id	sid	tid	token	lemma	pos
cana-3894	1	1	communications	communication	NOUN
cana-3894	1	2	on	on	ADP
cana-3894	1	3	applied	apply	VERB
cana-3894	1	4	nonlinear	nonlinear	ADJ
cana-3894	1	5	analysis	analysis	NOUN
cana-3894	1	6	issn	issn	NOUN
cana-3894	1	7	:	:	PUNCT
cana-3894	1	8	1074	1074	NUM
cana-3894	1	9	-	-	PUNCT
cana-3894	1	10	133x	133x	NUM
cana-3894	1	11	vol	vol	NOUN
cana-3894	1	12	32	32	NUM
cana-3894	1	13	no	no	NOUN
cana-3894	1	14	.	.	PUNCT
cana-3894	2	1	9s(2025	9s(2025	NUM
cana-3894	2	2	)	)	PUNCT
cana-3894	2	3	generalized	generalize	VERB
cana-3894	2	4	q	q	ADJ
cana-3894	2	5	-	-	ADJ
cana-3894	2	6	mittag	mittag	ADJ
cana-3894	2	7	-	-	PUNCT
cana-3894	2	8	leffler	leffler	NOUN
cana-3894	2	9	matrix	matrix	NOUN
cana-3894	2	10	function	function	NOUN
cana-3894	2	11	and	and	CCONJ
cana-3894	2	12	its	its	PRON
cana-3894	2	13	properties	property	NOUN
cana-3894	2	14	cynthia	cynthia	VERB
cana-3894	2	15	v.	v.	ADP
cana-3894	2	16	rodrigues1,2	rodrigues1,2	PROPN
cana-3894	2	17	and	and	CCONJ
cana-3894	2	18	bharti	bharti	PROPN
cana-3894	2	19	v.	v.	ADP
cana-3894	2	20	nathwani2	nathwani2	PROPN
cana-3894	2	21	,	,	PUNCT
cana-3894	2	22	*	*	PROPN
cana-3894	2	23	1mukesh	1mukesh	NUM
cana-3894	2	24	patel	patel	NOUN
cana-3894	2	25	school	school	NOUN
cana-3894	2	26	of	of	ADP
cana-3894	2	27	technology	technology	NOUN
cana-3894	2	28	management	management	NOUN
cana-3894	2	29	&	&	CCONJ
cana-3894	2	30	engineering	engineering	PROPN
cana-3894	2	31	,	,	PUNCT
cana-3894	2	32	svkm	svkm	VERB
cana-3894	2	33	’s	’s	PART
cana-3894	2	34	nmims	nmim	NOUN
cana-3894	2	35	,	,	PUNCT
cana-3894	2	36	mumbai	mumbai	NOUN
cana-3894	2	37	400056	400056	NUM
cana-3894	2	38	,	,	PUNCT
cana-3894	2	39	maharashtra	maharashtra	PROPN
cana-3894	2	40	,	,	PUNCT
cana-3894	2	41	india	india	PROPN
cana-3894	2	42	2amity	2amity	PROPN
cana-3894	2	43	school	school	NOUN
cana-3894	2	44	of	of	ADP
cana-3894	2	45	applied	apply	VERB
cana-3894	2	46	sciences	science	NOUN
cana-3894	2	47	,	,	PUNCT
cana-3894	2	48	amity	amity	NOUN
cana-3894	2	49	university	university	PROPN
cana-3894	2	50	maharashtra	maharashtra	PROPN
cana-3894	2	51	,	,	PUNCT
cana-3894	2	52	mumbai	mumbai	PROPN
cana-3894	2	53	,	,	PUNCT
cana-3894	2	54	panvel	panvel	NOUN
cana-3894	2	55	410206	410206	NUM
cana-3894	2	56	,	,	PUNCT
cana-3894	2	57	maharashtra	maharashtra	PROPN
cana-3894	2	58	,	,	PUNCT
cana-3894	2	59	india	india	PROPN
cana-3894	2	60	*	*	PUNCT
cana-3894	2	61	corresponding	correspond	VERB
cana-3894	2	62	author	author	NOUN
cana-3894	2	63	article	article	NOUN
cana-3894	2	64	history	history	NOUN
cana-3894	2	65	:	:	PUNCT
cana-3894	2	66	received	receive	VERB
cana-3894	2	67	:	:	PUNCT
cana-3894	2	68	13	13	NUM
cana-3894	2	69	-	-	SYM
cana-3894	2	70	11	11	NUM
cana-3894	2	71	-	-	PUNCT
cana-3894	2	72	2024	2024	NUM
cana-3894	2	73	revised	revise	VERB
cana-3894	2	74	:	:	PUNCT
cana-3894	2	75	25	25	NUM
cana-3894	2	76	-	-	SYM
cana-3894	2	77	12	12	NUM
cana-3894	2	78	-	-	PUNCT
cana-3894	2	79	2024	2024	NUM
cana-3894	2	80	accepted	accept	VERB
cana-3894	2	81	:	:	PUNCT
cana-3894	2	82	09	09	NUM
cana-3894	2	83	-	-	SYM
cana-3894	2	84	01	01	NUM
cana-3894	2	85	-	-	PUNCT
cana-3894	2	86	2025	2025	NUM
cana-3894	2	87	abstract	abstract	NOUN
cana-3894	2	88	:	:	PUNCT
cana-3894	2	89	motivated	motivate	VERB
cana-3894	2	90	essentially	essentially	ADV
cana-3894	2	91	by	by	ADP
cana-3894	2	92	the	the	DET
cana-3894	2	93	success	success	NOUN
cana-3894	2	94	of	of	ADP
cana-3894	2	95	the	the	DET
cana-3894	2	96	applications	application	NOUN
cana-3894	2	97	of	of	ADP
cana-3894	2	98	the	the	DET
cana-3894	2	99	mittag	mittag	ADJ
cana-3894	2	100	-	-	PUNCT
cana-3894	2	101	leffler	leffler	NOUN
cana-3894	2	102	functions	function	NOUN
cana-3894	2	103	and	and	CCONJ
cana-3894	2	104	matrix	matrix	NOUN
cana-3894	2	105	theory	theory	NOUN
cana-3894	2	106	in	in	ADP
cana-3894	2	107	science	science	NOUN
cana-3894	2	108	and	and	CCONJ
cana-3894	2	109	engineering	engineering	NOUN
cana-3894	2	110	,	,	PUNCT
cana-3894	2	111	we	we	PRON
cana-3894	2	112	propose	propose	VERB
cana-3894	2	113	here	here	ADV
cana-3894	2	114	a	a	DET
cana-3894	2	115	unification	unification	NOUN
cana-3894	2	116	of	of	ADP
cana-3894	2	117	certain	certain	ADJ
cana-3894	2	118	q	q	NOUN
cana-3894	2	119	-	-	PUNCT
cana-3894	2	120	extensions	extension	NOUN
cana-3894	2	121	of	of	ADP
cana-3894	2	122	generalizations	generalization	NOUN
cana-3894	2	123	of	of	ADP
cana-3894	2	124	mittag	mittag	ADJ
cana-3894	2	125	-	-	PUNCT
cana-3894	2	126	leffler	leffler	NOUN
cana-3894	2	127	function	function	NOUN
cana-3894	2	128	together	together	ADV
cana-3894	2	129	with	with	ADP
cana-3894	2	130	saxena	saxena	PROPN
cana-3894	2	131	-	-	PUNCT
cana-3894	2	132	nishimoto	nishimoto	PROPN
cana-3894	2	133	’s	’s	PART
cana-3894	2	134	function	function	NOUN
cana-3894	2	135	,	,	PUNCT
cana-3894	2	136	bessel	bessel	NOUN
cana-3894	2	137	-	-	PUNCT
cana-3894	2	138	maitland	maitland	PROPN
cana-3894	2	139	function	function	NOUN
cana-3894	2	140	,	,	PUNCT
cana-3894	2	141	dotsenko	dotsenko	ADJ
cana-3894	2	142	function	function	NOUN
cana-3894	2	143	,	,	PUNCT
cana-3894	2	144	elliptic	elliptic	ADJ
cana-3894	2	145	function	function	NOUN
cana-3894	2	146	,	,	PUNCT
cana-3894	2	147	etc	etc	X
cana-3894	2	148	.	.	X
cana-3894	3	1	we	we	PRON
cana-3894	3	2	obtain	obtain	VERB
cana-3894	3	3	mellin	mellin	NOUN
cana-3894	3	4	-	-	PUNCT
cana-3894	3	5	barnes	barne	VERB
cana-3894	3	6	contour	contour	ADJ
cana-3894	3	7	integral	integral	ADJ
cana-3894	3	8	representation	representation	NOUN
cana-3894	3	9	,	,	PUNCT
cana-3894	3	10	q	q	ADJ
cana-3894	3	11	-	-	PUNCT
cana-3894	3	12	difference	difference	NOUN
cana-3894	3	13	equation	equation	NOUN
cana-3894	3	14	and	and	CCONJ
cana-3894	3	15	eigen	eigen	PROPN
cana-3894	3	16	function	function	NOUN
cana-3894	3	17	property	property	NOUN
cana-3894	3	18	.	.	PUNCT
cana-3894	4	1	keywords	keyword	NOUN
cana-3894	4	2	:	:	PUNCT
cana-3894	4	3	mittag	mittag	ADJ
cana-3894	4	4	-	-	PUNCT
cana-3894	4	5	leffler	leffler	NOUN
cana-3894	4	6	matrix	matrix	NOUN
cana-3894	4	7	function	function	NOUN
cana-3894	4	8	,	,	PUNCT
cana-3894	4	9	q	q	ADJ
cana-3894	4	10	-	-	PUNCT
cana-3894	4	11	mittag	mittag	ADJ
cana-3894	4	12	-	-	PUNCT
cana-3894	4	13	leffler	leffler	NOUN
cana-3894	4	14	function	function	NOUN
cana-3894	4	15	,	,	PUNCT
cana-3894	4	16	q	q	ADJ
cana-3894	4	17	-	-	PUNCT
cana-3894	4	18	difference	difference	NOUN
cana-3894	4	19	equation	equation	NOUN
cana-3894	4	20	,	,	PUNCT
cana-3894	4	21	eigen	eigen	PROPN
cana-3894	4	22	function	function	PROPN
cana-3894	4	23	1	1	NUM
cana-3894	4	24	.	.	PUNCT
cana-3894	4	25	preliminaries	preliminary	NOUN
cana-3894	4	26	let	let	VERB
cana-3894	4	27	the	the	DET
cana-3894	4	28	spectrum	spectrum	NOUN
cana-3894	4	29	of	of	ADP
cana-3894	4	30	a	a	DET
cana-3894	4	31	matrix	matrix	NOUN
cana-3894	4	32	in	in	ADP
cana-3894	4	33	cr×r	cr×r	NOUN
cana-3894	4	34	,	,	PUNCT
cana-3894	4	35	denoted	denote	VERB
cana-3894	4	36	by	by	ADP
cana-3894	4	37	σ	σ	PROPN
cana-3894	4	38	(	(	PUNCT
cana-3894	4	39	a	a	NOUN
cana-3894	4	40	)	)	PUNCT
cana-3894	4	41	,	,	PUNCT
cana-3894	4	42	be	be	AUX
cana-3894	4	43	the	the	DET
cana-3894	4	44	set	set	NOUN
cana-3894	4	45	of	of	ADP
cana-3894	4	46	all	all	DET
cana-3894	4	47	eigenvalues	eigenvalue	NOUN
cana-3894	4	48	of	of	ADP
cana-3894	4	49	a.	a.	NOUN
cana-3894	4	50	recall	recall	NOUN
cana-3894	4	51	that	that	SCONJ
cana-3894	4	52	a	a	DET
cana-3894	4	53	matrix	matrix	NOUN
cana-3894	4	54	a	a	DET
cana-3894	4	55	∈	∈	PROPN
cana-3894	4	56	cr×r	cr×r	NOUN
cana-3894	4	57	is	be	AUX
cana-3894	4	58	said	say	VERB
cana-3894	4	59	to	to	PART
cana-3894	4	60	be	be	AUX
cana-3894	4	61	positive	positive	ADJ
cana-3894	4	62	stable	stable	ADJ
cana-3894	4	63	when	when	SCONJ
cana-3894	4	64	β	β	X
cana-3894	4	65	(	(	PUNCT
cana-3894	4	66	a	a	X
cana-3894	4	67	)	)	PUNCT
cana-3894	4	68	=	=	SYM
cana-3894	4	69	min	min	NOUN
cana-3894	4	70	{	{	PUNCT
cana-3894	4	71	a	a	DET
cana-3894	4	72	(	(	PUNCT
cana-3894	4	73	z	z	NOUN
cana-3894	4	74	)	)	PUNCT
cana-3894	4	75	/z	/z	PUNCT
cana-3894	5	1	∈	∈	PROPN
cana-3894	5	2	σ	σ	PROPN
cana-3894	5	3	(	(	PUNCT
cana-3894	5	4	a	a	NOUN
cana-3894	5	5	)	)	PUNCT
cana-3894	5	6	}	}	PUNCT
cana-3894	5	7	>	>	X
cana-3894	5	8	0	0	PUNCT
cana-3894	5	9	(	(	PUNCT
cana-3894	5	10	1.1	1.1	NUM
cana-3894	5	11	)	)	PUNCT
cana-3894	5	12	for	for	ADP
cana-3894	5	13	a	a	DET
cana-3894	5	14	positive	positive	ADJ
cana-3894	5	15	stable	stable	ADJ
cana-3894	5	16	matrix	matrix	NOUN
cana-3894	5	17	a	a	DET
cana-3894	5	18	∈	∈	PROPN
cana-3894	5	19	cr×r	cr×r	NOUN
cana-3894	5	20	,	,	PUNCT
cana-3894	5	21	the	the	DET
cana-3894	5	22	q	q	ADJ
cana-3894	5	23	-	-	PUNCT
cana-3894	5	24	gamma	gamma	NOUN
cana-3894	5	25	matrix	matrix	NOUN
cana-3894	5	26	function	function	NOUN
cana-3894	5	27	is	be	AUX
cana-3894	5	28	defined	define	VERB
cana-3894	5	29	by	by	ADP
cana-3894	5	30	[	[	X
cana-3894	5	31	10	10	NUM
cana-3894	5	32	,	,	PUNCT
cana-3894	5	33	eq.(3.13	eq.(3.13	PROPN
cana-3894	5	34	)	)	PUNCT
cana-3894	5	35	]	]	PUNCT
cana-3894	6	1	γq	γq	ADP
cana-3894	6	2	(	(	PUNCT
cana-3894	6	3	a	a	X
cana-3894	6	4	)	)	PUNCT
cana-3894	6	5	=	=	SYM
cana-3894	6	6	1	1	NUM
cana-3894	6	7	1−q∫	1−q∫	NUM
cana-3894	6	8	0	0	NUM
cana-3894	6	9	ta−ie−qt	ta−ie−qt	PROPN
cana-3894	6	10	q	q	X
cana-3894	6	11	dt	dt	X
cana-3894	6	12	(	(	PUNCT
cana-3894	6	13	1.2	1.2	NUM
cana-3894	6	14	)	)	PUNCT
cana-3894	6	15	and	and	CCONJ
cana-3894	6	16	the	the	DET
cana-3894	6	17	reciprocal	reciprocal	ADJ
cana-3894	6	18	q	q	ADJ
cana-3894	6	19	-	-	PUNCT
cana-3894	6	20	gamma	gamma	NOUN
cana-3894	6	21	matrix	matrix	NOUN
cana-3894	6	22	function	function	NOUN
cana-3894	6	23	is	be	AUX
cana-3894	6	24	defined	define	VERB
cana-3894	6	25	as	as	ADP
cana-3894	6	26	[	[	X
cana-3894	6	27	10	10	NUM
cana-3894	6	28	,	,	PUNCT
cana-3894	6	29	eq.(3.20	eq.(3.20	PROPN
cana-3894	6	30	)	)	PUNCT
cana-3894	6	31	]	]	PUNCT
cana-3894	7	1	γ−1	γ−1	PROPN
cana-3894	7	2	q	q	X
cana-3894	7	3	(	(	PUNCT
cana-3894	7	4	a	a	NOUN
cana-3894	7	5	)	)	PUNCT
cana-3894	7	6	=	=	PUNCT
cana-3894	8	1	[	[	X
cana-3894	8	2	a]q	a]q	NOUN
cana-3894	8	3	[	[	X
cana-3894	8	4	a+	a+	X
cana-3894	8	5	i]q	i]q	X
cana-3894	8	6	.	.	PUNCT
cana-3894	8	7	.	.	PUNCT
cana-3894	8	8	.	.	PUNCT
cana-3894	8	9	.	.	PUNCT
cana-3894	8	10	.	.	PUNCT
cana-3894	8	11	.	.	PUNCT
cana-3894	9	1	[	[	X
cana-3894	9	2	a+	a+	X
cana-3894	9	3	(	(	PUNCT
cana-3894	9	4	n−	n−	NOUN
cana-3894	9	5	1	1	NUM
cana-3894	9	6	)	)	PUNCT
cana-3894	9	7	i]q	i]q	PROPN
cana-3894	9	8	γq	γq	ADP
cana-3894	9	9	−1	−1	NOUN
cana-3894	9	10	(	(	PUNCT
cana-3894	9	11	a+	a+	X
cana-3894	9	12	ni	ni	PROPN
cana-3894	9	13	)	)	PUNCT
cana-3894	9	14	,	,	PUNCT
cana-3894	9	15	n	n	X
cana-3894	9	16	≥	≥	NOUN
cana-3894	9	17	1	1	NUM
cana-3894	9	18	(	(	PUNCT
cana-3894	9	19	1.3	1.3	NUM
cana-3894	9	20	)	)	PUNCT
cana-3894	9	21	https://internationalpubls.com	https://internationalpubls.com	X
cana-3894	9	22	329	329	NUM
cana-3894	9	23	communications	communication	NOUN
cana-3894	9	24	on	on	ADP
cana-3894	9	25	applied	apply	VERB
cana-3894	9	26	nonlinear	nonlinear	ADJ
cana-3894	9	27	analysis	analysis	NOUN
cana-3894	9	28	issn	issn	NOUN
cana-3894	9	29	:	:	PUNCT
cana-3894	9	30	1074	1074	NUM
cana-3894	9	31	-	-	PUNCT
cana-3894	9	32	133x	133x	NUM
cana-3894	9	33	vol	vol	NOUN
cana-3894	9	34	32	32	NUM
cana-3894	9	35	no	no	NOUN
cana-3894	9	36	.	.	PUNCT
cana-3894	10	1	9s(2025	9s(2025	NUM
cana-3894	10	2	)	)	PUNCT
cana-3894	10	3	if	if	SCONJ
cana-3894	10	4	a	a	PRON
cana-3894	10	5	and	and	CCONJ
cana-3894	10	6	b	b	NOUN
cana-3894	10	7	are	be	AUX
cana-3894	10	8	positive	positive	ADJ
cana-3894	10	9	stable	stable	ADJ
cana-3894	10	10	matrices	matrix	NOUN
cana-3894	10	11	in	in	ADP
cana-3894	10	12	cr×r	cr×r	NOUN
cana-3894	10	13	then	then	ADV
cana-3894	10	14	the	the	DET
cana-3894	10	15	q	q	ADJ
cana-3894	10	16	-	-	PUNCT
cana-3894	10	17	beta	beta	ADJ
cana-3894	10	18	matrix	matrix	NOUN
cana-3894	10	19	function	function	NOUN
cana-3894	10	20	is	be	AUX
cana-3894	10	21	defined	define	VERB
cana-3894	10	22	as	as	ADP
cana-3894	10	23	[	[	X
cana-3894	10	24	10	10	NUM
cana-3894	10	25	,	,	PUNCT
cana-3894	10	26	eq.(4.5	eq.(4.5	PROPN
cana-3894	10	27	)	)	PUNCT
cana-3894	10	28	]	]	PUNCT
cana-3894	11	1	bq	bq	INTJ
cana-3894	11	2	(	(	PUNCT
cana-3894	11	3	a	a	DET
cana-3894	11	4	,	,	PUNCT
cana-3894	11	5	b	b	NOUN
cana-3894	11	6	)	)	PUNCT
cana-3894	11	7	=	=	PUNCT
cana-3894	12	1	1∫	1∫	NUM
cana-3894	12	2	0	0	NUM
cana-3894	12	3	(	(	PUNCT
cana-3894	12	4	tq	tq	ADV
cana-3894	12	5	;	;	PUNCT
cana-3894	12	6	q)∞	q)∞	ADJ
cana-3894	12	7	(	(	PUNCT
cana-3894	12	8	tqb	tqb	NOUN
cana-3894	12	9	;	;	PUNCT
cana-3894	12	10	q	q	NOUN
cana-3894	12	11	)	)	PUNCT
cana-3894	12	12	−1	−1	NOUN
cana-3894	12	13	∞	∞	NOUN
cana-3894	12	14	ta−i	ta−i	NOUN
cana-3894	12	15	dqt	dqt	NOUN
cana-3894	12	16	(	(	PUNCT
cana-3894	12	17	1.4	1.4	NUM
cana-3894	12	18	)	)	PUNCT
cana-3894	12	19	furthermore	furthermore	ADV
cana-3894	12	20	,	,	PUNCT
cana-3894	12	21	if	if	SCONJ
cana-3894	12	22	a	a	DET
cana-3894	12	23	,	,	PUNCT
cana-3894	12	24	b	b	NOUN
cana-3894	12	25	and	and	CCONJ
cana-3894	12	26	a+b	a+b	NUM
cana-3894	12	27	are	be	AUX
cana-3894	12	28	positive	positive	ADJ
cana-3894	12	29	stable	stable	ADJ
cana-3894	12	30	matrices	matrix	NOUN
cana-3894	12	31	in	in	ADP
cana-3894	12	32	cr×rsuch	cr×rsuch	NOUN
cana-3894	13	1	that	that	PRON
cana-3894	13	2	ab	ab	PROPN
cana-3894	13	3	=	=	SYM
cana-3894	13	4	ba	ba	PROPN
cana-3894	13	5	then	then	ADV
cana-3894	13	6	the	the	DET
cana-3894	13	7	beta	beta	ADJ
cana-3894	13	8	matrix	matrix	NOUN
cana-3894	13	9	function	function	NOUN
cana-3894	13	10	is	be	AUX
cana-3894	13	11	defined	define	VERB
cana-3894	13	12	as	as	ADP
cana-3894	13	13	[	[	X
cana-3894	13	14	10	10	NUM
cana-3894	13	15	,	,	PUNCT
cana-3894	13	16	eq.(4.6	eq.(4.6	NOUN
cana-3894	13	17	)	)	PUNCT
cana-3894	13	18	]	]	PUNCT
cana-3894	14	1	bq	bq	INTJ
cana-3894	14	2	(	(	PUNCT
cana-3894	14	3	a	a	DET
cana-3894	14	4	,	,	PUNCT
cana-3894	14	5	b	b	NOUN
cana-3894	14	6	)	)	PUNCT
cana-3894	14	7	=	=	PUNCT
cana-3894	14	8	γq	γq	ADP
cana-3894	14	9	(	(	PUNCT
cana-3894	14	10	a	a	NOUN
cana-3894	14	11	)	)	PUNCT
cana-3894	14	12	γq	γq	ADP
cana-3894	14	13	(	(	PUNCT
cana-3894	14	14	b	b	NOUN
cana-3894	14	15	)	)	PUNCT
cana-3894	14	16	γ−1	γ−1	PROPN
cana-3894	14	17	q	q	X
cana-3894	14	18	(	(	PUNCT
cana-3894	14	19	a+b	a+b	NUM
cana-3894	14	20	)	)	PUNCT
cana-3894	14	21	(	(	PUNCT
cana-3894	14	22	1.5	1.5	NUM
cana-3894	14	23	)	)	PUNCT
cana-3894	14	24	2	2	NUM
cana-3894	14	25	.	.	X
cana-3894	14	26	introduction	introduction	NOUN
cana-3894	14	27	a	a	DET
cana-3894	14	28	generalized	generalized	ADJ
cana-3894	14	29	structure	structure	NOUN
cana-3894	14	30	of	of	ADP
cana-3894	14	31	the	the	DET
cana-3894	14	32	mittag	mittag	ADJ
cana-3894	14	33	-	-	PUNCT
cana-3894	14	34	leffler	leffler	NOUN
cana-3894	14	35	matrix	matrix	NOUN
cana-3894	14	36	function	function	NOUN
cana-3894	14	37	is	be	AUX
cana-3894	14	38	given	give	VERB
cana-3894	14	39	by	by	ADP
cana-3894	14	40	[	[	PUNCT
cana-3894	14	41	11	11	NUM
cana-3894	14	42	,	,	PUNCT
cana-3894	14	43	eq.(2.9	eq.(2.9	PROPN
cana-3894	14	44	)	)	PUNCT
cana-3894	14	45	]	]	X
cana-3894	14	46	:	:	PUNCT
cana-3894	14	47	ea	ea	NUM
cana-3894	14	48	,	,	PUNCT
cana-3894	14	49	b	b	PROPN
cana-3894	14	50	,	,	PUNCT
cana-3894	14	51	c	c	PROPN
cana-3894	14	52	αi	αi	PROPN
cana-3894	14	53	,	,	PUNCT
cana-3894	14	54	δi,µi	δi,µi	NOUN
cana-3894	14	55	(	(	PUNCT
cana-3894	14	56	λz	λz	X
cana-3894	14	57	;	;	PUNCT
cana-3894	14	58	s	s	X
cana-3894	14	59	,	,	PUNCT
cana-3894	14	60	r	r	NOUN
cana-3894	14	61	)	)	PUNCT
cana-3894	14	62	=	=	SYM
cana-3894	15	1	∞∑	∞∑	NUM
cana-3894	15	2	n=0	n=0	PUNCT
cana-3894	16	1	[	[	X
cana-3894	16	2	(	(	PUNCT
cana-3894	16	3	a)δn	a)δn	PROPN
cana-3894	16	4	]	]	X
cana-3894	16	5	s	s	VERB
cana-3894	16	6	γ−1	γ−1	PROPN
cana-3894	16	7	(	(	PUNCT
cana-3894	16	8	αni	αni	PROPN
cana-3894	16	9	+	+	PROPN
cana-3894	16	10	b	b	NOUN
cana-3894	16	11	)	)	PUNCT
cana-3894	16	12	[	[	PUNCT
cana-3894	16	13	(	(	PUNCT
cana-3894	16	14	c)µn	c)µn	PROPN
cana-3894	16	15	]	]	X
cana-3894	16	16	−r	−r	PROPN
cana-3894	16	17	(	(	PUNCT
cana-3894	16	18	λz)n	λz)n	PROPN
cana-3894	16	19	n	n	CCONJ
cana-3894	16	20	!	!	PUNCT
cana-3894	16	21	(	(	PUNCT
cana-3894	16	22	2.1	2.1	NUM
cana-3894	16	23	)	)	PUNCT
cana-3894	16	24	where	where	SCONJ
cana-3894	16	25	a	a	DET
cana-3894	16	26	,	,	PUNCT
cana-3894	16	27	b	b	NOUN
cana-3894	16	28	,	,	PUNCT
cana-3894	16	29	c	c	PROPN
cana-3894	16	30	are	be	AUX
cana-3894	16	31	positive	positive	ADJ
cana-3894	16	32	stable	stable	ADJ
cana-3894	16	33	matrices	matrix	NOUN
cana-3894	16	34	in	in	ADP
cana-3894	16	35	cp×p	cp×p	PROPN
cana-3894	16	36	,	,	PUNCT
cana-3894	16	37	α	α	PROPN
cana-3894	16	38	,	,	PUNCT
cana-3894	16	39	λ	λ	PROPN
cana-3894	16	40	,	,	PUNCT
cana-3894	16	41	z	z	PROPN
cana-3894	16	42	∈	∈	PROPN
cana-3894	16	43	c	c	NOUN
cana-3894	16	44	with	with	ADP
cana-3894	16	45	ℜ(α	ℜ(α	NOUN
cana-3894	16	46	)	)	PUNCT
cana-3894	16	47	>	>	X
cana-3894	16	48	0	0	NUM
cana-3894	16	49	,	,	PUNCT
cana-3894	16	50	δ	δ	PROPN
cana-3894	16	51	,	,	PUNCT
cana-3894	16	52	µ	µ	X
cana-3894	16	53	>	>	X
cana-3894	16	54	0	0	NUM
cana-3894	16	55	,	,	PUNCT
cana-3894	16	56	r	r	NOUN
cana-3894	16	57	∈	∈	PROPN
cana-3894	16	58	{	{	PUNCT
cana-3894	16	59	−1	−1	NOUN
cana-3894	16	60	,	,	PUNCT
cana-3894	16	61	0	0	NUM
cana-3894	16	62	}	}	PUNCT
cana-3894	16	63	∪	∪	NOUN
cana-3894	16	64	n	n	NOUN
cana-3894	16	65	and	and	CCONJ
cana-3894	16	66	s	s	PROPN
cana-3894	16	67	∈	∈	NOUN
cana-3894	16	68	{	{	PUNCT
cana-3894	16	69	0	0	NUM
cana-3894	16	70	}	}	PUNCT
cana-3894	16	71	∪	∪	NOUN
cana-3894	16	72	n.	n.	NOUN
cana-3894	16	73	interestingly	interestingly	ADV
cana-3894	16	74	,	,	PUNCT
cana-3894	16	75	the	the	DET
cana-3894	16	76	proposed	propose	VERB
cana-3894	16	77	function	function	NOUN
cana-3894	16	78	(	(	PUNCT
cana-3894	16	79	(	(	PUNCT
cana-3894	16	80	2.13	2.13	NUM
cana-3894	16	81	)	)	PUNCT
cana-3894	16	82	below	below	ADV
cana-3894	16	83	)	)	PUNCT
cana-3894	16	84	also	also	ADV
cana-3894	16	85	enables	enable	VERB
cana-3894	16	86	us	we	PRON
cana-3894	16	87	to	to	PART
cana-3894	16	88	define	define	VERB
cana-3894	16	89	and	and	CCONJ
cana-3894	16	90	include	include	VERB
cana-3894	16	91	the	the	DET
cana-3894	16	92	q	q	NOUN
cana-3894	16	93	-	-	PUNCT
cana-3894	16	94	analogues	analogue	NOUN
cana-3894	16	95	of	of	ADP
cana-3894	16	96	(	(	PUNCT
cana-3894	16	97	i	i	NOUN
cana-3894	16	98	)	)	PUNCT
cana-3894	16	99	bessel	bessel	NOUN
cana-3894	16	100	-	-	PUNCT
cana-3894	16	101	maitland	maitland	NOUN
cana-3894	16	102	matrix	matrix	NOUN
cana-3894	16	103	function	function	NOUN
cana-3894	16	104	[	[	X
cana-3894	16	105	11	11	NUM
cana-3894	16	106	]	]	PUNCT
cana-3894	16	107	:	:	PUNCT
cana-3894	16	108	jµi	jµi	NOUN
cana-3894	16	109	νi	νi	PROPN
cana-3894	16	110	(	(	PUNCT
cana-3894	16	111	z	z	NOUN
cana-3894	16	112	)	)	PUNCT
cana-3894	16	113	=	=	PUNCT
cana-3894	17	1	∞∑	∞∑	NUM
cana-3894	17	2	n=0	n=0	NUM
cana-3894	17	3	(	(	PUNCT
cana-3894	17	4	−1)n	−1)n	PROPN
cana-3894	17	5	γ−1(νi	γ−1(νi	PROPN
cana-3894	17	6	+	+	PROPN
cana-3894	17	7	nµi	nµi	PROPN
cana-3894	17	8	+	+	CCONJ
cana-3894	17	9	i	i	PROPN
cana-3894	17	10	)	)	PUNCT
cana-3894	17	11	zn	zn	PROPN
cana-3894	17	12	n	n	CCONJ
cana-3894	17	13	!	!	PROPN
cana-3894	17	14	,	,	PUNCT
cana-3894	17	15	(	(	PUNCT
cana-3894	17	16	ii	ii	NOUN
cana-3894	17	17	)	)	PUNCT
cana-3894	17	18	dotsenko	dotsenko	ADJ
cana-3894	17	19	matrix	matrix	NOUN
cana-3894	17	20	function	function	NOUN
cana-3894	17	21	[	[	X
cana-3894	17	22	11	11	NUM
cana-3894	17	23	]	]	PUNCT
cana-3894	17	24	:	:	PUNCT
cana-3894	17	25	2r1(ai	2r1(ai	NUM
cana-3894	17	26	,	,	PUNCT
cana-3894	17	27	bi	bi	NOUN
cana-3894	17	28	;	;	PUNCT
cana-3894	17	29	ci	ci	PROPN
cana-3894	17	30	,	,	PUNCT
cana-3894	17	31	ωi	ωi	NOUN
cana-3894	17	32	;	;	PUNCT
cana-3894	17	33	ν	ν	X
cana-3894	17	34	;	;	PUNCT
cana-3894	17	35	z	z	X
cana-3894	17	36	)	)	PUNCT
cana-3894	17	37	=	=	SYM
cana-3894	18	1	∞∑	∞∑	PRON
cana-3894	18	2	n=0	n=0	NUM
cana-3894	18	3	γ(ai	γ(ai	PROPN
cana-3894	18	4	+	+	CCONJ
cana-3894	18	5	ni)γ−1(ai	ni)γ−1(ai	PROPN
cana-3894	18	6	)	)	PUNCT
cana-3894	19	1	γ(bi	γ(bi	PROPN
cana-3894	19	2	+	+	PROPN
cana-3894	19	3	n	n	PROPN
cana-3894	19	4	ω	ω	NUM
cana-3894	19	5	ν	ν	NOUN
cana-3894	19	6	i)γ−1(bi	i)γ−1(bi	PROPN
cana-3894	19	7	)	)	PUNCT
cana-3894	19	8	γ(ci	γ(ci	PROPN
cana-3894	19	9	)	)	PUNCT
cana-3894	19	10	γ−1(ci	γ−1(ci	PROPN
cana-3894	19	11	+	+	CCONJ
cana-3894	19	12	n	n	NUM
cana-3894	19	13	ω	ω	NUM
cana-3894	19	14	ν	ν	X
cana-3894	19	15	i	i	PROPN
cana-3894	19	16	)	)	PUNCT
cana-3894	19	17	zn	zn	PROPN
cana-3894	19	18	n	n	CCONJ
cana-3894	19	19	!	!	PROPN
cana-3894	19	20	,	,	PUNCT
cana-3894	19	21	(	(	PUNCT
cana-3894	19	22	iii	iii	X
cana-3894	19	23	)	)	PUNCT
cana-3894	19	24	saxena	saxena	PROPN
cana-3894	19	25	and	and	CCONJ
cana-3894	19	26	nishimoto	nishimoto	PROPN
cana-3894	19	27	’s	’s	PART
cana-3894	19	28	matrix	matrix	NOUN
cana-3894	19	29	function	function	NOUN
cana-3894	20	1	[	[	X
cana-3894	20	2	11	11	NUM
cana-3894	20	3	]	]	SYM
cana-3894	20	4	:	:	PUNCT
cana-3894	20	5	eγi	eγi	PROPN
cana-3894	20	6	,	,	PUNCT
cana-3894	20	7	k	k	PROPN
cana-3894	21	1	[	[	X
cana-3894	21	2	(	(	PUNCT
cana-3894	21	3	αji	αji	NOUN
cana-3894	21	4	,	,	PUNCT
cana-3894	21	5	bj)1,2	bj)1,2	ADJ
cana-3894	21	6	;	;	PUNCT
cana-3894	21	7	z	z	X
cana-3894	21	8	]	]	X
cana-3894	21	9	=	=	PUNCT
cana-3894	22	1	∞∑	∞∑	NUM
cana-3894	22	2	n=0	n=0	NUM
cana-3894	22	3	(	(	PUNCT
cana-3894	22	4	γi)knγ	γi)knγ	NOUN
cana-3894	22	5	−1(α1ni	−1(α1ni	NOUN
cana-3894	22	6	+	+	PROPN
cana-3894	22	7	b1)γ	b1)γ	PROPN
cana-3894	22	8	−1(α2ni	−1(α2ni	PROPN
cana-3894	22	9	+	+	NOUN
cana-3894	22	10	b2	b2	NOUN
cana-3894	22	11	)	)	PUNCT
cana-3894	22	12	zn	zn	PROPN
cana-3894	22	13	n	n	CCONJ
cana-3894	22	14	!	!	PROPN
cana-3894	22	15	,	,	PUNCT
cana-3894	22	16	where	where	SCONJ
cana-3894	22	17	z	z	NOUN
cana-3894	22	18	,	,	PUNCT
cana-3894	22	19	γ	γ	PROPN
cana-3894	22	20	,	,	PUNCT
cana-3894	22	21	αj	αj	NOUN
cana-3894	22	22	,	,	PUNCT
cana-3894	22	23	βj	βj	PROPN
cana-3894	22	24	∈	∈	PROPN
cana-3894	22	25	c,ℜ(α1	c,ℜ(α1	NOUN
cana-3894	22	26	+	+	CCONJ
cana-3894	22	27	α2	α2	ADJ
cana-3894	22	28	)	)	PUNCT
cana-3894	22	29	>	>	PUNCT
cana-3894	22	30	ℜ(k)−	ℜ(k)−	PROPN
cana-3894	22	31	1,ℜ(k	1,ℜ(k	PROPN
cana-3894	22	32	)	)	PUNCT
cana-3894	22	33	>	>	X
cana-3894	22	34	0	0	NUM
cana-3894	22	35	,	,	PUNCT
cana-3894	22	36	and	and	CCONJ
cana-3894	22	37	(	(	PUNCT
cana-3894	22	38	iv	iv	X
cana-3894	22	39	)	)	PUNCT
cana-3894	22	40	the	the	DET
cana-3894	22	41	elliptic	elliptic	ADJ
cana-3894	22	42	matrix	matrix	NOUN
cana-3894	22	43	function	function	NOUN
cana-3894	22	44	[	[	X
cana-3894	22	45	11	11	NUM
cana-3894	22	46	]	]	PUNCT
cana-3894	22	47	:	:	PUNCT
cana-3894	22	48	k(i	k(i	PROPN
cana-3894	22	49	;	;	PUNCT
cana-3894	22	50	k	k	X
cana-3894	22	51	)	)	PUNCT
cana-3894	22	52	=	=	PUNCT
cana-3894	23	1	π	π	NOUN
cana-3894	23	2	2	2	NUM
cana-3894	23	3	2f1	2f1	NUM
cana-3894	23	4	(	(	PUNCT
cana-3894	23	5	1	1	NUM
cana-3894	23	6	2	2	NUM
cana-3894	23	7	i	i	NOUN
cana-3894	23	8	,	,	PUNCT
cana-3894	23	9	1	1	NUM
cana-3894	23	10	2	2	NUM
cana-3894	23	11	i	i	NOUN
cana-3894	23	12	;	;	PUNCT
cana-3894	23	13	k2	k2	PROPN
cana-3894	23	14	i	i	PROPN
cana-3894	23	15	;	;	PUNCT
cana-3894	23	16	)	)	PUNCT
cana-3894	23	17	.	.	PUNCT
cana-3894	24	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3894	24	2	330	330	NUM
cana-3894	24	3	communications	communication	NOUN
cana-3894	24	4	on	on	ADP
cana-3894	24	5	applied	apply	VERB
cana-3894	24	6	nonlinear	nonlinear	ADJ
cana-3894	24	7	analysis	analysis	NOUN
cana-3894	24	8	issn	issn	NOUN
cana-3894	24	9	:	:	PUNCT
cana-3894	24	10	1074	1074	NUM
cana-3894	24	11	-	-	PUNCT
cana-3894	24	12	133x	133x	NUM
cana-3894	24	13	vol	vol	NOUN
cana-3894	24	14	32	32	NUM
cana-3894	24	15	no	no	NOUN
cana-3894	24	16	.	.	PUNCT
cana-3894	25	1	9s(2025	9s(2025	NUM
cana-3894	25	2	)	)	PUNCT
cana-3894	25	3	the	the	DET
cana-3894	25	4	following	follow	VERB
cana-3894	25	5	definitions	definition	NOUN
cana-3894	25	6	and	and	CCONJ
cana-3894	25	7	formulas	formula	NOUN
cana-3894	25	8	will	will	AUX
cana-3894	25	9	be	be	AUX
cana-3894	25	10	used	use	VERB
cana-3894	25	11	in	in	ADP
cana-3894	25	12	this	this	DET
cana-3894	25	13	work	work	NOUN
cana-3894	25	14	.	.	PUNCT
cana-3894	26	1	for	for	ADP
cana-3894	26	2	a	a	DET
cana-3894	26	3	∈	∈	PROPN
cana-3894	26	4	cr×r	cr×r	NOUN
cana-3894	26	5	and	and	CCONJ
cana-3894	26	6	q	q	NOUN
cana-3894	26	7	̸=	̸=	PROPN
cana-3894	26	8	1	1	NUM
cana-3894	26	9	,	,	PUNCT
cana-3894	26	10	qa	qa	PROPN
cana-3894	26	11	=	=	SYM
cana-3894	26	12	ea	ea	PROPN
cana-3894	26	13	log	log	VERB
cana-3894	26	14	q	q	PROPN
cana-3894	27	1	then	then	ADV
cana-3894	27	2	the	the	DET
cana-3894	27	3	q	q	ADJ
cana-3894	27	4	-	-	PUNCT
cana-3894	27	5	shifted	shift	VERB
cana-3894	27	6	factorial	factorial	ADJ
cana-3894	27	7	matrix	matrix	NOUN
cana-3894	27	8	function	function	NOUN
cana-3894	27	9	is	be	AUX
cana-3894	27	10	defined	define	VERB
cana-3894	27	11	by	by	ADP
cana-3894	27	12	[	[	X
cana-3894	27	13	10	10	NUM
cana-3894	27	14	]	]	PUNCT
cana-3894	27	15	(	(	PUNCT
cana-3894	27	16	a	a	PRON
cana-3894	27	17	;	;	PUNCT
cana-3894	27	18	q)n	q)n	SYM
cana-3894	27	19	=	=	SYM
cana-3894	27	20	{	{	PUNCT
cana-3894	27	21	i	i	PRON
cana-3894	27	22	if	if	SCONJ
cana-3894	27	23	n	n	X
cana-3894	27	24	=	=	SYM
cana-3894	27	25	0	0	PUNCT
cana-3894	28	1	(	(	PUNCT
cana-3894	28	2	i	i	PRON
cana-3894	28	3	−	−	PROPN
cana-3894	28	4	a)(i	a)(i	PROPN
cana-3894	28	5	−	−	PROPN
cana-3894	28	6	aq)	aq)	NUM
cana-3894	28	7	...	...	PUNCT
cana-3894	29	1	(i	(i	PRON
cana-3894	29	2	−	−	PROPN
cana-3894	29	3	aqn−1	aqn−1	PROPN
cana-3894	29	4	)	)	PUNCT
cana-3894	29	5	if	if	SCONJ
cana-3894	29	6	n	n	NUM
cana-3894	29	7	∈	∈	PROPN
cana-3894	29	8	n.	n.	NOUN
cana-3894	29	9	(	(	PUNCT
cana-3894	29	10	2.2	2.2	NUM
cana-3894	29	11	)	)	PUNCT
cana-3894	29	12	for	for	ADP
cana-3894	29	13	any	any	DET
cana-3894	29	14	n	n	CCONJ
cana-3894	29	15	,	,	PUNCT
cana-3894	29	16	(	(	PUNCT
cana-3894	29	17	a	a	X
cana-3894	29	18	;	;	PUNCT
cana-3894	29	19	q)n	q)n	SYM
cana-3894	29	20	=	=	SYM
cana-3894	29	21	(	(	PUNCT
cana-3894	29	22	q	q	ADJ
cana-3894	29	23	;	;	PUNCT
cana-3894	29	24	q)∞(aqn	q)∞(aqn	NOUN
cana-3894	29	25	;	;	PUNCT
cana-3894	29	26	q)−1	q)−1	NOUN
cana-3894	29	27	∞	∞	PROPN
cana-3894	29	28	,	,	PUNCT
cana-3894	29	29	where	where	SCONJ
cana-3894	29	30	(	(	PUNCT
cana-3894	29	31	a	a	X
cana-3894	29	32	;	;	PUNCT
cana-3894	29	33	q)∞	q)∞	ADJ
cana-3894	29	34	=	=	SYM
cana-3894	29	35	∞∏	∞∏	X
cana-3894	29	36	k=0	k=0	PROPN
cana-3894	29	37	(	(	PUNCT
cana-3894	29	38	i	i	PRON
cana-3894	29	39	−	−	PROPN
cana-3894	29	40	aqk	aqk	PROPN
cana-3894	29	41	)	)	PUNCT
cana-3894	29	42	,	,	PUNCT
cana-3894	29	43	|q|	|q|	VERB
cana-3894	29	44	<	<	X
cana-3894	29	45	1	1	NUM
cana-3894	29	46	.	.	PUNCT
cana-3894	29	47	(	(	PUNCT
cana-3894	29	48	a	a	PRON
cana-3894	29	49	;	;	PUNCT
cana-3894	29	50	q)−1	q)−1	NOUN
cana-3894	29	51	∞	∞	NOUN
cana-3894	29	52	=	=	SYM
cana-3894	29	53	∞∏	∞∏	X
cana-3894	29	54	k=0	k=0	PROPN
cana-3894	29	55	(	(	PUNCT
cana-3894	29	56	i	i	PRON
cana-3894	29	57	−	−	PROPN
cana-3894	29	58	aqk)−1	aqk)−1	NOUN
cana-3894	29	59	,	,	PUNCT
cana-3894	29	60	||a||	||a||	ADP
cana-3894	29	61	<	<	X
cana-3894	29	62	1	1	NUM
cana-3894	29	63	,	,	PUNCT
cana-3894	29	64	|q|	|q|	VERB
cana-3894	29	65	<	<	X
cana-3894	29	66	1	1	NUM
cana-3894	29	67	.	.	PUNCT
cana-3894	30	1	a	a	DET
cana-3894	30	2	q	q	ADJ
cana-3894	30	3	-	-	PUNCT
cana-3894	30	4	binomial	binomial	ADJ
cana-3894	30	5	coefficient	coefficient	NOUN
cana-3894	30	6	is	be	AUX
cana-3894	30	7	(	(	PUNCT
cana-3894	30	8	cf	cf	NOUN
cana-3894	30	9	.	.	PUNCT
cana-3894	31	1	[	[	X
cana-3894	31	2	2	2	NUM
cana-3894	31	3	,	,	PUNCT
cana-3894	31	4	ex.(1.2	ex.(1.2	ADJ
cana-3894	31	5	)	)	PUNCT
cana-3894	31	6	,	,	PUNCT
cana-3894	31	7	p.20	p.20	X
cana-3894	31	8	]	]	X
cana-3894	31	9	with	with	ADP
cana-3894	31	10	r	r	NOUN
cana-3894	31	11	=	=	SYM
cana-3894	31	12	1	1	NUM
cana-3894	31	13	):	):	PUNCT
cana-3894	31	14	[	[	PUNCT
cana-3894	31	15	n	n	X
cana-3894	31	16	m	m	NOUN
cana-3894	31	17	]	]	X
cana-3894	31	18	r	r	NOUN
cana-3894	31	19	=	=	PUNCT
cana-3894	31	20	(	(	PUNCT
cana-3894	31	21	qr	qr	NOUN
cana-3894	31	22	;	;	PUNCT
cana-3894	31	23	qr)n	qr)n	PROPN
cana-3894	31	24	(	(	PUNCT
cana-3894	31	25	qr	qr	NOUN
cana-3894	31	26	;	;	PUNCT
cana-3894	31	27	qr)n−m	qr)n−m	PROPN
cana-3894	31	28	(	(	PUNCT
cana-3894	31	29	qr	qr	NOUN
cana-3894	31	30	;	;	PUNCT
cana-3894	31	31	qr)m	qr)m	NOUN
cana-3894	31	32	,	,	PUNCT
cana-3894	31	33	r	r	NOUN
cana-3894	31	34	̸=	̸=	PROPN
cana-3894	31	35	0	0	NUM
cana-3894	31	36	.	.	PUNCT
cana-3894	32	1	(	(	PUNCT
cana-3894	32	2	2.3	2.3	NUM
cana-3894	32	3	)	)	PUNCT
cana-3894	32	4	a	a	DET
cana-3894	32	5	q	q	ADJ
cana-3894	32	6	-	-	PUNCT
cana-3894	32	7	gamma	gamma	NOUN
cana-3894	32	8	function	function	NOUN
cana-3894	32	9	is	be	AUX
cana-3894	32	10	defined	define	VERB
cana-3894	32	11	as	as	ADP
cana-3894	32	12	[	[	X
cana-3894	32	13	10	10	NUM
cana-3894	32	14	,	,	PUNCT
cana-3894	32	15	eq.(3.18	eq.(3.18	PROPN
cana-3894	32	16	)	)	PUNCT
cana-3894	32	17	]	]	X
cana-3894	32	18	:	:	PUNCT
cana-3894	32	19	γq(a	γq(a	PROPN
cana-3894	32	20	)	)	PUNCT
cana-3894	33	1	=	=	SYM
cana-3894	33	2	(	(	PUNCT
cana-3894	33	3	q	q	X
cana-3894	33	4	;	;	PUNCT
cana-3894	33	5	q)∞	q)∞	INTJ
cana-3894	33	6	(	(	PUNCT
cana-3894	33	7	qa	qa	NOUN
cana-3894	33	8	;	;	PUNCT
cana-3894	33	9	q	q	X
cana-3894	33	10	)	)	PUNCT
cana-3894	33	11	−1	−1	NOUN
cana-3894	33	12	∞	∞	NUM
cana-3894	33	13	;	;	PUNCT
cana-3894	33	14	(	(	PUNCT
cana-3894	33	15	1−	1−	NUM
cana-3894	33	16	q)i−a	q)i−a	NUM
cana-3894	33	17	,	,	PUNCT
cana-3894	33	18	(	(	PUNCT
cana-3894	33	19	2.4	2.4	NUM
cana-3894	33	20	)	)	PUNCT
cana-3894	33	21	q−n	q−n	NOUN
cana-3894	33	22	/∈	/∈	PUNCT
cana-3894	34	1	σ	σ	PROPN
cana-3894	34	2	(	(	PUNCT
cana-3894	34	3	qa	qa	PROPN
cana-3894	34	4	)	)	PUNCT
cana-3894	34	5	,	,	PUNCT
cana-3894	34	6	n	n	NOUN
cana-3894	34	7	=	=	SYM
cana-3894	34	8	0	0	NUM
cana-3894	34	9	,	,	PUNCT
cana-3894	34	10	1	1	NUM
cana-3894	34	11	,	,	PUNCT
cana-3894	34	12	2	2	NUM
cana-3894	34	13	,	,	PUNCT
cana-3894	34	14	·	·	PUNCT
cana-3894	34	15	·	·	PUNCT
cana-3894	34	16	·	·	PUNCT
cana-3894	34	17	for	for	ADP
cana-3894	34	18	a	a	DET
cana-3894	34	19	∈	∈	PROPN
cana-3894	34	20	cr×r	cr×r	NOUN
cana-3894	34	21	the	the	DET
cana-3894	34	22	q	q	NOUN
cana-3894	34	23	-	-	PUNCT
cana-3894	34	24	analogue	analogue	NOUN
cana-3894	34	25	of	of	ADP
cana-3894	34	26	legendre	legendre	PROPN
cana-3894	34	27	’s	’s	PART
cana-3894	34	28	duplication	duplication	NOUN
cana-3894	34	29	formula	formula	NOUN
cana-3894	34	30	is	be	AUX
cana-3894	34	31	of	of	ADP
cana-3894	34	32	the	the	DET
cana-3894	34	33	form	form	NOUN
cana-3894	34	34	[	[	X
cana-3894	34	35	10	10	NUM
cana-3894	34	36	,	,	PUNCT
cana-3894	34	37	eq.(3.23	eq.(3.23	NOUN
cana-3894	34	38	)	)	PUNCT
cana-3894	34	39	]	]	PUNCT
cana-3894	34	40	γq	γq	ADP
cana-3894	34	41	(	(	PUNCT
cana-3894	34	42	2a	2a	NUM
cana-3894	34	43	)	)	PUNCT
cana-3894	34	44	γq2	γq2	NOUN
cana-3894	34	45	(	(	PUNCT
cana-3894	34	46	1	1	NUM
cana-3894	34	47	2	2	NUM
cana-3894	34	48	)	)	PUNCT
cana-3894	35	1	=	=	VERB
cana-3894	35	2	γq2	γq2	NOUN
cana-3894	35	3	(	(	PUNCT
cana-3894	35	4	a	a	X
cana-3894	35	5	)	)	PUNCT
cana-3894	35	6	γq2	γq2	NOUN
cana-3894	35	7	(	(	PUNCT
cana-3894	35	8	a+	a+	X
cana-3894	35	9	1	1	NUM
cana-3894	35	10	2	2	NUM
cana-3894	35	11	i	i	NOUN
cana-3894	35	12	)	)	PUNCT
cana-3894	35	13	(	(	PUNCT
cana-3894	35	14	1	1	NUM
cana-3894	35	15	+	+	NOUN
cana-3894	35	16	q)2a−i	q)2a−i	NOUN
cana-3894	35	17	(	(	PUNCT
cana-3894	35	18	2.5	2.5	NUM
cana-3894	35	19	)	)	PUNCT
cana-3894	35	20	where	where	SCONJ
cana-3894	35	21	q−n	q−n	PROPN
cana-3894	35	22	/∈	/∈	PROPN
cana-3894	35	23	σ	σ	PROPN
cana-3894	35	24	(	(	PUNCT
cana-3894	35	25	q2a	q2a	PROPN
cana-3894	35	26	)	)	PUNCT
cana-3894	35	27	,	,	PUNCT
cana-3894	35	28	q−2n	q−2n	PROPN
cana-3894	35	29	/∈	/∈	PUNCT
cana-3894	36	1	σ	σ	PROPN
cana-3894	36	2	(	(	PUNCT
cana-3894	36	3	q2a	q2a	PROPN
cana-3894	36	4	)	)	PUNCT
cana-3894	36	5	,	,	PUNCT
cana-3894	36	6	q−2n	q−2n	PROPN
cana-3894	36	7	/∈	/∈	PUNCT
cana-3894	37	1	σ	σ	PROPN
cana-3894	37	2	(	(	PUNCT
cana-3894	37	3	qa+i/2	qa+i/2	PROPN
cana-3894	37	4	)	)	PUNCT
cana-3894	37	5	,	,	PUNCT
cana-3894	37	6	n	n	NOUN
cana-3894	37	7	=	=	SYM
cana-3894	37	8	1	1	NUM
cana-3894	37	9	,	,	PUNCT
cana-3894	37	10	2	2	NUM
cana-3894	37	11	,	,	PUNCT
cana-3894	37	12	·	·	PUNCT
cana-3894	37	13	·	·	PUNCT
cana-3894	37	14	·	·	PUNCT
cana-3894	38	1	in	in	ADP
cana-3894	38	2	view	view	NOUN
cana-3894	38	3	of	of	ADP
cana-3894	38	4	[	[	X
cana-3894	38	5	3	3	NUM
cana-3894	38	6	,	,	PUNCT
cana-3894	38	7	eq.(6	eq.(6	NOUN
cana-3894	38	8	)	)	PUNCT
cana-3894	38	9	]	]	PUNCT
cana-3894	38	10	,	,	PUNCT
cana-3894	38	11	we	we	PRON
cana-3894	38	12	can	can	AUX
cana-3894	38	13	propose	propose	VERB
cana-3894	38	14	the	the	DET
cana-3894	38	15	the	the	DET
cana-3894	38	16	following	following	NOUN
cana-3894	38	17	theorem	theorem	NOUN
cana-3894	38	18	for	for	ADP
cana-3894	38	19	matrix	matrix	NOUN
cana-3894	38	20	function	function	NOUN
cana-3894	38	21	.	.	PUNCT
cana-3894	39	1	theorem	theorem	VERB
cana-3894	39	2	2.1	2.1	NUM
cana-3894	39	3	.	.	PUNCT
cana-3894	40	1	if	if	SCONJ
cana-3894	40	2	f(z	f(z	NOUN
cana-3894	40	3	)	)	PUNCT
cana-3894	41	1	=	=	PUNCT
cana-3894	42	1	∞∑	∞∑	DET
cana-3894	42	2	n=0	n=0	NUM
cana-3894	42	3	vnz	vnz	NOUN
cana-3894	42	4	n	n	X
cana-3894	42	5	is	be	AUX
cana-3894	42	6	an	an	DET
cana-3894	42	7	entire	entire	ADJ
cana-3894	42	8	function	function	NOUN
cana-3894	42	9	then	then	ADV
cana-3894	42	10	the	the	DET
cana-3894	42	11	order	order	NOUN
cana-3894	42	12	ϱ(f	ϱ(f	NOUN
cana-3894	42	13	)	)	PUNCT
cana-3894	42	14	of	of	ADP
cana-3894	42	15	f	f	PROPN
cana-3894	42	16	is	be	AUX
cana-3894	42	17	given	give	VERB
cana-3894	42	18	by	by	ADP
cana-3894	42	19	ϱ(f	ϱ(f	NOUN
cana-3894	42	20	)	)	PUNCT
cana-3894	42	21	=	=	SYM
cana-3894	42	22	lim	lim	PROPN
cana-3894	42	23	n→∞	n→∞	NUM
cana-3894	42	24	supn	supn	NOUN
cana-3894	42	25	log	log	NOUN
cana-3894	42	26	n	n	PRON
cana-3894	42	27	log(∥vn∥)−1	log(∥vn∥)−1	PROPN
cana-3894	42	28	.	.	PUNCT
cana-3894	43	1	(	(	PUNCT
cana-3894	43	2	2.6	2.6	NUM
cana-3894	43	3	)	)	PUNCT
cana-3894	43	4	and	and	CCONJ
cana-3894	43	5	the	the	DET
cana-3894	43	6	type	type	NOUN
cana-3894	43	7	of	of	ADP
cana-3894	43	8	the	the	DET
cana-3894	43	9	function	function	NOUN
cana-3894	43	10	σ	σ	PROPN
cana-3894	43	11	is	be	AUX
cana-3894	43	12	given	give	VERB
cana-3894	43	13	by	by	ADP
cana-3894	43	14	[	[	X
cana-3894	43	15	3	3	NUM
cana-3894	43	16	]	]	X
cana-3894	43	17	eϱσ	eϱσ	PROPN
cana-3894	43	18	=	=	SYM
cana-3894	43	19	lim	lim	PROPN
cana-3894	43	20	n→∞	n→∞	NUM
cana-3894	43	21	sup	sup	NOUN
cana-3894	43	22	(	(	PUNCT
cana-3894	43	23	n	n	NOUN
cana-3894	43	24	∥vn∥ϱ/n	∥vn∥ϱ/n	NUM
cana-3894	43	25	)	)	PUNCT
cana-3894	43	26	.	.	PUNCT
cana-3894	44	1	(	(	PUNCT
cana-3894	44	2	2.7	2.7	NUM
cana-3894	44	3	)	)	PUNCT
cana-3894	44	4	https://internationalpubls.com	https://internationalpubls.com	X
cana-3894	44	5	331	331	NUM
cana-3894	44	6	communications	communication	NOUN
cana-3894	44	7	on	on	ADP
cana-3894	44	8	applied	apply	VERB
cana-3894	44	9	nonlinear	nonlinear	ADJ
cana-3894	44	10	analysis	analysis	NOUN
cana-3894	44	11	issn	issn	NOUN
cana-3894	44	12	:	:	PUNCT
cana-3894	44	13	1074	1074	NUM
cana-3894	44	14	-	-	PUNCT
cana-3894	44	15	133x	133x	NUM
cana-3894	44	16	vol	vol	NOUN
cana-3894	44	17	32	32	NUM
cana-3894	44	18	no	no	NOUN
cana-3894	44	19	.	.	PUNCT
cana-3894	45	1	9s(2025	9s(2025	NUM
cana-3894	45	2	)	)	PUNCT
cana-3894	45	3	for	for	ADP
cana-3894	45	4	every	every	DET
cana-3894	45	5	positive	positive	ADJ
cana-3894	45	6	ϵ	ϵ	NOUN
cana-3894	45	7	,	,	PUNCT
cana-3894	45	8	the	the	DET
cana-3894	45	9	asymptotic	asymptotic	ADJ
cana-3894	45	10	estimate	estimate	NOUN
cana-3894	45	11	[	[	X
cana-3894	45	12	3	3	NUM
cana-3894	45	13	,	,	PUNCT
cana-3894	45	14	eq.(8	eq.(8	NUM
cana-3894	45	15	)	)	PUNCT
cana-3894	45	16	]	]	PUNCT
cana-3894	46	1	|f(z)|	|f(z)|	PROPN
cana-3894	46	2	<	<	X
cana-3894	46	3	exp	exp	NOUN
cana-3894	46	4	(	(	PUNCT
cana-3894	46	5	(	(	PUNCT
cana-3894	46	6	σ	σ	X
cana-3894	46	7	+	+	NUM
cana-3894	46	8	ϵ	ϵ	X
cana-3894	46	9	)	)	PUNCT
cana-3894	46	10	|z|ϱ	|z|ϱ	NOUN
cana-3894	46	11	)	)	PUNCT
cana-3894	46	12	,	,	PUNCT
cana-3894	46	13	|z|	|z|	VERB
cana-3894	46	14	≥	≥	NOUN
cana-3894	46	15	r0	r0	VERB
cana-3894	46	16	>	>	X
cana-3894	46	17	0	0	PUNCT
cana-3894	47	1	(	(	PUNCT
cana-3894	47	2	2.8	2.8	NUM
cana-3894	47	3	)	)	PUNCT
cana-3894	47	4	holds	hold	VERB
cana-3894	47	5	with	with	ADP
cana-3894	47	6	ϱ	ϱ	PROPN
cana-3894	47	7	,	,	PUNCT
cana-3894	47	8	σ	σ	NOUN
cana-3894	47	9	as	as	ADP
cana-3894	47	10	in	in	ADP
cana-3894	47	11	(	(	PUNCT
cana-3894	47	12	2.6	2.6	NUM
cana-3894	47	13	)	)	PUNCT
cana-3894	47	14	,	,	PUNCT
cana-3894	47	15	(	(	PUNCT
cana-3894	47	16	2.7	2.7	NUM
cana-3894	47	17	)	)	PUNCT
cana-3894	47	18	for	for	ADP
cana-3894	47	19	|z|	|z|	NOUN
cana-3894	47	20	≥	≥	NOUN
cana-3894	47	21	r0(ϵ	r0(ϵ	NOUN
cana-3894	47	22	)	)	PUNCT
cana-3894	47	23	,	,	PUNCT
cana-3894	47	24	r0(ϵ	r0(ϵ	NOUN
cana-3894	47	25	)	)	PUNCT
cana-3894	47	26	sufficiently	sufficiently	ADV
cana-3894	47	27	large	large	ADJ
cana-3894	47	28	.	.	PUNCT
cana-3894	48	1	for	for	ADP
cana-3894	48	2	any	any	DET
cana-3894	48	3	complex	complex	ADJ
cana-3894	48	4	square	square	ADJ
cana-3894	48	5	matrix	matrix	NOUN
cana-3894	48	6	a	a	PRON
cana-3894	48	7	and	and	CCONJ
cana-3894	48	8	|q|	|q|	VERB
cana-3894	48	9	<	<	X
cana-3894	48	10	1	1	NUM
cana-3894	48	11	the	the	DET
cana-3894	48	12	q	q	NOUN
cana-3894	48	13	-	-	PUNCT
cana-3894	48	14	analogues	analogue	NOUN
cana-3894	48	15	of	of	ADP
cana-3894	48	16	the	the	DET
cana-3894	48	17	exponential	exponential	ADJ
cana-3894	48	18	matrix	matrix	NOUN
cana-3894	48	19	functions	function	NOUN
cana-3894	48	20	are	be	AUX
cana-3894	48	21	defined	define	VERB
cana-3894	48	22	as	as	ADP
cana-3894	48	23	[	[	X
cana-3894	48	24	10	10	NUM
cana-3894	48	25	,	,	PUNCT
cana-3894	48	26	eq.(3.11	eq.(3.11	NOUN
cana-3894	48	27	)	)	PUNCT
cana-3894	48	28	]	]	PUNCT
cana-3894	48	29	eq(a	eq(a	NOUN
cana-3894	48	30	)	)	PUNCT
cana-3894	48	31	=	=	PUNCT
cana-3894	49	1	∞∑	∞∑	NUM
cana-3894	49	2	n=0	n=0	NUM
cana-3894	49	3	an	an	DET
cana-3894	49	4	(	(	PUNCT
cana-3894	49	5	q	q	NOUN
cana-3894	49	6	;	;	PUNCT
cana-3894	49	7	q)n	q)n	SYM
cana-3894	49	8	=	=	SYM
cana-3894	49	9	(	(	PUNCT
cana-3894	49	10	(	(	PUNCT
cana-3894	49	11	1−	1−	NUM
cana-3894	49	12	q)a	q)a	NOUN
cana-3894	49	13	;	;	PUNCT
cana-3894	49	14	q)−1	q)−1	NOUN
cana-3894	49	15	∞	∞	PROPN
cana-3894	49	16	,	,	PUNCT
cana-3894	49	17	(	(	PUNCT
cana-3894	49	18	2.9	2.9	NUM
cana-3894	49	19	)	)	PUNCT
cana-3894	49	20	and	and	CCONJ
cana-3894	49	21	[	[	X
cana-3894	49	22	10	10	NUM
cana-3894	49	23	,	,	PUNCT
cana-3894	49	24	eq.(3.10	eq.(3.10	PROPN
cana-3894	49	25	)	)	PUNCT
cana-3894	49	26	]	]	PUNCT
cana-3894	49	27	eq(a	eq(a	NOUN
cana-3894	49	28	)	)	PUNCT
cana-3894	49	29	=	=	PUNCT
cana-3894	50	1	∞∑	∞∑	DET
cana-3894	50	2	n=0	n=0	NUM
cana-3894	50	3	qn(n−1)/2	qn(n−1)/2	PROPN
cana-3894	50	4	an	an	DET
cana-3894	50	5	(	(	PUNCT
cana-3894	50	6	q	q	NOUN
cana-3894	50	7	;	;	PUNCT
cana-3894	50	8	q)n	q)n	SYM
cana-3894	50	9	=	=	SYM
cana-3894	50	10	(	(	PUNCT
cana-3894	50	11	−(1−	−(1−	X
cana-3894	50	12	q)a	q)a	NOUN
cana-3894	50	13	;	;	PUNCT
cana-3894	50	14	q)∞	q)∞	ADJ
cana-3894	50	15	,	,	PUNCT
cana-3894	50	16	(	(	PUNCT
cana-3894	50	17	2.10	2.10	NUM
cana-3894	50	18	)	)	PUNCT
cana-3894	50	19	let	let	VERB
cana-3894	50	20	a	a	DET
cana-3894	50	21	∈	∈	NOUN
cana-3894	50	22	cr×r	cr×r	NOUN
cana-3894	50	23	be	be	AUX
cana-3894	50	24	a	a	DET
cana-3894	50	25	positive	positive	ADJ
cana-3894	50	26	stable	stable	ADJ
cana-3894	50	27	matrix	matrix	NOUN
cana-3894	50	28	then	then	ADV
cana-3894	50	29	the	the	DET
cana-3894	50	30	q	q	ADJ
cana-3894	50	31	-	-	PUNCT
cana-3894	50	32	beta	beta	ADJ
cana-3894	50	33	matrix	matrix	NOUN
cana-3894	50	34	function	function	NOUN
cana-3894	50	35	is	be	AUX
cana-3894	50	36	defined	define	VERB
cana-3894	50	37	as	as	ADP
cana-3894	50	38	[	[	X
cana-3894	50	39	10	10	NUM
cana-3894	50	40	,	,	PUNCT
cana-3894	50	41	eq.(4.5	eq.(4.5	PROPN
cana-3894	50	42	)	)	PUNCT
cana-3894	50	43	]	]	PUNCT
cana-3894	50	44	bq(a	bq(a	NOUN
cana-3894	50	45	,	,	PUNCT
cana-3894	50	46	b	b	X
cana-3894	50	47	)	)	PUNCT
cana-3894	50	48	=	=	SYM
cana-3894	51	1	∫	∫	PROPN
cana-3894	51	2	1	1	NUM
cana-3894	51	3	0	0	NUM
cana-3894	51	4	(	(	PUNCT
cana-3894	51	5	tq	tq	ADV
cana-3894	51	6	;	;	PUNCT
cana-3894	51	7	q)∞	q)∞	ADJ
cana-3894	51	8	(	(	PUNCT
cana-3894	51	9	tqb	tqb	NOUN
cana-3894	51	10	;	;	PUNCT
cana-3894	51	11	q)−1	q)−1	NOUN
cana-3894	51	12	∞	∞	PROPN
cana-3894	51	13	ta−idqt	ta−idqt	NOUN
cana-3894	51	14	,	,	PUNCT
cana-3894	51	15	(	(	PUNCT
cana-3894	51	16	2.11	2.11	NUM
cana-3894	51	17	)	)	PUNCT
cana-3894	51	18	the	the	DET
cana-3894	51	19	q	q	NOUN
cana-3894	51	20	-	-	NOUN
cana-3894	51	21	derivative	derivative	NOUN
cana-3894	51	22	of	of	ADP
cana-3894	51	23	a	a	DET
cana-3894	51	24	function	function	NOUN
cana-3894	51	25	f(x	f(x	PROPN
cana-3894	51	26	)	)	PUNCT
cana-3894	51	27	is	be	AUX
cana-3894	51	28	defined	define	VERB
cana-3894	51	29	by	by	ADP
cana-3894	51	30	[	[	X
cana-3894	51	31	2	2	NUM
cana-3894	51	32	,	,	PUNCT
cana-3894	51	33	ex.1.12	ex.1.12	NOUN
cana-3894	51	34	,	,	PUNCT
cana-3894	51	35	p.22	p.22	NOUN
cana-3894	51	36	]	]	X
cana-3894	51	37	dqf(a	dqf(a	ADJ
cana-3894	51	38	)	)	PUNCT
cana-3894	51	39	=	=	NOUN
cana-3894	52	1	[	[	X
cana-3894	52	2	f(a)−	f(a)−	VERB
cana-3894	52	3	f(aq)][a(1−	f(aq)][a(1−	ADJ
cana-3894	52	4	q)]−1	q)]−1	NOUN
cana-3894	52	5	.	.	PUNCT
cana-3894	53	1	(	(	PUNCT
cana-3894	53	2	2.12	2.12	NUM
cana-3894	53	3	)	)	PUNCT
cana-3894	53	4	in	in	ADP
cana-3894	53	5	view	view	NOUN
cana-3894	53	6	of	of	ADP
cana-3894	53	7	two	two	NUM
cana-3894	53	8	q	q	NOUN
cana-3894	53	9	-	-	PUNCT
cana-3894	53	10	analogues	analogue	NOUN
cana-3894	53	11	of	of	ADP
cana-3894	53	12	generalized	generalized	ADJ
cana-3894	53	13	mittag	mittag	ADJ
cana-3894	53	14	-	-	PUNCT
cana-3894	53	15	leffler	leffler	NOUN
cana-3894	53	16	function	function	NOUN
cana-3894	54	1	[	[	X
cana-3894	54	2	3	3	NUM
cana-3894	54	3	,	,	PUNCT
cana-3894	54	4	4	4	NUM
cana-3894	54	5	]	]	PUNCT
cana-3894	54	6	,	,	PUNCT
cana-3894	54	7	we	we	PRON
cana-3894	54	8	define	define	VERB
cana-3894	54	9	qgeneralized	qgeneralized	ADJ
cana-3894	54	10	mittag	mittag	ADJ
cana-3894	54	11	-	-	PUNCT
cana-3894	54	12	leffler	leffler	NOUN
cana-3894	54	13	matrix	matrix	NOUN
cana-3894	54	14	functions	function	NOUN
cana-3894	54	15	in	in	ADP
cana-3894	54	16	the	the	DET
cana-3894	54	17	form	form	NOUN
cana-3894	54	18	:	:	PUNCT
cana-3894	54	19	definition	definition	NOUN
cana-3894	54	20	1	1	NUM
cana-3894	54	21	.	.	PUNCT
cana-3894	55	1	let	let	VERB
cana-3894	55	2	a	a	DET
cana-3894	55	3	,	,	PUNCT
cana-3894	55	4	b	b	NOUN
cana-3894	55	5	,	,	PUNCT
cana-3894	55	6	c	c	AUX
cana-3894	55	7	be	be	AUX
cana-3894	55	8	positive	positive	ADJ
cana-3894	55	9	stable	stable	ADJ
cana-3894	55	10	matrices	matrix	NOUN
cana-3894	55	11	in	in	ADP
cana-3894	55	12	cr×r	cr×r	PROPN
cana-3894	55	13	,	,	PUNCT
cana-3894	55	14	α	α	PROPN
cana-3894	55	15	,	,	PUNCT
cana-3894	55	16	δ	δ	PROPN
cana-3894	55	17	,	,	PUNCT
cana-3894	55	18	µ	µ	X
cana-3894	55	19	∈	∈	PROPN
cana-3894	55	20	c	c	NOUN
cana-3894	55	21	with	with	ADP
cana-3894	55	22	ℜ(α	ℜ(α	NOUN
cana-3894	55	23	)	)	PUNCT
cana-3894	55	24	>	>	X
cana-3894	55	25	0	0	NUM
cana-3894	55	26	,	,	PUNCT
cana-3894	55	27	δ	δ	PROPN
cana-3894	55	28	,	,	PUNCT
cana-3894	55	29	µ	µ	X
cana-3894	55	30	>	>	X
cana-3894	55	31	0	0	NUM
cana-3894	55	32	,	,	PUNCT
cana-3894	56	1	r	r	NOUN
cana-3894	56	2	∈	∈	PROPN
cana-3894	56	3	{	{	PUNCT
cana-3894	56	4	−1	−1	NOUN
cana-3894	56	5	,	,	PUNCT
cana-3894	56	6	0	0	NUM
cana-3894	56	7	}	}	PUNCT
cana-3894	56	8	∪	∪	NOUN
cana-3894	56	9	n	n	CCONJ
cana-3894	56	10	,	,	PUNCT
cana-3894	56	11	s	s	VERB
cana-3894	56	12	∈	∈	PROPN
cana-3894	56	13	n	n	NOUN
cana-3894	56	14	∪	∪	X
cana-3894	56	15	{	{	PUNCT
cana-3894	56	16	0	0	NUM
cana-3894	56	17	}	}	PUNCT
cana-3894	56	18	then	then	ADV
cana-3894	56	19	ea	ea	NUM
cana-3894	56	20	,	,	PUNCT
cana-3894	56	21	b	b	PROPN
cana-3894	56	22	,	,	PUNCT
cana-3894	56	23	c	c	PROPN
cana-3894	56	24	αi	αi	PROPN
cana-3894	56	25	,	,	PUNCT
cana-3894	56	26	δi	δi	ADV
cana-3894	56	27	,	,	PUNCT
cana-3894	56	28	µi(λz	µi(λz	PROPN
cana-3894	56	29	;	;	PUNCT
cana-3894	56	30	s	s	X
cana-3894	56	31	,	,	PUNCT
cana-3894	56	32	r|q	r|q	ADJ
cana-3894	56	33	)	)	PUNCT
cana-3894	56	34	=	=	PUNCT
cana-3894	57	1	∞∑	∞∑	NUM
cana-3894	57	2	n=0	n=0	NUM
cana-3894	57	3	(	(	PUNCT
cana-3894	57	4	−1)pni	−1)pni	PROPN
cana-3894	57	5	qpn(n−1)i/2	qpn(n−1)i/2	PROPN
cana-3894	58	1	[	[	X
cana-3894	58	2	γq(δni	γq(δni	X
cana-3894	58	3	+	+	NOUN
cana-3894	58	4	a)]s	a)]s	INTJ
cana-3894	58	5	×	×	NOUN
cana-3894	59	1	[	[	X
cana-3894	59	2	γq(αni	γq(αni	X
cana-3894	59	3	+	+	ADJ
cana-3894	59	4	b)]−1	b)]−1	X
cana-3894	59	5	[	[	X
cana-3894	59	6	γq(µni	γq(µni	NOUN
cana-3894	59	7	+	+	NOUN
cana-3894	59	8	c)]−r	c)]−r	NOUN
cana-3894	59	9	(	(	PUNCT
cana-3894	59	10	λz)n	λz)n	PROPN
cana-3894	59	11	(	(	PUNCT
cana-3894	59	12	q	q	NOUN
cana-3894	59	13	;	;	PUNCT
cana-3894	59	14	q)n	q)n	X
cana-3894	59	15	,	,	PUNCT
cana-3894	59	16	(	(	PUNCT
cana-3894	59	17	2.13	2.13	NUM
cana-3894	59	18	)	)	PUNCT
cana-3894	60	1	where	where	SCONJ
cana-3894	60	2	p	p	NOUN
cana-3894	60	3	=	=	SYM
cana-3894	60	4	α2	α2	PROPN
cana-3894	60	5	+	+	CCONJ
cana-3894	60	6	rµ2	rµ2	NOUN
cana-3894	60	7	−	−	PROPN
cana-3894	60	8	sδ2	sδ2	NOUN
cana-3894	60	9	+	+	CCONJ
cana-3894	60	10	1	1	NUM
cana-3894	60	11	with	with	ADP
cana-3894	60	12	ℜ(p	ℜ(p	NOUN
cana-3894	60	13	)	)	PUNCT
cana-3894	60	14	>	>	X
cana-3894	60	15	0	0	X
cana-3894	60	16	.	.	PUNCT
cana-3894	61	1	definition	definition	NOUN
cana-3894	61	2	2	2	NUM
cana-3894	61	3	.	.	PUNCT
cana-3894	62	1	let	let	VERB
cana-3894	62	2	a	a	DET
cana-3894	62	3	,	,	PUNCT
cana-3894	62	4	b	b	NOUN
cana-3894	62	5	,	,	PUNCT
cana-3894	62	6	c	c	AUX
cana-3894	62	7	be	be	AUX
cana-3894	62	8	positive	positive	ADJ
cana-3894	62	9	stable	stable	ADJ
cana-3894	62	10	matrices	matrix	NOUN
cana-3894	62	11	in	in	ADP
cana-3894	62	12	cr×r	cr×r	PROPN
cana-3894	62	13	,	,	PUNCT
cana-3894	62	14	α	α	PROPN
cana-3894	62	15	,	,	PUNCT
cana-3894	62	16	δ	δ	PROPN
cana-3894	62	17	,	,	PUNCT
cana-3894	62	18	µ	µ	X
cana-3894	62	19	∈	∈	PROPN
cana-3894	62	20	c	c	NOUN
cana-3894	62	21	with	with	ADP
cana-3894	62	22	ℜ(α	ℜ(α	NOUN
cana-3894	62	23	)	)	PUNCT
cana-3894	62	24	>	>	X
cana-3894	62	25	0	0	NUM
cana-3894	62	26	,	,	PUNCT
cana-3894	62	27	δ	δ	PROPN
cana-3894	62	28	,	,	PUNCT
cana-3894	62	29	µ	µ	X
cana-3894	62	30	>	>	X
cana-3894	62	31	0	0	NUM
cana-3894	62	32	,	,	PUNCT
cana-3894	63	1	r	r	NOUN
cana-3894	63	2	∈	∈	PROPN
cana-3894	63	3	{	{	PUNCT
cana-3894	63	4	−1	−1	NOUN
cana-3894	63	5	,	,	PUNCT
cana-3894	63	6	0	0	NUM
cana-3894	63	7	}	}	PUNCT
cana-3894	63	8	∪	∪	NOUN
cana-3894	63	9	n	n	CCONJ
cana-3894	63	10	,	,	PUNCT
cana-3894	63	11	s	s	VERB
cana-3894	63	12	∈	∈	PROPN
cana-3894	63	13	n	n	NOUN
cana-3894	63	14	∪	∪	X
cana-3894	63	15	{	{	PUNCT
cana-3894	63	16	0	0	NUM
cana-3894	63	17	}	}	PUNCT
cana-3894	63	18	and	and	CCONJ
cana-3894	63	19	(	(	PUNCT
cana-3894	63	20	α2	α2	ADJ
cana-3894	63	21	+	+	CCONJ
cana-3894	63	22	rµ2	rµ2	NOUN
cana-3894	63	23	+	+	CCONJ
cana-3894	63	24	1)i	1)i	NUM
cana-3894	63	25	=	=	SYM
cana-3894	63	26	sδ2i	sδ2i	PROPN
cana-3894	63	27	then	then	ADV
cana-3894	63	28	ea	ea	NUM
cana-3894	63	29	,	,	PUNCT
cana-3894	63	30	b	b	PROPN
cana-3894	63	31	,	,	PUNCT
cana-3894	63	32	c	c	PROPN
cana-3894	63	33	αi	αi	PROPN
cana-3894	63	34	,	,	PUNCT
cana-3894	63	35	δi	δi	ADV
cana-3894	63	36	,	,	PUNCT
cana-3894	63	37	µi(λz	µi(λz	PROPN
cana-3894	63	38	;	;	PUNCT
cana-3894	63	39	s	s	X
cana-3894	63	40	,	,	PUNCT
cana-3894	63	41	r|q	r|q	ADJ
cana-3894	63	42	)	)	PUNCT
cana-3894	63	43	=	=	PUNCT
cana-3894	64	1	∞∑	∞∑	NUM
cana-3894	64	2	n=0	n=0	NUM
cana-3894	65	1	[	[	X
cana-3894	65	2	γq(δni	γq(δni	X
cana-3894	65	3	+	+	NUM
cana-3894	65	4	a)]s	a)]s	ADJ
cana-3894	66	1	[	[	X
cana-3894	66	2	γq(αni	γq(αni	PROPN
cana-3894	66	3	+	+	ADJ
cana-3894	66	4	b)]−1	b)]−1	NOUN
cana-3894	66	5	×[γq(µni	×[γq(µni	NOUN
cana-3894	66	6	+	+	CCONJ
cana-3894	66	7	c)]−r	c)]−r	NOUN
cana-3894	66	8	(	(	PUNCT
cana-3894	66	9	λz)n	λz)n	PROPN
cana-3894	66	10	(	(	PUNCT
cana-3894	66	11	q	q	NOUN
cana-3894	66	12	;	;	PUNCT
cana-3894	66	13	q)n	q)n	X
cana-3894	66	14	.	.	PUNCT
cana-3894	67	1	(	(	PUNCT
cana-3894	67	2	2.14	2.14	NUM
cana-3894	67	3	)	)	PUNCT
cana-3894	67	4	alternatively	alternatively	ADV
cana-3894	67	5	in	in	ADP
cana-3894	67	6	view	view	NOUN
cana-3894	67	7	of	of	ADP
cana-3894	67	8	the	the	DET
cana-3894	67	9	definition	definition	NOUN
cana-3894	67	10	of	of	ADP
cana-3894	67	11	q	q	ADJ
cana-3894	67	12	-	-	PUNCT
cana-3894	67	13	gamma	gamma	NOUN
cana-3894	67	14	function	function	NOUN
cana-3894	67	15	(	(	PUNCT
cana-3894	67	16	2.4	2.4	NUM
cana-3894	67	17	)	)	PUNCT
cana-3894	67	18	these	these	DET
cana-3894	67	19	q	q	NOUN
cana-3894	67	20	-	-	NOUN
cana-3894	67	21	forms	form	NOUN
cana-3894	67	22	can	can	AUX
cana-3894	67	23	also	also	ADV
cana-3894	67	24	be	be	AUX
cana-3894	67	25	put	put	VERB
cana-3894	67	26	in	in	ADP
cana-3894	67	27	the	the	DET
cana-3894	67	28	form	form	NOUN
cana-3894	67	29	:	:	PUNCT
cana-3894	67	30	ea	ea	NUM
cana-3894	67	31	,	,	PUNCT
cana-3894	67	32	b	b	PROPN
cana-3894	67	33	,	,	PUNCT
cana-3894	67	34	c	c	PROPN
cana-3894	67	35	αi	αi	PROPN
cana-3894	67	36	,	,	PUNCT
cana-3894	67	37	δi	δi	ADV
cana-3894	67	38	,	,	PUNCT
cana-3894	67	39	µi(λz	µi(λz	PROPN
cana-3894	67	40	;	;	PUNCT
cana-3894	67	41	s	s	X
cana-3894	67	42	,	,	PUNCT
cana-3894	67	43	r|q	r|q	ADJ
cana-3894	67	44	)	)	PUNCT
cana-3894	67	45	=	=	PUNCT
cana-3894	68	1	∞∑	∞∑	NUM
cana-3894	68	2	n=0	n=0	NUM
cana-3894	68	3	(	(	PUNCT
cana-3894	68	4	−1)pni	−1)pni	PROPN
cana-3894	68	5	qpn(n−1)i/2	qpn(n−1)i/2	X
cana-3894	68	6	(	(	PUNCT
cana-3894	68	7	qαni+b	qαni+b	X
cana-3894	68	8	;	;	PUNCT
cana-3894	68	9	q)∞	q)∞	ADJ
cana-3894	68	10	×[(qµni+c	×[(qµni+c	PROPN
cana-3894	68	11	;	;	PUNCT
cana-3894	68	12	q)∞]r	q)∞]r	X
cana-3894	69	1	[	[	X
cana-3894	69	2	(	(	PUNCT
cana-3894	69	3	qδni+a	qδni+a	PROPN
cana-3894	69	4	;	;	PUNCT
cana-3894	69	5	q)∞]−s	q)∞]−s	X
cana-3894	69	6	(	(	PUNCT
cana-3894	69	7	λz)n	λz)n	PROPN
cana-3894	69	8	(	(	PUNCT
cana-3894	69	9	q	q	NOUN
cana-3894	69	10	;	;	PUNCT
cana-3894	69	11	q)n	q)n	X
cana-3894	69	12	,	,	PUNCT
cana-3894	69	13	(	(	PUNCT
cana-3894	69	14	2.15	2.15	NUM
cana-3894	69	15	)	)	PUNCT
cana-3894	69	16	https://internationalpubls.com	https://internationalpubls.com	X
cana-3894	69	17	332	332	NUM
cana-3894	69	18	communications	communication	NOUN
cana-3894	69	19	on	on	ADP
cana-3894	69	20	applied	apply	VERB
cana-3894	69	21	nonlinear	nonlinear	ADJ
cana-3894	69	22	analysis	analysis	NOUN
cana-3894	69	23	issn	issn	NOUN
cana-3894	69	24	:	:	PUNCT
cana-3894	69	25	1074	1074	NUM
cana-3894	69	26	-	-	PUNCT
cana-3894	69	27	133x	133x	NUM
cana-3894	69	28	vol	vol	NOUN
cana-3894	69	29	32	32	NUM
cana-3894	69	30	no	no	NOUN
cana-3894	69	31	.	.	PUNCT
cana-3894	70	1	9s(2025	9s(2025	NUM
cana-3894	70	2	)	)	PUNCT
cana-3894	70	3	and	and	CCONJ
cana-3894	70	4	ea	ea	NUM
cana-3894	70	5	,	,	PUNCT
cana-3894	70	6	b	b	PROPN
cana-3894	70	7	,	,	PUNCT
cana-3894	70	8	c	c	PROPN
cana-3894	70	9	αi	αi	PROPN
cana-3894	70	10	,	,	PUNCT
cana-3894	70	11	δi	δi	ADV
cana-3894	70	12	,	,	PUNCT
cana-3894	70	13	µi(λz	µi(λz	PROPN
cana-3894	70	14	;	;	PUNCT
cana-3894	70	15	s	s	X
cana-3894	70	16	,	,	PUNCT
cana-3894	70	17	r|q	r|q	ADJ
cana-3894	70	18	)	)	PUNCT
cana-3894	70	19	=	=	PUNCT
cana-3894	71	1	∞∑	∞∑	NUM
cana-3894	71	2	n=0	n=0	PUNCT
cana-3894	71	3	[	[	PUNCT
cana-3894	71	4	(	(	PUNCT
cana-3894	71	5	qαni+b	qαni+b	X
cana-3894	71	6	;	;	PUNCT
cana-3894	71	7	q)∞	q)∞	ADJ
cana-3894	71	8	]	]	PUNCT
cana-3894	72	1	[	[	X
cana-3894	72	2	(	(	PUNCT
cana-3894	72	3	qµni+c	qµni+c	NOUN
cana-3894	72	4	;	;	PUNCT
cana-3894	72	5	q)∞]r	q)∞]r	X
cana-3894	72	6	×[(qδni+a	×[(qδni+a	PROPN
cana-3894	72	7	;	;	PUNCT
cana-3894	72	8	q)∞]−s	q)∞]−s	X
cana-3894	72	9	(	(	PUNCT
cana-3894	72	10	λz)n	λz)n	PROPN
cana-3894	72	11	(	(	PUNCT
cana-3894	72	12	q	q	NOUN
cana-3894	72	13	;	;	PUNCT
cana-3894	72	14	q)n	q)n	X
cana-3894	72	15	.	.	PUNCT
cana-3894	73	1	(	(	PUNCT
cana-3894	73	2	2.16	2.16	NUM
cana-3894	73	3	)	)	PUNCT
cana-3894	73	4	we	we	PRON
cana-3894	73	5	shall	shall	AUX
cana-3894	73	6	refer	refer	VERB
cana-3894	73	7	to	to	ADP
cana-3894	73	8	these	these	DET
cana-3894	73	9	functions	function	NOUN
cana-3894	73	10	as	as	ADP
cana-3894	73	11	q	q	NOUN
cana-3894	73	12	-	-	NOUN
cana-3894	73	13	gmlm	gmlm	NOUN
cana-3894	73	14	.	.	PUNCT
cana-3894	74	1	the	the	DET
cana-3894	74	2	objective	objective	NOUN
cana-3894	74	3	of	of	ADP
cana-3894	74	4	constructing	construct	VERB
cana-3894	74	5	this	this	DET
cana-3894	74	6	function	function	NOUN
cana-3894	74	7	is	be	AUX
cana-3894	74	8	to	to	PART
cana-3894	74	9	(	(	PUNCT
cana-3894	74	10	i	i	NOUN
cana-3894	74	11	)	)	PUNCT
cana-3894	74	12	include	include	VERB
cana-3894	74	13	certain	certain	ADJ
cana-3894	74	14	existing	exist	VERB
cana-3894	74	15	generalizations	generalization	NOUN
cana-3894	74	16	of	of	ADP
cana-3894	74	17	mittag	mittag	ADJ
cana-3894	74	18	-	-	PUNCT
cana-3894	74	19	leffler	leffler	NOUN
cana-3894	74	20	matrix	matrix	NOUN
cana-3894	74	21	function	function	NOUN
cana-3894	74	22	[	[	X
cana-3894	74	23	3	3	NUM
cana-3894	74	24	,	,	PUNCT
cana-3894	74	25	11	11	NUM
cana-3894	74	26	,	,	PUNCT
cana-3894	74	27	4	4	NUM
cana-3894	74	28	,	,	PUNCT
cana-3894	74	29	7	7	NUM
cana-3894	74	30	,	,	PUNCT
cana-3894	74	31	8	8	NUM
cana-3894	74	32	,	,	PUNCT
cana-3894	74	33	9	9	NUM
cana-3894	74	34	,	,	PUNCT
cana-3894	74	35	5	5	NUM
cana-3894	74	36	,	,	PUNCT
cana-3894	74	37	6	6	NUM
cana-3894	74	38	]	]	NUM
cana-3894	74	39	,	,	PUNCT
cana-3894	74	40	(	(	PUNCT
cana-3894	74	41	ii	ii	NOUN
cana-3894	74	42	)	)	PUNCT
cana-3894	74	43	also	also	ADV
cana-3894	74	44	include	include	VERB
cana-3894	74	45	the	the	DET
cana-3894	74	46	matrix	matrix	NOUN
cana-3894	74	47	functions	function	NOUN
cana-3894	74	48	such	such	ADJ
cana-3894	74	49	as	as	ADP
cana-3894	74	50	bessel	bessel	NOUN
cana-3894	74	51	maitland	maitland	PROPN
cana-3894	74	52	function	function	PROPN
cana-3894	74	53	,	,	PUNCT
cana-3894	74	54	dotsenko	dotsenko	ADJ
cana-3894	74	55	function	function	NOUN
cana-3894	74	56	,	,	PUNCT
cana-3894	74	57	bessel	bessel	ADJ
cana-3894	74	58	function	function	NOUN
cana-3894	74	59	,	,	PUNCT
cana-3894	74	60	generalized	generalized	ADJ
cana-3894	74	61	bessel	bessel	NOUN
cana-3894	74	62	maitland	maitland	PROPN
cana-3894	74	63	function	function	PROPN
cana-3894	74	64	,	,	PUNCT
cana-3894	74	65	lommel	lommel	PROPN
cana-3894	74	66	function	function	PROPN
cana-3894	74	67	etc	etc	X
cana-3894	74	68	.	.	X
cana-3894	74	69	especially	especially	ADV
cana-3894	74	70	by	by	ADP
cana-3894	74	71	means	mean	NOUN
cana-3894	74	72	of	of	ADP
cana-3894	74	73	parameters	parameter	NOUN
cana-3894	74	74	r	r	NOUN
cana-3894	74	75	,	,	PUNCT
cana-3894	74	76	γ	γ	X
cana-3894	74	77	,	,	PUNCT
cana-3894	74	78	λ	λ	PROPN
cana-3894	74	79	(	(	PUNCT
cana-3894	74	80	table-1	table-1	NUM
cana-3894	74	81	below	below	ADV
cana-3894	74	82	)	)	PUNCT
cana-3894	74	83	(	(	PUNCT
cana-3894	74	84	iii	iii	X
cana-3894	74	85	)	)	PUNCT
cana-3894	74	86	obtain	obtain	VERB
cana-3894	74	87	inverse	inverse	NOUN
cana-3894	74	88	inequality	inequality	NOUN
cana-3894	74	89	relations	relation	NOUN
cana-3894	74	90	and	and	CCONJ
cana-3894	74	91	some	some	DET
cana-3894	74	92	other	other	ADJ
cana-3894	74	93	inequalities	inequality	NOUN
cana-3894	74	94	by	by	ADP
cana-3894	74	95	means	mean	NOUN
cana-3894	74	96	of	of	ADP
cana-3894	74	97	the	the	DET
cana-3894	74	98	integer	integer	NOUN
cana-3894	74	99	′s′.	′s′.	X
cana-3894	75	1	the	the	DET
cana-3894	75	2	q	q	NOUN
cana-3894	75	3	-	-	PUNCT
cana-3894	75	4	analogues	analogue	NOUN
cana-3894	75	5	of	of	ADP
cana-3894	75	6	the	the	DET
cana-3894	75	7	above	above	ADV
cana-3894	75	8	stated	state	VERB
cana-3894	75	9	shukla	shukla	NOUN
cana-3894	75	10	and	and	CCONJ
cana-3894	75	11	prajapati	prajapati	PROPN
cana-3894	75	12	’s	’s	PART
cana-3894	75	13	function	function	NOUN
cana-3894	75	14	(	(	PUNCT
cana-3894	75	15	2.1	2.1	NUM
cana-3894	75	16	)	)	PUNCT
cana-3894	75	17	and	and	CCONJ
cana-3894	75	18	those	those	DET
cana-3894	75	19	functions	function	NOUN
cana-3894	75	20	listed	list	VERB
cana-3894	75	21	above	above	ADP
cana-3894	75	22	from	from	ADP
cana-3894	75	23	(	(	PUNCT
cana-3894	75	24	i	i	NOUN
cana-3894	75	25	)	)	PUNCT
cana-3894	75	26	through	through	ADP
cana-3894	75	27	(	(	PUNCT
cana-3894	75	28	iv	iv	X
cana-3894	75	29	)	)	PUNCT
cana-3894	75	30	are	be	AUX
cana-3894	75	31	all	all	PRON
cana-3894	75	32	yielded	yield	VERB
cana-3894	75	33	by	by	ADP
cana-3894	75	34	the	the	DET
cana-3894	75	35	q	q	NOUN
cana-3894	75	36	-	-	NOUN
cana-3894	75	37	gmlm	gmlm	NOUN
cana-3894	75	38	(	(	PUNCT
cana-3894	75	39	2.13	2.13	NUM
cana-3894	75	40	)	)	PUNCT
cana-3894	75	41	or	or	CCONJ
cana-3894	75	42	(	(	PUNCT
cana-3894	75	43	2.14	2.14	NUM
cana-3894	75	44	)	)	PUNCT
cana-3894	75	45	.	.	PUNCT
cana-3894	76	1	they	they	PRON
cana-3894	76	2	are	be	AUX
cana-3894	76	3	tabulated	tabulate	VERB
cana-3894	76	4	below	below	ADP
cana-3894	76	5	together	together	ADV
cana-3894	76	6	with	with	ADP
cana-3894	76	7	the	the	DET
cana-3894	76	8	indicated	indicate	VERB
cana-3894	76	9	substitutions	substitution	NOUN
cana-3894	76	10	.	.	PUNCT
cana-3894	77	1	table-1	table-1	DET
cana-3894	77	2	q	q	NOUN
cana-3894	77	3	-	-	PUNCT
cana-3894	77	4	function	function	NOUN
cana-3894	77	5	of	of	ADP
cana-3894	77	6	r	r	NOUN
cana-3894	77	7	s	s	PROPN
cana-3894	77	8	α	α	NOUN
cana-3894	77	9	b	b	PROPN
cana-3894	77	10	a	a	DET
cana-3894	77	11	δ	δ	PROPN
cana-3894	77	12	c	c	PROPN
cana-3894	77	13	µ	µ	X
cana-3894	77	14	particular	particular	ADJ
cana-3894	77	15	case	case	NOUN
cana-3894	77	16	of	of	ADP
cana-3894	77	17	mittag	mittag	ADJ
cana-3894	77	18	-	-	PUNCT
cana-3894	77	19	leffler	leffler	NOUN
cana-3894	77	20	0	0	NUM
cana-3894	77	21	1	1	NUM
cana-3894	77	22	α	α	NOUN
cana-3894	77	23	1	1	NUM
cana-3894	77	24	1	1	NUM
cana-3894	77	25	1	1	NUM
cana-3894	77	26	(	(	PUNCT
cana-3894	77	27	2.13	2.13	NUM
cana-3894	77	28	)	)	PUNCT
cana-3894	77	29	wiman	wiman	NOUN
cana-3894	77	30	0	0	NUM
cana-3894	77	31	1	1	NUM
cana-3894	77	32	α	α	NOUN
cana-3894	77	33	b	b	NOUN
cana-3894	77	34	1	1	NUM
cana-3894	77	35	1	1	NUM
cana-3894	77	36	(	(	PUNCT
cana-3894	77	37	2.13	2.13	NUM
cana-3894	77	38	)	)	PUNCT
cana-3894	77	39	prabhakar	prabhakar	NOUN
cana-3894	77	40	0	0	NUM
cana-3894	77	41	1	1	NUM
cana-3894	77	42	α	α	NOUN
cana-3894	77	43	b	b	NOUN
cana-3894	77	44	γi	γi	INTJ
cana-3894	77	45	1	1	NUM
cana-3894	77	46	(	(	PUNCT
cana-3894	77	47	2.13	2.13	NUM
cana-3894	77	48	)	)	PUNCT
cana-3894	77	49	shukla	shukla	NOUN
cana-3894	77	50	and	and	CCONJ
cana-3894	77	51	0	0	NUM
cana-3894	77	52	1	1	NUM
cana-3894	77	53	α	α	NOUN
cana-3894	77	54	b	b	NOUN
cana-3894	77	55	γi	γi	X
cana-3894	77	56	q	q	PROPN
cana-3894	78	1	(	(	PUNCT
cana-3894	78	2	2.13	2.13	NUM
cana-3894	78	3	)	)	PUNCT
cana-3894	78	4	prajapati	prajapati	PROPN
cana-3894	78	5	bessel	bessel	NOUN
cana-3894	78	6	-	-	PUNCT
cana-3894	78	7	maitland	maitland	PROPN
cana-3894	78	8	0	0	NUM
cana-3894	78	9	0	0	NUM
cana-3894	78	10	µ	µ	X
cana-3894	78	11	(	(	PUNCT
cana-3894	78	12	ν	ν	X
cana-3894	78	13	+	+	X
cana-3894	78	14	1)i	1)i	NUM
cana-3894	78	15	(	(	PUNCT
cana-3894	78	16	2.13	2.13	NUM
cana-3894	78	17	)	)	PUNCT
cana-3894	78	18	dotsenko	dotsenko	ADJ
cana-3894	78	19	-1	-1	ADP
cana-3894	78	20	1	1	NUM
cana-3894	78	21	ω	ω	NOUN
cana-3894	78	22	/	/	SYM
cana-3894	78	23	ν	ν	X
cana-3894	78	24	ci	ci	NOUN
cana-3894	78	25	a	a	PRON
cana-3894	78	26	i	i	PROPN
cana-3894	78	27	bi	bi	PROPN
cana-3894	78	28	ω	ω	PROPN
cana-3894	78	29	/	/	SYM
cana-3894	78	30	ν	ν	X
cana-3894	78	31	(	(	PUNCT
cana-3894	78	32	2.14	2.14	NUM
cana-3894	78	33	)	)	PUNCT
cana-3894	78	34	saxena1	saxena1	NOUN
cana-3894	78	35	1	1	NUM
cana-3894	78	36	α1	α1	PROPN
cana-3894	78	37	b1	b1	NOUN
cana-3894	78	38	γi	γi	X
cana-3894	78	39	k	k	PROPN
cana-3894	78	40	b2	b2	PROPN
cana-3894	78	41	α2	α2	PROPN
cana-3894	78	42	(	(	PUNCT
cana-3894	78	43	2.13	2.13	NUM
cana-3894	78	44	)	)	PUNCT
cana-3894	78	45	nishimoto	nishimoto	NOUN
cana-3894	78	46	elliptic	elliptic	ADJ
cana-3894	78	47	-1	-1	NOUN
cana-3894	78	48	1	1	NUM
cana-3894	78	49	1	1	NUM
cana-3894	78	50	i	i	NOUN
cana-3894	78	51	1	1	NUM
cana-3894	78	52	2	2	NUM
cana-3894	78	53	i	i	NOUN
cana-3894	78	54	1	1	NUM
cana-3894	78	55	1	1	NUM
cana-3894	78	56	2	2	NUM
cana-3894	78	57	i	i	NOUN
cana-3894	78	58	1	1	NUM
cana-3894	78	59	(	(	PUNCT
cana-3894	78	60	2.14	2.14	NUM
cana-3894	78	61	)	)	PUNCT
cana-3894	78	62	the	the	DET
cana-3894	78	63	explicit	explicit	ADJ
cana-3894	78	64	forms	form	NOUN
cana-3894	78	65	of	of	ADP
cana-3894	78	66	the	the	DET
cana-3894	78	67	functions	function	NOUN
cana-3894	78	68	mentioned	mention	VERB
cana-3894	78	69	in	in	ADP
cana-3894	78	70	this	this	DET
cana-3894	78	71	table	table	NOUN
cana-3894	78	72	are	be	AUX
cana-3894	78	73	as	as	SCONJ
cana-3894	78	74	stated	state	VERB
cana-3894	78	75	below	below	ADV
cana-3894	78	76	.	.	PUNCT
cana-3894	79	1	•	•	NUM
cana-3894	79	2	q	q	ADJ
cana-3894	79	3	-	-	PUNCT
cana-3894	79	4	mittag	mittag	ADJ
cana-3894	79	5	-	-	PUNCT
cana-3894	79	6	leffler	leffler	NOUN
cana-3894	79	7	function	function	NOUN
cana-3894	79	8	:	:	PUNCT
cana-3894	79	9	eαi(λz|q	eαi(λz|q	ADJ
cana-3894	79	10	)	)	PUNCT
cana-3894	79	11	=	=	PUNCT
cana-3894	80	1	∞∑	∞∑	NUM
cana-3894	80	2	n=0	n=0	PUNCT
cana-3894	80	3	[	[	PUNCT
cana-3894	80	4	(	(	PUNCT
cana-3894	80	5	−1)n	−1)n	PROPN
cana-3894	80	6	qn(n−1)/2	qn(n−1)/2	PROPN
cana-3894	80	7	]	]	PUNCT
cana-3894	80	8	α2i	α2i	X
cana-3894	80	9	(	(	PUNCT
cana-3894	80	10	qαni+i	qαni+i	INTJ
cana-3894	80	11	;	;	PUNCT
cana-3894	80	12	q)∞	q)∞	INTJ
cana-3894	80	13	(	(	PUNCT
cana-3894	80	14	λz)n	λz)n	PROPN
cana-3894	80	15	.	.	PUNCT
cana-3894	81	1	•	•	NUM
cana-3894	82	1	q	q	NOUN
cana-3894	82	2	-	-	PUNCT
cana-3894	82	3	analogue	analogue	NOUN
cana-3894	82	4	of	of	ADP
cana-3894	82	5	wiman	wiman	PROPN
cana-3894	82	6	’s	’s	PART
cana-3894	82	7	function	function	PROPN
cana-3894	82	8	:	:	PUNCT
cana-3894	82	9	eb	eb	PROPN
cana-3894	82	10	αi(λz|q	αi(λz|q	PROPN
cana-3894	82	11	)	)	PUNCT
cana-3894	83	1	=	=	PUNCT
cana-3894	84	1	∞∑	∞∑	NUM
cana-3894	84	2	n=0	n=0	PUNCT
cana-3894	84	3	[	[	PUNCT
cana-3894	84	4	(	(	PUNCT
cana-3894	84	5	−1)n	−1)n	PROPN
cana-3894	84	6	qn(n−1)/2	qn(n−1)/2	PROPN
cana-3894	84	7	]	]	SYM
cana-3894	84	8	α2i	α2i	X
cana-3894	84	9	(	(	PUNCT
cana-3894	84	10	qαni+b	qαni+b	X
cana-3894	84	11	;	;	PUNCT
cana-3894	84	12	q)∞	q)∞	INTJ
cana-3894	84	13	(	(	PUNCT
cana-3894	84	14	λz)n	λz)n	PROPN
cana-3894	84	15	.	.	PUNCT
cana-3894	85	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3894	85	2	333	333	NUM
cana-3894	85	3	communications	communication	NOUN
cana-3894	85	4	on	on	ADP
cana-3894	85	5	applied	apply	VERB
cana-3894	85	6	nonlinear	nonlinear	ADJ
cana-3894	85	7	analysis	analysis	NOUN
cana-3894	85	8	issn	issn	NOUN
cana-3894	85	9	:	:	PUNCT
cana-3894	85	10	1074	1074	NUM
cana-3894	85	11	-	-	PUNCT
cana-3894	85	12	133x	133x	NUM
cana-3894	85	13	vol	vol	NOUN
cana-3894	85	14	32	32	NUM
cana-3894	85	15	no	no	NOUN
cana-3894	85	16	.	.	PUNCT
cana-3894	86	1	9s(2025	9s(2025	NUM
cana-3894	86	2	)	)	PUNCT
cana-3894	86	3	•	•	PRON
cana-3894	86	4	q	q	NOUN
cana-3894	86	5	-	-	PUNCT
cana-3894	86	6	analogue	analogue	NOUN
cana-3894	86	7	of	of	ADP
cana-3894	86	8	prabhakar	prabhakar	PROPN
cana-3894	86	9	’s	’s	PART
cana-3894	86	10	generalized	generalize	VERB
cana-3894	86	11	ml	ml	NOUN
cana-3894	86	12	-	-	PUNCT
cana-3894	86	13	function	function	NOUN
cana-3894	86	14	:	:	PUNCT
cana-3894	86	15	ea	ea	NUM
cana-3894	86	16	,	,	PUNCT
cana-3894	86	17	b	b	NOUN
cana-3894	86	18	αi	αi	X
cana-3894	86	19	(	(	PUNCT
cana-3894	86	20	λz|q	λz|q	PROPN
cana-3894	86	21	)	)	PUNCT
cana-3894	86	22	=	=	PUNCT
cana-3894	87	1	∞∑	∞∑	NUM
cana-3894	87	2	n=0	n=0	PUNCT
cana-3894	87	3	[	[	PUNCT
cana-3894	87	4	(	(	PUNCT
cana-3894	87	5	−1)n	−1)n	PROPN
cana-3894	87	6	qn(n−1)/2	qn(n−1)/2	PROPN
cana-3894	87	7	]	]	SYM
cana-3894	87	8	α2i	α2i	X
cana-3894	87	9	(	(	PUNCT
cana-3894	87	10	qαni+b	qαni+b	X
cana-3894	87	11	;	;	PUNCT
cana-3894	87	12	q)∞	q)∞	PART
cana-3894	87	13	×	×	NOUN
cana-3894	87	14	[	[	PUNCT
cana-3894	87	15	(	(	PUNCT
cana-3894	87	16	qa+ni	qa+ni	ADJ
cana-3894	87	17	;	;	PUNCT
cana-3894	87	18	q)∞	q)∞	ADJ
cana-3894	87	19	]	]	X
cana-3894	87	20	−1	−1	NOUN
cana-3894	87	21	(	(	PUNCT
cana-3894	87	22	λz)n	λz)n	PROPN
cana-3894	87	23	(	(	PUNCT
cana-3894	87	24	q	q	NOUN
cana-3894	87	25	;	;	PUNCT
cana-3894	87	26	q)n	q)n	X
cana-3894	87	27	.	.	PUNCT
cana-3894	88	1	•	•	NUM
cana-3894	88	2	q	q	NOUN
cana-3894	88	3	-	-	PUNCT
cana-3894	88	4	ml	ml	NOUN
cana-3894	88	5	-	-	PUNCT
cana-3894	88	6	function	function	NOUN
cana-3894	88	7	of	of	ADP
cana-3894	88	8	shukla	shukla	NOUN
cana-3894	88	9	and	and	CCONJ
cana-3894	88	10	prajapati	prajapati	PROPN
cana-3894	88	11	(	(	PUNCT
cana-3894	88	12	q	q	NOUN
cana-3894	88	13	is	be	AUX
cana-3894	88	14	replaced	replace	VERB
cana-3894	88	15	by	by	ADP
cana-3894	88	16	δ	δ	PROPN
cana-3894	88	17	):	):	PUNCT
cana-3894	88	18	ea	ea	PROPN
cana-3894	88	19	,	,	PUNCT
cana-3894	88	20	b	b	PROPN
cana-3894	88	21	αi	αi	NOUN
cana-3894	88	22	,	,	PUNCT
cana-3894	88	23	δi(λz|q	δi(λz|q	NUM
cana-3894	88	24	)	)	PUNCT
cana-3894	88	25	=	=	NOUN
cana-3894	89	1	∞∑	∞∑	NUM
cana-3894	89	2	n=0	n=0	PUNCT
cana-3894	89	3	[	[	PUNCT
cana-3894	89	4	(	(	PUNCT
cana-3894	89	5	−1)n	−1)n	PROPN
cana-3894	89	6	qn(n−1)/2	qn(n−1)/2	PROPN
cana-3894	89	7	]	]	PUNCT
cana-3894	89	8	(	(	PUNCT
cana-3894	89	9	α2−	α2−	NOUN
cana-3894	89	10	δ2	δ2	VERB
cana-3894	89	11	+	+	NOUN
cana-3894	89	12	1)i	1)i	NOUN
cana-3894	89	13	(	(	PUNCT
cana-3894	89	14	qαni+b	qαni+b	X
cana-3894	89	15	;	;	PUNCT
cana-3894	89	16	q)∞.	q)∞.	VERB
cana-3894	89	17	×(qa+δni	×(qa+δni	PROPN
cana-3894	89	18	;	;	PUNCT
cana-3894	89	19	q)∞	q)∞	ADJ
cana-3894	89	20	−1	−1	NOUN
cana-3894	89	21	(	(	PUNCT
cana-3894	89	22	λz)n	λz)n	PROPN
cana-3894	89	23	(	(	PUNCT
cana-3894	89	24	q	q	NOUN
cana-3894	89	25	;	;	PUNCT
cana-3894	89	26	q)n	q)n	SYM
cana-3894	89	27	•	•	ADP
cana-3894	89	28	q	q	ADJ
cana-3894	89	29	-	-	PUNCT
cana-3894	89	30	bessel	bessel	NOUN
cana-3894	89	31	-	-	PUNCT
cana-3894	89	32	maitland	maitland	NOUN
cana-3894	89	33	function	function	NOUN
cana-3894	89	34	:	:	PUNCT
cana-3894	89	35	jµ	jµ	PROPN
cana-3894	89	36	νii(−z	νii(−z	PROPN
cana-3894	89	37	;	;	PUNCT
cana-3894	89	38	q	q	X
cana-3894	89	39	)	)	PUNCT
cana-3894	89	40	=	=	SYM
cana-3894	90	1	∞∑	∞∑	NUM
cana-3894	90	2	n=0	n=0	PUNCT
cana-3894	90	3	[	[	PUNCT
cana-3894	90	4	(	(	PUNCT
cana-3894	90	5	−1)n	−1)n	PROPN
cana-3894	90	6	qn(n−1)/2	qn(n−1)/2	PROPN
cana-3894	90	7	]	]	PUNCT
cana-3894	90	8	(	(	PUNCT
cana-3894	90	9	µ2	µ2	PROPN
cana-3894	90	10	+	+	PROPN
cana-3894	90	11	1)i	1)i	NUM
cana-3894	90	12	(	(	PUNCT
cana-3894	90	13	qµni+νi+i	qµni+νi+i	PROPN
cana-3894	90	14	;	;	PUNCT
cana-3894	90	15	q)∞	q)∞	INTJ
cana-3894	90	16	(	(	PUNCT
cana-3894	90	17	q	q	ADJ
cana-3894	90	18	;	;	PUNCT
cana-3894	90	19	q)n	q)n	X
cana-3894	90	20	zn	zn	X
cana-3894	90	21	.	.	PROPN
cana-3894	90	22	•	•	NUM
cana-3894	90	23	q	q	ADJ
cana-3894	90	24	-	-	ADJ
cana-3894	90	25	dotsenko	dotsenko	ADJ
cana-3894	90	26	function	function	NOUN
cana-3894	90	27	:	:	PUNCT
cana-3894	90	28	2r1(ai	2r1(ai	NUM
cana-3894	90	29	,	,	PUNCT
cana-3894	90	30	bi	bi	NOUN
cana-3894	90	31	;	;	PUNCT
cana-3894	90	32	ci	ci	PROPN
cana-3894	90	33	,	,	PUNCT
cana-3894	90	34	ω	ω	PROPN
cana-3894	90	35	;	;	PUNCT
cana-3894	90	36	ν	ν	NOUN
cana-3894	90	37	;	;	PUNCT
cana-3894	90	38	z	z	NOUN
cana-3894	90	39	;	;	PUNCT
cana-3894	90	40	q	q	X
cana-3894	90	41	)	)	PUNCT
cana-3894	90	42	=	=	SYM
cana-3894	91	1	∞∑	∞∑	NUM
cana-3894	91	2	n=0	n=0	NUM
cana-3894	91	3	(	(	PUNCT
cana-3894	91	4	qci+	qci+	PROPN
cana-3894	91	5	ω	ω	PROPN
cana-3894	91	6	ν	ν	PROPN
cana-3894	91	7	ni	ni	PROPN
cana-3894	91	8	;	;	PUNCT
cana-3894	91	9	q)∞	q)∞	PROPN
cana-3894	91	10	[	[	PUNCT
cana-3894	91	11	(	(	PUNCT
cana-3894	91	12	qbi+	qbi+	PROPN
cana-3894	91	13	ω	ω	PROPN
cana-3894	91	14	ν	ν	X
cana-3894	91	15	ni	ni	PROPN
cana-3894	91	16	;	;	PUNCT
cana-3894	91	17	q)∞	q)∞	ADJ
cana-3894	91	18	]	]	X
cana-3894	91	19	−1	−1	NOUN
cana-3894	91	20	×	×	NOUN
cana-3894	91	21	[	[	PUNCT
cana-3894	91	22	(	(	PUNCT
cana-3894	91	23	qni+ai	qni+ai	PROPN
cana-3894	91	24	;	;	PUNCT
cana-3894	91	25	q)∞	q)∞	ADJ
cana-3894	91	26	]	]	X
cana-3894	91	27	−1	−1	NOUN
cana-3894	91	28	zn	zn	X
cana-3894	91	29	(	(	PUNCT
cana-3894	91	30	q	q	NOUN
cana-3894	91	31	;	;	PUNCT
cana-3894	91	32	q)n	q)n	X
cana-3894	91	33	.	.	PUNCT
cana-3894	92	1	•	•	NUM
cana-3894	92	2	q	q	NOUN
cana-3894	92	3	-	-	PUNCT
cana-3894	92	4	form	form	NOUN
cana-3894	92	5	of	of	ADP
cana-3894	92	6	the	the	DET
cana-3894	92	7	particular	particular	ADJ
cana-3894	92	8	case	case	NOUN
cana-3894	92	9	m	m	VERB
cana-3894	92	10	=	=	SYM
cana-3894	92	11	2	2	NUM
cana-3894	92	12	of	of	ADP
cana-3894	92	13	the	the	DET
cana-3894	92	14	function	function	NOUN
cana-3894	92	15	due	due	ADP
cana-3894	92	16	to	to	ADP
cana-3894	92	17	saxena	saxena	PROPN
cana-3894	92	18	and	and	CCONJ
cana-3894	92	19	nishimoto	nishimoto	PROPN
cana-3894	92	20	eγi	eγi	PROPN
cana-3894	92	21	,	,	PUNCT
cana-3894	92	22	k	k	PROPN
cana-3894	93	1	[	[	X
cana-3894	93	2	(	(	PUNCT
cana-3894	93	3	αji	αji	NOUN
cana-3894	93	4	,	,	PUNCT
cana-3894	93	5	bj)1,2	bj)1,2	ADJ
cana-3894	93	6	;	;	PUNCT
cana-3894	93	7	z|q	z|q	X
cana-3894	93	8	]	]	X
cana-3894	93	9	=	=	PUNCT
cana-3894	94	1	∞∑	∞∑	NUM
cana-3894	94	2	n=0	n=0	PUNCT
cana-3894	94	3	[	[	PUNCT
cana-3894	94	4	(	(	PUNCT
cana-3894	94	5	−1)n	−1)n	PROPN
cana-3894	94	6	qn(n−1)/2	qn(n−1)/2	PROPN
cana-3894	94	7	]	]	PUNCT
cana-3894	94	8	(	(	PUNCT
cana-3894	94	9	α2	α2	ADJ
cana-3894	94	10	1+α2	1+α2	NUM
cana-3894	94	11	2−k2	2−k2	NUM
cana-3894	94	12	+	+	SYM
cana-3894	94	13	1)i	1)i	NOUN
cana-3894	94	14	×(qα1ni+b1	×(qα1ni+b1	ADJ
cana-3894	94	15	;	;	PUNCT
cana-3894	94	16	q)∞	q)∞	INTJ
cana-3894	94	17	(	(	PUNCT
cana-3894	94	18	qα2ni+b2	qα2ni+b2	PROPN
cana-3894	94	19	;	;	PUNCT
cana-3894	94	20	q)∞	q)∞	ADJ
cana-3894	94	21	×	×	NOUN
cana-3894	94	22	[	[	PUNCT
cana-3894	94	23	(	(	PUNCT
cana-3894	94	24	qγi+kn	qγi+kn	NOUN
cana-3894	94	25	;	;	PUNCT
cana-3894	94	26	q)∞	q)∞	ADJ
cana-3894	94	27	]	]	X
cana-3894	94	28	−1	−1	NOUN
cana-3894	94	29	zn	zn	X
cana-3894	94	30	(	(	PUNCT
cana-3894	94	31	q	q	NOUN
cana-3894	94	32	;	;	PUNCT
cana-3894	94	33	q)n	q)n	X
cana-3894	94	34	.	.	PUNCT
cana-3894	95	1	•	•	NUM
cana-3894	95	2	q	q	ADJ
cana-3894	95	3	-	-	ADJ
cana-3894	95	4	elliptic	elliptic	ADJ
cana-3894	95	5	function	function	NOUN
cana-3894	95	6	:	:	PUNCT
cana-3894	95	7	k	k	X
cana-3894	95	8	(	(	PUNCT
cana-3894	95	9	√	√	NUM
cana-3894	95	10	z|q	z|q	NUM
cana-3894	95	11	)	)	PUNCT
cana-3894	95	12	=	=	PUNCT
cana-3894	96	1	π	π	NOUN
cana-3894	96	2	2	2	NUM
cana-3894	96	3	2ϕ1	2ϕ1	NUM
cana-3894	96	4	(	(	PUNCT
cana-3894	96	5	1	1	NUM
cana-3894	96	6	2	2	NUM
cana-3894	96	7	i	i	NOUN
cana-3894	96	8	,	,	PUNCT
cana-3894	96	9	1	1	NUM
cana-3894	96	10	2	2	NUM
cana-3894	96	11	i	i	NOUN
cana-3894	96	12	;	;	PUNCT
cana-3894	96	13	z	z	PROPN
cana-3894	96	14	i	i	NOUN
cana-3894	96	15	;	;	PUNCT
cana-3894	96	16	)	)	PUNCT
cana-3894	96	17	.	.	PUNCT
cana-3894	97	1	we	we	PRON
cana-3894	97	2	first	first	ADV
cana-3894	97	3	show	show	VERB
cana-3894	97	4	the	the	DET
cana-3894	97	5	convergence	convergence	NOUN
cana-3894	97	6	of	of	ADP
cana-3894	97	7	series	series	NOUN
cana-3894	97	8	in	in	ADP
cana-3894	97	9	(	(	PUNCT
cana-3894	97	10	2.13	2.13	NUM
cana-3894	97	11	)	)	PUNCT
cana-3894	97	12	and	and	CCONJ
cana-3894	97	13	(	(	PUNCT
cana-3894	97	14	2.14	2.14	NUM
cana-3894	97	15	)	)	PUNCT
cana-3894	97	16	;	;	PUNCT
cana-3894	97	17	this	this	PRON
cana-3894	97	18	is	be	AUX
cana-3894	97	19	followed	follow	VERB
cana-3894	97	20	by	by	ADP
cana-3894	97	21	mellinbarnes	mellinbarne	NOUN
cana-3894	97	22	integral	integral	ADJ
cana-3894	97	23	representation	representation	NOUN
cana-3894	97	24	,	,	PUNCT
cana-3894	97	25	q	q	ADJ
cana-3894	97	26	-	-	PUNCT
cana-3894	97	27	difference	difference	NOUN
cana-3894	97	28	equation	equation	NOUN
cana-3894	97	29	and	and	CCONJ
cana-3894	97	30	eigen	eigen	PROPN
cana-3894	97	31	function	function	NOUN
cana-3894	97	32	property	property	NOUN
cana-3894	97	33	.	.	PUNCT
cana-3894	98	1	3	3	X
cana-3894	98	2	.	.	X
cana-3894	98	3	main	main	ADJ
cana-3894	98	4	results	result	NOUN
cana-3894	98	5	in	in	ADP
cana-3894	98	6	this	this	DET
cana-3894	98	7	section	section	NOUN
cana-3894	98	8	,	,	PUNCT
cana-3894	98	9	we	we	PRON
cana-3894	98	10	prove	prove	VERB
cana-3894	98	11	the	the	DET
cana-3894	98	12	following	follow	VERB
cana-3894	98	13	results	result	NOUN
cana-3894	98	14	.	.	PUNCT
cana-3894	99	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3894	99	2	334	334	NUM
cana-3894	99	3	communications	communication	NOUN
cana-3894	99	4	on	on	ADP
cana-3894	99	5	applied	apply	VERB
cana-3894	99	6	nonlinear	nonlinear	ADJ
cana-3894	99	7	analysis	analysis	NOUN
cana-3894	99	8	issn	issn	NOUN
cana-3894	99	9	:	:	PUNCT
cana-3894	99	10	1074	1074	NUM
cana-3894	99	11	-	-	PUNCT
cana-3894	99	12	133x	133x	NUM
cana-3894	99	13	vol	vol	NOUN
cana-3894	99	14	32	32	NUM
cana-3894	99	15	no	no	NOUN
cana-3894	99	16	.	.	PUNCT
cana-3894	100	1	9s(2025	9s(2025	NUM
cana-3894	100	2	)	)	PUNCT
cana-3894	100	3	3.1	3.1	NUM
cana-3894	100	4	convergence	convergence	NOUN
cana-3894	100	5	theorem	theorem	VERB
cana-3894	100	6	3.1	3.1	NUM
cana-3894	100	7	.	.	PUNCT
cana-3894	101	1	let	let	VERB
cana-3894	101	2	a	a	DET
cana-3894	101	3	,	,	PUNCT
cana-3894	101	4	b	b	NOUN
cana-3894	101	5	,	,	PUNCT
cana-3894	101	6	c	c	AUX
cana-3894	101	7	be	be	AUX
cana-3894	101	8	positive	positive	ADJ
cana-3894	101	9	stable	stable	ADJ
cana-3894	101	10	matrices	matrix	NOUN
cana-3894	101	11	in	in	ADP
cana-3894	101	12	cp×p	cp×p	PROPN
cana-3894	101	13	,	,	PUNCT
cana-3894	101	14	α	α	PROPN
cana-3894	101	15	,	,	PUNCT
cana-3894	101	16	δ	δ	PROPN
cana-3894	101	17	,	,	PUNCT
cana-3894	101	18	µ	µ	X
cana-3894	101	19	∈	∈	PROPN
cana-3894	101	20	c	c	NOUN
cana-3894	101	21	with	with	ADP
cana-3894	101	22	ℜ(α	ℜ(α	NOUN
cana-3894	101	23	)	)	PUNCT
cana-3894	101	24	>	>	X
cana-3894	101	25	0	0	NUM
cana-3894	101	26	,	,	PUNCT
cana-3894	101	27	ℜ(α2	ℜ(α2	PROPN
cana-3894	101	28	)	)	PUNCT
cana-3894	102	1	+	+	NUM
cana-3894	102	2	rµ2	rµ2	NOUN
cana-3894	102	3	−	−	PROPN
cana-3894	102	4	sδ2	sδ2	NOUN
cana-3894	102	5	+	+	CCONJ
cana-3894	102	6	1	1	NUM
cana-3894	102	7	>	>	SYM
cana-3894	102	8	0	0	NUM
cana-3894	102	9	,	,	PUNCT
cana-3894	102	10	δ	δ	PROPN
cana-3894	102	11	,	,	PUNCT
cana-3894	102	12	µ	µ	X
cana-3894	102	13	>	>	X
cana-3894	102	14	0	0	NUM
cana-3894	102	15	,	,	PUNCT
cana-3894	102	16	r	r	NOUN
cana-3894	102	17	∈	∈	PROPN
cana-3894	102	18	{	{	PUNCT
cana-3894	102	19	−1	−1	NOUN
cana-3894	102	20	,	,	PUNCT
cana-3894	102	21	0	0	NUM
cana-3894	102	22	}	}	PUNCT
cana-3894	102	23	∪	∪	NOUN
cana-3894	102	24	n	n	CCONJ
cana-3894	102	25	,	,	PUNCT
cana-3894	102	26	s	s	VERB
cana-3894	102	27	∈	∈	PROPN
cana-3894	102	28	n	n	NOUN
cana-3894	102	29	∪	∪	X
cana-3894	102	30	{	{	PUNCT
cana-3894	102	31	0	0	NUM
cana-3894	102	32	}	}	PUNCT
cana-3894	102	33	and	and	CCONJ
cana-3894	102	34	0	0	NUM
cana-3894	102	35	<	<	X
cana-3894	102	36	q	q	X
cana-3894	102	37	<	<	X
cana-3894	102	38	1	1	NUM
cana-3894	102	39	.	.	PUNCT
cana-3894	102	40	then	then	ADV
cana-3894	102	41	ea	ea	NUM
cana-3894	102	42	,	,	PUNCT
cana-3894	102	43	b	b	PROPN
cana-3894	102	44	,	,	PUNCT
cana-3894	102	45	c	c	PROPN
cana-3894	102	46	αi	αi	PROPN
cana-3894	102	47	,	,	PUNCT
cana-3894	102	48	δi	δi	ADV
cana-3894	102	49	,	,	PUNCT
cana-3894	102	50	µi(λz	µi(λz	PROPN
cana-3894	102	51	;	;	PUNCT
cana-3894	102	52	s	s	X
cana-3894	102	53	,	,	PUNCT
cana-3894	102	54	r|q	r|q	ADJ
cana-3894	102	55	)	)	PUNCT
cana-3894	102	56	is	be	AUX
cana-3894	102	57	an	an	DET
cana-3894	102	58	entire	entire	ADJ
cana-3894	102	59	function	function	NOUN
cana-3894	102	60	of	of	ADP
cana-3894	102	61	order	order	NOUN
cana-3894	102	62	zero	zero	NUM
cana-3894	102	63	.	.	PUNCT
cana-3894	103	1	proof	proof	NOUN
cana-3894	103	2	.	.	PUNCT
cana-3894	104	1	put	put	VERB
cana-3894	104	2	vn	vn	NOUN
cana-3894	104	3	=	=	SYM
cana-3894	104	4	(	(	PUNCT
cana-3894	104	5	−1)pni	−1)pni	PROPN
cana-3894	104	6	qpn(n−1)i/2	qpn(n−1)i/2	PROPN
cana-3894	105	1	[	[	X
cana-3894	105	2	γq(δni	γq(δni	X
cana-3894	105	3	+	+	NOUN
cana-3894	105	4	a)]s	a)]s	ADJ
cana-3894	105	5	γq	γq	ADP
cana-3894	105	6	−1(αni	−1(αni	PROPN
cana-3894	105	7	+	+	PROPN
cana-3894	105	8	b)[γq	b)[γq	X
cana-3894	105	9	−1(µni	−1(µni	PROPN
cana-3894	105	10	+	+	NUM
cana-3894	105	11	c)]r	c)]r	NOUN
cana-3894	105	12	×	×	NOUN
cana-3894	105	13	1	1	NUM
cana-3894	105	14	(	(	PUNCT
cana-3894	105	15	q	q	NOUN
cana-3894	105	16	;	;	PUNCT
cana-3894	105	17	q)n	q)n	X
cana-3894	105	18	(	(	PUNCT
cana-3894	105	19	3.1	3.1	NUM
cana-3894	105	20	)	)	PUNCT
cana-3894	105	21	to	to	PART
cana-3894	105	22	get	get	VERB
cana-3894	105	23	ea	ea	ADP
cana-3894	105	24	,	,	PUNCT
cana-3894	105	25	b	b	PROPN
cana-3894	105	26	,	,	PUNCT
cana-3894	105	27	c	c	PROPN
cana-3894	105	28	αi	αi	PROPN
cana-3894	105	29	,	,	PUNCT
cana-3894	105	30	δi	δi	ADV
cana-3894	105	31	,	,	PUNCT
cana-3894	105	32	µi(λz	µi(λz	PROPN
cana-3894	105	33	;	;	PUNCT
cana-3894	105	34	s	s	X
cana-3894	105	35	,	,	PUNCT
cana-3894	105	36	r|q	r|q	ADJ
cana-3894	105	37	)	)	PUNCT
cana-3894	105	38	=	=	PUNCT
cana-3894	106	1	∞∑	∞∑	NUM
cana-3894	106	2	n=0	n=0	NUM
cana-3894	106	3	vn	vn	NOUN
cana-3894	106	4	(	(	PUNCT
cana-3894	106	5	λz)n	λz)n	PROPN
cana-3894	106	6	.	.	PUNCT
cana-3894	107	1	then	then	ADV
cana-3894	107	2	in	in	ADP
cana-3894	107	3	view	view	NOUN
cana-3894	107	4	of	of	ADP
cana-3894	107	5	(	(	PUNCT
cana-3894	107	6	2.4	2.4	NUM
cana-3894	107	7	)	)	PUNCT
cana-3894	107	8	and	and	CCONJ
cana-3894	107	9	applying	apply	VERB
cana-3894	107	10	norm	norm	NOUN
cana-3894	107	11	,	,	PUNCT
cana-3894	107	12	we	we	PRON
cana-3894	107	13	get	get	VERB
cana-3894	107	14	after	after	ADP
cana-3894	107	15	some	some	DET
cana-3894	107	16	simplification	simplification	NOUN
cana-3894	107	17	,	,	PUNCT
cana-3894	107	18	n	n	CCONJ
cana-3894	107	19	√	√	PROPN
cana-3894	107	20	∥vn∥	∥vn∥	NOUN
cana-3894	107	21	∼	∼	NOUN
cana-3894	107	22	∥∥∥∥∥(−1)pi	∥∥∥∥∥(−1)pi	NOUN
cana-3894	107	23	qp(n−1)i/2	qp(n−1)i/2	NOUN
cana-3894	107	24	×(1−	×(1−	PROPN
cana-3894	107	25	q)s(i−a)−r(i−c)−(i−b)/n	q)s(i−a)−r(i−c)−(i−b)/n	PROPN
cana-3894	107	26	(	(	PUNCT
cana-3894	107	27	1−	1−	NUM
cana-3894	107	28	q)(−sδ+rµ+α)i	q)(−sδ+rµ+α)i	ADJ
cana-3894	107	29	×	×	NOUN
cana-3894	107	30	[	[	PUNCT
cana-3894	107	31	∞∏	∞∏	X
cana-3894	107	32	h=0	h=0	PROPN
cana-3894	107	33	(	(	PUNCT
cana-3894	107	34	i	i	PRON
cana-3894	107	35	−	−	PROPN
cana-3894	107	36	qδni+a+hi	qδni+a+hi	NOUN
cana-3894	107	37	)	)	PUNCT
cana-3894	107	38	]	]	X
cana-3894	107	39	s	s	X
cana-3894	107	40	[	[	PUNCT
cana-3894	107	41	∞∏	∞∏	X
cana-3894	107	42	m=0	m=0	PROPN
cana-3894	107	43	(	(	PUNCT
cana-3894	107	44	i	i	NOUN
cana-3894	107	45	−	−	PROPN
cana-3894	107	46	qαni+b+mi	qαni+b+mi	NOUN
cana-3894	107	47	)	)	PUNCT
cana-3894	107	48	]	]	PUNCT
cana-3894	108	1	×	×	PROPN
cana-3894	108	2	[	[	PUNCT
cana-3894	108	3	∞∏	∞∏	X
cana-3894	108	4	j=0	j=0	PROPN
cana-3894	108	5	(	(	PUNCT
cana-3894	108	6	i	i	PRON
cana-3894	108	7	−	−	PROPN
cana-3894	108	8	qµni+c+ji	qµni+c+ji	NOUN
cana-3894	108	9	)	)	PUNCT
cana-3894	108	10	]	]	PUNCT
cana-3894	108	11	−r	−r	ADJ
cana-3894	108	12	1	1	NUM
cana-3894	108	13	(	(	PUNCT
cana-3894	108	14	q	q	NOUN
cana-3894	108	15	;	;	PUNCT
cana-3894	108	16	q)n	q)n	X
cana-3894	108	17	∥∥∥∥∥	∥∥∥∥∥	PUNCT
cana-3894	108	18	now	now	ADV
cana-3894	108	19	by	by	ADP
cana-3894	108	20	applying	apply	VERB
cana-3894	108	21	limn	limn	NOUN
cana-3894	108	22	→	→	SYM
cana-3894	108	23	∞	∞	PROPN
cana-3894	108	24	,	,	PUNCT
cana-3894	108	25	we	we	PRON
cana-3894	108	26	get	get	VERB
cana-3894	108	27	1	1	NUM
cana-3894	108	28	r	r	NOUN
cana-3894	108	29	=	=	SYM
cana-3894	108	30	lim	lim	PROPN
cana-3894	108	31	n→∞	n→∞	NUM
cana-3894	108	32	n	n	CCONJ
cana-3894	108	33	√	√	PROPN
cana-3894	108	34	∥vn∥	∥vn∥	NOUN
cana-3894	108	35	∼	∼	NOUN
cana-3894	108	36	0	0	PUNCT
cana-3894	108	37	when	when	SCONJ
cana-3894	108	38	|q|	|q|	VERB
cana-3894	108	39	<	<	X
cana-3894	108	40	1	1	NUM
cana-3894	108	41	,	,	PUNCT
cana-3894	108	42	ℜ(α2	ℜ(α2	PROPN
cana-3894	108	43	)	)	PUNCT
cana-3894	108	44	+	+	NUM
cana-3894	108	45	rµ2	rµ2	NOUN
cana-3894	108	46	−	−	PROPN
cana-3894	108	47	sδ2	sδ2	NOUN
cana-3894	108	48	+	+	CCONJ
cana-3894	108	49	1	1	NUM
cana-3894	108	50	>	>	SYM
cana-3894	108	51	0	0	NUM
cana-3894	108	52	.	.	PUNCT
cana-3894	109	1	thus	thus	ADV
cana-3894	109	2	,	,	PUNCT
cana-3894	109	3	the	the	DET
cana-3894	109	4	function	function	NOUN
cana-3894	109	5	(	(	PUNCT
cana-3894	109	6	2.13	2.13	NUM
cana-3894	109	7	)	)	PUNCT
cana-3894	109	8	is	be	AUX
cana-3894	109	9	an	an	DET
cana-3894	109	10	entire	entire	ADJ
cana-3894	109	11	function	function	NOUN
cana-3894	109	12	.	.	PUNCT
cana-3894	110	1	its	its	PRON
cana-3894	110	2	order	order	NOUN
cana-3894	110	3	may	may	AUX
cana-3894	110	4	be	be	AUX
cana-3894	110	5	determined	determine	VERB
cana-3894	110	6	by	by	ADP
cana-3894	110	7	using	use	VERB
cana-3894	110	8	theorem	theorem	NOUN
cana-3894	110	9	2.1	2.1	NUM
cana-3894	110	10	.	.	PUNCT
cana-3894	111	1	in	in	ADP
cana-3894	111	2	fact	fact	NOUN
cana-3894	111	3	,	,	PUNCT
cana-3894	111	4	by	by	ADP
cana-3894	111	5	choosing	choose	VERB
cana-3894	111	6	f(z	f(z	NOUN
cana-3894	111	7	)	)	PUNCT
cana-3894	111	8	=	=	SYM
cana-3894	111	9	ea	ea	PROPN
cana-3894	111	10	,	,	PUNCT
cana-3894	111	11	b	b	PROPN
cana-3894	111	12	,	,	PUNCT
cana-3894	111	13	c	c	PROPN
cana-3894	111	14	αi	αi	PROPN
cana-3894	111	15	,	,	PUNCT
cana-3894	111	16	δi	δi	ADV
cana-3894	111	17	,	,	PUNCT
cana-3894	111	18	µi(λz	µi(λz	PROPN
cana-3894	111	19	;	;	PUNCT
cana-3894	111	20	s	s	X
cana-3894	111	21	,	,	PUNCT
cana-3894	111	22	r|q	r|q	ADJ
cana-3894	111	23	)	)	PUNCT
cana-3894	111	24	and	and	CCONJ
cana-3894	111	25	un	un	PROPN
cana-3894	111	26	=	=	PROPN
cana-3894	111	27	vn	vn	PROPN
cana-3894	111	28	,	,	PUNCT
cana-3894	111	29	theorem	theorem	VERB
cana-3894	111	30	2.1	2.1	NUM
cana-3894	111	31	gets	get	AUX
cana-3894	111	32	particularized	particularize	VERB
cana-3894	111	33	to	to	ADP
cana-3894	111	34	ϱ(ea	ϱ(ea	PROPN
cana-3894	111	35	,	,	PUNCT
cana-3894	111	36	b	b	NOUN
cana-3894	111	37	,	,	PUNCT
cana-3894	111	38	c	c	PROPN
cana-3894	111	39	αi	αi	PROPN
cana-3894	111	40	,	,	PUNCT
cana-3894	111	41	δi	δi	ADV
cana-3894	111	42	,	,	PUNCT
cana-3894	111	43	µi(λz	µi(λz	PROPN
cana-3894	111	44	;	;	PUNCT
cana-3894	111	45	s	s	X
cana-3894	111	46	,	,	PUNCT
cana-3894	111	47	r|q	r|q	ADJ
cana-3894	111	48	)	)	PUNCT
cana-3894	111	49	)	)	PUNCT
cana-3894	112	1	=	=	SYM
cana-3894	112	2	lim	lim	PROPN
cana-3894	112	3	n→∞	n→∞	NUM
cana-3894	112	4	sup	sup	NOUN
cana-3894	112	5	n	n	NOUN
cana-3894	112	6	log	log	NOUN
cana-3894	112	7	n	n	PRON
cana-3894	112	8	log(∥vn∥−1	log(∥vn∥−1	PROPN
cana-3894	112	9	)	)	PUNCT
cana-3894	112	10	,	,	PUNCT
cana-3894	112	11	where	where	SCONJ
cana-3894	112	12	log	log	NOUN
cana-3894	112	13	(	(	PUNCT
cana-3894	112	14	∥vn∥−1	∥vn∥−1	PROPN
cana-3894	112	15	)	)	PUNCT
cana-3894	112	16	=	=	VERB
cana-3894	112	17	log	log	NOUN
cana-3894	112	18	(	(	PUNCT
cana-3894	112	19	∥∥∥∥∥γq(αni	∥∥∥∥∥γq(αni	PROPN
cana-3894	112	20	+	+	NOUN
cana-3894	112	21	b	b	NOUN
cana-3894	112	22	)	)	PUNCT
cana-3894	113	1	[	[	X
cana-3894	113	2	γq(µni	γq(µni	NOUN
cana-3894	113	3	+	+	NUM
cana-3894	113	4	c)]r	c)]r	NOUN
cana-3894	113	5	γq(n+	γq(n+	NOUN
cana-3894	113	6	1	1	NUM
cana-3894	113	7	)	)	PUNCT
cana-3894	113	8	×q−n(n−1)(α2+rµ2−sδ2	×q−n(n−1)(α2+rµ2−sδ2	NOUN
cana-3894	113	9	+	+	PROPN
cana-3894	113	10	1)i/2	1)i/2	NUM
cana-3894	113	11	[	[	X
cana-3894	113	12	γq(δni	γq(δni	PROPN
cana-3894	113	13	+	+	NUM
cana-3894	113	14	a)]−s	a)]−s	PROPN
cana-3894	113	15	∥∥∥∥∥	∥∥∥∥∥	NUM
cana-3894	113	16	)	)	PUNCT
cana-3894	114	1	=	=	SYM
cana-3894	114	2	log	log	VERB
cana-3894	114	3	∥γq(αni	∥γq(αni	NOUN
cana-3894	114	4	+	+	NOUN
cana-3894	114	5	b)∥+	b)∥+	ADJ
cana-3894	114	6	r	r	NOUN
cana-3894	114	7	log	log	NOUN
cana-3894	114	8	∥γq(µni	∥γq(µni	ADV
cana-3894	114	9	+	+	CCONJ
cana-3894	114	10	c)∥	c)∥	X
cana-3894	115	1	+	+	CCONJ
cana-3894	115	2	log	log	VERB
cana-3894	115	3	|γq(n+	|γq(n+	NOUN
cana-3894	115	4	1)|	1)|	NUM
cana-3894	115	5	−	−	NOUN
cana-3894	115	6	1	1	NUM
cana-3894	115	7	2	2	NUM
cana-3894	115	8	n(n−	n(n−	NOUN
cana-3894	115	9	1	1	NUM
cana-3894	115	10	)	)	PUNCT
cana-3894	115	11	[	[	PUNCT
cana-3894	115	12	ℜ(α2	ℜ(α2	PROPN
cana-3894	116	1	+	+	CCONJ
cana-3894	116	2	rµ2	rµ2	NOUN
cana-3894	116	3	−	−	PROPN
cana-3894	116	4	sδ2	sδ2	PROPN
cana-3894	116	5	+	+	CCONJ
cana-3894	116	6	1)∥i∥	1)∥i∥	X
cana-3894	116	7	]	]	PUNCT
cana-3894	116	8	log	log	VERB
cana-3894	116	9	q	q	PROPN
cana-3894	116	10	−s	−s	NOUN
cana-3894	116	11	log	log	NOUN
cana-3894	116	12	∥γq(δni	∥γq(δni	PROPN
cana-3894	116	13	+	+	CCONJ
cana-3894	116	14	a)∥.	a)∥.	ADJ
cana-3894	116	15	(	(	PUNCT
cana-3894	116	16	3.2	3.2	NUM
cana-3894	116	17	)	)	PUNCT
cana-3894	116	18	https://internationalpubls.com	https://internationalpubls.com	X
cana-3894	116	19	335	335	NUM
cana-3894	116	20	communications	communication	NOUN
cana-3894	116	21	on	on	ADP
cana-3894	116	22	applied	apply	VERB
cana-3894	116	23	nonlinear	nonlinear	ADJ
cana-3894	116	24	analysis	analysis	NOUN
cana-3894	116	25	issn	issn	NOUN
cana-3894	116	26	:	:	PUNCT
cana-3894	116	27	1074	1074	NUM
cana-3894	116	28	-	-	PUNCT
cana-3894	116	29	133x	133x	NUM
cana-3894	116	30	vol	vol	NOUN
cana-3894	116	31	32	32	NUM
cana-3894	116	32	no	no	NOUN
cana-3894	116	33	.	.	PUNCT
cana-3894	117	1	9s(2025	9s(2025	NUM
cana-3894	117	2	)	)	PUNCT
cana-3894	117	3	from	from	ADP
cana-3894	117	4	the	the	DET
cana-3894	117	5	definition	definition	NOUN
cana-3894	117	6	(	(	PUNCT
cana-3894	117	7	2.4	2.4	NUM
cana-3894	117	8	)	)	PUNCT
cana-3894	117	9	of	of	ADP
cana-3894	117	10	q	q	ADJ
cana-3894	117	11	-	-	PUNCT
cana-3894	117	12	gamma	gamma	NOUN
cana-3894	117	13	function	function	NOUN
cana-3894	117	14	,	,	PUNCT
cana-3894	117	15	one	one	PRON
cana-3894	117	16	finds	find	VERB
cana-3894	117	17	log	log	VERB
cana-3894	117	18	∥γq(αni	∥γq(αni	NOUN
cana-3894	117	19	+	+	PROPN
cana-3894	117	20	b)∥	b)∥	PUNCT
cana-3894	117	21	=	=	PRON
cana-3894	117	22	log	log	NOUN
cana-3894	117	23	∥∥∥(q	∥∥∥(q	SYM
cana-3894	117	24	;	;	PUNCT
cana-3894	117	25	q)∞[(qαni+b	q)∞[(qαni+b	X
cana-3894	117	26	;	;	PUNCT
cana-3894	117	27	q)∞	q)∞	ADJ
cana-3894	117	28	]	]	X
cana-3894	117	29	−1	−1	NOUN
cana-3894	117	30	(	(	PUNCT
cana-3894	117	31	1−	1−	NUM
cana-3894	117	32	q)i−αni−b	q)i−αni−b	NOUN
cana-3894	117	33	∥∥∥	∥∥∥	PROPN
cana-3894	117	34	=	=	PRON
cana-3894	117	35	log	log	PROPN
cana-3894	117	36	∥∥∥(q	∥∥∥(q	PUNCT
cana-3894	117	37	;	;	PUNCT
cana-3894	117	38	q)∞	q)∞	ADJ
cana-3894	118	1	[	[	X
cana-3894	118	2	(	(	PUNCT
cana-3894	118	3	qαni+b	qαni+b	X
cana-3894	118	4	;	;	PUNCT
cana-3894	118	5	q)∞	q)∞	PRON
cana-3894	118	6	]	]	X
cana-3894	118	7	−1	−1	NOUN
cana-3894	118	8	(	(	PUNCT
cana-3894	118	9	1−	1−	NUM
cana-3894	118	10	q)i−αni−b	q)i−αni−b	NOUN
cana-3894	118	11	∥∥∥	∥∥∥	PROPN
cana-3894	118	12	=	=	SYM
cana-3894	118	13	log	log	NOUN
cana-3894	118	14	|(q	|(q	NOUN
cana-3894	118	15	;	;	PUNCT
cana-3894	118	16	q)∞|+	q)∞|+	PROPN
cana-3894	118	17	∥i	∥i	PROPN
cana-3894	118	18	−	−	NOUN
cana-3894	118	19	αi	αi	PART
cana-3894	118	20	−b∥	−b∥	PROPN
cana-3894	118	21	log	log	VERB
cana-3894	118	22	|(1−	|(1−	NOUN
cana-3894	118	23	q)|	q)|	PROPN
cana-3894	118	24	−	−	PROPN
cana-3894	118	25	log	log	NOUN
cana-3894	118	26	∥∥(qαni+b	∥∥(qαni+b	NOUN
cana-3894	118	27	;	;	PUNCT
cana-3894	118	28	q)∞	q)∞	ADV
cana-3894	118	29	∥∥	∥∥	X
cana-3894	118	30	;	;	PUNCT
cana-3894	118	31	(	(	PUNCT
cana-3894	118	32	3.3	3.3	NUM
cana-3894	118	33	)	)	PUNCT
cana-3894	118	34	in	in	ADP
cana-3894	118	35	which	which	PRON
cana-3894	118	36	log	log	NOUN
cana-3894	118	37	∥∥(qαni+b	∥∥(qαni+b	NOUN
cana-3894	118	38	;	;	PUNCT
cana-3894	118	39	q)∞	q)∞	ADV
cana-3894	118	40	∥∥	∥∥	X
cana-3894	118	41	=	=	PRON
cana-3894	118	42	log	log	PROPN
cana-3894	118	43	(	(	PUNCT
cana-3894	118	44	∞∏	∞∏	PROPN
cana-3894	118	45	k=0	k=0	PROPN
cana-3894	118	46	∥∥i	∥∥i	VERB
cana-3894	118	47	−	−	PROPN
cana-3894	118	48	qαni+b+k	qαni+b+k	X
cana-3894	118	49	∥∥	∥∥	X
cana-3894	118	50	)	)	PUNCT
cana-3894	118	51	=	=	SYM
cana-3894	118	52	log	log	NOUN
cana-3894	118	53	(	(	PUNCT
cana-3894	118	54	lim	lim	PROPN
cana-3894	118	55	m→∞	m→∞	NOUN
cana-3894	118	56	m∏	m∏	PROPN
cana-3894	118	57	k=0	k=0	PUNCT
cana-3894	118	58	∥∥i	∥∥i	VERB
cana-3894	118	59	−	−	PROPN
cana-3894	118	60	qαni+b+k	qαni+b+k	X
cana-3894	118	61	∥∥	∥∥	X
cana-3894	118	62	)	)	PUNCT
cana-3894	118	63	=	=	SYM
cana-3894	118	64	lim	lim	PROPN
cana-3894	118	65	m→∞	m→∞	NOUN
cana-3894	118	66	m∑	m∑	AUX
cana-3894	118	67	k=0	k=0	PROPN
cana-3894	118	68	log	log	VERB
cana-3894	118	69	∥∥i	∥∥i	ADV
cana-3894	118	70	−	−	PROPN
cana-3894	118	71	qαni+b+k	qαni+b+k	VERB
cana-3894	118	72	∥∥	∥∥	X
cana-3894	118	73	=	=	SYM
cana-3894	119	1	∞∑	∞∑	PRON
cana-3894	119	2	k=0	k=0	PROPN
cana-3894	119	3	log	log	VERB
cana-3894	119	4	∥∥i	∥∥i	ADV
cana-3894	119	5	−	−	PROPN
cana-3894	119	6	qαni+b+k	qαni+b+k	X
cana-3894	119	7	∥∥	∥∥	X
cana-3894	119	8	.	.	PUNCT
cana-3894	120	1	here	here	ADV
cana-3894	120	2	it	it	PRON
cana-3894	120	3	may	may	AUX
cana-3894	120	4	be	be	AUX
cana-3894	120	5	noted	note	VERB
cana-3894	120	6	that	that	SCONJ
cana-3894	120	7	[	[	X
cana-3894	120	8	1	1	NUM
cana-3894	120	9	,	,	PUNCT
cana-3894	120	10	p.207	p.207	NOUN
cana-3894	120	11	]	]	PUNCT
cana-3894	120	12	log	log	NOUN
cana-3894	120	13	∥∥i	∥∥i	NOUN
cana-3894	120	14	−	−	PROPN
cana-3894	120	15	qαni+b+k	qαni+b+k	VERB
cana-3894	120	16	∥∥	∥∥	X
cana-3894	120	17	≤	≤	NUM
cana-3894	120	18	1−	1−	NUM
cana-3894	120	19	∥qαni+b∥	∥qαni+b∥	X
cana-3894	120	20	|q|k	|q|k	PROPN
cana-3894	120	21	which	which	PRON
cana-3894	120	22	leads	lead	VERB
cana-3894	120	23	us	we	PRON
cana-3894	120	24	to	to	ADP
cana-3894	120	25	∞∑	∞∑	PROPN
cana-3894	120	26	k=0	k=0	PROPN
cana-3894	120	27	log	log	VERB
cana-3894	120	28	∥∥i	∥∥i	ADV
cana-3894	120	29	−	−	PROPN
cana-3894	120	30	qαni+b+k	qαni+b+k	VERB
cana-3894	120	31	∥∥	∥∥	X
cana-3894	120	32	≤	≤	NOUN
cana-3894	120	33	∥qαni+b∥	∥qαni+b∥	PUNCT
cana-3894	121	1	∞∑	∞∑	NUM
cana-3894	121	2	k=0	k=0	PUNCT
cana-3894	121	3	|q|k	|q|k	PROPN
cana-3894	121	4	=	=	SYM
cana-3894	121	5	∥qαni+b∥	∥qαni+b∥	X
cana-3894	121	6	1−	1−	NUM
cana-3894	121	7	|q|	|q|	NOUN
cana-3894	121	8	.	.	PUNCT
cana-3894	122	1	this	this	PRON
cana-3894	122	2	implies	imply	VERB
cana-3894	122	3	that	that	SCONJ
cana-3894	122	4	lim	lim	PROPN
cana-3894	122	5	n→∞	n→∞	NUM
cana-3894	122	6	log	log	NOUN
cana-3894	122	7	∥∥(qαni+b	∥∥(qαni+b	NOUN
cana-3894	122	8	;	;	PUNCT
cana-3894	122	9	q)∞	q)∞	ADV
cana-3894	122	10	∥∥	∥∥	X
cana-3894	122	11	n	n	PRON
cana-3894	122	12	log	log	VERB
cana-3894	122	13	n	n	NOUN
cana-3894	122	14	=	=	SYM
cana-3894	122	15	0	0	X
cana-3894	122	16	.	.	PUNCT
cana-3894	123	1	consequently	consequently	ADV
cana-3894	123	2	from	from	ADP
cana-3894	123	3	(	(	PUNCT
cana-3894	123	4	3.3	3.3	NUM
cana-3894	123	5	)	)	PUNCT
cana-3894	123	6	,	,	PUNCT
cana-3894	123	7	it	it	PRON
cana-3894	123	8	follows	follow	VERB
cana-3894	123	9	that	that	SCONJ
cana-3894	123	10	lim	lim	PROPN
cana-3894	123	11	n→∞	n→∞	PRON
cana-3894	123	12	log	log	VERB
cana-3894	123	13	∥γq(αni	∥γq(αni	NOUN
cana-3894	123	14	+	+	PROPN
cana-3894	123	15	b)∥	b)∥	PUNCT
cana-3894	123	16	n	n	PRON
cana-3894	123	17	log	log	VERB
cana-3894	123	18	n	n	NOUN
cana-3894	123	19	=	=	SYM
cana-3894	123	20	0	0	PROPN
cana-3894	123	21	.	.	PUNCT
cana-3894	124	1	this	this	DET
cana-3894	124	2	last	last	ADJ
cana-3894	124	3	limit	limit	NOUN
cana-3894	124	4	and	and	CCONJ
cana-3894	124	5	the	the	DET
cana-3894	124	6	trivial	trivial	ADJ
cana-3894	124	7	limit	limit	NOUN
cana-3894	124	8	lim	lim	PROPN
cana-3894	124	9	n→∞	n→∞	NUM
cana-3894	124	10	n−	n−	NOUN
cana-3894	124	11	1	1	NUM
cana-3894	124	12	log	log	NOUN
cana-3894	124	13	n	n	NOUN
cana-3894	124	14	=	=	SYM
cana-3894	124	15	∞	∞	PROPN
cana-3894	124	16	when	when	SCONJ
cana-3894	124	17	used	use	VERB
cana-3894	124	18	in	in	ADP
cana-3894	124	19	(	(	PUNCT
cana-3894	124	20	3.2	3.2	NUM
cana-3894	124	21	)	)	PUNCT
cana-3894	124	22	,	,	PUNCT
cana-3894	124	23	yields	yield	NOUN
cana-3894	124	24	lim	lim	PROPN
cana-3894	124	25	n→∞	n→∞	PRON
cana-3894	124	26	log	log	PROPN
cana-3894	124	27	(	(	PUNCT
cana-3894	124	28	∥vn∥)−1	∥vn∥)−1	NOUN
cana-3894	124	29	n	n	NOUN
cana-3894	124	30	log	log	VERB
cana-3894	124	31	n	n	NOUN
cana-3894	124	32	=	=	SYM
cana-3894	124	33	∞.	∞.	PROPN
cana-3894	124	34	thus	thus	ADV
cana-3894	124	35	,	,	PUNCT
cana-3894	124	36	ϱ(ea	ϱ(ea	PROPN
cana-3894	124	37	,	,	PUNCT
cana-3894	124	38	b	b	NOUN
cana-3894	124	39	,	,	PUNCT
cana-3894	124	40	c	c	PROPN
cana-3894	124	41	αi	αi	PROPN
cana-3894	124	42	,	,	PUNCT
cana-3894	124	43	δi	δi	ADV
cana-3894	124	44	,	,	PUNCT
cana-3894	124	45	µi(λz	µi(λz	PROPN
cana-3894	124	46	;	;	PUNCT
cana-3894	124	47	s	s	X
cana-3894	124	48	,	,	PUNCT
cana-3894	124	49	r|q	r|q	ADJ
cana-3894	124	50	)	)	PUNCT
cana-3894	124	51	)	)	PUNCT
cana-3894	125	1	=	=	PUNCT
cana-3894	125	2	0	0	X
cana-3894	125	3	.	.	PUNCT
cana-3894	126	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3894	126	2	336	336	NUM
cana-3894	126	3	communications	communication	NOUN
cana-3894	126	4	on	on	ADP
cana-3894	126	5	applied	apply	VERB
cana-3894	126	6	nonlinear	nonlinear	ADJ
cana-3894	126	7	analysis	analysis	NOUN
cana-3894	126	8	issn	issn	NOUN
cana-3894	126	9	:	:	PUNCT
cana-3894	126	10	1074	1074	NUM
cana-3894	126	11	-	-	PUNCT
cana-3894	126	12	133x	133x	NUM
cana-3894	126	13	vol	vol	NOUN
cana-3894	126	14	32	32	NUM
cana-3894	126	15	no	no	NOUN
cana-3894	126	16	.	.	PUNCT
cana-3894	127	1	9s(2025	9s(2025	NUM
cana-3894	127	2	)	)	PUNCT
cana-3894	127	3	theorem	theorem	VERB
cana-3894	127	4	3.2	3.2	NUM
cana-3894	127	5	.	.	PUNCT
cana-3894	128	1	the	the	DET
cana-3894	128	2	function	function	NOUN
cana-3894	128	3	ea	ea	PROPN
cana-3894	128	4	,	,	PUNCT
cana-3894	128	5	b	b	PROPN
cana-3894	128	6	,	,	PUNCT
cana-3894	128	7	c	c	PROPN
cana-3894	128	8	αi	αi	PROPN
cana-3894	128	9	,	,	PUNCT
cana-3894	128	10	δi	δi	ADV
cana-3894	128	11	,	,	PUNCT
cana-3894	128	12	µi(λz	µi(λz	PROPN
cana-3894	128	13	;	;	PUNCT
cana-3894	128	14	s	s	X
cana-3894	128	15	,	,	PUNCT
cana-3894	128	16	r|q	r|q	ADJ
cana-3894	128	17	)	)	PUNCT
cana-3894	128	18	represents	represent	VERB
cana-3894	128	19	the	the	DET
cana-3894	128	20	series	series	NOUN
cana-3894	128	21	which	which	PRON
cana-3894	128	22	converges	converge	VERB
cana-3894	128	23	absolutely	absolutely	ADV
cana-3894	128	24	for	for	ADP
cana-3894	128	25	|z|	|z|	NOUN
cana-3894	128	26	<	<	X
cana-3894	128	27	∣∣(1−	∣∣(1−	PROPN
cana-3894	128	28	q)(sδ−α−rµ−1	q)(sδ−α−rµ−1	NUM
cana-3894	128	29	)	)	PUNCT
cana-3894	128	30	∣∣	∣∣	PUNCT
cana-3894	128	31	and	and	CCONJ
cana-3894	128	32	|q|	|q|	VERB
cana-3894	128	33	<	<	X
cana-3894	128	34	1	1	NUM
cana-3894	128	35	.	.	PUNCT
cana-3894	128	36	proof	proof	NOUN
cana-3894	128	37	.	.	PUNCT
cana-3894	129	1	take	take	VERB
cana-3894	129	2	un	un	PROPN
cana-3894	129	3	=	=	PUNCT
cana-3894	130	1	[	[	X
cana-3894	130	2	γq(γ	γq(γ	X
cana-3894	130	3	+	+	CCONJ
cana-3894	130	4	δn)]s	δn)]s	PROPN
cana-3894	131	1	[	[	X
cana-3894	131	2	γq(β	γq(β	X
cana-3894	131	3	+	+	X
cana-3894	131	4	αn)]−1	αn)]−1	NUM
cana-3894	131	5	[	[	PUNCT
cana-3894	131	6	γq(λ+	γq(λ+	ADP
cana-3894	131	7	µn)]−r	µn)]−r	PROPN
cana-3894	131	8	[	[	X
cana-3894	131	9	γq(n+	γq(n+	NOUN
cana-3894	131	10	1	1	NUM
cana-3894	131	11	)	)	PUNCT
cana-3894	131	12	]	]	PUNCT
cana-3894	131	13	(	(	PUNCT
cana-3894	131	14	3.4	3.4	NUM
cana-3894	131	15	)	)	PUNCT
cana-3894	131	16	then	then	ADV
cana-3894	131	17	eγ	eγ	ADP
cana-3894	131	18	,	,	PUNCT
cana-3894	131	19	δα	δα	PRON
cana-3894	131	20	,	,	PUNCT
cana-3894	131	21	β	β	X
cana-3894	131	22	,	,	PUNCT
cana-3894	131	23	λ	λ	PROPN
cana-3894	131	24	,	,	PUNCT
cana-3894	131	25	µ(z	µ(z	PROPN
cana-3894	131	26	;	;	PUNCT
cana-3894	131	27	s	s	X
cana-3894	131	28	,	,	PUNCT
cana-3894	131	29	r|q	r|q	ADJ
cana-3894	131	30	)	)	PUNCT
cana-3894	131	31	=	=	PUNCT
cana-3894	132	1	∞∑	∞∑	PRON
cana-3894	132	2	n=0	n=0	NUM
cana-3894	132	3	un	un	PROPN
cana-3894	132	4	zn	zn	PROPN
cana-3894	132	5	.	.	PUNCT
cana-3894	133	1	now	now	ADV
cana-3894	133	2	in	in	ADP
cana-3894	133	3	view	view	NOUN
cana-3894	133	4	of	of	ADP
cana-3894	133	5	(	(	PUNCT
cana-3894	133	6	2.4	2.4	NUM
cana-3894	133	7	)	)	PUNCT
cana-3894	133	8	,	,	PUNCT
cana-3894	133	9	we	we	PRON
cana-3894	133	10	get	get	VERB
cana-3894	133	11	n	n	PRON
cana-3894	133	12	√	√	NOUN
cana-3894	133	13	∥un∥	∥un∥	NOUN
cana-3894	133	14	∼	∼	NOUN
cana-3894	133	15	∥∥(1−	∥∥(1−	PROPN
cana-3894	133	16	q)(sδ−ℜ(α)−rµ)i−1	q)(sδ−ℜ(α)−rµ)i−1	NOUN
cana-3894	133	17	∥∥	∥∥	PUNCT
cana-3894	133	18	whence	whence	ADV
cana-3894	133	19	1	1	NUM
cana-3894	133	20	r	r	NOUN
cana-3894	133	21	=	=	SYM
cana-3894	133	22	lim	lim	PROPN
cana-3894	133	23	n→∞	n→∞	NOUN
cana-3894	133	24	n	n	CCONJ
cana-3894	133	25	√	√	VERB
cana-3894	133	26	|un|	|un|	NOUN
cana-3894	133	27	∼	∼	NOUN
cana-3894	133	28	∣∣(1−	∣∣(1−	ADJ
cana-3894	133	29	q)α+rµ−sδ+1	q)α+rµ−sδ+1	NUM
cana-3894	133	30	∣∣	∣∣	ADJ
cana-3894	133	31	.	.	PUNCT
cana-3894	134	1	thus	thus	ADV
cana-3894	134	2	,	,	PUNCT
cana-3894	134	3	the	the	DET
cana-3894	134	4	series	series	NOUN
cana-3894	134	5	in	in	ADP
cana-3894	134	6	(	(	PUNCT
cana-3894	134	7	2.14	2.14	NUM
cana-3894	134	8	)	)	PUNCT
cana-3894	134	9	converges	converge	VERB
cana-3894	134	10	absolutely	absolutely	ADV
cana-3894	134	11	if	if	SCONJ
cana-3894	134	12	|z|	|z|	NOUN
cana-3894	134	13	<	<	X
cana-3894	134	14	r	r	NOUN
cana-3894	134	15	=	=	PUNCT
cana-3894	134	16	(	(	PUNCT
cana-3894	134	17	1−	1−	NUM
cana-3894	134	18	q)sδ−ℜ(α)−rµ−1	q)sδ−ℜ(α)−rµ−1	NOUN
cana-3894	134	19	.	.	PROPN
cana-3894	134	20	3.2	3.2	NUM
cana-3894	134	21	contour	contour	NOUN
cana-3894	134	22	integral	integral	ADJ
cana-3894	134	23	theorem	theorem	NOUN
cana-3894	134	24	3.3	3.3	NUM
cana-3894	134	25	.	.	PUNCT
cana-3894	135	1	let	let	VERB
cana-3894	135	2	a	a	DET
cana-3894	135	3	,	,	PUNCT
cana-3894	135	4	b	b	NOUN
cana-3894	135	5	,	,	PUNCT
cana-3894	135	6	c	c	AUX
cana-3894	135	7	be	be	AUX
cana-3894	135	8	positive	positive	ADJ
cana-3894	135	9	stable	stable	ADJ
cana-3894	135	10	matrices	matrix	NOUN
cana-3894	135	11	in	in	ADP
cana-3894	135	12	cp×p	cp×p	PROPN
cana-3894	135	13	,	,	PUNCT
cana-3894	135	14	α	α	PROPN
cana-3894	135	15	,	,	PUNCT
cana-3894	135	16	δ	δ	PROPN
cana-3894	135	17	,	,	PUNCT
cana-3894	135	18	µ	µ	X
cana-3894	135	19	∈	∈	PROPN
cana-3894	135	20	c	c	NOUN
cana-3894	135	21	with	with	ADP
cana-3894	135	22	ℜ(α	ℜ(α	NOUN
cana-3894	135	23	)	)	PUNCT
cana-3894	135	24	>	>	X
cana-3894	135	25	0	0	NUM
cana-3894	135	26	,	,	PUNCT
cana-3894	135	27	ℜ(α2)+rµ2−sδ2	ℜ(α2)+rµ2−sδ2	PUNCT
cana-3894	136	1	+	+	PROPN
cana-3894	136	2	1	1	NUM
cana-3894	136	3	>	>	SYM
cana-3894	136	4	0	0	NUM
cana-3894	136	5	,	,	PUNCT
cana-3894	136	6	δ	δ	PROPN
cana-3894	136	7	,	,	PUNCT
cana-3894	136	8	µ	µ	X
cana-3894	136	9	>	>	X
cana-3894	136	10	0	0	NUM
cana-3894	136	11	,	,	PUNCT
cana-3894	136	12	r	r	NOUN
cana-3894	136	13	∈	∈	PROPN
cana-3894	136	14	{	{	PUNCT
cana-3894	136	15	−1	−1	NOUN
cana-3894	136	16	,	,	PUNCT
cana-3894	136	17	0}∪n	0}∪n	X
cana-3894	136	18	,	,	PUNCT
cana-3894	136	19	s	s	PROPN
cana-3894	136	20	∈	∈	PROPN
cana-3894	136	21	n∪{0	n∪{0	NOUN
cana-3894	136	22	}	}	PUNCT
cana-3894	136	23	and	and	CCONJ
cana-3894	136	24	0	0	NUM
cana-3894	136	25	<	<	X
cana-3894	136	26	q	q	X
cana-3894	136	27	<	<	X
cana-3894	136	28	1	1	NUM
cana-3894	136	29	.	.	PUNCT
cana-3894	137	1	then	then	ADV
cana-3894	137	2	the	the	DET
cana-3894	137	3	function	function	NOUN
cana-3894	137	4	ea	ea	PROPN
cana-3894	137	5	,	,	PUNCT
cana-3894	137	6	b	b	PROPN
cana-3894	137	7	,	,	PUNCT
cana-3894	137	8	c	c	PROPN
cana-3894	137	9	αi	αi	PROPN
cana-3894	137	10	,	,	PUNCT
cana-3894	137	11	δi	δi	ADV
cana-3894	137	12	,	,	PUNCT
cana-3894	137	13	µi(λz	µi(λz	PROPN
cana-3894	137	14	;	;	PUNCT
cana-3894	137	15	s	s	X
cana-3894	137	16	,	,	PUNCT
cana-3894	137	17	r|q	r|q	ADJ
cana-3894	137	18	)	)	PUNCT
cana-3894	137	19	is	be	AUX
cana-3894	137	20	expressible	expressible	ADJ
cana-3894	137	21	as	as	ADP
cana-3894	137	22	the	the	DET
cana-3894	137	23	mellin	mellin	PROPN
cana-3894	137	24	barnes	barnes	PROPN
cana-3894	137	25	q	q	ADJ
cana-3894	137	26	-	-	PUNCT
cana-3894	137	27	integral	integral	AUX
cana-3894	137	28	given	give	VERB
cana-3894	137	29	by	by	ADP
cana-3894	137	30	ea	ea	ADP
cana-3894	137	31	,	,	PUNCT
cana-3894	137	32	b	b	PROPN
cana-3894	137	33	,	,	PUNCT
cana-3894	137	34	c	c	PROPN
cana-3894	137	35	αi	αi	PROPN
cana-3894	137	36	,	,	PUNCT
cana-3894	137	37	δi	δi	ADV
cana-3894	137	38	,	,	PUNCT
cana-3894	137	39	µi(λz	µi(λz	PROPN
cana-3894	137	40	;	;	PUNCT
cana-3894	137	41	s	s	X
cana-3894	137	42	,	,	PUNCT
cana-3894	137	43	r|q	r|q	ADJ
cana-3894	137	44	)	)	PUNCT
cana-3894	137	45	=	=	SYM
cana-3894	137	46	1	1	NUM
cana-3894	137	47	2πi	2πi	ADJ
cana-3894	137	48	∫	∫	PROPN
cana-3894	137	49	l	l	NOUN
cana-3894	137	50	(	(	PUNCT
cana-3894	137	51	−1)−psq−ps(−s−1)/2	−1)−psq−ps(−s−1)/2	X
cana-3894	137	52	γq(s	γq(s	NUM
cana-3894	137	53	)	)	PUNCT
cana-3894	138	1	[	[	X
cana-3894	138	2	γq(a−	γq(a−	NOUN
cana-3894	138	3	δis)]s	δis)]s	ADV
cana-3894	138	4	×[γq(b	×[γq(b	ADV
cana-3894	138	5	−	−	PROPN
cana-3894	138	6	αis	αis	ADV
cana-3894	138	7	)	)	PUNCT
cana-3894	138	8	]	]	PUNCT
cana-3894	139	1	[	[	X
cana-3894	139	2	γq(c	γq(c	NUM
cana-3894	139	3	−	−	PROPN
cana-3894	139	4	µis)]−r	µis)]−r	NOUN
cana-3894	139	5	(	(	PUNCT
cana-3894	139	6	−z)−s	−z)−s	NOUN
cana-3894	139	7	dqs	dqs	NOUN
cana-3894	139	8	,	,	PUNCT
cana-3894	139	9	(	(	PUNCT
cana-3894	139	10	3.5	3.5	NUM
cana-3894	139	11	)	)	PUNCT
cana-3894	139	12	where	where	SCONJ
cana-3894	139	13	|argz|	|argz|	ADJ
cana-3894	139	14	<	<	X
cana-3894	139	15	π	π	X
cana-3894	139	16	.	.	PUNCT
cana-3894	140	1	the	the	DET
cana-3894	140	2	contour	contour	ADJ
cana-3894	140	3	l	l	NOUN
cana-3894	140	4	of	of	ADP
cana-3894	140	5	integration	integration	NOUN
cana-3894	140	6	begins	begin	VERB
cana-3894	140	7	from	from	ADP
cana-3894	140	8	−i∞	−i∞	NOUN
cana-3894	140	9	and	and	CCONJ
cana-3894	140	10	proceeds	proceed	NOUN
cana-3894	140	11	towards	towards	ADP
cana-3894	140	12	+	+	PROPN
cana-3894	140	13	i∞	i∞	PROPN
cana-3894	140	14	,	,	PUNCT
cana-3894	140	15	and	and	CCONJ
cana-3894	140	16	is	be	AUX
cana-3894	140	17	indented	indent	VERB
cana-3894	140	18	to	to	PART
cana-3894	140	19	keep	keep	VERB
cana-3894	140	20	the	the	DET
cana-3894	140	21	poles	pole	NOUN
cana-3894	140	22	of	of	ADP
cana-3894	140	23	integrand	integrand	NOUN
cana-3894	140	24	at	at	ADP
cana-3894	140	25	s	s	NOUN
cana-3894	140	26	=	=	NOUN
cana-3894	140	27	−ni	−ni	NOUN
cana-3894	140	28	to	to	ADP
cana-3894	140	29	the	the	DET
cana-3894	140	30	left	left	NOUN
cana-3894	140	31	;	;	PUNCT
cana-3894	140	32	and	and	CCONJ
cana-3894	140	33	the	the	DET
cana-3894	140	34	poles	pole	NOUN
cana-3894	140	35	at	at	ADP
cana-3894	140	36	s	s	NOUN
cana-3894	140	37	=	=	PUNCT
cana-3894	140	38	(	(	PUNCT
cana-3894	140	39	a+	a+	X
cana-3894	140	40	ni)/δ	ni)/δ	NOUN
cana-3894	140	41	to	to	ADP
cana-3894	140	42	the	the	DET
cana-3894	140	43	right	right	NOUN
cana-3894	140	44	of	of	ADP
cana-3894	140	45	the	the	DET
cana-3894	140	46	path	path	NOUN
cana-3894	140	47	for	for	ADP
cana-3894	140	48	all	all	PRON
cana-3894	140	49	n	n	PRON
cana-3894	140	50	∈	∈	NOUN
cana-3894	140	51	n	n	NOUN
cana-3894	140	52	∪	∪	X
cana-3894	140	53	{	{	PUNCT
cana-3894	140	54	0	0	NUM
cana-3894	140	55	}	}	PUNCT
cana-3894	140	56	.	.	PUNCT
cana-3894	141	1	proof	proof	NOUN
cana-3894	141	2	.	.	PUNCT
cana-3894	142	1	the	the	DET
cana-3894	142	2	integral	integral	ADJ
cana-3894	142	3	on	on	ADP
cana-3894	142	4	the	the	DET
cana-3894	142	5	right	right	ADJ
cana-3894	142	6	hand	hand	NOUN
cana-3894	142	7	side	side	NOUN
cana-3894	142	8	of	of	ADP
cana-3894	142	9	(	(	PUNCT
cana-3894	142	10	3.5	3.5	NUM
cana-3894	142	11	)	)	PUNCT
cana-3894	142	12	may	may	AUX
cana-3894	142	13	be	be	AUX
cana-3894	142	14	evaluated	evaluate	VERB
cana-3894	142	15	as	as	ADP
cana-3894	142	16	the	the	DET
cana-3894	142	17	sum	sum	NOUN
cana-3894	142	18	of	of	ADP
cana-3894	142	19	the	the	DET
cana-3894	142	20	residues	residue	NOUN
cana-3894	142	21	at	at	ADP
cana-3894	142	22	the	the	DET
cana-3894	142	23	poles	pole	NOUN
cana-3894	142	24	s	s	PART
cana-3894	142	25	=	=	NOUN
cana-3894	142	26	0,−1,−2	0,−1,−2	NUM
cana-3894	142	27	,	,	PUNCT
cana-3894	142	28	.	.	PUNCT
cana-3894	142	29	.	.	PUNCT
cana-3894	142	30	.	.	PUNCT
cana-3894	143	1	.	.	PUNCT
cana-3894	144	1	in	in	ADP
cana-3894	144	2	fact	fact	NOUN
cana-3894	144	3	,	,	PUNCT
cana-3894	144	4	in	in	ADP
cana-3894	144	5	view	view	NOUN
cana-3894	144	6	of	of	ADP
cana-3894	144	7	the	the	DET
cana-3894	144	8	definition	definition	NOUN
cana-3894	144	9	of	of	ADP
cana-3894	144	10	residue	residue	NOUN
cana-3894	144	11	,	,	PUNCT
cana-3894	144	12	i	i	PRON
cana-3894	144	13	=	=	NOUN
cana-3894	144	14	1	1	NUM
cana-3894	144	15	2πi	2πi	ADJ
cana-3894	144	16	∫	∫	PROPN
cana-3894	144	17	l	l	NOUN
cana-3894	144	18	(	(	PUNCT
cana-3894	144	19	−1)−ps	−1)−ps	PROPN
cana-3894	144	20	q−ps(−s−1)/2	q−ps(−s−1)/2	NOUN
cana-3894	144	21	γq(s	γq(s	NUM
cana-3894	144	22	)	)	PUNCT
cana-3894	145	1	[	[	X
cana-3894	145	2	γq(a−	γq(a−	NOUN
cana-3894	145	3	δis)]s	δis)]s	ADV
cana-3894	145	4	(	(	PUNCT
cana-3894	145	5	−z)−s	−z)−s	ADJ
cana-3894	145	6	×[γq(b	×[γq(b	ADV
cana-3894	145	7	−	−	PROPN
cana-3894	145	8	αis	αis	NOUN
cana-3894	145	9	)	)	PUNCT
cana-3894	145	10	]	]	PUNCT
cana-3894	146	1	[	[	X
cana-3894	146	2	γq(c	γq(c	NUM
cana-3894	146	3	−	−	PROPN
cana-3894	146	4	µis)]−r	µis)]−r	NOUN
cana-3894	146	5	dqs	dqs	NOUN
cana-3894	146	6	=	=	NOUN
cana-3894	146	7	∞∑	∞∑	NUM
cana-3894	146	8	n=0	n=0	NUM
cana-3894	146	9	res	re	NOUN
cana-3894	146	10	s	s	PART
cana-3894	146	11	=	=	NOUN
cana-3894	146	12	−n	−n	NOUN
cana-3894	146	13	[	[	PUNCT
cana-3894	146	14	(	(	PUNCT
cana-3894	146	15	−1)−ps	−1)−ps	PROPN
cana-3894	146	16	q−ps(−s−1)/2	q−ps(−s−1)/2	NOUN
cana-3894	146	17	γq(s	γq(s	NUM
cana-3894	146	18	)	)	PUNCT
cana-3894	146	19	(	(	PUNCT
cana-3894	146	20	−z)−s	−z)−s	NOUN
cana-3894	146	21	[	[	X
cana-3894	146	22	γq(b	γq(b	NOUN
cana-3894	146	23	−	−	ADP
cana-3894	146	24	αis)]−1	αis)]−1	ADJ
cana-3894	146	25	https://internationalpubls.com	https://internationalpubls.com	X
cana-3894	146	26	337	337	NUM
cana-3894	146	27	communications	communication	NOUN
cana-3894	146	28	on	on	ADP
cana-3894	146	29	applied	apply	VERB
cana-3894	146	30	nonlinear	nonlinear	ADJ
cana-3894	146	31	analysis	analysis	NOUN
cana-3894	146	32	issn	issn	NOUN
cana-3894	146	33	:	:	PUNCT
cana-3894	146	34	1074	1074	NUM
cana-3894	146	35	-	-	PUNCT
cana-3894	146	36	133x	133x	NUM
cana-3894	146	37	vol	vol	NOUN
cana-3894	146	38	32	32	NUM
cana-3894	146	39	no	no	NOUN
cana-3894	146	40	.	.	PUNCT
cana-3894	147	1	9s(2025	9s(2025	NUM
cana-3894	147	2	)	)	PUNCT
cana-3894	147	3	×[γq(c	×[γq(c	VERB
cana-3894	147	4	−	−	NOUN
cana-3894	147	5	µis)]−r	µis)]−r	NOUN
cana-3894	147	6	[	[	X
cana-3894	147	7	γq(a−	γq(a−	NOUN
cana-3894	147	8	δis)]s	δis)]s	ADV
cana-3894	147	9	]	]	PUNCT
cana-3894	147	10	=	=	PUNCT
cana-3894	148	1	∞∑	∞∑	NUM
cana-3894	148	2	n=0	n=0	PUNCT
cana-3894	148	3	lim	lim	PROPN
cana-3894	148	4	s→−n	s→−n	PROPN
cana-3894	148	5	π(s	π(s	PROPN
cana-3894	148	6	+	+	CCONJ
cana-3894	148	7	n	n	CCONJ
cana-3894	148	8	)	)	PUNCT
cana-3894	148	9	sinπs	sinπs	PROPN
cana-3894	148	10	(	(	PUNCT
cana-3894	148	11	−1)−ps	−1)−ps	PROPN
cana-3894	148	12	q−ps(−s−1)/2	q−ps(−s−1)/2	PROPN
cana-3894	149	1	[	[	X
cana-3894	149	2	γq(a−	γq(a−	NOUN
cana-3894	149	3	δis)]s	δis)]s	ADV
cana-3894	149	4	(	(	PUNCT
cana-3894	149	5	−z)−s	−z)−s	ADJ
cana-3894	149	6	×[γq(b	×[γq(b	ADV
cana-3894	149	7	−	−	X
cana-3894	149	8	αis)]−1	αis)]−1	X
cana-3894	149	9	[	[	X
cana-3894	149	10	γq(c	γq(c	PUNCT
cana-3894	149	11	−	−	PROPN
cana-3894	149	12	µis)]−r	µis)]−r	NOUN
cana-3894	149	13	[	[	PUNCT
cana-3894	149	14	γq(1−	γq(1−	PROPN
cana-3894	149	15	s)]−1	s)]−1	NOUN
cana-3894	149	16	=	=	NOUN
cana-3894	149	17	∞∑	∞∑	NUM
cana-3894	149	18	n=0	n=0	NUM
cana-3894	149	19	(	(	PUNCT
cana-3894	149	20	−1)pn	−1)pn	PROPN
cana-3894	149	21	qpn(n−1)/2	qpn(n−1)/2	PROPN
cana-3894	150	1	[	[	X
cana-3894	150	2	γq(a+	γq(a+	NOUN
cana-3894	150	3	δin)]s	δin)]s	ADJ
cana-3894	150	4	[	[	PUNCT
cana-3894	150	5	γq(b	γq(b	PUNCT
cana-3894	150	6	+	+	NUM
cana-3894	150	7	αin)]−1	αin)]−1	PRON
cana-3894	150	8	[	[	X
cana-3894	150	9	γq(c	γq(c	X
cana-3894	150	10	+	+	CCONJ
cana-3894	150	11	µin)]−r	µin)]−r	PROPN
cana-3894	150	12	×	×	PROPN
cana-3894	150	13	zn	zn	PROPN
cana-3894	150	14	γq(n+	γq(n+	NOUN
cana-3894	150	15	1	1	NUM
cana-3894	150	16	)	)	PUNCT
cana-3894	150	17	=	=	SYM
cana-3894	150	18	ea	ea	PROPN
cana-3894	150	19	,	,	PUNCT
cana-3894	150	20	b	b	PROPN
cana-3894	150	21	,	,	PUNCT
cana-3894	150	22	c	c	PROPN
cana-3894	150	23	αi	αi	PROPN
cana-3894	150	24	,	,	PUNCT
cana-3894	150	25	δi	δi	ADV
cana-3894	150	26	,	,	PUNCT
cana-3894	150	27	µi(λz	µi(λz	PROPN
cana-3894	150	28	;	;	PUNCT
cana-3894	150	29	s	s	X
cana-3894	150	30	,	,	PUNCT
cana-3894	150	31	r|q	r|q	ADJ
cana-3894	150	32	)	)	PUNCT
cana-3894	150	33	.	.	PUNCT
cana-3894	151	1	theorem	theorem	VERB
cana-3894	151	2	3.4	3.4	NUM
cana-3894	151	3	.	.	PUNCT
cana-3894	152	1	let	let	VERB
cana-3894	152	2	a	a	DET
cana-3894	152	3	,	,	PUNCT
cana-3894	152	4	b	b	NOUN
cana-3894	152	5	,	,	PUNCT
cana-3894	152	6	c	c	AUX
cana-3894	152	7	be	be	AUX
cana-3894	152	8	positive	positive	ADJ
cana-3894	152	9	stable	stable	ADJ
cana-3894	152	10	matrices	matrix	NOUN
cana-3894	152	11	in	in	ADP
cana-3894	152	12	cr×r	cr×r	PROPN
cana-3894	152	13	,	,	PUNCT
cana-3894	152	14	α	α	PROPN
cana-3894	152	15	,	,	PUNCT
cana-3894	152	16	δ	δ	PROPN
cana-3894	152	17	,	,	PUNCT
cana-3894	152	18	µ	µ	X
cana-3894	152	19	∈	∈	PROPN
cana-3894	152	20	c	c	NOUN
cana-3894	152	21	with	with	ADP
cana-3894	152	22	ℜ(α	ℜ(α	NOUN
cana-3894	152	23	)	)	PUNCT
cana-3894	152	24	>	>	X
cana-3894	152	25	0	0	NUM
cana-3894	152	26	,	,	PUNCT
cana-3894	152	27	δ	δ	PROPN
cana-3894	152	28	,	,	PUNCT
cana-3894	152	29	µ	µ	X
cana-3894	152	30	>	>	X
cana-3894	152	31	0	0	NUM
cana-3894	152	32	,	,	PUNCT
cana-3894	152	33	r	r	NOUN
cana-3894	152	34	∈	∈	PROPN
cana-3894	152	35	{	{	PUNCT
cana-3894	152	36	−1	−1	NOUN
cana-3894	152	37	,	,	PUNCT
cana-3894	152	38	0	0	NUM
cana-3894	152	39	}	}	PUNCT
cana-3894	152	40	∪	∪	NOUN
cana-3894	152	41	n	n	CCONJ
cana-3894	152	42	,	,	PUNCT
cana-3894	152	43	s	s	VERB
cana-3894	152	44	∈	∈	PROPN
cana-3894	152	45	n	n	NOUN
cana-3894	152	46	∪	∪	X
cana-3894	152	47	{	{	PUNCT
cana-3894	152	48	0	0	NUM
cana-3894	152	49	}	}	PUNCT
cana-3894	152	50	and	and	CCONJ
cana-3894	152	51	(	(	PUNCT
cana-3894	152	52	α2	α2	ADJ
cana-3894	152	53	+	+	CCONJ
cana-3894	152	54	rµ2	rµ2	NOUN
cana-3894	152	55	+	+	CCONJ
cana-3894	152	56	1)i	1)i	NUM
cana-3894	152	57	=	=	SYM
cana-3894	152	58	sδ2i	sδ2i	PROPN
cana-3894	152	59	,	,	PUNCT
cana-3894	152	60	0	0	PUNCT
cana-3894	153	1	<	<	X
cana-3894	153	2	q	q	X
cana-3894	153	3	<	<	X
cana-3894	153	4	1	1	NUM
cana-3894	153	5	.	.	PUNCT
cana-3894	154	1	then	then	ADV
cana-3894	154	2	the	the	DET
cana-3894	154	3	function	function	NOUN
cana-3894	154	4	ea	ea	PROPN
cana-3894	154	5	,	,	PUNCT
cana-3894	154	6	b	b	PROPN
cana-3894	154	7	,	,	PUNCT
cana-3894	154	8	c	c	PROPN
cana-3894	154	9	αi	αi	PROPN
cana-3894	154	10	,	,	PUNCT
cana-3894	154	11	δi	δi	ADV
cana-3894	154	12	,	,	PUNCT
cana-3894	154	13	µi(λz	µi(λz	PROPN
cana-3894	154	14	;	;	PUNCT
cana-3894	154	15	s	s	X
cana-3894	154	16	,	,	PUNCT
cana-3894	154	17	r|q	r|q	ADJ
cana-3894	154	18	)	)	PUNCT
cana-3894	154	19	is	be	AUX
cana-3894	154	20	expressible	expressible	ADJ
cana-3894	154	21	as	as	ADP
cana-3894	154	22	the	the	DET
cana-3894	154	23	mellin	mellin	PROPN
cana-3894	154	24	barnes	barnes	PROPN
cana-3894	154	25	q	q	ADJ
cana-3894	154	26	-	-	PUNCT
cana-3894	154	27	integral	integral	AUX
cana-3894	154	28	given	give	VERB
cana-3894	154	29	by	by	ADP
cana-3894	154	30	ea	ea	ADP
cana-3894	154	31	,	,	PUNCT
cana-3894	154	32	b	b	PROPN
cana-3894	154	33	,	,	PUNCT
cana-3894	154	34	c	c	PROPN
cana-3894	154	35	αi	αi	PROPN
cana-3894	154	36	,	,	PUNCT
cana-3894	154	37	δi	δi	ADV
cana-3894	154	38	,	,	PUNCT
cana-3894	154	39	µi(λz	µi(λz	PROPN
cana-3894	154	40	;	;	PUNCT
cana-3894	154	41	s	s	X
cana-3894	154	42	,	,	PUNCT
cana-3894	154	43	r|q	r|q	ADJ
cana-3894	154	44	)	)	PUNCT
cana-3894	154	45	=	=	SYM
cana-3894	154	46	1	1	NUM
cana-3894	154	47	2πi	2πi	ADJ
cana-3894	154	48	∫	∫	PROPN
cana-3894	154	49	l	l	NOUN
cana-3894	154	50	γq(s	γq(s	PUNCT
cana-3894	154	51	)	)	PUNCT
cana-3894	155	1	[	[	X
cana-3894	155	2	γq(a−	γq(a−	NOUN
cana-3894	155	3	δis)]s	δis)]s	ADV
cana-3894	155	4	(	(	PUNCT
cana-3894	155	5	−z)−s	−z)−s	ADJ
cana-3894	155	6	×[γq(b	×[γq(b	ADV
cana-3894	155	7	−	−	X
cana-3894	155	8	αis)]−1	αis)]−1	X
cana-3894	155	9	[	[	X
cana-3894	155	10	γq(c	γq(c	NUM
cana-3894	155	11	−	−	NOUN
cana-3894	155	12	µis)]−rdqs	µis)]−rdqs	PROPN
cana-3894	155	13	,	,	PUNCT
cana-3894	155	14	(	(	PUNCT
cana-3894	155	15	3.6	3.6	NUM
cana-3894	155	16	)	)	PUNCT
cana-3894	155	17	where	where	SCONJ
cana-3894	155	18	|argz|	|argz|	ADJ
cana-3894	155	19	<	<	X
cana-3894	155	20	π	π	PROPN
cana-3894	155	21	;	;	PUNCT
cana-3894	155	22	the	the	DET
cana-3894	155	23	contour	contour	NOUN
cana-3894	155	24	l	l	NOUN
cana-3894	155	25	of	of	ADP
cana-3894	155	26	integration	integration	NOUN
cana-3894	155	27	begins	begin	VERB
cana-3894	155	28	from	from	ADP
cana-3894	155	29	−i∞	−i∞	NOUN
cana-3894	155	30	and	and	CCONJ
cana-3894	155	31	proceeds	proceed	NOUN
cana-3894	155	32	towards	towards	ADP
cana-3894	155	33	+	+	PROPN
cana-3894	155	34	i∞	i∞	PROPN
cana-3894	155	35	,	,	PUNCT
cana-3894	155	36	and	and	CCONJ
cana-3894	155	37	is	be	AUX
cana-3894	155	38	indented	indent	VERB
cana-3894	155	39	to	to	PART
cana-3894	155	40	keep	keep	VERB
cana-3894	155	41	the	the	DET
cana-3894	155	42	poles	pole	NOUN
cana-3894	155	43	of	of	ADP
cana-3894	155	44	integrand	integrand	NOUN
cana-3894	155	45	at	at	ADP
cana-3894	155	46	s	s	NOUN
cana-3894	155	47	=	=	NOUN
cana-3894	155	48	−ni	−ni	NOUN
cana-3894	155	49	to	to	ADP
cana-3894	155	50	the	the	DET
cana-3894	155	51	left	left	NOUN
cana-3894	155	52	;	;	PUNCT
cana-3894	155	53	and	and	CCONJ
cana-3894	155	54	the	the	DET
cana-3894	155	55	poles	pole	NOUN
cana-3894	155	56	at	at	ADP
cana-3894	155	57	s	s	NOUN
cana-3894	155	58	=	=	PUNCT
cana-3894	155	59	(	(	PUNCT
cana-3894	155	60	a+	a+	X
cana-3894	155	61	ni)/δ	ni)/δ	NOUN
cana-3894	155	62	to	to	ADP
cana-3894	155	63	the	the	DET
cana-3894	155	64	right	right	NOUN
cana-3894	155	65	of	of	ADP
cana-3894	155	66	the	the	DET
cana-3894	155	67	path	path	NOUN
cana-3894	155	68	,	,	PUNCT
cana-3894	155	69	for	for	ADP
cana-3894	155	70	all	all	DET
cana-3894	155	71	n	n	PRON
cana-3894	155	72	∈	∈	NOUN
cana-3894	155	73	n	n	NOUN
cana-3894	155	74	∪	∪	X
cana-3894	155	75	{	{	PUNCT
cana-3894	155	76	0	0	NUM
cana-3894	155	77	}	}	PUNCT
cana-3894	155	78	.	.	PUNCT
cana-3894	155	79	3.3	3.3	NUM
cana-3894	155	80	difference	difference	NOUN
cana-3894	155	81	equation	equation	NOUN
cana-3894	155	82	with	with	ADP
cana-3894	155	83	the	the	DET
cana-3894	155	84	aid	aid	NOUN
cana-3894	155	85	of	of	ADP
cana-3894	155	86	the	the	DET
cana-3894	155	87	following	follow	VERB
cana-3894	155	88	operators	operator	NOUN
cana-3894	155	89	,	,	PUNCT
cana-3894	155	90	the	the	DET
cana-3894	155	91	difference	difference	NOUN
cana-3894	155	92	equations	equation	NOUN
cana-3894	155	93	of	of	ADP
cana-3894	155	94	both	both	DET
cana-3894	155	95	q	q	NOUN
cana-3894	155	96	-	-	PUNCT
cana-3894	155	97	analogues	analogue	NOUN
cana-3894	155	98	will	will	AUX
cana-3894	155	99	be	be	AUX
cana-3894	155	100	derived	derive	VERB
cana-3894	155	101	.	.	PUNCT
cana-3894	156	1	put	put	VERB
cana-3894	156	2	λqf(a	λqf(a	PROPN
cana-3894	156	3	)	)	PUNCT
cana-3894	156	4	=	=	SYM
cana-3894	156	5	f(a)−	f(a)−	NOUN
cana-3894	156	6	f(aq−1	f(aq−1	NUM
cana-3894	156	7	)	)	PUNCT
cana-3894	156	8	,	,	PUNCT
cana-3894	156	9	θf(a	θf(a	NOUN
cana-3894	156	10	)	)	PUNCT
cana-3894	156	11	=	=	SYM
cana-3894	156	12	f(a)−	f(a)−	VERB
cana-3894	156	13	f(aq	f(aq	PROPN
cana-3894	156	14	)	)	PUNCT
cana-3894	156	15	,	,	PUNCT
cana-3894	156	16	(	(	PUNCT
cana-3894	156	17	3.7	3.7	NUM
cana-3894	156	18	)	)	PUNCT
cana-3894	156	19	dq	dq	NOUN
cana-3894	156	20	f(a	f(a	NOUN
cana-3894	156	21	)	)	PUNCT
cana-3894	157	1	=	=	PUNCT
cana-3894	157	2	(	(	PUNCT
cana-3894	157	3	1−	1−	NUM
cana-3894	157	4	q	q	NOUN
cana-3894	157	5	)	)	PUNCT
cana-3894	157	6	dqf(a	dqf(a	PROPN
cana-3894	157	7	)	)	PUNCT
cana-3894	157	8	:	:	PUNCT
cana-3894	158	1	=	=	SYM
cana-3894	158	2	(	(	PUNCT
cana-3894	158	3	1−	1−	NUM
cana-3894	158	4	q	q	NOUN
cana-3894	158	5	)	)	PUNCT
cana-3894	159	1	[	[	X
cana-3894	159	2	f(a)−	f(a)−	NOUN
cana-3894	159	3	f(aq)](a−	f(aq)](a−	PROPN
cana-3894	159	4	aq)−1	aq)−1	NOUN
cana-3894	160	1	=	=	PUNCT
cana-3894	161	1	[	[	X
cana-3894	161	2	f(a)−	f(a)−	NOUN
cana-3894	161	3	f(aq)](a)−1	f(aq)](a)−1	NOUN
cana-3894	161	4	,	,	PUNCT
cana-3894	161	5	(	(	PUNCT
cana-3894	161	6	3.8	3.8	NUM
cana-3894	161	7	)	)	PUNCT
cana-3894	161	8	{	{	PUNCT
cana-3894	161	9	a−1∏	a−1∏	NOUN
cana-3894	161	10	u=0	u=0	INTJ
cana-3894	161	11	a−1∏	a−1∏	NOUN
cana-3894	161	12	v=0	v=0	PUNCT
cana-3894	162	1	[	[	X
cana-3894	162	2	θi	θi	ADP
cana-3894	162	3	+	+	CCONJ
cana-3894	162	4	c−uqi−(b+vi)/a	c−uqi−(b+vi)/a	ADJ
cana-3894	162	5	−	−	NOUN
cana-3894	162	6	i]m	i]m	ADJ
cana-3894	162	7	}	}	PUNCT
cana-3894	162	8	{	{	PUNCT
cana-3894	162	9	a−1∏	a−1∏	NOUN
cana-3894	162	10	u=0	u=0	PROPN
cana-3894	162	11	a−1∏	a−1∏	NOUN
cana-3894	162	12	v=0	v=0	X
cana-3894	163	1	[	[	X
cana-3894	163	2	c−uqi−(b+vi)/a]m	c−uqi−(b+vi)/a]m	NOUN
cana-3894	163	3	}	}	PUNCT
cana-3894	163	4	−1	−1	NOUN
cana-3894	163	5	=	=	SYM
cana-3894	163	6	φ(a	φ(a	ADJ
cana-3894	163	7	,	,	PUNCT
cana-3894	163	8	b	b	NOUN
cana-3894	163	9	,	,	PUNCT
cana-3894	163	10	c;m	c;m	NUM
cana-3894	163	11	)	)	PUNCT
cana-3894	163	12	u	u	NOUN
cana-3894	163	13	,	,	PUNCT
cana-3894	163	14	v	v	X
cana-3894	163	15	(	(	PUNCT
cana-3894	163	16	3.9	3.9	NUM
cana-3894	163	17	)	)	PUNCT
cana-3894	163	18	and	and	CCONJ
cana-3894	163	19	{	{	PUNCT
cana-3894	163	20	a−1∏	a−1∏	NOUN
cana-3894	163	21	u=0	u=0	PROPN
cana-3894	163	22	a−1∏	a−1∏	NOUN
cana-3894	163	23	v=0	v=0	PUNCT
cana-3894	163	24	[	[	X
cana-3894	163	25	θi	θi	ADP
cana-3894	163	26	+	+	CCONJ
cana-3894	163	27	c−uq(b+vi)/a	c−uq(b+vi)/a	PROPN
cana-3894	163	28	−	−	PROPN
cana-3894	163	29	i]m	i]m	ADJ
cana-3894	163	30	}	}	PUNCT
cana-3894	163	31	{	{	PUNCT
cana-3894	163	32	a−1∏	a−1∏	NOUN
cana-3894	163	33	u=0	u=0	PROPN
cana-3894	163	34	a−1∏	a−1∏	NOUN
cana-3894	163	35	v=0	v=0	X
cana-3894	164	1	[	[	X
cana-3894	164	2	c−uq−(b+vi)/a]m	c−uq−(b+vi)/a]m	NOUN
cana-3894	164	3	}	}	PUNCT
cana-3894	164	4	−1	−1	NOUN
cana-3894	164	5	=	=	SYM
cana-3894	164	6	ψ(a	ψ(a	PROPN
cana-3894	164	7	,	,	PUNCT
cana-3894	164	8	b	b	NOUN
cana-3894	164	9	,	,	PUNCT
cana-3894	164	10	c;m	c;m	NUM
cana-3894	164	11	)	)	PUNCT
cana-3894	164	12	u	u	NOUN
cana-3894	164	13	,	,	PUNCT
cana-3894	164	14	v	v	NOUN
cana-3894	164	15	.	.	PUNCT
cana-3894	165	1	(	(	PUNCT
cana-3894	165	2	3.10	3.10	NUM
cana-3894	165	3	)	)	PUNCT
cana-3894	165	4	https://internationalpubls.com	https://internationalpubls.com	X
cana-3894	165	5	338	338	NUM
cana-3894	165	6	communications	communication	NOUN
cana-3894	165	7	on	on	ADP
cana-3894	165	8	applied	apply	VERB
cana-3894	165	9	nonlinear	nonlinear	ADJ
cana-3894	165	10	analysis	analysis	NOUN
cana-3894	165	11	issn	issn	NOUN
cana-3894	165	12	:	:	PUNCT
cana-3894	165	13	1074	1074	NUM
cana-3894	165	14	-	-	PUNCT
cana-3894	165	15	133x	133x	NUM
cana-3894	165	16	vol	vol	NOUN
cana-3894	165	17	32	32	NUM
cana-3894	165	18	no	no	NOUN
cana-3894	165	19	.	.	PUNCT
cana-3894	166	1	9s(2025	9s(2025	NUM
cana-3894	166	2	)	)	PUNCT
cana-3894	166	3	in	in	ADP
cana-3894	166	4	these	these	DET
cana-3894	166	5	notations	notation	NOUN
cana-3894	166	6	,	,	PUNCT
cana-3894	166	7	the	the	DET
cana-3894	166	8	q	q	ADJ
cana-3894	166	9	-	-	PUNCT
cana-3894	166	10	difference	difference	NOUN
cana-3894	166	11	equation	equation	NOUN
cana-3894	166	12	satisfied	satisfy	VERB
cana-3894	166	13	by	by	ADP
cana-3894	166	14	(	(	PUNCT
cana-3894	166	15	2.13	2.13	NUM
cana-3894	166	16	)	)	PUNCT
cana-3894	166	17	is	be	AUX
cana-3894	166	18	derived	derive	VERB
cana-3894	166	19	in	in	ADP
cana-3894	166	20	the	the	DET
cana-3894	166	21	following	follow	VERB
cana-3894	166	22	theorem	theorem	PROPN
cana-3894	166	23	.	.	PUNCT
cana-3894	166	24	theorem	theorem	NOUN
cana-3894	166	25	3.5	3.5	NUM
cana-3894	166	26	.	.	PUNCT
cana-3894	167	1	let	let	VERB
cana-3894	167	2	α	α	PRON
cana-3894	167	3	,	,	PUNCT
cana-3894	167	4	µ	µ	NUM
cana-3894	167	5	,	,	PUNCT
cana-3894	167	6	δ	δ	PROPN
cana-3894	167	7	∈	∈	PROPN
cana-3894	167	8	n	n	CCONJ
cana-3894	167	9	,	,	PUNCT
cana-3894	167	10	then	then	ADV
cana-3894	167	11	ea	ea	NUM
cana-3894	167	12	,	,	PUNCT
cana-3894	167	13	b	b	PROPN
cana-3894	167	14	,	,	PUNCT
cana-3894	167	15	c	c	PROPN
cana-3894	167	16	αi	αi	PROPN
cana-3894	167	17	,	,	PUNCT
cana-3894	167	18	δi	δi	ADV
cana-3894	167	19	,	,	PUNCT
cana-3894	167	20	µi(λz	µi(λz	PROPN
cana-3894	167	21	;	;	PUNCT
cana-3894	167	22	s	s	X
cana-3894	167	23	,	,	PUNCT
cana-3894	167	24	r|q	r|q	ADJ
cana-3894	167	25	)	)	PUNCT
cana-3894	167	26	satisfies	satisfy	VERB
cana-3894	167	27	the	the	DET
cana-3894	167	28	equation	equation	NOUN
cana-3894	167	29	[	[	PUNCT
cana-3894	167	30	φ	φ	PROPN
cana-3894	167	31	(	(	PUNCT
cana-3894	167	32	µ,c	µ,c	NOUN
cana-3894	167	33	,	,	PUNCT
cana-3894	167	34	η;r	η;r	PROPN
cana-3894	167	35	)	)	PUNCT
cana-3894	167	36	ℓ,k	ℓ,k	X
cana-3894	167	37	φ	φ	X
cana-3894	167	38	(	(	PUNCT
cana-3894	167	39	α	α	PROPN
cana-3894	167	40	,	,	PUNCT
cana-3894	167	41	b	b	NOUN
cana-3894	167	42	,	,	PUNCT
cana-3894	167	43	σ;1	σ;1	PROPN
cana-3894	167	44	)	)	PUNCT
cana-3894	167	45	h	h	NOUN
cana-3894	167	46	,	,	PUNCT
cana-3894	167	47	m	m	VERB
cana-3894	167	48	θ	θ	NOUN
cana-3894	167	49	]	]	PUNCT
cana-3894	168	1	ea	ea	NUM
cana-3894	168	2	,	,	PUNCT
cana-3894	168	3	b	b	PROPN
cana-3894	168	4	,	,	PUNCT
cana-3894	168	5	c	c	PROPN
cana-3894	168	6	αi	αi	PROPN
cana-3894	168	7	,	,	PUNCT
cana-3894	168	8	δi	δi	ADV
cana-3894	168	9	,	,	PUNCT
cana-3894	168	10	µi(λz	µi(λz	PROPN
cana-3894	168	11	;	;	PUNCT
cana-3894	168	12	s	s	X
cana-3894	168	13	,	,	PUNCT
cana-3894	168	14	r|q	r|q	ADJ
cana-3894	168	15	)	)	PUNCT
cana-3894	168	16	−	−	PROPN
cana-3894	169	1	[	[	PUNCT
cana-3894	169	2	(	(	PUNCT
cana-3894	169	3	−1)p	−1)p	PROPN
cana-3894	169	4	z	z	PROPN
cana-3894	169	5	ψ	ψ	PROPN
cana-3894	169	6	(	(	PUNCT
cana-3894	169	7	δ	δ	PROPN
cana-3894	169	8	,	,	PUNCT
cana-3894	169	9	a	a	PRON
cana-3894	169	10	,	,	PUNCT
cana-3894	169	11	ζ;s	ζ;s	NOUN
cana-3894	169	12	)	)	PUNCT
cana-3894	169	13	j	j	PROPN
cana-3894	169	14	,	,	PUNCT
cana-3894	169	15	i	i	PRON
cana-3894	169	16	]	]	PUNCT
cana-3894	169	17	ea	ea	NUM
cana-3894	169	18	,	,	PUNCT
cana-3894	169	19	b	b	PROPN
cana-3894	169	20	,	,	PUNCT
cana-3894	169	21	c	c	PROPN
cana-3894	169	22	αi	αi	PROPN
cana-3894	169	23	,	,	PUNCT
cana-3894	169	24	δi	δi	ADV
cana-3894	169	25	,	,	PUNCT
cana-3894	169	26	µi(λzq	µi(λzq	VERB
cana-3894	169	27	p	p	X
cana-3894	169	28	;	;	PUNCT
cana-3894	169	29	s	s	X
cana-3894	169	30	,	,	PUNCT
cana-3894	169	31	r|q	r|q	ADJ
cana-3894	169	32	)	)	PUNCT
cana-3894	170	1	=	=	SYM
cana-3894	170	2	0	0	NUM
cana-3894	170	3	(	(	PUNCT
cana-3894	170	4	3.11	3.11	NUM
cana-3894	170	5	)	)	PUNCT
cana-3894	170	6	in	in	ADP
cana-3894	170	7	which	which	PRON
cana-3894	170	8	ζ	ζ	NOUN
cana-3894	170	9	is	be	AUX
cana-3894	170	10	δth	δth	NOUN
cana-3894	170	11	root	root	NOUN
cana-3894	170	12	of	of	ADP
cana-3894	170	13	unity	unity	NOUN
cana-3894	170	14	,	,	PUNCT
cana-3894	170	15	η	η	PROPN
cana-3894	170	16	is	be	AUX
cana-3894	170	17	µth	µth	VERB
cana-3894	170	18	root	root	NOUN
cana-3894	170	19	of	of	ADP
cana-3894	170	20	unity	unity	NOUN
cana-3894	170	21	,	,	PUNCT
cana-3894	170	22	σ	σ	PROPN
cana-3894	170	23	is	be	AUX
cana-3894	170	24	αth	αth	NUM
cana-3894	170	25	root	root	NOUN
cana-3894	170	26	of	of	ADP
cana-3894	170	27	unity	unity	NOUN
cana-3894	170	28	.	.	PUNCT
cana-3894	171	1	proof	proof	NOUN
cana-3894	171	2	.	.	PUNCT
cana-3894	172	1	in	in	ADP
cana-3894	172	2	the	the	DET
cana-3894	172	3	first	first	ADJ
cana-3894	172	4	place	place	NOUN
cana-3894	172	5	,	,	PUNCT
cana-3894	172	6	the	the	DET
cana-3894	172	7	coefficient	coefficient	NOUN
cana-3894	172	8	of	of	ADP
cana-3894	172	9	zn	zn	PROPN
cana-3894	172	10	in	in	ADP
cana-3894	172	11	the	the	DET
cana-3894	172	12	series	series	NOUN
cana-3894	172	13	representation	representation	PROPN
cana-3894	172	14	ofea	ofea	PROPN
cana-3894	172	15	,	,	PUNCT
cana-3894	172	16	b	b	PROPN
cana-3894	172	17	,	,	PUNCT
cana-3894	172	18	c	c	PROPN
cana-3894	172	19	αi	αi	PROPN
cana-3894	172	20	,	,	PUNCT
cana-3894	172	21	δi	δi	ADV
cana-3894	172	22	,	,	PUNCT
cana-3894	172	23	µi(λz	µi(λz	PROPN
cana-3894	172	24	;	;	PUNCT
cana-3894	172	25	s	s	X
cana-3894	172	26	,	,	PUNCT
cana-3894	172	27	r|q	r|q	ADJ
cana-3894	172	28	)	)	PUNCT
cana-3894	172	29	will	will	AUX
cana-3894	172	30	be	be	AUX
cana-3894	172	31	expressed	express	VERB
cana-3894	172	32	in	in	ADP
cana-3894	172	33	q	q	ADJ
cana-3894	172	34	-	-	PUNCT
cana-3894	172	35	factorial	factorial	ADJ
cana-3894	172	36	notation	notation	NOUN
cana-3894	172	37	with	with	ADP
cana-3894	172	38	the	the	DET
cana-3894	172	39	help	help	NOUN
cana-3894	172	40	of	of	ADP
cana-3894	172	41	the	the	DET
cana-3894	172	42	set	set	NOUN
cana-3894	172	43	of	of	ADP
cana-3894	172	44	formulas	formula	NOUN
cana-3894	172	45	[	[	X
cana-3894	172	46	2	2	NUM
cana-3894	172	47	,	,	PUNCT
cana-3894	172	48	appendix	appendix	VERB
cana-3894	172	49	i	i	PRON
cana-3894	172	50	]	]	X
cana-3894	172	51	:	:	PUNCT
cana-3894	172	52	(	(	PUNCT
cana-3894	172	53	a	a	X
cana-3894	172	54	;	;	PUNCT
cana-3894	172	55	q)kn	q)kn	PROPN
cana-3894	172	56	=	=	SYM
cana-3894	172	57	(	(	PUNCT
cana-3894	172	58	a	a	DET
cana-3894	172	59	,	,	PUNCT
cana-3894	172	60	aq	aq	ADP
cana-3894	172	61	,	,	PUNCT
cana-3894	172	62	.	.	PUNCT
cana-3894	172	63	.	.	PUNCT
cana-3894	173	1	.	.	PUNCT
cana-3894	174	1	,	,	PUNCT
cana-3894	174	2	aqk−1	aqk−1	PROPN
cana-3894	174	3	;	;	PUNCT
cana-3894	174	4	qk)n	qk)n	X
cana-3894	174	5	,	,	PUNCT
cana-3894	174	6	(	(	PUNCT
cana-3894	174	7	ak	ak	PROPN
cana-3894	174	8	;	;	PUNCT
cana-3894	174	9	qk)n	qk)n	PROPN
cana-3894	174	10	=	=	SYM
cana-3894	174	11	(	(	PUNCT
cana-3894	174	12	a	a	PRON
cana-3894	174	13	,	,	PUNCT
cana-3894	174	14	aωk	aωk	NOUN
cana-3894	174	15	,	,	PUNCT
cana-3894	174	16	.	.	PUNCT
cana-3894	174	17	.	.	PUNCT
cana-3894	175	1	.	.	PUNCT
cana-3894	176	1	,	,	PUNCT
cana-3894	176	2	aω	aω	INTJ
cana-3894	176	3	k−1	k−1	PROPN
cana-3894	176	4	k	k	PROPN
cana-3894	176	5	;	;	PUNCT
cana-3894	176	6	qk)n	qk)n	PROPN
cana-3894	176	7	;	;	PUNCT
cana-3894	176	8	ωk	ωk	ADP
cana-3894	176	9	=	=	PROPN
cana-3894	176	10	e(2πi)/k	e(2πi)/k	PROPN
cana-3894	176	11	,	,	PUNCT
cana-3894	176	12	(	(	PUNCT
cana-3894	176	13	a	a	X
cana-3894	176	14	;	;	PUNCT
cana-3894	176	15	qn)νk	qn)νk	SYM
cana-3894	176	16	=	=	SYM
cana-3894	176	17	(	(	PUNCT
cana-3894	176	18	a1	a1	PROPN
cana-3894	176	19	/	/	SYM
cana-3894	176	20	n	n	CCONJ
cana-3894	176	21	;	;	PUNCT
cana-3894	176	22	q)νk	q)νk	PROPN
cana-3894	176	23	(	(	PUNCT
cana-3894	176	24	a	a	DET
cana-3894	176	25	1	1	NUM
cana-3894	176	26	/	/	SYM
cana-3894	176	27	nω	nω	NOUN
cana-3894	176	28	;	;	PUNCT
cana-3894	176	29	q)νk	q)νk	PROPN
cana-3894	176	30	.	.	PUNCT
cana-3894	176	31	.	.	PUNCT
cana-3894	176	32	.	.	PUNCT
cana-3894	177	1	(	(	PUNCT
cana-3894	177	2	a	a	DET
cana-3894	177	3	1	1	NUM
cana-3894	177	4	/	/	SYM
cana-3894	177	5	nωn−1	nωn−1	PROPN
cana-3894	177	6	;	;	PUNCT
cana-3894	177	7	q)νk	q)νk	PROPN
cana-3894	177	8	,	,	PUNCT
cana-3894	177	9	ωn	ωn	NOUN
cana-3894	177	10	=	=	SYM
cana-3894	177	11	1	1	NUM
cana-3894	177	12	,	,	PUNCT
cana-3894	177	13	and	and	CCONJ
cana-3894	177	14	(	(	PUNCT
cana-3894	177	15	qa	qa	INTJ
cana-3894	177	16	;	;	PUNCT
cana-3894	177	17	qδ)n	qδ)n	PROPN
cana-3894	177	18	=	=	SYM
cana-3894	177	19	(	(	PUNCT
cana-3894	177	20	qa	qa	PROPN
cana-3894	177	21	/	/	SYM
cana-3894	177	22	δ	δ	PROPN
cana-3894	177	23	;	;	PUNCT
cana-3894	177	24	q)n	q)n	X
cana-3894	177	25	(	(	PUNCT
cana-3894	177	26	ϖqa	ϖqa	PROPN
cana-3894	177	27	/	/	SYM
cana-3894	177	28	δ	δ	PROPN
cana-3894	177	29	;	;	PUNCT
cana-3894	177	30	q)n	q)n	PUNCT
cana-3894	177	31	.	.	PUNCT
cana-3894	177	32	.	.	PUNCT
cana-3894	177	33	.	.	PUNCT
cana-3894	178	1	(	(	PUNCT
cana-3894	178	2	ϖ	ϖ	NOUN
cana-3894	178	3	δ−1qa	δ−1qa	PROPN
cana-3894	178	4	/	/	SYM
cana-3894	178	5	δ	δ	PROPN
cana-3894	178	6	;	;	PUNCT
cana-3894	178	7	q)n	q)n	SYM
cana-3894	178	8	=	=	PUNCT
cana-3894	178	9	δ−1∏	δ−1∏	PROPN
cana-3894	178	10	i=0	i=0	PROPN
cana-3894	178	11	(	(	PUNCT
cana-3894	178	12	ϖiqa	ϖiqa	PROPN
cana-3894	178	13	/	/	SYM
cana-3894	178	14	δ	δ	PROPN
cana-3894	178	15	;	;	PUNCT
cana-3894	178	16	q)n	q)n	X
cana-3894	178	17	,	,	PUNCT
cana-3894	178	18	ϖδ	ϖδ	PRON
cana-3894	178	19	=	=	SYM
cana-3894	179	1	1	1	X
cana-3894	179	2	.	.	PUNCT
cana-3894	179	3	then	then	ADV
cana-3894	179	4	following	follow	VERB
cana-3894	179	5	the	the	DET
cana-3894	179	6	notation	notation	NOUN
cana-3894	179	7	used	use	VERB
cana-3894	179	8	in	in	ADP
cana-3894	179	9	(	(	PUNCT
cana-3894	179	10	3.1	3.1	NUM
cana-3894	179	11	)	)	PUNCT
cana-3894	179	12	for	for	ADP
cana-3894	179	13	the	the	DET
cana-3894	179	14	coefficient	coefficient	NOUN
cana-3894	179	15	of	of	ADP
cana-3894	179	16	zn	zn	PROPN
cana-3894	179	17	,	,	PUNCT
cana-3894	179	18	we	we	PRON
cana-3894	179	19	get	get	VERB
cana-3894	179	20	vn	vn	NOUN
cana-3894	179	21	=	=	PUNCT
cana-3894	179	22	(	(	PUNCT
cana-3894	179	23	−1)pn	−1)pn	PROPN
cana-3894	179	24	qpn(n−1)/2	qpn(n−1)/2	PROPN
cana-3894	179	25	[	[	X
cana-3894	179	26	(	(	PUNCT
cana-3894	179	27	qa	qa	PROPN
cana-3894	180	1	;	;	PUNCT
cana-3894	180	2	q)δn	q)δn	PROPN
cana-3894	180	3	]	]	PUNCT
cana-3894	180	4	s[(qc	s[(qc	ADV
cana-3894	180	5	;	;	PUNCT
cana-3894	180	6	q)µn	q)µn	PROPN
cana-3894	180	7	]	]	X
cana-3894	180	8	−r	−r	PROPN
cana-3894	180	9	[	[	X
cana-3894	180	10	(	(	PUNCT
cana-3894	180	11	qb	qb	PROPN
cana-3894	180	12	;	;	PUNCT
cana-3894	180	13	q)αn	q)αn	PROPN
cana-3894	180	14	]	]	X
cana-3894	180	15	−1	−1	NOUN
cana-3894	180	16	1	1	NUM
cana-3894	180	17	(	(	PUNCT
cana-3894	180	18	q	q	NOUN
cana-3894	180	19	;	;	PUNCT
cana-3894	180	20	q)n	q)n	SYM
cana-3894	180	21	=	=	SYM
cana-3894	180	22	(	(	PUNCT
cana-3894	180	23	−1)pn	−1)pn	PROPN
cana-3894	180	24	qpn(n−1)/2	qpn(n−1)/2	PROPN
cana-3894	181	1	[	[	X
cana-3894	181	2	(	(	PUNCT
cana-3894	181	3	qa	qa	INTJ
cana-3894	181	4	;	;	PUNCT
cana-3894	181	5	qδ)n	qδ)n	PROPN
cana-3894	181	6	]	]	X
cana-3894	181	7	s	s	X
cana-3894	182	1	[	[	X
cana-3894	182	2	(	(	PUNCT
cana-3894	182	3	qa+i	qa+i	ADV
cana-3894	182	4	;	;	PUNCT
cana-3894	182	5	qδ)n	qδ)n	PROPN
cana-3894	182	6	]	]	X
cana-3894	182	7	s	s	X
cana-3894	182	8	·	·	PUNCT
cana-3894	182	9	·	·	PUNCT
cana-3894	182	10	·	·	PUNCT
cana-3894	183	1	[	[	X
cana-3894	183	2	(	(	PUNCT
cana-3894	183	3	qa+δi−i	qa+δi−i	NOUN
cana-3894	183	4	;	;	PUNCT
cana-3894	183	5	qδ)n	qδ)n	PROPN
cana-3894	183	6	]	]	X
cana-3894	183	7	s	s	VERB
cana-3894	183	8	×[(qc	×[(qc	X
cana-3894	183	9	;	;	PUNCT
cana-3894	183	10	qµ)n	qµ)n	X
cana-3894	183	11	]	]	PUNCT
cana-3894	183	12	−r	−r	PROPN
cana-3894	183	13	[	[	X
cana-3894	183	14	(	(	PUNCT
cana-3894	183	15	qc+i	qc+i	PROPN
cana-3894	183	16	;	;	PUNCT
cana-3894	183	17	qµ)n	qµ)n	X
cana-3894	183	18	]	]	PUNCT
cana-3894	183	19	−r	−r	PROPN
cana-3894	183	20	·	·	PUNCT
cana-3894	183	21	·	·	PUNCT
cana-3894	183	22	·	·	PUNCT
cana-3894	184	1	[	[	X
cana-3894	184	2	(	(	PUNCT
cana-3894	184	3	qc+µi−i	qc+µi−i	X
cana-3894	184	4	;	;	PUNCT
cana-3894	184	5	qµ)n	qµ)n	X
cana-3894	184	6	]	]	PUNCT
cana-3894	184	7	−r	−r	PROPN
cana-3894	184	8	×[(qb	×[(qb	PROPN
cana-3894	184	9	;	;	PUNCT
cana-3894	184	10	qα)n	qα)n	X
cana-3894	184	11	]	]	PUNCT
cana-3894	184	12	−1	−1	NOUN
cana-3894	184	13	[	[	X
cana-3894	184	14	(	(	PUNCT
cana-3894	184	15	qb+i	qb+i	X
cana-3894	184	16	;	;	PUNCT
cana-3894	184	17	qα)n	qα)n	X
cana-3894	184	18	]	]	PUNCT
cana-3894	184	19	−1	−1	NOUN
cana-3894	184	20	·	·	PUNCT
cana-3894	184	21	·	·	PUNCT
cana-3894	184	22	·	·	PUNCT
cana-3894	185	1	[	[	X
cana-3894	185	2	(	(	PUNCT
cana-3894	185	3	qb+αi−i	qb+αi−i	NOUN
cana-3894	185	4	;	;	PUNCT
cana-3894	185	5	qα)n	qα)n	X
cana-3894	185	6	]	]	PUNCT
cana-3894	185	7	−1	−1	NOUN
cana-3894	185	8	1	1	NUM
cana-3894	185	9	(	(	PUNCT
cana-3894	185	10	q	q	NOUN
cana-3894	185	11	;	;	PUNCT
cana-3894	185	12	q)n	q)n	SYM
cana-3894	185	13	=	=	SYM
cana-3894	185	14	(	(	PUNCT
cana-3894	185	15	−1)pn	−1)pn	PROPN
cana-3894	185	16	qpn(n−1)/2	qpn(n−1)/2	PROPN
cana-3894	185	17	{	{	PUNCT
cana-3894	185	18	δ−1∏	δ−1∏	VERB
cana-3894	185	19	j=0	j=0	VERB
cana-3894	185	20	δ−1∏	δ−1∏	VERB
cana-3894	185	21	i=0	i=0	PROPN
cana-3894	185	22	[	[	X
cana-3894	185	23	(	(	PUNCT
cana-3894	185	24	ζj	ζj	PROPN
cana-3894	185	25	q(a+ii)/δ	q(a+ii)/δ	PROPN
cana-3894	185	26	;	;	PUNCT
cana-3894	185	27	q)n	q)n	X
cana-3894	185	28	]	]	X
cana-3894	185	29	s	s	PART
cana-3894	185	30	}	}	PUNCT
cana-3894	185	31	×	×	NOUN
cana-3894	185	32	{	{	PUNCT
cana-3894	185	33	µ−1∏	µ−1∏	PROPN
cana-3894	185	34	ℓ=0	ℓ=0	PROPN
cana-3894	185	35	µ−1∏	µ−1∏	ADP
cana-3894	185	36	k=0	k=0	PROPN
cana-3894	186	1	[	[	X
cana-3894	186	2	(	(	PUNCT
cana-3894	186	3	ηℓ	ηℓ	INTJ
cana-3894	186	4	q(c+ki)/µ	q(c+ki)/µ	NOUN
cana-3894	186	5	;	;	PUNCT
cana-3894	186	6	q)n	q)n	X
cana-3894	186	7	]	]	PUNCT
cana-3894	186	8	−r	−r	ADJ
cana-3894	186	9	}	}	PUNCT
cana-3894	186	10	×	×	NOUN
cana-3894	186	11	{	{	PUNCT
cana-3894	186	12	α−1∏	α−1∏	PROPN
cana-3894	186	13	h=0	h=0	PROPN
cana-3894	186	14	α−1∏	α−1∏	PROPN
cana-3894	186	15	m=0	m=0	PROPN
cana-3894	186	16	[	[	X
cana-3894	186	17	(	(	PUNCT
cana-3894	186	18	σh	σh	ADP
cana-3894	186	19	q(b+mi)/α	q(b+mi)/α	NOUN
cana-3894	186	20	;	;	PUNCT
cana-3894	186	21	q)n	q)n	X
cana-3894	186	22	]	]	X
cana-3894	186	23	−1	−1	NOUN
cana-3894	186	24	}	}	PUNCT
cana-3894	186	25	1	1	NUM
cana-3894	186	26	(	(	PUNCT
cana-3894	186	27	q	q	NOUN
cana-3894	186	28	;	;	PUNCT
cana-3894	186	29	q)n	q)n	X
cana-3894	186	30	,	,	PUNCT
cana-3894	186	31	(	(	PUNCT
cana-3894	186	32	3.12	3.12	NUM
cana-3894	186	33	)	)	PUNCT
cana-3894	186	34	where	where	SCONJ
cana-3894	186	35	ζ	ζ	NOUN
cana-3894	186	36	is	be	AUX
cana-3894	186	37	δth	δth	NOUN
cana-3894	186	38	root	root	NOUN
cana-3894	186	39	of	of	ADP
cana-3894	186	40	unity	unity	NOUN
cana-3894	186	41	,	,	PUNCT
cana-3894	186	42	η	η	PROPN
cana-3894	186	43	is	be	AUX
cana-3894	186	44	µth	µth	VERB
cana-3894	186	45	root	root	NOUN
cana-3894	186	46	of	of	ADP
cana-3894	186	47	unity	unity	NOUN
cana-3894	186	48	,	,	PUNCT
cana-3894	186	49	σ	σ	PROPN
cana-3894	186	50	is	be	AUX
cana-3894	186	51	αth	αth	NUM
cana-3894	186	52	root	root	NOUN
cana-3894	186	53	of	of	ADP
cana-3894	186	54	unity	unity	NOUN
cana-3894	186	55	.	.	PUNCT
cana-3894	187	1	now	now	ADV
cana-3894	187	2	take	take	VERB
cana-3894	187	3	δ−1∏	δ−1∏	ADJ
cana-3894	187	4	j=0	j=0	VERB
cana-3894	187	5	δ−1∏	δ−1∏	VERB
cana-3894	187	6	i=0	i=0	PROPN
cana-3894	188	1	[	[	X
cana-3894	188	2	(	(	PUNCT
cana-3894	188	3	ζj	ζj	PROPN
cana-3894	188	4	q(a+ii)/δ	q(a+ii)/δ	PROPN
cana-3894	188	5	;	;	PUNCT
cana-3894	188	6	q)n	q)n	X
cana-3894	188	7	]	]	X
cana-3894	188	8	s	s	X
cana-3894	188	9	=	=	X
cana-3894	188	10	an	an	PRON
cana-3894	188	11	,	,	PUNCT
cana-3894	188	12	µ−1∏	µ−1∏	PROPN
cana-3894	188	13	ℓ=0	ℓ=0	PROPN
cana-3894	188	14	µ−1∏	µ−1∏	ADP
cana-3894	188	15	k=0	k=0	PROPN
cana-3894	189	1	[	[	X
cana-3894	189	2	(	(	PUNCT
cana-3894	189	3	ηℓ	ηℓ	INTJ
cana-3894	189	4	q(c+ki)/µ	q(c+ki)/µ	NOUN
cana-3894	189	5	;	;	PUNCT
cana-3894	189	6	q)n	q)n	X
cana-3894	189	7	]	]	X
cana-3894	189	8	r	r	NOUN
cana-3894	189	9	=	=	SYM
cana-3894	189	10	bn	bn	NOUN
cana-3894	189	11	,	,	PUNCT
cana-3894	189	12	(	(	PUNCT
cana-3894	189	13	3.13	3.13	NUM
cana-3894	189	14	)	)	PUNCT
cana-3894	189	15	and	and	CCONJ
cana-3894	189	16	α−1∏	α−1∏	PROPN
cana-3894	189	17	h=0	h=0	PROPN
cana-3894	189	18	α−1∏	α−1∏	PROPN
cana-3894	189	19	m=0	m=0	PROPN
cana-3894	189	20	(	(	PUNCT
cana-3894	189	21	σh	σh	PROPN
cana-3894	189	22	q(b+mi)/α	q(b+mi)/α	NOUN
cana-3894	189	23	;	;	PUNCT
cana-3894	189	24	q)n	q)n	SYM
cana-3894	189	25	=	=	SYM
cana-3894	189	26	cn	cn	PROPN
cana-3894	189	27	,	,	PUNCT
cana-3894	189	28	(	(	PUNCT
cana-3894	189	29	−1)pn	−1)pn	NOUN
cana-3894	189	30	qpn(n−1)/2	qpn(n−1)/2	PROPN
cana-3894	189	31	=	=	PRON
cana-3894	189	32	dn	dn	NOUN
cana-3894	189	33	(	(	PUNCT
cana-3894	189	34	3.14	3.14	NUM
cana-3894	189	35	)	)	PUNCT
cana-3894	189	36	https://internationalpubls.com	https://internationalpubls.com	X
cana-3894	189	37	339	339	NUM
cana-3894	189	38	communications	communication	NOUN
cana-3894	189	39	on	on	ADP
cana-3894	189	40	applied	apply	VERB
cana-3894	189	41	nonlinear	nonlinear	ADJ
cana-3894	189	42	analysis	analysis	NOUN
cana-3894	189	43	issn	issn	NOUN
cana-3894	189	44	:	:	PUNCT
cana-3894	189	45	1074	1074	NUM
cana-3894	189	46	-	-	PUNCT
cana-3894	189	47	133x	133x	NUM
cana-3894	189	48	vol	vol	NOUN
cana-3894	189	49	32	32	NUM
cana-3894	189	50	no	no	NOUN
cana-3894	189	51	.	.	PUNCT
cana-3894	190	1	9s(2025	9s(2025	NUM
cana-3894	190	2	)	)	PUNCT
cana-3894	191	1	then	then	ADV
cana-3894	191	2	∞∑	∞∑	NUM
cana-3894	191	3	n=0	n=0	NUM
cana-3894	191	4	vn	vn	X
cana-3894	191	5	zn	zn	NOUN
cana-3894	191	6	=	=	PUNCT
cana-3894	192	1	∞∑	∞∑	PROPN
cana-3894	192	2	n=0	n=0	NUM
cana-3894	192	3	an	an	DET
cana-3894	192	4	dn	dn	NOUN
cana-3894	192	5	b−1	b−1	PROPN
cana-3894	192	6	n	n	CCONJ
cana-3894	192	7	c−1	c−1	PROPN
cana-3894	192	8	n	n	PROPN
cana-3894	192	9	zn	zn	PROPN
cana-3894	192	10	(	(	PUNCT
cana-3894	192	11	q	q	NOUN
cana-3894	192	12	;	;	PUNCT
cana-3894	192	13	q)n	q)n	SYM
cana-3894	192	14	=	=	SYM
cana-3894	192	15	w	w	X
cana-3894	192	16	,	,	PUNCT
cana-3894	192	17	say	say	INTJ
cana-3894	192	18	.	.	PUNCT
cana-3894	193	1	since	since	SCONJ
cana-3894	193	2	the	the	DET
cana-3894	193	3	series	series	NOUN
cana-3894	193	4	in	in	ADP
cana-3894	193	5	(	(	PUNCT
cana-3894	193	6	2.13	2.13	NUM
cana-3894	193	7	)	)	PUNCT
cana-3894	193	8	converges	converge	NOUN
cana-3894	193	9	,	,	PUNCT
cana-3894	193	10	we	we	PRON
cana-3894	193	11	have	have	VERB
cana-3894	193	12	θw	θw	VERB
cana-3894	193	13	=	=	PRON
cana-3894	193	14	∞∑	∞∑	PROPN
cana-3894	193	15	n=0	n=0	NUM
cana-3894	193	16	an	an	DET
cana-3894	193	17	dn	dn	NOUN
cana-3894	194	1	b−1	b−1	PROPN
cana-3894	194	2	n	n	CCONJ
cana-3894	194	3	c−1	c−1	PROPN
cana-3894	194	4	n	n	PRON
cana-3894	194	5	1	1	NUM
cana-3894	194	6	(	(	PUNCT
cana-3894	194	7	q	q	NOUN
cana-3894	194	8	;	;	PUNCT
cana-3894	194	9	q)n	q)n	X
cana-3894	194	10	θzn	θzn	X
cana-3894	194	11	=	=	X
cana-3894	195	1	∞∑	∞∑	PROPN
cana-3894	195	2	n=0	n=0	NUM
cana-3894	195	3	an	an	DET
cana-3894	195	4	dn	dn	NOUN
cana-3894	195	5	b−1	b−1	PROPN
cana-3894	195	6	n	n	CCONJ
cana-3894	195	7	c−1	c−1	PROPN
cana-3894	195	8	n	n	CCONJ
cana-3894	195	9	1−	1−	NUM
cana-3894	195	10	qn	qn	PROPN
cana-3894	195	11	(	(	PUNCT
cana-3894	195	12	q	q	NOUN
cana-3894	195	13	;	;	PUNCT
cana-3894	195	14	q)n	q)n	X
cana-3894	195	15	zn	zn	X
cana-3894	195	16	=	=	SYM
cana-3894	196	1	∞∑	∞∑	NUM
cana-3894	196	2	n=1	n=1	PROPN
cana-3894	196	3	an	an	DET
cana-3894	196	4	dn	dn	NOUN
cana-3894	196	5	b−1	b−1	PROPN
cana-3894	196	6	n	n	CCONJ
cana-3894	196	7	c−1	c−1	PROPN
cana-3894	196	8	n	n	PROPN
cana-3894	196	9	zn	zn	PROPN
cana-3894	196	10	(	(	PUNCT
cana-3894	196	11	q	q	NOUN
cana-3894	196	12	;	;	PUNCT
cana-3894	196	13	q)n−1	q)n−1	PROPN
cana-3894	196	14	.	.	PUNCT
cana-3894	197	1	next	next	ADJ
cana-3894	197	2	operating	operate	VERB
cana-3894	197	3	by	by	ADP
cana-3894	197	4	φ	φ	PROPN
cana-3894	197	5	(	(	PUNCT
cana-3894	197	6	α	α	PROPN
cana-3894	197	7	,	,	PUNCT
cana-3894	197	8	b	b	NOUN
cana-3894	197	9	,	,	PUNCT
cana-3894	197	10	σ;1	σ;1	PROPN
cana-3894	197	11	)	)	PUNCT
cana-3894	197	12	h	h	NOUN
cana-3894	197	13	,	,	PUNCT
cana-3894	197	14	m	m	VERB
cana-3894	197	15	,	,	PUNCT
cana-3894	197	16	we	we	PRON
cana-3894	197	17	get	get	VERB
cana-3894	197	18	φ	φ	PROPN
cana-3894	197	19	(	(	PUNCT
cana-3894	197	20	α	α	PROPN
cana-3894	197	21	,	,	PUNCT
cana-3894	197	22	b	b	NOUN
cana-3894	197	23	,	,	PUNCT
cana-3894	197	24	σ;1	σ;1	PROPN
cana-3894	197	25	)	)	PUNCT
cana-3894	197	26	h	h	PROPN
cana-3894	197	27	,	,	PUNCT
cana-3894	197	28	m	m	VERB
cana-3894	197	29	θi	θi	ADP
cana-3894	197	30	w	w	PROPN
cana-3894	197	31	=	=	PUNCT
cana-3894	197	32	∞∑	∞∑	PROPN
cana-3894	197	33	n=1	n=1	PROPN
cana-3894	197	34	an	an	DET
cana-3894	197	35	dn	dn	NOUN
cana-3894	197	36	b−1	b−1	PROPN
cana-3894	197	37	n	n	CCONJ
cana-3894	197	38	c−1	c−1	PROPN
cana-3894	197	39	n	n	PRON
cana-3894	197	40	1	1	NUM
cana-3894	197	41	(	(	PUNCT
cana-3894	197	42	q	q	NOUN
cana-3894	197	43	;	;	PUNCT
cana-3894	197	44	q)n−1	q)n−1	PROPN
cana-3894	197	45	×	×	PROPN
cana-3894	197	46	{	{	PUNCT
cana-3894	197	47	α−1∏	α−1∏	PROPN
cana-3894	197	48	h=0	h=0	PROPN
cana-3894	197	49	α−1∏	α−1∏	PROPN
cana-3894	197	50	m=0	m=0	PROPN
cana-3894	197	51	(	(	PUNCT
cana-3894	197	52	θi	θi	ADP
cana-3894	197	53	+	+	ADJ
cana-3894	197	54	σ−hqi−(b+mi)/α	σ−hqi−(b+mi)/α	ADJ
cana-3894	197	55	−	−	PROPN
cana-3894	197	56	i	i	NOUN
cana-3894	197	57	)	)	PUNCT
cana-3894	197	58	}	}	PUNCT
cana-3894	197	59	×	×	NOUN
cana-3894	197	60	{	{	PUNCT
cana-3894	197	61	α−1∏	α−1∏	PROPN
cana-3894	197	62	h=0	h=0	PROPN
cana-3894	197	63	α−1∏	α−1∏	PROPN
cana-3894	197	64	m=0	m=0	PROPN
cana-3894	197	65	(	(	PUNCT
cana-3894	197	66	σ−hqi−(b+mi)/α	σ−hqi−(b+mi)/α	NOUN
cana-3894	197	67	)	)	PUNCT
cana-3894	197	68	}	}	PUNCT
cana-3894	197	69	−1	−1	NOUN
cana-3894	198	1	zn	zn	NOUN
cana-3894	198	2	=	=	PUNCT
cana-3894	199	1	∞∑	∞∑	NUM
cana-3894	199	2	n=1	n=1	PROPN
cana-3894	199	3	an	an	DET
cana-3894	199	4	dn	dn	NOUN
cana-3894	199	5	b−1	b−1	PROPN
cana-3894	199	6	n	n	CCONJ
cana-3894	199	7	c−1	c−1	PROPN
cana-3894	199	8	n	n	PRON
cana-3894	199	9	1	1	NUM
cana-3894	199	10	(	(	PUNCT
cana-3894	199	11	q	q	NOUN
cana-3894	199	12	;	;	PUNCT
cana-3894	199	13	q)n−1	q)n−1	PROPN
cana-3894	199	14	×	×	PROPN
cana-3894	199	15	{	{	PUNCT
cana-3894	199	16	α−1∏	α−1∏	PROPN
cana-3894	199	17	h=0	h=0	PROPN
cana-3894	199	18	α−1∏	α−1∏	PROPN
cana-3894	199	19	m=0	m=0	PROPN
cana-3894	199	20	(	(	PUNCT
cana-3894	199	21	i	i	NOUN
cana-3894	199	22	−	−	PROPN
cana-3894	199	23	σhq(n−1)i+(b+mi)/α	σhq(n−1)i+(b+mi)/α	NOUN
cana-3894	199	24	)	)	PUNCT
cana-3894	199	25	}	}	PUNCT
cana-3894	199	26	×	×	NOUN
cana-3894	199	27	{	{	PUNCT
cana-3894	199	28	α−1∏	α−1∏	PROPN
cana-3894	199	29	h=0	h=0	PROPN
cana-3894	199	30	α−1∏	α−1∏	PROPN
cana-3894	199	31	m=0	m=0	PROPN
cana-3894	199	32	(	(	PUNCT
cana-3894	199	33	σhq(b+mi)/α	σhq(b+mi)/α	NOUN
cana-3894	199	34	)	)	PUNCT
cana-3894	199	35	}	}	PUNCT
cana-3894	199	36	−1	−1	NOUN
cana-3894	199	37	zn	zn	NOUN
cana-3894	199	38	=	=	PUNCT
cana-3894	200	1	∞∑	∞∑	NUM
cana-3894	200	2	n=1	n=1	PROPN
cana-3894	200	3	an	an	DET
cana-3894	200	4	dn	dn	NOUN
cana-3894	200	5	b−1	b−1	PROPN
cana-3894	200	6	n	n	CCONJ
cana-3894	200	7	c−1	c−1	PROPN
cana-3894	200	8	n	n	PRON
cana-3894	200	9	1	1	NUM
cana-3894	200	10	(	(	PUNCT
cana-3894	200	11	q	q	NOUN
cana-3894	200	12	;	;	PUNCT
cana-3894	200	13	q)n−1	q)n−1	PROPN
cana-3894	200	14	cn	cn	PROPN
cana-3894	200	15	c−1	c−1	PROPN
cana-3894	200	16	n−1	n−1	PROPN
cana-3894	200	17	zn	zn	PROPN
cana-3894	200	18	=	=	PUNCT
cana-3894	201	1	∞∑	∞∑	NUM
cana-3894	201	2	n=1	n=1	PROPN
cana-3894	201	3	an	an	DET
cana-3894	201	4	dn	dn	NOUN
cana-3894	201	5	b−1	b−1	PROPN
cana-3894	201	6	n	n	CCONJ
cana-3894	201	7	c−1	c−1	PROPN
cana-3894	201	8	n−1	n−1	PROPN
cana-3894	201	9	zn	zn	PROPN
cana-3894	201	10	(	(	PUNCT
cana-3894	201	11	q	q	NOUN
cana-3894	201	12	;	;	PUNCT
cana-3894	201	13	q)n−1	q)n−1	PROPN
cana-3894	201	14	finally	finally	ADV
cana-3894	201	15	,	,	PUNCT
cana-3894	201	16	φ	φ	PROPN
cana-3894	201	17	(	(	PUNCT
cana-3894	201	18	µ,c	µ,c	NOUN
cana-3894	201	19	,	,	PUNCT
cana-3894	201	20	η;r	η;r	PROPN
cana-3894	201	21	)	)	PUNCT
cana-3894	201	22	ℓ,k	ℓ,k	X
cana-3894	201	23	φ	φ	X
cana-3894	201	24	(	(	PUNCT
cana-3894	201	25	α	α	PROPN
cana-3894	201	26	,	,	PUNCT
cana-3894	201	27	b	b	NOUN
cana-3894	201	28	,	,	PUNCT
cana-3894	201	29	σ;1	σ;1	PROPN
cana-3894	201	30	)	)	PUNCT
cana-3894	201	31	h	h	PROPN
cana-3894	201	32	,	,	PUNCT
cana-3894	201	33	m	m	VERB
cana-3894	201	34	θi	θi	ADP
cana-3894	201	35	w	w	PROPN
cana-3894	201	36	=	=	PUNCT
cana-3894	201	37	∞∑	∞∑	PROPN
cana-3894	201	38	n=1	n=1	PROPN
cana-3894	201	39	an	an	DET
cana-3894	201	40	dn	dn	NOUN
cana-3894	201	41	c−1	c−1	PROPN
cana-3894	201	42	n−1	n−1	PROPN
cana-3894	201	43	b−1	b−1	PROPN
cana-3894	201	44	n	n	CCONJ
cana-3894	201	45	1	1	NUM
cana-3894	201	46	(	(	PUNCT
cana-3894	201	47	q	q	NOUN
cana-3894	201	48	;	;	PUNCT
cana-3894	201	49	q)n−1	q)n−1	PROPN
cana-3894	201	50	{	{	PUNCT
cana-3894	201	51	µ−1∏	µ−1∏	ADP
cana-3894	201	52	l=0	l=0	PROPN
cana-3894	201	53	µ−1∏	µ−1∏	ADP
cana-3894	201	54	k=0	k=0	PROPN
cana-3894	201	55	[	[	X
cana-3894	201	56	(	(	PUNCT
cana-3894	201	57	θi	θi	ADP
cana-3894	201	58	+	+	CCONJ
cana-3894	201	59	η−lqi−(c+ki)/µ	η−lqi−(c+ki)/µ	ADJ
cana-3894	201	60	−	−	PROPN
cana-3894	201	61	i)]r	i)]r	NOUN
cana-3894	201	62	}	}	PUNCT
cana-3894	201	63	×	×	NOUN
cana-3894	201	64	{	{	PUNCT
cana-3894	201	65	µ−1∏	µ−1∏	ADP
cana-3894	201	66	l=0	l=0	PROPN
cana-3894	201	67	µ−1∏	µ−1∏	ADP
cana-3894	201	68	k=0	k=0	PROPN
cana-3894	201	69	[	[	X
cana-3894	201	70	(	(	PUNCT
cana-3894	201	71	η−lqi−(c+ki)/µ)]r	η−lqi−(c+ki)/µ)]r	NOUN
cana-3894	201	72	}	}	PUNCT
cana-3894	201	73	−1	−1	NOUN
cana-3894	201	74	zn	zn	PROPN
cana-3894	201	75	https://internationalpubls.com	https://internationalpubls.com	X
cana-3894	201	76	340	340	NUM
cana-3894	201	77	communications	communication	NOUN
cana-3894	201	78	on	on	ADP
cana-3894	201	79	applied	apply	VERB
cana-3894	201	80	nonlinear	nonlinear	ADJ
cana-3894	201	81	analysis	analysis	NOUN
cana-3894	201	82	issn	issn	NOUN
cana-3894	201	83	:	:	PUNCT
cana-3894	201	84	1074	1074	NUM
cana-3894	201	85	-	-	PUNCT
cana-3894	201	86	133x	133x	NUM
cana-3894	201	87	vol	vol	NOUN
cana-3894	201	88	32	32	NUM
cana-3894	201	89	no	no	NOUN
cana-3894	201	90	.	.	PUNCT
cana-3894	202	1	9s(2025	9s(2025	NUM
cana-3894	202	2	)	)	PUNCT
cana-3894	203	1	=	=	NOUN
cana-3894	204	1	∞∑	∞∑	NUM
cana-3894	204	2	n=1	n=1	ADP
cana-3894	204	3	an	an	DET
cana-3894	204	4	dn	dn	NOUN
cana-3894	204	5	c−1	c−1	PROPN
cana-3894	204	6	n−1	n−1	PROPN
cana-3894	204	7	b−1	b−1	PROPN
cana-3894	204	8	n	n	CCONJ
cana-3894	204	9	1	1	NUM
cana-3894	204	10	(	(	PUNCT
cana-3894	204	11	q	q	NOUN
cana-3894	204	12	;	;	PUNCT
cana-3894	204	13	q)n−1	q)n−1	PROPN
cana-3894	204	14	{	{	PUNCT
cana-3894	204	15	µ−1∏	µ−1∏	ADP
cana-3894	204	16	l=0	l=0	PROPN
cana-3894	204	17	µ−1∏	µ−1∏	ADP
cana-3894	204	18	k=0	k=0	PROPN
cana-3894	205	1	[	[	X
cana-3894	205	2	−qn	−qn	X
cana-3894	205	3	+	+	CCONJ
cana-3894	205	4	η−lqi−(c+ki)/µ)]r	η−lqi−(c+ki)/µ)]r	NOUN
cana-3894	205	5	}	}	PUNCT
cana-3894	205	6	×	×	NOUN
cana-3894	205	7	{	{	PUNCT
cana-3894	205	8	µ−1∏	µ−1∏	ADP
cana-3894	205	9	l=0	l=0	PROPN
cana-3894	205	10	µ−1∏	µ−1∏	ADP
cana-3894	205	11	k=0	k=0	PROPN
cana-3894	206	1	[	[	X
cana-3894	206	2	η−lqi−(c+ki)/µ]r	η−lqi−(c+ki)/µ]r	ADP
cana-3894	206	3	}	}	PUNCT
cana-3894	206	4	−1	−1	NOUN
cana-3894	206	5	zn	zn	NOUN
cana-3894	206	6	=	=	PUNCT
cana-3894	207	1	∞∑	∞∑	NUM
cana-3894	207	2	n=1	n=1	ADP
cana-3894	207	3	an	an	DET
cana-3894	207	4	dn	dn	NOUN
cana-3894	207	5	c−1	c−1	PROPN
cana-3894	207	6	n−1	n−1	PROPN
cana-3894	207	7	b−1	b−1	PROPN
cana-3894	207	8	n	n	CCONJ
cana-3894	207	9	1	1	NUM
cana-3894	207	10	(	(	PUNCT
cana-3894	207	11	q	q	NOUN
cana-3894	207	12	;	;	PUNCT
cana-3894	207	13	q)n−1	q)n−1	PROPN
cana-3894	207	14	bn	bn	INTJ
cana-3894	207	15	b−1	b−1	PROPN
cana-3894	207	16	n−1	n−1	PROPN
cana-3894	207	17	zn	zn	PROPN
cana-3894	207	18	=	=	PUNCT
cana-3894	208	1	∞∑	∞∑	NUM
cana-3894	208	2	n=1	n=1	PROPN
cana-3894	208	3	an	an	DET
cana-3894	208	4	dn	dn	PROPN
cana-3894	208	5	b−1	b−1	PROPN
cana-3894	208	6	n−1	n−1	PROPN
cana-3894	208	7	c−1	c−1	PROPN
cana-3894	208	8	n−1	n−1	PROPN
cana-3894	208	9	zn	zn	PROPN
cana-3894	208	10	(	(	PUNCT
cana-3894	208	11	q	q	NOUN
cana-3894	208	12	;	;	PUNCT
cana-3894	208	13	q)n−1	q)n−1	PROPN
cana-3894	208	14	thus	thus	ADV
cana-3894	208	15	,	,	PUNCT
cana-3894	208	16	φ	φ	PROPN
cana-3894	208	17	(	(	PUNCT
cana-3894	208	18	µ,c	µ,c	NOUN
cana-3894	208	19	,	,	PUNCT
cana-3894	208	20	η;r	η;r	PROPN
cana-3894	208	21	)	)	PUNCT
cana-3894	208	22	ℓ,k	ℓ,k	X
cana-3894	208	23	φ	φ	X
cana-3894	208	24	(	(	PUNCT
cana-3894	208	25	α	α	PROPN
cana-3894	208	26	,	,	PUNCT
cana-3894	208	27	b	b	NOUN
cana-3894	208	28	,	,	PUNCT
cana-3894	208	29	σ;1	σ;1	PROPN
cana-3894	208	30	)	)	PUNCT
cana-3894	208	31	h	h	PROPN
cana-3894	208	32	,	,	PUNCT
cana-3894	208	33	m	m	VERB
cana-3894	208	34	θi	θi	ADP
cana-3894	208	35	w	w	PROPN
cana-3894	208	36	=	=	PUNCT
cana-3894	208	37	∞∑	∞∑	PROPN
cana-3894	208	38	n=0	n=0	NUM
cana-3894	208	39	an+1	an+1	NOUN
cana-3894	208	40	dn+1	dn+1	ADV
cana-3894	208	41	b−1	b−1	PROPN
cana-3894	208	42	n	n	CCONJ
cana-3894	208	43	c−1	c−1	PROPN
cana-3894	208	44	n	n	X
cana-3894	208	45	zn+1	zn+1	NUM
cana-3894	208	46	(	(	PUNCT
cana-3894	208	47	q	q	NOUN
cana-3894	208	48	;	;	PUNCT
cana-3894	208	49	q)n	q)n	X
cana-3894	208	50	(	(	PUNCT
cana-3894	208	51	3.15	3.15	NUM
cana-3894	208	52	)	)	PUNCT
cana-3894	208	53	on	on	ADP
cana-3894	208	54	the	the	DET
cana-3894	208	55	other	other	ADJ
cana-3894	208	56	hand	hand	NOUN
cana-3894	208	57	,	,	PUNCT
cana-3894	208	58	ψ	ψ	X
cana-3894	208	59	(	(	PUNCT
cana-3894	208	60	δ	δ	PROPN
cana-3894	208	61	,	,	PUNCT
cana-3894	208	62	a	a	PRON
cana-3894	208	63	,	,	PUNCT
cana-3894	208	64	ζ;s	ζ;s	NOUN
cana-3894	208	65	)	)	PUNCT
cana-3894	208	66	j	j	PROPN
cana-3894	208	67	,	,	PUNCT
cana-3894	208	68	i	i	PRON
cana-3894	208	69	ea	ea	PROPN
cana-3894	208	70	,	,	PUNCT
cana-3894	208	71	b	b	PROPN
cana-3894	208	72	,	,	PUNCT
cana-3894	208	73	c	c	PROPN
cana-3894	208	74	αi	αi	PROPN
cana-3894	208	75	,	,	PUNCT
cana-3894	208	76	δi	δi	ADV
cana-3894	208	77	,	,	PUNCT
cana-3894	208	78	µi(zq	µi(zq	VERB
cana-3894	208	79	p	p	PRON
cana-3894	208	80	;	;	PUNCT
cana-3894	208	81	s	s	X
cana-3894	208	82	,	,	PUNCT
cana-3894	208	83	r|q	r|q	ADJ
cana-3894	208	84	)	)	PUNCT
cana-3894	208	85	=	=	PUNCT
cana-3894	209	1	∞∑	∞∑	NUM
cana-3894	209	2	n=0	n=0	PUNCT
cana-3894	209	3	an	an	DET
cana-3894	209	4	dn	dn	NOUN
cana-3894	209	5	b−1	b−1	PROPN
cana-3894	209	6	n	n	CCONJ
cana-3894	209	7	c−1	c−1	PROPN
cana-3894	209	8	n	n	PRON
cana-3894	209	9	1	1	NUM
cana-3894	209	10	(	(	PUNCT
cana-3894	209	11	q	q	NOUN
cana-3894	209	12	;	;	PUNCT
cana-3894	209	13	q)n	q)n	X
cana-3894	209	14	{	{	PUNCT
cana-3894	209	15	δ−1∏	δ−1∏	PROPN
cana-3894	209	16	j=0	j=0	PROPN
cana-3894	209	17	δ−1∏	δ−1∏	ADJ
cana-3894	209	18	i=0	i=0	PROPN
cana-3894	210	1	[	[	X
cana-3894	210	2	(	(	PUNCT
cana-3894	210	3	θi	θi	ADP
cana-3894	210	4	+	+	CCONJ
cana-3894	210	5	ζ−jq−(a+ii)/δ	ζ−jq−(a+ii)/δ	NUM
cana-3894	210	6	−	−	NOUN
cana-3894	210	7	i)]s	i)]s	PROPN
cana-3894	210	8	}	}	PUNCT
cana-3894	210	9	×	×	NOUN
cana-3894	210	10	{	{	PUNCT
cana-3894	210	11	δ−1∏	δ−1∏	PROPN
cana-3894	210	12	j=0	j=0	VERB
cana-3894	210	13	δ−1∏	δ−1∏	ADJ
cana-3894	210	14	i=0	i=0	PROPN
cana-3894	211	1	[	[	X
cana-3894	211	2	(	(	PUNCT
cana-3894	211	3	ζ−jq−(a+ii)/δ)]s	ζ−jq−(a+ii)/δ)]s	PROPN
cana-3894	211	4	}	}	PUNCT
cana-3894	211	5	−1	−1	NOUN
cana-3894	211	6	zn	zn	NOUN
cana-3894	211	7	=	=	PUNCT
cana-3894	212	1	∞∑	∞∑	PRON
cana-3894	212	2	n=0	n=0	PUNCT
cana-3894	212	3	an	an	DET
cana-3894	212	4	dn	dn	NOUN
cana-3894	212	5	b−1	b−1	PROPN
cana-3894	212	6	n	n	CCONJ
cana-3894	212	7	c−1	c−1	PROPN
cana-3894	212	8	n	n	PRON
cana-3894	212	9	1	1	NUM
cana-3894	212	10	(	(	PUNCT
cana-3894	212	11	q	q	NOUN
cana-3894	212	12	;	;	PUNCT
cana-3894	212	13	q)n	q)n	X
cana-3894	212	14	{	{	PUNCT
cana-3894	212	15	δ−1∏	δ−1∏	PROPN
cana-3894	212	16	j=0	j=0	PROPN
cana-3894	212	17	δ−1∏	δ−1∏	ADJ
cana-3894	212	18	i=0	i=0	PROPN
cana-3894	213	1	[	[	X
cana-3894	213	2	(	(	PUNCT
cana-3894	213	3	i	i	PRON
cana-3894	213	4	−	−	PROPN
cana-3894	213	5	ζjqni+(a+ii)/δ)]s	ζjqni+(a+ii)/δ)]s	NOUN
cana-3894	213	6	}	}	PUNCT
cana-3894	213	7	zn	zn	NOUN
cana-3894	213	8	=	=	PUNCT
cana-3894	214	1	∞∑	∞∑	PRON
cana-3894	214	2	n=0	n=0	PUNCT
cana-3894	214	3	an	an	DET
cana-3894	214	4	dn	dn	NOUN
cana-3894	214	5	b−1	b−1	PROPN
cana-3894	214	6	n	n	CCONJ
cana-3894	214	7	c−1	c−1	PROPN
cana-3894	214	8	n	n	PRON
cana-3894	214	9	1	1	NUM
cana-3894	214	10	(	(	PUNCT
cana-3894	214	11	q	q	NOUN
cana-3894	214	12	;	;	PUNCT
cana-3894	214	13	q)n	q)n	X
cana-3894	214	14	an+1	an+1	PROPN
cana-3894	214	15	a−1	a−1	PROPN
cana-3894	214	16	n	n	NOUN
cana-3894	214	17	zn	zn	NOUN
cana-3894	214	18	=	=	PUNCT
cana-3894	215	1	∞∑	∞∑	NUM
cana-3894	215	2	n=0	n=0	NUM
cana-3894	215	3	an+1	an+1	NOUN
cana-3894	215	4	dn	dn	X
cana-3894	215	5	b−1	b−1	PROPN
cana-3894	215	6	n	n	CCONJ
cana-3894	215	7	c−1	c−1	PROPN
cana-3894	215	8	n	n	PROPN
cana-3894	215	9	zn	zn	PROPN
cana-3894	215	10	(	(	PUNCT
cana-3894	215	11	q	q	NOUN
cana-3894	215	12	;	;	PUNCT
cana-3894	215	13	q)n	q)n	SYM
cana-3894	215	14	that	that	PRON
cana-3894	215	15	is	be	AUX
cana-3894	215	16	,	,	PUNCT
cana-3894	215	17	z	z	PROPN
cana-3894	215	18	(	(	PUNCT
cana-3894	215	19	−1)p	−1)p	NOUN
cana-3894	215	20	ψ	ψ	X
cana-3894	215	21	(	(	PUNCT
cana-3894	215	22	δ	δ	PROPN
cana-3894	215	23	,	,	PUNCT
cana-3894	215	24	a	a	PRON
cana-3894	215	25	,	,	PUNCT
cana-3894	215	26	ζ;s	ζ;s	NOUN
cana-3894	215	27	)	)	PUNCT
cana-3894	215	28	j	j	PROPN
cana-3894	215	29	,	,	PUNCT
cana-3894	215	30	i	i	PRON
cana-3894	215	31	ea	ea	PROPN
cana-3894	215	32	,	,	PUNCT
cana-3894	215	33	b	b	PROPN
cana-3894	215	34	,	,	PUNCT
cana-3894	215	35	c	c	PROPN
cana-3894	215	36	αi	αi	PROPN
cana-3894	215	37	,	,	PUNCT
cana-3894	215	38	δi	δi	ADV
cana-3894	215	39	,	,	PUNCT
cana-3894	215	40	µi(zq	µi(zq	VERB
cana-3894	215	41	p	p	PRON
cana-3894	215	42	;	;	PUNCT
cana-3894	215	43	s	s	X
cana-3894	215	44	,	,	PUNCT
cana-3894	215	45	r|q	r|q	ADJ
cana-3894	215	46	)	)	PUNCT
cana-3894	215	47	=	=	PUNCT
cana-3894	216	1	∞∑	∞∑	PRON
cana-3894	216	2	n=0	n=0	NUM
cana-3894	216	3	an+1	an+1	NOUN
cana-3894	216	4	dn+1	dn+1	ADV
cana-3894	216	5	b−1	b−1	PROPN
cana-3894	216	6	n	n	CCONJ
cana-3894	216	7	c−1	c−1	PROPN
cana-3894	216	8	n	n	X
cana-3894	216	9	zn+1	zn+1	NUM
cana-3894	216	10	(	(	PUNCT
cana-3894	216	11	q	q	NOUN
cana-3894	216	12	;	;	PUNCT
cana-3894	216	13	q)n	q)n	X
cana-3894	216	14	.	.	PUNCT
cana-3894	217	1	(	(	PUNCT
cana-3894	217	2	3.16	3.16	NUM
cana-3894	217	3	)	)	PUNCT
cana-3894	217	4	on	on	ADP
cana-3894	217	5	comparing	compare	VERB
cana-3894	217	6	(	(	PUNCT
cana-3894	217	7	3.15	3.15	NUM
cana-3894	217	8	)	)	PUNCT
cana-3894	217	9	and	and	CCONJ
cana-3894	217	10	(	(	PUNCT
cana-3894	217	11	3.16	3.16	NUM
cana-3894	217	12	)	)	PUNCT
cana-3894	217	13	,	,	PUNCT
cana-3894	217	14	the	the	DET
cana-3894	217	15	equation	equation	NOUN
cana-3894	217	16	(	(	PUNCT
cana-3894	217	17	3.11	3.11	NUM
cana-3894	217	18	)	)	PUNCT
cana-3894	217	19	is	be	AUX
cana-3894	217	20	obtained	obtain	VERB
cana-3894	217	21	.	.	PUNCT
cana-3894	218	1	the	the	DET
cana-3894	218	2	q	q	ADJ
cana-3894	218	3	-	-	PUNCT
cana-3894	218	4	difference	difference	NOUN
cana-3894	218	5	equation	equation	NOUN
cana-3894	218	6	satisfied	satisfy	VERB
cana-3894	218	7	by	by	ADP
cana-3894	218	8	the	the	DET
cana-3894	218	9	function	function	NOUN
cana-3894	218	10	(	(	PUNCT
cana-3894	218	11	2.14	2.14	NUM
cana-3894	218	12	)	)	PUNCT
cana-3894	218	13	is	be	AUX
cana-3894	218	14	given	give	VERB
cana-3894	218	15	in	in	ADP
cana-3894	218	16	following	follow	VERB
cana-3894	218	17	theorem	theorem	VERB
cana-3894	218	18	whose	whose	DET
cana-3894	218	19	proof	proof	NOUN
cana-3894	218	20	follows	follow	VERB
cana-3894	218	21	line	line	NOUN
cana-3894	218	22	-	-	PUNCT
cana-3894	218	23	to	to	ADP
cana-3894	218	24	-	-	PUNCT
cana-3894	218	25	line	line	NOUN
cana-3894	218	26	just	just	ADV
cana-3894	218	27	dropping	drop	VERB
cana-3894	218	28	the	the	DET
cana-3894	218	29	factor	factor	NOUN
cana-3894	218	30	qn(n−1)/2	qn(n−1)/2	PROPN
cana-3894	218	31	that	that	PRON
cana-3894	218	32	is	be	AUX
cana-3894	218	33	,	,	PUNCT
cana-3894	218	34	dropping	drop	VERB
cana-3894	218	35	dn	dn	ADV
cana-3894	218	36	in	in	ADP
cana-3894	218	37	(	(	PUNCT
cana-3894	218	38	3.14	3.14	NUM
cana-3894	218	39	)	)	PUNCT
cana-3894	218	40	.	.	PUNCT
cana-3894	219	1	theorem	theorem	VERB
cana-3894	219	2	3.6	3.6	NUM
cana-3894	219	3	.	.	PUNCT
cana-3894	220	1	let	let	VERB
cana-3894	220	2	α	α	PRON
cana-3894	220	3	,	,	PUNCT
cana-3894	220	4	µ	µ	NUM
cana-3894	220	5	,	,	PUNCT
cana-3894	220	6	δ	δ	PROPN
cana-3894	220	7	∈	∈	PROPN
cana-3894	220	8	n	n	CCONJ
cana-3894	220	9	,	,	PUNCT
cana-3894	220	10	then	then	ADV
cana-3894	220	11	y	y	PROPN
cana-3894	220	12	=	=	SYM
cana-3894	220	13	eγ	eγ	PROPN
cana-3894	220	14	,	,	PUNCT
cana-3894	220	15	δα	δα	PRON
cana-3894	220	16	,	,	PUNCT
cana-3894	220	17	β	β	NOUN
cana-3894	220	18	,	,	PUNCT
cana-3894	220	19	λ,µ(z	λ,µ(z	X
cana-3894	220	20	;	;	PUNCT
cana-3894	220	21	s	s	X
cana-3894	220	22	,	,	PUNCT
cana-3894	220	23	r|q	r|q	ADJ
cana-3894	220	24	)	)	PUNCT
cana-3894	220	25	satisfies	satisfy	VERB
cana-3894	220	26	the	the	DET
cana-3894	220	27	equation	equation	NOUN
cana-3894	220	28	[	[	PUNCT
cana-3894	220	29	φ	φ	PROPN
cana-3894	220	30	(	(	PUNCT
cana-3894	220	31	µ,λ	µ,λ	PROPN
cana-3894	220	32	,	,	PUNCT
cana-3894	220	33	η;r	η;r	NOUN
cana-3894	220	34	)	)	PUNCT
cana-3894	220	35	ℓ,k	ℓ,k	X
cana-3894	220	36	φ	φ	X
cana-3894	220	37	(	(	PUNCT
cana-3894	220	38	α	α	X
cana-3894	220	39	,	,	PUNCT
cana-3894	220	40	β	β	X
cana-3894	220	41	,	,	PUNCT
cana-3894	220	42	σ;1	σ;1	PROPN
cana-3894	220	43	)	)	PUNCT
cana-3894	220	44	h	h	NOUN
cana-3894	220	45	,	,	PUNCT
cana-3894	220	46	m	m	VERB
cana-3894	220	47	θ−	θ−	PROPN
cana-3894	220	48	z	z	NOUN
cana-3894	220	49	ψ	ψ	PROPN
cana-3894	220	50	(	(	PUNCT
cana-3894	220	51	δ	δ	PROPN
cana-3894	220	52	,	,	PUNCT
cana-3894	220	53	γ	γ	PROPN
cana-3894	220	54	,	,	PUNCT
cana-3894	220	55	ζ;s	ζ;s	NOUN
cana-3894	220	56	)	)	PUNCT
cana-3894	221	1	j	j	PROPN
cana-3894	221	2	,	,	PUNCT
cana-3894	221	3	i	i	PRON
cana-3894	221	4	]	]	PUNCT
cana-3894	221	5	y	y	PROPN
cana-3894	221	6	=	=	SYM
cana-3894	221	7	0	0	PROPN
cana-3894	221	8	,	,	PUNCT
cana-3894	221	9	(	(	PUNCT
cana-3894	221	10	3.17	3.17	NUM
cana-3894	221	11	)	)	PUNCT
cana-3894	221	12	where	where	SCONJ
cana-3894	221	13	ζ	ζ	NOUN
cana-3894	221	14	is	be	AUX
cana-3894	221	15	δth	δth	NOUN
cana-3894	221	16	root	root	NOUN
cana-3894	221	17	of	of	ADP
cana-3894	221	18	unity	unity	NOUN
cana-3894	221	19	,	,	PUNCT
cana-3894	221	20	η	η	PROPN
cana-3894	221	21	is	be	AUX
cana-3894	221	22	µth	µth	VERB
cana-3894	221	23	root	root	NOUN
cana-3894	221	24	of	of	ADP
cana-3894	221	25	unity	unity	NOUN
cana-3894	221	26	,	,	PUNCT
cana-3894	221	27	σ	σ	PROPN
cana-3894	221	28	is	be	AUX
cana-3894	221	29	αth	αth	NUM
cana-3894	221	30	root	root	NOUN
cana-3894	221	31	of	of	ADP
cana-3894	221	32	unity	unity	NOUN
cana-3894	221	33	.	.	PUNCT
cana-3894	222	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3894	222	2	341	341	NUM
cana-3894	222	3	communications	communication	NOUN
cana-3894	222	4	on	on	ADP
cana-3894	222	5	applied	apply	VERB
cana-3894	222	6	nonlinear	nonlinear	ADJ
cana-3894	222	7	analysis	analysis	NOUN
cana-3894	222	8	issn	issn	NOUN
cana-3894	222	9	:	:	PUNCT
cana-3894	222	10	1074	1074	NUM
cana-3894	222	11	-	-	PUNCT
cana-3894	222	12	133x	133x	NUM
cana-3894	222	13	vol	vol	NOUN
cana-3894	222	14	32	32	NUM
cana-3894	222	15	no	no	NOUN
cana-3894	222	16	.	.	PUNCT
cana-3894	223	1	9s(2025	9s(2025	NUM
cana-3894	223	2	)	)	PUNCT
cana-3894	223	3	3.4	3.4	NUM
cana-3894	223	4	eigen	eigen	PROPN
cana-3894	223	5	function	function	NOUN
cana-3894	223	6	property	property	NOUN
cana-3894	223	7	take	take	NOUN
cana-3894	223	8	{	{	PUNCT
cana-3894	223	9	a−1∏	a−1∏	NOUN
cana-3894	223	10	u=0	u=0	PROPN
cana-3894	223	11	a−1∏	a−1∏	NOUN
cana-3894	223	12	v=0	v=0	ADP
cana-3894	224	1	[	[	X
cana-3894	224	2	(	(	PUNCT
cana-3894	224	3	λq	λq	INTJ
cana-3894	224	4	+	+	NUM
cana-3894	224	5	c−uqi−(b+vi)/a	c−uqi−(b+vi)/a	ADJ
cana-3894	224	6	−	−	NOUN
cana-3894	224	7	i)]m	i)]m	NOUN
cana-3894	224	8	}	}	PUNCT
cana-3894	224	9	{	{	PUNCT
cana-3894	224	10	a−1∏	a−1∏	PROPN
cana-3894	224	11	u=0	u=0	PROPN
cana-3894	224	12	a−1∏	a−1∏	NOUN
cana-3894	224	13	v=0	v=0	X
cana-3894	225	1	[	[	X
cana-3894	225	2	c−uqi−(b+vi)/a]m	c−uqi−(b+vi)/a]m	NOUN
cana-3894	225	3	}	}	PUNCT
cana-3894	225	4	−1	−1	NOUN
cana-3894	225	5	=	=	SYM
cana-3894	225	6	ω(a	ω(a	PROPN
cana-3894	225	7	,	,	PUNCT
cana-3894	225	8	b	b	NOUN
cana-3894	225	9	,	,	PUNCT
cana-3894	225	10	c;m	c;m	NUM
cana-3894	225	11	)	)	PUNCT
cana-3894	225	12	u	u	NOUN
cana-3894	225	13	,	,	PUNCT
cana-3894	225	14	v	v	NUM
cana-3894	225	15	,	,	PUNCT
cana-3894	225	16	(	(	PUNCT
cana-3894	225	17	3.18	3.18	NUM
cana-3894	225	18	)	)	PUNCT
cana-3894	225	19	and	and	CCONJ
cana-3894	225	20	∆q	∆q	PROPN
cana-3894	225	21	=	=	SYM
cana-3894	225	22	dq	dq	PROPN
cana-3894	225	23	ω	ω	PROPN
cana-3894	225	24	(	(	PUNCT
cana-3894	225	25	δ	δ	PROPN
cana-3894	225	26	,	,	PUNCT
cana-3894	225	27	a	a	PRON
cana-3894	225	28	,	,	PUNCT
cana-3894	225	29	ζ;−s	ζ;−s	NOUN
cana-3894	225	30	)	)	PUNCT
cana-3894	225	31	j	j	PROPN
cana-3894	225	32	,	,	PUNCT
cana-3894	225	33	i	i	PRON
cana-3894	225	34	φ	φ	PROPN
cana-3894	225	35	(	(	PUNCT
cana-3894	225	36	µ,c	µ,c	NOUN
cana-3894	225	37	,	,	PUNCT
cana-3894	225	38	η;r	η;r	PROPN
cana-3894	225	39	)	)	PUNCT
cana-3894	225	40	ℓ,k	ℓ,k	X
cana-3894	225	41	φ	φ	X
cana-3894	225	42	(	(	PUNCT
cana-3894	225	43	α	α	PROPN
cana-3894	225	44	,	,	PUNCT
cana-3894	225	45	b	b	NOUN
cana-3894	225	46	,	,	PUNCT
cana-3894	225	47	σ;1	σ;1	PROPN
cana-3894	225	48	)	)	PUNCT
cana-3894	225	49	h	h	NOUN
cana-3894	225	50	,	,	PUNCT
cana-3894	225	51	m	m	PROPN
cana-3894	225	52	.	.	PUNCT
cana-3894	226	1	(	(	PUNCT
cana-3894	226	2	3.19	3.19	NUM
cana-3894	226	3	)	)	PUNCT
cana-3894	226	4	here	here	ADV
cana-3894	226	5	the	the	DET
cana-3894	226	6	operators	operators	PROPN
cana-3894	226	7	ω	ω	PROPN
cana-3894	226	8	(	(	PUNCT
cana-3894	226	9	δ	δ	PROPN
cana-3894	226	10	,	,	PUNCT
cana-3894	226	11	γ	γ	X
cana-3894	226	12	,	,	PUNCT
cana-3894	226	13	ζ;−s	ζ;−s	NOUN
cana-3894	226	14	)	)	PUNCT
cana-3894	226	15	j	j	PROPN
cana-3894	226	16	,	,	PUNCT
cana-3894	226	17	i	i	PRON
cana-3894	226	18	,	,	PUNCT
cana-3894	226	19	φ	φ	PROPN
cana-3894	226	20	(	(	PUNCT
cana-3894	226	21	µ,λ	µ,λ	PROPN
cana-3894	226	22	,	,	PUNCT
cana-3894	226	23	η;r	η;r	NOUN
cana-3894	226	24	)	)	PUNCT
cana-3894	226	25	ℓ,k	ℓ,k	NOUN
cana-3894	226	26	,	,	PUNCT
cana-3894	226	27	φ	φ	PROPN
cana-3894	226	28	(	(	PUNCT
cana-3894	226	29	α	α	PROPN
cana-3894	226	30	,	,	PUNCT
cana-3894	226	31	β	β	X
cana-3894	226	32	,	,	PUNCT
cana-3894	226	33	σ;1	σ;1	PROPN
cana-3894	226	34	)	)	PUNCT
cana-3894	226	35	h	h	NOUN
cana-3894	226	36	,	,	PUNCT
cana-3894	226	37	m	m	VERB
cana-3894	226	38	in	in	ADP
cana-3894	226	39	(	(	PUNCT
cana-3894	226	40	3.19	3.19	NUM
cana-3894	226	41	)	)	PUNCT
cana-3894	226	42	are	be	AUX
cana-3894	226	43	not	not	PART
cana-3894	226	44	commutative	commutative	ADJ
cana-3894	226	45	with	with	ADP
cana-3894	226	46	the	the	DET
cana-3894	226	47	operator	operator	NOUN
cana-3894	226	48	dq	dq	PROPN
cana-3894	226	49	.	.	PUNCT
cana-3894	227	1	this	this	DET
cana-3894	227	2	property	property	NOUN
cana-3894	227	3	does	do	AUX
cana-3894	227	4	not	not	PART
cana-3894	227	5	hold	hold	VERB
cana-3894	227	6	for	for	SCONJ
cana-3894	227	7	the	the	DET
cana-3894	227	8	function	function	NOUN
cana-3894	227	9	eγ	eγ	ADP
cana-3894	227	10	,	,	PUNCT
cana-3894	227	11	δ	δ	PROPN
cana-3894	227	12	α	α	NOUN
cana-3894	227	13	,	,	PUNCT
cana-3894	227	14	β	β	X
cana-3894	227	15	,	,	PUNCT
cana-3894	227	16	λ,µ(z	λ,µ(z	X
cana-3894	227	17	;	;	PUNCT
cana-3894	227	18	s	s	X
cana-3894	227	19	,	,	PUNCT
cana-3894	227	20	r|q	r|q	ADJ
cana-3894	227	21	)	)	PUNCT
cana-3894	227	22	,	,	PUNCT
cana-3894	227	23	but	but	CCONJ
cana-3894	227	24	for	for	ADP
cana-3894	227	25	the	the	DET
cana-3894	227	26	other	other	ADJ
cana-3894	227	27	version	version	NOUN
cana-3894	227	28	:	:	PUNCT
cana-3894	227	29	eγ	eγ	ADP
cana-3894	227	30	,	,	PUNCT
cana-3894	227	31	δα	δα	PRON
cana-3894	227	32	,	,	PUNCT
cana-3894	227	33	β	β	NOUN
cana-3894	227	34	,	,	PUNCT
cana-3894	227	35	λ,µ(z	λ,µ(z	X
cana-3894	227	36	;	;	PUNCT
cana-3894	227	37	s	s	X
cana-3894	227	38	,	,	PUNCT
cana-3894	227	39	r|q	r|q	ADJ
cana-3894	227	40	)	)	PUNCT
cana-3894	227	41	,	,	PUNCT
cana-3894	227	42	it	it	PRON
cana-3894	227	43	is	be	AUX
cana-3894	227	44	established	establish	VERB
cana-3894	227	45	in	in	ADP
cana-3894	227	46	theorem	theorem	ADJ
cana-3894	227	47	3.7	3.7	NUM
cana-3894	227	48	.	.	PUNCT
cana-3894	228	1	let	let	VERB
cana-3894	228	2	α	α	PRON
cana-3894	228	3	,	,	PUNCT
cana-3894	228	4	µ	µ	NUM
cana-3894	228	5	,	,	PUNCT
cana-3894	228	6	δ	δ	PROPN
cana-3894	228	7	∈	∈	PROPN
cana-3894	228	8	n	n	PRON
cana-3894	228	9	and	and	CCONJ
cana-3894	228	10	q	q	ADJ
cana-3894	228	11	-	-	PUNCT
cana-3894	228	12	difference	difference	NOUN
cana-3894	228	13	operator	operator	NOUN
cana-3894	228	14	θ	θ	PROPN
cana-3894	228	15	be	be	AUX
cana-3894	228	16	defined	define	VERB
cana-3894	228	17	by	by	ADP
cana-3894	228	18	(	(	PUNCT
cana-3894	228	19	3.7	3.7	NUM
cana-3894	228	20	)	)	PUNCT
cana-3894	228	21	then	then	ADV
cana-3894	228	22	eγ	eγ	ADP
cana-3894	228	23	,	,	PUNCT
cana-3894	228	24	δα	δα	PRON
cana-3894	228	25	,	,	PUNCT
cana-3894	228	26	β	β	NOUN
cana-3894	228	27	,	,	PUNCT
cana-3894	228	28	λ,µ(z	λ,µ(z	X
cana-3894	228	29	;	;	PUNCT
cana-3894	228	30	s	s	X
cana-3894	228	31	,	,	PUNCT
cana-3894	228	32	r|q	r|q	ADJ
cana-3894	228	33	)	)	PUNCT
cana-3894	228	34	is	be	AUX
cana-3894	228	35	an	an	DET
cana-3894	228	36	eigen	eigen	PROPN
cana-3894	228	37	function	function	NOUN
cana-3894	228	38	with	with	ADP
cana-3894	228	39	respect	respect	NOUN
cana-3894	228	40	to	to	ADP
cana-3894	228	41	the	the	DET
cana-3894	228	42	operator	operator	NOUN
cana-3894	228	43	∆q	∆q	PROPN
cana-3894	228	44	defined	define	VERB
cana-3894	228	45	by	by	ADP
cana-3894	228	46	(	(	PUNCT
cana-3894	228	47	3.19	3.19	NUM
cana-3894	228	48	)	)	PUNCT
cana-3894	228	49	.	.	PUNCT
cana-3894	229	1	that	that	PRON
cana-3894	229	2	is	be	AUX
cana-3894	229	3	,	,	PUNCT
cana-3894	229	4	for	for	ADP
cana-3894	229	5	any	any	DET
cana-3894	229	6	non	non	ADJ
cana-3894	229	7	zero	zero	NUM
cana-3894	229	8	c	c	NOUN
cana-3894	229	9	,	,	PUNCT
cana-3894	229	10	∆q	∆q	PROPN
cana-3894	229	11	ea	ea	PROPN
cana-3894	229	12	,	,	PUNCT
cana-3894	229	13	b	b	PROPN
cana-3894	229	14	,	,	PUNCT
cana-3894	229	15	c	c	PROPN
cana-3894	229	16	αi	αi	PROPN
cana-3894	229	17	,	,	PUNCT
cana-3894	229	18	δi	δi	ADV
cana-3894	229	19	,	,	PUNCT
cana-3894	229	20	µi(cz	µi(cz	NOUN
cana-3894	229	21	;	;	PUNCT
cana-3894	229	22	s	s	X
cana-3894	229	23	,	,	PUNCT
cana-3894	229	24	r|q	r|q	ADJ
cana-3894	229	25	)	)	PUNCT
cana-3894	229	26	=	=	SYM
cana-3894	229	27	c	c	NOUN
cana-3894	229	28	ea	ea	PROPN
cana-3894	229	29	,	,	PUNCT
cana-3894	229	30	b	b	PROPN
cana-3894	229	31	,	,	PUNCT
cana-3894	229	32	c	c	PROPN
cana-3894	229	33	αi	αi	PROPN
cana-3894	229	34	,	,	PUNCT
cana-3894	229	35	δi	δi	ADV
cana-3894	229	36	,	,	PUNCT
cana-3894	229	37	µi(z	µi(z	X
cana-3894	229	38	;	;	PUNCT
cana-3894	229	39	s	s	X
cana-3894	229	40	,	,	PUNCT
cana-3894	229	41	r|q	r|q	ADJ
cana-3894	229	42	)	)	PUNCT
cana-3894	229	43	.	.	PUNCT
cana-3894	230	1	(	(	PUNCT
cana-3894	230	2	3.20	3.20	NUM
cana-3894	230	3	)	)	PUNCT
cana-3894	230	4	(	(	PUNCT
cana-3894	230	5	3.21	3.21	NUM
cana-3894	230	6	)	)	PUNCT
cana-3894	230	7	proof	proof	NOUN
cana-3894	230	8	.	.	PUNCT
cana-3894	231	1	with	with	ADP
cana-3894	231	2	an	an	DET
cana-3894	231	3	,	,	PUNCT
cana-3894	231	4	bn	bn	NOUN
cana-3894	231	5	and	and	CCONJ
cana-3894	231	6	cn	cn	PROPN
cana-3894	231	7	as	as	ADP
cana-3894	231	8	in	in	ADP
cana-3894	231	9	(	(	PUNCT
cana-3894	231	10	3.13	3.13	NUM
cana-3894	231	11	)	)	PUNCT
cana-3894	231	12	and	and	CCONJ
cana-3894	231	13	in	in	ADP
cana-3894	231	14	(	(	PUNCT
cana-3894	231	15	3.14	3.14	NUM
cana-3894	231	16	)	)	PUNCT
cana-3894	231	17	,	,	PUNCT
cana-3894	231	18	ea	ea	PROPN
cana-3894	231	19	,	,	PUNCT
cana-3894	231	20	b	b	PROPN
cana-3894	231	21	,	,	PUNCT
cana-3894	231	22	c	c	PROPN
cana-3894	231	23	αi	αi	PROPN
cana-3894	231	24	,	,	PUNCT
cana-3894	231	25	δi	δi	ADV
cana-3894	231	26	,	,	PUNCT
cana-3894	231	27	µi(cz	µi(cz	NOUN
cana-3894	231	28	;	;	PUNCT
cana-3894	231	29	s	s	X
cana-3894	231	30	,	,	PUNCT
cana-3894	231	31	r|q	r|q	ADJ
cana-3894	231	32	)	)	PUNCT
cana-3894	231	33	=	=	PUNCT
cana-3894	231	34	∞∑	∞∑	NUM
cana-3894	231	35	n=0	n=0	NUM
cana-3894	231	36	an	an	DET
cana-3894	231	37	b−1	b−1	PROPN
cana-3894	231	38	n	n	CCONJ
cana-3894	231	39	c−1	c−1	PROPN
cana-3894	231	40	n	n	PROPN
cana-3894	231	41	zn	zn	PROPN
cana-3894	231	42	(	(	PUNCT
cana-3894	231	43	q	q	NOUN
cana-3894	231	44	;	;	PUNCT
cana-3894	231	45	q)n	q)n	X
cana-3894	231	46	now	now	ADV
cana-3894	231	47	if	if	SCONJ
cana-3894	231	48	ea	ea	PROPN
cana-3894	231	49	,	,	PUNCT
cana-3894	231	50	b	b	PROPN
cana-3894	231	51	,	,	PUNCT
cana-3894	231	52	c	c	PROPN
cana-3894	231	53	αi	αi	PROPN
cana-3894	231	54	,	,	PUNCT
cana-3894	231	55	δi	δi	ADV
cana-3894	231	56	,	,	PUNCT
cana-3894	231	57	µi(cz	µi(cz	NOUN
cana-3894	231	58	;	;	PUNCT
cana-3894	231	59	s	s	X
cana-3894	231	60	,	,	PUNCT
cana-3894	231	61	r|q	r|q	ADJ
cana-3894	231	62	)	)	PUNCT
cana-3894	231	63	=	=	SYM
cana-3894	232	1	yc	yc	X
cana-3894	232	2	then	then	ADV
cana-3894	232	3	in	in	ADP
cana-3894	232	4	the	the	DET
cana-3894	232	5	notation	notation	NOUN
cana-3894	232	6	(	(	PUNCT
cana-3894	232	7	3.9	3.9	NUM
cana-3894	232	8	)	)	PUNCT
cana-3894	232	9	,	,	PUNCT
cana-3894	232	10	φ	φ	PROPN
cana-3894	232	11	(	(	PUNCT
cana-3894	232	12	α	α	PROPN
cana-3894	232	13	,	,	PUNCT
cana-3894	232	14	b	b	NOUN
cana-3894	232	15	,	,	PUNCT
cana-3894	232	16	σ;1	σ;1	PROPN
cana-3894	232	17	)	)	PUNCT
cana-3894	232	18	h	h	NOUN
cana-3894	232	19	,	,	PUNCT
cana-3894	232	20	m	m	VERB
cana-3894	232	21	yc	yc	NOUN
cana-3894	232	22	=	=	PUNCT
cana-3894	232	23	∞∑	∞∑	PROPN
cana-3894	232	24	n=0	n=0	NUM
cana-3894	232	25	cn	cn	NOUN
cana-3894	232	26	an	an	DET
cana-3894	232	27	b−1	b−1	PROPN
cana-3894	232	28	n	n	CCONJ
cana-3894	232	29	c−1	c−1	PROPN
cana-3894	232	30	n	n	PRON
cana-3894	232	31	1	1	NUM
cana-3894	232	32	(	(	PUNCT
cana-3894	232	33	q	q	NOUN
cana-3894	232	34	;	;	PUNCT
cana-3894	232	35	q)n	q)n	X
cana-3894	232	36	×	×	NOUN
cana-3894	232	37	{	{	PUNCT
cana-3894	232	38	α−1∏	α−1∏	PROPN
cana-3894	232	39	h=0	h=0	PROPN
cana-3894	232	40	α−1∏	α−1∏	PROPN
cana-3894	232	41	m=0	m=0	PROPN
cana-3894	232	42	(	(	PUNCT
cana-3894	232	43	θi	θi	X
cana-3894	232	44	+	+	CCONJ
cana-3894	232	45	σ−h	σ−h	NOUN
cana-3894	232	46	qi−(b+mi)/α	qi−(b+mi)/α	NOUN
cana-3894	232	47	−	−	PROPN
cana-3894	232	48	i	i	NOUN
cana-3894	232	49	)	)	PUNCT
cana-3894	232	50	}	}	PUNCT
cana-3894	232	51	×	×	NOUN
cana-3894	232	52	{	{	PUNCT
cana-3894	232	53	α−1∏	α−1∏	PROPN
cana-3894	232	54	h=0	h=0	PROPN
cana-3894	232	55	α−1∏	α−1∏	PROPN
cana-3894	232	56	m=0	m=0	PROPN
cana-3894	232	57	(	(	PUNCT
cana-3894	232	58	σ−hqi−(b+mi)/α	σ−hqi−(b+mi)/α	NOUN
cana-3894	232	59	)	)	PUNCT
cana-3894	232	60	}	}	PUNCT
cana-3894	232	61	−1	−1	NOUN
cana-3894	232	62	zn	zn	NOUN
cana-3894	232	63	=	=	PUNCT
cana-3894	233	1	∞∑	∞∑	PROPN
cana-3894	233	2	n=0	n=0	NUM
cana-3894	233	3	cn	cn	NOUN
cana-3894	233	4	an	an	DET
cana-3894	233	5	b−1	b−1	PROPN
cana-3894	233	6	n	n	CCONJ
cana-3894	233	7	c−1	c−1	PROPN
cana-3894	233	8	n	n	CCONJ
cana-3894	233	9	{	{	PUNCT
cana-3894	233	10	α−1∏	α−1∏	PROPN
cana-3894	233	11	h=0	h=0	PROPN
cana-3894	233	12	α−1∏	α−1∏	PROPN
cana-3894	233	13	m=0	m=0	PROPN
cana-3894	233	14	(	(	PUNCT
cana-3894	233	15	i	i	NOUN
cana-3894	233	16	−	−	PROPN
cana-3894	233	17	σhq(n−1)i+(b+mi)/α	σhq(n−1)i+(b+mi)/α	NOUN
cana-3894	233	18	)	)	PUNCT
cana-3894	233	19	}	}	PUNCT
cana-3894	233	20	×	×	NOUN
cana-3894	233	21	{	{	PUNCT
cana-3894	233	22	α−1∏	α−1∏	PROPN
cana-3894	233	23	h=0	h=0	PROPN
cana-3894	233	24	α−1∏	α−1∏	PROPN
cana-3894	233	25	m=0	m=0	PROPN
cana-3894	233	26	(	(	PUNCT
cana-3894	233	27	σhq(b+mi)/α	σhq(b+mi)/α	NOUN
cana-3894	233	28	)	)	PUNCT
cana-3894	233	29	}	}	PUNCT
cana-3894	233	30	−1	−1	NOUN
cana-3894	233	31	zn	zn	PROPN
cana-3894	233	32	(	(	PUNCT
cana-3894	233	33	q	q	NOUN
cana-3894	233	34	;	;	PUNCT
cana-3894	233	35	q)n	q)n	X
cana-3894	233	36	=	=	SYM
cana-3894	234	1	∞∑	∞∑	PROPN
cana-3894	234	2	n=0	n=0	NUM
cana-3894	234	3	cn	cn	NOUN
cana-3894	234	4	an	an	DET
cana-3894	234	5	b−1	b−1	PROPN
cana-3894	234	6	n	n	CCONJ
cana-3894	234	7	c−1	c−1	PROPN
cana-3894	234	8	n	n	PRON
cana-3894	234	9	1	1	NUM
cana-3894	234	10	(	(	PUNCT
cana-3894	234	11	q	q	NOUN
cana-3894	234	12	;	;	PUNCT
cana-3894	234	13	q)n	q)n	PUNCT
cana-3894	234	14	cn	cn	PROPN
cana-3894	234	15	c−1	c−1	PROPN
cana-3894	234	16	n−1	n−1	PROPN
cana-3894	234	17	zn	zn	PROPN
cana-3894	234	18	=	=	PUNCT
cana-3894	235	1	∞∑	∞∑	PROPN
cana-3894	235	2	n=0	n=0	NUM
cana-3894	235	3	cn	cn	NOUN
cana-3894	235	4	an	an	DET
cana-3894	235	5	b−1	b−1	PROPN
cana-3894	235	6	n	n	CCONJ
cana-3894	235	7	c−1	c−1	PROPN
cana-3894	235	8	n−1	n−1	PROPN
cana-3894	235	9	zn	zn	PROPN
cana-3894	235	10	(	(	PUNCT
cana-3894	235	11	q	q	NOUN
cana-3894	235	12	;	;	PUNCT
cana-3894	235	13	q)n	q)n	X
cana-3894	235	14	https://internationalpubls.com	https://internationalpubls.com	X
cana-3894	235	15	342	342	NUM
cana-3894	235	16	communications	communication	NOUN
cana-3894	235	17	on	on	ADP
cana-3894	235	18	applied	apply	VERB
cana-3894	235	19	nonlinear	nonlinear	ADJ
cana-3894	235	20	analysis	analysis	NOUN
cana-3894	235	21	issn	issn	NOUN
cana-3894	235	22	:	:	PUNCT
cana-3894	235	23	1074	1074	NUM
cana-3894	235	24	-	-	PUNCT
cana-3894	235	25	133x	133x	NUM
cana-3894	235	26	vol	vol	NOUN
cana-3894	235	27	32	32	NUM
cana-3894	235	28	no	no	NOUN
cana-3894	235	29	.	.	PUNCT
cana-3894	236	1	9s(2025	9s(2025	NUM
cana-3894	236	2	)	)	PUNCT
cana-3894	236	3	next	next	ADJ
cana-3894	236	4	φ	φ	PROPN
cana-3894	236	5	(	(	PUNCT
cana-3894	236	6	µ,c	µ,c	NOUN
cana-3894	236	7	,	,	PUNCT
cana-3894	236	8	η;r	η;r	PROPN
cana-3894	236	9	)	)	PUNCT
cana-3894	236	10	ℓ,k	ℓ,k	X
cana-3894	236	11	φ	φ	X
cana-3894	236	12	(	(	PUNCT
cana-3894	236	13	α	α	PROPN
cana-3894	236	14	,	,	PUNCT
cana-3894	236	15	b	b	NOUN
cana-3894	236	16	,	,	PUNCT
cana-3894	236	17	σ;1	σ;1	PROPN
cana-3894	236	18	)	)	PUNCT
cana-3894	236	19	h	h	NOUN
cana-3894	236	20	,	,	PUNCT
cana-3894	236	21	m	m	VERB
cana-3894	236	22	yc	yc	NOUN
cana-3894	236	23	=	=	PUNCT
cana-3894	237	1	∞∑	∞∑	PROPN
cana-3894	237	2	n=0	n=0	NUM
cana-3894	237	3	cn	cn	NOUN
cana-3894	237	4	an	an	DET
cana-3894	237	5	c−1	c−1	PROPN
cana-3894	237	6	n−1	n−1	PROPN
cana-3894	237	7	b−1	b−1	PROPN
cana-3894	237	8	n	n	CCONJ
cana-3894	237	9	1	1	NUM
cana-3894	237	10	(	(	PUNCT
cana-3894	237	11	q	q	NOUN
cana-3894	237	12	;	;	PUNCT
cana-3894	237	13	q)n	q)n	X
cana-3894	237	14	×	×	NOUN
cana-3894	237	15	{	{	PUNCT
cana-3894	237	16	µ−1∏	µ−1∏	ADP
cana-3894	237	17	l=0	l=0	PROPN
cana-3894	237	18	µ−1∏	µ−1∏	ADP
cana-3894	237	19	k=0	k=0	PROPN
cana-3894	238	1	[	[	X
cana-3894	238	2	(	(	PUNCT
cana-3894	238	3	θi	θi	ADP
cana-3894	238	4	+	+	CCONJ
cana-3894	238	5	η−lqi−(c+ki)/µ	η−lqi−(c+ki)/µ	ADJ
cana-3894	238	6	−	−	PROPN
cana-3894	238	7	i)]r	i)]r	NOUN
cana-3894	238	8	}	}	PUNCT
cana-3894	238	9	×	×	NOUN
cana-3894	238	10	{	{	PUNCT
cana-3894	238	11	µ−1∏	µ−1∏	ADP
cana-3894	238	12	l=0	l=0	PROPN
cana-3894	238	13	µ−1∏	µ−1∏	ADP
cana-3894	238	14	k=0	k=0	PROPN
cana-3894	239	1	[	[	X
cana-3894	239	2	(	(	PUNCT
cana-3894	239	3	η−lqi−(c+ki)/µ)]r	η−lqi−(c+ki)/µ)]r	NOUN
cana-3894	239	4	}	}	PUNCT
cana-3894	239	5	−1	−1	NOUN
cana-3894	239	6	zn	zn	NOUN
cana-3894	239	7	=	=	PUNCT
cana-3894	240	1	∞∑	∞∑	PROPN
cana-3894	240	2	n=0	n=0	NUM
cana-3894	240	3	cn	cn	NOUN
cana-3894	240	4	an	an	DET
cana-3894	240	5	c−1	c−1	PROPN
cana-3894	240	6	n−1	n−1	PROPN
cana-3894	240	7	b−1	b−1	PROPN
cana-3894	240	8	n	n	CCONJ
cana-3894	240	9	1	1	NUM
cana-3894	240	10	(	(	PUNCT
cana-3894	240	11	q	q	NOUN
cana-3894	240	12	;	;	PUNCT
cana-3894	240	13	q)n	q)n	X
cana-3894	240	14	×	×	NOUN
cana-3894	240	15	{	{	PUNCT
cana-3894	240	16	µ−1∏	µ−1∏	ADP
cana-3894	240	17	l=0	l=0	PROPN
cana-3894	240	18	µ−1∏	µ−1∏	ADP
cana-3894	240	19	k=0	k=0	PROPN
cana-3894	241	1	[	[	X
cana-3894	241	2	−qn	−qn	X
cana-3894	241	3	+	+	CCONJ
cana-3894	241	4	η−lqi−(c+ki)/µ)]r	η−lqi−(c+ki)/µ)]r	NOUN
cana-3894	241	5	}	}	PUNCT
cana-3894	241	6	×	×	NOUN
cana-3894	241	7	{	{	PUNCT
cana-3894	241	8	µ−1∏	µ−1∏	ADP
cana-3894	241	9	l=0	l=0	PROPN
cana-3894	241	10	µ−1∏	µ−1∏	ADP
cana-3894	241	11	k=0	k=0	PROPN
cana-3894	242	1	[	[	X
cana-3894	242	2	η−lqi−(c+ki)/µ]r	η−lqi−(c+ki)/µ]r	ADP
cana-3894	242	3	}	}	PUNCT
cana-3894	242	4	−1	−1	NOUN
cana-3894	242	5	zn	zn	NOUN
cana-3894	242	6	=	=	PUNCT
cana-3894	243	1	∞∑	∞∑	PROPN
cana-3894	243	2	n=0	n=0	NUM
cana-3894	243	3	cn	cn	NOUN
cana-3894	243	4	an	an	DET
cana-3894	243	5	c−1	c−1	PROPN
cana-3894	243	6	n−1	n−1	PROPN
cana-3894	243	7	b−1	b−1	PROPN
cana-3894	243	8	n	n	CCONJ
cana-3894	243	9	1	1	NUM
cana-3894	243	10	(	(	PUNCT
cana-3894	243	11	q	q	NOUN
cana-3894	243	12	;	;	PUNCT
cana-3894	243	13	q)n	q)n	SYM
cana-3894	243	14	bn	bn	X
cana-3894	243	15	b−1	b−1	PROPN
cana-3894	243	16	n−1	n−1	PROPN
cana-3894	243	17	zn	zn	NOUN
cana-3894	243	18	=	=	PUNCT
cana-3894	244	1	∞∑	∞∑	PROPN
cana-3894	244	2	n=0	n=0	NUM
cana-3894	244	3	cn	cn	NOUN
cana-3894	244	4	an	an	DET
cana-3894	244	5	b−1	b−1	PROPN
cana-3894	244	6	n−1	n−1	PROPN
cana-3894	244	7	c−1	c−1	PROPN
cana-3894	244	8	n−1	n−1	PROPN
cana-3894	244	9	zn	zn	PROPN
cana-3894	244	10	(	(	PUNCT
cana-3894	244	11	q	q	NOUN
cana-3894	244	12	;	;	PUNCT
cana-3894	244	13	q)n	q)n	X
cana-3894	244	14	further	far	ADV
cana-3894	244	15	using	use	VERB
cana-3894	244	16	(	(	PUNCT
cana-3894	244	17	3.18	3.18	NUM
cana-3894	244	18	)	)	PUNCT
cana-3894	244	19	,	,	PUNCT
cana-3894	244	20	ω	ω	PROPN
cana-3894	244	21	(	(	PUNCT
cana-3894	244	22	δ	δ	PROPN
cana-3894	244	23	,	,	PUNCT
cana-3894	244	24	a	a	PRON
cana-3894	244	25	,	,	PUNCT
cana-3894	244	26	ζ;−s	ζ;−s	NOUN
cana-3894	244	27	)	)	PUNCT
cana-3894	244	28	j	j	PROPN
cana-3894	244	29	,	,	PUNCT
cana-3894	244	30	i	i	PRON
cana-3894	244	31	φ	φ	PROPN
cana-3894	244	32	(	(	PUNCT
cana-3894	244	33	µ,c	µ,c	NOUN
cana-3894	244	34	,	,	PUNCT
cana-3894	244	35	η;r	η;r	PROPN
cana-3894	244	36	)	)	PUNCT
cana-3894	244	37	ℓ,k	ℓ,k	X
cana-3894	244	38	φ	φ	X
cana-3894	244	39	(	(	PUNCT
cana-3894	244	40	α	α	PROPN
cana-3894	244	41	,	,	PUNCT
cana-3894	244	42	b	b	NOUN
cana-3894	244	43	,	,	PUNCT
cana-3894	244	44	σ;1	σ;1	PROPN
cana-3894	244	45	)	)	PUNCT
cana-3894	244	46	h	h	NOUN
cana-3894	244	47	,	,	PUNCT
cana-3894	244	48	m	m	VERB
cana-3894	244	49	yc	yc	NOUN
cana-3894	244	50	=	=	PUNCT
cana-3894	245	1	∞∑	∞∑	PROPN
cana-3894	245	2	n=0	n=0	NUM
cana-3894	245	3	cn	cn	NOUN
cana-3894	245	4	an	an	DET
cana-3894	245	5	b−1	b−1	PROPN
cana-3894	245	6	n−1	n−1	PROPN
cana-3894	245	7	c−1	c−1	PROPN
cana-3894	245	8	n−1	n−1	PROPN
cana-3894	245	9	1	1	NUM
cana-3894	245	10	(	(	PUNCT
cana-3894	245	11	q	q	NOUN
cana-3894	245	12	;	;	PUNCT
cana-3894	245	13	q)n	q)n	X
cana-3894	245	14	{	{	PUNCT
cana-3894	245	15	δ−1∏	δ−1∏	PROPN
cana-3894	245	16	j=0	j=0	PROPN
cana-3894	245	17	δ−1∏	δ−1∏	ADJ
cana-3894	245	18	i=0	i=0	PROPN
cana-3894	246	1	[	[	X
cana-3894	246	2	(	(	PUNCT
cana-3894	246	3	∆qi	∆qi	X
cana-3894	246	4	+	+	CCONJ
cana-3894	246	5	ζ−jq−(a+ii)/δ	ζ−jq−(a+ii)/δ	NUM
cana-3894	246	6	−	−	NOUN
cana-3894	246	7	i)]−s	i)]−s	PROPN
cana-3894	246	8	}	}	PUNCT
cana-3894	246	9	×	×	NOUN
cana-3894	246	10	{	{	PUNCT
cana-3894	246	11	δ−1∏	δ−1∏	PROPN
cana-3894	246	12	j=0	j=0	VERB
cana-3894	246	13	δ−1∏	δ−1∏	VERB
cana-3894	246	14	i=0	i=0	PROPN
cana-3894	247	1	[	[	X
cana-3894	247	2	(	(	PUNCT
cana-3894	247	3	ζ−jq−(a+ii)/δ)]−s	ζ−jq−(a+ii)/δ)]−s	ADJ
cana-3894	247	4	}	}	PUNCT
cana-3894	247	5	−1	−1	NOUN
cana-3894	247	6	zn	zn	NOUN
cana-3894	247	7	=	=	PUNCT
cana-3894	248	1	∞∑	∞∑	PROPN
cana-3894	248	2	n=0	n=0	NUM
cana-3894	248	3	cn	cn	NOUN
cana-3894	248	4	an	an	DET
cana-3894	248	5	b−1	b−1	PROPN
cana-3894	248	6	n−1	n−1	PROPN
cana-3894	248	7	c−1	c−1	PROPN
cana-3894	248	8	n−1	n−1	PROPN
cana-3894	248	9	1	1	NUM
cana-3894	248	10	(	(	PUNCT
cana-3894	248	11	q	q	NOUN
cana-3894	248	12	;	;	PUNCT
cana-3894	248	13	q)n	q)n	X
cana-3894	248	14	{	{	PUNCT
cana-3894	248	15	δ−1∏	δ−1∏	PROPN
cana-3894	248	16	j=0	j=0	PROPN
cana-3894	248	17	δ−1∏	δ−1∏	ADJ
cana-3894	248	18	i=0	i=0	PROPN
cana-3894	249	1	[	[	X
cana-3894	249	2	(	(	PUNCT
cana-3894	249	3	i	i	PRON
cana-3894	249	4	−	−	PROPN
cana-3894	249	5	ζjqni+(a+ii)/δ)]s	ζjqni+(a+ii)/δ)]s	NOUN
cana-3894	249	6	}	}	PUNCT
cana-3894	249	7	zn	zn	NOUN
cana-3894	249	8	=	=	PUNCT
cana-3894	250	1	∞∑	∞∑	PROPN
cana-3894	250	2	n=0	n=0	NUM
cana-3894	250	3	cn	cn	NOUN
cana-3894	250	4	an	an	DET
cana-3894	250	5	b−1	b−1	PROPN
cana-3894	250	6	n−1	n−1	PROPN
cana-3894	250	7	c−1	c−1	PROPN
cana-3894	250	8	n−1	n−1	PROPN
cana-3894	250	9	1	1	NUM
cana-3894	250	10	(	(	PUNCT
cana-3894	250	11	q	q	NOUN
cana-3894	250	12	;	;	PUNCT
cana-3894	250	13	q)n	q)n	X
cana-3894	250	14	an−1	an−1	PROPN
cana-3894	250	15	a−1	a−1	PROPN
cana-3894	250	16	n	n	PROPN
cana-3894	250	17	zn	zn	NOUN
cana-3894	250	18	=	=	PUNCT
cana-3894	251	1	∞∑	∞∑	PROPN
cana-3894	251	2	n=0	n=0	NUM
cana-3894	251	3	cn	cn	NOUN
cana-3894	251	4	an−1	an−1	ADJ
cana-3894	251	5	b−1	b−1	PROPN
cana-3894	251	6	n−1	n−1	PROPN
cana-3894	251	7	c−1	c−1	PROPN
cana-3894	251	8	n−1	n−1	PROPN
cana-3894	251	9	zn	zn	PROPN
cana-3894	251	10	(	(	PUNCT
cana-3894	251	11	q	q	NOUN
cana-3894	251	12	;	;	PUNCT
cana-3894	251	13	q)n	q)n	X
cana-3894	251	14	https://internationalpubls.com	https://internationalpubls.com	X
cana-3894	251	15	343	343	NUM
cana-3894	251	16	communications	communication	NOUN
cana-3894	251	17	on	on	ADP
cana-3894	251	18	applied	apply	VERB
cana-3894	251	19	nonlinear	nonlinear	ADJ
cana-3894	251	20	analysis	analysis	NOUN
cana-3894	251	21	issn	issn	NOUN
cana-3894	251	22	:	:	PUNCT
cana-3894	251	23	1074	1074	NUM
cana-3894	251	24	-	-	PUNCT
cana-3894	251	25	133x	133x	NUM
cana-3894	251	26	vol	vol	NOUN
cana-3894	251	27	32	32	NUM
cana-3894	251	28	no	no	NOUN
cana-3894	251	29	.	.	PUNCT
cana-3894	252	1	9s(2025	9s(2025	NUM
cana-3894	252	2	)	)	PUNCT
cana-3894	252	3	finally	finally	ADV
cana-3894	252	4	,	,	PUNCT
cana-3894	252	5	∆q	∆q	PROPN
cana-3894	252	6	yc	yc	NOUN
cana-3894	252	7	=	=	PROPN
cana-3894	252	8	dq	dq	PROPN
cana-3894	252	9	ω	ω	PROPN
cana-3894	252	10	(	(	PUNCT
cana-3894	252	11	δ	δ	PROPN
cana-3894	252	12	,	,	PUNCT
cana-3894	252	13	a	a	PRON
cana-3894	252	14	,	,	PUNCT
cana-3894	252	15	ζ;−s	ζ;−s	NOUN
cana-3894	252	16	)	)	PUNCT
cana-3894	252	17	j	j	PROPN
cana-3894	252	18	,	,	PUNCT
cana-3894	252	19	i	i	PRON
cana-3894	252	20	φ	φ	PROPN
cana-3894	252	21	(	(	PUNCT
cana-3894	252	22	µ,c	µ,c	NOUN
cana-3894	252	23	,	,	PUNCT
cana-3894	252	24	η;r	η;r	PROPN
cana-3894	252	25	)	)	PUNCT
cana-3894	252	26	ℓ,k	ℓ,k	X
cana-3894	252	27	φ	φ	X
cana-3894	252	28	(	(	PUNCT
cana-3894	252	29	α	α	PROPN
cana-3894	252	30	,	,	PUNCT
cana-3894	252	31	b	b	NOUN
cana-3894	252	32	,	,	PUNCT
cana-3894	252	33	σ;1	σ;1	PROPN
cana-3894	252	34	)	)	PUNCT
cana-3894	252	35	h	h	NOUN
cana-3894	252	36	,	,	PUNCT
cana-3894	252	37	m	m	VERB
cana-3894	252	38	yc	yc	NOUN
cana-3894	252	39	=	=	NOUN
cana-3894	252	40	∞∑	∞∑	NUM
cana-3894	252	41	n=1	n=1	NUM
cana-3894	252	42	cn	cn	PROPN
cana-3894	252	43	an−1	an−1	PROPN
cana-3894	252	44	b−1	b−1	PROPN
cana-3894	252	45	n−1	n−1	PROPN
cana-3894	252	46	c−1	c−1	PROPN
cana-3894	252	47	n−1	n−1	PROPN
cana-3894	252	48	zn−1	zn−1	PROPN
cana-3894	252	49	(	(	PUNCT
cana-3894	252	50	q	q	NOUN
cana-3894	252	51	;	;	PUNCT
cana-3894	252	52	q)n−1	q)n−1	PROPN
cana-3894	252	53	=	=	PUNCT
cana-3894	253	1	∞∑	∞∑	PRON
cana-3894	253	2	n=0	n=0	NUM
cana-3894	253	3	cn+1	cn+1	VERB
cana-3894	253	4	an	an	DET
cana-3894	253	5	b−1	b−1	PROPN
cana-3894	253	6	n	n	CCONJ
cana-3894	253	7	c−1	c−1	PROPN
cana-3894	253	8	n	n	PROPN
cana-3894	253	9	zn	zn	PROPN
cana-3894	253	10	(	(	PUNCT
cana-3894	253	11	q	q	NOUN
cana-3894	253	12	;	;	PUNCT
cana-3894	253	13	q)n	q)n	SYM
cana-3894	253	14	=	=	SYM
cana-3894	253	15	c	c	NOUN
cana-3894	253	16	ea	ea	PROPN
cana-3894	253	17	,	,	PUNCT
cana-3894	253	18	b	b	PROPN
cana-3894	253	19	,	,	PUNCT
cana-3894	253	20	c	c	PROPN
cana-3894	253	21	αi	αi	PROPN
cana-3894	253	22	,	,	PUNCT
cana-3894	253	23	δi	δi	ADV
cana-3894	253	24	,	,	PUNCT
cana-3894	253	25	µi(cz	µi(cz	NOUN
cana-3894	253	26	;	;	PUNCT
cana-3894	253	27	s	s	X
cana-3894	253	28	,	,	PUNCT
cana-3894	253	29	r|q	r|q	ADJ
cana-3894	253	30	)	)	PUNCT
cana-3894	253	31	.	.	PUNCT
cana-3894	254	1	references	reference	NOUN
cana-3894	254	2	[	[	X
cana-3894	254	3	1	1	NUM
cana-3894	254	4	]	]	PUNCT
cana-3894	254	5	m.	m.	NOUN
cana-3894	254	6	h.	h.	PROPN
cana-3894	254	7	annaby	annaby	PROPN
cana-3894	254	8	and	and	CCONJ
cana-3894	254	9	z.	z.	PROPN
cana-3894	254	10	s.	s.	PROPN
cana-3894	254	11	mansour	mansour	PROPN
cana-3894	254	12	.	.	PROPN
cana-3894	255	1	q	q	ADJ
cana-3894	255	2	-	-	PUNCT
cana-3894	255	3	fractional	fractional	ADJ
cana-3894	255	4	calculus	calculus	NOUN
cana-3894	255	5	and	and	CCONJ
cana-3894	255	6	equations	equation	NOUN
cana-3894	255	7	.	.	PUNCT
cana-3894	256	1	springerverlag	springerverlag	PROPN
cana-3894	256	2	berlin	berlin	PROPN
cana-3894	256	3	heidelberg	heidelberg	PROPN
cana-3894	256	4	,	,	PUNCT
cana-3894	256	5	2012	2012	NUM
cana-3894	256	6	.	.	PUNCT
cana-3894	257	1	[	[	X
cana-3894	257	2	2	2	X
cana-3894	257	3	]	]	X
cana-3894	257	4	g.	g.	PROPN
cana-3894	257	5	gasper	gasper	PROPN
cana-3894	257	6	and	and	CCONJ
cana-3894	257	7	m.	m.	PROPN
cana-3894	257	8	rahman	rahman	PROPN
cana-3894	257	9	.	.	PUNCT
cana-3894	258	1	basic	basic	ADJ
cana-3894	258	2	hypergeometric	hypergeometric	ADJ
cana-3894	258	3	series	series	NOUN
cana-3894	258	4	.	.	PUNCT
cana-3894	259	1	cambridge	cambridge	PROPN
cana-3894	259	2	university	university	PROPN
cana-3894	259	3	press	press	PROPN
cana-3894	259	4	,	,	PUNCT
cana-3894	259	5	cambridge	cambridge	PROPN
cana-3894	259	6	,	,	PUNCT
cana-3894	259	7	1990	1990	NUM
cana-3894	259	8	.	.	PUNCT
cana-3894	260	1	[	[	X
cana-3894	260	2	3	3	X
cana-3894	260	3	]	]	X
cana-3894	260	4	b.	b.	PROPN
cana-3894	260	5	v.	v.	PROPN
cana-3894	260	6	nathwani	nathwani	PROPN
cana-3894	260	7	.	.	PUNCT
cana-3894	261	1	generalized	generalize	VERB
cana-3894	261	2	q	q	ADJ
cana-3894	261	3	-	-	ADJ
cana-3894	261	4	mittag	mittag	ADJ
cana-3894	261	5	-	-	PUNCT
cana-3894	261	6	leffler	leffler	NOUN
cana-3894	261	7	function	function	NOUN
cana-3894	261	8	and	and	CCONJ
cana-3894	261	9	its	its	PRON
cana-3894	261	10	properties	property	NOUN
cana-3894	261	11	.	.	PUNCT
cana-3894	262	1	journal	journal	PROPN
cana-3894	262	2	of	of	ADP
cana-3894	262	3	divulgaciones	divulgaciones	PROPN
cana-3894	262	4	matematicas	matematicas	PROPN
cana-3894	262	5	,	,	PUNCT
cana-3894	262	6	18(1):10–33	18(1):10–33	NUM
cana-3894	262	7	,	,	PUNCT
cana-3894	262	8	2017	2017	NUM
cana-3894	262	9	.	.	PUNCT
cana-3894	263	1	[	[	X
cana-3894	263	2	4	4	X
cana-3894	263	3	]	]	X
cana-3894	263	4	b.	b.	PROPN
cana-3894	263	5	v.	v.	PROPN
cana-3894	263	6	nathwani	nathwani	PROPN
cana-3894	263	7	.	.	PUNCT
cana-3894	264	1	inequalities	inequality	NOUN
cana-3894	264	2	involving	involve	VERB
cana-3894	264	3	mittag	mittag	ADJ
cana-3894	264	4	-	-	PUNCT
cana-3894	264	5	leffler	leffler	NOUN
cana-3894	264	6	type	type	NOUN
cana-3894	264	7	q	q	ADJ
cana-3894	264	8	-	-	PUNCT
cana-3894	264	9	konhauser	konhauser	ADJ
cana-3894	264	10	polynomial	polynomial	NOUN
cana-3894	264	11	.	.	PUNCT
cana-3894	265	1	studia	studia	PROPN
cana-3894	265	2	universitatis	universitatis	PROPN
cana-3894	265	3	babes	babes	PROPN
cana-3894	265	4	-	-	PUNCT
cana-3894	265	5	bolyai	bolyai	NOUN
cana-3894	265	6	mathematica	mathematica	PROPN
cana-3894	265	7	,	,	PUNCT
cana-3894	265	8	65(3):379–401	65(3):379–401	PROPN
cana-3894	265	9	,	,	PUNCT
cana-3894	265	10	2020	2020	NUM
cana-3894	265	11	.	.	PUNCT
cana-3894	266	1	[	[	X
cana-3894	266	2	5	5	NUM
cana-3894	266	3	]	]	X
cana-3894	266	4	b.	b.	PROPN
cana-3894	266	5	v.	v.	PROPN
cana-3894	266	6	nathwani	nathwani	PROPN
cana-3894	266	7	and	and	CCONJ
cana-3894	266	8	b.	b.	PROPN
cana-3894	266	9	i.	i.	PROPN
cana-3894	266	10	dave	dave	PROPN
cana-3894	266	11	.	.	PUNCT
cana-3894	267	1	generalized	generalize	VERB
cana-3894	267	2	mittag	mittag	ADJ
cana-3894	267	3	-	-	PUNCT
cana-3894	267	4	leffler	leffler	NOUN
cana-3894	267	5	function	function	NOUN
cana-3894	267	6	and	and	CCONJ
cana-3894	267	7	its	its	PRON
cana-3894	267	8	properties	property	NOUN
cana-3894	267	9	.	.	PUNCT
cana-3894	268	1	the	the	DET
cana-3894	268	2	mathematics	mathematics	PROPN
cana-3894	268	3	student	student	NOUN
cana-3894	268	4	journal	journal	PROPN
cana-3894	268	5	,	,	PUNCT
cana-3894	268	6	86(1	86(1	PROPN
cana-3894	268	7	-	-	PUNCT
cana-3894	268	8	2):63–76	2):63–76	NUM
cana-3894	268	9	,	,	PUNCT
cana-3894	268	10	2017	2017	NUM
cana-3894	268	11	.	.	PUNCT
cana-3894	269	1	[	[	X
cana-3894	269	2	6	6	NUM
cana-3894	269	3	]	]	X
cana-3894	269	4	b.	b.	PROPN
cana-3894	269	5	v.	v.	PROPN
cana-3894	269	6	nathwani	nathwani	PROPN
cana-3894	269	7	and	and	CCONJ
cana-3894	269	8	b.	b.	PROPN
cana-3894	269	9	i.	i.	PROPN
cana-3894	269	10	dave	dave	PROPN
cana-3894	269	11	.	.	PUNCT
cana-3894	270	1	fractional	fractional	ADJ
cana-3894	270	2	q	q	NOUN
cana-3894	270	3	-	-	INTJ
cana-3894	270	4	calculus	calculus	NOUN
cana-3894	270	5	of	of	ADP
cana-3894	270	6	anextended	anextende	VERB
cana-3894	270	7	qmittag	qmittag	ADJ
cana-3894	270	8	-	-	PUNCT
cana-3894	270	9	leffler	leffler	NOUN
cana-3894	270	10	function	function	NOUN
cana-3894	270	11	.	.	PUNCT
cana-3894	271	1	journal	journal	NOUN
cana-3894	271	2	of	of	ADP
cana-3894	271	3	fractional	fractional	ADJ
cana-3894	271	4	calculus	calculus	NOUN
cana-3894	271	5	and	and	CCONJ
cana-3894	271	6	applications	application	NOUN
cana-3894	271	7	,	,	PUNCT
cana-3894	271	8	9(1):64–81	9(1):64–81	NUM
cana-3894	271	9	,	,	PUNCT
cana-3894	271	10	2018	2018	NUM
cana-3894	271	11	.	.	PUNCT
cana-3894	272	1	[	[	X
cana-3894	272	2	7	7	X
cana-3894	272	3	]	]	X
cana-3894	272	4	j.	j.	PROPN
cana-3894	272	5	c.	c.	PROPN
cana-3894	272	6	prajapati	prajapati	PROPN
cana-3894	272	7	,	,	PUNCT
cana-3894	272	8	b.	b.	PROPN
cana-3894	272	9	i.	i.	PROPN
cana-3894	272	10	dave	dave	PROPN
cana-3894	272	11	,	,	PUNCT
cana-3894	272	12	and	and	CCONJ
cana-3894	272	13	b.	b.	PROPN
cana-3894	272	14	v.	v.	PROPN
cana-3894	272	15	nathwani	nathwani	PROPN
cana-3894	272	16	.	.	PUNCT
cana-3894	273	1	on	on	ADP
cana-3894	273	2	a	a	DET
cana-3894	273	3	unification	unification	NOUN
cana-3894	273	4	of	of	ADP
cana-3894	273	5	generalized	generalized	ADJ
cana-3894	273	6	mittag	mittag	ADJ
cana-3894	273	7	-	-	PUNCT
cana-3894	273	8	leffler	leffler	NOUN
cana-3894	273	9	function	function	NOUN
cana-3894	273	10	and	and	CCONJ
cana-3894	273	11	family	family	NOUN
cana-3894	273	12	of	of	ADP
cana-3894	273	13	bessel	bessel	NOUN
cana-3894	273	14	functions	function	NOUN
cana-3894	273	15	.	.	PUNCT
cana-3894	274	1	advances	advance	NOUN
cana-3894	274	2	in	in	ADP
cana-3894	274	3	pure	pure	ADJ
cana-3894	274	4	mathematics	mathematic	NOUN
cana-3894	274	5	,	,	PUNCT
cana-3894	274	6	3:127–137	3:127–137	NUM
cana-3894	274	7	,	,	PUNCT
cana-3894	274	8	2013	2013	NUM
cana-3894	274	9	.	.	PUNCT
cana-3894	275	1	[	[	X
cana-3894	275	2	8	8	X
cana-3894	275	3	]	]	X
cana-3894	275	4	j.	j.	PROPN
cana-3894	275	5	c.	c.	PROPN
cana-3894	275	6	prajapati	prajapati	PROPN
cana-3894	275	7	and	and	CCONJ
cana-3894	275	8	b.	b.	PROPN
cana-3894	275	9	v.	v.	PROPN
cana-3894	275	10	nathwani	nathwani	PROPN
cana-3894	275	11	.	.	PUNCT
cana-3894	276	1	recurrence	recurrence	NOUN
cana-3894	276	2	relation	relation	NOUN
cana-3894	276	3	of	of	ADP
cana-3894	276	4	a	a	DET
cana-3894	276	5	unified	unified	ADJ
cana-3894	276	6	generalized	generalized	ADJ
cana-3894	276	7	mittag	mittag	ADJ
cana-3894	276	8	-	-	PUNCT
cana-3894	276	9	leffler	leffler	NOUN
cana-3894	276	10	-	-	PUNCT
cana-3894	276	11	function	function	NOUN
cana-3894	276	12	.	.	PUNCT
cana-3894	277	1	palestine	palestine	PROPN
cana-3894	277	2	journal	journal	PROPN
cana-3894	277	3	of	of	ADP
cana-3894	277	4	mathematics	mathematic	NOUN
cana-3894	277	5	,	,	PUNCT
cana-3894	277	6	3(1):94––98	3(1):94––98	PROPN
cana-3894	277	7	,	,	PUNCT
cana-3894	277	8	2014	2014	NUM
cana-3894	277	9	.	.	PUNCT
cana-3894	278	1	[	[	X
cana-3894	278	2	9	9	NUM
cana-3894	278	3	]	]	PUNCT
cana-3894	278	4	j.	j.	PROPN
cana-3894	278	5	c.	c.	PROPN
cana-3894	278	6	prajapati	prajapati	PROPN
cana-3894	278	7	and	and	CCONJ
cana-3894	278	8	b.	b.	PROPN
cana-3894	278	9	v.	v.	PROPN
cana-3894	278	10	nathwani	nathwani	PROPN
cana-3894	278	11	.	.	PUNCT
cana-3894	279	1	fractional	fractional	ADJ
cana-3894	279	2	calculus	calculus	NOUN
cana-3894	279	3	of	of	ADP
cana-3894	279	4	a	a	DET
cana-3894	279	5	unified	unified	ADJ
cana-3894	279	6	mittag	mittag	ADJ
cana-3894	279	7	-	-	PUNCT
cana-3894	279	8	leffler	leffler	NOUN
cana-3894	279	9	function	function	NOUN
cana-3894	279	10	.	.	PUNCT
cana-3894	280	1	ukrainian	ukrainian	ADJ
cana-3894	280	2	mathematical	mathematical	ADJ
cana-3894	280	3	journal	journal	NOUN
cana-3894	280	4	,	,	PUNCT
cana-3894	280	5	66(8):1267–1280	66(8):1267–1280	NUM
cana-3894	280	6	,	,	PUNCT
cana-3894	280	7	2015	2015	NUM
cana-3894	280	8	.	.	PUNCT
cana-3894	281	1	[	[	X
cana-3894	281	2	10	10	NUM
cana-3894	281	3	]	]	X
cana-3894	281	4	ahmed	ahmed	PROPN
cana-3894	281	5	salem	salem	PROPN
cana-3894	281	6	.	.	PUNCT
cana-3894	282	1	on	on	ADP
cana-3894	282	2	a	a	DET
cana-3894	282	3	q	q	NOUN
cana-3894	282	4	-	-	PUNCT
cana-3894	282	5	gamma	gamma	NOUN
cana-3894	282	6	and	and	CCONJ
cana-3894	282	7	a	a	DET
cana-3894	282	8	q	q	ADJ
cana-3894	282	9	-	-	PUNCT
cana-3894	282	10	beta	beta	ADJ
cana-3894	282	11	matrix	matrix	NOUN
cana-3894	282	12	functions	function	NOUN
cana-3894	282	13	.	.	PUNCT
cana-3894	283	1	linear	linear	ADJ
cana-3894	283	2	and	and	CCONJ
cana-3894	283	3	multilinear	multilinear	PROPN
cana-3894	283	4	algebra	algebra	PROPN
cana-3894	283	5	,	,	PUNCT
cana-3894	283	6	60(6):683–696	60(6):683–696	NOUN
cana-3894	283	7	,	,	PUNCT
cana-3894	283	8	2012	2012	NUM
cana-3894	283	9	.	.	PUNCT
cana-3894	284	1	[	[	X
cana-3894	284	2	11	11	NUM
cana-3894	284	3	]	]	X
cana-3894	284	4	r.	r.	PROPN
cana-3894	284	5	r.	r.	PROPN
cana-3894	284	6	sanjhira	sanjhira	PROPN
cana-3894	284	7	,	,	PUNCT
cana-3894	284	8	b.	b.	PROPN
cana-3894	284	9	v.	v.	PROPN
cana-3894	284	10	nathwani	nathwani	PROPN
cana-3894	284	11	,	,	PUNCT
cana-3894	284	12	and	and	CCONJ
cana-3894	284	13	b.	b.	PROPN
cana-3894	284	14	i.	i.	PROPN
cana-3894	284	15	dave	dave	PROPN
cana-3894	284	16	.	.	PUNCT
cana-3894	285	1	generalized	generalize	VERB
cana-3894	285	2	mittag	mittag	ADJ
cana-3894	285	3	-	-	PUNCT
cana-3894	285	4	leffler	leffler	NOUN
cana-3894	285	5	matrix	matrix	NOUN
cana-3894	285	6	function	function	NOUN
cana-3894	285	7	and	and	CCONJ
cana-3894	285	8	associated	associated	ADJ
cana-3894	285	9	matrix	matrix	NOUN
cana-3894	285	10	polynomials	polynomial	NOUN
cana-3894	285	11	.	.	PUNCT
cana-3894	286	1	the	the	DET
cana-3894	286	2	journal	journal	NOUN
cana-3894	286	3	of	of	ADP
cana-3894	286	4	the	the	DET
cana-3894	286	5	indian	indian	PROPN
cana-3894	286	6	mathematical	mathematical	ADJ
cana-3894	286	7	society	society	NOUN
cana-3894	286	8	,	,	PUNCT
cana-3894	286	9	86(1	86(1	PROPN
cana-3894	286	10	-	-	PUNCT
cana-3894	286	11	2):161–178	2):161–178	NUM
cana-3894	286	12	,	,	PUNCT
cana-3894	286	13	2019	2019	NUM
cana-3894	286	14	.	.	PUNCT
cana-3894	287	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3894	287	2	344	344	NUM