id	sid	tid	token	lemma	pos
cana-5712	1	1	communications	communication	NOUN
cana-5712	1	2	on	on	ADP
cana-5712	1	3	applied	apply	VERB
cana-5712	1	4	nonlinear	nonlinear	ADJ
cana-5712	1	5	analysis	analysis	NOUN
cana-5712	1	6	issn	issn	NOUN
cana-5712	1	7	:	:	PUNCT
cana-5712	1	8	1074	1074	NUM
cana-5712	1	9	-	-	PUNCT
cana-5712	1	10	133x	133x	NUM
cana-5712	1	11	vol	vol	VERB
cana-5712	1	12	32	32	NUM
cana-5712	1	13	no	no	NOUN
cana-5712	1	14	.	.	PUNCT
cana-5712	2	1	10s	10	NOUN
cana-5712	2	2	(	(	PUNCT
cana-5712	2	3	2025	2025	NUM
cana-5712	2	4	)	)	PUNCT
cana-5712	2	5	2712	2712	NUM
cana-5712	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5712	2	7	computation	computation	NOUN
cana-5712	2	8	of	of	ADP
cana-5712	2	9	euler	euler	NOUN
cana-5712	2	10	-	-	PUNCT
cana-5712	2	11	type	type	NOUN
cana-5712	2	12	integrals	integral	NOUN
cana-5712	2	13	involving	involve	VERB
cana-5712	2	14	generalized	generalized	ADJ
cana-5712	2	15	m	m	PROPN
cana-5712	2	16	-	-	PUNCT
cana-5712	2	17	series	series	NOUN
cana-5712	2	18	m.	m.	NOUN
cana-5712	2	19	u.	u.	PROPN
cana-5712	2	20	siddiqui	siddiqui	PROPN
cana-5712	2	21	1	1	NUM
cana-5712	2	22	,	,	PUNCT
cana-5712	2	23	owais	owais	PROPN
cana-5712	2	24	khan2	khan2	PROPN
cana-5712	2	25	*	*	PUNCT
cana-5712	2	26	,	,	PUNCT
cana-5712	2	27	nafis	nafis	PROPN
cana-5712	2	28	ahmad3	ahmad3	PROPN
cana-5712	2	29	and	and	CCONJ
cana-5712	2	30	m.	m.	PROPN
cana-5712	2	31	kashif	kashif	PROPN
cana-5712	2	32	khan4	khan4	PROPN
cana-5712	2	33	1,2,4department	1,2,4department	NUM
cana-5712	2	34	of	of	ADP
cana-5712	2	35	mathematics	mathematic	NOUN
cana-5712	2	36	and	and	CCONJ
cana-5712	2	37	statistics	statistic	NOUN
cana-5712	2	38	,	,	PUNCT
cana-5712	2	39	integral	integral	ADJ
cana-5712	2	40	university	university	NOUN
cana-5712	2	41	,	,	PUNCT
cana-5712	2	42	lucknow-226026,india	lucknow-226026,india	PROPN
cana-5712	2	43	emails	email	NOUN
cana-5712	2	44	:	:	PUNCT
cana-5712	2	45	2uzairmohd931@gmail.com	2uzairmohd931@gmail.com	NUM
cana-5712	2	46	,	,	PUNCT
cana-5712	2	47	2owkhan05@gmail.com	2owkhan05@gmail.com	NUM
cana-5712	2	48	,	,	PUNCT
cana-5712	2	49	4mdkashifkhan85@gmail.com	4mdkashifkhan85@gmail.com	X
cana-5712	3	1	3department	3department	NUM
cana-5712	3	2	of	of	ADP
cana-5712	3	3	mathematics	mathematic	NOUN
cana-5712	3	4	,	,	PUNCT
cana-5712	3	5	shibli	shibli	PROPN
cana-5712	3	6	national	national	PROPN
cana-5712	3	7	college	college	NOUN
cana-5712	3	8	,	,	PUNCT
cana-5712	3	9	azamgarh-276001	azamgarh-276001	ADJ
cana-5712	3	10	,	,	PUNCT
cana-5712	3	11	india	india	PROPN
cana-5712	3	12	email	email	NOUN
cana-5712	3	13	:	:	PUNCT
cana-5712	3	14	3nafis.sncmaths@gmail.com	3nafis.sncmaths@gmail.com	NUM
cana-5712	3	15	article	article	NOUN
cana-5712	3	16	history	history	NOUN
cana-5712	3	17	:	:	PUNCT
cana-5712	3	18	received	receive	VERB
cana-5712	3	19	:	:	PUNCT
cana-5712	3	20	12	12	NUM
cana-5712	3	21	-	-	SYM
cana-5712	3	22	01	01	NUM
cana-5712	3	23	-	-	PUNCT
cana-5712	3	24	2025	2025	NUM
cana-5712	3	25	revised	revise	VERB
cana-5712	3	26	:	:	PUNCT
cana-5712	3	27	15	15	NUM
cana-5712	3	28	-	-	NUM
cana-5712	3	29	02	02	NUM
cana-5712	3	30	-	-	PUNCT
cana-5712	3	31	2025	2025	NUM
cana-5712	3	32	accepted	accept	VERB
cana-5712	3	33	:	:	PUNCT
cana-5712	3	34	01	01	NUM
cana-5712	3	35	-	-	SYM
cana-5712	3	36	03	03	NUM
cana-5712	3	37	-	-	PUNCT
cana-5712	3	38	2025	2025	NUM
cana-5712	3	39	abstract	abstract	NOUN
cana-5712	3	40	:	:	PUNCT
cana-5712	3	41	:	:	PUNCT
cana-5712	3	42	this	this	DET
cana-5712	3	43	research	research	NOUN
cana-5712	3	44	presents	present	VERB
cana-5712	3	45	new	new	ADJ
cana-5712	3	46	evaluations	evaluation	NOUN
cana-5712	3	47	of	of	ADP
cana-5712	3	48	euler	euler	NOUN
cana-5712	3	49	-	-	PUNCT
cana-5712	3	50	type	type	NOUN
cana-5712	3	51	integrals	integral	NOUN
cana-5712	3	52	that	that	PRON
cana-5712	3	53	encompass	encompass	VERB
cana-5712	3	54	the	the	DET
cana-5712	3	55	generalized	generalized	ADJ
cana-5712	3	56	m	m	PROPN
cana-5712	3	57	-	-	PUNCT
cana-5712	3	58	series	series	NOUN
cana-5712	3	59	,	,	PUNCT
cana-5712	3	60	a	a	DET
cana-5712	3	61	comprehensive	comprehensive	ADJ
cana-5712	3	62	extension	extension	NOUN
cana-5712	3	63	of	of	ADP
cana-5712	3	64	special	special	ADJ
cana-5712	3	65	functions	function	NOUN
cana-5712	3	66	.	.	PUNCT
cana-5712	4	1	these	these	DET
cana-5712	4	2	results	result	NOUN
cana-5712	4	3	not	not	PART
cana-5712	4	4	only	only	ADV
cana-5712	4	5	deepen	deepen	VERB
cana-5712	4	6	our	our	PRON
cana-5712	4	7	understanding	understanding	NOUN
cana-5712	4	8	of	of	ADP
cana-5712	4	9	the	the	DET
cana-5712	4	10	structural	structural	ADJ
cana-5712	4	11	properties	property	NOUN
cana-5712	4	12	of	of	ADP
cana-5712	4	13	the	the	DET
cana-5712	4	14	generalized	generalized	ADJ
cana-5712	4	15	m	m	PROPN
cana-5712	4	16	-	-	PUNCT
cana-5712	4	17	series	series	NOUN
cana-5712	4	18	but	but	CCONJ
cana-5712	4	19	also	also	ADV
cana-5712	4	20	suggest	suggest	VERB
cana-5712	4	21	potential	potential	ADJ
cana-5712	4	22	applications	application	NOUN
cana-5712	4	23	in	in	ADP
cana-5712	4	24	various	various	ADJ
cana-5712	4	25	fields	field	NOUN
cana-5712	4	26	,	,	PUNCT
cana-5712	4	27	including	include	VERB
cana-5712	4	28	mathematical	mathematical	ADJ
cana-5712	4	29	physics	physics	NOUN
cana-5712	4	30	,	,	PUNCT
cana-5712	4	31	engineering	engineering	NOUN
cana-5712	4	32	,	,	PUNCT
cana-5712	4	33	and	and	CCONJ
cana-5712	4	34	applied	applied	ADJ
cana-5712	4	35	mathematics	mathematic	NOUN
cana-5712	4	36	.	.	PUNCT
cana-5712	5	1	several	several	ADJ
cana-5712	5	2	specific	specific	ADJ
cana-5712	5	3	cases	case	NOUN
cana-5712	5	4	are	be	AUX
cana-5712	5	5	analysed	analyse	VERB
cana-5712	5	6	to	to	PART
cana-5712	5	7	illustrate	illustrate	VERB
cana-5712	5	8	the	the	DET
cana-5712	5	9	versatility	versatility	NOUN
cana-5712	5	10	and	and	CCONJ
cana-5712	5	11	utility	utility	NOUN
cana-5712	5	12	of	of	ADP
cana-5712	5	13	the	the	DET
cana-5712	5	14	derived	derive	VERB
cana-5712	5	15	integral	integral	ADJ
cana-5712	5	16	formulas	formula	NOUN
cana-5712	5	17	by	by	ADP
cana-5712	5	18	selecting	select	VERB
cana-5712	5	19	particular	particular	ADJ
cana-5712	5	20	parameter	parameter	NOUN
cana-5712	5	21	values	value	NOUN
cana-5712	5	22	of	of	ADP
cana-5712	5	23	the	the	DET
cana-5712	5	24	generalized	generalized	ADJ
cana-5712	5	25	m	m	PROPN
cana-5712	5	26	-	-	PUNCT
cana-5712	5	27	series	series	NOUN
cana-5712	5	28	.	.	PUNCT
cana-5712	6	1	keywords	keyword	NOUN
cana-5712	6	2	:	:	PUNCT
cana-5712	6	3	:	:	PUNCT
cana-5712	6	4	euler	euler	NOUN
cana-5712	6	5	-	-	PUNCT
cana-5712	6	6	type	type	NOUN
cana-5712	6	7	integrals	integral	NOUN
cana-5712	6	8	,	,	PUNCT
cana-5712	6	9	generalized	generalized	ADJ
cana-5712	6	10	m	m	NOUN
cana-5712	6	11	-	-	PUNCT
cana-5712	6	12	series	series	NOUN
cana-5712	6	13	and	and	CCONJ
cana-5712	6	14	fox	fox	PROPN
cana-5712	6	15	-	-	PUNCT
cana-5712	6	16	wright	wright	PROPN
cana-5712	6	17	functions	function	NOUN
cana-5712	6	18	.	.	PUNCT
cana-5712	7	1	1	1	X
cana-5712	7	2	.	.	X
cana-5712	7	3	introduction	introduction	NOUN
cana-5712	7	4	special	special	ADJ
cana-5712	7	5	functions	function	NOUN
cana-5712	7	6	are	be	AUX
cana-5712	7	7	mathematical	mathematical	ADJ
cana-5712	7	8	functions	function	NOUN
cana-5712	7	9	that	that	PRON
cana-5712	7	10	have	have	AUX
cana-5712	7	11	been	be	AUX
cana-5712	7	12	assigned	assign	VERB
cana-5712	7	13	specific	specific	ADJ
cana-5712	7	14	names	name	NOUN
cana-5712	7	15	and	and	CCONJ
cana-5712	7	16	symbols	symbol	NOUN
cana-5712	7	17	due	due	ADP
cana-5712	7	18	to	to	ADP
cana-5712	7	19	their	their	PRON
cana-5712	7	20	importance	importance	NOUN
cana-5712	7	21	in	in	ADP
cana-5712	7	22	various	various	ADJ
cana-5712	7	23	fields	field	NOUN
cana-5712	7	24	,	,	PUNCT
cana-5712	7	25	including	include	VERB
cana-5712	7	26	functional	functional	ADJ
cana-5712	7	27	analysis	analysis	NOUN
cana-5712	7	28	,	,	PUNCT
cana-5712	7	29	geometry	geometry	NOUN
cana-5712	7	30	,	,	PUNCT
cana-5712	7	31	physics	physics	NOUN
cana-5712	7	32	,	,	PUNCT
cana-5712	7	33	and	and	CCONJ
cana-5712	7	34	mathematical	mathematical	ADJ
cana-5712	7	35	analysis	analysis	NOUN
cana-5712	7	36	.	.	PUNCT
cana-5712	8	1	integral	integral	ADJ
cana-5712	8	2	transforms	transform	NOUN
cana-5712	8	3	are	be	AUX
cana-5712	8	4	widely	widely	ADV
cana-5712	8	5	used	use	VERB
cana-5712	8	6	in	in	ADP
cana-5712	8	7	many	many	ADJ
cana-5712	8	8	applied	apply	VERB
cana-5712	8	9	mathematics	mathematic	NOUN
cana-5712	8	10	and	and	CCONJ
cana-5712	8	11	mathematical	mathematical	ADJ
cana-5712	8	12	physics	physics	NOUN
cana-5712	8	13	problems	problem	NOUN
cana-5712	8	14	.	.	PUNCT
cana-5712	9	1	several	several	ADJ
cana-5712	9	2	mathematicians	mathematician	NOUN
cana-5712	9	3	have	have	AUX
cana-5712	9	4	developed	develop	VERB
cana-5712	9	5	integral	integral	ADJ
cana-5712	9	6	transforms	transform	NOUN
cana-5712	9	7	,	,	PUNCT
cana-5712	9	8	such	such	ADJ
cana-5712	9	9	as	as	ADP
cana-5712	9	10	the	the	DET
cana-5712	9	11	euler	euler	PROPN
cana-5712	9	12	integral	integral	ADJ
cana-5712	9	13	,	,	PUNCT
cana-5712	9	14	laplace	laplace	NOUN
cana-5712	9	15	transform	transform	NOUN
cana-5712	9	16	,	,	PUNCT
cana-5712	9	17	fourier	fourier	NOUN
cana-5712	9	18	transform	transform	NOUN
cana-5712	9	19	,	,	PUNCT
cana-5712	9	20	mellin	mellin	NOUN
cana-5712	9	21	transform	transform	NOUN
cana-5712	9	22	,	,	PUNCT
cana-5712	9	23	and	and	CCONJ
cana-5712	9	24	hankel	hankel	NOUN
cana-5712	9	25	transform	transform	NOUN
cana-5712	9	26	,	,	PUNCT
cana-5712	9	27	each	each	PRON
cana-5712	9	28	incorporating	incorporate	VERB
cana-5712	9	29	different	different	ADJ
cana-5712	9	30	special	special	ADJ
cana-5712	9	31	functions	function	NOUN
cana-5712	9	32	.	.	PUNCT
cana-5712	10	1	in	in	ADP
cana-5712	10	2	numerous	numerous	ADJ
cana-5712	10	3	studies	study	NOUN
cana-5712	10	4	,	,	PUNCT
cana-5712	10	5	the	the	DET
cana-5712	10	6	term	term	NOUN
cana-5712	10	7	exp(t	exp(t	PROPN
cana-5712	10	8	)	)	PUNCT
cana-5712	10	9	,	,	PUNCT
cana-5712	10	10	which	which	PRON
cana-5712	10	11	appears	appear	VERB
cana-5712	10	12	in	in	ADP
cana-5712	10	13	the	the	DET
cana-5712	10	14	integral	integral	ADJ
cana-5712	10	15	representation	representation	NOUN
cana-5712	10	16	of	of	ADP
cana-5712	10	17	the	the	DET
cana-5712	10	18	gamma	gamma	NOUN
cana-5712	10	19	function	function	NOUN
cana-5712	10	20	,	,	PUNCT
cana-5712	10	21	is	be	AUX
cana-5712	10	22	often	often	ADV
cana-5712	10	23	substituted	substitute	VERB
cana-5712	10	24	with	with	ADP
cana-5712	10	25	more	more	ADJ
cana-5712	10	26	complex	complex	ADJ
cana-5712	10	27	functions	function	NOUN
cana-5712	10	28	to	to	PART
cana-5712	10	29	facilitate	facilitate	VERB
cana-5712	10	30	generalizations	generalization	NOUN
cana-5712	10	31	.	.	PUNCT
cana-5712	11	1	these	these	DET
cana-5712	11	2	extensions	extension	NOUN
cana-5712	11	3	of	of	ADP
cana-5712	11	4	the	the	DET
cana-5712	11	5	beta	beta	ADJ
cana-5712	11	6	function	function	NOUN
cana-5712	11	7	are	be	AUX
cana-5712	11	8	presented	present	VERB
cana-5712	11	9	while	while	SCONJ
cana-5712	11	10	maintaining	maintain	VERB
cana-5712	11	11	its	its	PRON
cana-5712	11	12	symmetry	symmetry	NOUN
cana-5712	11	13	properties	property	NOUN
cana-5712	11	14	[	[	X
cana-5712	11	15	1	1	NUM
cana-5712	11	16	]	]	PUNCT
cana-5712	11	17	.	.	PUNCT
cana-5712	12	1	furthermore	furthermore	ADV
cana-5712	12	2	,	,	PUNCT
cana-5712	12	3	integral	integral	ADJ
cana-5712	12	4	and	and	CCONJ
cana-5712	12	5	derivative	derivative	ADJ
cana-5712	12	6	formulas	formula	NOUN
cana-5712	12	7	for	for	ADP
cana-5712	12	8	gauss	gauss	ADJ
cana-5712	12	9	hypergeometric	hypergeometric	ADJ
cana-5712	12	10	and	and	CCONJ
cana-5712	12	11	confluent	confluent	ADJ
cana-5712	12	12	hypergeometric	hypergeometric	ADJ
cana-5712	12	13	functions	function	NOUN
cana-5712	12	14	,	,	PUNCT
cana-5712	12	15	along	along	ADP
cana-5712	12	16	with	with	ADP
cana-5712	12	17	descriptions	description	NOUN
cana-5712	12	18	of	of	ADP
cana-5712	12	19	their	their	PRON
cana-5712	12	20	generalizations	generalization	NOUN
cana-5712	12	21	,	,	PUNCT
cana-5712	12	22	are	be	AUX
cana-5712	12	23	derived	derive	VERB
cana-5712	12	24	using	use	VERB
cana-5712	12	25	the	the	DET
cana-5712	12	26	generalized	generalized	ADJ
cana-5712	12	27	beta	beta	NOUN
cana-5712	12	28	function	function	NOUN
cana-5712	12	29	.	.	PUNCT
cana-5712	13	1	recently	recently	ADV
cana-5712	13	2	,	,	PUNCT
cana-5712	13	3	many	many	ADJ
cana-5712	13	4	researchers	researcher	NOUN
cana-5712	13	5	have	have	AUX
cana-5712	13	6	been	be	AUX
cana-5712	13	7	presenting	present	VERB
cana-5712	13	8	extensions	extension	NOUN
cana-5712	13	9	and	and	CCONJ
cana-5712	13	10	generalizations	generalization	NOUN
cana-5712	13	11	for	for	ADP
cana-5712	13	12	special	special	ADJ
cana-5712	13	13	functions	function	NOUN
cana-5712	13	14	,	,	PUNCT
cana-5712	13	15	such	such	ADJ
cana-5712	13	16	as	as	ADP
cana-5712	13	17	the	the	DET
cana-5712	13	18	pochhammer	pochhammer	NOUN
cana-5712	13	19	symbol	symbol	NOUN
cana-5712	13	20	,	,	PUNCT
cana-5712	13	21	gamma	gamma	NOUN
cana-5712	13	22	function	function	NOUN
cana-5712	13	23	,	,	PUNCT
cana-5712	13	24	k	k	PROPN
cana-5712	13	25	-	-	PUNCT
cana-5712	13	26	gamma	gamma	NOUN
cana-5712	13	27	function	function	NOUN
cana-5712	13	28	,	,	PUNCT
cana-5712	13	29	p	p	PROPN
cana-5712	13	30	-	-	PUNCT
cana-5712	13	31	k	k	NOUN
cana-5712	13	32	-	-	NOUN
cana-5712	13	33	gamma	gamma	NOUN
cana-5712	13	34	and	and	CCONJ
cana-5712	13	35	beta	beta	NOUN
cana-5712	13	36	functions	function	NOUN
cana-5712	13	37	,	,	PUNCT
cana-5712	13	38	along	along	ADP
cana-5712	13	39	with	with	ADP
cana-5712	13	40	the	the	DET
cana-5712	13	41	confluent	confluent	ADJ
cana-5712	13	42	hypergeometric	hypergeometric	ADJ
cana-5712	13	43	function	function	NOUN
cana-5712	13	44	(	(	PUNCT
cana-5712	13	45	see	see	VERB
cana-5712	13	46	[	[	X
cana-5712	13	47	2	2	NUM
cana-5712	13	48	-	-	SYM
cana-5712	13	49	5	5	NUM
cana-5712	13	50	,	,	PUNCT
cana-5712	13	51	9	9	NUM
cana-5712	13	52	-	-	SYM
cana-5712	13	53	10	10	NUM
cana-5712	13	54	,	,	PUNCT
cana-5712	13	55	15	15	NUM
cana-5712	13	56	]	]	NUM
cana-5712	13	57	)	)	PUNCT
cana-5712	13	58	.	.	PUNCT
cana-5712	14	1	sharma	sharma	PROPN
cana-5712	14	2	and	and	CCONJ
cana-5712	14	3	jain	jain	PROPN
cana-5712	15	1	[	[	X
cana-5712	15	2	12	12	NUM
cana-5712	15	3	]	]	PUNCT
cana-5712	15	4	characterized	characterize	VERB
cana-5712	15	5	a	a	DET
cana-5712	15	6	generalized	generalized	ADJ
cana-5712	15	7	m	m	NOUN
cana-5712	15	8	-	-	PUNCT
cana-5712	15	9	series	series	NOUN
cana-5712	15	10	,	,	PUNCT
cana-5712	15	11	which	which	PRON
cana-5712	15	12	extends	extend	VERB
cana-5712	15	13	various	various	ADJ
cana-5712	15	14	special	special	ADJ
cana-5712	15	15	functions	function	NOUN
cana-5712	15	16	such	such	ADJ
cana-5712	15	17	as	as	ADP
cana-5712	15	18	the	the	DET
cana-5712	15	19	mittag	mittag	ADJ
cana-5712	15	20	-	-	PUNCT
cana-5712	15	21	leffler	leffler	NOUN
cana-5712	15	22	function	function	NOUN
cana-5712	15	23	,	,	PUNCT
cana-5712	15	24	wright	wright	PROPN
cana-5712	15	25	function	function	PROPN
cana-5712	15	26	,	,	PUNCT
cana-5712	15	27	prabhaker	prabhaker	NOUN
cana-5712	15	28	function	function	NOUN
cana-5712	15	29	,	,	PUNCT
cana-5712	15	30	and	and	CCONJ
cana-5712	15	31	gauss	gauss	ADJ
cana-5712	15	32	hypergeometric	hypergeometric	ADJ
cana-5712	15	33	function	function	NOUN
cana-5712	15	34	.	.	PUNCT
cana-5712	16	1	in	in	ADP
cana-5712	16	2	2018	2018	NUM
cana-5712	16	3	,	,	PUNCT
cana-5712	16	4	suthar	suthar	VERB
cana-5712	16	5	et	et	PROPN
cana-5712	16	6	al	al	PROPN
cana-5712	16	7	.	.	PUNCT
cana-5712	17	1	[	[	X
cana-5712	17	2	15	15	NUM
cana-5712	17	3	]	]	PUNCT
cana-5712	17	4	assessed	assess	VERB
cana-5712	17	5	integral	integral	ADJ
cana-5712	17	6	expressions	expression	NOUN
cana-5712	17	7	of	of	ADP
cana-5712	17	8	the	the	DET
cana-5712	17	9	product	product	NOUN
cana-5712	17	10	of	of	ADP
cana-5712	17	11	m	m	PROPN
cana-5712	17	12	-	-	PUNCT
cana-5712	17	13	series	series	PROPN
cana-5712	17	14	and	and	CCONJ
cana-5712	17	15	jacobi	jacobi	PROPN
cana-5712	17	16	polynomials	polynomial	NOUN
cana-5712	17	17	.	.	PUNCT
cana-5712	18	1	subsequently	subsequently	ADV
cana-5712	18	2	,	,	PUNCT
cana-5712	18	3	sachan	sachan	VERB
cana-5712	18	4	et	et	PROPN
cana-5712	18	5	al	al	PROPN
cana-5712	18	6	.	.	PUNCT
cana-5712	19	1	[	[	X
cana-5712	19	2	11	11	NUM
cana-5712	19	3	]	]	PUNCT
cana-5712	19	4	presented	present	VERB
cana-5712	19	5	a	a	DET
cana-5712	19	6	new	new	ADJ
cana-5712	19	7	extension	extension	NOUN
cana-5712	19	8	of	of	ADP
cana-5712	19	9	the	the	DET
cana-5712	19	10	m	m	NOUN
cana-5712	19	11	-	-	PUNCT
cana-5712	19	12	series	series	NOUN
cana-5712	19	13	and	and	CCONJ
cana-5712	19	14	discovered	discover	VERB
cana-5712	19	15	its	its	PRON
cana-5712	19	16	properties	property	NOUN
cana-5712	19	17	,	,	PUNCT
cana-5712	19	18	including	include	VERB
cana-5712	19	19	recurrence	recurrence	NOUN
cana-5712	19	20	relations	relation	NOUN
cana-5712	19	21	,	,	PUNCT
cana-5712	19	22	integral	integral	ADJ
cana-5712	19	23	representation	representation	NOUN
cana-5712	19	24	,	,	PUNCT
cana-5712	19	25	and	and	CCONJ
cana-5712	19	26	formulas	formula	NOUN
cana-5712	19	27	for	for	ADP
cana-5712	19	28	mailto:2	mailto:2	X
cana-5712	19	29	mailto:2owkhan05@gmail.com	mailto:2owkhan05@gmail.com	X
cana-5712	20	1	mailto:4mdkashifkhan85@gmail.com	mailto:4mdkashifkhan85@gmail.com	X
cana-5712	20	2	mailto:3nafis.sncmaths@gmail.com	mailto:3nafis.sncmaths@gmail.com	X
cana-5712	21	1	communications	communication	NOUN
cana-5712	21	2	on	on	ADP
cana-5712	21	3	applied	apply	VERB
cana-5712	21	4	nonlinear	nonlinear	ADJ
cana-5712	21	5	analysis	analysis	NOUN
cana-5712	21	6	issn	issn	NOUN
cana-5712	21	7	:	:	PUNCT
cana-5712	21	8	1074	1074	NUM
cana-5712	21	9	-	-	PUNCT
cana-5712	21	10	133x	133x	NUM
cana-5712	21	11	vol	vol	VERB
cana-5712	21	12	32	32	NUM
cana-5712	21	13	no	no	NOUN
cana-5712	21	14	.	.	PUNCT
cana-5712	22	1	10s	10	NOUN
cana-5712	22	2	(	(	PUNCT
cana-5712	22	3	2025	2025	NUM
cana-5712	22	4	)	)	PUNCT
cana-5712	22	5	2713	2713	NUM
cana-5712	22	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5712	22	7	fractional	fractional	ADJ
cana-5712	22	8	integrals	integral	NOUN
cana-5712	22	9	and	and	CCONJ
cana-5712	22	10	derivatives	derivative	NOUN
cana-5712	22	11	.	.	PUNCT
cana-5712	23	1	following	follow	VERB
cana-5712	23	2	this	this	DET
cana-5712	23	3	excellent	excellent	ADJ
cana-5712	23	4	work	work	NOUN
cana-5712	23	5	,	,	PUNCT
cana-5712	23	6	we	we	PRON
cana-5712	23	7	obtained	obtain	VERB
cana-5712	23	8	composition	composition	NOUN
cana-5712	23	9	formulas	formula	NOUN
cana-5712	23	10	for	for	ADP
cana-5712	23	11	euler	euler	NOUN
cana-5712	23	12	-	-	PUNCT
cana-5712	23	13	type	type	NOUN
cana-5712	23	14	integrals	integral	NOUN
cana-5712	23	15	featuring	feature	VERB
cana-5712	23	16	a	a	DET
cana-5712	23	17	generalized	generalize	VERB
cana-5712	23	18	m	m	PROPN
cana-5712	23	19	-	-	PUNCT
cana-5712	23	20	series	series	NOUN
cana-5712	23	21	kernel	kernel	PROPN
cana-5712	23	22	.	.	PUNCT
cana-5712	24	1	additionally	additionally	ADV
cana-5712	24	2	,	,	PUNCT
cana-5712	24	3	we	we	PRON
cana-5712	24	4	demonstrated	demonstrate	VERB
cana-5712	24	5	applications	application	NOUN
cana-5712	24	6	of	of	ADP
cana-5712	24	7	our	our	PRON
cana-5712	24	8	findings	finding	NOUN
cana-5712	24	9	as	as	ADP
cana-5712	24	10	specific	specific	ADJ
cana-5712	24	11	instances	instance	NOUN
cana-5712	24	12	by	by	ADP
cana-5712	24	13	selecting	select	VERB
cana-5712	24	14	appropriate	appropriate	ADJ
cana-5712	24	15	values	value	NOUN
cana-5712	24	16	for	for	ADP
cana-5712	24	17	the	the	DET
cana-5712	24	18	parameters	parameter	NOUN
cana-5712	24	19	of	of	ADP
cana-5712	24	20	generalized	generalized	ADJ
cana-5712	24	21	m	m	PROPN
cana-5712	24	22	-	-	PUNCT
cana-5712	24	23	series	series	NOUN
cana-5712	24	24	sachan	sachan	NOUN
cana-5712	24	25	et	et	PROPN
cana-5712	24	26	al	al	PROPN
cana-5712	24	27	.	.	PUNCT
cana-5712	25	1	[	[	X
cana-5712	25	2	12	12	NUM
cana-5712	25	3	]	]	PUNCT
cana-5712	25	4	defined	define	VERB
cana-5712	25	5	generalized	generalized	ADJ
cana-5712	25	6	m	m	NOUN
cana-5712	25	7	-	-	PUNCT
cana-5712	25	8	series	series	NOUN
cana-5712	25	9	,	,	PUNCT
cana-5712	25	10	which	which	PRON
cana-5712	25	11	is	be	AUX
cana-5712	25	12	novel	novel	ADJ
cana-5712	25	13	an	an	DET
cana-5712	25	14	extension	extension	NOUN
cana-5712	25	15	of	of	ADP
cana-5712	25	16	generalized	generalized	ADJ
cana-5712	25	17	hypergeometric	hypergeometric	ADJ
cana-5712	25	18	function	function	NOUN
cana-5712	25	19	,	,	PUNCT
cana-5712	25	20	wright	wright	PROPN
cana-5712	25	21	function	function	PROPN
cana-5712	25	22	and	and	CCONJ
cana-5712	25	23	mittag	mittag	ADJ
cana-5712	25	24	-	-	PUNCT
cana-5712	25	25	leffler	leffler	NOUN
cana-5712	25	26	is	be	AUX
cana-5712	25	27	defined	define	VERB
cana-5712	25	28	as	as	ADP
cana-5712	25	29	:	:	PUNCT
cana-5712	25	30	mq	mq	PROPN
cana-5712	25	31	ρ	ρ	PROPN
cana-5712	25	32	p	p	PROPN
cana-5712	25	33	σ	σ	PROPN
cana-5712	25	34	=	=	PROPN
cana-5712	25	35	mq	mq	PROPN
cana-5712	25	36	ρ	ρ	PROPN
cana-5712	25	37	(	(	PUNCT
cana-5712	25	38	k1	k1	NOUN
cana-5712	25	39	,	,	PUNCT
cana-5712	25	40	…	…	PUNCT
cana-5712	25	41	.	.	PUNCT
cana-5712	26	1	,	,	PUNCT
cana-5712	26	2	kp	kp	PROPN
cana-5712	26	3	,	,	PUNCT
cana-5712	26	4	l1	l1	PROPN
cana-5712	26	5	…	…	PUNCT
cana-5712	26	6	.	.	PUNCT
cana-5712	27	1	lq	lq	INTJ
cana-5712	27	2	:	:	PUNCT
cana-5712	27	3	z)p	z)p	X
cana-5712	27	4	σ	σ	X
cana-5712	27	5	=	=	PUNCT
cana-5712	27	6	∑	∑	PROPN
cana-5712	27	7	(	(	PUNCT
cana-5712	27	8	k1)m	k1)m	PROPN
cana-5712	27	9	…	…	PUNCT
cana-5712	27	10	(kp)m	(kp)m	X
cana-5712	27	11	(	(	PUNCT
cana-5712	27	12	l1)m	l1)m	NOUN
cana-5712	27	13	…	…	SYM
cana-5712	27	14	(lq)m	(lq)m	PROPN
cana-5712	27	15	∞	∞	PROPN
cana-5712	27	16	m=0	m=0	PROPN
cana-5712	27	17	zm	zm	PROPN
cana-5712	27	18	⌈(ρ+σm	⌈(ρ+σm	PROPN
cana-5712	27	19	)	)	PUNCT
cana-5712	27	20	,	,	PUNCT
cana-5712	27	21	(	(	PUNCT
cana-5712	27	22	1.1	1.1	NUM
cana-5712	27	23	)	)	PUNCT
cana-5712	27	24	where	where	SCONJ
cana-5712	27	25	ρ	ρ	PROPN
cana-5712	27	26	,	,	PUNCT
cana-5712	27	27	σ	σ	PROPN
cana-5712	27	28	,	,	PUNCT
cana-5712	27	29	z	z	NOUN
cana-5712	27	30	ϵ	ϵ	X
cana-5712	27	31	c	c	X
cana-5712	27	32	,	,	PUNCT
cana-5712	27	33	r(σ	r(σ	PROPN
cana-5712	27	34	)	)	PUNCT
cana-5712	27	35	>	>	X
cana-5712	27	36	0	0	NUM
cana-5712	27	37	,	,	PUNCT
cana-5712	27	38	(	(	PUNCT
cana-5712	27	39	ki)m(i	ki)m(i	X
cana-5712	27	40	=	=	SYM
cana-5712	27	41	1	1	NUM
cana-5712	27	42	,	,	PUNCT
cana-5712	27	43	…	…	PUNCT
cana-5712	27	44	.	.	PUNCT
cana-5712	27	45	,	,	PUNCT
cana-5712	27	46	p	p	X
cana-5712	27	47	)	)	PUNCT
cana-5712	27	48	and	and	CCONJ
cana-5712	27	49	(	(	PUNCT
cana-5712	27	50	lj)m	lj)m	PROPN
cana-5712	27	51	(	(	PUNCT
cana-5712	27	52	j	j	NOUN
cana-5712	27	53	=	=	SYM
cana-5712	27	54	1	1	NUM
cana-5712	27	55	,	,	PUNCT
cana-5712	27	56	…	…	PUNCT
cana-5712	27	57	,	,	PUNCT
cana-5712	27	58	q	q	NOUN
cana-5712	27	59	)	)	PUNCT
cana-5712	27	60	.	.	PUNCT
cana-5712	28	1	well	well	INTJ
cana-5712	28	2	known	know	VERB
cana-5712	28	3	pochhamer	pochhamer	NOUN
cana-5712	28	4	symbols	symbol	NOUN
cana-5712	28	5	(	(	PUNCT
cana-5712	28	6	k)m	k)m	NOUN
cana-5712	28	7	defined	define	VERB
cana-5712	28	8	as	as	ADP
cana-5712	28	9	:	:	PUNCT
cana-5712	28	10	(	(	PUNCT
cana-5712	28	11	k)m	k)m	NOUN
cana-5712	28	12	=	=	PUNCT
cana-5712	28	13	{	{	PUNCT
cana-5712	28	14	1	1	NUM
cana-5712	28	15	m	m	NOUN
cana-5712	28	16	=	=	SYM
cana-5712	28	17	0	0	NUM
cana-5712	28	18	,	,	PUNCT
cana-5712	28	19	k	k	PROPN
cana-5712	28	20	≠	≠	PROPN
cana-5712	28	21	0	0	NUM
cana-5712	29	1	k(k	k(k	NOUN
cana-5712	29	2	+	+	NOUN
cana-5712	29	3	1	1	NUM
cana-5712	29	4	)	)	PUNCT
cana-5712	29	5	…	…	PUNCT
cana-5712	29	6	(	(	PUNCT
cana-5712	29	7	k	k	X
cana-5712	30	1	+	+	NOUN
cana-5712	30	2	m	m	VERB
cana-5712	30	3	−	−	NOUN
cana-5712	30	4	1	1	NUM
cana-5712	30	5	)	)	PUNCT
cana-5712	30	6	,	,	PUNCT
cana-5712	30	7	mϵn	mϵn	PROPN
cana-5712	30	8	,	,	PUNCT
cana-5712	30	9	kϵc	kϵc	NOUN
cana-5712	30	10	=	=	SYM
cana-5712	30	11	γ(k+m	γ(k+m	NUM
cana-5712	30	12	)	)	PUNCT
cana-5712	30	13	γ(k	γ(k	PROPN
cana-5712	30	14	)	)	PUNCT
cana-5712	30	15	.	.	PUNCT
cana-5712	31	1	the	the	DET
cana-5712	31	2	series	series	NOUN
cana-5712	31	3	(	(	PUNCT
cana-5712	31	4	1.1	1.1	NUM
cana-5712	31	5	)	)	PUNCT
cana-5712	31	6	is	be	AUX
cana-5712	31	7	convergent	convergent	ADJ
cana-5712	31	8	for	for	ADP
cana-5712	31	9	all	all	DET
cana-5712	31	10	z	z	NOUN
cana-5712	31	11	if	if	SCONJ
cana-5712	31	12	p	p	PRON
cana-5712	31	13	≤	≤	NUM
cana-5712	31	14	q.	q.	NOUN
cana-5712	31	15	it	it	PRON
cana-5712	31	16	is	be	AUX
cana-5712	31	17	convergent	convergent	NOUN
cana-5712	31	18	for	for	ADP
cana-5712	31	19	|z|	|z|	NOUN
cana-5712	31	20	<	<	X
cana-5712	31	21	η	η	PROPN
cana-5712	31	22	=	=	PROPN
cana-5712	32	1	σσ	σσ	ADV
cana-5712	33	1	if	if	SCONJ
cana-5712	33	2	p	p	NOUN
cana-5712	33	3	=	=	X
cana-5712	33	4	q	q	NOUN
cana-5712	34	1	+	+	NUM
cana-5712	34	2	1	1	NUM
cana-5712	34	3	and	and	CCONJ
cana-5712	34	4	divergent	divergent	ADJ
cana-5712	34	5	if	if	SCONJ
cana-5712	34	6	p	p	X
cana-5712	34	7	>	>	X
cana-5712	34	8	q	q	PROPN
cana-5712	35	1	+	+	NUM
cana-5712	35	2	1	1	NUM
cana-5712	35	3	.	.	PUNCT
cana-5712	35	4	when	when	SCONJ
cana-5712	35	5	p	p	NOUN
cana-5712	35	6	=	=	PUNCT
cana-5712	35	7	ν	ν	X
cana-5712	35	8	+	+	NUM
cana-5712	35	9	1	1	NUM
cana-5712	35	10	and	and	CCONJ
cana-5712	35	11	|z|	|z|	NOUN
cana-5712	35	12	=	=	SYM
cana-5712	35	13	η	η	NOUN
cana-5712	35	14	,	,	PUNCT
cana-5712	35	15	there	there	PRON
cana-5712	35	16	is	be	VERB
cana-5712	35	17	convergent	convergent	NOUN
cana-5712	35	18	under	under	ADP
cana-5712	35	19	conditions	condition	NOUN
cana-5712	35	20	that	that	PRON
cana-5712	35	21	depend	depend	VERB
cana-5712	35	22	on	on	ADP
cana-5712	35	23	parameters	parameter	NOUN
cana-5712	35	24	.	.	PUNCT
cana-5712	36	1	the	the	DET
cana-5712	36	2	detailed	detailed	ADJ
cana-5712	36	3	accound	accound	NOUN
cana-5712	36	4	of	of	ADP
cana-5712	36	5	the	the	DET
cana-5712	36	6	m	m	PROPN
cana-5712	36	7	-	-	PUNCT
cana-5712	36	8	series	series	NOUN
cana-5712	36	9	can	can	AUX
cana-5712	36	10	be	be	AUX
cana-5712	36	11	found	find	VERB
cana-5712	36	12	in	in	ADP
cana-5712	36	13	paper	paper	NOUN
cana-5712	36	14	written	write	VERB
cana-5712	36	15	by	by	ADP
cana-5712	36	16	sharma	sharma	PROPN
cana-5712	36	17	and	and	CCONJ
cana-5712	36	18	jain	jain	PROPN
cana-5712	37	1	[	[	X
cana-5712	37	2	12	12	NUM
cana-5712	37	3	]	]	PUNCT
cana-5712	37	4	.	.	PUNCT
cana-5712	38	1	the	the	DET
cana-5712	38	2	generalized	generalized	ADJ
cana-5712	38	3	m	m	PROPN
cana-5712	38	4	-	-	PUNCT
cana-5712	38	5	series	series	NOUN
cana-5712	38	6	can	can	AUX
cana-5712	38	7	be	be	AUX
cana-5712	38	8	represented	represent	VERB
cana-5712	38	9	as	as	ADP
cana-5712	38	10	a	a	DET
cana-5712	38	11	special	special	ADJ
cana-5712	38	12	case	case	NOUN
cana-5712	38	13	of	of	ADP
cana-5712	38	14	wright	wright	PROPN
cana-5712	38	15	generalized	generalize	VERB
cana-5712	38	16	hypergeometric	hypergeometric	ADJ
cana-5712	38	17	function	function	NOUN
cana-5712	38	18	,	,	PUNCT
cana-5712	38	19	called	call	VERB
cana-5712	38	20	fox	fox	PROPN
cana-5712	38	21	-	-	PUNCT
cana-5712	38	22	wright	wright	PROPN
cana-5712	38	23	function	function	PROPN
cana-5712	38	24	rψs[x	rψs[x	PROPN
cana-5712	38	25	]	]	X
cana-5712	38	26	,	,	PUNCT
cana-5712	38	27	of	of	ADP
cana-5712	38	28	the	the	DET
cana-5712	38	29	fox	fox	PROPN
cana-5712	38	30	h	h	NOUN
cana-5712	38	31	-	-	PUNCT
cana-5712	38	32	function	function	NOUN
cana-5712	38	33	,	,	PUNCT
cana-5712	38	34	and	and	CCONJ
cana-5712	38	35	of	of	ADP
cana-5712	38	36	meijer	meijer	NOUN
cana-5712	38	37	g	g	NOUN
cana-5712	38	38	-	-	PUNCT
cana-5712	38	39	function	function	NOUN
cana-5712	38	40	[	[	X
cana-5712	38	41	6	6	NUM
cana-5712	38	42	]	]	PUNCT
cana-5712	38	43	.	.	PUNCT
cana-5712	39	1	mq	mq	PROPN
cana-5712	39	2	ρ	ρ	PROPN
cana-5712	39	3	p	p	PROPN
cana-5712	39	4	σ	σ	PROPN
cana-5712	39	5	(	(	PUNCT
cana-5712	39	6	k1	k1	PROPN
cana-5712	39	7	,	,	PUNCT
cana-5712	39	8	…	…	PUNCT
cana-5712	39	9	.	.	PUNCT
cana-5712	39	10	,	,	PUNCT
cana-5712	39	11	kp	kp	PROPN
cana-5712	39	12	,	,	PUNCT
cana-5712	39	13	l1	l1	PROPN
cana-5712	39	14	…	…	PUNCT
cana-5712	39	15	.	.	PUNCT
cana-5712	40	1	lq	lq	INTJ
cana-5712	40	2	:	:	PUNCT
cana-5712	40	3	z	z	X
cana-5712	40	4	)	)	PUNCT
cana-5712	40	5	=	=	SYM
cana-5712	40	6	∏	∏	NUM
cana-5712	40	7	γ(lq	γ(lq	NUM
cana-5712	40	8	)	)	PUNCT
cana-5712	40	9	q	q	NOUN
cana-5712	41	1	j=1	j=1	PROPN
cana-5712	41	2	∏	∏	PROPN
cana-5712	41	3	γ(kp	γ(kp	PROPN
cana-5712	41	4	)	)	PUNCT
cana-5712	41	5	p	p	X
cana-5712	41	6	j=1	j=1	NOUN
cana-5712	41	7	∑	∑	PUNCT
cana-5712	41	8	γ(λ1+λ1k),	γ(λ1+λ1k),	PROPN
cana-5712	41	9	…	…	SYM
cana-5712	41	10	…	…	NUM
cana-5712	41	11	,γ(λr+λsk)xk	,γ(λr+λsk)xk	NOUN
cana-5712	41	12	γ(l1+l1k	γ(l1+l1k	PROPN
cana-5712	41	13	)	)	PUNCT
cana-5712	41	14	,	,	PUNCT
cana-5712	41	15	……	……	NOUN
cana-5712	41	16	,	,	PUNCT
cana-5712	41	17	γ(l1+l1k)k	γ(l1+l1k)k	PROPN
cana-5712	41	18	!	!	PUNCT
cana-5712	41	19	∞	∞	PROPN
cana-5712	42	1	k=0	k=0	X
cana-5712	42	2	,	,	PUNCT
cana-5712	42	3	(	(	PUNCT
cana-5712	42	4	1.2	1.2	NUM
cana-5712	42	5	)	)	PUNCT
cana-5712	42	6	=	=	SYM
cana-5712	42	7	p+1ψq+1	p+1ψq+1	PROPN
cana-5712	42	8	[	[	PUNCT
cana-5712	42	9	(	(	PUNCT
cana-5712	42	10	λ1	λ1	ADJ
cana-5712	42	11	,	,	PUNCT
cana-5712	42	12	λ1	λ1	ADJ
cana-5712	42	13	)	)	PUNCT
cana-5712	42	14	,	,	PUNCT
cana-5712	42	15	…	…	PUNCT
cana-5712	42	16	…	…	PUNCT
cana-5712	42	17	,	,	PUNCT
cana-5712	42	18	(	(	PUNCT
cana-5712	42	19	λr	λr	INTJ
cana-5712	42	20	,	,	PUNCT
cana-5712	42	21	λs	λs	NOUN
cana-5712	42	22	)	)	PUNCT
cana-5712	42	23	;	;	PUNCT
cana-5712	42	24	(	(	PUNCT
cana-5712	42	25	l1	l1	PROPN
cana-5712	42	26	,	,	PUNCT
cana-5712	42	27	l1	l1	PROPN
cana-5712	42	28	)	)	PUNCT
cana-5712	42	29	,	,	PUNCT
cana-5712	42	30	…	…	PUNCT
cana-5712	42	31	…	…	PUNCT
cana-5712	42	32	.	.	PUNCT
cana-5712	42	33	,	,	PUNCT
cana-5712	42	34	(	(	PUNCT
cana-5712	42	35	lr	lr	INTJ
cana-5712	42	36	,	,	PUNCT
cana-5712	42	37	ls	ls	PROPN
cana-5712	42	38	)	)	PUNCT
cana-5712	42	39	;	;	PUNCT
cana-5712	42	40	x	x	X
cana-5712	42	41	]	]	X
cana-5712	42	42	(	(	PUNCT
cana-5712	42	43	1.3	1.3	NUM
cana-5712	42	44	)	)	PUNCT
cana-5712	42	45	mq	mq	NOUN
cana-5712	42	46	ρ	ρ	PROPN
cana-5712	42	47	p	p	PROPN
cana-5712	42	48	σ	σ	PROPN
cana-5712	42	49	(	(	PUNCT
cana-5712	42	50	k1	k1	PROPN
cana-5712	42	51	,	,	PUNCT
cana-5712	42	52	…	…	PUNCT
cana-5712	42	53	.	.	PUNCT
cana-5712	42	54	,	,	PUNCT
cana-5712	42	55	kp	kp	PROPN
cana-5712	42	56	,	,	PUNCT
cana-5712	42	57	l1	l1	PROPN
cana-5712	42	58	…	…	PUNCT
cana-5712	42	59	.	.	PUNCT
cana-5712	43	1	lq	lq	INTJ
cana-5712	43	2	:	:	PUNCT
cana-5712	43	3	z	z	X
cana-5712	43	4	)	)	PUNCT
cana-5712	43	5	=	=	SYM
cana-5712	43	6	∏	∏	NUM
cana-5712	43	7	γ(lq	γ(lq	NUM
cana-5712	43	8	)	)	PUNCT
cana-5712	43	9	q	q	NOUN
cana-5712	44	1	j=1	j=1	PROPN
cana-5712	44	2	∏	∏	PROPN
cana-5712	44	3	γ(kp	γ(kp	PROPN
cana-5712	44	4	)	)	PUNCT
cana-5712	44	5	p	p	X
cana-5712	44	6	j=1	j=1	NOUN
cana-5712	44	7	hp+1,q+2	hp+1,q+2	X
cana-5712	44	8	1,p+1	1,p+1	NUM
cana-5712	45	1	[	[	X
cana-5712	45	2	−z|	−z|	X
cana-5712	45	3	(	(	PUNCT
cana-5712	45	4	1	1	NUM
cana-5712	45	5	−	−	PROPN
cana-5712	45	6	kj)1	kj)1	PROPN
cana-5712	45	7	p	p	PROPN
cana-5712	45	8	,	,	PUNCT
cana-5712	45	9	(	(	PUNCT
cana-5712	45	10	0,1	0,1	NOUN
cana-5712	45	11	)	)	PUNCT
cana-5712	45	12	(	(	PUNCT
cana-5712	45	13	0,1	0,1	NOUN
cana-5712	45	14	)	)	PUNCT
cana-5712	45	15	,	,	PUNCT
cana-5712	45	16	(	(	PUNCT
cana-5712	45	17	1	1	NUM
cana-5712	45	18	−	−	NOUN
cana-5712	45	19	lj)1	lj)1	PROPN
cana-5712	45	20	q	q	PROPN
cana-5712	45	21	,	,	PUNCT
cana-5712	45	22	(	(	PUNCT
cana-5712	45	23	0,1	0,1	NOUN
cana-5712	45	24	)	)	PUNCT
cana-5712	45	25	]	]	PUNCT
cana-5712	45	26	,	,	PUNCT
cana-5712	45	27	(	(	PUNCT
cana-5712	45	28	1.4	1.4	NUM
cana-5712	45	29	)	)	PUNCT
cana-5712	45	30	where	where	SCONJ
cana-5712	45	31	hr	hr	NOUN
cana-5712	45	32	,	,	PUNCT
cana-5712	45	33	s+1	s+1	PROPN
cana-5712	45	34	1,r	1,r	NUM
cana-5712	45	35	[	[	X
cana-5712	45	36	x	x	X
cana-5712	45	37	]	]	X
cana-5712	45	38	is	be	AUX
cana-5712	45	39	a	a	DET
cana-5712	45	40	fox	fox	NOUN
cana-5712	45	41	-	-	PUNCT
cana-5712	45	42	h	h	NOUN
cana-5712	45	43	function	function	NOUN
cana-5712	45	44	[	[	X
cana-5712	45	45	1	1	X
cana-5712	45	46	]	]	PUNCT
cana-5712	45	47	and	and	CCONJ
cana-5712	45	48	the	the	DET
cana-5712	45	49	coefficients	coefficient	NOUN
cana-5712	45	50	γ1	γ1	PROPN
cana-5712	45	51	′	′	NOUN
cana-5712	45	52	,	,	PUNCT
cana-5712	45	53	…	…	PUNCT
cana-5712	45	54	.	.	PUNCT
cana-5712	46	1	,	,	PUNCT
cana-5712	46	2	γ′r	γ′r	NOUN
cana-5712	46	3	,	,	PUNCT
cana-5712	46	4	l′1	l′1	ADJ
cana-5712	46	5	,	,	PUNCT
cana-5712	46	6	…	…	PUNCT
cana-5712	46	7	.	.	PUNCT
cana-5712	47	1	,	,	PUNCT
cana-5712	47	2	l′sϵ	l′sϵ	X
cana-5712	47	3	r+	r+	VERB
cana-5712	47	4	such	such	ADJ
cana-5712	47	5	that	that	SCONJ
cana-5712	47	6	1	1	NUM
cana-5712	47	7	+	+	CCONJ
cana-5712	47	8	∑	∑	PROPN
cana-5712	47	9	lj	lj	PROPN
cana-5712	47	10	′s	′s	PROPN
cana-5712	47	11	j=1	j=1	PUNCT
cana-5712	48	1	−	−	PROPN
cana-5712	48	2	∑	∑	PUNCT
cana-5712	48	3	γj	γj	SCONJ
cana-5712	48	4	′r	′r	PROPN
cana-5712	48	5	i=1	i=1	PROPN
cana-5712	49	1	for	for	ADP
cana-5712	49	2	suitable	suitable	ADJ
cana-5712	49	3	bounded	bounded	ADJ
cana-5712	49	4	value	value	NOUN
cana-5712	49	5	of	of	ADP
cana-5712	49	6	|x|	|x|	PROPN
cana-5712	49	7	.	.	PUNCT
cana-5712	50	1	taking	take	VERB
cana-5712	50	2	suitable	suitable	ADJ
cana-5712	50	3	values	value	NOUN
cana-5712	50	4	of	of	ADP
cana-5712	50	5	the	the	DET
cana-5712	50	6	parameters	parameter	NOUN
cana-5712	50	7	in	in	ADP
cana-5712	50	8	(	(	PUNCT
cana-5712	50	9	1.1	1.1	NUM
cana-5712	50	10	)	)	PUNCT
cana-5712	50	11	,	,	PUNCT
cana-5712	50	12	we	we	PRON
cana-5712	50	13	conclude	conclude	VERB
cana-5712	50	14	special	special	ADJ
cana-5712	50	15	cases	case	NOUN
cana-5712	50	16	and	and	CCONJ
cana-5712	50	17	connections	connection	NOUN
cana-5712	50	18	which	which	PRON
cana-5712	50	19	are	be	AUX
cana-5712	50	20	enumerated	enumerate	VERB
cana-5712	50	21	as	as	SCONJ
cana-5712	50	22	follows	follow	VERB
cana-5712	50	23	:	:	PUNCT
cana-5712	50	24	1	1	X
cana-5712	50	25	.	.	X
cana-5712	50	26	forσ	forσ	NOUN
cana-5712	50	27	=	=	SYM
cana-5712	50	28	1	1	NUM
cana-5712	50	29	,	,	PUNCT
cana-5712	50	30	the	the	DET
cana-5712	50	31	generalized	generalized	ADJ
cana-5712	50	32	m	m	PROPN
cana-5712	50	33	-	-	PUNCT
cana-5712	50	34	series	series	NOUN
cana-5712	50	35	reduces	reduce	VERB
cana-5712	50	36	in	in	ADP
cana-5712	50	37	the	the	DET
cana-5712	50	38	m	m	NOUN
cana-5712	50	39	-	-	PUNCT
cana-5712	50	40	series	series	NOUN
cana-5712	50	41	defined	define	VERB
cana-5712	50	42	by	by	ADP
cana-5712	50	43	sharma	sharma	PROPN
cana-5712	50	44	[	[	X
cana-5712	50	45	12	12	NUM
cana-5712	50	46	]	]	PUNCT
cana-5712	50	47	.	.	PUNCT
cana-5712	51	1	mq	mq	PROPN
cana-5712	51	2	ρ	ρ	PROPN
cana-5712	51	3	p	p	NOUN
cana-5712	51	4	1	1	NUM
cana-5712	51	5	(	(	PUNCT
cana-5712	51	6	k1	k1	NOUN
cana-5712	51	7	,	,	PUNCT
cana-5712	51	8	…	…	PUNCT
cana-5712	51	9	.	.	PUNCT
cana-5712	51	10	,	,	PUNCT
cana-5712	51	11	kp	kp	PROPN
cana-5712	51	12	,	,	PUNCT
cana-5712	51	13	l1	l1	PROPN
cana-5712	51	14	…	…	PUNCT
cana-5712	51	15	.	.	PUNCT
cana-5712	52	1	lq	lq	INTJ
cana-5712	52	2	:	:	PUNCT
cana-5712	52	3	z	z	X
cana-5712	52	4	)	)	PUNCT
cana-5712	52	5	=	=	SYM
cana-5712	52	6	∑	∑	PROPN
cana-5712	52	7	(	(	PUNCT
cana-5712	52	8	k1)m	k1)m	PROPN
cana-5712	52	9	…	…	PUNCT
cana-5712	52	10	…	…	PUNCT
cana-5712	52	11	(kp	(kp	SYM
cana-5712	52	12	)	)	PUNCT
cana-5712	52	13	m	m	PROPN
cana-5712	52	14	(	(	PUNCT
cana-5712	52	15	l1)m	l1)m	NOUN
cana-5712	52	16	…	…	SYM
cana-5712	52	17	…	…	SYM
cana-5712	52	18	.(lq	.(lq	SYM
cana-5712	52	19	)	)	PUNCT
cana-5712	52	20	m	m	VERB
cana-5712	52	21	∞	∞	NUM
cana-5712	52	22	m=0	m=0	PROPN
cana-5712	52	23	zm	zm	PROPN
cana-5712	52	24	γ(ρ+σm	γ(ρ+σm	PROPN
cana-5712	52	25	)	)	PUNCT
cana-5712	52	26	(	(	PUNCT
cana-5712	52	27	1.5	1.5	NUM
cana-5712	52	28	)	)	PUNCT
cana-5712	52	29	communications	communication	NOUN
cana-5712	52	30	on	on	ADP
cana-5712	52	31	applied	apply	VERB
cana-5712	52	32	nonlinear	nonlinear	ADJ
cana-5712	52	33	analysis	analysis	NOUN
cana-5712	52	34	issn	issn	NOUN
cana-5712	52	35	:	:	PUNCT
cana-5712	52	36	1074	1074	NUM
cana-5712	52	37	-	-	PUNCT
cana-5712	52	38	133x	133x	NUM
cana-5712	52	39	vol	vol	VERB
cana-5712	52	40	32	32	NUM
cana-5712	52	41	no	no	NOUN
cana-5712	52	42	.	.	PUNCT
cana-5712	53	1	10s	10	NOUN
cana-5712	53	2	(	(	PUNCT
cana-5712	53	3	2025	2025	NUM
cana-5712	53	4	)	)	PUNCT
cana-5712	53	5	2714	2714	NUM
cana-5712	53	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5712	53	7	=	=	PUNCT
cana-5712	53	8	pmq	pmq	VERB
cana-5712	53	9	ρ	ρ	PROPN
cana-5712	53	10	(	(	PUNCT
cana-5712	53	11	k1	k1	NOUN
cana-5712	53	12	,	,	PUNCT
cana-5712	53	13	…	…	PUNCT
cana-5712	53	14	.	.	PUNCT
cana-5712	54	1	,	,	PUNCT
cana-5712	54	2	kp	kp	PROPN
cana-5712	54	3	,	,	PUNCT
cana-5712	54	4	l1	l1	PROPN
cana-5712	54	5	…	…	PUNCT
cana-5712	54	6	.	.	PUNCT
cana-5712	55	1	lq	lq	INTJ
cana-5712	55	2	:	:	PUNCT
cana-5712	55	3	z	z	NOUN
cana-5712	55	4	)	)	PUNCT
cana-5712	55	5	2	2	NUM
cana-5712	55	6	.	.	X
cana-5712	56	1	for	for	ADP
cana-5712	56	2	p	p	NOUN
cana-5712	56	3	=	=	NOUN
cana-5712	56	4	q	q	NOUN
cana-5712	56	5	=	=	SYM
cana-5712	56	6	0	0	NUM
cana-5712	56	7	,	,	PUNCT
cana-5712	56	8	the	the	DET
cana-5712	56	9	generalized	generalized	ADJ
cana-5712	56	10	m	m	PROPN
cana-5712	56	11	-	-	PUNCT
cana-5712	56	12	series	series	NOUN
cana-5712	56	13	reduces	reduce	VERB
cana-5712	56	14	in	in	ADP
cana-5712	56	15	the	the	DET
cana-5712	56	16	mittag	mittag	ADJ
cana-5712	56	17	-	-	PUNCT
cana-5712	56	18	leffler	leffler	NOUN
cana-5712	56	19	function[17	function[17	PROPN
cana-5712	56	20	]	]	X
cana-5712	56	21	m0	m0	PROPN
cana-5712	56	22	ρ	ρ	PROPN
cana-5712	56	23	0	0	PROPN
cana-5712	57	1	σ	σ	PROPN
cana-5712	57	2	(	(	PUNCT
cana-5712	57	3	k1	k1	PROPN
cana-5712	57	4	,	,	PUNCT
cana-5712	57	5	…	…	PUNCT
cana-5712	57	6	.	.	PUNCT
cana-5712	57	7	,	,	PUNCT
cana-5712	57	8	kp	kp	PROPN
cana-5712	57	9	,	,	PUNCT
cana-5712	57	10	l1	l1	PROPN
cana-5712	57	11	…	…	PUNCT
cana-5712	57	12	.	.	PUNCT
cana-5712	58	1	lq	lq	INTJ
cana-5712	58	2	:	:	PUNCT
cana-5712	58	3	z	z	X
cana-5712	58	4	)	)	PUNCT
cana-5712	58	5	=	=	PUNCT
cana-5712	58	6	∑	∑	PUNCT
cana-5712	58	7	zm	zm	PROPN
cana-5712	58	8	γ(ρ+σm	γ(ρ+σm	PROPN
cana-5712	58	9	)	)	PUNCT
cana-5712	59	1	=	=	SYM
cana-5712	59	2	eρ	eρ	PROPN
cana-5712	59	3	,	,	PUNCT
cana-5712	59	4	σ(z)∞	σ(z)∞	VERB
cana-5712	59	5	m=0	m=0	PROPN
cana-5712	59	6	(	(	PUNCT
cana-5712	59	7	1.6	1.6	NUM
cana-5712	59	8	)	)	PUNCT
cana-5712	59	9	3	3	NUM
cana-5712	59	10	.	.	X
cana-5712	60	1	for	for	ADP
cana-5712	60	2	p	p	NOUN
cana-5712	60	3	=	=	NOUN
cana-5712	60	4	q	q	NOUN
cana-5712	60	5	=	=	SYM
cana-5712	60	6	1	1	NUM
cana-5712	60	7	,	,	PUNCT
cana-5712	60	8	k	k	NOUN
cana-5712	60	9	=	=	SYM
cana-5712	60	10	αϵ	αϵ	PROPN
cana-5712	60	11	c	c	NOUN
cana-5712	60	12	,	,	PUNCT
cana-5712	60	13	l	l	NOUN
cana-5712	60	14	=	=	SYM
cana-5712	60	15	1	1	NUM
cana-5712	60	16	,	,	PUNCT
cana-5712	60	17	equation	equation	NOUN
cana-5712	60	18	(	(	PUNCT
cana-5712	60	19	1.1	1.1	NUM
cana-5712	60	20	)	)	PUNCT
cana-5712	60	21	reduces	reduce	VERB
cana-5712	60	22	in	in	ADP
cana-5712	60	23	the	the	DET
cana-5712	60	24	generalized	generalized	ADJ
cana-5712	60	25	mittag	mittag	ADJ
cana-5712	60	26	-	-	PUNCT
cana-5712	60	27	leffler	leffler	NOUN
cana-5712	60	28	function	function	NOUN
cana-5712	60	29	[	[	X
cana-5712	60	30	14	14	NUM
cana-5712	60	31	]	]	X
cana-5712	60	32	m1	m1	PROPN
cana-5712	60	33	ρ	ρ	PROPN
cana-5712	60	34	1	1	NUM
cana-5712	60	35	σ	σ	NOUN
cana-5712	60	36	(	(	PUNCT
cana-5712	60	37	−	−	PROPN
cana-5712	60	38	,	,	PUNCT
cana-5712	60	39	−	−	NOUN
cana-5712	60	40	:	:	PUNCT
cana-5712	60	41	z	z	X
cana-5712	60	42	)	)	PUNCT
cana-5712	60	43	=	=	PUNCT
cana-5712	61	1	∑	∑	PUNCT
cana-5712	61	2	zm	zm	PROPN
cana-5712	61	3	γ(ρ+σm	γ(ρ+σm	PROPN
cana-5712	61	4	)	)	PUNCT
cana-5712	61	5	=	=	SYM
cana-5712	61	6	eρ	eρ	PROPN
cana-5712	61	7	,	,	PUNCT
cana-5712	61	8	σ	σ	PROPN
cana-5712	61	9	α	α	PROPN
cana-5712	61	10	(	(	PUNCT
cana-5712	61	11	z)∞	z)∞	NOUN
cana-5712	61	12	m=0	m=0	PROPN
cana-5712	61	13	(	(	PUNCT
cana-5712	61	14	1.7	1.7	NUM
cana-5712	61	15	)	)	PUNCT
cana-5712	61	16	4	4	NUM
cana-5712	61	17	.	.	X
cana-5712	62	1	for	for	ADP
cana-5712	62	2	p	p	NOUN
cana-5712	62	3	=	=	NOUN
cana-5712	62	4	q	q	NOUN
cana-5712	62	5	=	=	SYM
cana-5712	62	6	1	1	NUM
cana-5712	62	7	,	,	PUNCT
cana-5712	62	8	k	k	NOUN
cana-5712	62	9	=	=	SYM
cana-5712	62	10	αϵ	αϵ	PROPN
cana-5712	62	11	c	c	NOUN
cana-5712	62	12	,	,	PUNCT
cana-5712	62	13	l	l	NOUN
cana-5712	62	14	=	=	SYM
cana-5712	62	15	1	1	NUM
cana-5712	62	16	,	,	PUNCT
cana-5712	62	17	equation	equation	NOUN
cana-5712	62	18	(	(	PUNCT
cana-5712	62	19	1.1	1.1	NUM
cana-5712	62	20	)	)	PUNCT
cana-5712	62	21	reduces	reduce	VERB
cana-5712	62	22	in	in	ADP
cana-5712	62	23	the	the	DET
cana-5712	62	24	wright	wright	PROPN
cana-5712	62	25	function	function	NOUN
cana-5712	63	1	[	[	X
cana-5712	63	2	17	17	NUM
cana-5712	63	3	]	]	X
cana-5712	64	1	m1	m1	PROPN
cana-5712	64	2	ρ	ρ	PROPN
cana-5712	64	3	1	1	NUM
cana-5712	64	4	1	1	NUM
cana-5712	64	5	(	(	PUNCT
cana-5712	64	6	−,1	−,1	ADJ
cana-5712	64	7	:	:	PUNCT
cana-5712	64	8	z	z	X
cana-5712	64	9	)	)	PUNCT
cana-5712	64	10	=	=	PUNCT
cana-5712	64	11	∑	∑	PUNCT
cana-5712	64	12	zm	zm	PROPN
cana-5712	64	13	γ(ρ+m	γ(ρ+m	PROPN
cana-5712	64	14	)	)	PUNCT
cana-5712	64	15	=	=	SYM
cana-5712	64	16	wρ	wρ	NOUN
cana-5712	64	17	,	,	PUNCT
cana-5712	64	18	σ(z)∞	σ(z)∞	VERB
cana-5712	64	19	m=0	m=0	PROPN
cana-5712	64	20	(	(	PUNCT
cana-5712	64	21	1.8	1.8	NUM
cana-5712	64	22	)	)	PUNCT
cana-5712	64	23	5	5	NUM
cana-5712	64	24	.	.	X
cana-5712	64	25	for	for	ADP
cana-5712	64	26	ρ	ρ	PROPN
cana-5712	64	27	=	=	SYM
cana-5712	64	28	σ	σ	PROPN
cana-5712	64	29	=	=	SYM
cana-5712	64	30	1	1	NUM
cana-5712	64	31	,	,	PUNCT
cana-5712	64	32	equation	equation	NOUN
cana-5712	64	33	(	(	PUNCT
cana-5712	64	34	1.1	1.1	NUM
cana-5712	64	35	)	)	PUNCT
cana-5712	64	36	reduces	reduce	VERB
cana-5712	64	37	in	in	ADP
cana-5712	64	38	term	term	NOUN
cana-5712	64	39	of	of	ADP
cana-5712	64	40	gauss	gauss	ADJ
cana-5712	64	41	hypergeometric	hypergeometric	ADJ
cana-5712	64	42	function	function	NOUN
cana-5712	64	43	𝑀𝑞	𝑀𝑞	PROPN
cana-5712	64	44	1	1	NUM
cana-5712	64	45	𝑝	𝑝	NOUN
cana-5712	64	46	1	1	NUM
cana-5712	64	47	(	(	PUNCT
cana-5712	64	48	𝑘1	𝑘1	PROPN
cana-5712	64	49	,	,	PUNCT
cana-5712	64	50	…	…	PUNCT
cana-5712	64	51	.	.	PUNCT
cana-5712	65	1	,	,	PUNCT
cana-5712	65	2	𝑘𝑝	𝑘𝑝	PROPN
cana-5712	65	3	,	,	PUNCT
cana-5712	65	4	𝑙1	𝑙1	PROPN
cana-5712	65	5	…	…	PUNCT
cana-5712	65	6	.	.	PUNCT
cana-5712	66	1	𝑙𝑞	𝑙𝑞	NOUN
cana-5712	66	2	:	:	PUNCT
cana-5712	66	3	𝑧	𝑧	X
cana-5712	66	4	)	)	PUNCT
cana-5712	66	5	=	=	SYM
cana-5712	66	6	∑	∑	PROPN
cana-5712	66	7	(	(	PUNCT
cana-5712	66	8	k1)m	k1)m	PROPN
cana-5712	66	9	…	…	PUNCT
cana-5712	66	10	…	…	PUNCT
cana-5712	66	11	(kp	(kp	SYM
cana-5712	66	12	)	)	PUNCT
cana-5712	66	13	m	m	PROPN
cana-5712	66	14	(	(	PUNCT
cana-5712	66	15	l1)m	l1)m	NOUN
cana-5712	66	16	…	…	SYM
cana-5712	66	17	…	…	SYM
cana-5712	66	18	.(lq	.(lq	SYM
cana-5712	66	19	)	)	PUNCT
cana-5712	66	20	m	m	VERB
cana-5712	66	21	∞	∞	NUM
cana-5712	66	22	m=0	m=0	PROPN
cana-5712	66	23	zm	zm	PROPN
cana-5712	66	24	𝑚	𝑚	PROPN
cana-5712	66	25	!	!	PUNCT
cana-5712	66	26	=	=	SYM
cana-5712	67	1	=	=	NUM
cana-5712	67	2	𝑝f𝑞	𝑝f𝑞	NOUN
cana-5712	67	3	[	[	PUNCT
cana-5712	67	4	k1	k1	NOUN
cana-5712	67	5	,	,	PUNCT
cana-5712	67	6	…	…	PUNCT
cana-5712	67	7	.	.	PUNCT
cana-5712	67	8	.	.	PUNCT
cana-5712	68	1	kp	kp	PROPN
cana-5712	68	2	;	;	PUNCT
cana-5712	68	3	l1	l1	PROPN
cana-5712	68	4	,	,	PUNCT
cana-5712	68	5	…	…	PUNCT
cana-5712	68	6	…	…	PUNCT
cana-5712	68	7	.	.	PUNCT
cana-5712	69	1	lq	lq	INTJ
cana-5712	69	2	;	;	PUNCT
cana-5712	69	3	z	z	NOUN
cana-5712	69	4	]	]	X
cana-5712	69	5	.	.	PUNCT
cana-5712	70	1	(	(	PUNCT
cana-5712	70	2	1.9	1.9	NUM
cana-5712	70	3	)	)	PUNCT
cana-5712	70	4	in	in	ADP
cana-5712	70	5	the	the	DET
cana-5712	70	6	present	present	ADJ
cana-5712	70	7	study	study	NOUN
cana-5712	70	8	,	,	PUNCT
cana-5712	70	9	we	we	PRON
cana-5712	70	10	also	also	ADV
cana-5712	70	11	need	need	VERB
cana-5712	70	12	to	to	PART
cana-5712	70	13	recall	recall	VERB
cana-5712	70	14	the	the	DET
cana-5712	70	15	following	follow	VERB
cana-5712	70	16	interesting	interesting	ADJ
cana-5712	70	17	and	and	CCONJ
cana-5712	70	18	useful	useful	ADJ
cana-5712	70	19	integral	integral	ADJ
cana-5712	70	20	identities	identity	NOUN
cana-5712	70	21	in	in	ADP
cana-5712	70	22	term	term	NOUN
cana-5712	70	23	of	of	ADP
cana-5712	70	24	gamma	gamma	NOUN
cana-5712	70	25	function	function	NOUN
cana-5712	70	26	[	[	X
cana-5712	70	27	1	1	NUM
cana-5712	70	28	,	,	PUNCT
cana-5712	70	29	14	14	NUM
cana-5712	70	30	-	-	SYM
cana-5712	70	31	15	15	NUM
cana-5712	70	32	]	]	PUNCT
cana-5712	70	33	as	as	SCONJ
cana-5712	70	34	follows	follow	VERB
cana-5712	70	35	:	:	PUNCT
cana-5712	70	36	1	1	X
cana-5712	70	37	.	.	X
cana-5712	70	38	∫	∫	PROPN
cana-5712	70	39	e−αt[sinh	e−αt[sinh	PROPN
cana-5712	70	40	(	(	PUNCT
cana-5712	70	41	βt)]γdt	βt)]γdt	X
cana-5712	70	42	∞	∞	NOUN
cana-5712	70	43	0	0	NUM
cana-5712	70	44	=	=	SYM
cana-5712	70	45	β−12−γ−1	β−12−γ−1	NOUN
cana-5712	70	46	γ	γ	X
cana-5712	70	47	(	(	PUNCT
cana-5712	70	48	α	α	NOUN
cana-5712	70	49	2β	2β	NOUN
cana-5712	70	50	−	−	NOUN
cana-5712	70	51	γ	γ	X
cana-5712	70	52	2	2	NUM
cana-5712	70	53	)	)	PUNCT
cana-5712	70	54	γ(1+γ	γ(1+γ	NOUN
cana-5712	70	55	)	)	PUNCT
cana-5712	70	56	γ	γ	X
cana-5712	70	57	(	(	PUNCT
cana-5712	70	58	1	1	NUM
cana-5712	70	59	2β	2β	NOUN
cana-5712	70	60	+	+	CCONJ
cana-5712	70	61	γ	γ	X
cana-5712	70	62	2	2	NUM
cana-5712	70	63	+1	+1	PROPN
cana-5712	70	64	)	)	PUNCT
cana-5712	70	65	,	,	PUNCT
cana-5712	70	66	(	(	PUNCT
cana-5712	70	67	1.10	1.10	NUM
cana-5712	70	68	)	)	PUNCT
cana-5712	70	69	a.	a.	NOUN
cana-5712	70	70	𝑅(𝛾	𝑅(𝛾	PROPN
cana-5712	70	71	)	)	PUNCT
cana-5712	70	72	>	>	PUNCT
cana-5712	70	73	−1	−1	NOUN
cana-5712	70	74	,	,	PUNCT
cana-5712	70	75	𝑅(𝛽	𝑅(𝛽	NUM
cana-5712	70	76	)	)	PUNCT
cana-5712	70	77	>	>	X
cana-5712	70	78	0	0	NUM
cana-5712	70	79	,	,	PUNCT
cana-5712	70	80	𝑅	𝑅	NOUN
cana-5712	70	81	(	(	PUNCT
cana-5712	70	82	𝛼	𝛼	PROPN
cana-5712	70	83	𝛽	𝛽	NOUN
cana-5712	70	84	)	)	PUNCT
cana-5712	70	85	>	>	X
cana-5712	70	86	𝑅(𝛾	𝑅(𝛾	X
cana-5712	70	87	)	)	PUNCT
cana-5712	70	88	2	2	NUM
cana-5712	70	89	.	.	PUNCT
cana-5712	70	90	∫	∫	PROPN
cana-5712	70	91	xσ(1	xσ(1	PROPN
cana-5712	71	1	−	−	PROPN
cana-5712	72	1	x2)−	x2)−	PROPN
cana-5712	72	2	μ	μ	NUM
cana-5712	72	3	2pγ	2pγ	ADJ
cana-5712	72	4	μ(x)dx	μ(x)dx	PROPN
cana-5712	72	5	=	=	SYM
cana-5712	72	6	2μ−1	2μ−1	NUM
cana-5712	72	7	γ	γ	X
cana-5712	72	8	(	(	PUNCT
cana-5712	72	9	1	1	NUM
cana-5712	72	10	2	2	NUM
cana-5712	72	11	+	+	CCONJ
cana-5712	72	12	σ	σ	PROPN
cana-5712	72	13	2	2	NUM
cana-5712	72	14	)	)	PUNCT
cana-5712	73	1	γ(1	γ(1	PROPN
cana-5712	73	2	+	+	PROPN
cana-5712	73	3	σ	σ	PROPN
cana-5712	73	4	2	2	NUM
cana-5712	73	5	)	)	PUNCT
cana-5712	74	1	γ(1	γ(1	PROPN
cana-5712	74	2	+	+	PROPN
cana-5712	74	3	σ	σ	PROPN
cana-5712	74	4	2	2	NUM
cana-5712	74	5	−	−	NOUN
cana-5712	74	6	ν	ν	NOUN
cana-5712	74	7	2	2	NUM
cana-5712	74	8	−	−	PROPN
cana-5712	74	9	μ	μ	NOUN
cana-5712	74	10	2	2	NUM
cana-5712	74	11	)	)	PUNCT
cana-5712	74	12	γ	γ	PROPN
cana-5712	74	13	(	(	PUNCT
cana-5712	74	14	σ	σ	PROPN
cana-5712	74	15	2	2	NUM
cana-5712	74	16	+	+	CCONJ
cana-5712	74	17	ν	ν	NOUN
cana-5712	74	18	2	2	NUM
cana-5712	74	19	−	−	PROPN
cana-5712	74	20	μ	μ	NOUN
cana-5712	74	21	2	2	NUM
cana-5712	74	22	+	+	CCONJ
cana-5712	74	23	3	3	NUM
cana-5712	74	24	2	2	NUM
cana-5712	74	25	)	)	PUNCT
cana-5712	74	26	1	1	NUM
cana-5712	74	27	0	0	NUM
cana-5712	74	28	,	,	PUNCT
cana-5712	74	29	(	(	PUNCT
cana-5712	74	30	1.11	1.11	NUM
cana-5712	74	31	)	)	PUNCT
cana-5712	74	32	a.	a.	NOUN
cana-5712	74	33	𝑅𝑒(𝜇	𝑅𝑒(𝜇	NOUN
cana-5712	74	34	)	)	PUNCT
cana-5712	74	35	<	<	X
cana-5712	74	36	1	1	NUM
cana-5712	74	37	,	,	PUNCT
cana-5712	74	38	𝑅𝑒(𝜎	𝑅𝑒(𝜎	NOUN
cana-5712	74	39	)	)	PUNCT
cana-5712	74	40	>	>	X
cana-5712	74	41	−1	−1	NOUN
cana-5712	74	42	3	3	X
cana-5712	74	43	.	.	PUNCT
cana-5712	74	44	.	.	PUNCT
cana-5712	75	1	∫	∫	PROPN
cana-5712	76	1	𝑥−𝜌(𝑥2	𝑥−𝜌(𝑥2	NOUN
cana-5712	76	2	−	−	PROPN
cana-5712	76	3	1)−	1)−	PROPN
cana-5712	76	4	𝜇	𝜇	ADP
cana-5712	76	5	2	2	NUM
cana-5712	76	6	∞	∞	NUM
cana-5712	76	7	1	1	NUM
cana-5712	76	8	𝑃𝜈	𝑃𝜈	PROPN
cana-5712	76	9	𝜇(𝑥)𝑑𝑥	𝜇(𝑥)𝑑𝑥	ADJ
cana-5712	76	10	=	=	SYM
cana-5712	76	11	2𝜌+𝜇−2	2𝜌+𝜇−2	NUM
cana-5712	76	12	𝛤	𝛤	PROPN
cana-5712	76	13	(	(	PUNCT
cana-5712	76	14	𝜌+𝜇+𝜈	𝜌+𝜇+𝜈	NOUN
cana-5712	76	15	2	2	NUM
cana-5712	76	16	)	)	PUNCT
cana-5712	76	17	𝛤	𝛤	PROPN
cana-5712	76	18	(	(	PUNCT
cana-5712	76	19	𝜌+𝜇−𝜈−1	𝜌+𝜇−𝜈−1	PROPN
cana-5712	76	20	2	2	NUM
cana-5712	76	21	)	)	PUNCT
cana-5712	76	22	𝜋	𝜋	NOUN
cana-5712	76	23	1	1	NUM
cana-5712	76	24	2𝛤(𝜌	2𝛤(𝜌	NUM
cana-5712	76	25	)	)	PUNCT
cana-5712	76	26	,	,	PUNCT
cana-5712	76	27	(	(	PUNCT
cana-5712	76	28	1.12	1.12	NUM
cana-5712	76	29	)	)	PUNCT
cana-5712	76	30	𝑅𝑒(𝜇	𝑅𝑒(𝜇	ADJ
cana-5712	76	31	)	)	PUNCT
cana-5712	76	32	<	<	X
cana-5712	76	33	1	1	NUM
cana-5712	76	34	,	,	PUNCT
cana-5712	76	35	𝑅𝑒(𝜌	𝑅𝑒(𝜌	ADV
cana-5712	76	36	+	+	CCONJ
cana-5712	76	37	𝜇	𝜇	X
cana-5712	76	38	+	+	X
cana-5712	76	39	𝜈	𝜈	X
cana-5712	76	40	)	)	PUNCT
cana-5712	76	41	>	>	X
cana-5712	76	42	0	0	NUM
cana-5712	76	43	,	,	PUNCT
cana-5712	76	44	𝑅𝑒(𝜌	𝑅𝑒(𝜌	ADJ
cana-5712	76	45	+	+	ADV
cana-5712	76	46	𝜇	𝜇	ADP
cana-5712	76	47	−	−	ADP
cana-5712	76	48	𝜈	𝜈	X
cana-5712	76	49	)	)	PUNCT
cana-5712	76	50	>	>	SYM
cana-5712	76	51	1	1	NUM
cana-5712	76	52	integral	integral	ADJ
cana-5712	76	53	containing	contain	VERB
cana-5712	76	54	tchebichef	tchebichef	NOUN
cana-5712	76	55	polynomial	polynomial	ADJ
cana-5712	76	56	4	4	NUM
cana-5712	76	57	.	.	PUNCT
cana-5712	77	1	∫	∫	PROPN
cana-5712	78	1	(	(	PUNCT
cana-5712	78	2	1	1	NUM
cana-5712	78	3	−	−	NOUN
cana-5712	78	4	x	x	X
cana-5712	78	5	)	)	PUNCT
cana-5712	78	6	1	1	NUM
cana-5712	78	7	2(1	2(1	NUM
cana-5712	78	8	+	+	NUM
cana-5712	78	9	x)αun(x)dx	x)αun(x)dx	ADJ
cana-5712	78	10	=	=	SYM
cana-5712	78	11	1	1	NUM
cana-5712	78	12	−1	−1	NOUN
cana-5712	78	13	π	π	NOUN
cana-5712	78	14	1	1	NUM
cana-5712	78	15	22α+2μ+	22α+2μ+	NUM
cana-5712	78	16	3	3	NUM
cana-5712	78	17	2	2	NUM
cana-5712	79	1	[	[	X
cana-5712	79	2	n+1]2γ(α+	n+1]2γ(α+	ADJ
cana-5712	79	3	1	1	NUM
cana-5712	79	4	2	2	NUM
cana-5712	79	5	)	)	PUNCT
cana-5712	79	6	γ(α+1	γ(α+1	NOUN
cana-5712	79	7	)	)	PUNCT
cana-5712	79	8	(	(	PUNCT
cana-5712	79	9	2n+2)γ(α+n+	2n+2)γ(α+n+	NOUN
cana-5712	79	10	1	1	NUM
cana-5712	79	11	2	2	NUM
cana-5712	79	12	)	)	PUNCT
cana-5712	79	13	γ(α−n+	γ(α−n+	NOUN
cana-5712	79	14	1	1	NUM
cana-5712	79	15	2	2	NUM
cana-5712	79	16	)	)	PUNCT
cana-5712	79	17	(	(	PUNCT
cana-5712	79	18	1.13	1.13	NUM
cana-5712	79	19	)	)	PUNCT
cana-5712	79	20	a.	a.	NOUN
cana-5712	79	21	where	where	SCONJ
cana-5712	79	22	,	,	PUNCT
cana-5712	79	23	re(α	re(α	PROPN
cana-5712	79	24	)	)	PUNCT
cana-5712	79	25	>	>	X
cana-5712	80	1	−1	−1	NOUN
cana-5712	80	2	;	;	PUNCT
cana-5712	80	3	n	n	NOUN
cana-5712	80	4	=	=	SYM
cana-5712	80	5	1,2	1,2	NUM
cana-5712	80	6	,	,	PUNCT
cana-5712	80	7	…	…	PUNCT
cana-5712	80	8	…	…	PUNCT
cana-5712	80	9	5	5	X
cana-5712	80	10	.	.	PUNCT
cana-5712	80	11	∫	∫	PROPN
cana-5712	80	12	xλp2γ(x)dx	xλp2γ(x)dx	PROPN
cana-5712	81	1	=	=	PUNCT
cana-5712	81	2	(	(	PUNCT
cana-5712	81	3	−1)γγγ	−1)γγγ	PROPN
cana-5712	81	4	2γ(γ+	2γ(γ+	NUM
cana-5712	81	5	λ	λ	NOUN
cana-5712	81	6	2	2	NUM
cana-5712	81	7	+	+	CCONJ
cana-5712	81	8	3	3	NUM
cana-5712	81	9	2	2	NUM
cana-5712	81	10	)	)	PUNCT
cana-5712	81	11	γ(−	γ(−	NOUN
cana-5712	81	12	λ	λ	NOUN
cana-5712	81	13	2	2	NUM
cana-5712	81	14	)	)	PUNCT
cana-5712	81	15	1	1	NUM
cana-5712	81	16	0	0	NUM
cana-5712	81	17	,	,	PUNCT
cana-5712	81	18	re(λ	re(λ	NUM
cana-5712	81	19	)	)	PUNCT
cana-5712	81	20	>	>	X
cana-5712	82	1	−1	−1	NOUN
cana-5712	82	2	,	,	PUNCT
cana-5712	82	3	γ	γ	X
cana-5712	82	4	is	be	AUX
cana-5712	82	5	non	non	ADJ
cana-5712	82	6	-	-	ADJ
cana-5712	82	7	negative	negative	ADJ
cana-5712	82	8	integer	integer	NOUN
cana-5712	82	9	.	.	PUNCT
cana-5712	83	1	(	(	PUNCT
cana-5712	83	2	1.14	1.14	NUM
cana-5712	83	3	)	)	PUNCT
cana-5712	83	4	6	6	NUM
cana-5712	83	5	.	.	PUNCT
cana-5712	83	6	∫	∫	PROPN
cana-5712	84	1	xλp2ν+1(x)dx	xλp2ν+1(x)dx	PROPN
cana-5712	84	2	=	=	SYM
cana-5712	84	3	(	(	PUNCT
cana-5712	84	4	−1)ν	−1)ν	NOUN
cana-5712	84	5	γ	γ	X
cana-5712	84	6	(	(	PUNCT
cana-5712	84	7	1	1	NUM
cana-5712	84	8	2	2	NUM
cana-5712	84	9	−	−	NOUN
cana-5712	84	10	λ	λ	NOUN
cana-5712	84	11	2	2	NUM
cana-5712	84	12	+	+	NOUN
cana-5712	84	13	ν)γ(1	ν)γ(1	ADJ
cana-5712	84	14	+	+	NOUN
cana-5712	84	15	λ	λ	NOUN
cana-5712	84	16	2	2	NUM
cana-5712	84	17	)	)	PUNCT
cana-5712	84	18	γ	γ	X
cana-5712	84	19	(	(	PUNCT
cana-5712	84	20	1	1	NUM
cana-5712	84	21	2	2	NUM
cana-5712	84	22	−	−	NOUN
cana-5712	84	23	λ	λ	NOUN
cana-5712	84	24	2	2	NUM
cana-5712	84	25	)	)	PUNCT
cana-5712	84	26	γ(2+ν+	γ(2+ν+	PROPN
cana-5712	84	27	λ	λ	NOUN
cana-5712	84	28	2	2	NUM
cana-5712	84	29	)	)	PUNCT
cana-5712	84	30	1	1	NUM
cana-5712	84	31	0	0	NUM
cana-5712	84	32	,	,	PUNCT
cana-5712	84	33	re(λ	re(λ	NUM
cana-5712	84	34	)	)	PUNCT
cana-5712	84	35	>	>	X
cana-5712	84	36	−2	−2	X
cana-5712	84	37	(	(	PUNCT
cana-5712	84	38	1.15	1.15	NUM
cana-5712	84	39	)	)	PUNCT
cana-5712	84	40	.	.	PUNCT
cana-5712	85	1	integral	integral	ADJ
cana-5712	85	2	associated	associate	VERB
cana-5712	85	3	with	with	ADP
cana-5712	85	4	generalized	generalized	ADJ
cana-5712	85	5	laguerre	laguerre	NOUN
cana-5712	85	6	polynomial	polynomial	ADJ
cana-5712	85	7	as	as	ADP
cana-5712	85	8	:	:	PUNCT
cana-5712	85	9	7	7	NUM
cana-5712	85	10	.	.	NOUN
cana-5712	85	11	∫	∫	PROPN
cana-5712	85	12	xβ−1e−xln	xβ−1e−xln	PROPN
cana-5712	85	13	(	(	PUNCT
cana-5712	85	14	α)(x)dx	α)(x)dx	NOUN
cana-5712	85	15	=	=	SYM
cana-5712	85	16	γ(α−β+n+1)γ(β	γ(α−β+n+1)γ(β	NOUN
cana-5712	85	17	)	)	PUNCT
cana-5712	85	18	γ(α−β+1	γ(α−β+1	X
cana-5712	85	19	)	)	PUNCT
cana-5712	85	20	n	n	CCONJ
cana-5712	85	21	!	!	NOUN
cana-5712	85	22	,	,	PUNCT
cana-5712	85	23	re(β	re(β	X
cana-5712	85	24	)	)	PUNCT
cana-5712	85	25	>	>	X
cana-5712	85	26	0	0	NUM
cana-5712	85	27	,	,	PUNCT
cana-5712	85	28	∞	∞	PROPN
cana-5712	85	29	0	0	NUM
cana-5712	86	1	n	n	PRON
cana-5712	86	2	is	be	AUX
cana-5712	86	3	non	non	ADJ
cana-5712	86	4	negative	negative	ADJ
cana-5712	86	5	integer	integer	NOUN
cana-5712	86	6	.	.	PUNCT
cana-5712	87	1	(	(	PUNCT
cana-5712	87	2	1.16	1.16	NUM
cana-5712	87	3	)	)	PUNCT
cana-5712	87	4	communications	communication	NOUN
cana-5712	87	5	on	on	ADP
cana-5712	87	6	applied	apply	VERB
cana-5712	87	7	nonlinear	nonlinear	ADJ
cana-5712	87	8	analysis	analysis	NOUN
cana-5712	87	9	issn	issn	NOUN
cana-5712	87	10	:	:	PUNCT
cana-5712	87	11	1074	1074	NUM
cana-5712	87	12	-	-	PUNCT
cana-5712	87	13	133x	133x	NUM
cana-5712	87	14	vol	vol	VERB
cana-5712	87	15	32	32	NUM
cana-5712	87	16	no	no	NOUN
cana-5712	87	17	.	.	PUNCT
cana-5712	88	1	10s	10	NOUN
cana-5712	88	2	(	(	PUNCT
cana-5712	88	3	2025	2025	NUM
cana-5712	88	4	)	)	PUNCT
cana-5712	88	5	2715	2715	NUM
cana-5712	88	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5712	88	7	8	8	NUM
cana-5712	88	8	.	.	PUNCT
cana-5712	88	9	∫	∫	PROPN
cana-5712	89	1	uλ−1(1	uλ−1(1	PROPN
cana-5712	89	2	+	+	CCONJ
cana-5712	89	3	u)−μdu	u)−μdu	ADJ
cana-5712	89	4	=	=	SYM
cana-5712	89	5	γ(λ)γ(μ−1	γ(λ)γ(μ−1	NOUN
cana-5712	89	6	)	)	PUNCT
cana-5712	89	7	γ(μ	γ(μ	NOUN
cana-5712	89	8	)	)	PUNCT
cana-5712	89	9	∞	∞	PROPN
cana-5712	89	10	0	0	NUM
cana-5712	89	11	,	,	PUNCT
cana-5712	89	12	0	0	NUM
cana-5712	89	13	<	<	X
cana-5712	89	14	re(λ	re(λ	NOUN
cana-5712	89	15	)	)	PUNCT
cana-5712	89	16	<	<	X
cana-5712	89	17	re(μ	re(μ	NOUN
cana-5712	89	18	)	)	PUNCT
cana-5712	89	19	.	.	PUNCT
cana-5712	90	1	(	(	PUNCT
cana-5712	90	2	1.17	1.17	NUM
cana-5712	90	3	)	)	PUNCT
cana-5712	90	4	9	9	NUM
cana-5712	90	5	.	.	PUNCT
cana-5712	90	6	∫	∫	PROPN
cana-5712	90	7	sinμϑ.	sinμϑ.	PROPN
cana-5712	90	8	cosνϑdϑ	cosνϑdϑ	PROPN
cana-5712	91	1	=	=	PUNCT
cana-5712	91	2	π	π	NOUN
cana-5712	91	3	2	2	NUM
cana-5712	91	4	0	0	NUM
cana-5712	91	5	γ	γ	X
cana-5712	91	6	(	(	PUNCT
cana-5712	91	7	μ+1	μ+1	NUM
cana-5712	91	8	2	2	NUM
cana-5712	91	9	)	)	PUNCT
cana-5712	91	10	γ	γ	PROPN
cana-5712	91	11	(	(	PUNCT
cana-5712	91	12	ν+1	ν+1	PROPN
cana-5712	91	13	2	2	NUM
cana-5712	91	14	)	)	PUNCT
cana-5712	91	15	2γ	2γ	NOUN
cana-5712	91	16	(	(	PUNCT
cana-5712	91	17	μ+ν+2	μ+ν+2	PROPN
cana-5712	91	18	2	2	NUM
cana-5712	91	19	)	)	PUNCT
cana-5712	91	20	,	,	PUNCT
cana-5712	91	21	re(μ	re(μ	X
cana-5712	91	22	)	)	PUNCT
cana-5712	91	23	>	>	X
cana-5712	91	24	0	0	NUM
cana-5712	91	25	,	,	PUNCT
cana-5712	91	26	re(ν	re(ν	X
cana-5712	91	27	)	)	PUNCT
cana-5712	91	28	>	>	X
cana-5712	91	29	0	0	X
cana-5712	91	30	.	.	PUNCT
cana-5712	92	1	(	(	PUNCT
cana-5712	92	2	1.18	1.18	NUM
cana-5712	92	3	)	)	PUNCT
cana-5712	92	4	2	2	NUM
cana-5712	92	5	.	.	PUNCT
cana-5712	92	6	composition	composition	NOUN
cana-5712	92	7	of	of	ADP
cana-5712	92	8	euler	euler	NOUN
cana-5712	92	9	type	type	NOUN
cana-5712	92	10	integrals	integral	NOUN
cana-5712	92	11	:	:	PUNCT
cana-5712	92	12	theorem	theorem	NOUN
cana-5712	92	13	1	1	NUM
cana-5712	92	14	.	.	PUNCT
cana-5712	93	1	if	if	SCONJ
cana-5712	93	2	re(η	re(η	NOUN
cana-5712	93	3	)	)	PUNCT
cana-5712	93	4	>	>	X
cana-5712	94	1	−1	−1	NOUN
cana-5712	94	2	,	,	PUNCT
cana-5712	94	3	re(ξ	re(ξ	PUNCT
cana-5712	94	4	)	)	PUNCT
cana-5712	94	5	>	>	X
cana-5712	94	6	0	0	NUM
cana-5712	94	7	,	,	PUNCT
cana-5712	94	8	re(ν	re(ν	X
cana-5712	94	9	)	)	PUNCT
cana-5712	94	10	>	>	X
cana-5712	94	11	0	0	NUM
cana-5712	94	12	,	,	PUNCT
cana-5712	94	13	re	re	ADP
cana-5712	94	14	(	(	PUNCT
cana-5712	94	15	μ	μ	PROPN
cana-5712	94	16	ν	ν	PROPN
cana-5712	94	17	)	)	PUNCT
cana-5712	94	18	>	>	X
cana-5712	94	19	re(μ	re(μ	NOUN
cana-5712	94	20	)	)	PUNCT
cana-5712	94	21	,	,	PUNCT
cana-5712	94	22	σ	σ	PROPN
cana-5712	94	23	,	,	PUNCT
cana-5712	94	24	ρ	ρ	PROPN
cana-5712	94	25	∈	∈	PROPN
cana-5712	94	26	c	c	X
cana-5712	94	27	,	,	PUNCT
cana-5712	94	28	ξ	ξ	X
cana-5712	94	29	=	=	PUNCT
cana-5712	94	30	ϑ4	ϑ4	NOUN
cana-5712	94	31	,	,	PUNCT
cana-5712	94	32	re(σ	re(σ	X
cana-5712	94	33	)	)	PUNCT
cana-5712	94	34	>	>	X
cana-5712	95	1	0	0	NUM
cana-5712	95	2	,	,	PUNCT
cana-5712	95	3	we	we	PRON
cana-5712	95	4	get	get	AUX
cana-5712	95	5	following	follow	VERB
cana-5712	95	6	results	result	NOUN
cana-5712	95	7	∫	∫	PROPN
cana-5712	95	8	e−μt[sinh	e−μt[sinh	INTJ
cana-5712	95	9	(	(	PUNCT
cana-5712	95	10	νt)]η	νt)]η	NOUN
cana-5712	95	11	mq	mq	PROPN
cana-5712	96	1	p	p	NOUN
cana-5712	96	2	p	p	X
cana-5712	96	3	σ∞	σ∞	PROPN
cana-5712	96	4	0	0	NUM
cana-5712	96	5	(	(	PUNCT
cana-5712	96	6	k1	k1	NOUN
cana-5712	96	7	,	,	PUNCT
cana-5712	96	8	…	…	PUNCT
cana-5712	96	9	.	.	PUNCT
cana-5712	96	10	,	,	PUNCT
cana-5712	96	11	kp	kp	PROPN
cana-5712	96	12	,	,	PUNCT
cana-5712	96	13	l1	l1	PROPN
cana-5712	96	14	…	…	PUNCT
cana-5712	96	15	.	.	PUNCT
cana-5712	97	1	lq	lq	INTJ
cana-5712	97	2	:	:	PUNCT
cana-5712	97	3	ze−ξt)dt	ze−ξt)dt	X
cana-5712	97	4	=	=	PUNCT
cana-5712	97	5	ν−12−η−1	ν−12−η−1	ADP
cana-5712	97	6	∏	∏	PROPN
cana-5712	97	7	γ(lq	γ(lq	NUM
cana-5712	97	8	)	)	PUNCT
cana-5712	97	9	q	q	PROPN
cana-5712	97	10	i=1	i=1	PROPN
cana-5712	97	11	γ(1+η	γ(1+η	PROPN
cana-5712	97	12	)	)	PUNCT
cana-5712	97	13	∏	∏	PROPN
cana-5712	97	14	γ(kp	γ(kp	PROPN
cana-5712	97	15	)	)	PUNCT
cana-5712	97	16	p	p	X
cana-5712	97	17	j=1	j=1	PROPN
cana-5712	97	18	p+2ψq+2	p+2ψq+2	VERB
cana-5712	97	19	[	[	PUNCT
cana-5712	97	20	(	(	PUNCT
cana-5712	97	21	k1	k1	NOUN
cana-5712	97	22	,	,	PUNCT
cana-5712	97	23	1	1	NUM
cana-5712	97	24	)	)	PUNCT
cana-5712	97	25	,	,	PUNCT
cana-5712	97	26	…	…	PUNCT
cana-5712	97	27	…	…	PUNCT
cana-5712	97	28	,	,	PUNCT
cana-5712	97	29	(	(	PUNCT
cana-5712	97	30	kp	kp	INTJ
cana-5712	97	31	,	,	PUNCT
cana-5712	97	32	1	1	NUM
cana-5712	97	33	)	)	PUNCT
cana-5712	97	34	,	,	PUNCT
cana-5712	97	35	(	(	PUNCT
cana-5712	97	36	μ	μ	NUM
cana-5712	97	37	2ν	2ν	NOUN
cana-5712	97	38	−	−	PROPN
cana-5712	97	39	η	η	X
cana-5712	97	40	2	2	NUM
cana-5712	97	41	+	+	SYM
cana-5712	97	42	ξ	ξ	PROPN
cana-5712	97	43	2ν	2ν	NOUN
cana-5712	97	44	)	)	PUNCT
cana-5712	97	45	,	,	PUNCT
cana-5712	97	46	(	(	PUNCT
cana-5712	97	47	1,1	1,1	NUM
cana-5712	97	48	)	)	PUNCT
cana-5712	97	49	(	(	PUNCT
cana-5712	97	50	l1	l1	PROPN
cana-5712	97	51	,	,	PUNCT
cana-5712	97	52	1	1	NUM
cana-5712	97	53	)	)	PUNCT
cana-5712	97	54	,	,	PUNCT
cana-5712	97	55	…	…	PUNCT
cana-5712	97	56	…	…	PUNCT
cana-5712	97	57	.	.	PUNCT
cana-5712	97	58	,	,	PUNCT
cana-5712	97	59	(	(	PUNCT
cana-5712	97	60	lq	lq	INTJ
cana-5712	97	61	,	,	PUNCT
cana-5712	97	62	1	1	NUM
cana-5712	97	63	)	)	PUNCT
cana-5712	97	64	,	,	PUNCT
cana-5712	97	65	(	(	PUNCT
cana-5712	97	66	ρ	ρ	PROPN
cana-5712	97	67	,	,	PUNCT
cana-5712	97	68	σ	σ	PROPN
cana-5712	97	69	)	)	PUNCT
cana-5712	97	70	,	,	PUNCT
cana-5712	97	71	(	(	PUNCT
cana-5712	97	72	μ	μ	NUM
cana-5712	97	73	2ν	2ν	NOUN
cana-5712	97	74	+	+	CCONJ
cana-5712	97	75	η	η	X
cana-5712	97	76	2	2	NUM
cana-5712	97	77	+	+	SYM
cana-5712	97	78	1	1	NUM
cana-5712	97	79	+	+	SYM
cana-5712	97	80	ξ	ξ	PROPN
cana-5712	97	81	2ν	2ν	NOUN
cana-5712	97	82	)	)	PUNCT
cana-5712	98	1	z	z	NOUN
cana-5712	98	2	]	]	X
cana-5712	98	3	.	.	PUNCT
cana-5712	99	1	(	(	PUNCT
cana-5712	99	2	2.1	2.1	NUM
cana-5712	99	3	)	)	PUNCT
cana-5712	99	4	proof	proof	NOUN
cana-5712	99	5	.	.	PUNCT
cana-5712	100	1	to	to	PART
cana-5712	100	2	prove	prove	VERB
cana-5712	100	3	above	above	ADP
cana-5712	100	4	theorem	theorem	NOUN
cana-5712	100	5	1	1	NUM
cana-5712	100	6	,	,	PUNCT
cana-5712	100	7	expressing	express	VERB
cana-5712	100	8	mq	mq	PROPN
cana-5712	100	9	p	p	PROPN
cana-5712	100	10	p	p	PROPN
cana-5712	100	11	σ	σ	PROPN
cana-5712	100	12	is	be	AUX
cana-5712	100	13	the	the	DET
cana-5712	100	14	l.h.s	l.h.s	NOUN
cana-5712	100	15	.	.	PUNCT
cana-5712	101	1	of	of	ADP
cana-5712	101	2	(	(	PUNCT
cana-5712	101	3	2.1	2.1	NUM
cana-5712	101	4	)	)	PUNCT
cana-5712	101	5	.	.	PUNCT
cana-5712	102	1	changing	change	VERB
cana-5712	102	2	the	the	DET
cana-5712	102	3	order	order	NOUN
cana-5712	102	4	of	of	ADP
cana-5712	102	5	integral	integral	ADJ
cana-5712	102	6	and	and	CCONJ
cana-5712	102	7	on	on	ADP
cana-5712	102	8	evaluating	evaluate	VERB
cana-5712	102	9	the	the	DET
cana-5712	102	10	inner	inner	ADJ
cana-5712	102	11	integral	integral	NOUN
cana-5712	102	12	with	with	ADP
cana-5712	102	13	help	help	NOUN
cana-5712	102	14	of	of	ADP
cana-5712	102	15	(	(	PUNCT
cana-5712	102	16	1.10	1.10	NUM
cana-5712	102	17	)	)	PUNCT
cana-5712	102	18	.	.	PUNCT
cana-5712	103	1	∫	∫	PROPN
cana-5712	103	2	e−μt[sinh	e−μt[sinh	INTJ
cana-5712	103	3	(	(	PUNCT
cana-5712	103	4	νt)]η	νt)]η	NOUN
cana-5712	103	5	mq	mq	PROPN
cana-5712	104	1	p	p	NOUN
cana-5712	104	2	p	p	X
cana-5712	104	3	σ∞	σ∞	PROPN
cana-5712	104	4	0	0	NUM
cana-5712	104	5	(	(	PUNCT
cana-5712	104	6	k1	k1	NOUN
cana-5712	104	7	,	,	PUNCT
cana-5712	104	8	…	…	PUNCT
cana-5712	104	9	.	.	PUNCT
cana-5712	104	10	,	,	PUNCT
cana-5712	104	11	kp	kp	PROPN
cana-5712	104	12	,	,	PUNCT
cana-5712	104	13	l1	l1	PROPN
cana-5712	104	14	…	…	PUNCT
cana-5712	104	15	.	.	PUNCT
cana-5712	105	1	lq	lq	INTJ
cana-5712	105	2	:	:	PUNCT
cana-5712	105	3	ze−ξt)dt	ze−ξt)dt	X
cana-5712	105	4	=	=	SYM
cana-5712	106	1	∫	∫	PROPN
cana-5712	106	2	e−μt[sinh	e−μt[sinh	INTJ
cana-5712	106	3	(	(	PUNCT
cana-5712	106	4	νt)]η	νt)]η	PROPN
cana-5712	106	5	∑	∑	PROPN
cana-5712	106	6	(	(	PUNCT
cana-5712	106	7	k1)m	k1)m	PROPN
cana-5712	106	8	…	…	PUNCT
cana-5712	106	9	…	…	PUNCT
cana-5712	106	10	(kp	(kp	SYM
cana-5712	106	11	)	)	PUNCT
cana-5712	106	12	m	m	PROPN
cana-5712	106	13	(	(	PUNCT
cana-5712	106	14	l1)m	l1)m	NOUN
cana-5712	106	15	…	…	SYM
cana-5712	106	16	…	…	SYM
cana-5712	106	17	.(lq	.(lq	SYM
cana-5712	106	18	)	)	PUNCT
cana-5712	107	1	m	m	VERB
cana-5712	107	2	∞	∞	NUM
cana-5712	107	3	m=0	m=0	PROPN
cana-5712	107	4	zme−ξmt	zme−ξmt	PROPN
cana-5712	107	5	γ(ρ+σm	γ(ρ+σm	PROPN
cana-5712	107	6	)	)	PUNCT
cana-5712	108	1	dt	dt	X
cana-5712	109	1	∞	∞	NOUN
cana-5712	109	2	0	0	NUM
cana-5712	110	1	=	=	SYM
cana-5712	110	2	∑	∑	PROPN
cana-5712	110	3	(	(	PUNCT
cana-5712	110	4	k1)m	k1)m	PROPN
cana-5712	110	5	…	…	PUNCT
cana-5712	110	6	…	…	PUNCT
cana-5712	110	7	(kp	(kp	SYM
cana-5712	110	8	)	)	PUNCT
cana-5712	110	9	m	m	PROPN
cana-5712	110	10	(	(	PUNCT
cana-5712	110	11	l1)m	l1)m	NOUN
cana-5712	110	12	…	…	SYM
cana-5712	110	13	…	…	SYM
cana-5712	110	14	.(lq	.(lq	SYM
cana-5712	110	15	)	)	PUNCT
cana-5712	111	1	m	m	VERB
cana-5712	111	2	∞	∞	NUM
cana-5712	111	3	m=0	m=0	PROPN
cana-5712	111	4	zme−ξmt	zme−ξmt	PROPN
cana-5712	111	5	γ(ρ+σm	γ(ρ+σm	PROPN
cana-5712	111	6	)	)	PUNCT
cana-5712	111	7	∫	∫	PROPN
cana-5712	111	8	e−(μ+ξm)t[sinh	e−(μ+ξm)t[sinh	PROPN
cana-5712	111	9	(	(	PUNCT
cana-5712	111	10	νt)]ηdt	νt)]ηdt	X
cana-5712	111	11	∞	∞	X
cana-5712	111	12	0	0	NUM
cana-5712	112	1	=	=	SYM
cana-5712	112	2	∑	∑	PROPN
cana-5712	112	3	(	(	PUNCT
cana-5712	112	4	k1)m	k1)m	PROPN
cana-5712	112	5	…	…	PUNCT
cana-5712	112	6	…	…	PUNCT
cana-5712	112	7	(kp	(kp	SYM
cana-5712	112	8	)	)	PUNCT
cana-5712	112	9	m	m	PROPN
cana-5712	112	10	(	(	PUNCT
cana-5712	112	11	l1)m	l1)m	NOUN
cana-5712	112	12	…	…	SYM
cana-5712	112	13	…	…	SYM
cana-5712	112	14	.(lq	.(lq	SYM
cana-5712	112	15	)	)	PUNCT
cana-5712	113	1	m	m	VERB
cana-5712	113	2	∞	∞	NUM
cana-5712	113	3	m=0	m=0	PROPN
cana-5712	113	4	zme−ξmt	zme−ξmt	PROPN
cana-5712	113	5	γ(ρ+σm	γ(ρ+σm	PROPN
cana-5712	113	6	)	)	PUNCT
cana-5712	113	7	ν−12−η−1	ν−12−η−1	ADP
cana-5712	113	8	γ	γ	PROPN
cana-5712	113	9	(	(	PUNCT
cana-5712	113	10	μ+ξm	μ+ξm	PROPN
cana-5712	113	11	2ν	2ν	NOUN
cana-5712	113	12	−	−	PROPN
cana-5712	113	13	η	η	PROPN
cana-5712	113	14	2	2	NUM
cana-5712	113	15	)	)	PUNCT
cana-5712	113	16	γ(η+1	γ(η+1	SYM
cana-5712	113	17	)	)	PUNCT
cana-5712	114	1	γ	γ	PROPN
cana-5712	114	2	(	(	PUNCT
cana-5712	114	3	μ+ξm	μ+ξm	PROPN
cana-5712	114	4	2ν	2ν	NOUN
cana-5712	114	5	+	+	CCONJ
cana-5712	114	6	η	η	PROPN
cana-5712	114	7	2	2	NUM
cana-5712	114	8	+1	+1	PROPN
cana-5712	114	9	)	)	PUNCT
cana-5712	114	10	=	=	PUNCT
cana-5712	114	11	ν−12−η−1	ν−12−η−1	PRON
cana-5712	114	12	γ(η	γ(η	PROPN
cana-5712	114	13	+	+	CCONJ
cana-5712	114	14	1	1	X
cana-5712	114	15	)	)	PUNCT
cana-5712	114	16	∑	∑	PROPN
cana-5712	114	17	(	(	PUNCT
cana-5712	114	18	k1)m	k1)m	PROPN
cana-5712	114	19	…	…	PUNCT
cana-5712	114	20	…	…	PUNCT
cana-5712	114	21	(kp	(kp	SYM
cana-5712	114	22	)	)	PUNCT
cana-5712	114	23	m	m	PROPN
cana-5712	114	24	(	(	PUNCT
cana-5712	114	25	l1)m	l1)m	NOUN
cana-5712	114	26	…	…	SYM
cana-5712	114	27	…	…	SYM
cana-5712	114	28	.(lq	.(lq	SYM
cana-5712	114	29	)	)	PUNCT
cana-5712	114	30	m	m	VERB
cana-5712	114	31	∞	∞	NUM
cana-5712	114	32	m=0	m=0	PROPN
cana-5712	114	33	zme−ξmt	zme−ξmt	PROPN
cana-5712	114	34	γ(ρ+σm	γ(ρ+σm	PROPN
cana-5712	114	35	)	)	PUNCT
cana-5712	114	36	γ	γ	PROPN
cana-5712	114	37	(	(	PUNCT
cana-5712	114	38	μ	μ	PROPN
cana-5712	114	39	2ν	2ν	NOUN
cana-5712	114	40	−	−	PROPN
cana-5712	114	41	η	η	X
cana-5712	114	42	2	2	NUM
cana-5712	114	43	+	+	NUM
cana-5712	114	44	ξm	ξm	PROPN
cana-5712	114	45	2ν	2ν	NOUN
cana-5712	114	46	)	)	PUNCT
cana-5712	114	47	γ	γ	PROPN
cana-5712	114	48	(	(	PUNCT
cana-5712	114	49	μ	μ	PROPN
cana-5712	114	50	2ν	2ν	NOUN
cana-5712	114	51	+	+	CCONJ
cana-5712	114	52	η	η	PROPN
cana-5712	114	53	2	2	NUM
cana-5712	114	54	+1	+1	PROPN
cana-5712	114	55	+	+	NUM
cana-5712	114	56	ξm	ξm	NUM
cana-5712	114	57	2ν	2ν	NOUN
cana-5712	114	58	)	)	PUNCT
cana-5712	114	59	.	.	PUNCT
cana-5712	115	1	finally	finally	ADV
cana-5712	115	2	,	,	PUNCT
cana-5712	115	3	we	we	PRON
cana-5712	115	4	use	use	VERB
cana-5712	115	5	equation	equation	NOUN
cana-5712	115	6	(	(	PUNCT
cana-5712	115	7	1.3	1.3	NUM
cana-5712	115	8	)	)	PUNCT
cana-5712	115	9	,	,	PUNCT
cana-5712	115	10	and	and	CCONJ
cana-5712	115	11	we	we	PRON
cana-5712	115	12	get	get	AUX
cana-5712	115	13	desired	desire	VERB
cana-5712	115	14	result	result	NOUN
cana-5712	115	15	(	(	PUNCT
cana-5712	115	16	2.1	2.1	NUM
cana-5712	115	17	)	)	PUNCT
cana-5712	115	18	.	.	PUNCT
cana-5712	116	1	theorem	theorem	NOUN
cana-5712	116	2	2	2	NUM
cana-5712	116	3	.	.	PUNCT
cana-5712	117	1	if	if	SCONJ
cana-5712	117	2	re(ξ	re(ξ	VERB
cana-5712	117	3	)	)	PUNCT
cana-5712	117	4	>	>	X
cana-5712	117	5	0	0	NUM
cana-5712	117	6	,	,	PUNCT
cana-5712	117	7	re(η	re(η	PUNCT
cana-5712	117	8	)	)	PUNCT
cana-5712	117	9	>	>	X
cana-5712	118	1	−1	−1	NOUN
cana-5712	118	2	,	,	PUNCT
cana-5712	118	3	re(σ	re(σ	X
cana-5712	118	4	)	)	PUNCT
cana-5712	118	5	>	>	X
cana-5712	118	6	0	0	NUM
cana-5712	118	7	,	,	PUNCT
cana-5712	118	8	re	re	ADP
cana-5712	118	9	(	(	PUNCT
cana-5712	118	10	μ	μ	PROPN
cana-5712	118	11	2	2	NUM
cana-5712	118	12	)	)	PUNCT
cana-5712	118	13	>	>	X
cana-5712	118	14	re(η	re(η	X
cana-5712	118	15	):	):	PUNCT
cana-5712	118	16	σ	σ	PROPN
cana-5712	118	17	,	,	PUNCT
cana-5712	118	18	ρ	ρ	PROPN
cana-5712	118	19	∈	∈	PROPN
cana-5712	118	20	c	c	NOUN
cana-5712	118	21	,	,	PUNCT
cana-5712	118	22	following	follow	VERB
cana-5712	118	23	results	result	NOUN
cana-5712	118	24	holds	hold	VERB
cana-5712	118	25	:	:	PUNCT
cana-5712	118	26	∫	∫	PROPN
cana-5712	118	27	e−μ[sinh(νt)]η	e−μ[sinh(νt)]η	VERB
cana-5712	118	28	∞	∞	PROPN
cana-5712	118	29	0	0	NUM
cana-5712	119	1	mz	mz	PROPN
cana-5712	119	2	p(k1	p(k1	PROPN
cana-5712	119	3	,	,	PUNCT
cana-5712	119	4	…	…	PUNCT
cana-5712	119	5	.	.	PUNCT
cana-5712	119	6	,	,	PUNCT
cana-5712	119	7	kp	kp	PROPN
cana-5712	119	8	,	,	PUNCT
cana-5712	119	9	l1	l1	PROPN
cana-5712	119	10	…	…	PUNCT
cana-5712	119	11	.	.	PUNCT
cana-5712	120	1	lq	lq	INTJ
cana-5712	120	2	:	:	PUNCT
cana-5712	120	3	z(2	z(2	PROPN
cana-5712	120	4	sinh(νt))ξm)p	sinh(νt))ξm)p	NUM
cana-5712	120	5	σ	σ	X
cana-5712	120	6	dt	dt	NOUN
cana-5712	120	7	=	=	SYM
cana-5712	120	8	ν−12−η−1	ν−12−η−1	PRON
cana-5712	120	9	∏	∏	PROPN
cana-5712	120	10	γ(lq)q	γ(lq)q	NOUN
cana-5712	120	11	j=1	j=1	PROPN
cana-5712	120	12	∏	∏	PROPN
cana-5712	120	13	γ(kp)p	γ(kp)p	NOUN
cana-5712	120	14	i=1	i=1	PROPN
cana-5712	120	15	communications	communication	NOUN
cana-5712	120	16	on	on	ADP
cana-5712	120	17	applied	apply	VERB
cana-5712	120	18	nonlinear	nonlinear	ADJ
cana-5712	120	19	analysis	analysis	NOUN
cana-5712	120	20	issn	issn	NOUN
cana-5712	120	21	:	:	PUNCT
cana-5712	120	22	1074	1074	NUM
cana-5712	120	23	-	-	PUNCT
cana-5712	120	24	133x	133x	NUM
cana-5712	120	25	vol	vol	VERB
cana-5712	120	26	32	32	NUM
cana-5712	120	27	no	no	NOUN
cana-5712	120	28	.	.	PUNCT
cana-5712	121	1	10s	10	NOUN
cana-5712	121	2	(	(	PUNCT
cana-5712	121	3	2025	2025	NUM
cana-5712	121	4	)	)	PUNCT
cana-5712	121	5	2716	2716	NUM
cana-5712	121	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5712	121	7	×	×	NOUN
cana-5712	121	8	p+3ψq+2	p+3ψq+2	NOUN
cana-5712	121	9	[	[	PUNCT
cana-5712	121	10	(	(	PUNCT
cana-5712	121	11	k1	k1	NOUN
cana-5712	121	12	,	,	PUNCT
cana-5712	121	13	1	1	NUM
cana-5712	121	14	)	)	PUNCT
cana-5712	121	15	,	,	PUNCT
cana-5712	121	16	…	…	PUNCT
cana-5712	121	17	…	…	PUNCT
cana-5712	121	18	,	,	PUNCT
cana-5712	121	19	(	(	PUNCT
cana-5712	121	20	kp	kp	INTJ
cana-5712	121	21	,	,	PUNCT
cana-5712	121	22	1	1	NUM
cana-5712	121	23	)	)	PUNCT
cana-5712	121	24	,	,	PUNCT
cana-5712	121	25	(	(	PUNCT
cana-5712	121	26	μ	μ	NUM
cana-5712	121	27	2ν	2ν	NOUN
cana-5712	121	28	−	−	PROPN
cana-5712	121	29	η	η	X
cana-5712	121	30	2	2	NUM
cana-5712	121	31	+	+	SYM
cana-5712	121	32	ξ	ξ	PROPN
cana-5712	121	33	2	2	NUM
cana-5712	121	34	)	)	PUNCT
cana-5712	121	35	,	,	PUNCT
cana-5712	121	36	(	(	PUNCT
cana-5712	121	37	1	1	NUM
cana-5712	121	38	+	+	CCONJ
cana-5712	121	39	η	η	PROPN
cana-5712	121	40	,	,	PUNCT
cana-5712	121	41	ξ	ξ	NOUN
cana-5712	121	42	)	)	PUNCT
cana-5712	121	43	,	,	PUNCT
cana-5712	121	44	(	(	PUNCT
cana-5712	121	45	1,1	1,1	NUM
cana-5712	121	46	)	)	PUNCT
cana-5712	121	47	(	(	PUNCT
cana-5712	121	48	l1	l1	PROPN
cana-5712	121	49	,	,	PUNCT
cana-5712	121	50	1	1	NUM
cana-5712	121	51	)	)	PUNCT
cana-5712	121	52	,	,	PUNCT
cana-5712	121	53	…	…	PUNCT
cana-5712	121	54	…	…	PUNCT
cana-5712	121	55	.	.	PUNCT
cana-5712	121	56	,	,	PUNCT
cana-5712	121	57	(	(	PUNCT
cana-5712	121	58	lq	lq	INTJ
cana-5712	121	59	,	,	PUNCT
cana-5712	121	60	1	1	NUM
cana-5712	121	61	)	)	PUNCT
cana-5712	121	62	,	,	PUNCT
cana-5712	121	63	(	(	PUNCT
cana-5712	121	64	ρ	ρ	PROPN
cana-5712	121	65	,	,	PUNCT
cana-5712	121	66	σ	σ	PROPN
cana-5712	121	67	)	)	PUNCT
cana-5712	121	68	,	,	PUNCT
cana-5712	121	69	(	(	PUNCT
cana-5712	121	70	μ	μ	NUM
cana-5712	121	71	2ν	2ν	NOUN
cana-5712	121	72	+	+	CCONJ
cana-5712	121	73	η	η	X
cana-5712	121	74	2	2	NUM
cana-5712	121	75	+	+	CCONJ
cana-5712	121	76	1	1	NUM
cana-5712	121	77	+	+	SYM
cana-5712	121	78	ξ	ξ	NOUN
cana-5712	121	79	)	)	PUNCT
cana-5712	121	80	;	;	PUNCT
cana-5712	122	1	z	z	X
cana-5712	122	2	]	]	X
cana-5712	122	3	.	.	PUNCT
cana-5712	123	1	(	(	PUNCT
cana-5712	123	2	2.2	2.2	NUM
cana-5712	123	3	)	)	PUNCT
cana-5712	123	4	proof	proof	NOUN
cana-5712	123	5	.	.	PUNCT
cana-5712	124	1	for	for	ADP
cana-5712	124	2	solving	solve	VERB
cana-5712	124	3	the	the	DET
cana-5712	124	4	above	above	ADJ
cana-5712	124	5	integral	integral	ADJ
cana-5712	124	6	formula	formula	NOUN
cana-5712	124	7	(	(	PUNCT
cana-5712	124	8	2.2	2.2	NUM
cana-5712	124	9	)	)	PUNCT
cana-5712	124	10	,	,	PUNCT
cana-5712	124	11	using	use	VERB
cana-5712	124	12	definition	definition	NOUN
cana-5712	124	13	(	(	PUNCT
cana-5712	124	14	1.1	1.1	NUM
cana-5712	124	15	)	)	PUNCT
cana-5712	124	16	in	in	ADP
cana-5712	124	17	the	the	DET
cana-5712	124	18	l.h.s	l.h.s	NOUN
cana-5712	124	19	.	.	PUNCT
cana-5712	125	1	of	of	ADP
cana-5712	125	2	(	(	PUNCT
cana-5712	125	3	2.2	2.2	NUM
cana-5712	125	4	)	)	PUNCT
cana-5712	125	5	and	and	CCONJ
cana-5712	125	6	then	then	ADV
cana-5712	125	7	changing	change	VERB
cana-5712	125	8	order	order	NOUN
cana-5712	125	9	of	of	ADP
cana-5712	125	10	integration	integration	NOUN
cana-5712	125	11	,	,	PUNCT
cana-5712	125	12	we	we	PRON
cana-5712	125	13	have	have	VERB
cana-5712	125	14	=	=	PRON
cana-5712	125	15	∑	∑	PROPN
cana-5712	125	16	(	(	PUNCT
cana-5712	125	17	k1)m	k1)m	PROPN
cana-5712	125	18	…	…	PUNCT
cana-5712	125	19	…	…	PUNCT
cana-5712	125	20	(	(	PUNCT
cana-5712	125	21	kp	kp	INTJ
cana-5712	125	22	)	)	PUNCT
cana-5712	125	23	m	m	PROPN
cana-5712	125	24	(	(	PUNCT
cana-5712	125	25	l1)m	l1)m	NOUN
cana-5712	125	26	…	…	PUNCT
cana-5712	125	27	…	…	PUNCT
cana-5712	125	28	.	.	PUNCT
cana-5712	126	1	(	(	PUNCT
cana-5712	126	2	lq	lq	NOUN
cana-5712	126	3	)	)	PUNCT
cana-5712	126	4	m	m	PROPN
cana-5712	126	5	∞	∞	NUM
cana-5712	126	6	m=0	m=0	PROPN
cana-5712	126	7	zm2ξm(sinh	zm2ξm(sinh	PROPN
cana-5712	126	8	(	(	PUNCT
cana-5712	126	9	νt))ξm	νt))ξm	PROPN
cana-5712	126	10	γ(ρ	γ(ρ	PROPN
cana-5712	126	11	+	+	CCONJ
cana-5712	126	12	σm	σm	X
cana-5712	126	13	)	)	PUNCT
cana-5712	126	14	∫	∫	PROPN
cana-5712	126	15	e−μ[sinh	e−μ[sinh	PROPN
cana-5712	126	16	(	(	PUNCT
cana-5712	126	17	νt)]η	νt)]η	NOUN
cana-5712	126	18	∞	∞	PROPN
cana-5712	126	19	0	0	NUM
cana-5712	127	1	dt	dt	NOUN
cana-5712	127	2	=	=	SYM
cana-5712	127	3	∏	∏	PROPN
cana-5712	127	4	γ(lq)q	γ(lq)q	VERB
cana-5712	127	5	j=1	j=1	PROPN
cana-5712	127	6	∏	∏	PROPN
cana-5712	127	7	γ(kp	γ(kp	PROPN
cana-5712	127	8	)	)	PUNCT
cana-5712	127	9	p	p	X
cana-5712	127	10	i=1	i=1	PROPN
cana-5712	127	11	∑	∑	PUNCT
cana-5712	127	12	γ(1	γ(1	PROPN
cana-5712	127	13	+	+	NUM
cana-5712	127	14	k1	k1	NOUN
cana-5712	127	15	)	)	PUNCT
cana-5712	127	16	…	…	PUNCT
cana-5712	127	17	.	.	PUNCT
cana-5712	127	18	.	.	PUNCT
cana-5712	128	1	γ(m	γ(m	PROPN
cana-5712	128	2	+	+	CCONJ
cana-5712	128	3	kp	kp	PROPN
cana-5712	128	4	)	)	PUNCT
cana-5712	128	5	(	(	PUNCT
cana-5712	128	6	z2ξ)m	z2ξ)m	X
cana-5712	128	7	γ(1	γ(1	PROPN
cana-5712	128	8	+	+	NUM
cana-5712	128	9	l1	l1	PROPN
cana-5712	128	10	)	)	PUNCT
cana-5712	128	11	…	…	PUNCT
cana-5712	128	12	.	.	PUNCT
cana-5712	128	13	.	.	PUNCT
cana-5712	129	1	γ(m	γ(m	PROPN
cana-5712	129	2	+	+	CCONJ
cana-5712	129	3	lq)γ(ρ	lq)γ(ρ	PROPN
cana-5712	129	4	+	+	CCONJ
cana-5712	129	5	σm	σm	X
cana-5712	129	6	)	)	PUNCT
cana-5712	129	7	∫	∫	PROPN
cana-5712	129	8	e−μ[sinh	e−μ[sinh	PROPN
cana-5712	129	9	(	(	PUNCT
cana-5712	129	10	νt)]η+ξm	νt)]η+ξm	PROPN
cana-5712	129	11	∞	∞	NUM
cana-5712	129	12	0	0	NUM
cana-5712	130	1	dt	dt	NOUN
cana-5712	131	1	∞	∞	PROPN
cana-5712	131	2	m=0	m=0	PROPN
cana-5712	131	3	=	=	SYM
cana-5712	131	4	∏	∏	PROPN
cana-5712	131	5	γ(lq)q	γ(lq)q	VERB
cana-5712	131	6	j=1	j=1	PROPN
cana-5712	131	7	∏	∏	PROPN
cana-5712	131	8	γ(kp	γ(kp	PROPN
cana-5712	131	9	)	)	PUNCT
cana-5712	131	10	p	p	X
cana-5712	131	11	i=1	i=1	PROPN
cana-5712	131	12	∑	∑	PUNCT
cana-5712	131	13	γ(1	γ(1	PROPN
cana-5712	131	14	+	+	NUM
cana-5712	131	15	k1	k1	NOUN
cana-5712	131	16	)	)	PUNCT
cana-5712	131	17	…	…	PUNCT
cana-5712	131	18	.	.	PUNCT
cana-5712	131	19	.	.	PUNCT
cana-5712	132	1	γ(m	γ(m	PROPN
cana-5712	132	2	+	+	CCONJ
cana-5712	132	3	kp)(z2ξ)m	kp)(z2ξ)m	PROPN
cana-5712	132	4	γ(1	γ(1	PROPN
cana-5712	132	5	+	+	NUM
cana-5712	132	6	l1	l1	PROPN
cana-5712	132	7	)	)	PUNCT
cana-5712	132	8	…	…	PUNCT
cana-5712	132	9	.	.	PUNCT
cana-5712	132	10	.	.	PUNCT
cana-5712	133	1	γ(m	γ(m	PROPN
cana-5712	133	2	+	+	CCONJ
cana-5712	133	3	lq)γ(ρ	lq)γ(ρ	PROPN
cana-5712	133	4	+	+	CCONJ
cana-5712	133	5	σm	σm	X
cana-5712	133	6	)	)	PUNCT
cana-5712	133	7	∞	∞	NUM
cana-5712	133	8	m=0	m=0	PROPN
cana-5712	133	9	ν−12−(η+ξm)−1γ	ν−12−(η+ξm)−1γ	PROPN
cana-5712	133	10	(	(	PUNCT
cana-5712	133	11	μ	μ	PROPN
cana-5712	133	12	2ν	2ν	NOUN
cana-5712	133	13	−	−	PROPN
cana-5712	133	14	η	η	PROPN
cana-5712	133	15	+	+	PROPN
cana-5712	133	16	ξm	ξm	PROPN
cana-5712	133	17	2	2	NUM
cana-5712	133	18	)	)	PUNCT
cana-5712	134	1	γ(1	γ(1	PROPN
cana-5712	134	2	+	+	NUM
cana-5712	134	3	η	η	PROPN
cana-5712	134	4	+	+	PROPN
cana-5712	134	5	ξm	ξm	PROPN
cana-5712	134	6	)	)	PUNCT
cana-5712	134	7	γ	γ	PROPN
cana-5712	134	8	(	(	PUNCT
cana-5712	134	9	μ	μ	PROPN
cana-5712	134	10	2ν	2ν	NOUN
cana-5712	134	11	+	+	CCONJ
cana-5712	134	12	η	η	PROPN
cana-5712	134	13	+	+	PROPN
cana-5712	134	14	ξm	ξm	PROPN
cana-5712	134	15	2	2	NUM
cana-5712	134	16	+	+	NUM
cana-5712	134	17	1	1	NUM
cana-5712	134	18	)	)	PUNCT
cana-5712	134	19	=	=	PUNCT
cana-5712	134	20	ν−12−η−1	ν−12−η−1	ADP
cana-5712	134	21	∏	∏	PROPN
cana-5712	134	22	γ(lq	γ(lq	NUM
cana-5712	134	23	)	)	PUNCT
cana-5712	134	24	q	q	PUNCT
cana-5712	134	25	j=1	j=1	PROPN
cana-5712	134	26	∏	∏	PROPN
cana-5712	134	27	γ(kp	γ(kp	PROPN
cana-5712	134	28	)	)	PUNCT
cana-5712	134	29	p	p	X
cana-5712	134	30	i=1	i=1	PROPN
cana-5712	134	31	∑	∑	PUNCT
cana-5712	134	32	γ(1+k1)	γ(1+k1)	NOUN
cana-5712	134	33	…	…	PUNCT
cana-5712	134	34	..	..	PUNCT
cana-5712	134	35	γ(m+kp	γ(m+kp	NUM
cana-5712	134	36	)	)	PUNCT
cana-5712	134	37	γ(1+l1)	γ(1+l1)	NOUN
cana-5712	134	38	…	…	SYM
cana-5712	134	39	..	..	SYM
cana-5712	134	40	γ(m+lq)γ(ρ+σm	γ(m+lq)γ(ρ+σm	NOUN
cana-5712	134	41	)	)	PUNCT
cana-5712	134	42	γ	γ	PROPN
cana-5712	134	43	(	(	PUNCT
cana-5712	134	44	μ	μ	PROPN
cana-5712	134	45	2ν	2ν	NOUN
cana-5712	134	46	−	−	PROPN
cana-5712	134	47	η	η	X
cana-5712	134	48	2	2	NUM
cana-5712	134	49	+	+	NUM
cana-5712	134	50	ξm	ξm	PROPN
cana-5712	134	51	2	2	NUM
cana-5712	134	52	)	)	PUNCT
cana-5712	134	53	γ(1+η+ξm	γ(1+η+ξm	PROPN
cana-5712	134	54	)	)	PUNCT
cana-5712	134	55	γ	γ	PROPN
cana-5712	134	56	(	(	PUNCT
cana-5712	134	57	μ	μ	PROPN
cana-5712	134	58	2ν	2ν	NOUN
cana-5712	134	59	+	+	CCONJ
cana-5712	134	60	η	η	X
cana-5712	134	61	2	2	NUM
cana-5712	134	62	+1+ξm	+1+ξm	NUM
cana-5712	134	63	)	)	PUNCT
cana-5712	134	64	∞	∞	PROPN
cana-5712	134	65	m=0	m=0	PROPN
cana-5712	134	66	zm	zm	PROPN
cana-5712	134	67	m	m	PROPN
cana-5712	134	68	!	!	PUNCT
cana-5712	135	1	γ(1	γ(1	PROPN
cana-5712	135	2	+	+	NUM
cana-5712	135	3	m	m	NOUN
cana-5712	135	4	)	)	PUNCT
cana-5712	135	5	.	.	PUNCT
cana-5712	136	1	hence	hence	ADV
cana-5712	136	2	,	,	PUNCT
cana-5712	136	3	we	we	PRON
cana-5712	136	4	call	call	VERB
cana-5712	136	5	equation	equation	NOUN
cana-5712	136	6	(	(	PUNCT
cana-5712	136	7	1.3	1.3	NUM
cana-5712	136	8	)	)	PUNCT
cana-5712	136	9	and	and	CCONJ
cana-5712	136	10	then	then	ADV
cana-5712	136	11	reached	reach	VERB
cana-5712	136	12	at	at	ADP
cana-5712	136	13	desired	desire	VERB
cana-5712	136	14	result	result	NOUN
cana-5712	136	15	(	(	PUNCT
cana-5712	136	16	2.2	2.2	NUM
cana-5712	136	17	)	)	PUNCT
cana-5712	136	18	.	.	PUNCT
cana-5712	137	1	theorem	theorem	NOUN
cana-5712	137	2	3	3	NUM
cana-5712	137	3	.	.	PUNCT
cana-5712	138	1	if	if	SCONJ
cana-5712	138	2	re(ξ	re(ξ	VERB
cana-5712	138	3	)	)	PUNCT
cana-5712	138	4	>	>	X
cana-5712	138	5	0	0	NUM
cana-5712	138	6	,	,	PUNCT
cana-5712	138	7	re(ν	re(ν	X
cana-5712	138	8	)	)	PUNCT
cana-5712	138	9	<	<	X
cana-5712	138	10	1	1	NUM
cana-5712	138	11	,	,	PUNCT
cana-5712	138	12	re(μ	re(μ	NOUN
cana-5712	138	13	)	)	PUNCT
cana-5712	138	14	>	>	X
cana-5712	139	1	0	0	NUM
cana-5712	139	2	,	,	PUNCT
cana-5712	139	3	σ	σ	PROPN
cana-5712	139	4	,	,	PUNCT
cana-5712	139	5	ξ	ξ	PROPN
cana-5712	139	6	∈	∈	PROPN
cana-5712	139	7	c	c	NOUN
cana-5712	139	8	,	,	PUNCT
cana-5712	139	9	re(σ	re(σ	X
cana-5712	139	10	)	)	PUNCT
cana-5712	139	11	>	>	X
cana-5712	139	12	0	0	NUM
cana-5712	139	13	,	,	PUNCT
cana-5712	139	14	following	follow	VERB
cana-5712	139	15	integral	integral	ADJ
cana-5712	139	16	formula	formula	NOUN
cana-5712	139	17	holds	hold	VERB
cana-5712	139	18	∫	∫	PROPN
cana-5712	139	19	uμ(1	uμ(1	ADJ
cana-5712	139	20	−	−	PROPN
cana-5712	139	21	u2)−	u2)−	ADJ
cana-5712	139	22	ν	ν	X
cana-5712	139	23	2pη	2pη	ADJ
cana-5712	139	24	ν(u	ν(u	PROPN
cana-5712	139	25	)	)	PUNCT
cana-5712	139	26	1	1	NUM
cana-5712	139	27	0	0	NUM
cana-5712	139	28	mz	mz	PROPN
cana-5712	139	29	p(k1	p(k1	PROPN
cana-5712	139	30	,	,	PUNCT
cana-5712	139	31	…	…	PUNCT
cana-5712	139	32	.	.	PUNCT
cana-5712	140	1	,	,	PUNCT
cana-5712	140	2	kp	kp	PROPN
cana-5712	140	3	,	,	PUNCT
cana-5712	140	4	l1	l1	PROPN
cana-5712	140	5	…	…	PUNCT
cana-5712	140	6	.	.	PUNCT
cana-5712	141	1	lq	lq	INTJ
cana-5712	141	2	:	:	PUNCT
cana-5712	141	3	zuξ)dup	zuξ)dup	PROPN
cana-5712	141	4	σ	σ	NOUN
cana-5712	142	1	=	=	PUNCT
cana-5712	142	2	2ν−1	2ν−1	NUM
cana-5712	142	3	∏	∏	NUM
cana-5712	142	4	γ(lq)q	γ(lq)q	NOUN
cana-5712	142	5	j=1	j=1	PROPN
cana-5712	142	6	∏	∏	PROPN
cana-5712	142	7	γ(kp)p	γ(kp)p	NOUN
cana-5712	142	8	i=1	i=1	PROPN
cana-5712	142	9	×	×	NOUN
cana-5712	142	10	p+3ψq+3	p+3ψq+3	NUM
cana-5712	142	11	[	[	PUNCT
cana-5712	142	12	(	(	PUNCT
cana-5712	142	13	k1	k1	NOUN
cana-5712	142	14	,	,	PUNCT
cana-5712	142	15	1	1	NUM
cana-5712	142	16	)	)	PUNCT
cana-5712	142	17	,	,	PUNCT
cana-5712	142	18	…	…	PUNCT
cana-5712	142	19	…	…	PUNCT
cana-5712	142	20	,	,	PUNCT
cana-5712	142	21	(	(	PUNCT
cana-5712	142	22	kp	kp	INTJ
cana-5712	142	23	,	,	PUNCT
cana-5712	142	24	1	1	NUM
cana-5712	142	25	)	)	PUNCT
cana-5712	142	26	,	,	PUNCT
cana-5712	142	27	(	(	PUNCT
cana-5712	142	28	μ	μ	NOUN
cana-5712	142	29	2	2	NUM
cana-5712	142	30	+	+	CCONJ
cana-5712	142	31	1	1	NUM
cana-5712	142	32	2	2	NUM
cana-5712	142	33	,	,	PUNCT
cana-5712	142	34	ξ	ξ	PROPN
cana-5712	142	35	2	2	NUM
cana-5712	142	36	)	)	PUNCT
cana-5712	142	37	,	,	PUNCT
cana-5712	142	38	(	(	PUNCT
cana-5712	142	39	1	1	NUM
cana-5712	142	40	+	+	NUM
cana-5712	142	41	η	η	PROPN
cana-5712	142	42	2	2	NUM
cana-5712	142	43	,	,	PUNCT
cana-5712	142	44	ξ	ξ	PROPN
cana-5712	142	45	2	2	NUM
cana-5712	142	46	)	)	PUNCT
cana-5712	142	47	,	,	PUNCT
cana-5712	142	48	(	(	PUNCT
cana-5712	142	49	1,1	1,1	NUM
cana-5712	142	50	)	)	PUNCT
cana-5712	142	51	(	(	PUNCT
cana-5712	142	52	l1	l1	PROPN
cana-5712	142	53	,	,	PUNCT
cana-5712	142	54	1	1	NUM
cana-5712	142	55	)	)	PUNCT
cana-5712	142	56	,	,	PUNCT
cana-5712	142	57	…	…	PUNCT
cana-5712	142	58	…	…	PUNCT
cana-5712	142	59	.	.	PUNCT
cana-5712	143	1	,	,	PUNCT
cana-5712	143	2	(	(	PUNCT
cana-5712	143	3	lq	lq	INTJ
cana-5712	143	4	,	,	PUNCT
cana-5712	143	5	1	1	NUM
cana-5712	143	6	)	)	PUNCT
cana-5712	143	7	,	,	PUNCT
cana-5712	143	8	(	(	PUNCT
cana-5712	143	9	ρ	ρ	PROPN
cana-5712	143	10	,	,	PUNCT
cana-5712	143	11	σ	σ	PROPN
cana-5712	143	12	)	)	PUNCT
cana-5712	143	13	,	,	PUNCT
cana-5712	143	14	(	(	PUNCT
cana-5712	143	15	μ	μ	NOUN
cana-5712	143	16	2	2	NUM
cana-5712	143	17	−	−	PROPN
cana-5712	143	18	η	η	PROPN
cana-5712	143	19	2	2	NUM
cana-5712	143	20	−	−	NOUN
cana-5712	143	21	ν	ν	NOUN
cana-5712	143	22	2	2	NUM
cana-5712	143	23	+	+	CCONJ
cana-5712	143	24	1	1	NUM
cana-5712	143	25	,	,	PUNCT
cana-5712	143	26	ξ	ξ	PROPN
cana-5712	143	27	2	2	NUM
cana-5712	143	28	)	)	PUNCT
cana-5712	143	29	(	(	PUNCT
cana-5712	143	30	μ	μ	PROPN
cana-5712	143	31	2	2	NUM
cana-5712	143	32	+	+	SYM
cana-5712	143	33	η	η	PROPN
cana-5712	143	34	2	2	NUM
cana-5712	143	35	−	−	NOUN
cana-5712	143	36	ν	ν	NOUN
cana-5712	143	37	2	2	NUM
cana-5712	143	38	+	+	CCONJ
cana-5712	143	39	3	3	NUM
cana-5712	143	40	2	2	NUM
cana-5712	143	41	,	,	PUNCT
cana-5712	143	42	ξ	ξ	PROPN
cana-5712	143	43	2	2	NUM
cana-5712	143	44	)	)	PUNCT
cana-5712	143	45	;	;	PUNCT
cana-5712	144	1	z	z	X
cana-5712	144	2	]	]	X
cana-5712	144	3	.	.	PUNCT
cana-5712	145	1	(	(	PUNCT
cana-5712	145	2	2.3	2.3	NUM
cana-5712	145	3	)	)	PUNCT
cana-5712	145	4	𝐏𝐫𝐨𝐨𝐟.	𝐏𝐫𝐨𝐨𝐟.	PUNCT
cana-5712	145	5	to	to	PART
cana-5712	145	6	prove	prove	VERB
cana-5712	145	7	theorem	theorem	ADJ
cana-5712	145	8	3	3	NUM
cana-5712	145	9	,	,	PUNCT
cana-5712	145	10	using	use	VERB
cana-5712	145	11	definition	definition	NOUN
cana-5712	145	12	of	of	ADP
cana-5712	145	13	generalized	generalized	ADJ
cana-5712	145	14	m	m	PROPN
cana-5712	145	15	-	-	PUNCT
cana-5712	145	16	series	series	NOUN
cana-5712	145	17	in	in	ADP
cana-5712	145	18	the	the	DET
cana-5712	145	19	left	left	ADJ
cana-5712	145	20	hand	hand	NOUN
cana-5712	145	21	side	side	NOUN
cana-5712	145	22	of	of	ADP
cana-5712	145	23	(	(	PUNCT
cana-5712	145	24	2.3	2.3	NUM
cana-5712	145	25	)	)	PUNCT
cana-5712	145	26	.	.	PUNCT
cana-5712	146	1	after	after	ADP
cana-5712	146	2	simple	simple	ADJ
cana-5712	146	3	simplification	simplification	NOUN
cana-5712	146	4	,	,	PUNCT
cana-5712	146	5	we	we	PRON
cana-5712	146	6	get	get	VERB
cana-5712	146	7	∫	∫	PROPN
cana-5712	146	8	uμ(1	uμ(1	ADP
cana-5712	146	9	−	−	PROPN
cana-5712	146	10	u2)−	u2)−	ADJ
cana-5712	146	11	ν	ν	X
cana-5712	146	12	2pη	2pη	ADJ
cana-5712	146	13	ν(u	ν(u	PROPN
cana-5712	146	14	)	)	PUNCT
cana-5712	146	15	1	1	NUM
cana-5712	146	16	0	0	NUM
cana-5712	146	17	mz	mz	PROPN
cana-5712	146	18	p(k1	p(k1	PROPN
cana-5712	146	19	,	,	PUNCT
cana-5712	146	20	…	…	PUNCT
cana-5712	146	21	.	.	PUNCT
cana-5712	147	1	,	,	PUNCT
cana-5712	147	2	kp	kp	PROPN
cana-5712	147	3	,	,	PUNCT
cana-5712	147	4	l1	l1	PROPN
cana-5712	147	5	…	…	PUNCT
cana-5712	147	6	.	.	PUNCT
cana-5712	148	1	lq	lq	INTJ
cana-5712	148	2	:	:	PUNCT
cana-5712	148	3	zuξ)dup	zuξ)dup	PROPN
cana-5712	148	4	σ	σ	PROPN
cana-5712	148	5	communications	communication	NOUN
cana-5712	148	6	on	on	ADP
cana-5712	148	7	applied	apply	VERB
cana-5712	148	8	nonlinear	nonlinear	ADJ
cana-5712	148	9	analysis	analysis	NOUN
cana-5712	148	10	issn	issn	NOUN
cana-5712	148	11	:	:	PUNCT
cana-5712	148	12	1074	1074	NUM
cana-5712	148	13	-	-	PUNCT
cana-5712	148	14	133x	133x	NUM
cana-5712	148	15	vol	vol	VERB
cana-5712	148	16	32	32	NUM
cana-5712	148	17	no	no	NOUN
cana-5712	148	18	.	.	PUNCT
cana-5712	149	1	10s	10	NOUN
cana-5712	149	2	(	(	PUNCT
cana-5712	149	3	2025	2025	NUM
cana-5712	149	4	)	)	PUNCT
cana-5712	149	5	2717	2717	NUM
cana-5712	149	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5712	150	1	=	=	PUNCT
cana-5712	150	2	∑	∑	PROPN
cana-5712	150	3	(	(	PUNCT
cana-5712	150	4	k1)m	k1)m	PROPN
cana-5712	150	5	…	…	PUNCT
cana-5712	150	6	…	…	PUNCT
cana-5712	150	7	(	(	PUNCT
cana-5712	150	8	kp	kp	INTJ
cana-5712	150	9	)	)	PUNCT
cana-5712	150	10	m	m	PROPN
cana-5712	150	11	(	(	PUNCT
cana-5712	150	12	l1)m	l1)m	NOUN
cana-5712	150	13	…	…	PUNCT
cana-5712	150	14	…	…	PUNCT
cana-5712	150	15	.	.	PUNCT
cana-5712	151	1	(	(	PUNCT
cana-5712	151	2	lq	lq	NOUN
cana-5712	151	3	)	)	PUNCT
cana-5712	151	4	m	m	PROPN
cana-5712	151	5	∞	∞	PROPN
cana-5712	151	6	m=0	m=0	PROPN
cana-5712	151	7	zm	zm	PROPN
cana-5712	151	8	γ(ρ	γ(ρ	PROPN
cana-5712	152	1	+	+	CCONJ
cana-5712	152	2	σm	σm	X
cana-5712	152	3	)	)	PUNCT
cana-5712	152	4	∫	∫	PROPN
cana-5712	153	1	uμ+ξm(1	uμ+ξm(1	PROPN
cana-5712	154	1	−	−	PROPN
cana-5712	154	2	u2)−	u2)−	PROPN
cana-5712	154	3	ν	ν	X
cana-5712	154	4	2pη	2pη	ADJ
cana-5712	154	5	ν(u)du	ν(u)du	PROPN
cana-5712	154	6	1	1	NUM
cana-5712	154	7	0	0	NUM
cana-5712	154	8	=	=	SYM
cana-5712	154	9	∏	∏	PROPN
cana-5712	154	10	γ(lq)q	γ(lq)q	NOUN
cana-5712	154	11	j=1	j=1	PROPN
cana-5712	154	12	∏	∏	PROPN
cana-5712	154	13	γ(kp)p	γ(kp)p	NOUN
cana-5712	154	14	i=1	i=1	PROPN
cana-5712	154	15	∑	∑	PUNCT
cana-5712	154	16	γ(1	γ(1	PROPN
cana-5712	154	17	+	+	NUM
cana-5712	154	18	k1	k1	NOUN
cana-5712	154	19	)	)	PUNCT
cana-5712	154	20	…	…	PUNCT
cana-5712	154	21	.	.	PUNCT
cana-5712	154	22	.	.	PUNCT
cana-5712	155	1	γ(m	γ(m	PROPN
cana-5712	155	2	+	+	CCONJ
cana-5712	155	3	kp	kp	PROPN
cana-5712	155	4	)	)	PUNCT
cana-5712	156	1	γ(1	γ(1	PROPN
cana-5712	156	2	+	+	NUM
cana-5712	156	3	l1	l1	PROPN
cana-5712	156	4	)	)	PUNCT
cana-5712	156	5	…	…	PUNCT
cana-5712	156	6	.	.	PUNCT
cana-5712	156	7	.	.	PUNCT
cana-5712	157	1	γ(m	γ(m	PROPN
cana-5712	157	2	+	+	CCONJ
cana-5712	157	3	lq)γ(ρ	lq)γ(ρ	PROPN
cana-5712	157	4	+	+	CCONJ
cana-5712	157	5	σm	σm	X
cana-5712	157	6	)	)	PUNCT
cana-5712	157	7	2ν−1γ	2ν−1γ	NUM
cana-5712	157	8	(	(	PUNCT
cana-5712	157	9	1	1	NUM
cana-5712	157	10	2	2	NUM
cana-5712	157	11	+	+	NUM
cana-5712	157	12	μ	μ	PROPN
cana-5712	157	13	+	+	X
cana-5712	157	14	ξm	ξm	PROPN
cana-5712	157	15	2	2	NUM
cana-5712	157	16	)	)	PUNCT
cana-5712	157	17	γ	γ	X
cana-5712	157	18	(	(	PUNCT
cana-5712	157	19	1	1	NUM
cana-5712	157	20	+	+	NUM
cana-5712	157	21	μ	μ	PROPN
cana-5712	157	22	+	+	X
cana-5712	157	23	ξm	ξm	PROPN
cana-5712	157	24	2	2	NUM
cana-5712	157	25	)	)	PUNCT
cana-5712	158	1	γ(1	γ(1	NOUN
cana-5712	159	1	+	+	PUNCT
cana-5712	159	2	m)zm	m)zm	ADJ
cana-5712	159	3	γ	γ	X
cana-5712	159	4	(	(	PUNCT
cana-5712	159	5	1	1	NUM
cana-5712	159	6	+	+	NUM
cana-5712	159	7	μ	μ	PROPN
cana-5712	159	8	+	+	X
cana-5712	159	9	ξm	ξm	PROPN
cana-5712	159	10	2	2	NUM
cana-5712	159	11	−	−	PROPN
cana-5712	159	12	η	η	PROPN
cana-5712	159	13	2	2	NUM
cana-5712	159	14	−	−	PROPN
cana-5712	159	15	ν	ν	NOUN
cana-5712	159	16	2	2	NUM
cana-5712	159	17	)	)	PUNCT
cana-5712	159	18	γ	γ	PROPN
cana-5712	159	19	(	(	PUNCT
cana-5712	159	20	μ	μ	PROPN
cana-5712	159	21	+	+	PROPN
cana-5712	159	22	ξm	ξm	PROPN
cana-5712	159	23	2	2	NUM
cana-5712	159	24	+	+	SYM
cana-5712	159	25	η	η	PROPN
cana-5712	159	26	2	2	NUM
cana-5712	159	27	−	−	NOUN
cana-5712	159	28	ν	ν	NOUN
cana-5712	159	29	2	2	NUM
cana-5712	159	30	+	+	CCONJ
cana-5712	159	31	3	3	NUM
cana-5712	159	32	2)m	2)m	NOUN
cana-5712	159	33	!	!	PUNCT
cana-5712	160	1	∞	∞	PROPN
cana-5712	160	2	m=0	m=0	PROPN
cana-5712	160	3	hence	hence	ADV
cana-5712	160	4	proved	prove	VERB
cana-5712	160	5	.	.	PUNCT
cana-5712	161	1	theorem	theorem	VERB
cana-5712	161	2	4	4	NUM
cana-5712	161	3	.	.	PUNCT
cana-5712	162	1	if	if	SCONJ
cana-5712	162	2	re(ξ	re(ξ	VERB
cana-5712	162	3	)	)	PUNCT
cana-5712	162	4	>	>	X
cana-5712	162	5	0	0	NUM
cana-5712	162	6	,	,	PUNCT
cana-5712	162	7	re(ν	re(ν	X
cana-5712	162	8	)	)	PUNCT
cana-5712	162	9	<	<	X
cana-5712	162	10	1	1	NUM
cana-5712	162	11	,	,	PUNCT
cana-5712	162	12	re(μ	re(μ	PUNCT
cana-5712	163	1	+	+	CCONJ
cana-5712	163	2	ν	ν	X
cana-5712	163	3	+	+	CCONJ
cana-5712	163	4	η	η	PROPN
cana-5712	163	5	)	)	PUNCT
cana-5712	163	6	>	>	X
cana-5712	163	7	0	0	NUM
cana-5712	163	8	,	,	PUNCT
cana-5712	163	9	re(μ	re(μ	PUNCT
cana-5712	164	1	+	+	CCONJ
cana-5712	164	2	ν	ν	X
cana-5712	164	3	−	−	PROPN
cana-5712	164	4	η	η	PROPN
cana-5712	164	5	)	)	PUNCT
cana-5712	164	6	>	>	X
cana-5712	164	7	1	1	NUM
cana-5712	164	8	,	,	PUNCT
cana-5712	164	9	re(σ	re(σ	X
cana-5712	164	10	)	)	PUNCT
cana-5712	164	11	>	>	X
cana-5712	164	12	0	0	NUM
cana-5712	164	13	,	,	PUNCT
cana-5712	164	14	following	follow	VERB
cana-5712	164	15	integral	integral	ADJ
cana-5712	164	16	formulas	formula	NOUN
cana-5712	164	17	holds	hold	VERB
cana-5712	164	18	:	:	PUNCT
cana-5712	164	19	∫	∫	PROPN
cana-5712	165	1	u−μ(u2	u−μ(u2	PROPN
cana-5712	165	2	−	−	PROPN
cana-5712	166	1	1)−	1)−	NUM
cana-5712	166	2	ν	ν	PROPN
cana-5712	166	3	2pη	2pη	NOUN
cana-5712	166	4	ν(u	ν(u	PROPN
cana-5712	166	5	)	)	PUNCT
cana-5712	167	1	∞	∞	NUM
cana-5712	167	2	0	0	NUM
cana-5712	168	1	mz	mz	PROPN
cana-5712	168	2	p	p	PROPN
cana-5712	168	3	(	(	PUNCT
cana-5712	168	4	k1	k1	PROPN
cana-5712	168	5	,	,	PUNCT
cana-5712	168	6	…	…	PUNCT
cana-5712	168	7	.	.	PUNCT
cana-5712	168	8	,	,	PUNCT
cana-5712	168	9	kp	kp	PROPN
cana-5712	168	10	,	,	PUNCT
cana-5712	168	11	l1	l1	PROPN
cana-5712	168	12	…	…	PUNCT
cana-5712	168	13	.	.	PUNCT
cana-5712	169	1	lq	lq	INTJ
cana-5712	169	2	:	:	PUNCT
cana-5712	169	3	zu−ξ)dup	zu−ξ)dup	NUM
cana-5712	169	4	σ	σ	X
cana-5712	169	5	=	=	SYM
cana-5712	169	6	∏	∏	PROPN
cana-5712	169	7	γ(lq	γ(lq	NUM
cana-5712	169	8	)	)	PUNCT
cana-5712	169	9	q	q	NOUN
cana-5712	170	1	j=1	j=1	NOUN
cana-5712	170	2	(	(	PUNCT
cana-5712	170	3	π	π	NOUN
cana-5712	170	4	)	)	PUNCT
cana-5712	170	5	1	1	NUM
cana-5712	170	6	2	2	NUM
cana-5712	170	7	∏	∏	NUM
cana-5712	170	8	γ(kp	γ(kp	NUM
cana-5712	170	9	)	)	PUNCT
cana-5712	170	10	p	p	X
cana-5712	170	11	i=1	i=1	PROPN
cana-5712	170	12	p+3ψq+2	p+3ψq+2	NOUN
cana-5712	170	13	[	[	PUNCT
cana-5712	170	14	(	(	PUNCT
cana-5712	170	15	k1	k1	NOUN
cana-5712	170	16	,	,	PUNCT
cana-5712	170	17	1	1	NUM
cana-5712	170	18	)	)	PUNCT
cana-5712	170	19	,	,	PUNCT
cana-5712	170	20	…	…	PUNCT
cana-5712	170	21	…	…	PUNCT
cana-5712	170	22	,	,	PUNCT
cana-5712	170	23	(	(	PUNCT
cana-5712	170	24	kp	kp	INTJ
cana-5712	170	25	,	,	PUNCT
cana-5712	170	26	1	1	NUM
cana-5712	170	27	)	)	PUNCT
cana-5712	170	28	,	,	PUNCT
cana-5712	170	29	(	(	PUNCT
cana-5712	170	30	μ+ν+2	μ+ν+2	PROPN
cana-5712	170	31	2	2	NUM
cana-5712	170	32	,	,	PUNCT
cana-5712	170	33	ξ	ξ	PROPN
cana-5712	170	34	2	2	NUM
cana-5712	170	35	)	)	PUNCT
cana-5712	170	36	,	,	PUNCT
cana-5712	170	37	(	(	PUNCT
cana-5712	170	38	μ+ν−η−1	μ+ν−η−1	PROPN
cana-5712	170	39	2	2	NUM
cana-5712	170	40	,	,	PUNCT
cana-5712	170	41	ξ	ξ	PROPN
cana-5712	170	42	2	2	NUM
cana-5712	170	43	)	)	PUNCT
cana-5712	170	44	,	,	PUNCT
cana-5712	170	45	(	(	PUNCT
cana-5712	170	46	1,1	1,1	NUM
cana-5712	170	47	)	)	PUNCT
cana-5712	170	48	(	(	PUNCT
cana-5712	170	49	l1	l1	PROPN
cana-5712	170	50	,	,	PUNCT
cana-5712	170	51	1	1	NUM
cana-5712	170	52	)	)	PUNCT
cana-5712	170	53	,	,	PUNCT
cana-5712	170	54	…	…	PUNCT
cana-5712	170	55	…	…	PUNCT
cana-5712	170	56	.	.	PUNCT
cana-5712	170	57	,	,	PUNCT
cana-5712	170	58	(	(	PUNCT
cana-5712	170	59	lq	lq	INTJ
cana-5712	170	60	,	,	PUNCT
cana-5712	170	61	1	1	NUM
cana-5712	170	62	)	)	PUNCT
cana-5712	170	63	,	,	PUNCT
cana-5712	170	64	(	(	PUNCT
cana-5712	170	65	ρ	ρ	PROPN
cana-5712	170	66	,	,	PUNCT
cana-5712	170	67	σ	σ	PROPN
cana-5712	170	68	)	)	PUNCT
cana-5712	170	69	,	,	PUNCT
cana-5712	170	70	(	(	PUNCT
cana-5712	170	71	μ	μ	NOUN
cana-5712	170	72	,	,	PUNCT
cana-5712	170	73	ξ	ξ	PROPN
cana-5712	170	74	)	)	PUNCT
cana-5712	170	75	;	;	PUNCT
cana-5712	171	1	z	z	X
cana-5712	171	2	]	]	X
cana-5712	171	3	.	.	PUNCT
cana-5712	172	1	(	(	PUNCT
cana-5712	172	2	2.4	2.4	NUM
cana-5712	172	3	)	)	PUNCT
cana-5712	172	4	proof	proof	NOUN
cana-5712	172	5	.	.	PUNCT
cana-5712	173	1	using	use	VERB
cana-5712	173	2	equation	equation	NOUN
cana-5712	173	3	(	(	PUNCT
cana-5712	173	4	1.2	1.2	NUM
cana-5712	173	5	)	)	PUNCT
cana-5712	173	6	and	and	CCONJ
cana-5712	173	7	changing	change	VERB
cana-5712	173	8	the	the	DET
cana-5712	173	9	order	order	NOUN
cana-5712	173	10	of	of	ADP
cana-5712	173	11	integration	integration	NOUN
cana-5712	173	12	in	in	ADP
cana-5712	173	13	the	the	DET
cana-5712	173	14	left	left	ADJ
cana-5712	173	15	hand	hand	NOUN
cana-5712	173	16	side	side	NOUN
cana-5712	173	17	of	of	ADP
cana-5712	173	18	(	(	PUNCT
cana-5712	173	19	2.4	2.4	NUM
cana-5712	173	20	)	)	PUNCT
cana-5712	173	21	,	,	PUNCT
cana-5712	173	22	we	we	PRON
cana-5712	173	23	have	have	VERB
cana-5712	173	24	=	=	SYM
cana-5712	173	25	∏	∏	X
cana-5712	173	26	γ(lq)q	γ(lq)q	NOUN
cana-5712	173	27	j=1	j=1	PROPN
cana-5712	173	28	∏	∏	PROPN
cana-5712	173	29	γ(kp)p	γ(kp)p	NOUN
cana-5712	173	30	i=1	i=1	PROPN
cana-5712	173	31	∑	∑	PUNCT
cana-5712	173	32	γ(1	γ(1	PROPN
cana-5712	173	33	+	+	NUM
cana-5712	173	34	k1	k1	NOUN
cana-5712	173	35	)	)	PUNCT
cana-5712	173	36	…	…	PUNCT
cana-5712	173	37	.	.	PUNCT
cana-5712	173	38	.	.	PUNCT
cana-5712	174	1	γ(m	γ(m	PROPN
cana-5712	174	2	+	+	CCONJ
cana-5712	174	3	kp	kp	PROPN
cana-5712	174	4	)	)	PUNCT
cana-5712	174	5	zm	zm	PROPN
cana-5712	174	6	γ(1	γ(1	PROPN
cana-5712	174	7	+	+	NUM
cana-5712	174	8	l1	l1	PROPN
cana-5712	174	9	)	)	PUNCT
cana-5712	174	10	…	…	PUNCT
cana-5712	174	11	.	.	PUNCT
cana-5712	174	12	.	.	PUNCT
cana-5712	175	1	γ(m	γ(m	PROPN
cana-5712	175	2	+	+	CCONJ
cana-5712	175	3	lq)γ(ρ	lq)γ(ρ	PROPN
cana-5712	175	4	+	+	CCONJ
cana-5712	175	5	σm	σm	X
cana-5712	175	6	)	)	PUNCT
cana-5712	175	7	∞	∞	NUM
cana-5712	176	1	m=0	m=0	PROPN
cana-5712	176	2	∫	∫	PROPN
cana-5712	176	3	u−(μ+ξm)(u2	u−(μ+ξm)(u2	PROPN
cana-5712	177	1	−	−	PROPN
cana-5712	177	2	1)−	1)−	PROPN
cana-5712	177	3	ν	ν	PROPN
cana-5712	177	4	2pη	2pη	NOUN
cana-5712	177	5	ν(u)du	ν(u)du	PROPN
cana-5712	177	6	∞	∞	NOUN
cana-5712	177	7	0	0	NUM
cana-5712	178	1	=	=	SYM
cana-5712	178	2	∏	∏	PROPN
cana-5712	178	3	γ(lq)q	γ(lq)q	NOUN
cana-5712	178	4	j=1	j=1	PROPN
cana-5712	178	5	(	(	PUNCT
cana-5712	178	6	μ	μ	NOUN
cana-5712	178	7	)	)	PUNCT
cana-5712	178	8	1	1	NUM
cana-5712	178	9	2	2	NUM
cana-5712	178	10	∏	∏	NUM
cana-5712	178	11	γ(kp)p	γ(kp)p	NOUN
cana-5712	178	12	i=1	i=1	PROPN
cana-5712	178	13	∑	∑	PUNCT
cana-5712	178	14	γ(1	γ(1	PROPN
cana-5712	178	15	+	+	NUM
cana-5712	178	16	k1	k1	NOUN
cana-5712	178	17	)	)	PUNCT
cana-5712	178	18	…	…	PUNCT
cana-5712	178	19	.	.	PUNCT
cana-5712	178	20	.	.	PUNCT
cana-5712	179	1	γ(m	γ(m	PROPN
cana-5712	179	2	+	+	CCONJ
cana-5712	179	3	kp	kp	PROPN
cana-5712	179	4	)	)	PUNCT
cana-5712	179	5	zm	zm	PROPN
cana-5712	179	6	γ(1	γ(1	PROPN
cana-5712	179	7	+	+	NUM
cana-5712	179	8	l1	l1	PROPN
cana-5712	179	9	)	)	PUNCT
cana-5712	179	10	…	…	PUNCT
cana-5712	179	11	.	.	PUNCT
cana-5712	179	12	.	.	PUNCT
cana-5712	180	1	γ(m	γ(m	PROPN
cana-5712	180	2	+	+	CCONJ
cana-5712	180	3	lq)γ(ρ	lq)γ(ρ	PROPN
cana-5712	180	4	+	+	CCONJ
cana-5712	180	5	σm	σm	X
cana-5712	180	6	)	)	PUNCT
cana-5712	180	7	∞	∞	NUM
cana-5712	181	1	m=0	m=0	PROPN
cana-5712	181	2	×	×	PROPN
cana-5712	181	3	γ	γ	X
cana-5712	181	4	(	(	PUNCT
cana-5712	181	5	μ+ξm+ν+2	μ+ξm+ν+2	NOUN
cana-5712	181	6	2	2	NUM
cana-5712	181	7	)	)	PUNCT
cana-5712	181	8	γ	γ	PROPN
cana-5712	181	9	(	(	PUNCT
cana-5712	181	10	μ+ξm+ν−η−1	μ+ξm+ν−η−1	NUM
cana-5712	181	11	2	2	NUM
cana-5712	181	12	)	)	PUNCT
cana-5712	181	13	γ(1+m	γ(1+m	PROPN
cana-5712	181	14	)	)	PUNCT
cana-5712	181	15	γ(μ+ξm)m	γ(μ+ξm)m	PUNCT
cana-5712	181	16	!	!	PUNCT
cana-5712	182	1	thus	thus	ADV
cana-5712	182	2	,	,	PUNCT
cana-5712	182	3	from	from	ADP
cana-5712	182	4	equation	equation	NOUN
cana-5712	182	5	(	(	PUNCT
cana-5712	182	6	1.3	1.3	NUM
cana-5712	182	7	)	)	PUNCT
cana-5712	182	8	,	,	PUNCT
cana-5712	182	9	reached	reach	VERB
cana-5712	182	10	at	at	ADP
cana-5712	182	11	required	require	VERB
cana-5712	182	12	result	result	NOUN
cana-5712	182	13	of	of	ADP
cana-5712	182	14	theorem	theorem	ADJ
cana-5712	182	15	4	4	NUM
cana-5712	182	16	.	.	PUNCT
cana-5712	182	17	theorem	theorem	NOUN
cana-5712	182	18	5	5	NUM
cana-5712	182	19	.	.	PUNCT
cana-5712	182	20	if	if	SCONJ
cana-5712	182	21	re(μ	re(μ	NUM
cana-5712	182	22	)	)	PUNCT
cana-5712	182	23	>	>	X
cana-5712	182	24	−1	−1	NOUN
cana-5712	182	25	,	,	PUNCT
cana-5712	182	26	re(λ	re(λ	ADP
cana-5712	182	27	)	)	PUNCT
cana-5712	182	28	>	>	X
cana-5712	182	29	0	0	NUM
cana-5712	182	30	,	,	PUNCT
cana-5712	182	31	re(σ	re(σ	X
cana-5712	182	32	)	)	PUNCT
cana-5712	182	33	>	>	X
cana-5712	182	34	0	0	NUM
cana-5712	182	35	,	,	PUNCT
cana-5712	182	36	n	n	NOUN
cana-5712	182	37	=	=	SYM
cana-5712	182	38	1,2	1,2	NUM
cana-5712	182	39	.	.	NUM
cana-5712	182	40	,	,	PUNCT
cana-5712	182	41	,	,	PUNCT
cana-5712	182	42	following	follow	VERB
cana-5712	182	43	integral	integral	ADJ
cana-5712	182	44	formula	formula	NOUN
cana-5712	182	45	holds	holds	AUX
cana-5712	182	46	:	:	PUNCT
cana-5712	182	47	∫	∫	PROPN
cana-5712	182	48	(	(	PUNCT
cana-5712	182	49	1	1	NUM
cana-5712	182	50	−	−	PROPN
cana-5712	182	51	u	u	NOUN
cana-5712	182	52	)	)	PUNCT
cana-5712	182	53	1	1	NUM
cana-5712	182	54	2(1	2(1	NUM
cana-5712	182	55	+	+	CCONJ
cana-5712	182	56	u)μun(u	u)μun(u	X
cana-5712	182	57	)	)	PUNCT
cana-5712	182	58	1	1	NUM
cana-5712	182	59	0	0	NUM
cana-5712	182	60	mz	mz	PROPN
cana-5712	182	61	p(k1	p(k1	PROPN
cana-5712	182	62	,	,	PUNCT
cana-5712	182	63	…	…	PUNCT
cana-5712	182	64	.	.	PUNCT
cana-5712	183	1	,	,	PUNCT
cana-5712	183	2	kp	kp	PROPN
cana-5712	183	3	,	,	PUNCT
cana-5712	183	4	l1	l1	PROPN
cana-5712	183	5	…	…	PUNCT
cana-5712	183	6	.	.	PUNCT
cana-5712	184	1	lq	lq	PRON
cana-5712	184	2	:	:	PUNCT
cana-5712	184	3	z(1	z(1	PROPN
cana-5712	184	4	+	+	NUM
cana-5712	184	5	x)λ)dup	x)λ)dup	PROPN
cana-5712	185	1	σ	σ	NOUN
cana-5712	185	2	=	=	SYM
cana-5712	185	3	(	(	PUNCT
cana-5712	185	4	π	π	NOUN
cana-5712	185	5	)	)	PUNCT
cana-5712	185	6	1	1	NUM
cana-5712	185	7	22	22	NUM
cana-5712	185	8	2n+	2n+	NUM
cana-5712	185	9	3	3	NUM
cana-5712	185	10	2{(n+1)!}2	2{(n+1)!}2	NUM
cana-5712	185	11	(	(	PUNCT
cana-5712	185	12	2n+2	2n+2	PROPN
cana-5712	185	13	)	)	PUNCT
cana-5712	185	14	∏	∏	PROPN
cana-5712	185	15	γ(lq	γ(lq	NUM
cana-5712	185	16	)	)	PUNCT
cana-5712	185	17	q	q	NOUN
cana-5712	185	18	j=1	j=1	PROPN
cana-5712	185	19	∏	∏	PROPN
cana-5712	185	20	γ(kp	γ(kp	PROPN
cana-5712	185	21	)	)	PUNCT
cana-5712	185	22	p	p	X
cana-5712	185	23	i=1	i=1	PROPN
cana-5712	185	24	p+3ψq+2	p+3ψq+2	NOUN
cana-5712	185	25	[	[	PUNCT
cana-5712	185	26	(	(	PUNCT
cana-5712	185	27	k1	k1	NOUN
cana-5712	185	28	,	,	PUNCT
cana-5712	185	29	1	1	NUM
cana-5712	185	30	)	)	PUNCT
cana-5712	185	31	,	,	PUNCT
cana-5712	185	32	…	…	PUNCT
cana-5712	185	33	…	…	PUNCT
cana-5712	185	34	,	,	PUNCT
cana-5712	185	35	(	(	PUNCT
cana-5712	185	36	kp	kp	INTJ
cana-5712	185	37	,	,	PUNCT
cana-5712	185	38	1	1	NUM
cana-5712	185	39	)	)	PUNCT
cana-5712	185	40	,	,	PUNCT
cana-5712	185	41	(	(	PUNCT
cana-5712	185	42	2μ+1	2μ+1	PROPN
cana-5712	185	43	2	2	NUM
cana-5712	185	44	,	,	PUNCT
cana-5712	185	45	λ	λ	PROPN
cana-5712	185	46	)	)	PUNCT
cana-5712	185	47	,	,	PUNCT
cana-5712	185	48	(	(	PUNCT
cana-5712	185	49	μ	μ	NOUN
cana-5712	185	50	,	,	PUNCT
cana-5712	185	51	λ	λ	PROPN
cana-5712	185	52	)	)	PUNCT
cana-5712	185	53	,	,	PUNCT
cana-5712	185	54	(	(	PUNCT
cana-5712	185	55	1,1	1,1	NUM
cana-5712	185	56	)	)	PUNCT
cana-5712	185	57	(	(	PUNCT
cana-5712	185	58	l1	l1	PROPN
cana-5712	185	59	,	,	PUNCT
cana-5712	185	60	1	1	NUM
cana-5712	185	61	)	)	PUNCT
cana-5712	185	62	,	,	PUNCT
cana-5712	185	63	…	…	PUNCT
cana-5712	185	64	…	…	PUNCT
cana-5712	185	65	.	.	PUNCT
cana-5712	185	66	,	,	PUNCT
cana-5712	185	67	(	(	PUNCT
cana-5712	185	68	lq	lq	INTJ
cana-5712	185	69	,	,	PUNCT
cana-5712	185	70	1	1	NUM
cana-5712	185	71	)	)	PUNCT
cana-5712	185	72	,	,	PUNCT
cana-5712	185	73	(	(	PUNCT
cana-5712	185	74	ρ	ρ	PROPN
cana-5712	185	75	,	,	PUNCT
cana-5712	185	76	σ	σ	PROPN
cana-5712	185	77	)	)	PUNCT
cana-5712	185	78	,	,	PUNCT
cana-5712	185	79	(	(	PUNCT
cana-5712	185	80	μ	μ	NOUN
cana-5712	185	81	+	+	X
cana-5712	185	82	5	5	NUM
cana-5712	185	83	2	2	NUM
cana-5712	185	84	,	,	PUNCT
cana-5712	185	85	λ	λ	NOUN
cana-5712	185	86	)	)	PUNCT
cana-5712	185	87	,	,	PUNCT
cana-5712	185	88	(	(	PUNCT
cana-5712	185	89	μ	μ	NOUN
cana-5712	185	90	`	`	PUNCT
cana-5712	185	91	−	−	PROPN
cana-5712	185	92	n	n	NOUN
cana-5712	185	93	+	+	CCONJ
cana-5712	185	94	1	1	NUM
cana-5712	185	95	2	2	NUM
cana-5712	185	96	,	,	PUNCT
cana-5712	185	97	λ	λ	PROPN
cana-5712	185	98	)	)	PUNCT
cana-5712	185	99	;	;	PUNCT
cana-5712	185	100	z	z	X
cana-5712	185	101	]	]	PUNCT
cana-5712	185	102	.	.	PUNCT
cana-5712	186	1	(	(	PUNCT
cana-5712	186	2	2.5	2.5	NUM
cana-5712	186	3	)	)	PUNCT
cana-5712	186	4	proof	proof	NOUN
cana-5712	186	5	.	.	PUNCT
cana-5712	187	1	to	to	PART
cana-5712	187	2	prove	prove	VERB
cana-5712	187	3	above	above	ADP
cana-5712	187	4	theorem	theorem	NOUN
cana-5712	187	5	,	,	PUNCT
cana-5712	187	6	using	use	VERB
cana-5712	187	7	definition	definition	NOUN
cana-5712	187	8	(	(	PUNCT
cana-5712	187	9	1.1	1.1	NUM
cana-5712	187	10	)	)	PUNCT
cana-5712	187	11	and	and	CCONJ
cana-5712	187	12	relation	relation	NOUN
cana-5712	187	13	(	(	PUNCT
cana-5712	187	14	1.3	1.3	NUM
cana-5712	187	15	)	)	PUNCT
cana-5712	187	16	in	in	ADP
cana-5712	187	17	the	the	DET
cana-5712	187	18	left	left	ADJ
cana-5712	187	19	hand	hand	NOUN
cana-5712	187	20	side	side	NOUN
cana-5712	187	21	of	of	ADP
cana-5712	187	22	theorem	theorem	NOUN
cana-5712	187	23	5	5	NUM
cana-5712	187	24	,	,	PUNCT
cana-5712	187	25	and	and	CCONJ
cana-5712	187	26	then	then	ADV
cana-5712	187	27	simply	simply	ADV
cana-5712	187	28	,	,	PUNCT
cana-5712	187	29	we	we	PRON
cana-5712	187	30	get	get	VERB
cana-5712	187	31	required	require	VERB
cana-5712	187	32	result	result	NOUN
cana-5712	187	33	.	.	PUNCT
cana-5712	188	1	communications	communication	NOUN
cana-5712	188	2	on	on	ADP
cana-5712	188	3	applied	apply	VERB
cana-5712	188	4	nonlinear	nonlinear	ADJ
cana-5712	188	5	analysis	analysis	NOUN
cana-5712	188	6	issn	issn	NOUN
cana-5712	188	7	:	:	PUNCT
cana-5712	188	8	1074	1074	NUM
cana-5712	188	9	-	-	PUNCT
cana-5712	188	10	133x	133x	NUM
cana-5712	188	11	vol	vol	VERB
cana-5712	188	12	32	32	NUM
cana-5712	188	13	no	no	NOUN
cana-5712	188	14	.	.	PUNCT
cana-5712	189	1	10s	10	NOUN
cana-5712	189	2	(	(	PUNCT
cana-5712	189	3	2025	2025	NUM
cana-5712	189	4	)	)	PUNCT
cana-5712	189	5	2718	2718	NUM
cana-5712	189	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5712	189	7	=	=	SYM
cana-5712	189	8	∏	∏	PROPN
cana-5712	189	9	γ(lq	γ(lq	NUM
cana-5712	189	10	)	)	PUNCT
cana-5712	189	11	q	q	NOUN
cana-5712	190	1	j=1	j=1	PROPN
cana-5712	190	2	∏	∏	PROPN
cana-5712	190	3	γ(kp	γ(kp	PROPN
cana-5712	190	4	)	)	PUNCT
cana-5712	190	5	p	p	X
cana-5712	190	6	i=1	i=1	PROPN
cana-5712	190	7	∑	∑	PUNCT
cana-5712	190	8	γ(1+k1)	γ(1+k1)	NOUN
cana-5712	190	9	…	…	PUNCT
cana-5712	190	10	..	..	PUNCT
cana-5712	190	11	γ(m+kp	γ(m+kp	NUM
cana-5712	190	12	)	)	PUNCT
cana-5712	190	13	(	(	PUNCT
cana-5712	190	14	z	z	NOUN
cana-5712	190	15	2λ	2λ	NUM
cana-5712	190	16	)	)	PUNCT
cana-5712	190	17	m	m	PROPN
cana-5712	190	18	γ(1+l1)	γ(1+l1)	PROPN
cana-5712	190	19	…	…	SYM
cana-5712	190	20	..	..	PUNCT
cana-5712	190	21	γ(m+lq)γ(ρ+σm	γ(m+lq)γ(ρ+σm	PROPN
cana-5712	190	22	)	)	PUNCT
cana-5712	191	1	∞	∞	PROPN
cana-5712	191	2	m=0	m=0	PROPN
cana-5712	191	3	∫	∫	PROPN
cana-5712	191	4	(	(	PUNCT
cana-5712	191	5	1	1	NUM
cana-5712	191	6	−	−	PROPN
cana-5712	191	7	u	u	NOUN
cana-5712	191	8	)	)	PUNCT
cana-5712	191	9	1	1	NUM
cana-5712	191	10	2(1	2(1	NUM
cana-5712	191	11	+	+	NUM
cana-5712	191	12	u)μ+λnun(u	u)μ+λnun(u	NOUN
cana-5712	191	13	)	)	PUNCT
cana-5712	191	14	1	1	NUM
cana-5712	191	15	0	0	NUM
cana-5712	191	16	du	du	X
cana-5712	191	17	=	=	SYM
cana-5712	191	18	∏	∏	PROPN
cana-5712	191	19	γ(lq	γ(lq	NUM
cana-5712	191	20	)	)	PUNCT
cana-5712	192	1	q	q	NOUN
cana-5712	192	2	j=1	j=1	PROPN
cana-5712	192	3	∏	∏	PROPN
cana-5712	192	4	γ(kp	γ(kp	PROPN
cana-5712	192	5	)	)	PUNCT
cana-5712	192	6	p	p	X
cana-5712	192	7	i=1	i=1	PROPN
cana-5712	192	8	∑	∑	PUNCT
cana-5712	192	9	γ(1+k1)	γ(1+k1)	NOUN
cana-5712	192	10	…	…	PUNCT
cana-5712	192	11	..	..	PUNCT
cana-5712	192	12	γ(m+kp	γ(m+kp	NUM
cana-5712	192	13	)	)	PUNCT
cana-5712	192	14	(	(	PUNCT
cana-5712	192	15	z	z	NOUN
cana-5712	192	16	2λ	2λ	NUM
cana-5712	192	17	)	)	PUNCT
cana-5712	192	18	m	m	PROPN
cana-5712	192	19	γ(1+l1)	γ(1+l1)	PROPN
cana-5712	192	20	…	…	SYM
cana-5712	192	21	..	..	PUNCT
cana-5712	192	22	γ(m+lq)γ(ρ+σm	γ(m+lq)γ(ρ+σm	PROPN
cana-5712	192	23	)	)	PUNCT
cana-5712	193	1	∞	∞	PROPN
cana-5712	193	2	m=0	m=0	PROPN
cana-5712	193	3	(	(	PUNCT
cana-5712	193	4	π	π	NOUN
cana-5712	193	5	)	)	PUNCT
cana-5712	193	6	1	1	NUM
cana-5712	193	7	22	22	NUM
cana-5712	193	8	μ+λn+2n+	μ+λn+2n+	NUM
cana-5712	193	9	3	3	NUM
cana-5712	193	10	2{(n+1)!}2	2{(n+1)!}2	NUM
cana-5712	193	11	(	(	PUNCT
cana-5712	193	12	2n+2)γ(μ+λm+	2n+2)γ(μ+λm+	NUM
cana-5712	193	13	5	5	NUM
cana-5712	193	14	2	2	NUM
cana-5712	193	15	)	)	PUNCT
cana-5712	193	16	γ(μ+λm−	γ(μ+λm−	PROPN
cana-5712	193	17	n	n	CCONJ
cana-5712	193	18	2	2	NUM
cana-5712	193	19	+	+	CCONJ
cana-5712	193	20	1	1	NUM
cana-5712	193	21	2	2	NUM
cana-5712	193	22	)	)	PUNCT
cana-5712	193	23	=	=	SYM
cana-5712	193	24	(	(	PUNCT
cana-5712	193	25	π	π	NOUN
cana-5712	193	26	)	)	PUNCT
cana-5712	193	27	1	1	NUM
cana-5712	193	28	222n+	222n+	NUM
cana-5712	193	29	3	3	NUM
cana-5712	193	30	2{(n	2{(n	NUM
cana-5712	193	31	+	+	NUM
cana-5712	193	32	1)!}2	1)!}2	NUM
cana-5712	193	33	(	(	PUNCT
cana-5712	193	34	2n	2n	NUM
cana-5712	193	35	+	+	CCONJ
cana-5712	193	36	2	2	X
cana-5712	193	37	)	)	PUNCT
cana-5712	193	38	∏	∏	PROPN
cana-5712	193	39	γ(lq)q	γ(lq)q	VERB
cana-5712	193	40	j=1	j=1	PROPN
cana-5712	193	41	∏	∏	PROPN
cana-5712	193	42	γ(kp)p	γ(kp)p	NOUN
cana-5712	193	43	i=1	i=1	PROPN
cana-5712	193	44	∑	∑	PUNCT
cana-5712	193	45	γ(1	γ(1	PROPN
cana-5712	193	46	+	+	NUM
cana-5712	193	47	k1	k1	NOUN
cana-5712	193	48	)	)	PUNCT
cana-5712	193	49	…	…	PUNCT
cana-5712	193	50	.	.	PUNCT
cana-5712	193	51	.	.	PUNCT
cana-5712	194	1	γ(m	γ(m	PROPN
cana-5712	194	2	+	+	CCONJ
cana-5712	194	3	kp	kp	PROPN
cana-5712	194	4	)	)	PUNCT
cana-5712	194	5	(	(	PUNCT
cana-5712	194	6	z	z	NOUN
cana-5712	194	7	γ	γ	X
cana-5712	194	8	)	)	PUNCT
cana-5712	194	9	m	m	VERB
cana-5712	195	1	γ(1	γ(1	ADJ
cana-5712	195	2	+	+	NUM
cana-5712	195	3	l1	l1	PROPN
cana-5712	195	4	)	)	PUNCT
cana-5712	195	5	…	…	PUNCT
cana-5712	195	6	.	.	PUNCT
cana-5712	195	7	.	.	PUNCT
cana-5712	196	1	γ(m	γ(m	PROPN
cana-5712	196	2	+	+	CCONJ
cana-5712	196	3	lq)γ(ρ	lq)γ(ρ	PROPN
cana-5712	196	4	+	+	CCONJ
cana-5712	196	5	σm	σm	X
cana-5712	196	6	)	)	PUNCT
cana-5712	196	7	∞	∞	NUM
cana-5712	197	1	m=0	m=0	PROPN
cana-5712	197	2	×	×	PROPN
cana-5712	197	3	γ	γ	X
cana-5712	197	4	(	(	PUNCT
cana-5712	197	5	μ	μ	PROPN
cana-5712	197	6	+	+	PROPN
cana-5712	197	7	1	1	NUM
cana-5712	197	8	2	2	NUM
cana-5712	197	9	+	+	CCONJ
cana-5712	197	10	λm	λm	NOUN
cana-5712	197	11	)	)	PUNCT
cana-5712	197	12	γ(μ	γ(μ	PROPN
cana-5712	198	1	+	+	CCONJ
cana-5712	198	2	λm)zm	λm)zm	X
cana-5712	198	3	γ	γ	X
cana-5712	198	4	(	(	PUNCT
cana-5712	198	5	μ	μ	PROPN
cana-5712	198	6	+	+	PROPN
cana-5712	198	7	5	5	NUM
cana-5712	198	8	2	2	NUM
cana-5712	198	9	+	+	CCONJ
cana-5712	198	10	λm	λm	NOUN
cana-5712	198	11	)	)	PUNCT
cana-5712	198	12	γ(μ	γ(μ	NOUN
cana-5712	198	13	`	`	PUNCT
cana-5712	198	14	−	−	PROPN
cana-5712	198	15	n	n	NOUN
cana-5712	198	16	+	+	CCONJ
cana-5712	198	17	1	1	NUM
cana-5712	198	18	2	2	NUM
cana-5712	198	19	+	+	CCONJ
cana-5712	198	20	λm	λm	NOUN
cana-5712	198	21	)	)	PUNCT
cana-5712	198	22	theorem	theorem	VERB
cana-5712	198	23	6	6	NUM
cana-5712	198	24	.	.	PUNCT
cana-5712	198	25	letre(μ	letre(μ	NUM
cana-5712	198	26	)	)	PUNCT
cana-5712	198	27	>	>	X
cana-5712	198	28	0	0	NUM
cana-5712	198	29	,	,	PUNCT
cana-5712	198	30	re(σ	re(σ	X
cana-5712	198	31	)	)	PUNCT
cana-5712	198	32	>	>	X
cana-5712	198	33	0	0	NUM
cana-5712	198	34	,	,	PUNCT
cana-5712	198	35	re(α	re(α	X
cana-5712	198	36	−	−	PROPN
cana-5712	198	37	μ	μ	PROPN
cana-5712	198	38	+	+	CCONJ
cana-5712	198	39	n	n	CCONJ
cana-5712	198	40	)	)	PUNCT
cana-5712	198	41	>	>	X
cana-5712	199	1	−1	−1	NOUN
cana-5712	199	2	,	,	PUNCT
cana-5712	199	3	re(α	re(α	PUNCT
cana-5712	199	4	−	−	PROPN
cana-5712	199	5	μ	μ	NUM
cana-5712	199	6	)	)	PUNCT
cana-5712	199	7	>	>	X
cana-5712	199	8	−1	−1	NOUN
cana-5712	199	9	.	.	PUNCT
cana-5712	200	1	the	the	DET
cana-5712	200	2	identity	identity	NOUN
cana-5712	200	3	holds	hold	VERB
cana-5712	200	4	:	:	PUNCT
cana-5712	201	1	∫	∫	PROPN
cana-5712	201	2	uμ−1e−uln	uμ−1e−uln	ADJ
cana-5712	201	3	α	α	PROPN
cana-5712	201	4	(	(	PUNCT
cana-5712	201	5	u	u	NOUN
cana-5712	201	6	)	)	PUNCT
cana-5712	201	7	mz	mz	PROPN
cana-5712	201	8	p(k1	p(k1	PROPN
cana-5712	201	9	,	,	PUNCT
cana-5712	201	10	…	…	PUNCT
cana-5712	201	11	.	.	PUNCT
cana-5712	201	12	,	,	PUNCT
cana-5712	201	13	kp	kp	PROPN
cana-5712	201	14	,	,	PUNCT
cana-5712	201	15	l1	l1	PROPN
cana-5712	201	16	…	…	PUNCT
cana-5712	201	17	.	.	PUNCT
cana-5712	202	1	lq	lq	INTJ
cana-5712	202	2	:	:	PUNCT
cana-5712	202	3	z(2u)ξ)dup	z(2u)ξ)dup	ADP
cana-5712	202	4	σ∞	σ∞	NOUN
cana-5712	202	5	0	0	X
cana-5712	202	6	=	=	SYM
cana-5712	202	7	∏	∏	NUM
cana-5712	202	8	γ(lq	γ(lq	NUM
cana-5712	202	9	)	)	PUNCT
cana-5712	202	10	q	q	NOUN
cana-5712	203	1	j=1	j=1	PROPN
cana-5712	203	2	∏	∏	PROPN
cana-5712	203	3	γ(kp	γ(kp	PROPN
cana-5712	203	4	)	)	PUNCT
cana-5712	203	5	p	p	X
cana-5712	203	6	i=1	i=1	PROPN
cana-5712	203	7	p+3ψq+2	p+3ψq+2	NOUN
cana-5712	203	8	[	[	PUNCT
cana-5712	203	9	(	(	PUNCT
cana-5712	203	10	k1	k1	NOUN
cana-5712	203	11	,	,	PUNCT
cana-5712	203	12	1	1	NUM
cana-5712	203	13	)	)	PUNCT
cana-5712	203	14	,	,	PUNCT
cana-5712	203	15	…	…	PUNCT
cana-5712	203	16	…	…	PUNCT
cana-5712	203	17	,	,	PUNCT
cana-5712	203	18	(	(	PUNCT
cana-5712	203	19	kp	kp	INTJ
cana-5712	203	20	,	,	PUNCT
cana-5712	203	21	1	1	NUM
cana-5712	203	22	)	)	PUNCT
cana-5712	203	23	,	,	PUNCT
cana-5712	203	24	(	(	PUNCT
cana-5712	203	25	α	α	NOUN
cana-5712	203	26	−	−	PROPN
cana-5712	203	27	μ	μ	PROPN
cana-5712	203	28	+	+	PROPN
cana-5712	203	29	n	n	PROPN
cana-5712	203	30	+	+	NUM
cana-5712	203	31	1	1	NUM
cana-5712	203	32	,	,	PUNCT
cana-5712	203	33	−ξ	−ξ	NOUN
cana-5712	203	34	)	)	PUNCT
cana-5712	203	35	,	,	PUNCT
cana-5712	203	36	(	(	PUNCT
cana-5712	203	37	μ	μ	NOUN
cana-5712	203	38	,	,	PUNCT
cana-5712	203	39	ξ	ξ	NOUN
cana-5712	203	40	)	)	PUNCT
cana-5712	203	41	,	,	PUNCT
cana-5712	203	42	(	(	PUNCT
cana-5712	203	43	1,1	1,1	NUM
cana-5712	203	44	)	)	PUNCT
cana-5712	203	45	(	(	PUNCT
cana-5712	203	46	l1	l1	PROPN
cana-5712	203	47	,	,	PUNCT
cana-5712	203	48	1	1	NUM
cana-5712	203	49	)	)	PUNCT
cana-5712	203	50	,	,	PUNCT
cana-5712	203	51	…	…	PUNCT
cana-5712	203	52	…	…	PUNCT
cana-5712	203	53	.	.	PUNCT
cana-5712	203	54	,	,	PUNCT
cana-5712	203	55	(	(	PUNCT
cana-5712	203	56	lq	lq	INTJ
cana-5712	203	57	,	,	PUNCT
cana-5712	203	58	1	1	NUM
cana-5712	203	59	)	)	PUNCT
cana-5712	203	60	,	,	PUNCT
cana-5712	203	61	(	(	PUNCT
cana-5712	203	62	ρ	ρ	PROPN
cana-5712	203	63	,	,	PUNCT
cana-5712	203	64	σ	σ	PROPN
cana-5712	203	65	)	)	PUNCT
cana-5712	203	66	,	,	PUNCT
cana-5712	203	67	(	(	PUNCT
cana-5712	203	68	α	α	NOUN
cana-5712	203	69	−	−	PROPN
cana-5712	203	70	μ	μ	PROPN
cana-5712	203	71	+	+	PROPN
cana-5712	203	72	1	1	NUM
cana-5712	203	73	,	,	PUNCT
cana-5712	203	74	−ξ	−ξ	NOUN
cana-5712	203	75	)	)	PUNCT
cana-5712	203	76	;	;	PUNCT
cana-5712	204	1	z2ξ	z2ξ	PROPN
cana-5712	204	2	]	]	X
cana-5712	204	3	.	.	PUNCT
cana-5712	205	1	(	(	PUNCT
cana-5712	205	2	2.6	2.6	NUM
cana-5712	205	3	)	)	PUNCT
cana-5712	205	4	proof	proof	NOUN
cana-5712	205	5	.	.	PUNCT
cana-5712	206	1	using	use	VERB
cana-5712	206	2	(	(	PUNCT
cana-5712	206	3	1.1	1.1	NUM
cana-5712	206	4	)	)	PUNCT
cana-5712	206	5	in	in	ADP
cana-5712	206	6	the	the	DET
cana-5712	206	7	left	left	ADJ
cana-5712	206	8	hand	hand	NOUN
cana-5712	206	9	side	side	NOUN
cana-5712	206	10	of	of	ADP
cana-5712	206	11	(	(	PUNCT
cana-5712	206	12	2.6	2.6	NUM
cana-5712	206	13	)	)	PUNCT
cana-5712	206	14	and	and	CCONJ
cana-5712	206	15	simple	simple	ADJ
cana-5712	206	16	simplification	simplification	NOUN
cana-5712	206	17	,	,	PUNCT
cana-5712	206	18	we	we	PRON
cana-5712	206	19	get	get	AUX
cana-5712	206	20	following	follow	VERB
cana-5712	206	21	steps	step	NOUN
cana-5712	206	22	∫	∫	PROPN
cana-5712	206	23	uμ−1e−uln	uμ−1e−uln	ADJ
cana-5712	206	24	α	α	PROPN
cana-5712	206	25	(	(	PUNCT
cana-5712	206	26	u	u	NOUN
cana-5712	206	27	)	)	PUNCT
cana-5712	206	28	mz	mz	PROPN
cana-5712	206	29	p	p	PROPN
cana-5712	206	30	(	(	PUNCT
cana-5712	206	31	k1	k1	PROPN
cana-5712	206	32	,	,	PUNCT
cana-5712	206	33	…	…	PUNCT
cana-5712	206	34	.	.	PUNCT
cana-5712	207	1	,	,	PUNCT
cana-5712	207	2	kp	kp	PROPN
cana-5712	207	3	,	,	PUNCT
cana-5712	207	4	l1	l1	PROPN
cana-5712	207	5	…	…	PUNCT
cana-5712	207	6	.	.	PUNCT
cana-5712	208	1	lq	lq	INTJ
cana-5712	208	2	:	:	PUNCT
cana-5712	208	3	z(2u)ξ)dup	z(2u)ξ)dup	PROPN
cana-5712	208	4	σ	σ	NUM
cana-5712	208	5	∞	∞	NOUN
cana-5712	208	6	0	0	NUM
cana-5712	209	1	=	=	PUNCT
cana-5712	209	2	∑	∑	PUNCT
cana-5712	209	3	(	(	PUNCT
cana-5712	209	4	k1)1	k1)1	PROPN
cana-5712	209	5	…	…	PUNCT
cana-5712	209	6	.	.	PUNCT
cana-5712	209	7	.	.	PUNCT
cana-5712	210	1	(	(	PUNCT
cana-5712	210	2	kp)m	kp)m	PROPN
cana-5712	210	3	zm2ξm	zm2ξm	PROPN
cana-5712	210	4	(	(	PUNCT
cana-5712	210	5	l1)1	l1)1	PROPN
cana-5712	210	6	…	…	PUNCT
cana-5712	210	7	.	.	PUNCT
cana-5712	210	8	.	.	PUNCT
cana-5712	211	1	(	(	PUNCT
cana-5712	211	2	lq)mγ(ρ	lq)mγ(ρ	NOUN
cana-5712	211	3	+	+	CCONJ
cana-5712	211	4	σm	σm	NOUN
cana-5712	211	5	)	)	PUNCT
cana-5712	211	6	∞	∞	NUM
cana-5712	212	1	m=0	m=0	PROPN
cana-5712	212	2	∫	∫	PROPN
cana-5712	212	3	uμ+ξme−uln	uμ+ξme−uln	PROPN
cana-5712	212	4	α	α	PROPN
cana-5712	212	5	(	(	PUNCT
cana-5712	212	6	u)du	u)du	PROPN
cana-5712	212	7	∞	∞	PROPN
cana-5712	212	8	0	0	NUM
cana-5712	212	9	=	=	SYM
cana-5712	212	10	∏	∏	PROPN
cana-5712	212	11	γ(lq	γ(lq	NUM
cana-5712	212	12	)	)	PUNCT
cana-5712	212	13	q	q	NOUN
cana-5712	213	1	j=1	j=1	PROPN
cana-5712	213	2	∏	∏	PROPN
cana-5712	213	3	γ(kp	γ(kp	PROPN
cana-5712	213	4	)	)	PUNCT
cana-5712	213	5	p	p	X
cana-5712	213	6	i=1	i=1	PROPN
cana-5712	213	7	∑	∑	PUNCT
cana-5712	213	8	γ(1+k1)	γ(1+k1)	NOUN
cana-5712	213	9	…	…	PUNCT
cana-5712	213	10	..	..	PUNCT
cana-5712	213	11	γ(m+kp	γ(m+kp	NUM
cana-5712	213	12	)	)	PUNCT
cana-5712	213	13	(	(	PUNCT
cana-5712	213	14	z2ξ)m	z2ξ)m	NUM
cana-5712	213	15	γ(1+l1)	γ(1+l1)	NUM
cana-5712	213	16	…	…	SYM
cana-5712	213	17	..	..	PUNCT
cana-5712	213	18	γ(m+lq)γ(ρ+σm	γ(m+lq)γ(ρ+σm	PROPN
cana-5712	213	19	)	)	PUNCT
cana-5712	213	20	∞	∞	PROPN
cana-5712	213	21	m=0	m=0	PROPN
cana-5712	213	22	γ(α−(μ+ξm)+n+1)γ(μ+ξm)γ(1+m	γ(α−(μ+ξm)+n+1)γ(μ+ξm)γ(1+m	PROPN
cana-5712	213	23	)	)	PUNCT
cana-5712	213	24	γ((α−μ−ξm+1))n	γ((α−μ−ξm+1))n	NOUN
cana-5712	213	25	!	!	PUNCT
cana-5712	213	26	hence	hence	ADV
cana-5712	213	27	proved	prove	VERB
cana-5712	213	28	.	.	PUNCT
cana-5712	214	1	theorem	theorem	VERB
cana-5712	214	2	7	7	NUM
cana-5712	214	3	.	.	PUNCT
cana-5712	215	1	if	if	SCONJ
cana-5712	215	2	re(σ	re(σ	NOUN
cana-5712	215	3	)	)	PUNCT
cana-5712	215	4	>	>	X
cana-5712	216	1	0	0	NUM
cana-5712	216	2	,	,	PUNCT
cana-5712	216	3	0	0	NUM
cana-5712	216	4	<	<	X
cana-5712	216	5	re(λ	re(λ	NOUN
cana-5712	216	6	)	)	PUNCT
cana-5712	216	7	<	<	X
cana-5712	216	8	re(μ	re(μ	NOUN
cana-5712	216	9	)	)	PUNCT
cana-5712	216	10	,	,	PUNCT
cana-5712	216	11	following	follow	VERB
cana-5712	216	12	compostion	compostion	NOUN
cana-5712	216	13	formula	formula	NOUN
cana-5712	216	14	holds	hold	VERB
cana-5712	216	15	∫	∫	PROPN
cana-5712	216	16	uλ−1(1	uλ−1(1	PROPN
cana-5712	216	17	+	+	CCONJ
cana-5712	216	18	u)−μ	u)−μ	PRON
cana-5712	216	19	mz	mz	PROPN
cana-5712	216	20	p(k1	p(k1	NOUN
cana-5712	216	21	,	,	PUNCT
cana-5712	216	22	…	…	PUNCT
cana-5712	216	23	.	.	PUNCT
cana-5712	217	1	,	,	PUNCT
cana-5712	217	2	kp	kp	PROPN
cana-5712	217	3	,	,	PUNCT
cana-5712	217	4	l1	l1	PROPN
cana-5712	217	5	…	…	PUNCT
cana-5712	217	6	.	.	PUNCT
cana-5712	218	1	lq	lq	PRON
cana-5712	218	2	:	:	PUNCT
cana-5712	218	3	z(1	z(1	PROPN
cana-5712	218	4	+	+	NUM
cana-5712	218	5	u)−ν)dup	u)−ν)dup	ADJ
cana-5712	218	6	σ∞	σ∞	PROPN
cana-5712	218	7	0	0	NUM
cana-5712	218	8	=	=	SYM
cana-5712	218	9	∏	∏	PROPN
cana-5712	218	10	γ(lq	γ(lq	NUM
cana-5712	218	11	)	)	PUNCT
cana-5712	218	12	q	q	NOUN
cana-5712	218	13	j=1	j=1	PROPN
cana-5712	218	14	∏	∏	PROPN
cana-5712	218	15	γ(kp	γ(kp	PROPN
cana-5712	218	16	)	)	PUNCT
cana-5712	219	1	p	p	X
cana-5712	220	1	i=1	i=1	PROPN
cana-5712	220	2	p+2ψq+2	p+2ψq+2	VERB
cana-5712	220	3	[	[	PUNCT
cana-5712	220	4	(	(	PUNCT
cana-5712	220	5	k1	k1	NOUN
cana-5712	220	6	,	,	PUNCT
cana-5712	220	7	1	1	NUM
cana-5712	220	8	)	)	PUNCT
cana-5712	220	9	,	,	PUNCT
cana-5712	220	10	…	…	PUNCT
cana-5712	220	11	…	…	PUNCT
cana-5712	220	12	,	,	PUNCT
cana-5712	220	13	(	(	PUNCT
cana-5712	220	14	kp	kp	INTJ
cana-5712	220	15	,	,	PUNCT
cana-5712	220	16	1	1	NUM
cana-5712	220	17	)	)	PUNCT
cana-5712	220	18	,	,	PUNCT
cana-5712	220	19	(	(	PUNCT
cana-5712	220	20	μ	μ	PROPN
cana-5712	220	21	−	−	PROPN
cana-5712	220	22	λ	λ	PROPN
cana-5712	220	23	,	,	PUNCT
cana-5712	220	24	ν	ν	NOUN
cana-5712	220	25	)	)	PUNCT
cana-5712	220	26	,	,	PUNCT
cana-5712	220	27	(	(	PUNCT
cana-5712	220	28	1,1	1,1	NUM
cana-5712	220	29	)	)	PUNCT
cana-5712	220	30	(	(	PUNCT
cana-5712	220	31	l1	l1	PROPN
cana-5712	220	32	,	,	PUNCT
cana-5712	220	33	1	1	NUM
cana-5712	220	34	)	)	PUNCT
cana-5712	220	35	,	,	PUNCT
cana-5712	220	36	…	…	PUNCT
cana-5712	220	37	…	…	PUNCT
cana-5712	220	38	.	.	PUNCT
cana-5712	220	39	,	,	PUNCT
cana-5712	220	40	(	(	PUNCT
cana-5712	220	41	lq	lq	INTJ
cana-5712	220	42	,	,	PUNCT
cana-5712	220	43	1	1	NUM
cana-5712	220	44	)	)	PUNCT
cana-5712	220	45	,	,	PUNCT
cana-5712	220	46	(	(	PUNCT
cana-5712	220	47	ρ	ρ	PROPN
cana-5712	220	48	,	,	PUNCT
cana-5712	220	49	σ	σ	PROPN
cana-5712	220	50	)	)	PUNCT
cana-5712	220	51	,	,	PUNCT
cana-5712	220	52	(	(	PUNCT
cana-5712	220	53	μ	μ	NOUN
cana-5712	220	54	,	,	PUNCT
cana-5712	220	55	ν	ν	NOUN
cana-5712	220	56	)	)	PUNCT
cana-5712	220	57	;	;	PUNCT
cana-5712	221	1	z	z	X
cana-5712	221	2	]	]	X
cana-5712	221	3	.	.	PUNCT
cana-5712	222	1	(	(	PUNCT
cana-5712	222	2	2.7	2.7	NUM
cana-5712	222	3	)	)	PUNCT
cana-5712	222	4	communications	communication	NOUN
cana-5712	222	5	on	on	ADP
cana-5712	222	6	applied	apply	VERB
cana-5712	222	7	nonlinear	nonlinear	ADJ
cana-5712	222	8	analysis	analysis	NOUN
cana-5712	222	9	issn	issn	NOUN
cana-5712	222	10	:	:	PUNCT
cana-5712	222	11	1074	1074	NUM
cana-5712	222	12	-	-	PUNCT
cana-5712	222	13	133x	133x	NUM
cana-5712	222	14	vol	vol	VERB
cana-5712	222	15	32	32	NUM
cana-5712	222	16	no	no	NOUN
cana-5712	222	17	.	.	PUNCT
cana-5712	223	1	10s	10	NOUN
cana-5712	223	2	(	(	PUNCT
cana-5712	223	3	2025	2025	NUM
cana-5712	223	4	)	)	PUNCT
cana-5712	223	5	2719	2719	NUM
cana-5712	223	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5712	223	7	proof	proof	NOUN
cana-5712	223	8	.	.	PUNCT
cana-5712	224	1	for	for	ADP
cana-5712	224	2	evaluating	evaluate	VERB
cana-5712	224	3	(	(	PUNCT
cana-5712	224	4	2.7	2.7	NUM
cana-5712	224	5	)	)	PUNCT
cana-5712	224	6	,	,	PUNCT
cana-5712	224	7	applying	apply	VERB
cana-5712	224	8	definition	definition	NOUN
cana-5712	224	9	of	of	ADP
cana-5712	224	10	generalized	generalized	ADJ
cana-5712	224	11	m	m	PROPN
cana-5712	224	12	-	-	PUNCT
cana-5712	224	13	series	series	NOUN
cana-5712	224	14	in	in	ADP
cana-5712	224	15	the	the	DET
cana-5712	224	16	left	left	ADJ
cana-5712	224	17	hand	hand	NOUN
cana-5712	224	18	side	side	NOUN
cana-5712	224	19	of	of	ADP
cana-5712	224	20	(	(	PUNCT
cana-5712	224	21	2.7	2.7	NUM
cana-5712	224	22	)	)	PUNCT
cana-5712	224	23	,	,	PUNCT
cana-5712	224	24	we	we	PRON
cana-5712	224	25	get	get	VERB
cana-5712	224	26	=	=	PUNCT
cana-5712	224	27	∑	∑	PUNCT
cana-5712	224	28	(	(	PUNCT
cana-5712	224	29	k1)1	k1)1	PROPN
cana-5712	224	30	…	…	PUNCT
cana-5712	224	31	.	.	PUNCT
cana-5712	224	32	.	.	PUNCT
cana-5712	225	1	(	(	PUNCT
cana-5712	225	2	kp)m	kp)m	PROPN
cana-5712	225	3	zm	zm	PROPN
cana-5712	225	4	(	(	PUNCT
cana-5712	225	5	l1)1	l1)1	PROPN
cana-5712	225	6	…	…	PUNCT
cana-5712	225	7	.	.	PUNCT
cana-5712	225	8	.	.	PUNCT
cana-5712	226	1	(	(	PUNCT
cana-5712	226	2	lq)mγ(ρ	lq)mγ(ρ	NOUN
cana-5712	226	3	+	+	CCONJ
cana-5712	226	4	σm	σm	NOUN
cana-5712	226	5	)	)	PUNCT
cana-5712	226	6	∞	∞	PROPN
cana-5712	226	7	m=0	m=0	PROPN
cana-5712	226	8	∫	∫	PROPN
cana-5712	226	9	uλ−1(1	uλ−1(1	PROPN
cana-5712	226	10	+	+	CCONJ
cana-5712	226	11	u)−μ−2mdu	u)−μ−2mdu	PROPN
cana-5712	226	12	∞	∞	PROPN
cana-5712	226	13	0	0	NUM
cana-5712	227	1	=	=	PUNCT
cana-5712	227	2	∑	∑	PUNCT
cana-5712	227	3	(	(	PUNCT
cana-5712	227	4	k1)1	k1)1	PROPN
cana-5712	227	5	…	…	PUNCT
cana-5712	227	6	.	.	PUNCT
cana-5712	227	7	.	.	PUNCT
cana-5712	228	1	(	(	PUNCT
cana-5712	228	2	kp)m	kp)m	PROPN
cana-5712	228	3	zm	zm	PROPN
cana-5712	228	4	(	(	PUNCT
cana-5712	228	5	l1)1	l1)1	PROPN
cana-5712	228	6	…	…	PUNCT
cana-5712	228	7	.	.	PUNCT
cana-5712	228	8	.	.	PUNCT
cana-5712	229	1	(	(	PUNCT
cana-5712	229	2	lq)mγ(ρ	lq)mγ(ρ	NOUN
cana-5712	229	3	+	+	CCONJ
cana-5712	229	4	σm	σm	NOUN
cana-5712	229	5	)	)	PUNCT
cana-5712	229	6	∞	∞	NUM
cana-5712	229	7	m=0	m=0	PROPN
cana-5712	229	8	γ(λ)γ(μ	γ(λ)γ(μ	PROPN
cana-5712	230	1	+	+	CCONJ
cana-5712	230	2	νm	νm	PROPN
cana-5712	230	3	−	−	PROPN
cana-5712	230	4	λ	λ	NOUN
cana-5712	230	5	)	)	PUNCT
cana-5712	230	6	γ(μ	γ(μ	PROPN
cana-5712	231	1	+	+	CCONJ
cana-5712	231	2	νm	νm	ADJ
cana-5712	231	3	)	)	PUNCT
cana-5712	231	4	=	=	SYM
cana-5712	231	5	∏	∏	NUM
cana-5712	231	6	γ(lq)γ(λ)q	γ(lq)γ(λ)q	NUM
cana-5712	231	7	j=1	j=1	PROPN
cana-5712	231	8	∏	∏	PROPN
cana-5712	231	9	γ(kp	γ(kp	PROPN
cana-5712	231	10	)	)	PUNCT
cana-5712	231	11	p	p	X
cana-5712	231	12	i=1	i=1	PROPN
cana-5712	231	13	∑	∑	PUNCT
cana-5712	231	14	γ(1+k1)	γ(1+k1)	NOUN
cana-5712	231	15	…	…	PUNCT
cana-5712	231	16	..	..	PUNCT
cana-5712	231	17	γ(m+kp	γ(m+kp	NUM
cana-5712	231	18	)	)	PUNCT
cana-5712	231	19	zm	zm	PROPN
cana-5712	231	20	γ(1+l1)	γ(1+l1)	PROPN
cana-5712	231	21	…	…	SYM
cana-5712	231	22	..	..	SYM
cana-5712	231	23	γ(m+lq)γ(ρ+σm	γ(m+lq)γ(ρ+σm	PROPN
cana-5712	231	24	)	)	PUNCT
cana-5712	231	25	γ(μ+νm−λ)γ(1+m	γ(μ+νm−λ)γ(1+m	NOUN
cana-5712	231	26	)	)	PUNCT
cana-5712	231	27	γ(μ+νm)m	γ(μ+νm)m	PROPN
cana-5712	231	28	!	!	PUNCT
cana-5712	232	1	∞	∞	PROPN
cana-5712	232	2	m=0	m=0	PROPN
cana-5712	232	3	hence	hence	ADV
cana-5712	232	4	proved	prove	VERB
cana-5712	232	5	.	.	PUNCT
cana-5712	233	1	theorem	theorem	ADJ
cana-5712	233	2	8	8	NUM
cana-5712	233	3	.	.	PUNCT
cana-5712	234	1	let	let	VERB
cana-5712	234	2	re(μ	re(μ	X
cana-5712	234	3	)	)	PUNCT
cana-5712	234	4	>	>	X
cana-5712	234	5	0	0	NUM
cana-5712	234	6	,	,	PUNCT
cana-5712	234	7	re(ν	re(ν	X
cana-5712	234	8	)	)	PUNCT
cana-5712	234	9	>	>	X
cana-5712	234	10	0	0	NUM
cana-5712	234	11	,	,	PUNCT
cana-5712	234	12	re(σ	re(σ	X
cana-5712	234	13	)	)	PUNCT
cana-5712	234	14	>	>	X
cana-5712	234	15	0	0	NUM
cana-5712	234	16	,	,	PUNCT
cana-5712	234	17	re(η	re(η	PUNCT
cana-5712	234	18	)	)	PUNCT
cana-5712	234	19	>	>	X
cana-5712	234	20	0	0	NUM
cana-5712	234	21	,	,	PUNCT
cana-5712	234	22	re(ξ	re(ξ	PUNCT
cana-5712	234	23	)	)	PUNCT
cana-5712	234	24	>	>	X
cana-5712	235	1	0	0	X
cana-5712	235	2	.	.	PUNCT
cana-5712	236	1	then	then	ADV
cana-5712	236	2	∫	∫	PROPN
cana-5712	236	3	sinμϑ.	sinμϑ.	PROPN
cana-5712	236	4	cosνϑ	cosνϑ	PROPN
cana-5712	236	5	mz	mz	PROPN
cana-5712	236	6	p(k1	p(k1	PROPN
cana-5712	236	7	,	,	PUNCT
cana-5712	236	8	…	…	PUNCT
cana-5712	236	9	.	.	PUNCT
cana-5712	237	1	,	,	PUNCT
cana-5712	237	2	kp	kp	PROPN
cana-5712	237	3	,	,	PUNCT
cana-5712	237	4	l1	l1	PROPN
cana-5712	237	5	…	…	PUNCT
cana-5712	237	6	.	.	PUNCT
cana-5712	238	1	lq	lq	INTJ
cana-5712	238	2	:	:	PUNCT
cana-5712	238	3	z{sinηϑ.	z{sinηϑ.	ADJ
cana-5712	238	4	cosξϑ})dup	cosξϑ})dup	NOUN
cana-5712	238	5	σ	σ	PROPN
cana-5712	238	6	dϑ	dϑ	NOUN
cana-5712	238	7	π	π	PROPN
cana-5712	238	8	2	2	NUM
cana-5712	238	9	0	0	NUM
cana-5712	238	10	=	=	SYM
cana-5712	238	11	∏	∏	PROPN
cana-5712	238	12	γ(lq	γ(lq	NUM
cana-5712	238	13	)	)	PUNCT
cana-5712	238	14	q	q	NOUN
cana-5712	238	15	j=1	j=1	NOUN
cana-5712	238	16	2	2	NUM
cana-5712	238	17	∏	∏	PROPN
cana-5712	238	18	γ(kp	γ(kp	NUM
cana-5712	238	19	)	)	PUNCT
cana-5712	238	20	p	p	X
cana-5712	238	21	i=1	i=1	PROPN
cana-5712	238	22	p+3ψq+2	p+3ψq+2	NOUN
cana-5712	238	23	[	[	PUNCT
cana-5712	238	24	(	(	PUNCT
cana-5712	238	25	k1	k1	NOUN
cana-5712	238	26	,	,	PUNCT
cana-5712	238	27	1	1	NUM
cana-5712	238	28	)	)	PUNCT
cana-5712	238	29	,	,	PUNCT
cana-5712	238	30	…	…	PUNCT
cana-5712	238	31	…	…	PUNCT
cana-5712	238	32	,	,	PUNCT
cana-5712	238	33	(	(	PUNCT
cana-5712	238	34	kp	kp	INTJ
cana-5712	238	35	,	,	PUNCT
cana-5712	238	36	1	1	NUM
cana-5712	238	37	)	)	PUNCT
cana-5712	238	38	,	,	PUNCT
cana-5712	238	39	(	(	PUNCT
cana-5712	238	40	μ+1	μ+1	NUM
cana-5712	238	41	2	2	NUM
cana-5712	238	42	,	,	PUNCT
cana-5712	238	43	η	η	PROPN
cana-5712	238	44	2	2	NUM
cana-5712	238	45	)	)	PUNCT
cana-5712	238	46	(	(	PUNCT
cana-5712	238	47	ν+1	ν+1	PROPN
cana-5712	238	48	2	2	NUM
cana-5712	238	49	,	,	PUNCT
cana-5712	238	50	ξ	ξ	PROPN
cana-5712	238	51	2	2	NUM
cana-5712	238	52	)	)	PUNCT
cana-5712	238	53	,	,	PUNCT
cana-5712	238	54	(	(	PUNCT
cana-5712	238	55	1,1	1,1	NUM
cana-5712	238	56	)	)	PUNCT
cana-5712	238	57	(	(	PUNCT
cana-5712	238	58	l1	l1	PROPN
cana-5712	238	59	,	,	PUNCT
cana-5712	238	60	1	1	NUM
cana-5712	238	61	)	)	PUNCT
cana-5712	238	62	,	,	PUNCT
cana-5712	238	63	…	…	PUNCT
cana-5712	238	64	…	…	PUNCT
cana-5712	238	65	.	.	PUNCT
cana-5712	238	66	,	,	PUNCT
cana-5712	238	67	(	(	PUNCT
cana-5712	238	68	lq	lq	INTJ
cana-5712	238	69	,	,	PUNCT
cana-5712	238	70	1	1	NUM
cana-5712	238	71	)	)	PUNCT
cana-5712	238	72	,	,	PUNCT
cana-5712	238	73	(	(	PUNCT
cana-5712	238	74	ρ	ρ	PROPN
cana-5712	238	75	,	,	PUNCT
cana-5712	238	76	σ	σ	PROPN
cana-5712	238	77	)	)	PUNCT
cana-5712	238	78	,	,	PUNCT
cana-5712	238	79	(	(	PUNCT
cana-5712	238	80	μ+ν	μ+ν	NUM
cana-5712	238	81	2	2	NUM
cana-5712	238	82	,	,	PUNCT
cana-5712	238	83	η+ξ	η+ξ	NUM
cana-5712	238	84	2	2	NUM
cana-5712	238	85	)	)	PUNCT
cana-5712	238	86	;	;	PUNCT
cana-5712	239	1	z	z	X
cana-5712	239	2	]	]	X
cana-5712	239	3	.	.	PUNCT
cana-5712	240	1	(	(	PUNCT
cana-5712	240	2	2.8	2.8	NUM
cana-5712	240	3	)	)	PUNCT
cana-5712	240	4	proof	proof	NOUN
cana-5712	240	5	.	.	PUNCT
cana-5712	241	1	proof	proof	NOUN
cana-5712	241	2	of	of	ADP
cana-5712	241	3	theorem	theorem	ADJ
cana-5712	241	4	8	8	NUM
cana-5712	241	5	is	be	AUX
cana-5712	241	6	same	same	ADJ
cana-5712	241	7	as	as	ADP
cana-5712	241	8	the	the	DET
cana-5712	241	9	roof	roof	NOUN
cana-5712	241	10	of	of	ADP
cana-5712	241	11	theorem	theorem	ADJ
cana-5712	241	12	7	7	NUM
cana-5712	241	13	.	.	PUNCT
cana-5712	241	14	theorem	theorem	NOUN
cana-5712	241	15	9	9	NUM
cana-5712	241	16	.	.	PUNCT
cana-5712	242	1	if	if	SCONJ
cana-5712	242	2	re(ξ	re(ξ	VERB
cana-5712	242	3	)	)	PUNCT
cana-5712	242	4	>	>	X
cana-5712	242	5	0	0	NUM
cana-5712	242	6	,	,	PUNCT
cana-5712	242	7	re(ν	re(ν	X
cana-5712	242	8	)	)	PUNCT
cana-5712	242	9	<	<	X
cana-5712	242	10	1	1	NUM
cana-5712	242	11	,	,	PUNCT
cana-5712	242	12	re(μ	re(μ	NOUN
cana-5712	242	13	)	)	PUNCT
cana-5712	242	14	>	>	X
cana-5712	243	1	0	0	NUM
cana-5712	243	2	,	,	PUNCT
cana-5712	243	3	σ	σ	PROPN
cana-5712	243	4	,	,	PUNCT
cana-5712	243	5	ξ	ξ	PROPN
cana-5712	243	6	∈	∈	PROPN
cana-5712	243	7	c	c	NOUN
cana-5712	243	8	,	,	PUNCT
cana-5712	243	9	re(σ	re(σ	X
cana-5712	243	10	)	)	PUNCT
cana-5712	243	11	>	>	X
cana-5712	243	12	0	0	NUM
cana-5712	243	13	,	,	PUNCT
cana-5712	243	14	following	follow	VERB
cana-5712	243	15	integral	integral	ADJ
cana-5712	243	16	formula	formula	NOUN
cana-5712	243	17	holds	hold	VERB
cana-5712	243	18	∫	∫	PROPN
cana-5712	243	19	uμ−1e−	uμ−1e−	PROPN
cana-5712	243	20	au	au	PROPN
cana-5712	243	21	2	2	NUM
cana-5712	243	22	wη	wη	NOUN
cana-5712	243	23	,	,	PUNCT
cana-5712	243	24	v	v	NOUN
cana-5712	243	25	mq	mq	PROPN
cana-5712	243	26	σ(k1	σ(k1	PROPN
cana-5712	243	27	,	,	PUNCT
cana-5712	243	28	…	…	PUNCT
cana-5712	243	29	.	.	PUNCT
cana-5712	244	1	,	,	PUNCT
cana-5712	244	2	kp	kp	PROPN
cana-5712	244	3	,	,	PUNCT
cana-5712	244	4	l1	l1	PROPN
cana-5712	244	5	…	…	PUNCT
cana-5712	244	6	.	.	PUNCT
cana-5712	245	1	lq	lq	INTJ
cana-5712	245	2	:	:	PUNCT
cana-5712	245	3	zuξ)dup	zuξ)dup	PROPN
cana-5712	245	4	ρ	ρ	NUM
cana-5712	245	5	∞	∞	NOUN
cana-5712	245	6	0	0	PUNCT
cana-5712	245	7	=	=	SYM
cana-5712	245	8	∏	∏	PROPN
cana-5712	245	9	γ(lq	γ(lq	NUM
cana-5712	245	10	)	)	PUNCT
cana-5712	245	11	q	q	NOUN
cana-5712	246	1	j=1	j=1	PROPN
cana-5712	246	2	∏	∏	PROPN
cana-5712	246	3	γ(kp	γ(kp	PROPN
cana-5712	246	4	)	)	PUNCT
cana-5712	247	1	p	p	X
cana-5712	247	2	i=1	i=1	X
cana-5712	247	3	aμ	aμ	INTJ
cana-5712	247	4	p+3ψq+2	p+3ψq+2	PROPN
cana-5712	247	5	[	[	PUNCT
cana-5712	247	6	(	(	PUNCT
cana-5712	247	7	k1	k1	NOUN
cana-5712	247	8	,	,	PUNCT
cana-5712	247	9	1	1	NUM
cana-5712	247	10	)	)	PUNCT
cana-5712	247	11	,	,	PUNCT
cana-5712	247	12	…	…	PUNCT
cana-5712	247	13	…	…	PUNCT
cana-5712	247	14	,	,	PUNCT
cana-5712	247	15	(	(	PUNCT
cana-5712	247	16	kp	kp	INTJ
cana-5712	247	17	,	,	PUNCT
cana-5712	247	18	1	1	NUM
cana-5712	247	19	)	)	PUNCT
cana-5712	247	20	,	,	PUNCT
cana-5712	247	21	(	(	PUNCT
cana-5712	247	22	μ	μ	NOUN
cana-5712	247	23	+	+	NOUN
cana-5712	247	24	ν	ν	X
cana-5712	247	25	+	+	CCONJ
cana-5712	247	26	1	1	NUM
cana-5712	247	27	2	2	NUM
cana-5712	247	28	,	,	PUNCT
cana-5712	247	29	ξ	ξ	NOUN
cana-5712	247	30	)	)	PUNCT
cana-5712	247	31	(	(	PUNCT
cana-5712	247	32	μ	μ	NOUN
cana-5712	247	33	−	−	PROPN
cana-5712	248	1	ν	ν	NOUN
cana-5712	248	2	+	+	CCONJ
cana-5712	248	3	1	1	NUM
cana-5712	248	4	2	2	NUM
cana-5712	248	5	,	,	PUNCT
cana-5712	248	6	ξ	ξ	NOUN
cana-5712	248	7	)	)	PUNCT
cana-5712	248	8	,	,	PUNCT
cana-5712	248	9	(	(	PUNCT
cana-5712	248	10	1,1	1,1	NUM
cana-5712	248	11	)	)	PUNCT
cana-5712	248	12	(	(	PUNCT
cana-5712	248	13	l1	l1	PROPN
cana-5712	248	14	,	,	PUNCT
cana-5712	248	15	1	1	NUM
cana-5712	248	16	)	)	PUNCT
cana-5712	248	17	,	,	PUNCT
cana-5712	248	18	…	…	PUNCT
cana-5712	248	19	…	…	PUNCT
cana-5712	248	20	.	.	PUNCT
cana-5712	249	1	,	,	PUNCT
cana-5712	249	2	(	(	PUNCT
cana-5712	249	3	lq	lq	INTJ
cana-5712	249	4	,	,	PUNCT
cana-5712	249	5	1	1	NUM
cana-5712	249	6	)	)	PUNCT
cana-5712	249	7	,	,	PUNCT
cana-5712	249	8	(	(	PUNCT
cana-5712	249	9	ρ	ρ	PROPN
cana-5712	249	10	,	,	PUNCT
cana-5712	249	11	σ	σ	PROPN
cana-5712	249	12	)	)	PUNCT
cana-5712	249	13	,	,	PUNCT
cana-5712	249	14	(	(	PUNCT
cana-5712	249	15	μ	μ	NOUN
cana-5712	249	16	−	−	PROPN
cana-5712	250	1	k	k	PROPN
cana-5712	250	2	+	+	PROPN
cana-5712	250	3	1	1	NUM
cana-5712	250	4	,	,	PUNCT
cana-5712	250	5	ξ	ξ	NUM
cana-5712	250	6	)	)	PUNCT
cana-5712	250	7	;	;	PUNCT
cana-5712	250	8	z	z	NOUN
cana-5712	250	9	aξ	aξ	INTJ
cana-5712	250	10	]	]	PUNCT
cana-5712	250	11	(	(	PUNCT
cana-5712	250	12	2.9	2.9	NUM
cana-5712	250	13	)	)	PUNCT
cana-5712	250	14	proof	proof	NOUN
cana-5712	250	15	.	.	PUNCT
cana-5712	251	1	for	for	ADP
cana-5712	251	2	evaluating	evaluate	VERB
cana-5712	251	3	(	(	PUNCT
cana-5712	251	4	2.7	2.7	NUM
cana-5712	251	5	)	)	PUNCT
cana-5712	251	6	,	,	PUNCT
cana-5712	251	7	applying	apply	VERB
cana-5712	251	8	definition	definition	NOUN
cana-5712	251	9	of	of	ADP
cana-5712	251	10	generalized	generalized	ADJ
cana-5712	251	11	m	m	PROPN
cana-5712	251	12	-	-	PUNCT
cana-5712	251	13	series	series	NOUN
cana-5712	251	14	in	in	ADP
cana-5712	251	15	the	the	DET
cana-5712	251	16	left	left	ADJ
cana-5712	251	17	hand	hand	NOUN
cana-5712	251	18	side	side	NOUN
cana-5712	251	19	of	of	ADP
cana-5712	251	20	(	(	PUNCT
cana-5712	251	21	2.7	2.7	NUM
cana-5712	251	22	)	)	PUNCT
cana-5712	251	23	,	,	PUNCT
cana-5712	251	24	we	we	PRON
cana-5712	251	25	get	get	VERB
cana-5712	251	26	=	=	SYM
cana-5712	251	27	∏	∏	NUM
cana-5712	251	28	γ(lq)q	γ(lq)q	NOUN
cana-5712	251	29	j=1	j=1	PROPN
cana-5712	251	30	∏	∏	PROPN
cana-5712	251	31	γ(kp)p	γ(kp)p	NOUN
cana-5712	251	32	i=1	i=1	PRON
cana-5712	251	33	aμ	aμ	INTJ
cana-5712	251	34	∑	∑	PUNCT
cana-5712	251	35	γ(1	γ(1	PROPN
cana-5712	251	36	+	+	NUM
cana-5712	251	37	k1	k1	NOUN
cana-5712	251	38	)	)	PUNCT
cana-5712	251	39	…	…	PUNCT
cana-5712	251	40	.	.	PUNCT
cana-5712	251	41	.	.	PUNCT
cana-5712	252	1	γ(m	γ(m	PROPN
cana-5712	252	2	+	+	CCONJ
cana-5712	252	3	kp	kp	PROPN
cana-5712	252	4	)	)	PUNCT
cana-5712	252	5	zm	zm	PROPN
cana-5712	252	6	γ(1	γ(1	PROPN
cana-5712	252	7	+	+	NUM
cana-5712	252	8	l1	l1	PROPN
cana-5712	252	9	)	)	PUNCT
cana-5712	252	10	…	…	PUNCT
cana-5712	252	11	.	.	PUNCT
cana-5712	252	12	.	.	PUNCT
cana-5712	253	1	γ(m	γ(m	PROPN
cana-5712	253	2	+	+	CCONJ
cana-5712	253	3	lq)γ(ρ	lq)γ(ρ	PROPN
cana-5712	253	4	+	+	CCONJ
cana-5712	253	5	σm	σm	X
cana-5712	253	6	)	)	PUNCT
cana-5712	253	7	∞	∞	NUM
cana-5712	254	1	m=0	m=0	PROPN
cana-5712	254	2	∫	∫	PROPN
cana-5712	254	3	uμ+ξe−	uμ+ξe−	ADV
cana-5712	254	4	au	au	ADP
cana-5712	254	5	2	2	NUM
cana-5712	254	6	wη	wη	NOUN
cana-5712	254	7	,	,	PUNCT
cana-5712	254	8	vdu	vdu	PROPN
cana-5712	254	9	∞	∞	PROPN
cana-5712	254	10	0	0	NUM
cana-5712	254	11	communications	communication	NOUN
cana-5712	254	12	on	on	ADP
cana-5712	254	13	applied	apply	VERB
cana-5712	254	14	nonlinear	nonlinear	ADJ
cana-5712	254	15	analysis	analysis	NOUN
cana-5712	254	16	issn	issn	NOUN
cana-5712	254	17	:	:	PUNCT
cana-5712	254	18	1074	1074	NUM
cana-5712	254	19	-	-	PUNCT
cana-5712	254	20	133x	133x	NUM
cana-5712	254	21	vol	vol	VERB
cana-5712	254	22	32	32	NUM
cana-5712	254	23	no	no	NOUN
cana-5712	254	24	.	.	PUNCT
cana-5712	255	1	10s	10	NOUN
cana-5712	255	2	(	(	PUNCT
cana-5712	255	3	2025	2025	NUM
cana-5712	255	4	)	)	PUNCT
cana-5712	255	5	2720	2720	NUM
cana-5712	255	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5712	255	7	=	=	SYM
cana-5712	255	8	∏	∏	PROPN
cana-5712	255	9	γ(lq	γ(lq	NUM
cana-5712	255	10	)	)	PUNCT
cana-5712	255	11	q	q	NOUN
cana-5712	256	1	j=1	j=1	NOUN
cana-5712	256	2	∏	∏	PROPN
cana-5712	256	3	γ(kp)p	γ(kp)p	NOUN
cana-5712	256	4	i=1	i=1	PRON
cana-5712	256	5	aμ	aμ	INTJ
cana-5712	256	6	∑	∑	PUNCT
cana-5712	256	7	γ(1	γ(1	PROPN
cana-5712	256	8	+	+	NUM
cana-5712	256	9	k1	k1	NOUN
cana-5712	256	10	)	)	PUNCT
cana-5712	256	11	…	…	PUNCT
cana-5712	256	12	.	.	PUNCT
cana-5712	256	13	.	.	PUNCT
cana-5712	257	1	γ(m	γ(m	PROPN
cana-5712	257	2	+	+	CCONJ
cana-5712	257	3	kp	kp	PROPN
cana-5712	257	4	)	)	PUNCT
cana-5712	257	5	(	(	PUNCT
cana-5712	257	6	z	z	NOUN
cana-5712	257	7	aξ)m	aξ)m	PROPN
cana-5712	257	8	γ(1	γ(1	PROPN
cana-5712	257	9	+	+	NUM
cana-5712	257	10	l1	l1	PROPN
cana-5712	257	11	)	)	PUNCT
cana-5712	257	12	…	…	PUNCT
cana-5712	257	13	.	.	PUNCT
cana-5712	257	14	.	.	PUNCT
cana-5712	258	1	γ(m	γ(m	PROPN
cana-5712	258	2	+	+	CCONJ
cana-5712	258	3	lq)γ(ρ	lq)γ(ρ	PROPN
cana-5712	258	4	+	+	CCONJ
cana-5712	258	5	σm	σm	X
cana-5712	258	6	)	)	PUNCT
cana-5712	258	7	∞	∞	NUM
cana-5712	258	8	m=0	m=0	PROPN
cana-5712	258	9	γ	γ	PROPN
cana-5712	258	10	(	(	PUNCT
cana-5712	258	11	μ	μ	PROPN
cana-5712	258	12	+	+	PROPN
cana-5712	258	13	ξm	ξm	X
cana-5712	258	14	+	+	X
cana-5712	258	15	ν	ν	X
cana-5712	258	16	+	+	CCONJ
cana-5712	258	17	1	1	NUM
cana-5712	258	18	2	2	NUM
cana-5712	258	19	)	)	PUNCT
cana-5712	258	20	γ(μ	γ(μ	PROPN
cana-5712	258	21	+	+	NUM
cana-5712	258	22	ξm	ξm	PROPN
cana-5712	258	23	−	−	NOUN
cana-5712	258	24	v	v	NOUN
cana-5712	258	25	+	+	CCONJ
cana-5712	258	26	1	1	NUM
cana-5712	258	27	2	2	NUM
cana-5712	258	28	)	)	PUNCT
cana-5712	259	1	γ(1	γ(1	NOUN
cana-5712	259	2	−	−	PROPN
cana-5712	259	3	k	k	PROPN
cana-5712	260	1	+	+	PROPN
cana-5712	260	2	μ	μ	PROPN
cana-5712	260	3	+	+	X
cana-5712	260	4	ξm	ξm	NOUN
cana-5712	260	5	)	)	PUNCT
cana-5712	260	6	hence	hence	ADV
cana-5712	260	7	proved	prove	VERB
cana-5712	260	8	.	.	PUNCT
cana-5712	261	1	3	3	X
cana-5712	261	2	.	.	X
cana-5712	261	3	special	special	ADJ
cana-5712	261	4	cases	case	NOUN
cana-5712	261	5	:	:	PUNCT
cana-5712	261	6	corollary	corollary	ADJ
cana-5712	261	7	1	1	NUM
cana-5712	261	8	.	.	PUNCT
cana-5712	262	1	if	if	SCONJ
cana-5712	262	2	we	we	PRON
cana-5712	262	3	take	take	VERB
cana-5712	262	4	p	p	NOUN
cana-5712	262	5	=	=	NOUN
cana-5712	262	6	q	q	NOUN
cana-5712	262	7	=	=	SYM
cana-5712	262	8	0	0	NUM
cana-5712	262	9	in	in	ADP
cana-5712	262	10	theorem	theorem	NOUN
cana-5712	262	11	1	1	NUM
cana-5712	262	12	and	and	CCONJ
cana-5712	262	13	using	use	VERB
cana-5712	262	14	formula	formula	NOUN
cana-5712	262	15	(	(	PUNCT
cana-5712	262	16	1.6	1.6	NUM
cana-5712	262	17	)	)	PUNCT
cana-5712	262	18	,	,	PUNCT
cana-5712	262	19	we	we	PRON
cana-5712	262	20	get	get	VERB
cana-5712	262	21	the	the	DET
cana-5712	262	22	following	following	ADJ
cana-5712	262	23	result	result	PROPN
cana-5712	262	24	∫	∫	PROPN
cana-5712	262	25	e−μt[sinh(νt)]η∞	e−μt[sinh(νt)]η∞	PROPN
cana-5712	262	26	0	0	NUM
cana-5712	262	27	eρ	eρ	PROPN
cana-5712	262	28	,	,	PUNCT
cana-5712	262	29	σ(ze−ξt)dt	σ(ze−ξt)dt	NOUN
cana-5712	262	30	=	=	SYM
cana-5712	262	31	ν−12−η−1	ν−12−η−1	PRON
cana-5712	262	32	γ(1+η	γ(1+η	PROPN
cana-5712	262	33	)	)	PUNCT
cana-5712	262	34	1	1	NUM
cana-5712	262	35	2ψ2	2ψ2	NUM
cana-5712	262	36	[	[	PUNCT
cana-5712	262	37	(	(	PUNCT
cana-5712	262	38	μ	μ	NUM
cana-5712	262	39	2ν	2ν	NOUN
cana-5712	262	40	−	−	PROPN
cana-5712	262	41	η	η	PROPN
cana-5712	262	42	2	2	NUM
cana-5712	262	43	,	,	PUNCT
cana-5712	262	44	ξ	ξ	PROPN
cana-5712	262	45	2ν	2ν	NOUN
cana-5712	262	46	)	)	PUNCT
cana-5712	262	47	,	,	PUNCT
cana-5712	262	48	(	(	PUNCT
cana-5712	262	49	1,1	1,1	NUM
cana-5712	262	50	)	)	PUNCT
cana-5712	262	51	(	(	PUNCT
cana-5712	262	52	ρ	ρ	PROPN
cana-5712	262	53	,	,	PUNCT
cana-5712	262	54	σ	σ	PROPN
cana-5712	262	55	)	)	PUNCT
cana-5712	262	56	,	,	PUNCT
cana-5712	262	57	(	(	PUNCT
cana-5712	262	58	μ	μ	NUM
cana-5712	262	59	2ν	2ν	NOUN
cana-5712	262	60	+	+	CCONJ
cana-5712	262	61	η	η	X
cana-5712	262	62	2	2	NUM
cana-5712	262	63	+	+	SYM
cana-5712	262	64	1	1	NUM
cana-5712	262	65	+	+	SYM
cana-5712	262	66	ξ	ξ	PROPN
cana-5712	262	67	2ν	2ν	NOUN
cana-5712	262	68	)	)	PUNCT
cana-5712	263	1	z	z	X
cana-5712	263	2	]	]	X
cana-5712	263	3	.	.	PUNCT
cana-5712	264	1	corollary	corollary	ADJ
cana-5712	264	2	2	2	NUM
cana-5712	264	3	.	.	PUNCT
cana-5712	265	1	if	if	SCONJ
cana-5712	265	2	we	we	PRON
cana-5712	265	3	take	take	VERB
cana-5712	265	4	if	if	SCONJ
cana-5712	265	5	p	p	NOUN
cana-5712	265	6	=	=	NOUN
cana-5712	265	7	0	0	NUM
cana-5712	265	8	,	,	PUNCT
cana-5712	265	9	q	q	NOUN
cana-5712	265	10	=	=	SYM
cana-5712	265	11	1	1	NUM
cana-5712	265	12	in	in	ADP
cana-5712	265	13	theorem	theorem	NOUN
cana-5712	265	14	1	1	NUM
cana-5712	265	15	and	and	CCONJ
cana-5712	265	16	using	use	VERB
cana-5712	265	17	(	(	PUNCT
cana-5712	265	18	1.7	1.7	NUM
cana-5712	265	19	)	)	PUNCT
cana-5712	265	20	,	,	PUNCT
cana-5712	265	21	we	we	PRON
cana-5712	265	22	get	get	VERB
cana-5712	265	23	following	follow	VERB
cana-5712	265	24	result	result	NOUN
cana-5712	265	25	.	.	PUNCT
cana-5712	266	1	∫	∫	PROPN
cana-5712	267	1	e−μt[sinh(νt)]η∞	e−μt[sinh(νt)]η∞	PROPN
cana-5712	267	2	0	0	NUM
cana-5712	267	3	wρ	wρ	PROPN
cana-5712	267	4	,	,	PUNCT
cana-5712	267	5	σ(ze−ξt)dt	σ(ze−ξt)dt	NOUN
cana-5712	267	6	=	=	SYM
cana-5712	267	7	ν−12−η−1	ν−12−η−1	DET
cana-5712	267	8	γ(1+η	γ(1+η	PROPN
cana-5712	267	9	)	)	PUNCT
cana-5712	267	10	1	1	NUM
cana-5712	267	11	1ψ2	1ψ2	NUM
cana-5712	267	12	[	[	PUNCT
cana-5712	267	13	(	(	PUNCT
cana-5712	267	14	μ	μ	NUM
cana-5712	267	15	2ν	2ν	NOUN
cana-5712	267	16	−	−	PROPN
cana-5712	267	17	η	η	PROPN
cana-5712	267	18	2	2	NUM
cana-5712	267	19	,	,	PUNCT
cana-5712	267	20	ξ	ξ	PROPN
cana-5712	267	21	2ν	2ν	NOUN
cana-5712	267	22	)	)	PUNCT
cana-5712	267	23	,	,	PUNCT
cana-5712	267	24	(	(	PUNCT
cana-5712	267	25	ρ	ρ	PROPN
cana-5712	267	26	,	,	PUNCT
cana-5712	267	27	σ	σ	PROPN
cana-5712	267	28	)	)	PUNCT
cana-5712	267	29	,	,	PUNCT
cana-5712	267	30	(	(	PUNCT
cana-5712	267	31	μ	μ	NUM
cana-5712	267	32	2ν	2ν	NOUN
cana-5712	268	1	+	+	CCONJ
cana-5712	268	2	η	η	X
cana-5712	268	3	2	2	NUM
cana-5712	268	4	+	+	SYM
cana-5712	268	5	1	1	NUM
cana-5712	268	6	+	+	SYM
cana-5712	268	7	ξ	ξ	PROPN
cana-5712	268	8	2ν	2ν	NOUN
cana-5712	268	9	)	)	PUNCT
cana-5712	269	1	z	z	NOUN
cana-5712	269	2	]	]	PUNCT
cana-5712	269	3	.	.	PUNCT
cana-5712	270	1	corollary	corollary	ADJ
cana-5712	270	2	3	3	X
cana-5712	270	3	.	.	PUNCT
cana-5712	271	1	if	if	SCONJ
cana-5712	271	2	we	we	PRON
cana-5712	271	3	take	take	VERB
cana-5712	271	4	if	if	SCONJ
cana-5712	271	5	p	p	NOUN
cana-5712	271	6	=	=	X
cana-5712	271	7	q	q	NOUN
cana-5712	271	8	=	=	NOUN
cana-5712	271	9	1	1	NUM
cana-5712	271	10	,	,	PUNCT
cana-5712	271	11	k	k	NOUN
cana-5712	271	12	=	=	PUNCT
cana-5712	271	13	a	a	PROPN
cana-5712	271	14	and	and	CCONJ
cana-5712	271	15	l	l	NOUN
cana-5712	271	16	=	=	SYM
cana-5712	271	17	1	1	NUM
cana-5712	271	18	,	,	PUNCT
cana-5712	271	19	an	an	DET
cana-5712	271	20	equation	equation	NOUN
cana-5712	271	21	(	(	PUNCT
cana-5712	271	22	2.3	2.3	NUM
cana-5712	271	23	)	)	PUNCT
cana-5712	271	24	and	and	CCONJ
cana-5712	271	25	using	use	VERB
cana-5712	271	26	(	(	PUNCT
cana-5712	271	27	1.8	1.8	NUM
cana-5712	271	28	)	)	PUNCT
cana-5712	271	29	,	,	PUNCT
cana-5712	271	30	we	we	PRON
cana-5712	271	31	get	get	VERB
cana-5712	271	32	∫	∫	PROPN
cana-5712	271	33	uμ(1	uμ(1	ADP
cana-5712	271	34	−	−	PROPN
cana-5712	271	35	u2)−	u2)−	ADJ
cana-5712	271	36	ν	ν	X
cana-5712	271	37	2pη	2pη	ADJ
cana-5712	271	38	ν(u	ν(u	PROPN
cana-5712	271	39	)	)	PUNCT
cana-5712	271	40	1	1	NUM
cana-5712	271	41	0	0	NUM
cana-5712	271	42	eρ	eρ	PROPN
cana-5712	271	43	,	,	PUNCT
cana-5712	271	44	σ	σ	PROPN
cana-5712	271	45	a	a	X
cana-5712	271	46	(	(	PUNCT
cana-5712	271	47	zuξ)du	zuξ)du	NOUN
cana-5712	271	48	=	=	SYM
cana-5712	271	49	2ν−1	2ν−1	NUM
cana-5712	271	50	∏	∏	NUM
cana-5712	271	51	γ(lq	γ(lq	NUM
cana-5712	271	52	)	)	PUNCT
cana-5712	271	53	q	q	PUNCT
cana-5712	271	54	j=1	j=1	PROPN
cana-5712	271	55	∏	∏	PROPN
cana-5712	271	56	γ(kp	γ(kp	PROPN
cana-5712	271	57	)	)	PUNCT
cana-5712	271	58	p	p	X
cana-5712	271	59	i=1	i=1	PROPN
cana-5712	271	60	3ψ3	3ψ3	NUM
cana-5712	271	61	[	[	PUNCT
cana-5712	271	62	(	(	PUNCT
cana-5712	271	63	a	a	PRON
cana-5712	271	64	,	,	PUNCT
cana-5712	271	65	1	1	NUM
cana-5712	271	66	)	)	PUNCT
cana-5712	271	67	,	,	PUNCT
cana-5712	271	68	(	(	PUNCT
cana-5712	271	69	μ	μ	NOUN
cana-5712	271	70	2	2	NUM
cana-5712	271	71	+	+	CCONJ
cana-5712	271	72	1	1	NUM
cana-5712	271	73	2	2	NUM
cana-5712	271	74	,	,	PUNCT
cana-5712	271	75	ξ	ξ	PROPN
cana-5712	271	76	2	2	NUM
cana-5712	271	77	)	)	PUNCT
cana-5712	271	78	,	,	PUNCT
cana-5712	271	79	(	(	PUNCT
cana-5712	271	80	μ+1	μ+1	NUM
cana-5712	271	81	2	2	NUM
cana-5712	271	82	,	,	PUNCT
cana-5712	271	83	ξ	ξ	PROPN
cana-5712	271	84	2	2	NUM
cana-5712	271	85	)	)	PUNCT
cana-5712	271	86	(	(	PUNCT
cana-5712	271	87	ρ	ρ	PROPN
cana-5712	271	88	,	,	PUNCT
cana-5712	271	89	σ	σ	PROPN
cana-5712	271	90	)	)	PUNCT
cana-5712	271	91	,	,	PUNCT
cana-5712	271	92	(	(	PUNCT
cana-5712	271	93	μ	μ	NOUN
cana-5712	271	94	2	2	NUM
cana-5712	271	95	−	−	PROPN
cana-5712	271	96	η	η	PROPN
cana-5712	271	97	2	2	NUM
cana-5712	271	98	−	−	NOUN
cana-5712	271	99	ν	ν	NOUN
cana-5712	271	100	2	2	NUM
cana-5712	271	101	+	+	CCONJ
cana-5712	271	102	1	1	NUM
cana-5712	271	103	,	,	PUNCT
cana-5712	271	104	ξ	ξ	PROPN
cana-5712	271	105	2	2	NUM
cana-5712	271	106	)	)	PUNCT
cana-5712	271	107	(	(	PUNCT
cana-5712	271	108	μ	μ	PROPN
cana-5712	271	109	2	2	NUM
cana-5712	271	110	+	+	SYM
cana-5712	271	111	η	η	PROPN
cana-5712	271	112	2	2	NUM
cana-5712	271	113	−	−	NOUN
cana-5712	271	114	ν	ν	NOUN
cana-5712	271	115	2	2	NUM
cana-5712	271	116	+	+	CCONJ
cana-5712	271	117	3	3	NUM
cana-5712	271	118	2	2	NUM
cana-5712	271	119	,	,	PUNCT
cana-5712	271	120	ξ	ξ	PROPN
cana-5712	271	121	2	2	NUM
cana-5712	271	122	)	)	PUNCT
cana-5712	271	123	;	;	PUNCT
cana-5712	272	1	z	z	X
cana-5712	272	2	]	]	PUNCT
cana-5712	272	3	.	.	PUNCT
cana-5712	273	1	corollary	corollary	ADJ
cana-5712	273	2	4	4	NUM
cana-5712	273	3	.	.	PUNCT
cana-5712	274	1	if	if	SCONJ
cana-5712	274	2	we	we	PRON
cana-5712	274	3	take	take	VERB
cana-5712	274	4	ρ	ρ	NOUN
cana-5712	274	5	=	=	SYM
cana-5712	274	6	σ	σ	NOUN
cana-5712	274	7	=	=	NOUN
cana-5712	274	8	1	1	NUM
cana-5712	274	9	in	in	ADP
cana-5712	274	10	theorem	theorem	NOUN
cana-5712	274	11	3	3	NUM
cana-5712	274	12	and	and	CCONJ
cana-5712	274	13	using	use	VERB
cana-5712	274	14	(	(	PUNCT
cana-5712	274	15	1.5	1.5	NUM
cana-5712	274	16	)	)	PUNCT
cana-5712	274	17	,	,	PUNCT
cana-5712	274	18	we	we	PRON
cana-5712	274	19	get	get	VERB
cana-5712	274	20	∫	∫	PROPN
cana-5712	274	21	uμ(1	uμ(1	ADP
cana-5712	274	22	−	−	PROPN
cana-5712	274	23	u2)−	u2)−	ADJ
cana-5712	274	24	ν	ν	X
cana-5712	274	25	2pη	2pη	ADJ
cana-5712	274	26	ν(u	ν(u	PROPN
cana-5712	274	27	)	)	PUNCT
cana-5712	274	28	1	1	NUM
cana-5712	274	29	0	0	NUM
cana-5712	274	30	pfq	pfq	PROPN
cana-5712	274	31	[	[	PUNCT
cana-5712	274	32	k1	k1	NOUN
cana-5712	274	33	,	,	PUNCT
cana-5712	274	34	…	…	PUNCT
cana-5712	274	35	.	.	PUNCT
cana-5712	274	36	.	.	PUNCT
cana-5712	275	1	kp	kp	PROPN
cana-5712	275	2	;	;	PUNCT
cana-5712	275	3	l1	l1	PROPN
cana-5712	275	4	,	,	PUNCT
cana-5712	275	5	…	…	PUNCT
cana-5712	275	6	…	…	PUNCT
cana-5712	275	7	.	.	PUNCT
cana-5712	276	1	lq	lq	INTJ
cana-5712	276	2	;	;	PUNCT
cana-5712	276	3	z	z	X
cana-5712	276	4	]	]	X
cana-5712	276	5	du	du	X
cana-5712	276	6	=	=	SYM
cana-5712	276	7	2ν−1	2ν−1	NUM
cana-5712	276	8	∏	∏	NUM
cana-5712	276	9	γ(lq	γ(lq	NUM
cana-5712	276	10	)	)	PUNCT
cana-5712	276	11	q	q	PUNCT
cana-5712	277	1	j=1	j=1	PROPN
cana-5712	277	2	∏	∏	PROPN
cana-5712	277	3	γ(kp	γ(kp	PROPN
cana-5712	277	4	)	)	PUNCT
cana-5712	278	1	p	p	X
cana-5712	278	2	i=1	i=1	PROPN
cana-5712	278	3	p+2ψq+2	p+2ψq+2	VERB
cana-5712	278	4	[	[	PUNCT
cana-5712	278	5	(	(	PUNCT
cana-5712	278	6	k1	k1	NOUN
cana-5712	278	7	,	,	PUNCT
cana-5712	278	8	1	1	NUM
cana-5712	278	9	)	)	PUNCT
cana-5712	278	10	,	,	PUNCT
cana-5712	278	11	…	…	PUNCT
cana-5712	278	12	…	…	PUNCT
cana-5712	278	13	,	,	PUNCT
cana-5712	278	14	(	(	PUNCT
cana-5712	278	15	kp	kp	INTJ
cana-5712	278	16	,	,	PUNCT
cana-5712	278	17	1	1	NUM
cana-5712	278	18	)	)	PUNCT
cana-5712	278	19	,	,	PUNCT
cana-5712	278	20	(	(	PUNCT
cana-5712	278	21	μ	μ	NOUN
cana-5712	278	22	2	2	NUM
cana-5712	278	23	+	+	CCONJ
cana-5712	278	24	1	1	NUM
cana-5712	278	25	2	2	NUM
cana-5712	278	26	,	,	PUNCT
cana-5712	278	27	ξ	ξ	PROPN
cana-5712	278	28	2	2	NUM
cana-5712	278	29	)	)	PUNCT
cana-5712	278	30	,	,	PUNCT
cana-5712	278	31	(	(	PUNCT
cana-5712	278	32	1	1	NUM
cana-5712	278	33	+	+	NUM
cana-5712	278	34	μ	μ	PROPN
cana-5712	278	35	2	2	NUM
cana-5712	278	36	,	,	PUNCT
cana-5712	278	37	ξ	ξ	PROPN
cana-5712	278	38	2	2	NUM
cana-5712	278	39	)	)	PUNCT
cana-5712	278	40	(	(	PUNCT
cana-5712	278	41	l1	l1	PROPN
cana-5712	278	42	,	,	PUNCT
cana-5712	278	43	1	1	NUM
cana-5712	278	44	)	)	PUNCT
cana-5712	278	45	,	,	PUNCT
cana-5712	278	46	…	…	PUNCT
cana-5712	278	47	…	…	PUNCT
cana-5712	278	48	.	.	PUNCT
cana-5712	278	49	,	,	PUNCT
cana-5712	278	50	(	(	PUNCT
cana-5712	278	51	lq	lq	INTJ
cana-5712	278	52	,	,	PUNCT
cana-5712	278	53	1	1	NUM
cana-5712	278	54	)	)	PUNCT
cana-5712	278	55	,	,	PUNCT
cana-5712	278	56	(	(	PUNCT
cana-5712	278	57	μ	μ	NOUN
cana-5712	278	58	2	2	NUM
cana-5712	278	59	−	−	PROPN
cana-5712	278	60	η	η	PROPN
cana-5712	278	61	2	2	NUM
cana-5712	278	62	−	−	NOUN
cana-5712	278	63	ν	ν	NOUN
cana-5712	278	64	2	2	NUM
cana-5712	278	65	+	+	CCONJ
cana-5712	278	66	1	1	NUM
cana-5712	278	67	,	,	PUNCT
cana-5712	278	68	ξ	ξ	PROPN
cana-5712	278	69	2	2	NUM
cana-5712	278	70	)	)	PUNCT
cana-5712	278	71	(	(	PUNCT
cana-5712	278	72	μ	μ	PROPN
cana-5712	278	73	2	2	NUM
cana-5712	278	74	+	+	SYM
cana-5712	278	75	η	η	PROPN
cana-5712	278	76	2	2	NUM
cana-5712	278	77	−	−	NOUN
cana-5712	278	78	ν	ν	NOUN
cana-5712	278	79	2	2	NUM
cana-5712	278	80	+	+	CCONJ
cana-5712	278	81	3	3	NUM
cana-5712	278	82	2	2	NUM
cana-5712	278	83	,	,	PUNCT
cana-5712	278	84	ξ	ξ	PROPN
cana-5712	278	85	2	2	NUM
cana-5712	278	86	)	)	PUNCT
cana-5712	278	87	;	;	PUNCT
cana-5712	279	1	z	z	X
cana-5712	279	2	]	]	PUNCT
cana-5712	279	3	’	'	PUNCT
cana-5712	279	4	corollary	corollary	ADJ
cana-5712	279	5	5	5	NUM
cana-5712	279	6	.	.	PUNCT
cana-5712	280	1	if	if	SCONJ
cana-5712	280	2	we	we	PRON
cana-5712	280	3	take	take	VERB
cana-5712	280	4	p	p	NOUN
cana-5712	280	5	=	=	NOUN
cana-5712	280	6	q	q	NOUN
cana-5712	280	7	=	=	SYM
cana-5712	280	8	0	0	NUM
cana-5712	280	9	in	in	ADP
cana-5712	280	10	theorem	theorem	NOUN
cana-5712	280	11	4	4	NUM
cana-5712	280	12	and	and	CCONJ
cana-5712	280	13	using	use	VERB
cana-5712	280	14	(	(	PUNCT
cana-5712	280	15	1.6	1.6	NUM
cana-5712	280	16	)	)	PUNCT
cana-5712	280	17	,	,	PUNCT
cana-5712	280	18	we	we	PRON
cana-5712	280	19	get	get	AUX
cana-5712	280	20	following	follow	VERB
cana-5712	280	21	result	result	NOUN
cana-5712	280	22	∫	∫	PROPN
cana-5712	281	1	u−μ(u2	u−μ(u2	PROPN
cana-5712	281	2	−	−	PROPN
cana-5712	282	1	1)−	1)−	NUM
cana-5712	282	2	ν	ν	PROPN
cana-5712	282	3	2pη	2pη	NOUN
cana-5712	282	4	ν(u	ν(u	PROPN
cana-5712	282	5	)	)	PUNCT
cana-5712	283	1	∞	∞	PROPN
cana-5712	283	2	0	0	NUM
cana-5712	283	3	eρ	eρ	PROPN
cana-5712	283	4	,	,	PUNCT
cana-5712	283	5	σ(zu−ξ)du	σ(zu−ξ)du	PROPN
cana-5712	283	6	=	=	SYM
cana-5712	283	7	1	1	NUM
cana-5712	283	8	(	(	PUNCT
cana-5712	283	9	π	π	NOUN
cana-5712	283	10	)	)	PUNCT
cana-5712	283	11	1	1	NUM
cana-5712	283	12	2	2	NUM
cana-5712	283	13	3ψ2	3ψ2	NUM
cana-5712	283	14	[	[	PUNCT
cana-5712	283	15	(	(	PUNCT
cana-5712	283	16	μ+ν+2	μ+ν+2	PROPN
cana-5712	283	17	2	2	NUM
cana-5712	283	18	,	,	PUNCT
cana-5712	283	19	ξ	ξ	PROPN
cana-5712	283	20	2	2	NUM
cana-5712	283	21	)	)	PUNCT
cana-5712	283	22	,	,	PUNCT
cana-5712	283	23	(	(	PUNCT
cana-5712	283	24	μ+ν−η−1	μ+ν−η−1	PROPN
cana-5712	283	25	2	2	NUM
cana-5712	283	26	,	,	PUNCT
cana-5712	283	27	ξ	ξ	PROPN
cana-5712	283	28	2	2	NUM
cana-5712	283	29	)	)	PUNCT
cana-5712	283	30	,	,	PUNCT
cana-5712	283	31	(	(	PUNCT
cana-5712	283	32	1,1	1,1	NUM
cana-5712	283	33	)	)	PUNCT
cana-5712	283	34	,	,	PUNCT
cana-5712	283	35	(	(	PUNCT
cana-5712	283	36	ρ	ρ	PROPN
cana-5712	283	37	,	,	PUNCT
cana-5712	283	38	σ	σ	PROPN
cana-5712	283	39	)	)	PUNCT
cana-5712	283	40	,	,	PUNCT
cana-5712	283	41	(	(	PUNCT
cana-5712	283	42	μ	μ	NOUN
cana-5712	283	43	,	,	PUNCT
cana-5712	283	44	ξ	ξ	PROPN
cana-5712	283	45	)	)	PUNCT
cana-5712	283	46	;	;	PUNCT
cana-5712	284	1	z	z	X
cana-5712	284	2	]	]	PUNCT
cana-5712	284	3	.	.	PUNCT
cana-5712	285	1	corollary	corollary	ADJ
cana-5712	285	2	6	6	NUM
cana-5712	285	3	.	.	PUNCT
cana-5712	286	1	if	if	SCONJ
cana-5712	286	2	we	we	PRON
cana-5712	286	3	take	take	VERB
cana-5712	286	4	p	p	NOUN
cana-5712	286	5	=	=	NOUN
cana-5712	286	6	0	0	NUM
cana-5712	286	7	,	,	PUNCT
cana-5712	286	8	q	q	NOUN
cana-5712	286	9	=	=	SYM
cana-5712	286	10	1	1	NUM
cana-5712	286	11	in	in	ADP
cana-5712	286	12	theorem	theorem	NOUN
cana-5712	286	13	5	5	NUM
cana-5712	286	14	and	and	CCONJ
cana-5712	286	15	using	use	VERB
cana-5712	286	16	(	(	PUNCT
cana-5712	286	17	1.8	1.8	NUM
cana-5712	286	18	)	)	PUNCT
cana-5712	286	19	,	,	PUNCT
cana-5712	286	20	we	we	PRON
cana-5712	286	21	get	get	VERB
cana-5712	286	22	communications	communication	NOUN
cana-5712	286	23	on	on	ADP
cana-5712	286	24	applied	apply	VERB
cana-5712	286	25	nonlinear	nonlinear	ADJ
cana-5712	286	26	analysis	analysis	NOUN
cana-5712	286	27	issn	issn	NOUN
cana-5712	286	28	:	:	PUNCT
cana-5712	286	29	1074	1074	NUM
cana-5712	286	30	-	-	PUNCT
cana-5712	286	31	133x	133x	NUM
cana-5712	286	32	vol	vol	VERB
cana-5712	286	33	32	32	NUM
cana-5712	286	34	no	no	NOUN
cana-5712	286	35	.	.	PUNCT
cana-5712	287	1	10s	10	NOUN
cana-5712	287	2	(	(	PUNCT
cana-5712	287	3	2025	2025	NUM
cana-5712	287	4	)	)	PUNCT
cana-5712	287	5	2721	2721	NUM
cana-5712	287	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5712	287	7	∫	∫	PROPN
cana-5712	287	8	(	(	PUNCT
cana-5712	287	9	1	1	NUM
cana-5712	287	10	−	−	PROPN
cana-5712	287	11	u	u	NOUN
cana-5712	287	12	)	)	PUNCT
cana-5712	287	13	1	1	NUM
cana-5712	287	14	2(1	2(1	NUM
cana-5712	287	15	+	+	CCONJ
cana-5712	287	16	u)μun(u	u)μun(u	X
cana-5712	287	17	)	)	PUNCT
cana-5712	287	18	1	1	NUM
cana-5712	287	19	0	0	NUM
cana-5712	287	20	wρ	wρ	PROPN
cana-5712	287	21	,	,	PUNCT
cana-5712	287	22	σ	σ	PROPN
cana-5712	287	23	(	(	PUNCT
cana-5712	287	24	z	z	PROPN
cana-5712	287	25	(	(	PUNCT
cana-5712	287	26	1+μ	1+μ	NUM
cana-5712	287	27	2	2	NUM
cana-5712	287	28	)	)	PUNCT
cana-5712	287	29	λ	λ	NOUN
cana-5712	287	30	)	)	PUNCT
cana-5712	287	31	du	du	PROPN
cana-5712	287	32	=	=	SYM
cana-5712	287	33	(	(	PUNCT
cana-5712	287	34	π	π	NOUN
cana-5712	287	35	)	)	PUNCT
cana-5712	287	36	1	1	NUM
cana-5712	287	37	22	22	NUM
cana-5712	287	38	2n+	2n+	NUM
cana-5712	287	39	3	3	NUM
cana-5712	287	40	2{(n+1)!}2	2{(n+1)!}2	NUM
cana-5712	287	41	(	(	PUNCT
cana-5712	287	42	2n+2	2n+2	PROPN
cana-5712	287	43	)	)	PUNCT
cana-5712	287	44	2ψ3	2ψ3	NOUN
cana-5712	287	45	[	[	PUNCT
cana-5712	287	46	(	(	PUNCT
cana-5712	287	47	2μ+1	2μ+1	PROPN
cana-5712	287	48	2	2	NUM
cana-5712	287	49	,	,	PUNCT
cana-5712	287	50	λ	λ	PROPN
cana-5712	287	51	)	)	PUNCT
cana-5712	287	52	,	,	PUNCT
cana-5712	287	53	(	(	PUNCT
cana-5712	287	54	μ	μ	NOUN
cana-5712	287	55	,	,	PUNCT
cana-5712	287	56	λ	λ	NOUN
cana-5712	287	57	)	)	PUNCT
cana-5712	287	58	(	(	PUNCT
cana-5712	287	59	ρ	ρ	PROPN
cana-5712	287	60	,	,	PUNCT
cana-5712	287	61	σ	σ	PROPN
cana-5712	287	62	)	)	PUNCT
cana-5712	287	63	,	,	PUNCT
cana-5712	287	64	(	(	PUNCT
cana-5712	287	65	μ	μ	NOUN
cana-5712	287	66	+	+	X
cana-5712	287	67	5	5	NUM
cana-5712	287	68	2	2	NUM
cana-5712	287	69	,	,	PUNCT
cana-5712	287	70	λ	λ	NOUN
cana-5712	287	71	)	)	PUNCT
cana-5712	287	72	,	,	PUNCT
cana-5712	287	73	(	(	PUNCT
cana-5712	287	74	μ	μ	NOUN
cana-5712	287	75	`	`	PUNCT
cana-5712	287	76	−	−	PROPN
cana-5712	287	77	n	n	NOUN
cana-5712	287	78	+	+	CCONJ
cana-5712	287	79	1	1	NUM
cana-5712	287	80	2	2	NUM
cana-5712	287	81	,	,	PUNCT
cana-5712	287	82	λ	λ	PROPN
cana-5712	287	83	)	)	PUNCT
cana-5712	287	84	;	;	PUNCT
cana-5712	288	1	z	z	X
cana-5712	288	2	]	]	PUNCT
cana-5712	288	3	.	.	PUNCT
cana-5712	289	1	corollary	corollary	ADJ
cana-5712	289	2	7	7	NUM
cana-5712	289	3	.	.	PUNCT
cana-5712	290	1	if	if	SCONJ
cana-5712	290	2	we	we	PRON
cana-5712	290	3	take	take	VERB
cana-5712	290	4	p	p	NOUN
cana-5712	290	5	=	=	NOUN
cana-5712	290	6	q	q	NOUN
cana-5712	290	7	=	=	NOUN
cana-5712	290	8	1	1	NUM
cana-5712	290	9	,	,	PUNCT
cana-5712	290	10	k=1	k=1	X
cana-5712	290	11	in	in	ADP
cana-5712	290	12	theorem	theorem	NOUN
cana-5712	290	13	8	8	NUM
cana-5712	290	14	and	and	CCONJ
cana-5712	290	15	(	(	PUNCT
cana-5712	290	16	1.7	1.7	NUM
cana-5712	290	17	)	)	PUNCT
cana-5712	290	18	,	,	PUNCT
cana-5712	290	19	we	we	PRON
cana-5712	290	20	get	get	VERB
cana-5712	290	21	∫	∫	PROPN
cana-5712	290	22	sinμϑ.	sinμϑ.	PROPN
cana-5712	290	23	cosνϑeρ	cosνϑeρ	PROPN
cana-5712	290	24	,	,	PUNCT
cana-5712	290	25	σ	σ	PROPN
cana-5712	290	26	a	a	PROPN
cana-5712	290	27	(	(	PUNCT
cana-5712	290	28	zsinμϑ.	zsinμϑ.	NOUN
cana-5712	290	29	cosνϑ)dϑ	cosνϑ)dϑ	PROPN
cana-5712	290	30	=	=	PUNCT
cana-5712	290	31	γ(l	γ(l	PROPN
cana-5712	290	32	)	)	PUNCT
cana-5712	290	33	2γ(k	2γ(k	NUM
cana-5712	290	34	)	)	PUNCT
cana-5712	290	35	3ψ2	3ψ2	NUM
cana-5712	290	36	[	[	PUNCT
cana-5712	290	37	(	(	PUNCT
cana-5712	290	38	a	a	DET
cana-5712	290	39	,	,	PUNCT
cana-5712	290	40	1	1	NUM
cana-5712	290	41	)	)	PUNCT
cana-5712	290	42	,	,	PUNCT
cana-5712	290	43	(	(	PUNCT
cana-5712	290	44	μ+1	μ+1	NUM
cana-5712	290	45	2	2	NUM
cana-5712	290	46	,	,	PUNCT
cana-5712	290	47	η	η	PROPN
cana-5712	290	48	2	2	NUM
cana-5712	290	49	)	)	PUNCT
cana-5712	290	50	(	(	PUNCT
cana-5712	290	51	ν+1	ν+1	PROPN
cana-5712	290	52	2	2	NUM
cana-5712	290	53	,	,	PUNCT
cana-5712	290	54	ξ	ξ	PROPN
cana-5712	290	55	2	2	NUM
cana-5712	290	56	)	)	PUNCT
cana-5712	290	57	(	(	PUNCT
cana-5712	290	58	ρ	ρ	PROPN
cana-5712	290	59	,	,	PUNCT
cana-5712	290	60	σ	σ	PROPN
cana-5712	290	61	)	)	PUNCT
cana-5712	290	62	,	,	PUNCT
cana-5712	290	63	(	(	PUNCT
cana-5712	290	64	μ+ν	μ+ν	NUM
cana-5712	290	65	2	2	NUM
cana-5712	290	66	,	,	PUNCT
cana-5712	290	67	η+ξ	η+ξ	NUM
cana-5712	290	68	2	2	NUM
cana-5712	290	69	)	)	PUNCT
cana-5712	290	70	;	;	PUNCT
cana-5712	291	1	z	z	X
cana-5712	291	2	]	]	X
cana-5712	291	3	π	π	PROPN
cana-5712	291	4	2	2	NUM
cana-5712	291	5	0	0	NUM
cana-5712	291	6	.	.	PUNCT
cana-5712	292	1	corollary	corollary	ADJ
cana-5712	292	2	8	8	NUM
cana-5712	292	3	.	.	PUNCT
cana-5712	293	1	if	if	SCONJ
cana-5712	293	2	we	we	PRON
cana-5712	293	3	take	take	VERB
cana-5712	293	4	p	p	NOUN
cana-5712	293	5	=	=	NOUN
cana-5712	293	6	q	q	NOUN
cana-5712	293	7	=	=	NOUN
cana-5712	293	8	0	0	X
cana-5712	293	9	.	.	PUNCT
cana-5712	294	1	in	in	ADP
cana-5712	294	2	theorem	theorem	NOUN
cana-5712	294	3	9	9	NUM
cana-5712	294	4	and	and	CCONJ
cana-5712	294	5	using	use	VERB
cana-5712	294	6	(	(	PUNCT
cana-5712	294	7	1.6	1.6	NUM
cana-5712	294	8	)	)	PUNCT
cana-5712	294	9	,	,	PUNCT
cana-5712	294	10	we	we	PRON
cana-5712	294	11	get	get	VERB
cana-5712	294	12	∫	∫	PROPN
cana-5712	294	13	𝑢𝜇−1𝑒−	𝑢𝜇−1𝑒−	PROPN
cana-5712	294	14	𝑎𝑢	𝑎𝑢	PRON
cana-5712	294	15	2	2	NUM
cana-5712	294	16	𝑊𝜂,𝑣(𝑎𝑢)𝐸𝜌,𝜎(𝑧𝑢𝜉	𝑊𝜂,𝑣(𝑎𝑢)𝐸𝜌,𝜎(𝑧𝑢𝜉	NUM
cana-5712	294	17	)	)	PUNCT
cana-5712	295	1	∞	∞	NOUN
cana-5712	295	2	0	0	NUM
cana-5712	296	1	𝑑𝑢	𝑑𝑢	NOUN
cana-5712	297	1	=	=	NOUN
cana-5712	297	2	𝑎𝜇	𝑎𝜇	PROPN
cana-5712	297	3	3𝛹2	3𝛹2	NUM
cana-5712	297	4	[	[	PUNCT
cana-5712	297	5	(	(	PUNCT
cana-5712	297	6	𝜇	𝜇	X
cana-5712	297	7	+	+	X
cana-5712	297	8	𝜈	𝜈	X
cana-5712	297	9	+	+	CCONJ
cana-5712	297	10	1	1	NUM
cana-5712	297	11	2	2	NUM
cana-5712	297	12	,	,	PUNCT
cana-5712	297	13	𝜉	𝜉	NOUN
cana-5712	297	14	)	)	PUNCT
cana-5712	297	15	,	,	PUNCT
cana-5712	297	16	(	(	PUNCT
cana-5712	297	17	𝜇	𝜇	ADP
cana-5712	297	18	−	−	ADP
cana-5712	297	19	𝜈	𝜈	X
cana-5712	297	20	+	+	CCONJ
cana-5712	297	21	1	1	NUM
cana-5712	297	22	2	2	NUM
cana-5712	297	23	,	,	PUNCT
cana-5712	297	24	ξ	ξ	NOUN
cana-5712	297	25	)	)	PUNCT
cana-5712	297	26	,	,	PUNCT
cana-5712	297	27	(	(	PUNCT
cana-5712	297	28	1,1	1,1	NUM
cana-5712	297	29	)	)	PUNCT
cana-5712	297	30	(	(	PUNCT
cana-5712	297	31	𝜌	𝜌	X
cana-5712	297	32	,	,	PUNCT
cana-5712	297	33	𝜎	𝜎	NOUN
cana-5712	297	34	)	)	PUNCT
cana-5712	297	35	,	,	PUNCT
cana-5712	297	36	(	(	PUNCT
cana-5712	297	37	𝜇	𝜇	ADP
cana-5712	297	38	−	−	PROPN
cana-5712	297	39	𝑘	𝑘	PROPN
cana-5712	297	40	+	+	NOUN
cana-5712	297	41	1	1	NUM
cana-5712	297	42	,	,	PUNCT
cana-5712	297	43	𝜉	𝜉	NOUN
cana-5712	297	44	)	)	PUNCT
cana-5712	297	45	;	;	PUNCT
cana-5712	297	46	z	z	X
cana-5712	297	47	/	/	SYM
cana-5712	297	48	aξ	aξ	VERB
cana-5712	297	49	]	]	X
cana-5712	297	50	4	4	NUM
cana-5712	297	51	.	.	X
cana-5712	297	52	conclusion	conclusion	NOUN
cana-5712	297	53	remark	remark	NOUN
cana-5712	297	54	in	in	ADP
cana-5712	297	55	this	this	DET
cana-5712	297	56	investigation	investigation	NOUN
cana-5712	297	57	,	,	PUNCT
cana-5712	297	58	we	we	PRON
cana-5712	297	59	have	have	AUX
cana-5712	297	60	managed	manage	VERB
cana-5712	297	61	to	to	PART
cana-5712	297	62	obtain	obtain	VERB
cana-5712	297	63	new	new	ADJ
cana-5712	297	64	forms	form	NOUN
cana-5712	297	65	for	for	ADP
cana-5712	297	66	the	the	DET
cana-5712	297	67	eulerian	eulerian	ADJ
cana-5712	297	68	type	type	NOUN
cana-5712	297	69	integrals	integral	NOUN
cana-5712	297	70	that	that	PRON
cana-5712	297	71	are	be	AUX
cana-5712	297	72	associated	associate	VERB
cana-5712	297	73	with	with	ADP
cana-5712	297	74	the	the	DET
cana-5712	297	75	generalized	generalized	ADJ
cana-5712	297	76	m	m	PROPN
cana-5712	297	77	-	-	PUNCT
cana-5712	297	78	series	series	NOUN
cana-5712	297	79	,	,	PUNCT
cana-5712	297	80	which	which	PRON
cana-5712	297	81	in	in	ADP
cana-5712	297	82	turn	turn	NOUN
cana-5712	297	83	has	have	AUX
cana-5712	297	84	enriched	enrich	VERB
cana-5712	297	85	the	the	DET
cana-5712	297	86	theory	theory	NOUN
cana-5712	297	87	of	of	ADP
cana-5712	297	88	the	the	DET
cana-5712	297	89	special	special	ADJ
cana-5712	297	90	functions	function	NOUN
cana-5712	297	91	.	.	PUNCT
cana-5712	298	1	the	the	DET
cana-5712	298	2	integral	integral	ADJ
cana-5712	298	3	expressions	expression	NOUN
cana-5712	298	4	derived	derive	VERB
cana-5712	298	5	not	not	PART
cana-5712	298	6	only	only	ADV
cana-5712	298	7	extend	extend	VERB
cana-5712	298	8	our	our	PRON
cana-5712	298	9	knowledge	knowledge	NOUN
cana-5712	298	10	of	of	ADP
cana-5712	298	11	the	the	DET
cana-5712	298	12	structural	structural	ADJ
cana-5712	298	13	properties	property	NOUN
cana-5712	298	14	of	of	ADP
cana-5712	298	15	the	the	DET
cana-5712	298	16	generalised	generalise	VERB
cana-5712	298	17	m	m	PROPN
cana-5712	298	18	-	-	PUNCT
cana-5712	298	19	series	series	NOUN
cana-5712	298	20	,	,	PUNCT
cana-5712	298	21	but	but	CCONJ
cana-5712	298	22	also	also	ADV
cana-5712	298	23	reveal	reveal	VERB
cana-5712	298	24	the	the	DET
cana-5712	298	25	flexibility	flexibility	NOUN
cana-5712	298	26	by	by	ADP
cana-5712	298	27	analysing	analyse	VERB
cana-5712	298	28	special	special	ADJ
cana-5712	298	29	cases	case	NOUN
cana-5712	298	30	involving	involve	VERB
cana-5712	298	31	special	special	ADJ
cana-5712	298	32	parameter	parameter	NOUN
cana-5712	298	33	values	value	NOUN
cana-5712	298	34	.	.	PUNCT
cana-5712	299	1	these	these	DET
cana-5712	299	2	results	result	NOUN
cana-5712	299	3	offer	offer	VERB
cana-5712	299	4	opportunities	opportunity	NOUN
cana-5712	299	5	for	for	ADP
cana-5712	299	6	possible	possible	ADJ
cana-5712	299	7	applications	application	NOUN
cana-5712	299	8	in	in	ADP
cana-5712	299	9	a	a	DET
cana-5712	299	10	broad	broad	ADJ
cana-5712	299	11	range	range	NOUN
cana-5712	299	12	of	of	ADP
cana-5712	299	13	disciplines	discipline	NOUN
cana-5712	299	14	such	such	ADJ
cana-5712	299	15	as	as	ADP
cana-5712	299	16	mathematical	mathematical	ADJ
cana-5712	299	17	physics	physics	NOUN
cana-5712	299	18	,	,	PUNCT
cana-5712	299	19	engineering	engineering	NOUN
cana-5712	299	20	,	,	PUNCT
cana-5712	299	21	and	and	CCONJ
cana-5712	299	22	applied	applied	ADJ
cana-5712	299	23	mathematics	mathematic	NOUN
cana-5712	299	24	.	.	PUNCT
cana-5712	300	1	future	future	ADJ
cana-5712	300	2	research	research	NOUN
cana-5712	300	3	may	may	AUX
cana-5712	300	4	explore	explore	VERB
cana-5712	300	5	further	further	ADJ
cana-5712	300	6	generalizations	generalization	NOUN
cana-5712	300	7	and	and	CCONJ
cana-5712	300	8	applications	application	NOUN
cana-5712	300	9	of	of	ADP
cana-5712	300	10	these	these	DET
cana-5712	300	11	integrals	integral	NOUN
cana-5712	300	12	in	in	ADP
cana-5712	300	13	solving	solve	VERB
cana-5712	300	14	complex	complex	ADJ
cana-5712	300	15	problems	problem	NOUN
cana-5712	300	16	across	across	ADP
cana-5712	300	17	different	different	ADJ
cana-5712	300	18	scientific	scientific	ADJ
cana-5712	300	19	disciplines	discipline	NOUN
cana-5712	300	20	.	.	PUNCT
cana-5712	301	1	we	we	PRON
cana-5712	301	2	concluded	conclude	VERB
cana-5712	301	3	from	from	ADP
cana-5712	301	4	the	the	DET
cana-5712	301	5	present	present	ADJ
cana-5712	301	6	research	research	NOUN
cana-5712	301	7	work	work	NOUN
cana-5712	301	8	by	by	ADP
cana-5712	301	9	giving	give	VERB
cana-5712	301	10	some	some	DET
cana-5712	301	11	comments	comment	NOUN
cana-5712	301	12	on	on	ADP
cana-5712	301	13	the	the	DET
cana-5712	301	14	results	result	NOUN
cana-5712	301	15	of	of	ADP
cana-5712	301	16	theorem	theorem	ADJ
cana-5712	301	17	1	1	NUM
cana-5712	301	18	-	-	PUNCT
cana-5712	301	19	theorem	theorem	ADJ
cana-5712	301	20	9and	9and	PROPN
cana-5712	301	21	their	their	PRON
cana-5712	301	22	corollaries	corollary	NOUN
cana-5712	301	23	.	.	PUNCT
cana-5712	302	1	the	the	DET
cana-5712	302	2	integrals	integral	NOUN
cana-5712	302	3	can	can	AUX
cana-5712	302	4	be	be	AUX
cana-5712	302	5	further	far	ADV
cana-5712	302	6	generalized	generalize	VERB
cana-5712	302	7	and	and	CCONJ
cana-5712	302	8	applied	apply	VERB
cana-5712	302	9	in	in	ADP
cana-5712	302	10	solving	solve	VERB
cana-5712	302	11	some	some	DET
cana-5712	302	12	long	long	ADV
cana-5712	302	13	-	-	PUNCT
cana-5712	302	14	standing	stand	VERB
cana-5712	302	15	problems	problem	NOUN
cana-5712	302	16	in	in	ADP
cana-5712	302	17	that	that	PRON
cana-5712	302	18	has	have	AUX
cana-5712	302	19	been	be	AUX
cana-5712	302	20	presented	present	VERB
cana-5712	302	21	in	in	ADP
cana-5712	302	22	this	this	DET
cana-5712	302	23	letter	letter	NOUN
cana-5712	302	24	.	.	PUNCT
cana-5712	303	1	we	we	PRON
cana-5712	303	2	ended	end	VERB
cana-5712	303	3	present	present	ADJ
cana-5712	303	4	research	research	NOUN
cana-5712	303	5	work	work	NOUN
cana-5712	303	6	with	with	ADP
cana-5712	303	7	comments	comment	NOUN
cana-5712	303	8	of	of	ADP
cana-5712	303	9	theorem	theorem	NOUN
cana-5712	303	10	1theorem	1theorem	NUM
cana-5712	303	11	9and	9and	PROPN
cana-5712	303	12	their	their	PRON
cana-5712	303	13	corollaries	corollary	NOUN
cana-5712	303	14	.	.	PUNCT
cana-5712	304	1	the	the	DET
cana-5712	304	2	proposed	propose	VERB
cana-5712	304	3	generalized	generalize	VERB
cana-5712	304	4	m	m	PROPN
cana-5712	304	5	-	-	PUNCT
cana-5712	304	6	series	series	NOUN
cana-5712	304	7	is	be	AUX
cana-5712	304	8	an	an	DET
cana-5712	304	9	interesting	interesting	ADJ
cana-5712	304	10	function	function	NOUN
cana-5712	304	11	which	which	PRON
cana-5712	304	12	is	be	AUX
cana-5712	304	13	equivalent	equivalent	ADJ
cana-5712	304	14	to	to	ADP
cana-5712	304	15	one	one	NUM
cana-5712	304	16	of	of	ADP
cana-5712	304	17	the	the	DET
cana-5712	304	18	several	several	ADJ
cana-5712	304	19	families	family	NOUN
cana-5712	304	20	of	of	ADP
cana-5712	304	21	transcendental	transcendental	ADJ
cana-5712	304	22	and	and	CCONJ
cana-5712	304	23	special	special	ADJ
cana-5712	304	24	functions	function	NOUN
cana-5712	304	25	namely	namely	ADV
cana-5712	304	26	exponential	exponential	ADJ
cana-5712	304	27	function	function	NOUN
cana-5712	304	28	,	,	PUNCT
cana-5712	304	29	binomial	binomial	ADJ
cana-5712	304	30	series	series	NOUN
cana-5712	304	31	,	,	PUNCT
cana-5712	304	32	cosine	cosine	NOUN
cana-5712	304	33	function	function	NOUN
cana-5712	304	34	,	,	PUNCT
cana-5712	304	35	sine	sine	ADJ
cana-5712	304	36	function	function	NOUN
cana-5712	304	37	,	,	PUNCT
cana-5712	304	38	mittag	mittag	ADJ
cana-5712	304	39	-	-	PUNCT
cana-5712	304	40	leffer	leffer	NOUN
cana-5712	304	41	function	function	NOUN
cana-5712	304	42	,	,	PUNCT
cana-5712	304	43	wright	wright	PROPN
cana-5712	304	44	function	function	PROPN
cana-5712	304	45	,	,	PUNCT
cana-5712	304	46	gauss	gauss	ADJ
cana-5712	304	47	hypergeometric	hypergeometric	ADJ
cana-5712	304	48	function	function	NOUN
cana-5712	304	49	,	,	PUNCT
cana-5712	304	50	fox	fox	NOUN
cana-5712	304	51	-	-	PUNCT
cana-5712	304	52	h	h	NOUN
cana-5712	304	53	function	function	NOUN
cana-5712	304	54	and	and	CCONJ
cana-5712	304	55	meijer	meijer	NOUN
cana-5712	304	56	g	g	NOUN
cana-5712	304	57	-	-	PUNCT
cana-5712	304	58	function	function	NOUN
cana-5712	304	59	which	which	PRON
cana-5712	304	60	appears	appear	VERB
cana-5712	304	61	to	to	PART
cana-5712	304	62	be	be	AUX
cana-5712	304	63	new	new	ADJ
cana-5712	304	64	even	even	ADV
cana-5712	304	65	in	in	ADP
cana-5712	304	66	the	the	DET
cana-5712	304	67	case	case	NOUN
cana-5712	304	68	of	of	ADP
cana-5712	304	69	special	special	ADJ
cana-5712	304	70	cases	case	NOUN
cana-5712	304	71	.	.	PUNCT
cana-5712	305	1	thus	thus	ADV
cana-5712	305	2	,	,	PUNCT
cana-5712	305	3	we	we	PRON
cana-5712	305	4	can	can	AUX
cana-5712	305	5	deduce	deduce	VERB
cana-5712	305	6	more	more	ADV
cana-5712	305	7	useful	useful	ADJ
cana-5712	305	8	results	result	NOUN
cana-5712	305	9	and	and	CCONJ
cana-5712	305	10	their	their	PRON
cana-5712	305	11	equivalent	equivalent	ADJ
cana-5712	305	12	forms	form	NOUN
cana-5712	305	13	from	from	ADP
cana-5712	305	14	theorem	theorem	ADJ
cana-5712	305	15	1	1	NUM
cana-5712	305	16	to	to	PART
cana-5712	305	17	theorem	theorem	VERB
cana-5712	305	18	9	9	NUM
cana-5712	305	19	in	in	ADP
cana-5712	305	20	terms	term	NOUN
cana-5712	305	21	of	of	ADP
cana-5712	305	22	fox	fox	PROPN
cana-5712	305	23	h	h	NOUN
cana-5712	305	24	-	-	PUNCT
cana-5712	305	25	function	function	NOUN
cana-5712	305	26	and	and	CCONJ
cana-5712	305	27	meijer	meijer	NOUN
cana-5712	305	28	g	g	NOUN
cana-5712	305	29	-	-	PUNCT
cana-5712	305	30	function	function	NOUN
cana-5712	305	31	.	.	PUNCT
cana-5712	306	1	acknowledgement	acknowledgement	NOUN
cana-5712	306	2	:	:	PUNCT
cana-5712	306	3	all	all	DET
cana-5712	306	4	authors	author	NOUN
cana-5712	306	5	would	would	AUX
cana-5712	306	6	like	like	VERB
cana-5712	306	7	to	to	ADP
cana-5712	306	8	thanks	thanks	NUM
cana-5712	306	9	integral	integral	ADJ
cana-5712	306	10	university	university	NOUN
cana-5712	306	11	,	,	PUNCT
cana-5712	306	12	lucknow	lucknow	PROPN
cana-5712	306	13	,	,	PUNCT
cana-5712	306	14	india	india	PROPN
cana-5712	306	15	for	for	ADP
cana-5712	306	16	providing	provide	VERB
cana-5712	306	17	the	the	DET
cana-5712	306	18	manuscript	manuscript	NOUN
cana-5712	306	19	(	(	PUNCT
cana-5712	306	20	mcn	mcn	PROPN
cana-5712	306	21	):	):	PUNCT
cana-5712	306	22	iu	iu	PROPN
cana-5712	306	23	/	/	SYM
cana-5712	306	24	r&d/2025	r&d/2025	NOUN
cana-5712	306	25	-	-	PUNCT
cana-5712	306	26	mcn0003703	mcn0003703	NOUN
cana-5712	306	27	for	for	ADP
cana-5712	306	28	this	this	DET
cana-5712	306	29	work	work	NOUN
cana-5712	306	30	.	.	PUNCT
cana-5712	307	1	conflict	conflict	NOUN
cana-5712	307	2	of	of	ADP
cana-5712	307	3	interest	interest	NOUN
cana-5712	307	4	:	:	PUNCT
cana-5712	307	5	the	the	DET
cana-5712	307	6	authors	author	NOUN
cana-5712	307	7	declare	declare	VERB
cana-5712	307	8	that	that	SCONJ
cana-5712	307	9	there	there	PRON
cana-5712	307	10	is	be	VERB
cana-5712	307	11	no	no	DET
cana-5712	307	12	conflict	conflict	NOUN
cana-5712	307	13	of	of	ADP
cana-5712	307	14	interest	interest	NOUN
cana-5712	307	15	.	.	PUNCT
cana-5712	308	1	references	reference	NOUN
cana-5712	308	2	[	[	X
cana-5712	308	3	1	1	NUM
cana-5712	308	4	]	]	PUNCT
cana-5712	308	5	a.	a.	NOUN
cana-5712	308	6	erdelyi	erdelyi	NOUN
cana-5712	308	7	,	,	PUNCT
cana-5712	308	8	transformation	transformation	NOUN
cana-5712	308	9	of	of	ADP
cana-5712	308	10	hypergeometric	hypergeometric	ADJ
cana-5712	308	11	function	function	NOUN
cana-5712	308	12	of	of	ADP
cana-5712	308	13	two	two	NUM
cana-5712	308	14	variables	variable	NOUN
cana-5712	308	15	,	,	PUNCT
cana-5712	308	16	proc	proc	NOUN
cana-5712	308	17	.	.	PUNCT
cana-5712	309	1	roy	roy	PROPN
cana-5712	309	2	.	.	PROPN
cana-5712	309	3	soc	soc	PROPN
cana-5712	309	4	.	.	PUNCT
cana-5712	310	1	edinburg	edinburg	PROPN
cana-5712	310	2	a	a	PRON
cana-5712	310	3	,	,	PUNCT
cana-5712	310	4	62	62	NUM
cana-5712	310	5	,	,	PUNCT
cana-5712	310	6	378	378	NUM
cana-5712	310	7	-	-	SYM
cana-5712	310	8	385	385	NUM
cana-5712	310	9	,	,	PUNCT
cana-5712	310	10	1948	1948	NUM
cana-5712	310	11	.	.	PUNCT
cana-5712	311	1	communications	communication	NOUN
cana-5712	311	2	on	on	ADP
cana-5712	311	3	applied	apply	VERB
cana-5712	311	4	nonlinear	nonlinear	ADJ
cana-5712	311	5	analysis	analysis	NOUN
cana-5712	311	6	issn	issn	NOUN
cana-5712	311	7	:	:	PUNCT
cana-5712	311	8	1074	1074	NUM
cana-5712	311	9	-	-	PUNCT
cana-5712	311	10	133x	133x	NUM
cana-5712	311	11	vol	vol	VERB
cana-5712	311	12	32	32	NUM
cana-5712	311	13	no	no	NOUN
cana-5712	311	14	.	.	PUNCT
cana-5712	312	1	10s	10	NOUN
cana-5712	312	2	(	(	PUNCT
cana-5712	312	3	2025	2025	NUM
cana-5712	312	4	)	)	PUNCT
cana-5712	312	5	2722	2722	NUM
cana-5712	312	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5712	313	1	[	[	X
cana-5712	313	2	2	2	NUM
cana-5712	313	3	]	]	PUNCT
cana-5712	313	4	m.	m.	NOUN
cana-5712	313	5	kamarujjama	kamarujjama	PROPN
cana-5712	313	6	,	,	PUNCT
cana-5712	313	7	o.	o.	PROPN
cana-5712	313	8	khan	khan	PROPN
cana-5712	313	9	,	,	PUNCT
cana-5712	313	10	computation	computation	NOUN
cana-5712	313	11	of	of	ADP
cana-5712	313	12	new	new	ADJ
cana-5712	313	13	class	class	NOUN
cana-5712	313	14	of	of	ADP
cana-5712	313	15	integrals	integral	NOUN
cana-5712	313	16	involving	involve	VERB
cana-5712	313	17	generalized	generalized	ADJ
cana-5712	313	18	galue	galue	ADJ
cana-5712	313	19	type	type	NOUN
cana-5712	313	20	struve	struve	PROPN
cana-5712	313	21	function	function	NOUN
cana-5712	313	22	,	,	PUNCT
cana-5712	313	23	j.	j.	PROPN
cana-5712	313	24	comput	comput	PROPN
cana-5712	313	25	.	.	PUNCT
cana-5712	314	1	appl	appl	PROPN
cana-5712	314	2	.	.	PROPN
cana-5712	314	3	math	math	PROPN
cana-5712	314	4	.	.	PUNCT
cana-5712	315	1	,	,	PUNCT
cana-5712	315	2	351	351	NUM
cana-5712	315	3	(	(	PUNCT
cana-5712	315	4	2019	2019	NUM
cana-5712	315	5	)	)	PUNCT
cana-5712	315	6	228	228	NUM
cana-5712	315	7	-	-	SYM
cana-5712	315	8	236	236	NUM
cana-5712	315	9	.	.	PUNCT
cana-5712	316	1	[	[	X
cana-5712	316	2	3	3	X
cana-5712	316	3	]	]	X
cana-5712	316	4	n.	n.	PROPN
cana-5712	316	5	u.	u.	PROPN
cana-5712	316	6	khan	khan	PROPN
cana-5712	316	7	,	,	PUNCT
cana-5712	316	8	m.	m.	PROPN
cana-5712	316	9	iqbal	iqbal	PROPN
cana-5712	316	10	khan	khan	PROPN
cana-5712	316	11	,	,	PUNCT
cana-5712	316	12	o.	o.	PROPN
cana-5712	316	13	khan	khan	PROPN
cana-5712	316	14	,	,	PUNCT
cana-5712	316	15	certain	certain	ADJ
cana-5712	316	16	finite	finite	ADJ
cana-5712	316	17	integrals	integral	NOUN
cana-5712	316	18	involving	involve	VERB
cana-5712	316	19	generalized	generalize	VERB
cana-5712	316	20	wright	wright	PROPN
cana-5712	316	21	function	function	NOUN
cana-5712	316	22	,	,	PUNCT
cana-5712	316	23	advanced	advanced	ADJ
cana-5712	316	24	mathematical	mathematical	ADJ
cana-5712	316	25	models	model	NOUN
cana-5712	316	26	&	&	CCONJ
cana-5712	316	27	applications	application	NOUN
cana-5712	316	28	,	,	PUNCT
cana-5712	316	29	6	6	NUM
cana-5712	316	30	,	,	PUNCT
cana-5712	316	31	(	(	PUNCT
cana-5712	316	32	3	3	NUM
cana-5712	316	33	)	)	PUNCT
cana-5712	316	34	,	,	PUNCT
cana-5712	316	35	(	(	PUNCT
cana-5712	316	36	2021	2021	NUM
cana-5712	316	37	)	)	PUNCT
cana-5712	316	38	,	,	PUNCT
cana-5712	316	39	292301	292301	NUM
cana-5712	316	40	[	[	X
cana-5712	316	41	4	4	NUM
cana-5712	316	42	]	]	X
cana-5712	316	43	n.	n.	PROPN
cana-5712	316	44	khan	khan	PROPN
cana-5712	316	45	,	,	PUNCT
cana-5712	316	46	s.	s.	PROPN
cana-5712	316	47	husain	husain	PROPN
cana-5712	316	48	,	,	PUNCT
cana-5712	316	49	o.	o.	PROPN
cana-5712	316	50	khan	khan	PROPN
cana-5712	316	51	,	,	PUNCT
cana-5712	316	52	a	a	DET
cana-5712	316	53	novel	novel	ADJ
cana-5712	316	54	kind	kind	NOUN
cana-5712	316	55	of	of	ADP
cana-5712	316	56	beta	beta	ADJ
cana-5712	316	57	logarithmic	logarithmic	ADJ
cana-5712	316	58	function	function	NOUN
cana-5712	316	59	and	and	CCONJ
cana-5712	316	60	their	their	PRON
cana-5712	316	61	properties	property	NOUN
cana-5712	316	62	,	,	PUNCT
cana-5712	316	63	hacet	hacet	PROPN
cana-5712	316	64	.	.	PUNCT
cana-5712	317	1	j.	j.	PROPN
cana-5712	317	2	math	math	PROPN
cana-5712	317	3	.	.	PUNCT
cana-5712	318	1	stat	stat	PROPN
cana-5712	318	2	.	.	PUNCT
cana-5712	319	1	52	52	NUM
cana-5712	319	2	(	(	PUNCT
cana-5712	319	3	4	4	NUM
cana-5712	319	4	)	)	PUNCT
cana-5712	319	5	(	(	PUNCT
cana-5712	319	6	2023	2023	NUM
cana-5712	319	7	)	)	PUNCT
cana-5712	319	8	,	,	PUNCT
cana-5712	320	1	945–955	945–955	NUM
cana-5712	320	2	[	[	X
cana-5712	320	3	5	5	X
cana-5712	320	4	]	]	X
cana-5712	320	5	o.	o.	PROPN
cana-5712	320	6	khan	khan	PROPN
cana-5712	320	7	,	,	PUNCT
cana-5712	320	8	m.	m.	NOUN
cana-5712	320	9	kamarujjama	kamarujjama	PROPN
cana-5712	320	10	,	,	PUNCT
cana-5712	320	11	n.u	n.u	PROPN
cana-5712	320	12	.	.	PROPN
cana-5712	320	13	khan	khan	PROPN
cana-5712	320	14	,	,	PUNCT
cana-5712	320	15	d.	d.	PROPN
cana-5712	320	16	baleanu	baleanu	PROPN
cana-5712	320	17	,	,	PUNCT
cana-5712	320	18	k.s	k.s	PROPN
cana-5712	320	19	.	.	PROPN
cana-5712	320	20	nisar	nisar	PROPN
cana-5712	320	21	,	,	PUNCT
cana-5712	320	22	computable	computable	ADJ
cana-5712	320	23	solution	solution	NOUN
cana-5712	320	24	of	of	ADP
cana-5712	320	25	fractional	fractional	ADJ
cana-5712	320	26	kinetic	kinetic	ADJ
cana-5712	320	27	equations	equation	NOUN
cana-5712	320	28	using	use	VERB
cana-5712	320	29	mathieu	mathieu	NOUN
cana-5712	320	30	-	-	PUNCT
cana-5712	320	31	type	type	NOUN
cana-5712	320	32	series	series	NOUN
cana-5712	320	33	,	,	PUNCT
cana-5712	320	34	adv	adv	PROPN
cana-5712	320	35	.	.	PROPN
cana-5712	320	36	differ	differ	VERB
cana-5712	320	37	equ	equ	PROPN
cana-5712	320	38	.	.	PROPN
cana-5712	320	39	2019	2019	NUM
cana-5712	320	40	,	,	PUNCT
cana-5712	320	41	234	234	NUM
cana-5712	320	42	(	(	PUNCT
cana-5712	320	43	2019	2019	NUM
cana-5712	320	44	)	)	PUNCT
cana-5712	320	45	.	.	PUNCT
cana-5712	321	1	[	[	X
cana-5712	321	2	6	6	NUM
cana-5712	321	3	]	]	PUNCT
cana-5712	321	4	e.	e.	PROPN
cana-5712	321	5	ilhan	ilhan	PROPN
cana-5712	321	6	and	and	CCONJ
cana-5712	321	7	i.o	i.o	PROPN
cana-5712	321	8	.	.	PROPN
cana-5712	321	9	kiymaz	kiymaz	PROPN
cana-5712	321	10	,	,	PUNCT
cana-5712	321	11	a	a	DET
cana-5712	321	12	generalization	generalization	NOUN
cana-5712	321	13	of	of	ADP
cana-5712	321	14	truncated	truncated	ADJ
cana-5712	321	15	m	m	PROPN
cana-5712	321	16	-	-	PUNCT
cana-5712	321	17	fractional	fractional	ADJ
cana-5712	321	18	derivatives	derivative	NOUN
cana-5712	321	19	and	and	CCONJ
cana-5712	321	20	applications	application	NOUN
cana-5712	321	21	to	to	ADP
cana-5712	321	22	fractional	fractional	ADJ
cana-5712	321	23	differential	differential	ADJ
cana-5712	321	24	equation	equation	NOUN
cana-5712	321	25	,	,	PUNCT
cana-5712	321	26	appl	appl	PROPN
cana-5712	321	27	.	.	PROPN
cana-5712	321	28	math	math	PROPN
cana-5712	321	29	.	.	PUNCT
cana-5712	322	1	nonlinear	nonlinear	PROPN
cana-5712	322	2	sci	sci	PROPN
cana-5712	322	3	.	.	PROPN
cana-5712	322	4	,	,	PUNCT
cana-5712	322	5	5	5	NUM
cana-5712	322	6	(	(	PUNCT
cana-5712	322	7	1	1	NUM
cana-5712	322	8	)	)	PUNCT
cana-5712	322	9	(	(	PUNCT
cana-5712	322	10	2020	2020	NUM
cana-5712	322	11	)	)	PUNCT
cana-5712	322	12	,	,	PUNCT
cana-5712	322	13	pp	pp	PROPN
cana-5712	322	14	.	.	PUNCT
cana-5712	323	1	171	171	NUM
cana-5712	323	2	-	-	SYM
cana-5712	323	3	188	188	NUM
cana-5712	323	4	.	.	PUNCT
cana-5712	324	1	[	[	X
cana-5712	324	2	7	7	X
cana-5712	324	3	]	]	X
cana-5712	324	4	e.d	e.d	PROPN
cana-5712	324	5	.	.	PROPN
cana-5712	324	6	,rainville,:special	,rainville,:special	ADJ
cana-5712	324	7	functions	function	NOUN
cana-5712	324	8	,	,	PUNCT
cana-5712	324	9	the	the	DET
cana-5712	324	10	macmillan	macmillan	PROPN
cana-5712	324	11	company	company	PROPN
cana-5712	324	12	,	,	PUNCT
cana-5712	324	13	new	new	PROPN
cana-5712	324	14	york	york	PROPN
cana-5712	324	15	,	,	PUNCT
cana-5712	324	16	2013	2013	NUM
cana-5712	324	17	.	.	PUNCT
cana-5712	325	1	[	[	X
cana-5712	325	2	8	8	NUM
cana-5712	325	3	]	]	PUNCT
cana-5712	325	4	m.	m.	NOUN
cana-5712	325	5	kamarujjama	kamarujjama	PROPN
cana-5712	325	6	,	,	PUNCT
cana-5712	325	7	n.	n.	PROPN
cana-5712	325	8	u.	u.	PROPN
cana-5712	325	9	khan	khan	PROPN
cana-5712	325	10	,	,	PUNCT
cana-5712	325	11	o.	o.	PROPN
cana-5712	325	12	khan	khan	PROPN
cana-5712	325	13	,	,	PUNCT
cana-5712	325	14	juan	juan	PROPN
cana-5712	325	15	j.	j.	PROPN
cana-5712	325	16	nieto	nieto	PROPN
cana-5712	325	17	,	,	PUNCT
cana-5712	325	18	extended	extend	VERB
cana-5712	325	19	type	type	NOUN
cana-5712	325	20	k	k	NOUN
cana-5712	325	21	-	-	ADJ
cana-5712	325	22	mittag	mittag	ADJ
cana-5712	325	23	–	–	PUNCT
cana-5712	325	24	leffler	leffler	NOUN
cana-5712	325	25	function	function	NOUN
cana-5712	325	26	and	and	CCONJ
cana-5712	325	27	its	its	PRON
cana-5712	325	28	applications	application	NOUN
cana-5712	325	29	,	,	PUNCT
cana-5712	325	30	int	int	NOUN
cana-5712	325	31	.	.	PUNCT
cana-5712	326	1	j.	j.	PROPN
cana-5712	326	2	appl	appl	PROPN
cana-5712	326	3	.	.	PUNCT
cana-5712	327	1	comput	comput	PROPN
cana-5712	327	2	.	.	PUNCT
cana-5712	328	1	math	math	NOUN
cana-5712	328	2	(	(	PUNCT
cana-5712	328	3	2019	2019	NUM
cana-5712	328	4	):	):	PUNCT
cana-5712	328	5	72	72	NUM
cana-5712	328	6	,	,	PUNCT
cana-5712	328	7	1	1	NUM
cana-5712	328	8	-	-	SYM
cana-5712	328	9	14	14	NUM
cana-5712	328	10	.	.	PUNCT
cana-5712	328	11	https://doi.org/10.1007/s40819-019-0656-5	https://doi.org/10.1007/s40819-019-0656-5	NUM
cana-5712	328	12	.	.	PUNCT
cana-5712	329	1	[	[	X
cana-5712	329	2	9	9	NUM
cana-5712	329	3	]	]	PUNCT
cana-5712	329	4	s.	s.	PROPN
cana-5712	329	5	kumar	kumar	PROPN
cana-5712	329	6	,	,	PUNCT
cana-5712	329	7	o.	o.	PROPN
cana-5712	329	8	khan	khan	PROPN
cana-5712	329	9	,	,	PUNCT
cana-5712	329	10	n.u	n.u	PROPN
cana-5712	329	11	.	.	PROPN
cana-5712	329	12	khan	khan	PROPN
cana-5712	329	13	,	,	PUNCT
cana-5712	329	14	caputo	caputo	PROPN
cana-5712	329	15	derivative	derivative	ADJ
cana-5712	329	16	formulas	formula	NOUN
cana-5712	329	17	of	of	ADP
cana-5712	329	18	hurwitz	hurwitz	PROPN
cana-5712	329	19	-	-	PUNCT
cana-5712	329	20	lerch	lerch	PROPN
cana-5712	329	21	zeta	zeta	PROPN
cana-5712	329	22	function	function	PROPN
cana-5712	329	23	and	and	CCONJ
cana-5712	329	24	applications	application	NOUN
cana-5712	329	25	,	,	PUNCT
cana-5712	329	26	communication	communication	NOUN
cana-5712	329	27	on	on	ADP
cana-5712	329	28	applied	apply	VERB
cana-5712	329	29	nonlinear	nonlinear	ADJ
cana-5712	329	30	analysis	analysis	NOUN
cana-5712	329	31	.	.	PUNCT
cana-5712	330	1	,	,	PUNCT
cana-5712	330	2	32	32	NUM
cana-5712	330	3	(	(	PUNCT
cana-5712	330	4	10	10	NUM
cana-5712	330	5	)	)	PUNCT
cana-5712	330	6	(	(	PUNCT
cana-5712	330	7	2025	2025	NUM
cana-5712	330	8	)	)	PUNCT
cana-5712	330	9	,	,	PUNCT
cana-5712	330	10	2434	2434	NUM
cana-5712	330	11	-	-	SYM
cana-5712	330	12	2441	2441	NUM
cana-5712	330	13	.	.	PUNCT
cana-5712	331	1	[	[	X
cana-5712	331	2	10	10	NUM
cana-5712	331	3	]	]	X
cana-5712	331	4	d.s	d.s	PROPN
cana-5712	331	5	.	.	PROPN
cana-5712	331	6	sachan	sachan	PROPN
cana-5712	331	7	,	,	PUNCT
cana-5712	331	8	d.	d.	PROPN
cana-5712	331	9	kumar	kumar	PROPN
cana-5712	331	10	,	,	PUNCT
cana-5712	331	11	k.s	k.s	PROPN
cana-5712	331	12	.	.	PROPN
cana-5712	331	13	,	,	PUNCT
cana-5712	331	14	nisar	nisar	PROPN
cana-5712	331	15	,	,	PUNCT
cana-5712	331	16	certain	certain	ADJ
cana-5712	331	17	properties	property	NOUN
cana-5712	331	18	associated	associate	VERB
cana-5712	331	19	with	with	ADP
cana-5712	331	20	generalized	generalized	ADJ
cana-5712	331	21	mseries	mserie	NOUN
cana-5712	331	22	using	use	VERB
cana-5712	331	23	hadamard	hadamard	ADJ
cana-5712	331	24	product	product	NOUN
cana-5712	331	25	,	,	PUNCT
cana-5712	331	26	sahand	sahand	NOUN
cana-5712	331	27	communications	communication	NOUN
cana-5712	331	28	in	in	ADP
cana-5712	331	29	mathematical	mathematical	ADJ
cana-5712	331	30	analysis	analysis	NOUN
cana-5712	331	31	,	,	PUNCT
cana-5712	331	32	21	21	NUM
cana-5712	331	33	(	(	PUNCT
cana-5712	331	34	1	1	NUM
cana-5712	331	35	)	)	PUNCT
cana-5712	331	36	(	(	PUNCT
cana-5712	331	37	2024	2024	NUM
cana-5712	331	38	)	)	PUNCT
cana-5712	331	39	,	,	PUNCT
cana-5712	331	40	pp	pp	PROPN
cana-5712	331	41	.	.	PUNCT
cana-5712	332	1	151	151	NUM
cana-5712	332	2	-	-	SYM
cana-5712	332	3	171	171	NUM
cana-5712	332	4	.	.	PUNCT
cana-5712	333	1	[	[	X
cana-5712	333	2	11	11	NUM
cana-5712	333	3	]	]	X
cana-5712	333	4	d.s	d.s	PROPN
cana-5712	333	5	.	.	PROPN
cana-5712	333	6	sachan	sachan	PROPN
cana-5712	333	7	,	,	PUNCT
cana-5712	333	8	h.	h.	PROPN
cana-5712	333	9	jalori	jalori	PROPN
cana-5712	333	10	and	and	CCONJ
cana-5712	333	11	s.	s.	PROPN
cana-5712	333	12	jaloree	jaloree	PROPN
cana-5712	333	13	,	,	PUNCT
cana-5712	333	14	fractional	fractional	ADJ
cana-5712	333	15	calculus	calculus	NOUN
cana-5712	333	16	of	of	ADP
cana-5712	333	17	product	product	NOUN
cana-5712	333	18	of	of	ADP
cana-5712	333	19	m	m	NOUN
cana-5712	333	20	-	-	PUNCT
cana-5712	333	21	series	series	NOUN
cana-5712	333	22	and	and	CCONJ
cana-5712	333	23	ifunction	ifunction	NOUN
cana-5712	333	24	of	of	ADP
cana-5712	333	25	two	two	NUM
cana-5712	333	26	variables	variable	NOUN
cana-5712	333	27	,	,	PUNCT
cana-5712	333	28	jnanabha	jnanabha	PROPN
cana-5712	333	29	,	,	PUNCT
cana-5712	333	30	52	52	NUM
cana-5712	333	31	(	(	PUNCT
cana-5712	333	32	1	1	NUM
cana-5712	333	33	)	)	PUNCT
cana-5712	333	34	(	(	PUNCT
cana-5712	333	35	2022	2022	NUM
cana-5712	333	36	)	)	PUNCT
cana-5712	333	37	,	,	PUNCT
cana-5712	333	38	pp	pp	ADP
cana-5712	333	39	.	.	PUNCT
cana-5712	334	1	189	189	NUM
cana-5712	334	2	-	-	SYM
cana-5712	334	3	202	202	NUM
cana-5712	334	4	.	.	PUNCT
cana-5712	335	1	[	[	X
cana-5712	335	2	12	12	NUM
cana-5712	335	3	]	]	PUNCT
cana-5712	335	4	m.	m.	NOUN
cana-5712	335	5	sharma	sharma	PROPN
cana-5712	335	6	,	,	PUNCT
cana-5712	335	7	r.	r.	PROPN
cana-5712	335	8	jain	jain	PROPN
cana-5712	335	9	,	,	PUNCT
cana-5712	335	10	a	a	DET
cana-5712	335	11	note	note	NOUN
cana-5712	335	12	on	on	ADP
cana-5712	335	13	generalized	generalized	ADJ
cana-5712	335	14	m	m	PROPN
cana-5712	335	15	-	-	PUNCT
cana-5712	335	16	series	series	NOUN
cana-5712	335	17	,	,	PUNCT
cana-5712	335	18	fract	fract	PROPN
cana-5712	335	19	.	.	PUNCT
cana-5712	336	1	calc	calc	PROPN
cana-5712	336	2	.	.	PUNCT
cana-5712	337	1	appl	appl	PROPN
cana-5712	337	2	.	.	PUNCT
cana-5712	338	1	anal	anal	PROPN
cana-5712	338	2	.	.	PUNCT
cana-5712	339	1	12	12	NUM
cana-5712	339	2	(	(	PUNCT
cana-5712	339	3	1	1	NUM
cana-5712	339	4	)	)	PUNCT
cana-5712	339	5	,	,	PUNCT
cana-5712	339	6	2009	2009	NUM
cana-5712	339	7	,	,	PUNCT
cana-5712	339	8	449	449	NUM
cana-5712	339	9	-	-	SYM
cana-5712	339	10	452	452	NUM
cana-5712	339	11	.	.	PUNCT
cana-5712	340	1	[	[	X
cana-5712	340	2	13	13	NUM
cana-5712	340	3	]	]	X
cana-5712	340	4	a.k	a.k	PROPN
cana-5712	340	5	.	.	PROPN
cana-5712	340	6	shukla	shukla	PROPN
cana-5712	340	7	,	,	PUNCT
cana-5712	340	8	a.k	a.k	PROPN
cana-5712	340	9	.	.	PROPN
cana-5712	340	10	,	,	PUNCT
cana-5712	340	11	and	and	CCONJ
cana-5712	340	12	j.c	j.c	PROPN
cana-5712	340	13	.	.	PROPN
cana-5712	340	14	prajapati	prajapati	PROPN
cana-5712	340	15	.	.	PUNCT
cana-5712	341	1	on	on	ADP
cana-5712	341	2	a	a	DET
cana-5712	341	3	generalization	generalization	NOUN
cana-5712	341	4	of	of	ADP
cana-5712	341	5	mittag	mittag	ADJ
cana-5712	341	6	-	-	PUNCT
cana-5712	341	7	leffler	leffler	NOUN
cana-5712	341	8	function	function	NOUN
cana-5712	341	9	and	and	CCONJ
cana-5712	341	10	its	its	PRON
cana-5712	341	11	prop	prop	NOUN
cana-5712	341	12	-	-	PUNCT
cana-5712	341	13	erties	ertie	NOUN
cana-5712	341	14	.	.	PUNCT
cana-5712	342	1	journal	journal	PROPN
cana-5712	342	2	of	of	ADP
cana-5712	342	3	mathematical	mathematical	ADJ
cana-5712	342	4	analysis	analysis	NOUN
cana-5712	342	5	and	and	CCONJ
cana-5712	342	6	applications	application	NOUN
cana-5712	342	7	336	336	NUM
cana-5712	342	8	(	(	PUNCT
cana-5712	342	9	2	2	NUM
cana-5712	342	10	)	)	PUNCT
cana-5712	342	11	(	(	PUNCT
cana-5712	342	12	2007	2007	NUM
cana-5712	342	13	):	):	PUNCT
cana-5712	342	14	797–811	797–811	NUM
cana-5712	342	15	.	.	PUNCT
cana-5712	343	1	[	[	X
cana-5712	343	2	14	14	NUM
cana-5712	343	3	]	]	X
cana-5712	343	4	d.l	d.l	PROPN
cana-5712	343	5	.	.	PROPN
cana-5712	343	6	suthar	suthar	PROPN
cana-5712	343	7	,	,	PUNCT
cana-5712	343	8	h.	h.	PROPN
cana-5712	343	9	tadesse	tadesse	PROPN
cana-5712	343	10	and	and	CCONJ
cana-5712	343	11	k.	k.	PROPN
cana-5712	343	12	tilahun	tilahun	PROPN
cana-5712	343	13	,	,	PUNCT
cana-5712	343	14	integrals	integral	NOUN
cana-5712	343	15	involving	involve	VERB
cana-5712	343	16	jacobi	jacobi	PROPN
cana-5712	343	17	polynomials	polynomial	NOUN
cana-5712	343	18	and	and	CCONJ
cana-5712	343	19	mseries	mserie	NOUN
cana-5712	343	20	,	,	PUNCT
cana-5712	343	21	j.	j.	PROPN
cana-5712	343	22	fract	fract	PROPN
cana-5712	343	23	.	.	PUNCT
cana-5712	344	1	calc	calc	PROPN
cana-5712	344	2	.	.	PUNCT
cana-5712	345	1	appl	appl	PROPN
cana-5712	345	2	.	.	PROPN
cana-5712	345	3	,	,	PUNCT
cana-5712	345	4	9	9	NUM
cana-5712	345	5	(	(	PUNCT
cana-5712	345	6	2	2	NUM
cana-5712	345	7	)	)	PUNCT
cana-5712	345	8	(	(	PUNCT
cana-5712	345	9	2018	2018	NUM
cana-5712	345	10	)	)	PUNCT
cana-5712	345	11	,	,	PUNCT
cana-5712	345	12	287	287	NUM
cana-5712	345	13	-	-	SYM
cana-5712	345	14	294	294	NUM
cana-5712	345	15	.	.	PUNCT
cana-5712	345	16	.	.	PUNCT
cana-5712	346	1	[	[	X
cana-5712	346	2	15	15	NUM
cana-5712	346	3	]	]	X
cana-5712	346	4	i.n	i.n	PROPN
cana-5712	346	5	.	.	PROPN
cana-5712	346	6	sneddon	sneddon	PROPN
cana-5712	346	7	,	,	PUNCT
cana-5712	346	8	the	the	DET
cana-5712	346	9	use	use	NOUN
cana-5712	346	10	of	of	ADP
cana-5712	346	11	integral	integral	ADJ
cana-5712	346	12	transforms	transform	NOUN
cana-5712	346	13	.	.	PUNCT
cana-5712	347	1	new	new	PROPN
cana-5712	347	2	york	york	PROPN
cana-5712	347	3	:	:	PUNCT
cana-5712	347	4	tata	tata	PROPN
cana-5712	347	5	mcgraw	mcgraw	PROPN
cana-5712	347	6	-	-	PUNCT
cana-5712	347	7	hill	hill	PROPN
cana-5712	347	8	,	,	PUNCT
cana-5712	347	9	1979	1979	NUM
cana-5712	347	10	.	.	PUNCT
cana-5712	348	1	[	[	X
cana-5712	348	2	16	16	NUM
cana-5712	348	3	]	]	X
cana-5712	348	4	m.r	m.r	PROPN
cana-5712	348	5	.	.	PROPN
cana-5712	348	6	spiegel	spiegel	PROPN
cana-5712	348	7	,	,	PUNCT
cana-5712	348	8	theory	theory	NOUN
cana-5712	348	9	and	and	CCONJ
cana-5712	348	10	problem	problem	NOUN
cana-5712	348	11	of	of	ADP
cana-5712	348	12	laplace	laplace	NOUN
cana-5712	348	13	transforms	transform	VERB
cana-5712	348	14	,	,	PUNCT
cana-5712	348	15	schums	schum	VERB
cana-5712	348	16	outline	outline	NOUN
cana-5712	348	17	series	series	NOUN
cana-5712	348	18	.	.	PUNCT
cana-5712	349	1	new	new	PROPN
cana-5712	349	2	york	york	PROPN
cana-5712	349	3	:	:	PUNCT
cana-5712	349	4	mcgraw	mcgraw	PROPN
cana-5712	349	5	-	-	PUNCT
cana-5712	349	6	hill	hill	PROPN
cana-5712	349	7	,	,	PUNCT
cana-5712	349	8	1965	1965	NUM
cana-5712	349	9	.	.	PUNCT
cana-5712	350	1	[	[	X
cana-5712	350	2	17	17	NUM
cana-5712	350	3	]	]	X
cana-5712	350	4	h.m	h.m	PROPN
cana-5712	350	5	.	.	PROPN
cana-5712	350	6	srivastava	srivastava	PROPN
cana-5712	350	7	,	,	PUNCT
cana-5712	350	8	and	and	CCONJ
cana-5712	350	9	p.w	p.w	PROPN
cana-5712	350	10	.	.	PROPN
cana-5712	350	11	karlsson	karlsson	PROPN
cana-5712	350	12	,	,	PUNCT
cana-5712	350	13	multiple	multiple	ADJ
cana-5712	350	14	gaussian	gaussian	ADJ
cana-5712	350	15	hypergeometric	hypergeometric	ADJ
cana-5712	350	16	series	series	NOUN
cana-5712	350	17	,	,	PUNCT
cana-5712	350	18	halstedpress(ellis	halstedpress(ellis	PROPN
cana-5712	350	19	horwood	horwood	NOUN
cana-5712	350	20	limited	limit	VERB
cana-5712	350	21	,	,	PUNCT
cana-5712	350	22	chichester	chichester	PROPN
cana-5712	350	23	)	)	PUNCT
cana-5712	350	24	.	.	PUNCT
cana-5712	351	1	new	new	PROPN
cana-5712	351	2	york	york	PROPN
cana-5712	351	3	:	:	PUNCT
cana-5712	351	4	wiley	wiley	PROPN
cana-5712	351	5	,	,	PUNCT
cana-5712	351	6	1985	1985	NUM
cana-5712	351	7	.	.	PUNCT
cana-5712	352	1	[	[	X
cana-5712	352	2	18	18	NUM
cana-5712	352	3	]	]	PUNCT
cana-5712	352	4	a.	a.	NOUN
cana-5712	352	5	wiman	wiman	PROPN
cana-5712	352	6	,	,	PUNCT
cana-5712	352	7	uber	uber	ADJ
cana-5712	352	8	den	den	PROPN
cana-5712	352	9	fundamental	fundamental	ADJ
cana-5712	352	10	satz	satz	PROPN
cana-5712	352	11	in	in	ADP
cana-5712	352	12	der	der	PROPN
cana-5712	352	13	theorie	theorie	PROPN
cana-5712	352	14	der	der	PROPN
cana-5712	352	15	funktionen	funktionen	PROPN
cana-5712	352	16	acta	acta	PROPN
cana-5712	352	17	mathematica29	mathematica29	PROPN
cana-5712	352	18	(	(	PUNCT
cana-5712	352	19	1	1	NUM
cana-5712	352	20	):	):	PUNCT
cana-5712	352	21	191–201	191–201	NUM
cana-5712	352	22	,	,	PUNCT
cana-5712	352	23	1905	1905	NUM
cana-5712	352	24	.	.	PUNCT
cana-5712	353	1	https://doi.org/10.1007/s40819-019-0656-5	https://doi.org/10.1007/s40819-019-0656-5	PROPN
cana-5712	353	2	https://www.scopus.com/record/display.uri?eid=2-s2.0-85182790769&origin=reflist&sort=plf-f&src=s&imp=t&sid=2d344b666f7fe6dedcff0518b8ad3e75&sot=cite&sdt=a&sl=23&s=ref%282-s2.0-85182790769%29	https://www.scopus.com/record/display.uri?eid=2-s2.0-85182790769&origin=reflist&sort=plf-f&src=s&imp=t&sid=2d344b666f7fe6dedcff0518b8ad3e75&sot=cite&sdt=a&sl=23&s=ref%282-s2.0-85182790769%29	PROPN
cana-5712	353	3	https://www.scopus.com/record/display.uri?eid=2-s2.0-85182790769&origin=reflist&sort=plf-f&src=s&imp=t&sid=2d344b666f7fe6dedcff0518b8ad3e75&sot=cite&sdt=a&sl=23&s=ref%282-s2.0-85182790769%29	https://www.scopus.com/record/display.uri?eid=2-s2.0-85182790769&origin=reflist&sort=plf-f&src=s&imp=t&sid=2d344b666f7fe6dedcff0518b8ad3e75&sot=cite&sdt=a&sl=23&s=ref%282-s2.0-85182790769%29	PROPN