id	sid	tid	token	lemma	pos
cana-3291	1	1	communications	communication	NOUN
cana-3291	1	2	on	on	ADP
cana-3291	1	3	applied	apply	VERB
cana-3291	1	4	nonlinear	nonlinear	ADJ
cana-3291	1	5	analysis	analysis	NOUN
cana-3291	1	6	issn	issn	NOUN
cana-3291	1	7	:	:	PUNCT
cana-3291	1	8	1074	1074	NUM
cana-3291	1	9	-	-	PUNCT
cana-3291	1	10	133x	133x	NUM
cana-3291	1	11	vol	vol	NOUN
cana-3291	1	12	32	32	NUM
cana-3291	1	13	no	no	NOUN
cana-3291	1	14	.	.	PUNCT
cana-3291	2	1	6s	6s	NUM
cana-3291	2	2	(	(	PUNCT
cana-3291	2	3	2025	2025	NUM
cana-3291	2	4	)	)	PUNCT
cana-3291	3	1	253	253	NUM
cana-3291	3	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-3291	3	3	jacobi	jacobi	PROPN
cana-3291	3	4	matrix	matrix	NOUN
cana-3291	3	5	polynomial	polynomial	ADJ
cana-3291	3	6	and	and	CCONJ
cana-3291	3	7	its	its	PRON
cana-3291	3	8	integral	integral	ADJ
cana-3291	3	9	results	result	NOUN
cana-3291	3	10	v.sri	v.sri	NOUN
cana-3291	3	11	lakshmi1	lakshmi1	NOUN
cana-3291	3	12	,	,	PUNCT
cana-3291	3	13	n.	n.	PROPN
cana-3291	3	14	srimannarayana2	srimannarayana2	PROPN
cana-3291	3	15	*	*	PUNCT
cana-3291	3	16	,	,	PUNCT
cana-3291	3	17	m.v	m.v	PROPN
cana-3291	3	18	.	.	PROPN
cana-3291	3	19	chakradhar	chakradhar	PROPN
cana-3291	3	20	rao3	rao3	PROPN
cana-3291	3	21	,	,	PUNCT
cana-3291	3	22	m.	m.	NOUN
cana-3291	3	23	radha	radha	PROPN
cana-3291	3	24	madhavi4	madhavi4	PROPN
cana-3291	3	25	,	,	PUNCT
cana-3291	3	26	d.k.pavan	d.k.pavan	VERB
cana-3291	3	27	kumar5	kumar5	PROPN
cana-3291	3	28	1research	1research	NUM
cana-3291	3	29	scholar	scholar	NOUN
cana-3291	3	30	,	,	PUNCT
cana-3291	3	31	department	department	NOUN
cana-3291	3	32	of	of	ADP
cana-3291	3	33	engineering	engineering	NOUN
cana-3291	3	34	mathematics	mathematic	NOUN
cana-3291	3	35	,	,	PUNCT
cana-3291	3	36	college	college	NOUN
cana-3291	3	37	of	of	ADP
cana-3291	3	38	engineering	engineering	PROPN
cana-3291	3	39	,	,	PUNCT
cana-3291	3	40	koneru	koneru	PROPN
cana-3291	3	41	lakshmaiah	lakshmaiah	PROPN
cana-3291	3	42	education	education	PROPN
cana-3291	3	43	foundation	foundation	PROPN
cana-3291	3	44	,	,	PUNCT
cana-3291	3	45	vaddeswaram	vaddeswaram	PROPN
cana-3291	3	46	,	,	PUNCT
cana-3291	3	47	guntur	guntur	PROPN
cana-3291	3	48	(	(	PUNCT
cana-3291	3	49	dt	dt	PROPN
cana-3291	3	50	.	.	PUNCT
cana-3291	3	51	,	,	PUNCT
cana-3291	3	52	)	)	PUNCT
cana-3291	3	53	,	,	PUNCT
cana-3291	3	54	a.p	a.p	PROPN
cana-3291	3	55	.	.	PROPN
cana-3291	3	56	,	,	PUNCT
cana-3291	3	57	india	india	PROPN
cana-3291	3	58	.	.	PUNCT
cana-3291	4	1	associate	associate	PROPN
cana-3291	4	2	professor	professor	NOUN
cana-3291	4	3	in	in	ADP
cana-3291	4	4	the	the	DET
cana-3291	4	5	department	department	NOUN
cana-3291	4	6	of	of	ADP
cana-3291	4	7	mathematics	mathematic	NOUN
cana-3291	4	8	,	,	PUNCT
cana-3291	4	9	g.pulla	g.pulla	NOUN
cana-3291	4	10	reddy	reddy	PROPN
cana-3291	4	11	degree	degree	NOUN
cana-3291	4	12	and	and	CCONJ
cana-3291	4	13	p.g	p.g	PROPN
cana-3291	4	14	.	.	PROPN
cana-3291	4	15	college	college	PROPN
cana-3291	4	16	,	,	PUNCT
cana-3291	4	17	mehdipatnam	mehdipatnam	NOUN
cana-3291	4	18	,	,	PUNCT
cana-3291	4	19	hyderabad	hyderabad	PROPN
cana-3291	4	20	,	,	PUNCT
cana-3291	4	21	telangana	telangana	PROPN
cana-3291	4	22	,	,	PUNCT
cana-3291	5	1	india	india	PROPN
cana-3291	5	2	.	.	PUNCT
cana-3291	5	3	email	email	NOUN
cana-3291	5	4	:	:	PUNCT
cana-3291	6	1	kanurisrilakshmi@gmail.com	kanurisrilakshmi@gmail.com	X
cana-3291	6	2	2professor	2professor	NUM
cana-3291	6	3	,	,	PUNCT
cana-3291	6	4	department	department	NOUN
cana-3291	6	5	of	of	ADP
cana-3291	6	6	engineering	engineering	NOUN
cana-3291	6	7	mathematics	mathematic	NOUN
cana-3291	6	8	,	,	PUNCT
cana-3291	6	9	college	college	NOUN
cana-3291	6	10	of	of	ADP
cana-3291	6	11	engineering	engineering	PROPN
cana-3291	6	12	,	,	PUNCT
cana-3291	6	13	koneru	koneru	PROPN
cana-3291	6	14	lakshmaiah	lakshmaiah	PROPN
cana-3291	6	15	education	education	PROPN
cana-3291	6	16	foundation	foundation	PROPN
cana-3291	6	17	,	,	PUNCT
cana-3291	6	18	vaddeswaram	vaddeswaram	PROPN
cana-3291	6	19	,	,	PUNCT
cana-3291	6	20	guntur	guntur	PROPN
cana-3291	6	21	(	(	PUNCT
cana-3291	6	22	dt	dt	PROPN
cana-3291	6	23	.	.	PUNCT
cana-3291	6	24	,	,	PUNCT
cana-3291	6	25	)	)	PUNCT
cana-3291	6	26	,	,	PUNCT
cana-3291	6	27	andhra	andhra	PROPN
cana-3291	6	28	pradesh	pradesh	PROPN
cana-3291	6	29	,	,	PUNCT
cana-3291	6	30	india-522502	india-522502	PROPN
cana-3291	6	31	.	.	PUNCT
cana-3291	7	1	email	email	NOUN
cana-3291	7	2	:	:	PUNCT
cana-3291	7	3	sriman72@kluniversity.in	sriman72@kluniversity.in	PROPN
cana-3291	7	4	3m.v.chakradhara	3m.v.chakradhara	NUM
cana-3291	7	5	rao	rao	PROPN
cana-3291	7	6	,	,	PUNCT
cana-3291	7	7	professor	professor	NOUN
cana-3291	7	8	,	,	PUNCT
cana-3291	7	9	department	department	NOUN
cana-3291	7	10	of	of	ADP
cana-3291	7	11	mathematics	mathematics	PROPN
cana-3291	7	12	,	,	PUNCT
cana-3291	7	13	presidency	presidency	NOUN
cana-3291	7	14	university	university	NOUN
cana-3291	7	15	,	,	PUNCT
cana-3291	7	16	bangalore	bangalore	PROPN
cana-3291	7	17	,	,	PUNCT
cana-3291	7	18	india	india	PROPN
cana-3291	7	19	.	.	PUNCT
cana-3291	7	20	email	email	NOUN
cana-3291	7	21	:	:	PUNCT
cana-3291	7	22	chakrimv@yahoo.com	chakrimv@yahoo.com	PROPN
cana-3291	7	23	4professor	4professor	NUM
cana-3291	7	24	,	,	PUNCT
cana-3291	7	25	department	department	NOUN
cana-3291	7	26	of	of	ADP
cana-3291	7	27	engineering	engineering	NOUN
cana-3291	7	28	mathematics	mathematic	NOUN
cana-3291	7	29	,	,	PUNCT
cana-3291	7	30	college	college	NOUN
cana-3291	7	31	of	of	ADP
cana-3291	7	32	engineering	engineering	PROPN
cana-3291	7	33	,	,	PUNCT
cana-3291	7	34	koneru	koneru	PROPN
cana-3291	7	35	lakshmaiah	lakshmaiah	PROPN
cana-3291	7	36	education	education	PROPN
cana-3291	7	37	foundation	foundation	PROPN
cana-3291	7	38	,	,	PUNCT
cana-3291	7	39	vaddeswaram	vaddeswaram	PROPN
cana-3291	7	40	,	,	PUNCT
cana-3291	7	41	guntur	guntur	PROPN
cana-3291	7	42	(	(	PUNCT
cana-3291	7	43	dt	dt	PROPN
cana-3291	7	44	.	.	PUNCT
cana-3291	7	45	,	,	PUNCT
cana-3291	7	46	)	)	PUNCT
cana-3291	7	47	,	,	PUNCT
cana-3291	7	48	andhra	andhra	PROPN
cana-3291	7	49	pradesh	pradesh	PROPN
cana-3291	7	50	,	,	PUNCT
cana-3291	7	51	india-522502	india-522502	PROPN
cana-3291	7	52	email	email	NOUN
cana-3291	7	53	:	:	PUNCT
cana-3291	7	54	mrmadhavi5@gmail.com	mrmadhavi5@gmail.com	X
cana-3291	7	55	5asst.professor	5asst.professor	NUM
cana-3291	7	56	,	,	PUNCT
cana-3291	7	57	department	department	NOUN
cana-3291	7	58	of	of	ADP
cana-3291	7	59	mathematics	mathematic	NOUN
cana-3291	7	60	,	,	PUNCT
cana-3291	7	61	seshadri	seshadri	NOUN
cana-3291	7	62	rao	rao	PROPN
cana-3291	7	63	gudlavalleru	gudlavalleru	PROPN
cana-3291	7	64	engineering	engineering	PROPN
cana-3291	7	65	college	college	PROPN
cana-3291	7	66	,	,	PUNCT
cana-3291	7	67	gudlavalleru	gudlavalleru	NOUN
cana-3291	7	68	521356	521356	NUM
cana-3291	7	69	,	,	PUNCT
cana-3291	7	70	andhra	andhra	PROPN
cana-3291	7	71	pradesh	pradesh	PROPN
cana-3291	7	72	,	,	PUNCT
cana-3291	7	73	india	india	PROPN
cana-3291	7	74	.	.	PUNCT
cana-3291	8	1	e	e	X
cana-3291	8	2	-	-	NOUN
cana-3291	8	3	mail	mail	NOUN
cana-3291	8	4	:	:	PUNCT
cana-3291	8	5	krish.pav@gmail.com	krish.pav@gmail.com	PROPN
cana-3291	8	6	article	article	PROPN
cana-3291	8	7	history	history	NOUN
cana-3291	8	8	:	:	PUNCT
cana-3291	8	9	received	receive	VERB
cana-3291	8	10	:	:	PUNCT
cana-3291	8	11	18	18	NUM
cana-3291	8	12	-	-	SYM
cana-3291	8	13	10	10	NUM
cana-3291	8	14	-	-	PUNCT
cana-3291	8	15	2024	2024	NUM
cana-3291	8	16	revised	revise	VERB
cana-3291	8	17	:	:	PUNCT
cana-3291	8	18	02	02	NUM
cana-3291	8	19	-	-	SYM
cana-3291	8	20	12	12	NUM
cana-3291	8	21	-	-	PUNCT
cana-3291	8	22	2024	2024	NUM
cana-3291	8	23	accepted	accept	VERB
cana-3291	8	24	:	:	PUNCT
cana-3291	8	25	10	10	NUM
cana-3291	8	26	-	-	SYM
cana-3291	8	27	12	12	NUM
cana-3291	8	28	-	-	PUNCT
cana-3291	8	29	2024	2024	NUM
cana-3291	8	30	abstract	abstract	NOUN
cana-3291	8	31	:	:	PUNCT
cana-3291	8	32	introduction	introduction	NOUN
cana-3291	8	33	:	:	PUNCT
cana-3291	8	34	recent	recent	ADJ
cana-3291	8	35	advancements	advancement	NOUN
cana-3291	8	36	in	in	ADP
cana-3291	8	37	matrix	matrix	NOUN
cana-3291	8	38	polynomial	polynomial	ADJ
cana-3291	8	39	structures	structure	NOUN
cana-3291	8	40	associated	associate	VERB
cana-3291	8	41	with	with	ADP
cana-3291	8	42	special	special	ADJ
cana-3291	8	43	functions	function	NOUN
cana-3291	8	44	have	have	AUX
cana-3291	8	45	gained	gain	VERB
cana-3291	8	46	significant	significant	ADJ
cana-3291	8	47	traction	traction	NOUN
cana-3291	8	48	,	,	PUNCT
cana-3291	8	49	showcasing	showcase	VERB
cana-3291	8	50	a	a	DET
cana-3291	8	51	diverse	diverse	ADJ
cana-3291	8	52	array	array	NOUN
cana-3291	8	53	of	of	ADP
cana-3291	8	54	applications	application	NOUN
cana-3291	8	55	across	across	ADP
cana-3291	8	56	various	various	ADJ
cana-3291	8	57	engineering	engineering	NOUN
cana-3291	8	58	disciplines	discipline	NOUN
cana-3291	8	59	.	.	PUNCT
cana-3291	9	1	this	this	DET
cana-3291	9	2	paper	paper	NOUN
cana-3291	9	3	primarily	primarily	ADV
cana-3291	9	4	aims	aim	VERB
cana-3291	9	5	to	to	PART
cana-3291	9	6	explore	explore	VERB
cana-3291	9	7	and	and	CCONJ
cana-3291	9	8	derive	derive	VERB
cana-3291	9	9	multiple	multiple	ADJ
cana-3291	9	10	integral	integral	ADJ
cana-3291	9	11	representations	representation	NOUN
cana-3291	9	12	for	for	ADP
cana-3291	9	13	the	the	DET
cana-3291	9	14	modified	modify	VERB
cana-3291	9	15	jacobi	jacobi	PROPN
cana-3291	9	16	matrix	matrix	NOUN
cana-3291	9	17	polynomial	polynomial	NOUN
cana-3291	9	18	.	.	PUNCT
cana-3291	10	1	specifically	specifically	ADV
cana-3291	10	2	,	,	PUNCT
cana-3291	10	3	we	we	PRON
cana-3291	10	4	will	will	AUX
cana-3291	10	5	delve	delve	VERB
cana-3291	10	6	into	into	ADP
cana-3291	10	7	both	both	CCONJ
cana-3291	10	8	finite	finite	ADJ
cana-3291	10	9	and	and	CCONJ
cana-3291	10	10	infinite	infinite	VERB
cana-3291	10	11	single	single	ADJ
cana-3291	10	12	integral	integral	ADJ
cana-3291	10	13	representations	representation	NOUN
cana-3291	10	14	,	,	PUNCT
cana-3291	10	15	as	as	ADV
cana-3291	10	16	well	well	ADV
cana-3291	10	17	as	as	ADP
cana-3291	10	18	double	double	ADJ
cana-3291	10	19	integral	integral	ADJ
cana-3291	10	20	representations	representation	NOUN
cana-3291	10	21	of	of	ADP
cana-3291	10	22	the	the	DET
cana-3291	10	23	polynomial	polynomial	NOUN
cana-3291	10	24	.	.	PUNCT
cana-3291	11	1	by	by	ADP
cana-3291	11	2	examining	examine	VERB
cana-3291	11	3	these	these	DET
cana-3291	11	4	integral	integral	ADJ
cana-3291	11	5	forms	form	NOUN
cana-3291	11	6	,	,	PUNCT
cana-3291	11	7	we	we	PRON
cana-3291	11	8	seek	seek	VERB
cana-3291	11	9	to	to	PART
cana-3291	11	10	enhance	enhance	VERB
cana-3291	11	11	the	the	DET
cana-3291	11	12	understanding	understanding	NOUN
cana-3291	11	13	of	of	ADP
cana-3291	11	14	their	their	PRON
cana-3291	11	15	mathematical	mathematical	ADJ
cana-3291	11	16	properties	property	NOUN
cana-3291	11	17	and	and	CCONJ
cana-3291	11	18	implications	implication	NOUN
cana-3291	11	19	,	,	PUNCT
cana-3291	11	20	thereby	thereby	ADV
cana-3291	11	21	providing	provide	VERB
cana-3291	11	22	valuable	valuable	ADJ
cana-3291	11	23	insights	insight	NOUN
cana-3291	11	24	that	that	PRON
cana-3291	11	25	can	can	AUX
cana-3291	11	26	be	be	AUX
cana-3291	11	27	leveraged	leverage	VERB
cana-3291	11	28	in	in	ADP
cana-3291	11	29	practical	practical	ADJ
cana-3291	11	30	engineering	engineering	NOUN
cana-3291	11	31	scenarios	scenario	NOUN
cana-3291	11	32	.	.	PUNCT
cana-3291	12	1	the	the	DET
cana-3291	12	2	exploration	exploration	NOUN
cana-3291	12	3	of	of	ADP
cana-3291	12	4	these	these	DET
cana-3291	12	5	representations	representation	NOUN
cana-3291	12	6	not	not	PART
cana-3291	12	7	only	only	ADV
cana-3291	12	8	enriches	enrich	VERB
cana-3291	12	9	the	the	DET
cana-3291	12	10	theoretical	theoretical	ADJ
cana-3291	12	11	framework	framework	NOUN
cana-3291	12	12	surrounding	surround	VERB
cana-3291	12	13	modified	modified	ADJ
cana-3291	12	14	jacobi	jacobi	NOUN
cana-3291	12	15	matrix	matrix	NOUN
cana-3291	12	16	polynomials	polynomial	NOUN
cana-3291	12	17	but	but	CCONJ
cana-3291	12	18	also	also	ADV
cana-3291	12	19	highlights	highlight	VERB
cana-3291	12	20	their	their	PRON
cana-3291	12	21	potential	potential	ADJ
cana-3291	12	22	utility	utility	NOUN
cana-3291	12	23	in	in	ADP
cana-3291	12	24	solving	solve	VERB
cana-3291	12	25	complex	complex	ADJ
cana-3291	12	26	problems	problem	NOUN
cana-3291	12	27	within	within	ADP
cana-3291	12	28	the	the	DET
cana-3291	12	29	engineering	engineering	NOUN
cana-3291	12	30	domain	domain	NOUN
cana-3291	12	31	.	.	PUNCT
cana-3291	13	1	keywords	keyword	NOUN
cana-3291	13	2	:	:	PUNCT
cana-3291	13	3	finite	finite	VERB
cana-3291	13	4	and	and	CCONJ
cana-3291	13	5	infinite	infinite	VERB
cana-3291	13	6	single	single	ADJ
cana-3291	13	7	integral	integral	ADJ
cana-3291	13	8	representation	representation	NOUN
cana-3291	13	9	,	,	PUNCT
cana-3291	13	10	hypergeometric	hypergeometric	ADJ
cana-3291	13	11	function	function	NOUN
cana-3291	13	12	,	,	PUNCT
cana-3291	13	13	jacobi	jacobi	PROPN
cana-3291	13	14	polynomial	polynomial	PROPN
cana-3291	13	15	(	(	PUNCT
cana-3291	13	16	modified	modified	ADJ
cana-3291	13	17	)	)	PUNCT
cana-3291	13	18	,	,	PUNCT
cana-3291	13	19	jacobi	jacobi	PROPN
cana-3291	13	20	matrix	matrix	NOUN
cana-3291	13	21	polynomial	polynomial	ADJ
cana-3291	13	22	1	1	NUM
cana-3291	13	23	.	.	PUNCT
cana-3291	13	24	introduction	introduction	NOUN
cana-3291	13	25	in	in	ADP
cana-3291	13	26	the	the	DET
cana-3291	13	27	past	past	ADJ
cana-3291	13	28	few	few	ADJ
cana-3291	13	29	years	year	NOUN
cana-3291	13	30	,	,	PUNCT
cana-3291	13	31	many	many	ADJ
cana-3291	13	32	authors	author	NOUN
cana-3291	13	33	extended	extend	VERB
cana-3291	13	34	classical	classical	ADJ
cana-3291	13	35	polynomials	polynomial	NOUN
cana-3291	13	36	to	to	PART
cana-3291	13	37	matrix	matrix	VERB
cana-3291	13	38	polynomials	polynomial	NOUN
cana-3291	13	39	.	.	PUNCT
cana-3291	14	1	many	many	ADJ
cana-3291	14	2	authors	author	NOUN
cana-3291	14	3	generalized	generalize	VERB
cana-3291	14	4	the	the	DET
cana-3291	14	5	hypergeometric	hypergeometric	ADJ
cana-3291	14	6	series	series	NOUN
cana-3291	14	7	,	,	PUNCT
cana-3291	14	8	appell	appell	PROPN
cana-3291	14	9	’s	’s	PART
cana-3291	14	10	hypergeometric	hypergeometric	ADJ
cana-3291	14	11	functions	function	NOUN
cana-3291	14	12	also	also	ADV
cana-3291	14	13	to	to	PART
cana-3291	14	14	matrix	matrix	VERB
cana-3291	14	15	version	version	NOUN
cana-3291	14	16	of	of	ADP
cana-3291	14	17	the	the	DET
cana-3291	14	18	functions	function	NOUN
cana-3291	14	19	.	.	PUNCT
cana-3291	15	1	recently	recently	ADV
cana-3291	15	2	,	,	PUNCT
cana-3291	15	3	a	a	DET
cana-3291	15	4	good	good	ADJ
cana-3291	15	5	number	number	NOUN
cana-3291	15	6	of	of	ADP
cana-3291	15	7	authors	author	NOUN
cana-3291	15	8	studied	study	VERB
cana-3291	15	9	matrix	matrix	NOUN
cana-3291	15	10	version	version	NOUN
cana-3291	15	11	of	of	ADP
cana-3291	15	12	jacobi	jacobi	PROPN
cana-3291	15	13	,	,	PUNCT
cana-3291	15	14	hermite	hermite	PROPN
cana-3291	15	15	,	,	PUNCT
cana-3291	15	16	legendre	legendre	PROPN
cana-3291	15	17	and	and	CCONJ
cana-3291	15	18	other	other	ADJ
cana-3291	15	19	polynomials	polynomial	NOUN
cana-3291	15	20	[	[	X
cana-3291	15	21	1]-[4	1]-[4	NUM
cana-3291	15	22	]	]	PUNCT
cana-3291	15	23	.	.	PUNCT
cana-3291	16	1	the	the	DET
cana-3291	16	2	theory	theory	NOUN
cana-3291	16	3	of	of	ADP
cana-3291	16	4	matrix	matrix	NOUN
cana-3291	16	5	polynomials	polynomial	NOUN
cana-3291	16	6	provides	provide	VERB
cana-3291	16	7	a	a	DET
cana-3291	16	8	way	way	NOUN
cana-3291	16	9	to	to	PART
cana-3291	16	10	solve	solve	VERB
cana-3291	16	11	many	many	ADJ
cana-3291	16	12	problems	problem	NOUN
cana-3291	16	13	in	in	ADP
cana-3291	16	14	mathematical	mathematical	ADJ
cana-3291	16	15	physics	physics	NOUN
cana-3291	16	16	which	which	PRON
cana-3291	16	17	have	have	VERB
cana-3291	16	18	real	real	ADJ
cana-3291	16	19	time	time	NOUN
cana-3291	16	20	applications	application	NOUN
cana-3291	16	21	.	.	PUNCT
cana-3291	17	1	l.jodar	l.jodar	X
cana-3291	18	1	[	[	X
cana-3291	18	2	5]-[8	5]-[8	X
cana-3291	18	3	]	]	X
cana-3291	18	4	introduced	introduce	VERB
cana-3291	18	5	matrix	matrix	NOUN
cana-3291	18	6	form	form	NOUN
cana-3291	18	7	of	of	ADP
cana-3291	18	8	laguerre	laguerre	NOUN
cana-3291	18	9	and	and	CCONJ
cana-3291	18	10	hermite	hermite	ADJ
cana-3291	18	11	and	and	CCONJ
cana-3291	18	12	hypergeometric	hypergeometric	ADJ
cana-3291	18	13	function	function	NOUN
cana-3291	18	14	.	.	PUNCT
cana-3291	19	1	subhi	subhi	PROPN
cana-3291	19	2	khan	khan	PROPN
cana-3291	19	3	and	and	CCONJ
cana-3291	19	4	others	other	NOUN
cana-3291	19	5	mailto:kanurisrilakshmi@gmail.com	mailto:kanurisrilakshmi@gmail.com	PROPN
cana-3291	19	6	mailto:sriman72@kluniversity.in	mailto:sriman72@kluniversity.in	X
cana-3291	19	7	mailto:chakrimv@yahoo.com	mailto:chakrimv@yahoo.com	X
cana-3291	19	8	mailto:mrmadhavi5@gmail.com	mailto:mrmadhavi5@gmail.com	VERB
cana-3291	19	9	mailto:krish.pav@gmail.com	mailto:krish.pav@gmail.com	X
cana-3291	19	10	communications	communication	NOUN
cana-3291	19	11	on	on	ADP
cana-3291	19	12	applied	apply	VERB
cana-3291	19	13	nonlinear	nonlinear	ADJ
cana-3291	19	14	analysis	analysis	NOUN
cana-3291	19	15	issn	issn	NOUN
cana-3291	19	16	:	:	PUNCT
cana-3291	19	17	1074	1074	NUM
cana-3291	19	18	-	-	PUNCT
cana-3291	19	19	133x	133x	NUM
cana-3291	19	20	vol	vol	NOUN
cana-3291	19	21	32	32	NUM
cana-3291	19	22	no	no	NOUN
cana-3291	19	23	.	.	PUNCT
cana-3291	20	1	6s	6s	NUM
cana-3291	20	2	(	(	PUNCT
cana-3291	20	3	2025	2025	NUM
cana-3291	20	4	)	)	PUNCT
cana-3291	20	5	254	254	NUM
cana-3291	20	6	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-3291	20	7	extended	extend	VERB
cana-3291	20	8	laguerre	laguerre	NOUN
cana-3291	20	9	polynomials	polynomial	NOUN
cana-3291	20	10	with	with	ADP
cana-3291	20	11	two	two	NUM
cana-3291	20	12	variables	variable	NOUN
cana-3291	20	13	[	[	X
cana-3291	20	14	9	9	NUM
cana-3291	20	15	]	]	PUNCT
cana-3291	20	16	.	.	PUNCT
cana-3291	21	1	parihar	parihar	PROPN
cana-3291	21	2	and	and	CCONJ
cana-3291	21	3	patel	patel	PROPN
cana-3291	22	1	[	[	X
cana-3291	22	2	10	10	NUM
cana-3291	22	3	]	]	PUNCT
cana-3291	22	4	introduced	introduce	VERB
cana-3291	22	5	the	the	DET
cana-3291	22	6	modified	modify	VERB
cana-3291	22	7	jacobi	jacobi	NOUN
cana-3291	22	8	polynomials	polynomial	NOUN
cana-3291	22	9	and	and	CCONJ
cana-3291	22	10	derived	derived	ADJ
cana-3291	22	11	generating	generating	NOUN
cana-3291	22	12	function	function	NOUN
cana-3291	22	13	and	and	CCONJ
cana-3291	22	14	recurrence	recurrence	NOUN
cana-3291	22	15	relations	relation	NOUN
cana-3291	22	16	of	of	ADP
cana-3291	22	17	modified	modify	VERB
cana-3291	22	18	jacobi	jacobi	PROPN
cana-3291	22	19	polynomial	polynomial	NOUN
cana-3291	22	20	.	.	PUNCT
cana-3291	23	1	later	later	ADV
cana-3291	23	2	on	on	ADV
cana-3291	23	3	,	,	PUNCT
cana-3291	23	4	sri	sri	ADJ
cana-3291	23	5	lakshmi	lakshmi	NOUN
cana-3291	23	6	,	,	PUNCT
cana-3291	23	7	v	v	X
cana-3291	23	8	[	[	X
cana-3291	23	9	4	4	NUM
cana-3291	23	10	]	]	PUNCT
cana-3291	23	11	introduced	introduce	VERB
cana-3291	23	12	matrix	matrix	NOUN
cana-3291	23	13	form	form	NOUN
cana-3291	23	14	of	of	ADP
cana-3291	23	15	modified	modify	VERB
cana-3291	23	16	jacobi	jacobi	PROPN
cana-3291	23	17	polynomial	polynomial	ADJ
cana-3291	23	18	and	and	CCONJ
cana-3291	23	19	derived	derived	ADJ
cana-3291	23	20	generating	generating	NOUN
cana-3291	23	21	function	function	NOUN
cana-3291	23	22	,	,	PUNCT
cana-3291	23	23	recurrence	recurrence	NOUN
cana-3291	23	24	relations	relation	NOUN
cana-3291	23	25	of	of	ADP
cana-3291	23	26	matrix	matrix	NOUN
cana-3291	23	27	version	version	NOUN
cana-3291	23	28	of	of	ADP
cana-3291	23	29	modified	modify	VERB
cana-3291	23	30	jacobi	jacobi	PROPN
cana-3291	23	31	polynomial	polynomial	NOUN
cana-3291	23	32	.	.	PUNCT
cana-3291	24	1	srimanarayana	srimanarayana	PROPN
cana-3291	24	2	,	,	PUNCT
cana-3291	24	3	n	n	X
cana-3291	24	4	et.al	et.al	NOUN
cana-3291	25	1	[	[	X
cana-3291	25	2	11	11	NUM
cana-3291	25	3	]	]	PUNCT
cana-3291	25	4	,	,	PUNCT
cana-3291	25	5	[	[	X
cana-3291	25	6	12	12	NUM
cana-3291	25	7	]	]	PUNCT
cana-3291	25	8	,	,	PUNCT
cana-3291	25	9	derived	derive	VERB
cana-3291	25	10	integral	integral	ADJ
cana-3291	25	11	representations	representation	NOUN
cana-3291	25	12	for	for	ADP
cana-3291	25	13	generalized	generalized	ADJ
cana-3291	25	14	hypergeometric	hypergeometric	ADJ
cana-3291	25	15	function	function	NOUN
cana-3291	25	16	and	and	CCONJ
cana-3291	25	17	modified	modify	VERB
cana-3291	25	18	konhauser	konhauser	NOUN
cana-3291	25	19	’s	’s	PART
cana-3291	25	20	polynomial	polynomial	ADJ
cana-3291	25	21	.	.	PUNCT
cana-3291	26	1	in	in	ADP
cana-3291	26	2	the	the	DET
cana-3291	26	3	present	present	ADJ
cana-3291	26	4	study	study	NOUN
cana-3291	26	5	finite	finite	NOUN
cana-3291	26	6	and	and	CCONJ
cana-3291	26	7	infinite	infinite	VERB
cana-3291	26	8	integral	integral	ADJ
cana-3291	26	9	representations	representation	NOUN
cana-3291	26	10	and	and	CCONJ
cana-3291	26	11	double	double	ADJ
cana-3291	26	12	integral	integral	ADJ
cana-3291	26	13	representations	representation	NOUN
cana-3291	26	14	has	have	AUX
cana-3291	26	15	been	be	AUX
cana-3291	26	16	established	establish	VERB
cana-3291	26	17	for	for	ADP
cana-3291	26	18	(	(	PUNCT
cana-3291	26	19	)	)	PUNCT
cana-3291	26	20	(	(	PUNCT
cana-3291	26	21	,	,	PUNCT
cana-3291	26	22	)	)	PUNCT
cana-3291	26	23	a	a	DET
cana-3291	26	24	nj	nj	PROPN
cana-3291	26	25	x	x	SYM
cana-3291	27	1	w	w	X
cana-3291	27	2	.	.	PUNCT
cana-3291	27	3	useful	useful	ADJ
cana-3291	27	4	functions	function	NOUN
cana-3291	27	5	and	and	CCONJ
cana-3291	27	6	integral	integral	ADJ
cana-3291	27	7	formulae	formulae	NOUN
cana-3291	27	8	:	:	PUNCT
cana-3291	27	9	in	in	ADP
cana-3291	27	10	the	the	DET
cana-3291	27	11	present	present	ADJ
cana-3291	27	12	article	article	NOUN
cana-3291	27	13	,	,	PUNCT
cana-3291	27	14	we	we	PRON
cana-3291	27	15	abide	abide	VERB
cana-3291	27	16	by	by	ADP
cana-3291	27	17	the	the	DET
cana-3291	27	18	rules	rule	NOUN
cana-3291	27	19	of	of	ADP
cana-3291	27	20	matrix	matrix	NOUN
cana-3291	27	21	theory	theory	NOUN
cana-3291	27	22	.	.	PUNCT
cana-3291	28	1	assume	assume	VERB
cana-3291	28	2	0	0	NUM
cana-3291	28	3	1	1	NUM
cana-3291	28	4	,	,	PUNCT
cana-3291	28	5	,	,	PUNCT
cana-3291	28	6	...	...	PUNCT
cana-3291	28	7	,	,	PUNCT
cana-3291	28	8	m	m	VERB
cana-3291	28	9	m	m	VERB
cana-3291	28	10	np	np	INTJ
cana-3291	28	11	p	p	X
cana-3291	28	12	p	p	PROPN
cana-3291	28	13	c	c	NOUN
cana-3291	28	14			NOUN
cana-3291	28	15	,	,	PUNCT
cana-3291	28	16	where	where	SCONJ
cana-3291	28	17	ip	ip	NOUN
cana-3291	28	18	be	be	AUX
cana-3291	28	19	the	the	DET
cana-3291	28	20	matrix	matrix	NOUN
cana-3291	28	21	of	of	ADP
cana-3291	28	22	size	size	NOUN
cana-3291	28	23	‘	'	PUNCT
cana-3291	28	24	m	m	NOUN
cana-3291	28	25	’	'	PUNCT
cana-3291	28	26	and	and	CCONJ
cana-3291	28	27	the	the	DET
cana-3291	28	28	matrix	matrix	NOUN
cana-3291	28	29	polynomial	polynomial	NOUN
cana-3291	28	30	of	of	ADP
cana-3291	28	31	degree	degree	NOUN
cana-3291	28	32	‘	'	PUNCT
cana-3291	28	33	n	n	CCONJ
cana-3291	28	34	’	'	PUNCT
cana-3291	28	35	as	as	ADP
cana-3291	28	36	1	1	NUM
cana-3291	28	37	1	1	NUM
cana-3291	28	38	1	1	NUM
cana-3291	28	39	0	0	NUM
cana-3291	28	40	(	(	PUNCT
cana-3291	28	41	)	)	PUNCT
cana-3291	28	42	...	...	PUNCT
cana-3291	29	1	n	n	CCONJ
cana-3291	29	2	n	n	CCONJ
cana-3291	29	3	n	n	CCONJ
cana-3291	29	4	n	n	CCONJ
cana-3291	29	5	nf	nf	NOUN
cana-3291	29	6	z	z	NOUN
cana-3291	30	1	p	p	NOUN
cana-3291	30	2	z	z	PROPN
cana-3291	30	3	p	p	NOUN
cana-3291	30	4	z	z	PROPN
cana-3291	30	5	p	p	NOUN
cana-3291	30	6	z	z	NOUN
cana-3291	30	7	p−	p−	NOUN
cana-3291	30	8	−=	−=	NOUN
cana-3291	30	9	+	+	X
cana-3291	31	1	+	+	PUNCT
cana-3291	31	2	+	+	CCONJ
cana-3291	31	3	+	+	CCONJ
cana-3291	31	4	,	,	PUNCT
cana-3291	31	5	where	where	SCONJ
cana-3291	31	6	np	np	PRON
cana-3291	31	7	is	be	AUX
cana-3291	31	8	not	not	PART
cana-3291	31	9	a	a	DET
cana-3291	31	10	null	null	ADJ
cana-3291	31	11	matrix	matrix	NOUN
cana-3291	31	12	.	.	PUNCT
cana-3291	32	1	also	also	ADV
cana-3291	32	2	,	,	PUNCT
cana-3291	32	3	i	i	PRON
cana-3291	32	4	and	and	CCONJ
cana-3291	32	5	o	o	NOUN
cana-3291	32	6	be	be	AUX
cana-3291	32	7	the	the	DET
cana-3291	32	8	identity	identity	NOUN
cana-3291	32	9	and	and	CCONJ
cana-3291	32	10	null	null	ADJ
cana-3291	32	11	matrices	matrix	NOUN
cana-3291	32	12	in	in	ADP
cana-3291	32	13	m	m	PROPN
cana-3291	32	14	mc	mc	PROPN
cana-3291	32	15			PROPN
cana-3291	32	16	.	.	PUNCT
cana-3291	33	1	for	for	ADP
cana-3291	33	2	a	a	DET
cana-3291	33	3	matrix	matrix	NOUN
cana-3291	33	4	m	m	NOUN
cana-3291	33	5	mp	mp	NOUN
cana-3291	33	6	c	c	NOUN
cana-3291	33	7			NOUN
cana-3291	33	8	,	,	PUNCT
cana-3291	33	9	(	(	PUNCT
cana-3291	33	10	)	)	PUNCT
cana-3291	33	11	p	p	PROPN
cana-3291	33	12	is	be	AUX
cana-3291	33	13	the	the	DET
cana-3291	33	14	spectrum	spectrum	NOUN
cana-3291	33	15	of	of	ADP
cana-3291	33	16	p	p	PROPN
cana-3291	33	17	and	and	CCONJ
cana-3291	33	18	the	the	DET
cana-3291	33	19	matrix	matrix	NOUN
cana-3291	33	20	p	p	NOUN
cana-3291	33	21	is	be	AUX
cana-3291	33	22	a	a	DET
cana-3291	33	23	positive	positive	ADJ
cana-3291	33	24	stable	stable	ADJ
cana-3291	33	25	matrix	matrix	NOUN
cana-3291	33	26	.	.	PUNCT
cana-3291	34	1	in	in	ADP
cana-3291	34	2	[	[	X
cana-3291	34	3	13	13	NUM
cana-3291	34	4	]	]	PUNCT
cana-3291	34	5	,	,	PUNCT
cana-3291	34	6	for	for	ADP
cana-3291	34	7	all	all	DET
cana-3291	34	8	m	m	VERB
cana-3291	34	9	mp	mp	NOUN
cana-3291	34	10	c	c	NOUN
cana-3291	34	11			NOUN
cana-3291	34	12	and	and	CCONJ
cana-3291	34	13	p	p	PROPN
cana-3291	34	14	n	n	PRON
cana-3291	34	15	i+	i+	NOUN
cana-3291	34	16	is	be	AUX
cana-3291	34	17	invertible	invertible	ADJ
cana-3291	34	18	,	,	PUNCT
cana-3291	34	19	where	where	SCONJ
cana-3291	34	20	‘	'	PUNCT
cana-3291	34	21	n	n	CCONJ
cana-3291	34	22	’	'	PUNCT
cana-3291	34	23	is	be	AUX
cana-3291	34	24	an	an	DET
cana-3291	34	25	integer	integer	NOUN
cana-3291	34	26	,	,	PUNCT
cana-3291	34	27	then	then	ADV
cana-3291	34	28	the	the	DET
cana-3291	34	29	pochhammer	pochhammer	NOUN
cana-3291	34	30	symbol	symbol	NOUN
cana-3291	34	31	is	be	AUX
cana-3291	34	32	defined	define	VERB
cana-3291	34	33	by	by	ADP
cana-3291	34	34	1	1	NUM
cana-3291	34	35	(	(	PUNCT
cana-3291	34	36	)	)	PUNCT
cana-3291	34	37	...	...	PUNCT
cana-3291	35	1	(	(	PUNCT
cana-3291	35	2	(	(	PUNCT
cana-3291	35	3	1	1	NUM
cana-3291	35	4	)	)	PUNCT
cana-3291	35	5	)	)	PUNCT
cana-3291	35	6	;	;	PUNCT
cana-3291	35	7	0	0	NUM
cana-3291	35	8	(	(	PUNCT
cana-3291	35	9	)	)	PUNCT
cana-3291	35	10	(	(	PUNCT
cana-3291	35	11	)	)	PUNCT
cana-3291	35	12	(	(	PUNCT
cana-3291	35	13	)	)	PUNCT
cana-3291	35	14	;	;	PUNCT
cana-3291	35	15	0	0	NUM
cana-3291	35	16	;	;	PUNCT
cana-3291	35	17	0	0	NUM
cana-3291	35	18	n	n	PRON
cana-3291	36	1	p	p	X
cana-3291	36	2	p	p	X
cana-3291	37	1	i	i	PRON
cana-3291	37	2	p	p	NOUN
cana-3291	37	3	n	n	INTJ
cana-3291	37	4	i	i	PRON
cana-3291	37	5	n	n	VERB
cana-3291	37	6	p	p	X
cana-3291	37	7	p	p	X
cana-3291	37	8	ni	ni	PROPN
cana-3291	37	9	p	p	PROPN
cana-3291	37	10	n	n	PROPN
cana-3291	37	11	i	i	PRON
cana-3291	37	12	n	n	ADV
cana-3291	37	13	−	−	PROPN
cana-3291	38	1	+	+	CCONJ
cana-3291	38	2	+	+	CCONJ
cana-3291	38	3	−	−	X
cana-3291	38	4			NOUN
cana-3291	38	5			NUM
cana-3291	38	6	=	=	SYM
cana-3291	38	7			VERB
cana-3291	38	8	+	+	CCONJ
cana-3291	38	9			VERB
cana-3291	38	10			PROPN
cana-3291	38	11			NUM
cana-3291	38	12	=	=	SYM
cana-3291	38	13			PROPN
cana-3291	38	14	(	(	PUNCT
cana-3291	38	15	1.1	1.1	NUM
cana-3291	38	16	)	)	PUNCT
cana-3291	38	17	for	for	ADP
cana-3291	38	18	preliminary	preliminary	ADJ
cana-3291	38	19	matrix	matrix	NOUN
cana-3291	38	20	version	version	NOUN
cana-3291	38	21	of	of	ADP
cana-3291	38	22	gamma	gamma	NOUN
cana-3291	38	23	,	,	PUNCT
cana-3291	38	24	beta	beta	NOUN
cana-3291	38	25	,	,	PUNCT
cana-3291	38	26	and	and	CCONJ
cana-3291	38	27	hypergeometric	hypergeometric	ADJ
cana-3291	38	28	functions	function	NOUN
cana-3291	38	29	one	one	PRON
cana-3291	38	30	can	can	AUX
cana-3291	38	31	refer	refer	VERB
cana-3291	38	32	[	[	NOUN
cana-3291	38	33	2	2	NUM
cana-3291	38	34	]	]	PUNCT
cana-3291	38	35	,	,	PUNCT
cana-3291	38	36	[	[	X
cana-3291	38	37	5	5	NUM
cana-3291	38	38	]	]	PUNCT
cana-3291	38	39	,	,	PUNCT
cana-3291	38	40	[	[	X
cana-3291	38	41	6	6	NUM
cana-3291	38	42	]	]	PUNCT
cana-3291	38	43	,	,	PUNCT
cana-3291	38	44	[	[	X
cana-3291	38	45	7	7	NUM
cana-3291	38	46	]	]	PUNCT
cana-3291	38	47	,	,	PUNCT
cana-3291	38	48	and	and	CCONJ
cana-3291	38	49	[	[	X
cana-3291	38	50	13	13	NUM
cana-3291	38	51	]	]	PUNCT
cana-3291	38	52	.	.	PUNCT
cana-3291	39	1	in	in	ADP
cana-3291	39	2	[	[	X
cana-3291	39	3	10	10	NUM
cana-3291	39	4	]	]	PUNCT
cana-3291	39	5	,	,	PUNCT
cana-3291	39	6	parihar	parihar	PROPN
cana-3291	39	7	and	and	CCONJ
cana-3291	39	8	patel	patel	PROPN
cana-3291	39	9	defined	define	VERB
cana-3291	39	10	modified	modified	ADJ
cana-3291	39	11	jacobi	jacobi	PROPN
cana-3291	39	12	polynomial	polynomial	NOUN
cana-3291	39	13	using	use	VERB
cana-3291	39	14	a	a	DET
cana-3291	39	15	difference	difference	NOUN
cana-3291	39	16	operator	operator	NOUN
cana-3291	39	17	[	[	X
cana-3291	39	18	14	14	NUM
cana-3291	39	19	]	]	PUNCT
cana-3291	39	20	.	.	PUNCT
cana-3291	40	1	later	later	ADV
cana-3291	40	2	,	,	PUNCT
cana-3291	40	3	sri	sri	PROPN
cana-3291	40	4	lakshmi	lakshmi	NOUN
cana-3291	40	5	,	,	PUNCT
cana-3291	40	6	v	v	NOUN
cana-3291	40	7	,	,	PUNCT
cana-3291	40	8	et.al	et.al	NOUN
cana-3291	40	9	extended	extend	VERB
cana-3291	40	10	the	the	DET
cana-3291	40	11	same	same	ADJ
cana-3291	40	12	as	as	ADP
cana-3291	40	13	modified	modify	VERB
cana-3291	40	14	jacobi	jacobi	PROPN
cana-3291	40	15	matrix	matrix	NOUN
cana-3291	40	16	polynomial	polynomial	NOUN
cana-3291	40	17	,	,	PUNCT
cana-3291	40	18	(	(	PUNCT
cana-3291	40	19	)	)	PUNCT
cana-3291	40	20	(	(	PUNCT
cana-3291	40	21	,	,	PUNCT
cana-3291	40	22	)	)	PUNCT
cana-3291	40	23	a	a	DET
cana-3291	40	24	nj	nj	PROPN
cana-3291	40	25	x	x	SYM
cana-3291	40	26	w	w	NOUN
cana-3291	40	27	as	as	SCONJ
cana-3291	40	28	follows	follow	VERB
cana-3291	40	29	[	[	X
cana-3291	40	30	4	4	NUM
cana-3291	40	31	]	]	PUNCT
cana-3291	40	32	.	.	PUNCT
cana-3291	41	1	(	(	PUNCT
cana-3291	41	2	)	)	PUNCT
cana-3291	41	3	2	2	NUM
cana-3291	41	4	1	1	NUM
cana-3291	41	5	(	(	PUNCT
cana-3291	41	6	)	)	PUNCT
cana-3291	41	7	(	(	PUNCT
cana-3291	41	8	,	,	PUNCT
cana-3291	41	9	)	)	PUNCT
cana-3291	41	10	,	,	PUNCT
cana-3291	41	11	;	;	PUNCT
cana-3291	41	12	;	;	PUNCT
cana-3291	41	13	!	!	PUNCT
cana-3291	42	1	a	a	DET
cana-3291	42	2	n	n	CCONJ
cana-3291	42	3	n	n	ADP
cana-3291	42	4	a	a	PRON
cana-3291	43	1	i	i	NOUN
cana-3291	43	2	x	x	PROPN
cana-3291	43	3	j	j	NOUN
cana-3291	43	4	x	x	SYM
cana-3291	43	5	w	w	PROPN
cana-3291	43	6	f	f	PROPN
cana-3291	43	7	ni	ni	PROPN
cana-3291	44	1	i	i	PROPN
cana-3291	44	2	a	a	PROPN
cana-3291	44	3	w	w	NOUN
cana-3291	44	4	n	n	ADP
cana-3291	44	5	w	w	PROPN
cana-3291	45	1	+	+	NUM
cana-3291	45	2			NUM
cana-3291	45	3			NOUN
cana-3291	45	4	=	=	PUNCT
cana-3291	46	1	−	−	PUNCT
cana-3291	46	2	+	+	NOUN
cana-3291	46	3			NOUN
cana-3291	46	4			NOUN
cana-3291	46	5			NOUN
cana-3291	46	6			PROPN
cana-3291	46	7	(	(	PUNCT
cana-3291	46	8	1.2	1.2	NUM
cana-3291	46	9	)	)	PUNCT
cana-3291	46	10	(	(	PUNCT
cana-3291	46	11	)	)	PUNCT
cana-3291	46	12	0	0	NUM
cana-3291	46	13	(	(	PUNCT
cana-3291	46	14	)	)	PUNCT
cana-3291	46	15	(	(	PUNCT
cana-3291	46	16	)	)	PUNCT
cana-3291	46	17	!	!	PUNCT
cana-3291	46	18	!	!	PUNCT
cana-3291	47	1	(	(	PUNCT
cana-3291	47	2	)	)	PUNCT
cana-3291	47	3	r	r	NOUN
cana-3291	47	4	n	n	NOUN
cana-3291	47	5	r	r	NOUN
cana-3291	47	6	n	n	NOUN
cana-3291	47	7	r	r	NOUN
cana-3291	47	8	r	r	NOUN
cana-3291	47	9	r	r	NOUN
cana-3291	47	10	x	x	SYM
cana-3291	47	11	ni	ni	PROPN
cana-3291	47	12	w	w	PROPN
cana-3291	47	13	a	a	PROPN
cana-3291	47	14	i	i	NOUN
cana-3291	47	15	w	w	PROPN
cana-3291	47	16	n	n	ADP
cana-3291	47	17	r	r	NOUN
cana-3291	48	1	i	i	PRON
cana-3291	48	2	a=	a=	VERB
cana-3291	48	3			NOUN
cana-3291	48	4			PROPN
cana-3291	48	5	−	−	PROPN
cana-3291	49	1			PROPN
cana-3291	49	2			PROPN
cana-3291	50	1	+	+	CCONJ
cana-3291	50	2			PROPN
cana-3291	50	3			NOUN
cana-3291	50	4	=	=	SYM
cana-3291	51	1	+	+	CCONJ
cana-3291	51	2			X
cana-3291	51	3	(	(	PUNCT
cana-3291	51	4	1.3	1.3	NUM
cana-3291	51	5	)	)	PUNCT
cana-3291	51	6	to	to	PART
cana-3291	51	7	obtain	obtain	VERB
cana-3291	51	8	different	different	ADJ
cana-3291	51	9	integral	integral	ADJ
cana-3291	51	10	representations	representation	NOUN
cana-3291	51	11	,	,	PUNCT
cana-3291	51	12	the	the	DET
cana-3291	51	13	following	follow	VERB
cana-3291	51	14	well	well	ADV
cana-3291	51	15	-	-	PUNCT
cana-3291	51	16	known	know	VERB
cana-3291	51	17	results	result	NOUN
cana-3291	51	18	have	have	AUX
cana-3291	51	19	been	be	AUX
cana-3291	51	20	used	use	VERB
cana-3291	51	21	:	:	PUNCT
cana-3291	51	22	maclaurin	maclaurin	NOUN
cana-3291	51	23	’s	’s	PART
cana-3291	51	24	theorem	theorem	NOUN
cana-3291	51	25	is	be	AUX
cana-3291	51	26	(	(	PUNCT
cana-3291	51	27	)	)	PUNCT
cana-3291	51	28	0	0	NUM
cana-3291	51	29	(	(	PUNCT
cana-3291	51	30	0	0	NUM
cana-3291	51	31	)	)	PUNCT
cana-3291	51	32	(	(	PUNCT
cana-3291	51	33	)	)	PUNCT
cana-3291	51	34	!	!	PUNCT
cana-3291	52	1	l	l	NOUN
cana-3291	53	1	l	l	PUNCT
cana-3291	53	2	l	l	NOUN
cana-3291	53	3	f	f	X
cana-3291	53	4	s	s	X
cana-3291	53	5	f	f	PROPN
cana-3291	53	6	s	s	PART
cana-3291	53	7	l	l	NOUN
cana-3291	53	8			NOUN
cana-3291	53	9	=	=	SYM
cana-3291	54	1	=	=	AUX
cana-3291	54	2			X
cana-3291	54	3	(	(	PUNCT
cana-3291	54	4	1.4	1.4	NUM
cana-3291	54	5	)	)	PUNCT
cana-3291	54	6	so	so	SCONJ
cana-3291	54	7	that	that	SCONJ
cana-3291	54	8	the	the	DET
cana-3291	54	9	coefficients	coefficient	NOUN
cana-3291	54	10	(	(	PUNCT
cana-3291	54	11	)	)	PUNCT
cana-3291	54	12	(	(	PUNCT
cana-3291	54	13	0	0	NUM
cana-3291	54	14	)	)	PUNCT
cana-3291	54	15	;	;	PUNCT
cana-3291	54	16	0,1	0,1	NUM
cana-3291	54	17	,	,	PUNCT
cana-3291	54	18	2,lf	2,lf	NUM
cana-3291	54	19	l	l	NOUN
cana-3291	54	20	=	=	PUNCT
cana-3291	55	1	−	−	NOUN
cana-3291	56	1	−	−	NOUN
cana-3291	56	2	−	−	NOUN
cana-3291	56	3	are	be	AUX
cana-3291	56	4	obtained	obtain	VERB
cana-3291	56	5	by	by	ADP
cana-3291	56	6	the	the	DET
cana-3291	56	7	integrals	integral	NOUN
cana-3291	56	8	communications	communication	NOUN
cana-3291	56	9	on	on	ADP
cana-3291	56	10	applied	apply	VERB
cana-3291	56	11	nonlinear	nonlinear	ADJ
cana-3291	56	12	analysis	analysis	NOUN
cana-3291	56	13	issn	issn	NOUN
cana-3291	56	14	:	:	PUNCT
cana-3291	56	15	1074	1074	NUM
cana-3291	56	16	-	-	PUNCT
cana-3291	56	17	133x	133x	NUM
cana-3291	56	18	vol	vol	NOUN
cana-3291	56	19	32	32	NUM
cana-3291	56	20	no	no	NOUN
cana-3291	56	21	.	.	PUNCT
cana-3291	57	1	6s	6s	NUM
cana-3291	57	2	(	(	PUNCT
cana-3291	57	3	2025	2025	NUM
cana-3291	57	4	)	)	PUNCT
cana-3291	57	5	255	255	NUM
cana-3291	57	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3291	57	7	(	(	PUNCT
cana-3291	57	8	0	0	NUM
cana-3291	57	9	)	)	PUNCT
cana-3291	57	10	(	(	PUNCT
cana-3291	57	11	)	)	PUNCT
cana-3291	57	12	1	1	X
cana-3291	57	13	!	!	PUNCT
cana-3291	58	1	(	(	PUNCT
cana-3291	58	2	)	)	PUNCT
cana-3291	58	3	(	(	PUNCT
cana-3291	58	4	0	0	NUM
cana-3291	58	5	)	)	PUNCT
cana-3291	58	6	;	;	PUNCT
cana-3291	59	1	0,1,2	0,1,2	X
cana-3291	59	2	...	...	SYM
cana-3291	59	3	2	2	NUM
cana-3291	59	4	l	l	NOUN
cana-3291	59	5	n	n	NUM
cana-3291	59	6	l	l	NOUN
cana-3291	59	7	f	f	X
cana-3291	59	8	s	s	X
cana-3291	59	9	ds	ds	INTJ
cana-3291	59	10	f	f	X
cana-3291	59	11	s	s	VERB
cana-3291	59	12	i	i	PRON
cana-3291	59	13	s	s	VERB
cana-3291	60	1	+	+	CCONJ
cana-3291	60	2	+	+	PUNCT
cana-3291	60	3	=	=	SYM
cana-3291	60	4	=	=	NOUN
cana-3291	60	5			X
cana-3291	60	6	(	(	PUNCT
cana-3291	60	7	1.5	1.5	NUM
cana-3291	60	8	)	)	PUNCT
cana-3291	60	9	for	for	ADP
cana-3291	60	10	re	re	VERB
cana-3291	60	11	(	(	PUNCT
cana-3291	60	12	)	)	PUNCT
cana-3291	60	13	m	m	VERB
cana-3291	60	14	and	and	CCONJ
cana-3291	60	15	re	re	ADP
cana-3291	60	16	(	(	PUNCT
cana-3291	60	17	)	)	PUNCT
cana-3291	60	18	0n	0n	NOUN
cana-3291	61	1	m−	m−	PROPN
cana-3291	62	1			INTJ
cana-3291	62	2	,	,	PUNCT
cana-3291	62	3	we	we	PRON
cana-3291	62	4	have	have	VERB
cana-3291	62	5	1	1	NUM
cana-3291	62	6	1	1	NUM
cana-3291	62	7	1	1	NUM
cana-3291	62	8	0	0	NUM
cana-3291	62	9	(	(	PUNCT
cana-3291	62	10	)	)	PUNCT
cana-3291	62	11	(	(	PUNCT
cana-3291	62	12	)	)	PUNCT
cana-3291	62	13	(	(	PUNCT
cana-3291	62	14	1	1	X
cana-3291	62	15	)	)	PUNCT
cana-3291	62	16	(	(	PUNCT
cana-3291	62	17	)	)	PUNCT
cana-3291	62	18	(	(	PUNCT
cana-3291	62	19	)	)	PUNCT
cana-3291	62	20	(	(	PUNCT
cana-3291	62	21	)	)	PUNCT
cana-3291	62	22	j	j	PROPN
cana-3291	62	23	m	m	VERB
cana-3291	62	24	j	j	PROPN
cana-3291	62	25	n	n	CCONJ
cana-3291	62	26	m	m	PROPN
cana-3291	62	27	j	j	NOUN
cana-3291	62	28	m	m	VERB
cana-3291	62	29	n	n	PROPN
cana-3291	62	30	d	d	PROPN
cana-3291	62	31	n	n	CCONJ
cana-3291	62	32	m	m	VERB
cana-3291	62	33	n	n	PRON
cana-3291	62	34	m	m	PRON
cana-3291	62	35			NOUN
cana-3291	62	36			NOUN
cana-3291	62	37	+	+	VERB
cana-3291	62	38	−	−	NOUN
cana-3291	62	39	−	−	PROPN
cana-3291	62	40	−	−	PROPN
cana-3291	62	41	=	=	SYM
cana-3291	63	1	−	−	PROPN
cana-3291	63	2			NOUN
cana-3291	63	3			VERB
cana-3291	63	4	−	−	NOUN
cana-3291	63	5			X
cana-3291	63	6	(	(	PUNCT
cana-3291	63	7	1.6	1.6	NUM
cana-3291	63	8	)	)	PUNCT
cana-3291	63	9	2	2	NUM
cana-3291	63	10	2	2	NUM
cana-3291	63	11	1	1	NUM
cana-3291	63	12	(	(	PUNCT
cana-3291	63	13	)	)	PUNCT
cana-3291	63	14	t	t	AUX
cana-3291	63	15	nn	nn	PROPN
cana-3291	63	16	e	e	PROPN
cana-3291	63	17	t	t	PROPN
cana-3291	63	18	dt	dt	AUX
cana-3291	63	19			VERB
cana-3291	63	20	−	−	PROPN
cana-3291	63	21	−	−	NOUN
cana-3291	63	22	−	−	NOUN
cana-3291	63	23			VERB
cana-3291	63	24	=	=	SYM
cana-3291	63	25			X
cana-3291	63	26	(	(	PUNCT
cana-3291	63	27	1.7	1.7	NUM
cana-3291	63	28	)	)	PUNCT
cana-3291	63	29	if	if	SCONJ
cana-3291	63	30	real	real	ADJ
cana-3291	63	31	(	(	PUNCT
cana-3291	63	32	,	,	PUNCT
cana-3291	63	33	)	)	PUNCT
cana-3291	63	34	0	0	NUM
cana-3291	63	35	m	m	VERB
cana-3291	63	36	n	n	PRON
cana-3291	63	37			INTJ
cana-3291	63	38	,	,	PUNCT
cana-3291	63	39	then	then	ADV
cana-3291	63	40	1	1	NUM
cana-3291	63	41	1	1	NUM
cana-3291	63	42	1	1	NUM
cana-3291	63	43	1	1	NUM
cana-3291	63	44	1	1	NUM
cana-3291	63	45	0	0	NUM
cana-3291	63	46	0	0	NUM
cana-3291	63	47	(	(	PUNCT
cana-3291	63	48	1	1	NUM
cana-3291	63	49	)	)	PUNCT
cana-3291	63	50	(	(	PUNCT
cana-3291	63	51	1	1	X
cana-3291	63	52	)	)	PUNCT
cana-3291	63	53	(	(	PUNCT
cana-3291	63	54	,	,	PUNCT
cana-3291	63	55	)	)	PUNCT
cana-3291	63	56	(	(	PUNCT
cana-3291	63	57	1	1	X
cana-3291	63	58	)	)	PUNCT
cana-3291	63	59	k	k	NOUN
cana-3291	64	1	k	k	PUNCT
cana-3291	64	2	l	l	PUNCT
cana-3291	65	1	k	k	X
cana-3291	65	2	l	l	PUNCT
cana-3291	66	1	x	x	X
cana-3291	66	2	y	y	PROPN
cana-3291	66	3	y	y	PROPN
cana-3291	66	4	dxdy	dxdy	PROPN
cana-3291	66	5	k	k	PROPN
cana-3291	66	6	l	l	PROPN
cana-3291	66	7	xy	xy	PROPN
cana-3291	67	1			NOUN
cana-3291	67	2	−	−	PROPN
cana-3291	68	1	−	−	PROPN
cana-3291	69	1	+	+	CCONJ
cana-3291	69	2	−	−	PROPN
cana-3291	69	3	−	−	PRON
cana-3291	69	4	−	−	PROPN
cana-3291	70	1	=	=	SYM
cana-3291	70	2	−	−	PROPN
cana-3291	70	3			X
cana-3291	71	1			X
cana-3291	71	2	(	(	PUNCT
cana-3291	71	3	1.8	1.8	NUM
cana-3291	71	4	)	)	PUNCT
cana-3291	71	5	if	if	SCONJ
cana-3291	71	6	real	real	ADJ
cana-3291	71	7	(	(	PUNCT
cana-3291	71	8	k	k	NOUN
cana-3291	71	9	,	,	PUNCT
cana-3291	71	10	l)>0	l)>0	PROPN
cana-3291	71	11	,	,	PUNCT
cana-3291	71	12	real(𝜆)>0	real(𝜆)>0	PROPN
cana-3291	71	13	then	then	ADV
cana-3291	71	14	1	1	NUM
cana-3291	71	15	1	1	NUM
cana-3291	71	16	1	1	NUM
cana-3291	71	17	(	(	PUNCT
cana-3291	71	18	)	)	PUNCT
cana-3291	71	19	(	(	PUNCT
cana-3291	71	20	)	)	PUNCT
cana-3291	71	21	(	(	PUNCT
cana-3291	71	22	)	)	PUNCT
cana-3291	71	23	(	(	PUNCT
cana-3291	71	24	1	1	X
cana-3291	71	25	)	)	PUNCT
cana-3291	71	26	(	(	PUNCT
cana-3291	71	27	)	)	PUNCT
cana-3291	72	1	k	k	X
cana-3291	72	2	l	l	PUNCT
cana-3291	72	3	a	a	DET
cana-3291	72	4	k	k	X
cana-3291	72	5	l	l	NOUN
cana-3291	72	6	u	u	NOUN
cana-3291	72	7	v	v	ADP
cana-3291	72	8	u	u	NOUN
cana-3291	72	9	v	v	NOUN
cana-3291	72	10	dudv	dudv	NOUN
cana-3291	72	11	k	k	PROPN
cana-3291	72	12	l	l	PROPN
cana-3291	72	13			X
cana-3291	72	14			ADJ
cana-3291	72	15			ADJ
cana-3291	72	16	−	−	PROPN
cana-3291	72	17	−	−	NOUN
cana-3291	72	18	−	−	PROPN
cana-3291	72	19			NOUN
cana-3291	72	20			NOUN
cana-3291	72	21			NOUN
cana-3291	72	22	−	−	NOUN
cana-3291	72	23	−	−	NOUN
cana-3291	72	24	=	=	PUNCT
cana-3291	73	1			VERB
cana-3291	73	2	+	+	CCONJ
cana-3291	73	3	+	+	ADJ
cana-3291	73	4			ADJ
cana-3291	73	5	(	(	PUNCT
cana-3291	73	6	1.9	1.9	NUM
cana-3291	73	7	)	)	PUNCT
cana-3291	73	8	where	where	SCONJ
cana-3291	73	9	‘	'	PUNCT
cana-3291	73	10	a	a	PRON
cana-3291	73	11	’	'	PUNCT
cana-3291	73	12	is	be	AUX
cana-3291	73	13	the	the	DET
cana-3291	73	14	area	area	NOUN
cana-3291	73	15	lies	lie	VERB
cana-3291	73	16	between	between	ADP
cana-3291	73	17	u	u	PROPN
cana-3291	73	18	,	,	PUNCT
cana-3291	73	19	v	v	DET
cana-3291	73	20	≥	≥	NOUN
cana-3291	73	21	0	0	NUM
cana-3291	73	22	and	and	CCONJ
cana-3291	73	23	u+v	u+v	NUM
cana-3291	73	24	≤	≤	NUM
cana-3291	73	25	1	1	NUM
cana-3291	73	26	.	.	PUNCT
cana-3291	73	27	/2	/2	NOUN
cana-3291	74	1	2	2	NUM
cana-3291	74	2	1	1	NUM
cana-3291	74	3	2	2	NUM
cana-3291	74	4	1	1	NUM
cana-3291	74	5	0	0	NUM
cana-3291	74	6	(	(	PUNCT
cana-3291	74	7	,	,	PUNCT
cana-3291	74	8	)	)	PUNCT
cana-3291	74	9	2	2	NUM
cana-3291	74	10	(	(	PUNCT
cana-3291	74	11	sin	sin	NOUN
cana-3291	74	12	)	)	PUNCT
cana-3291	74	13	(	(	PUNCT
cana-3291	74	14	cos	cos	PROPN
cana-3291	74	15	)	)	PUNCT
cana-3291	74	16	a	a	DET
cana-3291	74	17	ba	ba	PROPN
cana-3291	74	18	b	b	PROPN
cana-3291	74	19	t	t	PROPN
cana-3291	74	20	t	t	PROPN
cana-3291	74	21	dt	dt	X
cana-3291	74	22			PROPN
cana-3291	74	23			PROPN
cana-3291	74	24	−	−	PROPN
cana-3291	74	25	−=	−=	NOUN
cana-3291	74	26			X
cana-3291	74	27	(	(	PUNCT
cana-3291	74	28	1.10	1.10	NUM
cana-3291	74	29	)	)	PUNCT
cana-3291	74	30	2	2	NUM
cana-3291	74	31	2	2	NUM
cana-3291	74	32	1	1	NUM
cana-3291	74	33	(	(	PUNCT
cana-3291	74	34	)	)	PUNCT
cana-3291	74	35	2	2	NUM
cana-3291	74	36	2	2	NUM
cana-3291	74	37	2	2	NUM
cana-3291	74	38	r	r	NOUN
cana-3291	74	39	r	r	NOUN
cana-3291	74	40	r	r	NOUN
cana-3291	74	41	r	r	NOUN
cana-3291	74	42			X
cana-3291	74	43			ADJ
cana-3291	74	44			ADJ
cana-3291	74	45	+	+	PROPN
cana-3291	74	46			NOUN
cana-3291	74	47			NOUN
cana-3291	74	48			NOUN
cana-3291	74	49			PROPN
cana-3291	74	50	=	=	SYM
cana-3291	74	51			PROPN
cana-3291	75	1			INTJ
cana-3291	76	1			PROPN
cana-3291	76	2			PROPN
cana-3291	77	1			ADJ
cana-3291	77	2			PROPN
cana-3291	77	3			PROPN
cana-3291	77	4			NOUN
cana-3291	77	5	(	(	PUNCT
cana-3291	77	6	1.11	1.11	NUM
cana-3291	77	7	)	)	PUNCT
cana-3291	77	8	provided	provide	VERB
cana-3291	77	9	re(s)>0	re(s)>0	PROPN
cana-3291	77	10	and	and	CCONJ
cana-3291	77	11	re	re	ADJ
cana-3291	77	12	(	(	PUNCT
cana-3291	77	13	𝛼)>0	𝛼)>0	X
cana-3291	77	14	[	[	X
cana-3291	77	15	15	15	NUM
cana-3291	77	16	]	]	PUNCT
cana-3291	77	17	,	,	PUNCT
cana-3291	77	18	[	[	X
cana-3291	77	19	16	16	NUM
cana-3291	77	20	]	]	SYM
cana-3291	77	21	2	2	NUM
cana-3291	77	22	.	.	X
cana-3291	77	23	integral	integral	ADJ
cana-3291	77	24	representation	representation	NOUN
cana-3291	77	25	for	for	ADP
cana-3291	77	26	(	(	PUNCT
cana-3291	77	27	)	)	PUNCT
cana-3291	77	28	(	(	PUNCT
cana-3291	77	29	,	,	PUNCT
cana-3291	77	30	)	)	PUNCT
cana-3291	77	31	a	a	DET
cana-3291	77	32	nj	nj	PROPN
cana-3291	77	33	x	x	PUNCT
cana-3291	77	34	w	w	ADP
cana-3291	77	35	integral	integral	ADJ
cana-3291	77	36	representation	representation	NOUN
cana-3291	77	37	by	by	ADP
cana-3291	77	38	a	a	DET
cana-3291	77	39	contour	contour	NOUN
cana-3291	77	40	integral	integral	NOUN
cana-3291	77	41	by	by	ADP
cana-3291	77	42	the	the	DET
cana-3291	77	43	generating	generate	VERB
cana-3291	77	44	function	function	NOUN
cana-3291	77	45	of	of	ADP
cana-3291	77	46	(	(	PUNCT
cana-3291	77	47	)	)	PUNCT
cana-3291	77	48	(	(	PUNCT
cana-3291	77	49	,	,	PUNCT
cana-3291	77	50	)	)	PUNCT
cana-3291	77	51	a	a	DET
cana-3291	77	52	nj	nj	PROPN
cana-3291	77	53	x	x	SYM
cana-3291	77	54	w	w	INTJ
cana-3291	77	55	,	,	PUNCT
cana-3291	77	56	we	we	PRON
cana-3291	77	57	have	have	AUX
cana-3291	77	58	(	(	PUNCT
cana-3291	77	59	)	)	PUNCT
cana-3291	77	60	1	1	NUM
cana-3291	77	61	1	1	NUM
cana-3291	77	62	0	0	NUM
cana-3291	77	63	(	(	PUNCT
cana-3291	77	64	,	,	PUNCT
cana-3291	77	65	)	)	PUNCT
cana-3291	77	66	(	(	PUNCT
cana-3291	77	67	,	,	PUNCT
cana-3291	77	68	;	;	PUNCT
cana-3291	77	69	)	)	PUNCT
cana-3291	77	70	(	(	PUNCT
cana-3291	77	71	)	)	PUNCT
cana-3291	77	72	a	a	DET
cana-3291	77	73	n	n	ADP
cana-3291	77	74	tn	tn	PROPN
cana-3291	77	75	n	n	PROPN
cana-3291	77	76	n	n	PRON
cana-3291	77	77	j	j	NOUN
cana-3291	77	78	x	x	PUNCT
cana-3291	77	79	w	w	PROPN
cana-3291	77	80	x	x	SYM
cana-3291	77	81	t	t	NOUN
cana-3291	77	82	e	e	X
cana-3291	77	83	f	f	X
cana-3291	77	84	i	i	PRON
cana-3291	77	85	a	a	INTJ
cana-3291	77	86	wt	wt	INTJ
cana-3291	77	87	i	i	PRON
cana-3291	77	88	a	a	DET
cana-3291	77	89	w	w	NOUN
cana-3291	77	90			NOUN
cana-3291	77	91	=	=	PUNCT
cana-3291	78	1	=	=	PUNCT
cana-3291	79	1	+	+	NUM
cana-3291	79	2	−	−	PROPN
cana-3291	79	3	+	+	CCONJ
cana-3291	79	4			X
cana-3291	79	5	(	(	PUNCT
cana-3291	79	6	2.1	2.1	NUM
cana-3291	79	7	)	)	PUNCT
cana-3291	79	8	assume	assume	VERB
cana-3291	79	9	1	1	NUM
cana-3291	79	10	1	1	NUM
cana-3291	79	11	(	(	PUNCT
cana-3291	79	12	)	)	PUNCT
cana-3291	79	13	(	(	PUNCT
cana-3291	79	14	,	,	PUNCT
cana-3291	79	15	;	;	PUNCT
cana-3291	79	16	)	)	PUNCT
cana-3291	79	17	u	u	NOUN
cana-3291	79	18	x	x	X
cana-3291	79	19	f	f	X
cana-3291	79	20	u	u	X
cana-3291	79	21	e	e	X
cana-3291	79	22	f	f	PROPN
cana-3291	79	23	i	i	PRON
cana-3291	79	24	a	a	PRON
cana-3291	79	25	wu	wu	PROPN
cana-3291	79	26	w	w	PROPN
cana-3291	79	27	=	=	PUNCT
cana-3291	80	1	+	+	NUM
cana-3291	80	2	−	−	PROPN
cana-3291	80	3	(	(	PUNCT
cana-3291	80	4	2.2	2.2	NUM
cana-3291	80	5	)	)	PUNCT
cana-3291	80	6	using	use	VERB
cana-3291	80	7	maclaurin	maclaurin	NOUN
cana-3291	80	8	’s	’s	PART
cana-3291	80	9	theorem	theorem	NOUN
cana-3291	80	10	(	(	PUNCT
cana-3291	80	11	1.4	1.4	NUM
cana-3291	80	12	)	)	PUNCT
cana-3291	80	13	and	and	CCONJ
cana-3291	80	14	using	use	VERB
cana-3291	80	15	(	(	PUNCT
cana-3291	80	16	1.5	1.5	NUM
cana-3291	80	17	)	)	PUNCT
cana-3291	80	18	,	,	PUNCT
cana-3291	80	19	we	we	PRON
cana-3291	80	20	arrive	arrive	VERB
cana-3291	80	21	at	at	ADP
cana-3291	80	22	the	the	DET
cana-3291	80	23	following	following	NOUN
cana-3291	80	24	:	:	PUNCT
cana-3291	80	25	theorem	theorem	ADJ
cana-3291	80	26	:	:	PUNCT
cana-3291	80	27	assume	assume	VERB
cana-3291	80	28	‘	'	PUNCT
cana-3291	80	29	a	a	PRON
cana-3291	80	30	’	'	PUNCT
cana-3291	80	31	be	be	AUX
cana-3291	80	32	any	any	DET
cana-3291	80	33	square	square	ADJ
cana-3291	80	34	matrix	matrix	NOUN
cana-3291	80	35	of	of	ADP
cana-3291	80	36	order	order	NOUN
cana-3291	80	37	‘	'	PUNCT
cana-3291	80	38	n	n	CCONJ
cana-3291	80	39	’	'	PUNCT
cana-3291	80	40	,	,	PUNCT
cana-3291	80	41	0a	0a	NUM
cana-3291	80	42	communications	communication	NOUN
cana-3291	80	43	on	on	ADP
cana-3291	80	44	applied	apply	VERB
cana-3291	80	45	nonlinear	nonlinear	ADJ
cana-3291	80	46	analysis	analysis	NOUN
cana-3291	80	47	issn	issn	NOUN
cana-3291	80	48	:	:	PUNCT
cana-3291	80	49	1074	1074	NUM
cana-3291	80	50	-	-	PUNCT
cana-3291	80	51	133x	133x	NUM
cana-3291	80	52	vol	vol	NOUN
cana-3291	80	53	32	32	NUM
cana-3291	80	54	no	no	NOUN
cana-3291	80	55	.	.	PUNCT
cana-3291	81	1	6s	6s	NUM
cana-3291	81	2	(	(	PUNCT
cana-3291	81	3	2025	2025	NUM
cana-3291	81	4	)	)	PUNCT
cana-3291	81	5	256	256	NUM
cana-3291	81	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3291	81	7	0	0	NUM
cana-3291	81	8	(	(	PUNCT
cana-3291	81	9	)	)	PUNCT
cana-3291	81	10	1	1	NUM
cana-3291	81	11	1	1	NUM
cana-3291	81	12	1	1	NUM
cana-3291	81	13	(	(	PUNCT
cana-3291	81	14	)	)	PUNCT
cana-3291	81	15	(	(	PUNCT
cana-3291	81	16	,	,	PUNCT
cana-3291	81	17	)	)	PUNCT
cana-3291	81	18	,	,	PUNCT
cana-3291	81	19	;	;	PUNCT
cana-3291	81	20	2	2	NUM
cana-3291	81	21	a	a	PRON
cana-3291	81	22	n	n	X
cana-3291	81	23	un	un	PROPN
cana-3291	81	24	n	n	PROPN
cana-3291	81	25	a	a	PRON
cana-3291	82	1	i	i	NOUN
cana-3291	82	2	x	x	PROPN
cana-3291	82	3	j	j	NOUN
cana-3291	82	4	x	x	X
cana-3291	83	1	w	w	NOUN
cana-3291	83	2	u	u	NOUN
cana-3291	83	3	e	e	NOUN
cana-3291	83	4	f	f	PROPN
cana-3291	84	1	i	i	PRON
cana-3291	84	2	a	a	PRON
cana-3291	84	3	wu	wu	INTJ
cana-3291	84	4	du	du	NOUN
cana-3291	85	1	i	i	PRON
cana-3291	85	2	w	w	VERB
cana-3291	86	1	+	+	CCONJ
cana-3291	86	2	−	−	PROPN
cana-3291	86	3	−+	−+	PROPN
cana-3291	86	4			NOUN
cana-3291	86	5			NOUN
cana-3291	87	1	=	=	PUNCT
cana-3291	88	1	+	+	NUM
cana-3291	88	2	−	−	PROPN
cana-3291	88	3			CCONJ
cana-3291	89	1			PROPN
cana-3291	89	2			NOUN
cana-3291	89	3			PUNCT
cana-3291	89	4	where	where	SCONJ
cana-3291	89	5	the	the	DET
cana-3291	89	6	contour	contour	NOUN
cana-3291	89	7	integral	integral	NOUN
cana-3291	89	8	is	be	AUX
cana-3291	89	9	around	around	ADP
cana-3291	89	10	the	the	DET
cana-3291	89	11	u	u	NOUN
cana-3291	89	12	-	-	NOUN
cana-3291	89	13	plane	plane	NOUN
cana-3291	89	14	in	in	ADP
cana-3291	89	15	anti	anti	ADJ
cana-3291	89	16	-	-	ADJ
cana-3291	89	17	clockwise	clockwise	ADJ
cana-3291	89	18	sense	sense	NOUN
cana-3291	89	19	.	.	PUNCT
cana-3291	90	1	proof	proof	NOUN
cana-3291	90	2	:	:	PUNCT
cana-3291	90	3	using	use	VERB
cana-3291	90	4	maclaurin	maclaurin	NOUN
cana-3291	90	5	’s	’s	PART
cana-3291	90	6	theorem	theorem	NOUN
cana-3291	90	7	,	,	PUNCT
cana-3291	90	8	we	we	PRON
cana-3291	90	9	have	have	VERB
cana-3291	90	10	(	(	PUNCT
cana-3291	90	11	)	)	PUNCT
cana-3291	90	12	0	0	NUM
cana-3291	91	1	(	(	PUNCT
cana-3291	91	2	0	0	NUM
cana-3291	91	3	)	)	PUNCT
cana-3291	91	4	(	(	PUNCT
cana-3291	91	5	)	)	PUNCT
cana-3291	91	6	!	!	PUNCT
cana-3291	92	1	n	n	CCONJ
cana-3291	92	2	n	n	CCONJ
cana-3291	92	3	n	n	NOUN
cana-3291	92	4	f	f	NOUN
cana-3291	92	5	u	u	NOUN
cana-3291	92	6	f	f	PROPN
cana-3291	92	7	u	u	NOUN
cana-3291	92	8	n	n	ADV
cana-3291	92	9			VERB
cana-3291	92	10	=	=	PUNCT
cana-3291	93	1	=	=	NOUN
cana-3291	93	2			X
cana-3291	93	3	0	0	NUM
cana-3291	93	4	(	(	PUNCT
cana-3291	93	5	)	)	PUNCT
cana-3291	93	6	1	1	NUM
cana-3291	93	7	!	!	PUNCT
cana-3291	94	1	(	(	PUNCT
cana-3291	94	2	)	)	PUNCT
cana-3291	94	3	(	(	PUNCT
cana-3291	94	4	0	0	NUM
cana-3291	94	5	)	)	PUNCT
cana-3291	94	6	;	;	PUNCT
cana-3291	95	1	0,1	0,1	NUM
cana-3291	95	2	,	,	PUNCT
cana-3291	95	3	2	2	NUM
cana-3291	95	4	n	n	NOUN
cana-3291	95	5	n	n	CCONJ
cana-3291	95	6	n	n	NOUN
cana-3291	95	7	f	f	NOUN
cana-3291	95	8	u	u	X
cana-3291	95	9	f	f	PROPN
cana-3291	95	10	du	du	PROPN
cana-3291	95	11	n	n	PROPN
cana-3291	95	12	i	i	PRON
cana-3291	95	13	u	u	ADJ
cana-3291	96	1	+	+	CCONJ
cana-3291	96	2	+	+	CCONJ
cana-3291	96	3			NOUN
cana-3291	96	4	=	=	NOUN
cana-3291	97	1	=	=	SYM
cana-3291	97	2	−−−	−−−	VERB
cana-3291	97	3	if	if	SCONJ
cana-3291	97	4	(	(	PUNCT
cana-3291	97	5	)	)	PUNCT
cana-3291	97	6	1	1	NUM
cana-3291	97	7	1	1	NUM
cana-3291	97	8	0	0	NUM
cana-3291	97	9	(	(	PUNCT
cana-3291	97	10	,	,	PUNCT
cana-3291	97	11	)	)	PUNCT
cana-3291	97	12	;	;	PUNCT
cana-3291	97	13	;	;	PUNCT
cana-3291	97	14	(	(	PUNCT
cana-3291	97	15	)	)	PUNCT
cana-3291	97	16	a	a	DET
cana-3291	97	17	u	u	NOUN
cana-3291	97	18	nn	nn	PROPN
cana-3291	97	19	n	n	PROPN
cana-3291	97	20	n	n	PRON
cana-3291	97	21	j	j	PROPN
cana-3291	97	22	x	x	SYM
cana-3291	97	23	wx	wx	PROPN
cana-3291	97	24	e	e	X
cana-3291	97	25	f	f	PROPN
cana-3291	97	26	i	i	PRON
cana-3291	97	27	a	a	DET
cana-3291	97	28	wu	wu	NOUN
cana-3291	97	29	u	u	PROPN
cana-3291	97	30	w	w	PROPN
cana-3291	97	31	i	i	PRON
cana-3291	97	32	a	a	DET
cana-3291	97	33			X
cana-3291	97	34	=	=	SYM
cana-3291	97	35			NOUN
cana-3291	97	36			NOUN
cana-3291	97	37	+	+	CCONJ
cana-3291	97	38	−	−	X
cana-3291	97	39	=	=	SYM
cana-3291	97	40			NOUN
cana-3291	97	41			NOUN
cana-3291	97	42	+	+	ADP
cana-3291	97	43			NOUN
cana-3291	97	44			PROPN
cana-3291	97	45			X
cana-3291	97	46	0	0	NUM
cana-3291	97	47	(	(	PUNCT
cana-3291	97	48	)	)	PUNCT
cana-3291	97	49	1	1	NUM
cana-3291	97	50	!	!	PUNCT
cana-3291	98	1	(	(	PUNCT
cana-3291	98	2	,	,	PUNCT
cana-3291	98	3	)	)	PUNCT
cana-3291	98	4	!	!	PUNCT
cana-3291	99	1	(	(	PUNCT
cana-3291	99	2	)	)	PUNCT
cana-3291	99	3	(	(	PUNCT
cana-3291	99	4	)	)	PUNCT
cana-3291	99	5	2	2	NUM
cana-3291	99	6	a	a	DET
cana-3291	99	7	n	n	CCONJ
cana-3291	99	8	n	n	CCONJ
cana-3291	99	9	n	n	CCONJ
cana-3291	99	10	n	n	ADV
cana-3291	99	11	j	j	NOUN
cana-3291	99	12	x	x	SYM
cana-3291	99	13	w	w	VERB
cana-3291	99	14	n	n	PROPN
cana-3291	99	15	f	f	NOUN
cana-3291	99	16	u	u	X
cana-3291	99	17	du	du	PROPN
cana-3291	99	18	i	i	PRON
cana-3291	99	19	a	a	PRON
cana-3291	100	1	i	i	NOUN
cana-3291	100	2	u	u	ADJ
cana-3291	101	1	+	+	CCONJ
cana-3291	101	2	+	+	CCONJ
cana-3291	101	3			NOUN
cana-3291	101	4	=	=	X
cana-3291	102	1	+	+	NUM
cana-3291	102	2			PUNCT
cana-3291	102	3	,	,	PUNCT
cana-3291	102	4	which	which	PRON
cana-3291	102	5	leads	lead	VERB
cana-3291	102	6	to	to	ADP
cana-3291	102	7	0	0	NUM
cana-3291	102	8	(	(	PUNCT
cana-3291	102	9	)	)	PUNCT
cana-3291	102	10	1	1	NUM
cana-3291	102	11	1	1	NUM
cana-3291	102	12	1	1	NUM
cana-3291	102	13	(	(	PUNCT
cana-3291	102	14	)	)	PUNCT
cana-3291	102	15	(	(	PUNCT
cana-3291	102	16	,	,	PUNCT
cana-3291	102	17	)	)	PUNCT
cana-3291	102	18	,	,	PUNCT
cana-3291	102	19	;	;	PUNCT
cana-3291	102	20	2	2	NUM
cana-3291	102	21	a	a	PRON
cana-3291	102	22	n	n	X
cana-3291	102	23	un	un	PROPN
cana-3291	102	24	n	n	PROPN
cana-3291	102	25	a	a	PRON
cana-3291	103	1	i	i	NOUN
cana-3291	103	2	x	x	PROPN
cana-3291	103	3	j	j	NOUN
cana-3291	103	4	x	x	X
cana-3291	104	1	w	w	NOUN
cana-3291	104	2	u	u	NOUN
cana-3291	104	3	e	e	NOUN
cana-3291	104	4	f	f	PROPN
cana-3291	105	1	i	i	PRON
cana-3291	105	2	a	a	PRON
cana-3291	105	3	wu	wu	INTJ
cana-3291	105	4	du	du	NOUN
cana-3291	106	1	i	i	PRON
cana-3291	106	2	w	w	VERB
cana-3291	107	1	+	+	CCONJ
cana-3291	107	2	−	−	PROPN
cana-3291	107	3	−+	−+	PROPN
cana-3291	107	4			NOUN
cana-3291	107	5			NOUN
cana-3291	108	1	=	=	PUNCT
cana-3291	109	1	+	+	NUM
cana-3291	109	2	−	−	PROPN
cana-3291	109	3			CCONJ
cana-3291	110	1			PROPN
cana-3291	110	2			NOUN
cana-3291	110	3			PUNCT
cana-3291	110	4	2	2	X
cana-3291	110	5	.	.	X
cana-3291	110	6	real	real	ADJ
cana-3291	110	7	integral	integral	ADJ
cana-3291	110	8	representation	representation	NOUN
cana-3291	110	9	theorem	theorem	VERB
cana-3291	110	10	:	:	PUNCT
cana-3291	110	11	if	if	SCONJ
cana-3291	110	12	‘	'	PUNCT
cana-3291	110	13	a	a	PRON
cana-3291	110	14	’	'	PUNCT
cana-3291	110	15	be	be	AUX
cana-3291	110	16	any	any	DET
cana-3291	110	17	square	square	ADJ
cana-3291	110	18	matrix	matrix	NOUN
cana-3291	110	19	of	of	ADP
cana-3291	110	20	order	order	NOUN
cana-3291	110	21	n	n	PRON
cana-3291	110	22	n	n	VERB
cana-3291	110	23	and	and	CCONJ
cana-3291	110	24	(	(	PUNCT
cana-3291	110	25	)	)	PUNCT
cana-3291	110	26	(	(	PUNCT
cana-3291	110	27	,	,	PUNCT
cana-3291	110	28	)	)	PUNCT
cana-3291	110	29	a	a	DET
cana-3291	110	30	nj	nj	PROPN
cana-3291	111	1	x	x	PUNCT
cana-3291	111	2	w	w	NOUN
cana-3291	111	3	be	be	AUX
cana-3291	111	4	the	the	DET
cana-3291	111	5	modified	modify	VERB
cana-3291	111	6	jacobi	jacobi	NOUN
cana-3291	111	7	matrix	matrix	NOUN
cana-3291	111	8	polynomial	polynomial	NOUN
cana-3291	111	9	,	,	PUNCT
cana-3291	111	10	then	then	ADV
cana-3291	111	11	the	the	DET
cana-3291	111	12	real	real	ADJ
cana-3291	111	13	integral	integral	ADJ
cana-3291	111	14	representations	representation	NOUN
cana-3291	111	15	of	of	ADP
cana-3291	111	16	this	this	DET
cana-3291	111	17	polynomial	polynomial	NOUN
cana-3291	111	18	are	be	AUX
cana-3291	111	19	as	as	SCONJ
cana-3291	111	20	follows	follow	VERB
cana-3291	111	21	:	:	PUNCT
cana-3291	111	22	(	(	PUNCT
cana-3291	111	23	)	)	PUNCT
cana-3291	111	24	,	,	PUNCT
cana-3291	111	25	0	0	NUM
cana-3291	111	26	0	0	NUM
cana-3291	111	27	(	(	PUNCT
cana-3291	111	28	)	)	PUNCT
cana-3291	111	29	(	(	PUNCT
cana-3291	111	30	)	)	PUNCT
cana-3291	111	31	(	(	PUNCT
cana-3291	111	32	,	,	PUNCT
cana-3291	111	33	)	)	PUNCT
cana-3291	111	34	(	(	PUNCT
cana-3291	111	35	)	)	PUNCT
cana-3291	111	36	!	!	PUNCT
cana-3291	112	1	(	(	PUNCT
cana-3291	112	2	)	)	PUNCT
cana-3291	112	3	r	r	NOUN
cana-3291	112	4	a	a	PRON
cana-3291	112	5	n	n	NOUN
cana-3291	112	6	r	r	NOUN
cana-3291	112	7	n	n	NOUN
cana-3291	112	8	r	r	NOUN
cana-3291	112	9	m	m	VERB
cana-3291	112	10	r	r	NOUN
cana-3291	112	11	x	x	PUNCT
cana-3291	112	12	w	w	ADP
cana-3291	112	13	a	a	PRON
cana-3291	112	14	i	i	NOUN
cana-3291	112	15	w	w	PROPN
cana-3291	112	16	j	j	PROPN
cana-3291	112	17	x	x	X
cana-3291	112	18	w	w	VERB
cana-3291	112	19	cis	cis	NOUN
cana-3291	112	20	m	m	PROPN
cana-3291	112	21	r	r	NOUN
cana-3291	112	22	n	n	NOUN
cana-3291	112	23	d	d	NOUN
cana-3291	112	24	r	r	NOUN
cana-3291	112	25	i	i	PRON
cana-3291	113	1	a	a	DET
cana-3291	113	2			X
cana-3291	113	3			X
cana-3291	113	4			X
cana-3291	113	5			PROPN
cana-3291	113	6			X
cana-3291	113	7	=	=	PUNCT
cana-3291	114	1			NOUN
cana-3291	114	2			PROPN
cana-3291	114	3	−	−	PROPN
cana-3291	114	4			PROPN
cana-3291	115	1	+	+	CCONJ
cana-3291	115	2			PROPN
cana-3291	115	3			NOUN
cana-3291	115	4	=	=	PUNCT
cana-3291	116	1	+	+	CCONJ
cana-3291	116	2	−	−	PROPN
cana-3291	116	3	+	+	CCONJ
cana-3291	116	4			X
cana-3291	116	5			PUNCT
cana-3291	116	6	(	(	PUNCT
cana-3291	116	7	3.1	3.1	NUM
cana-3291	116	8	)	)	PUNCT
cana-3291	116	9	proof	proof	NOUN
cana-3291	116	10	:	:	PUNCT
cana-3291	116	11	using	use	VERB
cana-3291	116	12	(	(	PUNCT
cana-3291	116	13	1.14	1.14	NUM
cana-3291	116	14	)	)	PUNCT
cana-3291	116	15	,	,	PUNCT
cana-3291	116	16	it	it	PRON
cana-3291	116	17	reduces	reduce	VERB
cana-3291	116	18	to	to	PART
cana-3291	116	19	(	(	PUNCT
cana-3291	116	20	by	by	ADP
cana-3291	116	21	choosing	choose	VERB
cana-3291	116	22	the	the	DET
cana-3291	116	23	contour	contour	NOUN
cana-3291	116	24	iu	iu	ADP
cana-3291	116	25	e	e	NOUN
cana-3291	116	26	=	=	X
cana-3291	116	27	(	(	PUNCT
cana-3291	116	28	)	)	PUNCT
cana-3291	116	29	2	2	NUM
cana-3291	116	30	(	(	PUNCT
cana-3291	116	31	)	)	PUNCT
cana-3291	116	32	(	(	PUNCT
cana-3291	116	33	1	1	NUM
cana-3291	116	34	)	)	PUNCT
cana-3291	116	35	00	00	PUNCT
cana-3291	117	1	(	(	PUNCT
cana-3291	117	2	)	)	PUNCT
cana-3291	117	3	(	(	PUNCT
cana-3291	117	4	,	,	PUNCT
cana-3291	117	5	)	)	PUNCT
cana-3291	117	6	!	!	PUNCT
cana-3291	118	1	(	(	PUNCT
cana-3291	118	2	2	2	NUM
cana-3291	118	3	)	)	PUNCT
cana-3291	118	4	!	!	PUNCT
cana-3291	119	1	(	(	PUNCT
cana-3291	119	2	)	)	PUNCT
cana-3291	120	1	i	i	PRON
cana-3291	120	2	r	r	NOUN
cana-3291	120	3	r	r	NOUN
cana-3291	120	4	i	i	PRON
cana-3291	120	5	a	a	DET
cana-3291	120	6	e	e	NOUN
cana-3291	120	7	i	i	PRON
cana-3291	120	8	n	n	PROPN
cana-3291	120	9	in	in	ADP
cana-3291	120	10	r	r	NOUN
cana-3291	120	11	n	n	CCONJ
cana-3291	120	12	r	r	NOUN
cana-3291	120	13	r	r	NOUN
cana-3291	120	14	x	x	PUNCT
cana-3291	120	15	w	w	NOUN
cana-3291	120	16	e	e	NOUN
cana-3291	120	17	a	a	PRON
cana-3291	120	18	i	i	PROPN
cana-3291	120	19	w	w	PROPN
cana-3291	120	20	j	j	PROPN
cana-3291	120	21	x	x	X
cana-3291	120	22	w	w	PROPN
cana-3291	120	23	e	e	X
cana-3291	120	24	e	e	X
cana-3291	120	25	ie	ie	X
cana-3291	120	26	d	d	PROPN
cana-3291	120	27	n	n	NOUN
cana-3291	121	1	i	i	PRON
cana-3291	121	2	r	r	VERB
cana-3291	121	3	i	i	PRON
cana-3291	121	4	a	a	PRON
cana-3291	121	5			X
cana-3291	121	6			X
cana-3291	121	7			PROPN
cana-3291	121	8			X
cana-3291	121	9			X
cana-3291	121	10			PROPN
cana-3291	122	1			PROPN
cana-3291	122	2			NOUN
cana-3291	122	3	−	−	ADP
cana-3291	122	4	−	−	NOUN
cana-3291	123	1	=	=	NOUN
cana-3291	123	2			NOUN
cana-3291	123	3			NOUN
cana-3291	123	4			PROPN
cana-3291	123	5			PROPN
cana-3291	124	1	+	+	CCONJ
cana-3291	124	2			PROPN
cana-3291	124	3			NOUN
cana-3291	124	4	=	=	PUNCT
cana-3291	125	1	+	+	NUM
cana-3291	125	2			NUM
cana-3291	125	3	2	2	NUM
cana-3291	125	4	0	0	NUM
cana-3291	125	5	00	00	PUNCT
cana-3291	125	6	(	(	PUNCT
cana-3291	125	7	)	)	PUNCT
cana-3291	125	8	(	(	PUNCT
cana-3291	125	9	)	)	PUNCT
cana-3291	125	10	(	(	PUNCT
cana-3291	125	11	)	)	PUNCT
cana-3291	125	12	!	!	PUNCT
cana-3291	126	1	(	(	PUNCT
cana-3291	126	2	2	2	X
cana-3291	126	3	)	)	PUNCT
cana-3291	126	4	!	!	PUNCT
cana-3291	126	5	!	!	PUNCT
cana-3291	127	1	(	(	PUNCT
cana-3291	127	2	)	)	PUNCT
cana-3291	127	3	r	r	NOUN
cana-3291	127	4	ri	ri	INTJ
cana-3291	128	1	i	i	PRON
cana-3291	128	2	m	m	VERB
cana-3291	128	3	nin	nin	NOUN
cana-3291	128	4	r	r	NOUN
cana-3291	128	5	m	m	NOUN
cana-3291	128	6	r	r	NOUN
cana-3291	128	7	r	r	NOUN
cana-3291	128	8	x	x	PUNCT
cana-3291	128	9	w	w	NOUN
cana-3291	128	10	e	e	NOUN
cana-3291	128	11	a	a	X
cana-3291	128	12	i	i	NOUN
cana-3291	128	13	e	e	NOUN
cana-3291	128	14	w	w	PROPN
cana-3291	128	15	e	e	PROPN
cana-3291	128	16	d	d	PROPN
cana-3291	128	17	n	n	PROPN
cana-3291	128	18	m	m	VERB
cana-3291	128	19	r	r	NOUN
cana-3291	128	20	i	i	PRON
cana-3291	128	21	a	a	DET
cana-3291	128	22			X
cana-3291	128	23			X
cana-3291	128	24			X
cana-3291	128	25			X
cana-3291	128	26			PROPN
cana-3291	129	1			PROPN
cana-3291	129	2			VERB
cana-3291	129	3			VERB
cana-3291	129	4	−	−	NOUN
cana-3291	129	5	=	=	SYM
cana-3291	130	1	=	=	NOUN
cana-3291	130	2			NOUN
cana-3291	130	3			PROPN
cana-3291	130	4	−	−	PROPN
cana-3291	130	5			PROPN
cana-3291	131	1	+	+	CCONJ
cana-3291	131	2			PROPN
cana-3291	131	3			NOUN
cana-3291	131	4	=	=	SYM
cana-3291	132	1	+	+	CCONJ
cana-3291	132	2			X
cana-3291	132	3			NUM
cana-3291	132	4	by	by	ADP
cana-3291	132	5	changing	change	VERB
cana-3291	132	6	the	the	DET
cana-3291	132	7	order	order	NOUN
cana-3291	132	8	of	of	ADP
cana-3291	132	9	summation	summation	NOUN
cana-3291	132	10	and	and	CCONJ
cana-3291	132	11	integration	integration	NOUN
cana-3291	132	12	,	,	PUNCT
cana-3291	132	13	we	we	PRON
cana-3291	132	14	obtain	obtain	VERB
cana-3291	132	15	communications	communication	NOUN
cana-3291	132	16	on	on	ADP
cana-3291	132	17	applied	apply	VERB
cana-3291	132	18	nonlinear	nonlinear	ADJ
cana-3291	132	19	analysis	analysis	NOUN
cana-3291	132	20	issn	issn	NOUN
cana-3291	132	21	:	:	PUNCT
cana-3291	132	22	1074	1074	NUM
cana-3291	132	23	-	-	PUNCT
cana-3291	132	24	133x	133x	NUM
cana-3291	132	25	vol	vol	NOUN
cana-3291	132	26	32	32	NUM
cana-3291	132	27	no	no	NOUN
cana-3291	132	28	.	.	PUNCT
cana-3291	133	1	6s	6s	NUM
cana-3291	133	2	(	(	PUNCT
cana-3291	133	3	2025	2025	NUM
cana-3291	133	4	)	)	PUNCT
cana-3291	133	5	257	257	NUM
cana-3291	133	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3291	133	7	2	2	NUM
cana-3291	133	8	(	(	PUNCT
cana-3291	133	9	)	)	PUNCT
cana-3291	133	10	,	,	PUNCT
cana-3291	133	11	0	0	NUM
cana-3291	133	12	0	0	NUM
cana-3291	134	1	(	(	PUNCT
cana-3291	134	2	)	)	PUNCT
cana-3291	134	3	(	(	PUNCT
cana-3291	134	4	)	)	PUNCT
cana-3291	134	5	!	!	PUNCT
cana-3291	135	1	(	(	PUNCT
cana-3291	135	2	2	2	NUM
cana-3291	135	3	)	)	PUNCT
cana-3291	135	4	!	!	PUNCT
cana-3291	136	1	(	(	PUNCT
cana-3291	136	2	)	)	PUNCT
cana-3291	136	3	r	r	NOUN
cana-3291	136	4	m	m	VERB
cana-3291	136	5	n	n	ADV
cana-3291	136	6	r	r	NOUN
cana-3291	136	7	in	in	ADP
cana-3291	136	8	r	r	NOUN
cana-3291	136	9	r	r	NOUN
cana-3291	136	10	m	m	NOUN
cana-3291	136	11	r	r	NOUN
cana-3291	136	12	x	x	PUNCT
cana-3291	136	13	w	w	ADP
cana-3291	136	14	a	a	PRON
cana-3291	136	15	i	i	NOUN
cana-3291	136	16	w	w	PROPN
cana-3291	136	17	e	e	PROPN
cana-3291	136	18	d	d	PROPN
cana-3291	136	19	n	n	NOUN
cana-3291	136	20	r	r	NOUN
cana-3291	136	21	i	i	PRON
cana-3291	137	1	a	a	DET
cana-3291	137	2			X
cana-3291	137	3			X
cana-3291	137	4			X
cana-3291	137	5			PROPN
cana-3291	137	6			VERB
cana-3291	137	7	−	−	ADP
cana-3291	138	1	+	+	CCONJ
cana-3291	138	2	=	=	NOUN
cana-3291	138	3			NOUN
cana-3291	138	4			PROPN
cana-3291	138	5	−	−	PROPN
cana-3291	138	6			PROPN
cana-3291	139	1	+	+	CCONJ
cana-3291	139	2			PROPN
cana-3291	139	3			NOUN
cana-3291	139	4	=	=	SYM
cana-3291	140	1	+	+	CCONJ
cana-3291	140	2			X
cana-3291	140	3			ADP
cana-3291	140	4	2	2	NUM
cana-3291	140	5	,	,	PUNCT
cana-3291	140	6	0	0	NUM
cana-3291	140	7	0	0	NUM
cana-3291	140	8	(	(	PUNCT
cana-3291	140	9	)	)	PUNCT
cana-3291	140	10	(	(	PUNCT
cana-3291	140	11	)	)	PUNCT
cana-3291	140	12	(	(	PUNCT
cana-3291	140	13	)	)	PUNCT
cana-3291	140	14	(	(	PUNCT
cana-3291	140	15	2	2	NUM
cana-3291	140	16	)	)	PUNCT
cana-3291	140	17	!	!	PUNCT
cana-3291	141	1	(	(	PUNCT
cana-3291	141	2	)	)	PUNCT
cana-3291	141	3	r	r	NOUN
cana-3291	141	4	n	n	NOUN
cana-3291	141	5	r	r	NOUN
cana-3291	141	6	r	r	NOUN
cana-3291	141	7	m	m	VERB
cana-3291	141	8	r	r	NOUN
cana-3291	141	9	x	x	PUNCT
cana-3291	141	10	w	w	ADP
cana-3291	141	11	a	a	X
cana-3291	141	12	i	i	NOUN
cana-3291	141	13	w	w	VERB
cana-3291	141	14	cis	cis	NOUN
cana-3291	141	15	m	m	PROPN
cana-3291	141	16	r	r	NOUN
cana-3291	141	17	n	n	NOUN
cana-3291	142	1	d	d	NOUN
cana-3291	142	2	r	r	NOUN
cana-3291	142	3	i	i	PRON
cana-3291	143	1	a	a	DET
cana-3291	143	2			ADJ
cana-3291	143	3			X
cana-3291	143	4			NOUN
cana-3291	143	5			NOUN
cana-3291	143	6	=	=	PUNCT
cana-3291	143	7			NOUN
cana-3291	143	8			PROPN
cana-3291	143	9	−	−	PROPN
cana-3291	143	10			PROPN
cana-3291	144	1	+	+	CCONJ
cana-3291	144	2			PROPN
cana-3291	144	3			NOUN
cana-3291	144	4	=	=	PUNCT
cana-3291	145	1	+	+	CCONJ
cana-3291	145	2	−	−	PROPN
cana-3291	145	3	+	+	CCONJ
cana-3291	145	4			X
cana-3291	145	5			PUNCT
cana-3291	145	6	consequently	consequently	ADV
cana-3291	145	7	,	,	PUNCT
cana-3291	145	8	we	we	PRON
cana-3291	145	9	arrive	arrive	VERB
cana-3291	145	10	at	at	ADP
cana-3291	145	11	(	(	PUNCT
cana-3291	145	12	)	)	PUNCT
cana-3291	145	13	,	,	PUNCT
cana-3291	145	14	0	0	NUM
cana-3291	145	15	0	0	NUM
cana-3291	145	16	(	(	PUNCT
cana-3291	145	17	)	)	PUNCT
cana-3291	145	18	(	(	PUNCT
cana-3291	145	19	)	)	PUNCT
cana-3291	145	20	(	(	PUNCT
cana-3291	145	21	,	,	PUNCT
cana-3291	145	22	)	)	PUNCT
cana-3291	145	23	(	(	PUNCT
cana-3291	145	24	)	)	PUNCT
cana-3291	145	25	!	!	PUNCT
cana-3291	146	1	(	(	PUNCT
cana-3291	146	2	)	)	PUNCT
cana-3291	146	3	r	r	NOUN
cana-3291	146	4	a	a	PRON
cana-3291	146	5	n	n	NOUN
cana-3291	146	6	r	r	NOUN
cana-3291	146	7	n	n	NOUN
cana-3291	146	8	r	r	NOUN
cana-3291	146	9	m	m	VERB
cana-3291	146	10	r	r	NOUN
cana-3291	146	11	x	x	PUNCT
cana-3291	146	12	w	w	ADP
cana-3291	146	13	a	a	PRON
cana-3291	146	14	i	i	NOUN
cana-3291	146	15	w	w	PROPN
cana-3291	146	16	j	j	PROPN
cana-3291	146	17	x	x	X
cana-3291	146	18	w	w	VERB
cana-3291	146	19	cis	cis	NOUN
cana-3291	146	20	m	m	PROPN
cana-3291	146	21	r	r	NOUN
cana-3291	146	22	n	n	NOUN
cana-3291	146	23	d	d	NOUN
cana-3291	146	24	r	r	NOUN
cana-3291	146	25	i	i	PRON
cana-3291	147	1	a	a	DET
cana-3291	147	2			X
cana-3291	147	3			X
cana-3291	147	4			X
cana-3291	147	5			PROPN
cana-3291	147	6			X
cana-3291	147	7	=	=	PUNCT
cana-3291	148	1			NOUN
cana-3291	148	2			PROPN
cana-3291	148	3	−	−	PROPN
cana-3291	148	4			PROPN
cana-3291	149	1	+	+	CCONJ
cana-3291	149	2			PROPN
cana-3291	149	3			NOUN
cana-3291	149	4	=	=	PUNCT
cana-3291	150	1	+	+	CCONJ
cana-3291	150	2	−	−	PROPN
cana-3291	151	1	+	+	CCONJ
cana-3291	151	2			X
cana-3291	151	3			PUNCT
cana-3291	151	4	4	4	X
cana-3291	151	5	.	.	X
cana-3291	151	6	finite	finite	VERB
cana-3291	151	7	single	single	ADJ
cana-3291	151	8	integral	integral	ADJ
cana-3291	151	9	representation	representation	NOUN
cana-3291	151	10	theorem	theorem	NOUN
cana-3291	151	11	1	1	NUM
cana-3291	151	12	:	:	PUNCT
cana-3291	151	13	assume	assume	VERB
cana-3291	151	14	‘	'	PUNCT
cana-3291	151	15	a	a	DET
cana-3291	151	16	’	'	PUNCT
cana-3291	151	17	be	be	AUX
cana-3291	151	18	any	any	DET
cana-3291	151	19	square	square	ADJ
cana-3291	151	20	matrix	matrix	NOUN
cana-3291	151	21	of	of	ADP
cana-3291	151	22	order	order	NOUN
cana-3291	151	23	‘	'	PUNCT
cana-3291	151	24	n	n	CCONJ
cana-3291	151	25	’	'	PUNCT
cana-3291	151	26	,	,	PUNCT
cana-3291	151	27	0a	0a	NUM
cana-3291	151	28	.	.	PUNCT
cana-3291	152	1	if	if	SCONJ
cana-3291	152	2	re	re	VERB
cana-3291	152	3	(	(	PUNCT
cana-3291	152	4	)	)	PUNCT
cana-3291	152	5	a	a	PRON
cana-3291	152	6	and	and	CCONJ
cana-3291	152	7	re	re	ADP
cana-3291	152	8	(	(	PUNCT
cana-3291	152	9	)	)	PUNCT
cana-3291	152	10	b	b	NOUN
cana-3291	152	11	a−	a−	PROPN
cana-3291	152	12	are	be	AUX
cana-3291	152	13	positive	positive	ADJ
cana-3291	152	14	,	,	PUNCT
cana-3291	152	15	then	then	ADV
cana-3291	152	16	(	(	PUNCT
cana-3291	152	17	)	)	PUNCT
cana-3291	152	18	(	(	PUNCT
cana-3291	152	19	)	)	PUNCT
cana-3291	152	20	(	(	PUNCT
cana-3291	152	21	)	)	PUNCT
cana-3291	152	22	1	1	NUM
cana-3291	152	23	1	1	NUM
cana-3291	152	24	1	1	NUM
cana-3291	152	25	(	(	PUNCT
cana-3291	152	26	)	)	PUNCT
cana-3291	152	27	3	3	NUM
cana-3291	152	28	2	2	NUM
cana-3291	152	29	0	0	NUM
cana-3291	152	30	,	,	PUNCT
cana-3291	152	31	,	,	PUNCT
cana-3291	152	32	;	;	PUNCT
cana-3291	152	33	(	(	PUNCT
cana-3291	152	34	1	1	X
cana-3291	152	35	)	)	PUNCT
cana-3291	152	36	(	(	PUNCT
cana-3291	152	37	,	,	PUNCT
cana-3291	152	38	)	)	PUNCT
cana-3291	152	39	,	,	PUNCT
cana-3291	152	40	;	;	PUNCT
cana-3291	152	41	a	a	DET
cana-3291	152	42	b	b	NOUN
cana-3291	152	43	a	a	PRON
cana-3291	152	44	a	a	DET
cana-3291	152	45	n	n	NOUN
cana-3291	152	46	x	x	SYM
cana-3291	152	47	b	b	PROPN
cana-3291	152	48	ni	ni	PROPN
cana-3291	152	49	bt	bt	PROPN
cana-3291	152	50	t	t	PROPN
cana-3291	152	51	j	j	PROPN
cana-3291	152	52	x	x	X
cana-3291	152	53	w	w	PROPN
cana-3291	152	54	f	f	PROPN
cana-3291	152	55	wt	wt	PROPN
cana-3291	152	56	dtw	dtw	PROPN
cana-3291	152	57	a	a	DET
cana-3291	152	58	b	b	PROPN
cana-3291	152	59	a	a	PRON
cana-3291	152	60	i	i	PRON
cana-3291	152	61	a	a	DET
cana-3291	152	62	a	a	DET
cana-3291	152	63	−	−	NOUN
cana-3291	152	64	−	−	NOUN
cana-3291	152	65	−	−	PROPN
cana-3291	152	66			PROPN
cana-3291	152	67			ADJ
cana-3291	152	68			ADJ
cana-3291	152	69	−−	−−	NOUN
cana-3291	152	70			NOUN
cana-3291	152	71	=	=	SYM
cana-3291	152	72			NOUN
cana-3291	152	73			NOUN
cana-3291	152	74			VERB
cana-3291	153	1	−	−	PROPN
cana-3291	153	2	+	+	NOUN
cana-3291	153	3			PROPN
cana-3291	153	4			PROPN
cana-3291	153	5			X
cana-3291	153	6	(	(	PUNCT
cana-3291	153	7	4.1	4.1	NUM
cana-3291	153	8	)	)	PUNCT
cana-3291	153	9	proof	proof	NOUN
cana-3291	153	10	:	:	PUNCT
cana-3291	153	11	by	by	ADP
cana-3291	153	12	using	use	VERB
cana-3291	153	13	(	(	PUNCT
cana-3291	153	14	1.3	1.3	NUM
cana-3291	153	15	)	)	PUNCT
cana-3291	153	16	(	(	PUNCT
cana-3291	153	17	)	)	PUNCT
cana-3291	153	18	(	(	PUNCT
cana-3291	153	19	)	)	PUNCT
cana-3291	153	20	0	0	NUM
cana-3291	154	1	(	(	PUNCT
cana-3291	154	2	)	)	PUNCT
cana-3291	154	3	(	(	PUNCT
cana-3291	154	4	,	,	PUNCT
cana-3291	154	5	)	)	PUNCT
cana-3291	154	6	!	!	PUNCT
cana-3291	155	1	!	!	PUNCT
cana-3291	156	1	(	(	PUNCT
cana-3291	156	2	)	)	PUNCT
cana-3291	156	3	r	r	NOUN
cana-3291	156	4	n	n	NOUN
cana-3291	156	5	r	r	NOUN
cana-3291	156	6	a	a	PRON
cana-3291	156	7	n	n	NOUN
cana-3291	156	8	r	r	NOUN
cana-3291	156	9	n	n	NOUN
cana-3291	156	10	r	r	NOUN
cana-3291	156	11	r	r	NOUN
cana-3291	156	12	x	x	SYM
cana-3291	156	13	ni	ni	PROPN
cana-3291	156	14	w	w	PROPN
cana-3291	156	15	a	a	PROPN
cana-3291	156	16	i	i	PROPN
cana-3291	156	17	w	w	PROPN
cana-3291	156	18	j	j	PROPN
cana-3291	156	19	x	x	SYM
cana-3291	156	20	w	w	PROPN
cana-3291	156	21	n	n	ADP
cana-3291	156	22	r	r	NOUN
cana-3291	156	23	i	i	PRON
cana-3291	156	24	a=	a=	VERB
cana-3291	156	25			NOUN
cana-3291	156	26			PROPN
cana-3291	156	27	−	−	PROPN
cana-3291	157	1			PROPN
cana-3291	157	2			PROPN
cana-3291	158	1	+	+	CCONJ
cana-3291	158	2			PROPN
cana-3291	158	3			NOUN
cana-3291	158	4	=	=	SYM
cana-3291	159	1	+	+	CCONJ
cana-3291	159	2			X
cana-3291	159	3	(	(	PUNCT
cana-3291	159	4	)	)	PUNCT
cana-3291	159	5	(	(	PUNCT
cana-3291	159	6	)	)	PUNCT
cana-3291	159	7	(	(	PUNCT
cana-3291	159	8	)	)	PUNCT
cana-3291	159	9	(	(	PUNCT
cana-3291	159	10	)	)	PUNCT
cana-3291	159	11	(	(	PUNCT
cana-3291	159	12	)	)	PUNCT
cana-3291	159	13	0	0	NUM
cana-3291	159	14	(	(	PUNCT
cana-3291	159	15	)	)	PUNCT
cana-3291	159	16	!	!	PUNCT
cana-3291	159	17	!	!	PUNCT
cana-3291	160	1	(	(	PUNCT
cana-3291	160	2	)	)	PUNCT
cana-3291	160	3	r	r	NOUN
cana-3291	160	4	n	n	NOUN
cana-3291	160	5	r	r	NOUN
cana-3291	160	6	r	r	NOUN
cana-3291	160	7	r	r	NOUN
cana-3291	160	8	n	n	NOUN
cana-3291	160	9	r	r	NOUN
cana-3291	160	10	r	r	NOUN
cana-3291	160	11	r	r	NOUN
cana-3291	160	12	r	r	NOUN
cana-3291	160	13	r	r	NOUN
cana-3291	160	14	x	x	SYM
cana-3291	160	15	ni	ni	PROPN
cana-3291	160	16	w	w	PROPN
cana-3291	160	17	b	b	PROPN
cana-3291	160	18	a	a	PRON
cana-3291	160	19	a	a	DET
cana-3291	160	20	i	i	NOUN
cana-3291	160	21	w	w	PROPN
cana-3291	161	1	n	n	ADP
cana-3291	162	1	r	r	NOUN
cana-3291	163	1	i	i	PRON
cana-3291	164	1	a	a	DET
cana-3291	164	2	a	a	DET
cana-3291	164	3	b=	b=	NOUN
cana-3291	164	4			NOUN
cana-3291	164	5			PROPN
cana-3291	164	6	−	−	PROPN
cana-3291	164	7			PROPN
cana-3291	164	8			PROPN
cana-3291	165	1	+	+	CCONJ
cana-3291	165	2			PROPN
cana-3291	165	3			NOUN
cana-3291	165	4	=	=	SYM
cana-3291	166	1	+	+	CCONJ
cana-3291	166	2			X
cana-3291	166	3	on	on	ADP
cana-3291	166	4	using	use	VERB
cana-3291	166	5	(	(	PUNCT
cana-3291	166	6	1.5	1.5	NUM
cana-3291	166	7	)	)	PUNCT
cana-3291	166	8	,	,	PUNCT
cana-3291	166	9	we	we	PRON
cana-3291	166	10	have	have	VERB
cana-3291	166	11	(	(	PUNCT
cana-3291	166	12	)	)	PUNCT
cana-3291	166	13	(	(	PUNCT
cana-3291	166	14	)	)	PUNCT
cana-3291	166	15	(	(	PUNCT
cana-3291	166	16	)	)	PUNCT
cana-3291	166	17	(	(	PUNCT
cana-3291	166	18	)	)	PUNCT
cana-3291	166	19	(	(	PUNCT
cana-3291	166	20	)	)	PUNCT
cana-3291	166	21	(	(	PUNCT
cana-3291	166	22	)	)	PUNCT
cana-3291	166	23	1	1	NUM
cana-3291	166	24	1	1	NUM
cana-3291	166	25	1	1	NUM
cana-3291	166	26	0	0	NUM
cana-3291	166	27	0	0	NUM
cana-3291	166	28	(	(	PUNCT
cana-3291	166	29	)	)	PUNCT
cana-3291	166	30	(	(	PUNCT
cana-3291	166	31	1	1	NUM
cana-3291	166	32	)	)	PUNCT
cana-3291	166	33	!	!	PUNCT
cana-3291	166	34	!	!	PUNCT
cana-3291	167	1	(	(	PUNCT
cana-3291	167	2	)	)	PUNCT
cana-3291	167	3	r	r	NOUN
cana-3291	167	4	n	n	NOUN
cana-3291	167	5	r	r	NOUN
cana-3291	167	6	r	r	NOUN
cana-3291	167	7	a	a	DET
cana-3291	167	8	r	r	NOUN
cana-3291	167	9	b	b	NOUN
cana-3291	167	10	an	an	DET
cana-3291	167	11	r	r	NOUN
cana-3291	167	12	r	r	NOUN
cana-3291	167	13	r	r	NOUN
cana-3291	167	14	r	r	NOUN
cana-3291	167	15	x	x	SYM
cana-3291	167	16	ni	ni	PROPN
cana-3291	167	17	w	w	PROPN
cana-3291	167	18	b	b	PROPN
cana-3291	167	19	b	b	PROPN
cana-3291	167	20	a	a	PRON
cana-3291	168	1	i	i	NOUN
cana-3291	168	2	w	w	PROPN
cana-3291	168	3	t	t	PROPN
cana-3291	168	4	t	t	PROPN
cana-3291	168	5	dt	dt	X
cana-3291	168	6	n	n	CCONJ
cana-3291	168	7	r	r	NOUN
cana-3291	168	8	i	i	PRON
cana-3291	168	9	a	a	DET
cana-3291	168	10	a	a	DET
cana-3291	168	11	a	a	DET
cana-3291	168	12	b	b	NOUN
cana-3291	168	13	a	a	NOUN
cana-3291	168	14	+	+	NOUN
cana-3291	168	15	−	−	ADP
cana-3291	168	16	−	−	NOUN
cana-3291	168	17	−	−	NOUN
cana-3291	169	1	=	=	NOUN
cana-3291	169	2			NOUN
cana-3291	169	3			NOUN
cana-3291	169	4	−	−	PROPN
cana-3291	169	5			PROPN
cana-3291	169	6			PROPN
cana-3291	169	7	+	+	CCONJ
cana-3291	169	8			PROPN
cana-3291	169	9			NOUN
cana-3291	169	10	=	=	SYM
cana-3291	169	11	−	−	PROPN
cana-3291	170	1	+	+	CCONJ
cana-3291	170	2			PROPN
cana-3291	170	3			VERB
cana-3291	170	4	−	−	NOUN
cana-3291	170	5			X
cana-3291	170	6			PUNCT
cana-3291	170	7	by	by	ADP
cana-3291	170	8	interchanging	interchange	VERB
cana-3291	170	9	the	the	DET
cana-3291	170	10	order	order	NOUN
cana-3291	170	11	of	of	ADP
cana-3291	170	12	integration	integration	NOUN
cana-3291	170	13	and	and	CCONJ
cana-3291	170	14	summation	summation	NOUN
cana-3291	170	15	,	,	PUNCT
cana-3291	170	16	we	we	PRON
cana-3291	170	17	have	have	VERB
cana-3291	170	18	(	(	PUNCT
cana-3291	170	19	)	)	PUNCT
cana-3291	170	20	(	(	PUNCT
cana-3291	170	21	)	)	PUNCT
cana-3291	170	22	(	(	PUNCT
cana-3291	170	23	)	)	PUNCT
cana-3291	170	24	(	(	PUNCT
cana-3291	170	25	)	)	PUNCT
cana-3291	170	26	(	(	PUNCT
cana-3291	170	27	)	)	PUNCT
cana-3291	170	28	(	(	PUNCT
cana-3291	170	29	)	)	PUNCT
cana-3291	170	30	1	1	NUM
cana-3291	170	31	1	1	NUM
cana-3291	170	32	1	1	NUM
cana-3291	170	33	00	00	NUM
cana-3291	170	34	(	(	PUNCT
cana-3291	170	35	)	)	PUNCT
cana-3291	170	36	(	(	PUNCT
cana-3291	170	37	)	)	PUNCT
cana-3291	170	38	(	(	PUNCT
cana-3291	170	39	1	1	NUM
cana-3291	170	40	)	)	PUNCT
cana-3291	170	41	!	!	PUNCT
cana-3291	170	42	!	!	PUNCT
cana-3291	171	1	(	(	PUNCT
cana-3291	171	2	)	)	PUNCT
cana-3291	171	3	r	r	NOUN
cana-3291	171	4	n	n	NOUN
cana-3291	171	5	r	r	NOUN
cana-3291	171	6	r	r	NOUN
cana-3291	171	7	a	a	DET
cana-3291	171	8	b	b	NOUN
cana-3291	171	9	a	a	PRON
cana-3291	171	10	n	n	NOUN
cana-3291	171	11	r	r	NOUN
cana-3291	171	12	r	r	NOUN
cana-3291	171	13	r	r	NOUN
cana-3291	171	14	r	r	NOUN
cana-3291	171	15	x	x	SYM
cana-3291	171	16	ni	ni	PROPN
cana-3291	171	17	b	b	PROPN
cana-3291	171	18	wt	wt	PROPN
cana-3291	171	19	b	b	PROPN
cana-3291	171	20	a	a	PRON
cana-3291	172	1	i	i	NOUN
cana-3291	172	2	w	w	PROPN
cana-3291	172	3	t	t	PROPN
cana-3291	172	4	t	t	X
cana-3291	172	5	dt	dt	PROPN
cana-3291	172	6	a	a	DET
cana-3291	172	7	b	b	PROPN
cana-3291	172	8	a	a	PRON
cana-3291	172	9	n	n	NOUN
cana-3291	172	10	r	r	NOUN
cana-3291	172	11	i	i	PRON
cana-3291	172	12	a	a	PRON
cana-3291	172	13	a	a	DET
cana-3291	172	14	−	−	NOUN
cana-3291	172	15	−	−	NOUN
cana-3291	172	16	−	−	PROPN
cana-3291	173	1	=	=	NOUN
cana-3291	173	2			NOUN
cana-3291	173	3			NOUN
cana-3291	173	4	−	−	PROPN
cana-3291	174	1			PROPN
cana-3291	174	2			PROPN
cana-3291	174	3	+	+	PROPN
cana-3291	174	4			PROPN
cana-3291	174	5			NOUN
cana-3291	174	6	=	=	SYM
cana-3291	174	7	−	−	PROPN
cana-3291	174	8			NOUN
cana-3291	174	9			VERB
cana-3291	174	10	−	−	NOUN
cana-3291	174	11	+	+	NUM
cana-3291	174	12			NOUN
cana-3291	174	13	communications	communication	NOUN
cana-3291	174	14	on	on	ADP
cana-3291	174	15	applied	apply	VERB
cana-3291	174	16	nonlinear	nonlinear	ADJ
cana-3291	174	17	analysis	analysis	NOUN
cana-3291	174	18	issn	issn	NOUN
cana-3291	174	19	:	:	PUNCT
cana-3291	174	20	1074	1074	NUM
cana-3291	174	21	-	-	PUNCT
cana-3291	174	22	133x	133x	NUM
cana-3291	174	23	vol	vol	NOUN
cana-3291	174	24	32	32	NUM
cana-3291	174	25	no	no	NOUN
cana-3291	174	26	.	.	PUNCT
cana-3291	175	1	6s	6s	NUM
cana-3291	175	2	(	(	PUNCT
cana-3291	175	3	2025	2025	NUM
cana-3291	175	4	)	)	PUNCT
cana-3291	175	5	258	258	NUM
cana-3291	175	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3291	175	7	(	(	PUNCT
cana-3291	175	8	)	)	PUNCT
cana-3291	175	9	(	(	PUNCT
cana-3291	175	10	)	)	PUNCT
cana-3291	175	11	(	(	PUNCT
cana-3291	175	12	)	)	PUNCT
cana-3291	176	1	1	1	NUM
cana-3291	176	2	1	1	NUM
cana-3291	176	3	1	1	NUM
cana-3291	176	4	3	3	NUM
cana-3291	176	5	2	2	NUM
cana-3291	176	6	0	0	NUM
cana-3291	176	7	,	,	PUNCT
cana-3291	176	8	,	,	PUNCT
cana-3291	176	9	;	;	PUNCT
cana-3291	176	10	(	(	PUNCT
cana-3291	176	11	1	1	X
cana-3291	176	12	)	)	PUNCT
cana-3291	176	13	,	,	PUNCT
cana-3291	176	14	(	(	PUNCT
cana-3291	176	15	)	)	PUNCT
cana-3291	176	16	;	;	PUNCT
cana-3291	176	17	a	a	DET
cana-3291	176	18	b	b	NOUN
cana-3291	176	19	a	a	PRON
cana-3291	176	20	x	x	X
cana-3291	176	21	b	b	PROPN
cana-3291	176	22	ni	ni	PROPN
cana-3291	176	23	b	b	PROPN
cana-3291	176	24	t	t	PROPN
cana-3291	176	25	t	t	PROPN
cana-3291	176	26	f	f	X
cana-3291	176	27	wt	wt	INTJ
cana-3291	176	28	dtw	dtw	PROPN
cana-3291	176	29	a	a	DET
cana-3291	176	30	b	b	NOUN
cana-3291	176	31	a	a	DET
cana-3291	176	32	a	a	DET
cana-3291	176	33	i	i	PRON
cana-3291	176	34	a	a	DET
cana-3291	176	35	−	−	NOUN
cana-3291	176	36	−	−	NOUN
cana-3291	177	1	−	−	PROPN
cana-3291	177	2			NOUN
cana-3291	177	3			NOUN
cana-3291	177	4			VERB
cana-3291	177	5	−	−	ADP
cana-3291	177	6	=	=	NUM
cana-3291	177	7	−	−	PROPN
cana-3291	177	8			NOUN
cana-3291	177	9			NOUN
cana-3291	177	10			VERB
cana-3291	177	11	−	−	PROPN
cana-3291	178	1	+	+	NOUN
cana-3291	178	2			PROPN
cana-3291	178	3			PROPN
cana-3291	178	4			PUNCT
cana-3291	178	5	theorem	theorem	VERB
cana-3291	178	6	2	2	NUM
cana-3291	178	7	:	:	PUNCT
cana-3291	178	8	assume	assume	VERB
cana-3291	178	9	‘	'	PUNCT
cana-3291	178	10	a	a	DET
cana-3291	178	11	’	'	PUNCT
cana-3291	178	12	be	be	AUX
cana-3291	178	13	any	any	DET
cana-3291	178	14	square	square	ADJ
cana-3291	178	15	matrix	matrix	NOUN
cana-3291	178	16	of	of	ADP
cana-3291	178	17	order	order	NOUN
cana-3291	178	18	‘	'	PUNCT
cana-3291	178	19	n	n	CCONJ
cana-3291	178	20	’	'	PUNCT
cana-3291	178	21	,	,	PUNCT
cana-3291	178	22	0a	0a	NUM
cana-3291	179	1	if	if	SCONJ
cana-3291	179	2	real	real	ADJ
cana-3291	179	3	part	part	NOUN
cana-3291	179	4	of	of	ADP
cana-3291	179	5	1	1	NUM
cana-3291	179	6	,	,	PUNCT
cana-3291	179	7	2	2	NUM
cana-3291	179	8	a	a	DET
cana-3291	179	9	b−	b−	NOUN
cana-3291	179	10	,	,	PUNCT
cana-3291	179	11	then	then	ADV
cana-3291	179	12	/2	/2	PUNCT
cana-3291	179	13	(	(	PUNCT
cana-3291	179	14	)	)	PUNCT
cana-3291	179	15	2	2	NUM
cana-3291	179	16	1	1	NUM
cana-3291	179	17	2	2	NUM
cana-3291	179	18	1	1	NUM
cana-3291	179	19	2	2	NUM
cana-3291	179	20	2	2	NUM
cana-3291	179	21	4	4	NUM
cana-3291	179	22	3	3	NUM
cana-3291	179	23	0	0	NUM
cana-3291	179	24	1	1	NUM
cana-3291	179	25	,	,	PUNCT
cana-3291	179	26	,	,	PUNCT
cana-3291	179	27	,	,	PUNCT
cana-3291	179	28	;	;	PUNCT
cana-3291	179	29	2	2	NUM
cana-3291	179	30	(	(	PUNCT
cana-3291	179	31	)	)	PUNCT
cana-3291	179	32	(	(	PUNCT
cana-3291	179	33	)	)	PUNCT
cana-3291	179	34	(	(	PUNCT
cana-3291	179	35	,	,	PUNCT
cana-3291	179	36	)	)	PUNCT
cana-3291	179	37	(	(	PUNCT
cana-3291	179	38	sin	sin	NOUN
cana-3291	179	39	)	)	PUNCT
cana-3291	179	40	(	(	PUNCT
cana-3291	179	41	cos	cos	X
cana-3291	179	42	)	)	PUNCT
cana-3291	179	43	sin	sin	NOUN
cana-3291	179	44	cos2	cos2	NOUN
cana-3291	179	45	2	2	NUM
cana-3291	179	46	!	!	PUNCT
cana-3291	179	47	(	(	PUNCT
cana-3291	179	48	)	)	PUNCT
cana-3291	179	49	(	(	PUNCT
cana-3291	179	50	)	)	PUNCT
cana-3291	179	51	(	(	PUNCT
cana-3291	179	52	)	)	PUNCT
cana-3291	179	53	,	,	PUNCT
cana-3291	179	54	,	,	PUNCT
cana-3291	179	55	;	;	PUNCT
cana-3291	179	56	a	a	DET
cana-3291	179	57	a	a	DET
cana-3291	179	58	b	b	NOUN
cana-3291	179	59	n	n	NOUN
cana-3291	179	60	x	x	NOUN
cana-3291	179	61	a	a	DET
cana-3291	179	62	b	b	NOUN
cana-3291	179	63	a	a	DET
cana-3291	179	64	b	b	NOUN
cana-3291	179	65	nia	nia	PROPN
cana-3291	179	66	b	b	PROPN
cana-3291	180	1	i	i	PRON
cana-3291	180	2	a	a	DET
cana-3291	180	3	j	j	NOUN
cana-3291	180	4	x	x	SYM
cana-3291	180	5	w	w	PROPN
cana-3291	180	6	t	t	PROPN
cana-3291	180	7	t	t	PROPN
cana-3291	180	8	f	f	PROPN
cana-3291	180	9	w	w	PROPN
cana-3291	180	10	t	t	PROPN
cana-3291	180	11	t	t	PROPN
cana-3291	180	12	dtw	dtw	PROPN
cana-3291	180	13	n	n	PROPN
cana-3291	180	14	a	a	PROPN
cana-3291	180	15	b	b	NOUN
cana-3291	181	1	i	i	PRON
cana-3291	181	2	a	a	PRON
cana-3291	181	3	a	a	DET
cana-3291	181	4	b	b	NOUN
cana-3291	181	5			NOUN
cana-3291	181	6	−	−	NOUN
cana-3291	181	7	−	−	PROPN
cana-3291	182	1	+	+	CCONJ
cana-3291	182	2	+	+	PUNCT
cana-3291	183	1	+	+	ADJ
cana-3291	183	2			ADJ
cana-3291	183	3			NOUN
cana-3291	183	4	−	−	PROPN
cana-3291	183	5	+	+	CCONJ
cana-3291	183	6	+	+	CCONJ
cana-3291	183	7			NOUN
cana-3291	183	8	=	=	NUM
cana-3291	183	9			NOUN
cana-3291	183	10			NOUN
cana-3291	183	11			VERB
cana-3291	183	12	+	+	NOUN
cana-3291	183	13			NOUN
cana-3291	183	14			PROPN
cana-3291	183	15			ADP
cana-3291	183	16	proof	proof	NOUN
cana-3291	183	17	:	:	PUNCT
cana-3291	183	18	by	by	ADP
cana-3291	183	19	the	the	DET
cana-3291	183	20	equation	equation	NOUN
cana-3291	183	21	(	(	PUNCT
cana-3291	183	22	1.3	1.3	NUM
cana-3291	183	23	)	)	PUNCT
cana-3291	183	24	of	of	ADP
cana-3291	183	25	(	(	PUNCT
cana-3291	183	26	)	)	PUNCT
cana-3291	183	27	(	(	PUNCT
cana-3291	183	28	,	,	PUNCT
cana-3291	183	29	)	)	PUNCT
cana-3291	183	30	a	a	DET
cana-3291	183	31	nj	nj	PROPN
cana-3291	183	32	x	x	SYM
cana-3291	183	33	w	w	INTJ
cana-3291	183	34	,	,	PUNCT
cana-3291	183	35	we	we	PRON
cana-3291	183	36	have	have	AUX
cana-3291	183	37	2	2	NUM
cana-3291	183	38	1	1	NUM
cana-3291	183	39	(	(	PUNCT
cana-3291	183	40	)	)	PUNCT
cana-3291	183	41	(	(	PUNCT
cana-3291	183	42	,	,	PUNCT
cana-3291	183	43	)	)	PUNCT
cana-3291	183	44	,	,	PUNCT
cana-3291	183	45	;	;	PUNCT
cana-3291	183	46	;	;	PUNCT
cana-3291	183	47	!	!	PUNCT
cana-3291	184	1	a	a	DET
cana-3291	184	2	n	n	CCONJ
cana-3291	184	3	n	n	NOUN
cana-3291	184	4	i	i	PRON
cana-3291	184	5	a	a	X
cana-3291	184	6	x	x	X
cana-3291	184	7	j	j	PROPN
cana-3291	184	8	x	x	PROPN
cana-3291	184	9	w	w	PROPN
cana-3291	184	10	f	f	PROPN
cana-3291	184	11	ni	ni	PROPN
cana-3291	184	12	i	i	PROPN
cana-3291	184	13	a	a	PROPN
cana-3291	184	14	w	w	NOUN
cana-3291	184	15	n	n	ADP
cana-3291	184	16	w	w	PROPN
cana-3291	184	17	+	+	NUM
cana-3291	184	18			NUM
cana-3291	184	19			NOUN
cana-3291	184	20	=	=	PUNCT
cana-3291	185	1	−	−	PUNCT
cana-3291	185	2	+	+	NOUN
cana-3291	185	3			NOUN
cana-3291	185	4			NOUN
cana-3291	185	5			NOUN
cana-3291	185	6			PROPN
cana-3291	185	7	(	(	PUNCT
cana-3291	185	8	)	)	PUNCT
cana-3291	185	9	0	0	NUM
cana-3291	185	10	(	(	PUNCT
cana-3291	185	11	)	)	PUNCT
cana-3291	185	12	(	(	PUNCT
cana-3291	185	13	2	2	X
cana-3291	185	14	)	)	PUNCT
cana-3291	185	15	(	(	PUNCT
cana-3291	185	16	)	)	PUNCT
cana-3291	185	17	(	(	PUNCT
cana-3291	185	18	)	)	PUNCT
cana-3291	185	19	!	!	PUNCT
cana-3291	186	1	(	(	PUNCT
cana-3291	186	2	)	)	PUNCT
cana-3291	186	3	!	!	PUNCT
cana-3291	187	1	(	(	PUNCT
cana-3291	187	2	)	)	PUNCT
cana-3291	187	3	(	(	PUNCT
cana-3291	187	4	)	)	PUNCT
cana-3291	187	5	(	(	PUNCT
cana-3291	187	6	2	2	X
cana-3291	187	7	)	)	PUNCT
cana-3291	187	8	r	r	NOUN
cana-3291	187	9	n	n	ADP
cana-3291	187	10	r	r	NOUN
cana-3291	187	11	n	n	NOUN
cana-3291	187	12	r	r	NOUN
cana-3291	187	13	rr	rr	NOUN
cana-3291	187	14	r	r	NOUN
cana-3291	187	15	r	r	NOUN
cana-3291	187	16	r	r	NOUN
cana-3291	187	17	r	r	NOUN
cana-3291	187	18	x	x	SYM
cana-3291	187	19	ni	ni	PROPN
cana-3291	187	20	w	w	PROPN
cana-3291	187	21	i	i	PRON
cana-3291	187	22	a	a	DET
cana-3291	187	23	a	a	DET
cana-3291	187	24	b	b	NOUN
cana-3291	187	25	r	r	NOUN
cana-3291	187	26	a	a	DET
cana-3291	187	27	bw	bw	NOUN
cana-3291	187	28	n	n	CCONJ
cana-3291	187	29	i	i	PRON
cana-3291	187	30	a	a	DET
cana-3291	187	31	r	r	NOUN
cana-3291	187	32	a	a	DET
cana-3291	187	33	b	b	NOUN
cana-3291	187	34	a	a	DET
cana-3291	187	35	b	b	NOUN
cana-3291	187	36	r=	r=	ADJ
cana-3291	187	37			NOUN
cana-3291	187	38			PROPN
cana-3291	187	39	−	−	PROPN
cana-3291	188	1			PROPN
cana-3291	188	2			PROPN
cana-3291	189	1	+	+	CCONJ
cana-3291	190	1			VERB
cana-3291	190	2	+	+	ADJ
cana-3291	190	3	+	+	ADJ
cana-3291	190	4			ADJ
cana-3291	190	5			NOUN
cana-3291	190	6	=	=	SYM
cana-3291	190	7	+	+	CCONJ
cana-3291	190	8			VERB
cana-3291	190	9	+	+	CCONJ
cana-3291	190	10	+	+	CCONJ
cana-3291	190	11			X
cana-3291	190	12	(	(	PUNCT
cana-3291	190	13	)	)	PUNCT
cana-3291	190	14	/2	/2	PUNCT
cana-3291	191	1	2	2	NUM
cana-3291	191	2	2	2	NUM
cana-3291	191	3	1	1	NUM
cana-3291	191	4	2	2	NUM
cana-3291	191	5	2	2	NUM
cana-3291	191	6	1	1	NUM
cana-3291	191	7	0	0	NUM
cana-3291	191	8	0	0	NUM
cana-3291	191	9	(	(	PUNCT
cana-3291	191	10	)	)	PUNCT
cana-3291	191	11	2	2	NUM
cana-3291	191	12	(	(	PUNCT
cana-3291	191	13	2	2	NUM
cana-3291	191	14	)	)	PUNCT
cana-3291	191	15	(	(	PUNCT
cana-3291	191	16	sin	sin	NOUN
cana-3291	191	17	)	)	PUNCT
cana-3291	191	18	(	(	PUNCT
cana-3291	191	19	cos	cos	PROPN
cana-3291	191	20	)	)	PUNCT
cana-3291	191	21	!	!	PUNCT
cana-3291	192	1	(	(	PUNCT
cana-3291	192	2	)	)	PUNCT
cana-3291	192	3	!	!	PUNCT
cana-3291	193	1	(	(	PUNCT
cana-3291	193	2	)	)	PUNCT
cana-3291	193	3	(	(	PUNCT
cana-3291	193	4	)	)	PUNCT
cana-3291	193	5	r	r	NOUN
cana-3291	193	6	n	n	NOUN
cana-3291	193	7	r	r	NOUN
cana-3291	193	8	a	a	DET
cana-3291	193	9	r	r	NOUN
cana-3291	193	10	b	b	X
cana-3291	193	11	rn	rn	NOUN
cana-3291	193	12	r	r	NOUN
cana-3291	193	13	r	r	NOUN
cana-3291	193	14	r	r	NOUN
cana-3291	193	15	x	x	SYM
cana-3291	193	16	ni	ni	PROPN
cana-3291	193	17	w	w	PROPN
cana-3291	193	18	i	i	PRON
cana-3291	193	19	a	a	PRON
cana-3291	193	20	a	a	DET
cana-3291	193	21	b	b	PROPN
cana-3291	193	22	rw	rw	NOUN
cana-3291	193	23	t	t	PROPN
cana-3291	193	24	t	t	PROPN
cana-3291	193	25	dt	dt	X
cana-3291	194	1	n	n	CCONJ
cana-3291	194	2	i	i	PRON
cana-3291	194	3	a	a	DET
cana-3291	194	4	r	r	NOUN
cana-3291	194	5	a	a	DET
cana-3291	194	6	b	b	X
cana-3291	194	7			NOUN
cana-3291	194	8	+	+	NOUN
cana-3291	194	9	−	−	PROPN
cana-3291	194	10	+	+	CCONJ
cana-3291	194	11	−	−	PROPN
cana-3291	195	1	=	=	SYM
cana-3291	195	2			NOUN
cana-3291	195	3			NOUN
cana-3291	195	4	−	−	PROPN
cana-3291	195	5			PROPN
cana-3291	195	6			PROPN
cana-3291	196	1	+	+	CCONJ
cana-3291	197	1			VERB
cana-3291	197	2	+	+	ADJ
cana-3291	197	3	+	+	ADJ
cana-3291	197	4			ADJ
cana-3291	197	5			NOUN
cana-3291	197	6	=	=	SYM
cana-3291	198	1	+	+	CCONJ
cana-3291	198	2			VERB
cana-3291	198	3			VERB
cana-3291	198	4			X
cana-3291	198	5			PUNCT
cana-3291	198	6	on	on	ADP
cana-3291	198	7	interchanging	interchange	VERB
cana-3291	198	8	the	the	DET
cana-3291	198	9	order	order	NOUN
cana-3291	198	10	of	of	ADP
cana-3291	198	11	integration	integration	NOUN
cana-3291	198	12	and	and	CCONJ
cana-3291	198	13	summation	summation	NOUN
cana-3291	198	14	,	,	PUNCT
cana-3291	198	15	we	we	PRON
cana-3291	198	16	have	have	VERB
cana-3291	198	17	(	(	PUNCT
cana-3291	198	18	)	)	PUNCT
cana-3291	198	19	/2	/2	PROPN
cana-3291	199	1	2	2	NUM
cana-3291	199	2	1	1	NUM
cana-3291	199	3	2	2	NUM
cana-3291	199	4	1	1	NUM
cana-3291	199	5	2	2	NUM
cana-3291	199	6	2	2	NUM
cana-3291	199	7	00	00	NUM
cana-3291	199	8	1	1	NUM
cana-3291	199	9	(	(	PUNCT
cana-3291	199	10	)	)	PUNCT
cana-3291	199	11	(	(	PUNCT
cana-3291	199	12	)	)	PUNCT
cana-3291	199	13	2	2	NUM
cana-3291	199	14	2	2	NUM
cana-3291	199	15	2	2	NUM
cana-3291	199	16	(	(	PUNCT
cana-3291	199	17	sin	sin	NOUN
cana-3291	199	18	)	)	PUNCT
cana-3291	199	19	(	(	PUNCT
cana-3291	199	20	cos	cos	PROPN
cana-3291	199	21	)	)	PUNCT
cana-3291	199	22	(	(	PUNCT
cana-3291	199	23	sin	sin	NOUN
cana-3291	199	24	)	)	PUNCT
cana-3291	199	25	(	(	PUNCT
cana-3291	199	26	cos	cos	PROPN
cana-3291	199	27	)	)	PUNCT
cana-3291	199	28	!	!	PUNCT
cana-3291	200	1	(	(	PUNCT
cana-3291	200	2	)	)	PUNCT
cana-3291	200	3	(	(	PUNCT
cana-3291	200	4	)	)	PUNCT
cana-3291	200	5	(	(	PUNCT
cana-3291	200	6	)	)	PUNCT
cana-3291	200	7	!	!	PUNCT
cana-3291	201	1	(	(	PUNCT
cana-3291	201	2	)	)	PUNCT
cana-3291	201	3	(	(	PUNCT
cana-3291	201	4	)	)	PUNCT
cana-3291	201	5	n	n	CCONJ
cana-3291	201	6	r	r	NOUN
cana-3291	201	7	a	a	DET
cana-3291	201	8	b	b	NOUN
cana-3291	201	9	r	r	NOUN
cana-3291	201	10	r	r	NOUN
cana-3291	201	11	rn	rn	NOUN
cana-3291	201	12	r	r	NOUN
cana-3291	201	13	r	r	NOUN
cana-3291	201	14	r	r	NOUN
cana-3291	201	15	r	r	NOUN
cana-3291	201	16	r	r	NOUN
cana-3291	201	17	r	r	NOUN
cana-3291	201	18	r	r	NOUN
cana-3291	201	19	x	x	NOUN
cana-3291	201	20	a	a	DET
cana-3291	201	21	b	b	NOUN
cana-3291	201	22	a	a	DET
cana-3291	201	23	b	b	X
cana-3291	201	24	ni	ni	NOUN
cana-3291	201	25	i	i	PRON
cana-3291	201	26	a	a	PRON
cana-3291	201	27	a	a	DET
cana-3291	201	28	b	b	PROPN
cana-3291	201	29	w	w	PROPN
cana-3291	201	30	t	t	PROPN
cana-3291	201	31	t	t	PROPN
cana-3291	201	32	t	t	PROPN
cana-3291	201	33	t	t	PROPN
cana-3291	201	34	w	w	PROPN
cana-3291	201	35	dt	dt	PROPN
cana-3291	201	36	n	n	PROPN
cana-3291	201	37	a	a	DET
cana-3291	201	38	b	b	NOUN
cana-3291	202	1	i	i	PRON
cana-3291	202	2	a	a	DET
cana-3291	202	3	r	r	NOUN
cana-3291	202	4	a	a	DET
cana-3291	202	5	b	b	NOUN
cana-3291	202	6			NOUN
cana-3291	202	7	−	−	NOUN
cana-3291	202	8	−	−	NOUN
cana-3291	203	1	=	=	SYM
cana-3291	204	1	+	+	PUNCT
cana-3291	205	1	+	+	CCONJ
cana-3291	205	2	+	+	ADJ
cana-3291	205	3			NOUN
cana-3291	205	4			NOUN
cana-3291	205	5			NOUN
cana-3291	205	6			PROPN
cana-3291	205	7			NOUN
cana-3291	205	8			PROPN
cana-3291	205	9	−	−	PROPN
cana-3291	206	1			PROPN
cana-3291	206	2			PROPN
cana-3291	207	1			PROPN
cana-3291	208	1			INTJ
cana-3291	209	1			PROPN
cana-3291	209	2			PROPN
cana-3291	210	1	+	+	CCONJ
cana-3291	210	2			VERB
cana-3291	210	3	+	+	CCONJ
cana-3291	210	4			PROPN
cana-3291	210	5			NOUN
cana-3291	210	6			PROPN
cana-3291	210	7			NOUN
cana-3291	210	8			PROPN
cana-3291	210	9			NOUN
cana-3291	210	10	=	=	SYM
cana-3291	210	11			VERB
cana-3291	210	12			VERB
cana-3291	210	13	+	+	NUM
cana-3291	210	14			NOUN
cana-3291	210	15	/2	/2	NOUN
cana-3291	210	16	2	2	NUM
cana-3291	210	17	1	1	NUM
cana-3291	210	18	2	2	NUM
cana-3291	210	19	1	1	NUM
cana-3291	210	20	2	2	NUM
cana-3291	210	21	2	2	NUM
cana-3291	210	22	4	4	NUM
cana-3291	210	23	3	3	NUM
cana-3291	210	24	0	0	NUM
cana-3291	210	25	1	1	NUM
cana-3291	210	26	,	,	PUNCT
cana-3291	210	27	,	,	PUNCT
cana-3291	210	28	,	,	PUNCT
cana-3291	210	29	;	;	PUNCT
cana-3291	210	30	2	2	NUM
cana-3291	210	31	(	(	PUNCT
cana-3291	210	32	)	)	PUNCT
cana-3291	210	33	(	(	PUNCT
cana-3291	210	34	)	)	PUNCT
cana-3291	210	35	(	(	PUNCT
cana-3291	210	36	sin	sin	NOUN
cana-3291	210	37	)	)	PUNCT
cana-3291	210	38	(	(	PUNCT
cana-3291	210	39	cos	cos	X
cana-3291	210	40	)	)	PUNCT
cana-3291	210	41	sin	sin	NOUN
cana-3291	210	42	cos2	cos2	NOUN
cana-3291	210	43	2	2	NUM
cana-3291	210	44	!	!	PUNCT
cana-3291	210	45	(	(	PUNCT
cana-3291	210	46	)	)	PUNCT
cana-3291	210	47	(	(	PUNCT
cana-3291	210	48	)	)	PUNCT
cana-3291	210	49	(	(	PUNCT
cana-3291	210	50	)	)	PUNCT
cana-3291	210	51	,	,	PUNCT
cana-3291	210	52	,	,	PUNCT
cana-3291	210	53	;	;	PUNCT
cana-3291	210	54	a	a	DET
cana-3291	210	55	b	b	X
cana-3291	210	56	x	x	SYM
cana-3291	210	57	a	a	DET
cana-3291	210	58	b	b	NOUN
cana-3291	210	59	a	a	DET
cana-3291	210	60	b	b	NOUN
cana-3291	210	61	nia	nia	PROPN
cana-3291	210	62	b	b	PROPN
cana-3291	211	1	i	i	PRON
cana-3291	212	1	a	a	DET
cana-3291	212	2	t	t	NOUN
cana-3291	212	3	t	t	X
cana-3291	212	4	f	f	PROPN
cana-3291	212	5	w	w	PROPN
cana-3291	212	6	t	t	PROPN
cana-3291	212	7	t	t	PROPN
cana-3291	212	8	dtw	dtw	PROPN
cana-3291	212	9	n	n	PROPN
cana-3291	212	10	a	a	PROPN
cana-3291	212	11	b	b	NOUN
cana-3291	213	1	i	i	PRON
cana-3291	213	2	a	a	PRON
cana-3291	213	3	a	a	DET
cana-3291	213	4	b	b	NOUN
cana-3291	213	5			NOUN
cana-3291	213	6	−	−	NOUN
cana-3291	213	7	−	−	PROPN
cana-3291	214	1	+	+	CCONJ
cana-3291	214	2	+	+	PUNCT
cana-3291	215	1	+	+	ADJ
cana-3291	215	2			ADJ
cana-3291	215	3			NOUN
cana-3291	215	4	−	−	PROPN
cana-3291	215	5	+	+	CCONJ
cana-3291	215	6	+	+	CCONJ
cana-3291	215	7			NOUN
cana-3291	215	8	=	=	NUM
cana-3291	215	9			NOUN
cana-3291	215	10			NOUN
cana-3291	215	11			VERB
cana-3291	215	12	+	+	NOUN
cana-3291	215	13			NOUN
cana-3291	215	14			PROPN
cana-3291	215	15			PUNCT
cana-3291	215	16	hence	hence	ADV
cana-3291	215	17	the	the	DET
cana-3291	215	18	proof	proof	NOUN
cana-3291	215	19	.	.	PUNCT
cana-3291	216	1	5	5	X
cana-3291	216	2	.	.	X
cana-3291	216	3	infinite	infinite	ADJ
cana-3291	216	4	single	single	ADJ
cana-3291	216	5	integral	integral	ADJ
cana-3291	216	6	representation	representation	NOUN
cana-3291	216	7	if	if	SCONJ
cana-3291	216	8	‘	'	PUNCT
cana-3291	216	9	a	a	DET
cana-3291	216	10	’	'	PUNCT
cana-3291	216	11	be	be	AUX
cana-3291	216	12	any	any	DET
cana-3291	216	13	square	square	ADJ
cana-3291	216	14	matrix	matrix	NOUN
cana-3291	216	15	of	of	ADP
cana-3291	216	16	order	order	NOUN
cana-3291	216	17	n	n	PRON
cana-3291	216	18	n	n	VERB
cana-3291	216	19	and	and	CCONJ
cana-3291	216	20	(	(	PUNCT
cana-3291	216	21	)	)	PUNCT
cana-3291	216	22	(	(	PUNCT
cana-3291	216	23	,	,	PUNCT
cana-3291	216	24	)	)	PUNCT
cana-3291	216	25	a	a	DET
cana-3291	216	26	nj	nj	PROPN
cana-3291	217	1	x	x	PUNCT
cana-3291	217	2	w	w	AUX
cana-3291	217	3	be	be	AUX
cana-3291	217	4	the	the	DET
cana-3291	217	5	modified	modify	VERB
cana-3291	217	6	jacobi	jacobi	NOUN
cana-3291	217	7	matrix	matrix	NOUN
cana-3291	217	8	polynomial	polynomial	NOUN
cana-3291	217	9	,	,	PUNCT
cana-3291	217	10	then	then	ADV
cana-3291	217	11	infinite	infinite	VERB
cana-3291	217	12	single	single	ADJ
cana-3291	217	13	integral	integral	ADJ
cana-3291	217	14	representation	representation	NOUN
cana-3291	217	15	of	of	ADP
cana-3291	217	16	this	this	DET
cana-3291	217	17	polynomial	polynomial	NOUN
cana-3291	217	18	is	be	AUX
cana-3291	217	19	as	as	SCONJ
cana-3291	217	20	follows	follow	VERB
cana-3291	217	21	:	:	PUNCT
cana-3291	217	22	theorem	theorem	NOUN
cana-3291	217	23	assume	assume	VERB
cana-3291	217	24	a	a	DET
cana-3291	217	25	be	be	AUX
cana-3291	217	26	any	any	DET
cana-3291	217	27	square	square	ADJ
cana-3291	217	28	matrix	matrix	NOUN
cana-3291	217	29	of	of	ADP
cana-3291	217	30	order	order	NOUN
cana-3291	217	31	‘	'	PUNCT
cana-3291	217	32	n	n	CCONJ
cana-3291	217	33	’	'	PUNCT
cana-3291	217	34	0a	0a	NUM
cana-3291	217	35	.	.	PUNCT
cana-3291	218	1	communications	communication	NOUN
cana-3291	218	2	on	on	ADP
cana-3291	218	3	applied	apply	VERB
cana-3291	218	4	nonlinear	nonlinear	ADJ
cana-3291	218	5	analysis	analysis	NOUN
cana-3291	218	6	issn	issn	NOUN
cana-3291	218	7	:	:	PUNCT
cana-3291	218	8	1074	1074	NUM
cana-3291	218	9	-	-	PUNCT
cana-3291	218	10	133x	133x	NUM
cana-3291	218	11	vol	vol	NOUN
cana-3291	218	12	32	32	NUM
cana-3291	218	13	no	no	NOUN
cana-3291	218	14	.	.	PUNCT
cana-3291	219	1	6s	6s	NUM
cana-3291	219	2	(	(	PUNCT
cana-3291	219	3	2025	2025	NUM
cana-3291	219	4	)	)	PUNCT
cana-3291	219	5	259	259	NUM
cana-3291	219	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3291	219	7	2	2	NUM
cana-3291	219	8	(	(	PUNCT
cana-3291	219	9	)	)	PUNCT
cana-3291	219	10	2	2	NUM
cana-3291	219	11	1	1	NUM
cana-3291	219	12	2	2	NUM
cana-3291	219	13	2	2	NUM
cana-3291	219	14	2	2	NUM
cana-3291	219	15	,	,	PUNCT
cana-3291	219	16	;	;	PUNCT
cana-3291	219	17	(	(	PUNCT
cana-3291	219	18	)	)	PUNCT
cana-3291	219	19	(	(	PUNCT
cana-3291	219	20	,	,	PUNCT
cana-3291	219	21	)	)	PUNCT
cana-3291	219	22	(	(	PUNCT
cana-3291	219	23	)	)	PUNCT
cana-3291	219	24	!	!	PUNCT
cana-3291	220	1	,	,	PUNCT
cana-3291	220	2	;	;	PUNCT
cana-3291	220	3	a	a	DET
cana-3291	220	4	t	t	NOUN
cana-3291	220	5	an	an	DET
cana-3291	220	6	n	n	PROPN
cana-3291	220	7	x	x	PROPN
cana-3291	220	8	nii	nii	PROPN
cana-3291	220	9	a	a	DET
cana-3291	220	10	j	j	PROPN
cana-3291	220	11	x	x	SYM
cana-3291	220	12	w	w	PROPN
cana-3291	220	13	e	e	PROPN
cana-3291	220	14	t	t	PROPN
cana-3291	220	15	f	f	PROPN
cana-3291	220	16	wt	wt	INTJ
cana-3291	220	17	dtw	dtw	PROPN
cana-3291	220	18	a	a	PRON
cana-3291	220	19	n	n	NOUN
cana-3291	220	20	a	a	PRON
cana-3291	220	21	i	i	PRON
cana-3291	220	22	a	a	DET
cana-3291	220	23			NOUN
cana-3291	220	24	−	−	ADP
cana-3291	220	25	−	−	NUM
cana-3291	221	1	−	−	PRON
cana-3291	221	2			PROPN
cana-3291	221	3			NOUN
cana-3291	221	4	−+	−+	PROPN
cana-3291	221	5			PROPN
cana-3291	221	6	=	=	X
cana-3291	221	7			NOUN
cana-3291	221	8			NOUN
cana-3291	221	9	+	+	NOUN
cana-3291	221	10			PROPN
cana-3291	221	11			PROPN
cana-3291	221	12			X
cana-3291	221	13	(	(	PUNCT
cana-3291	221	14	5.1	5.1	NUM
cana-3291	221	15	)	)	PUNCT
cana-3291	221	16	proof	proof	NOUN
cana-3291	221	17	:	:	PUNCT
cana-3291	221	18	from	from	ADP
cana-3291	221	19	the	the	DET
cana-3291	221	20	equation	equation	NOUN
cana-3291	221	21	(	(	PUNCT
cana-3291	221	22	1.3	1.3	NUM
cana-3291	221	23	)	)	PUNCT
cana-3291	221	24	of	of	ADP
cana-3291	221	25	(	(	PUNCT
cana-3291	221	26	)	)	PUNCT
cana-3291	221	27	(	(	PUNCT
cana-3291	221	28	,	,	PUNCT
cana-3291	221	29	)	)	PUNCT
cana-3291	221	30	a	a	DET
cana-3291	221	31	nj	nj	PROPN
cana-3291	221	32	x	x	SYM
cana-3291	221	33	w	w	INTJ
cana-3291	221	34	,	,	PUNCT
cana-3291	221	35	we	we	PRON
cana-3291	221	36	have	have	VERB
cana-3291	221	37	2	2	NUM
cana-3291	221	38	1	1	NUM
cana-3291	221	39	(	(	PUNCT
cana-3291	221	40	)	)	PUNCT
cana-3291	221	41	(	(	PUNCT
cana-3291	221	42	,	,	PUNCT
cana-3291	221	43	)	)	PUNCT
cana-3291	221	44	,	,	PUNCT
cana-3291	221	45	;	;	PUNCT
cana-3291	221	46	;	;	PUNCT
cana-3291	221	47	!	!	PUNCT
cana-3291	222	1	a	a	DET
cana-3291	222	2	n	n	CCONJ
cana-3291	222	3	n	n	NOUN
cana-3291	222	4	i	i	PRON
cana-3291	222	5	a	a	X
cana-3291	222	6	x	x	X
cana-3291	222	7	j	j	PROPN
cana-3291	222	8	x	x	PROPN
cana-3291	222	9	w	w	PROPN
cana-3291	222	10	f	f	PROPN
cana-3291	222	11	ni	ni	PROPN
cana-3291	222	12	i	i	PROPN
cana-3291	222	13	a	a	PROPN
cana-3291	222	14	w	w	NOUN
cana-3291	222	15	n	n	ADP
cana-3291	222	16	w	w	PROPN
cana-3291	222	17	+	+	NUM
cana-3291	222	18			NUM
cana-3291	222	19			NOUN
cana-3291	222	20	=	=	PUNCT
cana-3291	223	1	−	−	PUNCT
cana-3291	223	2	+	+	NOUN
cana-3291	223	3			NOUN
cana-3291	223	4			NOUN
cana-3291	223	5			NOUN
cana-3291	223	6			PROPN
cana-3291	223	7	(	(	PUNCT
cana-3291	223	8	)	)	PUNCT
cana-3291	223	9	0	0	NUM
cana-3291	223	10	(	(	PUNCT
cana-3291	223	11	)	)	PUNCT
cana-3291	223	12	(	(	PUNCT
cana-3291	223	13	)	)	PUNCT
cana-3291	223	14	!	!	PUNCT
cana-3291	224	1	(	(	PUNCT
cana-3291	224	2	a	a	X
cana-3291	224	3	)	)	PUNCT
cana-3291	224	4	(	(	PUNCT
cana-3291	224	5	)	)	PUNCT
cana-3291	224	6	!	!	PUNCT
cana-3291	225	1	(	(	PUNCT
cana-3291	225	2	)	)	PUNCT
cana-3291	225	3	r	r	NOUN
cana-3291	225	4	n	n	NOUN
cana-3291	225	5	r	r	NOUN
cana-3291	225	6	n	n	NOUN
cana-3291	225	7	r	r	NOUN
cana-3291	225	8	r	r	NOUN
cana-3291	225	9	r	r	NOUN
cana-3291	225	10	r	r	NOUN
cana-3291	225	11	x	x	SYM
cana-3291	225	12	ni	ni	PROPN
cana-3291	225	13	w	w	PROPN
cana-3291	225	14	a	a	DET
cana-3291	225	15	r	r	NOUN
cana-3291	226	1	i	i	PRON
cana-3291	226	2	a	a	DET
cana-3291	226	3	w	w	NOUN
cana-3291	226	4	n	n	VERB
cana-3291	226	5	i	i	PRON
cana-3291	226	6	a	a	DET
cana-3291	226	7	r	r	NOUN
cana-3291	227	1	a=	a=	NOUN
cana-3291	227	2			NOUN
cana-3291	227	3			NOUN
cana-3291	227	4	−	−	PROPN
cana-3291	228	1			VERB
cana-3291	229	1	+	+	NOUN
cana-3291	229	2			PROPN
cana-3291	229	3			PROPN
cana-3291	230	1	+	+	CCONJ
cana-3291	230	2			PROPN
cana-3291	230	3			NOUN
cana-3291	230	4	=	=	SYM
cana-3291	230	5			VERB
cana-3291	230	6	+	+	NUM
cana-3291	230	7			X
cana-3291	230	8	(	(	PUNCT
cana-3291	230	9	)	)	PUNCT
cana-3291	230	10	2	2	NUM
cana-3291	230	11	2	2	NUM
cana-3291	230	12	2	2	NUM
cana-3291	230	13	1	1	NUM
cana-3291	230	14	0	0	NUM
cana-3291	230	15	(	(	PUNCT
cana-3291	230	16	)	)	PUNCT
cana-3291	230	17	!	!	PUNCT
cana-3291	231	1	(	(	PUNCT
cana-3291	231	2	)	)	PUNCT
cana-3291	231	3	(	(	PUNCT
cana-3291	231	4	)	)	PUNCT
cana-3291	231	5	!	!	PUNCT
cana-3291	232	1	(	(	PUNCT
cana-3291	232	2	)	)	PUNCT
cana-3291	232	3	r	r	NOUN
cana-3291	232	4	n	n	NUM
cana-3291	232	5	r	r	NOUN
cana-3291	232	6	t	t	NOUN
cana-3291	232	7	a	a	DET
cana-3291	232	8	rn	rn	NOUN
cana-3291	232	9	r	r	NOUN
cana-3291	233	1	r	r	NOUN
cana-3291	233	2	r	r	NOUN
cana-3291	233	3	r	r	NOUN
cana-3291	233	4	x	x	SYM
cana-3291	233	5	ni	ni	PROPN
cana-3291	233	6	w	w	PROPN
cana-3291	233	7	i	i	PROPN
cana-3291	233	8	a	a	DET
cana-3291	233	9	w	w	NOUN
cana-3291	233	10	e	e	PROPN
cana-3291	233	11	t	t	NOUN
cana-3291	233	12	dt	dt	X
cana-3291	233	13	n	n	PROPN
cana-3291	234	1	a	a	PRON
cana-3291	234	2	i	i	PRON
cana-3291	234	3	a	a	DET
cana-3291	234	4	r	r	NOUN
cana-3291	234	5	a	a	DET
cana-3291	234	6			NOUN
cana-3291	234	7	−	−	NOUN
cana-3291	234	8	+	+	CCONJ
cana-3291	234	9	−	−	PROPN
cana-3291	234	10	=	=	SYM
cana-3291	234	11	−	−	PROPN
cana-3291	234	12			NOUN
cana-3291	234	13			PROPN
cana-3291	234	14	−	−	PROPN
cana-3291	235	1			PROPN
cana-3291	235	2			PROPN
cana-3291	236	1	+	+	CCONJ
cana-3291	236	2			PROPN
cana-3291	236	3			NOUN
cana-3291	236	4	=	=	SYM
cana-3291	236	5			VERB
cana-3291	236	6	+	+	NUM
cana-3291	236	7			X
cana-3291	236	8			PUNCT
cana-3291	236	9	on	on	ADP
cana-3291	236	10	interchanging	interchange	VERB
cana-3291	236	11	the	the	DET
cana-3291	236	12	order	order	NOUN
cana-3291	236	13	of	of	ADP
cana-3291	236	14	integration	integration	NOUN
cana-3291	236	15	and	and	CCONJ
cana-3291	236	16	summation	summation	NOUN
cana-3291	236	17	,	,	PUNCT
cana-3291	236	18	we	we	PRON
cana-3291	236	19	have	have	VERB
cana-3291	236	20	(	(	PUNCT
cana-3291	236	21	)	)	PUNCT
cana-3291	236	22	2	2	NUM
cana-3291	236	23	2	2	NUM
cana-3291	236	24	2	2	NUM
cana-3291	236	25	1	1	NUM
cana-3291	236	26	0	0	NUM
cana-3291	236	27	(	(	PUNCT
cana-3291	236	28	)	)	PUNCT
cana-3291	236	29	(	(	PUNCT
cana-3291	236	30	)	)	PUNCT
cana-3291	236	31	(	(	PUNCT
cana-3291	236	32	)	)	PUNCT
cana-3291	236	33	!	!	PUNCT
cana-3291	237	1	(	(	PUNCT
cana-3291	237	2	)	)	PUNCT
cana-3291	237	3	(	(	PUNCT
cana-3291	237	4	)	)	PUNCT
cana-3291	237	5	!	!	PUNCT
cana-3291	238	1	r	r	NOUN
cana-3291	238	2	n	n	NUM
cana-3291	238	3	r	r	NOUN
cana-3291	238	4	t	t	NOUN
cana-3291	238	5	an	an	DET
cana-3291	238	6	r	r	NOUN
cana-3291	239	1	r	r	NOUN
cana-3291	239	2	r	r	NOUN
cana-3291	239	3	r	r	NOUN
cana-3291	239	4	x	x	SYM
cana-3291	239	5	ni	ni	NOUN
cana-3291	239	6	wt	wt	INTJ
cana-3291	239	7	i	i	PRON
cana-3291	239	8	a	a	PRON
cana-3291	239	9	w	w	NOUN
cana-3291	239	10	e	e	PROPN
cana-3291	239	11	t	t	X
cana-3291	239	12	dt	dt	X
cana-3291	239	13	a	a	DET
cana-3291	239	14	n	n	NOUN
cana-3291	240	1	a	a	DET
cana-3291	240	2	i	i	PRON
cana-3291	240	3	a	a	DET
cana-3291	240	4	r	r	NOUN
cana-3291	240	5			NOUN
cana-3291	240	6	−	−	ADP
cana-3291	240	7	−	−	NOUN
cana-3291	240	8	=	=	SYM
cana-3291	240	9	−	−	PROPN
cana-3291	240	10			NOUN
cana-3291	240	11			PROPN
cana-3291	240	12	−	−	PROPN
cana-3291	241	1			PROPN
cana-3291	241	2			PROPN
cana-3291	242	1	+	+	CCONJ
cana-3291	242	2			PROPN
cana-3291	242	3			NOUN
cana-3291	242	4	=	=	SYM
cana-3291	242	5			VERB
cana-3291	242	6	+	+	NUM
cana-3291	242	7			NUM
cana-3291	242	8	2	2	NUM
cana-3291	242	9	2	2	NUM
cana-3291	242	10	1	1	NUM
cana-3291	242	11	2	2	NUM
cana-3291	242	12	2	2	NUM
cana-3291	242	13	2	2	NUM
cana-3291	242	14	,	,	PUNCT
cana-3291	242	15	;	;	PUNCT
cana-3291	242	16	(	(	PUNCT
cana-3291	242	17	)	)	PUNCT
cana-3291	242	18	(	(	PUNCT
cana-3291	242	19	)	)	PUNCT
cana-3291	242	20	!	!	PUNCT
cana-3291	243	1	,	,	PUNCT
cana-3291	243	2	;	;	PUNCT
cana-3291	243	3	t	t	PROPN
cana-3291	243	4	an	an	DET
cana-3291	243	5	x	x	X
cana-3291	243	6	nii	nii	PROPN
cana-3291	243	7	a	a	PROPN
cana-3291	243	8	e	e	PROPN
cana-3291	243	9	t	t	PROPN
cana-3291	243	10	f	f	PROPN
cana-3291	243	11	wt	wt	INTJ
cana-3291	243	12	dtw	dtw	PROPN
cana-3291	243	13	a	a	DET
cana-3291	243	14	n	n	NOUN
cana-3291	243	15	a	a	DET
cana-3291	243	16	i	i	PRON
cana-3291	243	17	a	a	DET
cana-3291	243	18			NOUN
cana-3291	243	19	−	−	ADP
cana-3291	243	20	−	−	NUM
cana-3291	244	1	−	−	PRON
cana-3291	244	2			PROPN
cana-3291	244	3			NOUN
cana-3291	244	4	−+	−+	PROPN
cana-3291	244	5			PROPN
cana-3291	244	6	=	=	X
cana-3291	244	7			NOUN
cana-3291	244	8			NOUN
cana-3291	244	9	+	+	NOUN
cana-3291	244	10			PROPN
cana-3291	244	11			PROPN
cana-3291	244	12			PUNCT
cana-3291	244	13	hence	hence	ADV
cana-3291	244	14	the	the	DET
cana-3291	244	15	theorem	theorem	NOUN
cana-3291	244	16	.	.	PROPN
cana-3291	244	17	6	6	NUM
cana-3291	244	18	.	.	X
cana-3291	244	19	double	double	ADJ
cana-3291	244	20	integral	integral	ADJ
cana-3291	244	21	representation	representation	NOUN
cana-3291	244	22	theorem	theorem	NOUN
cana-3291	244	23	:	:	PUNCT
cana-3291	244	24	assume	assume	VERB
cana-3291	244	25	‘	'	PUNCT
cana-3291	244	26	a	a	PRON
cana-3291	244	27	’	'	PUNCT
cana-3291	244	28	be	be	AUX
cana-3291	244	29	any	any	DET
cana-3291	244	30	square	square	ADJ
cana-3291	244	31	matrix	matrix	NOUN
cana-3291	244	32	of	of	ADP
cana-3291	244	33	order	order	NOUN
cana-3291	244	34	‘	'	PUNCT
cana-3291	244	35	n	n	CCONJ
cana-3291	244	36	’	'	PUNCT
cana-3291	244	37	,	,	PUNCT
cana-3291	244	38	0a	0a	NUM
cana-3291	244	39	.	.	PUNCT
cana-3291	245	1	if	if	SCONJ
cana-3291	245	2	real	real	ADJ
cana-3291	245	3	part	part	NOUN
cana-3291	245	4	of	of	ADP
cana-3291	245	5	a	a	DET
cana-3291	245	6	,	,	PUNCT
cana-3291	245	7	b	b	NOUN
cana-3291	245	8	,	,	PUNCT
cana-3291	245	9	𝜆	𝜆	X
cana-3291	245	10	>	>	X
cana-3291	245	11	0	0	NUM
cana-3291	245	12	then	then	ADV
cana-3291	245	13	(	(	PUNCT
cana-3291	245	14	)	)	PUNCT
cana-3291	245	15	1	1	NUM
cana-3291	245	16	1	1	NUM
cana-3291	245	17	1	1	NUM
cana-3291	245	18	4	4	NUM
cana-3291	245	19	3	3	NUM
cana-3291	245	20	1	1	NUM
cana-3291	245	21	,	,	PUNCT
cana-3291	245	22	,	,	PUNCT
cana-3291	245	23	,	,	PUNCT
cana-3291	245	24	;	;	PUNCT
cana-3291	245	25	(	(	PUNCT
cana-3291	245	26	)	)	PUNCT
cana-3291	245	27	(	(	PUNCT
cana-3291	245	28	)	)	PUNCT
cana-3291	245	29	(	(	PUNCT
cana-3291	245	30	,	,	PUNCT
cana-3291	245	31	)	)	PUNCT
cana-3291	245	32	(	(	PUNCT
cana-3291	245	33	1	1	X
cana-3291	245	34	)	)	SYM
cana-3291	245	35	2	2	NUM
cana-3291	245	36	2	2	NUM
cana-3291	245	37	2	2	NUM
cana-3291	245	38	!	!	PUNCT
cana-3291	246	1	(	(	PUNCT
cana-3291	246	2	)	)	PUNCT
cana-3291	246	3	(	(	PUNCT
cana-3291	246	4	)	)	PUNCT
cana-3291	246	5	(	(	PUNCT
cana-3291	246	6	)	)	PUNCT
cana-3291	246	7	,	,	PUNCT
cana-3291	246	8	,	,	PUNCT
cana-3291	246	9	;	;	PUNCT
cana-3291	246	10	a	a	DET
cana-3291	246	11	a	a	DET
cana-3291	246	12	b	b	NOUN
cana-3291	246	13	a	a	DET
cana-3291	246	14	bn	bn	NOUN
cana-3291	246	15	n	n	CCONJ
cana-3291	246	16	a	a	DET
cana-3291	246	17	x	x	X
cana-3291	246	18	nii	nii	PROPN
cana-3291	246	19	a	a	DET
cana-3291	246	20	j	j	PROPN
cana-3291	246	21	x	x	SYM
cana-3291	246	22	w	w	NOUN
cana-3291	246	23	u	u	NOUN
cana-3291	246	24	v	v	ADP
cana-3291	246	25	u	u	NOUN
cana-3291	246	26	v	v	ADP
cana-3291	246	27	f	f	PROPN
cana-3291	246	28	uvw	uvw	PROPN
cana-3291	246	29	dudvw	dudvw	PROPN
cana-3291	246	30	n	n	CCONJ
cana-3291	246	31	a	a	PRON
cana-3291	246	32	b	b	NOUN
cana-3291	246	33	a	a	DET
cana-3291	246	34	b	b	NOUN
cana-3291	246	35	a	a	DET
cana-3291	246	36	b	b	NOUN
cana-3291	246	37	i	i	PRON
cana-3291	246	38	a	a	DET
cana-3291	246	39			ADJ
cana-3291	246	40			ADJ
cana-3291	246	41			ADJ
cana-3291	246	42			ADJ
cana-3291	246	43			ADJ
cana-3291	246	44	−	−	PROPN
cana-3291	246	45	−	−	PROPN
cana-3291	246	46	−	−	PROPN
cana-3291	246	47	−	−	PROPN
cana-3291	246	48	−	−	PROPN
cana-3291	246	49			PROPN
cana-3291	246	50			NOUN
cana-3291	246	51	−	−	PROPN
cana-3291	247	1	+	+	ADJ
cana-3291	247	2			VERB
cana-3291	247	3	+	+	ADJ
cana-3291	247	4			NOUN
cana-3291	247	5	=	=	NOUN
cana-3291	247	6	−	−	NOUN
cana-3291	247	7	−	−	NOUN
cana-3291	247	8			NOUN
cana-3291	247	9			NOUN
cana-3291	247	10			VERB
cana-3291	247	11			VERB
cana-3291	247	12	−	−	NOUN
cana-3291	247	13	−	−	NOUN
cana-3291	248	1	+	+	NOUN
cana-3291	248	2			PROPN
cana-3291	248	3			PROPN
cana-3291	248	4			X
cana-3291	248	5	(	(	PUNCT
cana-3291	248	6	6.1	6.1	NUM
cana-3291	248	7	)	)	PUNCT
cana-3291	248	8	proof	proof	NOUN
cana-3291	248	9	:	:	PUNCT
cana-3291	248	10	from	from	ADP
cana-3291	248	11	the	the	DET
cana-3291	248	12	equation	equation	NOUN
cana-3291	248	13	(	(	PUNCT
cana-3291	248	14	1.3	1.3	NUM
cana-3291	248	15	)	)	PUNCT
cana-3291	248	16	of	of	ADP
cana-3291	248	17	(	(	PUNCT
cana-3291	248	18	)	)	PUNCT
cana-3291	248	19	(	(	PUNCT
cana-3291	248	20	,	,	PUNCT
cana-3291	248	21	)	)	PUNCT
cana-3291	248	22	a	a	DET
cana-3291	248	23	nj	nj	PROPN
cana-3291	248	24	x	x	PUNCT
cana-3291	249	1	w	w	X
cana-3291	249	2	we	we	PRON
cana-3291	249	3	have	have	VERB
cana-3291	249	4	(	(	PUNCT
cana-3291	249	5	)	)	PUNCT
cana-3291	249	6	2	2	NUM
cana-3291	249	7	1	1	NUM
cana-3291	249	8	(	(	PUNCT
cana-3291	249	9	)	)	PUNCT
cana-3291	249	10	(	(	PUNCT
cana-3291	249	11	,	,	PUNCT
cana-3291	249	12	)	)	PUNCT
cana-3291	249	13	,	,	PUNCT
cana-3291	249	14	;	;	PUNCT
cana-3291	249	15	;	;	PUNCT
cana-3291	249	16	!	!	PUNCT
cana-3291	250	1	a	a	DET
cana-3291	250	2	n	n	CCONJ
cana-3291	250	3	n	n	NOUN
cana-3291	250	4	i	i	PRON
cana-3291	250	5	a	a	X
cana-3291	250	6	x	x	X
cana-3291	250	7	j	j	PROPN
cana-3291	250	8	x	x	PROPN
cana-3291	250	9	w	w	PROPN
cana-3291	250	10	f	f	PROPN
cana-3291	250	11	ni	ni	PROPN
cana-3291	250	12	i	i	PROPN
cana-3291	250	13	a	a	PROPN
cana-3291	250	14	w	w	NOUN
cana-3291	250	15	n	n	ADP
cana-3291	250	16	w	w	PROPN
cana-3291	250	17	+	+	NUM
cana-3291	250	18			NUM
cana-3291	250	19			NOUN
cana-3291	250	20	=	=	PUNCT
cana-3291	251	1	−	−	PUNCT
cana-3291	251	2	+	+	NOUN
cana-3291	251	3			NOUN
cana-3291	251	4			NOUN
cana-3291	251	5			NOUN
cana-3291	251	6			PROPN
cana-3291	251	7	(	(	PUNCT
cana-3291	251	8	)	)	PUNCT
cana-3291	251	9	1	1	NUM
cana-3291	251	10	1	1	NUM
cana-3291	251	11	1	1	NUM
cana-3291	251	12	0	0	NUM
cana-3291	251	13	1	1	NUM
cana-3291	251	14	(	(	PUNCT
cana-3291	251	15	)	)	PUNCT
cana-3291	251	16	(	(	PUNCT
cana-3291	251	17	)	)	PUNCT
cana-3291	251	18	2	2	NUM
cana-3291	251	19	2	2	NUM
cana-3291	251	20	2	2	NUM
cana-3291	251	21	(	(	PUNCT
cana-3291	251	22	1	1	NUM
cana-3291	251	23	)	)	PUNCT
cana-3291	251	24	!	!	PUNCT
cana-3291	251	25	(	(	PUNCT
cana-3291	251	26	)	)	PUNCT
cana-3291	251	27	(	(	PUNCT
cana-3291	251	28	)	)	PUNCT
cana-3291	251	29	(	(	PUNCT
cana-3291	251	30	)	)	PUNCT
cana-3291	251	31	(	(	PUNCT
cana-3291	251	32	)	)	PUNCT
cana-3291	251	33	!	!	PUNCT
cana-3291	252	1	(	(	PUNCT
cana-3291	252	2	)	)	PUNCT
cana-3291	252	3	(	(	PUNCT
cana-3291	252	4	)	)	PUNCT
cana-3291	252	5	r	r	NOUN
cana-3291	252	6	n	n	NOUN
cana-3291	252	7	r	r	NOUN
cana-3291	252	8	a	a	DET
cana-3291	252	9	r	r	NOUN
cana-3291	252	10	b	b	NOUN
cana-3291	252	11	r	r	NOUN
cana-3291	252	12	a	a	DET
cana-3291	252	13	bn	bn	NOUN
cana-3291	252	14	r	r	NOUN
cana-3291	252	15	r	r	NOUN
cana-3291	252	16	r	r	NOUN
cana-3291	252	17	r	r	NOUN
cana-3291	252	18	r	r	NOUN
cana-3291	252	19	r	r	NOUN
cana-3291	252	20	r	r	NOUN
cana-3291	252	21	a	a	DET
cana-3291	252	22	x	x	SYM
cana-3291	252	23	ni	ni	PROPN
cana-3291	252	24	w	w	PROPN
cana-3291	252	25	i	i	PROPN
cana-3291	252	26	a	a	PRON
cana-3291	252	27	w	w	NOUN
cana-3291	252	28	u	u	NOUN
cana-3291	252	29	v	v	ADP
cana-3291	252	30	u	u	NOUN
cana-3291	252	31	v	v	ADP
cana-3291	252	32	du	du	PROPN
cana-3291	252	33	dv	dv	PROPN
cana-3291	252	34	n	n	PROPN
cana-3291	252	35	a	a	DET
cana-3291	252	36	b	b	NOUN
cana-3291	252	37	a	a	DET
cana-3291	252	38	b	b	NOUN
cana-3291	253	1	i	i	PRON
cana-3291	253	2	a	a	DET
cana-3291	253	3	r	r	NOUN
cana-3291	253	4	a	a	DET
cana-3291	253	5	b	b	PROPN
cana-3291	253	6			X
cana-3291	253	7			ADJ
cana-3291	253	8			ADJ
cana-3291	253	9			ADJ
cana-3291	253	10			X
cana-3291	253	11	+	+	CCONJ
cana-3291	253	12	−	−	PROPN
cana-3291	254	1	+	+	CCONJ
cana-3291	254	2	−	−	PROPN
cana-3291	254	3	−	−	NUM
cana-3291	254	4	−	−	NOUN
cana-3291	255	1	−	−	PROPN
cana-3291	255	2	=	=	NOUN
cana-3291	256	1			NOUN
cana-3291	256	2			PROPN
cana-3291	256	3			NOUN
cana-3291	256	4			PROPN
cana-3291	256	5			NOUN
cana-3291	256	6			NOUN
cana-3291	256	7	−	−	PROPN
cana-3291	257	1	+	+	ADV
cana-3291	257	2			PROPN
cana-3291	258	1			PROPN
cana-3291	259	1			PROPN
cana-3291	260	1			INTJ
cana-3291	261	1			PROPN
cana-3291	262	1			INTJ
cana-3291	262	2			VERB
cana-3291	262	3	+	+	CCONJ
cana-3291	262	4			PROPN
cana-3291	262	5			NOUN
cana-3291	262	6			PROPN
cana-3291	262	7			NOUN
cana-3291	262	8			PROPN
cana-3291	262	9			NOUN
cana-3291	262	10	=	=	PUNCT
cana-3291	262	11	−	−	NOUN
cana-3291	262	12	−	−	PROPN
cana-3291	262	13			NOUN
cana-3291	262	14			NOUN
cana-3291	262	15			NOUN
cana-3291	262	16	−	−	NOUN
cana-3291	262	17	−	−	NOUN
cana-3291	263	1	+	+	CCONJ
cana-3291	263	2			X
cana-3291	263	3			ADJ
cana-3291	263	4	communications	communication	NOUN
cana-3291	263	5	on	on	ADP
cana-3291	263	6	applied	apply	VERB
cana-3291	263	7	nonlinear	nonlinear	ADJ
cana-3291	263	8	analysis	analysis	NOUN
cana-3291	263	9	issn	issn	NOUN
cana-3291	263	10	:	:	PUNCT
cana-3291	263	11	1074	1074	NUM
cana-3291	263	12	-	-	PUNCT
cana-3291	263	13	133x	133x	NUM
cana-3291	263	14	vol	vol	NOUN
cana-3291	263	15	32	32	NUM
cana-3291	263	16	no	no	NOUN
cana-3291	263	17	.	.	PUNCT
cana-3291	264	1	6s	6s	NUM
cana-3291	264	2	(	(	PUNCT
cana-3291	264	3	2025	2025	NUM
cana-3291	264	4	)	)	PUNCT
cana-3291	264	5	260	260	NUM
cana-3291	264	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3291	264	7	on	on	ADP
cana-3291	264	8	interchanging	interchange	VERB
cana-3291	264	9	the	the	DET
cana-3291	264	10	order	order	NOUN
cana-3291	264	11	of	of	ADP
cana-3291	264	12	integration	integration	NOUN
cana-3291	264	13	and	and	CCONJ
cana-3291	264	14	summation	summation	NOUN
cana-3291	264	15	,	,	PUNCT
cana-3291	264	16	we	we	PRON
cana-3291	264	17	have	have	VERB
cana-3291	264	18	1	1	NUM
cana-3291	264	19	1	1	NUM
cana-3291	264	20	1	1	NUM
cana-3291	264	21	4	4	NUM
cana-3291	264	22	3	3	NUM
cana-3291	264	23	1	1	NUM
cana-3291	264	24	,	,	PUNCT
cana-3291	264	25	,	,	PUNCT
cana-3291	264	26	,	,	PUNCT
cana-3291	264	27	;	;	PUNCT
cana-3291	264	28	(	(	PUNCT
cana-3291	264	29	)	)	PUNCT
cana-3291	264	30	(	(	PUNCT
cana-3291	264	31	)	)	PUNCT
cana-3291	264	32	(	(	PUNCT
cana-3291	264	33	1	1	X
cana-3291	264	34	)	)	SYM
cana-3291	264	35	2	2	NUM
cana-3291	264	36	2	2	NUM
cana-3291	264	37	2	2	NUM
cana-3291	264	38	!	!	PUNCT
cana-3291	265	1	(	(	PUNCT
cana-3291	265	2	)	)	PUNCT
cana-3291	265	3	(	(	PUNCT
cana-3291	265	4	)	)	PUNCT
cana-3291	265	5	(	(	PUNCT
cana-3291	265	6	)	)	PUNCT
cana-3291	265	7	,	,	PUNCT
cana-3291	265	8	,	,	PUNCT
cana-3291	265	9	;	;	PUNCT
cana-3291	265	10	a	a	DET
cana-3291	265	11	b	b	NOUN
cana-3291	265	12	a	a	DET
cana-3291	265	13	bn	bn	NOUN
cana-3291	265	14	a	a	DET
cana-3291	265	15	x	x	X
cana-3291	265	16	nii	nii	PROPN
cana-3291	265	17	a	a	DET
cana-3291	265	18	u	u	NOUN
cana-3291	265	19	v	v	ADP
cana-3291	265	20	u	u	NOUN
cana-3291	265	21	v	v	ADP
cana-3291	265	22	f	f	PROPN
cana-3291	265	23	uvw	uvw	PROPN
cana-3291	265	24	dudvw	dudvw	PROPN
cana-3291	265	25	n	n	CCONJ
cana-3291	265	26	a	a	PRON
cana-3291	265	27	b	b	NOUN
cana-3291	265	28	a	a	DET
cana-3291	265	29	b	b	NOUN
cana-3291	265	30	a	a	DET
cana-3291	265	31	b	b	NOUN
cana-3291	265	32	i	i	PRON
cana-3291	265	33	a	a	DET
cana-3291	265	34			ADJ
cana-3291	265	35			ADJ
cana-3291	265	36			ADJ
cana-3291	265	37			ADJ
cana-3291	265	38			ADJ
cana-3291	265	39	−	−	PROPN
cana-3291	265	40	−	−	PROPN
cana-3291	265	41	−	−	PROPN
cana-3291	265	42	−	−	PROPN
cana-3291	265	43	−	−	PROPN
cana-3291	265	44			PROPN
cana-3291	265	45			NOUN
cana-3291	265	46	−	−	PROPN
cana-3291	266	1	+	+	ADJ
cana-3291	266	2			VERB
cana-3291	266	3	+	+	ADJ
cana-3291	266	4			NOUN
cana-3291	266	5	=	=	NOUN
cana-3291	266	6	−	−	NOUN
cana-3291	266	7	−	−	NOUN
cana-3291	266	8			NOUN
cana-3291	266	9			NOUN
cana-3291	266	10			VERB
cana-3291	266	11			VERB
cana-3291	266	12	−	−	NOUN
cana-3291	266	13	−	−	NOUN
cana-3291	267	1	+	+	NOUN
cana-3291	267	2			PROPN
cana-3291	267	3			PROPN
cana-3291	267	4			ADV
cana-3291	267	5	hence	hence	ADV
cana-3291	267	6	the	the	DET
cana-3291	267	7	theorem	theorem	VERB
cana-3291	267	8	.	.	PUNCT
cana-3291	267	9	special	special	ADJ
cana-3291	267	10	cases	case	NOUN
cana-3291	267	11	:	:	PUNCT
cana-3291	267	12	if	if	SCONJ
cana-3291	267	13	‘	'	PUNCT
cana-3291	267	14	a	a	DET
cana-3291	267	15	’	'	PUNCT
cana-3291	267	16	be	be	AUX
cana-3291	267	17	any	any	DET
cana-3291	267	18	square	square	ADJ
cana-3291	267	19	matrix	matrix	NOUN
cana-3291	267	20	of	of	ADP
cana-3291	267	21	order	order	NOUN
cana-3291	267	22	n	n	PRON
cana-3291	267	23	n	n	VERB
cana-3291	267	24	and	and	CCONJ
cana-3291	267	25	(	(	PUNCT
cana-3291	267	26	)	)	PUNCT
cana-3291	267	27	(	(	PUNCT
cana-3291	267	28	,	,	PUNCT
cana-3291	267	29	)	)	PUNCT
cana-3291	267	30	a	a	DET
cana-3291	267	31	nj	nj	PROPN
cana-3291	268	1	x	x	PUNCT
cana-3291	268	2	w	w	NOUN
cana-3291	268	3	be	be	AUX
cana-3291	268	4	the	the	DET
cana-3291	268	5	modified	modify	VERB
cana-3291	268	6	jacobi	jacobi	NOUN
cana-3291	268	7	matrix	matrix	NOUN
cana-3291	268	8	polynomial	polynomial	NOUN
cana-3291	268	9	,	,	PUNCT
cana-3291	268	10	then	then	ADV
cana-3291	268	11	the	the	DET
cana-3291	268	12	applications	application	NOUN
cana-3291	268	13	of	of	ADP
cana-3291	268	14	the	the	DET
cana-3291	268	15	above	above	ADJ
cana-3291	268	16	theorems	theorem	NOUN
cana-3291	268	17	of	of	ADP
cana-3291	268	18	this	this	DET
cana-3291	268	19	polynomial	polynomial	NOUN
cana-3291	268	20	are	be	AUX
cana-3291	268	21	as	as	SCONJ
cana-3291	268	22	follows	follow	VERB
cana-3291	268	23	:	:	PUNCT
cana-3291	268	24	theorem	theorem	ADJ
cana-3291	268	25	:	:	PUNCT
cana-3291	268	26	1	1	NUM
cana-3291	268	27	1	1	NUM
cana-3291	268	28	(	(	PUNCT
cana-3291	268	29	)	)	PUNCT
cana-3291	268	30	(	(	PUNCT
cana-3291	268	31	)	)	PUNCT
cana-3291	268	32	0	0	NUM
cana-3291	269	1	(	(	PUNCT
cana-3291	269	2	,	,	PUNCT
cana-3291	269	3	)	)	PUNCT
cana-3291	269	4	(	(	PUNCT
cana-3291	269	5	,	,	PUNCT
cana-3291	269	6	)	)	PUNCT
cana-3291	269	7	(	(	PUNCT
cana-3291	269	8	1	1	X
cana-3291	269	9	)	)	PUNCT
cana-3291	269	10	a	a	DET
cana-3291	269	11	a	a	DET
cana-3291	269	12	a	a	DET
cana-3291	269	13	n	n	CCONJ
cana-3291	269	14	n	n	NOUN
cana-3291	269	15	t	t	NOUN
cana-3291	270	1	j	j	X
cana-3291	270	2	x	x	X
cana-3291	270	3	w	w	PROPN
cana-3291	270	4	j	j	PROPN
cana-3291	270	5	x	x	INTJ
cana-3291	270	6	wt	wt	PROPN
cana-3291	270	7	dt	dt	NOUN
cana-3291	270	8	t	t	PROPN
cana-3291	270	9	−	−	PROPN
cana-3291	270	10	=	=	NOUN
cana-3291	270	11	−	−	NOUN
cana-3291	270	12	proof	proof	NOUN
cana-3291	270	13	:	:	PUNCT
cana-3291	270	14	by	by	ADP
cana-3291	270	15	setting	set	VERB
cana-3291	270	16	a	a	DET
cana-3291	270	17	=	=	SYM
cana-3291	270	18	b	b	NOUN
cana-3291	270	19	,	,	PUNCT
cana-3291	270	20	in	in	ADP
cana-3291	270	21	(	(	PUNCT
cana-3291	270	22	1.15	1.15	NUM
cana-3291	270	23	)	)	PUNCT
cana-3291	270	24	,	,	PUNCT
cana-3291	270	25	we	we	PRON
cana-3291	270	26	come	come	VERB
cana-3291	270	27	across	across	ADV
cana-3291	270	28	at	at	ADP
cana-3291	270	29	1	1	NUM
cana-3291	270	30	1	1	NUM
cana-3291	270	31	(	(	PUNCT
cana-3291	270	32	)	)	PUNCT
cana-3291	270	33	00	00	PUNCT
cana-3291	271	1	(	(	PUNCT
cana-3291	271	2	)	)	PUNCT
cana-3291	271	3	(	(	PUNCT
cana-3291	271	4	)	)	PUNCT
cana-3291	271	5	(	(	PUNCT
cana-3291	271	6	)	)	PUNCT
cana-3291	271	7	(	(	PUNCT
cana-3291	271	8	,	,	PUNCT
cana-3291	271	9	)	)	PUNCT
cana-3291	271	10	(	(	PUNCT
cana-3291	271	11	1	1	NUM
cana-3291	271	12	)	)	PUNCT
cana-3291	271	13	!	!	PUNCT
cana-3291	271	14	!	!	PUNCT
cana-3291	272	1	(	(	PUNCT
cana-3291	272	2	)	)	PUNCT
cana-3291	272	3	r	r	NOUN
cana-3291	272	4	ra	ra	PROPN
cana-3291	272	5	n	n	ADP
cana-3291	272	6	a	a	DET
cana-3291	272	7	n	n	NOUN
cana-3291	272	8	r	r	NOUN
cana-3291	272	9	n	n	NOUN
cana-3291	272	10	r	r	NOUN
cana-3291	272	11	r	r	NOUN
cana-3291	272	12	x	x	SYM
cana-3291	272	13	ni	ni	PROPN
cana-3291	272	14	wt	wt	PROPN
cana-3291	272	15	t	t	PROPN
cana-3291	272	16	a	a	PRON
cana-3291	273	1	i	i	NOUN
cana-3291	273	2	w	w	PROPN
cana-3291	273	3	j	j	PROPN
cana-3291	273	4	x	x	SYM
cana-3291	273	5	w	w	NOUN
cana-3291	273	6	dt	dt	X
cana-3291	273	7	t	t	PROPN
cana-3291	274	1	n	n	CCONJ
cana-3291	274	2	r	r	NOUN
cana-3291	274	3	i	i	PRON
cana-3291	274	4	a	a	DET
cana-3291	274	5	−	−	NOUN
cana-3291	274	6	=	=	PUNCT
cana-3291	274	7			NOUN
cana-3291	274	8			NOUN
cana-3291	274	9	−	−	PROPN
cana-3291	275	1			PROPN
cana-3291	275	2			PROPN
cana-3291	276	1	+	+	CCONJ
cana-3291	276	2			PROPN
cana-3291	276	3			NOUN
cana-3291	276	4	=	=	SYM
cana-3291	276	5	−	−	PROPN
cana-3291	276	6	+	+	NUM
cana-3291	276	7			NUM
cana-3291	276	8	1	1	NUM
cana-3291	276	9	1	1	NUM
cana-3291	276	10	(	(	PUNCT
cana-3291	276	11	)	)	PUNCT
cana-3291	276	12	0	0	NUM
cana-3291	277	1	(	(	PUNCT
cana-3291	277	2	,	,	PUNCT
cana-3291	277	3	)	)	PUNCT
cana-3291	277	4	(	(	PUNCT
cana-3291	277	5	1	1	X
cana-3291	277	6	)	)	PUNCT
cana-3291	277	7	a	a	DET
cana-3291	277	8	a	a	PRON
cana-3291	277	9	n	n	NOUN
cana-3291	277	10	t	t	NOUN
cana-3291	277	11	j	j	NOUN
cana-3291	277	12	x	x	SYM
cana-3291	277	13	wt	wt	PROPN
cana-3291	277	14	dt	dt	NOUN
cana-3291	277	15	t	t	PROPN
cana-3291	278	1	−	−	PROPN
cana-3291	278	2	=	=	NOUN
cana-3291	278	3	−	−	NOUN
cana-3291	278	4	theorem	theorem	VERB
cana-3291	278	5	:	:	PUNCT
cana-3291	278	6	1	1	NUM
cana-3291	278	7	1	1	NUM
cana-3291	278	8	(	(	PUNCT
cana-3291	278	9	)	)	PUNCT
cana-3291	278	10	(	(	PUNCT
cana-3291	278	11	)	)	PUNCT
cana-3291	278	12	0	0	NUM
cana-3291	278	13	(	(	PUNCT
cana-3291	278	14	,	,	PUNCT
cana-3291	278	15	)	)	PUNCT
cana-3291	278	16	(	(	PUNCT
cana-3291	278	17	)	)	PUNCT
cana-3291	278	18	(	(	PUNCT
cana-3291	278	19	1	1	X
cana-3291	278	20	)	)	PUNCT
cana-3291	278	21	a	a	DET
cana-3291	278	22	a	a	DET
cana-3291	278	23	a	a	DET
cana-3291	278	24	n	n	CCONJ
cana-3291	278	25	n	n	NOUN
cana-3291	278	26	t	t	NOUN
cana-3291	279	1	j	j	X
cana-3291	279	2	x	x	X
cana-3291	279	3	w	w	PROPN
cana-3291	279	4	l	l	NOUN
cana-3291	279	5	xt	xt	PROPN
cana-3291	279	6	dt	dt	PROPN
cana-3291	279	7	t	t	PROPN
cana-3291	280	1	−	−	PROPN
cana-3291	280	2	=	=	NOUN
cana-3291	280	3	−	−	NOUN
cana-3291	280	4	proof	proof	NOUN
cana-3291	280	5	:	:	PUNCT
cana-3291	280	6	by	by	ADP
cana-3291	280	7	considering	consider	VERB
cana-3291	280	8	0w→	0w→	PROPN
cana-3291	280	9	and	and	CCONJ
cana-3291	280	10	setting	set	VERB
cana-3291	280	11	a	a	DET
cana-3291	280	12	b=	b=	NOUN
cana-3291	280	13	in	in	ADP
cana-3291	280	14	(	(	PUNCT
cana-3291	280	15	1.15	1.15	NUM
cana-3291	280	16	)	)	PUNCT
cana-3291	280	17	,	,	PUNCT
cana-3291	280	18	we	we	PRON
cana-3291	280	19	arrive	arrive	VERB
cana-3291	280	20	at	at	ADP
cana-3291	280	21	the	the	DET
cana-3291	280	22	following	following	NOUN
cana-3291	280	23	:	:	PUNCT
cana-3291	280	24	1	1	NUM
cana-3291	280	25	1	1	NUM
cana-3291	280	26	(	(	PUNCT
cana-3291	280	27	)	)	PUNCT
cana-3291	280	28	00	00	PUNCT
cana-3291	281	1	(	(	PUNCT
cana-3291	281	2	)	)	PUNCT
cana-3291	281	3	(	(	PUNCT
cana-3291	281	4	)	)	PUNCT
cana-3291	281	5	(	(	PUNCT
cana-3291	281	6	)	)	PUNCT
cana-3291	281	7	(	(	PUNCT
cana-3291	281	8	,	,	PUNCT
cana-3291	281	9	)	)	PUNCT
cana-3291	281	10	(	(	PUNCT
cana-3291	281	11	1	1	NUM
cana-3291	281	12	)	)	PUNCT
cana-3291	281	13	!	!	PUNCT
cana-3291	281	14	!	!	PUNCT
cana-3291	282	1	(	(	PUNCT
cana-3291	282	2	)	)	PUNCT
cana-3291	282	3	a	a	DET
cana-3291	282	4	rn	rn	PROPN
cana-3291	282	5	a	a	PRON
cana-3291	282	6	n	n	NOUN
cana-3291	282	7	r	r	NOUN
cana-3291	282	8	n	n	NOUN
cana-3291	282	9	r	r	NOUN
cana-3291	282	10	r	r	NOUN
cana-3291	282	11	t	t	NOUN
cana-3291	282	12	a	a	PRON
cana-3291	283	1	i	i	PRON
cana-3291	283	2	ni	ni	PROPN
cana-3291	283	3	xt	xt	PROPN
cana-3291	284	1	j	j	PROPN
cana-3291	284	2	x	x	PUNCT
cana-3291	284	3	w	w	VERB
cana-3291	284	4	dt	dt	X
cana-3291	284	5	t	t	PROPN
cana-3291	284	6	n	n	PROPN
cana-3291	284	7	n	n	PROPN
cana-3291	284	8	i	i	PRON
cana-3291	284	9	a	a	DET
cana-3291	284	10	−	−	NOUN
cana-3291	285	1	=	=	SYM
cana-3291	285	2	+	+	NUM
cana-3291	285	3	−	−	PROPN
cana-3291	285	4	=	=	SYM
cana-3291	286	1	−	−	PROPN
cana-3291	286	2	+	+	NUM
cana-3291	286	3			NUM
cana-3291	286	4	1	1	NUM
cana-3291	286	5	1	1	NUM
cana-3291	286	6	(	(	PUNCT
cana-3291	286	7	)	)	PUNCT
cana-3291	286	8	0	0	NUM
cana-3291	287	1	(	(	PUNCT
cana-3291	287	2	)	)	PUNCT
cana-3291	287	3	(	(	PUNCT
cana-3291	287	4	1	1	X
cana-3291	287	5	)	)	PUNCT
cana-3291	287	6	a	a	DET
cana-3291	287	7	a	a	NOUN
cana-3291	287	8	n	n	ADP
cana-3291	287	9	t	t	PROPN
cana-3291	287	10	l	l	NOUN
cana-3291	287	11	xt	xt	PROPN
cana-3291	288	1	dt	dt	PROPN
cana-3291	288	2	t	t	PROPN
cana-3291	288	3	−	−	PROPN
cana-3291	289	1	=	=	PUNCT
cana-3291	289	2	−	−	NOUN
cana-3291	289	3	where	where	SCONJ
cana-3291	289	4	(	(	PUNCT
cana-3291	289	5	)	)	PUNCT
cana-3291	289	6	(	(	PUNCT
cana-3291	289	7	)	)	PUNCT
cana-3291	289	8	a	a	DET
cana-3291	289	9	nl	nl	NOUN
cana-3291	289	10	x	x	PROPN
cana-3291	289	11	is	be	AUX
cana-3291	289	12	the	the	DET
cana-3291	289	13	laguerre	laguerre	NOUN
cana-3291	289	14	matrix	matrix	NOUN
cana-3291	289	15	polynomial	polynomial	NOUN
cana-3291	289	16	of	of	ADP
cana-3291	289	17	one	one	NUM
cana-3291	289	18	variable	variable	NOUN
cana-3291	289	19	[	[	X
cana-3291	289	20	2	2	NUM
cana-3291	289	21	]	]	PUNCT
cana-3291	289	22	.	.	PUNCT
cana-3291	290	1	theorem	theorem	VERB
cana-3291	290	2	:	:	PUNCT
cana-3291	290	3	communications	communication	NOUN
cana-3291	290	4	on	on	ADP
cana-3291	290	5	applied	apply	VERB
cana-3291	290	6	nonlinear	nonlinear	ADJ
cana-3291	290	7	analysis	analysis	NOUN
cana-3291	290	8	issn	issn	NOUN
cana-3291	290	9	:	:	PUNCT
cana-3291	290	10	1074	1074	NUM
cana-3291	290	11	-	-	PUNCT
cana-3291	290	12	133x	133x	NUM
cana-3291	290	13	vol	vol	NOUN
cana-3291	290	14	32	32	NUM
cana-3291	290	15	no	no	NOUN
cana-3291	290	16	.	.	PUNCT
cana-3291	291	1	6s	6s	NUM
cana-3291	291	2	(	(	PUNCT
cana-3291	291	3	2025	2025	NUM
cana-3291	291	4	)	)	PUNCT
cana-3291	291	5	261	261	NUM
cana-3291	291	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3291	291	7	2	2	NUM
cana-3291	291	8	(	(	PUNCT
cana-3291	291	9	)	)	PUNCT
cana-3291	291	10	2	2	NUM
cana-3291	291	11	1	1	NUM
cana-3291	291	12	2	2	NUM
cana-3291	291	13	1	1	NUM
cana-3291	291	14	2	2	NUM
cana-3291	291	15	;	;	PUNCT
cana-3291	291	16	(	(	PUNCT
cana-3291	291	17	)	)	PUNCT
cana-3291	291	18	(	(	PUNCT
cana-3291	291	19	,	,	PUNCT
cana-3291	291	20	)	)	PUNCT
cana-3291	291	21	,	,	PUNCT
cana-3291	291	22	;	;	PUNCT
cana-3291	291	23	!	!	PUNCT
cana-3291	292	1	(	(	PUNCT
cana-3291	292	2	)	)	PUNCT
cana-3291	292	3	a	a	DET
cana-3291	292	4	t	t	NOUN
cana-3291	292	5	an	an	DET
cana-3291	292	6	n	n	X
cana-3291	292	7	nii	nii	PROPN
cana-3291	292	8	a	a	DET
cana-3291	292	9	j	j	PROPN
cana-3291	292	10	x	x	SYM
cana-3291	292	11	w	w	PROPN
cana-3291	292	12	e	e	PROPN
cana-3291	292	13	t	t	PROPN
cana-3291	292	14	f	f	X
cana-3291	292	15	xt	xt	PROPN
cana-3291	292	16	dt	dt	PROPN
cana-3291	293	1	a	a	DET
cana-3291	293	2	i	i	PRON
cana-3291	293	3	an	an	DET
cana-3291	293	4	a	a	DET
cana-3291	293	5			NOUN
cana-3291	293	6	−	−	ADP
cana-3291	293	7	−	−	NOUN
cana-3291	293	8	−	−	NOUN
cana-3291	293	9	−	−	NOUN
cana-3291	293	10	+	+	NOUN
cana-3291	293	11	=	=	SYM
cana-3291	293	12			NOUN
cana-3291	293	13			NOUN
cana-3291	293	14	+	+	ADP
cana-3291	293	15			VERB
cana-3291	293	16			NOUN
cana-3291	293	17			PROPN
cana-3291	293	18			ADP
cana-3291	293	19	proof	proof	NOUN
cana-3291	293	20	:	:	PUNCT
cana-3291	293	21	by	by	ADP
cana-3291	293	22	assuming	assume	VERB
cana-3291	293	23	0w→	0w→	NUM
cana-3291	293	24	,	,	PUNCT
cana-3291	293	25	we	we	PRON
cana-3291	293	26	have	have	VERB
cana-3291	293	27	2	2	NUM
cana-3291	293	28	2	2	NUM
cana-3291	293	29	(	(	PUNCT
cana-3291	293	30	)	)	PUNCT
cana-3291	293	31	2	2	NUM
cana-3291	293	32	1	1	NUM
cana-3291	293	33	0	0	NUM
cana-3291	293	34	(	(	PUNCT
cana-3291	293	35	)	)	PUNCT
cana-3291	293	36	(	(	PUNCT
cana-3291	293	37	)	)	PUNCT
cana-3291	293	38	(	(	PUNCT
cana-3291	293	39	)	)	PUNCT
cana-3291	293	40	(	(	PUNCT
cana-3291	293	41	,	,	PUNCT
cana-3291	293	42	)	)	PUNCT
cana-3291	293	43	!	!	PUNCT
cana-3291	294	1	(	(	PUNCT
cana-3291	294	2	)	)	PUNCT
cana-3291	294	3	(	(	PUNCT
cana-3291	294	4	)	)	PUNCT
cana-3291	294	5	(	(	PUNCT
cana-3291	294	6	)	)	PUNCT
cana-3291	294	7	!	!	PUNCT
cana-3291	295	1	rn	rn	PROPN
cana-3291	295	2	a	a	DET
cana-3291	295	3	t	t	NOUN
cana-3291	295	4	an	an	DET
cana-3291	295	5	r	r	NOUN
cana-3291	295	6	n	n	CCONJ
cana-3291	295	7	r	r	NOUN
cana-3291	295	8	r	r	NOUN
cana-3291	295	9	r	r	NOUN
cana-3291	295	10	i	i	PRON
cana-3291	295	11	a	a	DET
cana-3291	295	12	ni	ni	PROPN
cana-3291	295	13	xt	xt	PROPN
cana-3291	295	14	j	j	PROPN
cana-3291	296	1	x	x	PUNCT
cana-3291	296	2	w	w	PROPN
cana-3291	296	3	e	e	PROPN
cana-3291	296	4	t	t	NOUN
cana-3291	296	5	dt	dt	X
cana-3291	296	6	n	n	PROPN
cana-3291	296	7	a	a	PRON
cana-3291	296	8	a	a	PRON
cana-3291	296	9	i	i	PRON
cana-3291	296	10	a	a	DET
cana-3291	296	11	r	r	NOUN
cana-3291	296	12			NOUN
cana-3291	296	13	−	−	NOUN
cana-3291	296	14	−	−	NOUN
cana-3291	297	1	=	=	NUM
cana-3291	297	2	−	−	NOUN
cana-3291	297	3	+	+	CCONJ
cana-3291	297	4	−	−	NOUN
cana-3291	297	5	=	=	SYM
cana-3291	298	1			VERB
cana-3291	298	2	+	+	NUM
cana-3291	298	3			NUM
cana-3291	298	4	2	2	NUM
cana-3291	298	5	2	2	NUM
cana-3291	298	6	1	1	NUM
cana-3291	298	7	2	2	NUM
cana-3291	298	8	1	1	NUM
cana-3291	298	9	2	2	NUM
cana-3291	298	10	;	;	PUNCT
cana-3291	298	11	(	(	PUNCT
cana-3291	298	12	)	)	PUNCT
cana-3291	298	13	,	,	PUNCT
cana-3291	298	14	;	;	PUNCT
cana-3291	298	15	!	!	PUNCT
cana-3291	299	1	(	(	PUNCT
cana-3291	299	2	)	)	PUNCT
cana-3291	299	3	t	t	PROPN
cana-3291	299	4	an	an	DET
cana-3291	299	5	nii	nii	PROPN
cana-3291	299	6	a	a	PRON
cana-3291	299	7	e	e	PROPN
cana-3291	299	8	t	t	PROPN
cana-3291	300	1	f	f	X
cana-3291	301	1	xt	xt	PROPN
cana-3291	302	1	dt	dt	PROPN
cana-3291	303	1	a	a	DET
cana-3291	303	2	i	i	PRON
cana-3291	303	3	an	an	DET
cana-3291	303	4	a	a	DET
cana-3291	303	5			NOUN
cana-3291	303	6	−	−	ADP
cana-3291	303	7	−	−	NOUN
cana-3291	303	8	−	−	NOUN
cana-3291	303	9	−	−	NOUN
cana-3291	303	10	+	+	NOUN
cana-3291	303	11	=	=	SYM
cana-3291	303	12			NOUN
cana-3291	303	13			NOUN
cana-3291	303	14	+	+	ADP
cana-3291	303	15			VERB
cana-3291	303	16			NOUN
cana-3291	303	17			PROPN
cana-3291	303	18			ADP
cana-3291	303	19	conclusion	conclusion	VERB
cana-3291	303	20	recent	recent	ADJ
cana-3291	303	21	advancements	advancement	NOUN
cana-3291	303	22	in	in	ADP
cana-3291	303	23	matrix	matrix	NOUN
cana-3291	303	24	polynomial	polynomial	ADJ
cana-3291	303	25	structures	structure	NOUN
cana-3291	303	26	associated	associate	VERB
cana-3291	303	27	with	with	ADP
cana-3291	303	28	special	special	ADJ
cana-3291	303	29	functions	function	NOUN
cana-3291	303	30	have	have	AUX
cana-3291	303	31	gained	gain	VERB
cana-3291	303	32	significant	significant	ADJ
cana-3291	303	33	traction	traction	NOUN
cana-3291	303	34	,	,	PUNCT
cana-3291	303	35	showcasing	showcase	VERB
cana-3291	303	36	a	a	DET
cana-3291	303	37	diverse	diverse	ADJ
cana-3291	303	38	array	array	NOUN
cana-3291	303	39	of	of	ADP
cana-3291	303	40	applications	application	NOUN
cana-3291	303	41	across	across	ADP
cana-3291	303	42	various	various	ADJ
cana-3291	303	43	engineering	engineering	NOUN
cana-3291	303	44	disciplines	discipline	NOUN
cana-3291	303	45	.	.	PUNCT
cana-3291	304	1	this	this	DET
cana-3291	304	2	paper	paper	NOUN
cana-3291	304	3	primarily	primarily	ADV
cana-3291	304	4	intended	intend	VERB
cana-3291	304	5	to	to	PART
cana-3291	304	6	explore	explore	VERB
cana-3291	304	7	and	and	CCONJ
cana-3291	304	8	derive	derive	VERB
cana-3291	304	9	multiple	multiple	ADJ
cana-3291	304	10	integral	integral	ADJ
cana-3291	304	11	representations	representation	NOUN
cana-3291	304	12	for	for	ADP
cana-3291	304	13	the	the	DET
cana-3291	304	14	modified	modify	VERB
cana-3291	304	15	jacobi	jacobi	PROPN
cana-3291	304	16	matrix	matrix	NOUN
cana-3291	304	17	polynomial	polynomial	NOUN
cana-3291	304	18	.	.	PUNCT
cana-3291	305	1	specifically	specifically	ADV
cana-3291	305	2	,	,	PUNCT
cana-3291	305	3	we	we	PRON
cana-3291	305	4	will	will	AUX
cana-3291	305	5	delve	delve	VERB
cana-3291	305	6	into	into	ADP
cana-3291	305	7	both	both	CCONJ
cana-3291	305	8	finite	finite	ADJ
cana-3291	305	9	and	and	CCONJ
cana-3291	305	10	infinite	infinite	VERB
cana-3291	305	11	single	single	ADJ
cana-3291	305	12	integral	integral	ADJ
cana-3291	305	13	representations	representation	NOUN
cana-3291	305	14	,	,	PUNCT
cana-3291	305	15	as	as	ADV
cana-3291	305	16	well	well	ADV
cana-3291	305	17	as	as	ADP
cana-3291	305	18	double	double	ADJ
cana-3291	305	19	integral	integral	ADJ
cana-3291	305	20	representations	representation	NOUN
cana-3291	305	21	of	of	ADP
cana-3291	305	22	the	the	DET
cana-3291	305	23	polynomial	polynomial	NOUN
cana-3291	305	24	.	.	PUNCT
cana-3291	306	1	by	by	ADP
cana-3291	306	2	examining	examine	VERB
cana-3291	306	3	these	these	DET
cana-3291	306	4	integral	integral	ADJ
cana-3291	306	5	forms	form	NOUN
cana-3291	306	6	,	,	PUNCT
cana-3291	306	7	we	we	PRON
cana-3291	306	8	seek	seek	VERB
cana-3291	306	9	to	to	PART
cana-3291	306	10	enhance	enhance	VERB
cana-3291	306	11	the	the	DET
cana-3291	306	12	understanding	understanding	NOUN
cana-3291	306	13	of	of	ADP
cana-3291	306	14	their	their	PRON
cana-3291	306	15	mathematical	mathematical	ADJ
cana-3291	306	16	properties	property	NOUN
cana-3291	306	17	and	and	CCONJ
cana-3291	306	18	implications	implication	NOUN
cana-3291	306	19	,	,	PUNCT
cana-3291	306	20	thereby	thereby	ADV
cana-3291	306	21	providing	provide	VERB
cana-3291	306	22	valuable	valuable	ADJ
cana-3291	306	23	insights	insight	NOUN
cana-3291	306	24	that	that	PRON
cana-3291	306	25	can	can	AUX
cana-3291	306	26	be	be	AUX
cana-3291	306	27	leveraged	leverage	VERB
cana-3291	306	28	in	in	ADP
cana-3291	306	29	practical	practical	ADJ
cana-3291	306	30	engineering	engineering	NOUN
cana-3291	306	31	scenarios	scenario	NOUN
cana-3291	306	32	like	like	ADP
cana-3291	306	33	applying	apply	VERB
cana-3291	306	34	laplace	laplace	NOUN
cana-3291	306	35	transforms	transform	VERB
cana-3291	306	36	.	.	PUNCT
cana-3291	307	1	the	the	DET
cana-3291	307	2	exploration	exploration	NOUN
cana-3291	307	3	of	of	ADP
cana-3291	307	4	these	these	DET
cana-3291	307	5	representations	representation	NOUN
cana-3291	307	6	not	not	PART
cana-3291	307	7	only	only	ADV
cana-3291	307	8	enriches	enrich	VERB
cana-3291	307	9	the	the	DET
cana-3291	307	10	theoretical	theoretical	ADJ
cana-3291	307	11	framework	framework	NOUN
cana-3291	307	12	surrounding	surround	VERB
cana-3291	307	13	modified	modified	ADJ
cana-3291	307	14	jacobi	jacobi	NOUN
cana-3291	307	15	matrix	matrix	NOUN
cana-3291	307	16	polynomials	polynomial	NOUN
cana-3291	307	17	but	but	CCONJ
cana-3291	307	18	also	also	ADV
cana-3291	307	19	highlights	highlight	VERB
cana-3291	307	20	their	their	PRON
cana-3291	307	21	potential	potential	ADJ
cana-3291	307	22	utility	utility	NOUN
cana-3291	307	23	in	in	ADP
cana-3291	307	24	solving	solve	VERB
cana-3291	307	25	complex	complex	ADJ
cana-3291	307	26	problems	problem	NOUN
cana-3291	307	27	within	within	ADP
cana-3291	307	28	the	the	DET
cana-3291	307	29	engineering	engineering	NOUN
cana-3291	307	30	domain	domain	NOUN
cana-3291	307	31	[	[	X
cana-3291	307	32	17	17	NUM
cana-3291	307	33	,	,	PUNCT
cana-3291	307	34	18	18	NUM
cana-3291	307	35	]	]	PUNCT
cana-3291	307	36	.	.	PUNCT
cana-3291	308	1	acknowledgment	acknowledgment	NOUN
cana-3291	308	2	the	the	DET
cana-3291	308	3	authors	author	NOUN
cana-3291	308	4	are	be	AUX
cana-3291	308	5	very	very	ADV
cana-3291	308	6	thankful	thankful	ADJ
cana-3291	308	7	to	to	ADP
cana-3291	308	8	the	the	DET
cana-3291	308	9	reviewers	reviewer	NOUN
cana-3291	308	10	for	for	ADP
cana-3291	308	11	their	their	PRON
cana-3291	308	12	comments	comment	NOUN
cana-3291	308	13	and	and	CCONJ
cana-3291	308	14	suggestions	suggestion	NOUN
cana-3291	308	15	.	.	PUNCT
cana-3291	309	1	and	and	CCONJ
cana-3291	309	2	they	they	PRON
cana-3291	309	3	are	be	AUX
cana-3291	309	4	very	very	ADV
cana-3291	309	5	thankful	thankful	ADJ
cana-3291	309	6	to	to	ADP
cana-3291	309	7	their	their	PRON
cana-3291	309	8	corresponding	correspond	VERB
cana-3291	309	9	organizations	organization	NOUN
cana-3291	309	10	for	for	ADP
cana-3291	309	11	their	their	PRON
cana-3291	309	12	encouragement	encouragement	NOUN
cana-3291	309	13	references	reference	NOUN
cana-3291	309	14	[	[	X
cana-3291	309	15	1	1	NUM
cana-3291	309	16	]	]	SYM
cana-3291	309	17	m.m.makky.(2021	m.m.makky.(2021	NOUN
cana-3291	309	18	)	)	PUNCT
cana-3291	309	19	extended	extend	VERB
cana-3291	309	20	of	of	ADP
cana-3291	309	21	legendre	legendre	PROPN
cana-3291	309	22	matrix	matrix	NOUN
cana-3291	309	23	polynomials	polynomial	NOUN
cana-3291	309	24	of	of	ADP
cana-3291	309	25	two	two	NUM
cana-3291	309	26	variables	variable	NOUN
cana-3291	309	27	.	.	PUNCT
cana-3291	310	1	international	international	ADJ
cana-3291	310	2	journal	journal	PROPN
cana-3291	310	3	of	of	ADP
cana-3291	310	4	mathematical	mathematical	ADJ
cana-3291	310	5	analysis	analysis	NOUN
cana-3291	310	6	.	.	PUNCT
cana-3291	311	1	15(2).85	15(2).85	NUM
cana-3291	311	2	-	-	SYM
cana-3291	311	3	93	93	NUM
cana-3291	311	4	.	.	PUNCT
cana-3291	312	1	doi	doi	NOUN
cana-3291	312	2	:	:	PUNCT
cana-3291	312	3	10.12988	10.12988	NUM
cana-3291	312	4	/	/	SYM
cana-3291	312	5	ijma.2021.912102	ijma.2021.912102	PRON
cana-3291	312	6	[	[	X
cana-3291	312	7	2	2	NUM
cana-3291	312	8	]	]	PUNCT
cana-3291	312	9	fuli	fuli	NOUN
cana-3291	312	10	he	he	PRON
cana-3291	312	11	,	,	PUNCT
cana-3291	312	12	ahmed	ahmed	PROPN
cana-3291	312	13	bakhet	bakhet	PROPN
cana-3291	312	14	,	,	PUNCT
cana-3291	312	15	m.hidan	m.hidan	PROPN
cana-3291	312	16	&	&	CCONJ
cana-3291	312	17	m.abdalla	m.abdalla	NOUN
cana-3291	312	18	.	.	PUNCT
cana-3291	313	1	(	(	PUNCT
cana-3291	313	2	2019	2019	NUM
cana-3291	313	3	)	)	PUNCT
cana-3291	313	4	two	two	NUM
cana-3291	313	5	variables	variable	NOUN
cana-3291	313	6	shivley	shivley	PROPN
cana-3291	313	7	’s	’s	PART
cana-3291	313	8	matrix	matrix	NOUN
cana-3291	313	9	polynomials	polynomial	NOUN
cana-3291	313	10	.	.	PUNCT
cana-3291	314	1	symmetry.11(2	symmetry.11(2	PROPN
cana-3291	314	2	)	)	PUNCT
cana-3291	315	1	https://doi.org/10.3390/sym11020151	https://doi.org/10.3390/sym11020151	NOUN
cana-3291	316	1	[	[	X
cana-3291	316	2	3	3	X
cana-3291	316	3	]	]	X
cana-3291	316	4	g.yasmin	g.yasmin	NOUN
cana-3291	316	5	&	&	CCONJ
cana-3291	316	6	s	s	PROPN
cana-3291	316	7	khan	khan	PROPN
cana-3291	316	8	.	.	PUNCT
cana-3291	317	1	(	(	PUNCT
cana-3291	317	2	2014	2014	NUM
cana-3291	317	3	)	)	PUNCT
cana-3291	317	4	hermite	hermite	ADJ
cana-3291	317	5	matrix	matrix	NOUN
cana-3291	317	6	-	-	PUNCT
cana-3291	317	7	based	base	VERB
cana-3291	317	8	polynomial	polynomial	NOUN
cana-3291	317	9	of	of	ADP
cana-3291	317	10	two	two	NUM
cana-3291	317	11	variables	variable	NOUN
cana-3291	317	12	and	and	CCONJ
cana-3291	317	13	lie	lie	VERB
cana-3291	317	14	algebraic	algebraic	ADJ
cana-3291	317	15	techniques	technique	NOUN
cana-3291	317	16	.	.	PUNCT
cana-3291	318	1	southeast	southeast	ADJ
cana-3291	318	2	asian	asian	PROPN
cana-3291	318	3	bullmath.38.603	bullmath.38.603	PROPN
cana-3291	318	4	-	-	SYM
cana-3291	318	5	618	618	NUM
cana-3291	318	6	.	.	PUNCT
cana-3291	319	1	https://www.researchgate.net/publication/264236643_hermite_matrix_based_polynomials_of_two_variables_and	https://www.researchgate.net/publication/264236643_hermite_matrix_based_polynomials_of_two_variables_and	NOUN
cana-3291	319	2	_	_	PUNCT
cana-3291	320	1	lie_algebraic_techniques	lie_algebraic_technique	NOUN
cana-3291	320	2	.	.	PUNCT
cana-3291	321	1	[	[	X
cana-3291	321	2	4	4	X
cana-3291	321	3	]	]	X
cana-3291	321	4	v.	v.	ADP
cana-3291	321	5	sri	sri	PROPN
cana-3291	321	6	lakshmi	lakshmi	PROPN
cana-3291	321	7	,	,	PUNCT
cana-3291	321	8	n.	n.	PROPN
cana-3291	321	9	srimannarayana	srimannarayana	PROPN
cana-3291	321	10	,	,	PUNCT
cana-3291	321	11	b.satyanarayana	b.satyanarayana	PROPN
cana-3291	321	12	,	,	PUNCT
cana-3291	321	13	m.radha	m.radha	PROPN
cana-3291	321	14	madhavi	madhavi	PROPN
cana-3291	321	15	&	&	CCONJ
cana-3291	321	16	d.ramesh	d.ramesh	PROPN
cana-3291	321	17	.(2020	.(2020	PUNCT
cana-3291	321	18	on	on	ADP
cana-3291	321	19	modified	modify	VERB
cana-3291	321	20	jacobi	jacobi	NOUN
cana-3291	321	21	matrix	matrix	NOUN
cana-3291	321	22	polynomials.international	polynomials.international	PROPN
cana-3291	321	23	journal	journal	NOUN
cana-3291	321	24	of	of	ADP
cana-3291	321	25	advanced	advanced	ADJ
cana-3291	321	26	science	science	NOUN
cana-3291	321	27	and	and	CCONJ
cana-3291	321	28	technology.29(18s)924	technology.29(18s)924	NOUN
cana-3291	321	29	-	-	PUNCT
cana-3291	321	30	932	932	NUM
cana-3291	321	31	https://www.researchgate.net/publication/343650134_on_modified_jacobi_matrix_polynomials	https://www.researchgate.net/publication/343650134_on_modified_jacobi_matrix_polynomial	NOUN
cana-3291	321	32	[	[	X
cana-3291	321	33	5	5	NUM
cana-3291	321	34	]	]	PUNCT
cana-3291	321	35	l.jodar	l.jodar	X
cana-3291	321	36	&	&	CCONJ
cana-3291	321	37	e.defez.(1998	e.defez.(1998	PROPN
cana-3291	321	38	)	)	PUNCT
cana-3291	321	39	a	a	DET
cana-3291	321	40	connection	connection	NOUN
cana-3291	321	41	between	between	ADP
cana-3291	321	42	laguerre	laguerre	NOUN
cana-3291	321	43	’s	’s	PART
cana-3291	321	44	and	and	CCONJ
cana-3291	321	45	hermite	hermite	PROPN
cana-3291	321	46	’s	’s	PART
cana-3291	321	47	matrix	matrix	NOUN
cana-3291	321	48	polynomials	polynomial	NOUN
cana-3291	321	49	.	.	PUNCT
cana-3291	322	1	appl.math	appl.math	ADP
cana-3291	322	2	lett.11(1	lett.11(1	NOUN
cana-3291	322	3	)	)	PUNCT
cana-3291	322	4	13	13	NUM
cana-3291	322	5	-	-	SYM
cana-3291	322	6	17	17	NUM
cana-3291	322	7	..	..	PUNCT
cana-3291	322	8	https://doi.org/10.1016/s0893	https://doi.org/10.1016/s0893	NUM
cana-3291	322	9	9659(97)00125	9659(97)00125	NUM
cana-3291	322	10	-	-	SYM
cana-3291	322	11	0	0	PUNCT
cana-3291	323	1	[	[	X
cana-3291	323	2	6	6	NUM
cana-3291	323	3	]	]	PUNCT
cana-3291	323	4	l.jordar	l.jordar	PROPN
cana-3291	323	5	&	&	CCONJ
cana-3291	323	6	j.c.cortes	j.c.cortes	PROPN
cana-3291	323	7	.	.	PUNCT
cana-3291	324	1	(	(	PUNCT
cana-3291	324	2	1998	1998	NUM
cana-3291	324	3	)	)	PUNCT
cana-3291	324	4	on	on	ADP
cana-3291	324	5	the	the	DET
cana-3291	324	6	hypergeometric	hypergeometric	ADJ
cana-3291	324	7	matrix	matrix	NOUN
cana-3291	324	8	function	function	NOUN
cana-3291	324	9	,	,	PUNCT
cana-3291	324	10	j.comp	j.comp	NOUN
cana-3291	324	11	.	.	PUNCT
cana-3291	325	1	anal	anal	PROPN
cana-3291	325	2	.	.	PUNCT
cana-3291	325	3	math	math	PROPN
cana-3291	325	4	,	,	PUNCT
cana-3291	325	5	99	99	NUM
cana-3291	325	6	.	.	PUNCT
cana-3291	325	7	205217	205217	NUM
cana-3291	325	8	.	.	PUNCT
cana-3291	326	1	https://doi.org/10.1016/s0377-0427(98)00158-7	https://doi.org/10.1016/s0377-0427(98)00158-7	VERB
cana-3291	327	1	[	[	X
cana-3291	327	2	7	7	NUM
cana-3291	327	3	]	]	X
cana-3291	327	4	l.jordar	l.jordar	NOUN
cana-3291	327	5	&	&	CCONJ
cana-3291	327	6	j.sastre,(2000	j.sastre,(2000	X
cana-3291	327	7	)	)	PUNCT
cana-3291	327	8	the	the	DET
cana-3291	327	9	growth	growth	NOUN
cana-3291	327	10	of	of	ADP
cana-3291	327	11	laguerre	laguerre	NOUN
cana-3291	327	12	matrix	matrix	NOUN
cana-3291	327	13	polynomials	polynomial	NOUN
cana-3291	327	14	of	of	ADP
cana-3291	327	15	bounder	bounder	NOUN
cana-3291	327	16	intervals	interval	NOUN
cana-3291	327	17	.	.	PUNCT
cana-3291	328	1	appl.math	appl.math	ADP
cana-3291	328	2	lett.13	lett.13	PROPN
cana-3291	328	3	,	,	PUNCT
cana-3291	328	4	2126	2126	NUM
cana-3291	328	5	.	.	PUNCT
cana-3291	329	1	https://core.ac.uk/download/pdf/82551946.pdf	https://core.ac.uk/download/pdf/82551946.pdf	ADJ
cana-3291	329	2	communications	communication	NOUN
cana-3291	329	3	on	on	ADP
cana-3291	329	4	applied	apply	VERB
cana-3291	329	5	nonlinear	nonlinear	ADJ
cana-3291	329	6	analysis	analysis	NOUN
cana-3291	329	7	issn	issn	NOUN
cana-3291	329	8	:	:	PUNCT
cana-3291	329	9	1074	1074	NUM
cana-3291	329	10	-	-	PUNCT
cana-3291	329	11	133x	133x	NUM
cana-3291	329	12	vol	vol	NOUN
cana-3291	329	13	32	32	NUM
cana-3291	329	14	no	no	NOUN
cana-3291	329	15	.	.	PUNCT
cana-3291	330	1	6s	6s	NUM
cana-3291	330	2	(	(	PUNCT
cana-3291	330	3	2025	2025	NUM
cana-3291	330	4	)	)	PUNCT
cana-3291	330	5	262	262	NUM
cana-3291	330	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3291	331	1	[	[	X
cana-3291	331	2	8	8	NUM
cana-3291	331	3	]	]	PUNCT
cana-3291	331	4	l.jordar	l.jordar	NOUN
cana-3291	331	5	,	,	PUNCT
cana-3291	331	6	r.company	r.company	PRON
cana-3291	331	7	,	,	PUNCT
cana-3291	331	8	e.navarro.(1994	e.navarro.(1994	ADJ
cana-3291	331	9	)	)	PUNCT
cana-3291	331	10	laguerre	laguerre	NOUN
cana-3291	331	11	matrix	matrix	NOUN
cana-3291	331	12	polynomials	polynomial	NOUN
cana-3291	331	13	and	and	CCONJ
cana-3291	331	14	system	system	NOUN
cana-3291	331	15	of	of	ADP
cana-3291	331	16	second	second	ADJ
cana-3291	331	17	order	order	NOUN
cana-3291	331	18	differential	differential	NOUN
cana-3291	331	19	equations	equation	NOUN
cana-3291	331	20	,	,	PUNCT
cana-3291	331	21	appl.num	appl.num	X
cana-3291	331	22	.	.	PUNCT
cana-3291	331	23	math,15	math,15	NOUN
cana-3291	331	24	,	,	PUNCT
cana-3291	331	25	53	53	NUM
cana-3291	331	26	-	-	SYM
cana-3291	331	27	63	63	NUM
cana-3291	331	28	.	.	PUNCT
cana-3291	331	29	https://www.sciencedirect.com/science/article/pii/0168927494000123	https://www.sciencedirect.com/science/article/pii/0168927494000123	PUNCT
cana-3291	332	1	[	[	X
cana-3291	332	2	9	9	NUM
cana-3291	332	3	]	]	SYM
cana-3291	332	4	subi	subi	X
cana-3291	332	5	khan	khan	PROPN
cana-3291	332	6	&	&	CCONJ
cana-3291	332	7	n.a.m	n.a.m	PROPN
cana-3291	332	8	hassan	hassan	PROPN
cana-3291	332	9	.	.	PUNCT
cana-3291	333	1	(	(	PUNCT
cana-3291	333	2	2010	2010	NUM
cana-3291	333	3	)	)	PUNCT
cana-3291	333	4	2	2	NUM
cana-3291	333	5	-	-	PUNCT
cana-3291	333	6	variables	variable	NOUN
cana-3291	333	7	laguerre	laguerre	NOUN
cana-3291	333	8	polynomials	polynomial	NOUN
cana-3291	333	9	and	and	CCONJ
cana-3291	333	10	lie	lie	NOUN
cana-3291	333	11	-	-	PUNCT
cana-3291	333	12	algebraic	algebraic	ADJ
cana-3291	333	13	techniques	technique	NOUN
cana-3291	333	14	.	.	PUNCT
cana-3291	334	1	j.phys.a	j.phys.a	NOUN
cana-3291	334	2	,	,	PUNCT
cana-3291	334	3	43	43	NUM
cana-3291	334	4	.	.	PUNCT
cana-3291	335	1	204	204	NUM
cana-3291	335	2	-	-	SYM
cana-3291	335	3	235	235	NUM
cana-3291	335	4	.	.	PUNCT
cana-3291	335	5	https://www.sciencedirect.com/science/article/pii/0168927494000123	https://www.sciencedirect.com/science/article/pii/0168927494000123	PUNCT
cana-3291	336	1	[	[	X
cana-3291	336	2	10	10	NUM
cana-3291	336	3	]	]	X
cana-3291	336	4	c.l.parihar	c.l.parihar	PROPN
cana-3291	336	5	&	&	CCONJ
cana-3291	336	6	v.c.patel	v.c.patel	PROPN
cana-3291	336	7	,	,	PUNCT
cana-3291	336	8	(	(	PUNCT
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cana-3291	336	10	)	)	PUNCT
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cana-3291	337	2	acad	acad	PROPN
cana-3291	337	3	.	.	PUNCT
cana-3291	338	1	math	math	NOUN
cana-3291	338	2	.	.	PUNCT
cana-3291	339	1	,1.1	,1.1	PROPN
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cana-3291	341	3	]	]	PUNCT
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cana-3291	341	11	)	)	PUNCT
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cana-3291	343	6	and	and	CCONJ
cana-3291	343	7	engineering	engineering	NOUN
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cana-3291	343	10	-	-	SYM
cana-3291	343	11	3878	3878	NUM
cana-3291	343	12	.	.	PUNCT
cana-3291	344	1	8	8	NUM
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cana-3291	344	4	.	.	PUNCT
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cana-3291	345	2	12	12	NUM
cana-3291	345	3	]	]	X
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cana-3291	345	13	)	)	PUNCT
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cana-3291	345	19	’s	’s	PART
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cana-3291	345	21	.	.	PUNCT
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cana-3291	346	8	)	)	PUNCT
cana-3291	346	9	,	,	PUNCT
cana-3291	346	10	6473	6473	NUM
cana-3291	346	11	-	-	SYM
cana-3291	346	12	6481	6481	NUM
cana-3291	346	13	.	.	PUNCT
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cana-3291	348	3	]	]	PUNCT
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cana-3291	348	9	)	)	PUNCT
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cana-3291	349	5	,	,	PUNCT
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cana-3291	349	7	)	)	PUNCT
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cana-3291	353	2	17	17	NUM
cana-3291	353	3	]	]	PUNCT
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cana-3291	353	20	i	i	NOUN
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cana-3291	353	23	,	,	PUNCT
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cana-3291	353	30	,	,	PUNCT
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cana-3291	353	32	on	on	ADP
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cana-3291	353	36	,	,	PUNCT
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cana-3291	353	38	,	,	PUNCT
cana-3291	353	39	no.2s	no.2s	INTJ
cana-3291	353	40	,	,	PUNCT
cana-3291	353	41	687	687	NUM
cana-3291	353	42	-	-	PUNCT
cana-3291	353	43	695(2024	695(2024	NOUN
cana-3291	353	44	)	)	PUNCT
cana-3291	353	45	.	.	PUNCT
cana-3291	354	1	doi	doi	NOUN
cana-3291	354	2	:	:	PUNCT
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cana-3291	354	5	18	18	NUM
cana-3291	354	6	]	]	PUNCT
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cana-3291	354	8	,	,	PUNCT
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cana-3291	354	10	kumar	kumar	PROPN
cana-3291	354	11	,	,	PUNCT
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cana-3291	354	16	ayant	ayant	PROPN
cana-3291	354	17	,	,	PUNCT
cana-3291	354	18	n.	n.	PROPN
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cana-3291	354	20	,	,	PUNCT
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cana-3291	354	22	of	of	ADP
cana-3291	354	23	a	a	DET
cana-3291	354	24	boundary	boundary	ADJ
cana-3291	354	25	value	value	NOUN
cana-3291	354	26	problem	problem	NOUN
cana-3291	354	27	involving	involve	VERB
cana-3291	354	28	general	general	ADJ
cana-3291	354	29	class	class	NOUN
cana-3291	354	30	of	of	ADP
cana-3291	354	31	polynomial	polynomial	ADJ
cana-3291	354	32	,	,	PUNCT
cana-3291	354	33	struve	struve	PROPN
cana-3291	354	34	’s	’s	PART
cana-3291	354	35	function	function	NOUN
cana-3291	354	36	and	and	CCONJ
cana-3291	354	37	psi	psi	NOUN
cana-3291	354	38	function	function	NOUN
cana-3291	354	39	of	of	ADP
cana-3291	354	40	one	one	NUM
cana-3291	354	41	variable	variable	NOUN
cana-3291	354	42	,	,	PUNCT
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cana-3291	354	44	on	on	ADP
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cana-3291	354	46	nonlinear	nonlinear	ADJ
cana-3291	354	47	analysis	analysis	NOUN
cana-3291	354	48	,	,	PUNCT
cana-3291	354	49	v.31	v.31	X
cana-3291	354	50	,	,	PUNCT
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cana-3291	354	54	-	-	PUNCT
cana-3291	354	55	659(2024	659(2024	NUM
cana-3291	354	56	)	)	PUNCT
cana-3291	354	57	.	.	PUNCT
cana-3291	355	1	doi	doi	NOUN
cana-3291	355	2	:	:	PUNCT
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