	ADP
cuesj-478	122	108	finding	find	VERB
cuesj-478	122	109	n+1	n+1	NUM
cuesj-478	122	110	equation	equation	NOUN
cuesj-478	122	111	we	we	PRON
cuesj-478	122	112	need	need	VERB
cuesj-478	122	113	use	use	VERB
cuesj-478	122	114	the	the	DET
cuesj-478	122	115	root	root	NOUN
cuesj-478	122	116	of	of	ADP
cuesj-478	122	117	the	the	DET
cuesj-478	122	118	polynomial	polynomial	ADJ
cuesj-478	122	119	e	e	NOUN
cuesj-478	122	120	x	x	PUNCT
cuesj-478	122	121	e	e	NOUN
cuesj-478	122	122	x	x	SYM
cuesj-478	122	123	x	x	SYM
cuesj-478	122	124	x	x	SYM
cuesj-478	122	125	n	n	PRON
cuesj-478	122	126	�	�	PROPN
cuesj-478	122	127	�	�	PROPN
cuesj-478	122	128	�	�	PROPN
cuesj-478	122	129	�	�	PROPN
cuesj-478	122	130	�	�	PROPN
cuesj-478	122	131	�	�	PROPN
cuesj-478	122	132	�	�	PROPN
cuesj-478	122	133	�	�	PROPN
cuesj-478	122	134	1	1	NUM
cuesj-478	122	135	1	1	NUM
cuesj-478	122	136	2	2	NUM
cuesj-478	122	137	1	1	NUM
cuesj-478	122	138	0	0	NUM
cuesj-478	122	139	0	0	NUM
cuesj-478	122	140	5	5	NUM
cuesj-478	122	141	�	�	PROPN
cuesj-478	122	142	(	(	PUNCT
cuesj-478	122	143	)	)	PUNCT
cuesj-478	122	144	(	(	PUNCT
cuesj-478	122	145	)	)	PUNCT
cuesj-478	122	146	.	.	PUNCT
cuesj-478	123	1	so	so	ADV
cuesj-478	123	2	we	we	PRON
cuesj-478	123	3	put	put	VERB
cuesj-478	123	4	the	the	DET
cuesj-478	123	5	root	root	NOUN
cuesj-478	123	6	in	in	ADP
cuesj-478	123	7	the	the	DET
cuesj-478	123	8	equation	equation	NOUN
cuesj-478	123	9	(	(	PUNCT
cuesj-478	123	10	19	19	NUM
cuesj-478	123	11	)	)	PUNCT
cuesj-478	123	12	after	after	ADP
cuesj-478	123	13	,	,	PUNCT
cuesj-478	123	14	we	we	PRON
cuesj-478	123	15	calculate	calculate	VERB
cuesj-478	123	16	all	all	DET
cuesj-478	123	17	structure	structure	NOUN
cuesj-478	123	18	instead	instead	ADV
cuesj-478	123	19	each	each	DET
cuesj-478	123	20	x	x	SYM
cuesj-478	123	21	variable	variable	NOUN
cuesj-478	124	1	so	so	SCONJ
cuesj-478	124	2	our	our	PRON
cuesj-478	124	3	equation	equation	NOUN
cuesj-478	124	4	is	be	AUX
cuesj-478	124	5	a	a	DET
cuesj-478	124	6	a	a	DET
cuesj-478	124	7	a	a	DET
cuesj-478	124	8	a0	a0	NOUN
cuesj-478	124	9	2	2	NUM
cuesj-478	124	10	4	4	NUM
cuesj-478	124	11	3	3	NUM
cuesj-478	124	12	42	42	NUM
cuesj-478	124	13	3	3	NUM
cuesj-478	124	14	8	8	NUM
cuesj-478	124	15	1680	1680	NUM
cuesj-478	124	16	840	840	NUM
cuesj-478	124	17	2	2	NUM
cuesj-478	124	18	1	1	NUM
cuesj-478	124	19	512	512	NUM
cuesj-478	124	20	0	0	NUM
cuesj-478	124	21	1	1	NUM
cuesj-478	124	22	�	�	PROPN
cuesj-478	124	23	�	�	PROPN
cuesj-478	124	24	�	�	PROPN
cuesj-478	124	25	�	�	PROPN
cuesj-478	124	26	�	�	PROPN
cuesj-478	124	27	�	�	PROPN
cuesj-478	124	28	�	�	PROPN
cuesj-478	124	29	�	�	PROPN
cuesj-478	124	30	�	�	PROPN
cuesj-478	124	31	�	�	PROPN
cuesj-478	124	32	�	�	PROPN
cuesj-478	124	33	�	�	PROPN
cuesj-478	124	34	�	�	PROPN
cuesj-478	124	35	�	�	PROPN
cuesj-478	124	36	�	�	PROPN
cuesj-478	124	37	(	(	PUNCT
cuesj-478	124	38	)	)	PUNCT
cuesj-478	124	39	so	so	ADV
cuesj-478	124	40	by	by	ADP
cuesj-478	124	41	initial	initial	ADJ
cuesj-478	124	42	condition	condition	NOUN
cuesj-478	124	43	,	,	PUNCT
cuesj-478	124	44	we	we	PRON
cuesj-478	124	45	have	have	VERB
cuesj-478	124	46	α	α	PRON
cuesj-478	124	47	equation	equation	NOUN
cuesj-478	124	48	h	h	NOUN
cuesj-478	124	49	a	a	DET
cuesj-478	124	50	a	a	DET
cuesj-478	124	51	a	a	DET
cuesj-478	124	52	a	a	DET
cuesj-478	124	53	a	a	DET
cuesj-478	124	54	h	h	NOUN
cuesj-478	124	55	a	a	DET
cuesj-478	124	56	a	a	DET
cuesj-478	124	57	a	a	DET
cuesj-478	124	58	ad	ad	NOUN
cuesj-478	124	59	4	4	NUM
cuesj-478	124	60	0	0	NUM
cuesj-478	124	61	1	1	NUM
cuesj-478	124	62	2	2	NUM
cuesj-478	124	63	3	3	NUM
cuesj-478	124	64	4	4	NUM
cuesj-478	124	65	1	1	NUM
cuesj-478	124	66	4	4	NUM
cuesj-478	124	67	1	1	NUM
cuesj-478	124	68	2	2	NUM
cuesj-478	124	69	3	3	NUM
cuesj-478	124	70	4	4	NUM
cuesj-478	124	71	0	0	NUM
cuesj-478	124	72	0	0	NUM
cuesj-478	124	73	2	2	NUM
cuesj-478	124	74	0	0	NUM
cuesj-478	124	75	2	2	NUM
cuesj-478	124	76	6	6	NUM
cuesj-478	124	77	12	12	NUM
cuesj-478	124	78	20	20	NUM
cuesj-478	124	79	0	0	NUM
cuesj-478	124	80	3	3	NUM
cuesj-478	124	81	(	(	PUNCT
cuesj-478	124	82	)	)	PUNCT
cuesj-478	124	83	(	(	PUNCT
cuesj-478	124	84	)	)	PUNCT
cuesj-478	124	85	(	(	PUNCT
cuesj-478	124	86	(	(	PUNCT
cuesj-478	124	87	)	)	PUNCT
cuesj-478	124	88	)	)	PUNCT
cuesj-478	125	1	(	(	PUNCT
cuesj-478	125	2	�	�	PROPN
cuesj-478	125	3	�	�	PROPN
cuesj-478	125	4	�	�	PROPN
cuesj-478	125	5	�	�	PROPN
cuesj-478	125	6	�	�	PROPN
cuesj-478	125	7	�	�	PROPN
cuesj-478	125	8	�	�	PROPN
cuesj-478	125	9	�	�	PROPN
cuesj-478	125	10	�	�	PROPN
cuesj-478	125	11	�	�	PROPN
cuesj-478	125	12	�	�	PROPN
cuesj-478	125	13	�	�	PROPN
cuesj-478	125	14	�	�	PROPN
cuesj-478	125	15	)	)	PUNCT
cuesj-478	125	16	)	)	PUNCT
cuesj-478	126	1	(	(	PUNCT
cuesj-478	126	2	(	(	PUNCT
cuesj-478	126	3	)	)	PUNCT
cuesj-478	126	4	)	)	PUNCT
cuesj-478	126	5	(	(	PUNCT
cuesj-478	126	6	)	)	PUNCT
cuesj-478	126	7	(	(	PUNCT
cuesj-478	126	8	(	(	PUNCT
cuesj-478	126	9	)	)	PUNCT
cuesj-478	126	10	)	)	PUNCT
cuesj-478	127	1	d	d	X
cuesj-478	128	1	d	d	X
cuesj-478	128	2	h	h	NOUN
cuesj-478	128	3	a	a	DET
cuesj-478	128	4	a	a	DET
cuesj-478	128	5	a	a	DET
cuesj-478	128	6	h	h	NOUN
cuesj-478	128	7	a	a	DET
cuesj-478	128	8	a	a	DET
cuesj-478	128	9	2	2	NUM
cuesj-478	128	10	4	4	NUM
cuesj-478	128	11	2	2	NUM
cuesj-478	128	12	3	3	NUM
cuesj-478	128	13	4	4	NUM
cuesj-478	128	14	3	3	NUM
cuesj-478	128	15	4	4	NUM
cuesj-478	128	16	3	3	NUM
cuesj-478	128	17	4	4	NUM
cuesj-478	128	18	0	0	NUM
cuesj-478	128	19	12	12	NUM
cuesj-478	128	20	60	60	NUM
cuesj-478	128	21	180	180	NUM
cuesj-478	128	22	0	0	NUM
cuesj-478	128	23	4	4	NUM
cuesj-478	128	24	0	0	NUM
cuesj-478	128	25	120	120	NUM
cuesj-478	128	26	840	840	NUM
cuesj-478	128	27	6	6	NUM
cuesj-478	128	28	0	0	NUM
cuesj-478	128	29	�	�	PROPN
cuesj-478	128	30	�	�	PROPN
cuesj-478	128	31	�	�	PROPN
cuesj-478	128	32	�	�	PROPN
cuesj-478	128	33	�	�	PROPN
cuesj-478	128	34	�	�	PROPN
cuesj-478	128	35	�	�	PROPN
cuesj-478	128	36	�	�	PROPN
cuesj-478	128	37	�	�	PROPN
cuesj-478	128	38	�	�	PROPN
cuesj-478	128	39	�	�	PROPN
cuesj-478	128	40	(	(	PUNCT
cuesj-478	128	41	)	)	PUNCT
cuesj-478	128	42	5	5	NUM
cuesj-478	128	43	now	now	ADV
cuesj-478	128	44	use	use	VERB
cuesj-478	128	45	newton	newton	PROPN
cuesj-478	128	46	iteration	iteration	NOUN
cuesj-478	128	47	method	method	NOUN
cuesj-478	128	48	for	for	ADP
cuesj-478	128	49	finding	find	VERB
cuesj-478	128	50	the	the	DET
cuesj-478	128	51	messing	mess	VERB
cuesj-478	128	52	variable	variable	NOUN
cuesj-478	128	53	and	and	CCONJ
cuesj-478	128	54	our	our	PRON
cuesj-478	128	55	result	result	NOUN
cuesj-478	128	56	will	will	AUX
cuesj-478	128	57	be	be	AUX
cuesj-478	128	58	a	a	DET
cuesj-478	128	59	a	a	DET
cuesj-478	128	60	a	a	DET
cuesj-478	128	61	a	a	NOUN
cuesj-478	128	62	and	and	CCONJ
cuesj-478	128	63	a0	a0	NOUN
cuesj-478	128	64	1	1	NUM
cuesj-478	128	65	2	2	NUM
cuesj-478	128	66	3	3	NUM
cuesj-478	128	67	4	4	NUM
cuesj-478	128	68	1	1	NUM
cuesj-478	128	69	4	4	NUM
cuesj-478	128	70	9	9	NUM
cuesj-478	128	71	20	20	NUM
cuesj-478	128	72	1	1	NUM
cuesj-478	128	73	4	4	NUM
cuesj-478	128	74	1	1	NUM
cuesj-478	128	75	20	20	NUM
cuesj-478	128	76	0=	0=	NUM
cuesj-478	129	1	=	=	PUNCT
cuesj-478	129	2	=	=	PUNCT
cuesj-478	130	1	=	=	PUNCT
cuesj-478	130	2	=	=	PROPN
cuesj-478	130	3	,	,	PUNCT
cuesj-478	130	4	,	,	PUNCT
cuesj-478	130	5	,	,	PUNCT
cuesj-478	130	6	mahmood	mahmood	PROPN
cuesj-478	130	7	,	,	PUNCT
cuesj-478	130	8	et	et	PROPN
cuesj-478	130	9	al	al	PROPN
cuesj-478	130	10	.	.	PUNCT
cuesj-478	130	11	:	:	PUNCT
cuesj-478	131	1	multi	multi	ADJ
cuesj-478	131	2	-	-	ADJ
cuesj-478	131	3	order	order	NOUN
cuesj-478	131	4	fde	fde	NOUN
cuesj-478	131	5	based	base	VERB
cuesj-478	131	6	on	on	ADP
cuesj-478	131	7	cd	cd	PROPN
cuesj-478	131	8	by	by	ADP
cuesj-478	131	9	shifted	shift	VERB
cuesj-478	131	10	lp	lp	NUM
cuesj-478	131	11	67	67	NUM
cuesj-478	131	12	http://journals.cihanuniversity.edu.iq/index.php/cuesj	http://journals.cihanuniversity.edu.iq/index.php/cuesj	ADJ
cuesj-478	131	13	cuesj	cuesj	ADJ
cuesj-478	131	14	2021	2021	NUM
cuesj-478	131	15	,	,	PUNCT
cuesj-478	131	16	5	5	NUM
cuesj-478	131	17	(	(	PUNCT
cuesj-478	131	18	2	2	NUM
cuesj-478	131	19	):	):	PUNCT
cuesj-478	131	20	64	64	NUM
cuesj-478	131	21	-	-	SYM
cuesj-478	131	22	68	68	NUM
cuesj-478	131	23	if	if	SCONJ
cuesj-478	131	24	we	we	PRON
cuesj-478	131	25	put	put	VERB
cuesj-478	131	26	those	those	DET
cuesj-478	131	27	number	number	NOUN
cuesj-478	131	28	in	in	ADP
cuesj-478	131	29	our	our	PRON
cuesj-478	131	30	h4	h4	NOUN
cuesj-478	131	31	(	(	PUNCT
cuesj-478	131	32	x	x	X
cuesj-478	131	33	)	)	PUNCT
cuesj-478	131	34	our	our	PRON
cuesj-478	131	35	result	result	NOUN
cuesj-478	131	36	will	will	AUX
cuesj-478	131	37	be	be	AUX
cuesj-478	131	38	h4	h4	PROPN
cuesj-478	131	39	(	(	PUNCT
cuesj-478	131	40	x)=x3	x)=x3	NUM
cuesj-478	131	41	which	which	PRON
cuesj-478	131	42	is	be	AUX
cuesj-478	131	43	the	the	DET
cuesj-478	131	44	precise	precise	ADJ
cuesj-478	131	45	solution	solution	NOUN
cuesj-478	131	46	to	to	ADP
cuesj-478	131	47	this	this	DET
cuesj-478	131	48	issue	issue	NOUN
cuesj-478	131	49	.	.	PUNCT
cuesj-478	132	1	conclusion	conclusion	NOUN
cuesj-478	132	2	in	in	ADP
cuesj-478	132	3	this	this	DET
cuesj-478	132	4	paper	paper	NOUN
cuesj-478	132	5	,	,	PUNCT
cuesj-478	132	6	using	use	VERB
cuesj-478	132	7	the	the	DET
cuesj-478	132	8	method	method	NOUN
cuesj-478	132	9	and	and	CCONJ
cuesj-478	132	10	technique	technique	NOUN
cuesj-478	132	11	for	for	ADP
cuesj-478	132	12	get	get	VERB
cuesj-478	132	13	approximate	approximate	ADJ
cuesj-478	132	14	solution	solution	NOUN
cuesj-478	132	15	of	of	ADP
cuesj-478	132	16	fractional	fractional	ADJ
cuesj-478	132	17	differential	differential	ADJ
cuesj-478	132	18	equations	equation	NOUN
cuesj-478	132	19	with	with	ADP
cuesj-478	132	20	initial	initial	ADJ
cuesj-478	132	21	conditions	condition	NOUN
cuesj-478	132	22	and	and	CCONJ
cuesj-478	132	23	conformable	conformable	ADJ
cuesj-478	132	24	sense	sense	NOUN
cuesj-478	132	25	are	be	AUX
cuesj-478	132	26	used	use	VERB
cuesj-478	132	27	to	to	PART
cuesj-478	132	28	characterize	characterize	VERB
cuesj-478	132	29	the	the	DET
cuesj-478	132	30	fractional	fractional	ADJ
cuesj-478	132	31	derivatives	derivative	NOUN
cuesj-478	132	32	,	,	PUNCT
cuesj-478	132	33	the	the	DET
cuesj-478	132	34	solution	solution	NOUN
cuesj-478	132	35	can	can	AUX
cuesj-478	132	36	be	be	AUX
cuesj-478	132	37	easily	easily	ADV
cuesj-478	132	38	analyzed	analyze	VERB
cuesj-478	132	39	for	for	ADP
cuesj-478	132	40	any	any	DET
cuesj-478	132	41	number	number	NOUN
cuesj-478	132	42	of	of	ADP
cuesj-478	132	43	different	different	ADJ
cuesj-478	132	44	values	value	NOUN
cuesj-478	132	45	of	of	ADP
cuesj-478	132	46	x	x	PRON
cuesj-478	132	47	since	since	SCONJ
cuesj-478	132	48	it	it	PRON
cuesj-478	132	49	is	be	AUX
cuesj-478	132	50	written	write	VERB
cuesj-478	132	51	as	as	ADP
cuesj-478	132	52	a	a	DET
cuesj-478	132	53	truncated	truncated	ADJ
cuesj-478	132	54	legendre	legendre	PROPN
cuesj-478	132	55	series	series	PROPN
cuesj-478	132	56	.	.	PUNCT
cuesj-478	133	1	furthermore	furthermore	ADV
cuesj-478	133	2	,	,	PUNCT
cuesj-478	133	3	the	the	DET
cuesj-478	133	4	suggested	suggest	VERB
cuesj-478	133	5	strategy	strategy	NOUN
cuesj-478	133	6	’s	’s	PART
cuesj-478	133	7	validity	validity	NOUN
cuesj-478	133	8	and	and	CCONJ
cuesj-478	133	9	applicability	applicability	NOUN
cuesj-478	133	10	are	be	AUX
cuesj-478	133	11	proved	prove	VERB
cuesj-478	133	12	by	by	ADP
cuesj-478	133	13	numerical	numerical	ADJ
cuesj-478	133	14	findings	finding	NOUN
cuesj-478	133	15	.	.	PUNCT
cuesj-478	134	1	the	the	DET
cuesj-478	134	2	numerical	numerical	ADJ
cuesj-478	134	3	results	result	NOUN
cuesj-478	134	4	show	show	VERB
cuesj-478	134	5	that	that	SCONJ
cuesj-478	134	6	as	as	SCONJ
cuesj-478	134	7	the	the	DET
cuesj-478	134	8	number	number	NOUN
cuesj-478	134	9	of	of	ADP
cuesj-478	134	10	n	n	PRON
cuesj-478	134	11	terms	term	NOUN
cuesj-478	134	12	is	be	AUX
cuesj-478	134	13	raised	raise	VERB
cuesj-478	134	14	,	,	PUNCT
cuesj-478	134	15	the	the	DET
cuesj-478	134	16	method	method	NOUN
cuesj-478	134	17	converges	converge	VERB
cuesj-478	134	18	.	.	PUNCT
cuesj-478	135	1	with	with	ADP
cuesj-478	135	2	tiny	tiny	ADJ
cuesj-478	135	3	n	n	CCONJ
cuesj-478	135	4	,	,	PUNCT
cuesj-478	135	5	we	we	PRON
cuesj-478	135	6	get	get	VERB
cuesj-478	135	7	the	the	DET
cuesj-478	135	8	precise	precise	ADJ
cuesj-478	135	9	answer	answer	NOUN
cuesj-478	135	10	for	for	ADP
cuesj-478	135	11	several	several	ADJ
cuesj-478	135	12	examples	example	NOUN
cuesj-478	135	13	,	,	PUNCT
cuesj-478	135	14	all	all	DET
cuesj-478	135	15	examples	example	NOUN
cuesj-478	135	16	are	be	AUX
cuesj-478	135	17	achieved	achieve	VERB
cuesj-478	135	18	by	by	ADP
cuesj-478	135	19	the	the	DET
cuesj-478	135	20	use	use	NOUN
cuesj-478	135	21	of	of	ADP
cuesj-478	135	22	python	python	NOUN
cuesj-478	135	23	programming	programming	NOUN
cuesj-478	135	24	to	to	PART
cuesj-478	135	25	create	create	VERB
cuesj-478	135	26	quick	quick	ADJ
cuesj-478	135	27	algorithms	algorithm	NOUN
cuesj-478	135	28	.	.	PUNCT
cuesj-478	136	1	the	the	DET
cuesj-478	136	2	method	method	NOUN
cuesj-478	136	3	presented	present	VERB
cuesj-478	136	4	here	here	ADV
cuesj-478	136	5	can	can	AUX
cuesj-478	136	6	be	be	AUX
cuesj-478	136	7	used	use	VERB
cuesj-478	136	8	to	to	PART
cuesj-478	136	9	solve	solve	VERB
cuesj-478	136	10	the	the	DET
cuesj-478	136	11	high	high	ADJ
cuesj-478	136	12	order	order	NOUN
cuesj-478	136	13	of	of	ADP
cuesj-478	136	14	n	n	PRON
cuesj-478	136	15	for	for	ADP
cuesj-478	136	16	conformable	conformable	ADJ
cuesj-478	136	17	fractional	fractional	ADJ
cuesj-478	136	18	differential	differential	ADJ
cuesj-478	136	19	equations	equation	NOUN
cuesj-478	136	20	as	as	ADV
cuesj-478	136	21	well	well	ADV
cuesj-478	136	22	as	as	ADP
cuesj-478	136	23	conformable	conformable	ADJ
cuesj-478	136	24	fractional	fractional	ADJ
cuesj-478	136	25	partial	partial	ADJ
cuesj-478	136	26	differential	differential	NOUN
cuesj-478	136	27	equations	equation	NOUN
cuesj-478	136	28	.	.	PUNCT
cuesj-478	137	1	references	reference	NOUN
cuesj-478	137	2	1	1	NUM
cuesj-478	137	3	.	.	PUNCT
cuesj-478	137	4	h.	h.	PROPN
cuesj-478	137	5	khalil	khalil	PROPN
cuesj-478	137	6	,	,	PUNCT
cuesj-478	137	7	r.	r.	PROPN
cuesj-478	137	8	h.	h.	PROPN
cuesj-478	137	9	ali	ali	PROPN
cuesj-478	137	10	khan	khan	PROPN
cuesj-478	137	11	,	,	PUNCT
cuesj-478	137	12	m.	m.	NOUN
cuesj-478	137	13	a	a	DET
cuesj-478	137	14	al	al	PROPN
cuesj-478	137	15	-	-	PUNCT
cuesj-478	137	16	smadi	smadi	NOUN
cuesj-478	137	17	,	,	PUNCT
cuesj-478	137	18	a.	a.	NOUN
cuesj-478	137	19	freihat	freihat	PROPN
cuesj-478	137	20	and	and	CCONJ
cuesj-478	137	21	n.	n.	PROPN
cuesj-478	137	22	shawagfeh	shawagfeh	NOUN
cuesj-478	137	23	.	.	PUNCT
cuesj-478	138	1	new	new	ADJ
cuesj-478	138	2	operational	operational	ADJ
cuesj-478	138	3	matrix	matrix	NOUN
cuesj-478	138	4	for	for	ADP
cuesj-478	138	5	shifted	shift	VERB
cuesj-478	138	6	legendre	legendre	PROPN
cuesj-478	138	7	polynomials	polynomial	NOUN
cuesj-478	138	8	.	.	PUNCT
cuesj-478	139	1	punjab	punjab	PROPN
cuesj-478	139	2	university	university	PROPN
cuesj-478	139	3	journal	journal	NOUN
cuesj-478	139	4	of	of	ADP
cuesj-478	139	5	mathematics	mathematics	PROPN
cuesj-478	139	6	,	,	PUNCT
cuesj-478	139	7	vol	vol	NOUN
cuesj-478	139	8	.	.	PROPN
cuesj-478	140	1	47	47	NUM
cuesj-478	140	2	,	,	PUNCT
cuesj-478	140	3	no	no	INTJ
cuesj-478	140	4	.	.	NOUN
cuesj-478	140	5	1	1	NUM
cuesj-478	140	6	,	,	PUNCT
cuesj-478	140	7	pp	pp	ADJ
cuesj-478	140	8	.	.	PUNCT
cuesj-478	141	1	1	1	NUM
cuesj-478	141	2	-	-	SYM
cuesj-478	141	3	23	23	NUM
cuesj-478	141	4	,	,	PUNCT
cuesj-478	141	5	2020	2020	NUM
cuesj-478	141	6	.	.	PUNCT
cuesj-478	142	1	2	2	X
cuesj-478	142	2	.	.	X
cuesj-478	142	3	r.	r.	PROPN
cuesj-478	142	4	a.	a.	PROPN
cuesj-478	142	5	khalil	khalil	PROPN
cuesj-478	142	6	.	.	PUNCT
cuesj-478	143	1	a	a	DET
cuesj-478	143	2	new	new	ADJ
cuesj-478	143	3	definition	definition	NOUN
cuesj-478	143	4	of	of	ADP
cuesj-478	143	5	fractional	fractional	ADJ
cuesj-478	143	6	derivative	derivative	NOUN
cuesj-478	143	7	.	.	PUNCT
cuesj-478	144	1	journal	journal	PROPN
cuesj-478	144	2	of	of	ADP
cuesj-478	144	3	computational	computational	ADJ
cuesj-478	144	4	and	and	CCONJ
cuesj-478	144	5	applied	applied	ADJ
cuesj-478	144	6	mathematics	mathematic	NOUN
cuesj-478	144	7	,	,	PUNCT
cuesj-478	144	8	vol	vol	NOUN
cuesj-478	144	9	.	.	PROPN
cuesj-478	144	10	264	264	NUM
cuesj-478	144	11	,	,	PUNCT
cuesj-478	144	12	pp	pp	ADJ
cuesj-478	144	13	.	.	PUNCT
cuesj-478	145	1	65	65	NUM
cuesj-478	145	2	-	-	SYM
cuesj-478	145	3	70	70	NUM
cuesj-478	145	4	,	,	PUNCT
cuesj-478	145	5	2014	2014	NUM
cuesj-478	145	6	.	.	PUNCT
cuesj-478	146	1	3	3	X
cuesj-478	146	2	.	.	PUNCT
cuesj-478	146	3	a.	a.	PROPN
cuesj-478	146	4	b.	b.	PROPN
cuesj-478	146	5	kisabo	kisabo	PROPN
cuesj-478	146	6	,	,	PUNCT
cuesj-478	146	7	u.	u.	PROPN
cuesj-478	146	8	c.	c.	PROPN
cuesj-478	146	9	uchenna	uchenna	PROPN
cuesj-478	146	10	,	,	PUNCT
cuesj-478	146	11	and	and	CCONJ
cuesj-478	146	12	f.	f.	PROPN
cuesj-478	146	13	a.	a.	PROPN
cuesj-478	146	14	adebimpe	adebimpe	PROPN
cuesj-478	146	15	.	.	PUNCT
cuesj-478	147	1	newton	newton	PROPN
cuesj-478	147	2	’s	’s	PART
cuesj-478	147	3	method	method	NOUN
cuesj-478	147	4	for	for	ADP
cuesj-478	147	5	solving	solve	VERB
cuesj-478	147	6	non	non	ADJ
cuesj-478	147	7	-	-	ADJ
cuesj-478	147	8	linear	linear	ADJ
cuesj-478	147	9	system	system	NOUN
cuesj-478	147	10	of	of	ADP
cuesj-478	147	11	algebraic	algebraic	ADJ
cuesj-478	147	12	equations	equation	NOUN
cuesj-478	147	13	(	(	PUNCT
cuesj-478	147	14	nlsaes	nlsaes	NOUN
cuesj-478	147	15	)	)	PUNCT
cuesj-478	147	16	with	with	ADP
cuesj-478	147	17	matlab	matlab	PROPN
cuesj-478	147	18	/	/	SYM
cuesj-478	147	19	simulink	simulink	PROPN
cuesj-478	147	20	®	®	PROPN
cuesj-478	147	21	and	and	CCONJ
cuesj-478	147	22	maple	maple	PROPN
cuesj-478	147	23	®	®	PROPN
cuesj-478	147	24	.	.	PUNCT
cuesj-478	148	1	american	american	PROPN
cuesj-478	148	2	journal	journal	PROPN
cuesj-478	148	3	of	of	ADP
cuesj-478	148	4	mathematical	mathematical	ADJ
cuesj-478	148	5	and	and	CCONJ
cuesj-478	148	6	computer	computer	NOUN
cuesj-478	148	7	modelling	modelling	NOUN
cuesj-478	148	8	,	,	PUNCT
cuesj-478	148	9	vol	vol	NOUN
cuesj-478	148	10	.	.	PROPN
cuesj-478	148	11	2	2	NUM
cuesj-478	148	12	,	,	PUNCT
cuesj-478	148	13	no	no	INTJ
cuesj-478	148	14	.	.	NOUN
cuesj-478	148	15	4	4	NUM
cuesj-478	148	16	,	,	PUNCT
cuesj-478	148	17	pp	pp	ADJ
cuesj-478	148	18	.	.	PUNCT
cuesj-478	149	1	117	117	NUM
cuesj-478	149	2	-	-	SYM
cuesj-478	149	3	131	131	NUM
cuesj-478	149	4	,	,	PUNCT
cuesj-478	149	5	2017	2017	NUM
cuesj-478	149	6	.	.	PUNCT
cuesj-478	150	1	4	4	X
cuesj-478	150	2	.	.	X
cuesj-478	150	3	s.	s.	PROPN
cuesj-478	150	4	s.	s.	PROPN
cuesj-478	150	5	ezz	ezz	PROPN
cuesj-478	150	6	-	-	PUNCT
cuesj-478	150	7	eldien	eldien	PROPN
cuesj-478	150	8	,	,	PUNCT
cuesj-478	150	9	j.	j.	PROPN
cuesj-478	150	10	a.	a.	PROPN
cuesj-478	150	11	machado	machado	PROPN
cuesj-478	150	12	,	,	PUNCT
cuesj-478	150	13	y.	y.	PROPN
cuesj-478	150	14	wang	wang	PROPN
cuesj-478	150	15	and	and	CCONJ
cuesj-478	150	16	a.	a.	NOUN
cuesj-478	150	17	a.	a.	NOUN
cuesj-478	150	18	aldraiweesh	aldraiweesh	PROPN
cuesj-478	150	19	.	.	PUNCT
cuesj-478	151	1	an	an	DET
cuesj-478	151	2	algorithm	algorithm	NOUN
cuesj-478	151	3	for	for	ADP
cuesj-478	151	4	the	the	DET
cuesj-478	151	5	approximate	approximate	ADJ
cuesj-478	151	6	solution	solution	NOUN
cuesj-478	151	7	of	of	ADP
cuesj-478	151	8	the	the	DET
cuesj-478	151	9	fractional	fractional	ADJ
cuesj-478	151	10	riccati	riccati	PROPN
cuesj-478	151	11	differential	differential	NOUN
cuesj-478	151	12	equation	equation	NOUN
cuesj-478	151	13	.	.	PUNCT
cuesj-478	152	1	international	international	ADJ
cuesj-478	152	2	journal	journal	PROPN
cuesj-478	152	3	of	of	ADP
cuesj-478	152	4	nonlinear	nonlinear	PROPN
cuesj-478	152	5	sciences	sciences	PROPN
cuesj-478	152	6	and	and	CCONJ
cuesj-478	152	7	numerical	numerical	PROPN
cuesj-478	152	8	simulation	simulation	PROPN
cuesj-478	152	9	,	,	PUNCT
cuesj-478	152	10	vol	vol	NOUN
cuesj-478	152	11	.	.	PROPN
cuesj-478	152	12	20	20	NUM
cuesj-478	152	13	,	,	PUNCT
cuesj-478	152	14	no	no	INTJ
cuesj-478	152	15	.	.	NOUN
cuesj-478	152	16	6	6	NUM
cuesj-478	152	17	,	,	PUNCT
cuesj-478	152	18	pp	pp	ADJ
cuesj-478	152	19	.	.	PUNCT
cuesj-478	153	1	661	661	NUM
cuesj-478	153	2	-	-	SYM
cuesj-478	153	3	674	674	NUM
cuesj-478	153	4	,	,	PUNCT
cuesj-478	153	5	2019	2019	NUM
cuesj-478	153	6	.	.	PUNCT
cuesj-478	154	1	5	5	NUM
cuesj-478	154	2	.	.	X
cuesj-478	154	3	l.	l.	PROPN
cuesj-478	154	4	yuanlu	yuanlu	PROPN
cuesj-478	154	5	.	.	PUNCT
cuesj-478	155	1	solving	solve	VERB
cuesj-478	155	2	a	a	DET
cuesj-478	155	3	nonlinear	nonlinear	ADJ
cuesj-478	155	4	fractional	fractional	ADJ
cuesj-478	155	5	differential	differential	NOUN
cuesj-478	155	6	equation	equation	NOUN
cuesj-478	155	7	using	use	VERB
cuesj-478	155	8	chebyshev	chebyshev	NOUN
cuesj-478	155	9	wavelets	wavelet	NOUN
cuesj-478	155	10	.	.	PUNCT
cuesj-478	156	1	communications	communication	NOUN
cuesj-478	156	2	in	in	ADP
cuesj-478	156	3	nonlinear	nonlinear	ADJ
cuesj-478	156	4	science	science	NOUN
cuesj-478	156	5	and	and	CCONJ
cuesj-478	156	6	numerical	numerical	PROPN
cuesj-478	156	7	simulation	simulation	PROPN
cuesj-478	156	8	,	,	PUNCT
cuesj-478	156	9	vol	vol	NOUN
cuesj-478	156	10	.	.	PROPN
cuesj-478	156	11	15	15	NUM
cuesj-478	156	12	,	,	PUNCT
cuesj-478	156	13	no	no	INTJ
cuesj-478	156	14	.	.	NOUN
cuesj-478	156	15	9	9	NUM
cuesj-478	156	16	,	,	PUNCT
cuesj-478	156	17	pp	pp	ADJ
cuesj-478	156	18	.	.	PUNCT
cuesj-478	156	19	2284	2284	NUM
cuesj-478	156	20	-	-	SYM
cuesj-478	156	21	2292	2292	NUM
cuesj-478	156	22	,	,	PUNCT
cuesj-478	156	23	2010	2010	NUM
cuesj-478	156	24	.	.	PUNCT
cuesj-478	157	1	6	6	NUM
cuesj-478	157	2	.	.	X
cuesj-478	157	3	e.	e.	PROPN
cuesj-478	157	4	hesameddini	hesameddini	PROPN
cuesj-478	157	5	and	and	CCONJ
cuesj-478	157	6	e.	e.	PROPN
cuesj-478	157	7	asadollahifar	asadollahifar	PROPN
cuesj-478	157	8	.	.	PUNCT
cuesj-478	158	1	numerical	numerical	ADJ
cuesj-478	158	2	solution	solution	NOUN
cuesj-478	158	3	of	of	ADP
cuesj-478	158	4	multi	multi	ADJ
cuesj-478	158	5	-	-	ADJ
cuesj-478	158	6	order	order	ADJ
cuesj-478	158	7	fractional	fractional	ADJ
cuesj-478	158	8	differential	differential	NOUN
cuesj-478	158	9	equation	equation	NOUN
cuesj-478	158	10	.	.	PUNCT
cuesj-478	159	1	ijnao	ijnao	PROPN
cuesj-478	159	2	,	,	PUNCT
cuesj-478	159	3	vol	vol	NOUN
cuesj-478	159	4	.	.	PROPN
cuesj-478	159	5	5	5	NUM
cuesj-478	159	6	,	,	PUNCT
cuesj-478	159	7	no	no	INTJ
cuesj-478	159	8	.	.	NOUN
cuesj-478	159	9	1	1	NUM
cuesj-478	159	10	,	,	PUNCT
cuesj-478	159	11	pp	pp	ADJ
cuesj-478	159	12	.	.	PUNCT
cuesj-478	160	1	37	37	NUM
cuesj-478	160	2	-	-	SYM
cuesj-478	160	3	48	48	NUM
cuesj-478	160	4	,	,	PUNCT
cuesj-478	160	5	2015	2015	NUM
cuesj-478	160	6	.	.	PUNCT
cuesj-478	161	1	7	7	X
cuesj-478	161	2	.	.	X
cuesj-478	161	3	m.	m.	PROPN
cuesj-478	161	4	abul	abul	PROPN
cuesj-478	161	5	-	-	PUNCT
cuesj-478	161	6	ez	ez	PROPN
cuesj-478	161	7	,	,	PUNCT
cuesj-478	161	8	m.	m.	NOUN
cuesj-478	161	9	zayed	zayed	PROPN
cuesj-478	161	10	,	,	PUNCT
cuesj-478	161	11	a.	a.	PROPN
cuesj-478	161	12	youssef	youssef	PROPN
cuesj-478	161	13	and	and	CCONJ
cuesj-478	161	14	m.	m.	PROPN
cuesj-478	161	15	de	de	PROPN
cuesj-478	161	16	la	la	PROPN
cuesj-478	161	17	sen	sen	PROPN
cuesj-478	161	18	.	.	PROPN
cuesj-478	161	19	on	on	ADP
cuesj-478	161	20	conformable	conformable	ADJ
cuesj-478	161	21	fractional	fractional	ADJ
cuesj-478	161	22	legendre	legendre	NOUN
cuesj-478	161	23	polynomials	polynomial	NOUN
cuesj-478	161	24	and	and	CCONJ
cuesj-478	161	25	their	their	PRON
cuesj-478	161	26	convergence	convergence	NOUN
cuesj-478	161	27	properties	property	NOUN
cuesj-478	161	28	with	with	ADP
cuesj-478	161	29	applications	application	NOUN
cuesj-478	161	30	.	.	PUNCT
cuesj-478	162	1	alexandria	alexandria	PROPN
cuesj-478	162	2	engineering	engineering	PROPN
cuesj-478	162	3	journal	journal	PROPN
cuesj-478	162	4	,	,	PUNCT
cuesj-478	162	5	vol	vol	NOUN
cuesj-478	162	6	.	.	PROPN
cuesj-478	162	7	59	59	NUM
cuesj-478	162	8	,	,	PUNCT
cuesj-478	162	9	no	no	INTJ
cuesj-478	162	10	.	.	NOUN
cuesj-478	162	11	6	6	NUM
cuesj-478	162	12	,	,	PUNCT
cuesj-478	162	13	pp	pp	ADJ
cuesj-478	162	14	.	.	PUNCT
cuesj-478	163	1	5231	5231	NUM
cuesj-478	163	2	-	-	SYM
cuesj-478	163	3	5245	5245	NUM
cuesj-478	163	4	,	,	PUNCT
cuesj-478	163	5	2020	2020	NUM
cuesj-478	163	6	.	.	PUNCT
cuesj-478	164	1	8	8	NUM
cuesj-478	164	2	.	.	PUNCT
cuesj-478	164	3	h.	h.	PROPN
cuesj-478	164	4	çerdik	çerdik	PROPN
cuesj-478	164	5	yaslan	yaslan	PROPN
cuesj-478	164	6	and	and	CCONJ
cuesj-478	164	7	f.	f.	PROPN
cuesj-478	164	8	mutlu	mutlu	PROPN
cuesj-478	164	9	.	.	PUNCT
cuesj-478	165	1	numerical	numerical	ADJ
cuesj-478	165	2	solution	solution	NOUN
cuesj-478	165	3	of	of	ADP
cuesj-478	165	4	the	the	DET
cuesj-478	165	5	conformable	conformable	ADJ
cuesj-478	165	6	differential	differential	ADJ
cuesj-478	165	7	equations	equation	NOUN
cuesj-478	165	8	via	via	ADP
cuesj-478	165	9	shifted	shift	VERB
cuesj-478	165	10	legendre	legendre	PROPN
cuesj-478	165	11	polynomials	polynomial	NOUN
cuesj-478	165	12	.	.	PUNCT
cuesj-478	166	1	international	international	ADJ
cuesj-478	166	2	journal	journal	PROPN
cuesj-478	166	3	of	of	ADP
cuesj-478	166	4	computer	computer	NOUN
cuesj-478	166	5	mathematics	mathematic	NOUN
cuesj-478	166	6	,	,	PUNCT
cuesj-478	166	7	vol	vol	NOUN
cuesj-478	166	8	.	.	PROPN
cuesj-478	166	9	97	97	NUM
cuesj-478	166	10	,	,	PUNCT
cuesj-478	166	11	no.5	no.5	PROPN
cuesj-478	166	12	,	,	PUNCT
cuesj-478	166	13	pp	pp	ADP
cuesj-478	166	14	.	.	PUNCT
cuesj-478	167	1	1016	1016	NUM
cuesj-478	167	2	-	-	SYM
cuesj-478	167	3	1028	1028	NUM
cuesj-478	167	4	,	,	PUNCT
cuesj-478	167	5	2020	2020	NUM
cuesj-478	167	6	.	.	PUNCT
cuesj-478	168	1	9	9	X
cuesj-478	168	2	.	.	X
cuesj-478	168	3	m.	m.	NOUN
cuesj-478	168	4	m.	m.	PROPN
cuesj-478	168	5	khader	khader	PROPN
cuesj-478	168	6	,	,	PUNCT
cuesj-478	168	7	t.	t.	PROPN
cuesj-478	168	8	s.	s.	PROPN
cuesj-478	168	9	el	el	PROPN
cuesj-478	168	10	danaf	danaf	PROPN
cuesj-478	168	11	and	and	CCONJ
cuesj-478	168	12	a.	a.	PROPN
cuesj-478	168	13	s.	s.	PROPN
cuesj-478	168	14	hendy	hendy	PROPN
cuesj-478	168	15	.	.	PUNCT
cuesj-478	169	1	efficient	efficient	ADJ
cuesj-478	169	2	spectral	spectral	ADJ
cuesj-478	169	3	collocation	collocation	NOUN
cuesj-478	169	4	method	method	NOUN
cuesj-478	169	5	for	for	ADP
cuesj-478	169	6	solving	solve	VERB
cuesj-478	169	7	multi	multi	ADJ
cuesj-478	169	8	-	-	ADJ
cuesj-478	169	9	term	term	ADJ
cuesj-478	169	10	fractional	fractional	ADJ
cuesj-478	169	11	differential	differential	NOUN
cuesj-478	169	12	equations	equation	NOUN
cuesj-478	169	13	based	base	VERB
cuesj-478	169	14	on	on	ADP
cuesj-478	169	15	the	the	DET
cuesj-478	169	16	generalized	generalized	ADJ
cuesj-478	169	17	laguerre	laguerre	NOUN
cuesj-478	169	18	polynomials	polynomial	NOUN
cuesj-478	169	19	.	.	PUNCT
cuesj-478	170	1	j.	j.	PROPN
cuesj-478	170	2	fractional	fractional	PROPN
cuesj-478	170	3	calc	calc	PROPN
cuesj-478	170	4	.	.	PUNCT
cuesj-478	171	1	appl	appl	PROPN
cuesj-478	171	2	,	,	PUNCT
cuesj-478	171	3	vol	vol	NOUN
cuesj-478	171	4	.	.	PROPN
cuesj-478	172	1	3	3	NUM
cuesj-478	172	2	,	,	PUNCT
cuesj-478	172	3	pp	pp	ADJ
cuesj-478	172	4	.	.	PUNCT
cuesj-478	173	1	1	1	NUM
cuesj-478	173	2	-	-	SYM
cuesj-478	173	3	14	14	NUM
cuesj-478	173	4	,	,	PUNCT
cuesj-478	173	5	2012	2012	NUM
cuesj-478	173	6	.	.	PUNCT
cuesj-478	174	1	appendix	appendix	NOUN
cuesj-478	174	2	result	result	NOUN
cuesj-478	174	3	of	of	ADP
cuesj-478	174	4	python	python	PROPN
cuesj-478	174	5	code	code	NOUN
cuesj-478	174	6	for	for	ADP
cuesj-478	174	7	example	example	NOUN
cuesj-478	174	8	1	1	NUM
cuesj-478	174	9	mahmood	mahmood	NOUN
cuesj-478	174	10	,	,	PUNCT
cuesj-478	174	11	et	et	PROPN
cuesj-478	174	12	al	al	PROPN
cuesj-478	174	13	.	.	PUNCT
cuesj-478	174	14	:	:	PUNCT
cuesj-478	175	1	multi	multi	ADJ
cuesj-478	175	2	-	-	ADJ
cuesj-478	175	3	order	order	NOUN
cuesj-478	175	4	fde	fde	NOUN
cuesj-478	175	5	based	base	VERB
cuesj-478	175	6	on	on	ADP
cuesj-478	175	7	cd	cd	PROPN
cuesj-478	175	8	by	by	ADP
cuesj-478	175	9	shifted	shift	VERB
cuesj-478	175	10	lp	lp	PROPN
cuesj-478	175	11	68	68	NUM
cuesj-478	175	12	http://journals.cihanuniversity.edu.iq/index.php/cuesj	http://journals.cihanuniversity.edu.iq/index.php/cuesj	ADJ
cuesj-478	175	13	cuesj	cuesj	ADJ
cuesj-478	175	14	2021	2021	NUM
cuesj-478	175	15	,	,	PUNCT
cuesj-478	175	16	5	5	NUM
cuesj-478	175	17	(	(	PUNCT
cuesj-478	175	18	2	2	NUM
cuesj-478	175	19	):	):	PUNCT
cuesj-478	175	20	64	64	NUM
cuesj-478	175	21	-	-	SYM
cuesj-478	175	22	68	68	NUM
cuesj-478	175	23	result	result	NOUN
cuesj-478	175	24	of	of	ADP
cuesj-478	175	25	python	python	PROPN
cuesj-478	175	26	code	code	NOUN
cuesj-478	175	27	for	for	ADP
cuesj-478	175	28	example	example	NOUN
cuesj-478	175	29	2	2	NUM
cuesj-478	175	30	result	result	NOUN
cuesj-478	175	31	of	of	ADP
cuesj-478	175	32	python	python	PROPN
cuesj-478	175	33	code	code	NOUN
cuesj-478	175	34	for	for	ADP
cuesj-478	175	35	example	example	NOUN
cuesj-478	175	36	3	3	NUM