id	sid	tid	token	lemma	pos
iajs-3076	1	1	ihjpas	ihjpas	PROPN
iajs-3076	1	2	.	.	PUNCT
iajs-3076	2	1	36	36	NUM
iajs-3076	2	2	(	(	PUNCT
iajs-3076	2	3	3	3	NUM
iajs-3076	2	4	)	)	PUNCT
iajs-3076	2	5	2023	2023	NUM
iajs-3076	2	6	382	382	NUM
iajs-3076	2	7	this	this	DET
iajs-3076	2	8	work	work	NOUN
iajs-3076	2	9	is	be	AUX
iajs-3076	2	10	licensed	license	VERB
iajs-3076	2	11	under	under	ADP
iajs-3076	2	12	a	a	DET
iajs-3076	2	13	creative	creative	ADJ
iajs-3076	2	14	commons	common	NOUN
iajs-3076	2	15	attribution	attribution	NOUN
iajs-3076	2	16	4.0	4.0	NUM
iajs-3076	2	17	international	international	ADJ
iajs-3076	2	18	license	license	NOUN
iajs-3076	2	19	*	*	PUNCT
iajs-3076	2	20	corresponding	correspond	VERB
iajs-3076	2	21	author	author	NOUN
iajs-3076	2	22	:	:	PUNCT
iajs-3076	2	23	ghada.h.i@ihcoedu.uobaghdad.edu.iq	ghada.h.i@ihcoedu.uobaghdad.edu.iq	PROPN
iajs-3076	2	24	abstract	abstract	NOUN
iajs-3076	2	25	this	this	DET
iajs-3076	2	26	work	work	NOUN
iajs-3076	2	27	describes	describe	VERB
iajs-3076	2	28	two	two	NUM
iajs-3076	2	29	efficient	efficient	ADJ
iajs-3076	2	30	and	and	CCONJ
iajs-3076	2	31	useful	useful	ADJ
iajs-3076	2	32	methods	method	NOUN
iajs-3076	2	33	for	for	ADP
iajs-3076	2	34	solving	solve	VERB
iajs-3076	2	35	fractional	fractional	ADJ
iajs-3076	2	36	pantograph	pantograph	NOUN
iajs-3076	2	37	delay	delay	NOUN
iajs-3076	2	38	equations	equation	NOUN
iajs-3076	2	39	(	(	PUNCT
iajs-3076	2	40	fpdes	fpde	NOUN
iajs-3076	2	41	)	)	PUNCT
iajs-3076	2	42	with	with	ADP
iajs-3076	2	43	initial	initial	ADJ
iajs-3076	2	44	and	and	CCONJ
iajs-3076	2	45	boundary	boundary	ADJ
iajs-3076	2	46	conditions	condition	NOUN
iajs-3076	2	47	.	.	PUNCT
iajs-3076	3	1	these	these	DET
iajs-3076	3	2	two	two	NUM
iajs-3076	3	3	methods	method	NOUN
iajs-3076	3	4	depend	depend	VERB
iajs-3076	3	5	mainly	mainly	ADV
iajs-3076	3	6	on	on	ADP
iajs-3076	3	7	orthogonal	orthogonal	ADJ
iajs-3076	3	8	polynomials	polynomial	NOUN
iajs-3076	3	9	,	,	PUNCT
iajs-3076	3	10	which	which	PRON
iajs-3076	3	11	are	be	AUX
iajs-3076	3	12	the	the	DET
iajs-3076	3	13	method	method	NOUN
iajs-3076	3	14	of	of	ADP
iajs-3076	3	15	the	the	DET
iajs-3076	3	16	operational	operational	ADJ
iajs-3076	3	17	matrix	matrix	NOUN
iajs-3076	3	18	of	of	ADP
iajs-3076	3	19	the	the	DET
iajs-3076	3	20	fractional	fractional	ADJ
iajs-3076	3	21	derivative	derivative	NOUN
iajs-3076	3	22	that	that	PRON
iajs-3076	3	23	depends	depend	VERB
iajs-3076	3	24	on	on	ADP
iajs-3076	3	25	bernstein	bernstein	PROPN
iajs-3076	3	26	polynomials	polynomial	NOUN
iajs-3076	3	27	and	and	CCONJ
iajs-3076	3	28	the	the	DET
iajs-3076	3	29	operational	operational	ADJ
iajs-3076	3	30	matrix	matrix	NOUN
iajs-3076	3	31	of	of	ADP
iajs-3076	3	32	the	the	DET
iajs-3076	3	33	fractional	fractional	ADJ
iajs-3076	3	34	derivative	derivative	NOUN
iajs-3076	3	35	with	with	ADP
iajs-3076	3	36	shifted	shift	VERB
iajs-3076	3	37	legendre	legendre	PROPN
iajs-3076	3	38	polynomials	polynomial	NOUN
iajs-3076	3	39	.	.	PUNCT
iajs-3076	4	1	the	the	DET
iajs-3076	4	2	basic	basic	ADJ
iajs-3076	4	3	procedure	procedure	NOUN
iajs-3076	4	4	of	of	ADP
iajs-3076	4	5	this	this	DET
iajs-3076	4	6	method	method	NOUN
iajs-3076	4	7	is	be	AUX
iajs-3076	4	8	to	to	PART
iajs-3076	4	9	convert	convert	VERB
iajs-3076	4	10	the	the	DET
iajs-3076	4	11	pantograph	pantograph	NOUN
iajs-3076	4	12	delay	delay	NOUN
iajs-3076	4	13	equation	equation	NOUN
iajs-3076	4	14	to	to	ADP
iajs-3076	4	15	a	a	DET
iajs-3076	4	16	system	system	NOUN
iajs-3076	4	17	of	of	ADP
iajs-3076	4	18	linear	linear	PROPN
iajs-3076	4	19	equations	equation	NOUN
iajs-3076	4	20	,	,	PUNCT
iajs-3076	4	21	and	and	CCONJ
iajs-3076	4	22	by	by	ADP
iajs-3076	4	23	using	use	VERB
iajs-3076	4	24	,	,	PUNCT
iajs-3076	4	25	the	the	DET
iajs-3076	4	26	operational	operational	ADJ
iajs-3076	4	27	matrices	matrix	NOUN
iajs-3076	4	28	,	,	PUNCT
iajs-3076	4	29	we	we	PRON
iajs-3076	4	30	get	get	AUX
iajs-3076	4	31	rid	rid	VERB
iajs-3076	4	32	of	of	ADP
iajs-3076	4	33	the	the	DET
iajs-3076	4	34	integration	integration	NOUN
iajs-3076	4	35	and	and	CCONJ
iajs-3076	4	36	differentiation	differentiation	NOUN
iajs-3076	4	37	operations	operation	NOUN
iajs-3076	4	38	,	,	PUNCT
iajs-3076	4	39	which	which	PRON
iajs-3076	4	40	makes	make	VERB
iajs-3076	4	41	solving	solve	VERB
iajs-3076	4	42	the	the	DET
iajs-3076	4	43	problem	problem	NOUN
iajs-3076	4	44	easier	easy	ADJ
iajs-3076	4	45	.	.	PUNCT
iajs-3076	5	1	the	the	DET
iajs-3076	5	2	concept	concept	NOUN
iajs-3076	5	3	of	of	ADP
iajs-3076	5	4	caputo	caputo	PROPN
iajs-3076	5	5	has	have	AUX
iajs-3076	5	6	been	be	AUX
iajs-3076	5	7	used	use	VERB
iajs-3076	5	8	to	to	PART
iajs-3076	5	9	describe	describe	VERB
iajs-3076	5	10	fractional	fractional	ADJ
iajs-3076	5	11	derivatives	derivative	NOUN
iajs-3076	5	12	.	.	PUNCT
iajs-3076	6	1	finally	finally	ADV
iajs-3076	6	2	,	,	PUNCT
iajs-3076	6	3	some	some	DET
iajs-3076	6	4	numerical	numerical	ADJ
iajs-3076	6	5	examples	example	NOUN
iajs-3076	6	6	are	be	AUX
iajs-3076	6	7	identified	identify	VERB
iajs-3076	6	8	to	to	PART
iajs-3076	6	9	show	show	VERB
iajs-3076	6	10	the	the	DET
iajs-3076	6	11	utility	utility	NOUN
iajs-3076	6	12	and	and	CCONJ
iajs-3076	6	13	capability	capability	NOUN
iajs-3076	6	14	of	of	ADP
iajs-3076	6	15	the	the	DET
iajs-3076	6	16	two	two	NUM
iajs-3076	6	17	proposed	propose	VERB
iajs-3076	6	18	approaches	approach	NOUN
iajs-3076	6	19	.	.	PUNCT
iajs-3076	7	1	the	the	DET
iajs-3076	7	2	mathematica	mathematica	PROPN
iajs-3076	7	3	®	®	PROPN
iajs-3076	7	4	12	12	NUM
iajs-3076	7	5	program	program	NOUN
iajs-3076	7	6	has	have	AUX
iajs-3076	7	7	been	be	AUX
iajs-3076	7	8	relied	rely	VERB
iajs-3076	7	9	upon	upon	SCONJ
iajs-3076	7	10	in	in	ADP
iajs-3076	7	11	the	the	DET
iajs-3076	7	12	calculations	calculation	NOUN
iajs-3076	7	13	.	.	PUNCT
iajs-3076	8	1	keywords	keyword	NOUN
iajs-3076	8	2	:	:	PUNCT
iajs-3076	8	3	bernstein	bernstein	PROPN
iajs-3076	8	4	polynomials	polynomials	PROPN
iajs-3076	8	5	,	,	PUNCT
iajs-3076	8	6	legendre	legendre	PROPN
iajs-3076	8	7	polynomials	polynomial	NOUN
iajs-3076	8	8	,	,	PUNCT
iajs-3076	8	9	pantograph	pantograph	NOUN
iajs-3076	8	10	delay	delay	NOUN
iajs-3076	8	11	equations	equation	NOUN
iajs-3076	8	12	.	.	PUNCT
iajs-3076	9	1	1	1	X
iajs-3076	9	2	.	.	X
iajs-3076	9	3	introduction	introduction	NOUN
iajs-3076	9	4	fractional	fractional	ADJ
iajs-3076	9	5	calculus	calculus	NOUN
iajs-3076	9	6	has	have	AUX
iajs-3076	9	7	recently	recently	ADV
iajs-3076	9	8	been	be	AUX
iajs-3076	9	9	increasingly	increasingly	ADV
iajs-3076	9	10	used	use	VERB
iajs-3076	9	11	due	due	ADP
iajs-3076	9	12	to	to	ADP
iajs-3076	9	13	its	its	PRON
iajs-3076	9	14	wide	wide	ADJ
iajs-3076	9	15	applications	application	NOUN
iajs-3076	9	16	in	in	ADP
iajs-3076	9	17	real	real	ADJ
iajs-3076	9	18	-	-	PUNCT
iajs-3076	9	19	world	world	NOUN
iajs-3076	9	20	problems	problem	NOUN
iajs-3076	9	21	.	.	PUNCT
iajs-3076	10	1	it	it	PRON
iajs-3076	10	2	has	have	AUX
iajs-3076	10	3	been	be	AUX
iajs-3076	10	4	used	use	VERB
iajs-3076	10	5	as	as	ADP
iajs-3076	10	6	a	a	DET
iajs-3076	10	7	powerful	powerful	ADJ
iajs-3076	10	8	tool	tool	NOUN
iajs-3076	10	9	in	in	ADP
iajs-3076	10	10	various	various	ADJ
iajs-3076	10	11	fields	field	NOUN
iajs-3076	10	12	such	such	ADJ
iajs-3076	10	13	as	as	ADP
iajs-3076	10	14	chemistry	chemistry	NOUN
iajs-3076	10	15	,	,	PUNCT
iajs-3076	10	16	physics	physics	NOUN
iajs-3076	10	17	,	,	PUNCT
iajs-3076	10	18	engineering	engineering	NOUN
iajs-3076	10	19	,	,	PUNCT
iajs-3076	10	20	and	and	CCONJ
iajs-3076	10	21	applied	applied	ADJ
iajs-3076	10	22	sciences	science	NOUN
iajs-3076	10	23	,	,	PUNCT
iajs-3076	10	24	where	where	SCONJ
iajs-3076	10	25	it	it	PRON
iajs-3076	10	26	can	can	AUX
iajs-3076	10	27	be	be	AUX
iajs-3076	10	28	seen	see	VERB
iajs-3076	10	29	in	in	ADP
iajs-3076	10	30	thermal	thermal	ADJ
iajs-3076	10	31	modeling	modeling	NOUN
iajs-3076	10	32	[	[	X
iajs-3076	10	33	1	1	NUM
iajs-3076	10	34	]	]	PUNCT
iajs-3076	10	35	,	,	PUNCT
iajs-3076	10	36	networks	network	NOUN
iajs-3076	10	37	[	[	X
iajs-3076	10	38	2	2	NUM
iajs-3076	10	39	]	]	PUNCT
iajs-3076	10	40	,	,	PUNCT
iajs-3076	10	41	optics	optic	NOUN
iajs-3076	10	42	[	[	X
iajs-3076	10	43	3	3	NUM
iajs-3076	10	44	]	]	PUNCT
iajs-3076	10	45	,	,	PUNCT
iajs-3076	10	46	optimal	optimal	ADJ
iajs-3076	10	47	control	control	NOUN
iajs-3076	11	1	[	[	X
iajs-3076	11	2	4	4	NUM
iajs-3076	11	3	]	]	PUNCT
iajs-3076	11	4	,	,	PUNCT
iajs-3076	11	5	elasticity	elasticity	NOUN
iajs-3076	11	6	[	[	X
iajs-3076	11	7	5	5	NUM
iajs-3076	11	8	]	]	PUNCT
iajs-3076	11	9	,	,	PUNCT
iajs-3076	11	10	fluid	fluid	ADJ
iajs-3076	11	11	mechanics	mechanic	NOUN
iajs-3076	11	12	[	[	X
iajs-3076	11	13	6	6	NUM
iajs-3076	11	14	]	]	PUNCT
iajs-3076	11	15	,	,	PUNCT
iajs-3076	11	16	and	and	CCONJ
iajs-3076	11	17	many	many	ADJ
iajs-3076	11	18	other	other	ADJ
iajs-3076	11	19	applications	application	NOUN
iajs-3076	11	20	.	.	PUNCT
iajs-3076	12	1	the	the	DET
iajs-3076	12	2	fractional	fractional	ADJ
iajs-3076	12	3	nature	nature	NOUN
iajs-3076	12	4	of	of	ADP
iajs-3076	12	5	this	this	DET
iajs-3076	12	6	class	class	NOUN
iajs-3076	12	7	of	of	ADP
iajs-3076	12	8	problems	problem	NOUN
iajs-3076	12	9	makes	make	VERB
iajs-3076	12	10	the	the	DET
iajs-3076	12	11	solution	solution	NOUN
iajs-3076	12	12	very	very	ADV
iajs-3076	12	13	difficult	difficult	ADJ
iajs-3076	12	14	.	.	PUNCT
iajs-3076	13	1	as	as	ADP
iajs-3076	13	2	a	a	DET
iajs-3076	13	3	result	result	NOUN
iajs-3076	13	4	,	,	PUNCT
iajs-3076	13	5	many	many	ADJ
iajs-3076	13	6	researchers	researcher	NOUN
iajs-3076	13	7	and	and	CCONJ
iajs-3076	13	8	authors	author	NOUN
iajs-3076	13	9	try	try	VERB
iajs-3076	13	10	to	to	PART
iajs-3076	13	11	generalize	generalize	VERB
iajs-3076	13	12	and	and	CCONJ
iajs-3076	13	13	develop	develop	VERB
iajs-3076	13	14	the	the	DET
iajs-3076	13	15	current	current	ADJ
iajs-3076	13	16	methods	method	NOUN
iajs-3076	13	17	to	to	PART
iajs-3076	13	18	simply	simply	ADV
iajs-3076	13	19	apply	apply	VERB
iajs-3076	13	20	them	they	PRON
iajs-3076	13	21	numerically	numerically	ADV
iajs-3076	13	22	or	or	CCONJ
iajs-3076	13	23	analytically	analytically	ADV
iajs-3076	13	24	and	and	CCONJ
iajs-3076	13	25	find	find	VERB
iajs-3076	13	26	approximate	approximate	ADJ
iajs-3076	13	27	solutions	solution	NOUN
iajs-3076	13	28	to	to	ADP
iajs-3076	13	29	them	they	PRON
iajs-3076	13	30	.	.	PUNCT
iajs-3076	14	1	these	these	DET
iajs-3076	14	2	methods	method	NOUN
iajs-3076	14	3	include	include	VERB
iajs-3076	14	4	the	the	DET
iajs-3076	14	5	collocation	collocation	NOUN
iajs-3076	14	6	method	method	NOUN
iajs-3076	14	7	[	[	X
iajs-3076	14	8	7	7	NUM
iajs-3076	14	9	,	,	PUNCT
iajs-3076	14	10	8	8	NUM
iajs-3076	14	11	]	]	PUNCT
iajs-3076	14	12	,	,	PUNCT
iajs-3076	14	13	adomian	adomian	NOUN
iajs-3076	14	14	’s	’s	PART
iajs-3076	14	15	decomposition	decomposition	NOUN
iajs-3076	14	16	method	method	NOUN
iajs-3076	14	17	[	[	X
iajs-3076	14	18	9–11	9–11	NOUN
iajs-3076	14	19	]	]	PUNCT
iajs-3076	14	20	,	,	PUNCT
iajs-3076	14	21	homotopy	homotopy	VERB
iajs-3076	14	22	perturbation	perturbation	NOUN
iajs-3076	14	23	method	method	NOUN
iajs-3076	14	24	[	[	X
iajs-3076	14	25	12	12	NUM
iajs-3076	14	26	,	,	PUNCT
iajs-3076	14	27	13	13	NUM
iajs-3076	14	28	]	]	PUNCT
iajs-3076	14	29	,	,	PUNCT
iajs-3076	14	30	and	and	CCONJ
iajs-3076	14	31	other	other	ADJ
iajs-3076	14	32	methods	method	NOUN
iajs-3076	14	33	[	[	X
iajs-3076	14	34	14–16	14–16	NUM
iajs-3076	14	35	]	]	PUNCT
iajs-3076	14	36	.	.	PUNCT
iajs-3076	15	1	fractional	fractional	ADJ
iajs-3076	15	2	delay	delay	NOUN
iajs-3076	15	3	differential	differential	ADJ
iajs-3076	15	4	equations	equation	NOUN
iajs-3076	15	5	(	(	PUNCT
iajs-3076	15	6	fddes	fdde	NOUN
iajs-3076	15	7	)	)	PUNCT
iajs-3076	15	8	are	be	AUX
iajs-3076	15	9	used	use	VERB
iajs-3076	15	10	in	in	ADP
iajs-3076	15	11	a	a	DET
iajs-3076	15	12	variety	variety	NOUN
iajs-3076	15	13	of	of	ADP
iajs-3076	15	14	technical	technical	ADJ
iajs-3076	15	15	systems	system	NOUN
iajs-3076	15	16	,	,	PUNCT
iajs-3076	15	17	including	include	VERB
iajs-3076	15	18	characterizing	characterize	VERB
iajs-3076	15	19	propagation	propagation	NOUN
iajs-3076	15	20	,	,	PUNCT
iajs-3076	15	21	transport	transport	NOUN
iajs-3076	15	22	development	development	NOUN
iajs-3076	15	23	,	,	PUNCT
iajs-3076	15	24	or	or	CCONJ
iajs-3076	15	25	population	population	NOUN
iajs-3076	15	26	gestures	gesture	NOUN
iajs-3076	15	27	[	[	X
iajs-3076	15	28	17	17	NUM
iajs-3076	15	29	,	,	PUNCT
iajs-3076	15	30	18	18	NUM
iajs-3076	15	31	]	]	PUNCT
iajs-3076	15	32	.	.	PUNCT
iajs-3076	16	1	the	the	DET
iajs-3076	16	2	pantograph	pantograph	NOUN
iajs-3076	16	3	equation	equation	NOUN
iajs-3076	16	4	is	be	AUX
iajs-3076	16	5	one	one	NUM
iajs-3076	16	6	of	of	ADP
iajs-3076	16	7	the	the	DET
iajs-3076	16	8	most	most	ADV
iajs-3076	16	9	important	important	ADJ
iajs-3076	16	10	types	type	NOUN
iajs-3076	16	11	of	of	ADP
iajs-3076	16	12	delay	delay	NOUN
iajs-3076	16	13	differential	differential	ADJ
iajs-3076	16	14	equations	equation	NOUN
iajs-3076	16	15	,	,	PUNCT
iajs-3076	16	16	and	and	CCONJ
iajs-3076	16	17	it	it	PRON
iajs-3076	16	18	is	be	AUX
iajs-3076	16	19	used	use	VERB
iajs-3076	16	20	to	to	PART
iajs-3076	16	21	describe	describe	VERB
iajs-3076	16	22	a	a	DET
iajs-3076	16	23	wide	wide	ADJ
iajs-3076	16	24	range	range	NOUN
iajs-3076	16	25	of	of	ADP
iajs-3076	16	26	phenomena	phenomenon	NOUN
iajs-3076	16	27	.	.	PUNCT
iajs-3076	17	1	various	various	ADJ
iajs-3076	17	2	applications	application	NOUN
iajs-3076	17	3	of	of	ADP
iajs-3076	17	4	these	these	DET
iajs-3076	17	5	equations	equation	NOUN
iajs-3076	17	6	in	in	ADP
iajs-3076	17	7	practical	practical	ADJ
iajs-3076	17	8	doi.org/10.30526/36.3.3076	doi.org/10.30526/36.3.3076	ADJ
iajs-3076	17	9	article	article	NOUN
iajs-3076	17	10	history	history	NOUN
iajs-3076	17	11	:	:	PUNCT
iajs-3076	17	12	received	receive	VERB
iajs-3076	17	13	16	16	NUM
iajs-3076	17	14	october	october	PROPN
iajs-3076	17	15	2022	2022	NUM
iajs-3076	17	16	,	,	PUNCT
iajs-3076	17	17	accepted	accept	VERB
iajs-3076	17	18	9	9	NUM
iajs-3076	17	19	january	january	NOUN
iajs-3076	17	20	2023	2023	NUM
iajs-3076	17	21	,	,	PUNCT
iajs-3076	17	22	published	publish	VERB
iajs-3076	17	23	in	in	ADP
iajs-3076	17	24	july	july	PROPN
iajs-3076	17	25	2023	2023	NUM
iajs-3076	17	26	.	.	PUNCT
iajs-3076	18	1	ibn	ibn	PROPN
iajs-3076	18	2	al	al	PROPN
iajs-3076	18	3	-	-	PUNCT
iajs-3076	18	4	haitham	haitham	PROPN
iajs-3076	18	5	journal	journal	PROPN
iajs-3076	18	6	for	for	ADP
iajs-3076	18	7	pure	pure	ADJ
iajs-3076	18	8	and	and	CCONJ
iajs-3076	18	9	applied	applied	ADJ
iajs-3076	18	10	sciences	sciences	PROPN
iajs-3076	18	11	journal	journal	PROPN
iajs-3076	18	12	homepage	homepage	NOUN
iajs-3076	18	13	:	:	PUNCT
iajs-3076	18	14	jih.uobaghdad.edu.iq	jih.uobaghdad.edu.iq	VERB
iajs-3076	18	15	fractional	fractional	ADJ
iajs-3076	18	16	pantograph	pantograph	NOUN
iajs-3076	18	17	delay	delay	NOUN
iajs-3076	18	18	equations	equation	NOUN
iajs-3076	18	19	solving	solve	VERB
iajs-3076	18	20	by	by	ADP
iajs-3076	18	21	the	the	DET
iajs-3076	18	22	meshless	meshless	ADJ
iajs-3076	18	23	methods	method	NOUN
iajs-3076	18	24	shefaa	shefaa	NOUN
iajs-3076	18	25	m.	m.	PROPN
iajs-3076	18	26	n.	n.	PROPN
iajs-3076	18	27	jasim	jasim	PROPN
iajs-3076	18	28	department	department	PROPN
iajs-3076	18	29	of	of	ADP
iajs-3076	18	30	mathematics	mathematics	PROPN
iajs-3076	18	31	,	,	PUNCT
iajs-3076	18	32	college	college	NOUN
iajs-3076	18	33	of	of	ADP
iajs-3076	18	34	education	education	NOUN
iajs-3076	18	35	for	for	ADP
iajs-3076	18	36	pure	pure	ADJ
iajs-3076	18	37	science	science	NOUN
iajs-3076	18	38	ibn	ibn	PROPN
iajs-3076	18	39	al	al	PROPN
iajs-3076	18	40	-	-	PUNCT
iajs-3076	18	41	haytham	haytham	PROPN
iajs-3076	18	42	,	,	PUNCT
iajs-3076	18	43	university	university	NOUN
iajs-3076	18	44	of	of	ADP
iajs-3076	18	45	baghdad	baghdad	PROPN
iajs-3076	18	46	,	,	PUNCT
iajs-3076	18	47	baghdad	baghdad	PROPN
iajs-3076	18	48	,	,	PUNCT
iajs-3076	18	49	iraq	iraq	PROPN
iajs-3076	18	50	.	.	PUNCT
iajs-3076	19	1	shefaa.mohammed1203a@ihcoedu.uobaghdad.edu.i	shefaa.mohammed1203a@ihcoedu.uobaghdad.edu.i	PROPN
iajs-3076	19	2	q	q	PROPN
iajs-3076	19	3	ghada	ghada	PROPN
iajs-3076	19	4	h.	h.	PROPN
iajs-3076	19	5	ibraheem	ibraheem	PROPN
iajs-3076	19	6	*	*	PROPN
iajs-3076	19	7	department	department	PROPN
iajs-3076	19	8	of	of	ADP
iajs-3076	19	9	mathematics	mathematics	PROPN
iajs-3076	19	10	,	,	PUNCT
iajs-3076	19	11	college	college	NOUN
iajs-3076	19	12	of	of	ADP
iajs-3076	19	13	education	education	NOUN
iajs-3076	19	14	for	for	ADP
iajs-3076	19	15	pure	pure	ADJ
iajs-3076	19	16	science	science	NOUN
iajs-3076	19	17	ibn	ibn	PROPN
iajs-3076	19	18	al	al	PROPN
iajs-3076	19	19	-	-	PUNCT
iajs-3076	19	20	haytham	haytham	PROPN
iajs-3076	19	21	,	,	PUNCT
iajs-3076	19	22	university	university	NOUN
iajs-3076	19	23	of	of	ADP
iajs-3076	19	24	baghdad	baghdad	PROPN
iajs-3076	19	25	,	,	PUNCT
iajs-3076	19	26	baghdad	baghdad	PROPN
iajs-3076	19	27	,	,	PUNCT
iajs-3076	19	28	iraq	iraq	PROPN
iajs-3076	19	29	.	.	PUNCT
iajs-3076	20	1	ghada.h.i@ihcoedu.uobaghdad.edu.iq	ghada.h.i@ihcoedu.uobaghdad.edu.iq	PROPN
iajs-3076	20	2	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-3076	20	3	mailto:ghada.h.i@ihcoedu.uobaghdad.edu.iq	mailto:ghada.h.i@ihcoedu.uobaghdad.edu.iq	PROPN
iajs-3076	20	4	http://en.uobaghdad.edu.iq/?page_id=15060	http://en.uobaghdad.edu.iq/?page_id=15060	NOUN
iajs-3076	20	5	http://en.uobaghdad.edu.iq/?page_id=15060	http://en.uobaghdad.edu.iq/?page_id=15060	NOUN
iajs-3076	20	6	mailto:shefaa.mohammed1203a@ihcoedu.uobaghdad.edu.iq	mailto:shefaa.mohammed1203a@ihcoedu.uobaghdad.edu.iq	NOUN
iajs-3076	20	7	mailto:shefaa.mohammed1203a@ihcoedu.uobaghdad.edu.iq	mailto:shefaa.mohammed1203a@ihcoedu.uobaghdad.edu.iq	NOUN
iajs-3076	20	8	mailto:shefaa.mohammed1203a@ihcoedu.uobaghdad.edu.iq	mailto:shefaa.mohammed1203a@ihcoedu.uobaghdad.edu.iq	NOUN
iajs-3076	20	9	http://en.uobaghdad.edu.iq/?page_id=15060	http://en.uobaghdad.edu.iq/?page_id=15060	NOUN
iajs-3076	20	10	http://en.uobaghdad.edu.iq/?page_id=15060	http://en.uobaghdad.edu.iq/?page_id=15060	NOUN
iajs-3076	20	11	mailto:ghada.h.i@ihcoedu.uobaghdad.edu.iq	mailto:ghada.h.i@ihcoedu.uobaghdad.edu.iq	PROPN
iajs-3076	20	12	mailto:ghada.h.i@ihcoedu.uobaghdad.edu.iq	mailto:ghada.h.i@ihcoedu.uobaghdad.edu.iq	NOUN
iajs-3076	20	13	ihjpas	ihjpa	VERB
iajs-3076	20	14	.	.	PUNCT
iajs-3076	21	1	36	36	NUM
iajs-3076	21	2	(	(	PUNCT
iajs-3076	21	3	3	3	NUM
iajs-3076	21	4	)	)	PUNCT
iajs-3076	21	5	2023	2023	NUM
iajs-3076	21	6	383	383	NUM
iajs-3076	21	7	disciplines	discipline	NOUN
iajs-3076	21	8	such	such	ADJ
iajs-3076	21	9	as	as	ADP
iajs-3076	21	10	biology	biology	NOUN
iajs-3076	21	11	,	,	PUNCT
iajs-3076	21	12	physics	physics	NOUN
iajs-3076	21	13	,	,	PUNCT
iajs-3076	21	14	economics	economic	NOUN
iajs-3076	21	15	,	,	PUNCT
iajs-3076	21	16	and	and	CCONJ
iajs-3076	21	17	electrodynamics	electrodynamic	NOUN
iajs-3076	21	18	have	have	AUX
iajs-3076	21	19	been	be	AUX
iajs-3076	21	20	researched	research	VERB
iajs-3076	21	21	by	by	ADP
iajs-3076	21	22	many	many	ADJ
iajs-3076	21	23	scholars	scholar	NOUN
iajs-3076	21	24	[	[	X
iajs-3076	21	25	19–21	19–21	NUM
iajs-3076	21	26	]	]	PUNCT
iajs-3076	21	27	.	.	PUNCT
iajs-3076	22	1	researchers	researcher	NOUN
iajs-3076	22	2	have	have	AUX
iajs-3076	22	3	been	be	AUX
iajs-3076	22	4	interested	interested	ADJ
iajs-3076	22	5	in	in	ADP
iajs-3076	22	6	finding	find	VERB
iajs-3076	22	7	strategies	strategy	NOUN
iajs-3076	22	8	to	to	PART
iajs-3076	22	9	solve	solve	VERB
iajs-3076	22	10	these	these	DET
iajs-3076	22	11	kinds	kind	NOUN
iajs-3076	22	12	of	of	ADP
iajs-3076	22	13	problems	problem	NOUN
iajs-3076	22	14	and	and	CCONJ
iajs-3076	22	15	have	have	AUX
iajs-3076	22	16	presented	present	VERB
iajs-3076	22	17	a	a	DET
iajs-3076	22	18	number	number	NOUN
iajs-3076	22	19	of	of	ADP
iajs-3076	22	20	papers	paper	NOUN
iajs-3076	22	21	on	on	ADP
iajs-3076	22	22	the	the	DET
iajs-3076	22	23	subject	subject	NOUN
iajs-3076	22	24	,	,	PUNCT
iajs-3076	22	25	where	where	SCONJ
iajs-3076	22	26	rabiei	rabiei	PROPN
iajs-3076	22	27	and	and	CCONJ
iajs-3076	22	28	ordok	ordok	NOUN
iajs-3076	22	29	[	[	X
iajs-3076	22	30	22	22	NUM
iajs-3076	22	31	]	]	PUNCT
iajs-3076	22	32	introduce	introduce	VERB
iajs-3076	22	33	fractional	fractional	ADJ
iajs-3076	22	34	-	-	PUNCT
iajs-3076	22	35	order	order	NOUN
iajs-3076	22	36	boubaker	boubaker	NOUN
iajs-3076	22	37	polynomials	polynomial	NOUN
iajs-3076	22	38	related	relate	VERB
iajs-3076	22	39	to	to	ADP
iajs-3076	22	40	the	the	DET
iajs-3076	22	41	boubaker	boubaker	NOUN
iajs-3076	22	42	polynomials	polynomial	NOUN
iajs-3076	22	43	to	to	PART
iajs-3076	22	44	achieve	achieve	VERB
iajs-3076	22	45	the	the	DET
iajs-3076	22	46	numerical	numerical	ADJ
iajs-3076	22	47	result	result	NOUN
iajs-3076	22	48	for	for	ADP
iajs-3076	22	49	pantograph	pantograph	NOUN
iajs-3076	22	50	differential	differential	NOUN
iajs-3076	22	51	equations	equation	NOUN
iajs-3076	22	52	of	of	ADP
iajs-3076	22	53	fractional	fractional	ADJ
iajs-3076	22	54	order	order	NOUN
iajs-3076	22	55	in	in	ADP
iajs-3076	22	56	any	any	DET
iajs-3076	22	57	arbitrary	arbitrary	ADJ
iajs-3076	22	58	interval	interval	NOUN
iajs-3076	22	59	.	.	PUNCT
iajs-3076	23	1	yuttanan	yuttanan	PROPN
iajs-3076	23	2	et	et	PROPN
iajs-3076	23	3	al	al	PROPN
iajs-3076	23	4	.	.	PUNCT
iajs-3076	24	1	[	[	X
iajs-3076	24	2	23	23	NUM
iajs-3076	24	3	]	]	PUNCT
iajs-3076	24	4	presented	present	VERB
iajs-3076	24	5	a	a	DET
iajs-3076	24	6	new	new	ADJ
iajs-3076	24	7	class	class	NOUN
iajs-3076	24	8	of	of	ADP
iajs-3076	24	9	functions	function	NOUN
iajs-3076	24	10	called	call	VERB
iajs-3076	24	11	fractional	fractional	ADJ
iajs-3076	24	12	-	-	PUNCT
iajs-3076	24	13	order	order	NOUN
iajs-3076	24	14	generalized	generalize	VERB
iajs-3076	24	15	taylor	taylor	PROPN
iajs-3076	24	16	wavelets	wavelet	NOUN
iajs-3076	24	17	(	(	PUNCT
iajs-3076	24	18	fogtw	fogtw	PROPN
iajs-3076	24	19	)	)	PUNCT
iajs-3076	24	20	for	for	ADP
iajs-3076	24	21	the	the	DET
iajs-3076	24	22	nonlinear	nonlinear	ADJ
iajs-3076	24	23	fractional	fractional	ADJ
iajs-3076	24	24	delay	delay	NOUN
iajs-3076	24	25	and	and	CCONJ
iajs-3076	24	26	nonlinear	nonlinear	ADJ
iajs-3076	24	27	fractional	fractional	ADJ
iajs-3076	24	28	pantograph	pantograph	NOUN
iajs-3076	24	29	differential	differential	NOUN
iajs-3076	24	30	equations	equation	NOUN
iajs-3076	24	31	.	.	PUNCT
iajs-3076	25	1	in	in	ADP
iajs-3076	25	2	[	[	X
iajs-3076	25	3	24	24	NUM
iajs-3076	25	4	]	]	PUNCT
iajs-3076	25	5	,	,	PUNCT
iajs-3076	25	6	a	a	DET
iajs-3076	25	7	method	method	NOUN
iajs-3076	25	8	utilizing	utilize	VERB
iajs-3076	25	9	the	the	DET
iajs-3076	25	10	chebyshev	chebyshev	NOUN
iajs-3076	25	11	cardinal	cardinal	ADJ
iajs-3076	25	12	functions	function	NOUN
iajs-3076	25	13	(	(	PUNCT
iajs-3076	25	14	ccfs	ccfs	NOUN
iajs-3076	25	15	)	)	PUNCT
iajs-3076	25	16	is	be	AUX
iajs-3076	25	17	formulated	formulate	VERB
iajs-3076	25	18	to	to	PART
iajs-3076	25	19	find	find	VERB
iajs-3076	25	20	an	an	DET
iajs-3076	25	21	accurate	accurate	ADJ
iajs-3076	25	22	result	result	NOUN
iajs-3076	25	23	for	for	ADP
iajs-3076	25	24	fractional	fractional	ADJ
iajs-3076	25	25	pantograph	pantograph	NOUN
iajs-3076	25	26	delay	delay	NOUN
iajs-3076	25	27	differential	differential	ADJ
iajs-3076	25	28	equations	equation	NOUN
iajs-3076	25	29	;	;	PUNCT
iajs-3076	25	30	see	see	VERB
iajs-3076	25	31	more	more	ADJ
iajs-3076	25	32	works	work	NOUN
iajs-3076	25	33	[	[	X
iajs-3076	25	34	25–27	25–27	NUM
iajs-3076	25	35	]	]	X
iajs-3076	25	36	.	.	PUNCT
iajs-3076	26	1	operational	operational	ADJ
iajs-3076	26	2	matrices	matrix	NOUN
iajs-3076	26	3	are	be	AUX
iajs-3076	26	4	one	one	NUM
iajs-3076	26	5	of	of	ADP
iajs-3076	26	6	the	the	DET
iajs-3076	26	7	most	most	ADV
iajs-3076	26	8	widely	widely	ADV
iajs-3076	26	9	used	use	VERB
iajs-3076	26	10	numerical	numerical	ADJ
iajs-3076	26	11	methods	method	NOUN
iajs-3076	26	12	for	for	ADP
iajs-3076	26	13	solving	solve	VERB
iajs-3076	26	14	fractional	fractional	ADJ
iajs-3076	26	15	differential	differential	ADJ
iajs-3076	26	16	equations	equation	NOUN
iajs-3076	26	17	(	(	PUNCT
iajs-3076	26	18	fdes	fde	NOUN
iajs-3076	26	19	)	)	PUNCT
iajs-3076	26	20	because	because	SCONJ
iajs-3076	26	21	they	they	PRON
iajs-3076	26	22	are	be	AUX
iajs-3076	26	23	based	base	VERB
iajs-3076	26	24	on	on	ADP
iajs-3076	26	25	polynomials	polynomial	NOUN
iajs-3076	26	26	,	,	PUNCT
iajs-3076	26	27	which	which	PRON
iajs-3076	26	28	are	be	AUX
iajs-3076	26	29	one	one	NUM
iajs-3076	26	30	of	of	ADP
iajs-3076	26	31	the	the	DET
iajs-3076	26	32	simplest	simple	ADJ
iajs-3076	26	33	functions	function	NOUN
iajs-3076	26	34	in	in	ADP
iajs-3076	26	35	terms	term	NOUN
iajs-3076	26	36	of	of	ADP
iajs-3076	26	37	structure	structure	NOUN
iajs-3076	26	38	.	.	PUNCT
iajs-3076	27	1	as	as	ADP
iajs-3076	27	2	a	a	DET
iajs-3076	27	3	result	result	NOUN
iajs-3076	27	4	,	,	PUNCT
iajs-3076	27	5	the	the	DET
iajs-3076	27	6	benefit	benefit	NOUN
iajs-3076	27	7	of	of	ADP
iajs-3076	27	8	this	this	DET
iajs-3076	27	9	method	method	NOUN
iajs-3076	27	10	is	be	AUX
iajs-3076	27	11	that	that	SCONJ
iajs-3076	27	12	it	it	PRON
iajs-3076	27	13	transforms	transform	VERB
iajs-3076	27	14	the	the	DET
iajs-3076	27	15	problem	problem	NOUN
iajs-3076	27	16	into	into	ADP
iajs-3076	27	17	a	a	DET
iajs-3076	27	18	set	set	NOUN
iajs-3076	27	19	of	of	ADP
iajs-3076	27	20	algebraic	algebraic	ADJ
iajs-3076	27	21	equations	equation	NOUN
iajs-3076	27	22	.	.	PUNCT
iajs-3076	28	1	using	use	VERB
iajs-3076	28	2	the	the	DET
iajs-3076	28	3	operational	operational	ADJ
iajs-3076	28	4	matrix	matrix	NOUN
iajs-3076	28	5	,	,	PUNCT
iajs-3076	28	6	we	we	PRON
iajs-3076	28	7	get	get	VERB
iajs-3076	28	8	rid	rid	VERB
iajs-3076	28	9	of	of	ADP
iajs-3076	28	10	the	the	DET
iajs-3076	28	11	derivations	derivation	NOUN
iajs-3076	28	12	and	and	CCONJ
iajs-3076	28	13	integrals	integral	NOUN
iajs-3076	28	14	,	,	PUNCT
iajs-3076	28	15	making	make	VERB
iajs-3076	28	16	the	the	DET
iajs-3076	28	17	solution	solution	NOUN
iajs-3076	28	18	easier	easy	ADJ
iajs-3076	28	19	and	and	CCONJ
iajs-3076	28	20	simpler	simple	ADJ
iajs-3076	28	21	.	.	PUNCT
iajs-3076	29	1	studies	study	NOUN
iajs-3076	29	2	that	that	PRON
iajs-3076	29	3	relied	rely	VERB
iajs-3076	29	4	on	on	ADP
iajs-3076	29	5	operational	operational	ADJ
iajs-3076	29	6	matrices	matrix	NOUN
iajs-3076	29	7	methods	method	NOUN
iajs-3076	29	8	can	can	AUX
iajs-3076	29	9	be	be	AUX
iajs-3076	29	10	seen	see	VERB
iajs-3076	29	11	in	in	ADP
iajs-3076	29	12	[	[	X
iajs-3076	29	13	28–32	28–32	NUM
iajs-3076	29	14	]	]	PUNCT
iajs-3076	29	15	.	.	PUNCT
iajs-3076	30	1	the	the	DET
iajs-3076	30	2	main	main	ADJ
iajs-3076	30	3	objective	objective	NOUN
iajs-3076	30	4	of	of	ADP
iajs-3076	30	5	this	this	DET
iajs-3076	30	6	work	work	NOUN
iajs-3076	30	7	is	be	AUX
iajs-3076	30	8	to	to	PART
iajs-3076	30	9	apply	apply	VERB
iajs-3076	30	10	the	the	DET
iajs-3076	30	11	operational	operational	ADJ
iajs-3076	30	12	matrix	matrix	NOUN
iajs-3076	30	13	method	method	NOUN
iajs-3076	30	14	for	for	ADP
iajs-3076	30	15	derivatives	derivative	NOUN
iajs-3076	30	16	that	that	PRON
iajs-3076	30	17	depend	depend	VERB
iajs-3076	30	18	on	on	ADP
iajs-3076	30	19	bernstein	bernstein	PROPN
iajs-3076	30	20	polynomials	polynomials	PROPN
iajs-3076	30	21	,	,	PUNCT
iajs-3076	30	22	as	as	ADV
iajs-3076	30	23	well	well	ADV
iajs-3076	30	24	as	as	ADP
iajs-3076	30	25	the	the	DET
iajs-3076	30	26	operational	operational	ADJ
iajs-3076	30	27	matrix	matrix	NOUN
iajs-3076	30	28	method	method	NOUN
iajs-3076	30	29	,	,	PUNCT
iajs-3076	30	30	which	which	PRON
iajs-3076	30	31	depends	depend	VERB
iajs-3076	30	32	on	on	ADP
iajs-3076	30	33	shifted	shift	VERB
iajs-3076	30	34	legendre	legendre	PROPN
iajs-3076	30	35	polynomials	polynomial	NOUN
iajs-3076	30	36	,	,	PUNCT
iajs-3076	30	37	for	for	ADP
iajs-3076	30	38	solving	solve	VERB
iajs-3076	30	39	fractional	fractional	ADJ
iajs-3076	30	40	pantograph	pantograph	NOUN
iajs-3076	30	41	delay	delay	NOUN
iajs-3076	30	42	equations	equation	NOUN
iajs-3076	30	43	(	(	PUNCT
iajs-3076	30	44	fpdes	fpde	NOUN
iajs-3076	30	45	)	)	PUNCT
iajs-3076	30	46	with	with	ADP
iajs-3076	30	47	initial	initial	ADJ
iajs-3076	30	48	and	and	CCONJ
iajs-3076	30	49	boundary	boundary	ADJ
iajs-3076	30	50	conditions	condition	NOUN
iajs-3076	30	51	.	.	PUNCT
iajs-3076	31	1	the	the	DET
iajs-3076	31	2	rest	rest	NOUN
iajs-3076	31	3	of	of	ADP
iajs-3076	31	4	this	this	DET
iajs-3076	31	5	paper	paper	NOUN
iajs-3076	31	6	is	be	AUX
iajs-3076	31	7	organized	organize	VERB
iajs-3076	31	8	as	as	SCONJ
iajs-3076	31	9	follows	follow	VERB
iajs-3076	31	10	:	:	PUNCT
iajs-3076	31	11	in	in	ADP
iajs-3076	31	12	section	section	NOUN
iajs-3076	31	13	2	2	NUM
iajs-3076	31	14	,	,	PUNCT
iajs-3076	31	15	we	we	PRON
iajs-3076	31	16	provide	provide	VERB
iajs-3076	31	17	some	some	DET
iajs-3076	31	18	basic	basic	ADJ
iajs-3076	31	19	definitions	definition	NOUN
iajs-3076	31	20	of	of	ADP
iajs-3076	31	21	fractional	fractional	ADJ
iajs-3076	31	22	calculus	calculus	NOUN
iajs-3076	31	23	.	.	PUNCT
iajs-3076	32	1	in	in	ADP
iajs-3076	32	2	section	section	NOUN
iajs-3076	32	3	3	3	NUM
iajs-3076	32	4	,	,	PUNCT
iajs-3076	32	5	bernstein	bernstein	PROPN
iajs-3076	32	6	polynomials	polynomials	PROPN
iajs-3076	32	7	and	and	CCONJ
iajs-3076	32	8	their	their	PRON
iajs-3076	32	9	operational	operational	ADJ
iajs-3076	32	10	matrices	matrix	NOUN
iajs-3076	32	11	(	(	PUNCT
iajs-3076	32	12	bom	bom	NOUN
iajs-3076	32	13	)	)	PUNCT
iajs-3076	32	14	are	be	AUX
iajs-3076	32	15	introduced	introduce	VERB
iajs-3076	32	16	.	.	PUNCT
iajs-3076	33	1	also	also	ADV
iajs-3076	33	2	,	,	PUNCT
iajs-3076	33	3	in	in	ADP
iajs-3076	33	4	section	section	NOUN
iajs-3076	33	5	4	4	NUM
iajs-3076	33	6	,	,	PUNCT
iajs-3076	33	7	shifted	shift	VERB
iajs-3076	33	8	legendre	legendre	NOUN
iajs-3076	33	9	polynomials	polynomial	NOUN
iajs-3076	33	10	and	and	CCONJ
iajs-3076	33	11	their	their	PRON
iajs-3076	33	12	operational	operational	ADJ
iajs-3076	33	13	matrices	matrix	NOUN
iajs-3076	33	14	(	(	PUNCT
iajs-3076	33	15	lom	lom	NOUN
iajs-3076	33	16	)	)	PUNCT
iajs-3076	33	17	are	be	AUX
iajs-3076	33	18	considered	consider	VERB
iajs-3076	33	19	.	.	PUNCT
iajs-3076	34	1	in	in	ADP
iajs-3076	34	2	section	section	NOUN
iajs-3076	34	3	5	5	NUM
iajs-3076	34	4	,	,	PUNCT
iajs-3076	34	5	some	some	DET
iajs-3076	34	6	numerical	numerical	ADJ
iajs-3076	34	7	examples	example	NOUN
iajs-3076	34	8	of	of	ADP
iajs-3076	34	9	pantograph	pantograph	NOUN
iajs-3076	34	10	equations	equation	NOUN
iajs-3076	34	11	with	with	ADP
iajs-3076	34	12	prime	prime	ADJ
iajs-3076	34	13	and	and	CCONJ
iajs-3076	34	14	boundary	boundary	ADJ
iajs-3076	34	15	conditions	condition	NOUN
iajs-3076	34	16	will	will	AUX
iajs-3076	34	17	be	be	AUX
iajs-3076	34	18	solved	solve	VERB
iajs-3076	34	19	by	by	ADP
iajs-3076	34	20	the	the	DET
iajs-3076	34	21	proposed	propose	VERB
iajs-3076	34	22	methods	method	NOUN
iajs-3076	34	23	.	.	PUNCT
iajs-3076	35	1	finally	finally	ADV
iajs-3076	35	2	,	,	PUNCT
iajs-3076	35	3	we	we	PRON
iajs-3076	35	4	discuss	discuss	VERB
iajs-3076	35	5	our	our	PRON
iajs-3076	35	6	findings	finding	NOUN
iajs-3076	35	7	and	and	CCONJ
iajs-3076	35	8	conclusions	conclusion	NOUN
iajs-3076	35	9	.	.	PUNCT
iajs-3076	36	1	2	2	X
iajs-3076	36	2	.	.	X
iajs-3076	36	3	basic	basic	ADJ
iajs-3076	36	4	definitions	definition	NOUN
iajs-3076	36	5	the	the	DET
iajs-3076	36	6	riemann	riemann	PROPN
iajs-3076	36	7	-	-	PUNCT
iajs-3076	36	8	liouville	liouville	PROPN
iajs-3076	36	9	and	and	CCONJ
iajs-3076	36	10	caputo	caputo	PROPN
iajs-3076	36	11	operators	operators	PROPN
iajs-3076	37	1	[	[	X
iajs-3076	37	2	33	33	NUM
iajs-3076	37	3	]	]	PUNCT
iajs-3076	37	4	are	be	AUX
iajs-3076	37	5	the	the	DET
iajs-3076	37	6	two	two	NUM
iajs-3076	37	7	most	most	ADV
iajs-3076	37	8	commonly	commonly	ADV
iajs-3076	37	9	used	use	VERB
iajs-3076	37	10	definitions	definition	NOUN
iajs-3076	37	11	in	in	ADP
iajs-3076	37	12	fractional	fractional	ADJ
iajs-3076	37	13	calculus	calculus	NOUN
iajs-3076	37	14	.	.	PUNCT
iajs-3076	38	1	this	this	DET
iajs-3076	38	2	section	section	NOUN
iajs-3076	38	3	will	will	AUX
iajs-3076	38	4	give	give	VERB
iajs-3076	38	5	the	the	DET
iajs-3076	38	6	definitions	definition	NOUN
iajs-3076	38	7	and	and	CCONJ
iajs-3076	38	8	some	some	PRON
iajs-3076	38	9	of	of	ADP
iajs-3076	38	10	their	their	PRON
iajs-3076	38	11	properties	property	NOUN
iajs-3076	38	12	.	.	PUNCT
iajs-3076	39	1	definition	definition	NOUN
iajs-3076	39	2	1	1	NUM
iajs-3076	39	3	:	:	PUNCT
iajs-3076	39	4	the	the	DET
iajs-3076	39	5	riemann	riemann	PROPN
iajs-3076	39	6	–	–	PUNCT
iajs-3076	39	7	liouville	liouville	VERB
iajs-3076	39	8	fractional	fractional	ADJ
iajs-3076	39	9	integration	integration	NOUN
iajs-3076	39	10	of	of	ADP
iajs-3076	39	11	order	order	NOUN
iajs-3076	39	12	α	α	NOUN
iajs-3076	39	13	is	be	AUX
iajs-3076	39	14	defined	define	VERB
iajs-3076	39	15	as	as	ADP
iajs-3076	39	16	[	[	X
iajs-3076	39	17	33	33	NUM
iajs-3076	39	18	]	]	PUNCT
iajs-3076	39	19	𝐼𝛼𝑦(𝑥	𝐼𝛼𝑦(𝑥	NOUN
iajs-3076	39	20	)	)	PUNCT
iajs-3076	40	1	=	=	PRON
iajs-3076	40	2	{	{	PUNCT
iajs-3076	40	3	1	1	NUM
iajs-3076	40	4	𝛤(𝛼	𝛤(𝛼	NUM
iajs-3076	40	5	)	)	PUNCT
iajs-3076	40	6	∫	∫	NOUN
iajs-3076	41	1	𝑥	𝑥	NOUN
iajs-3076	41	2	0	0	NUM
iajs-3076	41	3	  	  	SPACE
iajs-3076	41	4	𝑦(𝑠	𝑦(𝑠	PROPN
iajs-3076	41	5	)	)	PUNCT
iajs-3076	41	6	(	(	PUNCT
iajs-3076	41	7	𝑥−𝑠)1−𝛼	𝑥−𝑠)1−𝛼	NOUN
iajs-3076	41	8	𝑑𝑠	𝑑𝑠	NOUN
iajs-3076	41	9	,	,	PUNCT
iajs-3076	41	10	𝛼	𝛼	X
iajs-3076	41	11	>	>	X
iajs-3076	41	12	0	0	PROPN
iajs-3076	41	13	,	,	PUNCT
iajs-3076	41	14	𝑥	𝑥	PROPN
iajs-3076	41	15	>	>	X
iajs-3076	41	16	0	0	NUM
iajs-3076	41	17	,	,	PUNCT
iajs-3076	41	18	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-3076	41	19	)	)	PUNCT
iajs-3076	41	20	,	,	PUNCT
iajs-3076	41	21	𝛼	𝛼	NOUN
iajs-3076	41	22	=	=	NOUN
iajs-3076	41	23	0	0	NUM
iajs-3076	41	24	.	.	PUNCT
iajs-3076	42	1	(	(	PUNCT
iajs-3076	42	2	1	1	X
iajs-3076	42	3	)	)	PUNCT
iajs-3076	42	4	for	for	ADP
iajs-3076	42	5	the	the	DET
iajs-3076	42	6	riemann	riemann	PROPN
iajs-3076	42	7	–	–	PUNCT
iajs-3076	42	8	liouville	liouville	VERB
iajs-3076	42	9	integral	integral	ADJ
iajs-3076	42	10	1	1	NUM
iajs-3076	42	11	.	.	PUNCT
iajs-3076	42	12	𝐼𝛼1𝐼𝛼2𝑦(𝑥	𝐼𝛼1𝐼𝛼2𝑦(𝑥	NOUN
iajs-3076	42	13	)	)	PUNCT
iajs-3076	42	14	=	=	PUNCT
iajs-3076	43	1	𝐼𝛼1+𝛼2𝑦(𝑥	𝐼𝛼1+𝛼2𝑦(𝑥	NOUN
iajs-3076	43	2	)	)	PUNCT
iajs-3076	43	3	,	,	PUNCT
iajs-3076	43	4	2	2	X
iajs-3076	43	5	.	.	PUNCT
iajs-3076	43	6	𝐼𝛼(𝜆1𝑦(𝑥	𝐼𝛼(𝜆1𝑦(𝑥	NOUN
iajs-3076	43	7	)	)	PUNCT
iajs-3076	44	1	+	+	CCONJ
iajs-3076	44	2	𝜆2𝑔(𝑥	𝜆2𝑔(𝑥	PROPN
iajs-3076	44	3	)	)	PUNCT
iajs-3076	44	4	)	)	PUNCT
iajs-3076	45	1	=	=	PUNCT
iajs-3076	45	2	𝜆1𝐼𝛼𝑦(𝑥	𝜆1𝐼𝛼𝑦(𝑥	PRON
iajs-3076	45	3	)	)	PUNCT
iajs-3076	45	4	+	+	CCONJ
iajs-3076	45	5	𝜆2𝐼𝛼𝑔(𝑥	𝜆2𝐼𝛼𝑔(𝑥	CCONJ
iajs-3076	45	6	)	)	PUNCT
iajs-3076	45	7	,	,	PUNCT
iajs-3076	45	8	3	3	X
iajs-3076	45	9	.	.	PUNCT
iajs-3076	46	1	𝐼𝛼𝑥𝛽	𝐼𝛼𝑥𝛽	NOUN
iajs-3076	46	2	=	=	PUNCT
iajs-3076	46	3	𝛤(𝛽+1	𝛤(𝛽+1	NOUN
iajs-3076	46	4	)	)	PUNCT
iajs-3076	46	5	𝛤(𝛽+𝛼+1	𝛤(𝛽+𝛼+1	NOUN
iajs-3076	46	6	)	)	PUNCT
iajs-3076	46	7	𝑥𝛼+𝛽	𝑥𝛼+𝛽	NUM
iajs-3076	46	8	,	,	PUNCT
iajs-3076	46	9	𝛽	𝛽	PROPN
iajs-3076	46	10	>	>	X
iajs-3076	46	11	−1	−1	NOUN
iajs-3076	46	12	,	,	PUNCT
iajs-3076	46	13	where	where	SCONJ
iajs-3076	46	14	𝛼1	𝛼1	NOUN
iajs-3076	46	15	,	,	PUNCT
iajs-3076	46	16	𝛼2	𝛼2	PROPN
iajs-3076	46	17	,	,	PUNCT
iajs-3076	46	18	𝜆1	𝜆1	VERB
iajs-3076	46	19	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
iajs-3076	46	20	𝜆2	𝜆2	NOUN
iajs-3076	46	21	are	be	AUX
iajs-3076	46	22	constants	constant	NOUN
iajs-3076	46	23	.	.	PUNCT
iajs-3076	47	1	definition	definition	NOUN
iajs-3076	47	2	2	2	NUM
iajs-3076	47	3	:	:	PUNCT
iajs-3076	47	4	caputo	caputo	PROPN
iajs-3076	47	5	’s	’s	PART
iajs-3076	47	6	fractional	fractional	ADJ
iajs-3076	47	7	derivative	derivative	ADJ
iajs-3076	47	8	operator	operator	NOUN
iajs-3076	47	9	of	of	ADP
iajs-3076	47	10	order	order	NOUN
iajs-3076	47	11	𝛼	𝛼	NOUN
iajs-3076	47	12	is	be	AUX
iajs-3076	47	13	defined	define	VERB
iajs-3076	47	14	as	as	ADP
iajs-3076	47	15	[	[	X
iajs-3076	47	16	33	33	NUM
iajs-3076	47	17	]	]	PUNCT
iajs-3076	47	18	𝐷𝛼𝑦(𝑥	𝐷𝛼𝑦(𝑥	PROPN
iajs-3076	47	19	)	)	PUNCT
iajs-3076	47	20	=	=	SYM
iajs-3076	47	21	1	1	NUM
iajs-3076	47	22	𝛤(𝑛−𝛼	𝛤(𝑛−𝛼	VERB
iajs-3076	47	23	)	)	PUNCT
iajs-3076	47	24	∫	∫	NOUN
iajs-3076	48	1	𝑥	𝑥	NOUN
iajs-3076	48	2	0	0	NUM
iajs-3076	48	3	  	  	SPACE
iajs-3076	48	4	𝑦(𝑛)(𝑠	𝑦(𝑛)(𝑠	NOUN
iajs-3076	48	5	)	)	PUNCT
iajs-3076	48	6	(	(	PUNCT
iajs-3076	48	7	𝑥−𝑠)𝛼+1−𝑛	𝑥−𝑠)𝛼+1−𝑛	X
iajs-3076	48	8	𝑑𝑠	𝑑𝑠	NOUN
iajs-3076	48	9	,	,	PUNCT
iajs-3076	48	10	𝑛	𝑛	PRON
iajs-3076	48	11	−	−	PROPN
iajs-3076	48	12	1	1	NUM
iajs-3076	48	13	<	<	X
iajs-3076	48	14	𝛼	𝛼	PROPN
iajs-3076	48	15	≤	≤	NUM
iajs-3076	48	16	𝑛	𝑛	PROPN
iajs-3076	48	17	,	,	PUNCT
iajs-3076	48	18	𝑛	𝑛	DET
iajs-3076	48	19	∈	∈	NOUN
iajs-3076	48	20	𝑁.	𝑁.	PROPN
iajs-3076	48	21	(	(	PUNCT
iajs-3076	48	22	2	2	NUM
iajs-3076	48	23	)	)	PUNCT
iajs-3076	48	24	ihjpas	ihjpa	NOUN
iajs-3076	48	25	.	.	PUNCT
iajs-3076	49	1	36	36	NUM
iajs-3076	49	2	(	(	PUNCT
iajs-3076	49	3	3	3	NUM
iajs-3076	49	4	)	)	PUNCT
iajs-3076	49	5	2023	2023	NUM
iajs-3076	49	6	384	384	NUM
iajs-3076	49	7	the	the	DET
iajs-3076	49	8	characteristics	characteristic	NOUN
iajs-3076	49	9	of	of	ADP
iajs-3076	49	10	caputo	caputo	PROPN
iajs-3076	49	11	derivative	derivative	PROPN
iajs-3076	49	12	are	be	AUX
iajs-3076	49	13	1	1	NUM
iajs-3076	49	14	.	.	PUNCT
iajs-3076	49	15	𝐷𝛼𝐼𝛼𝑦(𝑥	𝐷𝛼𝐼𝛼𝑦(𝑥	NOUN
iajs-3076	49	16	)	)	PUNCT
iajs-3076	50	1	=	=	SYM
iajs-3076	50	2	𝑦(𝑥	𝑦(𝑥	PROPN
iajs-3076	50	3	)	)	PUNCT
iajs-3076	50	4	,	,	PUNCT
iajs-3076	50	5	2	2	X
iajs-3076	50	6	.	.	X
iajs-3076	50	7	𝐼𝛼𝐷𝛼𝑦(𝑥	𝐼𝛼𝐷𝛼𝑦(𝑥	PROPN
iajs-3076	50	8	)	)	PUNCT
iajs-3076	50	9	=	=	SYM
iajs-3076	50	10	𝑦(𝑥	𝑦(𝑥	PROPN
iajs-3076	50	11	)	)	PUNCT
iajs-3076	50	12	−	−	PROPN
iajs-3076	51	1	∑𝑛−1	∑𝑛−1	PRON
iajs-3076	51	2	𝑖=0	𝑖=0	PROPN
iajs-3076	51	3	 	 	SPACE
iajs-3076	51	4	𝑦(𝑖)(0	𝑦(𝑖)(0	PROPN
iajs-3076	51	5	)	)	PUNCT
iajs-3076	51	6	𝑥𝑖	𝑥𝑖	ADP
iajs-3076	52	1	𝑖	𝑖	PROPN
iajs-3076	52	2	!	!	PROPN
iajs-3076	52	3	,	,	PUNCT
iajs-3076	53	1	3	3	X
iajs-3076	53	2	.	.	X
iajs-3076	53	3	𝐷𝛼𝜆	𝐷𝛼𝜆	PROPN
iajs-3076	53	4	=	=	SYM
iajs-3076	53	5	0	0	NUM
iajs-3076	53	6	,	,	PUNCT
iajs-3076	53	7	where	where	SCONJ
iajs-3076	53	8	𝜆	𝜆	NOUN
iajs-3076	53	9	is	be	AUX
iajs-3076	53	10	constant	constant	ADJ
iajs-3076	53	11	.	.	PUNCT
iajs-3076	54	1	in	in	ADP
iajs-3076	54	2	this	this	DET
iajs-3076	54	3	study	study	NOUN
iajs-3076	54	4	,	,	PUNCT
iajs-3076	54	5	the	the	DET
iajs-3076	54	6	concept	concept	NOUN
iajs-3076	54	7	of	of	ADP
iajs-3076	54	8	caputo	caputo	PROPN
iajs-3076	54	9	was	be	AUX
iajs-3076	54	10	relied	rely	VERB
iajs-3076	54	11	upon	upon	SCONJ
iajs-3076	54	12	to	to	PART
iajs-3076	54	13	define	define	VERB
iajs-3076	54	14	the	the	DET
iajs-3076	54	15	fractional	fractional	ADJ
iajs-3076	54	16	derivative	derivative	NOUN
iajs-3076	54	17	.	.	PUNCT
iajs-3076	55	1	3	3	X
iajs-3076	55	2	.	.	X
iajs-3076	55	3	bernstein	bernstein	PROPN
iajs-3076	55	4	polynomials	polynomials	PROPN
iajs-3076	55	5	and	and	CCONJ
iajs-3076	55	6	their	their	PRON
iajs-3076	55	7	operational	operational	ADJ
iajs-3076	55	8	matrix	matrix	NOUN
iajs-3076	56	1	[	[	X
iajs-3076	56	2	34,35	34,35	NOUN
iajs-3076	56	3	]	]	PUNCT
iajs-3076	56	4	in	in	ADP
iajs-3076	56	5	this	this	DET
iajs-3076	56	6	section	section	NOUN
iajs-3076	56	7	,	,	PUNCT
iajs-3076	56	8	we	we	PRON
iajs-3076	56	9	will	will	AUX
iajs-3076	56	10	go	go	VERB
iajs-3076	56	11	over	over	ADP
iajs-3076	56	12	bernstein	bernstein	PROPN
iajs-3076	56	13	's	's	PART
iajs-3076	56	14	polynomial	polynomial	NOUN
iajs-3076	56	15	and	and	CCONJ
iajs-3076	56	16	some	some	PRON
iajs-3076	56	17	of	of	ADP
iajs-3076	56	18	its	its	PRON
iajs-3076	56	19	fundamental	fundamental	ADJ
iajs-3076	56	20	properties	property	NOUN
iajs-3076	56	21	,	,	PUNCT
iajs-3076	56	22	as	as	ADV
iajs-3076	56	23	well	well	ADV
iajs-3076	56	24	as	as	ADP
iajs-3076	56	25	a	a	DET
iajs-3076	56	26	description	description	NOUN
iajs-3076	56	27	of	of	ADP
iajs-3076	56	28	an	an	DET
iajs-3076	56	29	operational	operational	ADJ
iajs-3076	56	30	matrix	matrix	NOUN
iajs-3076	56	31	with	with	ADP
iajs-3076	56	32	integer	integer	NOUN
iajs-3076	56	33	and	and	CCONJ
iajs-3076	56	34	fractional	fractional	ADJ
iajs-3076	56	35	derivatives	derivative	NOUN
iajs-3076	56	36	,	,	PUNCT
iajs-3076	56	37	and	and	CCONJ
iajs-3076	56	38	explain	explain	VERB
iajs-3076	56	39	how	how	SCONJ
iajs-3076	56	40	to	to	PART
iajs-3076	56	41	apply	apply	VERB
iajs-3076	56	42	the	the	DET
iajs-3076	56	43	approach	approach	NOUN
iajs-3076	56	44	(	(	PUNCT
iajs-3076	56	45	bom	bom	PROPN
iajs-3076	56	46	)	)	PUNCT
iajs-3076	56	47	for	for	ADP
iajs-3076	56	48	solving	solve	VERB
iajs-3076	56	49	the	the	DET
iajs-3076	56	50	pantograph	pantograph	NOUN
iajs-3076	56	51	equation	equation	NOUN
iajs-3076	56	52	.	.	PUNCT
iajs-3076	57	1	3	3	NUM
iajs-3076	57	2	.	.	NOUN
iajs-3076	57	3	1	1	NUM
iajs-3076	57	4	.	.	X
iajs-3076	57	5	bernstein	bernstein	PROPN
iajs-3076	57	6	polynomials	polynomial	VERB
iajs-3076	57	7	the	the	DET
iajs-3076	57	8	bernstein	bernstein	PROPN
iajs-3076	57	9	polynomials	polynomial	NOUN
iajs-3076	57	10	of	of	ADP
iajs-3076	57	11	degree	degree	NOUN
iajs-3076	57	12	𝑛	𝑛	PROPN
iajs-3076	57	13	on	on	ADP
iajs-3076	57	14	the	the	DET
iajs-3076	57	15	interval	interval	NOUN
iajs-3076	57	16	[	[	X
iajs-3076	57	17	0,1	0,1	NUM
iajs-3076	57	18	]	]	PUNCT
iajs-3076	57	19	are	be	AUX
iajs-3076	57	20	defined	define	VERB
iajs-3076	57	21	by	by	ADP
iajs-3076	57	22	𝐵𝑖,𝑛(𝑥	𝐵𝑖,𝑛(𝑥	NOUN
iajs-3076	57	23	)	)	PUNCT
iajs-3076	58	1	=	=	PUNCT
iajs-3076	58	2	(	(	PUNCT
iajs-3076	58	3	𝑛	𝑛	PROPN
iajs-3076	58	4	𝑖	𝑖	X
iajs-3076	58	5	)	)	PUNCT
iajs-3076	59	1	𝑥𝑖(1	𝑥𝑖(1	NOUN
iajs-3076	59	2	−	−	PROPN
iajs-3076	59	3	𝑥)𝑛−𝑖	𝑥)𝑛−𝑖	ADP
iajs-3076	59	4	,	,	PUNCT
iajs-3076	59	5	for	for	ADP
iajs-3076	59	6	𝑖	𝑖	PRON
iajs-3076	59	7	=	=	SYM
iajs-3076	59	8	0	0	NUM
iajs-3076	59	9	,	,	PUNCT
iajs-3076	59	10	1	1	NUM
iajs-3076	59	11	,	,	PUNCT
iajs-3076	59	12	…	…	PUNCT
iajs-3076	59	13	,	,	PUNCT
iajs-3076	59	14	𝑛	𝑛	NOUN
iajs-3076	59	15	,	,	PUNCT
iajs-3076	59	16	where	where	SCONJ
iajs-3076	59	17	(	(	PUNCT
iajs-3076	59	18	𝑛	𝑛	NOUN
iajs-3076	59	19	𝑖	𝑖	PROPN
iajs-3076	59	20	)	)	PUNCT
iajs-3076	59	21	=	=	SYM
iajs-3076	60	1	𝑛	𝑛	PROPN
iajs-3076	60	2	!	!	PUNCT
iajs-3076	60	3	𝑖	𝑖	X
iajs-3076	60	4	!	!	PUNCT
iajs-3076	61	1	(	(	PUNCT
iajs-3076	61	2	𝑛	𝑛	PRON
iajs-3076	61	3	−	−	NOUN
iajs-3076	61	4	𝑖	𝑖	SYM
iajs-3076	61	5	)	)	PUNCT
iajs-3076	61	6	!	!	PUNCT
iajs-3076	61	7	.	.	PUNCT
iajs-3076	62	1	bernstein	bernstein	PROPN
iajs-3076	62	2	basis	basis	NOUN
iajs-3076	62	3	polynomials	polynomial	NOUN
iajs-3076	62	4	in	in	ADP
iajs-3076	62	5	a	a	DET
iajs-3076	62	6	linear	linear	ADJ
iajs-3076	62	7	combination	combination	NOUN
iajs-3076	62	8	𝐵𝑛(𝑥	𝐵𝑛(𝑥	NOUN
iajs-3076	62	9	)	)	PUNCT
iajs-3076	62	10	=	=	SYM
iajs-3076	63	1	∑𝑛	∑𝑛	ADJ
iajs-3076	63	2	𝑖=0	𝑖=0	PROPN
iajs-3076	63	3	  	  	SPACE
iajs-3076	63	4	𝑐𝑖𝐵𝑖,𝑛(𝑥	𝑐𝑖𝐵𝑖,𝑛(𝑥	NOUN
iajs-3076	63	5	)	)	PUNCT
iajs-3076	63	6	,	,	PUNCT
iajs-3076	63	7	are	be	AUX
iajs-3076	63	8	called	call	VERB
iajs-3076	63	9	a	a	DET
iajs-3076	63	10	bernstein	bernstein	PROPN
iajs-3076	63	11	polynomial	polynomial	PROPN
iajs-3076	63	12	or	or	CCONJ
iajs-3076	63	13	polynomial	polynomial	ADJ
iajs-3076	63	14	in	in	ADP
iajs-3076	63	15	bernstein	bernstein	PROPN
iajs-3076	63	16	form	form	PROPN
iajs-3076	63	17	of	of	ADP
iajs-3076	63	18	degree	degree	NOUN
iajs-3076	63	19	,	,	PUNCT
iajs-3076	63	20	and	and	CCONJ
iajs-3076	63	21	𝑐𝑖	𝑐𝑖	NOUN
iajs-3076	63	22	are	be	AUX
iajs-3076	63	23	called	call	VERB
iajs-3076	63	24	bernstein	bernstein	PROPN
iajs-3076	63	25	coefficients	coefficients	PROPN
iajs-3076	63	26	.	.	PUNCT
iajs-3076	64	1	now	now	ADV
iajs-3076	64	2	we	we	PRON
iajs-3076	64	3	can	can	AUX
iajs-3076	64	4	approximate	approximate	VERB
iajs-3076	64	5	any	any	DET
iajs-3076	64	6	polynomial	polynomial	NOUN
iajs-3076	64	7	of	of	ADP
iajs-3076	64	8	degree	degree	NOUN
iajs-3076	64	9	𝑛	𝑛	ADP
iajs-3076	64	10	to	to	ADP
iajs-3076	64	11	the	the	DET
iajs-3076	64	12	form	form	NOUN
iajs-3076	64	13	of	of	ADP
iajs-3076	64	14	linear	linear	ADJ
iajs-3076	64	15	combination	combination	NOUN
iajs-3076	64	16	,	,	PUNCT
iajs-3076	64	17	as	as	SCONJ
iajs-3076	64	18	given	give	VERB
iajs-3076	64	19	below	below	ADP
iajs-3076	64	20	[	[	PUNCT
iajs-3076	64	21	34	34	NUM
iajs-3076	64	22	]	]	SYM
iajs-3076	64	23	𝑦(𝑥	𝑦(𝑥	PROPN
iajs-3076	64	24	)	)	PUNCT
iajs-3076	64	25	=	=	SYM
iajs-3076	65	1	∑𝑛	∑𝑛	ADJ
iajs-3076	65	2	𝑖=1	𝑖=1	PUNCT
iajs-3076	65	3	  	  	SPACE
iajs-3076	65	4	𝑐𝑖𝐵𝑖,𝑛	𝑐𝑖𝐵𝑖,𝑛	NOUN
iajs-3076	65	5	=	=	SYM
iajs-3076	66	1	𝐶𝑇𝛷(𝑥	𝐶𝑇𝛷(𝑥	PROPN
iajs-3076	66	2	)	)	PUNCT
iajs-3076	66	3	,	,	PUNCT
iajs-3076	66	4	(	(	PUNCT
iajs-3076	66	5	3	3	X
iajs-3076	66	6	)	)	PUNCT
iajs-3076	67	1	where	where	SCONJ
iajs-3076	67	2	𝐶𝑇	𝐶𝑇	PROPN
iajs-3076	67	3	=	=	PUNCT
iajs-3076	68	1	[	[	X
iajs-3076	68	2	𝑐0	𝑐0	NOUN
iajs-3076	68	3	,	,	PUNCT
iajs-3076	68	4	𝑐1	𝑐1	NOUN
iajs-3076	68	5	,	,	PUNCT
iajs-3076	68	6	…	…	PUNCT
iajs-3076	68	7	,	,	PUNCT
iajs-3076	68	8	𝑐𝑛	𝑐𝑛	ADP
iajs-3076	68	9	]	]	PUNCT
iajs-3076	68	10	,	,	PUNCT
iajs-3076	68	11	𝛷(𝑥	𝛷(𝑥	NOUN
iajs-3076	68	12	)	)	PUNCT
iajs-3076	68	13	=	=	PUNCT
iajs-3076	69	1	[	[	X
iajs-3076	69	2	𝐵0,𝑛	𝐵0,𝑛	PROPN
iajs-3076	69	3	,	,	PUNCT
iajs-3076	69	4	𝐵1,𝑛	𝐵1,𝑛	PROPN
iajs-3076	69	5	,	,	PUNCT
iajs-3076	69	6	…	…	PUNCT
iajs-3076	69	7	,	,	PUNCT
iajs-3076	69	8	𝐵𝑛,𝑛],𝑇	𝐵𝑛,𝑛],𝑇	PROPN
iajs-3076	69	9	or	or	CCONJ
iajs-3076	69	10	in	in	ADP
iajs-3076	69	11	the	the	DET
iajs-3076	69	12	form	form	NOUN
iajs-3076	69	13	of	of	ADP
iajs-3076	69	14	a	a	DET
iajs-3076	69	15	matrix	matrix	NOUN
iajs-3076	69	16	resulting	result	VERB
iajs-3076	69	17	from	from	ADP
iajs-3076	69	18	multiplying	multiply	VERB
iajs-3076	69	19	a	a	DET
iajs-3076	69	20	square	square	ADJ
iajs-3076	69	21	matrix	matrix	NOUN
iajs-3076	69	22	(	(	PUNCT
iajs-3076	69	23	𝑛	𝑛	PROPN
iajs-3076	69	24	+	+	NOUN
iajs-3076	69	25	1	1	X
iajs-3076	69	26	)	)	PUNCT
iajs-3076	69	27	×	×	NOUN
iajs-3076	69	28	(	(	PUNCT
iajs-3076	69	29	𝑛	𝑛	PROPN
iajs-3076	69	30	+	+	ADJ
iajs-3076	69	31	1	1	NUM
iajs-3076	69	32	)	)	PUNCT
iajs-3076	69	33	and	and	CCONJ
iajs-3076	69	34	vector	vector	NOUN
iajs-3076	69	35	(	(	PUNCT
iajs-3076	69	36	𝑛	𝑛	PROPN
iajs-3076	69	37	+	+	NOUN
iajs-3076	69	38	1	1	X
iajs-3076	69	39	)	)	PUNCT
iajs-3076	69	40	×	×	NOUN
iajs-3076	69	41	1	1	NUM
iajs-3076	69	42	:	:	PUNCT
iajs-3076	69	43	𝛷(𝑥	𝛷(𝑥	X
iajs-3076	69	44	)	)	PUNCT
iajs-3076	69	45	=	=	SYM
iajs-3076	69	46	𝐴𝑋	𝐴𝑋	PROPN
iajs-3076	69	47	,	,	PUNCT
iajs-3076	69	48	𝐴	𝐴	NOUN
iajs-3076	69	49	=	=	PUNCT
iajs-3076	70	1	[	[	X
iajs-3076	70	2	(	(	PUNCT
iajs-3076	70	3	−1)0(𝑛	−1)0(𝑛	NOUN
iajs-3076	70	4	0	0	NUM
iajs-3076	70	5	)	)	PUNCT
iajs-3076	70	6	(	(	PUNCT
iajs-3076	70	7	−1)1(𝑛	−1)1(𝑛	PROPN
iajs-3076	70	8	0	0	NUM
iajs-3076	70	9	)	)	PUNCT
iajs-3076	70	10	(	(	PUNCT
iajs-3076	70	11	𝑛	𝑛	PRON
iajs-3076	70	12	−	−	NUM
iajs-3076	70	13	0	0	NUM
iajs-3076	70	14	1	1	NUM
iajs-3076	70	15	)	)	PUNCT
iajs-3076	70	16	…	…	PUNCT
iajs-3076	70	17	(	(	PUNCT
iajs-3076	70	18	−1)𝑛−0(𝑛	−1)𝑛−0(𝑛	PROPN
iajs-3076	70	19	0	0	NUM
iajs-3076	70	20	)	)	PUNCT
iajs-3076	70	21	(	(	PUNCT
iajs-3076	70	22	𝑛	𝑛	PROPN
iajs-3076	70	23	−	−	PROPN
iajs-3076	70	24	0	0	NUM
iajs-3076	70	25	𝑛	𝑛	PRON
iajs-3076	70	26	−	−	PROPN
iajs-3076	70	27	0	0	NUM
iajs-3076	70	28	)	)	PUNCT
iajs-3076	70	29	0	0	PUNCT
iajs-3076	71	1	(	(	PUNCT
iajs-3076	71	2	−1)0(𝑛	−1)0(𝑛	PROPN
iajs-3076	71	3	𝑖	𝑖	PROPN
iajs-3076	71	4	)	)	PUNCT
iajs-3076	71	5	…	…	PUNCT
iajs-3076	71	6	(	(	PUNCT
iajs-3076	71	7	−1)𝑛−𝑖(𝑛	−1)𝑛−𝑖(𝑛	ADV
iajs-3076	71	8	𝑖	𝑖	X
iajs-3076	71	9	)	)	PUNCT
iajs-3076	71	10	(	(	PUNCT
iajs-3076	71	11	𝑛	𝑛	PROPN
iajs-3076	71	12	−	−	PROPN
iajs-3076	71	13	𝑖	𝑖	SYM
iajs-3076	71	14	𝑛	𝑛	PRON
iajs-3076	71	15	−	−	PROPN
iajs-3076	71	16	𝑖	𝑖	SYM
iajs-3076	71	17	)	)	PUNCT
iajs-3076	71	18	⋮	⋮	ADJ
iajs-3076	71	19	⋮	⋮	NOUN
iajs-3076	71	20	⋱	⋱	PUNCT
iajs-3076	71	21	⋮	⋮	NOUN
iajs-3076	71	22	0	0	X
iajs-3076	71	23	0	0	NUM
iajs-3076	71	24	…	…	PUNCT
iajs-3076	71	25	(	(	PUNCT
iajs-3076	71	26	−1)0(𝑛	−1)0(𝑛	NOUN
iajs-3076	71	27	𝑛	𝑛	PROPN
iajs-3076	71	28	)	)	PUNCT
iajs-3076	71	29	]	]	PUNCT
iajs-3076	71	30	(	(	PUNCT
iajs-3076	71	31	𝑛+1)×(𝑛+1	𝑛+1)×(𝑛+1	NOUN
iajs-3076	71	32	)	)	PUNCT
iajs-3076	71	33	,	,	PUNCT
iajs-3076	71	34	𝑋	𝑋	NOUN
iajs-3076	71	35	=	=	PUNCT
iajs-3076	72	1	[	[	PUNCT
iajs-3076	72	2	1	1	NUM
iajs-3076	72	3	𝑥	𝑥	PRON
iajs-3076	72	4	𝑥2	𝑥2	NOUN
iajs-3076	72	5	⋮	⋮	NOUN
iajs-3076	72	6	𝑥𝑛	𝑥𝑛	PROPN
iajs-3076	72	7	]	]	PUNCT
iajs-3076	72	8	(	(	PUNCT
iajs-3076	72	9	𝑛+1)×1	𝑛+1)×1	INTJ
iajs-3076	72	10	.	.	PUNCT
iajs-3076	73	1	we	we	PRON
iajs-3076	73	2	note	note	VERB
iajs-3076	73	3	that	that	SCONJ
iajs-3076	73	4	the	the	DET
iajs-3076	73	5	‖𝐴‖	‖𝐴‖	PROPN
iajs-3076	73	6	≠	≠	PROPN
iajs-3076	73	7	0	0	NUM
iajs-3076	73	8	,	,	PUNCT
iajs-3076	73	9	which	which	PRON
iajs-3076	73	10	indicates	indicate	VERB
iajs-3076	73	11	that	that	SCONJ
iajs-3076	73	12	the	the	DET
iajs-3076	73	13	matrix	matrix	NOUN
iajs-3076	73	14	𝐴	𝐴	PROPN
iajs-3076	73	15	is	be	AUX
iajs-3076	73	16	invertible	invertible	ADJ
iajs-3076	73	17	.	.	PUNCT
iajs-3076	74	1	on	on	ADP
iajs-3076	74	2	the	the	DET
iajs-3076	74	3	other	other	ADJ
iajs-3076	74	4	hand	hand	NOUN
iajs-3076	74	5	,	,	PUNCT
iajs-3076	74	6	when	when	SCONJ
iajs-3076	74	7	using	use	VERB
iajs-3076	74	8	the	the	DET
iajs-3076	74	9	bernstein	bernstein	PROPN
iajs-3076	74	10	polynomials	polynomial	NOUN
iajs-3076	74	11	in	in	ADP
iajs-3076	74	12	the	the	DET
iajs-3076	74	13	least	least	ADJ
iajs-3076	74	14	-	-	PUNCT
iajs-3076	74	15	squares	square	NOUN
iajs-3076	74	16	approximation	approximation	NOUN
iajs-3076	74	17	,	,	PUNCT
iajs-3076	74	18	the	the	DET
iajs-3076	74	19	fact	fact	NOUN
iajs-3076	74	20	that	that	SCONJ
iajs-3076	74	21	they	they	PRON
iajs-3076	74	22	are	be	AUX
iajs-3076	74	23	not	not	PART
iajs-3076	74	24	orthogonal	orthogonal	ADJ
iajs-3076	74	25	becomes	become	VERB
iajs-3076	74	26	a	a	DET
iajs-3076	74	27	disadvantage	disadvantage	NOUN
iajs-3076	74	28	.	.	PUNCT
iajs-3076	75	1	according	accord	VERB
iajs-3076	75	2	to	to	ADP
iajs-3076	75	3	[	[	X
iajs-3076	75	4	35	35	NUM
iajs-3076	75	5	]	]	PUNCT
iajs-3076	75	6	,	,	PUNCT
iajs-3076	75	7	one	one	NUM
iajs-3076	75	8	method	method	NOUN
iajs-3076	75	9	for	for	ADP
iajs-3076	75	10	direct	direct	ADJ
iajs-3076	75	11	least	least	ADJ
iajs-3076	75	12	-	-	PUNCT
iajs-3076	75	13	squares	square	NOUN
iajs-3076	75	14	approximation	approximation	NOUN
iajs-3076	75	15	by	by	ADP
iajs-3076	75	16	polynomials	polynomial	NOUN
iajs-3076	75	17	in	in	ADP
iajs-3076	75	18	bernstein	bernstein	PROPN
iajs-3076	75	19	form	form	PROPN
iajs-3076	75	20	relies	rely	VERB
iajs-3076	75	21	on	on	ADP
iajs-3076	75	22	the	the	DET
iajs-3076	75	23	construction	construction	NOUN
iajs-3076	75	24	of	of	ADP
iajs-3076	75	25	the	the	DET
iajs-3076	75	26	ihjpas	ihjpa	NOUN
iajs-3076	75	27	.	.	PUNCT
iajs-3076	76	1	36	36	NUM
iajs-3076	76	2	(	(	PUNCT
iajs-3076	76	3	3	3	NUM
iajs-3076	76	4	)	)	PUNCT
iajs-3076	76	5	2023	2023	NUM
iajs-3076	76	6	385	385	NUM
iajs-3076	76	7	basis	basis	NOUN
iajs-3076	76	8	{	{	PUNCT
iajs-3076	76	9	𝑑0	𝑑0	NOUN
iajs-3076	76	10	𝑛(𝑥	𝑛(𝑥	PROPN
iajs-3076	76	11	)	)	PUNCT
iajs-3076	76	12	,	,	PUNCT
iajs-3076	76	13	𝑑1	𝑑1	NOUN
iajs-3076	76	14	𝑛(𝑥	𝑛(𝑥	PROPN
iajs-3076	76	15	)	)	PUNCT
iajs-3076	76	16	,	,	PUNCT
iajs-3076	76	17	…	…	PUNCT
iajs-3076	76	18	,	,	PUNCT
iajs-3076	76	19	𝑑𝑛	𝑑𝑛	X
iajs-3076	76	20	𝑛(𝑥	𝑛(𝑥	PROPN
iajs-3076	76	21	)	)	PUNCT
iajs-3076	76	22	}	}	PUNCT
iajs-3076	76	23	that	that	PRON
iajs-3076	76	24	is	be	AUX
iajs-3076	76	25	"	"	PUNCT
iajs-3076	76	26	dual	dual	ADJ
iajs-3076	76	27	"	"	PUNCT
iajs-3076	76	28	to	to	ADP
iajs-3076	76	29	the	the	DET
iajs-3076	76	30	bernstein	bernstein	PROPN
iajs-3076	76	31	basis	basis	NOUN
iajs-3076	76	32	of	of	ADP
iajs-3076	76	33	degree	degree	NOUN
iajs-3076	76	34	𝑛	𝑛	NOUN
iajs-3076	76	35	on	on	ADP
iajs-3076	76	36	to	to	ADP
iajs-3076	76	37	[	[	X
iajs-3076	76	38	0,1	0,1	NUM
iajs-3076	76	39	]	]	PUNCT
iajs-3076	76	40	.	.	PUNCT
iajs-3076	77	1	the	the	DET
iajs-3076	77	2	attribute	attribute	NOUN
iajs-3076	77	3	that	that	PRON
iajs-3076	77	4	distinguishes	distinguish	VERB
iajs-3076	77	5	this	this	DET
iajs-3076	77	6	dual	dual	ADJ
iajs-3076	77	7	basis	basis	NOUN
iajs-3076	77	8	is	be	AUX
iajs-3076	77	9	∫	∫	PROPN
iajs-3076	77	10	1	1	NUM
iajs-3076	77	11	0	0	NUM
iajs-3076	77	12	 	 	SPACE
iajs-3076	77	13	𝑏𝑖	𝑏𝑖	ADP
iajs-3076	77	14	𝑛(𝑥)𝑑𝑗	𝑛(𝑥)𝑑𝑗	PROPN
iajs-3076	77	15	𝑛(𝑥)𝑑𝑥	𝑛(𝑥)𝑑𝑥	ADV
iajs-3076	77	16	=	=	PUNCT
iajs-3076	77	17	{	{	PUNCT
iajs-3076	77	18	1	1	NUM
iajs-3076	77	19	𝑓𝑜𝑟	𝑓𝑜𝑟	NOUN
iajs-3076	77	20	𝑖	𝑖	X
iajs-3076	77	21	=	=	SYM
iajs-3076	77	22	𝑗	𝑗	PROPN
iajs-3076	77	23	,	,	PUNCT
iajs-3076	77	24	0	0	NUM
iajs-3076	78	1	𝑓𝑜𝑟	𝑓𝑜𝑟	NOUN
iajs-3076	78	2	𝑖	𝑖	PUNCT
iajs-3076	78	3	≠	≠	PROPN
iajs-3076	78	4	𝑗	𝑗	PROPN
iajs-3076	78	5	,	,	PUNCT
iajs-3076	78	6	for	for	ADP
iajs-3076	78	7	𝑖	𝑖	SYM
iajs-3076	78	8	,	,	PUNCT
iajs-3076	78	9	𝑗	𝑗	NOUN
iajs-3076	78	10	=	=	SYM
iajs-3076	78	11	0,1	0,1	NUM
iajs-3076	78	12	,	,	PUNCT
iajs-3076	78	13	.	.	PUNCT
iajs-3076	78	14	.	.	PUNCT
iajs-3076	78	15	.	.	PUNCT
iajs-3076	78	16	.	.	PUNCT
iajs-3076	78	17	.	.	PUNCT
iajs-3076	78	18	.	.	PUNCT
iajs-3076	79	1	.	.	PUNCT
iajs-3076	80	1	,	,	PUNCT
iajs-3076	80	2	𝑛	𝑛	NOUN
iajs-3076	80	3	,	,	PUNCT
iajs-3076	80	4	where	where	SCONJ
iajs-3076	80	5	𝑑𝑗	𝑑𝑗	PROPN
iajs-3076	80	6	𝑛(𝑥	𝑛(𝑥	PROPN
iajs-3076	80	7	)	)	PUNCT
iajs-3076	81	1	=	=	PUNCT
iajs-3076	82	1	∑𝑛	∑𝑛	ADJ
iajs-3076	82	2	𝑘=0	𝑘=0	VERB
iajs-3076	82	3	 	 	SPACE
iajs-3076	82	4	𝜆𝑗𝑘𝐵𝑘	𝜆𝑗𝑘𝐵𝑘	ADJ
iajs-3076	82	5	𝑛(𝑥	𝑛(𝑥	PROPN
iajs-3076	82	6	)	)	PUNCT
iajs-3076	82	7	,	,	PUNCT
iajs-3076	82	8	𝑗	𝑗	NOUN
iajs-3076	82	9	=	=	SYM
iajs-3076	82	10	0,1	0,1	NUM
iajs-3076	82	11	,	,	PUNCT
iajs-3076	82	12	…	…	PUNCT
iajs-3076	82	13	,	,	PUNCT
iajs-3076	82	14	𝑛	𝑛	NOUN
iajs-3076	82	15	,	,	PUNCT
iajs-3076	82	16	𝜆𝑗𝑘	𝜆𝑗𝑘	PUNCT
iajs-3076	82	17	=	=	SYM
iajs-3076	82	18	(	(	PUNCT
iajs-3076	82	19	−1)𝑗+𝑘	−1)𝑗+𝑘	X
iajs-3076	82	20	(	(	PUNCT
iajs-3076	82	21	𝑛	𝑛	PROPN
iajs-3076	82	22	𝑗	𝑗	NOUN
iajs-3076	82	23	)	)	PUNCT
iajs-3076	82	24	(	(	PUNCT
iajs-3076	82	25	𝑛	𝑛	PROPN
iajs-3076	82	26	𝑘	𝑘	NOUN
iajs-3076	82	27	)	)	PUNCT
iajs-3076	82	28	∑𝑚𝑖𝑛(𝑗,𝑘	∑𝑚𝑖𝑛(𝑗,𝑘	PUNCT
iajs-3076	82	29	)	)	PUNCT
iajs-3076	83	1	𝑖=0	𝑖=0	SYM
iajs-3076	83	2	  	  	SPACE
iajs-3076	83	3	(	(	PUNCT
iajs-3076	83	4	2𝑖	2𝑖	NOUN
iajs-3076	83	5	+	+	CCONJ
iajs-3076	83	6	1)(𝑛	1)(𝑛	NUM
iajs-3076	84	1	+	+	CCONJ
iajs-3076	84	2	𝑖	𝑖	SYM
iajs-3076	84	3	+	+	NOUN
iajs-3076	84	4	1	1	NUM
iajs-3076	84	5	𝑛	𝑛	DET
iajs-3076	84	6	−	−	NOUN
iajs-3076	84	7	𝑗	𝑗	NOUN
iajs-3076	84	8	)	)	PUNCT
iajs-3076	84	9	(	(	PUNCT
iajs-3076	84	10	𝑛	𝑛	PROPN
iajs-3076	84	11	−	−	PROPN
iajs-3076	84	12	𝑖	𝑖	SYM
iajs-3076	84	13	𝑛	𝑛	PRON
iajs-3076	84	14	−	−	NOUN
iajs-3076	84	15	𝑗	𝑗	NOUN
iajs-3076	84	16	)	)	PUNCT
iajs-3076	84	17	(	(	PUNCT
iajs-3076	84	18	𝑛	𝑛	PROPN
iajs-3076	84	19	+	+	NOUN
iajs-3076	84	20	𝑖	𝑖	SYM
iajs-3076	84	21	+	+	NOUN
iajs-3076	84	22	1	1	NUM
iajs-3076	84	23	𝑛	𝑛	DET
iajs-3076	84	24	−	−	PROPN
iajs-3076	84	25	𝑘	𝑘	NOUN
iajs-3076	84	26	)	)	PUNCT
iajs-3076	84	27	(	(	PUNCT
iajs-3076	84	28	𝑛	𝑛	PROPN
iajs-3076	84	29	−	−	PROPN
iajs-3076	84	30	𝑖	𝑖	SYM
iajs-3076	84	31	𝑛	𝑛	PRON
iajs-3076	84	32	−	−	NOUN
iajs-3076	84	33	𝑘	𝑘	NOUN
iajs-3076	84	34	)	)	PUNCT
iajs-3076	84	35	,	,	PUNCT
iajs-3076	84	36	(	(	PUNCT
iajs-3076	84	37	4	4	X
iajs-3076	84	38	)	)	PUNCT
iajs-3076	84	39	for	for	ADP
iajs-3076	84	40	𝑗	𝑗	PROPN
iajs-3076	84	41	,	,	PUNCT
iajs-3076	84	42	𝑘	𝑘	NOUN
iajs-3076	84	43	=	=	SYM
iajs-3076	84	44	0,1	0,1	NUM
iajs-3076	84	45	,	,	PUNCT
iajs-3076	84	46	.	.	PUNCT
iajs-3076	84	47	.	.	PUNCT
iajs-3076	84	48	.	.	PUNCT
iajs-3076	84	49	.	.	PUNCT
iajs-3076	85	1	,	,	PUNCT
iajs-3076	85	2	𝑛.	𝑛.	NOUN
iajs-3076	85	3	3	3	NUM
iajs-3076	85	4	.	.	SYM
iajs-3076	85	5	2	2	NUM
iajs-3076	85	6	operational	operational	ADJ
iajs-3076	85	7	matrix	matrix	NOUN
iajs-3076	85	8	of	of	ADP
iajs-3076	85	9	fractional	fractional	ADJ
iajs-3076	85	10	derivative	derivative	NOUN
iajs-3076	85	11	for	for	ADP
iajs-3076	85	12	bernstein	bernstein	PROPN
iajs-3076	85	13	polynomial	polynomial	PROPN
iajs-3076	85	14	(	(	PUNCT
iajs-3076	85	15	bom	bom	PROPN
iajs-3076	85	16	)	)	PUNCT
iajs-3076	85	17	in	in	ADP
iajs-3076	85	18	the	the	DET
iajs-3076	85	19	beginning	beginning	NOUN
iajs-3076	85	20	,	,	PUNCT
iajs-3076	85	21	we	we	PRON
iajs-3076	85	22	will	will	AUX
iajs-3076	85	23	present	present	VERB
iajs-3076	85	24	the	the	DET
iajs-3076	85	25	operational	operational	ADJ
iajs-3076	85	26	matrix	matrix	NOUN
iajs-3076	85	27	𝐷	𝐷	NOUN
iajs-3076	85	28	of	of	ADP
iajs-3076	85	29	derivatives	derivative	NOUN
iajs-3076	85	30	for	for	ADP
iajs-3076	85	31	bernstein	bernstein	PROPN
iajs-3076	85	32	polynomials	polynomial	NOUN
iajs-3076	85	33	,	,	PUNCT
iajs-3076	85	34	which	which	PRON
iajs-3076	85	35	is	be	AUX
iajs-3076	85	36	a	a	DET
iajs-3076	85	37	square	square	ADJ
iajs-3076	85	38	matrix	matrix	NOUN
iajs-3076	85	39	of	of	ADP
iajs-3076	85	40	degree	degree	NOUN
iajs-3076	85	41	(	(	PUNCT
iajs-3076	85	42	𝑛	𝑛	PROPN
iajs-3076	85	43	+	+	NOUN
iajs-3076	85	44	1	1	X
iajs-3076	85	45	)	)	PUNCT
iajs-3076	85	46	×	×	NOUN
iajs-3076	85	47	(	(	PUNCT
iajs-3076	85	48	𝑛	𝑛	PROPN
iajs-3076	85	49	+	+	NOUN
iajs-3076	85	50	1	1	NUM
iajs-3076	85	51	)	)	PUNCT
iajs-3076	85	52	,	,	PUNCT
iajs-3076	85	53	then	then	ADV
iajs-3076	85	54	the	the	DET
iajs-3076	85	55	derivative	derivative	NOUN
iajs-3076	85	56	of	of	ADP
iajs-3076	85	57	the	the	DET
iajs-3076	85	58	vector	vector	NOUN
iajs-3076	85	59	𝛷(𝑥	𝛷(𝑥	NOUN
iajs-3076	85	60	)	)	PUNCT
iajs-3076	85	61	is	be	AUX
iajs-3076	85	62	ⅆ𝛷(𝑥	ⅆ𝛷(𝑥	PROPN
iajs-3076	85	63	)	)	PUNCT
iajs-3076	85	64	ⅆ𝑥	ⅆ𝑥	NOUN
iajs-3076	85	65	=	=	PROPN
iajs-3076	85	66	𝐷𝛷(𝑥	𝐷𝛷(𝑥	PROPN
iajs-3076	85	67	)	)	PUNCT
iajs-3076	85	68	,	,	PUNCT
iajs-3076	85	69	(	(	PUNCT
iajs-3076	85	70	5	5	X
iajs-3076	85	71	)	)	PUNCT
iajs-3076	85	72	where	where	SCONJ
iajs-3076	85	73	𝐷	𝐷	NOUN
iajs-3076	85	74	is	be	AUX
iajs-3076	85	75	given	give	VERB
iajs-3076	85	76	in	in	ADP
iajs-3076	85	77	[	[	PUNCT
iajs-3076	85	78	34	34	NUM
iajs-3076	85	79	]	]	PUNCT
iajs-3076	85	80	,	,	PUNCT
iajs-3076	85	81	𝐷	𝐷	PROPN
iajs-3076	85	82	=	=	SYM
iajs-3076	85	83	𝐴𝜎𝐵∗	𝐴𝜎𝐵∗	PROPN
iajs-3076	85	84	,	,	PUNCT
iajs-3076	85	85	where	where	SCONJ
iajs-3076	85	86	𝜎	𝜎	PROPN
iajs-3076	85	87	is	be	AUX
iajs-3076	85	88	(	(	PUNCT
iajs-3076	85	89	𝑛	𝑛	PROPN
iajs-3076	85	90	+	+	NOUN
iajs-3076	85	91	1	1	NUM
iajs-3076	85	92	)	)	PUNCT
iajs-3076	85	93	×	×	NOUN
iajs-3076	85	94	(	(	PUNCT
iajs-3076	85	95	𝑛	𝑛	NOUN
iajs-3076	85	96	)	)	PUNCT
iajs-3076	85	97	matrix	matrix	NOUN
iajs-3076	85	98	given	give	VERB
iajs-3076	85	99	in	in	ADP
iajs-3076	85	100	[	[	NOUN
iajs-3076	85	101	35	35	NUM
iajs-3076	85	102	]	]	PUNCT
iajs-3076	85	103	as	as	ADP
iajs-3076	85	104	𝜎	𝜎	NOUN
iajs-3076	85	105	=	=	PUNCT
iajs-3076	86	1	[	[	X
iajs-3076	86	2	0	0	NUM
iajs-3076	86	3	0	0	NUM
iajs-3076	86	4	0	0	NUM
iajs-3076	86	5	…	…	PUNCT
iajs-3076	86	6	0	0	NUM
iajs-3076	86	7	1	1	NUM
iajs-3076	86	8	0	0	NUM
iajs-3076	86	9	0	0	NUM
iajs-3076	86	10	…	…	SYM
iajs-3076	86	11	0	0	NUM
iajs-3076	86	12	0	0	NUM
iajs-3076	86	13	2	2	NUM
iajs-3076	86	14	0	0	NUM
iajs-3076	86	15	…	…	SYM
iajs-3076	86	16	0	0	NUM
iajs-3076	86	17	⋮	⋮	NOUN
iajs-3076	86	18	⋮	⋮	ADJ
iajs-3076	86	19	⋮	⋮	NOUN
iajs-3076	86	20	⋱	⋱	PUNCT
iajs-3076	86	21	0	0	NUM
iajs-3076	86	22	0	0	NUM
iajs-3076	86	23	0	0	NUM
iajs-3076	86	24	0	0	NUM
iajs-3076	86	25	…	…	PUNCT
iajs-3076	86	26	𝑛	𝑛	X
iajs-3076	86	27	]	]	PUNCT
iajs-3076	86	28	and	and	CCONJ
iajs-3076	86	29	,	,	PUNCT
iajs-3076	86	30	𝐵∗	𝐵∗	PROPN
iajs-3076	86	31	is	be	AUX
iajs-3076	86	32	(	(	PUNCT
iajs-3076	86	33	𝑛	𝑛	NOUN
iajs-3076	86	34	)	)	PUNCT
iajs-3076	86	35	×	×	NOUN
iajs-3076	86	36	(	(	PUNCT
iajs-3076	86	37	𝑛	𝑛	PROPN
iajs-3076	86	38	+	+	ADJ
iajs-3076	86	39	1	1	NUM
iajs-3076	86	40	)	)	PUNCT
iajs-3076	86	41	matrix	matrix	NOUN
iajs-3076	86	42	define	define	NOUN
iajs-3076	86	43	as	as	ADP
iajs-3076	86	44	𝐵∗	𝐵∗	NUM
iajs-3076	86	45	=	=	PUNCT
iajs-3076	87	1	[	[	X
iajs-3076	87	2	𝐴[1	𝐴[1	X
iajs-3076	87	3	]	]	X
iajs-3076	87	4	−1	−1	NOUN
iajs-3076	87	5	𝐴[2	𝐴[2	PROPN
iajs-3076	87	6	]	]	PUNCT
iajs-3076	87	7	−1	−1	NOUN
iajs-3076	87	8	⋮	⋮	NOUN
iajs-3076	87	9	𝐴[𝑛	𝐴[𝑛	X
iajs-3076	87	10	]	]	PUNCT
iajs-3076	87	11	−1	−1	NOUN
iajs-3076	87	12	]	]	PUNCT
iajs-3076	87	13	,	,	PUNCT
iajs-3076	87	14	𝐴[𝑘	𝐴[𝑘	PROPN
iajs-3076	87	15	]	]	PUNCT
iajs-3076	87	16	−1	−1	NOUN
iajs-3076	87	17	𝑖𝑠	𝑖𝑠	NOUN
iajs-3076	87	18	𝑘𝑡ℎ	𝑘𝑡ℎ	VERB
iajs-3076	87	19	𝑟𝑜𝑤	𝑟𝑜𝑤	PROPN
iajs-3076	87	20	𝑜𝑓	𝑜𝑓	ADP
iajs-3076	87	21	𝐴−1	𝐴−1	PROPN
iajs-3076	87	22	,	,	PUNCT
iajs-3076	87	23	𝑘	𝑘	NOUN
iajs-3076	87	24	=	=	SYM
iajs-3076	87	25	1,2	1,2	NUM
iajs-3076	87	26	,	,	PUNCT
iajs-3076	87	27	⋯	⋯	NOUN
iajs-3076	87	28	,	,	PUNCT
iajs-3076	87	29	𝑛.	𝑛.	NOUN
iajs-3076	87	30	we	we	PRON
iajs-3076	87	31	can	can	AUX
iajs-3076	87	32	generalize	generalize	VERB
iajs-3076	87	33	eq	eq	ADP
iajs-3076	87	34	.	.	PUNCT
iajs-3076	88	1	(	(	PUNCT
iajs-3076	88	2	5	5	NUM
iajs-3076	88	3	)	)	PUNCT
iajs-3076	88	4	as	as	SCONJ
iajs-3076	88	5	follows	follow	VERB
iajs-3076	88	6	ⅆ𝑛	ⅆ𝑛	PROPN
iajs-3076	88	7	ⅆ𝑥𝑛	ⅆ𝑥𝑛	PROPN
iajs-3076	88	8	𝛷(𝑥	𝛷(𝑥	PROPN
iajs-3076	88	9	)	)	PUNCT
iajs-3076	88	10	=	=	SYM
iajs-3076	88	11	(	(	PUNCT
iajs-3076	88	12	𝐷)𝑛𝛷(𝑥	𝐷)𝑛𝛷(𝑥	PROPN
iajs-3076	88	13	)	)	PUNCT
iajs-3076	88	14	,	,	PUNCT
iajs-3076	88	15	𝑤ℎ𝑒𝑟𝑒	𝑤ℎ𝑒𝑟𝑒	NOUN
iajs-3076	88	16	𝑛	𝑛	NOUN
iajs-3076	88	17	=	=	SYM
iajs-3076	88	18	1	1	NUM
iajs-3076	88	19	,	,	PUNCT
iajs-3076	88	20	2	2	NUM
iajs-3076	88	21	,	,	PUNCT
iajs-3076	88	22	.	.	PUNCT
iajs-3076	88	23	.	.	PUNCT
iajs-3076	89	1	..	..	PUNCT
iajs-3076	90	1	(	(	PUNCT
iajs-3076	90	2	6	6	X
iajs-3076	90	3	)	)	PUNCT
iajs-3076	90	4	let	let	VERB
iajs-3076	90	5	us	we	PRON
iajs-3076	90	6	now	now	ADV
iajs-3076	90	7	introduce	introduce	VERB
iajs-3076	90	8	the	the	DET
iajs-3076	90	9	operational	operational	ADJ
iajs-3076	90	10	matrix	matrix	NOUN
iajs-3076	90	11	of	of	ADP
iajs-3076	90	12	the	the	DET
iajs-3076	90	13	fractional	fractional	ADJ
iajs-3076	90	14	derivatives	derivative	NOUN
iajs-3076	90	15	𝐷(𝛼	𝐷(𝛼	NOUN
iajs-3076	90	16	)	)	PUNCT
iajs-3076	90	17	,	,	PUNCT
iajs-3076	90	18	𝛼	𝛼	X
iajs-3076	90	19	>	>	X
iajs-3076	90	20	0	0	NUM
iajs-3076	90	21	,	,	PUNCT
iajs-3076	90	22	of	of	ADP
iajs-3076	90	23	size	size	NOUN
iajs-3076	90	24	(	(	PUNCT
iajs-3076	90	25	𝑛	𝑛	PROPN
iajs-3076	90	26	+	+	NOUN
iajs-3076	90	27	1	1	NUM
iajs-3076	90	28	)	)	PUNCT
iajs-3076	90	29	×	×	NOUN
iajs-3076	90	30	(	(	PUNCT
iajs-3076	90	31	𝑛	𝑛	PROPN
iajs-3076	90	32	+	+	NOUN
iajs-3076	90	33	1	1	NUM
iajs-3076	90	34	)	)	PUNCT
iajs-3076	90	35	is	be	AUX
iajs-3076	90	36	defined	define	VERB
iajs-3076	90	37	by	by	ADP
iajs-3076	90	38	the	the	DET
iajs-3076	90	39	concept	concept	NOUN
iajs-3076	90	40	of	of	ADP
iajs-3076	90	41	caputo	caputo	PROPN
iajs-3076	90	42	in	in	ADP
iajs-3076	90	43	[	[	X
iajs-3076	90	44	35	35	NUM
iajs-3076	90	45	]	]	SYM
iajs-3076	90	46	𝐷(𝛼	𝐷(𝛼	NOUN
iajs-3076	90	47	)	)	PUNCT
iajs-3076	90	48	=	=	NOUN
iajs-3076	91	1	[	[	X
iajs-3076	91	2	∑𝑛	∑𝑛	ADJ
iajs-3076	91	3	𝑗=⌈𝛼⌉	𝑗=⌈𝛼⌉	NOUN
iajs-3076	91	4	 	 	SPACE
iajs-3076	91	5	𝜔0,𝑗,0	𝜔0,𝑗,0	PROPN
iajs-3076	91	6	∑𝑛	∑𝑛	PROPN
iajs-3076	91	7	𝑗=⌈𝛼⌉	𝑗=⌈𝛼⌉	PROPN
iajs-3076	91	8	 	 	SPACE
iajs-3076	91	9	𝜔0,𝑗,1	𝜔0,𝑗,1	PUNCT
iajs-3076	91	10	…	…	PUNCT
iajs-3076	91	11	∑𝑛	∑𝑛	ADJ
iajs-3076	91	12	𝑗=⌈𝛼⌉	𝑗=⌈𝛼⌉	NOUN
iajs-3076	91	13	 	 	SPACE
iajs-3076	91	14	𝜔0,𝑗,𝑛	𝜔0,𝑗,𝑛	PRON
iajs-3076	91	15	⋮	⋮	NOUN
iajs-3076	91	16	⋮	⋮	NOUN
iajs-3076	91	17	⋮	⋮	NOUN
iajs-3076	91	18	∑𝑛	∑𝑛	PROPN
iajs-3076	91	19	𝑗=⌈𝛼⌉	𝑗=⌈𝛼⌉	PROPN
iajs-3076	91	20	 	 	SPACE
iajs-3076	91	21	𝜔𝑖,𝑗,0	𝜔𝑖,𝑗,0	PROPN
iajs-3076	91	22	∑𝑛	∑𝑛	PROPN
iajs-3076	91	23	𝑗=⌈𝛼⌉	𝑗=⌈𝛼⌉	PROPN
iajs-3076	91	24	 	 	SPACE
iajs-3076	91	25	𝜔𝑖,𝑗,1	𝜔𝑖,𝑗,1	PROPN
iajs-3076	91	26	…	…	PUNCT
iajs-3076	91	27	∑𝑛	∑𝑛	ADJ
iajs-3076	91	28	𝑗=⌈𝛼⌉	𝑗=⌈𝛼⌉	NOUN
iajs-3076	91	29	 	 	SPACE
iajs-3076	91	30	𝜔𝑖,𝑗,𝑛	𝜔𝑖,𝑗,𝑛	PROPN
iajs-3076	91	31	⋮	⋮	NOUN
iajs-3076	91	32	⋮	⋮	ADJ
iajs-3076	91	33	⋮	⋮	ADJ
iajs-3076	91	34	∑𝑛	∑𝑛	ADJ
iajs-3076	91	35	𝑗=⌈𝛼⌉	𝑗=⌈𝛼⌉	PROPN
iajs-3076	91	36	 	 	SPACE
iajs-3076	91	37	𝜔𝑛,𝑗,0	𝜔𝑛,𝑗,0	PROPN
iajs-3076	91	38	∑𝑛	∑𝑛	PROPN
iajs-3076	91	39	𝑗=⌈𝛼⌉	𝑗=⌈𝛼⌉	NOUN
iajs-3076	91	40	 	 	SPACE
iajs-3076	91	41	𝜔𝑛,𝑗,1	𝜔𝑛,𝑗,1	PROPN
iajs-3076	91	42	…	…	PUNCT
iajs-3076	91	43	∑𝑛	∑𝑛	ADJ
iajs-3076	91	44	𝑗=⌈𝛼⌉	𝑗=⌈𝛼⌉	NOUN
iajs-3076	91	45	 	 	SPACE
iajs-3076	91	46	𝜔𝑛,𝑗,𝑛	𝜔𝑛,𝑗,𝑛	NOUN
iajs-3076	91	47	]	]	PUNCT
iajs-3076	91	48	here	here	ADV
iajs-3076	91	49	𝜔𝑖,𝑗,𝑙	𝜔𝑖,𝑗,𝑙	ADJ
iajs-3076	91	50	is	be	AUX
iajs-3076	91	51	given	give	VERB
iajs-3076	91	52	by	by	ADP
iajs-3076	91	53	:	:	PUNCT
iajs-3076	91	54	𝜔𝑖,𝑗,𝑙	𝜔𝑖,𝑗,𝑙	PROPN
iajs-3076	91	55	=	=	PUNCT
iajs-3076	91	56	(	(	PUNCT
iajs-3076	91	57	−1)𝑗−𝑖(𝑛	−1)𝑗−𝑖(𝑛	PROPN
iajs-3076	91	58	𝑖	𝑖	NOUN
iajs-3076	91	59	)	)	PUNCT
iajs-3076	91	60	(	(	PUNCT
iajs-3076	91	61	𝑛	𝑛	PROPN
iajs-3076	91	62	−	−	NOUN
iajs-3076	91	63	𝑖	𝑖	SYM
iajs-3076	91	64	𝑗	𝑗	INTJ
iajs-3076	91	65	−	−	NOUN
iajs-3076	91	66	𝑖	𝑖	SYM
iajs-3076	91	67	)	)	PUNCT
iajs-3076	92	1	𝛤(𝑗	𝛤(𝑗	PRON
iajs-3076	93	1	+	+	NOUN
iajs-3076	93	2	1	1	X
iajs-3076	93	3	)	)	PUNCT
iajs-3076	93	4	𝛤(𝑗	𝛤(𝑗	PRON
iajs-3076	93	5	+	+	CCONJ
iajs-3076	93	6	1	1	NUM
iajs-3076	93	7	−	−	PROPN
iajs-3076	93	8	𝑞	𝑞	NOUN
iajs-3076	93	9	)	)	PUNCT
iajs-3076	93	10	∑	∑	ADP
iajs-3076	93	11	𝑛	𝑛	PRON
iajs-3076	93	12	𝑘=0	𝑘=0	ADV
iajs-3076	93	13	 	 	SPACE
iajs-3076	93	14	𝜆𝑙𝑘𝜇𝑘𝑗	𝜆𝑙𝑘𝜇𝑘𝑗	ADJ
iajs-3076	93	15	,	,	PUNCT
iajs-3076	93	16	where	where	SCONJ
iajs-3076	93	17	𝜆𝑙𝑘	𝜆𝑙𝑘	PROPN
iajs-3076	93	18	is	be	AUX
iajs-3076	93	19	given	give	VERB
iajs-3076	93	20	in	in	ADP
iajs-3076	93	21	eq	eq	ADP
iajs-3076	93	22	.	.	PUNCT
iajs-3076	93	23	(	(	PUNCT
iajs-3076	93	24	4	4	NUM
iajs-3076	93	25	)	)	PUNCT
iajs-3076	93	26	and	and	CCONJ
iajs-3076	93	27	ihjpas	ihjpa	VERB
iajs-3076	93	28	.	.	PUNCT
iajs-3076	94	1	36	36	NUM
iajs-3076	94	2	(	(	PUNCT
iajs-3076	94	3	3	3	NUM
iajs-3076	94	4	)	)	PUNCT
iajs-3076	94	5	2023	2023	NUM
iajs-3076	94	6	386	386	NUM
iajs-3076	94	7	𝜇𝑘𝑗	𝜇𝑘𝑗	NOUN
iajs-3076	94	8	=	=	SYM
iajs-3076	94	9	∑	∑	PUNCT
iajs-3076	94	10	𝑛	𝑛	DET
iajs-3076	94	11	𝑠=𝑘	𝑠=𝑘	NOUN
iajs-3076	94	12	  	  	SPACE
iajs-3076	94	13	(	(	PUNCT
iajs-3076	94	14	−1)𝑠−𝑘(𝑛	−1)𝑠−𝑘(𝑛	NOUN
iajs-3076	94	15	𝑘	𝑘	PROPN
iajs-3076	94	16	)	)	PUNCT
iajs-3076	94	17	(	(	PUNCT
iajs-3076	94	18	𝑛	𝑛	PROPN
iajs-3076	94	19	−	−	NOUN
iajs-3076	94	20	𝑘	𝑘	INTJ
iajs-3076	94	21	𝑠	𝑠	INTJ
iajs-3076	94	22	−	−	PROPN
iajs-3076	94	23	𝑘	𝑘	PROPN
iajs-3076	94	24	)	)	PUNCT
iajs-3076	94	25	1	1	NUM
iajs-3076	94	26	𝑗	𝑗	NOUN
iajs-3076	94	27	−	−	NOUN
iajs-3076	94	28	𝛼	𝛼	NOUN
iajs-3076	95	1	+	+	NOUN
iajs-3076	95	2	𝑠	𝑠	PROPN
iajs-3076	95	3	+	+	NOUN
iajs-3076	95	4	1	1	NUM
iajs-3076	95	5	.	.	X
iajs-3076	96	1	3	3	NUM
iajs-3076	96	2	.	.	NOUN
iajs-3076	96	3	3	3	NUM
iajs-3076	96	4	the	the	DET
iajs-3076	96	5	steps	step	NOUN
iajs-3076	96	6	of	of	ADP
iajs-3076	96	7	applying	apply	VERB
iajs-3076	96	8	the	the	DET
iajs-3076	96	9	bom	bom	NOUN
iajs-3076	96	10	method	method	NOUN
iajs-3076	96	11	for	for	ADP
iajs-3076	96	12	solving	solve	VERB
iajs-3076	96	13	the	the	DET
iajs-3076	96	14	delay	delay	NOUN
iajs-3076	96	15	-	-	PUNCT
iajs-3076	96	16	pantograph	pantograph	NOUN
iajs-3076	96	17	equation	equation	NOUN
iajs-3076	96	18	in	in	ADP
iajs-3076	96	19	this	this	DET
iajs-3076	96	20	paper	paper	NOUN
iajs-3076	96	21	,	,	PUNCT
iajs-3076	96	22	we	we	PRON
iajs-3076	96	23	consider	consider	VERB
iajs-3076	96	24	the	the	DET
iajs-3076	96	25	fractional	fractional	ADJ
iajs-3076	96	26	neutral	neutral	ADJ
iajs-3076	96	27	pantograph	pantograph	NOUN
iajs-3076	96	28	differential	differential	NOUN
iajs-3076	96	29	equation	equation	NOUN
iajs-3076	96	30	𝐷𝛼𝑦(𝑥	𝐷𝛼𝑦(𝑥	NOUN
iajs-3076	96	31	)	)	PUNCT
iajs-3076	96	32	=	=	SYM
iajs-3076	96	33	𝑎(𝑥)𝑦(𝑝𝑥	𝑎(𝑥)𝑦(𝑝𝑥	ADJ
iajs-3076	96	34	)	)	PUNCT
iajs-3076	96	35	+	+	CCONJ
iajs-3076	96	36	𝑏(𝑥)𝐷𝛾𝑦(𝑝𝑥	𝑏(𝑥)𝐷𝛾𝑦(𝑝𝑥	PROPN
iajs-3076	96	37	)	)	PUNCT
iajs-3076	96	38	+	+	NUM
iajs-3076	96	39	𝑑(𝑥)𝑦(𝑥	𝑑(𝑥)𝑦(𝑥	X
iajs-3076	96	40	)	)	PUNCT
iajs-3076	96	41	+	+	CCONJ
iajs-3076	97	1	𝑔(𝑥	𝑔(𝑥	NUM
iajs-3076	97	2	)	)	PUNCT
iajs-3076	97	3	,	,	PUNCT
iajs-3076	97	4	(	(	PUNCT
iajs-3076	97	5	7	7	X
iajs-3076	97	6	)	)	PUNCT
iajs-3076	98	1	where	where	SCONJ
iajs-3076	98	2	𝑥	𝑥	PRON
iajs-3076	98	3	∈	∈	PROPN
iajs-3076	98	4	[	[	X
iajs-3076	98	5	0,1	0,1	NUM
iajs-3076	98	6	]	]	PUNCT
iajs-3076	98	7	,	,	PUNCT
iajs-3076	98	8	0	0	PUNCT
iajs-3076	98	9	<	<	X
iajs-3076	98	10	𝛾	𝛾	X
iajs-3076	98	11	≤	≤	NUM
iajs-3076	98	12	𝛼	𝛼	PRON
iajs-3076	98	13	≤	≤	NUM
iajs-3076	98	14	2	2	NUM
iajs-3076	98	15	,	,	PUNCT
iajs-3076	98	16	0	0	NUM
iajs-3076	98	17	<	<	X
iajs-3076	98	18	𝑝	𝑝	X
iajs-3076	98	19	<	<	X
iajs-3076	98	20	1	1	NUM
iajs-3076	98	21	.	.	PUNCT
iajs-3076	98	22	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-3076	98	23	)	)	PUNCT
iajs-3076	98	24	is	be	AUX
iajs-3076	98	25	the	the	DET
iajs-3076	98	26	unknown	unknown	ADJ
iajs-3076	98	27	function	function	NOUN
iajs-3076	98	28	,	,	PUNCT
iajs-3076	98	29	𝑎	𝑎	X
iajs-3076	98	30	,	,	PUNCT
iajs-3076	98	31	𝑏	𝑏	NOUN
iajs-3076	98	32	,	,	PUNCT
iajs-3076	98	33	𝑑	𝑑	NOUN
iajs-3076	98	34	,	,	PUNCT
iajs-3076	98	35	𝑔	𝑔	PROPN
iajs-3076	98	36	∈	∈	PROPN
iajs-3076	98	37	𝐶[0,1	𝐶[0,1	ADP
iajs-3076	98	38	]	]	PUNCT
iajs-3076	98	39	,	,	PUNCT
iajs-3076	98	40	with	with	ADP
iajs-3076	98	41	initial	initial	ADJ
iajs-3076	98	42	and	and	CCONJ
iajs-3076	98	43	boundary	boundary	ADJ
iajs-3076	98	44	conditions	condition	NOUN
iajs-3076	98	45	.	.	PUNCT
iajs-3076	99	1	now	now	ADV
iajs-3076	99	2	to	to	PART
iajs-3076	99	3	apply	apply	VERB
iajs-3076	99	4	the	the	DET
iajs-3076	99	5	bom	bom	PROPN
iajs-3076	99	6	method	method	NOUN
iajs-3076	99	7	,	,	PUNCT
iajs-3076	99	8	we	we	PRON
iajs-3076	99	9	follow	follow	VERB
iajs-3076	99	10	the	the	DET
iajs-3076	99	11	steps	step	NOUN
iajs-3076	99	12	below	below	ADV
iajs-3076	99	13	:	:	PUNCT
iajs-3076	99	14	iwe	iwe	PROPN
iajs-3076	99	15	will	will	AUX
iajs-3076	99	16	approximate	approximate	VERB
iajs-3076	99	17	unknown	unknown	ADJ
iajs-3076	99	18	function	function	NOUN
iajs-3076	99	19	𝑦	𝑦	PROPN
iajs-3076	99	20	(	(	PUNCT
iajs-3076	99	21	𝑥	𝑥	NOUN
iajs-3076	99	22	)	)	PUNCT
iajs-3076	99	23	by	by	ADP
iajs-3076	99	24	bernstein	bernstein	PROPN
iajs-3076	99	25	polynomials	polynomials	PROPN
iajs-3076	99	26	as	as	ADP
iajs-3076	99	27	(	(	PUNCT
iajs-3076	99	28	3	3	NUM
iajs-3076	99	29	)	)	PUNCT
iajs-3076	99	30	,	,	PUNCT
iajs-3076	99	31	and	and	CCONJ
iajs-3076	99	32	we	we	PRON
iajs-3076	99	33	have	have	VERB
iajs-3076	99	34	𝐷𝑦(𝑥	𝐷𝑦(𝑥	NOUN
iajs-3076	99	35	)	)	PUNCT
iajs-3076	99	36	=	=	PUNCT
iajs-3076	99	37	𝐶𝑇𝐷	𝐶𝑇𝐷	ADV
iajs-3076	99	38	𝛷(𝑥	𝛷(𝑥	NOUN
iajs-3076	99	39	)	)	PUNCT
iajs-3076	99	40	,	,	PUNCT
iajs-3076	99	41	𝐷𝑦(𝑝𝑥	𝐷𝑦(𝑝𝑥	ADV
iajs-3076	99	42	)	)	PUNCT
iajs-3076	99	43	=	=	PUNCT
iajs-3076	99	44	𝐶𝑇𝐷	𝐶𝑇𝐷	ADV
iajs-3076	99	45	𝛷(𝑝𝑥	𝛷(𝑝𝑥	NOUN
iajs-3076	99	46	)	)	PUNCT
iajs-3076	99	47	,	,	PUNCT
iajs-3076	99	48	…	…	PUNCT
iajs-3076	99	49	,	,	PUNCT
iajs-3076	99	50	𝐷𝑛𝑦(𝑥	𝐷𝑛𝑦(𝑥	NOUN
iajs-3076	99	51	)	)	PUNCT
iajs-3076	99	52	=	=	PUNCT
iajs-3076	99	53	𝐶𝑇𝐷𝑛	𝐶𝑇𝐷𝑛	NOUN
iajs-3076	99	54	𝛷(𝑥	𝛷(𝑥	NOUN
iajs-3076	99	55	)	)	PUNCT
iajs-3076	99	56	,	,	PUNCT
iajs-3076	99	57	𝐷𝑛𝑦(𝑝𝑥)𝐶𝑇𝐷𝑛	𝐷𝑛𝑦(𝑝𝑥)𝐶𝑇𝐷𝑛	PROPN
iajs-3076	99	58	𝛷(𝑝𝑥	𝛷(𝑝𝑥	PROPN
iajs-3076	99	59	)	)	PUNCT
iajs-3076	99	60	,	,	PUNCT
iajs-3076	99	61	𝐷𝛼𝑦(𝑥	𝐷𝛼𝑦(𝑥	VERB
iajs-3076	99	62	)	)	PUNCT
iajs-3076	99	63	=	=	SYM
iajs-3076	99	64	𝐶𝑇𝐷(𝛼)𝛷(𝑥	𝐶𝑇𝐷(𝛼)𝛷(𝑥	PROPN
iajs-3076	99	65	)	)	PUNCT
iajs-3076	99	66	,	,	PUNCT
iajs-3076	99	67	𝐷𝛼𝑦(𝑝𝑥	𝐷𝛼𝑦(𝑝𝑥	NOUN
iajs-3076	99	68	)	)	PUNCT
iajs-3076	99	69	=	=	PUNCT
iajs-3076	99	70	𝐶𝑇𝐷(𝛼)𝛷(𝑝𝑥	𝐶𝑇𝐷(𝛼)𝛷(𝑝𝑥	ADJ
iajs-3076	99	71	)	)	PUNCT
iajs-3076	99	72	,	,	PUNCT
iajs-3076	99	73	𝑤ℎ𝑒𝑟𝑒	𝑤ℎ𝑒𝑟𝑒	NOUN
iajs-3076	99	74	𝛼	𝛼	NOUN
iajs-3076	99	75	𝑖𝑠	𝑖𝑠	NOUN
iajs-3076	99	76	𝑜𝑟𝑑𝑒𝑟	𝑜𝑟𝑑𝑒𝑟	NOUN
iajs-3076	99	77	𝑜𝑓	𝑜𝑓	ADP
iajs-3076	99	78	𝑡ℎ𝑒	𝑡ℎ𝑒	NOUN
iajs-3076	99	79	𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑎𝑙	𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑎𝑙	NOUN
iajs-3076	99	80	𝑑𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒.	𝑑𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒.	NOUN
iajs-3076	99	81	iiwe	iiwe	NOUN
iajs-3076	99	82	will	will	AUX
iajs-3076	99	83	substitute	substitute	VERB
iajs-3076	99	84	all	all	DET
iajs-3076	99	85	initial	initial	ADJ
iajs-3076	99	86	or	or	CCONJ
iajs-3076	99	87	boundary	boundary	ADJ
iajs-3076	99	88	conditions	condition	NOUN
iajs-3076	99	89	given	give	VERB
iajs-3076	99	90	in	in	ADP
iajs-3076	99	91	the	the	DET
iajs-3076	99	92	problem	problem	NOUN
iajs-3076	99	93	.	.	PUNCT
iajs-3076	100	1	iiiwe	iiiwe	PROPN
iajs-3076	100	2	use	use	VERB
iajs-3076	100	3	the	the	DET
iajs-3076	100	4	roots	root	NOUN
iajs-3076	100	5	of	of	ADP
iajs-3076	100	6	chebyshev	chebyshev	NOUN
iajs-3076	100	7	polynomials	polynomial	NOUN
iajs-3076	100	8	to	to	PART
iajs-3076	100	9	help	help	VERB
iajs-3076	100	10	reduce	reduce	VERB
iajs-3076	100	11	interpolation	interpolation	NOUN
iajs-3076	100	12	errors	error	NOUN
iajs-3076	100	13	as	as	SCONJ
iajs-3076	100	14	the	the	DET
iajs-3076	100	15	collocation	collocation	NOUN
iajs-3076	100	16	node	node	VERB
iajs-3076	100	17	,	,	PUNCT
iajs-3076	100	18	𝑥𝑖	𝑥𝑖	PROPN
iajs-3076	100	19	=	=	NOUN
iajs-3076	101	1	1	1	NUM
iajs-3076	101	2	2	2	NUM
iajs-3076	101	3	+	+	CCONJ
iajs-3076	101	4	1	1	NUM
iajs-3076	101	5	2𝑐𝑜𝑠	2𝑐𝑜𝑠	NUM
iajs-3076	101	6	(	(	PUNCT
iajs-3076	101	7	(	(	PUNCT
iajs-3076	101	8	2𝑖	2𝑖	NOUN
iajs-3076	101	9	+	+	CCONJ
iajs-3076	101	10	1	1	X
iajs-3076	101	11	)	)	PUNCT
iajs-3076	101	12	𝜋	𝜋	NOUN
iajs-3076	101	13	2𝑛	2𝑛	NUM
iajs-3076	101	14	)	)	PUNCT
iajs-3076	101	15	,	,	PUNCT
iajs-3076	101	16	𝑖	𝑖	NOUN
iajs-3076	101	17	=	=	SYM
iajs-3076	101	18	0,1	0,1	NUM
iajs-3076	101	19	,	,	PUNCT
iajs-3076	101	20	…	…	PUNCT
iajs-3076	101	21	,	,	PUNCT
iajs-3076	101	22	𝑛	𝑛	PRON
iajs-3076	101	23	−	−	NOUN
iajs-3076	101	24	1	1	NUM
iajs-3076	101	25	.	.	X
iajs-3076	102	1	ivwe	ivwe	NOUN
iajs-3076	102	2	substitute	substitute	VERB
iajs-3076	102	3	the	the	DET
iajs-3076	102	4	approximate	approximate	ADJ
iajs-3076	102	5	polynomial	polynomial	ADJ
iajs-3076	102	6	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-3076	102	7	)	)	PUNCT
iajs-3076	102	8	and	and	CCONJ
iajs-3076	102	9	its	its	PRON
iajs-3076	102	10	derivatives	derivative	NOUN
iajs-3076	102	11	in	in	ADP
iajs-3076	102	12	eq	eq	ADP
iajs-3076	102	13	.	.	PUNCT
iajs-3076	103	1	(	(	PUNCT
iajs-3076	103	2	7	7	NUM
iajs-3076	103	3	)	)	PUNCT
iajs-3076	103	4	to	to	PART
iajs-3076	103	5	get	get	VERB
iajs-3076	103	6	the	the	DET
iajs-3076	103	7	system	system	NOUN
iajs-3076	103	8	of	of	ADP
iajs-3076	103	9	algebraic	algebraic	ADJ
iajs-3076	103	10	equations	equation	NOUN
iajs-3076	103	11	that	that	SCONJ
iajs-3076	103	12	we	we	PRON
iajs-3076	103	13	can	can	AUX
iajs-3076	103	14	solve	solve	VERB
iajs-3076	103	15	using	use	VERB
iajs-3076	103	16	computer	computer	NOUN
iajs-3076	103	17	programs	program	NOUN
iajs-3076	103	18	like	like	ADP
iajs-3076	103	19	mathematica	mathematica	PROPN
iajs-3076	103	20	and	and	CCONJ
iajs-3076	103	21	thus	thus	ADV
iajs-3076	103	22	get	get	VERB
iajs-3076	103	23	the	the	DET
iajs-3076	103	24	vector	vector	NOUN
iajs-3076	103	25	values	value	NOUN
iajs-3076	103	26	𝐶𝑇.	𝐶𝑇.	ADV
iajs-3076	103	27	as	as	ADP
iajs-3076	103	28	a	a	DET
iajs-3076	103	29	result	result	NOUN
iajs-3076	103	30	,	,	PUNCT
iajs-3076	103	31	we	we	PRON
iajs-3076	103	32	will	will	AUX
iajs-3076	103	33	get	get	VERB
iajs-3076	103	34	an	an	DET
iajs-3076	103	35	approximate	approximate	ADJ
iajs-3076	103	36	solution	solution	NOUN
iajs-3076	103	37	to	to	ADP
iajs-3076	103	38	the	the	DET
iajs-3076	103	39	problem	problem	NOUN
iajs-3076	103	40	.	.	PUNCT
iajs-3076	104	1	4	4	X
iajs-3076	104	2	.	.	X
iajs-3076	104	3	the	the	DET
iajs-3076	104	4	shifted	shift	VERB
iajs-3076	104	5	legendre	legendre	PROPN
iajs-3076	104	6	polynomials	polynomial	NOUN
iajs-3076	104	7	and	and	CCONJ
iajs-3076	104	8	their	their	PRON
iajs-3076	104	9	operational	operational	ADJ
iajs-3076	104	10	matrix	matrix	NOUN
iajs-3076	104	11	[	[	X
iajs-3076	104	12	36	36	NUM
iajs-3076	104	13	]	]	PUNCT
iajs-3076	104	14	shifted	shift	VERB
iajs-3076	104	15	legendre	legendre	PROPN
iajs-3076	104	16	polynomials	polynomial	NOUN
iajs-3076	104	17	will	will	AUX
iajs-3076	104	18	be	be	AUX
iajs-3076	104	19	discussed	discuss	VERB
iajs-3076	104	20	in	in	ADP
iajs-3076	104	21	this	this	DET
iajs-3076	104	22	section	section	NOUN
iajs-3076	104	23	.	.	PUNCT
iajs-3076	105	1	then	then	ADV
iajs-3076	105	2	we	we	PRON
iajs-3076	105	3	will	will	AUX
iajs-3076	105	4	describe	describe	VERB
iajs-3076	105	5	the	the	DET
iajs-3076	105	6	method	method	NOUN
iajs-3076	105	7	(	(	PUNCT
iajs-3076	105	8	lom	lom	NOUN
iajs-3076	105	9	)	)	PUNCT
iajs-3076	105	10	and	and	CCONJ
iajs-3076	105	11	how	how	SCONJ
iajs-3076	105	12	to	to	PART
iajs-3076	105	13	use	use	VERB
iajs-3076	105	14	it	it	PRON
iajs-3076	105	15	to	to	PART
iajs-3076	105	16	solve	solve	VERB
iajs-3076	105	17	the	the	DET
iajs-3076	105	18	problem	problem	NOUN
iajs-3076	105	19	.	.	PUNCT
iajs-3076	106	1	4	4	NUM
iajs-3076	106	2	.	.	NOUN
iajs-3076	106	3	1	1	NUM
iajs-3076	106	4	.	.	PUNCT
iajs-3076	106	5	legendre	legendre	PROPN
iajs-3076	106	6	polynomials	polynomials	PROPN
iajs-3076	106	7	legendre	legendre	PROPN
iajs-3076	106	8	polynomials	polynomial	NOUN
iajs-3076	106	9	are	be	AUX
iajs-3076	106	10	known	know	VERB
iajs-3076	106	11	for	for	ADP
iajs-3076	106	12	the	the	DET
iajs-3076	106	13	interval	interval	NOUN
iajs-3076	106	14	[	[	X
iajs-3076	106	15	-1,1	-1,1	X
iajs-3076	106	16	]	]	PUNCT
iajs-3076	106	17	and	and	CCONJ
iajs-3076	106	18	can	can	AUX
iajs-3076	106	19	be	be	AUX
iajs-3076	106	20	calculated	calculate	VERB
iajs-3076	106	21	using	use	VERB
iajs-3076	106	22	the	the	DET
iajs-3076	106	23	regression	regression	NOUN
iajs-3076	106	24	relationship	relationship	NOUN
iajs-3076	106	25	as	as	ADP
iajs-3076	106	26	following	follow	VERB
iajs-3076	106	27	𝐿𝑖+1(𝑧	𝐿𝑖+1(𝑧	VERB
iajs-3076	106	28	)	)	PUNCT
iajs-3076	107	1	=	=	SYM
iajs-3076	108	1	2𝑖	2𝑖	NOUN
iajs-3076	108	2	+	+	CCONJ
iajs-3076	108	3	1	1	NUM
iajs-3076	108	4	𝑖	𝑖	SYM
iajs-3076	108	5	+	+	NOUN
iajs-3076	108	6	1	1	NUM
iajs-3076	108	7	𝑧𝐿𝑖(𝑧	𝑧𝐿𝑖(𝑧	NOUN
iajs-3076	108	8	)	)	PUNCT
iajs-3076	109	1	−	−	NOUN
iajs-3076	109	2	𝑖	𝑖	SYM
iajs-3076	110	1	𝑖	𝑖	PUNCT
iajs-3076	111	1	+	+	NOUN
iajs-3076	111	2	1	1	NUM
iajs-3076	111	3	𝐿𝑖−1(𝑧	𝐿𝑖−1(𝑧	NOUN
iajs-3076	111	4	)	)	PUNCT
iajs-3076	111	5	,	,	PUNCT
iajs-3076	111	6	𝑖	𝑖	X
iajs-3076	111	7	=	=	SYM
iajs-3076	111	8	1,2	1,2	NUM
iajs-3076	111	9	,	,	PUNCT
iajs-3076	111	10	…	…	PUNCT
iajs-3076	111	11	(	(	PUNCT
iajs-3076	111	12	8)	8)	NUM
iajs-3076	111	13	where	where	SCONJ
iajs-3076	111	14	𝐿0(𝑧	𝐿0(𝑧	PROPN
iajs-3076	111	15	)	)	PUNCT
iajs-3076	111	16	=	=	SYM
iajs-3076	111	17	1	1	NUM
iajs-3076	111	18	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-3076	111	19	𝐿1(𝑧	𝐿1(𝑧	PROPN
iajs-3076	111	20	)	)	PUNCT
iajs-3076	111	21	=	=	SYM
iajs-3076	111	22	𝑧.	𝑧.	NOUN
iajs-3076	111	23	substitute	substitute	NOUN
iajs-3076	111	24	the	the	DET
iajs-3076	111	25	variable	variable	ADJ
iajs-3076	111	26	𝑧	𝑧	NOUN
iajs-3076	111	27	=	=	SYM
iajs-3076	111	28	2𝑥	2𝑥	NOUN
iajs-3076	111	29	−	−	NOUN
iajs-3076	111	30	1	1	NUM
iajs-3076	111	31	for	for	ADP
iajs-3076	111	32	these	these	DET
iajs-3076	111	33	polynomials	polynomial	NOUN
iajs-3076	111	34	in	in	ADP
iajs-3076	111	35	the	the	DET
iajs-3076	111	36	interval	interval	NOUN
iajs-3076	111	37	[	[	X
iajs-3076	111	38	0,1	0,1	NOUN
iajs-3076	111	39	]	]	PUNCT
iajs-3076	111	40	,	,	PUNCT
iajs-3076	111	41	and	and	CCONJ
iajs-3076	111	42	create	create	VERB
iajs-3076	111	43	the	the	DET
iajs-3076	111	44	socalled	socalle	VERB
iajs-3076	111	45	shifted	shift	VERB
iajs-3076	111	46	legendre	legendre	PROPN
iajs-3076	111	47	polynomial	polynomial	PROPN
iajs-3076	111	48	,	,	PUNCT
iajs-3076	111	49	let	let	VERB
iajs-3076	111	50	𝑃𝑖	𝑃𝑖	ADP
iajs-3076	111	51	(	(	PUNCT
iajs-3076	111	52	𝑥	𝑥	NOUN
iajs-3076	111	53	)	)	PUNCT
iajs-3076	111	54	be	be	AUX
iajs-3076	111	55	a	a	DET
iajs-3076	111	56	symbol	symbol	NOUN
iajs-3076	111	57	for	for	ADP
iajs-3076	111	58	the	the	DET
iajs-3076	111	59	shifted	shift	VERB
iajs-3076	111	60	legendre	legendre	PROPN
iajs-3076	111	61	polynomial	polynomial	ADJ
iajs-3076	111	62	.	.	PUNCT
iajs-3076	112	1	𝑃𝑖	𝑃𝑖	ADP
iajs-3076	112	2	(	(	PUNCT
iajs-3076	112	3	𝑥	𝑥	NOUN
iajs-3076	112	4	)	)	PUNCT
iajs-3076	112	5	is	be	AUX
iajs-3076	112	6	calculated	calculate	VERB
iajs-3076	112	7	as	as	ADP
iajs-3076	112	8	follows	follow	VERB
iajs-3076	112	9	:	:	PUNCT
iajs-3076	112	10	ihjpas	ihjpas	PROPN
iajs-3076	112	11	.	.	PUNCT
iajs-3076	113	1	36	36	NUM
iajs-3076	113	2	(	(	PUNCT
iajs-3076	113	3	3	3	NUM
iajs-3076	113	4	)	)	PUNCT
iajs-3076	113	5	2023	2023	NUM
iajs-3076	113	6	387	387	NUM
iajs-3076	113	7	𝑃𝑖+1(𝑥	𝑃𝑖+1(𝑥	NUM
iajs-3076	113	8	)	)	PUNCT
iajs-3076	113	9	=	=	SYM
iajs-3076	113	10	(	(	PUNCT
iajs-3076	113	11	2𝑖	2𝑖	NOUN
iajs-3076	113	12	+	+	CCONJ
iajs-3076	113	13	1)(2𝑥	1)(2𝑥	NUM
iajs-3076	113	14	−	−	NOUN
iajs-3076	113	15	1	1	NUM
iajs-3076	113	16	)	)	PUNCT
iajs-3076	113	17	(	(	PUNCT
iajs-3076	113	18	𝑖	𝑖	X
iajs-3076	114	1	+	+	NOUN
iajs-3076	114	2	1	1	X
iajs-3076	114	3	)	)	PUNCT
iajs-3076	114	4	𝑃𝑖(𝑥	𝑃𝑖(𝑥	PROPN
iajs-3076	114	5	)	)	PUNCT
iajs-3076	115	1	−	−	NOUN
iajs-3076	115	2	𝑖	𝑖	SYM
iajs-3076	116	1	𝑖	𝑖	PUNCT
iajs-3076	117	1	+	+	NOUN
iajs-3076	117	2	1	1	NUM
iajs-3076	117	3	𝑃𝑖−1(𝑥	𝑃𝑖−1(𝑥	NOUN
iajs-3076	117	4	)	)	PUNCT
iajs-3076	117	5	,	,	PUNCT
iajs-3076	117	6	𝑖	𝑖	NOUN
iajs-3076	117	7	=	=	SYM
iajs-3076	117	8	1,2	1,2	NUM
iajs-3076	117	9	,	,	PUNCT
iajs-3076	117	10	…	…	PUNCT
iajs-3076	117	11	,	,	PUNCT
iajs-3076	117	12	(	(	PUNCT
iajs-3076	117	13	9	9	NUM
iajs-3076	117	14	)	)	PUNCT
iajs-3076	117	15	here	here	ADV
iajs-3076	117	16	𝑃0(𝑥	𝑃0(𝑥	NUM
iajs-3076	117	17	)	)	PUNCT
iajs-3076	117	18	=	=	SYM
iajs-3076	117	19	1	1	NUM
iajs-3076	117	20	and	and	CCONJ
iajs-3076	117	21	𝑃1(𝑥	𝑃1(𝑥	NOUN
iajs-3076	117	22	)	)	PUNCT
iajs-3076	117	23	=	=	VERB
iajs-3076	118	1	𝑥.	𝑥.	VERB
iajs-3076	118	2	the	the	DET
iajs-3076	118	3	following	follow	VERB
iajs-3076	118	4	formulations	formulation	NOUN
iajs-3076	118	5	of	of	ADP
iajs-3076	118	6	the	the	DET
iajs-3076	118	7	shifted	shift	VERB
iajs-3076	118	8	legendre	legendre	PROPN
iajs-3076	118	9	polynomial	polynomial	PROPN
iajs-3076	118	10	of	of	ADP
iajs-3076	118	11	degree	degree	NOUN
iajs-3076	118	12	𝑖	𝑖	DET
iajs-3076	118	13	analytic	analytic	ADJ
iajs-3076	118	14	form	form	NOUN
iajs-3076	118	15	are	be	AUX
iajs-3076	118	16	found	find	VERB
iajs-3076	118	17	in	in	ADP
iajs-3076	118	18	the	the	DET
iajs-3076	118	19	source	source	NOUN
iajs-3076	118	20	[	[	X
iajs-3076	118	21	36	36	NUM
iajs-3076	118	22	]	]	X
iajs-3076	118	23	:	:	PUNCT
iajs-3076	118	24	𝑃𝑖(𝑥	𝑃𝑖(𝑥	PROPN
iajs-3076	118	25	)	)	PUNCT
iajs-3076	118	26	=	=	PUNCT
iajs-3076	119	1	∑	∑	PUNCT
iajs-3076	119	2	𝑖	𝑖	X
iajs-3076	119	3	𝑘=0	𝑘=0	VERB
iajs-3076	119	4	  	  	SPACE
iajs-3076	119	5	(	(	PUNCT
iajs-3076	119	6	−1)𝑖+𝑘	−1)𝑖+𝑘	NUM
iajs-3076	119	7	(	(	PUNCT
iajs-3076	119	8	𝑖	𝑖	PROPN
iajs-3076	119	9	+	+	NUM
iajs-3076	119	10	𝑘	𝑘	NOUN
iajs-3076	119	11	)	)	PUNCT
iajs-3076	119	12	!	!	PUNCT
iajs-3076	120	1	(	(	PUNCT
iajs-3076	120	2	𝑖	𝑖	X
iajs-3076	120	3	−	−	NOUN
iajs-3076	120	4	𝑘	𝑘	NOUN
iajs-3076	120	5	)	)	PUNCT
iajs-3076	120	6	!	!	PUNCT
iajs-3076	121	1	𝑥𝑘	𝑥𝑘	INTJ
iajs-3076	122	1	(	(	PUNCT
iajs-3076	122	2	𝑘!)2	𝑘!)2	INTJ
iajs-3076	122	3	.	.	PUNCT
iajs-3076	123	1	(	(	PUNCT
iajs-3076	123	2	10	10	NUM
iajs-3076	123	3	)	)	PUNCT
iajs-3076	123	4	whereas	whereas	SCONJ
iajs-3076	123	5	:	:	PUNCT
iajs-3076	123	6	𝑃𝑖(1	𝑃𝑖(1	X
iajs-3076	123	7	)	)	PUNCT
iajs-3076	123	8	=	=	SYM
iajs-3076	123	9	1	1	NUM
iajs-3076	123	10	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-3076	123	11	𝑃𝑖(0	𝑃𝑖(0	NOUN
iajs-3076	123	12	)	)	PUNCT
iajs-3076	123	13	=	=	PUNCT
iajs-3076	123	14	(	(	PUNCT
iajs-3076	123	15	−1)𝑖.	−1)𝑖.	NUM
iajs-3076	123	16	the	the	DET
iajs-3076	123	17	requirement	requirement	NOUN
iajs-3076	123	18	of	of	ADP
iajs-3076	123	19	orthogonality	orthogonality	NOUN
iajs-3076	123	20	is	be	AUX
iajs-3076	123	21	:	:	PUNCT
iajs-3076	123	22	∫	∫	PROPN
iajs-3076	123	23	1	1	NUM
iajs-3076	123	24	0	0	NUM
iajs-3076	123	25	 	 	SPACE
iajs-3076	123	26	𝑃𝑖(𝑥)𝑃𝑗(𝑥)𝑑𝑥	𝑃𝑖(𝑥)𝑃𝑗(𝑥)𝑑𝑥	NOUN
iajs-3076	123	27	=	=	SYM
iajs-3076	123	28	{	{	PUNCT
iajs-3076	123	29	1	1	NUM
iajs-3076	123	30	2𝑖+1	2𝑖+1	NOUN
iajs-3076	123	31	𝑓𝑜𝑟	𝑓𝑜𝑟	NOUN
iajs-3076	123	32	𝑖	𝑖	X
iajs-3076	123	33	=	=	SYM
iajs-3076	123	34	𝑗	𝑗	PROPN
iajs-3076	123	35	,	,	PUNCT
iajs-3076	123	36	0	0	NUM
iajs-3076	124	1	𝑓𝑜𝑟	𝑓𝑜𝑟	NOUN
iajs-3076	124	2	𝑖	𝑖	ADP
iajs-3076	124	3	≠	≠	PROPN
iajs-3076	124	4	𝑗.	𝑗.	NOUN
iajs-3076	124	5	the	the	DET
iajs-3076	124	6	shifted	shift	VERB
iajs-3076	124	7	legendre	legendre	PROPN
iajs-3076	124	8	polynomials	polynomials	PROPN
iajs-3076	124	9	'	'	PART
iajs-3076	124	10	power	power	NOUN
iajs-3076	124	11	series	series	NOUN
iajs-3076	124	12	is	be	AUX
iajs-3076	124	13	written	write	VERB
iajs-3076	124	14	as	as	SCONJ
iajs-3076	124	15	follows	follow	VERB
iajs-3076	124	16	:	:	PUNCT
iajs-3076	124	17	𝑃𝑖(𝑥	𝑃𝑖(𝑥	NOUN
iajs-3076	124	18	)	)	PUNCT
iajs-3076	124	19	=	=	PUNCT
iajs-3076	125	1	∑	∑	PUNCT
iajs-3076	125	2	𝑖	𝑖	X
iajs-3076	125	3	𝑘=0	𝑘=0	AUX
iajs-3076	125	4	  	  	SPACE
iajs-3076	125	5	(	(	PUNCT
iajs-3076	125	6	−1)𝑖+𝑘(𝑖	−1)𝑖+𝑘(𝑖	VERB
iajs-3076	125	7	+	+	PROPN
iajs-3076	125	8	𝑘	𝑘	DET
iajs-3076	125	9	𝑘	𝑘	NOUN
iajs-3076	125	10	)	)	PUNCT
iajs-3076	125	11	(	(	PUNCT
iajs-3076	125	12	𝑖	𝑖	X
iajs-3076	125	13	𝑘	𝑘	NOUN
iajs-3076	125	14	)	)	PUNCT
iajs-3076	125	15	𝑥𝑘.	𝑥𝑘.	ADP
iajs-3076	125	16	now	now	ADV
iajs-3076	125	17	we	we	PRON
iajs-3076	125	18	can	can	AUX
iajs-3076	125	19	approximate	approximate	VERB
iajs-3076	125	20	any	any	DET
iajs-3076	125	21	function	function	NOUN
iajs-3076	125	22	based	base	VERB
iajs-3076	125	23	on	on	ADP
iajs-3076	125	24	shifted	shift	VERB
iajs-3076	125	25	legendre	legendre	PROPN
iajs-3076	125	26	polynomial	polynomial	PROPN
iajs-3076	125	27	as	as	SCONJ
iajs-3076	125	28	follows	follow	VERB
iajs-3076	125	29	:	:	PUNCT
iajs-3076	125	30	𝑦(𝑥	𝑦(𝑥	X
iajs-3076	125	31	)	)	PUNCT
iajs-3076	125	32	=	=	PUNCT
iajs-3076	125	33	∑	∑	PUNCT
iajs-3076	125	34	∞	∞	PROPN
iajs-3076	125	35	𝑗=0	𝑗=0	PUNCT
iajs-3076	125	36	  	  	SPACE
iajs-3076	125	37	𝑐𝑗𝑃𝑗(𝑥	𝑐𝑗𝑃𝑗(𝑥	PROPN
iajs-3076	125	38	)	)	PUNCT
iajs-3076	125	39	,	,	PUNCT
iajs-3076	125	40	where	where	SCONJ
iajs-3076	125	41	𝑐𝑗	𝑐𝑗	ADV
iajs-3076	125	42	=	=	X
iajs-3076	125	43	(	(	PUNCT
iajs-3076	125	44	2𝑗	2𝑗	NOUN
iajs-3076	125	45	+	+	NOUN
iajs-3076	125	46	1	1	X
iajs-3076	125	47	)	)	PUNCT
iajs-3076	125	48	∫	∫	NOUN
iajs-3076	125	49	1	1	NUM
iajs-3076	125	50	0	0	NUM
iajs-3076	125	51	 	 	SPACE
iajs-3076	125	52	𝑦(𝑥)𝑃𝑗(𝑥)𝑑𝑥	𝑦(𝑥)𝑃𝑗(𝑥)𝑑𝑥	PROPN
iajs-3076	125	53	,	,	PUNCT
iajs-3076	125	54	𝑗	𝑗	NOUN
iajs-3076	125	55	=	=	SYM
iajs-3076	125	56	1,2	1,2	NUM
iajs-3076	125	57	,	,	PUNCT
iajs-3076	125	58	…	…	PUNCT
iajs-3076	125	59	only	only	ADV
iajs-3076	125	60	the	the	DET
iajs-3076	125	61	first	first	ADJ
iajs-3076	125	62	(	(	PUNCT
iajs-3076	125	63	𝑛	𝑛	PROPN
iajs-3076	125	64	+	+	NOUN
iajs-3076	125	65	1	1	NUM
iajs-3076	125	66	)	)	PUNCT
iajs-3076	125	67	terms	term	NOUN
iajs-3076	125	68	of	of	ADP
iajs-3076	125	69	shifted	shift	VERB
iajs-3076	125	70	legendre	legendre	PROPN
iajs-3076	125	71	polynomials	polynomial	NOUN
iajs-3076	125	72	are	be	AUX
iajs-3076	125	73	considered	consider	VERB
iajs-3076	125	74	in	in	ADP
iajs-3076	125	75	practice	practice	NOUN
iajs-3076	125	76	.	.	PUNCT
iajs-3076	126	1	next	next	ADV
iajs-3076	126	2	,	,	PUNCT
iajs-3076	126	3	there	there	PRON
iajs-3076	126	4	is	be	VERB
iajs-3076	126	5	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-3076	126	6	)	)	PUNCT
iajs-3076	126	7	=	=	PUNCT
iajs-3076	126	8	∑	∑	PUNCT
iajs-3076	126	9	𝑛	𝑛	PRON
iajs-3076	126	10	𝑗=0	𝑗=0	PROPN
iajs-3076	126	11	  	  	SPACE
iajs-3076	126	12	𝑐𝑗𝑃𝑗(𝑥	𝑐𝑗𝑃𝑗(𝑥	NOUN
iajs-3076	126	13	)	)	PUNCT
iajs-3076	126	14	=	=	PUNCT
iajs-3076	127	1	𝐶𝑇𝛷(𝑥	𝐶𝑇𝛷(𝑥	NUM
iajs-3076	127	2	)	)	PUNCT
iajs-3076	127	3	,	,	PUNCT
iajs-3076	127	4	(	(	PUNCT
iajs-3076	127	5	11	11	NUM
iajs-3076	127	6	)	)	PUNCT
iajs-3076	127	7	where	where	SCONJ
iajs-3076	127	8	𝐶𝑇	𝐶𝑇	PROPN
iajs-3076	127	9	=	=	PUNCT
iajs-3076	128	1	[	[	X
iajs-3076	128	2	𝑐0	𝑐0	NOUN
iajs-3076	128	3	,	,	PUNCT
iajs-3076	128	4	…	…	PUNCT
iajs-3076	128	5	,	,	PUNCT
iajs-3076	128	6	𝑐𝑛	𝑐𝑛	ADP
iajs-3076	128	7	]	]	PUNCT
iajs-3076	128	8	,	,	PUNCT
iajs-3076	128	9	𝑡ℎ𝑒	𝑡ℎ𝑒	ADJ
iajs-3076	128	10	𝑠ℎ𝑖𝑓𝑡𝑒𝑑	𝑠ℎ𝑖𝑓𝑡𝑒𝑑	ADJ
iajs-3076	128	11	𝐿𝑒𝑔𝑒𝑛𝑑𝑟𝑒	𝐿𝑒𝑔𝑒𝑛𝑑𝑟𝑒	ADJ
iajs-3076	128	12	𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡	𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡	ADJ
iajs-3076	128	13	𝑣𝑒𝑐𝑡𝑜𝑟	𝑣𝑒𝑐𝑡𝑜𝑟	NOUN
iajs-3076	128	14	,	,	PUNCT
iajs-3076	128	15	𝛷(𝑥	𝛷(𝑥	NOUN
iajs-3076	128	16	)	)	PUNCT
iajs-3076	128	17	=	=	PUNCT
iajs-3076	129	1	[	[	X
iajs-3076	129	2	𝑃0(𝑥	𝑃0(𝑥	NUM
iajs-3076	129	3	)	)	PUNCT
iajs-3076	129	4	,	,	PUNCT
iajs-3076	129	5	𝑃1(𝑥	𝑃1(𝑥	NOUN
iajs-3076	129	6	)	)	PUNCT
iajs-3076	129	7	,	,	PUNCT
iajs-3076	129	8	…	…	PUNCT
iajs-3076	129	9	,	,	PUNCT
iajs-3076	129	10	𝑃𝑛(𝑥)]𝑇	𝑃𝑛(𝑥)]𝑇	VERB
iajs-3076	129	11	𝑡ℎ𝑒	𝑡ℎ𝑒	ADP
iajs-3076	129	12	𝑠ℎ𝑖𝑓𝑡𝑒𝑑	𝑠ℎ𝑖𝑓𝑡𝑒𝑑	ADJ
iajs-3076	129	13	𝐿𝑒𝑔𝑒𝑛𝑑𝑟𝑒	𝐿𝑒𝑔𝑒𝑛𝑑𝑟𝑒	ADJ
iajs-3076	129	14	𝑣𝑒𝑐𝑡𝑜𝑟.	𝑣𝑒𝑐𝑡𝑜𝑟.	NOUN
iajs-3076	129	15	4	4	NUM
iajs-3076	129	16	.	.	NOUN
iajs-3076	129	17	2	2	NUM
iajs-3076	129	18	.	.	PUNCT
iajs-3076	129	19	operational	operational	ADJ
iajs-3076	129	20	matrix	matrix	NOUN
iajs-3076	129	21	of	of	ADP
iajs-3076	129	22	fractional	fractional	ADJ
iajs-3076	129	23	derivative	derivative	NOUN
iajs-3076	129	24	for	for	ADP
iajs-3076	129	25	shifted	shift	VERB
iajs-3076	129	26	legendre	legendre	PROPN
iajs-3076	129	27	polynomials	polynomials	PROPN
iajs-3076	129	28	(	(	PUNCT
iajs-3076	129	29	lom	lom	PROPN
iajs-3076	129	30	)	)	PUNCT
iajs-3076	129	31	the	the	DET
iajs-3076	129	32	operational	operational	ADJ
iajs-3076	129	33	matrix	matrix	NOUN
iajs-3076	129	34	of	of	ADP
iajs-3076	129	35	derivatives	derivative	NOUN
iajs-3076	129	36	defined	define	VERB
iajs-3076	129	37	based	base	VERB
iajs-3076	129	38	on	on	ADP
iajs-3076	129	39	shifted	shift	VERB
iajs-3076	129	40	legendre	legendre	PROPN
iajs-3076	129	41	polynomials	polynomial	NOUN
iajs-3076	129	42	is	be	AUX
iajs-3076	129	43	denoted	denote	VERB
iajs-3076	129	44	by	by	ADP
iajs-3076	129	45	𝐷(1	𝐷(1	NUM
iajs-3076	129	46	)	)	PUNCT
iajs-3076	129	47	of	of	ADP
iajs-3076	129	48	degree	degree	NOUN
iajs-3076	129	49	(	(	PUNCT
iajs-3076	129	50	𝑛	𝑛	PROPN
iajs-3076	129	51	+	+	NOUN
iajs-3076	129	52	1	1	X
iajs-3076	129	53	)	)	PUNCT
iajs-3076	129	54	×	×	NOUN
iajs-3076	129	55	(	(	PUNCT
iajs-3076	129	56	𝑛	𝑛	PROPN
iajs-3076	129	57	+	+	NOUN
iajs-3076	129	58	1	1	NUM
iajs-3076	129	59	)	)	PUNCT
iajs-3076	129	60	and	and	CCONJ
iajs-3076	129	61	can	can	AUX
iajs-3076	129	62	be	be	AUX
iajs-3076	129	63	expressed	express	VERB
iajs-3076	129	64	in	in	ADP
iajs-3076	129	65	the	the	DET
iajs-3076	129	66	following	follow	VERB
iajs-3076	129	67	form	form	NOUN
iajs-3076	129	68	[	[	X
iajs-3076	129	69	36	36	NUM
iajs-3076	129	70	]	]	PUNCT
iajs-3076	129	71	ihjpas	ihjpa	NOUN
iajs-3076	129	72	.	.	PUNCT
iajs-3076	130	1	36	36	NUM
iajs-3076	130	2	(	(	PUNCT
iajs-3076	130	3	3	3	NUM
iajs-3076	130	4	)	)	PUNCT
iajs-3076	130	5	2023	2023	NUM
iajs-3076	130	6	388	388	NUM
iajs-3076	130	7	𝐷(1	𝐷(1	NUM
iajs-3076	130	8	)	)	PUNCT
iajs-3076	130	9	=	=	PRON
iajs-3076	130	10	(	(	PUNCT
iajs-3076	130	11	𝑑𝑖𝑗	𝑑𝑖𝑗	ADJ
iajs-3076	130	12	)	)	PUNCT
iajs-3076	130	13	=	=	PUNCT
iajs-3076	130	14	{	{	PUNCT
iajs-3076	130	15	2(2𝑗	2(2𝑗	NUM
iajs-3076	130	16	+	+	NUM
iajs-3076	130	17	1	1	NUM
iajs-3076	130	18	)	)	PUNCT
iajs-3076	130	19	,	,	PUNCT
iajs-3076	130	20	𝑓𝑜𝑟	𝑓𝑜𝑟	ADV
iajs-3076	130	21	𝑗	𝑗	X
iajs-3076	131	1	=	=	SYM
iajs-3076	131	2	𝑖	𝑖	SYM
iajs-3076	131	3	−	−	PROPN
iajs-3076	131	4	𝑘	𝑘	PROPN
iajs-3076	131	5	,	,	PUNCT
iajs-3076	131	6	0	0	NUM
iajs-3076	131	7	,	,	PUNCT
iajs-3076	131	8	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	VERB
iajs-3076	131	9	{	{	PUNCT
iajs-3076	131	10	𝑘	𝑘	NOUN
iajs-3076	131	11	=	=	SYM
iajs-3076	131	12	1,3	1,3	NUM
iajs-3076	131	13	,	,	PUNCT
iajs-3076	131	14	…	…	PUNCT
iajs-3076	131	15	,	,	PUNCT
iajs-3076	131	16	𝑛	𝑛	PROPN
iajs-3076	131	17	,	,	PUNCT
iajs-3076	131	18	𝑖𝑓	𝑖𝑓	ADP
iajs-3076	131	19	𝑛	𝑛	ADP
iajs-3076	131	20	𝑜𝑑𝑑.	𝑜𝑑𝑑.	NOUN
iajs-3076	132	1	𝑘	𝑘	X
iajs-3076	132	2	=	=	SYM
iajs-3076	132	3	1,3	1,3	NUM
iajs-3076	132	4	,	,	PUNCT
iajs-3076	132	5	…	…	PUNCT
iajs-3076	132	6	,	,	PUNCT
iajs-3076	132	7	𝑛	𝑛	PRON
iajs-3076	132	8	−	−	PROPN
iajs-3076	132	9	1	1	NUM
iajs-3076	132	10	,	,	PUNCT
iajs-3076	132	11	𝑖𝑓	𝑖𝑓	ADP
iajs-3076	132	12	𝑛	𝑛	DET
iajs-3076	132	13	𝑒𝑣𝑒𝑛.	𝑒𝑣𝑒𝑛.	NOUN
iajs-3076	132	14	the	the	DET
iajs-3076	132	15	vector	vector	NOUN
iajs-3076	132	16	's	's	PART
iajs-3076	132	17	derivative	derivative	ADJ
iajs-3076	132	18	𝛷(𝑥	𝛷(𝑥	NOUN
iajs-3076	132	19	)	)	PUNCT
iajs-3076	132	20	can	can	AUX
iajs-3076	132	21	be	be	AUX
iajs-3076	132	22	written	write	VERB
iajs-3076	132	23	as	as	SCONJ
iajs-3076	132	24	follows	follow	VERB
iajs-3076	132	25	𝑑𝛷(𝑥	𝑑𝛷(𝑥	NOUN
iajs-3076	132	26	)	)	PUNCT
iajs-3076	132	27	𝑑𝑥	𝑑𝑥	VERB
iajs-3076	132	28	=	=	VERB
iajs-3076	132	29	𝐷(1)𝛷.	𝐷(1)𝛷.	NOUN
iajs-3076	132	30	(	(	PUNCT
iajs-3076	132	31	12	12	NUM
iajs-3076	132	32	)	)	PUNCT
iajs-3076	132	33	we	we	PRON
iajs-3076	132	34	can	can	AUX
iajs-3076	132	35	generalize	generalize	VERB
iajs-3076	132	36	equation	equation	NOUN
iajs-3076	132	37	(	(	PUNCT
iajs-3076	132	38	12	12	NUM
iajs-3076	132	39	)	)	PUNCT
iajs-3076	132	40	as	as	ADP
iajs-3076	132	41	𝑑𝑛𝛷(𝑥	𝑑𝑛𝛷(𝑥	PROPN
iajs-3076	132	42	)	)	PUNCT
iajs-3076	132	43	𝑑𝑥𝑛	𝑑𝑥𝑛	VERB
iajs-3076	132	44	=	=	PUNCT
iajs-3076	132	45	(	(	PUNCT
iajs-3076	132	46	𝐷(1	𝐷(1	NUM
iajs-3076	132	47	)	)	PUNCT
iajs-3076	132	48	)	)	PUNCT
iajs-3076	132	49	𝑛	𝑛	DET
iajs-3076	132	50	𝛷(𝑥	𝛷(𝑥	NOUN
iajs-3076	132	51	)	)	PUNCT
iajs-3076	132	52	,	,	PUNCT
iajs-3076	132	53	𝑛	𝑛	NOUN
iajs-3076	132	54	=	=	SYM
iajs-3076	132	55	1	1	NUM
iajs-3076	132	56	,	,	PUNCT
iajs-3076	132	57	2	2	NUM
iajs-3076	132	58	,	,	PUNCT
iajs-3076	132	59	.	.	PUNCT
iajs-3076	132	60	.	.	PUNCT
iajs-3076	132	61	.	.	PUNCT
iajs-3076	132	62	.	.	PUNCT
iajs-3076	132	63	.	.	PUNCT
iajs-3076	132	64	.	.	PUNCT
iajs-3076	133	1	(	(	PUNCT
iajs-3076	133	2	13	13	NUM
iajs-3076	133	3	)	)	PUNCT
iajs-3076	133	4	let	let	VERB
iajs-3076	133	5	us	we	PRON
iajs-3076	133	6	now	now	ADV
iajs-3076	133	7	represent	represent	VERB
iajs-3076	133	8	the	the	DET
iajs-3076	133	9	fractional	fractional	ADJ
iajs-3076	133	10	derivative	derivative	ADJ
iajs-3076	133	11	operational	operational	ADJ
iajs-3076	133	12	matrix	matrix	NOUN
iajs-3076	133	13	𝐷(𝛼	𝐷(𝛼	NOUN
iajs-3076	133	14	)	)	PUNCT
iajs-3076	133	15	,	,	PUNCT
iajs-3076	133	16	𝛼	𝛼	X
iajs-3076	133	17	>	>	X
iajs-3076	133	18	0	0	NUM
iajs-3076	133	19	,	,	PUNCT
iajs-3076	133	20	of	of	ADP
iajs-3076	133	21	size	size	NOUN
iajs-3076	133	22	(	(	PUNCT
iajs-3076	133	23	𝑛	𝑛	PROPN
iajs-3076	133	24	+	+	NOUN
iajs-3076	133	25	1	1	NUM
iajs-3076	133	26	)	)	PUNCT
iajs-3076	133	27	×	×	NOUN
iajs-3076	133	28	(	(	PUNCT
iajs-3076	133	29	𝑛	𝑛	PROPN
iajs-3076	133	30	+	+	NOUN
iajs-3076	133	31	1	1	NUM
iajs-3076	133	32	)	)	PUNCT
iajs-3076	133	33	defined	define	VERB
iajs-3076	133	34	by	by	ADP
iajs-3076	133	35	the	the	DET
iajs-3076	133	36	caputo	caputo	PROPN
iajs-3076	133	37	concept	concept	NOUN
iajs-3076	133	38	in	in	ADP
iajs-3076	133	39	the	the	DET
iajs-3076	133	40	source	source	NOUN
iajs-3076	133	41	[	[	X
iajs-3076	133	42	36	36	NUM
iajs-3076	133	43	]	]	PUNCT
iajs-3076	133	44	as	as	SCONJ
iajs-3076	133	45	follows	follow	VERB
iajs-3076	133	46	:	:	PUNCT
iajs-3076	134	1	𝐷𝛼	𝐷𝛼	NOUN
iajs-3076	134	2	=	=	PUNCT
iajs-3076	135	1	[	[	X
iajs-3076	135	2	0	0	NUM
iajs-3076	135	3	0	0	NUM
iajs-3076	135	4	⋯	⋯	NOUN
iajs-3076	135	5	0	0	NUM
iajs-3076	135	6	⋮	⋮	NOUN
iajs-3076	135	7	⋮	⋮	NOUN
iajs-3076	135	8	⋯	⋯	VERB
iajs-3076	135	9	⋮	⋮	NOUN
iajs-3076	135	10	0	0	NUM
iajs-3076	135	11	0	0	NUM
iajs-3076	135	12	⋯	⋯	NOUN
iajs-3076	135	13	0	0	NUM
iajs-3076	135	14	∑⌈𝛼⌉	∑⌈𝛼⌉	PROPN
iajs-3076	135	15	𝑘=⌈𝛼⌉	𝑘=⌈𝛼⌉	PROPN
iajs-3076	135	16	 	 	SPACE
iajs-3076	135	17	𝜃⌈𝛼⌉,0,𝑘	𝜃⌈𝛼⌉,0,𝑘	NOUN
iajs-3076	135	18	∑	∑	PUNCT
iajs-3076	135	19	⌈𝛼⌉	⌈𝛼⌉	ADJ
iajs-3076	135	20	𝑘=⌈𝛼⌉	𝑘=⌈𝛼⌉	PROPN
iajs-3076	135	21	 	 	SPACE
iajs-3076	135	22	𝜃⌈𝛼⌉,1,𝑘	𝜃⌈𝛼⌉,1,𝑘	NOUN
iajs-3076	135	23	⋯	⋯	VERB
iajs-3076	135	24	∑	∑	PROPN
iajs-3076	135	25	⌈𝛼⌉	⌈𝛼⌉	ADJ
iajs-3076	135	26	𝑘=⌈𝛼⌉	𝑘=⌈𝛼⌉	PROPN
iajs-3076	135	27	 	 	SPACE
iajs-3076	135	28	𝜃⌈𝛼⌉,𝑛,𝑘	𝜃⌈𝛼⌉,𝑛,𝑘	NOUN
iajs-3076	135	29	⋮	⋮	NOUN
iajs-3076	135	30	⋮	⋮	NOUN
iajs-3076	135	31	⋯	⋯	NOUN
iajs-3076	135	32	⋮	⋮	NOUN
iajs-3076	135	33	∑𝑖	∑𝑖	PROPN
iajs-3076	135	34	𝑘=⌈𝛼⌉	𝑘=⌈𝛼⌉	PROPN
iajs-3076	135	35	 	 	SPACE
iajs-3076	135	36	𝜃𝑖,0,𝑘	𝜃𝑖,0,𝑘	PUNCT
iajs-3076	136	1	∑𝑖	∑𝑖	PROPN
iajs-3076	136	2	𝑘=⌈𝛼⌉	𝑘=⌈𝛼⌉	PROPN
iajs-3076	136	3	 	 	SPACE
iajs-3076	136	4	𝜃𝑖,1,𝑘	𝜃𝑖,1,𝑘	NOUN
iajs-3076	136	5	⋯	⋯	PUNCT
iajs-3076	136	6	∑𝑖	∑𝑖	PROPN
iajs-3076	136	7	𝑘=⌈𝛼⌉	𝑘=⌈𝛼⌉	PROPN
iajs-3076	136	8	 	 	SPACE
iajs-3076	136	9	𝜃𝑖,𝑛,𝑘	𝜃𝑖,𝑛,𝑘	NOUN
iajs-3076	136	10	⋮	⋮	NOUN
iajs-3076	136	11	⋮	⋮	NOUN
iajs-3076	136	12	⋯	⋯	VERB
iajs-3076	136	13	⋮	⋮	NOUN
iajs-3076	136	14	∑𝑛	∑𝑛	PROPN
iajs-3076	136	15	𝑘=⌈𝛼⌉	𝑘=⌈𝛼⌉	PROPN
iajs-3076	136	16	 	 	SPACE
iajs-3076	136	17	𝜃𝑛,0,𝑘	𝜃𝑛,0,𝑘	NOUN
iajs-3076	136	18	∑𝑛	∑𝑛	PROPN
iajs-3076	136	19	𝑘=⌈𝛼⌉	𝑘=⌈𝛼⌉	PROPN
iajs-3076	136	20	 	 	SPACE
iajs-3076	136	21	𝜃𝑛,1,𝑘	𝜃𝑛,1,𝑘	NOUN
iajs-3076	136	22	⋯	⋯	ADP
iajs-3076	136	23	∑𝑛	∑𝑛	PROPN
iajs-3076	136	24	𝑘=⌈𝛼⌉	𝑘=⌈𝛼⌉	PROPN
iajs-3076	136	25	 	 	SPACE
iajs-3076	136	26	𝜃𝑛,𝑛,𝑘	𝜃𝑛,𝑛,𝑘	NOUN
iajs-3076	136	27	]	]	PUNCT
iajs-3076	136	28	,	,	PUNCT
iajs-3076	136	29	where	where	SCONJ
iajs-3076	136	30	𝜃𝑖,𝑗,𝑘	𝜃𝑖,𝑗,𝑘	X
iajs-3076	136	31	𝑖𝑠	𝑖𝑠	CCONJ
iajs-3076	136	32	𝑑𝑒𝑓𝑖𝑛𝑒𝑑	𝑑𝑒𝑓𝑖𝑛𝑒𝑑	ADJ
iajs-3076	136	33	𝑏𝑦	𝑏𝑦	NOUN
iajs-3076	136	34	𝜃𝑖,𝑗,𝑘	𝜃𝑖,𝑗,𝑘	PROPN
iajs-3076	136	35	=	=	PUNCT
iajs-3076	136	36	(	(	PUNCT
iajs-3076	136	37	2𝑗	2𝑗	NOUN
iajs-3076	136	38	+	+	NOUN
iajs-3076	136	39	1	1	NUM
iajs-3076	136	40	)	)	PUNCT
iajs-3076	136	41	∑	∑	NOUN
iajs-3076	136	42	𝑗	𝑗	INTJ
iajs-3076	136	43	𝑙=0	𝑙=0	NOUN
iajs-3076	136	44	  	  	SPACE
iajs-3076	136	45	(	(	PUNCT
iajs-3076	136	46	−1)𝑖+𝑗+𝑘+𝑙(𝑖	−1)𝑖+𝑗+𝑘+𝑙(𝑖	NUM
iajs-3076	136	47	+	+	CCONJ
iajs-3076	136	48	𝑘	𝑘	NOUN
iajs-3076	136	49	)	)	PUNCT
iajs-3076	136	50	!	!	PUNCT
iajs-3076	137	1	(	(	PUNCT
iajs-3076	137	2	𝑙	𝑙	X
iajs-3076	137	3	+	+	CCONJ
iajs-3076	137	4	𝑗	𝑗	NOUN
iajs-3076	137	5	)	)	PUNCT
iajs-3076	137	6	!	!	PUNCT
iajs-3076	138	1	(	(	PUNCT
iajs-3076	138	2	𝑖	𝑖	X
iajs-3076	138	3	−	−	NOUN
iajs-3076	138	4	𝑘	𝑘	NOUN
iajs-3076	138	5	)	)	PUNCT
iajs-3076	138	6	!	!	PUNCT
iajs-3076	139	1	𝑘	𝑘	X
iajs-3076	139	2	!	!	PUNCT
iajs-3076	140	1	𝛤(𝑘	𝛤(𝑘	NUM
iajs-3076	140	2	−	−	PROPN
iajs-3076	140	3	𝛼	𝛼	NOUN
iajs-3076	140	4	+	+	NOUN
iajs-3076	140	5	1)(𝑗	1)(𝑗	NUM
iajs-3076	140	6	−	−	PROPN
iajs-3076	140	7	𝑙	𝑙	NOUN
iajs-3076	140	8	)	)	PUNCT
iajs-3076	140	9	!	!	PUNCT
iajs-3076	141	1	(	(	PUNCT
iajs-3076	141	2	𝑙!)2(𝑘	𝑙!)2(𝑘	X
iajs-3076	142	1	+	+	NOUN
iajs-3076	143	1	𝑙	𝑙	PART
iajs-3076	143	2	−	−	NOUN
iajs-3076	143	3	𝛼	𝛼	NOUN
iajs-3076	143	4	+	+	NOUN
iajs-3076	143	5	1	1	NUM
iajs-3076	143	6	)	)	PUNCT
iajs-3076	143	7	.	.	PUNCT
iajs-3076	144	1	it	it	PRON
iajs-3076	144	2	is	be	AUX
iajs-3076	144	3	worth	worth	ADJ
iajs-3076	144	4	noting	note	VERB
iajs-3076	144	5	that	that	SCONJ
iajs-3076	144	6	the	the	DET
iajs-3076	144	7	initial	initial	ADJ
iajs-3076	144	8	⌈𝛼⌉	⌈𝛼⌉	NOUN
iajs-3076	144	9	rows	row	VERB
iajs-3076	144	10	in	in	ADP
iajs-3076	144	11	𝐷(𝛼)are	𝐷(𝛼)are	PROPN
iajs-3076	144	12	all	all	DET
iajs-3076	144	13	zero	zero	NUM
iajs-3076	144	14	.	.	PUNCT
iajs-3076	145	1	4.3	4.3	NUM
iajs-3076	145	2	the	the	DET
iajs-3076	145	3	steps	step	NOUN
iajs-3076	145	4	of	of	ADP
iajs-3076	145	5	applying	apply	VERB
iajs-3076	145	6	the	the	DET
iajs-3076	145	7	lom	lom	NOUN
iajs-3076	145	8	method	method	NOUN
iajs-3076	145	9	for	for	ADP
iajs-3076	145	10	solving	solve	VERB
iajs-3076	145	11	the	the	DET
iajs-3076	145	12	delay	delay	NOUN
iajs-3076	145	13	-	-	PUNCT
iajs-3076	145	14	pantograph	pantograph	NOUN
iajs-3076	145	15	equation	equation	NOUN
iajs-3076	145	16	iwe	iwe	PROPN
iajs-3076	145	17	will	will	AUX
iajs-3076	145	18	approximate	approximate	VERB
iajs-3076	145	19	unknown	unknown	ADJ
iajs-3076	145	20	function	function	NOUN
iajs-3076	145	21	𝑦	𝑦	PROPN
iajs-3076	145	22	(	(	PUNCT
iajs-3076	145	23	𝑥	𝑥	NOUN
iajs-3076	145	24	)	)	PUNCT
iajs-3076	145	25	by	by	ADP
iajs-3076	145	26	legendre	legendre	PROPN
iajs-3076	145	27	polynomials	polynomial	NOUN
iajs-3076	145	28	as	as	ADP
iajs-3076	145	29	eq	eq	ADJ
iajs-3076	145	30	.	.	PUNCT
iajs-3076	146	1	(	(	PUNCT
iajs-3076	146	2	11	11	NUM
iajs-3076	146	3	)	)	PUNCT
iajs-3076	146	4	,	,	PUNCT
iajs-3076	146	5	and	and	CCONJ
iajs-3076	146	6	we	we	PRON
iajs-3076	146	7	have	have	VERB
iajs-3076	146	8	𝐷𝑦(𝑥	𝐷𝑦(𝑥	NOUN
iajs-3076	146	9	)	)	PUNCT
iajs-3076	147	1	=	=	PUNCT
iajs-3076	147	2	𝐶𝑇𝐷	𝐶𝑇𝐷	ADV
iajs-3076	147	3	𝛷(𝑥	𝛷(𝑥	NOUN
iajs-3076	147	4	)	)	PUNCT
iajs-3076	147	5	,	,	PUNCT
iajs-3076	147	6	𝐷𝑦(𝑝𝑥	𝐷𝑦(𝑝𝑥	ADV
iajs-3076	147	7	)	)	PUNCT
iajs-3076	147	8	=	=	PUNCT
iajs-3076	147	9	𝐶𝑇𝐷	𝐶𝑇𝐷	ADV
iajs-3076	147	10	𝛷(𝑝𝑥	𝛷(𝑝𝑥	NOUN
iajs-3076	147	11	)	)	PUNCT
iajs-3076	147	12	,	,	PUNCT
iajs-3076	147	13	…	…	PUNCT
iajs-3076	147	14	,	,	PUNCT
iajs-3076	147	15	𝐷𝑛𝑦(𝑥	𝐷𝑛𝑦(𝑥	NOUN
iajs-3076	147	16	)	)	PUNCT
iajs-3076	147	17	=	=	PUNCT
iajs-3076	147	18	𝐶𝑇𝐷𝑛	𝐶𝑇𝐷𝑛	NOUN
iajs-3076	147	19	𝛷(𝑥	𝛷(𝑥	NOUN
iajs-3076	147	20	)	)	PUNCT
iajs-3076	147	21	,	,	PUNCT
iajs-3076	147	22	𝐷𝑛𝑦(𝑝𝑥)𝐶𝑇𝐷𝑛	𝐷𝑛𝑦(𝑝𝑥)𝐶𝑇𝐷𝑛	PROPN
iajs-3076	147	23	𝛷(𝑝𝑥	𝛷(𝑝𝑥	PROPN
iajs-3076	147	24	)	)	PUNCT
iajs-3076	147	25	,	,	PUNCT
iajs-3076	147	26	𝐷𝛼𝑦(𝑥	𝐷𝛼𝑦(𝑥	VERB
iajs-3076	147	27	)	)	PUNCT
iajs-3076	147	28	=	=	SYM
iajs-3076	148	1	𝐶𝑇𝐷(𝛼)𝛷(𝑥	𝐶𝑇𝐷(𝛼)𝛷(𝑥	PROPN
iajs-3076	148	2	)	)	PUNCT
iajs-3076	148	3	,	,	PUNCT
iajs-3076	148	4	𝐷𝛼𝑦(𝑝𝑥	𝐷𝛼𝑦(𝑝𝑥	NOUN
iajs-3076	148	5	)	)	PUNCT
iajs-3076	148	6	=	=	PUNCT
iajs-3076	148	7	𝐶𝑇𝐷(𝛼)𝛷(𝑝𝑥	𝐶𝑇𝐷(𝛼)𝛷(𝑝𝑥	ADJ
iajs-3076	148	8	)	)	PUNCT
iajs-3076	148	9	,	,	PUNCT
iajs-3076	148	10	𝑤ℎ𝑒𝑟𝑒	𝑤ℎ𝑒𝑟𝑒	NOUN
iajs-3076	148	11	𝛼	𝛼	NOUN
iajs-3076	148	12	𝑖𝑠	𝑖𝑠	NOUN
iajs-3076	148	13	𝑜𝑟𝑑𝑒𝑟	𝑜𝑟𝑑𝑒𝑟	NOUN
iajs-3076	148	14	𝑜𝑓	𝑜𝑓	ADP
iajs-3076	148	15	𝑡ℎ𝑒	𝑡ℎ𝑒	NOUN
iajs-3076	148	16	𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑎𝑙	𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑎𝑙	NOUN
iajs-3076	148	17	𝑑𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒.	𝑑𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒.	NOUN
iajs-3076	148	18	iiwe	iiwe	NOUN
iajs-3076	148	19	will	will	AUX
iajs-3076	148	20	substitute	substitute	VERB
iajs-3076	148	21	all	all	DET
iajs-3076	148	22	initial	initial	ADJ
iajs-3076	148	23	or	or	CCONJ
iajs-3076	148	24	boundary	boundary	ADJ
iajs-3076	148	25	conditions	condition	NOUN
iajs-3076	148	26	given	give	VERB
iajs-3076	148	27	in	in	ADP
iajs-3076	148	28	the	the	DET
iajs-3076	148	29	problem	problem	NOUN
iajs-3076	148	30	.	.	PUNCT
iajs-3076	149	1	iiiwe	iiiwe	PROPN
iajs-3076	149	2	use	use	VERB
iajs-3076	149	3	the	the	DET
iajs-3076	149	4	roots	root	NOUN
iajs-3076	149	5	of	of	ADP
iajs-3076	149	6	chebyshev	chebyshev	NOUN
iajs-3076	149	7	polynomials	polynomial	NOUN
iajs-3076	149	8	can	can	AUX
iajs-3076	149	9	help	help	VERB
iajs-3076	149	10	reduce	reduce	VERB
iajs-3076	149	11	interpolation	interpolation	NOUN
iajs-3076	149	12	errors	error	NOUN
iajs-3076	149	13	as	as	SCONJ
iajs-3076	149	14	the	the	DET
iajs-3076	149	15	collocation	collocation	NOUN
iajs-3076	149	16	node	node	VERB
iajs-3076	149	17	,	,	PUNCT
iajs-3076	149	18	𝑥𝑖	𝑥𝑖	PROPN
iajs-3076	149	19	=	=	NOUN
iajs-3076	150	1	1	1	NUM
iajs-3076	150	2	2	2	NUM
iajs-3076	150	3	+	+	CCONJ
iajs-3076	150	4	1	1	NUM
iajs-3076	150	5	2𝑐𝑜𝑠	2𝑐𝑜𝑠	NUM
iajs-3076	150	6	(	(	PUNCT
iajs-3076	150	7	(	(	PUNCT
iajs-3076	150	8	2𝑖	2𝑖	NOUN
iajs-3076	150	9	+	+	CCONJ
iajs-3076	150	10	1	1	X
iajs-3076	150	11	)	)	PUNCT
iajs-3076	150	12	𝜋	𝜋	NOUN
iajs-3076	150	13	2𝑛	2𝑛	NUM
iajs-3076	150	14	)	)	PUNCT
iajs-3076	150	15	,	,	PUNCT
iajs-3076	150	16	𝑖	𝑖	NOUN
iajs-3076	150	17	=	=	SYM
iajs-3076	150	18	0,1	0,1	NUM
iajs-3076	150	19	,	,	PUNCT
iajs-3076	150	20	…	…	PUNCT
iajs-3076	150	21	,	,	PUNCT
iajs-3076	150	22	𝑛	𝑛	PRON
iajs-3076	150	23	−	−	NOUN
iajs-3076	150	24	1	1	NUM
iajs-3076	150	25	.	.	X
iajs-3076	151	1	ivwe	ivwe	NOUN
iajs-3076	151	2	substitute	substitute	VERB
iajs-3076	151	3	the	the	DET
iajs-3076	151	4	approximate	approximate	ADJ
iajs-3076	151	5	polynomial	polynomial	ADJ
iajs-3076	151	6	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-3076	151	7	)	)	PUNCT
iajs-3076	151	8	and	and	CCONJ
iajs-3076	151	9	its	its	PRON
iajs-3076	151	10	derivatives	derivative	NOUN
iajs-3076	151	11	in	in	ADP
iajs-3076	151	12	eq	eq	ADP
iajs-3076	151	13	.	.	PUNCT
iajs-3076	152	1	(	(	PUNCT
iajs-3076	152	2	7	7	NUM
iajs-3076	152	3	)	)	PUNCT
iajs-3076	152	4	to	to	PART
iajs-3076	152	5	get	get	VERB
iajs-3076	152	6	the	the	DET
iajs-3076	152	7	system	system	NOUN
iajs-3076	152	8	of	of	ADP
iajs-3076	152	9	algebraic	algebraic	ADJ
iajs-3076	152	10	equations	equation	NOUN
iajs-3076	152	11	that	that	SCONJ
iajs-3076	152	12	we	we	PRON
iajs-3076	152	13	can	can	AUX
iajs-3076	152	14	solve	solve	VERB
iajs-3076	152	15	using	use	VERB
iajs-3076	152	16	computer	computer	NOUN
iajs-3076	152	17	programs	program	NOUN
iajs-3076	152	18	like	like	ADP
iajs-3076	152	19	mathematica	mathematica	PROPN
iajs-3076	152	20	and	and	CCONJ
iajs-3076	152	21	thus	thus	ADV
iajs-3076	152	22	get	get	VERB
iajs-3076	152	23	the	the	DET
iajs-3076	152	24	vector	vector	NOUN
iajs-3076	152	25	values	value	NOUN
iajs-3076	152	26	𝐶𝑇	𝐶𝑇	PROPN
iajs-3076	152	27	as	as	ADP
iajs-3076	152	28	a	a	DET
iajs-3076	152	29	result	result	NOUN
iajs-3076	152	30	,	,	PUNCT
iajs-3076	152	31	we	we	PRON
iajs-3076	152	32	will	will	AUX
iajs-3076	152	33	get	get	VERB
iajs-3076	152	34	an	an	DET
iajs-3076	152	35	approximate	approximate	ADJ
iajs-3076	152	36	solution	solution	NOUN
iajs-3076	152	37	to	to	ADP
iajs-3076	152	38	the	the	DET
iajs-3076	152	39	problem	problem	NOUN
iajs-3076	152	40	.	.	PUNCT
iajs-3076	153	1	5	5	X
iajs-3076	153	2	.	.	X
iajs-3076	153	3	illustrative	illustrative	ADJ
iajs-3076	153	4	examples	example	NOUN
iajs-3076	153	5	ihjpas	ihjpa	VERB
iajs-3076	153	6	.	.	PUNCT
iajs-3076	154	1	36	36	NUM
iajs-3076	154	2	(	(	PUNCT
iajs-3076	154	3	3	3	NUM
iajs-3076	154	4	)	)	PUNCT
iajs-3076	154	5	2023	2023	NUM
iajs-3076	154	6	389	389	NUM
iajs-3076	154	7	in	in	ADP
iajs-3076	154	8	this	this	DET
iajs-3076	154	9	section	section	NOUN
iajs-3076	154	10	,	,	PUNCT
iajs-3076	154	11	some	some	DET
iajs-3076	154	12	numerical	numerical	ADJ
iajs-3076	154	13	examples	example	NOUN
iajs-3076	154	14	are	be	AUX
iajs-3076	154	15	given	give	VERB
iajs-3076	154	16	to	to	PART
iajs-3076	154	17	demonstrate	demonstrate	VERB
iajs-3076	154	18	the	the	DET
iajs-3076	154	19	applicability	applicability	NOUN
iajs-3076	154	20	and	and	CCONJ
iajs-3076	154	21	accuracy	accuracy	NOUN
iajs-3076	154	22	of	of	ADP
iajs-3076	154	23	the	the	DET
iajs-3076	154	24	proposed	propose	VERB
iajs-3076	154	25	method	method	NOUN
iajs-3076	154	26	.	.	PUNCT
iajs-3076	155	1	𝑀𝑎𝑡ℎ𝑒𝑚𝑎𝑡𝑖𝑐𝑎	𝑀𝑎𝑡ℎ𝑒𝑚𝑎𝑡𝑖𝑐𝑎	NOUN
iajs-3076	155	2	®	®	NOUN
iajs-3076	155	3	12	12	NUM
iajs-3076	155	4	is	be	AUX
iajs-3076	155	5	used	use	VERB
iajs-3076	155	6	for	for	ADP
iajs-3076	155	7	all	all	DET
iajs-3076	155	8	numerical	numerical	ADJ
iajs-3076	155	9	calculations	calculation	NOUN
iajs-3076	155	10	.	.	PUNCT
iajs-3076	156	1	example	example	NOUN
iajs-3076	156	2	1	1	NUM
iajs-3076	156	3	:	:	PUNCT
iajs-3076	156	4	consider	consider	VERB
iajs-3076	156	5	the	the	DET
iajs-3076	156	6	following	follow	VERB
iajs-3076	156	7	fractional	fractional	ADJ
iajs-3076	156	8	neutral	neutral	ADJ
iajs-3076	156	9	pantograph	pantograph	NOUN
iajs-3076	156	10	differential	differential	NOUN
iajs-3076	156	11	equation	equation	NOUN
iajs-3076	156	12	𝐷𝛼𝑦(𝑥	𝐷𝛼𝑦(𝑥	NOUN
iajs-3076	156	13	)	)	PUNCT
iajs-3076	156	14	=	=	PUNCT
iajs-3076	156	15	−𝑦(𝑥	−𝑦(𝑥	NOUN
iajs-3076	156	16	)	)	PUNCT
iajs-3076	156	17	+	+	NUM
iajs-3076	156	18	0.1𝑦(0.8𝑥	0.1𝑦(0.8𝑥	NUM
iajs-3076	156	19	)	)	PUNCT
iajs-3076	157	1	+	+	CCONJ
iajs-3076	157	2	0.5𝐷𝛼𝑦(0.8𝑥	0.5𝐷𝛼𝑦(0.8𝑥	NUM
iajs-3076	157	3	)	)	PUNCT
iajs-3076	158	1	+	+	CCONJ
iajs-3076	158	2	𝑔(𝑥	𝑔(𝑥	NUM
iajs-3076	158	3	)	)	PUNCT
iajs-3076	158	4	,	,	PUNCT
iajs-3076	158	5	𝑥	𝑥	PROPN
iajs-3076	158	6	∈	∈	NOUN
iajs-3076	158	7	(	(	PUNCT
iajs-3076	158	8	0,1	0,1	NOUN
iajs-3076	158	9	]	]	PUNCT
iajs-3076	158	10	,	,	PUNCT
iajs-3076	158	11	(	(	PUNCT
iajs-3076	158	12	14	14	NUM
iajs-3076	158	13	)	)	PUNCT
iajs-3076	158	14	𝑦(0	𝑦(0	PROPN
iajs-3076	158	15	)	)	PUNCT
iajs-3076	158	16	=	=	SYM
iajs-3076	158	17	0	0	NUM
iajs-3076	158	18	,	,	PUNCT
iajs-3076	158	19	𝑤𝑖𝑡ℎ	𝑤𝑖𝑡ℎ	NOUN
iajs-3076	158	20	0	0	PUNCT
iajs-3076	159	1	<	<	X
iajs-3076	159	2	𝛼	𝛼	X
iajs-3076	159	3	≤	≤	NUM
iajs-3076	159	4	1	1	NUM
iajs-3076	159	5	.	.	PUNCT
iajs-3076	160	1	now	now	ADV
iajs-3076	160	2	to	to	PART
iajs-3076	160	3	solve	solve	VERB
iajs-3076	160	4	eq	eq	ADP
iajs-3076	160	5	.	.	PUNCT
iajs-3076	161	1	(	(	PUNCT
iajs-3076	161	2	14	14	NUM
iajs-3076	161	3	)	)	PUNCT
iajs-3076	161	4	by	by	ADP
iajs-3076	161	5	(	(	PUNCT
iajs-3076	161	6	bom	bom	PROPN
iajs-3076	161	7	)	)	PUNCT
iajs-3076	161	8	,	,	PUNCT
iajs-3076	161	9	the	the	DET
iajs-3076	161	10	exact	exact	ADJ
iajs-3076	161	11	solution	solution	NOUN
iajs-3076	161	12	to	to	ADP
iajs-3076	161	13	this	this	DET
iajs-3076	161	14	problem	problem	NOUN
iajs-3076	161	15	for	for	ADP
iajs-3076	161	16	𝛼	𝛼	NOUN
iajs-3076	161	17	=	=	SYM
iajs-3076	161	18	0.8	0.8	NUM
iajs-3076	161	19	is	be	AUX
iajs-3076	161	20	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-3076	161	21	)	)	PUNCT
iajs-3076	161	22	=	=	PUNCT
iajs-3076	162	1	𝑥3.8	𝑥3.8	ADJ
iajs-3076	162	2	with	with	ADP
iajs-3076	162	3	(	(	PUNCT
iajs-3076	162	4	𝑥	𝑥	NOUN
iajs-3076	162	5	)	)	PUNCT
iajs-3076	162	6	=	=	SYM
iajs-3076	162	7	2.211894885744887𝑥3	2.211894885744887𝑥3	NUM
iajs-3076	162	8	+	+	CCONJ
iajs-3076	162	9	0.9571706039258614𝑥3.8	0.9571706039258614𝑥3.8	NOUN
iajs-3076	162	10	,	,	PUNCT
iajs-3076	162	11	and	and	CCONJ
iajs-3076	162	12	with	with	ADP
iajs-3076	162	13	𝑛	𝑛	PROPN
iajs-3076	162	14	=	=	SYM
iajs-3076	162	15	2	2	NUM
iajs-3076	162	16	,	,	PUNCT
iajs-3076	162	17	by	by	ADP
iajs-3076	162	18	applying	apply	VERB
iajs-3076	162	19	the	the	DET
iajs-3076	162	20	suggested	suggest	VERB
iajs-3076	162	21	method	method	NOUN
iajs-3076	162	22	in	in	ADP
iajs-3076	162	23	section	section	NOUN
iajs-3076	162	24	(	(	PUNCT
iajs-3076	162	25	3	3	NUM
iajs-3076	162	26	-	-	SYM
iajs-3076	162	27	2	2	NUM
iajs-3076	162	28	)	)	PUNCT
iajs-3076	162	29	,	,	PUNCT
iajs-3076	162	30	we	we	PRON
iajs-3076	162	31	have	have	VERB
iajs-3076	162	32	𝐷0.8	𝐷0.8	NOUN
iajs-3076	162	33	=	=	PUNCT
iajs-3076	163	1	[	[	X
iajs-3076	163	2	−1.14334	−1.14334	X
iajs-3076	163	3	−	−	PROPN
iajs-3076	163	4	1.55	1.55	NUM
iajs-3076	163	5	−	−	NOUN
iajs-3076	163	6	0.276996	0.276996	NUM
iajs-3076	163	7	1.17281	1.17281	NUM
iajs-3076	163	8	0.872243	0.872243	NUM
iajs-3076	163	9	−	−	PROPN
iajs-3076	163	10	1.55	1.55	NUM
iajs-3076	163	11	−	−	PROPN
iajs-3076	163	12	0.0294677	0.0294677	NUM
iajs-3076	163	13	0.677756	0.677756	NUM
iajs-3076	163	14	1.82699	1.82699	NUM
iajs-3076	163	15	]	]	PUNCT
iajs-3076	163	16	by	by	ADP
iajs-3076	163	17	applying	apply	VERB
iajs-3076	163	18	the	the	DET
iajs-3076	163	19	condition	condition	NOUN
iajs-3076	163	20	given	give	VERB
iajs-3076	163	21	in	in	ADP
iajs-3076	163	22	the	the	DET
iajs-3076	163	23	problem	problem	NOUN
iajs-3076	163	24	and	and	CCONJ
iajs-3076	163	25	following	follow	VERB
iajs-3076	163	26	the	the	DET
iajs-3076	163	27	solution	solution	NOUN
iajs-3076	163	28	steps	step	NOUN
iajs-3076	163	29	mentioned	mention	VERB
iajs-3076	163	30	in	in	ADP
iajs-3076	163	31	section	section	NOUN
iajs-3076	163	32	)	)	PUNCT
iajs-3076	163	33	3	3	NUM
iajs-3076	163	34	-	-	SYM
iajs-3076	163	35	3	3	NUM
iajs-3076	163	36	)	)	PUNCT
iajs-3076	163	37	,	,	PUNCT
iajs-3076	163	38	a	a	DET
iajs-3076	163	39	system	system	NOUN
iajs-3076	163	40	of	of	ADP
iajs-3076	163	41	algebraic	algebraic	ADJ
iajs-3076	163	42	equations	equation	NOUN
iajs-3076	163	43	will	will	AUX
iajs-3076	163	44	be	be	AUX
iajs-3076	163	45	produced	produce	VERB
iajs-3076	163	46	,	,	PUNCT
iajs-3076	163	47	and	and	CCONJ
iajs-3076	163	48	by	by	ADP
iajs-3076	163	49	solving	solve	VERB
iajs-3076	163	50	this	this	DET
iajs-3076	163	51	system	system	NOUN
iajs-3076	163	52	,	,	PUNCT
iajs-3076	163	53	we	we	PRON
iajs-3076	163	54	get	get	VERB
iajs-3076	163	55	the	the	DET
iajs-3076	163	56	values	value	NOUN
iajs-3076	163	57	of	of	ADP
iajs-3076	163	58	𝑐0	𝑐0	NOUN
iajs-3076	163	59	=	=	SYM
iajs-3076	163	60	0	0	NUM
iajs-3076	163	61	,	,	PUNCT
iajs-3076	163	62	𝑐1	𝑐1	NOUN
iajs-3076	163	63	=	=	NOUN
iajs-3076	163	64	0.0118614	0.0118614	NUM
iajs-3076	163	65	,	,	PUNCT
iajs-3076	163	66	𝑐2	𝑐2	NOUN
iajs-3076	163	67	=	=	SYM
iajs-3076	163	68	0.472083	0.472083	NUM
iajs-3076	163	69	,	,	PUNCT
iajs-3076	163	70	the	the	DET
iajs-3076	163	71	approximate	approximate	ADJ
iajs-3076	163	72	solution	solution	NOUN
iajs-3076	163	73	is	be	AUX
iajs-3076	163	74	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-3076	163	75	)	)	PUNCT
iajs-3076	164	1	=	=	SYM
iajs-3076	165	1	0.0237227𝑥	0.0237227𝑥	PROPN
iajs-3076	165	2	+	+	NUM
iajs-3076	165	3	0.44836𝑥2	0.44836𝑥2	NUM
iajs-3076	165	4	.	.	PUNCT
iajs-3076	166	1	if	if	SCONJ
iajs-3076	166	2	𝑛	𝑛	PROPN
iajs-3076	166	3	=	=	SYM
iajs-3076	166	4	15	15	NUM
iajs-3076	166	5	,	,	PUNCT
iajs-3076	166	6	we	we	PRON
iajs-3076	166	7	have	have	VERB
iajs-3076	166	8	the	the	DET
iajs-3076	166	9	following	follow	VERB
iajs-3076	166	10	approximate	approximate	ADJ
iajs-3076	166	11	solution	solution	NOUN
iajs-3076	166	12	:	:	PUNCT
iajs-3076	166	13	𝑦(𝑥	𝑦(𝑥	NUM
iajs-3076	166	14	)	)	PUNCT
iajs-3076	166	15	=	=	NUM
iajs-3076	167	1	9.543602968653811	9.543602968653811	NUM
iajs-3076	167	2	×	×	NOUN
iajs-3076	167	3	10−17	10−17	NUM
iajs-3076	167	4	+	+	NOUN
iajs-3076	167	5	0.000006511676397407056𝑥	0.000006511676397407056𝑥	NUM
iajs-3076	167	6	−	−	NUM
iajs-3076	167	7	0.0007034719961872769𝑥2	0.0007034719961872769𝑥2	NUM
iajs-3076	168	1	+	+	NOUN
iajs-3076	168	2	0.03467000244609836𝑥3	0.03467000244609836𝑥3	NUM
iajs-3076	169	1	+	+	CCONJ
iajs-3076	169	2	1.4120584194534938𝑥4	1.4120584194534938𝑥4	NUM
iajs-3076	169	3	−	−	NOUN
iajs-3076	169	4	1.2900408484650545𝑥5	1.2900408484650545𝑥5	NUM
iajs-3076	170	1	+	+	CCONJ
iajs-3076	170	2	2.1428840263535394𝑥6	2.1428840263535394𝑥6	NUM
iajs-3076	170	3	−	−	NOUN
iajs-3076	170	4	2.118319283516632𝑥7	2.118319283516632𝑥7	NUM
iajs-3076	170	5	−	−	NOUN
iajs-3076	170	6	0.6752474254279832𝑥8	0.6752474254279832𝑥8	NUM
iajs-3076	170	7	+	+	PUNCT
iajs-3076	170	8	6.081788398525532𝑥9	6.081788398525532𝑥9	NUM
iajs-3076	170	9	−	−	NOUN
iajs-3076	170	10	10.489702105988727𝑥10	10.489702105988727𝑥10	NOUN
iajs-3076	170	11	+	+	CCONJ
iajs-3076	171	1	10.517845113990916𝑥11	10.517845113990916𝑥11	NUM
iajs-3076	171	2	−	−	NOUN
iajs-3076	172	1	7.003103640066911𝑥12	7.003103640066911𝑥12	NUM
iajs-3076	172	2	+	+	NUM
iajs-3076	172	3	3.1968135804363556𝑥13	3.1968135804363556𝑥13	NUM
iajs-3076	172	4	−	−	NOUN
iajs-3076	172	5	0.9498166132520964𝑥14	0.9498166132520964𝑥14	NOUN
iajs-3076	173	1	+	+	CCONJ
iajs-3076	173	2	0.14086738703346668𝑥15	0.14086738703346668𝑥15	NUM
iajs-3076	173	3	.	.	PUNCT
iajs-3076	174	1	table	table	NOUN
iajs-3076	174	2	1	1	NUM
iajs-3076	174	3	shows	show	VERB
iajs-3076	174	4	the	the	DET
iajs-3076	174	5	absolute	absolute	ADJ
iajs-3076	174	6	error|𝑦𝑒𝑥𝑎𝑐𝑡	error|𝑦𝑒𝑥𝑎𝑐𝑡	PROPN
iajs-3076	174	7	−	−	PROPN
iajs-3076	174	8	𝑦𝑎𝑝𝑝.|	𝑦𝑎𝑝𝑝.|	NOUN
iajs-3076	174	9	value	value	NOUN
iajs-3076	174	10	for	for	ADP
iajs-3076	174	11	the	the	DET
iajs-3076	174	12	some	some	PRON
iajs-3076	174	13	𝑥	𝑥	PRON
iajs-3076	174	14	∈	∈	NOUN
iajs-3076	174	15	(	(	PUNCT
iajs-3076	174	16	0,1	0,1	NOUN
iajs-3076	174	17	]	]	PUNCT
iajs-3076	174	18	at	at	ADP
iajs-3076	174	19	𝑛=	𝑛=	NOUN
iajs-3076	174	20	9	9	NUM
iajs-3076	174	21	,	,	PUNCT
iajs-3076	174	22	11	11	NUM
iajs-3076	174	23	,	,	PUNCT
iajs-3076	174	24	13	13	NUM
iajs-3076	174	25	,	,	PUNCT
iajs-3076	174	26	and	and	CCONJ
iajs-3076	174	27	15	15	NUM
iajs-3076	174	28	.	.	PUNCT
iajs-3076	174	29	table	table	NOUN
iajs-3076	174	30	1	1	NUM
iajs-3076	174	31	:	:	PUNCT
iajs-3076	174	32	the	the	DET
iajs-3076	174	33	absolute	absolute	ADJ
iajs-3076	174	34	error	error	NOUN
iajs-3076	174	35	of	of	ADP
iajs-3076	174	36	ex	ex	PROPN
iajs-3076	174	37	.	.	PROPN
iajs-3076	174	38	1	1	NUM
iajs-3076	174	39	for	for	ADP
iajs-3076	174	40	𝑛=9,11,13,15	𝑛=9,11,13,15	NOUN
iajs-3076	174	41	by	by	ADP
iajs-3076	174	42	(	(	PUNCT
iajs-3076	174	43	bom	bom	PROPN
iajs-3076	174	44	)	)	PUNCT
iajs-3076	174	45	𝒙	𝒙	PROPN
iajs-3076	174	46	𝒏	𝒏	PROPN
iajs-3076	174	47	=	=	SYM
iajs-3076	174	48	𝟗	𝟗	NUM
iajs-3076	174	49	𝒏	𝒏	PROPN
iajs-3076	175	1	=	=	X
iajs-3076	176	1	𝟏𝟏	𝟏𝟏	NUM
iajs-3076	176	2	𝒏	𝒏	PROPN
iajs-3076	176	3	=	=	SYM
iajs-3076	176	4	𝟏𝟑	𝟏𝟑	NUM
iajs-3076	176	5	𝒏	𝒏	X
iajs-3076	176	6	=	=	PROPN
iajs-3076	176	7	𝟏𝟓	𝟏𝟓	NUM
iajs-3076	176	8	0.1	0.1	NUM
iajs-3076	176	9	1.21756×10	1.21756×10	NUM
iajs-3076	176	10	-	-	SYM
iajs-3076	176	11	7	7	NUM
iajs-3076	176	12	2.92165×10	2.92165×10	NOUN
iajs-3076	176	13	-	-	SYM
iajs-3076	176	14	8	8	NUM
iajs-3076	176	15	6.77509×10	6.77509×10	NOUN
iajs-3076	176	16	-	-	SYM
iajs-3076	176	17	8	8	NUM
iajs-3076	176	18	3.19953×10	3.19953×10	NUM
iajs-3076	176	19	-	-	SYM
iajs-3076	176	20	8	8	NUM
iajs-3076	176	21	0.2	0.2	NUM
iajs-3076	176	22	1.07484×10	1.07484×10	NUM
iajs-3076	176	23	-	-	SYM
iajs-3076	176	24	7	7	NUM
iajs-3076	176	25	3.66589×10	3.66589×10	NUM
iajs-3076	176	26	-	-	SYM
iajs-3076	176	27	8	8	NUM
iajs-3076	176	28	7.85818×10	7.85818×10	NOUN
iajs-3076	176	29	-	-	SYM
iajs-3076	176	30	8	8	NUM
iajs-3076	176	31	3.32075×10	3.32075×10	NOUN
iajs-3076	176	32	-	-	SYM
iajs-3076	176	33	8	8	NUM
iajs-3076	176	34	0.3	0.3	NUM
iajs-3076	176	35	1.40511×10	1.40511×10	NUM
iajs-3076	176	36	-	-	SYM
iajs-3076	176	37	7	7	NUM
iajs-3076	176	38	5.90616×10	5.90616×10	NUM
iajs-3076	176	39	-	-	SYM
iajs-3076	176	40	8	8	NUM
iajs-3076	176	41	5.80438×10	5.80438×10	NOUN
iajs-3076	176	42	-	-	PUNCT
iajs-3076	176	43	8	8	NUM
iajs-3076	176	44	2.87904×10	2.87904×10	NUM
iajs-3076	176	45	-	-	PUNCT
iajs-3076	176	46	8	8	NUM
iajs-3076	176	47	0.4	0.4	NUM
iajs-3076	176	48	3.05621×10	3.05621×10	NUM
iajs-3076	176	49	-	-	SYM
iajs-3076	176	50	7	7	NUM
iajs-3076	176	51	6.14799×10	6.14799×10	NOUN
iajs-3076	176	52	-	-	PUNCT
iajs-3076	176	53	8	8	NUM
iajs-3076	176	54	2.5095×10	2.5095×10	NOUN
iajs-3076	176	55	-	-	SYM
iajs-3076	176	56	8	8	NUM
iajs-3076	176	57	1.82177×10	1.82177×10	NUM
iajs-3076	176	58	-	-	SYM
iajs-3076	176	59	8	8	NUM
iajs-3076	176	60	0.5	0.5	NUM
iajs-3076	176	61	5.54154×10	5.54154×10	NUM
iajs-3076	176	62	-	-	SYM
iajs-3076	176	63	8	8	NUM
iajs-3076	176	64	2.54537×10	2.54537×10	NUM
iajs-3076	176	65	-	-	SYM
iajs-3076	176	66	8	8	NUM
iajs-3076	176	67	9.48675×10	9.48675×10	NUM
iajs-3076	176	68	-	-	SYM
iajs-3076	176	69	9	9	NUM
iajs-3076	176	70	4.38442×10	4.38442×10	NOUN
iajs-3076	176	71	-	-	SYM
iajs-3076	176	72	9	9	NUM
iajs-3076	176	73	0.6	0.6	NUM
iajs-3076	176	74	2.92554×10	2.92554×10	NOUN
iajs-3076	176	75	-	-	SYM
iajs-3076	176	76	7	7	NUM
iajs-3076	176	77	3.27859×10	3.27859×10	NUM
iajs-3076	176	78	-	-	SYM
iajs-3076	176	79	8	8	NUM
iajs-3076	176	80	2.82086×10	2.82086×10	NUM
iajs-3076	176	81	-	-	SYM
iajs-3076	176	82	8	8	NUM
iajs-3076	176	83	6.08513×10	6.08513×10	NUM
iajs-3076	176	84	-	-	SYM
iajs-3076	176	85	10	10	NUM
iajs-3076	176	86	0.7	0.7	NUM
iajs-3076	176	87	3.1252×10	3.1252×10	NUM
iajs-3076	176	88	-	-	SYM
iajs-3076	176	89	7	7	NUM
iajs-3076	176	90	8.2099×10	8.2099×10	NOUN
iajs-3076	176	91	-	-	PUNCT
iajs-3076	176	92	8	8	NUM
iajs-3076	176	93	3.73298×10	3.73298×10	NUM
iajs-3076	176	94	-	-	SYM
iajs-3076	176	95	8	8	NUM
iajs-3076	176	96	1.17502×10	1.17502×10	NUM
iajs-3076	176	97	-	-	SYM
iajs-3076	176	98	8	8	NUM
iajs-3076	176	99	0.8	0.8	NUM
iajs-3076	176	100	6.18788×10	6.18788×10	NUM
iajs-3076	176	101	-	-	SYM
iajs-3076	176	102	8	8	NUM
iajs-3076	176	103	1.2187×10	1.2187×10	NUM
iajs-3076	176	104	-	-	SYM
iajs-3076	176	105	7	7	NUM
iajs-3076	176	106	3.22221×10	3.22221×10	NUM
iajs-3076	176	107	-	-	SYM
iajs-3076	176	108	8	8	NUM
iajs-3076	176	109	1.2558×10	1.2558×10	NOUN
iajs-3076	176	110	-	-	SYM
iajs-3076	176	111	9	9	NUM
iajs-3076	176	112	0.9	0.9	NUM
iajs-3076	176	113	2.07441×10	2.07441×10	NOUN
iajs-3076	176	114	-	-	SYM
iajs-3076	176	115	7	7	NUM
iajs-3076	176	116	1.90066×10	1.90066×10	NUM
iajs-3076	176	117	-	-	SYM
iajs-3076	176	118	7	7	NUM
iajs-3076	176	119	1.81549×10	1.81549×10	NUM
iajs-3076	176	120	-	-	SYM
iajs-3076	176	121	8	8	NUM
iajs-3076	176	122	1.60439×10	1.60439×10	NUM
iajs-3076	176	123	-	-	SYM
iajs-3076	176	124	8	8	NUM
iajs-3076	176	125	in	in	ADP
iajs-3076	176	126	order	order	NOUN
iajs-3076	176	127	to	to	PART
iajs-3076	176	128	use	use	VERB
iajs-3076	176	129	the	the	DET
iajs-3076	176	130	lom	lom	NOUN
iajs-3076	176	131	approach	approach	NOUN
iajs-3076	176	132	to	to	PART
iajs-3076	176	133	solve	solve	VERB
iajs-3076	176	134	example	example	NOUN
iajs-3076	176	135	1	1	NUM
iajs-3076	176	136	,	,	PUNCT
iajs-3076	176	137	we	we	PRON
iajs-3076	176	138	must	must	AUX
iajs-3076	176	139	follow	follow	VERB
iajs-3076	176	140	the	the	DET
iajs-3076	176	141	steps	step	NOUN
iajs-3076	176	142	outlined	outline	VERB
iajs-3076	176	143	in	in	ADP
iajs-3076	176	144	section	section	NOUN
iajs-3076	176	145	(	(	PUNCT
iajs-3076	176	146	4	4	NUM
iajs-3076	176	147	-	-	SYM
iajs-3076	176	148	3	3	NUM
iajs-3076	176	149	)	)	PUNCT
iajs-3076	176	150	.	.	PUNCT
iajs-3076	177	1	if	if	SCONJ
iajs-3076	177	2	we	we	PRON
iajs-3076	177	3	assume	assume	VERB
iajs-3076	177	4	𝑛	𝑛	ADJ
iajs-3076	177	5	=	=	SYM
iajs-3076	177	6	2	2	NUM
iajs-3076	177	7	,	,	PUNCT
iajs-3076	177	8	we	we	PRON
iajs-3076	177	9	get	get	VERB
iajs-3076	177	10	𝐷0.8	𝐷0.8	VERB
iajs-3076	177	11	=	=	PUNCT
iajs-3076	178	1	[	[	X
iajs-3076	178	2	0	0	NUM
iajs-3076	178	3	0	0	NUM
iajs-3076	178	4	0	0	NUM
iajs-3076	178	5	1.81521	1.81521	NUM
iajs-3076	178	6	0.495057	0.495057	NUM
iajs-3076	178	7	−	−	PROPN
iajs-3076	178	8	0.206274	0.206274	NUM
iajs-3076	178	9	−	−	PROPN
iajs-3076	178	10	0.495057	0.495057	NUM
iajs-3076	178	11	4.08422	4.08422	NUM
iajs-3076	178	12	1.06084	1.06084	NUM
iajs-3076	178	13	]	]	PUNCT
iajs-3076	178	14	the	the	DET
iajs-3076	178	15	approximate	approximate	ADJ
iajs-3076	178	16	solution	solution	NOUN
iajs-3076	178	17	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-3076	178	18	)	)	PUNCT
iajs-3076	178	19	=	=	SYM
iajs-3076	179	1	0.0237227𝑥	0.0237227𝑥	PROPN
iajs-3076	179	2	+	+	NUM
iajs-3076	179	3	0.44836𝑥2	0.44836𝑥2	NUM
iajs-3076	179	4	,	,	PUNCT
iajs-3076	179	5	and	and	CCONJ
iajs-3076	179	6	the	the	DET
iajs-3076	179	7	value	value	NOUN
iajs-3076	179	8	of	of	ADP
iajs-3076	179	9	𝑐0	𝑐0	NOUN
iajs-3076	179	10	=	=	SYM
iajs-3076	179	11	0.161315	0.161315	NUM
iajs-3076	179	12	,	,	PUNCT
iajs-3076	179	13	𝑐1	𝑐1	NOUN
iajs-3076	179	14	=	=	NOUN
iajs-3076	179	15	0.236041	0.236041	NUM
iajs-3076	179	16	,	,	PUNCT
iajs-3076	179	17	𝑐2	𝑐2	NOUN
iajs-3076	179	18	=	=	SYM
iajs-3076	179	19	0.0747266	0.0747266	NUM
iajs-3076	179	20	.	.	PUNCT
iajs-3076	180	1	if	if	SCONJ
iajs-3076	180	2	𝑛	𝑛	PROPN
iajs-3076	180	3	=	=	SYM
iajs-3076	180	4	15	15	NUM
iajs-3076	180	5	,	,	PUNCT
iajs-3076	180	6	the	the	DET
iajs-3076	180	7	approximate	approximate	ADJ
iajs-3076	180	8	solution	solution	NOUN
iajs-3076	180	9	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-3076	180	10	)	)	PUNCT
iajs-3076	180	11	=	=	SYM
iajs-3076	181	1	−5.917880389286895	−5.917880389286895	NUM
iajs-3076	181	2	×	×	NOUN
iajs-3076	181	3	10−17	10−17	NUM
iajs-3076	181	4	+	+	CCONJ
iajs-3076	181	5	0.000004941255572793077𝑥	0.000004941255572793077𝑥	ADJ
iajs-3076	181	6	−	−	NOUN
iajs-3076	181	7	0.0005604595883997804𝑥2	0.0005604595883997804𝑥2	NUM
iajs-3076	182	1	+	+	PUNCT
iajs-3076	182	2	0.030640435190110164𝑥3	0.030640435190110164𝑥3	X
iajs-3076	183	1	+	+	CCONJ
iajs-3076	183	2	1.4662615402598584𝑥4	1.4662615402598584𝑥4	NUM
iajs-3076	183	3	−	−	NOUN
iajs-3076	183	4	1.7082026330161135𝑥5	1.7082026330161135𝑥5	NUM
iajs-3076	184	1	+	+	NUM
iajs-3076	184	2	4.183434690591156𝑥6	4.183434690591156𝑥6	NUM
iajs-3076	184	3	−	−	NOUN
iajs-3076	184	4	8.78814674633918𝑥7	8.78814674633918𝑥7	NUM
iajs-3076	184	5	+	+	CCONJ
iajs-3076	184	6	ihjpas	ihjpa	NOUN
iajs-3076	184	7	.	.	PUNCT
iajs-3076	185	1	36	36	NUM
iajs-3076	185	2	(	(	PUNCT
iajs-3076	185	3	3	3	NUM
iajs-3076	185	4	)	)	PUNCT
iajs-3076	185	5	2023	2023	NUM
iajs-3076	185	6	390	390	NUM
iajs-3076	185	7	14.437646065525456𝑥8	14.437646065525456𝑥8	NUM
iajs-3076	186	1	−	−	NOUN
iajs-3076	186	2	18.130978138638397𝑥9	18.130978138638397𝑥9	NUM
iajs-3076	187	1	+	+	CCONJ
iajs-3076	187	2	17.216360479207815𝑥10	17.216360479207815𝑥10	NUM
iajs-3076	187	3	−	−	NUM
iajs-3076	187	4	12.200969372917305𝑥11	12.200969372917305𝑥11	NUM
iajs-3076	187	5	+	+	CCONJ
iajs-3076	187	6	6.3079153582312015𝑥12	6.3079153582312015𝑥12	NUM
iajs-3076	187	7	−	−	NUM
iajs-3076	187	8	2.277429378098255𝑥13	2.277429378098255𝑥13	NUM
iajs-3076	188	1	+	+	CCONJ
iajs-3076	189	1	0.5224877022689723𝑥14	0.5224877022689723𝑥14	ADJ
iajs-3076	189	2	−	−	NOUN
iajs-3076	189	3	0.058464614185574325𝑥15	0.058464614185574325𝑥15	NOUN
iajs-3076	189	4	.	.	PUNCT
iajs-3076	190	1	we	we	PRON
iajs-3076	190	2	present	present	VERB
iajs-3076	190	3	table	table	NOUN
iajs-3076	190	4	2	2	NUM
iajs-3076	190	5	,	,	PUNCT
iajs-3076	190	6	in	in	ADP
iajs-3076	190	7	which	which	PRON
iajs-3076	190	8	we	we	PRON
iajs-3076	190	9	will	will	AUX
iajs-3076	190	10	show	show	VERB
iajs-3076	190	11	the	the	DET
iajs-3076	190	12	absolute	absolute	ADJ
iajs-3076	190	13	error	error	NOUN
iajs-3076	190	14	value	value	NOUN
iajs-3076	190	15	of	of	ADP
iajs-3076	190	16	𝑛=9,11,13	𝑛=9,11,13	NOUN
iajs-3076	190	17	,	,	PUNCT
iajs-3076	190	18	and	and	CCONJ
iajs-3076	190	19	15	15	NUM
iajs-3076	190	20	table	table	NOUN
iajs-3076	190	21	2	2	NUM
iajs-3076	190	22	:	:	PUNCT
iajs-3076	190	23	the	the	DET
iajs-3076	190	24	absolute	absolute	ADJ
iajs-3076	190	25	error	error	NOUN
iajs-3076	190	26	of	of	ADP
iajs-3076	190	27	ex	ex	PROPN
iajs-3076	190	28	.	.	PROPN
iajs-3076	190	29	1	1	NUM
iajs-3076	190	30	for	for	ADP
iajs-3076	190	31	𝑛=9,11,13,15	𝑛=9,11,13,15	NOUN
iajs-3076	190	32	by	by	ADP
iajs-3076	190	33	(	(	PUNCT
iajs-3076	190	34	lom	lom	PROPN
iajs-3076	190	35	)	)	PUNCT
iajs-3076	190	36	𝒙	𝒙	PROPN
iajs-3076	190	37	𝒏	𝒏	PROPN
iajs-3076	190	38	=	=	SYM
iajs-3076	190	39	𝟗	𝟗	NUM
iajs-3076	190	40	𝒏	𝒏	PROPN
iajs-3076	191	1	=	=	X
iajs-3076	192	1	𝟏𝟏	𝟏𝟏	NUM
iajs-3076	192	2	𝒏	𝒏	PROPN
iajs-3076	192	3	=	=	SYM
iajs-3076	192	4	𝟏𝟑	𝟏𝟑	NUM
iajs-3076	192	5	𝒏	𝒏	X
iajs-3076	192	6	=	=	PROPN
iajs-3076	192	7	𝟏𝟓	𝟏𝟓	NUM
iajs-3076	192	8	0.1	0.1	NUM
iajs-3076	192	9	1.21719×10	1.21719×10	NOUN
iajs-3076	192	10	-	-	SYM
iajs-3076	192	11	7	7	NUM
iajs-3076	192	12	2.88811×10	2.88811×10	NUM
iajs-3076	192	13	-	-	SYM
iajs-3076	192	14	8	8	NUM
iajs-3076	192	15	2.34826×10	2.34826×10	NUM
iajs-3076	192	16	-	-	SYM
iajs-3076	192	17	9	9	NUM
iajs-3076	192	18	1.72445×10	1.72445×10	NUM
iajs-3076	192	19	-	-	SYM
iajs-3076	192	20	8	8	NUM
iajs-3076	192	21	0.2	0.2	NUM
iajs-3076	192	22	1.07453×10	1.07453×10	NOUN
iajs-3076	192	23	-	-	SYM
iajs-3076	192	24	7	7	NUM
iajs-3076	192	25	3.60137×10	3.60137×10	NUM
iajs-3076	192	26	-	-	SYM
iajs-3076	192	27	8	8	NUM
iajs-3076	192	28	1.13909×10	1.13909×10	NUM
iajs-3076	192	29	-	-	SYM
iajs-3076	192	30	8	8	NUM
iajs-3076	192	31	1.44977×10	1.44977×10	NUM
iajs-3076	192	32	-	-	SYM
iajs-3076	192	33	8	8	NUM
iajs-3076	192	34	0.3	0.3	NUM
iajs-3076	192	35	1.40539×10	1.40539×10	NUM
iajs-3076	192	36	-	-	SYM
iajs-3076	192	37	7	7	NUM
iajs-3076	192	38	5.78547×10	5.78547×10	NOUN
iajs-3076	192	39	-	-	SYM
iajs-3076	192	40	8	8	NUM
iajs-3076	192	41	9.88362×10	9.88362×10	NUM
iajs-3076	192	42	-	-	SYM
iajs-3076	192	43	9	9	NUM
iajs-3076	192	44	1.44738×10	1.44738×10	NOUN
iajs-3076	192	45	-	-	SYM
iajs-3076	192	46	8	8	NUM
iajs-3076	192	47	0.4	0.4	NUM
iajs-3076	192	48	3.05492×10	3.05492×10	NOUN
iajs-3076	192	49	-	-	SYM
iajs-3076	192	50	7	7	NUM
iajs-3076	192	51	6.08407×10	6.08407×10	NOUN
iajs-3076	192	52	-	-	SYM
iajs-3076	192	53	8	8	NUM
iajs-3076	192	54	9.05138×10	9.05138×10	NUM
iajs-3076	192	55	-	-	SYM
iajs-3076	192	56	9	9	NUM
iajs-3076	192	57	1.08162×10	1.08162×10	NUM
iajs-3076	192	58	-	-	SYM
iajs-3076	192	59	8	8	NUM
iajs-3076	192	60	0.5	0.5	NUM
iajs-3076	192	61	5.55965×10	5.55965×10	NUM
iajs-3076	192	62	-	-	SYM
iajs-3076	192	63	8	8	NUM
iajs-3076	192	64	2.58773×10	2.58773×10	NOUN
iajs-3076	192	65	-	-	SYM
iajs-3076	192	66	8	8	NUM
iajs-3076	192	67	3.71809×10	3.71809×10	NUM
iajs-3076	192	68	-	-	PUNCT
iajs-3076	192	69	8	8	NUM
iajs-3076	192	70	1.03386×10	1.03386×10	NUM
iajs-3076	192	71	-	-	SYM
iajs-3076	192	72	9	9	NUM
iajs-3076	192	73	0.6	0.6	NUM
iajs-3076	192	74	2.92938×10	2.92938×10	NUM
iajs-3076	192	75	-	-	SYM
iajs-3076	192	76	7	7	NUM
iajs-3076	192	77	3.09694×10	3.09694×10	NUM
iajs-3076	192	78	-	-	SYM
iajs-3076	192	79	8	8	NUM
iajs-3076	192	80	6.09679×10	6.09679×10	NUM
iajs-3076	192	81	-	-	PUNCT
iajs-3076	192	82	8	8	NUM
iajs-3076	192	83	8.16747×10	8.16747×10	NUM
iajs-3076	192	84	-	-	SYM
iajs-3076	192	85	9	9	NUM
iajs-3076	192	86	0.7	0.7	NUM
iajs-3076	192	87	3.1172×10	3.1172×10	NOUN
iajs-3076	192	88	-	-	SYM
iajs-3076	192	89	7	7	NUM
iajs-3076	192	90	8.21428×10	8.21428×10	NOUN
iajs-3076	192	91	-	-	PUNCT
iajs-3076	192	92	8	8	NUM
iajs-3076	192	93	6.37435×10	6.37435×10	NOUN
iajs-3076	192	94	-	-	SYM
iajs-3076	192	95	8	8	NUM
iajs-3076	192	96	1.17671×10	1.17671×10	NUM
iajs-3076	192	97	-	-	SYM
iajs-3076	192	98	8	8	NUM
iajs-3076	192	99	0.8	0.8	NUM
iajs-3076	192	100	6.3123×10	6.3123×10	NUM
iajs-3076	192	101	-	-	PUNCT
iajs-3076	192	102	8	8	NUM
iajs-3076	192	103	1.21236×10	1.21236×10	NUM
iajs-3076	192	104	-	-	SYM
iajs-3076	192	105	7	7	NUM
iajs-3076	192	106	5.67603×10	5.67603×10	NOUN
iajs-3076	192	107	-	-	SYM
iajs-3076	192	108	8	8	NUM
iajs-3076	192	109	5.21886×10	5.21886×10	NUM
iajs-3076	192	110	-	-	SYM
iajs-3076	192	111	9	9	NUM
iajs-3076	192	112	0.9	0.9	NUM
iajs-3076	192	113	2.09417×10	2.09417×10	NOUN
iajs-3076	192	114	-	-	SYM
iajs-3076	192	115	7	7	NUM
iajs-3076	192	116	1.93688×10	1.93688×10	NOUN
iajs-3076	192	117	-	-	SYM
iajs-3076	192	118	7	7	NUM
iajs-3076	192	119	6.72274×10	6.72274×10	NOUN
iajs-3076	192	120	-	-	SYM
iajs-3076	192	121	8	8	NUM
iajs-3076	192	122	5.09303×10	5.09303×10	NUM
iajs-3076	192	123	-	-	SYM
iajs-3076	192	124	9	9	NUM
iajs-3076	192	125	in	in	ADP
iajs-3076	192	126	figure	figure	NOUN
iajs-3076	192	127	1	1	NUM
iajs-3076	192	128	,	,	PUNCT
iajs-3076	192	129	we	we	PRON
iajs-3076	192	130	show	show	VERB
iajs-3076	192	131	a	a	DET
iajs-3076	192	132	plot	plot	NOUN
iajs-3076	192	133	of	of	ADP
iajs-3076	192	134	both	both	CCONJ
iajs-3076	192	135	the	the	DET
iajs-3076	192	136	exact	exact	ADJ
iajs-3076	192	137	solution	solution	NOUN
iajs-3076	192	138	and	and	CCONJ
iajs-3076	192	139	the	the	DET
iajs-3076	192	140	approximate	approximate	ADJ
iajs-3076	192	141	solution	solution	NOUN
iajs-3076	192	142	of	of	ADP
iajs-3076	192	143	the	the	DET
iajs-3076	192	144	two	two	NUM
iajs-3076	192	145	proposed	propose	VERB
iajs-3076	192	146	methods	method	NOUN
iajs-3076	192	147	for	for	ADP
iajs-3076	192	148	𝑛=15	𝑛=15	PROPN
iajs-3076	192	149	.	.	PROPN
iajs-3076	192	150	figure	figure	NOUN
iajs-3076	192	151	1	1	NUM
iajs-3076	192	152	:	:	PUNCT
iajs-3076	192	153	the	the	DET
iajs-3076	192	154	comparison	comparison	NOUN
iajs-3076	192	155	of	of	ADP
iajs-3076	192	156	the	the	DET
iajs-3076	192	157	exact	exact	ADJ
iajs-3076	192	158	solution	solution	NOUN
iajs-3076	192	159	and	and	CCONJ
iajs-3076	192	160	the	the	DET
iajs-3076	192	161	approximate	approximate	ADJ
iajs-3076	192	162	solution	solution	NOUN
iajs-3076	192	163	of	of	ADP
iajs-3076	192	164	(	(	PUNCT
iajs-3076	192	165	bom	bom	PROPN
iajs-3076	192	166	,	,	PUNCT
iajs-3076	192	167	lom	lom	NOUN
iajs-3076	192	168	)	)	PUNCT
iajs-3076	192	169	methods	method	NOUN
iajs-3076	192	170	for	for	ADP
iajs-3076	192	171	ex	ex	NOUN
iajs-3076	192	172	.	.	PROPN
iajs-3076	192	173	1	1	NUM
iajs-3076	192	174	at	at	ADP
iajs-3076	192	175	𝑛=15	𝑛=15	ADV
iajs-3076	192	176	also	also	ADV
iajs-3076	192	177	,	,	PUNCT
iajs-3076	192	178	in	in	ADP
iajs-3076	192	179	figure	figure	NOUN
iajs-3076	192	180	2	2	NUM
iajs-3076	192	181	,	,	PUNCT
iajs-3076	192	182	logarithmic	logarithmic	ADJ
iajs-3076	192	183	plots	plot	NOUN
iajs-3076	192	184	of	of	ADP
iajs-3076	192	185	the	the	DET
iajs-3076	192	186	greatest	great	ADJ
iajs-3076	192	187	absolute	absolute	ADJ
iajs-3076	192	188	error	error	NOUN
iajs-3076	192	189	of	of	ADP
iajs-3076	192	190	the	the	DET
iajs-3076	192	191	approximate	approximate	ADJ
iajs-3076	192	192	solution	solution	NOUN
iajs-3076	192	193	are	be	AUX
iajs-3076	192	194	given	give	VERB
iajs-3076	192	195	using	use	VERB
iajs-3076	192	196	bernstein	bernstein	PROPN
iajs-3076	192	197	or	or	CCONJ
iajs-3076	192	198	legendre	legendre	PROPN
iajs-3076	192	199	polynomials	polynomial	NOUN
iajs-3076	192	200	with	with	ADP
iajs-3076	192	201	operational	operational	ADJ
iajs-3076	192	202	matrices	matrix	NOUN
iajs-3076	192	203	to	to	PART
iajs-3076	192	204	solve	solve	VERB
iajs-3076	192	205	example	example	NOUN
iajs-3076	192	206	1	1	NUM
iajs-3076	192	207	from	from	ADP
iajs-3076	192	208	𝑛	𝑛	PROPN
iajs-3076	192	209	=	=	SYM
iajs-3076	192	210	2	2	NUM
iajs-3076	192	211	to	to	PART
iajs-3076	192	212	𝑛	𝑛	PROPN
iajs-3076	192	213	=	=	SYM
iajs-3076	192	214	15	15	NUM
iajs-3076	192	215	.	.	PUNCT
iajs-3076	193	1	ihjpas	ihjpas	PROPN
iajs-3076	193	2	.	.	PUNCT
iajs-3076	194	1	36	36	NUM
iajs-3076	194	2	(	(	PUNCT
iajs-3076	194	3	3	3	NUM
iajs-3076	194	4	)	)	PUNCT
iajs-3076	194	5	2023	2023	NUM
iajs-3076	194	6	391	391	NUM
iajs-3076	194	7	figure	figure	NOUN
iajs-3076	194	8	2	2	NUM
iajs-3076	194	9	:	:	PUNCT
iajs-3076	194	10	logarithmic	logarithmic	ADJ
iajs-3076	194	11	plots	plot	NOUN
iajs-3076	194	12	for	for	ADP
iajs-3076	194	13	the	the	DET
iajs-3076	194	14	𝑀𝐴𝐸𝑛	𝑀𝐴𝐸𝑛	PROPN
iajs-3076	194	15	of	of	ADP
iajs-3076	194	16	ex	ex	PROPN
iajs-3076	194	17	.	.	NOUN
iajs-3076	194	18	1	1	NUM
iajs-3076	194	19	form	form	NOUN
iajs-3076	194	20	𝑛=2	𝑛=2	NOUN
iajs-3076	194	21	to	to	PART
iajs-3076	194	22	𝑛=15	𝑛=15	SCONJ
iajs-3076	194	23	we	we	PRON
iajs-3076	194	24	note	note	VERB
iajs-3076	194	25	from	from	ADP
iajs-3076	194	26	the	the	DET
iajs-3076	194	27	above	above	ADJ
iajs-3076	194	28	results	result	NOUN
iajs-3076	194	29	that	that	SCONJ
iajs-3076	194	30	the	the	DET
iajs-3076	194	31	two	two	NUM
iajs-3076	194	32	proposed	propose	VERB
iajs-3076	194	33	methods	method	NOUN
iajs-3076	194	34	are	be	AUX
iajs-3076	194	35	efficient	efficient	ADJ
iajs-3076	194	36	because	because	SCONJ
iajs-3076	194	37	their	their	PRON
iajs-3076	194	38	results	result	NOUN
iajs-3076	194	39	are	be	AUX
iajs-3076	194	40	highly	highly	ADV
iajs-3076	194	41	accurate	accurate	ADJ
iajs-3076	194	42	compared	compare	VERB
iajs-3076	194	43	to	to	ADP
iajs-3076	194	44	the	the	DET
iajs-3076	194	45	results	result	NOUN
iajs-3076	194	46	of	of	ADP
iajs-3076	194	47	the	the	DET
iajs-3076	194	48	exact	exact	ADJ
iajs-3076	194	49	solution	solution	NOUN
iajs-3076	194	50	,	,	PUNCT
iajs-3076	194	51	as	as	SCONJ
iajs-3076	194	52	shown	show	VERB
iajs-3076	194	53	in	in	ADP
iajs-3076	194	54	figure	figure	NOUN
iajs-3076	194	55	1	1	NUM
iajs-3076	194	56	.	.	PUNCT
iajs-3076	195	1	also	also	ADV
iajs-3076	195	2	,	,	PUNCT
iajs-3076	195	3	we	we	PRON
iajs-3076	195	4	can	can	AUX
iajs-3076	195	5	see	see	VERB
iajs-3076	195	6	the	the	DET
iajs-3076	195	7	efficiency	efficiency	NOUN
iajs-3076	195	8	of	of	ADP
iajs-3076	195	9	the	the	DET
iajs-3076	195	10	two	two	NUM
iajs-3076	195	11	proposed	propose	VERB
iajs-3076	195	12	methods	method	NOUN
iajs-3076	195	13	in	in	ADP
iajs-3076	195	14	figure	figure	NOUN
iajs-3076	195	15	2	2	NUM
iajs-3076	195	16	,	,	PUNCT
iajs-3076	195	17	which	which	PRON
iajs-3076	195	18	shows	show	VERB
iajs-3076	195	19	the	the	DET
iajs-3076	195	20	decrease	decrease	NOUN
iajs-3076	195	21	in	in	ADP
iajs-3076	195	22	absolute	absolute	ADJ
iajs-3076	195	23	error	error	NOUN
iajs-3076	195	24	when	when	SCONJ
iajs-3076	195	25	the	the	DET
iajs-3076	195	26	value	value	NOUN
iajs-3076	195	27	of	of	ADP
iajs-3076	195	28	𝑛	𝑛	PROPN
iajs-3076	195	29	is	be	AUX
iajs-3076	195	30	increased	increase	VERB
iajs-3076	195	31	.	.	PUNCT
iajs-3076	196	1	in	in	ADP
iajs-3076	196	2	order	order	NOUN
iajs-3076	196	3	to	to	PART
iajs-3076	196	4	show	show	VERB
iajs-3076	196	5	which	which	PRON
iajs-3076	196	6	of	of	ADP
iajs-3076	196	7	the	the	DET
iajs-3076	196	8	two	two	NUM
iajs-3076	196	9	methods	method	NOUN
iajs-3076	196	10	is	be	AUX
iajs-3076	196	11	more	more	ADV
iajs-3076	196	12	efficient	efficient	ADJ
iajs-3076	196	13	,	,	PUNCT
iajs-3076	196	14	we	we	PRON
iajs-3076	196	15	present	present	VERB
iajs-3076	196	16	table	table	NOUN
iajs-3076	196	17	3	3	NUM
iajs-3076	196	18	,	,	PUNCT
iajs-3076	196	19	in	in	ADP
iajs-3076	196	20	which	which	PRON
iajs-3076	196	21	we	we	PRON
iajs-3076	196	22	will	will	AUX
iajs-3076	196	23	show	show	VERB
iajs-3076	196	24	the	the	DET
iajs-3076	196	25	absolute	absolute	ADJ
iajs-3076	196	26	error	error	NOUN
iajs-3076	196	27	values	value	NOUN
iajs-3076	196	28	of	of	ADP
iajs-3076	196	29	the	the	DET
iajs-3076	196	30	two	two	NUM
iajs-3076	196	31	proposed	propose	VERB
iajs-3076	196	32	methods	method	NOUN
iajs-3076	196	33	at	at	ADP
iajs-3076	196	34	𝑛	𝑛	PROPN
iajs-3076	196	35	=	=	SYM
iajs-3076	196	36	15	15	NUM
iajs-3076	196	37	table	table	NOUN
iajs-3076	196	38	3	3	NUM
iajs-3076	196	39	:	:	PUNCT
iajs-3076	196	40	the	the	DET
iajs-3076	196	41	absolute	absolute	ADJ
iajs-3076	196	42	error	error	NOUN
iajs-3076	196	43	|𝑦𝑒𝑥𝑎𝑐𝑡	|𝑦𝑒𝑥𝑎𝑐𝑡	NOUN
iajs-3076	196	44	−	−	NOUN
iajs-3076	196	45	𝑦𝑎𝑝𝑝.|	𝑦𝑎𝑝𝑝.|	VERB
iajs-3076	196	46	of	of	ADP
iajs-3076	196	47	(	(	PUNCT
iajs-3076	196	48	bom	bom	PROPN
iajs-3076	196	49	,	,	PUNCT
iajs-3076	196	50	lom	lom	PROPN
iajs-3076	196	51	)	)	PUNCT
iajs-3076	196	52	for	for	ADP
iajs-3076	196	53	ex	ex	PROPN
iajs-3076	196	54	.	.	PROPN
iajs-3076	196	55	1	1	NUM
iajs-3076	196	56	at	at	ADP
iajs-3076	196	57	𝑛=15	𝑛=15	ADP
iajs-3076	196	58	𝒙	𝒙	PRON
iajs-3076	196	59	absolute	absolute	ADJ
iajs-3076	196	60	error	error	NOUN
iajs-3076	196	61	(	(	PUNCT
iajs-3076	196	62	b	b	NOUN
iajs-3076	196	63	)	)	PUNCT
iajs-3076	196	64	absolute	absolute	ADJ
iajs-3076	196	65	error	error	NOUN
iajs-3076	196	66	(	(	PUNCT
iajs-3076	196	67	l	l	NOUN
iajs-3076	196	68	)	)	PUNCT
iajs-3076	196	69	0.1	0.1	NUM
iajs-3076	196	70	3.19953×10	3.19953×10	NUM
iajs-3076	196	71	-	-	SYM
iajs-3076	196	72	8	8	NUM
iajs-3076	196	73	1.72445×10	1.72445×10	NUM
iajs-3076	196	74	-	-	SYM
iajs-3076	196	75	8	8	NUM
iajs-3076	196	76	0.2	0.2	NUM
iajs-3076	196	77	3.32075×10	3.32075×10	NOUN
iajs-3076	196	78	-	-	SYM
iajs-3076	196	79	8	8	NUM
iajs-3076	196	80	1.44977×10	1.44977×10	NUM
iajs-3076	196	81	-	-	SYM
iajs-3076	196	82	8	8	NUM
iajs-3076	196	83	0.3	0.3	NUM
iajs-3076	196	84	2.87904×10	2.87904×10	NUM
iajs-3076	196	85	-	-	SYM
iajs-3076	196	86	8	8	NUM
iajs-3076	196	87	1.44738×10	1.44738×10	NOUN
iajs-3076	196	88	-	-	SYM
iajs-3076	196	89	8	8	NUM
iajs-3076	196	90	0.4	0.4	NUM
iajs-3076	196	91	1.82177×10	1.82177×10	NUM
iajs-3076	196	92	-	-	SYM
iajs-3076	196	93	8	8	NUM
iajs-3076	196	94	1.08162×10	1.08162×10	NUM
iajs-3076	196	95	-	-	SYM
iajs-3076	196	96	8	8	NUM
iajs-3076	196	97	0.5	0.5	NUM
iajs-3076	196	98	4.38442×10	4.38442×10	NOUN
iajs-3076	196	99	-	-	SYM
iajs-3076	196	100	9	9	NUM
iajs-3076	196	101	1.03386×10	1.03386×10	NUM
iajs-3076	196	102	-	-	SYM
iajs-3076	196	103	9	9	NUM
iajs-3076	196	104	0.6	0.6	NUM
iajs-3076	196	105	6.08513×10	6.08513×10	NUM
iajs-3076	196	106	-	-	SYM
iajs-3076	196	107	10	10	NUM
iajs-3076	196	108	8.16747×10	8.16747×10	NUM
iajs-3076	196	109	-	-	SYM
iajs-3076	196	110	9	9	NUM
iajs-3076	196	111	0.7	0.7	NUM
iajs-3076	196	112	1.17502×10	1.17502×10	NUM
iajs-3076	196	113	-	-	SYM
iajs-3076	196	114	8	8	NUM
iajs-3076	196	115	1.17671×10	1.17671×10	NUM
iajs-3076	196	116	-	-	SYM
iajs-3076	196	117	8	8	NUM
iajs-3076	196	118	0.8	0.8	NUM
iajs-3076	196	119	1.2558×10	1.2558×10	NUM
iajs-3076	196	120	-	-	SYM
iajs-3076	196	121	9	9	NUM
iajs-3076	196	122	5.21886×10	5.21886×10	NUM
iajs-3076	196	123	-	-	SYM
iajs-3076	196	124	9	9	NUM
iajs-3076	196	125	0.9	0.9	NUM
iajs-3076	196	126	1.60439×10	1.60439×10	NUM
iajs-3076	196	127	-	-	SYM
iajs-3076	196	128	8	8	NUM
iajs-3076	196	129	5.09303×10	5.09303×10	NUM
iajs-3076	196	130	-	-	SYM
iajs-3076	196	131	9	9	NUM
iajs-3076	196	132	we	we	PRON
iajs-3076	196	133	notice	notice	VERB
iajs-3076	196	134	from	from	ADP
iajs-3076	196	135	table	table	NOUN
iajs-3076	196	136	3	3	NUM
iajs-3076	196	137	that	that	SCONJ
iajs-3076	196	138	the	the	DET
iajs-3076	196	139	values	value	NOUN
iajs-3076	196	140	of	of	ADP
iajs-3076	196	141	legendre	legendre	PROPN
iajs-3076	196	142	's	's	PART
iajs-3076	196	143	absolute	absolute	ADJ
iajs-3076	196	144	error	error	NOUN
iajs-3076	196	145	are	be	AUX
iajs-3076	196	146	less	less	ADJ
iajs-3076	196	147	than	than	ADP
iajs-3076	196	148	those	those	PRON
iajs-3076	196	149	of	of	ADP
iajs-3076	196	150	bernstein	bernstein	PROPN
iajs-3076	196	151	’s	’s	PART
iajs-3076	196	152	absolute	absolute	ADJ
iajs-3076	196	153	error	error	NOUN
iajs-3076	196	154	,	,	PUNCT
iajs-3076	196	155	which	which	PRON
iajs-3076	196	156	indicates	indicate	VERB
iajs-3076	196	157	that	that	SCONJ
iajs-3076	196	158	(	(	PUNCT
iajs-3076	196	159	lom	lom	NOUN
iajs-3076	196	160	)	)	PUNCT
iajs-3076	196	161	method	method	NOUN
iajs-3076	196	162	is	be	AUX
iajs-3076	196	163	more	more	ADV
iajs-3076	196	164	efficient	efficient	ADJ
iajs-3076	196	165	than	than	ADP
iajs-3076	196	166	(	(	PUNCT
iajs-3076	196	167	bom	bom	NOUN
iajs-3076	196	168	)	)	PUNCT
iajs-3076	196	169	method	method	NOUN
iajs-3076	196	170	in	in	ADP
iajs-3076	196	171	solving	solve	VERB
iajs-3076	196	172	example	example	NOUN
iajs-3076	196	173	1	1	NUM
iajs-3076	196	174	.	.	PUNCT
iajs-3076	196	175	example	example	NOUN
iajs-3076	196	176	2	2	NUM
iajs-3076	196	177	:	:	PUNCT
iajs-3076	196	178	consider	consider	VERB
iajs-3076	196	179	the	the	DET
iajs-3076	196	180	following	follow	VERB
iajs-3076	196	181	fractional	fractional	ADJ
iajs-3076	196	182	pantograph	pantograph	NOUN
iajs-3076	196	183	equation	equation	NOUN
iajs-3076	196	184	𝐷2𝑦(𝑥	𝐷2𝑦(𝑥	NOUN
iajs-3076	196	185	)	)	PUNCT
iajs-3076	197	1	+	+	CCONJ
iajs-3076	197	2	𝐷	𝐷	PROPN
iajs-3076	197	3	3	3	NUM
iajs-3076	197	4	2𝑦(𝑥	2𝑦(𝑥	NUM
iajs-3076	197	5	)	)	PUNCT
iajs-3076	198	1	+	+	NUM
iajs-3076	199	1	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-3076	199	2	)	)	PUNCT
iajs-3076	199	3	=	=	SYM
iajs-3076	199	4	𝑦	𝑦	NOUN
iajs-3076	199	5	(	(	PUNCT
iajs-3076	199	6	𝑥	𝑥	PROPN
iajs-3076	199	7	2	2	NUM
iajs-3076	199	8	)	)	PUNCT
iajs-3076	199	9	+	+	CCONJ
iajs-3076	199	10	3𝑥2	3𝑥2	NUM
iajs-3076	199	11	4	4	NUM
iajs-3076	199	12	+	+	CCONJ
iajs-3076	200	1	4√	4√	ADV
iajs-3076	200	2	𝑥	𝑥	PRON
iajs-3076	200	3	𝜋	𝜋	NOUN
iajs-3076	201	1	+	+	ADJ
iajs-3076	201	2	2	2	NUM
iajs-3076	201	3	,	,	PUNCT
iajs-3076	201	4	𝑥	𝑥	DET
iajs-3076	201	5	∈	∈	NOUN
iajs-3076	202	1	[	[	X
iajs-3076	202	2	0,1	0,1	NUM
iajs-3076	202	3	]	]	PUNCT
iajs-3076	202	4	,	,	PUNCT
iajs-3076	202	5	(	(	PUNCT
iajs-3076	202	6	15	15	NUM
iajs-3076	202	7	)	)	PUNCT
iajs-3076	202	8	subject	subject	NOUN
iajs-3076	202	9	to	to	ADP
iajs-3076	202	10	𝑦(0	𝑦(0	PROPN
iajs-3076	202	11	)	)	PUNCT
iajs-3076	202	12	=	=	SYM
iajs-3076	202	13	0	0	NUM
iajs-3076	202	14	,	,	PUNCT
iajs-3076	202	15	𝑦(1	𝑦(1	PROPN
iajs-3076	202	16	)	)	PUNCT
iajs-3076	202	17	=	=	SYM
iajs-3076	202	18	1	1	NUM
iajs-3076	202	19	,	,	PUNCT
iajs-3076	202	20	and	and	CCONJ
iajs-3076	202	21	the	the	DET
iajs-3076	202	22	exact	exact	ADJ
iajs-3076	202	23	solution	solution	NOUN
iajs-3076	202	24	to	to	ADP
iajs-3076	202	25	this	this	DET
iajs-3076	202	26	problem	problem	NOUN
iajs-3076	202	27	is	be	AUX
iajs-3076	202	28	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-3076	202	29	)	)	PUNCT
iajs-3076	202	30	=	=	SYM
iajs-3076	202	31	𝑥2	𝑥2	NOUN
iajs-3076	202	32	.	.	PUNCT
iajs-3076	203	1	when	when	SCONJ
iajs-3076	203	2	applying	apply	VERB
iajs-3076	203	3	the	the	DET
iajs-3076	203	4	(	(	PUNCT
iajs-3076	203	5	bom	bom	NOUN
iajs-3076	203	6	)	)	PUNCT
iajs-3076	203	7	method	method	NOUN
iajs-3076	203	8	for	for	ADP
iajs-3076	203	9	solving	solve	VERB
iajs-3076	203	10	eq	eq	ADJ
iajs-3076	203	11	.	.	PUNCT
iajs-3076	204	1	(	(	PUNCT
iajs-3076	204	2	15	15	NUM
iajs-3076	204	3	)	)	PUNCT
iajs-3076	204	4	at	at	ADP
iajs-3076	204	5	𝑛	𝑛	PROPN
iajs-3076	204	6	=	=	SYM
iajs-3076	204	7	2	2	NUM
iajs-3076	204	8	,	,	PUNCT
iajs-3076	204	9	we	we	PRON
iajs-3076	204	10	have	have	VERB
iajs-3076	204	11	𝐷	𝐷	PROPN
iajs-3076	204	12	3	3	NUM
iajs-3076	204	13	2	2	NUM
iajs-3076	204	14	=	=	SYM
iajs-3076	204	15	[	[	PUNCT
iajs-3076	204	16	24	24	NUM
iajs-3076	204	17	35√𝜋	35√𝜋	NUM
iajs-3076	204	18	24	24	NUM
iajs-3076	204	19	7√𝜋	7√𝜋	NOUN
iajs-3076	204	20	136	136	NUM
iajs-3076	204	21	35√𝜋	35√𝜋	NUM
iajs-3076	204	22	−	−	NOUN
iajs-3076	204	23	48	48	NUM
iajs-3076	204	24	35√𝜋	35√𝜋	NUM
iajs-3076	204	25	−	−	NUM
iajs-3076	204	26	48	48	NUM
iajs-3076	204	27	7√𝜋	7√𝜋	NOUN
iajs-3076	204	28	−	−	PROPN
iajs-3076	204	29	272	272	NUM
iajs-3076	204	30	35√𝜋	35√𝜋	NUM
iajs-3076	204	31	24	24	NUM
iajs-3076	204	32	35√𝜋	35√𝜋	NUM
iajs-3076	204	33	24	24	NUM
iajs-3076	204	34	7√𝜋	7√𝜋	NOUN
iajs-3076	204	35	136	136	NUM
iajs-3076	204	36	35√𝜋	35√𝜋	NUM
iajs-3076	204	37	]	]	PUNCT
iajs-3076	204	38	,	,	PUNCT
iajs-3076	204	39	we	we	PRON
iajs-3076	204	40	also	also	ADV
iajs-3076	204	41	obtained	obtain	VERB
iajs-3076	204	42	the	the	DET
iajs-3076	204	43	values	value	NOUN
iajs-3076	204	44	of	of	ADP
iajs-3076	204	45	the	the	DET
iajs-3076	204	46	unknown	unknown	ADJ
iajs-3076	204	47	vector	vector	NOUN
iajs-3076	204	48	𝐶𝑇	𝐶𝑇	PROPN
iajs-3076	204	49	,	,	PUNCT
iajs-3076	204	50	which	which	PRON
iajs-3076	204	51	are	be	AUX
iajs-3076	204	52	as	as	SCONJ
iajs-3076	204	53	follows	follow	VERB
iajs-3076	204	54	𝑐0	𝑐0	NOUN
iajs-3076	204	55	=	=	SYM
iajs-3076	204	56	1.18599	1.18599	NUM
iajs-3076	204	57	×	×	NOUN
iajs-3076	204	58	10−17	10−17	NOUN
iajs-3076	204	59	,	,	PUNCT
iajs-3076	204	60	𝑐1	𝑐1	NOUN
iajs-3076	204	61	=	=	NOUN
iajs-3076	204	62	0.00228219	0.00228219	NUM
iajs-3076	204	63	,	,	PUNCT
iajs-3076	204	64	𝑐2	𝑐2	NOUN
iajs-3076	204	65	=	=	SYM
iajs-3076	204	66	1	1	X
iajs-3076	204	67	.	.	NUM
iajs-3076	204	68	ihjpas	ihjpas	PROPN
iajs-3076	204	69	.	.	PUNCT
iajs-3076	205	1	36	36	NUM
iajs-3076	205	2	(	(	PUNCT
iajs-3076	205	3	3	3	NUM
iajs-3076	205	4	)	)	PUNCT
iajs-3076	205	5	2023	2023	NUM
iajs-3076	205	6	392	392	NUM
iajs-3076	205	7	we	we	PRON
iajs-3076	205	8	also	also	ADV
iajs-3076	205	9	come	come	VERB
iajs-3076	205	10	up	up	ADP
iajs-3076	205	11	with	with	ADP
iajs-3076	205	12	the	the	DET
iajs-3076	205	13	following	follow	VERB
iajs-3076	205	14	approximate	approximate	ADJ
iajs-3076	205	15	solution	solution	NOUN
iajs-3076	205	16	:	:	PUNCT
iajs-3076	205	17	𝑦(𝑥	𝑦(𝑥	X
iajs-3076	205	18	)	)	PUNCT
iajs-3076	205	19	=	=	NUM
iajs-3076	205	20	1.18599	1.18599	NUM
iajs-3076	205	21	×	×	NOUN
iajs-3076	205	22	10−17	10−17	NUM
iajs-3076	205	23	+	+	NUM
iajs-3076	205	24	0.00456438𝑥	0.00456438𝑥	NOUN
iajs-3076	205	25	+	+	PUNCT
iajs-3076	205	26	0.995436𝑥2	0.995436𝑥2	NUM
iajs-3076	205	27	.	.	PUNCT
iajs-3076	206	1	if	if	SCONJ
iajs-3076	206	2	𝑛	𝑛	PROPN
iajs-3076	206	3	=	=	SYM
iajs-3076	206	4	20	20	NUM
iajs-3076	206	5	,	,	PUNCT
iajs-3076	206	6	we	we	PRON
iajs-3076	206	7	have	have	VERB
iajs-3076	206	8	the	the	DET
iajs-3076	206	9	following	follow	VERB
iajs-3076	206	10	approximate	approximate	ADJ
iajs-3076	206	11	solution	solution	NOUN
iajs-3076	206	12	:	:	PUNCT
iajs-3076	206	13	𝑦(𝑥	𝑦(𝑥	X
iajs-3076	206	14	)	)	PUNCT
iajs-3076	206	15	=	=	PUNCT
iajs-3076	207	1	−2.786853970684164	−2.786853970684164	NUM
iajs-3076	207	2	×	×	NOUN
iajs-3076	207	3	10−15	10−15	NOUN
iajs-3076	207	4	−	−	PROPN
iajs-3076	207	5	0.000030030531854295995𝑥	0.000030030531854295995𝑥	PROPN
iajs-3076	208	1	+	+	CCONJ
iajs-3076	208	2	1.006670875743893𝑥2	1.006670875743893𝑥2	NUM
iajs-3076	208	3	−	−	NOUN
iajs-3076	208	4	0.31622314969631304𝑥3	0.31622314969631304𝑥3	PUNCT
iajs-3076	209	1	+	+	CCONJ
iajs-3076	209	2	7.39417733179431𝑥4	7.39417733179431𝑥4	NUM
iajs-3076	209	3	−	−	NOUN
iajs-3076	209	4	101.22636028238139𝑥5	101.22636028238139𝑥5	PROPN
iajs-3076	210	1	+	+	CCONJ
iajs-3076	211	1	882.5852080762097𝑥6	882.5852080762097𝑥6	NUM
iajs-3076	211	2	−	−	NOUN
iajs-3076	212	1	5099.047105444493𝑥7	5099.047105444493𝑥7	NUM
iajs-3076	213	1	+	+	NUM
iajs-3076	213	2	19465.37892066044𝑥8	19465.37892066044𝑥8	PROPN
iajs-3076	213	3	−	−	NUM
iajs-3076	213	4	44677.52886989678𝑥9	44677.52886989678𝑥9	NOUN
iajs-3076	214	1	+	+	CCONJ
iajs-3076	214	2	27582.502303316025𝑥10	27582.502303316025𝑥10	NUM
iajs-3076	214	3	+	+	CCONJ
iajs-3076	214	4	211915.94892108513𝑥11	211915.94892108513𝑥11	NUM
iajs-3076	214	5	−	−	NOUN
iajs-3076	215	1	939140.5398020139𝑥12	939140.5398020139𝑥12	NUM
iajs-3076	215	2	+	+	CCONJ
iajs-3076	215	3	2196019.891017601𝑥13	2196019.891017601𝑥13	NUM
iajs-3076	215	4	−	−	NUM
iajs-3076	215	5	3463946.68783369𝑥14	3463946.68783369𝑥14	NUM
iajs-3076	216	1	+	+	CCONJ
iajs-3076	216	2	3900531.650722769𝑥15	3900531.650722769𝑥15	NUM
iajs-3076	216	3	−	−	NOUN
iajs-3076	216	4	3162032.689661729𝑥16	3162032.689661729𝑥16	NUM
iajs-3076	216	5	+	+	SYM
iajs-3076	216	6	1810684.418812781𝑥17	1810684.418812781𝑥17	NUM
iajs-3076	216	7	−	−	NOUN
iajs-3076	216	8	696899.7151342098𝑥18	696899.7151342098𝑥18	NUM
iajs-3076	216	9	+	+	NOUN
iajs-3076	216	10	162020.35868317497𝑥19	162020.35868317497𝑥19	NUM
iajs-3076	216	11	−	−	NOUN
iajs-3076	216	12	17212.384417226098𝑥20	17212.384417226098𝑥20	NOUN
iajs-3076	216	13	.	.	PUNCT
iajs-3076	217	1	table	table	NOUN
iajs-3076	217	2	4	4	NUM
iajs-3076	217	3	shows	show	VERB
iajs-3076	217	4	the	the	DET
iajs-3076	217	5	absolute	absolute	ADJ
iajs-3076	217	6	error|𝑦𝑒𝑥𝑎𝑐𝑡	error|𝑦𝑒𝑥𝑎𝑐𝑡	PROPN
iajs-3076	217	7	−	−	PROPN
iajs-3076	217	8	𝑦𝑎𝑝𝑝.|	𝑦𝑎𝑝𝑝.|	NOUN
iajs-3076	217	9	value	value	NOUN
iajs-3076	217	10	for	for	ADP
iajs-3076	217	11	the	the	DET
iajs-3076	217	12	some	some	PRON
iajs-3076	217	13	𝑥	𝑥	PRON
iajs-3076	217	14	∈	∈	PROPN
iajs-3076	218	1	[	[	X
iajs-3076	218	2	0,1	0,1	NUM
iajs-3076	218	3	]	]	PUNCT
iajs-3076	218	4	at	at	ADP
iajs-3076	218	5	𝑛=	𝑛=	NOUN
iajs-3076	218	6	14,16,18	14,16,18	NUM
iajs-3076	218	7	,	,	PUNCT
iajs-3076	218	8	and	and	CCONJ
iajs-3076	218	9	20	20	NUM
iajs-3076	218	10	table	table	NOUN
iajs-3076	218	11	4	4	NUM
iajs-3076	218	12	:	:	PUNCT
iajs-3076	218	13	the	the	DET
iajs-3076	218	14	absolute	absolute	ADJ
iajs-3076	218	15	error	error	NOUN
iajs-3076	218	16	of	of	ADP
iajs-3076	218	17	ex	ex	PROPN
iajs-3076	218	18	.	.	PROPN
iajs-3076	218	19	2	2	NUM
iajs-3076	218	20	for	for	ADP
iajs-3076	218	21	𝑛=14,16,18,20	𝑛=14,16,18,20	NUM
iajs-3076	218	22	by	by	ADP
iajs-3076	218	23	(	(	PUNCT
iajs-3076	218	24	bom	bom	NOUN
iajs-3076	218	25	)	)	PUNCT
iajs-3076	218	26	𝒙	𝒙	PROPN
iajs-3076	218	27	𝒏	𝒏	PROPN
iajs-3076	218	28	=	=	SYM
iajs-3076	218	29	𝟏𝟒	𝟏𝟒	NUM
iajs-3076	218	30	𝒏	𝒏	PROPN
iajs-3076	218	31	=	=	SYM
iajs-3076	218	32	𝟏𝟔	𝟏𝟔	NUM
iajs-3076	218	33	𝒏	𝒏	X
iajs-3076	218	34	=	=	SYM
iajs-3076	218	35	𝟏𝟖	𝟏𝟖	NUM
iajs-3076	218	36	𝒏	𝒏	PROPN
iajs-3076	218	37	=	=	NOUN
iajs-3076	218	38	𝟐𝟎	𝟐𝟎	NUM
iajs-3076	218	39	0.1	0.1	NUM
iajs-3076	218	40	3.3016×10	3.3016×10	NOUN
iajs-3076	218	41	-	-	SYM
iajs-3076	218	42	6	6	NUM
iajs-3076	218	43	2.0304×10	2.0304×10	NOUN
iajs-3076	218	44	-	-	SYM
iajs-3076	218	45	6	6	NUM
iajs-3076	218	46	1.679×10	1.679×10	NUM
iajs-3076	218	47	-	-	SYM
iajs-3076	218	48	6	6	NUM
iajs-3076	218	49	1.42028×10	1.42028×10	NOUN
iajs-3076	218	50	-	-	SYM
iajs-3076	218	51	6	6	NUM
iajs-3076	218	52	0.2	0.2	NUM
iajs-3076	218	53	5.64738×10	5.64738×10	NUM
iajs-3076	218	54	-	-	SYM
iajs-3076	218	55	6	6	NUM
iajs-3076	218	56	3.96901×10	3.96901×10	NOUN
iajs-3076	218	57	-	-	PUNCT
iajs-3076	218	58	6	6	NUM
iajs-3076	218	59	2.44675×10	2.44675×10	NUM
iajs-3076	218	60	-	-	SYM
iajs-3076	218	61	6	6	NUM
iajs-3076	218	62	1.92033×10	1.92033×10	NUM
iajs-3076	218	63	-	-	SYM
iajs-3076	218	64	6	6	NUM
iajs-3076	218	65	0.3	0.3	NUM
iajs-3076	218	66	5.90691×10	5.90691×10	NUM
iajs-3076	218	67	-	-	SYM
iajs-3076	218	68	6	6	NUM
iajs-3076	218	69	4.01465×10	4.01465×10	NOUN
iajs-3076	218	70	-	-	SYM
iajs-3076	218	71	6	6	NUM
iajs-3076	218	72	3.34437×10	3.34437×10	NUM
iajs-3076	218	73	-	-	SYM
iajs-3076	218	74	6	6	NUM
iajs-3076	218	75	2.143×10	2.143×10	NOUN
iajs-3076	218	76	-	-	SYM
iajs-3076	218	77	6	6	NUM
iajs-3076	218	78	0.4	0.4	NUM
iajs-3076	218	79	6.08868×10	6.08868×10	NUM
iajs-3076	218	80	-	-	SYM
iajs-3076	218	81	6	6	NUM
iajs-3076	218	82	4.68942×10	4.68942×10	NUM
iajs-3076	218	83	-	-	PUNCT
iajs-3076	218	84	6	6	NUM
iajs-3076	218	85	2.963×10	2.963×10	NUM
iajs-3076	218	86	-	-	SYM
iajs-3076	218	87	6	6	NUM
iajs-3076	218	88	2.48202×10	2.48202×10	NOUN
iajs-3076	218	89	-	-	SYM
iajs-3076	218	90	6	6	NUM
iajs-3076	218	91	0.5	0.5	NUM
iajs-3076	218	92	6.6422×10	6.6422×10	NOUN
iajs-3076	218	93	-	-	SYM
iajs-3076	218	94	6	6	NUM
iajs-3076	218	95	3.86708×10	3.86708×10	NUM
iajs-3076	218	96	-	-	SYM
iajs-3076	218	97	6	6	NUM
iajs-3076	218	98	3.25554×10	3.25554×10	PROPN
iajs-3076	218	99	-	-	SYM
iajs-3076	218	100	6	6	NUM
iajs-3076	218	101	2.06817×10	2.06817×10	NUM
iajs-3076	218	102	-	-	SYM
iajs-3076	218	103	6	6	NUM
iajs-3076	218	104	0.6	0.6	NUM
iajs-3076	218	105	4.61383×10	4.61383×10	NOUN
iajs-3076	218	106	-	-	PUNCT
iajs-3076	218	107	6	6	NUM
iajs-3076	218	108	4.11001×10	4.11001×10	NUM
iajs-3076	218	109	-	-	PUNCT
iajs-3076	218	110	6	6	NUM
iajs-3076	218	111	2.54331×10	2.54331×10	NOUN
iajs-3076	218	112	-	-	SYM
iajs-3076	218	113	6	6	NUM
iajs-3076	218	114	1.97996×10	1.97996×10	NUM
iajs-3076	218	115	-	-	SYM
iajs-3076	218	116	6	6	NUM
iajs-3076	218	117	0.7	0.7	NUM
iajs-3076	218	118	4.97604×10	4.97604×10	NUM
iajs-3076	218	119	-	-	PUNCT
iajs-3076	218	120	6	6	NUM
iajs-3076	218	121	2.68729×10	2.68729×10	NUM
iajs-3076	218	122	-	-	SYM
iajs-3076	218	123	6	6	NUM
iajs-3076	218	124	2.29425×10	2.29425×10	NUM
iajs-3076	218	125	-	-	SYM
iajs-3076	218	126	6	6	NUM
iajs-3076	218	127	1.58232×10	1.58232×10	NUM
iajs-3076	218	128	-	-	SYM
iajs-3076	218	129	6	6	NUM
iajs-3076	218	130	0.8	0.8	NUM
iajs-3076	218	131	2.62815×10	2.62815×10	NUM
iajs-3076	218	132	-	-	SYM
iajs-3076	218	133	6	6	NUM
iajs-3076	218	134	2.43508×10	2.43508×10	NUM
iajs-3076	218	135	-	-	SYM
iajs-3076	218	136	6	6	NUM
iajs-3076	218	137	1.62869×10	1.62869×10	NUM
iajs-3076	218	138	-	-	SYM
iajs-3076	218	139	6	6	NUM
iajs-3076	218	140	9.01401×10	9.01401×10	NOUN
iajs-3076	218	141	-	-	SYM
iajs-3076	218	142	7	7	NUM
iajs-3076	218	143	0.9	0.9	NUM
iajs-3076	218	144	2.04652×10	2.04652×10	NUM
iajs-3076	218	145	-	-	SYM
iajs-3076	218	146	6	6	NUM
iajs-3076	218	147	1.1369×10	1.1369×10	NUM
iajs-3076	218	148	-	-	SYM
iajs-3076	218	149	6	6	NUM
iajs-3076	218	150	6.75106×10	6.75106×10	NOUN
iajs-3076	218	151	-	-	SYM
iajs-3076	218	152	7	7	NUM
iajs-3076	218	153	3.45435×10	3.45435×10	NOUN
iajs-3076	218	154	-	-	PUNCT
iajs-3076	218	155	7	7	NUM
iajs-3076	218	156	to	to	PART
iajs-3076	218	157	solve	solve	VERB
iajs-3076	218	158	example	example	NOUN
iajs-3076	218	159	2	2	NUM
iajs-3076	218	160	using	use	VERB
iajs-3076	218	161	the	the	DET
iajs-3076	218	162	(	(	PUNCT
iajs-3076	218	163	lom	lom	NOUN
iajs-3076	218	164	)	)	PUNCT
iajs-3076	218	165	technique	technique	NOUN
iajs-3076	218	166	,	,	PUNCT
iajs-3076	218	167	we	we	PRON
iajs-3076	218	168	must	must	AUX
iajs-3076	218	169	follow	follow	VERB
iajs-3076	218	170	the	the	DET
iajs-3076	218	171	steps	step	NOUN
iajs-3076	218	172	indicated	indicate	VERB
iajs-3076	218	173	in	in	ADP
iajs-3076	218	174	section	section	NOUN
iajs-3076	218	175	(	(	PUNCT
iajs-3076	218	176	43	43	NUM
iajs-3076	218	177	)	)	PUNCT
iajs-3076	218	178	.	.	PUNCT
iajs-3076	219	1	if	if	SCONJ
iajs-3076	219	2	we	we	PRON
iajs-3076	219	3	take	take	VERB
iajs-3076	219	4	n=2	n=2	ADV
iajs-3076	219	5	,	,	PUNCT
iajs-3076	219	6	we	we	PRON
iajs-3076	219	7	get	get	VERB
iajs-3076	219	8	𝐷	𝐷	PROPN
iajs-3076	219	9	3	3	NUM
iajs-3076	219	10	2	2	NUM
iajs-3076	219	11	=	=	SYM
iajs-3076	220	1	[	[	X
iajs-3076	220	2	0	0	NUM
iajs-3076	220	3	0	0	NUM
iajs-3076	220	4	0	0	NUM
iajs-3076	220	5	0	0	NUM
iajs-3076	220	6	0	0	NUM
iajs-3076	220	7	0	0	NUM
iajs-3076	220	8	16	16	NUM
iajs-3076	220	9	√𝜋	√𝜋	SYM
iajs-3076	220	10	48	48	NUM
iajs-3076	220	11	5√𝜋	5√𝜋	NOUN
iajs-3076	220	12	−	−	NOUN
iajs-3076	221	1	16	16	NUM
iajs-3076	221	2	7√𝜋	7√𝜋	NOUN
iajs-3076	221	3	]	]	X
iajs-3076	221	4	,	,	PUNCT
iajs-3076	221	5	we	we	PRON
iajs-3076	221	6	also	also	ADV
iajs-3076	221	7	obtain	obtain	VERB
iajs-3076	221	8	the	the	DET
iajs-3076	221	9	values	value	NOUN
iajs-3076	221	10	of	of	ADP
iajs-3076	221	11	the	the	DET
iajs-3076	221	12	unknown	unknown	ADJ
iajs-3076	221	13	vector	vector	NOUN
iajs-3076	221	14	𝐶𝑇	𝐶𝑇	PROPN
iajs-3076	221	15	,	,	PUNCT
iajs-3076	221	16	which	which	PRON
iajs-3076	221	17	are	be	AUX
iajs-3076	221	18	as	as	SCONJ
iajs-3076	221	19	follows	follow	VERB
iajs-3076	221	20	𝑐0	𝑐0	NOUN
iajs-3076	221	21	=	=	SYM
iajs-3076	221	22	0.334094	0.334094	NUM
iajs-3076	221	23	,	,	PUNCT
iajs-3076	221	24	𝑐1	𝑐1	NOUN
iajs-3076	221	25	=	=	NOUN
iajs-3076	221	26	0.5	0.5	NUM
iajs-3076	221	27	,	,	PUNCT
iajs-3076	221	28	𝑐2	𝑐2	NOUN
iajs-3076	221	29	=	=	SYM
iajs-3076	221	30	0.165906	0.165906	NUM
iajs-3076	221	31	.	.	PUNCT
iajs-3076	222	1	and	and	CCONJ
iajs-3076	222	2	their	their	PRON
iajs-3076	222	3	approximate	approximate	ADJ
iajs-3076	222	4	solution	solution	NOUN
iajs-3076	222	5	is	be	AUX
iajs-3076	222	6	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-3076	222	7	)	)	PUNCT
iajs-3076	222	8	=	=	SYM
iajs-3076	223	1	2.77555756	2.77555756	NUM
iajs-3076	223	2	×	×	NOUN
iajs-3076	223	3	10−17	10−17	NUM
iajs-3076	223	4	+	+	NUM
iajs-3076	223	5	0.00456438𝑥	0.00456438𝑥	NOUN
iajs-3076	223	6	+	+	PUNCT
iajs-3076	223	7	0.995436𝑥2	0.995436𝑥2	NUM
iajs-3076	223	8	.	.	PUNCT
iajs-3076	224	1	if	if	SCONJ
iajs-3076	224	2	𝑛	𝑛	PROPN
iajs-3076	224	3	=	=	SYM
iajs-3076	224	4	20	20	NUM
iajs-3076	224	5	,	,	PUNCT
iajs-3076	224	6	the	the	DET
iajs-3076	224	7	approximate	approximate	ADJ
iajs-3076	224	8	solution	solution	NOUN
iajs-3076	224	9	will	will	AUX
iajs-3076	224	10	be	be	AUX
iajs-3076	224	11	as	as	SCONJ
iajs-3076	224	12	follows	follow	VERB
iajs-3076	224	13	:	:	PUNCT
iajs-3076	224	14	𝑦(𝑥	𝑦(𝑥	X
iajs-3076	224	15	)	)	PUNCT
iajs-3076	224	16	=	=	PUNCT
iajs-3076	225	1	−7.827619401012162	−7.827619401012162	NOUN
iajs-3076	225	2	×	×	NOUN
iajs-3076	225	3	10−17	10−17	NUM
iajs-3076	225	4	−	−	PROPN
iajs-3076	225	5	0.000030068562737359008𝑥	0.000030068562737359008𝑥	PROPN
iajs-3076	226	1	+	+	CCONJ
iajs-3076	226	2	1.0066701273460272𝑥2	1.0066701273460272𝑥2	NUM
iajs-3076	226	3	−	−	NOUN
iajs-3076	226	4	0.3161559593254199𝑥3	0.3161559593254199𝑥3	NOUN
iajs-3076	226	5	+	+	CCONJ
iajs-3076	227	1	7.391520839002448𝑥4	7.391520839002448𝑥4	NUM
iajs-3076	227	2	−	−	NUM
iajs-3076	227	3	101.1675850252221𝑥5	101.1675850252221𝑥5	NOUN
iajs-3076	228	1	+	+	CCONJ
iajs-3076	228	2	881.7639994208571𝑥6	881.7639994208571𝑥6	NUM
iajs-3076	228	3	−	−	NOUN
iajs-3076	229	1	5091.2533573008905𝑥7	5091.2533573008905𝑥7	NUM
iajs-3076	229	2	+	+	CCONJ
iajs-3076	229	3	19412.68134451585𝑥8	19412.68134451585𝑥8	NUM
iajs-3076	230	1	−	−	NUM
iajs-3076	230	2	44415.30443366349𝑥9	44415.30443366349𝑥9	X
iajs-3076	231	1	+	+	CCONJ
iajs-3076	231	2	26600.722236690082𝑥10	26600.722236690082𝑥10	NUM
iajs-3076	231	3	+	+	CCONJ
iajs-3076	231	4	214722.2039331961𝑥11	214722.2039331961𝑥11	NUM
iajs-3076	231	5	−	−	PROPN
iajs-3076	232	1	945315.3904772103𝑥12	945315.3904772103𝑥12	NUM
iajs-3076	232	2	+	+	NUM
iajs-3076	232	3	2206507.388919022𝑥13	2206507.388919022𝑥13	NUM
iajs-3076	232	4	−	−	NOUN
iajs-3076	232	5	3477652.419776158𝑥14	3477652.419776158𝑥14	NUM
iajs-3076	232	6	+	+	NUM
iajs-3076	232	7	3914177.755634204𝑥15	3914177.755634204𝑥15	NUM
iajs-3076	232	8	−	−	NOUN
iajs-3076	232	9	3172189.258528861𝑥16	3172189.258528861𝑥16	NUM
iajs-3076	232	10	+	+	NUM
iajs-3076	232	11	1816152.725780014𝑥17	1816152.725780014𝑥17	NUM
iajs-3076	232	12	−	−	PROPN
iajs-3076	232	13	698910.3552130745𝑥18	698910.3552130745𝑥18	NUM
iajs-3076	233	1	+	+	NUM
iajs-3076	233	2	162471.92620954153𝑥19	162471.92620954153𝑥19	NUM
iajs-3076	233	3	−	−	NOUN
iajs-3076	233	4	17259.100690250787𝑥20	17259.100690250787𝑥20	NUM
iajs-3076	233	5	.	.	PUNCT
iajs-3076	234	1	ihjpas	ihjpas	PROPN
iajs-3076	234	2	.	.	PUNCT
iajs-3076	235	1	36	36	NUM
iajs-3076	235	2	(	(	PUNCT
iajs-3076	235	3	3	3	NUM
iajs-3076	235	4	)	)	PUNCT
iajs-3076	235	5	2023	2023	NUM
iajs-3076	235	6	393	393	NUM
iajs-3076	235	7	table	table	NOUN
iajs-3076	235	8	5	5	NUM
iajs-3076	235	9	shows	show	VERB
iajs-3076	235	10	the	the	DET
iajs-3076	235	11	absolute	absolute	ADJ
iajs-3076	235	12	error|𝑦𝑒𝑥𝑎𝑐𝑡	error|𝑦𝑒𝑥𝑎𝑐𝑡	PROPN
iajs-3076	235	13	−	−	PROPN
iajs-3076	235	14	𝑦𝑎𝑝𝑝.|	𝑦𝑎𝑝𝑝.|	NOUN
iajs-3076	235	15	value	value	NOUN
iajs-3076	235	16	for	for	ADP
iajs-3076	235	17	the	the	DET
iajs-3076	235	18	some	some	PRON
iajs-3076	235	19	𝑥	𝑥	PRON
iajs-3076	235	20	∈	∈	PROPN
iajs-3076	236	1	[	[	X
iajs-3076	236	2	0,1	0,1	NUM
iajs-3076	236	3	]	]	PUNCT
iajs-3076	236	4	at	at	ADP
iajs-3076	236	5	𝑛=	𝑛=	NOUN
iajs-3076	236	6	14,16,18	14,16,18	NUM
iajs-3076	236	7	,	,	PUNCT
iajs-3076	236	8	and	and	CCONJ
iajs-3076	236	9	20	20	NUM
iajs-3076	236	10	table	table	NOUN
iajs-3076	236	11	5	5	NUM
iajs-3076	236	12	:	:	PUNCT
iajs-3076	236	13	the	the	DET
iajs-3076	236	14	absolute	absolute	ADJ
iajs-3076	236	15	error	error	NOUN
iajs-3076	236	16	of	of	ADP
iajs-3076	236	17	ex	ex	PROPN
iajs-3076	236	18	.	.	PROPN
iajs-3076	236	19	2	2	NUM
iajs-3076	236	20	for	for	ADP
iajs-3076	236	21	𝑛=14,16,18,20	𝑛=14,16,18,20	NUM
iajs-3076	236	22	by	by	ADP
iajs-3076	236	23	(	(	PUNCT
iajs-3076	236	24	lom	lom	PROPN
iajs-3076	236	25	)	)	PUNCT
iajs-3076	236	26	𝒙	𝒙	PROPN
iajs-3076	236	27	𝒏	𝒏	PROPN
iajs-3076	236	28	=	=	SYM
iajs-3076	236	29	𝟏𝟒	𝟏𝟒	NUM
iajs-3076	236	30	𝒏	𝒏	PROPN
iajs-3076	236	31	=	=	SYM
iajs-3076	236	32	𝟏𝟔	𝟏𝟔	NUM
iajs-3076	236	33	𝒏	𝒏	X
iajs-3076	236	34	=	=	SYM
iajs-3076	236	35	𝟏𝟖	𝟏𝟖	NUM
iajs-3076	236	36	𝒏	𝒏	PROPN
iajs-3076	236	37	=	=	NOUN
iajs-3076	236	38	𝟐𝟎	𝟐𝟎	NUM
iajs-3076	236	39	0.1	0.1	NUM
iajs-3076	236	40	3.30159×10	3.30159×10	NUM
iajs-3076	236	41	-	-	SYM
iajs-3076	236	42	6	6	NUM
iajs-3076	236	43	2.03041×10	2.03041×10	NUM
iajs-3076	236	44	-	-	SYM
iajs-3076	236	45	6	6	NUM
iajs-3076	236	46	1.67929×10	1.67929×10	NUM
iajs-3076	236	47	-	-	SYM
iajs-3076	236	48	6	6	NUM
iajs-3076	236	49	1.41633×10	1.41633×10	NUM
iajs-3076	236	50	-	-	SYM
iajs-3076	236	51	6	6	NUM
iajs-3076	236	52	0.2	0.2	NUM
iajs-3076	236	53	5.64737×10	5.64737×10	NUM
iajs-3076	236	54	-	-	SYM
iajs-3076	236	55	6	6	NUM
iajs-3076	236	56	3.96904×10	3.96904×10	NUM
iajs-3076	236	57	-	-	SYM
iajs-3076	236	58	6	6	NUM
iajs-3076	236	59	2.44733×10	2.44733×10	NUM
iajs-3076	236	60	-	-	SYM
iajs-3076	236	61	6	6	NUM
iajs-3076	236	62	1.91244×10	1.91244×10	NUM
iajs-3076	236	63	-	-	SYM
iajs-3076	236	64	6	6	NUM
iajs-3076	236	65	0.3	0.3	NUM
iajs-3076	236	66	5.9069×10	5.9069×10	NUM
iajs-3076	236	67	-	-	SYM
iajs-3076	236	68	6	6	NUM
iajs-3076	236	69	4.0147×10	4.0147×10	NOUN
iajs-3076	236	70	-	-	PUNCT
iajs-3076	236	71	6	6	NUM
iajs-3076	236	72	3.34525×10	3.34525×10	PROPN
iajs-3076	236	73	-	-	NUM
iajs-3076	236	74	6	6	NUM
iajs-3076	236	75	2.13118×10	2.13118×10	NUM
iajs-3076	236	76	-	-	SYM
iajs-3076	236	77	6	6	NUM
iajs-3076	236	78	0.4	0.4	NUM
iajs-3076	236	79	6.08866×10	6.08866×10	NUM
iajs-3076	236	80	-	-	SYM
iajs-3076	236	81	6	6	NUM
iajs-3076	236	82	4.68948×10	4.68948×10	PROPN
iajs-3076	236	83	-	-	SYM
iajs-3076	236	84	6	6	NUM
iajs-3076	236	85	2.96416×10	2.96416×10	NUM
iajs-3076	236	86	-	-	SYM
iajs-3076	236	87	6	6	NUM
iajs-3076	236	88	2.4665×10	2.4665×10	NUM
iajs-3076	236	89	-	-	SYM
iajs-3076	236	90	6	6	NUM
iajs-3076	236	91	0.5	0.5	NUM
iajs-3076	236	92	6.64218×10	6.64218×10	NOUN
iajs-3076	236	93	-	-	PUNCT
iajs-3076	236	94	6	6	NUM
iajs-3076	236	95	3.86716×10	3.86716×10	NOUN
iajs-3076	236	96	-	-	PUNCT
iajs-3076	236	97	6	6	NUM
iajs-3076	236	98	3.25698×10	3.25698×10	NUM
iajs-3076	236	99	-	-	SYM
iajs-3076	236	100	6	6	NUM
iajs-3076	236	101	2.04886×10	2.04886×10	NOUN
iajs-3076	236	102	-	-	SYM
iajs-3076	236	103	6	6	NUM
iajs-3076	236	104	0.6	0.6	NUM
iajs-3076	236	105	4.6138×10	4.6138×10	NOUN
iajs-3076	236	106	-	-	PUNCT
iajs-3076	236	107	6	6	NUM
iajs-3076	236	108	4.11011×10	4.11011×10	NUM
iajs-3076	236	109	-	-	SYM
iajs-3076	236	110	6	6	NUM
iajs-3076	236	111	2.54504×10	2.54504×10	NOUN
iajs-3076	236	112	-	-	SYM
iajs-3076	236	113	6	6	NUM
iajs-3076	236	114	1.95697×10	1.95697×10	NUM
iajs-3076	236	115	-	-	SYM
iajs-3076	236	116	6	6	NUM
iajs-3076	236	117	0.7	0.7	NUM
iajs-3076	236	118	4.97601×10	4.97601×10	NUM
iajs-3076	236	119	-	-	PUNCT
iajs-3076	236	120	6	6	NUM
iajs-3076	236	121	2.6874×10	2.6874×10	NUM
iajs-3076	236	122	-	-	SYM
iajs-3076	236	123	6	6	NUM
iajs-3076	236	124	2.29617×10	2.29617×10	NUM
iajs-3076	236	125	-	-	SYM
iajs-3076	236	126	6	6	NUM
iajs-3076	236	127	1.55857×10	1.55857×10	NUM
iajs-3076	236	128	-	-	SYM
iajs-3076	236	129	6	6	NUM
iajs-3076	236	130	0.8	0.8	NUM
iajs-3076	236	131	2.62812×10	2.62812×10	NUM
iajs-3076	236	132	-	-	SYM
iajs-3076	236	133	6	6	NUM
iajs-3076	236	134	2.43526×10	2.43526×10	NOUN
iajs-3076	236	135	-	-	SYM
iajs-3076	236	136	6	6	NUM
iajs-3076	236	137	1.63045×10	1.63045×10	NUM
iajs-3076	236	138	-	-	SYM
iajs-3076	236	139	6	6	NUM
iajs-3076	236	140	8.94486×10	8.94486×10	NUM
iajs-3076	236	141	-	-	SYM
iajs-3076	236	142	7	7	NUM
iajs-3076	236	143	0.9	0.9	NUM
iajs-3076	236	144	2.04649×10	2.04649×10	NUM
iajs-3076	236	145	-	-	SYM
iajs-3076	236	146	6	6	NUM
iajs-3076	236	147	1.13714×10	1.13714×10	NUM
iajs-3076	236	148	-	-	SYM
iajs-3076	236	149	6	6	NUM
iajs-3076	236	150	6.78982×10	6.78982×10	NOUN
iajs-3076	236	151	-	-	SYM
iajs-3076	236	152	7	7	NUM
iajs-3076	236	153	4.05584×10	4.05584×10	NOUN
iajs-3076	236	154	-	-	PUNCT
iajs-3076	236	155	7	7	NUM
iajs-3076	236	156	in	in	ADP
iajs-3076	236	157	figure	figure	NOUN
iajs-3076	236	158	3	3	NUM
iajs-3076	236	159	,	,	PUNCT
iajs-3076	236	160	we	we	PRON
iajs-3076	236	161	show	show	VERB
iajs-3076	236	162	a	a	DET
iajs-3076	236	163	plot	plot	NOUN
iajs-3076	236	164	of	of	ADP
iajs-3076	236	165	both	both	CCONJ
iajs-3076	236	166	the	the	DET
iajs-3076	236	167	exact	exact	ADJ
iajs-3076	236	168	solution	solution	NOUN
iajs-3076	236	169	and	and	CCONJ
iajs-3076	236	170	the	the	DET
iajs-3076	236	171	approximate	approximate	ADJ
iajs-3076	236	172	solution	solution	NOUN
iajs-3076	236	173	of	of	ADP
iajs-3076	236	174	the	the	DET
iajs-3076	236	175	two	two	NUM
iajs-3076	236	176	proposed	propose	VERB
iajs-3076	236	177	methods	method	NOUN
iajs-3076	236	178	of	of	ADP
iajs-3076	236	179	example	example	NOUN
iajs-3076	236	180	2	2	NUM
iajs-3076	236	181	for	for	ADP
iajs-3076	236	182	𝑛=20	𝑛=20	PROPN
iajs-3076	236	183	.	.	PUNCT
iajs-3076	237	1	figure	figure	VERB
iajs-3076	237	2	3	3	NUM
iajs-3076	237	3	:	:	PUNCT
iajs-3076	237	4	the	the	DET
iajs-3076	237	5	comparison	comparison	NOUN
iajs-3076	237	6	of	of	ADP
iajs-3076	237	7	the	the	DET
iajs-3076	237	8	exact	exact	ADJ
iajs-3076	237	9	solution	solution	NOUN
iajs-3076	237	10	and	and	CCONJ
iajs-3076	237	11	the	the	DET
iajs-3076	237	12	approximate	approximate	ADJ
iajs-3076	237	13	solution	solution	NOUN
iajs-3076	237	14	of	of	ADP
iajs-3076	237	15	(	(	PUNCT
iajs-3076	237	16	bom	bom	PROPN
iajs-3076	237	17	,	,	PUNCT
iajs-3076	237	18	lom	lom	NOUN
iajs-3076	237	19	)	)	PUNCT
iajs-3076	237	20	methods	method	NOUN
iajs-3076	237	21	for	for	ADP
iajs-3076	237	22	ex	ex	NOUN
iajs-3076	237	23	.	.	PROPN
iajs-3076	237	24	2	2	NUM
iajs-3076	237	25	at	at	ADP
iajs-3076	237	26	𝑛=20	𝑛=20	PROPN
iajs-3076	237	27	in	in	ADP
iajs-3076	237	28	figure	figure	NOUN
iajs-3076	237	29	4	4	NUM
iajs-3076	237	30	,	,	PUNCT
iajs-3076	237	31	logarithmic	logarithmic	ADJ
iajs-3076	237	32	plots	plot	NOUN
iajs-3076	237	33	of	of	ADP
iajs-3076	237	34	the	the	DET
iajs-3076	237	35	greatest	great	ADJ
iajs-3076	237	36	absolute	absolute	ADJ
iajs-3076	237	37	error	error	NOUN
iajs-3076	237	38	of	of	ADP
iajs-3076	237	39	the	the	DET
iajs-3076	237	40	approximate	approximate	ADJ
iajs-3076	237	41	solution	solution	NOUN
iajs-3076	237	42	are	be	AUX
iajs-3076	237	43	given	give	VERB
iajs-3076	237	44	using	use	VERB
iajs-3076	237	45	bernstein	bernstein	PROPN
iajs-3076	237	46	or	or	CCONJ
iajs-3076	237	47	legendre	legendre	PROPN
iajs-3076	237	48	polynomials	polynomial	NOUN
iajs-3076	237	49	with	with	ADP
iajs-3076	237	50	operational	operational	ADJ
iajs-3076	237	51	matrices	matrix	NOUN
iajs-3076	237	52	to	to	PART
iajs-3076	237	53	solve	solve	VERB
iajs-3076	237	54	example	example	NOUN
iajs-3076	237	55	2	2	NUM
iajs-3076	237	56	from	from	ADP
iajs-3076	237	57	𝑛	𝑛	NOUN
iajs-3076	237	58	=	=	SYM
iajs-3076	237	59	2	2	NUM
iajs-3076	237	60	to	to	ADP
iajs-3076	237	61	𝑛	𝑛	NOUN
iajs-3076	237	62	=	=	SYM
iajs-3076	237	63	20	20	NUM
iajs-3076	237	64	.	.	PUNCT
iajs-3076	238	1	ihjpas	ihjpas	PROPN
iajs-3076	238	2	.	.	PUNCT
iajs-3076	239	1	36	36	NUM
iajs-3076	239	2	(	(	PUNCT
iajs-3076	239	3	3	3	NUM
iajs-3076	239	4	)	)	PUNCT
iajs-3076	239	5	2023	2023	NUM
iajs-3076	239	6	394	394	NUM
iajs-3076	239	7	figure	figure	NOUN
iajs-3076	239	8	4	4	NUM
iajs-3076	239	9	:	:	PUNCT
iajs-3076	239	10	logarithmic	logarithmic	ADJ
iajs-3076	239	11	plots	plot	NOUN
iajs-3076	239	12	for	for	ADP
iajs-3076	239	13	the	the	DET
iajs-3076	239	14	𝑀𝐴𝐸𝑛	𝑀𝐴𝐸𝑛	PROPN
iajs-3076	239	15	of	of	ADP
iajs-3076	239	16	ex	ex	PROPN
iajs-3076	239	17	.	.	NOUN
iajs-3076	239	18	2	2	NUM
iajs-3076	239	19	form	form	NOUN
iajs-3076	239	20	𝑛=2	𝑛=2	PUNCT
iajs-3076	239	21	to	to	ADP
iajs-3076	239	22	𝑛=20	𝑛=20	PROPN
iajs-3076	239	23	the	the	DET
iajs-3076	239	24	two	two	NUM
iajs-3076	239	25	proposed	propose	VERB
iajs-3076	239	26	approaches	approach	NOUN
iajs-3076	239	27	are	be	AUX
iajs-3076	239	28	efficient	efficient	ADJ
iajs-3076	239	29	,	,	PUNCT
iajs-3076	239	30	as	as	SCONJ
iajs-3076	239	31	seen	see	VERB
iajs-3076	239	32	by	by	ADP
iajs-3076	239	33	the	the	DET
iajs-3076	239	34	above	above	ADJ
iajs-3076	239	35	results	result	NOUN
iajs-3076	239	36	because	because	SCONJ
iajs-3076	239	37	their	their	PRON
iajs-3076	239	38	results	result	NOUN
iajs-3076	239	39	are	be	AUX
iajs-3076	239	40	accurate	accurate	ADJ
iajs-3076	239	41	when	when	SCONJ
iajs-3076	239	42	compared	compare	VERB
iajs-3076	239	43	to	to	ADP
iajs-3076	239	44	the	the	DET
iajs-3076	239	45	precise	precise	ADJ
iajs-3076	239	46	solution	solution	NOUN
iajs-3076	239	47	's	's	PART
iajs-3076	239	48	results	result	NOUN
iajs-3076	239	49	,	,	PUNCT
iajs-3076	239	50	as	as	SCONJ
iajs-3076	239	51	shown	show	VERB
iajs-3076	239	52	in	in	ADP
iajs-3076	239	53	figure	figure	NOUN
iajs-3076	239	54	1	1	NUM
iajs-3076	239	55	.	.	PUNCT
iajs-3076	239	56	figure	figure	NOUN
iajs-3076	239	57	2	2	NUM
iajs-3076	239	58	demonstrates	demonstrate	VERB
iajs-3076	239	59	the	the	DET
iajs-3076	239	60	decrease	decrease	NOUN
iajs-3076	239	61	in	in	ADP
iajs-3076	239	62	absolute	absolute	ADJ
iajs-3076	239	63	error	error	NOUN
iajs-3076	239	64	when	when	SCONJ
iajs-3076	239	65	the	the	DET
iajs-3076	239	66	value	value	NOUN
iajs-3076	239	67	of	of	ADP
iajs-3076	239	68	𝑛	𝑛	PROPN
iajs-3076	239	69	is	be	AUX
iajs-3076	239	70	increased	increase	VERB
iajs-3076	239	71	,	,	PUNCT
iajs-3076	239	72	demonstrating	demonstrate	VERB
iajs-3076	239	73	the	the	DET
iajs-3076	239	74	efficacy	efficacy	NOUN
iajs-3076	239	75	of	of	ADP
iajs-3076	239	76	the	the	DET
iajs-3076	239	77	two	two	NUM
iajs-3076	239	78	proposed	propose	VERB
iajs-3076	239	79	techniques	technique	NOUN
iajs-3076	239	80	.	.	PUNCT
iajs-3076	240	1	table	table	NOUN
iajs-3076	240	2	6	6	NUM
iajs-3076	240	3	illustrates	illustrate	VERB
iajs-3076	240	4	the	the	DET
iajs-3076	240	5	absolute	absolute	ADJ
iajs-3076	240	6	error	error	NOUN
iajs-3076	240	7	numbers	number	NOUN
iajs-3076	240	8	for	for	ADP
iajs-3076	240	9	(	(	PUNCT
iajs-3076	240	10	bom	bom	PROPN
iajs-3076	240	11	,	,	PUNCT
iajs-3076	240	12	lom	lom	NOUN
iajs-3076	240	13	)	)	PUNCT
iajs-3076	240	14	methods	method	NOUN
iajs-3076	240	15	at	at	ADP
iajs-3076	240	16	𝑛	𝑛	NOUN
iajs-3076	240	17	=	=	SYM
iajs-3076	240	18	20	20	NUM
iajs-3076	240	19	to	to	PART
iajs-3076	240	20	determine	determine	VERB
iajs-3076	240	21	which	which	PRON
iajs-3076	240	22	of	of	ADP
iajs-3076	240	23	the	the	DET
iajs-3076	240	24	two	two	NUM
iajs-3076	240	25	strategies	strategy	NOUN
iajs-3076	240	26	is	be	AUX
iajs-3076	240	27	superior	superior	ADJ
iajs-3076	240	28	for	for	ADP
iajs-3076	240	29	solving	solve	VERB
iajs-3076	240	30	example	example	NOUN
iajs-3076	240	31	2	2	NUM
iajs-3076	240	32	.	.	PUNCT
iajs-3076	240	33	table	table	NOUN
iajs-3076	240	34	6	6	NUM
iajs-3076	240	35	:	:	PUNCT
iajs-3076	240	36	the	the	DET
iajs-3076	240	37	absolute	absolute	ADJ
iajs-3076	240	38	error	error	NOUN
iajs-3076	240	39	|𝑦𝑒𝑥𝑎𝑐𝑡	|𝑦𝑒𝑥𝑎𝑐𝑡	NOUN
iajs-3076	240	40	−	−	NOUN
iajs-3076	240	41	𝑦𝑎𝑝𝑝.|	𝑦𝑎𝑝𝑝.|	VERB
iajs-3076	240	42	of	of	ADP
iajs-3076	240	43	(	(	PUNCT
iajs-3076	240	44	bom	bom	PROPN
iajs-3076	240	45	,	,	PUNCT
iajs-3076	240	46	lom	lom	PROPN
iajs-3076	240	47	)	)	PUNCT
iajs-3076	240	48	for	for	ADP
iajs-3076	240	49	ex	ex	PROPN
iajs-3076	240	50	.	.	PROPN
iajs-3076	240	51	2	2	NUM
iajs-3076	240	52	at	at	ADP
iajs-3076	240	53	𝑛=20	𝑛=20	PROPN
iajs-3076	240	54	𝒙	𝒙	VERB
iajs-3076	240	55	absolute	absolute	ADJ
iajs-3076	240	56	error	error	NOUN
iajs-3076	240	57	(	(	PUNCT
iajs-3076	240	58	b	b	NOUN
iajs-3076	240	59	)	)	PUNCT
iajs-3076	240	60	absolute	absolute	ADJ
iajs-3076	240	61	error	error	NOUN
iajs-3076	240	62	(	(	PUNCT
iajs-3076	240	63	l	l	NOUN
iajs-3076	240	64	)	)	PUNCT
iajs-3076	240	65	0.1	0.1	NUM
iajs-3076	240	66	1.42028×10	1.42028×10	NOUN
iajs-3076	240	67	-	-	SYM
iajs-3076	240	68	6	6	NUM
iajs-3076	240	69	1.41633×10	1.41633×10	NUM
iajs-3076	240	70	-	-	SYM
iajs-3076	240	71	6	6	NUM
iajs-3076	240	72	0.2	0.2	NUM
iajs-3076	240	73	1.92033×10	1.92033×10	NUM
iajs-3076	240	74	-	-	SYM
iajs-3076	240	75	6	6	NUM
iajs-3076	240	76	1.91244×10	1.91244×10	NOUN
iajs-3076	240	77	-	-	SYM
iajs-3076	240	78	6	6	NUM
iajs-3076	240	79	0.3	0.3	NUM
iajs-3076	240	80	2.143×10	2.143×10	NUM
iajs-3076	240	81	-	-	SYM
iajs-3076	240	82	6	6	NUM
iajs-3076	240	83	2.13118×10	2.13118×10	NUM
iajs-3076	240	84	-	-	SYM
iajs-3076	240	85	6	6	NUM
iajs-3076	240	86	0.4	0.4	NUM
iajs-3076	240	87	2.48202×10	2.48202×10	NOUN
iajs-3076	240	88	-	-	SYM
iajs-3076	240	89	6	6	NUM
iajs-3076	240	90	2.4665×10	2.4665×10	NUM
iajs-3076	240	91	-	-	SYM
iajs-3076	240	92	6	6	NUM
iajs-3076	240	93	0.5	0.5	NUM
iajs-3076	240	94	2.06817×10	2.06817×10	NUM
iajs-3076	240	95	-	-	SYM
iajs-3076	240	96	6	6	NUM
iajs-3076	240	97	2.04886×10	2.04886×10	NOUN
iajs-3076	240	98	-	-	SYM
iajs-3076	240	99	6	6	NUM
iajs-3076	240	100	0.6	0.6	NUM
iajs-3076	240	101	1.97996×10	1.97996×10	NUM
iajs-3076	240	102	-	-	SYM
iajs-3076	240	103	6	6	NUM
iajs-3076	240	104	1.95697×10	1.95697×10	NUM
iajs-3076	240	105	-	-	SYM
iajs-3076	240	106	6	6	NUM
iajs-3076	240	107	0.7	0.7	NUM
iajs-3076	240	108	1.58232×10	1.58232×10	NUM
iajs-3076	240	109	-	-	SYM
iajs-3076	240	110	6	6	NUM
iajs-3076	240	111	1.55857×10	1.55857×10	NUM
iajs-3076	240	112	-	-	SYM
iajs-3076	240	113	6	6	NUM
iajs-3076	240	114	0.8	0.8	NUM
iajs-3076	240	115	9.01401×10	9.01401×10	NUM
iajs-3076	240	116	-	-	SYM
iajs-3076	240	117	7	7	NUM
iajs-3076	240	118	8.94486×10	8.94486×10	NUM
iajs-3076	240	119	-	-	SYM
iajs-3076	240	120	7	7	NUM
iajs-3076	240	121	0.9	0.9	NUM
iajs-3076	240	122	3.45435×10	3.45435×10	NOUN
iajs-3076	240	123	-	-	SYM
iajs-3076	240	124	7	7	NUM
iajs-3076	240	125	4.05584×10	4.05584×10	NOUN
iajs-3076	240	126	-	-	SYM
iajs-3076	240	127	7	7	NUM
iajs-3076	240	128	we	we	PRON
iajs-3076	240	129	notice	notice	VERB
iajs-3076	240	130	from	from	ADP
iajs-3076	240	131	the	the	DET
iajs-3076	240	132	above	above	ADJ
iajs-3076	240	133	table	table	NOUN
iajs-3076	240	134	that	that	SCONJ
iajs-3076	240	135	the	the	DET
iajs-3076	240	136	greatest	great	ADJ
iajs-3076	240	137	absolute	absolute	ADJ
iajs-3076	240	138	error	error	NOUN
iajs-3076	240	139	we	we	PRON
iajs-3076	240	140	acquired	acquire	VERB
iajs-3076	240	141	in	in	ADP
iajs-3076	240	142	the	the	DET
iajs-3076	240	143	method	method	NOUN
iajs-3076	240	144	(	(	PUNCT
iajs-3076	240	145	bom	bom	NOUN
iajs-3076	240	146	)	)	PUNCT
iajs-3076	240	147	is	be	AUX
iajs-3076	240	148	2.48202×10	2.48202×10	NOUN
iajs-3076	240	149	-	-	SYM
iajs-3076	240	150	6	6	NUM
iajs-3076	240	151	,	,	PUNCT
iajs-3076	240	152	but	but	CCONJ
iajs-3076	240	153	in	in	ADP
iajs-3076	240	154	the	the	DET
iajs-3076	240	155	method	method	NOUN
iajs-3076	240	156	(	(	PUNCT
iajs-3076	240	157	lom	lom	NOUN
iajs-3076	240	158	)	)	PUNCT
iajs-3076	240	159	is	be	AUX
iajs-3076	240	160	2.4665×10	2.4665×10	NOUN
iajs-3076	240	161	-	-	SYM
iajs-3076	240	162	6	6	NUM
iajs-3076	240	163	,	,	PUNCT
iajs-3076	240	164	indicating	indicate	VERB
iajs-3076	240	165	that	that	SCONJ
iajs-3076	240	166	the	the	DET
iajs-3076	240	167	method	method	NOUN
iajs-3076	240	168	(	(	PUNCT
iajs-3076	240	169	lom	lom	NOUN
iajs-3076	240	170	)	)	PUNCT
iajs-3076	240	171	is	be	AUX
iajs-3076	240	172	the	the	DET
iajs-3076	240	173	best	good	ADJ
iajs-3076	240	174	in	in	ADP
iajs-3076	240	175	solving	solve	VERB
iajs-3076	240	176	ex	ex	NOUN
iajs-3076	240	177	.	.	PROPN
iajs-3076	240	178	2	2	NUM
iajs-3076	240	179	.	.	NOUN
iajs-3076	240	180	6	6	NUM
iajs-3076	240	181	.	.	X
iajs-3076	240	182	conclusion	conclusion	NOUN
iajs-3076	240	183	in	in	ADP
iajs-3076	240	184	this	this	DET
iajs-3076	240	185	study	study	NOUN
iajs-3076	240	186	,	,	PUNCT
iajs-3076	240	187	we	we	PRON
iajs-3076	240	188	propose	propose	VERB
iajs-3076	240	189	the	the	DET
iajs-3076	240	190	methods	method	NOUN
iajs-3076	240	191	of	of	ADP
iajs-3076	240	192	operational	operational	ADJ
iajs-3076	240	193	matrices	matrix	NOUN
iajs-3076	240	194	that	that	PRON
iajs-3076	240	195	depend	depend	VERB
iajs-3076	240	196	on	on	ADP
iajs-3076	240	197	bernstein	bernstein	PROPN
iajs-3076	240	198	polynomials	polynomial	NOUN
iajs-3076	240	199	and	and	CCONJ
iajs-3076	240	200	shifted	shift	VERB
iajs-3076	240	201	legendre	legendre	PROPN
iajs-3076	240	202	polynomials	polynomial	NOUN
iajs-3076	240	203	for	for	ADP
iajs-3076	240	204	fractional	fractional	ADJ
iajs-3076	240	205	derivatives	derivative	NOUN
iajs-3076	240	206	in	in	ADP
iajs-3076	240	207	solving	solve	VERB
iajs-3076	240	208	fractional	fractional	ADJ
iajs-3076	240	209	delay	delay	NOUN
iajs-3076	240	210	pantograph	pantograph	NOUN
iajs-3076	240	211	equations	equation	NOUN
iajs-3076	240	212	.	.	PUNCT
iajs-3076	241	1	the	the	DET
iajs-3076	241	2	numerical	numerical	ADJ
iajs-3076	241	3	results	result	NOUN
iajs-3076	241	4	of	of	ADP
iajs-3076	241	5	the	the	DET
iajs-3076	241	6	approximate	approximate	ADJ
iajs-3076	241	7	solutions	solution	NOUN
iajs-3076	241	8	in	in	ADP
iajs-3076	241	9	examples	example	NOUN
iajs-3076	241	10	1	1	NUM
iajs-3076	241	11	and	and	CCONJ
iajs-3076	241	12	2	2	NUM
iajs-3076	241	13	were	be	AUX
iajs-3076	241	14	given	give	VERB
iajs-3076	241	15	accuracy	accuracy	NOUN
iajs-3076	241	16	when	when	SCONJ
iajs-3076	241	17	compared	compare	VERB
iajs-3076	241	18	with	with	ADP
iajs-3076	241	19	the	the	DET
iajs-3076	241	20	exact	exact	ADJ
iajs-3076	241	21	solutions	solution	NOUN
iajs-3076	241	22	,	,	PUNCT
iajs-3076	241	23	proving	prove	VERB
iajs-3076	241	24	the	the	DET
iajs-3076	241	25	effectiveness	effectiveness	NOUN
iajs-3076	241	26	and	and	CCONJ
iajs-3076	241	27	efficiency	efficiency	NOUN
iajs-3076	241	28	of	of	ADP
iajs-3076	241	29	the	the	DET
iajs-3076	241	30	proposed	propose	VERB
iajs-3076	241	31	methods	method	NOUN
iajs-3076	241	32	.	.	PUNCT
iajs-3076	242	1	figures	figure	NOUN
iajs-3076	242	2	2	2	NUM
iajs-3076	242	3	and	and	CCONJ
iajs-3076	242	4	4	4	NUM
iajs-3076	242	5	showed	show	VERB
iajs-3076	242	6	the	the	DET
iajs-3076	242	7	absolute	absolute	ADJ
iajs-3076	242	8	error	error	NOUN
iajs-3076	242	9	of	of	ADP
iajs-3076	242	10	the	the	DET
iajs-3076	242	11	two	two	NUM
iajs-3076	242	12	examples	example	NOUN
iajs-3076	242	13	for	for	ADP
iajs-3076	242	14	more	more	ADJ
iajs-3076	242	15	than	than	ADP
iajs-3076	242	16	𝑛	𝑛	PROPN
iajs-3076	242	17	,	,	PUNCT
iajs-3076	242	18	where	where	SCONJ
iajs-3076	242	19	when	when	SCONJ
iajs-3076	242	20	the	the	DET
iajs-3076	242	21	values	value	NOUN
iajs-3076	242	22	of	of	ADP
iajs-3076	242	23	𝑛	𝑛	DET
iajs-3076	242	24	increase	increase	NOUN
iajs-3076	242	25	,	,	PUNCT
iajs-3076	242	26	the	the	DET
iajs-3076	242	27	value	value	NOUN
iajs-3076	242	28	of	of	ADP
iajs-3076	242	29	the	the	DET
iajs-3076	242	30	absolute	absolute	ADJ
iajs-3076	242	31	error	error	NOUN
iajs-3076	242	32	decreases	decrease	NOUN
iajs-3076	242	33	,	,	PUNCT
iajs-3076	242	34	which	which	PRON
iajs-3076	242	35	shows	show	VERB
iajs-3076	242	36	the	the	DET
iajs-3076	242	37	accuracy	accuracy	NOUN
iajs-3076	242	38	and	and	CCONJ
iajs-3076	242	39	success	success	NOUN
iajs-3076	242	40	of	of	ADP
iajs-3076	242	41	the	the	DET
iajs-3076	242	42	proposed	propose	VERB
iajs-3076	242	43	methods	method	NOUN
iajs-3076	242	44	.	.	PUNCT
iajs-3076	243	1	tables	table	NOUN
iajs-3076	243	2	3	3	NUM
iajs-3076	243	3	and	and	CCONJ
iajs-3076	243	4	6	6	NUM
iajs-3076	243	5	show	show	VERB
iajs-3076	243	6	that	that	SCONJ
iajs-3076	243	7	the	the	DET
iajs-3076	243	8	method	method	NOUN
iajs-3076	243	9	(	(	PUNCT
iajs-3076	243	10	lom	lom	NOUN
iajs-3076	243	11	)	)	PUNCT
iajs-3076	243	12	is	be	AUX
iajs-3076	243	13	the	the	DET
iajs-3076	243	14	best	good	ADJ
iajs-3076	243	15	solution	solution	NOUN
iajs-3076	243	16	for	for	ADP
iajs-3076	243	17	the	the	DET
iajs-3076	243	18	two	two	NUM
iajs-3076	243	19	examples	example	NOUN
iajs-3076	243	20	.	.	PUNCT
iajs-3076	244	1	mathematica	mathematica	PROPN
iajs-3076	244	2	®	®	PROPN
iajs-3076	244	3	12	12	NUM
iajs-3076	244	4	program	program	NOUN
iajs-3076	244	5	was	be	AUX
iajs-3076	244	6	used	use	VERB
iajs-3076	244	7	to	to	PART
iajs-3076	244	8	find	find	VERB
iajs-3076	244	9	the	the	DET
iajs-3076	244	10	numerical	numerical	ADJ
iajs-3076	244	11	results	result	NOUN
iajs-3076	244	12	.	.	PUNCT
iajs-3076	245	1	ihjpas	ihjpas	PROPN
iajs-3076	245	2	.	.	PUNCT
iajs-3076	246	1	36	36	NUM
iajs-3076	246	2	(	(	PUNCT
iajs-3076	246	3	3	3	NUM
iajs-3076	246	4	)	)	PUNCT
iajs-3076	246	5	2023	2023	NUM
iajs-3076	246	6	395	395	NUM
iajs-3076	246	7	references	reference	NOUN
iajs-3076	246	8	1	1	NUM
iajs-3076	246	9	.	.	PUNCT
iajs-3076	247	1	jamil	jamil	PROPN
iajs-3076	247	2	.	.	PUNCT
iajs-3076	247	3	b.	b.	PROPN
iajs-3076	247	4	;	;	PUNCT
iajs-3076	248	1	anwar	anwar	PROPN
iajs-3076	248	2	.	.	PUNCT
iajs-3076	249	1	m.s	m.s	PROPN
iajs-3076	249	2	.	.	PROPN
iajs-3076	250	1	;	;	PUNCT
iajs-3076	250	2	rasheed	rasheed	PROPN
iajs-3076	250	3	.	.	PUNCT
iajs-3076	250	4	a.	a.	PROPN
iajs-3076	250	5	;	;	PUNCT
iajs-3076	250	6	irfan	irfan	PROPN
iajs-3076	250	7	.	.	PUNCT
iajs-3076	250	8	m.	m.	PROPN
iajs-3076	250	9	mhd	mhd	PROPN
iajs-3076	250	10	maxwell	maxwell	PROPN
iajs-3076	250	11	flow	flow	NOUN
iajs-3076	250	12	modeled	model	VERB
iajs-3076	250	13	by	by	ADP
iajs-3076	250	14	fractional	fractional	ADJ
iajs-3076	250	15	derivatives	derivative	NOUN
iajs-3076	250	16	with	with	ADP
iajs-3076	250	17	chemical	chemical	ADJ
iajs-3076	250	18	reaction	reaction	NOUN
iajs-3076	250	19	and	and	CCONJ
iajs-3076	250	20	thermal	thermal	ADJ
iajs-3076	250	21	radiation	radiation	NOUN
iajs-3076	250	22	.	.	PUNCT
iajs-3076	251	1	chinese	chinese	ADJ
iajs-3076	251	2	journal	journal	PROPN
iajs-3076	251	3	of	of	ADP
iajs-3076	251	4	physics	physics	PROPN
iajs-3076	251	5	.	.	PUNCT
iajs-3076	252	1	2020	2020	NUM
iajs-3076	252	2	,	,	PUNCT
iajs-3076	252	3	67	67	NUM
iajs-3076	252	4	,	,	PUNCT
iajs-3076	252	5	512	512	NUM
iajs-3076	252	6	-	-	SYM
iajs-3076	252	7	533	533	NUM
iajs-3076	252	8	,	,	PUNCT
iajs-3076	252	9	doi	doi	NOUN
iajs-3076	252	10	:	:	PUNCT
iajs-3076	252	11	org/10.1016	org/10.1016	PROPN
iajs-3076	252	12	/	/	SYM
iajs-3076	252	13	j.cjph.2020.08.012	j.cjph.2020.08.012	PROPN
iajs-3076	252	14	.	.	PUNCT
iajs-3076	253	1	2	2	X
iajs-3076	253	2	.	.	X
iajs-3076	253	3	alzubaidi	alzubaidi	NOUN
iajs-3076	253	4	.	.	PUNCT
iajs-3076	254	1	w.k	w.k	PROPN
iajs-3076	254	2	.	.	PROPN
iajs-3076	254	3	;	;	PUNCT
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iajs-3076	302	4	)	)	PUNCT
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iajs-3076	302	7	-	-	SYM
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iajs-3076	303	4	.	.	PUNCT
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iajs-3076	308	13	.	.	PUNCT
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iajs-3076	309	2	.	.	PUNCT
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iajs-3076	310	2	,	,	PUNCT
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iajs-3076	310	7	,	,	PUNCT
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iajs-3076	310	9	:	:	PUNCT
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iajs-3076	310	11	.	.	PUNCT
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iajs-3076	311	2	.	.	PUNCT
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iajs-3076	311	4	.	.	PUNCT
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iajs-3076	312	4	.	.	PUNCT
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iajs-3076	315	4	)	)	PUNCT
iajs-3076	315	5	,	,	PUNCT
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iajs-3076	315	7	-	-	SYM
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iajs-3076	315	9	,	,	PUNCT
iajs-3076	315	10	doi	doi	NOUN
iajs-3076	315	11	:	:	PUNCT
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iajs-3076	317	2	.	.	PUNCT
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iajs-3076	322	7	-	-	SYM
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iajs-3076	322	9	,	,	PUNCT
iajs-3076	322	10	doi	doi	NOUN
iajs-3076	322	11	:	:	PUNCT
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iajs-3076	322	13	.	.	PUNCT
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iajs-3076	323	2	.	.	X
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iajs-3076	335	7	-	-	SYM
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iajs-3076	335	9	,	,	PUNCT
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iajs-3076	341	2	.	.	PUNCT
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iajs-3076	350	13	differential	differential	NOUN
iajs-3076	350	14	equation	equation	NOUN
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iajs-3076	351	11	doi	doi	NOUN
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iajs-3076	355	4	,	,	PUNCT
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iajs-3076	355	6	:	:	PUNCT
iajs-3076	355	7	https://doi.org/10.1016/j.camwa.2009.08.039	https://doi.org/10.1016/j.camwa.2009.08.039	NOUN
iajs-3076	355	8	.	.	PUNCT
iajs-3076	356	1	21	21	NUM
iajs-3076	356	2	.	.	PUNCT
iajs-3076	357	1	aiello	aiello	PROPN
iajs-3076	357	2	.	.	PUNCT
iajs-3076	357	3	w.	w.	PROPN
iajs-3076	357	4	g.	g.	PROPN
iajs-3076	357	5	;	;	PUNCT
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iajs-3076	357	7	.	.	PUNCT
iajs-3076	358	1	h.	h.	PROPN
iajs-3076	358	2	i.	i.	PROPN
iajs-3076	358	3	;	;	PUNCT
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iajs-3076	358	5	.	.	PUNCT
iajs-3076	359	1	j.	j.	PROPN
iajs-3076	359	2	analysis	analysis	NOUN
iajs-3076	359	3	of	of	ADP
iajs-3076	359	4	a	a	DET
iajs-3076	359	5	model	model	NOUN
iajs-3076	359	6	representing	represent	VERB
iajs-3076	359	7	stage	stage	NOUN
iajs-3076	359	8	-	-	PUNCT
iajs-3076	359	9	structured	structure	VERB
iajs-3076	359	10	population	population	NOUN
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iajs-3076	359	13	state	state	NOUN
iajs-3076	359	14	-	-	PUNCT
iajs-3076	359	15	dependent	dependent	ADJ
iajs-3076	359	16	time	time	NOUN
iajs-3076	359	17	delay	delay	NOUN
iajs-3076	359	18	.	.	PUNCT
iajs-3076	360	1	siam	siam	PROPN
iajs-3076	360	2	journal	journal	PROPN
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iajs-3076	360	6	.	.	PUNCT
iajs-3076	361	1	1992	1992	NUM
iajs-3076	361	2	,	,	PUNCT
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iajs-3076	361	4	)	)	PUNCT
iajs-3076	361	5	,	,	PUNCT
iajs-3076	361	6	855	855	NUM
iajs-3076	361	7	-	-	SYM
iajs-3076	361	8	869	869	NUM
iajs-3076	361	9	,	,	PUNCT
iajs-3076	361	10	doi	doi	NOUN
iajs-3076	361	11	:	:	PUNCT
iajs-3076	361	12	https://doi.org/10.1137/0152048	https://doi.org/10.1137/0152048	PROPN
iajs-3076	361	13	22	22	NUM
iajs-3076	361	14	.	.	PUNCT
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iajs-3076	362	2	.	.	PUNCT
iajs-3076	363	1	k.	k.	PROPN
iajs-3076	363	2	;	;	PUNCT
iajs-3076	363	3	ordokhani	ordokhani	PROPN
iajs-3076	363	4	.	.	PUNCT
iajs-3076	364	1	y.	y.	NOUN
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iajs-3076	364	4	pantograph	pantograph	NOUN
iajs-3076	364	5	delay	delay	NOUN
iajs-3076	364	6	differential	differential	ADJ
iajs-3076	364	7	equations	equation	NOUN
iajs-3076	364	8	via	via	ADP
iajs-3076	364	9	fractional	fractional	ADJ
iajs-3076	364	10	-	-	PUNCT
iajs-3076	364	11	order	order	NOUN
iajs-3076	364	12	boubaker	boubaker	NOUN
iajs-3076	364	13	polynomials	polynomial	NOUN
iajs-3076	364	14	.	.	PUNCT
iajs-3076	365	1	engineering	engineer	VERB
iajs-3076	365	2	with	with	ADP
iajs-3076	365	3	computers	computer	NOUN
iajs-3076	365	4	.	.	PUNCT
iajs-3076	366	1	2019	2019	NUM
iajs-3076	366	2	,	,	PUNCT
iajs-3076	366	3	35(4	35(4	NUM
iajs-3076	366	4	)	)	PUNCT
iajs-3076	366	5	,	,	PUNCT
iajs-3076	366	6	14311441	14311441	NUM
iajs-3076	366	7	.	.	PUNCT
iajs-3076	367	1	doi	doi	NOUN
iajs-3076	367	2	:	:	PUNCT
iajs-3076	367	3	https://doi.org/10.1007	https://doi.org/10.1007	ADJ
iajs-3076	367	4	/	/	SYM
iajs-3076	367	5	s00366	s00366	ADJ
iajs-3076	367	6	-	-	PUNCT
iajs-3076	367	7	018	018	NUM
iajs-3076	367	8	-	-	PUNCT
iajs-3076	367	9	0673	0673	NUM
iajs-3076	367	10	-	-	PUNCT
iajs-3076	367	11	8	8	NUM
iajs-3076	367	12	.	.	NUM
iajs-3076	367	13	23	23	NUM
iajs-3076	367	14	.	.	PUNCT
iajs-3076	368	1	yuttanan	yuttanan	PROPN
iajs-3076	368	2	.	.	PUNCT
iajs-3076	369	1	b.	b.	PROPN
iajs-3076	369	2	;	;	PUNCT
iajs-3076	370	1	razzaghi	razzaghi	PROPN
iajs-3076	370	2	.	.	PUNCT
iajs-3076	371	1	m.	m.	NOUN
iajs-3076	371	2	;	;	PUNCT
iajs-3076	371	3	vo	vo	X
iajs-3076	371	4	.	.	PUNCT
iajs-3076	372	1	t.	t.	PROPN
iajs-3076	372	2	n.	n.	PROPN
iajs-3076	372	3	a	a	DET
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iajs-3076	372	5	generalized	generalize	VERB
iajs-3076	372	6	taylor	taylor	PROPN
iajs-3076	372	7	wavelet	wavelet	NOUN
iajs-3076	372	8	method	method	NOUN
iajs-3076	372	9	for	for	ADP
iajs-3076	372	10	nonlinear	nonlinear	ADJ
iajs-3076	372	11	fractional	fractional	ADJ
iajs-3076	372	12	delay	delay	NOUN
iajs-3076	372	13	and	and	CCONJ
iajs-3076	372	14	nonlinear	nonlinear	ADJ
iajs-3076	372	15	fractional	fractional	ADJ
iajs-3076	372	16	pantograph	pantograph	NOUN
iajs-3076	372	17	differential	differential	PROPN
iajs-3076	372	18	equations	equation	NOUN
iajs-3076	372	19	.	.	PUNCT
iajs-3076	373	1	mathematical	mathematical	ADJ
iajs-3076	373	2	methods	method	NOUN
iajs-3076	373	3	in	in	ADP
iajs-3076	373	4	the	the	DET
iajs-3076	373	5	applied	applied	ADJ
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iajs-3076	373	7	,	,	PUNCT
iajs-3076	373	8	44(5	44(5	NOUN
iajs-3076	373	9	)	)	PUNCT
iajs-3076	373	10	,	,	PUNCT
iajs-3076	373	11	4156	4156	NUM
iajs-3076	373	12	-	-	SYM
iajs-3076	373	13	4175	4175	NUM
iajs-3076	373	14	,	,	PUNCT
iajs-3076	373	15	doi	doi	NOUN
iajs-3076	373	16	:	:	PUNCT
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iajs-3076	373	18	.	.	PROPN
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iajs-3076	373	20	.	.	PUNCT
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iajs-3076	374	2	.	.	PUNCT
iajs-3076	375	1	z.	z.	PROPN
iajs-3076	375	2	;	;	PUNCT
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iajs-3076	375	4	.	.	PUNCT
iajs-3076	376	1	m.	m.	PROPN
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iajs-3076	376	3	;	;	PUNCT
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iajs-3076	376	5	.	.	PUNCT
iajs-3076	377	1	m.	m.	PROPN
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iajs-3076	377	6	for	for	ADP
iajs-3076	377	7	the	the	DET
iajs-3076	377	8	generalized	generalized	ADJ
iajs-3076	377	9	variable	variable	ADJ
iajs-3076	377	10	-	-	PUNCT
iajs-3076	377	11	order	order	NOUN
iajs-3076	377	12	fractional	fractional	ADJ
iajs-3076	377	13	pantograph	pantograph	NOUN
iajs-3076	377	14	equation	equation	NOUN
iajs-3076	377	15	.	.	PUNCT
iajs-3076	378	1	alexandria	alexandria	PROPN
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iajs-3076	378	3	journal	journal	PROPN
iajs-3076	378	4	.	.	PUNCT
iajs-3076	379	1	2020	2020	NUM
iajs-3076	379	2	,	,	PUNCT
iajs-3076	379	3	59(4	59(4	NUM
iajs-3076	379	4	)	)	PUNCT
iajs-3076	379	5	,	,	PUNCT
iajs-3076	379	6	2347	2347	NUM
iajs-3076	379	7	-	-	SYM
iajs-3076	379	8	2354	2354	NUM
iajs-3076	379	9	.	.	PUNCT
iajs-3076	379	10	,	,	PUNCT
iajs-3076	379	11	doi	doi	NOUN
iajs-3076	379	12	:	:	PUNCT
iajs-3076	379	13	https://doi.org/10.1016/j.aej.2020.02.028	https://doi.org/10.1016/j.aej.2020.02.028	NOUN
iajs-3076	379	14	.	.	PROPN
iajs-3076	380	1	25	25	NUM
iajs-3076	380	2	.	.	X
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iajs-3076	381	2	.	.	PUNCT
iajs-3076	382	1	s.	s.	PROPN
iajs-3076	382	2	;	;	PUNCT
iajs-3076	382	3	ordokhani	ordokhani	NOUN
iajs-3076	382	4	.	.	PUNCT
iajs-3076	383	1	y.	y.	PROPN
iajs-3076	383	2	;	;	PUNCT
iajs-3076	383	3	dehghan	dehghan	PROPN
iajs-3076	383	4	.	.	PUNCT
iajs-3076	384	1	m.	m.	PROPN
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iajs-3076	384	4	of	of	ADP
iajs-3076	384	5	the	the	DET
iajs-3076	384	6	delay	delay	NOUN
iajs-3076	384	7	differential	differential	ADJ
iajs-3076	384	8	equations	equation	NOUN
iajs-3076	384	9	of	of	ADP
iajs-3076	384	10	pantograph	pantograph	NOUN
iajs-3076	384	11	type	type	NOUN
iajs-3076	384	12	via	via	ADP
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iajs-3076	384	14	polynomials	polynomial	NOUN
iajs-3076	384	15	.	.	PUNCT
iajs-3076	385	1	communications	communication	NOUN
iajs-3076	385	2	in	in	ADP
iajs-3076	385	3	nonlinear	nonlinear	ADJ
iajs-3076	385	4	science	science	NOUN
iajs-3076	385	5	and	and	CCONJ
iajs-3076	385	6	numerical	numerical	PROPN
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iajs-3076	385	8	.	.	PUNCT
iajs-3076	386	1	2012	2012	NUM
iajs-3076	386	2	,	,	PUNCT
iajs-3076	386	3	17(12	17(12	NUM
iajs-3076	386	4	)	)	PUNCT
iajs-3076	386	5	,	,	PUNCT
iajs-3076	386	6	4815	4815	NUM
iajs-3076	386	7	-	-	SYM
iajs-3076	386	8	4830	4830	NUM
iajs-3076	386	9	,	,	PUNCT
iajs-3076	386	10	https://doi.org/10.1016/j.cnsns.2012.05.009	https://doi.org/10.1016/j.cnsns.2012.05.009	PROPN
iajs-3076	386	11	26	26	NUM
iajs-3076	386	12	.	.	PUNCT
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iajs-3076	386	14	.	.	PUNCT
iajs-3076	387	1	m.	m.	PROPN
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iajs-3076	387	3	;	;	PUNCT
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iajs-3076	387	5	.	.	PUNCT
iajs-3076	387	6	a.	a.	PROPN
iajs-3076	387	7	;	;	PUNCT
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iajs-3076	387	9	.	.	PUNCT
iajs-3076	388	1	s.	s.	PROPN
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iajs-3076	388	3	fractional	fractional	ADJ
iajs-3076	388	4	pantograph	pantograph	NOUN
iajs-3076	388	5	delay	delay	NOUN
iajs-3076	388	6	equations	equation	NOUN
iajs-3076	388	7	by	by	ADP
iajs-3076	388	8	an	an	DET
iajs-3076	388	9	effective	effective	ADJ
iajs-3076	388	10	computational	computational	ADJ
iajs-3076	388	11	method	method	NOUN
iajs-3076	388	12	.	.	PUNCT
iajs-3076	389	1	mathematics	mathematic	NOUN
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iajs-3076	389	3	computers	computer	NOUN
iajs-3076	389	4	in	in	ADP
iajs-3076	389	5	simulation	simulation	NOUN
iajs-3076	389	6	.	.	PUNCT
iajs-3076	390	1	2020	2020	NUM
iajs-3076	390	2	,	,	PUNCT
iajs-3076	390	3	177	177	NUM
iajs-3076	390	4	,	,	PUNCT
iajs-3076	390	5	295	295	NUM
iajs-3076	390	6	-	-	SYM
iajs-3076	390	7	305	305	NUM
iajs-3076	390	8	,	,	PUNCT
iajs-3076	390	9	doi	doi	NOUN
iajs-3076	390	10	:	:	PUNCT
iajs-3076	390	11	https://doi.org/10.1016/j.matcom.2020.04.026	https://doi.org/10.1016/j.matcom.2020.04.026	PROPN
iajs-3076	390	12	.	.	PUNCT
iajs-3076	391	1	27	27	NUM
iajs-3076	391	2	.	.	PUNCT
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iajs-3076	392	2	.	.	PUNCT
iajs-3076	393	1	w.	w.	PROPN
iajs-3076	393	2	;	;	PUNCT
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iajs-3076	393	4	,	,	PUNCT
iajs-3076	393	5	z.	z.	PROPN
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iajs-3076	393	7	a	a	DET
iajs-3076	393	8	new	new	ADJ
iajs-3076	393	9	design	design	NOUN
iajs-3076	393	10	of	of	ADP
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iajs-3076	393	12	second	second	ADJ
iajs-3076	393	13	-	-	PUNCT
iajs-3076	393	14	order	order	NOUN
iajs-3076	393	15	lane	lane	NOUN
iajs-3076	393	16	–	–	PUNCT
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iajs-3076	393	18	pantograph	pantograph	NOUN
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iajs-3076	393	20	differential	differential	PROPN
iajs-3076	393	21	model	model	NOUN
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iajs-3076	393	25	method	method	NOUN
iajs-3076	393	26	.	.	PUNCT
iajs-3076	394	1	the	the	DET
iajs-3076	394	2	european	european	PROPN
iajs-3076	394	3	physical	physical	PROPN
iajs-3076	394	4	journal	journal	PROPN
iajs-3076	394	5	plus	plus	CCONJ
iajs-3076	394	6	.	.	PUNCT
iajs-3076	394	7	2020	2020	NUM
iajs-3076	394	8	,	,	PUNCT
iajs-3076	394	9	135(5	135(5	NUM
iajs-3076	394	10	)	)	PUNCT
iajs-3076	394	11	,	,	PUNCT
iajs-3076	394	12	1	1	NUM
iajs-3076	394	13	-	-	SYM
iajs-3076	394	14	12	12	NUM
iajs-3076	394	15	,	,	PUNCT
iajs-3076	394	16	doi	doi	NOUN
iajs-3076	394	17	:	:	PUNCT
iajs-3076	394	18	https://doi.org/10.1140/epjp/s13360-020-00449-x	https://doi.org/10.1140/epjp/s13360-020-00449-x	PROPN
iajs-3076	394	19	28	28	NUM
iajs-3076	394	20	.	.	PUNCT
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iajs-3076	394	22	.	.	PUNCT
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iajs-3076	395	2	;	;	PUNCT
iajs-3076	395	3	qasemi	qasemi	PROPN
iajs-3076	395	4	.	.	PUNCT
iajs-3076	396	1	s.	s.	PROPN
iajs-3076	396	2	discontinuous	discontinuous	PROPN
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iajs-3076	396	4	-	-	PUNCT
iajs-3076	396	5	galerkin	galerkin	PROPN
iajs-3076	396	6	and	and	CCONJ
iajs-3076	396	7	bernstein	bernstein	PROPN
iajs-3076	396	8	-	-	PUNCT
iajs-3076	396	9	legendre	legendre	PROPN
iajs-3076	396	10	polynomials	polynomial	NOUN
iajs-3076	396	11	method	method	NOUN
iajs-3076	396	12	for	for	ADP
iajs-3076	396	13	solving	solve	VERB
iajs-3076	396	14	fractional	fractional	ADJ
iajs-3076	396	15	damped	damp	VERB
iajs-3076	396	16	heat	heat	NOUN
iajs-3076	396	17	-	-	PUNCT
iajs-3076	396	18	and	and	CCONJ
iajs-3076	396	19	wave	wave	NOUN
iajs-3076	396	20	-	-	PUNCT
iajs-3076	396	21	like	like	ADJ
iajs-3076	396	22	equations	equation	NOUN
iajs-3076	396	23	.	.	PUNCT
iajs-3076	397	1	journal	journal	NOUN
iajs-3076	397	2	of	of	ADP
iajs-3076	397	3	computational	computational	ADJ
iajs-3076	397	4	and	and	CCONJ
iajs-3076	397	5	theoretical	theoretical	ADJ
iajs-3076	397	6	transport	transport	NOUN
iajs-3076	397	7	.	.	PUNCT
iajs-3076	398	1	2015	2015	NUM
iajs-3076	398	2	,	,	PUNCT
iajs-3076	398	3	44(1	44(1	PROPN
iajs-3076	398	4	)	)	PUNCT
iajs-3076	398	5	,	,	PUNCT
iajs-3076	398	6	1	1	NUM
iajs-3076	398	7	-	-	SYM
iajs-3076	398	8	23	23	NUM
iajs-3076	398	9	,	,	PUNCT
iajs-3076	398	10	doi	doi	NOUN
iajs-3076	398	11	:	:	PUNCT
iajs-3076	398	12	https://doi.org/10.1080/23324309.2014.955207	https://doi.org/10.1080/23324309.2014.955207	NOUN
iajs-3076	398	13	.	.	PUNCT
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iajs-3076	399	2	.	.	PUNCT
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iajs-3076	399	4	.	.	PUNCT
iajs-3076	400	1	m.	m.	PROPN
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iajs-3076	400	5	.	.	PUNCT
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iajs-3076	401	4	for	for	ADP
iajs-3076	401	5	solving	solve	VERB
iajs-3076	401	6	fractional	fractional	ADJ
iajs-3076	401	7	differential	differential	ADJ
iajs-3076	401	8	equations	equation	NOUN
iajs-3076	401	9	using	use	VERB
iajs-3076	401	10	shifted	shift	VERB
iajs-3076	401	11	chebyshev	chebyshev	PROPN
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iajs-3076	401	13	.	.	PUNCT
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iajs-3076	402	6	.	.	PUNCT
iajs-3076	403	1	2017	2017	NUM
iajs-3076	403	2	,	,	PUNCT
iajs-3076	403	3	3(2	3(2	NUM
iajs-3076	403	4	)	)	PUNCT
iajs-3076	403	5	,	,	PUNCT
iajs-3076	403	6	101	101	NUM
iajs-3076	403	7	-	-	SYM
iajs-3076	403	8	110	110	NUM
iajs-3076	403	9	.	.	PUNCT
iajs-3076	404	1	30	30	NUM
iajs-3076	404	2	.	.	PUNCT
iajs-3076	405	1	doha	doha	PROPN
iajs-3076	405	2	.	.	PUNCT
iajs-3076	406	1	e.	e.	PROPN
iajs-3076	406	2	h.	h.	PROPN
iajs-3076	406	3	;	;	PUNCT
iajs-3076	406	4	bhrawy	bhrawy	PROPN
iajs-3076	406	5	.	.	PUNCT
iajs-3076	407	1	a.	a.	PROPN
iajs-3076	407	2	h.	h.	PROPN
iajs-3076	407	3	;	;	PUNCT
iajs-3076	407	4	ezz	ezz	PROPN
iajs-3076	407	5	-	-	PUNCT
iajs-3076	407	6	eldien	eldien	NOUN
iajs-3076	407	7	.	.	PUNCT
iajs-3076	408	1	s.	s.	PROPN
iajs-3076	408	2	s.	s.	PROPN
iajs-3076	408	3	a	a	DET
iajs-3076	408	4	new	new	ADJ
iajs-3076	408	5	jacobi	jacobi	PROPN
iajs-3076	408	6	operational	operational	ADJ
iajs-3076	408	7	matrix	matrix	NOUN
iajs-3076	408	8	:	:	PUNCT
iajs-3076	408	9	an	an	DET
iajs-3076	408	10	application	application	NOUN
iajs-3076	408	11	for	for	ADP
iajs-3076	408	12	solving	solve	VERB
iajs-3076	408	13	fractional	fractional	ADJ
iajs-3076	408	14	differential	differential	ADJ
iajs-3076	408	15	equations	equation	NOUN
iajs-3076	408	16	.	.	PUNCT
iajs-3076	409	1	applied	apply	VERB
iajs-3076	409	2	mathematical	mathematical	ADJ
iajs-3076	409	3	modelling	modelling	NOUN
iajs-3076	409	4	.	.	PUNCT
iajs-3076	410	1	2012	2012	NUM
iajs-3076	410	2	,	,	PUNCT
iajs-3076	410	3	36(10	36(10	NUM
iajs-3076	410	4	)	)	PUNCT
iajs-3076	410	5	,	,	PUNCT
iajs-3076	410	6	4931	4931	NUM
iajs-3076	410	7	-	-	SYM
iajs-3076	410	8	4943	4943	NUM
iajs-3076	410	9	,	,	PUNCT
iajs-3076	410	10	doi	doi	NOUN
iajs-3076	410	11	:	:	PUNCT
iajs-3076	410	12	https://doi.org/10.1016/j.apm.2011.12.031	https://doi.org/10.1016/j.apm.2011.12.031	NOUN
iajs-3076	410	13	.	.	PUNCT
iajs-3076	411	1	https://doi.org/10.1186/s42787-019-0039-4	https://doi.org/10.1186/s42787-019-0039-4	NUM
iajs-3076	411	2	about	about	ADP
iajs-3076	411	3	:	:	PUNCT
iajs-3076	411	4	blank	blank	ADJ
iajs-3076	411	5	about	about	ADP
iajs-3076	411	6	:	:	PUNCT
iajs-3076	411	7	blank	blank	ADJ
iajs-3076	411	8	https://doi.org/10.1088/0031-8949/78/06/065004	https://doi.org/10.1088/0031-8949/78/06/065004	PROPN
iajs-3076	411	9	https://doi.org/10.1016/j.camwa.2009.08.039	https://doi.org/10.1016/j.camwa.2009.08.039	PROPN
iajs-3076	411	10	https://doi.org/10.1137/0152048	https://doi.org/10.1137/0152048	ADV
iajs-3076	411	11	https://doi.org/10.1007/s00366-018-0673-8	https://doi.org/10.1007/s00366-018-0673-8	NUM
iajs-3076	411	12	https://doi.org/10.1002/mma.7020	https://doi.org/10.1002/mma.7020	DET
iajs-3076	411	13	https://doi.org/10.1016/j.aej.2020.02.028	https://doi.org/10.1016/j.aej.2020.02.028	NOUN
iajs-3076	411	14	https://doi.org/10.1016/j.cnsns.2012.05.009	https://doi.org/10.1016/j.cnsns.2012.05.009	X
iajs-3076	411	15	https://doi.org/10.1016/j.matcom.2020.04.026	https://doi.org/10.1016/j.matcom.2020.04.026	PROPN
iajs-3076	411	16	https://doi.org/10.1140/epjp/s13360-020-00449-x	https://doi.org/10.1140/epjp/s13360-020-00449-x	PROPN
iajs-3076	411	17	https://doi.org/10.1080/23324309.2014.955207	https://doi.org/10.1080/23324309.2014.955207	PROPN
iajs-3076	411	18	https://doi.org/10.1016/j.apm.2011.12.031	https://doi.org/10.1016/j.apm.2011.12.031	X
iajs-3076	411	19	.	.	PUNCT
iajs-3076	412	1	ihjpas	ihjpas	PROPN
iajs-3076	412	2	.	.	PUNCT
iajs-3076	413	1	36	36	NUM
iajs-3076	413	2	(	(	PUNCT
iajs-3076	413	3	3	3	NUM
iajs-3076	413	4	)	)	PUNCT
iajs-3076	413	5	2023	2023	NUM
iajs-3076	413	6	397	397	NUM
iajs-3076	413	7	31	31	NUM
iajs-3076	413	8	.	.	PUNCT
iajs-3076	413	9	mohammadi	mohammadi	NOUN
iajs-3076	413	10	.	.	PUNCT
iajs-3076	414	1	f.	f.	PROPN
iajs-3076	414	2	;	;	PUNCT
iajs-3076	414	3	hosseini	hosseini	PROPN
iajs-3076	414	4	.	.	PROPN
iajs-3076	414	5	m.	m.	PROPN
iajs-3076	414	6	m.	m.	PROPN
iajs-3076	414	7	a	a	DET
iajs-3076	414	8	new	new	ADJ
iajs-3076	414	9	legendre	legendre	PROPN
iajs-3076	414	10	wavelet	wavelet	PROPN
iajs-3076	414	11	operational	operational	ADJ
iajs-3076	414	12	matrix	matrix	NOUN
iajs-3076	414	13	of	of	ADP
iajs-3076	414	14	derivative	derivative	NOUN
iajs-3076	414	15	and	and	CCONJ
iajs-3076	414	16	its	its	PRON
iajs-3076	414	17	applications	application	NOUN
iajs-3076	414	18	in	in	ADP
iajs-3076	414	19	solving	solve	VERB
iajs-3076	414	20	the	the	DET
iajs-3076	414	21	singular	singular	ADJ
iajs-3076	414	22	ordinary	ordinary	ADJ
iajs-3076	414	23	differential	differential	ADJ
iajs-3076	414	24	equations	equation	NOUN
iajs-3076	414	25	.	.	PUNCT
iajs-3076	415	1	journal	journal	NOUN
iajs-3076	415	2	of	of	ADP
iajs-3076	415	3	the	the	DET
iajs-3076	415	4	franklin	franklin	PROPN
iajs-3076	415	5	institute	institute	PROPN
iajs-3076	415	6	.	.	PUNCT
iajs-3076	416	1	2011	2011	NUM
iajs-3076	416	2	,	,	PUNCT
iajs-3076	416	3	348(8	348(8	NUM
iajs-3076	416	4	)	)	PUNCT
iajs-3076	416	5	,	,	PUNCT
iajs-3076	416	6	1787	1787	NUM
iajs-3076	416	7	-	-	SYM
iajs-3076	416	8	1796	1796	NUM
iajs-3076	416	9	.	.	PUNCT
iajs-3076	416	10	,	,	PUNCT
iajs-3076	416	11	doi	doi	PROPN
iajs-3076	416	12	:	:	PUNCT
iajs-3076	416	13	https://doi.org/10.1016/j.jfranklin.2011.04.017	https://doi.org/10.1016/j.jfranklin.2011.04.017	PROPN
iajs-3076	416	14	32	32	NUM
iajs-3076	416	15	.	.	PUNCT
iajs-3076	417	1	ibraheem	ibraheem	PROPN
iajs-3076	417	2	.	.	PUNCT
iajs-3076	418	1	g.h	g.h	PROPN
iajs-3076	418	2	.	.	PROPN
iajs-3076	418	3	;	;	PUNCT
iajs-3076	418	4	al	al	PROPN
iajs-3076	418	5	-	-	PUNCT
iajs-3076	418	6	jawary	jawary	PROPN
iajs-3076	418	7	.	.	PUNCT
iajs-3076	419	1	m.a	m.a	PROPN
iajs-3076	419	2	.	.	PUNCT
iajs-3076	420	1	the	the	DET
iajs-3076	420	2	operational	operational	ADJ
iajs-3076	420	3	matrix	matrix	NOUN
iajs-3076	420	4	of	of	ADP
iajs-3076	420	5	legendre	legendre	PROPN
iajs-3076	420	6	polynomials	polynomial	NOUN
iajs-3076	420	7	for	for	ADP
iajs-3076	420	8	solving	solve	VERB
iajs-3076	420	9	nonlinear	nonlinear	ADJ
iajs-3076	420	10	thin	thin	ADJ
iajs-3076	420	11	film	film	NOUN
iajs-3076	420	12	flow	flow	NOUN
iajs-3076	420	13	problems	problem	NOUN
iajs-3076	420	14	.	.	PUNCT
iajs-3076	421	1	alexandria	alexandria	PROPN
iajs-3076	421	2	engineering	engineering	PROPN
iajs-3076	421	3	journal	journal	PROPN
iajs-3076	421	4	.	.	PUNCT
iajs-3076	422	1	2020	2020	NUM
iajs-3076	422	2	,	,	PUNCT
iajs-3076	422	3	59,5	59,5	NUM
iajs-3076	422	4	,	,	PUNCT
iajs-3076	422	5	4027	4027	NUM
iajs-3076	422	6	-	-	SYM
iajs-3076	422	7	4033	4033	NUM
iajs-3076	422	8	,	,	PUNCT
iajs-3076	422	9	doi	doi	NOUN
iajs-3076	422	10	:	:	PUNCT
iajs-3076	422	11	org/10.1016	org/10.1016	PROPN
iajs-3076	422	12	/	/	SYM
iajs-3076	422	13	j.aej.2020.07.008	j.aej.2020.07.008	NOUN
iajs-3076	422	14	.	.	PUNCT
iajs-3076	423	1	33	33	NUM
iajs-3076	423	2	.	.	X
iajs-3076	423	3	alshbool	alshbool	NOUN
iajs-3076	423	4	.	.	PUNCT
iajs-3076	424	1	m.	m.	PROPN
iajs-3076	424	2	h.	h.	PROPN
iajs-3076	424	3	t.	t.	PROPN
iajs-3076	424	4	;	;	PUNCT
iajs-3076	424	5	bataineh	bataineh	PROPN
iajs-3076	424	6	.	.	PUNCT
iajs-3076	425	1	a.	a.	PROPN
iajs-3076	425	2	s.	s.	PROPN
iajs-3076	425	3	;	;	PUNCT
iajs-3076	425	4	hashim	hashim	PROPN
iajs-3076	425	5	.	.	PUNCT
iajs-3076	426	1	i.	i.	PROPN
iajs-3076	426	2	;	;	PUNCT
iajs-3076	426	3	isik	isik	NOUN
iajs-3076	426	4	.	.	PUNCT
iajs-3076	427	1	o.	o.	PROPN
iajs-3076	427	2	r.	r.	PROPN
iajs-3076	427	3	solution	solution	NOUN
iajs-3076	427	4	of	of	ADP
iajs-3076	427	5	fractional	fractional	ADJ
iajs-3076	427	6	-	-	PUNCT
iajs-3076	427	7	order	order	NOUN
iajs-3076	427	8	differential	differential	ADJ
iajs-3076	427	9	equations	equation	NOUN
iajs-3076	427	10	based	base	VERB
iajs-3076	427	11	on	on	ADP
iajs-3076	427	12	the	the	DET
iajs-3076	427	13	operational	operational	ADJ
iajs-3076	427	14	matrices	matrix	NOUN
iajs-3076	427	15	of	of	ADP
iajs-3076	427	16	new	new	ADJ
iajs-3076	427	17	fractional	fractional	PROPN
iajs-3076	427	18	bernstein	bernstein	PROPN
iajs-3076	427	19	functions	function	NOUN
iajs-3076	427	20	.	.	PUNCT
iajs-3076	428	1	journal	journal	PROPN
iajs-3076	428	2	of	of	ADP
iajs-3076	428	3	king	king	PROPN
iajs-3076	428	4	saud	saud	PROPN
iajs-3076	428	5	university	university	PROPN
iajs-3076	428	6	-	-	PUNCT
iajs-3076	428	7	science	science	NOUN
iajs-3076	428	8	.	.	PUNCT
iajs-3076	429	1	2017	2017	NUM
iajs-3076	429	2	,	,	PUNCT
iajs-3076	429	3	29(1	29(1	NUM
iajs-3076	429	4	)	)	PUNCT
iajs-3076	429	5	,	,	PUNCT
iajs-3076	429	6	1	1	NUM
iajs-3076	429	7	-	-	SYM
iajs-3076	429	8	18	18	NUM
iajs-3076	429	9	,	,	PUNCT
iajs-3076	429	10	doi	doi	NOUN
iajs-3076	429	11	:	:	PUNCT
iajs-3076	429	12	https://doi.org/10.1016/j.jksus.2015.11.004	https://doi.org/10.1016/j.jksus.2015.11.004	X
iajs-3076	429	13	.	.	PUNCT
iajs-3076	430	1	34	34	NUM
iajs-3076	430	2	.	.	PUNCT
iajs-3076	431	1	al	al	PROPN
iajs-3076	431	2	-	-	PUNCT
iajs-3076	431	3	jawary	jawary	PROPN
iajs-3076	431	4	.	.	PUNCT
iajs-3076	432	1	m.a	m.a	PROPN
iajs-3076	432	2	.	.	PROPN
iajs-3076	432	3	;	;	PUNCT
iajs-3076	432	4	ibraheem	ibraheem	ADJ
iajs-3076	432	5	.	.	PUNCT
iajs-3076	433	1	g.h	g.h	PROPN
iajs-3076	433	2	.	.	PROPN
iajs-3076	433	3	tow	tow	VERB
iajs-3076	433	4	meshless	meshless	ADJ
iajs-3076	433	5	methods	method	NOUN
iajs-3076	433	6	for	for	ADP
iajs-3076	433	7	solving	solve	VERB
iajs-3076	433	8	nonlinear	nonlinear	ADJ
iajs-3076	433	9	ordinary	ordinary	ADJ
iajs-3076	433	10	differential	differential	ADJ
iajs-3076	433	11	equations	equation	NOUN
iajs-3076	433	12	in	in	ADP
iajs-3076	433	13	engineering	engineering	NOUN
iajs-3076	433	14	and	and	CCONJ
iajs-3076	433	15	applied	apply	VERB
iajs-3076	433	16	sciences	science	NOUN
iajs-3076	433	17	.	.	PUNCT
iajs-3076	434	1	nonlinear	nonlinear	PROPN
iajs-3076	434	2	eng	eng	PROPN
iajs-3076	434	3	.	.	PUNCT
iajs-3076	435	1	j.	j.	PROPN
iajs-3076	435	2	2020	2020	PROPN
iajs-3076	435	3	,	,	PUNCT
iajs-3076	435	4	9,1	9,1	NUM
iajs-3076	435	5	,	,	PUNCT
iajs-3076	435	6	244255	244255	NUM
iajs-3076	435	7	,	,	PUNCT
iajs-3076	435	8	doi	doi	NOUN
iajs-3076	435	9	:	:	PUNCT
iajs-3076	435	10	org/10.1515	org/10.1515	PROPN
iajs-3076	435	11	/	/	SYM
iajs-3076	435	12	nleng-2020	nleng-2020	NOUN
iajs-3076	435	13	-	-	PUNCT
iajs-3076	435	14	0012	0012	NUM
iajs-3076	435	15	.	.	PUNCT
iajs-3076	436	1	35	35	NUM
iajs-3076	436	2	.	.	PUNCT
iajs-3076	436	3	saadatmandi	saadatmandi	PROPN
iajs-3076	436	4	.	.	PUNCT
iajs-3076	437	1	a.	a.	PROPN
iajs-3076	437	2	;	;	PUNCT
iajs-3076	437	3	bernstein	bernstein	PROPN
iajs-3076	437	4	operational	operational	PROPN
iajs-3076	437	5	matrix	matrix	NOUN
iajs-3076	437	6	of	of	ADP
iajs-3076	437	7	fractional	fractional	ADJ
iajs-3076	437	8	derivatives	derivative	NOUN
iajs-3076	437	9	and	and	CCONJ
iajs-3076	437	10	its	its	PRON
iajs-3076	437	11	applications	application	NOUN
iajs-3076	437	12	.	.	PUNCT
iajs-3076	438	1	applied	apply	VERB
iajs-3076	438	2	mathematical	mathematical	ADJ
iajs-3076	438	3	modelling	modelling	NOUN
iajs-3076	438	4	.	.	PUNCT
iajs-3076	439	1	2014	2014	NUM
iajs-3076	439	2	,	,	PUNCT
iajs-3076	439	3	38(4	38(4	NUM
iajs-3076	439	4	)	)	PUNCT
iajs-3076	439	5	,	,	PUNCT
iajs-3076	439	6	1365	1365	NUM
iajs-3076	439	7	-	-	SYM
iajs-3076	439	8	1372	1372	NUM
iajs-3076	439	9	,	,	PUNCT
iajs-3076	439	10	doi	doi	NOUN
iajs-3076	439	11	:	:	PUNCT
iajs-3076	439	12	https://doi.org/10.1016/j.apm.2013.08.007	https://doi.org/10.1016/j.apm.2013.08.007	ADJ
iajs-3076	439	13	.	.	PUNCT
iajs-3076	440	1	36	36	NUM
iajs-3076	440	2	.	.	X
iajs-3076	440	3	saadatmandi	saadatmandi	PROPN
iajs-3076	440	4	.	.	PUNCT
iajs-3076	441	1	a.	a.	NOUN
iajs-3076	441	2	;	;	PUNCT
iajs-3076	442	1	dehghan	dehghan	PROPN
iajs-3076	442	2	.	.	PUNCT
iajs-3076	442	3	m.	m.	PROPN
iajs-3076	442	4	a	a	DET
iajs-3076	442	5	new	new	ADJ
iajs-3076	442	6	operational	operational	ADJ
iajs-3076	442	7	matrix	matrix	NOUN
iajs-3076	442	8	for	for	ADP
iajs-3076	442	9	solving	solve	VERB
iajs-3076	442	10	fractional	fractional	ADJ
iajs-3076	442	11	-	-	PUNCT
iajs-3076	442	12	order	order	NOUN
iajs-3076	442	13	differential	differential	ADJ
iajs-3076	442	14	equations	equation	NOUN
iajs-3076	442	15	.	.	PUNCT
iajs-3076	443	1	computers	computer	NOUN
iajs-3076	443	2	mathematics	mathematic	NOUN
iajs-3076	443	3	with	with	ADP
iajs-3076	443	4	applications	application	NOUN
iajs-3076	443	5	.	.	PUNCT
iajs-3076	444	1	2010	2010	NUM
iajs-3076	444	2	,	,	PUNCT
iajs-3076	444	3	59(3	59(3	NUM
iajs-3076	444	4	)	)	PUNCT
iajs-3076	444	5	,	,	PUNCT
iajs-3076	444	6	1326	1326	NUM
iajs-3076	444	7	-	-	SYM
iajs-3076	444	8	1336	1336	NUM
iajs-3076	444	9	,	,	PUNCT
iajs-3076	444	10	doi	doi	NOUN
iajs-3076	444	11	:	:	PUNCT
iajs-3076	444	12	https://doi.org/10.1016	https://doi.org/10.1016	PROPN
iajs-3076	444	13	/	/	SYM
iajs-3076	444	14	j.camwa.2009.07.006	j.camwa.2009.07.006	NOUN
iajs-3076	444	15	https://doi.org/10.1016/j.jfranklin.2011.04.017	https://doi.org/10.1016/j.jfranklin.2011.04.017	VERB
iajs-3076	444	16	about	about	ADP
iajs-3076	444	17	:	:	PUNCT
iajs-3076	444	18	blank	blank	ADJ
iajs-3076	444	19	https://doi.org/10.1016/j.jksus.2015.11.004	https://doi.org/10.1016/j.jksus.2015.11.004	X
iajs-3076	444	20	https://doi.org/10.1515/nleng-2020-0012	https://doi.org/10.1515/nleng-2020-0012	PROPN
iajs-3076	444	21	https://doi.org/10.1016/j.apm.2013.08.007	https://doi.org/10.1016/j.apm.2013.08.007	ADJ
iajs-3076	444	22	https://doi.org/10.1016/j.camwa.2009.07.006	https://doi.org/10.1016/j.camwa.2009.07.006	NOUN